Mascotte : A few Maple Routines for Real-Time Code Generation
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Texte intégral
(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Mascotte : A few Maple Routines for Real-Time Code Generation Thierry Vie´ville. N 2826 Mars 1996 THE`ME 3. ISSN 0249-6399. apport de recherche.
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(61) çGbLR T[GbL0L" ubVlLKflflZ]\^R Z]RB^\ å ^Lf #WYVlZdWYq å LKfck\^R å æ WìXK\^RIgIZ]TlZd\YRhW å "L ubVlLKf[fZd\YR X=WYR qrL Zdflf[ébLg @FGZdfMZdf}T[GbL0X=WYflL GILKV[L#c M!GILKV[L TUGILVl\^éITlZdRbL0T[VlZ]LKf}TU\è\^éIT[ubéIT/WèflZ]JMu å L XK\^RIgIZ]TlZd\YRhW å "L ubVlLKflflZ]\^R M!GIZ]XaG_"L YW å éhWT[Z]\^R X\^V[VlLKflu¾\^RIgbf2TU\MTUGbL eYQZ ^LR fZde^RbW#TUébVl L . < MX ; = B XÐ I>= â ; â C I=B Þ ; ã Þ Y â Y K IM9 A@7 =@? FGbLKVlL2Zdfk\ T[LKR/W¢RbLKLgMT[\ J7W#RIZduIé å WTUL ^LXTU\YV[f²WYRbgMJ/W#TUVZdXLKf % M2Z¶TUGb\YéITkTUGbL2X\^JMu¾\^RILKRDTUf % c<L" u¾LXZdW å¶å æ ZdR TUGILXKWYf[L \ tZ å qrLKVT!f[uhW#XKLKfc M2Z¶TUG Z]R'hRIZ¶TUL gIZ]JMLKRbfZd\^RIf QS$ R BWYXTpf["L ^LVUW å flZ]J/u å QZ hX=WT[Z]\^Rbf¢X=W#R_qrLJ/WYgbL#:c ÐVl\^J%flæ×Jqr\ å ZdX¬W å eYLKqbV[W#ZdXPubV[\Yu¾LVlT[Z]LKfp\ J/W#T[VlZ]XKLKf WYf2ZdJMu å LKJMLR<T[LKg_Z]R TUGIZ]f!V[\^éITlZdRI L t\ M"L ^LKVXc M°LpJPébflTV[LKJ}Z]Rbg¥T[GhW#T°XK\^RDTUV[WYVlæ}T[\PT[GbLpur\ å æ×Rb\^J}Z®W å f Ð\^VZdRbfTaWYRIXKLYc×TUGbLtJ/W#TUVQZ 7W å e^LqbVUW ZdGf ^LVlæ ébR BW#Zd1V )kRb\^R`±XK\^JMJéTaW#TlZ YLYc)Rb\^R` ZdRDT[LKe^V[W å chL4TU!X Q °fl\/T[GhW#T!fZdJMu å Z bX=W#TlZd\^RIfpZ]ftJM\^VlLW/GbLébVlZ]flTlZdX TUGhW#RT[GbL e^LKRbLVUW#TlZd\YR \ WYRDæ0ubflLKébgI\#`SXKWYRb\^RIZ]X=W å Ð\YV[0 J FGZdftJ}Zde^GDTpq¾L¢T[GbLPVlL=WYfl\^R M!GDæ % eY\\×g % J/W#TUGbLJ/W#T[Z]XZdWYRbfpGh
(62) W ^LRb1L YLKVuIV[\^e^V[WYJflébXaGìWMV[\^éITlZdRILYc M!GIZ å L MLGh
(63) W ^L gb\YRbL¢Z]TtqrLKX=W#ébf[L ML RbLLKgZ]T , hébVTUGbLV[JM\^VlLYc M°L¦Gh
(64) W YLYcIZ]R¥TUGZdfVl\^éITlZdRbL#cb* W Ð\YV[J/W å gbLKVZ #W#T[\^1V M!GIZ]XaG X=WYR ^LKVæ LKWYflZ å æ7flZ]JMu å Z æ7TUGbL XK\^JMubéTaW#TlZd\^RIfp \ ^WYX\^qIZdWYRbf â. b,bdc ef3eg.
(65) Ø$ $3P+ + 2$ 1 K.0. 8. >. E
(66) H ;J6548T_:F@;:UB4<H. ;M4 ; K M 9JAJF84!; ;'K K:9 ;'K8H AJU84<H4!2 ; K 7 9 S K A') AV;'K 7. ~ . : G 0] & U@; = 7:AB45?
(67). . E : ¼. K M9JA F84<; ;'K K:9J;'K H AJUB4<H UBA 9 A@7 9 A K ; 4!2 7 9 S K 654 _ ; U@H'K'A & UJF K:9 ;'K H'T ; K F89 S 9<C:U UV;:U!K'A 4!2 ; K 9 F@; _M9 7 9 S K A'):AV;'K!7 ( 6 K^)9!6 K 7 9 TJK 4!2 29_ H:F@; U84<H A ;M4 7 9<H U S _ 9!;'K ;'K:9 ;AV;J6_:F@;_J6'K'AL K H5K8659<;'K S 6M4 F!KBT_ 6 K'AL S _ A U@HM9 ^ 2_ H:F@;:UB4<H A ( 6 K 4<C'DJK5F@;:U@I5K 4!2 ; K'A K 92 _ H:FV;:U84<H A UBA ;M4 K H'KB659<;'K 6 K 9'F@;:U@I'K 7:4 T_ K5A UVH 654<C 4<;:U FBA 9<H'T I:U AJU84<H 'A ) A<;'K!7:AL C _J; 7 9 ) 9!I'K 9 AB4 AB4V75K 4<; K86 9 S S UJF89<;:U84!H A 6 K S 6 K5A K H ;M9!;:U84<H UBA 9 AV;M9<H T59!6JT S 9 F - 9 K L & U@; A 4V75 K 6 K 98T U@C TJK82 U@H5KB T 654 _J;:U@H'K'A TJKB2 U@H'KBTU@H U@; ( ; UBA ; _ A AJU
(68) 7 S ) 4 9 TJK T I U89 & U@; = 7 AB4'? " 6 K U@H 9 S 9 F - 9 K 7 _ AV; C'K 4 9 T KB, T _ AJU@H & U@; = U@H 9 0/ ? ( 6 K ;J659 F K 2 _ H:F@;:UB4<H UBA 6 K HM9<75KBT S 654 FV;J659 F!K ;M4 9<IM4'U<TF84<HJ2 U F & U@; U@HM9 ;J6M9 F!K IM9'U 9<C K 654 _ ;:UVH'K'A U@H ; UBA :K 9 ;'K8H AJU84<H9!6'K " 6. . ! ~
(69) . S 654 F@; 659 F!K L 65;'4 $KF!9TJ;JK862 KU@H598TK LL ';52 K:4!9687:; &9<;6 U@L ;'KF84JL AV;;) L S K UV HM29_9 H:F" 3L F84<H I'KB6B; S 0/. %$. 5? @ADC. 6 87 #6 L. DA'&. ] )( :
(70) . AB9<I'K5UVH U@C AV;M4!6 K 9 7 9 S K 4<C'D KMF@; & @U ; U@; A K !S UVH 9 @U CM9!6). ~ : G 0] . . >@?Hb>BA.
