The Remaining 40% Of Ramanujan's Lost Notebook


 

   



!#"%$& " '()+*-, .0/214357698:.05;/<>=4? >@ A+B;CDAFEHGJILKNMPO;KRQSKMSMPGUTLVXW#AYCZMPOLK\[-]^MSKCDGJ]Y_HI;GJQD`a;QPQSKbIcGJTMPO;KRQSKbdeaLKb_gf^hRK\i;CDGjKlknm ILKbQD`lCDGjioK MPOLKpO;GUQSMSAYCPmAYWoq&]Y[)]YTratsP]YTuvQw_jAxQPMyTLAYMSKioArAYz2{Z|}Mwh&GU_J_~ioK`lAxTrEYKbT;GjKbTrMyMSA€ioKVxGJT9GJT9MPOLKmYKb]^C b‚xƒ^„-]YTnI…MPOLKbT…B;CDAe`lKKbI…i]Y`PzehR]^CDI { |†T‡MPOLKQSB;CDGUTLV…AYWb‚xƒ^„efRˆ0KAYCDVYKŠ‰XT;I;CPKh&Q€EHGJQPGJMSKbI7@4CDGJT;GjM}m7‹RAx_J_jKVYKYfN‹\]Y[ci;CDGJI;VYKYf:MSA KlŒL]Y[-GJTLK MPOLKBn]^BoKCDQ_jKWŽM9iemˆ{wc{:‘]^MPQPAxT{‡‰0[AxTLV’‘]^MPQSAxTuvQ-Bn]^BoKCDQfyOLK WŽAxanT;I‡] [-]YTea;QP`lCDGJB;M-`lAxT~MP]YGUT;GJTLV“b”Y•Bn]^VYKbQ GJT–MPOLKO;]YTnILhpCDGjMPGUTLV’AYW€q&]Y[-]YTeatsP]YT{—|†T–EeGjKh˜AYW MPOLK+W™]Y[K AYW4qX]Y[-]YTra^sS]YTuvQT;AYMSKi2AeAYzHQfHBnaLin_JGUQPOLKbI)GUT]9BnO;AYMSAe`lAYBem)KbI;GJMPGjAxT irmMPOLK @4]^MP] |šT;QSMPGjMPaLMSKNAYW;›;a;T;I;]Y[-KbT~MP]Y_rqpKbQSKb]^CD`œO9GJT€RAx[i]bmcGUT-b‚YžxƒŸ l¡^¢£fxGJM>h\]YQ4T;]^MPa;CD]Y_YMSA+`]Y_J_xMPO;GUQ TLKh&_JmW#Axa;T;I[-]YTea;QP`lCœGjB;M…¤Sq&]Y[-]YTeatsP]YTuvQ_JAxQSMTLAYMSKioAeAYz{v¥§¦&A¨h©I;GUIMPOnGJQ€[-]YTea;QP`lCDGJB;M CPKb]Y`œO@4CDGJT;GjM}m‹RAx_U_jKVYK¨ª ‘]^MPQSAxTInGjKbIGJT’b‚Y„Yž]^MpMPOLK ]^VYK€AYWyƒ^‚e{R«HOLAYCDMP_jm-MPOLKCPKb]^W#MSKCbf;AxT…QPKBn]^CD]^MSK AH``]YQPGjAxT;Qf ¬ {y­‡{w‘—O;GjMSMP]^zYKC)]YT;I®q{y‰{yqX]YTLzHGJT¯EeGUQPGjMSKbI¯­CœQ{w‘]^MPQSAxT{°@pO;K_U]^MSK ¬ {y­‡{w‘“O;GJMš± MP]^zYKCh\]YQ]BO~mHQPGJ`GJQPM]YT;I¯QSAxTAYW&²p{Z@ {Z‘—O;GjMSMP]^zYKCbfyhXOLA³`lAx]Ya;MPOLAYCPKbIh&GjMPO‡‘]^MPQSAxT B;CPAYi]^in_jmMPO;K)[AxQSMcB2AYBa;_J]^C ]YT;IW#CPKbdeaLKbTrMP_jm³anQSKbI(MSKlŒHMAxT7]YTn]Y_jmeQDGJQ€GJT’MPOLK ´^µ^MPO‡`lKbTH± MPaLCPm(Ÿ¶´Yž¨¢£{·qX]YTLzHGJTfHh&OLAO;]YQioKKbT]^MpMPOLK€¸0T;GjEYKCœQPGjM¹mAYWwˆ _J]YQSVYAFhºWŽAYC&[)]YT~mmYKb]^CDQfnO;]YI QPa;``lKKbI;KbI(‘]^MPQSAxT7]YQ»yCPAYW#KbQPQSAYC€AYW\­³]^MPOLKb[-]^MPGJ`Q€]^MMPOLK-¸XTnGjEYKCDQPGjM}mAYW\\GjCD[-GJT;VxO;]Y[…f h&OLKCDK‘]^MPQSAxTQPKCPEYKbI³WŽAYC+[AxQSM0AYWNO;GJQ0`]^CPKKCb{ RAYMPO³‘“OnGjMSMP]^zYKC€]YT;I³q&]YTLzHGJTŠhRKbTrM0MSA ‘]^MPQSAxTuvQ0]^MSMPGJ` A^¼ `lKMSA-KlŒL]Y[-GJTLKMPOLK Bn]^BoKCDQp_jKW#MiemOnGJ[…fL]YT;I…ioAYMPO…W#Axa;T;IMPOLKc]^WŽAYCPKl± [KbTrMPGjAxTLKbIŠ[)]YTra;QD`lCDGjB;M\iem qX]Y[-]YTra^sS]YT{yqX]YTLzHGJT…QPaLVYVYKbQSMSKbIMSA)­CDQ{y‘]^MPQSAxTMPO;]^M&OLKC _J]^MSK&Oea;QSi]YT;IuvQ:Bn]^BoKCDQwioKQSAYCPMSKbI]YT;IQSKbTrMyMSA@4CDGJT;GjM}m9‹RAx_U_jKVYKp½>GjinCD]^CPmYfr‹\]Y[ci;CDGJI;VYKYfxWŽAYC B;CPKbQPKCPEt]^MPGJAxT{y¾+aLCDGJTLVcMPOLK TLKlŒHMMPOLCPKK+mYKb]^CDQf;qX]YTLzeGUT QPKbT~M\‘]^MPQSAxTuvQ&Bn]^BoKCDQfHGJT;`_JanI;GJTLV MPOLKq&]Y[)]YTratsP]YT([-]YTea;QP`lCDGJB;Mf2QPKbT~M+AxT´Y„¾0Kb`lKb[ioKC-b‚Y„Y•ef:GJTi]^MP`DOLKbQ MSAŠ@4CDGJTnGjM¹m2uvQX_UG ± i;CD]^CDmY{yq&]YTLzHGJTO;]YIŠTLAYMCDKb]Y_JGj¿KbIMPOLK€GJ[-B2AYCDMP]YT;`lK+AYW:qX]Y[-]YTra^sS]YTuvQ&[-]YTranQP`lCDGjB;M\]YT;I…QSA I;GJITLAYMp[-KbT~MPGjAxT…GJMRMSA]YT~mYAxTLKY{N|†TBn]^CDMPGJ`a;_J]^CbfHOLK€I;GUI T;AYMCPKEYKb]Y_MPOLK€[-]YTea;QP`lCœGjB;MuvQRKlŒr± GJQSMSKbTn`lK&GJTO;GJQyAYinGjMPa;]^CPmŠŸ FƒF¢2AYW2‘]^MPQPAxT)hpCœGjMSMSKbTW#AYCyMPOLK0À>Á^ÂÃxÁ^ÂÄÅYÆ#ÇHÈÉ-ÅYƙʙ˜Å^Ì2Í2ÁbËbÊgÈbƙÎt{ @pOea;Qf2MPOLK9TLKlŒeM+deaLKbQSMPGjAxT’GJQÏp¦XAFhÐI;GUI‘]^MPQSAxT(`lAx[-K9GUT~MSA BoAxQPQSKbQPQPGJAxTŠAYWNMPOnGJQXQDOLKb]^WwAYW b”Y•B]^VYKbQpAYWZq&]Y[-]YTeatsP]YTuvQhRAYCPzLª ‰&W#MSKCqX]Y[-]YTra^sS]YTInGjKbI(GJT¯b‚Y´^µHfNˆ{ ¦{4¦X]^CDI;mQSMSCPAxT;Vx_jm³a;CPVYKbI’MPO;]^MqX]Y[-]YTra^sS]YTuvQ BnaLi_JGJQPOLKbI9B]^B2KCœQfeT;AYMSKi2AeAYzHQfe]YTnIAYMPO;KC\anTLBnaLin_UGJQPOLKbIhRAYCPz-ioKX`lAx_J_JKb`lMSKbIMSAYVYKMPO;KCpWŽAYC BnaLi_JGJ`]^MPGjAxT{Z‰ºOn]YT;ILhpCDGJMSMSKbT`lAYBem)AYW:q&]Y[-]YTeatsP]YTuvQTLAYMSKioArAYzHQ€Ÿ l¡^¢ h\]YQQPO;GjB;BoKbI)WŽCPAx[ MPOLKp¸0T;GjEYKCDQDGjM¹mcAYW­³]YILCD]YQwMSA¦0]^CDILmGJTb‚Y´Y”efe]YTnI]^MwMPOLKpQP]Y[KMPGJ[-KRAYMPO;KCN[-]YTea;QP`lCDGjBnMPQ ]YT;IB]^B2KCœQZAYWoqX]Y[-]YTeatsS]YT-h·KCPKX]Y_JQSA€QSKbTrM{y@pOLKCPKp]^BnBn]^CPKbTrMP_jmcGJQNTLA CPKb`lAYCDIAYWoB;CDKb`GJQSKb_jm h&O;]^Mh\]YQ&GUT;`_Ja;ILKbIGJTMPOnGJQQPO;GjB[KbT~M{y@&Ora;QbfH[-AxQSM&_JGjzYKb_JmYfLMPOLK_jAxQSMpT;AYMSKi2AeAYz hR]YQXQSKbT~M MSA)¦0]^CDILmGJT(b‚Y´Y”e{ |†T–MPOLK7b‚Y´^µYQ]YT;Iсb‚Y”^µYQfp‘]^MPQSAxT“hpCPAYMSK]Y_J[AxQSM¡xµBn]^BoKCDQAxTÒMPOLKŠhRAYCPz®AYW q&]t± [-]YTeatsP]YTf[AxQSM+AYWyMPOLKb[Ó]^CDGUQPGJTLV-W#CPAx[ÔKbGjMPOLKC qX]Y[-]YTra^sS]YTuvQ _JKMSMSKCDQ0MSAŠ¦X]^CDI;mŠAYC+WŽCPAx[ q&]Y[)]YTratsP]YTuvQRTLAYMSKioArAYzHQ{w|šT)B]^CPMPGJ`a;_J]^CFfrOLKXhpCPAYMSK0AxT qX]Y[-]YTeatsS]YT uvQ·[AH`PzMPOLKMP]cW#a;Tn`Õ± MPGjAxT;Qbf>h&O;GU`DOqX]Y[-]YTra^sS]YT‡I;GJQP`lA¨EYKCPKbI‡GUT(MPOLK)_J]YQPM€mYKb]^CcAYWpOnGJQ€_JGjW#K-]YT;II;KbQP`lCDGjioKbI(GJT] ÖnרØYنÚgنÛ:Ü×&ÝHފßràŽÖ¨á¨â ã




