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Déterminant microlocal d'un faisceau pervers

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(1)Déterminant microlocal d’un faisceau pervers Raphaël Bondu. To cite this version: Raphaël Bondu. Déterminant microlocal d’un faisceau pervers. Mathématiques [math]. Université Nice Sophia Antipolis, 2002. Français. �tel-00011209�. HAL Id: tel-00011209 https://tel.archives-ouvertes.fr/tel-00011209 Submitted on 15 Dec 2005. 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..

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(27) .   8. 95:. <;. t:n hc3x ovf cia.x g a¶abn5 g ` qÏxlc3a o x ]i^ ` g ³h` q g dm} ` _ fh^ `!Ê ~N` ]3^E` _ s<`!_ q3` c²d f c/q ` _ ~ f c²d ^ ` g c x g d ^ ` ^E`!_ a g3o d x|dznv~ ](fh^ d xlc²d y o ` aza µ a¶d `!Ê ~N`!a ovfEs x g Î  b ab` s f ~ ]<fh^ db` c²d k nv` cž~ f + q g3ovf<  ] x ^)g c3`Œd ^ xlc3a ÉCfh^ ~Nx|dmn f c s xlc f c3nv g `Nq3`¹W`6l` c3q ^ `¬ g n ^ xl~ ` Ê c3` b `!c ](f a¶nKdbn f c  ` _ c ` _ ^ nK g ` C³ f n ^ o `db} ` _ fh^ ` Ê ~ `°:·  ±i· ° ]<fhg3^ g c ` _ c f c s<` _ ]3^E` _ s nKa ·W f ~ ~N` o ` É xlnKd ^ ` ~Nx ^  g ` ^ ¸z·-¹Gx gi^ ` c²d6 s ` ^E` _ a gio d x8dc Ë `!a¶dzabxlc3a+q fhg db` ] x|a ] x ^ dmn s g3o nv` ^Nx Ê o x d ^ xlcia ÉCfh^ ~Œx|dbn f cq3`)¹G`7h` ciq ^ `¬y7n of- ^ `)q3`!a ] ` ^ a ] ` s dmnO³h`!a nvc²d ` _ ^ `!abamx|cedb` a.a g3^ o x q3` a s ^ n ] dmn f c~Nn s ^¶fhovfEs x o ` q3`!a É xlnva s ` x g Î ] ` ^ ³l` ^ a ·. .

