2?t bt?vD ? 1c ? ?? ê T? ?| @msE ? 4.1 ¨??? , ??  TV U¥? ?f ? ? 4.2 í÷? ? ? E F¥? ê T ? 4.3 í÷? ?Mf ?¥? ê T ? 4.4 Y? ?¥? ê T ? 4.5 ¨? ?E FV U¥? ê T ? 4.6 ??? , ?¥? ?μ_m ? 4.7 μ÷? ?¥? ê T ? 4.8 ?| @m# MD?5 ? 4.9 Mason T ? 4.10 L?? ?¥ SFGs# ?Mm ? 4.1 ¨??? , ??  TV U¥? ?f ? ? 4.2 í÷? ? ? E F¥? ê T ? 4.3 í÷? ?Mf ?¥? ê T ??? , ?¥? ?μ_m ? 4.7 μ÷? ?¥? ê T ? 4.8 ?| @m# MD?5 ? 4.9 Mason T 2?t bt?vD 2?t bt?vD ?4-1 ¨ Y n ¥?  TV U¥? ?f ? Ba  g¥|??f ? Y n U n = J n 1 1' k k' j j' m m' I k U k N J n =[0, …, I k , - I k , 0, …, 0] T kkkkkkkkk n kkkkkkkkkkkk n nknkk I IIII UUU )( 1 )]()[( 1 '''' '''' ' ?????+? ? = ??????? ? = ?= 2?t bt?vD n kkkkkkkk k k kk I U Z ? ?????+? == '''' '''' kkkkkkkk n k k kk U I Y ?????+? ? == | k ' 1? I?? kk n k k kk n kk k k kk U I Y I U Z ? ? == ? ? == Y n ¥?  T Y n ¥í í y kk ¥ } ??0 T 2?t bt?vD =a  gW¥ME FDMèa1 n jkjkjkjk k j jk I U Z ? ?????+? == '' '' U j 1 1' k k' j j' m m' I k U k N | k ' 1? I?? n jkjk k j jk I U Z ? ??? == ' ' ' ' ' '' '' kkkkkkkk jkjkjkjk k j jk U U ?????+? ?????+? ==μ | k ' 1? I?? kk jkjk k j jk U U ? ??? == ' μ ?a= g? ? Z? ?D Y? ? 1 1' 2 2' I 1 I 2 U 1 U 2 N ? ? ? ? ? ? ?????+???? ???? ? = ? ? ? ? ? ? = 2'2'22'2'222'1212 1'22111 2221 1211 1 n zz zz Z 2?t bt?vD 2?t bt?vD ? go^? ? ? ? ? ? ? ? ? ? ? ? ? ? ???+? ? ???+? ??? ???+? ??? ???+? ???+? = ? ? ? ? ? ? = '1122'2'1121122 11 '1122'2'1121122 12'12 '1122'2'1121122 12'12 '1122'2'1211122 '22'2'222 2221 1211 22 22 2 yy yy Y ? kjpq 1? n ?? ?? k?a? p?[#? j a? q ¥= ¨} ??0 T 2?t bt?vD + è? 2'  D 1'  1]B O¤1 H5?? ? ? ???¥ ? g¥ Z? Y? ?¥} ? T1 ? ? ? ? ? ? ??? ??? ? = ? ? ? ? ? ? ?? ?? ? = 1121 1222 1122 2212 2111 1 ; 1 YZ n ? ?¥|??E F?Mf ??  ?? ?f ?¥} ? Vr T? ?¨??? , ?¥} ??0 TD?  T -1V Ub ?? ? ?f ?¥} ? Ta? ?f ?¥? ê Tù 5üM1 Y n ¥?  T# } ??0 T¥? ê Tù5  ?42 í÷? ? ? E F¥? ê T Ba? n ¥? ê T Topological formulas Binet-Cauchy? ? ! PaQsY1 n?m? m?n¨ ? O m?n 5 det(P·Q )= P¥v0 Te[?¥ Q¥v0 T ? ? 5 ?Ym G¥ A¥ n?n0?d s N0?¥  ??¥| ^?? G¥B? ? O?0? ¥?  T-′1 1 b w ? det(AA T )= (1) (1)= ? ? " 2?t bt?vD 2?t bt?vD ?? Y b = diag(y 1 , y 2 , …, y b ) A# A T ¥d ,v0 T (major)D ?? O1 +1 -1   1 ?AY b ¥d ,v0 TgD ?? O ′1 (1) y j1 y j2 … y jn ,? ú j 1 , j 2 , … j n V UB? ?¥ ?| ?AY b # A T ¥?d ,v0 T¥e?? (1) 2 y j1 y j2 … y jn = y j1 y j2 … y jn ?T ( j) ( y) ? n = det Y n = det AY b A T )()( ) ()()()( ) ( 21 YW yTyyy t j j j jnjj j j T j b ≡= == ∑ ∑∑∑ ?? ? ?|? , LAAY íBL P1 ? ? ?? ? ? X ?3 TV U? ?¥B? ?¥ ? |? ,¥e?1 “ ?? , ” (tree admittance product) ,e? “ ? ” (tree product) 2?t bt?vD 2?t bt?vD =a? kk ¥? ê T ? kk ' det AY b A T ? ?? k?ak a-′'? ? ? (AY b )¥? k?(9ü ^? ? A¥? k?:1 A – k )a? ? ? (A T )¥? k  ( V:1 A – k T )a  ?-¥?  T  7? ?? ? A¥? k?M??| ?? kD? I? ? ¤ (| ¤a¥? ?:1 N – k )b? ^ )() ( )( ) ()()( 0 , ) ( , ) ( 0 YWyT yT rk j j rk k j j k N j j T -k j b-kkk N ≡= = ==? ∑ ∑ ∑∑ ? ? ¥ ?? ? ?|? , AYA ?l12- ? ' ?Ym G¥ ? ? T ??  ? ??B ?|¥0mb 2- ??é  c G¥ ????  ?cí ^  s ?1 ? ?Y ? ?B?sg V1B? ??? ·N – k ¥ ?'1e? ? k?? I?? r 0 ?]B ?Y ? ¥ ? :T T k  ro b ?N – k ¥ ?? V ?cem?] H ?Y?? k? r 0 ¥| ^ (?t| ^ N – k ?XM?1ì ) O N – k 1e N¥? ??? ? B?' N – k e N¥ ?| ? B?b 2?t bt?vD 2?t bt?vD )() ( ) ()()( 0 , ) ( , ) ( 0 YWyT yT rk j j rk j j k N j j T -k j b-kkk ≡= ==? ∑ ∑∑ ? AYA ? ? k?M??|?? kD? I??M¤b 8 p¥ H ?o1|? k??D? I?? r 0  ¤  ?ü?? N – k b ?¥? ? N – k ?s ?? ?i p ?? ?¥ ? |? ,e-?b )( ∑ ? =? ¥ ?? ? ?|? , k kk N 2?t bt?vD è1 C 1 =1F R 2 R 1 1 1' 1$ 2$ C 2 2F 1H L m Uè ^ k p ?  ?E F Z i (s) b 4 ? ?' 2 3 1 5 4 ??' 2 3 1 5 3 2?t bt?vD 4 ? ?' 2 3 1 5 4 ??' 2 3 1 5 T N -? j ( y) s 1s 0.5 2s 2 0.5s 2 s 12s ? j 123 124 134 135 145 234 235 245 T j ( y) 2s 2 1 2 s 1/2s 2ss 2 0.5 N -? ? 12 14 15 23 25 34 35 45 2?t bt?vD T N -? j ( y) s 1s 0.5 2s 2 0.5s 2 s 12s ? j 123 124 134 135 145 234 235 245 T j ( y) 2s 2 1 2 s 1/2s 2ss 2 0.5 N -? ? 12 14 15 23 25 34 35 45 1766 3554 5.02 2 1 212 2 1 25.025.0 1 )( )( 23 23 22 2 '1 , 1 11 +++ +++ = +++++++ +++++++ == ? ? = sss sss ss s ss s sss s s YW YW Z tn i 2?t bt?vD  ? ê TEí3 Y n ? ?  ?|? ,¥ ? VE ??  TZ 7 HyC?Mo·h[7/?¥?  ?  ?1  ?? ?# 2- ?? t a?? v¥? ?b 2?t bt?vD ?43 í÷? ?Mf ?¥? ê T Ba? k j ¥? ê T ? k j = (-1) k + j det [(A -k Y b )(A -j ) T ] )() ( ) ()1()1( )()()1( 0 , ) ( , ) ( , 0 0 YWyT yT rkj l l rkj l l rkj jkjk l l T -j l b-k jk ≡= ??= ?= ∑ ∑ ∑ ++ + AYA 2?t bt?vD )() ( 0 , ) ( , 0 YWyT rkj l l rkjkj ≡=? ∑ L= p3 H¥ZE sY9 ? 2 ? T k,r0 ? 2 ? T j,r0  p ? F 2 ??" ?¤? T kj,r0 ? ? ? ? ? ? ? ? ? ? ? ? = ∑∑∑ q q rj p p rk l l rkj yTyTyT ) () () ( ) ( , ) ( , ) ( , 000 I 000 , , , rjrkrkjkj WWW I==? 2?t bt?vD è2 1 1' 2 3 4 2' 1 y 2 y 3 y 4 y 5 y 6 y L y p? ? N¥? ?? , ??  T¥B¨ } ??0 T  12 b? I? ? 1’ 3 n5 ¤?? 1D? I?? 1’ ¤? G 11’ ? pW 1,1’ 11' 2 3 4 2' 1 y 2 y 3 y 4 y 5 y 6 y L y 2?t bt?vD 11' 2 3 4 2' 1 y 2 y 3 y 4 y 5 y 6 y L y y 1 y 3 y 4 y L y 1 y 3 y 4 y 6 y 1 y 3 y 5 y 6 y 1 y 3 y 5 y L y 1 y 3 y 6 y L y 1 y 4 y 5 y 6 y 1 y 4 y 5 y L y 1 y 4 y 6 y L y 2 y 3 y 4 y 6 y 2 y 3 y 4 y L y 2 y 3 y 5 y 6 y 2 y 3 y 5 y L y 2 y 3 y 6 y L y 2 y 4 y 5 y 6 y 2 y 4 y 5 y L y 2 y 4 y 6 y L y 3 y 4 y 5 y 6 y 3 y 4 y 5 y 6 y 3 y 4 y 5 y L  ? p W 2,1’  ¤ G? 2? 1’ ???¤?m G 21’ 2?t bt?vD 1 1’,2 3 4 2' 1 y 2 y 3 y 4 y 5 y 6 y L y 1 1' 2 3 4 2' 1 y 2 y 3 y 4 y 5 y 6 y L y y 1 y 2 y 3 y 4 y 1 y 2 y 3 y 5 y 1 y 2 y 4 y 5 y 1 y 2 y 3 y L y 1 y 2 y 4 y 6 y 1 y 2 y 5 y 6 y 1 y 2 y 5 y L y 1 y 2 y 6 y L y 1 y 3 y 4 y 5 y 1 y 3 y 4 y 6 y 1 y 3 y 5 y 6 y 1 y 3 y 5 y L y 1 y 3 y 6 y L LL yyyyyyyyyyyyyyyy WW 63153165316431 '1 ,2'1 ,112 +++= =? I 2?t bt?vD =aMf ?¥? ê T [/) ? | k ’1? I??b ME F )( )()( )( )()( )( )()( ' ,' '' , ' ,' ' , ''' , ' , ' ' ,' ' , ' YW YWYW YW WWWW YW YWYW I U Z t jkjkjkjk t jkjkkjjkjkjkkjjk t kjkkjk n jkjk k j jk ? = +?+ = ? = ? ??? == 2.o^ ? g? ? Z? ? )( )()( )( )( , , )( )( 2'1 , '12'2'1 , 12 '1212 2112 '2 , 2 22 '1 , 1 11 11 YW YWYW ZZ YW YW Z YW YW Z tn ttn ? = ? ??? == == ? ? = ] ? Mèa1 )( )()( ' , ' ,' ' ' , ' YW YWYW kk jkjkjkjk kk jkjk jk ? = ? ??? =μ 2?t bt?vD 2?t bt?vD è3 C 1 =1F R 2 R 1 1 1' 1$ 2$ C 2 2F 1H L 2' 2 k p 1) Z? ? ? 2) Mèa1b 4 ? ?' 2 3 1 5 ? 3 2?t bt?vD T 12 ', 1' 2 í ? j 123 124 134 135 145 234 235 245 T 2, 2 ' 12 13 15 23 25 T 12, 1 '2 ' 12 15 23 25 T 12, 1 '2 ' j ( y) s 0.5 2s 2 0.5s T 12 ', 1' 2 j ( y)0 T j ( y) 2s 2 1 2 s 1/2s 2ss 2 0.5 T 1, 1 ' j ( y) s 1/s 0.5 2s 2 0.5s 2 s 1/2s T 1, 1 ' 12 14 15 23 25 34 35 45 T 2, 2 ' j ( y) s 2s 0.5 2s 2 0.5s 2?t bt?vD 1766 34 1766 74 1766 3554 23 23 21 1221 12 2112 23 23 2 2 22 23 23 1 1 11 +++ ++ = ? == +++ ++ == +++ +++ == sss sss YW YWYW ZZ sss sss YW YW Z sss sss YW YW Z t t t )( )()( )( )( )( )( ',''', ', ', 3554 34 )( )()( 23 23 '1 , 1 2'1 ,' 21' 2'1 , 21 21 +++ ++ = ? = sss sss YW YWYW μ 2) 2?t bt?vD  ?|? ,? T¥? ê Tg?1 ? X ?3 T  ? 4-5?|e?o  ?|E F? T¥? ê T ( : ? T )  ? ??cμo? s e÷ H Y b ? ^?? μ1¥? ê Tü?ˉb - ?) ?¥? ê T #  ?? 2- ?¥ ?|? , 7 Y? ?¥? ê T5 # 3- ?¥à Qb 2?t bt?vD ?44 Y? ?¥? ê T Ba Y? ?¥} ? T ? ? ? ? ? ? ? ? ? ? ? ? ???+? ? ???+? ??? ???+? ??? ???+? ???+? = ? ? ? ? ? ? = '1122'2'1121122 11 '1122'2'1121122 12'12 '1122'2'1121122 12'12 '1122'2'1211122 '22'2'222 2221 1211 22 22 2 yy yy Y 2?t bt?vD =a 3- ? T k, j, ro ?l23- ? ' ?Ym G¥ ? 2- ? ??  ? ??B ?|¥0mb 3- ??é (1)c G¥ ???? (2)?cí ^ (3)s ?1 ?? ?Y ? ?B?sg V1B? ???b T k, j, ro 'V U?? kaj?? I?? r o sY)?  ? ? ? ?Y ??¥ 3- ?b ?a Y? ?¥? ê T ZE 1 ?¨ g 7 ^¥ ? gYV 3- ? ?9 ? )()( )()()( : )( )()( )( )( , )( )( 2'1 , '2 , 1'1 , '2 , 12 '2'1 , 2 , 1'1 , 2 , '12 '2'1 , 122'1 , '12 2112 '1 , 1 22 '2 , 2 11 YWYW YWYWYW YW YWYW yy YW YW y YW YW y ++ += ? == == ∑ ∑ ∑∑ T? 2?t bt?vD 2?t bt?vD ZE 2 ?¨ g ^ ? g¥ ?|? , ?9 ? W  (Y) ¥ ?|? ,-? g ( ^¥ ? g? ?= = ∑ )()( " YWYW t ¨?? 3- ?¥à Q  2?t bt?vD ?4-5 ¨? ?E FV U¥? ê T ? l = det Z f l = det B f Z e B f T ∑ ∑ ? ? ≡ ¥ ??? ? ?? ?¥? ? ?|E F ? ? ?|E F  }1  }1 )( )()( j jj l N ZW T? N -j }VM<? jH ?|¥? ?b ) ? ∑∑ ==? ?? ? ?? ? ?|E F ?|? , )( )()()(det 21 bne ZZZ LQ Z ?? l = (det Z e )? n (í ^E F ?D??? , ??  T¥1" T ) 7L?? ?