M S U L I B R A R I E S . m — \ ' R E T U R N I N G M A T E R I A L S : P I a c e i n b o o k d r o p t o r e m o v e t h i s c h e c k o u t f r o m y o u r r e c o r d . F I N E S w i l ] b e c h a r g e d i f b o o k i s r e t u r n e d a f t e r t h e d a t e s t a m p e d b e 1 0 w . C O L L I S I O N I N D U C E D H E A T I N G O F A W E A K L Y I O N I Z E D D I L U T E G A S I N S T E A D Y F L O W B Y T e r r e n c e J o s e p h M o r i n A D I S S E R T A T I O N S u b m i t t e d t o M i c h i g a n S t a t e U n i v e r s i t y i n p a r t i a l f u l f i l l m e n t o f t h e r e q u i r e m e n t s f o r t h e d e g r e e o f D O C T O R O F P H I L O S O P H Y D e p a r t m e n t o f C h e m i c a l E n g i n e e r i n g 1 9 8 5 C o p y r i g h t b y T E R R E N C E J O S E P H M O R I N 1 9 8 5 C O L L I S I O N I N D U C E D H E A T I N G O F A W E A K L Y I O N I Z E D D I L U T E G A S I N S T E A D Y F L O W B Y T e r r e n c e J o s e p h M o r i n C o l l i s i o n i n d u c e d h e a t i n g i s a s e q u e n c e o f c o l l i s i o n a l e x c i t a t i o n a n d r e l a x a t i o n p r o c e s s e s i n i t i a t e d b y e l e c t r o n i m p a c t e x c i t a t i o n a n d r e s u l t i n g i n a n i n c r e a s e i n g a s t e m p e r a t u r e . I n t h i s w o r k a s u i t a b l e w o r k i n g f l u i d i s i d e n t i f i e d a n d t h e e f f i c a c y o f c o l l i s i o n i n d u c e d h e a t i n g i n a l o w p r e s s u r e , m i c r o w a v e f r e q u e n c y e l e c t r i c a l d i s c h a r g e e n v i r o n m e n t i s e v a l u a t e d . A f t e r c o n s i d e r a t i o n o f s e v e r a l l o w m o l e c u l a r w e i g h t d i a t o m i c g a s e s , m o l e c u l a r h y d r o g e n i s s e l e c t e d a s t h e w o r k i n g f l u i d o f c h o i c e o n t h e b a s i s o f t h e p r e s e n c e o f s e v e r a l o p e n s c a t t e r i n g c h a n n e l s w h i c h r e s u l t i n k i n e t i c a l l y e x c i t e d p r o d u c t s , e s p e c i a l l y t h a t o f d i s s o c i a t i o n g i g e x c i t a t i o n o f t h e E ; 3 Z : : s t a t e . T h e k i n e t i c e n e r g y d i s t r i b u t i o n s o f t h e p r o d u c t s a r e c a l c u l a t e d i n t h e C o n d o n r e f l e c t i o n a p p r o x i m a t i o n f o r d i s s o c i a t i o n f r o m X 1 2 ; ( v = 0 - 1 3 ) . T h e F r a n c k - C o n d o n e n v e l o p e f o r v = 0 i s i n g o o d a g r e e m e n t w i t h p r e v i o u s w o r k s . A v e r a g e p r o d u c t k i n e t i c e n e r g i e s r a n g e f r o m 6 . 1 9 e v f o r X I X ; ( v = 0 ) t o 9 . 6 1 e v f o r x 1 X ; ( v = 1 3 ) . C a l c u l a t i o n s i n v o l v i n g t w o d i s t i n c t r e a c t o r m o d e l s f o r H 2 i n s t e a d y f l o w a t 1 0 0 - 7 0 0 N / m 2 i n d i c a t e t h a t t h e T e r r e n c e J o s e p h M o r i n h i g h e n e r g y d i s s o c i a t i o n p r o d u c t s m a k e a m a j o r c o n t r i b u t i o n t o g a s h e a t i n g . T h e e x i s t e n c e o f p a t h r e s h h o l d f o r e q u i l i b r a t i o n o f v i b r a t i o n a l a n d k i n e t i c t e m p e r a t u r e s i s a l s o i n d i c a t e d . I n a n o t h e r s e t o f c a l c u l a t i o n s t h e s e l f - c o n s i s t e n t e l e c t r o n g a s a n d n e u t r a l g a s p r o p e r t i e s a r e c a l c u l a t e d b y s i m u l t a n e o u s s o l u t i o n o f t h e B o l t z m a n n e q u a t i o n a n d m a c r o s c o p i c b a l a n c e e q u a t i o n s . A n e w s i m i l a r i t y v a r i a b l e i s i d e n t i f i e d t o e x t e n d t h e c r i t e r i a o f M a r g e n a u t o c o n s t a n t p r e s s u r e , s t e a d y f l o w d i s c h a r g e s . E n h a n c e m e n t , i n h i b i t i o n a n d r e s o n a n c e e f f e c t s a r e d e t e c t e d , a n d t h e n e c e s s i t y o f s u c h s e l f - c o n s i s t e n t c a l c u l a t i o n s i s e s t a b l i s h e d . T o e x a m i n e r e l a x a t i o n t i m e s c a l e s o f t h e h i g h e n e r g y d i s s o c i a t i o n p r o d u c t s t h e n o n l i n e a r B o l t z m a n n e q u a t i o n i s s o l v e d b y t h e m e t h o d o f o r t h o g o n a l c o l l o c a t i o n w i t h a L a g u e r r e p o l y n o m i a l b a s i s s e t . T h e r e s u l t i n g d i s t r i b u t i o n s e v i d e n c e n o n - p e r i o d i c o s c i l l a t o r y t r a j e c t o r i e s , i n v i o l a t i o n o f t h e K r o o k - W u c o n j e c t u r e . T h e s e t r a j e c t o r i e s a r e c o r r e l a t e d t o t h e r o b u s t p r e s e n c e o f a n u n s t a b l e m a n i f o l d i n t h e e i g e n s p a c e o f t h e l i n e a r i z e d p r o b l e m . T o t h e O n e i n w h o m a r e h i d d e n a l l t h e t r e a s u r e s o f w i s d o m a n d k n o w l e d g e , t h i s w o r k a n d w o r k e r a r e g r a t e f u l l y d e d i c a t e d . i i A C K N O W L E D G M E N T S " A n d w h a t d o y o u h a v e t h a t y o u d i d n o t r e c e i v e ? " I C o r i n t h i a n s 4 : 7 . O v e r t h e c o u r s e o f t h i s w o r k I h a v e r e c e i v e d m u c h f r o m m a n y a n d w i s h t o a c k n o w l e d g e t h e m h e r e : t o D r . M a r t i n C . H a w l e y f o r p r o v i s i o n o f a n e n v i r o n m e n t c o n d u c i v e t o r e s e a r c h o f t h i s k i n d . t o t h e N a t i o n a l A e r o n a u t i c s a n d S p a c e A d m i n i s t r a t i o n , D u P o n t G r a d u a t e F e l l o w s h i p P r o g r a m a n d t h e D i v i s i o n o f E n g i n e e r i n g R e s e a r c h f o r f i n a n c i a l s u p p o r t . t o m y p a r e n t s , R o b e r t a n d R o s e M o r i n , f o r t h e i r c o n s i s t e n t e x a m p l e o f e x c e l l e n c e a n d h a r d w o r k . t o N a o m i E v a n s f o r h e r p a t i e n t , n i m b l e - f i n g e r e d t r a n s f o r m a t i o n o f m a n u s c r i p t i n t o t y p e d c o p y . t o m y w i f e , L i n d a , f o r h e r g e n t l e f o r b e a r a n c e a n d e n c o u r a g e m e n t d u r i n g t h e c o m p l e t i o n o f t h i s w o r k . i i i 3 8 . 2 3 % N . H H . H h o m e o m u m ” 8 3 5 “ a . 5 a s a . m o a s T A B L E O F C O N T E N T S L I S T O F T A B L E S v i L I S T O F F I G U R E S v i i N O T A T I O N X I N T R O D U C T I O N 1 1 . 1 O v e r v i e w o f e l e c t r i c a l d i s c h a r g e p h y s i c s 5 1 . 2 P r o b l e m d e f i n i t i o n 8 B A C K G R O U N D A N D R E L A T E D W O R K 1 2 2 . 1 K i n e t i c a n d t r a n s p o r t t h e o r y 1 3 2 . 2 C o l l i s i o n t h e o r y 6 2 2 . 3 R e v i e w o f r e l a t e d w o r k 8 0 D E V E L O P M E N T A N D A N A L Y S I S 3 . 1 M o d e l s y s t e m i d e n t i f i c a t i o n 9 3 3 . 2 U n c o u p l e d c a l c u l a t i o n o f c o l l i s i o n i n d u c e d h e a t i n g o f H 2 1 1 9 3 . 3 . C o u p l e d c a l c u l a t i o n o f c o l l i s i o n i n d u c e d h e a t i n g o f H 2 1 4 4 3 . 4 C a l c u l a t i o n o f r e l a x a t i o n t i m e s c a l e s 1 7 0 S U M M A R Y A N D D I S C U S S I O N O F R E S U L T S 4 . 1 S u m m a r y o f e s s e n t i a l r e s u l t s 1 9 8 4 . 2 C o n c l u s i o n s 2 0 3 4 . 3 R e c o m m e n d a t i o n s f o r f u t u r e c o n s i d e r a t i o n 2 0 6 A P P E N D I X A C o m p u t e r p r o g r a m s t a t e m e n t s f o r 2 0 8 c a l c u l a t i o n o f t h e k i n e t i c e n e r g y d i s t r i b u t i o n a n d a v e r a g e k i n e t i c e n e r g y o f d i s s o c i a t i o n f r a g m e n t s . A P P E N D I X B C o m p u t e r p r o g r a m s t a t e m e n t s f o r 2 1 7 c a l c u l a t i o n o f n e u t r a l g a s d e n s i t y , t e m p e r a t u r e a n d v i b r a t i o n a l t e m p e r a t u r e i n t h e u n c o u p l e d a p p r o x i m a t i o n . i v A P P E N D I X A P P E N D I X D E A P P E N D I X C A P P E N J : x F 1 9 4 . r . r E . \ D I X G A P P E N D I X C A P P E N D I X D A P P E N D I X E A P P E N D I X F A P P E N D I X G C o m p u t e r p r o g r a m s t a t e m e n t s f o r c a l c u l a t i o n o f n e u t r a l g a s d e n s i t y a n d t e m p e r a t u r e , e l e c t r o n g a s e n e r g y a n d i n e l a s t i c e x c i t a t i o n r a t e s i n t h e c o u p l e d a p p r o x i m a t i o n . C o m p u t e r p r o g r a m s t a t e m e n t s f o r c a l c u l a t i o n o f t h e A c o u p l i n g m a t r i x o f t h e c o l l o c a t e d n o n l i n e a r B o l t z m a n n e q u a t i o n . C o m p u t e r p r o g r a m s t a t e m e n t s f o r t h e a n a l y s i s o f t h e l i n e a r i z e d B o l t z m a n n e q u a t i o n . C o m p u t e r p r o g r a m s t a t e m e n t s f o r t h e i n t e g r a t i o n o f t h e c o l l o c a t e d n o n l i n e a r B o l t z m a n n e q u a t i o n . N o t e s o n t h e L i o u v i l l e e q u a t i o n I J S T O F R E F E R E N C E S 2 2 2 2 2 6 2 3 6 3 8 9 4 0 3 4 0 5 T a b l e I : T a b l e I I : T a b l e I I I : L I S T O F T A B L E S S t a t i s t i c s o f t w o c a l c u l a t e d F r a n c k - C o n d o n e n v e l o p e s A v e r a g e r e l a t i v e k i n e t i c e n e r g y c a l c u l a t e d i n t h e C o n d o n r e f l e c t i o n a p p r o x i m a t i o n . V i b r a t i o n a l c o n t r i b u t i o n ( f v ) t o t h e t o t a l d i s s o c i a t i o n r a t e . v i 1 0 9 1 1 0 1 3 4 F i g u r e 1 F i g u r e 2 F i g u r e 3 F i g u r e 4 F i g u r e 5 F i g u r e 7 : 9 ; “ W e 8 ' F i g u r e F i g u r e F i g u r e F i g u r e F i g u r e F i g u r e F i g u r e F i g u r e F i g u r e F i S u r e 7 : 1 0 : L I S T O F F I G U R E S D e t a i l e d d e s c r i p t i o n o f t h e t w o - b o d y i n t e r a c t i o n s p h e r e I l l u s t r a t i o n o f t h e n o r m a l v e c t o r s k ? a n d k 9 A 1 a ] P o t e n t i a l e n e r g y c r v e s f o r s o m e s t a t e s o f N 2 a n d N 2 . ( M a s s e y , 1 9 6 9 ) P o t e n t i a l e n e r g y c r v e s f o r s o m e s t a t e s o f O 2 a n d O 2 . ( M a s s e y , 1 9 6 9 ) P o t e n t i a l e n e r g y c u r v e s f o r s o m e s t a t e s o f H 2 , H 2 a n d H 2 . ( S h a r p , 1 9 7 1 ) T i m e s c a l e s f o r a v a r i e t y o f t r a n s p o r t , e l e c t r o d y n a m i c a n d k i n e t i c p r o c e s s e s f o r p r e s s u r e s o f 1 - 1 ( 1 0 5 ) N / m 2 i n p u r e H 2 . T i m e s c a l e s f o r a v a r i e t y o f t r a n s p o r t , e l e c t r o d y n a m i c a n d k i n e t i c p r o c e s s e s f o r p r e s s u r e s o f 1 - 1 ( 1 0 5 ) N / m 2 a n d t h e e x t e n t o f d i s s o c i a t i o n a t 0 . 2 T i m e s c a l e s f o r a v a r i e t y o f t r a n s p o r t , e l e c t r o d y n a m i c a n d k i n e t i c p r o c e s s e s f o r t e m p e r a t u r e s o f 2 0 0 - 1 2 0 0 K a n d t h e e x t e n t o f d i s s o c i a t i o n a t 0 . 2 C o l l i s i o n e f f i c i e n c i e s o f v i b r a t i o n a l a n d e l e c t r o n i c e x c i t a t i o n p r o c e s s e s i n p u r e H c o m p a r e d w i t h t h e r e s u l t s o f a M a x w e l l i a n c u r v e - f i t R e l a t i v e c o n t r i b u t i o n o f t h r e e r e l a x a t i o n p r o c e s s e s t o t h e t o t a l g a s h e a t i n g r a t e f o r p r e s s u r e s o f 1 0 0 - 7 0 0 N / m 2 a n d a H z m o l a r f l o w r a t e o f 1 ( 1 0 ‘ 3 ) m o l e s / s . _ v i i 4 3 6 4 9 6 9 8 9 9 1 1 4 1 1 5 1 1 6 1 2 7 1 3 6 F i g u r e 1 1 . u r e 1 2 " j ‘ 1 2 F i g u r e 1 3 F i w r e 1 4 “ W e 1 5 F i g u r e 1 6 : P i g u r e 1 7 ; F i m l r e 1 8 : F i g l - ‘ I ' e 1 9 : F i g u r e F i g u r e F i g u r e F i g u r e F i g u r e F i g u r e F i g u r e F i g u r e F i g u r e F i g u r e l l : 1 2 : 1 3 : 1 4 : 1 5 : 1 6 : 1 7 : 1 8 : 1 9 : 2 0 : R e l a t i v e c o n t r i b u t i o n o f t h r e e r e l a x a t i o n p r o c e s s e s t o t h e t o t a l g a s h e a t i n g r a t e f o r p r e s s u r e s o f _ 1 0 0 - 7 0 0 N / m 2 a n d a H 2 m o l a r f l o w r a t e o f 1 ( 1 0 ‘ 4 ) m o l e s / s . a ) E x t e n t o f c o n v e r s i o n f o r p r e s s u r e s o f 5 0 - 7 0 0 N / m 2 c o m p a r e d i n t h e P F R a n d C S T R a p p r o x i m a t i o n . b ) G a s t e m p e r a t u r e f o r p r e s s u r e s o f 5 0 - 7 0 0 N / m c o m p a r e d i n t h e P F R a n d C S T R a p p r o x i m a t i o n . c ) V i b r a t i o n a l t e m p e r a t u r e f o r p r e s s u r e s o f 5 0 - 7 0 0 N / m c o m p a r e d i n t h e P F R a n d C S T R a p p r o x i m a t i o n . P F R p r o f i l e s o f e x t e n t o f c o n v e r s i o n , g a s t e m p e r a t u r e a n d v i b r a t i o n a l 2 t e m p e r a t u r e f o r a p r e s s u r e o f 5 0 N / m a n d m o l a r f l o w r a t e o f 1 ( 1 0 ’ 3 ) m o l e s / s . P F R p r o f i l e s o f e x t e n t o f c o n v e r s i o n , g a s t e m p e r a t u r e a n d v i b r a t i o n a l 2 t e m p e r a t u r e f o r a p r e s s u r e o f 4 0 0 N / m a n d m o l a r f l o w r a t e o f 1 ( 1 0 ' 3 ) m o l e / s . N o r m a l i z e d n e u t r a l g a s t e m p e r a t u r e f o r c e [ 0 , l ] a n d d o = 0 . 1 , 1 . 0 , 1 0 . 0 . N o r m a l i z e d a v e r a g e e l e c t r o n e n e r g y f o r c e [ 0 . 1 ] , « o = 0 . 1 a n d ¢ 2 = 0 . , 1 . 0 . N o r m a l i z e d a v e r a g e e l e c t r o n e n e r g y f o r c e [ 0 , 1 ] , « o = 1 . 0 a n d ¢ 2 = 0 . , 0 . 1 , 1 . 0 . N o r m a l i z e d a v e r a g e e l e c t r o n e n e r g y f o r C € [ 0 p 1 ] , “ o = 1 0 0 0 a n d ¢ 2 = 0 0 1 ‘ 0 0 1 ' 1 . 0 0 N o r m a l i z e d a v e r a g e i n e l a s t i c e x c i t a t i o n r a t e f o r c ‘ [ 0 , 1 ] , ¢ 2 = 0 . 1 a n d ‘ x o = 0 . 1 , 1 . 0 , 1 0 . 0 . C o m p a r i s o n o f t h e c a l c u l a t e d a n d c l o s e d f o r m r e d u c e d d i s t r i b u t i o n f u n c t i o n f o r b , = 0 . 2 a n d s e v e r a l v a l u e s o f e n e r g y . v i i i 1 3 7 1 3 8 1 4 0 1 4 1 1 5 9 1 6 2 1 6 3 1 6 4 1 6 7 1 8 4 F i g u r e 2 2 F i g u r e 2 . F i g u r e 2 . ‘ F i g u r e 2 4 F i g u r e 2 5 F i g u r e F i g u r e F i g u r e F i g u r e F i g u r e F i g u r e 2 1 : E v o l u t i o n o f t h e a v e r a g e e n e r g y a n d B o l t z m a n n H - f u n c t i o n a l f o r b e = 0 . 2 ( c a l c u l a t e d v a l u e s ) . 2 2 : E v o l u t i o n o f t h e . L a n d E u c l i d e a n n o r m f o r b O = 0 . 2 ( c a l c u I a t e d v a l u e s ) 2 3 : E v o l u t i o n o f t h e r e d u c e d d i s t r i b u t i o n f r o m a n o n - K B K W i n i t i a l c o n d i t i o n . 2 4 : E v o l u t i o n o f t h e a v e r a g e e n e r g y a n d B o l t z m a n n H - f u n c t i o n a l f o r a d i s t r i b u t i o n e v o l v i n g f r o m a n o n - K B K W i n i t i a l c o n d i t i o n . 2 5 : E v o l u t i o n o f t h e . 4 1 a n d E u c l i d e a n n o r m o f a d i s t r i b u t i o n e v o l v i n g f r o m a n o n - K B K W i n i t i a l c o n d i t i o n . 2 6 : R a t i o o f t h e E u c l i d e a n n o r m o f t h e p r o j e c t i o n o f t h e i n i t i a l c o n d i t i o n o n t o t h e u n s t a b l e m a n i f o l d t o t h e E u c l i d e a n n o r m o f t h e i n i t i a l c o n d i t i o n . i x 1 8 5 1 8 6 1 8 9 1 9 1 1 9 2 1 9 4 W ’ 3 ’ U O D U N O T A T I O N M o r s e c o n s t a n t c r o s s - s e c t i o n a l a r e a K B K W s o l u t i o n p a r a m e t e r r e f e r e n c e c o n c e n t r a t i o n h a r d s p h e r e d i a m e t e r d i s s o c i a t i o n e n e r g y e l e c t r o n i c c h a r g e i n e l a s t i c c o l l i s i o n e n e r g y d e f e c t e n e r g y o f f o r m a t i o n o f H a t o m s r o o t - m e a n - s q u a r e e l e c t r i c f i e l d s t r e n g t h d i s t r i b u t i o n f u n c t i o n v i b r a t i o n a l l e v e l p o p u l a t i o n f r a c t i o n a l v i b r a t i o n a l c o n t r i b u t i o n m o l a r f l o w r a t e o v e r a l l h e a t t r a n s f e r c o e f f i c i e n t P l a n c k ' s c o n s t a n t P l a n c k ' s c o n s t a n t / . 2 1 1 d i f f e r e n t i a l s c a t t e r i n g c r o s s - s e c t i o n B o l t z m a n n ' s c o n s t a n t c r o s s - s e c t i o n p a r a m e t e r m a s s m a s s o f H 2 C S < 4 ! N m a s s o f H n u m b e r o f p a r t i c l e s e l e c t r o n d e n s i t y L e g e n d r e p o l y n o m i a l p r e s s u r e N - b o d y d i s t r i b u t i o n n - b o d y d i s t r i b u t i o n g e n e r a l i z e d f l u x F r a n c k - C o n d o n f a c t o r c h a r g e g e n e r a l i z e d s o u r c e e q u i l i b r i u m i n t e r n u c l e a r s e p a r a t i o n g a s c o n s t a n t t u b e r a d i u s n o r m a l i z e d a x i a l d i m e n s i o n t i m e t e m p e r a t u r e v i b r a t i o n a l t e m p e r a t u r e r e f e r e n c e t e m p e r a t u r e f e e d t e m p e r a t u r e n o r m a l i z e d H 2 c o n c e n t r a t i o n n o r m a l i z e d H c o n c e n t r a t i o n f l u i d v e l o c i t y v o l u m e p o s i t i v e i n t e g e r s x i G r e e k L e t t e r s s u b s e t o f p o s i t i v e i n t e g e r s s u b s e t o f p o s i t i v e i n t e g e r s J o u l e s / e v d i s s o c i a t i v e e x c i t a t i o n f r e q u e n c y v i b r a t i o n a l e x c i t a t i o n f r e q u e n c y i n c o m p l e t e g a m m a f u n c t i o n a c c o m m o d a t i o n c o e f f i c i e n t c r o s s - s e c t i o n p a r a m e t e r K r o n e c k e r d e l t a D i r a c d e l t a e n e r g y d e v i a t i o n v a r i a b l e a v e r a g e e n e r g y o f d i s s o c i a t i o n p r o d u c t s s c a t t e r i n g a n g l e e i g e n v a l u e r e d u c e d m a s s c o l l i s i o n f r e q u e n c y f u n d a m e n t a l o s c i l l a t o r f r e q u e n c y m o m e n t u m t r a n s f e r f r e q u e n c y e x t e n t o f i o n i z a t i o n d e n s i t y f e e d d e n s i t y i n t e r a c t i o n s p h e r e r a d i u s t o t a l c r o s s - s e c t i o n x i i s a fi x fi S ‘ e O E n o r m a l i z e d t i m e n o r m a l i z e d t e m p e r a t u r e n o r m a l i z e d v i b r a t i o n a l t e m p e r a t u r e f l u i d p r o p e r t y d i s t r i b u t i o n p a r a m e t e r p e r t u r b a t i o n p a r a m e t e r s c a t t e r i n g a n g l e s c a t t e r i n g a n g l e w a v e f u n c t i o n f r e q u e n c y s o l i d a n g l e x i i i m ' m , ) “ n fi “ P ) ' — t , V e c t o r c ’ 8 2 , y m 1 m a m 0 ) ? 7 > ‘ t > 5 : 1 0 > < » N 0 H " V e c t o r q u a n t i t i e s m a g n e t i c f i e l d s t r e n g t h e l e c t r i c f i e l d s t r e n g t h f o r c e c e n t e r o f m a s s v e l o c i t y u n i t n o r m a l a n g u l a r m o m e n t u m u n i t n o r m a l s u r f a c e e l e m e n t v o l u m e e l e m e n t r e l a t i v e v e l o c i t y p o s i t i o n v e l o c i t y x i v ' I d i l u t e g c a r r y 0 1 ; a n d M i l l o n t h e r I N T R O D U C T I O N T h e n o n e q u i l i b r i u m e n v i r o n m e n t o f a w e a k l y i o n i z e d d i l u t e g a s h a s b e e n s t u d i e d f o r s o m e t i m e a s o n e i n w h i c h t o c a r r y o u t c h e m i c a l s y n t h e s i s . W i t h n o t a b l e e x c e p t i o n s ( U r e y a n d M i l l e r , 1 9 5 3 ) t h e f o c u s o f s u c h i n v e s t i g a t i o n s i s g e n e r a l l y o n t h e p r o d u c t i o n o f s e l e c t e d s p e c i e s b y d i r e c t e l e c t r o n i m p a c t e x c i t a t i o n a n d r e a r r a n g e m e n t p r o c e s s e s . I n s u c h a n e n v i r o n m e n t , e l e c t r o n s a r e ” h e a t e d " b y a n e x t e r n a l f i e l d t o a v e r a g e e n e r g i e s m u c h a b o v e t h a t o f t h e n e u t r a l g a s c o m p o n e n t , a n d t h e n s c a t t e r o f f t h e n e u t r a l g a s m o l e c u l e s , r e s u l t i n g i n e x c i t a t i o n o f t h e g a s m o l e c u l e s z i g _ m o m e n t u m t r a n s f e r a n d i n t e r n a l s t a t e t r a n s i t i o n s . F o r e x a m p l e , t h e p r o d u c t i o n o f a t o m i c h y d r o g e n a n d e x c i t e d a t o m i c a n d m o l e c u l a r s t a t e s f r o m m o l e c u l a r h y d r o g e n i n a n e l e c t r i c a l d i s c h a r g e h a s b e e n t h e s u b j e c t o f a g r e a t n u m b e r o f e x p e r i m e n t a l a n d c a l c u l a t i o n a l w o r k s s i n c e t h e f i r s t d e c a d e o f t h i s c e n t u r y . M o s t o f t h e s e w o r k s h a v e c o n c e n t r a t e d o n m e a s u r e m e n t o r c a l c u l a t i o n s o f e x c i t a t i o n r a t e s a n d s t e a d y s t a t e c o n c e n t r a t i o n s o f a t o m i c h y d r o g e n i n w e a k l y i o n i z e d , d i l u t e H z . I n s o m e o f t h e w o r k s t h e p r o d u c t i o n o f a t o m i c h y d r o g e n a n d e x c i t e d a t o m i c o r m o l e c u l a r s t a t e s i s o n e s t e p i n a s y n t h e s i s p r o c e s s a s i n , f o r e x a m p l e , t h e p r o d u c t i o n o f C 2 H 2 a n d H C N ( C a p e z z u t o , 1 9 7 3 ) o r r e d u c t i o n o f m e t a l o x i d e s ( M o l i n a r i , 1 9 7 4 ) . I t i s p o s s i b l e , h o w e v e r , t o c o n s i d e r t h e c o l l i s i o n a n d t r a n s p o r t p h e n o m e n a o f a w e a T h e i n t e : t w e e n : e n e r g e t i : s t a t e . ' p a t h s i n f r o m t h e g a s t o t ‘ . e x i t p l e , t h e d i g s i n e X C e s C 0 3 5 0 } ; 1 ‘ . “ G r e e n 5 r e a s o n o f a w e a k l y i o n i z e d d i l u t e g a s f r o m a n o t h e r p o i n t o f v i e w . T h e i n t e r m e d i a t e s a n d p r o d u c t s o f i n e l a s t i c c o l l i s i o n s b e t w e e n f r e e e l e c t r o n s a n d m o l e c u l e s a r e o f t e n h i g h l y e n e r g e t i c w i t h r e s p e c t t o t r a n s l a t i o n a l m o t i o n o r i n t e r n a l s t a t e . T h e s e c o l l i s i o n p r o c e s s e s a r e n o t o n l y s y n t h e s i s p a t h s b u t a r e a l s o p o t e n t i a l p a t h s f o r e n e r g y t r a n s f e r f r o m t h e d i r e c t e d m o t i o n o f t h e h i g h l y e n e r g e t i c e l e c t r o n g a s t o t h e r a n d o m t h e r m a l m o t i o n o f t h e n e u t r a l g a s . F o r e x a m p l e , i n t h e e l e c t r o n i m p a c t d i s s o c i a t i o n o f H 2 ( v = 0 ) t h e d i s s o c i a t i o n p r o d u c t s m a y h a v e a s h a r e d k i n e t i c e n e r g y i n e x c e s s o f 4 e v . T h i s e s t i m a t e i s m a d e a s s u m i n g a F r a n c k — C o n d o n t r a n s i t i o n f r o m X ' 2 : t o b 3 X : . I f t h e s e e n e r g e t i c p r o d u c t s a r e a b l e t o t h e r m a l i z e t h e i r e n e r g y o n a r e a s o n a b l e t i m e s c a l e , t h e n t h e p r o d u c t i o n o f t h e s e p r o d u c t s m a y b e a m e c h a n i s m f o r e f f i c i e n t h e a t i n g o f d i l u t e g a s e s . A m o n g t h e p o s s i b l e a p p l i c a t i o n s o f s u c h a h e a t i n g m e c h a n i s m i s t h a t o f t h e e l e c t r o t h e r m a l t h r u s t e r ( H a w k i n s , 1 9 8 1 ) . O n t h e o t h e r h a n d , i f t h e p r o d u c t s d o n o t e q u i l i b r a t e w i t h t h e o t h e r g a s m o l e c u l e s a n d c a n b e s e p a r a t e d t h e n o t h e r a p p l i c a t i o n s c o m e i n t o v i e w . O n c e s u f f i c i e n t l y m o t i v a t e d , t h e d e v e l o p m e n t o f t h e s e p o s s i b i l i t i e s r e s t s o n e f f o r t s i n s e v e r a l a r e a s . F o r a s p e c i f i c m o l e c u l e o n e m u s t i d e n t i f y t h o s e p r o d u c t s a n d c o r r e s p o n d i n g c o l l i s i o n e v e n t s h a v i n g t h e " a p p r o p r i a t e " t i m e a n d e n e r g y s c a l e s . F o r e x a m p l e , i n a m i c r o w a v e d i s c h a r g e i n f l o w i n g d i l u t e H z t h e t i m e s c a l e f o r r e c o m b i n a t i o n o f h y d r o g e n a t o m s i s m u c h l o n g e r t h a n t h e t m e s c a a t o m i c : e v e n t 1 : d i s c h a r ; E O I E C U I I g a s i n ' h i ’ d r o g e i d e n s i t y t i m e s c a l e o f f l o w t h r o u g h t h e e l e c t r i c a l d i s c h a r g e a n d s o a t o m i c r e c o m b i n a t i o n i s n e g l e c t e d a s a n a p p r o p r i a t e c o l l i s i o n e v e n t i n a d e s c r i p t i o n o f t h e e n e r g y t r a n s f e r p r o c e s s i n t h e d i s c h a r g e . O n e m u s t a l s o r e l a t e t h e r a t e s o f t h e s e e l e c t r o n - m o l e c u l e e x c i t a t i o n p r o c e s s e s t o t h e m a c r o s c o p i c s t a t e o f t h e g a s i n t h e d i s c h a r g e . I n t h e e l e c t r o n i m p a c t d i s s o c i a t i o n o f h y d r o g e n o n e m u s t r e l a t e t h e r a t e o f t h e d i s s o c i a t i o n t o t h e d e n s i t y a n d a v e r a g e e n e r g y o f t h e e l e c t r o n g a s a n d n e u t r a l g a s . T h e e l e c t r o n - m o l e c u l e e x c i t a t i o n p r o c e s s e s p r o d u c e a v a r i e t y o f _ e x c i t e d p r o d u c t s w h i c h r e l a x b y i n t e r a c t i o n w i t h o t h e r g a s m o l e c u l e s a n d s o o n e m u s t a l s o r e l a t e t h e r e l a x a t i o n r a t e s o f t h e s e p r o d u c t s w i t h t h e c o n d i t i o n o f t h e g a s m i x t u r e . I n s o m e c a s e s , t h e e s t i m a t e d r e l a x a t i o n t i m e s c a l e s a r e m u c h s h o r t e r t h a n t h e e x c i t a t i o n t i m e s c a l e s a n d s o a n e a r - e q u i l i b r i u m m o d e l m a y b e u s e d t o r e l a t e e x c i t a t i o n r a t e s , r e l a x a t i o n r a t e s a n d t h e s t a t e o f t h e d i l u t e g a s . I n g e n e r a l , h o w e v e r , t h e m a c h i n e r y o f a k i n e t i c t h e o r e t i c a l a p p r o a c h m u s t b e d e v e l o p e d a n d a p p l i e d i n o r d e r t o i n t e g r a t e t h e e x c i t a t i o n , r e l a x a t i o n a n d t r a n s p o r t p r o c e s s e s i n a s e l f - c o n s i s t e n t a n a l y s i s o f e l e c t r o n i m p a c t " h e a t i n g " o f a w e a k l y i o n i z e d d i l u t e g a s . T h e t e r m ” s e l f - c o n s i s t e n t " i s u s e d h e r e t o d e s c r i b e c a l c u l a t i o n s o f e l e c t r o n i m p a c t e x c i t a t i o n r a t e s a n d n e u t r a l g a s p r o p e r t i e s m a d e f r o m a s i m u l t a n e o u s s o l u t i o n o f t h e a p p r o p r i a t e k i n e t i c e q u a t i o n s f o r t h e m u l t i c o m p o n e n t d i l u t e g a s . T h e d e v e l o p m e n t a n d a p p l i c a t i o n o f a k i n e t i c t h e o r e t i c a l a p p r o a c h t o t h e a n a l y s i s o f e l e c t r o n i m p a c t h e a t i n g o f w e a k l y i o n i z e d d i l u t e h y d r o g e n o f t h e w : r e v i e w s , a n d a l s o a p p r o a c h ! n e c e s s a r j t h e C U I I ‘ a s e l f - c d i s c h a r g a n a l y z e d b e t ' v l e e n r e s u l t s P r e s e n t s a n d c h e : S E V e r a l f l u i d o f c a 1 9 3 1 5 1 1 d i s - t u b : n e w s e t ” i t e m . h y d r o g e n f o r m s t h e c o n t e n t o f t h i s w o r k . T h e p r e s e n t a t i o n o f t h e w o r k i s a s f o l l o w s , f i r s t , t h e i n t r o d u c t o r y m a t e r i a l r e v i e w s , i n a g e n e r a l w a y , t h e p h y s i c s o f e l e c t r i c a l d i s c h a r g e s a n d a l s o d e f i n e s a h i e r a r c h y o f r e l a t e d p r o b l e m s t o b e a p p r o a c h e d . S e c o n d , t h e b a c k g r o u n d m a t e r i a l r e v i e w s t h e n e c e s s a r y k i n e t i c t h e o r y , c o l l i s i o n t h e o r y a n d t h e n r e v i e w s t h e c u r r e n t s t a t e o f a t t e m p t s t o i n t e g r a t e t h e m a t e r i a l i n t o a s e l f e c o n s i s t e n t a n a l y s i s o f a w e a k l y i o n i z e d d i l u t e g a s d i s c h a r g e . T h i r d , e a c h o f t h e s e l e c t e d p r o b l e m s i s s p e c i f i e d , a n a l y z e d , a n d p r e l i m i n a r y r e s u l t s g i v e n . T h e r e l a t i o n s h i p s b e t w e e n t h e p r o b l e m s a r e d i s c u s s e d . F o u r t h , t h e c o m p l e t e r e s u l t s a r e p r e s e n t e d a n d d i s c u s s e d . T h e c a l c u l a t i o n a l a n a l y s i s p r e s e n t e d i n t h i s w o r k c o v e r s s e v e r a l t o p i c s o f c h e m i c a l p h y s i c s a n d c h e m i c a l e n g i n e e r i n g a n d i s a n o r i g i n a l c o n t r i b u t i o n i n s e v e r a l r e s p e c t s . M o l e c u l a r h y d r o g e n i s s e l e c t e d a s t h e w o r k i n g f l u i d o f c h o i c e f o r a c o l l i s i o n i n d u c e d h e a t i n g s y s t e m . D e t a i l e d c a l c u l a t i o n s o f t h e e l e c t r o n i m p a c t d i s s o c i a t i o n p r o d u c t e n e r g y d i s t r i b u t i o n i s m a d e f o r e x c i t a t i o n o f t h e b - s t a t e o f H 2 . A n e w s e t o f s i m i l a r i t y v a r i a b l e s i s i d e n t i f i e d t o e x t e n d t h e c r i t e r i a o f M a r g e n a u t o d i s c h a r g e s i n w o r k i n g f l u i d s w h i c h a r e i n s t e a d y f l o w . F o r t h e f i r s t t i m e , . s e l f - c o n s i s t e n t c a l c u l a t i o n s O f e l e c t r o n g a s a n d n e u t r a l g a s p r o p e r t i e s a r e p r e s e n t e d a n d t h e n e c e s s i t y o f s u c h c a l c u l a t i o n s i s e s t a b l i s h e d . T h e n o n l i n e a r B o l t z m a n n e q u a t i o n f o r M a x w e l l m o l e c u l e s i s s o l v e d b y t h e I m a ‘ t h o d o f o r t h o g o n a l c o l l o c a t i o n , r e s u l t i n g i n s o m e u n a n t i c i p a t e d q u a l i t a t i v e b e h a v i o r . 1 . 1 0 v : i o n i z e d t r a n s f e ; a n d " a : m i 0 8 1 1 ' W e a k l y t o m e n : 4 0 2 1 3 3 : n e u t r a l p r t i c i t h e i n t 1 . 1 O v e r v i e w o f e l e c t r i c a l d i s c h a r g e p h y s i c s I n t h e i n t r o d u c t o r y m a t e r i a l t h e e n v i r o n m e n t o f a w e a k l y i o n i z e d d i l u t e g a s i s p r o p o s e d a s o n e i n w h i c h t o e f f e c t e n e r g y t r a n s f e r f r o m t h e e l e c t r o n t o n e u t r a l g a s t h r o u g h e l e c t r o n i m p a c t e x c i t a t i o n o f g a s m o l e c u l e s . B o t h t e r m s " w e a k l y i o n i z e d " a n d " d i l u t e g a s " d e s c r i b e c o n c e n t r a t i o n r e g i m e s f o r t h e c h a r g e d a n d n e u t r a l g a s c o m p o n e n t s r e s p e c t i v e l y . A g a s i s c o n s i d e r e d w e a k l y i o n i z e d i f t h e r a t i o o f c o n c e n t r a t i o n s o f c h a r g e d s p e c i e s t o n e u t r a l s p e c i e s i s l e s s t h a n 1 0 - 3 . F o r t h i s r e g i m e t h e d o m i n a n t c o l l i s i o n e v e n t s a r e t h o s e b e t w e e n a c h a r g e d a n d a n e u t r a l p a r t i c l e a n d b e t w e e n a n e u t r a l a n d a n o t h e r n e u t r a l p a r t i c l e . A g a s m a y b e s a i d t o b e p h e n o m e l o g i c a l l y d i l u t e i f t h e i n t e r c o l l i s i o n t i m e s c a l e i s m u c h l o n g e r t h a n t h e t i m e s c a l e o f t h e c o l l i s i o n i t s e l f . S u c h a d e f i n i t i o n m a y t h u s b e a p p l i e d o n l y t o g a s e s f o r w h i c h a n i n t e r c o l l i s i o n t i m e s c a l e m a k e s s e n s e , i . e . s c a t t e r i n g c r o s s - s e c t i o n s h a v e r a d i a l o r a n g u l a r c u t - o f f s . T h e m o t i v a t i o n f o r r e s t r i c t i o n o f t h e s c o p e o f t h i s w o r k t o t h e w e a k l y i o n i z e d d i l u t e g a s r e g i m e s p r i n g s b o t h f r o m a p p l i c a t i o n s i n t e r e s t a n d f r o m t h e o r e t i c a l t r a c t a b i l i t y . A n a p p l i c a t i o n o f e l e c t r o n i m p a c t h e a t i n g o f a m o l e c u l a r g a s w h i c h i s o f g r e a t i n t e r e s t i s f o u n d i n t h e e l e c t r o t h e r m a l p r o p u l s i o n c o n c e p t ( H a w k i n s , 1 9 8 1 ) . I n t h i s c o n c e p t a s e l f - s u s t a i n e d m i c r o w a v e f r e q u e n c y e l e c t r i c a l d i s c h a r g e i n a r e s o n a n t c a v i t y i s u s e d t o s u s t a i n a c o n d i t i o n o f w e a k i o n i z a 1 p a r t i a l t o r e l s e o t i t h e r e k n e s ‘ C E V I t j 1 0 2 : ; 4 V ! “ c V ‘ u i I / O ‘ i o n i z a t i o n i n a d i l u t e l o w m o l e c u l a r w e i g h t g a s . T h e g a s i s p a r t i a l l y d i s s o c i a t e d i n t h e p l a s m a r e g i o n a n d t h e n r e c o m b i n e s t o r e l e a s e a n a m o u n t o f e n e r g y c o r r e s p o n d i n g t o i t s d i s s o c i a t i o n e n e r g y . T h e e n e r g y r e l e a s e d i s t h e r m a l i z e d i n t h e c o n v e r g i n g s e c t i o n o f a n o z z l e a n d t h e h o t g a s e s t h e n e x p a n d t h r o u g h t h e d i v e r g i n g s e c t i o n o f t h e n o z z l e t o p r o v i d e t h r u s t . I n m o s t i n v e s t i g a t i o n s t o d a t e , t h e p l a s m a s f o r m e d i n t h e r e s o n a n t c a v i t y a r e n o t m a g n e t i c a l l y c o n f i n e d a n d s o l o w e x t e n t s o f i o n i z a t i o n a r e t h e r u l e . T h e a n a l y s i s o f t h e e l e c t r o n g a s c o m p o n e n t o f t h e i o n i z e d d i l u t e g a s i s s i m p l i f i e d g r e a t l y b y t h e w e a k i o n i z a t i o n r e s t r i c t i o n i n t h a t t h e c h a r g e d p a r t i c l e m i c r o f i e l d s a r e s t r o n g l y d a m p e d , ( i . e . , d e b y e s p h e r e s a r e m u c h s m a l l e r t h a n d i m e n s i o n o f g a s r e g i o n ) . A s a r e s u l t , t h e c h a r g e d p a r t i c l e s a r e g r e a t l y i n f l u e n c e d b y t h e e x t e r n a l e l e c t r o m a g n e t i c f i e l d a n d b y c o l l i s i o n s w i t h u n c h a r g e d s p e c i e s b u t a r e a f f e c t e d l i t t l e b y t h e c o u l o m b f i e l d s o f o t h e r c h a r g e d p a r t i c l e s . T h e d i l u t e g a s r e s t r i c t i o n i s a l s o r e l a t e d t o i n t e r e s t i n t h e e l e c t r o t h e r m a l p r o p u l s i o n c o n c e p t , b u t m o r e f u n d a m e n t a l l y t o t h e c u r r e n t s t a t e o f a f f a i r s i n t h e k i n e t i c t h e o r y o f f l u i d s . W i t h o u t e s t i m a t e s o f e x c i t a t i o n a n d r e l a x a t i o n t i m e s c a l e s t h e r e i s n o r e a s o n t o a s s u m e t h a t t h e n e u t r a l g a s c o m p o n e n t s i n c o n t a c t w i t h a n e l e c t r o n g a s a r e c h a r a c t e r i z e d b y a M a x w e l l - B o l t z m a n n d i s t r i b u t i o n a n d s o a n e v o l u t i o n e q u a t i o n f o r t h e d i s t r i b u t i o n s i s r e q u i r e d . T h e o n l y s u c h e v o l u t i o n e q u a t i o n w i t h a g o o d d e a l o f g a s d y n a m i c s u p p o r t i s t h e B o l t z m a n n t r a n s p o h e r e a f t r i g o r 1 l i m i t ( V o l . 1 0 S 6 5 m e A < . i n a 0 1 2 9 3 5 f l o w t o a , 9 6 e x t e r n a l W i t h t h e E X C i t e j b “ r e d 1 1 3 0 O C C 3 3 9 t o t i f b : a t } ; a n : w e : o n e . F o r a n i d e a l g a s a t c o n s t a n t p r e s s u r e , t h e g a s I — ~ _ . _ . - — A t r a n s p o r t e q u a t i o n . T h e B o l t z m a n n t r a n s p o r t e q u a t i o n , k n o w n h e r e a f t e r a s t h e B o l t z m a n n e q u a t i o n , o n l y t a k e s o n t h e s c a n t y r i g o r i t p o s s e s s e s i n t h e z e r o d e n s i t y ( B o l t z m a n n - G r a d ) l i m i t ( C e r c i g n a n i , 1 9 7 5 , a l s o S t u d i e s i n S t a t . M e c h . , V o l . 1 0 ) . T h u s t h e z e r o d e n s i t y l i m i t p r o s c r i b e s t h e d i l u t e g a s r e s t r i c t i o n . A g e n e r a l m e t h o d t o m a i n t a i n a c o n d i t i o n o f w e a k i o n i z a t i o n i n a d i l u t e g a s i s t h r o u g h a n e l e c t r i c a l d i s c h a r g e i n a s t e a d y g a s f l o w . A l o w d e n s i t y e l e c t r o n g a s i s f o r m e d a n d e n e r g i z e d t o a , g e n e r a l l y , s t r o n g l y n o n e q u i l i b r i u m c o n d i t i o n b y t h e e x t e r n a l e l e c t r o m a g n e t i c f i e l d . T h e e n e r g e t i c e l e c t r o n s s c a t t e r w i t h t h e m o l e c u l e s o f t h e d i l u t e g a s t o p r o d u c e a v a r i e t y o f e x c i t e d s t a t e s w h i c h t h e n r e l a x b y o t h e r s c a t t e r i n g e v e n t s o r b y a r a d i a t i v e t r a n s i t i o n . R e l a x a t i o n a n d e n e r g y e x c h a n g e m a y a l s o o c c u r b y i n t e r a c t i o n w i t h t h e b o u n d a r y o f t h e g a s f l o w . D u e t o t h e l o w d e n s i t y o f t h e e l e c t r o n g a s , t h e c o n t r i b u t i o n s o f b l a c k b o d y r a d i a t i o n a n d b r e m s s t r g h l u n g t o t h e r e l a x a t i o n a n d e n e r g y t r a n s f e r r a t e s a r e n e g l i g i b l e . T h e p r e s e n c e o f a s t e a d y f l o w v e l o c i t y f i e l d i n t h e d i s c h a r g e i n t r o d u c e s s o m e t r a n s p o r t p h e n o m e n a n o t u s u a l l y f o u n d i n e l e c t r i c a l d i s c h a r g e s , t h a t o f b u l k t r a n s p o r t i n a n d o u t o f t h e i o n i z e d g a s r e g i o n . M o s t l a b o r a t o r y e l e c t r i c a l d i s c h a r g e s O p e r a t e a t a n d a r e m o d e l e d a s c l o s e d s y s t e m s a n d s o t h e d i s c h a r g e i s m a i n t a i n e d u n d e r c o n s t a n t g a s d e n s i t y . I n a s t e a d y f l o w ' d i s c h a r g e t h e c o n d i t i o n i s m o r e n e a r l y a c o n s t a n t p r e s s u r e d e n s i t y i s t h e c o n s t a : b e t w e e n e x c c o n s t a n t d e p r o c e s s e s 9 t h e r e l a x a t d i l u t e g a s { I 0 0 t h i s I ° f c o l l i s i c f l o w m u s t j f i e l d , c o o ; t r a n s f e r a : fi e S c r i p t i o : P a r t i c l e d j i fl d u c e d h e : 1 ' 2 P r o b l , T h i s c a l l i S i o n 9 m m a n d £ 0 : . s i g n i f j “ t h a t ‘ s 0 1 i f ) : . j ‘ 5 ' » : f e t e e r d e n s i t y i s i n v e r s e l y p r o p o r t i o n a l t o t h e t e m p e r a t u r e a n d s o i n t h e c o n s t a n t p r e s s u r e d i s c h a r g e t h e r e i s a s t r o n g c o u p l i n g b e t w e e n e x c i t a t i o n a n d r e l a x a t i o n p r o c e s s e s n o t f o u n d i n c o n s t a n t d e n s i t y d i s c h a r g e s . T h e r a t e s o f t h e e x c i t a t i o n p r o c e s s e s g e n e r a l l y a r e p r o p o r t i o n a l t o t h e g a s d e n s i t y w h e r e a s t h e r e l a x a t i o n p r o c e s s e s c o n t r i b u t e t o t h e a v e r a g e e n e r g y o f t h e d i l u t e g a s a n d t h u s t o i t s t e m p e r a t u r e . I t i s a p p a r e n t e v e n f r o m t h i s b r i e f d i s c u s s i o n t h a t a n y s e l f - c o n s i s t e n t d e s c r i p t i o n o f c o l l i s i o n i n d u c e d h e a t i n g o f a w e a k l y i o n i z e d g a s i n s t e a d y f l o w m u s t i n t e g r a t e t h e e f f e c t s o f a n e x t e r n a l e l e c t r o m a g n e t i c f i e l d , c o u p l e d k i n e t i c a n d t r a n s p o r t p r o c e s s e s a n d e n e r g y t r a n s f e r a c r o s s b o u n d a r i e s . T h e a p p r o p r i a t e , f i n e s t l e v e l o f d e s c r i p t i o n f o r a p h e n o m e n o l o g i c a l l y d i l u t e g a s i s t h e o n e - p a r t i c l e d i s t r i b u t i o n f u n c t i o n a n d t h e a n a l y s i s o f c o l l i s i o n i n d u c e d h e a t i n g m u s t b e i n t e r m s o f t h i s c o n s t r u c t . 1 . 2 P r o b l e m d e f i n i t i o n T h i s w o r k i s a t h e o r e t i c a l a n d c a l c u l a t i o n a l s t u d y o f c o l l i s i o n i n d u c e d h e a t i n g o f a w e a k l y i o n i z e d d i l u t e g a s i n s t e a d y f l o w . I t b e g i n s w i t h s e l e c t i o n o f a s u i t a b l e m o d e l s Y s t e m a n d i d e n t i f i c a t i o n o f t h e p r o b a b l e c o l l i s i o n a l p a t h w a y s f o r s i g n i f i c a n t e n e r g y t r a n s f e r . A l s o n e c e s s a r y h e r e i s a n e s t i m a t e o f t h e e n e r g y d i s t r i b u t i o n f o r t h e e x c i t e d s t a t e s W h i c h a r e o p e n t o t h e m o d e l s y s t e m . M a n y e x c i t e d s t a t e s h a v e d i s c r e t e e n e r g y l e v e l s s o s u c h e s t i m a t e s a r e e a s i l y o b t a i n e d , v i b r a t i o n a l S t a t t e r i n o e h o w e v e r , f o r o f s t a t e s e : r e q u i r e d . O n c e a n d r e l a x a t ; p o s s i b l e e f : 9 3 5 s t r e a m . 8 1 3 1 1 8 5 p r o : fi e s e P r o d u c a : i n V e s t i c z a h o w e v e r , f o r d i s s o c i a t i o n a n d i o n i z a t i o n p r o d u c t s a c o n t i n u u m o f s t a t e s e x i s t a n d s o s o m e m o r e d e t a i l e d c a l c u a t i o n s m a y b e r e q u i r e d . O n c e t h e m o d e l s y s t e m i s s e l e c t e d a n d t h e e x c i t a t i o n a n d r e l a x a t i o n p r o c e s s e s i d e n t i f i e d , t h e a n a l y s i s a d d r e s s e s p o s s i b l e e f f e c t s o f t h e e x c i t e d p r o d u c t s p r e s e n t i n t h e i o n i z e d g a s s t r e a m . I n a w e a k l y i o n i z e d d i l u t e d i a t o m i c g a s t h e e x c i t e d p r o d u c t s i n c l u d e t h e n o n e q u i l i b r i u m p o p u l a t i o n s i n t h e v i b r a t i o n a l a n d r o t a t i o n a l d e g r e e s o f f r e e d o m a s w e l l a s t h e a t o m s a n d i o n s f o r m e d i n d i s s o c i a t i o n , a t t a c h m e n t a n d i o n i z a t i o n s c a t t e r i n g e v e n t s . T h e a n a l y s i s o f t h e p o s s i b l e e f f e c t s o f t h e s e p r o d u c t s i s d i v i d e d i n t o t h r e e c a t e g o r i e s . T h e f i r s t i s a n i n v e s t i g a t i o n o f t h e e f f e c t o f t h e s e p r o d u c t s o n t h e m a c r o s c o p i c c o n d i t i o n o f t h e d i l u t e g a s , t h a t i s , h o w d o t h e e x c i t a t i o n p r o c e s s e s a f f e c t t h e d e n s i t y , a v e r a g e e n e r g y a n d v e l o c i t y o f t h e d i l u t e g a s ? W e m u s t f i r s t e s t a b l i s h t h a t c o l l i s i o n i n d u c e d h e a t i n g o f a w e a k l y i o n i z e d d i l u t e g a s i s f e a s i b l e f o r t h e m o d e l s y s t e m . I f t h e a v e r a g e e n e r g y o f t h e d i l u t e g a s i n c r e a s e s , t h e n t h e g a s d e n s i t y w i l l d r o p a n d t h e b u l k v e l o c i t y o f t h e g a s w i l l i n c r e a s e . T h e e x c i t a t i o n r a t e s a r e d i r e c t l y p r o p o r t i o n a l t o t h e n e u t r a l g a s d e n s i t y a n d s o t h e n e x t s t e p i n t h e a n a l y s i s i s a n i n v e s t i g a t i o n o f t h e C o u p l e d e v o l u t i o n o f t h e e l e c t r o n g a s a n d t h e d i l u t e n e u t r a l g a s . A s t h e d i l u t e n e u t r a l g a s i s h e a t e d a n d t h u s a s i t s d e n s i t y d e c r e a s e s , h o w d o t h e v a r i o u s e l e c t r o n i m p a c t e x c i t a t i o n r a t e s c h a n g e a n d w h a t e f f e c t , i n t u r n , d o t h e s e c h a n g e s i n a n d t h e m a e x c i t a t i o n p h a s e o f t c o n s i s t e n t i o n i z e d d i e x c i t a t i o n T h e r e l a t i o n s h 1 0 e x c i t a t i o n r a t e s h a v e o n t h e g a s h e a t i n g ? T h e g o a l o f t h i s p h a s e o f t h e i n v e s t i g a t i o n t h e n i s t o e s t a b l i s h a s e l f - c o n s i s t e n t r e l a t i o n s h i p b e t w e e n t h e c o n d i t i o n o f t h e w e a k l y i o n i z e d d i l u t e g a s i n s t e a d y f l o w a n d t h e c o l l i s i o n i n d u c e d e x c i t a t i o n r a t e s . T h e s e f i r s t t w o p h a s e s o f i n v e s t i g a t i o n f o c u s o n t h e r e l a t i o n s h i p b e t w e e n t h e c o l l i s i o n i n d u c e d h e a t i n g p r o c e s s e s a n d t h e m a c r o s c o p i c c o n d i t i o n o f t h e d i l u t e n e u t r a l g a s a n d o n e - p a r t i c l e d i s t r i b u t i o n f u n c t i o n o f t h e e l e c t r o n g a s . I n t h e t h i r d p h a s e o f i n v e s t i g a t i o n , t h e r e l a x a t i o n o f a n o n e q u i l i b r i u m o n e - p a r t i c l e d i s t r i b u t i o n o f a d i l u t e n e u t r a l e x c i t e d p r o d u c t i s e x a m i n e d . I n t h i s e x a m i n a t i o n w e d e p a r t f r o m t h e m a c r o s c o p i c d e s c r i p t i o n o f t h e n e u t r a l d i l u t e g a s . R e c a l l t h a t f o r a w e a k l y i o n i z e d d i l u t e s t r e a m o f m o l e c u l a r h y d r o g e n , t h e c o l l i s i o n i n d u c e d d i s s o c i a t i o n p r o d u c t s s h a r e a p p r o x i m a t e l y 4 . 4 e v o f k i n e t i c e n e r g y . T h e t h e r m a l e n e r g y o f t h e h y d r o g e n a t o m s i s m u c h s m a l l e r a n d s o t h e r e l a x a t i o n t i m e s c a l e s f o r t h e h i g h e n e r g y p r o d u c t s a r e n o t l i k e l y t o b e t h a t o f t h e a t o m s i n t h e t h e r m a l r e g i o n o f t h e d i s t r i b u t i o n f u n c t i o n . T h e m a n n e r o f r e l a x a t i o n a n d t h e r e l a x a t i o n t i m e s c a l e s f o r t h e h i g h e n e r g y t a i l o f t h e d i s t r i b u t i o n a r e a c c e s s i b l e t h r o u g h s o l u t i o n o f t h e a p p r o p r i a t e k i n e t i c e q u a t i o n f o r t h e o n e - p a r t i c l e d i s t r i b u t i o n f u n c t i o n . T h e s e t i m e s c a l e s h a v e c o n s i d e r a b l e s i g n i f i c a n c e f o r c o l l i s i o n i n d u c e d h e a t i n g a s i t i s t h e r e l a x a t i o n s t e p t h a t r e c o v e r s t h e e n e r g y o f e x c i t e d p r o d u c t s a s t h e r m a l e n e r g y . F o r t h i s e x a m i n a t i o n o f e m 8 1 ; m 2 . 0 ” g a m e “ m a y 8 5 3 9 $ 2 . 3 m w e » : 1 . a t ; " t o a 9 m 1 1 t h e r e l a x a t i o n p r o b l e m a v e r y s i m p l e m o d e l p r o b l e m i s s e l e c t e d . T h e e v o l u t i o n o f a s y s t e m o f d i l u t e M a x w e l l m o l e c u l e s a t c o n s t a n t d e n s i t y a n d t e m p e r a t u r e f r o m a n o n e q u i l i b r i u m d i s t r i b u t i o n t o t h e e q u i l i b r i u m M a x w e l l i a n i s s t u d i e d b y s o l u t i o n o f t h e f u l l y n o n l i n e a r B o l t z m a n n e q u a t i o n . T h e s e f o u r b r i e f o u t l i n e s d e f i n e t h e s c o p e o f t h i s w o r k . B e c a u s e e l e m e n t s o f k i n e t i c t h e o r y , s c a t t e r i n g t h e o r y a n d t r a n s p o r t t h e o r y a r e i n v o l v e d i n t h e i n v e s t i g a t i o n , a r e v i e w o f t h e r e l e v a n t w o r k i n e a c h f i e l d i s s u p p l i e d i n t h e f o l l o w i n g s e c t i o n . F o l l o w i n g t h e r e v i e w o f t h e t h e o r e t i c a l f r a m e w o r k w i t h i n w h i c h t h i s w o r k i s d o n e i s a r e v i e w o f r e c e n t c a l c u l a t i o n a l w o r k i n t h e t h e o r y a n d m o d e l i n g o f e l e c t r i c a l d i s c h a r g e s . f r ) 4 0 T o m " . w M p 1 : ‘ A n r B A C K G R O U N D A N D R E L A T E D W O R K T h i s c h a p t e r i s a r e v i e w o f t h e r e l e v a n t a r e a s o f k i n e t i c t h e o r y , s c a t t e r i n g t h e o r y a n d t r a n s p o r t t h e o r y , a s w e l l a s a r e v i e w o f p r o g r e s s t o d a t e i n a p p l i c a t i o n o f t h i s t h e o r e t i c a l b a c k g r o u n d t o s t u d y o f c h e m i c a l s y n t h e s i s a n d e n e r g y t r a n s f e r i n w e a k l y i o n i z e d d i l u t e g a s e s . A s s u c h , t h e d i v i s i o n o f t h e c h a p t e r i s a s f o l l o w s , t h e f i r s t s e c t i o n i s d e v o t e d t o r e v i e w o f r e l e v a n t k i n e t i c a n d t r a n s p o r t t h e o r y b e g i n n i n g w i t h t h e g e n e r a l m a n y - b o d y p r o b l e m a n d c l o s i n g w i t h d e r i v a t i o n o f t h e m a c r o s c 0 p i c t r a n s p o r t e q u a t i o n s . A l s o d i s c u s s e d i s t h e t r a n s p o r t t h e o r y o f w e a k l y i o n i z e d m e d i a . T h e s e c o n d s e c t i o n r e v i e w s s c a t t e r i n g t h e o r y a n d e x p e r i m e n t a l r e s u l t s f o r c r o s s s e c t i o n s a n d d i s c u s s e s t h e p a t h w a y s f o r c o l l i s i o n i n d u c e d h e a t i n g o f s e v e r a l l o w m o l e c u l a r w e i g h t d i a t o m i c g a s e s . T h e m i c r o s c o p i c d y n a m i c s o f e l a s t i c a n d i n e l a s t i c s c a t t e r i n g i s d i s c u s s e d . I n t h e t h i r d s e c t i o n s e v e r a l a r e a s o f w o r k t o d a t e i n a n a l y s i s o f e l e c t r i c a l d i s c h a r g e s a r e r e v i e w e d . B o t h c a l c u l a t i o n a l a p p r o a c h e s a n d r e s u l t s o f c a l c u l a t i o n s o f e x c i t a t i o n a n d r e l a x a t i o n r a t e s a s w e l l a s o f m a c r o s c o p i c f l u i d v a r i a b l e s a n d e x c i t e d p r o d u c t d i s t r i b u t i o n s a r e c o v e r e d . A l t h o u g h d i l u t e g a s d i s c h a r g e s i n t h e m i c r o w a v e f r e q u e n c y r e g i o n a r e o f c h i e f i n t e r e s t , l o w f r e q u e n c y a n d d . c . e l e c t r i c a l c h a r g e s a r e a l s o m e n t i o n e d w h e r e r e l e v a n t . 1 2 2 . 1 K i n e K i g r o u p e d t a l t h o u g h e a c h a t t e - k i n e t i c t h e o r y i s t h e d e s c r i p t i o n o f t h e e v o l u t i o n o f t h i s 1 3 2 . 1 K i n e t i c a n d t r a n s p o r t t h e o r y K i n e t i c t h e o r y a n d s t a t i s t i c a l m e c h a n i c s a r e g e n e r a l l y g r o u p e d t o g e t h e r i n w h a t i s k n o w n a s s t a t i s t i c a l p h y s i c s , a n d a l t h o u g h t h e t w o a p p r o a c h e s h a v e i m p o r t a n t d i f f e r e n c e s , t h e y e a c h a t t e m p t t o d e s c r i b e t h e m a c r o s c o p i c p r o p e r t i e s a n d b e h a v i o r i n t e r m s o f m i c r o s c o p i c s t r u c t u r e a n d d y n a m i c s . S p e c i f i c a l l y , s t a t i s t i c a l m e c h a n i c s d e s c r i b e s t h e a v e r a g e , o v e r a n a p p r o p r i a t e l y d e f i n e d e n s e m b l e o f s y s t e m s i n e q u i l i b r i u m , o f s o m e p r o p e r t y o f t h e s y s t e m . I n f i n i t e t i m e s c a l e s a r e i n v i e w i n a s t a t i s t i c a l m e c h a n i c a l a p p r o a c h . O n t h e o t h e r h a n d , k i n e t i c t h e o r y d e s c r i b e s t h e d y n a m i c a l e v o l u t i o n o f a p a r t i c u l a r m i c r o s t a t e f r o m o n e n o n e q u i l i b r i u m c o n d i t i o n t o a n o t h e r . U n l e s s a n e n s e m b l e o f i n i t i a l o r f i n a l s t a t e s i s j u s t i f i e d a n d d e f i n e d , t h e c o n c e p t o f e n s e m b l e i s a b s e n t . I n d e e d , f o r n o n e q u i l i b r i u m s y s t e m s , " W e d o n o t h a v e a n y g e n e r a l p r e s c r i p t i o n f o r c h o o s i n g a p p r o p r i a t e e n s e m b l e s . . . " ( M o n t r o l l a n d L e b o w i t z , 1 9 8 3 ) . F i n i t e t i m e s c a l e s a r e a p p r o p r i a t e i n a k i n e t i c t h e o r e t i c a l f r a m e w o r k . A l t h o u g h s t a t i s t i c a l m e c h a n i c s i s a p p l i e d t o w e a k l y n o n e q u i l i b r i u m s y s t e m s v i a p e r t u r b a t i o n a n a l y s i s , e . g . l i n e a r r e s p o n s e t h e o r y ( S e e 2 w a n z i g , 1 9 6 5 ) , t h e m a c h i n e r y o f k i n e t i c t h e o r y i s m o r e a p p r o p r i a t e f o r t h e s t u d y o f s t r o n g l y n o n e q u i l i b r i u m s y s t e m s . T h e m a t h e m a t i c a l c o n s t r u c t o f k i n e t i c t h e o r y i s t h e N t b o d y d i s t r i b u t i o n f u n c t i o n , a n o n n e g a t i v e c o n t i n u o u s f u n c t i o n O f ‘ t h e p o s i t i o n a n d v e l o c i t y o f N p a r t i c l e s . O n e g o a l o f “ H m fl u a w l a w m a n m o w m n u “ n m m a “ s h r h _ F . . . r f . s a s ” fl u fl 0 ) ; ) m m ( : 1 1 1 4 d i s t r i b u t i o n f u n c t i o n i n t e r m s o f t h e d y n a m i c s o f t h e N i n t e r - a c t i n g p a r t i c l e s . O n e a p p r o a c h i n t h i s p u r s u i t i s t h a t o f a m o l e c u l a r d y n a m i c s c a l c u l a t i o n . T h e t r a j e c t o r i e s o f a s m a l l n u m b e r ( n . 1 0 3 ) o f i n t e r a c t i n g p a r t i c l e s a r e c a l c u l a t e d w i t h t h e e q u a t i o n s o f m o t i o n , p e r i o d i c b o u n d a r y c o n d i t i o n s , a n d a n i n i t i a l c o n d i t i o n . F r o m t h e p o s i t i o n s a n d v e l o c i t i e s c a l c u l a t e d i n t h i s w a y , a n y p r o p e r t y o f t h e a s s e m b l y o f p a r t i c l e s m a y a l s o b e c a l c u l a t e d f o r a n y t i m e . S e v e r a l p r o b l e m s m u s t b e f a c e d i f t h i s m e t h o d i s t o b e a p p l i e d t o a s s e m b l i e s o f m o l e c u l e s w i t h i n t e r n a l s t r u c t u r e . T h e f i r s t r e a l l y h a s n o t h i n g t o d o w i t h t h e e x i s t e n c e o f i n t e r n a l s t r u c t u r e , b u t i s r e l a t e d t o t h e c o n c e p t o f t h e G i b b s e n s e m b l e . F o r t h e c a l c u l a t i o n o f s o m e p r o p e r t y o f t h e p a r t i c l e a s s e m b l y , o n e m u s t d e f i n e a n e n s e m b l e o f i n i t i a l m i c r o s t a t e s , f o l l o w t h e e v o l u t i o n ( p o s s i b l y n o n l i n e a r ) o f e a c h m i c r o s t a t e a n d t h e n a v e r a g e o v e r t h e r e s u l t s . T h e p r o b l e m s w i t h t h i s p r o c e d u r e a r e c o n c e p t u a l a n d c a l c u l a t i o n a l . C o n c e p t u a l l y o n e h a s t h e p r o b l e m o f t h e d e f i n i t i o n o f t h e a p p r o p r i a t e e n s e m b l e a s w e l l a s t h e i s s u e o f t h e v a l i d i t y o f e q u a l a _ p r i o r i p r o b a b i l i t i e s f o r t h e e l e m e n t s o f t h e e n s e m b l e . C a l c u l a t i o n a l l y o n e m u s t d e a l W i t h a t r e m e n d o u s n u m b e r o f m i c r o s t a t e s f o r a n y r e a s o n a b l e a s s e m b l y . A f u r t h e r p r o b l e m w h i c h i s r e l a t e d t o t h e e x i s t e n c e O f i n t e r n a l s t r u c t u r e i s a l s o c a l c u l a t i o n a l i n n a t u r e . A m o l e c u l a r d y n a m i c s s i m u l a t i o n o f a w e a k l y i o n i z e d d i l u t e g a s w o u l d r e Q u i r e s i m u l a t i o n o f a g r e a t v a r i e t y o f s c a t t e r i n g p h e n o m e n a , m u c h g r e a t e r t h a n t h e c u r r e n t s t a t e o f M D s i m u l a t i o n s p e r m i t . t h e e v o l i s n o t 1 ( E a r l y ! f u n c t i o : i n t h i s l i t h t h a n d t h e L i o u v i l k i i e t i c 0 1 t o a 6 ) . ; M S a ' 1 5 R e c a l l t h a t t h e g o a l o f k i n e t i c t h e o r y i s t o d e s c r i b e t h e e v o l u t i o n o f t h e n - b o d y d i s t r i b u t i o n f u n c t i o n , w h e r e n i s n o t n e c e s s a r i l y t h e n u m b e r o f p a r t i c l e s o f a n a s s e m b l y . ( E a r l y M D c a l c u l a t i o n s f o c u s e d o n t h e r a d i a l d i s t r i b u t i o n f u n c t i o n ( n = 2 ) a n d t r a n s p o r t c o e f f i c i e n t s ) . A n o t h e r a p p r o a c h i n t h i s p u r s u i t i s t h a t o f t h e k i n e t i c e q u a t i o n . O n e b e g i n s w i t h t h e e q u a t i o n s o f m o t i o n , b o u n d a r y a n d i n i t i a l c o n d i t i o n s a n d t h e n c o n t r a c t s t h e l e v e l o f d e s c r i p t i o n f r o m t h e N - b o d y L i o u v i l l e e q u a t i o n f o r t h e N - b o d y d i s t r i b u t i o n f u n c t i o n t o t h e k i n e t i c e q u a t i o n f o r a n n - b o d y d i s t r i b u t i o n f u n c t i o n ( n N ) o r t o a h i e r a r c h y o f s u c h e q u a t i o n s . T h e p r e m i e r e x a m p l e o f t h i s a p p r o a c h i s t h e a t t e m p t b y s e v e r a l w o r k e r s t o d e r i v e t h e B o l t z m a n n t r a n s p o r t e q u a t i o n f o r t h e s i n g l e p a r t i c l e d i s t r i b u t i o n f u n c t i o n f r o m t h e L i o u v i l l e e q u a t i o n ( K i r k w o o d a n d R o s s ( 1 9 5 8 ) , B o g o l i u b o v ( 1 9 4 6 ) , G r a d ( 1 9 5 8 ) ) . T h e c o n t r a c t i o n f r o m t h e N - b o d y d e s c r i p t i o n t o t h e s i n g l e p a r t i c l e d i s t r i b u t i o n , w h e t h e r b y t h e i n t u i t i v e c o n t i n u u m m e t h o d o f B o l t z m a n n ( 1 8 7 2 ) o r t h e l a t e r a t t e m p t s a t a r i g o r o u s r e d u c t i o n r e s u l t i n a B o l t z m a n n o r B o l t z m a n n - l i k e k i n e t i c e q u a t i o n . T h e k i n e t i c e q u a t i o n d e s c r i b e s t h e e v o l u t i o n o f t h e s i n g l e p a r t i c l e d i s t r i b u t i o n f u n c t i o n i n t e r m s o f t h e e f f e c t s o f f o r c e s , g r a d i e n t s , a n d b i n a r y c o l l i s i o n s . I n t h e z e r o d e n s i t y ( B o l t z m a n n - G r a d ) l i m i t t h e s i n g l e p a r t i c l e d i s t r i b u t i o n c o n t a i n s a l l t h e i n f o r m a t i o n t o b e h a d a b o u t t h e g a s . F r o m v e l o c i t y m o m e n t s o f t h e d i s t r i b u t i o n f u n c t i o n o n e m a y c a l c u l a t e a n « a v e r a g e d e n s i t y , m o m e n t u m a n d e n e r g y . F r o m i n t e g r a l s o f 1 6 p r o d u c t s o f t h e d i s t r i b u t i o n f u n c t i o n a n d c r o s s - s e c t i o n s o n e m a y c a l c u l a t e c o l l i s i o n , a n d t h u s , r e a c t i o n r a t e s . K n o w l e d g e o f t h e d i s t r i b u t i o n i s t h e b a s i s f o r i n t e r p r e t a t i o n o f a w i d e r a n g e o f e x p e r i m e n t a l r e s u l t s , f o r e x a m p l e , r e l a t i v e i n t e n s i t i e s o f e m i s s i o n l i n e s , D o p p l e r b r o a d e n i n g a n d V I c h a r a c t e r i s t i c s o f a L a n g m u i r e l e c t r i c p r o b e . C a l c u l a t i o n o f t h e s i n g l e p a r t i c l e d i s t r i b u t i o n f u n c t i o n o f t h e e l e c t r o n c o m p o n e n t a n d o f t h e e x c i t e d p r o d u c t c o m p o n e n t i n a s e l f - c o n s i s t e n t m a n n e r i s , t h e r e f o r e , o n e a p p r o a c h t o a n a l y s i s o f c o l l i s i o n i n d u c e d h e a t i n g i n a w e a k l y i o n i z e d d i l u t e g a s i n s t e a d y f l o w a n d i s t h e a p p r o a c h p u r s u e d i n t h i s w o r k . I t i s a p p r o p r i a t e h e r e t o p r o c e e d f r o m t h e N - b o d y d e s c r i p t i o n , t h r o u g h t h e c o n t r a c t i o n t o t h e e v o l u t i o n e q u a t i o n f o r t h e s i n g l e p a r t i c l e d i s t r i b u t i o n f u n c t i o n . W h a t f o l l o w s i s a n e x t e n s i o n a n d c l a r i f i c a t i o n o f a d e r i v a t i o n b y C e r c i g n a n i ( 1 9 7 5 ) w h i c h i s , i n t u r n , a n e x t e n s i o n o f t h e d e r i v a t i o n b y G r a d ( 1 9 5 8 ) o f t h e B o l t z m a n n e q u a t i o n f r o m t h e L i o u v i l l e e q u a t i o n . C o n s i d e r a n a s s e m b l y o f m c o m p o n e n t s i n a p h e n o m e n o l o g i c a l l y d i l u t e g a s . E a c h o f t h e m c o m p o n e n t s h a s m a s s m i a n d c h a r g e q i a n d f u r t h e r , t h e r e i s a o n e t o o n e c o r r e s p o n d e n c e b e t w e e n t h e m a s s p o i n t s o r p a r t i c l e s o f c o m p o n e n t i a n d a i a s u b s e t o f t h e p o s i t i v e i n t e g e r s 2 + . T h e m a x i m a l e l e m e n t o f e a c h c x i i s t h e n u m b e r o f m a s s p o i n t s o f c o m p o n e n t i i n t h e a s s e m b l y . L e t t h e a s s e m b l y e v o l v e u n d e r t h e i n f l u e n c e o f a f o r c e w h i c h m a y b e d e c o m p o s e d i n t o f o r c e s o n m a s s p o i n t j , a n e l e m e n t o f 0 1 ‘ , o f a n e x t e r n a l o r i g i n , d u e t o t h e b o u n d a r y a n d d u e t o o t h e r m t h e c l a a s s s s p o i i c a l L P Q . « , » . + E m n L t i s o u ' , - , a : ' « } ( a s s u m e d t o b e o n i X ? e + < ¥ t e fi q u a E g ~ t c v g 5 7 1 i 5 l ) P - 9 , l , p ( a S i r w i s e a d d i t i v e ) . e e A p A p e n d i x G X P U ' . ) A I M ‘ 1 ‘ ) h ' fi ; 3 ' 6 ) 1 7 F 2 F e + Z X F ‘ k ‘ . . 1 . I . J " ’ ’ ( 1 ) ( E ) K e n , ( 1 , 5 3 % ( s i t ) T h e f u l l m a n y b o d y d i s t r i b u t i o n i s a s s u m e d t o s a t i s f y f ¢ = ' k e a , x ‘ “ ( 2 ) u . 0 N o t e h e r e t h a t t h e i n d e p e n d e n t v a r i a b l e s a r e p o s i t i o n a n d v e l o c i t y o n l y . F o r t h e m o m e n t w e h a v e e x c l u d e d a n g u l a r m o m e n t u m a s a v a r i a b l e a s w e l l a s i n t e r n a l s t a t e d e s i g n a t i o n s . T h e s e w i l l b e a d d r e s s e d l a t e r . W e a r e n o t r e a l l y i n t e r e s t e d i n t h e e v o l u t i o n o f t h e m a n y b o d y d i s t r i b u t i o n b u t o n l y t h a t o f s o m e s m a l l s u b s e t / 3 ’ i o f c t i . W i t h t h i s i n m i n d w e d e f i n e t h e f o l l o w i n g r e d u c e d d i s t r i b u t i o n ( t r u n c a t e d d i s t r i b u t i o n i n G r a d ' s w o r k ) . I n ‘ B a n d { ( 1 . . J i n t h e u s e b e t w e e n 1 ; } : a n d K i r k w o G r a d a n d W i i e r a r c h y . R 3 x 3 3 w h V a r i a b l e a , “ f . i s p a r t . i t . i o n e d . i n t o t w o r e g . i o n s , j i ! x S a n d E 3 - S i k ' 1 8 ( D I n t h i s d e f i n i t i o n t h e r e a r e t w o s e t s t o b e s p e c i f i e d , D a n d { a j - / 3 j } . T h e s e t { o r j - fl j } i s d e f i n e d a s { l i k e d i ’ l f / S i } i n t h e u s u a l f a s h i o n . T h e d e f i n i t i o n o f D i s t h e w a t e r s h e d b e t w e e n t h e a p p r o a c h o f G r a d ( 1 9 5 8 ) a n d t h a t o f B o g o l i u b o v ( 1 9 4 6 ) a n d K i r k w o o d a n d R o s s ( 1 9 5 8 ) . I t i s a l s o , o f c o u r s e , w h e r e G r a d a n d w e p a r t w a y s w i t h t h e d e v e l o p m e n t o f t h e B B G K Y h i e r a r c h y . I n t h e d e v e l o p m e n t o f t h e B B G K Y h i e r a r c h y , D i s 3 3 3 R x E w h e r e R i s t h e t h r e e - s p a c e d o m a i n o f t h e v e l o c i t y v a r i a b l e a n d E 3 i s t h e t h r e e - s p a c e d o m a i n o f t h e c o o r d i n a t e v a r i a b l e . I n t h i s d e v e l o p m e n t t h e c o o r d i n a t e d o m a i n f o r e a c h 3 ' ! j : - - w h e r e S i k i s t h e s p h e r e d e f i n e d b y ' 2 ‘ “ - X “ I < a - . 3 3 _ j R x ( E S i k ) f o r e a c h ( x u ) : 9 " ) . A T h e d o m a i n D i s t h u s R F o r c o n v e n i e n c e i n l a t e r m a n i p u l a t i o n s t h e f o l l o w i n g d e c o m p o s i t i o n o f e q u a t i o n 2 i s m a d e . s i t [ = 1 K 6 « i 1 } ; [ = 1 K e p t : ) P H B i t ’ 2 1 + t o ) a s R c / ” K F . r , 3 I s ( I Q / . 3 1 . Q / : H I « x c / _ ‘ 1 7 . 4 . 3 1 R i n o ‘ 4 ’ “ i t o f ti T 0 . f o r P I m u l i n t e g r a t e 4 t h e n b e c h ? i s N o t 1 9 T o d e r i v e t h e e v o l u t i o n e q u a t i o n f o r P r f r o m t h a t d f u d A " a n d f o r P , m u l t i p l y e q u a t i o n 4 b y I ] 1 } . p } , 3 3 M 3 ( E 3 - 5 2 : ) . T h e f i r s t t e r m o f e q u a t i o n i n t e g r a t e o v e r R x 4 t h e n b e c o m e s t h e f o l l o w i n g L " . H c ' x . W a r ” ) - ' [ t i e r F } ‘ " D E P - T i - T r d e l : 2 . . h e " r fi ‘ i ‘ f ‘ 1 5 ' } b e I s ) T h e s e c o n d t e r m b e c o m e s t h e f o l l o w i n g e q u a t i o n . ‘ 7 } - T I " € 1 5 1 } ? a n ( 6 ) 3 ' " “ F F / 5 4 ' } [ X 1 . 9 . 3 . £ 1 . 1 9 . H 9 ‘ “ 7 ' : ) 3 , “ ( = 1 K é i d fl N o t e t h a t w e m a y w r i t e t h e i n t e g r a n d o f t h e f i r s t S A P s i n c e Y “ . i f 0 . p a r t o f t h i s t e r m a s V 2 } : - ( f i l i a l ) 3 2 0 C o n s i d e r t h i s f i r s t p a r t o f t h e t e r m . A A a : ‘ q u s - l s } . J X d i l l E 3 “ 5 , " : ( 7 ) = . . . . . . " fl “ T F m i x ” z A “ , V ‘ k { 1 P a x “ 0 1 1 ; ” * ‘ a d s v l ’ “ . ( 8 ) — s e ‘ * i t ) # ( < ' , k > : . . . . . . 7 ? 1 7 ‘ 1 a v g , d d E P A } J - I l ‘ i o r j - A ' } d ‘ i 5 3 ' : fi g ; ( 5 £ ) ? ’ ( ¢ k ) ( 9 ) ’ “ r - 9 Z [ _ _ d 5 } : P d ; A , ‘ K ( K P " 1 ‘ “ ? 2 1 I n t h i s l a s t e x p r e s s i o n t h e d i v e r g e n c e t h e o r e m h a s b e e n u s e d , i n t r o d u c i n g t h e s u r f a c e v a r i a b l e s d R a n d d s g g T h e f i r s t c o r r e s p o n d s t o t h e s u r f a c e e l e m e n t o f t h e g a s e n c l o s u r e o r b o u n d a r y a n d t h e s e c o n d c o r r e s p o n d s t o t h e d i f f e r e n t i a l s u r f a c e e l e m e n t o f a s p h e r e o f r a d i u s ‘ 6 ' a n d w i t h c e n t e r f i x e d a t q u . F u r t h e r m a n i p u l a t i o n o f t h e i n t e g r a l g i v e s A t h e f o l l o w i n g e q u a t i o n . : - F i - ‘ T F . 4 5 ” a s ” a n - 3 , , P a s , j = s 1 . 5 2 9 3 7 3 3 } . . 3 a ' I £ 3 _ 3 5 : R < ; , 1 ) # ( £ " k ) ( 1 0 ) P 1 P 2 . [ E d E ‘ k ' f i t P d ? “ v } : E d § k ‘ 5 k P d i k F “ 3 ‘ 1 8 ) : { ( 3 s . ” 1 F “ 3 ‘ f ‘ r 7 ‘ r 3 4 3 5 3 ” ( a d d e d ) D e f i n e , a n d n o t e t h a t k 9 E a t . . . A . g 2 2 W i t h t h i s d e f i n i t i o n t h e i n t e g r a l b e c o m e s t h e f o l l O W i n g 3 3 £ 4 - P 1 0 . . Z X { § d 3 5 k f a t 8 ( f ‘ k , g r , [ 5 ) d e ( 1 1 ) 9 : : g a f f 8 ‘ ! 5 : } P ? ~ 2 : E g d f t ' k . ‘ l k P " ( § ‘ k I i i : I X P Q 2 ’ 3 1 / 3 ) d “ : A M P . “ I ‘ i q f ‘ F f } S P 1 ( k ( @ 1 0 7 ‘ ( [ 5 9 ) n o r m a l v e c t o r s : ( 1 2 ) D e f i n e t h e f o l l o w i n g o u t w a r d n o r m a l t o S P q A l k P g : x - - x = R i k f i t ‘ 9 9 a . n = o u t w a r d n o r m a l t o g a s b o u n d a r y A S o , w i t h t h e s e d e f i n i t i o n s t h e r e s u l t f o r t h e f i r s t P = l R E P ? R 3 3 ‘ 9 3 . 2 3 t e r m o f e q u a t i o n 6 i s a s f o l l o w s : ( 1 3 ) _ X X g 9 : 1 ' i t 8 ( i ‘ t k ; £ 1 I F ) d 0 } ? a f t ) : m P ! ' 2 : z 9 ‘ } . i t ! ) F ( X t ' § u $ 1 1 : “ P i S ' p g fl ) a ° } k P 1 P a s e t s - n } s ” ( 4 0 1 4 9 . 2 ) " “ . d § , - , d g m d f fl N o w o n e m a y m a k e u s e o f t h e p a r t i t i o n i n g o f t h e c o o r d i n a t e d o m a i n o f e a c h p a r t i c l e a n d r e s t r i c t t h e d e v e l o p m e n t t o t h o s e a s s e m b l i e s f o r w h i c h t h e l o n g r a n g e f o r c e s , i . e . t h o s e f e l t b y p a r t i c l e s n o t w i t h i n a ' o f a n o t h e r p a r t i c l e , a r e o f t h e L o r e n t z t y p e . S o t h e e x p r e s s i o n f o r t h e f o r c e o n p a r t i c l e ( i , k ) m a y b e w r i t t e n a s t h e f o l l o w i n g : f r o n t h v t e r n F , . ‘ A l . S o w i t h o f e q u a ' F . ” A ( 1 " ( s f — ( ’ 9 1 : ) + i n x 2 4 ( 1 4 ) ( 5 0 : 0 ) 5 ; ? < 5 . . . ) T h e e l e c t r i c a n d m a g n e t i c f i e l d s t r e n g t h s a r e c a l c u l a t e d f r o m t h e c h a r g e d e n s i t i e s a n d t h e b o u n d a r y c o n d i t i o n s . t e r m f : k S o w i t h t h i s d e c o m p o s i t i o n i n m i n d , o f e q u a t i o n 6 . T h e i s t h e s h o r t r a n g e b o u n d a r y i n t e r a c t i o n t e r m . t u r n t o t h e s e c o n d t e r m ( . _ ‘ K . 3 . 9 ) 7 T T T a m a s ” ( 1 5 ) m ‘ D i “ : 5 " ” “ Z “ J ' f s i ' } ‘ ‘ 5 3 . S 4 5 : k f i q ‘ fl ' f s g _ _ m : ( ( X ‘ ) + f “ X 5 0 1 . 1 ) * 3 “ A " ( 1 5 ) _ 3 _ 5 ‘ 1 1 V P T T ’ 7 7 ‘ d x w d 5 ? “ . . n : J " ( E d e - fl } “ A V ’ 3 " : B ( x . . > ) + 3 7 % ) } = o ( 1 7 ) ( £ 0 . . . ) + I t x 7 d x 3 Q “ ; 7 3 ; } R a f i ! 3 7 / 5 . l h ’ Y L . : 1 - . " " " " - “ ( $ 5 m V A s k ' I ‘ : ) L k P + V . K L ] : F m 1 " P T 3 : ) 1 6 7 ) 7 “ - ; 7 3 ; } d f i fl d ( ? 2 0 “ ) 2 5 N o w l e t n ; . b e a n o u t w a r d n o r m a l v e c t o r o n a s p h e r e o f L k f i n i t e r a d i u s i n v e l o c i t y s p a c e . B y t h e d i v e r g e n c e t h e o r e m t h e v o l u m e i n t e g r a l o f V ' 5 . , P i s t r a n s f o r m e d t o a s u r f a c e 2 i t i n t e g r a l . S i n c e w e r e q u i r e t h a t f o r a l l ( i , k ) , / r m F o r . 5 . . ) = o ( 1 9 ) [ E I I E ' O O t h e n t h e i n t e g r a l v a n i s h e s . N o w c o n s i d e r t h e t h i r d t e r m o f e q u a t i o n 4 . ) I ) S i n c e w e w a n t t o p u l l t h e d e r i v a t i v e o p e r a t o r o u t o f t h e i n t e g r a l , c o n s i d e r t h e f o l l o w i n g r e l a t e d d e r i v a t i v e . U \ — - _ d n a _ . _ \ 3 2 6 - E . P T H d x u 0 ’ ; e r 3 3 ' “ f a r / 5 5 . 1 ‘ 1 ‘ [ a 5 5 1 ( 2 1 ) f n “ - f P d O ' : d ; T T F d x m d 1 ; . P s 9 - 1 _ ' 1 4 “ # 1 } “ ( M i ( m a m ) A n d s o t h e f i r s t t e r m o f e q u a t i o n 2 0 b e c o m e s t h e f o l l o w i n g : [ L 3 7 2 . . ¥ . < F ) + Z Z “ 5 " ; i i “ ) 4 : : I r e / 5 ; ( 3 3 3 6 8 4 9 7 1 9 3 3 ; ) : i t ( 2 2 ) € 0 9 1 , fi i , fl ) d 0 ~ fi d i p i Z ( n h o t n i = ( k e e t s f f e i 5 . t 2 D o o a E b i h o t f T l , 0 g n c i n r t o a e w h f 3 i e o ) e m f E [ = [ g o p s — m l r l r u a e b m k . t t s l G d l r : < fl § f ‘ k f h a 3 ( u e n ‘ p o l y u e e e d t T m / ; / S g w . ; . _ : m 2 l ) : l e - f L a d l h v b m o o t e n y u e g b y t - i d p s x “ : t ) . L b P f o n s r ) fi i a b o < “ : l v o o i n n l p f e r u d t t y i e r L u b l i a u o t t u i i e s . q i c . _ . _ m o a e i s s e c s q t e e u i n a t o d t e n i d . o b a e n u h . e t t r , . k » e n n > ( 2 3 ) ( 2 4 ) 2 7 T h e s e c o n d t e r m o f e q u a t i o n 2 0 i n t e g r a t e s e a s i l y t o b e c o m e t h e f o l l o w i n g : i z Y i n . [ Z — i ( 5 ( x > + 5 3 K X ( 3 ( X , , ) + _ g i f v h d fl p 9 3 ) _ i z : Z S P , ( x , , , § , , , / v ) d o ; : § d £ e t a - 7 a : a s o » : 2 3 ‘ 3 ’ “ P " f ’ " ‘ 1 ‘ { ° ‘ r ' l g r l S “ 1 P “ , ( I M k : ) =2! P “ ( 3 m 6 ) 2 % } s } ? 2 8 ( k 4 . . + Z Z [ 2 9 9 ? . £ - , fl ( x m . ; p g . / 3 ) d ¢ , ; M m 3 “ Z X E : - X g g f 9 4 : . $ 4 1 p r ( x t } . , S 2 1 , x P fl 1 ; ” : fi ) d 0 1 : 1 d ; ; k d x fi d g p i T h e f i r s t t w o t e r m s o f e q u a t i o n 2 4 c o r r e s p o n d t o e f f e c t s o f g r a d i e n t s a n d f o r c e s a c t i n g o n t h e " t e s t " p a r t i c l e s , t h a t i s , t h o s e p a r t i c l e s i d e n t i f i e d w i t h t h e s u b s e t / 3 . T h e t h i r d t e r m a c c o u n t s f o r i n t e r a c t i o n s b e t w e e n t h e " f i e l d ” p o i n t s a n d t h e b o u n d a r y . H i s t o r i c a l l y t h i s t e r m e i t h e r w a s n e g l e c t e d i n t h e d e r i v a t i o n o r d r o p p e d f r o m l a t e r c o n s i d e r a t i o n b y a s s u m p t i o n o f s p e c u l a r r e f l e c t i o n o f t h e f i e l d p o i n t s f r o m t h e b o u n d a r y . T h i s w a s d o n e i n s p i t e o f l a t e r a p p l i c a t i o n o f n o n s p e c u l a r b o u n d a r y c o n d i t i o n s o n t h e t e s t p a r t i c l e d i s t r i b u t i o n . T h e f o u r t h a n d f i f t h t e r m s a c c o u n t f o r t h e e f f e c t o f t e s t p o i n t - f i e l d p o i n t i n t e r a c t i o n a n d t h e l a s t t e r m c o r r e s p o n d s t o t h e e f f e c t o f f i e l d p o i n t - f i e l d p o i n t i n t e r a c t i o n . N o t e t h a t i f t h e i n d i c e s i n t h e f o u r t h t e r m a r e s w i t c h e d , t h e n i f o n e . . - P q = - d e f i n e s a r e l a t i v e v e l o c 1 t y a s Y i k S p q E i k t h e f o u r t h a n d f i f t h t e r m s m a y b e c o m b i n e d t o f o r m t h e f o l l o w i n g s i n g l e t e r m : I n M ( K P 5 . L o k Z E : E 2 f ’ P i ' Y 4 “ ’ 5 9 ? ’ 5 ) d u h d f p e ( 2 5 ) “ P I P . . . 2 c m : 3 . . . P i n t ‘ 1 ? T w p h a i e c r d a f l “ l i n s r o y z s r . a y S r m l t e m t m s 9 l a e 5 a n t 9 3 f e r / 3 ’ ) = t d r i i o t c n h s e m h a s i n e p y c - f o b o n o l d d ' o r P l y Q w e d E s l i P ? : € f t t r i r o o i a s 9 m n b 5 s u ’ 1 h i t h t i ‘ o e p “ . f d r e e n . t f s fl n l o ) i t w i u N ( 2 o m r f i 7 t a ) e t s i w n r f o e o w t m h i e c r o o u s t o 5 " “ 4 ‘ 4 “ P ” S e g a ? ? ? " S , ”K 2 9 N o w c o n s i d e r t h e l a s t t e r m o f e q u a t i o n 2 4 . O b s e r v e t h e f o l l o w i n g s y m m e t r i c a n d a n t i s y m m e t r i c r e l a t i o n s h i p s . p q _ _ i k B i k — q u ( 2 6 ) t h e l a s t t e r m a s t h e s u m o f t w o t e r m s . m M ‘ p g 9 2 5 z 2 : X X g “ 9 “ “ . f 1 } n ( § " " £ b § f ’ i ' ? c ’ i - / 3 ) A V E : 3 & 3 q u 4 5 9 3 ( 2 8 ) N o w i n t h e s e c o n d t e r m o f e q u a t i o n 2 8 s w i t c h t h e i n d i c e s a n d t h e n m a k e u s e o f s y m m e t r y a n d a n t i s y m m e t r y p r o p e r t i e s o f t h e i n t e g r a n d a n d t h e e q u a t i o n b e c o m e s t h e f o l l o w i n g , w h e r e w e h a v e n o t e d t h a t t h e i n d i c e s k a n d q a r e d u m m y i n d i c e s f o r i d e n t i c a l i n t e g r a l s a n d s o t h e s u m o v e r t h e m i s - 4 5 a 1 1 2 : _ i E : ( M 2 “ “ M ’ Y % ‘ Y M ‘ ' w ' fl / f r ) ( é h f é - % ) { ( o f f $ 9 M 0 ) M < " " " ’ x ” ° ’ § 9 » ; p » W fi fl ) ° ) 3 0 r e p l a c e d b y a c o n s t a n t m u l t i p l e o f o n e o f t h e i n t e g r a l s . m m 5 , : d o } ? d i g , d i g , d f p o ( 2 9 ) ( ‘ 3 ! P : ' 3 p a i f - d o ? » d 5 , d x I n t h e f i r s t p a r t o f e q u a t i o n 2 9 § i * i s v a r i e d o v e r t h e s u r f a c e o f t h e s p h e r e c e n t e r e d a t § p o a n d t h e f l u x o f ( i , * ) i s c a l c u l a t e d , t h e n § p o i s v a r i e d o v e r t h e i n t e g r a t i o n r e g i o n . I n t h e s e c o n d p a r t o f § p o i s v a r i e d o v e r t h e s p h e r e c e n t e r e d a t § i * a n d t h e f l u x o f ( p , o ) i s c a l c u l a t e d . S o , w h e t h e r § i * i s v a r i e d o v e r S E 3 o r § p o i s v a r i e d o v e r 8 : ; t h e r e s u l t a f t e r i n t e g r a t i o n i s t h e s a m e a n d s o w e w r i t e f o r e q u a t i o n 2 9 t h e f o l l o w i n g . 5 " ” ( 3 0 ) t i l - ( N o t e t h a t N “ i = n u m b e r o f e l e m e n t s o f « 1 . ) T h e e n t i r e e q u a t i o n f o r P r s fi ) t h e n b e c o m e s t h e f o l l o w i n g : 5 ‘ ( 3 1 ) ( = 1 £ 4 | _ _ P 0 . f + 1 2 £ < ¢ t A / A ‘ Y A / J ' f f ) 9 " . Y p o P l ' ( x l l - J ‘ _ . & k 1 ¥ ‘ p , § ’ p F ) J U L - : 0 r " s ” ” ' d f a d i ‘ d f e o E a c h i n t e g r a l o v e r t h e s p h e r e 8 2 2 m a y b e d e c o m p o s e d ' * i n t o t w o r e g i o n s , t h a t f o r w h i c h n 5 3 . Y p o ) O a n d t h a t f o r w h i c h ' * h i s . v ; o < 0 . T h e h e m i s p h e r e s i s . . . i s t h a t p a r t o f S E ? f o r ' * w h i c h n p o . Y p o ) 0 a n d i s i d e n t i f i e d w i t h p a r t i c l e s w h i c h h a v e j u s t l e f t t h e i n t e r a c t i o n s p h e r e a n d s o h a v e j u s t s c a t t e r e d . T h e h e m i s p h e r e S g g - i s t h a t p a r t o f S E : f o r w h i c h b f “ z [ [ X “ F " fi g W W ) i { 5 . ; I : k v : ° z r » , < ; , . , ; . fl ) a ¢ w ; . ‘ fi / C ‘ F a / P , ( { . , , £ - . , fl ) d e f . - , 3 2 ' * 9 E 3 . v ; 0 ( O a n d i s i d e n t i f i e d w i t h p a r t i c l e s j u s t e n t e r i n g e a c h o t h e r s i n t e r a c t i o n s p h e r e a n d a r e j u s t a b o u t t o s c a t t e r . W i t h t h i s d e c o m p o s i t i o n w e m a y r e w r i t e e q u a t i o n 3 1 i n t h e f o l l o w i n g w a y . D i ’ ” " A D X l ' k ( = 1 K e fi y ‘ - a P ° S i k — ( 3 2 ) p a ‘ X ( M ; - A / / 3 £ { g § l f ’ i 1 / fl ( § ¢ k a § l k , / S ) C J R d f m - { : 1 5 + ‘ 1 — — k l : ° Y : / P r a m ? » 5 9 0 . ? » . fl ) d ° 2 : ° d § ' w 4 3 9 ° ‘ 5 ’ ? » 3 3 m M ( F + i [ M m - m m I 2 5 - > 4 » M H W W a “ ! ' P - ‘ a t » . I » S “ ; 0 J 0 1 } d f ‘ ! d ‘ Y P O d f ' P o a " A t t h i s p o i n t w e r e a c h a n o t h e r w a t e r s h e d , a s i t w e r e , i n t h e d e r i v a t i o n o f a k i n e t i c e q u a t i o n . T h e r o a d w e l l t r a v e l l e d , n o t o n l y b y B o l t z m a n n b u t a l s o b y G r a d a n d C e r c i g n a n i , i s t o e x p r e s s t h e " a f t e r s c a t t e r i n g " v a r i a b l e s o f p o s i t i o n a n d v e l o c i t y i n t e r m s o f t h e " b e f o r e s c a t t e r i n g " v a r i a b l e s a s s u m i n g e l a s t i c s c a t t e r i n g o f t w o s p h e r e s o f r a d i u s ( T . T h i s r e l a t i o n s h i p i n t r o d u c e s a t i m e d i r e c t i o n o r i n f o r m a t i o n f l o w d i r e c t i o n i n t o a n o t h e r w i s e c o m p l e t e l y r e v e r s i b l e d e s c r i p t i o n o f d y n a m i c a l e v o l u t i o n . T h e r e s t r i c t i o n t o e l a s t i c s c a t t e r i n g r e s u l t s i n c a n c e l l a t i o n o f t h e f i f t h a n d s i x t h t e r m s o n t h e r i g h t h a n d s i d e o f e q u a t i o n 3 2 . A s s u m p t i o n o f s p e c u l a r r e f l e c t i o n o f t h e f i e l d p o i n t s f r o m t h e g a s b o u n d a r y r e s u l t s i n c a n c e l l a t i o n o f t h e t h i r d a n d f o u r t h t e r m s o n t h e r . h . s . o f e q u a t i o n 3 2 . ' 1 1 f f t o t h e p r e - c o l l i s i o n f l u x , n o t b y t h e l a w s o f e l a s t i c i m p a c t 3 4 T h e n i n t h e l i m i t t h a t t h e n u m b e r o f p a r t i c l e s i n t h e a s s e m b l y g o e s t o i n f i n i t y a n d t h e p a r t i c l e r a d i u s a v a n i s h e s s u c h t h a t ( N 0 3 ) — ) 0 a n d ( N 0 2 ) — 5 f i n i t e , t h e r e m a i n i n g p o r t i o n o f t h e e q u a t i o n b e c o m e s i d e n t i c a l w i t h t h e B o l t z m a n n e q u a t i o n . A f t e r t h e s o - c a l l e d B o l t z m a n n - G r a d l i m i t i s t a k e n t h e n t h e e q u a t i o n i s o f t e n g e n e r a l i z e d t o a c c o u n t f o r p o l y a t o m i c p a r t i c l e s , i n e l a s t i c a n d r e a r r a n g e m e n t s c a t t e r i n g p r o c e s s e s b y t h e a d d i t i o n o f h e u r i s t i c a l l y c o n s t r u c t e d c o l l i s i o n t e r m s . I t i s n o t a t a l l c l e a r t h a t s u c h t e r m s a r e c o r r e c t o r t h a t i t i s c o n s i s t e n t t o a d d t h e m a t t h i s p o i n t i n t h e d e r i v a t i o n . A n o t h e r o b j e c t i o n t o t h e c o n v e n t i o n a l a p p r o a c h i s t h a t o f l a c k o f i n t e r n a l c o n s i s t e n c y . I n t h e c o n v e n t i o n a l a p p r o a c h a s i n g l e d i s t i n g u i s h a b l e c l a s s i c a l d y n a m i c a l t r a j e c t o r y i s u s e d t o c o n n e c t t h e p r e - a n d p o s t - c o l l i s i o n c o n d i t i o n s . A f u n d a m e n t a l a s s u m p t i o n i n t h e r e d u c t i o n o f o r d e r f r o m t h e f u l l m a n y - b o d y d i s t r i b u t i o n t o a s i n g l e p a r t i c l e o r p a i r d i s t r i b u t i o n i s t h a t o f m i c r o s c o p i c s y m m e t r y o f t h e d i s t r i b u t i o n w i t h r e s p e c t t o i n t e r c h a n g e o f a p a i r o f p a r t i c l e i n d i c e s . T h e u s e o f a d i s t i n g u i s h a b l e t r a j e c t o r y t o r e l a t e t w o p o i n t s i n a n a s s e m b l y o f i n d i s t i n g u i s h a b l e p a r t i c l e s i s i n c o n s i s t e n t . B e c a u s e o f i t s p a r t i t i o n i n g o f t h e c o o r d i n a t e d o m a i n t h e m e t h o d o f G r a d p r o v i d e s t h e p o s s i b i l i t y o f e s c a p e f r o m t h i s i n c o n s i s t e n c y . T h o u g h g e n e r a l i z a t i o n t o i n e l a s t i c a n d r e a r r a n g e m e n t s c a t t e r i n g p r o c e s s e s w i l l b e g i v e n i n a l a t e r w o r k , t h e e s s e n c e o f t h e a p p r o a c h i s d e v e l o p e d h e r e . T h e p o s t - c o l l i s i o n f l u x i s r e l a t e d : X X Z W « . ' ) " / 3 r 9 ; " x 4 ; ° / fi - ( g < . . , f . . , / s " , e ’ ) R ( x r o , . n , x u . ; § j £ : t : X P o ; P ) x " k 3 2 * f ) d c — ; ( J ; P a d ! ” d i n e ] ! 3 5 b u t t h r o u g h a g e n e r a l i z e d p r o p a g a t o r . T h e f o r m o f t h e p r o p a g a t o r i s t h e r e s u l t o f a t w o b o d y s c a t t e r i n g p r o b l e m a n d s e r v e s t o c o n n e c t t h e m i c r o s c o p i c s c a t t e r i n g d y n a m i c s t o t h e e v o l u t i o n o f t h e d i s t r i b u t i o n f u n c t i o n . p o s t - c o l l i s i o n f l u x o f . . . k p - t e a r t i c l e s w 1 t h r e l a t i v e _ < _ W ) ‘ . Y ? P - M P H , K / W ‘ m o f ) v e l o c i t y 2 ? : a n d e x i t i n g t h r o u g h 1 . . s u r f a c e e l e m e n t d 0 ’ ” 5 ‘ “ r e ( 3 3 ) T h i s f o r m u l a t i o n o f t h e p o s t - c o l l i s i o n f l u x i n t e r m s O f a p r o p a g a t o r f o r t h e t w o p a r t i c l e s y s t e m a l l o w s f o r t r a n s i t i o n s f r o m a ( r , o ) - 9 ( p , o ) b u t i n w h a t f o l l o w s w e w i l l r e s t r i c t t h e p r o p a g a t o r t o e l a s t i c c e n t r a l f o r c e s c a t t e r i n g . C o n s i d e r n e x t t h e p a r t i c l e f l u x f r o m t h e b o u n d a r y . ( M y A é ) / 9 . § ‘ } / fi ( } a , § . - . , fl ) z [ ( M f / ‘ l / S j i f f / p . § , ~ , / / . ’ - ( x . - . , I J . . , / s : £ ’ ) . T ( ! $ # 1 5 . 5 5 1 5 1 ° ) ; ' é J x ' g 4 } I 5 P 0 ( 5 - 9 0 I t > d a - S k d e f d x fl o d g i o d f I 9 0 I 3 6 i n . 5 4 - ( 3 4 ) X . 0 " I . E ; < x . < 5 . A 5 * ) A J * ’ 2 X , , t ’ , t > d R d f ” c / é ’ z f i é ( e 0 9 ) 6 ’ ) F o r t h e l a s t t w o t e r m s o f e q u a t i o n 3 2 w e h a v e t h e f o l l o w i n g e x p r e s s i o n f o r t h e p o s t - c o l l i s i o n f l u x . ( fi é i v A é ‘ ) < A ‘ / X P - A / P P ) / 9 ‘ 2 0 . Y P : ’ / B ‘ ( 5 ¢ } I § Z } , ‘ X p o , § p o , / 3 > Z ( 3 5 ) m m 9 0 3 ‘ ' ’ X Z ( ‘ 4 ’ . ” fi x / 4 1 4 % ) W “ ‘ 3 ’ ' Y i o / F r a g , ’ 1 ‘ " ’ K i o é i m / S f ) ' : l 3 : ! O - ’ 8 3 . ‘ 1 9 ’ ‘ 5 ? ) t r l n - \ h u h . . . [ = l K ‘ P ‘ . ‘ V “ 2 2 _ . m E < M 9 ~ A fi j fi fi a fl » \ 4 2 / fi < § p ~ . . ; m fi ) d ° ' p . A ? » ( 3 6 ) L . k ° S < x a a g i n x P J S P » 1 * . { > d k d ; 9 c l t ' d a d ? “ 3 7 T h e s e p o s t - c o l l i s i o n f l u x e x p r e s s i o n s a r e s u b s t i t u t e d i n t o e q u a t i o n 3 2 t o y i e l d t h e f o l l o w i n g . i n D P U J P . ) 1 . - . . “ ) P S ? F X [ { f . . . 3 ; ? “ + 4 , 5 0 5 . . ) 5 . , x : 3 0 ) ) 3 3 9 : ) R o m ; . , . . . § , - . . i ’ . z < . . . § . , x n o d e - i " a w n - . 4 1 ; M a fi a . x e p z P " . - . . - 5 } , + 2 Z < M 3 ~ A f l j ) { { I f } ? § $ a / P r ( ¥ £ ; o , 3 , , F , 1 ‘ ) 1 : ! 5 8 ! £ 1 . 5 + — ! » 7 M . . — m { U w a g / 2 3 . x P r < 5 . . . § . . , / 2 > A R A § . . 3 8 P " + a M M n m 1 0 4 ' 1 " X X [ X ( M i - A ¢ J ) ( M 1 - A fi s ) l 9 5 ' \ / 1 : / R ( x * " ; " ’ x 1 ° ’ ; 1 ° “ H / g f ) ( ‘ 8 ! P I 3 : : 1 : ! 5 " ? " S i r . . . T < ¥ . . . . . . § s . , § g . . t 1 3 ~ . m x m f m f f é w 4 . ? 4 ! : 4 ? . . . c “ o r : e l f ” d 1 . . . d i p . » " ‘ ” P o r ! 2 2 % / < r a n H p ” ° P S r ; d V ‘ ; J ? ” a x ” d f ? ‘ T h e g e n e r a l i z e d p r o p a g a t o r t h u s m a y a c c o u n t f o r i n e l a s t i c a n d r e a r r a n g e m e n t s c a t t e r i n g e v e n t s a s w e l l a s e l a s t i c e v e n t s . S o f a r t h e e x a c t n a t u r e o f t h e s e t / 9 h a s b e e n l e f t u n d e f i n e d e x c e p t t h a t i t i s s p e c i f i e d b y a n o r d e r e d m - t u p l e g i v i n g t h e o r d e r o f t h e d i s t r i b u t i o n f u n c t i o n i n e a c h t y p e o f p a r t i c l e . I n w h a t f o l l o w s w e l e t P = ( 1 , 0 , 0 , . . . . 0 ) m s o t h a t t h e . t i E v a = : : . 5 o » E “ ‘ a ! + ' 2 ’ ? ’ ' 2 i ‘ s a c o n , d o n , s R $ 9 P ; u = » ’ l k ‘ l ' ( , k , 9 - J V t r u c t e d s u m i , ” a X 4 s . < 0 § f ° 1 1 l 6 5 - ‘ ’ 5 5 < § $ “ g } ) ! a ‘ 2 { I P . n . g ' ’ t ” r ‘ o _ - w 9 ( 9 . p i 1 u ( o u < ( I k o ( ( I c \ k p { - h i t . x P ' ) ; “ 9 " 1 . t " 1 t ° * + P 2 ( 1 ‘ : P ) ” . “ “ . ° s I ) o s ' ) a ' . P " ; ° P : P . . a . o f c k ; ( ? ' ) Y Y f ) . ) 3 1 ‘ 9 0 5 ‘ 1 : g e n e r a l i : t y H * r o ) ‘ S v ( e X ““ ~ - : ( l i 5 1 ' ” ° I } 9 “ x t n ( ( ( ( 3 3 3 4 7 3 9 0 ) ) ) ) h a t t h e x ‘ k ) ) 5 6 J ‘ “ 9 " 0 - » k . : I ) . V " 1 4 . . V m : 7 y . i o ¢ ( , I . t l I ' ¥ Y 3 9 d i s t r i b u t i o n f u n c t i o n i s a s i n g l e p a r t i c l e d i s t r i b u t i o n f o r s p e c i e s i . F o r t h e e l a s t i c s c a t t e r i n g o f r i g i d s p h e r e s , t h e f o l l o w i n g r e l a t i o n s h i p s m a y b e d e r i v e d f r o m p r i n c i p l e s o f c o n s e r v a t i o n o f l i n e a r m o m e n t u m a n d e n e r g y . U s i n g e q u a t i o n s 3 7 , 3 8 , 4 0 t h e f o l l o w i n g p r o p a g a t o r s a r e p a r t i c l e s a r e o f e q u a l m a s s . ’ A S O L E » , i ‘ u . P n ’ 1 ‘ ? ) " 5 ( 5 3 » ‘ 2 ‘ ” ) 5 ( i l f ) 5 ( § ; , ’ F r “ 2 9 0 2 ' ? ” W u i a t t h i h t n e 3 s 6 e , o t t h h r e e e f s l c l a o t w t i e n r g o i n e g q t a e t r i m o s n u i d f e o f r n P e r d ( § a i n f d ‘ s u b ; i ) s r t e i s t u u l t t e s d . i n t o e q 4 0 T U . . . 3 5 * : 1 ‘ 3 0 . i . . . f ' . z r . . § ~ . 5 p . . § ~ , é ) = 5 ( 5 . . - 2 r . . ) f ( § , . - 2 r . . ) ' « 6 2 0 3 1 1 5 5 3 5 . # 9 3 7 9 : " y é ‘ ) ) 5 ( f s o ‘ { h r 9 5 X 9 . " : - y x » 2 5 . " . I r . - - 2 ? : + 3 : < § ( x , ) + a x 8 0 . 3 ) . e r . P “ . b e . _ n u ‘ ‘ ‘ “ ' N ’ > 1 0 ) 5 . 7 ; } 3 1 5 . - Z ( M u m ) 3 4 / 9 ; : ~ 2 ’ 3 7 / [ fi ( a » . ? . . - e m e i i - m f x z w a . + fl a x - x ? ) " 5 ‘ : 4 " ( 4 1 ) - a ( 3 5 9 0 , 1 . 9 9 0 . 2 5 6 1 » . £ 3 ) 0 " ? ! » a g ' p o S o , t h e e n t i r e c o l l i s i o n t e r m i s n o w g i v e n a s a d i f f e r e n c e o f t w o t e r m s w r i t t e n i n p r e - c o l l i s i o n v a r i a b l e s . W i t h t h e a s s u m p t i o n o f c o m p l e t e l a c k o f c o r r e l a t i o n b e t w e e n t h e " t a r g e t " s t a t e a n d t h e i n c o m i n g " b u l l e t " s t a t e , t h e p a i r d i s t r i b u t i o n i s d e c o m p o s e d i n t o t h e u s u a l p r o d u c t o f t w o s i n g l e p a r t i c l e d i s t r i b u t i o n s . T h i s a s s u m p t i o n o f a b s e n c e o f c o r r e l a t i o n i s d i f f e r e n t f r o m t h e a s s u m p t i o n o f B o l t z m a n n a n d o t h e r s t h a t t h e s i n g l e p a r t i c l e d i s t r i b u t i o n s o f t h e o u t g o i n g p a r t i c l e s a r e u n c o r r e l a t e d . T h e d i s t i n c t i o n i s i m p o r t a n t . I t i s a t t h i s p o i n t t h a t t h e B o l t z m a n n - G r a d l i m i t i s i n v o k e d . A l l a l o n g w e h a v e a s s u m e d i n 5 3 [ ( M - 9 - P . ( x A . I / ‘ P ) 0 2 : f / p ; - . ? + n i x 9 2 : - Y ‘ : / { e < ¥ P o y . 1 ‘ > > - P e r : f § P - P e o V S ’ ( ? : . y : : ) ) e r f a > 4 5 3 : 4 % . 4 1 t h a t t h e p a r t i c l e o f i n t e r e s t , ( i , * ) , i s o u t s i d e o f a G ' - b a l l o f e a c h o f t h e o t h e r p a r t i c l e s i n t h e a s s e m b l y . I n o r d e r t o i n s u r e t h i s w e , r a t h e r f o r m a l l y , l e t N a p ' * c o a n d 0 1 * - 9 0 3 - - 9 O a n d N a p 5 - 1 3 , , — — 9 f i n i t e , n o n z e r o s u c h t h a t N a p 0 1 * . ( k w h e r e ( i v ; = 0 " : J 9 9 . . W h e n s u c h a l i m i t i s t a k e n t h e f o r m o f t h e k i n e t i c e q u a t i o n r e m a i n s t h e s a m e . m . . 1 : + i ‘ ( § < x . - > + § . - x 9 < m ) - 2 _ e + 5 % : E t . b M " . } § , ‘ m ‘ . S } : A P " ( 4 2 ) T h i s i s e s s e n t i a l l y t h e B o l t z m a n n e q u a t i o n i n i t s u s u a l f o r m . F o r a o n e c o m p o n e n t d i l u t e g a s t h e e q u a t i o n b e c o m e s t h e f o l l o w i n g e q u a t i o n , w h e r e £ - < f , E “ ) 5 ( M g - M g ) p r ( 3 ‘ , f ) - D E . s - Q E . $ - ( 5 < . s + ; x g < g > ) . § _ £ . g i g “ = M ‘ E W “ “ b ; — m - ) t ‘ s A I r e ; - W M . - " “ C ( L ‘ ~ m ‘ i 0 ‘ 9 . : - : a x > I ? o n ; - . H i “ ) v : . - 7 " ° ) > > ¥ < } 0 § 3 . - 0 , 1 } . 5 + } a i m - w ; “ H P 4 2 F o r e l a s t i c s c a t t e r i n g o f r i g i d s p h e r e s o f r a d i u s 0 ‘ t h e c o o r d i n a t e s f p a n d f 1 a r e r e l a t e d b y t h e o u t w a r d n o r m a l a n d t h e r a d i u s 0 ‘ i n t h e m a n n e r 3 5 p = § i - 0 ' 5 1 ; a n d s o o n e m a y w r i t e f o r e q u a t i o n 4 3 t h e f o l l o w i n g . 2 f + f - E + 3 5 ( £ ( 5 > + ¥ x 9 ( 5 > > . § £ + 5 3 ) } = 3 + 3 ! " ‘ 6 ‘ ‘ M - m . 2 " h ( 4 4 ) T h i s r e s e m b l e s t h e E n s k o g e q u a t i o n b u t i n t h e B o l t z m a n n - G r a d l i m i t ( t r - 9 0 ) t h e c o o r d i n a t e v a r i a b l e s a r e a l l i n t e r m s o f § i o n l y . T h e B o l t z m a n n - G r a d l i m i t o f e q u a t i o n 4 4 m a y b e g e n e r a l i z e d t o e l a s t i c c e n t r a l f o r c e s c a t t e r i n g . I n t h e f o l l o w i n g f i g u r e t h e g e n e r a l i z a t i o n i s i l l u s t r a t e d . T h e i n c o m i n g f l u x o f p a r t i c l e s i s p r o j e c t e d o n t o t h e p l a n e n o r m a l t o Y ? a n d t h e n t h e e l a s t i c d i f f e r e n t i a l c r o s s - s e c t i o n i s u s e d t o r e l a t e t h e t o t a l o u t g o i n g f l u x i n t e r m s o f t h e p r o j e c t e d a r e a . 4 3 ‘ I l a - " l r d r d y I v f / r - / 3 _ _ ; / d 9 d 9 ! q p ’ 3 ‘ 9 " t “ ' 9 K Q . I = l ‘ C - P y I ( 6 , I \ / : ' / ) s i n e c l e d p ’ I 0 9 , I V . - " / ) = F l a n 6 9 / E S ? b r - D e t a i l e d d e s c r i p t i o n o f t h e t w o - b o d y i n t e r a c t i o n s p h e r e F i g u r e 1 : ; n £ 1 I ’ fi I { 4 0 5 . . p - . o n p i ' Y . - / y f / : 1 9 ' ) ) ) ~ ' ( § . i ' + o [ M - P l ) s i n : 6 < o ‘ . ¥ 0 ’ 9 . o v f / » d - e ~ p ‘ < x . £ ~ > ¥ < x , % . ) } f u n c t i o n a u t o n o m o u s i n t i m e . I n w h a t s e n s e d o e s t h i s s i n g l e 4 4 I t i s a t t h i s p o i n t t h a t t h e h e u r i s t i c a l l y c o n s t r u c t e d c o l l i s i o n t e r m s a r e a d d e d ( C e r c i g n a n i , 1 9 7 5 ) . B y a n a l o g y w i t h t h e e l a s t i c s c a t t e r i n g c a s e d i f f e r e n t i a l c r o s s - s e c t i o n s f o r a l l t y p e s o f i n e l a s t i c a n d r e a r r a n g e m e n t e v e n t s a r e a d d e d o n t h e r . h . s . o f e q u a t i o n 4 4 . W i t h t h e g e n e r a l i z a t i o n t o t h e c e n t r a l f o r c e e l a s t i c s c a t t e r i n g p r o b l e m i n a s i n g l e c o m p o n e n t g a s t h e f a m i l i a r B o l t z m a n n e q u a t i o n r e s u l t s . b i + y a ; + % ( { ( § \ + § X § ( x ) > - ) 5 6 " . ) ? = _ . ' + > W ) f — + 3 ' § ( 4 5 ) T h i s r e s u l t i s e a s i l y g e n e r a l i z e d t o a m u l t i c o m p o n e n t a s s e m b l y o f p a r t i c l e s i n t e r a c t i n g g i g c e n t r a l f o r c e s . T h i s d e r i v a t i o n h a s p r o c e e d e d f r o m e q u a t i o n 2 t o e q u a t i o n 4 4 b y a n u m b e r o f s t e p s , s o m e m e r e l y f o r m a l . W e h a v e g o n e f r o m t h e f u l l m a n y - b o d y d e s c r i p t i o n o f t h e e v o l u t i o n o f t h e a s s e m b l y t o a n e v o l u t i o n e q u a t i o n f o r a s i n g l e p a r t i c l e d i s t r i b u t i o n 4 5 p a r t i c l e e v o l u t i o n e q u a t i o n a c c u r a t e l y d e s c r i b e t h e e v o l u t i o n o f t h e m a n y - b o d y s y s t e m ? T h e c u r r e n t s t a t e o f a n a n s w e r t o t h i s q u e s t i o n i s d e s c r i b e d b y L a n f o r d - ( 1 9 8 3 ) i n a p r o o f t h a t t h e B o l t z m a n n d e s c r i p t i o n o f a m a n y - b o d y s y s t e m h o l d s f o r t i m e s u p t o 1 / 5 o f a m e a n f r e e t i m e . T h o u g h a t t h i s p o i n t t h e r e i s n o c o m p l e t e l y r i g o r o u s b a s i s f o r u s e o f t h e B o l t z m a n n e q u a t i o n i n t h e d e s c r i p t i o n o f t h e l o n g t i m e e x c i t a t i o n a n d r e l a x a t i o n p r o c e s s e s i n a d i l u t e g a s , t h e e q u a t i o n r e m a i n s a s a p r a c t i c a l t o o l o f g r e a t v a l u e a n d " a m o d e l o f w h a t a k i n e t i c e q u a t i o n s h o u l d b e l i k e " ( M o n t r o l l a n d L e b o w i t z , 1 9 8 3 ) . T h e B o l t z m a n n e q u a t i o n a l s o h a s a l o n g h i s t o r y o f s u c c e s s i n g a s d y n a m i c s . T w o i m p l i c a t i o n s o f t h e e q u a t i o n s , w h i c h h a v e r i g o r o u s f o u n d a t i o n s a r e t h e M a x w e l l i a n e q u i l i b r i u m d i s t r i b u t i o n a n d t h e e q u a t i o n s o f h y d r o d y n a m i c s . I f t h e B o l t z m a n n e q u a t i o n i s t a k e n a s a b a s i s f o r a r e d u c e d d e s c r i p t i o n o f a m a n y - b o d y s y s t e m , o n e m u s t a l s o f a c e t h e q u e s t i o n s o f e x i s t e n c e , u n i q u e n e s s a n d p o s i t i v i t y o f s o l u t i o n s . M o d e r n t r e a t m e n t o f t h e s e q u e s t i o n s i s f o u n d e d p r i m a r i l y i n t h e t h e o r y o f a b s t r a c t n o n l i n e a r d i f f e r e n t i a l e q u a t i o n s i n B a n a c h s p a c e . F o r a f o r c e - f r e e , s p a t i a l l y u n i f o r m a s s e m b l y o f p a r t i c l e s , A r k e r y d ( 1 9 8 0 ) h a s o b t a i n e d g l o b a l ( i n t i m e ) e x i s t e n c e a n d u n i q u e n e s s o f s o l u t i o n f o r a f a i r l y g e n e r a l c o l l i s i o n k e r n e l . G l i c k s o n ( 1 9 7 2 ) h a s o b t a i n e d l o c a l e x i s t e n c e a n d u n i q u e n e s s f o r a s p a t i a l l y u n i f o r m g a s h a v i n g i n i t i a l c o n d i t i o n s b o u n d e d b y a M a x w e l l i a n a n d i n t e r a c t i n g 3 1 3 a p o t e n t i a l w i t h c u t o f f . T h e f i r s t g l o b a l e x i s t e n c e p r o o f f o r t h e s p a t i a l l y i n h o m o g e n e o u s c a s e w a s 4 6 g i v e n b y U k a i ( 1 9 7 4 ) f o r i n i t i a l c o n d i t i o n s i n t h e n e i g h b o r - h o o d o f a M a x w e l l i a n . T h e c u r r e n t s t a t e o f t h e a p p r o a c h e s t o t h e s e v e r y o p e n p r o b l e m s i s r e v i e w e d i n d e t a i l b y G r e e n b e r g ( 1 9 8 3 ) a n d 2 w e i f e l ( 1 9 8 4 ) . I n l e a v i n g t h e d i s c u s s i o n o f e x i s t e n c e t h e o r y f o r t h e n o n l i n e a r B o l t z m a n n e q u a t i o n , i t s h o u l d b e n o t e d t h a t q u e s t i o n s o f g l o b a l e x i s t e n c e , u n i q u e n e s s a n d p o s i t i v i t y f o r s o l u t i o n s o f t h e l i n e a r i z e d p r o b l e m h a v e b e e n s e t t l e d ( N i s h i d a a n d I m a i , 1 9 7 7 ) . I n t h e s p i r i t o f B o l t z m a n n ( 1 8 7 2 ) , w h o i n t r o d u c e d h i s f a m o u s e q u a t i o n a s a s t e p i n h i s p r o o f o f t h e m i n i m u m o r H - t h e o r e m , w e m o v e o n t o a d i s c u s s i o n o f a p p l i c a t i o n o f t h e B o l t z m a n n e q u a t i o n t o n o n e q u i l i b r i u m o f a w e a k l y i o n i z e d d i l u t e g a s . O f p a r t i c u l a r i n t e r e s t i s t h e v e l o c i t y o r e n e r g y d i s t r i b u t i o n o f t h e e l e c t r o n c o m p o n e n t w h i c h i s v e r y p r o b a b l y s t r o n g l y n o n e q u i l i b r i u m , a n d s u c h d i s t r i b u t i o n s f o r t h e c o l l i s i o n i n d u c e d e x c i t a t i o n p r o d u c t s . A s m i g h t b e e x p e c t e d f r o m a n e x a m i n a t i o n o f e q u a t i o n 4 5 , t h e m a j o r c o m p l i c a t i o n i n a B o l t z m a n n a n a l y s i s o f d i l u t e g a s e s i s t h e c o l l i s i o n t e r m . T h e s o - c a l l e d c o l l i s i o n i n t e g r a l i s a n o n l i n e a r f u n c t i o n o f t h e d e s i r e d d i s t r i b u t i o n f u n c t i o n , i n v o l v e s t h e g e n e r a l l y u n - k n o w n d i f f e r e n t i a l s c a t t e r i n g c r o s s - s e c t i o n a n d t h e c o m p l i c a t i o n o f t h e a b s o l u t e v a l u e o f t h e r e l a t i v e S p e e d . F o r s e v e r a l p h y s i c a l l y i n t e r e s t i n g p r o b l e m s t h e r e a r e c o r r e s p o n d i n g a s s u m p t i o n s o f a m a t h e m a t i c a l n a t u r e w h i c h s i m p l i f y t h e c o l l i s i o n t e r m i n o n e w a y o r a n o t h e r . T h r e e s u c h m o d e l p r o b l e m s a r e d i s c u s s e d h e r e i n p r e p a r a t i o n f o r a B o l t z m a n n a n a l y s i s o f A . . . ‘ I n 2 P : m w m t n e n c i E t t 4 e i a e x h o o e v h h 6 f t i e u m n a p u e e f p h t n i e t n t w e o r e z t c r t i c e l d i l e e f f e h n a l r a e t a h o t i t g I c n t n s t s r i v n t u C h / b e n [ L o s l t c l i e } e y - ' e t T a y l c v e n d 7 e e h n e e a t l e . e L n d e o c l a e u c t g e n p d h m t t / e . r a e i d e a s h f h l I 0 9 . - c o l l s e o e r i a h p r e e e a r h c t r s T u n o e e x n o t l e l o d n t o g c t t o n 4 " 3 t c n o o w s n l n n f d o r e r r a e o a a i I R t i f m c e c t y n s e z p t t e l n g i w s ) r . e n t n h a d d d e t h 5 . ) e r n - i l t t e . a o t n c g o a n h s s . 4 t a n e h e c e e o e t 9 p m - s u l b t u p w { 0 $ 3 0 ; 1 , 5 9 ) - 3 3 r n l r r c i o l n r t e e e s t i e e o o a a t e m a e s n t d e e a d p r i i c c u l l t i t c o r o m d z r t i s f r e i m h c a e r a c o t s l o o t a c o y o n r e e u n l t i g m n m i a d a i b q n t l l o n o s p § o u t e i y n e r i p u n e ( a s s t e n w p n t z ‘ t w i i d i t o e i r t i ' $ ¢ o t n h r t l x n n e t e s n n i i o c l o e o h 1 i f t r e s n h e a s i 4 a c n i t h r b m m " i a 4 i a h e t r e a g e e > r t 6 e i r t r l e e l i n ¥ ( ) , c p v n s . a h i u a o s m i c d t e m e / Y v v 5 o y e t o a c c e e e E . m c i e n h r q l l / £ + p t n s d e t g u o o ' o e I g h e a c c o n u t n w n a a d l r i i ‘ é C e ‘ é - K ’ ( 4 6 t a t l l t p t e l e w h d e e e h e s e t o e o n n l i e t t n r s a g d u y n a y i i e c e e c r n q t a i e u s p a e k e r a t c ) b i h t e d l s g s y . e a i c t n o i n 4 7 c o l l i s i o n i n d u c e d h e a t i n g o f a w e a k l y i o n i z e d d i l u t e g a s . T h e t h r e e m o d e l p r o b l e m s a r e t h o s e o f t h e L o r e n t z g a s ( L o r e n t z , 1 9 0 5 ) , t h e M a x w e l l g a s ( M a x w e l l , 1 8 6 7 ) a n d t h e " n e a r l y e q u i l i b r i u m " g a s . T h e t h r e e m o d e l s a r e i d e a l i z a t i o n s o f e l e c t r o n - n e u t r a l , e x c i t e d p r o d u c t - n e u t r a l a n d n e u t r a l - n e u t r a l i n t e r a c t i o n s , r e s p e c t i v e l y . B e c a u s e t h e c h o i c e o f t h e m o d e l a f f e c t s o n l y t h e r . h . s . o f e q u a t i o n 4 5 , c o n s i d e r h e r e t h e m u l t i c o m p o n e n t f o r m o f t h a t p a r t o f t h e e q u a t i o n . M r a m / § . - / I ( 0 4 x 3 4 / § . / I < e , / § . - I e > X " 2 P , I a ! ) s m e f fl a i m x n i - ¥ M a fi a , i - + 2 9 : ( n i - . H - / ) — + ‘ ( a < ( I + 2 5 ; ) ° . d £ - > ] J - 9 $ 0 d . 5 % ’ ¢ G 5 ° } ( 4 8 ) 4 8 a n d t h e e q u a t i o n s i m p l i f i e s t o t h e f o l l o w i n g , a f t e r i n t e g r a t i n g o v e r t h e v e l o c i t y v a r i a b l e f o r p . P " ( 4 7 ) T h i s r e s u l t i s l i n e a r i n t h e d i s t r i b u t i o n f u n c t i o n f o r t h e e l e c t r o n c o m p o n e n t . N o w r e c a l l t h a t t h e d e r i v a t i o n s r e s u l t i n g i n e q u a t i o n 4 5 a r e f o r p a r t i c l e s o f e q u a l m a s s b u t u s i n g e q u a t i o n s 3 7 a n d 3 8 , a r e e a s i l y g e n e r a l i z e d t o p a r t i c l e s o f d i s p a r a t e m a s s . F o r p u r e l y e l a s t i c e l e c t r o n - m o l e c u l e s c a t t e r i n g r e c a l l t h a t t h e e n e r g y e x c h a n g e i n s u c h a c o l l i s i o n i s o f t h e o r d e r 2 m i / m p , a s m a l l n u m b e r . F o r a n i s o t r o p i c d i s t r i b u t i o n f u n c t i o n , e q u a t i o n 4 8 m a y b e t r a n s f o r m e d i n t o a n e n e r g y c o o r d i n a t e a n d t h e t e r m ‘ R Z ‘ ; i t + 1 9 : ( _ _ C “ 6 _ ' _ § _ 1 _ ' > ) e x p a n d e d i n a T a y l o r s e r i e s ( ( + fl m h m ) a r o u n d £ ( 5 ’ 5 2 ) t o y i e l d a t e r m w h i c h i s l i n e a r i n t h e f i r s t d e r i v a t i v e o f t h e d i s t r i b u t i o n w i t h r e s p e c t t o e n e r g y . S u c h a n a p p r o a c h i s t h e b a s i s o f t r e a t m e n t s o f e l a s t i c s c a t t e r i n g i n w e a k l y i o n i z e d d i l u t e g a s e s f r o m t h a t o f _ M o r s e ( 1 9 3 5 ) t o t h e p r e s e n t . F o r i n e l a s t i c s c a t t e r i n g w i t h s m a l l e n e r g y e x c h a n g e a T a y l o r s e r i e s e x p a n s i o n i s p o s s i b l e b u t i n g e n e r a l e q u a t i o n 4 8 4 9 i s t h e b a s i s f o r c a l c u l a t i o n s f o r t h e L o r e n t z g a s . A f u r t h e r a p p r o x i m a t i o n a s s o c i a t e d w i t h t h e w o r k o f L o r e n t z i s t h a t o f t h e e x p a n s i o n o f t h e e l e c t r o n d i s t r i b u t i o n f u n c t i o n i n s p h e r i c a l h a r m o n i c s . T h e p h y s i c a l b a s i s f o r t h e a s s u m p t i o n i s t h e e f f e c t o f e l e c t r o n - n e u t r a l c o l l i s i o n s i n r a n d o m i z i n g t h e d i r e c t e d e l e c t r o n m o t i o n . S o i t i s a s s u m e d t h a t t h e d i s t r i b u t i o n i s n e a r l y i s o t r o p i c i n v e l o c i t y s p a c e a n d t h u s o n l y t h e f i r s t t w o t e r m s o f t h e e x p a n s i o n a r e r e t a i n e d . C a l c u l a t i o n s o f t h e e l e c t r o n d i s t r i b u t i o n f u n c t i o n u s i n g t h e t w o t e r m e x p a n s i o n a r e r e v i e w e d b y M o r i n ( 1 9 8 2 ) . T h e L o r e n t z a p p r o x i m a t i o n i s g e n e r a l i z e d t o a n e i g h t t e r m e x p a n s i o n b y P i t c h f o r d ( 1 9 8 1 ) a n d t h e n a p p l i e d i n c a l c u l a t i o n s o f t r a n s p o r t c o e f f i c i e n t s o f N 2 i n d . c . e l e c t r i c a l d i s c h a r g e s b y P i t c h f o r d ( 1 9 8 2 ) . T h e M a x w e l l g a s m o d e l i s a n i d e a l i z a t i o n o f b i n a r y i n t e r a c t i o n o f t w o n e u t r a l m a s s e s v i a a n i n v e r s e f o u r t h p o w e r r e p u l s i v e i n t e r m o l e c u l a r p o t e n t i a l . M a x w e l l ( 1 8 6 7 ) d e m o n s t r a t e d t h a t f o r s u c h a p o t e n t i a l t h e p r o d u c t [ \ [ L P / I ( 6 , / } / . " / ) i n e q u a t i o n 4 6 r e d u c e s t o t h e s p e e d i n d e p e n d e n t t e r m 1 ( 9 ) . T h i s r e s u l t g r e a t l y s i m p l i f i e s a n a l y s i s o f t h e c o l l i s i o n t e r m a n d i n f a c t a l l o w s e x a c t s o l u t i o n o f t h e B o l t z m a n n e q u a t i o n f o r c e r t a i n c a s e s . M a x w e l l m a d e m u c h u s e o f t h e i n v e r s e f o u r t h p o w e r p o t e n t i a l i n h i s c a l c u l a t i o n s o f t r a n s p o r t c o e f f i c i e n t s a s t h e e q u a t i o n s o f t r a n s f e r c o u l d b e s o l v e d i n c l o s e d f o r m f o r s u c h a p o t e n t i a l . A l t h o u g h a n i n v e r s e f o u r t h p o w e r p o t e n t i a l i s p h y s i c a l l y u n r e a l i s t i c ( i t i s t o o s o f t , i n v e r s e n i n t h t o f i f t e e n t h f i t s t r a n s p o r t d a t a b e t t e r ) t h e i n v e r s e d e p e n d e n c e o f t h e d i f f e r e n t i a l w r i t t e n i n t h e f o l l o w i n g f o r m , w h e r e t h e d i s t r i b u t i o n f u n c t i o n 5 0 c r o s s - s e c t i o n o n t h e r e l a t i v e v e l o c i t y i s a n o b s e r v e d f e a t u r e i n l o w e n e r g y s c a t t e r i n g o f e l e c t r o n s a n d H , H e , 8 2 ' D 2 ( K i e f f e r , 1 9 7 1 ) . T h e i n v e r s e v e l o c i t y d e p e n d e n c e o f t h e t o t a l e l a s t i c c r o s s — s e c t i o n i s a l s o i m p l i e d b y t h e o p t i c a l t h e o r e m o f q u a n t u m c e n t r a l f o r c e s c a t t e r i n g t h e o r y ( C h i l d , 1 9 7 4 ) . T h e B o l t z m a n n e q u a t i o n f o r t h e r e l a x a t i o n o f a n o n - e q u i l i b r i u m , s p a t i a l l y h o m o g e n o u s a s s e m b l y o f M a x w e l l m o l e c u l e s a d m i t s c l o s e d f o r m s o l u t i o n , t h e f i r s t o f w h i c h w a s f o u n d b y K r u p p ( 1 9 6 7 ) . H e f o u n d o n e m e m b e r o f a c l a s s o f s i m i l a r i t y s o l u t i o n s . T h e g e n e r a l c l a s s o f s o l u t i o n s w a s r e d i s c o v e r e d a n d i d e n t i f i e d b y B o b y l e v ( 1 9 7 6 ) , p o p u l a r i z e d b y K r o o k a n d W u ( 1 9 7 6 ) , a n d k n o w n h e r e a f t e r a s t h e K B K W ( K r u p p - B o b y l e V - K r o o k - W u ) c l a s s o f s o l u t i o n s . F o l l o w i n g t h e s e m i n a l w o r k s o f K a c ( 1 9 5 5 ) a n d G r a d ( 1 9 4 9 ) , T r u e s d e l l ( 1 9 5 6 ) s h o w e d t h a t t h e m o m e n t e q u a t i o n s g e n e r a t e d b y t a k i n g v e l o c i t y m o m e n t s o f t h e B o l t z m a n n e q u a t i o n f o r M a x w e l l m o l e c u l e s a r e s u c c e s s i v e l y i n t e g r a b l e , a n d s o i n p r i n c i p l e t h e e n t i r e d i s t r i b u t i o n f u n c t i o n m a y b e r e c o n s t r u c t e d . I t r e m a i n e d f o r K r u p p t o a c t u a l l y f i n d a c l o s e d f o r m e x p r e s s i o n f o r t h e d i s t r i b u t i o n . K r u p p , B o b y l e v , K r o o k a n d W u c o n s i d e r e d a o n e c o m p o n e n t , s p a t i a l l y h o m o g e n o u s , d i l u t e M a x w e l l g a s a t c o n s t a n t n u m b e r d e n s i t y a n d a v e r a g e e n e r g y a n d w i t h a d i s t r i b u t i o n f u n c t i o n i s o t r o p i c i n v e l o c i t y s p a c e . T h e B o l t z m a n n e q u a t i o n c o r r e s p o n d i n g t o t h e s e c o n d i t i o n s m a y b e n o r m a l i z e s t o u n i t y ( i n s t e a d o f t o / O ) . . p r ] 1 a M / s . ' / = = q y 0 n u y , - ’ I I ( i a , / y . - ' a 9 3 o = ) g I 5 — I ) M ; ‘ . a ¥ ( N T § ) x . h . . w , - . . > £ < § . , é > ] x ¢ ( I a v x e e / w / h m o m x s > a § . e : ( « . 5 5 5 0 1 2 ) ) . 2 4 : 8 . 0 M 4 ) . . ‘ - 2 g ( v ’ r ) 4 . £ ( V T ) ‘ = — - { ' d ’ l S m X d i r f f J Q ‘ F z V ' fl ' ) £ 0 9 2 ? ) ( 5 4 ) 5 1 ' S M ’ X 4 1 6 5 - ( 4 9 ) 1 . [ R f fi n ‘ h l f = 1 5 { 5 “ k i t ‘ fl f : 3 5 - 1 - — ( 5 3 ) A f t e r t r a n s f o r m a t i o n t o d i m e n s i o n l e s s v a r i a b l e s v = ‘ 5 " ( m / k T ) ; i a n d ¢ ' = 4 4 7 K S F t h e f o l l o w i n g e q u a t i o n r e s u l t s . 1 « ) 1 - O T i o h e m i r e s n t t i r n a m t n e e s t g f h r o o o r d d m s i f m f e e t r h ( K r o t s e o o n d k i a a n ( l d K r a , e u W q p u u p , t 1 i 9 1 o 9 7 b o y r F b o y u r m b : b e e x p ( ‘ " 7 6 ) , ' b . n 6 6 E m ; 7 ) a t y o B o b b y e i y s o l l e e l , v d v t e h 1 d 9 e 7 6 e s x o ) a l c u t t l i y o n [ 0 ; ' 7 5 ] ( 5 6 ) 5 2 g i v e n h e r e . 