Probability Around the Quantum Gravity Part III.1: Planar Pure Gravity
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(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Probability Around the Quantum Gravity. Part III.1: Planar Pure Gravity. Vadim Malyshev. N ˚ 3493 16 September 1998 ` THEME 1. ISSN 0249-6399. apport de recherche.
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(19) p,VYL oWVYi H c VYplhXCiVk]a c plU I K K©i®KMplY] I U KMmlhKMUV K©o plU]VYp@] ¥ a H I K c m p¶] I KTU0KMo pCm VkjCj VYo I UV¦i ]]0i®KN| ]&L Ui®KWVYm plf| KMoWVYXlU0K{] I K K Up m[_p,VYL oMUVk] VYii p\a ] Il U*Vkjlj ac VYo I ³«L{ V p\]0KMo I p XlaKMU*XlUKMU |C|CaUnc KM@X i | a XlLm a U] a |,X[] c plU c pfi¡V a hK L{Vk] oMKMUM H*I Vk] U I _ a ii±oWVYa ii I a K K] I cKMUKsVkjlj a cVYo I KMU*KMX c i | chXC L\ H I K©m[_(pCVYL oMU*Vkjlj KWV KMm KWV i K pfe p@]0K£nV i U LXliVk] plU @XCVYp@]0XlL a VMg ]_h K I a K ] a _s] c I gwa K V j ac c |±Vkc | i Ä U0] cW o p c a ]% pXlaLNa K acY aoWc VYi¡¥.U0a ]0Xlm[_ chC a KMi®K^I ghVYp ]be¦ V a0Äwc gc j a c oMKMc U0UKMUM c Vk] UÏpCKa K K m p ] p KWa V c i K XCU KMUXli ]0chU ¥ UÏ] Vk] ac K VYp]¨] VYm[g oWVk]0K p ac ]&pXlLNK oWVYi%|CX[]&VYpC VYi®_@] c o{cVYplmj |,c Vk| i U] oa U]0Xlc m KMU a U0Xlc o I j a oMKMU0U0KMUW\ I _U0c Xlo I j oMKMUU0KMI UoWcYVYa p | KsXl UK ¡cYXla iÏp ] c pCi _ H* pfI o a L j,a X[]0K e ap@]0K¢¤£nc V i K¢Z(jK LNI KMp@a ]0U |CX[I ]cYVYa i®U VYU g pC&] K K^] oWVYi p L{Vk] p K KV KLVYp@_ KWVYU plU° K gwK K K©VU ] i U]M KM i®i Ä p cW p\c m oMXli ]µ_ p\c VMgwK a IlVY Ipl ac gwK Ä a VYcyi® i±] c j c c i c KMU cYU°a ] I I Vk]Mª pTu m LNKMc plU c plUMª ] ploMi®XlmlKMU*U LNKsXlKMU] plU o V K p pf] | K&VYi® ] L oWVYii _{XlpCU i ghVk|Ci®KY J_pCVYL oMUsU0Xl|CU] ]0X[]0KMU] IC Uj ac |,i®KML ] I VfplK c plKY³ plU]0KWVYm ch VMgwK a VY pC K V c a Kc i cc cYÄ pC ;cYa V{j a c oMa KMU0U ] I V a a| c ] a V a _ c p ] VYiÏU0]Vk]0Kyc¥ Il o I i®iÏa hKMplK a Vk]0KNVYi®c i ] j ci KMU ]%oWVYp{hKMplK Vk]0KY ;cYH a IC U j oMKMU0U%Uc I Xli®m I c VMgwKU LNK c U0_LNLK^] a KMc U |CX[]bVYiU ] U I XCi®m§|K©VNi®KM ] LVk]0K K¢ZlVYL jCiKp p(K¢Z(jCi m pl¥bU] o I VYU] oj oMKMU0UM I Vk] c pCcYK a °c Xli®m+ i Ä K] c a I VMgwK VYU p¶] I K{U] c o I VYU] oT@X,VYp] 21 Vk] c p p¶aÄwXCc VYp]0XCaLc ¬ KMi®mf] I K _fVYplm iVYX[| K ml_pCVYL oMU pU]Vk] U] oWVYi¨LNKMo I VYp oMU ¥ UV{eV gfj oMKMU0U©cYa i®KWVW g pl