(71) AB9<I5K5U@H UVC>= U@C HM9V75KL 4<C'D HM9V75K ? E ~ ~ W ( P U@C HM9V75K ; K HM9V7MK 4!2 ; K U@C 659!69) U@H & U F ; K 4!C'D K5F@; UBA ;M4 C'K A<;M4!6 KBT 4<C'D HM9V75K ; K HM9V75K 4!2 ; K 4<C'D KMF@; ;M4-C'K AV;M4 6 KBT
(72). E : ¼. AB9<I'KMU@H U@C AV; 4!6 K 9 7 9 S K S 654 F KBT_J6 K 9<H'T 9 U@;:A A _ C 4<C5D K5F@; A 9!H T K <S 2 U K U@H 9 7 9 S K U@CJ659 69) ( 9<H C'K 4!2 ; K 254!687 HM9V7MK L 4!6 HM9V75K HM9V7MK 6 K H 9 64<C'KD KM4<F@;C'DA 8HM4!29V75KHM9V75F8 K 4<C'D HM9V75K 4!6 4!C'D HM9<75K $ & U C'/K$ AV;M4!6 K T ( UVH ; K 2 U K 4 2 HM9V75 K UV C HM9V7MK $ 4<C'D HM9V75K ( _ 6B; K86B7 4!6 K ; K 6 K5A'_ ;:UVH K <S HM9V7MK & U 9<I'K ; K HM9V75 K K ;'$K 9 ; HM9<75K 4!6 K HM9<75K ;5K:9 ; H 9V75K 9<H T C'K AV;M4!6'KBTU@H ; K F84!6 6'K'A S 4<H'<STM$U@H 2 $U K L 9!2B;'KB6 F84!H<SI'K8$ 6MA U84<H /$ I:U89 $F84<HJI'K86B; 6 =7 6# ( KU@H:F K 2 )MU 4 _K 9!F86'9!HK C'9 K A K8FV66 K'UB49<_;'KBA T 7 9 S K S 6M4 659V7J75K863L U@; 9 '& 9 ) A F84V7 S 9 U@H A U<2 HM4 <S ( . ! ~
(73) . 7 9 -'K K < S L F84<HJI'K86B;.
(74). 6 =7 #6 . . < . ] )( :
(75) . ;'K:9 ;J6'K 9 T 6 K'9 T 9-;'K:9J; T'9!;M9 AV;J69_:FV;_J6 K 2 654<7 9 2 U K. ~ . : G 0] ;'K:9 ;J6'K 9 T= 2:U K HM9<75KM?. E~ ~ W ( P . 2 U K8HM9V75K.
(76). E : ¼. b,bdc ef3eg. . . ; K HM9<75K 4!2 9 2 U K.
(77) K 29_ H:FV;:U84<H ;'K:9J;J6 K 9 T =@? 6 K ;_ 6BH A ; K ;'K:9 ; 6 K 98T UVH ; K A KMF UV2 U!K T 2 U K ; BU A-6 K8;_J6BH'K T 9JA 9 ;'K:9 ; T'9<; 9 AV; 69_:F@;_ 6 K 4!2 ; K 254!687 " S 6 87 6 = U@H'K / 4!2 ;'K:9 ; L ? (((k$ ((( 6. . (. ! ~
(78) . 3L F89<; L$;'K$9 ; & 6 UV;'K. 6 = 7 6. . . . . < A . ] )( :
(79) . ;'K:9 ; & 6 U@;'K. &. . 6 U@;'K 9 ;'K:9 ; T'9<;M9 AV;J6_:F@;_J6'KU@H 9 2 U K. ~ : G 0] ;'K:9 ; & 6 U@;'KE=2 U K H 9V75K. E~ ~ W ( P . 2 U K8HM9V75K ;'K:9 ;.
(80). . . . . L ;'K:9 ; ? ; K HM9<75K 4!2 9 2 U K 9 ;'K:9 ; T'9<; 9 AV; 69_:F@;_ 6 K 4!2 ; K 254!687 6 87 6 = U@H'K / 4!2 ;'K:9 ; L ? (((k$ ((( ". E : ¼. K 29_ H:FV;:U84<H ;'K:9J; & 6 U@;5KE=@? & 6 UV;'K'A ; K ;'K:9 ; U@H ; 4 ; K A S K5F UV2:U!KBT 2 U K. 6. ! ~
(81) . 3L F89<; L & 6:U@;'K ;M4. 6 = 7 6. >@?Hb>BA.
(82) . :.
(83) FC. . ] )( :
(84) . ;) S K $ 29_ H:F. . K H'K86M9 U K T F K5F - 254!6 9 29_ H:F@; U84<H. . ~ . : G 0] ;) S KE= K:9 S 63L 29_ H F = HM9V7MK L H CM9 6 . A'?J?. E~ ~ W ( P :K 9 S 6 HM9V7MK H CM9 6 A.
(85). . ;9<H )K . :K 9 S 6 K'A A U84<H HM9<75K 4!2 ; K K8H'K8659 U KBT 29_JH:F@;:U84!H=14 ;:UB4<HM9 ? 4!6 9 A K ; 4!2 HM9<75K'A 4!2 ; K K H'K86M9 U K T 29_ SH:F@; U84<H ; K H_ 7JC'K86 4!2 9!6 _ 75K H ; A 4!2 ; K 29_ H F@;:U84<H=4 S ;:U84!HM9 ?. E : ¼. N MK F - UV2 ; K K:9 S 6 K'A A U84<H UBA 9 K8H'K8659 U KBT 29_JH:F@;:U84!H 4!2 K I'K HJ;_M9 ) 4!2 9 U@I'K8H HM9<75K 9<H T K I'K8H ;_M9 ) 4!2 9 U@I5K H H_B7JC'KB6 4!2 9!6 _B75K H ; =A ? ( 6 K 254 4 & U@H ;) S K'A " U AV;L A K ;L JL L L L * L L 9 JL L 9<H T L !4 6 L MH 4!; 9!6 K F84<H:AJU<TJK86'KBT 9JA K H'K86M9 U K T 29_ H:F@; U84<H ( . . ! ~
(86) . ;) S K 29_ H:F@; U84<H . . 0>UC ? <
(87) . ] )( :
(88) . F84<H I'KB6B; $ 6 87 6 F84!H I'K86B; AV; 6 U@H 4!6 :K 9 S 6 ;M4 9-;'K$9 ; T'9<;M9 AV;J69_ F@;_J6 K. ~ : G 0] F84<H I'KB6B;>=AV; 6 U@H L 6 =7 6:? E ~ ~ W ( P b,bdc ef3eg. .