9 / . . . I . . . “ 2 3 6 + v a e R m ) = ( M r ) c x P ( " " / 1 I . ’ 5 6 : ) 1 5 : 1 3 . : fl z i y ‘ b ) ) ( 5 5 ) ( - T h e K B K W s o l u t i o n i s r e m a r k a b l e f o r s e v e r a l r e a s o n s . I t i s t h e f i r s t c l o s e d f o r m n o n e q u i l i b r i u m s o l u t i o n t o t h e n o n l i n e a r B o l t z m a n n e q u a t i o n s i n c e B o l t z m a n n p r o p o s e d t h e k i n e t i c e q u a t i o n i n 1 8 7 2 . T h e f a c t t h a t i t l a y u n d i s c o v e r e d f o r o n e h u n d r e d y e a r s d e s p i t e t h e e f f o r t s o f B o l t z m a n n , h i s s t u d e n t s a n d o t h e r s s i n c e t o f i n d s u c h s o l u t i o n s i s a l s o r e m a r k a b l e . ' T w o p r o p e r t i e s , o n e d e m o n s t r a b l e a n d t h e o t h e r c o n j e c t u r e d , w a r r a n t f u r t h e r d i s c u s s i o n . T h e f i r s t p r o p e r t y r e l a t e s t o t h e w a y i n w h i c h t h e n o n e q u i l i b r i u m s o l u t i o n a p p r o a c h e s i t s e q u i l i b r i u m a s y m p t o t e a n d b e a r s o n t h e r e l i a b i l i t y o f l i n e a r i z a t i o n s c h e m e s i n t h e a s y m p t o t i c r e g i o n . P l o t s o f t h e r a t i o o f t h e d i s t r i b u t i o n f u n c t i o n t o i t s e q u i l i b r i u m v a l u e a s a f u n c t i o n o f v e l o c i t y f o r a r a n g e o f t i m e p a r a m e t e r s r e v e a l s t h a t t h e a p p r o a c h t o u n i t y i s v e r y n o n u n i f o r m , t h a t i s , r e l a x a t i o n t i m e s c a l e s f o r t h e h i g h e n e r g y t a i l a r e m u c h l o n g e r t h a n f o r t h e r n o n u . f ( v , 2 : 6 2 ) ) = [ l ” 3 % ) H O T B V J W P ( 2 . ” ( u 3 - V 0 ” ? ( 5 7 ) 5 3 t h e r m a l e n e r g i e s ( v r v l ) . M o r e p r e c i s e d e s c r i p t i o n s o f t h i s n o n u n i f o r m a p p r o a c h m a y b e f o u n d b y e x a m i n a t i o n o f t h e r a t i o f ( V , ’ T ’ ) / f ( v p m ) . 2 ( [ I + 1 ] e x p < ‘ ‘ 2 ’ ) ( 5 8 ) N o w n o t e f o r a n y t i m e T a n d £ < 1 t h e r e i s a V ( € ) s u c h t h a t t h e f o l l o w i n g i n e q u a l i t y h o l d s f o r a l l ‘ V ) W V ( E ) . ‘ F T s w ‘ , ‘ 2 5 5 : 3 ) ‘ < [ H % ] 8 * P ( W ) ” S o , f o r a n y t i m e i n t h e e v o l u t i o n o f t h e n o n e q u i l i b r i u m s o l u t i o n w e h a v e d i s t r i b u t i o n f u n c t i o n s w h i c h a r e b o u n d e d a w a y f r o m t h e e q u i l i b r i u m v a l u e t o a n y d e s i r e d d e g r e e . E r n s t ( 1 9 8 5 ) c o n c l u d e s t h a t t h i s n o n u n i f o r m i t y f o r a l l t i m e t h u s d e n i e s u s r e c o u r s e t o l i n e a r i z a t i o n a r o u n d t h e e q u i l i b r i u m a s a s o l u t i o n t e c h n i q u e . T h i s o b j e c t i o n t o l i n e a r a n a l y s i s w i l l b e d i s c u s s e d l a t e r . T h e s e c o n d p r o p e r t y d i s c u s s e d i n c o n t e x t o f t h e K B K W s o l u t i o n i s o n e a t t r i b u t e d t o t h e s o l u t i o n b y K r o o k a n d W u . I n a n u m b e r o f p h y s i c a l p r o b l e m s s u c h a s s h o c k w a v e s , s i m i l a r i t y s o l u t i o n s p l a y a s p e c i a l r o l e i n r e l a t i o n t o t h e g e n e r a l i n i t i a l v a l u e p r o b l e m , a n d i n t h e f o l l o w i n g s e n s e . A n a r b i t r a r y i n i t i a l s t a t e t e n d s A n t r e l s o l l i k 5 4 f i r s t t o r e l a x t o w a r d s a s t a t e c h a r a c t e r i z e d b y t h e s i m i l a r i t y s o l u t i o n . T h e s u b s e q u e n t s t a g e o f t h e r e l a x a t i o n i s e s s e n t i a l l y r e p r e s e n t e d b y t h e s i m i l a r i t y s o l u t i o n w i t h a p p r o p r i a t e p h a s e . W e c o n j e c t u r e t h a t t h i s p r o p e r t y i s s h a r e d b y r e l a x a t i o n p r o b l e m s o f t h e B o l t z m a n n e q u a t i o n . A n d s o K r o o k a n d W u c o n j e c t u r e t h a t r e l a x a t i o n p r o c e s s e s d e s c r i b e d b y t h e B o l t z m a n n e q u a t i o n a r e c h a r a c t e r i z e d b y t w o s e t s o f v e r y d i f f e r e n t t i m e s c a l e s . T h e y s u g g e s t t h a t v e r y f a s t p r o c e s s e s r e l a x t h e a r b i t r a r y i n i t i a l d i s b r i b u t i o n t o t h e s i m i l a r i t y s o l u t i o n w h i c h t h e n e v o l v e s o n m u c h l o n g e r t i m e s c a l e s , m u c h l i k e t h e " n o r m a l s o l u t i o n s " o f H i l b e r t ( 1 9 1 2 ) . N o e v i d e n c e f o r t h e c o n j e c t u r e w a s p r e s e n t e d a n d t h e p r e s e n t a t i o n o f e v i d e n c e b o t h f o r a n d a g a i n s t t h e K r o o k - W u c o n j e c t u r e h a s o c c u p i e d m a n y a u t h o r s i n t h e l a s t f i v e y e a r s . T h e K B K W s o l u t i o n a n d t h e K r o o k - W u c o n j e c t u r e h a v e m o t i v a t e d w o r k i n s e v e r a l d i r e c t i o n s i n k i n e t i c t h e o r y . T h e d i s c o v e r y o f o n e s i m i l a r i t y s o l u t i o n o f t h e n o n l i n e a r B o l t z m a n n e q u a t i o n r a i s e s t h e p o s s i b i l i t y o f o t h e r s u c h s o l u t i o n s . T e n t i a n d H u i ( 1 9 7 8 ) h a v e u s e d g e n e r a l g r o u p t h e o r e t i c m e t h o d s t o g e n e r a t e s e v e r a l o t h e r s i m i l a r i t y s o l u t i o n s o f t h e s a m e e q u a t i o n . T h e s e o t h e r s o l u t i o n s d o n o t , h o w e v e r , p r e s e r v e t h e n u m b e r d e n s i t y a n d e n e r g y c o n s e r v a t i o n p r o p e r t y . T h e K r o o k - W u c o n j e c t u r e h a s m o t i v a t e d i n t e r e s t i n n u m e r i c a l s o l u t i o n o f t h e n o n l i n e a r B o l t z m a n n e q u a t i o n f o r s e v e r a l r e a s o n s . F i r s t , t h e p r o b l e m h a s a c l o s e d f o r m s o l u t i o n f o r a c e r t a i n c l a s s o f i n i t i a l c o n d i t i o n s , a n d s o m a k e s e v a l u a t i o n o f a n u m e r i c a l t e c h n i q u e p o s s i b l e . S e c o n d , w i t h a s u i t a b l e n u m e r i c a l t e c h d i s t o n n t h i s a n d ; n o n l : Q U O t G A " ! o f t h t o t h E q u i l ~ 0 r a ; f ( v , T 5 1 1 V { C g é ) / f ( v , o o ) b u t i n t e r m s o f f ( v , t ) a n d s o i n t h i n k i n g a b o u t 5 5 t e c h n i q u e t h e K r o o k - W u c o n j e c t u r e m a y b e t e s t e d o n i n i t i a l d i s t r i b u t i o n s o u t s i d e o f t h e K B K W c l a s s a n d a p p l i e d a s w e l l o n m o r e g e n e r a l n o n l i n e a r p r o b l e m s i n k i n e t i c t h e o r y . A t t h i s p o i n t a r e v i e w o f t h e d i f f i c u l t i e s o f n u m e r i c a l s o l u t i o n a n d p r e v i o u s a t t e m p t s a t i t i s a p p r o p r i a t e . I n a n y a t t e m p t t o o b t a i n a n u m e r i c a l s o l u t i o n o f t h e n o n l i n e a r B o l t z m a n n e q u a t i o n o n e s h o u l d k e e p t h e f o l l o w i n g q u o t e f r o m T j o n a n d W u ( 1 9 7 9 ) i n m i n d . B e c a u s e t h e n o n l i n e a r B o l t z m a n n e q u a t i o n i s n o t o r i o u s l y c o m p l i c a t e d , n o t m u c h i s k n o w n a b o u t i t e v e n a c e n t u r y a f t e r i t s i n c e p t i o n . W e h a v e r e c e n t l y l e a r n e d i n a h a r d w a y t h a t i t i s a l s o v e r y d i f f i c u l t t o s t u d y n u m e r i c a l l y . S e v e r a l m a j o r a r e a s o f d i f f i c u l t y c o n f r o n t t h e a n a l y s i s o f t h i s p a r t i c u l a r n o n l i n e a r p r o b l e m . T h e f i r s t i s r e l a t e d t o t h e n o n u n i f o r m r e l a x a t i o n o f t h e K B K W s o l u t i o n t o i t s e q u i l i b r i u m v a l u e . F r o m t h e c l o s e d f o r m s o l u t i o n w e k n o w t h a t f o r a n y t i m e T a n d a n y € < L t h e r e i s a V ( £ ) s u c h t h a t f ( y , T ) / f ( v , o o ) i s b o u n d e d a w a y f r o m i t s e q u i l i b r i u m v a l u e f o r a l l v > V ( £ ) , t h a t i s : E L I . ) . . l . > e $ ( v , m ) ( 6 0 ) O n f i r s t o b s e r v a t i o n t h i s r e s u l t w o u l d i n d i c a t e t h a t l i n e a r i z a t i o n a r o u n d t h e e q u i l i b r i u m v a l u e i s n o t a p p r o p r i a t e . T h e B o l t z m a n n e q u a t i o n i s n o t f o r m u l a t e d i n t e r m s o f l i n e f o r t I R m ? ) r $ 0 0 0 0 ) , ( 6 1 ) L + ( ' . 3 O ‘ u m 5 6 l i n e a r i z a t i o n i t m a y b e b e t t e r t o l o o k a t d i f f e r e n c e s o f t h e f o r m g i v e n b e l o w . S u c h d i f f e r e n c e s a r e d o m i n a t e d b y t e r m s w h i c h f a l l o f f e x p o n e n t i a l l y w i t h t h e s q u a r e o f t h e v e l o c i t y w i t h t h e r e s u l t t h a t t h e v e l o c i t y r e g i o n m o s t n o n u n i f o r m i n a p p r o a c h t o e q u i l i b r i u m i s a l s o t h e r e g i o n c o n t r i b u t i n g l e a s t t o t h e e v o l u t i o n o f t h e d i s t r i b u t i o n f u n c t i o n . W i t h t h i s a r g u m e n t i n h a n d t h e l i n e a r i z e d p r o b l e m w i l l b e a n a l y z e d . A n o t h e r p r o b l e m c o n f r o n t i n g b o t h t h e l i n e a r i z e d a n d n o n l i n e a r p r o b l e m i s t h a t o f s t a b i l i t y o f t h e e q u i l i b r i u m . T o b e g i n s t u d y o f t h e s t a b i l i t y o f t h e e q u i l i b r i u m w e t u r n t o t h e n o r m a l i z e d m o m e n t s o f t h e d i s t r i b u t i o n f u n c t i o n , w h i c h a r e d e s c r i b e d b y t h e f o l l o w i n g n o n l i n e a r o r d i n a r y d i f f e r e n t i a l e q u a t i o n . n l $ . 0 3 “ + M " = F r i - Z M K M fl - K " = 0 ’ L ‘ 1 V ' " ( 6 2 ) K 3 0 I n i t i a l c o n d i t i o n s o n M O ( T ) a n d M 1 ( ¢ ) a r e g i v e n b y r e l a t i n g t h e n o r m a l i z e d m o m e n t s t o t h e c o n s t a n t v a l u e s o f d e n s i t y a n d t e m p e r a t u r e . T h e m o m e n t e q u a t i o n s a r e s u c c e s s i v e l y i n t e g r a b l e a n d s o w e m a y w r i t e f o r t h e f i r s t t w o d i f f e r e n t i a l e q u a t i o n s . a . . 3 m . ( m . - I ) m . ( o ) = 1 . ( 6 3 ) . ( m . ~ : ) m . ( o ) = 1 . O . Q ( 6 4 ) 5 7 T h e d i f f e r e n t i a l e q u a t i o n f o r M D h a s a s t a b l e c r i t i c a l p o i n t a t M o = 0 a n d a n u n s t a b l e o n e a t M o = 1 , t h e e q u i l i b r i u m p o i n t . T h i s i n s t a b i l i t y i s a l s o r e f l e c t e d i n t h e b e h a v i o r o f M 1 a n d s h o u l d b e e x p e c t e d i n a n y a t t e m p t t o i n t e g r a t e t h e e q u a t i o n f o r t h e d i s t r i b u t i o n f u n c t i o n . E x a m i n a t i o n o f t h e i n t e g r a n d o f t h e i n t e g r o d i f f e r e n t i a l e q u a t i o n f o r t h e d i s t r i b u t i o n f u n c t i o n r e v e a l s a t h i r d p r o b l e m . T h e c o n s e r v a t i o n o f l i n e a r m o m e n t u m r e q u i r e s a u n i q u e r e l a t i o n - s h i p b e t w e e n p o s t - c o l l i s i o n a n d p r e - c o l l i s i o n v e l o c i t i e s a n d t h e r e s u l t i n g r e l a t i o n s h i p g r e a t l y c o m p l i c a t e s t h e c o l l i s i o n i n t e g r a l . T j o n a n d W u s e t o u t t o e x a m i n e t h e a p p r o a c h o f t h e t a i l o f t h e d i s t r i b u t i o n f u n c t i o n t o t h e e q u i l i b r i u m v a l u e . T h e t a i l i s m o s t i n t e r e s t i n g i f o n e i s i n t e r e s t e d i n r a t e s o f i n e l a s t i c p r o c e s s e s . T h e y n o t e t h a t t h e c o l l i s i o n i n t e g r a l o f t h e B o l t z m a n n e q u a t i o n f o r M a x w e l l m o l e c u l e s i s v e r y c o m p l i c a t e d a n d s o t h e y c h o o s e a " s i m p l e r e q u a t i o n t h a t i s b o t h p h y s i c a l l y m e a n i n g f u l a n d n u m e r i c a l l y t r a c t a b l e " . T h e m o d e l e q u a t i o n t h e y c h o o s e i s a t w o - d i m e n s i o n a l d i f f u s i v e s c a t t e r i n g e q u a t i o n w h i c h s a t i s f i e s e n e r g y c o n s e r v a t i o n b u t n o t l i n e a r m o m e n t u m c o n s e r v a t i o n . T h e i n t e g r o d i f f e r e n t i a l e q u a t i o n i s s o l v e d b y E u l e r ' s m e t h o d i n t h e t i m e d o m a i n a n d t r a p e z o i d a l q u a d r a t u r e i n t h e v e l o c i t y d o m a i n . B e c a u s e t h e s e l e c t e d m o d e l e q u a t i o n i s n o t t h e e v o l u t i o n e q u a t i o n f o r t h e K B K W s o l u t i o n , n o c o m p a r i s o n o f t h e n u m e r i c a l r e s u l t s w i t h t h e K B K W s o l u t i o n i s p o s s i b l e . I n s p i t e o f t h i s d i s p a r i t y 5 8 T j o n a n d W u p r e s e n t t h e n u m e r i c a l r e s u l t s o f t h e i r a n a l y s i s a s e v i d e n c e i n f a v o r o f t h e K r o o k - W u c o n j e c t u r e . A s s u p p o r t f o r t h e i r a p p r o a c h T j o n a n d W u c i t e t h e m o d e l s o f L o r e n t z a n d t h e E h r e n f e s t s a s e x a m p l e s o f m o m e n t u m c o n s e r v a t i o n v i o l a t i n g m o d e l s w h i c h q u a l i t a t i v e l y r e f l e c t t h e p r o p e r t i e s o f m o m e n t u m c o n s e r v i n g m o d e l s . I n a l a t e r w o r k T j o n ( 1 9 7 9 ) c o n t i n u e s c a l c u l a t i o n s u s i n g t h e s i m p l i f i e d m o d e l e q u a t i o n a n d h e r e p o r t s t h a t f o r c e r t a i n n o n - K B K W i n i t i a l c o n d i t i o n s t h e r e l a x a t i o n t o e q u i l i b r i u m v i o l a t e s t h e K r o o k - W u c o n j e c t u r e . I n p a r t i c u l a r , f o r c e r t a i n i n i t i a l c o n d i t i o n s , t h e p o p u l a t i o n o f c e r t a i n r e g i o n s i n t h e h i g h e n e r g y t a i l o v e r s h o o t s t h e e q u i l i b r i u m v a l u e a n d s o a p p r o a c h e s t h e e q u i l i b r i u m f r o m a b o v e r a t h e r t h a n f r o m b e l o w . S u c h o v e r p o p u l a t i o n e f f e c t s h a v e b e e n r e p o r t e d i n m o l e c u l a r d y n a m i c s s i m u l a t i o n o f a d i l u t e m o n a t o m i c g a s i n t e r a c t i n g g i g t h e L e n n a r d - J o n e s 6 - 1 2 p o t e n t i a l ( B r e y , 1 9 8 2 ) . I n a r e c e n t r e v i e w o f a n a l y t i c a l a n a l y s i s o f t h e K r o o k - W u c o n j e c t u r e E r n s t c o n c l u d e s t h a t t h e c o n j e c t u r e i s f a l s e w i t h v e r y h i g h p r o b a b i l i t y . W i t h t h e v a l i d i t y o f t h e K r o o k - W u c o n j e c t u r e s e t t l e d o n o t h e r g r o u n d s t h e w o r k o f T j o n a n d W u s t i l l l e a v e s t h e d i r e c t n u m e r i c a l s o l u t i o n o f t h e n o n l i n e a r , m o m e n t u m c o n s e r v i n g B o l t z m a n n e q u a t i o n u n t o u c h e d . F o r b o t h t h e L o r e n t z a n d M a x w e l l g a s m o d e l s t h e c o l l i s i o n i n t e g r a l i s s i m p l i f i e d b y t h e n a t u r e o f t h e s c a t t e r i n g i t s e l f , t h a t i s , o n s o m e p h y s i c a l b a s i s . T h e l a s t m o d e l p r o b l e m 5 9 r e v i e w e d h e r e i s o f a m o r e f o r m a l v a r i e t y , t h a t o f t h e n e a r l y e q u i l i b r i u m g a s . I n t h i s m o d e l p r o b l e m t h e d i s t r i b u t i o n f u n c t i o n i s d e c o m p o s e d i n t o t h e p r o d u c t o f e i t h e r a l o c a l o r a n a b s o l u t e M a x w e l l i a n d i s t r i b u t i o n a n d t h e t e r m ( 1 + f ( v , t ) ) f ( v , t ) = f m ( t h ) ( 1 + f ( v , t ) ) ( 6 5 ) T h i s d e c o m p o s i t i o n i s s u b s t i t u t e d i n t o t h e c o l l i s i o n i n t e g r a l . S i n c e t h e c o l l i s i o n i n t e g r a l i s q u a d r a t i c i n t h e d i s t r i b u t i o n f u n c t i o n t h e r e a r e t e r m s w h i c h a r e z e r o , f i r s t a n d s e c o n d o r d e r i n € ( v , t ) . T h e n t h e m a j o r a s s u m p t i o n i s m a d e t h a t f m £ ( v , t ) i s u n i f o r m l y s m a l l w i t h r e s p e c t t o f m , t h a t i s , I M M E H < < I N . . . “ w i t h a n a p p r o p r i a t e d e f i n i t i o n o f " ' ( l . T h e c o n s e q u e n c e o f t h i s a s s u m p t i o n i s t h a t t e r m s q u a d r a t i c i n C ( v , t ) a r e n e g l e c t e d w i t h r e s p e c t t o t h o s e z e r o a n d f i r s t o r d e r a n d s o a c o l l i s i o n i n t e g r a l r e s u l t s w h i c h i s l i n e a r i n t h e v a r i a b l e ( C ( v y t ) . W a n g C h a n g a n d U h l e n b e c k ( 1 9 5 2 ) a n d W a l d m a n n ( 1 9 5 8 ) a n a l y z e d t h e n e a r l y e q u i l i b r i u m s o ~ c a l l e d o r l i n e a r i z e d p r o b l e m f o r a M a x w e l l g a s w i t h a n g u l a r c u t o f f a n d f o u n d t h a t t h e a s s o c i a t e d L a g u e r r e p o l y n o m i a l s a r e t h e e i g e n f u n c t i o n s o f t h e l i n e a r c o l l i s i o n o p e r a t o r . T h e y a l s o r e p o r t e d t h e c o r r e s p o n d i n g e i g e n v a l u e s , w h i c h r a n g e f r o m z e r o t o t h e l i m i t p o i n t a t - 1 ( U h l e n b e c k a n d F o r d , 1 9 6 3 ) . I f t h e c u t o f f i s r e m o v e d t h e n t h e l i m i t p o i n t i s r e m o v e d t o - a o a n d t h e e i g e n v a l u e s , ‘ , , g o a s t h e f o u r t h r o o t o f t h e i r i n d e x , D . A s i n t h e n o n l i n e a r p r o b l e m t h e o n l y c o m p l e t e s o l u t i o n i s f o r t h e c a s e o f M a x w e l l m o l e c u l e s . R e s u l t s o f 6 0 t h e l i n e a r i z e d a n a l y s i s f o r o t h e r t y p e s o f p o t e n t i a l s a r e g i v e n b y C e r c i g n a n i ( 1 9 7 5 ) i n h i s e x t e n s i v e r e v i e w o f l i n e a r t r a n s p o r t t h e o r y . T h o u g h l i n e a r i z a t i o n o f t h e c o l l i s i o n t e r m i s a n o f t - u s e d t o o l i n k i n e t i c t h e o r y t h e v a l i d i t y o f t h e a p p r o a c h i s q u e s t i o n a b l e o n s e v e r a l g r o u n d s . F i r s t , o n e c o u l d a r g u e , t h e v a l i d i t y o f t h e n o n l i n e a r B o l t z m a n n e q u a t i o n a s a n a c c u r a t e d e s c r i p t i o n o f t h e a s s e m b l y o f i n t e r a c t i n g p a r t i c l e s i s o p e n . S e c o n d , i f t h e s y s t e m i s n o t i n c o m p l e t e t h e r m o d y n a m i c e q u i l i b r i u m , t h e d e c o m p o s i t i o n o f t h e d i s t r i b u t i o n f u n c t i o n i s n o t u n i q u e a n d n o p r i o r i t y m a y b e a s s i g n e d t o t h e M a x w e l l i a n . T h i r d , t h e r e a r e c a s e s , e . g . K B K W s o l u t i o n , f o r w h i c h n o u n i f o r m b o u n d o n £ ( v , T ) e x i s t s , c o n t r a r y t o w h a t i s r e q u i r e d b y t h e l i n e a r i z a t i o n a p p r o a c h . T h i s i s s u e i s a d d r e s s e d l a t e r i n t h i s w o r k . W i t h t h i s t h e d i s c u s s i o n a n d r e v i e w o f r e l e v a n t k i n e t i c t h e o r y i s b r o u g h t t o a c l o s e . W e t u r n n e x t t o a b r i e f r e v i e w o f t r a n s p o r t t h e o r y o n a m a c r o s c o p i c l e v e l . D e r i v a t i o n o f m a c r o s c o p i c t r a n s p o r t e q u a t i o n s m a y p r o c e e d f r o m M a x w e l l ' s e q u a t i o n s o f c h a n g e , t h e E n s k o g e x p a n s i o n o f t h e B o l t z m a n n e q u a t i o n o r g i g a c o n t i n u u m a p p r o a c h a n d i t i s t h e l a s t t h a t i s u s e d h e r e . I t i s p r i m a r i l y t h e n e u t r a l d i l u t e g a s i n s t e a d y f l o w w h i c h w e h a v e i n m i n d i n t h i s d e v e l o p m e n t . T h e e f f e c t s o f f l o w , m i x i n g , w a l l i n t e r a c t i o n , a n d t h e v a r i o u s e x c i t a t i o n p r o c e s s e s a r e i m p o r t a n t f a c t o r s t o b e i n c o r p o r a t e d i n t h e d e s c r i p t i o n . I n t h e u s u a l m a c r o s c o p i c f l u i d d e s c r i p t i o n w e a s s u m e t h a t t h e f l u i d i s c h a r a c t e r i z e d b y a l o c a l M a x w e l l i a n o f d e n s i t y / O ( x , t ) , v e l o c i t y v ( x , t ) a n d t e m p e r a t u r e T ( x , t ) . C o n s t r u c t i o n o f t h e m a s s a n d i n t e r n a l s t a t e e n e r g y b a l a n c e s i s 6 1 F o r a w e a k l y i o n i z e d d i l u t e m o l e c u l a r g a s t h e d i s t r i b u t i o n o v e r t h e r o t a t i o n a l a n d v i b r a t i o n a l e n e r g y s t a t e s m a y n o t b e i n e q u i l i b r i u m w i t h t h e t e m p e r a t u r e T ( x , t ) a n d t h e s e d i s t r i b u t i o n s m a y n o t e v e n b e M a x w e l l - B o l t z m a n n . F o r t h e p r e s e n t w e a s s u m e t h a t t h e i n t e r n a l s t a t e d i s t r i b u t i o n s a r e M a x w e l l - B o l t z m a n n a n d c h a r a c t e r i z e d b y a s i n g l e t e m p e r a t u r e f o r e a c h d e g r e e o f f r e e d o m . W i t h t h e s e r e s t r i c t i o n s t h e s p e c i f i c i n t e r n a l e n e r g y o f t h e d i l u t e g a s m a y b e d e c o m p o s e d , i n t h e B o r n - O p p e n h e i m e r s e p a r a t i o n , i n t o t h e s u m o f t h e t r a n s l a t i o n a l , r o t a t i o n a l a n d v i b r a t i o n a l e i g e n e n e r g i e s a s w e l l a s t h e e n e r g y o f f o r m a t i o n o f a n y e x c i t e d s t a t e s o r p r o d u c t s . C o r r e s p o n d i n g b a l a n c e e q u a t i o n s m a y b e c o n s t r u c t e d i n t h e u s u a l m a n n e r , i n c o r p o r a t i n g c o n s e r v a t i o n o f m a s s , m o m e n t u m a n d e n e r g y . I n s t e a d o f o n e e n e r g y b a l a n c e o n e m a y c o n s t r u c t b a l a n c e s o v e r e a c h d e g r e e o f f r e e d o m a n d t h e n i n c l u d e t h e t e r m s w h i c h c o u p l e t h e m . W i t h t h i s a p p r o a c h t h e d e g r e e o f e q u i l i b r i u m o f t w o d e g r e e s o f f r e e d o m a p p e a r s a s a n a t u r a l c o n s e q u e n c e o f t h e r e l a t i v e s i z e o f t h e t i m e s c a l e s f o r e x c i t a t i o n a n d r e l a x a t i o n b e t w e e n t h e t w o . A l t h o u g h t h e u s e o f a M a x w e l l - B o l t z m a n n m o d e l w i t h a " v i b r a t i o n a l " t e m p e r a t u r e i s n o t n e w , a n d t h e d e c o m p o s i t i o n o f t h e m a c r o s c o p i c s p e c i f i c i n t e r n a l e n e r g y i s s u g g e s t e d b y t h e B o r n - O p p e n h e i m e r s e p a r a t i o n o f t h e s i n g l e m o l e c u l e w a v e f u n c t i o n i n t o p r o d u c t s o f i n t e r n a l s t a t e w a v e f u n c t i o n s , t h e c o n s t r u c t i o n o f b a l a n c e e q u a t i o n s o v e r e a c h d e g r e e o f f r e e d o m o f t h e e n e r g y a p p e a r s t o b e a n o v e l a p p r o a c h i n a n a l y s i s o f w e a k l y i o n i z e d d i l u t e g a s e s . A ) f x . . t ¢ J ( a l ) a v A - - _ m A ( 3 5 . 6 M S , + 0 ‘ “ 2 , 1 0 4 ! ( 6 6 ) 6 2 i d e n t i c a l a n d p r o c e e d s i n t h e f o l l o w i n g m a n n e r . L e t fi g h t ) b e t h e f l u i d p r o p e r t y o f i n t e r e s t a n d l e t Y ( x ) a n d § ( x ) b e a f i x e d v o l u m e a n d b o u n d i n g s u r f a c e i n t h e l a b o r a t o r y f r a m e . T h e f o l l o w i n g b a l a n c e e q u a t i o n m a y t h e n b e w r i t t e n . Y O . " s q ) 1 1 ( 5 ) T h i s b a l a n c e e q u a t i o n r e l a t e s t h e a c c u m u l a t i o n o f m a s s o r e n e r g y i n t h e v o l u m e t o t h e t r a n s p o r t p r o c e s s e s a c r o s s t h e b o u n d a r y a n d t o t h e n e t p r o d u c t i o n i n t h e v o l u m e . U s e o f G a u s s ' s d i v e r g e n c e t h e o r e m l e a d s t o a d i f f e r e n t i a l f o r m o f e q u a t i o n 6 6 b u t s u c h a f o r m i s n o t a s g e n e r a l i n a p p l i c a t i o n , p a r t i c u l a r l y t o s y s t e m s i n w h i c h t h e fi g h t ) a r e s p a t i a l l y h o m o g e n e o u s . T h e c o n s t i t u t i v e r e l a t i o n b e t w e e n Q j ( x , t ) , t h e f l u x v e c t o r f o r 4 % ( x , t ) , a n d ( 4 4 3 9 1 : ) i t s e l f r e m a i n s t o b e s p e c i f i e d , a s d o e s t h e n e t p r o d u c t i o n t e r m R j ( x , t ) . T h e p r o d u c t i o n t e r m i s r e l a t e d t o l ¢ 5 ( x , t ) t h r o u g h c o n s i d e r a t i o n o f t h e i n e l a s t i c a n d r e a r r a n g e m e n t c o l l i s i o n p r o c e s s e s w h i c h c o n t r i b u t e t o p r o d u c t i o n o f e x c i t e d s t a t e s . 2 . 2 C o l l i s i o n t h e o r y C o l l i s i o n p r o c e s s e s a r e t h e m e c h a n i s m s f o r e n e r g y t r a n s f e r i n a w e a k l y i o n i z e d d i l u t e g a s a n d d e t e r m i n e t h e f o r m o f b o t h t h e n e t p r o d u c t i o n t e r m R j ( x , t ) i n t h e m a c r o s c o p i c b a l a n c e 6 3 e q u a t i o n a n d t h e c o l l i s i o n i n t e g r a l o f t h e B o l t z m a n n e q u a t i o n ( e q n . 4 6 ) . I t i s a p p r o p r i a t e a t t h i s p o i n t t o r e v i e w t h e q u a n t i t a t i v e d e s c r i p t i o n o f b i n a r y c o l l i s i o n s o n b o t h t h e m i c r o s c o p i c a n d m a c r o s c o p i c l e v e l . O n a m i c r o s c o p i c l e v e l o f d e s c r i p t i o n , i . e . c o l l i s i o n i n t e g r a l o f B o l t z m a n n e q u a t i o n , t h e a n a l y s i s m u s t u l t i m a t e l y y i e l d a d i f f e r e n t i a l s c a t t e r i n g c r o s s - s e c t i o n a n d a r e l a t i o n s h i p b e t w e e n t h e p r e - c o l l i s i o n a n d p o s t - c o l l i s i o n p a r t i c l e v e l o c i t i e s a n d e n e r g i e s . O n t h e m a c r o s c o p i c l e v e l t h e r e s u l t i s a d i s t r i b u t i o n a v e r a g e d t o t a l c r o s s - s e c t i o n o r k i n e t i c r a t e c o n s t a n t . T h i s m a c r o s c o p i c l e v e l f o l l o w s d i r e c t l y f r o m t h e m i c r o s c o p i c l e v e l b y t h e a p p r o p r i a t e s u m m a t i o n a n d i n t e g r a t i o n o v e r p h a s e s p a c e . T h e c o l l i s i o n p r o c e s s e s o f p r i m a r y i n t e r e s t i n a c o n s i d e r a t i o n o f c o l l i s i o n i n d u c e d h e a t i n g o f a w e a k l y i o n i z e d g a s a r e e l a s t i c a n d i n e l a s t i c e l e c t r o n - m o l e c u l e c o l l i s i o n s a n d c o l l i s i o n s b e t w e e n t w o n e u t r a l p a r t i c l e s . C o n s i d e r t h e c l a s s i c a l d e s c r i p t i o n o f a c o l l i s i o n o f t w o p a r t i c l i e s i n t e r a c t i n g b y a c e n t r a l p o t e n t i a l . T h e i n d i c e s ( i , r ) r e f e r t o t h e p r e - c o l l i s i o n i d e n t i t y o f t h e t a r g e t a n d b u l l e t s p e c i e s r e s p e c t i v e l y a n d t h e i n d i c e s ( j , p ) r e f e r t o t h e c o r r e s p o n d i n g p o s t - c o l l i s i o n q u a n t i t i e s . S o , f o r e x a m p l e , t h e p a i r x i i i , i s t h e p o s i t i o n a n d v e l o c i t y o f t h e t a r g e t 5 a t t h e p o i n t w h e n p a r t i c l e s 5 a n d r a r e w i t h i n a d i s t a n c e 0 ; , o f e a c h o t h e r . M r : 7 Y 1 P ' m ‘ . = m . ( 7 0 ) 6 4 F i g u r e 2 : I l l u s t r a t i o n o f t h e n o r m a l v e c t o r s k : a n d k ? T h e v e c t o r s k : a n d k j p a r e o u t w a r d u n i t n o r m a l v e c t o r s m a r k i n g t h e p o i n t s w h e r e t h e b u l l e t p a r t i c l e e n t e r s a n d e x i t s t h e s p h e r e o f r a d i u s 6 c e n t e r e d o n t h e t a r g e t . L e t n b e a u n i t v e c t o r o r i e n t e d i n t h e d i r e c t i o n o f f , “ 2 ' . - t h a t i s , n - ( § p - f r H C w h e r e C i s a n o r m a l i z a t i o n c o n s t a n t t o b e d e t e r m i n e d . ‘ E p = 1 ; + n C ( 6 7 ) N o w u s e t h i s e x p r e s s i o n i n t h e l a b c o o r d i n a t e f o r m o f t h e e n e r g y a n d l i n e a r m o m e n t u m c o n s e r v a t i o n e q u a t i o n s . : 3 - + £ 5 - ° £ ; = E E P § " : ; * - : 3 “ ; " $ - 1 . - E ' f " . 1 f ‘ ~ 1 . * ' “ P . z ’ " ~ ’ ( 6 8 ) m r ‘ 3 - + " N ? 4 = m ? E ' P + M 3 E S ( 6 9 ) H \ 4 3 l l 4 + : ~ ’ : K 3 3 ' 3 ( ‘ / > A ) V 6 5 A f t e r s u b s t i t u t i n g e q n . 6 7 i n t o e q n . 6 9 a n d t h e r e s u l t i n t o e q n . 6 8 t h e f o l l o w i n g e q u a t i o n f o r C r e s u l t s . c = - 2 ( n . v l i ’ ) “ ‘ ( 7 1 ) ( 1 + , 3 ) m . 1 W i t h t h i s e x p r e s s i o n f o r C t h e f o l l o w i n g r e l a t i o n s h i p s f o r t h e l a b c o o r d i n a t e a n d c e n t e r o f m a s s f r a m e v e l o c i t i e s m a y b e m a d e . ( n u - m . ) ‘ 7 2 ) z — V ' f ? { F ' ‘ 2 9 ( ' 2 ‘ ) m . ( ' 7 3 ) ( " ‘ 9 ‘ M t ) P r ( ' - . i ’ . £ ‘ 2 1 ‘ ( 5 " y i ) ( 7 4 ) T h e p r e c e d i n g a n a l y s i s m a y b e r e p e a t e d f o r t h e c a s e o f i n e l a s t i c i n t e r a c t i o n i n w h i c h t h e d i f f e r e n c e o f t o t a l i n t e r n a l s t a t e e n e r g y o f t h e f i n a l c o n f i g u r a t i o n a n d i n i t i a l c o n f i g u r a t i o n i s d e n o t e s a s A E . T h e f o l l o w i n g e x p r e s s i o n s f o r C a n d X ? a r e o b t a i n e d . V 2 . p 1 " 1 " “ ; z - 4 . . ‘ r - — l ( r . ) A E ] C ( Q A ) [ ( 9 a ) M r M ‘ ( . 7 5 ) ( l + 3 3 — 7 — m l . 1 . Y : 2 g r “ ( ' 2 ' Y r ) ? - 9 R ' 3 ' f ) - 2 ( M ; r + : : ‘ ) A E ] ( 7 6 ) F r o m e q n . 7 5 o n e m a y o b t a i n t h e f o l l o w i n g r e l a t i o n s h i p b e t w e e n n . v . p a n d n . v . r . A A ] A A l l V : P ~ I ’ — M r - r M L ' ) A E ( Q . Y . ) ) - ~ ( 9 O Y " ) [ l 2 " \ t h ( 9 . 3 4 3 7 1 ] ( 7 7 ) F o r h a r d s p h e r e e l a s t i c s c a t t e r i n g t h e u n i t v e c t o r n i s i d e n t i c a l t o t h e o u t w a r d n o r m a l v e c t o r k , n o t i n g t h a t k i t = k j p . I n t h i s c a s e A . E = O s o e q n . 7 7 r e d u c e s t o t h e f o l l o w i n g r e s u l t . 1 3 : . r _ 9 ’ Y j 2 ° Y 1 ( 7 8 ) . ( “ S - : < Q " E r ) ’ § ’ ( 9 £ ) ) — * ( A L X i ? ) ( 8 0 ) 6 7 E q u a t i o n 7 8 i s t h e u s u a l r e l a t i o n s h i p e m p l o y e d i n d e r i v a t i o n o f t h e B o l t z m a n n e q u a t i o n a l t h o u g h a p p l i c a t i o n o f t h e e q u a t i o n i s m a d e t o m u c h m o r e t h a n h a r d s p h e r e e l a s t i c s c a t t e r i n g . T h e a n a l y s i s m a y a l s o b e e x t e n d e d t o r e a r r a n g e m e n t c o l l i s i o n s i f e q n . 7 0 i s r e p l a c e d b y t h e f o l l o w i n g e x p r e s s i o n o f t o t a l m a s s c o n s e r v a t i o n . m r + m i = m j 4 ' m p ( 7 9 ) T h e e x p r e s s i o n f o r C m a y t h e n b e g i v e n a s i n e q n . 8 0 . — l c : - ( - . i . , , + ( W : m — m ) - — ( i n : 1 2 ) U p t o t h i s p o i n t t h e f i n a l r e l a t i v e v e l o c i t y h a s b e e n r e l a t e d t o t h e i n i t i a l r e l a t i v e v e l o c i t y t h r o u g h t h e d e f i n e d v e c t o r n . F o r h a r d s p h e r e e l a s t i c s c a t t e r i n g n i s e a s i l y i d e n t i f i e d a s t h e o u t w a r d n o r m a l v e c t o r E . F o r e l a s t i c a n d i n e l a s t i c c e n t r a l f o r c e s c a t t e r i n g t h e r e l a t i o n s h i p " ‘ r ‘ E r ‘ " i f " " ‘ 9 f r * ” ' 5 f 5 i n t e r m s o f r e l a t h W i i v t e e e q l n o s c . i v 8 i 4 e s t a d i n V A 8 5 r a i n t d y p a j m V A a l s o b e e x p r e s s e d 6 8 b e t w e e n k . r , V . r A l A l a n d k P , v 9 A ] . 3 i s n o t a s c l e a r . C o n s i d e r t h e c e n t r a l f o r c e s c a t t e r i n g p r o b l e m i n c e n t e r o f m a s s c o o r d i n a t e f r a m e . L e t G b e t h e v e l o c i t y c e n t e r o f t h e m a s s o f t h e t w o p a r t i c l e s . ( ; = 4 m r + M “ m ! 9 M ‘ 9 ¥ ‘ . = G - M r V ; a A . f “ M " a S . : G ) - ” V P ‘ ) A ~ — 3 M r ? M 3 ‘ 5 , = G + . _ . _ — " i f ; P = = G + M d f M f Q - M i 5 ‘ R e c a l l t h a t t h e u n i t v e c t o r n o f l i p a n d f r “ ’ 3 I I t h e o f t h e ( 8 1 ) ( 8 2 ) ( 8 3 ) ( 8 4 ) ( 8 5 ) i s d e f i n e d i n t e r m s ( 8 6 ) m - - I v s ) [ I - 2 ( 2 : 2 3 3 ) . 3 6 : . 7 ' T ( ( Y y 7 c ° 5 / 4 1 f a 6 9 S o t h e u n i t v e c t o r 9 d i v i d e s t h e a n g l e f o r m e d b e t w e e n f p a n d f r a s w e l l a s t h a t b e t w e e n Y . P a n d y i r . F o r e l a s t i c c o l l i s i o n s ( Y 3 ? ) = ( Y t r l a n d s o n b i s e c t s t h e a n g l e b e t w e e n y j p a n d y i r , s o t h a t n . V i r = [ V i r ] c o s 9 w h e r e 2 9 i s e q u a l t o t h e a n g l e f o r m e d b y y j p a n d Y i r ' F u r t h e r , o n e m a y s u b s t i t u t e e q n s . 8 2 - 8 5 i n t o t h e l a b f r a m e e n e r g y b a l a n c e f o r t h e f o l l o w i n g . F o r i n c r e a s e d i n t e r n a l e x c i t a t i o n ( A B ) 0 ) t h e s e c o n d t e r m i n b r a c k e t s i s b o u n d e d a b o v e b y u n i t y a n d r e p r e s e n t s t h e f r a c t i o n o f t h e i n i t i a l r e l a t i v e k i n e t i c e n e r g y w h i c h i s l o s t i n t h e e x c i t a t i o n . T o a d d r e s s a n g u l a r m o m e n t u m c o n s e r v a t i o n t h e f o l l o w i n g a n g l e s a r e d e f i n e d . ) 5 . " Y . " [ W m f . ( 8 8 ) . 7 ' ) ( 8 9 ) 7 x : k n 0 ) / ~ \ : 4 4 s o t h a t , ’ 5 : ' Y 3 ? = / Y s ' / 6 ° > ( fi r e ) ( 9 0 ) [ 9 : 9 “ o f / , 1 ) 5 " “ [ 3 1 : s w a g - 9 4 : ] - . Z ( m z v m g ) [ i f / 1 ] ( 9 6 ) 7 0 T h e t o t a l o r b i t a l a n g u l a r m o m e n t u m i n t h e c e n t e r o f m a s s s y s t e m i s g i v e n a s t h e f o l l o w i n g . M ‘ H m e ( 9 1 ) J 4 } - : M k t r x i f I . " ( ( 1 - m r . A A ( 9 2 ) g . . . = 0 1 m m . 9 5 , - " x y ! M ‘ J M , ( 9 3 ) A s s u m i n g t h a t t h e c o l l i s i o n d o e s n o t i n v o l v e r o t a t i o n a l d e g r e e s o f f r e e d o m t h e n w e m a y w r i t e t h e f o l l o w i n g e x p r e s s i o n o f c o n s e r v a t i o n o f o r b i t a l a n g u l a r m o m e n t u m . H t " / 5 9 / ( 9 4 ) U S P / " h ( N 9 ) ( 9 5 ) / Y ‘ r / 9 " “ { 5 . 2 . U s i n g e q n . 8 7 i n e q n . 9 5 o n e m a y e l i m i n a t e t h e f a c t o r l y i r / f r o m e a c h s i d e t o y i e l d e q n . 9 6 . ' I L ( " ‘ 5 ( 4 . : - 3 . _ - / . t ( / f c o s ‘ 1 / 3 ‘ \ f . r / C ° 5 / 1 3 — 2 ( m _ - z [ ' 2 1 1 i ” . ' 1 n ( ‘ n : ' . * f t M f > J — / . Q - v E : - - I A . ‘ ( V t . ‘ ) c o s A z E - y / V f / z ] ‘ ( ( 1 1 0 0 1 2 ) ) 7 1 F r o m t h i s , a n d t r i g o n o m e t r i c i d e n t i t i e s , a n e x p r e s s i o n f o r c o s ( / S , - 9 ) i s f o u n d a n d s u b s t i t u t e d i n e q n . 9 0 t o r e l a t e k . p . v . p t o k . r . v . r . A 3 A ] A 1 A 1 I / - 1 1 L C o s ( fi , - a ) : [ I - S a n a / 5 i ) - 2 ( € % ’ ” — ) fi % 1 ] } ( 9 7 ) P P - p ( ‘ 3 Y ; ‘ ( V 3 ) 0 “ ( fi r - 9 ) ( 9 8 ) I / " I . - u I . k . ' . \ / . P : V . " _ ( m + m 3 ) £ _ l , 2 _ _ M g r - ‘ 3 ) _ A _ § . 5 ‘ 4 I , ( [ 1 2 “ a n ; “ I f ! " I S « I S , ~ I 1 ( " P M . I n ” : ( 9 9 ) " L r m H M ; , 1 : I ‘ L / [ l " ) ( i f “ ) . ) I ' A ' T E ' T I " " S M # 1 } ( 1 0 0 ) I / 1 ' - n M . E : i k . . V I ~ 2 ( fl ) ; — : - M r - M : [ 9 ( . ' R ’ A ( fi r § P ° ) a l 5 ; - ? ! ” + 9 C 4 » ' ; : ° ¥ £ " ‘ / [ l 5 4 ‘ : - , ; . ‘ 4 - s M N ‘ N ) - J ‘ [ M 3 — , 2 Q ( C ) ( 5 " ( 3 9 ‘ A fi 2 E - g f fl o £ x " ‘ 3 ] l ; ‘ . ‘ ) ( 1 0 4 ) 7 2 S i n c e f i r . Y i r i s i d e n t i f i e d a s t h e i n c o m i n g f l u x a n d k j p . y g a s t h e o u t g o i n g , t h e n e g a t i v e s i g n i s c h o s e n i n e q n . 1 0 3 . C o m p a r i n g e q n s . 1 0 3 a n d 7 7 , i t i s a p p a r e n t t h a t t h e y a r e i d e n t i c a l e x c e p t f o r t h e v a r i a b l e l a b e l s 9 a n d k . T h e r e s u l t i n e q n . 1 0 3 r e l a t e s t h e t e r m m k j p . Y j p t o k i t . y i r a n d p r e p a r e s t h e w a y f o r e x t e n s i o n o f t h e d e r i v a t i o n o f t h e B o l t z m a n n c o l l i s i o n t e r m t o i n e l a s t i c c e n t r a l f o r c e s c a t t e r i n g . T h e c o l l i s i o n i n t e g r a l o f e q n . 4 1 b e c o m e s t h e f o l l o w i n g . ’ 3 % » O - d 0 } ? 4 4 ; , T h u s f a r , r e l a t i o n s h i p s b e t w e e n k . r . V . r a n d k . p . V . p A l A 1 A ] A ] h a v e b e e n e s t a b l i s h e d , a s w e l l a s t h o s e f o r / Y i r / a n d l y j p l . I t r e m a i n s n o w t o r e l a t e k i r , k j p a n d n , t h e u n i t v e c t o r d e f i n e d e a r l i e r ( e q n . 6 7 , 8 6 ) . T a k i n g t h e v e c t o r p r o d u c t o f k j p w i t h t h e f o l l o w i n g e x p r e s s i o n f o r Y j p r e s u l t s i n e q n . 1 0 6 . A P M r V . - = Y 5 + ( ' " T i t - ) C Z . ‘ ( 1 0 5 ) P r , g s ‘ Y f ‘ ( I V Y . + ( ’ * § 1 ) C f f ” } ( 1 0 6 ) . . [ 1 ( i j y H . ’ - : 7 a ’ X ; [ + ( 1 * a I + [ ( H m — i : ) C ( 5 5 ‘ k ' 1 ‘ 5 “ 9 ? ) " ? ) ( ( 1 1 0 0 8 9 ) ) 7 3 C o n s e r v a t i o n o f o r b i t a l a n g u l a r m o m e n t u m r e q u i r e s t h a t ( 1 0 7 ) I W I ( r 1 - 9 ) = M / 9 % l T h e s t e p f r o m e q n . 1 0 8 t o 1 0 9 w a s m a d e b y o b s e r v i n g t h a t k j p , y i r a n d n a r e a l l i n t h e s a m e p l a n e a n d s o t h e v e c t o r p r o d u c t s o f a n y t w o w i l l b e i d e n t i c a l i n d i r e c t i o n . E q u a t i n g e q n s . 1 0 7 a n d 1 0 9 g i v e s e q n . 1 1 0 . ( Y i p ) S W ‘ ( F ' — 9 > : / \ / ‘ _ " / a n / S ‘ + ( H ’ % ) C S o ' n fl g ( 1 1 0 ) T h e a n g l e / 3 3 i s t h a t f o r m e d b e t w e e n k j p a n d t h e u n i t v e c t o r n . O n e m a y e x p r e s s l y j p / i n t e r m s o f / Y i r / w i t h e q n . 8 7 . V M V P - 2 6 9 9 , 2 3 ) 1 5 " “ ‘ ( F r 9 ) - l l ’ f / 5 " ‘ / " z ( “ ' fi k v h fl z ( 1 1 1 ) N o w r e c a l l t h a t t h e c o n s t a n t C i s g i v e n i n t e r m s o f n , V i r a n d t h e c h a n g e i n i n t e r n a l s t a t e e n e r g y . T h e a n g l e A r b e t w e e n 9 a n d Y i m a y n o w b e e x p r e s s e d a s / 3 1 t / 6 3 a n d o n e m a y w r i t e t h e f o l l o w i n g f o r C . HC ) l l ” » 9 5 7 7 A p v ' C = ~ 1 / ( E l f / ( 5 m { 5 1 ‘ " " fl c y ) f / c o s ( l 6 = " 1 / K " , / * ¢ / S , ) ° S ( fl . " / ‘ r ) $ " “ / ’ 3 ( ( 1 1 1 1 4 5 ) ) 7 4 ” L ’ / Y ~ ' r / C O S ( / 3 ( 1 7 9 3 ) " [ l ‘ é ‘ r / z e o s z o s c t f z ) ’ 1 ( M n m ' A 5 ] ( 1 1 2 ) “ ( M r ( 1 + 9 1 : ) A s c a t t e r i n g e v e n t m a y b e s p e c i f i e d i n t e r m s o f / 3 2 ( d e f i n i n g t h e i m p a c t p a r a m e t e r ) , t h e s c a t t e r i n g a n g l e 8 a n d t h e r e l a t i v e v e l o c i t y / Y i r / a s w e l l a s p a r t i c l e m a s s e s a n d 1 1 3 . F r o m t h i s i n f o r m a t i o n o n e m a y c a l c u l a t e l y j p / f r o m e q n . 8 7 ; / 3 1 f r o m e q n . 9 5 a n d t h e n / 3 3 f r o m e q n s . 1 1 1 a n d 1 1 2 . T h e s e c a l c u l a t i o n s n o t o n l y f i x t h e o u t c o m e o f t h e c o l l i s i o n b u t a l s o e s t a b l i s h t h e r e l a t i o n s h i p b e t w e e n k i r , k j p a n d t h e u n i q u e u n i t v e c t o r 9 . C o n s i d e r f o r e x a m p l e t h e c a s e o f e l a s t i c , c e n t r a l f o r c e s c a t t e r i n g . I n t h i s p r o b l e m t h e t r a j e c t o r y i s s y m m e t r i c a b o u t t h e s c a t t e r i n g c e n t e r a n d s o # 1 - 0 = 1 1 ' - fl 2 . ( 1 1 3 ) 5 1 . n ( / 5 ' — 9 F r o m e q n . 1 1 2 r e s u l t s t h e f o l l o w i n g . ( M g . . . ) S u b s t i t u t i n g t h i s i n t o e q n . 1 1 1 g i v e s t h e f o l l o w i n g . 7 5 A n d w i t h a t r i g o n o m e t r i c i d e n t i t y w e h a v e t h e r e s u l t g i v e n b e l o w . C o s ( / 3 _ ( _ E £ ; ) S M ( 5 % ) = c o s ( , 5 . 1 % , ) s y n / 3 3 ( 1 1 6 ) T h i s i d e n t i t y i s s a t i s f i e d i f , f o r e x a m p l e , # 3 = ( fl z - ’ 3 1 ) ” , G e o m e t r i c a l l y t h i s m e a n s t h a t t h e u n i t v e c t o r 1 3 b i s e c t s t h e a n g l e b e t w e e n k i r a n d k j p . F o r e l a s t i c , c e n t r a l f o r c e s c a t t e r i n g t h i s m a k e s i n t u i t i v e s e n s e . T h e s a m e g e n e r a l p r o c e d u r e h o l d s f o r i n e l a s t i c s c a t t e r i n g p r o b l e m s . T h u s f a r t h e a n a l y s i s o f t h e b i n a r y c o l l i s i o n h a s b e e n w i t h i n t h e f r a m e w o r k o f t h e c o n s e r v a t i o n l a w s f o r m a s s , e n e r g y , l i n e a r a n d a n g u l a r m o m e n t u m w i t h n o d i s c u s s i o n o f t h e a c t u a l t r a j e c t o r y o r d y n a m i c s w h i c h c o n n e c t t h e e n t e r i n g a n d l e a v i n g p a r t i c l e s t a t e s . I n t h e r e m a r k s f o l l o w i n g e q n . 1 1 2 i t w a s s t a t e d t h a t s p e c i f i c a t i o n o f t h e i m p a c t p a r a m e t e r ( o r k i t ) , t h e r e l a t i v e v e l o c i t y l y i r / a n d t h e s c a t t e r i n g a n g l e 0 f i x t h e o u t c o m e o f t h e s c a t t e r i n g e v e n t . T h e s c a t t e r i n g a n g l e 0 i s n o t , h o w e v e r , i n d e p e n d e n t o f t h e i m p a c t p a r a m e t e r a n d r e l a t i v e v e l o c i t y b u t i s r e l a t e d t o t h e m t h r o u g h i n t e g r a t i o n o f t h e e q u a t i o n s o f m o t i o n f o r t h e t w o p a r t i c l e s y s t e m . T h e i n t e g r a t i o n s m a y b e d o n e e i t h e r m a t h e m a t i c a l l y , g i v e n a p o t e n t i a l f u n c t i o n , o r a s i t w e r e , e x p e r i m e n t a l l y t o y i e l d a d i f f e r e n t i a l c r o s s - s e c t i o n . W i t h t h e d i f f e r e n t i a l c r o s s - s e c t i o n a n d t h e r e l a t i o n - s h i p s d e v e l o p e d i n F i g . l , t h e c o l l i s i o n i n t e g r a l o f e q n . 1 0 4 i s t r a n s f o r m e d i n t o t h e f o l l o w i n g f o r m . i “ 9 5 P ) £ 7 : / n . / I ( e ( 1 4 5 ° , 1 < 3 ) ) fl “ ' “ ( M W ) V 5 ) ] . P t — ( fi P ' I z g - P ’ . - D C ’ § , - , " “ , ‘ ’ 3 C fl fi ) [ 3 " ( X N 1 . J ° I . . X " ’ ; ‘ } ) } C I R C I ; P ° 7 6 ' 4 . ( 1 1 7 ) I t s h o u l d b e n o t e d t h a t e q n . 1 1 7 i s n o t t h e u s u a l f o r m o f t h e B o l t z m a n n c o l l i s i o n t e r m b u t t h a t i t d o e s r e d u c e t o t h e u s u a l f o r m f o r t h e c a s e A E = 0 , e . g . e l a s t i c c o l l i s i o n s . R e c a l l n o w t h a t t h e p r i m a r y m o t i v a t i o n f o r a d i s c u s s i o n o f s c a t t e r i n g t h e o r y i s a q u a n t i t a t i v e d e s c r i p t i o n o f e l a s t i c a n d i n e l a s t i c e l e c t r o n - m o l e c u l e e x c i t a t i v e c o l l i s i o n s a n d a l s o o f n e u t r a l - n e u t r a l c o l l i s i o n s c o n t r i b u t i n g t o r e l a x a t i o n o f e x c i t e d p r o d u c t s . I t i s e v i d e n t t h a t s u c h a d e s c r i p t i o n r e q u i r e s s c a t t e r i n g c r o s s - s e c t i o n i n f o r m a t i o n a s w e l l a s d e t a i l s o f t h e i n t e r n a l e n e r g y s t a t e s o f t a r g e t s a n d b u l l e t s . T h e q u a n t u m m e c h a n i c a l t r e a t m e n t o f e l a s t i c , i n e l a s t i c a n d r e - a r r a n g e m e n t s c a t t e r i n g o f e l e c t r o n s w i t h a t o m i c a n d m o l e c u l a r s p e c i e s i s d i s c u s s e d i n d e t a i l b y M a s s e y a n d B u r h o p ( 1 9 6 9 ) a n d M a s s e y ( 1 9 6 9 ) . H o w e v e r , b e c a u s e o f t h e t r e m e n d o u s d i f f i c u l t y o f s u c h c a l c u l a t i o n s e v e n f o r h i g h e n e r g y e l e c t r o n - H 2 s c a t t e r i n g , n o t t o m e n t i o n t h e p a u c i t y o f p o t e n t i a l s u r f a c e s , c a l c u l a t i o n s h e r e r e l y h e a v i l y o n e x p e r i m e n t a l l y o b t a i n e d d i f f e r e n t i a l c r o s s - s e c t i o n s a n d i n e l a s t i c a n g l e - a v e r a g e d c r o s s - s e c t i o n s . S u c h c r o s s - s e c t i o n s m a y b e f o u n d i n w o r k s w h i c h c o n s i d e r s i n g l e D i s s o c i a t i v e i o n i z a t i o n o f | { + : 3 X b y e x c i t a t i o n t o 1 { : 9 7 7 e x c i t a t i o n s o r s p e c i e s o r i n e x t e n s i v e c o m p i l a t i o n s l i k e t h a t o f K i e f f e r ( 1 9 7 1 ) . T o t h i s p o i n t t h e t e r m A E , i n t r o d u c e d i n e q n . 7 5 , h a s b e e n r e g a r d e d a s a n i n d e p e n d e n t l y v a r i a b l e p a r a m e t e r . I t i s , h o w e v e r , d e p e n d e n t o n t h e p r e - a n d p o s t - c o l l i s i o n i n t e r n a l s t a t e s o f t h e t a r g e t a n d b u l l e t s p e c i e s . F o r t r a n s i t i o n s b e t w e e n s t a t e s r e p r e s e n t e d b y t h e d i s c r e t e s p e c t r u m o f t h e s i n g l e p a r t i c l e h a m i l t o n i a n t h e s p e c i f i c a t i o n o f A E i s s t r a i g h t f o r w a r d , a s s u m i n g t h a t t h e e n e r g y e i g e n v a l u e s a r e k n o w n . A s a n e x a m p l e c o n s i d e r t h e s c a t t e r i n g o f e l e c t r o n s i n H 2 . F o r e l a s t i c s c a t t e r i n g o r s c a t t e r i n g e v e n t s w h i c h r e s u l t i n v i b r a t i o n a l a n d r o t a t i o n a l t r a n s i t i o n s i n t h e g r o u n d e l e c t r o n i c s t a t e t h e v a l u e o f A B m a y b e c a l c u l a t e d . I t m a y a l s o b e c a l c u l a t e d f o r t r a n s i t i o n s f r o m t h e g r o u n d e l e c t r o n i c s t a t e t o b o u n d s t a t e s o f e x c i t e d f o r m s o f H 2 . T h e r e a r e e x c e p t i o n s t o t h i s , h o w e v e r , a n d a m o n g t h e m a r e v a r i o u s d i s s o c i a t i v e p r o c e s s e s . D i s s o c i a t i v e a t t a c h m e n t o f a n e l e c t r o n t o H 2 i n t h e X . 2 ; s t a t e r e s u l t s i n e x c i t a t i o n e i t h e r t o t h e 2 : ; o r t h e . 1 2 ” M s t a t e o f t h e H ; i o n f o l l o w e d b y d i s s o c i a t i o n i n t o H - a n d H ( l s ) p o s s i b l y s h a r i n g s e v e r a l e v o f k i n e t i c e n e r g y . E x c i t a t i o n o f u + 1 + g r o u n d s t a t e H 2 { : 3 t o t h e l o w e s t t r i p l e t s t a t e ‘ 3 2 : “ r e s u l t s i n d i s s o c i a t i o n i n t o t w o e n e r g e t i c H ( l s ) a t o m s . + s t a t e o f t h e H 2 + m o l e c u l a r i o n i s f o l l o w e d b y d i s s o c i a t i o n i n t o H ( l s ) a n d H + p o s s i b l y s h a r i n g c l o s e t o 1 0 e v o f k i n e t i c e n e r g y . T h e s e t h r e e p r o c e s s e s a r e o f g r e a t i n t e r e s t f o r c o l l i s i o n 7 8 i n d u c e d h e a t i n g o f h y d r o g e n b e c a u s e o f t h e k i n e t i c e n e r g y o f t h e p r o d u c t s t a t e s . E x p e r i m e n t a l m e a s u r e m e n t s b y S c h u l z ( 1 9 5 9 ) a n d l a t e r b y R a p p ( 1 9 6 5 ) o f t h e c r o s s - s e c t i o n f o r p r o d u c t i o n o f H - b y d i s s o c i a t i v e a t t a c h m e n t a l s o c o n f i r m e d t h a t t h e r e s u l t i n g H - i o n s h a v e k i n e t i c e n e r g y o f a b o u t 2 . 5 e v . D u n n ( 1 9 6 3 ) f o u n d t h a t t h e e n e r g e t i c p r o t o n s r e s u l t i n g f r o m d i s s o c i a t i v e i o n i z a t i o n o f H 2 c a r r y a w a y u p t o 1 0 e v . o f k i n e t i c 3 + e n e r g y . F o r d i s s o c i a t i o n o f H b y e x c i t a t i o n t o b 2 : “ t h e r e 2 a r e n o e x p e r i m e n t a l i n d i c a t i o n s o f t h e e n e r g y d i s t r i b u t i o n o f t h e n e u t r a l p r o d u c t s , b u t o b v i o u s l y a n e s t i m a t e o f t h e m e a n v a l u e i s b a s i c t o a n a l y s i s o f c o l l i s i o n i n d u c e d h e a t i n g o f h y d r o g e n . S u c h a c a l c u l a t i o n i s p r e s e n t e d l a t e r . T h e m i c r o s c o p i c d e s c r i p t i o n o f c o l l i s i o n s w h i c h i s m a d e i n t e r m s o f e n e r g y a n d m o m e n t u m c o n s e r v a t i o n r e l a t i o n s , a c r o s s - s e c t i o n a n d t h e c h a n g e i n i n t e r n a l s t a t e e n e r g y i s f u n d a m e n t a l i n t h e c o n s t r u c t i o n o f t h e c o l l i s i o n t e r m o f t h e B o l t z m a n n e q u a t i o n . F o r t h e m a c r o s c o p i c d e s c r i p t i o n o f t r a n s p o r t p h e n o m e n a i n a w e a k l y i o n i z e d g a s t h e c o l l i s i o n t e r m s a r e c o r r e s p o n d i n g l y c o a r s e r . T h e n e t p r o d u c t i o n t e r m R j ( x , t ) o f e q n . 6 6 i s i n t e r m s o f p r o d u c t s o f c o n c e n t r a t i o n s o r d e n s i t i e s a n d a r e a c t i o n r a t e c o n s t a n t d e r i v a b l e f r o m d i s t r i b u t i o n a v e r a g e d c r o s s - s e c t i o n s . R a t e c o n s t a n t s m a y a l s o b e d e v e l o p e d i n t e r m s o f t h e p r o d u c t o f a h a r d s p h e r e c o l l i s i o n f r e q u e n c y a n d a t r a n s i t i o n p r o b a b i l i t y ( Y a r d l e y , 1 9 8 0 ) . T h e d i s t r i b u t i o n f u n c t i o n u s e d i n c a l c u l a t i o n o f t h e r a t e c o n s t a n t i s t y p i c a l l y a l o c a l M a x w e l l i a n , g i v i n g a r a t e c o n s t a n t d e p e n d e n t o n t h e 7 9 l o c a l t e m p e r a t u r e . U s e o f t h i s a p p r o a c h i n c a l c u l a t i o n s o f e l e c t r o n i m p a c t i n d u c e d e x c i t a t i o n r a t e c o n s t a n t s i s c o m m o n ( E r w i n , 1 9 8 3 ) b u t o f q u e s t i o n a b l e a c c u r a c y f o r e x c i t a t i o n p r o c e s s e s i n H 2 w h i c h i n v o l v e t r a n s i t i o n s f r o m o n e p o t e n t i a l s u r f a c e t o a n o t h e r ( M o r i n , 1 9 8 2 ) . U s e o f t h e M a x w e l l i a n d i s t r i b u t i o n i n c a l c u l a t i o n s o f r a t e c o n s t a n t s f o r e x c i t a t i o n a n d r e l a x a t i o n p r o c e s s e s w h i c h i n v o l v e n e u t r a l m o l e c u l e s i s c o m m o n a n d i s a d o p t e d h e r e . T h e p r i m a r y m o t i v a t i o n f o r d i s c u s s i o n o f t h e m a c r o s c o p i c d i s c r i p t i o n o f c o l l i s i o n i n d u c e d s y n t h e s i s a n d e n e r g y t r a n s f e r p r o c e s s e s i s r e l a t e d t o t h e o b s e r v a t i o n t h a t t h e m a c r o s c o p i c l e v e l o f d e s c r i p t i o n i s a p p r o p r i a t e f o r t h e n e u t r a l c o m p o n e n t s o f a w e a k l y i o n i z e d d i l u t e g a s . B e c a u s e o f t h e g r e a t d i s p a r i t y i n c o n c e n t r a t i o n b e t w e e n f r e e e l e c t r o n s a n d n e u t r a l s , t h e r e l a x a t i o n t i m e s c a l e s o f t h e n e u t r a l s a r e g e n e r a l l y m u c h s h o r t e r t h a n t h e e x c i t a t i o n t i m e s c a l e s o r i n v e r s e c o l l i s i o n f r e q u e n c i e s . T h e m a c r o s c o p i c l e v e l i s n o t a t a l l a p p r O p r i a t e f o r t h e f r e e e l e c t r o n c o m p o n e n t a n d s o t h e m a c h i n e r y o f k i n e t i c t h e o r y , t h e B o l t z m a n n e q u a t i o n i n p a r t i c u l a r , h a s b e e n r e v i e w e d a n d c l a r i f i e d w h e r e n e c e s s a r y . T h e u s u a l p l a c e w h e r e t h e m i c r o s c o p i c d e s c r i p t i o n o f a n e l e c t r o n g a s a n d t h e m a c r o s c o p i c d e s c r i p t i o n o f t h e n e u t r a l g a s m e e t i s t h e m o d e l i n g o f e l e c t r i c a l d i s c h a r g e s i n g a s e s a n d s o i n t h e l a s t p a r t o f t h e r e v i e w t h e h i s t o r y a n d c u r r e n t s t a t e o f s u c h m o d e l i n g e f f o r t s i s a d d r e s s e d . m i c r o s c o p i c B o l t z m a n n e q u a t i o n a r e d e c o u p l e d a n d t h e e l e c t r o n 8 0 2 . 3 R e v i e w o f r e l a t e d w o r k T h e p u r p o s e o f t h i s s e c t i o n i s t o s u r v e y w o r k s w h i c h c o n t r i b u t e t o t h e u n d e r s t a n d i n g o f t h e r e l a t i o n s h i p b e t w e e n m a c r o s c o p i c f l u i d p r o p e r t i e s , s u c h a s c o n c e n t r a t i o n s a n d t e m p e r a t u r e , a n d t h e i n t e r a c t i o n o f a n e x t e r n a l e l e c t r o m a g n e t i c f i e l d , d i l u t e e l e c t r o n g a s , n e u t r a l g a s a n d b o u n d a r i e s . N o n e o f t h e w o r k s c i t e d h e r e e x a m i n e t h e f e a s i b i l i t y o f c o l l i s i o n i n d u c e d h e a t i n g o r c o n s i d e r t h e e f f e c t s o f t h e r m a l i z a t i o n o f e x c i t e d p r o d u c t s b u t t h e y d o t r e a t s o m e a s p e c t s o f a w e a k l y i o n i z e d d i l u t e g a s . T h e m a j o r i t y o f l i t e r a t u r e i n t h i s a r e a i s s p e c i f i c t o w e a k l y i o n i z e d d i l u t e h y d r o g e n ( H 2 ) a n d s o f o r t h i s r e a s o n a n d r e a s o n s d i s c u s s e d l a t e r i n t h i s w o r k t h e r e v i e w h e r e f o c u s e s o n c a l c u l a t i o n a l a n d e x p e r i m e n t a l s t u d i e s o f e l e c t r i c a l d i s c h a r g e s i n H 2 . T h e r e v i e w i s d e v e l o p e d i n t h r e e p a r t s , w i t h t h e f i r s t p a r t d e v o t e d t o w o r k s w h i c h r e p o r t c a l c u l a t i o n s o f t h e e l e c t r o n d i s t r i b u t i o n f u n c t i o n v i a t h e B o l t z m a n n e q u a t i o n f o r a w e a k l y i o n i z e d d i l u t e g a s o f c o n s t a n t d e n s i t y a n d / o r t e m p e r a t u r e . I n t h i s c l a s s o f i n v e s t i g a t i o n s t h e e l e c t r o n g a s a n d n e u t r a l g a s a r e e s s e n t i a l l y d e c o u p l e d . T h e s e c o n d p a r t o f t h e r e v i e w , b y c o n t r a s t , i s d e v o t e d t o w o r k s w h i c h r e p o r t c a l c u l a t i o n s o f m a c r o s c o p i c g a s d e n s i t i e s , t e m p e r a t u r e s a n d c o m p o s i t i o n s f o r n e u t r a l g a s e s w h i c h a r e i n c o n t a c t w i t h a n e l e c t r o n g a s o f c o n s t a n t d e n s i t y a n d a v e r a g e e n e r g y . H e r e a g a i n t h e m a c r o s c o p i c t r a n s p o r t e q u a t i o n s a n d t h e 8 1 g a s d e n s i t y a n d d i s t r i b u t i o n f u n c t i o n a r e p a r a m e t e r s i n a p l a s m a r e a c t o r m o d e l . T h e t h i r d p a r t o f t h i s r e v i e w i s d e v o t e d t o t h e f e w w o r k s r e p o r t i n g c a l c u l a t i o n s o f b o t h e l e c t r o n g a s a n d n e u t r a l g a s p r o p e r t i e s v i a t h e c o u p l e d s o l u t i o n o f t h e B o l t z m a n n e q u a t i o n a n d t h e m a c r o s c o p i c b a l a n c e e q u a t i o n s . C a l c u l a t i o n s o f t h e e l e c t r o n d i s t r i b u t i o n f u n c t i o n v i a t h e B o l t z m a n n e q u a t i o n h a v e b e e n m a d e a n d r e p o r t e d f o r a v a r i e t y o f i n v e s t i g a t i o n s f r o m 1 9 3 5 t o t h e p r e s e n t . M o r s e _ e _ t _ 1 1 . . ( 1 9 3 5 ) i n t r o d u c e d t h e a p p r o x i m a t e m e t h o d o f L o r e n t z ( t h e t w o t e r r n e x p a n s i o n o f t h e d i s t r i b u t i o n f u n c t i o n i n L e g e n d r e P O l y n o m i n a l s i n t h e s p e e d ) t o t r a n s p o r t t h e o r y o f e l e c t r o n s i n d - C - d i s c h a r g e s . M o r s e c o n s i d e r e d t w o c a s e s , t h a t o f a h o m o g e n e o u s e l e c t r o n g a s i n t e r a c t i n g e l a s t i c a l l y w i t h a n e u t r a l b a c k g r o u n d i n a u n i f o r m e l e c t r i c f i e l d a n d a l s o t h a t o f t h e e l a S t i c r e l a x a t i o n o f a n e l e c t r o n b e a m i n a f i e l d - f r e e r e g i o n . C l o S e d f o r m e x p r e s s i o n s f o r t h e s o l u t i o n o f t h e B o l t z m a n n e q u a t i o n w e r e o b t a i n e d a n d a r e o f t h e D r u y v e s t u y n t y p e , i . e . , e ’ " F ‘ C D I ‘ l e n t i a l o f t h e s q u a r e o f t h e e n e r g y . T h e w o r k w a s a f o r e r u n n e r o f s e v e r a l o t h e r w o r k s a d d r e s s i n g t h e r e l a x a t i o n o f a n o n e q u i l i b r i u m e l e c t r o n d i s t r i b u t i o n t o t h e e q u i l i b r i u m a n d h a s a p p l i c a t i o n i n n o t o n l y e l e c t r i c a l d i s c h a r g e a f t e r g l o w s b u t a l s o i n e l e c t r o n b e a m p l a s m a m o d e l s a n d t h o s e f o r t h e e l e c t r o m a g n e t i c p u l s e ( E M P ) p h e n o m e n a a s s o c i a t e d w i t h a n a h “ 0 8 p h e r i c n u c l e a r b l a s t . F i e l d - f r e e r e l a x a t i o n o f a n o n - e . . . q “ a l l i b r i u m e l e c t r o n g a s i s n o t o f p r i m a r y i n t e r e s t h e r e a n d s o t h e v o l u b y p a s s e d d i s t r i b u l a t e r i n H b y r e f o r . p r o c e s s e e q u a t i o n a S p a t i a w e r e s i m ; a n d a V e a n o n z e r . t h e e v o l . o f t ‘ q u o t . H O l s t e i n d i s c h a r g W o r l d w a a n d c a l c L i b e r a t e ( 1 9 4 3 ) O “ E r e G a v . f o r t h e . t h a t O f 2 2 6 9 8 m m f u n n i e r } 8 2 t h e v o l u m i n o u s b o d y o f l i t e r a t u r e a s s o c i a t e d w i t h i t w i l l b e b y p a s s e d , n o t i n g t h a t t h e r e l a x a t i o n o f a n o n e q u i l i b r i u m d i s t r i b u t i o n o f n e u t r a l M a x w e l l m o l e c u l e s w i l l b e a d d r e s s e d l a t e r i n t h i s w o r k . H o l s t e i n ( 1 9 4 6 ) e x t e n d e d t h e w o r k o f M o r s e _ e _ t a _ l _ b y r e f o r m u l a t i n g t h e p r o b l e m t o i n c l u d e i n e l a s t i c c o l l i s i o n p r o c e s s e s . H o l s t e i n p r e s e n t e d a d e r i v a t i o n o f t h e B o l t z m a n n e q u a t i o n i n t h e L o r e n t z a p p r o x i m a t i o n f o r t h e g e n e r a l c a s e o f a s p a t i a l l y i n h o m o g e n e o u s p l a s m a . T h e c o l l i s i o n m o d e l s a d o p t e d w e r e s i m p l e , w i t h a v e l o c i t y i n d e p e n d e n t e l a s t i c c r o s s - s e c t i o n a n d a v e l o c i t y i n d e p e n d e n t t o t a l i n e l a s t i c c r o s s - s e c t i o n w i t h a n o n z e r o t h r e s h h o l d . A l t h o u g h n o c a l c u l a t i o n s w e r e p r e s e n t e d , t h e e v o l u t i o n e q u a t i o n f o r t h e e l e c t r o n d i s t r i b u t i o n h a s b e e n o f t — q u o t e d s i n c e t h e n ( B r u n e t a n d V i n c e n t ( 1 9 7 9 ) , f o r e x a m p l e ) . H o : l - S t e i n ' s w o r k w a s t h e f i r s t t o t r e a t t h e h i g h - f r e q u e n c y g a s d i s c h a r g e m a d e p o s s i b l e b y t h e d e v e l o p m e n t o f r a d a r d u r i n g W o r l d W a r I I a n d w a s q u i c k l y f o l l o w e d b y a s e r i e s o f e x p e r i m e n t a l a n d c a l c u l a t i o n a l w o r k s f r o m w o r k e r s a t Y a l e , M I T , a n d B e l l L a b o r a t o r i e s . I n a s e r i e s o f p a p e r s b y M a r g e n a u a n d H a r t m a n ( 1 9 4 8 ) o f Y a l e , s e v e r a l a s p e c t s o f h i g h f r e q u e n c y g a s d i s c h a r g e s w e r e d e v e l o p e d . T h e i r d e r i v a t i o n o f t h e e v o l u t i o n e q u a t i o n f o r t h e e l e c t r o n g a s f r o m t h e B o l t z m a n n e q u a t i o n p a r a l l e l s t h a t o f H o l s t e i n . I n a d d i t i o n t h e y d i s c u s s g e n e r a l n - t h o r d e r L e g e n d r e p o l y n o m i a l e x p a n s i o n s o f t h e e l e c t r o n d i s t r i b u t i o n f “ f i c t i o n , t h u s a n t i c i p a t i n g t h e w o r k o f P i t c h f o r d e ; a ; ( 1 9 8 1 ) b y O v e r 3 0 y e a r s , a n d d e v e l o p a s i m i l a r i t y p r i n c i p l e f o r 8 3 c o m p a r i s o n o f h i g h f r e q u e n c y a n d d . c . d i s c h a r g e s . T h e s i m i l a r i t y l a w w a s d e v e l o p e d f r o m s c a l i n g o f t e r m s o f t h e B o l t z m a n n e q u a t i o n a n d s t a t e d t h a t t h e d e p e n d e n c e o f t h e d i s t r i b u t i o n f u n c t i o n o n e l e c t r o n e n e r g y i s u n c h a n g e d i f t h e f o l l o w i n g p a r a m e t e r s a r e u n c h a n g e d , E / N , w / N , N L , n / N w h e r e E i s t h e e l e c t r i c f i e l d s t r e n g t h , w , t h e a . c . f r e q u e n c y , N t h e n e u t r a l g a s d e n s i t y , L a c h a r a c t e r i s t i c l e n g t h a n d n t h e e l e c t r o n d e n s i t y . A n o t h e r r e s u l t o f t h e i r w o r k i s t h e p r e d i c t i o n o f a m i n i m u m b r e a k d o w n v o l t a g e a t a p r e s s u r e f o r w h i c h t h e e l e c t r o n - n e u t r a l c o l l i s i o n f r e q u e n c y a n d a n g u l a r f i e l d f r e q u e n c y a r e o f t h e s a m e o r d e r o f m a g n i t u d e . T h i s w a s c o n f i r m e d b y m e a s u r e m e n t s o f M a c D o n a l d a n d B r o w n ( 1 9 4 9 ) w h o a l s o p r e s e n t e d c a l c u l a t i o n s o f t h e e l e c t r o n d i s t r i b u t i o n f u n c t i o n . T h e t w o t e r m e x p a n s i o n o f t h e e l e c t r o n d i s t r i b u t i o n f u n c t i o n w a s m a d e a n d t h e l u m p e d i n e l a s t i c e x c i t a t i o n f r e q u e n c i e s o f R a m i e n ( 1 9 3 1 ) w e r e u s e d i n a s o l u t i o n o f t h e B o l t z m a n n e q u a t i o n f o r a n e l e c t r o n g a s i n c o n t a c t w i t h a n e u t r a l g a s o f c o n s t a n t p r e s s u r e a n d t e m p e r a t u r e . I n d i v i d u a l e x c i t a t i o n p r o c e s s e s w e r e n o t e x a m i n e d . T h e g o a l o f t h e w o r k w a s a p r e d i c t i o n o f t h e b r e a k - d o w n f i e l d s t r e n g t h f o r h y d r o g e n o f g i v e n p r e s s u r e a n d c o m p a r i s o n o f t h e c a l c u l a t i o n s w i t h e x p e r i m e n t a l f i e l d s t r e n g t h s . T h e r e s u l t s o f t h e a n a l y s i s w e r e i n g o o d a g r e e m e n t w i t h e x p e r i m e n t a l r e s u l t s . A l l i s a n d B r o w n ( 1 9 5 2 ) d e r i v e d a s i m p l e r s o l u t i o n t o t h e p r o b l e m a d d r e s s e d b y M a c D o n a l d a n d B r o w n b y n e g l e c t i n g t h e e l e c t r o n f r e e d i f f u s i o n t e r m w i t h r e s p e c t t o i n e l a s t i c e n e r g y t r a n s f e r i n t h e h i g h e n e r g y r e g i o n o f t h e d i s t r i b u t i o n n e 9 a l l o 9 9 9 e s r e e c v n e d a f f t 8 8 o c c c g e T L n t i s f t d a d o u i h ( 1 f . . a o r ( 1 a l h o h o s u u e h n e f c l 5 s n c l s 6 e c s e c s l t e h t e d - p i s u 5 t u i s g x 3 n l t e t c h ) ) t i a v s - l n r t o c w o i t m a r s c h 1 o a i s o a z i u m o p o w l e i n . T h t o g r s e e 6 w t o e d H t d a n l n r m n c i e e e n c a y e r 2 i k u t i a v e n c e e r o p a e t r d s t t n i l h , c s n e h e i f v e p i t a o z n s o g o r f i a c e r t o m o f e d t d t p t f a n r n r w n t t x o o o i a d n i . i e h e l o g s l k e c h x b f g i o c c r e i c t e e e s o e g w a a a e h r d i l e M t f s m i g t n r y i i e i r b a n . s l z h a r f h t t e t m e n y t . a , s n D d d c h s r o t k M o t e o q o i c u I o e l s a t d u u e e i r i d a n w s l n n s h t i e v s o k o o c s o c e u t e l y t a c d h n d w e e n n w D r h n c u v c d a s l e r a d o d w c o t n k a d o o u a o t c a g w a k s e f a o l n t b v a o p u a g d e h l h o s i s r l t n i h t e s c n t e o o c t d c d e d f i e i i n n d u h t f w u r u o h o w o n g o . r a d l i t i o c f y l l a r i n i f s r r e r h b a a l i e o n f h n B o c t a o B a e o R y o s a e s l r g m t v r r e s a l s v t h e e ( 1 9 o h f l e t o e M e e l a c p o e m t - a e n 6 r l q h o f w d i a l r i w o r z s l 6 i u e c e a e s y e p s n e ) o a l o m e u a s a q r c t . n . a r r i i r r b e c a c a l i t e L u r . k s e n t y t c o i a c n o e o n o o p r w w c g s t e n i s u e n o r n f s e T i o e l E h T o s s l o r n e c i d d h r s e T b e n t i h i y f t - e a n i s n n i e e k s h e q g h g e n h s s t s c t . e r c e e e s e c u e h e z f d g b e e t x f l f w s a a l - r s c p u o a d r t o a c g o i a u t h v r c s f r e e t . b a o i r e e s i B p s r i a a r i e a e i r n k t n t n e a o r l l p h m e d k o o t e g i a i r n d i e v d M q a h r a d u n n o t a e c a t o r i t d u u r h e o o s v s k f h c f s a i f f b i c e y e x w e d o l p e o l f r t n h i n o a t e b a e o e t w d o h a t y d e i e a m o o e e R o f u r t r n r c l y l d n a y c t m p f s n r a n e c e n o n c c a i n f n o t l a s h q s g t a B e t a h w o n e h s i o e e t e l s r a h t i n t o r t r r t r r e e e e o g f t g s P d d n t t l i a B o e n s e u e y m c u l l s a n . l h e c b e l n w c u d e c e s e k p e h u i i x t , s t r e r n n h c a s w a t c t d p z r e B f b a t c o s t n a S o r i s h t i e m r f e n i y f r b d n h r s i a r g o ( o e l o c o d i t n h n g a o k e n e w c o e f u n 1 9 s r c m a n n n t m w i 6 s o i e e v e s 3 o n f b n e ) . o n u t t a i l 8 4 a n a l y s i s o f d . c . s w a r m d a t a , c a l c u l a t i o n o f s t a t e - t o - s t a t e e x c i t a t c o m p a r i e l e c t r c r a n g e c g a s i n t d e n s i t y d a t a i n R e s e a r c e s t i m a t E X p e r i x t h e e l e a n 6 5 8 1 c o l l i s j f u n c t i c d i f f u s j C O e f f i c d a t a a : s e t s 0 1 S t r e n g 1 t e t h n i c a n d m o : ( 1 m 2 t h e 5 e ‘ t h e g 8 5 e x c i t a t i o n r a t e s g i v e n a s e t o f c r o s s - s e c t i o n s a n d f i n a l l y , c o m p a r i s o n o f r a t e s o f e l e c t r o n - e l e c t r o n i n t e r a c t i o n w i t h e l e c t r o n - m o l e c u l e e l a s t i c a n d i n e l a s t i c i n t e r a c t i o n o v e r a r a n g e o f i o n i z a t i o n d e g r e e . I n a l l o f t h e s e w o r k s t h e e l e c t r o n g a s i n t e r a c t s w i t h a w e a k l y i o n i z e d n e u t r a l g a s o f c o n s t a n t d e n s i t y a n d t e m p e r a t u r e . D u e t o t h e p a u c i t y o f c r o s s - s e c t i o n d a t a i n t h e e a r l y 1 9 6 0 ' s , P h e l p s a n d c o - w o r k e r s a t W e s t i n g h o u s e R e s e a r c h L a b o r a t o r i e s d e v e l o p e d a c a l c u l a t i o n a l t e c h n i q u e t o e s t i m a t e a s e t o f c r o s s - s e c t i o n s w h i c h a r e c o n s i s t e n t w i t h e x p e r i m e n t a l m e a s u r e m e n t s o f t h e e l e c t r o n d r i f t v e l o c i t y a n d t h e e l e c t r o n d i f f u s i o n c o e f f i c i e n t . I n a n i t e r a t i v e p r o c e d u r e a n a s s u m e d s e t o f c r o s s - s e c t i o n s i s i n c l u d e d i n t h e B o l t z m a n n c o l l i s i o n o p e r a t o r a n d t h e i s o t r o p i c p o r t i o n o f t h e d i s t r i b u t i o n f u n c t i o n i s c a l c u l a t e d f r o m w h i c h t h e d r i f t v e l o c i t y a n d d i f f u s i o n c o e f f i c i e n t a r e c a l c u l a t e d . T h e s e c a l c u l a t e d t r a n s p o r t c o e f f i c i e n t s a r e c o m p a r e d w i t h e x p e r i m e n t a l d . c . s w a r m t r a n s p o r t d a t a a n d t h e a s s u m e d c r o s s - s e c t i o n s a r e v a r i e d u n t i l t h e t w o s e t s o f t r a n s p o r t d a t a a g r e e o v e r a r a n g e o f e l e c t r i c f i e l d s t r e n g t h a n d g a s p r e s s u r e . F r o s t a n d P h e l p s ( 1 9 6 2 ) a p p l i e d t h e t e c h n i q u e t o c a l c u l a t e r o t a t i o n a l a n d v i b r a t i o n a l e x c i t a t i o n a n d m o m e n t u m t r a n s f e r c r o s s - s e c t i o n s f o r l o w e n e r g y e l e c t r o n s ( k T ‘ ( 2 e v ) i n h y d r o g e n . E n g e l h a r d t a n d P h e l p s ( 1 9 6 3 ) e x t e n d e d t h e s e c a l c u l a t i o n s t o i n c l u d e c r o s s - s e c t i o n s f o r e x c i t a t i o n t o 3 t h e l > Z I J s t a t e o f H t h e g r o u n d s t a t e o f H 2 + a n d t o a I 2 , + g e n e r i c s t a t e w h i c h d e c a y s r a d i a t i v e l y t o t h e ) 0 E “ s t a t e . T h e s e c a l c u l a t i o n s w e r e s o o n r e p l a c e d b y e x p e r i m e n t a l c r o s s - s e c t i o n s o f S c h u l f o r e x c i G o l d e n . a p p l i e d o f e l a s t s c a t t e r i R u m b l e l e x p a n s i c a n a l y s i s a c c u r a t e c o u i s i c 8 6 o f S c h u l z ( 1 9 6 4 ) f o r v i b r a t i o n a l e x c i t a t i o n , C o r r i g a n ( 1 9 6 5 ) 3 + f o r e x c i t a t i o n t o t h e L . X L . s t a t e , a n d R a p p a n d E n g l a n d e r - G o l d e n ( 1 9 6 5 ) f o r i o n i z a t i o n o f H T h e m e t h o d o f P h e l p s w a s 2 . a p p l i e d b y R o c k w o o d ( 1 9 7 3 ) t o d e t e r m i n e a s e l f - c o n s i s t e n t s e t o f e l a s t i c a n d i n e l a s t i c c r o s s - s e c t i o n s f o r e l e c t r o n - H g s c a t t e r i n g a n d w a s l a t e r e x t e n d e d b y P i t c h f o r d , O ' N e i l a n d R u m b l e ( 1 9 8 1 ) a n d P i t c h f o r d a n d P h e l p s ( 1 9 8 2 ) t o a n e i g h t — t e r m e x p a n s i o n o f t h e d i s t r i b u t i o n f u n c t i o n f o r a p p l i c a t i o n t o a n a l y s i s o f N 2 s w a r m d a t a . W i t h i n c r e a s i n g a v a i l a b i l i t y o f a c c u r a t e c r o s s - s e c t i o n s f o r a w i d e v a r i e t y o f e l e c t r o n - H 2 c o l l i s i o n p h e n o m e n a t h e c a l c u l a t i o n o f e x c i t a t i o n r a t e s f r o m a s o l u t i o n o f t h e B o l t z m a n n e q u a t i o n w a s p o s s i b l e , w i t h s e v e r a l p a p e r s a p p e a r i n g o n t h e t o p i c . M u c h o f t h e w o r k w a s r e p o r t e d b y w o r k e r s a t t h e U n i v e r s i t y o f B a r i i n I t a l y . C a c c i a t o r e , C a p i t e l l i a n d D i l o n a r d o ( 1 9 7 8 ) s o l v e d t h e B o l t z m a n n e q u a t i o n f o r a n e l e c t r o n g a s i n c o n t a c t w i t h H 2 , t a k i n g t h e v i b r a t i o n a l s t r u c t u r e i n t o a c c o u n t a n d t h e n u s e d t h e c a l c u l a t e d v i b r a t i o n a l a n d e l e c t r o n i c e x c i t a t i o n r a t e s i n a s e t o f v i b r a t i o n a l m a s t e r e q u a t i o n s t o c a l c u l a t e d i s s o c i a t i o n r a t e s f o r H 2 a t c o n s t a n t p r e s s u r e a n d t e m p e r a t u r e . C a c c i a t o r e 2 ; 3 1 r e p o r t e d d i s s o c i a t i o n r a t e s t h a t a r e l a r g e r t h a n t h o s e c a l c u l a t e d f o r e x c i t a t i o n o f l + 3 + H f r o m , 2 : ( v = o ) t o l s z : u , w i t h t h e i n c r e a s e d u e t o 9 2 t + d i s s o c i a t i o n f r o m h i g h v i b r a t i o n a l l e v e l s o f X 2 : 3 . T h e i r m o d e l d i d n o t , h o w e v e r , t a k e i n t o a c c o u n t t h e p r e s e n c e o f a t o m i c h y d r o g e n a n d i n p a r t i c u l a r , t h e g r e a t e f f e c t i v e n e s s o f a t o m i c h y d r o g e n i n d e p o p u l a t i o n o f h i g h v i b r a t i o n a l l e v e l s o f 8 7 H 2 b y V - T p r o c e s s e s ( A u d i b e r t 2 5 E l ! 1 9 7 5 ) . B r u n e t a n d V i n c e n t ( 1 9 7 9 ) u s e d e x p e r i m e n t a l a n d t h e o r e t i c a l c r o s s - s e c t i o n s f o r r o t a t i o n a l , v i b r a t i o n a l a n d e l e c t r o n i c e x c i t a t i o n t o c a l c u l a t e e x c i t a t i o n r a t e s o f e l e c t r o n - m o l e c u l e p r o c e s s e s i n H 2 v i a t h e e v o l u t i o n e q u a t i o n o f H o l s t e i n . T h e e x c i t a t i o n r a t e s a r e f o r e l e c t r o n s i n a d . c . h y d r o g e n d i s c h a r g e o f c o n s t a n t d e n s i t y a n d t e m p e r a t u r e . E x c i t a t i o n o f X ' Z ; H z t o t h e 5 . x : , C ‘ T r u , D ' T T “ , ' Z : f ] : a n d B U Z Z s t a t e s o f H z w a s i n c l u d e d a s w e l l a s e x c i t a t i o n t o t h e t r i p l e t s t a t e s . B r u n e t a n d V i n c e n t r e p o r t e x c e l l e n t a g r e e m e n t b e t w e e n c a l c u l a t e d i o n i z a t i o n r a t e s a n d t h e e x p e r i m e n t a l v a l u e s o f R o s e ( 1 9 5 6 ) a n d o t h e r s . G a r s c a d d e n a n d B a i l e y ( 1 9 8 0 ) c a l c u l a t e d t h e e l e c t r o n d i s t r i b u t i o n f u n c t i o n a n d v i b r a t i o n a l d i s t r i b u t i o n f u n c t i o n f o r a d . c . d i s c h a r g e i n H a t c o n s t a n t d e n s i t y a n d t e m p e r a t u r e o v e r 2 a r a n g e o f e l e c t r i c f i e l d s t r e n g t h s i d e n t i c a l t o t h a t o f B r u n e t a n d V i n c e n t . G a r s c a d d e n a n d B a i l e y u s e d t h e l u m p e d e l e c t r o n i c e x c i t a t i o n c r o s s - s e c t i o n o f E n g e l h a r d t a n d P h e l p s i n s t e a d o f t h e m e a s u r e d c r o s s - s e c t i o n s o f S r i v a s t a v a a n d J e n s e n ( 1 9 7 7 ) , S t o n e a n d Z i p f ( 1 9 7 2 ) a n d o t h e r s . T h e y i n c o r p o r a t e d , h o w e v e r , c r o s s - s e c t i o n s f o r d i s s o c i a t i v e a t t a c h m e n t o f H 2 g i g e x c i t a t i o n t h r o u g h t h e ‘ 1 2 : : a n d 1 X ; s t a t e s o f H 2 - f r o m s e v e r a l v i b r a t i o n a l l e v e l s o f H 2 ' 2 ; . C r o s s - s e c t i o n s f o r s u c h p r o c e s s e s , c a l c u l a t e d b y W a d e h r a a n d B a r d s l e y ( 1 9 7 8 ) , s h o w i n c r e a s e s o f f o u r o r d e r s o f m a g n i t u d e a s t h e i n i t i a l v i b r a t i o n a l s t a t e o f t h e H 2 t a r g e t m o l e c u l e c h a n g e s f r o m v = o t o v = 4 . G a r s c a d d e n a n d t h a t f o r m o l e c u l a r g a s d i s c h a r g e s s u c h c o u l o m b e f f e c t s m a y b e 8 8 B a i l e y r e p o r t e d n o n - B o l t z m a n n v i b r a t i o n a l p o p u l a t i o n s w i t h o v e r p o p u l a t i o n o f s t a t e s v = 5 - 7 d u e t o a n h a r m o n i c p u m p i n g b u t g a v e n o i n d i c a t i o n o f h o w t h e p r e s e n c e o f h y d r o g e n a t o m s a f f e c t e d t h e c a l c u l a t e d d i s s o c i a t i v e a t t a c h m e n t r a t e s f r o m h i g h v i b r a t i o n a l l e v e l s . C a c c i a t o r e , C a p i t e l l i a n d G o r s e ( 1 9 8 0 ) c a l c u l a t e i o n i z a t i o n e x c i t a t i o n r a t e s f o r a d . c . h y d r o g e n d i s c h a r g e a t c o n s t a n t d e n s i t y a n d t e m p e r a t u r e f r o m a s o l u t i o n o f t h e B o l t z m a n n e q u a t i o n c o u p l e d w i t h v i b r a t i o n a l m a s t e r e q u a t i o n s . T h e c a l c u l a t e d i o n i z a t i o n r a t e s w e r e m u c h g r e a t e r t h a n i o n i z a t i o n f r o m I E ; ( v = o ) w o u l d i n d i c a t e a t l o w e l e c t r i c f i e l d s t r e n g t h s b u t t h e i n f l u e n c e o f i o n i z a t i o n f r o m h i g h v i b r a t i o n a l l e v e l s o f g r o u n d s t a t e H d r a m a t i c a l l y d e c r e a s e d a s t h e e l e c t r i c f i e l d 2 s t r e n g t h a n d t h u s t h e d i s s o c i a t i o n r a t e i n c r e a s e d . I n a l a t e r w o r k C a p i t e l l i , G o r s e a n d R i c a r d ( 1 9 8 1 ) c a l c u l a t e d t h e e l e c t r o n a n d n e u t r a l m o l e c u l e v i b r a t i o n a l d i s t r i b u t i o n f u n c t i o n f o r a d . c . n i t r o g e n d i s c h a r g e o f c o n s t a n t d e n s i t y a n d t e m p e r a t u r e . N i t r o g e n i s m u c h m o r e s t a b l e w i t h r e s p e c t t o d e p o p u l a t i o n o f e x c i t e d v i b r a t i o n a l l e v e l s 2 3 3 V - T p r o c e s s e s t h a n i s h y d r o g e n a n d t h e c a l c u l a t e d e l e c t r o n d i s t r i b u t i o n f u n c t i o n a n d v i b r a t i o n a l d i s t r i b u t i o n f u n c t i o n s e v i d e n c e d t h i s . T h e w o r k s c i t e d h e r e i n d i c a t e c o n s i d e r a b l e a c t i v i t y i n c a l c u l a t i o n o f e x c i t a t i o n r a t e s f o r i n e l a s t i c e l e c t r o n - H 2 p r o c e s s e s i n w e a k l y i o n i z e d d . c . d i s c h a r g e s . A f e w w o r k s , t h a t o f D r e i c e r ( 1 9 6 0 ) a n d R o c k w o o d ( 1 9 7 4 ) i n p a r t i c u l a r , h a v e c o n s i d e r e d e l e c t r o n - e l e c t r o n p r o c e s s e s a l s o a n d h a v e c o n c l u d e d g l o w d i s c h a r g e i n H 2 . H e w a s p r i m a r i l y i n t e r e s t e d i n t h e e f f e c t 8 9 n e g l e c t e d i n c a l c u l a t i o n s o f t h e e l e c t r o n d i s t r i b u t i o n f u n c t i o n i f t h e e x t e n t o f i o n i z a t i o n i s l e s s t h a n 1 0 — 3 . T h e s e c a l c u l a t i o n s o f e l e c t r o n d i s t r i b u t i o n f u n c t i o n s a n d e x c i t a t i o n r a t e s f o r d . c . d i s c h a r g e s a t c o n s t a n t d e n s i t y a n d t e m p e r a t u r e p r o v i d e s o m e i n s i g h t i n t o e l e c t r o n - m o l e c u l e k i n e t i c s b u t l e a v e u s f a r f r o m a n a n a l y s i s o f c o l l i s i o n i n d u c e d h e a t i n g i n h i g h f r e q u e n c y g a s d i s c h a r g e s . M o r i n ( 1 9 8 2 ) c a l c u l a t e d t h e e l e c t r o n d i s t r i b u t i o n f u n c t i o n f o r a n e l e c t r o n g a s i n a b o u n d e d , m i c r o w a v e f r e q u e n c y e l e c t r i c a l d i s c h a r g e . M o r i n a l s o c o m p a r e d t h e v i b r a t i o n a l a n d e l e c t r o n i c e x c i t a t i o n r a t e s c a l c u l a t e d f r o m t h e r e s u l t i n g e l e c t r o n d i s t r i b u t i o n f u n c t i o n w i t h t h o s e f r o m c a l c u l a t i o n s u s i n g a M a x w e l l i a n d i s t r i b u t i o n a t t h e s a m e a v e r a g e e n e r g y . H e c o n c l u d e d t h a t u s e o f a M a x w e l l i a n a p p r o x i m a t i o n f o r v i b r a t i o n a l e x c i t a t i o n r a t e s g a v e g o o d r e s u l t s b u t t h a t s u c h a n a p p r o a c h w a s n o t a c c e p t a b l e f o r e l e c t r o n i c e x c i t a t i o n r a t e s . T h e u s e o f a M a x w e l l i a n i s c o n v e n i e n t a n d e v e n j u s t i f i e d i n t h e c a s e o f s t r o n g l y i o n i z e d g a s d i s c h a r g e s . E r w i n a n d K u n c ( 1 9 8 3 ) h a v e c a l c u l a t e d r a t e c o e f f i c i e n t s f o r a w i d e v a r i e t y o f e l e c t r o n - H 2 p r o c e s s e s u s i n g t h e M a x w e l l i a n a p p r o x i m a t i o n f o r t h e d i s t r i b u t i o n f u n c t i o n . I n t h e s e c o n d p a r t o f t h i s r e v i e w m a c r o s c o p i c m o d e l s o f d . c . a n d h i g h f r e q u e n c y e l e c t r i c a l d i s c h a r g e s i n h y d r o g e n a r e d i s c u s s e d . R o g o f f ( 1 9 7 2 ) c a l c u l a t e d g a s d e n s i t i e s , t e m p e r a t u r e a n d t h e c u r r e n t d i s t r i b u t i o n f o r a h i g h p r e s s u r e ( 5 0 0 t o r r ) n t w h a a s a u s g s t e h s e t g r d e e s b u y l t C o p f e a z e z l u e t c o t r 2 n o 3 i E c l t ( r 1 a 9 n 7 s 3 i ) t i o n i n s . t h r e T e h e p m p a e e c r h s a m n a i n s d 9 0 o f g a s h e a t i n g b y e l a s t i c c o l l i s i o n s o n t h e f o r m a t i o n o f f i l a m e n t a r y a r c s i n h y d r o g e n . N o i n e l a s t i c e l e c t r o n - m o l e c u l e c o l l i s i o n s o r t h e r m a l d i s s o c i a t i o n e f f e c t s a r e c o n s i d e r e d . T h e c a l c u l a t i o n s i n d i c a t e a c o n t i n u o u s c o n s t r i c t i o n o f t h e p o s i t i v e c o l u m n , w h i c h i s o b s e r v e d e x p e r i m e n t a l l y i n a t o m i c g a s e s , b u t d o n o t i n d i c a t e t h e s u d d e n a p p e a r a n c e o f a h i g h l y c o n d u c t i v e c o r e , w h i c h i s o b s e r v e d i n H a n d o t h e r m o l e c u l a r 2 g a s d i s c h a r g e s . R o g o f f a t t r i b u t e s t h i s f e a t u r e o f h i g h p r e s s u r e d i s c h a r g e s i n h y d r o g e n t o t h e p r e s e n c e o f a t o m s w h i c h r e s u l t f r o m e l e c t r o n i m p a c t a n d t h e r m a l d i s s o c i a t i o n . T h e e f f e c t o f g a s h e a t i n g i s t o c a u s e g a s e x p a n s i o n a n d t h u s d e c r e a s e d g a s d e n s i t y . W i t h a l o w e r g a s d e n s i t y t h e e l e c t r o n - n e u t r a l c o l l i s i o n f r e q u e n c y d r o p s a n d t h e d r i f t v e l o c i t y a n d h e n c e c u r r e n t i n c r e a s e , r e s u l t i n g i n c o n s t r i c t i o n o f t h e d i s c h a r g e . B e l l ( 1 9 7 2 ) d e v e l o p e d a r e a c t o r m o d e l t o p r e d i c t t h e e x t e n t o f d i s s o c i a t i o n o f h y d r o g e n i n a h i g h f r e q u e n c y d i s c h a r g e b a s e d o n a h y b r i d o f c o l d p l a s m a t h e o r y ( s e e , f o r e x a m p l e , R o g e r s , 1 9 8 2 ) a n d t h e w o r k o f R o s e a n d B r o w n ( 1 9 5 5 ) . A c o n s t a n t t e m p e r a t u r e a n d p r e s s u r e w e r e a s s u m e d a n d t h e i n f l u e n c e o f i n t e r n a l s t r u c t u r e w a s n e g l e c t e d . I n a s e r i e s o f p a p e r s b y w o r k e r s a t t h e U n i v e r s i t y o f B a r i r e s u l t s o f e x p e r i m e n t a l s t u d i e s o f t h e s y n t h e s i s o f H C N a n d C 2 H 2 f r o m C H 4 a n d N 2 i n a m e g a h e r t z f r e q u e n c y d i s c h a r g e w e r e i n t e r p r e t e d i n t e r m s o f a v i b r a t i o n a l l a d d e r c l i m b i n g d i s s o c i a t i o n m e c h a n i s m r a t h e r 9 1 d e v e l o p e d i n g r e a t e r d e t a i l b y M o l i n a r i ( 1 9 7 4 ) f o r a p p l i c a t i o n t o h o m o g e n e o u s a n d h e t e r o g e n e o u s r e a c t i o n s o c c u r i n g i n a w e a k l y i o n i z e d d i s c h a r g e . C a p e z z u t o , C r a m a r o s s a , D ' A g o s t i n o a n d M o l i n a r i ( 1 9 7 3 ) , i n p a r t i c u l a r , m a k e a p p l i c a t i o n t o d i s s o c i a t i o n o f H 2 a n d c l a i m t h a t s u c h a m e c h a n i s m w o u l d r e s u l t i n d i s s o c i a t i o n r a t e s m u c h g r e a t e r t h a n t h a t v i a e x c i t a t i o n t o t h e 5 3 1 : : s t a t e o f H 2 . I n l i g h t o f t h e V - T p r o b a b i l i t i e s f o r H - H 2 c o l l i s i o n s s u c h a c l a i m h a s l i t t l e v a l i d i t y . M e a r n s a n d E k i n c i ( 1 9 7 7 ) r e c o n s i d e r e d t h e m o d e l o f B e l l a n d c o m p a r e d e x p e r i m e n t a l d a t a o f h y d r o g e n d i s s o c i a t i o n i n a m i c r o w a v e f r e q u e n c y d i s c h a r g e w i t h t h e m o d e l p r e d i c t i o n s o f B e l l b u t c a m e t o n o d e f i n i t e c o n c l u s i o n . M e a r n s a n d E k i n c i t r e a t e d t e m p e r a t u r e a s a n a d j u s t a b l e p a r a m e t e r a n d n o d i s c u s s i o n o f c o l l i s i o n i n d u c e d h e a t i n g e f f e c t s w a s m a d e . T h e f i r s t c a l c u l a t i o n a l w o r k t o i n c o r p o r a t e a n e n e r g y b a l a n c e i n a s e t o f s e l f - c o n s i s t e n t m a c r o s c o p i c b a l a n c e e q u a t i o n s f o r a d i s s o c i a t i n g h y d r o g e n s t r e a m i n t h e p o s i t i v e c o l u m n o f a d . c . d i s c h a r g e w a s t h a t o f B r u n e t , R o c c a S e r r a a n d M a b r u ( 1 9 8 1 ) . T h e y c o n s i d e r e d a c y l i n d r i c a l d i s c h a r g e a t l o w p r e s s u r e ( 5 - 3 0 t o r r ) i n a h y d r o g e n f l o w a n d c a l c u l a t e d t h e e l e c t r i c f i e l d , g a s t e m p e r a t u r e a n d d e n s i t y a n d e l e c t r o n d e n s i t y a s f u n c t i o n s o f a x i a l a n d r a d i a l p o s i t i o n i n t h e d i s c h a r g e t u b e b y a n i t e r a t i v e s o l u t i o n o f t h e n e u t r a l g a s m a c r o s c o p i c e q u a t i o n s a n d a f i v e l e v e l v i b r a t i o n a l m a s t e r e q u a t i o n . S e l f - c o n s i s t e n t e x c i t a t i o n r a t e s w e r e o b t a i n e d f r o m t h e c a l c u l a t i o n s o f B r u n e t a n d V i n c e n t a n d t h e e l e c t r i c f i e l d w a s c a l c u l a t e d f r o m t h e c u r r e n t c o n s e r v a t i o n 9 2 e q u a t i o n . T h e e n e r g y t r a n s f e r f r o m e l e c t r o n t o n e u t r a l g a s w a s a c c o u n t e d f o r b y a t e r m i n v o l v i n g t h e p r o d u c t o f t h e e l e c t r o n m o b i l i t y a n d t h e s q u a r e o f t h e e l e c t r i c f i e l d b u t t h e y d i d n o t d e a l i n d e t a i l w i t h t h e c o l l i s i o n p r o c e s s e s w h i c h e f f e c t e n e r g y t r a n s f e r . B r u n e t g t _ g l c o m p a r e d t h e i r c a l c u l a t i o n s w i t h e x p e r i m e n t a l e l e c t r i c f i e l d s t r e n g t h s a n d a g r e e d t o w i t h i n 1 5 % . T h e y c o n c l u d e d t h a t g a s h e a t i n g i s p r i m a r i l y r e s p o n s i b l e f o r t h e s h a p e o f t h e e l e c t r i c f i e l d p r o f i l e b e c a u s e o f t h e s t r o n g c o u p l i n g b e t w e e n g a s t e m p e r a t u r e , d e n s i t y a n d i o n i z a t i o n r a t e . N o d e t a i l e d a n a l y s i s o f t h e h e a t i n g e f f e c t w a s p r e s e n t e d b e c a u s e o f t h e g e n e r a l w a y i n w h i c h c o l l i s i o n i n d u c e d h e a t i n g w a s t r e a t e d i n t h e e n e r g y b a l a n c e e q u a t i o n . T h e w o r k o f B r u n e t , R o c c a - S e r r a a n d M a b r u i s , h o w e v e r , a s i g n i f i c a n t c o n t r i b u t i o n t o t h e s e l f - c o n s i s t e n t a n a l y s i s o f a d . c . d i s c h a r g e . T h e r e i s l i t t l e r e p o r t e d e x p e r i m e n t a l w o r k w h i c h f o c u s e s o n c o l l i s i o n i n d u c e d h e a t i n g o f h y d r o g e n i n a h i g h f r e q u e n c y d i s c h a r g e . T h e w o r k o f C h a p m a n ( 1 9 8 4 ) i n d i s c h a r g e c a l o r i m e t r y a n d g a s t e m p e r a t u r e e s t i m a t e s f o r m i c r o w a v e e l e c t r i c a l d i s c h a r g e s i n H 2 i s t h e o n l y r e c e n t e x c e p t i o n . T h i s r e v i e w o f w o r k s d e v o t e d t o w e a k l y i o n i z e d d i s c h a r g e s s h o u l d l e a v e t h e j u s t i f i a b l e i m p r e s s i o n t h a t t h e a r e a o f c o l l i s i o n i n d u c e d h e a t i n g o f a w e a k l y i o n i z e d g a s s t r e a m i s e s s e n t i a l l y u n e x p l o r e d . I n t h e f o l l o w i n g s e c t i o n t h e m o d e l p r o b l e m s i d e n t i f i e d e a r l i e r ( S e c t i o n 1 . 2 ) a r e d e v e l o p e d a n d c a l c u l a t i o n a l r e s u l t s a r e p r e s e n t e d . D E V E L O P M E N T A N D A N A L Y S I S I n t h e i n t r o d u c t o r y m a t e r i a l a s e r i e s o f p r o b l e m s w a s p r e s e n t e d w h i c h d e f i n e t h e p u r p o s e a n d s c o p e o f t h i s w o r k . T h e d e v e l o p m e n t a n d a n a l y s i s o f t h e s e p r o b l e m s f o r m s t h e c o n t e n t o f t h i s c h a p t e r . I t b e g i n s w i t h s e l e c t i o n o f a s u i t a b l e m o d e l s y s t e m , i d e n t i f i c a t i o n o f p r o b a b l e c o l l i s i o n e v e n t s w h i c h c o n t r i b u t e t o c o l l i s i o n i n d u c e d h e a t i n g a n d e s t i m a t i o n o f e x c i t e d s t a t e e n e r g y d i s t r i b u t i o n s . 3 . 1 . M o d e l s y s t e m i d e n t i f i c a t i o n T h i s f i r s t p r o b l e m m a y a p p e a r a r t i f i c i a l i n l i g h t o f t h e r e s t r i c t i o n o f t h e l i t e r a t u r e r e v i e w t o e l e c t r i c a l d i s c h a r g e s i n h y d r o g e n b u t t h e e v i d e n c e i n f a v o r o f s e l e c t i o n o f h y d r o g e n a s t h e m o d e l s y s t e m i s c o n v i n c i n g . F o r c o l l i s i o n i n d u c e d h e a t i n g t o b e p h y s i c a l l y r e a l i z a b l e t h e n e u t r a l p a r t i c l e s i n t h e w e a k l y i o n i z e d d i l u t e g a s m u s t i n t e r a c t w i t h t h e n o n e q u i l i b r i u m e l e c t r o n g a s i n p r o c e s s e s w h i c h i n c r e a s e t h e i r k i n e t i c e n e r g y . S u c h p r o c e s s e s m a y b e e l a s t i c o r i n e l a s t i c . C o n s i d e r e l a s t i c c o l l i s i o n s f i r s t a n d r e f e r t o e q n s . 3 7 a n d 3 8 o f s e c t i o n 2 . 1 . L e t i n d e x i b e i d e n t i f i e d w i t h t h e e l e c t r o n a n d i n d e x p w i t h t h e n e u t r a l m o l e c u l e o r a t o m . T h e e n e r g y e x c h a n g e i n t h e c o l l i s i o n i s o f t h e o r d e r Z / v g g l z m i / m p f o r m i < < m p . T h e e l a s t i c c r o s s - s e c t i o n a c c o u n t s f o r m o s t o f t h e t o t a l c r o s s - s e c t i o n a n d s o t h e m o d e l s y s t e m s h o u l d m a x i m i z e t h e r a t i o o f m a s s e s . H y d r o g e n , b e i n g t h e l i g h t e s t e l e m e n t , i s t h e l o g i c a l c h o i c e o n e l a s t i c c o n s i d e r a t i o n s a l o n e , a s s u m i n g t h a t t h e e l a s t i c 9 3 c s r u o b m a b e o a d c T f i i t l o e d v 1 o r o i t e x n e r h s h p i x 9 f a e n c o c d t o e g e c l e a l 7 s s a m h v e q t i e s h n i t u 1 s t t f i u a a r u p h z s t c ) t o e - a c s n r m e r e e h i c u - a m . s n e n e g i i o d r d h o l s t i e C t o e c o n d f h s i a e e i c c r i o o t e g a n d u y e u t V . c o s t a n f s c d a a t n i h t t n , a i i i m t s r i . t t s o e h b o o e i r p s b e t S o n o i e m l H e r n l e y o d d h o s o n n s i s 2 a s f e e e p s h i t C , , , g c t a y a g u h i i o h a h o n N t t t t r i r r t b m l e l e h h h a e t s r s 2 a n t e e i a i a d e e t e n i i l a a e t n i i n l w e e t n c , n i e h t a o r l r i n o v d a a e l s l l o t l l i o t n h b r d r e c o p i y o l v e w t h e t t o o x r o m i r c t s a r g e i d r h s i e 2 t f p i i i k e r l m y c e e - t i . n f i e t e e t o o q p s n s a a o t e l l o a e t s n r e h u r h e t l n . a a h l y y r r n x t F e e a o h c i e t a m e d c c h n c o o t o l i s o p t t l i n h l r t e l r i n , f a e o l e i e e r s c h g c h t 0 s a b t t f r c s r h t z o o i o o t f T a h f h i n e a a i s d e o s a n i e e h r m c c e a d r g y i r k r a c n t s e s n g y e s n e e a o l r o h e m m a s l r t o s e l i o . c a c f e o l y b h s s t t e a f o o o n t y d a t h o o w t s K l r l n e e s 1 i i o t n o - t h r l i l d l t T t h e l d t f o b s c h r - e e i i h h a l s d e e h n o e e 3 e s f s r s s e e t t p n a e c o e o w o e e o s n o h i i i s e a m i f i i e h r s t y a c t l t m l ( f r n h n t x n d l r m d a g x 1 0 o o e i u c c e o s i l e a e n h - l n u . r e n s o e u n e c a r p o o m m f s i o t m c r f i s d t r r 1 e s a g n i t ( 1 i r h e g s h y t h l . i e c 9 9 s e t a l y e i 7 a q i t h o i z e d h s u b d ) f o t l e i i r m i e n s l e c m 1 n r e u T n s l o ) o o i e e h x a d s 2 t a s h m . d e , e n r s o c v h g t r c m t b ( y a p c c a o e o F a i o h e e e o a n u g l o e r r c e l n m o r f r c o t s t . o t u e m a n e a i K w s m n a l s e o t e o f i c p f h s w t p d t i s d r h q r v l e f e i c h o l i s e - u e t x e e e a e e o i s i i a a k r e b h A p e n x n o e s s n e e k r e , a e s n c . c l l r i c r t y y o i s h g i w m y o e n n t s 9 4 p e a k a t 3 ( 1 0 - 2 0 ) m 2 f o r a n e l e c t r o n e n e r g y o f 2 . 3 e v i n N 2 a n d a t h r e s h h o l d o f 1 . 8 e v , a n d p e a k a t 6 ( 1 0 - 2 1 ) m 2 f o r a n e l e c t r o n e n e r g y o f 2 . 0 e v i n H 2 a n d a t h r e s h h o l d o f 1 . 0 e v ( S c h u l z , 1 9 6 4 ) . V i b r a t i o n a l e x c i t a t i o n c r o s s - s e c t i o n s f o r e l e c t r o n s i n 0 2 f r o m 9 5 t h e s w a r m a n a l y s i s o f H a k e a n d P h e l p s ( 1 9 6 7 ) s h o w a p e a k a t 1 . 5 ( 1 0 _ 2 1 ) f o r a n e l e c t r o n e n e r g y o f 1 . 3 e v a n d a t h r e s h h o l d o f 0 . 3 e v . T h e l e v e l s p a c i n g o f v i b r a t i o n a l l e v e l s o f g r o u n d s t a t e 0 2 a n d N 2 i s s m a l l e r t h a n f o r H 2 a n d s o v - T r e l a x a t i o n o f t h e v i b r a t i o n a l m a n i f o l d i s e x p e c t e d a n d o b s e r v e d t o b e f a s t e r . N o w c o n s i d e r t h e e l e c t r o n i c c h a n n e l s b e l o w t h e i o n i z a t i o n t h r e s h h o l d f o r e a c h s p e c i e s . S u c h a c o n s i d e r a t i o n m a y b e m a d e o n t h e b a s i s o f a s e t o f p o t e n t i a l c u r v e s f o r t h e d i a t o m i c a n d i t s i o n s . F i g u r e 3 s h o w s t h e p o t e n t i a l e n e r g y c u r v e s f o r s e v e r a l e l e c t r o n i c s t a t e s o f N 2 a n d N 2 + . N i t r o g e n h a s n o s t a b l e n e g a t i v e i o n s a l t h o u g h t h e f o r m a t i o n o f N 2 - a s a n i n t e r m e d i a t e h a s b e e n u s e d i n t h e r a t i o n a l i z a t i o n o f t h e v i b r a t i o n a l e x c i t a t i o n t h r e s h h o l d e n e r g y ( S c h u l z , 1 9 6 4 ) . I o n i z a t i o n o f N 2 g i g e x c i t a t i o n t o t h e g r o u n d s t a t e o f N + o c c u r s a t 1 5 . 9 e v a n d t h e r e a r e m a n y 2 e l e c t r o n i c c h a n n e l s o p e n u n d e r t h i s t h r e s h h o l d . T h e e x c i t a t i o n s p e c t r u m o f N 2 ( S c h u l z , 1 9 5 9 ) h a s s e v e r a l p e a k s b e t w e e n 7 a n d 1 4 e v w h i c h c o r r e s p o n d t o e x c i t a t i o n f r o m t h e g r o u n d s t a t e t o t h e A 3 2 : : , a l T T g , C B T T u a n d b l T T u s t a t e s , w i t h t h r e s h h o l d s a t 6 . 2 , 9 . 1 , 1 1 . 2 a n d 1 2 . 8 5 e v r e s p e c t i v e l y . E x a m i n a t i o n o f t h e p o t e n t i a l c u r v e s w o u l d i n d i c a t e t h a t v e r t i c a l t r a n s i t i o n s f r o m t h e g r o u n d s t a t e t o t h e r e p u l s i v e p a r t o f t h e u p p e r e l e c t r o n i c s t a t e p o t e n t i a l a r e v e r y u n l i k e l y , c o n f i r m e d b y t h e e x p e r i m e n t a l o b s e r v a t i o n o f e x t r e m e l y l o w e x t e n t s o f d i s s o c i a t i o n i n n i t r o g e n d i s c h a r g e s . T h e m o s t l i k e l y s o u r c e o f a t o m s i n a n i t r o g e n d i s c h a r g e i s d i s s o c i a t i v e i o n i z a t i o n a t a t h r e s h h o l d o f 2 4 . 3 e v . T h e e l e c t r o n i c c h a n n e l s o p e n b e l o w 1 5 . 9 e v i n v o l v e e x c i t e d s t a t e s 2 0 - x ‘ z ) v e ( y g r e n e l a i t n e t o P 0 . 4 0 . 8 1 . 2 1 . 6 2 . 0 2 . 4 2 . 8 ‘ 3 . 2 3 . 6 F i g u r e 3 : 9 6 2 4 - 2 2 r 1 2 1 0 l e J n g l l l l l l l 1 1 1 1 4 g I n t e r n u c l e a r d i s t a n c e ( X ) P o t e n t i a l e n e r g y c u r v e s f o r s o m e s t a t e s o f N 2 a n d N 3 . ( M a s s e y , 1 9 6 9 ) . 9 7 w h i c h d o n o t c h a n g e a p p r e c i a b l y i n k i n e t i c e n e r g y b u t w h i c h d e c a y v i a r a d i a t i v e o r s u p e r e l a s t i c p r o c e s s e s . F o r N t h e n , 2 t h e r e a r e n o c o l l i s i o n a l p a t h w a y s w h i c h r e s u l t i n p r o d u c t s w i t h h i g h k i n e t i c e n e r g y , e . g . o n t h e o r d e r o f 1 e v . F i g u r e 4 g i v e s t h e p o t e n t i a l e n e r g y c u r v e s f o r s t a t e s o f O 2 a n d 0 2 + . I o n i z a t i o n o f 0 2 o c c u r s v i a e x c i t a t i o n t o t h e ) ( Z T T g s t a t e o f 0 2 + a t a t h r e s h h o l d o f 1 2 . 0 5 e v . S o m e v e r t i c a l t r a n s i t i o n s f r o m t h e g r o u n d s t a t e l e a d t o d i s s o c i a t i o n i n t o o x y g e n a t o m s . I n p a r t i c u l a r , e x c i t a t i o n f r o m g r o u n d s t a t e 0 2 t o t h e B 3 : : 1 s t a t e r e s u l t s i n t w o o x y g e n a t o m s w h i c h s h a r e 0 . 5 - 2 . 0 e v o f k i n e t i c e n e r g y , a s s u m i n g a v e r t i c a l t r a n s i t i o n . T h e t h r e s h h o l d f o r t h i s i s 8 . 0 e v a n d c o i n c i d e s w i t h t h e o n s e t p o t e n t i a l i n e x p e r i m e n t a l s t u d i e s o f d i s s o c i a t i o n o f 0 2 ( G l o c k l e r a n d W i l s o n , 1 9 3 2 ) . U n l i k e N 2 , o x y g e n d o e s e v i d e n c e n e g a t i v e i o n s t a t e s w h i c h a r e p r o d u c e d b y s e v e r a l p r o c e s s e s . T h e d i s s o c i a t i v e a t t a c h m e n t c r o s s - s e c t i o n o f R a p p a n d B r i g l i a ( 1 9 6 5 ) h a s a t h r e s h h o l d a t 4 e v a n d p e a k s a t 6 . 4 a n d 3 4 e v w i t h v a l u e s o f 1 . 4 ( 1 0 - 2 2 ) a n d 0 . 4 6 ( 1 0 - 2 2 ) m 2 r e s p e c t i v e l y . T h e l o w e n e r g y p e a k c o r r e s p o n d s t o p r o d u c t i o n o f O a n d 0 ' a n d t h e h i g h e n e r g y p e a k t o p r o d u c t i o n o f 0 + a n d 0 - . T h e 0 ' i o n s p r o d u c e d i n t h e l o w e n e r g y a t t a c h m e n t p r o c e s s a p p e a r t o h a v e 1 - 2 e v o f k i n e t i c e n e r g y . I n c o n t r a s t t h e n w i t h n i t r o g e n t h e r e a r e s e v e r a l p r o c e s s e s i n o x y g e n w h i c h p r o d u c e e x c i t e d s t a t e s t h a t d e c a y i n t o k i n e t i c a l l y e x c i t e d p r o d u c t s . F i g u r e 5 s h o w s t h e p o t e n t i a l e n e r g y c u r v e s f o r s t a t e s o f H 2 , H + , H - ( S h a r p , 1 9 7 1 ) . I o n i z a t i o n o f H t o t h e 2 2 : 9 2 2 2 ) v e ( y g r e n e l a i t n e t o P o c 9 8 2 0 . 1 8 1 6 - 1 4 - 1 2 _ 1 0 - J l L l L l L 0 . 8 1 . 2 1 . 6 2 . 0 2 . 4 2 . 8 3 . 2 3 . 6 I n t e r n u c l e a r d i s t a n c e ( A ) F i g u r e 4 : P o t e n t i a l e n e r g y _ c u r v e s f o r s o m e s t a t e s o f 0 2 a n d 0 2 + . ( M a s s e y , 1 9 6 9 ) ) v e ( y g r e n e l a i t n e t o P 9 9 2 0 r - 1 8 . 1 6 . 1 2 L l l J l l 1 . 4 . 8 1 . 2 1 . 6 2 . 0 2 . 4 2 . 8 3 . 2 3 . 6 I n t e r n u c l e a r d i s t a n c e ( A ) F i g u r e 5 : P o t e n t i a l e n e r g y c u r v e s f o r s o m e s t a t e s o f H 2 , H 2 a n d H z - o ( S h a r p , 1 9 7 1 ) . p r o d u c e t w o H ( l S ) a t o m s s h a r i n g s e v e r a l e v o f k i n e t i c e n e r g y . 1 0 0 s t a t e o f H 2 + o c c u r s a t a t h r e s h h o l d o f 1 5 . 6 e v . A s f o r t h e N 2 a n d 0 2 t h e r e a r e s e v e r a l e l e c t r o n i c c h a n n e l s o p e n b e l o w t h e i o n i z a t i o n t h r e s h h o l d , t h e l o w e s t o f * w h i c h i s d i s s o c i a t i v e a t t a c h m e n t v i a e x c i t a t i o n t o t h e 2 2 : ; : s t a t e o f H 2 - w h i c h h a s a t h r e s h h o l d o f 3 . 4 e v a n d p e a k s a t 3 . 8 , 1 0 a n d 1 4 . 2 e v w i t h c r o s s - s e c t i o n s o f 1 . 8 ( 1 0 - 2 5 ) m 2 ( S c h u l t z a n d A s u n d i , 1 9 6 7 ) , 1 . 3 ( 1 0 ' 2 4 ) m 2 a n d 2 . 1 ( 1 0 ' 2 4 ) m 2 ( R a p p , B r i g l i a a n d S h a r p , 1 9 6 5 ) r e s p e c t i v e l y . T h e i o n s p r o d u c e d i n t h e f i r s t a n d t h i r d p r o c e s s e s h a v e l i t t l e k i n e t i c e n e r g y w h e r e a s t h o s e p r o d u c e d i n t h e s e c o n d p r o c e s s a p p e a r t o h a v e a b o u t 2 . 5 e v o f k i n e t i c e n e r g y . I n c o m p a r i s o n w i t h 0 2 , t h e d i s s o c i a t i v e a t t a c h m e n t p r o c e s s e s o c c u r a t l o w e r t h r e s h h o l d s i n H 2 , e j e c t i o n s w i t h g r e a t e r k i n e t i c e n e r g y , b u t h a v e m u c h s m a l l e r p e a k c r o s s - s e c t i o n s . D i s s o c i a t i o n o f H 2 g i g e x c i t a t i o n t o t h e b 3 z : : s t a t e o f H 2 p r o c e e d s a t a t h r e s h h o l d o f 8 . 8 e v a n d t h e c r o s s - s e c t i o n p e a k s a t 0 . 9 ( 1 0 - 2 0 ) m 2 a t 1 6 e v ( C o r r i g a n , 1 9 6 5 ) . D i s s o c i a t i o n o f H 2 a t t h e t h r e s h h o l d e n e r g y r e s u l t s i n t w o H ( I s ) a t o m s s h a r i n g 4 . 4 e v o f k i n e t i c e n e r g y . A t a t h r e s h h o l d o f 1 1 . 3 7 e v e x c i t a t i o n o f t h e g r o u n d s t a t e 1 Z ; t o t h e B 1 z 3 s t a t e o c c u r s ( A j e l l o , S r i v a s t a v a a n d Y u n g , 1 9 8 2 ) . T h e c r o s s - 2 1 ) m 2 . T h e s e c t i o n f o r t h e p r o c e s s p e a k s a t 4 0 e v a t 3 . 2 ( 1 0 - l 3 s t a t e d e c a y s r a d i a t i v e l y t o t h e g r o u n d s t a t e t o p r o d u c e t h e L y m a n - b a n d s y s t e m . A t a t h r e s h h o l d o f 1 1 . 7 2 e v e x c i t a t i o n o f t h e g r o u n d s t a t e t o t h e a B ‘ Z : ; s t a t e o f H 2 o c c u r s . T h i s s t a t e d e c a y s r a d i a t i v e l y t o t h e r e p u l s i v e t r i p l e t b 3 z : : s t a t e t o 1 0 1 A t 1 2 . 4 1 e v t h e g r o u n d s t a t e i s e x c i t e d t o t h e C l T T ' u s t a t e . 2 1 2 T h e c r o s s - s e c t i o n f o r t h i s p r o c e s s p e a k s a t 5 0 . e v a t 3 . 5 ( 1 0 - ) m ( A j e l l o , S r i v a s t a v a a n d Y u n g , 1 9 8 2 ) . T h i s s t a t e d e c a y s r a d i a t i v e l y t o t h e g r o u n d s t a t e t o g i v e t h e W e r n e r - b a n d s y s t e m . I n h y d r o g e n t h e n t h e r e a r e t h r e e e l e c t r o n i c c h a n n e l s b e l o w t h e i o n i z a t i o n t h r e s h h o l d w h i c h r e s u l t i n p r o d u c t s h a v i n g a t l e a s t 2 . 5 e v o f k i n e t i c e n e r g y . F u r t h e r , t h e d i s s o c i a t i o n c r o s s - s e c t i o n o f H 2 h a s a l o w t h r e s h h o l d , a n d i s l a r g e e n o u g h t o a s s u r e a s i g n i f i c a n t e x t e n t o f d i s s o c i a t i o n i n a n e l e c t r i c a l d i s c h a r g e , a s i s o b s e r v e d ( C h a p m a n 3 3 3 1 , 1 9 8 2 ) . E x p e r i m e n t a l m e a s u r e m e n t s o f H e a l e y a n d R e e d ( 1 9 4 1 ) o f t h e a v e r a g e f r a c t i o n a l e n e r g y l o s s o f a n e l e c t r o n b y c o l l i s i o n w i t h a g a s m o l e c u l e i n a d . c . d i s c h a r g e i n d i c a t e d t h e h i g h e s t e l e c t r o n - m o l e c u l e e n e r g y t r a n s f e r r a t e s i n H 2 f o l l o w e d b y N 2 a n d t h e n 0 2 o v e r a n e l e c t r o n e n e r g y r a n g e o f 1 - 5 e v . O n t h e b a s i s o f t h e s e c o n s i d e r a t i o n s o f e l a s t i c a n d i n e l a s t i c e l e c t r o n - m o l e c u l e c o l l i s i o n p r o c e s s e s i n H 2 , 0 2 a n d N 2 , H 2 w a s s e l e c t e d a s t h e m o d e l s y s t e m f o r f u r t h e r c a l c u l a t i o n a l s t u d y o f c o l l i s i o n i n d u c e d h e a t i n g i n a w e a k l y i o n i z e d e l e c t r i c a l d i s c h a r g e . T h e s e l e c t i o n o f H 2 h a s b e e n m a d e o n c o n s i d e r a t i o n o f e s t i m a t e s o f t i m e a n d e n e r g y s c a l e s a s s o c i a t e d w i t h a v a r i e t y o f e l e c t r o n - m o l e c u l e p r o c e s s e s . T h e e s t i m a t e s o f t i m e s c a l e s a r e m a d e o n t h r e s h h o l d s , w h i c h d e t e r m i n e s h o w m u c h o f t h e e l e c t r o n d i s t r i b u t i o n m a y p a r t i c i p a t e i n t h e c o l l i s i o n a n d o n c r o s s - s e c t i o n s , w h i c h d e t e r m i n e h o w l i k e l y t h e c o l l i s i o n i s o n a p e r e l e c t r o n b a s i s . T h e e n e r g y s c a l e s 1 0 2 a r e e s t i m a t e d a s s u m i n g t h e F r a n c k - C o n d o n p r i n c i p l e f o r t r a n s i t i o n s b e t w e e n p o t e n t i a l c u r v e s . T h e s e e s t i m a t e s a r e s u f f i c i e n t l y r e s o l v e d t o s e r v e a s t h e b a s i s o n w h i c h t o s e l e c t H 2 a s t h e m o d e l s y s t e m . A n e v a l u a t i o n o f c o l l i s i o n i n d u c e d h e a t i n g i n H 2 , h o w e v e r , r e q u i r e s b e t t e r t h a n t h e s e . S p e c i f i c a l l y , i t r e q u i r e s c a l c u l a t i o n o f t h e k i n e t i c e n e r g y d i s t r i b u t i o n o r m e a n k i n e t i c e n e r g y o f t h e c o l l i s i o n p r o d u c t s o f e x c i t a t i o n t o t h e 2 2 : ; s t a t e o f 1 1 - , a n d t o t h e b 3 X : a n d a 3 2 : ; s t a t e s o f H 2 . T h e s e p r o c e s s e s a r e t h e c a n d i d a t e s f o r s i g n i f i c a n t c o l l i s i o n i n d u c e d h e a t i n g a n d a q u a n t i t a t i v e d e s c r i p t i o n o f t h e p r o d u c t e n e r g y i s c r i t i c a l . E v a l u a t i o n o f c o l l i s i o n i n d u c e d h e a t i n g i n H 2 a l s o r e q u i r e s , a t t h e b e g i n n i n g , c o m p a r i s o n o f t h e e x c i t a t i o n t i m e s c a l e e s t i m a t e s w i t h t i m e s c a l e s f o r m a s s t r a n s p o r t , f l o w w i t h i n t h e d i s c h a r g e , a n d c o l l i s i o n a l r e l a x a t i o n p r o c e s s e s . S u c h a c o m p a r i s o n g r e a t l y s i m p l i f i e s t h e c a l c u l a t i o n a l w o r k a n d f o c u s e s t h e a n a l y s i s o n a s m a l l e r g r o u p o f c o m p e t i t i v e p r o c e s s e s . F o r e x a m p l e , a c o m p a r i s o n o f t i m e s c a l e s o f e l e c t r o n m o t i o n a n d n u c l e a r m o t i o n i s f u n d a m e n t a l t o t h e u s e o f a p o t e n t i a l c u r v e i n s e m i c l a s s i c a l s c a t t e r i n g t h e o r y . I n t h i s w o r k , c o m p a r i s o n o f t i m e s c a l e s o f e x c i t a t i o n , r e l a x a t i o n a n d t r a n s p o r t p r o c e s s e s i s f u n d a m e n t a l t o t h e c o n s t r u c t i o n o f t h e m o d e l . I n t h e r e m a i n d e r o f t h i s s e c t i o n t h e c a l c u l a t i o n o f t h e m e a n k i n e t i c e n e r g y o f d i s s o c i a t i o n p r o d u c t s a n d a c o m p a r i s o n o f t i m e s c a l e s f o r e x c i t a t i o n , r e l a x a t i o n a n d t r a n s p o r t a r e t a k e n u p . O f t h e t h r e e e l e c t r o n i c e x c i t a t i o n p r o c e s s e s r e s u l t i n g i n d i s s o c i a t i o n o f H 2 a n d p r o d u c t i o n o f k i n e t i c a l l y e n e r g e t i c 1 Z ; ( v = o ) t o b 3 X a w e r e c a l c u l a t e d b y R e s c i g n o e 5 . a _ l _ ( 1 9 7 6 ) 1 0 3 a t o m s ( o r i o n s i n t h e c a s e o f d i s s o c i a t i v e a t t a c h m e n t ) e x c i t a t i o n o f t h e b 3 X : h a s t h e l a r g e s t c r o s s - s e c t i o n b y f a r . T h e t o t a l c r o s s - s e c t i o n f o r e x c i t a t i o n o f t h e a 3 2 : g s t a t e , a s c a l c u l a t e d b y R e s c i g n o , M c C u r d y , M c K o y a n d B e n d e r ( 1 9 7 6 ) i n t h e d i s t o r t e d - w a v e a p p r o x i m a t i o n , i s u n i f o r m l y 1 0 - 1 5 % o f t h e m a g n i t u d e o f t h e c a l c u l a t e d c r o s s - s e c t i o n f o r e x c i t a t i o n o f t h e b 3 X : 1 s t a t e . T h e s u m o f t h e t w o t o t a l c r o s s - s e c t i o n s i s v e r y c l o s e t o t h e d i s s o c i a t i o n c r o s s - s e c t i o n m e a s u r e d b y C o r r i g a n ( 1 9 6 5 ) , i n d i c a t i n g t h a t a l a r g e m a j o r i t y o f d i s s o c i a t i o n i n H 2 i s e f f e c t e d y _ i _ a _ e x c i t a t i o n t o t h e b 3 2 : : 1 - s t a t e . T h e c r o s s - s e c t i o n f o r d i s s o c i a t i v e a t t a c h m e n t v i a e x c i t a t i o n t o t h e 2 E L ; s t a t e o f H 2 - i s s e v e r a l o r d e r s o f m a g n i t u d e s m a l l e r , w i t h t h e s p e c i f i c v a l u e v a r y i n g w i d e l y w i t h t h e i n i t i a l v i b r a t i o n a l l e v e l o f t h e t a r g e t m o l e c u l e . B e c a u s e o f t h e d o m i n a n c e o f d i s s o c i a t i o n g i g e x c i t a t i o n t o t h e l o w e s t t r i p l e t s t a t e o f H i t i s t h i s p r o c e s s w h i c h i s h e r e c o n s i d e r e d . O f 2 i n t e r e s t i s t h e c a l c u l a t i o n o f t h e a v e r a g e k i n e t i c e n e r g y o f t h e p r o d u c t s o f d i s s o c i a t i o n v i a e x c i t a t i o n t o t h e b 3 ‘ Z : : s t a t e . + 3 + g t o b Z u ’ t h e r e l a t i v e k i n e t i c e n e r g y o f t h e t w o a t o m s i s d e t e r m i n e d m a i n l y A s s u m i n g v e r t i c a l t r a n s i t i o n s f r o m 1 Z b y t h e r e l a t i v e s e p a r a t i o n o f t h e t w o g r o u n d s t a t e n u c l e i ( e s s e n t i a l l y t h e f i r s t B o r n a p p r o x i m a t i o n ) a n d s o t h e r e l a t i v e k i n e t i c e n e r g y d i s t r i b u t i o n i s j u s t p r o p o r t i o n a l t o t h e F r a n c k - C o n d o n f a c t o r f o r a t r a n s i t i o n f r o m t h e b o u n d i n i t i a l s t a t e v t o t h e c o n t i n u u m . F r a n c k - C o n d o n f a c t o r s f o r t r a n s i t i o n s f r o m a l g c l c M r t s f f f g a a t e e a h h r f k s k c e r u u u u r l r n i e p c e u u F F a t T a l " w c F i a f w w w n r o T w m n s r e s r n a h h h n h o a a o h e o a f a d i a v a d t v e e a i r v v t F r l e n r v n n e n e e c e e e r m a r t e n b n r x n i t i i i i i C t y p i d d t e c i r o z s o o o i e o f o y s i e t r e t t - a t i o n s t - - K q a a c " t n a n n i v c n o h o C C o u n e r h c l c c z e k c k i : i y i t v ; a m i ’ t a n E l I n o n o o m i i e d a n n n o n i e b F 1 t v n n o e t d e n r , . d n a e e l e o X i f f n l e n s e a e n n e k o t l ( v b t t d i s n p c i c = n i t v x f a a i s d i y t s l o T s n h c 0 i e c l ; c c n s f i e a f t n h e e ) a d i e t t f v t s w o i n c a e a s e t c l t o o o t o a a e n t e o c n t k a t i d r f r e e o s p s u i l e y n b y a n b , a c a u s s t v e e a o r r t n d d n u v m i u e f w l o h b e r w o g t , r h n r a r l t s v d i d t p e e e n a c v o e r n e o n t e y w v l e y a e r M n p i a t c h c a t i h e e r s c s o o t o c e t e r o i o m s f g c s t K t r " a o f n i h x e n d c u y o u o o r t l t o h n i p f t e t o t m m y f a b t t e n c e d h h b r o i n g e i l f c p i l h h d a s h c e n t e e i t a n i ( a o i n b l s w y s t u o a t e i 1 9 d l t c b y C c f q i e m p l r g n f s K s e a e e l i a g l t c u s r c r s 8 r o i u 3 o " g o t u u t d o o r c i u o 0 s o l { e R n s n a r h o w r o a u b n o m e n p a : d c i ) v e a p r c n l u d a s s s o t o ; o i n t u e v o e a d t w b n c i r n n l e e i t i i s a , n r y d f i o l l e t i o a g t d f o i o t t e g n r s r t y a h i u n f n n h m r d t e n o g n o W t s e n h t p f e . c n u m o o o a t f a a h o a t l c e t e m l f t l a t r e p p h i t w a h m t a e n h g e e t f l y e i r p h f l e e r i £ c A e i t i i e o r o n c e i n , c w h a t e o i , p i n a u w d x d r l u i e g l _ h d t s w n i w d n o o u p e t a i e o n o t e h l i v c i i i i m a b b l c r o c f s n t o e t t i n m t s t a t l e i n t 1 ( v g n n a s n e o u l s t t i a i r d s w i h d t p e t s m n i n l z t h i a h e b p i e s i c a i a e o b e e g 6 a h l u t t o a o o a l e t i i 9 e t r r F n m s t t a s a n t t t u d n c n r 5 t t e i u a x t v t a t i l v m o o a ) i f m o a t s i e o t e c h o a e n n t t l n . o m e n e r u i l a s s n m i e d a a s l y l s u n . . z e d u a o r f a a i h l t o e i t o a e t t t a i o a e n l i e e a p e f t s o t s l i n . d o n 1 0 4 v a l u e s , u s e d t o e s t i m a t e m e a n v a l u e s f o r t r a n s i t i o n s f r o m v = 1 a n d a b o v e . 