Stabilité des conditions aux limites pour l'équation des ondes par des méthodes énergetiques : le cas des bords courbes
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(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Stabilit´e des conditions aux limites pour l’´equation des ondes par des m´ethodes e´ nergetiques : le cas des bords courbes Patrick Joly, Olivier Vacus. N ˚ 2849 Mars 1996 ` THEME 4. ISSN 0249-6399. apport de recherche.
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(146) µ R & µW >G xyy K µ & yy & I A mr` x yy KNM yy µ 8 X y C D F F G 8 & > mr` x z H I A 8C&¢á > yy \ yy &
(147) µ 8 \ R24 > mr` x yy & 8 R24 R;A > I yy K y{ & 8 \ R24R A > I & µW 8 \ R24 > mr` x KNM. .§ WmrW u
(148) gji p l x gjba WtU XWkW m:ekah`b^?Wti x W¡ c ah^_esW p W ¥Ais^ p c iAm «¦Wteka_W x W mrefWlAWti p c i&e acKX1WtF X¨W p ` x Wt W ¬¢A£Ca¬W m:eklAgj` x u WtefenW x c ^mrgoi W I`b^_ªjc ahWti&e c U G K K K xyy K µ & µ µ & & & yy 1 8 W P > mr` x O K P K S K S I A yyy KNM µ X µ X µ yy mr` x z C H D
(149) F iF 8 & > I A 8C&¢áo > yy yy mr` x &
(150) µ 8QPR S)> yy & 8QPR SR;A > I yy K y{ & 8PR SR A> I & µW 8QPR S)> mr` x KNM. |§ ±W¡mreu Wl x gjba WtU XW I`b^kW m:ea±gj&ynWYe cU l x gol x WtXWti¦elAc x ahW x p W/isgje x W Wt ef` p WI« lb`b^dmnI`bW uj W mrelAgj` x u Wl x goba WtU XW¨M`E ^hi&enW x ª¦^_Wti&e[a_WAg x p Wtv&esW x ^hWY` x Wte p goiAu ahW¡mku gji p ^hen^_gjiAmTa_^hX^_enW m.c Amrg x Ac i¦efW m ¢ B ` Agj`se p ±`si/efWtXlAm ¬«b^ha'm:`¦¯ x cKb^hWtimW` F x p WKmrgoXXW x a_W mku gji&e x ^hb`sen^hgoiAm x W mC lAW u en^_ªIW m p W|u S cou `bi p W m p WY`bvKl x goba WYU XW m «tls`b^m p W x W u
(151) gjXK XW
(152) iAu W x ahWkX1WtF XWl x g&u?W p W ctªIW uTlAgj` x ibgj`bªIWYahahW¡mu gji p ^hef^hgji¤m^his^hen^dc a_W m & 8 \ Rw4 R >EWte KN& M 8 \ R24 R >²¢Iz|iibgjefW x c)I`bW acKibgjii&`ba_ah^hesW p W ¬«bgj` p W)X c ib^ WU x W W I`b^_ªjc ahWti&enW®aC±WYv¦^dmrenWYiAu W p W «?mrgoi¦e|b^_WtiWm ` F x p ^ x W u efWtXWti&eah^YW mkc `utc x cou e WU x W)6g x iW p W)acKu go` x s` x WI¢ Å i x W mr`bXWI «¬gjil6WY`be x W m:`bXW x c ^hi¤mr^Ta_We x ctªoc ^_akI`bWisgj`Am,l x W mrWYi¦efgjiAm p c iAm,adc mr`b^_enW p W u
(153) W x c lblAg x e Ggoi m:W lbacou W mr` x lAWti p c i&eKahWefWtXlAm 2I`bWibgo`AmctªIgoiAm p W ¥Ais^6lsah`Am S c `bet«&Wte.gji u goiAmr^ p W U x Wk`bibW®mrgja_`ben^_gji p `l x goba WYU XWku go`blbaYW W I`Ac en^hgoi p W m gji p W mÆ'u
(154) gji p ^_en^_gji,a_^hX^_enWI¢tz|iKmfc ^_e.M`sWku WtefenWOmrgoah`bef^hgoiKW mre'i¦`sahahWOc ^hiAm:^bI`bWTefgj`befW mm:W m p W x ^hªOWt W mm:` x ac[ x gji&en^ WU x WT^_i¦esW x ^_Wt` x WTlAWti p c i¦e.adc p ` x Wt W p W|aC±WYv¦lW x ^hWYiAu WI«
(155) Wtegji¨enWYi¦efW p ±WYv S ^_AW x `bibWWt ibW x j^hWÒ«buj W mre: ctU p ^ x W)`bibW{¹g x XWI`Ac p x c ef^I`bW p W ¥Aib^_W)l6gÒmr^_en^hªIWÒ«AM`b^ ÕÖ×EÕØ.