(89) AV;J6 UVH AV;J6:U@H 4!6 BU AV; 4!2 AV;J6 U@H 4!6 6 =7 6 T'9!;M9 AV;J69_:FV;_J6 K'A & U@; AB4<75K S 4JA AJUVC K_ H'K I 9 _M9<;5KBT 29_ H:FV;:U84<H A
(90). E : ¼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~ W E + K 9JA8K 96 _JH " F84<H I5K86B; $ 6 =7 6 $ $K 9M9V7 S K !=@? . 6. (. ! ~
(91) . 3L F89<; L$;'K$9 ; & 6 UV;'K L ;'K:9J;J6 K 9 T. 6 = 7 6. . . 0>UC ? <
(92) 8 : $ ADC <8 . ] )( :
(93) . F84<H I'KB6B; $ 7 9 S K!7 AB4<;'K:9J; F84<H I'KB6B;9 7 9 S K 4<C'D K5FV; ; 4 9<H 7:AB4<;5K:9 ; F84<H I5K86B; $ 7 AB4<;'K:9J; !7 9 S K F84<H I5K86B;9<H 7:AB4<;'K$9 ; ;M4 9!H 7 9 S K 4<C'D K5FV; F84<H I5K86B; $ 7:9 S KMU@H'K86B; F84<H I5K86B;9 7 9 S K 4<C'D KMF@; ;M4 9!H U@H'KB6B; 254!687 F84<H I5K86B; $ UVH'K86B; 7 9 S K F84<H I5K86B; CM9 F - ;M4 9-7:9 S K 4<C'D KMF@;. ~ : G 0] F84<H I'KB6B;>= K:9 S 63L 7 9 S K!7:A 4<;'K:9 ; F84<H I'KB6B;>= ;'K$9 ;L 7:AB4!;'K:9 ; 7 9 S K F84<H I'KB6B;>= K:9 S 63L 7 9 S K5U@H5K86B; ? F84<H I'KB6B;>= K:9 S 63L U@H'KB6B; !7 9 S KM?. E~ ~ W ( P . ?. ?. >@?Hb>BA.
(94) K:9 6 ;'K:S9 ;
(95). 9 7 9 S K K:9 S 6MA AJU84!H ( 9 ;'K:9 ; T'9<;M9 AV;J6_:F@;_J6'K . (. E : ¼. 'K A8K F84<7 S K!7MK H ;M9!6) S 9 UV6 A 4!2 29_ H F@;:U84<H:A 9 4 & A ; 4 F84<HJI'K86B;9 7 9 S K 4<C'DJK5F@; U@H ;M4 " 9<H U@H5K86B; 254!687RL U@HJIM4 I:UVH 4<H )AV;J6:U@H 9<H T 29_ H:FV;:U84<H 9<H K 9 AJU ) S 9!6 A KBT ;'K:9 ; L 9JA _ A K T C) ; K 7:AB4 N $ N U@CJ659 69) ( H 259 F@;L ; K5A K 654 _ ;:UVH'K'A 9!6 K HM4<; 6 K 9 ) _ A K829_ 2M4!6 9-7 9 S K _:A K863L C_ ; 9!6 K S 9!6B; 4!2 ; K U@H ;'KB6 259 F!K & UV; ; K N $ N U@C 659!69) ( 6. . . . . . . : <. . ] )( :
(96) . ;'K:9 ; S 9!6MA K TJK82 U@H5K'A 9-;'K:9J; S 9 6MA K86 I:U89 9 254!687 9 659V7 7 9 6. ~ : G 0] ;'K:9 ; S 9!6MA KE= 659V7 7:9!69_ K / L . 6M9V7 7 9!6J69_ KL. ((( ?. E~ ~ W ( P . 659V7J7 9!6 69_ K ( U 9<H K _M9<; U84<H TJK82 UVH:U@H 9 659V7 7:9!6 69_ K. .
(97). &. . =. E : ¼. K 92 _ H:FV;:U84<H ;'K:9J; S 9!6MA8K TJK82 U@H5K'A 9 7 9 S K S 654 F!K T_J6 K !4 2 ; K 254!687 " SU F 654 9 F 6M= ;A K'" 6A 879 6:6? (6 (( T'K 9<H;MT9 " AV;J6_:F@;_J6'K L 9 F F84 6JTMU@H ; 4 9 254!687 9 659V7 7 9 6 =7 S ( $K 9:U F89 K K!75K H ;4!2 ; K 659<7 7 9!6 UBA TJK82 UVH'KBT C) ; K 6 K _ 9!6 K:9 S 6 K5A AJU84<H. 6. . (. . &. U F UBA 'A -:U S S KBT. 9 . . 1 = l
(98) ( ?^1 l
(99) = K l
(100) ?^1 ?. ;# .1 $ * 1 " ( . = = . ? ? HM4<; ') K ; U
(101) 7 S K!75K HJ;'KBT l =V? . = . . ;# .1. b,bdc ef3eg. ".