1 0 5 F o r c a l c u l a t i o n o f t h e i n i t i a l s t a t e v i b r a t i o n a l w a v e f u n c t i o n a M o r s e p o t e n t i a l w a s f i t t o t h e 1 Z 3 c u r v e o f K o l o s a n d W o l n i e w i c z . T h e M o r s e c o n s t a n t s w e r e o b t a i n e d f r o m t h e c o m p i l a t i o n o f S h a r p ( 1 9 7 1 ) . V ( r ) = D £ e x p ( - 2 a ( r - r o ) ) - 2 e x p ( - a ( r - r o ) ) } ( 1 1 8 ) r 0 = . 7 4 1 6 ( 1 o ' 1 ° ) m a = 1 . 9 4 2 8 ( 1 0 1 ° ) m ’ 1 D = 7 . 6 0 5 4 ( 1 0 ’ 1 9 ) J T h e r a d i a l S c h r o d i n g e r e q u a t i o n f o r k = 0 t a k e s t h e f o l l o w i n g f o r m . f i g “ ) + 3 % . g £ - V ( r ) } w r h o ( 1 1 9 ) . W i t h t h e f o l l o w i n g s u b s t i t u t i o n s t h e S c h r o d i n g e r e q u a t i o n t a k e s o n a m o r e f a m i l i a r f o r m . L e t : t = K e x p ( - a r ) - ( 2 = 2 1 4 E E < O f o r b o u n d s t a t e s 2 2 a h K 2 = 8 . 4 4 D e x p ( 2 a r ° ) ‘ 2 2 a / 5 2 = 8 / ‘ D a 2 ‘ 2 t 2 d z f + t g j + ( - 3 2 + fi i ’ x 2 W ‘ = 0 ( 1 2 0 ) d t 2 d t 1 2 1 0 6 A t t h i s p o i n t , e q n . 1 2 0 i s r e c o g n i z e d a s a v a r i a n t o f t h e G a u s s h y p e r g e o m e t i c e q u a t i o n , t h e c o n f l u e n t h y p e r g e o m e t r i c e q u a t i o n i n f a c t a n d s o t h e w a y t o t h e s o l u t i o n i s c l e a r . I n p r e s e n t a t i o n s o f t h e s o l u t i o n t o t h e S c h r o d i n g e r e q u a t i o n f o r t h e M o r s e p o t e n t i a l s e v e r a l a u t h o r s t a k e a n o t h e r a p p r o a c h w h i c h d e s e r v e s c o m m e n t . R a p p ( 1 9 7 3 ) , f o r e x a m p l e , a p p l i e s t h e m e t h o d o f F r o e b e n i u s t o e q n . 1 2 0 b u t i s o n l y a b l e t o t r u n c a t e t h e p o w e r s e r i e s a n d o b t a i n a d i s c r e t e s p e c t r u m b y e x t e n d i n g t h e d o m a i n o f r f r o m ( o , + o o ) t o ( - o o , + o o ) a n d t h e n r e q u i r i n g t h a t ¢ ( r ) v a n i s h a s r d e - o o . S y m m e t r y c o n d i t i o n s o n i n v e r s i o n t h r o u g h t h e o r i g i n a p p l y t o t h e S p h e r i c a l h a r m o n i c t e r m i n t h e f a c t o r i z a t i o n o f t h e t o t a l w a v e f u n c t i o n , n o t t o t h e r a d i a l c o m p o n e n t . T h e e i g e n f u n c t i o n s g i v e n b y R a p p a r e i n c o r r e c t b u t t h e e i g e n v a l u e s a r e c o r r e c t . T h e a d h o g e x t e n s i o n o f t h e d o m a i n i s b o t h u n n e c e s s a r y a n d m i s l e a d i n g . T h e p o l y n o m i a l e i g e n f u n c t i o n s a n d d i s c r e t e s p e c t r u m f o l l o w n a t u r a l l y f r o m t h e p r o p e r t i e s o f t h e c o n f l u e n t h y p e r g e o m e t r i c f u n c t i o n , a s d e t a i l e d b y F l u g g e ( 1 9 7 4 ) T h e s o l u t i o n t o e q n . 1 2 0 i s o f t h e f o r m g i v e n i n e q n . 1 2 1 , w i t h M a n d U a s t h e t w o l i n e a r l y i n d e p e n d e n t s o l u t i o n s o f t h e c o n f l u e n t h y p e r g e o m e t i c e q u a t i o n . f V V p ~ 2 X I ¢ ( f ) ' 3 8 X P ( ' / 1 ) 2 ‘ [ C l M [ . 2 + Y - / 1 ’ I + 2 3 : { - ] " - C 2 6 U [ { + x ” 6 é " * 2 y ) t j ] ( 1 2 1 ) N o w r e c a l l t h a t w e r e q u i r e ¢ ( t ) - ; O a s t - a O ( r - » + o o ) 2 Y a n d s o C 2 = O a s t - i s s i n g u l a r a t t = O . T h e s e c o n d c o n d i t i o n o n f ( t ) i s t h a t ¥ v a n i s h a t r = 0 , t h u s V ( K ) = O . 4 0 0 - ? " P C ’ 9 2 ) K Y M E K ‘ Y ‘ A / a fl u ’ ; K ] 5 0 . ( 1 2 2 ) V < & _ ( 1 2 3 ) E . 3 - D + ( 3 . _ . _ _ D “ 2 J ) “ % . ( V + ' / ) - % ) < W é ) ) 1 ( 1 2 5 ) 1 0 7 T h u s , t h e z e r o e s o f M d e t e r m i n e t h e e n e r g y e i g e n v a l u e s F o r H 2 t h e r a t i o o f K t o ( 1 + 2 ! ) c a n b e e s t i m a t e d b y n o t i n g t h a t I i s b o u n d e d a b o v e b y f / Z a n d b e l o w b y O f o r a l l b o u n d s t a t e s . T h i s r a t i o h a s a m i n i m u m v a l u e o f 4 . 1 a n d s o t h e a s y m p t o t i c e x p a n s i o n o f t h e c o n f l u e n t h y p e r g e o m e t r i c f u n c t i o n i s u s e d t o l o c a t e t h e z e r o e s . T h e f u n c t i o n h a s z e r o e s f o r 8 + X - f / Z = - v w h e r e v i s z e r o o r a p o s i t i v e i n t e g e r . F r o m t h e l o w e r b o u n d o n Y a n u p p e r b o u n d o n v r e s u l t s , g i v i n g a f i n i t e , d i s c r e t e s p e c t r u m . 2 F o r H t h i s u p p e r b o u n d r e s t r i c t s a M o r s e m o d e l t o 1 6 2 v i b r a t i o n a l l e v e l s . T h e v i b r a t i o n a l w a v e f u n c t i o n m a y b e w r i t t e n t h e n a s t h e f o l l o w i n g e q u a t i o n . ( H t ) = t ‘ I ” ’ 2 " ’ " ” e X p ( - t / 2 ) M I - v , / $ - 2 v . t ] ( 1 2 4 ) T h e e n e r g y e i g e n v a l u e s a r e o b t a i n e d b y s o l v i n g t h e P / e q u a t i o n 8 + X ’ 2 = - v f o r t h e e n e r g y v a r i a b l e i n Y . N o t e h e r e a l s o t h a t M l — v , p - 2 v , t ] m a y b e w r i t t e n a s a p o l y n o m i a l o f o r d e r v i n t . T h e F r a n c k - C o n d o n f a c t o r i n t h e r e f l e c t i o n a p p r o x i m a t i o n , t o w i t h i n a n o r m a l i z a t i o n c o n s t a n t , i s g i v e n b y t h e s q u a r e o f t h e v i b r a t i o n a l w a v e f u n c t i o n e v a l u a t e d a t t h e i n t e r n u c l e a r s e p a r a t i o n w h i c h c o r r e s p o n d s t o a r e l a t i v e k i n e t i c e n e r g y w 1 0 8 o f t w o a t o m s w i t h r e s p e c t t o t w o H ( 1 s ) a t o m s a t i n f i n i t e s e p a r a t i o n . g 2 q ( V . W ) — < / ( V ' R w ) ( 1 2 6 ) w { q ( v , w ) d w = 1 ( 1 2 7 ) 0 W i t h t h e n o r m a l i z a t i o n a s s u m e d i n e q n . 1 2 7 t h e k i n e t i c e n e r g y d i s t r i b u t i o n i s g i v e n b y q ( v , w ) a n d t h e a v e r a g e k i n e t i c e n e r g y i s g i v e n b y t h e i n t e g r a l o f t h e p r o d u c t o f q ( v , w ) a n d W . o n q ( v , w ( r ) ) d u - . - q ( v ) w ( r ) ) > 4 9 . ( J r 3 " ( 1 2 8 ) T h e e x p l i c i t r e l a t i o n f o r w i n t e r m s o f i n t e r n u c l e a r s e p a r a t i o n i s o b t a i n e d f r o m a c u r v e - f i t o f t h e p o t e n t i a l o f K o l o s a n d W o l n i e w i c z ( 1 9 6 5 ) f o r t h e b 3 Z 1 4 1 s t a t e t o t h e f o l l o w i n g t w o p a r a m e t e r i n v e r s e H u l t h é n p o t e n t i a l . - 1 w = fl z f e x p ( / S 3 r ) - 1 ] ( 1 2 9 ) U s i n g t h e f o l l o w i n g p o l y n o m i a l f o r m o f M l - v , l + 2 ¥ , t ] t h e a v e r a g e r e l a t i v e k i n e t i c e n e r g y o f t h e d i s s o c i a t i o n p r o d u c t s i s g i v e n i n e q n . 1 3 1 . V n M [ - v , 1 + 2 x , t ] = 2 : a n ” ) t ( 1 3 0 ) b n ( v ) n ! 1 1 : 0 v : w 2 Z 0 t : 0 o V Z M m ° : v o . . Q 5 “ ( a ) ( 9 ~ V “ I ) ( ( _ v _ v ) ) _ b ) _ 5 o a , , . < . v . , < . ( ) 0 v ' m ' . n ( v ) ) n ! m ! 2 ( ‘ a . 2 K r K fl x d h m “ n ~ v y / + . e q D M Z 7 1 2 4 : ‘ A L V I ' ' ) I ‘ M - + M é 1 5 1 / 4 ) { a C O O “ x p N é 3 e ' A é ) d J é r ( 1 3 1 ) < ~ > - = / s a n ( v ) b n ( v ) 1 0 9 = ( - v ) ( - v + 1 ) ( - v + 2 ) . . . . ( - v + n - l ) = ( 1 + 2 X ) ( 1 + 2 ! + 1 ) . . . . ( 1 + 2 ¥ + n - 1 ) T h e i n t e g r a l s m a y b e r e l a t e d t o t h e i n c o m p l e t e g a m m a f u n c t i o n b y r e c u r r e n c e r e l a t i o n s ( A b r a m o w i t z a n d S t e g u n , 1 9 7 2 ) s o t h a t o n l y t h e i n c o m p l e t e g a m m a f u n c t i o n X ( 2 k ’ + 2 / 6 3 / a , K ) n e e d b e c a l c u l a t e d . T h e r e q u i r e d i n t e g r a t i o n w a s p e r f o r m e d b y a 9 6 - p o i n t G a u s s i a n q u a d r a t u r e . T h e r e s u l t s o f t h e c a l c u l a t i o n f o r V : O a r e c o m p a r e d w i t h t h o s e o f R e s c i g n o i n t h e f o l l o w i n g t a b l e . T a b l e I : S t a t i s t i c s o f t w o c a l c u l a t e d F r a n c k - C o n d o n e n v e l o p e s . l R e s c i g n o M o r i n l M o s t p r o b a b l e r e l a t i v e k i n e t i c e n e r g y 5 . 7 0 e v 5 . 7 1 e v E n e r g y a t h a l f - h e i g h t ( e v ) 4 . 4 2 4 . 4 6 7 . 2 5 7 . 4 6 i s b y f a r t h e m o s t p r o m i s i n g o p e n c h a n n e l f o r c o l l i s i o n i n d u c e d 1 1 0 B o t h F r a n c k - C o n d o n e n v e l o p e s f o r e x c i t a t i o n f r o m 1 + _ . 3 + . Z ( v — o ) t o t h e c o n t i n u u m o f b i n a r e G a u s s 1 a n , r e f l e c t i n g t h e G a u s s i a n n a t u r e o f t h e v i b r a t i o n a l w a v e f u n c t i o n . A l t h o u g h t h e p r e s e n t c a l c u l a t i o n i s c o n s i d e r a b l y e a s i e r t o p e r f o r m t h a n t h a t o f R e s c i g n o £ 2 3 1 t h e r e s u l t s f o r t h e ( v = o ) c a s e a r e v e r y c l o s e t o t h e i r s . I n t h e f o l l o w i n g t a b l e t h e a v e r a g e r e l a t i v e k i n e t i c e n e r g i e s f o r e x c i t a t i o n f r o m 1 + 3 + . ' E g v t o b Z 9 a r e g i v e n . T a b l e I I : A v e r a g e r e l a t i v e k i n e t i c e n e r g y c a l c u l a t e d i n t h e C o n d o n r e f l e c t i o n a p p r o x i m a t i o n . V W 6 V V W 6 V 0 6 . 1 9 1 7 8 . 5 1 5 1 6 . 5 1 8 8 8 . 7 6 3 2 6 . 9 4 9 9 8 . 9 8 5 3 7 . 3 0 2 1 0 9 . 1 8 3 4 7 . 6 3 7 1 1 9 . 3 5 4 5 7 . 9 5 1 1 2 9 . 4 9 8 6 8 . 2 4 4 1 3 9 . 6 1 5 T h e s e a v e r a g e s a r e c o n s i d e r a b l y l a r g e r t h a n t h e i n i t i a l e s t i m a t e o f 4 . 4 4 e v b a s e d o n a t r a n s i t i o n a t t h e o u t e r c l a s s i c a l t u r n i n g p o i n t f o r v = o . T h e s e v a l u e s a l s o i n d i c a t e t h a t d i s s o c i a t i o n o f H 2 g i g e x c i t a t i o n o f t h e l o w e s t t r i p l e t s t a t e 1 1 1 h e a t i n g o f H 2 . A t t h i s p o i n t i t i s a p p r o p r i a t e t o c o n s i d e r e x p e r i m e n t a l e v i d e n c e f o r c o l l i s i o n i n d u c e d h e a t i n g g i g e x c i t a t i o n t o t h e b 3 z : : s t a t e o f H 2 . M e a s u r e m e n t s o f k i n e t i c e n e r g y d i s t r i b u t i o n s o f i o n i c f r a g m e n t s o f d i s s o c i a t i v e a t t a c h m e n t i n H 2 h a v e b e e n m a d e b u t n o s u c h m e a s u r e m e n t s e x i s t f o r n e u t r a l a t o m s . T h e c r o s s - s e c t i o n o f C o r r i g a n i s t h e o n l y e x p e r i m e n t a l c r o s s - s e c t i o n f o r e l e c t r o n i m p a c t d i s s o c i a t i o n o f H a n d w a s o b t a i n e d b y 2 m e a s u r i n g t h e p r e s s u r e d e c r e a s e i n a t u b e o f d i s s o c i a t i n g H 2 c a u s e d b y t r a p p i n g o u t t h e a t o m s i n a l a y e r o f m o l y b d e n u m t r i o x i d e o n t h e t u b e ' s i n n e r s u r f a c e . T h i s r a t e o f p r e s s u r e d e c r e a s e w a s r e l a t e d b y a m o d e l t o t h e c r o s s - s e c t i o n f o r d i s s o c i a t i o n g i g e x c i t a t i o n t o b 3 X 3 s t a t e . T h e m o d e l C o r r i g a n u s e d a s s u m e d t h a t t h e p r e s s u r e d e c r e a s e w a s c a u s e d b y t h e d e c r e a s e i n c o n c e n t r a t i o n o f H 2 a n d d i d n o t c o n s i d e r t h e p o s s i b i l i t y t h a t t h e e x c i t e d a t o m i c p r o d u c t s w o u l d t r a n s f e r s o m e p a r t o f t h e i r k i n e t i c e n e r g y t o t h e H H i s m e a s u r e m e n t s , 2 . h o w e v e r , w e r e a t p r e s s u r e s o f 6 . 7 - 2 7 ( 1 0 - 4 ) N / m 2 a n d i n t h i s p r e s s u r e r a n g e t h e m e a n f r e e p a t h o f H i s l o n g e r t h a n t h e 2 d i m e n s i o n s o f t h e v e s s e l a n d s o t h e d i s s o c i a t i o n p r o d u c t s w o u l d b e m o r e l i k e l y t o e x c h a n g e e n e r g y w i t h t h e w a l l t h a n w i t h f r e e m o l e c u l e s . T h u s , C o r r i g a n ' s d a t a l e a v e s t h e q u e s t i o n o f c o l l i s i o n i n d u c e d h e a t i n g u n t o u c h e d . T h e o n l y o t h e r w o r k r e l a t e d t o s t u d y i n g t h e k i n e t i c e n e r g y d i s t r i b u t i o n o f n e u t r a l H a t o m f r a g m e n t s i s t h a t o f P o l y a k o v a , F i z g e e r a n d E r k o ( 1 9 7 4 ) w h o m e a s u r e t h e D o p p l e r b r o a d e n i n g o f t h e B a l m e r l i n e s i n e l e c t r o n 1 1 2 i m p a c t d i s s o c i a t i o n o f h y d r o c a r b o n s . A v e r a g e H a t o m k i n e t i c e n e r g i e s r a n g e f r o m 3 . 9 t o 6 . 1 e v d e p e n d i n g o n t h e h o s t h y d r o c a r b o n . S i m i l a r m e a s u r e m e n t s f o r h i g h f r e q u e n c y H 2 d i s c h a r g e s a r e i n p r o g r e s s b y C h a p m a n ( 1 9 8 5 ) . I n t h e d e v e l o p m e n t o f t h e c a l c u l a t i o n a l s c h e m e s , w h i c h a r e p r e s e n t e d l a t e r , a n e x a m i n a t i o n o f t h e t i m e s c a l e s f o r e x c i t a t i o n , r e l a x a t i o n a n d t r a n s p o r t p h e n o m e n a i s p r o f i t a b l e a n d i s t a k e n u p i n t h i s l a s t p o r t i o n o f s e c t i o n 3 . 1 . T h e t i m e s c a l e d i s c u s s e d h e r e i s t h e i n v e r s e o f a c h a r a c t e r i s t i c f r e q u e n c y o f t h e p r o c e s s o f i n t e r e s t . F o r p e r i o d i c p r o c e s s e s , l i k e v i b r a t i o n a l m o t i o n o f a d i a t o m i c o r t h e o s c i l l a t i o n o f a n e l e c t r o m a g n e t i c f i e l d , t h e p e r i o d o f t h e m o t i o n i s t h e a p p r o p r i a t e t i m e s c a l e . F o r e x c i t a t i o n a n d r e l a x a t i o n p r o c e s s e s t h e i n v e r s e o f t h e c o l l i s i o n f r e q u e n c y i s a m e a s u r e o f t h e i n t e r c o l l i s i o n t i m e s c a l e . F o r t r a n s p o r t p r o c e s s e s s u c h a s c o n v e c t i v e f l o w t h e m e a n r e s i d e n c e t i m e i s t h e a p p r o p r i a t e t i m e s c a l e . F o r w a v e p r o p a g a t i o n i n a n i o n i z e d g a s t h e i n v e r s e o f t h e p l a s m a f r e q u e n c y i s t h e c h a r a c t e r i s t i c t i m e s c a l e . I n F i g u r e s 6 , 7 a n d 8 t h e t i m e s c a l e s f o r a v a r i e t y o f e x c i t a t i o n , r e l a x a t i o n a n d t r a n s p o r t p r o c e s s e s a r e p r e s e n t e d o v e r a r a n g e o f d i s c h a r g e c o n d i t i o n s f o r a w e a k l y i o n i z e d d i l u t e H 2 m i c r o w a v e f r e q u e n c y d i s c h a r g e . T h e e x c i t a t i o n a n d r e l a x a t i o n t i m e s c a l e s a r e c a l c u l a t e d f r o m c o l l i s i o n f r e q u e n c i e s p e r m o l e c u l e o f H 2 . T h e d a s h e d l i n e i n e a c h f i g u r e i s t h e e l e c t r o n - H 2 m o m e n t u m t r a n s f e r t i m e s c a l e o n a s i n g l e e l e c t r o n b a s i s i n s t e a d o f o n a s i n g l e H 2 m o l e c u l e b a s i s . 1 1 3 T h e r e s i d e n c e t i m e i s c a l c u l a t e d f o r a t u b u l a r d i s c h a r g e 1 0 . 0 c m l o n g a n d 1 . 0 c m i n r a d i u s . F i g u r e 6 p r e s e n t s t h e v a r i a t i o n o f t h e s e t i m e s c a l e s w i t h p r e s s u r e ( 1 - 1 0 0 0 0 0 N / m z ) f o r a p u r e H 2 d i s c h a r g e a t 3 0 0 K w i t h a g a s f l o w o f 3 0 0 ( 1 0 - 6 ) m o l e s / s a n d a n e l e c t r o n t o n e u t r a l c o n c e n t r a t i o n r a t i o o f 1 0 - 6 . F o r p r e s s u r e s b e t w e e n 1 0 0 a n d 1 0 , 0 0 0 N / m 2 t h e r e a r e f i v e g r o u p s o f t i m e s c a l e s . T h e s m a l l e s t i s t h a t o f t h e v i b r a t i o n a l m o t i o n o f H 2 . T h e s e c o n d i s t h a t c o r r e s p o n d i n g t o t h e f i e l d f r e q u e n c y , p l a s m a f r e q u e n c y a n d e l e c t r o n - H 2 m o m e n t u m t r a n s f e r f r e q u e n c y o n a s i n g l e e l e c t r o n b a s i s . I n t h e c o l d p l a s m a a p p r o x i m a t i o n t h e w e a k l y i o n i z e d g a s c o n d u c t i v i t y i s a m a x i m u m w h e n t h e f i e l d f r e q u e n c y a n d e l e c t r o n - H 2 m o m e n t u m t r a n s f e r f r e q u e n c y a r e e q u a l . I n F i g u r e 6 t h i s e q u a l i t y o c c u r s a t a b o u t 3 2 0 N / m z . T h e t h i r d r e g i o n o f t i m e s c a l e s i s t h a t o f t h e H 2 - H 2 e l a s t i c c o l l i s i o n . C o m p a r i s o n o f t h i s t i m e s c a l e w i t h t h a t o f t h e e l e c t r o n - H 2 e l a s t i c a n d v i b r a t i o n a l e x c i t a t i o n t i m e s c a l e s i n d i c a t e s t h a t a n H 2 m o l e c u l e " s e e s ” o n l y o t h e r H 2 m o l e c u l e s e x c e p t f o r a n o c c a s i o n a l c o l l i s i o n w i t h a n e l e c t r o n . S o u n d e r t h e s e c o n d i t i o n s o n e m a y e x p e c t t h a t H i s e s s e n t i a l l y c h a r a c t e r i z e d b y a n 2 e q u i l i b r i u m v e l o c i t y d i s t r i b u t i o n . T h e l a s t g r o u p o f t i m e s c a l e s i s t h a t o f t h e H z - H 2 v i b r a t i o n - t o - t r a n s l a t i o n r e l a x a t i o n a n d t h a t o f t h e a v e r a g e r e s i d e n c e t i m e i n t h e d i s c h a r g e . T h e t i m e s c a l e o f V - T r e l a x a t i o n i n H 2 i s v e r y s l o w w i t h r e s p e c t t o H z - e e l a s t i c , H Z - e v i b r a t i o n a l e x c i t a t i o n a n d v i b r a t i o n - t o - v i b r a t i o n r e l a x a t i o n p r o c e s s e s a n d t h i s s e p a r a t i o n i n t i m e s c a l e s i s t h e b a s i s o f m o d e l i n g t h e v i b r a t i o n a l m a n i f o l d a s a ) s , e m i t ( g o l L _ - . - _ - - 1 1 1 1 - 1 1 2 3 4 5 _ = 3 - : F ; a n ) ’ ( - 9 i ‘ 3 1 O 2 ( ( 4 i - . V ‘ 1 \ \ \ \ I O - ' > m o l e / $ “ I O 5 b ' m f G u ) ' H : o n e l p e n ' o d ‘ 2 l 3 g 4 \ J 5 F i g u r e 6 : 1 1 4 l o g ( P r e s s u r e , N / m z ) T i m e s c a l e s f o r a v a r i e t y o f t r a n s p o r t , e l e c t r o d y n a m i c a n d k i n e t i c p r o c e s s e s f o r p r e s s u r e s o f l - 1 ( 1 0 5 ) N / m 2 i n p u r e H 2 . 1 1 5 T ; a ? E - a 3 3 . m o H g : 3 . 0 0 " " ) m o l e / $ - 1 2 _ 2 ; : ’ - ( / 0 . ‘ ) \ \ x = 0 . 1 0 \ \ - 1 3 L 5 ! , : 1 7 ’ 6 - C l " ! a w . — 1 4 v i b r a ' h ' o n a l p e t - { a d ' 1 5 [ 1 1 1 1 1 2 3 4 5 l o g ( P r e s s u r e , N / m z ) F i g u r e 7 : T i m e s c a l e s f o r a v a r i e t y o f t r a n s p o r t , e l e c t r g d y n a m i c ) a n d k i n e t i c p r o c e s s e s f o r p r e s s u r e s o f 1 - 1 ( 1 0 N / m 2 a n d t h e e x t e n t o f d i s s o c i a t i o n a t 0 . 2 . H 0 ' ” ; " ' 5 " ‘ 1 1 6 H : - H , e l u s i v e . : 1 A _ 6 " U : _ 7 _ 1 4 3 - 1 4 e h s f u ' c . m E ~ r - 1 a - 3 - U ) - 9 _ ) 9 ) [ Q u a d ‘ F r ‘ l u e n c y P \ e - H ; c h s fl ‘ c - 1 0 - _ _ ¥ 3 a F i e l d ' 1 1 ‘ P 7 0 0 I V / m ‘ F r q u c n c y E : 3 . 0 0 " ) m o l e / s - 2 _ - 1 i s [ ( m ‘ ) - 1 3 _ X : 0 . 2 0 U - _ 1 4 u ) " M : G i l : ‘ 1 5 7 1 1 i 1 1 1 1 4 1 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0 T e m p e r a t u r e ( K ) F i g u r e 8 : T i m e s c a l e s f o r a v a r i e t y o f t r a n s p o r t , e l e c t r o - d y n a m i c a n d k i n e t i c p r o c e s s e s f o r t e m p e r a t u r e s o f 2 0 0 - 1 2 0 0 K a n d t h e e x t e n t o f d i s s o c i a t i o n a t 0 . 2 . 1 1 7 p s e u d o e q u i l i b r i u m o n e , w i t h t h e p o p u l a t i o n s d e s c r i b e d b y a B o l t z m a n n d i s t r i b u t i o n a t t e m p e r a t u r e T v ' w h e r e T V # T . A p a r t f r o m m o d e l i n g q u e s t i o n s t h i s s e p a r a t i o n i n t i m e s c a l e s i n d i c a t e s a c o n d i t i o n o f n o n e q u i l i b r i u m b e t w e e n t h e t r a n s l a t i o n a l a n d v i b r a t i o n a l d e g r e e s o f f r e e d o m . B e l o w 1 0 0 N / m 2 t h e r e s i d e n c e t i m e s c a l e i s o f t h e s a m e o r d e r o f m a g n i t u d e a s t h e e x c i t a t i o n t i m e s c a l e s , i n d i c a t i n g t h a t f o r a g i v e n g a s f l o w r a t e t h e r e i s a t h r e s h h o l d p r e s s u r e f o r p r o d u c t i o n o f a p l a s m a . T h i s e x p e c t a t i o n i s c o n f i r m e d b y l o w p r e s s u r e e x p e r i m e n t s i n t h e a u t h o r ' s l a b o r a t o r y . A t a r o u n d 1 N / m 2 ( a ~ 7 m i c r o n ) t h e r e s i d e n c e t i m e s c a l e i s o f t h e s a m e o r d e r o f m a g n i t u d e a s t h e H Z - H 2 e l a s t i c c o l l i s i o n t i m e s c a l e , p r e d i c t i n g f r e e m o l e c u l a r f l o w o n t h e l e n g t h s c a l e o f t h e d i s c h a r g e . I n F i g u r e 7 t h e e f f e c t o f f i n i t e d i s s o c i a t i o n i s i n c l u d e d i n t h e c a l c u l a t i o n o f t h e v a r i o u s t i m e s c a l e s . T h r e e a d d i t i o n a l p r o c e s s e s a r e i n c l u d e d , H - H e l a s t i c c o l l i s i o n s , H Z - H V T 2 r e l a x a t i o n p r o c e s s e s a n d H + H + H r e c o m b i n a t i o n p r o c e s s e s . T h e 2 H z - H e l a s t i c c o l l i s i o n t i m e s c a l e i s t h e s a m e o r d e r o f m a g n i t u d e a s t h e H Z - H 2 p r o c e s s a n d s o e q u i l i b r a t i o n o f H 2 a n d H i s e x p e c t e d . T h e H z - H V T r e l a x a t i o n t i m e s c a l e i s n o w o f t h e s a l ' n e o r d e r o f m a g n i t u d e a s t h e e - H 2 v i b r a t i o n a l e x c i t a t i o n r a t e a n d s o o n e w o u l d e x p e c t t o f i n d a m u c h g r e a t e r d e g r e e o f e Q u i l i b r a t i o n o f t h e v i b r a t i o n a l l e v e l p o p u l a t i o n s t o t h e t r a n s l a t i o n a l t e m p e r a t u r e t h a n w o u l d b e f o u n d i n t h e c a s e o f P u r e H z . T h i s i s s u p p o r t e d b y t h e c a l c u l a t i o n a l r e s u l t s o f B r u n e t 9 3 g i ( 1 9 8 1 ) . B e l o w a b o u t 2 0 0 0 u m 2 t h e n z + n + n 1 1 8 r e c o m b i n a t i o n t i m e s c a l e i s l o n g e r t h a n t h a t f o r f l o w t h r o u g h t h e d i s c h a r g e a n d s o i n t h a t p r e s s u r e r a n g e t h r e e - b o d y r e c o m b i n a t i o n e f f e c t s h a v e l i t t l e e f f e c t o n t h e r e a r r a n g e m e n t p r o c e s s e s . I n F i g u r e 8 t h e s a m e t i m e s c a l e s a r e g i v e n a s a f u n c t i o n o f t e m p e r a t u r e ( 2 0 0 - 1 2 0 0 K ) f o r a d i s c h a r g e a t 4 0 0 N / m 2 w i t h a n H 2 f e e d r a t e o f 3 0 0 ( 1 0 - 6 ) m o l e s / s , e x t e n t o f d i s s o c i a t i o n 6 ) o f 0 . 2 0 , a n d e x t e n t o f i o n i z a t i o n o f l . ( 1 0 - . A t t e m p e r a t u r e s a b o v e 3 0 0 K t h e s e p a r a t i o n b e t w e e n t i m e s c a l e s i n t h e u p p e r h a l f o f F i g u r e 8 c h a n g e s g r e a t l y d u e t o t h e t e m p e r a t u r e d e p e n d e n c e o f t h e V T t i m e s c a l e s . C o m p a r i s o n o f t h e t i m e s c a l e s p r e s e n t e d i n F i g u r e s 6 , 7 a n d 8 p l a y a u s e f u l r o l e i n t h e c o n s t r u c t i o n o f t h e m a c r o s c o p i c b a l a n c e e q u a t i o n s f o r t h e d i l u t e n e u t r a l g a s i n a h i g h f r e q u e n c y d i s c h a r g e a s w e l l a s i n t h e s e l e c t i o n o f o p e r a t i n g c o n d i t i o n s , p r i m a r i l y t h e p r e s s u r e a n d f e e d g a s f l o w r a t e . F o r e x a m p l e , f o r a n e x t e r n a l f i e l d f r e q u e n c y o f 2 . 4 5 G H z t h e o p e r a t i n g P r e s s u r e a t 3 0 0 K s h o u l d b e b e t w e e n 1 0 0 a n d 1 0 0 0 N / m 2 w i t h a f l o w ’ r e s i d e n c e t i m e o f n o l e s s t h a n 1 0 - 2 s . F o r a m o d e l o f t h i s s Y s t e m V T s e l f - r e l a x a t i o n a n d t h r e e - b o d y r e c o m b i n a t i o n p r o c e s s e s m a y s a f e l y b e n e g l e c t e d . T h e s e e s t i m a t e s o f t i m e s c a l e s a r e r e f e r r e d t o i n l a t e r d e v e l o p m e n t s . 1 1 9 3 . 2 U n c o u p l e d c a l c u l a t i o n o f c o l l i s i o n i n d u c e d h e a t i n g o f H 2 . I n t h i s s e c t i o n t h e e f f e c t o f e l e c t r o n - H 2 e x c i t a t i o n p r o c e s s e s o n t h e n e u t r a l g a s d e n s i t y t e m p e r a t u r e a n d v i b r a t i o n a l p o p u l a t i o n d i s t r i b u t i o n i s i n v e s t i g a t e d i n a n a t t e m p t t o e v a l u a t e t h e c r e d i b i l i t y o f c o l l i s i o n i n d u c e d h e a t i n g u n d e r d i s c h a r g e c o n d i t i o n s s i m i l a r t o t h o s e o f a h i g h - f r e q u e n c y l a b o r a t o r y d i s c h a r g e . T h e r e s u l t s o f t h e p r e v i o u s s e c t i o n p r o v i d e a b a s i s f o r s e l e c t i o n o f i m p o r t a n c e e x c i t a t i o n , r e l a x a t i o n a n d t r a n s p o r t p r o c e s s e s a n d a l s o a s a b a s i s f o r i d e n t i f i c a t i o n o f e x c i t e d p r o d u c t e n e r g i e s . G i v e n t h e g r e a t s e p a r a t i o n b e t w e e n t i m e s c a l e s f o r e l e c t r o n - m o l e c u l e a n d m o l e c u l e - m o l e c u l e e n c o u n t e r s t h e d e v e l o p m e n t o f e n e r g y t r a n s f e r m o d e l s p r o c e e d s o n t w o l e v e l s . M a s s a n d e n e r g y t r a n s p o r t p r o c e s s e s i n t h e n e u t r a l c o m p o n e n t o f t h e w e a k l y i o n i z e d g a s a r e m o d e l e d o n a m a c r o s c o p i c l e v e l w i t h t h e n e u t r a l m o l e c u l e s c h a r a c t e r i z e d b y a l o c a l M a x w e l l i a n v e l o c i t y d i s t r i b u t i o n a n d a B o l t z m a n n d i s t r i b u t i o n o v e r ' v i b r a t i o n a l a n d r o t a t i o n a l d e g r e e s o f f r e e d o m . T h e B o l t z m a n n d e s c r i p t i o n i s a c o m p r o m i s e b e t w e e n t h e m a s t e r e q u a t i o n a p p r o a c h a n d a s s u m p t i o n o f c o m p l e t e e q u i l i b r a t i o n b e t w e e n t h e t r a n s l a t i o n a l t e m p e r a t u r e , T , a n d t h e v i b r a t i o n a l t e m p e r a t u r e T v ' T h e d i l u t e e l e c t r o n g a s i s s t r o n g l y n o n - e q u i l i b r i u m a n d i s m o d e l e d o n a m i c r o s c o p i c l e v e l b y s o l u t i o n o f t h e B o l t z m a n n e q u a t i o n f o r ' t h e d i l u t e e l e c t r o n g a s . T h e c a l c u l a t i o n a l a p p r o a c h i s t o s O l v e t h e B o l t z m a n n e q u a t i o n f o r a n e l e c t r o n g a s i n c o l l i s i o n a l c O n t a c t w i t h a n e u t r a l g a s o f c o n s t a n t p r e s s u r e a n d t e m p e r a t u r e . 1 2 0 F r o m t h e e l e c t r o n d i s t r i b u t i o n f u n c t i o n t h e e l a s t i c a n d i n - e l a s t i c e x c i t a t i o n r a t e s a r e c a l c u l a t e d , a s w e l l a s t h e i o n i — z a t i o n a n d d i f f u s i o n c o e f f i c i e n t s . T h e s e e x c i t a t i o n r a t e s a r e t h e n u s e d i n a s e t o f s t e a d y - s t a t e m a s s a n d e n e r g y b a l a n c e e q u a t i o n s f o r t h e n e u t r a l c o m p o n e n t s . T h e s e e q u a t i o n s a r e s o l v e d t o g i v e c o n c e n t r a t i o n a n d t e m p e r a t u r e p r o f i l e s i n a t u b u l a r d i s c h a r g e . T h e e x t e r n a l f i e l d s t r e n g t h s p e c i f i e d i n t h e B o l t z m a n n e q u a t i o n i s m a i n t a i n e d b e l o w t h a t w h i c h r e s u l t s i n a n e x t e n t o f d i s s o c i a t i o n o f 2 0 % . T h i s c a l c u l a t i o n a l a p p r o a c h i s e s s e n t i a l l y a r e g u l a r p e r t u r b a t i o n m e t h o d , a n d i s s i m i l a r t o t h a t o f B r u n e t a n d V i n c e n t . T h e f i r s t p a r t o f t h i s p r o c e d u r e , t h e c a l c u l a t i o n o f e x c i t a t i o n r a t e s f r o m s o l u t i o n o f t h e B o l t z m a n n e q u a t i o n h a s b e e n d e s c r i b e d a n d c a r r i e d o u t b y t h e a u t h o r ( M o r i n , 1 9 8 2 ) . T h e e x c i t a t i o n p r o c e s s e s c o n s i d e r e d a r e t h o s e o f e l a s t i c c o l l i s i o n , X I Z ; ( v = o ) - ) X I Z ; ( v = 1 ) , X 1 : ; ( v = o ) — v b B Z : r e s u l t i n g i n d i s s o c i a t i o n a n d X 1 2 ; ( v = o ) — ~ , g r o u n d s t a t e o f 3 2 + } T h e e f f e c t s o f d i f f u s i o n a n d i o n i z a t i o n a r e a l s o i n c l u d e d . T h e s o l u t i o n t e c h n i q u e i s b a s e d o n t h e L o r e n t z a p p r o x i m a t i o n f o i f t h e d i s t r i b u t i o n f u n c t i o n . T h e s p h e r i c a l h a r m o n i c e x p a n s i o n i s e s s e n t i a l l y a r e g u l a r p e r t u r b a t i o n a p p r o a c h i n w h i c h a n i s o t r o p i c d i s t r i b u t i o n i s t h e r e d u c e d t e r m o f t h e s e r i e s . F o r a O n e - d i m e n s i o n a l , e x t e r n a l e l e c t r i c f i e l d w h i c h i s p e r i o d i c ‘ W i t h f r e q u e n c y w t h e e x p a n s i o n i n s p h e r i c a l h a r m o n i c s c o l l a p s e s i n t o a n e x p a n s i o n i n L e g e n d r e p o l y n o m i a l s . ( a . e + 5 . ) 5 % : + ( 8 . 6 + 5 . 5 3 % * ( “ 4 “ 5 4 5 5 ; = 0 ( 1 3 2 ) 1 2 1 f ( r , v , t ) = 3 ? f k ( r , v , t ) P k ( c o s 8 ) 1 4 : 0 S u b s t i t u t i o n o f t h e i n f i n i t e s e r i e s i n t o t h e B o l t z m a n n e q u a t i o n y i e l d s a n i n f i n i t e s e t o f c o u p l e d i n t e g r o - p a r t i a l d i f f e r e n t i a l e q u a t i o n s , e a c h o f a f i n i t e n u m b e r o f t e r m s . T h e L o r e n t z a p p r o x i m a t i o n i s b a s e d o n t h e n a t u r e o f e l e c t r o n - m o l e c u l e c o l l i s i o n s t o r a n d o m i z e t h e d i r e c t i o n a l e l e c t r o n m o t i o n . I f t h e h i e r a r c h y i s t r u n c a t e d a f t e r t h e s e c o n d e q u a t i o n t h e n t h e t w o e q u a t i o n s m a y b e c o m b i n e d t o g i v e o n e e q u a t i o n . A d e t a i l e d d e s c r i p t i o n o f t h e e x p a n s i o n p r o c e d u r e m a y b e f o u n d i n t h e a u t h o r ' s p r e v i o u s w o r k . T h e r e s u l t i s a l i n e a r s e c o n d o r d e r h o m o g e n e o u s o r d i n a r y d i f f e r e n t i a l e q u a t i o n w i t h v a r i a b l e c o - e f f i c i e n t s . T h e i n d e p e n d e n t v a r i a b l e h a s b e e n c h a n g e d f r o m s p e e d t o e n e r g y ( u n i t s o f e v ) . T h e c o e f f i c i e n t s o f e q n . 1 3 2 , e u g . 0 , a r e c o n s t a n t , b u t w i t h v a l u e s t h a t a r e d i f f e r e n t o v e r e a c h o f S e V e n i n t e r v a l s o f t h e e n e r g y d o m a i n . T h e d i v i s i o n o f t h e d c ” m a i n i n t o i n t e r v a l s i s d i r e c t l y r e l a t e d t o t h e t h r e s h h o l d s f o l ? t h e t h r e e i n e l a s t i c c o l l i s i o n s . T h e s o l u t i o n s o n e a c h i n t e r v a l a r e o b t a i n e d b y m a t c h i n g t h e d i s t r i b u t i o n f u n c t i o n a n d . i t s f i r s t d e r i v a t i v e a t e a c h t h r e s h h o l d . T h e g e n e r a l s o l u t i o n ‘ 1 5 e q n . 1 3 2 i s g i v e n b y t h e f o l l o w i n g e x p r e s s i o n a n d i n v o l v e s t h e c o n f l u e n t h y p e r g e o m e t r i c f u n c t i o n . £ 6 ) : . 4 4 ) . . ) M L - . . ¢ I l ¢ 2 - E i ; Q E . I n ‘ n o r m i ' . l - » a O ) + ¢ ‘ : " ‘ ~ f ° - c * " “ " 7 } ( 1 3 3 ) 1 . 1 ( Q . - y q o “ ) V " r + c ' o m c o n s i a w f s M [ a t , f , 7 ] E C O W ‘ H H C W " h y p e r g e o m h o ’ c 1 2 2 ( 1 , 0 1 3 + 5 1 + e , ) / ( 2 q , , ) . + a . ) 0 l l ( 3 ( I ( G a l a , " ‘ ( 3 . 5 0 ) / Q : 1 ] : - r : < 5 4 5 1 ¢ q u 0 . 1 — 7 4 0 4 , ) / 0 . ‘ F u n c . ( ' I ' o V \ F r o m t h e d i s t r i b u t i o n f u n c t i o n t h e d i f f u s i o n c o - e f f i c i e n t , e l e c t r o n m o b i l i t y a n d i n e l a s t i c c o l l i s i o n f r e q u e n c i e s 3 1 1 2 c a l c u l a t e d . T h e c o l l i s i o n f r e q u e n c i e s a r e a c t u a l l y r e p o r t e d a s c o l l i s i o n e f f i c i e n c i e s , t h a t i s , a s t h e r a t i o o f t h e C D l l i s i o n f r e q u e n c y f o r t h e p a r t i c u l a r i n e l a s t i c c o l l i s i o n t o t h e t o t a l m o m e n t u m t r a n s f e r c o l l i s i o n f r e q u e n c y . T h e r e s u l t s O f t h e c a l c u l a t i o n s a r e g i v e n i n F i g u r e 9 a s p l o t s o f t h e c O l l i s i o n e f f i c i e n c i e s 3 g t h e e f f e c t i v e e l e c t r i c f i e l d t o P r e s s u r e r a t i o . n a ( ° ‘ H 1 , . “ ) P 1 L 3 + r a f ' A l s o p l o t t e d a r e r e s u l t s o f a M a x w e l l i a n a p p r o x i m a t i o n t o t h e d i s t r i b u t i o n f u n c t i o n . A l l c o l l i s i o n e f f i c i e n c i e s a r e c a l c u l a t e d f o r w e a k l y i o n i z e d d i l u t e H a t 3 0 0 K a n d s o i n 2 c a l c u l a t i o n s w h i c h f o l l o w , e v e r y a t t e m p t i s m a d e t o m a i n t a i n d i s c h a r g e c o n d i t i o n s n e a r t h i s p o i n t . T h e d e v e l o p m e n t o f t h e b a l a n c e e q u a t i o n s f o r t h e t u b u l a r d i s c h a r g e i s m a d e f r o m e q n . 6 6 . B a l a n c e e q u a t i o n s f o r m a s s a n d e n e r g y a r e d e v e l o p e d b u t a c o n s t a n t p r e s s u r e c o n d i t i o n i s p l a c e d o n t h e m o d e l , a r e a s o n a b l e c o n d i t i o n f o r d i l u t e g a s i n s h o r t ( A ' l O c m ) t u b e s . T h e s t e a d y - s t a t e m a s s b a l a n c e o n H 2 i s g i v e n b y t h e f o l l o w i n g e q u a t i o n . . d e . - R . d v ( 1 3 4 ) A v N 1 m a s s f l u x o f H 2 R 1 m a s s p r o d u c t i o n r a t e o f H 2 T h e f o r m o f t h e m a s s f l u x t e r m d e p e n d s o n t h e w a y t r a n s p o r t e f f e c t s a r e m o d e l e d . B o t h t h e f u l l y h o m o g e n e o u s ( C S T R ) a n d a x i a l l y s e g r e g a t e d t u b u l a r ( P F R ) m o d e l s a r e i n v e s t i g a t e d a s s i m p l e l i m i t i n g c a s e s . I n l i g h t o f t h e g r e a t s e p a r a t i o n b e t w e e n e l e c t r o n - m o l e c u l e a n d m o l e c u l e - m o l e c u l e t i m e s c a l e s i t i s e x p e c t e d t h a t t h e e l e c t r o n - m o l e c u l e p r o c e s s e s R = R ( u . ’ r ) / R ( u o r ’ 7 0 ) 1 2 4 d o m i n a t e t h e t r a n s p o r t e f f e c t s . F o r t h e C S T R m o d e l t h e v o l u m e V i n e q n . 1 3 4 i s t h e e n t i r e d i s c h a r g e v o l u m e a n d t h e s u r f a c e i n t e g r a l v a n i s h e s e v e r y w h e r e e x c e p t a t t h e e n t r a n c e a n d e x i t t o t h e d i s c h a r g e . T h e m a s s b a l a n c e o n H t a k e s t h e 2 f o l l o w i n g f o r m f o r a c o n s t a n t p r e s s u r e d i s c h a r g e . 1 ' fl — + D a R = 0 ( 1 3 5 ) 1 + u ? u = d i m e n s i o n l e s s c o n c e n t r a t i o n o f H 2 7 = d i m e n s i o n l e s s t e m p e r a t u r e D a - V R ( u ° , ' 1 ' . ) / f o = D a m k o h l e r n u m b e r F o r t h e a x i a l l y s e g r e g a t e d P F R m o d e l t h e d i f f e r e n t i a l f o r m o f e q n . 1 3 4 i s u s e d b y t r a n s f o r m i n g t h e s u r f a c e i n t e g r a l i n t o a v o l u m e i n t e g r a l . F o r t h e P F R m o d e l t h e m a s s f l u x o f H 2 i s g i v e n b y t h e p r o d u c t o f t h e a v e r a g e v e l o c i t y a n d t h e H 2 c o n c e n t r a t i o n . T h e r e s u l t i n g b a l a n c e e q u a t i o n , i n d i m e n s i o n l e s s f o r m , i s g i v e n b y t h e f o l l o w i n g e q u a t i o n . d ( u T ) = Q g ( l + u 7 ) 2 R ( 1 3 6 ) d s 2 T h e d i m e n s i o n l e s s r a t e e x p r e s s i o n s i n e q n s . 1 3 5 a n d 1 3 6 i n v o l v e d i s s o c i a t i o n o f H b y d i r e c t e l e c t r o n i m p a c t t o t h e 2 b 3 z : : s t a t e a n d a l s o b y a v i b r a t i o n a l l a d d e r - c l i m b i n g m o d e l . T h e r a t e e x p r e s s i o n s a l s o i n v o l v e r e c o m b i n a t i o n b y r e a c t i o n a t t h e t u b e w a l l a n d t h r e e b o d y h o m o g e n e o u s p r o c e s s e s . T h r e e r e c o m b i n a t i o n r e a c t i o n s a r e c o n s i d e r e d . 1 2 5 H + H + H - l — ( — 2 — 2 - ) H 2 + H 1 1 2 + H + H 3 5 3 - 1 4 2 1 5 H + H H w a l l 2 2 1 a n d k 2 2 a r e c a l c u l a t e d f r o m h a r d s p h e r e k i n e t i c t h e o r y a n d k w i s c a l c u l a t e d T h e r e c o m b i n a t i o n c o e f f i c i e n t s k i n t e r m s o f a t h e r m a l s p e e d o f a h y d r o g e n a t o m a n d a n a c c o m m o d a t i o n c o e f f i c i e n t 1 ' . T h e m o l a r p r o d u c t i o n r a t e o f H 2 d u e t o r e c o m b i n a t i o n p r o c e s s e s i s t h e n g i v e n i n e q n . 1 3 7 . v 3 1 z - T ; W . R a e ” C ° ( k m u , * k a u a ) ” . 1 1 ' ( £ 7 7 7 7 ) _ C O X ’ 1 ’ “ a . ( 1 3 7 ) ‘ R 1 A s s u m i n g c o n s t a n t p r e s s u r e ( ( u + u 2 ) 7 = l ) , e q n . 1 3 7 I m a y b e t r a n s f o r m e d t o t h e f o l l o w i n g . 3 1 W . R , “ = C 0 k m ( ( 1 1 - + a r ( l - u 1 ' ) X ( - u + ) + ( K T , ) ( I ) ! ( ( - u ? ) ( 1 3 8 ) ’ f ' 4 ' a t ” ; ( f « ' V L N o w t h e e x p r e s s i o n i s d i v i d e d t h r o u g h b y t h e l e a d c o e f f i c i e n t C o 3 k 2 1 ( T o ) . T h e c o e f f i c i e n t s k 2 1 a n d k 2 2 h a v e a f a c t o r o f T a 5 w h i c h i s f a c t o r e d o u t b e f o r e t h e e x p r e s s i o n i s d i v i d e d t h r o u g h . T h e f i n a l r e s u l t i s t h e d i m e n s i o n l e s s p r o d u c t i o n r a t e o f H 2 d u e t o r e c o m b i n a t i o n . _ S fi 1 _ V i R m = 4 ' ( d u u r C I - a n y h m ) + 0 ( S . ( l - u ’ ) ' ) ’ r V t I ( 1 3 9 ) . . k ( W t r ) x a - 1 1 0 q : O 1 2 6 N o w c o n s i d e r t h e r a t e t e r m s c o r r e s p o n d i n g t o d i s s o c i a t i o n o f H T h e d i r e c t e l e c t r o n i m p a c t d i s s o c i a t i o n r a t e c o n s t a n t 2 . i s o b t a i n e d f r o m t h e e x c i t a t i o n e f f i c i e n c y c a l c u l a t e d i n e a r l i e r w o r k a n d p r e s e n t e d i n F i g u r e 9 . T h e m o l a r l o s s r a t e o f H 2 d u e t o e x c i t a t i o n o f t h e b B Z f : s t a t e m a y b e w r i t t e n a s e q n . 1 4 0 . R 0 3 = “ 6 2 1 / ( 1 3 ) ( 1 4 0 ) N A 1 ’ I ) = m o m e n t u m t r a n s f e r c o l l i s i o n f r e q u e n c y n e = e l e c t r o n d e n s i t y N A = A v o g a d r o s n u m b e r D i s s o c i a t i o n t h r o u g h t r a n s i t i o n s f r o m X 1 2 : ; ( v = 1 3 ) t o t h e c o n t i n u u m i s c a l c u l a t e d b y m o d e l i n g t h e v i b r a t i o n a l d i s t r i b u t i o n a s a B o l t z m a n n d i s t r i b u t i o n a t t e m p e r a t u r e T k j l h F o r n n o n d e g e n e r a t e v i b r a t i o n a l l e v e l s t h e f r a c t i o n o f H 2 i n l e v e l v = j i s r e p r e s e n t e d b y t h e f o l l o w i n g . f j = e x p ( - E § / R T ) ( 1 4 1 ) i e x p ( - ( S i / R T ) i = o F o r d i s s o c i a t i o n f r o m t h e u p p e r m o s t l e v e l , t h e d i m e n s i o n l e s s r a t e e x p r e s s i o n m a y b e w r i t t e n a s t h e f o l l o w i n g . 1 2 7 . 1 0 . 0 9 _ , _ _ S o l u t i o n - - - M a x w e l l i a n f i t . 0 7 - . 0 6 b . 0 5 - . 0 4 v I v I ’ \ o I . . . , ’ D i s s o m a t l v e . 0 3 . . - - ° 2 ‘ V i b r a t i o n a l , I , . 0 1 r ' I o n i z a t i o n ' 7 5 . 0 1 0 0 . 1 2 5 . 1 5 0 . 1 7 5 . E / p ( m 2 - c ' 1 ) F i g u r e 9 : C o l l i s i o n e f f i c i e n c i e s o f v i b r a t i o n a l a n d e l e c t r o n i c e x c i t a t i o n p r o c e s s e s i n p u r e H 2 c o m p a r e d w i t h t h e r e s u l t s o f a M a x w e l l i a n c u r v e - f i t . 3 3 u . z ; ( “ " 0 x e 1 2 8 - V t 6 % + ‘ r l ~ d . 0 v “ 3 U ‘ ? ' S u < ) ) . 8 7 3 7 ' 0 1 : 0 a ) = ’ k u < 7 3 > / / k H C T Z ) a , = m m / c . k , . < 7 : ) T h e d i m e n s i o n l e s s r a t e e x p r e s s i o n i n e q n . 1 3 5 a n d 1 3 6 m a y n o w b e w r i t t e n i n t e r m s o f e q n . 1 3 9 , 1 4 0 a n d 1 4 2 . 5 ’ 2 v 5 7 R : O l a ? + 0 6 . ? + u t - ( ’ l ' < l ~ 3 a l a > - d 5 3 7 - ) - r / _ / + ” 2 1 % ? 1 6 ‘ 5 " » * “ 3 1 % 1 : 1 ( l ‘ 8 1 ) ) ( 1 4 3 ) - V L — c l ° 7 / n e " a l s o ) ? ( f ' w fl r o ‘ d m E n - fi g 2 3 % . 1 . . . ) « ( 8 ) — ' — ° 1 ’ 6 3 4 / . 8 . 0 3 ) N o w c o n s i d e r t h e s t e a d y - s t a t e e n e r g y b a l a n c e s . O n e I n a y w r i t e b a l a n c e s o v e r t h e t r a n s l a t i o n a l - r o t a t i o n a l a n d ‘ V i b r a t i o n a l d e g r e e s o f f r e e d o m s e p a r a t e l y a n d c o u p l e t h e t w o e q u a t i o n s w i t h t h e V T t e r m s . T h e g e n e r a l b a l a n c e e q u a t i o n I n a y b e w r i t t e n a s t h e f o l l o w i n g . [ € 2 9 . 8 4 = S s d l ’ A ( 1 4 4 ) S t = e + W ) 6 a " " . 1 4 . + Z R 1 2 1 ( 6 . u . + 4 . u , ) + m u m “ ) ( 1 4 7 ) 1 2 9 A s b e f o r e , f o r t h e C S T R m o d e l t h e s u r f a c e i n t e g r a l v a n i s h e s e v e r y w h e r e e x c e p t a t t h e e n t r a n c e a n d e x i t . A 6 1 / - A ( 7 1 1 / e v s . ( 1 4 5 ) f ’ e x i ' l ’ l 0 J fl h u t t J F o r t h e P F R m o d e l t h e s u r f a c e i n t e g r a l i s t r a n s f o r m e d t o a v o l u m e i n t e g r a l , t h e i n t e g r a n d i s c o l l e c t e d i n t o o n e t e r m a n d t h e f o l l o w i n g d i f f e r e n t i a l b a l a n c e e q u a t i o n r e s u l t s . g _ 0 1 1 . ) = 5 . d z ) ” 3 3 ( 1 4 6 ) F o r a p a r t i a l l y d i s s o c i a t e d d i a t o m i c g a s t h e t r a n s l a t i o n a l a n d r o t a t i o n a l c o m p o n e n t o f t h e t o t a l s p e c i f i c e n t h a l p y m a y b e e x p r e s s e d i n t e r m s o f t h e c o m p o s i t i o n . C O “ 0 m ) * C o a l m 1 F o r p u r e H a t f e e d c o n d i t i o n s t h e e n t h a l p y r e d u c e s t o 2 7 R T . / 2 M , a s e x p e c t e d . T h e f i r s t t e r m o n t h e r i g h t - h a n d s i d e i s t h e e n e r g y o f f o r m a t i o n o f h y d r o g e n a t o m s . T h e s e c o n d t e r m i s t h e t r a n s l a t i o n a l t e r m a n d t h e t h i r d i s t h e r o t a t i o n a l t e r m . T h e l a s t t e r m c o r r e s p o n d s t o t h e p r e s s u r e . T h e e x p r e s s i o n f o r t h e t r a n s l a t i o n a l - r o t a t i o n a l e n t h a l p y i s n o r m a l i z e d t o t h e f e e d c o n d i t i o n v a l u e . k z a fi ) ( | - u + ) + ( 1 1 3 + ’ 4 4 ) T 7 I + u ) : ( 1 4 8 ) ( e 5 ( 5 3 ) ( _ g _ 1 1 7 . = = = ” “ 4 1 “ ? ) ( $ 3 5 ) 0 " N ' o _ > 3 9 0 % . ) ' 4 . J r t . f o i p f fi ) ( x k ) ' é - . E ( ( 1 1 5 5 0 1 ) ) R V T ‘ : ( E l - 6 ° ) ( K ) ; + K ; ) C , u , 1 e ( v = ( ) 1 3 0 T h e v i b r a t i o n a l c o n t r i b u t i o n t o t h e t o t a l s p e c i f i c e n t h a l p y i s b a s e d o n t h e h a r m o n i c o s c i l l a t o r a p p r o x i m a t i o n f o r t h e v i b r a t i o n a l p a r t i t i o n f u n c t i o n . I n t h e n o r m a l i z e d f o r m i t i s g i v e n b y e q n . 1 4 9 . ( 1 4 9 ) I - e x P ( a t } I n t h e b a l a n c e o v e r t h e t r a n s l a t i o n a l - r o t a t i o n a l m o d e t h e r e a r e t h r e e s o u r c e t e r m s a n d o n e e n e r g y l o s s t e r m . E n e r g y i s t r a n s f e r e d t o t h i s m o d e b y e l a s t i c e l e c t r o n - n e u t r a l c o l l i s i o n s , V T r e l a x a t i o n p r o c e s s e s a n d t h e r m a l i z a t i o n o f t h e k i n e t i c e n e r g y o f d i s s o c i a t i o n p r o d u c t s . E n e r g y i s r e m o v e d E E Q E t h i s m o d e b y c o n t a c t w i t h t h e d i s c h a r g e b o u n d a r y . T h e s o u r c e t e r m i d e n t i f i e d w i t h e l a s t i c c o l l i s i o n s b e t w e e n e l e c t r o n s a n d n e u t r a l s m a y b e c a l c u l a t e d i n t h e f o l l o w i n g w a y . ‘ ” Q Q ' 4 ! ( 1 1 6 ) 6 ‘ ( 4 : 7 5 : 4 2 ) : . 1 : [ V M T h e s e c o n d s o u r c e t e r m i s t h a t d u e t o V T r e l a x a t i o n . . + T h e r a t e o f e n e r g y e x c h a n g e d u e t o r e l a x a t 1 o n f r o m X l z : g ( v = l ) m a y b e w r i t t e n a s t h e f o l l o w i n g . ( 1 5 2 ) T h e r a t e c o e f f i c i e n t s i n e q n . 1 5 2 a r e r e l a t e d t o 1 3 1 t r a n s i t i o n p r o b a b i l i t i e s t h r o u g h t h e f o l l o w i n g . V 1 . _ ' 1 E l ” k I a . P l o fi c l ( “ # 1 ) M 6 0 ” . ( 1 5 3 ) I I , - 2 1 1 K 1 0 = P i a " d L k T ) M C ) “ ; ( 1 5 4 ) 0 , 4 T h e t r a n s i t i o n p r o b a b i l i t i e s h a v e b e e n m e a s u r e d b y A u d i b e r t g i g i ( 1 9 7 5 ) a n d H e i d n e r a n d K a s p a r ( 1 9 7 2 ) . T h e f o l l o w i n g e x p r e s s i o n s a r e c u r v e f i t s o f t h e i r d a t a . 1 - V 3 P “ , = E X P < ~ 9 7 ' 1 - ‘ - 1 . 5 . 3 3 ) ( 1 5 5 ) 1 - ‘ V ’ 9 7 ) ( 1 5 6 ) p “ , - e x p < - S ’ W T + ‘ 5 - T h e e n t i r e s o u r c e t e r m m a y t h e n b e w r i t t e n a s t h e f o l l o w i n g . 1 1 - 2 2 . 1 I z 1 R V r = 4 r d 1 4 c . , , . ( ( 5 5 , ) ( u 1 » ( P . . - P . . ) + w r ( 0 . . ) 0 ‘ e x p ( { I I - 8 . ) . ) 1 : 0 R e l a x a t i o n o f l e v e l s a b o v e v = 1 a l s o o c c u r a n d t r a n s i t i o n ‘ p r o b a b i l i t i e s f o r t h e s e a r e c a l c u l a t e d b y l i n e a r s c a l i n g i n v . T h e t o t a l V T r e l a x a t i o n e n e r g y t r a n s f e r r a t e i s g i v e n i n e q n . 1 5 8 . s e u o s l u p a r o t c n e e d d i r t n i e n g m t t o e f r o V m r T s r X o e f = t Z l a g t ( x h v a e - n i o e ) o x 1 6 0 ) ? ( V — 1 ) ( — . c i t a t i o n ’ l r a c a r e o ‘ n a s = r a r u a c n d l t h e a l e A V t o e t l t a w s e o s m d A a ( e e a t t e y T r r b r f o l l o w i ) r m a r r . - T d c f e o o r m e l m n i s g , . f e T e t r x h f e c e f e i i d e t c o x a i m t c e t h e i i n o t c a n y t i h e n g i v e n 1 3 2 R ’ fi d z M C ’ : 0 1 , 1 1 " ‘ e ( 9 “ ’ ) % ’ . u + " ( . u r ) r > ( “ 7 7 ’ Z V ( E v - f a ) £ ( V ) V ‘ — ' l T h e t h i r d s o u r c e t e r m c o r r e s p o n d s t o t h e t h e r m a l i z a t i o n ( 1 5 8 ) o f t h e k i n e t i c e n e r g y o f d i s s o c i a t i o n p r o d u c t s . 7 7 ‘ _ . 3 ’ 6 1 ' ( ~ ) ” " 6 6 " ( 1 5 9 ) ‘ l / E } = a v e r a g e e n e r g y o f d i s s o c i a t i o n p r o d u c t T h e e n e r g y l o s s t e r m i n t h e t r a n s l a t i o n a l - r o t a t i o n a l e n e r g y b a l a n c e i s t h a t c o r r e s p o n d i n g t o t h e e f f e c t o f t h e d i s c h a r g e b o u n d a r y a n d i s c o n s t r u c t e d i n t e r m s o f a t e m p e r a t u r e d r o p a n d a n o v e r a l l t r a n s f e r c o e f f i c i e n t . 3 F o r t h e e n e r g y b a l a n c e o v e r t h e v i b r a t i o n a l d e g r e e o f 1 4 / ” c E ' ” ( I ’ ( 7 ) 4 4 ( 6 ' ° ) ( 1 6 1 ) T h e r e l a x a t i o n t e r m i s i d e n t i c a l t o e q n . 1 5 7 o r 1 5 8 . T h e c O m p l e t e s e t o f b a l a n c e e q u a t i o n s f o r t h e C S T R m o d e l i s 8 ) ) I E h r / _ _ L r / . _ _ 4 { M e t V 1 . 7 F R T ; ( 1 1 ' + R " , + 1 1 1 ~ 0 3 ) ( 1 6 2 ) V i b r a t i o n a l t e m p e r a t u r e o f t h e C S T R a n d P F R m o d e l s . F i g u r e s 1 3 a n d 1 3 3 - 2 V _ L ‘ v / - ' L ‘ v “ * 7 : ( 4 T ‘ I R V ? ) ( 1 6 3 ) c m " ) i n l e ‘ l ’ 7 F 0 ° F o r t h e P F R m o d e l t h e b a l a n c e e q u a t i o n s a r e i d e n t i c a l e x c e p t t h a t t h e l e f t h a n d s i d e o f e q n s . 1 6 2 a n d 1 6 3 a r e r e p l a c e d b y d h / d s . d — k T ’ : “ 2 v “ 1 + R V ? + fi 1 ~ ” 3 ) ( 1 6 4 ) a s 7 ‘ 5 “ — V é l ‘ u ' = i . _ _ _ . ( fl . , ‘ R u e ( 1 6 5 ) d s 7 5 . " E q u a t i o n s 1 3 5 , 1 6 2 a n d 1 6 3 a n d e q n s . 1 3 6 , 1 6 4 a n d 1 6 5 c o n s t i t u t e t w o s e t s o f m o d e l e q u a t i o n s f o r t h e c o n c e n t r a t i o n a n d t e m p e r a t u r e v a l u e s ( C S T R ) o r f i e l d s ( P F R ) i n a w e a k l y i o n i z e d d i l u t e g a s d i s c h a r g e i n H 2 . T h e r e s u l t s o f n u m e r i c a l s o l u t i o n o f t h e t w o s e t s o f m o d e l e q u a t i o n s a r e p r e s e n t e d i n F i g u r e s 1 0 - 1 4 a n d T a b l e I I I . F i g u r e s 1 0 a n d 1 1 p r e s e n t t h e r e l a t i v e c o n t r i b u t i o n s o f e l a s t i c a n d t h e t w o i n e l a s t i c p r ‘ 3 ‘ = e ( S s e s t o t h e g a s h e a t i n g r a t e a s a f u n c t i o n o f p r e s s u r e ( 1 0 0 ‘ 7 0 0 N / m 2 ) a t t w o H 2 f e e d r a t e s . F i g u r e 1 2 , a , b a n d c c o m p a r e s r e s u l t s f o r e x i t s t r e a m c o n v e r s i o n , t e m p e r a t u r e a n d r a t e s a t h i g h e r p r e s s u r e s , r e s u l t i n g i n d e p o p u l a t i o n o f u p p e r 1 3 4 1 J 4 p r e s e n t c o n c e n t r a t i o n a n d t e m p e r a t u r e p r o f i l e s a t t w o d d n f f e r e n t p r e s s u r e s . T a b l e I I I p r e s e n t s t h e c a l c u l a t e d c c u a t r i b u t i o n o f t h e v i b r a t i o n a l l a d d e r - c l i m b i n g m e c h a n i s m t c > t h e t o t a l d i s s o c i a t i o n r a t e . M o l i n a r i ( 1 9 7 4 ) d e v e l o p e d a m o d e l f o r d i s s o c i a t i o n o f d i j a t o m i c s i n a w e a k l y i o n i z e d d i l u t e g a s w h i c h i n c l u d e d o n l y t h e c o n t r i b u t i o n f r o m c o l l i s i o n i n d u c e d d i s s o c i a t i o n f r o m t J i e z n e a r - c o n t i n u u m v i b r a t i o n a l l e v e l s . H e c l a i m e d t h a t d i r e c t e l e c t r o n i m p a c t d i s s o c i a t i o n w a s n o t s u f f i c i e n t t o e x p l a i n e x p e r i m e n t a l m e a s u r e m e n t s . T o e x a m i n e M o l i n a r i ' s c l a i m t h e f r t a c t i o n o f t h e d i s s o c i a t i o n r a t e c o n t r i b u t e d b y t h e v i b r a t i o n a l l a x i d e r - c l i m b i n g m e c h a n i s m w a s c a l c u l a t e d a n d t a b u l a t e d i n T a b l e I I I f o r a r a n g e o f p r e s s u r e ( 5 0 - 7 0 0 N / m z ) . T a b l e I I I . V i b r a t i o n a l c o n t r i b u t i o n ( f v ) t o t h e t o t a l d i s s o c i a t i o n r a t e P r e s s u r e N / m 2 f v 5 0 . 0 0 9 5 1 0 0 5 . 5 ( 1 0 ' 5 ) 4 0 0 0 . 0 7 0 0 0 . 0 T h e g a s f l o w r a t e h a d n o e f f e c t o n t h e o r d e r o f m a g n i t u d e o f t h e v a l u e s o f f v ' T h e r e d u c t i o n o f f v t o e s s e n t i a l l y z e r o a t 4 0 0 N / m 2 i s d u e t o i n c r e a s e d V T r e l a x a t i o n 1 3 5 v i b r a t i o n a l s t a t e s . T h e h i g h d i s s o c i a t i o n r a t e s o f C a c c i a t o r e g i g a _ l ( 1 9 7 8 ) a r e v e r y u n l i k e l y i n l i g h t o f t h i s e f f e c t . B a s e d o n t h e s e c a l c u l a t i o n s , t h e p r e s e n c e o f v i b r a t i o n a l s t r u c t u r e p l a y s n o d i r e c t r o l e i n d i s s o c i a t i o n o f H 2 a t p r e s s u r e s o f l O O — 7 0 0 N / m z . T h e t h r e e c o l l i s i o n p r o c e s s e s i n t h i s m o d e l w h i c h c o n t r i b u t e t o c o l l i s i o n i n d u c e d h e a t i n g a r e t h o s e o f e l a s t i c c o l l i s i o n s , V T r e l a x a t i o n a n d d i s s o c i a t i o n b y e x c i t a t i o n o f t h e l o w e s t t r i p l e t s t a t e o f H 2 . I n F i g u r e s 1 0 a n d 1 1 t h e f r a c t i o n e a c h c o n t r i b u t e s t o t h e t o t a l h e a t i n g r a t e i s g i v e n o v e r a r a n g e o f p r e s s u r e ( 1 0 0 - 7 0 0 N / m z ) a n d f e e d g a s f l o w r a t e ( 1 0 0 - 1 0 0 0 m o l e s / s ) . T h e e l e c t r o n d e n s i t y i s c o n s t a n t a t 3 6 . 7 ( 1 0 1 6 ) m — a n d t h e a v e r a g e e l e c t r o n e n e r g y i s 6 . 2 5 e v , c a l c u l a t e d f r o m t h e w o r k o f M o r i n f o r a n e f f e c t i v e H e l p o f 7 5 m 2 . c - 1 . U n d e r t h e s e c o n d i t i o n s i t i s p o s s i b l e t h a t t h e t h e r m a l i z a t i o n o f h y d r o g e n a t o m s h a v i n g h i g h k i n e t i c e n e r g y d o m i n a t e s t h e e n e r g y t r a n s f e r f r o m t h e e l e c t r o n g a s t o t h e n e u t r a l g a s . T h e r e l a t i v e c o n t r i b u t i o n t o g a s h e a t i n g d u e t o V T r e l a x a t i o n i s l e s s t h a n 1 0 % , w i t h e l a s t i c h e a t i n g i n t e r m e d i a t e b ( i f - W e e n V T r e l a x a t i o n a n d t h e r m a l i z a t i o n o f d i s s o c i a t i o n p r o d u c t s . A l t h o u g h F i g u r e s 1 0 a n d 1 1 p r e s e n t c a l c u l a t i o n s f o r t h e C S T R “ “ 3 5 9 1 , F i g u r e 1 2 a , b , c i n d i c a t e t h a t t h e P F R a n d C S T R m o d e l s g i v e e s s e n t i a l l y i d e n t i c a l r e s u l t s f o r t h e c o n d i t i o n o f t h e g a s s t r e a m a t t h e d i s c h a r g e e x i t . T h e t i m e s c a l e s f o r e l e c t r o n - m o l e c u l e P r o c e s s e s a r e s i m p l y t o o s h o r t i n c o m p a r i s o n t o t h a t O f a x i a l c o n v e c t i v e t r a n s p o r t f o r t h e a x i a l s e g r e t a t i o n t o 1 3 6 1 . 0 0 . 9 0 . 8 e f 0 - 7 " D i s s o c i a t i o n 0 . 6 ) - F o = 1 . ( 1 0 ’ 3 ) m o l e s / s I 0 . 5 ) - 0 . 4 h 0 ' 2 i ' E l a s t i c 0 . 1 I f / . l J 1 1 1 1 1 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 P r e s s u r e ( N / m z ) I 1 fi g u r e 1 0 : R e l a t i v e c o n t r i b u t i o n o f t h r e e r e l a x a t i o n p r o c e s s e s t o t h e t o t a l g a s h e a t i n g r a t e f o r p r e s s u r e s o f 1 0 0 - 7 0 0 u m 2 a n d a H 2 m o l a r f l o w r a t e o f 1 ( 1 0 - 3 ) m o l e s / s . 1 3 7 1 . 0 0 . 9 _ F o = l . ( 1 0 ' 4 ) m o l e s / s 0 . 8 , . 0 , 7 D i s s o c i a t i o n / 0 . 6 0 . 5 . 0 . 4 ) - 0 . 3 ) - 0 . 2 _ E l a s t i c 0 . 1 i ’ _ _ [ V T 1 1 1 1 1 L l 1 0 0 . 2 0 0 . 3 0 0 . 4 0 0 . 5 0 0 . 6 0 0 . 7 0 0 . 8 0 0 . 2 ) P r e s s u r e ( N / m F l g u I r e z l l : R e l a t i v e c o n t r i b u t i o n o f t h r e e r e l a x a t i o n p r o c e s s e s t o t h e t o t a i g a s h e a t i n g r a t e f o r p r e s s u r e s o f _ 4 1 0 0 - 7 0 0 N / m a n d a H 2 m o l a r f l o r r a t e o f l ( 1 0 ) m o l e s / s . 1 3 8 . 2 5 c . 2 0 a . g r P F R g . . 1 5 _ 5 l O U ' 1 0 ’ C S T R . 0 5 . . b a , 3 . 0 _ 5 P F R ‘ é \ \ o g ' 2 0 C S T R m b ) — 2 1 . 0 1 1 1 1 1 e L a b . . P F R c m - I a 1 1 ) - Q ) - E . . 2 ) - 3 6 . 0 ) - ‘ é . . c : ' - fl > 1 . 0 l L 1 i L 1 1 1 F i g u l f e 1 2 : a ) b ) C ) 1 0 0 . 2 0 0 . 3 0 0 . 4 0 0 . 5 0 0 . 6 0 0 . 7 0 0 . P r e s s u r e ( N / m z ) E x t e n t o f c o n v e r s i o n f o r p r e s s u r e s o f 5 0 - 7 0 N / m 2 c o m p a r e d i n t h e P F R a n d C S T R a p p r o x i m a t i o n . 2 G a s t e m p e r a t u r e f o r p r e s s u r e s o f 5 0 - 7 0 0 N / m c o m p a r e d i n t h e P F R a n d C S T R a p p r o x i m a t i o n . V i b r a t i o n a l t e m p e r a t u r e f o r p r e s s u r e s o f 5 0 - 7 0 0 N / m c o m p a r e d i n t h e P F R a n d C S T R a p p r o x i m a t i o n . 1 3 9 p r o d u c e m u c h e f f e c t . T h e r e s u l t s o f c a l c u l a t e d t e m p e r a t u r e a n d v i b r a t i o n a l t e m p e r a t u r e p r e s e n t e d i n F i g u r e 1 2 b a n d c i n d i c a t e t h a t t h e t r a n s i t i o n f r o m n o n e q u i l i b r i u m c o n d i t i o n s b e t w e e n t r a n s l a t i o n a l - r o t a t i o n a l a n d v i b r a t i o n a l d e g r e e s o f f r e e d o m t o a n e q u i l i b r i u m o n e t a k e s p l a c e i n a p r e s s u r e r e g i m e o f t h e s a m e o r d e r a s t h e o p e r a t i n g r a n g e o f a m i c r o w a v e f r e q u e n c y d i s c h a r g e . A b o v e 6 0 0 N / m 2 t h e t w o t e m p e r a t u r e s h a v e e s s e n t i a l l y e q u i l i b r a t e d , a l t h o u g h t h e v a l u e o f t h e t h r e s h h o l d p r e s s u r e d e p e n d s o n g a s f l o w r a t e a n d e l e c t r o n g a s p r o p e r t i e s a l s o . A b o v e t h i s t h r e s h h o l d t h e h e a t c a p a c i t y o f m o l e c u l a r h y d r o g e n i s e f f e c t i v e l y 7 R / 2 . T h e e x i s t e n c e o f t h i s l o w p r e s s u r e t h r e s h h o l d i s i m p o r t a n t f o r t h o s e p r o c e s s e s , e . g . g a s h e a t i n g , w h i c h r e q u i r e t h a t e n e r g y i n P u t s t o i n t e r n a l d e g r e e s o f f r e e d o m b e t h e r m a l i z e d . I n F i g u r e s 1 3 a n d 1 4 t h e c o u p l i n g b e t w e e n c o n v e r s i o n 0 f H 2 a n d H , g a s t e m p e r a t u r e a n d v i b r a t i o n a l t e m p e r a t u r e i s i l l u s t r a t e d . I n F i g u r e 1 3 t h e o p e r a t i n g p r e s s u r e i s l o w ( S O N / m 2 ) a n d t h e c o n v e r s i o n , g a s t e m p e r a t u r e a n d v i b r a t i o n a l t e m p e r a t u r e i n c r e a s e i n a m o n o t o n e f a s h i o n d o w n t h e l e n g t h o f t h e d i s c h a r g e z o n e . A t t h i s p r e s s u r e t h e r a t e o f V T r e l a x a t i o n i s l o w a n d s o t h e v i b r a t i o n a l t e m p e r a t u r e i s m u c h h i g h e r t h a n t h e g a s t e m p e r a t u r e . T h e e l e c t r o n - m o l e c u l e c o l l i s i o n f r e q u e n c y i s S m a l l e r a n d s o t h e s o u r c e t e r m s i n t h e t r a n s l a t i o n a l - r o t a t i o n a l e n e r g y b a l a n c e b a r e l y e x c e e d t h e h e a t t r a n s f e r r a t e f r o m t h e d i s c h a r g e z o n e b y c o n v e c t i o n a n d c o n d u c t i o n a n d t h e g a s l e a v e s t h e d i s c h a r g e o n l y 5 0 K h o t t e r t h a n w h e n i t e n t e r e d . ! “ ! 0 O e r s i n 0 F i g u r e 1 3 1 4 0 1 . 0 F 1 ( 1 0 ‘ 3 ) l / 2 0 ' = m o C S 5 . 9 O a 0 " P = 5 0 . N / m z ‘ ' 8 ' 0 8 * « 1 6 0 . 7 . . a 1 4 - 0 6 V i b r a t i o n a l ~ 1 g ' ’ t e m p e r a t u r e " 2 ' 3 0 . 5 - \ . 1 0 . 5 E 0 . 4 ~ J 8 - S 0 . 3 p « 4 0 . 2 _ C o n v e r s u o n T e m p e r a t u r e 0 1 r J 2 . 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1 . 0 A x i a l p o s i t i o n : P F R p r o f i l e s o f e x t e n t o f c o n v e r s i o n , g a s t e m p e r a t u r e a n d v i b r a t i o n a l t e m p e r a t u r e f o r a p r e s s u r e o f 5 0 N / m 2 1 ( 1 0 ' 3 ) m o l e s / s . a n d m o l a r f l o w r a t e o f 1 4 1 L 0 3 2 0 0 9 _ F 0 = 1 . ( 1 0 ) r g o l e s / s b q 1 8 . P = 4 0 0 . N / m 0 8 , ‘ 1 5 0 . 7 . _ 4 1 4 . . 5 0 . 6 . . 1 2 . g ‘ 3 0 . 5 . . 1 0 8 c 8 8 . . . Q 4 " V i b r a t i o n a l 4 8 . S 0 . 3 » / t e m p e r a t u r e < 6 . 0 . 2 » T e m p e r a t u r e . 4 4 . 0 . 1 \ l 2 . ‘ 1 L 1 L C o n v e r s i o n + 1 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1 . 0 A x i a l p o s i t i o n F i g u r e 1 4 : P F R p r o f i l e s o f e x t e n t o f c o n v e r s i o n g a s t e m p e r a t u r e a n d v i b r a t i o n a l t e m p e r a t u r e f o r a p r e s s u r e o f 4 0 0 N / m 2 a n d m o l a r f l o w r a t e o f 1 ( 1 0 ’ 3 ) m o l e S / s . 1 4 2 A t a h i g h e r p r e s s u r e ( 4 0 0 N / m z ) t h e V T r e l a x a t i o n r a t e i s h i g h e r a s a r e t h e e l e c t r o n - H 2 e x c i t a t i o n r a t e s . E a r l y i n t h e d i s c h a r g e z o n e t h e i n c r e a s i n g c o n c e n t r a t i o n o f h y d r o g e n a t o m s c a u s e s r a p i d r e l a x a t i o n o f t h e H v i b r a t i o n a l 2 m a n i f o l d a n d r e s u l t s i n e v e n t u a l e q u i l i b r a t i o n o f t h e k i n e t i c a n d v i b r a t i o n a l t e m p e r a t u r e s . N e a r t h e e n d o f t h e d i s c h a r g e z o n e t h e g a s t e m p e r a t u r e g o e s t h r o u g h a m a x i m u m a n d t h e n s l o w l y d e c r e a s e s . T h i s t e m p e r a t u r e d r o p r e s u l t s i n a n i n c r e a s e i n t h e e l e c t r o n - m o l e c u l e c o l l i s i o n f r e q u e n c y a n d t h u s a n i n c r e a s e i n t h e e x c i t a t i o n r a t e s . T h i s r e s u l t s i n a s l i g h t i n c r e a s e i n t h e c o n v e r s i o n o f H z t o a t o m i c h y d r o g e n a s t h e s t r e a m e x i t s t h e d i s c h a r g e z o n e . T h e r e s u l t s p r e s e n t e d i n F i g u r e 1 4 , i n p a r t i c u l a r , i l l u s t r a t e t h e s t r o n g c o u p l i n g b e t w e e n t h e c o n d i t i o n o f t h e g a s a n d t h e e l e c t r o n - H e x c i t a t i o n r a t e s . 2 T h e r e a r e s e v e r a l p o i n t s t o b e m a d e f r o m t h e s e c a l c u l a t i o n s c o n c e r n i n g t h e f e a s i b i l i t y o f c o l l i s i o n i n d u c e d h e a t i n g o f a w e a k l y i o n i z e d g a s . F i r s t , t h o u g h , r e c a l l t h e t w o m a j o r a s s u m p t i o n s o f t h e m o d e l . T h e f i r s t a s s u m p t i o n h a s t o d o w i t h t h e d e c o u p l i n g o f t h e B o l t z m a n n e q u a t i o n f r o m t h e m a c r o s c o p i c b a l a n c e e q u a t i o n s . T h e e s s e n t i a l a s s u m p t i o n i s t h a t t h e e n e r g y t r a n s f e r r a t e s c a l c u l a t e d f r o m s o l u t i o n o f t h e B o l t z m a n n e q u a t i o n f o r e l e c t r o n m o t i o n i n a g a s o f t e m p e r a t u r e T m a y b e u s e d i n a m a c r o s c o p i c r e a c t o r m o d e l h a v i n g s t e a d y - s t a t e t e m p e r a t u r e s h i g h e r t h a n T . I n t h e s e c o n d a s s u m p t i o n , t h e d i s s o c i a t i o n p r o d u c t s t h e r m a l i z e a l l e x c e s s k i n e t i c e n e r g y o n a t i m e s c a l e o f f l o w t h r o u g h t h e d i s c h a r g e . T h i s i s a 1 4 3 r e a s o n a b l e a s s u m p t i o n i f t h e h i g h e n e r g y a t o m s r e l a x o n a t i m e s c a l e c h a r a c t e r i s t i c o f t h e r m a l a t o m s . T h e s e t w o a s s u m p t i o n s a r e e x a m i n e d i n g r e a t e r d e t a i l l a t e r . O n t h e b a s i s o f t h e s e c a l c u l a t i o n s t h e f o l l o w i n g p o i n t s m a y b e m a d e . 1 . T h e r m a l i z a t i o n o f d i s s o c i a t i o n p r o d u c t s i s a s i g n i f i c a n t c o n t r i b u t i o n t o g a s h e a t i n g i n a l o w p r e s s u r e ( 1 0 0 - 7 0 0 N / M Z ) m i c r o w a v e d i s c h a r g e i n H 2 . 2 . T h e p r i m a r y d i s s o c i a t i o n m e c h a n i s m f o r w e a k l y i o n i z e d H 2 i s g i g e x c i t a t i o n t o t h e b 3 z : : s t a t e . T h e m e c h a n i s m o f C a c c i a t o r e 2 3 E l ( 1 9 7 8 ) i s u n l i k e l y . 3 . A l o w p r e s s u r e t h r e s h h o l d e x i s t s f o r e q u i l i b r a t i o n o f t h e v i b r a t i o n a l a n d t r a n s l a t i o n a l - r o t a t i o n a l d e g r e e s o f f r e e d o m . 4 . T h e p r e s e n c e o f a x i a l s e g r e g a t i o n i n a g a s d i s c h a r g e m o d e l o f H 2 a t l o w p r e s s u r e h a s n o s i g n i f i c a n t e f f e c t o n t h e m o d e l r e s u l t s . 5 . T h e r e i s s t r o n g c o u p l i n g b e t w e e n t h e g a s c o n d i t i o n e . g . t e m p e r a t u r e , a n d t h e e l e c t r o n - m o l e c u l e k i n e t i c s . I n s u m m a r y , t h e r e s u l t s o f t h e s e c a l c u l a t i o n s i n d i c a t e t h a t s i g n i f i c a n t g a s h e a t i n g i s p o s s i b l e i n a l o w p r e s s u r e m i c r o w a v e f r e q u e n c y d i s c h a r g e i n H 2 i n s t e a d y f l o w . B e f o r e d e t a i l e d c a l c u l a t i o n s c o n c e r n i n g a s p e c i f i c l a b o r a t o r y d i s c h a r g e a r e m a d e t h e t w o a s s u m p t i o n s r e f e r r e d t o e a r l i e r r e q u i r e a t t e n t i o n a n d a r e d i s c u s s e d i n t h e l a s t t w o s e c t i o n s o f t h i s c h a p t e r . 1 4 4 3 . 3 . C o u p l e d c a l c u l a t i o n o f c o l l i s i o n i n d u c e d h e a t i n g o f H 2 H i s t o r i c a l l y , m a c r o s c o p i c m o d e l s o f c h e m i c a l r e a c t o r s i n v o l v i n g e l e c t r o n i m p a c t p h e n o m e n a a s s u m e t h a t t h e a v e r a g e e l e c t r o n e n e r g y a n d e l e c t r o n d e n s i t y a r e u n a f f e c t e d b y t h e e n e r g y t r a n s f e r p r o c e s s e s , w h e r e a s t h e e l e c t r o n t r a n s p o r t m o d e l s , b a s e d o n t h e B o l t z m a n n e q u a t i o n , a s s u m e a c o n s t a n t v a l u e f o r t h e n e u t r a l g a s t e m p e r a t u r e a n d d e n s i t y . T h i s m o d e l d i c h o t o m y i s c h a r a c t e r i s t i c o f t h e l i t e r a t u r e o n g a s e o u s e l e c t r o n i c s . A n i m p o r t a n t c o n s i d e r a t i o n i n t h e a n a l y s i s o f c o l l i s i o n i n d u c e d h e a t i n g i s t h e e f f e c t o f t h e g a s h e a t i n g o n t h e s t e a d y - s t a t e d e n s i t y a n d a v e r a g e e n e r g y o f b o t h t h e e l e c t r o n a n d n e u t r a l g a s e s . I n t h e w o r k o f M o r i n a n d H a w l e y ( 1 9 8 4 a , 1 9 8 4 b ) t h e e f f e c t o f t h i s c o u p l i n g o n t h e t e m p o r a l e v o l u t i o n a n d s t e a d y - s t a t e v a l u e s o f t h e e l e c t r o n g a s a n d n e u t r a l g a s d e n s i t i e s a n d a v e r a g e e n e r g i e s i s a n a l y z e d f o r a s p a t i a l l y h o m o g e n e o u s d i l u t e e l e c t r o n g a s i n t e r a c t i n g b y e l a s t i c a n d i n e l a s t i c p r o c e s s e s w i t h a n e u t r a l g a s h a v i n g i n t e r n a l s t r u c t u r e . T h e e f f e c t o f t h i s c o u p l i n g o n t h e i n e l a s t i c e x c i t a t i o n r a t e s i s a l s o s t u d i e d . T h e a n a l y s i s a n d r e s u l t s o f M o r i n a n d H a w l e y a r e r e p r o d u c e d h e r e . T h e p u r p o s e o f t h i s a n a l y s i s i s t o m a k e s e l f - c o n s i s t e n t c a l c u l a t i o n s o f e l e c t r o n g a s a n d n e u t r a l g a s p r o p e r t i e s , g i v e n a n e l e c t r i c f i e l d s t r e n g t h . S i n c e c o u p l e d s o l u t i o n o f t h e B o l t z m a n n e q u a t i o n a n d t h e m a c r o s c o p i c b a l a n c e e q u a t i o n s i s i n v i e w , a s i m p l e r c o l l i s i o n m o d e l i s a t t r a c t i v e . T h e c o l l i s i o n m o d e l i n c o r p o r a t e s e l a s t i c s c a t t e r i n g a n d a w e a k A 3 1 " . A V l 6 l 1 4 5 i n e l a s t i c c h a n n e l w h i c h c o u l d b e i d e n t i f i e d w i t h a r o t a t i o n a l o r e v e n v i b r a t i o n a l e x c i t a t i o n p r o c e s s . A n a l y s i s o f t h i s c o u p l e d p r o b l e m p r o c e e d s w i t h d e f i n i t i o n o f t h e a p p r o p r i a t e f o r m o f t h e B o l t z m a n n e q u a t i o n a n d t h e n t o d e r i v a t i o n o f t h e m a c r o s c o p i c b a l a n c e e q u a t i o n s a n d s i m u l t a n e o u s s o l u t i o n o f t h e e q u a t i o n s i n c l o s e d f o r m . A s i n s e c t i o n 3 . 2 t h e B o l t z m a n n e q u a t i o n f o r t h e e l e c t r o n g a s i s r e d u c e d g i g t h e s p h e r i c a l h a r m o n i c e x p a n s i o n a n d t h e L o r e n t z t r u n c a t i o n a p p r o x i m a t i o n t o a s e t o f p a r t i a l d i f f e r e n t i a l e q u a t i o n s f o r t h e f i r s t t w o c o e f f i c i e n t s o f t h e e x p a n s i o n . T h e s e p a r t i a l d i f f e r e n t i a l e q u a t i o n s a r e r e d u c e d t o o r d i n a r y d i f f e r e n t i a l e q u a t i o n s b y c o m p a r i n g t h e t i m e s c a l e s o f e l e c t r o n - m o l e c u l e , e l e c t r o n - f i e l d p r o c e s s e s a n d t h o s e f o r m o l e c u l e - m o l e c u l e p r o c e s s e s . O n t h e m a c r o s c o p i c r e l a x a t i o n a n d t r a n s p o r t t i m e s c a l e s t h e n e u t r a l g a s e s s e n t i a l l y " s e e s " a n e l e c t r o n g a s a t s t e a d y - s t a t e , a n d s o t h e s t e a d y - s t a t e B o l t z m a n n e q u a t i o n f o r t h e e l e c t r o n g a s i s t h e a p p r o p r i a t e e q u a t i o n . T h e t i m e h a r m o n i c r e s p o n s e o f t h e d i s t r i b u t i o n f u n c t i o n o c c u r s o n a m u c h s h o r t e r t i m e s c a l e t h a n t h a t o f t h e r e l a x a t i o n a n d t r a n s p o r t p r o c e s s e s a n d s o i s a v e r a g e d o n t h e t i m e s c a l e o f t h e s e s l o w e r p r o c e s s e s . T h e e l a s t i c a n d i n e l a s t i c c r o s s - s e c t i o n s a r e a p p r o x i m a t e d b y t h e f o l l o w i n g f u n c t i o n s . 4 4 f ) = a - M E ( 1 6 6 ) ; 1 3 6 9 " $ 9 0 5 5 ) ( 1 6 7 ) c c s o r e n o c s s t i s i s - o t s n e t t T e e h n c s , r h e t s . e w o q 3 ; i n n n : i e g f 1 y 3 t o + d e h r 2 e e p l e m a 0 e l e y 4 n a c 1 d s t b e r t e i n o c c n r , e - e % : H p + o r 2 l f o a t a o h t l e d e i l e t c c A u e { $ 4 5 ) E V ‘ J E = S m x , i a c b t t r h o t t n i h s o e n s s l i a e c r o w i n g . s o i b e n s y a i c r l o t n h o a s e p ( - 5 € s n . ) s d f - o s v W l > = e i i l 0 o ( s 1 s - 5 3 ) ( 1 7 0 ) 1 4 6 G i t e q ; i n n / W A , : e M { 0 n e r g y h a m p e r { n i ’ n c l q s i ‘ i ' c c o l l i s i o n d = : : 3 r n 1 j r fi d l a i r ( é § ) / o z 4 ' “ ; L ) M [ i / ‘ e T h e p a r a m e t e r s ¢ 2 a n d fi e a r e c o n s t a n t s r e l a t e d t o m a s s e s , c r o s s - s e c t i o n s a n d e n e r g i e s . T h e d i f f e r e n t i a l e q u a t i o n a n d h e n c e , i t s s o l u t i o n , a r e p a r a m e t e r i z e d b y t h e n e u t r a l g a s d e n s i t y , , 0 , t h r o u g h t h e d e n s i t y d e p e n d e n c e o f « 1 . F o r a w e a k i n e l a s t i c c h a n n e l o n e e x p e c t s 9 1 6 ‘ ! a n d s o t h e f o r m a l a p p r o a c h o f a r e g u l a r p e r t u r b a t i o n e x p a n s i o n i s a p p l i e d . ' R C ) 3 i é ” 4 “ ” ( 1 6 9 ) o f g e n l s o l ' P e r t b e ( 3 ‘ + « . 9 i d ; “ c 0 ( O 1 9 0 ( 5 0 ) < 2 : $ 0 8 V 1 : w 4 3 e 0 6 0 : = 1 e x p % 3 I n . ) ~ ° ( £ ) = ” P C ' 1 “ ) : 7 ‘ : : ( ( ; : ( 1 7 1 ) . ( - 0 ( . E ) ( 1 7 2 ) o - W . ) ‘ ) ' : , f " ( ° ) ( % ) fl - M ( " ¢ ‘ P ( ' S ‘ ) ) ( 1 7 4 ) 1 “ 1 4 7 T h e n e u t r a l g a s d e n s i t y a n d t h u s “ 1 a r e i n d e p e n d e n t o f t h e e n e r g y v a r i a b l e E a n d s o t h e d i f f e r e n t i a l e q u a t i o n s g e n e r a t e d b y s u b s t i t u t i o n o f e q n . 1 6 9 i n t o e q n . 1 6 8 m a y b e s o l v e d s u c c e s s i v e l y , b e g i n n i n g w i t h t h e e q u a t i o n f o r f ° ( € ) . T h e r e s u l t f o r t h e f i r s t c o e f f i c i e n t o f t h e r e g u l a r p e r t u r b a t i o n e x p a n s i o n i s g i v e n b y t h e f o l l o w i n g e x p r e s s i o n . ‘ 3 / 1 A g e n e r a l e x p r e s s i o n f o r f n ( £ ) m a y b e f o u n d i n d u c t i v e l y a n d i s g i v e n i n t n h e f o l l o w i n g e q u a t i o n . m = o ( ” fl “ ) ! F r o m t h i s e x p r e s s i o n t h e f u l l d i s t r i b u t i o n f u n c t i o n m a y b e c o n s t r u c t e d a n d a n y d e s i r e d m o m e n t o f t h e d i s t r i b u t i o n f u n c t i o n c a l c u l a t e d . " _ m n - M M “ , ° ° v E { R e n e w s a v e : f r e q g a s e x c j D e u t P a r t n o w a n d t h e t h e W a l l ! ) u 0 1 4 8 m m n - v m l i f " X L a ) { a c e } ( i f - M m 2 . ) ( 1 7 5 ) : 9 S x " ( “ m " ) ! ( « n 5 0 " " I n t o 1 : 9 c c V . = I V A / ’ 0 : ( i f ? C 8 % W e ) " 9 6 5 5 1 4 ‘ I " ! ‘ N V 1 ” fl - M : : N 0 ’ 2 ( ' 3 3 ) ( ' 4 ) L X I ? ) i " ) A l p H ; ¢ : X " X X I . ( r u m - 1 ) . , ( S ( 1 7 6 ) M 8 0 ( = 0 . P g fi ) < 8 ; + 5 3 + 5 1 f a N o t o n l y t h e d i s t r i b u t i o n f u n c t i o n , b u t a l s o t h e a v e r a g e e n e r g y E a n d t h e a v e r a g e i n e l a s t i c e x c i t a t i o n f r e q u e n c y , J e ' a r e p a r a m e t e r i z e d b y « 1 a n d t h u s b y t h e n e u t r a l g a s d e n s i t y l p . T h e a v e r a g e e n e r g y a n d a v e r a g e i n e l a s t i c e x c i t a t i o n f r e q u e n c y d e t e r m i n e t h e e n e r g y t r a n s f e r t o t h e n e u t r a l g a s b y e l a s t i c a n d i n e l a s t i c p r o c e s s e s a n d s o a r e p a r t o f t h e b a l a n c e e q u a t i o n s f o r t h e n e u t r a l g a s . I t r e m a i n s n o w t o d e t e r m i n e t h e e x p l i c i t d e p e n d e n c e o f n e u t r a l g a s d e n s i t y a n d t e m p e r a t u r e o n t h e e l e c t r o n g a s p r o p e r t i e s a n d t o f o l l o w t h e e v o l u t i o n o f t h e s e p r o p e r t i e s f r o m t h e i n i t i a l d a t a t o t h e s t e a d y s t a t e ( s ) . C o n s i d e r a w e l l - m i x e d , c o n s t a n t p r e s s u r e r e a c t o r w i t h e n e r g y a d d i t i o n b y e l a s t i c c o l l i s i o n s a n d b y t h e r a p i d l y t h e r m a l i z e d p r o d u c t s o f t h e w e a k i n e l a s t i c s c a t t e r i n g c h a n n e l . E n e r g y e x t r a c t i o n o c c u r s b y c o n v e c t i o n a n d t h r o u g h a c o o l e d w a l l . T h e m a s s a n d e n e r g y b a l a n c e e q u a t i o n s m a y b e w r i t t e n V i Q C J fi l e e - 6 , 1 : - ~ p U . C p T * V H ‘ “ 9 ( 1 7 8 ) 1 4 9 : i n . t e r m s o f a m o l a r d e n s i t y , / o , a v o l u m e t r i c f l o w r a t e , w , a n d t e m p e r a t u r e T . V d = : ( k % - A % 5 5 f l 0 ( 1 7 7 ) T h e e n e r g y i n p u t d u e t o e l e c t r o n i m p a c t , H , i s m a d e u p o f t w o t e r m s , o n e c o r r e s p o n d i n g t o e l a s t i c c o l l i s i o n s , f o r w h i c h t h e e n e r g y t r a n s f e r p e r c o l l i s i o n i s Z m E / M , a n d i n e l a s t i c c o l l i s i o n s , f o r w h i c h t h e e n e r g y t r a n s f e r p e r c o l l i s i o n i s a f i x e d C e . fl . H = / 5 " e " ’ A ( ° ' ~ < % ? e ) E / ‘ M ‘ Q M / M * 7 7 4 : 5 “ ) ( 1 7 9 ) T h e e n e r g y o u t p u t t o t h e c o o l e d w a l l i s b a s e d o n a N e w t o n ' s c o o l i n g l a w m o d e l a n d i s c o n s t r u c t e d i n t e r m s o f a t e m p e r a t u r e d i f f e r e n c e a n d a n o v e r a l l h e a t t r a n s f e r c o e f f i c i e n t . Q = 6 5 1 ( 1 " 1 1 ) ( 1 8 0 ) B e c a u s e i o n i z a t i o n k i n e t i c s a r e n o t e x p l i c i t i n t h e s o l u t i o n o f t h e B o l t z m a n n e q u a t i o n s o m e a s s u m p t i o n s c o n c e r n i n g t h e e l e c t r o n d e n s i t y i n e q n . 1 7 9 a r e r e q u i r e d . T w o s i m p l e m o d e l s a r e t h o s e o f c o n s t a n t d e n s i t y o r c o n s t a n t e x t e n t o f i o n i z a t i o n , a n d b o t h a r e e x p l o r e d . r c s m t e n r b t d i e u h e n a i r i e q s e n n e n t i n T l r f e y . g g h e a 1 e c y n 8 f d 2 t , o a t e i m n h t f s c h e f t e e e a h l c t l e l f o t s a a t i o i o t c t a v r t e i l a v p n t e e a l e o a e e l f t r c a h n l i s g t b u t n y r l m e o i e m r t c a m m r f t s a a f r i t n i o o n s f e l t s e i m i n r . r e d a s o w m t i s c T h c m h r e e h f e o f c c x e r e i s l o h o e x l y a d p p l n r i w e o o s o n f f e c i l r s r e t h i a n g t i n u o r a e i n e r o t g c g n e . u i v o o i e y f s v e r b e n a s H l a n c e 1 5 0 T o c o m p l e t e t h e d e r i v a t i o n , n o t e t h a t f o r a n i d e a l g a s a t c o n s t a n t p r e s s u r e , l 0 T = c o n s t a n t , a n d s o t h e t i m e ( d e r i v a t i v e i n e q n . 1 7 8 v a n i s h e s . E q u a t i o n s 1 7 7 a n d 1 7 8 I n a y t h e n b e c o m b i n e d i n t o a s i n g l e o r d i n a r y d i f f e r e n t i a l e q u a t i o n i n v o l v i n g t h e a v e r a g e e n e r g y a n d a v e r a g e i n e l a s t i c e x c i t a t i o n f r e q u e n c y , w h i c h a r e i n t u r n , e x p l i c i t f u n c t i o n s o f f ) a n d T . S u b s t i t u t i o n o f e q n . 1 7 5 a n d 1 7 6 i n t o e q n . 1 7 9 y i e l d s t h e f o l l o w i n g e x p r e s s i o n f o r H . m I t n - H fl “ ‘ 1 ‘ “ 1 V 7 . _ o . n - M H w t ) ” . W e e - . 2 ) Z X Z f j g g j m f y v ( 9 ; ) m o a i r - ' 0 1 : 0 ( 1 8 1 ) 1 ‘ 7 2 . J 7 2 . P ( % ) ( ( q . + $ 1 ) + fi t ( a t , ( 1 5 2 + S ) ) W h e n t h e t e r m s o f e q u a l o r d e r i n ¢ 2 a r e c o l l e c t e d i t c a n b e s h o w n t h a t d u e t o c a n c e l l a t i o n o f t e r m s t h e o n l y t e r m H = / $ n - r * 4 ’ ” ~ ( fi ) ( % > " ‘ - . i o n t ? s u b S ‘ t r a n : t h e y o r d i r f o l l c 1 5 1 ( o n t h e e l e c t r o n g a s b u t e q n s . 1 7 5 a n d 1 7 6 a r e n o t . T h e m o d e l o f t h e c o u p l e d p r o b l e m i s c o n s t r u c t e d b y s u b s t i t u t i o n o f e q n s . 1 8 0 a n d 1 8 2 i n t o 1 7 7 a n d 1 7 8 . A f t e r t r a n s f o r m a t i o n t o d i m e n s i o n l e s s v a r i a b l e s f o r / o a n d T i n w h i c h t h e y a r e n o r m a l i z e d b y t h e f e e d v a l u e s , a s i n g l e n o n l i n e a r o r d i n a r y d i f f e r e n t i a l e q u a t i o n f o r / 0 ( t ) r e s u l t s . 3 2 . i f = 7 ' ( fi ‘ c ) ” H " ' 1 “ ‘ e ) ( 1 8 3 ) a t ( I F / 0 2 + a ) c h , e , £ , 3 ) o l 0 6 [ 0 , ' ] F o r c o n s t a n t e l e c t r o n d e n s i t y t h e c o n s t a n t s h a v e t h e f o l l o w i n g v a l u e s . 1 A h f H Q S E ' e n e ” i C = i “ , 0 , - u , - C p , o , - u . - P C , a - . . M ( % § ) l 4 . T E A K 7 9 ‘ 1 7 1 C r 2 d = a t . . _ A A _ 1 I + . u J - C ’ e 2 d o ’ 0 ' ‘ P l + 7 2 M fi w % 1 ? C % T - i i = 1 + M ' 3 fl ' w i T Z ' c P J H o n » - + § t h e f ( 1 5 2 F o r c o n s t a n t e x t e n t o f i o n i z a t i o n t h e c o n s t a n t s h a v e ' t h e f o l l o w i n g v a l u e s . A h + C = A l f i u ‘ . C P 1 ” " ” ( ' T i c r “ ’ 1 ' P e r ' 7 ' ) ( ‘ 1 ' ? ) V ‘ + A R T . d = l l a t ' u i n C P 1 a 1 o I + A k T g « W E E S ' " ' I “ ‘ — — ‘ c f ‘ . o f ‘ 1 : - C F M U " P C P 0 . ” < % ) 2 e = « a c - l t : l + ( m e + 3 9 5 3 2 . A u x - C e 0 . P e w . ( 1 . 9 % o 9 u 9 . p v f o 1 5 3 A l t h o u g h t h e e v o l u t i o n o f t h e d e n s i t y a n d t h u s t h e a v e r a g e e l e c t r o n e n e r g y a n d i n e l a s t i c e x c i t a t i o n r a t e i s n o w a c c e s s i b l e t h r o u g h t h e c l o s e d f o r m s o l u t i o n o f e q n . 1 8 3 ( s e e M o r i n a n d H a w l e y , 1 9 8 4 a ) i t i s t h e s t e a d y - s t a t e s e l f - c o n s i s t e n t v a l u e s o f / D , E a n d 5 % w h i c h a r e o f i n t e r e s t . L e t t h e r i g h t h a n d s i d e o f e q n . 1 8 3 b e d e f i n e d a s g ( / > ) . N o t e t h a t t h e f u n c t i o n g i s b o u n d e d f o r a l l / o a n d t h a t g i s c o n t i n u o u s w i t h r e s p e c t t o f ) , e . g . d g / d f e x i s t s f o r a l l / 0 , a n d s o t h e e x i s t e n c e o f a u n i q u e [ 0 ( t , t m f ° ) i s a s s u r e d , w i t h 7 p ° a s t h e i n i t i a l v a l u e a t t i m e t o . G i v e n t h a t a u n i q u e t r a j e c t o r y e x i s t s f o r e a c h i n i t i a l c o n d i t i o n , h o w m a n y s t a t i o n a r y t r a j e c t o r i e s e x i s t , t h a t i s , a r e t h e r e m u l t i p l e s t e a d y - s t a t e v a l u e s o f ’ 0 , E a n d 1 7 a ? T o a n s w e r t h i s , l e t t h e n u m e r a t o r o f t h e r i g h t h a n d s i d e o f e q n . 1 8 3 b e d e f i n e d a s l h g p ) . T h e z e r o e s o f h i p ) d e t e r m i n e t h e s t a t i o n a r y p o i n t s o f t h e d i f f e r e n t i a l e q u a t i o n a n d a s u b s e t , a t l e a s t , o f t h e z e r o e s o f h a r e t h e s t a b l e s t e a d y s t a t e s . S i n c e h i f ) i s c u b i c i n / n a n e x a c t e x p r e s s i o n f o r i t s t h r e e r o o t s i s a v a i l a b l e . A n a l y s i s o f t h e c a s e s o f c o n s t a n t e l e c t r o n d e n s i t y a n d c o n s t a n t e x t e n t o f i o n i z a t i o n r e v e a l s t h a t t h e r e i s o n l y o n e r e a l p o s i t i v e r o o t o f h ( P ) a n d t h e r e f o r e o n l y o n e s t e a d y - s t a t e v a l u e o f f ) , E a n d 5 % , i n d e p e n d e n t o f t h e i n i t i a l c o n d i t i o n o f f u t ) . T h e s t e a d y - s t a t e s m a y b e f o u n d b y a n a l y s i s o f h g p ) . i ) ( ) = 3 - 6 1 + d ~ e ( 1 3 4 ) 7 ° / 9 f ’ r i o n i z a c o n s t a s s u m i d e n t i s t h e 1 5 4 T h e c o n s t a n t s c , d , e h a v e t h e f o l l o w i n g v a l u e s f o r c o n s t a n t e l e c t r o n d e n s i t y a n d c o n s t a n t e x t e n t o f i o n i z a t i o n a s s u m i n g t h a t t h e c o o l a n t a n d i n i t i a l f e e d t e m p e r a t u r e s a r e i d e n t i c a l . C o n s t a n t e l e c t r o n d e n s i t y 1 1 C = l - O ( 3 ; d = o ( , ; e = ° ( , , C o n s t a n t i o n i z a t i o n e x t e n t . ( 1 1 C : ( I + d 3 ) ; d : q c c " e : q o c 1 q : ‘ fl V E e ; " o q : U 3 I . - - — - . m % ( ' E . - § ) / ‘ ( E C , T , + M T . ) M fi ' fi G — f ) " F o r c o n s t a n t e l e c t r o n d e n s i t y 5 i i s t h e e x t e n t o f i o n i z a t i o n a t , 0 = , q ; f o r c o n s t a n t e x t e n t o f i o n i z a t i o n ; i i s t h e e x t e n t o f i o n i z a t i o n f o r a l l f ) . E s s e n t i a l l y t h e n , t h e s e l f - c o n s i s t e n t n e u t r a l g a s d e n s i t y i s d e t e r m i n e d b y t h r e e d i m e n s i o n l e s s p a r a m e t e r s , t h e e x t e n t o f i o n i z a t i o n , * 1 , t h e r a t i o o f f i e l d f r e q u e n c y t o t o t a l m o m e n t u m t r a n s f e r c o l l i s i o n f r e q u e n c y , 0 ( 0 , a n d t h e p a r a m e t e r a t 3 , w h i c h i s t h e r a t i o o f a c h a r a c t e r i s t i c g a s h e a t i n g r a t e t o a c h a r a c t e r i s t i c e n e r g y t r a n s p o r t a n d r e m o v a l r a t e s . O n c e t h e v a r i a b l e s i n v o l v e d i n e a c h o f t h e s e p a r a m e t e r s h a v e b e e n s p e c i f i e d t h e n t h e v a l u e o f t h e p a r a m e t e r t n , w h i c h i s e s s e n t i a l l y t h e i n v e r s e o f ( E . / N ) 2 , i s f i x e d . T h e s i m i l a r i t y c o n d i t i o n s o f M a r g e n a u r e q u i r e d t h a t $ 1 , « 0 a n d E e l N b e e q u a l f o r t w o d i s c h a r g e s t o b e t o a n e l e c t r o n g a s i n t e r a c t i n g e l a s t i c a l l y w i t h a n e u t r a l g a s 1 5 5 c o n s i d e r e d " k i n e t i c a l l y " s i m i l a r . I n M a r g e n a u ' s a n a l y s i s o f t h e B o l t z m a n n e q u a t i o n t h e n e u t r a l g a s d e n s i t y w a s a f i x e d p a r a m e t e r . I n t h e a n a l y s i s h e r e t h e n e u t r a l g a s d e n s i t y i s d e t e r m i n e d i n a s e l f - c o n s i s t e n t c a l c u l a t i o n a n d i s d e p e n d e n t o n t h e m o r e f u n d a m e n t a l v a r i a b l e s a s s o c i a t e d w i t h c o l l i s i o n r a t e s , g a s f l o w a n d h e a t t r a n s f e r . W i t h t h e s e p a r a m e t e r s o n e m a y r e f o r m u l a t e t h e s i m i l a r i t y l a w s o f M a r g e n a u i n t e r m s o f « 6 , $ i , E / N i w h e r e N i i s t h e f e e d g a s d e n s i t y i n s t e a d o f t h e d i s c h a r g e g a s d e n s i t y a n d , a n a d d i t i o n a l t e r m , ¢ x 3 . E q u a l i t y o f t h e s e p a r a m e t e r s f o r t w o d i s c h a r g e s i d e n t i f i e s t h e m a s k i n e t i c a l l y a n d m a c r o s c o p i c a l l y s i m i l a r . I n a d d i t i o n t o t h e i d e n t i f i c a t i o n o f s i m i l a r i t y l a w s , t h e m o d e l e q u a t i o n s a r e a b a s i s f o r c a l c u l a t i o n o f a s e l f - c o n s i s t e n t n e u t r a l g a s d e n s i t y , a n d e x c i t a t i o n f r e q u e n c y . T h e c a l c u l a t i o n s p r e s e n t e d h e r e b y n o m e a n s e x h a u s t t h e u t i l i t y o f t h e m o d e l b u t f o c u s o n t h e e f f e c t o f g a s h e a t i n g o n t h e g a s h e a t i n g r a t e , g a s t e m p e r a t u r e , a v e r a g e e l e c t r o n e n e r g y a n d a v e r a g e i n e l a s t i c e x c i t a t i o n f r e q u e n c y . T h e c a l c u l a t e d t e m p e r a t u r e s a r e n o r m a l i z e d b y t h e f e e d g a s t e m p e r a t u r e a n d t h e a v e r a g e e l e c t r o n e n e r g y a n d i n e l a s t i c e x c i t a t i o n f r e q u e n c y a r e n o r m a l i z e d b y t h e v a l u e s c o r r e s p o n d i n g o f d e n s i t y / fi k , t h e f e e d g a s d e n s i t y . I = l - ( 1 8 5 ) = / ) l ] _ “ _ : : - 0 + u i f l 2 q x o : 1 l 1 o + 1 z o d h + l o d : ° 0 Z " _ o n é Y “ ( 1 8 7 ) 1 5 6 : Z [ 4 a t : l — ( N u / A / E a P 1 1 4 0 : I ‘ d ' / { 0 ° m » ) ( 1 8 6 ) Z 9 4 1 ‘ “ n — M n + k - M n u n . 7 7 : : Z 0 ) ( 2 . 1 9 1 ? ( a t ) L i l / f . ) 1 ( 1 8 , , m o k 0 k ' . ( m m 1 ) ! 1 3 , , ( 0 ) 5 H k + ( 1 % , A l s o o f i n t e r e s t i s t h e g a s h e a t i n g r a t e H , n o r m a l i z e d b y t h e h e a t i n g r a t e a t t h e g a s f e e d c o n d i t i o n s , H o ' H _ 1 + 0 ! . I f - I O [ 0 1 + « o z . c o n s t a n t e l e c t r o n d e n s i t y ( 1 8 9 ) O _ _ _ 1 % 2 / ( ’ 1 0 “ + 0 ‘ : ) c o n s t a n t e x t e n t o f i o n i z a t i o n ( 1 9 0 ) T h e v a l u e o f t h i s r a t i o w i t h r e s p e c t t o u n i t y i n d i c a t e s h o w g a s h e a t i n g , e . g . c h a n g e s i n / O , a f f e c t t h e g a s h e a t i n g r a t e . E v e n w i t h o u t d e t a i l e d c a l c u l a t i o n s , s o m e q u a l i t a t i v e f e a t u r e s o f t h e r a t i o m a y b e d e t e r m i n e d . C o n s i d e r t h e h i g h - p r e s s x e l e c t : i n g a c a s e I g a s h h e a t i i n e l g a s 0 e x c h a e n e r g o f t h r e g i o C o n s t P o i n t C o n d u t h e a m o m e n e x t e n m a X i m . C a l c u . f i n d . 1 5 7 p r e s s u r e l i m i t , e . g . ( x o < < ' 1 , t h e n f o r t h e c a s e o f c o n s t a n t e l e c t r o n d e n s i t y t h e n o r m a l i z e d g a s h e a t i n g r a t e i s l i n e a r i n g a s t e m p e r a t u r e , e v i d e n c i n g e n h a n c e d h e a t i n g . F o r t h e c a s e o f t h e c o n s t a n t e x t e n t o f i o n i z a t i o n t h e n o r m a l i z e d g a s h e a t i n g r a t e i s u n i t y , i n d i c a t i n g t h a t t h e t o t a l g a s h e a t i n g i s u n a f f e c t e d b y t h e d e n s i t y c h a n g e . T h e d e c r e a s e i n e l e c t r o n - m o l e c u l e c o l l i s i o n r a t e d u e t o t h e d r o p i n n e u t r a l g a s d e n s i t y i s e x a c t l y c o m p e n s a t e d b y t h e i n c r e a s e i n e n e r g y e x c h a n g e d p e r c o l l i s i o n b y t h e e n h a n c e d a v e r a g e e l e c t r o n e n e r g y . T h e s e q u a l i t a t i v e f e a t u r e s a r e d r a w n f r o m a n a l y s i s o f t h e h i g h - p r e s s u r e l i m i t b u t d i s c u s s i o n o f o t h e r p r e s s u r e r e g i o n s m a y a l s o b e m a d e . T h e f u n c t i o n H / H o , f o r t h e c a s e o f c o n s t a n t e l e c t r o n d e n s i t y , h a s a m a x i m u m e n h a n c e m e n t a t t h e p o i n t / > = d o . T h i s i s c o n s i s t e n t w i t h t h e c o l d p l a s m a c o n d u c t i v i t y m a x i m u m . T h i s c o r r e s p o n d s t o t h e c o n d i t i o n t h a t t h e a n g u l a r f r e q u e n c y o f t h e e x t e r n a l f i e l d b e e q u a l t o t h e m o m e n t u m t r a n s f e r c o l l i s i o n f r e q u e n c y . F o r t h e c a s e o f c o n s t a n t e x t e n t o f i o n i z a t i o n t h e f u n c t i o n H / H o d o e s n o t e x h i b i t a m a x i m u m b u t i s m o n o t o n e i n c r e a s i n g i n / 0 . R e s u l t s o f c a l c u l a t i o n s a r e p r e s e n t e d i n F i g u r e s 1 5 - 1 9 . R e c a l l t h a t t o f i n d t h e s t e a d y - s t a t e , s e l f - c o n s i s t e n t g a s d e n s i t y a l l o n e m u s t s p e c i f y i s « 3 , “ o a n d 5 1 . T o f i n d E , 7 7 a , h o w e v e r , o n e m u s t a l s o s p e c i f y a , . T h e p a r a m e t e r a . , m a y b e w r i t t e n a s t h e f o l l o w i n g f u n c t i o n o f 0 ( 3 , a a n d 5 ’ 1 a s w e l l a s o f a O f e w o t h e r v a r i a b l e s . c c b 1 0 1 a : r e W e i s t o ( 1 + r e s 1 1 1 i s h i g t h e t h e : t h e a " _ ' ” 2 " 3 f } g 1 1 ( ) S } ; ? O ; 3 1 ‘ l J “ < / ’ ( 1 9 1 ) 1 5 8 ” - 1 ( % ) " * ( 6 C e : - + W ? ) S p e c i f i c a t i o n o f : E i ' 0 ( 3 , 0 ( 0 r e s u l t s i n a s e l f - c o n s i s t e n t v a l u e o f / p a n d t h e n s p e c i f i c a t i o n o f t h e f i r s t b r a c k e t e d t e r m i n e q n . 1 9 1 c o m p l e t e l y d e t e r m i n e s t h e v a l u e s o f . § a n d ' i 2 . T h e c a l c u l a t i o n s p r e s e n t e d i n F i g u r e s 1 5 - 1 9 a r e f o r a p u r e H 2 f e e d s t r e a m a t 3 0 0 K e n t e r i n g a d i s c h a r g e r e g i o n . 0 2 5 4 m i n d i a m e t e r a n d . 2 5 4 m i n l e n g t h a t a r a t e o f 2 . 5 - 7 . 5 ( 1 0 ' 4 ) m o l e s / s . T h e e x t e n t o f i o n i z a t i o n o f t h e 6 w e a k l y i o n i z e d g a s i s l . ( 1 0 - ) . I n F i g u r e 1 5 - 1 9 t h e a b s c i s s a i s t h e p a r a m e t e r C i n e q u a t i o n 1 8 4 . T h i s p a r a m e t e r i s r e l a t e d t o « 3 e i t h e r a s C = 1 — 0 ( 3 1 f o r c o n s t a n t e l e c t r o n d e n s i t y o r a s C = ( 1 + a s ) - f o r c o n s t a n t e x t e n t o f i o n i z a t i o n . N o t e t h a t a s 1 - < x 3 a r e t h e f i r s t t w o t e r m s o f t h e s e r i e s e x p a n s i o n o f ( 1 + « 3 ) . , o n e w o u l d e x p e c t t h a t f o r s m a l l 0 1 3 ( 0 & 3 “ l ) , t h e r e s p e c t i v e v a l u e s o f c w o u l d b e c l o s e , a n d t h e z e r o f i e l d l i m i t s o f t h e t w o c a s e s t o b e i d e n t i c a l . I n F i g u r e 1 5 t h e s e l f - c o n s i s t e n t n o r m a l i z e d g a s t e m p e r a t u r e i s p r e s e n t e d , o v e r a r a n g e o f p r e s s u r e f r o m l o w ( 0 ( 0 ) ) 1 ) t o h i g h ( c x o ( ( l ) a n d f o r a r a n g e o f c o n t h e u n i t i n t e r v a l . F o r t h e c o n s t a n t e l e c t r o n d e n s i t y c a s e c m a y t a k e o n v a l u e s l e s s t h a n z e r o b u t t h i s i n t r o d u c e s n o n e w q u a l i t a t i v e f e a t u r e s i n t h e r e s u l t s . T o c a l c u l a t e t h e s e t e m p e r a t u r e s o n l y c a n d 6 ( 0 P 1 9 0 3 l e r u t a r e p m e t s a g d e z i l a m r o N 1 5 9 I O T 9 _ — - a , = 0 . 1 - - a t . = 1 . 0 8 - — - - a , = 1 0 . 0 F i g u r e 1 5 : N o r m a l i z e d n e u t r a l g a s t e m p e r a t u r e f o r c c [ 0 , 1 ] a n d “ O = 0 . 1 , 1 . 0 , 1 0 . 0 . m 1 O I £ 1 T h e e : 1 6 0 m u s t b e s p e c i f i e d . T h e t e m p e r a t u r e i s n o t d i r e c t l y d e p e n d e n t o n i n d i v i d u a l v a r i a b l e s s u c h a s g a s f l o w r a t e o r f i e l d f r e q u e n c y a n d s o i s v a l i d f o r a w i d e v a r i e t y o f g a s d i s c h a r g e s . A s t h e v a l u e o f c g o e s f r o m 1 t o 0 . t h e n o r m a l i z e d t e m p e r a t u r e i n c r e a s e s i n a m o n o t o n e f a s h i o n f o r a w i d e r a n g e o f p r e s s u r e . T h e h i g h e r t h e p r e s s u r e , t h e m o r e p r o n o u n c e d t h e h e a t i n g e f f e c t i s . C h a n g e s i n a n u m b e r o f v a r i a b l e s m a y r e s u l t i n c d e c r e a s i n g f r o m 1 t o O , f o r e x a m p l e , i n c r e a s i n g t h e e l e c t r i c f i e l d s t r e n g t h o r d e c r e a s i n g t h e f e e d f l o w r a t e . I n t h e l o w p r e s s u r e r e g i o n , ¢ x o ) ) 1 , v e r y l i t t l e g a s h e a t i n g t a k e s p l a c e , t h e n e u t r a l g a s t e m p e r a t u r e a n d d e n s i t y a r e e s s e n t i a l l y u n c h a n g e d f r o m t h e f e e d c o n d i t i o n s a n d s o E / N i s a r e a s o n a b l e p a r a m e t e r f o r c h a r a c t e r i z a t i o n o f t h e d i s c h a r g e . A s t h e p r e s s u r e i n c r e a s e s t h e v a r i a t i o n i n c h a s a m o r e p r o n o u n c e d e f f e c t o n t h e g a s t e m p e r a t u r e a n d E / N n o l o n g e r a c c u r a t e l y c h a r a c t e r i z e s t h e c o n d i t i o n o f t h e d i s c h a r g e s i n c e N i s n o w a s t r o n g f u n c t i o n o f E . F i g u r e 1 5 m a y a l s o b e u s e f u l i n l o c a t i n g t h e o p t i m u m O p e r a t i n g p o i n t s ( v a l u e s o f c ) g i v e n a n c x o . I n t h e c a s e o f c o n s t a n t e l e c t r o n d e n s i t y t h e h e a t i n g r a t e g o e s t h r o u g h a m a x i m u m a t ‘ p = « O . I n t e r m s o f t e m p e r a t u r e , t h i s c o n d i t i o n r e q u i r e s q u = 1 . S o , f o r d o = 0 . 1 , T = 1 0 a n d f r o m F i g u r e 1 5 , c = . 0 6 . L i k e w i s e , f o r d o = l t h e o p t i m u m o p e r a t i n g p o i n t i s a t t h e f e e d c o n d i t i o n . T h i s o p t i m u m v a l u e f o r c m a y , i n t u r n , b e r e l a t e d t o e x p e r i m e n t a l v a r i a b l e s t h r o u g h e x p r e s s i o n s d e r i v e d e a r l i e r . ‘ t } r e 1 6 1 C o n s i d e r F i g u r e s 1 6 — 1 8 , w h i c h p r e s e n t c a l c u l a t i o n s o f n o r m a l i z e d s e l f - c o n s i s t e n t , s t e a d y - s t a t e , a v e r a g e e l e c t r o n e n e r g i e s . I n t h e s e c a l c u l a t i o n s t h e s p e c i f i c a t i o n o f g a s l o w r a t e , e x t e n t o f i o n i z a t i o n , a n d d i s c h a r g e g e o m e t r y i s n e c e s s a r y a n d t h o s e s p e c i f i e d v a l u e s w e r e r e f e r r e d t o e a r l i e r . T h e c u r v e s i n e a c h o f t h e t h r e e f i g u r e s a r e p a r a m e t e r i z e d b y ¢ 2 , t h e r e l a t i v e s t r e n g t h o f t h e i n e l a s t i c c h a n n e l . T h i s p a r a m e t e r a s s u m e s v a l u e s o f 0 . 0 , e l a s t i c c o l l i s i o n s o n l y , 0 . 1 a n d 1 . 0 , w h i c h s i m u l a t e r o t a t i o n a l e x c i t a t i o n . I n F i g u r e 1 6 t h e h i g h p r e s s u r e ( a x o < < 1 ) c a l c u l a t i o n s a r e p r e s e n t e d . F o r b o t h t h e p u r e l y e l a s t i c c o l l i s i o n m o d e l ( ¢ 2 = 0 . 0 ) a n d t h e m o d e l w i t h t h e i n e l a s t i c c h a n n e l o p e n t h e n o r m a l i z e d a v e r a g e e l e c t r o n e n e r g y i s m o n o t o n e i n c r e a s i n g i n « ' 3 o r m o n o t o n e d e c r e a s i n g w i t h c . Q u a n t i t a t i v e l y , t h e s t r o n g e r t h e i n e l a s t i c c h a n n e l i s , t h e l o w e r t h e n o r m a l i z e d a v e r a g e e l e c t r o n e n e r g y i s . T h e n o r m a l i z e d a v e r a g e e l e c t r o n e n e r g y c u r v e s i n F i g u r e 1 7 a n d 1 8 e v i d e n c e b o t h e n h a n c e m e n t a n d i n h i b i t i o n . I n c o n t r a s t t o F i g u r e 1 5 , t h e r e a r e v a l u e s o f t h e p a r a m e t e r c f o r w h i c h t h e a v e r a g e e l e c t r o n e n e r g y i s b e l o w t h a t w h i c h c o r r e s p o n d s t o t h e f e e d g a s c o n d i t i o n . I n F i g u r e 1 7 t h e e l a s t i c c a s e ( ¢ 2 = o ) e v i d e n c e s o n l y e n h a n c e m e n t , a s e x p e c t e d . I f t h e i n e l a s t i c c h a n n e l i s o p e n t h e n a s t h e p a r a m e t e r c i s d e c r e a s e d f r o m 1 t h e n o r m a l i z e d a v e r a g e e l e c t r o n e n e r g y g o e s t o a m i n i m u m a n d t h e n i n c r e a s e s t o a v a l u e o f 1 a n d t h e n i n t o t h e e n h a n c e m e n t r e g i m e . T h e r e i s a m i n i m u m v a l u e o f c f o r e n h a n c e m e n t o f y g r e n e n o r t c e l e e g a r e v a d e z i l a m r o N 1 6 2 5 0 F i g u r e 1 6 : N o r m a l i z e d a v e r a g e e l e c t r o n e n e r g y f o r c € [ 0 , 1 ] , 0 ( 0 = 0 . 1 a n d ¢ 2 = 0 . , 1 . 0 . y g r e n e n o r t c e l e e g a r e v a d e z i l a m r o N 1 6 3 1 . 5 - 1 . 0 . 5 1 . 0 P J ‘ Q U r e 1 7 : N o r m a l i z e d a v e r a g e e l e c t r o n e n e r g y f o r c € [ 0 , 1 ] , a 0 = 1 . 0 a n d ¢ 2 = 0 . , 0 . 1 , 1 . 0 . 1 6 4 1 . 2 a o = 1 0 0 * 8 H l . 0 ) — V _ G ) x \ s \ ~ ~ ~ I 0 a \ u ' ” ° 8 \ 0 r - s \ - S 0 6 " \ . I g , - ¢ 1 = _ — \ g 3 ¢ : . = - - 3 0 . 4 . . ¢ 1 - — , _ — « 4 H ( U ) — E z 0 0 2 l l l l L l 4 l l . 5 1 . 0 F e i g n i t e 1 8 : N o r m a l i z e d a v e r a g e e l e c t r o n e n e r g y f o r c € [ O , l ] , a O = 1 0 . 0 a n d ¢ 2 = 0 . , 0 . 1 , 1 . 0 . A n a l y s i s o f t h e f o r m o f t : a l s o i n d i c a t e s a m a x i m u m v a l u e 1 6 5 t h e a v e r a g e e l e c t r o n e n e r g y t o o c c u r . F i g u r e s 1 7 a n d 1 8 i n d i c a t e t h a t a s t h e p r e s s u r e i s d e c r e a s e d ( ( x o 2 , 1 ) t h e v a l u e o f t h i s t h r e s h h o l d c i n c r e a s e s . T h e o n s e t o f i n h i b i t i o n m a y a l s o b e a n a l y z e d b y c o n s i d e r i n g t h e f i r s t f e w t e r m s o f t h e s e r i e s e x p r e s s i o n f o r t h e n o r m a l i z e d a v e r a g e e l e c t r o n e n e r g y . I n e q n . 1 8 6 t h e f u l l e x p r e s s i o n i s g i v e n . I t i s a p p a r e n t t h a t f o r s m a l l v a l u e s o f 0 5 2 t h e o n s e t o f i n h i b i t i o n i s i n d i c a t e d b y a c h a n g e i n t h e s i g n o f 3 ’ , f r o m p o s i t i v e t o n e g a t i v e . A n a l y s i s o f t h e f o r m o f ( i n d i c a t e s f o r O < I § 3 < 1 . 0 8 6 2 ' 5 t h a t [ ) 0 a n d f o r S ? ) 1 . 0 8 6 2 , D ” < 0 . R e c a l l n o w t h a t S i s a n i n v e r s e e n e r g y s c a l e o f t h e i n e l a s t i c p r o c e s s a n d c a n b e r e l a t e d t o t h e e n e r g y o f t h e p e a k v a l u e o f t h e i n e l a s t i c c r o s s - s e c t i o n s i m p l y b y d i f f e r e n t i a t i o n o f e q n . 1 6 7 . T h e r e s u l t i s t h a t S = 1 / 2 E m w h e r e E m i s t h e e n e r g y a t w h i c h t h e i n e l a s t i c c r o s s - s e c t i o n p e a k s . A l s o r e c a l l t h a t 3 / 2 q , i s t h e a v e r a g e e n e r g y o f a n e l e c t r o n g a s a s s u m i n g o n l y e l a s t i c c o l l i s i o n s . T h e e a r l i e r i n e q u a l i t y t a k e s o n t h e f o l l o w i n g f o r m . 0 < — — < 7 3 ( 1 9 2 ) I f t h i s e q u a l i t y i s s a t i s f i e d t h e n e n h a n c e m e n t o f t h e a v e r a g e e l e c t r o n e n e r g y m a y b e e x p e c t e d . T h e i n e q u a l i t y e s s e n t i a l l y r e q u i r e s t h a t t h e i n e l a s t i c c r o s s - s e c t i o n p e a k a t o r b e l o w o n e - t h i r d t h e a v e r a g e e n e r g y o f t h e e l e c t r o n g a s . d ' - 0 4 6 £ “ — 1 5 ‘ - . ( o r 2 , - ' ) ' T h u s f a r t h e r e s u l t s h a v e c o n c e r n e d n e u t r a l g a s a n d f o r m a t e l e c t r o n e n e r g i e s , w i t h e n h a n c e m e n t o f t h e n o r m a l i z e d v a l u e s f o r s o m e v a r i a b l e r a n g e s . W i t h e n h a n c e m e n t o f e l a s t i c c o l l i s i o n p r o c e s s e s o n e m i g h t a l s o e x p e c t s o m e e n h a n c e d i n e l a s t i c c o l l i s i o n r a t e s . C a l c u l a t i o n s o f n o r m a l i z e d i n e l a s t i c e x c i t a t i o n r a t e s a r e p r e s e n t e d i n F i g u r e 1 9 f o r l o w , m e d i u m a n d h i g h p r e s s u r e , F 1 o v e r a r a n g e o f c a n d f o r ¢ 2 = 0 . 1 . A t l o w p r e s s u r e ( d ; ) ) 1 ) _ V Z L T A . ‘ ( p r f ‘ - . . . I t h e n o r m a l i z e d i n e l a s t i c e x c i t a t i o n r a t e i s e s s e n t i a l l y u n - c h a n g e d f r o m i t s v a l u e a t f e e d c o n d i t i o n s , c o r r e s p o n d i n g t o t h e p r e v i o u s r e s u l t s . A t m e d i u m p r e s s u r e ( c x o = 1 . 0 ) t h e n o r m a l i z e d e x c i t a t i o n r a t e i s m o n o t o n e i n c r e a s i n g w i t h 0 ( 3 o r m o n o t o n e d e c r e a s i n g w i t h c a n d i s e n h a n c e d f o r a l l v a l u e s o f c . A t h i g h p r e s s u r e ( c x o < < 1 ) t h e n o r m a l i z e d c u r v e s h o w s a m i n i m u m a t C ~ 0 . 3 a n d r e g i o n s o f e n h a n c e m e n t a n d a l s o i n h i b i t i o n . S e v e r a l p o i n t s a r e t o b e m a d e f r o m t h i s f i g u r e . F i r s t , t h e r e i s a p r e s s u r e t h r e s h h o l d a b o v e w h i c h i n h i b i t i o n o f t h e e x c i t a t i o n r a t e o c c u r s f o r s o m e v a l u e s o f c . S e c o n d , f o r a g i v e n v a l u e o f c x o o r p r e s s u r e t h e r e i s a t h r e s h h o l d v a l u e o f c f o r w h i c h o n s e t o f e n h a n c e m e n t o c c u r s . F o r c x o = 0 . 1 t h i s o n s e t i s v e r y s h a r p . T h i r d , f r o m t h e s h a p e o f t h e t h r e e c u r v e s i n F i g u r e 1 9 t h e r e i s a v a l u e o f t x o b e t w e e n 0 . 1 a n d 1 0 . 0 f o r w h i c h t h e n o r m a l i z e d i n e l a s t i c e x c i t a t i o n r a t e h a s a m a x i m u m a t a g i v e n v a l u e o f c . A n i n e l a s t i c r e s o n a n c e , l i k e t h e c o l d p l a s m a c o n d u C t i v i t y r e s o n a n c e , i s e v i d e n c e d 1 6 7 5 . 0 9 5 , = 0 . 1 ' 8 — d o = 0 . 1 g 4 . 0 . . — - a t : 1 . 0 g \ . _ . _ . a t = 1 0 . 0 " - 1 " u 3 3 . 0 , \ - H O X ( D . . O " J m 2 0 0 ’ ( 0 F ( ( D . - £ 2 - H ' 8 1 . 0 - N - H H . - ( 0 g l A 1 J 1 l 1 A l . 5 1 . 0 C F i g u r e 1 9 : N o r m a l i z e d a v e r a g e i n e l a s t i c e x c i t a t i o n r a t e f o r c a [ 0 , 1 ] , 9 5 2 = 0 . 1 a n d a 0 = 0 . 1 . 1 . 0 , 1 0 . 0 1 6 8 i n F i g u r e 1 9 a n d i s i n t e r e s t i n g a s a p o s s i b l e s e l e c t i v e e x c i t a t i o n t e c h n i q u e . T h e p r e s e n c e o f t h i s r e s o n a n c e a l s o r a i s e s q u e s t i o n s c o n c e r n i n g t h e e f f e c t o f e l e c t r o n i c e x c i t a t i o n i n a s e l f - c o n s i s t e n t c a l c u l a t i o n o f a v e r a g e e n e r g i e s a n d e x c i t a t i o n r a t e s . T h e p e r t u r b a t i o n a p p r o a c h u s e d h e r e i s n o t a m e n a b l e t o h i g h e n e r g y e v e n t s l i k e d i s s o c i a t i o n a n d i o n i z a t i o n . B e f o r e s u m m a r i z i n g t h e r e s u l t s p r e s e n t e d h e r e , r e c a l l t h a t t h e p u r p o s e o f t h i s s e c t i o n i s a n a n a l y s i s o f t h e e f f e c t o f g a s h e a t i n g o n t h e s e l f - c o n s i s t e n t g a s h e a t i n g r a t e , n e u t r a l g a s t e m p e r a t u r e , a v e r a g e e l e c t r o n e n e r g y a n d a v e r a g e i n e l a s t i c e x c i t a t i o n r a t e . A s i g n i f i c a n t f e a t u r e o f t h e s e r e s u l t s i s t h a t t h e y r e p r e s e n t s e l f - c o n s i s t e n t c a l c u l a t i o n s . F i r s t , a s e t o f s i m i l a r i t y v a r i a b l e s h a s b e e n i d e n t i f i e d f o r t h e d i s c h a r g e s c o n s i d e r e d h e r e . T h e s e t i n c l u d e s t h o s e o f M a r g e n a u a s a s u b s e t a n d h a s , i n a d d i t i o n , a v a r i a b l e c o r r e s p o n d i n g t o g a s f l o w a n d h e a t t r a n s f e r . T h e s e v a r i a b l e s m a k e c o r r e l a t i o n o f c a l c u l a t i o n a l a n d e x p e r i m e n t a l d a t a p o s s i b l e f o r a w i d e v a r i e t y o f g a s e s a n d d i s c h a r g e c o n d i t i o n s . T h e c a l c u l a t i o n a l r e s u l t s p r e s e n t e d e a r l i e r i n t h i s s e c t i o n a r e i n t e r m s o f t h e s e s i m i l a r i t y v a r i a b l e s a n d t h e i r u s e g r e a t l y s i m p l i f i e s t h e p r e s e n t a t i o n . S e c o n d , t h e d e p e n d e n c e o f t h e n o r m a l i z e d g a s h e a t i n g r a t e o n t h e v a r i a b l e S ( x 3 , d o a n d 3 1 h a s b e e n i d e n t i f i e d f o r c o n s t a n t e l e c t r o n d e n s i t y a n d c o n s t a n t e x t e n t o f i o n i z a t i o n . T h e h e a t i n g r a t e a t c o n s t a n t e l e c t r o n d e n s i t y h a s a m a x i m u m 1 6 9 f o r , 0 = d o c o r r e s p o n d i n g t o t h e c o l d p l a s m a r e s o n a n c e . T h e r e f o r e , i n p l a s m a s w i t h a n i n i t i a l c o n d i t i o n / 0 i ) ( V 0 t h e e f f e c t o f t h e g a s h e a t i n g i s t o d r i v e t h e d i s c h a r g e t o w a r d t h e r e s o n a n c e . T h e v a l u e o f c t o d o t h i s m a y b e o b t a i n e d f r o m F i g u r e 1 5 . F o r c o n s t a n t e x t e n t o f i o n i z a t i o n n o m a x i m u m i n t h e n o r m a l i z e d g a s h e a t i n g r a t e o c c u r s a n d t h e h e a t i n g r a t e d e c r e a s e s a s g a s t e m p e r a t u r e i n c r e a s e s . T h i r d , t r a n s i t i o n s f r o m e n h a n c e m e n t t o d e p r e s s i o n o f t h e a v e r a g e e l e c t r o n e n e r g y a n d i n e l a s t i c e x c i t a t i o n r a t e h a v e b e e n i d e n t i f i e d a n d t h e c o n d i t i o n s f o r o n s e t o f e n h a n c e m e n t m a y b e o b t a i n e d f r o m F i g u r e s 1 6 - 1 8 . C o n d i t i o n s f o r t h e o n s e t o f i n h i b i t i o n h a v e a l s o b e e n d e t e r m i n e d i n t e r m s o f q “ a n d 5 ' a n d r e l a t e d t o t h e e n e r g y s c a l e s i n v o l v e d . F o u r t h , t h e p r e s e n c e o f a n i n e l a s t i c r e s o n a n c e h a s b e e n i d e n t i f i e d a n d a s s o c i a t e d w i t h t h e g a s h e a t i n g e f f e c t . o f M a x w e l l m o l e c u l e s i n a f i e l d f r e e r e g i o n t h e B o l t z m a n n 1 7 0 3 . 