HAL Id: hal-00080808
https://hal.archives-ouvertes.fr/hal-00080808
Submitted on 20 Jun 2006
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished 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.
AF equivalence relations and their cocycles
Jean Renault
To cite this version:
Jean Renault. AF equivalence relations and their cocycles. Proceedings Operator and Mathematical Physics Conference, 2003, Constanza, Romania. pp.365-377. �hal-00080808�
(*),+*-/.0),-1+*21354
687:9<;<=>,?;
@ACBEDGFHIFED<JLKMDNPOQASRTOQUDBEV,DU8HQKMWXFEDRTY,Z[BERHQ\]OY^B'V`_ba]DGFTcdW,K[BEDDfe`Y,KMJHgZMD<W,h<D
FED<ZiHgBEKMOWbRjHQW,kBEV,D<K[FhO`h_^h<ZMD<RKMWlBEV,DIUDfHgRTYbFEDfklRTDBTBEKMWbmbn]N1DmKMJoDH8kbDc,W,K[BEKMOW
OQA'HBEOa]OQZiOQmKMhfHgZ1@pqDfe`Y,KMJHgZMD<W,h<DFED<ZiHgBEKMOWsrut!DRTV,OfNvBEVdHBjD<JoDGFT_0h<O`h_^h<ZMDwKMR
h<OVbOUOZMOQmOYbRBEOHe`Y,HQRTK[xyabFEOLkbYbhBh<O`h_^h<ZMDrt!DBEV,DWRzBEYdkL_8BEV,DjabFEOQ\,ZMD<U{OQA
kbDBEDFEUKMWbKiWbm%BEV,D|eLY,HQRTK[xyKMW^JQHgFEKiHgWLBuabFEOQ\dHQ\bKMZiK[B5_}UDfHQRTY^FED<RwHQkbUK[BTBEKMW,m~H%mKMJoD<W
h<O`h_^h<ZMDHQRBEV,D<K[FHkbOQWbxyKMoOLkL_^UkbDGFEKiJQHgBEKMJoDQri
10!1g|
llL``bP%¡ ¢g£C£¤¦¥d` j§¢QG£l^¨©b]0ªbl¢«¬¡PE<`¢QL®G¯¢¡°,G±
L£C²^¢Q¨<^Q³|´j¢µgL£C£¶G¯sLG¯¢ °sb±%L£C²^¢g¨s!·¸¹y¯¢g¢%º!C »sG¢%C,G¢Q²^¢gLw£C¢QbE
¢Q¼,s^£SG0½^¾G¯s¢|°j¿<¤TL£C²^¢Q¨|²^¢Q¢g<`¢QÀ~¨,Áºl¢g£C¢gl¢g,<ÂÄÃoÅQÆgÆQÆŸ8GLGE®ÇÁdC²sÈ
¿
É
Â:Ê ËÍÌQÊ
É^Î
Ï ¸
ÊÐ Ã Â:ʦ¿
Ê Ë Î Æ
Ñ
¯¢²b^²^¢X^]Gbl^Ò¯ª²^^sÒC¯¢|b¢¤zÒs^^¢gG¢QLG^lbGÒ¯sCG²^^Ò¡ÓÔ
L®'·¸8À¢»s¢À¨,Á
ÓÔ¹5 ʾËÍÕ ÊÔÂ Ê Æ
Ñ ¯¢Q ÓÖ¯sb|¼,¢«¬¡0ªLG¢wLsÀ~ij]µgµg<LCd^¢QG¢I¢glÒ©¢QLG¢u×ËÍ£C^²º
¹yG¢g¢%ؽLÙoÚǾf³
Ñ
¯¢QG£µg^0¨*¢¢Û]Ò¢QG¢QÀlC%G¯¢®Ç<Ll¢g ^¥X^®:G^Ò*^£C^²bCµQL£sÀÁ,©LlCµQg³
Ñ
¯¢
°,G±uL£C²^¢Q¨8·¸'¯¢w° ¿ ¤TL£C²^¢g¨suL®:¯¢b¢¤TGCÀ]¢À®Ç£C£*G¯®Üݸ^lG¯s¢Ò]À]sµf
GÒs^µg¢Þ0¸uËàßâá
Ã~ã
Î
ÅgÆgÆQÆ:ÅGºsäb³1åb¢ÛLlÒ£C¢^æb^¢IµQLlsG¢G¯¢I²bGbÒ*^À|µg^sªGsµfb
®Ç^P·¸v²^C^¢gâCÖG¯¢~d¢µfbâçGçªçf³[½!L®Ø½`è`Ú¹5ª¢Q¢0L£ª*ؽbéQÚܾ³~êvG¯§!dC¢g ë^Öl^¢
²^¢Q¢g<L£²^<LÒs¯ìL£C²^¢Q¨<^Qæ ¢G¢L£C±Q¢ ÞíËîÞ ¸ bG¯¢!C]»sG¢!ÒsLG¯ïªÒ©^µ¢L®G¯¢
^C¢g,G¢À¡²b^Ò¯µ^©ªEs²^®I}ªC²^£C¢%^¢Qª¢ÛÖLsÀÖº¢À]²^¢gæ£C^¨©¢Q££C¢QÀÖ¨dÁ
Î
ÅgÆQÆgÆ:źs³
Ñ ¯dsLâ¢g£C¢gl¢Qb8^®ÞðC^qC]»ssi¢0Òs`¯qñPËëñ à ñ*ò'ÆgÆQÆó³ Ñ ¯¢%^s¢¤TªÀ]¢QÀqª¯si®Ü
ÝÍËïÝ ¸ ^µbÞô^µQµbÀ]C²|G©È
ÝIñSÃfñ ò ÆgÆgÆdËïñ ò ñ©õÆgÆQÆ
ög÷÷öøXùfúûüGýùúCþCÿ ªü¦ÿGúùzþ*ÿzùfúþ !"$#%'&&)(*"$+,-+&/.103245)6 !7"$+,-8$91(
"$+,;:&)(<"$+,-==)>
?