a |l|Ca ULNa KWVYU0X a K pghV a VYp@]M c H*Il U U@X ]0K&p,Vk]0X a VYi p¦@X,VYp]0XlL ¬ KMai®m ] II K a _ I K K&] a I K K V K IC ]0KML VYp¹VGcYZ a LN U©VYplm pU]Vk] I U] oWVYi I LNKM o I VYp oMU I K a K ] K K U VmlK^]0K L p U0] a om[_(pCVYL c oMUL K XlpCmCcYaVYLNKMa p@]VYiÏ] VYp] K |l|,U*LNa KWVYU0X K ]0U0KMi p+XCVYp@]0XlL VMg ]µ_>| ] I ] I KMU0K VYo^] UV K\Vk|CU0KMp@]NVYplm VYp VYi ]0K pCVk] gwK g K j c p]«o c Xli®I m{|KIVYm[gw K a ] UKMm ³ ] I Vk]«a ] I K*j a c oMKMU0U ]0U0KMi oWVYp| K ]V Ä KMpT] c | K*L cYa K XCplmCVYLNKMp@]VYi] VYp\] K |l|CUnLKWVYU0X K ]0UKMi J_pCVYL oMUVYii cW U&] c o c plU mCK a ] I K a KM c p>| KMi cW ] I K§o a ] oWVYibj c p] I K a K{KM@X i | a Xla L ¡m cY a U] a |CX[] c p I VYUp c UÄ KMplU0KY acy p¶] I Ko c p@] a a V a _ ] IC U a KMc c p U&a K^gwKMp+L cYa K pCVka ]0X VYi ] I Ä K©m[cy_(3pC¡VYaL c oMU°bi K©a VN pl XCp gwK U0K cYa pTc ] I K©a o L jCXl]0K ] LNKYªC] I cK ]0Kc L Il o I c p a L#Vc j,Vkj K |_ ¯sa (e hmCVYi¡c ¥ %e K gwc K m[_(pCaVY;cYL a oMUb gwKMUVYiU U LNK UKM plU0KTc ] c m Ä U] cW |,X[] plU p ] I K o c ] oWVYai°j a pch] ] I X[]j K L plaU0oWVYi pl ia L c ]0UM ac m p ] p c ] chI Kj I _(U oWVYi¨o Xlp]0K j,V ] VYii] IC U|CX[] ]0UpCVk]0X VYi®pCKMU0U L~j |,Vk| i ]µ_Nj p] g K U K^g mlKMp@]M . . . . . ;=<4U>;?.
(20)
(21) !"#%$&'( . . I WV gwKNVk|CU c i®Xl]0KMi _fp c j I _U oWVYi V a hXlLNKMp@]0U ¡cYa ] I Ko I c oMKNVYplmK^gwKMp a KMi®K^ghVYploMK ch ] Ic K\m[_(pCVYL Ä oWchVY inL c mlKMa iUMªb|CXl]] I c Vk] a UNVYi®U c c ] a XlK ¡cYa VYi®inL c mlK a p a Vkjlj a c VYo Ic KMUNmCXlK ] ac ] I Ki¡VYo K¢Zj K c LKMp]VYio p ¬ L{Vk] p H I KfiKWc VYm pla ¶] I KWVYm oWVYp pla i _ | K j |,Vk| i a U] o p]0X ] c p{VYpl m{ | KWVYX[]a _h«Q*KMi®a K^ghVYp]°XlKMU] pTV KY³ I Vkc ] UXlp a gwK UVYi ]µ_ VYcplmThKMplK oUc ]0XCVk] a c p ] VYa U V hXCKMm KMoMKMp]0cYi _ha ªlUKMK `b8 thatc 9Òª[] I Vk]no L jCX[]0K U0o KMploMK o Xli®mjCi¡VM_U a LNK Ä i®K p X[a ]0X Kc j I _(U oWVYi ] I K KMUM |,a Vk| i U] oa VYUj cKMo^]0U ch Il o I Km Ua oMXlU0U acWI K K*LV K]c Il U KMa iVk] p§@a X ]0K cYaK^g mlKMp@]b|_V©j a KMi L a p,V _sL a mlKMi ] a I K Xlc p gwK U0a K° c plgc VU c LKnch VYLNLV L KnK¢Z[VYo^]0i®_V Vkj I VYLNLV ¥¨U L iV i _ ] ] I K VYplm L~K^g i®X[] p V iVYplhXCVYhKY eVk] I KMLVk] I oWVYcYia ] I K aa cL c mlI _pCVYL o ] I K cYa _K¢Z U ] pl ;c cYa U]Vk] a U] a oWVYiI LKMo I VYp oMUTVYpCm @X,VYp]0XlL ] K _{| Xl ]«L{VYp_§plK mlKWVYUM ] UU LNKU0X j U0K°] Vk]nVYp\Vk]]0KML jC] ] c o c c plU0] a Xlo^]s U L iV a ] I K cYa _ ;c cYa a cW pC o c L jCc i®K¢Z[KMU©| ac Xl I ]s@X ]0K XlplK¢Z(j KMo^ ]0KMm jch I KMpI L3KMpCV UKMK 8 I uwt 9Òª 8 c uhu 9¡¥ I j c K XC¬ i®i _ I VMg cY a pl § U LNK&j I _U ¬ oWVY iU hp ¬ oWa VYpCoMKy ¥ I c plK ] KNK KMo^]0U U©] Vk] plKNoWVYpCp ] ZVYp p pVYp p p ]0K&Xlp gwK U0K ] X[] K a LNKMi c VGZ c L\ªlVYp@_o c plU] a XCo^] gwK p] a c mlXCo pl ch V&i c oWVYi c |CU0K a gwK a o I VYplhKMUnm a VYU' ] oWVYi®i _{] I K©Uj±VYoMK] LNK p IC UnplK I | cYa I cc m ]5oWVYplp c ]5|KKWVYU_] c ¬ plmo a ] oWVYi(K¢Z(j c plKMp]0U |_e c p@]0K¢¤£nV a i c U L&XCiVk] c p&|KMoWVYXCU0K ]c I K©VYU_(L jl] c ] o ch Unm c L pCc Vk]0KMmT|_] I KK¢Zj c plKMp@] VYi]0K a L Il o I mlK^j KMpl;mCcYUa U0] ac plha i _ p¦] cI Kmlc K^]V i®U ] IchKL a mlKMiÒ cI Vk] UXlU0XCVYi®i®_TU L&XCiVk]0aKMm ch U] I KXC p L c m U] a |CX[] a cW p p] Ic KU0K^] I ] VYpl hXli¡Vkc ] plU c ] ¬ If¬ Z(KMm¦p@XCaÄwLsc | K ac oMKMi®i®UM KI o plU mlK Va pl c o L jCi K¢Z{] KMp c Ko Xli®m\p ] plm V c eV c gTj a oMKMU0c Un g a pl] ;cYa KplKMoMKMc U I chUV LN_¹KWK¢VYZ(U0j X a pCKMUWKMªlp] ]0I U Vk] ] U K oWVYVYi®L i®KMm XlXCUsU0· XCVY¸ i®i _TºV »¼ p ¥c |CplX[i ] plKWV pla i _e¦U V a0LNÄwc K g\jVYpCa c m oMKML U0UKM] UMª,VYpl U g plL]VkI ] KMUp K K¢Zj c plKMp@]0UM A  . ¾ . y  ¾ ? ? ¾ plK¢m LNKMpCU c pCVYi.oWVYUK U0KMo^] c p ; ¥ UXCU0K XCi pfj,V a ] oMXCiV a VYaU§KML j I VYU 2 1M pl¶i p Ä U | K^] KMKMp oMiVYU0U oWVYi j ac |±Vk| i ]µ_ VYpCm2] c m LNKMplU c p,VYi*XCVYp]0XCL VMg ]_h c pU0a KMo^] p a t* ] I K«L c p LXlL chc plKMoMKMU0UV a _&mlK ¬ p ] c plUÏV a K° gwKMpo c ploMK a p pl*o c LNjCi®K¢Z[KMU VYpCm oMX ghc Vk]0X K c pT] m LNaKMc plU pCcYVYa ioWVYU0KY c a c z( c KMo^] ;puo p@ ]V plU I p@cY] a mlXlo^] c _© cmCK ¬ chp ] pCUMH ªyj |Cai®c KMLNIU¨VYplc mU c a LNK Ä p cy a p aa KMU0Xl i®]0UM I p Uc KMo^] pfc t ch K© gwKsVc U c ] K¢Z(j c U ] p Qe c Vkjlj c VYo a ] j,X Kc jCiVYpCV c VMg ]_hª,cYa ] K pCi _sac VYi ] Il U5K¢Z(j U ] p U ] KML j I VYU 2 1 K°U LNKj p]0UWª KMiVk]0KMm] ] I Kno L&| pCVk] VYi VkjCj VYo I c oWVYiL c mlKMiÒª I K a K©] I K&oMKMi®iUV a KVkjlj KMplmlKMm p a VYp( ¦ p 0 U M K ^ o ] p K U 0 ] l X [ m f _ { V [ m ( _ C p Y V L m c L²] c ] I K | c XlpCmCV a _ ch ] I Km U Ä H Il UL c mlKMi U©U c i ghVk|Ci®K g V a VYplm c L VYi Ä U ¥VYpCm . . . . UVUXW7Y[Z]\[^]Z.
