Maxwell's Equations in a 1D Ferromagnetic Medium : Existence and Uniqueness of Strong Solutions

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(1)Maxwell’s Equations in a 1D Ferromagnetic Medium : Existence and Uniqueness of Strong Solutions Patrick Joly, Olivier Vacus. To cite this version: Patrick Joly, Olivier Vacus. Maxwell’s Equations in a 1D Ferromagnetic Medium : Existence and Uniqueness of Strong Solutions. [Research Report] RR-3052, INRIA. 1996. �inria-00073640�. HAL Id: inria-00073640 https://hal.inria.fr/inria-00073640 Submitted on 24 May 2006. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Maxwell's equations in a 1D ferromagnetic medium : existence and uniqueness of strong solutions Patrick Joly, Olivier Vacus. N˚ 3052 Novembre 1996. THÈME 4. ISSN 0249-6399. apport de recherche.

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(204) h \5o Y g enePm w jD

(205) \anloi\ shpanjSl9^|© r 50 ¸ D ¯R & µ IJ@5 V " #.84=< % )"j (* [ W(X ÄÈ|DÄ. Á G + } ¹ &5± ¯ » ¼ ½9» ¾ µ À ¿ ½ + ¼ ¹ -5±¯ » ¼ µ À ¿ $ Á D ¯ ¸ µ ) a "J5J@ $ !" D ¯B &µ @ + } ¹ &7±¯ » ¼ ½» ¾ µ À ¿½ + ¼ ¹ &7±¯ » ¼ µ À ¿ '_!t"#! 6 @aJ |' U ÁÂ¯F µ U D U Á = ¯F µ U 4 E 4 FW9G ³ ´ 7 ¯Êf©æSµ A 9Ä ED

(206) uJ5J* ^V!#S_ J7J@ ' ê " ! j ]' !5`L J ' !j " ! !" SS_J7J !J !" 4C

(207) H $

(208) 6 @!*`) % C {"! C } V '%R <}4984 ] ' g$ #.8t4

(209) > % tj3_ J7J y" ! 3O _ ^ "\J@ ' 'Sey@!* J !J (e "! '6 v J@!>)'% ( ' ¯Êf© bµ ? Á ¯F A µ ?d ÁÂ¯F A µ D ?&A / (" ! C' ' [) 4 Gw jb]8h Y \k \ lfj en\ q

(210) \"j |Á 6G + } ¹ &7±¯ » ¼ ½» ¾ µ À ¿

(211) ½ + ¼ ¹ &5± ¯ » ¼ µ À ¿ \ q \«=lf\ ¯R¶ ¸ µPg

(212) o2h Y \(dlfacdf\oij

(213) ecdfhpanjSl j

(214) 3h Y \&ekaclf\?g w m w jSfen\ ] 899 ¶ FHGM³ ´ AJI 99 <%= ? s d w e ¸ D B 9 ?&¸ A sd w eP¶ D KL=@? Á FHGM³ ´ : KL=@? AJI ¯Êf©[

(215) Z µ 99 ?&AwM B ?&A D 99 ¶7¯F iµ ¶ = ¯F µ FHMG ³ ´ 9; ¸ ¯F iµ D ¸ = ¯[F µ FHMG ³ ´ X4Y (\ \uacoihp\ l|s1\4g

(216) l q dlfacdf\ lf\?oioj

(217) ¯R¶ ¸ µ2aco\ lo¦d w \ q br5h Y \4g

(218) lg

(219) ekrfoianoj Gekaclf\?g w gDu \eneB o3\ dg

(220) hpanjSlo ©2.j w \(m w \ sanoi\enr \ Y gè

(221) \h Y \ ¥j

(222) enekj aclf'h Y \ j w \ ] ~50 Á W(X ÄÈ|DÄ. G+ } ¹ -5±¯ » ¼ ½9» ¾ µ À ¿ ½ + ¼ ¹ -5±¯ » ¼ µ À ¿ ¯R¶ = ¸ = µ @!* '&)t'&)jè # ik% J@5V "[#.84CB % )"jj *@k [ ¯B¶ ¸ µ + } ¹ &5± ¯ » ¼ µ À ¿½ + = ¯R &7±i® ¯ '* µiµ 4 g$ ¶ D ¯RÁ µ ) ¸ D i¯RÁ µ #)"a [ &(&)t'@ "J5J@ g$ J!" + } ¹ &5± ¯ » ¼ ½9» ¾ µ À ¿x½ + ¼ ¹ &7±¯ » ¼ µ À ¿ + } ¹ &7±¯ » ¼ µ À ¿L½ + = ¯B &5±¦® ¯ '* µpµ &)!D ¯B &µ ! .J'