á

 
á   ZÖ

_jKMSMSKC-MSA‡¦X]^CDI;m‡AxT;_Jm‡]^ioAxaLMMPOLCPKKŠ[-AxT~MPO;Q-i2KW#AYCPKŠOLK…I;GJKbI Ÿvƒrf·B;B>{N´Y´^µe´Y´Y”¨¢£{ґ]^Mš± QSAxT(O;]YI([)]YILK-QSAx[K-`lAxTtsSKb`lMPaLCPKbQ€AxT’MPOLKKlŒHGUQSMSKbT;`lKAYW\`lKCPMP]YGJT([AH`Pz³MPOLKMP]…W™a;T;`lMPGjAxTnQ{ |†W+O;KO;]YIÒO;]YI–GJT–O;GJQ-BoAxQPQPKbQPQPGjAxT®MPO;K_jAxQSMTLAYMSKioArAYz2fpOLKhRAxa;_JI–O;]bEYK’QSKKbTÒMPO;]^MO;GUQ `lAxTtsSKb`lMPaLCPKbQ0hRKCPK`lAYCPCPKb`lM{ @pOea;QfnBnCPAYin]^in_jm…QSAx[-KMPGJ[K9]^WŽMSKC+‘]^MPQSAxTuvQGJT~MSKCDKbQSM0GUTq&]t± [-]YTeatsP]YTuvQ:h·AYCPzchR]YT;KbIGUTcMPO;K\_U]^MSK+b‚Y”^µYQbfxinaLM:ioKWŽAYCPKO;GUQ4ILKb]^MPOGUTb‚t¡rƒrfe¦X]^CDI;m€Bn]YQPQSKbI q&]Y[)]YTratsP]YTuvQc[-]YTranQP`lCDGjB;M MSA‘]^MPQSAxT{«HGUT;`lK-[-]YTrm’GUILKbT~MPGJMPGjKbQ€GJTrEYAx_jEHGJTLVŠ[AH`Pz(MPOLKMP] W™a;T;`lMPGjAxT;Qc]^B;BoKb]^CGUT7MPOLK_jAxQSMTLAYMSKioArAYz2fyGjMGJQc`lKCDMP]YGJTMPO;]^McMPO;K _jAxQPMcTLAYMSKioAeAYz7]^CDGJQSKbQ W#CPAx[ MPOLK€_J]YQPMpmYKb]^C&AYWZq&]Y[-]YTeatsP]YTuvQ&_UGjWŽKY{ ›ZGJT;]Y_J_jmYfRGJT®Kb]^CD_Jm“b‚Y•Y•efZsPa;QSM-]^W#MSKC)MPO;K`lKbT~MSKbTn]^CPm®AYW q&]Y[-]YTeatsP]YTuvQ-inGJCPMPOf·0]^CPAxQP] »Na;in_JGJQPOnGJTLV ¦&AxanQSK0GUTXKh ¾XKb_UO;G;Bna;in_JGJQPO;KbI]cBOLAYMSAe`lAYBem-KbI;GJMPGjAxT)AYW>MPOLK0_JAxQSMRT;AYMSKi2AeAYz Ÿ b„¨¢£{Z|†Tn`_Ja;ILKbI GJT€MPOLKNKbI;GJMPGjAxT€]^CPKR]WŽKhAYMPOLKC:a;TLBnaLi_JGJQPOLKbI0[-]YTea;QP`lCDGJB;MPQiem+qX]Y[-]YTeatsS]YT ]YQ·h·Kb_J_]YQ·_JKMSMSKCDQNioKM}h·KKbT q&]Y[-]YTeatsP]YT]YTnI)¦0]^CDILmY{·«HOLAYCDMP_jmcMPO;KCPKb]^WŽMSKCFfHqX]YTLzHGJThpCPAYMSK ]-EYKCDmŠGJT~MSKCDKbQSMPGJTLVBn]^BoKCpAxTMPO;KAYCDGjVxGUTŠ]YT;I³`lAxT~MSKbTrMXAYWwMPO;Kc_jAxQSM0TLAYMSKioArAYz2fo]YQ&hRKb_J_ ]YQ AYMPOLKC0[-]YTranQP`lCDGjB;MPQ\_jKW#Mpiem qX]Y[-]YTeatsS]YT‡Ÿ b•¨¢£{ ‰&ioAxaLM „^µ AYW