(22) K
(23) ] ['. }. #. \K oWVYi®oMXli¡Vk]0K§U c LNK\LV p XCVYp] ] KMUM H I K§K¢Zj c plKMp@] ¡cYa ] IC UL c mCKMi U\º ; VYplm ] I XCU ] |KMi c plhU] c V¹m 43 K a KMp]NXlp gwK a UVYi ]_¶oMiVYUUN] I VYp L c mlKMiUNVYoMoMK^jl]0KMm p j I _U oMUMX[] o c p@ ] pXlI XlL I i L ] p§] cIl U°L c mlKMi U KMii±mCK ¬ plKMm ª( gwKMU Uj±VYoMK ] I V&o c pCU]VYp] oMX a gYVk]0X a K VYU pT] Kc j _(U oWVYi L mlKMiÒa a c a c a a0Äwc I I aj c oMz(KMKMUo^U0] KMU p x I K Ua K©] VYKi®U oMc KMp@o ] I VYVYpli hp§KMU] V a KKj,j Vkc j U0K U |C5i®K c Kplo i _ plc U0p] Xl] I o^]*K©VY| plc m\XCplUmC]0XCV m[a _l_¥ p Ilpli o plI KWaV KMplemlK V a ] I g K KMcX a i c | a XCL²m cU] a |CX[] c p pghV a VYc p@]M¹K\XlU0K§] I K c H X[]]0 K Xlc pCo^] c pCVYi°cYa KM@X,Vk] c p LNK^] I c mc ] j gwc K] I Vk] cYaa plKhK^c ]0U º ¼§» K¢Z(c j pCKMp]M©KmlK^gwKMi jplK o Ls| pCVk] VYi¨]0KMo I p XlKMU] U0]0Xlm[ _{i oWVYi.c o KM iVk] c p Xlplo^a ] plUM a c I a I I I co LNjCpi®K¢U0ZKM5o^] KspU ]0XlmlK_{o iV pCa hU K©ml] K LNm[K_(| pCK VYI L VMg oM U cYa ch K U0KXlo o I VYe¦plhV a0KMÄwUc oWg\VYpj a | c K&oMKMm U0UKMpCUMK& KMi®UK K K p] K § . ÂÁ ¾ Và 6 ¾ . y ] I VYp Ä D% ` VYU]0X a¡cYa KMi®Xlo m,Vk] pl\] c LNKU c LNKj c p@]0U ch ] I K Qc VYplm c L=e¦Vk] a Z H I K cYa _ VYplm2z±bz I i c ULVYp ¡cYa a KWVYm pl¦] I K§j,Vkj K a VYplm gwK a _ I KMi j Xli o LLNKMp]0UW ~N !´ b * 0
(24) 5$& '( 5 cYa ] I K jc I _(U oWVYi a p@ ]0aK a j c a K^]I Vk] c p a ch; ] chI K c pCK¢dm cY aLNKMplU c pCVYia a VMg ]µ_¹VY pCm¹a Lc VYp_¦I | KWa VYX[ ] Xlc i oWVYioMXliVk] ac plU K K K ] o c Vkjl]0K ¯L&| p U&iKMo^]0X KMU 8 tO 9Ò X VYi K K Us] c gwKsV j |±Vkc | i U0] I o g K j a p@]*VYplma m U0oMa XlU0Un plK c Vkjlj ac VYo I KMUMc H*I K a K Unp c c ] c j c i c Y _ p a a pCVkKj m I LNKMplU p.³.] KXlplmlK i®_ pCU] Xlo^]0X K oMKMi®i±o L jCi®K¢ZC¥ U plK¢m LNKMplU pCVYi[5Vsi plKWV σ. 1. σ. 2. σ. 3. .......... σ. N. 5 hX a KOh³ D plKWV a U0j pT a Vkj I. c ac U c LNKVYi j I Vk| K^]ToWVYp | Ko c plU mlK a KMm VYUV XlpCo^] c p c p I ch agwK ] ¯´ oMKMo U chV p U0Xlo I U0 _a L&Vkj | I U i®U U0KMK L 5 hX a KOG¥
(25) !#" Ks gwK©p cy ] I K|,VYU omlK ¬ p ] c p p\L cYcYa0a a KsVk|Cc U0] a VYo^] ]0cYK a a LNU c] ` I VYc p p Äwc 8 tO 9Òª a ] I c X[]°j a cYa KML&c | KMmlm pC p <bc XCoMi mlKWa VYp\Uj±a VYoMKY³] c IC U*c o KMUj plmlchU L K©] a i _V ga U] pl c XCVYp] 1 VG ] p ÏK«U I VYi®iho plU mlK m U] |CXl] plU p©] I KbU0K^] ¬ p ]0K5i plKWV Uj p Vkj I U U LNK^] LNKMU. ;=<4U>;?.