(102) ?. K 659V7J7 9!6 UBA TJK82 U@H5KBT C) 9 A K _5K H:F!K 4!2 659V7J7 9!6 69_ K5A 4 2 ; K 254!6B7 " HM4<HJ;'K8687 UVHM9 = K$9 S 6:? S 9<;J;'K86BH & K86'K K:9 S 6 UBA 9<H U@H'KB6B; K:9 S 6 K5A AJU84<H & U F 6 K S 6'K'A K H ; ; K A ) H ;M9 9AV;J6_:F@;_J6'K 9<H T 7 U ;F84!H ;M9 U@H AB4<75K IM9!6 U89!C K'A HM9V7MK'A 9JA TJKB2 U@H'KBT UVH ; K A K 9_'K & K86'K 9 S 9<; ;5K86BH UBA K5U@; KB6 9 " 9 A K 9_'K H:F!K 4!2 =A'_JC ? S 9<;J;'K86BH ; ; ( = I ? & KB6 K I UBA 9<H 4 S ;:U84!HM9 IM9!6 UB9<C K HM9V7MK 9<H ) U F :K 9:UU FB9 7 9!K ;: K!F 75K8H; K :K 9:UJF89 K K!7MK H ; & 9 AV;J6:U@&H L F84!6J6 K'A S 4!H TMU@H ;M4 9 U@I'K8H K$( 9:U F89 _JH:U@; HM4<HJ;'K8687 UVHM9 6 K S 6 K'A K HJ;'KBT C) 9<H U@H'K86B; 29_ H F@;:U84<H & U@; 9JA 4 S ;:U84<H 9 99!6 _B7MK H ;L 9 IM9!6 U89!C K HM9V75K UJF U 7 9<;:F ; K A ) H ;M9 9AV;J6_:F@;_J6'K ; K ; = S 9!; ;'K86BH ? ;M4 TJK8HM4<;'K &l L / 4!&6 74!6'K 4 FJF _J6 K H F!K 4!2 ; K S 9<; ;'KB6BH ; K ; = S 9!; ;'K86BH ? ;M4 TJK8HM4<;'K / 4!6 7 4 6 K 4 F F _J6'K H:F!K 4!2 ; K S 9<; ;5K86BH ;; KK ;; 1
(103) == S 9!;9<;;';'K86BK8H6 H ? ;M4 L TJK8HM9<;4<;';'K8K 6 Hl 4!6 L / 4 F? F _ 4 6 K K8H:659!F!;MK 4!6 4 2 ;M;4 KTJK SHM9<4<;J;5;'K K86B9 H ;'K86BH 9<;:U@I'KL F89!H C' SK _ A K T ;M/ 4 A K S 9!659<;'K C'K8; K (K ( H ( TMU<S2 2 K86 K8H ; A K _5K H:F!K 4!2 9<; ;5K86BH S UBA ; K HM4<&H ;5K8687 U@H 9 4!2 ; K 2 UV6MAV; 659<7S 7 9!6 96 _ ( K 6 K 5 6 4 < 4 ; ! 4 2 ; K 5 6 V 9 J 7 7 ! 9 6 ( ~ W E * " ;':K 9 ; S 9!6MA KE=9 T T=198T T= 9L ) ? ? = ; ( = 9 ? L L ; ( k= ) ? ?J? S4 6M;:4 FU84<=@H ? A I'K C'K K H FV6 K'9<;'KBT U@; ;'$K 9 ; 9!6 A KE=@? L 6 K 75K!7JC'KB6 S UV2 ; ) KE=19!6 A L 6 6:? ; & K H S = 7 S / ;5K:9 ; S 9 6MA K $ ) 9 F F != 9 T T3L 9 T T =19 T T= 9nL ) ? ? = ; ( != 9 ? L JL ; ( k= ) ? ? 3L ;'$K 9 ; S 9 6MA8K $ $K 9 =19 6 A / : ? ? K A K = 59 T 9!6 _B75K HJ; ; ) S K 1? 2U K H'T * = 6 =7 6 = 9 C 1? ? 9 T T =19 L C ? . 6. . . . . . . . . 8. >&. . ] )( :
(104) . 7:AB4<C'D K K!75K8H ;M9!69) 75KMF 9<H:U A@7 4!2 4<C'D K5FV; TJKB2 U@H:U@; U84<H A. ~ . : G 0] . . >@?Hb>BA.
(105) :7 " AB4<C'D=14<C'D L 9<;J; L AB9<; ; ( (( ? ;M4 6 K ;J6 U K I'K ; K IM9 _5K 4 2 9<H 9<; ;J6:U@C_ ;'K 7:AB4<C'D=14<C'D L 9<;J; IM9 L ((( ? ;M4 TJK82 U@H5K ; K IM9 _'K 4!2 9<H 9!; ;J6 U@C _ ;'K E~ ~ W ( P 4<C'D ; K HM9<75K 4!2 9<H 4<C'DJK5F@; 9<; ; ; K HM9<75K 4!2 9<H 9<; ; 6 U@C_ ;5K AB9<; ; ; K HM9<75K 4!2 A'_JCM9<; ;J6:U@C_ ;'K5AL K5U@; K86 254!6 T)B7 9!H:U F 9<; ;J6:U@C_ ;'K5A 4!6 ;M4 6 K82'K86 K H:F K 9<H 9<;J;J6 U@C_J;'K 4!2 9 A'_ C 4<C'D K5FV; ( IM9 9< H ) IM9 _'K.
(106). E : ¼. 654!I:U<TJK 9<H K K!7MK H ;M9!6) 75K5F 9!H:UBA@7 4!2 4<C'D KMF@; TJK82 U@H U@;:U84<H ( H 4<C'D KMF@; UBA TJKB2 U@H'KBT C) 9 UBAV; 4!2 9<; ;J6 UVC_ ;'K'A 4 2 9 U@I'K H IM9 _'K ( 6 K IM9 _'K 4!2 9<H 4<C'DJK5F@; F89<H C'K 9-HM9V7MK L 9<H K:9 S 6 K'A A U84<H 4!6 9<HM4<; K86 'A _ C 4<C'D K5FV; ( C'DJK5F@; A 9!6 K AJU
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~ W E * 7:A 4<C'DE= 7 )M4<C'D L9 / L C K 4 L F 4 = 9 / ?J? " * 4 S = 7 )M4<C5DM? ;M9<C KE= 9 / C K 4 F H>= 9 / ? 59V7MK 7 )M4<C5D ? * 7:A 4<C'DEk= ) 4 _J654<C5D L 69) S K 7 ) 4<C'DL9<HM4!; K86M4!C'D 3L9 L T / L L o ? " * 7:A 4<C'DEk= ) 4 _J654<C5D L 9'? +. . . . . b,bdc ef3eg. (.