¥ det Z e "? RasLa1sC?Me?A?? ks p  2?t bt?vD 46 ??? , ?¥? ?μ_m Associated Directed Graph ? Ba??? , ?¥? ?μ_m 21 22221 11211 ? ? ? ? ? ? ? ? ? ? ? ? ? ? == t n t n t n t n t n t n T abai yyy yyy yyy L MMMM L L AYAY 2?t bt?vD ?l3F ?? ?μ_m G d ?? ?¥?? H ? ? kaj-W¥μ ?μ_H ?sY1 - y kj ? -y jk b D Y i ¥?1" - y kj k j - y jk ?μ_HXsY?? Y i ¥d?í7 Y i ¥ ?í??]? (  )d?í-?¥μ′' G d ?Xc??y7 G d D Y i BB?b ?i? Y i ¥d?íYè? 0V7 G d μ_H¥ ?Yè ?0N? Z_? ^àZ_b 2?t bt?vD k?m Uè ^¥F ?? ?μ_mb C 2 ? G 1 è % I 2 ? G 2 C 1 I 2 L é è 1 122 1 1 2 )1( 2 )1( 1 0 1 2 1 2 1 22 112211 ? ? ? ? ? ? ? ? ? ? = ++??? +?++? +??+? ???++ sLsCGGsLsC GGGG GsLGsLsCsC sCGsCsCsCG i   αα αα Y C 2 ? G 1 è % I 2 ? G 2 C 1 I 2 L é 3 2?t bt?vD ?N V¤ F ?? ?μ_m1 é è ? G 1 G 1 % G 2 sC 2 ? (1+% )G 2 sC 2 G 2 1sL % G 2 1sL sC 1 sC 1 m? 1??¥ (  ) d out GQ1 3, 3, 2, 3 b 2?t bt?vD 2?t bt?vD =aμ÷? ?? n ¥? ê T ?l4 μ_ ? T ro μ_m G d ?@/ Hq¥0m?1μ_ ?  ??Z_a ˉ? ^B? ? 2)r 0 1 d out ro = 0¥? I? (?1? )  ??¥   d out = 1 b é (a) è ? G 1 sC 2 ? 1sL -% G 2 é (b) è % G 2 ? sC 2 ? (1+% )G 2 [/òm (1  èμ_m[é1? I?¥μ_ ? è é (c) è ? ? sC 1 1sL -% G 2 2 )1( Gα+ 2?t bt?vD 2?t bt?vD ?l5 μ_ 2- ? T k , ro  μ_ ? 7B ?|¥0m?1μ_ ? ?@  ??Z_a ˉ? ^B? 2- ?  ?B? ??sμ?? I? (k r o ) ? ì¥ d out ro = 0  ??¥ d out =1 μ÷? ???? , ?¥?  T?? G d ¥μ_ ? ?-?b ?l5 μ_m 2- ? T k , ro  "μ_ ? 7B ?|¥0m ?@  ??Z_a ˉ? ^B? 2- ?  ?B? ??sμ?? I? (k r o ) ? ì¥  d out ro = 0  ??¥ d out =1 . ( V¨  è¥μ_ ? 7  ?|F[ a ü ) μ÷? ???? , ?¥?  T?? G d ¥μ_ ? ? -?b · ? P.65-P.67£ ü  /SEV Uμ_ ?  2?t bt?vD 2?t bt?vD ? ? Y i ¥? n t ?? n t M1?? , ? Y d  Y d ü ^[ n t ?1? I¥??? , ?b ! A d + ^μ_m G d ¥?¨1 ó ? A d ? (-1) ??? , a¥ ? b d ^ G d ¥9H ? A d ¥¨1 n t  ?b d  ' ^?¥ G d H ??¥?? 7 T dd D AA γ + = ? ?eE?5?? D¥í d ij ' A d + ' ¥? i?? A d + ¥? j ?íe-?b? i?j Ho1 I n A d + ¥ ? i? A d ¥? j?] H1d ,¥í9'o31 I n ?? i·_? j¥HbN H A d + ? i?í1(+1) A d ¥? j ?1(-1) A d + ' ¥M?í' i·_? j¥H ? (-y ij ) # ijij yd = 2?t bt?vD  T a ü D¥d?í' Y d ¥d?íb? i" j H5 () ∑∑ ≠ = ?= t n ik k ik i dij yGd 1 )( "¥H ? ?  H  ?? Vn D¥?í9' Y d ¥?íb#μ T dddn YY AA γ + == ( ) T ddnn Y AA detdet γ + ==? ¨1 , O? ?9 ? d H 2?t bt?vD (1)V A d ? n(=n t -1) ?v0 T ????B ? ?A1 s ??v0 T1 ,?A I n9?A  ?)?¥ A d + ^? sb (2) ? n ??B? ?5μ V ? ^μ_ ?d μ_ ?b ?| ?1 n? ? n t = n+ 1ò? d out 9 ?9 ^ n ?μB??V 15Aμ ?1 ,yNdμ_ ?"? I?-?à ?μB?1 ,? f ?/ A d + ?D???¥?1 ? ,yNd μ_ ??¥v0?9 ^ s¥ v0 T1 ,? A I ndμ_ ?b (3)?μ_ ? ??[Xê¥? I? n t 1?5 A d + 1 ,¥??¥?1 ? ,v0 T1 ,9?A I nb 2?t bt?vD (4)Ka I n[ n t 1?¥μ_ ?b??[ n t 1?¥μ _m?¥v0 T A t + ?? ? ?μB?d ,í (+1) ?[ detA t + " 1 v0 T A t d ,í (+1) C¥ê? ? A t + ? ?B"? ? ? V ?CB?d ,í (-1) ??d ,í (-1)? V[YV?MF¥? ? (′?? |?M )7 ?? Vn A t + ? A t o ?] H1 (+1) (-1) V7£¤ ∑ =? 1?¤μ_ ? ??[ μ_ ? ?- t n n )(   T·He1 dtn W=? 2?t bt?vD ?/S d}Vμ_ ? W dt ' ??[ n t 1?¥μ_ ? ?e-9?by? I??]??Y n ′#?A·  n t b?o^? ???? , ?yNμ_m G d ¥μ_HA?7 O ?μ_H ?M]?" V [ ??s Oo?BHH?1í_m G u i G u ? ^ G d ¥? ?í_mb ? ? è é ? ? è é 2?t bt?vD ?do^? ??i? ?í_m ?μ_ ?¥?l? G d ¥μ_ ? ?Z_a'1 G u ¥ ? 7 G u ¥ ?S Z_a9 V[M1·?? I?¥ μ_ ?byN?o^? ? V¤ ∑ =? ?μ ? ? ?- u G un G )( L= ?í s e÷?o?¥ RLC? ? G u D ?Y LmBá G u ü ^e ?¥? ? ??¥Lm G u ¥ ?ü ^| ^? ,V7  TD? 4-2?¥? ê TB á 7 O  T? a??co?¥o^? ?b7? 4-2 ?¥? ê T5? ? a¨?co?? ?b ?¨μ÷? ?¥? ?μ_maμ_ ?#μ_ 2- ?? à QCá ì V[) ? 2?t bt?vD ?4-7 μ÷? ?¥? ê T Ba? k k # z?f ?¥? ê T ? T dddn AAY detdet γ + ==? ? T kdkdkk )()( det ? + ? =? AA γ ? sY ^? ? ¥? k?a ??¥9ü ^| k??? I? r 0  ¤aμ_m¥ 1 ó ?? ^ ? ?1? 2 ?¥ ? ? V? )()( kdkd ? + ? AA ? dd AA ? + 2?t bt?vD )( ) , ( 0 0 0 )2( , , )2( YW krd kk kr kr T T ≡ =? ∑ ? ? ? ??μ_ ¥ ? ?μ_ )()( kdkd ? + ? AA ?  T·H Ve1  ? d}Vμ_ ? r 0 ? ksY}V ?s¥?b W d(ab,cd) }Vμ_ ? T ab,cd ¥ ?-9?b ),( 0 krd W μ÷B g? ? ? E F? ? ? ,? ê T )( )( ) '1 , 1( 1 ) '1 , 1( 1 YW W Y W YW Z d td i td d i == 2?t bt?vD è k pm U ? g¥ z 11 (s)az 22 (s) b i L 1H 4i L 1 2 2 2' 1$ 1F 3 | CCCS 1VCCSa?°4E V¤  ??? , ?1 2?t bt?vD ? ? ? ? ? ? ? ? = +? +?+?? ??+ ? s ss s s ss s ss i 11 4 1 4 1 5 1 5 1 Y M?¥? ?μ_m1 [? ' 1? I?