(156)
(157) . rm go^he p W Mu x gj^dmnmnc i¦efWKc `#u go` x m p `enWtXlAm ¢Ez|iWti p W p `s^he®c ahg x m)I`bWKu WYenenWWt ibW x j^_WKc ` enWtXlAm lAWt`ber WtF e x W)u goi¦e x goF atWt WkWti¨¹gjiAu ef^hgoi p W|ibg x XW m p W m p gjibiWt W m^_ib^hef^c ahW m
(158) «ju W M`b^ u gji¤mren^_en`bW)a_W x W mr`sahe²c e p Wmrec b^_ah^hesW[ ¹g x enWc isibgjiAu?WI ¢. ×Q×*àZY\[
(159) ðE]^.
(160) t. W W
(161) . ". #. $&%. ,. ')(+*-, 6 2 0. 3. ')(+'2 0. 3. 2. *+3. *1,. .. , (. . |z i u goXXWti¤u WTlAc x e x c ^hefW x ahW®utcom p W mku goi p ^hef^hgoiAmTahW m.lbah`¤m r¥AibW¡m ¦«Auo±W m:er c¡U p ^ x W ctªIW ua_WTenW x XW p W|u go` x s` x WI«ol6go` x ahW mfM`sWtaha_W m¬ahW m p Wt XgjiAm:e x c en^_gjiAmm:gji&e`biKlAWt`¨enW u S ib^I`bW mTX°c ^m.ahWutcomTWt iW x c a«blAgj` x M`sWtau goiAI`bWI« x Wta WYU ªIW x c p W)enWta_ahW menW¡u S is^I`bW m ¢ R gj`befW ¹gj^dm « gjiXgji&e x W x c c[U adc¥¤i p Wku WOu S c ls^he x WkI`E±^_ajWtv&^m:enW p W mEc u C goiAmQlba_`Am)WY atW Ic i¦efW m p W®u goiAu ah` x WklAgj` x ahW mu gji p ^hen^_gjiAm p ±g x p x W) [WteO)mnc iAmefW x XW m p W{u go` x s` x W m
(162) « Wte|u WI«&Wti e x c¡ªoc ^hahadc i&e|mr` x `si p goX c ^_ibW)u goi¦ªIWtv&WI¢ ]I^Iisgj`Am'u gjXXWti u C goiAm¬ctªIW u'ac|u gji p ^hen^_gji p g x p x W{ ²u
(163) acjmfmr^dM`bW ¦« uj W mre'm:Wt`bahWYXWti&e lAc x u WM`V±^haVm »c j^_e p ±`biutcomTWtv¦e x WtF XWtXWYi¦el¤c x ef^u `sah^hW x ¢ . % $ $ Y ( ! !# £CaEW m:e{u goibi&+ ` 8Cu²f¢ :± <El¤c x Wtv&WtXlsahWW>I`bWu Wutcjm[isWl x W m:Wti¦efW)lAcjm p W p ^ ¯ u `sahesW¡ m ¢ ¼ cu goi p ^hef^hgoi p WAg x p m
(164) fW u x ^he K & K& I A C D 8 & > 8 &¢h > W I K M O K S w gj` x adc p Wt XgoiAmre x c ef^hgoiE«¦^_a'mr`¦¯e p fW¡ u x ^ x W|aC±^ p Wti&en^_ebW 8C¦¢_ >G K K K µ µ 8 &¢á > K M K 4 KNM O I M. . . . ÕÖ×EÕØ.
