Linear Growth for Greedy Lattice Animals
31
0
0
Texte intégral
(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Linear Growth for Greedy Lattice Animals James B. Martin. N° 4035 Octobre 2000. ISSN 0249-6399. ISRN INRIA/RR--4035--FR+ENG. THÈME 1. apport de recherche.
(3)
(4)
(5)
(6) !#"$&%')(* -+ ,/.103245768,:9<;>=@? ACBED&FHGHIKJMLN<OPG<QSRUTGVWOPXUOYVZD&FHG<O [7\P]S^YGV_a`bL LQScdc:]e\fVWgdGK\ZG<hiBEG&\ihiBdGkj/lm3nSoepqJ rKhsVZ]Std\ZG uvnSnen J uew)cEQvxeG<O. y z {<|&}~dS|S G&V U7QSjEgGV<H-fWt/GQSj g QSFHX]vjd]ejUjEG&xeQvVP SG¡\iQvj:gU]SF QS\P¢QvtdG<O£¤VZBqh]eFFH]ej¥gUOfVP\ZtdRUVP]Sja¦H G&VK§¨©«ªt/G)VPBEG¬FQTUF¬RdF QvRdG¬]S¯® U°v± H²] SG<\ QSh&]SjdjdG³hsVZG<g´OfRdt:OfG&VZOµa]S¶ ]SKOP·<G©£BdhiBh]ej3VZQvjVZBdG¸]S\Zxej«¹ACBd¢OHFH]ºgdG&]vC»Yxe\PG<G<gUX ¢QVPVP¢hG¬QSjdFHQSOY¼K£CQSOj3VP\Z]UgUREh&G<gtºX²`!]>TGV¶QS@«½fI<¾e¾Soe¿CQSjEg²À QvjEgd]SÁqQvjEg¸Â G<OfVPG<j½YI³¾S¾vmº¿sU£Bd] OPBd]£bG<g¥VPBEQvV)¤CÃ Ä ¨ÆÅÇSÈeÉ Ä ª ɫʬËÌ Æ]e\)Of]eFGÍHÎÏd VZBdG&j§¨©«ªPЩ´ÑÒ§ÓQE O<«QSjEgqjÔCÕ Æ]e\Of]eFG § ËÖÌ 7×WOPjdxØ\ZG&¢QVZG<gtdRUVcEQS\fVZXOPFcEG<\bFHG&VPBd]UÕfgdä O<d£bGKgUG<\P SG¶VPBEG)OPQSFG h]ejEhREOP]ej REjEgUG&\ØVPBEGOPxSB3VZÕPXä £bG<QvÙeG&\h]Sj:gU¤VZ]ejVPB:QV¡ÚÜÝß Û ÞPà)á ¦¨Æâ-ªfã eâ Ë$Ì 7QSjEg1OPBd]£VPBEQvVH§æå ç Ú Ý Û Þ à á ¦¨Æâ-ª ã eâÆ]S\¬OP]SFHGh]ejEOfVZQvj3V ç èaGQSOP]¸xS SGQvj:Qv]SxS]eREOK\PG³OfRE¤ViOKÆ]S\ VZBdG¡\ZG&¢QVPG³g »fxS\ZG&G³gUX¢QVfVZh&G cEQVZBEOé¼ FH]ºgdG& ê²ë3ì-íZî¬ï }ð {S QvVfVP¢hG QSjdFQSO<dOfG<¤ñéQ> S]egdjdxØcEQVZBEO<EOfREc:G<\ZQegdgUVP 3VYXSdh&]SjEh&G&j3VP\iQVZ]ejjdG<ò3REQSVYX. Unité de recherche INRIA Rocquencourt Domaine de Voluceau, Rocquencourt, BP 105, 78153 Le Chesnay Cedex (France) Téléphone : +33 1 39 63 55 11 — Télécopie : +33 1 39 63 53 30.
(7) )**«)!#)s a (* Ò ! "$&%')(* ]SV $UGV¡OP]SV³ P ¶sREjdGQvFHG g¹gUG Qv\ZQStdG<OQvN<QVZ]S\PG³O¬gUG.
(8) { gdOfVP\ZtERUVP]SjHh]eFFØRdjdGC¦H ]SV7§¨Æ©«ª¢QW QSG<Rd\FHQvTUFQvGCgUG ® U°v± H¬OPRd\ VP]eREOÜOP]SREOfG<jEOPG&F¬tEG³O h&]SjdjEGTUG<O«µgUG!K gUG¯VZQvG!©¡òeRE3h&]SFHcd\ZG&jdjdG<j3V ]e\PxSjdGS`!G¯FH]UgUD&G!gdG sxe\PG<G<gUX¶QvVfVZh&G!QvjEFQv¢O QNVZNHj3VP\Z]UgURdV cEQv\¬`!]>T¥GV)QS@7½fI<¾S¾eoe¿GV¬À QvjEgd]SÁ G&V  G³OYVZG&j´½YI<¾e¾vmº¿s ò3RdÜ]Sj3V F]ej3VP\ZNò3RdGe Of à aÄ ¨ÆÅÇSÈ É Ä ªf É«Ê Ë Ì c/]SRd\Rdj ͹ΠÏdCQv]S\iO¡§¨©«ªPÐ>©Ñ § c O&bGV²gdQSjEO¡Ô Õ « eG<hagUG<O FHN&VPBd]UgUG³OOfFH¢Qv\PG³OØò3Rd]eò3R Rdj´c:G<R¹cEREOOPFcEG³O&Üjd]eREOÕf]Sä tUVZG&jd]ejEOQ F &FHG²h]ejEhREOP]ej¹OP]SREO B3Xºc/]vVZBdD<OPG¸N<xSD&\ZG&FHG<ÕPjeä VcdREOHQStEG²ò3RdG Ú Ýß Û Þ àØá ¦¨Æâ-ª ã eâ Ë Ì 7GVjd]eREOFH]Sj3VP\Z]Sj:Oò3RdG § å ç ÚÜÝ Û Þ à á ¦¨Æâ-ª ã Sâc/]SRd\ÜREjdGh]ejEOYViQvj3VPG ç W]SREOÜgU]ejdjd]ejEOÜQvREOZOPºgdG<O\ZN<OPRd¤ViQViOÜQvjEQS]exSRdG³O c/]SRE\G FH]UgUD&G gUG sxe\PG<G<gUX¢QVPVP¢hG cEQvVPBEO ï |³{ í "! { ¢QVfVZh&G)QvjdFQv¢O&dhiBEG&FHj:OOPQSjEOC\PN<c:N&VPVP]Sj :OfRdc/G&\iQSgEgU¤VZ ºVPNedjEN&xeQSVPN gUG)h&]SjEh&G&jU VZ\ZQvVP]Sj.
(9)
(10) !"#$
(11) %'&. o. Ø« ¯) GV¶ d:QSjEg¸G&V¬³ P¹q¶s¬t/GØQSj²@ g :QvFHX]vÜjd]ejU jdG&x3QVP SG \iQvj:gU]SF >QS\P¢QvtEG³O&d£VPB h&]SFHFH]Sj¸gU¢OYVZ\PtdRUVZ]ej¦H+ *E]S\QØÁEjdVPG)OPRdtEOPGVµ]v¶sdVPBdG
(12) ,-/.0132¨ÆµSªb]SµOgdGÁEjdG³gt3X 2¨µS+ ª 465 H8 7 ½YISI³¿ d°v± 9.:
(13) %;< = >$?%@A&B;C0 ©aOQh]ejdjdG³hsVPG³gOPRdtEOPGV]S ]S OP·<G¶© h]Sj3ViQvjdjEx¬VZBdG ]S\Zxej £BE]eOPGK£bG&xSB3VCOFHQvTUFQv QSFH]SjdxHQv«OPREhiBOPGViO& GVW§¨©«ªbt:G VZBdOFHQvTUFØRdF £bG&xSB3V< ACBd¢OKFH]ºgdG&O¶cd\ZG<OPG&j3VPG³g²tºX²tºX¥`!]>T À Qvj:gU]SÁ« ÀK\P; DjqQvj:gq G<OfVPG<j1½YI³¾S¾eoe¿s-Qvj:gqQ¡ QS\PGVYX ]S QScdcdh<QVP]Sj:OCj²OfVZQVZOfVP¢h&QS cdBºXUOf¢h&O<dò3RdG&RdG<jExHVPBdG<]S\ZX¡QvjEgc/G&\ih]S¢QVZ]ejQS\PG gUG³OPh&\Pt:G³g 7×j:gUG&\ VZBdG)h]ejEgUVP]SjVPBEQvV Ã Ä ¨ÆÅÇSÈ É Ä ª É«Ê ËÌ Æ]S\OP]SFHG ÍιÏE ½YIS uS¿ VZBdG&XOfBE]£ÖVPBEQvVVPBdG<\PG G&Tº¢OfVZOQSj§ ËÌ OfREhiBVPB:QV §¨Æ©«ª å§ QvF]3OYVOPRd\ZG&>X 7 FÅ E;GIHJLK ½YIS oe¿ © MON Û À QSjEgU]SÁQSjEg¡Â G³OYVZG&jq½fI<¾S¾Sm3¿cE\P]UhG<G<gHVZ]OPBd]£´VPB:QV<UREjEgUG&\!VPBEGKOZQvFHG¶h&]SjEgd¤VZ]ej º]SjdG¶jQShsV B:QSOCFH]S\ZG OYVZ\P]ejdxSXHVPBEQvVVPBdG<\PG G&Tº¢OfVZOQvj¸§ ËÖÌ OPREhiBVPB:QV §¨©«ª Ñ#§ QvF]3OYVOPRd\ZG&XQvjEgjÔ Õ 7 ½YIS m3¿ © PéjVZBd¢OØc:Qvc/G&\³ £bG\ZG&cE\P]UgUREh&GVPBEGh]ejEhREOP]ejEO)]SK`!]>T G&VQS@C½YI³¾S¾So3¿ Qvj:g]v¶À QSjEgU]SÁ1Qvj:g  G³OYVZG&j½fI<¾S¾Sm3¿CREjEgUG&\ QOPxeBeVZX¸£bG<QSÙSG&\¶h]Sj:gU¤VZ]ej -QvjEg²jaQegdgUVP]Sj¥]etUVZQSj¥QSj¥GTUcd¢hVKt/]SRdj:g Æ]e\ VPBdGFV¬§ j VZG&\ZFHO ]S!VZBdG¡gU¢OYVZ\PtdRUVZ]ej ¦H¡ACBEGFG&VPBd]UgdO)REOfG³gQv\ZGØ\ZG&¢QVZG<gqVP]¸VPBE]eOPG]S VZBdG¡Qvt/] SGHcEQSc:G<\ZO<«tERUV¬Qv\ZG¡OfFHcdG&\ jcEQv\PVZRO QjcEQv\PVP¢hREQS\ VPBdGjdG<G<g Æ]e\ VPBdG¡\iQVZBdG&\ j3VP\Zh<QVZG cE\P]etEQvtd¤VYXG³OYVZFQVZG<OCREOPG<gVZBdG&\ZG OQ> e]S¢gUG<g r¶Rd\RE¤VZFQVZG \PG³OfRE¤V¢OCVPBdG Æ]e]£jdx#S ¦ &<]&edfB& T=U ëºï } ë WVX VZY L- [\O]&B<&^_ L&B` > ç ËÖÌ &Ba# b# , Wc g Û ¦¨Æâ/ª ã Õfä Sâ ËÖÌ ½YIS pS¿ à á Þ Ý eL-heL- [\O]&B & i § e §1¨Æ©«ª Ñ j § %'$
(14) k&B,&Ba1 -%'l
(15) Ô Õ ½YIS me¿ © (. ). nnco pLqrBsBt.