4 C a l c u l a t i o n o f r e l a x a t i o n t i m e s c a l e s I n t h e u n c o u p l e d c a l c u l a t i o n s o f s e c t i o n 3 . 2 a n a s s u m p t i o n i s m a d e a b o u t t h e r e l a x a t i o n t i m e s c a l e o f t h e h i g h - e n e r g y d i s s o c i a t i o n p r o d u c t s . I t i s a s s u m e d t h a t t h e h i g h - e n e r g y a t o m s t h e r m a l i z e t h e i r e x c e s s k i n e t i c e n e r g y o n t h e t i m e s c a l e o f t h e d i s c h a r g e r e s i d e n c e t i m e . F o r a t o m s i n t h e t h e r m a l v e l o c i t y r a n g e t h i s i s r e a s o n a b l e i n l i g h t o f t h e t i m e s c a l e s p r e s e n t e d i n F i g u r e s 6 - 8 . I t i s n o t c e r t a i n , h o w e v e r , t h a t t h e t i m e s c a l e f o r r e l a x a t i o n o f " t a i l " a t o m s i s o f t h e s a m e o r d e r o f m a g n i t u d e a s t h a t f o r t h e r m a l a t o m s . M a c r o s c o p i c c o n s i d e r a t i o n s g i v e n o i n f o r m a t i o n a b o u t t h i s . H o w e v e r , i n f o r m a t i o n a b o u t r e l a x a t i o n o f n o n e q u i l i b r i u m a t o m d i s t r i b u t i o n s i s a c c e s s i b l e t h r o u g h s o l u t i o n o f t h e f u l l y n o n l i n e a r B o l t z m a n n e q u a t i o n . T h e p r o d u c t i o n o f e x c i t e d a t o m s i s e s s e n t i a l l y a s o u r c e t e r m i n t h e h i g h e n e r g y t a i l o f t h e a t o m d i s t r i b u t i o n . T h e t i m e s c a l e f o r r e l a x a t i o n o f t h e h i g h e n e r g y r e g i o n o f t h e d i s t r i b u t i o n t o i t s e q u i l i b r i u m v a l u e i s o b t a i n e d b y f o l l o w i n g t h e e v o l u t i o n o f t h e i n i t i a l n o n e q u i l i b r i u m s y s t e m g i g a m i c r o s c o p i c k i n e t i c e q u a t i o n l i k e t h e B o l t z m a n n e q u a t i o n . T h e s t u d y o f r e l a x a t i o n o f n o n e q u i l i b r i u m d i s t r i b u t i o n s h a s a w i d e r a n g e o f a p p l i c a t i o n o u t s i d e o f c o l l i s i o n i n d u c e d h e a t i n g a n d E r n s t ( 1 9 8 3 ) h a s r e v i e w e d s o m e o f t h e m . S u c h s t u d y r e q u i r e s n u m e r i c a l s o l u t i o n o f t h e n o n l i n e a r B o l t z m a n n e q u a t i o n i n g e n e r a l . F o r t h e c a s e o f a s p a t i a l l y h o m o g e n e o u s a s s e m b l y 1 7 1 e q u a t i o n a d m i t s a s o l u t i o n i n c l o s e d f o r m f o r a s p e c i a l c l a s s o f i n i t i a l c o n d i t i o n s . T h e b a c k g r o u n d o f t h i s s o l u t i o n , t h e K B K W s o l u t i o n , h a s b e e n r e v i e w e d e a r l i e r . T h e n o n e q u i l i b r i u m i n i t i a l d i s t r i b u t i o n o f i n t e r e s t i n c a l c u l a t i o n o f r e l a x a t i o n t i m e s c a l e s f o r f a s t H a t o m s a r e n o t i n t h e f a v o r e d c l a s s o f i n i t i a l c o n d i t i o n s , b u t t h e K B K W s o l u t i o n i s o f i n t e r e s t b e c a u s e i t g i v e s o n e a n o p p o r t u n i t y t o e v a l u a t e a n u m e r i c a l t e c h n i q u e . T h e t e c h n i q u e m a y t h e n b e a p p l i e d t o t h e i n i t i a l d i s t r i b u t i o n s o f i n t e r e s t a n d t h e r e l a x a t i o n o f n o n - K B K W d i s t r i b u t i o n s m a y b e s t u d i e d . N o d i r e c t c o m p a r i s o n s b e t w e e n t h e c l o s e d f o r m s o l u t i o n o f K r u p p , B o b y l e v , K r o o k a n d W u a n d a n u m e r i c a l s o l u t i o n h a v e b e e n m a d e . T h e p u r p o s e o f t h i s s e c t i o n i s t o d e m o n s t r a t e t h a t t h e m e t h o d o f o r t h o g o n a l c o l l o c a t i o n i s a n a p p r o p r i a t e a p p r o x i m a t i o n m e t h o d f o r s o l u t i o n o f t h e n o n l i n e a r B o l t z m a n n e q u a t i o n a n d t h e n t o a p p l y t h e m e t h o d t o a n a l y z e t h e r e l a x a t i o n o f n o n e q u i l i b r i u m v e l o c i t y d i s t r i b u t i o n s t o t h e e q u i l i b r i u m . I n d e p a r t i n g f r o m t h e m a c r o s c o p i c d e s c r i p t i o n o f t h e n e u t r a l a t o m s a s i m p l e r p h y s i c a l m o d e l o f r e l a x a t i o n i s c o n s i d e r e d . T h e c a s e o f a o n e c o m p o n e n t , s p a t i a l l y h o m o g e n e o u s , d i l u t e M a x w e l l g a s a t c o n s t a n t d e n s i t y a n d a v e r a g e e n e r g y a n d c h a r a c t e r i z e d b y a d i s t r i b u t i o n f u n c t i o n w h i c h i s i s o t r o p i c i n v e l o c i t y s p a c e i s c o n s i d e r e d . T h e B o l t z m a n n e q u a t i o n f o r t h i s m o d e l c a s e i s g i v e n i n e q n . 4 9 , a n d t h e c l o s e d f o r m s o l u t i o n f o r t h e K B K W i n i t i a l c o n d i t i o n s i n e q n . 5 5 a n d 5 6 . T h i s m o d e l r e t a i n s t h e e s s e n t i a l f e a t u r e s o f , a n o n e q u i l i b r i u m i n i t i a l c o n d i t i o n , n o n l i n e a r r e l a x a t i o n v i a b i n a r y c o l l i s i o n s , a n d c T i h o n e l v l o i B l s o v s m l i i t o n z n g w n i h n m a d i e e c n q h s u i s a o a t n t i l i o e s n s f s y f o v m r a o r m t i e h a n i b t s l u e m m s o d a f e n o l d r , r t e t n a h e f e g e t y r i o o c s e n m a s e n m e d r t . r v r e a a n t n e i s r o f g n o y m a t i o n s 1 7 2 s c a l e s , i s g i v e n i n e q n . 5 4 a n d r e p e a t e d h e r e . ( r 1 1 ) £ 3 3 0 ? ) + . 9 6 7 7 ) = { ' A 1 s m x o l e “ d e g £ 0 1 ? ) { 3 0 0 1 1 ) ( 1 9 3 ) o o a . 1 v ' . - . - i < v 1 2 + u ) + 1 ( v 1 - ~ 1 9 ) c o s l + [ y x o g l s i ' n j t ’ c o s e ( 1 9 4 ) [ r z _ ) Q 1 ) , ( 1 1 x . 1 " . “ c . ) - 1 ( v + w - 3 v ~ w ) c o s - l n y / s m x ' c o s f ( 1 9 5 ) A n y n u m e r i c a l m e t h o d c o n s i d e r e d f o r t h e n o n l i n e a r B o l t z m a n n e q u a t i o n m u s t b e a m e n a b l e t o i n t e r p o l a t i o n , i n t e g r a t i o n o v e r a s e m i i n f i n i t e d o m a i n a n d , i f e x t e r n a l f i e l d s a r e a n t i c i p a t e d , d i f f e r e n t i a t i o n o f t h e d i s t r i b u t i o n f u n c t i o n w i t h r e s p e c t t o v e l o c i t y . I n l i g h t o f t h e s e r e q u i r e m e n t s t h e m e t h o d o f o r t h o g o n a l c o l l o c a t i o n w i t h a L a g u e r r e p o l y n o m i a l b a s i s s e t w a s s e l e c t e d . T h e m e t h o d h a s b e e n a l m o s t e x c l u s i v e l y a p p l i e d w i t h i n t h e c h e m i c a l e n g i n e e r i n g l i t e r a t u r e a l t h o u g h S l a t e r ( 1 9 4 3 ) a p p l i e d t h e m e t h o d t o s o l v e t h e r a d i a l S c h r 5 d i n g e r e q u a t i o n f o r e x c i t e d b a n d s o f e l e c t r o n s i n s o d i u m . F o r a r e c e n t r e v i e w o f t h e m e t h o d a n d a c o m p a r i s o n w i t h f i n i t e d i f f e r e n c e a n d G a l e r k i n a p p r o x i m a t i o n t e c h n i q u e s t h e w o r k o f B o t h a a n d P i n d e r ( 1 9 8 3 ) i s s u g g e s t e d . 1 7 3 E v e n w i t h o u t k n o w i n g t h e f o r m o f t h e K B K W s o l u t i o n o f e q n . 1 9 3 t w o c h a r a c t e r i s t i c s a r e k n o w n a b o u t t h e s o l u t i o n . F i r s t , t h e H - t h e o r e m g u a r a n t e e s t h a t t h e i n i t i a l c o n d i t i o n e v e n t u a l l y r e l a x e s t o a M a x w e l l i a n , a n d s e c o n d , t h a t t h e d i s t r i b u t i o n f u n c t i o n m a y b e r e w r i t t e n a s a f u n c t i o n o f e n e r g y s i n c e t h e f u n c t i o n i s i s o t r o p i c i n v e l o c i t y s p a c e . W i t h t h e s e i n m i n d t h e f o l l o w i n g t r i a l f u n c t i o n i s p r o p o s e d . n + 1 - V L 1 a { . ( v ’ n ) = ( 3 1 ' ) “ P P / ( 1 ) 2 : 5 0 7 “ " ) ! 3 ’ ) ( 1 9 6 ) i = 1 T h e f a c t o r o u t s i d e t h e s u m m a t i o n i s t h e e q u i l i b r i u m v a l u e o f t h e d i s t r i b u t i o n f u n c t i o n a n d t h e s u m m a t i o n i s a L a g r a n g e i n t e r p o l a t i o n p o l y n o m i a l i n w h i c h t h e v a l u e s o f t h e r e d u c e d d i s t r i b u t i o n f u n c t i o n a t t h e z e r o e s o f t h e L a g u e r r e p o l y n o m i a l , + ( n “ ( 1 7 2 ) . a ( d i s t r i b u t i o n f u n c t i o n i s j u s t t h e d i s t r i b u t i o n f u n c t i o n a r e u s e d f o r i n t e r p o l a t i o n . T h e r e d u c e d n o r m a l i z e d b y t h e e q u i l i b r i u m d i s t r i b u t i o n f u n c t i o n . T h e t r i a l f u n c t i o n i s s u b s t i t u t e d i n t o t h e B o l t z m a n n e q u a t i o n a n d t h e e n t i r e e q u a t i o n i s i n t e g r a t e d b y t h e f o l l o w i n g p o i n t m e a s u r e . 1 . 1 a . 5 ( v - ) 5 ) v a A v ( 1 9 7 ) I n t e g r a t i o n o v e r t h e s e m i i n f i n i t e d o m a i n g e n e r a t e s t h e n + 1 m o m e n t e q u a t i o n s g i v e n i n e q n . 1 9 8 . d 1 . : 1 ! K t ) = U ' 1 V [ 1 \ 7 u = v A . ' 1 ( x s ) = ( 2 1 1 7 5 0 0 ) 8 ' . 3 ) " 1 a o d ” ) - v O . s fi O 1 1 3 : c ; ! z 4 ‘ Y = ' ” x “ : £ V J 1 9 Y " “ 9 ° X L % ) u ( 1 9 9 F ( “ ( " ° Y ) ) F ( v < x “ y ) > t ( ‘ ) ( 2 0 0 ) ) < P : - u # ( X ! ) 7 n 2 1 7 4 n + l A H $ 0 2 5 . 7 ) + « V i i / V ) = i i [ w v i y fl q u k ’ Q / i z k ( V 1 4 ) ( 1 9 8 ) h 1 0 ( n V . 3 4 A U G ! ) = ( . 2 1 ? ) { ' J X M X E ‘ E F J u I J G s m e e x f < ” / ) F < v ( v : - ( 0 ) ) ° . . m . ) ) V } : i V i i - ( 9 1 ) + i < v 1 3 - U z ) c o s ¥ ‘ 1 ' ( V l a fi u s f n e fi n ‘ x w ' s f 1 ‘ 4 ( J ' = £ 6 1 2 ; + ( . 2 1 ) - . 1 1 0 1 ; - 0 1 ) c o s ’ X - ( V 2 3 ) 1 . ) S M Q S M X c o S E O n c e t h e A . i k ( V 2 3 ) a r e d e t e r m i n e d t h e i n t e g r a t i o n o f e q n . 1 9 8 i s s t r a i g h t f o r w a r d . T o c a l c u l a t e t h e A i k w 2 5 ) t h e f o l l o w i n g v a r i a b l e t r a n s f o r m a t i o n s a r e m a d e . A 5 3 0 5 » C ” 3 : { £ 7 6 E d O e i m - ' s m e u a n J ( x e x P < m ) ” V m ( 2 0 0 M , V n - fi p l M a " a ! m + A A - M 3 H ! C X ' " - ’ M M ) ( 1 M f ' , M * M I ' M ” * ( ’ m M 4 ) - ! M ( , l ) u . a ” c - * ! M g ( ( + ‘ M M H a - ) M . ! w ) I I 3 k ) N ) m a - n n ) " “ 2 " ) M . 1 - M , ! ( t n W ‘ + U : [ 4 ‘ l e M X - A Z M / i k Z u . fi l I ( M f M a ) ! 4 " . ( a f l . ) ! < A / , + M 1 7 5 n n + 1 m — - " ' x " fl C V U L Y » : ” ( V ) 3 § V 5 . . . “ ) ( 2 0 1 ) M a c X K ‘ X M K i m ” “ 0 E q u a t i o n 1 9 9 m a y b e r e w r i t t e n i n t h e f o l l o w i n g f o r m . . v n “ A i K C X J : ( 1 ” ) 1 2 z b £ ( < ) B M ( K ) A : : ( X ) ( 2 0 2 ) [ = 0 M 8 0 1 7 . 2 1 1 o n r O O % . % . , u = [ i ( X ; + y ) + 3 ( x s ‘ 7 ) ° ° ’ 7 + x 5 7 “ " Q S " " x ‘ ° S E ] ( 2 0 4 ) < H I I V ' - V ; - . m [ : ( X fi - y ) - 1 ( X 3 - Y > C O S ' X - X 3 y S m é S m ’ X C O S E J ( 2 0 5 ) A f t e r s u b s t i t u t i o n o f e q n . 2 0 4 a n d 2 0 5 i n t o e q n . 2 0 3 , u s e o f t h e b i n o m i a l e x p a n s i o n a n d m a n y l o n g i n t e g r a t i o n s t h e f o l l o w i n g e x p r e s s i o n f o r A 1 m ( X . 3 ) r e s u l t s . # 5 0 M 5 0 # 8 0 M = O 1 : 0 . L I ) ( 1 " ( M * M , A 4 ’ M 1 ) ) . ( J + l a - l ) ‘ ! ( 2 ( l + m + l ) - ( fi t h + A 6 ‘ M a ) ~ I ) ” x ; _ ( 1 4 - m d u n / “ M r M - M , » ( 2 0 6 ) l . 1 . = i Z Z A A “ ) ( 2 0 7 ) 1 7 6 M + M , ’ I \ G - M 1 ' - ‘ e v e n { W i n n e r K + i - p I ! e v e n s k i e g e r T h e s e c a l c u l a t i o n s o f A i fi ( x j ) m a y b e c h e c k e d b y h a n d c a l c u l a t i o n f o r l o w e s t o r d e r c o l l o c a t i o n . C h e c k i n g t h e h i g h o r d e r c o l l o c a t i o n r e s u l t s i s f a c i l i t a t e d b y n o t i n g t h a t t h e s t e a d y - s t a t e f o r m o f e q n . 1 9 8 i s g i v e n i n t e r m s o f A 1 ? ( X j ) a l o n e s i n c e t h e s t e a d y - s t a t e d i s t r i b u t i o n f u n c t i o n i s u n i t y e v e r y w h e r e . n + | r m [ 8 ! = 1 T h e c a l c u l a t e d a n d c h e c k e d v a l u e s f o r A i k ( x j ) a r e p r e s e n t e d i n t h e a p p e n d e d m a t e r i a l . W i t h t h i s c o u p l i n g m a t r i x A , i n t e g r a t i o n o f t h e m o m e n t e q u a t i o n s p r o c e e d s , g i v e n t h e i n i t i a l d i s t r i b u t i o n a n d a n o r m a l i z a t i o n . I n t e g r a t i o n o f e q n . 1 9 8 i s p e r f o r m e d w i t h t h e I M S L i n t e g r a t o r D G E A R . T h e s o l u t i o n o f t h e B o l t z m a n n e q u a t i o n m u s t s a t i s f y d e n s i t y a n d e n e r g y n o r m a l i z a t i o n . I n t h e c a l c u l a t i o n s p r e s e n t e d h e r e t h e d i s t r i b u t i o n f u n c t i o n i s r e n o r m a l i z e d o f t e n i n t h e i n t e g r a t i o n t o s a t i s f y t h e c o n s t a n t d e n s i t y r e q u i r e m e n t a n d t h e e n e r g y i s c a l c u l a t e d a n d u s e d t o e v a l u a t e t h e a c c u r a c y o f t h e i n t e g r a t i o n a n d a p p r o x i m a t i o n m e t h o d s . A l l i n t e g r a t i o n s i n v e l o c i t y a r e d o n e b y G a u s s i a n L a g u e r r e q u a d r a t u r e . 1 7 7 C O c o . 2 l l ! " 0 2 - 9 0 1 ) + ) A v = 1 5 ( a n z i x v z i fl v J V : 3 . ( 2 0 8 ) 0 O T h e d i f f i c u l t s t e p i n s o l u t i o n o f t h e n o n l i n e a r p r o b l e m i s t h e c a l c u l a t i o n o f t h e c o u p l i n g m a t r i x A . O n c e i t i s I E c o n s t r u c t e d , a l i n e a r a n a l y s i s a r o u n d t h e s t e a d y - s t a t e m a y j E E E E E i F 1 . a l s o b e d o n e . F o r t h e l i n e a r i z e d p r o b l e m d e f i n e t h e f o l l o w i n g d e v i a t i o n v a r i a b l e . c i v i l / r ) : £ ( v z , ’ r ) — l . ( 2 0 9 ) S u b s t i t u t i o n o f e q n . 2 0 9 i n t o e q n . 1 9 8 a n d s i m p l i f i c a t i o n o f t h e r e s u l t t o t e r m s z e r o o r f i r s t o r d e r i n E l e a d s t o t h e f o l l o w i n g a u t o n o m o u s o r d i n a r y d i f f e r e n t i a l e q u a t i o n . n + 4 ( £ 0 3 ? ) = Z € 3 , 8 0 1 , ” ( 2 1 0 ) d 1 » 2 : . A H C 5 ; = Z A i d “ ) - $ 4 5 ( 2 1 1 ) ' 6 ' ! A n a l y s i s o f t h e l i n e a r i z e d p r o b l e m a m o u n t s t o a s t u d y o f t h e m a t r i x o p e r a t o r C , s p e c i f i c a l l y , i d e n t i f i c a t i o n o f t h e e i g e n v a l u e s a n d e i g e n v e c t o r s o f C . W i t h t h e e i g e n v a l u e s a n d e i g e n v e c t o r s o f C t h e f o r m o f t h e s o l u t i o n i s d e t e r m i n e d g i v e n t h e i n i t i a l c o n d i t i o n s . T h e e i g e n s o f C w e r e d e t e r m i n e d w i t h t h e I M S L E I G R F r o u t i n e , w h i c h i s b a s e d o n t h e Q R a l g o r i t h m . T m e t e h a i i h e g g t e e e e d f c n r n o n o i v r v r a a a d m l l l e a s u r u l e e f i o s z f o i r o e s o e t l d i l h l d g l e e o e o c d c n C a t v a a e t o i s c i p o n t o e t o n r h , r a e c o a o s w t a d r r t r e h d e r a e r o o i r t r p o e h r f e o e i f 4 n s e v e x c - a n c o t r e l 1 e i p l d a 1 o t i p t a o n o n t i w i s h e a t t n i o h h t t n . t i n c i a r n p e a c p T s r e h p n e n e e e a d c w s e t e d s t o b y 1 7 8 o n e . T h e s p e c t r u m o f C f o r a n N o r d e r c o l l o c a t i o n i s m a d e u p o f t h e f o l l o w i n g , + 1 , 0 , — n / ( n + 2 ) w h e r e n = 1 , 2 , 3 . . . , N - 2 . T h e i n v a r i a n c e o f t h e s p e c t r u m i s a r e s u l t o f t h e s u c c e s s i v e i n t e g r a b i l i t y p r o p e r t y o f t h e L a g u e r r e m o m e n t s , f o u n d b y T r u e s d e l l . T h e s p e c t r u m o f C t h u s h a s a l i m i t p o i n t a t - l , i n a g r e e m e n t w i t h t h e r e s u l t s o f W a n g C h a n g a n d U h l e n b e c k . T h e s i n g l e p o s i t i v e e i g e n v a l u e i n d i c a t e s t h a t t h e e q u i l i b r i u m p o i n t ( £ I = 0 ) i s a s a d d l e p o i n t . T h e e i g e n s p a c e o f C m a y b e d e c o m p o s e d i n t o t h e u n s t a b l e m a n i f o l d , i n v a r i a n t m a n i f o l d a n d s t a b l e m a n i f o l d , c o r r e s p o n d i n g t o t h e p o s i t i v e , z e r o a n d n e g a t i v e e i g e n v a l u e s , r e s p e c t i v e l y . F o r a n N p o i n t c o l l o c a t i o n , c o n s i d e r a ! - n e i g h b o r h o o d a r o u n d t h e o r i g i n , w h e r e 5 4 ‘ ! . A n y v e c t o r w i t h i n t h e X - b a l l a n d o n t h e s t a b l e m a n i f o l d r e m a i n s o n t h e s t a b l e m a n i f o l d a n d a p p r o a c h e s t h e o r i g i n a s y m p t o t i c a l l y , t h a t i s , i n i n f i n i t e t i m e . A n y v e c t o r w i t h i n t h e 5 - b a l l a n d o n t h e i n v a r i a n t m a n i f o l d i s i n v a r i a n t i n t i m e a n d s o n e i t h e r r e l a x e s n o r g r o w s b u t i s m a p p e d b y C o n t o t h e o r i g i n . A n y v e c t o r w i t h i n t h e 5 ’ - b a l l a n d o n t h e u n s t a b l e m a n i f o l d m a y a p p r o a c h t h e o r i g i n a r b i t r a r i l y c l o s e b u t i n f i n i t e t i m e w i l l l e a v e t h e J - n e i g h b o r h o o d . B e c a u s e t h e l i n e a r i z a t i o n i s a r t 6 E L . ‘ A . P 2 “ . . . . . . 2 . ~ L 2 “ " I v a ” / . J [ ' 6 ‘ E X P ( A ? ) 1 ’ I . C ” “ ( D O A / I ' M ( 2 1 2 ) 1 7 9 l o c a l a n a l y s i s n o c o n c l u s i o n m a y b e d r a w n a b o u t t h e t r a j e c t o r y o n c e i t l e a v e s t h e 5 , - n e i g h b o r h o o d o f t h e o r i g i n . I n a n y c a s e , i f t h e l i n e a r i z e d r e s u l t s d e s c r i b e t h e r e l a x a t i o n t o t h e e q u i l i b r i u m e . g . t h e K B K W s o l u t i o n a f t e r l o n g t i m e , t h e n t h e p r o j e c t i o n s o f t h e d i s t r i b u t i o n f u n c t i o n o n t o t h e i n v a r i a n t a n d u n s t a b l e m a n i f o l d s m u s t v a n i s h . T h i s e x p e c t a t i o n i s e x a m i n e d l a t e r . F r o m t h e e i g e n s o f C t h e f o l l o w i n g s o l u t i o n o f t h e l i n e a r i z e d p r o b l e m i s c o n s t r u c t e d . T h e c o l u m n s o f ‘ Z _ a r e t h e n o r m a l i z e d e i g e n v e c t o r s o f C . W i t h o u t l o s s o f g e n e r a l i t y , a s s u m e t h a t t h e l a s t k e i g e n v e c t o r s s p a n t h e u n s t a b l e a n d i n v a r i a n t m a n i f o l d s , s o i t i s r e q u i r e d t h a t t h e s o l u t i o n i s s p a n n e d o n l y b y t h e f i r s t N - k e i g e n v e c t o r s , 8 0 C N ' C N - l , . . . . , C a r e s e t t o z e r o . T o f i x t h e r e m a i n i n g N - k + 1 c o e f f i c i e n t s i t i s r e q u i r e d t h a t t h e i n i t i a l c o n d i t i o n b e s p e c i f i e d . T h i s f i x e s t h e v a l u e o f t h e c o l u m n v e c t o r o n t h e l e f t h a n d s i d e o f e q n . 2 1 2 , a n d o n e m a y w r i t e f o r e q n . 2 1 2 t h e f o l l o w i n g s y m b o l i c e q u a t i o n . E = S y “ A l u U V - K ) ( A l - k ) ! ! ! ( 2 1 3 ) 1 8 0 T h e m a t r i x o p e r a t o r m a p s t h e u n k n o w n N — k d i m e n s i o n a l v e c t o r C i n t o t h e N d i m e n s i o n a l i n i t i a l v a l u e v e c t o r E . T h e c o r r e s p o n d i n g l e a s t e r r o r s o l u t i o n o f e q n . 2 1 3 i s g i v e n b y C = ( S T S ‘ ) - 1 S T E a n d t h e p r o j e c t i o n m a t r i x o p e r a t o r i s 9 ( S T $ ) — . S T T h e e r r o r i n t h e p r o j e c t i o n i s t h e n o r m o f t h e v e c t o r w h i c h i s p r o j e c t e d o u t a n d i s e q u a l t o ( E T E - E T S ( S T S ) - 1 5 T E ) , w h e r e S i s t h e N x ( n - k ) m a t r i x o f e i g e n v e c t o r s w h i c h s p a n t h e s t a b l e m a n i f o l d . F o r a g i v e n i n i t i a l c o n d i t i o n , o n e m a y n o w p r o j e c t t h e i n i t i a l v e c t o r o n t o t h e s t a b l e m a n i f o l d , f o l l o w t h e r e l a x a t i o n o f t h e v e c t o r o n t h e s t a b l e m a n i f o l d a n d c o m p a r e t h e c a l c u l a t e d d i s t r i b u t i o n w i t h t h e a v a i l a b l e c l o s e d f o r m s o l u t i o n . T h e r e s u l t s a n d d i s c u s s i o n o f r e s u l t s a r e p r e s e n t e d i n f o u r p a r t s . I n t h e f i r s t , t h e s p e c t r u m a n d e i g e n s p a c e o f C a r e d i s c u s s e d a n d c o m p a r e d w i t h t h e w o r k o f W a n g C h a n g a n d U h l e n b e c k . S e c o n d , a c o m p a r i s o n i s m a d e o f t h e c a l c u l a t e d a n d t h e c l o s e d f o r m e v o l u t i o n o f t h e d i s t r i b u t i o n f r o m K B K W i n i t i a l c o n d i t i o n s t o t h e e q u i l i b r i u m . T h i r d , t h e c o m p a r i s o n i s r e p e a t e d f o r t h e l i n e a r i z e d c a l c u l a t i o n s . F o u r t h , t h e c a l c u l a t i o n s o f t h e e v o l u t i o n o f a d i s t r i b u t i o n f u n c t i o n f r o m n o n - K B K W i n i t i a l c o n d i t i o n s a r e p r e s e n t e d a n d d i s c u s s e d . W a n g C h a n g a n d U h l e n b e c k ( 1 9 5 2 ) f o u n d t h a t t h e a s s o c i a t e d L a g u e r r e p o l y n o m i a l s a r e t h e e n e r g y e i g e n f u n c t i o n s o f t h e l i n e a r i z e d B o l t z m a n n c o l l i s i o n i n t e g r a l f o r M a x w e l l m o l e c u l e s , w i t h d i s c r e t e e i g e n v a l u e s i n t h e s e t { 0 , - 1 1 w i t h - 1 a s a l i m i t p o i n t . ‘ T h i s p r o b l e m i s i d e n t i c a l t o t h e l i n e a r i z e d p r o b l e m 1 8 1 u n d e r c o n s i d e r a t i o n h e r e a n d c o m p a r i s o n o f r e s u l t s i s u s e f u l . I n t h e a n a l y s i s o f W a n g C h a n g a n d U h l e n b e c k a n i n f i n i t e b a s i s s e t i s u s e d w h e r e a s i n t h i s w o r k o n l y a f i n i t e d i m e n s i o n a l e i g e n s p a c e i s u s e d . T h e e s s e n t i a l s p e c t r u m , i . e . t h e s e t o f l i m i t p o i n t s o f t h e d i s c r e t e s p e c t r u m , i s i d e n t i c a l i n e a c h w o r k . T h e o n l y , b u t s u b s t a n t i a l , d i f f e r e n c e b e t w e e n t h i s w o r k a n d t h a t o f W a n g C h a n g a n d U h l e n b e c k i s t h e p r e s e n c e o f t h e s i n g l e p o s i t i v e e i g e n v a l u e , + 1 , i n t h e s p e c t r u m o f l i n e a r i z e d , c o l l o c a t e d c o l l i s i o n o p e r a t o r . T h i s s i n g l e e i g e n v a l u e c h a n g e s t h e c h a r a c t e r o f t h e e q u i l i b r i u m p o i n t f r o m t h a t o f a s t a b l e n o d e ( W a n g C h a n g a n d U h l e n b e c k ) t o a s a d d l e p o i n t . T h e p r e s e n c e o f t h e p o s i t i v e e i g e n v a l u e i s r o b u s t w i t h r e s p e c t t o c h a n g e s i n t h e o r d e r o f t h e c o l l o c a t i o n a n d i t c a n b e s h o w n t h a t + 1 i s a n e l e m e n t o f t h e s p e c t r u m o f t h e c o l l i s i o n o p e r a t o r f o r a n y o r d e r N . C o n s i d e r t h e e v o l u t i o n e q u a t i o n f o r £ 1 x , ’ r ) . A 6 4 " : 9 ? ( 2 1 4 ) A ? * N o w c o n s i d e r t h e v e c t o r o f t h e f o r m Z E N - 8 w h e r e I I i s t h e c o l u m n v e c t o r w i t h e a c h e l e m e n t s e t t o u n i t y . ' 4 - V . N Q I I = I V Q ( 2 1 5 ) I n e q n . 2 1 5 t h e c o l u m n v e c t o r D i s f o r m e d b y s u m m i n g B o l t z m a n n e q u a t i o n . 1 8 2 t h e r o w s o f C . y D , - = Z C s " ' ( 2 1 6 ) ( i t ) v ) v = . X - - - . Z Z A ‘ “ ( ’ 3 S " ( 2 1 7 ) 4 % : k = 1 2 1 . A n d s o , N J 5 I I i s a n o r m a l i z e d e i g e n v e c t o r o f C w i t h t h e e i g e n v a l u e o f + 1 , f o r a l l N . R e c o n c i l i a t i o n o f t h e s e r e s u l t s w i t h t h o s e o f W a n g C h a n g a n d U h l e n b e c k i s p o s s i b l e i f i t i s n o t e d t h a t t h e n o r m a l i z a t i o n f a c t o r f o r t h i s e i g e n v e c t o r i s d e p e n d e n t o n t h e o r d e r o f c o l l o c a t i o n a n d t h a t , u n l i k e t h e o t h e r e i g e n v e c t o r s , t h e v a l u e o f e a c h e l e m e n t o f t h e e i g e n v e c t o r g o e s t o z e r o a s N - % . I n t h e l i m i t o f a n i n f i n i t e b a s i s s e t e x p a n s i o n , l i k e t h a t o f W a n g C h a n g a n d U h l e n b e c k , t h e u n s t a b l e m a n i f o l d v a n i s h e s a n d t h e p o s i t i v e e i g e n v a l u e i s n o l o n g e r a n i m p o r t a n t f e a t u r e . N u m e r i c a l c a l c u l a t i o n s , h o w e v e r , a l w a y s i n v o l v e t r u n c a t i o n o f t h e b a s i s s e t a n d s o t h e p r e s e n c e o f t h e u n s t a b l e m a n i f o l d r e m a i n s a s a r e l e v a n t f e a t u r e o f n u m e r i c a l s o l u t i o n o f t h e l i n e a r i z e d 1 8 3 R e c a l l t h a t o n e r e a s o n f o r a d o p t i n g t h e M a x w e l l m o d e l i n t h i s a n a l y s i s o f r e l a x a t i o n o f a n o n e q u i l i b r i u m d i s t r i b u t i o n i s t h a t a c l o s e d f o r m s o l u t i o n o f t h e c o r r e s p o n d i n g B o l t z m a n n e q u a t i o n e x i s t s f o r a s p e c i a l c l a s s o f i n i t i a l c o n d i t i o n s , i . e . t h e K B K W c l a s s . A n u m e r i c a l t e c h n i q u e m a y t h u s b e t e s t e d o n t h e K B K W i n i t i a l c o n d i t i o n s a n d t h e n a p p l i e d t o t h e s t u d y o f r e l a x a t i o n o f i n i t i a l c o n d i t i o n s m o r e l i k e t h o s e c h a r a c t e r i s t i c o f a d i s s o c i a t e d g a s . W i t h t h i s g o a l i n m i n d t h e r e s u l t s o f c a l c u l a t i o n s o f r e l a x a t i o n o f t h e d i s t r i b u t i o n f u n c t i o n f r o m K B K W i n i t i a l c o n d i t i o n s a r e c o n s i d e r e d . T h e e v o l u t i o n o f t h e f u l l r a n g e o f K B K W i n i t i a l c o n d i t i o n s w a s c a l c u l a t e d f o r a l l t i m e s o u t t o e q u i l i b r a t i o n a n d c o m p a r e d w i t h t h e c l o s e d f o r m r e s u l t s . C a l c u l a t i o n s w e r e m a d e f o r f r o m 4 t o 1 1 c o l l o c a t i o n p o i n t s a n d t h e r e s u l t i n g d i s t r i b u t i o n f u n c t i o n s e s s e n t i a l l y r e p r o d u c e t h e c l o s e d f o r m s o l u t i o n o v e r t h e r a n g e o f 1 % , t i m e a n d e n e r g y . I n F i g u r e 2 0 t h e c a l c u l a t i o n r e d u C e d d i s t r i b u t i o n f u n c t i o n i s c o m p a r e d w i t h t h e c l o s e d f o r m r e s u l t a s a f u n c t i o n o f t i m e f o r h , = o . 2 a n d v a r i o u s v a l u e s o f e n e r g y . S e v e r a l p r o p e r t i e s o f t h e d i s t r i b u t i o n f u n c t i o n w e r e c a l c u l a t e d a n d a r e p r e s e n t e d i n F i g u r e s 2 1 a n d 2 2 . I n F i g u r e 2 1 t h e a v e r a g e e n e r g y o f t h e d i s t r i b u t i o n i s p l o t t e d a s a f u n c t i o n o f t i m e . T h e c a l c u l a t i o n o f t h e e n e r g y i s a c h e c k o n t h e d e g r e e t o w h i c h t h e e n e r g y i s c o n s e r v e d d u r i n g i n t e g r a t i o n a n d r e n o r m a l i z a t i o n . ' I n F i g u r e 2 1 t h i s v a l u e i s c o n s t a n t a t 3 , i n d i c a t i n g t h a t e n e r g y c o n s e r v a t i o n i s s a t i s f i e d . T h i s i s a l s o r e p r e s e n t a t i v e o f o t h e r c a l c u l a t i o n s . l n o i n t 4 3 u b i 1 r 2 3 t s i l 0 d 3 n 8 2 d e . c y u g d r e e j n 6 r 2 e n 4 m r f o o 2 f n 2 2 s d e e u s l o a 0 l v 1 2 c l d a 8 n r 1 1 a e v d e 6 s e n 1 t a d l n 4 u a 1 1 c l 2 a . 2 0 c 1 1 _ e = h = 0 t b n 1 b 1 8 l 6 f o r o n f o s n i o r i a t p c m n 7 I 1 6 . [ 3 5 X u o r q o u n ; u o r q n q u q s r p p e o n p a u 4 o u C f l 2 1 . : 0 2 e r u g i F N o r m a l i z e d t i m e 1 8 4 4 6 5 2 . 4 P 5 2 . 4 L 1 . 8 5 2 . 4 1 n 1 A l a n L r o f l a n o i t c n u f - H n n a m z t l o B d o i + c n u £ 1 n a - y L g H 1 . r ) e s n e e u l e a g v 1 a r d e e v t 1 a a " 3 r e n E 4 4 1 l e u h c t l a c f ( o n 2 o . i 0 t u = l o . J v b E : 1 2 e r u g i F 1 0 9 . . . 3 3 2 l K b x e u e B B P I B A E p a z r r e m x o u 2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0 2 2 2 4 2 6 2 8 N o r m a l i z e d t i m e H - f u n c t i o n a l 1 8 5 4 2 3 0 0 0 0 . . 0 0 . ‘ 1 1 0 0 . 0 . 2 0 3 E r o f m r o n n a e d i l c u E d n a 0 1 L s e e u h l 8 t a v f o d 6 e n t o a i l 4 t u u c l l a o c 2 v ( E : 2 2 e r u g i F 1 1 1 1 0 “ U P S P T “ [ 0 1 1 3 I O o H 1 2 1 4 1 6 1 8 2 0 2 2 2 4 N o r m a l i z e d t i m e 2 6 0 . 2 . 2 8 n o r m 1 8 6 1 8 7 T h e o t h e r v a l u e p r e s e n t e d i n F i g u r e 2 1 i s t h e H f u n c t i o n a l o f B o l t z m a n n . T h e H f u n c t i o n a l i s d e f i n e d i n t h e f o l l o w i n g e x p r e s s i o n . a : 2 _ 1 1 1 H [ ¥ T ( v , + ) ] - { / 1 7 { V £ . ( V ’ T ) I n f r ( v , fi ’ ) c ’ v ( 2 1 8 ) O B o l t z m a n n ( 1 8 7 2 ) s h o w e d t h a t d H / d 7 ( 0 f o r a l l " r a n d u s e d t h e r e s u l t t o s h o w t h a t a n y a r b i t r a r y i n i t i a l d i s t r i b u t i o n r e l a x e s t o t h e M a x w e l l i a n i n i n f i n i t e t i m e . F o r t h e M a x w e l l i a n d i s t r i b u t i o n t h e v a l u e o f H i s - 4 . 2 5 6 8 1 o r ( - % ( l n ( 2 ¢ r ) + l ) ) . T o c h e c k t h i s v a l u e a g a i n s t t h e c a l c u l a t i o n a M a x w e l l i a n w a s u s e d a s t h e i n i t i a l c o n d i t i o n . T h e c a l c u l a t e d v a l u e o f H i s - 4 . 2 5 6 2 0 , a n d t h i s v a l u e i s a l s o p r e s e n t e d i n F i g u r e 2 1 a s t h e b a s e l i n e . A s e x p e c t e d , t h e H - c u r v e r e l a x e s m o n o t o n i c a l l y t o t h e M a x w e l l i a n b a s e l i n e , p r o v i d i n g a n a d d i t i o n a l c h e c k o n t h e c a l c u l a t i o n a l r e s u l t s . T w o f u n c t i o n n o r m s a r e p r e s e n t e d i n F i g u r e 2 2 , t h e A i - n o r m f o r t h e f u n c t i o n s p a c e o f t h e f u l l d i s t r i b u t i o n f T ( v 3 , ? ’ ) a n d t h e E u c l i d e a n n o r m o f t h e N - d i m e n s i o n a l v e c t o r s p a c e o f t h e c o l l o c a t e d p r o b l e m . T h e s e n o r m s a r e d i s c u s s e d l a t e r b u t n o t e h e r e t h a t t h e y d e c r e a s e i n a m o n o t o n e f a s h i o n t o z e r o . I n s u m m a r y , t h e m e t h o d o f o r t h o g o n a l c o l l o c a t i o n a p p e a r s t o b e a n e x c e l l e n t n u m e r i c a l m e t h o d f o r a n a l y s i s o f t h e n o n l i n e a r B o l t z m a n n e q u a t i o n f o r M a x w e l l m o l e c u l e s . I t i s 1 - ‘ " . ' _ m — — c — E 1 A 2 1 8 8 w i t h a d e g r e e o f c o n f i d e n c e t h e n t h a t t h e e v o l u t i o n o f n o n - K B K W i n i t i a l d i s t r i b u t i o n s i s c o n s i d e r e d . T h e p a r t i c u l a r t y p e o f n o n - K B K W i n i t i a l d i s t r i b u t i o n s e l e c t e d f o r c a l c u l a t i o n s h o u l d r e p r e s e n t t h e m a j o r f e a t u r e o f a n o n e q u i l i b r i u m ' d i s t r i b u t i o n o f h y d r o g e n a t o m s , t h a t i s , i t s h o u l d h a v e a n o v e r p o p u l a t e d t a i l r e g i o n c o r r e s p o n d i n g t o t h e h i g h e n e r g y d i s s o c i a t i o n f r a g m e n t s . T h e r e s u l t s o f c a l c u l a t i o n s f o r t h e e v o l u t i o n o f j u s t s u c h a n i n i t i a l c o n d i t i o n a r e p r e s e n t e d i n F i g u r e 2 3 a s c u r v e s o f t h e r e d u c e d d i s t r i b u t i o n a s a f u n c t i o n o f t i m e f o r v a r i o u s e n e r g i e s . I n c o n t r a s t t o t h e K B K W i n i t i a l c o n d i t i o n , w h i c h h a s a s i n g l e m a x i m u m i n t h e r e d u c e d d i s t r i b u t i o n t h e n o n - K B K W i n i t i a l c o n d i t i o n s e l e c t e d f o r c a l c u l a t i o n s h a s t w o l o c a l m a x i m a . I n t h e c a l c u l a t i o n s p r e s e n t e d i n F i g u r e 2 3 t h i s o s c i l l a t o r y f e a t u r e i s p r o p a g a t e d a n d a m p l i f i e d . T h e o v e r s h o o t o f t h e e q u i l i b r i u m a n d s l o w d e c a y , c h a r a c t e r i s t i c o f t h e T j o n e f f e c t , i s i n e v i d e n c e i n t h e h i g h e r e n e r g y r e g i o n s o f t h e d i s t r i b u t i o n , w i t h s m a l l a m p l i t u d e , n o n p e r i o d i c o s c i l l a t o r y p h e n o m e n a i n t h e l o w e r e n e r g y r a n g e s . S u c h r e l a x a t i o n b e h a v i o r i s q u a l i t a t i v e l y d i s t i n c t f r o m K B K W r e l a x a t i o n . R e c a l l t h a t i n t h e K B K W s o l u t i o n t h e r e i s o n l y o n e r e l a x a t i o n t i m e s c a l e , ’ r ~ 6 , w h i c h m a y b e i d e n t i f i e d b y e x a m i n a t i o n o f t h e p a r a m e t e r k ) . T h i s s i n g l e - m o d e r e l a x a t i o n r e s u l t s i n t h e h i g h l y n o n u n i f O r m r e l a x a t i o n o f t h e h i g h e n e r g y t a i l r e f e r r e d t o e a r l i e r . F o r n o n - K B K W i n i t i a l d i s t r i b u t i o n s o f t h e t y p e c o n s i d e r e d i n F i g u r e 2 3 t h e r e a p p e a r s t o b e a s p e c t r u m o f r e l a x a t i o n t i m e s c a l e s , s o m e o f w h i c h a r e v e r y s h o r t a n d . n o i t 6 i 1 3 d n o 4 c 1 3 l a 2 i 1 3 t i n 0 i 1 3 W K _ L 1 8 B 2 K - n 6 o 2 n a 1 4 2 m o r 2 e f 1 2 m i n t o 0 i 1 2 d t e u z b 1 8 i i 1 l r a t m s 1 6 r i 1 o d N d 1 4 e 1 c u d 1 2 e 1 r e 1 0 h 1 t 8 o 4 f n o 6 i J t u l 1 4 o _ 2 l _ _ 9 , v E : 3 2 e r u g i F 0 5 I - h ‘ - . , 3 4 1 3 . 1 1 + 1 m u m i x a M 0 7 6 5 1 2 1 1 1 . . . u o r q o u n ; u o r q n q r x q s r p p e o n p e u 2 . 1 1 8 9 1 9 0 c h a r a c t e r i z e p r o c e s s e s w h i c h r e s u l t i n h i g h e n e r g y p r o d u c t s . I n F i g u r e 2 4 t h e c a l c u l a t e d v a l u e s o f e n e r g y a n d t h e H - f u n c t i o n a l a r e p r e s e n t e d . T h e c a l c u l a t e d e n e r g y i s w i t h i n 0 . 2 % o f t h e M a x w e l l i a n v a l u e f o r a l l t i m e a n d t h e v a l u e o f t h e H - f u n c t i o n a l r e l a x e s m o n o t o n i c a l l y t o a b a s e l i n e w h i c h i s w i t h i n 0 . 1 % o f t h e M a x w e l l i a n b a s e l i n e . I n F i g u r e 2 5 t h e c a l c u l a t e d A ; a n d E u c l i d e a n n o r m s a r e p r e s e n t e d o v e r t h e r a n g e o f t i m e s b e g i n n i n g w i t h t h e i n i t i a l d i s t r i b u t i o n o n o u t t o e q u i l i b r a t i o n . T h e J ; n o r m i n i t i a l l y f a l l s t o w a r d z e r o , p a s s e s t h r o u g h a m i n i m u m a t ¢ w ~ 2 . 1 a n d t h e n t h r o u g h a m a x i m u m a t ‘ ? ‘ ~ 2 8 . 6 a n d t h e n s l o w l y d e c a y s t o z e r o . T h e E u c l i d e a n n o r m o f t h e d e v i a t i o n i n c r e a s e s f r o m t h e i n i t i a l v a l u e t o a m a x i m u m a t ? ' ~ 1 . 5 a n d t h e n d e c r e a s e s t o z e r o . B o t h n o r m s r e f l e c t t h e o v e r s h o o t b e h a v i o r a n d n o n - K B K W r e l a x a t i o n p h e n o m e n a i l l u s t r a t e d i n F i g u r e 2 3 . T h e s e r e s u l t s i n d i c a t e t h a t t h e T j o n e f f e c t o c c u r s i n t h e e v o l u t i o n o f d i s t r i b u t i o n f u n c t i o n s w h i c h r e s u l t f r o m t h e n o n l i n e a r B o l t z m a n n e q u a t i o n w i t h a m o m e n t u m c o n s e r v i n g k e r n e l . S o f o r t h i s m o d e l t h e r e l a x a t i o n o f t h e d i s t r i b u t i o n f u n c t i o n i s n o t o n l y h i g h l y n o n u n i f o r m b u t a l s o o s c i l l a t o r y . T h e t i m e s c a l e s f o r r e l a x a t i o n v a r y g r e a t l y f r o m t h e t h e r m a l t o t a i l r e g i o n . R e c a l l t h a t t h e l i n e a r i z e d a n a l y s i s o f t h e r e l a x a t i o n p r o b l e m r e s u l t e d i n ‘ a l i n e a r e v o l u t i o n e q u a t i o n a n d t h e c o r r e s p o n d i n g e i g e n v a l u e s a n d e i g e n v e c t o r s . F r o m t h e e i g e n v e c t o r s a p r o j e c t i o n m a t r i x o p e r a t o r m a y b e c o n s t r u c t e d a n d t h e n u s e d t o m a p a n y i n i t i a l d i s t r i b u t i o n o n t o t h e s t a b l e 6 5 2 . 4 ” I « 8 5 2 . 4 - a r o f 0 l 3 a n . o n L o 8 i 2 t i c t n i 1 6 d u 2 f n - o H c 1 4 2 n l n a a i 1 2 m t 2 z i t n l i l 0 o 2 B W K d B 1 _ 1 8 e n K 1 m a - i n t o y 6 g n 1 d r e e a z n 1 e m 4 i 1 o l 1 1 1 1 1 a e r m g f 2 r a 1 o r g N e n v i 0 a v 1 l e o h v 8 t e f n o o 6 i n t o u i b 4 t i u r l t o s 1 2 v i _ E d 9 4 : 1 . 3 . 2 2 e r u g i F 3 . 0 - 4 . 2 5 4 s z e u a S E P I G A P p a z r t e m x o m H - f u n c t i o n a l 1 9 1 ) ) ' ‘ 0 0 1 1 ( ( 4 3 ) 6 ' 0 1 1 2 . " 0 1 ( 1 8 A 2 6 1 2 4 2 2 2 L 1 1 _ 0 L 2 8 l 1 e m i 6 t j 1 L A I l A d e 4 z 1 i l a m 2 r 1 o N 0 L o 1 n e h a 8 t m f o o r 6 f n o g i n 4 4 t i u v l l o o l 2 v v E e : 5 2 e r u g i F P . 4 ( M J O U u e e p r f o n g ) b o q T ) n o r m I 3 ( a n d E u c l i d e a n n o r m o f a d i s t r i b u t i o n - K B K W i n i t i a l c o n d i t i o n . 1 9 2 1 9 3 m a n i f o l d . S u c h c a l c u l a t i o n s w e r e m a d e f o r K B K W i n i t i a l d i s t r i b u t i o n s o f ’ b o ’ b e t w e e n 1 ( 1 0 - 6 ) a n d 0 . 1 a n d t h e s o l u t i o n o f t h e l i n e a r i z e d p r o b l e m w a s c o m p a r e d w i t h t h e K B K W c l o s e d f o r m s o l u t i o n . T h e a g r e e m e n t b e t w e e n t h e t w o w a s e x c e l l e n t , s u p e r i o r i n e a s e o f c a l c u l a t i o n a n d i n a c c u r a c y t o t h e n o n - l i n e a r c a l c u l a t i o n s . T h i s i s p r o b a b l y d u e t o t h e a b s e n c e o f n o r m a l i z a t i o n s t e p s i n t h e l i n e a r i z e d s o l u t i o n . T h e a g r e e m e n t a l s o i n d i c a t e s t h a t K B K W i n i t i a l d i s t r i b u t i o n s h a v e z e r o p r o j e c t i o n o n t o t h e i n v a r i a n t a n d u n s t a b l e m a n i f o l d s . T h e p o s s i b i l i t y o f a c o r r e l a t i o n b e t w e e n t h e p r e s e n c e o f a n o n z e r o p r o j e c t i o n o f a n i n i t i a l d i s t r i b u t i o n o n t o t h e u n s t a b l e m a n i f o l d a n d t h e o s c i l l a t o r y e v o l u t i o n o f t h e d i s t r i b u t i o n i s i n t r i g u i n g a n d w a s i n v e s t i g a t e d b y c a l c u l a t i o n o f t h e E u c l i d e a n n o r m o f t h e p r o j e c t i o n o f b o t h K B K W a n d n o n - K B K W i n i t i a l d i s t r i b u t i o n s o n t o t h e u n s t a b l e m a n i f o l d . T h e r e s u l t s o f t h e s e c a l c u l a t i o n s a r e p r e s e n t e d i n F i g u r e 2 6 a n d g i v e t h e r a t i o o f t h e E u c l i d e a n n o r m o f t h e p r o j e c t i o n o n t o t h e u n s t a b l e m a n i f o l d t o t h e E u c l i d e a n n o r m o f t h e i n i t i a l d i s t r i b u t i o n a s a f u n c t i o n o f t h e E u c l i d e a n n o r m o f t h e i n i t i a l d i s t r i b u t i o n . T h e r a n g e o n t h e a b s c i s s a c o r r e s p o n d s t o K B K W d i s t r i b u t i o n s o f b e f r o m 1 ( 1 0 - 6 ) t o 0 . 1 . F o r t h e K B K W i n i t i a l d i s t r i b u t i o n t h e r a t i o i n c r e a s e s m o n o t o n i c a l l y f r o m z e r o f o r ‘ 3 0 = O a n d h a s a m a x i m u m v a l u e o f 8 . 2 ( 1 0 _ 6 ) a t . h , = . 1 . T h i s b e h a v i o r r e f l e c t s t h e f a c t t h a t t h e l i n e a r i z a t i o n a r o u n d t h e M a x w e l l i a n i s s t r i c t l y c o r r e c t o n l y i n t h e l i m i t t h a t 5 0 ‘ 5 0 . T h e s m a l l v a l u e o f t h e r a t i o e v e n a t b e = . 1 c o r r e s p o n d s w i t h t h e 1 9 4 - l n o n - K B K W - 2 ’ 6 2 3 - 3 . m H E ’ 4 r 8 I - 5 - E x 8 ‘ - 6 L K B K W q — 7 L 1 1 1 1 1 - 7 - 6 - s - 4 - 3 - 2 - 1 0 L o g ( I n i t i a l E - n o r m ) F i g u r e 2 6 : R a t i o o f t h e E u c l i d e a n n o r m o f t h e p r o j e c t i o n o f t h e i n i t i a l c o n d i t i o n o n t o t h e u n s t a b l e m a n i f o l d t o t h e E u c l i d e a n n o r m o f t h e i n i t i a l c o n d i t i o n . w h i c h i s i n i t i a l l y o n t h e u n s t a b l e m a n i f o l d , a p p r o a c h e s t h e 1 9 5 e x c e l l e n t a g r e e m e n t b e t w e e n t h e l i n e a r i z e d K B K W a n d c l o s e d f o r m r e s u l t s r e f e r r e d t o e a r l i e r . T h e v a r i a t i o n o f t h e r a t i o w i t h n o r m i s o f a d i f f e r e n t f o r m f o r t h e n o n - K B K W i n i t i a l c o n d i t i o n s . T h e r a t i o o f t h e n o r m o f t h e p r o j e c t i o n o n t o t h e u n s t a b l e m a n i f o l d t o t h e n o r m o f t h e i n i t i a l n o n - K B K W d i s t r i b u t i o n i s u n i f o r m l y a b o u t 1 ( 1 0 - 2 ) o v e r t h e e n t i r e r a n g e o f F i g u r e 2 6 . T h e r e l a t i v e s i z e o f t h e u n s t a b l e c o m p o n e n t i s t h r e e o r d e r s o f m a g n i t u d e l a r g e r t h a n t h a t o f t h e m a x i m u m K B K W v a l u e a n d m a n y , m a n y o r d e r s o f m a g n i t u d e l a r g e r t h a n t h e c o r r e s p o n d i n g K B K W v a l u e a s t h e M a x w e l l i a n i s a p p r o a c h e d . B a s e d o n t h e s e r e s u l t s o n e m a y i n f e r a c o r r e l a t i o n b e t w e e n t h e p r e s e n c e o f t h e u n s t a b l e m a n i f o l d i n t h e e i g e n s p a c e o f t h e l i n e a r i z e d p r o b l e m a n d t h e p r e s e n c e o f o s c i l l a t o r y a n d l o c a l l y n o n - r e l a x i n g t r a j e c t o r i e s i n t h e s o l u t i o n t o t h e n o n l i n e a r p r o b l e m . R e c a l l t h a t a n y v e c t o r w h i c h i s o n t h e u n s t a b l e m a n i f o l d a n d w i t h i n a 5 - n e i g h b o r h o o d o f t h e o r i g i n w i l l , i n f i n i t e t i m e , l e a v e t h e S - n e i g h b o r h o o d . T h i s b e h a v i o r i s i l l u s t r a t e d i n t h e b e h a v i o r o f b o t h n o r m s p l o t t e d i n F i g u r e 2 5 , b u t i s n o t s e e n i n F i g u r e 2 2 . I n F i g u r e 2 2 t h e n o r m s o f t h e K B K W s o l u t i o n a r e p r e s e n t e d a n d s h o w o n l y m o n o t o n e d e c r e a s e w i t h t i m e . F o r t h e p a r t i c u l a r n o n - K B K W i n i t i a l d i s t r i b u t o n c o n s i d e r e d i n F i g u r e 2 5 t h e . L 2 n o r m a p p r o a c h e s t h e o r i g i n , t h e n r e t r e a t s a n d f i n a l l y r e l a x e s t o t h e e q u i l i b r i u m . T h e E u c l i d e a n n o r m r e t r e a t s f r o m t h e o r i g i n a n d t h e n r e l a x e s . T h e b e h a v i o r o f b o t h n o r m s r e s e m b l e s t h a t o f p a t r a j e c t o r y 1 9 6 o r i g i n , t h e n l e a v e s a n d f i n a l l y r e a p p r o a c h e s t h e o r i g i n , t h i s t i m e o n t h e s t a b l e m a n i f o l d . W h e t h e r o r n o t s u c h a t r a n s i t i o n f r o m t h e u n s t a b l e t o s t a b l e m a n i f o l d o c c u r s c a n n o t b e d e t e r m i n e d f r o m t h e l o c a l l i n e a r a n a l y s i s . I n s u m m a r y , t h e r e a r e a t l e a s t t h r e e s i g n i f i c a n t r e s u l t s f r o m t h e s e c a l c u l a t i o n s . F i r s t , a s u i t a b l e n u m e r i c a l a p p r o x i m a t i o n m e t h o d h a s b e e n t e s t e d a n d f o u n d t o e s s e n t i a l l y r e p r o d u c e t h e c l o s e d f o r m K B K W s o l u t i o n o f t h e n o n l i n e a r B o l t z m a n n e q u a t i o n w i t h a m o m e n t u m c o n s e r v i n g k e r n e l o v e r a w i d e r a n g e o f t i m e , v e l o c i t y a n d i n i t i a l c o n d i t o n . T h e m e t h o d o f o r t h o g o n a l c o l l o c a t i o n w i t h L a g u e r r e p o l y n o m i a l s i s a l s o g e n e r a l e n o u g h t o t r e a t n o n - M a x w e l l m o l e c u l e s , a s w e l l a s s y s t e m s w i t h e x t e r n a l f o r c e s a n d d e n s i t y g r a d i e n t s . T h e c a l c u l a t e d d i s t r i b u t i o n s a r e e a s i l y u s e d t o c a l c u l a t e t r a n s i e n t v a l u e s o f r e a c t i o n r a t e s , t r a n s p o r t c o e f f i c i e n t s a n d o t h e r q u a n t i t i e s r e l a t e d t o t h e d i s t r i b u t i o n f u n c t i o n , e . g . D o p p l e r b r o a d e n i n g o f e m i s s i o n l i n e s . S e c o n d , t h e s o l u t i o n o f t h e n o n l i n e a r B o l t z m a n n e q u a t i o n f o r c e r t a i n i n i t i a l d i s t r i b u t i o n s e x h i b i t s t h e t r a n s i e n t o v e r p o p u l a t i o n e f f e c t o f T j o n a s w e l l a s s o m e l o w a m p l i t u d e n o n - p e r i o d i c o s c i l l a t i o n s . T h e p r e s e n c e o f t h e s e t r a j e c t o r i e s v i o l a t e s t h e K r o o k - W u c o n j e c t u r e c o n c e r n i n g r e l a x a t i o n o f _ n o n e q u i l i b r i u m d i s t r i b u t i o n s . T h i r d , t h e p r e s e n c e o f t h e u n s t a b l e m a n i f o l d i n t h e e i g e n s p a c e o f t h e l i n e a r i z e d p r o b l e m a n t i c i p a t e s t h e e x i s t e n c e o f t h e n o n - r e l a x i n g t r a j e c t o r i e s d i s c o v e r e d i n t h e s e c a l c u l a t i o n s . T h e u n s t a b l e m a n i f o l d i s a r o b u s t f e a t u r e o f t h e e i g e n s p a c e a n d i s p r e s e n t 1 9 7 i n a n y f i n i t e o r d e r L a g u e r r e b a s i s s e t e x p a n s i o n o f t h e d i s t r i b u t i o n f u n c t i o n . T h e p r e s e n c e o f _ t h e u n s t a b l e m a n i f o l d r a i s e s q u e s t i o n s a b o u t t h e v a l i d i t y o f t h e g e n e r a l l i n e a r i z e d a n a l y s i s o f t h e B o l t z m a n n e q u a t i o n . T h e d e c o m p o s i t i o n o f t h e e i g e n s p a c e o f t h e l i n e a r i z e d p r o b l e m d o e s , h o w e v e r , p r o v i d e a m e a n s t o a p r i o r i p a r t i t i o n t h e c l a s s o f i n i t i a l d i s t r i b u t i o n s i n t o t h o s e w h i c h r e l a x m o n o t o n i c a l l y t o t h e e q u i l i b r i u m a n d t h o s e w h i c h d i v e r g e f r o m t h e e q u i l i b r i u m i n f i n i t e t i m e . T h e K B K W i n i t i a l d i s t r i b u t i o n i s c o n t a i n e d i n t h e s t a b l e m a n i f o l d b u t d o e s n o t e x h a u s t t h e s e t o f p o s s i b l e i n i t i a l v a l u e s w h i c h r e l a x m o n o t o n i c a l l y ( i n n o r m ) . S U M M A R Y A N D D I S C U S S I O N O F R E S U L T S T h e c a l c u l a t i o n a l a n a l y s i s p r e s e n t e d i n t h e p r e v i o u s c h a p t e r c o v e r s s e v e r a l t o p i c s o f c h e m i c a l p h y s i c s a n d c h e m i c a l e n g i n e e r i n g . T h e r e s u l t s o f e a c h s e c t i o n , a l t h o u g h o r i g i n a l , i n t e r e s t i n g a n d w o r t h w h i l e o n t h e i r o w n m e r i t , c o n t r i b u t e i n v a r y i n g d e g r e e s t o t h e u n d e r s t a n d i n g o f c o l l i s i o n i n d u c e d h e a t i n g i n w e a k l y i o n i z e d d i l u t e g a s e s . I n t h i s c h a p t e r t h e s e r e s u l t s a r e s u m m a r i z e d a n d t h e i r p a r t i c u l a r r e l e v a n c e t o t h e e v a l u a t i o n o f c o l l i s i o n i n d u c e d h e a t i n g i s d i s c u s s e d . T h i s s e c t i o n i s f o l l o w e d b y r e c o m m e n d a t i o n s o f e x p e r i m e n t a l , c a l c u l a t i o n a l a n d t h e o r e t i c a l a s p e c t s f o r c o n s i d e r a t i o n i n t h e f u t u r e . 4 . 1 S u m m a r y o f e s s e n t i a l r e s u l t s T h i s s u m m a r y i s p r e s e n t e d i n t h e s a m e f a s h i o n a s t h e t o p i c s w e r e t r e a t e d i n t h e p r e v i o u s c h a p t e r a n d s o b e g i n s w i t h a s u m m a r y o f t h e m o d e l s y s t e m i d e n t i f i c a t i o n w o r k . T h e i n t e n t o f t h e m o d e l s y s t e m i d e n t i f i c a t i o n w o r k w a s t o s u r v e y s e v e r a l l o w m o l e c u l a r w e i g h t d i a t o m i c g a s e s , e x a m i n e a n d c o m p a r e t h e e l a s t i c a n d i n e l a s t i c s c a t t e r i n g c h a n n e l s o p e n t o e a c h a n d s e l e c t a m o d e l m o l e c u l e f o r f u r t h e r c a l c u l a t i o n a l w o r k . O n t h e b a s i s o f c o n s i d e r a t i o n o f t h e s c a t t e r i n g p r o c e s s e s a n d p r o d u c t e n e r g i e s m o l e c u l a r h y d r o g e n w a s . s e l e c t e d f o r f u r t h e r c a l c u l a t i o n a l w o r k a n d i s s u g g e s t e d a s t h e s p e c i e s o f c h o i c e f o r e x p e r i m e n t a l i n v e s t i g a t i o n s o f c o l l i s i o n i n d u c e d h e a t i n g . 1 9 8 1 9 9 T h e e n e r g i e s o f t h e a t o m s r e s u l t i n g f r o m e x c i t a t i o n o f X 1 2 : ; H z t o b 3 2 : : H z w e r e o n l y r o u g h l y e s t i m a t e d i n t h e i n i t i a l s u r v e y o f p o s s i b l e m o d e l s y s t e m s . F o r t h e p u r p o s e o f l a t e r w o r k t h e F r a n c k - C o n d o n o v e r l a p s i n t h e C o n d o n r e f l e c t i o n a p p r o x i m a t i o n w e r e c a l c u l a t e d a n d t h e d i s s o c i a t i o n p r o d u c t k i n e t i c e n e r g y w a s c a l c u l a t e d f o r d i s s o c i a t i v e t r a n s i t i o n s f r o m t h e g n o u n d e l e c t r o n i c s t a t e t o t h e l o w e s t t r i p l e t s t a t e . T h e s e e n e r g i e s r a n g e f r o m 6 . 2 t o 9 . 6 e v a n d t h e s t a t i s t i c s o f t h e n o r m a l i z e d F r a n c k - C o n d o n e n v e l o p e f o r t r a n s i t i o n f r o m X 1 Z ; ( v = 0 ) a r e i n g o o d a g r e e m e n t w i t h p u b l i s h e d w o r k . I n t h e f i n a l p a r t o f t h e s e c t i o n t h e i n t e r c o l l i s i o n a l t i m e s c a l e s f o r s e v e r a l c o l l i s i o n p r o c e s s e s w e r e c o m p a r e d w i t h t i m e s c a l e s f o r e l e c t r o d y n a m i c a n d t r a n s p o r t p r o c e s s e s . T h e t i m e s c a l e c o m p a r i s o n i s a u s e f u l b a s i s f r o m w h i c h t o d r a w c o n c l u s i o n s a b o u t t h e q u a l i t a t i v e b e h a v i o r o f a w e a k l y i o n i z e d d i l u t e g a s i n s t e a d y f l o w . O f p a r t i c u l a r r e l e v a n c e t o c o l l i s i o n i n d u c e d h e a t i n g i s t h e p r e s e n c e o f t w o t h r e s h h o l d s . A l o w p r e s s u r e t h r e s h h o l d f o r d i s c h a r g e i n i t i a t i o n i n H 2 i n s t e a d y f l o w i s i n d i c a t e d f r o m c o m p a r i s o n o f t h e t i m e s c a l e s f o r g a s f l o w a n d e l e c t r o n - m o l e c u l e k i n e t i c s . T h e p r e s e n c e o f t h i s t h r e s h h o l d h a s b e e n e x p e r i m e n t a l l y c o n f i r m e d . T h e s e c o n d t h r e s h h o l d i s a h i g h t e m p e r a t u r e o n e f o r e q u i l i b r a t i o n o f v i b r a t i o n a l a n d t r a n s l a t i o n a l d e g r e e s o f f r e e d o m . T h e p r e s e n c e o f t h i s f e a t u r e i s c o n f i r m e d b y l a t e r c a l c u l a t i o n a l w o r k . T h e r e l e v a n t r e s u l t s o f t h i s s e c t i o n a r e t h r e e f o l d . M o l e c u l a r h y d r o g e n i s t h e b e s t c a n d i d a t e f o r a w o r k i n g f l u i d i n a 2 0 0 c o l l i s i o n i n d u c e d h e a t i n g s y s t e m ; t h e p r o d u c t s o f e l e c t r o n i m p a c t d i s s o c i a t i o n o f H s h a r e f r o m 6 . 2 t o 9 . 6 e v o f k i n e t i c 2 e n e r g y a n d a r e p o s s i b l y t h e m a j o r c o n t r i b u t i o n t o t h e g a s h e a t i n g e f f e c t ; c o m p a r i s o n o f k i n e t i c , t r a n s p o r t a n d e l e c t r o d y n a m i c t i m e s c a l e s a n t i c i p a t e s q u a l i t a t i v e f e a t u r e s o f l a b o r a t o r y d i s c h a r g e s . T h e p u r p o s e o f t h e s o - c a l l e d u n c o u p l e d c a l c u l a t i o n s o f s e c t i o n 3 . 2 w a s t o c o m p a r e t w o d i s s o c i a t i o n m e c h a n i s m s , i i i — 4 “ “ 1 “ ” ; e s t i m a t e g a s t e m p e r a t u r e s t o s e e i f s i g n i f i c a n t g a s h e a t i n g c o u l d t a k e p l a c e , a n d e v a l u a t e t h e e f f e c t s o f v i b r a t i o n a l s t r u c t u r e , m a c r o s c o p i c t r a n s p o r t a n d e x t e r n a l h e a t t r a n s f e r . T h e r e s u l t s o f c a l c u l a t i o n s i n v o l v i n g t w o d i s t i n c t r e a c t o r m o d e l s i n d i c a t e t h a t d i s s o c i a t i o n o f H 2 i n a p r e s s u r e r a n g e o f 1 0 0 - 7 0 0 N / m ‘ 2 i s b y e x c i t a t i o n o f t h e b 3 2 : H 2 s t a t e . T h e l a d d e r m o d e l i s a v e r y u n l i k e l y e x p l a n a t i o n o f d i s s o c i a t i o n r a t e s i n l i g h t o f t h e h i g h e f f i c i e n c y o f H - H V T ' p r o c e s s e s . 2 A s e x p e c t e d , t h e h i g h e n e r g y d i s s o c i a t i o n p r o d u c t s m a k e a m a j o r c o n t r i b u t i o n t o t h e g a s h e a t i n g e f f e c t , a s s u m i n g t h a t t h e h i g h e n e r g y p r o d u c t s a r e r a p i d l y t h e r m a l i z e d . T h e e q u i l i b r a t i o n t h r e s h h o l d f o r v i b r a t i o n a l - t r a n s l a t i o n a l e q u i l i b r a t i o n a n t i c i p a t e d i n t h e t i m e s c a l e a n a l y s i s i s c o n f i r m e d i n t h e u n c o u p l e d c a l c u l a t i o n s . T h e c o n c e n t r a t i o n s a n d t e m p e r a t u r e s c a l c u l a t e d i n t h e P F R a n d C S T R m o d e l s a r e c l o s e , i n d i c a t i n g t h a t t h e e f f e c t o f a x i a l l y s e g r e g a t e d t r a n s p o r t i s s w a m p e d b y t h e f a s t e l e c t r o n - m o l e c u l e k i n e t i c 2 0 1 p r o c e s s e s . T h e p r e s e n c e o f v i b r a t i o n a l s t r u c t u r e d o e s n o t s i g n i f i c a n t l y a f f e c t t h e d i s S o c i a t i o n r a t e b u t d o e s e n h a n c e t h e g a s h e a t i n g r a t e a s p r e s s u r e i s i n c r e a s e d . T h i s i s p r i m a r i l y d u e t o t h e i n c r e a s e d e f f e c t i v e n e s s o f H - H V T 2 r e l a x a t i o n a s t h e p r e s s u r e a n d h e n c e t h e t e m p e r a t u r e i s i n c r e a s e d . T h e s e c a l c u l a t i o n s i l l u s t r a t e t h a t f o r c o n d i t i o n s r e p r e s e n t a t i v e o f l a b o r a t o r y d i s c h a r g e s n o t o n l y d o t h e e l e c t r o n - m o l e c u l e k i n e t i c s r e s u l t i n s i g n i f i c a n t g a s h e a t i n g , b u t t h e g a s h e a t i n g i s l i k e l y t o a f f e c t t h e k i n e t i c s t h r o u g h t h e d e n s i t y c h a n g e s e f f e c t e d b y t h e h e a t i n g . T h e p u r p o s e o f t h e t h i r d s e c t i o n o f t h e p r e v i o u s c h a p t e r w a s t o e x a m i n e t h e c o u p l e d e v o l u t i o n o f t h e e l e c t r o n a n d n e u t r a l g a s e s a n d t o p r e s e n t a s e l f - c o n s i s t e n t c a l c u l a t i o n o f t h e p r o p e r t i e s o f b o t h c o m p o n e n t s . T h e f i r s t s i g n i f i c a n t r e s u l t f r o m t h e d e v e l o p m e n t o f t h e s e l f — c o n s i s t e n t m o d e l w a s t h e i d e n t i f i c a t i o n o f a n e w s e t o f s i m i l a r i t y v a r i a b l e s f o r e l e c t r i c a l d i s c h a r g e s i n w e a k l y i o n i z e d g a s e s i n s t e a d y f l o w . T h e E / N c o r r e l a t i o n o f M a r g e n a u i s c l e a r l y i n a d e q u a t e i n l i g h t o f t h e d e p e n d e n c e o f N o n E i n c e r t a i n p r e s s u r e r a n g e s . T h e n o r m a l i z e d g a s h e a t i n g r a t e m a y h a v e a m a x i m u m v a l u e a t f > = = 0 g , c o r r e s p o n d i n g t o t h e c o l d p l a s m a r e s o n a n c e a n d s o c h o i c e o f t h e i n i t i a l O p e r a t i n g p r e s s u r e i s c r i t i c a l i n d e t e r m i n i n g w h e t h e r t h e g a s h e a t i n g w i l l d r i v e t h e d i s c h a r g e t o w a r d o r a w a y f r o m t h e r e s o n a n t c o n d i t i o n . T h e c a l c u l a t i o n s p r e s e n t e d i n F i g u r e s 1 5 - 1 9 p r o v i d e a b a s i s f o r s e l e c t i o n o f _ o p e r a t i n g c o n d i t i o n s t o m a x i m i z e t h e n o r m a l i z e d h e a t i n g 2 0 2 r a t e , a v e r a g e e l e c t r o n e n e r g y o r t h e a v e r a g e i n e l a s t i c e x c i t a t i o n r a t e . T h e p r e s e n c e o f i n e l a s t i c s c a t t e r i n g i n t r o d u c e s t h e p o s s i b i l i t y o f d e p r e s s i o n o f t h e a v e r a g e e l e c t r o n e n e r g y a n d i n e l a s t i c e x c i t a t i o n r a t e b e l o w t h e v a l u e s c o r r e s p o n d i n g t o a d i s c h a r g e a t t h e f e e d c o n d i t i o n s . C o n d i t i o n s f o r t h e o n s e t o f i n h i b i t i o n h a v e b e e n d e t e r m i n e d i n t e r m s o f t h e r e l a t i v e p o s i t i o n o f t h e p e a k s o f t h e e l e c t r o n e n e r g y d i s t r i b u t i o n a n d t h e i n e l a s t i c c r o s s - s e c t i o n . A n i n e l a s t i c r e s o n a n c e h a s b e e n i d e n t i f i e d w h i c h i s d i s t i n c t f r o m t h e c o l d p l a s m a r e s o n a n c e . T h e e n h a n c e m e n t a n d i n h i b i t i o n e f f e c t s d u e t o g a s h e a t i n g h a v e c o n s i d e r a b l e r e l e v a n c e t o c o l l i s i o n i n d u c e d h e a t i n g a n d e s t a b l i s h t h e n e c e s s i t y f o r s e l f - c o n s i s t e n t c a l c u l a t i o n s o f d i s c h a r g e p r o p e r t i e s . T h e a n a l y s i s a n d r e s u l t s p r e s e n t e d i n t h e f o u r t h s e c t i o n o f t h e p r e v i o u s c h a p t e r a r e m o r e g e n e r a l i n a p p l i c a t i o n t h a n p u r e l y t o c o l l i s i o n i n d u c e d h e a t i n g e f f e c t s i n w e a k l y i o n i z e d d i l u t e g a s d i s c h a r g e s t h o u g h t h e r e l e v a n c e t o c o l l i s i o n i n d u c e d h e a t i n g i s c l e a r . T h e m e t h o d o f o r t h o g o n a l c o l l o c a t i o n w i t h a f i n i t e L a g u e r r e p o l y n o m i a l b a s i s s e t i s a n a t u r a l a n d a c c u r a t e n u m e r i c a l a p p r o x i m a t i o n m e t h o d t o s o l v e t h e n o n l i n e a r B o l t z m a n n e q u a t i o n w i t h a m o m e n t u m c o n s e r v i n g k e r n e l . T h e r e s u l t s o f c a l c u l a t i o n s o f e v o l u t i o n o f t h e d i s t r i b u t i o n f u n c t i o n f r o m n o n - K B K W i n i t i a l v a l u e s d e m o n s t r a t e t h e e x i s t e n c e o f _ n o n - p e r i o d i c o s c i l l a t o r y r e l a x a t i o n t o t h e e q u i l i b r i u m a n d p r o v i d e f u r t h e r e v i d e n c e a g a i n s t t h e K r o o k - w u c o n j e c t u r e . M o r e i m p o r t a n t l y , t h e s e n o n - K B K W t r a j e c t o r i e s a r e c o r r e l a t e d t o 2 0 3 t h e p r e s e n c e o f a r o b u s t u n s t a b l e m a n i f o l d i n t h e e i g e n s p a c e o f t h e l i n e a r i z e d B o l t z m a n n e q u a t i o n . T h e r e s u l t s o f t h e l i n e a r i z e d a n a l y s i s p r e s e n t e d h a v e f e a t u r e s i n c o m m o n w i t h t h a t o f t h e i n f i n i t e b a s i s s e t e x p a n s i o n o f W a n g C h a n g a n d U h l e n b e c k b u t a l s o p r o v i d e a m e t h o d o f p a r t i t i o n i n g t h e i n i t i a l v a l u e s p a c e i n t o r e l a x i n g a n d n o n r e l a x i n g m a n i f o l d s . T h e p r e s e n c e o f t h e o s c i l l a t o r y t r a j e c t o r i e s i n t r o d u c e s t h e p o s s i b i l i t y t h a t t h e h i g h e n e r g y d i s s o c i a t i o n p r o d u c t s , p r e s e n t i n a w e a k l y i o n i z e d d i l u t e H 2 d i s c h a r g e , t h e r m a l i z e t h e i r e n e r g y o n t i m e s c a l e s m u c h l a r g e r t h a n t h a t o f f l o w t h r o u g h t h e d i s c h a r g e . I t a l s o r a i s e s t h e p o s s i b i l i t y t h a t a t o m i c r e c o m b i n a t i o n k i n e t i c s a r e v e r y d i f f e r e n t i n H z - H m i x t u r e s i n d u c e d b y t h e r m a l d i s s o c i a t i o n a n d b y e l e c t r o n i m p a c t d i s s o c i a t i o n . 4 . 2 C o n c l u s i o n s 1 . M o l e c u l a r h y d r o g e n i s s u p e r i o r t o O 2 a n d N a s a w o r k i n g 2 f l u i d i n a c o l l i s i o n i n d u c e d h e a t i n g s y s t e m . 2 . T h e p r o d u c t s o f e l e c t r o n i m p a c t d i s s o c i a t i o n o f H 2 s h a r e f r o m 6 . 2 t o 9 . 6 e v o f k i n e t i c e n e r g y . 3 . C o m p a r i s o n o f k i n e t i c , t r a n s p o r t a n d e l e c t r o d y n a m i c t i m e s c a l e s a n t i c i p a t e s q u a l i t a t i v e f e a t u r e s o f l a b o r a t o r y d i s c h a r g e s . ’ 4 . I n a l a b o r a t o r y d i s c h a r g e t h e d i s s o c i a t i o n o f H 2 i s o v e r w h e l m i n g l y v i a e x c i t a t i o n o f t h e x s t a t e t o t h e b 3 2 : : s t a t e . ’ T h e c o n t r i b u t i o n o f t h e r m a l C I D i s 1 0 . 1 1 . 2 0 4 i n s i g n i f i c a n t i n c o m p a r i s o n . ‘ T h e g a s h e a t i n g e f f e c t i s s i g n i f i c a n t , w i t h e l a s t i c c o l l i s i o n s a n d t h e r m a l i z e d d i s s o c i a t i o n p r o d u c t s m a k i n g t h e m a j o r c o n t r i b u t i o n s . T h e c a l c u l a t i o n s o f c o n c e n t r a t i o n a n d t e m p e r a t u r e i n t h e P F R a n d C S T R m o d e l s a r e d o m i n a t e d b y e l e c t r o n - m o l e c u l e k i n e t i c s . T h e t h r e s h h o l d f o r e q u i l i b r a t i o n o f v i b r a t i o n a l , r o t a t i o n a l a n d t r a n s l a t i o n a l d e g r e e s o f f r e e d o m a n t i c i p a t e d i n t h e t i m e s c a l e a n a l y s i s i s c o n f i r m e d . A n e w s i m i l a r i t y v a r i a b l e i s i d e n t i f i e d f r o m t h e s e l f e c o n s i s t e n t m o d e l c a l c u l a t i o n w h i c h e x t e n d s t h e c r i t e r i a o f M a r g e n a u t o c o n s t a n t p r e s s u r e , s t e a d y f l o w d i s c h a r g e s . T h e s e l f - c o n s i s t e n t m o d e l c a l c u l a t i o n s i n d i c a t e t h e e x i s t e n c e o f j a r e s o n a n c e i n t h e g a s h e a t i n g r a t e a n d a l s o p r o v i d e a b a s i s f o r s e l e c t i o n o f o p e r a t i n g c o n d i t i o n s t o m a x i m i z e t h e n o r m a l i z e d h e a t i n g r a t e . C o n d i t i o n s f o r e n h a n c e m e n t a n d d e p r e s s i o n o f t h e g a s h e a t i n g r a t e , a v e r a g e e l e c t r o n e n e r g y a n d a v e r a g e i n e l a s t i c e x c i t a t i o n r a t e a r e i d e n t i f i e d . A r e s o n a n c e i n t h e i n e l a s t i c e x c i t a t i o n r a t e i s i d e n t i f i e d . ( T h e ' c o n d i t i o n s u n d e r w h i c h t h e r e s o n a n c e o c c u r s a r e d i s t i n c t f r o m t h e c o l d p l a s m a r e s o n a n c e . ' 1 2 . 1 3 . 1 4 . 1 5 . 1 6 . 2 0 5 T h e m e t h o d o f o r t h o g o n a l c o l l o c a t i o n w i t h a f i n i t e L a g u e r r e p o l y n o m i a l b a s i s s e t i s a n a t u r a l a n d a c c u r a t e n u m e r i c a l a p p r o x i m a t i o n m e t h o d t o s o l v e t h e n o n l i n e a r B o l t z m a n n e q u a t i o n w i t h a m o m e n t u m c o n s e r v i n g k e r n e l . R e s u l t s o f c a l c u l a t i o n s o f t h e e v o l u t i o n o f t h e d i s t r i b u t i o n f u n c t i o n f r o m n o n - K B K W i n i t i a l v a l u e s d e m o n s t r a t e t h e e x i s t e n c e o f n o n - p e r i o d i c o s c i l l a t o r y r e l a x a t i o n t o t h e e q u i l i b r i u m a n d p r o v i d e f u r t h e r e v i d e n c e a g a i n s t t h e K r o o k - w u c o n j e c t u r e . C e r t a i n n o n - K B K W t r a j e c t o r i e s a r e c o r r e l a t e d t o t h e p r e s e n c e o f a r o b u s t u n s t a b l e m a n i f o l d i n t h e e i g e n s p a c e o f t h e l i n e a r i z e d B o l t z m a n n e q u a t i o n . T h e e i g e n s p a c e o f t h e l i n e a r i z e d p r o b l e m m a y b e u s e d t o p a r t i t i o n t h e i n i t i a l v a l u e s p a c e i n t o r e l a x i n g a n d n o n - r e l a x i n g m a n i f o l d s . T h e p r e s e n c e o f n o n - p e r i o d i c o s c i l l a t o r y t r a j e c t o r i e s r a i s e s a t l e a s t t w o q u e s t i o n s a b o u t r e l a x a t i o n o f h i g h e n e r g y h y d r o g e n a t o m s . F i r s t , t h e t h e r m a l i z a t i o n t i m e s c a l e s m a y b e v e r y l o n g w i t h r e s p e c t t o o t h e r c o l l i s i o n p r o c e s s e s , a n d s e c o n d , t h a t a t o m i c r e c o m b i n a t i o n k i n e t i c s m a y b e v e r y d i f f e r e n t i n H Z - H m i x t u r e s i n d u c e d b y t h e r m a l a n d e l e c t r o n i m p a c t C I D . 2 0 6 4 . 3 R e c o m m e n d a t i o n s f o r f u t u r e c o n s i d e r a t i o n T h e s e r e c o m m e n d a t i o n s c o v e r e x p e r i m e n t a l , c a l c u l a t i o n a l a n d t h e o r e t i c a l a s p e c t s o f t h e p r o b l e m a n d a r e p r e s e n t e d h e r e . T h e g r e a t d i f f i c u l t y o f d i r e c t , n o n i n t r u s i v e e x p e r i m e n t a l m e a s u r e m e n t o f m a c r o s c o p i c d i s c h a r g e p r o p e r t i e s i s t h e p r i m a r y o b s t a c l e i n c h a r a c t e r i z a t i o n o f e l e c t r i c a l d i s c h a r g e s o f a l l k i n d s . T w o p o s s i b l e e x p e r i m e n t s s u g g e s t e d b y t h e r e s u l t s o f t h i s w o r k a r e t h e d e t e c t i o n o f t h e h i g h e n e r g y p r o d u c t s o f e l e c t r o n i m p a c t d i s s o c i a t i o n o f H a n d t h e c o r r e l a t i o n o f 2 g a s t e m p e r a t u r e w i t h t h e s i m i l a r i t y v a r i a b l e s p r e s e n t e d i n s e c t i o n 3 . 3 . T h e s e e x p e r i m e n t s , h o w e v e r , r e s t o n m e a s u r e m e n t s o f g a s t e m p e r a t u r e , e l e c t r i c f i e l d s t r e n g t h a n d e l e c t r o n d e n s i t y , w h i c h a r e v e r y d i f f i c u l t t o m a k e a t t h e p r e s e n t . T h e r e a r e t w o i m p o r t a n t c a l c u l a t i o n a l i n v e s t i g a t i o n s s u g g e s t e d a s c o n t i n u a t i o n o f t h e w o r k p r e s e n t e d h e r e . I n t h e f i r s t , t h e s e l f - c o n s i s t e n c y o f t h e e l e c t r o n e n e r g y , n e u t r a l g a s t e m p e r a t u r e a n d d e n s i t y i s e x t e n d e d t o s e l f — c o n s i s t e n t c a l c u l a t i o n s o f e l e c t r o n e n e r g y , e l e c t r o n d e n s i t y a n d n e u t r a l g a s p r o p e r t i e s f o r a r e s o n a n t c a v i t y c o u p l i n g s t r u c t u r e t y p i c a l o f l a b o r a t o r y d i s c h a r g e s . I n t h e s e c o n d , t h e r e l a x a t i o n t i m e s c a l e a n a l y s i s i s e x t e n d e d t o a t w o c o m p o n e n t M a x w e l l g a s i n w h i c h r e a r r a n g e m e n t c o l l i s i o n s t a k e p l a c e . T h e e f f e c t o f t h e m u l t i c o m p o n e n t f e a t u r e o n t h e p r e s e n c e o f t h e u n s t a b l e m a n i f o l d i n t h e l i n e a r i z e d p r o b l e m a n d t h e n o n - r e l a x i n g t r a j e c t o r i e s i n t h e n o n l i n e a r p r o b l e m 2 0 7 s h o u l d b e a d d r e s s e d . S o m e t h e o r e t i c a l w o r k i s s u g g e s t e d b y t h e r e v i e w o f k i n e t i c t h e o r y p r e s e n t e d i n s e c t i o n 2 . 1 a n d i s i n p r o g r e s s b y t h e a u t h o r . T h e p r e s e n t s t a t e o f t h e t h e o r y o n w h i c h t h e B o l t z m a n n e q u a t i o n i s " b a s e d " i s r e s t r i c t e d t o e l a s t i c a n d w e a k l y i n e l a s t i c c o l l i s i o n s a n d b e g s t o b e e x t e n d e d t o s t r o n g l y i n e l a s t i c a n d r e a r r a n g e m e n t s c a t t e r i n g e v e n t s . A P P E N D I C E S A P P E N D I X A C o m p u t e r p r o g r a m s t a t e m e n t s f o r c a l c u l a t i o n o f t h e k i n e t i c e n e r g y d i s t r i b u t i o n a n d a v e r a g e k i n e t i c e n e r g y o f d i s s o c i a t i o n f r a g m e n t s . 2 0 8 O O O O O O O O O O O O O O O O O O 0 0 0 O 2 0 9 P R O G R A M M O R S E ( I N P U T , O U T P U T , T A P E 2 0 , T A P E 3 0 , T A P E 4 0 , T A P E 5 0 , T A P E 6 0 ) D I M E N S I O N E ( 0 : 1 3 ) , S U M 2 ( 0 : 1 3 ) , Y ( 2 0 0 ) , R ( 2 0 0 ) , P H ( 0 : 1 3 , 2 0 0 ) , + P H 2 ( 0 : 1 3 , 2 0 0 ) , D G A M ( 0 : 2 6 ) , E E ( 0 : 1 3 , 2 0 0 ) C O M M O N A ( 0 : 1 3 , 0 : 1 3 ) , B ( O : 1 3 , 0 : 1 3 ) , F A C T ( 0 : 1 4 ) , A L ( O : 1 3 ) + , N O R M C ( 0 : 1 3 ) , E E N ( 0 : 1 3 ) I N T E G E R v , V M A x R E A L N O R M C T H I S P R O G R A M C A L C U L A T E S T H E E N E R G Y E I G E N V A L U E S , V I E R A T I O N A L W A V E F U N C T I O N S F O R T H E H Y D R O G E N M O L E C U L E M O D E L L E D A S A M O R S E O S C I L L A T O R . I T A L S O C A L C U L A T E S T H E D I S T R I B U T I O N O F K I N E T I C E N E R G Y O F T H E P R O D U C T S O F A D I S S O C I A T I V E T R A N S I T I O N F R O M A B O U N D ( M O R S E ) S T A T E T O A C O N T I N U U M S T A T E ( R E P U L S I V E E X P O N E N T I A L P O T E N T I A L ) . T H E R E S U L T S O F T H E C A L C U L A T I O N A R E W R I T T E N O N C O N N E C T E D F I L E S I N A F O R M W H I C H I S A P P R O P R I A T E F O R U S E O F T H E R D S O O S B A T C H P L O T T I N G P R O G R A M . T A P E 4 0 = I N T E R N U C L E A R D I S T A N C E , W A V E F U N C T I O N T A P E 3 0 = I N T E R N U C L E A R D I S T A N C E , P R O E A E I L I T Y D E N S I T Y T A P E 2 0 = I N T E R N U C L E A R D I S T A N C E , E X C E S S E N E R G Y D I S T R I B U T I O N T A P E 5 0 = V , E N E R G Y , A L ( V ) E X P A N S I O N C O E F F I C I E N T S I N T E R N U C L E A R D I S T A N C E , P R O E A B I L I T Y D E N S I T Y T A P E 6 0 = V I E R A T I O N A L Q U A N T U M N O . , A V E R A G E E X C E S S E N E R G Y P H Y S I C A L C O N S T A N T S R M = R E D U C E D M A S S O F D I A T O M I C M O L E C U L E R M = 8 . 3 6 E - 2 8 H B = P L A N C K ' S C O N S T A N T / ( 2 . * P I ) H E = 1 . 0 5 4 E - 3 4 M O R S E P O T E N T I A L = D E * ( E X P ( - 2 . * A 1 * ( R - R 0 ) ) - 2 . * E X P ( - A 1 * ( R - R 0 ) ) ) A 2 = E X P ( A 1 * R 0 ) D E = P O T E N T I A L W E L L D E P T H I N J O U L E S D E = 7 . 6 0 5 4 E — 1 9 R a n Q U I L I D R I U M I N T E R N U C L E A R S E P A R A T I O N R 0 = . 7 4 1 2 E - 1 0 A 1 - 1 . 9 4 2 8 E 1 0 A 2 = 4 . 2 2 0 7 E X C E S S E N E R G Y = P 1 / ( E X P ( P 2 * R ) - l . ) P 1 = 1 8 . 0 0 9 8 P 2 = 1 . 8 7 4 5 3 E 1 0 V M A X = 1 3 C X = ( 8 . * R M * D E * A 2 * * 2 ) * * . 5 / ( H E * A 1 ) E I - ( B . * R M * D E ) * * . 5 / ( H E * A 1 ) F A C T O R I A L C A L C U L A T I O N F A C T ( 0 ) = 1 . D O 1 0 v = o , V M A X F A C T ( v + 1 ) - ( v + 1 ) * F A C T ( v ) E ( v ) = E N E R G Y O F L E V E L v E ( v ) = - D E + ( 2 . * D E / R M ) * * . 5 * A 1 * H B * ( v + . 5 ) - ( A 1 * H B * + ( v + . 5 ) ) * * 2 / ( 2 . * R M ) A L ( v ) = ( - 2 . * R M * E ( V ) ) * * . 5 / ( A 1 * H E ) A ( v , J ) , B ( v , J ) A R E T H E E X P A N S I O N C O E F F I C I E N T S F O R T H E C O N F L U E N T M ( a 2 1 0 C H Y P E R G E O M E T R I C S E R I E S M ( - V , B 1 - 2 V , C K * E X P ( - A 1 * R ) ) A ( v , 0 ) = 1 . B ( V , 0 ) = 1 . I F ( v . E Q . 0 ) T H E N A ( 0 , 0 ) = 1 . B ( 0 , 0 ) = 1 . E L S E D O 2 0 J = 1 , V A ( V , J ) = A ( v , J - 1 ) * ( J - 1 - v ) B ( v , J ) = B ( v , J - 1 ) * ( B 1 - 2 . * v + J - 1 ) 2 0 C O N T I N U E E N D I F S U M 2 ( v ) = o . c T H E I N T I S U D R O U T I N E I s A 9 6 P O I N T G A U S S I A N I N T E G R A T I O N C R O U T I N E . S E E P . 9 1 9 A B R A M . A N D S T E G U N C A L L I N T 1 ( V A L , C K , A L ( V ) , 0 , 0 ) C D G A M ( M ) I S T H E I N C O M P L E T E G A M M A F U N C T I O N O F A R G U M E N T C G I V E N B Y 2 * A L ( v ) + M D G A M ( 0 ) = V A L D O 2 5 M = 1 , 2 * V D G A M ( M ) = ( 2 . * A L ( V ) + M - 1 ) * D G A M ( M - 1 ) - C K * * ( 2 . * A L ( V ) + M - 1 ) + * E X P ( - C K ) 2 5 C O N T I N U E D O 5 0 I s o , v D O 6 0 J = 0 , V S U M 2 ( V ) = A ( V , I ) * A ( V , J ) * D G A M ( I + J ) / ( A 1 * B ( V , I ) * B ( V , J ) * F A C T ( I ) + * F A C T ( J ) ) + S U M 2 ( V ) 6 0 C O N T I N U E s o C O N T I N U E C N O R M C ( v ) I S T H E N O R M A L I Z A T I O N C O N S T A N T F O R T H E W A V E F U N C T I O N C O F L E V E L v N O R M C ( V ) = 1 . / S U M 2 ( V ) * * . 1 0 C O N T I N U E - C R ( K ) I S T H E I N T E R N U C L E A R D I S T A N C E D O 8 5 x = 1 , 2 o o R ( K ) = K * 2 . E - 1 2 Y ( N ) = C K * E X P ( - A 1 * R ( K ) ) 8 5 C O N T I N U E D o 8 0 V = O , V M A X D o 1 0 0 J = 1 , 2 0 0 S U M = 0 . 0 D O 1 1 0 I = 0 , V S U M = S U M + A ( V , I ) * Y ( J ) * * I / ( B ( V , I ) * F A C T ( I ) ) 1 1 0 C O N T I N U E c P H ( V , J ) I s T H E V A L U E O F T H E N O R M A L I Z E D W A V E F U N C T I O N F O R L E V E L c v A T I N T E R N U C L E A R D I S T A N C E R ( J ) . c P H 2 ( V , J ) I S T H E S Q U A R E O F T H E N O R M A L I Z E D W A V E F U N C T I O N c E E ( V , J ) I s T H E P R O D U C T O F T H E P R O B A B I L I T Y D E N S I T Y ( W A V E F U N C T I O N c S Q U A R E D ) A N D T H E E X C E S S E N E R G Y O F T H E C O N T I N U U M S T A T E . T H I S C A S S U M E S A F R A N K - C O N D O N T R A N S I T I O N . l e c c ‘ I ‘ 2 : 1 0 0 8 0 2 1 1 P H ( V , J ) = Y ( J ) * * A L ( v ) * E X P ( - Y ( J ) / 2 . ) * S U M * N O R M C ( V ) P H 2 ( V , J ) = P H ( V , J ) * * 2 E E ( V , J ) = P H 2 ( v , J ) * P 1 / ( E X P ( P 2 * R ( J ) ) - 1 . ) C O N T I N U E C O N T I N U E C I N T 2 I S A 9 6 - P O I N T G A U S S I A N I N T E G R A T I O N R O U T I N E A N D C I S U S E D T O E V A L U A T E Q U A D R A T U R E S O N T H E I N T E R V A L ( 0 , C K ) 1 5 0 1 4 0 1 3 0 2 0 0 C A L L I N T 2 ( A 1 , P 1 , P 2 , C K ) D O 1 3 0 V = 0 , V M A X W R I T E ( 5 0 , * ) V , E ( v ) , A L ( v ) D O 1 5 0 I = 0 , V W R I T E < 5 0 , * ) A ( V , I ) , B ( V , I ) C O N T I N U E W R I T E ( 4 0 , * ) 1 W R I T E ( 2 0 , * ) 1 W R I T E ( 3 0 , * ) 1 D O 1 4 0 J 2 1 , 2 0 0 W R I T E ( 4 0 , * ) R ( J ) , P H ( V , J ) W R I T E ( 5 0 , * ) R ( J ) , P H 2 ( V , J ) W R I T E ( 3 0 , * ) R ( J ) , P H 2 ( V , J ) W R I T E ( 2 0 , * ) R ( J ) , E E ( V , J ) C O N T I N U E W R I T E ( 4 0 , * ) ' I N T E R N U C . D I S T . ‘ W R I T E ( 3 0 , * ) ' I N T E R N U C . D I S T . ‘ W R I T E ( 2 0 , * ) ' I N T E R N U C . D I S T . ‘ W R I T E ( 3 0 , * ) ' S Q U A R E O F W A V E . ’ W R I T E ( 2 0 , * ) ' E X C E S S E N E R G Y ' W R I T E ( 3 0 , * ) ' M O R S E P O T E N T I A L ' W R I T E ( 2 0 , * ) ' E X P . P O T E N T I A L ' W R I T E ( 3 0 , * ) ' V = ' , V W R I T E ( 2 0 , * ) ' V = ' , V W R I T E ( 3 0 , * ) 8 . , 5 . W R I T E ( 4 0 , * ) ' V I B . W A V E F U N C T I O N ' W R I T E ( 2 0 , * ) 8 . , 5 . W R I T E ( 4 0 , * ) ' M O R S E O S C I L L A T O R W A V E F U N C T I O N ' W R I T E ( 4 0 , * ) ' V = ' , V W R I T E ( 4 0 , * ) 8 . , 5 . C O N T I N U E D O 2 0 0 V = O , V M A X W R I T E ( 6 0 , * ) V , E E N ( v ) C O N T I N U E S T O P E N D S U B R O U T I N E I N T 1 ( S U M , C K , A L , I , J ) D I M E N S I O N x ( 9 6 ) , W ( 9 6 ) , Y ( 9 6 ) D O U B L E P R E C I S I O N X , W F 1 ( A , B , C , D ) = E X P ( - A ) * A * * ( 2 . * B + C + D ) / A X ( 1 ) = - . 9 9 9 6 8 9 5 0 3 8 8 3 2 3 0 D 0 x ( 2 ) = - . 9 9 8 3 6 4 3 7 5 8 6 3 1 8 1 D 0 X ( 3 ) = - . 9 9 5 9 8 1 8 4 2 9 8 7 2 0 9 D 0 8 5 x ( 4 ) = - . 9 9 2 5 4 3 9 0 0 3 2 3 7 6 2 D 0 X ( 5 ) = - . 9 8 8 0 5 4 1 2 6 3 2 9 6 2 3 D 0 X ( 6 ) = - . 9 8 2 5 1 7 2 6 3 5 6 3 0 1 4 D o X ( 7 ) = ’ . 9 7 5 9 3 9 1 7 4 5 8 5 1 3 6 D 0 X ( 8 ) = - . 9 6 8 3 2 6 8 2 8 4 6 3 2 6 4 D 0 X ( 9 ) = - . 9 5 9 6 8 8 2 9 1 4 4 8 7 4 2 D 0 x ( 1 0 ) = - . 9 5 0 0 3 2 7 1 7 7 8 4 4 3 7 D 0 X ( 1 1 ) = - . 9 3 9 3 7 0 3 3 9 7 5 2 7 5 5 D 0 X ( l Z ) = - . 9 2 7 7 1 2 4 5 6 7 2 2 3 0 8 D 0 x ( 1 3 ) = - . 9 1 5 0 7 1 4 2 3 1 2 0 8 9 8 D 0 x ( 1 4 ) = - . 9 0 1 4 6 0 6 3 5 3 1 5 8 5 2 D o x ( 1 5 ) = - . 8 8 6 8 9 4 5 1 7 4 0 2 4 2 0 D 0 X ( 1 6 ) = - . 8 7 1 3 8 8 5 0 5 9 0 9 2 9 6 D 0 X ( 1 7 ) = - . 8 5 4 9 5 9 0 3 3 4 3 4 6 0 1 D 0 x ( 1 8 ) = - . 8 3 7 6 2 3 5 1 1 2 2 8 1 8 7 D 0 X ( 1 9 ) = - . 8 1 9 4 0 0 3 1 0 7 3 7 9 3 I D 0 X ( 2 0 ) = - . 8 0 0 3 0 8 7 4 4 1 3 9 1 4 0 D 0 X ( 2 1 ) = - . 7 8 0 3 6 9 0 4 3 8 6 7 4 3 3 D 0 x ( 2 2 ) = - . 7 5 9 6 0 2 3 4 1 1 7 6 6 4 7 D 0 x ( 2 3 ) = - . 7 3 8 0 3 0 6 4 3 7 4 4 4 0 0 D o x ( 2 4 ) = - . 7 1 5 6 7 6 8 1 2 3 4 8 9 6 7 D o x ( 2 5 ) = - . 6 9 2 5 6 4 5 3 6 6 4 2 1 7 1 D 0 X ( 2 6 ) = - . 6 6 8 7 I B 3 1 0 0 4 3 9 1 6 D 0 X ( 2 7 ) = - . 6 4 4 1 6 3 4 0 3 7 B 4 9 6 7 D 0 X ( 2 8 ) = - . 6 1 8 9 2 5 8 4 0 1 2 5 4 6 8 D 0 x ( 2 9 ) = - . 5 9 3 0 3 2 3 6 4 7 7 7 5 7 2 D 0 x ( 3 0 ) = - . 5 6 6 5 1 0 4 1 8 5 6 1 3 9 7 D o x ( 3 1 ) = - . 5 3 9 3 8 8 1 0 8 3 2 4 3 5 7 D 0 x ( 3 2 ) = - . 5 1 1 6 9 4 1 7 7 1 5 4 6 6 7 D o X ( 3 3 ) = - . 4 B 3 4 5 7 9 7 3 9 2 0 5 9 5 D o X ( 3 4 ) = - . 4 5 4 7 0 9 4 2 2 1 6 7 7 4 3 D o X ( 3 5 ) = - . 4 2 5 4 7 8 9 8 8 4 0 7 3 0 0 D 0 x ( 3 6 ) = - . 3 9 5 7 9 7 6 4 9 8 2 8 9 0 8 D 0 x ( 3 7 ) - - . 3 6 5 6 9 6 8 6 1 4 7 2 3 1 3 D 0 X ( 3 8 ) = - . 3 3 5 2 0 8 5 2 2 8 9 2 6 2 5 D 0 x ( 3 9 ) = - . 3 0 4 3 6 4 9 4 4 3 5 4 4 9 6 D o x ( 4 0 ) = - . 2 7 3 1 9 8 8 1 2 5 9 1 0 4 9 D 0 x ( 4 1 ) = - . 2 4 1 7 4 3 1 5 6 1 6 3 8 4 0 D 0 x ( 4 2 ) = - . 2 1 0 0 3 1 3 1 0 4 6 0 5 6 7 D 0 x ( 4 3 ) = - . 1 7 8 0 9 6 8 8 2 3 6 7 6 1 8 D o x ( 4 4 ) = - . 1 4 5 9 7 3 7 1 4 6 5 4 8 9 6 D o x ( 4 5 ) = - . 1 1 3 6 9 5 8 5 0 1 1 0 6 6 5 D 0 x ( 4 6 ) = - . 0 8 1 2 9 7 4 9 5 4 6 4 4 2 5 D 0 x ( 4 7 ) = - . 0 4 8 8 1 2 9 8 5 1 3 6 0 4 9 D 0 X ( 4 8 ) = - . 0 1 6 2 7 6 7 4 4 8 4 9 6 0 2 D o D O 8 5 K = 1 , 4 8 X ( 9 7 - K ) = - X ( K ) C O N T I N U E W ( 1 ) = . 0 0 0 7 9 6 7 9 2 0 6 5 5 5 2 D 0 w ( 2 ) = . 0 0 1 8 5 3 9 6 0 7 8 8 9 4 6 D 0 2 1 2 1 5 W ( 3 ) = . 0 0 2 9 1 0 7 3 1 8 1 7 9 3 4 D 0 w ( 4 ) = . 0 0 3 9 6 4 5 5 4 3 3 8 4 4 4 D 0 w ( 5 ) = . 0 0 5 0 1 4 2 0 2 7 4 2 9 2 7 D 0 w ( 6 ) = . 0 0 6 0 5 8 5 4 5 5 0 4 2 3 5 D 0 w ( 7 ) = . 0 0 7 0 9 6 4 7 0 7 9 1 1 5 3 D 0 w ( 8 ) = . 0 0 8 1 2 6 8 7 6 9 2 5 6 9 B D O w ( 9 ) = . 0 0 9 1 4 8 6 7 1 2 3 0 7 8 3 D 0 w ( 1 0 ) = . 0 1 0 1 6 0 7 7 0 5 3 5 0 0 8 D 0 w ( 1 1 ) = . 0 1 1 1 6 2 1 0 2 0 9 9 8 3 B D O w ( 1 2 ) = . 0 1 2 1 5 1 6 0 4 6 7 1 0 8 8 D o w ( 1 3 ) = . 0 1 3 1 2 8 2 2 9 5 6 6 9 6 1 D 0 w ( 1 4 ) = . 0 1 4 0 9 0 9 4 1 7 7 2 3 1 4 D 0 w ( 1 5 ) = . 0 1 5 0 3 8 7 2 1 0 2 6 9 9 4 D 0 w ( 1 6 ) = . 0 1 5 9 7 0 5 6 2 9 0 2 5 6 2 D 0 W ( 1 7 ) = . 0 1 6 8 8 5 4 7 9 8 6 4 2 4 5 D 0 w ( 1 8 ) = . 0 1 7 7 8 2 5 0 2 3 1 6 0 4 5 D 0 w ( 1 9 ) = . 0 1 8 6 6 0 6 7 9 6 2 7 4 1 1 D 0 w ( 2 0 ) = . 0 1 9 5 1 9 0 8 1 1 4 0 1 4 5 D 0 w ( 2 1 ) = . 0 2 0 3 5 6 7 9 7 1 5 4 3 3 3 D 0 w ( 2 2 ) = . 0 2 1 1 7 2 9 3 9 8 9 2 1 9 1 D o w ( 2 3 ) = . 0 2 1 9 6 6 6 4 4 4 3 8 7 4 4 D 0 w ( 2 4 ) = . 0 2 2 7 3 7 0 6 9 6 5 8 3 2 9 D o w ( 2 5 ) = . 0 2 3 4 8 3 3 9 9 0 8 5 9 2 6 D 0 w ( 2 6 ) = . 0 2 4 2 0 4 8 4 1 7 9 2 3 6 4 D o w ( 2 7 ) = . 0 2 4 9 0 0 6 3 3 2 2 2 4 8 3 D 0 w ( 2 8 ) - . 0 2 5 5 7 0 0 3 6 0 0 5 3 4 9 D 0 W ( 2 9 ) = . 0 2 6 2 1 2 3 4 0 7 3 5 6 7 2 D 0 w ( 3 0 ) - . 0 2 6 8 2 6 8 6 6 7 2 5 5 9 1 D o w ( 3 1 ) = . 0 2 7 4 1 2 9 6 2 7 2 6 0 2 9 D o W ( 3 2 ) = . 0 2 7 9 7 0 0 0 7 6 1 6 8 4 8 D 0 w ( 3 3 ) - . 0 2 8 4 9 7 4 1 1 0 6 5 0 8 5 D o w ( 3 4 ) = . 0 2 8 9 9 4 6 1 4 1 5 0 5 5 5 D 0 w ( 3 5 ) = . 0 2 9 4 6 1 0 8 9 9 5 8 1 6 7 D 0 W ( 3 6 ) = . 0 2 9 8 9 6 3 4 4 1 3 6 3 2 8 D 0 W ( 3 7 ) - . 0 3 0 2 9 9 9 1 5 4 2 0 8 2 7 D 0 w ( 3 8 ) = . 0 3 0 6 7 1 3 7 6 1 2 3 6 6 9 D 0 w ( 3 9 ) = . 0 3 1 0 1 0 3 3 2 5 8 6 3 1 3 D 0 w ( 4 0 ) = . 0 3 1 3 1 6 4 2 5 5 9 6 8 6 1 D o W ( 4 1 ) = . 0 3 1 5 8 9 3 3 0 7 7 0 7 2 7 D 0 W ( 4 2 ) = . 0 3 1 8 2 8 7 5 8 8 9 4 4 1 1 D 0 W ( 4 3 ) - . 0 3 2 0 3 4 4 5 6 2 3 1 9 9 2 D 0 W ( 4 4 ) = . 0 3 2 2 0 6 2 0 4 7 9 4 0 3 0 D 0 w ( 4 5 ) = . 0 3 2 3 4 3 8 2 2 5 6 8 5 7 5 D 0 w ( 4 6 ) = . 0 3 2 4 4 7 1 6 3 7 1 4 0 6 4 D 0 W ( 4 7 ) - . 0 3 2 5 1 6 1 1 8 7 1 3 8 6 8 D 0 w ( 4 8 ) = . 0 3 2 5 5 0 6 1 4 4 9 2 3 6 3 D 0 D O 1 5 K = l , 4 8 w ( 9 7 - K ) = W ( K ) C O N T I N U E S U M = 0 . 2 1 3 2 1 4 D 0 1 0 K = 1 , 9 6 Y ( K ) = . 5 * C K * ( X ( K ) + 1 . ) S U M = S U M + W ( K ) * F 1 ( Y ( K ) , A L , I , J ) C O N T I N U E S U M = . 5 * C K * S U M R E T U R N E N D S U B R O U T I N E I N T 2 ( A 1 , P 1 , P 2 , C K ) D I M E N S I O N X ( 9 6 ) , W ( 9 6 ) , Y ( 9 6 ) , W 1 ( 0 : l 3 , 9 6 ) D O U B L E P R E C I S I O N X , W C O M M O N A ( 0 : 1 3 , 0 : 1 3 ) , B ( 0 : 1 3 , 0 : l 3 ) , F A C T ( 0 : 1 4 ) , A L ( 0 : 1 3 ) , + N O R M C ( 0 : 1 3 ) , E E N ( 0 : 1 3 ) I N T E G E R v F 1 ( A , B , C , D , E ) = A * * 2 * B * * ( 2 . * C / D - 1 . ) / ( E * * ( C / D ) - + B * * ( C / D ) ) * * 3 F 2 ( A , B , C , D , E ) = A * * 2 * B * * ( C / D - I . ) / ( E * * ( C / D ) - B * * ( C / D ) ) * * 2 X ( 1 ) - - . 9 9 9 6 8 9 5 0 3 8 8 3 2 3 0 D o X ( 2 ) = - . 9 9 8 3 6 4 3 7 5 8 6 3 1 8 1 D 0 x ( 3 ) = — . 9 9 5 9 8 1 8 4 2 9 8 7 2 0 9 D 0 x ( 4 ) - - . 9 9 2 5 4 3 9 0 0 3 2 3 7 6 2 D 0 x ( 5 ) = - . 9 8 8 0 5 4 1 2 6 3 2 9 6 2 3 D 0 x ( 6 ) = - . 9 8 2 5 1 7 2 6 3 5 6 3 0 1 4 D 0 x ( 7 ) = - . 9 7 5 9 3 9 1 7 4 5 8 5 1 3 6 D 0 x ( 8 ) - - . 9 6 8 3 2 6 8 2 8 4 6 3 2 6 4 D 0 x ( 9 ) - - . 9 5 9 6 8 8 2 9 1 4 4 B 7 4 2 D 0 x ( 1 0 ) = - . 9 5 0 0 3 2 7 1 7 7 8 4 4 3 7 D 0 X ( 1 1 ) - - . 9 3 9 3 7 0 3 3 9 7 5 2 7 5 5 D 0 x ( 1 2 ) = - . 9 2 7 7 1 2 4 5 6 7 2 2 3 0 8 D 0 x ( 1 3 ) = - . 9 1 5 0 7 1 4 2 3 1 2 0 8 9 8 D 0 X ( 1 4 ) - - . 9 0 1 4 6 0 6 3 5 3 1 5 8 5 2 D 0 x ( 1 5 ) = - . 8 8 6 8 9 4 5 1 7 4 0 2 4 2 0 D o x ( 1 6 ) - - . 8 7 1 3 8 8 5 0 5 9 0 9 2 9 6 D 0 x ( 1 7 ) = - . 8 5 4 9 5 9 0 3 3 4 3 4 6 0 1 D 0 x ( 1 8 ) - - . 8 3 7 6 2 3 5 1 1 2 2 8 1 8 7 D 0 X ( 1 9 ) - - . 8 1 9 4 0 0 3 1 0 7 3 7 9 3 1 D 0 X ( 2 0 ) = - . 8 0 0 3 0 8 7 4 4 1 3 9 1 4 0 D 0 x ( 2 1 ) - - . 7 8 0 3 6 9 0 4 3 8 6 7 4 3 3 D 0 x ( 2 2 ) = - . 7 5 9 6 0 2 3 4 1 1 7 6 6 4 7 D o x ( 2 3 ) - - . 7 3 8 0 3 0 6 4 3 7 4 4 4 0 0 0 0 X ( 2 4 ) = - . 7 1 5 6 7 6 8 1 2 3 4 8 9 6 7 D 0 X ( 2 5 ) = - . 6 9 2 5 6 4 5 3 6 6 4 2 1 7 1 D 0 X ( 2 6 ) = - . 6 6 8 7 1 8 3 1 0 0 4 3 9 1 6 D 0 X ( 2 7 ) = - . 6 4 4 1 6 3 4 0 3 7 8 4 9 6 7 D 0 x ( 2 8 ) = - . 6 1 8 9 2 5 8 4 0 1 2 5 4 6 8 D 0 X ( 2 9 ) - - . 5 9 3 0 3 2 3 6 4 7 7 7 5 7 2 D o X ( 3 0 ) = - . 5 6 6 5 1 0 4 1 8 5 6 1 3 9 7 D 0 x ( 3 1 ) = - . 5 3 9 3 8 8 1 0 8 3 2 4 3 5 7 D 0 X ( 3 2 ) = - . 5 1 1 6 9 4 1 7 7 1 5 4 6 6 7 D o x ( 3 3 ) = - . 4 8 3 4 5 7 9 7 3 9 2 0 5 9 6 D 0 x ( 3 4 ) = - . 4 5 4 7 0 9 4 2 2 1 6 7 7 4 3 D 0 8 5 x ( 3 5 ) = - . 4 2 5 4 7 8 9 8 8 4 0 7 3 0 0 D 0 x ( 3 6 ) = - . 3 9 5 7 9 7 6 4 9 8 2 8 9 0 8 D 0 X ( 3 7 ) = - . 3 6 5 6 9 6 8 6 1 4 7 2 3 1 3 D 0 x ( 3 8 ) = - . 3 3 5 2 0 8 5 2 2 8 9 2 6 2 5 D 0 x ( 3 9 ) = - . 3 0 4 3 6 4 9 4 4 3 5 4 4 9 6 D o X ( 4 o ) = - . 2 7 3 1 9 8 8 1 2 5 9 1 0 4 9 D 0 X ( 4 1 ) = - . 2 4 1 7 4 3 1 5 6 1 6 3 8 4 0 D 0 x ( 4 2 ) = - . 2 1 0 0 3 1 3 1 0 4 6 0 5 6 7 D 0 x ( 4 3 ) = - . 1 7 8 0 9 6 8 8 2 3 6 7 6 1 8 D 0 x ( 4 4 ) - - . 1 4 5 9 7 3 7 1 4 6 5 4 8 9 6 D 0 X ( 4 5 ) = - . 1 1 3 6 9 5 8 5 0 1 1 0 6 6 5 D 0 X ( 4 6 ) = - . 0 8 1 2 9 7 4 9 5 4 6 4 4 2 5 D 0 x ( 4 7 ) - - . 0 4 8 8 1 2 9 8 5 1 3 6 0 4 9 D 0 x ( 4 8 ) = - . 0 1 6 2 7 6 7 4 4 8 4 9 6 0 2 D 0 D O 8 5 K = 1 , 4 8 X ( 9 7 - K ) = - X ( K ) C O N T I N U E w ( 1 ) = . 0 0 0 7 9 6 7 9 2 0 6 5 5 5 2 D 0 w ( 2 ) - . 0 0 1 8 5 3 9 6 0 7 8 8 9 4 6 D 0 w ( 3 ) - . 0 0 2 9 1 0 7 3 1 8 1 7 9 3 4 D 0 w ( 4 ) = . 0 0 3 9 6 4 5 5 4 3 3 8 4 4 4 D 0 w ( 5 ) - . 0 0 5 0 1 4 2 0 2 7 4 2 9 2 7 D 0 w ( 6 ) = . 0 0 6 0 5 8 5 4 5 5 0 4 2 3 5 D 0 w ( 7 ) - . 0 0 7 0 9 6 4 7 0 7 9 1 1 5 3 D 0 w ( 8 ) = . 0 0 8 1 2 6 8 7 6 9 2 5 6 9 8 D o w ( 9 ) = . 0 0 9 1 4 8 6 7 1 2 3 0 7 8 3 D 0 w ( 1 0 ) = . 0 1 0 1 6 0 7 7 0 5 3 5 0 0 8 D 0 w ( 1 1 ) = . 0 1 1 1 6 2 1 0 2 0 9 9 8 3 8 D 0 w ( 1 2 ) - . 0 1 2 1 5 1 6 0 4 6 7 1 0 8 8 D 0 w ( 1 3 ) - . 0 1 3 1 2 8 2 2 9 5 6 6 9 6 1 D o W ( 1 4 ) - . 0 1 4 0 9 0 9 4 1 7 7 2 3 1 4 D 0 w ( 1 5 ) c . 0 1 5 0 3 8 7 2 1 0 2 6 9 9 4 D 0 w ( 1 6 ) - . 0 1 5 9 7 0 5 6 2 9 0 2 5 6 2 D 0 w ( 1 7 ) - . 0 1 6 8 8 5 4 7 9 8 6 4 2 4 5 D 0 W ( 1 8 ) - . 0 1 7 7 8 2 5 0 2 3 1 6 0 4 5 D 0 w ( 1 9 ) - . 0 1 8 6 6 0 6 7 9 6 2 7 4 1 1 D 0 w ( 2 0 ) = . 0 1 9 5 1 9 0 8 1 1 4 0 1 4 5 D o w ( 2 1 ) = . 0 2 0 3 5 6 7 9 7 1 5 4 3 3 3 D 0 w ( 2 2 ) = . 0 2 1 1 7 2 9 3 9 8 9 2 1 9 1 D 0 w ( 2 3 ) - . 0 2 1 9 6 6 6 4 4 4 3 8 7 4 4 D 0 W ( 2 4 ) - . 0 2 2 7 3 7 0 6 9 6 5 8 3 2 9 D 0 w ( 2 5 ) = . 0 2 3 4 8 3 3 9 9 0 8 5 9 2 6 D 0 w ( 2 6 ) = . 0 2 4 2 0 4 8 4 1 7 9 2 3 6 4 D 0 w ( 2 7 ) = . 0 2 4 9 0 0 6 3 3 2 2 2 4 8 3 D o W ( 2 8 ) = . 0 2 5 5 7 0 0 3 6 0 0 5 3 4 9 D 0 w ( 2 9 ) = . 0 2 6 2 1 2 3 4 0 7 3 5 6 7 2 D 0 w ( 3 0 ) = . 0 2 6 8 2 6 8 6 6 7 2 5 5 9 1 D 0 w ( 3 1 ) = . 0 2 7 4 1 2 9 6 2 7 2 6 0 2 9 D 0 w ( 3 2 ) = . 0 2 7 9 7 0 0 0 7 6 1 6 8 4 B D O w ( 3 3 ) = . 0 2 8 4 9 7 4 1 1 0 6 5 0 8 5 D 0 2 1 5 " ( w ‘ 9 I s ‘ n ' o 9 U ; 2 1 6 w ( 3 4 ) = . 0 2 8 9 9 4 6 1 4 1 5 0 5 5 5 D 0 w ( 3 s ) = . 0 2 9 4 6 1 0 8 9 9 5 8 1 6 7 D 0 w ( 3 6 ) = . 0 2 9 8 9 6 3 4 4 1 3 6 3 2 8 D 0 w ( 3 7 ) = . 0 3 0 2 9 9 9 1 5 4 2 0 8 2 7 D 0 w ( 3 8 ) = . 0 3 0 6 7 1 3 7 6 1 2 3 6 6 9 D o w ( 3 9 ) = . 0 3 1 0 1 0 3 3 2 5 8 6 3 1 3 D 0 w ( 4 0 ) = . 0 3 1 3 1 6 4 2 5 5 9 6 8 6 1 D o w ( 4 1 ) = . 0 3 1 5 8 9 3 3 0 7 7 0 7 2 7 D 0 w ( 4 2 ) = . 0 3 1 8 2 8 7 5 8 8 9 4 4 1 1 D 0 w ( 4 3 ) = . 0 3 2 0 3 4 4 5 6 2 3 1 9 9 2 D 0 w ( 4 4 ) = . 0 3 2 2 0 6 2 0 4 7 9 4 0 3 0 D 0 w ( 4 5 ) = . 0 3 2 3 4 3 8 2 2 5 6 8 5 7 5 D 0 w ( 4 6 ) = . 0 3 2 4 4 7 1 6 3 7 1 4 0 6 4 D 0 w ( 4 7 ) = . 0 3 2 5 1 6 1 1 8 7 1 3 8 6 8 D 0 w ( 4 8 ) = . 0 3 2 5 5 0 6 1 4 4 9 2 3 6 3 D 0 D O 1 5 X = 1 , 4 8 W ( 9 7 - K ) = W ( K ) 1 5 C O N T I N U E D O 5 0 0 X = 1 , 9 6 Y ( N ) = . 5 * C N * ( X ( N ) + I . ) D O 5 1 0 V = o , 1 3 S U M 1 = 0 . 0 D O 5 2 0 I = 0 , v S U M I x S U M 1 + A ( v , I ) * Y ( K ) * * I / ( B ( V , I ) * F A C T ( I ) ) 5 2 0 C O N T I N U E W 1 ( V , K ) - S U M 1 * E X P ( - Y ( K ) * . 5 ) * Y ( K ) * * A L ( V ) * N O R M C ( V ) 5 1 0 C O N T I N U E 5 0 0 C O N T I N U E D O 5 4 0 V = o , 1 3 s u m - 0 . 0 S U M 3 - 0 . 0 D O 5 3 0 I = 1 , 9 6 S U M 2 = S U M 2 + F 1 ( W 1 ( V , I ) , Y ( I ) , P 2 , A 1 , C K ) * W ( I ) S U M 3 = S U M 3 + F 2 ( W 1 ( V , I ) , Y ( I ) , P 2 , A 1 , C K ) * W ( I ) 5 3 0 C O N T I N U E E E N ( V ) = P 1 * S U M 2 / S U M 3 5 4 o C O N T I N U E R E T U R N E N D A P P E N D I X B C o m p u t e r p r o g r a m s t a t e m e n t s f o r c a l c u l a t i o n o f n e u t r a l g a s d e n s i t y , t e m p e r a t u r e a n d v i b r a t i o n a l t e m p e r a t u r e i n t h e u n c o u p l e d a p p r o x i m a t i o n . 2 1 7 2 1 8 P R O G R A M I N T E G ( I N P U T , O U T P U T , T A P E 7 0 ) I N T E G E R N , M E T H , M I T E R , I N D E X , I W K ( 3 ) , I E R , K R E A L Y ( 3 ) , W K ( 5 2 ) , X , T O L , X E N D , H E X T E R N A L F C N , F C N J C O M M O N A ( 1 0 0 ) C T H I S P R O G R A M I N T E G R A T E s T H E P F R R E A C T O R E Q U A T I O N S D E S C R I B E D C I N S E C T I O N 3 . 2 O F T H E D I S S E R T A T I O N O F T . J . M O R I N , P H D , M I C H I G A N C S T A T E U N I V E R S I T Y , 1 9 8 5 . T H E I M S L I N T E G R A T O R D G E A R I s U S E D . 2 0 N = 3 X = 0 . Y ( 1 ) = 1 . Y ( 2 ) = I . Y ( 3 ) = 1 . M E T H = 1 M I T E R = 0 I N D E X = 1 P R I N T * , ' P R = ' R E A D * , A ( 1 ) P R I N T * , ' F 0 = ' R E A D * , A ( 2 ) P R I N T * , ' H 1 = ' R E A D * , A ( 3 ) P R I N T * , ' E N = ' R E A D * , A ( 4 ) P R I N T * , ' A E N = ' R E A D * , A ( 5 ) P R I N T * , ' V V = ' R E A D * , A ( 6 > P R I N T * , ' V E = ' R E A D * , A ( 7 ) P R I N T * , ' V I = ' R E A D * , A ( 8 ) P R I N T * , ' D F = ' R E A D * , A ( 9 ) 2 1 P R I N T * , ' T O L = ' R E A D * , T O L P R I N T * , ' H = ' R E A D * , H W R I T E ( 7 0 , F M T = 2 ) A ( 1 ) , A ( 2 ) , A ( 3 ) , A ( 4 ) , A ( 5 ) W R I T E ( 7 0 , F M T = 3 ) A ( 6 ) , A ( 7 ) , A ( 8 ) , A ( 9 ) 2 F O R M A T ( 2 X , ' P R = ' , E 1 0 . 4 , 2 X , ' F 0 = ' , E 1 0 . 4 , 2 X , ' H 1 = ' , E 1 0 . 4 , + 2 X , ' E N = ' , E 1 0 . 4 , 2 X , ' A E N = ' , E 1 0 . 4 ) 3 F O R M A T ( 2 X , ' V V = ' , E 1 0 . 4 , 2 x , ' V E = ' , E 1 0 . 4 , 2 X , ' V I = ' , E 1 0 . 4 , + 2 X , ' D F = ' , E 1 0 . 4 ) D O 1 0 K = l , 1 0 X E N D = F L O A T ( K ) / 1 0 . C A L L D G E A R ( N , F C N , F C N J , X , H , Y , X E N D , T O L , M E T H , M I T E R , + I N D E X , I W K , W K , I E R ) I F ( I E R . G T . 1 2 8 ) G O T O 3 0 x 1 = ( 1 . - Y ( 1 ) ) / Y ( 2 ) ‘ A d l l 1 0 3 0 1 2 2 1 9 X 2 = X 1 / ( 2 . - x 1 ) P R I N T * , X , ' ' , X 2 , ' ' , Y ( 2 ) , ' ' , Y ( 3 ) W R I T E ( 7 0 , F M T = 1 1 ) X , X 2 , Y ( 2 ) , Y ( 3 ) , Y ( 1 ) F O R M A T ( 2 X , E 1 0 . 4 , 2 X , E 1 0 . 4 , 2 X , E 1 0 . 4 , 2 X , E 1 0 . 4 , 2 X , E 1 0 . 4 ) C O N T I N U E P R I N T * , ' T Y P E 1 T O C O N T I N U E , 0 T O S T O P ' R E A D * , L 1 I F ( L I . E Q . 1 ) G O T O 2 0 S T O P C O N T I N U E P R I N T * , ' T O L = ' , T O L P R I N T * , ' H = ' , H P R I N T * , ' X E N D = ' , X E N D P R I N T * , ' X = ' , X D O 1 2 J = l , 3 P R I N T * , ' Y ( ' , J , ' ) = ' , Y ( J ) C O N T I N U E P R I N T * , ' T Y P E 1 T O C O N T I N U E , 0 T O S T O P ' R E A D * , L 2 I F ( L 2 . E Q . 1 ) G O T O 2 1 S T O P E N D S U B R O U T I N E F C N ( N , X , Y , Y P R I M E ) I N T E G E R N R E A L Y ( N ) , Y P R I M E ( N ) , X C O M M O N A ( 1 0 0 ) D I M E N S I O N F V l 4 ( l 4 ) D I M E N S I O N E J ( 0 : 1 4 ) E J ( 0 ) = 2 5 6 2 2 . 9 E J ( 1 ) = 7 5 4 0 4 . 8 E J ( 2 ) = 1 2 3 7 2 3 . E J ( 3 ) = 1 6 6 9 1 6 . E J ( 4 ) = 2 0 8 6 4 4 . E J ( 5 ) = 2 4 8 1 7 7 . E J ( 6 ) = 2 8 4 0 4 9 . E J ( 7 ) = 3 1 6 2 6 1 . E J ( 8 ) = 3 4 7 0 0 9 . E J ( 9 ) = 3 7 5 5 6 0 . E J ( 1 0 ) = 4 0 1 1 8 3 . E J ( 1 1 ) = 4 2 0 2 1 7 . E J ( 1 2 ) = 4 3 6 3 2 3 . E J ( 1 3 ) = 4 4 9 5 0 1 . E J ( 1 4 ) = 4 5 9 7 5 0 . P R = A ( 1 ) F 0 = A ( 2 ) H 1 = A ( 3 ) E N = A ( 4 ) A E N = A ( 5 ) = A ( 6 ) V E = A ( 7 ) t A . » b 5 0 2 2 2 0 V I = A ( 8 ) D F = A ( 9 ) T L = . 1 T R = . 0 1 2 5 P I = 3 . 1 4 1 5 9 R G = 8 . 3 1 4 B X = 1 . 3 8 0 6 E - 2 3 A N = 6 . 0 2 3 E 2 3 E D = E J ( 1 4 ) - E J ( 0 ) T D = 1 . T 0 = 3 0 0 . T A = P I * T R * * 2 R V = T A * T L W A = 2 . * P I * T R * T L C 0 = P R / ( R G * T 0 ) G l o = 1 . 5 9 4 E - 1 3 * C 0 * A N T N = C 0 * A N R K W = . 0 0 0 0 1 R K l l = l . l S E 6 * T 0 * * . 5 R X 1 2 = 2 . 7 3 2 E 6 * T 0 * * . 5 R X 2 1 = 3 . 0 3 * T 0 * * . 5 R X 2 2 = 4 . 4 5 * T 0 * * . 5 E M = 9 . 1 1 E — 3 1 H M = 3 . 2 E — 2 7 5 3 2 3 . 1 6 8 - 1 9 H D = 2 . E - 1 0 E C = 1 . 6 E - 1 9 A l = R K 1 2 / R K l l A 2 = R K 2 2 / R K 2 1 A 3 = R K l l / ( C 0 * R K 2 1 ) A 4 = E D / ( 2 . * R G * T 0 ) A 5 = ( B K * T 0 / ( P I * H M ) ) * * . 5 * R K W / ( C 0 * * 2 * R K 2 1 * T R ) A D = V E / ( C 0 * * 3 * R K 2 1 * A N ) D A = R V * C 0 * * 3 * R K 2 1 / F 0 A 6 = ( E J ( 1 ) - E J ( 0 ) ) / ( R G * T 0 ) S U M 3 = 0 . S U M 4 = 0 . D O 5 K l = 0 , 1 4 S U M 3 = S U M 3 + E X P ( ( E J ( 1 4 ) - E J ( K 1 ) ) / ( R G * T 0 * Y ( 3 ) ) ) S U M 4 = S U M 4 + ( E J ( 1 4 ) - E J ( K 1 ) ) * E X P ( ( E J ( 1 4 ) - E J ( K 1 ) ) / ( R G * T 0 * Y ( 3 ) ) ) + / ( R G * T 0 * Y ( 3 ) * * 2 ) C O N T I N U E S W 2 4 = 0 0 D O 5 0 1 J v = 1 , 1 4 S U M 1 4 = 0 . D O 5 0 2 J J = 0 , 1 4 S U M 1 4 = S U M 1 4 + E X P ( ( E J ( J v ) - E J ( J J ) ) / ( R G * T 0 * Y ( 3 ) ) ) C O N T I N U E F v 1 4 ( J V ) = J V * ( E J ( J v ) - E J ( 0 ) ) / S U M 1 4 S U M 2 4 = S U M 2 4 + F V 1 4 ( J V ) 5 0 1 2 2 1 C O N T I N U E G l = G l O * Y ( l ) / Y ( 2 ) P 1 0 1 = E X P ( - 8 9 . 1 / ( T 0 * Y ( 2 ) ) * * . 3 3 - 2 . 5 3 3 ) P 1 0 2 = E X P ( - 8 9 . 1 / ( T 0 * Y ( 2 ) ) * * . 3 3 + 3 . 5 7 ) U M 1 = H M / 2 . U M 2 = H M / 3 . E x = 7 . 0 4 9 E - 1 9 F O T 1 = C 0 * * 2 * A N * P I * H D * * 2 * S U M 2 4 * ( Y ( 1 ) * * 2 * P 1 0 1 + * ( 8 . * B K * T 0 / ( P I * U M 1 ) ) * * . 5 + Y ( l ) * ( l . - Y ( l ) ) + * P 1 0 2 * ( 8 . * B K * T 0 / ( P I * U M 2 ) ) * * . 5 ) / Y ( 2 ) * * 1 . 5 F O T = 2 . * R V * ( B N * S I N ( X * P I ) * T N * S E * 2 . * E M * A B N * ( 2 . * E C / E M ) * * . S / H M + + F O T 1 - H 1 * W A * T 0 * ( Y ( 2 ) - T D ) / R v ) / ( 7 . * R G * T 0 * F 0 ) + + 2 . * R V * E N * S I N ( X * P I ) * V E * G 1 * E X / ( 7 . * R G * T 0 * F 0 ) F O V = 2 . * R V * ( E N * S I N ( X * P I ) * v v * G 1 * ( E J ( 1 ) - E J ( 0 ) ) / A N - F O T 1 ) / + ( 7 . * R G * T 0 * F 0 ) R 0 = A 2 / Y ( 2 ) * * 2 . 5 + A 5 / Y ( 2 ) * * . 5 + Y ( 1 ) * ( ( 1 . - 3 . * A 2 ) / Y ( 2 ) + * * 2 . 5 - A 5 / Y ( 2 ) * * . 5 ) + Y ( 1 ) * * 2 * ( 3 . * A 2 - 2 . ) / Y ( 2 ) * * 2 . 5 + + Y ( 1 ) * * 3 * ( 1 . - A 2 ) / Y ( 2 ) * * 2 . 5 - A D * G I * E N * S I N ( X * P I ) + - A 3 * Y ( 1 ) * ( A 1 + Y ( 1 ) * ( 1 . - A 1 ) ) / ( Y ( 2 ) * * 1 . 5 * S U M 3 ) Y 1 0 = ( 2 . * A 4 + 1 . 5 * Y ( 2 ) ) * 4 . / ( 7 . * ( 1 . + Y ( 1 ) ) * * 2 ) Y 1 1 = 7 . * ( 1 . + Y ( 1 ) ) / ( 4 . * A 6 * * 2 * Y ( 1 ) ) Y 1 2 = Y ( 3 ) * * 2 * ( E X P ( A 6 / Y ( 3 ) ) - 1 . ) * * 2 * E X P ( - A 6 / Y ( 3 ) ) * F O V Y 1 3 = Y ( 3 ) * * 2 * ( 1 . - E X P ( - A 6 / Y ( 3 ) ) ) / ( A 6 * Y ( 1 ) * ( 1 . + Y ( 1 ) ) ) Y P R I M E ( 1 ) = . 5 * D A * R 0 * ( 1 . + Y ( 1 ) ) * * 2 Y P R I M E ( 2 ) = ( F O T + Y 1 0 * Y P R I M E ( 1 ) ) * 7 . * ( 1 . + Y ( 1 ) ) / + ( 4 . * ( 2 . 5 + Y ( 1 ) ) ) Y P R I M E < 3 ) = Y 1 1 * Y 1 2 - Y 1 3 * Y P R I M E ( 1 ) R E T U R N E N D S U B R O U T I N E F C N J ( N , X , Y , P D ) I N T E G E R N R E A L Y ( N ) , P D ( N , N ) , X R E T U R N E N D A P P E N D I X C C o m p u t e r p r o g r a m s t a t e m e n t s f o r c a l c u l a t i o n o f n e u t r a l g a s d e n s i t y a n d t e m p e r a t u r e , e l e c t r o n g a s e n e r g y a n d i n e l a s t i c e x c i t a t i o n r a t e s i n t h e c o u p l e d a p p r o x i m a t i o n . 2 2 2 C C C C C 2 2 3 P R O G R A M V I B E X I ( I N P U T , O U T P U T , T A P E 6 0 ) I N T E G E R N M A X R E A L F A C T ( 0 : 2 0 ) , F 0 ( 0 : 2 0 ) , v v ( 0 : 2 0 ) , V I B E X ( 1 0 ) c T H I S P R O G R A M C A L C U L A T E S S E L F - C O N S I S T E N T V A L U E S O F G A S C D E N S I T Y , T E M P E R A T U R E , A N D E L E C T R O N A V E R A G E E N E R G Y A N D I N E L A S T I C C E X C I T A T I O N R A T E S . T H E E Q U A T I O N S S O L V E D H E R E A R E D E S C R I B E D C I N F U L L I N T H E D I S S E R T A T I O N O F T . J . M O R I N , P H D , M I C H I G A N S T A T E C U N I V E R S I T Y , 1 9 8 5 . N M A X = 1 5 C F A C T O R I A L C A L C U L A T I O N F A C T ( 0 ) = 1 . D O 1 0 I = 1 , N M A X F A C T ( I ) = I * F A C T ( I - 1 ) 1 0 C O N T I N U E C P H Y S I C A L C O N S T A N T S P I = 3 . 1 4 1 5 9 R G = B . 3 1 4 C P = 3 . 5 * R G A N = 6 . 0 2 2 E 2 3 B E T A = 1 . 6 0 2 E - 1 9 E M = 2 . 7 2 3 E - 4 D E L T A = . 2 5 D L = 1 0 . D I A = . 0 2 5 4 V O L = . 2 5 * P I * D L * D I A * * 3 W = 1 . 5 4 E 1 0 S I G M = 1 . 5 9 4 E - 1 3 X S I = 1 . E - 6 E v = . 5 4 A R E A = P I * D L * D I A * * 2 H E A T C = 1 0 . T E M P = 3 0 0 . D O 2 0 I = 1 , 1 F L = 2 . 5 E - 4 * I D O 3 0 J = 1 , 1 0 A 0 = 1 . * J D O 4 0 x = 1 , 1 9 , 1 C = . 0 5 * X D = C * A o * * 2 C S O L V E F O R R O O T S O F C U B I C A 1 = ( 3 . * D - C * * 2 ) / 3 . B 1 = ( - 2 . * C * * 3 + 9 . * D * C - 2 7 . * D ) / 2 7 . A 3 = - B 1 / 2 . + ( A 1 * * 3 / 2 7 . + B 1 * * 2 / 4 . ) * * . 5 B 3 = - B 1 / 2 . - ( A 1 * * 3 / 2 7 . + B 1 * * 2 / 4 . ) * * . 5 I F ( A 3 . L T . 0 . ) T H E N A 2 = - ( - A 3 ) * * ( 1 . / 3 . ) E L S E A 2 = A 3 * * ( 1 . / 3 . ) E N D I F I F ( B B . L T . 0 . ) T H E N N A I l , l ” 0 C S i " . U V ‘ 1 ' \ s 2 2 4 B 2 = - ( - B 3 ) * * ( 1 . / 3 . ) E L S E B 2 = B 3 * * ( 1 . / 3 . ) E N D I F R 1 = A 2 + B Z + C / 3 . C S O L V E F O R P H I 7 0 6 0 5 0 1 0 0 9 0 8 0 1 3 0 R 1 0 = W / ( A N * A 0 * S I G M ) P R E S S = R G * T E M P * R 1 0 P H 1 0 = ( C / ( 1 . - C ) ) * 1 . 5 * B E T A * 2 . * E M * X S I * A N * * 2 * R 1 0 * * 2 + * S I G M / ( F L * C P * T E M P / V O L + A R E A * H E A T C * T E M P / V O L ) P H 1 = P H 1 0 * ( R 1 * * 2 + A 0 * * 2 ) X = P H 1 / D E L T A F 0 ( 0 ) = 1 . D O 5 0 L = 1 , N M A X S U M 1 = 0 . D O 6 0 L 1 = 0 , L - l D O 7 0 L 2 = o , L - L 1 S U M 1 = S U M 1 + ( - 1 ) * * ( L + 1 + L 2 ) * x * * ( L — L 1 ) * F 0 ( L 1 ) + * ( X / ( L 2 + X ) ) * * l . 5 / ( ( - 1 ) * * L l * F A C T ( L 2 ) * F A C T ( L - L l - L 2 ) ) C O N T I N U E C O N T I N U E F 0 ( L ) = S U M 1 C O N T I N U E D O 8 0 L = 1 , N M A X S U M 2 = 0 . D O 9 0 M = 0 , L _ D O 1 0 0 N = 0 , L - M ‘ S U M 2 = S U M 2 + ( - 1 > * * ( N + L ) * F 0 ( M ) * X * * ( L - M ) * ( ( 1 . + X ) / + ( 1 . + X + N ) ) * * 2 . 5 / ( ( - 1 ) * * M * F A C T ( N ) * F A C T ( L - M — N ) ) C O N T I N U E C O N T I N U E V V ( L ) = S U M 2 C O N T I N U E W R I T E ( 6 0 , 1 1 0 ) F L , A 0 , C W R I T E ( 6 0 , 1 2 0 ) R 1 , 1 . / R 1 W R I T E ( 6 0 , 2 0 0 ) P H 1 , X D O 1 3 0 N 1 = 0 , N M A X W R I T E ( 6 0 , 1 4 0 ) N 1 , V V ( N 1 ) C O N T I N U E D O 1 7 0 I l = l , 4 , l I F ( 1 1 . E Q . 1 ) T H E N P H 2 = . 1 E L S E I F ( I I . E Q . 2 ) T H E N P H 2 = 1 . E L S E I F < I I . E Q . 3 ) T H E N P H 2 = 1 0 . E L S E P H 2 = 0 . E N D I F S U M 3 = 1 . 2 2 5 S I G V = P H 2 * S I G M * 2 . * E M / E V v v ( 0 ) = A N * R 1 * R 1 0 * S I G V * 1 . 5 * ( x / ( x + 1 . ) ) * * 2 . 5 / P H 1 D O 1 5 0 N 2 = 1 , N M A X S U M 3 O L D = S U M 3 S U M 3 = S U M 3 + P H 2 * * N 2 * V v ( N 2 ) I F ( A B S ( ( S U M 3 - S U M 3 O L D ) / S U M 3 ) . L E . . 0 0 1 ) T H E N W R I T E ( 6 0 , 1 9 0 ) N 2 A E 1 = 1 . - 2 . * P H 1 * E V * S U M 3 * V V ( 0 ) / ( 3 . * A N * R 1 * R 1 0 * S I G M * 2 . * E M ) W R I T E ( 6 0 , 2 1 0 ) A E 1 A E 2 = ( 1 . + A 0 * * 2 ) / ( R 1 * * 2 + A 0 * * 2 ) - 2 . * P H 1 0 * ( 1 . + A 0 * * 2 ) * E V * + S U M 3 * v v ( 0 ) / ( 3 . * A N * R 1 * R 1 0 * S I G M * 2 . * E M ) W R I T E < 6 0 , 2 2 0 ) A E 2 X 1 = P H 1 0 * ( 1 . + A 0 * * 2 ) / D E L T A v v 1 = R 1 * X 1 / X * ( X * ( 1 . + X 1 ) / ( X 1 * ( 1 . + X ) ) ) * * 2 . 5 * V v ( 0 ) * S U M 3 W R I T E ( 6 0 , 2 3 0 ) V V 1 G O T O 1 6 0 E L S E E N D I F C O N T I N U E V I B E X ( I l ) = V V ( O ) * S U M 3 W R I T E ( 6 0 , 1 8 0 ) P H 2 , V I B B x ( 1 1 ) C O N T I N U E F O R M A T ( 5 X , ' F L O W R A T E = ' , E 1 0 . 4 , 5 X , ' A o = ' , E 1 0 . 4 , 5 X , + ' C = ' , E 1 0 . 4 ) F O R M A T ( 5 X , ‘ D E N S I T Y = ' , E l O . 4 , 5 X , ' T E M P = ' , E l O . 4 ) F O R M A T ( 1 0 X , 1 2 , 5 X , ' V V / v o = ' , E 1 0 . 4 ) F O R M A T ( 5 X , ' P H 2 = ' , E 1 0 . 4 , 5 X , ' E X C I T A T I O N R A T E = ' , E 1 0 . 4 ) F O R M A T ( 5 X , ' S E R I E S C O N V E R G E S A T N = ' , 1 2 ) F O R M A T ( 5 X , ' P H 1 = ' , E 1 0 . 4 , 5 X , ‘ P H 1 / D E L T A = ' , E 1 0 . 4 ) F O R M A T ( 1 0 X , ' A V E R A G E E N E R G Y , W / O V I B R . = ' , E 1 0 . 4 ) F O R M A T ( 1 0 X , ' A V E R A G E E N E R G Y , W / O E L A S T I C , V I B R . = ' , E 1 0 . 4 ) F O R M A T ( 1 0 X , ' R E D U C E D E X C I T A T I O N R A T E , W / O E L A S T I C , V I B R = ' + E 1 0 . 4 ) C O N T I N U E C O N T I N U E C O N T I N U E S T O P E N D A P P E N D I X D C o m p u t e r p r o g r a m s t a t e m e n t s f o r c a l c u l a t i o n o f t h e c o u p l i n g m a t r i x A o f t h e c o l l o c a t e d n o n l i n e a r B o l t z m a n n e q u a t i o n . 2 2 6 H . . I V A V R V R ‘ A ‘ ‘ l ‘ C C F ‘ 2 2 7 P R O G R A M O R T H O l ( I N P U T , O U T P U T , T A P E 5 0 , T A P E 6 0 ) D I M E N S I O N C ( 0 : 1 5 ) , A ( 0 : 1 5 , 0 : 1 5 ) , B ( 0 : 1 5 , 0 : 1 5 ) , + C A l ( 0 : 1 5 , 0 : 1 5 , 0 : 1 5 ) , C A 2 ( O : 1 5 , 0 : 1 5 , 0 : 1 5 ) D I M E N S I O N F A C T 1 ( 0 : 1 0 0 ) , F A C T 2 ( - 1 : 1 0 0 ) D I M E N S I O N W L ( 0 : 1 5 ) R E A L L ( 1 5 , 0 : 1 5 ) C T H I S P R O G R A M C A C U L A T E S T H E C O U P L I N G M A T R I X A ( * , * , * , * ) C U S E D I N T H E N U M E R I C A L I N T E G R A T I O N O F T H E B O L T Z M A N N E Q U A T I O N C , W H I C H I s D E S C R I B E D I N S E C T I O N 3 . 4 O F T H E D I S S E R T A T I O N O F C T . J . M O R I N , P H D , M I C H I G A N S T A T E U N I V E R S I T Y , 1 9 8 5 . D O 1 0 1 : 1 , 1 5 L ( I , 0 ) = 0 . o 1 0 C O N T I N U E C T H E F O L L O W I N G N U M B E R S A R E T H E R O O T S O F T H E F I R S T C F I F T E E N L A G U E R R E P O L Y N O M I A L S . C B U L L . A M E R . M A T H . S O C . V O L . 5 5 ( 1 9 4 9 ) P . 1 0 0 4 - 1 0 1 2 L ( 1 , 1 ) = 1 . L ( 2 , l ) = . 5 8 5 7 8 6 4 3 7 6 2 7 L ( 2 , 2 ) = 3 . 4 1 4 2 1 3 5 6 2 3 7 3 L ( 3 , 1 ) = . 4 1 5 7 7 4 5 5 6 7 8 3 L ( 3 , 2 ) = 2 . 2 9 4 2 8 0 3 6 0 2 7 9 L ( 3 , 3 ) = 6 . 2 8 9 9 4 5 0 8 2 9 3 7 L ( 4 , 1 ) = . 3 2 2 5 4 7 6 8 9 6 1 9 L ( 4 , 2 ) = 1 . 7 4 5 7 6 1 1 0 1 1 5 8 L ( 4 , 3 ) = 4 . 5 3 6 6 2 0 2 9 6 9 2 1 L ( 4 , 4 ) = 9 . 3 9 5 0 7 0 9 1 2 3 0 1 L ( 5 , l ) = . 2 6 3 5 6 0 3 1 9 7 1 8 L ( 5 , 2 ) = 1 . 4 1 3 4 0 3 0 5 9 1 0 7 L ( 5 , 3 ) = 3 . 5 9 6 4 2 5 7 7 1 0 4 1 L ( 5 , 4 ) = 7 . 0 8 5 8 1 0 0 0 5 8 5 9 L ( 5 , 5 ) - - 1 2 . 6 4 0 8 0 0 8 4 4 2 7 6 L ( 6 , 1 ) = . 2 2 2 8 4 6 6 0 4 1 7 9 L ( 6 , 2 ) = 1 . 1 8 8 9 3 2 1 0 1 6 7 3 L ( 6 , 3 ) = 2 . 9 9 2 7 3 6 3 2 6 0 5 9 L ( 6 , 4 ) = 5 . 7 7 5 1 4 3 5 6 9 1 0 5 L ( 6 , 5 ) = 9 . 8 3 7 4 6 7 4 1 8 3 8 3 L ( 6 , 6 ) = 1 5 . 9 8 2 8 7 3 9 8 0 6 0 2 L ( 7 , 1 ) = . 1 9 3 0 4 3 6 7 6 5 6 0 . L ( 7 , 2 ) = 1 . 0 2 6 6 6 4 8 9 5 3 3 9 L ( 7 , 3 ) = 2 . 5 6 7 B 7 6 7 4 4 9 5 1 L ( 7 , 4 ) = 4 . 9 0 0 3 5 3 0 8 4 5 2 6 L ( 7 , 5 ) = 8 . 1 8 2 1 5 3 4 4 4 5 6 3 L ( 7 , 6 ) = 1 2 . 7 3 4 1 8 0 2 9 1 7 9 8 L ( 7 , 7 ) = 1 9 . 3 9 5 7 2 7 8 6 2 2 6 3 L ( 8 , 1 ) = . 1 7 0 2 7 9 6 3 2 3 0 5 L ( 8 , 2 ) = . 9 0 3 7 0 1 7 7 6 7 9 9 L ( 8 , 3 ) = 2 . 2 5 1 0 8 6 6 2 9 8 6 6 L ( 8 , 4 ) = 4 . 2 6 6 7 0 0 1 7 0 2 8 8 L ( 8 , 5 ) = 7 . 0 4 5 9 0 5 4 0 2 3 9 3 L ( 8 , 6 ) = 1 0 . 7 5 8 5 1 6 0 1 0 1 8 1 L ( 8 , 7 ) = 1 5 . 7 4 0 6 7 8 6 4 1 2 7 8 L ( 8 , 8 ) = 2 2 . 8 6 3 1 3 1 7 3 6 8 8 9 L ( 9 , 1 ) = . 1 5 2 3 2 2 2 2 7 7 3 2 L ( 9 , 2 ) = . 8 0 7 2 2 0 0 2 2 7 4 2 L ( 9 , 3 ) = 2 . 0 0 5 1 3 5 1 5 5 6 1 9 L ( 9 , 4 ) = 3 . 7 8 3 4 7 3 9 7 3 3 3 1 L ( 9 , 5 ) = 6 . 2 0 4 9 5 6 7 7 7 8 7 7 L ( 9 , 6 ) = 9 . 3 7 2 9 8 5 2 5 1 6 8 8 L ( 9 , 7 ) = 1 3 . 4 6 6 2 3 6 9 1 1 0 9 2 L ( 9 , 8 ) = 1 8 . 8 3 3 5 9 7 7 8 8 9 9 2 L ( 9 , 9 ) = 2 6 . 3 7 4 0 7 1 8 9 0 9 2 7 L ( 1 0 , l ) = . 1 3 7 7 9 3 4 7 0 5 4 0 L ( 1 0 , 2 ) = . 7 2 9 4 5 4 5 4 9 5 0 3 L ( 1 0 , 3 ) = 1 . 8 0 8 3 4 2 9 0 1 7 4 0 L ( 1 0 , 4 ) = 3 . 4 0 1 4 3 3 6 9 7 8 5 5 L ( l O , 5 ) = 5 . 5 5 2 4 9 6 l 4 0 0 6 4 L ( 1 0 , 6 ) = 8 . 3 3 0 1 5 2 7 4 6 7 6 4 L ( 1 0 , 7 ) = l l . 8 4 3 7 8 5 8 3 7 9 0 0 L ( 1 0 , 8 ) = 1 6 . 2 7 9 2 5 7 8 3 1 3 7 8 L ( 1 0 , 9 ) = 2 1 . 9 9 6 5 8 5 8 1 1 9 8 1 L ( 1 0 , 1 0 ) = 2 9 . 9 2 0 6 9 7 0 1 2 2 7 4 L ( 1 1 , 1 ) = . 1 2 5 7 9 6 4 4 2 1 8 8 L ( 1 1 , 2 ) = . 6 6 5 4 1 8 2 5 5 8 3 9 L ( 1 1 , 3 ) = 1 . 6 4 7 1 5 0 5 4 5 8 7 2 L ( 1 1 , 4 ) = 3 . 0 9 1 1 3 8 1 4 3 0 3 5 L ( 1 1 , 5 ) = 5 . 0 2 9 2 8 4 4 0 1 5 8 0 L ( 1 1 , 6 ) = 7 . 5 0 9 8 8 7 8 6 3 8 0 7 L ( 1 1 , 7 ) = 1 0 . 6 0 5 9 5 0 9 9 9 5 4 7 L ( 1 1 , 8 ) = l 4 . 4 3 1 6 1 3 7 5 8 0 6 4 L ( l l , 9 ) = l 9 . l 7 8 8 5 7 4 0 3 2 1 5 L ( 1 1 , 1 0 ) = 2 5 . 2 1 7 7 0 9 3 3 9 6 7 8 L ( 1 1 , 1 1 ) = 3 3 . 4 9 7 1 9 2 8 4 7 1 7 6 L ( 1 2 , 1 ) = . 1 1 5 7 2 2 1 1 7 3 5 8 L ( 1 2 , 2 ) = . 6 1 1 7 5 7 4 8 4 5 1 5 L ( 1 2 , 3 ) = 1 . 5 1 2 6 1 0 2 6 9 7 7 6 L ( 1 2 , 4 ) = 2 . 8 3 3 7 5 1 3 3 7 7 4 4 L ( 1 2 , 5 ) = 4 . 5 9 9 2 2 7 6 3 9 4 1 8 L ( 1 2 , 6 ) = 6 . 8 4 4 5 2 5 4 5 3 1 1 5 L ( 1 2 , 7 ) = 9 . 6 2 1 3 1 6 8 4 2 4 5 7 L ( 1 2 , B ) = l 3 . 0 0 6 0 5 4 9 9 3 3 0 6 L ( 1 2 , 9 ) = 1 7 . 1 1 6 8 5 5 1 8 7 4 6 2 L ( 1 2 , 1 0 ) = 2 2 . 1 5 1 0 9 0 3 7 9 3 9 7 L ( 1 2 , 1 1 ) = 2 8 . 4 8 7 9 6 7 2 5 0 9 8 4 L ( 1 2 , 1 2 ) = 3 7 . 0 9 9 1 2 1 0 4 4 4 6 7 L ( 1 3 , 1 ) = . 1 0 7 1 4 2 3 8 8 4 7 2 L ( 1 3 , 2 ) = . 5 6 6 1 3 1 8 9 9 0 4 0 L ( 1 3 , 3 ) = 1 . 3 9 8 5 6 4 3 3 6 4 5 1 L ( l 3 , 4 ) = 2 . 6 1 6 5 9 7 1 0 8 4 0 6 L ( 1 3 , 5 ) = 4 . 2 3 8 8 4 5 9 2 9 0 1 7 L ( 1 3 , 6 ) = 6 . 2 9 2 2 5 6 2 7 1 1 4 0 2 2 8 2 0 3 0 L ( 1 3 , 7 ) = 8 . 8 1 5 0 0 1 9 4 1 1 8 7 L ( 1 3 , 8 ) = 1 1 . 8 6 1 4 0 3 5 8 8 8 1 1 L ( 1 3 , 9 ) = 1 5 . 5 1 0 7 6 2 0 3 7 7 0 4 L ( 1 3 , 1 0 ) = 1 9 . 8 8 4 6 3 5 6 6 3 8 8 0 L ( 1 3 , 1 1 ) = 2 5 . 1 8 5 2 6 3 8 6 4 6 7 B L ( 1 3 , 1 2 ) = 3 1 . 8 0 0 3 8 6 3 0 1 9 4 7 L ( 1 3 , 1 3 ) = 4 0 . 7 2 3 0 0 8 6 6 9 2 6 6 L ( 1 4 , 1 ) = . 0 9 9 7 4 7 5 0 7 0 3 3 L ( 1 4 , 2 ) = . 5 2 6 8 5 7 6 4 8 8 5 2 L ( l 4 , 3 ) = 1 . 3 0 0 6 2 9 1 2 1 2 5 1 L ( 1 4 , 4 ) = 2 . 4 3 0 8 0 1 0 7 B 7 3 1 L ( l 4 , 5 ) = 3 . 9 3 2 1 0 2 8 2 2 2 9 3 L ( l 4 , 6 ) = 5 . 8 2 5 5 3 6 2 1 8 3 0 2 L ( 1 4 , 7 ) = 8 . 1 4 0 2 4 0 1 4 1 5 6 5 L ( l 4 , 8 ) = 1 0 . 9 1 6 4 9 9 5 0 7 3 6 6 L ( 1 4 , 9 ) = l 4 . 2 1 0 8 0 5 0 1 1 1 6 1 L ( 1 4 , 1 0 ) = 1 8 . 1 0 4 8 9 2 2 2 0 2 1 8 L ( 1 4 , 1 1 ) = 2 2 . 7 2 3 3 8 1 6 2 8 2 6 9 L ( 1 4 , 1 2 ) = 2 8 . 2 7 2 9 8 1 7 2 3 2 4 8 L ( 1 4 , 1 3 ) = 3 5 . 