(108) *. 7:A 4<C'DE=k) 4 _J654<C5D L C ? *. 7:A 4<C'DE=k) 4 _J654<C5D LOT ? *. 7:A 4<C'DE=k) 4 _J654<C5D L KM?. K 4 /. L L. o . K. ! ~
(109) . 9JA A'_ 75K L ;M9<C K. . > CU? <8
(110) . ] )( :
(111) . F84<H I'KB6B; $ N F84<H I'KB6B;9<H :K 9 S 6 K'A A U84<H ;M4 9 S U K5F!K 4!2 N F84 T K. ~ : G 0] . . F84<H I'KB6B;>= K:9 S 63L NL HM9V75K ? E~ ~ W ( P :K 9 S 6 9<H :K 9 S 6 K'A AJUB4<HL 9<H 9!6 659) 4!2 K:9 S 6 K'A AJUB4<H 4!6 9 UBA<; 4 2 K _ 9<;:U84<H:A HM9V75K ; K HM9<75K 4!2 ; K N 654 _ ;:UVH'K ;M4 C'K K8H'K8659<;5KBT
(112). E : ¼. N'4<HJI'K86B; ; K U@H S _ ; ;M4 N F84 TJK 254!6 K IM9 _M9<;:UVH U@; ( ; 4 _ ; S _J; A 9 & UJF F84<H ;M9'U@H A 9 29_ N S 6M4 F!KBT_ 6 K ( 6 9 K AJU@U@HH S _ ;K 7 9 _ AV;K C C'65K9 U K5FEU@L ; H_KB756 K8" 6 U F 4!6 4 U F K:9 6 K5A AJU84<H L S 9 HM9V75K T 9!6J659 )4!2 A'_:F K:9 6'K'A AJU84!H A L 9 UBAV; 4!2 K _M9!;:U84<H A 4!2 ; S K 254!6B7 HM9<75K K:9 6 K'A AJUB4<H _ H'TJ K86MAV; 4 4 T 9JA 9 A K _'K H:F K 4!2 9JAJAJU HB7MK H ; AV;MS9!;'K!75K HJ; A ( 6 K 4 _ _ ; B U A 9 9 ) A 4 ;
(113) U 7 U K T L _ J A @ U H S & S U " ; K M9 K 4 ;:U@7 U K 92 _ H F@;:U84<H TMU S U@; A F8S4<H A<;M9<H ; A 254 6 T'4_ C K 6 KMF UBAJU84!H 7 o4!HM4 TMU
(114) 7MK H AJU84!HM9 9!6J659 ) A U@H T :K 9'KB T S2 654<H 7 l" = UEL D L UBA 6 K 9 F!KBT C ) =
(115) U / ? = D / ? 654 & TMU
(116) 7 =
(117) U ? (( ( :? ((( S . . . 3L. 6 = 7 6. >@?Hb>BA.
(118) K 52 4 4 & U@H T'4 F _ 75K H ;M9!;:U84<H UBA S 6M4<I:U<TJK T U@H ; K FB4 TJK K 9 TJKB6 " 6 KK 7 9 K NK:9 U@H ;56'K'K86A 25AJ9U84!F HK ;M4-C'K K IM9 _M9<;'K T 6 K F84 SAV; L U SK ; K H_B7 C'K86 4!2 4 K8659!;:U84<H A ( ( SA 9!6'K 254 4 K T 6 K 5 2 4 4 @ U H M H V 9 7 @ U H 8 F ! 4 H ' I K H ; 8 U < 4 H .; lL ; L & IM 9!6 UB9<C K'A 9!6'K 6 K5A K86BI'K T 254!6U@H;' K8&6 HM9 " ;'K!7 4!659!69) I 9!6 U89<C K'A S 6 K'A KB6BI'KBT 254!6 IM9 6 U89</ C ( K'(A ( HM9V75K5A AV; 9!6B;:U@H U@; L K 9 L ^ L ! 9 6 K & ( U ( U@H'TJK'A KBT IM9 6 U89<C K'A 4!2U@; A IM9!6 UB9<H ;L ; U A 29N'_4V7H:S FV;:9!6 U84<U@HH 7 ;M9<H4 U ; _ K 9!;'4!6K'AU U@HMK'9AJA 6NK5=VAV? ;J6654U _FV;:;:U@U@I'H'KK 4!6 U K54<F!H'K K 4!2 F84 TJK'A L 9JA 9 AJU
(119) 7 S K86 S S U@H ;'KB6 259 F!K 9<H'T 9 C'K ; ;5K86 4 S ;:U
(120) 7 U 59<;:UB4<H ( 6 K F84<H'TMU@;:U84!HM9 :K 9 S 6 K'A AJUB4<H ; UV2 =V? UBA _ H TJK86 AV;M4 4 T 9<H'T _ A8KBT ;M4-;J6M9<H A 9!;'K 4 UJF :K 9 S 6 K'A A U84<H A ( 4 & K I5K863L ; K K H'KB659<;'KBTF848TJK UBA K5A A S 6 K ;J; ) ; 9<H & U@; N=V? L K ( U(0S 9!6 K8H ; K'A U!K'A 9!6 K 'A ) AV;5K!7 9<;:UJF89 ) U@H A K86 ;'KBT 9JA U@H F84!H I'K86B; =5LAV;J6:U@H ? ( ~ W E * A " H>= 9 ? H = 9 ? H>= 9 ? o " * ;'$K 9 ; & 6 UV;'KE= ; 7 S /@( F L F84<HJI'K86 ; =AL N3L ;B7 SW/ ? ? " * A " 9!6 659 ) = 9 L H>=
(121) AJU@H>= 9 M? ? 3L A UVH>= 9 M? L 9 = ? # ? " * ;'$K 9 ; & 6 UV;'KE= ; 7 S ( F L F84<HJI'K86 ; =AL N3L ;B7 S M? ? " * A " I ; U<2 =k_ *9 l L _ L FBAJF =k_ M?J? L & I $ F84JA =k_ M? L 9 / 9 6 F@;M9<H = & $ 2 = _L & ? ?" * ;'$K 9 ; & 6 UV;'KE= ; 7 S o ( F L F84<HJI'K86 ; =AL N3L ;B7 S o ? ? " . 6. 6. . . . . . . . . . . ! ~
(122) . 4 S ;:U@7 U K L F84 AV;L NL 254!6B;J6M9<HL ;'K:9 ; & 6 U@;'KL. . :=< > C. 6 = 7 6. . ] )( :
(123) . S 654 F<T K82 U@H'K TJK82 UVH'K <9 H 4 S K8659<;M4 6 :I U89 S 654 S KB6B;:U!K'A 9!H T 6_ K'A. ~ : G 0] S 654 F<T K82 U@H'K= S 654 S K86B;) / L S. E~ ~ W ( P . 654 S K86B;) L. ((( ?. S 654 S K86B;) ( U JTK5K8U@;2:U@H:K86U@H HM9V759 KL 65K4 9_MK86B9<;:;)U84!H4!6 4!69 5296 _4 65K9 F84<H:AV;J69_:FV; S S (. b,bdc ef3eg. ".
(124) E : ¼.