(16) m. $?& B< &©²Ñ Ì . § å ç g Û Þ àá ¦¨Æâ-ª ã ÕPä eâ 7 ½YIS wv¿ Ý `!]ejEgUVP]Sj½YIS pS¿!¢OQØVP]SR:hiB£bG<QSÙSG&\!VPB:Qvj½YIe ue¿BQºÆ]S\CG&TUQSFHcdGeU¤V¢OCFcEG<gtºXVPBEG h&]SjEgd¤VZ]ej Ã Ä ¨ÅÇeÈ É Ä ª Õ É«Ê ËÖÌ Æ]e\Of]eFHG ÍWδ#Ï 7 G&G G<hVP]Sj
(17) ØÆ]S\gUG&VZQS¢O& PéjaVPBdGØÁE\iOYV cEQS\fV ]vb]SRd\Kcd\Z]3]S¶½h&]S\Z\PG³Ofc/]Sj:gUjExVP]VPBdGVZBdGH\PG³OfRdVZO¶]v`!]>T²GV)QvI³¾S¾So3¿s/£!G gdG&\Z eGQt:]eRdjEg ]Sjqà §1¨Æ©«ªPЩ jaVPBdGh&QeOfG£BdG<\PG¦ ¢O Q !G<\PjE]SRdÜgU¢OfVP\ZtdRdVP]Sj½ñVPBEG\ZG<OPRdV O \ZG&¢QVZG<gqVP]VPBEG¬»Yc/]£!G<\ Q>£b¼Hcd\P] eG<gqt3X G<GSÜI<¾e¾3wt:¿sACBd¢O Qv]£O R:OKVP]¥h]ej3VP\Z]S VPBdGG /G³hsV)]ej §1¨Æ©«ªÜ]S VPBdG¶VZQS/]v«?¦ QdQSjGTdhiBEQSjdxSG]S«Q)FQTUF¬RdF QSjEg¡Qvjj3VPG<xS\iQv:X3G&¢gdO¯VPBdGKt/]SRdjEgdG<gUjdG³OPO!j ©]SÜà §¨©«ªPЩÖÆ]S\¶xSG&jEG&\iQv«¦ OZQVZOfÆXºjdxa½YIS pS¿K`!]SFHcEQS\Pjdx¡§¨©«ªCVZ]Q¡\ZG&¢QVZG<g¸cd\Z]UhG<OZO£VPBqQ OPRdc/G&\iQSgdgd¤VZ eGKcE\P]ec:G<\fVYXHVZBdG&j¸XºG<gEObVPBdG)QSFH]eOfVOfRE\PGKt:]eRdjEgUG³gUjdG³OPO]S §¨©«ªPЩaQSOCj½YIe o3¿sdQvj:g xe eG<OCQt:]eRdjEg]v VPBEG Æ]S\ZF ]vC½YIS wv¿!Æ]e\;Å EFGIH JLK§1¨Æ©«ªPÐ©Ü *E\P]eF VPBEQvVc:]ej3V]Sj !¤V£b]SRd¢gt/G¸c:]3OPOPtdGVZ] h&]SFHcdGVPGVZBdG¸cd\P]º]SWREOPjdxQaFH]ºgd¤Á:h<QVZ]ej ]SÜVPBdGHQv\ZxSREFG<j3VZOjaÀ QSjEgU]SÁaQSjEgq G³OYVZG&j1½fI<¾S¾Sm3¿EtEQeOfG³g²]Sj¥FQS\fVZjdx3QvG)jdG<ò3REQSVPG<OKQvjEg¥VPBdG »fFHGVZBd]Ug]vt/]SRdj:gUG<ggd -G&\ZG&jEh&G<OY¼i PéjEOfVPG<Qeg£!GgUG<gdREhGÆ\P]eF VZBdGt/]SREjEg]SVPBdGÆ]S\ZF'½fIS wv¿ Q \iQVZBdG&\ OfVP\Z]SjdxeG&\VZ\PREjEh&QvVP]Sj¥\ZG<OPRdV¶VZBEQvja£bQeOWREOPG<g¥VPBdG<\PGe QvjEgqtEQSOPG)VZBdG\PG³OYV ]v7VZBdGcd\P]º]S¯]SjqQ c/]£bG&\PÆRdE»fh&]SjEh&G&j3VP\iQVZ]ej]S FHG<QeOfRE\PG¼K\ZG<OPRd¤VWgdRdG VP]¡A Qv¢Qvxe\ZQSjEgq½fI<¾S¾3pS¿ÜèaG¬gd]Bd]£!G< SG<\!Æ]e]£ À QSjEgU]e¤Á¸QvjEg G<OfVPG&jtºXcEQv\PVPVP]SjEjdxØVPBEG OPGVC]vÆG<QeOftdG¶¢QVPVP¢hG QvjdFQv¢Ob]vQxS SG<jOP·<GK©qj3VP] OPGViOHG<QehiB¹h]ej3VZQvjdjdx QvVfVP¢hG¥QSjdFHQSO]SKQ xS SG<j1£¢gºVP B à å æå$©Übj´]S\igUG<\ØVZ]QvcdcdX OPRdc/G&\iQSgdgd¤VZ ºVYXQv\ZxSREFG<j3VZO<W½WG&\ZG VPBdGl e²]S µH¢O]SjdG xe\PG³QVZG&\CVPB:Qvj¸VPBEG¬gU/G<\PG<jEhG t/GVY£bG&G<j VZBdGKFHQvTUFØRdF QvjEgFjdF¬RdF QSRdG³O¯]S VPBEGWÁE\iOfVCh&]3]e\ZgdjEQvVPG -¨ à ª¯QSFH]Sjdx¬VPBdGKFHG&F¬t/G&\iO!a]S µS¿s Péj G<hVP]Sj¥w¬£!G h]ejEOf¢gUG<\!VZBdG \PG<QvVPG³g .:
(18) %; L¸F]UgUG< £Bd¢hiB£CQSOCQv¢OP]¬VZ\PG³QVPG³g¡tºX À QSjEgU]e¤Á1QSjEg G<OfVPG<j GV ¨Æ©«ª t/G¡VZBdGFQvTºFQv7£bG&xSB3V¬]SQ¥OfG<¤ñéQ> S]egdjdx¸cEQvVPB]SG<jdxvVZB © OYViQv\PVPjdxaQvVØVZBdG¸]S\Zxej ACBdG<]S\ZG&F wºIxe eG<OQq\ZG<OPRdVHQSjEQv]Sxe]SREO)VP] ACBdG&]e\PG<F ISIS7OPBd]£jEx h&]Sjº SG<\PxeG&jEh&GW]S ¨©«ªPÐ>©aRdjEgUG<\Wh]ejEgUVP]Sj½YIe pe¿s7_²REhiB¸]SVZBdG cd\Z]3]S h<Qv\Z\PG<Ob] SG<\gU\ZG<hVPXÆ\Z]SF VZBEQVC]vACBdG&]e\PG<F$IS:I QUhG<\fViQvjcEQS\fViObQS\PG¶BEQv\igUG<\!t/G<h<QvREOPGKOPRdc/G&\iQSgdgd¤VZ ºVYX¡Qv\ZxSRdFHG&j3ViO!QS\PG¶jd]vVOP] G³QSOPX¥QvcEcd¢h&QStdGS)è GOfFHcdÆX¥VZBdGHcEQVZBagUG³h]eFc/]eOPVP]SjQv\ZxSRdFHG&j3VK£BdhiB £CQSO¶REOfG³g¥VZ]¸cd\P] eG VZBdG)h]ejº SG&\ZxSG<jEhG¶RdjEgUG<\h]ejEgUVP]Sj½YIS uS¿bj¥À QvjEgd]SÁ¸QSjEg G³OYVZG&j½YI³¾S¾vmº¿s A]]SRd\HÙºjd]£G<gUxeGS¯VPBdG¥OfVP\Z]SjdxeG<OfVÙ3jE]£j1jdG³hG<OZOZQv\ZXh]Sj:gU¤VZ]ej´Æ]S\¥½YIe o3¿Ø]S\¥½YIe mº¿ØOHVZBEQV à ËkÌ ½OPG&G¬[¯\P]ec:]3OfVP]SjqoE mQvjEg¸VZBdG\PG<FHQS\PÙ£Bd¢hiB¥Æ]S]£OZ¿¶ACBdGØxeQvc²t/GVY£bG&G<j¥VZBdOKQvj:g h&]SjEgd¤VZ]ej´½fIS pS¿¶O¬gUOZhR:OPOPG<gaj G³hsVP]Sj¾E«Qv]Sjdx£VPB Qv\Z]eREO FH]ºgdG&¢O QvjEga\PG³OfRE¤ViO \PG<QvVPG<gqVP] VZBd]eOPG FHG&j3VP]SjdG³gQSt:] eGS ! n" $#.