¥μ_ ?μ 5 s 1+4s ? 1 ? s4s 1 s s ?' # s ss s s ssss s dt W 15 ) 4 ( 55 ) 4 1() 4 (1 2 ++ =?+++?= 2?t bt?vD 5 s 1+4s ? ? ?' ?' ? 1 ? s4s ?' ? ? 5 s4s s 2- ? T 1, 1' μ 1+4s ? ? ?' ?' ?? s4s # W d(1, 1') =1+1+4s+ s –4s =s+2 ] ? W d(2, 1') =1 + 5s =(s+5)s 2?t bt?vD 2?t bt?vD 15 5 15 2 )'1,2( 22 2 2 )'1,1( 11 ++ + == ++ + == ss s W W Z ss ss W W Z dt d dt d ? ^ =a? k j #Mf ?¥? ê T )( det)1( ) , ( 0 0 )()( 0 )2( , , )( YW jkrd T jdkd jk jk jkr jkr T T ≡ = ?=? ∑ ? ? + ? + ? ??μ_ ¥ ? AA γ 2?t bt?vD  g ? | k ' 1? I??5?} ? T dt jkjkdjkjkd dt jjkkdjkjkdjjkkdjkjkd dt jkkdjkkd n kjjk jk W WW W WWWW W WW Z ) ' ,' () '' , ( ) ' ,'() ' ,'() ' ,'() ,''( ) ' ,'() ,'(' ? = +?? = ? = ? ??? = ] ?¤ dt j'kjkdj'kjkd jk W WW Z ) ,'() ' ,( ? = 2?t bt?vD ?4-8 ?| @m# MD?5 (signal-flow graph) SFG Ba?| @m ?| @m ^B?V UL?} ?Z?FM 1"¥F ?μ _m ????? ?¤??-W¥μ_| ^?b x a y B??| @m??B?yT? T¥L?} ?Z?Fb y=ax  1 ??¥ ?′}V ? í ?"d¥M 9? ??M  b ? ′ x¥?? V?1?? xb 2?t bt?vD x a y | ^ ?¤?iyT1"¥M  ??¥??-W¨ μ_L V U Z_ ? 7T1y¥M ??·_T 1T¥M ??V U?|o ?| ^Z_. {b | ^¥ ?′ü ^Z?F?T1y¥M  ?e¥" ?9 ?| ^. {′?|| ^. { He[?| ^¥. {′ y=ax  1 ?T x i μ H H[ ¥ ?| ^ ?Z?1 x i =?( ?| ^. {′?? ?| ^  S)¥??M  )  ? p? ^?? x i ¥ ?μ ?| ^é?¥b ??? x i μ  H H[ ¥| ^5?| (x i )1?? x i ¥ ?BH | ^. {b 2?t bt?vD B?cμ n?M ¥L?} ?Z? (2) 0 1 ∑ = = n i ii xa V¨[/ZE?[ x j 1 { ¥yT? TZ? (3) )1( 1 ∑ ≠ = ×++= n ji i jjiij xaxax YVM[9 ?¤?yT? T¥Z?' (4) 1 1 ∑ ≠ = ?= n ji i ii j j xa a x 2?t bt?vD (5) 4422113 xaxaxax ++= x 2 a 2 x 1 x 4 x 3 a 1 a 4 x 2 a 2 x 1 x 4 x 3 a 1 a 4 344 322 311 (6) xax xax xax = = = 2?t bt?vD x 2 a 2 x 1 x 4 x 3 a 1 a 4 a 5 a 6 x 5 x 6 366 355 4422113 (7) xax xax xaxaxax = = ++= ?N Vn[ M T1T¥M ¥Z? H o3 I n???¥ ?| ^¥?Y7D | ^í1 2?t bt?vD ¨ SFG p3L?Z?F HA? n5| ??Z?1 yT? T¥Z?b31?i¥ ^Z?F¥ ??M  A?μ O?μBQT1TCB?yT? T¥Z? ?  ?Z??5o ?T1yCb?"??¥ SFG? ^? ?¥?5|?áp¥2Tb è / Z?F¥yT? Ti?M?¥ SFG s s s fxxx f xxx fxxx 79104 10424 310172 321 321 321 ?=++? =?? =++? 2?t bt?vD s s s fxxx f xxx fxxx 9 7 9 10 9 4 522 5.155.8 213 312 321 ??= ??= ?+= 3 ?B?? T s f 1 x 2 x 3 x 5.1 9 7 ? 9 10 ? 2? 9 4 5? 5.8 2 5 2?t bt?vD ?=?? T s s s fxxxx f xxxx fxxxx 710104 1044 31017 3213 3212 3211 +++?= ????= ?++?= B?L?Z?F ??¥ SFG? ^?B¥? ? ì ^ Mo?r¥b s f 1 x 2 x 3 x 3? 7 10 4? 4? 10? 17 2 10 1? 1? 10 2?t bt?vD ?}VL?} ?Z?F¥_ Z? (8) BFAX = nn× pn× n?M _  p? { ?_  [] (9) F X BA1BFA)X(1X ? ? ? ? ? ? ?+=?+= [ ] (10) B-A1C += (11) F X CX ? ? ? ? ? ? = ó¤ ? n?(n+p)9< ? í ? m¥1 ó?é?| ^¥ ?′ 2?t bt?vD C ?¥ ?B???B?T1yT¥M  ?B  ??yTT1y¥M b ?¥í í C ij 1 , HV U ?? jD?? iW àμ| ^ í í C ij d , HV U?? j à?? iWμBH ?′1 C ij ¥μ_| ^b è X? è ^??èaZ?1 UU iUU s 092 1628 21 21 =+? =? ??Z?F?¥ SFGb 2?t bt?vD 3 UU iUU s 092 1628 21 21 =+? =? s i U U × ? ? ? ? ? ? = ? ? ? ? ? ? ? ? ? ? ? ? 0 16 9 2- 2- 8 2 1 0 10 2- 16- 2- 9 C ? ? ? ? ? ? = i s U 1 U 2 -16 9 -2 -2 10 2?t bt?vD SFGs?¥Btè¨ ?? ÷?? oμ| ^¥?? i s U 1 U 2 -16 9 -2 -2 10 ??? oμ ?| ^¥?? i s U 1 U 2 -16 9 -2 -2 10 U 2 * 1 V B???| ^Z_ ??üVBt?]¥| ^???7?? 6B???"B?? ê2?1 7 ^? b 2?t bt?vD -_ ^? V÷??????¥ 7 ^? . {′ ü ^ ^?  ?μ| ^. {′-b i s U 1 U 2 -16 9 -2 -2 10 í ^ì V B???| ^Z_ ??üV ?]¥| ^????í????¥> ^?b í ^?M¤( V B???oüBH| ^?? ?]B?? ¥ì?11ìbí ^Dí ^-Wí  ??b 2?t bt?vD =a?| @m¥MD?5 1a]Z_i ó| ^e??5 x i t 2 x j t 1 t n M (a) x i x j (b) ∑ = n k k t 1 i n k kj xtx ? ? ? ? ? ? ? ? = ∑ iniij xtxtxtx +++= L 21 nH]Z_i ó| ^ V¨BH| ^}9?| ^¥. { ′?? nHi ó| ^¥| ^. {′-?b 2?t bt?vD 2a]Z_) ó| ^e??5 x 0 x n (b) ∏ = n k k t 1 x 0 x n (a) t 1 t 2 t n ll x 1 x 2 x n-1 1 122 011 ? = = = nnn xtx xtx xtx M 0 1 0321 xtxttttx n k knj ? ? ? ? ? ? ? ? == ∏ = L nH]Z_) ó| ^ V¨BH| ^}9?| ^¥. { ′?? nH) ó| ^¥| ^. {′-b 2?t bt?vD è X?L?Z?F1 09 38 11 21 11 1 =? =? = UI UIU UU s s ? U s " 1V¨ SFGsE pèa U 2 -′b 3 (1)|L?Z?F?1_ Z?1 P SFG? ?? U 1 í1ì T?X|eZ?F¥?BZ?  ] HQ|b s U U I U × ? ? ? ? ? ? ? ? ? ? ? = ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 0 3 11 1- 9 0 0 1- 8 0 0 1- 2 1 1 2?t bt?vD (2) ó¤ ? ? ? ? ? ? ? ? ? ? ? = ? ? ? ? ? ? ? ? ? ? + + + = 0 0 9 0 3- 0 0 8 11 0 0 0 0 11- 9 0 3- 0 11- 8 11 0 0 11- C (3)? ó¤ ? C? ?