Singularités de frontière et conditions limites absorbantes : le problème du coin
Texte intégral
(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Singularit´es de fronti`ere et conditions limites absorbantes : le probl`eme du coin Olivier Vacus. N ˚ 2851 Mars 1996 ` THEME 4. ISSN 0249-6399. apport de recherche.
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(49) KSKSA¢X ` >_e RUT_RUKSRZyUHNJLA
(50) BCA TO xyUJ e A TOVKSAXO e RZHXVX^J_HSZMPTOYAX 3 M$W e A
(51) BCH A ? e AiAX1O [ JLA M ? EKMHST MPBxA e yZA e _d MPO e H` RZKS]A O AMPT k RZlA e OXJLH RUTOfBCA TªAf JLTLAA OYJ [ AO e
(52) A? X/`bRZBCWLK A
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(59) TLA e6M? _HSA T KÎMPTMPKS]_X^A$BMPO > A BMPOQH3JLA [ A KSA J e W e RZLK A? BA WxM e A cA BCWLKIAVJLTLA\`bRUT [ HSOQHSRUT [ A"KNM²»R e BA8 n _ l Ts Oiqn K-p A c)r HNX^OQnA Tx} `bA\r A On KJLTLHN`bHSO_A n. . n. . A`H<²MPHIO SH KNX [ A BCRUTO e A eW RZLK A
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(64) TM KIJLHLBCHNX A
(65) T$R3A JL e AVKMiOQA` > TLH3JLA [ AXA K
(66) A BCA TOXlxT_HX OYRUJ¢gYRUJ e X³WxRZJ e KIA W e RZLK A
(67) ? BCA [ J`bRZHSTM 3A` [ AXa`bRUT [ HSOYHIRUTxXMxX^R e xMT)OQAX [ JX^A`bRZT [ R e [ e A r P rbDxA O r
(68) oU KXbÎMWLWLJLHIAEWxRZJ e `bA KNMiX^J e K-A c)HNX^OQA Tx`bA [ QA TLA e yUHSA¢X [ R e [ e A [ RZTx`iX1JLWVA e HSA J e M? K-R e [ e A [ A¢X`bRZT [ HSOQHSRZTxX 3JLHVX1RUTO [ A¢ ` e RZHXYXQMPTOYAX"A TOQA BCWxX³GAXO e M ZMPJLc&X1RUTO MUXQX^'A COQA` > TLH3JLAX A O"TLRZJxXTÄA T ²»A e RZTxX3JÄJ_TLA e A ? 3A$W e A X^A
(69) T)OMPOYHIRUT MPJO e RZHX^H A ? BCA ` > MPWLHIO e A ¨ T)xT KIA`
(70) MUX [ A¢XE`bRZT [ HIOYHSRZTxX [ R e [ e A A KSA aAi A TW e A¢ X^A Tx`A [ A6`bRUHITxXEM§A O_A" O e MPHIOLA WxM e e MPT`bHX RUKIKSHITL R BMPHXjWlRZJ e J_TLA²»R e BJ_KMPOQHSRZT [ JW e RU_K A ? BCA\K
(71) A y A ? e A
(72) BCA TO [ H 5EA e A TOYA 8 [ H e A¢`bOYA BA T)O HSTxX1WLH e A A [ J [ RUBMHSTLA [ AXA JMPOYHIRUTxXWM e Mc)HNMPKIAX KRUWªA e M ¡ OYA J e [ AKM`bRUT [ HSOQHSRUT [ ACxR e [ XbA cW e HIBCA M? KÎMPH [ A [ JLT_A²MPBCHIKSKIA [ A 3 ²»RUTx`bOQHSRZTxX MPJLcHSKIHMH e A¢UX 8 . .