(26)
(27) !"#%$&'( . v. bK XCU0K5] I Kb]0K a L p c i c Y_ ¡ac L c X a j a K^g c XCUj,Vkj K a U.|CXl]ÏL c U]0i _ ]oWVYp©| K%U Ä jlj KMm,¥ H*I Vk] U%] I Km U] a |CX[] c pCU c ,p{ ] I KU0K^] . ch U] a plhU I K a KU0 ] a pl©o c LKMU ¡ac L#o c L jCX[]0K a U0o KMploMK ]0K a L p c i c Y_l¥ ¸cY a
(28) ª I K a K²¸ I E O ; I VYpla m
(29) * 7 ªcYa I K a K 7 U°VYp§VYi j I VGE | cYK^a] a Uj c p§Uj,VYoMc Ky¥ 5 K¢Z[VYLNjCa i®K oWVYp§| Kc ] KXlp ]bU0j a K a K p p «£nc VYU0K ¸ I I ¬ o KMUj a plc mlU5] ] K KML jC]_NU] pl ] p ËghVYi®XlKnj KMU0o | KMm 4JK plK ] I K p plplKMwVk] gwK LKWVYU0X K p . |@_ +-,. OG¥ .¥«¸3K¢Zj º º
(30) ,
(31) , -¥ ¼
(32)
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(34) OE. K
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(82) & * K a K cKj a KMU0KMp ]n] c I KL p LXlL ch |,VYU c omlK I¬ p a ] c plU°o c ploMK a p a pl c oMKMi®iÏ U] a Xlo^]0X a KMUM Ä ¯ o L jCi®K¢Z U |l]V plKMm|_hi®X pl] hK^] K ]0U«KMi®KMLKMp]V _{o plU] ]0XlKMp@]0U« oMKMii®UMª@i K I] KLVk]]0K a o c pCU U]0U ch L c i®KMoMXli®KMUM pCKU I c Xli®mN| KgwK a _oWV a K Xli p§mlK ¬ p pl] I K a XliKMU ch hI iX pl*c VYpCm&] I KV cha U plnj ac a |,Vk| a i ]_ma U0I ] a |CX[c ] c plUM a p cY] a I K c ] I K a I VYplm ]¨¡UaKMc KMLNU chm Ïc c X[|lI ] a Xli ] Vk] a U LNa K]_c j K oMKMi®iXliV U] Xla o^]0X c K VYUnc U a LN K©a°Vc j VYmlgYa VYp@]VYha KMU cYa p p@] a ] K UW H*I K K*V Kp mCK ¬ p ]0Knj I _(U oWVYi KWVYU plU«] j K K plK*oMKMiiCU] XCo^]0X K hi®X pC Xli®KnK^]0oY ª c gwK a VYp c ] I K a H I XlU ghV a c XlUj c UU | i ] KMUU I c Xli®m | K U0]0Xlm KMm ] c U0KMK I Vk]{Xlp gwK a UVYi i¡chV UI ] I K^_ U I c V a KY a p ] Il UI j±Vk jK a cWj, Vkj K acY a Kc U I VYa i®i I KMplo c Xlp@]0K c a ] °c Xlp gw K a UVY i¨oMiVYI U0cU0c KMUM ª c pCK ] KMaL U j a jCc XliV p j _(U oMUcYap e K gwK ª VWg plac U LK CK¢Z | i a ]_ pfc o U pl§V oMKMii±U0c ] Xlo^]0X K c plKoWVYp\wV pTL KU L jCi o ]_ p§] I Kj |,Vk| i U] onmlKMU0o jC] p§VYpCm§K^gwKMp hK^]U i ghVk|Ci®KL mlKMi®UM . . . . . .
(83) . . . . ;=<4U>;?.
(84)
(85) !"#%$&'( . OG. T MGGlh  ? ¾ C.¾ ¯c i¡Vk|KMii®KMm,¥o c L jCc iK¢Z ch U&VU0K^] ch KMiKMÄ LNKMp]0UoWVYi®i®KMm+ oMKM i®i®UWª ] I K a K UV Xlplo^] c c p>chm L U p ª ] I K{m LNKMpCU p ] I K{ oMKMi®i &ª5]V pl ghVYi®chXl KMU E O ch; H I Kc m $ LNKMplcYU a p m L ¸ U0X[ j sm L s DK^] 7
(86) | K] I KNU+-K^,] oMKMii®U m LNKMplU p /5 KWVYo I oMKMi®i 7 $ = E ª UnmlK ¬ plKMm\VU0Xl|CU0K^ ]
(87) 7