üA@CBDEGFùHF7I`û1EyùTüAJLK45NMO03P<5<5NQR03S<TA>UOVAWXQR03S<TA>ZY*1[H0G\5<] 0^03_1P)`Q035<230
03Qab] 45<TA>c,OdC03_eP<`Q035<230f 0Qab] 45<T>Ug4e2J)23Q03TA>h7 i4A`jj0TP)03TA>ck*6<45)WlMOi4e6))m6<03 `b] `$0$>
c03451Wld4SH035<P<TGWXk*P)0QQ0O]n<034 0^>
Ñ ¯¢Q
*%¹yÞŪÝu¾1Ë
ã
¹yñÄÅ,+.-0/Å,1¾32Þ54764ÞÈ8+qÅ,/92 :ÖŪÝ;IñËvÝ=<>1*ä
¯sb~s`^£¶ªGsµG¢|^®@?¢<L£C¢X²bGbÒ©bCÀ¡LsÀq·8¸|ËBA8¿^¹*%¹ÇÞÅGݾª¾IËBA8¿b¹ÇÞÅGݾf³
C
^G¢G¯©`G¯s¢¢¼,`^£¢Qsµ¢l¢g£`GC^âÀ]¢»©¢QÀâ¨dÁ9*%¹ÇޡŪݾ^âÞ§æ©Ll¢g£CÁ}ñ§LsÀ01
L¢w¢Q¼,C`L£C¢g,Ii®¶G¯s¢g¢¢Û]Cª+âÅD/Öªsµ<¯¯s`IÝ
;
ñ!ËÍÝ
<
1~G¯s¢7EE<LC£:¢Q¼,Co^£¢Qsµ¢
jG¯ £C^²>F³§¬^¢g`^¢QQ涯¢!²bLs²^¢ ^]Gbl^Ò¯ªô²^^sÒPX¯¢}À]s^£bµfb ¹yG¢g¢
d¢µfGC^ìçªçf³[é^®|ؽ`è`ÚǾ8^®=GóËIH6 ^A8¿L¹yÞŪÝu¾ jG¯ G¢ªÒ*¢Qµ|¡¯¢~®ÇssÀLl¢Qb<L£
µ]µgÁdµg£¢bÈ
J
È8*%¹yÞŪÝu¾LKM6
¹ÇñÅ)NSÅ,1¾ OKPNSÆ
çTsÀ]¢Q¢QÀ:æs ¢w¯sob¢^È
ÓÔf¹Q:¾¹R:¾'ËàÕ
Ê
ÔTS,UWVYX
Q1¹R:¾
®Ç^Q727A3S¹*%¹ÇÞÅGݾª¾ÅZR72[*%¹yÞŪÝu¾fÅZ\]2[^³
_ Ò^¨©L¨C£EÁ¡l¢^GG¢a`ïbÞ Ëb*
UdcX
À]¢»©¢Q|E<`¢fe"gqbhA8¿L¹*%¹ÇÞÅGݾª¾
Gsµ<¯~¯s`æ]®Ç^Q92 A S ¹*%¹ÇÞÅGݾª¾æ
e"g:¹Q:¾'Ëji.Qklnmporqzº8`Æ
çz'¥d` jq¹ªØ½`è`ÚzætsGbÒ©,ªGC^~é³èC d¢µfb0çªçfædª¢Q¢^£CG0ؽ8u`Úzæ Ñ ¯s¢g^¢g$½]³
Î
¾æ^¯s`
e"g§%Ö«¬¡PªLG¢®Ç^0Ó L%d^¢QG¢ G¢glÒ*¢g<`G¢!×/i®L©ÀPb£ÁPi®$`à%¼,s^Gi¤
C,`^GL,®Ç^*%¹ÇޡŪݾ jG¯´IbÀ]^]¤C C¥^]À]Ád À]¢QGC``b¢^È
v g ËàÕ>wx
S Æ ¹Ty$z¡¾
¬}bG¢Q`^¢gæ]sÀ¢g^¡^GlÒ]GC^}^®1¢GG¢g,C^£®Ç¢g¢gs¢QI j¯µ<¯}Cu`Gª»s¢QÀ!¯¢QG¢bæ©^££
«¬¡%ªLG¢^G¢L®:G¯s¢u^¨©`b¢j®Ç^!³¶çT~G¯µ^,¢ÛdQæ,G¯s¢uµg^,G¢QGÒ©LGL®:¯¢u«¬q
Ò^¨£C¢g CQÈ
G|{~}a^&~ ): T5~}|ZYrW# ¢¡d£¤¡ ¥¦&>¡§8¨, ©¦ Tª
*«"ªa¬¡ ¢¡£8¡W v 29
Ã
¹T*lÅ,^!¿
®
¾¯°±²ª@³©´µ¶Y¨%T²¦"¨, >·8·¸£¬¥aY´%©¨,´¹`
º»
T¡
»
8ª¥@ v Y´¼
»
¨=½>ª8 µT¾¼W¿> ¢ª£¥Àª8¨%Y¢Á
êv¯¢g*ËÂ*%¹ÇޡŪݾ1¯¢²bGbÒ*^ÀlL®:G¯s¢^s¢¤TªÀ]¢QÀ®Çs££Sª¯si®Ü¹ÇÞ0¸^ŪݸQ¾L©À
J
'¯¢I®Ç©ÀLl¢g,<L£Sµ]µÁ]µ£C¢^æbG¯s¢¢Q¼,sLGC^¹yÃzq¾¯sbb£ÁlXG^£C]bl®Ç^×ËÍ£C^²º
L©ÀÖG¯¢QÄ`v¼,¢^³ C ^G¢ G¯sL£C^²ºq|G¯¢ GbÒ©b£b²^µg^£¢g,GbÒ,ÁÖ^®jG¯¢!ª¯si®Ü
Ý ¸ ³j¢µg^!À¢QÀ]sµg¢w®ÇGb ¯¢Ås1¢g^]¤Tå^¨*¢gCsª¤z´I¢g£C£¢G¯¢Q^¢g llbG¢w²^¢Q¢g<L£
¢QG£iÈsÀ¢g1ª^¨£C¢bGGlÒ]GC^©ÄbG¯¢À]Áds^µg¹ÇޡŪݾÄLsÀX^ÅÆh2 Al¹yÞÅ,^¾fæ
G¯s¢µgdµgÁ]µ£C¢|Õ S¶Ç
À]¢g»s¢QÀq¨dÁ ÆïCw~´^À]b]¤C ¥b]À]ÁdÀ¢g``b¢8®L©À}^£CÁ!i®G¯¢
GbÒ©b£b²^µg^£,ÒsG¢GG¢~ȶ¹Tƾ1^®Æ¡C'±g¢gs³ Ñ ¯¢I^¨©`b¢µQ^G¢jµ^¢QGÒ©bsÀ¶G8µg^sª^,
Ñ ¯¢°,G± ^£²b¢g¨<¡·¸¯sbX¡ÒGCd£C¢g²b¢QÀ
_
媨©L£C²^¢g¨ss涩Ll¢g£CÁâG¯¢~»Û]¢QÀd¤
Ò*^CbI^£²b¢g¨<l·
¸
^®ÄG¯s¢²bLs²^¢wL]^l^Ò¯ª ²^^Òæd j¯µ<¯!Csi®ÇbGl£CÁ~¯dÁdÒ©¢Qª¤
»sG¢^®EÁdÒ*¢8º
á
³· ¸ G¯¢8µgG,GG¢QÀ~ÒdÀsµfI^®·
¸
¨dÁ%G¯¢8G¯®Ü¢g©À]^l^Ò¯G³
°^¢QGÒ©bsÀ]C²^£CÁ^æ:¯¢%²^^sÒ©bCÀ *%¹ÇÞÅGݾu¯sb8!ÒdC£¢Q²^¢QÀ _ å/G¨²^^sÒ©bCÀ:æÄG¯¢
¥^¢QGs¢g£±yl¹ÇÞÅGݾwË
J w Ã
¹b¾uL®G¯s¢%®ÇsÀ^l¢g,^£µ]µÁ]µg£¢b³0çzXwG¯¢q¹Ç²^<LÒs¯q^®¯¢¾
EE<LC£S¢Q¼,Co^£¢Qsµ¢%¹y ji¯^]I£L²d¾(F|G¢Q£CLGC^ ^ G¯¢wC]»sG¢ÒsLG¯!ªÒ©^µ¢wÞ ¸ ³Á À]¢®Ü¤
CibæsÀsµfb¢}£Cli%¢Qµ<¯¼,¢Q%^G¢}o`LC£L¨£C¢~®Çb _ å ¢Q¼,Co^£¢Qsµ¢!¢g£`bsg³
_ Ò*bªC¨£C¢8ELG¢g²bÁ%G%ªGsÀÁ~¯¢8´I^À^]¤ C C¥^]À]Ád Ò^¨s£¢Q ^[*%¹ÇޡŪݾµg^sGCª