(73). ~ m n y l n n . t _ q w x YrZSr n r nqp j w z n p . y ¥ L¥ ¥ r n y n y y l M 3A` y l y l j w. ERUJX BCA
(74) T)OQHSRUT_TLRUTxXa`bAXVO nqe M¢p yZMJLz c MZnUXY}X1A'y [ H 5A e A T)OX [ AXVT RU O e { AX WxRUJ r e [ A JLc e MPHX1RUTxX 3 M(W e A BCH A ? e A `UAX^O3JLA RZKSKIHSTLR A T `bRZTxX^H [ A e MPTO [ A¢XX1RUKSJ_OYHSRZTxXWxM e OQH`bJLKIH A ? e AX M [ A OQA e BCHITVA$ KSAW e A BHSA e [ AXgYA J_c [ A`bRUT [ HSOYHIRUTxX [ A`bRUHITxXWxRUJ e [ AX 43 [ R e [ e A A KSA
(75) aA `bRZT [ HIOYHSRZTxXjJLH KSJLHÄRZT)OVWxA e BCHXJLTLA"HSBWLK
(76) A BAT)OMPOYHIRUTA
(77) 5 A`bOQHS3A3 3 MX^A`bRZT [ A `UA¢X^O\J_ATLRX [ A
(78) JLcMWLW e R` > A¢X(A OMPTO [ H 5 A e A
(79) T)OQAX T_RUJxX\X^RUBBCAXEWxM e 3A TJxX M ? [ AX e A X1JLKSOMPOXO > A R e H3JLAX [ H 5 A e A
(80) T)OX 3RUH e AB
(81) A BA WM e ` > MPTx`A `bRUBCW_K A BCA
(82) T3OMPH e AX8. TLRUJX$M¢3RZTxXJ_T e A X^JLKIOMO [ A c)HNX^OQA Tx`bA6JLHKIJLHBMPTx3JLA HSKMJLT e A¢ X^JLKIOMPO [ J_TLH`bHIO_A J_HT_RUJxXi²MPHSO [ A ²MPJLO
(83) < jRUJxXi3A eQe RUTX MC? KNMT [ A`bA e MWLWxR e O6J_A KXiKSHIA TxXEWxA J_3A T)O A cHX^OQA e A
(84) T)O e A"TLR3X [ A J_cCW e RZLK A
(85) ? BCAXb ERZJxX$M 3RUTxXA
(86) T&`bA3JLHVTLRZJxX$`bRUT`bA e T_A`bRUTX^A e aA JLTLA²»R e BJLKNMPOYHIRUTO e M [ HSOQHSRUT¡ ? A
(87) OYA T [ e A"KSAX e A X^J_KSOMOXVA cHX^OMPTOXVMJ ` MZX [ A¢XE`bRZT [ HIOYHSRZTxX [ R e [ e A TLA KIKSA"A Oj` > A e ` > A M& Ã<à ͪ «ÝbÛÙ.
(88) u. FQ F. J_A K`bRZTx3JLA `bA$3JLH MC? TLRZO e A`RUTLTxMHXQXYMPT`bA e AX^OMPHIO M? ²MPH e A3 ERX e A X^J_KSOMOXiX1RUTO"MPJ TLRUB e A [ A"O e RUHXVA O M? ` > MU`JLTX^A e M`bRZTxXYMZ` e A" JLT` > MPW_HSO e A [ A\`bA e MWLWxR e O MPxR e [ RUT [ A BCRZT)O e AK-A
(89) c)HNX^OYA
(90) Tx`bA [ J_TLAX1RUKIJLOYHIRUT HST)xT_HSBCA TO e A
(91) yUJLKIH A ? e A MPJ eW RZLK A
(92) ? BCA [ J`bRUHITCWxRUJ e J_TLAE²MPBHSKSKIA [ A 43 A
(93) TLyUKIRUxMT)OVKIAX`bRUT [ HSOYHIRUTxXHNXYX1JLAX [ AX MPWLW e Rc)HIBMPOQHSRZTxX [ A d M [ A3 d RUJ e `bA²MH e A RZT(y A TLAxe MPKIHX1AKNM [ A BCRZTxX^O e MOYHSRZT [ Ao [ MPTX KIA`
(94) MUX [ JX^A`bRZT [ R e [ e A3 d JLHNXY3JÄJLT_AOYA
(95) KSKSA6X^RZKSJLOQHSRUT A
(96) c)HNX^OYA A KIKSA [ RUTLT_AJLT X1A TxX M ? [ A¢X A
(97) TLA e yZHSAX [ R e [ e A A KSA
(98) aAj M [ MPWLO_A AMPJCW e RULK A ? BCA [ J`bRZHSTÄ d KIJxXfW e A `HXA
(99) BCA TO RUTA c > HSxA e M [ AXA
(100) TLA e yZHSAX [ R e [ e A"o ¨ rjWxRUJ e [ A¢X`bRZT [ HSOQHSRZTxX [ AlR e [ X [ R e [ e A ¨ LhjT A OYA
(101) T [C[ RZTx`iMPJ` MZX y A TªA e MKÄKMW r e A BCH e? AiWM e OQHSA [ AX e A X1JLKSOMPOX RZTLy¦(R3RG > A A
(102) TÄLs MHXTLRZO e A"LJ_OVTÄAX1O WxMUX$KM `RUTxX1O e J`bOYHIRUT [ QA K
(103) A
(104) BCA TOX xT_HUX 8`bA e A X1JLKSOMPOT_RUJxXX^A e O [ MPxR e [ M ? MZXYX^J e A e K-JLTLH`HSO_A [ A"KMX^RZKSJLOQHSRZT e A yUJ_KSH A? e A3 A$TÄAX^O JLA [ MPTxXiKM [ A e T_H A ? e AWxM e OYHIAJ@RUT MPxR e [ AK-QA WLHST_A JxX^A6J_AX^OQHSRUT [ AX [ `bRUT HSOQHSRUTX [ A`bRUHITÄÄ ERZJxXETLRZJxXHIT)OQA e AXQX^RZTxXiMPJ_c `bRZT [ HSOQHSRZTxXC£ [ A [ JLHSOQAXEWxM e `RUB¡ WxMPOQHSLHIKSHIOLA ¤ `bRUT [ HSOQHSRUTX3JÄRUT XYMHSO A O e A$aA e H A
(105) AX WM e KIAXiX1RUKSJ_OYHSRZTxXX1J XYMPBBCA TO e A yZJLKSH A ? e A¢Xb ERZJxX [ A OQA e BHSTLRZTxXKSA J e TLRZB e AA c_MU`bOQAA OTLRUJX [ RUT_TLRUTxXCJLT MKSyZRP¡ e HIO > BCA\3JLHfWxA e BCA O [ A$KIAX A
(106) c)WLKIH`bHIOYA e
(107) `bA3JLA\TLRUJxXiBCRZT)O e RZTxXEMCO e M 3A e Xj3JLA K3JLAX A cA BCWLKIAXb ET W e RZy e MPBCBCA\s d 3 ¨ e A MKSHNXYMPTO`bA OYOQARZWVA e MOYHIRUT AX^OE²»RZJ e T_H<A T MT)¡ TLA cA3. ÁÂ ÃÄÁÅ.