(125). . . . S 654 F!TJ65K824 U@F H5=1K9!6 TJK8A'2? U@H5K'A K 9 H 7T 9 S K S 654 F!K T_J6 K 4!2 ; K 254!687 I:U89 SS 654 S K86B;:U!K5A 9<(H (T ( 69_ K'" A ( N'4<H ; 659!69) ;M4 TJK82 UVH'KE=@? L U@; 9JA HM4 AJU<TJK K82 2 KMF@; AL 9!H T T548K'A HM4<; 9!2 2 K5FV; 92 _ H:FV;:U84<H A 'A _ F 9JA AJU@7 S UV2)L K IM9 L K:9 S 9<H TL TMU<2 23L A K86 U K'AL 9<H T ;'K'AV;5K ( + 654 S K86B;:U!K5A 254!6 ; K 4 S K8659!;M4!6 F89<H C'K TJK82 U@H5KBTU@H 9 TJK5F 9!659<; U@I'K & 9 ) _ AJU@H ; UBA K H 9<H F!KBT 254!659 F84<H AV; 69_:F@; " 254 659 = <IM9!6MA L = 2 =9!6 A ?EL F84<H T:? 6 K5A ? TJK82 U@H5K 6'K & 6 U@;J;:U@H 69_ K'AL & K86'K <IM9!6MA UBA 9 U AV;4!2 HM9<75K'AL K I'K8H ;_M9 ) K!7 ; ) 2 =19!6 A ? UBA ; K S 9<; ;5K86BH4<H & U F ; U A 96 _ K S & U C'K _ A KBT ( 2 7 _ AV; C'K ; K 92 _ H F@;:U84<H TJKB2 U@H'KBT C ) S 654'F<TJK82 UVH'K ( ; 7 _ AV; 4!2B;5K86BH C'K U@H 9<H U@H'K86 ; 254 687 F84<H T UBA 9<H =14 S ;:UB4<HM9 ( ? U@H5K86B; CM4 4 K 9<H :K 9 S 6'K'A AJU84!H 6 K'A UBA ; K TJK'AJU<6 KBT 6 K'A'_ ; 6 = K ? 4 S; K86MK 9<;M4!9!66 SA 65 48T _:9<; F!;5K'K8A 6BH; 7K 9<;::K 9 F S 6A K';A A KU84<H 4 6K865K'9!A ;MK4!69 F 9!6 ; _ U
(126) 7575K K H " ; A 9!H T = M/ ? ; K F8 4<H'T S 6'SK F84<H'TMU@;:U84!H UBA K IM9 _ S9<;'KBT ;M4 ;J96 _' K 9!2B;5K86'A _ C AV; U@; _ ;:UB4<H U@H IM9!6 A 9!6'K _ A8KBT 9JA 7 9!;:F U@H 9!6 _B7MK H ; A & UJF F89<H ;M6 9 -'K K HM9V9<75H )K5A TJ4JKBAJ2AJU@U@CH'KBT S K IM9 _'K ( 6 K 'A _ C:AV;:U@; _J;:U84<H A 9!6 K ; K H T'4<H'K 254!6 9 S654J4 A AF84<U@CH AV;K 659A'_:U@HF 9<IMH 9 :K _'9 K'6'A K'( A AJU84!H 9 ;M4 C'K 4!2 9 F!K86B; 9 U@H ; ) K ; 9<H T 4 6 9<I'K 9 U@I'K H 654 K8S6B;) 9JA TJK82 U@H5KBTU@H ; K 9 A A'_B75K 25S9 FJU U@;) L $ ; K F84<H T :K 9 S 6 SK'A AJSUB4<H 7 _ SAV; F84<HJ;M9 U@H9 6 K 9<; U84<H4!2 ; K 254!68 7 " ; U A != 9L ; ? & K86'K ; K UBA 92 _ H F@;:U84<H UBA U@I5K H U@H 9 2 6 KJK KBT 2M4!687 H ) 4<; KB6 F84!H TMU@;:UB4<H A F89<H C'K U@H ;J6M4 T _:F!K TL _ AJU@H S 654 F
(127) 7 9 -'K 'A ) H ;M9 9 ( + 654 K86B;:U!K5A F89<H 9 AB4 C'K TJK82 U@H5KBTU@H 9 S 654'F!KBT _J6M9 & 9 ) I:U89 9 AV;M9<H T59!6JT 7 9 S S K S 6M4 F!KBT_ 6 K " S4!6M2 4 HMF!KB9V7MT _K 6 K S U F H ; U 9<; C'F8K9JA KF89 ; KBK T 4 S;MK84 6MK 9<;MIM4!9 6 _M9<UB;'A K 9 ; ABK4 TJ9!6K82:_BU@75H'KBK HT ;:CA ) 9 S 654 F!KB9T _J6 K ( ; KB6 & UBA K ,S; &K 254 &4 & UVH S 654 S K86B ;:U!K5A 9!6 K _ H TJK86 AV;M4 4 T " 6 K 75K!7JC'KB6 6 K 4 S K86M9<;M4!6 9JA ; K 6 K!7MK!7JC'K86 4 S ;:U84<H 9<H T 7 _ AV; 9<I5K / 9!6 _ 75K H ; ( _C:H UVHM9!969!)69) 6 6 K K 4 S 4 K865K8659<;M9!;M4 64!6 UBAUBA _ HC:9!U@96HM) 9!6) ( S 7 _:AV; C'K 4!2 ; K U@I5K H ; ) S K ;; )) S KK ; ; )6 L ; K L 9!6 _BL ;J75H K HJ;> =A ?9 F 9 FJS F84!6J TM UVH / ;M4 (; (( UBA UBAV; 6 K9!6 4 _ 75K865K H9<;;M4 A 6 7 _: 7 _AV; AV; C'K 9<I'4 2K ;H K9!6 _BU@7MI5K K HH ; ;A ) S K 9 JAJAB4 F U89!;:U@I'K 6 K 4 S K8659!;M( 4!6 UBA S9JA AB4 FJU89<;:U@I5K = H 9!6) ? L AB4 2 = 9L 2>=k)L :?J? 2 =2 = 9nL ) ? L :? 2 = 9L )L :? ( L A 4 2 = 9 nL ) ? 2>k= )L 9 ? ( 6 F84<7K 7 _ 9!;M6 9!;:_B75U@I'K HJK ; A 6 KU 4 S C'K865K 9!;M4!6J4!6TJKB62 KBT UBA ;M4F84V7J 7_M_ 9!;M659<9!;H ;'U@I'K K K _ H:U _'K H'K5A A ( & 9<HJ;:UB'A )B7J75K ;J6 UJF 6 K 4 S KB659<;M4!6 2UBA 9<H ;:UBA )B7 75K ; 6 U FEL A 4 2 = 9 nL ) ? 2 k= )L 9 ? 9<H'T 2 = 9L 9 ? l ( U<U@;T K!7 UBS A 4<;5F8K 4<HH ; A U< TJ6K86 K 9J4A S K89 65_9<;MH 4 9!696 )UB4A K8U<6MT K!9<7;M4! S6 4!;'K H ;L AB4 2>= 2 = 9 ?J? 9L S . . . . . . (. . >@?Hb>BA.