(28) ½j`#³h` c f c3a ki^ n `#Ê ³h`!~N`!cedja g3^¼o ` É xlnOdpq3`† g3f dmnK` c²dm` ^¼o ` a s!f ` / s nv`!cedba ] x ^   · r Ë g ci` ] x ^ d  s ` ]i^bfhk3oÌ` Ê ~ `qi`zabn0hc3`zx ]3] x ^ x ( djqÏxlcia o x q ` _ ~ f c3aÅd ^ x8dmn f c g xlciq f c g dmn o nva¶` o `!aBd ^ xlc3a ÉCfl^ ~Nx|dmn f c3a s xlc f c3nK g ` a ]<fhg3^ ab` ^ xl~N`!c3` ^ `!c ]<f a¶nKdmn f c  `!_ c ` _ ^ nv g `|· ¹G` s!f ~ ]<fh^ dm` ~ ` c²dqi` aa µ a¶d ` Ê ~ ` a ovfEs x g Î ] x ^ d ^ xlcia ÉCfh^ ~Œx|dbn f c s xlc f c3nv g `c Ë ` aÅd s f c²d 3^ fh o#`N_  g `Œ~ f q g3ovfg cTa¶n hc3`|·¾1cTd fhg db`  `!_ c ` _ ^ x o nOd `-_  g c3`Nd ^ xlc3a ÉCfh^ ~Nx|dbn f c s x + c f c3nK g ` ] ` g d É xln ^ `x ]3] x ^ x ( d ^ `qÏxlcia o x k xla¶` x Ê oÌË x ^b^ nK³ ` _ `q3`!aŒabnKc g3o x ^ nOd `!_ a g n c Ë `Î:nva¶dmxlnv`!c²d ] xlaÈx g q ` _ ] x ^ d%`!d s `!awc flg ³h` ovo `!a1abnvc  g3o x ^ nKd ` _ aR³ f c²dÈq f c3c3` ^ cÏx|nvababxlc s ` x Ê q3`!a  fhg +  · ÃRx ^ `#Î:`!~ ]3o ` B`!c‚qinv~ ` c3a¶n f c °  o xud ^ xlc3a ÉCfh^ ~Nx|dmn f cžq3`¹W6` l` c3q ^ ``!c²³ f nK` o ` s f + c fh^ ~Nx oˆx Ê g ci` s g3k nv g ` o nva¶ab`)a g3^ o ` s!f c fh^ ~Œx oˆx Ê g c s g a ] · º oÌË x ^b^ nK³ ` _ -`  f cIx g c3` abnvc  g3o x ^ nKd  ` _  o Ë fl^ n lnvc3`zq gPs!g a ] †qÏxlc3a o x k xlab` =} fl^ a+ab` s dmn f cPc g3oKo -`  o ` s f c fh^ ~Nx o x gs!g a ] ` aÅd o nva¶ab` È g nWc Ë `#_ d xlnOd ] xla ]3^E`!_ ab`!cedb`zx g q ` _ ] x ^ d · r Ë x g d ^ ` ] x ^ 6d Èq3`!a`#Î:` ~ ]3o `!a¬`#Î ]3o n s nKdm`!a  o ` s!g a ] ` c ]<f abnOdmn f c  `!_ c ` _ ^ nv g `IqÏxlcia o x ] x ^ dbnv`°:·   `!d oÌË `#Î:`!~ ]3o `q f c3c `_ qÏxlcia  0t  ~ f c²d ^ ` c²d  g ` o ` ]i^bfhoKf c h`!~N`!ced c Ë `Î:nva¶db` gªË x ]3^ ` Ê aÁx ³ f n ^  gif dmnK` c²d ` _ o `!a s f 7` / s nK` c²dma ] x ^   · ÂÈ` a`#Î:` ~ ]3o ` az~ f c²d ^ ` c²d g ` oÌË xl~ k n  g o( d `_ q3`¬a¶n hci`¬c Ë ` a¶d ] xla g c x ³|x|d x ^ q3` o x q ` _ ~ f c3aÅd ^ x8dmn f cª· ¹G`q `!_ dm` ^ ~ nvcÏx|cedz~Nn s ^bflovfEs x o ` aÅd g c3`  `!_ c ` _ ^ x o nKamx|dbn f cTqi` o x ]3^ ` ~ n `Ê ^ ` s!o xla¶ab` s x + ^ x s d ` _ ^ nvaÅdmnv g `†a¶` s f c3qÏxln ^ ` $   ¼x g Îab`!c3aja g nO³lx|cedba†y  abn  ` aÅd g cža µ a¶d ` Ê ~ ` ovfEs x o a g3^ 5 x ovfh^ a)a f c q `!_ db` ^ ~ nvc3xlc²dz~ n s ^¶fhovfEs x o `!c d xlc²dj g ` É x|nva s ` x g] ` ^ ³h` ^ a ^ ` q f c3c3` $   