1 4 9 4 4 3 6 6 0 5 9 2 L ( l 4 , l 4 ) = 4 4 . 3 6 6 0 8 1 7 l l l l 7 L ( 1 5 , 1 ) = . 0 9 3 3 0 7 8 1 2 0 1 7 L ( 1 5 , 2 ) = . 4 9 2 6 9 1 7 4 0 3 0 2 L ( 1 5 , 3 ) = 1 . 2 1 5 5 9 5 4 1 2 0 7 1 L ( 1 5 , 4 ) = 2 . 2 6 9 9 4 9 5 2 6 2 0 4 L ( 1 5 , 5 ) = 3 . 6 6 7 6 2 2 7 2 1 7 5 1 L ( 1 5 , 6 ) = 5 . 4 2 5 3 3 6 6 2 7 4 l 4 L ( 1 5 , 7 ) = 7 . 5 6 5 9 1 6 2 2 6 6 1 3 L ( 1 5 , 8 ) = 1 0 . 1 2 0 2 2 8 5 6 8 0 1 9 L ( 1 5 , 9 ) = 1 3 . 1 3 0 2 8 2 4 8 2 1 7 6 L ( 1 5 , 1 0 ) = 1 6 . 6 5 4 4 0 7 7 0 8 3 3 0 L ( 1 5 , 1 1 ) = 2 0 . 7 7 6 4 7 8 8 9 9 4 4 9 L ( 1 5 , 1 2 ) = 2 5 . 6 2 3 8 9 4 2 2 6 7 2 9 L ( 1 5 , 1 3 ) = 3 1 . 4 0 7 5 1 9 1 6 9 7 5 4 L ( 1 5 , 1 4 ) = 3 8 . 5 3 0 6 8 3 3 0 6 4 8 6 L ( 1 5 , 1 5 ) = 4 8 . 0 2 6 0 8 5 5 7 2 6 8 6 F A C T 1 ( 0 ) = 1 . . D O 2 0 I = 1 , 1 0 0 F A C T 1 ( I ) = I * F A C T 1 ( I - 1 ) C O N T I N U E F A C T 2 ( - 1 ) = 1 . F A C T 2 ( 0 ) = 1 . F A C T 2 ( 1 ) = 1 . D O 3 0 I = 2 , 1 0 0 F A C T 2 ( I ) = I * F A C T 2 ( I — 2 ) C O N T I N U E P R I N T * , ' I = ' R E A D * , I I I s I I W R I T E ( 5 0 , 2 1 ) 2 2 9 2 1 7 O 3 2 2 3 0 F O R M A T < 7 X , ' I ' , 4 X , ' J ' , 7 X , ' C ( I , J ) ' ) D O 6 0 J = l , I C ( J ) = l . D O 7 0 K = 1 , I I F ( J . E Q . K ) G O T O 7 0 C ( J ) = ( L ( I , J ) - L ( I , K ) ) * C ( J ) W R I T E ( 5 0 , 3 2 ) I , J , C ( J ) C O N T I N U E C O N T I N U E F O R M A T ( 3 X , 2 1 5 , 4 X , E l 5 . 8 ) D O 4 9 0 K = l , I l - 1 I = I l D O 5 1 0 J 1 = 1 , I S U M = 0 . 0 D O 5 2 0 J 2 = l , I I F ( J 2 . E Q . J 1 ) G O T O 5 2 0 I F ( K . E Q . 1 ) T H E N S U M = S U M - L ( I , J 2 ) G O T O 5 2 0 E L S E I F ( J 2 . E Q . I ) G O T O 5 2 0 E N D I F D O 5 3 0 J 3 = J 2 + l , I I F ( J 3 . E Q . J 1 ) G O T O 5 3 0 I F ( K . E Q . 2 ) T H E N S U M = S U M + L ( I , J 2 ) * L ( I , J 3 ) G O T O 5 3 0 E L S E I F ( J 3 . E Q . I ) G O T O 5 3 0 E N D I F D O 5 4 0 J 4 = J 3 + l , I I F ( J 4 . E Q . J 1 ) G O T O 5 4 0 I F ( K . E Q . 3 ) T H E N S U M = S U M - L ( I , J 2 ) * L ( I , J 3 ) * L ( I , J 4 ) G O T O 5 4 0 E L S E I F ( J 4 . E Q . I ) G O T O 5 4 0 E N D I F D O 5 5 0 J 5 = J 4 + 1 , I I F ( J 5 . E Q . J 1 ) G O T O 5 5 0 I F ( K . E Q . 4 ) T H E N S U M = S U M + L ( I , J 2 ) * L ( I , J 3 ) * L ( I , J 4 ) * L ( I , J 5 ) G O T O 5 5 0 E L S E I F ( J 5 . E Q . I ) G O T O 5 5 0 E N D I F D O 5 6 0 J 6 = J 5 + 1 , I I F ( J 6 . E Q . J 1 ) G O T O 5 6 0 I F ( K . E Q . 5 ) T H E N S U M = S U M - L ( I , J 2 ) * L ( I , J 3 ) * L ( I , J 4 ) * L ( I , J 5 ) * L ( I , J 6 ) 2 3 1 G O T O 5 6 0 E L S E I F ( J 6 . E Q . I ) G O T O 5 6 0 E N D I F D O 5 7 0 J 7 = J 6 + l , I I F ( J 7 . E Q . J 1 ) G O T O 5 7 0 I F ( X . E Q . 6 ) T H E N S U M = S U M + L ( I , J 2 ) * L ( I , J 3 ) * L ( I , J 4 ) * L ( I , J 5 ) * L ( I , J 6 ) * L ( I , J 7 ) G O T O 5 7 0 E L S E I F ( J 7 . E Q . I ) G O T O 5 7 0 E N D I F D O 5 8 0 J 8 = J 7 + l , I I F ( J 8 . E Q . J 1 ) G O T O 5 8 0 I F ( K . E Q . 7 ) T H E N S U M = S U M - L ( I , J 2 ) * L ( I , J 3 ) * L ( I , J 4 ) * L ( I , J 5 ) * L ( I , J 6 ) * L ( I , J 7 ) + * L ( I , J 8 ) G O T O 5 8 0 E L S E I F ( J 8 . E Q . I ) G O T O 5 8 0 E N D I F D O 5 9 0 J 9 = J 8 + 1 , I - I F ( J 9 . E Q . J 1 ) G O T O 5 9 0 I F ( K . E Q . 8 ) T H E N S U M = S U M + L ( I , J 2 ) * L ( I , J 3 ) * L ( I , J 4 ) * L ( I , J 5 ) * L ( I , J 6 ) * L ( I , J 7 ) + * L ( I , J 8 ) * L ( I , J 9 ) G O T O 5 9 0 E L S E I F ( J 9 . E Q . I ) G O T O 5 9 0 E N D I F D O 6 0 0 J 1 0 = J 9 + 1 , I I F ( J 1 0 . E Q . J 1 ) G O T O 6 0 0 I F ( K . E Q . 9 ) T H E N S U M = S U M - L ( I , J 2 ) * L ( I , J 3 ) * L ( I , J 4 ) * L ( I , J 5 ) * L ( I , J 6 ) * L ( I , J 7 ) + * L ( I , J 8 ) * L ( I , J 9 ) * L ( I , J 1 0 ) G O T O 6 0 0 E L S E I F ( J 1 0 . E Q . I ) G O T O 6 0 0 E N D I F D O 6 1 0 J 1 1 = J 1 0 + 1 , I I F ( J 1 1 . E Q . J 1 ) G O T O 6 1 0 I F ( K . E Q . 1 0 ) T H E N S U M = S U M + L ( I , J 2 ) * L ( I , J 3 ) * L ( I , J 4 ) * L ( I , J 5 ) * L ( I , J 6 ) * L ( I , J 7 ) + * L ( I , J 8 ) * L ( I , J 9 ) * L ( I , J 1 0 ) * L ( I , J 1 1 ) G O T O 6 1 0 E L S E I F ( J 1 1 . E Q . I ) G O T O 6 1 0 E N D I F D O 6 2 0 J 1 2 = J 1 1 + 1 , I I F ( J 1 2 . E Q . J 1 ) G O T O 6 2 0 6 6 0 6 5 0 6 4 0 6 3 0 2 3 2 I F ( K . E Q . 1 1 ) T H E N S U M = S U M - L ( I , J 2 ) * L ( I , J 3 ) * L ( I , J 4 ) * L ( I , J 5 ) * L ( I , J 6 ) * L ( I , J 7 ) + * L ( I , J 8 ) * L ( I , J 9 ) * L ( I , J l O ) * L ( I , J l l ) * L ( I , J l Z ) G O T O 6 2 0 E L S E I F ( J 1 2 . E Q . I ) G O T O 6 2 0 E N D I F D O 6 3 0 J 1 3 = J 1 2 + l , 1 I F ( J 1 3 . E Q . J 1 ) G O T O 6 3 0 I F ( K . E Q . 1 2 ) T H E N S U M = S U M + L ( I , J 2 ) * L ( I , J 3 ) * L ( I , J 4 ) * L ( I , J 5 ) * L ( I , J 6 ) * L ( I , J 7 ) + * L ( I , J 8 ) * L ( I , J 9 ) * L ( I , J l O ) * L ( I , J l l ) * L ( I , J 1 2 ) * L ( I , J l 3 ) G O T O 6 3 0 E L S E I F ( J 1 3 . E Q . I ) G O T O 6 3 0 E N D I F D O 6 4 0 J 1 4 = J l 3 + 1 , 1 I F ( J 1 4 . E Q . J 1 ) G O T O 6 4 0 I F ( K . E Q . 1 3 ) T H E N S U M = S U M - L ( I , J 2 ) * L ( I , J 3 ) * L ( I , J 4 ) * L ( I , J 5 ) * L ( I , J 6 ) * L ( I , J 7 ) + * L ( I , J 8 ) * L ( I , J 9 ) * L ( I , J l O ) * L ( I , J l l ) * L ( I , J 1 2 ) * L ( I , J 1 3 ) + * L ( I , J l 4 ) G O T O 6 4 0 E L S E I F ( J l 4 . E Q . I ) G O T O 6 4 0 E N D I F D O 6 5 0 J 1 5 = J 1 4 + l , I I F ( J 1 5 . E Q . J 1 ) G O T O 6 5 0 I F ( X . E Q . 1 4 ) T H E N S U M = S U M + L ( I , J 2 ) * L ( I , J 3 ) * L ( I , J 4 ) * L ( I , J 5 ) * L ( I , J 6 ) * L ( I , J 7 ) + * L ( I , J 8 ) * L ( I , J 9 ) * L ( I , J l O ) * L ( I , J l l ) * L ( I , J 1 2 ) * L ( I , J 1 3 ) + * L ( I , J l 4 ) * L ( I , J 1 5 ) G O T O 6 5 0 E L S E I F ( J I S . E Q . I ) G O T O 6 5 0 E N D I F D O 6 6 0 J 1 6 = J 1 5 + 1 , I I F ( J 1 6 . E Q . J 1 ) G O T O 6 6 0 I F ( X . E Q . 1 5 ) T H E N S U M = S U M - L ( I , J 2 ) * L ( I , J 3 ) * L ( I , J 4 ) * L ( I , J 5 ) * L ( I , J 6 ) * L ( I , J 7 ) + * L ( I , J 8 ) * L ( I , J 9 ) * L ( I , J 1 0 ) * L ( I , J l l ) * L ( I , J 1 2 ) * L ( I , J l 3 ) * + L ( I , J l 4 ) * L ( I , J 1 5 ) * L ( I , J 1 6 ) G O T O 6 6 0 E L S E I F ( J 1 6 . E Q . I ) G O T O 6 6 0 E N D I F C O N T I N U E C O N T I N U E C O N T I N U E C O N T I N U E 6 6 ( W V p h v : J : v P M ) . m m v . 9 . ) » P a d . 5 . \ u 4 e 2 3 3 6 2 0 C O N T I N U E 6 1 0 C O N T I N U E 6 0 0 C O N T I N U E 5 9 0 C O N T I N U E 5 8 0 C O N T I N U E 5 7 0 C O N T I N U E 5 6 0 C O N T I N U E 5 5 0 C O N T I N U E 5 4 0 C O N T I N U E 5 3 0 C O N T I N U E 5 2 0 C O N T I N U E A ( J I , I - 1 - X ) = S U M B ( J l , I - l - K ) = S U M / C ( J 1 ) 5 1 0 C O N T I N U E 4 9 0 C O N T I N U E 1 8 1 1 D O 6 8 0 3 1 : 1 , 1 A ( J 1 , I - 1 ) = 1 . 0 B ( J l , I - l ) = l . / C ( J l ) 6 8 0 C O N T I N U E W R I T E ( 5 0 , 2 2 ) 2 2 F O R M A T ( 7 X , ' I ' , 3 X , ' J 1 ' , 3 X , ' J 2 ' , 5 X , ' A ( J 1 , J 2 ) ' , 7 X , ' B ( J 1 , J 2 ) ' ) D O 3 8 3 1 : 1 , 1 1 D O 3 9 J 2 = l , I l W R I T E ( 5 0 , 3 3 ) I l , J 1 , J 2 , A ( J 1 , J 2 ) , B ( J 1 , J 2 ) 3 9 C O N T I N U E 3 8 C O N T I N U E 3 3 F O R M A T ( 3 X , 3 1 5 , 2 E 1 5 . 8 ) W R I T E ( 5 0 , 2 3 ) 2 3 F O R M A T ( 7 X , ' I ' , 6 X , ' W L ( I ) ' ) D O 3 5 I = 1 , I I S U M = 0 . 0 D O 3 6 J = l , I l - 1 S U M = S U M + B ( I , J ) * F A C T 2 ( 2 * J + 1 ) 3 6 C O N T I N U E W L ( I ) = S U M W R I T E ( 5 0 , 3 7 ) I , W L ( I ) 3 5 C O N T I N U E . 3 7 F O R M A T ( 3 X , 1 5 , 4 X , E 1 5 . 8 ) J l = I l W R I T E < 5 0 , 2 4 ) 2 4 F O R M A T ( 6 X , ' I l ' , 3 X , ' J 2 ' , 3 X , ' L 0 ' , 4 X , ' M ' , 5 X , ' C A 1 ( I l , J 2 , L 0 , M ) ' ) D O 9 9 5 J 2 = 1 , J 1 D O 1 0 0 0 L 0 = 0 , J l - 1 D O 1 0 1 0 M = 0 , J l - l S U M = 0 . 0 D O 1 0 2 0 N 1 = 0 , L 0 D O 1 0 3 0 N 2 = 0 , N 1 D O 1 0 4 0 M 1 - 0 , M D O 1 0 5 0 M 2 = 0 , M 1 1 0 7 0 1 0 6 0 1 0 5 0 1 0 4 0 1 0 3 0 1 0 2 0 1 0 1 0 1 0 0 0 9 9 5 3 4 2 5 1 1 3 0 1 1 2 0 2 3 4 D 0 1 0 6 0 L 1 = 0 , L 0 - N 1 + M 2 D O 1 0 7 0 L 2 = 0 , M - M 1 + N 2 L L 1 = 2 * ( ( L 1 + L 2 ) / 2 ) L L 2 = 2 * ( ( N 1 + M 1 - N 2 - M 2 ) / 2 ) I F ( L L 1 . L T . L 1 + L 2 ) G O T O 1 0 7 0 I F ( L L 2 . L T . N 1 + M 1 - N 2 — M 2 ) G O T O 1 0 7 0 I F ( J 2 . E Q . 0 ) T H E N I F ( N 1 + M 1 + N 2 + M 2 . E Q . 0 ) T H E N S U M = S U M + 2 . * ( - 1 ) * * L 1 * F A C T 1 ( L 0 ) * F A C T 1 ( M ) * F A C T 2 ( 2 * ( L 0 + M + 1 ) - 1 ) + / ( 2 * * ( L 0 + M ) * F A C T 1 ( L 1 ) * F A C T 1 ( L 2 ) * F A C T 1 ( L 0 - L 1 ) * F A C T 1 ( M - L 2 ) + * ( L 1 + L 2 + 1 ) ) E L S E S U M = S U M E N D I F E L S E S U M = S U M + 2 . * ( - 1 ) * * ( L 1 + M 1 - M 2 ) * F A C T 1 ( M ) * F A C T 1 ( L 0 ) * F A C T 1 ( L 0 - N 1 + M 2 ) + * 2 * * ( 3 * ( N 1 + M 1 - N 2 — M 2 ) / 2 ) + * F A C T l ( M - M 1 + N 2 ) * L ( J l , J 2 ) * * ( ( N 1 + M 1 + N 2 + M 2 ) / 2 ) * F A C T 1 ( ( N l + M l - N 2 + - M 2 ) / 2 ) * F A C T 2 ( L 1 + L 2 - 1 ) * F A C T 2 ( 2 * ( L 0 + M + 1 ) - N 1 - M 1 — N 2 - M 2 - 1 ) / + ( 2 * * ( L 0 + M ) * F A C T 1 ( N 2 ) * F A C T 1 ( M 2 ) * F A C T 1 ( L 1 ) + * F A C T 1 ( L 2 ) * F A C T 1 ( L 0 - N 1 + M 2 — L 1 ) * F A C T 1 ( M - M 1 + N 2 - L 2 ) + * ( N 1 + M 1 — N 2 — M 2 + 1 ) * F A C T 2 ( L 1 + L 2 + 1 + N 1 + M 1 - N 2 - M 2 ) + * F A C T 1 ( L 0 - N 1 ) * F A C T 1 ( M - M l ) * F A C T 1 ( N 1 - N 2 ) * F A C T 1 ( M 1 - M 2 ) ) E N D I F C O N T I N U E C O N T I N U E C O N T I N U E C O N T I N U E C O N T I N U E C O N T I N U E C A 1 ( J 2 , L 0 , M ) = S U M W R I T E ( 5 0 , 3 4 ) J 1 , J 2 , L 0 , M , S U M C O N T I N U E C O N T I N U E C O N T I N U E F O R M A T ( 3 X , 4 1 5 , 4 X , E 1 5 . 8 ) 3 1 : 1 1 W R I T E ( 5 0 , 2 5 ) _ F O R M A T < 6 X , ' 1 1 ' , 3 X , ' J 2 ' , 3 X , ' J 3 ' , 3 X , ' J 4 ' , 5 X , ' C A 2 ( J 1 , J 2 , J 3 , J 4 ) ' ) D O 1 1 1 0 J 2 = 1 , J 1 D O 1 1 1 1 J 3 = 1 , J 1 D O 1 1 1 2 J 4 = 1 , J l S U M = 0 . 0 D O 1 1 2 0 L 0 = 0 , J l - l D O 1 1 3 0 M = 0 , J 1 - l S U M = S U M + C A 1 ( J z , L 0 , M ) * B ( J 3 , L 0 ) * B ( J 4 , M ) C O N T I N U E C O N T I N U E C A 2 ( J 2 , J 3 , J 4 ) = S U M W R I T E ( 5 0 , 1 1 5 0 ) J 1 , J 2 , J 3 , J 4 , S U M 1 1 1 2 1 1 1 1 1 1 1 0 1 1 0 0 1 1 5 0 9 0 1 2 0 1 1 0 1 0 0 9 2 2 3 5 C O N T I N U E C O N T I N U E C O N T I N U E C O N T I N U E . F O R M A T ( 3 X , 4 1 5 , 4 X , E 1 5 . 8 ) D O 9 0 3 1 : 1 , 1 1 W R I T E ( 6 0 , 9 1 ) 1 1 , J 1 , W L ( J I ) ' C O N T I N U E D O 1 0 0 J 1 = l , I l D O 1 1 0 J 2 = l , I l D O 1 2 0 J 3 = 1 , I l W R I T E ( 6 0 , 9 2 ) 1 1 , J 1 , J 2 , J 3 , C A 2 ( J 1 , J 2 , J 3 ) C O N T I N U E C O N T I N U E C O N T I N U E F O R M A T ( 7 X , ' W L ( ' , I 2 , , F O R M A T ( 7 X , ' A ( ' , I 2 , ' , ' , I S T O P E N D 2 , ' ) ' , E l S . 8 ) I 2 , , 2 , ' , ' , I 2 , ' ) = ' , E 2 0 . 1 4 ) A P P E N D I X E C o m p u t e r p r o g r a m s t a t e m e n t s f o r t h e a n a l y s i s o f t h e l i n e a r i z e d B o l t z m a n n e q u a t i o n . 2 3 6 2 3 7 P R O G R A M C H E C K ( I N P U T , O U T P U T , T A P E 1 0 ) D I M E N S I O N A ( 8 : 1 1 , 1 1 , 1 1 , 1 1 ) , S U M ( 8 : 1 1 , 1 1 ) , B ( 8 : 1 1 , 1 1 , 1 1 ) C T H I S P R O G R A M C H E C K S T H E C O U P L I N G M A T R I X E L E M E N T S O F C T H E C O L L O C A T I O N O F T H E K R O O K - W U P R O B L E M . F O R A S E T C O F A ( I , J , K , L ) , T H E S U M O V E R T H E H A N D L I N D I C E S C S H O U L D E Q U A L 2 . 0 A ( 8 , 1 , l , 1 ) = . 1 4 0 8 6 8 3 7 7 7 8 6 5 5 8 + 0 0 A ( 8 , 1 , 1 , 2 ) = . 2 0 0 7 1 5 9 4 6 4 9 3 8 0 8 + 0 0 A ( 8 , 1 , 1 , 3 ) = . 9 0 1 8 5 8 9 5 8 8 6 6 3 4 E - O l A ( 8 , 1 , 1 , 4 ) = . 4 0 8 9 3 7 5 3 2 3 3 7 1 8 8 - 0 1 A ( 8 , l , 1 , 5 ) = . 8 9 5 5 1 4 5 4 4 2 5 4 1 8 8 - 0 2 A ( 8 , 1 , 1 , 6 ) = . 1 8 5 4 3 4 6 3 9 1 8 6 6 1 E - 0 2 A ( 8 , 1 , 1 , 7 ) = . 1 3 1 7 5 0 4 6 2 5 7 9 7 4 E ~ 0 3 A ( 8 , 1 , 1 , 8 ) = . 6 9 1 0 6 5 9 2 9 9 0 8 6 4 E - 0 5 A ( 8 , 1 , 2 , 1 ) = . 2 0 0 7 1 5 9 4 6 4 6 8 7 9 E + 0 0 A ( 8 , 1 , 2 , 2 ) = . 3 2 3 0 5 1 9 9 4 5 6 7 7 B E + 0 0 A ( 8 , 1 , 2 , 3 ) = . 1 7 6 6 7 6 2 8 5 6 8 4 6 1 E + 0 0 A ( 8 , 1 , 2 , 4 ) = . 8 0 2 3 1 6 7 1 8 7 9 5 7 4 E - 0 1 A ( 8 , 1 , 2 , 5 ) = . 1 9 0 3 1 8 0 5 4 5 6 0 5 2 8 - 0 1 A ( 8 , 1 , 2 , 6 ) = . 3 8 6 9 0 9 6 1 2 0 5 9 5 8 8 - 0 2 A ( 8 , 1 , 2 , 7 ) = . 2 8 9 1 6 6 6 3 5 5 5 2 0 1 E - 0 3 A ( 8 , 1 , 2 , 8 ) = . 1 4 9 4 0 7 4 9 7 3 6 8 4 7 3 - 0 4 A ( 8 , 1 , 3 , 1 ) = . 9 0 1 8 5 8 9 5 8 7 8 9 0 3 8 - 0 1 A ( 8 , 1 , 3 , 2 ) = . 1 7 6 6 7 6 2 8 5 6 7 7 3 3 3 + 0 0 A ( 8 , 1 , 3 , 3 ) = . 1 0 8 5 9 0 1 1 0 2 6 6 5 0 E + 0 0 A ( 8 , 1 , 3 , 4 ) = . 5 2 1 8 6 0 2 7 5 3 5 9 8 1 E - O l A ( 8 , 1 , 3 , 5 ) = . 1 2 8 6 9 1 4 7 1 9 7 5 9 l E - O l A ( 8 , 1 , 3 , 6 ) = . 2 6 4 4 2 1 2 9 3 6 9 8 5 5 E - 0 2 A ( 8 , 1 , 3 , 7 ) = . 2 0 0 6 2 5 9 7 0 0 5 2 2 2 8 - 0 3 A ( 8 , 1 , 3 , 8 ) = . 1 0 3 4 1 8 4 2 3 9 5 7 8 9 8 - 0 4 A ( 8 , 1 , 4 , 1 ) = . 4 0 8 9 3 7 5 3 2 3 5 0 8 2 8 - 0 1 A ( 8 , 1 , 4 , 2 ) = . 8 0 2 3 1 6 7 1 8 4 5 0 1 3 E - 0 1 A ( 8 , 1 , 4 , 3 ) = . 5 2 1 8 6 0 2 7 5 4 8 7 1 4 8 - 0 1 A ( 8 , 1 , 4 , 4 ) = . 2 6 4 9 0 7 6 0 0 7 6 5 1 3 8 - 0 1 A ( 8 , 1 , 4 , 5 ) = . 6 7 9 9 1 1 4 7 6 8 8 5 3 1 3 - 0 2 A ( 8 , 1 , 4 , 6 ) = . 1 4 5 0 7 9 0 3 8 6 6 5 5 9 E - 0 2 A ( 8 , 1 , 4 , 7 ) = . 1 1 2 6 2 6 1 8 6 1 0 5 3 0 8 - 0 3 A ( 8 , 1 , 4 , 8 ) = . 5 9 6 9 0 5 4 7 4 2 7 0 4 9 8 - 0 5 A ( 8 , 1 , 5 , 1 ) = . 8 9 5 5 1 4 5 4 3 4 0 1 5 3 3 - 0 2 A ( 8 , 1 , 5 , 2 ) ' . 1 9 0 3 1 8 0 5 4 7 9 6 9 9 3 - 0 1 A ( 8 , 1 , 5 , 3 ) = . 1 2 8 6 9 1 4 7 1 7 9 8 5 6 E - 0 1 A ( 8 , 1 , 5 , 4 ) = . 6 7 9 9 1 1 4 7 7 6 1 2 9 0 3 - 0 2 A ( 8 , 1 , 5 , 5 ) = . 1 7 8 3 6 9 4 1 8 1 4 5 5 1 8 - 0 2 A ( 8 , 1 , 5 , 6 ) = . 3 8 8 1 5 6 6 6 4 3 5 7 1 0 8 - 0 3 A ( 8 , 1 , 5 , 7 ) = . 3 0 4 2 4 4 2 2 6 5 0 5 5 5 8 - 0 4 A ( 8 , 1 , 5 , 8 ) = . 1 6 2 4 3 4 9 6 3 5 2 5 6 9 8 - 0 5 A ( 8 , 1 , 6 , 1 ) = . 1 8 5 4 3 4 6 3 9 7 0 6 7 3 8 - 0 2 A ( 8 , 1 , 6 , 2 ) = . 3 8 6 9 0 9 6 1 0 8 6 5 8 7 E - 0 2 A ( 8 , 1 , 6 , 3 ) = . 2 6 4 4 2 1 2 9 4 7 0 0 4 1 E - 0 2 A ( 8 , 1 , 6 , 4 ) = . 1 4 5 0 7 9 0 3 7 9 3 7 9 9 3 - 0 2 > H A o Q x o > H A V o “ 3 A H o § a m m o § v A H w o m > A H o q V “ > A q H o ‘ o “ q > V A H o > ‘ A o H q “ q > o A H h o I > “ A H s o \ > o ~ A H I fi o A V H \ ‘ m > q A o H ‘ fi > o A H s m m ‘ o A H § m o > > A m ‘ H fi m > o A H o o V > " o A H V o > m o A Q H ~ m , o A Q H o m 3 ‘ A o N fi o > c A ‘ N o “ > o A N a o > h m A N “ - > fi m I A N > m ~ ‘ H A N m h > m “ A N ‘ H H > n A N H > “ c A § N m H v o H A N - v o ‘ H A N o > N § ‘ c A N N > m A ‘ N - N > m A N n w > “ c ‘ w A N v m § w A N > m ~ w A N m ~ > w m “ A N w > - ) > A a N w - ‘ m w A N > m w A N “ V > m A m N > ~ u “ w m > A N w m § > A m N “ w > A m p - N m “ p > A N § m p > A “ N m ~ n > A N m m ~ “ e 5 N A m h > N w A m “ ‘ 2 3 8 . 3 8 8 1 5 6 6 6 5 4 8 3 3 1 8 - 0 3 . 8 8 0 7 6 9 6 7 8 5 2 4 0 2 E - 0 4 . 7 0 1 4 3 8 4 3 6 3 7 9 0 4 E - 0 5 . 3 8 8 9 3 7 7 5 8 5 1 0 2 0 8 - 0 6 . 1 3 1 7 5 0 4 6 1 6 6 0 4 7 3 - 0 3 . 2 8 9 1 6 6 6 3 7 6 6 2 3 2 E - 0 3 . 2 0 0 6 2 5 9 6 7 5 8 6 6 3 8 - 0 3 . 1 1 2 6 2 6 1 8 7 2 6 3 4 9 E - 0 3 . 3 0 4 2 4 4 2 2 2 7 9 2 9 6 E - 0 4 . 7 0 1 4 3 8 4 4 1 0 8 6 3 9 E - 0 5 . 5 6 1 8 8 9 0 0 3 2 4 2 1 7 E - 0 6 . 3 1 4 6 5 4 1 3 5 3 6 8 6 6 E - 0 7 . 6 9 1 0 6 5 9 3 4 5 9 1 0 1 3 - 0 5 . 1 4 9 4 0 7 4 9 6 2 3 3 8 2 8 - 0 4 . 1 0 3 4 1 8 4 2 5 1 7 2 4 7 E - 0 4 . 5 9 6 9 0 5 4 6 7 8 6 4 5 1 E - 0 5 . 1 6 2 4 3 4 9 6 5 7 1 8 3 8 8 - 0 5 . 3 8 8 9 3 7 7 5 5 1 2 7 4 9 E - 0 6 . 3 1 4 6 5 4 1 3 7 1 7 2 7 7 E - 0 7 . 1 8 3 3 7 0 3 0 2 2 6 7 6 4 8 ‘ 0 8 . 8 8 7 6 5 9 3 9 0 9 9 7 4 4 3 - 0 2 . 8 4 7 4 7 9 3 6 4 3 9 2 7 1 E - 0 1 . 7 9 5 9 7 7 9 2 7 8 3 9 4 3 E - 0 1 . 2 6 4 3 5 4 5 8 6 4 6 4 6 1 E - 0 1 . 7 2 8 5 9 9 8 9 3 1 8 2 0 4 E - 0 2 . 1 2 3 9 8 3 3 4 9 5 8 6 6 1 E - 0 2 . 1 0 3 7 0 5 0 9 3 0 3 3 9 2 E - 0 3 . 4 7 3 8 8 8 6 4 8 9 5 5 2 6 3 - 0 5 . 8 4 7 4 7 9 3 6 4 5 4 5 0 5 3 - 0 1 . 3 9 1 9 2 5 6 5 6 6 8 0 0 9 E + 0 0 . 2 5 2 3 7 5 7 5 2 3 5 1 3 B E + 0 0 . 1 0 5 0 8 7 7 6 3 0 7 7 5 6 3 + 0 0 . 2 6 0 8 9 8 1 4 6 8 4 0 4 2 E - 0 1 . 5 0 7 5 3 4 2 5 7 2 3 5 4 2 E T 0 2 . 3 9 1 6 4 5 9 8 2 8 9 0 7 6 E - 0 3 . 1 9 6 7 3 2 9 0 0 0 9 8 4 7 E - 0 4 . 7 9 5 9 7 7 9 2 7 6 3 9 3 4 8 - 0 1 . 2 5 2 3 7 5 7 5 2 3 8 0 8 9 E + 0 0 . 1 7 1 0 9 0 0 5 4 6 8 0 9 2 3 + 0 0 . 7 7 6 8 6 0 2 2 8 7 1 8 3 1 E - 0 1 . 1 9 5 7 3 1 5 9 6 2 0 5 6 3 E - 0 1 . 3 9 1 1 2 1 4 6 1 4 9 3 0 7 E - 0 2 . 3 0 1 4 2 9 7 4 1 9 1 7 0 5 8 - 0 3 . 1 5 2 7 0 6 5 1 2 0 8 9 8 7 E - 0 4 . 2 6 4 3 5 4 5 8 6 7 0 4 4 8 E - 0 1 . 1 0 5 0 8 7 7 6 3 0 1 4 8 1 E + 0 0 . 7 7 6 8 6 0 2 2 9 0 8 8 9 2 E - 0 1 . 3 7 6 4 1 0 4 7 8 1 3 3 9 5 8 - 0 1 . 9 9 1 5 1 8 6 4 4 7 9 8 3 6 E - 0 2 . 2 0 6 7 4 4 1 6 0 4 4 2 4 4 E - 0 2 m m D F W N H m Q a ‘ t h N H m fl m m b W N H Q O m ' h U N “ m u m m w a F - ‘ m \ l O ‘ C fl b W N F - ‘ a i fl m m v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v I n “ u l l l l u l l l l l l l l fl l l l l l l l l l l l l l l l l l l l l l l l l l l i l l I l l I I I I I I I I I I I I I I l l l l l l u l l l l i l l l l l u l l l l u l l l l 2 3 9 . 1 6 3 0 1 3 8 9 1 8 2 5 1 6 8 - 0 3 . 8 5 1 6 1 7 3 8 5 6 1 6 5 7 3 - 0 5 . 7 2 8 5 9 9 8 9 0 7 7 1 8 7 8 - 0 2 . 2 6 0 8 9 8 1 4 7 5 4 5 2 8 8 - 0 1 . 1 9 5 7 3 1 5 9 5 8 9 7 5 4 E - 0 1 . 9 9 1 5 1 8 6 4 5 5 3 1 6 4 8 - 0 2 . 2 6 5 1 9 1 8 5 5 8 9 6 7 7 E - 0 2 . 5 6 5 7 1 3 7 5 1 7 6 1 6 2 E - 0 3 . 4 4 8 5 0 6 4 2 5 0 7 9 2 1 8 - 0 4 . 2 3 6 5 3 6 4 6 4 2 6 8 1 3 8 - 0 5 . 1 2 3 9 8 3 3 5 0 4 3 4 2 9 E - 0 2 . 5 0 7 5 3 4 2 5 5 6 7 5 0 7 E - 0 2 . 3 9 1 1 2 1 4 6 2 8 0 3 3 1 E - 0 2 . 2 0 6 7 4 4 1 5 9 6 9 0 6 9 E - 0 2 . 5 6 5 7 1 3 7 5 4 0 3 5 3 6 E - 0 3 . 1 2 6 2 4 9 6 1 2 5 1 0 9 5 E - 0 3 . 1 0 1 7 4 4 9 1 3 4 4 5 5 0 8 - 0 4 . 5 5 8 5 6 6 3 9 3 6 7 9 6 8 8 - 0 6 . 1 0 3 7 0 5 0 9 1 7 9 1 3 6 E - 0 3 . 3 9 1 6 4 5 9 8 5 9 1 0 5 7 8 - 0 3 . 3 0 1 4 2 9 7 3 9 0 0 0 2 7 3 - 0 3 . 1 6 3 0 1 3 8 9 3 3 2 4 4 0 8 - 0 3 . 4 4 8 5 0 6 4 2 1 1 0 4 6 1 E - 0 4 . 1 0 1 7 4 4 9 1 3 9 1 5 1 2 E - 0 4 . 8 2 2 9 9 6 1 5 6 2 9 3 8 9 E - 0 6 . 4 5 6 4 9 7 7 8 3 9 3 1 5 0 E - 0 7 . 4 7 3 8 8 8 6 5 4 0 7 3 3 8 8 - 0 5 . 1 9 6 7 3 2 8 9 8 7 3 0 6 8 8 - 0 4 . 1 5 2 7 0 6 5 1 3 3 8 1 0 6 3 - 0 4 . 8 5 1 6 1 7 3 7 8 6 4 4 3 6 E - 0 5 . 2 3 6 5 3 6 4 6 6 3 4 1 4 7 8 - 0 5 . 5 5 8 5 6 6 3 9 0 6 4 7 3 9 8 - 0 6 . 4 5 6 4 9 7 7 8 5 1 2 8 4 6 8 - 0 7 . 2 6 3 9 7 5 7 0 5 7 3 9 3 1 8 - 0 8 . 4 5 2 4 7 5 2 6 6 7 5 2 1 2 E - 0 2 . 1 2 2 1 5 6 6 6 8 2 0 3 3 9 3 - 0 1 . 4 2 8 7 5 5 0 2 7 8 7 8 6 5 3 - 0 1 . 3 8 2 4 3 4 8 0 5 2 4 2 1 6 8 - 0 1 . 7 3 9 4 9 3 6 7 9 2 9 3 4 5 E - 0 2 . 1 6 2 7 0 0 2 2 0 0 4 6 4 7 8 - 0 2 . 1 0 9 5 4 1 2 3 2 8 2 7 5 8 E - 0 3 . 5 8 9 3 8 8 3 1 5 6 3 0 4 9 8 - 0 5 . 1 2 2 1 5 6 6 6 8 2 6 2 5 1 8 - 0 1 . 4 3 7 5 9 0 7 4 7 9 9 7 0 9 8 - 0 1 . 2 8 1 3 2 7 8 8 1 1 3 1 8 0 E + 0 0 . 1 4 6 6 8 6 3 8 6 2 1 1 0 6 E + 0 0 . 3 4 5 0 3 4 4 3 7 5 4 6 0 2 E - 0 1 . 6 9 2 5 5 7 3 2 4 6 6 3 3 1 E - 0 2 . 5 2 4 0 5 5 9 2 1 0 9 7 5 0 8 - 0 3 . 2 6 7 5 0 7 4 4 5 6 5 0 4 1 E - 0 4 m u m m fi W N H m e m fi w N q u m m fi w N q u m m l t h F - ‘ m fl m m l b w N H Q Q O ‘ U ' I P W N I — ‘ m \ l V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V > v > r > > v > v v > > v > v > > > w > > > > r v > > > > v > > > v w > > > r > w > > v > > > > r r A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A ’ V A A A A A m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V w u w w w w w w w w w w u w w w w w m w w m N N M N N N N w w w m w w w w m w m m w w w w m m m w m V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V M N N N M N N N H H H H H H H H m m m m m m m m q a q u a q q q m m m m m m m m m m m m m m m m p p m u > A V V w o n > A V V c u w > m u A V V w n c r A a V w V w > n o A V V u w ~ n A n a V V w > n A n v u w n V V A o w a V V w n A c > V V w E u > a A o V V O o > A n m o V » V > A u m > o A V V b u o o u V V v A c m > w V V h H V > V V a p o ’ o n > H A V V » b > u a V V m A u v n V » V m A n > n a V V m > A u n w V u u V V m c a > ’ w V V m n > V V m A m o u » m A » V V m o a n A o V V m v m o A V » V m I n n A a V V m y u n A » V V m r u n a V m V A a u n w V V m A » u e n A a V V m w n u A o V V m n o > A a V V g m ~ n A n n V V q z u A a V V q » > n A n > u V V q u A a ~ V V q n n A n z u V V q u A > a n V V q n A n v m q V V u > A m u > A w o V V q o V V w m v A m o > V V m n A o > m V V a u A n u > n A u V V m > a u A V V m v » u n u V V A m : a n A V V m > n n u u A V V m > G : > A V V u n a > b c H A V V 2 4 0 . 4 2 8 7 5 5 0 2 7 2 8 2 9 3 E - 0 1 . 2 8 1 3 2 7 8 8 1 1 2 8 1 6 E + 0 0 . 3 2 9 4 6 1 5 4 1 6 3 4 3 7 E + 0 0 . 1 5 0 0 7 6 9 7 7 7 2 3 9 8 3 + 0 0 . 3 7 9 1 5 2 3 2 7 3 6 6 2 3 E - 0 1 . 7 3 9 6 8 6 2 0 6 9 2 4 2 6 8 - 0 2 . 5 7 5 9 5 0 5 2 0 4 7 0 7 7 8 - 0 3 . 2 8 7 0 0 6 9 4 0 1 1 1 7 4 8 - 0 4 . 3 8 2 4 3 4 8 0 6 0 1 2 9 5 8 - 0 1 . 1 4 6 6 8 6 3 8 6 1 2 1 9 B E + 0 0 . 1 5 0 0 7 6 9 7 7 8 3 1 3 0 3 + 0 0 . 7 7 4 2 1 5 6 9 1 3 4 0 0 3 E - 0 1 . 1 9 8 8 2 5 9 2 9 3 5 5 7 3 8 - 0 1 . 4 1 5 8 2 7 2 5 4 9 4 8 9 1 E - 0 2 . 3 2 4 5 6 2 2 6 0 1 4 3 3 2 E - 0 3 . l 6 9 6 7 2 9 9 5 7 8 3 4 1 E - 0 4 . 7 3 9 4 9 3 6 7 6 5 6 4 9 6 E - 0 2 . 3 4 5 0 3 4 4 3 8 0 0 3 0 4 E - 0 1 . 3 7 9 1 5 2 3 2 6 3 9 0 7 9 8 - 0 1 . 1 9 8 8 2 5 9 2 9 5 5 2 4 1 E - 0 1 . 5 2 8 7 3 6 1 1 9 4 9 1 6 7 E - 0 2 . 1 1 2 0 7 8 7 1 4 2 9 9 4 6 8 - 0 2 . 8 8 8 5 1 5 0 8 1 5 3 6 3 1 8 - 0 4 . 4 6 6 0 1 9 5 4 1 8 5 0 4 4 8 - 0 5 . 1 6 2 7 0 0 2 2 0 7 5 1 3 3 8 - 0 2 . 6 9 2 5 5 7 3 2 3 3 9 0 0 2 E - 0 2 . 7 3 9 6 8 6 2 0 8 4 9 8 8 2 8 - 0 2 . 4 1 5 8 2 7 2 5 4 1 3 8 8 9 E - 0 2 . 1 1 2 0 7 8 7 1 4 4 4 8 6 7 E - 0 2 . 2 5 1 0 4 0 5 4 4 4 8 0 2 2 E - 0 3 . 2 0 1 1 9 8 3 3 2 7 0 5 4 9 8 - 0 4 . 1 1 0 4 8 4 3 3 8 7 9 7 2 3 8 - 0 5 . 1 0 9 5 4 1 2 3 1 6 4 2 7 5 8 - 0 3 . 5 2 4 0 5 5 9 2 2 8 9 5 1 7 8 - 0 3 . 5 7 5 9 5 0 5 1 8 6 0 9 1 5 E - 0 3 . 3 2 4 5 6 2 2 6 0 6 9 7 5 5 8 - 0 3 . 8 8 8 5 1 5 0 8 0 0 0 8 6 4 E - 0 4 . 2 0 1 1 9 8 3 3 2 7 3 8 7 9 E - 0 4 . 1 6 2 6 8 5 4 8 2 9 7 3 9 3 8 - 0 5 . 8 9 9 8 9 1 9 8 3 1 1 7 9 6 8 - 0 7 . 5 8 9 3 8 8 3 1 6 4 2 9 8 5 E - 0 5 . 2 6 7 5 0 7 4 4 5 8 7 2 4 5 8 - 0 4 . 2 8 7 0 0 6 9 4 0 2 0 0 5 6 E - 0 4 . 1 6 9 6 7 2 9 9 5 7 5 6 7 6 8 - 0 4 . 4 6 6 0 1 9 5 4 1 4 6 7 4 1 8 - 0 5 . 1 1 0 4 8 4 3 3 8 9 9 2 9 1 8 - 0 5 . 8 9 9 8 9 1 9 8 1 8 3 4 2 7 8 - 0 7 . 5 2 0 6 8 4 3 7 1 0 5 8 6 9 8 - 0 8 . 8 0 2 7 9 0 2 8 2 9 7 8 0 9 E - 0 2 . 1 8 6 5 4 9 2 5 1 9 7 5 5 2 8 - 0 2 ” - V V l H w v o o V l 3 ? H V b v l o V > V “ o v V l H m V l H V y m V V h O l v l o V J Q > u v l o V V - V H l > D o V t V v l 5 fi n N V o V V H v W l > m V h V V N v l > l o b b V N o v l m v V V fi V u o N V V m v l > o V fi N I V V q v > o l b N V > o V V v m l h N V l o ‘ > V V v l p N o V — l y V V o fi N l v V F > o V V w V h l I V n h V V w I V N c V V I W > w k V V I m V fi V > w I m V h V V > m m I w V I fi V V V m > o V w I > V I V V o w fi I fl V h o m V w V I V V V o fi V V V b ‘ l l > o V > o fi p — l V V V b » F V t 9 m l V o V b s N V l V > V l o V b a W V V l 3 V V o fi V - V b l > o l V fi l r V m o V V > o fi V u a V m V l > V o fl l V v o h V > l V o b V m v fi V u > m V h H v l fi m V l > V m V r v n w b > V m V m V u p fi v u > m V m V V m l y V l m m V V m fi v > V w m fi l v V V q l > m h m v ' V V V m m I b m > v m V V V ‘ " b I m V w v V V I V - > I m h m V V V m I F v m b > V > m V m V V N v I h I m v N V I m V V h m D I V m V v V fi I > m m V V m v I V I m V h ‘ s m v V O ’ V fi V w a O I V b V I v 3 m V m V ’ m V fi V q V m u u v 3 V fi V m v n q V H l m ’ h l V V N v m q V fl 3 # v V V I U m V fl > \ m # p v V V V I 2 4 1 . 1 6 1 8 3 2 3 1 2 0 6 9 2 4 E - 0 1 . 3 3 5 2 5 8 5 9 9 6 7 9 9 5 E - 0 1 . 1 8 0 8 8 5 4 1 1 8 9 4 0 0 3 - 0 1 . 2 7 6 6 4 4 9 2 8 8 9 6 9 9 3 - 0 2 . 2 4 1 6 8 6 6 3 6 9 1 1 7 1 8 - 0 3 . 1 0 6 0 6 2 7 0 9 9 8 3 5 9 8 - 0 4 . 1 8 6 5 4 9 2 4 6 8 8 2 3 5 E - 0 2 . 4 8 4 6 1 6 8 1 2 6 0 9 6 0 8 - 0 1 . 3 1 0 5 4 7 3 1 2 4 0 1 4 7 8 - 0 1 . 2 1 5 2 2 4 9 9 7 9 2 8 0 9 E + 0 0 . 7 4 6 7 2 6 0 5 2 8 3 0 1 3 E - 0 1 . 1 3 2 9 0 9 0 6 6 6 3 9 9 7 E - O l . 1 0 9 1 2 4 0 1 7 5 6 6 8 4 8 - 0 2 . 5 2 8 3 8 9 9 5 4 2 7 5 1 8 E - 0 4 . 1 6 1 8 3 2 3 1 5 0 8 8 7 6 E - 0 1 . 3 1 0 5 4 7 3 0 0 9 2 3 6 4 8 - 0 1 . 1 8 7 8 0 2 9 0 8 4 6 1 8 9 E + 0 0 . 2 9 7 2 2 4 7 1 3 6 1 8 5 6 E + 0 0 . 7 7 6 9 9 7 6 6 8 7 6 3 2 2 E - 0 1 . 1 5 3 3 0 7 2 0 4 4 1 5 1 1 3 - 0 1 . 1 1 6 9 8 1 1 2 0 6 8 9 2 7 E - 0 2 . 5 9 0 1 7 2 4 0 5 1 2 8 2 6 8 - 0 4 . 3 3 5 2 5 8 6 0 6 3 7 3 8 3 E - 0 1 . 2 1 5 2 2 4 9 9 6 6 3 2 9 7 E + 0 0 . 2 9 7 2 2 4 7 1 4 1 8 6 0 9 E + 0 0 . 2 0 4 2 3 2 6 6 1 1 9 8 1 5 E + 0 0 . 5 5 1 8 0 2 2 1 6 2 6 8 7 0 E - 0 1 . 1 1 1 9 3 0 2 2 3 4 5 4 2 4 E - O l . 8 8 0 8 9 1 2 5 9 7 2 6 0 1 E - 0 3 . 4 5 3 8 2 2 8 5 9 4 2 5 3 0 E - 0 4 . 1 8 0 8 8 5 4 0 7 9 5 5 8 8 E - 0 1 . 7 4 6 7 2 6 0 6 0 0 5 6 0 6 8 - 0 1 . 7 7 6 9 9 7 6 6 3 4 8 8 1 5 8 - 0 1 . 5 5 1 8 0 2 2 1 7 9 7 8 5 5 E - 0 1 . 1 5 1 2 1 2 3 0 4 2 6 4 1 6 E - 0 1 . 3 1 5 6 5 4 2 4 2 9 8 7 7 6 E - 0 2 . 2 4 9 6 3 5 3 8 4 1 8 2 7 7 E - 0 3 . 1 3 0 0 4 3 5 3 3 3 9 7 2 9 E - 0 4 . 2 7 6 6 4 4 9 3 8 7 4 7 9 5 8 - 0 2 . 1 3 2 9 0 9 0 6 4 5 3 4 4 9 3 - 0 1 . 1 5 3 3 0 7 2 0 6 0 6 5 8 5 E - 0 1 . 1 1 1 9 3 0 2 2 2 7 7 3 8 2 8 ‘ 0 1 . 3 1 5 6 5 4 2 4 4 1 7 0 1 0 E - 0 2 . 6 9 4 4 2 3 3 4 5 2 0 1 7 6 E - 0 3 . 5 5 9 4 1 7 6 2 5 6 9 8 4 4 8 - 0 4 . 3 0 4 5 1 8 6 9 4 3 9 1 1 9 E - 0 5 . 2 4 1 6 8 6 6 2 3 4 9 6 6 6 8 - 0 3 . 1 0 9 1 2 4 0 2 0 0 5 6 5 8 8 - 0 2 . 1 1 6 9 8 1 1 1 8 3 5 1 5 9 E - 0 2 . 8 8 0 8 9 1 2 7 0 1 3 5 4 6 E - 0 3 > V V l m 9 v > x m V V 9 v fi j l V V 9 v fl x \ v m V 9 V l v l ‘ v 9 \ V V y 9 V V - v q > h m # V V v m > h “ V V m v > t > V V m v % m > V V m v 9 m > u 0 m V V v m > 9 q V m V v > N p ‘ > w V V v l — > V V fi v m H ‘ m V V v — > m m V V v l ’ m l ‘ V V v 3 \ m — > m V V v m I ’ ‘ V V v H m 3 — V V v H m > e H > l H V V v m > m fi H V V v ’ v m V N V m 3 N m V V m v > N d V m V v ‘ N m > w H V m V v ‘ a m V V m v ) m w w V V V > m w m V V V > m w > u w V V V w ‘ q m V V w V > N V V V m w > w m w V V V w > - m V V V w > F m > H V V V w > ' V V V m fi m h > U V V V > ‘ m b V V h V > O m V V V b > Q m h ’ D V V V m b 3 ( V V V m h ‘ ‘ V t V V m > — V V V 1 m > I 0 > N m 1 V V V y V V » V m 0 ¥ ! V V m 1 V r h 0 V m V V > c 1 > t 0 V m V V > a 1 V V m V > m 0 m V V V 2 4 2 . 2 4 9 6 3 5 3 8 1 6 3 9 0 2 8 - 0 3 . 5 5 9 4 1 7 6 2 7 9 3 6 6 5 E - 0 4 . 4 5 2 7 2 6 5 2 4 8 0 2 2 2 8 - 0 5 . 2 4 9 2 0 7 5 5 4 6 1 3 1 6 8 - 0 6 . 1 0 6 0 6 2 7 1 4 0 9 8 0 8 E - 0 4 . 5 2 8 3 8 9 9 4 4 9 4 9 3 0 8 - 0 4 . 5 9 0 1 7 2 4 1 3 1 9 7 3 7 8 - 0 4 . 4 5 3 8 2 2 8 5 5 3 4 4 1 2 8 - 0 4 . 1 3 0 0 4 3 5 3 4 4 0 5 3 8 E - 0 4 . 3 0 4 5 1 8 6 9 3 3 6 1 4 6 8 - 0 5 . 2 4 9 2 0 7 5 5 4 8 9 0 7 2 8 - 0 6 . 1 4 3 4 2 0 7 4 5 0 8 9 1 3 8 - 0 7 . 1 1 0 9 8 4 1 3 7 9 7 2 9 9 8 - 0 2 . 4 4 4 4 4 6 0 7 0 4 6 8 9 8 8 - 0 2 . 2 1 8 9 7 5 9 0 8 2 1 0 2 7 8 - 0 1 . 2 5 4 8 9 1 8 6 3 5 6 9 3 6 E - 0 1 . 2 1 7 2 9 2 4 0 8 8 6 9 9 8 3 - 0 1 . 9 8 9 8 6 2 2 5 4 7 3 2 5 4 3 - 0 2 . 6 3 0 4 3 1 9 5 0 2 4 1 9 3 8 - 0 3 . 3 3 8 5 9 8 8 2 8 5 9 3 1 1 E - 0 4 . 4 4 4 4 4 6 2 7 7 1 0 6 1 8 3 - 0 2 . 4 5 7 1 9 8 4 3 6 9 2 4 9 5 E - 0 2 3 7 7 1 0 4 9 2 9 8 4 1 8 8 0 8 - 0 1 . 2 8 5 0 6 8 1 0 2 8 9 4 0 0 E - 0 1 . 1 4 9 8 6 3 4 1 6 5 7 0 9 S E + 0 0 . 4 7 0 2 9 6 5 8 8 1 6 8 8 2 8 - 0 1 . 3 2 1 7 7 3 7 1 7 6 0 4 4 0 8 - 0 2 . 1 7 5 8 2 0 8 2 0 9 1 9 2 7 E - 0 3 . 2 1 8 9 7 5 8 4 9 7 4 7 9 5 3 - 0 1 . 7 7 1 0 4 9 1 9 0 1 5 2 5 5 8 - 0 1 . 1 8 3 1 1 3 0 0 6 9 0 4 O Z E + 0 0 . 8 6 8 4 9 7 0 0 7 9 7 7 5 7 8 - 0 1 . 2 1 4 1 4 5 6 7 5 6 5 2 6 2 E + 0 0 . 4 6 8 3 3 3 6 8 8 2 5 9 0 1 E - 0 1 . 3 5 8 0 6 0 3 0 3 0 0 0 2 3 E - 0 2 . 1 7 8 2 3 6 1 2 0 5 4 7 1 3 3 - 0 3 . 2 5 4 8 9 1 9 1 0 5 5 3 8 5 8 - 0 1 . 2 8 5 0 6 8 2 0 8 8 3 1 9 4 E - 0 1 . 8 6 8 4 9 6 9 5 2 9 7 1 3 3 3 - 0 1 . 3 8 4 1 5 7 3 2 8 4 3 3 S O E + 0 0 . 1 7 3 8 1 6 8 7 9 5 4 9 1 2 8 + 0 0 . 3 6 7 1 2 9 5 0 6 2 9 6 3 5 3 - 0 1 . 2 8 9 2 3 6 6 3 3 3 9 5 2 6 E - 0 2 . 1 4 8 6 2 4 7 8 2 5 7 3 4 9 E - 0 3 . 2 1 7 2 9 2 4 3 5 4 6 3 6 1 8 - 0 1 . 1 4 9 8 6 3 4 1 0 3 2 0 9 0 E + 0 0 . 2 1 4 1 4 5 6 7 9 8 3 6 2 9 E + 0 0 . 1 7 3 8 1 6 8 7 8 4 5 7 7 B E + 0 0 . 5 9 2 5 0 0 4 1 6 7 4 6 5 9 E - 0 1 . 1 2 7 5 7 6 7 1 9 9 0 3 5 7 8 - 0 1 m m m m m m m c n m m m m m m m m m o a m m m o o m c o o o m m o o o o o o o o o o o o m o o o o c o c o o o o o o o o o o o o o o o o o m o o o o m w w u w w w w w w w m m w w m M H H H H H H H t - o m o o m m m m m m \ I \ n q q q q q q m m m m m m m m m m ‘ - ~ ‘ - ‘ - - - ~ “ “ ~ ‘ - ‘ ~ “ “ “ ‘ ~ ‘ Q “ ‘ - ~ ‘ ~ “ V “ “ m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m “ “ ‘ ~ “ “ “ ~ “ “ V ‘ V “ “ “ “ V ‘ V ~ V “ “ “ ‘ V “ “ ‘ V ‘ V ‘ > > > > > > > $ > > v > > > > > v > > > > > > > > > > > > > > t v a v > > > > > > r > > > v > v v > v > A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m ‘ ~ ~ ~ ~ ~ ~ ~ ‘ ~ ~ ‘ ~ ~ ‘ ~ ~ ‘ ‘ ‘ ‘ - ~ ‘ ‘ ~ ~ ~ ‘ ‘ ~ ‘ ~ ~ ~ ‘ ‘ ‘ ~ ~ ‘ ‘ ‘ ‘ ~ ‘ ~ ‘ ‘ ‘ Q Q O ‘ U ' I F U N H W Q O ‘ U ‘ I F M N H Q Q U ‘ U ‘ fi w N q u m m b C O N i - ‘ m \ l m m O p u N F - ‘ m q m m fi w w H m “ v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v V v v v v v v v v v v v v v v v v n u l l l l l l l l l l l l l l l l n u u u u l 2 4 3 . 9 9 3 9 1 1 9 8 0 8 8 4 8 3 E - 0 3 . 5 1 5 5 6 2 0 2 9 2 2 4 0 9 8 - 0 4 . 9 8 9 8 6 2 1 7 7 0 6 1 7 0 E - 0 2 . 4 7 0 2 9 6 6 0 5 3 4 0 0 8 8 - 0 1 . 4 6 8 3 3 3 6 7 4 7 4 3 9 2 8 - 0 1 . 3 6 7 1 2 9 5 1 1 8 9 8 8 4 E - 0 1 . 1 2 7 5 7 6 7 1 8 8 9 0 6 2 3 - 0 1 . 2 8 7 6 7 6 9 9 4 4 1 8 0 1 E - 0 2 . 2 2 9 9 7 8 3 4 0 1 5 1 1 5 8 - 0 3 . 1 2 4 4 7 6 0 9 9 9 7 1 9 0 E - 0 4 . 6 3 0 4 3 2 0 5 0 9 6 8 4 7 E - 0 3 . 3 2 1 7 7 3 6 9 5 2 5 9 2 5 E - 0 2 . 3 5 8 0 6 0 3 2 2 3 9 5 2 0 E - 0 2 . 2 8 9 2 3 6 6 2 4 8 5 7 3 8 E - 0 2 . 9 9 3 9 1 2 0 0 0 8 7 9 5 0 E - 0 3 . 2 2 9 9 7 8 3 3 8 1 7 5 8 4 3 - 0 3 . 1 8 4 3 9 0 7 2 1 8 4 6 8 4 8 - 0 4 . 1 0 1 2 8 5 9 2 9 9 9 7 3 l E - 0 5 . 3 3 8 5 9 8 7 8 7 0 2 6 3 6 E - 0 4 . 1 7 5 8 2 0 8 3 0 3 6 2 3 8 8 - 0 3 . 1 7 8 2 3 6 1 1 2 4 3 2 7 3 8 ' 0 3 . 1 4 8 6 2 4 7 8 6 3 7 4 9 0 3 - 0 3 . 5 1 5 5 6 2 0 1 9 5 4 7 3 9 E - 0 4 . 1 2 4 4 7 6 1 0 1 2 1 0 9 1 E - 0 4 . 1 0 1 2 8 5 9 2 9 4 1 4 4 4 8 - 0 5 . 5 8 2 1 1 5 7 9 3 9 9 6 6 3 8 - 0 7 . 6 6 8 9 8 3 8 9 0 2 0 9 3 5 E - 0 1 . 6 0 9 8 3 4 0 5 1 2 8 3 5 4 E - 0 1 . 2 0 6 9 4 1 8 7 4 5 2 3 1 8 E + 0 0 . 1 4 2 7 2 5 2 3 7 9 6 5 3 5 8 - 0 1 . 6 7 8 9 9 1 9 6 3 6 5 0 3 3 E - 0 1 . 2 1 3 0 4 4 5 8 5 5 2 5 4 9 8 - 0 1 . 3 8 2 1 2 0 5 0 8 5 8 4 1 9 E - 0 2 . 1 5 3 3 7 1 9 0 8 1 2 6 5 9 3 - 0 3 . 6 0 9 8 3 3 9 7 9 1 0 6 0 4 8 - 0 1 . 7 4 8 8 0 7 7 2 8 5 8 1 6 0 8 + 0 0 . 1 3 6 5 9 4 8 9 9 4 0 6 1 9 8 + 0 0 . 4 1 3 1 4 2 5 2 0 7 8 8 8 2 3 + 0 0 . 5 4 1 1 1 2 2 1 2 0 8 5 8 6 3 - 0 1 . 1 5 8 1 2 0 8 7 5 8 5 8 0 0 8 + 0 0 . 1 9 4 8 7 7 7 6 7 1 8 0 5 1 3 - 0 1 . 8 7 8 3 1 8 2 3 9 9 1 2 8 0 E - 0 3 . 2 0 6 9 4 1 8 9 1 7 2 3 5 5 8 + 0 0 . 1 3 6 5 9 4 8 7 3 5 6 1 9 9 3 + 0 0 . 5 8 5 2 6 1 6 2 7 2 1 6 8 2 E + 0 0 . 6 0 0 7 8 4 4 3 8 1 3 8 3 6 E - 0 1 . 1 3 7 6 2 5 1 2 1 7 7 3 4 5 E + 0 0 . 1 9 6 4 3 4 9 0 7 5 6 7 8 9 E + 0 0 . 1 9 0 4 1 6 1 3 9 2 1 6 7 2 8 - 0 1 . 8 9 0 1 3 7 6 0 6 1 3 4 5 4 E - 0 3 > A ‘ m p > ~ A m - p > A m ~ p > - A m ‘ p > A m n ‘ - > A m ~ p > “ > p A m ‘ > A m b ~ ~ > A m ‘ m ‘ > A m ~ m > A m ‘ m ~ > A m ~ m ‘ > A m ~ m > > A m ~ m ~ > A ‘ m m “ > A m ‘ m ‘ ~ A m ‘ m ) A m ~ m “ ’ A m ~ m 3 ~ A m ‘ m ’ 3 A ~ m “ m ’ A ‘ m m “ 3 A m ‘ m 7 A m ‘ m ‘ ’ A m ~ q 3 “ A m ‘ q > A m q ‘ “ 3 > A m q V ‘ v A m q ‘ v “ A m q ~ > A m q ~ ~ > A ‘ m q fi “ A ‘ m m 3 A ~ m m “ > > A ‘ m m > m m A ~ “ > A ‘ m ~ m > A ‘ m m > “ A ‘ m m ’ A ‘ m m ~ 3 A ~ m H > ‘ > A ~ m H > H A m ~ - > A ‘ m H ‘ V A ~ m H > ~ A ‘ m H ) A ‘ m H ‘ > A ~ m H ? > ~ A m M ~ > m N A ‘ ‘ q q q q q q q q q q m m m m m m m m m m m m m o m m m m m m m m m m m m m m m m m m m m m m m m m m 2 4 4 . l 4 2 7 2 5 3 7 5 7 7 l 9 9 E - 0 1 . 4 1 3 1 4 2 4 9 2 8 7 8 2 5 8 + 0 0 . 6 0 0 7 8 4 6 1 9 7 4 6 2 6 8 - 0 1 . 8 6 0 8 7 5 3 3 2 1 4 5 9 5 8 - 0 1 . 2 8 0 8 9 7 4 2 7 3 4 3 0 1 8 + 0 0 . 1 8 6 2 9 8 6 1 3 1 0 9 1 0 8 + 0 0 . 1 4 9 8 9 9 7 2 7 0 9 8 2 7 E - O l . 7 8 6 4 0 5 3 6 7 6 1 2 9 9 E - 0 3 - . 6 7 8 9 9 2 0 3 9 9 0 2 3 7 E - 0 1 . 5 4 1 1 1 2 0 1 8 9 8 1 9 5 8 - 0 1 ' . 1 3 7 6 2 5 1 3 5 6 8 5 0 8 8 + 0 0 . 2 8 0 8 9 7 4 3 2 0 2 8 7 Z E + 0 0 . 2 0 3 4 7 9 3 5 8 3 4 7 9 8 E + 0 0 . 6 4 1 9 4 1 0 2 6 3 7 8 8 4 E - O l . 5 2 7 7 8 5 3 1 0 4 5 3 0 5 8 - 0 2 . 2 6 8 3 7 2 1 6 4 4 9 4 9 3 8 - 0 3 . 2 1 3 0 4 4 6 1 1 8 6 4 4 6 8 - 0 1 . 1 5 8 1 2 0 8 6 9 7 3 1 6 5 E + 0 0 . 1 9 6 4 3 4 9 1 2 6 9 0 1 7 E + 0 0 . 1 8 6 2 9 8 6 1 1 1 4 2 7 7 E + 0 0 . 6 4 1 9 4 1 0 2 9 1 1 6 4 Z E - O l . 1 8 1 4 8 9 2 0 1 0 5 7 7 3 8 - 0 1 . 1 4 8 7 4 8 1 2 3 9 6 6 4 1 8 - 0 2 . 7 9 3 7 2 9 9 5 0 7 3 4 3 5 8 - 0 4 . 3 8 2 1 2 0 4 7 2 5 7 9 5 7 E - 0 2 . 1 9 4 8 7 7 7 7 5 7 6 6 1 4 E - O l . 1 9 0 4 1 6 1 3 1 9 0 8 9 3 3 - 0 1 . 1 4 9 8 9 9 7 3 0 2 4 5 1 2 8 - 0 1 . 5 2 7 7 8 5 3 0 2 6 3 1 4 0 8 - 0 2 . 1 4 8 7 4 8 1 2 4 7 7 7 8 5 8 - 0 2 . 1 2 2 7 5 7 1 9 3 0 1 8 6 9 8 - 0 3 . 6 6 2 7 8 4 9 2 1 8 1 2 1 5 8 - 0 5 . 1 5 3 3 7 1 9 2 4 9 7 3 5 6 8 - 0 3 . 8 7 8 3 1 8 2 0 0 7 6 1 9 0 8 - 0 3 . 8 9 0 1 3 7 6 4 0 3 5 4 2 8 3 - 0 3 . 7 8 6 4 0 5 3 5 1 3 5 5 7 7 E - 0 3 . 2 6 8 3 7 2 1 6 8 8 0 0 8 2 8 - 0 3 . 7 9 3 7 2 9 9 4 4 9 5 2 3 0 8 - 0 4 . 6 6 2 7 8 4 9 2 5 0 3 1 8 0 8 - 0 5 . 3 7 7 1 7 1 9 2 5 2 0 6 0 3 8 - 0 6 . 1 0 5 8 6 3 9 3 3 5 6 7 8 9 8 + 0 0 . 3 7 1 2 1 8 3 6 1 1 9 3 3 1 E + 0 0 . 7 1 9 4 2 1 2 8 9 3 9 5 5 4 E + 0 0 . 8 7 1 0 6 4 5 1 0 8 9 4 9 4 E + 0 0 . 3 3 0 1 4 4 5 9 3 8 9 9 6 0 8 + 0 0 . 8 7 9 4 7 3 9 0 7 9 8 9 4 5 E - 0 1 . 9 7 0 6 1 1 1 5 3 7 5 2 5 4 E - 0 2 . 1 6 6 2 0 7 1 8 0 7 5 1 6 0 E - 0 2 - . 3 7 1 2 1 8 3 7 7 0 2 5 8 0 8 + 0 0 . 2 4 3 3 9 7 7 9 3 3 6 O O S E + 0 1 w v h v m v m v fl v m v p v w v w v b v m v m v l v \ v m v H v N v h v t v ‘ v O v Q v m v H v N v M v D v m v m v fl v m v ‘ v - v i v N v W v b v m v O v Q v H v N v W D v m v m v u v q v N v U v h v “ “ ~ ‘ ~ “ “ ‘ ~ “ “ “ - “ “ “ “ “ “ “ ‘ § ~ “ V ‘ ~ ‘ V ‘ “ V ‘ 3 ) ) 3 ’ > 3 ’ y > ) > > 3 ’ ? 3 ’ 3 ’ > > > > , y > y > > > 3 3 " ” ) 7 3 ’ 3 > § > > > y > > > y > > y > > > A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m - - ~ § - - ~ s - ~ s - ~ s s u s - - - - - - - - - ~ s - ~ u - ~ \ J q q q q q q q q q q q q q \ ‘ q q q q q \ I Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q \ I Q V N Q Q Q N Q Q Q - ~ V - - s - - - - - - - s - - - s - s u s - - - - - - ~ s m m m e Q Q Q Q Q q q m m m m m m m m m m m m m m m m p p b b p P fi fi w w w w w w a N N N N N N 2 4 5 . 2 5 7 6 6 1 2 7 0 9 0 9 0 l E + 0 0 . 3 0 5 6 2 4 4 1 9 3 1 1 0 6 E + 0 1 . 5 8 6 8 0 6 4 9 3 2 2 9 2 3 E + 0 0 . 2 1 2 0 2 2 5 1 6 0 3 2 4 S E + 0 0 . 1 1 0 2 9 0 2 2 7 5 3 7 9 Z E + 0 0 . 9 8 3 0 3 2 7 1 9 8 1 8 7 7 3 - 0 2 . 7 1 9 4 2 1 2 4 6 5 5 4 7 O E + 0 0 . 2 5 7 6 6 1 1 7 7 7 7 6 7 S E + 0 0 . 3 0 9 7 0 6 2 4 1 0 7 8 6 7 E + 0 1 . 1 6 0 1 7 5 4 1 6 2 4 6 O G E + 0 1 . 1 2 3 2 7 7 2 8 1 2 4 8 0 1 3 + O l . 1 1 8 3 6 2 4 2 9 6 3 9 0 9 E + 0 0 . 1 2 0 7 4 0 3 9 6 8 9 1 0 5 E + 0 0 . 9 2 1 9 7 4 2 5 2 3 7 8 2 8 E - 0 2 . 8 7 1 0 6 4 5 3 0 3 3 6 B O E + 0 0 . 3 0 5 6 2 4 4 2 9 5 0 9 0 4 E + 0 1 . 1 6 0 1 7 5 4 1 8 4 8 1 2 3 E + 0 1 . 3 4 0 1 2 9 1 1 7 2 9 5 1 5 3 + 0 1 . 2 1 0 7 3 6 8 3 7 5 8 7 3 2 E + 0 0 . 4 7 8 6 1 9 9 0 6 8 1 8 4 9 E + 0 0 . 1 4 1 2 0 5 7 6 1 2 7 6 0 7 E + 0 0 . 8 0 0 8 3 5 0 1 9 8 4 5 1 8 3 - 0 2 . 3 3 0 1 4 4 5 7 9 6 9 6 9 3 E + 0 0 . 5 8 6 8 0 6 4 6 9 4 8 0 5 1 8 + 0 0 . 1 2 3 2 7 7 2 7 9 1 5 2 5 3 3 + 0 1 . 2 1 0 7 3 6 8 3 9 4 4 9 9 G E + 0 0 . 4 4 9 3 0 1 7 6 1 1 9 6 6 9 E + 0 0 . 3 0 9 9 6 6 4 0 6 9 6 6 8 5 8 + 0 0 . 4 8 9 3 3 5 6 6 9 4 8 1 0 8 E - 0 1 . 2 5 9 9 8 4 0 5 4 7 7 3 1 0 3 - 0 2 . 8 7 9 4 7 3 9 3 9 8 5 8 1 4 E - 0 1 . 2 1 2 0 2 2 5 2 6 7 4 2 6 6 E + 0 0 . 1 1 8 3 6 2 4 3 3 9 4 6 4 6 E + 0 0 . 4 7 8 6 1 9 9 1 0 2 6 7 3 0 E + 0 0 . 3 0 9 9 6 6 4 0 6 0 6 4 6 3 E + 0 0 . 1 4 3 7 8 9 1 4 2 4 6 8 4 S E + 0 0 . 1 4 8 4 4 8 3 6 4 4 8 2 1 9 E - 0 1 . 8 3 2 6 9 1 3 8 9 7 9 6 0 3 E - 0 3 . 9 7 0 6 1 1 1 8 2 1 2 8 7 8 8 - 0 2 . 1 1 0 2 9 0 2 2 6 4 6 1 0 7 E + 0 0 . 1 2 0 7 4 0 3 9 7 5 8 9 5 4 E + 0 0 . 1 4 1 2 0 5 7 6 0 8 2 3 1 4 E + 0 0 . 4 8 9 3 3 5 6 7 1 3 0 0 0 7 E ’ 0 1 . 1 4 8 4 4 8 3 6 4 3 1 8 4 8 3 - 0 1 . 1 4 6 0 1 8 2 7 6 5 3 8 4 8 E - 0 2 . 8 0 2 0 7 2 9 1 2 7 0 0 0 7 E - 0 4 . 1 6 6 2 0 7 1 7 7 7 1 0 4 8 8 - 0 2 . 9 8 3 0 3 2 7 2 6 0 7 1 5 4 3 - 0 2 . 9 2 1 9 7 4 2 4 5 6 4 8 0 2 8 - 0 2 . 8 0 0 8 3 5 0 2 3 2 1 0 3 1 8 - 0 2 2 4 6 A ( 8 , 7 , 8 , 5 ) = . 2 5 9 9 8 4 0 5 3 5 3 3 9 l E - 0 2 A ( 8 , 7 , 8 , 6 ) = . 8 3 2 6 9 1 3 9 1 3 0 2 3 8 8 - 0 3 A ( 8 , 7 , 8 , 7 ) = . 8 0 2 0 7 2 9 1 1 7 0 5 3 1 3 - 0 4 A ( 8 , 7 , 8 , 8 ) = . 4 6 7 8 2 9 2 9 5 3 8 6 3 6 8 - 0 5 A ( 8 , 8 , 1 , 1 ) = - . 1 5 8 9 6 5 4 8 8 5 7 9 1 2 8 + 0 2 A ( 8 , 8 , l , 2 ) = - . 1 8 8 5 1 9 8 8 4 4 9 6 9 3 E + 0 2 A ( 8 , 8 , 1 , 3 ) = - . 6 1 2 9 4 4 4 1 8 1 9 1 9 1 E + 0 2 A ( 8 , 8 , 1 , 4 ) = - . 1 3 6 6 1 9 8 0 1 5 5 8 5 5 2 + 0 2 A ( 8 , 8 , 1 , 5 ) = - . 1 2 6 9 1 2 1 0 7 8 4 9 4 9 E + 0 2 A ( 8 , 8 , 1 , 6 ) = - . 8 7 8 1 2 7 1 8 3 5 3 2 3 4 E + 0 0 A ( 8 , 8 , l , 7 ) = - . 5 4 2 5 5 3 0 9 1 4 7 9 9 3 E + 0 0 A ( 8 , 8 , 1 , 8 ) = . 1 8 0 7 1 7 3 4 3 7 0 0 9 6 E - 0 1 A ( 8 , 8 , 2 , 1 ) = - . 1 8 8 5 1 9 8 8 2 6 3 4 2 8 8 + 0 2 A ( 8 , 8 , 2 , 2 ) = . 1 9 5 4 8 0 9 2 7 4 5 2 4 5 E + 0 3 A ( 8 , 8 , 2 , 3 ) = - . 4 6 7 l 9 6 7 8 3 4 2 3 4 2 8 + 0 1 A ( 8 , 8 , 2 , 4 ) = . 1 3 6 9 5 4 1 9 2 6 8 3 1 0 3 + 0 3 A ( 8 , 8 , 2 , 5 ) = - . 1 1 2 3 8 4 3 2 6 8 3 0 5 1 8 + 0 2 A ( 8 , 8 , 2 , 6 ) = . 1 3 6 6 9 6 5 9 9 1 7 2 4 3 E + 0 2 A ( 8 , 8 , 2 , 7 ) = - . 4 8 6 7 0 8 7 5 0 4 8 2 6 5 3 + 0 0 A ( 8 , 8 , 2 , 8 ) = . 1 9 9 3 3 4 1 6 2 8 0 0 3 7 E + 0 0 A ( 8 , 8 , 3 , 1 ) = - . 6 1 2 9 4 4 4 2 1 1 7 2 1 4 E + 0 2 A ( 8 , 8 , 3 , 2 ) = - . 4 6 7 1 9 6 8 0 2 7 9 4 9 3 E + 0 1 A ( 8 , 8 , 3 , 3 ) = - . 2 1 4 5 9 2 0 2 4 1 3 2 6 l E + 0 3 A ( 8 , 8 , 3 , 4 ) = - . 4 4 4 0 7 7 3 9 7 8 8 2 9 4 E + 0 1 A ( 8 , 8 , 3 , 5 ) = - . 4 6 7 1 4 2 7 3 3 4 4 7 2 5 E + 0 2 A ( 8 , 8 , 3 , 6 ) = . 1 1 2 3 4 6 1 3 7 4 0 8 1 7 E + 0 1 A ( 8 , 8 , 3 , 7 ) = - . 1 9 7 2 7 3 5 3 5 0 3 6 9 5 8 + 0 1 A ( 8 , 8 , 3 , 8 ) = . 1 7 1 1 1 8 1 9 3 0 2 2 2 7 E + 0 0 A ( 8 , 8 , 4 , l ) = - . 1 3 6 6 1 9 7 9 4 2 5 6 9 Q E + 0 2 A ( 8 , 8 , 4 , 2 ) = . 1 3 6 9 5 4 1 9 2 0 6 4 7 O E + 0 3 A ( 8 , 8 , 4 , 3 ) = - . 4 4 4 0 7 7 3 4 4 2 3 8 7 6 8 + 0 1 A ( 8 , 8 , 4 , 4 ) = . 9 4 3 9 6 6 6 9 7 2 3 0 9 4 E + 0 2 A ( 8 , 8 , 4 , 5 ) = - . 8 3 0 3 7 6 7 7 5 9 3 5 2 9 B + 0 1 A ( 8 , 8 , 4 , 6 ) = . 9 1 1 1 1 0 4 2 7 1 3 7 4 6 8 + 0 1 A ( 8 , 8 , 4 , 7 ) - - . 1 4 4 2 9 6 2 7 2 1 3 3 9 4 E + 0 0 A ( 8 , 8 , 4 , 8 ) = . 2 0 8 1 8 1 9 2 0 7 0 1 4 6 E + 0 0 A ( 8 , 8 , 5 , 1 ) = - . 1 2 6 9 1 2 1 1 1 2 0 2 2 5 8 + 0 2 A ( 8 , 8 , 5 , 2 ) - - . 1 1 2 3 8 4 3 1 9 3 7 9 9 3 E + 0 2 A ( 8 , 8 , 5 , 3 ) = - . 4 6 7 1 4 2 7 3 8 1 0 3 8 7 E + 0 2 A ( 8 , 8 , 5 , 4 ) - - . 8 3 0 3 7 6 7 6 1 7 7 9 1 9 E + 0 1 A ( 8 , 8 , 5 , 5 ) - - . 8 3 4 5 0 0 3 4 3 0 7 3 1 6 E + 0 1 A ( 8 , 8 , 5 , 6 ) - - . 9 0 6 1 4 2 5 5 8 4 3 6 8 4 E + 0 0 A ( 8 , 8 , 5 , 7 ) : - . 4 4 4 1 3 8 4 9 8 4 2 3 8 5 8 - 0 1 A ( 8 , 8 , S , 8 ) - . 7 0 1 4 9 1 9 5 5 3 9 6 7 0 8 - 0 1 A ( 8 , 8 , 6 , 1 ) = - . 8 7 8 1 2 7 0 7 6 4 3 0 2 5 8 + 0 0 A ( 8 , 8 , 6 , 2 ) - . 1 3 6 6 9 6 5 9 6 8 4 4 1 2 8 + 0 2 A ( 8 , 8 , 6 , 3 ) = . 1 1 2 3 4 6 1 5 5 2 8 9 5 6 8 + 0 1 A ( 8 , 8 , 6 , 4 ) = . 9 1 1 1 1 0 4 2 0 2 4 5 6 8 E + 0 1 A ( 8 , 8 , 6 , 5 ) - - . 9 0 6 1 4 2 5 4 0 2 7 6 0 5 E + 0 0 A ( 8 , 8 , 6 , 6 ) = . 1 0 5 0 3 2 4 3 3 7 4 1 1 4 E + 0 1 > m m m A V V A v V V m m m A > m m q V V A r m m q V V A v u u u u m m q V V A u > m q m V V V > u ’ m q m V V > u V V V > m q m ’ > m q m V V A > V V m q m V § m m m V V ’ W m m m V V A > u u u u u m m m V V A u > > V m m m V V u ’ V V m m m ’ u A m m m V V 3 u A ’ m m m V V A 3 m m m V V A ’ u u m H H V V n A 3 m H V H V A u ? " m H V V H A n A m V H V H u 3 A m V H V H u 7 A m V V H H u > A > m V V H H u V > m V V H H u ’ > m V V H H u A v m V V H N u > A A m H M V V n > A m u H N V V > A m V V H N u > A m H N V V u > A > V V m H N u A > u m H N V V A m H m V V A u > > A m H w V V u > A m H w V V u V A m H w V V n > A m H w V V u > A m H w V V u > A > V V m H w u A y m H w V V V u > u ’ m H w V V > A u m H w V V > V m H w V V > ’ m H p V V ’ A m H 9 V V 3 A m H p V V ? A ’ A V V m H b 3 H m h A V V u u n u u u 2 4 7 . 2 3 0 9 5 1 9 6 9 5 6 6 3 8 E + 0 0 . 2 4 0 2 3 9 8 1 4 1 4 3 0 2 E - 0 1 - . 5 4 2 5 5 3 1 0 2 5 3 9 3 9 E + 0 0 - . 4 8 6 7 0 8 7 2 6 9 6 6 7 5 E + 0 0 ' . l 9 7 2 7 3 5 3 7 2 7 2 1 2 8 + 0 1 - . l 4 4 2 9 6 2 6 4 2 7 5 9 1 E + 0 0 . 4 4 4 1 3 8 5 1 4 8 6 7 5 2 3 - 0 1 . 2 3 0 9 5 1 9 6 9 6 2 4 S B E + 0 0 . 2 8 1 3 6 7 0 8 2 8 3 0 0 0 E - 0 1 . 2 2 4 1 2 4 8 7 8 5 1 6 8 2 8 - 0 2 . 1 8 0 7 1 7 3 4 7 5 5 7 2 2 E - 0 1 . 1 9 9 3 3 4 1 6 2 0 2 5 4 B E + 0 0 . 1 7 1 1 1 8 1 9 3 7 4 9 8 6 E + 0 0 . 2 0 8 1 8 1 9 2 0 4 3 4 0 7 E + 0 0 . 7 0 1 4 9 1 9 5 5 9 3 3 3 1 8 - 0 1 . 2 4 0 2 3 9 8 1 4 1 4 5 3 O E - O l . 2 2 4 1 2 4 8 7 8 5 0 2 6 1 E - 0 2 . 1 6 3 3 2 1 4 8 4 8 1 5 3 5 E - 0 3 . 1 2 2 3 7 0 6 8 7 7 8 8 3 6 8 + 0 0 . 1 7 7 2 0 3 2 1 3 1 4 B O O E + 0 0 . 9 0 7 9 5 1 3 4 5 7 4 8 1 9 E - 0 1 . 4 2 2 4 8 9 2 1 0 5 1 8 5 1 E - 0 1 . 1 2 7 4 4 8 0 0 0 5 2 9 2 8 E - 0 1 . 2 7 4 4 3 6 0 4 4 5 3 1 9 7 3 - 0 2 . 4 0 9 9 4 9 5 0 2 5 4 7 1 4 3 - 0 3 . 2 7 4 4 7 5 9 6 9 7 7 0 3 7 8 - 0 4 . 1 0 6 4 5 9 2 0 9 4 9 3 7 6 E - 0 5 . 1 7 7 2 0 3 2 1 3 0 8 0 7 0 E + 0 0 . 2 8 4 3 5 4 9 6 2 8 0 2 3 S E + 0 0 . 1 7 5 9 4 5 6 9 4 7 6 3 8 7 E + 0 0 . 8 0 3 8 5 3 9 1 1 3 1 5 8 5 E - 0 1 . 2 6 0 0 3 9 0 7 5 0 1 0 3 5 E - 0 1 . 5 4 0 2 7 1 4 3 1 5 3 2 3 5 E - 0 2 . 8 4 0 1 1 6 9 7 6 6 0 4 5 8 8 - 0 3 . 5 4 4 6 3 0 1 2 7 1 9 2 7 5 E - 0 4 . 2 1 6 5 0 2 8 9 0 8 9 2 9 2 E - 0 5 . 9 0 7 9 5 1 3 4 1 6 5 5 4 6 E - 0 1 . 1 7 5 9 4 5 6 9 6 1 1 3 5 6 8 + 0 0 . 1 2 5 9 0 9 3 5 0 8 2 4 2 6 8 + 0 0 . 6 0 8 2 8 2 3 8 8 7 6 1 8 4 3 - 0 1 . 2 1 0 6 8 0 0 8 2 1 8 6 6 3 8 - 0 1 . 4 4 3 1 5 3 5 0 5 2 8 4 5 0 8 - 0 2 . 7 1 8 5 5 3 0 5 6 7 9 9 4 6 8 - 0 3 . 4 6 5 9 9 1 4 3 3 8 1 3 4 3 8 - 0 4 . 1 9 0 9 9 9 3 4 9 4 3 0 9 0 3 - 0 5 . 4 2 2 4 8 9 2 1 8 7 9 7 1 8 8 - 0 1 . 8 0 3 8 5 3 8 9 6 7 2 7 5 6 E - 0 1 . 6 0 8 2 8 2 3 9 8 3 2 9 7 2 3 - 0 1 . 3 0 0 9 6 3 2 7 1 1 7 9 1 7 E ' 0 1 . 1 0 8 0 3 7 5 5 0 9 0 8 1 9 E - 0 1 2 4 8 . 2 2 8 7 8 8 5 5 0 8 5 6 5 1 E - 0 2 . 3 7 7 1 5 3 3 8 1 8 7 6 3 8 8 - 0 3 . 2 4 4 3 2 0 7 5 6 7 0 1 5 5 E - 0 4 . 1 0 0 7 7 1 5 3 2 5 8 2 3 7 3 - 0 5 . 1 2 7 4 4 7 9 9 6 1 3 6 4 2 E - 0 1 . 2 6 0 0 3 9 0 8 7 0 5 2 0 6 8 - 0 1 . 2 1 0 6 8 0 0 7 2 8 9 1 5 9 3 - 0 1 . 1 0 8 0 3 7 5 5 4 3 9 1 5 6 E - 0 1 . 4 1 0 4 0 0 4 8 6 8 5 0 9 0 3 - 0 2 . 8 8 5 6 0 5 7 4 4 7 9 8 5 7 3 - 0 3 . 1 5 2 4 7 2 5 5 7 5 5 5 6 8 8 - 0 3 . 9 9 6 7 3 6 2 8 3 4 6 5 0 8 E - 0 5 . 4 2 5 6 3 6 8 1 4 7 3 8 1 7 8 - 0 6 . 2 7 4 4 3 6 0 6 5 4 1 9 0 8 E - 0 2 . 5 4 0 2 7 1 3 8 3 0 5 6 2 8 8 - 0 2 . 4 4 3 1 5 3 5 5 2 0 3 2 5 3 E - 0 2 . 2 2 8 7 8 8 5 2 6 0 2 7 3 0 3 - 0 2 . 8 8 5 6 0 5 8 0 3 4 6 0 9 8 3 - 0 3 . 1 9 2 3 1 2 8 8 6 2 9 8 4 0 8 - 0 3 . 3 3 5 1 5 2 7 3 7 7 1 3 7 8 8 - 0 4 . 2 1 9 6 1 6 2 3 4 0 6 5 0 8 E - 0 5 . 9 4 3 0 7 3 7 1 4 1 2 1 3 9 8 - 0 7 . 4 0 9 9 4 9 4 5 8 7 1 3 7 5 8 - 0 3 . 8 4 0 1 1 7 0 9 1 1 5 8 2 8 E - 0 3 . 7 1 8 5 5 2 9 4 9 8 0 5 9 4 E - 0 3 . 3 7 7 1 5 3 4 4 0 0 8 4 0 4 8 - 0 3 . 1 5 2 4 7 2 5 3 9 2 9 4 7 3 8 - 0 3 . 3 3 5 1 5 2 7 6 3 9 4 1 6 9 E - 0 4 . 6 0 8 5 4 5 0 7 6 7 5 2 3 4 E - 0 5 . 4 0 2 2 5 2 5 5 4 3 4 9 0 0 8 - 0 6 . 1 7 9 2 5 6 3 8 1 7 0 0 0 5 3 - 0 7 . 2 7 4 4 7 6 0 1 6 1 6 8 8 1 3 - 0 4 . 5 4 4 6 3 0 0 1 0 4 2 3 9 3 E - 0 4 . 4 6 5 9 9 1 5 4 4 7 2 9 1 5 8 - 0 4 . 2 4 4 3 2 0 6 9 0 9 0 5 3 0 8 - 0 4 . 9 9 6 7 3 6 5 0 3 9 1 0 9 7 E - 0 5 . 2 1 9 6 1 6 1 9 2 1 4 3 0 6 3 - 0 5 . 4 0 2 2 5 2 5 8 7 6 2 7 9 4 8 - 0 6 . 2 6 6 3 9 3 0 7 0 6 4 0 7 7 8 - 0 7 . 1 1 9 4 3 6 0 3 6 9 3 9 4 4 3 - 0 8 . 1 0 6 4 5 9 1 9 3 5 0 6 5 5 E - 0 5 . 2 1 6 5 0 2 9 3 0 5 3 8 9 9 3 - 0 5 . 1 9 0 9 9 9 3 0 9 0 5 2 0 9 8 - 0 5 . 1 0 0 7 7 1 5 5 6 8 7 4 0 5 8 - 0 5 . 4 2 5 6 3 6 7 2 8 2 5 1 8 0 E - 0 6 . 9 4 3 0 7 3 8 8 6 7 6 1 0 7 8 - 0 7 . 1 7 9 2 5 6 3 6 1 9 8 4 9 2 E - 0 7 . 1 1 9 4 3 6 0 4 5 1 5 7 6 9 8 - 0 8 . 5 5 5 7 5 5 3 3 4 8 2 2 1 2 E - 1 0 ' . 5 6 8 4 5 1 2 5 4 7 7 5 9 4 E - 0 2 H ‘ q u m m t h H ‘ D m V a ‘ m b w N H m m fl m U ‘ p W N H m m q m m p r H m m q m m p r H m m q m v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v " I l l ! u u fl u fl fl u l l l l fl l l u l l l l l l l l l l fl n l l l l l l l l u I l l l l l u I I I I " I l l ! 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0 1 . 7 7 7 9 9 4 3 1 7 9 0 4 8 1 8 - 0 1 . 2 6 9 0 4 1 6 5 2 4 7 9 7 0 E - 0 1 . 1 0 1 7 5 1 3 3 9 9 4 3 8 0 8 - 0 1 . 1 8 1 9 4 9 7 8 4 9 2 2 6 1 8 - 0 2 . 3 1 9 1 2 1 2 1 5 2 7 7 1 1 3 - 0 3 . 1 8 6 1 9 7 9 0 1 6 6 5 9 6 E - 0 4 . 8 1 0 4 0 7 2 1 5 6 6 7 8 3 8 - 0 6 . 7 3 1 9 7 1 4 2 5 3 6 1 7 3 8 - 0 1 . 3 3 0 4 7 4 1 8 0 7 9 8 7 7 E + 0 0 . 2 4 0 7 5 3 7 6 9 7 4 7 2 4 E + 0 0 . 1 0 0 8 2 2 5 4 6 4 4 4 7 6 8 + 0 0 . 3 4 0 9 3 8 3 8 8 2 7 6 B O E - O l . 6 7 6 7 5 6 1 2 8 0 6 3 9 7 3 - 0 2 . 1 0 8 6 2 2 0 8 5 6 1 3 7 7 8 - 0 2 . 6 8 2 0 9 1 3 5 0 1 3 9 3 0 E - 0 4 . 2 7 7 3 4 9 8 5 0 9 8 5 6 0 3 - 0 5 . 7 7 7 9 9 4 3 1 5 3 4 0 0 4 E - O l . 2 4 0 7 5 3 7 7 0 4 2 3 9 1 8 + 0 0 . 1 8 9 7 4 3 3 1 4 6 9 6 9 O E + 0 0 . 8 6 9 2 1 3 9 1 7 0 3 9 8 1 E - O l . 3 0 6 7 1 6 5 0 2 9 3 6 9 8 3 - 0 1 . 6 2 8 9 8 9 5 1 4 7 0 0 6 1 8 - 0 2 . 1 0 3 3 4 5 7 8 3 2 9 8 8 9 E - 0 2 . 6 5 9 3 3 9 4 4 5 8 3 2 0 7 E - 0 4 . 2 7 2 7 9 9 5 0 1 7 1 0 4 4 8 - 0 5 . 2 6 9 0 4 1 6 5 3 8 4 3 9 4 E - O l . 1 0 0 8 2 2 5 4 6 2 9 5 6 0 3 + 0 0 . 8 6 9 2 1 3 9 1 9 7 6 8 3 0 E - 0 1 . 4 1 0 6 3 0 0 8 8 2 4 0 4 0 E - 0 1 . 1 5 1 2 1 8 9 7 1 9 4 1 4 9 E - 0 1 . 3 1 2 8 5 2 6 6 6 6 7 2 8 2 8 - 0 2 . 5 2 3 7 1 8 9 2 6 3 0 2 7 6 E - 0 3 . 3 3 4 0 0 5 8 9 3 1 6 5 5 7 E - 0 4 . 1 3 9 1 9 1 7 1 4 1 2 1 3 6 8 - 0 5 . 1 0 1 7 5 1 3 3 8 2 1 5 7 S E - O l . 3 4 0 9 3 8 3 9 2 4 9 6 3 5 8 - 0 1 . 3 0 6 7 1 6 4 9 9 9 7 2 0 3 8 - 0 1 . 1 5 1 2 1 8 9 7 3 5 9 6 7 7 8 - 0 1 . 5 8 4 6 2 5 3 5 8 6 8 1 0 2 E - 0 2 . 1 2 3 9 1 1 0 4 0 4 4 6 9 6 E - 0 2 . 2 1 5 4 4 6 2 3 0 0 7 9 4 1 3 - 0 3 . 1 3 9 2 6 3 1 7 2 7 7 1 4 6 E - 0 4 . 5 9 8 4 1 8 0 4 5 7 1 3 5 9 8 - 0 6 . 1 8 1 9 4 9 7 8 9 1 9 7 2 3 8 - 0 2 . 6 7 6 7 5 6 1 1 3 4 0 9 7 4 8 - 0 2 . 6 2 8 9 8 9 5 2 9 7 6 4 1 1 E - 0 2 . 3 1 2 8 5 2 6 5 7 8 5 0 7 3 8 - 0 2 . 1 2 3 9 1 1 0 4 2 7 5 4 8 0 3 - 0 2 . 2 6 4 5 2 7 9 1 4 5 2 4 1 4 8 - 0 3 V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V v v v v v > > v > > > > > > > > v > > v v > > v > > v v > w v v > > v v v > v v > > v v w v v > > > A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A m m m m m o m m m m m m m m m m m m m m m m m m m w m w m m m m m m m m m m m m m m m m m m m m m m V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V m m m m m m m m m m m m m m m p p b p p o o ¢ p w w w w w w w w w N N N N N M N N N H H H H H H H H 2 5 0 . 4 6 6 6 3 0 3 3 2 6 4 9 4 9 8 - 0 4 . 3 0 2 4 3 6 7 3 3 0 7 9 5 0 E - 0 5 . 1 3 0 8 3 7 0 0 1 6 0 0 9 4 E - 0 6 . 3 1 9 1 2 1 2 0 3 4 2 5 2 5 3 - 0 3 . 1 0 8 6 2 2 0 8 9 7 4 6 2 9 E - 0 2 . 1 0 3 3 4 5 7 7 9 5 3 5 8 6 8 - 0 2 . 5 2 3 7 1 8 9 4 9 0 9 6 9 7 3 - 0 3 . 2 1 5 4 4 6 2 2 3 7 7 6 8 9 8 - 0 3 . 4 6 6 6 3 0 3 4 3 7 3 3 9 5 E - 0 4 . 8 5 4 7 8 8 6 1 6 6 6 6 5 5 8 - 0 5 . 5 6 0 0 4 0 3 4 7 4 3 0 4 0 8 - 0 6 . 2 5 0 8 4 5 6 7 8 8 9 0 0 1 8 - 0 7 . 1 8 6 1 9 7 9 1 3 0 2 5 7 7 5 - 0 4 . 6 8 2 0 9 1 3 2 0 5 6 2 9 6 3 - 0 4 . 6 5 9 3 3 9 4 8 2 7 8 0 3 0 8 - 0 4 . 3 3 4 0 0 5 8 7 1 8 4 9 2 9 8 - 0 4 . 1 3 9 2 6 3 1 8 0 3 3 8 7 4 8 - 0 4 . 3 0 2 4 3 6 7 1 9 4 9 0 3 7 3 - 0 5 . 5 6 0 0 4 0 3 5 9 3 0 9 7 9 8 - 0 6 . 3 6 7 6 4 4 3 5 2 7 0 4 2 5 8 - 0 7 . 1 6 5 8 7 0 4 5 6 4 1 0 8 3 E - 0 8 . 8 1 0 4 0 7 1 7 9 7 5 2 1 2 8 - 0 6 . 2 7 7 3 4 9 8 6 0 7 8 3 3 2 8 - 0 5 . 2 7 2 7 9 9 4 9 1 7 6 2 8 4 E - 0 5 . 1 3 9 1 9 1 7 2 0 9 9 3 6 4 E - 0 5 . 5 9 8 4 1 8 0 1 6 8 4 7 7 9 E - 0 6 . 1 3 0 8 3 7 0 0 7 4 8 5 1 2 E - 0 6 . 2 5 0 8 4 5 6 7 3 9 6 3 4 0 E - 0 7 . 1 6 5 8 7 0 4 5 8 9 9 1 2 3 8 - 0 8 . 7 7 5 4 9 0 6 2 3 0 1 8 0 2 3 - 1 0 . 5 1 8 3 3 7 1 4 9 9 2 4 2 6 8 - 0 2 . 8 2 5 1 5 6 8 5 0 7 1 4 8 5 8 - 0 2 . 4 3 8 6 4 8 6 3 2 5 4 3 B S E - O l . 3 7 3 4 2 7 6 5 0 8 2 9 4 O E - O l . 1 0 2 4 6 1 7 7 6 0 0 4 9 3 3 - 0 1 . 2 3 4 4 4 6 8 5 0 2 5 9 9 3 E - 0 2 . 3 3 9 9 5 8 2 1 1 2 2 8 0 1 3 - 0 3 . 2 3 4 5 0 3 7 5 5 8 5 3 7 7 8 - 0 4 . 8 9 8 5 0 1 8 2 1 6 6 6 7 3 E - 0 6 . 8 2 5 1 5 6 7 4 5 9 4 1 0 6 E - 0 2 . 1 7 3 1 8 7 8 9 1 6 1 4 3 6 E - 0 1 . 2 4 6 4 8 4 6 9 4 2 6 2 1 1 8 + 0 0 . 1 2 8 8 7 8 9 4 6 2 5 2 3 7 E + 0 0 . 4 1 0 1 2 1 4 0 7 1 3 0 6 5 E - 0 1 . 8 3 8 4 5 1 9 4 4 8 1 0 0 0 8 - 0 2 . 1 3 1 2 6 4 1 0 0 7 7 8 5 9 3 - 0 2 . 8 3 6 8 9 2 8 1 1 9 3 9 5 5 E - 0 4 . 3 3 5 1 8 3 0 2 9 8 9 8 1 0 E - 0 5 . 4 3 8 6 4 8 6 1 8 3 6 4 8 2 8 - 0 1 . 2 4 6 4 8 4 6 9 5 9 3 3 7 G E + 0 0 N H ‘ D m m e b w w p m m fl m e W N H m m e m b U ’ N H m m q m m p r H m m e m D W N i - ‘ k o m q v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V > > > > > > > > > > > > > > > v v > > y y w > > > > > > > y > y y > w > v > > > > > > > y > y > y y A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A m w m m m m m m m m m m m m m m m m w w m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V w w w w w w w w u w w w w w w w w w w w N M N N N N N N N M N N N N N N M N N N N N N N N N N N N M V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V w w m w w N N N N N N H H H H H H H H H m m m m m m m m m m m m m m m m m m q fl u q q q q q q m m m m m m m m m m q “ V I V I V ’ V I V I V I \ l m m m m a ‘ m m a ‘ c ‘ m w m m m m m m m @ 9 9 9 p fi l fi h l fi w w w w w w w V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V G W ‘ W N H ‘ q u m U ‘ fi Q ’ N H m e O ‘ U ‘ p U N H m m q m m fi w N H K O G ’ Q U ‘ U ‘ I F W N H W Q Q O ‘ U T I F W v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v l u n u l l fl l l l l l l l l l l l l l u l l n u I I I I I I I I I I I I I I I l l l l l u l l u u l l l l l l l l u l l u l l l l u u u u u u u l l u l l V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V \ D k o x o x o \ o m m m m m m m m m w m m m m m m m m m m m m m m m m t o m x o x o x o x o x o x o x o k o \ o x o u n o x o x o x o x o t o V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w > 3 9 3 > > > > > v > > > y > > > > > > § > > > > F F > > > > > > > > > V > > V > > > > > > > > > i fi 2 5 1 . 3 3 8 6 8 9 4 7 9 7 9 6 B I E + 0 0 . 1 5 6 3 0 1 1 2 4 7 7 2 6 5 8 + 0 0 . 5 5 0 8 7 9 9 6 4 5 6 6 7 8 E - 0 1 . 1 1 0 7 9 7 3 1 5 7 9 4 5 7 E - 0 1 . 1 8 3 3 6 4 7 0 3 9 0 0 6 8 8 - 0 2 . 1 1 5 4 0 5 5 3 2 2 6 6 5 2 E - 0 3 . 4 8 0 6 9 0 8 1 4 4 5 2 7 9 8 - 0 5 . 3 7 3 4 2 7 6 7 0 9 0 6 4 9 E - 0 1 . 1 2 8 8 7 8 9 4 2 3 5 0 6 4 E + 0 0 . 1 5 6 3 0 1 1 2 6 5 5 7 O B E + 0 0 . 7 8 8 2 8 9 2 3 1 8 9 5 7 6 E - 0 1 . 2 8 1 5 4 9 0 2 6 7 9 4 8 9 3 - 0 1 . 5 8 6 6 0 4 8 3 5 7 8 0 2 4 E - 0 2 . 9 6 8 1 9 3 6 1 2 1 2 3 9 7 E - 0 3 . 6 2 0 2 6 6 7 1 0 4 0 2 7 2 8 - 0 4 . 2 5 6 2 8 3 5 4 0 7 0 0 5 1 8 - 0 5 . 1 0 2 4 6 1 7 6 3 7 2 9 0 2 8 - 0 1 . 4 1 0 1 2 1 4 3 5 6 5 2 4 0 3 - 0 1 . 5 5 0 8 7 9 9 4 3 6 8 4 7 8 8 - 0 1 . 2 8 1 5 4 9 0 3 4 7 5 7 5 2 8 - 0 1 . 1 0 7 9 0 3 6 5 3 6 9 5 3 0 8 - 0 1 . 2 2 7 9 8 0 5 2 8 5 6 9 5 6 3 - 0 2 . 3 9 5 4 1 2 6 0 8 4 8 3 5 3 E - 0 3 . 2 5 4 8 6 6 1 7 2 5 9 3 1 8 E - 0 4 . 1 0 9 3 7 8 4 8 1 3 3 6 0 8 8 - 0 5 . 2 3 4 4 4 6 8 9 0 7 7 2 2 3 E - 0 2 . 8 3 8 4 5 1 8 5 4 6 7 9 0 8 8 - 0 2 . 1 1 0 7 9 7 3 2 4 3 0 7 4 4 E - O l . 5 8 6 6 0 4 7 9 9 6 2 7 8 2 3 - 0 2 . 2 2 7 9 8 0 5 3 8 5 9 6 7 4 E - 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~ v N o H > fi ‘ A v ‘ ‘ ‘ N N > p m A v ~ N ~ W > p m A “ ~ ‘ N F v > m b A O v ‘ ~ N > o fi ~ A ‘ ‘ N ‘ ‘ v > p ‘ A ~ ‘ N ~ U v > p m A N ‘ ~ ~ v m m > p A N ~ v ~ ~ o e > b A m w v ~ ~ ~ m v k A w v ‘ ‘ ~ m H 3 fi m N A w v ‘ ‘ ~ > p m w A w v ‘ ~ ~ > fi m fi A w v ~ ‘ > fi ~ m m A ~ ~ ‘ w v > b m m A ‘ w v > fi m q A “ “ w v > m fi m A ~ w v ‘ > fi m m A “ “ fi v m > p p A - ~ m p v > fi ‘ w A ~ fi v m > p ~ w m ‘ A ~ ‘ h v > h fi m v fi A ~ ~ “ h v m o > fi A h v m ‘ ‘ v A - p - h v m ~ q > ‘ ‘ ~ A fi fi v m m v A fi h v m m ~ ‘ > A “ v m “ p m ‘ ~ > A F m N v o ~ ‘ ‘ > m m I “ A v ~ ‘ ~ 2 5 2 . 6 7 4 5 9 6 7 6 4 9 7 6 8 3 E - 0 7 . 3 0 3 2 5 4 2 3 4 2 0 2 3 8 E - 0 8 . 8 9 8 5 0 1 5 3 4 0 6 3 4 6 8 - 0 6 . 3 3 5 1 8 3 0 9 9 7 4 2 2 3 8 - 0 5 . 4 8 0 6 9 0 7 4 3 0 3 2 1 4 E - 0 5 . 2 5 6 2 8 3 5 8 0 5 7 4 1 7 8 - 0 5 . 1 0 9 3 7 8 4 6 6 7 2 5 5 4 E - 0 5 . 2 3 9 5 8 8 6 4 8 1 6 4 0 4 8 - 0 6 . 4 5 8 5 3 6 0 4 9 6 3 3 5 6 8 - 0 7 . 3 0 3 2 5 4 2 4 8 3 4 0 3 7 8 - 0 8 . 1 4 1 6 2 5 9 0 8 6 3 2 4 8 8 - 0 9 . 2 2 8 4 2 7 1 7 9 5 3 6 0 8 E - 0 2 . 3 9 3 8 6 9 7 7 5 8 7 1 2 8 E - 0 2 . 1 2 9 8 5 0 7 0 8 4 3 5 7 0 E - 0 2 . 3 1 8 6 4 5 2 6 6 2 8 8 5 1 8 - 0 1 . 2 2 3 2 0 6 3 9 0 6 1 4 9 1 8 - 0 1 . 3 7 2 4 2 5 9 6 1 1 0 9 0 0 E - 0 2 . 6 8 1 2 7 7 1 0 1 9 3 2 6 6 E - 0 3 . 3 9 2 0 2 1 9 6 2 7 6 7 3 3 E - 0 4 . 1 7 3 5 4 3 1 8 9 9 4 0 7 8 8 - 0 5 . 3 9 3 8 7 0 0 1 8 8 8 8 2 6 E - 0 2 . 3 0 3 8 5 9 0 6 5 7 5 2 4 8 8 - 0 3 . 2 6 9 1 4 4 0 6 8 4 4 2 9 8 3 - 0 1 . 1 5 7 6 8 8 0 6 2 1 0 6 9 0 8 + 0 0 . 7 6 7 9 5 4 9 2 7 1 5 9 7 4 E - 0 1 . 1 3 7 1 6 0 0 2 0 6 4 9 3 9 8 - 0 1 . 2 3 4 2 0 5 9 7 7 6 3 1 0 6 8 - 0 2 . 1 3 9 3 7 9 1 2 2 0 8 9 1 7 8 - 0 3 . 5 8 6 0 6 8 1 6 6 2 1 9 5 3 8 - 0 5 . 1 2 9 8 5 0 2 9 0 9 7 7 6 3 E - 0 2 . 2 6 9 1 4 4 0 0 7 6 8 8 7 4 E - O l . 2 1 3 5 4 6 7 0 8 7 4 2 8 0 8 + 0 0 . 2 8 0 3 6 0 3 8 7 2 3 8 0 3 8 + 0 0 . 1 0 2 5 6 9 7 5 4 2 4 2 7 2 E + 0 0 . 2 0 9 5 2 0 9 0 7 4 3 3 2 2 3 - 0 1 . 3 4 0 9 4 1 5 2 1 7 9 0 2 3 E - 0 2 . 2 1 8 1 6 8 5 4 7 2 9 1 9 5 E - 0 3 . 8 9 7 4 3 0 8 8 0 7 8 6 3 1 E - 0 5 . 3 1 8 6 4 5 3 0 6 7 4 2 8 4 8 - 0 1 . 1 5 7 6 8 8 0 5 5 5 3 3 0 7 E + 0 0 . 2 8 0 3 6 0 3 9 0 5 7 4 0 6 8 + 0 0 . 1 8 4 3 5 7 7 3 0 0 4 9 6 7 E + 0 0 . 6 9 1 6 4 5 2 1 5 6 6 5 6 3 8 - 0 1 . 1 4 0 1 3 7 0 7 4 0 9 5 0 4 8 - 0 1 . 2 3 2 4 5 0 4 6 1 4 5 3 4 8 8 - 0 2 . 1 4 6 9 6 5 5 3 5 1 6 5 5 8 8 - 0 3 . 6 0 8 9 3 7 9 1 3 4 9 3 2 6 8 - 0 5 . 2 2 3 2 0 6 3 6 3 8 4 3 9 3 8 ~ 0 1 . 7 6 7 9 5 4 9 8 5 5 1 2 9 2 3 - 0 1 . 1 0 2 5 6 9 7 4 9 5 8 4 2 9 E + 0 0 ) m p A v ‘ l m “ ’ A v m p “ u W “ m 1 l m 0 l 3 ‘ A v m m p “ ‘ l > V A v m p 0 u m “ > ~ “ A v m p ~ m l m “ l ‘ m > u A v m p m ~ O l > m “ A v m p ‘ ~ § l > > > m l A v o p ~ - m V I A v m m p ‘ ‘ i I w I A v m p ~ N w m ‘ fl V m I A v p m p ~ m I 3 “ A v ‘ q m p ‘ m I > I q m A v ‘ ~ I m a > fl “ q I A v m fi ‘ > q m I A v m p V q ~ > ‘ o I q K I > A v I ‘ m p “ ‘ I ‘ I > b m A v Q \ I — > ‘ A v i m o ~ “ 1 I I > ‘ A v I m o \ N - “ q U I > A v ~ m p > ~ l A v ‘ m p m m u b ‘ > o i m l A ~ v m o l - § o ? m l A v m ~ o ’ m l I “ “ m l A v m ‘ o 3 m \ u > > A v m ~ p Q l ~ o “ W l A v m ‘ p o l A m ~ b v m V i ‘ H > N o fl A m v ~ o V W u > o " l A m v ‘ p Q m > l A m v ‘ h ~ > ‘ O o l x ‘ l > A m v p ~ “ l o U “ > x A m p v ~ ‘ l u > ~ A p v m ~ - o O l x Q l > A p v m ‘ ~ l m ’ “ l > A v m p ‘ o G § l 3 x A v m p ‘ D l ~ > K A v m o ~ ‘ l m l o H § - l A v m o ‘ x - N l > o A v m h ~ w u ‘ > u l A v m b ‘ - b - l 7 > m o A v I ‘ m ~ l - l m A v m b ‘ l H > o l m m A v m ‘ ‘ — l > q ‘ A v m m u Q m l - > “ H l — m m l A v ‘ > N u “ l “ m m A v ‘ W > — l > ~ ~ m m u A v - D l — ‘ l > ~ m m l A v t u “ “ l > A v m m ‘ H q l > H m m m A v ‘ “ “ l 2 5 3 . 6 9 1 6 4 5 2 3 2 1 8 2 0 5 E - 0 1 . 2 7 2 4 3 9 0 8 8 8 0 7 9 1 8 - 0 1 . 5 7 0 0 9 4 1 7 9 8 0 6 8 0 8 - 0 2 . 9 8 2 8 8 5 1 3 8 7 1 1 2 5 8 - 0 3 . 6 3 2 0 6 3 1 4 8 1 1 3 8 2 3 - 0 4 . 2 6 9 9 0 5 1 1 6 2 3 4 7 0 8 - 0 5 . 3 7 2 4 2 6 0 6 0 6 0 7 7 2 8 - 0 2 . 1 3 7 1 5 9 9 9 8 5 1 6 8 4 8 - 0 1 . 2 0 9 5 2 0 9 2 7 3 6 9 3 4 E - 0 1 . 1 4 0 1 3 7 0 6 5 0 0 4 6 4 E - 0 1 . 5 7 0 0 9 4 2 0 4 8 9 7 4 9 8 - 0 2 . 1 2 0 5 5 0 9 0 3 2 2 1 7 8 8 - 0 2 . 2 1 1 4 1 1 9 0 9 3 4 0 6 0 8 - 0 3 . 1 3 6 4 5 8 9 7 1 5 8 9 0 9 8 - 0 4 . 5 8 7 2 2 0 5 3 3 8 6 5 2 8 3 - 0 6 . 6 8 1 2 7 6 8 8 0 4 7 0 7 0 8 - 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I " ‘ v m v 2 5 6 . 4 5 6 5 8 1 6 1 9 2 1 8 9 Z E - O l . 1 0 2 3 8 8 8 5 2 6 2 5 1 5 8 + 0 0 . 4 6 5 5 7 2 4 4 0 2 9 8 2 7 8 - 0 1 . 2 4 1 6 8 8 8 5 1 5 5 8 1 4 E + 0 0 . 2 4 1 5 5 5 6 8 7 8 1 1 3 4 E + 0 0 . 1 4 1 9 8 5 3 0 2 1 1 4 3 4 E + 0 0 . 2 3 9 5 7 5 0 4 4 5 6 1 2 1 E - 0 1 . 1 5 4 5 9 3 0 0 3 1 7 3 8 9 8 - 0 2 . 6 2 5 6 9 6 8 3 6 8 8 4 5 2 3 - 0 4 . 8 7 2 8 7 3 2 5 5 8 6 6 5 8 E - 0 2 . 5 7 6 9 5 0 3 4 9 2 0 4 7 l E - 0 1 . 1 1 0 5 0 7 8 2 2 7 1 1 9 5 3 + 0 0 . 2 4 1 5 5 5 6 9 0 2 5 6 0 6 E + 0 0 . 2 6 5 4 6 7 0 0 2 5 0 7 6 5 8 + 0 0 . 7 6 2 8 3 4 2 1 5 2 0 2 0 2 8 - 0 1 . l 3 6 5 1 7 0 9 8 7 8 5 5 9 E - 0 1 . 8 6 5 1 2 3 7 0 6 4 3 2 7 7 E - 0 3 . 3 6 9 9 9 7 4 4 4 1 8 5 0 9 8 - 0 4 . 2 3 8 1 0 3 0 7 1 8 2 4 3 0 E - 0 1 . 8 3 7 3 9 3 2 1 3 8 7 8 3 9 8 - 0 1 . 1 8 6 4 8 3 9 8 8 2 1 0 9 7 E + 0 0 . 1 4 1 9 8 5 3 0 1 1 4 6 6 3 E + 0 0 . 7 6 2 8 3 4 2 1 4 3 4 7 0 9 8 - 0 1 . 2 0 2 0 1 9 0 4 3 6 4 5 1 2 8 - 0 1 . 3 5 6 3 3 1 2 8 2 2 2 7 9 8 8 - 0 2 . 2 2 8 0 4 0 8 0 0 7 3 5 1 3 8 - 0 3 . 9 6 7 5 9 9 4 9 2 4 8 5 1 5 8 - 0 5 . 7 6 5 3 7 0 2 6 6 7 5 3 9 6 8 - 0 2 . 2 4 9 5 0 5 3 0 4 0 0 0 1 9 8 - 0 1 . 3 7 4 9 0 3 0 2 9 5 1 4 8 3 8 - 0 1 . 2 3 9 5 7 5 0 4 3 8 3 3 6 1 8 - 0 1 . 1 3 6 5 1 7 1 0 0 2 4 0 7 8 E - 0 1 . 3 5 6 3 3 1 2 8 1 3 6 3 9 6 8 - 0 2 . 6 5 9 5 5 4 7 8 8 8 8 2 1 3 3 - 0 3 . 4 2 7 4 2 3 2 2 7 2 1 1 6 8 E - 0 4 . 1 8 9 1 1 1 0 7 9 6 8 4 7 8 E - 0 5 . 4 2 4 5 4 8 3 6 5 1 7 4 3 6 8 - 0 3 . 1 3 3 8 0 2 3 2 0 1 3 5 6 0 8 - 0 2 . 2 2 7 4 7 8 7 7 2 5 8 0 9 8 8 - 0 2 . 1 5 4 5 9 3 0 0 7 3 1 2 0 9 8 - 0 2 . 8 6 5 1 2 3 6 8 5 6 8 4 9 2 8 - 0 3 . 2 2 8 0 4 0 8 0 9 4 4 6 3 8 8 - 0 3 . 4 2 7 4 2 3 2 1 8 3 2 9 8 9 3 - 0 4 . 2 7 8 6 4 8 4 5 9 9 5 0 4 0 8 - 0 5 . 1 2 4 2 8 8 1 0 4 3 0 8 4 2 8 - 0 6 . 1 9 1 0 4 9 7 3 7 4 8 7 9 6 8 - 0 4 . 5 9 1 8 3 7 0 1 7 3 3 1 9 0 E - 0 4 . 9 7 0 6 0 8 1 8 6 3 2 1 4 4 8 - 0 4 . 6 2 5 6 9 6 8 0 0 7 8 8 9 4 E - 0 4 . 3 6 9 9 9 7 4 6 1 7 3 5 4 9 8 - 0 4 V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V m a s a s a s m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V m m w m m m m m m m m m m m q q q q q q q q q m m m m m m m m m m m m m m m m m m # 9 9 0 0 3 : « > 9 4 : V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V \ D \ D \ D \ O \ D \ D \ O \ O \ D \ O \ D \ D \ O \ O \ D \ D O \ D \ D \ O \ D \ D \ O \ D \ D \ O \ D \ D \ D \ D \ O \ D \ D \ O \ O \ O \ O \ O \ O \ O \ O \ D \ O \ D \ D \ D \ O \ O \ D \ O > r > > : v w r w v v v w v t u v a » r > r r > > > > v r v v r v w v v r > > v > > z v > > z v y > 3 v > w > z ~ > 2 5 7 . 9 6 7 5 9 9 4 4 7 3 2 1 2 8 3 - 0 5 . 1 8 9 1 1 1 0 8 6 4 7 9 3 4 E - 0 5 . 1 2 4 2 8 8 1 0 0 5 3 3 6 6 8 - 0 6 . 5 7 7 8 4 3 2 3 9 8 3 7 2 0 E - 0 8 . 1 7 1 8 5 7 1 9 3 8 1 0 8 7 E + 0 0 . 6 4 0 6 6 9 3 4 1 6 6 4 7 6 E - O l . 6 3 3 7 7 1 1 9 6 2 4 0 5 6 8 + 0 0 . 5 5 2 0 6 3 3 1 8 9 0 0 7 6 E - 0 1 . 2 0 2 0 8 2 9 5 4 1 1 4 3 0 E + 0 0 . 4 4 6 9 5 9 3 6 3 7 6 2 2 9 8 - 0 2 . 2 8 8 9 9 7 1 1 0 5 4 6 9 2 8 - 0 1 . 3 2 5 5 3 9 4 8 1 3 0 9 5 3 8 - 0 2 . 1 2 0 0 2 7 8 1 5 0 8 6 1 3 8 - 0 3 . 6 4 0 6 6 8 8 9 4 6 2 9 9 3 E - 0 1 . 1 5 1 7 0 4 0 7 1 9 2 7 8 2 8 + 0 1 . 8 8 8 8 7 7 0 4 5 3 6 3 1 9 E - O l . 9 9 5 7 5 2 7 0 5 2 6 1 1 1 8 + 0 0 . 6 8 7 9 1 8 3 1 1 4 5 0 6 3 E - 0 1 . 2 1 8 1 7 3 9 5 0 9 6 8 7 B E + 0 0 . 8 6 3 7 8 7 6 9 0 6 1 4 1 2 3 - 0 1 . 1 0 0 0 4 3 1 0 5 2 6 7 1 0 8 - 0 1 . 3 4 6 6 1 3 2 3 1 1 8 7 1 2 3 - 0 3 . 6 3 3 7 7 1 6 3 3 9 6 2 1 7 E + 0 0 . 8 8 8 8 8 1 9 2 5 4 9 3 4 8 E - 0 1 . 2 2 2 5 0 4 4 9 2 5 6 9 7 l E + 0 1 . 4 3 4 3 7 6 7 2 6 3 9 2 6 6 8 + 0 0 . 6 9 1 9 4 8 1 6 7 9 7 9 7 Z E + 0 0 . 1 9 8 6 9 9 1 2 6 4 8 5 7 4 E - O l . 1 9 2 7 8 2 5 7 8 7 8 6 1 4 E + 0 0 . 1 6 0 3 2 0 3 7 2 4 0 6 2 0 E - 0 1 . 6 2 0 4 8 3 1 9 2 5 0 6 0 7 E - 0 3 . 5 5 2 0 6 7 4 0 7 4 0 6 8 7 8 - 0 1 . 9 9 5 7 5 1 7 5 5 3 1 2 0 9 E + 0 0 . 4 3 4 3 7 7 2 7 7 2 6 9 9 6 E + 0 0 . 4 3 3 0 5 1 9 4 1 9 1 6 3 5 8 + 0 0 . 1 6 8 3 8 1 3 0 3 1 9 9 5 7 E + 0 0 . 4 7 2 1 8 9 7 8 5 7 9 6 2 2 3 - 0 1 . 1 4 4 9 1 0 3 9 3 3 3 3 7 0 E + 0 0 . 9 6 9 2 5 0 1 5 7 5 9 5 5 2 3 - 0 2 . 4 0 1 2 5 1 9 8 9 5 5 8 2 0 8 - 0 3 . 2 0 2 0 8 3 2 6 1 9 1 6 4 l E + 0 0 . 6 8 7 9 1 0 4 6 9 7 1 4 5 5 E - 0 1 . 6 9 1 9 4 8 7 3 5 1 5 5 1 7 E + 0 0 . 1 6 8 3 8 1 5 6 3 0 3 8 5 7 E + 0 0 . 2 5 4 2 8 7 7 8 3 1 1 4 7 l E + 0 0 . 2 6 6 9 5 2 6 3 2 9 1 1 8 5 8 + 0 0 . 8 6 0 1 2 7 2 8 4 5 4 0 7 9 8 - 0 1 . 5 6 6 6 0 7 3 7 7 5 9 5 5 7 8 - 0 2 . 2 4 1 8 6 5 4 1 4 6 5 0 9 9 E - 0 3 - . 4 4 6 9 7 0 5 8 6 1 9 9 3 l E - 0 2 I » ) ? > > > > > > > > > > > > > v > > v > > > > > v > > > > > > > > r > > > > > > > v > > > > > v > A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A o m m m m m m m m m m m m m m m m m m m m m m \ D m m m o m m m m w m m m m m m m ‘ o m m m m m m m m m Q Q Q V N V Q Q Q V Q Q Q V V Q V Q Q V Q \ I V V V \ q u q \ I Q Q Q Q Q Q Q Q N Q Q Q Q Q Q V O ‘ O ‘ O ‘ O ‘ V V ‘ V V V V V V V V V V ‘ V ‘ V V V V V V V V ‘ V ‘ V V V V V V V V V V V V V V ‘ V V V V V ‘ V V m m m m m m m m m m # # D b h fi b fi fi w w w w w w w w w k ) N N N N N N M N H H H H H H H I — ‘ H m m m m > m q m V > m > m V V V q m V l l q m V l l > m q m V l V l > m l q m V v m > m > m > m > m V V V V V V q m V q m V l fl l l q m l V q q V l l l q q V l q q l > m V " V ! q q > m I V V q q I > m V V q q > m V V I q > m V V \ q > m V V q q I I I I I I I I > m V u m V I v m V " q m V l > m V l q m V > m V q m V ' I l > m V q m l V > m V q m V l l l > m V q m V l > m V q m l V l > m V m q V l l > m V q l m V l > m V l q m V w V m n m V > V m \ m V > m V q m l fl l l l V l > m V q m l V l > w V V q m q m > m V V q m l l l l > m V l V q H l > m V l V q H l > m V V m H l l > m V V I m H > m V V m H " l l > m V V m H ' > m V V m I I fl v m I V V m — I v m V I V m I I > m V V I m H > m V V m I H I > m V m N V I > m V m N V > m V m V N > m m N V V > m m N V V > m m N V V 2 5 8 = ’ . 2 1 8 1 7 3 6 8 2 7 4 7 8 7 E + 0 0 - . l 9 8 7 0 1 5 7 2 9 5 3 7 Z E - 0 1 . 4 7 2 1 9 1 0 1 9 2 1 6 5 5 8 - 0 1 . 2 6 6 9 5 2 6 0 9 8 7 6 1 7 E + 0 0 . 9 4 9 2 7 1 7 2 3 4 3 8 8 7 E - 0 1 . 2 2 4 5 6 9 4 6 7 9 5 5 0 1 E - 0 1 . 1 5 0 0 2 3 1 4 7 3 7 5 5 8 8 - 0 2 . 6 2 7 7 4 7 2 4 8 2 4 5 2 1 E - 0 4 . 2 8 8 9 9 7 3 7 1 2 8 0 8 6 E - O l . 8 6 3 7 8 7 0 5 3 2 4 0 2 3 3 - 0 1 . 1 9 2 7 8 2 6 3 7 7 9 4 1 5 3 + 0 0 . 1 4 4 9 1 0 3 5 7 8 3 4 3 l E + 0 0 . 8 6 0 1 2 7 3 8 0 2 5 6 0 2 E - 0 1 . 2 2 4 5 6 9 4 5 2 4 9 3 6 0 8 - 0 1 . 5 0 5 5 4 4 7 1 7 1 5 7 1 4 8 - 0 2 . 3 3 4 3 8 7 6 2 2 3 0 2 7 6 E - 0 3 . 1 4 6 2 5 3 2 1 6 2 5 7 7 2 8 - 0 4 . 3 2 5 5 3 9 1 8 7 5 8 8 2 2 E - 0 2 . 1 0 0 0 4 3 1 7 8 2 4 4 9 6 E - 0 1 . 1 6 0 3 2 0 3 0 1 5 4 7 4 7 8 - 0 1 . 9 6 9 2 5 0 5 7 0 1 4 2 3 2 E - 0 2 . 5 6 6 6 0 7 2 4 4 0 1 3 5 4 8 - 0 2 . 1 5 0 0 2 3 1 7 4 2 5 1 1 5 8 - 0 2 . 3 3 4 3 8 7 5 9 9 0 5 3 8 0 8 - 0 3 . 2 2 3 5 7 5 0 6 1 3 0 8 8 8 E - 0 4 . 9 8 2 7 4 9 9 5 1 8 6 1 0 9 8 - 0 6 . 1 2 0 0 2 7 9 1 9 9 0 5 4 0 8 - 0 3 . 3 4 6 6 1 2 9 7 0 5 0 3 2 0 8 - 0 3 . 6 2 0 4 8 3 4 5 6 3 7 3 2 2 E - 0 3 . 4 0 1 2 5 1 8 3 5 4 2 7 2 7 8 - 0 3 . 2 4 1 8 6 5 4 6 7 6 8 5 9 0 8 - 0 3 . 6 2 7 7 4 7 1 2 9 2 6 4 8 3 8 - 0 4 . 1 4 6 2 5 3 2 2 9 4 0 7 2 0 8 - 0 4 . 9 8 2 7 4 9 8 9 8 2 9 2 8 3 8 - 0 6 . 4 5 2 9 5 7 9 4 8 9 0 9 1 8 8 - 0 7 . 7 3 2 0 2 9 9 0 8 3 3 6 7 0 E + 0 0 . 9 4 8 0 0 2 8 5 9 9 5 0 0 7 E - 0 1 . 3 3 6 0 3 0 4 8 3 6 1 8 3 8 8 + 0 1 . 1 6 5 8 1 0 0 8 6 3 9 1 8 7 E + 0 1 . 1 9 6 0 4 0 6 5 9 8 6 3 5 0 8 + 0 1 . 2 8 1 7 0 0 5 8 3 6 4 0 4 9 8 + 0 0 . 9 0 1 7 0 5 0 4 5 8 3 5 1 2 8 - 0 1 . 2 0 8 3 4 2 1 8 0 6 6 7 3 9 E - 0 1 . 1 6 8 3 1 0 6 3 4 2 9 6 6 3 E - 0 2 . 9 4 7 9 9 3 3 2 3 2 0 6 9 0 E - 0 1 8 ' . 5 2 2 2 6 5 7 3 0 7 9 8 2 4 E + 0 1 8 - . 3 1 5 8 3 9 5 6 1 0 7 4 9 7 E + 0 1 = - . 7 9 2 5 5 2 6 0 9 7 4 1 6 9 E + 0 1 = - . 3 6 1 2 3 0 0 1 6 3 1 3 4 9 8 + 0 1 = - . 1 0 6 5 2 3 5 2 5 8 0 8 0 1 8 + 0 1 2 5 9 - . 2 3 5 9 7 4 4 8 8 4 3 0 6 6 E + 0 0 . 4 8 9 9 8 8 0 3 8 4 6 1 8 9 E - 0 1 . 4 6 6 1 1 7 6 3 4 9 6 0 0 3 E - 0 2 . 3 3 6 0 3 0 9 2 4 6 9 2 7 5 E + 0 1 “ . 3 1 5 8 4 0 5 2 2 9 4 4 9 3 E + 0 1 . 1 3 3 4 8 9 6 4 8 7 7 4 2 7 E + 0 2 . 2 3 6 7 6 9 9 1 9 0 9 7 4 2 E + 0 1 . 7 0 4 4 8 9 4 2 3 7 0 7 1 3 E + O l . 4 3 6 1 0 2 2 0 6 8 1 8 7 6 E + 0 0 . 3 4 8 9 5 0 7 8 5 5 8 4 7 5 E + 0 0 . 1 3 5 1 8 4 6 5 0 9 6 4 2 2 E + 0 0 . 8 3 6 5 4 8 7 4 5 2 4 6 5 5 E - 0 2 . 1 6 5 8 0 9 6 5 2 7 6 8 0 8 E + 0 1 . 7 9 2 5 5 1 3 9 9 7 6 7 4 O E + 0 1 . 2 3 6 7 6 9 4 0 0 5 3 7 0 1 E + O l . 9 8 7 0 6 7 7 2 4 7 6 4 3 5 E + 0 1 . 1 2 2 8 4 2 7 3 4 6 7 9 5 8 E + 0 1 . 1 5 1 3 3 5 5 7 9 6 2 2 5 4 E + 0 1 . 7 0 4 1 4 3 9 4 1 4 0 2 4 4 E - O l . 9 8 4 0 0 5 9 5 7 4 3 4 4 Z E - O l . 4 9 1 8 9 6 4 8 6 0 9 6 2 7 3 - 0 2 . 1 9 6 0 4 1 0 0 1 8 4 5 1 5 8 + 0 1 . 3 6 1 2 3 0 7 1 0 7 0 7 6 O E + 0 1 . 7 0 4 4 9 0 0 1 2 3 0 2 9 9 E + 0 1 . 1 2 2 8 4 2 9 1 5 7 2 8 6 9 E + 0 1 . 3 6 0 8 8 9 4 5 6 6 0 7 4 O E + 0 1 . 3 5 8 7 3 1 8 8 8 7 0 0 2 8 E + 0 0 . 4 5 8 9 7 1 1 1 6 0 2 2 4 4 E + 0 0 . 6 9 0 9 1 9 2 9 7 1 5 7 9 6 E - 0 1 . 3 0 2 9 7 3 0 7 4 3 7 1 9 5 8 - 0 2 . 2 8 1 6 9 9 4 0 4 5 8 6 l l E + 0 0 . 1 0 6 5 2 3 2 8 1 5 2 2 1 0 8 + 0 1 . 4 3 6 1 0 0 0 2 1 0 0 4 6 8 8 + 0 0 . 1 5 1 3 3 5 4 8 2 2 0 6 2 0 8 + 0 1 . 3 5 8 7 3 2 0 7 2 8 6 9 3 2 8 + 0 0 . 1 2 2 1 1 9 8 1 4 6 2 3 1 5 3 - 0 1 . 1 7 7 8 0 6 9 7 1 2 3 0 8 9 E + 0 0 . 1 7 0 8 2 3 4 3 3 7 7 2 9 7 E - 0 1 . 7 6 2 8 5 1 3 2 4 5 3 7 9 1 8 - 0 3 . 9 0 1 7 0 7 3 2 5 8 2 9 1 9 3 - 0 1 . 2 3 5 9 7 5 0 1 6 3 7 4 1 4 E + 0 0 . 3 4 8 9 5 1 2 3 4 9 4 7 8 9 E + 0 0 . 7 0 4 1 4 1 7 0 6 2 2 8 2 6 3 - 0 1 . 4 5 8 9 7 1 1 8 0 0 5 0 8 7 E + 0 0 . 1 7 7 8 0 6 9 6 4 3 0 4 1 8 3 + 0 0 . 5 1 4 0 2 1 7 0 3 0 7 4 8 3 3 - 0 1 . 4 1 6 5 3 7 4 4 9 8 3 7 0 5 8 - 0 2 . 1 8 8 8 2 2 6 6 5 9 7 5 8 6 8 - 0 3 . 2 0 8 3 4 1 9 8 9 1 6 4 1 8 3 - 0 1 . 4 8 9 9 8 8 4 7 3 2 7 3 1 2 E - 0 1 N H ‘ D m e U ‘ D W N H m m e U ‘ D w N F - ‘ m m V a ‘ m p w N H ‘ D G ’ V O ‘ U ‘ Q W N H m m V O ‘ m p r F - ‘ K o m q v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V > 3 " ) > > v > > > > > > v > > v v w > > > > > > > > > > > > > > > > 3 , » > > > > > > > > v > w v w > A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A \ o u a m n o u o « n o x o u a m n o u a u n o \ o u a m n o x o u a m n o x o u a m n o x o u a m n o x o u a m n o u a m n o x o u a m n o x o u a m n o x o u a m n o x o V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V c n a a a n n o n a n m c n a a a u m c n o o a n w c n o o a n m c n o a a u n o o a u m c n a a a n n c n a a a n m c n a a a u m c n a a a u n o o a n w c n a a a n n c n V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V m m q q u a q q q q q m m m m m m m m m m m m m m m m m m p h p p p p p o b w w w w w w w w u m m m 2 6 0 . 1 3 5 1 8 4 6 1 0 1 0 2 4 4 E + 0 0 . 9 8 4 0 0 6 1 6 5 5 2 6 8 1 8 - 0 1 . 6 9 0 9 1 9 2 3 9 6 7 7 9 O E - O l . 1 7 0 8 2 3 4 4 2 5 8 5 9 7 3 - 0 1 . 4 1 6 5 3 7 4 4 7 1 9 9 5 2 8 - 0 2 . 3 2 1 8 6 4 8 7 3 1 2 9 1 3 3 - 0 3 . 1 4 4 5 1 8 4 7 1 9 7 6 1 6 E - 0 4 . 1 6 8 3 1 0 6 8 7 3 7 7 0 2 E - 0 2 . 4 6 6 1 1 7 5 0 8 7 2 2 1 6 8 - 0 2 . 8 3 6 5 4 8 8 6 0 0 2 4 7 8 E - 0 2 . 4 9 1 8 9 6 4 2 4 5 0 0 7 4 E - 0 2 . 3 0 2 9 7 3 0 9 0 6 0 6 4 3 8 - 0 2 . 7 6 2 8 5 1 3 0 0 3 7 9 4 5 8 - 0 3 . 1 8 8 8 2 2 6 6 6 6 5 7 9 8 8 - 0 3 . 1 4 4 5 1 8 4 7 2 1 1 8 2 7 3 - 0 4 . 6 7 9 7 7 0 6 5 8 3 7 3 8 8 8 - 0 6 . 7 0 1 0 8 2 2 6 9 5 4 9 3 7 E + 0 2 . 2 9 5 1 2 2 0 6 0 7 7 5 7 6 E + 0 2 . 2 8 2 7 5 5 7 7 8 1 9 3 4 7 E + 0 3 . 3 8 4 7 3 2 2 0 6 4 6 3 8 1 8 + 0 2 . 8 3 7 8 6 3 3 4 4 8 4 8 1 6 E + 0 2 . 3 1 7 0 3 1 6 8 8 9 8 8 2 1 8 + 0 0 . 5 8 1 0 0 8 9 3 3 7 6 3 9 5 E + 0 1 . 3 8 5 9 5 9 3 0 7 8 9 5 9 7 E - O l . 4 3 0 9 2 8 3 3 3 2 6 2 2 7 E - 0 1 . 2 9 5 1 2 1 8 7 4 8 0 9 2 7 E + 0 2 . 6 2 6 0 8 8 4 3 6 8 4 1 9 G E + 0 3 . 1 0 8 4 9 8 7 3 3 2 8 2 0 9 E + 0 3 . 5 4 3 9 2 2 7 1 2 4 4 5 2 6 3 + 0 3 . 4 1 8 4 4 7 7 0 9 0 8 3 5 6 E + O l . 6 9 7 3 2 8 0 3 6 4 2 7 S O E + 0 2 . 3 8 2 7 1 2 9 2 2 9 9 0 3 2 3 + 0 0 . 1 7 9 9 9 2 8 2 7 9 3 6 0 8 E + 0 1 . 8 5 5 2 6 2 6 6 5 8 6 3 8 5 3 - 0 1 . 2 8 2 7 5 5 8 2 2 0 6 2 4 S E + 0 3 . 1 0 8 4 9 8 8 3 4 6 0 9 9 9 3 + 0 3 . 1 0 5 8 2 6 7 0 8 3 4 0 6 4 E + 0 4 . 4 5 3 1 0 9 9 3 0 7 5 3 7 l E + 0 2 . 3 2 0 9 9 3 3 5 2 9 4 9 6 2 E + 0 3 . 2 4 0 5 5 3 2 4 8 0 7 7 6 3 E + 0 2 . 2 2 2 7 6 1 3 7 3 5 1 9 9 0 3 + 0 2 . 7 5 8 6 3 8 5 5 8 9 0 9 3 0 E + 0 0 . 2 2 9 5 8 6 9 6 6 7 2 8 6 8 8 + 0 0 . 3 8 4 7 3 1 6 6 7 0 4 1 7 8 E + 0 2 . 5 4 3 9 2 2 5 7 2 6 1 2 7 6 8 + 0 3 . 4 5 3 1 1 0 6 9 3 6 9 3 1 6 8 + 0 2 . 4 6 6 8 9 1 6 6 3 4 3 2 1 2 3 + 0 3 . 1 2 0 6 1 6 2 9 5 9 3 3 7 Z E + 0 2 . 5 9 1 6 3 9 9 1 9 4 3 0 0 2 8 + 0 2 . 2 2 7 6 0 3 5 4 5 4 1 2 4 2 E + 0 0 p o o o fi fi b w w w w w w w w w w w w w w w w N N H H H H H H H H H m m m m m m m m m m m m m m m m > > > > > > z ~ > v v > > > > > > v > > v > > > v y > v n v > > a v > z v y > c y z v > v > a y : v a v n v z v z v v v r v n » A A A A A A A A A A A A A A A A A A A A A A A A A A ’ V A A A A A A A A A A A A A A A A A A A A A A A m n o u a m n o u a m n o u a m n o u a m n o u a m n o u a m n o u : m n o u a m n o u a m n o u a m n o u a m n o u a m n o u a m n o u a m n o u a m n o u a m n o V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V \ o u a m n o u a m u n u a m n n u a m n o u a m n o u a m n o u a m n o u a m u n u a m n o u a m n o u a m n o c n a n m c n a n m c n a n m c n a n m c n a n m c n V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V “ I I I u a l l " " I ! " a l l » I I I " a l l " " I ! “ " I n " " I I " n " I I " " I I " " I n " " I I " " I I " " I I " " I I " I p p m m m m m m m m m m m m m m m m m m q q q q q q q q q m m m m m m m m m m m m m o m m m m ‘ ‘ ‘ 2 6 1 = ' . l 3 9 7 4 4 0 4 8 9 8 4 7 2 8 + 0 1 = . 1 3 5 3 8 3 2 0 2 5 0 5 1 8 E + 0 0 = . 8 3 7 8 6 3 6 9 6 8 1 3 5 8 8 + 0 2 = - . 4 1 8 4 5 4 9 8 6 8 1 0 6 8 E + 0 1 = . 3 2 0 9 9 3 4 1 5 4 1 5 2 9 8 + 0 3 = . 1 2 0 6 1 6 0 4 7 9 7 8 4 O E + 0 2 = . 9 2 0 4 0 5 7 9 7 3 6 2 3 3 E + 0 2 = - . 3 3 0 1 2 3 1 6 4 5 0 4 7 7 E + 0 1 = . 6 0 5 3 3 8 9 5 3 4 3 5 4 Z E + 0 1 = . 1 5 5 8 6 2 4 6 3 1 7 2 5 3 E + 0 0 = . 1 0 6 6 1 5 9 3 4 3 8 9 9 9 8 + 0 0 = . 3 1 7 0 1 9 7 6 8 0 5 9 2 5 E + 0 0 = - . 6 9 7 3 2 7 7 3 5 4 2 4 0 4 E + 0 2 = ' . 2 4 0 5 5 3 4 8 0 5 3 5 7 5 E + 0 2 = - . 5 9 1 6 3 9 8 1 5 7 1 7 9 4 E + 0 2 = - . 3 3 0 1 2 3 3 4 0 3 3 8 4 7 E + 0 1 = - . 6 5 1 1 9 6 6 9 1 7 6 6 3 B E + 0 1 = * . 5 7 9 0 7 l 7 6 8 0 9 3 8 5 3 + 0 0 = . 1 2 5 2 4 7 4 0 9 1 0 1 5 8 8 + 0 0 = . 2 6 2 3 3 8 3 3 1 1 5 8 3 9 8 - 0 1 = . 5 8 1 0 0 9 1 8 1 5 8 8 8 9 E + 0 1 = - . 3 8 2 7 1 8 6 3 3 8 6 0 3 S E + 0 0 = . 2 2 2 7 6 1 4 3 0 8 8 9 3 7 E + 0 2 = . 2 2 7 6 0 0 5 5 5 8 6 6 9 6 E + 0 0 = . 6 0 5 3 3 9 0 2 6 0 7 8 5 8 3 + 0 1 = - . 5 7 9 0 7 1 8 8 2 8 7 9 3 6 8 + 0 0 = . 7 6 1 5 1 4 3 6 9 6 3 1 1 9 E + 0 0 = . 9 8 2 4 3 4 5 1 9 3 5 5 5 9 E - O l = . 6 8 2 8 4 2 7 7 5 6 3 1 8 0 3 - 0 2 = - . 3 8 5 9 6 1 9 5 7 5 0 8 7 0 E - 0 1 = - . 1 7 9 9 9 2 7 6 5 8 1 6 8 6 3 + 0 1 = - . 7 5 8 6 3 9 1 8 0 1 0 1 4 S E + 0 0 = - . 1 3 9 7 4 4 0 1 8 9 0 3 0 0 8 + 0 1 = . 1 5 5 8 6 2 3 5 5 6 0 4 7 7 E + 0 0 = . 1 2 5 2 4 7 4 2 8 5 4 2 9 3 E + 0 0 = . 9 8 2 4 3 4 5 0 3 4 9 4 0 1 8 - 0 1 = . 8 1 5 7 5 5 5 6 8 5 5 5 6 9 E - 0 2 = . 5 1 0 2 9 0 5 2 3 5 3 6 1 3 3 - 0 3 = . 4 3 0 9 2 8 4 0 8 6 4 1 1 9 3 - 0 1 8 . 8 5 5 2 6 2 4 8 4 5 4 6 9 8 8 - 0 1 = . 2 2 9 5 8 6 9 8 4 7 4 3 9 5 E + 0 0 = . 1 3 5 3 8 3 1 9 2 7 3 3 5 7 E + 0 0 = . 1 0 6 6 1 5 9 3 7 5 3 3 2 1 8 + 0 0 = . 2 6 2 3 3 8 3 2 5 0 4 6 5 8 8 - 0 1 = . 6 8 2 8 4 2 7 8 0 3 1 5 7 0 E - 0 2 = . 5 1 0 2 9 0 5 2 2 6 9 7 6 9 8 - 0 3 = . 2 9 2 9 0 6 9 8 1 6 8 2 6 1 8 - 0 4 ) 3 . 1 0 4 4 4 6 1 6 1 9 8 9 9 3 E + 0 0 ) = . 1 5 8 5 4 1 2 5 5 5 2 9 6 0 E + 0 0 ) 8 . 8 1 7 5 9 6 7 2 5 3 9 1 9 2 E - 0 1 ‘ ‘ ‘ m m m m m m m m m m m m m m m m m m m \ o x o \ o m m m m m m m m m m m m m m m m m m m m m m m m w H H H V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V O O O V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V a w n » > r > > > v v v v > > > v > v > > v > > > a v > > > > > > r > > > z v v v v v v v > > > > v v > > v H H H m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m 2 6 2 A ( 1 0 , l , l , 4 ) = . 4 4 5 0 8 1 0 8 9 3 1 9 5 0 8 - 0 1 A ( 1 0 , l , 1 , 5 ) = . 1 3 4 9 1 8 7 4 0 2 7 2 9 5 E - 0 1 A ( 1 0 , l , l , 6 ) = . 4 1 1 2 6 5 3 3 6 3 9 0 4 4 8 - 0 2 A ( 1 0 , 1 , l , 7 ) = . 6 2 5 2 5 9 8 1 3 2 0 5 0 5 8 - 0 3 A ( 1 0 , 1 , 1 , 8 ) = . 9 1 0 5 1 8 0 6 9 9 0 0 9 5 8 - 0 4 A ( 1 0 , 1 , l , 9 ) = . 4 4 6 3 9 3 4 6 7 2 5 7 1 7 E - 0 5 A ( 1 0 , l , l , 1 0 ) = . 1 5 9 0 7 1 5 2 4 8 4 1 1 8 8 - 0 6 A ( 1 0 , l , 2 , 1 ) = . 1 5 8 5 4 1 2 5 7 6 7 5 1 O E + 0 0 A ( 1 0 , 1 , 2 , 2 ) = . 2 7 0 5 4 7 8 2 0 3 7 8 8 5 8 + 0 0 A ( 1 0 , l , 2 , 3 ) = . 1 6 9 6 2 7 3 7 2 9 9 7 6 4 E + 0 0 A ( 1 0 , l , 2 , 4 ) = . 9 1 9 9 9 7 7 2 4 1 5 8 7 5 8 - 0 1 A ( 1 0 , 1 , 2 , 5 ) = . 3 0 2 0 6 8 2 8 5 0 1 8 3 2 8 - 0 1 A ( 1 0 , l , 2 , 6 ) = . 8 9 8 9 0 9 7 2 4 3 1 0 2 2 3 - 0 2 A ( 1 0 , 1 , 2 , 7 ) = . 1 4 3 9 2 8 7 6 2 5 5 4 4 2 3 - 0 2 A ( 1 0 , 1 , 2 , 8 ) = . 2 0 4 7 8 7 9 8 9 8 7 2 5 6 3 - 0 3 A ( 1 0 , l , 2 , 9 ) = . 1 0 4 3 5 3 3 1 2 4 2 6 7 5 3 - 0 4 A ( 1 0 , l , 2 , 1 0 ) = . 3 6 5 5 5 4 0 6 1 4 6 5 5 5 E - 0 6 A ( 1 0 , 1 , 3 , l ) = . 8 1 7 5 9 6 6 7 7 3 0 6 9 4 E - O l A ( 1 0 , l , 3 , 2 ) = . 1 6 9 6 2 7 3 8 0 3 6 0 9 1 E + 0 0 a ( 1 0 , 1 , 3 , 3 ) = . 1 1 9 9 4 1 0 5 3 3 9 5 4 5 3 + 0 0 A ( 1 0 , 1 , 3 , 4 ) = . 6 8 8 4 7 2 0 2 3 1 2 0 9 9 E - 0 1 A ( 1 0 , l , 3 , 5 ) = . 2 3 5 7 9 9 1 0 8 3 4 0 8 7 E - 0 1 A ( 1 0 , l , 3 , 6 ) = . 7 0 9 7 9 1 7 6 3 6 6 5 6 3 E - 0 2 A ( 1 0 , 1 , 3 , 7 ) = . 1 1 5 7 0 4 0 0 6 7 4 8 2 7 E - 0 2 A ( 1 0 , l , 3 , 8 ) = . 1 6 4 3 5 3 6 8 8 2 7 6 7 2 8 - 0 3 A ( 1 0 , l , 3 , 9 ) = . 8 4 5 4 2 1 1 5 1 3 0 7 5 9 3 - 0 5 A ( 1 0 , l , 3 , 1 0 ) = . 2 9 4 5 1 0 7 8 0 7 0 7 3 0 8 - 0 6 A ( 1 0 , 1 , 4 , 1 ) = . 4 4 5 0 8 1 1 4 2 5 7 9 5 1 8 - 0 1 A ( 1 0 , 1 , 4 , 2 ) = . 9 1 9 9 9 7 6 2 0 3 1 2 6 4 8 - 0 1 A ( 1 0 , 1 , 4 , 3 ) = . 6 8 8 4 7 2 0 7 4 7 9 8 4 8 8 - 0 1 a ( 1 0 , 1 , 4 , 4 ) = . 4 1 4 1 4 9 1 2 6 6 0 9 1 2 3 - 0 1 A ( 1 0 , 1 , 4 , 5 ) = . 1 4 7 6 1 7 9 2 3 0 2 1 2 4 3 - 0 1 A ( 1 0 , 1 , 4 , 6 ) = . 4 5 7 8 2 9 5 2 3 4 5 2 3 5 3 - 0 2 A ( 1 0 , 1 , 4 , 7 ) = . 7 6 3 5 0 9 9 2 5 3 7 7 5 5 3 - 0 3 A ( 1 0 , 1 , 4 , 8 ) = . 1 1 0 6 2 6 3 2 4 0 8 7 0 9 3 - 0 3 A ( 1 0 , 1 , 4 , 9 ) = . 5 7 7 2 5 9 7 3 7 4 3 3 1 7 8 - 0 5 A ( 1 0 , 1 , 4 , 1 0 ) = . 2 0 4 2 8 9 8 1 0 9 1 5 0 3 8 - 0 6 A ( 1 0 , 1 , 5 , 1 ) = . 1 3 4 9 1 8 7 0 0 0 0 0 5 3 E - 0 1 A ( 1 0 , 1 , 5 , 2 ) = . 3 0 2 0 6 8 3 7 9 8 3 3 1 4 E - 0 1 A ( 1 0 , 1 , 5 , 3 ) = . 2 3 5 7 9 9 0 2 3 1 3 0 3 1 3 - 0 1 A ( 1 0 , 1 , 5 , 4 ) = . 1 4 7 6 1 7 9 5 9 7 2 8 4 5 E - 0 1 A ( 1 0 , 1 , 5 , 5 ) = . 5 3 9 4 2 5 2 8 5 7 5 1 3 5 E - 0 2 A ( 1 0 , 1 , 5 , 6 ) = . 1 7 0 6 7 6 1 2 8 3 1 1 7 0 8 - 0 2 A ( 1 0 , 1 , 5 , 7 ) = . 2 8 8 0 4 8 0 9 0 0 2 7 3 6 8 - 0 3 A ( 1 0 , 1 , 5 , 8 ) = . 4 2 0 7 0 1 3 8 0 8 9 6 5 6 8 - 0 4 A ( 1 0 , 1 , 5 , 9 ) = . 2 2 0 6 8 4 0 8 3 4 5 1 7 7 8 - 0 5 A ( 1 0 , 1 , 5 , 1 0 ) = . 7 8 2 2 7 2 3 2 7 6 7 9 0 2 8 - 0 7 A ( 1 0 , 1 , 6 , 1 ) = . 4 1 1 2 6 5 5 2 9 4 6 4 8 0 8 - 0 2 A ( 1 0 , 1 , 6 , 2 ; = . 8 9 8 9 0 9 2 5 3 1 6 9 2 2 8 - 0 2 A ( 1 0 , 1 , 6 , 3 . 7 0 9 7 9 2 2 3 6 2 3 9 0 8 E - 0 2 2 6 3 A ( 1 0 , 1 , 6 , 4 ) = . 4 5 7 8 2 9 2 8 1 7 3 1 3 9 8 - 0 2 A ( 1 0 , 1 , 6 , 5 ) = . 1 7 0 6 7 6 1 9 0 0 6 6 3 9 E - 0 2 A ( 1 0 , 1 , 6 , 6 ) = . 5 5 8 0 2 4 9 7 4 7 9 3 6 3 E - 0 3 A ( 1 0 , 1 , 6 , 7 ) = . 9 5 6 2 8 3 5 9 2 1 8 8 3 6 8 - 0 4 A ( 1 0 , 1 , 6 , 8 ) = . 1 4 3 6 9 0 2 9 5 5 9 0 9 1 8 - 0 4 A ( 1 0 , 1 , 6 , 9 ) = . 7 6 1 8 9 9 0 2 5 6 4 7 4 9 8 - 0 6 A ( 1 0 , 1 , 6 , 1 0 ) = . 2 7 6 8 3 7 9 3 2 6 1 2 6 3 8 - 0 7 A ( 1 0 , 1 , 7 , l ) = . 6 2 5 2 5 9 2 9 6 6 4 0 4 8 8 - 0 3 A ( 1 0 , 1 , 7 , 2 ) = . 1 4 3 9 2 8 8 9 7 3 0 1 7 5 8 - 0 2 A ( 1 0 , 1 , 7 , 3 ) = . 1 1 5 7 0 3 8 7 9 9 6 4 7 1 E - 0 2 A ( 1 0 , 1 , 7 , 4 ) = . 7 6 3 5 1 0 6 9 2 0 2 4 7 4 8 - 0 3 A ( 1 0 , 1 , 7 , 5 ) = . 2 8 8 0 4 7 8 3 0 0 5 3 9 8 3 - 0 3 A ( 1 0 , 1 , 7 , 6 ) = . 9 5 6 2 8 3 9 8 2 1 3 4 2 1 8 - 0 4 A ( 1 0 , l , 7 , 7 ) = . 1 6 5 0 7 5 4 7 8 4 4 2 1 3 8 - 0 4 A ( 1 0 , 1 , 7 , 8 ) = . 2 5 0 2 5 9 5 3 8 7 3 6 5 9 8 - 0 5 A ( 1 0 , 1 , 7 , 9 ) = . 1 3 3 1 9 4 5 9 5 3 5 3 1 0 8 - 0 6 A ( 1 0 , 1 , 7 , 1 0 ) = . 4 8 5 9 4 8 8 4 9 6 4 9 6 1 8 - 0 8 A ( 1 0 , 1 , 8 , l ) = . 9 1 0 5 1 8 8 0 3 7 1 3 9 6 8 - 0 4 A ( 1 0 , 1 , 8 , 2 ) = . 2 0 4 7 8 7 8 1 2 0 5 2 1 3 E - 0 3 A ( l O , l , 8 , 3 ) = . 1 6 4 3 5 3 8 7 4 7 2 3 1 3 8 - 0 3 A ( 1 0 , 1 , 8 , 4 ) = . 1 1 0 6 2 6 2 1 1 1 9 6 0 6 8 - 0 3 A ( 1 0 , 1 , 8 , 5 ) = . 4 2 0 7 0 1 7 8 9 3 1 6 5 2 3 - 0 4 A ( 1 0 , 1 , 8 , 6 ) = . 1 4 3 6 9 0 2 2 0 8 4 1 8 2 3 - 0 4 A ( 1 0 , 1 , 8 , 7 ) = . 2 5 0 2 5 9 5 9 8 9 9 9 4 9 8 - 0 5 A ( 1 0 , 1 , 8 , 8 ) = . 3 9 0 5 9 5 8 6 7 3 1 6 7 1 E - 0 6 A ( 1 0 , 1 , 8 , 9 ) = . 2 0 9 5 7 0 2 2 2 2 5 2 3 8 3 - 0 7 A ( 1 0 , 1 , 8 , 1 0 ) = . 7 8 6 2 3 4 4 8 5 2 8 6 2 4 3 - 0 9 A ( 1 0 , 1 , 9 , 1 ) = . 4 4 6 3 9 3 0 0 2 9 1 7 4 9 8 - 0 5 A ( 1 0 , l , 9 , 2 ) = . 1 0 4 3 5 3 4 3 2 4 4 6 3 0 8 - 0 4 a ( 1 o , 1 , 9 , 3 ) = . 8 4 5 4 1 9 9 5 4 6 6 4 8 1 3 - 0 5 A ( 1 0 , 1 , 9 , 4 ) = . 5 7 7 2 6 0 4 9 2 7 4 0 0 9 8 - 0 5 A ( 1 0 , 1 , 9 , 5 ) = . 2 2 0 6 8 3 8 2 3 0 3 7 8 6 3 - 0 5 A ( 1 0 , 1 , 9 , 6 ) = . 7 6 1 8 9 9 5 7 8 9 8 2 6 5 8 - 0 6 A ( 1 0 , 1 , 9 , 7 ) = . 1 3 3 1 9 4 5 5 1 6 9 3 5 8 8 - 0 6 A ( 1 0 , l , 9 , 8 ) = . 2 0 9 5 7 0 2 3 1 1 6 8 8 5 E - 0 7 A ( 1 0 , 1 , 9 , 9 ) = . 1 1 2 7 2 0 9 8 9 8 7 7 2 0 8 - 0 8 A ( 1 o , 1 , 9 , 1 0 ) = A 2 5 2 2 8 0 4 0 5 7 7 6 0 3 - 1 0 a ( 1 o , 1 , 1 o , 1 ) = . 1 5 9 0 7 1 6 0 7 3 8 6 2 6 8 - 0 6 A ( 1 0 , 1 , 1 0 , 2 ) : . 3 6 5 5 5 3 8 4 5 7 4 9 2 1 E - 0 6 A ( 1 0 , 1 , 1 0 , 3 ) = . 2 9 4 5 1 0 9 9 9 3 3 7 9 7 3 - 0 6 A ( 1 0 , 1 , 1 0 , 4 ) = . 2 0 4 2 8 9 6 8 2 9 6 1 8 2 8 - 0 6 a ( 1 o , 1 , 1 0 , 5 ) = . 7 8 2 2 7 2 7 1 4 5 9 1 7 5 3 - 0 7 A ( 1 0 , 1 , 1 0 , 6 ) = . 2 7 6 8 3 7 8 8 0 0 1 5 8 1 8 - 0 7 A ( 1 0 , 1 , 1 0 , 7 ) : . 4 8 5 9 4 8 7 9 0 3 2 2 0 7 8 - 0 8 A ( 1 0 , 1 , 1 0 , 8 ) = . 7 8 6 2 3 4 6 4 7 9 1 6 5 6 8 - 0 9 A ( 1 0 , 1 , 1 0 , 9 ) = A 2 5 2 2 7 9 3 2 1 5 7 3 8 3 - 1 0 A ( 1 0 , 1 , 1 0 , 1 0 ) = . 1 6 5 1 3 5 1 5 7 8 1 3 1 1 E - l l A ( 1 0 , 2 , 1 , 1 ) = - . 5 8 2 6 7 3 6 6 7 8 9 5 5 1 8 - 0 2 A ( 1 0 , 2 , 1 , 2 ) - . 6 2 6 8 5 6 3 4 0 3 4 0 9 6 E - 0 1 A ( 1 0 , 2 , 1 , 3 ) = . 6 7 4 6 3 8 5 0 9 6 1 7 5 8 E - 0 1 I I I I I I I I I I V V V V V I V I V o l v l l v l v l l v l l v l l v l l v l I v I I v I I o V I v I I v I I v I I v I I v I I v I I v I I v I I v I V o I I V A ( 1 0 , 2 , 2 A ( 1 0 , 2 , 2 A ( 1 0 , 2 , 4 , 1 A ( 1 0 , 2 , 4 , 2 ) = A ( 1 0 , 2 , 4 , 3 ) = A ( 1 o , 2 , 4 , 4 ) = A ( 1 0 , 2 , 4 , 5 ) = A ( 1 0 , 2 , 4 , 6 ) = A ( 1 0 , 2 , 4 , 7 ) = A ( 1 0 , 2 , 4 , 8 ) = A ( 1 0 , 2 , 4 , 9 ) = A ( 1 0 , 2 , 4 , 1 0 ) - A ( 1 0 , 2 , 5 , 1 ) = A ( 1 0 , 2 , 5 , 2 ) - A ( 1 0 , 2 , 5 , 3 ) = a ( 1 0 , 2 , 5 , 4 ) - A ( 1 0 , 2 , 5 , 5 ) = A ( 1 0 , 2 , 5 , 6 ) = A ( 1 0 , 2 , 5 , 7 ) = A ( 1 0 , 2 , 5 , 8 ) = A ( 1 0 , 2 , 5 , 9 ) = A ( 1 0 , 2 , 5 , 1 0 ) = A ( 1 0 , 2 , 6 , 1 ) = A ( 1 0 , 2 , 6 , 2 ) = A ( 1 0 , 2 , 6 , 3 ) = 2 6 4 . 2 6 9 2 4 9 4 2 0 0 1 6 4 Z E - O l . 1 0 2 9 6 8 3 1 1 0 9 8 2 7 E - O l . 2 5 6 9 9 9 1 6 2 4 5 6 8 5 3 - 0 2 . 4 6 3 2 7 4 1 3 9 7 1 8 8 1 3 - 0 3 . 5 7 8 9 7 9 8 3 9 9 2 9 1 6 8 - 0 4 . 3 2 4 2 7 2 6 1 9 2 8 9 8 0 E - 0 5 . 1 0 3 1 2 4 9 1 2 9 5 6 2 8 8 - 0 6 . 6 2 6 8 5 6 3 4 2 8 8 7 S S E - O l . 3 0 5 6 6 1 7 3 4 9 9 3 9 2 3 + 0 0 . 2 2 5 6 2 7 2 6 7 8 1 3 2 5 E + 0 0 . 1 1 2 1 6 1 5 3 1 0 2 9 4 l E + 0 0 . 3 8 5 6 5 3 4 3 4 4 5 0 4 3 E - 0 1 . 1 0 9 6 5 6 5 3 2 0 4 4 9 4 E - 0 1 . 1 8 1 5 9 2 9 9 7 5 5 7 8 0 2 - 0 2 . 2 5 0 2 7 2 2 4 7 8 3 9 6 9 8 - 0 3 . 1 3 0 9 0 6 6 6 1 4 6 6 3 1 8 - 0 4 . 4 4 8 3 1 3 7 2 9 6 3 9 6 0 E - 0 6 . 6 7 4 6 3 8 4 3 8 9 5 8 9 4 E - O l . 2 2 5 6 2 7 2 8 1 2 3 3 7 6 8 + 0 0 . 1 7 5 9 4 5 3 0 8 3 7 9 6 O E + 0 0 . 9 5 4 5 5 8 9 8 6 5 5 9 2 8 E - 0 1 . 3 3 4 0 5 7 5 7 9 7 3 0 1 4 E - 0 1 . 9 7 7 6 9 4 8 8 3 0 6 7 6 7 8 - 0 2 . 1 6 1 9 9 3 2 5 5 3 6 9 4 5 E - 0 2 . 2 2 5 8 1 4 6 7 9 1 8 3 1 5 E - 0 3 . 1 1 7 6 8 2 0 2 0 3 6 8 5 5 8 - 0 4 . 4 0 4 5 9 2 1 9 0 1 9 5 1 7 8 - 0 6 . 2 6 9 2 4 9 5 1 2 7 2 1 2 2 8 - 0 1 . 1 1 2 1 6 1 5 0 8 8 2 3 1 9 E + 0 0 . 9 5 4 5 5 9 1 0 2 2 1 0 6 2 8 - 0 1 . 5 4 7 8 5 7 3 4 9 1 9 2 7 B E - O l . 2 0 0 5 2 6 6 8 7 4 2 2 1 0 8 - 0 1 . 6 0 7 2 3 6 0 2 5 3 7 1 0 9 3 - 0 2 . 1 0 2 9 6 3 7 6 1 2 5 3 2 5 8 - 0 2 . 1 4 6 7 9 0 7 4 9 1 2 7 4 9 3 - 0 3 . 7 7 5 3 9 0 2 5 7 8 6 7 7 7 E - 0 5 . 2 7 1 3 4 1 7 1 8 4 8 2 9 8 3 - 0 6 . 1 0 2 9 6 8 2 4 9 1 2 5 3 0 8 - 0 1 . 3 8 5 6 5 3 6 0 1 3 7 0 0 0 E - 0 1 . 3 3 4 0 5 7 4 3 8 8 8 5 7 9 8 - 0 1 . 2 0 0 5 2 6 7 3 6 5 3 4 8 1 E - 0 1 . 7 4 7 2 1 7 5 4 0 6 2 9 2 1 3 - 0 2 . 2 3 1 6 8 6 5 9 9 1 3 6 0 8 3 - 0 2 . 3 9 5 7 5 8 0 8 2 1 0 6 5 7 8 - 0 3 . 5 7 0 3 5 9 2 0 2 6 4 0 7 0 8 - 0 4 . 3 0 1 8 5 4 2 1 7 7 9 9 0 5 3 - 0 5 . 1 0 6 0 2 1 1 9 9 5 6 9 5 9 E - 0 6 . 2 5 6 9 9 9 4 7 0 9 5 7 4 5 8 - 0 2 . 1 0 9 6 5 6 4 5 2 8 6 4 3 3 8 - 0 1 . 9 7 7 6 9 5 6 1 5 3 4 7 3 3 E - 0 2 V V V V V V o v v v v v v v v V O V V V V V V V V V O V V V A ( 1 0 , 2 , 7 , A ( 1 0 , 2 , 7 , A ( 1 0 , 2 , 7 , A ( 1 0 , 2 , 8 , A ( l O , 2 , 8 , A ( 1 0 , 2 , 8 , A ( 1 0 , 2 , 8 , A ( 1 0 , 2 , L A ( 1 0 , 2 , L A ( 1 L 2 , L A ( 1 L 2 , L A ( 1 0 , L L A ( 1 L L L A ( 1 L 2 , 9 , A ( 1 0 , 2 , 9 , A ( 1 L 2 , 9 , 3 4 5 6 7 8 9 , l , l , 2 , 3 , 4 , 5 , 6 , 7 8 9 l l 2 3 4 5 6 7 8 9 1 1 2 I I I I I I V I I I I l l I I I I I I I I U ' N V N I ' I I I I I I I I I I I I I U V H I I I ' U I I I I I A ( 1 0 , 2 , 9 , 4 ) = A ( 1 0 , 2 , 9 , 5 ) = A ( 1 0 , 2 , 9 , 6 ) = A ( 1 0 , 2 , 9 , 7 ) - A ( 1 0 , 2 , 9 , 8 ) = A ( 1 0 , 2 , 9 , 9 ) = A ( 1 0 , 2 , 9 , 1 0 ) = A ( 1 0 , 2 , 1 0 , 1 ) = A ( 1 0 , 2 , 1 0 , 2 ) = A ( 1 0 , 2 , 1 0 , 3 ) = A ( 1 0 , 2 , 1 0 , 4 ) = A ( 1 0 , 2 , 1 0 , 5 ) - A ( 1 0 , 2 , 1 0 , 6 ) = A ( 1 0 , 2 , 1 o , 7 ) = A ( 1 0 , 2 , 1 0 , 8 ) = A ( 1 0 , 2 , 1 0 , 9 ) = A ( 1 0 , 2 , 1 0 , 1 0 ) = A ( 1 0 , 3 , 1 , 1 ) = A ( 1 0 , 3 , 1 , 2 ) = - . 7 6 5 9 1 4 8 0 2 2 8 6 7 Z E - 0 2 A ( 1 0 , 3 , 1 , 3 ) = 2 6 5 . 6 0 7 2 3 5 6 2 2 3 2 8 5 2 8 - 0 2 . 2 3 1 6 8 6 7 1 2 1 6 3 5 4 8 - 0 2 . 7 4 4 3 7 3 4 9 8 3 7 8 0 8 3 - 0 3 . 1 2 9 2 1 5 1 3 0 5 7 0 5 1 E - 0 3 . 1 9 1 9 5 1 7 0 8 8 9 2 1 9 3 - 0 4 . 1 0 2 6 7 1 1 1 3 4 2 2 2 1 3 - 0 5 . 3 7 0 1 7 6 3 0 8 4 9 5 1 2 3 - 0 7 . 4 6 3 2 7 3 2 6 5 6 6 5 9 8 8 - 0 3 . 1 8 1 5 9 3 2 3 1 2 9 7 9 4 3 - 0 2 . 1 6 1 9 9 3 0 2 9 8 1 4 7 7 8 - 0 2 , . 1 0 2 9 6 3 8 9 0 7 1 9 8 2 3 - 0 2 . 3 9 5 7 5 7 6 5 2 8 2 5 0 7 8 - 0 3 . 1 2 9 2 1 5 2 0 0 5 5 8 9 7 8 - 0 3 . 2 2 5 3 8 7 9 2 8 3 7 4 2 3 E - 0 4 . 3 3 8 1 0 0 9 8 2 7 2 1 9 1 8 - 0 5 . 1 8 1 2 2 1 4 7 4 7 7 0 9 5 E - 0 6 . 6 5 6 4 7 3 4 8 4 6 0 0 4 1 8 - 0 8 5 7 8 9 8 1 1 9 5 9 2 8 9 2 3 - 0 4 2 5 0 2 7 1 8 9 6 3 1 9 9 9 8 - 0 3 2 2 5 8 1 5 0 3 4 4 5 4 5 1 8 - 0 3 1 4 6 7 9 0 5 4 4 7 7 5 4 0 E - 0 3 5 7 0 3 5 9 9 6 8 6 0 5 7 7 8 - 0 4 1 9 1 9 5 1 5 5 8 6 1 2 4 0 8 - 0 4 3 3 8 1 0 1 1 2 6 6 0 6 8 2 8 - 0 5 5 2 2 8 8 7 9 9 3 8 4 7 9 2 3 - 0 6 2 8 2 5 7 3 0 1 2 9 7 4 6 3 8 - 0 7 . 1 0 5 3 7 6 5 6 2 0 6 6 0 6 8 - 0 8 3 2 4 2 7 1 5 9 6 1 5 2 6 7 8 - 0 5 1 3 0 9 0 6 9 2 7 5 6 4 5 7 8 - 0 4 1 1 7 6 8 1 7 4 2 7 7 7 2 6 E - 0 4 7 7 5 3 9 1 9 0 7 0 3 7 4 6 E - 0 5 3 0 1 8 5 3 5 5 9 4 8 1 2 0 E - 0 5 1 0 2 6 7 1 2 6 1 9 1 4 5 4 E - 0 5 1 8 1 2 2 1 2 9 9 3 8 3 4 7 8 - 0 6 2 8 2 5 7 3 1 3 5 3 0 7 3 3 E - 0 7 1 5 2 9 2 4 4 2 5 0 3 2 8 4 E - 0 8 . 5 7 3 5 0 3 0 5 8 6 0 0 8 8 8 - 1 0 . 1 0 3 1 2 5 1 5 8 8 7 0 6 8 8 - 0 6 . 4 4 8 3 1 3 1 0 9 9 9 6 3 8 E - 0 6 . 4 0 4 5 9 2 8 4 2 7 8 4 2 7 8 - 0 6 . 2 7 1 3 4 1 3 0 1 1 5 0 1 4 E - 0 6 . 1 0 6 0 2 1 3 5 9 9 4 1 3 1 E - 0 6 . 3 7 0 1 7 5 9 3 1 5 3 9 7 1 E - 0 7 . 6 5 6 4 7 3 9 8 8 0 1 7 1 6 8 - 0 8 . 1 0 5 3 7 6 5 2 6 5 5 8 4 4 8 - 0 8 . 5 7 3 5 0 3 1 1 4 4 3 7 2 9 8 - 1 0 . 2 2 1 6 1 3 7 8 9 7 1 6 7 3 3 - 1 1 . 2 9 3 9 6 2 7 2 5 1 1 8 0 4 8 - 0 2 . 3 2 6 9 6 9 0 2 0 1 3 4 1 3 3 - 0 1 p V m V m V q V m V m t V - O I V H V N V w V - c V - V m V m V l V \ O o o V o V u V — V u V — I V N V w V b V - O m V m q V e V m V H V n V a V m m V q V m O m V H V H r V p V V I I I I I I I I I I V I I I I I I I I I I I I I I I I I I V I I I I I I I I I I I I I I I I I I V I I I I I I I I I I I I I I I I I I V I I I I I I I I I I I I A ( 1 0 , 3 , 5 , 6 ) = A ( 1 0 , 3 , 5 , 7 ) = A ( 1 0 , 3 , 5 , 8 ) = A ( 1 0 , 3 , 5 , 9 ) = A ( 1 0 , 3 , 5 , 1 0 ) = A ( 1 0 , 3 , 6 , 1 ) = A ( 1 0 , 3 , 6 , 2 ) = A ( 1 0 , 3 , 6 , 3 ) = 2 6 6 . 3 4 4 1 9 2 2 6 7 8 2 1 2 0 8 - 0 1 . 9 2 5 6 7 2 2 7 2 7 5 1 4 0 3 - 0 2 . 3 0 0 3 8 4 6 5 2 3 3 7 0 2 E - 0 2 . 4 3 3 6 7 6 8 6 3 3 9 4 7 9 3 - 0 3 . 6 5 1 2 9 4 2 3 2 4 8 3 2 2 8 - 0 4 . 3 0 8 7 5 6 5 9 0 1 6 1 6 1 3 ‘ 0 5 . 1 1 1 9 5 0 5 7 9 5 7 0 4 7 3 - 0 6 . 7 6 5 9 1 4 9 2 3 2 4 9 5 1 E - 0 2 . 2 8 0 2 6 8 9 5 1 7 1 9 3 4 8 - 0 1 . 2 2 0 5 3 0 2 3 7 1 0 7 6 O E + 0 0 . 1 3 6 7 2 7 3 2 0 8 5 9 7 9 E + 0 0 . 4 4 5 4 7 3 3 1 7 1 0 4 1 9 E - 0 1 . 1 3 0 5 7 2 6 6 6 4 1 2 2 6 E - O l . 2 1 1 9 3 6 4 3 2 2 6 5 2 5 E - 0 2 . 2 9 6 9 4 3 3 7 9 3 1 1 1 9 3 - 0 3 . 1 5 3 5 0 8 3 1 7 8 2 6 1 2 E - 0 4 . 5 3 1 3 9 0 1 5 7 2 6 5 6 7 3 - 0 6 . 3 2 6 9 6 9 0 6 0 6 0 6 6 4 E - 0 1 . 2 2 0 5 3 0 2 3 2 1 3 0 8 4 E + 0 0 . 2 9 6 4 8 8 2 9 0 5 8 7 1 5 3 + 0 0 . 1 6 1 3 5 1 8 8 2 9 5 0 8 4 E + 0 0 . 5 6 6 2 9 3 9 6 1 6 9 2 2 8 8 - 0 1 . 1 6 1 8 3 5 6 7 8 8 1 8 5 3 8 - 0 1 . 2 7 1 0 6 8 5 0 4 2 9 8 4 6 8 - 0 2 . 3 7 1 3 4 6 1 3 2 4 8 2 1 3 5 - 0 3 . 1 9 5 5 7 1 7 5 6 9 0 4 6 6 3 - 0 4 . 6 6 3 9 0 1 4 4 6 1 5 1 8 0 8 - 0 6 . 3 4 4 1 9 2 2 3 9 2 8 1 2 6 8 - 0 1 . 1 3 6 7 2 7 3 2 5 7 2 3 7 7 E + 0 0 . 1 6 1 3 5 1 8 7 5 3 8 3 8 4 E + 0 0 ' . 9 8 6 4 1 1 3 3 4 7 4 3 0 2 E - 0 1 . 3 5 1 6 5 0 7 6 0 2 5 8 0 5 E - 0 1 . 1 0 6 9 2 2 0 2 9 2 1 2 9 1 8 - 0 1 . 1 7 9 3 2 1 0 8 3 5 2 1 7 0 E - 0 2 . 2 5 6 1 7 7 5 7 9 0 1 8 4 1 E - 0 3 . 1 3 4 4 6 6 4 3 5 1 2 4 3 8 3 - 0 4 . 4 7 1 1 5 2 9 0 3 3 0 3 0 2 8 - 0 6 . 9 2 5 6 7 2 5 4 2 7 8 0 3 8 8 - 0 2 . 4 4 5 4 7 3 2 4 9 2 9 2 2 6 E - 0 1 . 5 6 6 2 9 4 0 1 3 6 4 2 6 2 E - 0 1 . 3 5 1 6 5 0 7 2 9 9 7 1 8 8 E - 0 1 . 1 3 0 2 7 4 5 5 9 2 2 3 8 4 8 - 0 1 . 4 0 1 4 7 7 6 3 3 0 4 5 0 3 8 - 0 2 . 6 8 5 8 0 8 2 8 9 6 8 8 3 4 8 - 0 3 . 9 8 3 1 0 6 3 0 0 9 3 5 7 9 8 - 0 4 . 5 2 0 8 2 9 7 5 7 8 1 0 7 6 8 - 0 5 . 1 8 2 1 9 1 4 1 6 5 3 6 7 5 3 - 0 6 . 3 0 0 3 8 4 5 4 5 1 9 8 5 4 8 - 0 2 . 1 3 0 5 7 2 6 8 6 6 7 5 8 1 3 - 0 1 . 1 6 1 8 3 5 6 5 4 6 6 2 3 5 E - 0 1 2 6 7 A ( 1 0 , 3 , 6 , 4 ) = . 1 0 6 9 2 2 0 4 2 2 3 2 3 3 E - 0 1 A ( 1 0 , 3 , 6 , 5 ) = . 4 0 1 4 7 7 5 7 9 0 2 1 0 5 E - 0 2 A ( 1 0 , 3 , 6 , 6 ) = . 1 2 9 5 4 3 7 4 6 3 7 9 5 7 E - 0 2 A ( 1 0 , 3 , 6 , 7 ) = . 2 2 3 4 9 0 5 9 8 7 8 4 7 9 E - 0 3 A ( 1 0 , 3 , 6 , 8 ) = . 3 3 2 3 7 6 4 6 4 1 6 4 9 5 8 - 0 4 A ( 1 0 , 3 , 6 , 9 ) = . 1 7 7 1 5 2 2 8 1 5 5 5 2 4 8 - 0 5 A ( 1 0 , 3 , 6 , 1 0 ) = . 6 3 8 8 7 0 5 1 7 2 5 2 7 5 8 - 0 7 A ( 1 0 , 3 , 7 , l ) = . 4 3 3 6 7 7 2 3 4 5 2 5 4 8 E - 0 3 A ( 1 0 , 3 , 7 , 2 ) = . 2 1 1 9 3 6 3 5 0 6 8 3 5 7 E - 0 2 A ( 1 0 , 3 , 7 , 3 ) = . 2 7 1 0 6 8 5 8 7 0 3 9 7 4 E - 0 2 A ( 1 0 , 3 , 7 , 4 ) = . 1 7 9 3 2 1 0 2 1 9 4 8 9 1 3 - 0 2 A ( 1 0 , 3 , 7 , 5 ) = . 6 8 5 8 0 8 4 2 8 8 4 1 0 3 3 - 0 3 A ( 1 0 , 3 , 7 , 6 ) = . 2 2 3 4 9 0 5 7 0 8 1 7 8 3 E - 0 3 A ( 1 0 , 3 , 7 , 7 ) = . 3 8 9 7 2 3 4 4 7 1 8 5 0 2 3 - 0 4 A ( 1 0 , 3 , 7 , 8 ) = . 5 8 3 0 2 2 8 1 6 1 5 8 5 2 8 - 0 5 A ( 1 0 , 3 , 7 , 9 ) = . 3 1 2 5 8 2 8 4 1 2 7 7 5 5 8 - 0 6 A ( 1 0 , 3 , 7 , 1 0 ) = . 1 1 2 9 6 3 6 1 8 7 7 1 6 1 3 - 0 7 A ( 1 0 , 3 , 8 , l ) = . 6 5 1 2 9 3 5 4 0 1 3 0 3 8 8 - 0 4 A ( 1 0 , 3 , 8 , 2 ) = . 2 9 6 9 4 3 5 1 8 5 7 7 5 6 E - 0 3 A ( 1 0 , 3 , 8 , 3 ) = . 3 7 1 3 4 5 9 7 1 9 5 6 3 2 3 - 0 3 A ( 1 0 , 3 , 8 , 4 ) = . 2 5 6 1 7 7 6 7 7 0 1 6 4 7 E - 0 3 A I 1 0 , 3 , 8 , 5 ) = . 9 8 3 1 0 5 9 4 3 5 3 2 7 9 8 - 0 4 A ( 1 0 , 3 , 8 , 6 ) = . 3 3 2 3 7 6 5 6 1 2 2 5 0 9 8 - 0 4 A I 1 0 , 3 , 8 , 7 ) = . 5 8 3 0 2 2 7 0 2 1 1 6 4 1 E - 0 5 A ( 1 0 , 3 , 8 , 8 ) = . 9 0 2 7 8 0 8 4 2 9 7 0 6 9 8 - 0 6 A I 1 0 , 3 , 8 , 9 ) = . 4 8 6 7 4 6 7 1 8 4 1 7 2 0 8 - 0 7 A ( 1 0 , 3 , 8 , 1 0 ) = . 1 8 1 5 5 3 5 1 0 2 2 4 7 7 E - 0 8 A ( 1 0 , 3 , 9 , l ) = . 3 0 8 7 5 7 0 9 6 8 6 7 4 0 E - 0 5 A ( 1 0 , 3 , 9 , 2 ) = . 1 5 3 5 0 8 2 0 1 2 0 8 3 0 8 - 0 4 A ( 1 0 , 3 , 9 , 3 ) = . 1 9 5 5 7 1 8 7 7 5 5 4 8 1 8 - 0 4 A ( 1 0 , 3 , 9 , 4 ) = . 1 3 4 4 6 6 3 5 9 5 2 2 6 3 8 - 0 4 A ( 1 0 , 3 , 9 , 5 ) = . 5 2 0 8 3 0 0 8 1 5 5 1 7 9 3 - 0 5 A ( 1 0 , 3 , 9 , 6 ) = . 1 7 7 1 5 2 1 9 8 7 5 4 8 0 3 - 0 5 A ( 1 0 , 3 , 9 , 7 ) = . 3 1 2 5 8 2 9 5 5 0 1 9 9 0 8 - 0 6 A ( 1 0 , 3 , 9 , 8 ) = . 4 8 6 7 4 6 6 6 0 1 3 0 4 9 E - 0 7 A ( 1 0 , 3 , 9 , 9 ) = . 2 6 3 4 4 8 2 6 2 9 4 4 4 7 3 - 0 8 A ( 1 0 , 3 , 9 , 1 0 ) = . 9 8 6 6 0 0 7 4 7 2 5 2 6 4 8 - 1 0 A ( 1 0 , 3 , 1 0 , l ) = . 1 1 1 9 5 0 4 3 9 9 7 3 8 1 8 - 0 6 A ( 1 0 , 3 , 1 0 , 2 ) = . 5 3 1 3 9 0 5 1 9 4 2 0 4 2 3 - 0 6 A ( 1 0 , 3 , 1 0 , 3 ) = . 6 6 3 9 0 1 0 7 1 1 7 3 9 8 8 - 0 6 A ( 1 0 , 3 , 1 0 , 4 ) = . 4 7 1 1 5 3 1 4 2 6 1 1 5 9 E - 0 6 A ( 1 0 , 3 , 1 0 , 5 ) = . 1 8 2 1 9 1 3 1 3 6 4 6 8 3 E - 0 6 A ( 1 0 , 3 , 1 0 , 6 ) = . 6 3 8 8 7 0 7 8 3 6 3 6 8 9 E - 0 7 A ( 1 0 , 3 , 1 0 , 7 ) = . 1 1 2 9 6 3 5 7 2 2 1 1 6 3 E - 0 7 A ( 1 0 , 3 , 1 0 , 8 ) = . 1 8 1 5 5 3 5 5 0 2 7 5 2 0 E - 0 8 A ( 1 0 , 3 , 1 0 , 9 ) = . 9 8 6 6 0 0 5 6 0 4 9 8 8 1 8 - 1 0 A ( 1 0 , 3 , 1 0 , 1 0 ) = . 3 8 1 3 4 8 2 9 7 4 9 7 1 6 E - 1 1 A ( 1 0 , 4 , 1 , 1 ) = - . 3 5 1 4 7 0 8 1 9 9 8 7 3 0 8 - 0 2 A ( 1 0 , 4 , 1 , 2 ) = . 1 6 0 3 7 6 1 4 4 0 4 9 2 2 8 - 0 2 A ( 1 0 , 4 , 1 , 3 ) = ' . 7 6 7 2 0 4 7 4 3 1 6 9 7 1 3 - 0 2 o v v v I I V I I I I I I I I I I I I I I I I I I V I I I I I I I I I I I I I I I I I I V I I I I I I I I I I I I I I I I I I V I I I I I I I I I I I I A ( 1 0 , 4 , 5 , 2 ) = A ( 1 0 , 4 , 5 , 3 ) = A ( 1 0 , 4 , 5 , 4 ) = A ( 1 0 , 4 , 5 , 5 ) = A ( 1 0 , 4 , 5 , 6 ) = A ( 1 0 , 4 , 5 , 7 ) = A ( 1 0 , 4 , 5 , 8 ) = A ( 1 0 , 4 , 5 , 9 ) A ( 1 0 , 4 , 5 , 1 I I I I I I V I I 2 6 8 . 2 4 9 9 3 9 2 6 2 5 0 3 1 8 8 - 0 1 . 1 8 4 5 8 5 3 2 1 3 8 5 3 8 E - O l . 4 1 7 1 6 4 2 2 2 8 3 5 7 l E - 0 2 . 7 8 5 5 6 1 1 5 6 9 3 1 1 8 E - 0 3 . 9 4 6 7 9 7 1 0 1 1 6 4 5 2 E - 0 4 . 5 3 9 4 0 2 7 3 5 2 7 7 8 6 8 - 0 5 . 1 6 7 8 2 3 2 0 5 4 9 9 1 3 8 - 0 6 . 1 6 0 3 7 5 5 9 7 2 6 1 0 1 8 - 0 2 . 2 0 4 7 8 4 7 5 7 2 2 4 8 4 E - O l . 1 8 4 3 9 1 2 3 5 9 6 1 8 1 E - 0 1 . 1 6 2 2 1 3 2 8 6 8 5 0 6 0 E + 0 0 . 7 7 8 2 4 1 6 5 8 6 6 3 3 Z E - O l . 2 0 2 0 0 3 9 1 0 7 8 1 0 6 E - 0 1 . 3 5 6 3 7 2 5 0 2 6 1 9 7 1 8 - 0 2 . 4 7 0 5 1 0 2 5 3 1 3 7 4 9 8 - 0 3 . 2 5 5 9 3 9 3 7 5 5 0 6 3 9 E - 0 4 . 8 5 4 0 6 1 4 4 6 6 7 5 6 6 8 - 0 6 . 7 6 7 2 0 1 8 8 2 6 2 6 9 8 3 - 0 2 . 1 8 4 3 9 1 9 0 7 0 9 6 1 4 E - O l . 1 4 8 9 3 5 2 2 4 4 3 8 9 0 E + 0 0 . 2 6 1 3 6 1 6 1 8 5 9 9 0 4 E + 0 0 . 9 4 5 7 6 9 4 0 6 7 5 3 2 4 E - 0 1 . 2 7 4 2 5 2 1 9 7 4 5 0 5 5 8 - 0 1 . 4 4 9 4 8 7 8 0 2 4 1 6 1 2 8 - 0 2 . 6 2 5 7 7 6 1 5 8 9 2 6 7 8 E - 0 3 . 3 2 3 7 0 8 8 1 2 6 4 3 9 9 3 - 0 4 . 1 1 1 2 1 5 8 4 4 2 6 7 3 2 E - 0 5 . 2 4 9 9 3 8 7 9 0 3 2 9 9 l E - 0 1 . 1 6 2 2 1 3 3 8 8 0 6 6 4 S E + 0 0 . 2 6 1 3 6 1 5 3 7 6 9 0 3 9 B + 0 0 . 2 1 0 5 6 1 1 2 1 3 4 8 2 9 E + 0 0 . 7 9 0 2 1 4 1 7 4 5 9 4 4 4 3 - 0 1 . 2 3 2 9 9 2 8 3 5 3 3 5 6 1 8 - 0 1 . 3 9 4 2 8 5 8 6 0 6 0 2 3 9 E - 0 2 . 5 5 4 6 2 2 1 2 6 4 0 1 2 3 E - 0 3 . 2 9 3 0 5 4 5 2 3 1 9 0 5 1 8 - 0 4 . 1 0 1 6 8 6 3 8 1 6 2 6 1 1 8 - 0 5 . 1 8 4 5 8 5 6 6 6 8 2 9 6 6 8 - 0 1 . 7 7 8 2 4 0 9 0 1 3 4 5 2 7 3 - 0 1 . 9 4 5 7 7 0 0 1 9 0 9 7 8 4 3 - 0 1 . 7 9 0 2 1 3 9 3 5 0 3 3 5 3 E - O l . 3 0 1 1 9 5 5 8 7 3 2 6 2 2 E - 0 1 . 9 1 5 7 5 9 8 6 5 3 4 7 3 5 8 - 0 2 . 1 5 5 9 4 3 7 9 2 7 6 5 3 6 E - 0 2 . 2 2 2 3 4 6 2 7 6 9 5 6 3 9 3 - 0 3 . 1 1 7 5 0 4 1 9 7 7 1 4 1 7 E - 0 4 . 4 0 9 7 6 4 8 3 4 0 0 8 4 5 E - 0 6 . 4 1 7 1 6 2 8 5 6 1 3 8 0 2 E - 0 2 . 2 0 2 0 0 4 2 2 7 2 6 7 0 3 8 - 0 1 . 2 7 4 2 5 1 8 9 6 8 2 6 1 7 8 - 0 1 2 6 9 A ( 1 0 , 4 , 6 , 4 ) = . 2 3 2 9 9 2 9 6 6 5 2 1 1 2 3 - 0 1 A ( 1 0 , 4 , 6 , 5 ) = . 9 1 5 7 5 9 5 2 3 8 3 2 0 9 8 - 0 2 A ( 1 0 , 4 , 6 , 6 ) = . 2 9 0 1 5 1 4 4 1 2 3 1 5 0 3 - 0 2 A ( 1 0 , 4 , 6 , 7 ) = . 5 0 3 3 3 5 7 8 4 0 0 3 4 1 8 - 0 3 A ( 1 0 , 4 , 6 , 8 ) = . 7 4 1 8 0 1 0 9 8 3 4 2 8 8 E - 0 4 A ( l O , 4 , 6 , 9 ) = . 3 9 6 5 4 1 9 3 9 0 1 8 3 9 8 - 0 5 A ( 1 0 , 4 , 6 , 1 0 ) = . 1 4 2 1 7 0 1 4 4 4 6 2 6 1 3 - 0 6 A ( 1 0 , 4 , 7 , 1 ) = . 7 8 5 5 6 4 7 4 8 5 2 5 7 6 8 - 0 3 A ( 1 0 , 4 , 7 , 2 ) = . 3 5 6 3 7 1 6 3 3 8 7 0 3 7 8 - 0 2 A ( 1 0 , 4 , 7 , 3 ) = . 4 4 9 4 8 8 6 1 2 2 7 5 6 7 E - 0 2 A ( 1 0 , 4 , 7 , 4 ) = . 3 9 4 2 8 5 4 3 5 8 4 5 6 3 8 - 0 2 A ( 1 0 , 4 , 7 , 5 ) = . 1 5 5 9 4 3 9 3 6 7 3 8 3 7 8 - 0 2 A ( 1 0 , 4 , 7 , 6 ) = . 5 0 3 3 3 5 5 4 0 8 8 4 1 1 E - 0 3 A ( 1 0 , 4 , 7 , 7 ) = . 8 7 8 1 2 3 8 5 1 6 0 6 4 6 2 - 0 4 A ( 1 0 , 4 , 7 , 8 ) = . 1 3 0 8 1 4 8 2 0 8 6 0 0 8 E - 0 4 A ( 1 0 , 4 , 7 , 9 ) = . 7 0 0 9 6 4 3 2 7 6 9 3 4 0 3 - 0 6 A ( 1 0 , 4 , 7 , 1 0 ) = . 2 5 2 5 9 1 9 2 8 8 3 1 5 4 8 - 0 7 A ( 1 0 , 4 , 8 , l ) = . 9 4 6 7 9 1 6 1 9 1 8 5 2 1 3 - 0 4 A ( 1 0 , 4 , 8 , 2 ) = . 4 7 0 5 1 1 6 2 0 7 9 0 1 5 E - 0 3 A ( 1 0 , 4 , 8 , 3 ) = . 6 2 5 7 7 4 7 9 8 3 2 2 7 1 E - 0 3 A ( 1 0 , 4 , 8 , 4 ) = . 5 5 4 6 2 2 8 8 2 6 4 6 0 7 8 - 0 3 A ( 1 0 , 4 , 8 , 5 ) = . 2 2 2 3 4 6 0 1 0 9 2 9 1 9 3 - 0 3 A ( 1 0 , 4 , 8 , 6 ) = . 7 4 1 8 0 1 6 9 1 5 0 3 9 5 E - 0 4 A ( 1 0 , 4 , 8 , 7 ) = . 1 3 0 8 1 4 7 5 5 3 6 5 8 0 3 - 0 4 A ( 1 0 , 4 , 8 , 8 ) = . 2 0 1 3 2 3 0 0 0 6 0 3 7 1 3 - 0 5 A ( 1 0 , 4 , 8 , 9 ) = . 1 0 8 8 1 5 3 8 0 9 2 8 1 1 8 - 0 6 A ( 1 0 , 4 , 8 , 1 0 ) = . 4 0 4 2 4 3 6 9 9 5 8 2 0 7 E - 0 8 A ( 1 0 , 4 , 9 , l ) = . 5 3 9 4 0 6 9 2 2 5 0 6 2 0 E - 0 5 A ( 1 0 , 4 , 9 , 2 ) = . 2 5 5 9 3 8 3 3 9 5 3 5 0 8 3 - 0 4 A ( 1 0 , 4 , 9 , 3 ) = . 3 2 3 7 0 9 8 6 4 8 1 5 6 7 E - 0 4 A ( 1 0 , 4 , 9 , 4 ) = . 2 9 3 0 5 3 9 0 0 4 7 0 8 5 E - 0 4 A ( 1 0 , 4 , 9 , 5 ) = . 1 1 7 5 0 4 4 3 0 8 4 3 2 4 8 - 0 4 A ( 1 0 , 4 , 9 , 6 ) = . 3 9 6 5 4 1 3 9 2 5 6 6 6 2 3 - 0 5 A ( 1 0 , 4 , 9 , 7 ) = . 7 0 0 9 6 5 0 6 7 5 4 6 0 2 3 - 0 6 A ( 1 0 , 4 , 9 , 8 ) = . 1 0 8 8 1 5 3 3 3 8 5 4 6 5 3 - 0 6 A ( 1 0 , 4 , 9 , 9 ) = . 5 8 9 1 1 6 3 1 0 5 9 5 3 3 8 - 0 8 A ( 1 0 , 4 , 9 , 1 0 ) = . 2 2 0 1 3 8 7 2 3 6 5 6 2 5 8 - 0 9 A ( 1 0 , 4 , 1 0 , 1 ) = . 1 6 7 8 2 2 0 8 9 5 5 8 4 6 E - 0 6 A ( 1 0 , 4 , 1 0 , 2 ) = . 8 5 4 0 6 4 1 4 9 7 3 5 6 6 8 - 0 6 A ( 1 0 , 4 , 1 0 , 3 ) = . 1 1 1 2 1 5 5 6 4 4 0 2 3 0 E - 0 5 A I 1 0 , 4 , 1 0 , 4 ) = . 1 0 1 6 8 6 5 4 9 4 4 7 4 2 E - 0 5 A ( 1 0 , 4 , 1 0 , 5 ) = . 4 0 9 7 6 4 1 7 8 5 8 8 2 9 8 - 0 6 A ( 1 0 , 4 , 1 0 , 6 ) = . 1 4 2 1 7 0 3 1 2 2 7 2 8 2 E - 0 6 A ( 1 0 , 4 , 1 0 , 7 ) = . 2 5 2 5 9 1 6 7 2 5 4 3 4 9 8 - 0 7 A ( 1 0 , 4 , 1 0 , 8 ) = . 4 0 4 2 4 3 9 0 7 5 3 2 0 5 8 - 0 8 A ( 1 0 , 4 , 1 0 , 9 ) = . 2 2 0 1 3 8 6 4 8 6 8 3 6 7 E - 0 9 A ( 1 0 , 4 , 1 0 , 1 0 ) = . 8 4 8 6 1 7 8 8 9 3 0 1 2 9 E - 1 1 A ( 1 0 , 5 , 1 , 1 ) = . 1 2 1 1 8 8 8 3 0 2 3 5 0 4 8 - 0 2 A ( 1 0 , 5 , 1 , 2 ) = - . 9 9 3 0 6 5 5 3 6 0 2 2 1 9 E ' 0 3 A ( 1 0 , 5 , 1 , 3 ) = - . 5 8 0 8 2 1 6 2 8 6 8 2 3 Z E - 0 2 v v v v v v O V V V V V V V V V O V V V V V V V V V O V V V J V V V J V V V V I I I I I I I I I I I I I I I I I I V I I I I I I I I I I I I I I I I I I V I I I I I I I I I I I I I I I I I I V I I I I I I I I I I I I I A ( 1 0 , 5 , 4 , 1 0 A ( 1 0 , 5 , 5 , 1 ) = A ( 1 0 , 5 , 5 , 2 ) = A ( 1 0 , 5 , 5 , 3 ) = A ( 1 0 , 5 , 5 , 4 ) = A ( 1 0 , 5 , 5 , 5 ) = A ( 1 0 , 5 , 5 , 6 ) = A ( 1 0 , 5 , 5 , 7 ) = A ( 1 0 , 5 , 5 , 8 ) = A ( 1 0 , 5 , 5 , 9 ) = A ( 1 0 , 5 , 5 , 1 0 ) A ( 1 0 , 5 , 6 , 1 ) = A ( 1 0 , 5 , 6 , 2 ) - A ( 1 0 , 5 , 6 , 3 ) - 2 7 0 . 1 1 5 3 4 7 7 1 3 5 8 1 2 9 8 ‘ 0 1 . 1 7 6 0 0 0 7 9 9 8 3 8 2 2 E - 0 1 . 1 1 1 6 4 0 8 7 0 1 0 9 1 1 8 - 0 1 . 1 5 3 2 5 4 2 7 5 6 1 9 4 7 8 - 0 2 . 2 3 0 2 6 4 8 2 8 1 8 9 7 7 8 - 0 3 . 1 0 9 4 8 5 9 8 7 2 8 0 7 8 3 - 0 4 . 3 8 9 7 8 0 3 0 3 3 6 7 0 0 8 - 0 6 . 9 9 3 0 5 6 1 0 6 3 8 1 1 2 8 - 0 3 . 7 9 3 4 7 5 8 9 6 3 5 2 9 0 8 - 0 2 . 3 5 6 3 7 0 0 3 6 3 1 5 6 4 E - O l . 3 1 1 0 7 9 9 9 6 7 5 4 4 2 3 - 0 2 . 1 1 5 9 5 7 0 4 5 8 2 5 7 8 8 + 0 0 . 5 2 4 6 8 9 2 3 1 3 1 5 2 8 3 - 0 1 . 7 6 7 3 4 0 1 6 9 4 7 7 3 9 E - 0 2 . 1 1 5 5 8 1 3 5 6 5 3 3 3 1 8 - 0 2 . 5 6 9 4 0 8 8 2 8 2 8 3 7 1 8 - 0 4 . 2 0 5 3 9 4 4 5 4 2 8 9 0 2 8 - 0 5 . 5 8 0 8 2 4 3 9 9 3 6 6 9 7 8 - 0 2 . 3 5 6 3 7 0 2 3 6 2 5 8 9 5 E ' 0 1 . 8 2 8 7 1 1 2 7 1 1 6 9 6 0 8 - 0 1 . 6 9 3 1 4 8 9 6 5 0 7 4 2 2 8 - 0 1 . 1 9 5 9 0 7 5 2 4 6 1 2 2 7 E + 0 0 . 6 1 7 1 3 1 9 8 6 1 4 5 9 8 8 - 0 1 . 1 0 2 1 4 0 1 7 4 0 4 9 0 5 E - 0 1 . 1 3 9 5 2 6 2 2 9 4 8 6 3 6 8 - 0 2 . 7 3 4 5 6 8 5 0 0 8 8 8 6 0 3 - 0 4 . 2 4 7 9 3 9 3 9 0 0 8 5 6 1 3 - 0 5 . 1 1 5 3 4 7 5 6 3 4 0 5 5 2 3 - 0 1 . 3 1 1 0 7 0 6 6 0 2 4 5 6 0 E - 0 2 . 6 9 3 1 4 9 4 2 8 4 0 7 2 0 8 - 0 1 . 2 9 4 2 7 8 0 2 1 4 3 6 1 8 8 + 0 0 . 1 8 2 2 0 3 5 6 7 1 9 3 9 4 E + 0 0 . 5 5 8 9 3 5 5 5 3 0 5 3 7 4 E - O l . 9 4 5 6 2 5 5 1 2 8 4 9 8 0 3 - 0 2 . 1 3 2 6 9 8 8 4 4 9 5 9 1 2 8 - 0 2 . 7 0 3 2 6 8 0 5 6 8 3 8 6 2 8 - 0 4 . 2 4 3 5 4 6 4 1 2 8 8 1 3 8 8 - 0 5 . 1 7 6 0 0 0 6 8 1 6 7 6 6 7 8 - 0 1 . 1 1 5 9 5 7 0 7 9 3 9 7 0 5 E + 0 0 . 1 9 5 9 0 7 4 9 4 6 9 3 5 3 E + 0 0 . 1 8 2 2 0 3 5 8 5 1 0 7 3 S E + 0 0 . 8 6 4 1 2 1 3 0 5 4 2 1 5 8 8 - 0 1 . 2 7 0 7 4 1 4 0 7 9 8 5 0 4 E - O l . 4 5 4 3 5 3 1 3 7 1 3 8 2 4 3 - 0 2 . 6 4 5 9 0 4 5 2 8 2 5 5 4 1 E - 0 3 . 3 3 9 5 9 0 5 2 8 7 1 0 6 9 8 - 0 4 . 1 1 8 0 5 9 0 0 6 3 4 8 7 6 3 - 0 5 . 1 1 1 6 4 0 9 2 0 4 4 O S S E - O l . 5 2 4 6 8 9 1 0 5 0 4 1 0 3 8 - 0 1 . 6 1 7 1 3 2 0 8 0 2 2 4 1 1 8 - 0 1 V V I I I I I I I I I I I I I I I I I I V I I I I I I I I I I I I I I I I I I V I I I I I I I I I I I I I I I I I I V I I I I I I I I I I I I I I H O v v v v v v v v v o v v v v v v v v v o V V V V V V V V V O V V V V V V A ( 1 0 , 5 , 1 0 , 2 ) = A ( 1 0 , S , 1 0 , 3 ) = A ( 1 0 , 5 , 1 0 , 4 ) = A ( 1 0 , 5 , 1 0 , 5 ) = A ( 1 0 , 5 , 1 0 , 6 ) = A ( 1 0 , 5 , 1 0 , 7 ) = A ( 1 0 , 5 , 1 0 , 8 ) = A ( 1 0 , 5 , 1 0 , 9 ) = A ( 1 0 , 5 , 1 0 , 1 0 ) = 2 7 1 . 5 5 8 9 3 5 5 0 9 6 8 9 0 4 8 - 0 1 . 2 7 0 7 4 1 4 0 9 8 7 6 7 9 3 - 0 1 . 8 7 8 7 5 1 1 6 4 6 0 0 5 4 E - 0 2 . 1 5 1 2 1 5 4 5 5 1 3 9 2 1 8 - 0 2 . 2 2 1 7 9 4 2 5 3 2 9 2 2 7 E - 0 3 . 1 1 8 2 8 3 8 5 9 6 3 1 4 2 E - 0 4 . 4 2 2 2 7 3 6 0 5 5 8 2 5 6 8 - 0 6 . 1 5 3 2 5 4 2 2 7 4 6 1 7 3 E - 0 2 . 7 6 7 3 4 0 2 9 1 6 2 2 5 3 8 - 0 2 . 1 0 2 1 4 0 1 6 5 8 9 9 9 8 E - 0 1 . 9 4 5 6 2 5 5 2 8 1 2 9 3 1 E - 0 2 . 4 5 4 3 5 3 1 9 1 8 8 9 8 2 E - 0 2 . 1 5 1 2 1 5 4 4 4 4 7 5 3 8 3 - 0 2 . 2 6 1 3 5 3 0 1 1 9 5 0 4 0 8 - 0 3 . 3 8 8 8 3 8 0 1 7 3 5 7 7 8 8 - 0 4 . 2 0 7 6 4 0 2 0 3 2 5 3 5 9 E - 0 5 . 7 4 6 4 3 0 7 6 7 3 3 4 3 8 E - 0 7 . 2 3 0 2 6 4 6 4 1 5 1 5 9 9 E - 0 3 . 1 1 5 5 8 1 4 0 6 4 7 5 9 4 8 - 0 2 . 1 3 9 5 2 6 1 7 0 1 1 9 1 0 8 - 0 2 . 1 3 2 6 9 8 8 7 9 4 4 0 3 4 E - 0 2 . 6 4 5 9 0 4 3 1 2 2 5 0 4 2 8 - 0 3 . 2 2 1 7 9 4 3 2 4 9 1 4 9 8 E - 0 3 . 3 8 8 8 3 7 9 0 7 6 4 9 9 9 3 - 0 4 . 5 9 7 6 3 0 0 1 6 5 8 5 5 3 8 - 0 5 . 3 2 2 4 6 8 4 7 3 4 7 9 2 8 8 - 0 6 . 1 1 9 5 2 0 8 0 9 7 4 2 3 7 3 - 0 7 . 1 0 9 4 8 6 2 9 9 9 5 5 1 1 8 - 0 4 . 5 6 9 4 0 8 0 1 4 8 5 4 3 9 E - 0 4 . 7 3 4 5 6 9 3 9 6 7 4 0 8 8 8 - 0 4 . 7 0 3 2 6 7 4 5 3 7 2 9 9 5 E - 0 4 . 3 3 9 5 9 0 8 8 1 1 3 9 8 8 8 - 0 4 . 1 1 8 2 8 3 7 5 8 8 0 5 4 0 8 - 0 4 . 2 0 7 6 4 0 3 7 1 4 3 0 1 7 E - 0 5 . 3 2 2 4 6 8 3 3 1 8 1 4 8 2 3 - 0 6 . 1 7 4 1 8 1 8 5 8 0 3 4 1 9 8 - 0 7 . 6 5 0 0 3 3 5 7 2 1 0 8 2 4 8 - 0 9 . 3 8 9 7 7 8 9 9 8 6 3 2 9 1 E - 0 6 . 2 0 5 3 9 4 7 7 7 7 6 3 6 0 8 - 0 5 . 2 4 7 9 3 9 0 2 1 1 3 6 2 9 8 - 0 5 . 2 4 3 5 4 6 6 7 8 3 5 7 9 1 E - 0 5 . 1 1 8 0 5 8 8 7 5 8 4 2 0 4 8 - 0 5 . 4 2 2 2 7 4 0 2 0 5 8 3 9 2 E - 0 6 . 7 4 6 4 2 9 9 7 3 5 2 4 9 2 8 - 0 7 . 1 1 9 5 2 0 8 9 2 1 5 9 0 8 3 - 0 7 . 6 5 0 0 3 3 2 1 7 8 9 9 3 9 8 - 0 9 . 2 5 0 3 4 1 2 1 3 3 8 2 8 3 8 - 1 0 A I l O , 6 , 1 , 1 ) = - . 1 1 8 8 4 5 8 9 5 9 2 2 2 8 8 - 0 1 A ( 1 0 , 6 , 1 , 2 ) = - . 1 0 8 0 3 6 2 7 4 3 2 3 2 4 E - 0 1 A ( 1 0 , 6 , 1 , 3 ) - - . 3 9 1 0 4 2 6 6 8 4 8 8 8 1 8 - 0 1 A ( 1 0 , 6 , 1 , 4 ) = A ( 1 0 , 6 , l , 5 ) = - A ( 1 0 , 6 , 1 , 6 ) = A ( 1 0 , 6 , l , 7 ) = A ( 1 0 , 6 , l , 8 ) = A ( 1 0 , 6 , 1 , 9 ) - A ( 1 0 , 6 , l , 1 0 a » A H 0 C h N V q m m - b w w r - H — I x o m u m m a s w > A H O V 0 ‘ u p H m m V I O ‘ 0 1 0 . 5 w M H V O V V V V V V V V V O V V V V V V V V V O V V V V V V V V V I I I I V I I I I I I I I I I I I I I I I I I V I I I I I I I I I I I I I I I I I I V I I I I I I I I I I I I I I I I I I V I A ( 1 0 , 6 , 5 , 1 A ( 1 0 , 6 , 5 , 2 ) A ( 1 0 , 6 , 5 , 3 ) = - A ( 1 0 , 6 , 5 , 4 ) = A ( 1 0 , 6 , 5 , 5 ) = A ( 1 0 , 6 , 5 , 6 ) = A ( 1 0 , 6 , 5 , 7 ) = A ( 1 0 , 6 , 5 , 8 ) = A ( 1 0 , 6 , 5 , 9 ) = A ( 1 0 , 6 , 5 , 1 0 ) = A ( 1 0 , 6 , 6 , 1 ) = A ( 1 0 , 6 , 6 , 2 ) = A ( 1 0 , 6 , 6 , 3 ) = 2 7 2 . 8 6 5 7 5 1 2 3 7 1 4 2 8 3 E - 0 2 . 2 3 7 8 8 0 2 0 8 5 8 7 7 4 E - 0 1 . 1 6 0 0 8 0 1 9 5 2 7 3 6 2 E - 0 1 . 5 8 9 8 9 9 8 6 8 1 0 0 4 7 E - 0 2 . 6 6 1 2 4 0 9 6 4 7 4 5 9 6 E - 0 3 . 3 8 3 0 1 3 9 2 1 0 9 4 7 4 E - 0 4 . 1 1 7 3 7 8 0 6 3 0 0 2 6 0 8 - 0 5 . 1 0 8 0 3 4 7 6 7 9 0 8 9 8 3 - 0 1 . 1 4 8 2 6 2 0 2 3 4 6 0 1 2 E + 0 0 . 4 5 6 4 0 6 2 4 0 1 1 8 6 7 3 - 0 1 . 1 0 2 6 2 1 9 5 6 4 9 5 5 7 E + 0 0 . 2 3 3 9 9 3 6 2 5 1 5 1 9 2 8 - 0 1 . 1 0 8 4 1 2 0 0 3 7 2 6 7 0 E + 0 0 . 2 9 1 6 8 4 6 0 5 3 2 6 7 4 8 - 0 1 . 3 5 4 9 2 3 8 6 5 9 6 1 6 1 3 - 0 2 . 2 0 2 5 6 5 0 7 5 4 8 3 1 1 8 - 0 3 . 6 5 9 1 5 2 1 3 7 8 4 9 6 2 8 - 0 5 . 3 9 1 0 4 4 2 9 3 6 4 6 7 0 E - 0 1 . 4 5 6 4 0 7 3 1 1 1 3 9 6 3 B - O l . 1 0 8 7 8 0 5 9 8 2 6 7 9 1 E + 0 0 . 1 3 7 0 3 7 6 9 1 8 9 3 0 6 E - 0 1 . 3 1 2 4 3 9 0 8 6 2 6 4 9 3 8 - 0 1 . 1 7 0 1 5 3 7 3 4 3 3 2 4 Z E + 0 0 . 3 4 1 4 3 8 3 3 3 1 9 8 3 1 8 - 0 1 . 4 4 6 4 5 2 2 2 8 1 5 2 3 4 3 - 0 2 . 2 3 9 2 0 0 5 5 6 5 6 3 9 0 8 - 0 3 . 7 9 7 7 0 8 8 5 1 5 0 7 6 5 8 - 0 5 . 8 6 5 7 8 1 5 0 5 1 2 6 5 1 E - 0 2 . 1 0 2 6 2 1 4 5 4 5 1 2 7 0 E + 0 0 . 1 3 7 0 4 2 9 6 4 3 4 2 9 8 E - 0 1 . 3 5 6 1 0 1 2 0 9 7 6 3 4 4 8 - 0 2 . 2 1 6 8 7 3 4 7 0 8 6 8 4 S E + 0 0 . 1 7 8 9 0 3 9 4 8 8 0 6 6 9 E + 0 0 . 3 0 7 4 8 2 9 1 9 8 1 5 8 1 8 - 0 1 . 4 4 1 9 1 2 5 1 6 9 5 3 3 8 8 - 0 2 . 2 2 9 4 5 3 2 5 9 0 0 9 9 2 8 - 0 3 . 8 0 9 3 9 7 3 2 6 4 9 5 5 4 E - 0 5 . 2 3 7 8 8 3 0 5 8 4 3 4 8 2 E - 0 1 . 2 3 3 9 8 7 3 3 8 7 2 4 5 5 E - 0 1 . 3 1 2 4 4 5 7 2 6 5 9 4 8 9 E - 0 1 . 2 1 6 8 7 3 7 0 7 4 2 4 3 8 E + 0 0 . 1 9 9 7 4 7 0 6 8 2 5 4 5 1 8 + 0 0 . 8 6 6 1 4 0 6 3 7 1 5 3 8 8 3 - 0 1 . 1 5 3 5 8 7 5 9 7 9 0 6 1 5 E - 0 1 . 2 1 3 7 5 0 2 1 8 4 9 5 0 8 3 - 0 2 . 1 1 3 6 5 7 6 6 4 5 9 9 0 3 8 - 0 3 . 3 9 0 8 2 8 2 5 9 9 3 2 9 7 8 - 0 5 . 1 6 0 0 8 1 7 3 6 0 3 0 4 1 E - 0 1 . 1 0 8 4 1 1 6 2 2 3 5 0 1 0 3 + 0 0 . 1 7 0 1 5 4 1 4 3 7 6 5 1 0 E + 0 0 2 7 3 A ( 1 0 , 6 , 6 , 4 ) = . 1 7 8 9 0 3 7 1 7 0 2 3 7 9 8 + 0 0 A ( 1 0 , 6 , 6 , 5 ) = . 8 6 6 1 4 1 2 6 1 1 4 0 0 0 8 - 0 1 A ( 1 0 , 6 , 6 , 6 ) = . 3 4 7 9 2 2 8 5 3 3 6 1 5 2 3 - 0 1 A ( 1 0 , 6 , 6 , 7 ) = . 6 1 1 9 4 2 1 7 4 9 6 4 5 0 E - 0 2 A ( 1 0 , 6 , 6 , 8 ) = . 8 8 7 5 6 3 7 9 2 5 0 2 9 9 E - 0 3 A ( 1 0 , 6 , 6 , 9 ) = . 4 7 2 3 4 8 5 5 9 9 8 1 1 3 E - 0 4 A ( 1 0 , 6 , 6 , 1 0 ) = . 1 6 7 8 0 0 2 2 0 2 7 4 2 9 E - 0 5 A ( 1 0 , 6 , 7 , 1 ) = . 5 8 9 8 9 4 8 3 3 1 3 7 8 1 8 - 0 2 A ( 1 0 , 6 , 7 , 2 ) = . 2 9 1 6 8 5 8 7 5 1 2 6 8 6 E - 0 1 A ( 1 0 , 6 , 7 , 3 ) = . 3 4 1 4 3 6 9 7 5 5 0 4 6 Z E - O l A ( 1 0 , 6 , 7 , 4 ) = . 3 0 7 4 8 3 7 9 7 8 7 8 3 8 3 - 0 1 A ( 1 0 , 6 , 7 , 5 ) = . 1 5 3 5 8 7 2 9 3 5 5 2 8 5 8 - 0 1 A ( 1 0 , 6 , 7 , 6 ) = . 6 1 1 9 4 2 7 2 3 5 7 1 7 0 8 - 0 2 A ( 1 0 , 6 , 7 , 7 ) = . 1 0 8 8 7 1 8 0 7 7 4 2 6 2 8 - 0 2 A ( 1 0 , 6 , 7 , 8 ) = . 1 5 9 3 6 5 6 7 4 9 6 0 5 5 E - 0 3 A ( 1 0 , 6 , 7 , 9 ) = . 8 5 3 1 2 8 6 6 0 8 7 1 5 0 E - 0 5 A ( 1 0 , 6 , 7 , 1 0 ) = . 3 0 3 9 9 5 9 6 4 4 0 1 3 4 E - 0 6 A ( 1 0 , 6 , 8 , 1 ) = . 6 6 1 2 5 0 8 2 3 8 9 5 9 0 8 - 0 3 A ( 1 0 , 6 , 8 , 2 ) = . 3 5 4 9 2 1 3 7 9 3 1 2 1 5 8 - 0 2 A ( 1 0 , 6 , 8 , 3 ) = . 4 4 6 4 5 4 9 4 2 0 8 4 5 3 3 - 0 2 A ( 1 0 , 6 , 8 , 4 ) = . 4 4 1 9 1 0 7 5 3 9 4 3 3 8 E - 0 2 A ( 1 0 , 6 , 8 , 5 ) = . 2 1 3 7 5 0 9 2 2 8 3 0 5 1 8 - 0 2 A ( 1 0 , 6 , 8 , 6 ) = . 8 8 7 5 6 2 1 2 4 3 7 6 0 2 8 - 0 3 A ( 1 0 , 6 , 8 , 7 ) = . 1 5 9 3 6 5 8 7 1 0 7 0 3 5 8 - 0 3 A ( 1 0 , 6 , 8 , 8 ) = . 2 4 2 8 3 5 9 2 0 5 8 0 8 3 E - 0 4 A ( 1 0 , 6 , 8 , 9 ) = . 1 3 1 0 3 5 4 8 3 8 1 9 1 0 8 - 0 5 A ( 1 0 , 6 , 8 , 1 0 ) = . 4 8 3 5 9 4 3 9 0 1 5 7 6 6 E - 0 7 A ( 1 0 , 6 , 9 , l ) = . 3 8 3 0 0 4 5 1 6 9 1 9 5 3 E - 0 4 A ( 1 0 , 6 , 9 , 2 ) = . 2 0 2 5 6 7 4 5 9 2 6 8 7 2 E - 0 3 A ( 1 0 , 6 , 9 , 3 ) = . 2 3 9 1 9 7 9 7 8 6 0 1 1 7 8 - 0 3 A I 1 0 , 6 , 9 , 4 ) = . 2 2 9 4 5 4 9 5 4 5 3 5 4 1 8 - 0 3 A ( 1 0 , 6 , 9 , 5 ) = . 1 1 3 6 5 6 9 4 5 5 2 9 7 8 E - 0 3 A ( 1 0 , 6 , 9 , 6 ) = . 4 7 2 3 5 0 4 8 2 7 0 9 7 7 8 - 0 4 A ( 1 0 , 6 , 9 , 7 ) = . 8 5 3 1 2 5 6 5 3 1 4 4 1 0 E - 0 5 A ( 1 0 , 6 , 9 , 8 ) = . 1 3 1 0 3 5 7 0 1 4 8 9 4 2 E - 0 5 A ( 1 0 , 6 , 9 , 9 ) = . 7 0 9 7 7 6 4 4 0 2 6 0 8 2 3 - 0 7 A ( 1 0 , 6 , 9 , 1 0 ) = . 2 6 3 3 4 2 7 0 4 7 6 0 7 5 E - 0 8 A ( 1 0 , 6 , 1 0 , l ) = . 1 1 7 3 8 1 0 6 2 3 8 1 1 3 8 - 0 5 A ( 1 0 , 6 , 1 0 , 2 ) = . 6 5 9 1 4 4 4 7 1 0 9 3 5 0 8 - 0 5 A ( 1 0 , 6 , 1 0 , 3 ) = ; 7 9 7 7 1 7 3 8 5 1 2 5 9 l E - 0 5 A ( 1 0 , 6 , 1 0 , 4 ) = . 8 0 9 3 9 1 6 6 4 8 9 1 0 2 8 - 0 5 A ( 1 0 , 6 , 1 0 , 5 ) = . 3 9 0 8 3 0 7 2 3 0 2 9 3 7 8 - 0 5 A ( 1 0 , 6 , 1 0 , 6 ) = . 1 6 7 7 9 9 5 2 9 5 3 7 9 4 E - 0 5 A ( 1 L 6 , 1 0 , 7 ) 8 . 3 0 3 9 9 7 1 8 8 3 1 1 2 0 8 - 0 6 A ( 1 0 , 6 , 1 0 , 8 ) = . 4 8 3 5 9 3 2 2 8 9 3 3 7 7 8 - 0 7 A ( 1 0 , 6 , 1 0 , 9 ) = . 2 6 3 3 4 3 1 5 4 5 7 4 5 5 E - 0 8 A ( 1 0 , 6 , 1 0 , 1 0 ) = . 1 0 1 1 2 2 0 3 4 5 0 6 2 7 8 - 0 9 A ( 1 0 , 7 , 1 , 1 ) = ‘ . 2 6 8 0 9 7 7 4 5 7 2 0 3 0 8 - 0 2 A ( 1 0 , 7 , 1 , 2 ) = - . 2 4 5 3 9 7 8 2 8 9 8 5 0 1 E - 0 1 A ( 1 0 , 7 , 1 , 3 ) = - . 5 5 8 2 8 5 6 8 0 5 9 9 5 1 8 - 0 1 II I I I I I I I I I I I V I I I I I I I I I I I I I I I I I I V I I I I I I I I I I I I I I I I I I V I I I I I I I I I I I I I I I I I I V I I I I I I I I I I I I I A ( 1 0 , 7 , A ( 1 0 , 7 A ( 1 0 , 7 , A ( 1 0 , 7 , A ( 1 0 , 7 , A ( 1 0 , 7 A ( 1 0 , 7 , A ( 1 0 , L A ( 1 0 , 7 , A ( 1 0 , 7 A ( 1 0 , 7 , A ( 1 0 , 7 , A ( 1 0 , 7 , A ( 1 0 , 7 A ( 1 0 , 7 , A ( 1 0 , 7 , A ( 1 0 , 7 A ( 1 0 , 7 , A ( 1 0 , 7 , A ( 1 0 , L A ( 1 0 , 7 A ( 1 0 , 7 A ( 1 0 , 7 , A ( 1 0 , 7 , A ( 1 0 , 7 , A ( 1 0 , 7 , A ( 1 0 , 7 , A ( 1 0 , 7 , A ( 1 0 , 7 , A ( 1 0 , 7 , a ( 1 o , 7 , A ( 1 0 , 7 , A ( 1 0 , 7 , A ( 1 0 , 7 , A ( 1 0 , 7 , A ( 1 0 , 7 , A ( 1 0 , 7 , A ( 1 0 , 7 , A ( 1 0 , 7 , A ( 1 0 , 7 , A ( 1 o , 7 , A ( 1 0 , 7 , A ( 1 0 , 7 , A ( 1 0 , 7 , A ( 1 0 , 7 , A ( 1 0 , 7 , A ( 1 0 , 7 , 5 , 1 0 I = l , 1 1 1 1 , 1 1 2 2 , 2 2 2 2 , 2 2 2 , 2 3 3 3 , 3 , 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 5 5 5 , 5 , V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V 5 , 5 , 5 , 7 5 , 8 ) = 5 , 9 I = 4 5 6 7 8 9 1 l 2 3 4 5 6 7 8 9 1 1 2 3 4 5 6 7 8 9 1 1 2 3 4 5 6 7 8 9 1 1 2 3 4 5 6 I I I I I 0 I I I I I I I I I 0 I I I I I I I I I 0 I I I I : I I I I I 0 I - I I - I - I - I I 2 7 4 . 1 1 8 7 3 3 8 9 5 0 1 1 2 S E + 0 0 . 3 6 9 8 3 6 9 3 4 8 4 2 1 7 3 - 0 1 . 2 4 1 1 5 7 5 1 8 4 6 6 9 3 8 - 0 1 . 9 9 8 0 8 6 0 4 6 4 5 6 5 9 8 - 0 2 . 3 6 6 1 6 9 4 4 6 1 6 9 8 1 8 - 0 2 . 1 5 7 4 0 5 2 7 4 1 9 4 3 9 8 - 0 3 . 5 8 2 5 2 0 7 8 0 7 6 7 4 8 8 - 0 5 . 2 4 5 4 0 0 2 5 0 4 2 3 7 0 8 - 0 1 . 1 3 5 0 9 1 3 0 1 9 8 5 0 9 E + 0 0 . 7 6 3 4 2 1 2 0 7 6 6 6 4 0 8 - 0 1 . 3 4 8 4 2 9 5 4 4 8 2 8 8 3 8 + 0 0 . 1 1 2 1 3 3 4 2 4 7 2 9 1 1 E + 0 0 . 3 0 8 1 0 4 3 7 7 4 7 2 7 7 8 - 0 1 . 8 2 1 9 0 3 9 3 9 3 5 8 8 9 8 - 0 1 . 1 9 6 9 3 5 2 0 0 1 4 6 9 8 8 - 0 1 . 9 1 6 9 2 6 1 0 2 4 9 0 8 3 8 - 0 3 . 3 4 0 4 7 6 6 0 7 9 7 3 9 8 8 - 0 4 . 5 5 8 2 7 3 5 7 3 4 0 6 0 4 E - O l . 7 6 3 3 9 8 1 8 5 3 7 2 3 5 8 - 0 1 . 3 3 8 2 2 5 5 0 5 3 1 4 7 7 E + 0 0 . 2 6 2 4 2 6 0 6 7 1 4 3 6 8 E + 0 0 . 1 9 6 5 9 1 4 1 9 1 6 7 8 2 3 + 0 0 . 2 5 2 4 5 9 9 0 7 2 0 5 7 8 3 - 0 1 . 1 1 9 4 8 0 1 3 4 4 8 2 7 3 E + 0 0 . 2 2 7 4 3 6 6 9 0 4 0 2 1 0 8 - 0 1 . 1 0 8 8 9 9 5 7 4 8 8 8 7 1 8 - 0 2 . 3 8 7 8 9 7 5 6 3 5 2 7 4 2 E - 0 4 . 1 1 8 7 3 4 7 4 6 2 4 0 0 8 E + 0 0 . 3 4 8 4 3 1 4 6 3 3 5 3 3 4 E + 0 0 . 2 6 2 4 2 7 4 0 4 5 2 2 9 O E + 0 0 . 6 3 5 8 8 6 8 7 5 9 1 2 5 5 3 + 0 0 . 1 0 6 8 9 3 0 4 8 8 5 4 5 4 E + 0 0 . 2 3 7 0 6 4 4 6 2 3 8 7 9 3 E + 0 0 . 1 4 5 0 7 0 4 4 5 5 2 0 1 0 8 + 0 0 . 2 1 5 0 0 8 9 4 0 8 3 1 4 7 8 - 0 1 . 1 1 5 0 3 7 0 2 5 4 4 3 6 0 8 - 0 2 . 3 9 5 7 6 0 6 5 0 4 2 0 1 3 8 - 0 4 . 3 6 9 8 2 9 2 2 3 4 9 1 2 5 E - 0 1 . 