(19) p.
(20) !"#$
(21) %'&. .
(22) . è bG £\PVPG¬Æ]S\ VPBdGb]S\ZxSj)]v: vQSjEgKÆ]S\ VZBdG!c/]Sj3V ]S/ QSº]v:£Bd]eOPG!h&]3]e\ZgdjEQvVPG³O«Qv\ZGbG<ò3REQveVP] *d]e\ ¸¶s>£bGÜ£\PVPG -¨Yª/Æ]e\ VPBEGVPB)h]º]e\ZgUjEQvVPG]vU7 å!å¹:QvjEgi 4 G EÕ !" -¨Yª Q Æà ]e\&%C¬e£bGØ£\ZVPG'%ÆÆ]e\WVZBdGHc:]ej3V ]v!¶W£BE]eOPG(VPB hà ]º]S\igUjEQVZG)O)%/¨"éªÆ]S\ à å*Wå $E# *d]S# \ G + á WÆ]S\ G -Õ . # / ¨ Yª á -¨ Yª # +*d]e\ 幩 ¸)>£!G £\Z¤VZG0 f©.1ƶÆ]S\ + f²W&U£!G £\Z¤VZ, VZBdG hRdt/GØ<32 å /¨"YªCå¹©Ü à å4¯åEK]SOf·&GH¨Æ© á 65 à ªPSdQSjEg¡£\ZVPG)7¨Æ¯ ²ª!Æ]S\bVPBdG h&Rdt:G 9 8'2! 8 á $ Kå q ]SOP·<G¨@ :5 à ªfe è G\PG<xeQS\Zg¥¶ QSO QxS\iQvcdB¥jaVPBdGjd]e\PFQS £CQ>X Q VY£b]c/]Sj3VZO Qv\ZGØQeg>^fQSh&G&j3V VZBdG&XaQv\ZG"½ ;7RU h&¢gUG³Qvj:¿bgU¢OYViQvjEh&G GTdQShVPX²I)QvcEQS\f0V Q3VPBºREOQSj3Xc:]ej3VBEQSOCG&TdQShsVZXvjdG<xeBºt:]eRd\ZO< è GWQSOZOPRdFHG!VZBd\Z]SRdxeBd]SRUVVZBEQV³H/P¸¶sWQS\PGC g SQvjEgjd]ejU jdG&x3QVP SGe«è G£\PVPG <Æ]e\ÜVPBdG cE\P]etEQvtd¤VYXKFHG<QSOPRd\ZG7xS] eG&\Zjdjdx <H/evQSjEg à Æ]S\VPBdGbGTUc/G<hVZQVZ]ej)£VPB¬\ZG<OPc/G<hsVVP=] <,QOf]eFHGVPFHG<O £bGW£\ZVP&G <?>Qvj:gH@à > £BdG<j£bGW£¢OfBVP]HOYVZ\PG³OPO¯VPBdG gUG<c:G<jEgUG&j:hGK]Sj¡VZBdG h]SFHFH]SjgUOfVP\ZtdRUVP]Sj¦ ]SEVZBdG Qv\ZQStdG³O!<H-O QvBEG&\ZGC¦¨â/,ª 4A<!¨ Ä å¹â/ªeâ² Ïd èaG£U£\PVPG bG&\³C¨ B-ªÆ]S\VPBEG !G<\PjE]SRd gdOfVP\ZtERUVP]Sj£¤VZB¸cEQv\iQvFHGVZG&D\ B²RdjEgdG&\£Bd¢hiEB <!¨Æ 4 à +ª 4 àá <!¨ 4 Ïe+ª 4FB« %; < ^#$
(23) % ¢O¯Q ÁEjE¤VZGWh]ejdjdG<hVPG³gOfRdt:OfG&V!]v W& G&HV G¬¨©«ªÜt/GVPBEGWOfG&V¯]v ¢QVPVP¢hG¶QSjdFHQSO ]SCOP·&G¡©´£Bd¢hiBh]Sj3ViQvjaVZBdG¡c/]Sj3IV E J¶GÁEjdjdx²VZBdG¡£bG&xSB3V 2¨µSª ]vQ¸¢QVfVZh&GQvjEFQv¯µ¸QeO)QV ½fISI³¿U£!G BEQ> eG §¨©«,ª 4 ±&G°LK M 2¨µSBª 7 ½YIS e¿ MON. *«* SRUT ab ¬WV' Q C (&( )* ACBEGHÆ]S]£jdx¸\PG³OfRE¤V)¢O G<FHFHQI]S`!]>TaGVØQS@¯½fI<¾e¾Soe¿«Qvj:g gdG<OZh\Zt/G<O BE]£ Q¸¢QVfVZh&G¡QvjdFQv FQ>X¡t/G)h] eG&\ZG<gtºXQh&]SjUÁ:xSRd\iQVZ]ej]Sj¸QQvVfVZh&G ]v¢Qv\ZxSG<\OPh<QvG:S ~ Y X V - à [ X!ë Z å %å©
(24) %;- µ\ GبƩ« ª Y # eL- \O]&B &=?&--]-a# ) + Ý R7-7R7 + ^ ¶ L- )_
(25) 4a`@© Ð %b &Ba# # + Ý 46 &Ba# # = + á + cÕ )å à
(26) %% à d å å _ &Ba# eL P. Q. µIe. ^ f 7 ¨"% + hg Ý. ZL%@ª7. `!]ejEOf¢gUG<\7VPBEGWh&QeOfG£BEG&\ZGCVPBdG¶ BEQ> eG bG&\Zjd]SRdi½ B/¿ÜgU¢OfVP\ZtdRdVP]Sj ÜACBdGjEGTºV¯\ZG<OPRd¤V!cd\P] º¢gUG<O Q)»fc/]£!G<\Q>£b¼ Æ]S\VZBdG¬t/G&B:Q> 3]SRE\]v7§¨Æ©«ªQSOB¥t/G<h&]SFHG<OWOfFQv P VW£Qv]£ REOVP]t/]SRdj:g¸VPBdG G/G³hsV]S«VPBEG VZQv ]S ¦ ]Sjà > §¨Æ©«ªZÐ>©q£BEG&j²¦k¢OQHgU¢OYVZ\PtdRUVZ]ejOZQVZOfÆXºjdx²½fIS pS¿s. nnco pLqrBsBt.