(29)  # $  5 & ' 7 9   x g a¶nhci` ]i^ ` Ê a   a¶n 2 `!a¶d g c É xlnva s ` x gu] ` ^ ³l` ^ a.a g3^ 5 `!d abn 5 , `!a¶d abxŒa¶d ^ x|db`)q3`)q3nv~ ` c3a¶n f c ~Œx8Î:nK~Œx o ` =aÅd ^ x8dm` fhg ³h` ^ db` x ovfh^ a o `Nq `!_ dm` ^ ~ nvcÏx|ced+~ n s!^bfhoKf:s x o q3` 2  s f cedbnv`!ced) o x s o xlaba¶` $  G l _2  j g k   # $  5 , & ' 7 9  =x g a¶n hci` ]3^ `!Ê a   abn  ` a¶d g c3`a flg #a +̳lx ^ n `#_ d ` _ o nKaba¶`qi` 5 `!d  g `  ` aÅd g c¯a µ aÅd ` Ê ~ ` ovfEs x o a g3^ "x oKfh^ a x Ê g c¯q ` _ s x o x l` ]3^ ` Ê a o `a µ a¶d `!Ê ~N` ovfEs x o  `#_ dm`!c3q gŸ] x ^  ` _ ^bfMx Ê 5 ` a¶d g c É xlnva s ` x gŽ] ` ^ ³l` ^ a)a gi^ 5 q f c²d o `q `!_ db` ^ ~NnKcÏxlc²d+~Nn s ^bflovfEs x o ` aÅd $     # $  &(' 7%9   x g ab0n hc3` ]3^ ` Ê a  ¹G`uq `!_ db` ^ ~ nvc3xlc²d~Nn s ^¶fhovfEs x o `Î ]3^ nK~N` o ` É xlnOdŒ g ` o ` a¬a µ a¶d `!Ê ~N`!a ovfEs x g Î  b ic ` a f c²d ] xla†nvciq ` _ ] ` c3q3xlc²dmayªn o a a f ced o n ` _ a ` c²d ^ ` + ` g Î s x ^ n o a ]3^bf ³Env`!c3c3` c²d+q g ~ `! ~N` É xlnva s ` x g ] ` ^ ³h` ^ a*! f c x g ci` ^ ` o x|dmn f cu`!c²d ^ `  b `#d   a¶n oÌË nvc²dm` ^ a¶` s dbn f c b  ` a¶dÁq3` s f q3nK~N`!c3abn f c  qÏxlc3a · à ^E` _ s nva f c3a s `† g nWab` ] xlaba¶``!cqinv~ ` c3a¶n f c°:·. ±.

(30) t f nKd 2 g c É xlnKa s ` x g] ` ^ ³l` ^ aÁa g3^ 5 U '  ^ ` o x8dmnK³l` ~ ` c²d x Ê g ci` s!fhg3^¶k ` ]3o xlc3`QE x Ê abnvc g3o x ^ nKd ` _ nva fho#`!_ ` ` cu±i· Æ.cxyDEG _2  "g ) 5 " ) 5 "l ) 5 · ¿ f d f c3a s!f ~N~ ` ]3^E` _ s<` _ qi` ~ ~N`!ced !Mo ` s f ~ ]3o#`!_ ~N`!c²d xln ^ `¼qÏxlc3aSEG +2 5q3` o x ] x ^ dmnv` ^E6` _  g3o n ` Ê ^ `.qiH` EHG +2 #· Æ.cx ! U + g ) 5  ) 5  +  ) 5 l ) 5 #· t f nv`!c²d :E    $ 0 0 0 o ` a s f ~ ]<f amxlc²db` a¼n ^¶^E` _ q g3s dbn k3o ` apq3`

(31) E· ¹G`†q `#_ dm` ^ ~ nvcÏxlc²d¼~ n s!^bfhoKf:s x o `!a¶d s f c3a¶d ^bg nOdÁa g3^¼o `!ap~Nn s ^bflovfEs x o nva `!_ aÈa g nK³|xlc²dma†y 

(32) g +2 È g nWq f c3c3` o ` a µ a¶d ` Ê ~ ` oKf:s x o  g a g3^ g ) 5 o `!a

(33)  +2 È g nWq f c3c3`!c²d o ` apa µ aÅd ` Ê ~ ` a ovfEs x g Î  Ga g3^ )  5  ! 