(165)
(166) . ]&c i¤mc ^ x W ' ÃI % # ¿bÁ &t t Ä ¿ Á ¹ $ Ä ¿ %6Á «¦^_a¬ª&^hWti&e)G K µ K & µ & 8 &¢ > M _a K M O & µ eg I X KNM R u WM`s^E^hi p ^dM`sW{ac p W¡ u x go^mnmfc iAu
(167) W p WafWt isW x o^hW|Wti enWtXl¤m ¢ w `b^dmnI`E±goiWti©W m:e,c `bv x c lsl6WYam «E^_alAWt`se WYF e x W¨`bef^hahW p Wm:gj`ba_^hjisW x M`bW p c iAma_W m utc adu `badmXWtiW mQlAc x c,[`sgjibKWtejgja_q p c iAmTahW®utcom p ` Ag x p/p x gj^_et«IahW¡m p Wt`svlAgj^_i¦em ^hXlAg x e²c i¦emkmrgoi¦e|ahW mOmr`b^_ªoc i&e²m G ac x WE W u x ^hef` x W p WaC gjlW x c efWt` x p W acu
(168) gji p ^_en^_gji p WAg x p Xg p `bahganW I`Ac ef^hgoi p W mKgji p W m «.`bib^dM`sWtXWti&e{Wti p W x ^_ªOWY W mWti2efWtXlAm,WteKWYi p W x ^_ªOWt W¡mibg x X c ahW m · lAc x Wtv&WtXlsahWI«jlAgo` x adcKu gji p ^hef^hgji p g x p x W G K µ& K µ& K µ& I JvK & K & µ I JvK µ & K µ & K µ & K M O K S KNM K\ KNM µ O K S KNM O K 4 µ S X µ µ KNM O K 4vS §.WtefenW x WV W u x ^hef` x W¨m:W x c p c i¤mibgoe x WutcomaYWY W U x WtXWti&e p ^ ®W x WYi¦efW p `c ^_e p Wadc ibgo`bªIWtaha_W{Wtv&l x W¡mnmr^_gji p W)aCfW I`Ac ef^hgji p W mkgji p W¡9m 8C¦¢ >¢ U c lblba_^I`bW x aC±^ p Wti&en^_eb\W 8C&¢h > c U p W mQ¹gjiAu ef^hgoiAm aC»cjm:en`Au W p W|utc adu `baAI`b^su gjiAm:^m:enW c p yn` ^du ^hWY`AmrWtXWti¦e½u S go^m:^hW m.Wte|M`s^El6W x XWte p Wu gji¤u ah` x WI¢ R go` yngj` x m{lAgj` x adcu
(169) gji p ^_en^_gji p g x p x WKKlAc x Wtv&WtXlba_WI«IWtic lblbah^dM`¤c i&e 8¦¢h > c U K KN& M K Wte c U K &4 «b`bisW,m:^hXlsahW®mrgjXXW[X WtU ibW|Wti W ?Wte c U G . K K. µ & µ O O O M _a 4 µ eg K µ& µ K K µ & µ & KNM)K I KNM O K 4 S K M7K 4 I X µ µ 4 [WKibgo`bªIW c `V«6goi©cac p W u x go^mfmnc i¤u W p `bibWWt ibW x j^hWÒ« p W m[W m:en^_X c ef^hgji¤mkcl x ^_g x ^C«AWte²uj¢ §.Wmrgji&e®u W m p Wt`svlAgj^_i¦em[I`bW{isgj`Am|u S W x u S gji¤m c U x Wtl x Wti p x W p c iAmkahW¡mTutcom[I`b^¬isgj`Am ^hi&esW x W mnm:Wti&et¢ ×Q×*àZY\[
(170) ðE]^. µ & µ M µ. . µ K KNM)µK'& \ . K KNM)µK & 4 µ O J K µ&. . µ K K'\ µ K & 4 . K. K.