¥ SFG U s U 2 -3 I 1 9 11 8U 1 (4)| U s aI 1 W)| ^?e¤?m U SFG U s U 2 -3 I 1 9 11?8 2?t bt?vD U s U 2 I 1 9 88-3 (5)U s aI 1 W | ^1]Z_i ó| ^?ea¤?m U SFG (6)U s aI 1 W | ^1]Z_) ó| ^?ea¤?m U SFG U s U 2 85?9 (7)5èa U 2 -′1 U 2 =85?9=765V 2?t bt?vD 3a| ^M? (??h ? )?5 ?1h ?M  x 3 366 355 4422113 xax xax xaxaxax = = ++= () 44221166 44221155 xaxaxaax xaxaxaax ++= ++= x 2 x 1 x 4 x 3 a 1 a 4 a 2 a 5 a 6 x 5 x 6 x 1 x 2 x 4 x 5 x 6 a 1 a 5 a 2 a 5 a 1 a 6 a 2 a 6 a 4 a 5 a 4 a 6 2?t bt?vD M?¥?51 1 h ??? x 3  PD x 3 M ó¥ ?B H| ^¥ S ??7   5sY" ?BH| ^T?_M?Mà?| ^¥  ?? 3?2" 6 H?| ^b ?H?| ^¥. {′1$M?| ^D  M?| ^=| ^. {′-b ?T$h??μ mH ? | ^a nH| ^5| ^M?a¥?| ^ ?1 m?n è m U SFG? u1"d¥ { ? kS/ ?e (1) =?? x 1 ax 2 h ??? x 3  (2) =?? x 1 ax 3 h ??? x 2 b u x 1x 3 d x 2 a b c 2?t bt?vD 3 (1)h ??? x 3 u x 1 d x 2 ab bc u x 1 x 3 d x 2 a b c (2)h ??? x 2 u x 1 bd x 3 a bc u x 1 x 3 d x 2 a b c 2?t bt?vD 4a1ìh ??5 u x 1 d x 2 c a x 3 b 21 322 dxx cubxaxx = ++= u x 1 d x 2 x 3 a c ?1 a b ?1 21 32 11 dxx u a c x a b x = ? + ? = àh ??? x 0 . {′1 a¤1ì|?? x 0 M ó¤ ? H ?| ^. {′sY"[ (1-a)] H ??1ìbh ? 1ì?? x 0 ¥òH| ^í?Yb 2?t bt?vD 4a?_?5 4422113 xaxaxax ++= x 1 x 3 1 a x 4 2 a 4 a x 2 oDZ??M  x 3 D x 4 ¥ê? 1 3 4 2 4 2 1 4 1 4 x a x a a x a a x +? ? = x 4 4 1 a x 2 x 1 x 3 4 1 a a ? 4 2 a a? 2?t bt?vD SFG?| ^?_?5 (1)V÷???¥| ^ V[?_ ? ^÷? ??¥?| ^? ??_ (2)| ??-W¥| ^?_a| ^. {′ 1e| ^. {′¥? ? (3)|e ??2$?_| ^  ??¥  e | ^ ???1?2?_a| ^  ??   . {′1e| ^. {′e[?_| ^. {′¥μ? ?b 2?t bt?vD ?4 9 Mason T (1) ? ? == ∑ m mm j j P F X T Masonm9m T (e? Mason T ) ^ p SFGm9m ( . {′ ) ¥ Tb Mason T ???M  SFG¥m9m (. {′ ) b? SFG ?V U¥è? ? ? a SFG ¥m9mü ^ ? ?f ?b m?  T ÷??M  2?t bt?vD ( ) (2) 11 32 LL +?+?+?=? 1 ∑ k L ∑∑ ∑ i kk LL i k L L k i V U? kF i¨í ^¥. {′ p?? L k i V U ?? i¨í ^é? n?o?¤(í ^¥"?1 n¨í ^ ?¥. {′ü ^ ? n?o?¤(í ^. {′-bB?B¨í ^ü ^B ?í ^b 2?t bt?vD (1) ? ? == ∑ m mm j j P F X T ÷?????? ¥? mH -_ ^ ?¥. {′ ?? mH -_ ^ ??M¤(¥0 m¥m?  T p? ^V÷????? ?¥ ?μ -_ ^?é?¥ 2?t bt?vD Mason T V? L?Z?F¥} ?3¤?£ ü (3) BFAX = (4) det 1 F A b X n k kjk j ∑ = ? = ? { ?? ? p=1 (5) (-1)etA ?= n d (6) (-1) 1 m m m n kj n k k Pb ?=? ∑∑ = (7) det 1 ? ? = ? == ∑∑ = m mm n k kjk j j P A b F X T è ¨ Mason T p3m Uè ^¥í ^ 3¥è @b 1 2 3 1 z 2 z 3 z 4 z 5 z 6 z s U + ? 3 m Uè ^¥í ^Z? (*) 0 0 333232131 323222121 313212111 ? ? ? ? ? =++ =++ =++ IzIzIz IzIzIz UIzIzIz s 2?t bt?vD 2?t bt?vD ? 52111 zzzz ++= 43222 zzzz ++= 65433 zzzz ++= 22112 zzz ?== 43223 zzz ?== 53113 zzz ?== | T (*)1yT? T V¤ ó¤ ? 0 1 0 1 11 C 333131 232221 131211 ? ? ? ? ? ? ? ? ? ? + + ?+ = z z z zz z z zz 2?t bt?vD s U 1? 3 I 1 I 2 I 11 1 z+ 22 1 z+ 33 1 z+ 31 z 13 z 32 z 23 z 21 z 12 z 2?t bt?vD μ 8?í ^ 21 z 12 z 11 1 z+ 33 1 z+ 22 1 z+ 32 z 13 z 21 z 23 z 31 z 12 z 23 z 32 z 31 z 13 z 2?t bt?vD =¨í ^ μ 6F 11 1 z+ 22 1 z+ 22 1 z+ 33 1 z+ 31 z 13 z 22 1 z+ 11 1 z+ 33 1 z+ 11 1 z+ 23 z 32 z 21 z 12 z 33 1 z+ ?¨í ^oμBF? ??1ì? ( ) 11 321 LL +?+?+?=? ∑∑∑∑ i k i kkk LLLL 2?t bt?vD ()( ) ( ) ()()()()()() () () () ()()()[] 332211 122133133122322311 331133222211 31231221321331133223 1221332211 111 111 111111 111 1 zzz zzzzzzzzz zzzzzz zzzzzzzzzz zzzzz +++? ? ? ? ? ? ? ++++++ ++++++++ + ? ? ? ? ? ? ++++ ++++++ ?=? 2H -_ ^? s U 1? 3 I 1 I 31 z 311 zP ?= s U 1? 3 I 1 I 2 I 32 z 12 z 32212 zzP ?= 2?t bt?vD ^?y0 () 22221 11 zz =+?=? 1 2 =? ()()() ()()()()()() () () () ()()()[] 332211 122111133122322311 331133222211 31231221321332231221 332211 32212231 22113 3 111 111 111111 111 1 )( zzz zzzzzzzzz zzzzzz zzzzzzzzzz zzz zzzz PP U I T s +++? ? ? ? ? ? ? ++++++ ++++++++ + ? ? ? ? ? ? ++++ +++++ ? ??? = ? ?+? == s UTI 33 =5 2?t bt?vD ?L?? ??μ? ?] HT¨ H pjpjjj FTFTFTx +++= L 2211 ? ?¥ p? ? T ji (i=1,2,l Q)}V[ F i 1 { ?? ?a x j 1 {??¥m9mb ∑∑∑∑ ? ? == == m im m im p i iji p i ij PFTFx )()( 11 1 ?| @m¥?F? }VV { ??? F i ? {?? x j ¥? mH - _ ^?¥. {′ -_ ^?¥ ^?y0 2?t bt?vD 1  ?éB?e?sV SFG¥????