(27) $?& B< m. G&G¡½YI³¾S¾ºw>t UACBdG<]S\ZG&FuS¿COPBd]£O!VPB:QVVPBEG&\ZGKG&TUOfVZOQHh&]SjEOfVZQSjeV ç OfR:hiBVZBEQV B ÕPä FÅ E;GIH J#K §¨Æ©«ª å ç © M:N Û < M Qd O<3Æ]S\QS BACBEGKt:QSOPOb]v ]SRd\QS\PxeRdFHG&j3Vb¢OOPFHQS\!VZ]VPBEQvVC]S G&GSºtdRdV£!GKGTºVPG<jEg¤V VZ]Hcd\P]N ºá ¢gUG h]ejeVZ\P]e-] SG&\bà §¨Æ©«ª £BdhiB¢OCRdjdÆ]S\ZFj© QSOC£bG&«QSOb'j B S } ï ¯ï
(28) {
(29) | ï Y8X Y Y L- ]&=l #&B # ç Ë Ì &Ba# eL [ %%LB²¨ÏE à 1 l%%E© B ÕPä à M N §© ¨Æ©«ª å ç 7 R P © B. ÕPä å U VPBEG&j à. Õfä à M §¨©«ª å à Õfä à M 5 N © N U° "! !$# . © B M ¨ « © f ª B å © B Õfä 4 ¨ © B ÕPä ª Õ å´ 7 ½@uUI³¿ ]OfREcdc:]3OfG)VPBEQvV¶© B ÕPä Î à èaGØ£QvcdcdX G<FFQudI¬£¤VZZ B % 4&% B ÕPä 'e ]SVPG)VZBEQV¶VPBdG P Õ ä jºRdFØt:G<\¯]S OPG<ò3RdG<jEhG³O + Ý R 7-7-7 + ^ ½Æ-£,. VP,B _^4 `@©OÐ % b åv © B ³¿£Bd¢hiBOZQVZOfÆX¬VZBdGVZBdGWcd\Z]Sc/G&\PVPG<O xe eG&jj G&FHFQ¡uUI O)(e ^ + å *e M :Qvj:gVZBEQVWÆ]S\WQSj3XOfR:hiB¸OPG<ò3RdG<jEhGeUÕPVPä BEG)jºRdF¬Õfä t/G&\]S c/]Sj3VZO ^ h&]Sj3VZQSjEG<gj0/ g Ý 7¨ % + iO%@ª¯¢Ojd]HxS\ZG<QvVPG&\bVZBEQvj¨_ 5 à ª¨21 % 5 à ªP å3(S© B S¨4* B" ³ªfe *E]S\)5 ÎÏdU£bGKVPBdG<j¸BEQ> SG 7 §¨©«ª +5
(30) 8 4A<6 M9 N: ±&G M 5 H ´© B ÕPä 5
(31) ; <6 M N f Õ ä ° L. K. © B MON d°v± å <6 M9 N : G [ 5 ´ © B ÕPä 5 ; <>=@?AAAB? <>C U>° D C M"G G =FE <>HI? J N å 5 <6 M N : 5 ´ © B ÕPä 5 ; U° D C= E M"G <>HI? J G N <K=?AAA? <KC M -,4. NM å 5 Ã M NPOKQ K : 5 HS ;UT d ° " M G G D C < = ?AAA? < C L =RE < H ? J N B . ! n" $#.
(32) w.
(33) !"#$
(34) %'&. M -,4. NM Ã M9 N # D C= E M"G <KH? J G N # 5 <K=?AAA? <KC L L NM 4 , .. M å 5 Ã M9 N M -,4. M
(35) R,. N <K=?AAA? <KC L L N M 4 , . M 4 5 ¨ àá B 5 B ª M
(36) ,. M B
(37) R,4. N < = ?AAA? < C L L M
(38) , . , . å * M M Þ ¨ àá B 5\B ª ÕfäB ã M -,. å * M
(39) ,. L M -,. M Þ M Õ N ã M -,4L . -,4. 4 M -,. L M * L M Õ N M 7 L L W]£ÖVZQSÙSG¡QS\PxeGWG<jd]SRdxeB¡VZBEQV *e M Õ N å C½@ACBd¢Oh]Sj:gU¤VZ]ejgU]ºG³O!jE]vVgUG&c/G&j:g]ej 4. ©a]S\]ej -B ¿s7ACBdG<j. L. L.
(40) . à. § ¨Æ©«ª 8 å)5ÃU M §¨ÆÕP©«ä ª ÕPä ÃU M 7 N N © B á © É 7 §¨Æ©«ª g Û 4)5 < M N +5 8¥S5. © B ÕPä å )5 © B à ÕPä M -,4. *
(41) M Õ N M -,. L -,. L à . 4)5 *
(42) M Õ N M P Õ ä. © B å )5 à 7 L L ½@uU uS¿ ACBdG \ZxeB3VbBEQSjEgOf¢gUG<Ob]Sb½@udI>¿bQvjEga½@uU uS¿bQS\PG¶jEgdG&c/G&jEgUG<j3V]v B¸Qvj:g©ÜdOP]¬VZBdG gUG<OP\PG³g¡\ZG<OPRd¤V Æ]e]£O< kOfVP\iQvxSB3VPÆ]S\Z£bQS\ZgGTdhiBEQvjExSG ]v7QHFQTUF¬RdF$QvjEg¸QSj²j3VPG<xS\iQv jd]£8XºG<gEOVPBEG)t:]eRdjEgUG³gUjdG³OPO ]S«@à >§¨©«ªPЩ¥Æ]S\QS gdOfVP\ZtERUVP]SjEOW¦ OZQVP¢OfÆX3jdx²½YIe peB¿ S T=U ëºï } ë Y X Y L- A]&^[ L&B # ç ËÖÌ &Ba# l# !%%8]&B< B -a1< L&!¦ &- ]& .!#" %$'& HJLK ) à > §© ¨Æ©«ª å ç g Û ¨ àá ¦¨â/ªPª ÕPä eâ 7 ½@uU oe¿ Ý M R 3*E]S\QSj3XQvVfVP¢hG QSjdFQS µUd£!G B:Q> SG 2¨µS, ª4 5 U°v± B . nnco pLqrBsBt.
(43) . $?& B< 4. ACBdG<j. g. Û <µ e2 ι⫳eâ. Ý. 7. §¨©«ª+4 &± G° M 2¨ÆµSª MON 4 ±&G ° M MON g ÝÛ <µI2v δâ >Sâ å g Û ±G° OM <¸µ 2S Î1â« eâ 7 ½@uU m3¿ MON Ý jEh&G!VZBdGCj3VZG&xS\iQvj:g OQS£CQ>XUO«jd]ejU jdG&x3QVP SGe³QSjEg¬VPBdG<jØOPjEh&GbVPBdGb\ZQSjEgU]eF >QS\P¢QvtEG³O7:¨Î â-ªsP¸¶s)Qv\ZGK@ @ g d£VPB¥h&]SFHFH]Sj¸gU¢OYVZ\PtdRUVZ]ej bG&\³¨ àá ¦¨Æâ-ªfªE£bGKB:Q> SG à >§¨©«ªbå g Û )à > ±&G° M ³Iµ 2vHδâ Sâ MON Ý g Û 4 à M¢Õ >DM NN §¨©«ª eâ Ýg å Û 0 ç ©7¨ àá ¦¨Æâ-ªfª ÕPä 1¢eâ« Ý £BEG&\ZG ç ¢OCVPBdG)h&]SjEOfVZQSj3VCG³OYViQvtd¢OfBdG³gj¸[7\Z]Sc/]eOP¤VZ]ejuU uUUxe ºjdx²½@ud o3¿!QeOC\PG³ò3Rd\ZG<g "$(&%')*
(44) Q *«*:V
(45) aC )i VHs: *E]S\ f© 1) Ë ©Ü G&V¨! f©«ªKt/GVPBdGFQTUF¬RdF
(46) £!G<xeBeV ]vCQQvVfVP¢hGQSjdFQSÜ]vbOP·&GHjd]vV FH]e\PGWVPBEQSj ¨@ 5 à ª¨© á ²ªsdh]ej3VZQvjdG³gjVPBEG h&Rdt/GI0 aP©.1ñK]S OP·<G¨© á 65 à ªPSdQSjEg¡jEh&REgdjdx VZBdGc:]ej3V ²QvjEgqQ¡c/]SjeV QSg^fQShG<j3VVP]©E tdRdVKjd]SV¶jEhREgUjdxVPBdGc/]SjeVK©¸¤ViOfG<¤Y¬`!G&\PVZQSjEX VZBdG¬OPGVK]vÜQvVfVZh&G¬QvjdFQv¢OgUG³OPh&\Pt:G³g¸j¥VPBd¢OWgUG&ÁEjdVP]Sj¥¢OjE]SjU G&FHcUVYXe:OPjEh&G VPBEG&\ZG¬Qv\ZG cEQVZBEO]S G&jExvVPB¸/¨Æ© á ²ª 5 à Æ\P]eF ¡VP]H© ¡h]ejeViQvjdG<gj 0 f.© 1Æv ACBdG Æ]e]£jdxØcE\P]ec:G<\fVZG³OQv\ZGKFHFHG<gU¢QVZG¶Æ\Z]SFVPBdG gUG&ÁEjdVP]Sj¸]v¨aP©«ªBS W]SjU jdG<xeQVZ ºVYX S !¨ f©«ªb ÏØÆ]S\QS Ë © ½odI³¿ VZQVZ]ejEQv\ZVYX S ACBEG)h]SG<hsVZ]ejEOK ¡!¨ f©«ªs Ë ©)Qvj:gq !¨ :5 à f'© 5 à ª Ë © B:Q> SGKVPBdG)OZQvFHGb^Y]Sj3VgUOfVP\ZtdRUVP]Sj:-O Q ½od uS¿. ! n" $#.