MPOLK³]^B;B;CPAFŒHGU[-]^MSKb_jm°„Yž^µ‡`_U]YGJ[-Q)[)]YILKŠiem°q&]Y[-]YTeatsP]YT–GJTÒO;GJQ-_jAxQPM TLAYMSKioAeAYz-BoKCPMP]YGJT-MSA[AH`Pz)MPOLKMP]W#a;Tn`lMPGjAxT;QR]YT;I)AYMPO;KC rQSKCœGjKbQ{y­AxQSM·AYW4MPOLKbQSK0CPKbQPa;_JMPQ O;]FEYK7TLAFh i2KKbT“B;CDAFEYKbI iem“‰0T;ILCDKh&Q{%‘(K‡`GjMSK sSanQSMAxTLK(AYWOnGJQ Bn]^BoKCDQŸ Õ¢£f+h&O;GJ`œO B;CPA¨EeGUILKbQQSAx[K(AYWMPOLK(_jAxQSMŠTLAYMSKioAeAYzuvQ…O;GUQSMSAYCPm°MPO;]^M…hRKO;]FEYKCPKb_J]^MSKbI ]^ioAFEYKY{ @pO;K CPKb[-]YGUT;GJTLV0¡xµ GJQwILKEYAYMSKbI[AxQSMP_jmcMSA€MSAYBnGJ`QyKlŒH]Y[-GUTLKbI9irmq&]Y[-]YTeatsP]YT-GJTMPOLKAYCDInGJT;]^CPm TLAYMSKioAeAYzeQ{›LAYCKlŒL]Y[Bn_jKYf4MPOLKMP]…W™a;T;`lMPGjAxT7GJILKbTrMPGjMPGjKbQf [AHI;a;_U]^C Kbdra;]^MPGJAxT;Qf>²·GJQSKbT;QSMSKbGUT QSKCDGJKbQf~GJTrMSKVYCD]Y_JQNAYW2MPO;KMP]€W™a;T;`lMPGjAxT;Qbf~GJT;`lAx[B_jKMSKKb_J_JGjBnMPGJ`\GJT~MSKVYCœ]Y_JQwAYWMPOLK CDQSMwzHGJT;IfYMPOLK qpAYVYKCœQ rq&]Y[-]YTeatsP]YT7`lAxTrMPGJTeaLKbI(W#CD]Y`lMPGjAxTf>]YTnI’AYMPOLKC`lAxTrMPGJTra;KbI(WŽCœ]Y`lMPGjAxT;Q€]^CPK-QPAx[KAYW MPOLK·MSAYBnGJ`Q4WŽAxa;TnI€GJT€MPO;K·_jAxQSM4TLAYMSKioArAYz2{:@&O;GJQ¡xµ ™]YQ4h·Kb_J_r]YQ>MPO;KNAYMPOLKCw„^µ >GJQAYWLVYCPKb]^M GJTrMSKCPKbQSM0MSAMPO;KcB;CDKbQSKbT~M+]YaLMPOLAYCF{X|šTMPO;KcCPKb[)]YGJT;ILKCXAYWyMPO;GJQXBn]^BoKCbfnhRKi;CDGjKlknm…ILKbQD`lCDGjioK QSAx[KAYW2MPOLKbQSKCDKbQPa;_jMPQ{:­an`DOAYWMPOLKCPKbQSKb]^CD`œOAxTMPOLKbQPKKbT~MSCDGJKbQwGJQ:i2KbGUTLV0`lAxTnI;a;`lMSKbIh&GJMPO MPOLK ]YaLMPOLAYCFuvQ·CDKb`lKbT~M]YT;I`aLCPCDKbT~MRVYCD]YI;a;]^MSK QSMPanILKbT~MPQbfHGUT)Bn]^CDMPGJ`a;_J]^CbfH¦XKbTLV¦Xa;]^Mp‹\O;]YT f «eKbT H«LO;]YTc¦0a;]YTLVLf~«eAeAxT  G €]YTLVLf^‘(KbT H‹\O;GUTc½4GJ]bh€f ¬ ]^Kina;[ЫeAxO;Tf~«eKbanTLVX¦XhR]YT-«eAxT f ]YT;IŠ½4GJ]YTL!V H‹\O;KbTL# V "oO;]YTLVL{ ‰XQ&`a;QSMSAx[-]^CPmYf2QSKM