÷??9 @BH ?′1 (-B)¥μ_| ^b?| ^D ?B -_ ^ ? (?B??¥í ^??a¥ SFG?1>? SFG(closed signal-flow graph)b () 11 21 LL +?++?=? ∑∑∑ i kC i kCkCC LLL ?? L kC i ce SFG¥ i¨í ^¥. {′??9F¥ i ¨í ^¥. {′b 81 a?9F¥ i¨í ^ü ^c e -_ ^?D?9F| ^ ???í ^ =¥ i¨í ^ . {′?? (-BP k )?D ?¥ (i-1)¨í ^. {′- ebyN V| C ?1 ∑ ?+?=? m mmC PB 2?t bt?vD è ¨>? SFG pm Uèa¥ U 2 3 2 U 2? 16? s i 10 9 2? 1 U 3 (1)em ? U SFG?@FBHV U 2 ?i s ¥| ^  ?′1 (-B)¤?>?¥ SFG 2 U 2? 16? s i 10 9 2? B? 1 U 2?t bt?vD (2) ò¨í ^. {′1 L k 1 1 9 (-2)?(-2) (-B) ?(-16 )?(-2) L k 2 1 9?10 (3)>? SFG¥m?  T PBB B) mm C ∑ ?+?=+= +?++?=? 3268 90321049(1 (4)¨ Mason T9 ?m9m 68 32 2 2 = ? ? = ∑ mm s S P i U T (5)9 ?2T ss iiU 17 8 68 32 2 == 2?t bt?vD ?4 10 L?? ?¥ SFGs# ?Mm BaL?? ?¥ SFGs 1 sB?L?? ?A?ê4BF a?¥? ?M bê4?]¥? ?M  ? ¥Z?F?]y7 ?¥ SFG9?]bí ?  I 1Z?F1 ?? ?s L?? ?A? ?@?Z?F¥Z? ?DM  ? M] ?Z?F?¥Z? ^Mo? ?¥b ùsBF a?¥?M  P- ? a??] ??¥=  g? ?íq7 OYV? ?¥43ü ?°¤ yT? T¥? ?Z?b ê | ?|èaD ?|è @?¥?M T1? ?M b 2?t bt?vD ? ? ? ? ? ? = la ta b I I I ? ? ? ? ? ? = la ta b U U U ? ? ? ? ? ? = I l la I I I ? ? ? ? ? ? = V t ta I I I ? ? ? ? ? ? = V t ta U U U ? ? ? ? ? ? = I l la U U U U t aI t }V ?|?d÷| ^¥èa_ aè @_  U l aI l }V ?|?d÷| ^¥èa_ aè @_  ? KCLZ? (1) 0 = bf iQ (2) lalta IQI ?= 2?t bt?vD (3) 22 11 ? ? ? ? ? ? ? ? ? ? ? ? ?= ? ? ? ? ? ? = I l Il Il V t ta I I QQ QQ I I I T  ? Q l 1'é" ???? ?|¥s v|? TZ 71 ] ?? KVLZ? (4) 0 = bf uB (5) tatla UBU ?= T  ? B t 1'í ^ ???? ?|¥s v|? TZ 71 2?t bt?vD (6) 22 11 ? ? ? ? ? ? ? ? ? ? ? ? ?= ? ? ? ? ? ? = I l Vt Vt I l la U U BB BB U U U d÷| ^¥?M ? T¥| ^è @èa1" PZ?· _ ?¥í í1 ?|èa? ?|è @P  _ ?¥í í1 ?|è @? ?|èa' (7) 21 12 ? ? ? ? ? ? ? ? ? ? ? ? = ? ? ? ? ? ? t l t l t l I U ZG GY U I (8) - 1211 1112 1211 1112 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?= ? ? ? ? ? ? V I VIt VlI t l tlt tll t l U I BGQZ BYQG U I BGQZ BYQG U I 2?t bt?vD V 1 ¨ SFGs? ? H¥ê ??5 íq VCR í  VCCS 1221 , riuriu ?=?= ?| ?| e?| ^ s e| ^ 1221 , guigui ?== 12 gui = ?| ?| ?| ?| ?| ?| VCVS 12 uu μ= ?| ?| CCCS 12 ui β= ?| ?| CCVS 1221 , niinuu ?== ?| ( ?| ) ?| ( ?| ) ?| ?|12 riu = ?XMa  2?t bt?vD V 1 ¨ SFGs? ? H¥ê ??5 ? íq VCR μE F MD  122211 , ikiuku == ?| ?| e?| ^ s e| ^ (| ^ 2) ?| 122211 , ikiuku ?=?= 2 2 11 1 2 1 , 1 i k iu k u == 2 2 11 1 2 1 , 1 i k iu k u ?=?= (| ^ 2) ?| (| ^ 1) ?| (| ^ 1) ?| 2?t bt?vD è 3 ¨ SFGsEm U? ?¥Mf ? s U U T 6 = G 1 G 2 G 3I 1 I 3 I 5 s U + ? + + + + ? ? ? ? 2 U 4 U 6 U 1 sL 2 sL 3 sL 6 U 6 5 31 7 24 (1) ( ) () () () () 536 5324 3112 6435 4223 211 IsLU IIsLU IIsLU UUGI UUGI UUGI s = ?= ?= ?= ?= ?= (2) 2?t bt?vD s U B? 1 G? 2 G 3 G 2 G? 3 G? 1 G 6 U 1 I 3 I 5 I 4 U 2 U 1 sL 1 sL? 2 sL? 2 sL 3 sL (4) (3) [] [] () 332211 3 332211 3 33223312 2312331123112211 2 3323221211 332211 332233122312 331123112211 3322113323221211 1 ))()(( ))(())(())(( ))(())(())(( 1 LGLGLGBsLGLGLGs LGLGLGLG LGLGLGLGLGLGLGLG s LGLGLGLGLGs sLGsLGsLG sLGsLGsLGsLGsLGsLG sLGsLGsLGsLGsLGsLG sLGsLGsLBGsLGsLGsLGsLGsLG C ++ ? ? ? ? ? ? ? ? ++ +++ + +++++= ??? ??+??+?+ ??+??+?+ ??????? =? 2?t bt?vD ()1 3323221211 33223312 2312331123112211 2 332211 3 332211 3 6 ++++++ ? ? ? ? ? ? ? ? ++ +++ + = LGLGLGLGLGs LGLGLGLG LGLGLGLGLGLGLGLG s LGLGLGs LGLGLGs T è ¨ SFGsEm U? ?¥Mf ? s C U U T = R b i s u + ? + ? C u Ga R c C + ? C uμ iα 2?t bt?vD 6 5 3 1 7 2 4 8 3 (1) (2) ?|èa ?|è @ () 57 1 6 425 II R U U UUUGI C sa α= = ??= () 14 522 761 1 UU IRIRU II sC U bb μ= == +?= 2?t bt?vD (3)?   T? SFGiV U C ?U s @BH. {′ 1(-B)¥| ^??>?¥ SFG s U B? a G C UU = 1 a G? 2 U 4 U 6 I s I 7 I b R a G? α μ sC 1 ? sC 1 ? C R 1 (4) C baa C a baC sCR RG sC G B sCRsC G RG + ? ? ? ? ? ? +?+??=? αμα 1 1 2?t bt?vD #Mf ? CaCba Ca C ba C a ba a s C RGsCRRG RG sCR RG sCRsC G RG sC G U U T μα α μα ?+ ? = ++?+ ? == ))(1( 1 1 2?t bt?vD =a ?Mm (state transition diagram)  ?MmD ? ? í ?¥ H× ?Z?-Wμ b ¥ ?1"7 O ?? ?^? "d¥Mf ?¤? y7μ÷? ?8?? ^B??쨥y b í ?B?L?? ?? ?¥ ?Z?¥B?? T ^ (1) )()()( tBftAxtx += ?  é? ? fMDa (2) )0()()()( ?++= xsBFsAXssX ?M?