CE qE¢gÒsQÈG¯¢´I^À]b]¤C C¥^]À]Ád ÒsGb¨£¢Q ®Çb¤yl¹ÇޡŪݾ^sÀÖ¯¢~¢gÛ,¢gsGC^ÖG
*%¹ÇޡŪݾL®1µ]µÁ]µg£¢^[y¹yÞŪÝu¾f³
¢®Ç^¢!Ò¢QG¢g,GC²âG¯¢ª¢!E ÖE¢gÒsQæç|G¯sL£C£I¢gd¢Q G^l¢}¨s^Gµ~®ybµf<l^ï¯dÁb¤
Ò*¢gG»sG¢!l¢Q^G¢QÀ¢¼,`^£¢Qsµ¢G¢Q£CLGC^s j¯µ<¯ìµQL ª¢QGb¢ ^²bCÀ¢g£C¢|GâG¯¢
GbÒ©b£b²^µg^£SµQ^G¢^³
Ñ ¯¢wG¢^À]¢QG¯b£CÀ ¨*¢wo L¢I¯s`¯¢ªb£¢u^²b©L£CiEÁlL®G¯^£¥%%oÁ0¨*¢uG¯¢
¢glÒ¯©^G±Q¢j^lG¯s¢jGbÒ©b£b²^µgL£]²bGbÒ*^À±*%¹ÇޡŪݾ1^sÀayl¹ÇÞÅGݾf³ Ñ ¯¢QG¢j²^^sÒ©bCÀ
¯sob¢¨*¢g¢Q%,G]À]sµg¢QÀLsÀsG¢QÀC|¯¢jl¢Qbª¢¤¦G¯s¢g^¢CµQL£]G¢ªs²0¹yG¢g¢j¢^³²s³Ø½`Ús^
ؽ Î
ÚǾf³ Ñ ¯¢I«¬¡|Ò^¨s£¢Q{®Ç^°,G±^sÀ0°,G±¤T«w¢Q²^¢g^£²b¢g¨<^1L©À%ªb¢²,L²b¢
LG^lbGÒ¯sCG ²bGbÒs ^|EsÀ]C¢QÀ¨dÁX³'`L©8CàØ
Î
½ÚzæIØ
Î
ÙoÚ¦æ^sÀCÒsLGGµ£L
C§Ø
Î
è`ڦ橮Ç^%LG¯¢QGlC£C^Ò*^CbL®d¢Q ³d¢g¢X^£CG¡Ø
Î^Î Ú1LsÀØ
Î
Ú¦³¢|ª¯b£À
L£Gl¢Qbb!G¯sLIG¯s¢X´I^À^]¤C C¥^]À]Ád ÒsGb¨£¢Q ®Çbµ]µÁ]µg£¢j^!^sE®ÇbG%LGC^
²^^sÒs¶ b¶ªG©À]¢À¨,Á|«l³^]µ<¯lCÀ]1C}ؽQÚ¨]' ¢jÀ]wLµg^lÒs^G¢¯¢g¢¯C'G¢ª£
jG¯!^<Q³
çj¯¢Q^ª£CÁ0¯sLs¥ ¯¢°¢QbG¢8®Ç^
_
À]`Lsµg¢QÀ¡dGsÀ]ÁCâuª£C% j¯¢QG¢¯ jiGG¢Q
^¢QGC^~^®|Á0^£¥~¯s^¨*¢g¢Q!µg^lÒ£C¢¢QÀ:³
I¡}f~} !!"ó#$!u1&%
êâ¢0G¢µg^££¯¢g¢lG¯¢g¢0®ÇsÀ^¢Q,L£¢QG£i<^¯dÁdÒ*¢gG»sG¢0¢¼bs`L£C¢g©µ¢0¢g£`bsg³
¢QGCÀ¢QG¯¢Q¢g£C¢g`^sµ¢|G¯s¢ªG©À]Á8L®*¯dÁ,Ò*¢gG»sG¢®y^µGbQæoG¯¢QÁXªGCX£`¢®Çsª¯¢g
^¥%^&bG¢Q£LsÀ~GbÒ©b£b²^µg^£*¢¼,`^£¢Qsµ¢w¢g£`GC^©g³
')(+* ,.-0/2134657/831:9<;>=)?/2@BA61:CEDB/F/2G)H$CEI3#57/21:JK/L@M/2573DNC7OP1:QR(
Ñ ¯¢j¨sbªµ¢®Ç¢g¢g©µ¢j^ll¢QbªsG¢ÀX¢¼bs`L£C¢g©µ¢j¢g£`GC^©CØ
ÎTS
Ú¦³1ç¶G¢µg^££¨sGC¢VUsÁXG¯¢
G¢ªs²s³jêâ¢|^Gl¢wG¯sL¹ÇÞ¡Å+WuÅD`ľ0ª^sÀ^Àl¢Qbª¢QÀ}GÒsbµ¢8L©ÀG¯sLÃy C
L¢Q¼,C`L£C¢gsµg¢wG¢Q£CLGC^^ÞGsµ<¯ G¯sLQÈ
¹YX]¾Iµg£CbGG¢QL¢µb,L¨s£¢bæ
¹Z¾I²^<LÒ¯y{j[bG¢Q£ª¨©ª¢g^®¶Þ 4Þ§æ
¹J
¾¯¢l¢Qbª¢$`qj¼,s^G¤¦Cdo^GL,sÀ]¢Qy³
Ñ ¯¢j£^ª1µg^sÀ]GC^ll¢Q^sG¯sLG¯¢l¢QbªsG¢]\^¿`!LsÀ_^`¿%` ^¬yÍL¢¢¼,`^£¢Qb
¹Ç j¯s¢g¢6\`Å`^À]¢QL¢u¢QGÒ*¢Qµfb¢g£CÁlG¯¢w»©ªILsÀ~G¯¢8G¢Qµg^sÀ~ÒbaE¢QµGC^sbblÞ L©À
\^¿`'¹Q:¾'ËLc Ïed Q1¹ÇñÄÅ,1¾Eº>`'¹Çñ*¾G¾f³ ¯¢Qæ,^¢IÀ]¢g»s¢G¯s¢I´I^À]b]¤ C¥^]À]Ád À]¢QGC``b¢
L®]`ì^ v g Ë \^¿`
^`¿%`³ Ñ ¯¢l¢Q^G¢Å`ìCwµg^££C¢QÀ¡d`LL, j¯¢Q v g
Î ³ Ñ ¯¢
´IbÀ]^]¤ C C¥^]À]Ád À]¢QGC``b¢ v g
È8yjK ^!¿
®
`Cª»s¢¯¢8µ]µgÁdµg£¢wÀ]¢g,iEÁSÈ
v g ¹yñÄÅ,1]¾v g ¹1SÅd¾'Ë v g ¹ÇñÅd¾ ®Ç^Is³¢b³¹ÇñÅD1SÅd¾32 y Uò X Æ
}n~ ¢" _ %¢Q¼,Co^£¢Qsµ¢G¢Q£CLGC^ay b'L¨*`^¢jµQL£C£¢À¼°±r'i®:µg£CbGG¢Q
L¢w»sG¢b³jçzµg^££C¢QÀ
»
£)¦&¨°±rIi®¯¢g¢8¢gÛdª^!sµgG¢^Gs²0ª¢¼bs¢gsµg¢L®»sG¢
¢Q¼,C`L£C¢gsµg¢wG¢Q£CLGC^sw¹Ty
<
¾Gsµ<¯ G¯sLy/Ëny
<
Ò G0d££G¢Q³
¢®Ç^¢lE<`GC²~G¯¢»s<EuG¯s¢g^¢g!æS ¢|¢QµQL£C£b¢|^®'G¯s¢¢¼,`^£¢QbÀ]¢g»sGC^s
L®G¯¢8^l¢gs^¨£CEÁ0L®¢^G¢QÀ ¢Q¼,Co^£¢Qsµ¢w¢g£`b³
}n~ ¢ _ ~¢Q¼,C`L£C¢gsµg¢¢g£`b y/b^¨©`b¢IµQL£C£¢À0¥a"8·W®G¯¢QG¢
¢Û]E<X®y^l£CÁ
ã
+]ä
æ] j¯¢g¢=+Clª`¢b
á ØñsÚ¹ªØñÚÀ¢g^G¢Q¯¢µ£^^®
ñ*¾æ j¯µ<¯!C
¹Çܾ~Cd`LC^bÈj¹ÇñÄÅ,1¾Z2y5+XË+
d æ
¹ÇCܾ~l¢^G^¨£C¢^ȱQ 2
á
¹y¾ñOK5+¹Q:¾jl¢Qbªs^¨£¢b³
G|{~}}"! ± ²%´%µ#"#ª¥aµ%$ ´)´¯&')(+*-, yÀ·)¬ ³©YW"¡@¨,WT
Y´Å>·) YÁ/.