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(110) & $'& . e A? XaM¢3RZH e W e A `HXA JLA
(111) KSKSA¢X 43 TLRUJXEMKSKSRZTxXCA OQJ [ HSA e T_RUJxX [ A xTLHXQX^RZTxX [ MPTxX `bA OQOYAWxM e OYHSATLRUO e ACW e RULK A ? BCA$O1]WlAA OTLRZJxXBCRZT)O e RUTX3JLACKNM [ A
(112) BCRUTxX1O e MPOYHIRUT [ A K-A c)HNX^OQA Tx`bA [ A\X^RZKSJLOQHSRUTX e A yUJLKIH A? e AXA¢X^O²MU`HSKSA Mv? y A TVA e MPKSHNX^A e EW. P! $ ERZJxX [ A X^HIyUTLRZTxXWxM e k KM 43 [ R e [ e A ¨ WM e g7k hi KRZWVA e MOYA J e [ A`A OYOQA [ `bRUT HSOQHSRUTWlRZJ e JLTCxR e [[ AiTLR e BMKSA A
(113) OWM e\g7k hi j KRUWªA e MOYA J e [ A`bA OYOQAi`RUT [ HIOYHIRUT WxRUJ e J_T xR e [[ AT_R e BMPKSA d M e `bRUBBCR [ HSO_A KM [ A BRUTxX1O e MOYHIRUTJ_AiTLRUJXEMKSKSRZTxX [ RZTLTLA e [ MTxXj`bA"` > MPWLHIO e A AX^O `bA KIKSA [ JLT6` MUXÄWxM e OYHN`bJLKSHIA e ©TLRUJxX/MPKIKSRZTxX<`RUTxX1H [ A e A e [ MTxX<KMjX^J_HSOYA [ Aª`bA OQOYAfWxM e OQHSA KSAX 4 3 HNXYX^J_AX [ AXVMWLW e RcHSBMOYHIRUTxX [ A d M [ A k MPWLWxA KIRUTxXjJ_AiK-RUWªA e MPOQA J e [ A"`AX 3 mWxA JLOjX1A [ A xTLH e WxM eje A¢ ` `bJ e A Tx`bA 8 4 .
(114). . -oSr . g hi j l n x. n _ n p r n r g7hi j l n y n y_ o n y y n p y r nqpWn z Un } y g k hi j l n g khi j Nx r n y g k hi j ¥ ¨ D y n p z n} y. . . . Ã<à ͪ «ÝbÛÙ. . o.