(171) WA. . W W
(172) . . .
(173) % $ $ $ ¼ c¨u gji p ^hef^hgji W m:e p c i¤m[u Wutcom G. K . G DW 8 & >. I. K. ) $T k $. &KNMO KK &. O. S. &. A I. z|i X WtU si W[a_W mkutc adu `badm p ^ x W u efWtXWti&e cKU lAc x en^ x p W8C¦¢»¦ >G K K K K K & µ K & µ K & µ & & & & 8 > I K S KNMO K S KNM K M O K P O K S eg M _a X ¼ ±^ p Wt W ibgj`sªIWtaha_ W p goi¦e|gji ªocKmrWm:W x ª&^ x W mre|u WYahahW p `bibW p W u goXlAgIm:^hen^_gjil¤c x ef^u `& ah^ W U x W p W)aC gjlW x c efWt` x DW ¢A£:u ^C«&ahWutc au `ba'u
(174) gjiAm:^mrefW x c¨mr^_Xlba_WtXWYiIe c¨U ctyngo`benW x I`bWtaI`bW m enW x XW mOc ` XWtXK x W p W p x gj^_enW p W)aCfWt Ic ah^_ebW) u ^ p W mnm:`Am G K K K K K & µ K & µ K & µ & & & &M 8 > I M K M K K K N K M K N K O O O _a S S X P S eg . & K& &K& O KK S O K KNM & & & & K S X KNM X } c lblAWtahgoiAm|M`bW)a±gji lAgIm:W K µ K µ K µ M & & & 8 &¢±Z> 8& R > I B. . l Yx W U mcju efg x ^mnc en^_gjim:` 8 8& RM>> I M . KNM . O. x ha W)Ag x p «A^ha¬ª&^hWYi¦e K & JlK & & K S K S O S & X . K P . O JvK. K S . O. . K &. &. KNM O. JvK. KNM. K. &. K # S S. &. . & . O. KNM O. 8. X. . S. > K. K. S. & K&. KNM. ÕÖ×EÕØ.
(175)
(176) . Å i mrWmrW x ªoc i&e p W)adcKu gji p ^hen^_gjimr` x ahW)Ag x p «6goi c p goiAuXgoi¦e x W® M`sW 8 8& RM>> K & µ K & µ & µ 8 > K & K & R I K S KNM K S X K M O O M X X WtekgjilAWt`be p goiAuWti p W p `b^ x WI«¦ls`b^mfM`bW U W m:ek`bi X ctyng x c i&e p W,acKu
(177) gj` x b` x WÒ«AM`bW 8 8 & R M >> | & µ K & µ K & µ O O K S O KNM M ¶ gjefgjiAmkI`bW{adcKu gj` x b` x W p goiAu[Wtil¤c x ef^u `sah^hW x m:gjimr^_jibWYibW.yngj`sW x c,lba_`Amkc `¤u `bi x goF ahW p c i¤m adcm:`b^hefW p W m|utc adu `badm ¢6]ÒWt`baEu
(178) gjXlbefW{ahW|c ^he|I`E Wtaha_W)mrgo^hekAg x ikWt WI¢ §.goi¦e x c ^ x WtXWti¦e?c `Kutcom p `Ag x pp x go^heY«tibgj`Am'ibWOmrgjXXW mblAcjm'lAc x ªIWti¦` ckU Xgji&e x W x M`sWKaCfWY ibW x o^hW p ±g x p x W¨/comnm:g&u ^YWt W c U & enWta_ahWM`bWKisgj`Am{aC»ctªIgjiAm p W ¥Aib^_WKW mre p W u x go^mC mnc i¦efWI¢A£Ca¬c `bek^du ^ p »ctªjc i¦ec oW,e x ctªjc ^ha_ahW x l6go` x gjbefWtib^ x `sibW)W mref^hX c en^hgoi c,l x ^hg x ^C¢ §.goiAmrec engoiAm p »c Ag x p I`bWa_Wl x WtX^_W x enW x XW p `#XWYX x W)X ctyng x c i&e)W mre x W p W
(179) ªoc ba_W p ` e S Wt g xYWtU XW p W)e x cou WI«Au W M`b^ElAW x XWte p áct¯ x XW x M`sW K µ K µ & & & µ 8 &¢ > & µ | . . K P . O. K S . O. z|i Wti p W p `b^heM`bW
(180) K & µ K & µ K & µ |
(181)