(88) ª[] I K| c XlplmCV a _ ch &«z(X[| o c L jCiK¢Z J ch U*V U0X[|,U0K^] ch U0Xlo I ] I Vk] J±] I KMp J; U c L cYa j Il UL ch ] c o c L jCi®K¢Z[KMU U c plK¢Ë] c c pCK&LVkjCj pl a KMUj KMo^] pC m LNKMplU c p§VYpCm | a c XlpCmCV a KMUM <bX ghVYi®KMplc oMKNoMiVYUU0KMU ch o c L jCi®K¢Z[KMU ] I a KMUj KMo^]] c ] I KMUK U c L cYa j IC U0LNU V K©oWVYi®i®KMm\Xla pC iVk!^| KMi®i®KMchm§ o L jCi®K¢Z[KMUM H I K*U0]V ¥ ] I KoMKMi®i U%] I KU0Xl|o c LNjCi®K¢Z o c p]V p pl VYpCm§VYi®i,oMKMi®i®U U0Xlo I I] Vk]*K ] I K a cYa cYa ¸ 0c ]0K¹] I Vk ]fo c L jCi®K¢Z[KMU oWVYp | K¦o c pCU mlK a KMm VYU j,V a ] oMXli¡V a oWVYUKMU ch Uj p a Vkj I U ¸ ¥ G¥ ª U0KMK 8 uhu 9Ò H I Ko cYa0a KMUj c plmlKMpCoMKNoWVYp| KNo c plU0] a Xlo^]0KMm pm 43 K a KMp@] VW_UW 5 cY a K¢Z[VY L c j,i®chKY ª[i®IK^]°] I cYKa0a gwK a ] c oMKMU - ch o cYaa KMUj c plÄ m{] c a oMKMii®U¬ ch ª(] I K I Xl plo^] c p -¤¥ Ua ] I K m LNc KMplU a p ] Ko KMUchj plm pla sU c L jCi®K¢Z4 D p UnV KÄ ml2 K3 plKMm§ |_] K pCo mlKMploMKLVk] Z³ ] gwK ] oMKM U VYplm c J V K©o a pCpl KMo^ ]0KMm |_Ta VNi p c J & DVk| KMi®i®KMmNU0j pNo L j,i®K¢Z U«V©j,V G¥ I K K UV©o L j,i®K¢ZVYplm ³ ¥ U V Xlplo^] ch c p °c cp\] I KU0K^]c ¥ ch oMKMi®i®U chc cYa ] I gYVYi®chXC KMU p\U cc LNKUj pTUa j,VYoMK U c L cYa jH*IlI U0L ] Uj pfo L j,i®K¢Z(a KMU UVYp U L j IC U0L ] I Kc o L jCi®K¢Z[KMU KMUj KMo^] c pC{I Ua0j pl UM K\KM@X gYVYiKMploMK\oMiVYU0U0KMU§V K oWVYi®iKMm XlpliVk| KMi®iKMm,¥Uj p o L jCi®K¢Z[KMUM LpliKMU0U ] K U0K U0]Vk]0KMm K c o c plU mlchK a©c pCi _ Xlplo^] c pCU cN mlK ¬ pCKMc m c p¹a ] I K a oMKMi®i®U ch c LVGa Z LVYi5m LNKMplU c p |@_ mCXCVYi UVk] p ] U ]0KMpKM@X gYVYiKMp]n] Xlplo^] plU KMU] o^]0KMm\] gwK ] oMKMUM =, 2 #  ?   6 0¡ n  ? ¾ C.¾ H*I K a KsL{VYp_ ] c j c i c oWVYi pCoWV a pCVk] c plU ch Vk|CU] a VYo^]o c LNjCi®K¢Z[KMUM pKWVYo I ch ] I KML V§oMKMi®i U a K^j a KMU0KMp@]0KMm|_¹VYp c j KMpm U Ä N¯~£o c L jCi®K¢Z UsV\] c j c i c oWVYi%Uj,VYoMK Il o I¶ U mCK ¬ plKMm©|_©c ] I K plmCXlo^] gwKbch o c pCc U] a Xlo^] c pa ch ]0U $ m LNKMchpl U c pCVYiwU Ä KMc iK^] c pl!U 7 DÏK^!] a ¸ | c KNV\ m U0o ¡aplc plKMo^]0KMm¶+-,U0K^] ;c j cW p]0U gwK I ] oMKMU ¥choM KMi®i® U m c LNKM$ pCU p E ¬ p¹hKM pl K I VYiÒ"ª c 7 U $ |Cm ]V LNplKMKMpCm U c pC#LVYi. m 7U Ä% VY U VYpli®i mU UMc 4LN<KsVYo o c p@oM] KM pi®$i X c XlU m Vk]LN]VYKMo plIlU pCp ¥*L{+-, U Vkj mlKM( p@ ] $³ KMm % ] VY p 7 +-j , KM p U ¬ Z(KMm H I KM&p 7 U] I K VYo^] cYa U0j,VYoMK ch ] I KXlp c p ch 7 VYplm ')(+* 7 % g V mlKMp] ®¬ oWVk] c plU ch , % ] I ( ¥ cYa a I I a 1 ac c Ä KMmCh5 KMU ¥ ª K¢c Z[plVYK¢LNm jC i®LNKY,ª KMpl U c pCU¦VYibV3oMKM i®iUMVk j D p Ä ] gw UK V¦] oMi KMc@UMc ª j K ] Im KLN| c KMXlpCpCU mCVpCa VY_ ichoMKMi®i®UMª UVYplLm4Vkjli j p KMm U ]a c&c a plK gwcK a ]0a K¢Z± ]0c KMp§U c LNK a KMU] a o^ ] c pCU c pN] I ¡KcYa Vk]]VYo IC plsL{VkjCU«V a K L j c c U0KMm a K a K % K KMU] o^] X U0KMi gwKMU] ] I KoWVYU0Km L ¸ ; VYplm VYi®i m -L ¸ ; ª(] I K*| XlpCmCV ._ =,,. UVUXW7Y[Z]\[^]Z.