¥yT? T¥Z? (3) )0()()()( 111 ?++= ??? xssBFssAXssX 2?t bt?vD è ?ù?B?=¨? { ?L?? ?  ?Z?1 (4) )()()()( )()()()( 2222121 2 1212111 1 tfbtxatxatx tfbtxatxatx ++= ++= ? ?  ?Z?é? ? fMDμ (5) )0()()()()( )0()()()()( 222221212 112121111 ?+++= ?+++= xsFbsXasXassX xsFbsXasXassX |  T1yT? T¥Z? )0()()()()( )0()()()()( 2 1 2 1 222 1 121 1 2 1 1 1 1 212 1 111 1 1 ?+++= ?+++= ???? ???? xssFbssXassXassX xssFbssXassXassX 2?t bt?vD )(sU )( 1 sX )( 2 sX )0( 1 ?x )0( 2 ?x 2 1 bs ? 1 1 bs ? 1? s 1? s 21 1 as ? 12 1 as ? 11 1 as ? 22 1 as ? m ? U¥ SFG? ?| H×?ò  ?M D B¨? ? W¥1" üA1Vr ?Dy-? m 4?°¤  ?Z?b1  ?¤?B?D ?Z?μ üA? 1"¥?| @m" |ò ?M ? { ? ¥`f ? a[# ?′T1 SFG¥??M ? 6? ? sX 1 (s) asX 2 (s)T1??M b?"[ X 1 (s) asX 1 (s) a X 2 (s) asX 2 (s) T1M ¥? ?Z?F1 2?t bt?vD [] [])()( )()( )0()()()()( )0()()()()( 2 1 2 1 1 1 2 1 2 1 222 1 121 1 2 1 1 1 1 212 1 111 1 1 ssXssX ssXssX xssFbssXassXassX xssFbssXassXassX ? ? ???? ???? = = ?+++= ?+++= G  ?? SFG?m?1 ?Mmb )(sF )( 2 sX 12 a 22 a )( 1 sX )( 2 ssX )( 1 ssX 2 b 1 b 11 a 21 a 1? s 1 )0( 1 ?x )0( 2 ?x 2?t bt?vD  ?Mm?V?? sX j ?X j -W¥| ^. {′1 s -1 ?? H×¥s ? 7  e| ^. {′? ^ è ??? H×?e[è ? ?b" F(s) ^ SFG¥ ÷??? x 1 (0-)ax 2 (0-)9 ^ SFG¥÷??b ? Mm b 1 í ? "d?ò? ?M a ?M ¥ ? ?? { ? -W¥1"b? ?Mm?? ?ZL 1 ?Z?7 O V[ p¤? ?¥Mf ?b ?  ?Mm? V[ p¤ ? ? í ?¥ ?Z?¥? 3 ?é7¤ ?Z?¥ˉ ?×3? H×3C s ?/ )()()( tBftAxtx += ? / Té? ? fMD? ?a¤ ?Z?¤ˉ ?×3 2?t bt?vD ( ) [ ] [ ])()0()()()0(1)( 1 sBFxssBFxAssX +?Φ=+??= ? T? ( ) 1 1)( ? ?=Φ Ass ?1?3 ?b ?T? ?¥ { ?1 ,5 )0()()( ?Φ= xssX ?3 ??¥í í ),.,2,1(0)0( )0( )( )( jknkx j i ij k x sX s ≠==? ? ? =Φ L V[ A ?Mm? p { ??? x j (0-)à X i (s) { ??¥m9m?? b¨??ZE 7 i=1,2,…,n,j=1,2,…,n, L V p¤ ? ¥òí í )(s ij Φ )(sΦ 2?t bt?vD è 3 X? ?Z?1 )(2)( )(2)()(3)( 1 2 21 1 titi ttititi = +??= ? ? ε ? S′ i 1 (0-)=2 i 2 (0-)=3 b? ?¥ ? Mmi pMf ? T 1 =I 1 (s)E(s)a?3 ? ? è @ i 1 (t) )(sΦ (1)| ?Z?é? ? fMDμ )0()(2)( )0()(2)()(3)( 212 1211 ?+= ?++??= isIssI isEsIsIssI ? s sE 1 )( = 2?t bt?vD ? 1" [ ] [])()( )()( 2 1 2 1 1 1 ssIssI ssIssI ? ? = = ?M?¥ ?Mm )(sE )( 2 sI )( 1 sI )( 2 ssI )( 1 ssI 1? s )0( 1 ?i )0( 2 ?i 1? s 1? s 1 1 -1 2 2 -2 (2)YV?e SFG p I 1 (s) , n5h ??? I 2 (s) as I 2 (s)  ¤?/m 2?t bt?vD )(sE )( 1 sI )( 1 ssI )0( 1 ?i )0( 2 ?i 1? s 1 1 2 1 2 ? ? s -3 h ? m ? U SFG??? s I 1 (s) ¤?/m )(sE 1 2 ? s )( 1 sI )0( 1 ?i )0( 2 ?i 1? s 2? ? s ( ) 11 23 ?? ?? ss 2?t bt?vD Kah ? m ? U SFG??? I 1 (s) ¥1ì' V  I 1 (s)¥3 (*) 23 )0()0()(2 231 )0()0()(2 )( 2 21 21 2 2 1 11 1 ++ ???+ = ++ ???+ = ?? ??? ss isissE ss isissEs sI (3) 7 i 1 (0-) " i 2 (0-) =0 V¤Mf ? 23 2 )( )( )( 2 1 1 ++ == ss s sE sI sT (4)?  ?Mm p?3 ? b/ ?¨ Mason  T p ¤òí íb )(sΦ )(sΦ ? ? =Φ ∑ m ijmijm ij P s ())( )( T? P m(ij) 1V { ??? x j (0-)à X i (s)¥? mH -_ ^? . {′  m(ij) 1  ? -_ ^?¤ ^?y0bsY9 ?  T¤s0as  ?/ m?  T ( ) 2121 231231 ???? ++=??=? ssss V i 1 (0-)à X 1 (s)¥ -_ ^? P 1(11) =s -1  1(11) =1 V i 1 (0-)à X 2 (s)¥ -_ ^? P 1(21) =2s -2  1(21) =1 V i 2 (0-)à X 1 (s)¥ -_ ^? P 1(12) =-s -2  1(12) =1 2?t bt?vD V i 2 (0-)à X 2 (s)¥ -_ ^? P 1(22) =s -1  1(22) =1+3s -1 2?t bt?vD 23 1 )( 2 12 ++ ? =Φ ss s 23 )( 2 11 ++ =Φ ss s s 23 3 )( 2 21 ++ + =Φ ss s s 23 2 )( 2 21 ++ =Φ ss s ?3 ? 1 )(sΦ ? ? ? ? ? ? ? ? ? ? ? ? ++ + ++ ++ ? ++ =Φ 23 3 23 2 23 1 23 )( 22 22 ss s ss ssss s s 2?t bt?vD (5)| E (s) ai 1 (0-)ai 2 (0-) -′} ? T (*) 2 5 1 3 23 12 )( 2 1 + + + ? = ++ ? = ssss s sI é? ? fQMD ( ) )(53)( 2 1 teeti tt ε ?? +?= - ?o  ?  ?Z?y ?"d¥ ?Mm¥Z Eb?? { ?a? {¥L?? ?"d? H× { ? {Z?ˉ ?×Mf ?9 ??"d¥  ?Mmb I3B?? { ?a {¥L?? ?"d H×?¨B / { ? {Z? í ? 2?t bt?vD )( )()( )( )()( 0 1 1 1 0 1 1 1 teb dt ted b dt ted b tra dt trd a dt trd n n n n n n n n n n n +++= +++ ? ? ? ? ? ? L L ˉ ?×?M?¥Mf ?1 0 1 1 0 1 1 )( )( )( asas bsbsb sE sR sT n n n n n n n +++ +++ == ? ? ? ? L L 1 ?"d¥ SFG|Mf ?¥s0as ] e[?WM  s -n Z? ^ V|s0as sY1 2?t bt?vD ( ) ()ZsasassE ZsbsbsbsR nn n n nn n n n ?? ? ?? ? +++= +++= 0 1 1 0 1 1 )( )( L L ?lM "? {X i }(i=1,2,l,n) ZsX in i 1?+? = 5 (9) )1,,2,1( 1 ?