(115) p. FQ F. A O [ A"BMTLH A? e A A 3JLHSZMKSA TOYA . -oÎo . g hi l n x. n. . . nqp r n} rn 7 g hi l n y n y y_ o y qn p y r nqpWnU} z n r y g hi k k hi Ox D n _ y g k hi ¥ ¨ l n g y nqp z n y . o. k PM WLWxA KIRUTxXVX1J e OQRUJLO3JLA [ MPTxXj`bA"`
(116) MUX WxRZJ e KIAXX1RUKIJLOYHIRUTxX e A yZJLKSH A ? e A¢X [ A"K-QA 3JxM¢¡ OYHIRUT [ AXRUT [ AX RZT M$KSAXA J_HSZMPKIA Tx`bAXaX^JLHIZMPTOYAXU8 k k r r h i j g -oÎ g k hi k m n A O k o n p r nnU} t o k m n nqp r nn _ t A OYOQA"W e RZW e H
(117) A O_A" AX1OjMPJ ` J e [ A"TLRUO e A [ A BCRZTxX^O e MOYHSRZTÄ d RZJ e OMPTO T_RUJxXTLA(WxA TX^RUTX WxMZX3JLA `bA OQOYA > ])WxRUO >ÄA? X1AX1RUHSO e AX^O e H`OYHS3A ¨ T A
(118) 5 A O HIK<²MPJLO [ ÎMxR e [ TLRUOQA e JLAK-A cOYA TxX1HSRZT [ J e A X^J_KSOMO\X^A e MPHSO [ H e A`OYAWxRZJ e KIAX RUWªA e MPOQA J e X [ JO1])WxA 8 -oD . . . . g7k hi j u . k. m#n. n _ t. wqx n p r { n . . k. . . . M 3A` . 1 ¥ . . . {. ¨ TxX1JLHSOQA HSK²MJLO e A 3A TLH e MPJLc&`RUT [ HIOYHIRUTxX [ AX^OMPLHIKSHIOLA [ A¢X 43 X^J e JLT&xR e [ [ e RZHSO
(119) 8G3HÄRUT `bRUTxX1H [ A? e AiJLTRUWªA e MPOQA J e [ R e [ e A ¨ [ "A KM²»R e BCA k k u ~ g k h i j l mn v v n y u n y t n_ t m n y n y t n m n y v q w x v w H x O w v n p r s n n p y\z|{ nU} y z nqp nU} y n p y\z|{ nU} y. MPKIR e X `RUBCBCA/TLRZJxX KÎM 3RUTX e MPW_WlA
(120) K A A T"HSTO e R [ Jx`bOQHSRUT `bA OÄRUWªA e MOYA J e AX1O/`bA KSJ_H [ JLTLA 3 X1OMP_KSA\X^HÄA OjX1A JLKIA BCA TOaX^H 4 x ¢¡ ¡ ¡N k£ r y ¦§©¨ { v\¤ { =¥ r { 1 -oÎq k ~ v v vWwqx r s z|{ Á ÃÄÁÅ.
(121)
(122) . 3G H K-RUT`bRUTX^H [ A ? e A"JLTOYA
(123) KÄRUWªA e MPOQA J e HIK8AX1OVWxR3XYX1HSLKIA [ A"BCRUTO e A e 3JÄHIK8AX1OA 3JLH ¡ ZMPKSA
(124) T)OVWxRUJ e KIAXVX^RZKSJLOQHSRUTX e A yUJLKIH A? e AX M ? u m n y n g k hi j u m n o n y y y n y_ t _ nqp r n _ t nqp y r -oÎu r nqpWn r n M 3A` 1 WxRZJ e OQRUJLO ¥ 1 WxRUJ e OYRZJLy O A e A X^JLKIOMOVAX^OA OMPLKIH8A Oj`RUBCBCA
(125) T)O_A [ MPTxXVK- MPTLT_A c)A K e AX1OYA e MPHSOWlRZJ e 3JLA TLRZO e A O e M ZMPHIK"X^RZHSO`bRZBCWLKSA
(126) O 3RZH e KNM [ A BRUTxX1O e MOYHIRUT W e RZWxR3XA
(127) A`bH ¡ [ AXQX^RZJxX M? BCA T_A e KQA OQJ [ A6X^J e J_T [ RZBMPHITLAxR e TªA [ J W e RULK A ? BCA [ A MPJx` > ]CWxRUJ e KSAXRZWVA e MPOYA
(128) J e X [ JO1])WxA 8 -o w o n y n y y y n y_ _ r n y ERUJX TLA"KIAE²»A e RZTxXVWxMUXVHn `bHp y r nqpWn r . . . . . . . . . . . . .
(129) ' $#( ) ! `. g k h i j l . . . g k h i l . . o Sr N G q KC ERZJxX8TÄ MPKSKIRUTxXÄWxMZX<`bRZTxX^H [ A e A e [ A [ RUBMHSTLA [ MPTxX/X^RZT$A TxX^A
(130) BLKIA BMHXÄX1A JLKSA
(131) BCA TO KSA\`bRZHSTX^JLWªA e HIA J e [ e RUHSO [ JLT [ RZBMPHITLA3 d KIJxX W e A `bHNXA BA T)O [ A X^HIyUTLA"KNM3JxM e O [ A
(132). Ã<à ͪ «ÝbÛÙ. .