(89) K
(90) ] ['. Oyx. #. U°] I K©Xlp c p ch U c LK©oMKMi®i®U m L-4¸ E O p\U c LK| c@cYÄ UMªlU0KMK ;cYa K¢ZlVYL jCiK/8 O 9Òª±£ oc c LNjCi®K¢Z[KMUV c a KmlK ¬ plKMm§VYUnVYa i a KWVYm[c_ UVk] _ pl] Il U a KMU] a o^] c p,¥ ] I , UXlo I £ o% c L jCi®K¢Z pCKoWVYpVYU0U o Vk]0KsVYp¦Vkch|C U] VYo^]o L jCi®c K¢Z ] I ¸ a a ³ ( ¥@
(91) K§hK^] ] I K§oMi¡VYU0U U L j,i o VYi%o LNjCi®K¢Z[KMU I K K{] I KToMKMi®i®U V K§oWVYi®i®KMm U L j,i oMKMU ¥ «;cYa KWVYo I ; oMKMii ]0U©| c XlpCmCV a _ I VYU&t c pCK¢m LNKMplU c pCVYi5oMKMi®i®UVYplm¹] I K{U0K^] ch gwK a ] oMKMUXlp @XlKMi®_>mlK ¬ pCKMU s3¯p@_ a Vkj I ] I c X[]NLXli ] j,i®KTKMmlhKMUMªnp c i cc jCU U{V U L jCi o VYiCo c L j,i®K¢Z± =, = A ¾
(92) C ¾ pN] I Knj,Vkj K ab K*o c plU mlK a m 4 3 K a KMp]boMi¡VYU0U0KMU ch ] c m LNKMplU c pCVYi¡¥ o c L j,i®K¢Z(KMUW H I K oMiVYUU oWVYp3| K¦mlK ¬c plKMm3cYa K ] I K a c |@_ cL j c a U pl X a ] aI c K a{a KMUa ] a o^] c c pCU c p3] cI KoMiVYU0U ch o c LNjCi®K¢Z[KMU mCK ¬ pl KMm\Vk| gwI K |_§U a LNKo pla U ] XCo^] a gwKj ch oMKMmlX KMU] hK^]¬ VYii o L jCi®c K¢Z[KMU p§] Il UnoMi VYc UUM ¯p@_ aVM_sUXlo a oMiVYU0U0KMUa V K«V j,V ] oMXCiV oWVYU0K V iVYpChXCVYhKbmlK plKMm|_©U LNKbUX[|CU] ]0Xl] plU p V Vkj I VYLLV ªCU0KMK 8 uwt(ªCuhu 9Ò a c H I ;c cy a a c I c ;cYa c IC oMi c U0KMmK o c LNi®i j,VYo^pl] ¥N UX KMaU] VYoMo^KY] pl` U U0KMXCm imc U0X a VYoMVYK ii* o oMi cL UjCKMm3iK¢Z(o KMc U LNj,p VYo^] ] ¥ U U{j±VkV¶j]K c j³c o i c LN oWjCVYi®i*K¢Z Uj±VYU§oMVK U c L cYa j IC on] c V ¬ p ]0K ; m LNKMplU c pCVYiCU L jCi o VYi[o c L jCi®K¢Z ] I ] I K ;c i®i cy plj ac j K a ]_±³ KWVYo I ai p Ä U*o c p]V pCKMm pTc ] I K©| ac c XCplmCa V a _ ch K¢ZlVYo^]0i _\] c{c VYoMa KMU c@c ] °chc m LNKMplU c a pCVYi.oMKMi®iU c ¥ ¯U0c X cYVYa oMK IlI VYUc VYp¹VYml m Ä ] pCVYiÏj j K ]_f] I Vk]] I K&pCK I | X I m KWVYo I gwK ]0K¢Z U I LK L j o] V m U ch c H Il U U§] I K¦i U] VYi®io L j,VYo^] oM i c U0KMm ] I c Xl] I c iKMU ¥ ; m LNKMplU c pCVYiUX a VYoMKMUM a KMp@]Vk|Ci®KU0X a VYoMKMU%V a K d XlU] ¸ E O ; ÏUj I K a K ] I I VYpCmli®KMUM 0c p cYa KMp]Vk|,i®K UX c a VYoMKMaUV a K , j acGc d KMo^] gwK&chjC iVYplKy¥ ª ¼ c i®K pf| c ]]0i®Ky¥ ªa c ª , °Uj I K a K p c Il o I I i®KMUV K&oMX[]©VYplm] KWVYo I ] I KML V§e K^| XlU*|±VYplm o UU0oMX[j±¥ UVk]]VYo I KMmVYi pl ]0U | c Xl pCmCV a _h Il UoWVYU0,K , UV§ a Vkj I¦I c LNK c L cYa j IC oWVYi®i _ L&| KMmlmlKMmf] c ] I KU0X a VYoMK &z(Xlo I ¦ p ] o c LNajCi®K¢Z[c KMUbc V ca KnU]0Xlm c KMm p] I K°] c a j c i c oWVYil a Vkj I ] I Ka cYa _ U0KMK 8 x 9¡¥%c VYplm p c o c L&| pCVk¡] acYc a oMUMª I K K] j i oWVYi o L jCi®K¢Z[KMU V KoWVYi®iKMm§L{VkjCUM«z(X VYoMK ] ITI iKMU U |C]V plKMm L~V oM i c U0I