»
93´Å¥a²8·W¤0|"ª ¸£a0¼]´ »
£)¦¨°¹¶¢Á
')(' 1573#Q QC7A6JK3DNC7OP1 O2 ;P="?/ @NA61$C7DB/L/2G)H:CEI35+/21$JK/8@N/25+3DBC+OP1$QR(
3 ¢g¶©¢gdC¢g §¨sGC¢VUsÁw¯¢jµ£^ª»©µQ`GC^XL®s¯dÁdÒ©¢Qª»©i¢¢¼,`^£¢Qsµ¢G¢Q£CLGC^sQ³Äçz1¶
µ£^Gi»©µQ`b8Ò|GwCG^lbGÒ¯sCG!æ` j¯¢g¢^f´ ¥¬ ¨¦
» ´%¥à®ÇGb ywÃb¹yÞ0Ã`Å+WÃ`ÅD`þ
^,7y ò bv¹ÇÞ ò Å W ò ÅD` ò ¾wX ^¢g£ªbl^Ò¯ª e®Ç^µb,s££G¨sG¢8^®jÞ0Ã
^,¡¡µg^d£C£G¨sG¢lL®IÞ ò ªsµ<¯§G¯sL¬e
¿
`Ã54 ` ò L©Àhe 4 e¶¹TyÃQ¾Ë y ò sÒ§G
d£C£CG¢<g³ _ l¢QbªsG¢Àv¢Q¼,C`L£C¢gsµg¢¡¢g£`GC^ y`b¢gq¹yÞÅD`ľ0C!µQL£C£¢À ¨§> ªT¡®
G¯s¢¢Q^£`L£C¢QÀ^¢g£¶®ÇsµGC^swbqÞ ª©µ<¯¡¯s`ÅQ6\Ë Q6:^ X*ÆÕ0L¢µg^sª^,
X*ÆÕ,ÆdCsµ¢%^qL¨G<LÁ!¢^G¢QÀ}¢¼bs`L£C¢g©µ¢G¢Q£CLGC^qµQLq¨©¢%À]¢µ^lÒ*bG¢QÀ¡,G
¢g²^]À]µ0µg^lÒ©b¢g,<8`^¢QXE<LsÀsL<À¼bsLGC¢g,æilª870µg¢QXGqµg^sGÀ]¢g|¢g²^]À]µ
l¢Qbª¢QÀÍ¢Q¼,Co^£¢Qsµ¢â¢g£`GC^©g³ '²^]À]µl¢^GG¢Àv¢Q¼,C`L£C¢gsµg¢q¢g£`bsL¢
µ£^Gi»s¢À0»©ªj,G
¹Çܾ0EÁdÒ*¢:9
<
¹/¡Ë
Î
Ž]ÅQÆgÆQÆ:Å!;ì¾fÈÞ¯s^jµQL<À]©L£CiEÁa/ÖLsÀy G<L©ªGC^¢bæ
¹ÇCܾ0EÁdÒ*¢<9=9
<
¹T/Ë
Î
b>;ì¾fÈyë^^sGib¢XLsÀ}G¯¢QG¢|¢Û]CªuL¡d`LC^,
l¢^GG¢%¹Ç»sG¢^jC]»ssi¢¾¢¼bs`L£C¢g,G¬`³
¹yCܾ0EÁdÒ*¢:99=9©È1G¯¢QG¢wjld`LL,j¢^G¢¢¼bs`L£C¢g,j@`³
Ñ ¯¢EÁdÒ©¢!ç|G¢Q£CLGC^sL¢µg£¢L£Á¯dÁdÒ*¢gG»sG¢^³v°^sµg¢gC²¡¯¢!L¯¢gEÁdÒ©¢gæ ¢
¯sob¢^È
G|{~}} nWY´´%°]¡T ?0
»
£)¦¨°¹¶¬¨§t ªT¡¬³©W"¡Å¨,WT ´Á
r*@AÅ£85&CB8¯ED?(+*F¦ r ´ ¥a ¨¦
» ´%¥Å¯a
»
¨,7´9 " "ªÄ ¸£h ²
»
£)¦¨°±¶
¨§t ¢ªT¡¬)³©W"¡¤¨,WT G0$£)¦&H9=9
r*@¤¨%Tr§>¨:&!(+* .&£)¦&E99
á
"ª£)¦&E99=9
»
£)¦¨°±¶¨§t ¢ªT¡³©YW²¡a¨,µ
#T &´|¨)|¡ ¥¦"Wr¸£ ¡WY´´%°]ª·£a9Y´´ ¡Trª
º
¯±²¥ad£¤
»
9>¡)¿>£
¨)t§t¬ G0¼
»
ý>ª8 µT¾¼W¿> ª£¥ ª8¨%Y
v
g¯3²ªf£¨§t ¢ªT¡ Z
º
¡ ¢¡µ
¡©¨Á
3 ¢g1©1G¢µgL£C£,G¯¢Iµg^sªGsµGC^X^®s¯¢j¬^µ<¥b¢gÁ<L²b¢^®©wµ]µÁ]µ£C¢^³êq¢I^G¢²^C^¢Q
!l¢Qbª¢QÀ⢼bs`L£C¢g©µ¢0¢g£`b ¹yÞÅ+WuÅ,yÅD`ľæ¶!£C]µg^££CÁqµg^lÒs^µX²^^sÒ ji¯
bLIl¢^GG¢¡LsÀ} bG¢Q£Äµ]µÁ]µg£¢
J
ÈtyK8³¢XÀ¢»s¢j¯¢XG¥^¢g /Ò]À]sµf
¢Q¼,C`L£C¢gsµg¢wG¢Q£CLGC^[y¹
J
¾^¹4 ÞÅ[4`ľ¨,Á
¹YX
J
¹yñÄÅD1¾ÅD1¾4{¹X*Ūñ*¾"®Ç^8¹ÇñÅD1¾32 yÅ Xa28Æ
Ñ ¯¢8l¢^GG¢À¢Q¼,Co^£¢Qsµ¢XG¢Q£CLGC^7yl¹
J
¾jCLs¢Qµ¢GLC£Á ¢g²^]À]µLæs¢Q^¢Q®¹y C
Gs³ Ñ ¯¢0¢QG²b]À]Cµ%À¢QµblÒ©,ªGC^^®L§L¨G<LÁl¢Qbª¢QÀÖ¢¼,`^£¢Qsµ¢0¢g£`b
¹ÇÞ¡Å,yÅD`ľXÒ`,À]¢8¯¢ ´%r"ª8¨,ª ³© TjÞ
y³çz%Clâl¢Qbª¢QÀPªÒsbµ¢!ª©µ<¯
G¯©`QÈ
á
¹yÞ
y¾Ë
ã
Q 2
á
¹yÞq¾È>Q1¹yñ*¾ËÂQ1¹1¾ ®Ç^Is³¢b³C¹yñÄÅD1¾Z2[y|äbÆ
çT^sXµgbª¢bæį¢ ª^sÀL<ÀÖ¼,L¢Qb%¹
J
¾XË 4qÞ
yl¹
J
¾uC|}l¢Q^G¢QÀÖGÒs^µg¢
¢Q¼,CÒÒ*¢QÀ jG¯}£¢g®Ü^µfb!L®X³
}n~ ¢
Ñ
¯¢ul¢Qbª¢QÀj¤TªÒsbµ¢%¹
J
¾µQL£C£¢À%¯¢7>¡)¿>£a¨,§>^®G¯¢
µ]µgÁdµg£¢
J ³
çT¯¢%µg^G¢X^®G¯¢%´IbÀ]^¤