(128) . HM4 S 4 & K86 6 K 4 S K8659!;M4!6 6 KBT_ F!K'A S 4 & KB6MA AB4 L 2 = 9L 9 ? 2 = 9 ? 'A _ F 9JA U@H 9<H T $ 4!6 CM4 4 K 9<H4 S K86M9<;M4!6MA UVH'K 9!6 'KB2 U@H'K ; K 4 S KB659<;M4!6 9JA C'K5UVH U@H'K 9 63L U ( K (" = / 9 C L (( ( ? / =19 L ((( ? = CL ((( ? 9<H T = o L ((( ? o = / L ((( ? 254 6 9< H )F84!H AV;M9<HJ; A / L 9<H T o ( KB654 9 'KB2 U@H'K ; K K86M4 ;M4 C'K 9L AB4 UV2 9<H) 9!6 _B75K H ; U A 9 ; K H ; K 6 K5'A _ ; UBA 9 ( U<T K H ;:U@ ; ) 9 6 K :K 9 S 6 K'A A U84<H 9 UBA ;M4 C'K F84<H A U<TJK86 K T ; K K82B; 9<H T 6 U ; U<T K H ;:U@ ; ) 4!2 ; K 4 S K8659<;M4 6 ( U@HJI'K86MA K 'K82:U@H'K ; K U@H I'KB6MA K K82B; AJU<TJK 9<H'T 6:U ; AJU<TJK_ HM9 69) 4 S K8659<;M4 6 ;M4-C'K ; K 4 S KB659<;M4!6 U( SAB44 & 2K86 = 9 L 9 ? 'K82 2U@H5= K = 9; L K ? S? 4 L & K8K 6;:F C:U@HM9 96 )4 S K8659!;M4!6 ;M4 C'K ; K 4 S K8659<; 4!6 L 4S & K8654!2 'K82:U@H'K ; K ; UBA (C:(U@( H 9!96 )4 S K86M9<;M4!6 UBA ; K S 4 & KB6 4 2 9<H 4 S K8659<;M4 6 TJKB6 U@IM9<; U@I'K ; L 6 K 4 K8659<;M4 6 UBA 9 TJK86 UVIM9<;:U@I5K 4 K8659!;M4!6 254!6 ; K 7 _ ;:U S U F89<;:UV(I'( K 4 S KB659<;MS4!6>=A ? ; L ((( L AB4 UV2 / L S 9 6 K FB4<H AV;M9!H ;L U ( K ( T'4-HM4!;F84!H ;M9 U@H4<H5K 4!2 ; K TJK86:U@IM9<;:UVI'K IM9!6 UB9<C K " = / 9 C L (( ( ? / =19 L ((( ? = CL ((( ? 9<H T = / L ((( ? l & U K 254!6 ; K 7 _ ; U S U FB9<;:U@I'K4 S K8659!;M4!6 =A'? = 9 ; CL ? 9 ; = CL ? =19 L ? ; C AJFB9 9!6 S 65 4 T 6 (( K ( 4 S K8659<;M4 6 UBA 7 U 9'(KB(T ( & U@; AJF89 (9!( 6 S 654 9T _:F@; AL A 4 " 2 = 9 L C ? 2 =19>L C ? 254!6 9<H) F84<H A<;M9<H ;4!6 AJF89 9!6 :K 9 S 9<H T L (( ( 6 K 4 S K8659<;M4 6 K82B; 9<H T 6 U ; $K 9 S 9<H T KBT 4<I'K86 ; K 4 S K8659<;M4 6 =A ? L ((( L AB4 2 = (( ( L =k) L :? L ( (( ? = 2 = ((( L L ((( ?EL 2 = (( ( Ln)L ( (( ? ? HM4!;'K ; 9<; 9!6 _ 75K H ; A 4!2 9!6 K U@H I'K86 ;'KBT ( :K 9 S 9<H T'4!H L ((( 6 K 4 S K86M9<;M4!6 K82 ; 9<H'T 6 U ; :K 9 S 9!H TJKBT 4<I'KB6 ; K 4 S K8659<;M4 6 =A ? L ((( L AB4 2 = (( ( L k= ) L :? L ( (( ? = 2 = ((( L L ((( ?EL 2 = (( ( nL )L ( (( ? ? HM4!;'K ; 9<; 9!6 _ 75K H ; A 4!2 9!6 K U@H I'K86 ;'KBT K:9 S 9!H T=@? UBA-7 9 S 4<H 9!6 _B75K HJ; A ( I'KB6BCM4JA KMF89 6 K 4 S K8659!;M4!6 :K 9'K5'F _ ;'K'A 9 S 6 U@H ; = S 654'F@HM9V75K=19!6 A'? "? 4<H K 9'F F89 L 254!6 7 4 9T _ 9!6 TJK C _ U@H S _J6 S 4 A K ( . . . . . . . ! ~
(129) . TJK82 U@H5K L S 56 4 F
(130) 7:9 -'K L 7:AB4. $. >< 8 . ] )( :
(131) . 254!687 9!; 254!687:9<;9 A K ; $ 4 UJF :K 9 S 6 K5A AJU84<H4!2 U@H JK _M9 U@;:U!K5A. b,bdc ef3eg.