(34) l _2 È g nWq f c3c3` o `.a µ aÅd ` Ê ~ ` ovfEs x o  l a g3^ l ) 5  ! Æ.cc f db`  g G`!d  l o ` apq `#_ dm` ^ ~ nvcÏxlc²dbajqi` aja µ a¶d ` Ê ~ ` a ovfEs x g Î ]3^E` _ s<`!_ q3` c²dma!· ! l ) 5 s!f c²dmnK` c²d g cc f ~ k3^ ` & c3nWq3` s f q3n ^ ` s dmn f c3a  $    · Æ.cx o x ] x ^ dmnOdmn f c ! U ! g 6! l 8±  fGg Ê ! g U g ) 5 !    ± ! ±  "! E  8#± 4U $+E  a f c²d o ` a ](f nKc²dmaÈqi` o x+ab` s dmn f c  c giovo `.} fh^ a fh^ n hnKc3` ! l U l ) 5 !   =± ! ± %

(35) U &'  8#± -ˆa f c²d o ` a s f q3n ^ ` s dmn f c3a x Ê o Ë fh^ n hnKc3`  } fh^ a¼a¶` s dbn f cc g3ovo `  8#± q `!_ abn lc3` oÌË fh^ 0n hnvc3`ÁqÏxlc3a o xzab` s dmn f cc g3oKo `|· 8#± )`!a¶djd ^¶fh]] `#dmnKd Cq3` s f q3nv~ ` ciabn f c°  ](flg3^ nvc²dm` ^ ³l` c3n ^ q3xlc3a o ` ]3^¶fhovf c h` ~ ` c²d · ¾1cNd fhg d ]<f nvc²d%q3` ! g U$1E   o ` ]3^¶fhovf c h` ~ ` c²d s f c s ` ^ c3(`  g `!d g cŒa¶` g3o q3`!)a Ry o ` ^ ` s!fhovo ` ~ ` c²dj` c s ` a ](f nKc²dma ]3^bf ³Env`!ced q gÉ x|nKdj g ` o ` a s!µEs o ` a ]i^bfEs }3` a `#d s#µEs o `!a `#_ ³|xlc3` a s `!cedba o ` ovf c qiH` EG³Env`!c3c3`!ced ` _  g n ]w` _ a¼q3`!ajx g d f ~ fh^¶] }3nKab~ ` apcÏx|d g3^ ` o a *  ,+ x .^ - ˆxlc  `!d *   ˆxlc - + x ^  g n f c²dj~ `! ~N`!apq `!_ db` ^ ~ nvc3xlc²dma · ¾1cId fhg d ]<f nKced q3` ! l U /- 0  8#± - o ` ]3^¶fhovf c h` ~ ` c²d s f c s ` ^ c31`  l `!d s ` ^ dmxlnvcia q3` a  · t:n f c & Î:1` 2uqÏxlc33a   &    &%465  o ` a s!f ~ ]<f abxlc²dm` aq3$` E¦ g n1nKcedb` ^ ³:nK` c3ci` c²dza f c²d o ` a EWdb` ovo ` ap g 7`   )  5 · º ]<f aÅdm` ^ n fh^ n  f c ] ` g djq3n ^ `. g ` o `.a µ a¶d ` Ê ~ ` oKf:s x o  l xx g d flg3^ q3`  `Îix s db` ~ ` c²d o `.q `#_ dm` ^ ~NnKcÏxlc²djq3` o xz~ f c f q ^bf ~NnK`  g n s f ~ ] ` c3a¶` o ` ]3^bf q g nOd¼q3` a¼q `#_ dm` ^ ~ nvcÏxlc²dba q3` aj~ f c f q ^bf ~ nv`!aÈq3`!8a  s f c s ` ^ c `!_ a · à oKg a ]3^E` _ s nva `!_ ~N`!c²d la f nK/d 2 9  &    &%465  & Î `p_ `#d5a f nO;d :< g c ] `!dmnOd o x s `#dBq3N` l ) 5  !  g n ` c²d fhg3^ ` o x s!f q3n ^ ` s dmn f = c 0&·È> º :<` aÅdxlaba f:s n ` _ ] x ^Œo `ua µ aÅd `!Ê ~N` oKf:s x o  l g c c f ~ k3^ ` ?@! ' ) ·. ,.