(223) 6 74 6 |! 6"! "# ¸ =%l Q < < ¼ ? Á =l Q * ¯i <>=KL= µ ? ¼ Á ¼ =l Q * ¯Êf© bµ M M ?&A M M ?&A ) ' @ !'!C@ )AJ )H < = K = O &) W¸ V T J@! %))W@!* Á D ¯ ¸ µ T ! ! &) )t@!* D¯B¶ = ¸ = Á = µ > <4 X. T. Ø¥ÙÚ2ØÜÛ.

(224)

(225) !"#%$&'("#) *" Z. D ¯B µbr. \5sgSlMlj q \1«Glf\5g

(226) lg

(227) m|mfekacsg

(228) hpanjSl9anl. &. lMj

(229) h Y \ w( j w q o. B. _. D i. ¯Êf© bµ. D B¯ ¸ µ R¯ ©k?bµ X4Y \ w \ oi\ g w s Y j "genjfsg

(230) ePoph w jblf'oij

(231) ecdfhiakjblj

(232) ¯j7'µjbly2 -4 ano-\ dfanèg

(233) ek\?lbhxhijth Y \ w \ oi\ g w s Y j

(234) g«uf\ q m=j

(235) aclbh4j Bºacl9h Y \ oi\ loi\ j h Y \ ¥jSekenj aclf w \?oidfenh ¯ -Y jbop\&m w jj 3ano4h w anang

(236) e g

(237) l q en\1 ¥h4hpj¬h Y \ w \ g q \ w µ _ Ä. u ¯B¶ ¸ ¦Á µ # ! $# [Se ¯'7 µ 2 & 4 ¸ s a5 ) J k

(238) B 4 @ xuj ¸ a5 ) J* @/e B " ! ¯R¶ D ¯ ¸ µ ¸ Á D ¯ ¸ µpµ # g$ [Se ¯7'µ 2 &4 4 zd w SjSg

(239) eGaco4hijtgSmmfenrh Y \5s1jblSh w gSs1hiakjbl]tg

(240) mmanlfth Y \j w \?]ÂhpjB anloijS]'\&s1enjSoi\ q g enePj D ¯B &µá©3\h-do4sjSloia q \ w _ P =¯"µ D ¸ G D ¯B -µ ¸ =l Q 8 < < ¼ ¯R©kSèµ M M ¯ -Y \ w \ MgSl q q \ lfjShp\&s1jbloph¦g

(241) lbhio -Y ans Y jSlfenr q \?m|\?l q jSl <>= KL= O gSl q¸ V µä© X X4Y \ « w oih4ophi\ mMj 3h Y \5m w jj s1jSl|opacoph¦o(anlm w jDanlh Y g h( ¥j w o¦]tg T ene \ lfjbdf Y B ]tg

(242) mosP = ¯ µaclShijtakh¦op\ e¡ © Ä. QSb *"( $3" ! ? ¯R¶ = ¸ = Á = µ%>^ < " ! !! = } I ' ! " ! f m = } B¯CP = ¯" µpµP = ¯"µ (\1 ¥j w \&m w jDanlen\ ]t]tg¯Rbµä \ « w oih4lf\\ q g'm w jbm|\ w hýr¬j

(243) gSmmfenans g hpanjSl _ 'Ä @ o, Sb *"( $S@ !* ) ? ¯R¶ = ¸ !g= _' Á !`= µ%@> ) A J< )W )S " ! ¸ } O ) ¸ ¼ ¸WVV g$` ) < P = ¯"' !µ @ !*@ !* " ! H! j( J* j

(244) g $ = = + = = ! j) ' <= K = J _' !gj L

(245) ' @*j" "# U T X Q ? Á } ? Á ¼ ¯R©kèSµ ?&A B ?&A =%l Q * v =

(246) v = B x M O < x ¸ } B ¸ ¼ =%l Q Q ? ¼ Á } ? ¼ Á ¼ . . v v = x ¸ } ¸ ¼ =l Q + = ¯R©k?bµ ¼ B ¼ =%l Q = x B B ?&A ?&A M ¸. . `b\ \5oid|op\?s1hiakjbl^=© © 9Ä * " * @b N " ¸ } ¸ ¼ =%l Q ) * D B !¸ #"$"$_ % &' 2\ h do-oi\h ¸ D B¯ ¸ µä -Y \ w \ ¸ ED. GI!. . Á. ¯ µ. J. J. "!. !. . . !. . 4. ¸ =l Q <. M. . <. ¼. ¼ ? Á