(182) K & µ K & µ K & µ & µ K M O K P O K S KNM O K P O K S O M 8 &¢á > 8 B ªIW x ef^mfmrWtX¨Wti&e)G¦lAgj` x WY ª¦^_enW x p ác a_gj` x p ^ x ^hi&`ben^_ahWtX¨Wti&eTibgÒm,utc au `badm «Aibgj`¤m p W mr^ jibgoiAmlAc x K« p c iAm,ahW¡m,ibgjX¨ x WY`AmrW m)^hiWY Ic a_^hesW m,c `bvbI`bWta_ahW m)ibgj`¤mctªIgji¤m x W u go` x m
(183) « `bibWu gjiAm:e²c i¦efW`sib^hªIW x mrWta_ahWI« x Wt Wta_ahWI«&m:e x ^du enWYXWti&elAgImr^_en^_ªIWI«¦WtekªOW x ^ ¥?c i¦ekiW¡ c ibXgo^hiAm O I Wte I ¶ gj`¤m x WtXW x u ^hgoiAmlAc x ctªjc iAu W)ahW®ahW u efWt` x p Wmrgji c ^_X c ba_W)u goXl x W S WtiAm:^hgjiV¢ > £Ca¬isW,ibgo`Am x W mrefWKI`E c,U isgj`Am p Wt Ac xfx comnmrW x p `Xg p `ba_W p W & p c iAmkahW)XWYX x W p W p x go^hefWI¢6z|ic x W u
(184) gj` x mTl6go` x u W[c ^ x W c,U `sibW{^hiWt Ic ah^hesW p W w gj^hi¤utc xfx WI ¢ Å i W ?WteY«OWt ec i&e p gjisikWK I`bW & p WYXWt` x W[^ p Wti&en^I`bWtXW i&ei&`baha_W)mr` x D «bgji c
(185)
(186) K µ K µ & & & µ | K P O K S ×Q×*àZY\[
(187) ðE]^.
(188) j. W W
(189) . [gji¤u
(190) K & µ K & µ K & µ |
(191) K & µ K & µ KNM O K P O K S eg KNM O K P O M _a mrgo^he|WtiAu g x W M M 8 &¢ > M 8 8 & R >> | 8 & R > z|i lAWt`be|c ahg x m[c lblba_^I`bW x a_W)ahWtXX¨W p W x goi c aha¢¬z|i/WYi p W p `b^_e|M`bW 8 &¢á > 8 & R M >R| 8 & R;A > µ D R p gji¤uj«blAgj` x A } M } ¬« 8 &¢á > 8 & R M >R| 8 & R A> µ £CaQibW x W mrefW,lba_`Am|M`E cU ªOW x ^ ¥AW x I`bW 8 & R A > mrW¨u goi¦e x gjF a_W,W ?W u
(192) en^hªIWYXWti&e.Wti p W m p gjisikWt W mT^_ib^hef^c a_W m «su W)I`b^EW m:e p ^ x W u e)G µ 8 &¢h A> 8 & R A > | &
(193) µ & W
(194) O z|ic p goiAu©Wt ec ba_^EI`bW K µ K µ K µ & & & | &
(195) µ 8 &¢h j > & W µ. . K & µ K S . . . . . . . ¹gji¤u en^_gji. . ctªIW u. KNM . O. K P . O. K S . . O. . µ u W)I`b^Eu
(196) gjiAm:en^hef`bW)b^hWYi`bi x W m:`bahec e p W)mrec b^_ah^_ebW[ ¹g x enW p c iAmTac,XW mr` x Wkg `U acisg x XW p W Á ¿ Á & a_W m p W x ^_ªOWY W m p `l x WtX^_W x g x p x W p W|acmrgoah`bef^hgji & mrgoi¦eOX ctyng x Wt W mQl¤c x p W m ibg x XW mku goXlAc x c sahW m p W m p goibikWt W mk^his^hen^dc a_W m ¢ z|i#ibgoenW x c I`bWadc u goiAmrec i&enW iV±W m:e,lAcom¹gjiAu ef^hgoi p Wadc u go` x b` x WI« p c iAm,adc XW m:` x Wkg `U KW m:eT^hi&ªIW x mrWtXW
(197) i&eQl x gjlAg x en^_gjibibWYa c U )¢¤§.WYenenW|l x gjl x ^tWt esW[ ibW mrW x clba_`Am ªOW x ^ ¥ Wt W{lAgj` x ahW¡mku gji p ^hen^_gjiAm p ±g x p x W)lba_`AmWt a_WtªOWÒ ¢ . I. ÕÖ×EÕØ.