== + niXsX ii L ZsXXsXXsXXsX nnn ==== ? ,,,, 13221 L ' )( )( 1122110 11122110 sEXaXaXaXaZsX ZbXbXbXbXbsR nnnnn nnnnn +?????== +++++= ??? ??? L L ? [ + T V[? ?Mm 2?t bt?vD è ?X?Mf ? 01 2 2 3 01 2 2 3 3 )( )( )( asasas bsbsbsb sE sR sT +++ +++ == ¨ s -3 Ze  Ts0as i 7 ZsXZsXZsX 1 3 2 2 3 1 ,, ??? === 5μ 322110 3322110 3 32 21 )()( )( XaXaXasEsZ ZbXbXbXbsR ZsX XsX XsX ???= +++= = = = 2?t bt?vD ? [ + T V[? ?Mm )(sE )(sR 1 X 2 X 3 X 3 sX 2 sX 1 sX Z 0 a? 1 a? 2 a? 1 b 2 b 3 b 1 11 1 1? s 1? s 1? s 0 b 2?t bt?vD è X? ? ?Mf ?1 15177 45 )( )( )( 23 2 +++ ++ == sss ss sE sR sT ?? ?¥ ?MmiM?¥ ?Z?? [ r(t)1 {¥ {Z? 3 ¨ s -3 ZeMf ? T(s)¥s0as i 7 ZsXZsXZsX 1 3 2 2 3 1 ,, ??? === 321 321 33221 71715)()( 54)( XXXsEsZ XXXsR ZsXXsXXsX ???= ++= === 5μ 2?t bt?vD ? [   T V[? ?Mm )(sE )(sR 1 X 2 X 3 X 3 sX 2 sX 1 sX Z 15? 17? 7? 5 1 1 11 1 1? s 1? s 1? s 4 ?¥ ?Z?1 )(71715 321 3 3 2 2 1 texxxx xx xx +???= = = ? ? ? 2?t bt?vD {Z?1 321 54)( xxxtr ++= ?Mf ?? ?Mmaé7 ?Z?? {Z?¥V?? ??"d?? S ??1 ,5 T (9) ? U¥M "?? 7 (9) )1,,2,1( 1 ?== + niXsX ii L )0( 1 ?+= + iii xXsX ' SFG?¥?? sX i 9FB?. {′1 1¥ ?| ^ | ^ 6B ??M 1 S′ x i (0-) 2?t bt?vD ? 1c (? ?¥? ê T )1? Ba¨ Y n ¥?  TV U¥? ?f ? 1.  g¥|??f ? n kkkkkkkk k k kk I U Z ? ?????+? == '''' '''' kkkkkkkk n k k kk U I Y ?????+? ? == ? | k ' 1? I??5} ? T1 kk n k k kk n kk k k kk U I Y I U Z ? ? == ? ? == ; 2?t bt?vD   gW¥ME FDMèa1 n jkkjkjjk k j jk I U Z ? ?????+? == ' ' '' ' ' ' ' ' ' '' kkkkkkkk jkkjkjjk k j jk U U ?????+? ?????+? ==μ ? | k ' 1? I??5} ? T1 n kjjk k j jk I U Z ? ??? == ' kk kjjk k j jk U U ? ??? == ' μ 2?t bt?vD = g Z? ?D Y? ? ? ? ? ? ? ? ?????+???? ???? ? = ? ? ? ? ? ? = 2'2'22'2'222'1212 1'22111 2221 1211 1 n zz zz Z ? ? ? ? ? ? ? ? ? ? ? ? ???+? ? ???+? ??? ???+? ??? ???+? ???+? ? = ? ? ? ? ? ? = '1122'2'1121122 11 '1122'2'1121122 12'12 '1122'2'1121122 12'12 '1122'2'1211122 '22'2'222 2221 1211 22 22 2 1 n yy yy Y =aí÷? ? ? E F¥? ê T ? n ¥? ê T ? n = det Y n ∑ = j j yT ) ( ) ( )()( YW t ≡= ∑ ?? ? ?|? , ? kk ¥? ê T )( )( )() ( )( ) ()()( 0 , ) ( , ) ( 0 ZE= ZEB ¥ ?? ? ?|? , YWyT yT rk j j rk k j j k N j j T -k j e-kkk N ≡= = ==? ∑ ∑ ∑∑ ? ? AYA 2?t bt?vD 2?t bt?vD 2- ?' ?Ym(¥ ? ?5 ??  ? ??B ?|¥0mb &? c G¥ ????  ??é &a ?cí ^ &? s ?1 ? ?Y ? ?B?sg V1 B? ???b ?aí÷? ?Mf ?¥? ê T ? k j ¥? ê T )() ( 0 , ) ( , 0 YWyT rjk l l rjkjk ≡=? ∑ 2?t bt?vD Mf ?¥? ê T  ME F )( )()( ' ,' '' , YW YWYW Z t jkjkjkjk jk ? =  o^ ? g? ? Z? ? )( )()( , )( )( , )( )( 2'1 , '12'2'1 , 12 2112 '2 , 2 22 '1 , 1 11 YW YWYW ZZ YW YW Z YW YW Z t tt ? == == 2?t bt?vD  Mèa1 )( )()( ' , ' ,' ' ' , ' YW YWYW kk jkjkjkjk kk jkjk jk ? = ? ??? =μ 1aY? ?¥? ê T ZE 1 ?¨ g 7 ^¥ ? gYV 3- ? ?9 ? )()( )()()( : )( )()( )( )( , )( )( 2'1 , '2 , 1'1 , '2 , 12 '2'1 , 2 , 1'1 , 2 , '12 '2'1 , 122'1 , '12 2112 '1 , 1 22 '2 , 2 11 YWYW YWYWYW YW YWYW yy YW YW y YW YW y ++ += ? == == ∑ ∑ ∑∑ T? 2?t bt?vD ZE 2 ?¨ g ^ ? g¥ ?|? , ?9 ? W  (Y) ¥ ?|? ,-? g ( ^¥ ? g? ?= = ∑ )()( " YWYW t ?a¨? ?E FV U¥? ê T ? l = det Z f l = det B f Z e B f T ∑ ∑ ? ? ≡ ¥ ??? ? ?? ?¥? ? ?|E F ? ? ?|E F  }1  } 1 )( )()( j jj l N ZW 2?t bt?vD Ba??? , ?¥? ?μ_m ??? , ?¥? ?μ_m ? ? kaj-W¥μ ?μ_H ?sY1 -y kj ? -y jk  N? Z_? ^àZ_b μ÷? ?? n ¥? ê T _m ? T ro "μ_m G d ?@/ Hq¥0m 1) ??Z_a ˉ? ^B? ? 2)r 0 1 d out ro = 0¥? I? (?1? ) 3) ??¥ d out = 1 b _m 2- ? T k , ro  "μ_ ? 7B ?|¥0m ?@  ??Z_a ˉ? ^B? 2- ?  ?B? ??sμ?? I? (k r o ) ? ì¥  d out ro = 0  ??¥ d out =1 . td T dddn W )( )( detdet ≡ ∑ = ==? + _ ?[? I?1?¥ ?μμ μ_ ? ?- AAY γ 2?t bt?vD 2?t bt?vD taμ÷? ?¥? ê T ? k k # z?f ?¥? ê T )( ; )( );( ) '1 , 1( 1 ) '1 , 1( 1 ) , ( 0 YW W Y W YW Z YW d td i td d i krdkk == ≡? ? k j #Mf ?¥? ê T )( ) , ( 0 YW jkrdjk =?  g ? | k ' 1? I??5 2?t bt?vD dt jkjkdjkjkd n kjjk jk W WW Z ) ' ,' () '' , (' ? = ? ??? = dt j'kjkdj'kjkd jk W WW Z ) ,'() ' ,( ? = ? 1c (? ?¥? ê T )5 ?4.1 ¨? ê T pm U= g¥ ? ? , b( ! 2-2’ g 7 ^ )b 2?t bt?vD u 1  1$ 1F 1F 2F 1 1' 2 2' u 2  (2-T) Y in Z in Y in Z OC Y SC μ÷ Z OC Ex. 4.1a4.2a4.4a?4.1 4.5a4.6 4.7