(247) g l q ? Á ¼ © ( o ?&A ?&A ?Á ?A B \ q \ q ds1\&h Y g h g|© \S©-FW9G ³ ´7. M. . #.84

(248) 2 8 %. )O#.84

(249) 2 : % "! b '% @!* @!*t' @ !@ e.

(250) (. =\enjSlSo(hpj$P = "¯ µá© s s1j w q ca lfthpj¬h Y \j w ?\ ] f \ Y gèS\

(251) anh Y. ? Á =l Q ?&A. . M. ¯p. < = K = µ ? ¼ Á ¼ %= l Q M ?&A. ¯R©k ^µ. \h-do4S\h(\ oihpac]tg hi\ o(jSl. ÚÚ å öáò1ó . Á U Á U Á R ? D OG¸ Q R Á T ?A U ÁÂ¯F µ U ¼ D U Á = ¯F[µ U ¼ A ¼ OG¼ U ¯ ¸HQ R Á µ=¯F µ U ¼ Á ¯ F µ D i? i A ii ¼ A i & i ? A M i i T. ¯R©kèSµ ¯R©k?bµ ¯R©kZ

(252) µ.

(253) '* / [

(254) > @ ' . . bd|g hpanjSl¯R©k?bµ[aco3jSfh¦g aclf\ q br&hig \baclfh Y \4o¦sg ecg w m w j q ds1hj =\ dg hiakjbl¬¯R©k ^µ2br5Á+g

(255) l q \ dg

(256) hpanjSl¯Rf©n6ZSµ[aco3jSfh¦g aclf\ q br9o¦dg w aclf\?dg hiakjbl¯Êf©n^µá©Lzlh Y \&j

(257) h Y \ w4Y gSl q f w jS] ¯p

(258) © ^µ \ q \ q ds1\ _ U H¸ Q ¯F µ U U ¸ V ¯F[µ U U ¸ ¯F µ U U ¯F[µ U U ÁÂ¯F µ U ¯R©k>bµ A A M X A M X g \baclftanlbhpj¬gSss1jbdlbh ¯Rf©n µä \

(259) \h H¸ Q ¯

(260) d A µ% { ¸ V ¸ ¯!d A µ äÁ = ¯R©k?bµ X M M X4Y \?l |br.¯Êf©n6Z

(261) µá \&jbfhig

(262) anl. -Y acs Y r ak\ e q o h Y g h4aco4hpj¬o¦gèr

(263) oianl|s1\. ? Á ¯

(264) d µ O äÁ = ¯ ¸ V ?&A A * M ? Á =l Q O < ¸ V ?&A M ¸ =\enjSlSo(hpj 0= ¯ µ _ ? Á =l Q O < ¹ . . P. . . ?&A. . . . . ¸ !¯ d A µ äÁ = µ M X. ¯R©

(265) bµ. ¸ %= l Q < M X. ¯R© èµ. M. . <. . M. <. ¼¿. . ¯R© SSµ . ¸ V D g

(266) l q D g w \ m=jSoiakhiakS\sjSloihigSlSh¦o q \ m=\ l q anlftjblfekr¬jbl -Y \ w \ D W gSl q¸WV ©"äG\ M w \?lbhpacg hpaclf¯R©k ^µ M anh YX w \?oim=\ sh4hpjthpac]'\&ek \?g q o(hij _ ¼ ¼ ¸ Q ? Á ¼ D Oyv¸ Q R ? Á ? R Á x U Á U Á R ? Á ¼ M T ?&A ?&A M ?&A ?A w jS] -Y ans Y9 \S\h ¼ ¸ Q ?i Á ¼ ¯ F A µ i D O i v¸ Q R ? Á ? R Á x ¯F A µ i i ?&A i i i ?&A Á M ? A i i i i ¸ H Q i i i O U H¸ Q ¯ F A µ U i ? ¯ F A µ i i ? ¯ F A i µ i U Á ¯F A µ U Gw jb] ¯R©k>bµá \&