(36) t f nKd.*†y U      &    &%4  7 0 ] )  5 e·<à fhg3^ d flg d  qÏx|c3a(* o `†a µ aÅd ` Ê ~ ` ovfEs x o  -x g c3`+~ f c f q ^bf ~ nv`    x g d fhgi^ qi` o x s f q3n ^ ` s dmn f c  qÏxlcia" )  5  ! · ¹ Ë 6` _ hx o nOd ` _  g n ] ` ^ ~ `!d¼qi` ]i^bfhoKf ch` ^po `.q `#_ dm` ^ ~NnKcÏxlc²d¼~ n s ^¶fhovfEs x o a g3^  `!a¶d+y. ? "U c     . r xlc3a o ` s xla ] x ^ dmn s g3o nv` ^ q Ë g c É x|nva s ` x g ] ` ^ ³h` ^ aNa g3^  '  & ±   f c ] ` g d q f c s nvc + dm` ^¶]3^E`#_ dm` ^Áo `.q `!_ db` ^ ~ nvc3xlc²d¼~Nn s ^bflovfEs x o<s f ~ ~ ` a g nOd ·  g U G l +2  j g  `!a¶d g ca µ a¶d ` Ê ~ ` oKf:s x o a g3^ 5  E· t:n :E    $ 0 0 0 q ` _ a¶n hci` o ` a s!f ~ ](f abxlc²dm`!ajn ^b^E` _ q g3s dmn k3o `!aˆq3`IE% o ` ÉCf c s db` g3^  s#µEs o `!a `#_ ³|xlc3` a s `!cedba o ` ovf c Nq3` E ÉCfhg3^ c3nKd g c É xlnKa s ` x g 2  2 ] ` ^ ³h` ^ a.a gi^ E ^ ` o x|dmnO³h` + ~N`!ced x Ê oÌË fh^ n hnKc3`l·

(37) ± e·  Gy U G l  2  2  j    `!a¶d g ca µ a¶d ` Ê ~ ` oKf:s x o a g3^ E  y U E  8 ¹G`+q `#_ dm` ^ ~NnKcÏxlc²dj~Nn s ^¶fhovfEs x o q3I` 2 s f c²dmnK` c²d x g a¶n hc3` ]3^ ` Ê a o ` ajq `#_ dm` ^ ~NnKcÏxlc²dma¼q3`!a a µ a¶d ` Ê ~ ` a oKf:s x g Î  g `!d 

(38)  &   4 Ï`#d x g3s g ci`x g d ^ `+nKc ÉCfh^ ~Œx|dbn f c · ¹G`a µ aÅd `!Ê ~N` ovfEs x o  l a gi^ l ) 5  ! c Ë x ]i](fh^ dm` ] x|a+q Ë ` _ o#` _ ~ ` c²d†c flg ³h` x g y ` c g c s ` ^ d xlnKcab` ci6a ²n o ` aÅdw`Îix s db` ~ ` c²d o `ˆa µ aÅd `!Ê ~N

(39) ` ovfEs x o q f c²d o `ˆq `!_ db` ^ ~NnKcÏxlc²d s f ~ ] ` c3a¶` o ` a¼q `#_ dm` ^ ~ nvcÏxlc²dbapq3` aj

(40) a µ a¶d ` Ê ~ ` a ovfEs x g Î  Ì· Æ.c ] ` g d ] `!c3ab` ^ x g Î   s f ~N~ ` x Ê qi` a5a µ aÅd ` Ê ~ ` a oKf:s x g Îa g3^ qi` a5q3nKab g ` a ` _ ](f nvc²d `!_ a ! ) 3q3nKab g ` aj g nWa f