C
¥bdÀÁ,µ]µgÁdµg£¢
v
g*æ:iwCwµgsE^%LÁ G!µ^©ªÀ]¢g
G¯s¢0µ]µÁ]µ£C¢
J
Ëë£C^²
v
gÖÈybK ^¶i<8¬^µ<¥b¢gÁ}<L²b¢|8^£CGµQL£C£¢Àâi< ²¡¨n
º ³
_ /lÒ*^G^b¢ÛLlÒ£C¢¡^®|P¬¡^µ<¥^¢QÁï^²^¢ G¯¢ s1^ªbv¨©bsÀ^GÁïL®X
<LsÀ]bî L£C¥¡^}²bGbÒ﹪ؽ S
ÚǾf³}´j¢µgL£C£¯s`|!<L©À]^î L£C¥¡XÀ¢G¢QGlC¢QÀâ¨dÁ
Ò^¨s^¨£CEÁl¢Q^G¢¬+ó^Ö!²^^Ò8³~êq¢0bGGl¢l¯¢g¢lG¯sLG¯¢%²bGbÒ C
À]GµgG¢gG¢µg^,<L¨£C¢L©ÀwG¯sLį¢l¢QbªsG¢ +ë¯s^»sG¢GÁ,ll¢Gµ'GÒÒ*^G1³êq¢
µbsGCÀ]¢QG¯¢w<LC£¢Q¼,C`L£C¢gsµg¢G¢Q£CLGC^[y ^¯¢l¢Q^G¢ªÒsbµ¢0¹yÞîË ß áà Â1ÅD`Ë
ßqá
Ã
+}¾f³ çz §¯,ÁdÒ*¢gG»sG¢q¢g²^]À]µ}¢Q¼,C`L£C¢gsµg¢¡¢g£`GC^ij Ñ ¯¢¡<LsÀ^ð ^£¥
µ]µgÁdµg£¢
J
È8y K CjÀ¢»s¢À¨,Á
J
¹ÇñÅD1¾'Ë"£CC
<!
á ñ Ã ñ©òÆgÆQÆEñ
< 1 w Ã
<
ÆgÆQÆ(1 w Ã
ò 1 w Ã
Ã
¹Ü¯¢'£ClÄ¢Û]E<:¨*¢Qµg^sG¢G¯¢ª¢¼bs¢gsµg¢CªLGC^s^GÁ¾³ Ñ ¯¢l¢Qbª¢QÀI¤zGÒs^µg¢"%¹
J ¾
I¯¢¤s1bCªb!¨©bsÀ^GÁL®¯¢|<L©À]^ ^£¥Ö¹XÅD+}¾f³uçzuÀ]¢GµgGC¨*¢Qj¯¢¨©bsÀ]¢À
+ ¤¦¯s^GlbCµ®ÇsµGC^s^#8³¶çz ^GG¯L²w¯s`¯¢^£s¢Q¼,Co^£¢Qsµ¢j¢g£`b
yÍ1¯¢^£¢¼,`^£¢Qsµ¢j¢g£`b|^®©¯¢I²^<LÒs¯|¯sodC²ªC²b£¢^¢Qª¢ÛlLsÀlÂâ^
G¢^®¢QÀ]²b¢Q j¯C£C¢IG¯s¢G¥^¢g ïÒ]À]sµ j¯C£¢G¯¢uª¥b¢g ÒG]À]©µf¢¼,`^£¢Qsµ¢I¢g£`b
yl¹
J
¾G¯s¢wLC£¢¼bs`L£C¢g©µ¢wG¢Q£CLGC^ L®¶G¯¢|°oÁd£C¢gÁ%²^<LÒs¯ ^®¹XÅÂ'¾³
')(%$ & H3#Q C(' ?$@NO"9$H:JRD JKO"JR=J 57/2QR(
Ñ ¯¢%<LsÀ^î L£C¥qµgdµgÁ]µ£C¢lÀ¢»s¢ÀL¨*`^¢l8LÖ¢Û^Òs£¢%^®}¼,sbª¤¦ÒsG]À]sµ8µL¤
µÁ]µg£¢bæ j¯sCµ<¯v ¢¡À]¢g»s¢` ³ ¯¢¡À¢»sGC^©~²bb¢g﨩¢Q£` %L¥b¢ª¢Qsª¢®Ç^~^
L¨G<LÁ£]µQL£C£ÁP»sG¢¡bGC¢g,¢QÀ ²^<LÒ¯ I ¢}¢QªGµf0^sG¢g£C^¢G¯¢¡µgbª¢}^®w
Lª¢g£C¶À]L²b^!³u´j¢µg^££¶G¯©` Lª¢g£C1ÀC^²^<L CwL¡^¢Qb¢QÀ}²b^Ò¯ K
j¯¢QG¢j¯¢b¢gGGµ¢'L¢ª^µ<¥b¢QÀ^~£¢Q^¢g£ /ËesÅ
Î
Ž]ÅQÆgÆQÆ'LsÀ¯¢¢À]²^¢'l®ÇGbë
^¢Qª¢ÛX^®:£¢Q^¢g£/¼-
Î
GXwb¢gGG¢Û|L®:£¢Q^¢Q£&/³êâ¢À]¢QL¢I¨dÁ~¹/ľ¶¯¢G¢^®*b¢gGGµ¢Q
L®j¯¢£¢Q^¢g£Z/Í^sÀ§¨dÁ
¹/ľ8G¯s¢!G¢L®¢À]²^¢8®Ç^ô£C¢gb¢g£3/ - Î
G¡£C¢gb¢g£Z/³Öêq¢
^Gl¢wG¯sLI®Ç^I¢Q^¢QGÁ0b¢gGG¢gÛ*æG¯s¢g¢XL¢u»sG¢g£CÁ!%LdÁ^æ¨s]`£¢^ªI^¢bæs¢QÀ²^¢Q
ªLGGC²®Ç^*³ _ ~C]»sG¢Òs`¯08G¢Q¼,¢Qsµ¢L®Äµb¢µfG¢À%¢QÀ²^¢Qñ Ëvñ à ñ*òÆgÆQÆgæ
j¯¢QG¢8ñ:Ã8ª^ª<L£C¢gb¢g£³ Ñ ¯s¢|GÒs^µg¢XÞ L®'C]»ssi¢|ÒsLG¯su¯sb~s`^£L^££CÁ
À]Gµg^s¢Qµf¢QÀXGbÒ©b£b²^Á^æ^ ji¯|¯¢IµÁd£C©À]¢g'G¢<]8¹yñSÃñ ò ÆQÆgÆGñ
<
¾b¨©^GC ^ ¢¢Q¼,CÒ
Þî jG¯ G¯¢usÀ¢g£ÁdC²[bG¢Q£©ªGsµfG¢6Wu³ Ñ ¯¢u<LC£*¢¼,`^£¢Qsµ¢G¢Q£CLGC^y¯sb
^¢g£S²^<LÒs¯ C!Þ 4Þð¹ÇG¯j jC££Ä¨©¢%^À¢8µ£C¢QLCG¯¢¢gÛdª¢µfGC^*¾f³
}n~ ¢ _ µgdµgÁ]µ£C¢
J
Èy«K Xæ j¯¢QG¢ 8²^^sÒæĵg^££C¢QÀÖ ³©Y´%µ
¦"¨) ¢ª©¡¼¡ ¢¡£8¡#0¹Ç¢g£`b¢lG!¯¢ LªG¢Q£À]C^²^<L ¹'Å ¾ª¾i®G¯s¢g¢%¢Û]Cª!%^Ò
Q}È K 8æ^®ÜG¢Q!µQL£C£¢À £L¨*¢g£C£C²©æªsµ<¯¯s`
J
¹ÇñÅD1¾Ë £CC
<!