(267) \ h . i i. _. i. ?&A. i. i. i. M. i. i. i. ?&A. ¯R©

(268) bµ. ¯R© ^µ. i i i. ¸ Q ¯

(269) d A µ% ¸WV ¸ ¯!d A µ äÁ = % zlMh Y \&j

(270) h Y \ w4Y Sg l q q a G\ w \?lbhpacg hpaclf/¯i

(271) © ^µ ka h Yw \?oim=\ sM hxhij¬hpac]'\&

(272) an

(273) \ o M _ X ¸HQ D ¸ v?Á ? ? ?&A ?&A BSXY ?&A x gSl q h Y \?l ? ¸HQ ¯

(274) d µ ? ¸ ¯!d µ ? Á ¯

(275) d µ A A ?&A A M X & ? A ?&A £jSanlf¬gSs ¬ \ hpj/¯Êf©æD^fµä \&S\h _ ? ¼ Á ¯

(276) d µ O ¸HQ ¯

(277) d µ% ? Á ¯

(278) d µ O ? ¸HQ ¯

(279) d µ áÁ = A ?&A ¼ A ?&A A M ?&A A h Y g h4aco4hpj¬o¦gèr

(280) fh Y g

(281) l\ o(hij/¯Rf©æ

(282) bµ²gSl q ¯R© g

(283) Z µ. ? ¼ Á ¯

(284) d µ ? A ¼ A *. <=K = O T X. O ¯ ¸ V ¸ < µ ? Á ¯

(285) d A µ * M M X ?&A Oyv ? ¸ ¯

(286) d µ ? Á ¯!d µ < ? A A M X &? A A x M. ¯R© SSµ ¯R©

(287) bµ ¯R© gZ

(288) µ ¯R© b µ. ¯R©

(289) bµ Ø¥ÙÚ2ØÜÛ.

(290)

(291) !"#%$&'("#) *". (o \ q \ q ds1\ h Y g h. . ¸

(292) ¯ d A µ% 1 ® m ¯

(293) d A µ% 1 ® m ¯

(294) d A %µ f A m. M M. ¸. X4Y \ w \ ¥j w \

(295) doiaclf¯Rf©æ

(296) bµg

(297) l q R¯ ©

(298) ^µä ¯Êf©æ µLs g

(299) lM|\ -w anhphp\?l ? ¼ Á ¯!d µ O ¸WV ¸ ?&A ¼ A X M O ¼ ¸ V ¸ =%l Q . (o ¸ G 0=¯ µäfanh4ano M lfj

(300) h q a a¤sdfenh-hpj¬M oi\\&h Y g h P. . M X. ? ¼ Á ¼ =%l Q ?&A . . 1® o ¯

(301) d A µ 1® o ¯

(302) d A µ ¯

(303) d A µ . ä® p ¯

(304) d A µ% M ä® p ¯

(305) d A %µ M ¸ =%l Q . =l Q < ¸ =l Q < < ¸ M V X ¸ M =%l Q < M M X. < Y ¯ µ. ¯R© Sbµ ¯R© |èµ. ¯R© bSµ. -Y \ w \ ¯ < µxano g'm=j

(306) enrflfjS]'acg ePj

(307) q \ w \\ ^ anh Y/w \ o¦m|\?s1h4hpj { -Y jSoi\&s1j\a¤sak\?lSh¦o4jSlekr¤jbl <%= KL= O gSl q¸ V © { \ w jSdY m anlf¯Êf©æfèµLg

(308) l q ¯Êf© Sbµä \S\h _ X T ? Á ¯R© Sbµ ? A =%l Q M i¯ M <>=KL= µ ? ?&¼ AÁ ¼ =l Q Y ¯ < µ -Y \ w \ ¯ < µ7ano¬g§m=j

(309) enrljS]'ang

(310) e4j q \ w \ \^| q \ m=\ l q anl jSlfenr jSl ¯ <>= KL= O ¸ V µá anh Y =m jSoiakhiakS\sj\a¤s1an\ lbhio © v endfS

(311) aclfY M ¯Rf©

(312) µLanlbhpj/¯Êf©n?bµä \S\h _ X T ¸ =l Q ¯ < µ < < ¼ ¯R©

(313) ^µ Y M M -Y acs Y

(314) an

(315) \?oh Y \ w \ o¦dfekh-m w jDa q \ q h Y g

(316) h _ ¯R© bSµ = } D ¯< µ. Y ¼ 'Ä '% r 4 Sb *"( $3"! è¯R¶ = ¸ = Á = µ%> <("! !! j = } I '!t@!*" fF = B Q '% q 2\ hLdoop\ h ¸ } D B¯ ¸ Y } "µ g