(133) r. FQ F. WLKMT } C¥ _ KNM [ A BCH ¡ [ e RUHSOQA } l ¥ _ A O j KM [ A BCH ¡ [ e RUHIOYA C¥ _ l A O X1RUTO e AX^WxA`OYHS3A
(134) BCA T3O [ A$TLR e BMKSAX1R e OMPTOYA A O x KIAX }3A`bOQA J e X [ A"xMUX1A ¨ T)xT j KIAiWxRUHIT)O AX1OEW_KMU` A Mv ? KR e HSyZHSTLA EW e A? XKSAX e MPWLWxA KNXA OVKSAXW e A¢ `bHX1HSRUTXVMPWLWxR e O_A XjMPJW e A BCHIA e WxM e MPy e MPW > A KIAiW e RP¡ ? A OQJ [ HSA e AX1OVKSA\X^JLHIZMPTO#8 LK A
(135) ? BCA M& l X1J e n y k n r p y z X1J e j n _ t l ok m n r nqp=r n k -oÎp X1J e n t l o k m n nqp r n} X1J e ¥ _ ¥ l l } p X1J e n ¥_ ¥ l l x } p n p hjT X^JLWLWxRX^AJ_A$KSAX [ RZTLTVA AX"HSTLHIOYHNMPKSA¢X A O x X1RUTO M? X^JLW_WlR e OX1O e HN`bOYA
(136) BCA TO HSTx`KSJxX [ MPTX A O X^J XYMBCBCA TO e A yUJ_KSH A? e AX d RUJ e `bA KNM RZT$W e A T [ ¥ x
(137) 3 MPOYOQA TOYHSRZT [ J KIA`bOQA J e AX1OMPOQOYH e A A X1J e KÎMPX^A Tx`A [ MPTXKM [ Ab xTLHIOYHSRZT [ A `A W e A
(138) BCHSA e W e RULK A ? BCA [ A\`bRZT [ HIOYHSRZTxXVX^WªA `bH lJLA¢XVMPJ `RUHST@ . . . . . . . . . . . . . . . !
(139) V 3 M [ A BCRUTX^O e MPOQHSRUT6J_ATLRZJxXfW e A X1A TOYRUTX<H`bH3y A TªA e MPKIHX^AaKMEW e A JL3Aa3JLAKRZT$WlA
(140) JLO O e RUJL3A e [ MPTX"oP WxRUJ e KIA"` MUX xG3HÄ`AiO e M¢ZMHSKxTÄÎMWMUXCA O_AE A
(141) 5 A`OYJªAi W_KSJxXO RUO `UA¢X^OX^J e OYRUJ_OCWxM e `bA 3JLA X1A JLK y HSKjTÄ M¢y ZMHSOJLAWxA J [ HIT)O_A e A
(142) O =Äe RZW [ A e A¢ X^JLKIOMPOX BMPTJxMHSA T#O 8JLTLH`HSO_A [ AXjX^RZKSJLOQHSRZTxX A OjX1J e OQRUJLO`bRZT [ HSOQHSRZTxX [ A\`bRUHITxXb RZBCBCA T ` RUTxX<WM e JLT e MHX1RUTLTLA
(143) BCA TOW_J e A BA T)Of²»R e BCA K)GxHSKxA cHX^OMPHIOJLTLA X^RUKIJ)¡ OYHIRUT MPJ W e RZLK A? BA o) p X1J XQMPBCBA T)O e A yUJ_KSH A? e A RZT WlRZJ eYe MPHIOMKSR e X"`bRUTX^H [ A e A e KM²»RUTx`OYHSRZT [ Ab xT_HSAE²»R e BCA KIKSA BA T3OWxM e 8 k k r l o k m n n_ t m n n t l g hk y nqp r n nqp r n} . . y. . . . ÁÂ ÃÄÁÅ.
(144)
(145) . . H [ A AV`RUTxX1HX^OQAVMKSR e X M ? e A BM e 3JLA e JLAª`bA OQOYAf²»RUTx`OYHSRZT EAX1O<TJLKSKIAWxM e `RUTxX1O e J`bOYHIRUT X^J e KNM ² e RZT)OQH A ? e A [ ATLRUO e A [ RUBMHSTLA [ RUTx` X1RUKIJLOYHIRUT [ JLT§W e RZLK A
(146) ? BCA [ A MPJx` > ] X^HIBCWLKSA [ AVO1]WlAA 3JxMPOQHSRUT [ AX<RZT [ AX M¢3A¢``RUT [ HIOYHIRUTxX [ A H e H` > KIA O AX1O<WxRUJ e 3JLRUH RUTUM$WxRUJL3RZH e WxM e OQH e [ A WLJLHXA¢XYXYM ]3A e [ A
(147) T [ A [ JLH e A d KSJXW e A `HXA
(148) BCA TO TLRZO e AW e R` A [ A [ A`RUTxX1O e J`bOYHIRUT `RUBCWxR e OYAiO e RZHXCA OMPWxAXU8 rUVRUTW e A¢ `bHX1AiA OVRUT A OYJ [ HSAiKIA"W e RZLK A? BAi3JLH [ Ab TLHSO l o) [ A\`bA OQOYA\X^RZKSJLOQHSRZT RZTBCRZT)O e A"`RUBCBCA