á
Q^ÃL¹ÇñSÃQ¾DQ ò ¹Çñ ò ¾:ÆgÆgÆQ
<
¹Çñ
<
¾ØQ <
¹T1
<
¾zÚw
Ã
ÆgÆgÆQØQ ò ¹1 ò ¾zÚw
à ØQbÃ`¹1dþzÚw
Ã
j¯¢QG¢|Q
<
C¯¢¢QªGCµGC^~^® Q}G
¹T/ľf³
}n~ ¢ _ ÒsGb¨sL¨C£CiEÁì¢^G¢ `/bvÞ C µg^££C¢QÀv 9¨,¿> ¥aY´%©¨,
¹Ç¢g£`b¢0¡¯¢ <`GG¢Q£jÀ]L²b^ð¹'Å
¾ª¾®IG¯s¢g¢ ¢gÛdªl¡%^Ò9È È K ^¿
® æ
µg^££C¢QÀ!l^sGibÒsGb¨sL¨C£CiEÁbæsGLGE®ÇÁdC² Ï
U¶X Ð
ȶ¹yÕ`¾Ë
Î
®ÇbI¢gb¢gÁ2$L©À
8%^Ò ` c È0¹b¾±K ^!¿
®
æ]µgL£C£C¢QÀ0^0siC^£©Ò^¨©L¨C£EÁ^æd`Gª®ÇÁ,C² Ï
UdcX
` c ¹]¾Ë
Î
Gsµ<¯~¯s`
`'¹r8¹yñSÃñ ò ÆQÆgÆEñ
<
¾ª¾Ë`c 6)^,¹Çñ:Ãg¾ÈSÃL¹ÇñSÃQ¾È ò ¹yñ ò ¾SÆgÆQÆTÈ
<
¹yñ
<
¾Æ
C ^G¢ G¯sL%q¬L¥^`âl¢Qbª¢`àCl¼,s^G¤¦Cdo^GL,X jG¯ ¢QGÒ©¢µfGqG¯¢ ^£
¢Q¼,C`L£C¢gsµg¢¢g£`bfy ¹yi<I´IbÀ]^]¤C C¥^]À]Ád À]¢QGC``b¢ jC££:¨*¢²^C^¢Q~C~¯¢¢gÛ,
G¢Qµfb©¾f³ Ñ ¯dsgæ^i1GsGsnyïC,Gl¢^GG¢À¢Q¼,C`L£C¢gsµg¢¢g£`b³ Ñ ^²b¢¯¢g1 jG¯|
¼,s^G¤¦Ò]À]sµµ]µgÁdµg£¢bæ,G¯ÒG`dÀ]¢QG¯s¢lbª²^¢gs¢g<L£*]À]¢Q£*®Ç^jbG¢Q£*µgdµgÁ]µ£C¢
^!¯dÁ,Ò*¢gG»sG¢¢¼,`^£¢Qsµ¢w¢g£`GC^ÄÈ
G|{~}}&¯?(+*ÄZ »
£)¦¨°±¶ ³©#²¡) ¨,#T ͹ÇÞ¡Å,yÅD`ľ%¯|
W ¡¸£7¡ ¥¦&>¡¹§8¨, ©¦ "ª = ¨,±¡) ¡£8¡W
J
È&y K ¼¯Z
»
¨)a! >´%T´¬"¨,¶d
ªT¢§¨)¥ ¹#Å ¾ º
»
¢°¹¶@¦
»
´¦8¡ Þ "ª r=³©#²¡)0¨,WT Äy ¯a
9¨,¿> @¥¬´©¨)Z` 0Þ ²ª 9´ ¥¬ ¨¦
» ´¥.e50¨, ¥ y« ¶ ¼y ¡¨%¨%£t§
J
r
¡ ¡£8¡W¬¡
»
¥a W )§> ©´Å¶ ³©Y´%µ#¦"¨) ¢ª©¡¡ ¢¡£8¡W
J
È>y K «Á
$ %'& $~} V!" #$!u1&%
_ jC ¢g£C£i¤z¥d` jæ,G¯s¢¯¢gbGC¢Q^®¯dÁdÒ©¢Qª»ssi¢®ybµf^<^sÀ~^®¯dÁdÒ©¢Qª»©i¢w¢Q¼,Cb¤
L£C¢g©µ¢¢g²^]À]µ0¢Q¼,C`L£C¢gsµg¢ ¢g£`bsL¢~Cb%LG¢g£CÁ¢g£`G¢À:³ Ñ ¯¢°j¿f¤z^£²b¢g¨<Lµ
L©L£C^²X^®¯dÁ,Ò*¢gG»sG¢u^b C ¢g%Ls^£²b¢g¨<8L!LÒÒoÛ]%LG¢g£CÁ»sG¢À]Cl¢g]¤
GbsL£Ä¹y^
_
å¾°
¿
¤z^£²b¢g¨<³ Ñ ¯s¢g¢ICLblL®SGbÒ©b£b²^µgL£
_
åâ¢Q¼,Co^£¢Qsµ¢j¢g£`¤
G¯s¢X¯¢gbGC¢QuL®
_ å °j¿f¤z^£²b¢g¨<^LsÀ¡L®
_
åv¢Q¼,C`L£C¢gsµg¢|¢g£`bsuL¢XCb%LG¢g£CÁ
¢g£`G¢À:³uçTÒsLGGµs£C^Qæ©G¯¢QÁª¯©L¢8G¯s¢|Ll¢|µg^lÒ£C¢G¢C,`^GL,Qæ*s^¢Q£Á¯¢Ài¤
l¢gsGC^^²^¢b³
$)(+* , 3#1$9<, /]G H:CEI3#57/21:JK/L@N/]573DNC7OP1:Q (
çT0¯G¢QµGC^ædÞî8£C]µgL£C£CÁlµg^lÒsbµfjª¢µ^©À0µb,L¨s£¢ L©GÀ]b}GÒs^µg¢u^sÀ y
IL¢Q¼,C`L£C¢gsµg¢G¢Q£CLGC^^!Þ§³'åbG¯¢|G^¥^¢uL®ªClÒ£µEÁ^æ© ¢bGGl¢uG¯sLIG¯¢
¢Q¼,C`L£C¢gsµg¢µ£^ª¢jL¢wµg^,<L¨£C¢^³
_
j¨©¢g®Ç^¢^æ ¢L£ª%À]¢QL¢¨dÁfy Þ 4!Þ
²^<LÒs¯³
}n~ ¢ " Ñ ¯¢w¢¼bs`L£C¢g©µ¢wG¢Q£CLGC^[y ^!Þ j£C£¨*¢8µg^££C¢QÀ:È
¹Çܾa¦²¨, )¦¨i®²^<LÒs¯$y ĵg£,ª¢Àw8Þj4Þ ^sÀuG¯s¢¼,L¢Q,%LÒ âÈLÞÀKÞ y
I£CdµQL£:¯bl¢g^lbGÒ¯sCG
¹ÇCܾ ¦8¦²¨, >¥a¶¸£¦"¨) )¦¨~¹y^ _ s¾i®yîË ny
<
æ j¯s¢g¢¡¹Ty
<
¾X^§©µ¢Q^GC²
G¢Q¼,¢Qsµ¢w^®¶Ò^Ò*¢gj¢¼,`^£¢Qsµ¢w¢g£`GC^©
¹yCܾ ¦8¦²¨, >¥a¶¸£Ã°±rw¹y^ _ å¾®1iI _ sv^sÀ~ÞG^L£C£CÁ~À]Gµg^¢µf¢QÀ:³
½¥a¨,¿tÁ8Á ¹Çܾ Ñ ¯s¢|CsÀ]sµGC^¢|£CliwGbÒ©b£b²^Á GsuL _ sÍ¢¼bs`L£C¢g©µ¢X¢g£`¤