(317) l ¬q ¸w ¼ Y D w B¯ ¸ w ¼ µäÁ } D ¯ ¸ } µ"g

(318) l q Á ¼ D Y ¯ ¸ _ ¼ µä© a w oih²g

(319) ssj w q aclf&hpj5h Y \j w \?] tgSl h¦g \baclftanlbhpj¬gSss1jbdlbh(h \&enanl\ g s g g

(320) s1hi\ j gDu \eneB o(\ dg

(321) hpanjSlo \ gè

(322) \ ¼ ¼ ¸ } ¸ ¼ =%l Q ? Á } ? Á ¼ =%l Q ¯i <>=KL= µ ? Á ¼ } ? Á ¼ ¼ =l Q ¯R© Sbµ B ?&A B ? A M M ?A B ?A X4Y \ w \ ¥j w \

(323) doiaclft\ oihpac]'g

(324) hp\?o ¯Rf©n?bµg

(325) l q ¯R©k?bµ²j ek\?]t]'gt| Q . ¸ ¸¼ =l Q . v. = x ¸ } ¸ ¼ =%l Q = =B ¯R© Z

(326) µ }B B M anh Y = D = ¯i <>=KL= µ += gSl q = DO < ¯i <>=KL= µ =L© M M Q M M . . D. v. X4Y \ Od|ls1hiakjblj =L¯" µ = = B = x ano4sjSlbhpacldfjSd|ofacls w \ gSopaclftg

(327) l q o¦g hpacop«|\ o _ y{

(328) M =L¯Rbµ D q ekac] ¾ =L¯"µ D ¯R© bµ. M ¼ D _ Y Y ¨\1«=lanlf = g

(329) o(h \5dlfacdf\5opjSendhpanjSl9j = ¯ µ \ gèS\. ¼ f = B¯B® } µ B¯R® ¼ µ% =%l Q ¸ } ¸ ¼ =%l Q ¯R© Sbµ B B ÚÚ å öáò1ó .

(330) '* / [

(331) > @ ' . ?. 9Ä. EDF . =}. &) = ¼ e ""6 8 )$: @ ) 3J&)t <>= KL= . . . "D . . T. O . X. . ¸. V ). <. 4. (. \hd|ooi\h 6= ]'acl = } & = ¼ © ssj w q aclf5hpjek\?]t]'gSox7g

(332) l q b ¥j w D 6=² B acogs1jblSh w gSs1hiakjbl' w jb] P =²¯ µ aclbhpjakh¦op\ e¡ ©¬ªopaclfh Y \t«uf\ q m|jSanlbh&h Y \j w \ ]M \ q \ q ds1\¬h Y g h!B g q ]'anhio&gdlfacdf\t«uf\ q m|jSanlbh ¸ anl P0=¯" µ -Y ans Y ]'\ gSlo gSssj w q anl7hpj'en\ ]t]tgSbh Y g h¯B¶ ¸ ¦Á µ D ¯B¶ D ¯ ¸ µ ¸ Á D ¯ ¸ µiµ"aco(goih w jSlf'opjSendhpanjSl¤j

(333) L¯j7'µá© X4Y acog ecopj¬SakS\ o4h Y \dlandf\?lf\ o¦o-j

(334) h Y \oih w jSl¤opjSendfhiakjblanlh Y \oi\h\P0=¯"µá© X j9s1jSl|s1ecd q \5hij¤h Y \

(335) \?lf\ w g ePdlandf\?lf\ o¦o w \ o¦dfenhPanh5oi*d a¬s\ o hij w \ ]tg w \Mh Y g h&ak ¯B¶ ¸ ¦Á µ ano&goih w jSlfMopjSendhpanjSl jSl 2 &4 anh Y , = } h Y \ l ¸ lf\?s1\?oio¦g w akenr =\enjSlfbo(hp$ j P0=¯ µ ¯Bs1 ©"ek\?]']tg¤bµä© q a w \ s1h4sjSloi\ df\?ls1\ j 3h Y \ j w \ ] aco(h Y \5dlfacbd\ lf\?oio4j

(336) 3gSlSrekjfsg

(337) ePopjSendhpanjSl © È=èÈ ¥? Å S 0# ! $# ye j¯ 7'µ 2 & 4 *4 2\ h'¯R¶ ¸ iÁ µ gSl q ¯B¶ ¼ ¸ ¼ iÁ ¼ µ h jopjSendhpanjSlojSl 2 & 4 anh Y I 6=L©¯ v ,6= h Y \ l h Y \ j w \ ] gSmmfenak\?o© µ X4Y \?l} h Y \ } rMg w \&} acl/mg w hians dfeng w opjSendhpanjSlo4jb l 2 &6=L4Rk© (r9h Y \j w \?]