$&%')( *,+!*.-/( 0

5 9 21 3465 Ï87 š>?1 : A@ B CBDºFE :<;= q&]Y[)]YTratsP]YTuvQ+VYKbTLKCœ]Y_wMPOLKMP]…W™a;T;`lMPGjAxTHG)21 @JIKA@h&O;GJ`œO(O;]YQ+MPOLK-QP]Y[KVYKbT;KCD]Y_JGjM}m³]YQ+MPOLK VYKbTLKCD]Y_4`_J]YQPQPGU`]Y_ MPOLKMP])W#a;Tn`lMPGjAxTf;]YQXWŽAxa;TnIŠGJT7Ÿ¶´Yžef ‹\O;]^B {n´HÕ¢£f2W#AYC&KlŒL]Y[Bn_jKYf2GJQpILKL T;KbI

iem

5 N G)21M@JIK·Ï87 1 :QPR:<S TUWV4X I :QPR:QO TUWV4X @ 5 :<;O

š

B 1 IYB
|šTŠq&]Y[-]YTeatsP]YTuvQpTLAYMP]^MPGJAxTf;MPOLK MPOLCDKK[AxQSM&GU[BoAYCPMP]YT~MQSBoKb`GJ]Y_`]YQPKbQpAYWZš\]^CPK 5 N  :] @ 5 :<; 5O G)2@b_7 N  Q: PR:<S TUWV4X @ :<;=

[ 2RÏ87\G)2@4)7 ^ 2RÏ87

´



Ö á

 á
         
      FÖ  ZÖ

á


   

]YT;I

5 N g´ G)> ·Ï87\G)> <@K>  X )7 > :  :QP6:QO TUWV4X 7 234Y657Ï O T V4X "!MA@ 5 :<; O h&OLKCDK# 7 KlŒeB g´$#&%'!MA@Z|†[(! © ) µ Z @ ]YT;I ILKbTLAYMSKbQMPOLK ¾0KbILKzeGUT;I7KMP]~W™a;T;`lMPGJAxT{@pO;K BoKbTran_jMPGJ[-]^MSK+Kbdea;]Y_JGjM}m GJT?g ´p GJQ²Nan_jKCbuvQ\BoKbT~MP]^VYAxTn]Y_>Tea;[ioKCMPOLKAYCDKb[…{ |}W 7“KlŒHB >*#+ , Ax@ W#AYC·QPAx[KpBoAxQPGjMPGjEYKCœ]^MPGjAxT;]Y_;Tea;[ci2KC,)~@ @pOLKpqX]Y[-]YTra^sS]YT~‘(KioKC `_J]YQPQ&GJT~E^]^CDGJ]YTrM.- : GJQI;KL TLKbI…iem g” - : Ï87 ´ O T V  O T V4X > 34 X  5 E

@pOLK€q&AYVYKCDQrq&]Y[)]YTratsP]YT`lAxTrMPGJTeaLKbI…W#CD]Y`lMPGjAxT0/2\GUQILKLTLKbI…iem

#¡<

/2RÏ87

21   X    3 4 (  3 53 537666 @

B CBDºFE

98 %+;:   < (>=Y+*W-/( ? % (/+*.+*W%<0 |†TO;GJQp_JAxQSMXTLAYMSKioAeAYzf2q&]Y[-]YTeatsP]YTCDKL TLKbI…AYC0W#]Y`lMSAYCDKbIQSAx[-KcAYWZMPOLKcMPOLKMP])W™a;T;`lMPGJAxT