b y$,!^?¢^£¢l£C]µgL£C£CÁµ^lÒsbµf ^sÀ]^§²^^Ò*^À:æ j¯sCµ<¯âCG^Ò*L¤
£C^²bCµQL£C£Á§^l¢gs^¨£¢b³£C¢Q% ¢!GÒ©¢µ®ÇÁPL¯¢g jª¢bæ ¢¢¼,Òy jG¯ G¯sC
^Ò*^£C^²bÁ^³
¹ÇCܾ Ñ ¯s¢g¢}loÁP¢Û]Cª~À]E©µf%GbÒ©b£b²^C¢Qlb ^ ¢¼,`^£¢Qsµ¢!¢g£`GC^yî%^¥b¤
C²iwCb ^j?¢<L£C¢X£C]µgL£C£CÁ!µg^lÒsbµf²bGbÒ*^À:³6'ÛLlÒ£C¢QµQLq¨©¢lÀ]¢QÀsµ¢À
®Ç^ ؽb`Úzæ
Ñ
¯¢gbG¢Qô½³Ùs³
Ñ
¯¢g¢0Þ 8¯¢°L,^|GÒsbµ¢0L©À y ¯¢~bª¤
¨siw¢Q¼,C`L£C¢gsµg¢8G¢Q£CLGC^}^®%lC%L£¶¯^l¢Q^l^Ò¯ª Ý L®'Þ C,G i<ª¢Q£i®E³
Ñ
¯s¢|LG¯bª¯` /¯s`$y _ å ¨]wi< _ åìG^Ò*^£C^²bÁ uÀ]CªGCsµ®Ç^ G¯¢
^Ò*^£C^²bÁ0L®¶Þ5476I³
Ñ ¯¢^£j¢¼bs`L£C¢g©µ¢!G¢Q£CLGC^ì^ìG¯¢!C]»sG¢}ÒsLG¯ïªÒ©^µ¢L®w<`GG¢Q£IÀ]`¤
²^<L CL}¢Û^Òs£¢^®^ _ åì¢Q¼,C`L£C¢gsµg¢8G¢Q£CLGC^}L©À~¼b©^Gi¤zÒdÀsµfµgdµgÁ]µ£C¢
L¡¢ÛLlÒ£C¢X^®~µg^,GCd^sµ]µÁ]µg£¢b³çT¡®y^µfæ aEsªwbCâ½³Ù0^¨©`b¢^æ©G¯¢ª¢¢Û^|¤
Ò£C¢Qw¢gÛd¯©Lsª8L£C£ _ åÍ¢¼,`^£¢Qsµ¢l¢g£`GC^©LsÀ¡G¯¢Q|µ^,dbswµ]µÁ]µ£C¢Q%¹yl^¢
Ò¢QµgCG¢g£CÁ^æd¯¢gCIµb¯^l^£C^²bÁ%µ£^¾³ Ñ ¯¢wÒGd^®IªCl£LG¯sLIL®jØ
Î
]æ
Î
Úz³
G|{~}} ">,I¹yÞÅ,y¾@·)a " ³©YW²¡¬¨,WT
º
» Þ ¡ ¥¦&>¡"ª
W ·)@a# ¢¡d£¡ ¥¦&>¡ §8¨, ©¦Á
r*.
»
¨,f! >´%´¬¨,¶¸ªT§8¨,¥
º
»
¶¹³©YW"¡a¨,WT P¹ÇÞ Å)y ¾a"ª
»
¥¬ ¥a ¨¦
» ´%¥bÆPÈLÞ KÞ ¡¨%¨%£t§¤y ¶ |y Á
r*0 ¥a ¨, ¨
J 2 Ã
¹yÅ ¾9´0 ¡) © ©´7¡ ¡£8¡W ¶¢¿t§°±r¸£ ¥a£
d©%´Å 8¡
» y <
G0Å9"¡¨,Y´%§a´³©"¡¤ G0]¦"¨) )¦¨|¨)WT &´$´%©¡
» »
yË@ny
< ¯ » ¨,¶¸±ªT§8¨,¥ ¡9·Å¡
»
´ ´%©¡
» »
Æj¡¨%¨%T´
J
r
r*ZY¨%£ ¡ © ©´¡ ¡£8¡W
J 2 Ã
¹yÅ ¾f´f¡ © ©´%¸£ ¡)
»
¥¬ W ,§t ©´r
¡ © ©´f¡ ¡£8¡W7r¿§¬°±¶¸£0¥a£9¸©´[ )>¡
» y <
G0[§8
²¡¨))´%t§´)³©"¡Å ?03¦"¨, ¦&¨¼¨,WT ´¼´%©¡
» »
yË@ny
<
3¨, G0ÁuC^¢gGaE¢QµGC^¢%%LÒ /ÈÄÞ K0æ¶ ¢0oÁ¯s`}ª¨©ª¢g ëÞ C8
S¤Tª¢µfGC^¡i®'¯¢X¢QªGµfGC^¡L® ÍC aE¢QµGC^¢b³uêâ¢|oÁG¯sLu~ÒsLGGGC^ ^®
Þô¨dÁ S¤Tª¢µfbsIS¤zÒs^ªib®®Ç^uL£C£IÅ2 0æ©¢gG¯¢Q '¹¾ '¹Ü¾Ël^
'¹¾8Ë '¹ ¾³ êâ¢~À]¢QL¢0¨dÁ
¿
G¯¢~ÒsLGGGC^
ã
'¹¾fÅ 2 %ä0L®0³çz®jÞ C
µblÒs^µ^sÀqG^L£C£CÁqÀ]Gµg^s¢Qµf¢QÀÖL©À ï8!£CdµQL£¯bl¢g^lbGÒ¯sCG!æ®Ç^¢Q^¢QGÁ
Òs^ªib L®'Þ ¨dÁ}µ£C^Ò*¢g⪢gQæ*G¯¢QG¢¢Û]E< S¤¦Ò©LGGGC^^®Þó j¯µ<¯¡I»©¢g
G¯©L8³
3 ¢g¹ÇÞ¡Å,y¾w¨*¢~L _ å ¢¼,`^£¢Qsµ¢0¢g£`b³ Ñ ¯,©Åy Ë ny
<
j¯¢g¢¡¹y
<
¾C
LÖCsµ¢QbªC²G¢Q¼,¢Qsµ¢%^®ÒsGbÒ©¢Q8¢Q¼,C`L£C¢gsµg¢%G¢Q£CLGC^sbÞ ¹Ç ¢~^ªs¢l¯s`
y=cw¯¢%À]C^²^bsL£Ü¾8³lêâ¢% jGG¢lÞ
<
ËëÞ y <
^sÀq ¢%À]¢QL¢¨dÁ <
ÈSÞ K Þ <
G¯s¢0¼bsLGC¢g,%LÒsQ³%êâ¢0L£ª¯so^¢l%LÒ©
<< w Ã~È*Þ
< w
äK Þ <
ªsµ<¯â¯s`
< Ë
<< w à 6 < w
Ão³ Ñ ¯¢Qæ^¯¢g¢j¢Û]E<1®Ç^L£C£&/
Î
<< w
Ãf¤¦Òs^ªib
<
L®SÞ
< w èdÁ
µ£C^Ò*¢gÖG¢Qµfbswª©µ<¯G¯©`
<
G¢g»s¢%¹ < w à < w ò ¾ ¿ < w
ól¬}^¢g`b¢gæ©®ÒsLGGGC^s
<
^®Þ
< w
Ã|¨,Áqµ£C^Ò*¢gªs¨sª¢g¯©o^¢l¨©¢Q¢gGÒ©¢µ»s¢QÀ:æ¶^s¢0µgLÖµ<¯dbG¢}¹
<
¾wª©µ<¯
G¯©`
<
G¢g»s¢!