(149) T3O [ A [ JLH e A )VRUT aA e H xA MPW e
(150) A? X`bRUJ_W 3JLA `bA OQOYA²»RZTx`bOYHIRUT A¢X^OLHSA
(151) T X^RUKIJLOYHIRUT [ A TLRUO e A W e RULK A ? BCA [ A [ A
(152) WxM e O ® } RZTxX^H [ A e RZTxXVKSAiW e RULK A ? BCA [ A MJx` > ]X^JLHIZMPTO#8 n y l X^J e X^J e j nqp l y z -oÎt X^J e ¥ _ ¥ l l ¥ _ } p } ¥ ¥ n _ l l x ¥ _ X^J e } p } dfe A BCH A ? e A
(153) BA TO HSKU²MPJ_nqO p [ A xTLH e KIAX/`bRUT [ HSOYHIRUTxX8HITLHSOQHMKSAX A O x `RUBCBCAIJ»RUT`bOYHIRUTxX [ A A O & W e HIR e H `bA
(154) OYOYA [ Ab TLHSOQHSRUTWxR3X1A"W e RZLK A? BA©URUTTLA"WxA JLOaWxMUXjX^A"`RUTOYA TOYA e [ QA¢ ` e H e A"x 3JLA l g hk A O x l g hk x ` M e J_TLA"OYA KIKSA [ Ab xTLHIOYHIRUTC²MPHIOHSTOYy A e 3A TLH e [ AX [ A e HIaA A¢Xy OYA
(155) BCWxR e A
(156) KSKSA¢X [ A RUJ x
(157) = RZJLOYA²»RUHX RZTWxA JLO²MU`bHIKSA BA T3O<KIA 3A e `bA OQOYA [ H `bJ_KSO_A KIAX<²»RUTx`bOQHSRZTxX RUJ x M ]MPTO A O_A\ X1JLWLWxR3XA AX M? X1JLWLWxR e OiX1O e HN`bOYA
(158) BCA TOHITx`bKIJxX [ MTxX AX1OVO e HI)HNMPK WlRZJ e 8 -oSr n l x d RUJ e x + K/X1J CO [ YA ` e H e Ai3JLA aAnq e p H xAiKYA 3JxMPOQHSRZT [ AXRZT [ AUX 8 x -oSrUr n l n y l 3. . . . . . . . . . . . . . . . . . . nqp. Ã<à ͪ «ÝbÛÙ. . n py. . .
(159) ro. FQ F. ¨ T [ bA TLHSOQHS3A RUTWxA JLO [ Ab TLH e A O x `bRZBCBCAV²»RUTx`OYHSRZTxX [ A A
(160) O x A O [ A"KSA J e X [ A e HSaA AXX^WxMOYHNMPKSA¢XJLTLHNJ_A BCA TOÄ©KSAjW e RZLK A? BA -o) t AX1O [ RZTx`i`bR eYe A`bOYA
(161) BCA TO [ A xTLH- hjT XYMHSOj3JÄHIKÄM [ BCA OaJLTLA"JLTLHNJLA\X1RUKSJ_OYHSRZTJLA"TLRZJxXVTLRUOQA e RZTxXx ® } hjT` > A e ` > A M$? W e A¢ X^A TO M ? [ A OQA e BCHITLA e RUTxX1H [ A e RUTXEWxRUJ e `bA KNM [ MPTxXVKSA\3JxM e O [ A"WLKMT KSA"W e RULK A ? BCAX^JLHIUMT)O 8 . . . . -oSr o . g h k l y ¥ _ ¥ l l } p n ¥ _ ¥ l l } p nqp n y ¥ _ ¥ l l } p nq p y ¥ ¥ n _ l l p nqp } kNx n y kN x ¥ _ ¥ l l } p nqp y e Ao `bACW e RU_K A ? BCAAX1O$LHSA ¥ _ . . x. . . . . . . x. k Nx x . = RUJ_OC`bRZBCBCA M? KR e [ T WlRXA `
(162) M e RUT&HIT)O A ? y e A [ MPTXvKIA [ e JM O A"WLKNMPT l } hjT A T `bRUT`bKSJLO"TLRZTX1A JLKIA BCA TOjJ_A A¢X^O"MHSTxX1H_HSA T [ Ab xT_HSA BMPHNXiMPJXYX^Ha3JLA `bA OQOYAE²»RZTx`bOYHIRUT AX1O [ R J? KSAOYHSO e A [ A"`bA ` > MWLHSO e A83RUTMRZLOYA TJCJLT_AX1RUKIJLOYHIRUT HST)TLHSBCA
(163) T)O e A
(164) yUJLKIH A ? e A3 ® } A e H RUTxX<A
(165) T)xTJLAVKNME²»RUTx`bOQHSRZT OQA KSKIAV3JÄRZTKÎM [ A OQA e BHSTªA A AX^OLHIA TCX1RUKIJLOYHIRUT [ JW e RU_K A ? BCA -oÎp d RZJ e `A KM RUTWxR3X^A . . . . l. n y n py z. . . ÁÂ ÃÄÁÅ.