(198)
(199) . .
(200) % $ $ ) $T k $ $ ¼ c¨u gji p ^hef^hgjim:` x ahW)Ag x p W m:e c U l x W mrWYi¦e)G K K K K 8 &¢h t> G µD 8 & > I K µ M & O KNM)µK & S K µP & O KN& M I A X µ µ z|iu gjXXWtiAu W p c iAmk`bi l x WYX^hW x efWtXlAm.lAc x c lblsah^I`bW x aC ^ p Wti&en^_esW 8C&¢á¦ > c U W I K K & M Wte I KK & R µ S Wtekgji mrgoXXW|ahW m p WY`bv WY Ic a_^hesW mkc ^_iAmr^EgobenWti&`bW m
(201) ¢A£Ca¬ª&^hWti&)e G
(202) K µ& µ K µ & µ K µ& µ K µ & µ K µ & µ K M µ O K M7K P O KNM)K S O K P K S O K S µ I M K K µ& µ & K µ & K µ & 8 > K µ& K µ & 8 > K µ& K µ& K M7K S KNM O K S K M)K S O KNM)K S KNM O K S KNM)K S X X µ µ µ µ 8 &¢h > gj` Wti¤u g x W : 8 W R M > 8 R M >< K µ & J K µ & K µ & 8 > K µ & J K µ & K µ & O K M)K S KNM O K S S µ I K M7K S K M µ O K S µ S O M X µ µ 8 &¢h Z > z|i x WV W¡ u x ^_eTWtiAm:`b^hefW{acKu
(203) gji p ^_en^_gji p W)Ag x p Xg p `bahgaCfW M`¤c en^_gji p W mTgoi p W =m G K K µ& K µ & K & K & I A µ& 8 &¢h > D 8 & > I KNM O KNM)K O K K S O µ S S µ X KNM µ. J K K K K µ & & & & M I A D 8& > I K M O K K O K S&S X S µ ¶ gj`¤m Wtv&lba_gj^hefW x goiAmku WtefenW)u
(204) gji p ^_en^_gjimrgo`Am adc¹g x XW)mr`s^hªoc i&enWZG JvK K J K J K K µ µ µ & & & & & I A D 8& > I N K M O K O N K ) M K O K O K µ S#S S MS µ SµS X. . ×Q×*àZY\[
(205) ðE]^. . !.