1 1 2 1 3 1 6 0 1 1 9 9 5 1 8 + 0 0 . 1 9 6 5 9 0 2 4 0 1 1 3 4 4 E + 0 0 . 1 0 6 8 9 3 3 2 8 2 5 1 3 2 8 + 0 0 . 4 7 3 0 9 6 5 0 6 9 0 2 9 5 8 - 0 1 . 2 4 0 3 8 1 8 9 8 8 8 2 3 3 B + 0 0 . 7 0 1 8 4 2 0 3 2 1 4 0 1 2 8 - 0 1 . 1 0 2 4 5 1 1 7 2 6 2 4 5 7 8 - 0 1 . 5 4 1 0 5 4 7 3 2 1 3 8 9 5 E - 0 3 . 1 8 6 3 3 6 2 8 1 8 3 5 5 1 8 - 0 4 A ( 1 0 , 7 , 6 , 1 I = ' . 2 4 1 1 6 0 6 1 9 7 7 l l l E - 0 1 A ( 1 0 , 7 , A ( 1 0 , 7 , 6 , 2 ) = . 3 0 8 1 1 1 7 9 0 8 0 0 4 7 E - 0 1 6 , 3 ) 8 ' . 2 5 2 4 6 5 7 7 3 3 7 3 8 4 8 - 0 1 2 7 5 A ( 1 0 , 7 , 6 , 4 I = . 2 3 7 0 6 4 7 6 8 7 9 3 0 6 E + 0 0 A ( 1 0 , 7 , 6 , 5 I = . 2 4 0 3 8 1 8 4 6 0 2 9 7 B E + 0 0 A ( 1 0 , 7 , 6 , 6 I = . 1 3 4 9 3 7 4 4 6 7 9 7 2 7 E + 0 0 A ( 1 0 , 7 , 6 , 7 I = . 2 9 6 8 7 5 2 1 9 0 6 4 5 3 8 ’ 0 1 A ( 1 0 , 7 , 6 , 8 I = . 4 4 9 0 6 5 3 1 7 7 9 8 1 6 3 - 0 2 A ( 1 0 , 7 , 6 , 9 I = . 2 3 6 9 0 6 4 7 1 7 4 1 3 5 3 - 0 3 A ( 1 0 , 7 , 6 , 1 0 I = . 8 4 5 2 3 3 8 3 1 9 0 3 1 6 3 - 0 5 A ( 1 0 , 7 , 7 , 1 I = . 9 9 8 0 9 4 8 6 4 9 1 7 2 2 8 ’ 0 2 A ( 1 0 , 7 , 7 , 2 I = . 8 2 1 9 0 1 9 5 4 4 7 7 5 5 3 ‘ 0 1 A ( 1 0 , 7 , 7 , 3 I = . 1 1 9 4 8 0 2 9 3 2 7 3 2 3 E + 0 0 A ( 1 0 , 7 , 7 , 4 I = . 1 4 5 0 7 0 3 6 5 6 5 9 1 9 E + 0 0 A ( 1 0 , 7 , 7 , 5 I = . 7 0 1 8 4 2 2 5 1 5 8 3 0 0 3 ‘ 0 1 A ( 1 0 , 7 , 7 , 6 I = . 2 9 6 8 7 5 1 8 4 5 7 6 4 9 3 ‘ 0 1 A ( 1 0 , 7 , 7 , 7 I = . 6 2 4 2 6 9 2 0 5 6 7 3 0 4 E - 0 2 A ( 1 0 , 7 , 7 , 8 I = . 9 2 8 9 6 5 8 3 1 4 6 2 8 5 E ' 0 3 A ( 1 0 , 7 , 7 , 9 I = . 4 9 4 4 0 9 4 5 7 7 2 9 7 2 3 ' 0 4 A ( 1 0 , 7 , 7 , 1 0 I = . 1 7 5 0 1 8 4 9 8 6 9 3 7 2 3 ’ 0 5 A ( 1 0 , 7 , 8 , 1 I = . 3 6 6 1 5 8 2 0 9 9 8 4 6 1 3 ' 0 2 A ( 1 0 , 7 , 8 , 2 I = . 1 9 6 9 3 5 5 0 7 0 4 6 8 7 3 ' 0 1 A ( 1 0 , 7 , 8 , 3 I = . 2 2 7 4 3 6 4 5 1 4 5 9 6 5 3 ‘ 0 1 A ( 1 0 , 7 , 8 , 4 I = . 2 1 5 0 0 9 0 9 1 7 3 4 8 3 3 - 0 1 A ( 1 0 , 7 , 8 , 5 I = . 1 0 2 4 5 1 1 4 1 5 0 1 6 6 3 ' 0 1 A ( 1 0 , 7 , 8 , 5 I = . 4 4 9 0 6 5 3 7 5 6 4 2 0 2 E ‘ 0 2 A ( 1 0 , 7 , 8 , 7 I = . 9 2 8 9 5 5 7 8 8 5 0 2 9 1 3 - 0 3 A ( 1 0 , 7 , 8 , 8 I = . 1 4 4 6 7 8 2 8 2 8 3 6 7 1 3 ‘ 0 3 A ( 1 0 , 7 , 8 , 9 I = . 7 7 4 9 5 7 1 7 6 2 9 7 1 6 3 ’ 0 5 A ( 1 0 , 7 , 8 , 1 0 I = . 2 8 5 0 8 6 6 6 3 3 5 9 6 9 E ‘ 0 5 A ( 1 0 , 7 , 9 , 1 I = . 1 5 7 4 0 5 3 0 6 4 7 0 8 8 3 - 0 3 A ( 1 0 , 7 , 9 , 2 I = . 9 1 6 9 2 3 6 0 8 6 5 6 3 6 3 ' 0 3 , 3 I = r 4 ) : , 5 I = , 6 I = : 7 I = , 8 I = , 9 I = O I 1 ) I A ( 1 0 , 7 , 9 . 1 0 8 8 9 9 7 9 2 6 2 1 7 4 8 - 0 2 A ( 1 0 , 7 , 9 . 1 1 5 0 3 6 8 9 3 7 4 8 7 7 8 - 0 2 A ( 1 0 , 7 , 9 . 5 4 1 0 5 5 0 8 3 2 0 3 9 0 3 - 0 3 A ( 1 0 , 7 , 9 . 2 3 6 9 0 6 3 7 6 9 2 6 5 3 8 - 0 3 A ( 1 0 , 7 , 9 . 4 9 4 4 0 9 5 4 5 2 6 8 5 8 3 - 0 4 A ( 1 0 , 7 , 9 . 7 7 4 9 5 7 0 8 3 9 2 6 6 1 3 - 0 5 A ( 1 0 , 7 , 9 . 4 1 7 7 1 4 5 8 4 9 2 1 5 7 8 - 0 6 A ( 1 0 , 7 , 9 , 1 = . 1 5 4 4 5 6 3 5 3 1 5 8 8 6 8 - 0 7 A ( 1 0 , 7 , 1 0 , = . 5 8 2 5 1 7 0 4 8 9 9 7 0 3 8 - 0 5 A ( 1 0 , 7 , 1 0 , 2 = . 3 4 0 4 7 7 4 9 1 6 0 4 9 3 E - 0 4 A ( 1 0 , 7 , 1 0 , 3 I = . 3 8 7 8 9 6 6 8 5 5 8 0 8 1 8 - 0 4 A ( 1 0 , 7 , 1 0 , 4 I = . 3 9 5 7 6 1 1 7 1 9 5 8 5 0 8 - 0 4 A ( 1 0 , 7 , 1 0 , 5 I = . 1 8 6 3 3 6 0 9 4 5 3 6 4 4 E - 0 4 A ( 1 0 , 7 , 1 0 , 6 I = . 8 4 5 2 3 4 3 3 6 3 8 8 5 0 8 - 0 5 A ( 1 0 , 7 , 1 0 , 7 I = . 1 7 5 0 1 8 4 1 7 3 5 8 7 9 E - 0 5 A ( 1 0 , 7 , 1 0 , 8 I = . 2 8 5 0 8 6 7 7 1 5 7 8 6 8 8 - 0 6 A ( 1 0 , 7 , 1 0 , 9 I = . 1 5 4 4 5 6 2 9 0 5 7 0 0 4 8 - 0 7 A ( 1 0 , 7 , 1 0 , 1 0 I = . 5 9 2 5 5 6 3 8 5 4 6 9 5 9 E - 0 9 A ( 1 0 , 8 , 1 , 1 I = - . 3 5 3 2 7 6 0 5 9 0 3 1 4 9 E + 0 0 A ( 1 0 , 8 , 1 , 2 I = - . 3 3 6 2 6 6 1 3 9 5 2 2 1 9 8 + 0 0 A ( 1 0 , 8 , 1 , 3 I = - . 1 5 3 6 8 5 7 7 8 7 5 1 9 7 E + 0 1 I I V I I I I I I I I I I J I I I I I I I V I I I I I I I I I I I I I I I I I I V I I I I I I I I I I I I I I I I I I V I I I I I I I I I I I I A ( 1 0 , 8 , 5 , 1 A ( 1 0 , 8 , 5 , 2 I = - A ( 1 0 , 8 , 5 , 3 I = - A ( 1 0 , 8 , 5 , 4 I = - A ( 1 0 , 8 , 5 , 5 I = - A ( 1 0 , 8 , S , 6 I = - A ( 1 0 , 8 , 5 , 7 ) = A ( 1 0 , 8 , 5 , 8 I = A ( 1 0 , 8 , 5 , 9 I = A ( 1 0 , 8 , 5 , 1 0 I = A ( 1 0 , 8 , 6 , 1 I = ' A ( 1 0 , 8 , 6 , 2 ) = A ( 1 0 , 8 , 6 , 3 I = 2 7 6 . 1 6 2 5 0 7 1 2 2 3 8 2 5 2 8 + 0 0 . 4 9 9 0 8 8 7 9 0 2 6 7 7 1 E + 0 0 . 5 5 0 7 1 2 9 1 0 4 8 0 8 0 8 - 0 1 . 6 3 4 8 4 1 6 2 6 7 4 2 8 5 3 - 0 1 . 1 1 1 1 7 1 8 3 0 2 1 2 7 O E - O l . 1 4 5 9 9 8 0 4 7 9 0 1 2 3 8 - 0 2 . 3 9 9 2 8 5 1 8 9 8 7 1 5 3 E - 0 4 . 3 3 6 2 6 1 2 3 7 0 4 0 1 6 E + 0 0 . 4 3 4 5 4 5 7 7 5 5 0 2 9 Z E + 0 1 . 5 3 7 8 2 9 9 9 5 1 5 5 3 3 E - 0 1 . 3 6 7 7 9 5 4 0 4 7 9 1 8 3 E + 0 1 . 4 8 5 3 2 2 8 4 0 5 1 1 8 0 8 + 0 0 . 8 8 3 1 8 9 1 7 2 4 8 3 9 8 E + 0 0 . 6 1 8 7 0 7 1 5 3 4 8 0 5 0 8 - 0 1 . 9 7 3 1 4 6 9 1 1 1 2 8 4 2 8 - 0 1 . 8 3 6 1 5 9 3 8 4 5 6 2 0 5 E - 0 2 . 2 5 7 9 9 5 4 8 9 1 0 7 5 4 8 - 0 3 . 1 5 3 6 8 6 9 4 7 0 0 3 0 1 E + 0 1 . 5 3 7 6 0 2 3 0 5 4 1 2 2 9 8 - 0 1 . 6 2 0 6 9 4 7 3 4 9 0 1 1 9 E + 0 1 . 4 9 8 8 9 2 9 4 0 5 8 0 8 4 E + 0 0 . 2 0 6 8 0 5 4 0 0 5 5 0 3 7 E + O l . 6 3 7 2 5 6 6 3 3 4 9 0 3 2 3 - 0 2 . 2 3 9 5 1 1 9 1 5 7 1 5 4 l E + 0 0 . 1 2 1 0 3 5 4 4 2 7 7 4 8 8 8 + 0 0 . 9 3 9 7 8 0 1 3 2 8 3 0 4 9 E - 0 2 . 2 8 4 2 6 5 7 6 9 6 6 4 6 7 E - 0 3 . 1 6 2 4 8 9 2 9 8 7 3 1 0 9 E + 0 0 . 3 6 7 7 9 1 7 2 4 2 0 5 0 2 8 + 0 1 . 4 9 8 9 2 2 5 7 1 5 3 9 8 8 8 + 0 0 . 2 8 3 9 1 8 3 7 2 5 4 1 6 7 E + 0 1 . 1 7 1 1 8 6 4 9 1 8 4 7 0 4 E + 0 0 . 6 2 3 5 7 6 8 4 3 1 7 9 7 6 E + 0 0 . 9 1 8 7 4 4 3 0 6 5 4 5 7 0 3 - 0 1 . 1 5 6 3 4 2 9 6 1 3 8 8 8 7 E + 0 0 . 9 1 9 1 3 4 8 2 4 8 3 5 0 6 E - 0 2 . 3 1 5 1 7 1 9 5 1 6 2 6 7 8 8 - 0 3 . 4 9 9 1 0 5 5 1 6 8 2 1 1 5 8 + 0 0 . 4 8 5 2 8 7 0 1 8 1 2 0 2 9 E + 0 0 . 2 0 6 8 0 8 7 3 8 7 8 3 0 0 E + 0 1 . 1 7 1 1 7 2 7 8 2 7 7 8 7 4 E + 0 0 . 4 9 4 7 1 8 9 1 6 7 1 4 1 9 E + 0 0 . 1 7 8 2 3 3 3 5 0 6 2 7 1 2 3 + 0 0 . 1 6 2 7 7 2 6 5 5 8 3 6 3 1 3 + 0 0 . 7 7 3 5 2 1 1 6 3 3 5 5 3 3 8 - 0 1 . 4 1 2 1 4 6 9 0 1 9 9 9 2 2 E - 0 2 . 1 4 4 9 2 5 1 5 8 5 9 3 8 8 8 - 0 3 . 5 5 0 6 3 2 9 2 8 4 9 8 0 9 E - 0 1 . 8 8 3 1 6 9 1 1 4 5 8 9 6 9 E + 0 0 . 6 3 9 2 3 2 6 2 0 5 9 6 8 9 3 - 0 2 2 7 7 A ( 1 0 , 8 , 6 , 4 I = . 6 2 3 5 6 5 3 5 8 1 0 9 7 7 E + 0 0 A ( 1 0 , 8 , 6 , 5 I = - . 1 7 8 2 3 0 3 9 0 8 8 3 9 8 8 + 0 0 A ( 1 0 , 8 , 6 , 6 I = . 3 6 7 4 8 6 2 2 8 2 3 5 0 7 E + 0 0 A ( 1 0 , 8 , 6 , 7 I = . 1 5 8 4 0 1 4 7 8 9 5 5 0 6 E + 0 0 A ( 1 0 , 8 , 6 , 8 I = . 3 4 0 8 6 4 0 3 0 4 7 6 9 5 E - 0 1 A ( 1 0 , 8 , 6 , 9 I = . 1 8 9 7 6 3 1 8 2 2 8 8 5 2 8 - 0 2 A ( 1 0 , 8 , 6 , 1 0 I = . 6 6 6 7 2 5 1 7 7 7 5 1 4 6 3 ’ 0 4 A ( 1 0 , 8 , 7 , 1 I = - . 6 3 4 8 6 7 5 5 9 4 1 9 9 4 E - 0 1 A ( 1 0 , 8 , 7 , 2 I = - . 6 1 8 6 4 4 3 4 5 0 8 6 0 7 E - 0 1 A ( 1 0 , 8 , 7 , 3 I = - . 2 3 9 5 1 8 5 6 9 0 8 3 8 8 3 + 0 0 A ( 1 0 , 8 , 7 , 4 I = . 9 1 8 7 8 6 0 1 1 1 7 0 6 0 8 - 0 1 A ( 1 0 , 8 , 7 , 5 I = . 1 6 2 7 7 1 2 2 1 2 5 0 3 0 8 + 0 0 A ( 1 0 , 8 , 7 , 6 I = . 1 5 8 4 0 1 7 5 4 8 3 0 2 7 E + 0 0 A ( 1 0 , 8 , 7 , 7 I = . 3 7 0 1 2 7 1 2 8 9 9 0 1 3 8 - 0 1 A ( 1 0 , 8 , 7 , 8 I = . 7 1 6 6 8 2 8 8 7 1 9 5 9 3 3 - 0 2 A ( 1 0 , 8 , 7 , 9 I = . 3 9 1 5 2 4 4 1 6 0 4 5 2 9 8 - 0 3 A ( 1 0 , 8 , 7 , 1 0 I = . 1 3 7 8 9 4 0 7 9 8 8 7 9 6 8 - 0 4 A ( 1 0 , 8 , 8 , 1 I = . 1 1 1 1 7 6 7 7 7 8 6 3 8 8 E - 0 1 A ( 1 0 , 8 , 8 , 2 I = . 9 7 3 1 3 4 3 2 5 4 6 7 9 8 3 - 0 1 A ( 1 0 , 8 , 8 , 3 I = . 1 2 1 0 3 6 7 8 5 0 7 2 6 S E + 0 0 A ( 1 0 , 8 , 8 , 4 I = . 1 5 6 3 4 2 1 0 3 1 7 5 1 2 E + 0 0 A ( 1 0 , 8 , 8 , 5 I = . 7 7 3 5 2 4 6 4 6 5 0 1 7 6 8 - 0 1 A ( 1 0 , 8 , 8 , 6 I = . 3 4 0 8 6 3 1 9 6 3 6 1 1 7 8 - 0 1 A ( 1 0 , 8 , 8 , 7 I = . 7 1 6 6 8 3 9 2 4 7 4 7 4 9 8 - 0 2 A ( 1 0 , 8 , 8 , 8 I = . 1 3 1 4 5 0 8 8 6 4 5 3 8 8 E - 0 2 A ( 1 0 , 8 , 8 , 9 I = . 7 2 1 1 0 1 4 9 7 4 4 7 3 1 E - 0 4 A ( 1 0 , 8 , 8 , 1 0 ) = . 2 6 1 6 6 8 7 1 5 5 3 9 9 0 E - 0 5 A ( 1 0 , 8 , 9 , 1 I = . 1 4 5 9 9 3 2 1 7 0 2 9 1 7 8 - 0 2 A ( 1 0 , 8 , 9 , 2 I = . 8 3 6 1 7 1 6 2 9 9 9 8 7 2 8 - 0 2 A ( 1 0 , 8 , 9 , 3 I = . 9 3 9 7 6 6 6 8 1 0 4 0 0 6 8 - 0 2 A ( 1 0 , 8 , 9 , 4 I = . 9 1 9 1 4 3 6 4 3 8 4 1 3 8 3 - 0 2 A ( 1 0 , 8 , 9 , 5 I = . 4 1 2 1 4 3 1 5 5 6 0 8 6 5 8 - 0 2 A ( 1 0 , 8 , 9 , 6 I = . 1 8 9 7 6 4 2 1 6 5 2 0 4 2 8 - 0 2 A ( 1 0 , 8 , 9 , 7 I = . 3 9 1 5 2 2 7 5 2 1 2 4 7 3 3 - 0 3 A ( 1 0 , 8 , 9 , 8 I = . 7 2 1 1 0 2 7 5 0 1 3 4 1 5 8 - 0 4 A ( 1 0 , 8 , 9 , 9 I = . 3 9 6 0 7 1 9 1 4 5 5 4 6 0 8 - 0 5 A ( 1 0 , 8 , 9 , 1 0 I = . 1 4 4 9 0 6 4 4 4 8 7 1 0 8 8 - 0 6 A ( 1 0 , 8 , 1 0 , 1 I = . 3 9 9 3 0 1 2 0 4 0 8 3 7 1 8 - 0 4 A ( 1 0 , 8 , 1 0 , 2 I = . 2 5 7 9 9 1 4 0 0 1 8 9 8 9 8 - 0 3 A ( 1 0 , 8 , 1 0 , 3 I = . 2 8 4 2 7 0 2 7 4 4 4 8 7 7 3 - 0 3 A ( 1 0 , 8 , 1 0 , 4 I = . 3 1 5 1 6 8 8 9 4 5 8 7 7 1 8 - 0 3 A ( 1 0 , 8 , 1 0 , 5 I = . 1 4 4 9 2 6 4 9 4 4 1 4 2 2 8 - 0 3 A ( 1 0 , 8 , 1 0 , 6 I = . 6 6 6 7 2 1 2 8 8 3 1 1 5 8 3 - 0 4 A ( 1 0 , 8 , 1 0 , 7 I = . 1 3 7 8 9 4 7 8 0 8 3 8 3 7 E - 0 4 A ( 1 0 , 8 , 1 0 , 8 I = . 2 6 1 6 6 8 0 2 4 7 1 4 7 2 3 - 0 5 A ( 1 0 , 8 , 1 0 , 9 I = . 1 4 4 9 0 6 7 2 4 5 6 4 0 2 3 - 0 6 A ( 1 0 , 8 , 1 0 , 1 0 I = . 5 5 0 8 3 8 5 4 4 3 9 5 5 8 8 - 0 8 A ( 1 0 , 9 , 1 , 1 I 3 ‘ . 1 4 6 8 6 6 2 3 6 6 2 7 1 0 E + 0 1 A ( 1 0 , 9 , 1 , 2 I = - . 2 7 2 3 7 4 4 4 2 2 1 9 7 3 3 + 0 1 A ( 1 0 , 9 , 1 , 3 ) = - . 8 4 9 2 8 4 3 7 4 7 1 3 9 O E + 0 1 I I I I I I I I I I I I V I I I I I I I I I I I I I I I I I I V I I I I I I I I I I I I I I I I I I I V I I I I I I I I I I I I I I A ( 1 0 , 9 , 1 , A ( 1 0 , 9 , 1 , A ( 1 0 , 9 , 1 , A ( 1 0 , 9 , 1 , A ( 1 0 , 9 , 1 A ( 1 0 , 9 , 1 A ( 1 0 , 9 , 1 , A ( 1 0 , 9 , 2 , A ( 1 0 , 9 , 2 , A ( 1 0 , 9 , 2 , A ( 1 0 , 9 , 4 , 7 I A ( 1 0 , 9 , 4 , 8 I = A ( 1 0 , 9 , 4 , 9 I = A ( 1 0 , 9 , 4 , 1 0 I = A ( 1 0 , 9 , 5 , 1 I = - A ( 1 0 , 9 , 5 , 2 I = A ( 1 0 , 9 , 5 , 3 I = - A ( 1 0 , 9 , 5 , 4 I = A ( 1 0 , 9 , 5 , 5 I = - A ( 1 0 , 9 , 5 , 6 ) = A ( 1 0 , 9 , 5 , 7 I = - A ( 1 0 , 9 , 5 , 8 I = A ( 1 0 , 9 , 5 , 9 I = A ( 1 0 , 9 , 5 , 1 0 I = A ( 1 0 , 9 , 6 , 1 I = - A ( 1 0 , 9 , 6 , 2 I = A ( 1 0 , 9 , 6 , 3 I = - 2 7 8 . 6 8 6 8 3 7 9 2 9 4 8 7 2 3 E + 0 1 . 6 8 1 9 8 5 2 5 3 0 9 5 6 3 B + 0 1 . 2 0 3 9 1 3 1 3 9 5 5 1 8 8 E + 0 1 . 4 7 6 9 5 9 9 3 0 7 3 2 8 5 E + 0 0 . 9 5 0 0 7 5 3 9 4 9 3 9 6 3 8 - 0 1 . 5 1 9 1 8 0 9 7 8 8 8 1 2 0 3 - 0 2 . 6 4 9 6 2 9 7 9 4 6 7 9 6 4 8 - 0 3 . 2 7 2 3 6 6 9 0 5 2 1 2 4 0 E + 0 1 . 2 4 4 9 4 1 8 4 4 9 4 0 1 9 E + 0 2 . 2 2 3 8 5 6 6 7 5 6 2 4 8 5 8 + 0 1 . 3 3 0 5 4 7 8 5 6 6 8 8 5 0 3 + 0 2 . 1 0 9 1 6 5 4 1 3 6 7 7 6 9 E + 0 2 . 7 8 2 5 0 6 5 2 2 5 3 6 2 8 3 + 0 1 . 8 1 5 5 3 2 1 1 8 0 8 2 0 5 8 + 0 0 . 2 5 7 0 5 9 9 9 0 4 2 8 3 9 E + 0 0 . 6 7 2 9 8 4 8 4 7 3 3 3 2 8 3 - 0 1 . 4 3 1 8 9 7 9 8 7 8 9 1 7 2 8 - 0 2 . 8 4 9 3 0 8 2 8 8 0 9 7 3 8 E + 0 1 . 2 2 3 9 0 2 8 3 3 4 6 1 7 6 E + 0 1 . 3 8 8 1 6 4 2 4 6 0 8 2 3 1 E + 0 2 . 1 2 3 9 4 3 3 4 4 3 5 4 6 3 E + 0 2 . 2 6 7 2 9 9 5 8 3 5 5 4 2 7 E + 0 2 . 4 7 5 1 3 3 5 9 1 8 9 0 3 4 E + 0 1 . 1 9 1 7 9 2 4 2 0 2 9 7 8 6 8 + 0 1 . 2 3 9 3 0 8 4 6 9 9 2 8 8 0 E + 0 0 . 7 5 4 7 6 0 6 2 8 3 3 3 3 2 E - 0 1 . 4 5 4 4 7 8 2 3 8 5 8 9 2 2 8 - 0 2 . 6 8 6 8 0 3 5 2 5 6 8 6 2 6 8 + 0 1 . 3 3 0 5 4 0 2 9 9 4 1 5 5 9 E + 0 2 . 1 2 3 9 3 8 5 7 5 9 8 3 O S E + 0 2 . 4 0 6 5 4 9 3 0 2 9 3 5 6 0 8 + 0 2 . 4 3 7 7 8 9 4 4 6 1 1 5 4 9 E + 0 1 . 9 5 1 2 7 0 4 0 7 4 3 8 2 8 8 + 0 1 . 1 2 5 1 2 1 6 9 7 7 8 3 4 7 3 - 0 2 . 4 4 1 3 0 3 6 1 6 8 5 5 2 9 E + 0 0 . 1 1 2 6 7 0 2 8 8 4 5 0 3 2 8 + 0 0 . 4 9 5 5 2 0 3 4 8 9 7 7 1 5 E - 0 2 . 6 8 2 0 1 0 8 8 1 6 0 2 7 6 E + 0 1 . 1 0 9 1 7 1 3 4 5 2 3 3 9 2 E + 0 2 . 2 6 7 3 0 4 6 3 8 0 2 8 1 4 E + 0 2 . 4 3 7 8 0 8 2 8 1 1 8 3 2 4 E + 0 1 . 1 6 4 5 2 6 5 8 1 7 6 4 2 2 8 + 0 2 . 3 1 8 9 2 8 2 4 9 1 8 0 3 2 E + 0 0 . 1 5 0 1 8 7 3 3 8 1 4 3 5 9 E + 0 1 . 2 1 5 9 3 8 9 7 3 9 3 9 O S E + 0 0 . 5 7 6 6 9 4 3 4 9 4 3 8 1 8 8 - 0 1 . 2 1 0 3 0 5 8 0 9 7 8 7 3 1 8 - 0 2 . 2 0 3 9 0 0 9 2 9 5 4 0 4 0 E + 0 1 . 7 8 2 4 7 7 3 3 4 1 4 1 7 3 E + 0 1 . 4 7 5 1 0 5 7 8 1 8 5 3 2 0 8 + 0 1 2 7 9 A ( 1 0 , 9 , 6 , 4 ) = . 9 5 1 2 5 6 6 3 8 7 6 5 3 4 B + O l A ( 1 0 , 9 , 6 , 5 ) = . 3 1 8 9 6 5 3 8 2 8 7 4 0 l E + 0 0 A ( 1 0 , 9 , 6 , 6 ) = . 2 1 8 4 1 6 0 8 6 2 1 1 8 0 E + 0 1 A ( 1 0 , 9 , 6 , 7 ) = - . 6 2 3 5 4 2 4 8 4 8 2 7 3 4 E - 0 1 A ( 1 0 , 9 , 6 , 8 ) = . 3 0 9 3 2 4 8 6 3 4 8 3 2 0 E + 0 0 A ( 1 0 , 9 , 6 , 9 ) = . 2 7 6 9 3 6 9 2 9 7 3 1 1 6 8 - 0 1 A ( 1 0 , 9 , 6 , 1 0 I = . 1 0 1 9 7 0 9 6 0 5 6 5 7 2 8 - 0 2 A ( 1 0 , 9 , 7 , 1 ) = - . 4 7 6 9 9 4 5 8 3 3 8 3 2 0 8 + 0 0 A ( 1 0 , 9 , L 2 ) = . 8 1 5 6 1 7 5 2 7 8 1 2 7 2 E + 0 0 A ( 1 0 , 9 , 7 , 3 ) = - . 1 9 1 8 0 0 8 2 8 6 5 0 5 9 E + 0 1 A ( 1 0 , 9 , 7 , 4 ) = - . 1 2 0 2 4 6 0 3 7 8 4 0 8 4 E - 0 2 A ( 1 0 , 9 , 7 , 5 ) = - . 1 5 0 1 8 8 9 2 2 3 2 3 2 9 8 + 0 1 A ( 1 0 , 9 , 7 , 6 I = - . 6 2 3 5 1 4 5 9 6 3 7 2 8 4 E - 0 1 A ( 1 0 , 9 , 7 , 7 ) = . 1 5 4 3 9 0 6 9 2 1 2 8 8 0 E + 0 0 A ( 1 0 , 9 , 7 , 8 ) = . 7 6 6 8 1 7 6 0 4 4 5 3 5 4 E - O l A ( 1 0 , 9 , 7 , 9 ) = . 5 4 5 5 0 2 1 0 9 5 2 5 8 4 8 - 0 2 A ( 1 0 , 9 , 7 , 1 0 ) = . 2 0 3 3 3 9 2 9 8 6 5 0 4 6 E - 0 3 A ( 1 0 , 9 , 8 , 1 ) = - . 9 5 0 0 1 8 0 4 4 0 9 5 4 9 E - O l A ( 1 0 , 9 , 8 , 2 ) = . 2 5 7 0 4 5 8 0 2 1 9 4 6 3 E + 0 0 A ( 1 0 , 9 , 8 , 3 ) = - . 2 3 9 2 9 4 1 8 5 3 0 3 1 5 8 + 0 0 A ( 1 0 , 9 , 8 , 4 ) = . 4 4 1 2 9 4 9 4 7 6 3 9 1 1 E + 0 0 A ( 1 0 , 9 , 8 , 5 ) = . 2 1 5 9 4 2 1 8 0 7 1 5 5 0 8 + o o A ( 1 0 , 9 , 8 , 6 ) = . 3 0 9 3 2 4 1 5 7 1 9 1 4 4 E + 0 0 A ( 1 0 , 9 , 8 , 7 ) = . 7 6 6 8 1 8 3 6 2 8 9 9 3 6 8 - 0 1 A ( 1 0 , 9 , 8 , 8 ) = . 1 6 6 2 7 8 3 5 7 2 8 2 8 6 8 - 0 1 A ( 1 0 , 9 , 8 , 9 ) = . 1 0 9 0 3 6 3 3 2 7 4 2 1 1 8 - 0 2 A ( 1 0 , 9 , 8 , 1 0 ) = . 4 0 7 5 2 8 4 4 2 1 0 3 4 6 8 - 0 4 A ( 1 0 , 9 , 9 , 1 ) = . 5 1 9 1 3 2 9 6 4 8 3 6 9 0 E - 0 2 A ( 1 0 , 9 , 9 , 2 I = . 6 7 2 9 9 6 6 6 4 3 6 1 5 6 8 - 0 1 A ( 1 0 , 9 , 9 , 3 ) = . 7 5 4 7 4 8 2 6 0 3 6 9 5 2 8 - 0 1 A ( 1 0 , 9 , 9 , 4 ) = . 1 1 2 6 7 1 0 5 9 0 0 3 3 3 E + 0 0 A ( 1 0 , 9 , 9 , 5 ) = . 5 7 6 6 9 1 3 1 9 7 2 9 4 3 E - 0 1 A ( 1 0 , 9 , 9 , 6 ) = . 2 7 6 9 3 7 6 9 1 4 5 1 1 7 8 - 0 1 A ( 1 0 , 9 , 9 , 7 ) = . 5 4 5 5 0 1 0 3 3 4 1 1 7 1 E - 0 2 A ( 1 0 , 9 , 9 , 8 ) = . 1 0 9 0 3 6 4 0 8 6 8 4 9 1 E - 0 2 A ( 1 0 , 9 , 9 , 9 ) = . 6 8 0 6 3 0 3 7 1 7 6 1 0 3 E - 0 4 A ( 1 0 , 9 , 9 , 1 0 I = . 2 5 3 9 4 3 1 3 5 1 8 6 6 7 E - 0 5 A ( 1 0 , 9 , 1 0 , 1 I = . 6 4 9 6 4 2 8 4 4 1 0 9 6 2 E - 0 3 A ( 1 0 , 9 , 1 0 , 2 I = . 4 3 1 8 9 4 7 4 8 6 3 5 3 9 8 - 0 2 A ( 1 0 , 9 , 1 0 , 3 I = . 4 5 4 4 8 1 6 4 9 9 2 1 9 5 3 - 0 2 A ( 1 0 , 9 , 1 0 , 4 I - . 4 9 5 5 1 8 1 7 7 0 1 2 8 5 8 - 0 2 A ( 1 0 , 9 , 1 0 , 5 I = . 2 1 0 3 0 6 6 8 8 5 4 1 1 0 8 - 0 2 A ( 1 0 , 9 , 1 0 , 6 I = . 1 0 1 9 7 0 7 2 9 7 7 0 0 7 E - 0 2 A ( 1 0 , 9 , 1 0 , 7 I = . 2 0 3 3 3 9 6 6 5 0 6 3 1 4 E - 0 3 A ( 1 0 , 9 , 1 0 , 8 I = . 4 0 7 5 2 8 1 3 5 0 4 2 4 1 8 - 0 4 A ( 1 0 , 9 , 1 0 , 9 I = . 2 5 3 9 4 3 2 2 6 4 9 1 4 2 8 - 0 5 A ( 1 0 , 9 , 1 0 , 1 0 I = . 9 8 3 3 1 6 8 2 2 2 7 2 8 2 8 - 0 7 A ( 1 0 , 1 0 , 1 , 1 ) = - . 2 1 0 1 9 0 4 5 3 0 5 2 5 2 E + 0 3 A ( 1 0 , 1 0 , 1 , 2 I = ‘ . 2 4 8 6 4 3 5 8 1 3 9 0 3 8 8 + 0 3 A ( 1 0 , 1 0 , 1 , 3 ) = - . 9 9 1 4 7 0 7 8 7 0 4 8 3 4 E + 0 3 l l : I V " I I I I I I I I I I 2 8 0 A ( 1 0 , 1 0 , 1 , 4 ) = - . 3 2 1 1 8 0 8 0 7 1 1 3 6 5 8 + 0 3 A ( 1 0 , 1 0 , 1 , 5 ) = - . 3 7 9 6 7 6 9 7 2 3 8 9 2 2 3 + 0 3 A ( 1 0 , 1 0 , 1 , 6 ) = - . 3 0 4 5 1 7 9 4 6 2 4 3 2 9 E + 0 2 A ( 1 0 , 1 0 , l , 7 ) = - . 3 4 8 8 4 1 7 3 4 8 2 6 5 6 E + 0 2 A ( 1 0 , 1 0 , 1 , 8 ) = - . 1 7 3 5 7 1 4 8 3 0 4 5 8 2 8 + 0 1 A ( 1 0 , 1 0 , 1 , 9 ) = - . 5 3 1 7 3 5 6 0 5 5 6 0 2 4 E + 0 0 A ( 1 0 , 1 0 , 1 , 1 0 ) = A ( 1 0 , 1 0 , 2 , 1 ) = * . A ( 1 0 , 1 0 , 2 , 2 ) = A ( 1 0 , 1 0 , 2 , 3 ) = A ( 1 0 , 1 0 , 2 , 4 ) = A ( 1 0 , 1 0 , 2 , 5 ) = - . A ( 1 0 , 1 0 , 2 , 6 ) = A ( 1 0 , 1 0 , 2 , 7 ) = - A ( 1 0 , 1 0 , 2 , 8 ) A ( 1 o , 1 0 , 2 , 9 A ( 1 0 , 1 0 , 2 , 1 A ( 1 0 , 1 0 , 3 , 1 A ( 1 0 , 1 0 , 3 , 2 A ( 1 0 , 1 0 , 3 , 3 A ( 1 0 , 1 0 , 3 , 4 A ( 1 0 , 1 0 , 3 , 5 A ( 1 0 , 1 0 , 3 , 6 ) A ( 1 0 , 1 0 , 3 , 7 ) = - A ( 1 0 , 1 0 , 3 , 8 ) = A ( 1 0 , 1 0 , 3 , 9 ) = - A ( 1 0 , 1 0 , 3 , 1 0 ) A ( 1 0 , 1 0 , 4 , 1 ) = - A ( 1 0 , 1 0 , 4 , 2 ) = ) 0 ) ) ) ) ) A ( 1 0 , 1 0 , 4 , 3 ) = - . A ( 1 o , 1 o , 4 , 4 ) - A ( 1 0 , 1 0 , 4 , 5 ) = - A ( 1 0 , 1 0 , 4 , 6 ) = A ( 1 0 , 1 0 , 4 , 7 ) = - . A ( 1 0 , 1 0 , 4 , 8 ) = A ( 1 0 , 1 0 , 4 , 9 ) = - A ( 1 0 , 1 0 , 4 , 1 0 ) = A ( 1 0 , 1 0 , 5 , 1 ) = - A ( 1 0 , 1 0 , 5 , 2 ) = - A ( 1 0 , 1 0 , 5 , 3 ) = - . A ( 1 0 , 1 O , 5 , 4 ) = - a ( 1 o , 1 o , 5 , 5 ) = - A ( 1 0 , 1 0 , 5 , 6 ) = A ( 1 0 , 1 0 , 5 , 7 ) = ' . a ( 1 0 , 1 0 , 5 , 8 ) = - A ( 1 0 , 1 0 , 5 , 9 ) = - A ( 1 0 , 1 0 , 5 , 1 0 ) - A ( 1 0 , 1 0 , 6 , 1 ) = - A ( 1 0 , 1 0 , 6 , 2 ) = A ( 1 0 , 1 0 , 6 , 3 ) = . 1 0 6 2 0 4 4 3 9 2 1 6 5 3 8 - 0 1 2 4 8 6 4 3 6 0 4 2 7 8 5 6 E + 0 3 . 2 8 1 9 5 1 4 8 1 6 2 8 4 Z E + 0 4 . 6 3 7 6 7 8 5 6 5 9 7 9 O O E + 0 2 . 2 8 3 0 6 3 3 8 8 0 6 1 5 2 E + 0 4 4 3 1 0 6 0 8 5 7 7 7 2 8 3 E + 0 2 . 4 7 8 1 4 1 7 6 5 5 9 4 4 B E + 0 3 . 1 1 7 6 7 0 2 3 2 0 5 7 5 7 E + 0 2 . 2 2 8 8 1 8 6 0 7 6 2 8 3 5 3 + 0 2 . 5 3 1 0 3 2 7 3 7 3 4 4 S O E + 0 0 . 1 3 3 7 9 8 5 2 1 3 3 2 2 1 E + 0 0 . 9 9 1 4 7 0 6 4 2 0 8 9 8 4 B + 0 3 . 6 3 7 6 6 0 7 1 3 1 9 5 8 0 8 + 0 2 . 4 1 8 3 6 7 5 0 7 5 5 3 1 0 E + 0 4 . 2 3 7 1 5 7 7 4 9 1 7 6 0 3 8 + 0 3 . 1 6 2 2 4 1 9 0 3 4 9 5 7 9 E + 0 4 . 6 4 0 4 1 8 9 2 5 2 8 5 3 4 E + 0 2 . 1 5 2 0 2 6 7 7 4 4 0 6 4 3 E + 0 3 . 1 6 2 2 6 5 9 5 1 9 3 1 4 B E + 0 1 . 2 4 2 3 9 7 2 6 4 2 0 4 9 Z E + 0 1 . 1 2 1 1 6 2 9 3 4 2 8 6 9 9 E + 0 0 . 3 2 1 1 8 1 4 4 0 3 5 3 3 9 E + 0 3 . 2 8 3 0 6 3 4 5 8 2 5 1 9 5 E + 0 4 2 3 7 1 5 8 0 2 3 8 3 4 2 3 E + 0 3 . 2 8 1 0 6 9 9 2 2 0 6 5 7 3 8 + 0 4 . 1 6 2 8 9 0 5 6 2 0 5 7 S O E + 0 3 . 4 7 5 2 5 4 3 9 4 0 5 4 4 l E + 0 3 2 1 7 4 7 3 6 4 0 4 4 1 8 9 E + 0 2 . 2 2 5 1 4 2 3 1 7 8 6 1 3 2 E + 0 2 . 5 8 2 2 0 7 0 9 2 0 8 3 9 9 E + 0 0 . 1 8 2 5 7 0 1 3 6 4 7 2 3 S E + 0 0 . 3 7 9 6 7 6 7 9 4 5 2 8 9 6 E + 0 3 . 4 3 1 0 6 7 0 4 7 1 1 9 1 4 E + 0 2 1 6 2 2 4 1 8 6 9 7 3 5 7 Z E + 0 4 . 1 6 2 8 9 0 8 4 4 3 4 5 0 9 E + 0 3 . 6 1 6 0 7 4 5 9 9 2 6 6 0 5 E + 0 3 . 1 3 1 1 1 9 7 0 4 2 4 6 5 2 8 + 0 2 5 6 1 4 1 8 5 7 3 2 6 0 3 1 3 + 0 2 . 6 8 6 4 6 1 0 9 1 0 4 1 5 6 3 + 0 0 . 6 4 4 3 8 3 6 3 5 3 7 1 9 2 E + 0 0 . 8 1 0 0 5 0 0 3 9 4 3 5 7 4 8 - 0 1 . 3 0 4 5 1 9 3 8 6 2 9 1 5 0 3 + 0 2 . 4 7 8 1 4 2 2 4 4 3 3 8 9 9 E + 0 3 . 6 4 0 4 1 6 3 5 5 1 3 3 0 6 E + 0 2 2 8 1 A ( 1 0 , 1 0 , 6 , 4 ) = . 4 7 5 2 5 4 5 5 6 1 7 9 O S E + 0 3 A ( 1 0 , 1 0 , 6 , 5 ) = . 1 3 1 1 1 9 2 3 9 3 3 0 2 9 8 + 0 2 A ( 1 0 , 1 0 , 6 , 6 ) = . 7 2 8 3 6 3 9 9 5 5 5 2 0 6 E + 0 2 A ( l O , 1 0 , 6 , 7 ) = . 1 4 5 1 4 9 2 1 7 5 4 5 9 9 E + 0 1 A ( 1 0 , 1 0 , 6 , 8 ) = . 3 1 8 7 2 4 0 9 2 8 4 1 1 5 E + 0 1 A ( 1 0 , 1 0 , 6 , 9 ) = . 2 5 6 8 8 5 3 1 1 7 9 9 1 2 E + 0 0 A ( 1 0 , 1 0 , 6 , 1 0 ) = . 4 5 4 3 0 2 4 2 7 8 2 4 5 9 8 - 0 1 A ( 1 0 , 1 0 , 7 , 1 ) = — . 3 4 8 8 4 1 0 8 6 3 2 8 0 3 8 + 0 2 A ( 1 0 , 1 o , 7 , 2 ) = - . 1 1 7 6 7 1 7 9 1 3 1 5 0 8 8 + 0 2 A ( 1 0 , 1 0 , 7 , 3 ) = - . 1 5 2 0 2 6 6 2 8 6 1 3 4 7 E + 0 3 A ( 1 0 , 1 0 , L 4 ) = - . 2 1 7 4 7 4 6 7 3 9 8 6 4 B E + 0 2 1 ( 1 0 , 1 0 , 7 , 5 ) = - . 5 6 1 4 1 8 2 1 3 2 4 8 2 5 8 + 0 2 A ( 1 0 , 1 0 , L 6 ) = . 1 4 5 1 4 8 5 4 4 0 1 3 5 0 8 + 0 1 A ( 1 0 , 1 0 , 7 , 7 ) = - . 5 3 6 3 0 9 4 3 8 5 7 1 3 3 E + 0 1 A ( 1 0 , 1 0 , L 8 ) = . 3 0 2 9 9 5 8 6 2 4 3 9 2 7 E - 0 1 A ( 1 0 , 1 0 , L 9 ) = . 1 0 0 8 1 3 0 7 6 8 3 1 4 0 E + 0 0 A ( 1 0 , 1 0 , 7 , 1 0 ) = . 8 5 7 1 2 6 5 7 0 6 4 5 0 5 8 - 0 2 A ( 1 0 , 1 0 , 8 , 1 ) = - . 1 7 3 5 7 2 3 9 4 9 9 6 8 8 8 + 0 1 A ( 1 0 , 1 0 , 8 , 2 ) = . 2 2 8 8 1 8 8 8 4 1 9 3 9 0 E + 0 2 A ( 1 0 , 1 0 , 8 , 3 ) = . 1 6 2 2 6 3 2 8 7 6 0 3 8 6 E + 0 1 A ( 1 0 , 1 0 , 8 , 4 ) = . 2 2 5 1 4 2 4 8 8 9 2 6 6 5 8 + 0 2 A ( l O , 1 0 , 8 , 5 ) = - . 6 8 6 4 6 7 2 8 9 9 2 4 6 Z E + 0 0 A ( 1 0 , 1 0 , 8 , 6 ) = . 3 1 8 7 2 4 2 4 2 5 9 7 8 2 E + 0 1 A ( 1 0 , 1 0 , 8 , 7 ) = . 3 0 2 9 9 4 2 0 4 6 8 5 0 9 8 - 0 1 A ( 1 0 , 1 0 , 8 , 8 ) = . 4 1 8 9 1 2 3 4 3 9 7 1 9 0 8 + o o A ( 1 0 , 1 0 , 8 , 9 ) = . 3 4 2 6 5 2 6 4 1 9 9 3 4 8 E - 0 1 A ( 1 0 , 1 0 , 8 , 1 0 ) = . 1 8 1 7 6 4 8 5 8 0 7 5 4 4 8 - 0 2 A ( 1 0 , 1 0 , 9 , 1 ) = - . 5 3 1 7 3 4 7 6 5 5 0 7 2 8 E + 0 0 A ( 1 0 , 1 L 9 , 2 ) = - . 5 3 1 0 3 5 2 3 7 0 1 4 2 9 8 + 0 0 A ( 1 L 1 L 9 , 3 ) = - . 2 4 2 3 9 6 9 9 6 3 5 6 S S E + 0 1 A ( 1 0 , 1 L 9 , 4 ) = - . 5 8 2 2 0 8 8 0 5 7 1 7 5 3 E + 0 0 A ( 1 L 1 L 9 , 5 ) = - . 6 4 4 3 8 2 9 2 3 3 7 5 8 2 E + 0 0 A ( 1 L 1 0 , 9 , 6 ) = . 2 5 6 8 8 5 1 4 0 2 0 2 9 4 E + 0 0 A ( 1 L 1 0 , 9 , 7 ) = . 1 0 0 8 1 3 1 0 4 1 0 1 6 9 E + 0 0 A ( 1 L 1 0 , 9 , 8 ) = . 3 4 2 6 5 2 6 1 9 8 7 4 5 7 8 - 0 1 A ( 1 0 , 1 0 , 9 , 9 ) = . 2 2 1 3 4 9 4 2 5 0 0 9 9 8 E - 0 2 A ( 1 0 , 1 0 , 9 , 1 0 ) = . 1 1 0 5 9 9 4 9 9 6 0 6 6 8 8 - 0 3 A ( 1 0 , 1 0 , 1 0 , 1 ) = . 1 0 6 2 0 4 2 6 0 5 1 9 0 1 8 - 0 1 A ( 1 0 , 1 o , 1 o , 2 ) = . 1 3 3 7 9 8 5 7 2 4 6 7 6 4 E + 0 0 A ( 1 0 , 1 0 , 1 0 , 3 ) = . 1 2 1 1 6 2 8 8 8 5 0 6 6 6 E + o o a ( 1 o , 1 o , 1 o , 4 ) = . 1 8 2 5 7 0 1 7 3 2 5 9 5 9 E + 0 0 A ( 1 0 , 1 0 , 1 0 , 5 ) = . 8 1 0 0 4 9 8 7 8 7 8 2 5 9 E - 0 1 A ( 1 0 , 1 0 , 1 0 , 6 ) = . 4 5 4 3 0 2 4 7 0 9 3 4 6 4 8 - 0 1 A ( 1 0 , 1 0 , 1 0 , 7 ) = . 8 5 7 1 2 6 4 9 8 8 8 5 9 2 8 - 0 2 A ( 1 0 , 1 0 , 1 0 , 8 ) = . 1 8 1 7 6 4 8 6 4 0 7 8 1 0 E - 0 2 A ( 1 o , 1 o , 1 o , 9 ) = . 1 1 0 5 9 9 4 9 8 2 4 2 4 4 8 - 0 3 A ( 1 0 , 1 0 , 1 0 , 1 0 ) = . 5 1 3 7 8 9 2 8 8 0 0 3 6 1 E - 0 5 A ( l l , l , l , l ) = . 9 2 7 3 6 8 0 5 3 0 5 3 2 1 E - 0 1 A ( 1 1 , l , 1 , 2 ) = . 1 4 2 3 1 8 0 9 6 3 3 3 8 4 E + 0 0 A ( 1 1 , 1 , 1 , 3 ) = . 8 0 0 3 4 8 4 7 7 1 6 8 8 8 E - 0 1 A ( 1 1 , l , 1 , 4 ) = A ( l l , l , l , 5 ) = A ( l l , l , l , 6 ) = A ( l l , l , l , 7 ) = A ( l l , l , l , 8 ) = A ( l l , 1 , l , 9 ) = A ( l l , l , l , 1 0 ) = A ( l l , l , l , l l ) = A ( l l , l , 2 , l ) = A ( l l , l , 2 , 2 ) = A ( l l , 1 , 2 , 3 ) = A ( l l , l , 2 , 4 ) = A ( l l , l , 2 , 5 ) = A ( 1 1 , l , 2 , 6 ) = A ( l l , l , 2 , 7 ) = A ( l l , l , 2 , 8 ) = A ( l l , l , 2 , 9 ) = A ( l l , l , 2 , 1 0 ) = A ( l l , l , 2 , l l ) = A ( l l , l , 3 , l ) = A ( l l , l , 3 , 2 ) = A ( l l , l , 3 , 3 ) = A ( 1 1 , l , 3 , 4 ) = A ( 1 1 , 1 , 3 , 5 ) = A ( 1 1 , 1 , 3 , 6 ) = A ( 1 1 , l , 3 , 7 ) = A ( l l , 1 , 3 , 8 ) = A ( 1 1 , l , 3 , 9 ) = A ( l l , l , 3 , 1 0 ) = A ( l l , l , 3 , l l ) = A ( l l , 1 , 4 , l ) = A ( 1 1 , 1 , 4 , 2 ) = A ( 1 1 , 1 , 4 , 3 ) = A ( 1 1 , 1 , 4 , 4 ) = A ( 1 1 , 1 , 4 , 5 ) = A ( 1 1 , 1 , 4 , 6 ) = A ( 1 1 , 1 , 4 , 7 ) = A ( l l , l , 4 , 8 ) = A ( 1 1 , 1 , 4 , 9 ) = A ( 1 1 , 1 , 4 , 1 0 ) = A ' ( 1 1 , 1 , 4 , 1 1 ) = A ( 1 1 , l , 5 , 1 ) = A ( 1 1 , 1 , 5 , 2 ) = A ( 1 1 , 1 , 5 , 3 ) = A ( 1 1 , 1 , 5 , 4 ) = A ( 1 1 , 1 , 5 , 5 ) = A ( 1 1 , 1 , 5 , 6 ) = A ( l l , l , 5 , 7 ) = A ( 1 1 , 1 , 5 , 8 ) = A ( l l , l , 5 , 9 ) = 2 8 2 . 4 4 2 5 8 3 5 5 6 4 3 2 5 1 E - 0 1 . 1 6 3 5 7 9 4 8 6 9 8 8 9 7 8 - 0 1 . 5 0 4 8 0 5 9 6 7 0 5 7 l l E - 0 2 . 1 1 3 0 3 1 0 9 9 4 0 8 5 4 8 - 0 2 . 1 6 9 5 1 8 4 2 2 7 2 3 0 6 8 - 0 3 . 1 8 8 4 1 9 4 8 3 4 2 8 9 6 8 - 0 4 . 8 8 0 5 6 3 9 2 6 2 1 9 9 3 8 - 0 6 . 2 4 1 8 4 2 2 9 3 2 4 0 1 5 8 - 0 7 . 1 4 2 3 1 8 0 7 4 6 8 0 5 9 8 + 0 0 . 2 4 2 4 0 4 7 5 7 4 0 9 5 3 E + 0 0 . 1 6 4 8 6 4 1 7 0 5 9 0 5 9 8 + 0 0 . 8 9 6 0 9 4 7 2 0 5 9 2 3 7 E - O l . 3 5 6 2 6 3 9 1 5 3 0 9 6 B E - O l . 1 0 6 0 3 6 8 4 9 2 5 6 2 7 E - 0 1 . 2 4 8 2 6 2 2 5 6 5 8 2 1 7 E - 0 2 . 3 5 9 7 3 0 0 9 6 7 0 4 4 2 E - 0 3 . 4 1 2 7 0 4 8 3 2 9 3 9 4 3 8 - 0 4 . 1 8 7 2 8 6 4 4 8 1 7 2 2 3 8 - 0 5 . 5 2 5 6 8 6 9 9 3 6 5 7 6 3 8 - 0 7 . 8 0 0 3 4 9 2 3 9 2 5 2 6 B E - O l . 1 6 4 8 6 4 0 7 6 1 7 7 7 G E + 0 0 . 1 2 8 9 4 1 1 7 2 9 8 1 2 9 8 + 0 0 . 7 4 1 5 6 5 3 4 2 4 6 8 6 8 8 - 0 1 . 3 1 3 8 2 9 1 5 9 7 8 6 1 1 8 - 0 1 . 9 4 6 5 5 3 6 3 1 0 0 1 7 3 E - 0 2 . 2 2 9 8 7 6 3 6 6 9 8 4 1 7 8 - 0 2 . 3 3 3 4 1 7 4 1 5 7 3 1 6 7 8 - 0 3 . 3 9 2 6 4 9 7 6 7 8 4 6 3 6 8 - 0 4 . 1 7 7 7 7 6 4 9 4 4 5 8 8 3 8 - 0 5 . 5 0 9 2 6 2 0 2 6 9 9 3 0 8 3 - 0 7 . 4 4 2 5 8 2 5 3 0 2 4 9 6 4 E - 0 1 . 8 9 6 0 9 6 8 0 8 2 1 0 1 3 8 - 0 1 . 7 4 1 5 6 3 7 9 9 3 8 3 5 8 E - 0 1 . 4 3 7 4 8 0 0 7 2 4 3 2 6 6 8 - 0 1 . 1 9 2 1 9 6 7 4 5 4 1 0 9 1 E - 0 1 . 5 8 4 1 7 3 9 3 6 3 8 5 9 2 8 - 0 2 . 1 4 4 6 1 0 4 7 2 6 2 5 5 7 8 - 0 2 . 2 0 9 5 1 5 7 3 0 1 4 8 2 7 E - 0 3 . 2 4 9 1 6 7 0 3 5 3 0 6 6 4 8 - 0 4 . 1 1 2 3 4 1 5 1 8 5 7 6 6 4 8 - 0 5 . 3 2 3 2 6 9 5 7 8 7 4 4 7 3 8 - 0 7 . 1 6 3 5 8 0 3 5 8 2 8 4 8 9 8 - 0 1 . 3 5 6 2 6 1 8 7 7 6 0 4 9 9 E - O l . 3 1 3 8 3 1 0 4 4 0 0 4 4 7 8 - 0 1 . 1 9 2 1 9 5 9 6 0 8 8 0 7 8 E - 0 1 . 8 8 6 7 5 2 2 5 8 8 8 4 3 7 E - 0 2 . 2 7 5 0 3 6 4 0 9 8 5 7 4 2 E - 0 2 . 7 0 5 6 3 7 2 2 3 2 9 0 9 8 3 - 0 3 . 1 0 3 2 7 1 1 7 4 4 2 4 4 4 8 - 0 3 . 1 2 6 2 0 7 2 3 5 3 1 1 4 3 3 - 0 4 A ( 1 1 , 1 , 5 , 1 A ( 1 1 , l , 5 , 1 A ( 1 1 , 1 , 6 , 1 A ( 1 1 , L 6 , 2 A ( 1 1 , 1 , 6 , 3 A ( l l , l , 6 , 4 A ( 1 1 , L 6 , 5 A ( 1 l , 1 , 6 , 6 A ( 1 1 , 1 , 6 , 7 A ( l l , l , 6 , 8 A ( 1 1 , 1 , 6 , 9 A ( 1 1 , l , 6 , 1 A ( 1 1 , l , 6 , 1 A ( 1 1 , 1 , 7 , 1 A ( 1 1 , 1 , 7 , 2 A ( 1 1 , 1 , 7 , 3 A ( 1 1 , 1 , 7 , 4 A ( 1 1 , 1 , 7 , 5 A ( 1 1 , 1 , 7 , 6 A ( 1 1 , L 7 , 7 A ( 1 L 1 , 7 , 8 A ( 1 1 , l , 7 , 9 A ( 1 1 , 1 , 8 , 1 M 1 1 , 1 , ' 1 9 1 ) = A ( 1 1 , 1 , 9 , 2 ) = A ( 1 1 , 1 , 9 , 3 ) = A ( 1 1 , 1 , 9 , 4 ) = A ( 1 1 , 1 , 9 , 5 ) = A ( 1 1 , 1 , 9 , 6 ) = A ( 1 1 , 1 , 9 , 7 ) = A ( l l , l , 9 , 8 ) = A ( 1 1 , 1 , 9 , 9 ) = A ( 1 1 , 1 , 9 , 1 0 ) = A ( 1 1 , 1 , 9 , 1 1 ) = A ( 1 1 , 1 , 1 0 , 1 ) = A ( 1 1 , 1 , 1 0 , 2 ) = A ( 1 1 , 1 , 1 0 , 3 ) = A ( 1 1 , 1 , 1 0 , 4 ) = 2 8 3 . 5 7 2 1 7 8 4 3 9 2 9 5 3 6 8 - 0 6 . 1 6 8 3 3 6 7 8 2 1 5 2 5 6 8 - 0 7 . 5 0 4 8 0 0 9 6 9 2 4 7 3 0 8 - 0 2 . 1 0 6 0 3 8 0 8 3 1 7 6 8 3 8 - 0 1 . 9 4 6 5 4 1 0 6 4 6 9 5 3 4 8 - 0 2 . 5 8 4 1 8 1 2 6 6 1 8 5 6 2 8 - 0 2 . 2 7 5 0 3 4 1 1 3 2 9 2 3 5 8 - 0 2 . 8 5 8 9 2 5 0 4 2 1 6 6 4 5 E - 0 3 . 2 2 3 4 9 0 6 4 7 8 9 7 5 1 E - 0 3 . 3 2 7 8 0 3 3 0 4 0 0 3 2 8 8 - 0 4 . 4 0 3 8 4 9 2 7 7 9 3 0 1 4 3 - 0 5 . 1 8 2 9 3 5 3 1 9 3 3 7 2 2 8 - 0 6 . 5 4 0 2 3 2 7 5 5 7 5 2 4 3 8 - 0 8 . 1 1 3 0 3 3 0 6 7 1 7 9 9 1 8 - 0 2 . 2 4 8 2 5 7 3 7 9 7 3 5 1 5 8 - 0 2 . 2 2 9 8 8 1 6 2 3 3 6 3 3 3 8 - 0 2 . 1 4 4 6 0 7 0 7 6 9 3 6 1 5 8 - 0 2 . 7 0 5 6 5 0 7 0 6 3 2 2 5 6 3 - 0 3 . 2 2 3 4 8 7 7 5 8 8 8 7 5 9 8 - 0 3 . 6 0 0 7 3 4 9 0 2 3 2 0 7 1 8 - 0 4 . 8 8 9 6 5 0 9 3 5 6 7 5 9 5 8 - 0 5 . 1 1 2 7 2 7 5 9 0 1 9 5 7 6 8 - 0 5 . 5 1 4 2 2 7 2 7 4 0 9 5 4 5 8 - 0 7 . 1 5 5 6 3 8 1 4 7 1 6 1 8 0 8 - 0 8 . 1 6 9 5 1 3 3 6 1 3 8 5 0 4 8 - 0 3 . 3 5 9 7 4 2 9 6 1 9 6 1 7 3 8 - 0 3 . 3 3 3 4 0 3 0 0 5 1 2 9 1 8 8 - 0 3 . 2 0 9 5 2 5 4 6 9 5 2 9 1 3 8 - 0 3 1 J 3 2 6 6 8 1 7 2 6 2 6 9 8 - 0 3 . 3 2 7 8 1 5 5 5 4 3 2 8 4 8 8 - 0 4 . 8 8 9 6 3 2 2 2 2 4 6 7 1 8 8 - 0 5 . 1 3 1 8 9 7 1 6 9 3 6 4 2 4 8 - 0 5 . 1 6 8 2 8 8 3 4 6 8 1 3 4 8 8 - 0 6 . 7 6 7 2 8 5 2 2 7 7 1 5 1 9 8 - 0 8 . 2 3 3 1 9 7 6 0 5 5 4 0 0 9 8 - 0 9 . 1 8 8 4 2 7 1 7 9 3 1 7 3 3 8 - 0 4 . 4 1 2 6 8 5 0 7 0 1 8 7 9 9 8 - 0 4 . 3 9 2 6 7 2 1 4 4 8 2 6 6 3 8 - 0 4 . 2 4 9 1 5 1 3 8 2 9 0 2 8 2 8 - 0 4 . 1 2 6 2 1 4 5 8 2 8 9 1 7 5 8 ‘ 0 4 . 4 0 3 8 2 6 1 4 4 0 7 9 7 4 E - 0 5 . 1 1 2 7 3 2 1 5 4 4 1 1 4 3 8 - 0 5 . 1 6 8 2 8 3 9 5 5 6 5 9 3 8 8 - 0 6 . 2 2 0 6 0 9 3 0 5 9 6 2 0 2 3 - 0 7 . 1 0 1 2 2 7 5 4 1 3 6 6 5 7 8 - 0 8 . 3 1 5 6 1 7 3 2 5 9 7 5 5 8 8 - 1 0 . 8 8 0 5 0 4 6 7 1 3 9 6 6 6 E - 0 6 . 1 8 7 3 0 1 8 5 7 7 1 2 5 4 8 - 0 5 . 1 7 7 7 5 8 9 2 8 0 2 1 6 3 8 - 0 5 . 1 1 2 3 5 4 0 9 4 8 2 7 7 9 8 - 0 5 I I I I I I v v v I I v I I v v I I O V V I I I — I I I I a I v I I v I I v I I v I I v v I I v I I I I O V I I V A ( 1 1 , 1 , 1 0 , 5 ) A ( 1 1 , 1 , 1 0 , 6 ) A ( 1 1 , 1 , 1 0 , 7 ) A ( l l , 1 , 1 0 , 8 ) A ( l l , l , 1 0 , 9 ) A ( 1 1 , l , 1 0 , 1 0 A ( 1 1 , 1 , 1 0 , l l A ( l l , 1 , 1 1 , 1 ) A ( 1 1 , 1 , 1 1 , 2 ) A ( l l , 1 , l l , 3 ) A ( 1 1 , 1 , 1 1 , 4 ) A ( l l , l , 1 1 , 5 ) A ( 1 1 , 1 , l l , 6 ) A ( l l , l , l l , 7 ) A ( 1 1 , l , l l , 8 ) A ( l l , 1 , 1 1 , 9 ) A ( 1 1 , 1 , 1 1 , 1 0 A ( 1 1 , 1 , 1 1 , 1 l A ( 1 1 , 2 , 1 , 1 ) = - A ( 1 1 , 2 , 1 , 2 ) = A ( 1 1 , 2 , 1 , 3 ) = A ( 1 1 , 2 , 1 , 4 A ( l l , 2 , l , 5 A ( 1 1 , 2 , 1 , 6 A ( 1 1 , 2 , 1 , 7 A ( 1 1 , 2 , l , 8 A ( 1 1 , 2 , 1 , 9 A ( l l , 2 , 1 , 1 A ( 1 1 , 2 , 1 , 1 2 3 4 5 6 7 3 > 3 ) A ( 1 1 , 2 , 2 , A ( 1 1 , 2 , 2 , A ( l l , 2 , 2 , A ( 1 1 , 2 , 2 , A ( l l , 2 , 2 , A ( 1 1 , 2 , 2 , A ( 1 1 , 2 , 2 , A ( l l , 2 , 2 , 8 A ( 1 1 , 2 , 2 , 9 A ( l l , 2 , 2 , 1 A ( 1 1 , 2 , 2 , 1 1 A ( 1 1 , 2 , 3 , 1 ) = A ( 1 1 , 2 , 3 , 2 ) = A ( 1 1 , 2 , 3 , 3 ) = A ( 1 1 , 2 , 3 , 4 ) = A ( 1 1 , 2 , 3 , 5 ) = A ( 1 1 , 2 , 3 , 6 ) - A ( 1 1 , 2 , 3 , 7 ) A ( 1 1 , 2 , 3 , 8 ) A ( 1 1 , 2 , 3 , 9 ) = A ( 1 1 , 2 , 3 , 1 0 ) = 2 8 4 . 5 7 2 1 1 7 4 5 6 9 6 5 0 6 E - 0 6 . 1 8 2 9 5 5 6 2 6 6 4 8 6 1 E - 0 6 . 5 1 4 1 8 3 1 1 4 9 7 4 6 4 8 - 0 7 . 7 6 7 3 4 2 1 8 4 9 3 1 9 1 3 - 0 8 . 1 0 1 2 2 4 0 8 5 1 0 3 5 2 E - 0 8 . 4 6 4 1 1 5 9 5 0 5 3 2 5 3 8 - 1 0 = . 1 4 5 4 3 6 2 3 2 8 9 1 1 5 E - 1 1 . 2 4 1 8 5 7 6 2 8 3 6 9 1 5 E - 0 7 . 5 2 5 6 4 7 1 6 3 8 5 1 5 1 E - 0 7 . 5 0 9 3 0 7 7 5 8 8 8 3 5 8 8 - 0 7 . 3 2 3 2 3 6 3 5 0 3 2 4 7 2 E - 0 7 . 1 6 8 3 5 3 2 2 0 1 1 4 6 6 3 - 0 7 . 5 4 0 1 7 6 2 8 6 6 8 6 9 0 8 - 0 8 . 1 5 5 6 5 1 1 9 5 8 3 8 5 2 E - 0 8 . 2 3 3 1 7 8 6 1 8 1 2 4 2 9 E - 0 9 . 3 1 5 6 3 2 5 6 4 9 7 9 2 1 8 - 1 0 . 1 4 5 4 3 1 3 9 3 9 6 1 3 3 3 - 1 1 . 4 6 7 7 4 1 2 8 3 2 6 6 0 4 3 - 1 3 . 4 2 1 6 0 3 3 8 0 9 8 2 5 6 3 - 0 2 . 5 5 4 5 7 8 4 2 8 9 2 7 9 3 8 - 0 1 . 6 4 7 5 5 1 0 4 5 6 9 4 8 5 8 - 0 1 . 2 6 5 2 0 8 8 1 0 0 1 4 8 8 8 - 0 1 . 1 2 3 3 1 1 6 6 2 7 9 1 8 2 3 - 0 1 . 3 1 4 2 4 9 7 3 1 3 0 9 2 5 E - 0 2 . 8 3 2 1 1 2 0 2 0 1 3 4 4 5 8 - 0 3 . 1 0 7 7 1 6 4 9 9 7 1 2 7 5 3 - 0 3 . 1 3 6 5 8 6 1 9 7 7 8 3 1 2 8 - 0 4 . 5 6 8 2 2 9 0 4 2 9 2 9 8 6 E - 0 6 . 1 7 2 2 5 3 2 5 4 0 2 1 5 9 8 - 0 7 . 5 5 4 5 7 8 3 7 5 2 3 1 3 6 3 - 0 1 . 2 6 6 1 7 8 8 2 9 1 8 7 9 9 8 + 0 0 . 2 1 3 1 2 3 7 8 6 1 1 0 3 7 E + 0 0 . 1 0 6 1 5 9 2 9 9 2 1 1 8 7 E + 0 0 . 4 4 1 5 7 6 5 3 2 8 3 0 3 7 3 - 0 1 . 1 2 5 4 7 7 2 3 8 6 3 4 6 3 8 - 0 1 . 3 0 3 7 1 6 8 1 6 0 9 7 2 2 E - 0 2 . 4 2 5 6 2 6 1 0 6 7 8 9 4 2 E - 0 3 . 5 0 1 2 8 6 4 2 1 2 9 7 2 1 8 - 0 4 . 2 2 1 7 0 1 3 2 5 6 5 3 3 6 8 - 0 5 . 6 3 4 5 3 1 2 2 4 6 4 6 9 6 8 - 0 7 . 6 4 7 5 5 1 2 5 8 1 5 2 8 2 3 - 0 1 . 2 1 3 1 2 3 7 5 7 5 3 0 4 1 E + 0 0 . 1 8 3 6 3 5 3 3 5 0 5 1 8 0 8 + 0 0 . 1 0 0 0 6 3 3 1 6 9 3 8 7 6 E + 0 0 . 4 3 1 8 4 7 0 3 0 9 5 9 0 3 8 - 0 1 . 1 2 6 8 6 2 1 9 5 2 1 1 2 9 E - O l . 3 1 2 6 1 5 4 1 9 9 8 9 0 2 8 - 0 2 . 4 4 5 4 7 2 3 0 8 9 1 1 1 2 8 - 0 3 . 5 3 0 7 9 9 3 1 1 6 3 3 2 5 E - 0 4 . 2 3 7 1 9 0 9 3 2 8 5 0 2 4 8 - 0 5 A ( l l , 2 , 3 , A ( 1 1 , 2 , 4 , 1 ) ) = ) - . - . - ) = ) = ) = ) 2 ) = ) s I I I ) = A ( 1 1 , 2 , 4 , 1 0 ) A ( 1 1 , 2 , 4 , 1 1 ) A ( 1 1 , 2 , 5 , 1 ) = A ( 1 1 , 2 , 5 , 2 ) = A ( 1 l , 2 , 5 , 3 ) = A ( 1 1 , 2 , 5 , 4 ) = A ( 1 1 , 2 , 5 , 5 ) = A ( 1 1 , 2 , 5 , 6 ) = 7 ) = 8 ) = 9 ) = 1 0 ) 1 ) ) a A ( 1 1 , 2 , 6 , 2 ) = A ( 1 1 , 2 , 6 , 3 ) = A ( l l , 2 , 6 , 4 ) = A ( 1 1 , 2 , 6 , 5 ) = A ( 1 1 , 2 , 6 , 6 ) = A ( 1 1 , 2 , 6 , 7 ) = A ( 1 1 , 2 , 6 , 8 ) = A ( 1 1 , 2 , 6 , 9 ) = A ( 1 1 , 2 , 6 , 1 0 ) - A ( 1 1 , 2 , 6 , 1 1 ) = A ( 1 1 , 2 , 7 , 1 ) - A ( 1 1 , 2 , 7 , 2 ) = a ( 1 1 , 2 , 7 , 3 ) - A ( 1 1 , 2 , 7 , 4 ) = A ( 1 1 , 2 , 7 , 5 ) = A ( 1 1 , 2 , 7 , 6 ) = A ( 1 1 , 2 , 7 , 7 ) - A ( 1 1 , 2 , 7 , 8 ) = A ( 1 1 , 2 , 7 , 9 ) = A ( 1 1 , 2 , 7 , 1 0 ) - A ( 1 1 , 2 , 7 , 1 1 ) = A ( 1 1 , 2 , 8 , 1 ) = A ( 1 1 , 2 , 8 , 2 ) = A ( 1 1 , 2 , 8 , 3 ) = A ( 1 1 , 2 , 8 , 4 ) - A ( 1 1 , 2 , 8 , 5 ) - 2 8 5 . 6 8 5 4 4 0 8 8 5 5 7 8 3 1 3 - 0 7 . 2 6 5 2 0 8 4 2 1 0 4 2 1 9 8 - 0 1 . 1 0 6 1 5 9 3 7 0 6 3 2 6 7 E + 0 0 . 1 0 0 0 6 3 2 7 5 3 7 8 4 9 8 + 0 0 . 5 6 3 4 3 6 7 0 2 1 4 1 1 9 E - O l . 2 5 4 0 6 8 3 6 7 8 6 7 1 5 E - 0 1 . 7 5 4 0 7 2 4 8 3 3 2 3 4 0 E - 0 2 . 1 8 9 7 2 0 0 6 1 6 8 9 5 1 8 - 0 2 . 2 7 0 4 0 0 4 4 4 3 7 8 5 4 8 - 0 3 . 3 2 5 4 7 3 5 2 9 2 3 0 1 8 8 - 0 4 . 1 4 4 9 6 6 9 2 7 2 6 2 4 0 E - 0 5 . 4 2 0 7 8 4 4 4 7 8 4 0 9 9 E - 0 7 . 1 2 3 3 1 2 0 2 8 8 4 5 2 5 3 - 0 1 . 4 4 1 5 7 5 6 2 9 7 3 8 5 1 E - 0 1 . 4 3 1 8 4 8 0 1 0 5 5 7 5 9 8 - 0 1 . 2 5 4 0 6 8 0 2 0 6 9 4 8 3 E - 0 1 . 1 1 9 3 8 6 2 2 4 8 3 2 8 5 8 - 0 1 . 3 6 3 3 7 6 6 3 8 6 8 8 3 5 E - 0 2 . 9 4 2 5 1 4 8 7 5 9 8 7 4 0 3 - 0 3 . 1 3 6 2 4 3 0 0 3 9 0 8 0 2 8 - 0 3 . l 6 7 8 3 8 6 1 0 4 9 4 1 9 E - 0 4 . 7 5 4 1 1 3 9 9 0 3 6 4 4 0 8 - 0 6 . 2 2 3 1 3 6 5 5 9 9 2 3 6 8 3 - 0 7 . 3 1 4 2 4 7 5 7 8 7 1 7 1 9 8 - 0 2 . 1 2 5 4 7 7 8 2 1 8 7 5 3 9 8 - 0 1 . 1 2 6 8 6 1 5 8 2 4 3 0 1 4 8 - 0 1 . 7 5 4 0 7 6 2 3 0 4 4 1 5 7 8 - 0 2 . 3 6 3 3 7 5 7 1 1 6 4 0 4 0 E - 0 2 . 1 1 1 5 1 8 5 0 6 8 1 0 1 7 3 - 0 2 . 2 9 3 8 8 1 1 1 7 3 8 6 2 6 8 - 0 3 . 4 2 6 1 0 8 6 9 2 7 2 1 5 3 8 - 0 4 . 5 2 9 4 9 1 0 1 0 8 5 8 8 6 8 - 0 5 . 2 3 7 8 6 8 5 7 8 2 7 8 9 0 E - 0 6 . 7 0 6 5 5 1 6 2 4 4 9 9 1 7 8 - 0 8 . 8 3 2 1 2 2 3 5 1 0 8 4 7 6 8 - 0 3 . 3 0 3 7 1 4 1 7 4 9 2 4 6 1 8 - 0 2 . 3 1 2 6 1 8 2 9 2 9 0 0 8 8 E - 0 2 . 1 8 9 7 1 8 0 7 0 4 4 1 8 1 3 - 0 2 . 9 4 2 5 2 2 7 6 4 9 4 4 4 4 8 - 0 3 . 2 9 3 8 7 9 1 0 1 9 4 6 0 0 3 - 0 3 . 7 9 7 6 4 7 1 3 9 7 3 4 1 8 E - 0 4 . 1 1 6 9 6 5 9 0 3 4 8 7 2 0 8 - 0 4 . 1 4 9 1 8 0 1 4 2 5 0 5 7 6 E - 0 5 . 6 7 5 7 6 6 4 2 7 2 6 0 5 3 8 - 0 7 . 2 0 5 4 3 8 7 6 3 2 2 3 3 2 8 - 0 8 . 1 0 7 7 1 3 5 7 6 8 2 4 1 5 E - 0 3 . 4 2 5 6 3 3 6 3 8 7 6 9 8 0 8 - 0 3 . 4 4 5 4 6 3 8 3 1 0 5 6 2 6 8 - 0 3 . 2 7 0 4 0 6 4 4 0 2 2 2 3 6 8 - 0 3 . 1 3 6 2 4 0 2 9 4 0 1 1 7 1 E - 0 3 I I I I I I I I I I I I I I I I I I I I I I V V ) ) ) ) 0 1 ) ) ) ) ) ) I ) ) 0 1 1 , 2 , 3 A ( 1 L 2 , 1 0 , 4 A ( 1 1 , 2 , 1 0 , 5 A ( 1 1 , 2 , 1 0 , 6 A ( 1 1 , 2 , 1 0 , 7 A ( 1 1 , 2 , 1 0 , 8 A ( 1 L 2 , 1 0 , 9 A ( 1 1 , 2 , 1 0 , 1 A ( 1 1 , 2 , 1 0 , 1 1 A ( 1 1 , 2 , 1 1 , 1 ) = A ( 1 1 , 2 , 1 1 , 2 ) = A ( 1 1 , 2 , 1 1 , 3 ) = A ( 1 1 , 2 , 1 1 , 4 ) = A ( 1 1 , 2 , 1 1 , 5 ) = A ( 1 l , 2 , 1 1 , 6 ) = A ( 1 1 , 2 , 1 1 , 7 ) = A ( 1 1 , 2 , 1 1 , 8 ) = A ( 1 1 , 2 , 1 1 , 9 ) = ) ) ) ) ) ) ) ) ) ) ) ) ) 0 A ( 1 1 , 2 , 1 1 , 1 0 ) = A ( 1 1 , 2 , 1 1 , 1 1 ) = a ( 1 1 , 3 , 1 , 1 ) : A ( 1 1 , 3 , L 2 ) = - A ( 1 1 , 3 , L 3 ) = A ( 1 1 , 3 , 1 , 4 ) = A ( 1 1 , 3 , 1 , 5 ) = A ( 1 1 , 3 , 1 , 6 ) A ( 1 1 , 3 , 1 , 7 ) A ( 1 1 , 3 , 1 , 8 ) = A ( 1 1 , 3 , 1 , 9 ) = A ( 1 1 , 3 , 1 , 1 0 ) = A ( 1 1 , 3 , 1 , 1 1 ) = 2 8 6 . 4 2 6 1 1 7 0 2 2 4 1 4 0 2 8 - 0 4 . 1 1 6 9 6 4 6 0 0 8 4 9 2 0 E - 0 4 . 1 7 1 8 0 7 5 2 5 8 0 6 1 4 3 - 0 5 . 2 2 0 7 9 7 0 1 5 5 5 9 8 8 8 - 0 6 . 1 0 0 0 2 3 6 4 7 4 2 0 2 3 8 - 0 7 . 3 0 5 4 0 0 6 4 5 3 1 1 1 2 8 - 0 9 . 1 3 6 5 9 1 0 6 0 1 3 3 6 4 3 - 0 4 . 5 0 1 2 7 3 7 4 8 0 5 6 9 7 E - 0 4 . 5 3 0 8 1 4 0 0 2 6 7 2 7 4 8 - 0 4 . 3 2 5 4 6 3 0 2 6 2 7 1 6 8 8 - 0 4 . 1 6 7 8 4 3 5 9 9 8 5 4 2 2 8 - 0 4 . 5 2 9 4 7 4 6 5 2 9 2 1 6 4 E - 0 5 . 1 4 9 1 8 3 3 9 9 9 4 4 5 2 E - 0 5 . 2 2 0 7 9 3 6 2 0 6 0 8 8 9 E - 0 6 . 2 9 1 1 6 8 1 5 5 2 8 0 8 5 E - 0 7 . 1 3 2 8 1 7 4 7 0 3 8 9 9 0 E - 0 8 . 4 1 5 7 0 3 7 0 5 1 8 2 8 0 E - 1 0 . 5 6 8 1 8 8 7 1 0 7 4 7 8 2 8 - 0 6 . 2 2 1 7 1 1 8 3 8 8 4 3 6 7 8 ' 0 5 . 2 3 7 1 7 8 6 3 4 0 6 6 0 3 8 - 0 5 . 1 4 4 9 7 5 7 2 4 1 3 6 7 4 8 - 0 5 . 7 5 4 0 7 0 3 1 5 0 7 8 7 9 8 - 0 6 . 2 3 7 8 8 3 5 1 8 2 1 7 0 7 8 - 0 6 . 6 7 5 7 3 3 5 8 2 4 2 2 5 7 E - 0 7 . 1 0 0 0 2 7 9 5 4 2 5 2 9 0 3 - 0 7 . 1 3 2 8 1 4 8 1 4 0 9 4 5 8 8 - 0 8 . 6 0 5 6 8 8 9 9 8 8 4 7 4 4 E - 1 0 . 1 9 0 5 6 0 7 4 8 0 6 2 3 1 E - 1 1 . 1 7 2 2 6 4 1 8 1 9 4 6 8 2 8 - 0 7 . 6 3 4 5 0 2 4 1 9 3 5 5 4 8 8 - 0 7 . 6 8 5 4 7 4 3 6 2 1 3 3 1 8 E - 0 7 . 4 2 0 7 6 0 0 6 8 4 5 3 6 0 8 - 0 7 . 2 2 3 1 4 8 7 7 4 3 1 9 8 4 8 - 0 7 . 7 0 6 5 0 8 8 7 3 9 7 3 8 3 8 - 0 8 . 2 0 5 4 4 8 6 3 3 4 5 2 9 5 8 - 0 8 . 3 0 5 3 8 5 9 9 3 1 8 6 1 2 E - 0 9 . 4 1 5 7 1 5 4 9 7 2 3 6 6 8 3 - 1 0 . 1 9 0 5 5 6 9 7 5 7 1 6 3 7 3 - 1 1 . 6 1 5 0 3 9 1 3 3 0 3 5 4 9 8 - 1 3 3 1 4 8 3 5 4 6 9 5 4 4 0 5 E - 0 2 5 7 4 9 8 3 1 1 1 0 7 3 3 8 8 - 0 2 3 2 3 5 7 4 1 5 3 3 7 1 7 4 8 - 0 1 3 2 9 9 2 3 6 7 6 6 5 4 2 9 3 - 0 1 1 1 0 4 2 6 8 4 1 3 4 7 3 6 8 - 0 1 3 6 2 6 1 6 9 2 5 0 3 1 0 3 8 - 0 2 7 8 4 6 7 2 2 2 6 2 4 5 6 8 8 - 0 3 1 2 1 4 7 6 4 6 0 2 6 5 0 6 8 - 0 3 1 3 2 6 4 5 5 9 2 7 8 5 2 5 3 - 0 4 . 6 3 2 5 8 6 0 9 8 6 1 4 5 0 E - 0 6 . 1 7 2 1 7 2 4 4 3 1 7 7 4 7 8 - 0 7 I I I I I I I I I I I I I I I I I I V V I I I I I I I I I I I I I I I I I I V V I I I I I I I I I I I I I I I I I I V V I I I I I I I I ) I I A ( l l , 3 , 2 , M 1 1 , 3 , 2 , M 1 1 , 3 , 2 , M 1 1 , 3 , 2 , M 1 1 , 3 , 2 , M 1 1 , 3 , 2 , M 1 1 , 3 , 2 , M 1 1 , 3 , 2 , M 1 1 , 3 , 2 , M 1 1 , 3 , 2 , A ( 1 L 3 , 2 , M 1 1 , 3 , 3 , M 1 1 , 3 , 3 , M 1 1 , 3 , 3 , A ( 1 1 , 3 , 3 , M 1 1 , 3 , 3 , A ( l l , 3 , 3 , M 1 L 3 , 3 , M 1 1 , 3 , 3 , M 1 1 , 3 , 3 , A ( l l , 3 , 3 , M 1 1 , 3 , 3 , M 1 1 , 3 , 4 , M 1 1 , 3 , 4 , M 1 1 , 3 , 4 , M 1 L 3 , 4 , M 1 1 , 3 , 4 , a ( 1 1 , 3 , 4 , M 1 1 , 3 , 4 , M 1 1 , 3 , 4 , M 1 1 , 3 , 4 , M 1 1 , 3 , 4 , M 1 1 , 3 , 4 , M 1 1 , 3 , 5 , M 1 L 3 , 5 , A ( 1 1 , L 5 , M 1 1 , L 5 , M 1 1 , 3 , 5 , 1 2 3 4 5 6 7 8 9 1 1 1 2 3 4 S 6 7 8 9 l 1 1 2 3 4 5 6 7 8 9 1 1 1 2 3 4 5 ) ) ) ) ) ) ) ) ) 0 1 ) ) ) ) ) ) ) ) ) 0 1 ) ) ) ) ) ) ) ) ) 0 1 ) ) ) ) M 1 1 , 3 , s , 6 ) = M 1 1 , 3 , 5 , 7 ) = M 1 1 , 3 , 5 , 8 ) = M 1 1 , L 5 , 9 ) = M 1 L 3 , 5 , 1 0 ) = M 1 1 , 3 , 5 , 1 1 ) = M 1 1 , L 6 , 1 ) = A ( 1 1 , 3 , 6 , 2 ) = M 1 1 , 3 , 6 , 3 ) = M 1 L L 6 , 4 ) = M 1 1 , 3 , 6 , 5 ) = M 1 1 , 3 , 6 , 6 ) = 2 8 7 “ . 5 7 4 9 7 9 2 0 2 4 2 8 9 5 8 - 0 2 . 1 5 0 3 9 1 4 1 3 4 8 0 9 7 E - O l . 1 9 6 9 7 7 4 0 8 6 3 1 9 4 E + 0 0 . 1 2 2 1 7 3 7 9 8 3 2 8 7 3 E + 0 0 . 4 7 9 2 3 7 1 2 1 2 5 3 3 9 8 - 0 1 . 1 4 0 2 0 8 4 1 0 3 7 5 6 4 8 - 0 1 . 3 3 1 3 3 7 7 6 1 3 2 6 7 2 8 - 0 2 . 4 7 1 6 4 2 6 4 1 9 6 9 0 8 3 - 0 3 . 5 4 6 9 6 7 9 7 7 0 4 4 2 3 8 - 0 4 . 2 4 4 4 8 2 4 5 5 2 5 8 3 2 3 - 0 5 . 6 9 2 1 3 1 1 8 9 3 0 6 0 0 8 - 0 7 . 3 2 3 5 7 3 7 7 5 8 9 5 0 6 E - 0 1 . 1 9 6 9 7 7 5 1 0 4 8 0 7 9 E + 0 0 . 2 9 4 5 0 7 3 5 7 1 9 0 0 1 E + 0 0 . 1 6 1 4 2 6 9 1 1 1 7 4 2 0 E + 0 0 . 6 9 6 8 5 6 9 3 8 0 8 4 2 4 E - O l . 2 0 0 5 0 2 6 3 4 2 5 2 1 9 E - 0 1 . 4 9 8 4 4 7 4 3 2 1 6 4 5 4 3 - 0 2 . 6 9 9 5 8 4 8 8 6 8 8 8 2 6 E - 0 3 . 8 4 1 1 5 8 1 1 1 4 8 4 2 2 8 - 0 4 . 3 7 1 5 1 6 4 8 4 2 4 3 2 7 8 - 0 5 . 1 0 8 1 5 8 4 0 8 5 3 4 9 5 8 - 0 6 . 3 2 9 9 2 4 0 5 7 6 2 3 4 3 E - 0 1 . 1 2 2 1 7 3 7 7 6 5 4 4 5 1 E + 0 0 . 1 6 1 4 2 6 9 1 7 3 4 4 2 2 3 + 0 0 . 9 7 0 2 4 4 4 7 6 1 9 3 3 3 8 - 0 1 . 4 2 4 5 1 0 7 9 6 5 8 3 4 9 8 - 0 1 . 1 2 6 8 9 7 4 5 8 3 0 3 5 7 E - 0 1 . 3 1 4 7 8 4 7 1 4 5 5 5 5 7 E - 0 2 . 4 5 0 9 0 5 9 6 8 1 3 6 7 9 E - 0 3 . 5 3 7 8 1 7 9 9 0 8 1 7 7 6 8 - 0 4 . 2 4 0 5 6 4 2 5 1 1 8 6 0 2 8 - 0 5 . 6 9 3 8 2 8 3 8 8 9 0 9 0 8 E - 0 7 . 1 1 0 4 2 6 7 1 2 8 5 3 9 5 8 - 0 1 . 4 7 9 2 3 7 3 4 8 8 4 5 3 4 E - 0 1 . 6 9 6 8 5 7 0 9 0 5 1 5 5 5 E - 0 1 . 4 2 4 5 1 0 8 5 2 7 5 3 8 8 3 - 0 1 . 1 9 7 9 3 2 3 2 3 6 4 4 6 4 8 - 0 1 . 5 9 9 9 8 5 5 3 8 6 1 0 7 8 8 - 0 2 . 1 5 5 3 8 9 5 1 9 7 5 0 3 2 8 - 0 2 . 2 2 3 7 8 5 4 0 0 8 0 5 8 1 8 - 0 3 . 2 7 5 6 5 2 0 1 6 1 2 8 4 5 E - 0 4 . 1 2 3 4 8 8 7 6 2 1 9 3 7 0 8 - 0 5 . 3 6 5 4 8 8 3 4 9 4 4 6 3 9 8 - 0 7 . 3 6 2 6 1 6 7 6 3 4 1 3 8 3 E - 0 2 . 1 4 0 2 0 8 6 2 3 5 6 1 1 9 E - 0 1 . 2 0 0 5 0 2 3 1 0 2 9 0 1 8 8 - 0 1 . 1 2 6 8 9 7 7 3 6 7 1 8 O Q E - O l . 5 9 9 9 8 4 5 3 6 5 2 9 5 2 E - 0 2 . 1 8 5 3 5 5 0 4 7 2 3 3 3 2 E - 0 2 I I I I I I V V “ “ “ I I “ I I ~ “ “ V ‘ “ ~ “ V ~ ‘ I I I I I I I I I I I I I I V V I I I I I I I I I I I I I I I I “ I I V ~ V “ I I I I I I I I I I I I A ( l l , 3 , A ( 1 l , 3 , A ( l l , 3 , A ( 1 1 , 3 , A ( l l , 3 , A ( l l , 3 , A ( 1 1 , 3 , A ( l l , 3 , A ( 1 1 , 3 , A ( 1 1 , 3 , A ( l l , 3 , A ( l l , 3 , A ( 1 l , 3 , A ( l l , 3 , A ( l l , 3 , A ( 1 1 , 3 , A ( l l , 3 , A ( 1 1 , 3 , A ( 1 1 , 3 , A ( l l , 3 , A ( l l , 3 , A ( 1 1 , 3 , A ( 1 1 , 3 , A ( 1 1 , 3 , A ( l l , 3 , A ( 1 1 , 3 , A ( 1 1 , 3 , A ( 1 1 , 3 , 9 A ( 1 1 , 3 , 9 , A ( 1 1 , 3 , 9 , A ( l l , 3 , 9 , A ( 1 1 , 3 , 9 , A ( 1 1 , 3 , 9 , A ( 1 1 , 3 , 9 , A ( 1 1 , 3 , 9 , A ( 1 1 , 3 , 9 , A ( 1 1 , 3 , 9 , A ( 1 1 , 3 , 9 , m m m m m m m m m m m q u \ J q q q q q u q q m m o ‘ m m 2 8 8 . 4 8 4 1 8 1 7 3 2 0 7 6 6 5 8 - 0 3 . 7 0 4 4 9 3 5 0 1 4 7 3 2 8 E - 0 4 . 8 7 0 2 1 7 8 1 8 5 1 6 0 4 E - 0 5 . 3 9 1 9 7 5 7 7 5 8 3 7 4 9 8 - 0 6 . 1 1 5 9 2 4 5 6 7 0 9 8 4 1 3 - 0 7 . 7 8 4 6 7 8 6 9 7 9 8 2 6 0 8 - 0 3 . 3 3 1 3 3 6 1 0 6 0 4 6 3 6 E - 0 2 . 4 9 8 4 4 9 8 7 1 7 0 2 1 8 3 - 0 2 . 3 1 4 7 8 2 8 9 4 8 3 8 5 7 8 - 0 2 . 1 5 5 3 9 0 4 6 4 7 1 5 3 1 3 - 0 2 . 4 8 4 1 7 9 2 4 8 3 6 0 3 1 8 - 0 3 . 1 3 1 2 5 3 9 3 7 7 5 2 2 6 8 - 0 3 . 1 9 2 1 4 1 6 8 8 1 6 0 0 6 E - 0 4 . 2 4 4 9 6 0 9 3 1 5 3 9 1 4 8 - 0 5 . 1 1 0 7 8 2 3 1 7 5 4 1 6 9 E - 0 6 . 3 3 6 7 3 6 0 2 2 0 5 2 4 2 8 - 0 8 . 1 2 1 4 7 3 9 1 7 5 4 5 2 5 8 - 0 3 . 4 7 1 6 4 9 7 2 6 0 2 3 3 2 8 - 0 3 . 6 9 9 5 7 6 4 1 4 9 4 5 1 1 E - 0 3 . 4 5 0 9 1 2 6 1 3 0 1 8 7 7 E - 0 3 . 2 2 3 7 8 1 9 7 7 8 6 5 6 6 8 - 0 3 . 7 0 4 5 0 4 3 1 0 5 3 3 5 9 E - 0 4 . 1 9 2 1 3 9 9 1 6 8 4 8 0 8 8 - 0 4 . 2 8 3 1 4 7 6 6 6 9 1 2 9 5 8 - 0 5 . 3 6 2 2 7 0 1 4 8 9 9 0 2 6 E - 0 6 . 1 6 4 4 8 6 3 6 7 4 4 3 2 6 E - 0 7 . 5 0 0 5 3 1 2 0 0 6 8 8 1 0 3 - 0 9 . 1 3 2 6 5 0 4 7 1 0 8 7 4 6 E - 0 4 7 ) 8 ) 9 ) 1 0 1 1 1 ) 2 ) 3 ) 4 ) 5 ) 6 ) 7 ) 8 ) 9 ) 1 0 1 1 1 ) 2 ) 3 ) 4 ) 5 ) 6 ) 7 ) 8 ) 9 ) 1 0 1 1 1 ) 2 ) ) ) ) . 5 4 6 9 5 4 5 3 6 8 4 4 1 7 3 - 0 4 3 . 8 4 1 1 7 4 3 1 9 8 1 6 6 7 8 - 0 4 4 . 5 3 7 8 0 5 6 4 3 1 4 8 2 0 8 - 0 4 5 . 2 7 5 6 5 8 3 8 8 2 7 5 7 0 E - 0 4 6 ) . 8 7 0 1 9 5 9 2 1 0 1 0 0 1 E - 0 5 7 ) = . 2 4 4 9 6 5 5 6 2 8 5 6 6 9 E - 0 5 8 ) = . 3 6 2 2 6 5 2 3 2 9 2 2 7 1 3 - 0 6 9 ) = . 4 7 7 6 2 5 3 2 2 3 4 8 1 9 8 - 0 7 1 0 ) = . 2 1 7 6 4 5 8 5 0 9 9 4 4 9 8 - 0 8 1 1 ) = . 6 8 1 1 5 3 3 2 3 5 7 8 0 0 E - 1 0 A ( 1 1 , 3 , 1 0 , 1 ) = . 6 3 2 5 4 1 1 0 8 8 2 4 8 2 3 - 0 6 A ( 1 1 , 3 , 1 0 , 2 ) = . 2 4 4 4 9 4 5 5 4 3 8 0 0 3 8 - 0 5 A ( 1 1 , 3 , 1 0 , 3 ) = . 3 7 1 5 0 1 7 2 7 8 6 9 3 7 3 - 0 5 A ( 1 1 , 3 , 1 0 , 4 ) = . 2 4 0 5 7 5 3 0 8 6 5 2 0 7 E - 0 5 A ( 1 1 , 3 , 1 0 , 5 ) = . 1 2 3 4 8 2 9 1 5 1 3 7 5 3 8 - 0 5 A ( 1 1 , 3 , 1 0 , 6 ) = . 3 9 1 9 9 6 1 9 3 9 4 9 1 4 8 - 0 6 A ( 1 1 , 3 , 1 0 , 7 ) = . 1 1 0 7 7 7 5 9 4 6 5 2 9 4 3 - 0 6 A ( 1 1 , 3 , 1 0 , 8 ) = . 1 6 4 4 9 2 8 5 7 1 1 3 1 7 8 - 0 7 A ( 1 1 , 3 , 1 0 , 9 ) = . 2 1 7 6 4 1 7 2 8 7 7 1 0 9 8 - 0 8 A ( 1 1 , 3 , 1 0 , 1 0 ) = . 9 9 4 6 4 8 5 2 9 1 2 1 7 2 8 - 1 0 A ( 1 1 , 3 , 1 0 , 1 1 ) = . 3 1 2 0 8 7 3 2 6 5 0 1 6 9 8 - 1 1 A ( 1 1 , 3 , 1 1 , 1 ) = . 1 7 2 1 8 5 7 2 3 1 7 9 5 6 8 - 0 7 2 8 9 A ( 1 1 , 3 , 1 1 , 2 ) = . 6 9 2 0 9 5 5 5 4 4 7 7 5 8 8 - 0 7 A ( l l , 3 , l l , 3 ) = . 1 0 8 1 6 2 6 9 0 6 6 5 1 6 8 - 0 6 A ( l l , 3 , 1 1 , 4 ) = . 6 9 3 7 9 6 2 1 4 3 6 8 2 7 E - 0 7 A ( l l , 3 , 1 1 , 5 ) = . 3 6 5 5 0 5 3 1 4 7 6 4 4 2 8 - 0 7 A ( 1 1 , 3 , 1 1 , 6 ) = . 1 1 5 9 1 8 4 6 1 7 0 4 4 5 E - 0 7 A ( 1 1 , 3 , 1 1 , 7 ) = . 3 3 6 7 5 0 7 5 2 6 3 0 2 9 8 - 0 8 A ( 1 1 , 3 , l l , 8 ) = . 5 0 0 5 0 8 9 8 4 0 8 4 5 5 8 - 0 9 A ( 1 1 , 3 , 1 1 , 9 ) = . 6 8 1 1 7 1 9 7 3 2 1 0 6 2 E - 1 0 A ( l l , 3 , 1 1 , 1 0 ) = . 3 1 2 0 8 1 1 8 2 2 9 4 1 0 8 - 1 1 A ( l l , 3 , 1 1 , 1 1 ) = . 1 0 0 7 1 8 9 6 4 4 1 6 5 4 8 - 1 2 A ( 1 1 , 4 , 1 , l ) = ' . 1 5 0 3 5 2 8 8 4 5 2 0 5 4 E - 0 2 A ( l l , 4 , l , 2 ) = . 2 2 5 1 8 7 4 0 7 3 4 0 8 5 8 - 0 2 A ( 1 1 , 4 , 1 , 3 ) = - . 4 7 9 2 7 1 5 6 2 6 5 3 5 9 E - 0 3 A ( l l , 4 , 1 , 4 ) = . 2 3 6 5 1 5 0 6 6 6 4 4 6 4 E - O l A ( l l , 4 , l , 5 ) = . 2 0 4 5 5 5 8 8 8 3 4 0 1 1 8 - 0 1 A ( 1 1 , 4 , 1 , 6 ) = . 4 8 4 3 6 7 3 2 8 4 9 9 5 0 3 - 0 2 A ( l l , 4 , 1 , 7 ) = . 1 3 3 8 0 1 6 9 3 7 5 5 2 3 3 - 0 2 A ( 1 1 , 4 , 1 , 8 ) = . 1 7 0 3 4 3 9 0 4 0 7 3 8 9 8 - 0 3 A ( 1 1 , 4 , 1 , 9 ) = . 2 1 9 7 2 3 9 5 5 7 2 3 3 4 8 - 0 4 A ( 1 1 , 4 , 1 , 1 0 ) = . 9 0 9 4 9 5 1 2 5 4 3 4 0 3 8 - 0 6 A ( 1 1 , 4 , 1 , 1 1 ) = . 2 7 8 3 3 4 3 1 0 3 2 1 8 7 E - 0 7 A ( 1 1 , 4 , 2 , l ) = . 2 2 5 2 0 2 8 1 4 9 0 8 7 0 E - 0 2 A ( l l , 4 , 2 , 2 ) = . 2 1 5 9 8 9 1 5 0 4 5 6 1 5 8 - 0 2 A ( 1 l , 4 , 2 , 3 ) = ‘ . 1 6 7 3 9 0 5 1 6 7 2 6 3 0 E - 0 1 A ( 1 1 , 4 , 2 , 4 ) = . 1 2 9 0 2 6 6 2 6 4 4 0 4 6 E + 0 0 A ( 1 1 , 4 , 2 , 5 ) = . 7 6 3 8 9 5 9 2 4 4 6 5 0 3 8 - 0 1 A ( 1 1 , 4 , 2 , 6 ) = . 1 9 5 8 9 7 5 4 8 7 6 5 0 6 3 - 0 1 A ( 1 1 , 4 , 2 , 7 ) = . 5 0 5 0 3 6 6 8 3 8 9 8 6 5 E - 0 2 A ( 1 1 , 4 , 2 , 8 ) = . 6 7 0 7 6 8 9 6 7 4 3 8 5 6 8 - 0 3 A ( 1 l , 4 , 2 , 9 ) = . 8 2 1 2 2 6 0 7 0 6 8 4 1 3 8 - 0 4 A ( 1 1 , 4 , 2 , 1 0 ) = . 3 4 9 6 7 2 0 0 8 3 2 6 2 5 E - 0 5 A ( 1 1 , 4 , 2 , 1 1 ) = . 1 0 2 6 7 5 8 5 8 0 9 3 5 4 8 - 0 6 A ( 1 1 , 4 , 3 , 1 ) = - . 4 7 9 7 4 7 7 5 9 5 2 7 5 3 8 - 0 3 A ( 1 1 , 4 , 3 , 2 ) = - . 1 6 7 3 8 2 6 8 6 6 3 1 7 5 8 - 0 1 A ( 1 1 , 4 , 3 , 3 ) = . 1 5 7 0 0 2 2 7 9 9 7 1 4 9 E + 0 0 A ( l l , 4 , 3 , 4 ) = . 2 4 5 6 7 2 0 1 6 5 7 9 1 9 E + 0 0 A ( l l , 4 , 3 , 5 ) = . 1 0 9 6 0 9 4 9 6 1 1 0 3 5 8 + 0 0 A ( 1 1 , 4 , 3 , 6 ) = . 3 2 0 8 6 9 9 0 7 9 5 5 0 6 8 - 0 1 A ( 1 1 , 4 , 3 , 7 ) = . 7 8 2 3 1 5 6 2 7 6 5 7 2 3 3 - 0 2 A ( 1 1 , 4 , 3 , 8 ) = . 1 1 1 8 6 0 1 4 6 7 6 2 4 1 3 - 0 2 A ( 1 1 , 4 , 3 , 9 ) = . 1 3 2 3 6 3 6 7 7 9 4 8 8 9 8 - 0 3 A ( 1 1 , 4 , 3 , 1 0 ) = . 5 9 3 6 8 8 0 5 5 1 6 1 5 8 E - 0 5 A ( 1 1 , 4 , 3 , 1 l ) = . 1 7 0 8 1 4 2 7 4 4 4 7 2 1 E - 0 6 A ( 1 1 , 4 , 4 , 1 ) = . 2 3 6 5 2 1 4 4 9 6 9 6 7 4 E - 0 1 A ( 1 1 , 4 , 4 , 2 ) = . 1 2 9 0 2 5 4 1 5 0 2 2 6 2 8 + 0 0 A ( 1 1 , 4 , 4 , 3 ) = . 2 4 5 6 7 2 8 1 9 1 4 6 4 Z E + 0 0 A ( 1 1 , 4 , 4 , 4 ) = . 1 9 2 0 2 5 3 6 6 6 4 6 7 O E + 0 0 A ( 1 1 , 4 , 4 , 5 ) = . 8 8 3 5 7 6 4 1 7 5 4 5 5 6 E - O l A ( 1 1 , 4 , 4 , 6 ) = . 2 5 6 5 5 6 0 4 2 0 7 7 1 4 E - 0 1 A ( 1 1 , 4 , 4 , 7 ) = . 6 4 0 7 8 7 9 2 8 5 6 8 9 0 E - 0 2 2 9 0 A ( 1 1 , 4 , 4 , 8 ) = . 9 0 4 6 6 0 6 7 9 4 5 2 7 2 8 - 0 3 A ( l l , 4 , 4 , 9 ) = . 1 0 8 4 6 2 6 0 0 0 8 1 7 9 3 - 0 3 A ( l l , 4 , 4 , 1 0 ) = . 4 8 0 5 0 0 1 2 0 2 2 5 7 l E - 0 5 A ( 1 1 , 4 , 4 , l l ) = . 1 3 9 1 1 5 6 4 0 9 5 1 3 7 E - 0 6 A ( l l , 4 , 5 , l ) = . 2 0 4 5 5 1 1 6 3 3 3 3 2 4 E - O l A ( 1 1 , 4 , 5 , 2 ) = . 7 6 3 9 0 7 0 3 7 6 1 7 1 7 E - O l A ( l l , 4 , 5 , 3 ) = . 1 0 9 6 0 8 5 6 4 5 5 4 9 5 E + 0 0 A ( 1 1 , 4 , 5 , 4 ) = . 8 8 3 5 8 0 0 9 1 0 3 1 0 4 8 - 0 1 A ( l l , 4 , 5 , 5 ) = . 4 2 2 9 5 0 6 6 3 1 9 6 3 9 E - O l A ( 1 1 , 4 , 5 , 6 ) = . 1 2 7 0 1 7 9 0 6 6 3 4 1 4 E - O l A ( 1 1 , 4 , 5 , 7 ) = . 3 2 6 9 4 7 1 7 0 4 6 9 7 9 E - 0 2 A ( 1 1 , 4 , 5 , 8 ) = . 4 6 9 9 9 1 4 4 1 1 5 0 3 4 E - 0 3 A ( l l , 4 , 5 , 9 ) = . 5 7 5 9 3 9 2 8 2 8 9 6 3 4 3 - 0 4 A ( 1 1 , 4 , 5 , 1 0 ) = . 2 5 8 0 1 3 1 2 8 4 6 2 4 1 E - 0 5 A ( 1 1 , 4 , 5 , 1 1 ) = . 7 6 0 5 9 0 7 8 9 2 3 9 4 0 8 - 0 7 A ( 1 1 , 4 , 6 , l ) = . 4 8 4 3 8 8 7 5 1 8 2 9 1 0 3 - 0 2 A ( 1 1 , 4 , 6 , 2 ) = . 1 9 5 8 9 2 5 0 8 5 6 3 7 0 3 - 0 1 A ( 1 1 , 4 , 6 , 3 ) = . 3 2 0 8 7 4 4 1 5 1 9 2 5 2 3 - 0 1 A ( 1 1 , 4 , 6 , 4 ) = . 2 5 6 5 5 3 8 8 3 1 5 4 9 9 E - 0 1 A ( 1 1 , 4 , 6 , 5 ) = . 1 2 7 0 1 8 4 0 5 6 1 9 3 1 8 - 0 1 A ( l l , 4 , 6 , 6 ) = . 3 8 5 8 6 1 1 3 8 6 0 2 1 9 8 - 0 2 A ( 1 1 , 4 , 6 , 7 ) = . 1 0 1 1 9 0 1 1 0 6 7 2 1 8 3 - 0 2 A ( l l , 4 , 6 , 8 ) = . 1 4 6 0 6 5 0 5 7 8 9 0 6 1 E - 0 3 A ( 1 1 , 4 , 6 , 9 ) = . 1 8 0 7 3 6 9 3 3 1 1 7 4 9 3 - 0 4 A ( 1 1 , 4 , 6 , 1 0 ) = . 8 0 9 8 8 8 1 2 6 3 4 0 7 5 8 - 0 6 A ( 1 l , 4 , 6 , 1 1 ) = . 2 3 9 7 4 3 5 6 8 8 8 6 1 2 E - 0 7 A ( l l , 4 , 7 , 1 ) = . 1 3 3 7 9 5 5 0 3 3 7 0 4 9 8 - 0 2 A ( 1 l , 4 , 7 , 2 ) = . 5 0 5 0 5 1 4 9 4 1 1 0 3 8 8 - 0 2 A ( 1 1 , 4 , 7 , 3 ) = . 7 8 2 3 0 1 6 4 1 8 1 1 5 0 8 - 0 2 A ( l l , 4 , 7 , 4 ) = . 6 4 0 7 9 5 2 1 3 9 8 5 2 6 8 - 0 2 A ( 1 1 , 4 , 7 , 5 ) = . 3 2 6 9 4 5 0 9 5 3 6 6 6 8 E - 0 2 A ( 1 1 , 4 , 7 , 6 ) = . 1 0 1 1 9 0 4 0 2 9 8 3 7 8 8 - 0 2 A ( 1 1 , 4 , 7 , 7 ) = . 2 7 3 8 4 1 4 7 2 6 7 6 3 9 8 - 0 3 A ( 1 1 , 4 , 7 , 8 ) = . 4 0 0 2 6 7 7 1 3 8 7 1 4 7 3 - 0 4 A ( 1 1 , 4 , 7 , 9 ) = . 5 0 8 9 4 9 7 4 0 3 0 7 6 8 8 - 0 5 A ( 1 1 , 4 , 7 , 1 0 ) = . 2 3 0 0 8 2 1 6 8 8 7 2 7 7 8 - 0 6 A ( 1 1 , 4 , 7 , 1 1 ) = . 6 9 7 6 5 0 0 7 7 2 9 1 5 0 8 - 0 8 A ( 1 1 , 4 , 8 , 1 ) = . 1 7 0 3 5 4 2 2 7 1 7 9 8 1 E - 0 3 A ( 1 1 , 4 , 8 , 2 ) = . 6 7 0 7 4 4 3 9 2 8 9 1 7 2 3 - 0 3 A ( 1 1 , 4 , 8 , 3 ) = . 1 1 1 8 6 2 4 3 6 4 6 0 8 0 8 - 0 2 A ( 1 1 , 4 , 8 , 4 ) = . 9 0 4 6 4 8 6 3 2 5 1 3 2 7 8 - 0 3 A ( 1 1 , 4 , 8 , 5 ) = . 4 6 9 9 9 4 7 0 7 9 4 1 6 2 E - 0 3 A ( 1 1 , 4 , 8 , 6 ) = . 1 4 6 0 6 4 7 2 7 7 4 4 0 3 8 - 0 3 A ( 1 1 , 4 , 8 , 7 ) = . 4 0 0 2 6 7 4 7 3 8 5 0 1 4 3 - 0 4 A ( 1 1 , 4 , 8 , 8 ) = . 5 8 6 4 3 1 7 3 6 9 4 8 6 1 8 - 0 5 A ( 1 1 , 4 , 8 , 9 ) = . 7 5 1 7 7 4 0 0 1 7 1 7 1 1 E - 0 6 A ( 1 1 , 4 , 8 , 1 0 ) = . 3 4 0 0 1 7 7 5 5 3 4 0 3 2 8 - 0 7 A ( 1 1 , 4 , 8 , 1 1 ) = . 1 0 3 5 5 9 5 4 1 1 9 4 1 9 8 - 0 8 A ( 1 1 , 4 , 9 , 1 ) = . 2 1 9 7 1 4 4 4 0 1 3 5 0 2 8 - 0 4 A ( 1 1 , 4 , 9 , 2 ) = . 8 2 1 2 4 7 6 5 9 5 3 0 4 0 8 - 0 4 I I I I I I I I I I I I I I I I I I I I I I V V A ( 1 1 , 4 , 1 0 , 3 A ( 1 L 4 , 1 0 , 4 A ( 1 1 , 4 , 1 0 , 5 A ( l l , 4 , 1 L 6 A ( l l , 4 , 1 L 7 A ( 1 1 , 4 , 1 L 8 A ( 1 l , 4 , 1 L 9 A ( 1 1 , L 1 L 1 0 A ( l l , 4 , 1 L 1 1 A ( l l , 4 , 1 1 , 1 ) = A ( l l , 4 , 1 1 , 2 ) = A ( 1 1 , 4 , 1 1 , 3 ) = A ( 1 1 , 4 , l l , 4 ) = A ( 1 1 , 4 , 1 1 , 5 ) = ) ) ) ) ) ) ) ) ) ) ) A ( 1 1 , 4 , 1 1 : 8 ) = A ( l l , 4 , 1 1 , 9 ) = 2 9 1 . 1 3 2 3 6 1 7 6 5 0 5 4 1 6 E - 0 3 . 1 0 8 4 6 3 4 6 4 5 5 6 5 1 8 - 0 3 . 5 7 5 9 3 7 8 5 1 5 7 9 0 6 8 - 0 4 1 8 0 7 3 6 4 5 7 6 2 2 2 9 8 - 0 4 5 0 8 9 5 2 1 1 3 5 2 0 4 2 8 - 0 5 7 5 1 7 7 0 6 8 2 1 5 0 2 7 E - 0 6 9 8 9 9 0 3 4 2 3 6 7 6 0 0 E - 0 7 . 4 5 0 9 3 4 9 9 9 0 6 3 3 5 E - 0 8 . 1 4 0 9 1 0 3 3 6 3 5 0 6 1 8 - 0 9 . 9 0 9 5 2 9 3 0 1 6 5 1 4 5 E - 0 6 . 3 4 9 6 6 4 4 0 2 8 5 4 4 4 8 - 0 5 . 5 9 3 6 9 3 4 0 8 0 3 5 2 8 E - 0 5 . 4 8 0 4 9 9 3 6 5 6 2 9 3 3 8 - 0 5 . 2 5 8 0 1 1 7 8 3 3 1 6 1 9 8 - 0 5 . 8 0 9 8 9 8 1 4 1 4 4 0 6 1 8 - 0 6 . 2 3 0 0 7 8 8 2 1 2 1 7 2 8 3 - 0 6 . 3 4 0 0 2 3 3 6 0 8 5 6 3 7 8 - 0 7 . 4 5 0 9 3 1 1 2 2 6 5 0 2 7 8 - 0 8 . 2 0 5 4 3 7 0 8 9 8 6 5 6 9 3 - 0 9 . 6 4 5 3 0 9 5 9 0 0 6 5 5 7 E - 1 1 . 2 7 8 3 3 2 4 5 7 3 5 9 6 4 8 - 0 7 . 1 0 2 6 7 5 9 5 1 7 9 6 3 6 8 - 0 6 . 1 7 0 8 1 4 8 2 2 2 3 1 2 5 8 - 0 6 . 1 3 9 1 1 4 6 6 7 0 6 3 7 3 E - 0 6 . 7 6 0 5 9 9 4 2 1 2 2 3 4 2 3 - 0 7 . 2 3 9 7 3 9 3 7 4 6 0 2 3 1 8 - 0 7 ‘ . 6 9 7 6 6 2 2 9 3 9 0 8 1 1 3 - 0 8 . 1 0 3 5 5 7 4 8 9 7 5 3 5 8 E - 0 8 . 1 4 0 9 1 2 1 3 2 1 6 8 8 8 8 - 0 9 A ( 1 1 , 4 , 1 1 , 1 0 ) = . 6 4 5 3 0 3 4 8 6 3 4 6 1 5 E - 1 1 A ( 1 1 , 4 , 1 1 , 1 1 ) = . 2 0 8 1 1 6 1 9 1 9 6 9 6 6 8 - 1 2 a ( 1 1 , 5 , 1 , 1 ) = A ( 1 1 , 5 , 1 , 2 ) = A ( 1 1 , 5 , l , 3 ) = A ( 1 1 , 5 , 1 , 4 ) = - A ( 1 1 , 5 , 1 , 5 ) = A ( 1 1 , 5 , 1 , 6 ) = A ( 1 1 , 5 , 1 , 7 ) = A ( l l , 5 , 1 , 8 ) = A ( 1 1 , 5 , 1 , 9 ) = A ( 1 1 , 5 , 1 , 1 0 ) = A ( 1 1 , 5 , 1 , 1 1 ) = A ( 1 1 , 5 , 2 , 1 ) = A ( 1 1 , 5 , 2 , 2 ) = - A ( 1 1 , 5 , 2 , 3 ) = A ( 1 1 , 5 , 2 , 4 ) = ’ . A ( 1 1 , 5 , 2 , 5 ) = A ( 1 1 , 5 , 2 , 6 ) = A ( 1 1 , 5 , 2 , 7 ) = A ( 1 1 , 5 , 2 , 8 ) = . 3 1 8 6 1 6 0 5 0 2 0 8 2 2 8 - 0 2 . 1 2 4 8 1 3 6 6 8 6 6 2 6 8 3 - 0 2 . 7 4 7 3 1 9 3 3 7 0 9 7 0 0 3 - 0 2 . 4 9 3 2 2 0 1 0 3 0 8 9 7 0 3 - 0 2 . 2 1 5 9 2 7 0 3 0 6 5 8 3 5 E - 0 1 . 1 1 9 8 6 6 1 7 7 7 7 4 3 8 8 - 0 1 . 2 5 1 9 8 1 0 8 3 9 6 5 8 0 E - 0 2 . 3 9 0 5 9 8 1 5 3 2 1 7 0 7 E - 0 3 . 4 3 3 6 1 1 9 2 4 3 9 3 0 6 3 - 0 4 . 2 0 3 9 3 6 0 0 8 1 6 9 5 9 3 - 0 5 . 5 6 6 2 6 7 9 6 1 4 1 0 4 6 E - 0 7 . 1 2 4 8 1 8 2 0 8 8 6 0 2 3 3 - 0 2 . 3 3 7 5 9 0 8 1 7 9 4 4 1 5 8 - 0 1 . 2 3 1 7 4 8 1 6 6 2 6 1 2 4 8 - 0 1 3 1 7 5 0 0 9 4 9 0 2 2 3 6 8 - 0 1 . 1 0 0 1 8 9 6 9 1 1 1 8 4 3 E + 0 0 . 4 5 7 2 0 3 8 9 8 6 9 5 3 0 E - 0 1 . 9 5 6 3 5 5 7 5 8 1 7 1 4 1 E - 0 2 . 1 4 6 8 4 7 5 3 9 3 2 6 7 0 8 - 0 2 I I I I I I I I I I m q m m I I w V w V w m w p m m u m m u H A ( 1 1 , 5 , 2 , 9 ) = A ( l l , 5 , 2 , 1 0 ) = A ( l l , 5 , 2 , l l ) = A ( l l , 5 , 3 , l ) = A ( l l , 5 , 3 , 2 ) = A ( l l , 5 , 3 , 3 ) = - A ( l l , 5 , 3 , 4 ) A ( l l , 5 , 3 , 5 A ( 1 1 , 5 , 3 , A ( l l , 5 , 3 , A ( 1 1 , 5 , 3 , A ( 1 1 , 5 , 3 , A ( l l , 5 , 3 , A ( l l , 5 , 3 , A ( l l , 5 , 4 , A ( l l , 5 , 4 , A ( 1 1 , 5 , 4 , A ( l l , 5 , 4 , A ( l l , 5 , 4 , A ( 1 1 , 5 , 4 , A ( l l , 5 , 4 , A ( l l , 5 , 4 , A ( 1 1 , 5 , 4 , A ( 1 1 , 5 , 4 , A ( 1 1 , 5 , 4 , A ( 1 1 , 5 , 5 , 1 ) A ( l l , 5 , 5 , 2 ) = A ( 1 1 , 5 , 5 , 3 ) = A ( 1 1 , 5 , 5 , 4 ) = A ( 1 1 , 5 , 5 , 5 ) = A ( 1 1 , 5 , 5 , 6 ) = A ( 1 1 , 5 , 5 , 7 ) = A ( 1 1 , 5 , 5 , 8 ) = A ( 1 1 , 5 , 5 , 9 ) = A ( 1 1 , 5 , 5 , 1 0 ) = A ( 1 1 , 5 , 5 , 1 1 ) = A ( l l , 5 , 6 , l ) = A ( 1 1 , 5 , 6 , 2 ) = A ( 1 1 , 5 , 6 , 3 ) - A ( 1 1 , 5 , 6 , 4 ) = A ( 1 1 , 5 , 6 , 5 ) = A ( 1 1 , 5 , 6 , 6 ) = A ( l l , 5 , 6 , 7 ) = A ( 1 1 , 5 , 6 , 8 ) - A ( 1 1 , 5 , 6 , 9 ) = A ( 1 1 , 5 , 6 , 1 0 ) = A ( 1 1 , 5 , 6 , 1 1 ) = A ( 1 1 , S , 7 , 1 ) = A ( 1 1 , 5 , 7 , 2 ) = A ( 1 1 , 5 , 7 , 3 ) = I I V V I I I I I I I I I I I I I I I I I I 2 9 2 . 1 6 0 1 2 7 3 5 1 4 7 7 9 7 8 - 0 3 . 7 4 9 3 0 3 4 3 1 7 4 6 2 8 3 - 0 5 . 2 0 3 6 4 5 3 0 2 6 2 1 0 7 E - 0 6 . 7 4 7 2 8 8 9 2 6 5 0 4 5 5 8 - 0 2 . 2 3 1 7 5 5 6 3 0 8 1 1 6 8 E - 0 1 . 1 3 1 6 6 1 1 9 9 2 6 6 0 9 8 - 0 1 . 6 4 5 5 9 7 8 0 9 3 4 3 6 0 E - 0 1 . 2 1 0 4 4 4 2 0 8 1 1 8 1 3 E + 0 0 . 6 6 1 8 1 9 0 7 2 2 6 5 6 4 8 - 0 1 . 1 6 3 4 3 7 9 0 4 4 4 8 0 7 8 - 0 1 . 2 2 9 6 3 8 5 4 7 4 4 3 7 6 3 - 0 2 . 2 7 7 1 1 7 9 4 6 7 7 9 9 8 3 - 0 3 . 1 2 2 2 2 3 7 9 6 8 7 8 9 8 8 - 0 4 . 3 5 7 3 7 7 4 3 6 9 7 6 9 5 8 - 0 6 . 4 9 3 1 7 0 4 4 0 3 1 3 4 1 8 - 0 2 . 3 1 7 5 1 3 6 0 9 7 7 0 6 9 E - O l . 6 4 5 6 0 5 8 4 6 0 7 5 3 4 8 - 0 1 . 2 2 7 6 0 2 1 3 6 9 0 3 4 4 E + 0 0 . 1 8 1 3 4 1 8 9 2 3 1 2 0 5 8 + 0 0 . 5 4 6 4 3 3 9 0 7 5 8 4 2 9 E - 0 1 . 1 3 6 0 7 4 3 8 3 5 1 7 5 5 8 - 0 1 . 1 9 1 4 3 5 5 1 6 8 9 9 2 2 3 - 0 2 . 2 2 9 6 8 4 8 8 5 4 2 5 7 4 3 - 0 3 . 1 0 1 4 2 8 8 5 8 6 2 7 6 3 8 - 0 4 . 2 9 3 7 7 8 0 6 8 8 7 1 6 5 8 - 0 6 . 2 1 5 9 2 2 9 2 3 5 2 5 8 0 E - 0 1 . 1 0 0 1 9 0 8 1 9 1 8 2 9 0 8 + 0 0 . 2 1 0 4 4 3 2 8 7 7 3 8 6 O E + 0 0 . 1 8 1 3 4 2 2 4 5 0 5 0 4 7 E + 0 0 . 1 0 9 1 8 6 1 7 3 3 7 3 O Z E + 0 0 . 3 3 8 4 7 9 9 3 7 0 5 4 2 2 8 - 0 1 . 8 5 6 3 3 1 3 0 3 8 3 9 4 0 8 - 0 2 . 1 2 3 1 6 5 5 6 8 6 7 5 1 8 8 - 0 2 . 1 4 9 8 3 7 1 5 7 4 9 3 9 5 8 - 0 3 . 6 7 1 1 7 5 8 6 4 7 5 2 6 3 8 - 0 5 . 1 9 7 0 4 0 6 6 1 1 7 6 2 1 8 - 0 6 . 1 1 9 8 6 8 5 4 9 7 3 6 5 7 E - 0 1 . 4 5 7 1 9 7 9 1 7 2 7 6 0 6 3 - 0 1 . 6 6 1 8 2 5 2 9 3 5 0 0 4 4 E - 0 1 . 5 4 6 4 3 0 7 2 3 6 2 5 2 4 8 - 0 1 . 3 3 8 4 8 0 9 6 6 0 9 2 9 0 8 - 0 1 . 1 0 5 5 6 3 5 5 6 8 9 9 1 4 3 - 0 1 . 2 7 3 3 4 5 3 9 5 5 4 4 3 1 E - 0 2 . 3 9 4 1 2 1 2 9 2 1 7 4 5 3 3 - 0 3 . 4 8 4 6 7 9 3 1 0 0 9 1 0 0 8 - 0 4 . 2 1 6 9 8 5 1 0 4 0 1 7 9 1 E - 0 5 . 6 3 9 6 5 1 3 4 8 5 5 5 1 5 8 - 0 7 . 2 5 1 9 7 2 5 2 6 7 1 2 0 5 8 - 0 2 . 9 5 6 3 7 7 4 7 8 7 2 3 8 8 E - 0 2 . 1 6 3 4 3 5 5 7 7 0 1 4 7 5 E - 0 1 A ( 1 1 , 5 , 7 , 4 ) = A ( 1 1 , 5 , 7 , 5 ) = A ( 1 1 , 5 , 7 , 6 ) = A ( 1 1 , 5 , 7 , 7 ) = A ( l l , 5 , 7 , 8 ) = A ( 1 1 , 5 , 7 , 9 ) = A ( l l , 5 , 7 , 1 0 ) = A ( 1 1 , 5 , 7 , 1 1 ) = I I I I V V I I I I I I I I I I I I I I I A ( 1 1 , 5 , 9 , 2 A ( 1 1 , 5 , 9 , 3 ) = A ( 1 1 , 5 , 9 , 4 ) = A ( 1 1 , 5 , 9 , 5 ) = A ( 1 1 , 5 , 9 , 6 ) = A ( 1 1 , 5 , 9 , 7 ) = A ( l l , 5 , 9 , 8 ) = A ( 1 1 , 5 , 9 , 9 ) = A ( 1 1 , 5 , 9 , 1 0 ) = A ( 1 1 , 5 , 9 , 1 1 ) = A ( 1 1 , 5 , 1 0 , 1 ) = A ( 1 1 , 5 , 1 0 , 2 ) = A ( 1 1 , 5 , 1 0 , 3 ) = A ( 1 1 , 5 , 1 0 , 4 ) = A ( 1 l , 5 , 1 0 , 5 ) = A ( 1 1 , 5 , 1 0 , 6 ) = A ( 1 1 , 5 , 1 0 , 7 ) = A ( 1 1 , 5 , 1 0 , 8 ) = A ( 1 1 , 5 , 1 0 , 9 ) = A ( 1 1 , 5 , 1 0 , 1 0 ) = A ( 1 1 , 5 , 1 0 , 1 1 ) = A ( 1 1 , 5 , 1 1 , 1 ) = A ( 1 1 , 5 , 1 1 , 2 ) = A ( 1 1 , 5 , 1 1 , 3 ) = A ( 1 1 , 5 , 1 1 , 4 ) = A ( 1 1 , 5 , 1 1 , 5 ) = A ( 1 1 , 5 , 1 1 , 6 ) = A ( 1 1 , 5 , 1 1 , 7 ) = A ( 1 1 , 5 , 1 1 , 8 ) = A ( 1 1 , 5 , 1 1 , 9 ) = 2 9 3 . 1 3 6 0 7 5 8 1 6 3 3 5 5 1 3 - 0 1 . 8 5 6 3 2 5 6 9 2 6 2 0 8 9 8 - 0 2 . 2 7 3 3 4 6 4 5 8 9 2 5 5 2 3 - 0 2 . 7 3 1 2 2 2 7 7 5 1 2 9 9 4 3 - 0 3 . 1 0 7 0 1 9 2 7 0 5 0 1 5 0 3 - 0 3 . 1 3 5 3 6 0 7 7 8 5 1 4 8 4 3 - 0 4 . 6 1 1 9 0 9 8 1 3 4 8 6 0 2 3 - 0 6 . 1 8 4 9 1 8 6 9 2 7 1 9 4 2 3 - 0 7 . 3 9 0 6 1 5 7 8 4 6 8 1 3 6 8 - 0 3 . 1 4 6 8 4 2 6 9 3 5 3 8 9 3 8 - 0 2 . 2 2 9 6 4 3 7 4 6 7 5 2 1 2 8 - 0 2 . 1 9 1 4 3 2 1 6 9 9 5 8 7 2 2 - 0 2 . 1 2 3 1 6 6 9 9 5 1 2 6 6 7 8 - 0 2 . 3 9 4 1 1 7 6 9 4 2 1 3 4 9 8 - 0 3 . 1 0 7 0 1 9 7 2 6 1 5 8 3 4 8 - 0 3 . 1 5 6 9 7 3 9 1 3 3 3 4 4 7 E - 0 4 . 2 0 0 3 1 2 2 2 4 5 8 5 2 8 3 - 0 5 . 9 0 6 1 6 0 9 5 7 3 8 1 2 7 8 - 0 7 . 2 7 5 0 5 0 4 8 7 4 2 0 7 7 E - 0 8 . 4 3 3 5 8 8 4 3 4 1 3 4 4 4 3 - 0 4 . 1 6 0 1 3 3 4 5 5 0 9 6 9 1 8 - 0 3 . 2 7 7 1 1 1 3 4 1 1 1 9 9 6 3 - 0 3 . 2 2 9 6 8 9 3 6 6 6 1 9 8 2 8 - 0 3 . 1 4 9 8 3 5 1 1 1 5 8 5 6 2 8 - 0 3 . 4 8 4 6 8 5 0 9 5 7 5 6 2 8 8 - 0 4 . 1 3 5 3 5 9 7 5 9 5 2 5 5 0 2 - 0 4 . 2 0 0 3 1 3 0 8 5 8 5 1 8 9 3 - 0 5 . 2 6 2 8 6 4 2 7 1 6 8 2 8 7 3 - 0 6 . 1 1 9 7 7 0 6 0 0 6 5 9 4 9 3 - 0 7 . 3 7 3 4 1 9 5 0 5 8 2 0 4 0 3 - 0 9 . 2 0 3 9 5 0 8 2 1 5 6 4 5 5 8 - 0 5 . 7 4 9 2 6 5 1 6 8 3 0 9 4 2 2 - 0 5 . 1 2 2 2 2 8 0 2 7 4 5 0 4 3 3 - 0 4 . 1 0 1 4 2 5 9 0 7 3 1 7 3 2 3 - 0 4 . 6 7 1 1 8 9 6 8 3 3 8 7 7 5 8 - 0 5 . 2 1 6 9 8 0 9 7 7 8 9 6 2 4 8 - 0 5 . 6 1 1 9 1 8 1 9 4 3 3 7 5 9 8 - 0 6 . 9 0 6 1 5 1 2 2 7 3 8 6 6 9 E - 0 7 . 1 1 9 7 7 1 1 0 6 8 5 1 8 0 3 - 0 7 . 5 4 6 0 4 1 6 6 9 7 7 9 3 1 2 - 0 9 . 1 7 1 0 8 1 5 8 4 0 9 3 6 3 8 - 1 0 . 5 6 6 2 3 9 0 9 7 8 3 2 2 7 3 - 0 7 . 2 0 3 6 5 2 9 7 2 4 8 5 8 1 8 - 0 6 . 3 5 7 3 6 8 9 4 2 4 3 8 5 4 8 - 0 6 . 2 9 3 7 8 3 9 6 2 8 2 3 6 5 3 - 0 6 . 1 9 7 0 3 7 7 9 9 0 7 6 7 6 8 - 0 6 . 6 3 9 6 6 0 2 2 3 6 7 8 0 1 8 - 0 7 . 1 8 4 9 1 6 8 2 9 2 1 0 0 7 3 - 0 7 . 2 7 5 0 5 2 8 6 6 0 7 3 6 0 8 - 0 8 . 3 7 3 4 1 7 9 2 3 1 0 2 0 7 3 - 0 9 2 9 4 A ( 1 l , 5 , 1 1 , 1 0 ) = . 1 7 1 0 8 1 9 4 5 6 7 5 0 5 E - 1 0 A ( 1 1 , 5 , 1 1 , 1 1 ) = . 5 5 0 9 4 9 6 3 4 3 4 9 2 1 E - 1 2 A ( 1 l , 6 , l A ( 1 1 , 6 , 1 , , 1 ) = - . 2 1 4 8 0 8 7 9 5 1 3 5 4 7 E - 0 3 2 ) = - . 7 5 6 7 3 3 1 1 9 4 8 7 7 6 8 - 0 3 A ( 1 1 , 6 , l , 3 ) = . 9 4 1 9 0 2 7 1 3 3 8 4 4 8 E - 0 2 A ( 1 1 , 6 , 1 , 4 ) = . 1 6 8 6 6 9 7 6 7 4 4 4 9 5 8 - 0 1 A ( 1 1 , 6 , 1 , 5 ) = . 3 0 6 9 6 4 6 1 9 0 8 5 1 9 8 - 0 3 A ( 1 1 , 6 , 1 , 6 ) = . 1 7 0 9 1 5 4 4 4 4 6 8 8 5 8 - 0 1 A ( 1 L 6 , 1 , 7 ) = . 8 3 4 0 8 5 5 8 9 3 0 3 8 7 8 - 0 2 A ( 1 1 , 6 , 1 , 8 ) = . 1 0 2 1 0 8 3 8 2 7 2 5 4 2 E - 0 2 A ( 1 1 , 6 , 1 , 9 ) = . 1 3 3 6 4 5 5 3 5 3 5 6 6 6 E - 0 3 A ( 1 1 , 6 , L 1 0 ) = . 5 5 5 8 6 0 7 3 1 3 1 0 5 3 8 - 0 5 A ( 1 1 , 6 , 1 , 1 1 ) = . 1 6 9 9 0 9 4 3 8 2 9 6 7 6 8 - 0 6 A ( 1 1 , 6 , 2 , 1 ) = . 7 5 7 1 7 8 2 9 1 6 7 8 4 3 E - 0 3 A ( 1 1 , 6 , 2 , 2 ) = . 9 9 3 4 8 8 9 6 1 8 3 0 7 4 3 - 0 2 A ( 1 1 , 6 , 2 , 3 ) = . 4 0 3 6 2 6 0 0 7 0 2 7 9 Z E - 0 1 A ( 1 1 , 6 , 2 , 4 ) = . 2 5 6 6 8 3 9 5 2 1 7 5 0 8 8 - 0 1 A ( 1 1 , 6 , 2 , 5 ) = . 2 8 2 2 3 2 5 9 8 4 0 1 6 1 3 - 0 1 A ( 1 1 , 6 , 2 , 6 ) = . 7 1 0 9 0 8 8 1 5 9 6 3 1 9 E - O l A ( 1 1 , 6 , 2 , 7 ) = . 3 0 6 7 7 1 8 8 5 3 7 0 8 4 3 - 0 1 A ( 1 1 , 6 , 2 , 8 ) = . 3 6 7 9 6 0 6 1 5 0 3 9 9 2 3 - 0 2 A ( 1 L 6 , 2 , 9 ) = . 4 7 5 9 7 6 5 6 2 0 2 9 2 5 8 - 0 3 A ( 1 1 , 6 , 2 , 1 0 ) = . 1 9 4 5 0 2 4 8 1 4 6 3 1 3 8 - 0 4 A ( 1 1 , 6 , 2 , 1 1 ) = . 5 8 5 1 5 7 0 0 5 9 6 1 1 8 8 - 0 6 A ( 1 1 , 6 , 3 , 1 ) = . 9 4 2 0 6 9 4 0 8 4 8 3 8 0 3 - 0 2 A ( 1 1 , 6 , 3 , 2 ) = . 4 0 3 6 4 8 0 6 0 7 4 6 4 9 E - O l A ( 1 1 , 6 , 3 , 3 ) = . 8 0 6 6 1 8 6 0 7 6 0 3 0 1 8 - 0 1 A ( 1 1 , 6 , 3 , 4 ) = . 1 5 1 8 6 7 4 5 9 0 6 2 4 9 3 - 0 1 A I l l , 6 , 3 , 5 ) = . 5 7 0 7 6 9 1 0 7 4 3 4 9 0 E - 0 1 A ( 1 l , 6 , 3 , 6 ) = . 1 6 2 2 8 7 7 5 3 9 4 8 4 8 E + 0 0 A ( 1 1 , 6 , 3 , 7 ) = . 4 7 8 3 8 3 2 0 6 2 0 9 4 0 E - 0 1 A ( 1 1 , 6 , 3 , 8 ) = . 6 5 1 5 6 0 8 0 6 3 6 3 7 0 E - 0 2 A ( 1 1 , 6 , 3 , 9 ) = . 7 9 7 8 9 8 5 5 9 0 8 5 3 0 E - 0 3 A ( 1 L 6 , 3 , 1 0 ) = . 3 4 9 9 0 8 7 2 1 9 4 3 8 5 8 - 0 4 A ( 1 1 , 6 , 3 , 1 1 ) = J 0 2 7 5 3 1 0 7 3 5 6 0 8 8 - 0 5 A ( 1 1 , 6 , 4 , 1 ) = . 1 6 8 6 4 5 0 5 3 6 3 6 2 8 E - 0 1 A ( 1 1 , 6 , 4 , 2 ) = . 2 5 6 6 3 7 6 8 1 7 4 1 2 7 E - 0 1 A ( 1 1 , 6 , 4 , 3 ) = . 1 5 1 8 4 0 7 4 8 7 3 1 0 5 E - 0 1 A ( 1 1 , 6 , 4 , A ( 1 1 , 6 , 4 , A ( 1 1 , 6 , 4 A ( 1 1 , 6 , 4 A ( 1 1 , 6 , 4 A ( 1 1 , 6 , 4 A ( 1 1 , 6 , 4 A ( 1 1 , 6 , 5 4 ) = - . 1 0 7 7 5 6 3 5 3 2 1 6 2 5 8 + 0 0 5 ) = . 1 9 1 8 0 8 7 9 8 1 1 7 5 6 8 + 0 0 , 6 ) = . 1 4 8 1 3 1 3 2 9 2 7 5 2 0 8 + 0 0 , 7 ) = . 3 7 4 6 2 1 5 0 3 1 4 2 4 1 8 - 0 1 , 8 ) = . 5 4 0 6 1 1 1 1 7 6 8 5 3 3 E - 0 2 , 9 ) = . 6 3 2 5 9 6 1 1 3 0 6 4 2 1 8 - 0 3 A ( 1 1 , 6 , 4 , 1 0 ) = . 2 8 5 1 6 4 5 5 2 7 3 5 7 5 E - 0 4 , l l ) = . 8 1 0 9 7 8 8 7 1 1 6 8 5 4 E - 0 6 A ( 1 1 , 6 , 5 , A ( 1 1 , 6 , 5 , A ( 1 1 , 6 , 5 , 1 ) = . 3 0 8 5 9 6 5 2 9 0 6 6 5 6 8 - 0 3 2 ) = ‘ . 2 8 2 2 7 0 0 0 1 4 8 0 3 6 8 - 0 1 3 ) = . 5 7 0 7 9 9 4 9 7 6 5 4 6 6 E - 0 1 , 4 ) = . 1 9 1 8 0 7 8 6 5 8 6 3 6 7 E + 0 0 I " V V I I I I N I I I I I I I I I ' O I V V I I I I I I I I I I A ( 1 1 , 6 w A ( 1 1 , 6 , 7 , 3 ) = A ( l l , 6 , 7 , 4 ) = A ( 1 1 , 6 , 7 , 5 ) = A ( 1 1 , 6 , 7 , 6 ) = A ( 1 1 , 6 , 7 , 7 ) = A ( 1 1 , 6 , 7 , 8 ) = A ( 1 1 , 6 , 7 , 9 ) = A ( 1 1 , 6 , 7 , 1 0 O A ( 1 1 , 6 , 8 , 6 ) A ( 1 1 , 6 , 8 , 7 ) = A ( 1 1 , 6 , 8 , 8 ) = A ( 1 1 , 6 , 8 , 9 ) = A ( 1 1 , 6 , 8 , 1 0 ) = A ( 1 1 , 6 , 8 , 1 1 ) = A ( 1 1 , 6 , 9 , 1 ) = A ( 1 1 , 6 , 9 , 2 ) = A ( 1 1 , 6 , 9 , 3 ) = A ( 1 1 , 6 , 9 , 4 ) = A ( 1 1 , 6 , 9 , 5 ) = A ( 1 1 , 6 , 9 , 6 ) = A ( 1 1 , 6 , 9 , 7 ) = A ( 1 1 , 6 , 9 , 8 ) = A ( 1 1 , 6 , 9 , 9 ) = 2 9 5 . 2 3 2 5 4 2 7 6 1 9 5 0 7 S E + 0 0 . 9 4 8 2 9 1 0 9 9 9 2 1 3 B E - O l . 2 5 3 7 3 6 4 9 0 0 4 9 0 5 E - 0 1 . 3 5 8 4 7 0 5 0 4 9 4 3 4 0 3 - 0 2 . 4 4 1 2 3 4 7 8 3 9 2 0 6 6 8 - 0 3 . 1 9 5 8 8 7 2 9 3 5 8 5 8 8 8 - 0 4 . 5 7 9 1 8 3 9 8 0 3 3 1 5 2 E - 0 6 . 1 7 0 9 0 7 4 4 5 4 2 6 5 6 8 - 0 1 . 7 1 0 9 2 6 4 0 2 2 4 3 7 9 E - 0 1 . 1 6 2 2 8 5 9 8 5 8 3 2 5 7 E + 0 0 . 1 4 8 1 3 2 0 9 9 9 4 4 6 B E + 0 0 . 9 4 8 2 8 8 6 4 3 2 6 7 0 1 E - 0 1 . 3 6 0 6 1 0 5 1 5 1 9 9 3 7 3 - 0 1 . 9 5 0 4 9 5 3 7 9 9 4 7 8 2 8 - 0 2 . 1 3 6 1 8 5 2 5 0 0 3 9 4 9 E - 0 2 . 1 6 6 3 3 0 5 5 0 4 8 4 8 7 8 - 0 3 . 7 4 3 8 8 0 0 0 7 1 9 2 3 9 8 - 0 5 . 2 1 8 0 7 2 8 2 6 4 6 3 3 6 E - 0 6 . 8 3 4 1 1 1 8 5 3 3 2 8 0 7 8 - 0 2 . 3 0 6 7 6 5 9 8 0 2 0 3 6 4 8 - 0 1 . 4 7 8 3 8 9 0 7 9 5 0 7 9 1 8 - 0 1 . 3 7 4 6 1 8 3 3 7 0 8 2 2 1 3 - 0 1 . 2 5 3 7 3 7 6 9 7 8 5 8 0 1 8 - 0 1 . 9 5 0 4 9 3 3 4 2 6 7 9 6 9 8 - 0 2 . 2 6 1 0 1 1 2 9 2 2 4 1 1 6 E - 0 2 . 3 7 7 8 7 2 6 4 0 0 0 1 4 4 8 - 0 3 . 4 7 7 4 7 1 4 0 0 7 2 8 2 9 8 - 0 4 . 2 1 4 8 3 5 2 9 7 3 7 4 0 9 8 - 0 5 . 6 4 7 9 9 5 6 4 4 6 4 2 5 7 E - 0 7 . 1 0 2 1 0 2 7 8 6 6 9 5 4 7 3 - 0 2 . 3 6 7 9 7 4 4 2 0 4 4 1 9 0 3 - 0 2 . 6 5 1 5 4 7 1 4 3 2 0 6 7 0 E - 0 2 . 5 4 0 6 1 9 3 0 9 3 2 2 2 1 5 - 0 2 . 3 5 8 4 6 6 9 3 2 4 4 8 2 1 8 - 0 2 . 1 3 6 1 8 6 1 8 4 2 7 2 4 5 8 - 0 2 . 3 7 7 8 7 1 2 7 5 7 5 9 3 9 8 - 0 3 . 5 5 1 5 4 0 6 3 0 9 0 8 6 8 8 - 0 4 . 7 0 1 2 7 9 6 7 9 3 0 4 8 9 E - 0 5 . 3 1 6 8 6 5 3 5 0 4 0 2 6 5 8 - 0 6 . 9 5 8 2 0 0 5 4 3 9 1 0 1 6 8 - 0 8 . 1 3 3 6 5 3 2 3 3 3 1 9 8 2 8 - 0 3 . 4 7 5 9 5 7 7 7 9 1 4 4 6 6 8 - 0 3 . 7 9 7 9 1 9 3 7 1 9 6 2 0 5 8 - 0 3 . 6 3 2 5 8 3 1 6 3 6 7 8 6 5 8 - 0 3 . 4 4 1 2 4 0 6 8 4 7 2 2 2 9 3 - 0 3 . 1 6 6 3 2 8 8 0 9 2 5 7 2 7 8 - 0 3 . 4 7 7 4 7 4 9 6 5 8 0 5 4 1 3 - 0 4 . 7 0 1 2 7 5 9 9 1 9 4 3 3 6 3 - 0 5 . 9 2 0 7 6 8 7 8 6 9 9 3 8 8 8 - 0 6 A ( 1 1 , 6 , 9 , 1 0 ) = . 4 1 8 2 6 4 0 6 2 8 2 9 1 9 8 - 0 7 I I I I I I I I I I I I I I I I I I I I V V I I I I I I I I I I I I ) I I A ( 1 1 , 6 , 9 , A ( 1 1 , 6 , 1 0 , 1 A ( 1 1 , 6 , 1 0 , 2 A ( l l , 6 , 1 0 , 3 A ( 1 1 , 6 , 1 0 , 4 A ( 1 1 , 6 , 1 0 , 5 A ( 1 1 , 6 , 1 0 , 6 A ( l l , 6 , 1 0 , 7 A ( 1 1 , 6 , 1 0 , 8 A ( 1 1 , 6 , 1 0 , 9 A ( 1 1 , 6 , 1 0 , 1 A ( 1 1 , 6 , 1 0 , 1 A ( 1 1 , 6 , 1 1 , 1 A ( l l , 6 , 1 1 , 2 A ( 1 l , 6 , 1 1 , 3 A ( 1 1 , 6 , 1 1 , 4 A ( 1 1 , 6 , 1 1 , 5 A ( l l , 6 , l l , 6 A ( 1 1 , 6 , 1 1 , 7 1 1 ) ) ) ) ) ) ) ) ) ) 0 l ) ) ) ) ) ) A ( 1 1 , 6 , 1 L 1 0 ) = A ( 1 1 , 6 , 1 1 , 1 1 ) = A ( 1 1 , 7 , 1 , A ( 1 1 , 7 , 2 , A ( 1 1 , 7 , 2 , A ( 1 1 , 7 , 2 , A ( 1 1 , 7 , 2 , A ( 1 1 , 7 , 2 , A ( 1 1 , 7 , 2 A ( 1 1 , 7 , 2 , A ( 1 1 , 7 , 2 , A ( 1 1 , 7 , 2 , A ( 1 1 , 7 , 3 , A ( 1 1 , 7 , 3 , A ( 1 1 , 7 , L A ( 1 1 , L 3 , A ( 1 1 , 7 , 3 , 5 1 ) = I I I I V V I I I I I I I I I I I I I I I I I I 3 ) = 4 ) = - . 5 ) = 6 ) = - 7 ) = ' 8 ) : 9 ) = 1 0 ) = 1 1 ) = 1 ) = 2 ) = 3 ) 4 ) - 5 ) 2 9 6 . 1 3 0 2 6 8 8 5 7 9 4 0 3 5 8 - 0 8 . 5 5 5 8 0 1 5 9 7 1 0 1 8 9 8 - 0 5 . 1 9 4 5 1 7 7 8 3 7 1 1 4 9 E - 0 4 . 3 4 9 8 9 2 1 4 8 6 7 6 6 4 8 - 0 4 . 2 8 5 1 7 5 7 0 7 6 8 8 2 7 8 - 0 4 . 1 9 5 8 8 2 0 7 7 2 0 7 4 4 E - 0 4 . 7 4 3 8 9 7 1 4 7 9 7 0 0 7 3 - 0 5 . 2 1 4 8 3 1 4 6 9 7 6 9 1 9 3 - 0 5 . 3 1 6 8 7 0 5 4 6 0 2 4 3 6 3 - 0 6 . 4 1 8 2 6 0 5 2 4 5 4 8 4 1 3 - 0 7 . 1 9 0 5 2 2 2 7 1 7 4 3 8 2 E - 0 8 . 5 9 5 6 0 6 3 3 3 3 5 0 6 5 E - 1 0 . 1 6 9 9 2 5 5 1 7 8 7 8 8 7 E - 0 6 . 5 8 5 1 1 6 3 9 1 3 3 8 4 0 E - 0 6 . 1 0 2 7 5 7 6 7 5 0 8 0 0 6 8 - 0 5 . 8 1 0 9 4 7 0 4 9 5 1 2 1 2 8 - 0 6 . 5 7 9 1 9 9 7 3 3 0 6 3 9 7 E ~ 0 6 . 2 1 8 0 6 7 4 7 7 9 6 3 9 3 8 - 0 6 . 6 4 8 0 0 8 4 7 2 1 5 9 4 0 3 - 0 7 . 9 5 8 1 8 0 6 6 8 8 3 6 3 5 E - 0 8 . 1 3 0 2 7 0 5 7 0 8 0 6 3 1 8 - 0 8 . 5 9 5 6 0 0 4 8 0 8 2 7 3 2 8 - 1 0 . 1 9 1 7 4 5 4 3 8 1 5 7 9 0 8 - 1 1 . 2 4 7 0 9 9 8 0 5 8 5 6 1 2 8 - 0 1 . 1 0 8 5 9 3 9 2 1 1 7 7 0 9 E - 0 1 . 1 0 0 2 2 1 2 1 2 4 8 7 6 7 E + 0 0 . 2 0 3 1 6 4 7 8 7 9 6 3 0 3 E - 0 1 . 4 9 3 4 7 0 7 3 5 3 8 2 2 9 8 - 0 1 . 3 6 6 4 4 8 4 5 9 6 8 1 1 2 8 - 0 2 . 1 8 0 1 5 5 4 1 7 1 8 3 4 1 E - O l . 4 7 7 0 8 3 5 0 4 3 0 1 8 5 E - 0 2 . 4 9 7 8 9 3 1 0 8 3 3 1 4 8 8 - 0 3 . 2 4 1 3 1 9 6 1 6 5 2 0 7 4 E - 0 4 . 6 6 3 7 7 7 0 9 6 3 9 9 0 9 8 - 0 6 . 1 0 8 5 6 6 6 8 9 3 0 5 0 1 E - 0 1 . 2 4 9 8 1 9 4 7 8 9 5 1 3 9 3 + 0 0 . 7 2 1 9 2 6 8 0 0 9 0 6 6 6 E - 0 2 1 8 5 0 5 7 2 5 7 3 0 2 1 1 8 + 0 0 . 2 4 6 9 2 7 0 1 6 4 1 4 7 0 E - 0 1 . 7 7 8 9 2 6 6 4 5 8 7 1 2 5 3 - 0 1 . 6 6 8 1 3 5 3 4 9 9 8 8 0 1 8 - 0 1 . 1 6 8 7 1 3 3 4 8 9 7 5 8 7 8 - 0 1 . 1 6 9 5 4 8 3 7 5 0 1 5 4 4 8 - 0 2 . 8 2 0 4 0 5 1 5 1 6 7 1 3 7 8 - 0 4 . 2 1 7 8 5 9 1 9 2 5 5 2 7 9 E - O S ° . 1 0 0 2 3 3 5 3 9 9 3 8 9 B E + 0 0 . 7 1 9 4 8 0 0 3 0 2 3 8 6 3 E - 0 2 3 8 7 2 6 8 4 7 9 9 1 3 4 7 E + 0 0 . 1 1 3 3 7 1 5 8 2 7 0 1 B O E + 0 0 . 1 7 9 4 0 1 5 1 5 9 8 3 0 5 8 + 0 0 I I I I I I I I V V I I I I I I I I I I I I I I I I I I V V I I I I I I I I I I I I I I I I I I V V I I I I I I I I I I I I I I I A ( 1 1 , 7 , 4 A ( 1 1 , 7 , 4 A ( 1 1 , 7 , 6 , 8 ) = A ( 1 1 , 7 , 6 , 9 ) = A ( 1 1 , 7 , 6 , 1 0 ) = A ( 1 1 , 7 , 6 , 1 1 ) = A ( 1 1 , 7 , 7 , 1 ) = A ( 1 1 , 7 , 7 , 2 ) = A ( 1 1 , 7 , 7 , 3 ) = A ( 1 1 , 7 , 7 , 4 ) = A ( 1 1 , 7 , 7 , 5 ) = A ( 1 1 , 7 , 7 , 6 ) = A ( 1 1 , 7 , 7 , 7 ) = A ( 1 1 , 7 , 7 , 8 ) = A ( 1 1 , 7 , 7 , 9 ) = A ( 1 1 , 7 , 7 , 1 0 ) - A ( 1 1 , 7 , 7 , 1 1 ) - 2 9 7 . 1 2 3 2 9 0 9 0 3 8 6 6 2 9 8 - 0 2 . 1 5 2 1 6 1 8 1 7 7 6 4 8 6 8 + 0 0 . 2 7 6 7 7 8 7 5 9 5 8 0 3 4 E - 0 1 . 3 0 9 5 2 6 9 9 1 4 4 1 0 9 E - 0 2 . 1 4 3 6 5 6 0 7 4 5 5 6 0 2 8 - 0 3 . 4 0 6 6 1 0 4 6 4 0 5 4 3 2 8 - 0 5 . 2 0 3 3 2 7 5 6 4 5 2 2 6 2 8 - 0 1 J 8 5 0 2 7 6 7 8 4 9 7 1 4 E + 0 0 . 1 1 3 3 8 9 3 1 5 0 8 3 6 2 E + 0 0 . 4 2 5 6 8 9 9 1 8 9 2 0 4 0 8 - 0 1 . 8 9 4 2 2 0 4 9 0 0 0 8 5 9 3 - 0 1 . 8 6 3 5 5 0 6 9 1 8 6 5 3 8 8 - 0 1 J 4 2 1 6 3 5 7 0 4 4 6 4 3 E + 0 0 . 2 0 7 8 1 2 8 0 1 3 8 1 8 1 8 - 0 1 . 2 5 2 0 9 6 1 2 2 3 1 2 6 5 3 - 0 2 . 1 0 9 5 3 8 9 5 9 6 9 1 2 4 3 - 0 3 . 3 2 0 3 5 3 5 6 0 5 6 7 8 1 8 - 0 5 . 4 9 3 5 7 2 3 4 2 6 7 5 1 8 8 - 0 1 . 2 4 6 6 8 9 8 6 9 0 9 0 9 l E - O l . 1 7 9 4 1 9 5 0 8 2 0 3 8 6 8 + 0 0 . 8 9 4 2 7 2 4 1 5 8 9 8 7 4 E - O l . 1 4 2 9 6 8 5 7 2 2 1 0 5 2 8 + 0 0 . 2 2 2 9 6 9 2 9 9 2 9 8 7 l E + 0 0 . 9 7 0 8 0 9 6 7 3 3 0 8 3 9 8 - 0 1 . 1 4 3 4 8 1 1 0 1 9 1 3 4 9 8 - 0 1 . 1 7 5 2 6 2 9 1 7 0 3 6 8 9 8 - 0 2 . 7 8 2 1 9 3 0 5 9 7 6 2 9 0 E - 0 4 . 2 3 0 7 5 5 5 5 2 1 7 7 4 4 8 - 0 5 . 3 6 6 8 3 7 4 3 8 1 9 5 9 4 E - 0 2 . 7 7 8 8 4 6 8 1 2 9 0 0 1 6 8 - 0 1 . 1 2 2 5 7 2 4 8 1 6 3 2 2 3 E - 0 2 . 8 6 3 5 7 4 5 8 9 6 0 2 6 5 E - 0 1 . 2 2 2 9 6 9 1 3 4 4 5 4 6 Z E + 0 0 . 1 0 7 9 1 6 0 7 9 8 1 0 8 2 8 + 0 0 . 3 7 0 1 7 7 5 8 7 4 6 5 1 5 E - 0 1 . 5 5 0 8 8 5 1 5 1 4 6 0 5 3 E - 0 2 . 6 6 5 6 3 0 9 1 0 5 8 9 2 4 8 - 0 3 . 2 9 8 6 9 7 4 3 8 8 3 6 3 7 E - 0 4 . 8 7 2 0 2 5 9 0 2 5 9 8 4 9 3 - 0 6 . 1 8 0 1 6 3 9 3 1 8 0 0 0 5 3 - 0 1 . 6 6 8 1 1 6 3 6 0 3 2 0 7 1 E - 0 1 . 1 5 2 1 6 3 0 5 4 0 9 5 5 8 8 + 0 0 . 1 4 2 1 6 3 4 3 3 0 1 8 1 4 E + 0 0 . 9 7 0 8 0 8 0 6 2 4 1 1 3 8 3 - 0 1 . 3 7 0 1 7 8 1 9 2 2 4 2 7 5 8 - 0 1 . 1 2 1 5 3 2 6 9 1 3 7 3 4 3 8 - 0 1 . 1 7 9 4 8 8 8 5 6 7 0 1 9 4 8 - 0 2 . 2 2 4 4 6 4 8 1 7 1 6 5 4 3 8 - 0 3 . 1 0 0 8 8 7 9 0 5 6 7 4 0 9 8 - 0 4 . 3 0 2 7 7 7 1 8 7 5 4 4 1 2 8 - 0 6 A ( 1 1 , 7 , 8 , l ) = . 4 7 7 0 7 4 3 4 5 3 2 6 4 0 8 - 0 2 A ( l l , 7 , 8 , 2 ) = . 1 6 8 7 1 4 8 7 5 1 8 0 7 4 8 - 0 1 A ( l l , 7 , 8 , 3 ) = . 2 7 6 7 7 8 5 6 6 3 3 0 9 0 E - 0 1 A ( l l , 7 , 8 , 4 ) = : 2 0 7 8 1 1 8 9 3 9 2 4 3 7 E - 0 1 A ( l l , 7 , 8 , 5 ) = . 1 4 3 4 8 2 1 5 0 5 2 4 5 1 E - 0 1 A ( 1 1 , 7 , 8 , 6 ) = . 5 5 0 8 8 0 9 6 7 7 8 4 9 1 8 - 0 2 A ( l l , 7 , 8 , 7 ) = . 1 7 9 4 8 9 6 1 8 2 2 1 8 5 E - 0 2 A ( l l , 7 , 8 , 8 ) = . 2 6 8 2 1 4 2 1 9 7 7 2 7 4 8 - 0 3 A ( l l , 7 , 8 , 9 ) = . 3 3 6 8 1 8 1 1 9 8 4 8 2 0 8 - 0 4 A ( l l , 7 , 8 , 1 0 ) = . 1 5 2 3 0 4 8 4 7 4 8 9 4 0 8 - 0 5 A ( l l , 7 , 8 , l l ) = . 4 5 7 4 9 0 5 5 0 7 2 0 4 2 8 - 0 7 A ( 1 1 , 7 , 9 , l ) = . 4 9 7 8 9 2 0 3 5 1 2 7 7 3 E - 0 3 A ( l l , 7 , 9 , 2 ) = . 1 6 9 5 4 9 3 4 5 0 8 2 4 9 E - 0 2 A ( l l , 7 , 9 , 3 ) = . 3 0 9 5 2 3 8 7 4 4 2 0 8 5 E - 0 2 A ( l l , 7 , 9 , 4 ) = . 2 5 2 0 9 9 5 6 9 6 6 1 3 7 E - 0 2 A ( 1 1 , 7 , 9 , 5 ) = . l 7 5 2 6 0 5 2 3 6 1 0 6 3 E - 0 2 A ( l l , 7 , 9 , 6 ) = . 6 6 5 6 4 0 3 4 7 5 0 6 2 7 8 - 0 3 A ( 1 1 , 7 , 9 , 7 ) = . 2 2 4 4 6 2 7 7 9 4 4 2 5 5 8 - 0 3 A ( l l , 7 , 9 , 8 ) = . 3 3 6 8 2 0 2 8 2 0 2 9 7 5 8 - 0 4 A ( l l , 7 , 9 , 9 ) = . 4 3 8 5 8 0 5 0 3 6 4 7 7 6 3 - 0 5 A ( 1 1 , 7 , 9 , 1 0 ) = . 1 9 9 3 4 2 7 6 2 9 6 3 1 8 3 - 0 6 A ( l l , 7 , 9 , l l ) = . 6 1 8 1 4 3 3 2 2 2 9 2 3 7 3 - 0 8 A ( l l , 7 , 1 0 , 1 ) = . 2 4 1 3 2 6 7 1 2 5 6 8 9 3 E - 0 4 A ( l l , 7 , 1 0 , 2 ) = . 8 2 0 3 8 1 5 6 2 7 8 9 4 1 E - 0 4 A ( l l , 7 , 1 0 , 3 ) = . 1 4 3 6 5 9 7 8 8 0 2 2 8 9 8 - 0 3 A ( l l , 7 , 1 0 , 4 ) = . 1 0 9 5 3 5 5 7 3 6 4 2 4 6 3 - 0 3 A ( 1 1 , 7 , 1 0 , 5 ) = . 7 8 2 2 1 4 0 4 6 3 5 3 1 5 8 - 0 4 A ( l l , 7 , 1 0 , 6 ) = . 2 9 8 6 8 9 5 7 2 8 4 4 0 7 8 - 0 4 A ( l l , 7 , 1 0 , 7 ) = . 1 0 0 8 8 9 8 4 4 3 1 8 8 9 8 - 0 4 A ( l l , 7 , 1 0 , 8 ) = . 1 5 2 3 0 2 2 8 3 2 2 9 4 9 8 - 0 5 A ( l l , 7 , 1 0 , 9 ) = . 1 9 9 3 4 4 1 3 7 8 6 3 3 8 3 - 0 6 A ( l l , 7 , 1 0 , 1 0 ) = . 9 0 9 2 1 5 7 2 5 6 2 5 1 9 3 - 0 8 A ( 1 1 , 7 , 1 0 , l l ) = . 2 8 2 9 9 2 7 3 9 7 0 1 9 6 8 - 0 9 A ( 1 1 , 7 , 1 1 , 1 ) = . 6 6 3 7 5 2 2 0 3 4 2 2 5 2 3 - 0 6 A ( l l , 7 , l l , 2 ) = . 2 1 7 8 6 6 4 8 9 8 2 6 6 9 E - O S A ( l l , 7 , l l , 3 ) = . 4 0 6 5 9 9 8 9 9 7 0 4 9 3 8 - 0 5 A ( 1 1 , 7 , 1 1 , 4 ) = . 3 2 0 3 6 2 8 0 8 1 0 3 8 8 8 - 0 5 A ( 1 1 , 7 , 1 1 , 5 ) = . 2 3 0 7 5 0 0 8 3 9 2 9 3 7 E - 0 5 A ( 1 1 , 7 , 1 1 , 6 ) = . 8 7 2 0 4 6 6 3 6 2 3 5 5 2 E - 0 6 A ( 1 1 , 7 , 1 1 , 7 ) = . 3 0 2 7 7 2 1 9 4 6 4 9 1 4 3 - 0 6 A ( 1 1 , 7 , 1 1 , 8 ) = . 4 5 7 4 9 7 8 5 2 3 7 9 7 0 8 - 0 7 A ( 1 1 , 7 , 1 1 , 9 ) = . 6 1 8 1 3 8 0 0 8 4 8 7 4 2 8 - 0 8 2 9 8 A ( 1 1 , 7 , 1 1 , 1 0 ) = . 2 8 2 9 9 4 2 2 8 0 9 4 7 0 8 - 0 9 A ( 1 1 , 7 , 1 1 , 1 1 ) = . 9 0 8 3 6 6 4 2 7 1 2 0 9 4 8 - 1 1 A ( 1 1 , 8 , 1 , 1 ) = A ( 1 1 , 8 , 1 , 5 ) . 2 9 9 6 3 4 3 0 9 4 8 5 5 5 E - 0 1 . 1 3 6 3 7 7 1 4 0 8 7 9 6 3 E - 0 1 . 1 9 5 0 3 8 5 4 5 8 7 6 7 4 E + 0 0 . 2 0 7 8 0 8 8 4 8 4 7 0 4 5 E + 0 0 . 1 8 3 8 1 3 2 4 9 6 9 2 3 Z E + 0 0 . 4 7 6 7 1 3 1 6 1 9 1 5 5 4 3 - 0 1 I I I I I I I I I I I I I I V V I I I I I I I I I I I I I I I I I I V V I I I I I I I I I I I I I I I I I I V V I I I I I I I I I I I I I I I I I I I A ( 1 1 , 8 , 5 , 8 ) = A ( l l , 8 , 5 , 9 ) = A ( 1 1 , 8 , 5 , 1 0 ) = A ( 1 1 , 8 , 5 , 1 1 ) = A ( 1 1 , 8 , 6 , 1 ) = 2 9 9 . 1 5 8 7 2 7 8 8 1 4 9 8 6 3 E - 0 1 . 1 3 9 9 1 0 8 5 6 6 6 9 3 0 E - 0 1 . 3 3 4 7 4 2 6 0 5 9 9 1 7 8 E - 0 2 . 1 3 0 6 0 2 5 5 3 3 2 6 7 5 E - 0 3 . 4 1 3 6 7 1 4 9 3 5 0 4 3 5 E - 0 5 . 1 3 7 1 5 0 8 0 9 1 6 8 8 2 3 - 0 1 . 2 7 4 1 3 2 6 7 6 4 2 2 6 0 E + 0 0 . 2 5 0 1 3 3 1 7 1 6 7 7 5 9 8 + 0 0 . 7 5 3 8 6 9 6 1 5 4 9 5 2 0 8 + 0 0 . 4 3 9 4 5 6 0 4 5 6 2 7 5 9 E + 0 0 . 1 2 0 5 4 9 3 1 5 5 8 6 6 9 E + 0 0 . 7 3 9 4 5 5 0 2 2 8 4 9 1 4 E - 0 1 . 4 6 1 1 9 9 4 5 3 5 6 6 2 2 E - 0 1 . 1 1 0 6 9 7 9 6 0 0 4 4 4 9 E - O l . 4 1 9 8 5 6 1 5 4 6 2 1 8 1 8 - 0 3 . 1 2 9 8 5 1 7 0 3 2 9 2 1 6 8 - 0 4 . 1 9 4 8 1 7 4 4 2 4 4 6 9 5 8 + 0 0 . 2 4 9 7 0 8 8 5 3 6 6 2 0 1 8 + 0 0 . 9 7 3 8 9 3 2 5 4 9 9 5 3 5 E + 0 0 . 4 5 0 5 3 7 1 8 9 8 4 1 2 7 E + 0 0 . 7 9 5 1 6 7 2 9 7 1 2 4 8 6 E + 0 0 . 8 4 4 5 8 1 4 6 2 4 4 2 8 7 E - 0 1 . 8 5 9 0 7 5 4 8 6 6 6 0 0 0 8 - 0 1 . 1 1 5 3 8 6 8 6 2 5 4 0 6 2 8 + 0 0 . 1 9 6 4 7 3 4 0 7 2 6 8 0 6 8 - 0 1 . 7 9 9 0 2 4 5 0 8 5 2 3 8 7 8 - 0 3 . 2 4 5 9 8 3 1 9 8 6 8 1 1 9 E - 0 4 . 2 0 8 1 5 1 6 3 4 7 8 2 5 5 8 + 0 0 . 7 5 4 5 8 6 4 2 0 9 5 3 2 7 E + 0 0 . 4 5 1 0 3 3 3 9 8 5 0 9 0 3 8 + 0 0 . 1 3 8 5 2 3 4 0 8 0 2 5 5 0 8 + 0 1 . 7 2 0 5 2 5 7 5 6 4 7 8 3 1 8 ' 0 1 . 3 2 9 8 8 1 6 3 0 8 3 7 9 Z E + 0 0 . 7 6 9 4 4 9 4 9 1 0 5 3 8 2 3 - 0 1 . 1 0 8 2 4 1 3 3 7 5 8 4 3 B E + 0 0 . 1 4 4 0 1 0 9 4 1 0 0 3 2 2 8 - 0 1 . 6 3 2 3 2 0 4 1 5 2 0 6 7 8 E - 0 3 . 1 8 1 7 0 3 5 7 6 2 0 3 0 6 8 - 0 4 . 1 8 3 5 2 8 8 5 9 1 6 8 2 9 E + 0 0 . 4 3 8 7 9 3 9 2 7 4 3 1 l l E + 0 0 . 7 9 4 5 7 0 4 1 2 4 8 6 7 9 E + 0 0 . 7 1 8 0 1 2 8 2 4 6 5 4 S B E - O l . 6 1 5 1 3 6 2 3 2 2 2 7 0 9 E + 0 0 . 9 3 9 2 7 4 4 5 8 2 1 4 6 4 8 - 0 1 . 2 7 5 6 9 5 9 8 8 9 0 8 4 1 E + 0 0 . 8 2 0 8 0 9 9 8 7 4 9 0 0 7 8 - 0 1 . 1 0 2 2 2 0 3 4 6 5 9 8 1 9 3 - 0 1 . 4 6 4 2 4 1 3 7 1 9 0 1 1 5 E - 0 3 . 1 3 5 1 3 4 3 3 3 5 8 9 8 0 8 - 0 4 . 4 7 8 2 1 8 6 9 6 0 8 0 1 5 E - 0 1 M 1 1 M 1 1 M 1 1 M 1 1 M 1 1 M 1 1 M 1 1 M 1 1 3 0 0 , 8 , 6 , 2 ) = - . 1 2 0 9 1 3 0 1 5 6 7 8 5 2 3 + 0 0 , 8 , 6 , 3 ) = . 8 4 8 1 9 7 0 8 0 1 9 4 9 5 E ' 0 1 , 8 , 6 , 4 ) = - . 3 3 0 0 8 5 0 3 9 1 3 8 7 9 E + 0 0 , 8 , 6 , 5 ) = - . 9 3 8 7 0 5 2 8 0 4 2 3 1 6 E - 0 1 , 8 , 6 , 6 ) = . 1 3 5 6 0 0 5 5 8 9 4 7 7 7 E + 0 0 , 8 , 6 , 7 ) = . 1 5 0 4 0 2 4 9 4 7 0 6 2 1 E + 0 0 , 8 , 6 , 8 ) = . 2 9 8 9 2 1 0 5 9 0 0 2 1 7 E - 0 1 , 8 , 6 , 9 ) = . 3 8 4 5 6 8 2 7 5 3 3 0 8 2 3 - 0 2 , 8 , 6 , 1 0 ) = . 1 6 9 1 3 6 1 4 7 7 4 6 9 4 E - 0 3 , 8 , 6 , l l ) = . 4 9 9 4 9 6 8 8 9 7 1 6 5 1 E - 0 5 , 8 , 7 , 1 ) = . 1 5 8 2 0 1 5 9 1 1 1 1 7 2 8 - 0 1 , 8 , 7 , 2 ) = ' . 7 3 8 1 5 5 9 4 4 2 7 2 8 8 8 - 0 1 , 8 , 7 , 3 ) = . 8 5 7 7 1 9 4 4 3 7 3 8 4 6 E - 0 1 , 8 , 7 , 4 ) = . 7 7 0 2 9 2 6 5 4 6 3 3 5 2 8 - 0 1 , 8 , 7 , 5 ) = . 2 7 5 6 6 4 6 6 8 7 6 3 0 6 3 + 0 0 , 8 , 7 , 6 ) = . 1 5 0 4 0 8 6 9 0 9 1 1 7 Z E + 0 0 , 8 , 7 , 7 ) = . 5 8 1 1 3 3 5 2 6 8 6 6 3 2 E - 0 1 , 8 , 7 , 8 ) = . l O 4 8 2 6 6 5 1 0 7 7 0 2 E - 0 1 , 8 , 7 , 9 ) = . 1 3 4 6 2 5 1 2 6 4 7 4 9 3 8 - 0 2 , 8 , 7 , 1 0 ) = . 6 0 4 2 0 4 0 1 0 4 1 4 8 3 E - 0 4 , 8 , 7 , 1 1 ) = . 1 8 1 1 9 6 0 4 3 4 1 3 9 3 E - 0 5 , 8 , 8 , l ) = . 1 4 0 0 2 5 8 1 2 4 3 4 0 3 3 - 0 1 , 8 , 8 , 2 ) = . 4 6 0 9 0 8 6 7 6 0 3 1 9 8 8 - 0 1 , 8 , 8 , 3 ) = . 1 1 5 4 1 8 3 0 6 9 0 1 1 2 8 + 0 0 , 8 , 8 , 4 ) = . 1 0 8 2 2 0 7 9 9 1 2 7 5 9 E + 0 0 , 8 , 8 , 5 ) = . 8 2 0 8 9 5 3 3 1 5 6 2 5 0 8 - 0 1 , 8 , 8 , 6 ) = . 2 9 8 8 9 8 7 3 2 7 2 6 2 3 3 - 0 1 , 8 , 8 , 7 ) = . 1 0 4 8 2 9 6 8 8 0 6 1 7 3 8 - 0 1 , 8 , 8 , 8 ) = . 1 7 9 2 6 4 9 7 7 3 0 5 1 4 8 - 0 2 , 8 , 8 , 9 ) = . 2 3 0 1 0 2 0 4 2 7 9 2 1 7 8 - 0 3 , 8 , 8 , 1 0 ) = . 1 0 3 0 4 3 4 0 8 6 8 5 7 2 8 - 0 4 , 8 , 8 , 1 1 ) = . 3 0 8 8 2 6 0 0 5 6 5 7 1 8 E - 0 6 , 8 , 9 , l ) = . 3 3 4 5 9 1 8 6 1 2 4 6 7 4 8 - 0 2 , 8 , 9 , 2 ) = . 1 1 0 7 3 6 4 6 7 3 2 2 5 7 E - 0 1 , 8 , 9 , 3 ) = . 1 9 6 4 3 1 0 4 0 8 2 2 0 6 8 - 0 1 , 8 , 9 , 4 ) = . 1 4 4 0 3 9 5 9 8 3 8 0 9 1 E - 0 1 , 8 , 9 , 5 ) = . 1 0 2 2 0 7 6 5 6 4 5 4 9 9 8 - 0 1 , 8 , 9 , 6 ) = . 3 8 4 6 0 5 4 3 0 7 3 5 9 7 E - 0 2 , 8 , 9 , 7 ) = . 1 3 4 6 1 8 4 4 1 6 8 8 8 7 3 - 0 2 , 8 , 9 , 8 ) = . 2 3 0 1 0 8 0 5 7 1 6 6 9 4 3 - 0 3 , 8 , 9 , 9 ) = . 3 0 4 4 8 0 8 8 6 7 9 6 9 1 8 - 0 4 , 8 , 9 , 1 0 ) = . 1 3 7 8 2 0 5 6 8 7 3 5 2 4 3 - 0 5 , 8 , 9 , 1 1 ) = . 4 2 5 4 1 4 7 1 1 2 3 5 9 2 E - 0 7 , 8 , 1 0 , 1 ) = . 1 3 0 7 0 2 3 4 7 8 6 0 2 8 E - 0 3 , 8 , 1 0 , 2 ) = . 4 1 9 6 0 0 1 8 6 4 3 2 9 4 8 - 0 3 , 8 , 1 0 , 3 ) = . 7 9 9 3 1 1 0 8 3 9 3 7 9 4 8 - 0 3 , 8 , 1 0 , 4 ) = . 6 3 2 1 2 2 8 6 4 7 7 2 1 0 E - 0 3 , 8 , 1 0 , 5 ) = . 4 6 4 3 3 2 5 2 3 2 7 9 1 5 8 - 0 3 , 8 , 1 0 , 6 ) = . 1 6 9 1 0 7 5 8 8 5 9 0 1 2 3 - 0 3 , 8 , 1 0 , 7 ) = . 6 0 4 2 6 1 4 9 3 0 3 7 9 4 8 - 0 4 A ( l l A ( l l A ( 1 1 A ( 1 1 A ( l l A ( l l A ( 1 1 , 8 , 1 0 , 8 ) = , 8 , 1 0 , 9 ) = A ( l l , 8 , 1 0 , 1 0 ) = A ( l l , 8 , 1 0 , 1 1 ) = , 8 , 1 1 , 1 ) = , 8 , l l , 2 ) = A ( 1 1 , 8 , 1 1 , 3 ) = , 8 , 1 l , 4 ) = , 8 , l l , 5 ) = , 8 , l l , 6 ) = A ( 1 1 , 8 , l l , 1 1 ) A ( 1 1 , A ( 1 1 : , 9 , 1 , A ( l l A ( 1 1 , A ( 1 1 , A ( 1 1 , A ( l l ' r A ( 1 1 , A ( 1 1 , A ( 1 1 , A ( 1 1 , A ( 1 1 , A ( 1 1 , A ( 1 L A ( 1 1 , A ( 1 1 , A ( 1 1 , A ( 1 1 , A ( l l , A ( 1 1 9 , 1 , 1 ) 9 , 1 , 3 4 9 , 1 , 5 9 , 1 , 6 9 , 1 , 7 9 , 1 , 8 9 , 1 , 9 9 , 1 , 1 9 , 1 , 1 1 2 3 4 5 6 7 8 9 , 2 , 9 , 2 , 9 , 2 , 9 , 2 , 9 , L 9 , 2 , 9 , 2 , 9 , 2 , I I I I I I I I I I I I I I I I I I V V I I I I I I I I I I I I I I I I I I 9 , 2 , 1 0 ) = , 9 , 2 , 1 1 ) = A ( 1 1 , 9 , 3 , 1 ) = 3 0 1 . 1 0 3 0 3 6 5 0 5 0 5 2 5 0 8 - 0 4 . 1 3 7 8 2 4 4 2 7 4 2 6 3 8 3 - 0 5 . 6 2 4 3 9 3 5 7 4 0 6 6 8 5 3 - 0 7 . 1 9 4 0 8 5 1 2 2 4 5 2 7 3 E - 0 8 . 4 1 3 4 5 3 9 6 7 9 5 1 2 3 E - 0 5 . 1 2 9 9 0 7 7 1 1 1 1 2 7 6 E - 0 4 . 2 4 5 9 1 9 8 6 2 6 0 7 0 2 8 - 0 4 . 1 8 1 7 4 8 1 3 0 6 4 3 2 0 8 - 0 4 . 1 3 5 1 1 3 2 2 6 4 9 1 5 1 E - 0 4 . 4 9 9 5 6 5 1 9 2 7 6 8 6 1 8 - 0 5 . 1 8 1 1 8 1 3 6 3 6 0 1 0 1 8 - 0 5 . 3 0 8 8 4 5 7 8 5 3 9 0 5 9 8 - 0 6 . 4 2 5 4 0 0 2 2 0 6 0 5 0 0 E - 0 7 . 1 9 4 0 8 9 1 8 9 1 6 4 9 7 E - 0 8 . 6 2 1 8 9 1 2 3 0 4 6 1 0 9 E - 1 0 . 1 0 6 6 2 9 8 5 7 4 2 0 9 2 E + 0 1 . 6 1 0 4 0 7 6 2 0 6 6 8 4 l E + 0 0 4 9 0 9 3 4 6 1 0 3 6 6 8 2 3 + 0 1 . 5 8 1 0 4 3 9 5 8 6 6 3 9 4 E + 0 0 . 1 8 5 7 1 2 9 9 3 1 4 4 9 9 E + 0 1 . 1 2 5 4 2 4 3 1 0 5 6 4 9 9 E + 0 0 . 3 1 6 9 5 6 9 9 5 0 5 5 0 8 8 + 0 0 2 9 3 7 9 2 6 4 4 5 1 5 6 3 E - 0 2 . 1 8 6 7 8 2 9 0 0 7 0 9 6 6 8 - 0 1 . 1 4 2 9 6 1 0 1 9 6 2 8 2 7 E - 0 2 . 3 7 5 6 2 1 0 6 1 7 2 1 1 8 E - 0 4 . 6 0 9 9 0 4 7 9 5 8 8 5 0 9 E + 0 0 : . 1 1 3 2 5 0 4 6 9 5 6 5 3 9 E + 0 2 1 2 9 6 6 1 6 9 1 1 8 8 8 1 E + 0 1 1 1 5 8 1 6 6 6 8 8 6 8 0 6 E + 0 2 9 3 1 7 3 3 0 1 2 1 9 9 4 0 E + 0 0 2 9 8 1 8 5 0 8 1 7 7 9 9 6 E + 0 1 1 6 4 6 8 6 0 6 8 8 9 2 4 8 8 - 0 1 2 2 1 2 9 4 3 4 9 0 5 9 4 S E + 0 0 5 1 5 9 1 7 3 8 0 1 0 7 5 7 3 - 0 1 . 4 5 5 2 1 8 2 5 8 1 3 9 2 1 8 - 0 2 . 1 0 9 9 1 2 2 1 9 6 1 3 7 6 E - 0 3 4 9 1 1 0 2 2 6 6 3 1 1 6 5 8 + 0 1 A ( 1 1 , 9 , 3 , 2 ) = - 1 2 9 9 4 5 0 7 5 5 1 1 9 3 E + 0 1 A ( 1 1 A ( 1 1 A ( 1 1 , 9 , 3 , 3 ) = 1 9 1 3 0 4 ) : - , 9 , 3 , 5 ) = 2 1 0 7 7 4 5 1 4 6 7 5 1 4 E + 0 2 1 5 9 2 0 7 3 4 4 0 5 5 1 8 3 + 0 1 8 2 5 9 1 0 0 3 7 7 5 5 9 7 E + 0 1 A ( 1 1 , 9 , 3 , 6 ) = - 4 6 3 8 2 9 9 3 4 5 9 7 O Z E + 0 0 A ( 1 1 , 9 , 3 , 7 ) = 1 3 5 6 0 6 5 2 3 6 0 3 2 0 8 + 0 1 A ( 1 1 , 9 , 3 , 8 ) = ~ 7 0 8 7 0 4 4 0 4 5 3 2 9 1 8 - 0 1 A ( 1 1 . A ( 1 1 , A ( 1 l , A ( 1 1 , 9 , 3 , 9 ) 8 9 , 3 , 1 0 ) = 9 , 3 , 1 1 ) = 9 , 4 , 1 ) = 1 3 2 8 2 0 2 4 0 5 7 1 1 6 3 + 0 0 . 8 3 7 9 6 3 9 2 2 0 9 4 7 9 8 - 0 2 . 2 2 3 4 8 3 6 1 9 9 4 7 7 3 3 - 0 3 . 5 7 8 5 9 0 9 8 9 1 1 2 8 5 3 + 0 0 A ( 1 1 , 9 , 4 , 2 ) = ' . 1 1 5 7 6 2 5 0 0 7 6 2 9 4 E + 0 2 I I I I I I I I I I I I I I V V I I I I I I I I I I I I I I I I I I V V I I I I I I I I I I I I I I I I I I V V I I M 1 L 9 , 6 , 1 M 1 1 , 9 , 7 , 1 ) M 1 1 , 9 , 7 , 2 ) = M 1 1 , 9 , 7 , 3 ) = M 1 1 , 9 , 7 , 4 ) = - M 1 1 , 9 , 7 , 5 ) = M 1 1 , 9 , 7 , 6 ) = M 1 1 , 9 , 7 , 7 ) = M 1 1 , 9 , 7 , 8 ) = M 1 1 , 9 , 7 , 9 ) = M 1 L 9 , 7 , 1 0 ) = M 1 1 , 9 , 7 , 1 1 ) = M 1 1 , 9 , 8 , 1 ) = - M 1 1 , 9 , 8 , 2 ) = - M 1 1 , 9 , 8 , 3 ) = - M 1 1 , 9 , 8 , 4 ) = - M 1 1 , 9 , 8 , 5 ) = M 1 1 , 9 , 8 , 6 ) = M 1 L 9 , 8 , 7 ) = M 1 1 , 9 , 8 , 8 ) = 3 0 2 . 1 5 9 5 6 8 2 9 7 8 6 3 0 1 E + 0 1 . 1 1 4 7 9 6 3 1 4 8 3 5 5 5 E + 0 2 . 8 6 9 8 3 9 8 1 7 2 8 5 5 4 E + 0 0 . 2 8 3 4 1 5 3 2 0 5 1 5 6 3 E + 0 1 . 1 1 2 2 3 3 3 5 5 6 4 1 3 7 E + 0 0 . 1 2 5 4 3 1 8 0 8 6 4 3 0 4 E + 0 0 . 1 1 1 4 4 7 1 8 9 2 3 6 0 6 E + 0 0 . 6 0 3 1 9 5 3 1 0 3 9 5 6 8 8 - 0 2 . 1 6 4 3 5 2 6 1 2 2 7 3 4 3 8 - 0 3 . 1 8 5 9 2 2 0 3 7 0 6 5 0 3 E + 0 1 . 9 2 6 7 3 8 1 7 2 7 6 9 5 5 8 + 0 0 . 8 2 6 3 5 9 0 7 5 3 0 7 8 5 E + 0 1 . 8 6 7 9 3 0 0 8 4 4 6 6 9 3 E + 0 0 . 2 6 1 5 9 1 4 7 0 2 4 1 5 5 E + 0 1 . 3 9 3 9 1 8 2 0 8 7 7 7 9 O E + 0 0 . 3 6 3 3 0 1 5 7 7 0 4 6 5 1 3 + 0 0 . 1 8 8 4 0 2 5 6 3 3 3 3 5 1 8 + 0 0 . 9 4 2 7 2 7 6 2 2 4 5 9 6 4 E - 0 1 . 4 2 8 9 3 2 8 6 5 1 7 9 3 8 3 - 0 2 . 1 2 8 9 4 6 7 2 3 0 6 6 2 9 8 - 0 3 . 1 2 4 2 4 6 9 6 9 8 1 9 0 7 E + 0 0 . 2 9 7 8 9 6 9 8 8 6 8 9 9 O E + 0 1 . 4 6 6 7 4 3 3 0 5 3 2 5 5 1 8 + 0 0 . 2 8 3 2 4 9 6 3 0 0 3 3 9 7 E + 0 1 . 3 9 3 4 3 8 5 5 5 3 0 0 2 4 E + 0 0 . 7 6 2 9 2 2 5 3 2 8 5 6 4 6 3 + 0 0 . 5 0 7 4 4 7 6 2 6 4 4 1 7 2 E - 0 1 . 1 4 5 3 6 4 9 3 6 6 7 4 O I E + 0 0 . 3 3 9 2 9 8 7 0 2 6 0 1 8 1 E - 0 1 . 1 5 6 7 6 0 3 1 9 0 7 7 8 8 8 - 0 2 . 4 5 7 3 2 8 2 1 7 7 4 8 9 1 3 - 0 4 . 3 1 7 3 9 2 9 9 5 5 8 1 0 3 E + 0 0 . 1 5 3 8 0 2 5 5 8 7 7 9 7 2 8 - 0 1 . 1 3 5 7 2 1 9 1 8 9 4 0 5 4 E + 0 1 . 1 1 2 9 6 0 8 3 4 0 5 6 1 4 E + 0 0 . 3 6 3 5 8 5 6 0 9 9 4 2 6 7 E + 0 0 . 5 0 6 8 7 7 5 8 2 5 2 0 2 5 3 - 0 1 . 2 9 9 0 4 2 7 6 9 2 4 2 0 8 8 + 0 0 . 7 1 9 8 3 4 5 0 8 4 9 0 7 5 8 - 0 1 . 1 2 2 5 6 3 0 6 4 4 3 3 0 5 8 - 0 1 . 5 7 2 1 6 2 6 1 4 3 8 9 5 3 E - 0 3 . 1 7 0 1 1 9 6 1 6 3 8 5 0 2 8 - 0 4 . 3 0 4 0 3 1 2 3 2 3 7 1 9 3 E - 0 2 . 2 2 1 0 3 3 7 7 6 1 7 8 9 6 8 + 0 0 . 7 1 1 5 3 9 5 7 3 9 6 7 4 6 E - 0 1 . 1 2 5 2 4 4 2 6 5 4 2 2 2 2 E + 0 0 . 1 8 8 3 2 1 9 0 8 9 3 5 9 O E + 0 0 . 1 4 5 3 8 6 5 7 5 0 2 2 7 1 8 + 0 0 . 7 1 9 8 0 4 1 2 8 7 4 8 3 6 8 - 0 1 . 1 3 1 1 8 7 2 2 6 5 7 9 6 4 E - 0 1 3 0 3 A ( 1 1 , 9 , 8 , 9 ) = . 2 1 1 2 3 0 3 3 4 5 7 1 1 6 E - 0 2 A ( 1 1 , 9 , 8 , 1 0 ) = . 9 6 8 2 9 4 3 4 1 4 1 9 1 0 E - 0 4 A ( 1 1 , 9 , 8 , 1 1 ) = . 2 8 8 8 3 5 9 3 3 4 8 1 8 3 E - 0 5 A ( l l , 9 , 9 , 1 ) = . 1 8 6 9 2 7 4 4 6 6 2 9 8 5 8 - 0 1 A ( 1 1 , 9 , 9 , 2 ) = . 5 1 5 5 4 6 6 5 3 1 8 6 9 0 3 - 0 1 A ( l l , 9 , 9 , 3 ) = . 1 3 2 8 6 1 4 4 1 3 5 0 5 4 E + 0 0 A ( 1 1 , 9 , 9 , 4 ) = . 1 1 1 4 1 9 1 1 0 7 9 1 7 6 E + 0 0 A ( l l , 9 , 9 , 5 ) = . 9 4 2 8 5 5 0 0 4 6 8 6 8 6 8 - 0 1 A ( 1 1 , 9 , 9 , 6 ) = . 3 3 9 2 6 0 5 9 6 3 7 4 5 2 E - 0 1 A ( 1 1 , 9 , 9 , 7 ) = . 1 2 2 5 7 0 1 4 6 5 5 9 1 6 8 - 0 1 A ( 1 1 , 9 , 9 , 8 ) = . 2 1 1 2 2 3 7 2 8 8 2 0 1 9 3 - 0 2 A ( 1 1 , 9 , 9 , 9 ) = . 3 2 4 1 5 4 7 8 6 8 8 1 0 8 8 - 0 3 A ( 1 l , 9 , 9 , 1 0 ) = . 1 4 9 7 2 7 7 1 7 9 3 9 6 4 8 - 0 4 A ( l l , 9 , 9 , 1 1 ) = . 4 5 7 0 3 8 4 5 4 8 5 9 6 7 E - 0 6 A ( 1 1 , 9 , 1 0 , 1 ) = . 1 4 2 8 5 7 3 1 8 4 9 6 6 8 3 - 0 2 A ( 1 1 , 9 , 1 0 , 2 ) = . 4 5 5 4 8 4 5 6 6 9 1 9 0 4 3 - 0 2 A ( 1 1 , 9 , 1 0 , 3 ) = . 8 3 7 6 6 4 8 8 6 0 5 7 6 1 E - 0 2 A ( l l , 9 , 1 0 , 4 ) = . 6 0 3 4 0 4 2 7 0 8 0 5 1 9 8 - 0 2 A ( l l , 9 , 1 0 , 5 ) = . 4 2 8 8 3 5 2 5 8 2 0 7 9 8 8 - 0 2 A ( 1 1 , 9 , 1 0 , 6 ) = . 1 5 6 7 9 1 3 7 9 4 1 3 3 3 8 - 0 2 A ( 1 1 , 9 , 1 0 , 7 ) = . 5 7 2 0 9 8 1 2 7 5 7 7 1 9 8 - 0 3 A ( 1 1 , 9 , 1 0 , 8 ) = . 9 6 8 3 7 4 1 2 1 7 2 5 9 0 8 - 0 4 A ( 1 1 , 9 , 1 0 , 9 ) = . 1 4 9 7 2 3 1 5 9 6 6 5 8 8 8 - 0 4 A ( 1 1 , 9 , 1 0 , 1 0 ) = . 6 9 0 7 7 0 7 7 8 3 5 5 4 4 8 - 0 6 A ( 1 1 , 9 , 1 0 , 1 1 ) = . 2 1 2 5 2 6 7 8 1 3 1 2 4 5 E - 0 7 A ( 1 1 , 9 , 1 1 , l ) = . 3 7 5 8 6 8 8 7 9 1 3 2 2 1 8 - 0 4 A ( 1 1 , 9 , 1 1 , 2 ) = . 1 0 9 8 4 7 9 3 4 7 0 9 2 5 3 - 0 3 A ( l l , 9 , 1 1 , 3 ) = . 2 2 3 5 5 6 4 7 7 9 7 6 6 7 8 - 0 3 A ( 1 1 , 9 , 1 1 , 4 ) = . 1 6 4 3 0 1 0 3 5 9 6 5 7 6 8 - 0 3 A ( 1 1 , 9 , 1 1 , 5 ) = . 1 2 8 9 7 1 5 0 9 6 3 9 0 9 3 - 0 3 A ( 1 1 , 9 , 1 1 , 6 ) = . 4 5 7 2 4 6 3 5 4 9 8 3 4 5 3 - 0 4 A ( 1 1 , 9 , 1 1 , 7 ) = . 1 7 0 1 3 7 7 2 9 2 5 6 2 3 8 ~ 0 4 A ( l l , 9 , 1 1 , 8 ) = . 2 8 8 8 1 0 5 9 9 7 9 1 1 3 8 - 0 5 A ( 1 1 , 9 , 1 1 , 9 ) = . 4 5 7 0 5 8 1 9 9 0 6 5 9 4 8 - 0 6 A ( 1 1 , 9 , 1 1 , 1 0 ) = . 2 1 2 5 2 0 5 6 8 9 2 0 7 4 8 - 0 7 A ( 1 1 , 9 , 1 1 , 1 1 ) = . 6 7 5 6 9 8 0 1 6 4 1 9 3 0 8 - 0 9 A ( 1 1 , 1 0 , 1 , 1 ) = . 8 4 9 4 4 0 6 2 2 3 2 9 7 1 8 + 0 1 A ( 1 1 , 1 0 , 1 , 2 ) = . 3 2 3 7 9 6 7 4 9 1 1 4 9 9 E + 0 0 A ( 1 1 , 1 0 , 1 , 3 ) = . 4 1 5 8 1 3 9 0 3 8 0 8 5 9 E + 0 2 A ( 1 1 , 1 0 , 1 , 4 ) = . 1 4 3 5 7 5 5 4 9 1 2 5 6 7 E + 0 2 A ( 1 1 , 1 0 , 1 , 5 ) = . 3 1 5 0 6 0 4 5 5 7 9 9 1 0 8 + 0 2 A ( 1 1 , 1 0 , l , 6 ) = . 8 5 1 1 8 0 9 7 0 6 6 8 7 9 E + 0 1 A ( 1 1 , 1 0 , 1 , 7 ) B . 3 6 1 1 6 4 3 4 9 3 1 7 S S E + 0 1 A ( 1 1 , 1 0 , 1 , 8 ) = . 4 7 0 0 9 9 7 7 6 9 8 3 2 6 8 + 0 0 A ( 1 1 , 1 0 , 1 , 9 ) = . 9 3 8 8 5 0 7 0 6 4 4 3 1 9 3 - 0 1 A ( l l , 1 0 , 1 , 1 0 ) = . 1 3 2 9 4 4 0 9 2 0 3 8 0 9 8 - 0 1 A ( 1 1 , 1 0 , 1 , 1 1 ) = . 7 5 1 3 5 8 0 4 3 0 8 9 5 7 8 - 0 3 A ( 1 1 , 1 0 , 2 , 1 ) = . 3 1 7 8 3 1 0 3 9 4 2 8 7 1 8 + 0 0 A ( l l , 1 0 , 2 , 2 ) - ' . 6 3 6 7 7 5 9 9 9 0 6 9 2 1 3 + 0 2 A ( 1 1 , 1 0 , 2 , 3 ) = - . 3 5 5 6 3 8 7 7 1 0 5 7 1 3 3 + 0 2 I I I I I I V V I I I I I I I I I I I I I I I I I I V =V 3 0 4 A ( l l , 1 0 , 2 , 4 ) = - . 1 0 0 0 5 1 4 4 9 7 7 5 7 O E + 0 3 A ( 1 1 , 1 0 , 2 , 5 ) = - . 5 1 8 8 3 7 1 0 8 6 1 2 0 6 E + 0 2 A ( 1 1 , 1 0 , 2 , 6 ) = - . 3 6 6 7 8 9 2 5 7 5 2 6 4 O E + 0 2 A ( 1 1 , 1 0 , 2 , 7 ) = ’ . 6 l 8 8 2 2 2 8 2 5 5 2 7 2 E + 0 1 A ( l l , 1 0 , 2 , 8 ) = - . 1 8 5 8 4 3 0 7 1 3 4 1 5 1 E + 0 1 A ( 1 1 , 1 0 , 2 , 9 ) = - . 2 4 6 0 1 6 4 7 0 7 1 5 4 O E + 0 0 A ( 1 l , 1 0 , 2 , 1 0 ) = . 2 9 2 5 5 6 1 8 2 2 4 8 5 2 3 - 0 1 A ( 1 1 , 1 0 , 2 , 1 l ) = . 2 1 4 2 1 8 5 3 0 8 9 1 2 3 3 - 0 2 A ( 1 1 , 1 0 , 3 , 1 ) = . 4 1 5 9 9 1 3 2 5 3 7 8 4 Z E + 0 2 A ( 1 1 , 1 0 , 3 , 2 ) = - . 3 5 5 9 2 8 7 0 7 1 2 2 8 0 £ + 0 2 A ( 1 1 , 1 0 , 3 , 3 ) = . 1 8 3 1 4 7 1 6 1 4 8 3 7 6 8 + 0 3 A ( 1 1 , 1 0 , 3 , 4 ) = . 1 2 7 7 1 8 7 7 2 8 8 8 1 8 3 + 0 2 A ( 1 1 , 1 0 , 3 , 5 ) = . 1 2 7 0 2 5 4 2 0 1 8 8 9 O E + 0 3 A ( 1 1 , 1 0 , 3 , 6 ) = . 2 0 9 5 8 4 6 5 0 9 9 3 3 S E + 0 2 A ( 1 1 , 1 0 , 3 , 7 ) . 1 4 5 0 5 1 4 6 0 2 6 6 1 1 E + 0 2 A ( 1 1 , 1 0 , 3 , 8 . 1 1 3 9 4 2 6 4 9 9 6 0 5 2 E + 0 1 A ( 1 1 , 1 0 , 3 , 9 . 3 6 7 6 7 9 8 5 8 5 8 0 2 3 8 + 0 0 ) ) A ( 1 1 , 1 0 , 3 , 1 0 A ( 1 1 , 1 0 , 3 , 1 1 A ( 1 1 , 1 0 , 4 , 1 ) A ( 1 1 , 1 0 , 4 , 2 ) A ( 1 1 , 1 0 , 4 , , 3 ; : ) ) ) ) ) 0 A ( 1 1 , 1 0 , 4 , 4 A ( 1 1 . 1 0 , 4 , 5 A ( 1 1 , 1 0 , 4 , 6 A ( 1 1 , 1 0 , 4 , 7 A ( 1 1 , 1 0 , 4 , 8 A ( 1 1 , 1 0 , L 9 A ( 1 1 , 1 0 , L 1 A ( 1 1 , 1 0 , 4 , 1 1 A ( 1 1 , 1 0 , 5 , 1 ) A ( 1 1 , 1 0 , 5 , 2 ) = - . A ( 1 1 , 1 0 , 5 , 3 ) = A ( 1 1 , 1 0 , 5 , 5 ) = A ( 1 1 , 1 0 , 5 , 6 ) = A ( 1 1 , 1 0 , 5 , 7 ) = A ( 1 1 , 1 0 , 5 , 9 ) = A ( 1 1 , 1 0 , 5 , 1 0 ) = A ( 1 1 , 1 0 , 5 , 1 1 ) = A ( 1 1 , 1 0 , 6 , 1 ) = A ( 1 1 , 1 0 , 6 , 3 ) = A ( 1 1 , 1 0 , 6 , 4 ) = ' A ( 1 1 , 1 0 , 6 , 5 ) = A ( 1 1 , 1 0 , 6 , 6 ) = - A ( 1 1 , 1 0 , 6 , 7 ) = A ( 1 1 , 1 0 , 6 , 9 ) = . 9 2 8 3 5 9 9 3 2 7 3 1 8 4 8 - 0 1 . 4 3 7 2 9 1 0 5 7 4 6 0 2 4 8 - 0 2 . 1 4 3 3 1 4 8 7 1 7 8 8 0 2 E + 0 2 . 9 9 9 9 5 2 6 5 0 0 7 0 1 9 E + 0 2 . 1 2 7 3 1 7 1 4 2 4 8 6 5 7 E + 0 2 . 1 3 8 4 9 3 6 3 3 2 7 0 2 6 E + 0 3 . 3 0 4 1 2 9 4 6 7 0 1 O S O E + 0 2 . 4 7 3 8 9 7 6 5 5 0 1 0 2 2 3 + 0 2 . 2 9 2 4 5 4 0 6 9 8 5 2 8 3 8 + 0 1 . 2 6 6 2 4 7 5 7 2 0 0 4 8 0 E + 0 1 . 8 0 8 1 1 7 3 1 5 1 7 3 1 5 E - 0 1 . 7 4 0 7 8 6 7 5 7 0 8 7 3 3 8 - 0 1 . 3 0 2 6 9 0 3 9 7 8 0 2 5 1 E - 0 2 . 3 1 5 2 8 3 6 3 4 6 6 2 6 3 8 + 0 2 5 1 9 3 6 1 4 1 0 1 4 0 9 9 E + 0 2 . 1 2 7 0 7 3 3 9 3 8 2 1 7 2 8 + 0 3 A ( 1 1 , 1 0 , 5 , 4 ) = - . 3 0 4 3 3 3 6 2 9 6 0 8 1 5 E + 0 2 . 8 2 0 3 6 8 4 8 5 4 5 0 7 4 E + 0 2 . 5 4 4 7 7 2 1 4 8 1 3 2 3 2 3 + 0 0 . 1 0 0 6 4 8 3 4 8 9 2 7 S O E + 0 2 A ( 1 1 , 1 0 , 5 , 8 ) = - . 3 6 7 9 0 2 9 0 4 7 4 8 9 2 E + 0 0 . 4 5 2 3 1 0 9 1 9 7 6 1 6 6 E + 0 0 . 7 1 4 8 0 6 1 0 6 4 0 7 2 0 8 ' 0 1 . 2 3 3 8 3 8 8 9 6 0 1 9 7 3 E - 0 2 . 8 4 9 9 7 6 2 0 5 8 2 5 8 1 3 + 0 1 A ( 1 1 , 1 0 , 6 , 2 ) = - . 3 6 6 4 9 8 7 6 8 3 2 9 6 2 E + 0 2 . 2 0 9 2 9 3 1 6 9 9 7 5 2 8 8 + 0 2 . 4 7 3 7 3 5 3 6 1 0 9 9 2 4 E + 0 2 . 5 4 0 1 6 9 7 1 5 8 8 1 3 S E + 0 0 . 1 5 8 1 9 7 0 4 4 1 3 4 1 4 E + 0 2 . 7 4 5 9 6 0 4 1 4 4 0 9 6 4 E + 0 0 A ( 1 1 , 1 0 , 6 , 8 ) = - . . 2 2 7 7 2 7 3 8 2 9 0 9 5 1 8 + 0 0 1 0 3 9 9 4 2 8 4 1 9 7 6 9 E + 0 1 3 0 5 A ( 1 1 , 1 0 , 6 , 1 0 ) = . 2 6 6 7 7 5 4 7 1 1 0 0 1 2 3 - 0 1 A ( 1 l , 1 0 , 6 , 1 1 ) = . 7 9 3 7 3 0 5 2 9 0 3 9 7 5 8 - 0 3 A ( 1 1 , 1 0 , 7 , 1 ) = . 3 6 1 5 9 4 8 7 3 6 6 6 7 6 E + 0 1 A ( l l , 1 0 , 7 , 2 ) = ' . 6 1 9 8 9 0 4 5 1 4 3 1 2 7 E + 0 1 A ( 1 1 , 1 0 , 7 , 3 ) = . 1 4 5 1 6 3 8 8 4 1 6 2 9 0 E + 0 2 A ( 1 1 , 1 0 , 7 , 4 ) = - . 2 9 3 1 4 8 8 2 1 5 9 2 3 B E + 0 1 A ( 1 1 , 1 0 , 7 , 5 ) = . 1 0 0 6 7 4 4 3 6 6 8 8 4 Z E + 0 2 A ( 1 1 , 1 0 , 7 , 6 ) = . 7 4 5 4 3 5 2 8 2 5 8 8 0 1 E + 0 0 A ( 1 1 , 1 0 , 7 , 7 ) = . 9 7 2 1 1 2 8 5 6 8 0 5 3 Z E + 0 0 A ( 1 1 , 1 0 , 7 , 8 ) = . 1 9 4 6 2 6 5 2 6 9 0 7 0 9 E + 0 0 A ( 1 1 , 1 0 , 7 , 9 ) . 1 5 7 9 1 3 6 8 7 4 0 6 l l E + 0 0 A ( 1 1 , 1 0 , 7 , 1 . 9 8 3 3 2 5 7 5 5 0 7 8 1 1 8 - 0 2 A ( 1 1 , 1 0 , L 1 . 3 1 1 2 0 3 2 9 2 7 6 7 4 6 8 - 0 3 A ( 1 1 , 1 0 , 8 , l . 4 6 9 1 3 1 1 1 2 0 9 8 6 9 E + 0 0 A ( 1 1 , 1 0 , 8 , 2 . 1 8 5 5 9 8 5 5 9 6 7 7 6 O E + 0 1 A ( 1 1 , 1 0 , 8 , 3 . 1 1 3 6 7 8 2 9 1 4 4 0 0 1 E + 0 1 A ( 1 1 , 1 0 , L 4 . 2 6 6 0 7 5 2 7 8 8 1 8 6 1 E + 0 1 A ( 1 1 , 1 0 , 8 , 5 . 3 6 8 6 3 6 1 9 0 8 9 1 2 7 E + 0 0 A ( 1 1 , 1 0 , L 6 . 1 0 3 9 7 4 8 7 9 5 3 3 0 5 8 + 0 1 A ( 1 1 , 1 0 , 8 , 7 . 1 9 4 6 0 0 0 2 8 9 1 7 1 9 E + 0 0 . 1 1 4 2 1 8 8 3 2 4 5 9 3 O E + 0 0 M 1 1 , 1 0 , 8 , 9 M 1 1 , 1 0 , 8 , 1 M 1 1 , 1 0 , 8 , 1 A ( l l , 1 0 , 9 , l . 2 8 1 0 5 8 5 0 5 3 5 2 1 2 8 - 0 1 . 1 6 3 2 4 1 4 4 9 9 9 0 8 9 E - 0 2 . 5 0 5 7 1 7 3 8 9 1 0 3 2 1 E - 0 4 . 9 4 0 1 5 2 9 5 6 1 7 2 8 2 8 - 0 1 I I I I I I I I I I V V I I I I I I I I I I I I I I I I I I V V I I I I I I 0 1 ) ) ) ) ) ) ) A ( 1 1 , 1 0 , L , 8 ; 0 1 ) ) ) ) ) A ( 1 1 , 1 0 , 9 , 2 . 2 4 6 3 4 6 7 8 4 7 5 5 5 9 E + 0 0 A ( 1 1 , 1 0 , 9 , 3 . 3 6 8 0 4 5 0 4 1 3 3 7 6 1 8 + 0 0 A ( 1 1 , 1 0 , 9 , 4 . 8 1 0 5 9 4 6 1 4 5 9 5 1 7 E - 0 1 A ( 1 1 , 1 0 , 9 , 5 . 4 5 2 4 2 1 6 7 2 6 4 2 2 3 8 + 0 0 A ( 1 1 , 1 0 , 9 , 6 ) = . 2 2 7 6 9 4 8 9 2 7 9 0 1 7 E + 0 0 A ( 1 1 , 1 0 , 9 , 7 ) = . 1 5 7 9 1 9 6 0 9 2 2 0 7 O E + 0 0 A ( l l , 1 0 , 9 , 8 ) = . 2 8 1 0 5 3 1 1 7 6 5 1 0 3 E - 0 1 A ( 1 1 , 1 0 , 9 , 9 ) = . 5 0 1 0 8 6 9 8 7 2 4 2 1 6 8 - 0 2 A ( 1 1 , 1 0 , 9 , 1 0 ) = . 2 6 8 8 3 5 8 6 4 2 8 9 9 4 E - 0 3 A ( 1 1 , 1 0 , 9 , 1 1 ) = . 8 4 5 8 5 9 4 9 5 8 6 8 2 4 3 - 0 5 A ( 1 1 , 1 0 , 1 0 , 1 ) = . 1 3 2 8 5 5 6 2 5 7 0 6 7 2 8 - 0 1 A ( 1 1 , 1 0 , 1 0 , 2 ) = . 2 9 2 7 8 2 4 8 0 8 2 8 4 6 8 - 0 1 A ( 1 1 , 1 0 , 1 0 , 3 ) = . 9 2 8 1 0 5 6 8 1 6 6 8 9 7 E - 0 1 A ( 1 1 , 1 0 , 1 0 , 4 ) = . 7 4 0 9 6 2 4 4 9 9 2 6 8 8 3 - 0 1 A ( 1 1 , 1 0 , 1 0 , 5 ) = . 7 1 4 7 2 4 8 2 5 2 2 9 5 0 E - 0 1 A ( 1 1 , 1 0 , 1 0 , 6 ) = . 2 6 6 8 0 0 8 2 5 1 9 3 0 6 8 - 0 1 A ( 1 1 , 1 0 , 1 0 , 7 ) = . 9 8 3 2 7 4 5 0 0 3 2 2 3 0 3 - 0 2 A ( 1 1 , 1 0 , 1 0 , 8 ) = . 1 6 3 2 4 7 6 6 8 7 5 1 8 6 8 - 0 2 A ( 1 1 , 1 0 , 1 0 , 9 ) = . 2 6 8 8 3 2 4 5 2 7 7 5 3 1 8 - 0 3 A ( l l , 1 0 , 1 0 , 1 0 ) = . 1 3 9 7 9 7 3 0 6 9 5 7 2 3 8 - 0 4 A ( 1 1 , 1 0 , 1 0 , 1 1 ) = . 4 3 7 1 4 1 8 2 6 2 9 2 7 3 8 - 0 6 A ( 1 1 , 1 0 , 1 1 , 1 ) = . 7 5 1 5 5 7 4 5 5 2 5 9 9 0 E - 0 3 A ( 1 1 , 1 0 , 1 1 , 2 ) = . 2 1 4 1 6 7 1 2 4 7 9 5 4 9 E - 0 2 A ( 1 1 , 1 0 , 1 1 , 3 ) = . 4 3 7 3 4 9 0 2 0 6 4 8 9 8 8 - 0 2 A ( 1 1 , 1 0 , 1 1 , 4 ) = . 3 0 2 6 4 9 8 4 7 6 1 7 4 3 8 - 0 2 3 0 6 A ( 1 1 , 1 0 , 1 1 , 5 ) = . 2 3 3 8 5 8 1 4 8 2 0 3 5 8 8 - 0 2 A ( 1 1 , 1 0 , 1 1 , 6 ) = . 7 9 3 6 6 8 0 7 4 0 3 8 5 8 8 - 0 3 A ( 1 1 , 1 0 , 1 1 , 7 ) = . 3 1 1 2 1 6 7 7 9 0 9 5 9 6 8 - 0 3 A ( 1 1 , 1 0 , 1 1 , 8 ) = . 5 0 5 6 9 9 2 2 0 8 0 9 6 7 8 - 0 4 A ( 1 1 , 1 0 , 1 1 , 9 ) = . 8 4 5 8 7 3 0 3 7 3 9 1 7 0 E - 0 5 A ( 1 1 , 1 0 , 1 1 , 1 0 ) = . 4 3 7 1 3 7 9 1 7 4 1 9 5 1 8 - 0 6 A ( 1 1 , 1 0 , 1 1 , 1 1 ) = . 1 4 1 5 5 9 8 5 2 3 1 2 4 6 8 - 0 7 A ( 1 1 , 1 1 , 1 , 1 ) = . 1 0 4 0 4 1 8 8 9 9 5 3 6 l E + 0 4 A ( 1 1 , 1 1 , 1 , 2 ) = . 4 2 9 0 6 7 2 1 4 9 6 5 8 2 8 + 0 3 A ( l l , 1 1 , 1 , 3 ) = . 4 9 2 1 1 6 5 0 6 9 5 8 0 1 3 + 0 4 A ( 1 1 , 1 l , 1 , 4 ) = . 9 6 9 6 3 7 4 0 5 3 9 5 5 1 E + 0 3 A ( 1 1 , 1 1 , 1 , 5 ) = . 2 3 2 2 6 7 2 7 1 4 2 3 3 4 E + 0 4 A ( l l , l l , 1 , 6 ) = . 9 3 9 7 1 3 5 9 2 5 2 9 B O E + 0 2 A ( 1 l , 1 1 , 1 , 7 ) = . 2 6 2 9 0 4 8 7 0 0 3 3 2 6 E + 0 3 A ( 1 1 , 1 1 , 1 , 8 ) = . 1 0 2 5 0 4 4 1 0 7 4 3 7 1 E + 0 2 A ( 1 1 , 1 1 , 1 , 9 ) = . 8 2 4 4 7 3 9 8 9 0 0 9 8 6 E + 0 1 A ( 1 1 , 1 l , 1 , 1 0 ) = - . 2 3 1 2 5 1 7 1 6 6 1 3 7 7 8 - 0 1 A ( 1 1 , 1 1 , l , 1 1 ) = . 2 8 6 4 8 3 5 9 2 9 3 5 8 4 8 - 0 1 A ( 1 1 , 1 1 , 2 , l ) = . 4 2 9 1 8 9 0 5 6 3 9 6 4 8 8 + 0 3 A ( 1 1 , 1 1 , 2 , 2 ) = - . 1 0 0 6 6 2 7 9 9 0 7 2 2 7 E + 0 5 A ( 1 1 , 1 1 , 2 , 3 ) = ' . 2 3 2 6 4 5 9 0 4 5 4 1 0 2 8 + 0 4 A ( 1 1 , 1 1 , 2 , 4 ) = ' . 1 1 6 7 5 7 8 1 0 0 5 8 5 9 E + 0 5 A ( l l , 1 1 , 2 , 5 ) = - . 1 0 6 2 5 5 2 7 0 3 8 5 7 4 E + 0 4 A ( 1 1 , 1 1 , 2 , 6 ) = ' . 2 4 9 4 2 0 1 2 7 8 6 8 6 S E + 0 4 A ( 1 1 , 1 1 , 2 , 7 ) = - . 2 0 7 5 0 4 9 9 7 2 5 3 4 2 8 + 0 2 A ( 1 1 , 1 1 , 2 , 8 ) = ' . 1 7 9 9 1 0 1 7 4 8 4 6 6 5 8 + 0 3 A ( 1 1 , 1 1 , 2 , 9 ) = - . 2 0 3 3 2 9 l 4 5 9 0 8 3 6 E + 0 0 A ( 1 1 , 1 1 , 2 , 1 0 ) = - . 1 9 2 2 2 1 4 4 7 8 2 5 4 3 E + 0 1 A ( 1 1 , 1 1 , 2 , 1 1 ) = . 5 7 4 4 3 3 0 9 9 2 4 5 6 5 8 - 0 1 A ( 1 1 , 1 1 , 3 , 1 ) = . 4 9 2 0 7 6 7 1 2 0 3 6 1 3 E + 0 4 A ( 1 1 , 1 1 , 3 , 2 ) = - . 2 3 2 5 8 1 5 0 0 2 4 4 1 4 E + 0 4 A ( 1 1 , 1 1 , 3 , 3 ) = . 2 1 4 1 7 6 4 4 8 3 6 4 2 6 E + 0 5 A ( 1 1 , 1 l , 3 , 4 ) = - . 5 5 5 0 8 0 8 1 0 5 4 6 8 8 8 + 0 3 A ( 1 1 , 1 1 , 3 , 5 ) = . 1 0 1 0 4 2 6 8 8 5 9 8 6 3 E + 0 5 A ( 1 1 , 1 1 , 3 , 6 ) = “ . 6 4 6 1 1 2 4 7 2 5 3 4 1 8 8 + 0 3 A ( 1 1 , 1 1 , 3 , 7 ) = . 1 1 8 1 9 1 8 3 0 4 4 4 3 4 E + 0 4 A ( 1 1 , 1 1 , 3 , 8 ) = ‘ . 2 9 3 2 5 1 8 3 8 6 8 4 O B E + 0 2 A ( 1 1 , 1 1 , 3 , 9 ) = . 3 7 2 2 0 7 2 2 3 7 7 3 O O E + 0 2 A ( 1 1 , 1 1 , 3 , 1 0 ) = - . 8 9 8 5 1 3 7 8 6 4 9 4 7 3 8 + 0 0 A ( 1 1 , 1 1 , 3 , 1 1 ) = . 1 7 1 9 2 2 1 2 3 7 5 8 1 2 8 + 0 0 A ( 1 1 , 1 1 , 4 , 1 ) = . 9 7 0 2 0 3 8 1 1 6 4 5 5 1 3 + 0 3 A ( 1 1 , 1 1 , 4 , 2 ) = ' . 1 1 6 7 7 0 1 4 5 8 7 4 0 2 E + 0 5 A ( 1 1 , 1 1 , 4 , 3 ) = ' . 5 5 4 2 3 3 1 5 4 2 9 6 B B E + 0 3 A ( 1 1 , 1 1 , 4 , 4 ) = - . 1 3 3 0 9 4 3 5 5 4 6 8 7 S E + 0 5 A ( 1 1 , 1 1 , 4 , 5 ) = ’ . 2 1 1 0 9 2 3 1 5 6 7 3 8 3 E + 0 3 A ( 1 1 , 1 1 , 4 , 6 ) = - . 2 8 6 8 8 4 6 5 1 1 8 4 O B E + 0 4 A ( 1 1 , 1 1 , 4 , 7 ) = . 9 3 5 6 0 1 0 4 3 7 0 1 1 7 E + 0 2 A ( 1 1 , 1 1 , 4 , 8 ) = — . 2 0 5 6 4 5 0 2 3 3 4 5 9 S E + 0 3 A ( 1 1 , 1 1 , 4 , 9 ) = . 3 0 4 8 7 4 6 6 4 5 4 5 0 6 E + 0 1 A ( 1 1 , 1 1 , 4 , 1 0 ) - - . 2 1 5 6 9 2 0 3 0 2 6 5 9 3 8 + 0 1 3 0 7 A ( 1 1 , 1 1 , 4 , 1 1 ) = . 1 1 3 2 4 6 4 5 5 0 9 0 1 2 3 + 0 0 A ( 1 1 , 1 1 , 5 , 1 ) = . 2 3 2 2 1 9 0 8 9 5 0 8 0 6 E + 0 4 A ( 1 1 , 1 1 , 5 , 2 ) = - . 1 0 6 1 4 5 7 1 2 2 8 0 2 7 E + 0 4 A ( 1 1 , 1 1 , 5 , 3 ) = . 1 0 1 0 3 2 5 7 9 9 5 6 0 5 E + 0 5 A ( 1 1 , 1 1 , 5 , 4 ) = - . 2 1 0 6 7 2 7 6 0 0 0 9 7 7 E + 0 3 A ( 1 1 , 1 1 , 5 , 5 ) = . 4 7 2 9 2 5 5 8 7 4 6 3 3 8 E + 0 4 A ( 1 1 , 1 1 , 5 , 6 ) = - . 2 9 7 3 7 4 9 0 8 4 4 7 2 7 E + 0 3 A ( 1 1 , 1 1 , 5 , 7 ) = . 5 4 3 2 1 5 1 3 1 7 5 9 6 4 E + 0 3 A ( 1 1 , 1 1 , 5 , 8 ) = ' . 9 7 9 8 5 4 6 3 1 4 2 3 9 5 E + 0 1 A ( 1 1 , l l , 5 , 9 ) = . 1 6 5 1 3 4 3 1 6 3 8 4 7 9 E + 0 2 A ( 1 1 , l l , 5 , 1 0 ) = - . 1 8 1 6 2 4 8 5 3 9 8 3 5 2 E + 0 0 A ( 1 1 , 1 1 , 5 , 1 l ) = . 1 1 3 4 0 0 6 8 7 3 4 7 1 7 E + 0 0 A ( 1 1 , 1 1 , 6 , l ) = . 9 4 2 2 6 8 7 1 4 9 0 4 7 9 E + 0 2 A ( 1 l , l l , 6 , 2 ) = - . 2 4 9 4 8 1 5 9 6 3 7 4 5 1 E + 0 4 A ( 1 1 , 1 1 , 6 , 3 ) = - . 6 4 5 4 9 3 0 7 2 5 0 9 7 7 E + 0 3 A ( 1 l , l l , 6 , 4 ) = - . 2 8 6 9 1 8 0 9 9 2 1 2 6 S E + 0 4 A ( 1 1 , 1 1 , 6 , 5 ) = “ . 2 9 7 2 8 0 3 9 5 5 0 7 B I E + 0 3 A ( l l , l l , 6 , 6 ) = - . 5 8 3 8 1 2 6 1 0 6 2 6 2 2 E + 0 3 A ( l l , 1 1 , 6 , 7 ) = - . 1 2 1 1 0 8 9 5 6 3 3 6 9 B E + 0 2 A ( l l , 1 1 , 6 , 8 ) = - . 4 1 3 6 8 4 7 2 8 1 4 5 6 O E + 0 2 A ( 1 1 , 1 1 , 6 , 9 ) = - . 1 0 0 2 3 4 2 9 3 9 3 7 6 8 E + 0 1 A ( 1 1 , 1 1 , 6 , 1 0 ) = - . 1 5 0 6 4 9 8 9 2 1 6 6 2 6 E + 0 0 A ( 1 1 , 1 1 , 6 , 1 1 ) = . 3 9 8 7 6 0 6 1 1 1 3 3 1 8 E - 0 1 A ( 1 1 , l l , 7 , l ) = . 2 6 2 8 1 6 4 1 4 8 3 3 0 7 E + 0 3 A ( 1 l , 1 1 , 7 , 2 ) = - . 2 0 5 3 2 1 3 1 1 9 5 0 6 8 E + 0 2 A ( 1 1 , 1 1 , 7 , 3 ) = . 1 1 8 1 6 8 7 6 6 7 8 4 6 7 E + 0 4 A ( 1 l , 1 1 , 7 , 4 ) = . 9 3 7 0 0 2 6 0 1 6 2 3 5 4 E + 0 2 A ( l l , 1 1 , L 5 ) ‘ . 5 4 3 1 6 2 4 0 5 0 1 4 0 4 E + 0 3 A ( 1 l , 1 1 , L 6 ) = . 1 2 1 0 0 6 4 6 0 1 8 9 8 2 8 + 0 2 A ( 1 1 , 1 1 , L 7 ) = . 5 9 0 5 1 2 6 4 2 8 6 0 4 1 E + 0 2 A ( 1 1 , 1 1 , 7 , 8 ) = . 1 4 2 8 6 7 1 5 9 8 4 3 4 4 E + 0 1 A ( 1 1 , 1 1 , 7 , 9 ) = . 1 6 7 9 5 8 3 6 3 8 9 0 6 S E + 0 1 A ( 1 1 , 1 1 , 7 , 1 0 ) = . 2 0 3 6 6 9 2 0 0 1 8 5 6 9 E + 0 0 A ( 1 1 , 1 1 , 7 , 1 1 ) = . 1 6 7 8 0 9 7 9 3 9 2 9 3 4 8 - 0 1 A ( 1 1 , 1 1 , L 1 ) = . 1 0 2 6 9 9 5 7 0 6 5 5 8 2 E + 0 2 A ( 1 1 , 1 1 L 2 ) = - . 1 7 9 9 5 9 0 6 4 0 0 6 8 1 8 + 0 3 A ( 1 1 , 1 1 8 , 3 ) = - . 2 9 2 7 1 9 8 7 9 1 5 0 3 9 E + 0 2 A ( l l , 1 1 , 8 , 4 ) = - . 2 0 5 6 7 9 2 3 9 2 7 3 0 7 E + 0 3 A ( 1 1 , 1 1 , L 5 ) = ' . 9 7 8 4 3 6 7 3 2 2 9 2 1 8 E + 0 1 A ( l l , 1 1 , 8 , 6 ) = . 4 1 3 7 2 1 6 7 2 2 9 6 5 2 8 + 0 2 A ( 1 1 , 1 1 , L 7 ) = . 1 4 2 9 1 6 5 0 0 5 6 8 3 9 E + 0 1 A ( 1 1 , 1 1 , 8 , 8 ) = - . 3 4 4 4 1 4 5 2 9 2 0 4 3 7 E + 0 1 A ( 1 1 , 1 1 , 8 , 9 ) = . 2 7 9 1 8 4 3 0 7 9 0 3 0 5 E + 0 0 A ( 1 1 , 1 1 , 8 , 1 0 ) = . 4 8 4 9 8 2 2 6 0 3 8 6 4 6 E - 0 1 A ( 1 1 , 1 1 , 8 , 1 1 ) = . 2 5 7 7 4 2 7 7 3 4 6 5 0 0 8 - 0 2 A ( 1 1 , 1 1 , 9 , 1 ) = . 8 2 4 2 1 6 5 9 2 3 1 1 8 6 8 + 0 1 A ( 1 1 , 1 1 , 9 , 2 ) = ' . 1 9 6 8 1 3 2 2 5 7 4 6 1 5 E + 0 0 A ( 1 1 , 1 1 , 9 , 3 ) = . 3 7 2 1 3 5 4 3 5 9 3 8 8 4 E + 0 2 A ( 1 1 , 1 1 , 9 , 4 ) = . 3 0 5 3 5 3 1 4 6 7 9 1 4 6 E + 0 1 A ( 1 1 , 1 1 , 9 , 5 ) = . 1 6 5 1 1 3 2 8 9 3 5 6 2 3 8 + 0 2 3 0 8 A ( 1 1 , 1 1 , 9 , 6 ) = - . 1 0 0 1 7 2 7 8 7 9 0 4 7 4 E + 0 1 A ( 1 1 , 1 1 , 9 , 7 ) = . 1 6 7 9 4 7 5 2 1 8 0 5 7 6 E + 0 1 A ( 1 1 , 1 1 , 9 , 8 ) = . 2 7 9 1 9 3 9 3 0 3 2 7 8 9 E + 0 0 A ( 1 1 , 1 1 , 9 , 9 ) = . 1 8 2 5 3 4 5 5 3 2 2 7 0 1 E + 0 0 9 0 8 0 7 0 A ( 1 1 , 1 1 , 9 , 1 0 ) = . 1 0 6 5 9 3 7 0 9 7 8 8 2 9 E - 0 1 A ( 1 1 , 1 l , 9 , 1 1 ) = . 4 5 7 9 6 4 0 8 2 7 8 4 2 0 E - 0 3 A ( l l , l l , 1 0 , 1 ) = - . 2 2 9 5 4 0 9 7 0 l 7 6 4 6 E - O l A ( 1 1 , l l , 1 0 , 2 ) = - . 1 9 2 2 6 5 3 4 9 6 2 6 5 4 E + 0 1 A ( 1 1 , l l , 1 0 , 3 ) = - . 8 9 8 0 2 6 5 1 8 5 2 3 6 9 E + 0 0 A ( l l , l l , 1 0 , 4 ) = - . 2 1 5 7 2 5 4 4 9 1 0 0 1 4 E + 0 1 A ( l l , 1 1 , 1 0 , 5 ) = - . 1 8 1 4 7 2 3 7 9 7 1 4 Z S E + 0 0 A ( I I , 1 1 , 1 0 , 6 ) = - . 1 5 0 6 9 6 6 6 5 9 7 9 9 2 E + 0 0 A ( 1 1 , 1 l , 1 0 , 7 ) = . 2 0 3 6 7 8 5 5 5 3 2 0 9 5 E + 0 0 A ( 1 1 , 1 1 , 1 0 , 8 ) = . 4 8 4 9 7 1 2 8 0 0 9 3 3 0 E - 0 1 A ( 1 1 , l l , 1 0 , 9 ) = . 1 0 6 5 9 4 3 1 3 9 8 3 8 1 E - 0 1 A ( 1 1 , 1 1 , 1 0 , 1 0 ) = . 5 7 0 4 0 4 8 4 3 5 2 9 1 0 E - 0 3 A ( 1 1 , l l , 1 0 , l l ) = . 2 3 0 5 1 4 0 7 8 4 3 8 6 6 E - 0 4 A ( 1 1 , 1 1 , 1 1 , 1 ) = . 2 8 6 4 4 5 2 8 2 9 8 1 7 3 E - O l A ( 1 1 , l l , 1 1 , 2 ) = . 5 7 4 5 3 1 5 6 7 9 8 1 4 7 E - 0 1 A ( 1 1 , l l , 1 1 , 3 ) = . 1 7 1 9 1 1 0 8 6 1 8 8 6 3 E + o o A ( 1 1 , l l , 1 1 , 4 ) = . 1 1 3 2 5 4 1 0 8 3 4 9 7 9 E + 0 0 A ( 1 1 , 1 1 , 1 1 , 5 ) = . 1 1 3 3 9 7 1 0 1 1 1 4 9 7 E + 0 0 A ( l l , l l , 1 1 , 6 ) = . 3 9 8 7 7 2 0 6 8 1 4 7 O B E - O l A ( 1 1 , 1 1 , 1 1 , 7 ) = . 1 6 7 8 0 7 3 6 5 4 3 2 9 6 E - 0 1 A ( 1 1 , 1 1 , 1 1 , 8 ) = . 2 5 7 7 4 5 9 9 9 2 6 0 8 1 E - 0 2 A ( 1 1 , l l , 1 1 , 9 ) = . 4 5 7 9 6 1 7 6 7 5 5 1 7 5 E - 0 3 A ( 1 1 , 1 1 , 1 1 , 1 0 ) = . 2 3 0 5 1 4 7 2 5 1 0 3 6 0 E - 0 4 A ( 1 1 , 1 1 , 1 1 , 1 l ) = . 8 8 4 5 8 1 1 9 0 2 9 6 8 8 E - 0 6 D O 1 0 I = 8 , 1 1 D O 2 0 J = 1 , I S U M ( I , J ) = 0 . 0 D O 3 0 K = l , I D O 4 0 L = 1 , I S U M ( I , J ) = S U M ( I , J C O N T I N U E C O N T I N U E ) + A ( I , J , K , L ) W R I T E ( 1 0 , 5 0 ) I , J , S U M ( I , J ) C O N T I N U E C O N T I N U E F O R M A T ( 5 X , ' S U M ( ' D O 6 0 N = 8 , 1 1 D O 7 0 J = I , N D O 8 0 I = 1 , N B ( N , J , I ) = o . o D O 9 0 K = 1 , N B ( N , J , I ) = B ( N , J , I C O N T I N U E , I z , f , ' , 1 2 , ' ) = ' , E 2 0 . 1 4 ) ) + A ( N , J , I , K ) W R I T E ( 1 0 , 1 0 0 ) N , J , I , B ( N , J , I ) C O N T I N U E C O N T I N U E 3 0 9 6 0 C O N T I N U E 1 0 0 F O R M A T ( 1 0 X , ' B ( ' , 1 2 , ' , ' , 1 2 , ' , ' , 1 2 , ' ) = ' , E Z O . 1 4 ) S T O P E N D 3 1 0 P R O G R A M E V A L U E ( I N P U T , O U T P U T , T A P E 1 0 , T A P E z o ) I N T E G E R N , I A , I J O B , I z , I E R R E A L A ( l l , 1 1 ) , W K ( 2 0 0 ) , B ( 8 : l l , 1 1 , 1 1 ) R E A L W L ( 8 : 1 1 , 1 1 ) R E A L 2 1 ( 1 1 , 1 1 ) , 2 2 ( 1 1 , 1 1 ) C O M P L E X 2 ( 1 1 , 1 1 ) , w ( 1 1 ) C T H I S P R O G R A M C A L C U L A T E S T H E E I G E N S O F T H E L I N E A R I Z E D C O P E R A T O R C I N S E C T I O N 3 . 4 O F T H E D I S S E R T A T I O N O F T . J . C M O R I N . W L ( 8 , 1 ) = - 1 . 4 4 3 9 4 2 9 W L ( 8 , 2 ) = 1 . 0 1 8 9 0 1 5 W L ( 8 , 3 ) = - . 0 4 8 2 2 6 6 7 2 W L ( 8 , 4 ) = . 3 7 9 6 1 3 4 1 W L ( 8 , 5 ) = . 0 5 6 1 5 2 6 0 8 W L ( 8 , 6 ) = . 0 3 4 8 8 1 5 4 5 W L ( 8 , 7 ) = . 0 0 2 3 6 9 5 7 6 4 W L ( 8 , 8 ) = . 0 0 0 2 5 0 9 9 0 4 1 W L ( 9 , 1 ) = - 1 . 4 0 2 3 7 3 9 W L ( 9 , 2 ) = . 8 6 0 2 6 2 7 O W L ( 9 , 3 ) = . 0 7 6 8 6 9 6 4 3 W L ( 9 , 4 ) = . 2 9 5 7 4 5 2 4 W L ( 9 , 5 ) = . 1 2 2 4 6 0 6 3 W L ( 9 , 6 ) = . 0 3 7 0 1 2 3 3 3 W L ( 9 , 7 ) = . 9 2 7 6 7 9 6 E - 2 W L ( 9 , 8 ) = . 7 0 0 2 0 0 5 6 E - 3 W L ( 9 , 9 ) = . 4 6 3 7 9 0 4 3 E - 4 W L ( 1 0 , 1 ) = - 1 . 4 7 5 0 3 4 7 W L ( 1 0 , 2 ) = 1 . 0 0 7 8 6 9 W L ( 1 0 , 3 ) = - . 1 3 9 9 5 8 2 8 W L ( 1 0 , 4 ) = . 4 4 7 2 1 5 4 1 W L ( 1 0 , 5 ) = . 6 9 4 1 5 7 1 2 E - 1 W L ( 1 0 , 6 ) = . 7 7 5 0 4 0 7 4 E - 1 W L ( 1 0 , 7 ) = . 9 8 0 2 9 4 4 3 E - 2 W L ( 1 0 , 8 ) = . 3 0 3 1 1 2 0 2 E - 2 W L ( 1 0 , 9 ) = . 1 4 5 5 4 7 9 S E - 3 W L ( 1 0 , 1 0 ) = . 9 1 3 4 5 6 4 6 E - 5 W L ( 1 1 , 1 ) = - 1 . 4 4 1 8 3 6 3 W L ( 1 1 , 2 ) = . 8 8 3 0 2 4 3 8 W L ( 1 1 , 3 ) = - . 2 9 7 1 5 2 1 9 E — 1 W L ( 1 1 , 4 ) = . 3 4 8 3 5 6 3 2 W L ( 1 1 , 5 ) = . 1 4 1 0 6 0 6 3 W L ( 1 1 , 6 ) = . 7 0 2 2 2 8 5 4 E - 1 W L ( 1 1 , 7 ) = . 2 3 9 6 6 9 5 7 E - 1 W L ( 1 1 , 8 ) = . 4 1 4 5 2 7 4 l E - 2 W L ( 1 1 , 9 ) = . 7 3 6 7 5 0 7 l E - 3 W L ( 1 1 , 1 0 ) = . 3 6 7 2 0 4 7 4 E - 4 W L ( 1 1 , 1 1 ) = . 1 6 1 4 6 2 0 9 E - 5 B ( 8 , 1 , 1 ) = . 4 8 3 6 1 2 1 2 6 3 5 6 9 9 E + 0 0 B ( 8 , l , 2 ) = . 8 0 3 8 8 0 9 0 7 5 6 2 6 9 8 + 0 0 B ( 8 , 1 , 3 ) = . 4 4 3 3 6 2 6 4 7 3 0 5 7 4 E + 0 0 m m m m m m m m m m m m m m m o o m m o o o o o o o o m o o m m m O O O O O O O O c o c o o o m o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o ‘ - - - “ ~ “ “ ‘ - “ “ “ “ ‘ ~ “ ~ V ‘ V “ “ ~ “ § “ “ “ “ V q q q u q m m m m m m m m m m m m m m m m p n p a : - p u p - a : p w w w w w w u w N N N N N N N N t - J H H H H “ “ “ “ ~ ‘ ~ ‘ ~ “ “ V ~ V V ‘ ~ “ ‘ - “ “ “ ‘ ~ V “ “ ~ ‘ V “ ‘ - ‘ 3 1 1 . 2 0 8 1 7 0 7 1 3 1 0 1 6 B E + 0 0 . 4 9 8 5 9 1 1 2 4 8 7 7 9 7 E - O l . 1 0 3 0 2 0 8 2 7 8 7 5 6 8 8 - 0 1 . 7 7 2 2 0 1 4 1 5 2 7 9 8 5 3 - 0 3 . 4 0 2 0 8 8 9 2 6 9 4 2 3 6 3 - 0 4 . 1 9 0 5 3 8 8 7 0 3 6 6 9 l E + 0 0 . 8 6 5 7 1 3 5 8 5 0 9 2 7 8 E + 0 0 . 6 0 4 5 5 0 6 9 7 3 2 6 1 9 E + 0 0 . 2 5 9 0 0 4 4 5 0 5 2 5 6 4 E + 0 0 . 6 6 1 2 9 0 0 8 0 2 5 1 9 7 E - 0 1 . 1 2 9 9 6 5 2 8 7 1 0 3 1 8 8 - 0 1 . 1 0 1 5 6 8 8 4 8 9 4 6 3 3 8 - 0 2 . 5 1 1 7 1 2 2 2 1 2 7 9 8 4 8 - 0 4 . 8 2 5 6 5 4 4 3 2 6 8 6 4 6 3 - 0 1 . 5 0 1 5 3 7 4 9 8 9 8 3 2 1 E + 0 0 . 8 4 9 6 5 8 6 4 9 2 3 5 1 5 E + 0 0 . 4 3 6 8 1 0 8 0 8 7 3 3 3 1 E + 0 0 . 1 0 6 1 9 7 8 6 6 2 0 1 7 6 8 + 0 0 . 2 1 5 0 0 7 6 2 4 3 3 4 1 6 E - 0 1 . 1 6 4 4 7 9 8 1 1 9 1 4 7 4 3 - 0 2 . 8 4 1 7 2 8 5 6 1 9 3 7 7 3 8 - 0 4 . 3 2 2 8 7 5 0 1 8 3 7 3 2 5 E - 0 1 . 3 2 3 6 0 5 0 3 1 5 3 5 8 3 3 + 0 0 . 5 3 2 0 4 8 9 7 6 2 4 4 4 5 E + 0 0 . 8 1 7 5 0 7 7 5 0 1 7 2 5 6 E + 0 0 . 2 4 4 1 8 1 5 4 7 5 4 1 6 B E + 0 0 . 4 6 4 9 1 0 5 1 4 6 1 3 1 2 E - 0 1 . 3 6 9 3 9 8 2 8 9 4 9 4 9 1 3 - 0 2 . 1 8 4 1 5 7 8 8 2 7 6 2 4 4 E - 0 3 . 1 8 4 2 9 2 4 1 2 3 5 4 9 8 E - 0 1 . 3 0 6 0 2 5 8 9 5 1 1 4 2 6 E + 0 0 . 2 2 3 6 8 1 9 1 1 5 6 3 2 7 E + 0 0 . 6 8 7 5 9 5 4 7 4 8 5 3 7 2 E + 0 0 . 6 3 2 6 0 8 3 9 4 0 1 0 1 1 E + 0 0 . 1 5 6 3 5 1 4 6 8 7 5 2 2 9 E + 0 0 . 1 1 5 6 4 4 8 0 7 4 6 6 2 7 E - O l . 6 0 1 6 1 6 4 9 0 8 2 2 0 2 3 - 0 3 . 3 6 3 1 7 1 3 0 5 6 9 4 4 S E + 0 0 . 1 0 8 8 7 4 7 7 0 1 6 6 1 0 8 + 0 1 . 7 8 9 9 7 8 4 1 1 3 6 6 2 8 8 + 0 0 . 1 0 5 6 5 5 3 4 4 4 1 7 4 2 E + 0 1 . 2 9 4 4 8 1 5 7 6 7 1 0 1 0 8 + 0 0 . 6 4 6 0 6 8 7 3 2 0 0 3 1 9 E + 0 0 . 6 4 2 3 5 2 8 7 8 3 4 1 4 4 3 - 0 1 . 3 0 6 2 9 8 3 3 0 1 9 1 7 1 8 - 0 2 . 2 4 7 4 2 9 1 8 9 6 4 0 5 2 3 + 0 1 . 6 2 9 5 6 1 4 5 8 4 5 9 2 1 8 + 0 1 . 6 3 8 1 7 5 1 7 4 4 7 2 9 6 E + 0 1 . 4 4 0 1 8 1 3 9 3 3 5 9 9 O E + 0 1 ' . 1 2 7 4 6 4 9 6 8 7 9 2 5 7 E + 0 1 m m m m m m m m m m m m m o x o x o x o x o x o x o x o x o x o x o x o x o x o x o x m m m m m m m m m m m m m m m m m m m m o m “ “ “ “ ‘ V ~ “ - V - “ ~ “ V “ “ ‘ V V “ " V V ‘ V ‘ V “ ‘ - “ “ 0 1 0 1 0 1 9 » u n n a - b h p p h w w u w w w w w w m N N N N N M N N H H H H H H t — I w w m m m m m m m m q \ I \ I ‘ ~ “ “ ‘ V “ ‘ V “ ‘ V “ ‘ - V “ ~ V “ “ “ ~ V ‘ ~ “ V ‘ “ ‘ ~ ‘ V “ “ 3 1 2 . 9 5 3 7 6 5 6 8 5 4 4 8 7 8 E + 0 0 . 4 4 7 2 6 1 2 9 0 3 1 3 S S E + 0 0 . 3 2 2 3 7 9 0 9 2 3 7 1 6 9 8 - 0 1 . 1 2 3 7 9 8 7 7 8 6 0 8 2 4 E + 0 3 . 3 1 1 0 5 5 0 1 6 6 8 4 4 0 E + 0 3 . 3 3 2 3 9 1 6 3 7 3 8 4 5 9 E + 0 3 . 2 1 4 1 1 9 3 3 1 0 8 0 3 0 3 + 0 3 . 8 8 1 7 3 0 9 5 1 2 9 8 6 8 5 + 0 2 . 2 3 4 2 5 2 5 6 1 1 1 4 S O E + 0 2 . 2 9 2 9 3 7 7 3 9 1 2 9 7 3 E + 0 1 . 6 9 3 2 8 3 7 5 8 2 4 2 8 3 8 + 0 0 . 4 4 8 5 4 5 5 7 8 7 5 2 9 O E + 0 0 . 7 5 0 1 9 2 6 2 8 6 1 3 1 0 E + 0 0 . 4 7 9 7 4 5 0 2 5 4 4 4 7 3 8 + 0 0 . 2 2 7 0 5 3 1 1 2 2 7 5 6 2 8 + 0 0 . 7 5 7 7 2 9 4 7 2 1 7 6 7 6 8 - 0 1 . 1 5 9 8 0 2 1 9 6 9 8 5 9 5 E - 0 1 . 2 5 3 8 2 6 6 3 8 4 4 1 1 0 E - 0 2 . 1 6 5 5 3 5 4 3 9 4 3 8 3 2 8 - 0 3 . 6 6 8 6 4 4 9 5 8 8 8 2 8 3 E - 0 5 . 1 8 4 5 4 9 4 1 0 4 2 6 8 3 E + 0 0 . 7 8 7 2 6 6 2 4 3 1 2 4 8 7 E + 0 0 . 6 3 3 2 8 1 5 7 3 5 7 2 0 9 E + 0 0 . 2 7 4 5 2 0 0 4 7 7 7 4 S O E + 0 0 . 9 7 3 7 7 8 5 5 3 8 4 7 7 3 E - 0 1 . 1 9 5 5 8 9 3 7 4 8 1 8 8 8 E - 0 1 . 3 2 3 3 7 6 1 1 1 4 5 7 6 0 E - 0 2 . 2 0 3 7 1 2 6 0 7 5 4 9 7 6 E - 0 3 . 8 4 5 9 8 9 3 7 6 0 5 3 1 6 E - 0 5 . 9 1 0 9 4 3 8 4 5 2 1 1 4 7 E - 0 1 . 4 3 5 2 2 7 2 0 4 4 9 6 9 S E + 0 0 . 8 5 3 4 6 1 7 4 9 8 5 5 2 6 8 + 0 0 . 4 3 6 4 0 5 4 9 3 3 4 3 8 1 E + 0 0 . 1 4 7 9 9 3 3 8 1 4 4 8 1 5 8 + 0 0 . 3 0 5 3 5 8 1 4 8 3 5 3 2 4 8 - 0 1 . 4 9 5 2 2 4 7 4 9 3 9 6 3 1 8 - 0 2 . 3 1 6 7 2 2 1 4 5 7 4 4 2 9 3 - 0 3 . 1 3 0 0 2 4 7 6 8 5 6 3 2 4 8 - 0 4 . 6 1 5 8 4 5 7 3 0 7 9 2 5 0 E - 0 1 . 2 2 8 0 1 5 0 0 8 8 7 8 2 1 E + 0 0 . 5 9 5 4 4 9 6 0 1 1 8 1 7 8 E + 0 0 . 7 3 9 9 2 6 4 9 5 3 3 5 9 9 E + 0 0 . 3 0 4 8 4 4 0 4 8 9 2 1 7 2 E + 0 0 . 5 9 5 3 8 1 5 5 8 0 3 3 8 5 8 - 0 1 . 9 9 9 2 7 9 0 4 3 9 4 1 5 0 8 - 0 2 . 6 2 3 2 6 1 9 7 5 2 8 6 6 2 3 - 0 3 . 2 6 0 6 6 3 8 8 1 5 6 6 9 1 8 - 0 4 . 7 0 0 3 6 1 3 2 6 1 4 4 5 9 8 - 0 1 . 7 0 0 2 1 8 9 4 4 7 2 5 5 6 3 - 0 1 . 