(47)
(48) !"#$
(49) %'&. Rdc:G<\ZQegdgUVP º¤VYX. § S. X!ë. è. ¾. S. ¨"%f ²ª 5 ¨aP©«ª!å ¨ %YP©«ª7Æ]e\Qv % Ë Ë ©7 ½od oe¿ G £ REOPGKVPBdG)h&]SG³hsVP]Sj QeObt:]SVPB²QvjRdcdc/G&\t/]SRdj:gQSjEgQ]£!G<\Ct:]eRdjEgÆ]S\CVPBEGKcE\P]UhG³OPO. ~ . X V. ¨ÏEf©«ªbå´§¨f¨@&5 à ªé©«ª, %%d© &a§¨Æ©«ªå ¨ á ©Üf©«ª %%:© &. VZBdGHgUGÁEjE¤VZ]ejq]v ¡¨ÏdP©«ªs!*d]e\¶cEQS\fVH½Æ¢¿ jd]vVZG¬VZBEQV VPBEGc:]ej3V ©KVP])Q¶c:]ej3V¯QSg^fQShG<j3V VZ]²©:Qvj:gac:QSOZOfjdxVPBd\Z]SRExSB VPBdGc:]ej3VI P µ¸O¬QvjºXq¢QVPVP¢hG¡QvjEFQv¯á jVZBdGOPG(V G¬¨©«ª½Æ GSQ ¢QVPVP¢hGQvjdFQv«]S¯Of·&G¬©£BdhiBah]Sj3ViQvjEO=:¿s/VPBdG<j²VPBEGØRdjE]ej²]v7µ¡Qvj:g¥OfR:hiB¥Q¡cEQvVPB¥¢OWQQvVfVP¢hG QSjdFHQSU]v-Of·&GCjd] FH]S\ZGbVPBEQSj¨v?5 à ªY©aå8¨? 5 à ªP©ÜSh&]Sj3VZQSjdG³g¬j 0 á ©ÜP.© 1ñ <© dQSjEg¬jEh&REgdjdx VZBdG c/]SjeV á ©¡QSjEg¸QØc/]Sj3VWQSg>^fQehG<jeVCVZ]©/7ACBdG \ZG<OPRd¤VCÆ]e]£O& Ø X!ë ~ X Y Y L- \O]&B &Ø 0 Ïd Ì 1 &a# eLI à ¨@© ÏdP©«ª 4 & ;Å EFG M:N Û ¨ÏE© f©«ª 4h ;&+
(50) ÔÕ &'FÅ E;G M:N Û ¨ á ©©ÜP©«ª 4h ;&+ÔC Õ 7 &'FÅ E;G M:N Û R Ø[QS\fVH½Æñ¿Æ]e]£O¶FHFHG<gU¢QVZG&XÆ\P]eF. VZBdG&\ZGQv\ZG!c:QVPB:O]v:G&jExvVPBve©jE0 á ©ÜP©.1ñ ³©UxS]ejdx¶Æ\Z]SF. #" %$ &[# %; & #. Øå8¨@&5. ÕPä g Û à ª ç Ý Þ àá ¦¨â/ª ã eâ«. ½od m3¿. ç ]&^eL[ L&B` > .:k- - Y L -$
(51) R [ÜQv\PVZO¥½¢¿QvjEg ½ñ¿HÆ]e]£Æ\Z]SF cd\Z]Sc/G&\PVPG<O¥½@odI³¿ ½@od uS¿QSjEg ½oE o3¿Qvj:g1VZBdG¥QehsV¡VZBEQV ³ P¹WØQv\ZG)jEgUG<c:G<jEgUG&j3V³/R:Ofjdx jdxeFHQSj OOfREtEQSgdgd¤VZ eG¬G&\ZxS]UgU¢hKVPBEG&]S\ZG&F¸½Æ]e\¶\iQVZBdG&\WQ OPRdc/G&\iQSgdgd¤VZ eG¡ SG<\ZOP]ej]vWVi¿[QS\fV¸½Æñ¿)Æ]S]£OØOfFH¢Qv\ZX Æ\Z]SF Q»YVY£b]véOf¢gUG<gº¼H eG&\iOf]Sj]SVPBdG OZQvFHGVZBdG&]e\PG<Fk £BdhiBO<SÆ]e\7GTdQSFcEGe3Q)OPc/G<h¢Qv/h&QeOfG]S«ACBdG&]e\PG<FuU wK]S WÙeh&]SxSRQvjEg \ZG&jExSG& ½fI<¾ dI³¿ ACBEG t:]eRdjEg½oE mº¿¯¢OFHcdG<gtºX¡cEQS\fV)½¢¿b]S G&FHFQoEI QSjEgtºXACBdG&]e\PG<FuU od è G)h&QSjjd]£ ]StUViQvj¸FHFHG<gU¢QVZG&XVPBEG)QvF]3OYVOPRd\ZGKt/]SREjEgUG<gdjdG<OZOC]vܧ¨Æ©«ªZÐ>©S # . nnco pLqrBsBt.
(52) I³n T=U. $?& B<. ëºï } ë . X " %$ &[# %; & #. Õfä Sâ § ¨©«ª å´E¨)5 ª ç g Û Å;EFGIH JLK ¦ Æ ¨ / â P ª ã à P Þ à á © Ý M:N Û. ç ]&^eL[ L&B` # . - - Y # -$
(53) R WACBEG \PG³OfRdVCÆ]S]£O!Æ\Z]SF cEQv\PV)½Æñ¿b]v G<FFQHod uQvjEgcEQS\fV)½Æñ¿b]v G&FHFQHodIS Péj¸cEQeOPOPjExEU£bGKjE]vVPGKVZBdG Æ]S]£jdx>S } ï ¯ï
(54) {
(55) | ï X Y Lf%%; .b [-]a1 %;-# §1¨Æ©«ª 4 Ì ;& & ;Å EFGIH JLK © M:N Û 1 § Æ ¨ « © ª 4 Ì ;& & ;Å EFG M:N Û © §1¨Æ©«ª 4 Ì 7 &FÅ E;GIH J#K à © M:N Û § Æ ¨ « © ª &ÓFÅ EFG à © 4 Ì 7 M:N Û ACBdG G³ò3Rd QSG<jEhGKÆ]S]£OQvxeQSjÆ\P]eF G&FHFQSOodI QvjEgod uU Péj¸cEQS\fVZh&RdQS\<UV£CQSOCOfBE]£jtºX `!]>T²G&V QS@½YI³¾S¾So3¿CVZBEQVKÃK _ 4 Ì OKQOP1R D¡hG&j3V h]ejEgUVP]Sj²Æ]e\H½¢¿VP]Bd]eg j¥QShVKG< SG<j²Æ]S\ VZBdG)OfVP\Z]SjdxeG&\Ch]Sj:hREOf]Sj H 4 Ì Qd O& FÅ E;GIHJLK U° GO MS? M © M:N Û VZ]¥Bd]eg qVZBºREO VZBdGh]ejEhREOP]ej ½Æ¢¿½Æ£Bd¢hiB£CQSO cd\Z] SG³g jVZBdGOZQvFHGcEQSc:G<\¬RdjEgdG&\ØQqOYVZ\P]ejdxSG<\ h&]SjEgd¤VZ]ej:¿!OQSOP]ØVP\ZRdG £BdG&jEG& SG<\bà = 4 Ì %'$
(56) k&B,&Ba1 -%' # . . . . . . ! )* *E]S\Q¢QVfVZh&G QvjdFQv µQvjEgÆ]S\ ιÏEU£!G)gUG&ÁEjdGKVPBEGW» eVP\ZRdjEh<QVZG<g3¼¶£bG&xSB3V]vµ¬tºX 2 M N ¨µS+ ª 465 G?E 0 H 1 U°v± QSjEgVPBdG<j¸gdGÁEjdG § M N ¨©«,ª 4 ±&G°LK M 2 M N ¨ÆµSBª 7. . MON. ½ÆmEI³¿ ½ÆmE uS¿ ! n" $#.