(338) =h Y \ rMsj

(339) acls1a q \&jbl9h Y aco-aclShi\ w Dg ke 2 -6=&4Ê© l q h Y aco&g w Sd]'\?lSh&s g

(340) l=\ w \ m=\ g hi\ q g

(341) oenjSlfg

(342) o&lf\?s1\?oio¦g w r/Sr o Y ak ¥hpaclf/h Y \tanlfanhpacg eLhpac]\ A D Mhij A D 6=LgSl q opj jbl ©k©n©. . ( (. . ;. *,%(' 7 1, '9$ * '

(343) 5 +"5$ %(1'9$ * = ¸ = ¦ Á = µ(anl \7s1jbloph w d|s1h4h Y \7]tgDufan]tg

(344) e2opjSendhpanjSl ¯B¶ ¸ ¦Á q w _. \h5¯R¶ hiakjblo=Sr9s1jSl|opa \ aclf. µj 4¯7'µä=gSo( ¥j w j w q na l|g w r q aG\ w \?lbhpacg eP\?bd|gD. m D o¦dm z I ¯j7'µg q ]'anhio-gtoih w jSlftoij

(345) ecdfhpanjSl ¯B¶ Q ¸ Q iÁ Q µjSl`2 -4 | ¯ m 8 G ³ ´ z | µ M gSl qq \1«=l\&h Y \5]tgDufac]tg ePoij

(346) ecdfhpanjSl _ 89 : 9 ¯R¶ ¸ µ G + = ¯2 & m µá±i® ¯Rsd w e3µiµ ½ + } ¹ 2 - m µä±¯ » ¼ µ À ¿ ; Á G + } ¹ 2 - m µä±¯ » ¼ ½9» ¾ µ À ¿ ½ + ¼ ¹ 2 - m µä±¯ » ¼ µ À ¿ . br ¯ X4Y ano q h Y \j w \?]. R¯ ¶ ¸ iÁ µ =%l Q D ¯B¶ Q ¸ Q iÁ Q µ \1«GlfakhiakjblºanolfjSo¤gS]7fanSdjSdoth Y g

(347) l\o¬hij h Y \ dlfacbd\ lf\?oio w \ o¦dfenh¬j 5s1j w jSekecg w rº

(348) © µ j

(349) hp\/h Y g hh Y \/\uacoihp\ l|s1\ ¬oigèrfoxh Y g h _ D¯B¶ = ¸ = iÁ = µ < > m =. f. m. m. b. 4X Y \5]tg

(350) anl w \?oidekh(j h Y ano-o¦doi\ shpanjSl9ano _ ÄÈ|DÄ. ,5 ¯B¶ ¸ ¦Á µ Vt@!* " " [.

(351) ¯j'7 µ 6 %' )y W j k) R¯ ¶ = ¸ = iÁ = µ(G & *6 "! &

(352) 6' m D 'b" ! [ $ V! @ m M ) enan] ¾ è ¯B¶¯

(353) d A µ ¸ ¯

(354) d A µ iÁÂ¯!d A µpµ D q M M . W(X !. Ø¥ÙÚ2ØÜÛ.

(355)

(356) !"#%$&'("#) *".

(357) . 3 h4aco(

(358) \ w rsengSoioiacsg e gSl q. (. \5m w \ oi\ lbh(akh4jblfenr¬ ¥j w sjS]tmfen\hp\?lf\ o¦o © oio¦d]'\&h Y g h m gSl q h Y g h M ?¯B¶

(359) ¯ d A µ ¸ ¯!d A µ ¦ÁÂ¯

(360) d A µiµ>N < ¥j w oijS]'\ < I 5g

(361) l q ¥j w oijS]'\ oi\ df\ l|s1\ A m ¯Oh Y ano jbdfe q s1jSlbh w g q ansh"m|jSanlbh ¯ ).)µiµä© X g\banlf A D A gSo²h Y \-aclfakhiang