(41) cedjd flg ajx|dbdmx s } ` _ a¼`!c o ` g3^ps `!c²d ^ `|·<¹G`†a µ aÅd `!Ê ~N` ovfEs x 5o  l ` a¶d o x Ê ](fhgi^ |³:nKaba¶` ^  o `!a  G` c²d ^ ` + ` g Î(· È `†~ ` _ ~ f n ^ ` ` aÅd ^E` _ q3n0 ` _ s f ~N~ `.a g nOd · ¹x ]i^ ` ~ n `Ê ^ ` ] x ^ dbnv` ^ `7 ^bfhgi] ` g c s ` ^ d xlnKc¬c f ~ k3^ ` qi` ^E`!_ a g3o d x|dbawdm` s }3c3nK g ` a¼`!dpqi` ^ x ]3] ` o a¼ g nWab` ^¶f c²d g dmn o nva ` _ apqÏx|c3a o xza g nKdm`|· ¹xq3` g Î:n ` Ê ~ ` ] x ^ dmnv`.`!a¶d s f c3amx s!^E`!_ ` x Ê o x s!f c3a¶d ^bg3s dmn f c`#d x Ê o xzq ` _ ~ f c3aÅd ^ x8dmn f cqi` oÌË `#Î:nvaÅdm` c s `+q g q `!_ dm` ^ ~ nvcÏx|ced¼~ n s!^bfhoKf:s x o q Ë g c É xlnKa s ` x g] ` ^ ³l` ^ a · ¹G`Iq ` _ s flg3] x h`/q3` s `!d¶dm`Iq3` g Î:n ` Ê ~ ` ] x ^ dmnK`@a g nOd o nKc ` _ x|n ^ `!~N`!c²d o `!a `!_ dmx ] ` aq3` o x q ` _ ~ f c3aÅd ^ x8dmn f cª· Æ.c s!f ~ ~N`!c s ` ] x ^ ~ f c²d ^ ` ^  g ` o ` ]3^¶fhk3oÌ` Ê ~ `Nq gž]i^bfhoKf c h`!~N`!ced)` aÅd ovfEs x o a gi^ ) 5 `#d g `a¶n o ` ]3^¶fhovf c h` ~ ` c²d†`#Î:nKa¶dm-` Wn o `!a¶d g c3nK g `  ] x ^ dmnK` °:· °  ]3g nva. g ` o `. °.