(206) Z. W W
(207) . w gj` x b` en^_ah^m:W x u W®ibgj`bªIW¡c ` x Wt x gj`blAWtXWYi¦e p W m.enW x XW m
(208) « goi/ªoc p W u goXlAgImrW x ahW|enW x XW K µ& J K µ & K µ & I K µ& J K µ& K µ & KNM)K S KNM O K S S µ K µ JvZK K K M7K S K M µ O K S µ S 8 &¢h t > µ & µ& µ& O Z KNM)K S KNM O K S S µ µ Wtictyngj`se²c i&e|WtekWti x Wte x c iAu S c i&ek`biu W x ec ^_i/isgjX¨ x W p W fenW x XW m.X c iAI`Ac i¦em G . µ&. K. KNM)K. S. J K. µ&. KNM. µ. K O. S. µ&. µS. I. J K µ& J K & K & K M O K S S O Z KNM)K S S K S O S KNM S µ µ X J K µ & K µ & J<K µ & K µ & J K & K & KNM)K S#S K M O K S S O Z KNM O K S S O Z µ µ µ µ X K S O KNM S J K µ& J K & K & J K µ& K µ& J K & K & KNM)K SfS K S O K M O K S S KMS X Z X X Z µ µ X K S O KNM S 8 &¢h > Å i2gjlW x c i¦e¨c ^hiAm:^C«ibgo`AmKctªIgjiAmc ^he¨c lslAc x c LhF e x W aC gjlW x c efWt` x p W ac§ ¼=B «u WM`b^ ibgj`¤m lAW x XWtekc ahg x m p fW u x ^ x W K µ & J K µ & K µ& K µ & µ K µ& K µ & µ KNM)K S K M O K S S I µ µ X Z KNM)K S X Z K KNM µ O K K S µ & & µ O Z KNM X K S z|i x WYª¦^_Wti¦eOc ahg x m cKU aCfWt Ic ah^_ebW p W p Wt lAc x e 8 ¦¢_ Z >TlAgj` x gobenWtis^ x I`bW 8 8 W R M > 8 R M >> | K & K & µ 8 > K µ& J K µ& K µ & O KNM)K S KNM O K S S µ M Z KNM X K S O X µ µ 8 &¢h t > . J K µ& K M)K S Z J K µ&. K. J K. µ&. K. µ&. . ÕÖ×EÕØ.
(209)
(210) . Wte p og iAu 8 8 M . W. M. R > O. 8 . µR. K µ K . M > >&|. & µ O µ K & µ M K S K µ& O . J K. µ&. K. µ&. µ SµS §.WtefenWT¹go^mQWti¤u g x WI« isgj`AmiE»c¡ªIgoiAmQlAcomXgji&e x Wk I`bWkaCfWt ibW x j^hW.W m:e p W u x gj^mfmnc i¦efWI« X°c ^m p WTisgj`bªIW c `E« gjiKm
(211) ±W m:e p Wt Ac x cjmfm¦W p W mEenW x XW m p ±g x p x W 8ö^du ^d I >Vmr` x ahW.Ag x p{· gji ªoc x WY `Amnm:^ x®c,U u goiAu a_` x W®utc x a_W menW x XW m x W mrec i&e²mTm:gji&e p ±g x p x W{^hi¦ W x ^hWY` x ¢o£Ca¤c `beOc `Amfmr^ x WtX°c x I`bW x M`bW®ahW|mr^_jibW p W{ac)u go` x s` x W{iV±^hi&enW x ª&^hWti&eQl¤cjmku WtefenWT¹go^misgjilba_`Am p c iAm ibgje x W p Wt XgjiAm:e x c en^_gji · u W x W m:`bahec eTW¡mre p gjiAu[ªoc ac sahW{lAgj` x p W m p gjX c ^hibW m.u goi¦ªIWYv¦W m gj`ibgjiE¢ z|iu gjXXWtiAu Wkl¤c x ahW¡m p Wt`bvl x WtX^_W x mefW x XW¡m p ` XWtXK x W p W p x gj^hefWM`b^'m:gji&e u gji&e x gjF adc ba_W m l¤c x ahW)e S WY g xYWYU XW p W,e x cju WÒ«bWtekahW mkuYc au
(212) `bamkm:WX WtU ibWti&eku goXXW p c iAm[a_W lAc x c x c l S WKl x W¡ u¬W p Wti&)e G K µ