KMm&UX aa VYoMK%I|_©oMX[]] c pl c X[] a ¬ p I ]0K%pXlI Ls| K ca¨ch m U a Ä U ] c I p c p(c p@]0K , a U0KMo^] pl | c Xlplm,V a KMUM ] Kc U0X cYa VYoMIlK VYUchV | XCplmC V _{] KMc p\] cYa KIl| Xlplm,chV _| KMa i plhU°c ] c I acYa U L j UL LVkj,U U*VYp U L j U0L Vk|CU] VYo^]o L jCi®K¢Z[KMUM p ] K mCUMª ] c Lc Vkj,c U°V a Ka oWVYi®iKMm U c L cYc a j Il o ] I K a K c U°V I c LNK c L cYa j Il U0L ch U0Xlo I ] I Vk]gwK a ] oMKMU L{Vkj p] gwK ] oMKMUMª±KMmlhKM U p c KMmCchh KMUMIªCoMKMi®i®U poMKM i®i®UMI a I , ch q ¯ L k V j U, VU0Xl|m g U p ] & K L k V j ] K k V j ¥ UV{U0X[|C a Vkj I ch ] I K\ a Vkj I ¥ ch { «_!VYX[jC]gwK a L&Xl]0Xlpl ] c ] c j c i c oWVYino c L jCiK¢Z(KMUV a K I c LNK c L cYa j IC o¦VYUT] c j c i c oWVYiUj,VYoMKMU\] I K a K¹K¢Z U0]§] I K a U0X[| m g U c pCU U c L cYa j Il oVYU Vk|,U] a VYo^]*o c L j,i®K¢Z(KMUW . . . . . ;=<4U>;?.
(93) OG.
(94) !"#%$&'( . ] I K U0X a VYoMK UnoMi c U0KMm\] I K b< Xli®K a o I V a VYo^]0K a U] oMU ch ] I K©o c LNjCi®K¢Z UnmlK ¬ plKMm VYU ¸ º I K a K U] I Kp@XCLs| K anchÏ VYoMKMUMªbp@XCLs| K a°ch gwK a ] oMKMUMª bpXlLs| K a°ch i p Ä UM ]nm c KMU p I c ]mlK^j KMa plm I c p+a ] I K{a o c LNjCi®K¢Z¶|C; Xl] c ; pli _ c I p>a ] I K{ U0X aI VYoMK ]0U0KMi ³ ;cYacYa a KMchp ]VkI |,i®K{UX a VYoM;cYKMaU ] c K cY<«a Xli®K o V VYo^a ]0K U] oMU ¸ º a K K U] KhKMp@a XlchU pa Xlc L&| K VYplmli®KMU ¥ ª p p KMp@]Vk|Ci®KU0X VYoM KMU c ¸ ; º ;c I cyK K U°] I Ksp@XlL&| K o U0U0oMX[jCUW K©U I VYi®i XCU0K p VYo^] pli _{] I K i®i pluNoMiVYU0UKMUM TkV 0¡GGC ¿ > ? H Il U U©] I KNoMiVYU0U K I VMgwK d XlU]&mlK ¬ plKMm 0cf X a ] I K aa KMU] a o^] c plU V a K L j c U0KMm +c z L a jCi®KMU0]K¢ZlVYL jCi®KMUNV a K a V¦gwK a ]0K¢Z plU mCKN] I K\Uj I K a K gwK a ]0K¢Z LVkj±¥ ª°VYp KMmChK ] I ] gwK ] oMKMU plU mlK] I KUj I K K«KMmlhKsLVkj. > Â Â A ¾ > l ¾ z(L cc ] I oMKMiiU0X a VYoMK U0KMK 8 ; 9¡¥ UV{o c L j,VYo^]o c plplKMo^]0KMm UL c@c ] I ] °c m LNKMplU c pCVYi LVYp ¡c i®m ] IT¬ p ]0Kp@XlL&| K a ch oMi c U0KMm U0X[|,U0K^]0U oMKMi®i®U ¥
(95) UXlo I ] I Vk]M³ Oh
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(101)
(102) ¥ UTVYp KMmlhK cYa V¶gwK a ]0K¢Z ch ] I K o KMUj c plm pl&j c i®_ c p cc I a I
(103) H I ch a # I 0; . 6 ;[I 0 Â . H Il UoWVYi®iKMmVoMX[] ] I K a KnV U a KU ] °VcU0L U0X[|C] a VkoMj KMI ii@U U0 X ,, VY oMK ¼ UXl]o I VY] I i®i Vk ] ¸ , t ¼ ¸ KbU K^]
(104) , gw¼K ¸] oMKMU J U Ä Ë] a VYplhXliVk] c p UVU0L cc ] I oMKMi®iU0X a VYoMKYª I c LNK c L cYa j Il o%] c ] I KUj I K a KYª I K a Kb] I K a K U c plKm U] plhX U I KMm ] I Vk] i®i,| K] I K c X[]0K a VYoMKy¥ VYoMKsVYplm ;cYa VYi®i c ] I K a* VYoMKMU
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