(57)
(58) !"#$
(59) %'&. IeI. *E\P]eF. VPBEOgdGÁEjdVP]Sj«d£!G BEQ> eG¶FHFHG<gU¢QVZG&X¡VPB:QV<dÆ]S\Qv © 8QvjEg ÎÏd § M N ¨©«ªC幧¨©«ªbå´§ M N ¨Æ©«ª 5 ±G'L° K OM 5 0 H á c1 É 7 ½ÆmE oe¿ MON U°v± ACBEGWÆ]e]£jExØ\ZG<OPRdVbxe eG<ObQ¬t/]SRdj:g]ejVZBdG¶xe\P]£CVZB\iQVZGW]vVPBdG ¢QSOfV!VZG&\ZF ]SjVPBdG L ]S!½Æm: o3¿s ×WjEgUG<\¡h]Sj:gU¤VZ]ej ½fIS pS¿s!VPBEG¸L ]v½mE m3¿Ø£CVZG&jEg¹VP]n QSO ÖÑ Ì QCVPBd¢OH£Qv]M £ REOVP] QScdcd\Z]>TUFQVZGVZBdG)ò3REQvj3VPVYX¡FÅ E;GIHJLK M:N Û §¨©«ªPЩaQv\ZtdVP\iQv\ZX¡h]eOPG&XtºX¡FÅ E;GIH J#K M:N Û § N ¨Æ©«ªPЩ Æ]e\WQvcEcd\P]ecd\ZQvVPG //QvjEg¸OP]VP]¡£b]S\ZÙÆ]S\FH]3OYVW]S G<hsVZ]ebj mH£¤VZB¸VPBdG¬ò3REQSj3VPVPG<O \PG<cdQehG³gtºX VZBdG VP\ZRdjEh<QVZG<g SG&\iOP]ejEfO G[E 0 c1 X!ë ~ X V = > ¡Î´Ï ;Å EFG HJLK à ±G OM 5 0 H á c1 É åÖd¨@= 5 à ª ç g Û Þ àá ¦¨Æâ-ª ã Õfä eâ ;& ½ÆmE m3¿ L °. K © MON U°v± M:N Û R WACBEG GTUcd\ZG<OZOf]Sj ±GL° K M MLN U5 °v± 0 á c1 É h&]S\Z\PG³Ofc/]Sj:gdO7VZ]¡QvjGTUcd\ZG<OZOf]SjÆ]S\§¨©«ªbj¸£Bd¢hiBBEQeOCt:G<G&j¸\PG<cd¢QShG³g¡tºX 0 H á c1 É W]£VPBdGb\iQvjEgU]eF >QS\P¢QvtEG³O 0 á c1 É ¸¶vQS\PG!@ @ g Qvj:g)jd]ejUjEG&xeQvVP SG7£VPBgU¢OYVZ\PtdRUVZ]ej M ¦ NZd£BdG<\PG . . è G BEQ> SG. ¦ M N ƨ â-ª 4 ¦ ¨ÆâI5 d ªsd⥠´ÏL7. ¦ M N ¨Æâ-ª ã Õfä eâ 4 g Û Þ àá ¦¨Æâ-ª ã Õfä eâ« à á Þ Ý OP]½mE m3¿7Æ]S]£ObgU\PG³hsVZXHÆ\Z]SF ACBdG<M]S \ZG&F od odºQvcEcdG<g¡VP]ØVPBdG OP¤VZREQVZ]ej¡£BdG<\PG¶VPBdG gU¢OYVZtERUVP]Sj¸¦ ¢OC\ZG&cd¢QSh&G<gt3X¡VPBdG)gU¢OfVP\ZtdRdVP]Sj²¦ N . ë ~U}. g. Û. GV 2«K)Ñ É t:GQSjºX²ÆRdjEhVP]SjOPREhiBVPBEQvV ¨ÆªØÑ Ì QeO,i$Ñ Ì GV 4 G?E «< ¨ªi3 r¶jdGah<QvjgUG³gUREh&G OfVP\iQvxSB3VfÆ]e\P£CQv\igUXÆ\Z]SF G<FHH F Q¹mEI¥VZBEQV³WRdj:gUG&\ h&]SjEgd¤VZ]ej ½fIS pS¿s © à ±&G° M MON U5 °v± ¨ÆH á H
(60) Eª7Ñ#Ï QE O<-QSOK©1Ñ Ì ¬ACBd¢O¶£CQSO¶cd\Z] SG³g¸t3XqÀ QSjEgU]e¤ÁQvjEga G<OfVPG&j´½YI³¾S¾vmº¿Rdj:gUG&\ h]ejEgUVP]Sj´½YIS uS¿Æ]S\ VZBdG)h&QeOfG ¨Æ ,ª 4ÖÅÇSÈ/¨ s$ 5 à ªs
(61) . nnco pLqrBsBt. X Y.
(62) I>u. $?& B<. " ¬bØ« ) ) ¬(i: ACBEG)Æ]S]£jdxh]Sj:hG&j3VZ\ZQvVP]Sj¸jEG<ò3REQvVYX¢OWt:QSOPG<g²]ej¥Q¡\ZG<OPRd¤V¶]v¯A Qv¢QvxS\iQvj:g ½fI<¾e¾epS¿èÖBdG<j¥£!G R:OfG V< q£ h&]S\Z\PG³Ofc/]Sj:gHVP]QHOfG&V]v¢QVPVP¢hG QvjEFQv¢ObG<QehiB]vQ¬xe eG&j¸Of·&G dQvjEgVPBEGK QS\P¢QvtdG<O £ h&]S\Z\PG³Ofc/]SjEgVZ]¡VP\ZRdjEh<QVZG<g¸£bG&xSB3VZ3 O G[E 0 c1ACBEG¬cEQS\fVZh&RdQS\REOPGÆRdjdG³OPO¶]vVPBEG¬\ZG<OPRd¤V Æ]e\]SRd\cERd\Pc/]eOPG<Ob¢OCVPB:QVVPBEG t:]eRdjEgcd\P] º¢gUG<ggUG<c:G<jEgdO]ejdX]Sj Ø:QvjEgOjEgdG&c/G&jEgUG<j3V]v 1 ~ X V - !P à X!ë
(63) å ! å =O # :-#f :$ B %FB& &Ba# eL <!¨@Ï å å d+ª 4 à =: -
(64) &- @!&Ba &-<&^ K à iUR 7-7-7- &Ba# eL G°O # # å . %;. 4IG° 5 7 ° . Y #. Ãá # / ª!å Q 1K 7 á / J J 5 1 8 7 ½@pUI³¿ à R G&V t/G²Q¥FHG<gdQSj¹]SVPBdG\iQvjEgU]eF# >QS\P¢QvtEG ¯QSjEgGV 5Î ÏdACBdG<]S\ZG&F dISI]S A Qv¢Qvxe\ZQSjEg¥½fI<¾S¾3pS¿7VPBdG<j²FHcdG<ObVPB:QV 7 < Þ # á # 5 ã å 1 Q 1K á 5 J 8 7 @½ pU uS¿ 1 J è G VPBEG&j¸BEQ> SG à á # å1à # á # # g Û 4 < 5 ã R 5 Ý Þ # á7 # å g Û 1 Q 1K á 15 J J 8 R 5 Ý 4 g Û Q 1K«¨ á â J ªfSâ Ý å à 7 < Þ #. ! n" $#.
(65)
(66) !"#$
(67) %'&. e(
(68) Ø E£!G h&QSjh&]SFØtdjEG¶VZBd¢OQvx3Qvj£VPB½@pd ue¿¯VP]HxS SG < Þ # á à # /ã å < Þ # á # 5 # à á # / ã å < Þ # á # / á´à ã å < Þ # á # / Ðv ã å 1 Q 1K 7 á ¨ 1 / Ðve Bª J J 8 7 J 4+1 Q 1K á / 8 J à Ë Q 1K 7 á / J J 5 1 8 7 à L ¢OQVG<QeOYV à P / Ë (e
(69) ØdVPBdG<j½pUI³¿!Bd]egdObVZ\P ºQSXSdOPjEhG VZBdG). I³o. P /. . ) IV)C ¬b "$(&%')* (s )æ à *E]S\@8W QSjEg %Yf© 3b%Kå ©Ü gUGÁEjEG G¬
(70) ¨ 8df©Ü %@ª¶VZ]²t:GVZBdGOPGV)]Sb¢QVPVP¢hG¡QvjEFQv¢O µ]vOf·&G © OPREhiB´VPBEQvV 8 µUQvjEgOPREhiB´VPBEQvVG[E Ed°v± -¨ à ªb4:¨ à ªHQvj:g GO 3U°v± -¨ à ª_4:¨ à ªH5*% á à ½ G<\P
(71) G -¨ à ªQvjE g /¨ ª\PG<cd\PG³OfG<j3VVZBdG²ÁE\iOfVh]º]S\igUjEQVZG<O]v kQvj:g¹]S)83¿skr¶jdG¥h]eRd¢gÖOPQ>XVZBEQV
(72) Gب"8Ef©Ü %ª O7VPBdGOPGV!à ]v-QvVfVP¢hGQSjdFHQSO7]v Of·&G©Üe]v e%feQvj:gØjEh&REgdjdx@8¬QSO7Q?%;< $? & # >@ `!¢QSOZOP¤ÆXºjdxq¢QVPVP¢hG²QvjdFQv¢O¬tºXVZBdG&\H£gUVPB´j¹VPBd¢O£bQ>X£bG<jEQvtEGREOVP]QvcEcdXQS\PxeRdFHG&j3VZO t:QSOPG<g]Sj¸OfRdc/G&\iQSgEgU¤VZ ºVYXS *E]S \ b
(73) à δÏE H²WCQvjEg bgUG&ÁEjdG M N ¨ 8d , ª 4 ±° K M G'O 2 M N ¨ÆµSª 7 ½ mdI³¿ ? ? N WG&\Z G 2 M N ¨ÆµSª OKVZBdG 3@VZ\PRdj:h&QVZG<ga£!G<xeB3V ]S!µ¸QSO gUG&ÁEjdG³g QvV¡½ÆmEI³¿ACB3R: O M N "¨ 8E ª ¢O VPBdG FQvTºF¬REF ½ 3VP\ZRdjEh<QVPG³gE¿£bG&xSB3V7]v Q ¢QVPVP¢hGWQSjdFQSE]v OP·<G ` ,bKQvjEgH£¢gºVP B £Bd¢hiBjEh&R:gUG<O 8QeOQG&ñVPFH]eOfVc:]ej3V³ *E]S\G<Qehi B à ÎÏdU£bG¶VZBdG&j²gUG&ÁEjdG à M N ¨ « ª 7 M N 4 H J#K ½ md uS¿ * jEQvX£!G OPGV . . § nnco pLqrBsBt. M N 4 HJLK H JLK 7 Õ Ý. ½ md oe¿.