(213) K µ K µ K µ & & µ& µ& | 8 &¢áWA> 8. KNM)K. &¢h t>. Wte 8 &¢á¦ >. KNM . K K. &. K M . µ. &. µ. Wte 8 &¢á > ×Q×*àZY\[
(214) ðE]^. . |. KNM . K & KNM. S. . . . K. . . µ |. K. K. µ&. O. K. KNM)K S . O. µ. O. . S. P. . K µ &. K M7K P. µ. M7K. K. . O. K. M7K. K. . P. . . O. O. . K. µ&. µ. µ U u Wte £Ca{ibgj`¤m°c `seWti¦¥Ai¸ibgo`Am p Wt Ac xnx comnm:W x p W¡menW x XW m p W p Wt x W Wtegji¸`Am:W c2 W ?Wte p ±`bisW{^hiWY Ic a_^hesW p W w gj^hi¤utc xfx WI ¢ Å iW ?Wtet«bgoimnc ^_e{I`bW p c iAm a_Wutc p x W p W)ibgje x W l x goba WYU XWI« & W m:e{^ p Wti¦ef^I`bWtXW
(215) i&eTi&`baha_W,Wti p W S g x m p W « p goiAu i&`ba_ahWKc ^hiAm:^.I`bW¨mnc p W x ^hªOWt W{Wti enWYXlAmTm:` x D ¢¬z|i Wti p W p `b^he|I`bW K µ K µ K µ & µ & µ& | 8 &¢áj> S. . K . K. KNM)K P . O. S. KNM. S. . S. . µ& µ M7K S K. K.
(216) j. W W
(217) . ÇQ^_iAc a_WtXWti&et« gjigjbef^hWti&e|I`bW : 8 W R M > 8 R M ><+| O µ M . ctªIW u. . . 8 . 8 WRM> O. . 8 R M > >. µ. Wte,goi#lAWt`bec a_g x mKc lblba_^I`bW x a_Wa_WtXXW p W x og i c aha¢z[iibgjefW x c M`E cU l x W m:Wti&eadc u gji¤mre²c i¦efW =W m:eT¹gjiAu ef^hgoi p W { ¢ [W x ib^_W x
(218) lAgj^_i¦e c U p Wt Xgoi¦e x W x G a_W|u gji&e x gjF ahW p W 8 W R;A > O 8 µ R A >'lAc x &
(219) µ . I. Wte & W µ ¢ w go` x u Wtac&«¦goi gjl W U x W lAc x `bisWX°ctyng x c en^_gji p ^ x W u efW{lAgj` x ahW¡m p W x ^_ªOWY W m.mrlAc en^c ahW m ª&^c,aCfW I`Ac ef^hgji p W¡mTgji p W¡m lAgj` x a_W p W x ib^hW x enW x XW K µ & 8 ~ R A > µ | &
(220) µ . K M µ ÇQ^hi¤c ahWYXWti&et«jibgo`AmkXgji&e x W[cju ^_ahWtXWti¦e½M`bW
(221) K µ K µ K K K KNµ M & O K M7µ K & O K M)µ K & µ O K µK & µ O K µ & µ 8 &¢á Z > µ P S P S S µ | &
(222) µ O & W µ . R go`benW¡m ahW m p W x ^hªOWt W mK m:W u gji p W m p W & lAWt`bªIWti&e WYF e x W`bib^ ¹g x XWt XW
(223) i¦e)X ctyng x Wt W¡m,lAc x K µ& p U &
(224) µ. « c a ± t W s v u t W s l n e h ^ o g i W µ & W. O K P ¢Æ§.WtefenW)`ba_en^hXW{W mref^hX c en^_gjiW m:e[go¦ enWti&`bW)lAc x a_W{b^c ^m p W)anW I`Ac ef^hgoi p W mkgji p W m G µ K µ& I K µ& K µ & 18QPW> K & 8 &¢á > K P KNM K S µ µ X KSµ O K z|i x c lblAWtaha_W)I`bW K S& W m:ekb^hWtiu goi¦e x goF atW 8ußf¢ ¦¢»¦ >OWteM`bW W¡mrekX ctyng x WI ¢ §.W u
(225) ^Ecju SVWtU ªIW®ac p Wt XgjiAm:e x c en^_gjiE¢ . . . . . . . . . . . . ÕÖ×EÕØ.
(226)
(227) .
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