(166)
(167) . d. 3G HRUT&MWLWLKIH3JLA`bA O"RUWªA e MOYA J eM? KMCW e A
(168) BCH A? e A A 3JxMOYHSRZT [ A o)Sr
(169) o HIK)HIA T)O [ JLTLA WxM e O g h k l X1J e © -oSr y A O [ MPJLO e A"WxM e O o¨ -oSrbD r ¥ n ¥_ ¥ l l . } p n p A`bH/AX^O`bKNMPH e xW M e `bRUTX^O e Jx`bOQHSRUz T [ AXi`RUT [ HIOYHIRUTxVX HSTLHIOYHNMPKSA¢X [. J W e ZR LK A
(170) ? BCA-oÎp Äh e
(171) . X^J e ¥ U` AX^O1¡ M ? ¡ [ H e A\3JLA l X^J e -oSr q n y nqp y z 3 Mv²»RUT`bOYHIRUT aA e H xA [ RZTx`iK-QA JMPOYHIRUT [ AXRZT [ AXjX^J e KSA [ RUBMPHST_A K e AX1OYA M? BRUTO e A e 3JLAKSAX 43 X^RUTO$A KIKSAX"MPJXYX^HVaA e H A A¢Xb<hjT A OYJ [ HSAWxRUJ e `bA KNM x l g7k h i j AKMW e A BCH A ? e AA¢ JxMOYHIRUT [ A o)Ir o RUTOYH e A"3JLA g7k hi x l ¨ T(WxM e OQH`bJLKIHSA e
(172) KNM²»RUTx`bOQHSRZT ¥ l x ¥C¥ XYMPOQHX-²MPHSO »WLJLHXQJ_A x AX1O e A yUJ¡ } p } p KSH A ? e A g k hi x ¥C¥ l ¥C¥ l WxRZJ e j ¥ 1 RUBCBA [ A"WLKSJX KSAX } [ RZTLTªp A A¢X HITLHSOQH} MPKIAXp RUTOA O_A$ X^J_WLWxR3XA
(173) } AX M? X^JLWLp WxR e O"X1O e HN`bOYA
(174) BCA TO HSTx`KSJxX [ MTxX i RUT M } ¥ l n } ¥ l RUT` l `bAJ_HfAX^O"TLRZO e AC`bRZTx`bKIJxX^n HIRUp TÄ ¨ T(HIT)3A e XYMT)OKSAX e RUKIAX [ Ac A
(175) O [ A] RUT&RU_OYHSA
(176) T)O [ ACKNM B A
(177) BCA² M `b RUTKÎMJLO e A 4 3 3 M [ A BCRUTX^O e MPOQHSRUT [ A c)HNX^OQA Tx`bA$AX1O OYA e BCHSTªA A3 -oSr . A
(178) O - o)IrbD HIBCWLKSHNJ_A T)O³JLA . l . . . . . . . . Ã<à ͪ «ÝbÛÙ.
(179) rbD. FQ F. . . * &. . !#"%$'& & "'& * '!2, *. -. & . . &¢ "| , -. & . & * & $ &¢ "%!./ & . jh T [ HNX^WxR3X1A ME? W e A X1A T)O [ ÎMJBCRZHSTxXÄJLTLAjX1RUKIJLOYHIRUT Mi? TLRUO e AVW e RULK A ? BCAªo)Îp A O`A OYOQA X^RZKSJLOQHSRUTAX1O e A yUJ_KSH A? e A3 A`bHLT_RUJxXaMPJLOQR e HNX^A Mi? KSJLHxMWLWLKIH3JLA e [ A¢X³RZWVA e MPOYA
(180) J e X [ R e [ e A A KSA
(181) aA\ A OiZM [ RUTx` [ RUTLTLA e J_T X^A TxX"MJLcA TLA e yUHIAXE3JLA$TLRZJxX"MPKIKSRUTX [ Ab xTLH e [ MTxX`A ` > MPWLHIO e A³hjT§MPJ e M MPKIR e XA OYA T [ J&MPJ&W e RULK A ? BCA [ J§`bRUHITKMB A O > R [ A [ A
(182) 3A KSRZWLWVA A WxM e ¥iM RUT_yA O RZKS] [ MTxXCq A O"y A TVA e MPKSHNXA$ KIAX e A¢ X^JLKIOMPOX [ A G > A A T [ MPTX r oU 8 [ MPTXKSAjW e A BHSA e `
(183) MUX KM [ A ` e RUHXQXYMTx`bAiA TOYA
(184) BCWxX [ J_TLA A TLA e yUHIAiMZXYX1J e AiKIA"` M e MU`O A ? e A ²»R e OYA BCA
(185) T)OjLHSA
(186) T WlRXA [ J(W e RULK A ? BCA A OYJ [ H A [ MPTXKSAX1A`bRZT [ `
(187) MUX `UAX1OiKSA$W e A BCHIA e WxMUXV3A e XJLTLAi²»R e BJLKNMPOQHSRUTUM e HNMPOYHIRUTLT_A KSKIAiA OVKM$`RUTxX1O e J`bOYHIRUT [ QA
(188) K A BCA
(189) T)OX TLHX. . " b $ o o % ' ' AX e A X1JLKSOMPOXX^RZT)O [ JX M ? RZTLy ¦ R3RG > A A T JLH X^J e KSAX"xMUX1AX [ AX"O e M ZMPJ_c [ A RUKI]A Oª¥iM JLRUTLy [ MTxXq M$` > A e ` > A WxRUJ e [ AX 43 [ R e [ e A"o JLT_A A TLA e yUHIA MUXQX^R`bH
(190) A AMPJ W e RULK A ? BCA [ R e [ e A A
(191) OiTLRUT WLKSJxX [ R e [ e Ao `UAX^O1¡ M ? ¡ [ H e A [ JLT R e [ e A X^JLWªA e HIA J e\M? `bA KSJ_H [ AXE`RUT [ HIOYHIRUTxX [ A"xR e [ X ã3RUH e rDU r oÄA OjX^J e OYRZJLO$ r . . ÁÂ ÃÄÁÅ.