(74) I<m. $?& B<. @½ ACBd¢O!OPRdcd\ZG&FØRdF £:jd]SV!t/GÁEjE¤VZGÆ]S\CQv:¦HºtdRdV¯Æ]S\b¦ OPQvVP¢OYÆXºjdx½fIS pS¿s3£bGW£-OfBE]£¹VZBEQV!VPBdG t/]SREjEg½YIS wv¿!Bd]egEOZ¿ è G jd]vVZG VPBdG Æ]e]£jdxØcE\P]ec:G<\fVZG³OC]v VPBdG)ò3REQSjeVZ¤VZG³O M Ns¨ 8d ªs¯[QS\fV)½¢¿h]S\Z\ZG<OPc:]ejEgdO< G³OPOPG&j3VZQSXS/VP]VZBdGH]StEOPG&\Z QVP]Sj¥VPBEQvV QSjºX¢QVPVP¢hGQvjEFQv]S!Of·&GH©1h&]Sj3VZQSjEjdxVPBEGØ]e\PxSjqFØREOYV B:Q> SG QØGñVZFH]eOfVc:]ej3VWOP]SFHG&£BdG<\PGKj 0 á ©Üf.© 1Æ QSjEgB:Q> SG £gUVPB $Æ]S\OP]SFHG à å å´©Ü X!ë ~ X V = %% 1 à Î Ï & %% M N "¨ 8d a f ª L &feL &$?" ]&B B a1 k& M N ¨ « 8ª 3 %%O8¸¶ & = %% M N ¨ a ªbå§ M N ¨ ` ,bBª 7 ½ md m3¿ & = %%:©a § M N ¨Æ©«ªbå <° G Õ- G M N "¨ 8E f©Ð ¸ª 7 ½ md pS¿ . MS? M. . . M. R [ÜQv\PV ½Æñ¿ÜÆ]e]£O7Æ\Z]SFVZBdG¶QShsVbVPB:QVK<H-f²WKQv\ZGW @ g UQvjEgOf]hG<\fViQvjdX¡OfVZQvVP]SjEQS\PX ViQvÙºjEx'8H\iQVZBdG&\bVZBEQvj\²QSF]eRdj3VZObFHG&\ZG&XVP]¡QØVZ\ZQSjEOf¢QVZ]ej [ÜQv\PVZO ½ñ¿QSjEga½ñ¿!Æ]S]£Æ\P]eF VPBdG)gdGÁEjdVP]Sj:O)½Æm: ue¿!QSjEg½ mEI>¿!QSjEgVPBdG ]etEOfG<\P QvVP]SjEO!VPB:QV GØ
(75) ¨ «c ` be ²ªU G¬¨ ` b>ª Æ]e\Qv à b«Qvj:gVZBEQV f f G¬¨©«ª GØ
(76) "¨ 8dP©Ü ²ª <° MS? M Õ M Æ]e\Qv ©a b«\ZG<OPc:G³hsVZ eG&XS WGTºVK£bG¬QScdcdXVZBdGØh&]SjEh&G&j3VP\iQVZ]ej¸jdG³ò3REQv¤VYX¸]S G<hsVZ]ejapHVZ]h&]Sj3VP\Z]S VZBdGØgdG& ºQvVP]Sj¥]SÜVPBdG ò3REQSj3VPVPG< O M N ¨ 8d a ª!Æ\Z]SFVPBdG<\G&Tºc/G<hVZQvVP]SjERO S X!ë ~ X Y - Î¹Ï à 8K Y L- 7 / J < M N ¨ 8d ª á à M N ¨ 8d ª / å Q 1K á 5 18 7. J à . . . ! n" $#.
(77) I>p.
(78) !"#$
(79) %'& R è. G BEQ> eG. M N ¨ d8 ª,4. ±°K? M G'?O ? N d5 °v± G?E ?0 H c1 7 jEh&G GØ
(80) ¨ 8dc` be ¸ªK¢O QÁEjdVPG¡OPGV³«Qvj:g QSÜ]S¯VZBdGQvVfVZh&G¡QvjdFQv¢O h]Sj3ViQvjdG<gqjV)BEQ> SGHOf·&G jE]xS\ZG<QVZG&\CVZBEQvj a/QvjEg¸OPj:hG¬ÏåIG?E ?0 1å Æ]e\WQv 7/£bG)h&Qvj²QScdcdX G<FHFHQpUIK£VPB 4 VP]xe eGWVZBdG \ZG<OPRd¤V³ è G jd]£jE]vVPG)QHOPRdc/G&\iQSgdgUVP º¤VYXcd\P]ec:G<\fVYX]SVZBdG)OPG<ò3RdG&j:hG<O¶< à M N ¨ « ªs ¯ S X!ë ~ X = > ¡Î´Ï à 3 = %% ²Õ J à M N ¨ ²Õ 5 J ªb ¹ à M N ¨ « ¥Õ> ?ª 5à M N ¨ J Bª 7 R GVص³Õt/GQQvVfVP¢hGQvjdFQvÜj G¬
(81) ¨ «c ` ¥ Õ be ¥Õª¶Æ]e\)£Bd¢hiB M N ¨ « ¥Õ> ª)QVfViQvjEO VZO FQvTºF¬REF ½@OfG<G VPBdG¬gdGÁEjdVP]Sj<½ mdI³¿P¿ QvjEg¸G&V 8 t/GØQ B/.k $
(82) k&BL#]vܵ³ Õ Q: GS:QHc/]Sj3VWj µ>ÕOPREhiBHVPBEQvV ¨ à +ª 4 G'O 3d°v± , /¨ à ,ª 4²Õ áaà P VPBdG<\PG¢O7jE]SjU Rdjd¢ò3RdG&jdG³OPO7jVZBdG¶hiBE]S¢hG]v µ>ÕC]S\ ]S 8@dVPBdG<jFQSÙSGKVPBdG hiBd]eh&G t3XQvjºX¡FHGVZBd]Ug£BEhiB¸¢OCjEgdG&c/G&jEgUG<j3VW]v!<H-f¸¶s eÕK ¥Õe G?V 8vt/GÜVPBdG¯c:]ej3V«]etUVZQSjdG³g tºXWjEh\ZG<QeOfjdxbVPBdG¯ÁE\iOYV«h&]3]e\ZgdjEQvVPGÜ]S 8StºX:I Q³VPBdG<j ¨ à +ª 4¥Õ> QSjEg 8 ¢OQSg>^fQehG<jeVCVZ] 8@ GVµ J t/GaQ¢QVPVP¢hGqQSjdFQSWj GØ
(83) ¨ 8 c ` J be J ªHÆ]e\£Bd¢hiB M N ¨ 8 J ª¡QvVfViQvjEO¡VZO FQvTºF¬REF ACBdG<j²µ Õ QSjEgµ J Qv\ZG)gU¢OÆ^Y]ej3V¬½@OfjEhG µ Õ e8<F 2ºÏ å -¨ à ª Ë Õ ¬QvjEgµ J e ³3 2 Õ å -¨ à ª Ë
(84) Õ 5 J >¿eQvj:gHµ Õ µ J ¢O¯Q OPRdtEOPGV¯]S Q QvVfVP¢hG¶QvjdFQvdj Gب ` b¨! Õ 5 J ª be Õ 5 J ª/½@OfjEhG 8 µ Õ ¢OQSg>^fQehG<jeVCVZ' ] 8 µ J Qvj:gOPj:h\G ` b!¨ Õ 5 J ª b) ` Õ b$56` J b>¿s7ACBºREOC£bG BEQ> eG M N ¨ « ¥ Õ 5 J ªb 2 M N ¨µ³Õ µ J ª 462 M N ¨µ³Õ<ª 5 2 M N ¨Æµ J ª 4 M N ¨ Õ ª 5 M N "¨ 8 J Bª 7 ½ md me¿ bRUVHtºXaVZBdGjEgdG&c/G&jEgUG<jEhG]v¬<H- -¨ à ª Ë ¥Õ>¸QvjEgÖ<H- ¥Õ¥å -¨ à ª Ë ²Õ 5 J 3ÜVPBdG \iQvj:gU]SF Qv\ZQStdG M N "¨ 8 J ª7BEQeOÜVZBdGKOZQvFHGWgdOfVP\ZtERUVP]SjQeO M N ¨ « J ªs WG&jEh&GViQvÙºjEx G&TUc:G³h&QVZ]ejEOCj <½ md me¿bxS SG³O!VPBdG)gUG³Of\ZG<g\PG³OfRdV< M è G h]SFØtdjdGWVZBdG cd\ZG& º]eREO¯VY£!]ØG<FFQeO¯VZ]OPBdM ]£ÖVZBEQVCVZBdGKOPRdcd\ZG&FØRdF N gUGÁEjEG<gQV ½ md uS¿ jQShVC\ZG&cE\PG³OfG<jeViO!VPBdG jEG<Qv\xe\P]£CVZB\iQVZGK]S N ¨ « ªCQSO t/G<h&]SFHG<OC¢Qv\ZxSOG S. . . nnco pLqrBsBt. .