<
³]sµ<¯âG¢Q¼,¢g©µ¢L®Ò©LGGGC^sl¹
<
¾u jC£¶¨*¢0µg^££C¢QÀq0` ¢QQ³
_ ` ¢QXÀ]¢g»s¢Q <`ª¢g£CÀC^²^<L!³
C
^¢Q£Ábæ1 ¢À]¢»ss¢ 0¹b¾X^XGC²^£C¢0^¢Qª¢Û
L©À®Ç^@/"
Î æ ~¹/ľ0Ëô¹ < w à < w òo¾
¿ < w Ã æ ¹/ľ%Ë#
<
^sÀ®Çb$ 2%
< æ ^,¹¾
wG¯¢~¢g£C¢gl¢g,X^®w¹ < w à < w òQ¾
¿ < w à µ^,<LCs²&/ j¯C£C¢ \]¹¾8Ë
<< w à ¹¾f³ 3 ¢
¹ÇÞ Å)y ¾j¨*¢G¯¢ _ å ¢Q¼,C`L£C¢gsµg¢8¢g£`GC^}bGG]µ`G¢À G0¯$Lª¢g£CÀ]L²b^³ _
¢g£C¢gl¢Qb'^®:Þ G¢Q¼,¢Qsµ¢8¹
<
¾fæ, j¯¢QG¢'
<
'µ£C^Ò*¢g0G¨sG¢'^®*Þ
< w à ædª©µ<¯|¯s`
< ® à µb,LC¢À C
<< w à ¹
<
¾f³ Ñ ¯¢8%^Ò7ÆïÈ,Þ KóÞ bGG]µ`G¢w0ñ 2ÞôG¯¢
G¢Q¼,¢g©µ¢¹
<
¾fæ1 j¯¢QG¢!
<
w¯¢~¢Q£¢Q¢Q,8L®G¯¢~ÒsLGGGC^
< w
Ã| j¯sCµ<¯§µg^,^s
< w
Ã`¹yñ*¾³jçz®
ã w Ã
<
¹
<
¾<ä,ÅD/ 29: C%¨s^G®Ç^j¯¢^Ò*^£C^²^Á L®Þ§æ]¯¢g0ÆPCsÀ]sµg¢Q
LªbbGÒs¯CG$L®¶G¯s¢ _ 姢¼,`^£¢Qsµ¢w¢g£`GC^©¹ÇÞÅ)yw¾^sÀÖ¹ÇÞ Å,y ¾³
dÒÒ*bG¢%` G¯sL
J
Èy«K $}µbbdbswµ]µÁ]µg£¢^¥d²»ssi¢g£CÁq%LdÁ
`L£C¢QÄ^Åy
<
®ÇbL£C£t/¹Ç^G¢G¯sLÄG¯sC¢Qµg¢QG^GC£CÁ¯¢µQ^G¢' j¯¢QÅ*vÀ]µ¢G¢ªCsµ¢
y <
CµblÒs^µ<¾f³1ê⢵<¯dbG¢µbbdbsª¢µfGC^©)(
<< ®
Ãj®Ç^G¯¢w%LÒ©
<< ® ÃX¹Ç¨dÁ
GÒ©¢µ®ÇÁ,C²}G¢Qµfbsu®Ç^\¡È
¹/ľ$K 0¹T/ľª¾f³ Á¡µg^lÒ*bGibæÄ ¢l²^¢8µg^,GCd^s
G¢Qµfbs*(
<
®Ç^ <
È^ÞÀKôÞ
<
³¶êâ¢À]¢g»s¢:Z
<
ÈLÞ K v¨dÁ Z <
¹ÇñS¾Ë
J
¹ÇñÅ+(
< 6 <
¹ÇñS¾ª¾
L©À Z,
<
ÈÞ
< K ¨,ÁeZ,
<
¹yñ
<
¾qË
J <
¹yñ
<
Å-(
<< ® Ã 6
<< ® ÃL¹Çñ
<
¾ª¾æñ
< 2 Þ <
L©À
J <
¹yñ
<
Å,1
<
¾'Ë
J
¹.(
<
¹Çñ
<
¾fÅ+(
<
¹1
<
¾ª¾f³ Ñ ¯¢g
J
¹yñÄÅD1¾ËLZ
<
¹ÇñS¾+Z
<
¹1¾
w Ã
®Ç^^££'¹yñÄÅD1¾Z2 y
<
L©À Z < ® à ¹Çñ*¾Ë Z <
¹ÇñS¾+Z < 6 <
¹yñ*¾³âdCsµ¢ Z <
L¥b¢QX^£CÁ¡»©i¢g£CÁÖl^dÁq`L£C¢gæ¶ ¢
µg^0µbsEG©µf¨dÁ©À]sµfb w` ¢Q
<
ª©µ<¯lG¯sL)Z <
µg^sª^,^%¯¢¢Q£¢Ql¢g,
L®1¯¢8Òs^ªib
< ³ Ñ ¯¢gÄæ
J
%¼,s^G¤¦Ò]À]sµµ]µÁ]µ£C¢¢g£`GC^¢wlG¯¢[LªG¢Q£
À]L²b^ ^ª]µ`¢QÀ~ ji¯ ¯G` ¢g³
Ñ ¯¢0£^ªXÒs^ª8^®¯¢%¯¢gbG¢Q ^¨LC¢ÀÖ¨,Á⪩µgµ¢GGC^¢0LÒsÒ£µgLGC^s8L®G¯¢
£C¢gl%I¨*¢g£C` ³Äê⢵g^X^Gl¢'G¯©`ìÄl¢GC±Q^¨£C¢LsÀ8¢gsÀ]` ¢QÀ8 ji¯Xµg^lÒ£C¢G¢
²b¯bud`LL,ul¢gGCµºs³|êq¢%GÒ©¢µ®ÇÁ¡ª¢¼bs¢gsµg¢|^®Ò©,ªGC^¢dX¨*¢g<l¹./
<
¾ª©µ<¯
G¯©`
Ï /
<10
; L©À¡µbsªGsµfw¨dÁCsÀ]©µfGC^Öµb,GC,s^s®ÇsµGC^s$Æ
<
ÈsÞ K
Gsµ<¯~¯s`º*¹TÆ
<
¹yñ*¾Å
Î
¾2/
<
®ÇbIL£C£:ñ72Þ^sÀ
J Ë ¹TÆ 6>\L¾SÆQÆgÆQ¹Æ
Ã
6P\L¾
J
¹Æ
Ã
6)^o¾w
Ã
ÆgÆQÆQ¹TÆ 6)^o¾w
Ã