(132) ~ : G 0] . . 254!6B7 9<;>= K8H A ? 254!6B7 9<;>= K 8H AL 6'K 9 ? E~ ~ W ( P K 8H:A U84<H AL K5UV; K86 9 A K ; 4!2 K_M9<;:UB4<H 94!6 'A )9 AV;5CMK!4 7 4 K'4!29<H 6 K'K:99 6 K5K A _MAJ9<U8;4<H 4!2 K _ 9<;:U84<H:A 6K9 9 <H 4 S ; U84<HM 9 TMU<6 SK5F@;:UVI'K ;M4 9JA A'_B7MK 9 I ( 9!6 U89<C K'A 9!6 K 6 K 9 (
(133). E : ¼. UBA 29_ H F@;:U84<H 254 687 9<;9 A K ; 4!2 UVH JK _ 9 U@;:U K'A 4!6 9 4 U F F84V7JC U@HM9<;:UB4<H 4!2 ; K'A K 9<H T 9<; ;5K!7 S ; ;M4 6 KBT_ F!K ; K!7 ;M4 4<C ;M9 UVH 9 HM4!68 7:9 254!687 ( 6 K 2 U@HM9 254 687 UBA 9 ;54!6 = ;59<H T= (( ( ? ? K:9 S 6 K'A AJUB4<HL U ( K ( ; K _JH:U84<H 4!2F84<H'D 4!H:F@;:U84!H 4!2 K 9_M9<;:U84!H AL _ H K'A A _M9<HJ;:UV2 U FB9<;M4!6MA 4 F F _J6 ( 6 K 6 K 9 TMUV6'K5F@;:U@I5K 9JA 'A _B7MK'A ; 9<; 9 IM9!6 UB9<C K'A 9 6 K 6'K 9 ( H K _M9 U@;:U!K'A & U@; F84V7 S :K 9 IM9 _'K'A 9!6 K 259 A8K 6 K 254 4 & U@H ;J6M9<HJ254!6B7 9<;:U84!H A 9!6 K S K86J254!6875K T " HH JK _M_9 9 U@;:U@;:U!K5U K'A A 9!69!6K K K:9 S_ ;9!H TJU@HKBT 9-4<I'HMKB4 6687 I'9 KMF@;M254!4!6M6B7A L 9<H'U T K 7:9<;J6 U FJU!K'A S ( (" K l L K * l L K l L l * K L K 9 l L K *9 l 9<H'T ; K AJU H4!2 K UBA 6 KBT _:F KBT = I:U89 FBA H ? & K H S 4JA AJUVC K ( FBA H ( 4 4 66 :KF894<7 S6 K' :KA 9 A U8:K4<H9 SA 6 K'AUV;A U84<H 9 A TJ;K H K4V7 AJU@HMU 9!;MH 4!6 UBA ; _ H'K TJK8F86M4<H:AV; AV;J4 654 T9 UVH 9J; A ;254!6 9<; ; K ; K TJK8SHM4V7 U@H 9<;M4!6 & UBA HM4<; K86M4 UBA U@H ; 654 T_:F KBT 6. . . . . . _J6 HJUVHI AJU ; H _BK 7 l F84V7 S J_ ;Ml 9< ;:U84!HL & K 7 _ 9<H T 6 K'AV; 4!6 K U@; " A 4 T IM9 _5K 9<;. (. AV;A K ; " ; K K H T3L U@H 4!6JT K86 ;M4 K ;FB4 K86 K8H ; AJU H IM9 _5K'A 4 UJF K:9 S 6 K'A A U84<H A 9!6'K AJU@7 S UV2:U!KBT ( 6 ^K )9!6 K C_:U T KBT 2 654V7 ; K 254 4 & U@H S 6 U@7 9!69)4 S KB659<;M75K'4!69<HA A " 9 9<H T ) ;59<H T = 9Ln) ? ;54!6 = 9Ln) ? 75K'9<H A "" 9 4!,6 ) ; K:9:U AV; A = I L 9 ? 75K'9<H A " ; K86 K :K 9:UBA<; A IM9!6 U89!C KE=A'? IL 2M4!6 & U F 9U A ;J69_5K ; 254!6M9 = I L 9 ? 75K'9<H A " 254 6 9 IM9 6 U89<C KE=A ? IL 9 UBA-; 96 _'K 9<H T ; K 254 4 & U@H A KMF84<H T'9 96 ) 4 S K86M9<;M4!6MA L & U F 9!6 K 6 KB9T _:F!KBT " ;BHM4!; ; U@7 S U!K5A ; UV2 2 ;BHM4!6 ;BHM9!H T ;=9M4!6 T ) 9!6 K U@H JK _M9 U@;:U!K5A 4! H6 ;; K5K A CMK 4 44 S KK8659<H 9!;M4!F86M4<H:A AV;M9 9<H 9<;H 259 A K 4!6 ;J96 _'K L 4!6 'A _ C'$K 9 S 6 K'AJAJU84<H A 4!2 ; K'A K L U K I B U A ; K M H V 9 M 7 K ! 4 2 9 IM9!6 U89!C K 4!6 9 A K ; 4!2 IM9!6 UB9<C KE=
(134) A ? ( & ; ;59!H T=@? 9<H /T ;54!6>=@? 9!6 K F84V7 7 _J;M9<;:U@I5K 4 S K8659!;M4!6MA H ; U A F84!H ;':K 9 >@?Hb>BA.
(135) K I 9 _M9<;5KBT U@H 9<H) 4!6JTJK86L F84!H ;J659!6) ;M4-; K 7 9 S K 9<H T $ 4!6 4 S K8659!;M4!6MA ( U@H A K 4!;6JT K8UB6 A ;M;M94--'C'K HK 9JF84VA 7 9 9<;:;59!U@CH T K 4 S K8U@;659!;M4!AB64 I'9<HKET =@? 9 4 _ A ;K_'_ ;K H:A F K 9JA 9 ;54!6 4 S K86M9<;M4!6 S & S N';4<H UV2>T U@=
(136) ;:F84<U8H4<HT39 L K:9:K 9 S6 6'K'UV2A AJ;JU864!H_'K 9!L 6 KK:9 AJ6 U
(137) 7 SUV2 UV252 9U!KBT3A K L ? _ AJU@H ; K 4 S KB659<;M4!6 " S _B75 K HJ; A U@H ;5K86 S; UV2 4 K8659!;M4!6 6 K 7 _ : ; U ! 9 6 S " ; U<2 =
(138) F84<H'T / L :K 9 S 6 / L F84<H'T L :K 9 S 6 L F84!H T o L K:9 S 6 o ((( K:9 S 6 lM? UBA 6 KBT _ F!KBT ;M4 ; K o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l. /. . 6 =; ? 6. " 6. 6 K5A 4 T _JH:F@;:U84!H. ;/. $ ". . . l. ;. . $ /. 9<;>= ; ? " 9<;_ 659<;:U84!H _ H:F@; U84<H " ; / 4V75K H'K'A<;'KBTF84<H A<;J69_:F@; U84<H A & UV; 6 K 9<; 9 = C FJ? 75K'9<H A =19 C ? 9<H T 9 * = C * FJ? 75K'9<H A =19 * C ? 9<H T 9 * = C 9<H T FJ? 75K'9<H A =19 * C ? 9<H T T ; UV2>=
(139) FEL 9 L C ?-75K 9<H:A ; U<2 =
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lM? 22 * ll 9 * ;; $K$K 9:9:UBUBAVAV;; AA == ;;L0 ; 2 lM? 2 9 l 9 * ; $K 9:UBAV; A = ;L0 0 L ; 2 / lM? 9 * . . b,bdc ef3eg. . . ".
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