4 6 2 6 4 1 4 8 2 1 2 7 2 5 E + 0 0 w N H m m q m m - b w m w x o m q m m b w m H m m u m m p w m w m m u m m p w r o t — t o o q o x m p w m H o o q a s v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v " I ! " I l l l l l l l l l l l l l l l l l l l l ' l l I I I I I I I I I I I I I I I I I I I I l l l l l l l l fl l l l l l l l l l l l l l l I l l l l l l l fl l i fl fl l l fl l l l l l l ‘ fi ‘ ‘ ~ “ “ “ “ ~ “ “ “ “ “ “ “ ‘ - ‘ - “ “ “ “ “ m o m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m c o m m A A A H I — ‘ H C O O ‘ ‘ ‘ ~ ~ ~ ‘ ~ ‘ ~ ~ ~ ‘ ‘ ‘ ~ ‘ ~ ~ ‘ ~ ‘ ~ ~ ‘ ‘ ~ ‘ ~ ~ ‘ ‘ ~ ‘ ~ ~ ~ ‘ ‘ ‘ ‘ ~ ‘ ~ ‘ ~ ‘ ~ ‘ ‘ ‘ m fl m m p r H m m q u T O p W N H m m fl m m p r H m m fl m m D W N H m m q m e W N U - ‘ K o m q m m p v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v I l l l I l l I l I l l l l l l l n u n u u l l l l l l l l l l l l l l l l l l l l u l l l l I I n u l l u l l I I l l l l l l u I l l l l l l l l l l l l l l l u l l l l u H H H H H H H H m m m m m m m m m m m m m m m m m m q q q q q q u u q m m m m m m m m m m m m m m w 3 1 3 . 5 0 1 5 3 1 6 3 2 3 8 8 5 4 E + 0 0 . 6 9 7 6 8 4 3 0 5 7 1 9 7 0 E + 0 0 . 1 6 9 5 9 1 3 2 6 8 7 4 9 2 E + 0 0 . 2 6 6 9 1 7 5 7 3 8 7 1 2 0 E - 0 1 . 1 7 3 0 9 7 4 0 1 8 3 9 1 7 8 - 0 2 . 7 0 4 8 9 7 1 4 7 1 8 0 4 6 E - 0 4 . 1 3 2 7 1 8 8 6 2 5 7 7 3 Z E + 0 0 . 1 7 0 9 4 4 6 3 3 5 0 6 0 7 E + 0 0 . 5 6 6 2 9 4 3 3 7 5 9 6 9 6 E + 0 0 . 1 5 7 2 4 4 6 9 5 8 6 5 6 G E + 0 0 . 6 5 9 4 0 1 4 6 7 9 6 3 4 7 E + 0 0 . 5 3 6 3 0 5 2 7 3 3 4 5 0 3 E + 0 0 . 1 1 1 9 7 1 2 5 1 4 6 2 5 2 8 + 0 0 . 6 7 2 2 1 0 6 9 5 5 1 2 9 2 8 - 0 2 . 2 8 6 6 1 6 0 9 2 2 3 7 5 1 E - 0 3 . 1 0 4 4 3 7 7 4 8 6 4 8 7 4 E + 0 1 . 2 5 9 0 2 6 6 6 6 6 6 1 7 O E + 0 1 . 3 2 1 7 0 6 4 9 9 5 2 6 7 7 E + 0 1 . 1 8 8 4 5 4 5 8 9 2 9 5 9 B E + 0 1 . 1 4 0 7 6 0 2 5 6 4 6 7 5 7 E + 0 1 . 1 9 0 6 0 5 2 9 1 2 3 0 5 6 8 + 0 0 . 5 6 6 8 4 5 5 8 1 4 7 1 0 3 E + 0 0 . 4 6 5 0 8 2 7 7 5 9 4 3 3 2 8 - 0 1 . 1 8 0 8 6 6 9 7 3 1 4 5 5 4 8 - 0 2 . 8 2 0 0 0 3 0 9 0 5 7 0 2 9 E + 0 1 . 2 1 0 7 1 6 2 9 6 1 3 2 7 8 E + 0 2 . 2 3 8 9 2 0 6 5 4 5 3 7 7 l E + 0 2 . 1 6 3 3 8 4 4 9 9 0 0 5 4 3 E + 0 2 . 7 9 4 5 8 2 9 3 3 0 9 7 4 2 E + 0 1 . 2 0 1 1 6 5 6 1 3 7 1 6 6 5 8 + 0 1 . 9 6 6 0 9 5 6 3 3 6 0 6 3 B E + 0 0 . 3 9 4 0 9 4 2 3 2 3 1 7 5 6 E + 0 0 . 2 3 6 2 5 2 7 1 2 9 7 2 1 9 E - O l . 5 1 0 7 6 7 3 8 4 2 8 6 3 4 E + 0 3 . 1 3 2 5 0 1 2 0 9 0 7 5 7 7 E + 0 4 . 1 5 0 5 8 9 8 1 9 1 6 8 5 2 E + 0 4 . 1 0 6 5 7 8 8 9 5 4 8 0 1 6 8 + 0 4 . 5 0 7 7 1 2 0 5 6 0 4 9 4 8 E + 0 3 . 1 6 2 8 7 5 8 7 4 2 4 6 6 4 E + 0 3 . 3 4 2 7 2 0 2 1 4 5 4 0 6 Z E + 0 2 . 3 6 0 6 5 8 2 1 4 2 3 4 4 7 E + 0 1 . 6 3 3 8 0 7 0 4 5 8 5 8 2 3 E + 0 0 . 4 0 7 5 8 0 6 6 1 0 0 8 2 6 E + 0 0 . 7 3 1 5 6 7 0 2 5 7 1 3 1 2 E + 0 0 . 4 7 2 1 8 3 2 7 4 7 4 7 9 5 E + 0 0 . 2 6 6 9 9 0 1 9 7 1 0 3 2 7 E + 0 0 . 8 9 4 7 3 8 2 3 7 0 6 0 5 7 3 - 0 1 . 2 7 1 5 3 5 3 6 8 5 3 0 9 9 E - 0 1 . 4 3 8 7 9 2 2 1 8 6 9 1 2 6 3 - 0 2 . 6 3 0 1 7 3 9 1 4 4 7 2 5 7 E - 0 3 3 1 4 B ( 1 0 , 1 , 9 ) = . 3 2 2 5 0 1 3 6 8 6 4 7 2 8 3 - 0 4 B ( 1 0 , 1 , 1 0 ) = . 1 1 3 5 0 2 7 0 9 1 5 9 1 9 8 - 0 5 B ( 1 0 , 2 , 1 ) = . 1 6 4 6 3 9 0 3 1 0 2 7 7 S E + 0 0 B ( 1 0 , 2 , 2 ) = . 7 5 7 7 4 6 9 0 5 9 7 8 1 7 E + 0 0 B ( 1 0 , 2 , 3 ) = . 6 0 9 5 3 2 9 5 8 9 9 5 9 7 E + 0 0 B ( 1 0 , 2 , 4 ) = . 3 1 6 6 3 7 5 8 7 8 3 7 5 3 E + 0 0 B ( 1 0 , 2 , 5 ) = . 1 1 2 5 6 5 5 6 2 5 5 4 9 9 E + 0 0 B ( 1 0 , 2 , 6 ) = . 3 2 5 9 5 6 6 7 0 2 3 0 0 4 3 - 0 1 B ( 1 0 , 2 , 7 ) = . 5 4 7 9 8 5 5 2 2 6 2 4 9 6 E - 0 2 B ( 1 0 , 2 , 8 ) = . 7 6 0 9 3 9 9 5 8 1 9 1 4 4 8 - 0 3 B ( 1 0 , 2 , 9 ) = . 4 0 1 1 1 8 1 5 4 8 7 5 1 2 8 - 0 4 B ( 1 0 , 2 , 1 0 ) = . 1 3 7 8 0 8 9 4 3 7 4 9 1 8 E - 0 5 B ( 1 0 , 3 , 1 ) = . 7 5 1 5 9 1 8 3 0 7 7 8 5 4 8 - 0 1 B ( 1 0 , 3 , 2 ) = . 4 3 7 6 6 2 0 9 2 1 8 2 3 8 E + 0 0 B ( 1 0 , 3 , 3 ) = . 7 8 6 9 8 2 5 2 8 0 3 3 1 8 8 + 0 0 B ( 1 0 , 3 , 4 ) = . 4 7 9 0 6 0 1 4 3 6 6 7 7 9 E + 0 0 B ( 1 0 , 3 , 5 ) = . 1 6 3 4 3 0 2 6 6 3 8 0 0 9 E + 0 0 B ( 1 0 , 3 , 6 ) = . 4 8 5 0 5 6 6 0 7 1 8 1 0 9 3 - 0 1 B ( 1 0 , 3 , 7 ) = . 8 0 1 1 3 6 2 2 8 2 9 8 9 8 8 - 0 2 B ( 1 0 , 3 , 8 ) = . 1 1 2 7 9 2 8 2 7 0 1 1 0 3 8 - 0 2 B ( 1 0 , 3 , 9 ) = . 5 8 7 8 6 0 2 8 3 6 4 0 5 1 8 - 0 4 B ( 1 0 , 3 , 1 0 ) = . 2 0 3 7 6 8 7 9 3 1 4 5 3 3 E - 0 5 B ( 1 0 , 4 , 1 ) = . 3 8 9 2 6 9 0 9 1 4 3 7 4 1 E - 0 1 B ( 1 0 , 4 , 2 ) = . 2 6 7 9 4 1 6 3 5 1 7 2 2 8 E + 0 0 B ( 1 0 , 4 , 3 ) = . 5 1 1 3 4 1 9 3 1 1 4 5 2 3 E + 0 0 B ( 1 0 , 4 , 4 ) = . 7 6 5 9 7 8 4 3 0 1 7 9 6 9 E + 0 0 B ( 1 0 , 4 , 5 ) = . 3 1 0 9 5 2 1 5 4 0 0 5 9 4 E + 0 0 B ( 1 0 , 4 , 6 ) = . 8 7 7 3 7 2 7 0 7 5 6 8 2 0 E - 0 1 B ( 1 0 , 4 , 7 ) = . 1 4 9 5 1 4 1 6 5 6 7 4 7 8 E - 0 1 B ( 1 0 , 4 , 8 ) = . 2 0 5 7 3 2 2 2 0 7 1 1 7 6 8 - 0 2 B ( 1 0 , 4 , 9 ) = . 1 0 9 1 9 6 0 2 8 4 2 0 4 4 3 - 0 3 B ( 1 0 , 4 , 1 0 ) = . 3 7 3 2 3 7 2 0 9 9 8 0 9 7 8 - 0 5 B ( 1 0 , 5 , 1 ) = . 1 3 4 1 4 1 4 8 0 7 9 5 2 5 3 - 0 1 B ( 1 0 , 5 , 2 ) = . 2 0 7 1 3 4 1 6 7 5 7 3 9 B E + 0 0 B ( 1 0 , 5 , 3 ) = . 2 8 5 5 7 8 4 8 8 1 9 3 3 1 8 + 0 0 B ( 1 0 , 5 , 4 ) = . 6 0 4 1 2 2 0 4 2 8 8 6 0 2 E + 0 0 B ( 1 0 , 5 , 5 ) = . 6 3 0 3 7 9 0 7 4 2 4 8 8 3 E + 0 0 B ( 1 0 , 5 , 6 ) = . 2 1 8 8 4 7 6 1 3 6 3 7 4 l E + 0 0 B ( 1 0 , 5 , 7 ) = . 3 5 2 3 4 2 9 1 2 8 4 5 8 1 3 - 0 1 B ( 1 0 , 5 , 8 ) = . 5 0 2 1 2 2 2 3 5 0 5 2 0 5 8 - 0 2 B ( 1 0 , 5 , 9 ) = . 2 5 9 8 7 7 5 2 0 7 8 8 0 5 8 - 0 3 B ( 1 0 , 5 , 1 0 ) = . 9 0 4 8 7 1 6 7 0 4 1 2 2 9 8 - 0 5 B ( 1 0 , 6 , 1 ) = - . 5 4 3 1 5 2 5 8 0 1 4 9 2 6 3 - 0 1 B ( 1 0 , 6 , 2 ) = . 3 1 2 3 7 9 3 7 6 1 5 3 5 8 E + 0 0 B ( 1 0 , 6 , 3 ) = ’ . 2 0 5 6 6 3 0 6 0 4 8 7 8 4 E - 0 2 B ( 1 0 , 6 , 4 ) = . 5 5 9 7 2 6 9 6 2 1 5 4 4 Z E + 0 0 B ( 1 0 , 6 , 5 ) = . 4 4 2 4 1 7 0 5 4 9 4 1 6 Z E + 0 0 B ( 1 0 , 6 , 6 ) = . 6 0 1 9 3 9 9 6 6 5 9 2 5 3 E + 0 0 B ( 1 0 , 6 , 7 3 - . 1 2 2 6 9 4 6 8 8 8 0 8 3 3 3 + 0 0 6 , 8 I B ( 1 0 , . 1 6 3 0 4 2 0 1 1 0 7 3 8 3 E - 0 1 m m q q q q q q q q I \ q m m m m m m m m m m m m m m m w m m m m o H H W H ‘ H ~ H “ H H “ B ( 1 0 , B ( 1 0 , B ( 1 0 , B ( 1 0 , B ( 1 0 , B ( 1 0 , B ( 1 0 , B ( I o . B ( 1 0 , B ( 1 0 , B ( 1 0 , B ( 1 0 , B ( 1 0 , B ( 1 0 , B ( 1 0 , B ( 1 0 , B ( 1 0 , B ( 1 0 , B ( 1 0 , B ( 1 0 , B ( 1 0 , B ( 1 0 , B ( 1 0 , B ( 1 0 , B ( 1 0 , B ( 1 0 , B ( 1 0 , B ( 1 0 , B ( 1 0 , B ( 1 0 , B ( 1 0 , B ( 1 0 , E ( 1 0 . 1 B ( 1 0 , 1 B ( 1 0 , 1 B ( 1 0 , 1 B ( 1 0 , 1 B ( 1 0 , 1 B ( 1 0 , 1 B ( 1 0 , 1 B ( 1 0 , 1 “ - ‘ ~ “ ~ ‘ ~ ‘ - “ “ - “ - “ . “ - - 0 . 0 . 0 . 0 . 0 . 0 . 0 . 0 . H H H H B ( 1 0 , 1 0 , 1 0 ) = B ( l l , B ( l l , B ( l l , B ( l l , B ( l l , B ( l l , B ( l l , B ( l l , I I 1 ) = 2 ) = 3 ) = 4 ) - 5 ) = 6 ) = 7 ) = 8 ) = 3 1 5 . 8 8 0 3 2 8 0 6 2 5 1 5 4 2 8 - 0 3 . 2 9 7 7 7 7 3 9 4 2 5 3 7 4 8 - 0 4 . 2 4 9 0 7 6 8 8 3 3 4 9 S S E + 0 0 . 7 8 1 1 0 1 6 9 2 7 2 8 4 S E + 0 0 . 6 5 8 6 2 4 9 3 2 1 2 2 0 3 3 + 0 0 . 9 0 1 0 8 8 8 8 7 9 5 9 0 3 8 + 0 0 . 4 5 7 2 6 3 6 7 5 1 4 4 5 3 8 - 0 1 . 6 2 8 2 5 6 1 3 5 2 8 0 1 6 E + 0 0 . 4 6 3 8 1 6 3 9 5 6 6 4 2 6 E + 0 0 . 8 3 4 1 7 2 3 3 7 6 0 4 3 3 8 - 0 1 . 4 1 4 9 2 8 1 9 2 4 5 4 9 1 8 - 0 2 . 1 4 7 3 7 5 9 6 7 3 5 2 5 3 3 - 0 3 . 2 9 9 3 9 3 4 2 6 0 4 2 6 7 E + 0 1 . 8 0 7 5 2 9 7 4 6 3 4 6 3 S E + 0 1 . 9 4 6 9 1 5 9 9 5 4 0 1 3 7 E + 0 1 . 7 5 6 3 6 4 8 5 0 3 8 5 1 9 E + 0 1 . 3 6 5 2 2 1 3 8 0 6 5 4 l l E + 0 1 . 1 8 4 1 7 7 1 5 2 9 7 5 0 1 8 + 0 1 . 9 2 7 6 6 6 7 3 2 5 8 1 5 5 8 - 0 1 . 5 0 5 8 0 4 8 5 7 8 1 6 1 6 E + 0 0 . 3 4 8 9 7 5 6 4 0 9 3 1 1 2 8 - 0 1 . 1 1 2 5 5 1 5 8 8 6 3 2 1 1 8 - 0 2 . 2 8 9 7 8 7 3 9 7 8 7 5 9 B E + 0 2 . 7 6 9 4 9 6 8 4 0 3 3 2 4 B E + 0 2 . 9 1 0 2 3 3 1 9 6 9 2 0 6 9 E + 0 2 . 6 8 8 9 5 3 4 3 8 0 7 3 0 7 E + 0 2 . 3 5 6 1 5 2 4 7 1 2 5 3 1 4 E + 0 2 . 1 3 3 2 6 0 8 2 8 7 7 7 0 6 E + 0 2 . 2 9 0 8 0 9 7 6 7 2 3 5 6 9 E + 0 1 . 9 8 3 7 5 1 8 8 6 2 1 7 8 3 E + 0 0 . 3 5 2 6 1 5 7 5 9 1 3 2 3 6 E + 0 0 . 1 7 8 3 8 0 9 3 0 2 5 4 3 8 8 - 0 1 . 2 2 1 8 7 5 5 3 9 9 0 9 3 2 E + 0 4 . 5 9 1 1 0 2 6 2 3 2 3 7 7 O E + 0 4 . 7 0 5 9 6 2 1 4 6 2 5 0 1 6 E + 0 4 . 5 3 9 5 7 2 5 4 0 1 7 7 2 4 E + 0 4 . 2 8 6 8 4 4 7 3 6 6 8 3 3 l E + 0 4 . 1 0 7 7 8 7 5 8 6 9 5 4 8 9 E + 0 4 . 2 8 0 3 3 9 1 3 0 1 1 8 0 5 3 + 0 3 . 4 8 2 6 9 1 1 6 0 5 1 3 9 9 E + 0 2 . 4 3 1 9 0 4 4 0 9 5 1 3 8 6 E + 0 1 . 5 8 5 0 9 1 9 4 6 2 7 8 2 8 8 + 0 0 . 3 8 2 0 7 3 6 8 9 4 8 2 0 8 3 + 0 0 . 6 8 8 3 1 2 0 9 9 7 7 5 5 4 E + 0 0 . 4 9 1 5 1 8 4 3 4 3 7 3 3 Z E + 0 0 . 2 7 8 5 1 5 4 2 7 8 3 4 6 3 E + 0 0 . 1 1 5 0 2 6 9 2 8 8 9 8 3 O E + 0 0 . 3 4 8 2 8 8 0 5 3 0 2 7 7 9 E - 0 1 . 8 3 5 7 0 8 0 1 9 1 9 5 5 2 E - 0 2 . 1 2 1 8 6 2 4 6 5 9 0 1 5 6 8 ‘ 0 2 H H H N N M N M N N N N M N w w w w w w w w u w u p : a » p u : a p p u b a — p H — I p p m m m m m m m m m m m m m m B ( l l , B ( l l , B ( l l , B ( l l , B ( l l , B ( l l , B ( l l , B ( l l , B ( l l , B ( l l , B ( l l , B ( l l , B ( l l , B ( l l , B ( l l , B ( l l , B ( l l , B ( l l , B ( l l , B ( l l , B ( l l , B ( l l , 1 3 ( 1 1 , B ( l l , B ( l l , B ( l l , B ( l l , B ( l l , B ( l l , B ( l l , 1 3 ( 1 1 , B ( l l , B ( l l , B ( l l , B ( l l , B ( l l , B ( l l , 1 3 ( 1 1 , B ( 1 1 , B ( l l , B ( l l , 1 3 ( 1 1 . B ( l l , 1 3 ( 1 1 , B ( l l , B ( l l , B ( l l , B ( l l , B ( l l , B ( l l , 3 1 6 . 1 4 2 2 7 2 0 0 7 7 2 0 9 7 8 - 0 3 . 6 4 6 9 8 7 8 4 0 0 7 8 5 1 3 - 0 5 . 1 8 4 0 6 4 7 2 9 9 4 2 3 1 E - 0 6 . 1 5 8 9 4 5 5 3 0 8 4 0 2 1 E + 0 0 . 7 0 1 1 4 0 3 3 2 5 5 6 1 4 E + 0 0 . 6 2 1 0 7 5 6 0 4 8 4 6 6 7 E + 0 0 . 3 2 4 2 3 6 3 6 0 1 1 1 3 6 E + 0 0 . 1 4 1 7 4 9 0 7 6 0 2 2 3 8 E + 0 0 . 4 1 0 0 8 1 5 2 5 3 7 5 0 8 E - 0 1 . 1 0 2 2 2 0 5 2 3 3 7 4 2 6 E - 0 1 . 1 4 4 1 7 1 5 1 2 3 2 4 9 6 E - 0 2 . 1 7 3 2 3 6 4 0 4 4 0 8 8 0 3 - 0 3 . 7 6 7 7 7 7 1 2 9 0 8 2 3 9 8 - 0 5 . 2 2 3 0 8 3 4 8 0 3 1 1 7 4 E - 0 6 . 7 8 3 3 7 2 2 3 0 2 1 4 8 8 E - 0 1 . 3 9 4 2 2 7 3 4 0 5 3 7 9 9 E + 0 0 . 7 8 0 7 7 7 1 1 2 0 1 1 0 8 8 + 0 0 . 4 7 2 4 1 3 3 8 2 6 9 7 2 4 E + 0 0 . 1 9 8 7 0 2 8 0 5 4 8 3 8 2 E + 0 0 . 5 8 8 0 4 1 6 7 3 5 7 3 5 4 8 - 0 1 . 1 4 4 2 1 4 8 3 1 8 4 9 2 9 E - 0 1 . 2 0 6 0 2 6 9 7 6 8 1 2 2 3 8 - 0 2 . 2 4 4 9 8 8 2 2 3 0 9 4 8 9 E - 0 3 . 1 0 9 5 4 5 8 8 2 4 6 5 4 2 E - 0 4 . 3 1 6 0 5 2 1 7 2 7 5 3 0 8 8 - 0 6 . 5 0 7 5 1 1 1 3 0 1 4 7 7 5 3 - 0 1 . 2 1 8 4 8 5 6 9 9 5 5 3 9 Z E + 0 0 . 5 3 6 2 3 2 9 9 6 1 5 0 8 0 E + 0 0 . 7 1 1 8 1 4 9 3 8 4 2 9 7 S E + 0 0 . 3 5 3 6 0 8 9 6 4 0 0 0 6 S E + 0 0 . 9 9 9 1 3 2 9 3 8 7 7 7 7 2 E - 0 1 . 2 5 2 1 9 9 8 8 3 1 6 4 1 7 3 - 0 1 . 3 5 2 7 1 0 8 9 2 9 0 0 5 6 8 - 0 2 . 4 2 6 5 3 3 8 0 2 9 1 7 4 0 8 - 0 3 . 1 8 8 0 6 9 1 9 4 0 0 1 6 0 8 - 0 4 . 5 4 8 6 3 2 3 3 7 5 2 9 7 2 8 - 0 6 . 4 3 5 1 0 4 7 6 5 4 4 2 4 7 3 - 0 1 . 1 1 6 0 2 3 7 6 0 0 1 2 1 1 8 + 0 0 . 3 7 7 5 9 8 1 0 2 3 2 1 8 1 8 + 0 0 . 5 0 7 2 2 6 8 5 4 2 7 1 3 S E + 0 0 . 6 6 6 5 5 4 5 2 6 0 8 4 9 4 E + 0 0 . 2 2 6 1 1 4 9 7 7 7 0 7 8 4 E + 0 0 . 5 4 1 8 3 7 6 9 4 3 0 0 1 5 E - 0 1 . 7 8 2 0 4 0 3 1 3 8 9 9 7 5 3 - 0 2 . 9 2 4 4 1 0 9 4 8 9 7 3 7 1 8 - 0 3 . 4 1 4 9 4 3 3 3 5 6 5 9 4 4 E - 0 4 . 1 1 9 4 0 6 6 8 9 7 6 2 4 8 8 - 0 5 . 5 2 2 1 4 2 8 4 8 0 2 0 8 8 8 - 0 1 . 2 0 8 6 7 1 4 3 8 1 7 1 5 1 8 - 0 1 . 3 3 9 4 5 7 0 0 5 0 1 5 6 4 E + 0 0 H P H I — J s — u — a w M H H o m m q m m t h I - J p o m m q m m u p r H I - o n o m x l m m p u m w w o m m u m m n w m w w o m F J H v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v I I I I I I I I I I l l l l l l l l l l u l l l l l l l l l l l l l l l l u l l I I I I I I I I I I I I I I I I I I I I I I l l l l l l l l l l l l l l l l l l u l l l l l l l l l l l l l l l l ~ ‘ ~ “ - “ “ “ ~ “ ‘ ~ ‘ V ‘ ~ “ “ “ ‘ V “ ‘ V V ‘ V V “ “ “ ‘ ~ ‘ ~ “ 3 1 7 B ( l l , 6 , 4 ) = . 2 8 2 0 9 8 7 7 1 2 7 7 4 2 8 + 0 0 B ( l l , 6 , 5 ) = . 5 7 7 7 6 1 0 4 0 7 0 4 6 S E + 0 0 B ( l l , 6 , 6 ) = . 5 4 0 5 3 2 1 8 0 1 1 4 1 3 E + 0 0 B ( l l , 6 , 7 ) = . 1 6 2 2 3 5 1 0 7 2 8 0 2 8 8 + 0 0 B ( 1 1 , 6 , 8 ) = . 2 2 0 0 9 3 3 2 3 4 6 8 6 8 8 - 0 1 B ( l l , 6 , 9 ) = . 2 7 0 3 4 0 7 1 9 6 4 6 6 6 3 - 0 2 B ( 1 l , 6 , 1 0 ) = . 1 1 8 0 5 2 7 3 5 2 5 8 6 3 8 - 0 3 B ( l l , 6 , 1 1 ) = . 3 4 6 6 5 7 9 7 5 7 6 7 2 7 E - 0 5 B ( l l , 7 , 1 ) = . 1 8 4 4 6 5 7 6 0 9 4 4 5 5 8 + 0 0 B ( 1 1 , 7 , 2 ) = - . 3 8 4 5 3 6 1 8 9 5 0 5 9 S E + 0 0 B ( l l , 7 , 3 ) = . 7 4 5 0 4 2 3 4 8 2 9 1 2 0 8 + 0 0 B ( l l , 7 , 4 ) = - . 1 9 8 8 0 7 1 6 7 4 3 6 3 S E + 0 0 B ( l l , 7 , 5 ) = . 6 4 3 2 1 8 5 9 2 8 5 3 8 8 3 + 0 0 B ( l l , 7 , 6 ) = . 3 8 0 1 3 8 3 2 5 3 1 1 S S E + 0 0 B ( 1 1 , 7 , 7 ) = . 5 2 7 4 3 6 1 5 5 8 8 0 4 9 E + 0 0 B ( l l , 7 , 8 ) = . 9 2 0 5 6 6 6 2 7 3 8 6 7 l E - 0 1 B ( l l , 7 , 9 ) = . 1 0 4 9 0 6 0 1 6 4 7 2 6 6 8 - 0 1 B ( l l , 7 , 1 0 ) = . 4 7 9 2 7 7 2 7 7 6 7 2 9 5 8 - 0 3 B ( 1 1 , 7 , l l ) = . 1 3 6 4 6 5 8 7 0 9 3 1 7 1 3 - 0 4 B ( l l , 8 , 1 ) = . 7 1 1 2 7 9 1 4 4 4 1 2 5 5 E + 0 0 B ( l l , 8 , 2 ) = - . 1 8 4 0 7 4 8 6 6 3 4 9 1 7 E + 0 1 B ( l l , 8 , 3 ) = . 2 4 7 0 9 2 9 8 5 1 7 S Z S E + 0 1 B ( l l , 8 , 4 ) = “ . l 6 8 2 3 3 1 8 0 2 8 3 9 6 E + 0 1 B ( l l , 8 , 5 ) = . 1 3 5 7 1 8 9 6 2 5 2 8 6 6 E + 0 1 B ( l l , 8 , 6 ) = - . 9 2 3 1 2 0 3 1 8 0 7 9 6 8 E - 0 1 B ( l l , 8 , 7 ) = . 6 0 0 8 8 3 6 3 5 6 1 6 4 2 E + 0 0 B ( 1 1 , 8 , 8 ) = . 4 0 8 2 2 8 2 9 5 0 9 3 0 7 E + 0 0 B ( l l , 8 , 9 ) = . 6 4 1 4 1 6 1 0 5 2 7 7 7 4 E - 0 1 B ( 1 1 , 8 , 1 0 ) = . 2 6 8 7 3 4 9 0 1 9 1 6 4 5 8 - 0 2 B ( l l , 8 , 1 1 ) = . 8 0 5 6 4 2 8 7 2 1 7 1 2 3 E - 0 4 B ( l l , 9 , 1 ) = . 9 4 8 3 8 1 5 0 3 0 2 0 8 0 8 + 0 1 B ( l l , 9 , 2 ) = - . 2 5 7 9 2 1 1 5 6 7 4 3 0 7 E + 0 2 B ( l l , 9 , 3 ) = . 3 2 3 1 8 8 3 8 5 3 6 9 1 3 E + 0 2 B ( l l , 9 , 4 ) = - . 2 6 1 5 7 3 0 8 6 0 6 5 6 9 E + 0 2 B ( l l , 9 , 5 ) = . 1 5 5 7 7 7 0 7 4 7 0 1 6 O E + 0 2 B ( l l , 9 , 6 ) = “ . 6 2 9 1 7 9 3 5 9 4 7 1 0 4 E + 0 1 B ( 1 1 , 9 , 7 ) = . 2 3 7 5 1 7 6 6 7 6 1 1 3 4 E + 0 1 B ( 1 l , 9 , 8 ) = . 5 4 7 3 2 9 3 0 8 9 5 4 7 8 E - 0 3 B ( l l , 9 , 9 ) = . 4 5 7 4 4 8 3 5 8 7 7 1 3 6 E + 0 0 B ( l l , 9 , 1 0 ) = . 2 6 9 3 4 9 9 6 6 7 8 1 7 1 E - 0 1 B ( l l , 9 , 1 1 ) = . 7 3 0 3 6 9 3 4 6 5 7 9 8 4 3 - 0 3 B ( 1 1 , 1 0 , 1 ) = . 1 0 8 9 6 4 6 7 7 6 6 0 4 9 E + 0 3 B ( 1 1 , 1 0 , 2 ) = - . 2 9 5 7 9 9 0 0 4 5 6 8 8 7 E + 0 3 B ( 1 1 , 1 0 , 3 ) = . 3 6 6 0 1 8 6 4 7 1 7 S O Z E + 0 3 B ( 1 1 , 1 0 , 4 ) = ’ . 2 9 4 8 1 9 1 3 1 6 2 2 3 O E + 0 3 B ( 1 1 , 1 0 , 5 ) = . 1 6 9 0 3 6 9 3 5 9 1 3 6 4 E + 0 3 B ( 1 1 , 1 0 , 6 ) = - . 6 9 9 1 2 6 5 2 3 5 1 6 5 2 E + 0 2 B ( 1 1 , 1 0 , 7 ) = . 2 1 1 4 9 6 2 0 9 0 6 1 1 4 E + 0 2 B ( 1 1 , 1 0 , 8 ) = - . 3 9 8 0 6 0 1 6 4 6 5 3 4 6 E + 0 1 B ( 1 1 , 1 0 , 9 ) = . 1 0 0 6 0 8 3 7 4 1 4 8 9 7 E + 0 1 3 0 2 0 5 0 1 6 0 6 0 1 2 0 1 3 0 3 1 8 B ( 1 1 , 1 0 , 1 0 ) = . 3 1 9 3 7 1 6 5 9 8 7 1 4 0 E + 0 0 B ( 1 1 , 1 0 , 1 1 ) = . 1 3 7 9 6 1 6 3 6 6 7 4 0 7 8 - 0 1 B ( 1 1 , 1 1 , 1 ) = . 1 0 0 5 8 3 3 8 2 3 7 1 4 9 E + 0 5 B ( 1 1 , 1 1 , 2 ) = - . 2 7 3 9 8 8 1 3 6 5 9 5 3 0 8 + 0 5 B ( 1 1 , 1 1 , 3 ) = . 3 4 1 0 4 7 5 9 7 8 2 4 1 7 E + 0 5 B ( 1 1 , 1 1 , 4 ) = - . 2 7 7 6 1 4 9 8 1 5 0 6 2 1 E + 0 5 B ( 1 1 , 1 1 , 5 ) = . 1 6 1 3 5 0 6 1 7 6 6 9 7 7 E + 0 5 B ( 1 1 , 1 l , 6 ) = - . 6 8 5 0 9 4 8 6 4 8 2 4 3 6 E + 0 4 B ( 1 1 , 1 1 , 7 ) = . 2 1 1 1 1 1 3 9 4 0 3 4 5 1 8 + 0 4 B ( 1 1 , 1 l , 8 ) - . 4 5 7 4 8 1 5 8 9 0 0 6 5 9 E + 0 3 B ( 1 1 , 1 1 , 9 ; . 6 5 9 7 4 3 4 9 8 5 2 4 2 1 8 + 0 2 ) B ( l l , l l , l O - . 5 0 6 9 6 2 9 0 7 7 5 2 2 3 E + 0 1 B ( 1 1 , l l , l l . 5 4 4 3 7 7 2 8 1 9 2 1 5 8 E + 0 0 I A = 1 1 I J O B = 2 I Z = 1 1 D O 1 0 I = 8 , 1 1 N = I D O 2 0 J = 1 , N D O 3 0 K = 1 , N I F ( J . E Q . K ) T H E N A ( J , K ) = B ( I , J , K ) - 1 . - W L ( I , K ) E L S E A ( J , K ) = B ( I , J , K ) - W L ( I , K ) E N D I F C O N T I N U E C O N T I N U E C A L L E I G R F ( A , N , I A , I J O B , W , Z , I Z , W K , I E R ) W R I T E ( 1 0 , 5 0 ) I D O 4 0 L = 1 , N F O R M A T ( ' ' , s x , ' E I G E N V A L U E s O F T H E L I N E A R I Z E D - ' , I 2 , ' - P O I N T + C O L L O C A T I O N ' ) W R I T E ( 1 0 , 6 0 ) L , W ( L ) W R I T E ( 2 0 , 1 6 0 ) I , L , R E A L ( W ( L ) ) F O R M A T ( 7 X , ' W ( ' , 1 2 , ' , ' , I 2 , ' ) = ' , E 2 0 . 1 4 ) C O N T I N U E F O R M A T ( 1 0 X , ' W ( ' , I 2 , ' ) = ' , 2 E 2 0 . 1 4 ) D O 1 1 0 M 1 = 1 , N S U M = 0 . 0 D O 1 2 0 M 2 = 1 , N 2 1 ( M 2 , M 1 ) = R E A L ( Z ( M 2 , M 1 ) ) 2 2 ( M 2 , M 1 ) = A I M A G ( Z ( M 2 , M 1 ) ) S U M = S U M + 2 1 ( M 2 , M 1 ) * * 2 + 2 2 ( M 2 , M 1 ) * * 2 C O N T I N U E S U M l = 1 . / ( S U M * * . 5 ) D O 1 3 0 M 2 = 1 , N 2 1 ( M 2 , M 1 ) = 2 1 ( M 2 , M 1 ) * S U M 1 z 2 ( M 2 , M 1 ) = 2 2 ( M 2 , M 1 ) * S U M 1 2 ( M 2 , M 1 ) = C M P L x ( 2 1 ( M 2 , M 1 ) , 2 2 ( M 2 , M 1 ) ) C O N T I N U E 1 1 0 9 0 1 0 0 7 0 1 0 1 5 0 3 1 9 C O N T I N U E D O 8 0 M 1 = 1 , N D O 9 0 M 2 = 1 , N W R I T E ( 1 0 , 1 0 0 ) M 2 , M 1 , Z ( M 2 , M l ) W R I T E ( 2 0 , 1 5 0 ) I , M 2 , M l , Z l ( M 2 , M l ) C O N T I N U E C O N T I N U E F O R M A T ( 1 0 x , ' 2 ( ' , I z , ' , ' , I z , ' ) = ' , 2 E 2 0 . I 4 ) W R I T E ( 1 0 , 7 0 ) W K ( 1 ) F O R M A T ( 5 X , ' P E R F O R M A N C E I N D E x = ' , E 1 0 . 4 ) C O N T I N U E F O R M A T ( 7 X , ' Z ( ' , 1 2 , ' , ' , I 2 , ' , ' , 1 2 , ' ) = ' , E 2 0 . l 4 ) S T O P E N D m m V m V m V m m V m V m V m V H m V m V N W Q m I V V V m V ‘ m V U V ‘ V m V O m V Q V V m V Q m V H V N V m V U V V m V Q m V M m V O V Q V m V Q m V H V V m V m V N w V h V m V l m V m V V V m m q V m V m V m V ‘ m V m V V V - e l V m V fi V m V U m V V V ‘ U m V ‘ V m V O m V m V V V V N D C m V H V m N V V 3 2 0 P R O G R A M L E R R O R ( I N P U T , O U T P U T , T A P E 4 0 ) R E A L 2 ( 8 : 1 1 , 1 1 , I I ) , w ( 8 : 1 1 , 1 1 ) , s ( 1 1 , 1 1 ) , U ( 1 1 , 1 1 ) , A ( 1 1 , 1 1 ) , + A I N V ( 1 1 , 1 1 ) , W K A R E A ( 1 7 0 ) , A l ( 8 : 1 1 , l l , 1 1 ) , A 2 ( 8 : l l , 1 1 , 1 1 ) , + A 3 ( 8 : 1 1 , 1 1 , 1 1 ) , w s ( 1 1 , 1 1 ) I N T E G E R K ( 1 l ) , M ( 1 1 ) C T H I S P R O G R A M U S E S T H E E I G E N S C A L C U L A T E D I N T H E P R E V I O U S C P R O G R A M T O C O N S T R U C T T H E S T A B L E A N D U N S T A E L E M A N I F O L D S , A S C W E L L A S T H E P R O J E C T I O N M A T R I X O P E R A T O R . W ( , 1 ) = . 1 0 0 0 0 0 0 0 0 0 0 2 7 9 E + 0 1 W ( , 2 ) = . 1 7 1 4 9 1 9 7 6 1 7 5 2 8 8 - 0 8 W ( 3 ) = - . 3 3 3 3 3 3 3 3 2 3 8 2 1 3 8 + 0 0 W ( 4 ) = - . 6 6 6 6 6 6 7 2 2 5 3 9 S O E + 0 0 W ( 5 ) = - . 5 9 9 9 9 9 9 4 0 3 2 0 8 7 E + 0 0 W ( 6 ) = - . 7 1 4 2 8 5 6 9 0 0 7 5 2 4 E + 0 0 W ( 7 ) = - . 7 5 0 0 0 0 0 0 5 1 5 7 2 1 8 + 0 0 W ( 8 ) = * . 5 0 0 0 0 0 0 2 5 8 4 0 4 6 E + 0 0 Z ( , 1 ) = - . 3 5 3 5 5 3 4 2 0 1 7 7 1 9 E + 0 0 Z ( , 1 ) = - . 3 5 3 5 5 3 4 2 0 1 5 8 3 5 E + 0 0 Z ( l ) = ‘ . 3 5 3 5 5 3 4 2 0 1 9 6 6 6 E + 0 0 Z ( 1 ) = - . 3 5 3 5 5 3 4 2 0 2 0 9 4 Z E + 0 0 2 ( 1 ) = - . 3 5 3 5 5 3 4 2 0 5 2 7 3 1 E + 0 0 Z ( 1 ) = - . 3 5 3 5 5 3 4 2 2 5 3 0 1 8 E + 0 0 Z ( 1 ) = - . 3 5 3 5 5 3 4 3 2 9 0 7 9 5 E + 0 0 Z ( 1 ) = * . 3 5 3 5 5 3 1 6 8 0 3 9 0 4 E + 0 0 Z ( 2 ) = . 1 1 1 1 6 1 8 9 2 1 3 9 0 3 E + 0 0 Z ( 2 ) = . 8 2 3 5 0 3 5 5 1 4 6 0 9 O E - O l Z ( 2 ) = . 2 9 4 2 0 0 9 0 0 2 3 2 2 1 E - 0 1 Z ( 2 ) = - . 4 9 7 6 0 6 7 1 9 6 0 5 2 5 E - 0 1 Z ( 2 ) = - . 1 5 8 9 3 8 1 4 2 8 4 8 4 4 E + 0 0 Z ( 2 ) = “ . 3 0 4 7 8 3 2 3 3 4 3 7 2 0 8 + 0 0 z ( 2 ) = - . 5 0 0 5 0 1 0 4 1 1 5 1 6 9 E + o o z ( 2 ) = - . 7 8 0 2 9 7 5 9 8 1 9 0 5 7 E + o o z ( 3 ) = . 4 0 6 3 9 2 3 3 3 0 4 5 6 l E - O l z ( 3 ) = . 2 0 6 7 5 0 7 4 2 1 2 3 5 8 E - 0 1 z ( 3 ) = - . 7 4 5 1 5 5 9 3 3 2 9 9 4 6 E - 0 2 z ( 3 ) = - . 2 8 8 5 5 8 9 9 4 6 5 9 6 4 E - 0 1 z ( 3 ) = - . 1 7 7 3 1 0 5 1 8 4 1 0 2 1 E - 0 1 z ( 3 ) = . 7 0 6 2 9 6 8 5 5 2 9 3 7 4 E - 0 1 z ( 3 ) = . 3 2 1 3 0 9 7 8 5 1 5 7 9 5 E + 0 0 z ( 3 ) = . 9 4 2 5 9 7 4 1 3 8 6 3 6 8 E + o o z ( 4 ) = - . 4 0 8 4 8 8 1 4 4 1 8 5 2 4 E - 0 1 z ( 4 ) = . 1 5 8 5 8 1 3 9 9 3 2 5 4 l E - 0 2 z ( 4 ) = . 1 8 3 1 8 6 6 9 2 8 4 3 6 6 E - 0 1 z ( 4 ) = — . 1 3 6 2 9 3 8 5 6 3 2 5 3 5 E - 0 1 z ( 4 ) = - . 2 2 7 5 4 6 5 6 7 3 0 3 7 0 E - 0 1 z ( 4 ) = . 7 4 6 9 5 0 5 0 5 3 4 9 4 8 E - 0 1 z ( 4 ) = - . 2 0 2 2 9 8 8 3 9 1 0 8 4 3 E - 0 1 ' z ( 4 ) = - . 9 9 5 6 4 1 0 7 6 1 8 0 1 3 E + o o z ( 5 ; : . 5 5 0 5 6 6 0 0 0 6 3 1 8 5 8 - 0 1 5 : Z ( . 6 6 2 0 8 9 0 4 7 0 3 9 0 1 E - 0 2 m o o o o m m m o o o c o c m o o o o m o o o o o o o o o o o o m o c n c o o o o o c m a c m m m m m m m w m m m m m m m m m m m m m o m V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V N H m m q m m b w u w m m q a ‘ m w a I — o m q m m b w w q u m m u h w N q u m m m - w w w m q m m p w V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V 3 2 1 - . 2 6 8 0 4 7 1 5 4 9 2 0 5 3 8 - 0 1 . 1 0 7 7 8 1 5 1 5 5 8 7 3 7 E - 0 2 . 5 2 3 6 2 7 6 8 5 2 9 6 5 5 8 - 0 1 . 2 1 6 0 4 6 8 8 6 4 8 7 1 7 8 - 0 1 . 3 1 5 2 3 1 7 9 5 8 9 1 1 7 E + 0 0 . 9 4 5 3 1 7 7 1 0 0 3 2 0 6 E + 0 0 . 6 3 1 3 8 2 0 2 3 1 8 3 5 3 8 - 0 1 . 1 1 1 1 7 8 1 9 3 4 5 3 7 l E - 0 1 . 2 1 3 4 0 6 7 1 7 6 8 5 1 1 8 - 0 1 . 3 3 5 4 1 6 2 7 1 8 1 7 7 4 E - 0 1 . 6 5 5 0 6 2 3 6 2 5 9 5 0 6 8 - 0 2 . 9 4 4 9 2 9 0 8 6 9 6 4 5 0 8 - 0 1 . 3 3 5 9 2 6 1 9 1 5 9 7 1 3 E + 0 0 . 9 3 4 0 7 2 4 1 1 4 3 8 6 O E + 0 0 . 3 7 0 1 4 7 3 5 3 6 5 3 2 2 8 - 0 1 . 1 0 8 3 2 7 3 5 5 9 5 1 2 2 8 - 0 1 . 6 9 0 4 6 4 9 7 4 1 9 0 4 6 8 - 0 2 . 2 0 6 1 2 6 0 4 4 2 5 6 1 4 8 - 0 1 . 2 4 3 7 0 0 2 6 8 0 8 1 8 2 8 - 0 1 . 2 2 3 7 7 5 5 2 0 9 8 5 5 0 8 - 0 2 . l 4 1 5 8 8 1 6 3 7 6 9 5 2 8 + 0 0 . 9 8 8 6 3 2 3 3 4 9 3 6 2 3 E + 0 0 . 2 6 7 0 6 0 0 7 2 2 4 3 8 6 8 - 0 1 . 8 0 7 4 5 4 9 0 5 0 6 2 9 6 3 - 0 2 . 1 1 0 6 7 8 6 7 3 1 5 6 8 6 E - 0 1 . 1 1 6 8 3 5 0 8 9 8 6 2 5 1 E - 0 1 . 1 7 6 3 5 0 0 8 6 4 8 9 6 9 8 - 0 1 . 4 8 9 4 1 1 4 9 2 3 2 4 4 9 E - 0 1 8 ) = - . 7 4 4 8 6 3 8 1 1 5 5 4 2 9 E - 0 1 8 ) = - . 9 9 5 3 4 3 2 2 6 3 1 4 7 9 E + 0 0 . 1 0 0 0 0 0 0 0 0 3 9 2 0 3 3 + 0 1 . 1 6 9 9 4 9 6 7 4 5 6 4 8 7 E - 0 7 - . 3 3 3 3 3 3 4 5 2 6 2 3 1 5 E + 0 0 ' . 4 9 9 9 9 9 7 3 0 6 4 2 2 5 8 + 0 0 - . 6 0 0 0 0 0 5 1 0 4 4 0 4 l E + 0 0 ' . 7 7 7 7 7 7 6 8 4 9 7 1 5 1 E + 0 0 5 5 5 5 5 5 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 8 8 8 8 8 8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) - - - . 7 5 0 0 0 0 0 6 9 7 5 3 6 6 E + 0 0 - . 7 1 4 2 8 6 0 9 9 9 6 0 9 9 E + 0 0 - - . 6 6 6 6 6 5 9 6 6 7 4 2 4 6 8 + 0 0 1 ) = - . 3 3 3 3 3 4 4 5 5 0 1 3 8 0 8 + 0 0 1 ) = - . 3 3 3 3 3 4 4 5 5 3 2 9 4 2 8 + 0 0 1 ) = - . 3 3 3 3 3 4 4 5 5 4 5 9 6 0 E + 0 0 1 ) = - . 3 3 3 3 3 4 4 5 6 2 5 7 2 1 3 + 0 0 1 ) = - . 3 3 3 3 3 4 4 5 6 4 6 4 9 4 E + 0 0 1 ) = - . 3 3 3 3 3 4 4 5 9 0 5 8 6 I E + 0 0 1 ) = - . 3 3 3 3 3 4 5 4 3 1 5 3 1 9 E + 0 0 1 ) = - . 3 3 3 3 3 5 4 0 9 7 2 1 8 0 8 + 0 0 1 ) = - . 3 3 3 3 2 3 3 0 9 3 7 0 6 8 8 + 0 0 2 ) = ' . 9 1 3 3 8 4 8 1 9 9 4 9 9 9 E - 0 1 2 ) = - . 7 0 3 3 2 8 1 5 8 6 3 7 9 4 E - 0 1 o w x V V o o V V x c o V V - n x o V x V w V V o o x V V g o x V m V o V V o x m o V x V - o y V V x v o V V x I V V o w x V V h o x V V m o m V V x V m o q V m V V x m o V I x o \ V V V — s V m a m m V w V V m m m ‘ V V m m V V a m V V q m m V m V o m V m w V m V m V o V w m V o V p V x m V o m V x V o q V x V m V o o V x V x o V x J V V o - V x V t o V x V N o u V V x o V b V x V u V o m x - m V o \ V q V o V m V x m o V x H V V V N o x V V w o x V 9 V o - V V x n o V V w x o V a V \ d V V 3 2 2 2 ) = - . 3 1 9 1 0 0 1 8 1 0 5 1 9 5 8 - 0 1 2 ) = . 2 5 1 2 9 7 0 9 9 6 2 3 3 4 E - 0 1 2 ) = . 1 0 2 7 9 8 1 0 7 5 1 3 9 7 E + 0 0 2 ) = . 2 0 4 4 1 1 7 5 5 6 6 5 5 5 E + 0 0 2 ) = . 3 3 5 7 0 1 7 0 7 6 9 8 1 4 E + 0 0 2 ) = . 5 0 7 8 5 8 6 2 0 5 0 8 4 O E + 0 0 2 ) = . 7 4 9 7 2 8 7 4 6 5 4 9 3 0 E + 0 0 3 ) = . 2 7 7 3 9 8 9 3 2 3 2 9 9 5 3 - 0 1 3 ) = . 1 5 5 7 4 2 3 1 9 1 6 3 2 6 E - 0 1 3 ) = ” . 2 1 1 8 0 7 1 3 2 2 2 8 2 1 3 - 0 2 3 ) = - . 1 7 5 0 7 1 1 4 2 6 0 1 0 3 8 - 0 1 = - . 1 7 5 6 4 6 6 4 9 4 0 2 0 5 E - 0 1 . 1 8 7 4 6 0 6 6 6 8 0 7 8 1 E - 0 1 . 1 2 6 7 3 4 8 6 0 2 1 2 7 S E + 0 0 . 3 7 2 6 7 7 1 8 6 5 4 3 0 6 E + 0 0 . 9 1 8 1 8 6 8 0 7 6 3 4 7 8 E + 0 0 . 1 3 7 6 8 2 0 5 2 2 4 3 3 8 E - 0 1 . 5 1 3 8 6 0 3 4 4 8 4 0 2 6 8 - 0 2 . 4 4 8 7 7 1 6 6 3 3 8 3 7 8 8 - 0 2 . 7 0 4 8 8 6 2 4 8 5 8 2 0 1 3 - 0 2 . 3 5 5 5 6 1 1 6 5 3 2 4 8 9 8 - 0 2 . 2 1 8 9 3 6 1 9 7 0 6 9 0 2 E - 0 1 . 8 8 0 2 6 9 2 9 1 6 2 5 9 2 8 - 0 2 . 1 6 9 8 6 7 1 0 3 7 1 8 1 8 E + 0 0 . 9 8 5 0 3 2 9 4 9 6 6 7 3 O E + 0 0 . 1 4 0 4 6 2 4 9 9 6 6 9 7 7 E - O l . 2 8 7 1 0 9 5 9 0 3 5 3 0 7 E - 0 2 . 6 1 9 1 4 0 6 9 7 1 2 1 7 9 8 - 0 2 . 2 8 7 7 5 9 1 2 8 2 4 5 7 1 8 - 0 2 . 1 0 3 6 8 5 7 5 9 2 3 4 9 8 8 - 0 1 . 7 7 0 0 0 4 7 6 0 7 1 7 8 5 8 - 0 2 . 4 6 1 5 0 2 7 7 0 7 4 4 9 5 E - 0 1 . 6 2 4 1 5 1 3 2 1 7 8 5 6 3 E - 0 1 . 9 9 6 7 7 2 5 6 7 1 9 8 5 3 8 + 0 0 . 1 7 4 8 1 4 9 6 4 2 0 7 8 0 E - 0 1 . 5 1 4 9 3 1 5 2 9 3 0 7 2 7 8 - 0 2 . 2 9 1 2 4 1 2 1 4 8 8 6 8 6 8 - 0 2 6 ) = - . 8 6 3 2 5 9 4 8 9 3 5 5 8 4 E - 0 2 6 ) = . 9 5 0 9 0 7 5 7 5 5 7 0 0 3 8 - 0 2 6 ) = . 1 1 0 6 9 4 8 5 4 8 6 8 6 5 E - 0 2 6 ) = - . 4 1 5 1 5 7 9 5 3 0 1 2 8 6 3 - 0 1 6 ) ‘ . 1 8 1 5 8 7 2 0 2 1 7 9 4 O E + 0 0 6 ) = - . 9 8 2 2 4 0 1 7 2 7 0 9 3 6 E + 0 0 7 ) = - . 8 6 6 4 6 3 9 7 6 4 4 9 3 0 3 - 0 1 7 ) = . 1 6 8 6 3 7 4 7 7 2 5 6 4 5 3 - 0 1 7 ) = . 2 5 7 1 4 3 4 9 4 9 7 9 3 0 3 - 0 1 7 ) = - . 4 2 1 6 1 4 1 4 8 2 1 7 7 B E - 0 1 7 ) = . 1 3 7 4 9 8 5 9 5 7 2 8 1 4 E - 0 1 7 ) = . 8 4 3 5 8 3 6 9 0 8 2 3 0 6 8 - 0 1 7 ) = - . 2 6 6 2 7 6 6 8 6 9 8 4 5 7 E + 0 0 w v V V V V V V V V V V V V V V q v fl v m v m v m v m v m v m v m v m v m v m v m v m v m V m v V m v V m v V m v V D v \ v N A \ O \ O \ D \ O ® \ O \ D \ O \ D \ D \ D \ O \ O \ D \ D \ O \ O O \ D ® V 3 2 3 . 4 1 6 5 8 4 4 5 6 5 4 7 4 8 8 + 0 0 . 8 5 9 0 7 9 6 9 7 4 5 3 6 1 E + 0 0 . 1 5 6 4 8 3 5 4 1 5 8 9 4 8 8 - 0 1 - . 1 2 3 1 1 5 5 2 1 5 9 1 9 0 E - 0 2 - . 6 2 5 4 1 9 6 1 0 2 9 9 0 9 E - 0 2 . 5 6 3 3 5 4 0 8 2 2 0 2 8 4 3 - 0 2 . 5 0 0 5 6 0 5 1 3 3 3 1 2 6 E - 0 2 “ . 2 1 0 9 3 9 4 1 2 1 8 3 3 3 E - 0 1 . 1 6 7 7 3 7 0 8 0 2 7 4 1 8 E - 0 1 . 1 1 3 1 0 2 3 8 5 5 9 5 5 2 8 + 0 0 - . 9 9 3 0 4 5 4 3 9 1 2 6 8 2 8 + 0 0 “ . 7 6 8 9 2 7 0 5 8 5 0 8 6 1 8 - 0 1 - . 4 1 5 7 1 1 6 5 8 1 9 5 5 9 E - 0 2 . 3 5 0 3 8 3 9 4 2 0 4 0 2 3 8 - 0 1 - . 8 9 7 9 8 1 8 9 4 8 0 6 5 4 E - 0 2 - . 5 3 7 3 8 4 3 2 7 0 1 7 2 3 E - 0 1 . 6 0 4 9 4 2 7 5 0 6 9 5 1 0 8 - 0 1 . 1 7 4 6 0 2 0 1 8 2 9 9 4 8 E + 0 0 ’ . 7 6 6 9 6 0 5 6 5 9 4 2 7 2 E + 0 0 = - . 6 0 6 2 1 7 9 0 8 8 2 5 7 3 E + 0 0 . 1 0 0 0 0 0 0 0 3 4 9 6 6 4 E + 0 1 = ' . 1 6 6 0 1 2 3 3 2 4 2 8 2 0 8 - 0 6 = - . 3 3 3 3 3 3 0 8 2 0 2 2 1 9 E + 0 0 = ' . 4 9 9 9 9 9 4 1 7 2 1 8 4 4 E + 0 0 = - . 6 0 0 0 0 2 9 4 7 4 9 6 6 4 E + 0 0 = - . 7 1 4 2 8 2 0 6 0 7 1 7 3 7 E + 0 0 = - . 7 5 0 0 1 0 4 5 2 6 2 4 0 3 E + 0 0 = - . 7 7 7 7 7 0 1 2 5 0 6 0 1 7 B + 0 0 = - . 8 0 0 0 0 1 7 9 4 0 5 5 8 4 E + 0 0 = - . 6 6 6 6 6 3 4 6 4 8 2 7 3 1 8 + 0 0 1 ) = . 3 1 6 2 3 5 4 3 7 3 2 2 5 8 8 + 0 0 1 ) = . 3 1 6 2 3 5 4 3 8 1 7 1 3 5 8 + 0 0 1 ) = . 3 1 6 2 3 5 4 3 9 3 5 3 8 8 8 + 0 0 1 ) = . 3 1 6 2 3 5 4 4 7 0 0 3 5 5 E + 0 0 1 ) = . 3 1 6 2 3 5 4 5 7 3 8 6 0 1 E + 0 0 1 ) = . 3 1 6 2 3 5 5 7 1 6 9 4 1 3 8 + 0 0 1 ) = . 3 1 6 2 3 5 7 9 2 3 2 6 7 9 E + 0 0 1 ) = . 3 1 6 2 3 6 0 3 5 7 1 5 4 S E + 0 0 1 ) = . 3 1 6 2 1 8 6 2 7 6 6 6 4 5 E + 0 0 1 ) = . 3 1 6 1 7 4 4 0 8 1 2 2 1 7 E + 0 0 2 ) = . 7 6 7 7 5 1 2 2 0 0 7 1 3 6 E - 0 1 2 ) = . 6 0 9 0 4 5 4 6 3 8 2 0 6 0 E - 0 1 2 ) = . 3 1 9 6 4 7 0 3 3 4 3 0 5 0 E - 0 1 2 ) = ’ . 1 0 7 6 7 9 7 6 5 6 9 7 B O E - 0 1 2 ) = - . 6 8 4 6 7 5 3 8 1 8 7 3 8 4 E - 0 1 2 ) = - . 1 4 2 9 7 4 6 5 4 1 6 0 4 3 8 + 0 0 2 ) = - . 2 3 7 2 2 3 3 4 8 7 3 1 8 6 E + 0 0 2 ) = - . 3 5 6 1 9 8 6 3 5 0 4 1 4 3 8 + 0 0 2 ) = ‘ . 5 0 9 5 6 3 5 3 5 6 5 7 8 7 E + 0 0 2 ) = - . 7 2 2 0 2 6 0 3 0 0 7 9 7 7 E + 0 0 » p 9 9 - m p p b m m m m m m m m w m m m m m m m m m m m q q q q q q q )q 3 2 4 3 ) = - . 1 9 9 6 7 7 7 5 4 2 5 2 2 6 E - 0 1 3 ) = - . 1 2 0 5 8 1 4 4 0 5 2 6 6 4 E - 0 1 3 ) = - . 2 7 3 2 6 2 1 0 4 6 1 8 3 8 E - 0 3 3 ) = . 1 0 8 9 7 3 8 2 7 3 3 6 9 7 8 - 0 1 3 ) = . 1 4 1 9 1 1 8 7 2 1 6 0 6 6 8 - 0 1 3 ) = - . 1 5 9 5 3 8 0 6 7 0 4 5 9 3 E - 0 2 3 ) = - . 5 3 9 2 2 5 5 1 2 6 6 7 4 7 E - 0 1 3 ) = * . 1 7 1 5 8 9 1 4 0 6 6 7 6 2 E + 0 0 3 ) = - . 4 0 8 2 3 0 7 4 1 0 2 0 9 9 E + 0 0 3 ) = - . 8 9 4 5 0 0 0 3 5 6 6 5 2 5 8 + 0 0 4 ) = . 8 0 0 9 0 2 0 6 3 1 7 8 7 9 8 - 0 2 4 ) “ . 3 4 5 2 1 9 6 0 8 1 2 7 2 9 3 - 0 2 . 1 9 4 8 1 0 8 0 1 8 7 0 3 9 E - 0 2 . 4 2 7 5 4 1 8 1 9 5 6 9 9 9 8 - 0 2 . 1 5 5 2 4 5 9 9 5 0 6 2 0 0 8 - 0 3 . 9 6 4 6 0 1 0 4 4 5 5 4 3 4 8 - 0 2 . 1 2 8 4 1 7 0 9 8 9 2 2 2 9 E - 0 1 . 3 1 1 1 5 1 0 7 9 0 7 1 5 9 E - 0 1 . 2 3 6 6 6 0 0 8 6 3 6 3 4 9 E + 0 0 . 9 7 0 9 1 0 7 7 7 5 9 7 8 7 B + 0 0 . 5 5 9 7 7 8 2 5 3 3 2 6 7 5 3 - 0 2 . 1 5 3 4 0 0 2 1 4 4 6 3 1 0 E - 0 2 . 2 1 5 4 4 1 4 7 4 8 9 3 6 3 8 - 0 2 . 1 7 9 9 9 2 1 2 1 0 4 4 6 6 3 - 0 2 . 2 8 0 8 3 0 1 7 1 5 8 4 4 6 3 - 0 2 . 4 9 2 3 0 8 0 2 5 5 1 9 3 3 8 - 0 2 . 7 8 1 6 9 9 2 4 6 9 9 6 5 5 8 - 0 2 . 3 2 1 5 2 0 3 2 5 7 3 2 0 2 8 - 0 1 . 5 0 9 5 9 7 0 4 9 0 2 0 6 4 8 - 0 1 . 9 9 8 1 1 5 5 0 2 8 7 4 0 7 E + 0 0 . 9 7 3 9 5 6 6 3 2 8 2 8 9 4 E - 0 2 . 4 7 8 0 5 0 4 5 2 3 4 8 8 6 8 - 0 4 . 4 1 1 8 1 7 6 1 8 4 2 2 5 3 E - 0 2 . 1 8 9 2 0 5 4 4 0 9 5 8 7 5 E - 0 2 . 4 9 3 6 7 0 2 7 4 0 2 9 3 7 8 - 0 2 . 8 1 3 1 0 3 4 5 1 5 6 8 1 3 8 - 0 2 . 8 1 8 1 9 3 0 5 2 6 1 5 4 5 8 - 0 2 . 5 6 3 6 8 2 5 1 2 6 4 3 7 6 8 - 0 1 . 5 8 8 2 3 7 1 5 5 2 4 7 1 6 E - 0 1 . 9 9 6 5 3 8 7 9 0 6 7 2 6 6 E + 0 0 . 9 7 8 2 9 5 3 7 1 9 4 1 9 7 8 - 0 2 . 1 0 6 1 9 9 0 8 1 6 3 2 2 1 8 - 0 2 : . 3 5 2 4 2 5 2 1 1 9 5 2 0 6 8 - 0 2 . 3 5 9 3 0 2 6 7 9 0 0 0 0 2 8 - 0 2 . 1 7 2 7 7 7 6 8 2 4 4 4 6 9 3 - 0 2 J 0 1 0 4 5 3 5 8 6 6 4 9 3 8 - 0 1 J 0 7 8 6 5 4 0 8 2 6 3 7 8 8 - 0 1 . 2 8 4 8 7 3 6 7 8 0 4 4 4 7 E - 0 1 7 ) = - . 2 0 4 9 2 3 5 2 9 4 0 2 0 9 E + 0 0 7 ) = . 9 7 8 1 8 7 7 2 0 4 5 5 3 6 E + 0 0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) - ) 3 2 5 z ( 1 o , 1 , 8 ) = - . 9 9 1 1 9 9 1 4 1 1 8 7 2 4 E - 0 2 z ( 1 o , 2 , 8 ) = . 2 0 6 7 5 5 5 1 5 6 1 6 2 6 9 - 0 2 z ( 1 o , 3 , 8 ) = . 2 6 3 1 5 8 3 4 6 0 5 8 9 9 6 - 0 2 z ( 1 o , 4 , 8 ) = - . 4 4 7 4 9 5 5 4 4 6 0 4 7 4 E - 0 2 z ( 1 o , 5 , 8 ) = . 1 8 3 9 5 9 8 8 5 9 6 5 3 6 E - 0 2 z ( 1 o , 6 , 8 ) = . 6 8 2 9 1 9 7 7 2 1 7 9 4 9 E - 0 2 z ( 1 o , 7 , 8 ) = - . 2 0 6 4 2 4 2 3 5 0 0 9 5 5 E - 0 1 z ( 1 o , 8 , 8 ) = . 2 6 2 1 5 7 8 4 4 3 8 7 4 9 E - 0 1 z ( 1 o , 9 , 8 ) = . 6 1 2 6 9 2 7 0 9 6 2 2 1 7 E - 0 1 z ( 1 o , 1 o , 8 ) = - . 9 9 7 4 7 3 4 1 0 4 4 8 9 Z E + 0 0 z ( 1 o , 1 , 9 ) = - . 1 4 7 8 8 4 9 7 0 2 5 2 0 1 E - 0 1 z ( 1 o , 2 , 9 ) = . 4 3 7 6 7 7 1 4 5 2 4 2 6 8 E - 0 2 z ( 1 o , 3 , 9 ) = . 2 2 4 0 9 9 6 4 4 8 4 2 3 9 8 - 0 2 z ( 1 o , 4 , 9 ) = — . 6 6 3 5 9 3 0 7 6 9 8 7 5 9 9 - 0 2 z ( 1 o , 5 , 9 ) = . 6 9 6 2 5 8 2 3 9 4 0 9 1 5 E - 0 2 z ( 1 o , 6 , 9 ) = . 7 5 0 3 9 7 9 1 4 8 6 3 1 3 E - 0 3 z ( 1 o , 7 , 9 ) = - . 2 4 3 7 1 0 4 2 3 2 2 9 1 8 6 - 0 1 z ( 1 o , 8 , 9 ) = . 8 1 3 4 3 9 7 7 1 9 3 6 2 5 6 - 0 1 z ( 1 o , 9 , 9 ) = - . 2 2 5 4 4 3 2 8 3 3 2 3 0 1 s + o o z ( 1 o , 1 o , 9 ) = . 9 7 0 3 7 5 4 8 4 8 5 6 8 1 3 + 0 0 z ( 1 o , 1 , 1 0 ) = - . 1 0 9 5 4 7 0 0 5 7 8 3 9 6 8 - 0 1 z ( 1 o , 2 , 1 0 ) = - . 1 4 4 8 4 3 7 8 7 3 9 8 2 3 8 - 0 2 z ( 1 o , 3 , 1 0 ) = . 4 7 9 0 5 4 7 6 5 1 2 8 4 0 E - 0 2 z ( 1 o , 4 , 1 0 ) = . 5 5 1 7 9 5 5 0 6 6 1 2 6 1 8 - 0 3 z ( 1 o , 5 , 1 0 ) = - . 7 2 4 1 2 8 1 2 8 4 3 4 3 3 8 - 0 2 z ( 1 o , 6 , 1 0 ) = . 7 7 9 9 0 8 4 2 9 3 9 2 3 3 E - 0 3 z ( 1 o , 7 , 1 0 ) = . 2 4 6 0 5 7 8 1 3 2 2 7 0 9 E - O l z ( 1 o , 8 , 1 0 ) = - . 1 7 8 5 9 7 4 3 4 5 1 8 8 2 3 - 0 1 z ( 1 o , 9 , 1 0 ) = - . 2 3 1 6 7 5 2 0 5 9 2 0 2 6 6 + o o z ( 1 o , 1 o , 1 0 ) = . 9 7 2 1 6 8 2 3 2 5 0 6 5 1 E + 0 0 w ( 1 1 , 1 ) = . 9 9 9 9 9 9 9 1 6 8 9 2 6 4 E + 0 0 w ( 1 1 , 2 ) = . 1 6 3 0 9 5 5 4 7 7 3 3 8 6 8 - 0 6 w ( 1 1 , 3 ) = - . 3 3 3 3 2 7 6 8 1 2 3 0 4 G E + 0 0 w ( 1 1 , 4 ) = - . 5 0 0 0 5 2 4 6 5 8 6 6 5 0 E + 0 0 w ( 1 1 , 5 ) = - . 5 9 9 7 9 7 5 3 6 5 8 0 9 9 E + o o w ( 1 1 , 6 ) = - . 6 6 7 1 1 5 5 0 3 9 6 1 8 7 E + 0 0 w ( 1 1 , 7 ) = - . 8 1 8 1 6 9 6 0 1 9 3 1 0 1 E + o o W ( 1 1 , 8 ) = - . 8 0 0 0 9 5 7 7 0 6 0 7 3 4 E + 0 0 W ( 1 1 , 9 ) = - . 7 1 3 6 7 1 0 5 0 5 4 8 7 B E + 0 0 W ( 1 l , 1 0 ) = ‘ . 7 7 7 4 6 4 9 4 9 4 6 1 1 3 E + 0 0 W ( 1 1 , 1 1 ) = - . 7 5 0 5 5 0 9 8 7 5 8 3 4 9 E + 0 0 Z ( 1 1 , 1 , 1 ) = . 3 0 1 9 3 7 0 0 7 7 8 1 5 9 8 + 0 0 2 ( 1 1 , 2 , 1 ) = . 3 0 1 9 3 6 9 9 7 1 0 6 1 7 E + 0 0 2 ( 1 1 , 3 , 1 ) = . 3 0 1 9 3 7 0 0 5 3 3 1 1 2 8 + 0 0 2 ( 1 1 , 4 , 1 ) = . 3 0 1 9 3 6 9 8 6 2 7 2 8 9 8 + 0 0 2 ( 1 1 , 5 , 1 ) = . 3 0 1 9 3 6 9 6 0 5 6 7 9 2 E + 0 0 2 ( 1 1 , 6 , 1 ) = . 3 0 1 9 3 6 8 8 1 7 7 0 3 1 E + 0 0 2 ( 1 1 , 7 , 1 ) = . 3 0 1 9 3 6 5 0 0 1 9 9 l O E + 0 0 2 ( 1 1 , 8 , 1 ) = . 3 0 1 9 4 0 5 1 0 9 0 7 O O E + 0 0 2 ( 1 L 9 , 1 ) = . 3 0 1 9 2 3 0 3 2 6 7 0 7 8 E + 0 0 N J O D I “ ' U ~ ‘ O Q ‘ D G “ D : ‘ ~ “ “ H N N fi I I ’ U ‘ O Q Q O \ H N w fi I U ‘ O Q D C O \ w w b ~ c m ‘ m q - m “ o \ Z ( 1 1 , 1 0 , Z ( 1 1 , 1 1 , z ( 1 1 , z ( 1 1 , z ( 1 1 , z ( 1 1 , z ( 1 L 2 ( 1 1 , z ( 1 1 , z ( 1 1 , 2 ( 1 1 , 1 . ‘ z ( 1 1 , 1 0 , Z ( 1 1 , 1 1 , z ( 1 1 , 2 ( 1 L 2 ( 1 1 , z ( 1 1 , z ( 1 1 , z ( 1 1 , z ( 1 1 , z ( 1 1 , z ( 1 L ‘ V z ( 1 1 , 1 0 , z ( 1 1 , 1 1 , z ( 1 1 , z ( 1 L z ( 1 L z ( 1 1 , z ( 1 1 , z ( 1 1 , z ( 1 1 , z ( 1 1 , z ( 1 1 , I I “ “ ‘ ~ 2 ( 1 L 1 0 , Z ( 1 1 , 1 1 , z ( 1 1 , z ( 1 1 , z ( 1 1 , z ( 1 1 , z ( 1 L z ( 1 1 , z ( 1 L z ( 1 1 , z ( 1 1 , 1 . Q 2 ( 1 1 , 1 0 , Z ( 1 1 , 1 1 , z ( 1 1 , z ( 1 1 , z ( 1 1 , z ( 1 1 , 1 . 2 . 3 . 4 . 1 ) = 1 ) = 2 ) = 2 ) = 2 ) = 2 ) = 2 ) = 2 ) = 3 2 6 . 3 0 1 4 7 9 2 9 5 0 3 0 7 Z E + 0 0 . 2 9 7 6 9 6 7 9 2 4 6 4 7 O E + 0 0 2 ) = - . 2 ) = - . 2 ) = - . 6 5 6 0 4 1 7 5 4 2 0 8 2 2 3 - 0 1 5 3 2 8 7 2 1 8 9 9 2 2 5 5 E - 0 1 3 0 8 7 9 0 2 4 3 4 6 3 1 7 8 - 0 1 . 2 0 8 0 2 2 4 9 9 3 1 6 9 4 E - 0 2 . 4 6 3 1 8 7 4 1 8 3 9 1 8 3 E - 0 1 . 1 0 2 9 3 8 9 3 9 1 4 0 2 9 E + 0 0 . 1 7 3 6 0 7 1 0 3 3 3 8 4 l E + 0 0 . 2 6 0 9 2 9 1 8 7 3 8 6 8 0 3 + 0 0 . 3 6 9 2 8 7 2 9 9 0 5 4 8 8 3 + 0 0 . 5 0 7 2 6 1 9 5 2 3 4 9 9 3 E + 0 0 . 6 9 8 0 2 9 8 0 3 9 7 4 6 8 E + 0 0 . 1 4 9 3 4 5 8 1 9 2 9 5 8 1 E - 0 1 . 9 5 4 0 3 5 7 7 6 6 4 7 3 9 3 - 0 2 . 1 3 4 7 9 1 4 6 5 3 1 3 4 1 8 - 0 2 . 6 8 9 9 8 1 9 0 2 1 7 1 5 3 8 - 0 2 . 1 0 8 5 4 5 2 3 9 1 7 8 4 5 8 - 0 1 . 4 0 1 7 5 4 5 5 9 8 1 7 0 5 E - 0 2 . 2 3 2 5 8 4 4 8 5 9 4 2 6 2 E - 0 1 . 8 5 7 0 8 8 1 7 7 4 8 0 0 3 E - 0 1 . 2 0 7 3 9 5 3 1 2 0 9 6 1 5 E + 0 0 . 4 3 2 9 5 0 6 7 7 7 1 2 6 S E + 0 0 . 8 7 2 4 4 2 8 3 0 4 5 6 8 9 8 + 0 0 . 5 0 6 8 7 7 4 8 5 4 0 6 2 0 8 - 0 2 . 2 4 2 8 0 8 8 4 8 9 1 3 9 7 E - 0 2 . 8 5 0 2 3 1 1 5 8 6 0 6 6 3 E - 0 3 . 2 6 6 5 6 0 4 8 1 3 8 7 6 3 3 - 0 2 . 1 0 5 0 6 2 6 3 7 3 5 3 1 6 3 - 0 2 . 4 2 5 3 5 5 0 0 2 6 4 7 1 7 E - 0 2 . 8 8 3 1 3 9 2 1 6 7 9 2 0 4 8 - 0 2 . 2 3 4 3 3 0 2 4 0 8 9 1 3 3 8 - 0 2 . 6 8 1 8 2 9 1 6 8 5 6 6 4 7 3 - 0 1 . 2 8 7 2 9 6 9 2 8 2 6 6 0 5 8 + 0 0 . 9 5 5 3 3 7 3 5 7 8 8 2 6 1 E + 0 0 . 2 7 0 8 3 3 4 3 1 2 9 3 0 8 8 - 0 2 . 9 0 1 6 8 0 2 8 7 0 4 3 2 0 8 - 0 3 . 8 8 2 2 9 7 1 4 0 9 5 6 1 6 E - 0 3 . 1 0 6 0 8 3 9 6 6 8 9 9 6 7 3 - 0 2 . 7 8 1 2 1 6 6 0 0 6 6 6 1 5 3 - 0 3 . 2 5 1 1 9 8 5 9 0 9 7 4 5 9 8 - 0 2 . 6 5 0 8 1 7 4 6 5 0 7 1 0 8 8 - 0 3 . 1 1 4 1 6 5 3 7 8 5 6 4 3 1 8 - 0 1 . 9 8 6 0 5 4 3 5 8 3 3 3 0 7 3 - 0 2 . 1 2 4 9 0 4 9 0 8 8 0 4 3 6 E + 0 0 . 9 9 2 0 4 5 2 6 1 1 8 1 7 0 E + 0 0 . 2 8 2 0 9 2 8 4 9 4 9 1 5 1 8 - 0 2 . 5 5 7 6 8 4 3 3 7 2 6 4 9 8 3 - 0 3 . 1 1 4 3 7 1 1 9 7 6 7 9 9 9 8 - 0 2 . 4 8 3 9 3 4 7 4 5 8 5 1 1 1 8 - 0 3 3 2 7 z ( 1 L 5 , 6 ) = - . 1 5 5 5 3 2 8 6 2 2 1 2 4 4 E - 0 2 z ( 1 1 , 6 , 6 ) = - . 9 5 7 0 5 7 8 2 6 3 9 2 2 3 E — 0 3 z ( 1 1 , 7 , 6 ) = . 4 4 8 3 6 7 7 4 8 1 9 3 1 5 3 - 0 2 z ( 1 L 8 , 6 ) = . 4 0 3 8 7 9 4 2 5 3 7 0 9 8 E - 0 2 z ( 1 1 , 9 , 6 ) = - . 3 0 5 2 4 6 6 8 1 3 0 0 5 0 8 - 0 1 z ( 1 1 , 1 0 , 6 ) = - . 4 8 5 4 2 0 0 4 5 6 4 1 3 S E - 0 1 z ( 1 L 1 1 , 6 ) = . 9 9 8 3 2 9 7 8 3 8 2 8 7 3 E + 0 0 z ( 1 1 , 1 , 7 ) = - . 2 2 2 7 0 3 4 6 1 9 3 8 4 B E - 0 1 z ( 1 1 , 2 , 7 ) = . 6 6 1 3 2 1 8 6 7 3 7 7 4 6 3 - 0 2 z ( 1 1 , 3 , 7 ) = . 3 1 1 4 9 5 7 0 0 1 9 6 2 2 E - 0 2 z ( 1 L 4 , 7 ) = - . 9 2 4 1 1 2 1 7 9 2 0 2 3 7 E - 0 2 z ( 1 1 , 5 , 7 ) = . 9 3 5 4 1 1 7 5 4 1 3 9 7 2 8 - 0 2 z ( 1 1 , 6 , 7 ) = . 8 5 1 9 7 4 9 6 6 5 2 2 7 3 3 - 0 3 z ( 1 L 7 , 7 ) = - . 2 7 4 9 4 8 3 5 8 0 3 8 8 5 E - 0 1 z ( 1 L 8 , 7 ) = . 7 6 9 0 4 2 6 1 8 5 8 4 4 9 3 - 0 1 z ( 1 1 , 9 , 7 ) = - . 1 4 1 3 8 9 1 3 5 7 7 2 7 4 E + 0 0 z ( 1 1 , 1 0 , 7 ) = . 9 4 3 8 3 3 2 3 5 0 0 2 3 1 E - 0 1 z ( 1 L 1 1 , 7 ) = . 9 8 1 6 8 6 1 2 0 6 0 9 0 1 E + 0 0 z ( 1 1 , 1 , 8 ) = . 3 3 5 8 5 4 4 6 7 6 6 4 5 2 E - 0 2 z ( 1 1 , 2 , 8 ) = - . 7 3 8 6 1 9 3 1 4 4 6 4 3 3 E - 0 3 z ( 1 1 , 3 , 8 ) = - . 8 0 7 6 1 4 1 5 6 6 4 4 6 B E - 0 3 z ( 1 1 , 4 , 8 ) = . 1 4 2 2 0 5 9 7 0 7 0 4 1 7 3 - 0 2 z ( 1 1 , 5 , 8 ) = - . 6 7 3 8 2 6 6 6 1 4 6 5 6 O E - 0 3 z ( 1 1 , 6 , 8 ) = - . 1 7 2 3 5 9 9 6 1 1 2 5 4 3 E - 0 2 z ( 1 1 , 7 , 8 ) = . 5 1 9 1 1 0 9 4 5 1 4 0 1 4 9 - 0 2 z ( 1 1 , 8 , 8 ) = - . 6 0 8 9 3 5 7 7 5 1 4 3 7 1 E - 0 2 z ( 1 1 , 9 , 8 ) = - . 1 0 9 3 5 5 9 7 6 4 1 5 7 7 E - 0 1 z ( 1 1 , 1 0 , 8 ) = . 1 2 1 1 4 4 3 3 2 9 9 5 4 4 E + 0 0 z ( 1 1 , 1 1 , 8 ) = - . 9 9 2 5 3 3 3 8 0 1 3 3 3 2 2 + 0 0 z ( 1 1 , 1 , 9 ) = . 2 1 5 1 2 6 3 8 3 3 2 7 8 1 3 - 0 1 z ( 1 1 , 2 , 9 ) = . 1 6 9 5 1 6 7 7 3 3 1 4 2 5 2 - 0 2 z ( 1 1 , 3 , 9 ) = - . 9 0 8 3 2 0 8 7 4 9 1 2 8 2 E - 0 2 z ( 1 1 , 4 , 9 ) = . 1 0 4 8 9 1 1 9 0 8 6 1 0 2 E - 0 2 z ( 1 1 , 5 , 9 ) = . 1 1 9 3 2 0 7 2 1 9 2 5 4 1 2 — 0 1 z ( 1 1 , 6 , 9 ) = - . 7 3 6 3 2 3 3 4 4 6 9 1 7 B E - 0 2 z ( 1 1 , 7 , 9 ) = - . 2 9 8 9 4 7 1 5 8 5 9 1 9 8 8 - 0 1 z ( 1 L 8 , 9 ) = . 5 3 8 2 7 9 8 4 4 3 2 9 5 7 3 - 0 1 z ( 1 1 , 9 , 9 ) = . 1 4 0 4 6 2 9 3 0 3 3 0 5 1 a + 0 0 z ( 1 1 , 1 0 , 9 ) = - . 9 0 1 1 0 8 3 3 2 6 2 2 8 9 E + 0 0 z ( 1 1 , 1 L 9 ) = - . 4 0 4 6 4 4 1 9 9 8 6 3 8 8 3 + 0 0 z ( 1 1 , 1 , 1 0 ) = . 2 1 4 0 4 3 7 2 4 9 6 8 8 4 8 - 0 1 z ( 1 1 , 2 , 1 0 ) = - . 2 7 9 2 1 7 6 6 2 1 3 7 9 2 8 - 0 2 z ( 1 1 , 3 , 1 0 ) - - . 7 0 4 4 1 3 5 2 0 8 8 7 7 6 3 - 0 2 z ( 1 1 , 4 , 1 0 ) = . 7 8 0 5 1 0 3 5 1 7 4 7 6 7 8 - 0 2 z ( 1 1 , 5 , 1 0 ) = . 1 8 9 7 3 7 4 3 9 1 0 5 9 4 3 - 0 2 z ( 1 1 , 6 , 1 0 ) = - . 1 7 5 3 2 9 9 7 6 0 1 7 9 1 E - 0 1 z ( 1 1 , 7 , 1 0 ) = . 2 1 5 2 4 1 8 1 8 8 7 9 6 6 8 - 0 1 z ( 1 1 , 8 , 1 0 ) = . 2 8 7 1 9 9 2 0 1 3 9 2 7 8 E - 0 1 z ( 1 1 , 9 , 1 0 ) = - . 2 1 7 9 1 5 6 9 5 4 4 4 1 2 3 + 0 0 z ( 1 1 , 1 o , 1 0 ) = . 6 5 0 4 1 6 7 8 2 6 7 2 2 3 E + 0 0 3 2 8 z ( 1 1 , 1 1 , 1 0 ) = - . 7 2 6 1 5 0 9 1 0 8 6 5 0 4 E + 0 0 z ( 1 1 , 1 , 1 1 ) = - . 3 1 8 9 6 6 7 4 9 2 4 1 3 6 E - 0 2 z ( 1 1 , 2 , 1 1 ) = . 1 1 0 8 4 4 5 6 4 4 7 6 8 1 E - 0 3 z ( 1 1 , 3 , 1 1 ) = . 1 2 4 8 0 8 6 9 3 8 5 3 5 2 E - 0 2 z ( 1 1 , 4 , 1 1 ) = - . 7 7 2 8 1 1 4 1 2 9 6 1 7 2 E - 0 3 z ( 1 1 , 5 , 1 1 ) = - . 1 1 5 2 4 2 5 0 7 8 4 1 9 6 E - 0 2 z ( 1 1 , 6 , 1 1 ) = . 2 5 0 9 9 3 6 1 9 2 5 7 2 3 E - 0 2 z ( 1 1 , 7 , 1 1 ) = . 5 1 1 7 1 3 2 9 1 2 9 3 9 9 E - 0 3 z ( 1 1 , 8 , 1 1 ) = - . 1 1 2 0 4 8 9 7 7 2 1 7 0 3 E - 0 1 z ( 1 1 , 9 , 1 1 ) = . 1 9 7 2 1 0 6 9 5 5 9 3 3 3 E - 0 1 z ( 1 1 , 1 0 , 1 1 ) = . 6 3 8 3 2 3 6 5 8 0 4 6 6 2 E - 0 1 z ( 1 1 , 1 1 , 1 1 ) = - . 9 9 7 6 9 2 7 0 2 0 9 8 6 0 E + o o D O 1 0 I = 8 , 1 1 K ( I ) = 0 M ( I ) = 0 D O 2 0 J = 1 , I I F ( W ( I , J ) . L T . 0 . ) T H E N K ( I ) = K ( I ) + l w s ( I , K ( I ) ) = w ( I , J ) D O 3 0 L 1 = 1 , I S ( L 1 , K ( I ) ) = Z ( I , L 1 , J ) 3 0 C O N T I N U E - E L $ E M ( I ) = M ( I ) + l D O 4 0 M 1 = 1 , I U ( M 1 , M ( I ) ) = z ( I , M 1 , J ) 4 0 C O N T I N U E E N D I F 2 0 C O N T I N U E I F ( K ( I ) . L T . 2 ) G O T O 1 0 D O 5 0 J 1 = 1 , K ( I ) D O 6 0 J 2 = 1 , K ( I ) S U M = 0 . D O 7 0 J = 1 , I S U M = S U M + S ( J , J 1 ) * S ( J , J 2 ) 7 o C O N T I N U E A ( J 1 , J 2 ) = S U M 6 o C O N T I N U E 5 0 C O N T I N U E I D G T = 1 0 N = K ( I ) I A = 1 1 C A L L L I N V 2 F ( A , N , I A , A I N V , I D G T , W K A R E A , I E R ) D O 8 0 J 1 = 1 , K ( I ) D O 9 0 J 2 = 1 , I S U M = 0 . D O 1 0 0 J = 1 , K ( I ) S U M = S U M + A I N V ( J 1 , J ) * S ( J 2 , J ) 1 0 0 C O N T I N U E A 1 ( I , J 1 , J 2 ) = S U M 9 0 1 1 0 1 4 0 1 3 0 1 2 0 1 7 0 1 6 0 1 5 0 2 0 0 1 9 0 1 8 0 1 1 2 3 0 2 2 0 2 4 0 2 5 0 2 8 0 2 6 0 3 2 9 W R I T E ( 4 0 , 1 1 0 ) I , J 1 , J 2 , A 1 ( I , J 1 , J 2 ) C O N T I N U E C O N T I N U E F O R M A T ( 7 X , ' A 1 ( ' , I Z , ‘ , ' , 1 2 , ' , ' , I 2 , ' ) = ' , E Z O . 1 4 ) I F ( M ( I ) . L T . 2 ) G O T O 1 1 D O 1 2 0 J 1 = 1 , M ( I ) D O 1 3 0 J 2 = 1 , M ( I ) S U M = O . D O 1 4 0 J = 1 , I S U M = S U M + U ( J , J 1 ) * U ( J , J 2 ) C O N T I N U E A ( J 1 , J 2 ) = S U M C O N T I N U E C O N T I N U E I D G T = 1 0 N = M ( I ) I A = 1 1 C A L L L I N V 2 F ( A , N , I A , A I N V , I D G T , W K A R E A , I E R ) D O 1 5 0 J 1 = 1 , M ( I ) D O 1 6 0 J 2 = 1 , I S U M = 0 . D O 1 7 0 J = 1 , M ( I ) S U M = S U M + A I N V ( J 1 , J ) * U ( J 2 , J ) C O N T I N U E A 2 ( I , J 1 , J 2 ) = S U M C O N T I N U E C O N T I N U E D O 1 8 0 J 1 = 1 , I D O 1 9 0 J 2 = 1 , I S U M = O . D O 2 0 0 J = 1 , M ( I ) S U M = S U M + U ( J 1 , J ) * A 2 ( I , J , J 2 ) C O N T I N U E A 3 ( I , J 1 , J 2 ) = S U M W R I T E ( 4 0 , 2 1 0 ) I , J 1 , J 2 , A 3 ( I , J 1 , J 2 ) C O N T I N U E C O N T I N U E D O 2 2 0 J 1 = 1 , K ( I ) D O 2 3 0 J 2 = 1 , I W R I T E ( 4 0 , 2 4 0 ) I , J 2 , J 1 , S ( J 2 , J 1 ) C O N T I N U E C O N T I N U E F O R M A T ( 7 X , ' s ( ' , 1 2 , ' , , I 2 , ' , ' , 1 2 , ' ) = ' , E 2 0 . 1 4 ) W R I T E ( 4 0 , 2 5 0 ) I , K ( I ) F O R M A T ( 7 X , ' x ( ' , 1 2 , ' ) = ' , 1 2 ) W R I T E ( 4 0 , 2 8 0 ) I , M ( I ) F O R M A T ( 7 X , ' M ( ' , 1 2 , ' D O 2 6 0 J = L K ( I ) W R I T E ( 4 0 , 2 7 0 ) I , J , W S ( I , J ) C O N T I N U E ) = ' , I Z ) 3 3 0 2 7 0 F O R M A T ( 7 X , ' W S ( ' , I Z , ' , ' , I Z , ' ) = ' , E Z O . 1 4 ) 1 0 C O N T I N U E 2 1 0 F O R M A T ( 7 X , ' A 3 ( ' , 1 2 , ' , ' , 1 2 , ' , ' , I 2 , ' ) = ' , E 2 0 . 1 4 ) S T O P E N D 3 3 1 P R O G R A M L E R R 1 ( I N R U T , O U T R U T , T A R E 5 0 ) R E A L A 1 ( 8 : 1 1 , 1 1 , 1 1 ) , A 3 ( 8 : 1 1 , 1 1 , 1 1 ) , L ( 1 5 , 1 5 ) , E ( 1 5 , 1 5 ) , + C ( 1 5 , 1 5 , 6 ) , E R R ( 8 : 1 1 , 6 ) , S ( 8 : 1 1 , 1 l , 1 1 ) , W S ( 8 : 1 1 , 1 1 ) , E N O R M ( 8 : 1 1 , 1 1 ) R E A L Y N O R M ( 1 1 , 1 1 ) I N T E G E R K ( 1 1 ) , M ( 1 1 ) C T H I S P R O G R A M C A L C U L A T E S T H E E I G E N V E C T O R C O E F F I C I E N T S F O R T H E C L E A S T E R R O R S O L U T I O N T O T H E L I N E A R I z E D B O L T Z M A N N E Q U A T I O N . L ( 1 , 1 = 1 . L ( 2 , 1 ) = . 5 8 5 7 8 6 4 3 7 6 2 7 L ( 2 , 2 ) = 3 . 4 1 4 2 1 3 5 6 2 3 7 3 L ( 3 , 1 ) = . 4 1 5 7 7 4 5 5 6 7 8 3 L ( 3 , 2 ) = 2 . 2 9 4 2 8 0 3 6 0 2 7 9 L ( 3 , 3 ) = 6 . 2 8 9 9 4 5 0 8 2 9 3 7 L ( 4 , l ) = . 3 2 2 5 4 7 6 8 9 6 1 9 L ( 4 , 2 ) = 1 . 7 4 5 7 6 1 1 0 1 1 5 8 L ( 4 , 3 ) = 4 . 5 3 6 6 2 0 2 9 6 9 2 1 L ( 4 , 4 ) = 9 . 3 9 5 0 7 0 9 1 2 3 0 1 L ( 5 , l ) = . 2 6 3 5 6 0 3 1 9 7 1 8 L ( 5 , 2 ) = 1 . 4 1 3 4 0 3 0 5 9 1 0 7 L ( 5 , 3 ) = 3 . 5 9 6 4 2 5 7 7 1 0 4 1 L ( 5 , 4 ) = 7 . 0 8 5 8 1 0 0 0 5 8 5 9 L ( 5 , 5 ) = 1 2 . 6 4 0 8 0 0 8 4 4 2 7 6 L ( 6 , 1 ) = . 2 2 2 8 4 6 6 0 4 1 7 9 L ( 6 , 2 ) = 1 . 1 8 8 9 3 2 1 0 1 6 7 3 L ( 6 , 3 ) = 2 . 9 9 2 7 3 6 3 2 6 0 5 9 L ( 6 , 4 ) = 5 . 7 7 5 1 4 3 5 6 9 1 0 5 L ( 6 , 5 ) = 9 . 8 3 7 4 6 7 4 1 8 3 8 3 L ( 6 , 6 ) = 1 5 . 9 8 2 8 7 3 9 8 0 6 0 2 L ( 7 , l ) = . 1 9 3 0 4 3 6 7 6 5 6 0 L ( 7 , 2 ) = 1 . 0 2 6 6 6 4 8 9 5 3 3 9 L ( 7 , 3 ) = 2 . 5 6 7 8 7 6 7 4 4 9 5 1 L ( 7 , 4 ) = 4 . 9 0 0 3 5 3 0 8 4 5 2 6 L ( 7 , 5 ) = 8 . 1 8 2 1 5 3 4 4 4 5 6 3 L ( 7 , 6 ) = 1 2 . 7 3 4 1 8 0 2 9 1 7 9 8 L ( 7 , 7 ) = 1 9 . 3 9 5 7 2 7 8 6 2 2 6 3 L ( 8 , 1 ) = . 1 7 0 2 7 9 6 3 2 3 0 5 L ( 8 , 2 ) = . 9 0 3 7 0 1 7 7 6 7 9 9 L ( 8 , 3 ) = 2 . 2 5 1 0 8 6 6 2 9 8 6 6 L ( 8 , 4 ) = 4 . 2 6 6 7 0 0 1 7 0 2 8 8 L ( 8 , 5 ) = 7 . 0 4 5 9 0 5 4 0 2 3 9 3 L ( 8 , 6 ) = 1 0 . 7 5 8 5 1 6 0 1 0 1 8 1 L ( 8 , 7 ) = 1 5 . 7 4 0 6 7 8 6 4 1 2 7 8 L ( 8 , 8 ) = 2 2 . 8 6 3 1 3 1 7 3 6 8 8 9 L ( 9 , 1 ) = . 1 5 2 3 2 2 2 2 7 7 3 2 L ( 9 , 2 ) = . 8 0 7 2 2 0 0 2 2 7 4 2 L ( 9 , 3 ) = 2 . 0 0 5 1 3 5 1 5 5 6 1 9 L ( 9 , 4 ) = 3 . 7 8 3 4 7 3 9 7 3 3 3 1 L ( 9 , 5 ) = 6 . 2 0 4 9 5 6 7 7 7 8 7 7 L ( 9 , 6 ) = 9 . 3 7 2 9 8 5 2 5 1 6 8 8 L ( 9 , 7 ) = 1 3 . 4 6 6 2 3 6 9 1 1 0 9 2 L ( 9 , 8 ) = 1 8 . 8 3 3 5 9 7 7 8 8 9 9 2 L ( 9 , 9 ) = 2 6 . 3 7 4 0 7 1 8 9 0 9 2 7 L ( 1 0 , 1 ) = . 1 3 7 7 9 3 4 7 0 5 4 0 L ( 1 0 , 2 ) = . 7 2 9 4 5 4 5 4 9 5 0 3 L ( 1 0 , 3 ) = 1 . 8 0 8 3 4 2 9 0 1 7 4 0 L ( 1 0 , 4 ) = 3 . 4 0 1 4 3 3 6 9 7 8 5 5 L ( 1 0 , 5 ) = 5 . 5 5 2 4 9 6 1 4 0 0 6 4 L ( 1 0 , 6 ) = 8 . 3 3 0 1 5 2 7 4 6 7 6 4 L ( 1 0 , 7 ) = 1 1 . 8 4 3 7 8 5 8 3 7 9 0 0 L ( 1 0 , 8 ) = 1 6 . 2 7 9 2 5 7 8 3 1 3 7 8 L ( 1 0 , 9 ) = 2 1 . 9 9 6 5 8 5 8 1 1 9 8 1 L ( 1 0 , 1 0 ) = 2 9 . 9 2 0 6 9 7 0 1 2 2 7 4 L ( 1 1 , 1 ) = . 1 2 5 7 9 6 4 4 2 1 8 8 L ( 1 1 , 2 ) = . 6 6 5 4 1 8 2 5 5 8 3 9 L ( l l , 3 ) = 1 . 6 4 7 1 5 0 5 4 5 8 7 2 L ( 1 1 , 4 ) = 3 . 0 9 1 1 3 8 1 4 3 0 3 5 L ( 1 1 , 5 ) = 5 . 0 2 9 2 8 4 4 0 1 5 8 0 L ( 1 1 , 6 ) = 7 . 5 0 9 8 8 7 8 6 3 8 0 7 L ( 1 1 , 7 ) = 1 0 . 6 0 5 9 5 0 9 9 9 5 4 7 L ( l l , 8 ) = 1 4 . 4 3 1 6 1 3 7 5 8 0 6 4 L ( 1 1 , 9 ) = 1 9 . 1 7 8 8 5 7 4 0 3 2 1 5 L ( 1 1 , 1 0 ) = 2 5 . 2 1 7 7 0 9 3 3 9 6 7 8 L ( 1 1 , 1 1 ) = 3 3 . 4 9 7 1 9 2 8 4 7 1 7 6 L ( 1 2 , 1 ) = . 1 1 5 7 2 2 1 1 7 3 5 8 L ( 1 2 , 2 ) = . 6 1 1 7 5 7 4 8 4 5 1 5 L ( 1 2 , 3 ) = 1 . 5 1 2 6 1 0 2 6 9 7 7 6 L ( 1 2 , 4 ) = 2 . 8 3 3 7 5 1 3 3 7 7 4 4 L ( 1 2 , 5 ) = 4 . 5 9 9 2 2 7 6 3 9 4 1 8 L ( 1 2 , 6 ) = 6 . 8 4 4 5 2 5 4 5 3 1 1 5 L ( 1 2 , 7 ) = 9 . 6 2 1 3 1 6 8 4 2 4 5 7 L ( 1 2 , 8 ) = 1 3 . 0 0 6 0 5 4 9 9 3 3 0 6 L ( 1 2 , 9 ) = 1 7 . 1 1 6 8 5 5 1 8 7 4 6 2 L ( 1 2 , 1 0 ) = 2 2 . 1 5 1 0 9 0 3 7 9 3 9 7 L ( 1 2 , 1 1 ) = 2 8 . 4 8 7 9 6 7 2 5 0 9 8 4 L ( 1 2 , 1 2 ) = 3 7 . 0 9 9 1 2 1 0 4 4 4 6 7 L ( 1 3 , 1 ) = . 1 0 7 1 4 2 3 8 8 4 7 2 L ( 1 3 , 2 ) = . 5 6 6 1 3 1 8 9 9 0 4 0 L ( 1 3 , 3 ) = 1 . 3 9 8 5 6 4 3 3 6 4 5 1 L ( 1 3 , 4 ) = 2 . 6 1 6 5 9 7 1 0 8 4 0 6 L ( 1 3 , 5 ) = 4 . 2 3 8 8 4 5 9 2 9 0 1 7 L ( 1 3 , 6 ) = 6 . 2 9 2 2 5 6 2 7 1 1 4 0 L ( 1 3 , 7 ) = 8 . 8 1 5 0 0 1 9 4 1 1 8 7 L ( 1 3 , 8 ) = 1 1 . 8 6 1 4 0 3 5 8 8 8 1 1 L ( 1 3 , 9 ) = 1 5 . 5 1 0 7 6 2 0 3 7 7 0 4 L ( l 3 , 1 0 ) = 1 9 . 8 8 4 6 3 5 6 6 3 8 8 0 L ( 1 3 , 1 1 ) = 2 5 . 1 8 5 2 6 3 8 6 4 6 7 8 L ( 1 3 , 1 2 ) = 3 1 . 8 0 0 3 8 6 3 0 1 9 4 7 L ( 1 3 , 1 3 ) = 4 0 . 7 2 3 0 0 8 6 6 9 2 6 6 L ( 1 4 , 1 ) = . 0 9 9 7 4 7 5 0 7 0 3 3 L ( 1 4 , 2 ) = . 5 2 6 8 5 7 6 4 8 8 5 2 3 3 2 L ( 1 4 , 3 ) = 1 . 3 0 0 6 2 9 1 2 1 2 5 1 L ( 1 4 , 4 ) = 2 . 4 3 0 8 0 1 0 7 8 7 3 1 L ( 1 4 , 5 ) = 3 . 9 3 2 1 0 2 8 2 2 2 9 3 L ( 1 4 , 6 ) = 5 . 8 2 5 5 3 6 2 1 8 3 0 2 L ( 1 4 , 7 ) = 8 . 1 4 0 2 4 0 1 4 1 5 6 5 L ( l 4 , 8 ) = 1 0 . 9 1 6 4 9 9 5 0 7 3 6 6 L ( 1 4 , 9 ) = 1 4 . 2 1 0 8 0 5 0 1 1 1 6 1 L ( 1 4 , 1 0 ) = 1 8 . 1 0 4 8 9 2 2 2 0 2 1 8 L ( 1 4 , 1 1 ) = 2 2 . 7 2 3 3 8 1 6 2 8 2 6 9 L ( 1 4 , 1 2 ) = 2 8 . 2 7 2 9 8 1 7 2 3 2 4 8 L ( 1 4 , 1 3 ) = 3 5 . 1 4 9 4 4 3 6 6 0 5 9 2 L ( 1 4 , 1 4 ) = 4 4 . 3 6 6 0 8 1 7 1 1 1 1 7 L ( 1 5 , l ) = . 0 9 3 3 0 7 8 1 2 0 1 7 L ( 1 5 , 2 ) = . 4 9 2 6 9 1 7 4 0 3 0 2 L ( 1 5 , 3 ) = 1 . 2 1 5 5 9 5 4 1 2 0 7 1 L ( 1 5 , 4 ) = 2 . 2 6 9 9 4 9 5 2 6 2 0 4 L ( 1 5 , 5 ) = 3 . 6 6 7 6 2 2 7 2 1 7 5 1 L ( 1 5 , 6 ) = 5 . 4 2 5 3 3 6 6 2 7 4 1 4 L ( 1 5 , 7 ) = 7 . 5 6 5 9 1 6 2 2 6 6 1 3 L ( 1 5 , 8 ) = 1 0 . 1 2 0 2 2 8 5 6 8 0 1 9 L ( 1 5 , 9 ) = 1 3 . 1 3 0 2 8 2 4 8 2 1 7 6 L ( 1 5 , 1 0 ) = 1 6 . 6 5 4 4 0 7 7 0 8 3 3 0 L ( 1 5 , 1 1 ) = 2 0 . 7 7 6 4 7 8 8 9 9 4 4 9 L ( 1 5 , 1 2 ) = 2 5 . 6 2 3 8 9 4 2 2 6 7 2 9 L ( 1 5 , 1 3 ) = 3 1 . 4 0 7 5 1 9 1 6 9 7 5 4 L ( 1 5 , 1 4 ) = 3 8 . 5 3 0 6 8 3 3 0 6 4 8 6 L ( 1 5 , 1 5 ) = 4 8 . 0 2 6 0 8 5 5 7 2 6 8 6 A 1 ( 8 , 1 , 1 ) = . 1 1 4 6 1 0 7 1 5 7 4 2 8 2 E + 0 2 A 1 ( 8 , 1 , 2 ) = . 3 6 4 2 5 8 4 6 4 7 0 9 3 3 8 + 0 2 A 1 ( 8 , 1 , 3 ) = . 2 3 5 3 0 3 5 0 7 8 6 5 8 6 8 + 0 0 A 1 ( 8 , 1 , 4 ) = - . 3 3 0 2 6 1 9 3 9 6 4 6 0 1 E + 0 2 A 1 ( 8 , 1 , 5 ) = : . 3 4 8 5 3 8 6 9 0 2 6 3 6 3 E + 0 2 A l ( 8 , 1 , 6 ) = . 1 3 2 5 6 0 3 3 2 9 7 8 7 6 8 + 0 2 A 1 ( 8 , 1 , 7 ) = - . 2 3 3 9 7 1 0 5 4 7 3 1 2 3 E + 0 1 A l ( 8 , 1 , 8 ) = . 1 0 6 1 7 2 3 6 2 5 7 5 3 1 E + 0 0 A 1 ( 8 , 2 , 1 ) = . 7 6 9 4 6 9 3 4 8 4 2 8 2 5 E + 0 2 A 1 ( 8 , 2 , 2 ) = . 3 1 9 0 0 8 2 9 0 6 3 8 1 3 E + 0 3 A 1 ( 8 , 2 , 3 ) = . 1 1 1 2 9 9 6 8 2 2 2 2 2 3 3 + 0 2 A 1 ( 8 , 2 , 4 ) = - . 2 8 5 8 0 6 4 8 7 2 4 4 2 6 E + 0 3 A 1 ( 8 , 2 , 5 ) = . 3 2 1 8 8 7 2 6 4 1 6 9 5 8 E + 0 3 A 1 ( 8 , 2 , 6 ) = - . 1 5 1 4 8 7 6 9 8 4 7 7 9 B E + 0 3 A 1 ( 8 , 2 , 7 ) = - . 3 1 6 1 8 3 8 2 1 8 3 5 4 4 E + 0 2 A 1 ( 8 , 2 , 8 ) = “ . 2 9 0 2 0 1 0 7 4 6 3 0 0 2 8 + 0 1 A 1 ( 8 , 3 , 1 ) = . 5 0 7 5 1 7 9 4 1 2 5 0 4 1 E + 0 2 A 1 ( 8 , 3 , 2 ) = . 1 7 7 5 6 2 3 0 2 5 5 4 1 8 8 + 0 3 A 1 ( 8 , 3 , 3 ) = . 4 4 1 1 2 9 1 7 4 8 5 2 5 4 E + 0 1 A 1 ( 8 , 3 , 4 ) = - . 1 5 7 4 0 9 8 8 5 2 2 7 5 3 3 + 0 3 A 1 ( 8 , 3 , 5 ) = - . 1 8 2 6 5 6 6 5 0 8 1 2 2 9 8 + 0 3 A 1 ( 8 , 3 , 6 ) = “ . 8 5 2 8 5 3 7 6 8 4 7 1 9 8 E + 0 2 A 1 ( 8 , 3 , 7 ) = ‘ . 1 9 1 0 6 9 5 0 3 2 0 8 5 6 8 + 0 2 3 3 3 A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( h w w w w w w w w w w m w w w N N H H H H H H H H m m m m m m m m m m m m m m m m b p o p p b p p w “ “ ‘ ~ ‘ - ‘ - V ‘ ~ ‘ ~ § ‘ ~ ‘ ~ ‘ “ ~ “ - ‘ ‘ V - V ~ § ~ ‘ ~ ‘ “ V “ ‘ Q ~ V “ “ “ “ - “ - ~ ‘ - - ~ V ‘ . ‘ ~ fi “ “ - “ “ ~ “ ‘ ~ V “ ‘ ‘ V “ m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m o o o o c n m o o o o o o o o 3 3 4 - . 1 3 9 9 0 3 3 8 5 1 4 5 5 9 E + 0 1 - . 3 5 9 7 l 7 8 5 0 1 2 0 0 7 E + 0 2 - . 1 5 7 2 4 7 9 6 1 7 1 9 1 4 E + 0 3 . 3 2 7 9 7 9 5 1 8 9 1 7 7 l E + 0 1 . 1 4 2 2 0 6 7 6 9 9 5 1 5 3 8 + 0 3 . 1 4 4 5 0 0 3 6 4 6 3 1 6 6 8 + 0 3 . 7 8 7 7 8 0 3 6 6 0 5 1 3 O E + 0 2 . 1 3 4 6 6 2 7 1 8 8 9 0 7 G E + 0 2 . 1 5 5 2 3 8 5 2 0 4 4 7 1 6 8 + 0 1 . 9 5 5 4 6 8 6 2 7 4 0 2 3 O E + 0 1 . 1 0 0 8 2 4 6 2 4 0 1 9 5 7 E + 0 3 . 1 3 5 4 2 3 2 4 3 7 2 3 2 0 3 + 0 1 . 9 6 2 4 0 4 0 7 1 1 4 8 2 3 E + 0 2 . 6 6 5 8 0 3 3 6 5 9 2 0 8 7 E + 0 2 . 4 9 1 6 4 9 7 8 5 1 6 8 7 O E + 0 2 . 6 4 6 2 2 9 8 0 4 7 5 3 9 7 E + 0 1 . 9 2 4 5 6 9 5 8 9 0 8 5 8 8 E + 0 0 . 4 2 1 8 2 7 1 3 3 9 4 8 2 5 E + 0 2 . 1 6 3 3 9 2 7 6 0 3 2 7 8 9 E + 0 3 . 8 4 5 4 4 0 9 2 8 3 0 4 7 4 E + 0 1 . 1 4 2 9 7 9 4 4 4 1 0 3 0 0 E + 0 3 . 1 8 4 9 7 4 0 9 8 5 8 1 4 3 E + 0 3 . 8 3 0 7 5 7 7 7 5 7 6 0 1 4 E + 0 2 . 1 7 4 8 4 0 7 7 2 1 5 5 4 4 E + 0 2 . 1 0 0 7 4 2 5 5 2 1 9 6 6 1 3 + 0 1 . 2 6 1 8 4 0 3 7 8 0 0 8 0 3 8 + 0 0 . 2 4 9 0 2 2 3 2 7 8 6 1 5 3 E + 0 0 . 2 2 5 4 7 4 0 2 5 2 6 6 0 4 E + 0 0 . 1 9 0 2 4 7 0 6 1 2 5 9 3 O E + 0 0 . 1 4 1 6 7 4 7 7 2 6 5 4 3 7 E + 0 0 . 7 6 7 8 9 3 1 8 9 9 2 8 3 1 8 - 0 1 . 1 0 2 8 4 1 5 0 6 6 0 4 7 2 8 - 0 1 . 1 3 4 7 6 3 8 2 9 7 8 6 5 6 8 + 0 0 . 2 4 9 0 2 2 3 2 7 8 6 1 5 3 E + 0 0 . 2 3 7 4 0 4 9 6 4 5 0 7 1 5 E + 0 0 . 2 1 6 0 6 2 4 6 8 2 2 4 7 S E + 0 0 . 1 8 4 1 3 5 2 6 8 9 9 9 2 1 8 + 0 0 . 1 4 0 1 1 2 8 2 2 6 0 0 4 Z E + 0 0 . 8 1 3 0 5 2 9 0 8 7 0 3 1 3 3 - 0 1 . 2 3 8 8 1 2 9 5 6 5 2 1 6 8 8 - 0 2 . 1 1 0 4 3 1 3 5 2 2 1 8 3 S E + 0 0 . 2 2 5 4 7 4 0 2 5 2 6 6 0 4 E + 0 0 . 2 1 6 0 6 2 4 6 8 2 2 4 7 4 E + 0 0 . 1 9 8 7 7 2 3 0 3 9 2 6 5 8 E + 0 0 . 1 7 2 9 0 7 1 7 0 2 0 7 O I E + 0 0 . 1 3 7 2 4 3 3 3 2 1 7 0 9 9 E + 0 0 . 8 9 6 0 1 6 7 5 3 8 3 9 5 1 8 - 0 1 . 2 5 6 6 8 6 3 5 3 0 3 2 7 4 3 - 0 1 - . 6 5 7 2 9 6 5 8 9 7 4 6 1 S E - 0 1 . 1 9 0 2 4 7 0 6 1 2 5 9 3 0 E + 0 0 q u m m i p w N q u m m t h H m fl m m i fi w m e fl m m p U N H m Q O ‘ U ‘ I fi w N fi - ‘ m q u ‘ D W N H m v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( - - - - - ~ m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m Q i fi u s w u ‘ s u u u V u u w h ‘ u w s V ‘ s u w ‘ s u s s s s u u - - - - - - - ~ m m m m m m m m q q q q q u q \ l m m m m m m m m m m m m m m m m n p b h h b b - - - - - - s - § ~ w s s - - - ~ s s ~ s - - - - m m m m m m m m m m m w w w m q m m o w w w N N N H H H H H H H H 3 3 5 . 1 8 4 1 3 5 2 6 8 9 9 9 2 1 E + 0 0 . 1 7 2 9 0 7 1 7 0 2 0 7 O Z E + 0 0 . 1 5 6 1 1 0 5 5 2 6 7 5 5 8 3 + 0 0 . 1 3 2 9 5 0 7 3 2 4 8 1 8 6 E + 0 0 . 1 0 2 0 1 2 6 0 9 7 5 8 5 8 8 + 0 0 . 6 0 4 9 4 9 8 9 9 2 6 0 9 4 3 - 0 1 . 1 1 4 1 6 1 2 5 9 4 8 4 7 8 8 - 0 2 . 1 4 1 6 7 4 7 7 2 6 5 4 3 7 E + 0 0 . 1 4 0 1 1 2 8 2 2 6 0 0 4 Z E + 0 0 . 1 3 7 2 4 3 3 3 2 1 7 0 9 9 E + 0 0 . 1 3 2 9 5 0 7 3 2 4 8 1 8 S E + 0 0 . 1 2 7 0 3 1 9 3 1 5 4 1 7 1 E + 0 0 . 1 1 9 1 2 5 2 8 2 0 6 3 9 1 3 + 0 0 . 1 0 8 5 1 4 9 0 3 1 6 3 8 9 E + 0 0 . 9 3 3 4 6 2 8 6 0 4 5 2 2 7 8 - 0 1 . 7 6 7 8 9 3 1 8 9 9 2 8 3 2 8 - 0 1 . 8 1 3 0 5 2 9 0 8 7 0 3 1 2 8 - 0 1 . 8 9 6 0 1 6 7 5 3 8 3 9 5 1 E - 0 1 . 1 0 2 0 1 2 6 0 9 7 5 8 5 8 8 + 0 0 . 1 1 9 1 2 5 2 8 2 0 6 3 9 1 E + 0 0 . 1 4 1 9 8 5 3 0 3 1 6 7 2 0 E + 0 0 . 1 7 2 6 6 2 4 6 5 4 5 9 3 7 E + 0 0 . 2 1 6 5 1 8 2 0 8 0 7 9 9 4 E + 0 0 . 1 0 2 8 4 1 5 0 6 6 0 4 7 2 E - 0 1 . 2 3 8 8 1 2 9 5 6 5 2 1 7 1 3 - 0 2 . 2 5 6 6 8 6 3 5 3 0 3 2 7 4 E - 0 1 . 6 0 4 9 4 9 8 9 9 2 6 0 9 3 E - 0 1 . 1 0 8 5 1 4 9 0 3 1 6 3 8 8 E + 0 0 . 1 7 2 6 6 2 4 6 5 4 5 9 3 7 E + 0 0 . 2 5 8 7 4 5 7 2 2 2 5 2 5 4 E + 0 0 . 3 8 1 8 0 9 6 0 2 7 0 6 9 8 8 + 0 0 . 1 3 4 7 6 3 8 2 9 7 8 6 5 6 E + 0 0 . 1 1 0 4 3 1 3 5 2 2 1 8 3 5 E + 0 0 . 6 5 7 2 9 6 5 8 9 7 4 6 1 6 8 - 0 1 . 1 1 4 1 6 1 2 5 9 4 8 4 7 4 E - 0 2 . 9 3 3 4 6 2 8 6 0 4 5 2 2 8 E - 0 1 . 2 1 6 5 1 8 2 0 8 0 7 9 9 4 E + 0 0 . 3 8 1 8 0 9 6 0 2 7 0 6 9 8 8 + 0 0 . 6 1 8 1 0 8 8 4 3 9 2 1 2 1 E + 0 0 . 4 0 6 3 9 2 3 3 3 0 4 5 6 1 3 - 0 1 . 2 0 6 7 5 0 7 4 2 1 2 3 5 8 E - 0 1 . 7 4 5 1 5 5 9 3 3 2 9 9 4 6 8 - 0 2 . 2 8 8 5 5 8 9 9 4 6 5 9 6 4 8 - 0 1 . 1 7 7 3 1 0 5 1 8 4 1 0 2 1 E - 0 1 . 7 0 6 2 9 6 8 5 6 2 9 3 7 4 8 - 0 1 . 3 2 1 3 0 9 7 8 5 1 5 7 9 5 3 + 0 0 . 9 4 2 5 9 7 4 1 3 8 6 3 6 8 8 + 0 0 . 4 0 8 4 8 8 1 4 4 1 8 5 2 4 E - 0 1 . 1 5 8 5 8 1 3 9 9 3 2 5 4 1 8 - 0 2 . 1 8 3 1 8 6 6 9 2 8 4 3 6 6 8 - 0 1 v v v v v v v v v v v m u a s m u w a q u o x m u a - w n H a : q m m b w m w m u m m p w w w m w o m b - u m w w w w w w w p p p h p p b fi m m m m m m m m m m m m m )m v ~ v “ “ v v v V v ‘ ‘ “ ~ ‘ V ‘ ‘ ‘ A 1 ( A 1 ( A 1 ( m fl m m e N I - ‘ C D Q G U ‘ I Q W N H Q Q O N M D M N H C D Q O ‘ U ‘ I I t h l — ‘ ( D \ l m m b H H H H H m u ‘ p r H N m “ V ‘ V § “ “ V ‘ fi ‘ Q ‘ V V ~ “ ‘ - “ V ‘ V ‘ V V V “ V V c o c o o o m o o o o m m o o o o m o o o o m o o m m o o m o o o o o o o o m o o o o o o o o m o o o o o o o o o o o o O O O O O O O O m m m m m m m m m m m v v - - - - - V ‘ V § ~ § ‘ ~ ‘ \ ‘ § ‘ § “ “ “ “ ‘ ~ ‘ § V 3 3 6 2 ) = - . 1 3 6 2 9 3 8 5 6 3 2 5 3 5 E - 0 1 2 ) = - . 2 2 7 5 4 6 5 6 7 3 0 3 7 0 E - 0 1 2 ) = . 7 4 6 9 5 0 5 0 5 3 4 9 4 8 8 - 0 1 2 ) = - . 2 0 2 2 9 8 8 3 9 1 0 8 4 3 E - 0 1 2 ) = - . 9 9 5 6 4 1 0 7 6 1 8 0 1 3 8 + 0 0 . 5 5 0 5 6 6 0 0 0 6 3 1 8 5 E - 0 1 . 6 6 2 0 8 9 0 4 7 0 3 9 0 1 E - 0 2 - . 2 6 8 0 4 7 1 5 4 9 2 0 5 3 E - 0 1 ' . 1 0 7 7 8 1 5 1 5 5 8 7 3 7 E - 0 2 . 5 2 3 6 2 7 6 8 5 2 9 6 5 5 E - 0 1 ' . 2 1 6 0 4 6 8 8 6 4 8 7 1 7 E - 0 1 ‘ . 3 1 5 2 3 1 7 9 5 8 9 1 1 7 E + 0 0 . 9 4 5 3 1 7 7 1 0 0 3 2 0 6 E + 0 0 ‘ . 6 3 1 3 8 2 0 2 3 1 8 3 5 3 E - 0 1 . 1 1 1 1 7 8 1 9 3 4 5 3 7 1 E - 0 1 . 2 1 3 4 0 6 7 1 7 6 8 5 1 1 3 - 0 1 - . 3 3 5 4 1 6 2 7 1 8 1 7 7 4 E - 0 1 . 6 5 5 0 6 2 3 6 2 5 9 5 0 6 8 - 0 2 . 9 4 4 9 2 9 0 8 6 9 6 4 5 0 8 - 0 1 - . 3 3 5 9 2 6 1 9 1 5 9 7 1 3 E + 0 0 . 9 3 4 0 7 2 4 1 1 4 3 8 6 0 3 + 0 0 - . 3 7 0 1 4 7 3 5 3 6 5 3 2 2 8 - 0 1 . 1 0 8 3 2 7 3 5 5 9 5 1 2 2 E - 0 1 . 6 9 0 4 6 4 9 7 4 1 9 0 4 6 8 - 0 2 - . 2 0 6 1 2 6 0 4 4 2 5 6 1 4 E - 0 1 . 2 4 3 7 0 0 2 6 8 0 8 1 8 2 E - 0 1 . 2 2 3 7 7 5 5 2 0 9 8 5 5 0 3 - 0 2 ' . 1 4 1 5 8 8 1 6 3 7 6 9 5 2 E + 0 0 . 9 8 8 6 3 2 3 3 4 9 3 6 2 3 E + 0 0 . 2 6 7 0 6 0 0 7 2 2 4 3 8 6 E - 0 1 . 8 0 7 4 5 4 9 0 5 0 6 2 9 6 E - 0 2 - . 1 1 0 6 7 8 6 7 3 1 5 6 8 6 E - 0 1 - . 1 1 6 8 3 5 0 8 9 8 6 2 5 1 3 - 0 1 . 1 7 6 3 5 0 0 8 6 4 8 9 6 9 8 - 0 1 . 4 8 9 4 1 1 4 9 2 3 2 4 4 9 E - 0 1 6 ) = - . 7 4 4 8 6 3 8 1 1 5 5 4 2 9 E - 0 1 6 ) = ' . 9 9 5 3 4 3 2 2 6 3 1 4 7 9 E + 0 0 ( A ) V N ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ' . 3 3 3 3 3 3 3 3 2 3 8 2 1 3 8 + 0 0 - . 6 6 6 6 6 6 7 2 2 5 3 9 5 0 £ + 0 0 - . 5 9 9 9 9 9 9 4 0 3 2 0 8 7 E + 0 0 ' . 7 1 4 2 8 5 6 9 0 0 7 5 2 4 E + 0 0 - . 7 5 0 0 0 0 0 0 5 1 5 7 2 1 E + 0 0 - . 5 0 0 0 0 0 0 2 5 8 4 0 4 6 E + 0 0 1 ) = . 2 2 2 6 4 7 3 3 1 3 9 0 7 G E + 0 2 2 ) = . 4 1 0 5 7 0 9 3 7 4 2 9 3 l E + 0 2 3 ) = . 2 9 5 3 2 4 8 9 9 5 9 5 4 3 E + 0 2 4 ) = - . 5 4 4 3 1 4 1 3 4 2 5 5 6 9 8 + 0 2 5 ) = - . 5 4 6 2 2 5 3 0 7 1 3 4 0 1 E + 0 2 o Q a x ~ — o x H § ~ — - I o § x ~ H o V x V H N ‘ o - x N V V N o x N “ ~ o M V V x N o ~ w “ x - w o “ \ § w w m m m - ~ w u V m ‘ w m w m V w m w m ‘ w ~ ‘ “ V m u V m p ‘ m m m m - b V p “ h ‘ - V o “ m : m “ a m h o - p \ h m ‘ h ‘ “ “ V m - m - ‘ m ~ m m ‘ m m “ ‘ m m ~ w m m ~ ‘ m m m - “ m m w m ‘ m ~ ‘ m m m “ m ~ m m m ~ ‘ m m “ ‘ m m m m ~ “ m m “ m “ m o “ m \ u “ ~ A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( 3 3 7 ’ . 3 2 9 7 6 1 4 0 2 5 2 7 0 7 E + 0 2 ' . 8 2 6 9 9 4 1 5 2 2 4 4 8 8 £ + 0 1 - . 1 0 9 7 5 2 0 6 4 5 9 4 0 7 E + 0 1 “ . 3 4 3 9 5 8 6 8 4 2 4 3 2 6 3 - 0 1 - . 1 4 9 9 4 7 4 6 5 0 0 9 0 6 E + 0 3 - . 2 8 2 8 2 5 8 0 8 8 0 6 3 2 E + 0 3 . 2 3 9 0 6 4 3 4 0 8 0 9 8 3 E + 0 3 . 3 7 7 2 4 7 8 4 5 4 9 1 3 9 E + 0 3 . 4 4 6 0 7 7 8 0 0 1 0 8 4 7 E + O 3 . 3 0 0 4 1 2 5 7 5 9 4 0 2 5 E + 0 3 . 8 9 2 4 5 4 2 4 4 1 9 6 4 1 E + 0 2 . 1 3 5 4 8 8 6 4 4 6 3 3 4 4 E + 0 2 . 5 5 1 3 9 2 1 7 7 1 1 9 8 5 8 + 0 0 . 4 2 2 3 6 0 7 7 8 5 3 8 0 4 E + 0 3 . 7 5 8 9 9 8 2 1 0 3 8 2 4 7 E + 0 3 . 6 0 6 3 5 0 0 1 2 0 4 3 2 6 E + 0 3 . 1 0 0 8 3 9 6 3 0 3 7 8 8 9 E + 0 4 . 1 1 3 3 9 7 8 3 8 3 5 3 8 8 E + 0 4 . 7 5 0 8 4 9 6 8 9 0 6 8 2 7 E + 0 3 . 2 3 3 9 5 2 3 7 9 1 2 0 5 1 E + 0 3 . 3 8 4 5 9 9 1 7 5 7 8 8 4 6 E + 0 2 . 1 9 2 3 6 7 1 6 7 3 9 8 3 3 E + 0 1 . 1 4 7 5 4 2 8 3 9 8 2 8 8 8 3 + 0 3 . 1 3 4 2 0 1 8 4 6 2 1 5 4 O E + 0 3 . 1 6 9 0 2 8 7 4 0 6 9 6 3 8 E + 0 3 . 1 8 9 9 9 5 5 9 5 5 9 9 3 1 8 + 0 3 . 3 7 8 9 8 7 6 4 0 8 2 9 9 9 E + 0 3 . 1 5 1 7 2 8 2 1 4 3 3 0 2 7 E + 0 3 . 7 4 8 5 1 4 4 3 1 4 8 9 1 7 E + 0 2 . 7 4 1 0 2 7 8 0 4 4 6 4 1 0 8 + 0 1 . 7 7 9 5 0 1 4 1 3 9 2 6 4 8 E + 0 0 . 8 7 4 2 0 8 3 9 8 1 8 1 9 5 E + 0 2 . 1 2 5 5 7 7 5 6 8 9 0 1 9 1 E + 0 3 . 1 1 9 1 8 7 6 3 7 3 5 8 0 9 E + 0 3 “ . 1 7 0 8 8 9 9 2 8 2 3 7 4 Z E + 0 3 - . 2 3 9 6 3 7 2 9 1 8 6 8 7 4 E + 0 3 - . 1 2 6 5 9 7 5 8 8 9 6 2 4 I E + 0 3 - . 4 9 2 3 3 2 2 2 0 3 5 6 9 1 8 + 0 2 - ' . 5 9 8 3 2 7 8 9 5 6 2 6 4 3 E + 0 1 = ' . 5 3 0 0 7 2 2 5 6 9 2 2 7 Z E + 0 0 . 7 3 5 1 0 0 2 3 9 3 9 4 2 3 E + 0 3 . 1 1 8 0 5 0 3 1 5 4 4 1 3 1 8 + 0 4 3 ) = . 1 0 2 5 0 3 6 8 7 5 3 1 0 4 E + 0 4 4 ) = - . 1 5 8 3 6 5 2 3 8 4 5 0 2 1 E + 0 4 5 ) = - . 1 9 8 9 4 3 2 6 5 7 0 8 6 3 8 + 0 4 6 ) = - . 1 2 0 0 5 2 2 3 3 2 5 3 0 5 E + 0 4 7 ) = ‘ . 4 0 2 9 5 2 2 2 4 6 6 0 6 6 E + 0 3 8 ) = ” . 5 8 3 5 5 3 4 1 4 0 4 6 7 6 3 + 0 2 9 ) = ‘ . 4 3 0 6 2 7 1 9 5 5 3 7 0 9 8 + 0 1 1 ) = . 1 3 0 6 1 3 2 6 4 3 9 5 7 4 E + 0 3 N H m e m m w a i - m e \ l m m o w a o n m x l m w u w a l - J m m q m m n b w N H m m d m v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v O \ fl V N v D V l \ \ V D V O v \ V v l O V D \ , V b \ v V l O I \ V \ v V O ) I \ V D V v \ ' \ ) V v V U D \ V V \ v N D l \ V O v \ O V \ v Q V I D V ‘ \ \ V v D V m — \ O v V D V m ‘ \ V v D V — ‘ \ D V v D V — \ V v H U D ‘ V \ V v N — D V \ e v O V D V ‘ \ V v m D V — \ l V v m O V ‘ e \ V v O V — m \ V v I D V H \ V v ‘ D V - N \ V v D V fi W \ v ‘ D O V V — \ v V m D V O \ V v H ‘ D V \ v V M O O N V e \ v V V D N N m \ v V V O H N \ V v V M N D \ N V V V D N W \ V V Q V N D \ m V W V D V \ V m w V V O w \ V V e V w D \ V V w m V O w H \ V V w V D N \ w V V V O w w \ V V fi O fi V \ V V l m D V \ V fi m V D fi V \ q V V b V O \ b m V V V D fi m \ V V V D b H \ V fi V V D a b \ V V V O m w \ D V m V V 1 \ m V V V 0 D m \ V V V ‘ D m \ m 0 V V V A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( 3 ' 3 8 . 2 3 1 3 4 5 1 6 3 3 0 8 3 2 8 + 0 3 . 1 9 3 8 3 4 8 0 4 0 2 9 S S E + 0 3 . 3 0 9 3 1 4 8 7 3 3 1 1 7 7 E + 0 3 . 3 6 6 8 6 6 2 1 5 7 4 5 6 9 E + 0 3 . 2 3 1 3 3 3 7 3 7 2 5 0 5 3 3 + 0 3 . 7 3 1 8 7 9 1 8 6 1 8 3 2 1 5 + 0 2 . 1 1 8 0 9 0 8 3 5 7 3 5 2 0 E + 0 2 . 7 2 0 6 8 5 5 3 2 3 1 6 5 7 E + 0 0 . 2 3 1 9 1 2 8 6 1 3 8 8 0 1 E + 0 0 . 2 2 2 9 7 1 2 7 2 5 8 1 3 0 E + 0 0 . 2 0 6 6 1 5 6 4 4 4 5 4 3 9 E + 0 0 . 1 8 2 3 3 5 2 5 3 0 7 9 8 1 8 + 0 0 . 1 4 9 2 7 3 7 5 0 4 5 8 8 5 8 + 0 0 . 1 0 6 0 1 9 3 5 2 3 2 3 2 0 E + 0 0 . 5 0 1 3 2 5 3 7 8 2 0 7 6 1 8 - 0 1 . 2 3 1 4 9 8 7 1 0 8 9 8 4 6 E - 0 1 . 1 2 6 1 1 4 9 6 7 9 5 5 5 2 8 + 0 0 . 2 2 2 9 7 1 2 7 2 5 8 1 3 0 E + 0 0 . 2 1 4 6 9 1 5 3 2 6 8 8 2 8 E + 0 0 . 1 9 9 5 4 6 5 3 4 4 4 4 2 5 3 + 0 0 . 1 7 7 0 6 3 3 5 7 2 9 9 6 5 8 + 0 0 . 1 4 6 4 4 9 0 3 9 3 8 5 5 7 E + 0 0 . 1 0 6 3 9 6 2 9 5 5 9 4 8 8 E + 0 0 . 5 4 6 4 6 1 7 8 3 1 5 3 9 1 3 - 0 1 . 1 3 2 1 1 9 0 6 7 5 4 3 8 2 8 - 0 1 . 1 0 8 5 5 5 9 1 2 0 4 0 4 7 E + 0 0 . 2 0 6 6 1 5 6 4 4 4 5 4 3 9 E + 0 0 . 1 9 9 5 4 6 5 3 4 4 4 4 2 5 3 + 0 0 . 1 8 6 6 1 5 9 7 6 2 0 7 6 3 E + 0 0 . 1 6 7 4 2 0 1 9 7 7 5 4 4 3 E + 0 0 . 1 4 1 2 8 2 1 8 0 8 1 1 4 7 E + 0 0 . 1 0 7 0 8 5 7 8 6 3 2 4 Z O E + 0 0 . 6 2 9 0 2 3 6 4 6 6 2 0 3 2 8 - 0 1 . 4 9 6 6 2 5 4 8 3 5 1 2 9 8 E - 0 2 . 7 6 4 3 7 5 2 7 8 1 7 6 6 5 E - 0 1 . 1 8 2 3 3 5 2 5 3 0 7 9 8 1 E + 0 0 . 1 7 7 0 6 3 3 5 7 2 9 9 6 5 3 + 0 0 . 1 6 7 4 2 0 1 9 7 7 5 4 4 B E + 0 0 . 1 5 3 1 0 4 6 5 5 4 4 2 2 2 E + 0 0 . 1 3 3 6 1 1 8 3 3 6 3 0 1 2 3 + 0 0 . 1 0 8 1 0 9 3 5 4 9 7 3 5 2 E + 0 0 . 7 5 1 5 8 9 0 6 5 1 7 8 7 5 8 - 0 1 . 3 1 9 5 2 2 4 8 9 7 7 0 8 3 E - O l . 2 8 7 5 6 8 7 9 7 2 7 4 1 1 8 - 0 1 . 1 4 9 2 7 3 7 5 0 4 5 8 8 5 E + 0 0 . 1 4 6 4 4 9 0 3 9 3 8 5 5 7 E + 0 0 . 1 4 1 2 8 2 1 8 0 8 1 1 4 7 E + 0 0 . 1 3 3 6 1 1 8 3 3 6 3 0 1 2 E + 0 0 . 1 2 3 1 6 7 4 7 1 1 6 5 3 4 E + 0 0 . 1 0 9 5 0 3 1 0 1 4 6 0 2 2 E + 0 0 m m V m m V m m V ~ s m ~ V m m V m s m V m - m V m V V m ‘ - o - m V s m m V m u m m m m m D V V s m V m u V q s V q V u u u \ V q m s V q - q § q q ‘ q § m V m V V m V m V m V m ~ m V m m § V m m ~ V m m V - m m V m V m V m V - m m - m - m m V u m V m u V m m h ‘ V m V m V ~ m m m m o H n m u m H u o m w H m x w H o D m H a ‘ x \ m o m — x H ~ ~ o m — n - - q I u m m - - ‘ — o x o - m - I - - p H o M \ N N - - A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( 5 ( S ( S ( S ( S ( S ( S ( S ( S ( 3 3 9 . 9 1 8 4 8 0 8 0 6 6 4 2 8 8 8 - 0 1 . 6 8 6 9 7 8 4 6 9 8 9 8 6 5 E - 0 1 . 3 6 1 6 7 6 8 5 3 8 4 2 7 1 8 - 0 1 . 1 0 6 0 1 9 3 5 2 3 2 3 2 0 E + 0 0 . 1 0 6 3 9 6 2 9 5 5 9 4 8 8 8 + 0 0 . 1 0 7 0 8 5 7 8 6 3 2 4 Z O E + 0 0 . 1 0 8 1 0 9 3 5 4 9 7 3 5 2 8 + 0 0 . 1 0 9 5 0 3 1 0 1 4 6 0 2 2 8 + 0 0 . 1 1 1 3 2 6 5 4 2 2 3 9 4 B E + 0 0 . 1 1 3 6 8 2 5 4 5 6 5 7 1 7 E + 0 0 . 1 1 6 7 7 2 1 5 2 5 7 8 0 8 8 + 0 0 . 1 2 1 1 0 8 5 6 3 4 8 5 2 3 E + 0 0 . 5 0 1 3 2 5 3 7 8 2 0 7 6 1 3 - 0 1 . 5 4 6 4 6 1 7 8 3 1 5 3 9 0 3 - 0 1 . 6 2 9 0 2 3 6 4 6 6 2 0 3 1 8 - 0 1 . 7 5 1 5 8 9 0 6 5 1 7 8 7 4 8 - 0 1 . 9 1 8 4 8 0 8 0 6 6 4 2 8 9 3 - 0 1 . 1 1 3 6 8 2 5 4 5 6 5 7 1 7 E + 0 0 . 1 4 1 8 9 3 7 9 1 2 0 1 0 3 8 + 0 0 . 1 7 8 8 8 6 5 8 1 9 2 2 1 9 E + 0 0 . 2 3 0 8 5 6 4 4 4 6 9 4 8 S E + 0 0 . 2 3 1 4 9 8 7 1 0 8 9 8 4 7 3 - 0 1 . 1 3 2 1 1 9 0 6 7 5 4 3 8 2 8 - 0 1 . 4 9 6 6 2 5 4 8 3 5 1 3 0 4 3 - 0 2 . 3 1 9 5 2 2 4 8 9 7 7 0 8 4 E - 0 1 . 6 8 6 9 7 8 4 6 9 8 9 8 6 6 3 - 0 1 . 1 1 6 7 7 2 1 5 2 5 7 8 0 8 8 + 0 0 . 1 7 8 8 8 6 5 8 1 9 2 2 1 9 E + 0 0 . 2 6 0 3 3 5 5 7 4 8 4 0 1 8 8 + 0 0 . 3 7 4 7 6 5 7 1 8 0 2 7 8 1 E + 0 0 . 1 2 6 1 1 4 9 6 7 9 5 5 5 2 E + 0 0 . 1 0 8 5 5 5 9 1 2 0 4 0 4 7 E + 0 0 . 7 6 4 3 7 5 2 7 8 1 7 6 6 5 8 - 0 1 . 2 8 7 5 6 8 7 9 7 2 7 4 1 0 8 - 0 1 . 3 6 1 6 7 6 8 5 3 8 4 2 7 3 3 - 0 1 . 1 2 1 1 0 8 5 6 3 4 8 5 2 3 E + 0 0 . 2 3 0 8 5 6 4 4 4 6 9 4 8 S E + 0 0 . 3 7 4 7 6 5 7 1 8 0 2 7 8 1 E + 0 0 . 5 7 6 9 5 1 5 9 4 8 2 7 8 1 8 + 0 0 . 2 7 7 3 9 8 9 3 2 3 2 9 9 5 8 - 0 1 . 1 5 5 7 4 2 3 1 9 1 6 3 2 6 E - 0 1 - . 2 1 1 8 0 7 1 3 2 2 2 8 2 1 8 - 0 2 ‘ . 1 7 5 0 7 1 1 4 2 6 0 1 0 3 E - 0 1 - . 1 7 5 6 4 6 6 4 9 4 0 2 0 5 3 - 0 1 . 1 8 7 4 6 0 6 6 6 8 0 7 8 1 3 - 0 1 . 1 2 6 7 3 4 8 6 0 2 1 2 7 G E + 0 0 . 3 7 2 6 7 7 1 8 6 5 4 3 0 6 E + 0 0 . 9 1 8 1 8 6 8 0 7 6 3 4 7 8 E + 0 0 . 1 3 7 6 8 2 0 5 2 2 4 3 3 8 8 - 0 1 . 5 1 3 8 6 0 3 4 4 8 4 0 2 6 8 - 0 2 V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V q m m b w m e m q m m - b w m w m m q m m p w N t - u o m x l m m p w w H m m q m m p w m w m m q a ‘ m h w V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V \ O k O k O W K O k D U ) \ D \ D \ D ‘ D \ O \ D \ O \ D \ D \ D \ D \ D \ D \ D \ D \ D \ O \ D \ O \ D \ D & D \ D K D \ O \ D \ D \ O \ O \ D k D \ O \ O \ O \ D \ D \ D \ O \ O \ D \ D \ D K O 3 4 0 2 ) = - . 4 4 8 7 7 1 6 6 3 3 8 3 7 8 8 - 0 2 2 ) = - . 7 0 4 8 8 6 2 4 8 5 8 2 0 1 8 - 0 2 . 3 5 5 5 6 1 1 6 5 3 2 4 8 9 3 - 0 2 . 2 1 8 9 3 6 1 9 7 0 6 9 0 2 3 - 0 1 . 8 8 0 2 6 9 2 9 1 6 2 5 9 2 8 - 0 2 . 1 6 9 8 6 7 1 0 3 7 1 8 1 8 E + 0 0 . 9 8 5 0 3 2 9 4 9 6 6 7 3 0 8 + 0 0 . 1 4 0 4 6 2 4 9 9 6 6 9 7 7 E - 0 1 . 2 8 7 1 0 9 5 9 0 3 5 3 0 7 E - 0 2 . 6 1 9 1 4 0 6 9 7 1 2 1 7 9 8 - 0 2 . 2 8 7 7 5 9 1 2 8 2 4 5 7 1 E - 0 2 . 1 0 3 6 8 5 7 5 9 2 3 4 9 8 E - 0 1 . 7 7 0 0 0 4 7 6 0 7 1 7 8 5 3 - 0 2 . 4 6 1 5 0 2 7 7 0 7 4 4 9 5 3 - 0 1 . 6 2 4 1 5 1 3 2 1 7 8 5 6 3 8 - 0 1 . 9 9 6 7 7 2 5 6 7 1 9 8 5 3 8 + 0 0 . 1 7 4 8 1 4 9 6 4 2 0 7 8 0 E - 0 1 . 5 1 4 9 3 1 5 2 9 3 0 7 2 7 8 - 0 2 . 2 9 1 2 4 1 2 1 4 8 8 6 8 6 E - 0 2 . 8 6 3 2 5 9 4 8 9 3 5 5 8 4 3 - 0 2 . 9 5 0 9 0 7 5 7 5 5 7 0 0 3 3 - 0 2 . 1 1 0 6 9 4 8 5 4 8 6 8 6 5 E ‘ 0 2 . 4 1 5 1 5 7 9 5 3 0 1 2 8 6 E - 0 1 . 1 8 1 5 8 7 2 0 2 1 7 9 4 0 E + 0 0 . 9 8 2 2 4 0 1 7 2 7 0 9 3 6 E + 0 0 . 8 6 6 4 6 3 9 7 6 4 4 9 3 0 3 - 0 1 . 1 6 8 6 3 7 4 7 7 2 5 6 4 5 8 - 0 1 . 2 5 7 1 4 3 4 9 4 9 7 9 3 0 8 - 0 1 . 4 2 1 6 1 4 1 4 8 2 1 7 7 3 8 - 0 1 . 1 3 7 4 9 8 5 9 5 7 2 8 1 4 8 - 0 1 . 8 4 3 5 8 3 6 9 0 8 2 3 0 6 3 - 0 1 . 2 6 6 2 7 6 6 8 6 9 8 4 5 7 E + 0 0 . 4 1 6 5 8 4 4 5 6 5 4 7 4 8 8 + 0 0 . 8 5 9 0 7 9 6 9 7 4 5 3 6 I E + 0 0 . 1 5 6 4 8 3 5 4 1 5 8 9 4 8 8 - 0 1 . 1 2 3 1 1 5 5 2 1 5 9 1 9 0 3 - 0 2 . 6 2 5 4 1 9 6 1 0 2 9 9 0 9 E - 0 2 . 5 6 3 3 5 4 0 8 2 2 0 2 8 4 8 - 0 2 . 5 0 0 5 6 0 5 1 3 3 3 1 2 6 8 - 0 2 6 ) = - . 2 1 0 9 3 9 4 1 2 1 8 3 3 3 8 - 0 1 6 ) = . 1 6 7 7 3 7 0 8 0 2 7 4 1 8 8 - 0 1 6 ) = . 1 1 3 1 0 2 3 8 5 5 9 5 5 2 E + 0 0 6 ) = - . 9 9 3 0 4 5 4 3 9 1 2 6 8 2 8 + 0 0 7 ) = - . 7 6 8 9 2 7 0 5 8 5 0 8 6 1 8 - 0 1 7 ) = ' . 4 1 5 7 1 1 6 5 8 1 9 5 5 9 8 - 0 2 7 ) = . 3 5 0 3 8 3 9 4 2 0 4 0 2 3 8 - 0 1 7 ) = - . 8 9 7 9 8 1 8 9 4 8 0 6 5 4 E - 0 2 7 ) - ‘ . 5 3 7 3 8 4 3 2 7 0 1 7 2 3 E - 0 1 7 ) = . 6 0 4 9 4 2 7 5 0 6 9 5 1 0 3 - 0 1 7 ) = . 1 7 4 6 0 2 0 1 8 2 9 9 4 8 E + 0 0 3 4 1 7 ) = - . 7 6 6 9 6 0 5 6 5 9 4 2 7 2 E + 0 0 s ( 9 , 8 , S ( 9 , 9 , 7 ) = “ . 6 0 6 2 1 7 9 0 8 8 2 5 7 3 8 + 0 0 K ( 9 ) = 7 M ( 9 ) = 2 N S ( 9 , 1 ) = - . 3 3 3 3 3 3 4 5 2 6 2 3 1 5 E + 0 0 W S ( 9 , 2 ) = - . 4 9 9 9 9 9 7 3 0 6 4 2 2 5 E + 0 0 W S ( 9 , 3 ) = - . 6 0 0 0 0 0 5 1 0 4 4 0 4 l E + 0 0 w s ( 9 , 4 ) = - . 7 7 7 7 7 7 6 8 4 9 7 1 5 1 E + 0 0 W S ( 9 , 5 ) = - . 7 5 0 0 0 0 0 6 9 7 5 3 6 6 8 + 0 0 W S ( 9 , 6 ) = - . 7 1 4 2 8 6 0 9 9 9 6 0 9 9 E + 0 0 W S ( 9 , 7 ) = - . 6 6 6 6 6 5 9 6 6 7 4 2 4 B E + 0 0 A 1 ( 1 0 , 1 , 1 ) = . 7 3 2 1 3 4 7 9 6 9 8 1 7 0 E + 0 1 A 1 ( 1 0 , 1 , 2 ) = - . 9 5 0 0 3 5 4 7 2 6 0 2 7 6 E + 0 1 A 1 ( 1 0 , 1 , 3 ) = . 2 4 9 0 1 3 8 8 6 8 6 6 7 4 E + 0 2 A 1 ( 1 0 , 1 , 4 ) = - . 1 0 7 1 5 9 9 1 4 5 0 0 6 6 E + 0 2 A 1 ( 1 0 , 1 , 5 ) = . 7 3 2 9 5 4 8 9 4 5 0 1 0 2 E + 0 1 A 1 ( 1 0 , 1 , 6 ) = - . 3 7 4 5 2 2 7 0 7 9 4 3 8 3 E + 0 1 A 1 ( 1 0 , l , 7 ) = . 1 3 9 1 6 3 0 1 2 1 5 0 6 8 8 + 0 0 A 1 ( 1 0 , 1 , 8 ) = - . 2 7 6 9 1 2 7 1 0 6 2 9 4 O E + 0 0 A 1 ( 1 0 , 1 , 9 ) = - . 9 3 8 3 3 7 2 9 6 2 4 7 4 8 E - 0 2 A 1 ( 1 0 , 1 , 1 0 ) = - . 1 8 1 3 5 8 3 0 7 6 0 0 0 2 E - 0 2 A 1 ( 1 0 , 2 , 1 ) = . 2 0 5 7 0 4 4 1 6 6 1 7 7 S E + 0 3 A 1 ( 1 0 , 2 , 2 ) = - . 3 8 1 2 0 7 8 0 8 1 3 6 0 1 8 + 0 3 A 1 ( 1 0 , 2 , 3 ) = . 7 4 4 3 4 9 2 1 0 2 9 0 2 4 E + 0 3 A 1 ( 1 0 , 2 , 4 ) = - . 2 8 6 8 5 0 3 5 1 7 2 7 B O E + 0 3 A 1 ( 1 0 , 2 , 5 ) = . 3 2 3 8 2 9 8 6 0 1 7 6 8 9 3 + 0 3 A 1 ( 1 0 , 2 , 6 ) = - . 5 5 4 6 5 3 4 8 2 2 7 8 8 1 E + 0 2 A 1 ( 1 0 , 2 , 7 ) = . 2 7 7 6 1 9 2 8 9 7 5 5 8 2 E + 0 2 A 1 ( 1 0 , 2 , 8 ) = - . 4 0 0 6 8 7 2 7 1 3 5 6 5 8 8 + 0 1 A 1 ( 1 0 , 2 , 9 ) = . 1 6 3 0 6 7 8 1 7 6 8 7 9 9 E + 0 0 A 1 ( 1 0 , 2 , 1 0 ) = - . 3 5 4 7 7 8 7 6 6 6 3 2 0 8 E - 0 1 A 1 ( 1 0 , 3 , 1 ) = . 2 5 5 3 4 8 7 5 8 7 1 5 3 9 E + 0 4 A 1 ( 1 0 , 3 , 2 ) = - . 4 4 7 0 3 7 9 0 0 5 1 6 0 2 E + 0 4 A 1 ( 1 0 , 3 , 3 ) = . 9 0 4 7 3 6 7 8 8 7 3 6 2 8 3 + 0 4 A 1 ( 1 0 , 3 , 4 ) = - . 3 6 0 4 4 1 5 0 7 9 2 7 1 4 E + 0 4 A 1 ( 1 0 , 3 , 5 ) = . 3 8 4 4 3 4 3 6 2 8 1 0 8 5 E + 0 4 A 1 ( 1 0 , 3 , 6 ) = - . 6 4 6 9 7 5 1 7 5 8 4 8 2 3 3 + 0 3 A 1 ( 1 0 , 3 , 7 ) = . 3 7 9 3 3 2 9 9 8 1 5 6 5 5 8 + 0 3 A 1 ( 1 0 , 3 , 8 ) = - . 3 1 1 1 1 2 0 3 6 7 0 5 0 2 3 + 0 2 A 1 ( 1 0 , 3 , 9 ) = . 4 7 1 0 3 4 4 3 1 4 5 7 S Z E + 0 1 A 1 ( 1 0 , 3 , 1 0 ) = - . 3 1 8 9 6 5 9 1 1 8 6 5 2 3 E + 0 0 A 1 ( 1 0 , 4 , 1 ) = . 1 1 4 5 3 4 4 9 7 2 9 3 2 3 E + 0 5 A 1 ( 1 0 , 4 , 2 ) = - . 2 0 2 9 0 0 3 8 4 7 1 7 B B E + 0 5 A 1 ( 1 0 , 4 , 3 ) = . 4 0 8 2 9 6 6 8 3 4 9 6 2 4 E + 0 5 A 1 ( 1 0 , 4 , 4 ) = - . 1 6 1 1 5 8 2 5 1 3 0 6 4 1 E + 0 5 A 1 ( 1 0 , 4 , 5 ) = . 1 7 2 5 8 2 4 6 3 5 9 1 1 0 8 + 0 5 A 1 ( 1 0 , 4 , 6 ) = - . 2 9 8 3 2 6 0 9 2 7 9 0 0 7 E + 0 4 A 1 ( 1 0 , 4 , 7 ) = . 1 6 8 4 4 8 6 4 4 7 8 1 1 1 3 + 0 4 A 1 ( 1 0 , 4 , 8 ) = - . 1 2 6 2 5 4 8 7 3 2 7 5 7 6 8 + 0 3 A 1 ( 1 0 , 4 , 9 ) = . 2 5 9 9 1 7 2 9 7 3 6 3 2 8 8 + 0 2 3 4 2 A 1 ( 1 0 , 4 , 1 0 ) = - . 1 0 3 0 0 1 4 0 3 8 0 8 5 9 E + 0 1 A 1 ( 1 0 , 5 , 1 ) = . 1 9 8 4 6 3 5 9 3 3 3 0 3 8 8 + 0 5 A 1 ( 1 0 , 5 , 2 ) = - . 3 5 0 9 6 7 9 7 1 4 9 9 8 6 8 + 0 5 A 1 ( 1 0 , 5 , 3 ) = . 7 0 3 7 6 4 5 9 2 6 8 4 5 1 E + 0 5 A 1 ( 1 0 , 5 , 4 ) = - . 2 7 6 4 6 8 8 7 1 0 7 5 8 1 E + 0 5 A 1 ( 1 0 , 5 , 5 ) = . 2 9 5 3 7 7 0 6 1 0 0 2 Z S E + 0 5 A 1 ( 1 0 , 5 , 6 ) = - . 4 9 3 8 2 5 1 6 2 4 9 1 2 O E + 0 4 A 1 ( 1 0 , 5 , 7 ) = . 2 8 2 2 2 1 1 5 9 2 6 7 4 3 E + 0 4 A 1 ( 1 0 , 5 , 8 ) = - . 2 0 6 7 0 3 4 5 2 1 1 0 2 9 E + 0 3 A 1 ( 1 0 , 5 , 9 ) = . 4 2 7 8 3 4 3 9 6 3 6 2 3 0 3 + 0 2 A 1 ( 1 0 , 5 , 1 0 ) = - . 8 0 5 0 5 3 7 1 0 9 3 7 S O E + 0 0 A 1 ( 1 0 , 6 , 1 ) = . 1 8 3 2 8 9 3 1 7 2 6 6 9 4 E + 0 5 A 1 ( 1 0 , 6 , 2 ) = - . 3 2 4 0 0 1 8 2 1 0 3 0 3 8 E + 0 5 A 1 ( 1 0 , 6 , 3 ) = . 6 4 6 1 8 6 4 8 9 2 9 4 7 7 E + 0 5 A 1 ( 1 0 , 6 , 4 ) = - . 2 5 1 9 3 2 1 1 5 0 2 4 3 3 E + 0 5 A 1 ( 1 0 , 6 , 5 ) = . 2 6 8 9 1 5 3 4 4 2 8 5 9 6 E + 0 5 A 1 ( 1 0 , 6 , 6 ) = - . 4 3 7 7 1 5 0 6 1 8 4 6 3 8 3 + 0 4 A 1 ( 1 0 , 6 , 7 ) = . 2 5 1 5 8 4 8 4 6 0 6 7 4 3 E + 0 4 A 1 ( 1 0 , 6 , 8 ) = - . 1 6 5 5 7 8 4 9 4 5 4 8 8 0 3 + 0 3 A 1 ( 1 0 , 6 , 9 ) = . 3 4 9 0 0 9 3 2 3 1 2 0 1 2 8 + 0 2 A 1 ( 1 0 , 6 , 1 0 ) = - . 4 3 7 0 4 2 2 3 6 3 2 8 1 3 8 + 0 0 A 1 ( 1 0 , 7 , 1 ) = . 9 9 4 1 6 2 3 2 5 9 0 6 7 S E + 0 4 A 1 ( 1 0 , 7 , 2 ) = - . 1 7 5 9 2 7 5 5 5 6 8 4 O O E + 0 5 A 1 ( 1 0 , 7 , 3 ) = . 3 4 8 1 9 5 4 0 9 4 2 3 7 1 E + 0 5 A 1 ( 1 0 , 7 , 4 ) = - . 1 3 4 1 0 0 0 2 5 5 8 9 7 6 E + 0 5 A 1 ( 1 0 , 7 , 5 ) = . 1 4 2 3 0 5 5 0 2 8 1 5 2 5 8 + 0 5 A 1 ( 1 0 , 7 , 6 ) = - . 2 1 7 6 5 5 8 6 1 3 6 5 8 O E + 0 4 A 1 ( 1 0 , 7 , 7 ) = . 1 2 7 5 2 6 1 8 4 3 2 0 4 5 E + 0 4 A 1 ( 1 0 , 7 , 8 ) = - . 6 9 1 1 3 6 7 1 0 6 4 3 7 7 E + 0 2 A 1 ( 1 0 , 7 , 9 ) = . 1 6 1 3 6 4 6 6 9 7 9 9 8 0 E + 0 2 A 1 ( 1 0 , 7 , 1 0 ) = - . 1 0 9 1 6 1 3 7 6 9 5 3 1 3 E + 0 0 A 1 ( 1 0 , 8 , 1 ) = - . 1 6 7 8 5 1 5 3 2 5 6 9 5 3 E + 0 4 A 1 ( 1 0 , 8 , 2 ) = . 2 9 7 0 1 3 4 3 9 7 4 5 4 6 E + 0 4 A 1 ( 1 0 , 8 , 3 ) = ‘ . 5 7 5 0 3 5 0 0 6 7 8 6 8 8 E + 0 4 A 1 ( 1 0 , 8 , 4 ) = . 2 1 4 0 6 1 7 9 9 0 1 3 1 5 8 + 0 4 A 1 ( 1 0 , 8 , 5 ) = - . 2 2 5 9 1 1 0 5 3 0 9 2 7 8 E + 0 4 A 1 ( 1 0 , 8 , 6 ) = . 3 0 5 5 9 2 3 7 6 9 2 8 7 8 E + 0 3 A 1 ( 1 0 , 8 , 7 ) = - . 1 9 1 1 8 7 9 9 9 5 4 6 5 3 E + 0 3 A 1 ( 1 0 , 8 , 8 ) = . 7 4 2 2 5 4 1 1 4 1 5 1 0 0 3 + 0 1 A 1 ( 1 0 , 8 , 9 ) = - . 2 2 3 5 5 6 9 4 7 7 0 8 1 B E + 0 1 A 1 ( 1 0 , 8 , 1 0 ) = . 1 9 5 1 2 1 7 6 5 1 3 6 7 2 E - 0 2 A 1 ( 1 0 , 9 , 1 ) = - . 1 2 4 0 6 4 3 7 8 1 9 2 4 2 8 + 0 5 A 1 ( 1 0 , 9 , 2 ) = . 2 1 9 0 8 0 7 8 0 7 4 7 8 3 E + 0 5 A 1 ( 1 0 , 9 , 3 ) = - . 4 4 0 3 5 3 4 5 2 2 1 5 1 9 E + 0 5 A 1 ( 1 0 , 9 , 4 ) = . 1 7 3 7 5 8 1 5 7 9 4 3 4 9 E + 0 5 A 1 ( 1 0 , 9 , 5 ) = - . 1 8 6 1 8 6 5 1 8 2 1 1 3 6 E + 0 5 A 1 ( 1 0 , 9 , 6 ) = . 3 1 6 5 2 1 7 1 1 8 9 1 8 9 E + 0 4 A 1 ( 1 0 , 9 , 7 ) = - . 1 7 9 1 1 5 8 5 1 9 2 6 8 0 8 + 0 4 A 1 ( 1 0 , 9 , 8 ) = . 1 3 5 5 7 9 3 3 1 1 5 9 5 9 E + 0 3 A 1 ( 1 0 , 9 , 9 ) = - . 2 8 6 5 2 2 7 5 0 8 5 4 4 9 E + 0 2 n — V t V m V w V o m V m V q V m V m V o V w V m w b m m q m m o w w V V V V V V V V V V V w V o m V m V q V m V m V o V H V w V w p m m q m m o w w V V V V V V V V V V w V b n V a V m V d V a V m V A 1 ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 , 1 S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 , 1 S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 . S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 . S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 . S ( 1 0 . S ( 1 0 , S ( 1 0 , 3 4 3 9 , 1 0 ) = . 7 6 9 6 2 2 8 0 2 7 3 4 3 8 E + 0 0 I 1 ) = 1 ) = 1 ) = 1 ) = - 1 ) = - 1 ) = - 1 ) = - 1 ) = - 1 ) = - 1 ) = - 2 ) = 2 ) = - 2 ) = 2 ) = 2 ) = 2 ) = 2 ) = 2 ) = 2 ) = 2 ) = 3 ) = 3 ) = 3 ) = - 3 ) = 3 ) = 3 ) = 3 ) = 3 ) = 3 ) = 3 ) = 4 ) = 4 ) = 4 ) = 4 ) = 4 ) = - 4 ) = - 4 ) = 4 ) - 4 ) = 4 ) = 5 ) = 5 ) = 5 ) = 5 ) = - 5 ) = - 5 ) = 5 ) = 5 ) = - 5 ) = . 7 6 7 7 5 1 2 2 0 0 7 1 3 6 3 - 0 1 . 6 0 9 0 4 5 4 6 3 8 2 0 6 0 E - 0 1 . 3 1 9 6 4 7 0 3 3 4 3 0 5 0 E - 0 1 . 1 0 7 6 7 9 7 6 5 6 9 7 8 0 8 - 0 1 . 6 8 4 6 7 5 3 8 1 8 7 3 8 4 E - 0 1 . 1 4 2 9 7 4 6 5 4 1 6 0 4 3 E + 0 0 . 2 3 7 2 2 3 3 4 8 7 3 1 8 6 E + 0 0 . 3 5 6 1 9 8 6 3 5 0 4 1 4 3 E + 0 0 . 5 0 9 5 6 3 5 3 5 6 5 7 8 7 E + 0 0 . 7 2 2 0 2 6 0 3 0 0 7 9 7 7 E + 0 0 . 1 9 9 6 7 7 7 5 4 2 5 2 2 6 8 - 0 1 . 1 2 0 5 8 1 4 4 0 5 2 6 6 4 E - 0 1 . 2 7 3 2 6 2 1 0 4 6 1 8 3 8 8 - 0 3 . 1 0 8 9 7 3 8 2 7 3 3 6 9 7 8 - 0 1 . 1 4 1 9 1 1 8 7 2 1 6 0 6 6 E - O l . 1 5 9 5 3 8 0 6 7 0 4 5 9 3 E - 0 2 . 5 3 9 2 2 5 5 1 2 6 6 7 4 7 8 - 0 1 . 1 7 1 5 8 9 1 4 0 6 6 7 6 Z E + 0 0 . 4 0 8 2 3 0 7 4 1 0 2 0 9 9 E + 0 0 . 8 9 4 5 0 0 0 3 5 6 6 5 2 5 8 + 0 0 . 8 0 0 9 0 2 0 6 3 1 7 8 7 9 8 - 0 2 . 3 4 5 2 1 9 6 0 8 1 2 7 2 9 8 - 0 2 . 1 9 4 8 1 0 8 0 1 8 7 0 3 9 E - 0 2 . 4 2 7 5 4 1 8 1 9 5 6 9 9 9 8 - 0 2 . 1 5 5 2 4 5 9 9 5 0 6 2 0 0 8 - 0 3 . 9 6 4 6 0 1 0 4 4 5 5 4 3 4 E - 0 2 . 1 2 8 4 1 7 0 9 8 9 2 2 2 9 3 - 0 1 . 3 1 1 1 5 1 0 7 9 0 7 1 5 9 3 - 0 1 . 2 3 6 6 6 0 0 8 6 3 6 3 4 9 E + 0 0 . 9 7 0 9 1 0 7 7 7 5 9 7 8 7 E + 0 0 . 5 5 9 7 7 8 2 5 3 3 2 6 7 5 8 - 0 2 . 1 5 3 4 0 0 2 1 4 4 6 3 1 0 8 - 0 2 . 2 1 5 4 4 1 4 7 4 8 9 3 6 3 8 - 0 2 . 1 7 9 9 9 2 1 2 1 0 4 4 6 6 8 - 0 2 . 2 8 0 8 3 0 1 7 1 5 8 4 4 6 3 - 0 2 . 4 9 2 3 0 8 0 2 5 5 1 9 3 3 8 - 0 2 . 7 8 1 6 9 9 2 4 6 9 9 6 5 5 E ‘ 0 2 . 3 2 1 5 2 0 3 2 5 7 3 2 0 2 E - 0 1 . 5 0 9 5 9 7 0 4 9 0 2 0 6 4 E - 0 1 . 9 9 8 1 1 5 5 0 2 8 7 4 0 7 E + 0 0 . 9 7 3 9 5 6 6 3 2 8 2 8 9 4 8 - 0 2 . 4 7 8 0 5 0 4 5 2 3 4 8 8 6 E - 0 4 . 4 1 1 8 1 7 6 1 8 4 2 2 5 3 8 - 0 2 . 1 8 9 2 0 5 4 4 0 9 5 8 7 5 8 - 0 2 . 4 9 3 6 7 0 2 7 4 0 2 9 3 7 3 - 0 2 . 8 1 3 1 0 3 4 5 1 5 6 8 1 3 8 - 0 2 . 8 1 8 1 9 3 0 5 2 6 1 5 4 5 E - 0 2 . 5 6 3 6 8 2 5 1 2 6 4 3 7 6 8 - 0 1 . 5 8 8 2 3 7 1 5 5 2 4 7 1 6 8 - 0 1 H N w p m m q o o o x o a - I r p m m q m m o H N w p m m q m m o I — I w w o m m q m o \ s ( 1 0 , 1 0 S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 , s ( 1 0 , s ( 1 0 , S ( 1 0 , s ( 1 0 , s ( 1 0 , 1 s ( 1 0 , S ( 1 0 , s ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 , s ( 1 0 , S ( 1 0 , s ( 1 0 , s ( 1 0 , 1 s ( 1 0 , s ( 1 o . S ( 1 0 , s ( 1 0 . S ( 1 0 , S ( 1 0 , S ( 1 0 , s ( 1 0 , s ( 1 0 , s ( 1 0 , 1 S ( 1 0 , s ( 1 0 . s ( 1 0 , S ( 1 0 , S ( 1 0 , s ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 , s ( 1 0 , 1 0 K ( 1 0 ) = M ( 1 0 ) = w s ( 1 o , w s ( 1 0 , w s ( 1 0 , w s ( 1 o , w s ( 1 o , w s ( 1 0 , w s < 1 0 , I V I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I 9 1 1 2 3 9 ) = - 9 ) = - 9 ) = 3 4 4 . 9 9 6 5 3 8 7 9 0 6 7 2 6 6 E + 0 0 . 9 7 8 2 9 5 3 7 1 9 4 1 9 7 E - 0 2 . 1 0 6 1 9 9 0 8 1 6 3 2 2 1 E - 0 2 . 3 5 2 4 2 5 2 1 1 9 5 2 0 6 E - 0 2 . 3 5 9 3 0 2 6 7 9 0 0 0 0 2 8 - 0 2 . 1 7 2 7 7 7 6 8 2 4 4 4 6 9 2 - 0 2 . 1 0 1 0 4 5 3 5 8 6 6 4 9 3 8 - 0 1 . 1 0 7 8 6 5 4 0 8 2 6 3 7 8 E - 0 1 . 2 8 4 8 7 3 6 7 8 0 4 4 4 7 8 - 0 1 . 2 0 4 9 2 3 5 2 9 4 0 2 0 9 E + 0 0 . 9 7 8 1 8 7 7 2 0 4 5 5 3 6 E + 0 0 . 9 9 1 1 9 9 1 4 1 1 8 7 2 4 E - 0 2 . 2 0 6 7 5 5 5 1 5 6 1 6 2 6 E - 0 2 . 2 6 3 1 5 8 3 4 8 0 5 8 9 9 3 - 0 2 . 4 4 7 4 9 5 5 4 4 6 0 4 7 4 E - 0 2 ‘ . 1 8 3 9 5 9 8 8 5 9 6 5 3 6 E - 0 2 . 6 8 2 9 1 9 7 7 2 1 7 9 4 9 E - 0 2 . 2 0 6 4 2 4 2 3 5 0 0 9 5 5 8 - 0 1 . 2 6 2 1 5 7 8 4 4 3 8 7 4 9 E - 0 1 . 6 1 2 6 9 2 7 0 9 6 2 2 1 7 3 - 0 1 . 9 9 7 4 7 3 4 1 0 4 4 8 9 Z E + 0 0 . 1 4 7 8 8 4 9 7 0 2 5 2 0 1 8 - 0 1 . 4 3 7 6 7 7 1 4 5 2 4 2 6 8 8 - 0 2 . 2 2 4 0 9 9 6 4 4 8 4 2 3 9 E - 0 2 . 6 6 3 5 9 3 0 7 6 9 8 7 5 9 E - 0 2 . 6 9 6 2 5 8 2 3 9 4 0 9 1 5 3 - 0 2 . 7 5 0 3 9 7 9 1 4 8 6 3 1 3 E - 0 3 . 2 4 3 7 1 0 4 2 3 2 2 9 1 8 8 - 0 1 . 8 1 3 4 3 9 7 7 1 8 3 6 2 5 E - 0 1 . 2 2 5 4 4 3 2 8 3 3 2 3 0 1 E + 0 0 . 9 7 0 3 7 5 4 8 4 8 5 6 8 1 E + 0 0 . 1 0 9 5 4 7 0 0 5 7 8 3 9 6 8 - 0 1 . 1 4 4 8 4 3 7 8 7 3 9 8 2 3 8 - 0 2 . 4 7 9 0 5 4 7 6 5 1 2 8 4 0 E - 0 2 . 5 5 1 7 9 5 5 0 6 6 1 2 6 1 E - 0 3 . 7 2 4 1 2 8 1 2 8 4 3 4 3 3 3 ‘ 0 2 . 7 7 9 9 0 8 4 2 9 3 9 2 3 3 8 - 0 3 . 2 4 6 0 5 7 8 1 3 2 2 7 0 9 E - 0 1 . 1 7 8 5 9 7 4 3 4 5 1 8 8 2 3 - 0 1 . 2 3 1 8 7 5 2 0 5 9 2 0 2 6 E + 0 0 . 9 7 2 1 6 8 2 3 2 5 0 6 5 1 E + 0 0 = - . 1 6 6 0 1 2 3 3 2 4 2 8 2 0 E - 0 6 = - . 3 3 3 3 3 3 0 8 2 0 2 2 1 9 E + 0 0 ) = ' . 4 9 9 9 9 9 4 1 7 2 1 8 4 4 E + 0 0 4 ) = ’ . 6 0 0 0 0 2 9 4 7 4 9 6 6 4 E + 0 0 5 ) = - . 7 1 4 2 8 2 0 6 0 7 1 7 3 7 E + 0 0 6 ) = * . 7 5 0 0 1 0 4 5 2 6 2 4 0 3 3 + 0 0 7 ) = - . 7 7 7 7 7 0 1 2 5 0 6 0 1 7 E + 0 0 V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V w s ( 1 0 , w s ( 1 0 , A 1 ( 1 1 , A 1 ( 1 1 , A 1 ( 1 1 , A 1 ( 1 1 , A 1 ( 1 1 , A 1 ( 1 1 , A 1 ( 1 1 , A 1 ( 1 1 , A 1 ( 1 1 , A 1 ( 1 1 , A 1 ( 1 1 , A 1 ( 1 1 , A 1 ( 1 1 , A 1 ( 1 1 , A 1 ( 1 1 , A 1 ( 1 1 , A 1 ( 1 1 , A 1 ( 1 1 , A 1 ( 1 1 , A 1 ( 1 1 , A 1 ( 1 1 , A 1 ( 1 1 , A 1 ( 1 1 , A 1 ( 1 1 , A 1 ( 1 1 , A 1 ( 1 1 , A 1 ( 1 1 , A 1 ( 1 1 , A 1 ( 1 1 , A 1 ( 1 1 , A 1 ( 1 1 , A 1 ( 1 1 , A 1 ( 1 1 , A 1 ( 1 1 , A 1 ( 1 1 , A 1 ( 1 1 , A 1 ( 1 1 , A 1 ( 1 1 , A 1 ( 1 1 , A 1 ( 1 1 , A 1 ( 1 1 , A 1 ( 1 1 , A 1 ( 1 1 , A 1 ( 1 1 , A 1 ( 1 1 , A 1 ( 1 1 , A 1 ( 1 1 , A 1 ( 1 1 , 8 9 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 3 4 5 : . 8 0 0 0 0 1 7 9 4 0 5 5 8 4 E + 0 0 . 6 6 6 6 6 3 4 6 4 8 2 7 3 1 E + 0 0 1 ) = “ . 3 8 2 6 7 1 0 9 8 7 7 8 9 6 E + 0 2 2 ) = ” . 9 0 7 9 6 2 2 1 6 8 9 4 5 2 8 + 0 2 - . 8 9 5 8 1 0 5 4 1 6 1 7 6 B E + 0 2 . 7 1 3 0 5 2 7 0 6 5 9 9 7 O E + 0 2 . 1 1 8 7 4 7 0 8 0 6 8 7 7 8 8 + O 3 . 1 0 8 6 6 5 5 0 9 2 9 2 8 6 8 + 0 3 . 4 7 0 8 5 7 4 5 9 8 3 6 4 1 E + 0 2 . 1 3 6 9 6 8 5 5 2 4 5 1 5 8 E + 0 2 . 2 0 8 4 5 4 5 4 3 1 6 5 8 6 8 + 0 1 . 1 6 5 6 2 9 2 7 5 1 4 3 1 5 E + 0 0 . 3 8 7 4 7 7 8 7 4 7 5 5 8 6 8 - 0 2 . 5 2 6 0 1 5 3 1 0 7 6 4 3 1 E + 0 3 . 1 2 4 7 2 3 3 2 5 6 3 2 7 9 E + 0 4 . 1 3 5 5 1 7 7 0 3 1 8 6 9 1 8 + 0 4 . 9 4 2 2 3 1 6 2 7 1 4 7 6 4 E + 0 3 . 1 7 8 0 4 8 7 3 3 7 6 5 6 3 E + 0 4 . 1 7 6 8 9 2 3 7 9 2 0 9 0 3 E + 0 4 . 8 5 0 1 6 7 3 5 0 6 1 1 6 5 E + 0 3 . 2 7 0 3 2 0 9 3 1 2 7 0 7 2 E + 0 3 . 4 6 7 0 9 1 4 9 0 3 2 8 3 1 8 + 0 2 . 4 1 5 3 5 4 8 9 5 5 9 1 7 4 E + 0 1 . 9 9 5 1 9 7 2 9 6 1 4 2 5 8 E - 0 1 . 3 7 2 5 9 3 0 1 5 5 6 6 4 7 E + 0 4 . 8 6 8 3 2 5 9 3 2 7 0 7 2 7 E + 0 4 . 9 1 7 4 8 8 7 0 9 0 2 0 6 1 E + 0 4 . 6 6 3 7 9 5 1 2 5 2 6 6 1 6 E + 0 4 . 1 2 0 7 5 9 3 5 5 7 1 0 7 4 E + 0 5 . 1 1 7 4 0 3 9 7 9 0 0 7 6 0 8 + 0 5 . 5 6 8 4 0 8 4 3 3 9 7 2 3 0 8 + 0 4 . 1 8 4 0 0 1 0 3 9 8 3 8 7 9 E + 0 4 . 3 3 8 0 3 7 6 4 6 0 5 5 2 2 8 + 0 3 . 3 2 5 1 1 0 7 2 1 5 8 8 1 3 E + 0 2 . 9 2 7 9 7 8 5 1 5 6 2 5 0 0 E + 0 0 . 9 1 6 3 0 9 6 9 7 7 8 2 9 9 E + 0 4 . 2 1 0 4 1 2 9 5 6 6 9 6 9 7 E + 0 5 . 2 2 7 8 0 4 7 3 7 2 7 1 6 7 E + 0 5 - . 1 6 0 6 1 9 5 0 2 3 0 3 6 O E + 0 5 - . 3 0 1 5 2 4 5 9 0 3 2 8 9 3 E + 0 5 - . 2 8 8 3 1 8 4 3 5 2 9 9 4 O E + 0 5 - . 1 4 0 7 1 7 3 8 1 9 1 6 9 4 E + 0 5 - . 4 4 6 0 4 8 5 5 8 8 0 7 3 7 E + 0 4 . 8 4 0 3 8 8 2 9 3 2 6 6 3 0 E + 0 3 . 8 3 0 2 4 0 3 4 5 0 0 1 2 2 E + 0 2 = - . 2 7 6 8 4 6 3 1 3 4 7 6 5 6 E + 0 1 = - . 2 8 2 4 5 3 6 4 8 2 4 6 8 2 E + 0 3 = - . 3 2 9 0 5 4 3 3 2 8 2 4 9 S E + 0 3 . 5 7 1 6 9 1 3 0 7 0 1 1 0 6 E + 0 3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) : ) ) ) ) ) ) ) ) ) ) ) ) ) ) = ) = ) ) l _ ; ) . 2 5 5 9 4 7 0 8 7 7 7 8 7 l E + 0 3 3 4 6 A 1 ( 1 1 , 5 , 5 ) = . 8 5 5 2 5 9 4 7 4 9 1 9 1 8 8 + 0 3 A 1 ( 1 1 , 5 , 6 ) = . 5 1 1 1 3 8 1 0 0 5 9 2 4 2 E + 0 3 A 1 ( 1 1 , 5 , 7 ) = . 3 8 3 9 7 0 1 9 9 9 6 9 6 O E + 0 3 A 1 ( 1 1 , 5 , 8 ) = . 8 0 1 3 0 3 4 6 9 8 3 6 7 l E + 0 2 A 1 ( 1 1 , 5 , 9 ) = . 2 2 8 5 6 1 9 1 3 2 2 2 0 7 E + 0 2 A 1 ( 1 1 , 5 , 1 0 ) = . 1 4 1 7 0 6 6 2 7 6 0 7 3 S E + 0 1 A 1 ( 1 1 , 5 , 1 1 ) = . 9 0 4 8 7 4 8 0 1 6 3 5 7 4 8 - 0 1 A 1 ( 1 1 , 6 , 1 ) = - . 7 2 7 0 0 6 7 5 9 9 0 5 8 2 8 + 0 4 A 1 ( 1 1 , 6 , 2 ) = - . 1 2 0 0 2 4 3 5 6 3 9 8 6 6 8 + 0 5 A 1 ( 1 1 , 6 , 3 ) = - . 1 6 2 4 6 4 l 4 7 0 9 3 5 9 E + 0 5 A 1 ( 1 1 , 6 , 4 ) = . 9 2 9 0 1 5 1 3 5 2 1 6 7 1 E + 0 4 A 1 ( 1 1 , 6 , 5 ) = . 2 2 9 7 3 7 3 6 2 6 1 8 4 S E + 0 5 A 1 ( 1 1 , 6 , 6 ) = . 1 7 1 0 2 1 8 6 2 2 1 9 5 7 E + 0 5 A 1 ( 1 1 , 6 , 7 ) = . 1 0 6 3 7 2 7 2 7 3 9 8 2 0 3 + 0 5 A 1 ( 1 1 , 6 , 8 ) = . 2 6 1 5 7 0 2 1 7 4 4 2 5 1 E + 0 4 A 1 ( 1 1 , 6 , 9 ) = . 6 4 4 1 7 3 1 4 3 3 8 6 8 4 E + 0 3 A 1 ( 1 1 , 6 , 1 0 ) = . 4 5 4 9 5 5 7 3 0 4 3 8 2 3 E + 0 2 A 1 ( 1 1 , 6 , 1 1 ) = . 2 6 0 0 6 4 6 9 7 2 6 5 6 3 E + 0 1 A 1 ( 1 1 , 7 , 1 ) = . 2 1 0 5 9 7 6 4 8 3 6 4 3 l E + 0 4 A 1 ( 1 1 , 7 , 2 ) = . 4 6 6 3 4 8 9 9 0 5 6 7 4 O E + 0 4 A 1 ( 1 1 , 7 , 3 ) = . 5 1 3 5 6 5 4 9 6 4 9 6 1 1 £ + 0 4 A 1 ( 1 1 , 7 , 4 ) = - . 3 5 6 3 4 6 4 9 1 9 1 5 7 3 8 + 0 4 A 1 ( 1 1 , 7 , 5 ) = - . 6 8 4 1 9 7 8 1 6 6 3 4 9 2 E + 0 4 A 1 ( 1 1 , 7 , 6 ) = * . 6 4 0 3 4 5 0 8 9 7 3 9 5 6 E + 0 4 A 1 ( 1 1 , 7 , 7 ) = * . 3 2 0 7 1 3 7 9 9 9 8 0 2 8 E + 0 4 A 1 ( 1 1 , 7 , 8 ) = - . 9 8 9 4 7 5 6 7 1 5 8 9 3 7 E + 0 3 A 1 ( 1 1 , 7 , 9 ) = - . 1 9 0 4 3 8 5 8 9 6 9 2 1 2 8 + 0 3 A 1 ( 1 1 , 7 , 1 0 ) = - . 1 8 3 2 5 7 3 9 3 8 3 6 9 8 E + 0 2 A 1 ( 1 1 , 7 , 1 1 ) = - . 7 0 5 4 1 3 8 1 8 3 5 9 3 8 8 + 0 0 A 1 ( 1 1 , 8 , 1 ) = . 2 2 7 0 6 2 5 9 3 5 8 2 2 7 E + 0 4 A 1 ( 1 1 , 8 , 2 ) = . 4 3 5 3 5 6 7 5 3 6 4 4 7 Z E + 0 4 A 1 ( 1 1 , 8 , 3 ) = . 5 2 8 7 7 0 2 0 7 9 1 8 4 4 E + 0 4 A 1 ( 1 1 , 8 , 4 ) = - . 3 3 4 3 3 4 2 6 5 2 8 7 9 7 E + 0 4 A 1 ( 1 1 , 8 , 5 ) = - . 7 2 6 1 6 1 2 3 6 3 3 0 1 Z E + 0 4 A 1 ( 1 1 , 8 , 6 ) = - . 6 0 9 1 5 8 8 8 2 7 9 9 7 4 E + 0 4 A 1 ( 1 1 , 8 , 7 ) = “ . 3 3 7 9 0 6 2 7 1 4 8 8 9 G E + 0 4 A 1 ( 1 1 , 8 , 8 ) = - . 9 3 5 0 5 5 7 7 9 5 7 6 3 O E + 0 3 A 1 ( 1 1 , 8 , 9 ) = - . 2 0 4 3 2 7 0 1 2 6 5 8 1 2 8 + 0 3 A 1 ( 1 1 , 8 , 1 0 ) = - . 1 6 4 0 4 8 6 3 8 3 4 3 8 1 E + 0 2 A 1 ( 1 1 , 8 , 1 1 ) = ' . 8 2 8 2 5 4 6 9 9 7 0 7 0 3 8 + 0 0 A 1 ( 1 1 , 9 , 1 ) = . 1 7 8 5 8 7 1 2 9 7 5 5 0 2 8 + 0 5 A 1 ( 1 1 , 9 , 2 ) = . 3 7 5 1 9 0 3 7 8 2 3 1 7 0 E + 0 5 A 1 ( 1 1 , 9 , 3 ) = . 4 2 9 6 2 3 6 6 0 5 8 3 5 0 E + 0 5 A 1 ( 1 1 , 9 , 4 ) = - . 2 8 7 4 8 7 8 1 1 3 3 7 1 1 3 + 0 5 A 1 ( 1 1 , 9 , 5 ) = - . 5 7 9 4 1 2 3 6 9 0 1 9 9 9 E + 0 5 A 1 ( 1 1 , 9 , 6 ) = ‘ . 5 1 7 9 3 1 0 1 2 3 9 5 6 Z E + 0 5 A 1 ( 1 1 , 9 , 7 ) = - . 2 7 0 3 2 2 0 2 6 6 9 5 9 I E + 0 5 A 1 ( 1 1 , 9 , 8 ) = - . 8 0 0 5 2 0 8 6 9 3 0 2 7 S E + 0 4 A 1 ( 1 1 , 9 , 9 ) = - . 1 6 1 5 9 9 7 1 5 8 0 5 0 5 3 + 0 4 A 1 ( 1 1 , 9 , 1 0 ) = ’ . 1 4 4 0 1 9 5 9 9 9 1 4 5 5 8 + 0 3 Q H H H H H H H H H H H H N H N N N N N N N N N N s W — n — w s w w w w w w w w w b h b D # # 0 # # 9 9 1 0 1 I a r 0 H 1 0 1 0 1 0 A 1 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , - A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( l l , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( l l , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , H H H l V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V 3 4 7 - . 6 4 0 3 1 9 8 2 4 2 1 8 7 5 E + 0 1 . 1 8 7 9 3 3 7 7 1 4 6 2 8 6 E + 0 0 . 1 8 3 1 2 6 7 1 0 1 6 7 1 0 E + 0 0 . 1 7 4 3 8 1 2 5 5 6 5 9 7 l E + 0 0 . 1 6 1 5 1 7 9 2 6 1 6 8 2 1 E + 0 0 . 1 4 4 2 5 2 5 2 6 2 5 7 1 5 8 + 0 0 . 1 2 2 1 5 4 7 8 1 7 8 5 1 5 8 + 0 0 . 9 4 5 7 4 2 4 1 0 8 2 7 2 4 8 - 0 1 . 6 0 4 9 6 3 7 8 3 3 4 8 1 3 8 - 0 1 . 1 8 1 9 7 0 3 2 2 5 4 7 2 8 8 - 0 1 . 3 5 8 9 0 2 1 1 8 0 1 9 7 3 3 - 0 1 . 1 1 2 3 7 6 5 7 2 4 3 4 9 2 E + 0 0 . 1 8 3 1 2 6 7 1 0 1 6 7 1 0 8 + 0 0 . 1 7 8 5 5 8 4 4 5 2 8 6 8 7 E + 0 0 . 1 7 0 2 4 7 4 3 1 9 1 7 9 4 E + 0 0 . 1 5 8 0 2 3 1 0 3 5 6 8 9 Z E + 0 0 . 1 4 1 6 1 5 3 8 2 8 6 5 3 9 E + 0 0 . 1 2 0 6 1 5 3 6 9 3 5 6 9 6 E + 0 0 . 9 4 4 0 4 9 1 9 6 0 1 4 5 8 8 - 0 1 . 6 2 0 1 9 9 7 6 0 0 0 4 1 8 8 - 0 1 . 2 1 8 2 1 6 3 8 8 6 7 0 4 6 8 - 0 1 . 2 9 5 8 5 4 1 1 6 7 0 6 8 0 E - 0 1 . 1 0 2 3 2 8 9 5 4 0 0 0 9 6 E + 0 0 . 1 7 4 3 8 1 2 5 5 6 5 9 7 1 E + 0 0 . 1 7 0 2 4 7 4 3 1 9 1 7 9 4 E + 0 0 . 1 6 2 7 2 6 7 9 5 1 6 4 8 2 E + 0 0 . 1 5 1 6 6 4 9 9 8 4 3 5 8 5 E + 0 0 . 1 3 6 8 1 7 6 4 9 2 7 5 2 3 E + 0 0 . 1 1 7 8 1 4 7 3 2 2 8 2 9 6 E + 0 0 . 9 4 0 9 6 8 8 2 2 1 5 0 6 0 8 - 0 1 . 6 4 7 9 1 8 5 8 0 5 0 2 4 1 8 - 0 1 . 2 8 4 1 5 8 7 6 1 0 8 2 3 5 3 - 0 1 . 1 8 1 1 5 1 1 1 6 2 0 3 9 6 3 - 0 1 . 8 4 0 4 9 3 6 3 2 1 7 2 8 4 E - 0 1 . 1 6 1 5 1 7 9 2 6 1 6 8 2 l E + 0 0 . 1 5 8 0 2 3 1 0 3 5 6 8 9 Z E + 0 0 . 1 5 1 6 6 4 9 9 8 4 3 5 8 5 E + 0 0 . 1 4 2 3 1 3 1 2 0 4 2 2 2 8 8 + 0 0 . 1 2 9 7 6 0 8 5 5 9 3 5 6 S E + 0 0 . 1 1 3 6 9 5 3 8 3 9 5 6 1 0 8 + 0 0 . 9 3 6 4 3 7 9 3 6 1 1 6 7 2 8 - 0 1 . 6 8 8 6 8 8 9 3 0 1 0 7 6 9 8 - 0 1 . 3 8 1 1 5 0 5 2 0 6 3 9 4 2 E - 0 1 . 1 2 4 3 9 4 0 5 7 4 8 0 8 2 E - 0 2 . 5 7 1 6 2 6 9 3 5 8 2 3 6 6 8 - 0 1 . 1 4 4 2 5 2 5 2 6 2 5 7 1 5 8 + 0 0 . 1 4 1 6 1 5 3 8 2 8 6 5 3 9 E + 0 0 . 1 3 6 8 1 7 6 4 9 2 7 5 2 3 E + 0 0 . 1 2 9 7 6 0 8 5 5 9 3 5 6 5 E + 0 0 . 1 2 0 2 8 9 0 9 6 7 4 6 3 4 E + 0 0 ‘ v l l o v l J l v fl \ l v l m v fl m l v l o fl v I fl l v — l v v l l I v fl — l v l t fl v a I v I w I v I m I v ‘ I o o v I — I u — q I v o m v I l m l v l o v l H u v l w l v m fl l v w l v fl b fl m v l ‘ v l l o l v a q l — v l I m l H v l m l v o l v l a l v I — I v I I H v I I h v I I t v I m I v I m U I q I - — I . m . I . s w H I I v o ' H v I I H v I w v I I w I v I o v I m I m v I I v q I I v m I m v I I o v I H v " A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 l , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 . A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 l , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( l l , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , 3 4 8 . 1 0 8 1 6 6 3 1 8 0 4 7 2 7 E + 0 0 . 9 3 0 3 5 6 4 9 6 3 1 1 4 8 E - 0 1 . 7 4 3 4 1 1 6 5 0 5 7 7 3 5 3 - 0 1 . 5 1 1 3 3 4 6 6 2 2 6 8 0 9 8 - 0 1 . 2 1 4 0 0 8 5 8 6 6 9 7 3 9 3 - 0 1 . 2 1 0 7 4 9 0 6 0 1 9 9 9 9 8 - 0 1 . 1 2 2 1 5 4 7 8 1 7 8 5 1 5 E + 0 0 . 1 2 0 6 1 5 3 6 9 3 5 6 9 6 E + 0 0 . 1 1 7 8 1 4 7 3 2 2 8 2 9 6 E + 0 0 . 1 1 3 6 9 5 3 8 3 9 5 6 1 0 8 + 0 0 . 1 0 8 1 6 6 3 1 8 0 4 7 2 7 E + 0 0 . 1 0 1 0 8 9 7 3 4 3 0 7 6 7 E + 0 0 . 9 2 2 5 7 2 8 1 2 6 4 6 4 8 E - 0 1 . 8 1 3 4 5 0 3 1 4 5 4 5 9 6 E - 0 1 . 6 7 7 9 5 5 2 8 5 8 3 3 5 1 3 - 0 1 . 5 0 3 8 3 5 8 9 2 8 5 6 6 7 E - 0 1 . 2 5 1 1 3 3 0 7 1 8 0 5 9 2 E - 0 1 . 9 4 5 7 4 2 4 1 0 8 2 7 2 4 E - 0 1 . 9 4 4 0 4 9 1 9 6 0 1 4 5 7 8 - 0 1 . 9 4 0 9 6 8 8 2 2 1 5 0 6 0 E - 0 1 . 9 3 6 4 3 7 9 3 6 1 1 6 7 2 8 - 0 1 . 9 3 0 3 5 6 4 9 6 3 1 1 4 8 8 - 0 1 . 9 2 2 5 7 2 8 1 2 6 4 6 4 7 E - O l . 9 1 2 8 5 7 0 5 0 2 1 8 8 4 8 - 0 1 . 9 0 0 8 6 5 5 4 0 9 3 5 6 6 3 - 0 1 . 8 8 5 9 1 5 5 9 3 7 8 0 9 3 E - 0 1 . 8 6 5 5 7 1 9 1 3 9 8 0 8 7 8 - 0 1 . 8 2 7 6 1 2 7 5 8 5 8 7 9 4 3 - 0 1 . 6 0 4 9 6 3 7 8 3 3 4 8 1 5 E - 0 1 . 6 2 0 1 9 9 7 6 0 0 0 4 1 8 3 - 0 1 . 6 4 7 9 1 8 5 8 0 5 0 2 4 1 8 - 0 1 . 6 8 8 6 8 8 9 3 0 1 0 7 6 9 E - 0 1 . 7 4 3 4 1 1 6 5 0 5 7 7 3 5 8 - 0 1 . 8 1 3 4 5 0 3 1 4 5 4 5 9 6 8 - 0 1 . 9 0 0 8 6 5 5 4 0 9 3 5 6 7 3 - 0 1 . 1 0 0 8 8 9 1 5 4 6 7 9 9 S E + 0 0 . 1 1 4 2 8 9 0 1 6 1 0 6 8 2 8 + 0 0 . 1 3 1 2 5 5 5 6 3 5 4 0 7 8 E + 0 0 . 1 5 3 9 9 3 9 0 3 3 9 5 7 0 E + 0 0 . 1 8 1 9 7 0 3 2 2 5 4 7 2 8 8 - 0 1 . 2 1 8 2 1 6 3 8 8 6 7 0 4 6 E - 0 1 . 2 8 4 1 5 8 7 6 1 0 8 2 3 5 8 - 0 1 . 3 8 1 1 5 0 5 2 0 6 3 9 4 1 3 - 0 1 . 5 1 1 3 3 4 6 6 2 2 6 8 0 8 8 - 0 1 . 6 7 7 9 5 5 2 8 5 8 3 3 5 1 8 - 0 1 . 8 8 5 9 1 5 5 9 3 7 8 0 9 2 3 - 0 1 . 1 1 4 2 8 9 0 1 6 1 0 6 8 2 8 + 0 0 . 1 4 6 1 7 4 2 4 1 5 4 7 5 5 8 + 0 0 . 1 8 6 7 2 2 0 1 5 6 5 6 6 1 E + 0 0 . 2 4 2 3 9 0 9 6 0 5 3 7 2 2 8 + 0 0 l — ‘ H V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V \ o m m m m m m m m m m m m m m m m m m m m m q \ I q q q q q q u q q m m m m m m m m m m m m m m m m m F H H 3 4 9 A 3 ( 1 1 , 1 0 , 1 ) = - . 3 5 8 9 0 2 1 1 8 0 1 9 7 3 E - 0 1 A 3 ( 1 1 , 1 0 , 2 ) = - . 2 9 5 8 5 4 1 1 6 7 0 6 8 1 E - 0 1 A 3 ( 1 1 , 1 0 , 3 ) = - . 1 8 1 1 5 1 1 1 6 2 0 3 9 5 8 - 0 1 A 3 ( 1 1 , 1 0 , 4 ) = - . 1 2 4 3 9 4 0 5 7 4 8 0 7 9 E - 0 2 A 3 ( 1 1 , 1 0 , 5 ) = . 2 1 4 0 0 8 5 8 6 6 9 7 3 9 E - 0 1 A 3 ( 1 1 , 1 0 , 6 ) = . 5 0 3 8 3 5 8 9 2 8 5 6 6 6 E - 0 1 A 3 ( 1 1 , 1 0 , 7 ) = . 8 6 5 5 7 1 9 1 3 9 8 0 8 6 E ~ 0 1 A 3 ( 1 1 , 1 0 , 8 ) = . 1 3 1 2 5 5 5 6 3 5 4 0 7 B E + 0 0 A 3 ( 1 1 , 1 0 , 9 ) = . 1 8 6 7 2 2 0 1 5 6 5 6 6 l E + 0 0 A 3 ( 1 1 , 1 0 , 1 0 ) = . 2 5 7 3 5 1 8 3 3 8 2 6 0 1 8 + 0 0 A 3 ( 1 1 , 1 0 , 1 1 ) = . 3 5 5 0 3 0 9 4 8 8 1 0 3 9 E + 0 0 A 3 ( 1 1 , 1 1 , 1 ) = . 1 1 2 3 7 6 5 7 2 4 3 4 9 2 E + 0 0 A 3 ( 1 1 , 1 1 , 2 ) = . 1 0 2 3 2 8 9 5 4 0 0 0 9 6 E + 0 0 A 3 ( 1 1 , 1 1 , 3 ) = . 8 4 0 4 9 3 6 3 2 1 7 2 8 4 8 - 0 1 A 3 ( 1 1 , 1 1 , 4 ) = . 5 7 1 6 2 6 9 3 5 8 2 3 6 7 8 - 0 1 A 3 ( 1 1 , 1 1 , 5 ) = . 2 1 0 7 4 9 0 6 0 2 0 0 0 0 3 - 0 1 A 3 ( 1 1 , 1 1 , 6 ) = . 2 5 1 1 3 3 0 7 1 8 0 5 9 1 8 - 0 1 A 3 ( 1 1 , 1 1 , 7 ) = . 8 2 7 6 1 2 7 5 8 5 8 7 9 4 8 - 0 1 A 3 ( 1 1 , 1 1 , 8 ) = . 1 5 3 9 9 3 9 0 3 3 9 5 7 0 E + 0 0 A 3 ( 1 1 , 1 1 , 9 ) = . 2 4 2 3 9 0 9 6 0 5 3 7 2 2 8 + 0 0 A 3 ( 1 1 , 1 1 , 1 0 ) = . 3 5 5 0 3 0 9 4 8 8 1 0 3 9 E + 0 0 A 3 ( 1 1 , 1 1 , 1 1 ) = . 5 1 1 3 8 8 1 0 1 5 3 3 7 6 E + 0 0 S ( 1 1 , 1 , 1 ) = - . 1 4 9 3 4 5 8 1 9 2 9 5 8 1 E - 0 1 S ( 1 1 , 2 , 1 ) = - . 9 5 4 0 3 5 7 7 6 6 4 7 3 9 E - 0 2 S ( 1 1 , 3 , 1 ) = - . 1 3 4 7 9 1 4 6 5 3 1 3 4 1 3 - 0 2 S ( 1 1 , 4 , 1 ) = . 6 8 9 9 8 1 9 0 2 1 7 1 5 3 3 - 0 2 S ( 1 1 , 5 , 1 ) = . 1 0 8 5 4 5 2 3 9 1 7 8 4 5 E - 0 1 S ( 1 1 , 6 , 1 ) = . 4 0 1 7 5 4 5 5 9 8 1 7 0 5 E - 0 2 S ( 1 1 , 7 , 1 ) = - . 2 3 2 5 8 4 4 8 5 9 4 2 6 2 3 - 0 1 S ( 1 L 8 , 1 ) = . 8 5 7 0 8 8 1 7 7 4 8 0 0 3 E - 0 1 S ( l l , 9 , 1 ) = - . 2 0 7 3 9 5 3 1 2 0 9 6 1 5 E + 0 0 S ( 1 1 , 1 0 , 1 ) = . 4 3 2 9 5 0 6 7 7 7 1 2 6 S E + 0 0 S ( 1 1 , 1 1 , 1 ) = . 8 7 2 4 4 2 8 3 0 4 5 6 8 9 E + 0 0 S ( 1 1 , 1 , 2 ) = . 5 0 6 8 7 7 4 8 5 4 0 6 2 0 E - 0 2 S ( 1 1 , 2 , 2 ) = . 2 4 2 8 0 8 8 4 8 9 1 3 9 7 3 - 0 2 S ( 1 L 3 , 2 ) = - . 8 5 0 2 3 1 1 5 8 6 0 6 6 3 E - 0 3 S ( 1 1 , 4 , 2 ) = “ . 2 6 6 5 6 0 4 8 1 3 8 7 6 3 E - 0 2 S ( 1 L 5 , 2 ) = . 1 0 5 0 6 2 6 3 7 3 5 3 1 6 8 - 0 2 S ( l L 6 , 2 ) = . 4 2 5 3 5 5 0 0 2 6 4 7 1 7 8 - 0 2 S ( 1 1 , 7 , 2 ) = . 8 8 3 1 3 9 2 1 6 7 9 2 0 4 8 - 0 2 S ( 1 1 , 8 , 2 ) = . 2 3 4 3 3 0 2 4 0 8 9 1 3 3 E - 0 2 S ( 1 1 , 9 , 2 ) = . 6 8 1 8 2 9 1 6 8 5 6 6 4 7 8 - 0 1 S ( 1 1 , 1 0 , 2 ) = . 2 8 7 2 9 6 9 2 8 2 6 6 O S E + 0 0 S ( 1 1 , 1 1 , 2 ) = - . 9 5 5 3 3 7 3 5 7 8 8 2 6 1 8 + 0 0 S ( l l , 1 , 3 ) = . 2 7 0 8 3 3 4 3 1 2 9 3 0 8 E - 0 2 S ( l l , 2 , 3 ) = . 9 0 1 6 8 0 2 8 7 0 4 3 2 0 8 - 0 3 S ( l l , 3 , 3 ) = - . 8 8 2 2 9 7 1 4 0 9 5 6 1 6 8 - 0 3 S ( l l , 4 , 3 ) = “ . 1 0 6 0 8 3 9 6 6 8 9 9 6 7 3 - 0 2 S ( l l , 5 , 3 ) = . 7 8 1 2 1 6 6 0 0 6 6 6 1 5 E - 0 3 S ( l l , 6 , 3 ) = . 2 5 1 1 9 8 5 9 0 9 7 4 5 9 E - 0 2 H N W D ‘ U ‘ O Q D C D \ N J U F O I U ‘ O Q D C O \ w m w o ‘ m m - q m “ o \ “ “ “ “ ~ ‘ ~ “ “ ‘ 3 5 0 3 ) = ’ . 6 5 0 8 1 7 4 6 5 0 7 1 0 8 E - 0 3 3 ) = - . 1 1 4 1 6 5 3 7 8 5 6 4 3 1 E - 0 1 3 ) = - . 9 8 6 0 5 4 3 5 8 3 3 3 0 7 E - 0 2 3 ) = . 1 2 4 9 0 4 9 0 8 8 0 4 3 6 E + 0 0 3 ) = . 9 9 2 0 4 5 2 6 1 1 8 1 7 O B + 0 0 4 ) = ‘ . 2 8 2 0 9 2 8 4 9 4 9 1 5 l E - 0 2 4 ) = - . 5 5 7 6 8 4 3 3 7 2 6 4 9 8 E - 0 3 4 ) = . 1 1 4 3 7 1 1 9 7 6 7 9 9 9 8 - 0 2 4 ) = . 4 8 3 9 3 4 7 4 5 8 5 1 1 1 8 - 0 3 4 ) = - . 1 5 5 5 3 2 8 6 2 2 1 2 4 4 E - 0 2 4 ) = - . 9 5 7 0 5 7 8 2 6 3 9 2 2 3 E - 0 3 4 ) = . 4 4 8 3 6 7 7 4 8 1 9 3 1 5 8 - 0 2 4 ) = . 4 0 3 8 7 9 4 2 5 3 7 0 9 8 E - 0 2 4 ) = - . 3 0 5 2 4 6 6 8 1 3 0 0 5 0 E - 0 1 4 ) = - . 4 8 5 4 2 0 0 4 5 6 4 1 3 S E - 0 1 4 ) = . 9 9 8 3 2 9 7 8 3 8 2 8 7 B E + 0 0 5 ) = - . 2 2 2 7 0 3 4 6 1 9 3 8 4 B E - 0 1 5 ) = . 6 6 1 3 2 1 8 6 7 3 7 7 4 6 E - 0 2 5 ) = . 3 1 1 4 9 5 7 0 0 1 9 6 2 2 E - 0 2 5 ) = - . 9 2 4 1 1 2 1 7 9 2 0 2 3 7 E - 0 2 5 ) = . 9 3 5 4 1 1 7 5 4 1 3 9 7 2 E - 0 2 5 ) = . 8 5 1 9 7 4 9 6 6 5 2 2 7 3 8 - 0 3 5 ) = - . 2 7 4 9 4 8 3 5 8 0 3 8 8 5 E - 0 1 5 ) = . 7 6 9 0 4 2 6 1 8 5 8 4 4 9 8 - 0 1 . 1 4 1 3 8 9 1 3 5 7 7 2 7 4 E + 0 0 . 9 4 3 8 3 3 2 3 5 0 0 2 3 1 8 - 0 1 . 9 8 1 6 8 6 1 2 0 6 0 9 0 1 8 + 0 0 . 3 3 5 8 5 4 4 6 7 6 6 4 5 2 8 - 0 2 . 7 3 8 6 1 9 3 1 4 4 6 4 3 3 8 - 0 3 - . 8 0 7 6 1 4 1 5 6 6 4 4 6 8 8 - 0 3 . 1 4 2 2 0 5 9 7 0 7 0 4 1 7 8 - 0 2 . 6 7 3 8 2 6 6 6 1 4 6 5 6 0 8 - 0 3 . 1 7 2 3 5 9 9 6 1 1 2 5 4 3 E - 0 2 . 5 1 9 1 1 0 9 4 5 1 4 0 1 4 E - 0 2 . 6 0 8 9 3 5 7 7 5 1 4 3 7 1 3 - 0 2 “ . 1 0 9 3 5 5 9 7 6 4 1 5 7 7 8 - 0 1 . 1 2 1 1 4 4 3 3 2 9 9 5 4 4 E + 0 0 . 9 9 2 5 3 3 3 8 0 1 3 3 3 Z E + 0 0 . 2 1 5 1 2 6 3 8 3 3 2 7 8 1 E - 0 1 . 1 6 9 5 1 6 7 7 3 3 1 4 2 5 E - 0 2 . 9 0 8 3 2 0 8 7 4 9 1 2 8 2 8 - 0 2 . 1 0 4 8 9 1 1 9 0 8 6 1 0 2 8 - 0 2 . 1 1 9 3 2 0 7 2 1 9 2 5 4 1 8 - 0 1 . 7 3 6 3 2 3 3 4 4 6 9 1 7 8 8 - 0 2 . 2 9 8 9 4 7 1 5 8 5 9 1 9 8 8 - 0 1 . 5 3 8 2 7 9 8 4 4 3 2 9 5 7 8 - 0 1 Q Q Q Q Q Q q u m m m m m m m m m m m m m v v v v v v v v v v v v v v v v v v v v v v , 7 ) = . 1 4 0 4 6 2 9 3 0 3 3 0 5 1 3 + 0 0 7 ) = - . 9 0 1 1 0 8 3 3 2 6 2 2 8 9 E + 0 0 7 ) = - . 4 0 4 6 4 4 1 9 9 8 6 3 8 8 8 + 0 0 8 ) = . 2 1 4 0 4 3 7 2 4 9 6 8 8 4 E - 0 1 3 5 1 S ( 1 1 , 2 , 8 ) = - . 2 7 9 2 1 7 6 6 2 1 3 7 9 2 E - 0 2 S ( 1 1 , 3 , 8 ) = - . 7 0 4 4 1 3 5 2 0 8 8 7 7 6 E - 0 2 S ( 1 1 , 4 , 8 ) = . 7 8 0 5 1 0 3 5 1 7 4 7 6 7 8 - 0 2 S ( 1 1 , 5 , 8 ) = . 1 8 9 7 3 7 4 3 9 1 0 5 9 4 3 - 0 2 S ( 1 1 , 6 , 8 ) = ' . 1 7 5 3 2 9 9 7 6 0 1 7 9 1 E - 0 1 S ( 1 1 , 7 , 8 ) = . 2 1 5 2 4 1 8 1 8 8 7 9 6 6 E - 0 1 S ( 1 1 , 8 , 8 ) = . 2 8 7 1 9 9 2 0 1 3 9 2 7 B E - O l S ( 1 1 , 9 , 8 ) = - . 2 1 7 9 1 5 6 9 5 4 4 4 1 2 8 + 0 0 S ( 1 1 , 1 0 , 8 ) = . 6 5 0 4 1 6 7 8 2 6 7 2 2 3 E + 0 0 S ( 1 1 , 1 1 , 8 ) = - . 7 2 6 1 5 0 9 1 0 8 6 5 0 4 E + 0 0 S ( 1 1 , 1 , 9 ) = - . 3 1 8 9 6 6 7 4 9 2 4 1 3 6 8 - 0 2 S ( 1 1 , 2 , 9 ) = . 1 1 0 8 4 4 5 6 4 4 7 6 8 1 8 - 0 3 S ( 1 1 , 3 , 9 ) = . 1 2 4 8 0 8 6 9 3 8 5 3 5 2 3 - 0 2 S ( 1 1 , 4 , 9 ) = - . 7 7 2 8 1 1 4 1 2 9 6 l 7 Z E - 0 3 S ( 1 1 , 5 , 9 ) = - . 1 1 5 2 4 2 5 0 7 8 4 1 9 6 E - 0 2 S ( 1 1 , 6 , 9 ) = . 2 5 0 9 9 3 6 1 9 2 5 7 2 3 E - 0 2 S ( 1 1 , 7 , 9 ) = . 5 1 1 7 1 3 2 9 1 2 9 3 9 9 8 - 0 3 S ( 1 1 , 8 , 9 ) = - . 1 1 2 0 4 8 9 7 7 2 1 7 0 3 E - 0 1 S ( 1 1 , 9 , 9 ) = . 1 9 7 2 1 0 6 9 5 5 9 3 3 3 8 - 0 1 S ( 1 1 , 1 0 , 9 ) = . 6 3 8 3 2 3 6 5 8 0 4 6 6 2 8 - 0 1 S ( 1 1 , 1 1 , 9 ) = - . 9 9 7 6 9 2 7 0 2 0 9 8 6 O E + 0 0 K ( l l ) = 9 M ( 1 1 ) = 2 W S ( 1 1 , 1 ) = - . 3 3 3 3 2 7 6 8 1 2 3 0 4 6 E + 0 0 W S ( 1 1 , 2 ) = - . 5 0 0 0 5 2 4 6 5 8 6 6 5 0 8 + 0 0 W S ( 1 1 , 3 ) = ' . 5 9 9 7 9 7 5 3 8 5 8 0 9 9 E + 0 0 W S ( 1 1 , 4 ) = - . 6 6 7 1 1 5 5 0 3 9 6 1 8 7 E + 0 0 W S ( 1 1 , 5 ) = ‘ . 8 1 8 1 6 9 6 0 1 9 3 1 0 1 E + 0 0 W S ( 1 1 , 6 ) = - . 8 0 0 0 9 5 7 7 0 6 0 7 3 4 E + 0 0 W S ( 1 1 , 7 ) = - . 7 1 3 6 7 1 0 5 0 5 4 8 7 B E + 0 0 W S ( 1 1 , 8 ) = - . 7 7 7 4 6 4 9 4 9 4 6 1 1 3 E + 0 0 w s ( 1 1 , 9 ) = - . 7 5 0 5 5 0 9 8 7 5 8 3 4 9 E + 0 0 n o 1 0 I = 8 , l l I F ( K ( I ) . L T . 2 ) G O T O 1 0 D O 2 0 I l = l , 6 B O = 2 . * 1 0 . * * ( - I l ) W R I T E ( 5 0 , 1 1 0 ) B O S U M 5 = 0 . 0 D O 3 0 J = l , I B ( I , J ) = E X P ( - B O * . 5 * L ( I , J ) / ( 1 . - B O ) ) * ( l . - 1 . 5 * B O / ( 1 . - B O ) + + . 5 * B O * L ( I , J ) / ( 1 . - B O ) * * 2 ) / ( 1 . - B O ) * * 1 . 5 - 1 . S U M 5 = S U M 5 + E ( I , J ) * * 2 C O N T I N U E E N O R M ( I , 1 1 ) = S U M 5 D O 4 0 J = 1 , K ( I ) S U M = 0 . D O 5 0 J 1 = 1 , I S U M = S U M + A 1 ( I , J , J 1 ) * E ( I , J l ) C O N T I N U E C ( I , J , I 1 ) = S U M 4 0 7 0 6 0 2 2 0 2 1 0 2 3 0 1 1 8 0 2 0 0 1 0 0 1 1 0 1 0 3 5 2 C O N T I N U E I F ( M ( I ) . L T . 2 ) G O T O 1 1 S U M = O . D O 6 0 J = 1 , I D O 7 0 J 1 = 1 , I S U M = S U M + E ( I , J ) * E ( I , J l ) * A 3 ( I , J , J l ) C O N T I N U E C O N T I N U E E R R ( I , I l ) = S U M S U M 6 = 0 . 0 D O 2 1 0 J = 1 , I D O 2 2 0 J 1 = 1 , K ( I ) S U M 6 = S U M 6 + E ( I , J ) * S ( I , J , J l ) * C ( I , J l , I l ) C O N T I N U E C O N T I N U E Y N O R M ( I , 1 1 ) = S U M 6 W R I T E ( 5 0 , 2 3 0 ) Y N O R M ( I , 1 1 ) F O R M A T ( 7 X , ' S T A B L E N O R M = ' , E Z O . 1 4 ) W R I T E ( 5 0 , 1 0 0 ) E R R ( I , I 1 ) W R I T E ( 5 0 , 2 0 0 ) E N O R M ( I , 1 1 ) D O 8 0 J = 1 , K ( I ) W R I T E ( 5 0 , 9 0 ) I , J , 1 1 , C ( I , J , I l ) C O N T I N U E F O R M A T ( 7 X , ' C ( ' , 1 2 , ' , ' , 1 2 , ' , ' , 1 2 , ' ) = ' , E 2 0 . 1 4 ) F O R M A T ( 7 X , ' V E C T O R N O R M O F I N I T I A L D A T A = ' , E Z O . 1 4 ) F O R M A T ( 7 X , ' E R R O R I N L E A S T - E R R O R F I T = ' , E 2 0 . 1 4 ) F O R M A T ( 7 X , ' B O = ' , E Z O . 1 4 ) C O N T I N U E C O N T I N U E S T O P E N D 3 5 3 p R O G R A H L E R R 2 ( I N P U T , O U T P U T , T A P E 6 0 ) R E A L C ( 1 5 , 1 5 , 6 ) , S ( 8 : l l , 1 1 , 1 1 ) , F C ( 1 1 ) , F K W ( 1 1 ) , L ( 1 5 , 1 5 ) , + w s ( 8 : 1 1 , 1 1 ) , R ( 1 1 ) I N T E G E R K ( 1 1 ) , M ( l l ) C T H I S P R O G R A M C A L C U L A T E S T H E L E A S T E R R O R S O L U T I O N A N D C C O M P A R E S T H E C A L C U L A T I O N W I T H T H E C L O S E D F O R M K B K W S O L U T I O N . L 1 , 1 = 1 . L ( 2 , 1 ) = . 5 8 5 7 8 6 4 3 7 6 2 7 L ( 2 , 2 ) = 3 . 4 1 4 2 1 3 5 6 2 3 7 3 L ( 3 , 1 ) = . 4 1 5 7 7 4 5 5 6 7 8 3 L ( 3 , 2 ) - 2 . 2 9 4 2 8 0 3 6 0 2 7 9 L ( 3 , 3 ) = 6 . 2 8 9 9 4 5 0 8 2 9 3 7 L ( 4 , 1 ) = . 3 2 2 5 4 7 6 8 9 6 1 9 L ( 4 , 2 ) = 1 . 7 4 5 7 6 1 1 0 1 1 5 8 L ( 4 , 3 ) = 4 . 5 3 6 6 2 0 2 9 6 9 2 1 L ( 4 , 4 ) - 9 . 3 9 5 0 7 0 9 1 2 3 0 1 L ( 5 , 1 ) = . 2 6 3 5 6 0 3 1 9 7 1 8 L ( 5 , 2 ) = 1 . 4 1 3 4 0 3 0 5 9 1 0 7 L ( 5 , 3 ) - 3 . 5 9 6 4 2 5 7 7 1 0 4 1 L ( 5 , 4 ) = 7 . 0 8 5 8 1 0 0 0 5 8 5 9 L ( 5 , 5 ) = 1 2 . 6 4 0 8 0 0 8 4 4 2 7 6 L ( 6 , 1 ) = . 2 2 2 8 4 6 6 0 4 1 7 9 L ( 6 , 2 ) = 1 . 1 8 8 9 3 2 1 0 1 6 7 3 L ( 6 , 3 ) = 2 . 9 9 2 7 3 6 3 2 6 0 5 9 L ( 6 , 4 ) = 5 . 7 7 5 1 4 3 5 6 9 1 0 5 L ( 6 , 5 ) = 9 . 8 3 7 4 6 7 4 1 8 3 8 3 L ( 6 , 6 ) = 1 5 . 9 8 2 8 7 3 9 8 0 6 0 2 L ( 7 , 1 ) - . 1 9 3 0 4 3 6 7 6 5 6 0 L ( 7 , 2 ) = 1 . 0 2 6 6 6 4 8 9 5 3 3 9 L ( 7 , 3 ) = 2 . 5 6 7 8 7 6 7 4 4 9 5 1 L ( 7 , 4 ) - 4 . 9 0 0 3 5 3 0 8 4 5 2 6 L ( 7 , 5 ) - 8 . 1 8 2 1 5 3 4 4 4 5 6 3 L ( 7 , 6 ) - 1 2 . 7 3 4 1 8 0 2 9 1 7 9 8 L ( 7 , 7 ) = 1 9 . 3 9 5 7 2 7 8 6 2 2 6 3 L ( 8 , 1 ) = . 1 7 0 2 7 9 6 3 2 3 0 5 L ( 8 , 2 ) - . 9 0 3 7 0 1 7 7 6 7 9 9 L ( 8 , 3 ) - 2 . 2 5 1 0 8 6 6 2 9 8 6 6 L ( 8 , 4 ) = 4 . 2 6 6 7 0 0 1 7 0 2 8 8 L ( 8 , 5 ) = 7 . 0 4 5 9 0 5 4 0 2 3 9 3 L ( 8 , 6 ) - 1 0 . 7 5 8 5 1 6 0 1 0 1 8 1 L ( 8 , 7 ) = 1 5 . 7 4 0 6 7 8 6 4 1 2 7 8 L ( 8 , 8 ) - 2 2 . 8 6 3 1 3 1 7 3 6 8 8 9 L ( 9 , 1 ) = . 1 5 2 3 2 2 2 2 7 7 3 2 L ( 9 , 2 ) - . 8 0 7 2 2 0 0 2 2 7 4 2 L ( 9 , 3 ) = 2 . 0 0 5 1 3 5 1 5 5 6 1 9 L ( 9 , 4 ) = 3 . 7 8 3 4 7 3 9 7 3 3 3 1 L ( 9 , 5 ) = 6 . 2 0 4 9 5 6 7 7 7 8 7 7 L ( 9 , 6 ) = 9 . 3 7 2 9 8 5 2 5 1 6 8 8 L ( 9 , 7 ) = 1 3 . 4 6 6 2 3 6 9 1 1 0 9 2 L ( 9 , 8 ) = 1 8 . 8 3 3 5 9 7 7 8 8 9 9 2 L ( 9 , 9 ) = 2 6 . 3 7 4 0 7 1 8 9 0 9 2 7 L ( 1 0 , 1 ) = . 1 3 7 7 9 3 4 7 0 5 4 0 L ( 1 0 , 2 ) = . 7 2 9 4 5 4 5 4 9 5 0 3 L ( 1 0 , 3 ) = 1 . 8 0 8 3 4 2 9 0 1 7 4 0 L ( 1 0 , 4 ) = 3 . 4 0 1 4 3 3 6 9 7 8 5 5 L ( 1 0 , 5 ) = 5 . 5 5 2 4 9 6 1 4 0 0 6 4 L ( 1 0 , 6 ) = 8 . 3 3 0 1 5 2 7 4 6 7 6 4 L ( 1 0 , 7 ) = 1 1 . 8 4 3 7 8 5 8 3 7 9 0 0 L ( 1 0 , 8 ) = 1 6 . 2 7 9 2 5 7 8 3 1 3 7 8 L ( 1 0 , 9 ) = 2 1 . 9 9 6 5 8 5 8 1 1 9 8 1 L ( 1 0 , 1 0 ) = 2 9 . 9 2 0 6 9 7 0 1 2 2 7 4 L ( 1 1 , 1 ) = . 1 2 5 7 9 6 4 4 2 1 8 8 L ( 1 1 , 2 ) = . 6 6 5 4 1 8 2 5 5 8 3 9 L ( 1 1 , 3 ) = 1 . 6 4 7 1 5 0 5 4 5 8 7 2 L ( 1 1 , 4 ) = 3 . 0 9 1 1 3 8 1 4 3 0 3 5 L ( 1 1 , 5 ) = 5 . 0 2 9 2 8 4 4 0 1 5 8 0 L ( 1 1 , 6 ) = 7 . 5 0 9 8 8 7 8 6 3 8 0 7 L ( 1 1 , 7 ) = 1 0 . 6 0 5 9 5 0 9 9 9 5 4 7 L ( 1 1 , 8 ) = 1 4 . 4 3 1 6 1 3 7 5 8 0 6 4 L ( 1 1 , 9 ) = 1 9 . 1 7 8 8 5 7 4 0 3 2 1 5 L ( 1 l , 1 0 ) = 2 5 . 2 1 7 7 0 9 3 3 9 6 7 8 L ( 1 1 , 1 1 ) = 3 3 . 4 9 7 1 9 2 8 4 7 1 7 6 L ( 1 2 , 1 ) ' . 1 1 5 7 2 2 1 1 7 3 5 8 L ( 1 2 , 2 ) = . 6 1 1 7 5 7 4 8 4 5 1 5 L ( 1 2 , 3 ) ‘ 1 . 5 1 2 6 1 0 2 6 9 7 7 6 L ( 1 2 , 4 ) = 2 . 8 3 3 7 5 1 3 3 7 7 4 4 L ( 1 2 , 5 ) = 4 . 5 9 9 2 2 7 6 3 9 4 1 8 L ( 1 2 , 6 ) = 6 . 8 4 4 5 2 5 4 5 3 1 1 5 L ( 1 2 , 7 ) = 9 . 6 2 1 3 1 6 8 4 2 4 5 7 L ( 1 2 , 8 ) = 1 3 . 0 0 6 0 5 4 9 9 3 3 0 6 L ( 1 2 , 9 ) ¢ 1 7 . 1 1 6 8 5 5 1 8 7 4 6 2 L ( 1 2 , 1 0 ) = 2 2 . 1 5 1 0 9 0 3 7 9 3 9 7 L ( 1 2 , 1 1 ) = 2 8 . 4 8 7 9 6 7 2 5 0 9 8 4 L ( 1 2 , 1 2 ) = 3 7 . 0 9 9 1 2 1 0 4 4 4 6 7 L ( 1 3 , 1 ) = . 1 0 7 1 4 2 3 8 8 4 7 2 L ( 1 3 , 2 ) - . 5 6 6 1 3 1 8 9 9 0 4 0 L ( 1 3 , 3 ) = 1 . 3 9 8 5 6 4 3 3 6 4 5 1 L ( 1 3 , 4 ) = 2 . 6 1 6 5 9 7 1 0 8 4 0 6 L ( 1 3 , 5 ) = 4 . 2 3 8 8 4 5 9 2 9 0 1 7 L ( 1 3 , 6 ) = 6 . 2 9 2 2 5 6 2 7 1 1 4 0 L ( 1 3 , 7 ) ' 8 . 8 1 5 0 0 1 9 4 1 1 8 7 L ( 1 3 , 8 ) = 1 1 . 8 6 1 4 0 3 5 8 8 8 1 1 L ( 1 3 , 9 ) = 1 5 . 5 1 0 7 6 2 0 3 7 7 0 4 L ( 1 3 , 1 0 ) = 1 9 . 8 8 4 6 3 5 6 6 3 8 8 0 L ( 1 3 , 1 1 ) = 2 5 . 1 8 5 2 6 3 8 6 4 6 7 8 L ( 1 3 , 1 2 ) = 3 1 . 8 0 0 3 8 6 3 0 1 9 4 7 L ( 1 3 , 1 3 ) = 4 0 . 7 2 3 0 0 8 6 6 9 2 6 6 L ( 1 4 , 1 ) = . 0 9 9 7 4 7 5 0 7 0 3 3 L ( 1 4 , 2 ) = . 5 2 6 8 5 7 6 4 8 8 5 2 L ( 1 4 , 3 ) = 1 . 3 0 0 6 2 9 1 2 1 2 5 1 3 5 4 3 5 5 L ( 1 4 , 4 ) = 2 . 4 3 0 8 0 1 0 7 8 7 3 1 L ( 1 4 , 5 ) = 3 . 9 3 2 1 0 2 8 2 2 2 9 3 L ( 1 4 , 6 ) = 5 . 8 2 5 5 3 6 2 1 8 3 0 2 L ( l 4 , 7 ) = 8 . 1 4 0 2 4 0 1 4 1 5 6 5 L ( 1 4 , 8 ) = 1 0 . 9 1 6 4 9 9 5 0 7 3 6 6 L ( 1 4 , 9 ) = 1 4 . 2 1 0 8 0 5 0 1 1 1 6 1 L ( 1 4 , 1 0 ) = 1 8 . 1 0 4 8 9 2 2 2 0 2 1 8 L ( 1 4 , 1 1 ) = 2 2 . 7 2 3 3 8 1 6 2 8 2 6 9 L ( 1 4 , 1 2 ) = 2 8 . 2 7 2 9 8 1 7 2 3 2 4 8 L ( 1 4 , 1 3 ) = 3 5 . 1 4 9 4 4 3 6 6 0 5 9 2 L ( 1 4 , 1 4 ) = 4 4 . 3 6 6 0 8 1 7 1 1 1 1 7 L ( 1 5 , 1 ) = . 0 9 3 3 0 7 8 1 2 0 1 7 L ( 1 5 , 2 ) = . 4 9 2 6 9 1 7 4 0 3 0 2 L ( 1 5 , 3 ) = 1 . 2 1 5 5 9 5 4 1 2 0 7 1 L ( 1 5 , 4 ) = 2 . 2 6 9 9 4 9 5 2 6 2 0 4 L ( 1 5 , 5 ) = 3 . 6 6 7 6 2 2 7 2 1 7 5 1 L ( 1 5 , 6 ) = 5 . 4 2 5 3 3 6 6 2 7 4 1 4 L ( 1 5 , 7 ) = 7 . 5 6 5 9 1 6 2 2 6 6 1 3 L ( 1 5 , 8 ) = 1 0 . 1 2 0 2 2 8 5 6 8 0 1 9 L ( 1 5 , 9 ) = 1 3 . 1 3 0 2 8 2 4 8 2 1 7 6 L ( 1 5 , 1 0 ) = 1 6 . 6 5 4 4 0 7 7 0 8 3 3 0 L ( 1 5 , 1 1 ) = 2 0 . 7 7 6 4 7 8 8 9 9 4 4 9 L ( 1 5 , 1 2 ) = 2 5 . 6 2 3 8 9 4 2 2 6 7 2 9 L ( 1 5 , 1 3 ) = 3 1 . 4 0 7 5 1 9 1 6 9 7 5 4 L ( 1 5 , 1 4 ) = 3 8 . 5 3 0 6 8 3 3 0 6 4 8 6 L ( 1 5 , 1 5 ) = 4 8 . 0 2 6 0 8 5 5 7 2 6 8 6 S ( 8 , 1 , 1 ) = . 4 0 6 3 9 2 3 3 3 0 4 5 6 1 8 - 0 1 S ( 8 , 2 , 1 ) = . 2 0 6 7 5 0 7 4 2 1 2 3 5 8 E - 0 1 S ( 8 , 3 , 1 ) = ' . 7 4 5 1 5 5 9 3 3 2 9 9 4 6 E - 0 2 S ( 8 , 4 , 1 ) = - . 2 8 8 5 5 8 9 9 4 6 5 9 6 4 E - 0 1 S ( 8 , 5 , 1 ) = - . 1 7 7 3 1 0 5 1 8 4 1 0 2 1 E - 0 1 S ( 8 , 6 , 1 ) = . 7 0 6 2 9 6 8 5 6 2 9 3 7 4 E - 0 1 S ( 8 , 7 , 1 ) = . 3 2 1 3 0 9 7 8 5 1 5 7 9 S E + 0 0 S ( 8 , 8 , 1 ) = . 9 4 2 5 9 7 4 1 3 8 6 3 6 B E + 0 0 S ( 8 , 1 , 2 ) = - . 4 0 8 4 8 8 1 4 4 1 8 5 2 4 E - 0 1 S ( 8 , 2 , 2 ) = . 1 5 8 5 8 1 3 9 9 3 2 5 4 1 8 - 0 2 S ( 8 , 3 , 2 ) = . 1 8 3 1 8 6 6 9 2 8 4 3 6 6 8 - 0 1 S ( 8 , 4 , 2 ) = - . 1 3 6 2 9 3 8 5 6 3 2 5 3 5 8 - 0 1 S ( 8 , 5 , 2 ) = - . 2 2 7 5 4 6 5 6 7 3 0 3 7 O E - 0 1 S ( 8 , 6 , 2 ) = . 7 4 6 9 5 0 5 0 5 3 4 9 4 8 3 - 0 1 S ( 8 , 7 , 2 ) = ” . 2 0 2 2 9 8 8 3 9 1 0 8 4 B E - 0 1 S ( 8 , 8 , 2 ) = - . 9 9 5 6 4 1 0 7 6 1 8 0 1 3 3 + 0 0 S ( 8 , 1 , 3 ) = . 5 5 0 5 6 6 0 0 0 6 3 1 8 5 E - 0 1 S ( 8 , 2 , 3 ) = . 6 6 2 0 8 9 0 4 7 0 3 9 0 1 E - 0 2 S ( 8 , 3 , 3 ) = - . 2 6 8 0 4 7 1 5 4 9 2 0 5 3 E - 0 1 S ( 8 , 4 , 3 ) = - . 1 0 7 7 8 1 5 1 5 5 8 7 3 7 E - 0 2 S ( 8 , 5 , 3 ) = . 5 2 3 6 2 7 6 8 5 2 9 6 5 5 E - 0 1 S ( 8 , 6 , 3 ) = - . 2 1 6 0 4 6 8 8 6 4 8 7 1 7 E - 0 1 S ( 8 , 7 , 3 ) = - . 3 1 5 2 3 1 7 9 5 8 9 1 1 7 E + 0 0 8 , 8 , 3 ) = . 9 4 5 3 1 7 7 1 0 0 3 2 0 6 E + 0 0 O O p o o o o m w o - o m c o c o m b n v u m u p o v o u o o q 1 0 " v n l c l v m a o o N v u o u n w v m n o v " fi u o I n m m I c v m o n I " m u v o v u x u a m m a v " q h ! o C v o m h I " o o m u v t o v I x o v m I a h I o o m " ( v o u m o o m m m m H N m ’ ‘ m U ‘ Q m ‘ Q m ‘ U ‘ m O V m Q Q ‘ m O V ‘ m ‘ — m F ~ N m ‘ ’ m h ~ m fi I m ‘ “ U m ~ Q m Q ~ o Q ‘ O m \ V N m - - - - - - - V - V - ~ V - 3 5 6 4 ) = - . 6 3 1 3 8 2 0 2 3 1 8 3 5 3 E - 0 1 4 ) = . 1 1 1 1 7 8 1 9 3 4 5 3 7 1 E - 0 1 4 ) = . 2 1 3 4 0 6 7 1 7 6 8 5 1 1 8 - 0 1 4 ) = - . 3 3 5 4 1 6 2 7 1 8 1 7 7 4 E - 0 1 4 ) = . 6 5 5 0 6 2 3 6 2 5 9 5 0 6 8 - 0 2 4 ) = . 9 4 4 9 2 9 0 8 6 9 6 4 5 0 8 - 0 1 - . 3 3 5 9 2 6 1 9 1 5 9 7 1 3 E + 0 0 . 9 3 4 0 7 2 4 1 1 4 3 8 6 0 E + 0 0 - . 3 7 0 1 4 7 3 5 3 6 5 3 2 2 8 - 0 1 . 1 0 8 3 2 7 3 5 5 9 5 1 2 2 8 - 0 1 . 6 9 0 4 6 4 9 7 4 1 9 0 4 6 8 - 0 2 - . 2 0 6 1 2 6 0 4 4 2 5 6 1 4 E - 0 1 . 2 4 3 7 0 0 2 6 8 0 8 1 8 2 8 - 0 1 . 2 2 3 7 7 5 5 2 0 9 8 5 5 0 8 - 0 2 . 1 4 1 5 8 8 1 6 3 7 6 9 5 2 8 + 0 0 . 9 8 8 6 3 2 3 3 4 9 3 6 2 3 E + 0 0 . 2 6 7 0 6 0 0 7 2 2 4 3 8 6 8 - 0 1 . 8 0 7 4 5 4 9 0 5 0 6 2 9 6 3 - 0 2 - . 1 1 0 6 7 8 6 7 3 1 5 6 8 6 8 - 0 1 - . 1 1 6 8 3 5 0 8 9 8 6 2 5 1 E - 0 1 . 1 7 6 3 5 0 0 8 6 4 8 9 6 9 8 - 0 1 . 4 8 9 4 1 1 4 9 2 3 2 4 4 9 8 - 0 1 6 ) = - . 7 4 4 8 6 3 8 1 1 5 5 4 2 9 E - 0 1 6 ) = - . 9 9 5 3 4 3 2 2 6 3 1 4 7 9 E + 0 0 1 ) = - . 3 3 3 3 3 3 3 3 2 3 8 2 1 3 E + 0 0 2 ) = - . 6 6 6 6 6 6 7 2 2 5 3 9 S O E + 0 0 3 ) = - . 5 9 9 9 9 9 9 4 0 3 2 0 8 7 E + 0 0 4 ) = - . 7 1 4 2 8 5 6 9 0 0 7 5 2 4 E + 0 0 5 ) = “ . 7 5 0 0 0 0 0 0 5 1 5 7 2 1 E + 0 0 6 ) = - . 5 0 0 0 0 0 0 2 5 8 4 0 4 6 8 + 0 0 “ “ ‘ ~ - § - - - - - - ~ § ~ m m m m m m v v - - - - - s u - u u s V - - - Q 1 ) = . 2 7 7 3 9 8 9 3 2 3 2 9 9 5 8 - 0 1 1 ) = . 1 5 5 7 4 2 3 1 9 1 6 3 2 6 8 - 0 1 1 ) = - . 2 1 1 8 0 7 1 3 2 2 2 8 2 1 E - 0 2 1 ) = - . 1 7 5 0 7 1 1 4 2 6 0 1 0 3 E - 0 1 1 ) = - . 1 7 5 6 4 6 6 4 9 4 0 2 0 5 8 - 0 1 1 ) = . 1 8 7 4 6 0 6 6 6 8 0 7 8 1 8 - 0 1 1 ) = . 1 2 6 7 3 4 8 6 0 2 1 2 7 6 8 + 0 0 1 ) = . 3 7 2 6 7 7 1 8 6 5 4 3 0 6 E + 0 0 1 ) = . 9 1 8 1 8 6 8 0 7 6 3 4 7 B E + 0 0 2 ) = . 1 3 7 6 8 2 0 5 2 2 4 3 3 8 E - 0 1 2 ) = . 5 1 3 8 6 0 3 4 4 8 4 0 2 6 8 - 0 2 2 ) = - . 4 4 8 7 7 1 6 6 3 3 8 3 7 B E - 0 2 2 ) = “ . 7 0 4 8 8 6 2 4 8 5 8 2 0 1 3 - 0 2 2 ) = . 3 5 5 5 6 1 1 6 5 3 2 4 8 9 8 - 0 2 2 ) = . 2 1 8 9 3 6 1 9 7 0 6 9 0 2 8 - 0 1 ‘ 2 ) = . 8 8 0 2 6 9 2 9 1 6 2 5 9 2 8 - 0 2 2 ) = * . 1 6 9 8 6 7 1 0 3 7 1 8 1 8 E + 0 0 2 ) = - . 9 8 5 0 3 2 9 4 9 6 6 7 3 O E + 0 0 H m w n m ‘ o q m m H m w o m m q m m w w w b m m q m m w n w b - m m q m m H h t l a m i x a m N Q V - - ~ Q s Q V - - - - - - V - - - - u - - - - - V - \ o \ o x o m x o m m o m m m m m o m m m m m m m m m m m m m m m m m m m m w m w m m m m m m m m m m 3 5 7 3 ) = . 1 4 0 4 6 2 4 9 9 6 6 9 7 7 E - 0 1 ) = . 2 8 7 1 0 9 5 9 0 3 5 3 0 7 E - 0 2 ) = - . 6 1 9 1 4 0 6 9 7 1 2 1 7 9 E - 0 2 ) - - . 