(42) ]3^bfhoKf ch`!~N`!c²d ` cIqi` } fh^ a.q Ë g cIa fhg #a + `!c3ab`!~ k3o `q3` s f q3nK~N`!c3abn f cI°ŒqÏx|c3a a g /d  ] x ^ dmnK`+°:· 8 #· ¹G` ]3^¶fhk3oÌ` Ê ~ ` q g]3^bfhoKf ch`!~N`!c²dpa g3^¼o ` a ](f nvc²dmaˆqi` o xzab` s dmn f cc giovo ` g ) 5  ] x ^ dmnv` °:· ;} fh^ a s f q3nv~ ` ciabn f c °uab` ^ xl~ `!Ê c3`  ^3x  s ` x/Ê °:· + x gžs xla/  X 5 U   g nÈ` aÅd d ^ x|nKd `._ q3xlc3a o x ] x ^ dmnK`+°:· :· à fhg3^ d ^ x|nKdm` ^o ` ]3^¶fhovf c h` ~ ` c²d} fh^ azab` s dmn f cTc g3oKo ` f c ^ xl~ ` Ê c3` o ` ]3^bfhkioÌ` Ê ~ `Œ`!c ](f a¶nKdbn f c  `!_ c ` _ ^ nv g `  ] x ^ dbnv`+°:· = · à fhg3^ a¶` ^ xl~ ` c3` ^ ` c ](f abnKdbn f c  ` _ c ` _ ^ nK g `  o xŒd ^ xlcia ÉCfh^ ~Œx|dbn f c s xlc f c3nv g `q3`¹W` + h` c3q ^ `+a g /d  ] x ^ dmnK`+°:<·  #· Æ.c s!f c²d 3^ fh o `)x ovfh^ a o ` s f ~ ]<fh^ db` ~ ` c²dÁq3` a.~ n s!^bfhoKf:s x o nKa ` _ apqi`tix|d f q Ë g c É xlnva s ` x g ] ` ^ ³h` ^ a ] x ^ˆo xd ^ xlc3a ÉCfh^ ~Nx|dmn f c s xlc f c3nK g ` É xlnva s ` x g dmnK g `.xla¶a fEs n `!_ ` x Ê o x)d ^ xlc3a ÉCfh^ + ~Œx|dbn f cPq3`¹W6` l` c3q ^ `  ] x ^ dbnv`°E·  ± +` cž`Îixl~NnKcÏxlc²dqÏxlc3a g c ]3^ `!~NnK` ^ db` ~ ] a s `  g nªab` ] xlaba¶` ](fhgi^ˆo `!a É xlnKa s ` x g Î s f c3aÅd xlc²dba 9  fWgÊ  `!a¶d g ca fhg #a + ` a ] x s `.qi` 5  ] x ^ dmnK`+°:·  #· t:` o nv~ nKdm` ^ x gs xlaÁq3` 9 ] ` ^ ~N`#djq Ë x8dbd ^ x ]3] ` ^jo `!a    g ` oÌË f ca fhg }Ïx|nKdm`+ g n ]3^bf + ³:nK` c3ci` c²d†x oKfh^ ajq Ë g c3` ÉCfh^ ~ g3o `+qi`Ã5n s x ^ q + ¹G` É a s }3`#d  ]ig nva¶ g ` o `!aÁa¶` g3o ` a a¶nvc  gio x + ^ nKd ` _ aj g nBx ]i] x ^ x|nvaba¶` c²dÁ g xlc3q g ci`d ^ xlc3a ÉCfh^ ~Nx|dmn f c s xlc f c3nv g ` ^ xl~ ` Ê ci`)` c ](f ab,n + dmn f c  ` _ c ` _ ^ nv g `†a f c²dÁ g x|q ^ x|dbnv g `!a · Æ.c g dbn o nKab`.x ovfh^ a o ` ÉCf c s dm` gi.^

(43) GDR'X qi`  0t  ](flg3^`!_ dm`!c3q ^ ` o ` ^E` _ a g3o dmx|d x Ê g c É xlnK#a + s ` x g] ` ^ ³h` ^ ap g ` ovs f c3 g ` ^ xl~ ` c ` _ ` c ]<f a¶nKdmn f c  ` _ c ` _ ^ nK g ` ] x ^wo x+d ^ xlcia ÉCfh^ ~Œx|dbn f c q3`+¹G7` h` ciq ^ `|· ¾1c ](f abnKdbn f  c  `!_ c ` _ ^ nv g -` (} fl^ a s f q3nv~ ` c3a¶n f c°  o ` ]3^bfhkioÌ` Ê ~ `†ab` ^ xl~ ` Ê ci` ] x ^ °E· + x Ê  °  ] x ^ dbnv`+°:·  ° · s ` oKg nWq3`  X 5 U  ¹G` ]3^¶fhk3oÌ` Ê ~ `z` c/q3nK~N`!c3abn f c °¬` c ](f abnKdbn f c  ` _ c ` _ ^ nK g ` ^ `!³Env`!c²d x¬Ê ~ f c²d ^ ` ^  gªË g c s ` ^ d xlnKc ]i^bf q g nKd+q3` q `#_ dm` ^ ~NnKcÏxlc²dma†q3` ~ f c f q ^bf ~ nv`!a ³|x g d    ] x ^ dmnK`N°:·  8   s `  g n-`!a¶d É xlnKd¼qÏx|c3a o x ] x ^ dbnv`°:·    fWgÊ oÌË f c g dmn o nva¶` o `!ajqi` a s!^ n ] dmn f c3a s f ~ k nvcÏx|d f n ^ ` a q3` a É xlnva s ` x g Î ] ` ^ ³h` ^ aÁ`!cdb` ^ ~N`!ajqi` s x|d 7` _  fh^ nK` apq3` ^ ` ]3^E` _ ab`!c²d x|dbn f c3ajq3` s x ^  g3f nKa q3`+Ã1} · {xlnva f c fhk `l·. 8.