(192)
(193) . AVW e RULK A ? BCA6A
(194) OYJ [ H
(195) A AX1OfKSAaB A BCA 3JLA [ MPTXVo KMi`bRZT [ HIOYHSRZT [ AV`RUHST$A
(196) TBCRZHSTxXU8 3.
(197) . nUy ny _ nqp y r n pn z. o. r. ny l n} y. . n y n y n y_ l nqp y z nU} y z n y. n y n y nqp y r n pWnU} z. o. r. n y_ l n y. M TxXCqP OQRUJxX"KSAX"` MK`bJ_KX"X^RZT)O"²»RUT [ A¢ XX^J e JLTLAB A BCA"H [ A T)OQHSO_A& A TLA e yfA OQH3JLA3 KX^J O [ J_TLA$HSTO_A y e MOYHSRZT(WM e WxM e OYHIAXEA O [ A$KNM²»R e BJLKSA [ A e A A
(198) T(WxRUJ e aA e H xA e ²MU`bHIKSA BA T)O³JLA"OQRUJLOQA$X^RZKSJLOQHSRZT [ AKQA 3JxMOYHSRZT [ AXVRUT [ AXaA e H xA r n y -Sr n n l o y
(199) nqp r nqp n p ERUJXEMWLWxA KSA e RUTxXVWxM e KMX^JLHIOYA n y l -Îo n p r y
(200) MPTX JLTW e A BCHIA e OYA
(201) BCWxX KIAX` MK`bJ_KX [ A r
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(287) yUJLKIH A ? e A3 o) 3 M`bRUTxX1O e Jx`bOYHIRUT [ QA K
(288) A BCA T3OX<xTLHX QA
(289) OMPHIOEKNMW e HSTx`bHIWxMPKIA"BCRUOQHSZMPOQHSRUT [ A ¦ G > A A T 3JLA [ A$BCA OQO e A\MJ WlRZHSTO JLTLA²MBCHSKIKSA [ YA K
(290) A BCA T3OX³xTLHNXiMPW_W e RZW e H
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(292) JLHNX3JLA [ A¢X e A¢ X^JLKIOMPOXCA 3JLHSZMPKIA TOXfWLJLHNXYX^A
(293) T)O [ A `bRZJLKSA e [ A$y TLRZO e y A&A TLA e yUHSA [ R e [ e Ao ¨ rU ETLA"²»R e BJLKNMPOYHIRUTUM e HNMPOYHIRUTLT_A KSKIA e AX^OQA M ? A ` e H e AiA OjX^RZTHIBCWLK
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(303) A BA T)OMPH e AX8KIJLHLM [ gYRUHIT [ e AVWxM e A
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(306) 5 A O MPW e
(307) A? X [ HNXY` e A OYHNXYMOYHSRZT$X1J e JLTLAVy e HIKSKSA e A yUJLKIH A? e A KSA²MPHIOf3JLA K-RUWªA e MPOQA J e [ AX 43 MPHIOJLTOQA e BA [ A [ A e HIaA AOMTLyUA
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(309) 5 A O X1HRZT&`bRZTxX^H [ A ? e AKSA¢XET "J [ X `bH ¡ [ AXQX^RZJxX RUT3RUHSOa3JLA WxRZJ e KIAXfT "J [ X e A W e A X1A T)O_A XfWxM e [ A¢X`A e `bKIAX KSAVKMWLKMZ`bHSA
(310) T [ A KQA 3JxMOYHSRZT [ AXRZT [ AX$WxA JLO A O e A` MK`bJLK
(311) A [ J²MPHIO [ AiKM"W e A X1A Tx`bA [ JLTT "J [ MPJ [ A¢XYX^JX MJ [ AXYX1RUJxX /M ? [ e RUHIOYAiA
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(313) T)O_A X WM e [ AXi`
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(317) A [ A"`RUHSTX [ RUTOVMPJ e MPHIOxAX1RUHSTMPJCBCRZBCA TO [ J_TLAiHSBWLK
(318) Ab ¡ ¡BCA TOMOYHIRUTÄ d RUJ e JLTLA 43 [ RUTO KRUWªA e MOYA J e `RUTOYHSA
(319) T)OÄJLT_A [ A e HIaA
(320) AOMPTLyZA TOYHSA
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