2 8 7 7 5 9 1 2 8 2 4 5 7 1 E - 0 2 ) = . 1 0 3 6 8 5 7 5 9 2 3 4 9 8 E - 0 1 ) : . 7 7 0 0 0 4 7 6 0 7 1 7 8 5 E - 0 2 ) = - . 4 6 1 5 0 2 7 7 0 7 4 4 9 5 E - 0 1 ) = - . 6 2 4 1 5 1 3 2 1 7 8 5 6 3 E - 0 1 ) = . 9 9 6 7 7 2 5 6 7 1 9 8 5 3 E + 0 0 ) = - . 1 7 4 8 1 4 9 6 4 2 0 7 8 0 E - 0 1 ) = . 5 1 4 9 3 1 5 2 9 3 0 7 2 7 E - 0 2 ) - . 2 9 1 2 4 1 2 1 4 8 8 6 8 6 E - 0 2 ) = — . 8 6 3 2 5 9 4 8 9 3 5 5 8 4 E - 0 2 ) . . 9 5 0 9 0 7 5 7 5 5 7 0 0 3 E - 0 2 4 ) = . 1 1 0 6 9 4 8 5 4 8 6 8 6 5 E - 0 2 ) = - . 4 1 5 1 5 7 9 5 3 0 1 2 8 6 E - 0 1 ) = . 1 8 1 5 8 7 2 0 2 1 7 9 4 O E + 0 0 ) = - . 9 8 2 2 4 0 1 7 2 7 0 9 3 6 E + 0 0 ) = - . 8 6 6 4 6 3 9 7 6 4 4 9 3 0 E - 0 1 ) 2 . 1 6 8 6 3 7 4 7 7 2 5 6 4 5 E - 0 1 ) = . 2 5 7 1 4 3 4 9 4 9 7 9 3 0 E - 0 1 ) = - . 4 2 1 6 1 4 1 4 8 2 1 7 7 3 E - 0 1 ) . . 1 3 7 4 9 8 5 9 5 7 2 8 1 4 E - 0 1 ) . . 8 4 3 5 8 3 6 9 0 8 2 3 0 6 E - 0 1 ) - - . 2 6 6 2 7 6 6 8 6 9 8 4 5 7 E + 0 0 ) - . 4 1 6 5 8 4 4 5 6 5 4 7 4 8 E + 0 0 ) - . 8 5 9 0 7 9 6 9 7 4 5 3 6 1 E + 0 0 6 ) = . 1 5 6 4 8 3 5 4 1 5 8 9 4 8 E - 0 1 6 ) = - . 1 2 3 1 1 5 5 2 1 5 9 1 9 0 E - 0 2 6 ) = - . 6 2 5 4 1 9 6 1 0 2 9 9 0 9 E - 0 2 6 ) = . 5 6 3 3 5 4 0 8 2 2 0 2 8 4 E - 0 2 6 ) = . 5 0 0 5 6 0 5 1 3 3 3 1 2 6 E - 0 2 6 ) - - . 2 1 0 9 3 9 4 1 2 1 8 3 3 3 3 - 0 1 6 ) = . 1 6 7 7 3 7 0 8 0 2 7 4 1 8 E - 0 1 6 ) - . 1 1 3 1 0 2 3 8 5 5 9 5 5 2 E + 0 0 6 ) - - . 9 9 3 0 4 5 4 3 9 1 2 6 8 2 E + o o 7 ) = - . 7 6 8 9 2 7 0 5 8 5 0 8 6 1 E - 0 1 7 ) = - . 4 1 5 7 1 1 6 5 8 1 9 5 5 9 E - 0 2 7 ) - . 3 5 0 3 8 3 9 4 2 0 4 0 2 3 E - 0 1 7 ) = - . 8 9 7 9 8 1 8 9 4 8 0 6 5 4 E - 0 2 7 ) = - . 5 3 7 3 8 4 3 2 7 0 1 7 2 3 E - 0 1 7 ) = . 6 0 4 9 4 2 7 5 0 6 9 5 1 0 E - 0 1 7 ) = . 1 7 4 6 0 2 0 1 8 2 9 9 4 B E + 0 0 7 ) = — . 7 6 6 9 6 0 5 6 5 9 4 2 7 2 E + 0 0 7 ) = ' . 6 0 6 2 1 7 9 0 8 8 2 5 7 B E + 0 0 1 ) = - . 3 3 3 3 3 3 4 5 2 6 2 3 1 5 E + 0 0 2 ) = - . 4 9 9 9 9 9 7 3 0 6 4 2 2 5 E + 0 0 3 ) = - . 6 0 0 0 0 0 5 1 0 4 4 0 4 I E + 0 0 m m m v v - ~ V - ~ ‘ - - - - - - - - ~ V ~ Q ‘ s - - - V - - - - 3 5 8 W S ( 9 , 4 ) = - . 7 7 7 7 7 7 6 8 4 9 7 1 5 1 E + 0 0 W S ( 9 , 5 ) = - . 7 5 0 0 0 0 0 6 9 7 5 3 6 6 E + 0 0 W S ( 9 , 6 ) = - . 7 1 4 2 8 6 0 9 9 9 6 0 9 9 E + 0 0 W S ( 9 , 7 ) = - . 6 6 6 6 6 5 9 6 6 7 4 2 4 6 E + 0 0 S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 . S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 : S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( I O . S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( I O . S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 , s ( 1 0 , S ( 1 0 , S ( 1 0 , S ( 1 0 . S ( 1 0 , 6 , V + 4 F 0 0 4 I - ‘ m h e » N H o w m q m m h w w w o m m q m m h w n w o m m g o w n - h u m H o m m q m m . c - w N I - a ‘ “ “ “ “ “ ‘ ~ ‘ - “ ~ ‘ ~ “ ‘ - ‘ ~ “ ~ “ ‘ - ~ V ‘ V ‘ ~ V ‘ 1 ) = 1 ) = 1 ) = 1 ) = - 1 ) = - 1 ) = - 1 ) = - 1 ) = - 1 ) = - 1 ) = - 2 ) = - 2 ) = - 2 ) = - 2 ) = 2 ) - 2 ) : - 2 ) = - 2 ) = - 2 ) = - 2 ) - - 3 ) - 3 ) - 3 ) = - 3 ) = - 3 ) - - 3 ) - 3 ) - 3 ) = - 3 ) = - 3 ) = - 4 ) = - 4 ) = - 4 ) - 4 ) - 4 ) - - 4 ) - - 4 ) - 4 ) - 4 ) = - 4 ) = - 5 ) = - 5 ) = - 5 ) - 5 ) = - 5 ) = - 5 ) = . 7 6 7 7 5 1 2 2 0 0 7 1 3 6 8 ' 0 1 . 6 0 9 0 4 5 4 6 3 8 2 0 6 0 8 - 0 1 . 3 1 9 6 4 7 0 3 3 4 3 0 5 0 E - 0 1 . 1 0 7 6 7 9 7 6 5 6 9 7 8 0 E - 0 1 . 6 8 4 6 7 5 3 8 1 8 7 3 8 4 8 - 0 1 . 1 4 2 9 7 4 6 5 4 1 6 0 4 3 E + 0 0 . 2 3 7 2 2 3 3 4 8 7 3 1 8 6 E + 0 0 . 3 5 6 1 9 8 6 3 5 0 4 1 4 3 8 + 0 0 . 5 0 9 5 6 3 5 3 5 6 5 7 8 7 E + 0 0 . 7 2 2 0 2 6 0 3 0 0 7 9 7 7 E + 0 0 . 1 9 9 6 7 7 7 5 4 2 5 2 2 6 E - 0 1 . 1 2 0 5 8 1 4 4 0 5 2 6 6 4 8 - 0 1 . 2 7 3 2 6 2 1 0 4 6 1 8 3 8 8 - 0 3 . 1 0 8 9 7 3 8 2 7 3 3 6 9 7 E - 0 1 . 1 4 1 9 1 1 8 7 2 1 6 0 6 6 3 - 0 1 . 1 5 9 5 3 8 0 6 7 0 4 5 9 3 8 - 0 2 . 5 3 9 2 2 5 5 1 2 6 6 7 4 7 E - O l . 1 7 1 5 8 9 1 4 0 6 6 7 6 Z E + 0 0 . 4 0 8 2 3 0 7 4 1 0 2 0 9 9 E + 0 0 . 8 9 4 5 0 0 0 3 5 6 6 5 2 5 8 + 0 0 . 8 0 0 9 0 2 0 6 3 1 7 8 7 9 3 - 0 2 . 3 4 5 2 1 9 6 0 8 1 2 7 2 9 8 - 0 2 . 1 9 4 8 1 0 8 0 1 8 7 0 3 9 E - 0 2 . 4 2 7 5 4 1 8 1 9 5 6 9 9 9 E - 0 2 . 1 5 5 2 4 5 9 9 5 0 6 2 0 0 8 - 0 3 . 9 6 4 6 0 1 0 4 4 5 5 4 3 4 8 - 0 2 . 1 2 8 4 1 7 0 9 8 9 2 2 2 9 8 - 0 1 . 3 1 1 1 5 1 0 7 9 0 7 1 5 9 3 - 0 1 . 2 3 6 6 6 0 0 8 6 3 6 3 4 9 E + 0 0 . 9 7 0 9 1 0 7 7 7 5 9 7 8 7 E + 0 0 . 5 5 9 7 7 8 2 5 3 3 2 6 7 5 E - 0 2 . 1 5 3 4 0 0 2 1 4 4 6 3 1 0 E - 0 2 . 2 1 5 4 4 1 4 7 4 8 9 3 6 3 E - 0 2 . 1 7 9 9 9 2 1 2 1 0 4 4 6 6 8 - 0 2 . 2 8 0 8 3 0 1 7 1 5 8 4 4 6 8 - 0 2 . 4 9 2 3 0 8 0 2 5 5 1 9 3 3 8 - 0 2 . 7 8 1 6 9 9 2 4 6 9 9 6 5 5 8 - 0 2 . 3 2 1 5 2 0 3 2 5 7 3 2 0 2 8 - 0 1 . 5 0 9 5 9 7 0 4 9 0 2 0 6 4 E - 0 1 . 9 9 8 1 1 5 5 0 2 8 7 4 0 7 E + 0 0 . 9 7 3 9 5 6 6 3 2 8 2 8 9 4 E - 0 2 . 4 7 8 0 5 0 4 5 2 3 4 8 8 6 3 - 0 4 . 4 1 1 8 1 7 6 1 8 4 2 2 5 3 8 - 0 2 . 1 8 9 2 0 5 4 4 0 9 5 8 7 5 3 - 0 2 . 4 9 3 6 7 0 2 7 4 0 2 9 3 7 8 - 0 2 . 8 1 3 1 0 3 4 5 1 5 6 8 1 3 8 - 0 2 J - I ) s t u b ! U ‘ O Q D C W O H N W fi ‘ U G Q G W O ‘ — I N ’ U é I ‘ U ‘ O Q Q D O H N N F I ‘ U ‘ O Q O D \ 3 5 9 S ( 1 0 , 7 , 5 ) = . 8 1 8 1 9 3 0 5 2 6 1 5 4 5 8 - 0 2 S ( 1 0 , 8 , 5 ) = - . 5 6 3 6 8 2 5 1 2 6 4 3 7 6 E - 0 1 S ( 1 0 , 9 , 5 ) = . 5 8 8 2 3 7 1 5 5 2 4 7 1 6 E - 0 1 S ( 1 0 , 1 0 , 5 ) = . 9 9 6 5 3 8 7 9 0 6 7 2 6 6 E + 0 0 S ( 1 0 , , 6 ) = . 9 7 8 2 9 5 3 7 1 9 4 1 9 7 E - 0 2 S ( 1 0 , , 6 ) = - . 1 0 6 1 9 9 0 8 1 6 3 2 2 1 8 - 0 2 S ( 1 0 , 6 ) = - . 3 5 2 4 2 5 2 1 1 9 5 2 0 6 8 - 0 2 S ( 1 0 , 6 ) = . 3 5 9 3 0 2 6 7 9 0 0 0 0 2 E - 0 2 S ( 1 0 , 6 ) = . 1 7 2 7 7 7 6 8 2 4 4 4 6 9 E - 0 2 S ( 1 0 , 6 ) = - . 1 0 1 0 4 5 3 5 8 6 6 4 9 3 E - 0 1 S ( 1 0 , 6 ) ' . 1 0 7 8 6 5 4 0 8 2 6 3 7 8 E - 0 1 S ( 1 0 , 6 ) = . 2 8 4 8 7 3 6 7 8 0 4 4 4 7 8 - 0 1 S ( 1 0 , 6 ) = - . 2 0 4 9 2 3 5 2 9 4 0 2 0 9 E + 0 0 S ( 1 0 , 1 6 ) = . 9 7 8 1 8 7 7 2 0 4 5 5 3 6 3 + 0 0 S ( 1 0 , 7 ) = - . 9 9 1 1 9 9 1 4 1 1 8 7 2 4 E - 0 2 S ( 1 0 , 7 ) = . 2 0 6 7 5 5 5 1 5 6 1 6 2 6 E - 0 2 S ( 1 0 , 7 ) = . 2 6 3 1 5 8 3 4 8 0 5 8 9 9 8 - 0 2 S ( 1 0 , 7 ) = - . 4 4 7 4 9 5 5 4 4 6 0 4 7 4 E - 0 2 S ( 1 0 , 7 ) = . 1 8 3 9 5 9 8 8 5 9 6 5 3 6 E - 0 2 S ( 1 0 , 7 ) = . 6 8 2 9 1 9 7 7 2 1 7 9 4 9 E - 0 2 S ( 1 0 , 7 ) = - . 2 0 6 4 2 4 2 3 5 0 0 9 5 5 E - 0 1 S ( 1 0 , 7 ) - . 2 6 2 1 5 7 8 4 4 3 8 7 4 9 3 - 0 1 S ( 1 0 , 7 ) = . 6 1 2 6 9 2 7 0 9 6 2 2 1 7 3 - 0 1 S ( 1 0 , 1 7 ) ' - . 9 9 7 4 7 3 4 1 0 4 4 8 9 2 E + 0 0 S ( 1 0 , 8 ) = - . 1 4 7 8 8 4 9 7 0 2 5 2 0 1 E - 0 1 S ( 1 0 , 8 ) = . 4 3 7 6 7 7 1 4 5 2 4 2 6 8 8 - 0 2 S ( 1 0 , 8 ) = . 2 2 4 0 9 9 6 4 4 8 4 2 3 9 8 - 0 2 S ( 1 0 , 8 ) = - . 6 6 3 5 9 3 0 7 6 9 8 7 5 9 8 - 0 2 S ( 1 0 , 8 ) = . 6 9 6 2 5 8 2 3 9 4 0 9 1 5 3 - 0 2 S ( 1 0 , 8 ) = . 7 5 0 3 9 7 9 1 4 8 6 3 1 3 8 - 0 3 S ( 1 0 , 8 ) : - . 2 4 3 7 1 0 4 2 3 2 2 9 1 8 E - 0 1 S ( 1 0 , 8 ) = . 8 1 3 4 3 9 7 7 1 8 3 6 2 5 8 - 0 1 S ( 1 0 , 8 ) " . 2 2 5 4 4 3 2 8 3 3 2 3 0 1 8 + 0 0 S ( 1 0 , 1 8 ) 8 . 9 7 0 3 7 5 4 8 4 8 5 6 8 1 E + 0 0 S ( 1 0 , 9 ) * ' . 1 0 9 5 4 7 0 0 5 7 8 3 9 6 E - 0 1 I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I é 1 S ( 1 0 , 9 ) = - . 1 4 4 8 4 3 7 8 7 3 9 8 2 3 E - 0 2 S ( 1 0 , 9 ) = . 4 7 9 0 5 4 7 6 5 1 2 8 4 0 E - 0 2 S ( 1 0 , 9 ) = . 5 5 1 7 9 5 5 0 6 6 1 2 6 1 E - 0 3 s ( 1 0 , 9 ) - - . 7 2 4 1 2 8 1 2 8 4 3 4 3 3 E - 0 2 S ( 1 0 , 9 ) = . 7 7 9 9 0 8 4 2 9 3 9 2 3 3 E - 0 3 S ( 1 0 , 9 ) - . 2 4 6 0 5 7 8 1 3 2 2 7 0 9 E - 0 1 S ( 1 0 , 9 ) - - . 1 7 8 5 9 7 4 3 4 5 1 8 8 2 E - 0 1 s ( 1 0 , 9 ) = - . 2 3 1 8 7 5 2 0 5 9 2 0 2 6 E + o o s ( 1 0 , 1 o 9 ) = . 9 7 2 1 6 8 2 3 2 5 0 6 5 1 E + 0 0 R ( 1 0 ) = - m ( 1 0 ) = w s ( 1 0 , 1 ) = - . 1 6 6 0 1 2 3 3 2 4 2 8 2 0 E - 0 6 W S ( 1 0 , 2 ) s - . 3 3 3 3 3 3 0 8 2 0 2 2 1 9 E + 0 0 W S ( 1 0 , 3 ) = - . 4 9 9 9 9 9 4 1 7 2 1 8 4 4 E + 0 0 W S ( 1 0 , 4 ) = ” . 6 0 0 0 0 2 9 4 7 4 9 6 6 4 E + 0 0 “ “ “ V H V u H V n H ‘ v u v u v l v u H H N M v u M v n N v w u w u v m v u ‘ ~ ‘ V w v u ~ m v u w “ v u m v u w w w v l v u “ v u w v u w v n w w v u w v n w l v w u v w u v h n v p n v - w o p n v n v l v l v n u a v u m v « v n Q U ! A H H \ D Q Q O ‘ U ‘ I D U ’ N H ‘ V I n A g . . . - H ‘ \ o m q m m w a I — n ( I ) A | - - ' H ‘ D O Q G O I I F O O N H ‘ Q ‘ V ‘ Q V 1 ) = - 1 ) = - 1 ) = - 1 ) = 1 ) = H V I I 4 ) = 4 ) = - 4 ) = - 4 ) - 5 ) = - 3 6 0 5 ) = - . 7 1 4 2 8 2 0 6 0 7 1 7 3 7 E + 0 0 6 ) = - . 7 5 0 0 1 0 4 5 2 6 2 4 O B E + 0 0 7 ) = - . 7 7 7 7 7 0 1 2 5 0 6 0 1 7 E + 0 0 8 ) = - . 8 0 0 0 0 1 7 9 4 0 5 5 8 4 E + 0 0 9 ) = - . 6 6 6 6 6 3 4 6 4 8 2 7 3 1 8 + 0 0 . 1 4 9 3 4 5 8 1 9 2 9 5 8 1 8 - 0 1 . 9 5 4 0 3 5 7 7 6 6 4 7 3 9 8 - 0 2 . 1 3 4 7 9 1 4 6 5 3 1 3 4 1 E - 0 2 . 6 8 9 9 8 1 9 0 2 1 7 1 5 3 E ’ 0 2 . 1 0 8 5 4 5 2 3 9 1 7 8 4 5 3 - 0 1 . 4 0 1 7 5 4 5 5 9 8 1 7 0 5 8 - 0 2 . 2 3 2 5 8 4 4 8 5 9 4 2 6 2 E - 0 1 . 8 5 7 0 8 8 1 7 7 4 8 0 0 3 8 - 0 1 . 2 0 7 3 9 5 3 1 2 0 9 6 1 5 8 + 0 0 . 4 3 2 9 5 0 6 7 7 7 1 2 6 S E + 0 0 . 8 7 2 4 4 2 8 3 0 4 5 6 8 9 8 + 0 0 . 5 0 6 8 7 7 4 8 5 4 0 6 2 0 E - 0 2 . 2 4 2 8 0 8 8 4 8 9 1 3 9 7 8 - 0 2 - . 8 5 0 2 3 1 1 5 8 6 0 6 6 3 8 - 0 3 . 2 6 6 5 6 0 4 8 1 3 8 7 6 3 8 - 0 2 - . 1 0 5 0 6 2 6 3 7 3 5 3 1 6 E - 0 2 . 4 2 5 3 5 5 0 0 2 6 4 7 1 7 8 - 0 2 . 8 8 3 1 3 9 2 1 6 7 9 2 0 4 3 - 0 2 . 2 3 4 3 3 0 2 4 0 8 9 1 3 3 3 - 0 2 . 6 8 1 8 2 9 1 6 8 5 6 6 4 7 8 - 0 1 . 2 8 7 2 9 6 9 2 8 2 6 6 O S E + 0 0 . 9 5 5 3 3 7 3 5 7 8 8 2 6 1 8 + 0 0 . 2 7 0 8 3 3 4 3 1 2 9 3 0 8 8 - 0 2 . 9 0 1 6 8 0 2 8 7 0 4 3 2 0 8 - 0 3 . 8 8 2 2 9 7 1 4 0 9 5 6 1 6 3 - 0 3 . 1 0 6 0 8 3 9 6 6 8 9 9 6 7 E - 0 2 . 7 8 1 2 1 6 6 0 0 6 6 6 1 5 E - 0 3 . 2 5 1 1 9 8 5 9 0 9 7 4 5 9 8 - 0 2 " . 6 5 0 8 1 7 4 6 5 0 7 1 0 8 8 - 0 3 . 1 1 4 1 6 5 3 7 8 5 6 4 3 1 E - 0 1 . 9 8 6 0 5 4 3 5 8 3 3 3 0 7 3 - 0 2 . 1 2 4 9 0 4 9 0 8 8 0 4 3 6 E + 0 0 . 9 9 2 0 4 5 2 6 1 1 8 1 7 O E + 0 0 . 2 8 2 0 9 2 8 4 9 4 9 1 5 1 3 - 0 2 . 5 5 7 6 8 4 3 3 7 2 6 4 9 8 3 - 0 3 . 1 1 4 3 7 1 1 9 7 6 7 9 9 9 3 ’ 0 2 . 4 8 3 9 3 4 7 4 5 8 5 1 1 1 E - 0 3 . 1 5 5 5 3 2 8 6 2 2 1 2 4 4 8 - 0 2 . 9 5 7 0 5 7 8 2 6 3 9 2 2 3 3 - 0 3 . 4 4 8 3 6 7 7 4 8 1 9 3 1 5 E - 0 2 . 4 0 3 8 7 9 4 2 5 3 7 0 9 8 3 - 0 2 . 3 0 5 2 4 6 6 8 1 3 0 0 5 0 8 - 0 1 . 4 8 5 4 2 0 0 4 5 6 4 1 3 5 E - 0 1 . 9 9 8 3 2 9 7 8 3 8 2 8 7 3 E + 0 0 . 2 2 2 7 0 3 4 6 1 9 3 8 4 8 E - 0 1 N O O “ F O ~ ' U “ ‘ O Q ~ D C ‘ O \ ~ w ‘ m Q w p m m q " V ‘ Q m ‘ o ‘ \ ‘ 5 ) = - 5 ) = 5 ) = - 5 ) = 5 ) = 6 ) = 6 ) = - 6 ) = - 6 ) = 6 ) = - 6 ) = - 6 ) = 6 ) = - 6 ) = - 6 ) = 6 ) - - 7 ) = 7 ) = 7 ) = - 7 ) = 7 ) - 7 ) = - 7 ) = - 7 ) - 7 ) - 7 ) - - 7 ) - - 8 ) = 8 ) = - 8 ) = - 8 ) = 8 ) = 8 ) = - 8 ) = 8 ) - 8 ) = - 8 ) = 8 ) = - 9 ) = - 9 ) - 9 ) = 9 ) = - 9 ) = - 9 ) - 9 ) = 3 6 1 = . 6 6 1 3 2 1 8 6 7 3 7 7 4 6 8 - 0 2 . 3 1 1 4 9 5 7 0 0 1 9 6 2 2 E - 0 2 - . 9 2 4 1 1 2 1 7 9 2 0 2 3 7 E - 0 2 . 9 3 5 4 1 1 7 5 4 1 3 9 7 2 8 - 0 2 = . 8 5 1 9 7 4 9 6 6 5 2 2 7 3 E - 0 3 . 2 7 4 9 4 8 3 5 8 0 3 8 8 5 8 - 0 1 . 7 6 9 0 4 2 6 1 8 5 8 4 4 9 E - 0 1 . 1 4 1 3 8 9 1 3 5 7 7 2 7 4 E + 0 0 . 9 4 3 8 3 3 2 3 5 0 0 2 3 1 3 - 0 1 . 9 8 1 6 8 6 1 2 0 6 0 9 O I E + 0 0 . 3 3 5 8 5 4 4 6 7 6 6 4 5 2 E - 0 2 . 7 3 8 6 1 9 3 1 4 4 6 4 3 3 8 - 0 3 . 8 0 7 6 1 4 1 5 6 6 4 4 6 8 3 - 0 3 . 1 4 2 2 0 5 9 7 0 7 0 4 1 7 E - 0 2 . 6 7 3 8 2 6 6 6 1 4 6 5 6 0 E - 0 3 . 1 7 2 3 5 9 9 6 1 1 2 5 4 3 3 - 0 2 . 5 1 9 1 1 0 9 4 5 1 4 0 1 4 8 - 0 2 . 6 0 8 9 3 5 7 7 5 1 4 3 7 1 E - 0 2 . 1 0 9 3 5 5 9 7 6 4 1 5 7 7 8 - 0 1 . 1 2 1 1 4 4 3 3 2 9 9 5 4 4 E + 0 0 . 9 9 2 5 3 3 3 8 0 1 3 3 3 2 E + 0 0 . 2 1 5 1 2 6 3 8 3 3 2 7 8 1 8 - 0 1 . 1 6 9 5 1 6 7 7 3 3 1 4 2 5 E - 0 2 . 9 0 8 3 2 0 8 7 4 9 1 2 8 2 8 - 0 2 . 1 0 4 8 9 1 1 9 0 8 6 1 0 2 E - 0 2 . 1 1 9 3 2 0 7 2 1 9 2 5 4 1 E - 0 1 . 7 3 6 3 2 3 3 4 4 6 9 1 7 8 8 - 0 2 . 2 9 8 9 4 7 1 5 8 5 9 1 9 8 8 - 0 1 . 5 3 8 2 7 9 8 4 4 3 2 9 5 7 E - O l . 1 4 0 4 6 2 9 3 0 3 3 0 5 1 E + 0 0 . 9 0 1 1 0 8 3 3 2 6 2 2 8 9 E + 0 0 . 4 0 4 6 4 4 1 9 9 8 6 3 8 8 8 + 0 0 . 2 1 4 0 4 3 7 2 4 9 6 8 8 4 8 - 0 1 . 2 7 9 2 1 7 6 6 2 1 3 7 9 2 E - 0 2 . 7 0 4 4 1 3 5 2 0 8 8 7 7 6 E - 0 2 . 7 8 0 5 1 0 3 5 1 7 4 7 6 7 E - 0 2 . 1 8 9 7 3 7 4 3 9 1 0 5 9 4 E - 0 2 . 1 7 5 3 2 9 9 7 6 0 1 7 9 1 8 - 0 1 ' . 2 1 5 2 4 1 8 1 8 8 7 9 6 6 3 - 0 1 . 2 8 7 1 9 9 2 0 1 3 9 2 7 8 E - 0 1 . 2 1 7 9 1 5 6 9 5 4 4 4 1 2 E + 0 0 . 6 5 0 4 1 6 7 8 2 6 7 2 2 3 8 + 0 0 . 7 2 6 1 5 0 9 1 0 8 6 5 0 4 E + 0 0 . 3 1 8 9 6 6 7 4 9 2 4 1 3 6 8 - 0 2 . 1 1 0 8 4 4 5 6 4 4 7 6 8 1 8 - 0 3 . 1 2 4 8 0 8 6 9 3 8 5 3 5 2 E - 0 2 . 7 7 2 8 1 1 4 1 2 9 6 1 7 2 8 - 0 3 . 1 1 5 2 4 2 5 0 7 8 4 1 9 6 8 - 0 2 . 2 5 0 9 9 3 6 1 9 2 5 7 2 3 E - 0 2 . 5 1 1 7 1 3 2 9 1 2 9 3 9 9 E - 0 3 m H m N A m V ( ~ m - ‘ fi m ‘ l m “ “ l m ~ ‘ ~ m U ‘ m ‘ “ ~ O m ‘ V “ m — ~ ~ m D m ‘ N “ ’ m ~ U m D ‘ m M - ‘ ~ “ m m - O “ H “ m N ‘ m V h m ‘ “ t m m “ ~ H m h ‘ V m t Q m m ‘ V m m H - m C h m ‘ t ‘ I V ~ U m m G ‘ m H Q N m ‘ m W - “ F ~ m V O m W ‘ “ 3 6 2 S ( 1 1 , 8 , 9 ) = - . 1 1 2 0 4 8 9 7 7 2 1 7 0 3 E - 0 1 S ( 1 1 , 9 , 9 ) = . 1 9 7 2 1 0 6 9 5 5 9 3 3 3 3 - 0 1 S ( 1 1 , 1 0 , 9 ) = . 6 3 8 3 2 3 6 5 8 0 4 6 6 2 8 - 0 1 S ( 1 1 , 1 1 , 9 ) = - . 9 9 7 6 9 2 7 0 2 0 9 8 6 O E + 0 0 K ( 1 1 ) = m u ) : w s ( 1 1 , w s ( 1 1 , w s ( 1 1 , w s ( 1 1 , w s < 1 1 , w s ( 1 1 , w s ( 1 1 , w s ( 1 1 , w s ( 1 1 , V V 9 2 1 ) = - . 3 3 3 3 2 7 6 8 1 2 3 0 4 S E + 0 0 2 ) = - . 5 0 0 0 5 2 4 6 5 8 6 6 5 0 8 + 0 0 3 ) = - . 5 9 9 7 9 7 5 3 8 5 8 0 9 9 E + 0 0 4 ) = - . 6 6 7 1 1 5 5 0 3 9 6 1 8 7 E + 0 0 5 ) = - . 8 1 8 1 6 9 6 0 1 9 3 1 0 1 3 + 0 0 6 ) = - . 8 0 0 0 9 5 7 7 0 6 0 7 3 4 E + 0 0 7 ) = * . 7 1 3 6 7 1 0 5 0 5 4 8 7 3 8 + 0 0 8 ) = - . 7 7 7 4 6 4 9 4 9 4 6 1 1 3 8 + 0 0 9 ) = - . 7 5 0 5 5 0 9 8 7 5 8 3 4 9 E + 0 0 ‘ 1 ) = - . 1 6 3 9 5 3 7 8 0 4 1 0 4 3 E + 0 1 1 ) = 1 ) = - 1 ) = l ) - 1 ) = - 2 ) = - 2 ) = 2 ) = - 2 ) - 2 ) = 2 ) = - 3 ) = - 3 ) - 3 ) = - 3 ) - - 3 ) = 3 ) = - 4 ) - - 4 ) - 4 ) - 4 ) = - 4 ) - 4 ) = - 5 ) = - 5 ) = 5 ) - 5 ) = - 5 ) - 5 ) = - 6 ) = - 6 ) = - 6 ) = - 6 ) = 6 ) = . 6 4 7 4 5 3 2 2 2 6 5 3 3 1 8 - 0 1 . 1 6 7 6 2 2 6 4 2 9 4 0 3 7 E + 0 0 . 7 8 6 3 0 5 1 4 3 6 8 1 4 3 3 - 0 2 . 7 5 2 4 7 3 9 7 7 2 9 5 0 5 8 - 0 2 . 1 0 9 5 3 0 7 9 2 5 7 2 7 7 E + 0 1 . 1 6 3 9 5 7 3 0 8 8 4 0 0 6 8 - 0 1 . 6 2 6 9 4 1 2 5 5 3 5 5 0 1 E - 0 6 . 1 6 8 2 6 7 6 3 8 0 6 4 3 2 8 - 0 4 . 8 7 2 6 5 0 4 4 0 7 9 7 4 3 3 - 0 8 . 1 1 5 9 8 3 6 9 4 8 7 0 5 4 8 - 0 8 . 1 0 9 4 9 4 4 1 1 5 8 9 1 4 8 - 0 2 . 1 6 3 9 5 7 3 0 8 6 9 4 2 1 E - 0 3 . 3 4 8 3 3 6 3 2 5 0 6 2 2 6 E - 1 0 . 1 6 6 6 3 0 8 9 0 8 5 6 2 8 8 - 0 8 . 1 2 6 1 2 4 5 9 6 8 7 7 5 5 E - 1 0 . 6 2 4 5 3 0 3 7 5 3 3 1 6 1 E - 1 1 . 1 0 9 4 9 5 7 8 0 7 0 4 6 4 E - 0 5 . 1 6 3 9 5 7 3 0 1 7 7 0 3 3 E - 0 5 . 7 4 6 8 4 0 3 3 3 7 1 6 9 3 E - 1 2 . 2 7 9 8 1 3 2 8 1 9 1 9 8 4 3 - 1 2 . 3 9 0 3 5 4 5 3 7 4 3 0 9 5 E - 1 2 . 2 6 4 7 5 2 6 8 3 7 5 1 9 5 8 - 1 2 . 1 0 9 5 2 7 2 8 0 2 5 9 5 6 8 - 0 8 . 1 6 3 9 5 2 6 4 1 6 2 7 6 3 E - 0 7 . 4 1 0 8 8 5 5 3 4 1 1 4 8 6 3 - 1 1 . 2 2 7 7 6 0 0 2 6 6 6 2 8 2 E - 1 1 . 1 9 8 1 6 8 6 8 3 1 4 7 4 6 3 - 1 1 . 1 2 3 1 3 6 3 0 9 6 7 3 2 0 3 - 1 1 . 3 2 3 2 8 0 1 0 4 0 0 8 8 5 E - 1 1 . 1 6 3 9 4 2 4 2 5 0 5 4 9 9 3 - 0 9 . 3 0 4 7 4 1 1 9 2 8 9 0 9 2 E - 1 2 . 1 5 4 6 1 7 6 0 0 1 5 9 7 7 3 - 1 2 . 9 6 5 3 6 0 1 3 6 6 4 7 6 1 8 - 1 3 . 3 0 0 7 7 6 7 8 7 3 1 0 1 7 8 - 1 3 m m m m m m m m o x m o x o x o x o x o x o t o x o x o x o \ m m m m m m m m m m m m m m m m m m m m m m m H 0 0 A ‘ — l 0 A 0 “ H ‘ 0 A 0 — D ~ 0 A 0 ‘ — 0 I 0 A “ “ “ “ ~ “ “ - ‘ - “ ‘ V “ “ “ “ ‘ V V ~ “ “ ‘ ~ ‘ ~ ‘ V ‘ ~ ‘ - " - “ ‘ ~ ‘ ~ V V ~ ‘ ~ “ ~ “ “ V “ ‘ - ‘ V ‘ V V Q ~ ‘ fi ‘ V ‘ “ V “ ‘ \ l m m fi w N O - ‘ Q O ‘ U ' I I F U J N H \ l O ‘ U I fi U N F - ‘ N I O ‘ U I I F U N H Q O ‘ W I t h H \ J m m l w a H \ l O ‘ U ’ I O h U J N I - ‘ O fl 3 6 3 6 ) = . 2 8 9 8 5 1 0 6 7 1 9 1 7 8 E - 1 2 1 ) = - . 2 4 3 3 3 3 6 2 9 4 2 7 6 0 E + 0 1 1 ) = - . 2 1 6 6 3 8 3 6 2 2 0 7 2 5 E + 0 1 1 ) = - . 6 7 8 6 1 6 6 6 6 0 0 4 5 7 E + 0 0 1 ) = . 4 3 9 7 2 3 1 2 2 0 5 4 4 0 3 - 0 2 1 ) = . 1 1 9 0 4 6 6 8 6 2 5 0 8 9 E - 0 2 1 ) = - . 4 6 3 4 6 6 9 8 5 4 6 4 8 6 8 - 0 1 1 ) = . 3 3 9 4 0 7 9 3 7 5 6 2 8 7 8 - 0 1 2 ) = - . 2 4 3 3 3 1 8 2 7 5 0 4 3 0 E - 0 1 2 ) = - . 2 1 6 6 3 7 6 3 5 0 1 7 3 1 E - 0 2 2 ) = - . 6 8 1 6 3 2 7 5 2 6 9 0 4 0 E - 0 4 2 ) = . 6 6 8 2 3 9 8 7 5 6 5 6 3 4 E - 0 7 2 ) = - . 5 0 6 4 4 2 7 7 7 1 5 9 S O E - 0 7 2 ) = - . 5 2 6 5 0 9 9 5 6 9 6 6 2 4 E - 0 6 2 ) = . 2 4 3 1 4 2 3 8 9 4 4 4 4 5 8 - 0 6 3 ) = - . 2 4 3 3 3 1 8 3 0 1 4 4 5 5 8 - 0 3 3 ) = - . 2 1 6 4 5 8 3 4 6 8 1 0 6 5 E - 0 5 3 ) = - . 1 0 3 8 1 4 5 5 6 6 5 6 0 6 E - 0 7 3 ) = . 6 5 0 3 0 4 4 2 1 4 2 3 4 4 E - 0 9 3 ) = - . 4 9 3 4 8 2 2 6 1 9 9 8 4 l E - 0 9 3 ) = - . 4 6 8 5 5 0 3 8 4 6 0 2 4 7 E - 0 8 3 ) = - . 9 6 0 9 1 5 5 0 1 6 8 2 6 5 E - 0 9 4 ) = ' . 2 4 3 3 3 1 7 9 3 1 0 9 7 1 E - 0 5 4 ) = - . 2 1 4 9 6 3 1 9 1 2 0 8 3 1 3 - 0 8 4 ) = - . 2 8 8 8 1 0 9 2 0 4 3 7 3 3 E - 1 0 4 ) = . 4 2 7 3 7 0 6 6 9 3 7 1 1 7 3 - 1 1 4 ) = ’ . 3 3 9 8 4 9 8 5 4 3 9 4 3 5 3 - 1 1 4 ) = - . 3 3 7 0 9 0 3 6 4 3 0 2 4 l E - 1 0 4 ) = - . 7 1 6 5 4 1 2 1 4 3 8 3 6 4 E - 1 1 5 ) = - . 2 4 3 3 2 4 3 7 2 3 6 9 5 3 E - 0 7 5 ) = - . 7 4 4 2 1 0 3 6 7 5 6 6 4 7 E - 1 1 5 ) = . 1 4 1 9 2 3 7 9 7 2 4 2 5 9 E - 1 0 5 ) = - . 3 2 5 0 3 2 7 8 5 2 8 2 1 l E - 1 1 5 ) = . 2 5 8 3 9 3 2 7 9 1 9 6 2 2 8 - 1 1 5 ) = . 2 3 0 6 2 0 9 8 8 7 5 4 3 9 8 - 1 0 5 ) = . 4 4 1 8 5 7 4 4 2 9 1 9 6 0 8 - 1 1 6 ) = - . 2 4 3 3 4 7 4 3 2 6 4 1 6 3 E - 0 9 6 ) = . 3 1 3 3 3 6 7 4 9 4 1 3 4 2 3 - 1 2 6 ) = - . 6 0 6 3 8 3 5 6 4 6 6 5 4 3 8 ~ 1 2 6 ) = . 8 4 9 0 8 9 2 3 8 8 8 9 1 3 8 - 1 3 6 ) = - . 1 1 8 1 3 8 8 8 1 4 0 3 4 3 E - 1 2 6 ) = - . 9 9 1 4 7 8 8 6 9 1 7 1 7 l E - 1 2 6 ) = - . 2 2 4 0 9 9 8 5 3 0 4 5 8 7 E - 1 2 1 ) = . 2 0 9 6 4 3 2 3 6 8 7 7 6 3 E - 0 3 1 ) = . 3 4 1 5 2 8 8 0 9 2 0 2 1 3 3 + 0 1 1 ) = - . 3 7 8 5 6 7 2 1 7 1 2 6 8 0 E + 0 1 1 ) = . 1 7 3 2 1 8 9 1 4 9 3 1 9 9 E + 0 1 1 ) = . 6 0 2 0 1 8 8 4 5 0 6 0 8 2 E - 0 1 1 ) = - . 2 8 6 5 6 9 5 2 9 9 0 8 1 1 E - 0 1 1 ) = - . 3 0 1 1 6 7 0 2 6 5 6 4 4 2 8 - 0 2 C ( 1 0 , C ( 1 0 , C ( 1 0 , C ( 1 0 , C ( 1 0 , C ( 1 0 , C ( 1 0 , C ( 1 0 , C ( 1 0 , C ( 1 0 , C ( 1 0 , C ( 1 0 , C ( 1 0 . C ( 1 0 , C ( 1 0 , C ( 1 0 , C ( 1 0 , C ( 1 0 , C ( 1 0 , C ( 1 0 , C ( 1 0 , C ( 1 0 , C ( 1 0 , C ( 1 0 : C ( 1 0 . C ( 1 0 , C ( 1 0 , C ( 1 0 , C ( 1 0 , C ( 1 0 : C ( 1 0 , C ( 1 0 , C ( 1 0 , C ( 1 0 , C ( 1 0 , C ( 1 0 , C ( 1 0 , C ( 1 0 , C ( 1 0 . C ( 1 0 , C ( 1 0 : C ( 1 0 . C ( 1 0 , C ( 1 0 , C ( 1 0 , C ( 1 0 , C ( 1 0 , C ( 1 1 , C ( 1 1 , C ( 1 1 , V “ “ “ “ ~ ‘ ~ “ “ ~ “ ‘ - - - “ ‘ - “ “ V “ V ‘ ~ “ V ‘ V ‘ V Q ‘ w N H m m q m m h w u w m m q m m o w w H m m q m m p w m H m m q m m o w w w m m \ J m m w a o - u o m 3 6 4 1 ) 8 . 2 1 8 6 5 7 4 1 7 4 7 4 4 6 8 - 0 2 1 ) = . 2 5 4 4 2 9 9 2 7 4 6 1 6 Z E + 0 0 2 ) = . 7 2 0 4 0 3 7 3 9 0 7 4 1 6 E - 0 5 2 ) 8 . 3 4 1 4 5 6 2 5 9 8 6 3 8 0 8 - 0 1 2 ) 8 ' . 3 7 8 1 2 2 3 2 8 1 6 0 2 6 E - 0 2 2 ) = . l 7 3 7 8 4 7 4 7 4 0 1 3 7 E - 0 3 2 ) 8 - . 3 7 8 1 1 7 8 7 2 5 4 5 9 4 E - 0 5 2 ) 8 - . 2 7 2 6 7 7 8 5 8 4 0 9 4 5 E - 0 5 2 ) 8 - . 2 5 0 1 7 3 9 8 6 3 5 7 5 2 8 - 0 5 2 ) 8 . 1 2 2 8 5 0 1 0 0 0 6 3 4 5 8 - 0 6 2 ) = . 5 7 8 2 4 5 7 2 4 6 2 5 0 6 3 - 0 5 8 . 8 0 5 9 1 3 8 9 8 2 8 7 8 7 8 - 0 7 8 . 3 4 1 4 4 2 2 6 5 3 4 7 2 3 8 - 0 3 = - , 3 7 4 3 1 4 8 5 3 0 2 7 1 0 3 - 0 5 8 . 2 0 8 8 2 9 8 4 3 1 0 5 5 0 E - 0 7 8 - . 3 8 4 0 7 9 6 2 8 3 8 8 0 6 E - 0 7 8 - . 2 6 7 4 6 7 4 3 0 4 6 9 3 1 8 - 0 7 8 8 . 2 6 1 7 0 6 4 6 1 3 1 9 6 6 E - 0 7 8 . 1 1 0 8 7 3 9 1 2 2 0 6 2 0 8 - 0 8 8 . 3 3 3 2 8 7 2 1 7 1 9 0 9 3 8 - 0 7 8 . 8 1 4 8 4 2 8 4 8 8 3 1 8 9 8 - 0 9 8 . 3 4 1 4 4 0 5 5 9 8 5 8 3 4 8 - 0 5 . 3 4 4 5 1 2 9 9 0 4 3 2 4 1 E - 0 8 . 8 4 9 3 6 2 9 1 6 1 5 4 4 1 8 - 1 0 . 6 0 2 5 8 5 9 0 7 3 8 7 4 3 3 - 0 9 . 4 6 9 0 8 4 5 2 6 8 5 0 5 9 8 - 0 9 . 3 7 3 2 9 7 3 5 5 4 6 8 4 3 8 - 0 9 8 . 2 9 6 2 6 4 2 8 5 7 5 4 5 8 3 - 1 0 8 . 4 6 9 5 5 7 2 9 5 1 5 9 4 7 8 - 0 9 8 . 8 0 5 4 2 4 5 3 6 3 5 4 7 1 8 - 1 1 8 . 3 4 1 4 0 6 5 5 3 7 1 3 5 4 8 - 0 7 . 4 1 9 4 5 5 9 0 1 1 3 5 6 8 E - 1 0 . 1 8 7 1 5 8 7 3 8 4 5 4 3 5 E - 0 9 . 3 2 6 0 5 9 1 2 7 2 4 8 4 9 8 - 0 9 . 2 9 7 0 7 4 2 4 0 6 3 7 6 6 8 - 0 9 . 1 5 9 7 4 3 5 2 2 1 9 9 6 8 3 - 0 9 8 . 2 5 4 5 5 0 3 7 7 3 0 7 7 6 8 - 1 0 8 . 2 0 5 7 9 5 5 8 8 6 4 2 4 4 E - 0 9 8 . 1 8 3 7 4 5 1 7 2 9 6 0 2 3 8 - 1 3 8 . 3 3 9 2 2 2 8 5 0 3 0 1 4 7 3 - 0 9 8 - . 2 6 2 3 2 7 3 0 0 9 3 8 8 6 E - 1 0 8 8 . 1 1 8 2 2 8 3 6 4 0 2 7 9 5 E - " 0 9 6 ) 8 - . 2 0 3 4 4 3 2 2 9 2 3 3 0 7 E - 0 9 6 ) = - . 1 8 5 8 9 7 2 7 3 2 7 9 3 7 E - 0 9 6 ) = ’ . 9 9 6 5 1 7 0 9 9 2 1 8 6 B E - 1 0 6 ) 8 . 1 6 0 5 4 8 8 2 0 3 0 9 8 8 8 - 1 0 6 ) = . 1 2 7 6 1 3 5 4 6 5 1 7 7 1 8 - 0 9 1 ) = . 4 6 0 5 3 0 1 5 7 2 7 8 9 7 E + 0 1 1 ) = - . 6 0 6 4 3 4 7 5 8 9 1 9 7 7 E + 0 1 1 ) = - . 3 6 0 5 4 4 1 6 6 4 5 1 5 3 8 + 0 1 C ( 1 1 , C ( 1 1 , C ( 1 1 , C ( 1 1 , C ( 1 1 , C ( 1 1 , C ( 1 1 , C ( 1 1 , C ( 1 1 , C ( 1 1 , C ( 1 1 , C ( 1 1 , C ( 1 1 , C ( 1 1 , C ( 1 1 , C ( 1 1 , C ( 1 1 , C ( 1 1 , C ( 1 1 , C ( 1 1 , C ( 1 1 , C ( 1 1 , C ( 1 1 , C ( 1 1 , C ( 1 1 , C ( 1 1 , C ( 1 1 , C ( 1 1 , C ( 1 1 , C ( 1 1 , C ( 1 1 , C ( 1 1 , C ( 1 1 , C ( 1 1 , C ( 1 1 , C ( 1 1 , C ( 1 1 , C ( 1 1 , C ( 1 1 , C ( 1 1 , C ( 1 1 , C ( 1 1 , C ( 1 1 , C ( 1 1 , C ( 1 1 , C ( 1 1 , C ( 1 1 , C ( 1 1 , C ( 1 1 , C ( 1 1 , m u m m p w N H m m q m m u c - u M I — u o m q o s m o w m u m m q m m h w m u m m q m m u b w M i - u o m x l m u n h ~ ‘ ~ ‘ - “ “ - ‘ Q “ - ‘ - “ “ “ ~ V ‘ ~ ‘ ~ ‘ § ~ V “ - V ‘ ~ “ “ “ 1 ) = - 1 ) = - 1 ) = - 6 ) = 5 ) = - 5 ) = - 6 ) = 5 ) = 6 ) = - 5 ) = - 3 6 5 “ . 1 0 9 3 5 5 6 1 3 3 1 0 2 7 E + 0 1 . 1 1 4 7 9 4 1 9 0 0 8 3 3 3 E - 0 2 . 4 6 0 6 3 5 8 0 9 4 0 1 9 9 8 - 0 1 . 1 2 2 3 6 5 6 6 8 9 5 2 2 6 8 - 0 1 . 1 4 3 5 1 4 8 4 2 6 0 6 0 8 8 - 0 1 . 2 0 5 8 3 1 7 4 2 6 6 8 2 7 E + 0 0 - . 4 6 0 3 6 6 9 7 3 0 1 6 6 B B - O l - . 6 0 6 0 8 4 7 9 2 8 8 2 6 9 E - 0 2 . 1 2 7 1 4 7 4 5 2 3 8 8 7 3 E - 0 3 . 4 7 6 6 8 6 4 0 9 9 3 5 9 2 8 - 0 3 8 . 7 8 7 4 2 4 9 0 1 6 0 7 6 6 E - 0 5 . 2 4 8 7 5 9 0 4 3 4 5 0 7 9 8 - 0 3 . 9 7 1 9 2 3 0 5 8 7 5 7 9 3 E - 0 4 . 8 7 1 2 2 0 3 0 0 0 1 4 9 6 3 - 0 4 . 7 5 8 2 5 1 0 2 7 5 1 9 9 2 8 8 0 3 . 4 6 0 3 3 7 4 7 0 8 1 6 9 7 8 - 0 3 . 5 9 8 7 5 9 7 0 3 1 3 5 4 5 E - 0 5 . 2 1 5 4 9 2 3 9 0 6 2 2 3 1 8 - 0 5 . 4 3 1 8 8 1 2 9 5 0 7 2 3 8 E - 0 5 8 . 7 5 0 5 4 4 7 9 7 1 5 4 3 2 8 - 0 7 . 2 3 6 5 4 5 1 5 0 5 2 4 7 1 8 - 0 5 . 9 1 0 3 2 1 3 8 0 1 0 2 8 9 8 - 0 6 . 8 2 4 0 4 5 2 6 5 0 4 8 6 2 8 - 0 6 . 7 1 4 7 9 3 1 7 3 7 6 0 2 8 3 - 0 5 . 4 6 0 3 3 4 2 3 5 4 5 0 3 5 E - 0 5 . 5 2 6 6 7 3 7 8 9 3 7 4 6 5 8 - 0 8 . 2 1 8 3 8 6 6 3 2 6 4 9 2 5 8 - 0 7 . 4 3 1 3 1 6 4 9 3 4 5 0 9 8 8 - 0 7 . 7 5 2 6 7 2 5 8 3 4 7 3 0 4 8 - 0 9 . 2 3 7 1 3 7 8 6 6 6 8 4 8 0 8 - 0 7 . 9 1 0 5 0 3 2 5 4 8 0 2 7 0 8 - 0 8 . 8 2 5 5 0 4 5 0 0 2 8 7 5 5 E - 0 8 . 7 1 5 6 2 2 5 3 3 4 2 7 6 8 E - 0 7 . 4 6 0 3 2 0 1 6 1 4 4 4 0 4 8 - 0 7 . 2 0 7 9 1 8 1 1 5 2 8 8 5 3 E - 1 0 . 3 6 9 5 6 8 9 5 1 2 6 4 3 4 E - 0 9 . 8 0 6 2 7 8 4 7 7 4 8 0 6 9 E - 0 9 . 1 6 2 6 7 9 5 5 9 6 1 6 3 0 3 - 1 0 . 4 9 3 3 1 2 6 8 6 3 7 0 4 1 3 - 0 9 . 1 7 5 3 0 7 5 0 2 4 4 0 4 8 3 - 0 9 . 1 6 7 6 9 3 6 0 3 8 9 1 3 2 8 - 0 9 . 1 4 1 4 3 5 7 1 8 6 5 3 1 0 3 - 0 8 . 4 6 0 9 1 2 9 8 9 9 6 2 1 4 8 - 0 9 . 1 0 2 4 2 6 0 8 0 1 7 6 2 3 8 - 1 0 . 6 4 5 9 8 2 7 0 9 3 0 8 9 2 8 - 1 0 . 1 6 0 5 7 7 8 1 9 0 7 5 4 2 8 - 0 9 . 3 0 3 8 7 3 2 1 0 9 5 8 2 2 8 - 1 1 . 1 0 0 1 3 7 8 1 8 7 2 6 1 7 8 - 0 9 . 3 5 7 9 4 7 2 3 4 8 6 3 4 3 3 - 1 0 . 3 4 7 4 7 9 7 7 3 1 4 5 2 4 E - 1 0 1 0 4 0 3 6 6 C ( 1 1 , 9 , 6 ) = - . 2 9 2 6 2 4 4 9 4 1 9 5 8 2 8 - 0 9 P R I N T * , ' O R D E R O F C O L L O C A T I O N = ' R E A D * , I P R I N T * , ' 1 1 = ? W H E R E E o = 2 * 1 0 * * ( - 1 1 ) ' R E A D * , 1 1 B O = 2 . * 1 0 * * ( - I l ) W R I T E ( 6 0 , 5 0 ) I , B O D O 2 0 T = . 0 1 , l . , . 0 1 S U M 1 = 0 . 0 S U M 2 = 0 . 0 D O 3 0 J = 1 , I S U M = 0 . 0 D O 4 0 J 1 = 1 , K ( I ) S U M = S U M + C ( I , J 1 , 1 1 ) * S ( I , J , J 1 ) * E X P ( W S ( I , J 1 ) * T ) C O N T I N U E F C ( J ) = S U M + 1 . B = B O * E X P ( - T / 6 . ) w a ( J ) = E X P ( - . 5 * E * L ( I , J ) / ( 1 . - B ) ) * ( 1 . - 1 . 5 * B / ( 1 . - B ) + + . 5 * B * L ( I , J ) / ( 1 . - B ) * * 2 ) / ( 1 . - B ) * * 1 . 5 R ( J ) = F C ( J ) / F K W ( J ) S U M 1 8 S U M 1 + ( F C ( J ) - 1 . ) * * 2 S U M 2 = S U M 2 + ( w a ( J ) — 1 . ) * * 2 C O N T I N U E W R I T E ( 6 0 , 6 0 ) T W R I T E ( 6 0 , 6 1 ) S U M 1 , S U M 2 P O R N A T ( 5 X , ' S T A E L E N O R M c ' , E 2 0 . 1 4 , 5 x , ' E K w N O R M 8 ' , E 2 0 . 1 4 ) D O 7 0 J = 1 , I W R I T E ( 6 0 , 8 0 ) J , F C ( J ) , F K W ( J ) , R ( J ) C O N T I N U E P O R M A T ( l o x , 1 2 , ' - P O I N T C O L L O C A T I O N ' , s x , ' E o = ' , E 2 0 . 1 4 ) P O R M A T < 7 x , ' D I M E N S I O N L E S S T I M E = ' , E 2 0 . 1 4 ) F O R M A T ( 7 X , 1 2 , S X , E 2 0 . 1 4 , 5 X , E Z O . 1 4 , S X , E Z O . 1 4 ) C O N T I N U E P R I N T * , ' T Y P E 1 T O S T O P , 0 T O C O N T I N U E ' R E A U * , 1 2 I F ( 1 2 . E Q . 0 ) G O T O 1 0 S T O P E N D 3 6 7 P R O G R A M L E R R I ( I N P U T , O U T P U T , T A P E 5 0 ) R E A L A 1 ( 8 : 1 1 , 1 1 , 1 1 ) , A 3 ( 8 : 1 1 , 1 1 , 1 1 ) , L ( 1 5 , 1 5 ) , E ( 1 5 , 1 5 ) , + C ( 1 5 , 1 5 , 6 ) , E R R ( 8 : 1 1 , 6 ) , S ( 8 : 1 1 , 1 1 , l l ) , W S ( 8 : 1 1 , 1 1 ) , E N O R M ( 8 : 1 1 , 1 1 ) R E A L Y N O R M ( 1 1 , 1 1 ) I N T E G E R K ( 1 l ) , M ( 1 l ) C T H I S P R O G R A M C A L C U L A T E S T H E N O R M O F T H E U N S T A B L E C O M P O N E N T C O F A N Y I N I T I A L D I S T R I B U T I O N . L ( 1 , 1 ) = l . L ( 2 , 1 ) = . 5 8 5 7 8 6 4 3 7 6 2 7 L ( 2 , 2 ) = 3 . 4 1 4 2 1 3 5 6 2 3 7 3 L ( 3 , 1 ) = . 4 1 5 7 7 4 5 5 6 7 8 3 L ( 3 , 2 ) = 2 . 2 9 4 2 8 0 3 6 0 2 7 9 L ( 3 , 3 ) = 6 . 2 8 9 9 4 5 0 8 2 9 3 7 L ( 4 , 1 ) = . 3 2 2 5 4 7 6 8 9 6 1 9 L ( 4 , 2 ) = 1 . 7 4 5 7 6 1 1 0 1 1 5 8 L ( 4 , 3 ) = 4 . 5 3 6 6 2 0 2 9 6 9 2 1 L ( 4 , 4 ) = 9 . 3 9 5 0 7 0 9 1 2 3 0 1 L ( 5 , 1 ) = . 2 6 3 5 6 0 3 1 9 7 1 8 L ( 5 , 2 ) = l . 4 1 3 4 0 3 0 5 9 1 0 7 L ( 5 , 3 ) = 3 . 5 9 6 4 2 5 7 7 1 0 4 1 L ( 5 , 4 ) = 7 . 0 8 5 8 1 0 0 0 5 8 5 9 L ( 5 , 5 ) = 1 2 . 6 4 0 8 0 0 8 4 4 2 7 6 L ( 6 , l ) 8 . 2 2 2 8 4 6 6 0 4 1 7 9 L ( 6 , 2 ) = 1 . 1 8 8 9 3 2 1 0 1 6 7 3 L ( 6 , 3 ) = 2 . 9 9 2 7 3 6 3 2 6 0 5 9 L ( 6 , 4 ) 8 5 . 7 7 5 1 4 3 5 6 9 1 0 5 L ( 6 , 5 ) = 9 . 8 3 7 4 6 7 4 1 8 3 8 3 L ( 6 , 6 ) = 1 5 . 9 8 2 8 7 3 9 8 0 6 0 2 L ( 7 , 1 ) 8 . l 9 3 0 4 3 6 7 6 5 6 0 L ( 7 , 2 ) = 1 . 0 2 6 6 6 4 8 9 5 3 3 9 L ( 7 , 3 ) = 2 . 5 6 7 8 7 6 7 4 4 9 5 1 L ( 7 , 4 ) 8 4 . 9 0 0 3 5 3 0 8 4 5 2 6 L ( 7 , 5 ) = 8 . 1 8 2 1 5 3 4 4 4 5 6 3 L ( 7 , 6 ) = 1 2 . 7 3 4 1 8 0 2 9 1 7 9 8 L ( 7 , 7 ) = 1 9 . 3 9 5 7 2 7 8 6 2 2 6 3 L ( 8 , 1 ) = . 1 7 0 2 7 9 6 3 2 3 0 5 L ( 8 , 2 ) = . 9 0 3 7 0 1 7 7 6 7 9 9 L ( 8 , 3 ) = 2 . 2 5 1 0 8 6 6 2 9 8 6 6 L ( 8 , 4 ) = 4 . 2 6 6 7 0 0 1 7 0 2 8 8 L ( 8 , S ) = 7 . 0 4 5 9 0 5 4 0 2 3 9 3 L ( 8 , 6 ) = 1 0 . 7 5 8 5 1 6 0 1 0 1 8 1 L ( 8 , 7 ) 8 1 5 . 7 4 0 6 7 8 6 4 1 2 7 8 L ( 8 , 8 ) = 2 2 . 8 6 3 1 3 1 7 3 6 8 8 9 L ( 9 , 1 ) = . 1 5 2 3 2 2 2 2 7 7 3 2 L ( 9 , 2 ) = . 8 0 7 2 2 0 0 2 2 7 4 2 L ( 9 , 3 ) = 2 . 0 0 5 1 3 5 1 5 5 6 1 9 L ( 9 , 4 ) 8 3 . 7 8 3 4 7 3 9 7 3 3 3 1 L ( 9 , 5 ) = 6 . 2 0 4 9 5 6 7 7 7 8 7 7 L ( 9 , 6 ) = 9 . 3 7 2 9 8 5 2 5 1 6 8 8 L ( 9 , 7 ) = 1 3 . 4 6 6 2 3 6 9 1 1 0 9 2 L ( 9 , 8 ) 8 1 8 . 8 3 3 5 9 7 7 8 8 9 9 2 L ( 9 , 9 ) = 2 6 . 3 7 4 0 7 1 8 9 0 9 2 7 L ( 1 0 , 1 ) = . l 3 7 7 9 3 4 7 0 5 4 0 L ( 1 0 , 2 ) = . 7 2 9 4 5 4 5 4 9 5 0 3 L ( 1 0 , 3 ) = 1 . 8 0 8 3 4 2 9 0 1 7 4 0 L ( 1 0 , 4 ) = 3 . 4 0 1 4 3 3 6 9 7 8 5 5 L ( 1 0 , 5 ) 8 5 . 5 5 2 4 9 6 1 4 0 0 6 4 L ( 1 0 , 6 ) 8 8 . 3 3 0 1 5 2 7 4 6 7 6 4 L ( 1 0 , 7 ) = 1 1 . 8 4 3 7 8 5 8 3 7 9 0 0 L ( 1 0 , 8 ) = 1 6 . 2 7 9 2 5 7 8 3 1 3 7 8 L ( 1 0 , 9 ) = 2 1 . 9 9 6 5 8 5 8 1 1 9 8 1 L ( 1 0 , 1 0 ) = 2 9 . 9 2 0 6 9 7 0 1 2 2 7 4 L ( 1 1 , 1 ) = . 1 2 5 7 9 6 4 4 2 1 8 8 L ( 1 1 , 2 ) = . 6 6 5 4 1 8 2 5 5 8 3 9 L ( 1 1 , 3 ) = 1 . 6 4 7 1 5 0 5 4 5 8 7 2 L ( 1 1 , 4 ) = 3 . 0 9 1 1 3 8 1 4 3 0 3 5 L ( 1 1 , 5 ) = 5 . 0 2 9 2 8 4 4 0 1 5 8 0 L ( l l , 6 ) = 7 . 5 0 9 8 8 7 8 6 3 8 0 7 L ( 1 1 , 7 ) = 1 0 . 6 0 5 9 5 0 9 9 9 5 4 7 L ( 1 1 , 8 ) = l 4 . 4 3 1 6 1 3 7 5 8 0 6 4 L ( l l , 9 ) = 1 9 . 1 7 8 8 5 7 4 0 3 2 1 5 L ( l l , 1 0 ) = 2 5 . 2 1 7 7 0 9 3 3 9 6 7 8 L ( l l , l l ) = 3 3 . 4 9 7 1 9 2 8 4 7 1 7 6 L ( 1 2 , 1 ) = . 1 1 5 7 2 2 1 1 7 3 5 8 L ( 1 2 , 2 ) = . 6 1 1 7 5 7 4 8 4 5 1 5 L ( 1 2 , 3 ) = 1 . 5 1 2 6 1 0 2 6 9 7 7 6 L ( 1 2 , 4 ) = 2 . 8 3 3 7 5 1 3 3 7 7 4 4 L ( 1 2 , 5 ) = 4 . 5 9 9 2 2 7 6 3 9 4 1 8 L ( 1 2 , 6 ) = 6 . 8 4 4 5 2 5 4 5 3 1 1 5 L ( 1 2 , 7 ) = 9 . 6 2 1 3 1 6 8 4 2 4 5 7 L ( 1 2 , 8 ) = 1 3 . 0 0 6 0 5 4 9 9 3 3 0 6 L ( 1 2 , 9 ) = 1 7 . 1 1 6 8 5 5 1 8 7 4 6 2 L ( 1 2 , 1 0 ) = 2 2 . 1 5 1 0 9 0 3 7 9 3 9 7 L ( 1 2 , 1 1 ) = 2 8 . 4 8 7 9 6 7 2 5 0 9 8 4 L ( 1 2 , 1 2 ) = 3 7 . 0 9 9 1 2 1 0 4 4 4 6 7 L ( 1 3 , 1 ) = . 1 0 7 1 4 2 3 8 8 4 7 2 L ( 1 3 , 2 ) = . 5 6 6 1 3 1 8 9 9 0 4 0 L ( 1 3 , 3 ) = 1 . 3 9 8 5 6 4 3 3 6 4 5 1 L ( 1 3 , 4 ) = 2 . 6 1 6 5 9 7 1 0 8 4 0 6 L ( l 3 , 5 ) = 4 . 2 3 8 8 4 5 9 2 9 0 1 7 L ( 1 3 , 6 ) 8 6 . 2 9 2 2 5 6 2 7 1 1 4 0 L ( 1 3 , 7 ) = 8 . 8 1 5 0 0 1 9 4 1 1 8 7 L ( 1 3 , 8 ) = 1 1 . 8 6 1 4 0 3 5 8 8 8 1 1 L ( 1 3 , 9 ) = 1 5 . 5 1 0 7 6 2 0 3 7 7 0 4 L ( 1 3 , 1 0 ) = 1 9 . 8 8 4 6 3 5 6 6 3 8 8 0 L ( 1 3 , 1 1 ) 8 2 5 . 1 8 5 2 6 3 8 6 4 6 7 8 L ( 1 3 , 1 2 ) = 3 1 . 8 0 0 3 8 6 3 0 1 9 4 7 L ( 1 3 , 1 3 ) 8 4 0 . 7 2 3 0 0 8 6 6 9 2 6 6 L ( 1 4 , 1 ) 8 . 0 9 9 7 4 7 5 0 7 0 3 3 L ( 1 4 , 2 ) = . 5 2 6 8 5 7 6 4 8 8 5 2 3 6 8 m w V ‘ m w m w ‘ V m u “ m w V m w - “ m w ‘ “ m w m w V “ m w ~ ~ m w ‘ ‘ m w m - m m w “ m w ~ m w m w ‘ m w ~ m w ‘ m w ~ ‘ ~ “ “ “ “ m w m w ~ “ L ( l 4 , 3 ) = 1 . 3 0 0 6 2 9 1 2 1 2 5 1 L ( 1 4 , 4 ) = 2 . 4 3 0 8 0 1 0 7 8 7 3 1 L ( 1 4 , 5 ) = 3 . 9 3 2 1 0 2 8 2 2 2 9 3 L ( l 4 , 6 ) = 5 . 8 2 5 5 3 6 2 1 8 3 0 2 L ( l 4 , 7 ) = 8 . l 4 0 2 4 0 1 4 1 5 6 5 L ( l 4 , 8 ) 8 1 0 . 9 1 6 4 9 9 5 0 7 3 6 6 L ( 1 4 , 9 ) = 1 4 . 2 1 0 8 0 5 0 1 1 1 6 1 L ( 1 4 , 1 0 ) = 1 8 . 1 0 4 8 9 2 2 2 0 2 1 8 L ( 1 4 , 1 1 ) 8 2 2 . 7 2 3 3 8 1 6 2 8 2 6 9 L ( 1 4 , 1 2 ) = 2 8 . 2 7 2 9 8 1 7 2 3 2 4 8 L ( l 4 , 1 3 ) = 3 5 . 1 4 9 4 4 3 6 6 0 5 9 2 L ( 1 4 , 1 4 ) 8 4 4 . 3 6 6 0 8 1 7 1 1 1 1 7 L ( 1 5 , l ) = . 0 9 3 3 0 7 8 1 2 0 1 7 L ( 1 5 , 2 ) = . 4 9 2 6 9 1 7 4 0 3 0 2 L ( 1 5 , 3 ) = 1 . 2 1 5 5 9 5 4 1 2 0 7 l L ( 1 5 , 4 ) = 2 . 2 6 9 9 4 9 5 2 6 2 0 4 L ( 1 5 , 5 ) = 3 . 6 6 7 6 2 2 7 2 1 7 5 1 L ( 1 5 , 6 ) = 5 . 4 2 5 3 3 6 6 2 7 4 1 4 L ( 1 5 , 7 ) = 7 . 5 6 5 9 1 6 2 2 6 6 1 3 L ( 1 5 , 8 ) = 1 0 . 1 2 0 2 2 8 5 6 8 0 1 9 L ( 1 5 , 9 ) = 1 3 . 1 3 0 2 8 2 4 8 2 1 7 6 L ( 1 5 , 1 0 ) = 1 6 . 6 5 4 4 0 7 7 0 8 3 3 0 L ( 1 5 , 1 1 ) 8 2 0 . 7 7 6 4 7 8 8 9 9 4 4 9 L ( 1 5 , 1 2 ) = 2 5 . 6 2 3 8 9 4 2 2 6 7 2 9 L ( 1 5 , 1 3 ) = 3 1 . 4 0 7 5 1 9 1 6 9 7 5 4 L ( 1 5 , 1 4 ) = 3 8 . 5 3 0 6 8 3 3 0 6 4 8 6 L ( 1 5 , 1 5 ) 8 4 8 . 0 2 6 0 8 5 5 7 2 6 8 6 A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( 8 . 1 I V 1 ) = . 1 1 4 6 1 0 7 1 5 7 4 2 8 2 E + 0 2 2 ) = . 3 6 4 2 5 8 4 6 4 7 0 9 3 3 E + 0 2 3 ) = . 2 3 5 3 0 3 5 0 7 8 6 5 8 6 E + 0 0 4 ) = - . 3 3 0 2 6 1 9 3 9 6 4 6 0 1 E + 0 2 5 ) = - . 3 4 8 5 3 8 6 9 0 2 6 3 6 3 8 + 0 2 6 ) = - . 1 3 2 5 6 0 3 3 2 9 7 8 7 6 E + 0 2 7 ) = " . 2 3 3 9 7 1 0 5 4 7 3 1 2 3 3 + 0 1 8 ) = - . 1 0 6 1 7 2 3 6 2 5 7 5 3 1 E + 0 0 1 ) = . 7 6 9 4 6 9 3 4 8 4 2 8 2 5 8 + 0 2 2 ) = . 3 1 9 0 0 8 2 9 0 6 3 8 1 3 E + 0 3 3 ) = . 1 1 1 2 9 9 6 8 2 2 2 2 2 3 8 + 0 2 4 ) = - . 2 8 5 8 0 6 4 8 7 2 4 4 2 6 E + 0 3 5 ) = - . 3 2 1 8 8 7 2 6 4 1 6 9 5 8 8 + 0 3 6 ) = - . 1 5 1 4 8 7 6 9 8 4 7 7 9 B E + 0 3 7 ) = - . 3 1 6 1 8 3 8 2 1 8 3 5 4 4 E + 0 2 8 ) = - . 2 9 0 2 0 1 0 7 4 6 3 O O Z E + 0 1 1 ) = . 5 0 7 5 1 7 9 4 1 2 5 0 4 l E + 0 2 2 ) = . 1 7 7 5 6 2 3 0 2 5 5 4 1 8 8 + 0 3 3 ) = . 4 4 1 1 2 9 1 7 4 8 5 2 5 4 E + 0 1 4 ) = - . 1 5 7 4 0 9 8 8 5 2 2 7 5 3 8 + 0 3 5 ) = - . 1 8 2 6 5 6 6 5 0 8 1 2 2 9 E + 0 3 6 ) = - . 8 5 2 8 5 3 7 6 8 4 7 1 9 8 E + 0 2 7 ) = - . 1 9 1 0 6 9 5 0 3 2 0 8 5 6 E + 0 2 A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( p u w w w w w w w m w w m w m m w H H H H H H H t - a o x m o x m m a x m m m m m m m m m m o n - a : - p p m - p « M P - w Q Q “ ~ ‘ - “ “ - “ V ‘ ~ ‘ V ‘ ~ V ‘ “ “ “ ‘ V “ - ~ “ “ ~ ‘ Q ‘ - ~ ‘ - - - - - - - - - § - - ~ § - ~ fi fi “ - ~ § - - ~ § ~ ‘ ~ § ~ § - m m m m m m m m m m m m m m m m m m m m m o o m o o m o o o o o o o o m m m o o o o m m o o m o o m o o o o o o o o m m o o o o o o m 3 7 0 - . 1 3 9 9 0 3 3 8 5 1 4 5 5 9 E + 0 1 - . 3 5 9 7 1 7 8 5 0 1 2 0 0 7 E + 0 2 - . 1 5 7 2 4 7 9 6 l 7 1 9 1 4 E + 0 3 . 3 2 7 9 7 9 5 1 8 9 1 7 7 l E + 0 1 . 1 4 2 2 0 6 7 6 9 9 5 1 5 3 E + 0 3 . 1 4 4 5 0 0 3 6 4 6 3 1 6 6 E + 0 3 . 7 8 7 7 8 0 3 6 6 0 5 1 3 0 8 + 0 2 . 1 3 4 6 6 2 7 1 8 8 9 0 7 G E + 0 2 . 1 5 5 2 3 8 5 2 0 4 4 7 1 6 E + 0 1 . 9 5 5 4 6 8 6 2 7 4 0 2 3 0 8 + 0 1 . 1 0 0 8 2 4 6 2 4 0 1 9 5 7 E + 0 3 . 1 3 5 4 2 3 2 4 3 7 2 3 2 0 8 + 0 1 . 9 6 2 4 0 4 0 7 1 1 4 8 2 3 E + 0 2 . 6 6 5 8 0 3 3 6 5 9 2 0 8 7 E + 0 2 . 4 9 1 6 4 9 7 8 5 1 6 8 7 O E + 0 2 . 6 4 6 2 2 9 8 0 4 7 5 3 9 7 E + 0 1 . 9 2 4 5 6 9 5 8 9 0 8 5 8 8 8 + 0 0 . 4 2 1 8 2 7 1 3 3 9 4 8 2 5 3 + 0 2 . 1 6 3 3 9 2 7 6 0 3 2 7 8 9 E + 0 3 . 8 4 5 4 4 0 9 2 8 3 0 4 7 4 E + 0 1 . 1 4 2 9 7 9 4 4 4 1 0 3 0 0 E + 0 3 . 1 8 4 9 7 4 0 9 8 5 8 1 4 3 E + 0 3 . 8 3 0 7 5 7 7 7 5 7 6 0 1 4 E + 0 2 . 1 7 4 8 4 0 7 7 2 1 5 5 4 4 E + 0 2 . 1 0 0 7 4 2 5 5 2 1 9 6 6 1 8 + 0 1 . 2 6 1 8 4 0 3 7 8 0 0 8 0 3 8 + 0 0 . 2 4 9 0 2 2 3 2 7 8 6 1 5 3 E + 0 0 . 2 2 5 4 7 4 0 2 5 2 6 6 0 4 E + 0 0 . 1 9 0 2 4 7 0 6 1 2 5 9 3 O E + 0 0 . 1 4 1 6 7 4 7 7 2 6 5 4 3 7 E + 0 0 . 7 6 7 8 9 3 1 8 9 9 2 8 3 1 8 - 0 1 . 1 0 2 8 4 1 5 0 6 6 0 4 7 2 8 - 0 1 . 1 3 4 7 6 3 8 2 9 7 8 6 5 6 8 + 0 0 . 2 4 9 0 2 2 3 2 7 8 6 1 5 B E + 0 0 . 2 3 7 4 0 4 9 6 4 5 0 7 1 5 E + 0 0 . 2 1 6 0 6 2 4 6 8 2 2 4 7 S E + 0 0 . 1 8 4 1 3 5 2 6 8 9 9 9 2 1 E + 0 0 . 1 4 0 1 1 2 8 2 2 6 0 0 4 2 8 + 0 0 . 8 1 3 0 5 2 9 0 8 7 0 3 1 3 8 - 0 1 . 2 3 8 8 1 2 9 5 6 5 2 1 6 8 8 - 0 2 . 1 1 0 4 3 1 3 5 2 2 1 8 3 S E + 0 0 . 2 2 5 4 7 4 0 2 5 2 6 6 0 4 E + 0 0 . 2 1 6 0 6 2 4 6 8 2 2 4 7 4 E + 0 0 . 1 9 8 7 7 2 3 0 3 9 2 6 5 8 E + 0 0 . 1 7 2 9 0 7 1 7 0 2 0 7 0 1 E + 0 0 . 1 3 7 2 4 3 3 3 2 1 7 0 9 9 E + 0 0 . 8 9 6 0 1 6 7 5 3 8 3 9 5 1 E - O l . 2 5 6 6 8 6 3 5 3 0 3 2 7 4 8 - 0 1 - . 6 5 7 2 9 6 5 8 9 7 4 6 1 6 E - 0 1 . 1 9 0 2 4 7 0 6 1 2 5 9 3 0 E + 0 0 q u m m t h q u m m fi w N q u m m t h D - q u m m w a I — ‘ m q m m w a I — I m q m m b u N I — l m v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v V V V V V V V V V V V V p N v p p W v Q v W v p Q p Q v v p p Q v ‘ v - m v I m N v m W v m m p v m v O v m Q m H v v m m N v W v D m v m m m v m fl v m m m v ‘ v — v m I m N v v q U v b q v ‘ q v U q ‘ v q O v q q Q v Q v H v q N m w v v m fi v m m v m m v q o o J m H m o - v m H o I v o H m I I I I I I o N I v I o m H h v o H m v t ~ I I I I m H o I m v - I H o fl v - I I o H m v o m H v - N I I I m I - N N v o o M N v - I I A 3 ( 8 8 8 8 8 8 8 8 8 8 8 m m m m m m m m m m m m m m m m m m m m m m O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V 3 7 1 . 1 8 4 1 3 5 2 6 8 9 9 9 2 1 E + 0 0 . 1 7 2 9 0 7 1 7 0 2 0 7 0 2 E + 0 0 . 1 5 6 1 1 0 5 5 2 6 7 5 5 8 8 + 0 0 . 1 3 2 9 5 0 7 3 2 4 8 1 8 6 E + 0 0 . 1 0 2 0 1 2 6 0 9 7 5 8 5 8 8 + 0 0 . 6 0 4 9 4 9 8 9 9 2 6 0 9 4 8 - 0 1 . 1 1 4 1 6 1 2 5 9 4 8 4 7 8 8 - 0 2 . 1 4 1 6 7 4 7 7 2 6 5 4 3 7 E + 0 0 . 1 4 0 1 1 2 8 2 2 6 0 0 4 Z E + 0 0 . 1 3 7 2 4 3 3 3 2 1 7 0 9 9 E + 0 0 . 1 3 2 9 5 0 7 3 2 4 8 1 8 6 E + 0 0 . 1 2 7 0 3 1 9 3 1 5 4 1 7 l E + 0 0 . 1 1 9 1 2 5 2 8 2 0 6 3 9 l E + 0 0 . 1 0 8 5 1 4 9 0 3 1 6 3 8 9 B + 0 0 . 9 3 3 4 6 2 8 6 0 4 5 2 2 7 3 - 0 1 . 7 6 7 8 9 3 1 8 9 9 2 8 3 2 E - 0 1 . 8 1 3 0 5 2 9 0 8 7 0 3 1 2 8 - 0 1 . 8 9 6 0 1 6 7 5 3 8 3 9 5 1 E - 0 1 . 1 0 2 0 1 2 6 0 9 7 5 8 5 8 8 + 0 0 . 1 1 9 1 2 5 2 8 2 0 6 3 9 l E + 0 0 . 1 4 1 9 8 5 3 0 3 1 6 7 2 0 8 + 0 0 . 1 7 2 6 6 2 4 6 5 4 5 9 3 7 E + 0 0 . 2 1 6 5 1 8 2 0 8 0 7 9 9 4 E + 0 0 . 1 0 2 8 4 1 5 0 6 6 0 4 7 2 3 - 0 1 . 2 3 8 8 1 2 9 5 6 5 2 1 7 1 E - 0 2 . 2 5 6 6 8 6 3 5 3 0 3 2 7 4 E - 0 1 . 6 0 4 9 4 9 8 9 9 2 6 0 9 3 8 - 0 1 . 1 0 8 5 1 4 9 0 3 1 6 3 8 8 3 + 0 0 . 1 7 2 6 6 2 4 6 5 4 5 9 3 7 E + 0 0 . 2 5 8 7 4 5 7 2 2 2 5 2 5 4 E + 0 0 . 3 8 1 8 0 9 6 0 2 7 0 6 9 8 8 + 0 0 . 1 3 4 7 6 3 8 2 9 7 8 6 5 6 E + 0 0 . 1 1 0 4 3 1 3 5 2 2 1 8 3 5 E + 0 0 . 6 5 7 2 9 6 5 8 9 7 4 6 1 6 8 - 0 1 . 1 1 4 1 6 1 2 5 9 4 8 4 7 4 8 - 0 2 . 9 3 3 4 6 2 8 6 0 4 5 2 2 8 8 - 0 1 . 2 1 6 5 1 8 2 0 8 0 7 9 9 4 E + 0 0 . 3 8 1 8 0 9 6 0 2 7 0 6 9 8 E + 0 0 . 6 1 8 1 0 8 8 4 3 9 2 1 2 1 8 + 0 0 . 4 0 6 3 9 2 3 3 3 0 4 5 6 1 8 - 0 1 . 2 0 6 7 5 0 7 4 2 1 2 3 5 8 8 - 0 1 . 7 4 5 1 5 5 9 3 3 2 9 9 4 6 3 - 0 2 . 2 8 8 5 5 8 9 9 4 6 5 9 6 4 8 - 0 1 . 1 7 7 3 1 0 5 1 8 4 1 0 2 1 8 ‘ 0 1 . 7 0 6 2 9 6 8 5 6 2 9 3 7 4 8 - 0 1 . 3 2 1 3 0 9 7 8 5 1 5 7 9 S E + 0 0 . 9 4 2 5 9 7 4 1 3 8 6 3 6 B E + 0 0 . 4 0 8 4 8 8 1 4 4 1 8 5 2 4 8 - 0 1 . 1 5 8 5 8 1 3 9 9 3 2 5 4 1 8 - 0 2 . 1 8 3 1 8 6 6 9 2 8 4 3 6 6 E - 0 1 m w p V ‘ m m m V V m m m V V m w V V u m m V q V m w V V - m w V V I m w V V r m w V V p m w V V m u m V V m m w V V m w u V V m o q V V m b V r V m b V p V m a V m V m p V V m m n V V u m b V V q m b V V N m m V V m m w V V m m b V V m m m V V m m V m V m m V q V m m V m V m m V w V m m V V m m m V V w m m V V p m m V V m m m V V m m V m V m m V u V m m m V V m m V m N V m m m m m m m m m m m w s ( w s ( A 1 ( V V V V V V V V V V V 3 7 2 - . 1 3 6 2 9 3 8 5 6 3 2 5 3 S E - 0 1 . 2 2 7 5 4 6 5 6 7 3 0 3 7 0 3 - 0 1 . 7 4 6 9 5 0 5 0 5 3 4 9 4 B E - O l . 2 0 2 2 9 8 8 3 9 1 0 8 4 3 E - 0 1 . 9 9 5 6 4 1 0 7 6 1 8 0 1 3 8 + 0 0 . 5 5 0 5 6 6 0 0 0 6 3 1 8 5 E - 0 1 . 6 6 2 0 8 9 0 4 7 0 3 9 0 1 3 - 0 2 . 2 6 8 0 4 7 1 5 4 9 2 0 5 3 8 - 0 1 . 1 0 7 7 8 1 5 1 5 5 8 7 3 7 E - 0 2 . 5 2 3 6 2 7 6 8 5 2 9 6 5 5 8 - 0 1 . 2 1 6 0 4 6 8 8 6 4 8 7 1 7 3 - 0 1 . 3 1 5 2 3 1 7 9 5 8 9 1 1 7 E + 0 0 . 9 4 5 3 1 7 7 1 0 0 3 2 0 6 E + 0 0 . 6 3 1 3 8 2 0 2 3 1 8 3 5 3 8 - 0 1 . 1 1 1 1 7 8 1 9 3 4 5 3 7 1 8 - 0 1 . 2 1 3 4 0 6 7 1 7 6 8 5 1 1 8 - 0 1 . 3 3 5 4 1 6 2 7 1 8 1 7 7 4 E - 0 1 . 6 5 5 0 6 2 3 6 2 5 9 5 0 6 8 - 0 2 . 9 4 4 9 2 9 0 8 6 9 6 4 5 0 3 - 0 1 . 3 3 5 9 2 6 1 9 1 5 9 7 1 3 E + 0 0 . 9 3 4 0 7 2 4 1 1 4 3 8 6 O E + 0 0 . 3 7 0 1 4 7 3 5 3 6 5 3 2 2 8 - 0 1 . 1 0 8 3 2 7 3 5 5 9 5 1 2 2 3 - 0 1 . 6 9 0 4 6 4 9 7 4 1 9 0 4 6 E - 0 2 . 2 0 6 1 2 6 0 4 4 2 5 6 1 4 8 - 0 1 . 2 4 3 7 0 0 2 6 8 0 8 1 8 2 E - 0 1 . 2 2 3 7 7 5 5 2 0 9 8 5 5 0 E - 0 2 . 1 4 1 5 8 8 1 6 3 7 6 9 5 2 8 + 0 0 . 9 8 8 6 3 2 3 3 4 9 3 6 2 3 E + 0 0 . 2 6 7 0 6 0 0 7 2 2 4 3 8 6 3 - 0 1 . 8 0 7 4 5 4 9 0 5 0 6 2 9 6 3 - 0 2 . 1 1 0 6 7 8 6 7 3 1 5 6 8 6 8 - 0 1 . 1 1 6 8 3 5 0 8 9 8 6 2 5 1 3 - 0 1 . 1 7 6 3 5 0 0 8 6 4 8 9 6 9 E - 0 1 . 4 8 9 4 1 1 4 9 2 3 2 4 4 9 3 - 0 1 8 . 7 4 4 8 6 3 8 1 1 5 5 4 2 9 3 - 0 1 - . 9 9 5 3 4 3 2 2 6 3 1 4 7 9 3 + 0 0 v v v v v v v v v v v v v v v v v v v v v v v v v v v v v V V V V V V V V u u u l l l l u l l l l I l l l l l l l l l l l l l l l l l u u I I l l l l fl l l u l l u u u u l l l l l l u l l l l l l I 1 ) = - . 3 3 3 3 3 3 3 3 2 3 8 2 1 3 E + 0 0 2 ) 8 ‘ . 6 6 6 6 6 6 7 2 2 5 3 9 S O E + 0 0 3 ) = - . 5 9 9 9 9 9 9 4 0 3 2 0 8 7 E + 0 0 4 ) = - . 7 1 4 2 8 5 6 9 0 0 7 5 2 4 E + 0 0 5 ) = - . 7 5 0 0 0 0 0 0 5 1 5 7 2 1 8 + 0 0 6 ) = - . 5 0 0 0 0 0 0 2 5 8 4 0 4 6 E + 0 0 1 , 1 ) = . 2 2 2 6 4 7 3 3 1 3 9 0 7 6 E + 0 2 1 , 2 ) = . 4 1 0 5 7 0 9 3 7 4 2 9 3 1 8 + 0 2 1 , 3 ) = . 2 9 5 3 2 4 8 9 9 5 9 5 4 3 E + 0 2 1 , 4 ) = - . 5 4 4 3 1 4 1 3 4 2 5 5 6 9 E + 0 2 1 , 5 ) 8 ' . 5 4 6 2 2 5 3 0 7 1 3 4 O I E + 0 2 I V — n V — V s V H V H N V m V m V w V w w V m V m V w V w V w w V w V w V w V w w V w V p V b V o - V : V s V n V r u V - V t V u V c V n u V o V m V m V m m V m V m V m V m m V m V m V m V ‘ V a m V m V m V m V m I V \ V A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V \ D W O W ‘ D O D O W O \ D \ D \ D $ D \ D \ O \ D \ D \ D \ D \ D \ D \ O \ D \ O \ D \ D \ O \ O \ D \ O \ O \ O \ O \ O \ D \ D \ D \ D \ D \ O \ D \ O \ D \ D \ D \ O \ O \ O \ O 3 7 3 “ . 3 2 9 7 6 1 4 0 2 5 2 7 0 7 E + 0 2 - . 8 2 6 9 9 4 1 5 2 2 4 4 8 8 E + 0 1 ’ . 1 0 9 7 5 2 0 6 4 5 9 4 0 7 E + 0 1 8 . 3 4 3 9 5 8 6 8 4 2 4 3 2 6 E - 0 1 “ . 1 4 9 9 4 7 4 6 5 0 0 9 0 6 E + 0 3 - . 2 8 2 8 2 5 8 0 8 8 0 6 3 2 E + O 3 8 . 2 3 9 0 6 4 3 4 0 8 0 9 8 3 E + 0 3 . 3 7 7 2 4 7 8 4 5 4 9 1 3 9 E + 0 3 . 4 4 6 0 7 7 8 0 0 1 0 8 4 7 E + 0 3 . 3 0 0 4 1 2 5 7 5 9 4 0 2 5 8 + 0 3 . 8 9 2 4 5 4 2 4 4 1 9 6 4 l E + 0 2 . 1 3 5 4 8 8 6 4 4 6 3 3 4 4 E + 0 2 . 5 5 1 3 9 2 1 7 7 1 1 9 8 5 3 + 0 0 . 4 2 2 3 6 0 7 7 8 5 3 8 0 4 E + 0 3 . 7 5 8 9 9 8 2 1 0 3 8 2 4 7 E + 0 3 . 6 0 6 3 5 0 0 1 2 0 4 3 2 6 E + 0 3 . 1 0 0 8 3 9 6 3 0 3 7 8 8 9 E + 0 4 . 1 1 3 3 9 7 8 3 8 3 5 3 8 8 3 + 0 4 . 7 5 0 8 4 9 6 8 9 0 6 8 2 7 E + 0 3 . 2 3 3 9 5 2 3 7 9 1 2 0 5 1 E + 0 3 . 3 8 4 5 9 9 1 7 5 7 8 8 4 6 E + 0 2 . 1 9 2 3 6 7 1 6 7 3 9 8 3 3 E + 0 1 . 1 4 7 5 4 2 8 3 9 8 2 8 8 8 E + 0 3 . 1 3 4 2 0 1 8 4 6 2 1 5 4 0 E + 0 3 . 1 6 9 0 2 8 7 4 0 6 9 6 3 B E + 0 3 . 1 8 9 9 9 5 5 9 5 5 9 9 3 l E + 0 3 . 3 7 8 9 8 7 6 4 0 8 2 9 9 9 E + 0 3 . 1 5 1 7 2 8 2 1 4 3 3 0 2 7 E + 0 3 . 7 4 8 5 1 4 4 3 1 4 8 9 1 7 E + 0 2 . 7 4 1 0 2 7 8 0 4 4 6 4 1 0 8 + 0 1 . 7 7 9 5 0 1 4 1 3 9 2 6 4 B E + 0 0 . 8 7 4 2 0 8 3 9 8 1 8 1 9 S E + 0 2 . 1 2 5 5 7 7 5 6 8 9 0 1 9 1 8 + 0 3 . 1 1 9 1 8 7 6 3 7 3 5 8 0 9 E + 0 3 . 1 7 0 8 8 9 9 2 8 2 3 7 4 2 E + 0 3 . 2 3 9 6 3 7 2 9 1 8 6 8 7 4 E + 0 3 . 1 2 6 5 9 7 5 8 8 9 6 2 4 1 E + 0 3 . 4 9 2 3 3 2 2 2 0 3 5 6 9 1 8 + 0 2 . 5 9 8 3 2 7 8 9 5 6 2 6 4 B E + 0 1 . 5 3 0 0 7 2 2 5 6 9 2 2 7 2 8 + 0 0 . 7 3 5 1 0 0 2 3 9 3 9 4 2 3 E + 0 3 . 1 1 8 0 5 0 3 1 5 4 4 1 3 l E + 0 4 . 1 0 2 5 0 3 6 8 7 5 3 1 0 4 E + 0 4 . 1 5 8 3 6 5 2 3 8 4 5 0 2 1 E + 0 4 . 1 9 8 9 4 3 2 6 5 7 0 8 6 3 E + 0 4 . 1 2 0 0 5 2 2 3 3 2 5 3 0 5 3 + 0 4 . 4 0 2 9 5 2 2 2 4 6 6 0 6 6 E + 0 3 . 5 8 3 5 5 3 4 1 4 0 4 6 7 6 E + 0 2 . 4 3 0 6 2 7 1 9 5 5 3 7 0 9 E + 0 1 . 1 3 0 6 1 3 2 6 4 3 9 5 7 4 E + 0 3 H m m q a ‘ m p w N H W G ’ Q O ‘ U ‘ I fi U N I - ‘ m m q m m fi w k ’ H m m q m m b w N H W C D Q O ‘ U ‘ D U N I — ‘ m m q m V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V Q Q w Q - w I p \ s Q m Q m ~ Q I q - m \ H o ‘ - — u I - s J — I i - r ‘ o § — I m H - ‘ J o — - I q ‘ m - — I m - H ‘ — N I - ‘ » — e - I N N b - 1 N 0 M s N m N ~ q N m N s N m w w s w w m w § w w p w ~ w m w m - w fi l q - m fi m fi u l w fi w - b w fi § l p fi m - h t m 1 V q 0 m 1 § 0 m 1 H § 0 1 n § w 0 1 o 0 - 1 m 0 m - A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 1 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V m m m m m m m m m m m m m m m w w m m m m m m m m m m m m m m m m x n m m m m m m m m m m m m m m m m 3 7 4 . 2 3 1 3 4 5 1 6 3 3 0 8 3 2 E + 0 3 . 1 9 3 8 3 4 8 0 4 0 2 9 5 5 E + 0 3 ' . 3 0 9 3 1 4 8 7 3 3 1 1 7 7 E + O 3 ' . 3 6 6 8 6 6 2 1 5 7 4 5 6 9 E + 0 3 - - . 2 3 1 3 3 3 7 3 7 2 5 0 5 3 E + 0 3 I I I \ I w I - - ‘ ( I ) \ I \ D I - J 0 ) 0 ‘ I - ' ( I ) m N I - ' I ? ! + O N 8 8 . 1 1 8 0 9 0 8 3 5 7 3 5 2 0 8 + 0 2 . 7 2 0 6 8 5 5 3 2 3 1 6 5 7 E + 0 0 . 2 3 1 9 1 2 8 6 1 3 8 8 0 1 E + 0 0 . 2 2 2 9 7 1 2 7 2 5 8 1 3 O E + 0 0 . 2 0 6 6 1 5 6 4 4 4 5 4 3 9 E + 0 0 . 1 8 2 3 3 5 2 5 3 0 7 9 8 1 E + 0 0 . 1 4 9 2 7 3 7 5 0 4 5 8 8 5 E + 0 0 . 1 0 6 0 1 9 3 5 2 3 2 3 2 0 E + 0 0 . 5 0 1 3 2 5 3 7 8 2 0 7 6 1 8 - 0 1 . 2 3 1 4 9 8 7 1 0 8 9 8 4 6 E - 0 1 . 1 2 6 1 1 4 9 6 7 9 5 5 5 2 E + 0 0 . 2 2 2 9 7 1 2 7 2 5 8 1 3 O E + 0 0 . 2 1 4 6 9 1 5 3 2 6 8 8 2 8 E + 0 0 . 1 9 9 5 4 6 5 3 4 4 4 4 2 5 3 + 0 0 . 1 7 7 0 6 3 3 5 7 2 9 9 6 5 E + 0 0 . 1 4 6 4 4 9 0 3 9 3 8 5 5 7 E + 0 0 . 1 0 6 3 9 6 2 9 5 5 9 4 8 8 8 + 0 0 . 5 4 6 4 6 1 7 8 3 1 5 3 9 1 8 - 0 1 . 1 3 2 1 1 9 0 6 7 5 4 3 8 2 8 - 0 1 . 1 0 8 5 5 5 9 1 2 0 4 0 4 7 E + 0 0 . 2 0 6 6 1 5 6 4 4 4 5 4 3 9 E + 0 0 . 1 9 9 5 4 6 5 3 4 4 4 4 2 5 E + 0 0 . 1 8 6 6 1 5 9 7 6 2 0 7 6 3 E + 0 0 . 1 6 7 4 2 0 1 9 7 7 5 4 4 3 8 + 0 0 . 1 4 1 2 8 2 1 8 0 8 1 1 4 7 E + 0 0 . 1 0 7 0 8 5 7 8 6 3 2 4 Z O E + 0 0 . 6 2 9 0 2 3 6 4 6 6 2 0 3 2 E - 0 1 . 4 9 6 6 2 5 4 8 3 5 1 2 9 8 8 - 0 2 . 7 6 4 3 7 5 2 7 8 1 7 6 6 5 8 - 0 1 . 1 8 2 3 3 5 2 5 3 0 7 9 8 1 8 + 0 0 . 1 7 7 0 6 3 3 5 7 2 9 9 6 5 E + 0 0 . 1 6 7 4 2 0 1 9 7 7 5 4 4 3 E + 0 0 . 1 5 3 1 0 4 6 5 5 4 4 2 2 2 8 + 0 0 . 1 3 3 6 1 1 8 3 3 6 3 0 1 2 E + 0 0 . 1 0 8 1 0 9 3 5 4 9 7 3 5 2 8 + 0 0 . 7 5 1 5 8 9 0 6 5 1 7 8 7 5 8 - 0 1 . 3 1 9 5 2 2 4 8 9 7 7 0 8 3 3 - 0 1 . 2 8 7 5 6 8 7 9 7 2 7 4 1 1 3 - 0 1 . 1 4 9 2 7 3 7 5 0 4 5 8 8 5 8 + 0 0 . 1 4 6 4 4 9 0 3 9 3 8 5 5 7 E + 0 0 . 1 4 1 2 8 2 1 8 0 8 1 1 4 7 E + 0 0 . 1 3 3 6 1 1 8 3 3 6 3 0 1 2 E + 0 0 . 1 2 3 1 6 7 4 7 1 1 6 5 3 4 E + 0 0 . 1 0 9 5 0 3 1 0 1 4 6 0 2 2 E + 0 0 V V m m m V V V V m V V m V V m m m V V V V m V m V m V m V q V V V V V V V V q V V V q V q V V V q V V V V V q V V u u u V V m V V m V V V m V m V V V V V V m m m m V V V V V V V V V V V m V m V m V m V m V m V m V m V V V V m V V m J 8 - 8 I h 8 t 8 I I 8 U 8 ‘ O 8 Q 8 D ‘ 8 O 8 H N 8 A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( A 3 ( S ( s ( S ( S ( S ( s ( S ( S ( S ( S ( \ O \ D \ D \ D \ O \ D \ D \ D \ D \ D \ D 8 8 8 8 8 8 8 8 8 8 8 \ O \ D I D \ D \ D \ D \ D \ O \ O \ O \ D \ D \ D \ D \ O \ D \ D \ D \ D \ O \ D \ O \ D \ D \ D \ O \ D \ O \ D I D \ O k O t h O k O k a O k O K O 3 7 5 . 9 1 8 4 8 0 8 0 6 6 4 2 8 8 8 - 0 1 . 6 8 6 9 7 8 4 6 9 8 9 8 6 5 E - 0 1 . 3 6 1 6 7 6 8 5 3 8 4 2 7 1 E - 0 1 . 1 0 6 0 1 9 3 5 2 3 2 3 2 0 E + 0 0 . 1 0 6 3 9 6 2 9 5 5 9 4 8 8 8 + 0 0 . 1 0 7 0 8 5 7 8 6 3 2 4 Z O E + 0 0 . 1 0 8 1 0 9 3 5 4 9 7 3 5 2 8 + 0 0 . 1 0 9 5 0 3 1 0 1 4 6 0 2 2 E + 0 0 . 1 1 1 3 2 6 5 4 2 2 3 9 4 B E + 0 0 . 1 1 3 6 8 2 5 4 5 6 5 7 1 7 E + 0 0 . 1 1 6 7 7 2 1 5 2 5 7 8 0 8 E + 0 0 . 1 2 1 1 0 8 5 6 3 4 8 5 2 3 E + 0 0 . 5 0 1 3 2 5 3 7 8 2 0 7 6 1 3 - 0 1 . 5 4 6 4 6 1 7 8 3 1 5 3 9 0 3 - 0 1 . 6 2 9 0 2 3 6 4 6 6 2 0 3 1 3 - 0 1 . 7 5 1 5 8 9 0 6 5 1 7 8 7 4 E - 0 1 . 9 1 8 4 8 0 8 0 6 6 4 2 8 9 E - 0 1 . 1 1 3 6 8 2 5 4 5 6 5 7 1 7 E + 0 0 . 1 4 1 8 9 3 7 9 1 2 0 1 0 3 8 + 0 0 . 1 7 8 8 8 6 5 8 1 9 2 2 1 9 B + 0 0 . 2 3 0 8 5 6 4 4 4 6 9 4 8 5 E + 0 0 . 2 3 1 4 9 8 7 1 0 8 9 8 4 7 E - 0 1 . 1 3 2 1 1 9 0 6 7 5 4 3 8 2 8 - 0 1 . 4 9 6 6 2 5 4 8 3 5 1 3 0 4 3 - 0 2 . 3 1 9 5 2 2 4 8 9 7 7 0 8 4 8 - 0 1 . 6 8 6 9 7 8 4 6 9 8 9 8 6 6 8 - 0 1 . 1 1 6 7 7 2 1 5 2 5 7 8 0 8 8 + 0 0 . 1 7 8 8 8 6 5 8 1 9 2 2 1 9 E + 0 0 . 2 6 0 3 3 5 5 7 4 8 4 0 1 8 E + 0 0 . 3 7 4 7 6 5 7 1 8 0 2 7 8 1 E + 0 0 . 1 2 6 1 1 4 9 6 7 9 5 5 5 2 8 + 0 0 . 1 0 8 5 5 5 9 1 2 0 4 0 4 7 E + 0 0 . 7 6 4 3 7 5 2 7 8 1 7 6 6 5 3 - 0 1 . 2 8 7 5 6 8 7 9 7 2 7 4 1 0 E - 0 1 . 3 6 1 6 7 6 8 5 3 8 4 2 7 3 E - 0 1 . 1 2 1 1 0 8 5 6 3 4 8 5 2 3 E + 0 0 . 2 3 0 8 5 6 4 4 4 6 9 4 8 5 3 + 0 0 . 3 7 4 7 6 5 7 1 8 0 2 7 8 1 E + 0 0 . 5 7 6 9 5 1 5 9 4 8 2 7 8 1 8 + 0 0 . 2 7 7 3 9 8 9 3 2 3 2 9 9 5 3 - 0 1 . 1 5 5 7 4 2 3 1 9 1 6 3 2 6 3 - 0 1 8 . 2 1 1 8 0 7 1 3 2 2 2 8 2 1 E - 0 2 8 8 . 1 7 5 0 7 1 1 4 2 6 0 1 0 3 5 3 8 0 1 8 8 . 1 7 5 6 4 6 6 4 9 4 0 2 0 5 E - 0 1 . 1 8 7 4 6 0 6 6 6 8 0 7 8 1 E - 0 1 . 1 2 6 7 3 4 8 6 0 2 1 2 7 6 E + 0 0 . 3 7 2 6 7 7 1 8 6 5 4 3 0 6 E + 0 0 . 9 1 8 1 8 6 8 0 7 6 3 4 7 B E + 0 0 . 1 3 7 6 8 2 0 5 2 2 4 3 3 8 8 - 0 1 . 5 1 3 8 6 0 3 4 4 8 4 0 2 6 8 - 0 2 m N w V V m b N m m V V N m m V V m l V V m x V V m m V V m m N N N N W V V U m a V V W m - m b V V m r V V m p V V I - Q U m m V V W m m V V W m q V V m m m m V V o H V V W N fi 5 x N V V 0 o w V V 9 x n V V o m V V x m V V o q 5 0 5 0 x m V V 5 m m V V “ o w h V V x m b V V o w fi V V L o m V V o m m V V m x m o V q V \ m V V m m V V m w V V m w m m m m m V V m m w V V m m p m m V V m V a V m g V V m m m m m l V V m m a V V m m m V V m a V V m - m V t V m o V V m m q q I m l V V \ m w V V m - V V I \ m P I V V m u \ V V m m “ m I V V m o q \ V V 3 7 6 - . 4 4 8 7 7 1 6 6 3 3 8 3 7 B E - 0 2 - . 7 0 4 8 8 6 2 4 8 5 8 2 0 1 8 - 0 2 . 3 5 5 5 6 1 1 6 5 3 2 4 8 9 8 - 0 2 . 2 1 8 9 3 6 1 9 7 0 6 9 0 2 E - 0 1 . 8 8 0 2 6 9 2 9 1 6 2 5 9 2 8 - 0 2 ' . 1 6 9 8 6 7 1 0 3 7 1 8 1 8 E + 0 0 - . 9 8 5 0 3 2 9 4 9 6 6 7 B O E + 0 0 . 1 4 0 4 6 2 4 9 9 6 6 9 7 7 E - 0 1 . 2 8 7 1 0 9 5 9 0 3 5 3 0 7 8 - 0 2 8 . 6 1 9 1 4 0 6 9 7 1 2 1 7 9 8 - 0 2 . 2 8 7 7 5 9 1 2 8 2 4 5 7 1 8 - 0 2 . 1 0 3 6 8 5 7 5 9 2 3 4 9 8 8 - 0 1 . 7 7 0 0 0 4 7 6 0 7 1 7 8 5 E - 0 2 . 4 6 1 5 0 2 7 7 0 7 4 4 9 5 8 - 0 1 . 6 2 4 1 5 1 3 2 1 7 8 5 6 3 3 - 0 1 . 9 9 6 7 7 2 5 6 7 1 9 8 5 3 E + 0 0 . 1 7 4 8 1 4 9 6 4 2 0 7 8 0 8 - 0 1 . 5 1 4 9 3 1 5 2 9 3 0 7 2 7 8 - 0 2 . 2 9 1 2 4 1 2 1 4 8 8 6 8 6 8 - 0 2 . 8 6 3 2 5 9 4 8 9 3 5 5 8 4 8 - 0 2 . 9 5 0 9 0 7 5 7 5 5 7 0 0 3 3 - 0 2 . 1 1 0 6 9 4 8 5 4 8 6 8 6 5 8 - 0 2 . 4 1 5 1 5 7 9 5 3 0 1 2 8 6 8 - 0 1 . 1 8 1 5 8 7 2 0 2 1 7 9 4 O E + 0 0 . 9 8 2 2 4 0 1 7 2 7 0 9 3 6 E + 0 0 . 8 6 6 4 6 3 9 7 6 4 4 9 3 0 E - 0 1 . 1 6 8 6 3 7 4 7 7 2 5 6 4 5 8 - 0 1 . 2 5 7 1 4 3 4 9 4 9 7 9 3 0 3 - 0 1 . 4 2 1 6 1 4 1 4 8 2 1 7 7 3 8 - 0 1 . 1 3 7 4 9 8 5 9 5 7 2 8 1 4 E - 0 1 . 8 4 3 5 8 3 6 9 0 8 2 3 0 6 8 - 0 1 . 2 6 6 2 7 6 6 8 6 9 8 4 5 7 E + 0 0 . 4 1 6 5 8 4 4 5 6 5 4 7 4 8 E + 0 0 . 8 5 9 0 7 9 6 9 7 4 5 3 6 l E + 0 0 . 1 5 6 4 8 3 5 4 1 5 8 9 4 8 8 - 0 1 . 1 2 3 1 1 5 5 2 1 5 9 1 9 0 8 - 0 2 . 6 2 5 4 1 9 6 1 0 2 9 9 0 9 E - 0 2 . 5 6 3 3 5 4 0 8 2 2 0 2 8 4 8 - 0 2 . 5 0 0 5 6 0 5 1 3 3 3 1 2 6 E - 0 2 . 2 1 0 9 3 9 4 1 2 1 8 3 3 3 E - 0 1 . 1 6 7 7 3 7 0 8 0 2 7 4 1 8 3 - 0 1 . 1 1 3 1 0 2 3 8 5 5 9 5 5 2 3 + 0 0 . 9 9 3 0 4 5 4 3 9 1 2 6 8 2 8 + 0 0 . 7 6 8 9 2 7 0 5 8 5 0 8 6 1 3 - 0 1 . 4 1 5 7 1 1 6 5 8 1 9 5 5 9 8 - 0 2 . 3 5 0 3 8 3 9 4 2 0 4 0 2 3 E - 0 1 . 8 9 7 9 8 1 8 9 4 8 0 6 5 4 3 - 0 2 . 5 3 7 3 8 4 3 2 7 0 1 7 2 3 8 - 0 1 . 6 0 4 9 4 2 7 5 0 6 9 5 1 0 E - 0 1 . 1 7 4 6 0 2 0 1 8 2 9 9 4 8 E + 0 0 m m I I I I v v v v v v v V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V a b h h h p h p o w w w w w w u w w w m w w m m m N N N N H H H H H H H H H H q m m p w w w m q - 0 0 0 0 0 0 0 0 0 0 0 8 8 8 8 8 8 V V V V V V V \ I Q 3 7 7 8 . 7 6 6 9 6 0 5 6 5 9 4 2 7 2 8 + 0 0 - . 6 0 6 2 1 7 9 0 8 8 2 5 7 3 E + 0 0 8 . 3 3 3 3 3 3 4 5 2 6 2 3 1 S E + 0 0 8 . 4 9 9 9 9 9 7 3 0 6 4 2 2 5 8 + 0 0 - . 6 0 0 0 0 0 5 1 0 4 4 0 4 1 E + 0 0 ‘ . 7 7 7 7 7 7 6 8 4 9 7 1 5 1 £ + 0 0 - . 7 5 0 0 0 0 0 6 9 7 5 3 6 6 E + 0 0 - . 7 1 4 2 8 6 0 9 9 9 6 0 9 9 E + 0 0 - . 6 6 6 6 6 5 9 6 6 7 4 2 4 6 E + 0 0 1 ) = 3 ) = 4 ) = - 5 ) = 7 ) = e > = - . 9 ) = - . 1 ) = 3 ) = 4 ) = - 5 ) = 6 ) 7 ) 8 ) 1 9 ) = ) 8 - . 1 1 ) 2 ) = - . 3 ) = 4 ) = - . 5 ) = 6 ) = - 7 ) 8 O 9 ) = 1 ) = 2 ) = - . 3 ) = 4 ) = - 5 ) = 6 ) = - 7 ) = 8 ) = - 9 ) = . 7 3 2 1 3 4 7 9 6 9 8 1 7 0 E + 0 1 2 ) = - . 9 5 0 0 3 5 4 7 2 6 0 2 7 G E + 0 1 . 2 4 9 0 1 3 8 8 6 8 6 6 7 4 E + 0 2 . 1 0 7 1 5 9 9 1 4 5 0 0 6 6 E + 0 2 . 7 3 2 9 5 4 8 9 4 5 0 1 0 2 E + 0 1 6 ) = - . . 1 3 9 1 6 3 0 1 2 1 5 0 6 8 E + 0 0 3 7 4 5 2 2 7 0 7 9 4 3 8 3 E + 0 1 2 7 6 9 1 2 7 1 0 6 2 9 4 O E + 0 0 9 3 8 3 3 7 2 9 6 2 4 7 4 8 3 - 0 2 1 0 ) = - . 1 8 1 3 5 8 3 0 7 6 0 0 0 2 8 - 0 2 ) . 2 0 5 7 0 4 4 1 6 6 1 7 7 S E + 0 3 2 8 ' . 3 8 1 2 0 7 8 0 8 1 3 6 0 1 8 + 0 3 . 7 4 4 3 4 9 2 1 0 2 9 0 2 4 E + 0 3 . 2 8 6 8 5 0 3 5 1 7 2 7 8 0 E + 0 3 . 3 2 3 8 2 9 8 6 0 1 7 6 8 9 E + 0 3 . 5 5 4 6 5 3 4 8 2 2 7 8 8 1 3 + 0 2 . 2 7 7 6 1 9 2 8 9 7 5 5 8 2 E + 0 2 . 4 0 0 6 8 7 2 7 1 3 5 6 5 8 E + 0 1 . 1 6 3 0 6 7 8 1 7 6 8 7 9 9 E + 0 0 3 5 4 7 7 8 7 6 6 6 3 2 0 8 E - 0 1 . 2 5 5 3 4 8 7 5 8 7 1 5 3 9 E + 0 4 4 4 7 0 3 7 9 0 0 5 1 6 O Z E + 0 4 . 9 0 4 7 3 6 7 8 8 7 3 6 2 8 E + 0 4 3 6 0 4 4 1 5 0 7 9 2 7 1 4 E + 0 4 . 3 8 4 4 3 4 3 6 2 8 1 0 8 5 8 + 0 4 . 6 4 6 9 7 5 1 7 5 8 4 8 2 3 E + 0 3 ) . 3 7 9 3 3 2 9 9 8 1 5 6 5 5 E + 0 3 8 3 - . ) . 4 7 1 0 3 4 4 3 1 4 5 7 5 2 E + 0 1 1 0 = - , . 1 1 4 5 3 4 4 9 7 2 9 3 2 3 E + 0 5 3 1 1 1 1 2 0 3 6 7 0 5 0 2 8 + 0 2 3 1 8 9 6 5 9 1 1 8 6 5 2 3 3 + 0 0 2 0 2 9 0 0 3 8 4 7 1 7 8 8 E + 0 5 . 4 0 8 2 9 6 6 8 3 4 9 6 2 4 E + 0 5 . 1 6 1 1 5 8 2 5 1 3 0 6 4 l E + 0 5 . 1 7 2 5 8 2 4 6 3 5 9 1 1 0 3 + 0 5 . 2 9 8 3 2 6 0 9 2 7 9 0 0 7 E + 0 4 . 1 6 8 4 4 8 6 4 4 7 8 1 l l E + 0 4 . 1 2 6 2 5 4 8 7 3 2 7 5 7 6 E + 0 3 . 2 5 9 9 1 7 2 9 7 3 6 3 2 8 E + 0 2 3 7 8 A 1 ( 1 0 , 4 , 1 0 ) = ' . 1 0 3 0 0 1 4 0 3 8 0 8 5 9 E + 0 1 A 1 ( 1 0 , 5 , 1 ) = . 1 9 8 4 6 3 5 9 3 3 3 0 3 B E + 0 5 A 1 ( 1 0 , 5 , 2 ) = - . 3 5 0 9 6 7 9 7 l 4 9 9 8 6 8 + 0 5 A 1 ( 1 0 , 5 , 3 ) = . 7 0 3 7 6 4 5 9 2 6 8 4 5 1 E + 0 5 A 1 ( 1 0 , 5 , 4 ) = - . 2 7 6 4 6 8 8 7 1 0 7 5 8 1 8 + 0 5 A 1 ( 1 0 , 5 , 5 ) = . 2 9 5 3 7 7 0 6 1 0 0 2 2 5 3 + 0 5 A 1 ( 1 0 , 5 , 6 ) = - . 4 9 3 8 2 5 1 6 2 4 9 1 2 0 8 + 0 4 A 1 ( 1 0 , 5 , 7 ) = . 2 8 2 2 2 1 1 5 9 2 6 7 4 3 8 + 0 4 A 1 ( 1 0 , 5 , 8 ) = ‘ . 2 0 6 7 0 3 4 5 2 1 1 0 2 9 E + 0 3 A 1 ( 1 0 , 5 , 9 ) = . 4 2 7 8 3 4 3 9 6 3 6 2 3 0 E + 0 2 A 1 ( 1 0 , 5 , 1 0 ) = - . 8 0 5 0 5 3 7 1 0 9 3 7 S O E + 0 0 A 1 ( 1 0 , 6 , 1 ) = . 1 8 3 2 8 9 3 1 7 2 6 6 9 4 E + 0 5 A 1 ( 1 0 , 6 , 2 ) = - . 3 2 4 0 0 1 8 2 1 0 3 0 3 8 8 + 0 5 A 1 ( 1 0 , 6 , 3 ) = . 6 4 6 1 8 6 4 8 9 2 9 4 7 7 E + 0 5 A 1 ( 1 0 , 6 , 4 ) = “ . 2 5 1 9 3 2 1 1 5 0 2 4 3 3 8 + 0 5 A 1 ( 1 0 , 6 , 5 ) = . 2 6 8 9 1 5 3 4 4 2 8 5 9 6 E + 0 5 A 1 ( 1 0 , 6 , 6 ) = - . 4 3 7 7 1 5 0 6 1 8 4 6 3 B E + 0 4 A 1 ( 1 0 , 6 , 7 ) = . 2 5 1 5 8 4 8 4 6 0 6 7 4 B E + 0 4 A 1 ( 1 0 , 6 , 8 ) = - . 1 6 5 5 7 8 4 9 4 5 4 8 8 0 E + 0 3 A 1 ( 1 0 , 6 , 9 ) = . 3 4 9 0 0 9 3 2 3 1 2 0 1 Z E + 0 2 A 1 ( 1 0 , 6 , 1 0 ) = - . 4 3 7 0 4 2 2 3 6 3 2 8 1 3 8 + 0 0 A 1 ( 1 0 , 7 , 1 ) = . 9 9 4 1 6 2 3 2 5 9 0 6 7 5 E + 0 4 A 1 ( 1 0 , 7 , 2 ) = - . 1 7 5 9 2 7 5 5 5 6 8 4 0 0 E + 0 5 A 1 ( 1 0 , 7 , 3 ) = . 3 4 8 1 9 5 4 0 9 4 2 3 7 l E + 0 5 A 1 ( 1 0 , 7 , 4 ) = - . 1 3 4 1 0 0 0 2 5 5 8 9 7 6 E + 0 5 A 1 ( 1 0 , 7 , 5 ) = . 1 4 2 3 0 5 5 0 2 8 1 5 2 5 E + 0 5 A 1 ( 1 0 , 7 , 6 ) = - . 2 1 7 6 5 5 8 6 1 3 6 5 8 0 8 + 0 4 A 1 ( 1 0 , 7 , 7 ) = . 1 2 7 5 2 6 1 8 4 3 2 0 4 5 8 + 0 4 A 1 ( 1 0 , 7 , 8 ) = - . 6 9 1 1 3 6 7 1 0 6 4 3 7 7 E + 0 2 A 1 ( 1 0 , 7 , 9 ) = . 1 6 1 3 6 4 6 6 9 7 9 9 8 0 8 + 0 2 A 1 ( 1 0 , 7 , 1 0 ) = ' . 1 0 9 1 6 1 3 7 6 9 5 3 1 3 8 + 0 0 A 1 ( 1 0 , 8 , 1 ) = - . 1 6 7 8 5 1 5 3 2 5 6 9 5 3 3 + 0 4 A 1 ( 1 0 , 8 , 2 ) = . 2 9 7 0 1 3 4 3 9 7 4 5 4 6 E + 0 4 A 1 ( 1 0 , 8 , 3 ) = - . 5 7 5 0 3 5 0 0 6 7 8 6 8 8 8 + 0 4 A 1 ( 1 0 , 8 , 4 ) = . 2 1 4 0 6 1 7 9 9 0 1 3 1 5 E + 0 4 A 1 ( 1 0 , 8 , 5 ) = ’ . 2 2 5 9 1 1 0 5 3 0 9 2 7 8 8 + 0 4 A 1 ( 1 0 , 8 , 6 ) = . 3 0 5 5 9 2 3 7 6 9 2 8 7 8 8 + 0 3 A 1 ( 1 0 , 8 , 7 ) = - . 1 9 1 1 8 7 9 9 9 5 4 6 5 3 E + 0 3 A 1 ( 1 0 , 8 , 8 ) = . 7 4 2 2 5 4 1 1 4 1 5 1 0 0 E + 0 1 A 1 ( 1 0 , 8 , 9 ) = - . 2 2 3 5 5 6 9 4 7 7 0 8 1 3 8 + 0 1 A 1 ( 1 0 , 8 , 1 0 ) = . 1 9 5 1 2 1 7 6 5 1 3 6 7 2 8 - 0 2 A 1 ( 1 0 , 9 , 1 ) = - . 1 2 4 0 6 4 3 7 8 1 9 2 4 Z E + 0 5 A 1 ( 1 0 , 9 , 2 ) = . 2 1 9 0 8 0 7 8 0 7 4 7 8 3 8 + 0 5 A 1 ( 1 0 , 9 , 3 ) = - . 4 4 0 3 5 3 4 5 2 2 1 5 1 9 E + 0 5 A 1 ( 1 0 , 9 , 4 ) = . 1 7 3 7 5 8 1 5 7 9 4 3 4 9 E + 0 5 A 1 ( 1 0 , 9 , 5 ) = - . 1 8 6 1 8 6 5 1 8 2 1 1 3 6 E + 0 5 A 1 ( 1 0 , 9 , 6 ) = . 3 1 6 5 2 1 7 1 1 8 9 1 8 9 8 + 0 4 A 1 ( 1 0 , 9 , 7 ) = - . 1 7 9 1 1 5 8 5 1 9 2 6 8 0 E + 0 4 A 1 ( 1 0 , 9 , 8 ) = . 1 3 5 5 7 9 3 3 1 1 5 9 5 9 8 + 0 3 A 1 ( 1 0 , 9 , 9 ) = - . 2 8 6 5 2 2 7 5 0 8 5 4 4 9 E + 0 2 3 7 9 S ( 1 0 , S ( 1 0 , 5 ) = ‘ . 5 6 3 6 8 2 5 1 2 6 4 3 7 6 8 - 0 1 5 ) = . 5 8 8 2 3 7 1 5 5 2 4 7 1 6 E - 0 1 A 1 ( 1 0 , 9 , 1 0 ) = . 7 6 9 6 2 2 8 0 2 7 3 4 3 8 8 + 0 0 S ( 1 0 , 1 , 1 ) = . 7 6 7 7 5 1 2 2 0 0 7 1 3 6 8 - 0 1 S ( 1 0 , 2 , 1 ) = . 6 0 9 0 4 5 4 6 3 8 2 0 6 0 3 - 0 1 S ( 1 0 , 3 , 1 ) = . 3 1 9 6 4 7 0 3 3 4 3 0 5 0 8 - 0 1 S ( 1 0 , 4 , 1 ) = - . 1 0 7 6 7 9 7 6 5 6 9 7 8 0 E - 0 1 S ( 1 0 , 5 , 1 ) = - . 6 8 4 6 7 5 3 8 1 8 7 3 8 4 E - 0 1 S ( 1 0 , 6 , 1 ) = - . 1 4 2 9 7 4 6 5 4 1 6 0 4 3 E + 0 0 S ( 1 0 , 7 , 1 ) = - . 2 3 7 2 2 3 3 4 8 7 3 1 8 6 E + 0 0 S ( 1 0 , 8 , 1 ) = - . 3 5 6 1 9 8 6 3 5 0 4 1 4 3 E + 0 0 S ( 1 0 , 9 , 1 ) = - . 5 0 9 5 6 3 5 3 5 6 5 7 8 7 E + 0 0 S ( 1 0 , 1 0 , l ) = - . 7 2 2 0 2 6 0 3 0 0 7 9 7 7 E + 0 0 S ( 1 0 , l , 2 ) = - . 1 9 9 6 7 7 7 5 4 2 5 2 2 6 E - 0 1 S ( 1 0 , 2 , 2 ) = - . 1 2 0 5 8 1 4 4 0 5 2 6 6 4 E - 0 1 S ( 1 0 , 3 , 2 ) = - . 2 7 3 2 6 2 1 0 4 6 1 8 3 B E - 0 3 S ( 1 0 , 4 , 2 ) = . 1 0 8 9 7 3 8 2 7 3 3 6 9 7 E - 0 1 S ( 1 0 , 5 , 2 ) = . 1 4 1 9 1 1 8 7 2 1 6 0 6 6 E - 0 1 S ( 1 0 , 6 , 2 ) = - . 1 5 9 5 3 8 0 6 7 0 4 5 9 3 E - 0 2 S ( 1 0 , 7 , 2 ) = - . 5 3 9 2 2 5 5 1 2 6 6 7 4 7 E - 0 1 S ( 1 0 , 8 , 2 ) = ' . 1 7 1 5 8 9 1 4 0 6 6 7 6 2 E + 0 0 S ( 1 0 , 9 , 2 ) = - . 4 0 8 2 3 0 7 4 1 0 2 0 9 9 E + 0 0 S ( 1 0 , 1 0 , 2 ) = - . 8 9 4 5 0 0 0 3 5 6 6 5 2 5 8 + 0 0 S ( 1 0 , 1 , 3 ) = . 8 0 0 9 0 2 0 6 3 1 7 8 7 9 E - 0 2 S ( 1 0 , 2 , 3 ) = . 3 4 5 2 1 9 6 0 8 1 2 7 2 9 8 - 0 2 S ( 1 0 , 3 , 3 ) = - . 1 9 4 8 1 0 8 0 1 8 7 0 3 9 E - 0 2 S ( 1 0 , 4 , 3 ) = - . 4 2 7 5 4 1 8 1 9 5 6 9 9 9 E - 0 2 S ( 1 0 , 5 , 3 ) = - . 1 5 5 2 4 5 9 9 5 0 6 2 0 0 3 - 0 3 S ( 1 0 , 6 , 3 ) = . 9 6 4 6 0 1 0 4 4 5 5 4 3 4 8 - 0 2 S ( 1 0 , 7 , 3 ) = . 1 2 8 4 1 7 0 9 8 9 2 2 2 9 8 - 0 1 S ( 1 0 , 8 , 3 ) = ' . 3 1 1 1 5 1 0 7 9 0 7 1 5 9 E - 0 1 S ( 1 0 , 9 , 3 ) = - . 2 3 6 6 6 0 0 8 6 3 6 3 4 9 E + 0 0 S ( 1 0 , 1 0 , 3 ) = - . 9 7 0 9 1 0 7 7 7 5 9 7 8 7 E + 0 0 S ( 1 0 , l , 4 ) = - . 5 5 9 7 7 8 2 5 3 3 2 6 7 S E - 0 2 S ( 1 0 , 2 , 4 ) = - . 1 5 3 4 0 0 2 1 4 4 6 3 1 0 E - 0 2 S ( 1 0 , 3 , 4 ) = . 2 1 5 4 4 1 4 7 4 8 9 3 6 3 E - 0 2 S ( 1 0 , 4 , 4 ) = . 1 7 9 9 9 2 1 2 1 0 4 4 6 6 3 - 0 2 S ( 1 0 , 5 , 4 ) = - . 2 8 0 8 3 0 1 7 1 5 8 4 4 G E - 0 2 S ( 1 0 , 6 , 4 ) = - . 4 9 2 3 0 8 0 2 5 5 1 9 3 3 8 - 0 2 S ( 1 0 , 7 , 4 ) = . 7 8 1 6 9 9 2 4 6 9 9 6 5 5 8 - 0 2 S ( 1 0 , 8 , 4 ) = . 3 2 1 5 2 0 3 2 5 7 3 2 0 2 E - 0 1 S ( 1 0 , 9 , 4 ) = “ . 5 0 9 5 9 7 0 4 9 0 2 0 6 4 E ' 0 1 S ( 1 0 , 1 0 , 4 ) = - . 9 9 8 1 1 5 5 0 2 8 7 4 0 7 E + 0 0 S ( 1 0 , l , 5 ) = - . 9 7 3 9 5 6 6 3 2 8 2 8 9 4 E - 0 2 S ( 1 0 , 2 , 5 ) = - . 4 7 8 0 5 0 4 5 2 3 4 8 8 6 E - 0 4 S ( 1 0 , 3 , 5 ) = . 4 1 1 8 1 7 6 1 8 4 2 2 5 3 E - 0 2 S ( 1 0 , 4 , 5 = - . 1 8 9 2 0 5 4 4 0 9 5 8 7 5 8 - 0 2 S ( 1 0 , 5 , 5 ) = - . 4 9 3 6 7 0 2 7 4 0 2 9 3 7 E - 0 2 S ( 1 0 , 6 , 5 ) = . 8 1 3 1 0 3 4 5 1 5 6 8 1 3 8 - 0 2 S ( 1 0 , 7 , 5 ) = . 8 1 8 1 9 3 0 5 2 6 1 5 4 5 E - 0 2 8 . 9 . w m w p m m q m m o w m w ¢ m m q m o x o J — h t - c u m x a q n c o x o H N w - c m m q m o \ S ( 1 0 , 1 0 , s ( 1 0 , s ( 1 0 , s ( 1 0 , s ( 1 0 , s ( 1 0 , s ( 1 0 , s ( 1 0 , s ( 1 0 , s ( 1 0 , s ( 1 0 , 1 s ( 1 0 , s ( 1 0 , s ( 1 0 , s ( 1 0 , s ( 1 0 , s ( 1 0 , s ( 1 0 , s ( 1 0 , s ( 1 0 , s ( 1 0 , 1 s ( 1 0 , s ( 1 0 . s ( 1 0 , s ( 1 0 , s ( 1 0 , s ( 1 o . s ( 1 0 , s ( 1 0 , S ( 1 0 , s ( 1 0 , 1 s ( 1 0 , S ( 1 0 , s ( 1 0 , s ( 1 0 , s ( 1 o . s ( 1 0 , s ( 1 0 , S ( 1 0 , s ( 1 0 , s ( 1 0 , 1 K ( 1 0 ) = m m ) : w s ( 1 o , w s ( 1 0 , w s ( 1 0 , W S ( 1 0 , w s ( 1 0 , w s ( 1 o , w s ( 1 0 , 0 V I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I 9 l l 2 3 4 5 3 8 0 . 9 9 6 5 3 8 7 9 0 6 7 2 6 6 E + 0 0 . 9 7 8 2 9 5 3 7 1 9 4 1 9 7 8 - 0 2 . 1 0 6 1 9 9 0 8 1 6 3 2 2 1 E - 0 2 . 3 5 2 4 2 5 2 1 1 9 5 2 0 6 E - 0 2 . 3 5 9 3 0 2 6 7 9 0 0 0 0 2 E - 0 2 . 1 7 2 7 7 7 6 8 2 4 4 4 6 9 8 - 0 2 . 1 0 1 0 4 5 3 5 8 6 6 4 9 3 E - 0 1 . 1 0 7 8 6 5 4 0 8 2 6 3 7 B E - O l . 2 8 4 8 7 3 6 7 8 0 4 4 4 7 E - 0 1 . 2 0 4 9 2 3 5 2 9 4 0 2 0 9 E + 0 0 . 9 7 8 1 8 7 7 2 0 4 5 5 3 6 3 + 0 0 . 9 9 1 1 9 9 1 4 1 1 8 7 2 4 E - 0 2 . 2 0 6 7 5 5 5 1 5 6 1 6 2 6 3 - 0 2 . 2 6 3 1 5 8 3 4 8 0 5 8 9 9 3 - 0 2 . 4 4 7 4 9 5 5 4 4 6 0 4 7 4 3 - 0 2 . 1 8 3 9 5 9 8 8 5 9 6 5 3 6 8 - 0 2 . 6 8 2 9 1 9 7 7 2 1 7 9 4 9 E - 0 2 . 2 0 6 4 2 4 2 3 5 0 0 9 5 5 8 - 0 1 . 2 6 2 1 5 7 8 4 4 3 8 7 4 9 E - 0 1 . 6 1 2 6 9 2 7 0 9 6 2 2 1 7 E - O l . 9 9 7 4 7 3 4 1 0 4 4 8 9 Z E + 0 0 . 1 4 7 8 8 4 9 7 0 2 5 2 0 1 8 - 0 1 . 4 3 7 6 7 7 1 4 5 2 4 2 6 8 E - 0 2 . 2 2 4 0 9 9 6 4 4 8 4 2 3 9 8 - 0 2 . 6 6 3 5 9 3 0 7 6 9 8 7 5 9 8 - 0 2 . 6 9 6 2 5 8 2 3 9 4 0 9 1 5 8 - 0 2 . 7 5 0 3 9 7 9 1 4 8 6 3 1 3 8 - 0 3 . 2 4 3 7 1 0 4 2 3 2 2 9 1 8 8 - 0 1 . 8 1 3 4 3 9 7 7 1 8 3 6 2 5 8 - 0 1 . 2 2 5 4 4 3 2 8 3 3 2 3 0 1 8 + 0 0 . 9 7 0 3 7 5 4 8 4 8 5 6 8 1 8 + 0 0 . 1 0 9 5 4 7 0 0 5 7 8 3 9 6 8 - 0 1 . 1 4 4 8 4 3 7 8 7 3 9 8 2 3 8 - 0 2 . 4 7 9 0 5 4 7 6 5 1 2 8 4 0 E - 0 2 . 5 5 1 7 9 5 5 0 6 6 1 2 6 1 8 - 0 3 - . 7 2 4 1 2 8 1 2 8 4 3 4 3 3 E - 0 2 . 7 7 9 9 0 8 4 2 9 3 9 2 3 3 8 - 0 3 . 2 4 6 0 5 7 8 1 3 2 2 7 0 9 E - 0 1 - . 1 7 8 5 9 7 4 3 4 5 1 8 8 2 E - 0 1 9 ) = - . 2 3 1 8 7 5 2 0 5 9 2 0 2 6 E + 0 0 9 ) = . 9 7 2 1 6 8 2 3 2 5 0 6 5 1 E + 0 0 = - . 1 6 6 0 1 2 3 3 2 4 2 8 2 0 8 - 0 6 8 ' . 3 3 3 3 3 3 0 8 2 0 2 2 1 9 E + 0 0 = - . 4 9 9 9 9 9 4 1 7 2 1 8 4 4 E + 0 0 = - . 6 0 0 0 0 2 9 4 7 4 9 6 6 4 E + 0 0 ) = - . 7 1 4 2 8 2 0 6 0 7 1 7 3 7 E + 0 0 6 ) = - . 7 5 0 0 1 0 4 5 2 6 2 4 0 3 E + 0 0 7 ) = ‘ . 7 7 7 7 7 0 1 2 5 0 6 0 1 7 E + 0 0 3 8 1 W S ( 1 0 , 8 ) = - . 8 0 0 0 0 1 7 9 4 0 5 5 8 4 E + 0 0 W S ( 1 0 , 9 ) = - . 6 6 6 6 6 3 4 6 4 8 2 7 3 1 B + 0 0 A 1 ( 1 1 , l , 1 ) = - . 3 8 2 6 7 1 0 9 8 7 7 8 9 6 E + 0 2 A 1 ( 1 1 , l , 2 ) = ' . 9 0 7 9 6 2 2 1 6 8 9 4 5 2 3 + 0 2 A 1 ( 1 1 , 1 , 3 ) = - . 8 9 5 8 1 0 5 4 1 6 1 7 6 8 8 + 0 2 A 1 ( 1 1 , 1 , 4 ) = . 7 1 3 0 5 2 7 0 6 5 9 9 7 O E + 0 2 A 1 ( 1 1 , 1 , 5 ) = . 1 1 8 7 4 7 0 8 0 6 8 7 7 8 8 + 0 3 A 1 ( 1 1 , 1 , 6 ) = . 1 0 8 6 6 5 5 0 9 2 9 2 8 6 E + 0 3 A 1 ( 1 1 , 1 , 7 ) = . 4 7 0 8 5 7 4 5 9 8 3 6 4 l E + 0 2 A 1 ( 1 1 , 1 , 8 ) = . 1 3 6 9 6 8 5 5 2 4 5 1 5 8 E + 0 2 A 1 ( 1 1 , l , 9 ) = . 2 0 8 4 5 4 5 4 3 1 6 5 8 6 E + 0 1 A 1 ( 1 1 , 1 , 1 0 ) = . 1 6 5 6 2 9 2 7 5 1 4 3 1 5 3 + 0 0 A 1 ( 1 1 , 1 , l l ) = . 3 8 7 4 7 7 8 7 4 7 5 5 8 6 8 - 0 2 A 1 ( 1 1 , 2 , 1 ) = - . 5 2 6 0 1 5 3 1 0 7 6 4 3 1 3 + 0 3 A 1 ( 1 1 , 2 , 2 ) = “ . 1 2 4 7 2 3 3 2 5 6 3 2 7 9 E + 0 4 A 1 ( 1 1 , 2 , 3 ) = - . 1 3 5 5 1 7 7 0 3 1 8 6 9 l E + 0 4 A 1 ( 1 1 , 2 , 4 ) = . 9 4 2 2 3 1 6 2 7 1 4 7 6 4 E + 0 3 A 1 ( 1 1 , 2 , 5 ) = . 1 7 8 0 4 8 7 3 3 7 6 5 6 B E + 0 4 A 1 ( 1 1 , 2 , 6 ) = . 1 7 6 8 9 2 3 7 9 2 0 9 0 3 E + 0 4 A 1 ( 1 1 , 2 , 7 ) = . 8 5 0 1 6 7 3 5 0 6 1 1 6 S E + 0 3 A 1 ( 1 1 , 2 , 8 ) = . 2 7 0 3 2 0 9 3 1 2 7 0 7 2 8 + 0 3 A 1 ( 1 1 , 2 , 9 ) = . 4 6 7 0 9 1 4 9 0 3 2 8 3 l E + 0 2 A 1 ( 1 1 , 2 , 1 0 ) = . 4 1 5 3 5 4 8 9 5 5 9 1 7 4 E + 0 1 A 1 ( 1 1 , 2 , 1 1 ) = . 9 9 5 1 9 7 2 9 6 1 4 2 5 8 8 - 0 1 A 1 ( 1 1 , 3 , 1 ) = . 3 7 2 5 9 3 0 1 5 5 6 6 4 7 E + 0 4 A 1 ( 1 1 , 3 , 2 ) = . 8 6 8 3 2 5 9 3 2 7 0 7 2 7 E + 0 4 A 1 ( 1 1 , 3 , 3 ) = . 9 1 7 4 8 8 7 0 9 0 2 0 6 1 E + 0 4 A 1 ( 1 1 , 3 , 4 ) = - . 6 6 3 7 9 5 1 2 5 2 6 6 1 6 8 + 0 4 A 1 ( 1 1 , 3 , 5 ) = - . 1 2 0 7 5 9 3 5 5 7 1 0 7 4 E + 0 5 A 1 ( 1 1 , 3 , 6 ) = ’ . 1 1 7 4 0 3 9 7 9 0 0 7 6 O E + 0 5 A 1 ( 1 1 , 3 , 7 ) = - . 5 6 8 4 0 8 4 3 3 9 7 2 3 0 8 + 0 4 A 1 ( 1 1 , 3 , 8 ) = * . 1 8 4 0 0 1 0 3 9 8 3 8 7 9 E + 0 4 A 1 ( 1 1 , 3 , 9 ) = - . 3 3 8 0 3 7 6 4 6 0 5 5 2 2 8 + 0 3 A 1 ( 1 1 , 3 , 1 0 ) = - . 3 2 5 1 1 0 7 2 1 5 8 8 1 3 E + 0 2 A 1 ( 1 1 , 3 , 1 1 ) = - . 9 2 7 9 7 8 5 1 5 6 2 5 0 0 E + 0 0 A 1 ( 1 1 , 4 , 1 ) = . 9 1 6 3 0 9 6 9 7 7 8 2 9 9 E + 0 4 A 1 ( 1 1 , 4 , 2 ) = . 2 1 0 4 1 2 9 5 6 6 9 6 9 7 E + 0 5 A 1 ( 1 1 , 4 , 3 ) = . 2 2 7 8 0 4 7 3 7 2 7 1 6 7 E + 0 5 A 1 ( 1 1 , 4 , 4 ) = ” . 1 6 0 6 1 9 5 0 2 3 0 3 6 O E + 0 5 A 1 ( 1 1 , 4 , 5 ) = - . 3 0 1 5 2 4 5 9 0 3 2 8 9 3 E + 0 5 A 1 ( 1 1 , 4 , 6 ) = - . 2 8 8 3 1 8 4 3 5 2 9 9 4 O E + 0 5 A 1 ( 1 1 , 4 , 7 ) = ‘ . 1 4 0 7 1 7 3 8 1 9 1 6 9 4 E + 0 5 A 1 ( 1 1 , 4 , 8 ) = - . 4 4 6 0 4 8 5 5 8 8 0 7 3 7 E + 0 4 A 1 ( 1 1 , 4 , 9 ) = - . 8 4 0 3 8 8 2 9 3 2 6 6 3 0 E + 0 3 A 1 ( 1 1 , 4 , 1 0 ) = - . 8 3 0 2 4 0 3 4 5 0 0 1 2 2 8 + 0 2 A 1 ( 1 1 , 4 , 1 1 ) = - . 2 7 6 8 4 6 3 1 3 4 7 6 5 6 3 + 0 1 A 1 ( 1 1 , 5 , 1 ) = - . 2 8 2 4 5 3 6 4 8 2 4 6 8 2 8 + 0 3 A 1 ( 1 1 , 5 , 2 ) = - . 3 2 9 0 5 4 3 3 2 8 2 4 9 5 E + 0 3 A 1 ( 1 1 , 5 , 3 ) = “ . 5 7 1 6 9 1 3 0 7 0 1 1 0 6 E + 0 3 A 1 ( 1 1 , 5 , 4 ) = . 2 5 5 9 4 7 0 8 7 7 7 8 7 1 8 + 0 3 3 8 2 A 1 ( 1 1 , 5 , 5 ) = . 8 5 5 2 5 9 4 7 4 9 1 9 1 8 E + 0 3 A 1 ( 1 1 , 5 , 6 ) = . 5 1 1 1 3 8 1 0 0 5 9 2 4 Z E + 0 3 A 1 ( 1 1 , 5 , 7 ) = . 3 8 3 9 7 0 1 9 9 9 6 9 6 0 E + 0 3 A 1 ( 1 1 , 5 , 8 ) = . 8 0 1 3 0 3 4 6 9 8 3 6 7 1 E + 0 2 A 1 ( 1 1 , 5 , 9 ) = . 2 2 8 5 6 1 9 1 3 2 2 2 0 7 E + 0 2 A 1 ( 1 1 , 5 , 1 0 ) = . 1 4 1 7 0 6 6 2 7 6 0 7 3 S E + 0 1 A 1 ( 1 1 , 5 , 1 1 ) = . 9 0 4 8 7 4 8 0 1 6 3 5 7 4 3 - 0 1 A 1 ( 1 1 , 6 , 1 ) = ‘ . 7 2 7 0 0 6 7 5 9 9 0 5 8 2 8 + 0 4 A 1 ( 1 1 , 6 , 2 ) = - . 1 2 0 0 2 4 3 5 6 3 9 8 6 6 E + 0 5 A 1 ( 1 1 , 6 , 3 ) = - . 1 6 2 4 6 4 1 4 7 0 9 3 5 9 8 + 0 5 A 1 ( 1 1 , 6 , 4 ) = . 9 2 9 0 1 5 1 3 5 2 1 6 7 l E + 0 4 A 1 ( 1 1 , 6 , 5 ) = . 2 2 9 7 3 7 3 6 2 6 1 8 4 5 E + 0 5 A 1 ( 1 1 , 6 , 6 ) = . 1 7 1 0 2 1 8 6 2 2 1 9 5 7 E + 0 5 A 1 ( 1 1 , 6 , 7 ) = . 1 0 6 3 7 2 7 2 7 3 9 8 2 0 E + 0 5 A 1 ( 1 1 , 6 , 8 ) = . 2 6 1 5 7 0 2 1 7 4 4 2 5 1 E + 0 4 A 1 ( 1 1 , 6 , 9 ) = . 6 4 4 1 7 3 1 4 3 3 8 6 8 4 E + 0 3 A 1 ( 1 1 , 6 , 1 0 ) = . 4 5 4 9 5 5 7 3 0 4 3 8 2 3 E + 0 2 A 1 ( 1 1 , 6 , 1 1 ) = . 2 6 0 0 6 4 6 9 7 2 6 5 6 3 E + 0 1 A 1 ( 1 1 , 7 , 1 ) = . 2 1 0 5 9 7 6 4 8 3 6 4 3 1 E + 0 4 A 1 ( 1 1 , 7 , 2 ) = . 4 6 6 3 4 8 9 9 0 5 6 7 4 0 E + 0 4 A 1 ( 1 1 , 7 , 3 ) = . 5 1 3 5 6 5 4 9 6 4 9 6 1 1 8 + 0 4 A 1 ( 1 1 , 7 , 4 ) = - . 3 5 6 3 4 6 4 9 1 9 1 5 7 3 E + 0 4 A 1 ( 1 1 , 7 , 5 ) = - . 6 8 4 1 9 7 8 1 6 6 3 4 9 2 E + 0 4 A 1 ( 1 1 , 7 , 6 ) = “ . 6 4 0 3 4 5 0 8 9 7 3 9 5 6 8 + 0 4 A 1 ( 1 1 , 7 , 7 ) = * . 3 2 0 7 1 3 7 9 9 9 8 0 2 8 8 + 0 4 A 1 ( 1 1 , 7 , 8 ) = - . 9 8 9 4 7 5 6 7 1 5 8 9 3 7 E + 0 3 A 1 ( 1 1 , 7 , 9 ) = ' . 1 9 0 4 3 8 5 8 9 6 9 2 1 2 E + 0 3 A 1 ( 1 1 , 7 , 1 0 ) = - . 1 8 3 2 5 7 3 9 3 8 3 6 9 8 E + 0 2 A 1 ( 1 1 , 7 , 1 1 ) = ‘ . 7 0 5 4 1 3 8 1 8 3 5 9 3 8 8 + 0 0 A 1 ( 1 1 , 8 , 1 ) = . 2 2 7 0 6 2 5 9 3 5 8 2 2 7 E + 0 4 A 1 ( 1 1 , 8 , 2 ) = . 4 3 5 3 5 6 7 5 3 6 4 4 7 Z E + 0 4 A 1 ( 1 1 , 8 , 3 ) = . 5 2 8 7 7 0 2 0 7 9 1 8 4 4 E + 0 4 A 1 ( 1 1 , 8 , 4 ) = - . 3 3 4 3 3 4 2 6 5 2 8 7 9 7 E + 0 4 A 1 ( 1 1 , 8 , 5 ) = * . 7 2 6 1 6 1 2 3 6 3 3 0 1 2 E + 0 4 A 1 ( 1 1 , 8 , 6 ) = - . 6 0 9 1 5 8 8 8 2 7 9 9 7 4 E + 0 4 A 1 ( 1 1 , 8 , 7 ) = - . 3 3 7 9 0 6 2 7 1 4 8 8 9 6 E + 0 4 A 1 ( 1 1 , 8 , 8 ) = - . 9 3 5 0 5 5 7 7 9 5 7 6 3 0 E + 0 3 A 1 ( 1 1 , 8 , 9 ) = ‘ . 2 0 4 3 2 7 0 1 2 6 5 8 1 2 E + 0 3 A 1 ( 1 1 , 8 , 1 0 ) = - . 1 6 4 0 4 8 6 3 8 3 4 3 8 1 8 + 0 2 A 1 ( 1 1 , 8 , 1 1 ) = ‘ . 8 2 8 2 5 4 6 9 9 7 0 7 0 3 E + 0 0 A 1 ( 1 1 , 9 , 1 ) = . 1 7 8 5 8 7 1 2 9 7 5 5 0 2 8 + 0 5 A 1 ( 1 1 , 9 , 2 ) = . 3 7 5 1 9 0 3 7 8 2 3 1 7 0 E + 0 5 A 1 ( 1 1 , 9 , 3 ) = . 4 2 9 6 2 3 6 6 0 5 8 3 S O E + 0 5 A 1 ( 1 1 , 9 , 4 ) = “ . 2 8 7 4 8 7 8 1 1 3 3 7 1 1 3 + 0 5 A 1 ( 1 1 , 9 , 5 ) = ’ . 5 7 9 4 1 2 3 6 9 0 1 9 9 9 3 + 0 5 A 1 ( 1 1 , 9 , 6 ) = - . 5 1 7 9 3 1 0 1 2 3 9 5 6 2 3 + 0 5 A 1 ( 1 1 , 9 , 7 ) = - . 2 7 0 3 2 2 0 2 6 6 9 5 9 1 E + 0 5 A 1 ( 1 1 , 9 , 8 ) = - . 8 0 0 5 2 0 8 6 9 3 0 2 7 S E + 0 4 A 1 ( 1 1 , 9 , 9 = - . 1 6 1 5 9 9 7 1 5 8 0 5 0 5 E + 0 4 A 1 ( 1 1 , 9 , 1 0 ) = ‘ . 1 4 4 0 1 9 5 9 9 9 1 4 5 5 E + 0 3 D a U ‘ — I H - t ‘ u — m I ‘ — I s « m ‘ m — q I J m H — I m ‘ H — o I H H w H ‘ — I m w - H c H u N m N N N N m q m N m N o N N N N H H N W w w o w w w w m m u w m w m w s — o w u — a s w h b — l b w b m fi b é h w b m b m 0 q 9 D I U m m o I I U — I I U I U H h I t U m A 1 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( l l , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( l l , A 3 ( 1 1 , A 3 ( l l , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( l l , A 3 ( 1 1 , A 3 ( l l , A 3 ( l l , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A _ 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , A 3 ( 1 1 , I - J H H I H H V V V V V V V V V V V V V V V V ‘ V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V 3 8 3 - . 6 4 0 3 1 9 8 2 4 2 1 8 7 S E + 0 1 . 1 8 7 9 3 3 7 7 1 4 6 2 8 6 E + 0 0 . 1 8 3 1 2 6 7 1 0 1 6 7 1 0 3 + 0 0 . 1 7 4 3 8 1 2 5 5 6 5 9 7 l E + 0 0 . 1 6 1 5 1 7 9 2 6 1 6 8 2 1 3 + 0 0 . 1 4 4 2 5 2 5 2 6 2 5 7 1 5 3 + 0 0 . 1 2 2 1 5 4 7 8 1 7 8 5 1 5 8 + 0 0 . 9 4 5 7 4 2 4 1 0 8 2 7 2 4 8 - 0 1 . 6 0 4 9 6 3 7 8 3 3 4 8 1 3 8 - 0 1 . 1 8 1 9 7 0 3 2 2 5 4 7 2 8 8 - 0 1 . 3 5 8 9 0 2 1 1 8 0 1 9 7 3 E - 0 1 . 1 1 2 3 7 6 5 7 2 4 3 4 9 Z E + 0 0 . 1 8 3 1 2 6 7 1 0 1 6 7 1 0 E + 0 0 . 1 7 8 5 5 8 4 4 5 2 8 6 8 7 E + 0 0 . 1 7 0 2 4 7 4 3 1 9 1 7 9 4 E + 0 0 . 1 5 8 0 2 3 1 0 3 5 6 8 9 Z E + 0 0 . 1 4 1 6 1 5 3 8 2 8 6 5 3 9 E + 0 0 . 1 2 0 6 1 5 3 6 9 3 5 6 9 6 E + 0 0 . 9 4 4 0 4 9 1 9 6 0 1 4 5 8 8 - 0 1 . 6 2 0 1 9 9 7 6 0 0 0 4 1 8 8 - 0 1 . 2 1 8 2 1 6 3 8 8 6 7 0 4 6 8 - 0 1 . 2 9 5 8 5 4 1 1 6 7 0 6 8 0 8 - 0 1 . 1 0 2 3 2 8 9 5 4 0 0 0 9 6 E + 0 0 . 1 7 4 3 8 1 2 5 5 6 5 9 7 1 E + 0 0 . 1 7 0 2 4 7 4 3 1 9 1 7 9 4 E + 0 0 . 1 6 2 7 2 6 7 9 5 1 6 4 8 2 E + 0 0 . 1 5 1 6 6 4 9 9 8 4 3 5 8 5 E + 0 0 . 1 3 6 8 1 7 6 4 9 2 7 5 2 3 E + 0 0 . 1 1 7 8 1 4 7 3 2 2 8 2 9 6 E + 0 0 . 9 4 0 9 6 8 8 2 2 1 5 0 6 0 8 - 0 1 . 6 4 7 9 1 8 5 8 0 5 0 2 4 1 E - 0 1 . 2 8 4 1 5 8 7 6 1 0 8 2 3 5 E - 0 1 . 1 8 1 1 5 1 1 1 6 2 0 3 9 6 8 - 0 1 . 8 4 0 4 9 3 6 3 2 1 7 2 8 4 E - 0 1 . 1 6 1 5 1 7 9 2 6 1 6 8 2 1 3 + 0 0 . 1 5 8 0 2 3 1 0 3 5 6 8 9 2 E + 0 0 . 1 5 1 6 6 4 9 9 8 4 3 5 8 5 E + 0 0 . 1 4 2 3 1 3 1 2 0 4 2 2 2 8 3 + 0 0 . 1 2 9 7 6 0 8 5 5 9 3 5 6 5 E + 0 0 . 1 1 3 6 9 5 3 8 3 9 5 6 I O E + 0 0 . 9 3 6 4 3 7 9 3 6 1 1 6 7 2 8 - 0 1 . 6 8 8 6 8 8 9 3 0 1 0 7 6 9 8 - 0 1 . 3 8 1 1 5 0 5 2 0 6 3 9 4 2 E ‘ 0 1 . 1 2 4 3 9 4 0 5 7 4 8 0 8 2 E - 0 2 . 5 7 1 6 2 6 9 3 5 8 2 3 6 6 8 - 0 1 . 1 4 4 2 5 2 5 2 6 2 5 7 1 5 8 + 0 0 . 1 4 1 6 1 5 3 8 2 8 6 5 3 9 E + 0 0 . 1 3 6 8 1 7 6 4 9 2 7 5 2 3 3 + 0 0 . 1 2 9 7 6 0 8 5 5 9 3 5 6 5 E + 0 0 . 1 2 0 2 8 9 0 9 6 7 4 6 3 4 E + 0 0 3 8 4 A 3 ( 1 1 , 5 , 6 ) = . 1 0 8 1 6 6 3 1 8 0 4 7 2 7 E + 0 0 A 3 ( 1 1 , 5 , 7 ) = . 9 3 0 3 5 6 4 9 6 3 1 1 4 8 8 - 0 1 A 3 ( 1 1 , 5 , 8 ) = . 7 4 3 4 1 1 6 5 0 5 7 7 3 5 8 - 0 1 A 3 ( 1 1 , 5 , 9 ) = . 5 1 1 3 3 4 6 6 2 2 6 8 0 9 E - O l A 3 ( 1 1 , 5 , 1 0 ) = . 2 1 4 0 0 8 5 8 6 6 9 7 3 9 8 - 0 1 A 3 ( l l , 5 , 1 1 ) : - . 2 1 0 7 4 9 0 6 0 1 9 9 9 9 8 - 0 1 A 3 ( 1 1 , 6 , 1 ) = . 1 2 2 1 5 4 7 8 1 7 8 5 1 5 8 + 0 0 A 3 ( 1 1 , 6 , 2 ) = . 1 2 0 6 1 5 3 6 9 3 5 6 9 6 E + 0 0 A 3 ( 1 1 , 6 , 3 ) = . 1 1 7 8 1 4 7 3 2 2 8 2 9 G E + 0 0 A 3 ( 1 1 , 6 , 4 ) = . 1 1 3 6 9 5 3 8 3 9 5 6 1 0 8 + 0 0 A 3 ( 1 1 , 6 , 5 ) = . 1 0 8 1 6 6 3 1 8 0 4 7 2 7 E + 0 0 A 3 ( 1 1 , 6 , 6 ) = . 1 0 1 0 8 9 7 3 4 3 0 7 6 7 E + 0 0 A 3 ( 1 l , 6 , 7 ) = . 9 2 2 5 7 2 8 1 2 6 4 6 4 8 8 - 0 1 A 3 ( 1 1 , 6 , 8 ) = . 8 1 3 4 5 0 3 1 4 5 4 5 9 6 3 - 0 1 A 3 ( l l , 6 , 9 ) = . 6 7 7 9 5 5 2 8 5 8 3 3 5 1 8 - 0 1 A 3 ( 1 1 , 6 , 1 0 ) = . 5 0 3 8 3 5 8 9 2 8 5 6 6 7 E - 0 1 A 3 ( 1 1 , 6 , 1 1 ) = . 2 5 1 1 3 3 0 7 1 8 0 5 9 2 E - 0 1 A 3 ( 1 1 , 7 , 1 ) = . 9 4 5 7 4 2 4 1 0 8 2 7 2 4 E - O l A 3 ( 1 1 , 7 , 2 ) = . 9 4 4 0 4 9 1 9 6 0 1 4 5 7 8 - 0 1 A 3 ( 1 1 , 7 , 3 ) = . 9 4 0 9 6 8 8 2 2 1 5 0 6 0 8 - 0 1 A 3 ( 1 1 , 7 , 4 ) = . 9 3 6 4 3 7 9 3 6 1 1 6 7 2 8 - 0 1 A 3 ( l l , 7 , 5 ) = . 9 3 0 3 5 6 4 9 6 3 1 1 4 8 8 - 0 1 A 3 ( 1 1 , 7 , 6 ) = . 9 2 2 5 7 2 8 1 2 6 4 6 4 7 3 - 0 1 A 3 ( 1 1 , 7 , 7 ) = . 9 1 2 8 5 7 0 5 0 2 1 8 8 4 E - O l A 3 ( 1 1 , 7 , 8 ) = . 9 0 0 8 6 5 5 4 0 9 3 5 6 6 3 - 0 1 A 3 ( 1 1 , 7 , 9 ) = . 8 8 5 9 1 5 5 9 3 7 8 0 9 3 E - O l A 3 ( l l , 7 , 1 0 ) = . 8 6 5 5 7 1 9 1 3 9 8 0 8 7 E - 0 1 A 3 ( 1 1 , 7 , 1 1 ) = . 8 2 7 6 1 2 7 5 8 5 8 7 9 4 E - 0 1 A 3 ( 1 1 , 8 , 1 ) = . 6 0 4 9 6 3 7 8 3 3 4 8 1 5 E - 0 1 A 3 ( 1 1 , 8 , 2 ) = . 6 2 0 1 9 9 7 6 0 0 0 4 1 8 E - 0 1 A 3 ( 1 1 , 8 , 3 ) = . 6 4 7 9 1 8 5 8 0 5 0 2 4 1 8 - 0 1 A 3 ( 1 1 , 8 , 4 ) = . 6 8 8 6 8 8 9 3 0 1 0 7 6 9 E - O l A 3 ( 1 1 , 8 , 5 ) = . 7 4 3 4 1 1 6 5 0 5 7 7 3 S E - O l A 3 ( 1 1 , 8 , 6 ) = . 8 1 3 4 5 0 3 1 4 5 4 5 9 6 8 - 0 1 A 3 ( 1 1 , 8 , 7 ) = . 9 0 0 8 6 5 5 4 0 9 3 5 6 7 8 - 0 1 A 3 ( 1 1 , 8 , 8 ) = . 1 0 0 8 8 9 1 5 4 6 7 9 9 5 E + 0 0 A 3 ( 1 1 , 8 , 9 ) = . 1 1 4 2 8 9 0 1 6 1 0 6 8 2 8 + 0 0 A 3 ( 1 1 , 8 , 1 0 ) = . 1 3 1 2 5 5 5 6 3 5 4 0 7 B E + 0 0 A 3 ( 1 1 , 8 , l l ) = . 1 5 3 9 9 3 9 0 3 3 9 5 7 O E + 0 0 A 3 ( 1 1 , 9 , 1 ) = . 1 8 1 9 7 0 3 2 2 5 4 7 2 8 8 - 0 1 A 3 ( 1 1 , 9 , 2 ) = . 2 1 8 2 1 6 3 8 8 6 7 0 4 6 8 - 0 1 A 3 ( 1 1 , 9 , 3 ) = . 2 8 4 1 5 8 7 6 1 0 8 2 3 5 8 - 0 1 A 3 ( 1 1 , 9 , 4 ) = . 3 8 1 1 5 0 5 2 0 6 3 9 4 1 E - 0 1 A 3 ( 1 1 , 9 , 5 ) = . 5 1 1 3 3 4 6 6 2 2 6 8 0 8 8 - 0 1 A 3 ( 1 1 , 9 , 6 ) = . 6 7 7 9 5 5 2 8 5 8 3 3 5 1 3 - 0 1 A 3 ( 1 1 , 9 , 7 ) = . 8 8 5 9 1 5 5 9 3 7 8 0 9 2 8 - 0 1 A 3 ( 1 1 , 9 , 8 ) = . 1 1 4 2 8 9 0 1 6 1 0 6 8 2 3 + 0 0 A 3 ( 1 1 , 9 , 9 ) = . 1 4 6 1 7 4 2 4 1 5 4 7 5 5 E + 0 0 A 3 ( 1 1 , 9 , 1 0 ) = . 1 8 6 7 2 2 0 1 5 6 5 6 6 l E + 0 0 A 3 ( 1 1 , 9 , 1 1 ) = . 2 4 2 3 9 0 9 6 0 5 3 7 2 2 E + 0 0 ' - I N M F | I U \ O I \ 3 0 0 V V V V V V V A 3 ( 1 1 , 1 0 , A 3 ( 1 1 , 1 0 , A 3 ( 1 1 , 1 0 , A 3 ( 1 1 , 1 0 , A 3 ( 1 1 , 1 0 , A 3 ( 1 1 , 1 0 , A 3 ( 1 1 , 1 0 , A 3 ( 1 1 , 1 0 , A 3 ( 1 1 , 1 0 , A 3 ( 1 1 , 1 0 , A 3 ( 1 1 , 1 0 , A 3 ( 1 1 , 1 1 , A 3 ( 1 1 , 1 1 , A 3 ( 1 1 , 1 1 , A 3 ( 1 1 , 1 1 , A 3 ( 1 1 , l l , A 3 ( 1 1 , 1 1 , A 3 ( 1 1 , 1 1 , A 3 ( 1 1 , 1 1 , A 3 ( 1 1 , 1 1 , , 1 0 A 3 ( 1 1 , 1 1 A 3 ( 1 1 , 1 1 , S ( 1 1 , S ( 1 1 , S ( 1 1 , S ( 1 1 , S ( 1 1 , S ( 1 1 , S ( 1 1 , S ( 1 1 , S ( 1 1 , V V V V V V V V V ‘ ( n A I - ' I - ' V 0 0 ) \ I O \ U I I D M N S ( l l p 1 ) 2 ) 3 ) 4 ) 5 ) 6 ) 7 ) 8 ) 9 ) 1 0 ) 1 1 ) 1 ) 2 ) 3 ) 4 ) 5 ) 6 ) 7 ) 8 ) 9 ) ) 1 1 ) = 1 ) = - . 1 ) = - . 1 ) = - . 1 ) = 1 ) - 3 8 5 - . 3 5 8 9 0 2 1 1 8 0 1 9 7 3 8 - 0 1 - . 2 9 5 8 5 4 1 1 6 7 0 6 8 1 E - 0 1 - . 1 8 1 1 5 1 1 1 6 2 0 3 9 5 E - 0 1 - . 1 2 4 3 9 4 0 5 7 4 8 0 7 9 8 - 0 2 . 2 1 4 0 0 8 5 8 6 6 9 7 3 9 E 0 1 . 5 0 3 8 3 5 8 9 2 8 5 6 6 6 8 - 0 1 . 8 6 5 5 7 1 9 1 3 9 8 0 8 6 E - 0 1 . 1 3 1 2 5 5 5 6 3 5 4 0 7 B E + 0 0 . 1 8 6 7 2 2 0 1 5 6 5 6 6 1 8 + 0 0 . 2 5 7 3 5 1 8 3 3 8 2 6 0 1 E + 0 0 . 3 5 5 0 3 0 9 4 8 8 1 0 3 9 E + 0 0 . 1 1 2 3 7 6 5 7 2 4 3 4 9 Z E + 0 0 . 1 0 2 3 2 8 9 5 4 0 0 0 9 6 E + 0 0 . 8 4 0 4 9 3 6 3 2 1 7 2 8 4 8 - 0 1 . 5 7 1 6 2 6 9 3 5 8 2 3 6 7 8 - 0 1 . 2 1 0 7 4 9 0 6 0 2 0 0 0 0 8 - 0 1 . 2 5 1 1 3 3 0 7 1 8 0 5 9 1 8 - 0 1 . 8 2 7 6 1 2 7 5 8 5 8 7 9 4 E - O l . 1 5 3 9 9 3 9 0 3 3 9 5 7 O E + 0 0 . 2 4 2 3 9 0 9 6 0 5 3 7 2 2 E + 0 0 . 3 5 5 0 3 0 9 4 8 8 1 0 3 9 E + 0 0 . 5 1 1 3 8 8 1 0 1 5 3 3 7 6 E + 0 0 1 4 9 3 4 5 8 1 9 2 9 5 8 1 3 - 0 1 9 5 4 0 3 5 7 7 6 6 4 7 3 9 8 - 0 2 1 3 4 7 9 1 4 6 5 3 1 3 4 1 E - 0 2 . 6 8 9 9 8 1 9 0 2 1 7 1 5 3 8 - 0 2 . 1 0 8 5 4 5 2 3 9 1 7 8 4 5 8 - 0 1 . 4 0 1 7 5 4 5 5 9 8 1 7 0 5 8 - 0 2 . 2 3 2 5 8 4 4 8 5 9 4 2 6 2 8 - 0 1 . 8 5 7 0 8 8 1 7 7 4 8 0 0 3 8 - 0 1 . 2 0 7 3 9 5 3 1 2 0 9 6 1 5 8 + 0 0 . 4 3 2 9 5 0 6 7 7 7 1 2 6 S E + 0 0 . 8 7 2 4 4 2 8 3 0 4 5 6 8 9 8 + 0 0 . 5 0 6 8 7 7 4 8 5 4 0 6 2 0 E - 0 2 . 2 4 2 8 0 8 8 4 8 9 1 3 9 7 8 - 0 2 . 8 5 0 2 3 1 1 5 8 6 0 6 6 3 E - 0 3 . 2 6 6 5 6 0 4 8 1 3 8 7 6 3 E - 0 2 . 1 0 5 0 6 2 6 3 7 3 5 3 1 6 8 - 0 2 . 4 2 5 3 5 5 0 0 2 6 4 7 1 7 8 - 0 2 . 8 8 3 1 3 9 2 1 6 7 9 2 0 4 3 - 0 2 . 2 3 4 3 3 0 2 4 0 8 9 1 3 3 8 - 0 2 . 6 8 1 8 2 9 1 6 8 5 6 6 4 7 E - 0 1 . 2 8 7 2 9 6 9 2 8 2 6 6 0 5 E + 0 0 . 9 5 5 3 3 7 3 5 7 8 8 2 6 1 8 + 0 0 . 2 7 0 8 3 3 4 3 1 2 9 3 0 8 E - 0 2 . 9 0 1 6 8 0 2 8 7 0 4 3 2 0 8 - 0 3 . 8 8 2 2 9 7 1 4 0 9 5 6 1 6 3 - 0 3 . 1 0 6 0 8 3 9 6 6 8 9 9 6 7 8 - 0 2 . 7 8 1 2 1 6 6 0 0 6 6 6 1 5 8 - 0 3 . 2 5 1 1 9 8 5 9 0 9 7 4 5 9 8 - 0 2 m u b ~ - ‘ m a d ~ ‘ a “ m ~ $ V 9 V 5 v “ w v m w p ‘ m V m ‘ v V m v m m v m v m v m v m m ~ v m o ‘ v m \ ~ m v m v m v m v m v N W m h v m I ~ v I m U N ‘ m v O m v Q “ m J v C ~ m D m v \ “ v q l v \ v l v \ v l v \ v q v l \ v q v fl v i v \ v ” v u m v V ‘ ‘ 3 8 6 3 ) = - . 6 5 0 8 1 7 4 6 5 0 7 1 0 8 E - 0 3 3 ) = - . 1 1 4 1 6 5 3 7 8 5 6 4 3 1 8 - 0 1 3 ) = . 9 8 6 0 5 4 3 5 8 3 3 3 0 7 3 - 0 2 3 ) “ . 1 2 4 9 0 4 9 0 8 8 0 4 3 6 E + 0 0 3 ) - . 9 9 2 0 4 5 2 6 1 1 8 1 7 O E + 0 0 4 ) = - . 2 8 2 0 9 2 8 4 9 4 9 1 5 1 8 - 0 2 ) ‘ - . 5 5 7 6 8 4 3 3 7 2 6 4 9 8 E - 0 3 4 ) ‘ . 1 1 4 3 7 1 1 9 7 6 7 9 9 9 3 - 0 2 4 ) = . 4 8 3 9 3 4 7 4 5 8 5 1 1 1 8 - 0 3 4 ) = - . 1 5 5 5 3 2 8 6 2 2 1 2 4 4 E - 0 2 4 ) = “ . 9 5 7 0 5 7 8 2 6 3 9 2 2 3 8 - 0 3 4 ) ‘ . 4 4 8 3 6 7 7 4 8 1 9 3 1 5 E - 0 2 . 4 0 3 8 7 9 4 2 5 3 7 0 9 8 8 - 0 2 - . 3 0 5 2 4 6 6 8 1 3 0 0 5 0 3 - 0 1 - . 4 8 5 4 2 0 0 4 5 6 4 1 3 5 8 - 0 1 . 9 9 8 3 2 9 7 8 3 8 2 8 7 B E + 0 0 - . 2 2 2 7 0 3 4 6 1 9 3 8 4 8 3 - 0 1 . 6 6 1 3 2 1 8 6 7 3 7 7 4 6 8 - 0 2 . 3 1 1 4 9 5 7 0 0 1 9 6 2 2 E - 0 2 . 9 2 4 1 1 2 1 7 9 2 0 2 3 7 3 - 0 2 . 9 3 5 4 1 1 7 5 4 1 3 9 7 2 8 - 0 2 . 8 5 1 9 7 4 9 6 6 5 2 2 7 3 8 - 0 3 . 2 7 4 9 4 8 3 5 8 0 3 8 8 5 8 - 0 1 . 7 6 9 0 4 2 6 1 8 5 8 4 4 9 3 - 0 1 . 1 4 1 3 8 9 1 3 5 7 7 2 7 4 E + 0 0 . 9 4 3 8 3 3 2 3 5 0 0 2 3 l E - O l . 9 8 1 6 8 6 1 2 0 6 0 9 0 1 E + 0 0 . 3 3 5 8 5 4 4 6 7 6 6 4 5 2 3 - 0 2 . 7 3 8 6 1 9 3 1 4 4 6 4 3 3 8 - 0 3 . 8 0 7 6 1 4 1 5 6 6 4 4 6 8 8 - 0 3 . 1 4 2 2 0 5 9 7 0 7 0 4 1 7 8 - 0 2 . 6 7 3 8 2 6 6 6 1 4 6 5 6 0 8 - 0 3 . 1 7 2 3 5 9 9 6 1 1 2 5 4 3 E - 0 2 . 5 1 9 1 1 0 9 4 5 1 4 0 1 4 E - 0 2 . 6 0 8 9 3 5 7 7 5 1 4 3 7 1 3 - 0 2 . 1 0 9 3 5 5 9 7 6 4 1 5 7 7 E - O l . 1 2 1 1 4 4 3 3 2 9 9 5 4 4 E + 0 0 . 9 9 2 5 3 3 3 8 0 1 3 3 3 Z E + 0 0 . 2 1 5 1 2 6 3 8 3 3 2 7 8 1 E - 0 1 . 1 6 9 5 1 6 7 7 3 3 1 4 2 5 8 - 0 2 . 9 0 8 3 2 0 8 7 4 9 1 2 8 2 E - 0 2 . 1 0 4 8 9 1 1 9 0 8 6 1 0 2 8 - 0 2 . 1 1 9 3 2 0 7 2 1 9 2 5 4 1 3 - 0 1 . 7 3 6 3 2 3 3 4 4 6 9 1 7 8 8 - 0 2 . 2 9 8 9 4 7 1 5 8 5 9 1 9 8 8 - 0 1 . 5 3 8 2 7 9 8 4 4 3 2 9 5 7 E - O l . 1 4 0 4 6 2 9 3 0 3 3 0 5 1 8 + 0 0 . 9 0 1 1 0 8 3 3 2 6 2 2 8 9 E + 0 0 - . 4 0 4 6 4 4 1 9 9 8 6 3 8 8 E + 0 0 . 2 1 4 0 4 3 7 2 4 9 6 8 8 4 8 - 0 1 . b p v I I 3 8 7 S ( 1 1 , 2 , 8 ) = - . 2 7 9 2 1 7 6 6 2 1 3 7 9 2 3 - 0 2 S ( 1 1 , 3 , 8 ) = - . 7 0 4 4 l 3 5 2 0 8 8 7 7 6 E - 0 2 S ( 1 1 , 4 , 8 ) = . 7 8 0 5 1 0 3 5 1 7 4 7 6 7 E - 0 2 S ( 1 1 , 5 , 8 ) = . 1 8 9 7 3 7 4 3 9 1 0 5 9 4 E - 0 2 S ( 1 1 , 6 , 8 ) = “ . l 7 5 3 2 9 9 7 6 0 1 7 9 1 8 - 0 1 S ( 1 1 , 7 , 8 ) = . 2 1 5 2 4 1 8 1 8 8 7 9 6 6 E - O l S ( 1 1 , 8 , 8 ) = . 2 8 7 1 9 9 2 0 1 3 9 2 7 8 E - 0 1 S ( 1 1 , 9 , 8 ) = - . 2 1 7 9 1 5 6 9 5 4 4 4 1 2 8 + 0 0 S ( 1 1 , 1 0 , 8 ) = . 6 5 0 4 1 6 7 8 2 6 7 2 2 3 E + 0 0 S ( 1 1 , 1 1 , 8 ) = * . 7 2 6 1 5 0 9 1 0 8 6 5 0 4 E + 0 0 S ( 1 1 , l , 9 ) = - . 3 1 8 9 6 6 7 4 9 2 4 1 3 6 8 - 0 2 S ( 1 1 , 2 , 9 ) = . 1 1 0 8 4 4 5 6 4 4 7 6 8 1 E - 0 3 S ( 1 1 , 3 , 9 ) = . 1 2 4 8 0 8 6 9 3 8 5 3 5 2 8 - 0 2 S ( 1 1 , 4 , 9 ) = - . 7 7 2 8 1 1 4 1 2 9 6 1 7 Z E - 0 3 S ( 1 1 , 5 , 9 ) = - . 1 1 5 2 4 2 5 0 7 8 4 1 9 6 3 - 0 2 S ( 1 1 , 6 , 9 ) = . 2 5 0 9 9 3 6 1 9 2 5 7 2 3 8 - 0 2 S ( 1 1 , 7 , 9 ) = . 5 1 1 7 1 3 2 9 1 2 9 3 9 9 E - 0 3 S ( 1 1 , 8 , 9 ) = - . 1 1 2 0 4 8 9 7 7 2 1 7 0 3 E - 0 1 S ( 1 1 , 9 , 9 ) = . 1 9 7 2 1 0 6 9 5 5 9 3 3 3 3 - 0 1 S ( 1 1 , 1 0 , 9 ) = . 6 3 8 3 2 3 6 5 8 0 4 6 6 2 3 - 0 1 S ( 1 1 , 1 1 , 9 ) = - . 9 9 7 6 9 2 7 0 2 0 9 8 6 0 E + 0 0 K ( 1 1 ) = 9 M ( l l ) = 2 w s ( 1 1 , 1 ) = - . 3 3 3 3 2 7 6 8 1 2 3 0 4 G E + 0 0 w s ( 1 1 , 2 ) = - . 5 0 0 0 5 2 4 6 5 8 6 6 5 0 E + 0 0 w s ( 1 1 , 3 ) = - . 5 9 9 7 9 7 5 3 8 5 8 0 9 9 3 + 0 0 w s ( 1 1 , 4 ) = - . 6 6 7 1 1 5 5 0 3 9 6 1 8 7 E + 0 0 w s ( 1 1 , 5 ) = - . 8 1 8 1 6 9 6 0 1 9 3 1 0 1 E + 0 0 w s ( 1 1 , 6 ) = - . 8 0 0 0 9 5 7 7 0 6 0 7 3 4 E + 0 0 w s < 1 1 , 7 ) = - . 7 1 3 6 7 1 0 5 0 5 4 8 7 3 E + 0 0 w s ( 1 1 , 8 ) = - . 7 7 7 4 6 4 9 4 9 4 6 1 1 3 E + 0 0 w s ( 1 1 , 9 ) = - . 7 5 0 5 5 0 9 8 7 5 8 3 4 9 E + 0 0 1 0 P R I N T * , ' N U M B E R O F C O L L O C A T I O N P O I N T S = ' R E A D * , I I F ( K ( I ) . L T . 2 ) G O T O 1 0 1 1 : 1 P R I N T * , ' T Y P E 0 F O R K B K W I N I T I A L D A T A , 1 F O R D E F A U L T ' R E A D * , I O I F ( I O . E Q . O ) T H E N P R I N T * , ' B O = ' R E A D * , B O W R I T E ( 5 0 , 3 0 0 ) B O E L S E E N D I F 3 0 0 F O R M A T ( 5 X , ' B O = ' , E Z O . 1 4 ) S U M 5 = 0 . 0 D O 3 0 ' J = 1 , I I F ( I O . E Q . 0 ) T H E N B ( I , J ) = E X P ( - . 5 * B O * L ( I M / 1 . - B O ) ) * ( 1 . - 1 . 5 * B O / ( 1 . - B O ) + + . 5 * B O * L ( I , J ) / ( ( 1 . - B O ) 2 ) ) ) / ( ( l . - B O ) * * 1 . 5 ) 3 0 5 0 4 0 7 0 6 0 2 2 0 2 1 0 2 3 0 l l 8 0 2 0 0 1 0 0 3 8 8 E L S E P R I N T * , ' Y ( ' , J , ' ) = ' R E A D * , E ( I , J ) E N D I F E ( I , J ) = E ( I , J ) - I . S U M 5 = S U M S + E ( I , J ) * * 2 C O N T I N U E E N O R M ( I , I 1 ) = S U M 5 D O 4 0 J = 1 , K ( I ) S U M = 0 . D O 5 0 J l = l , I S U M = S U M + A 1 ( I , J , J 1 ) * E ( I , J l ) C O N T I N U E C ( I , J , I l ) = S U M C O N T I N U E I F ( M ( I ) . L T . 2 ) G O T O 1 1 S U M = O . D O 6 0 J = 1 , I D O 7 0 J l = l , I S U M = S U M + E ( I , J ) * E ( I , J l ) * A 3 ( I , J , J l ) C O N T I N U E C O N T I N U E E R R ( I , I l ) = S U M S U M 6 = 0 . 0 D O 2 1 0 J = 1 , I D O 2 2 0 J l = l , K ( I ) S U M 6 = S U M 6 + E ( I , J ) * S ( I , J , J l ) * C ( I , J 1 , I l ) C O N T I N U E C O N T I N U E Y N O R M ( I , I l ) = S U M 6 W R I T E ( 5 0 , 2 3 0 ) Y N O R M ( I , 1 1 ) F O R M A T ( 7 X , ' S T A B L E N O R M = ' , E Z O . 1 4 ) W R I T E ( 5 0 , 1 0 0 ) E R R ( I , 1 1 ) W R I T E ( 5 0 , 2 0 0 ) E N O R M ( I , 1 1 ) D O 8 0 J = 1 , K ( I ) W R I T E ( 5 0 , 9 0 ) I , J , 1 1 , C ( I , J , I l ) C O N T I N U E E O R M A T ( 7 x , ' C ( ' , I z , ' , ' , I z , ' , ' , 1 2 , ' ) = ' , E z o . 1 4 ) F O R M A T ( 7 X , ' V E C T O R N O R M O E I N I T I A L D A T A a ' , E 2 0 . 1 4 ) F O R M A T ( 7 X , ' E R R O R I N L E A S T - E R R O R F I T = ' , E Z O . 1 4 ) P R I N T * , ' T Y P E 1 T O C O N T I N U E , 0 T O S T O P ' R E A D * , N 1 I F ( N 1 . E Q . 1 ) G O T O 1 0 S T O P E N D A P P E N D I X F C o m p u t e r p r o g r a m s t a t e m e n t s f o r t h e i n t e g r a t i o n o f t h e c o l l o c a t e d n o n l i n e a r B o l t z m a n n e q u a t i o n . 3 8 9 3 9 0 P R O G R A M N O R M A L ( I N P U T , O U T P U T , T A P E 1 0 ) R E A L W L ( 8 : 1 1 , 1 1 ) , L ( 1 5 , 1 5 ) , E ( l l ) , P I I N T E G E R N , K , J C T H I S P R O G R A M N O R M A L I Z E S A N Y D I S T R I B U T I O N W I T H R E S P E C T T O C D E N S I T Y A N D E N E R G Y . W L ( 8 , 1 ) = . 4 3 7 7 2 3 4 1 0 4 9 3 W L ( 8 , 2 ) = 1 . 0 3 3 8 6 9 3 4 7 6 7 W L ( 8 , 3 ) = 1 . 6 6 9 7 0 9 7 6 5 6 6 W L ( 8 , 4 ) = 2 . 3 7 6 9 2 4 7 0 1 7 6 W L ( 8 , 5 ) = 3 . 2 0 8 5 4 0 9 1 3 3 5 W L ( 8 , 6 ) = 4 . 2 6 8 5 7 5 5 1 0 8 3 W L ( 8 , 7 ) = 5 . 8 1 8 0 8 3 3 6 8 6 7 W L ( 8 , 8 ) = 8 . 9 0 6 2 2 6 2 1 5 2 9 W L ( 9 , 1 ) = . 3 9 1 4 3 1 1 2 4 3 1 6 W L ( 9 , 2 ) = . 9 2 1 8 0 5 0 2 8 5 2 9 W L ( 9 , 3 ) = 1 . 4 8 0 1 2 7 9 0 9 9 4 W L ( 9 , 4 ) = 2 . 0 8 6 7 7 0 8 0 7 5 5 W L ( 9 , 5 ) = 2 . 7 7 2 9 2 1 3 8 9 7 1 W L ( 9 , 6 ) = 3 . 5 9 1 6 2 6 0 6 8 0 9 W L ( 9 , 7 ) = 4 . 6 4 8 7 6 6 0 0 2 1 4 W L ( 9 , 8 ) = 6 . 2 1 2 2 7 5 4 1 9 7 5 W L ( 9 , 9 ) = 9 . 3 6 3 2 1 8 2 3 7 7 1 W L ( 1 0 , 1 ) = . 3 5 4 0 0 9 7 3 8 6 0 7 W L ( 1 0 , 2 ) = . 8 3 1 9 0 2 3 0 1 0 4 4 W L ( 1 0 , 3 ) = 1 . 3 3 0 2 8 8 5 6 1 7 5 W L ( 1 0 , 4 ) = 1 . 8 6 3 0 6 3 9 0 3 1 1 W L ( 1 0 , 5 ) = 2 . 4 5 0 2 5 5 5 5 8 0 8 W L ( 1 0 , 6 ) = 3 . 1 2 2 7 6 4 1 5 5 1 4 W L ( 1 0 , 7 ) = 3 . 9 3 4 1 5 2 6 9 5 5 6 W L ( 1 0 , 8 ) = 4 . 9 9 2 4 1 4 8 7 2 1 9 W L ( 1 0 , 9 ) = 6 . 5 7 2 2 0 2 4 8 5 1 3 W L ( 1 0 , 1 0 ) = 9 . 7 8 4 6 9 5 8 4 0 3 7 W L ( 1 1 , 1 ) = . 3 2 3 1 2 8 8 8 0 4 3 5 W L ( 1 1 , 2 ) = . 7 5 8 1 2 5 5 9 9 8 1 0 W L ( 1 1 , 3 ) = 1 . 2 0 8 6 4 1 4 2 2 9 0 W L ( 1 1 , 4 ) = 1 . 6 8 4 5 7 9 1 6 7 I 4 W L ( 1 1 , 5 ) = 2 . 1 9 9 6 3 3 4 7 8 6 2 W L ( 1 1 , 6 ) = 2 . 7 7 3 4 8 9 7 4 5 7 5 W L ( 1 1 , 7 ) = 3 . 4 3 7 1 2 1 4 1 6 5 2 W L ( 1 1 , 8 ) = 4 . 2 4 4 8 4 0 2 9 0 8 0 W L ( 1 1 , 9 ) = 5 . 3 0 6 8 2 6 0 1 9 4 8 W L ( 1 1 , 1 0 ) = 6 . 9 0 4 2 1 5 4 7 8 8 3 W L ( 1 1 , 1 1 ) = 1 0 . 1 7 6 7 1 2 7 4 6 9 L ( 1 , 1 ) = 1 . L ( 2 , 1 ) = . 5 8 5 7 8 6 4 3 7 6 2 7 L ( 2 , 2 ) = 3 . 4 1 4 2 1 3 5 6 2 3 7 3 L ( 3 , l ) = . 4 1 5 7 7 4 5 5 6 7 8 3 L ( 3 , 2 ) = 2 . 2 9 4 2 8 0 3 6 0 2 7 9 L ( 3 , 3 ) = 6 . 2 8 9 9 4 5 0 8 2 9 3 7 L ( 4 , l ) = . 3 2 2 5 4 7 6 8 9 6 1 9 L ( 4 , 2 ) = 1 . 7 4 5 7 6 1 1 0 1 1 5 8 L ( 4 , 3 ) = 4 . 5 3 6 6 2 0 2 9 6 9 2 1 L ( 4 , 4 ) = 9 . 3 9 5 0 7 0 9 1 2 3 0 1 L ( 5 , l ) = . 2 6 3 5 6 0 3 1 9 7 1 8 L ( 5 , 2 ) = l . 4 1 3 4 0 3 0 5 9 1 0 7 L ( 5 , 3 ) = 3 . 5 9 6 4 2 5 7 7 1 0 4 1 L ( 5 , 4 ) = 7 . 0 8 5 8 1 0 0 0 5 8 5 9 L ( 5 , 5 ) = 1 2 . 6 4 0 8 0 0 8 4 4 2 7 6 L ( 6 , l ) = . 2 2 2 8 4 6 6 0 4 l 7 9 L ( 6 , 2 ) = l . 1 8 8 9 3 2 1 0 1 6 7 3 L ( 6 , 3 ) = 2 . 9 9 2 7 3 6 3 2 6 0 5 9 L ( 6 , 4 ) = 5 . 7 7 5 1 4 3 5 6 9 1 0 5 L ( 6 , 5 ) = 9 . 8 3 7 4 6 7 4 1 8 3 8 3 L ( 6 , 6 ) = 1 5 . 9 8 2 8 7 3 9 8 0 6 0 2 L ( 7 , l ) = . 1 9 3 0 4 3 6 7 6 5 6 0 L ( 7 , 2 ) = 1 . 0 2 6 6 6 4 8 9 5 3 3 9 L ( 7 , 3 ) = 2 . 5 6 7 8 7 6 7 4 4 9 5 1 L ( 7 , 4 ) = 4 . 9 0 0 3 5 3 0 8 4 5 2 6 L ( 7 , 5 ) = 8 . 1 8 2 1 5 3 4 4 4 5 6 3 L ( 7 , 6 ) = 1 2 . 7 3 4 1 8 0 2 9 1 7 9 8 L ( 7 , 7 ) = 1 9 . 3 9 5 7 2 7 8 6 2 2 6 3 L ( 8 , 1 ) = . 1 7 0 2 7 9 6 3 2 3 0 5 L ( 8 , 2 ) = . 9 0 3 7 0 1 7 7 6 7 9 9 L ( 8 , 3 ) = 2 . 2 5 1 0 8 6 6 2 9 8 6 6 L ( 8 , 4 ) = 4 . 2 6 6 7 0 0 1 7 0 2 8 8 L ( 8 , 5 ) = 7 . 0 4 5 9 0 5 4 0 2 3 9 3 L ( 8 , 6 ) = 1 0 . 7 5 8 5 1 6 0 1 0 1 8 1 L ( 8 , 7 ) = 1 5 . 7 4 0 6 7 8 6 4 1 2 7 8 L ( 8 , 8 ) = 2 2 . 8 6 3 1 3 1 7 3 6 8 8 9 L ( 9 , l ) = . 1 5 2 3 2 2 2 2 7 7 3 2 L ( 9 , 2 ) = . 8 0 7 2 2 0 0 2 2 7 4 2 L ( 9 , 3 ) = 2 . 0 0 5 1 3 5 1 5 5 6 1 9 L ( 9 , 4 ) = 3 . 7 8 3 4 7 3 9 7 3 3 3 l L ( 9 , 5 ) = 6 . 2 0 4 9 5 6 7 7 7 8 7 7 L ( 9 , 6 ) = 9 . 3 7 2 9 8 5 2 5 1 6 8 8 L ( 9 , 7 ) = 1 3 . 4 6 6 2 3 6 9 1 1 0 9 2 L ( 9 , 8 ) = 1 8 . 8 3 3 5 9 7 7 8 8 9 9 2 L ( 9 , 9 ) = 2 6 . 3 7 4 0 7 1 8 9 0 9 2 7 L ( 1 0 , 1 ) = . 1 3 7 7 9 3 4 7 0 5 4 0 L ( 1 0 , 2 ) - . 7 2 9 4 5 4 5 4 9 5 0 3 L ( 1 0 , 3 ) = l . 8 0 8 3 4 2 9 0 1 7 4 0 L ( 1 0 , 4 ) = 3 . 4 0 1 4 3 3 6 9 7 8 5 5 L ( 1 0 , 5 ) = 5 . 5 5 2 4 9 6 1 4 0 0 6 4 L ( 1 0 , 6 ) = 8 . 3 3 0 1 5 2 7 4 6 7 6 4 L ( 1 0 , 7 ) = 1 1 . 8 4 3 7 8 5 8 3 7 9 0 0 L ( 1 0 , 8 ) = 1 6 . 2 7 9 2 5 7 8 3 1 3 7 8 L ( 1 0 , 9 ) = 2 1 . 9 9 6 5 8 5 8 1 1 9 8 1 L ( 1 0 , 1 0 ) = 2 9 . 9 2 0 6 9 7 0 1 2 2 7 4 L ( 1 1 , 1 ) = . 1 2 5 7 9 6 4 4 2 1 8 8 L ( 1 1 , 2 ) = . 6 6 5 4 1 8 2 5 5 8 3 9 3 9 1 L ( l l , 3 ) = l . 6 4 7 1 5 0 5 4 5 8 7 2 L ( l l , 4 ) = 3 . 0 9 l l 3 8 1 4 3 0 3 5 L ( 1 1 , 5 ) = 5 . 0 2 9 2 8 4 4 0 1 5 8 0 L ( l l , 6 ) = 7 . 5 0 9 8 8 7 8 6 3 8 0 7 L ( 1 1 , 7 ) = 1 0 . 6 0 5 9 5 0 9 9 9 5 4 7 L ( l l , 8 ) = l 4 . 4 3 1 6 1 3 7 5 8 0 6 4 L ( 1 1 , 9 ) = 1 9 . 1 7 8 8 5 7 4 0 3 2 1 5 L ( l l , 1 0 ) = 2 5 . 2 1 7 7 0 9 3 3 9 6 7 8 L ( l l , l l ) = 3 3 . 4 9 7 l 9 2 8 4 7 1 7 6 L ( 1 2 , 1 ) = . 1 1 5 7 2 2 1 1 7 3 5 8 L ( 1 2 , 2 ) = . 6 1 1 7 5 7 4 8 4 5 1 5 L ( 1 2 , 3 ) = 1 . 5 1 2 6 1 0 2 6 9 7 7 6 L ( 1 2 , 4 ) = 2 . 8 3 3 7 5 1 3 3 7 7 4 4 L ( 1 2 , 5 ) = 4 . 5 9 9 2 2 7 6 3 9 4 1 8 L ( 1 2 , 6 ) = 6 . 8 4 4 5 2 5 4 5 3 1 1 5 L ( 1 2 , 7 ) = 9 . 6 2 1 3 1 6 8 4 2 4 5 7 L ( 1 2 , 8 ) = 1 3 . 0 0 6 0 5 4 9 9 3 3 0 6 L ( 1 2 , 9 ) = l 7 . 1 1 6 8 5 5 1 8 7 4 6 2 L ( 1 2 , 1 0 ) = 2 2 . 1 5 1 0 9 0 3 7 9 3 9 7 L ( 1 2 , 1 1 ) = 2 8 . 4 8 7 9 6 7 2 5 0 9 8 4 L ( 1 2 , 1 2 ) = 3 7 . 0 9 9 1 2 1 0 4 4 4 6 7 L ( 1 3 , 1 ) = . 1 0 7 l 4 2 3 8 8 4 7 2 L ( 1 3 , 2 ) = . 5 6 6 1 3 1 8 9 9 0 4 0 L ( 1 3 , 3 ) = 1 . 3 9 8 5 6 4 3 3 6 4 5 1 L ( 1 3 , 4 ) = 2 . 6 1 6 5 9 7 1 0 8 4 0 6 L ( 1 3 , 5 ) = 4 . 2 3 8 8 4 5 9 2 9 0 1 7 L ( 1 3 , 6 ) = 6 . 2 9 2 2 5 6 2 7 1 1 4 0 L ( 1 3 , 7 ) = 8 . 8 1 5 0 0 1 9 4 1 1 8 7 L ( 1 3 , 8 ) = l l . 8 6 1 4 0 3 5 8 8 8 1 1 L ( 1 3 , 9 ) = 1 5 . 5 1 0 7 6 2 0 3 7 7 0 4 L ( 1 3 , 1 0 ) = 1 9 . 8 8 4 6 3 5 6 6 3 8 8 0 L ( l 3 , 1 1 ) = 2 5 . 1 8 5 2 6 3 8 6 4 6 7 8 L ( 1 3 , 1 2 ) = 3 1 . 8 0 0 3 8 6 3 0 1 9 4 7 L ( 1 3 , 1 3 ) = 4 0 . 7 2 3 0 0 8 6 6 9 2 6 6 L ( l 4 , 1 ) = . 0 9 9 7 4 7 5 0 7 0 3 3 L ( l 4 , 2 ) = . 5 2 6 8 5 7 6 4 8 8 5 2 L ( 1 4 , 3 ) = 1 . 3 0 0 6 2 9 1 2 1 2 5 1 L ( 1 4 , 4 ) = 2 . 4 3 0 8 0 1 0 7 8 7 3 1 L ( l 4 , 5 ) = 3 . 9 3 2 1 0 2 8 2 2 2 9 3 L ( 1 4 , 6 ) = 5 . 8 2 5 5 3 6 2 1 8 3 0 2 L ( l 4 , 7 ) = 8 . l 4 0 2 4 0 1 4 1 5 6 5 L ( 1 4 , 8 ) = 1 0 . 9 1 6 4 9 9 5 0 7 3 6 6 L ( 1 4 , 9 ) = 1 4 . 2 1 0 8 0 5 0 1 1 1 6 1 L ( l 4 , 1 0 ) = 1 8 . 1 0 4 8 9 2 2 2 0 2 1 8 L ( 1 4 , 1 1 ) = 2 2 . 7 2 3 3 8 1 6 2 8 2 6 9 L ( 1 4 , 1 2 ) = 2 8 . 2 7 2 9 8 1 7 2 3 2 4 8 L ( l 4 , 1 3 ) = 3 5 . 1 4 9 4 4 3 6 6 0 5 9 2 L ( l 4 , 1 4 ) = 4 4 . 3 6 6 0 8 1 7 1 1 1 1 7 L ( 1 5 , 1 ) = . 0 9 3 3 0 7 8 1 2 0 1 7 L ( 1 5 , 2 ) = . 4 9 2 6 9 1 7 4 0 3 0 2 3 9 2 2 0 1 0 3 0 4 0 3 9 3 L ( 1 5 , 3 ) = 1 . 2 1 5 5 9 5 4 1 2 0 7 1 L ( 1 5 , 4 ) = 2 . 2 6 9 9 4 9 5 2 6 2 0 4 L ( 1 5 , 5 ) = 3 . 6 6 7 6 2 2 7 2 1 7 5 1 L ( 1 5 , 6 ) = 5 . 4 2 5 3 3 6 6 2 7 4 1 4 L ( 1 5 , 7 ) = 7 . 5 6 5 9 1 6 2 2 6 6 1 3 L ( 1 5 , 8 ) = 1 0 . 1 2 0 2 2 8 5 6 8 0 1 9 L ( 1 5 , 9 ) = 1 3 . 1 3 0 2 8 2 4 8 2 1 7 6 L ( 1 5 , 1 0 ) = 1 6 . 6 5 4 4 0 7 7 0 8 3 3 0 L ( 1 5 , 1 1 ) = 2 0 . 7 7 6 4 7 8 8 9 9 4 4 9 L ( 1 5 , 1 2 ) = 2 5 . 6 2 3 8 9 4 2 2 6 7 2 9 L ( 1 5 , 1 3 ) = 3 1 . 4 0 7 5 1 9 1 6 9 7 5 4 L ( 1 5 , 1 4 ) = 3 8 . 5 3 0 6 8 3 3 0 6 4 8 6 L ( 1 5 , 1 5 ) = 4 8 . 0 2 6 0 8 5 5 7 2 6 8 6 P R I N T * , ' N U M B E R O F C O L L O C A T I O N P O I N T S = R E A D * , N P R I N T * , ' I N D E x O F F I R S T R O O T = ' R E A D * , J P R I N T * , ' I N D E X O F S E C O N D R O O T = ' R E A D * , K P I = 3 . 1 4 1 5 9 2 6 5 D O 2 0 I = I , N I F ( I . E Q . J ) G O T O 2 0 I F ( I . E Q . K ) G O T O 2 0 P R I N T * , ' E ( ' , I , ' ) = ' R E A D * , E ( I ) E ( I ) = E ( I ) - 1 . C O N T I N U E ' S U M 1 = 0 . S U M 2 = 0 . D O 1 0 I = I , N I F ( I . E Q . J ) G O T O 1 0 I F ( I . E Q . K ) G O T O 1 0 S U M 1 = S U M 1 + W L ( N , I ) * L ( N , I ) * * 1 . 5 * E X P ( - . 5 * L ( N , I ) ) S U M 2 = S U M 2 + W L ( N , I ) * L ( N , I ) * * . 5 * E X P ( - . 5 * L ( N , I ) ) * C O N T I N U E D 1 = W L ( N , J ) * W L ( N , K ) * L ( N , J ) * * . 5 * L ( N , K ) * * . 5 * ( L ( N , J ) - * E ( I ) E ( I ) + L ( N , x ) ) * E X P ( - . 5 * ( L ( N , J ) + L ( N , K ) ) ) E ( J ) = - ( - W L ( N , K ) * L ( N , K ) * * 1 . 5 * E X P ( - . 5 * L ( N , K ) ) * S U M 2 + W L ( N , K ) + * L ( N , K ) * * . 5 * E X P ( ’ . 5 * L ( N , K ) ) * S U M 1 ) / D l E ( N ) = W L ( N , J ) * L ( N , J ) * * . 5 * E X P ( - . 5 * L ( N , J ) ) * ( - L ( N , J ) * S U M 2 + S U M 1 ) / D 1 D O 3 0 I = I , N E ( I ) = E ( I ) + 1 . W R I T E ( 1 0 , 4 0 ) N , I , E ( I ) P R I N T * , E ( I ) C O N T I N U E F O R M A T ( 7 X , ' F ( ' , 1 2 , ' , ' , 1 2 , ' ) = ' , E 2 0 . 1 4 ) P R I N T * , ' T Y P E 0 T O S T O P , 1 T O C O N T I N U E ' R E A D * , L 1 I F ( L 1 . E Q . 1 ) G O T O 5 S T O P 3 9 4 E N D 3 9 5 M O R I N , P N 2 0 1 3 0 3 7 , R G 2 , J C 4 9 9 9 , L 2 0 0 , T 1 0 0 , C M 2 7 0 0 0 0 . F T N S . C A T A L O G , L G O , T J M L G 9 , R P = 9 9 9 , I D = T J M , T K = K R O O K . D I S P O S E , O U T P U T , P R . * E O S P R O G R A M K R O O K ( I N P U T , O U T P U T , T A P E 6 0 ) I N T E G E R N , M E T H , M I T E R , I N D E X , I E R , I W K ( 1 6 ) R E A L X , T O L , X E N D , H , L ( 1 5 , 0 : 1 5 ) , Y ( l 6 ) , Y K ( 1 6 ) , W K ( 5 4 4 ) R E A L W L ( 8 : 1 2 , 1 2 ) R E A L Y N E w ( 1 6 ) C O M M O N A ( 8 : 1 1 , I I , I I , I I ) E X T E R N A L F C N , F C N J T H I S P R O G R A M I N T E G R A T E S T H E N O N L I N E A R B O L T Z M A N N E Q U A T I O N U S I N G T H E A ( I , J , K , L ) C A L C U L A T E D E A R L I E R . T H E V A L U E S O F T H E C O U P L I N G M A T R I X A ( I , J , K , L ) A R E R E Q U I R E D F O R T H I S P R O G R A M . T H E V A L U E S O F A ( I , J , K , L ) M A Y B E F O U N D O N P A G E S 2 3 7 - 3 0 8 . T H E F O L L O W I N G A R E I N T E G R A T I O N W E I G H T S F O R T H E R E N O R M A L I Z A T I O N O F T H E D I S T R I B U T I O N F U N C T I O N . T H E Y W E R E O B T A I N E D F R O M S A L Z E R A N D Z U C K E R A N D A R E G I V E N I N T H E F O R M W L ( * , * ) = W * E X P ( X ) , W H E R E 3 I S T H E R O O T O F A L A G U E R R E P O L Y N O M I A L A N D W 1 5 T H E W E I G H T F A C T O R . W L ( 8 , 1 ) = . 4 3 7 7 2 3 4 1 0 4 9 3 W L ( 8 , 2 ) = 1 . 0 3 3 8 6 9 3 4 7 6 7 W L ( 8 , 3 ) = 1 . 6 6 9 7 0 9 7 6 5 6 6 W L ( 8 , 4 ) = 2 . 3 7 6 9 2 4 7 0 1 7 6 W L ( 8 , 5 ) = 3 . 2 0 8 5 4 0 9 1 3 3 5 W L ( 8 , 6 ) = 4 . 2 6 8 5 7 5 5 1 0 8 3 W L ( 8 , 7 ) = 5 . 8 1 8 0 8 3 3 6 8 6 7 W L ( 8 , 8 ) = 8 . 9 0 6 2 2 6 2 1 5 2 9 W L ( 9 , 1 ) = . 3 9 I 4 3 1 1 2 4 3 1 6 W L ( 9 , 2 ) = . 9 2 1 8 0 5 0 2 8 5 2 9 W L ( 9 , 3 ) = 1 . 4 8 0 1 2 7 9 0 9 9 4 W L ( 9 , 4 ) = 2 . 0 8 6 7 7 0 8 0 7 5 5 W L ( 9 , 5 ) = 2 . 7 7 2 9 2 1 3 8 9 7 1 W L ( 9 , 6 ) = 3 . 5 9 1 6 2 6 0 6 8 0 9 W L ( 9 , 7 ) = 4 . 6 4 8 7 6 6 0 0 2 1 4 W L ( 9 , 8 ) = 6 . 2 1 2 2 7 5 4 I 9 7 5 W L ( 9 , 9 ) = 9 . 3 6 3 2 1 8 2 3 7 7 1 W L ( 1 0 , 1 ) = . 3 5 4 0 0 9 7 3 8 6 0 7 W L ( I o , 2 ) = . B 3 1 9 0 2 3 0 1 0 4 4 W L ( 1 0 , 3 ) = 1 . 3 3 0 2 8 8 5 6 1 7 5 W L ( 1 0 , 4 ) = 1 . 8 6 3 0 6 3 9 0 3 1 1 W L ( 1 0 , 5 ) = 2 . 4 5 0 2 5 5 5 5 8 0 8 W L ( 1 0 , 6 ) = 3 . 1 2 2 7 6 4 1 5 5 1 4 W L ( 1 0 , 7 ) = 3 . 9 3 4 1 5 2 6 9 5 5 6 W L ( 1 0 , 8 ) = 4 . 9 9 2 4 1 4 8 7 2 1 9 W L ( 1 0 , 9 ) = 6 . 5 7 2 2 0 2 4 8 5 1 3 W L ( 1 0 , 1 0 ) = 9 . 7 8 4 6 9 5 8 4 0 3 7 W L ( 1 1 , 1 ) = . 3 2 3 1 2 8 8 8 0 4 3 5 W L ( 1 1 , 2 ) = . 7 5 8 1 2 5 5 9 9 8 1 0 0 0 0 0 0 0 0 0 0 3 9 6 W L ( 1 1 , 3 ) = 1 . 2 0 8 6 4 1 4 2 2 9 0 W L ( 1 1 , 4 ) = 1 . 6 8 4 5 7 9 1 6 7 1 4 W L ( 1 1 , S ) = 2 . 1 9 9 6 3 3 4 7 8 6 2 W L ( 1 1 , 6 ) = 2 . 7 7 3 4 8 9 7 4 5 7 5 W L ( 1 1 , 7 ) = 3 . 4 3 7 1 2 1 4 1 6 5 2 W L ( 1 1 , 8 ) = 4 . 2 4 4 8 4 0 2 9 0 8 0 W L ( 1 1 , 9 ) = 5 . 3 0 6 8 2 6 0 1 9 4 8 W L ( 1 1 , 1 0 ) = 6 . 9 0 4 2 1 5 4 7 8 8 3 W L ( 1 1 , 1 1 ) = 1 0 . 1 7 6 7 1 2 7 4 6 9 C T H E F O L L O W I N G N U M B E R S A R E T H E R O O T S O F T H E F I R S T C F I F T E E N L A G U E R R E P O L Y N O M I A L S . C B U L L . A M E R . M A T H . S O C . V O L . 5 5 ( 1 9 4 9 ) P . 1 0 0 4 - 1 0 1 2 L ( 1 , 1 ) = 1 . L ( 2 , 1 ) = . 5 8 5 7 8 6 4 3 7 6 2 7 L ( 2 , 2 ) = 3 . 4 l 4 2 1 3 5 6 2 3 7 3 L ( 3 , 1 ) = . 4 1 5 7 7 4 5 5 6 7 8 3 L ( 3 , 2 ) = 2 . 2 9 4 2 8 0 3 6 0 2 7 9 L ( 3 , 3 ) = 6 . 2 8 9 9 4 5 0 8 2 9 3 7 L ( 4 , 1 ) = . 3 2 2 5 4 7 6 8 9 6 1 9 L ( 4 , 2 ) = 1 . 7 4 S 7 6 1 1 0 1 1 5 8 L ( 4 , 3 ) = 4 . 5 3 6 6 2 0 2 9 6 9 2 1 L ( 4 , 4 ) = 9 . 3 9 5 0 7 0 9 1 2 3 0 1 L ( 5 , 1 ) = . 2 6 3 5 6 0 3 1 9 7 1 8 L ( 5 , 2 ) = 1 . 4 1 3 4 0 3 0 5 9 1 0 7 L ( 5 , 3 ) = 3 . 5 9 6 4 2 5 7 7 1 0 4 1 L ( 5 , 4 ) = 7 . 0 8 5 8 1 0 0 0 5 8 5 9 L ( 5 , 5 ) = 1 2 . 6 4 0 8 0 0 8 4 4 2 7 6 L ( 6 , 1 ) = . 2 2 2 8 4 6 6 0 4 1 7 9 L ( 6 , 2 ) = l . 1 8 8 9 3 2 1 0 1 6 7 3 L ( 6 , 3 ) = 2 . 9 9 2 7 3 6 3 2 6 0 5 9 L ( 6 , 4 ) = 5 . 7 7 5 1 4 3 5 6 9 1 0 5 L ( 6 , 5 ) = 9 . 8 3 7 4 6 7 4 1 8 3 8 3 L ( 6 , 6 ) = 1 5 . 9 8 2 8 7 3 9 8 0 6 0 2 L ( 7 , 1 ) = . 1 9 3 0 4 3 6 7 6 5 6 0 L ( 7 , 2 ) = l . 0 2 6 6 6 4 8 9 5 3 3 9 L ( 7 , 3 ) = 2 . 5 6 7 8 7 6 7 4 4 9 5 1 L ( 7 , 4 ) = 4 . 9 0 0 3 5 3 0 8 4 5 2 6 L ( 7 , 5 ) = 8 . 1 8 2 1 5 3 4 4 4 5 6 3 L ( 7 , 6 ) = 1 2 . 7 3 4 1 8 0 2 9 1 7 9 8 L ( 7 , 7 ) = 1 9 . 3 9 5 7 2 7 8 6 2 2 6 3 L ( 8 , 1 ) = . 1 7 0 2 7 9 6 3 2 3 0 5 L ( 8 , 2 ) = . 9 0 3 7 0 1 7 7 6 7 9 9 L ( 8 , 3 ) = 2 . 2 5 1 0 8 6 6 2 9 8 6 6 L ( 8 , 4 ) = 4 . 2 6 6 7 0 0 1 7 0 2 8 8 L ( 8 , 5 ) = 7 . 0 4 5 9 0 5 4 0 2 3 9 3 L ( 8 , 6 ) = 1 0 . 7 5 8 5 1 6 0 1 0 1 8 1 L ( 8 , 7 ) = 1 5 . 7 4 0 6 7 8 6 4 1 2 7 8 L ( 8 , 8 ) = 2 2 . 8 6 3 1 3 1 7 3 6 8 8 9 L ( 9 , 1 ) = . 1 5 2 3 2 2 2 2 7 7 3 2 L ( 9 , 2 ) = . 8 0 7 2 2 0 0 2 2 7 4 2 L ( 9 , 3 ) = 2 . 0 0 5 1 3 5 1 5 5 6 1 9 L ( 9 , 4 ) = 3 . 7 8 3 4 7 3 9 7 3 3 3 l L ( 9 , 5 ) = 6 . 2 0 4 9 5 6 7 7 7 8 7 7 L ( 9 , 6 ) = 9 . 3 7 2 9 8 5 2 5 1 6 8 8 L ( 9 , 7 ) = l 3 . 4 6 6 2 3 6 9 1 1 0 9 2 L ( 9 , 8 ) = 1 8 . 8 3 3 5 9 7 7 8 8 9 9 2 L ( 9 , 9 ) = 2 6 . 3 7 4 0 7 1 8 9 0 9 2 7 L ( 1 0 , 1 ) = . l 3 7 7 9 3 4 7 0 5 4 0 L ( 1 0 , 2 ) = . 7 2 9 4 5 4 5 4 9 5 0 3 L ( 1 0 , 3 ) = 1 . 8 0 8 3 4 2 9 0 1 7 4 0 L ( 1 0 , 4 ) = 3 . 4 0 1 4 3 3 6 9 7 8 5 5 L ( 1 0 , 5 ) = 5 . 5 5 2 4 9 6 1 4 0 0 6 4 L ( 1 0 , 6 ) = 8 . 3 3 0 1 5 2 7 4 6 7 6 4 L ( 1 0 , 7 ) = l l . 8 4 3 7 8 5 8 3 7 9 0 0 L ( 1 0 , 8 ) = 1 6 . 2 7 9 2 5 7 8 3 1 3 7 8 L ( 1 0 , 9 ) = 2 1 . 9 9 6 5 8 5 8 1 1 9 8 1 L ( 1 0 , 1 0 ) = 2 9 . 9 2 0 6 9 7 0 1 2 2 7 4 L ( l l , l ) = . 1 2 5 7 9 6 4 4 2 1 8 8 L ( l l , 2 ) = . 6 6 5 4 1 8 2 5 5 8 3 9 L ( l l , 3 ) = l . 6 4 7 1 5 0 5 4 5 8 7 2 L ( l l , 4 ) = 3 . 0 9 1 1 3 8 1 4 3 0 3 5 L ( 1 1 , 5 ) = 5 . 0 2 9 2 8 4 4 0 1 5 8 0 L ( l l , 6 ) = 7 . 5 0 9 8 8 7 8 6 3 8 0 7 L ( 1 1 , 7 ) = 1 0 . 6 0 5 9 5 0 9 9 9 5 4 7 L ( 1 1 , 8 ) = 1 4 . 4 3 1 6 1 3 7 5 8 0 6 4 L ( 1 1 , 9 ) = l 9 . 1 7 8 8 5 7 4 0 3 2 1 5 L ( l l , 1 0 ) = 2 5 . 2 1 7 7 0 9 3 3 9 6 7 8 L ( l l , 1 1 ) = 3 3 . 4 9 7 1 9 2 8 4 7 l 7 6 L ( 1 2 , 1 ) = . 1 1 5 7 2 2 1 1 7 3 5 8 L ( 1 2 , 2 ) = . 6 1 1 7 5 7 4 8 4 5 1 5 L ( 1 2 , 3 ) = 1 . 5 1 2 6 1 0 2 6 9 7 7 6 L ( 1 2 , 4 ) = 2 . 8 3 3 7 5 1 3 3 7 7 4 4 L ( 1 2 , 5 ) = 4 . 5 9 9 2 2 7 6 3 9 4 1 8 L ( 1 2 , 6 ) = 6 . 8 4 4 5 2 5 4 5 3 1 1 5 L ( 1 2 , 7 ) = 9 . 6 2 1 3 1 6 8 4 2 4 5 7 L ( 1 2 , 8 ) = 1 3 . 0 0 6 0 5 4 9 9 3 3 0 6 L ( 1 2 , 9 ) = 1 7 . 1 1 6 8 5 5 1 8 7 4 6 2 L ( 1 2 , 1 0 ) = 2 2 . 1 5 1 0 9 0 3 7 9 3 9 7 L ( 1 2 , 1 1 ) = 2 8 . 4 8 7 9 6 7 2 5 0 9 8 4 L ( 1 2 , 1 2 ) = 3 7 . 0 9 9 1 2 1 0 4 4 4 6 7 L ( 1 3 , 1 ) = . 1 0 7 1 4 2 3 8 8 4 7 2 L ( 1 3 , 2 ) = . 5 6 6 1 3 1 8 9 9 0 4 0 L ( 1 3 , 3 ) = 1 . 3 9 8 5 6 4 3 3 6 4 5 1 L ( 1 3 , 4 ) = 2 . 6 1 6 5 9 7 1 0 8 4 0 6 L ( 1 3 , 5 ) = 4 . 2 3 8 8 4 5 9 2 9 0 1 7 L ( 1 3 , 6 ) = 6 . 2 9 2 2 5 6 2 7 1 1 4 0 L ( 1 3 , 7 ) = 8 . 8 1 5 0 0 1 9 4 1 1 8 7 L ( 1 3 , 8 ) = 1 1 . 8 6 1 4 0 3 5 8 8 8 1 1 L ( l 3 , 9 ) = 1 5 . 5 1 0 7 6 2 0 3 7 7 0 4 L ( l 3 , 1 0 ) = l 9 . 8 8 4 6 3 5 6 6 3 8 8 0 3 9 7 . . . - ' - J P 3 9 8 L ( 1 3 , l l ) = 2 5 . 1 8 5 2 6 3 8 6 4 6 7 8 L ( 1 3 , 1 2 ) = 3 1 . 8 0 0 3 8 6 3 0 1 9 4 7 L ( 1 3 , I 3 ) = 4 0 . 7 2 3 0 0 8 6 6 9 2 6 6 L ( 1 4 , 1 ) = . 0 9 9 7 4 7 5 0 7 0 3 3 L ( 1 4 , 2 ) = . 5 2 6 8 5 7 6 4 8 8 5 2 L ( 1 4 , 3 ) = 1 . 3 0 0 6 2 9 1 2 1 2 5 1 L ( 1 4 , 4 ) = 2 . 4 3 0 8 0 1 0 7 8 7 3 I L ( 1 4 , 5 ) = 3 . 9 3 2 1 0 2 8 2 2 2 9 3 L ( 1 4 , 6 ) = 5 . 8 2 5 5 3 6 2 1 8 3 0 2 L ( 1 4 , 7 ) = 8 . 1 4 0 2 4 0 1 4 1 5 6 5 L ( 1 4 , 8 ) = 1 0 . 9 1 6 4 9 9 5 0 7 3 6 6 L ( l 4 , 9 ) = 1 4 . 2 1 0 8 0 5 0 1 1 1 6 1 L ( l 4 , 1 0 ) = 1 8 . 1 0 4 8 9 2 2 2 0 2 1 8 L ( 1 4 , 1 1 ) = 2 2 . 7 2 3 3 8 1 6 2 8 2 6 9 L ( 1 4 , 1 2 ) = 2 8 . 2 7 2 9 8 1 7 2 3 2 4 8 L ( 1 4 , 1 3 ) = 3 5 . 1 4 9 4 4 3 6 6 0 5 9 2 L ( 1 4 , 1 4 ) = 4 4 . 3 6 6 0 8 1 7 1 1 1 1 7 L ( 1 5 , 1 ) = . 0 9 3 3 0 7 8 1 2 0 1 7 L ( 1 5 , 2 ) = . 4 9 2 6 9 1 7 4 0 3 0 2 L ( 1 5 , 3 ) = 1 . 2 1 5 5 9 5 4 1 2 0 7 1 L ( 1 5 , 4 ) = 2 . 2 6 9 9 4 9 5 2 6 2 0 4 L ( 1 5 , 5 ) = 3 . 6 6 7 6 2 2 7 2 1 7 5 1 L ( 1 5 , 6 ) = 5 . 4 2 5 3 3 6 6 2 7 4 1 4 L ( 1 5 , 7 ) = 7 . 5 6 5 9 1 6 2 2 6 6 1 3 L ( 1 5 , 8 ) = 1 0 . 1 2 0 2 2 8 5 6 8 0 1 9 L ( 1 5 , 9 ) = l 3 . 1 3 0 2 8 2 4 8 2 1 7 6 L ( 1 5 , 1 0 ) = 1 6 . 6 5 4 4 0 7 7 0 8 3 3 0 L ( 1 5 , 1 1 ) = 2 0 . 7 7 6 4 7 8 8 9 9 4 4 9 L ( 1 5 , 1 2 ) = 2 5 . 6 2 3 8 9 4 2 2 6 7 2 9 L ( 1 5 , 1 3 ) = 3 1 . 4 0 7 5 1 9 1 6 9 7 5 4 L ( 1 5 , 1 4 ) = 3 8 . 5 3 0 6 8 3 3 0 6 4 8 6 L ( 1 5 , 1 5 ) = 4 8 . 0 2 6 0 8 5 5 7 2 6 8 6 D O 1 0 I = 1 , 1 5 L ( I , 0 ) = 0 . 0 1 0 C O N T I N U E C V A R I A B L E P A R A M E T E R V A L U E S A R E D E F I N E D B E L O W . I S P R I N T * , ' V A L U E O F K R O O K - W U P A R A M E T E R B O = ' R E A D * , B o P R I N T * , ' N U M B E R O F C O L L O C A T I O N P O I N T S = ' R E A D * , N P R I N T * , ' I N I T I A L I N C R E M E N T ( H ) = ' R E A D * , H P R I N T * , ' T O L = ' R E A D * , T O L P R I N T * , ' M I T E R = ' R E A D * , M I T E R P R I N T * , ' I N I T I A L X E N D = ' R E A D * , X E N D 1 P R I N T * , ' F I N A L X E N D = ' R E A D * , X E N D 2 3 9 9 P R I N T * , ' X E N D I N C R E M E N T = ' R E A D * , X E N D 3 P R I N T * , ' M E T H = ' R E A D * , M E T H P R I N T * , ' T Y P E 0 T O N O R M A L I Z E I N I T I A L C O N D I T I O N , 1 T O D E F A U L T ' R E A D * , I O I N D E x = I H 1 = H T O L 1 = T O L W R I T E ( 6 0 , 5 0 0 ) B O , N W R I T E ( 6 0 , 5 1 0 ) W R I T E ( s o , 5 3 0 ) T O L , M I T E R , M E T H 5 0 0 F O R M A T ( 5 x , ' B o = ' , F 1 0 . 4 , 5 x , ' N = ' , 1 2 ) 5 3 o F O R M A T ( S X , ' T O L = ' , E l O . 4 , 5 X , ' M I T E R = ' , I Z , 5 X , ' M E T H = ' , 1 2 ) 5 1 0 F O R M A T ( 5 x , ' Y ( I ) R E N O R M A L I z E D O N R E T U R N T O K R O O K ' ) C T H I S L O O P C A L C U L A T E S T H E I N I T I A L D I S T R I B U T I O N F O R C T H E B O B Y L E V / K R O O K / W U S O L U T I O N . C T O I N P U T A N I N I T I A L C O N D I T I O N O N Y ( I ) T Y P E 0 , C O T H E R W I S E T H E B K W I N I T I A L C O N D I T I O N I S U S E D . P R I N T * , ' T Y P E I T O I N P U T x A N D Y ( I , 0 ) , o F O R D E F A U L T ' R E A D * , M 2 I F ( M 2 . E Q . 0 ) T H E N x = o . o D O 2 0 I = I , N Y ( I ) = E X P ( - B O * . 5 * L ( N , I ) / ( 1 . - B O ) ) * ( 1 . - 1 . 5 * B 0 / ( 1 . - B O ) + + . 5 * B o * L ( N , I ) / ( ( 1 . - B O ) * * 2 ) ) / < ( 1 . - B O ) * * 1 . 5 ) W R I T E ( 6 0 , 7 2 ) I , Y ( I ) 2 0 C O N T I N U E E L S E P R I N T * , ' X = ' R E A D * , x D O 2 5 I = I , N P R I N T * , ' Y ( ' , I , ' ) = ' R E A D * , Y ( I ) 2 5 C O N T I N U E E N D I F C T H I S L O O P N O R M A L I z E S T H E I N I T I A L C O N D I T I O N . S U M I = o . 0 D O 7 1 1 : 1 , N S U M 1 = S U M 1 + W L ( N , I ) * E x P ( - . 5 * L ( N , I ) ) * Y ( I ) * + L ( N , I ) * * . 5 / ( 2 . * 3 . 1 4 1 5 9 2 6 5 ) * * . 5 7 1 C O N T I N U E D O 8 1 I = I , N I F ( I o . E Q . 0 ) T H E N Y ( I ) = Y ( I ) / S U M 1 E L S E Y ( I ) = Y ( I ) E N D I F W R I T E ( 6 0 , 7 2 ) I , Y ( I ) 8 1 C O N T I N U E 4 0 0 I F ( I o . E Q . 0 ) T H E N W R I T E ( 6 0 , 3 ) 3 F O R M A T ( 5 x , ' I N I T I A L D A T A I s N O R M A L I Z E D I N T E R N A L L Y ' ) E L S E E N D I F 7 2 F O R M A T ( s x , ' Y ( ' , 1 2 , ' ) = ' , E 1 5 . 8 ) C T H I S L O O P C A L C U L A T E S T H E T I M E E V O L U T I O N O F T H E B O B Y L E V / C K R O O K / W U S O L U T I O N , U S I N G D G E A R T O I N T E G R A T E T H E E Q U A T I O N S . D O 3 0 X E N D = X B N D 1 , X E N D Z , X E N D 3 I N D E x = 1 H = H 1 T O L = T O L I C A L L D G E A R ( N , F C N , F C N J , X , H , Y , X E N D , T O L , M E T H , M I T E R , I N D E X , I W K , + W K , I E R ) D O 6 0 I = I , N I F ( Y ( I ) . L T . 0 . ) T H E N P R I N T * , ' Y ( ' , I , ' ) < 0 ' G O T O 5 5 0 E L S E E N D I F 6 0 C O N T I N U E S U M = 0 . 0 S U M 1 = 0 . 0 D O 7 0 I = I , N S U M I = S U M 1 + W L ( N , I ) * E X P ( - . 5 * L ( N , I ) ) * Y ( I ) * + L ( N , I ) * * . 5 / ( 2 . * 3 . 1 4 1 5 9 2 6 5 ) * * . 5 7 0 C O N T I N U E D O 8 0 I = I , N Y N E w ( I ) = Y ( I ) / S U M 1 8 0 C O N T I N U E B = B O * E X P ( - X / 6 . ) S U M 2 = 0 . 0 S U M 3 = 0 . 0 S U M 4 = 0 . S U M 5 = 0 . D O 4 0 I = I , N Y K ( I ) = E X P ( - B * . 5 * L ( N , I ) / ( 1 . - B ) ) * ( l . - l . 5 * B / ( 1 . - B ) + + . 5 * B * L ( N , I ) / ( 1 . - B ) * * 2 ) / ( 1 . - B ) * * 1 . 5 S U M 2 = S U M 2 + W L ( N , I ) * E X P ( - L ( N , I ) ) * L ( N , I ) * * . S * ( Y N E W ( I ) - 1 . ) * * 2 S U M 3 = S U M 3 + ( Y N E w ( I ) - 1 . ) * * 2 S U M 4 = S U M 4 + W L ( N , I ) * E X P ( - . 5 * L ( N , I ) ) * L ( N , I ) * * 1 . 5 * Y N E w ( I ) + / ( 2 . * 3 . 1 4 1 5 9 2 6 5 ) * * . 5 S U M 5 = S U M 5 + W L ( N , I ) * E x P ( - . 5 * L ( N , I ) ) * L ( N , I ) * * . 5 * Y N E w ( I ) + * ( - 1 . 5 * A L O G ( 2 . * 3 . 1 4 1 5 9 2 6 5 ) - . 5 * L ( N , I ) + A L O G ( Y N E w ( I ) ) ) / + ( 2 . * 3 . I 4 1 5 9 2 6 5 ) * * . 5 4 0 C O N T I N U E Y N O R M = S U M 2 V N O R H = S U M 3 E N E R G Y = S U M 4 H F U N C T = S U M 5 4 3 4 1 4 6 3 5 4 5 5 0 3 0 5 5 0 5 6 0 1 1 0 1 0 0 9 0 4 0 1 W R I T E ( 6 0 , 4 1 ) Y N O R M W R I T E ( 6 0 , 4 3 ) V N O R M W R I T E ( 6 0 , 4 6 ) E N E R G Y , H F U N C T F O R M A T ( 1 0 x , ' V E C T O R N O R M O F D E V I A T I O N = ' , E 1 5 . 8 ) F O R M A T ( 1 0 x , ' S Q U A R E N O R M O F F ( x , T ) - 1 = ' , E 1 5 . 8 ) F O R M A T ( 1 0 x , ' E N E R G Y = ' , E 2 0 . 1 4 , 5 x , ' H F U N C T = ' , E 2 0 . I 4 ) W R I T E ( 6 0 , 3 5 ) X , H F O R M A T ( 5 x , ' x = ' , E 1 5 . 8 , 5 x , ' H = ' , E 1 5 . 8 ) D O 4 5 I = I , N W R I T E ( 6 0 , 5 0 ) I , Y K ( I ) , Y ( I ) , Y N E W ( I ) Y ( I ) = Y N E w ( I ) C O N T I N U E F O R M A T ( 3 x , 1 5 , 5 x , E 1 5 . 8 , 5 x , E 1 5 . 8 , 5 x , E 1 5 . 8 ) C O N T I N U E S T O P P R I N T * , ' T Y P E 1 T O C O N T I N U E , 0 T O S T O P ' R E A D * , M 1 I F ( M 1 . E Q . I ) T H E N P R I N T * , X D O 5 6 0 I = I , N P R I N T * , I , Y N E w ( I ) C O N T I N U E G O T O 1 5 E L S E S T O P E N D I F E N D S U B R O U T I N E F C N ( N , x , Y , Y P R I M E ) I N T E G E R N R E A L Y ( N ) , Y P R I M E ( N ) , x C O M M O N A ( 8 : 1 1 , 1 1 , 1 1 , 1 1 ) D O 9 0 I = I , N S U M = 0 . 0 D O 1 0 0 J = 1 , N D O 1 1 0 K = 1 , N S U M = S U M + Y ( J ) * Y ( K ) * A ( N , I , J , K ) C O N T I N U E C O N T I N U E Y P R I M E ( I ) = - Y ( I ) + . 5 * S U M C O N T I N U E R E T U R N E N D S U B R O U T I N E F C N J ( N , x , Y , P D ) I N T E G E R N R E A L Y ( N ) , P D ( N , N ) , x C O M M O N A ( 8 : 1 1 , 1 1 , 1 1 , 1 1 ) D O 1 3 0 I = I , N D O 1 3 5 K = 1 , N S U M = 0 . 0 D O 1 4 0 J = 1 , N 4 0 2 S U M = S U M + . S * Y ( J ) * ( A ( N , I , K , J ) + A ( N , I , J , K ) ) 1 4 0 C O N T I N U E I F ( I . E Q . K ) T H B N P D ( I , K ) = - l . + S U M E L S E P D ( I , K ) = S U M E N D I F 1 3 5 C O N T I N U E 1 3 0 C O N T I N U E R E T U R N E N D A P P E N D I X G N o t e s o n t h e L i o u v i l l e e q u a t i o n C o n s i d e r a s e t o f p a r t i c l e s { a i l i ‘ I ’ l r u fl n z N e w t o n ' s l a w s o f m o t i o n f o r t h e a s s e m b l y o f p a r t i c l e s m a y b e w r i t t e n a s t h e f o l l o w i n g . f ‘ 4 ' = f ‘ c ’ ; T V : ( 1 “ ) ' . . F . . Z “ . " fi f ‘ I f q i é l o ) T h e f u l l N - b o d y d i s t r i b u t i o n m a y t h e n b e w r i t t e n i n t e r m s o f t h e s e t r a j e c t o r i e s . C ” ( 5 , “ : 5 “ . , t / 5 w » , $ . 1 5 b e = 7 7 " 7 7 ‘ 5 Q . “ - g i m m e . » 4 3 ' ( : 4 ; g u m = i n ) + g u m ) ~ 3 x 5 “ = 3 , 1 . ) + k g . ) 4 0 3 9 5 j £ ‘ { ” : “ . ) . : . - C N O ) 9 5 % » ) T I " 7 7 " 4 5 “ “ ¢ £ ( ? ) < J S E z ; _ 4 . " . : 3 . Y ' Q ) 5 q o ; u n 4 5 5 ( 4 ) a t i , 2 o n h g s a e h e t 7 . 1 p a L a t J e i n I T h i t s e r m s r e s u o l f t e t i h s c h t o e o r d i n a t e s , / y F / e s t a r t i n g p t o h i i n s t b o a f l a n c e e q u 4 0 4 C n ( * ) d e s c r i b e s a s i n g l e t r a j e c t o r y i n a m a n y d i m e n s i o n a l p h a s e s p a c e . I f ¢ ~ ( x . ‘ . ( £ . 3 , fi t fi , » i s a d i s t r i b u t i o n o f p h a s e p o i n t s a t t O t h e n t h e p r o p a g a t e d p h a s e d i s t r i b u t i o n a t t i s g i v e n b y t h e f o l l o w i n g . ‘ 3 ’ * 6 ” : C o n s i d e r a f i x e d v o l u m e i n p h a s e s p a c e . T h e c o n s e r v a t i o n o f p h a s e p o i n t s m a y b e e x p r e s s e d i n t h e f o l l o w i n g w a y . ) 6 2 ) 3 v s v e l o c i t y i n p h a s e s p a c e T h i s i n t e g r a l b a l a n c e i s t r a n s f o r m e d t o a d i f f e r e n t i a l e q u i V a l e n t . é j é ’ + ‘ 7 ' E f fi L = = C > 3 1 ! - ‘ f o l l o w i n g f o r m . A . . . " 3 : : X } : ( . g ' k ‘ “ i A ' i n g ; ' * i n J . m - ‘ & % _ . 5 ‘ 7 5 ” = 0 ‘ k L I S T O F R E F E R E N C E S L I S T O F R E F E R E N C E S A b r a m o w i t z , M . a n d I . A . S t e g u n , " H a n d b o o k o f M a t h e m a t i c F u n c t i o n s " , D o v e r P u b l i c a t i o n s , N e w Y o r k , 1 9 7 2 , p . 2 6 0 . A j e l l o , J . M . , S . K . S r i v a s t a v a a n d Y . L . Y u n g , P h y s . R e v . A , 3 5 ( 1 9 8 2 ) . P P . 2 4 8 5 - 2 4 9 8 . A l l i s , W . P . , a n d S . C . B r o w n , P h y s . R e v . , § 1 _ ( 1 9 5 2 ) , p p . 4 1 9 - 4 2 4 . 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