(362) e hian]'\

(363) br¬g

(364) m|mfekraclf7h Y \j w \?]6

(365) \sgSl q \«=lf\g'oih w jSlf7oij

(366) ecdfhiakjbl¬j L¯ 7'µ anh Y anlakhiang

(367) e q g hig¯B¶¯

(368) d A µ ¸ ¯

(369) d A µ iÁÂ¯!d A µpµ²jSl h Y \7aclbhp\ w Dg eJ2 A A 6= 4R© X4Y \ w \ ¥j w \ \&jbfhig

(370) anl Gbr9Sendfaclf==g¬oih w jSlf¤oij

(371) ecdfhpanjSlMjbl 2 A #= 4Ê© o A m \ S\h A 6= I m M -Y acs Y sjSlbh w g q anshioxh Y \ q \«=lfanhpanjSl9j m © X4Y \h Y \j w \?]anoxh Y \ lMm w M jDS\ q br¤sjSlbh w g q acs1hiakjbl ©. (. M. . . . 794 '

(372) , 0

(373) 5.79 ' #7 '

(374) 5 %: 15'9$ *. . (ss1j w q anlfthij'h Y \j w \?]. . . |akh-o¦d ¤ a s1\?o(hpj¬jShig ca lMg'm w anj w a[\ oihpac]'g

(375) hp\?o -Y acs Y o Y g enePm w jD

(376) \h Y g

(377) h4h Y \5dgSlbhpanhýr ?¯B¶¯

(378) d A µ ¸ ¯!d A µ iÁ ¯

(379) d A µpµ%6 ¯Rop\ \¬¯p

(380) ©n µpµsgSl9lj

(381) h-fenj dmMacl9«=lfanhp\&hpac]'\

(382) ©. ? Ä c ¶ f ÄtÈ ¶ ¸ 0É Á \ Y gè

(383) \&g

(384) e w \ g q ¤r op\ \ l ¯Bs1 ©Lm w jbj

(385) j

(386) en\ ]t]tg¤SµLh Y g

(387) h U ÁÂ¯F µ U D Á = ¯F[µ U g© \

(388) -© FWGM³ ´ f A b A -Y acs Y m w jD

(389) \ oxacl9m|g w hpacsdfecg w h Y g h 1ÁÂ

(390) ¯ d A %µ D äÁ = D X4Y \?l \ \ gSopanenr¤

(391) \ h(g¬d|lfa¡ ¥j w ] \ oihpac]'g

(392) hp\&jbl9® m !¯ d µä© l q \\ q f w jb] w \ ]tg w \

(393) M \ q \ q ds1\&h Y g h _ A ® m ¯ F A µ m ¯F A µ D ¸ =%l m ¯F µ Á =%l m ¯F µ MN M X4Y \ w \ ¥j w \ _ á® m !¯ d A µ ¸ =%l m äÁ = % M j w jS] gDu \ ekeR o\?dg hiakjblo \ S\h _ 89 ¶ : < =@? d?¶ s d w e ¸ d?¶ D 9; ? ¸ A B ¶ d¸ D K = ? d ¸ sd w e2 K =? Á d¸ B ?&A ?&A M `d|]']'aclf5h Y \ oi\4h j \?bd|g enakhiak\?o"g

(394) l q aclShi\ w g

(395) hpaclf jD

(396) \ w ³ ´ºen\ g q obgD ¥hi\ w aclShi\ w g

(397) hpaclf&Sr'mg w hio hij&h Y (\ ¥jSekenj anla q d ¼ ¼ U U U U ¹ ¿ ¸ d F D K = ?Á d¸ dF ¶ * < K = = d B f g h ?&A M A f gh \5lfj d|op\&h Y \&gSl q g

(398) dfRa¡ Oo¦s Y anhp¢1p£anen=\ w h\?dg hiakjbl _ ? Á D OG¸HQSR Á U Á U Á R ? Á ?A M T ?&A X g \baclfth Y \5o¦sg

(399) eng w m w j q dsh akh Y ¸ Q g

(400) l q d|opaclfth Y \5lj

(401) hig

(402) hpanjSl

(403) ¯ d d d µL ¥j w h Y \5]'a¡uf\ q m w j q dsh \

(404) \h ? Á d ¸HQD U Á U v Á ? Á ¸HQ x ?&A T ?&A X g \baclfth Y \5o¦sg

(405) eng w m w j q dsh4j 3h Y \&3g

(406) l q gSdÊ2ak Oois Y anhp¢£anec|\ w h(\ dg

(407) hpanjSlMbr ? Á SakS\ o _ Q 9o

(408) ". ÚÚ å öáò1ó . ? i. i. i. i. ¼ Á. ?&A i. i. i. i. DOCv ?. ¸ Q i Á x ?&A Á. ?&A. ¯R© ^bbµ. ¯R© ^=èµ ¯R© ^Sµ \?lShiakhýr ¯R© ^bbµ ¯R© ^S^µ. _.