(44)

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(128)  ] x ^  iU,  X 5 & X 5 & 

(129)   5  3 5 , &  3 5 !  X 5 & X 5 

(130)  2  $  e· r f c s Ïa¶n f c ]3^ `!c3q ](fhgi^ps x ^ dm` $ g c3` s x ^ dm` d ^ nK³EnQx o nvabxlc²dm`Áq g &3k3^E`._ ³h` s d fh^ nK` o  f c x  KU,   && 

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(138) Ã hf g3^.s ` o x f c ] ` g d.ab` o nv~ nKdb` ^zx Ê ^ `7²x ^ q3` ^ s ` g nRa¶` ] xlaba¶` ](flg3^ g c É xlnKa s ` x g 2 x g q3`!aba g a q Ë g c fhg ³h` ^ djd ^ nK³EnQx o nvabxlc²d   3 5  q3`A  fWg Ê  `!a¶d g c fhg h³ ` ^ d qi` ! · Æ.cxx ovfl^ a o `.qinQx ^ xl~ ~N`y. 3 . 3 8±# .. 5 (. 3. /.  3 8 ±  & &±  3 . . . . 3. /. 3. 5 5 . . 5.  3 . o. 5. 35 ) . . m mmm m mm m mmm  vmmm. . 1¾ c g c ]<f nvc²d    5 3 8±#   A U A  o x &Ïk3^ `q g É x|nva s ` x g 2 ` a¶& dy &  $ 6  $ 2 *   l - U &+& &&o & nv&~ & &&& /  /    3  3  7 &  & 6  & $ 2  ]3g nva¶ g ` o `!a 83  3   7 &   fWg Ê  ` aÅd g cz³ f nvabnKcÏxh` fhg ³l` ^ dBq3`   ³ f nvabnKcÏxh` fhg ³h` ^ dq3`  

(139)  5 )  ÉCfh^ ~N`!c²d g c a µ a¶d ` Ê ~ ` ÉCf ciqÏxl~ ` c²d x o q3`I³ f nKabnvc3xh` aqi` r &  & ± wqÏxlcia A  · &  & &   Ë x g d ^ ` ] x ^ d  f cx  $ 2 ) 2 $ 6  $ 2* l - U & && & o & nv&~ & &&     3  3 v± &  & 6  & $ 2  & / / `!d & o x &Ï& k3^ `†q g ~ fh^¶] }3nva¶~N& ` q Ë x|q8& ´ f c s & dmn f c  $ 6  $ 2 *   l - 7 9  $  2 ) 2 $ 6  $ 2*   l -za¶` o nKda g3^o ` a o nK~NnOdm` aŒnvc3q gis dmnO³h`!a s f ~ ~N` g c ~ fh^¶] }3nva¶~N`uq3` ^ `!a¶d ^ n s dmn f *c ˆ g n `!a¶d g c nva f ~ fh^¶] }3nKab~ ` ]3g nKab g ` o `. É xlnva s ` x g 6  & $ 2 `!a¶d s f c3a¶dmxlc²dÁa g3^jo ` a &3k3^ `!a   3    3 5j· . . .  . . . . . . .  . . . . . . . .    0 ²D<F-D

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