(85) I0m X!ë. $?& B<. ~ X. -
(86) . à ¡ Î´Ï Ã . M N ¨ a ª. . Ñ . M N k& Ñ. Ì 7. ½ md wv¿. M N ¨ « ª. Ñ M N %'$? &B,&Ba1 -%' k& Ñ Ì 7 ½ md e¿ R b[7\Z]Sc/G&\PVYX¡½ md wv¿ Æ]S]£O Æ\Z]SF VZBdGgUGÁ:jd¤VZ]ej½<md uS¿ QvjEg)Æ\P]eF VPBdGOPRdc/G&\iQSgdgUVP º¤VYX cE\P]ec:G<\fVYX Æ]e\VPBdG²OPG<ò3RdG&j:hG &à M N¨ a ª æ à ¸G<OfVZQStdOPBdG<g¹j G&FHFQ¹½<md oe¿sK½OPG&GÆ]S\HG&TUQSFHcdG èQvVPG<\ZO< I<¾ eudºACBEG&]S\ZG&F m: ¾3¿s W]£ UxS SG&j¸QvjºXÍWιÏEdG&V Ý t/G QS\PxeG¶G<jd]SRExSBVPBEQvV à M N ¨ « ª á M N å Í Æ]e\Qv Ý 7 ½ md ¾e¿ ½ REhiB²Qvj Ý GTUOfVZOCtºXq<½ md wv¿P¿s7ACBdG<j UÆ]S\
(87) Ý U£bG h&Qvj²QScdcdX G<FF?Q md u¬VP]HxS SG 7 M N ¨ a ª M N ÍN8 å[< 7 M N ¨ « ª à M N ¨ « ª Í 8'½ÆtºXq½<md ¾e¿P¿ < á á M 4A< N ¨ « ª á à M N ¨ « ª Í . å Q 1K 7 á ¨@Í ² ÐSS ª JJ 5 1 8 à 7 ÍJ 5 18 7 <½ mdI<n3¿ 4 Q 1K á 1 J jEh&G VPBdG)OPRdF]S«VZBdG)L ]SC<½ mdI<ne¿!] eG&\CQv" OÁEjdVPGSE£!G BEQ> eG¶tºX b]e\PG<¤f`bQvj3VPG<:VPBEQvV M Å;EFG HJLK N ¨ « ª á M N åÍ N Û QSFH]3OYVOPRd\PG<XeÜACBdOCBE]S¢gdOCÆ]S\QS ÍWιÏEUxS 3jdxVPBEG \PG³òeRE\ZG<g\PG³OfRE¤V³ ACBdG cE\PG< 3]SR:O!G&FHFQH£ xe eG¶R:OCVPBdG ]£bG&\Ct:]eRdjEgVPB:QV£bGKM jEG&G<g 7A«]HxSG&VWQHh]S\Z\ZG<OPc:]ejEgUjdx REcdc:G<\t/]SREjEg v£bG!QS\PxeRdG¯OPFHQS\PXS>REOPjExWVZBdG¯RdcEc:G<\ t/]SREjEg Æ]e\ § N ¨Æ©«ª«xS SG<j t3X G&FHF3Q mEI3½ÆñB¿ S X!ë ~ X § M N å´§ ;& %% ¡ÎLÏ 7 ;Å EFG HJLK © M:N Û . ! n" $#.
(88) Iw.
(89) !"#$
(90) %'&. GVWÍWιÏd+*E\P]eF G<FHFHQ?mEI3½Æñ¿sd£bG BEQ> SGe3Æ]S\QvjºX¡©Ü 7 7 < à § M N ¨Æ©«ª ¹§ 5NÍ 8 å[< à <° GO Õ GO M N ¨"8d aP©Ð ²ªb ¹§ 51ÍN8 © © MS? M M 7 å 5 < à M N "¨ 8E f©Ð ²ªb § 51ÍN8 7 ½<mdISI>¿ 5 © &° MF? M Õ M W]£ ºÆ]S\QvjºX ! - à M N "¨ 8E ,ª 4Ö Ã M N ¨ « ª å M N å §² Æ\Z]SF VPBdG)gUG&ÁEjdVP]SjEO¬ ½ md uS¿bQSjEga<½ md oe¿b]S M N QvjEg¸§7ACBºREO<ºÆ]S\QS - 8E U©Ü à M N "¨ 8E f©Ð ²ªbå´© b§ 7 ½<mdI³ue¿ ACBdG<jÆ]S\Qv å´©Ü ¸¶sE£!G h&QSjQScdcdX G&FHF[Q mE uØ£VPB 4 ©Ð $VZ]xe eG 7 < à M N "¨ 8d aP©Ð ²ªb ¹§ 51Í 8 å < 7 © à Þ M N "¨ 8E f©Ð ²ª á à M N "¨ 8E f©Ð ¸ª ã ¹Í 8 © å < M N "¨ 8d aP©Ð ²ª á à M N "¨ 8d aP©Ð ²ª ¹© Í. å Q 1K 7 á ¨Æ© © Ísª J J 5 1 8 à 7 © Í J 4 Q 1K á 5 18 7 <½ mdI<o3¿ à J * jEQvXeUÆ\Z]SF
(91) <½ mdISI³¿bQSjEga<½ mdI<o3¿sU£bGKB:Q> SGKVPBEQvV 7 7 © Í J < à § M N ¨Æ©«ªb § 5NÍ 8 å Q 1K á 5 1K8 5 5 © <° MS? M Õ M àJ 7 © Í J 4©7¨©5 à ª Q 1K á 5 1>8 7 ½<mdI&mº¿ à J jEh&G VPBdG OPRdF]S«VPBEG)L ]vC ½ mEI<m3¿¯] SG&\QS ©aObÁEjE¤VZGSd£bG BEQ> SG¶Æ\P]eF b]S\ZG&Y`bQSj3VPG&:VZBEQV FÅ E;GIHJLK à § M N ¨©«ªbå´§ 51ÍWQd O< M:N Û © jEh&GKVPBd¢OBd]egdOÆ]S\Qv ÍδÏdºVZBdG \PG³OfRE¤VÆ]e]£O& R . . . . . . nnco pLqrBsBt. .
(92) I. $?& B<. CA BdG t/]SRdj:gdOb£!G BEQ> eGWG<OfVZQStdOPBdG<g¡Æ\P]eF Qvt/] SGKQvjEgt:G<]£G<OfVZQvtE¢OfBEG<gQS]£ÖREObVZ]h&]SFHcdGVPG VZBdG cd\Z]º]v]S«VZBdG FQvj\ZG<OPRdVRS R =@ Y # -$ " %"K. è ¸G gUGÁEjEG§MQSOQV²½ md oe¿ACBdG&j M ¯RdjEgUG<\Hh&]SjEgd¤VZ]ej ½YIe pe¿sM VZBdGt/]SREjEg ½fIS wv¿ Æ]S]£O¬Æ\P]eF#VPBdG gd]SFHj:QVP]Sj²]SÜVPBdGò3REQvj3VPVPG<O N tºXVPBdGòeR:Qvj3VPVPG<O¶§ N xS SG<j²tºX G&FHFQmdIe½ñ¿s-Qvj:g¸VPBdG t/]SREjEgH]SjÃ)§¨Æ©«ªZÐ>©Ö½QSjEgBdG&j:hGS3tºX½mE oe¿s3]Sjà § M N ¨Æ©«ªPЩ«¿xS SG<jØtºXHACBdG&]e\PG<Fud oEACBdG QSRdG ]S ç h&QSjt/G VZQSÙSG<jQeObVPBEQvVG<OfVZQvtE¢OfBEG<gj¸[7\Z]Sc/]eOP¤VZ]ej¸ud ud W]£ ºÆ]S\Qv à ¹ÏE §¨Æ©«ª ¹;Å EFG E § Þ ` &`Æ©Ð b b ã FÅ E;G E © © M:N Û M:N Û § ` &`Æ©Ð b bã 4Ö;Å EFG E Þ. )`ñ©Ð b M:N Û ¹Å;EFG E § Þ ` b ã N Û M à ÅFEFG E N ¨ a ª ½ÆÆ\P]eF G&FHFQ[mEI3½Æ¢¿P¿ N Û ½ÆÆ\P]eF <½ md e¿f¿ 7 à M N QE O< ACBºREO M § Æ ¨ « © ª N ;Å EFG E <½ mdI³pe¿ © H J#? K 4Ö§ M:N Û QeOgUG<OP\PG³g r¶jVPBdGK]vVZBdG&\bBEQvj:g U¤b½YIS pS¿¯Bd]egdO<3VPBdG<j ºtºX G&FHFQØmEISeÆ]S\CQvjºXÍÎÏ)£bGKh<QvjÁdTQ OfR:hiB VZBEQV FÅ E;GIHJLK à ±&G 5 0 H á c1 É å¹Í M:N Û © °LK M MON d°v± QSFH]3OYVOPRd\PG<XeÜACBdG&j dÆ\P]eF
(93) ½Æm: o3¿s ;Å EFGIH JLK à §¨©«ªCå1FÅ EFG HJLK à § M N ¨©«ª 51Í M:N Û © M:N Û © 幧 51ͳ <½ mdRI m3¿ QSFH]3OYVOPRd\PG<XedtºX G<FHFH
(94) Q mE pd7ACBd¢OBd]S¢gdOCÆ]e\Qv«ÍÎÖ#Ï QEh]eF¬tdjdjdxVPBd¢O£VPB ½ mEI>pS¿!xS SG³ObVPBdG QE O<dh]ejº SG&\ZxSG<jEhG¶j½fIS me¿s. . ! n" $#.
(95)
(96) !"#$
Documents relatifs
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des
[…] Chez nous, le parterre […] est composé communément des citoyens les moins riches, les moins maniérés, les moins raffinés dans leurs mœurs ; de ceux
But on another hand, increasing q at constant operative pressure results in decreasing the equilibrium pressure, by decreasing the operative temperature (Figure 9), and finally, it
R´ esum´ e : On pr´esente des r´esultats autour du probl`eme suivant: pour un point mat´eriel dont l’acc´el´eration est born´ee par une constante donn´ee, et pour un
Ensuite, pour déterminer lesquelles des voix créées pouvaient être qualifiées d’« androgynes », nous avons fait un test de perception dans lequel nous avons demandé
Toutefois, des améliorations sont à prévoir car bien que la protection induite par ces glycoconjugués soit significative, elle n’est cependant pas optimale pour mettre
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des
Venant compléter les nombreux guides spécialisés qui informent le touriste gay sur les différents lieux et structures qu’il pourra fréquenter s’il recherche son