(409) '* / [

(410) > @ ' . è X4Y \ w \ ¥j w \

(411) f\ ekac]'anlg

(412) hpaclfth Y \5]'akuf\ q m w j q ds1h. _ ¼ ? Á d ¸HQD O U Á U i ? Á i ?&A T iii &? A iii. ¯R© ^Sµ. ¯ X4Y ¬ \ ]\?g

(413) lfaclfMj Lh Y \ w an Y h Y

(414) g l q oia q \tj

(415) Lh Y aco 1\ um w \ o¦oiakjbl Y

(416) g ohpj/=\¬dl q \ w io hpjj q ca l.h Y \¬op\?lop\ \']tg q \'m w \ sanoi\'anl h Y \ w \?]tg w \t^|© µ j Sr q \1«=lakhiakjbl9j

(417) ¸ Q \ Y gè

(418) \ ¯BÁ 5µ d v ? Á x ¸ V d ? Á ? Á d ¸HQD ? Á d ¸. ?A ?&A BSXY D U Á = ¯F µ U \5lj

(419) hp\ h Y g h _ 89 ¸ V Á D U ¸ V d? ? : 9; &? A B v ?&A Á R¯ Á µ5d ? x B XY Y ?&A. ªopaclf¬h Y \ Og

(420) s1h(h Y g h U Â Á ¯F A µ U. Y. DB. ?&A M. ?&A. Á U¼ ? B ?&A. U B¯ Á µ U ¼ n lX Y X4Y \ w \ ¥j w \

(421) \ Y gè

(422) \ _ ? Á d ¸HQD ? Á d ¸ ? U ¸ V Á U ¼ U ¯RÁ µ U ¼ n &? A B ?&A l B M X Y h Y g h4aco4hpj¬o¦gèr

(423) doiaclf¯Rf© ^bbµ _ ? A ¼ ? Á d ¸ D O U Á U i ? Á i ? U ¸WV Á U ¼ U ¯RÁ µ U ¼_n B ?&A B T iii ?&A iii B ? A l B M X Y v endfS

(424) aclfM¯Rf© ^µLanlbhpj/¯Êf© ^Sµ"en\ g q o(hpj¬h Y \&\ lf\ w Sr¬a q \ lbhpanhýr _. Á ¼ dF D ¼ ¼ ¼ U U U U U U ¿ V ¸ ¸ d F Á B ¯ Á µ L K = L K = L K = ? d O U UIi i A f gh B M M M X Y M f g h Á T iii ?&A iii 9Ä EDF}q "! #.84=< % )6#.8t4=< % ! @!g g$ V J@!*! * ¯")pµ ) ¯").)pµ

(425) @!*! " 254 d. . *. ¹ <>= U ¶ U ¼. ¯R© ^bbµ ¯R© ^*Z

(426) µ ¯R© ^gbµ ¯R© ^bbµ. `b\ hphianlf. ¹ <>= U ¶ U ¼ KL= U ¸ U ¼ KL= U ¸ V Á U ¼ KL= U ¯RÁ µ U ¼ ¿ d F ¯B¶ ¸ ¦Á äµ ¯ A µ D fg h B M M M X Y e \?bd|g hpanjSl ¯R© ^bbµL\1um w \ o¦oi\ oxh Y g

(427) h B¯ ¶ ¸ ¦Á äµ ¯ A µano g q \ s w \ gSopaclf OdlshpanjSlMj 3hpac]\S© X4Y aco4]'\ g

(428) l|o4anlMmg w hians dfeng w h Y g

(429) h _ e 1¶7!¯ d A µ% ¸ ¯

(430) d A µ% w \ ]tg acl/=jSdl q \ q anh Y.w \ o¦m=\ s1h hpj¤hian]'\

(431) anh Y gSl/dmm=\ w =jSd|l q acl q \ m=\ l q \ lbh j