GJILKbTrMPGjMPGjKbQ0CPKb`lAYCœILKbI’irm³O;GJ[ GJT’O;GJQ+TLAYMSKioAeAYzeQb{c›LAYC€KlŒL]Y[Bn_JKYf>GJT’O;GJQ+TLAYMSKioAeAYzeQ-Ÿ¶´ef B>{ ´Y„Y´ef²·T~MSCDm³µt¢£f2q&]Y[-]YTeatsP]YT…CPKb`lAYCDILKbIŠMPOLKGJILKbTrMPGjM}m >  @ 34 T = 65 [ X 2Y>‡ž [ X 2A@)7 >p¡G X >  X   > 43  X  5 E B T Bn]^VYKžY„9GJT O;GJQ\_jAxQPM\T;AYMSKi2AeAYz2fHO;K0W™]Y`lMSAYCPKbI…MPOnGJQ\GJILKbTrMPGjM¹m)GUT~MSA9MPOLK+W#Ax_J_jAFhXGJTLV9GJILKbTrMPG ± MPGjKbQÏN|}WCH7 T4OEX D @ ]YT;IGFH7 TS>X D @ f;MPOLKbT š 3 + ž  G)> FX  @ [ 2 3 + ž [ 2 @  7 9 L  3 C  : 3  X :NM 9 L  >SF  : 3  X :TM

[ 2> +

ž

:IO'PQO'R š> + ž G)>  X  E [ 2  @  7 9 L Z>WC  : 3  X : M 9 L  3 F  : 3  X : M :IOUPVO'R :IHVJJ :IHKJJ

|†TO;GJQTLAYMSKioAeAYzeQŸ¶”efnB;B { b´ef>b”ef2²NTrMSCPm³Õ¢£fq&]Y[-]YTeatsP]YTŠGJTrMSCPAeIna;`lKbIMPOLK€Bn]^Cœ]Y[KMSKC X 8Ï 7Y/2Z/ X 2 X A@ ]YT;IŠQPMP]^MSKbIŠM¹hRA)Kb_JKVx]YT~M&[-AeI;an_J]^CKbdran]^MPGjAxT;Qf  > X X   X E / @ 2_7 XG[ ]YT;I / @ 2 X )7 X X [ 3  3 X\  > X\  |šT(O;GJQ+_jAxQSM€TLAYMSKioAeAYzf4q&]Y[-]YTeatsP]YT’VxGjEYKbQ€QSKEYKCD]Y_yAYMPOLKC€ioKb]YaLMPGjW™a;_:GJILKbTrMPGjMPGjKbQ+GJTrEYAx_jEeGUTLV MPOLK€B]^CD]Y[KMSKC X @;W#AYCpKlŒL]Y[Bn_jKYf X  X > X X @ 7 Q> 34 X5  E [ 3  > X X  >¡ X > X X \ 


 

á

 
á   ZÖ

@pOea;QfYq&]Y[)]YTratsP]YT9O;]YQZVxGjEYKbT9]0ioKb]YaLMPGjW™a;_xBn]^Cœ]Y[MSCDGJ¿b]^MPGjAxT9WŽAYCZMPOLKI;GUQP`lCDGJ[-GU]YT~M W™a;T;`lMPGJAxTf "!MR8Ï 7  2Ï  X5  @;h&OLKCP\ K  7ÒKlŒHB g$´ #&%'!MAE »yCPAeAYW™QAYW4MPO;K€CPKbQPa;_JMPQ`GjMSKbIŠ]^ioAFEYKO;]bEYKci2KKbTVxGJEYKbTŠiem €]YT;V³Ÿ YÕ¢£{ B T’Bn]^VYK)´^µx„…GUT³OnGJQ _jAxQSM TLAYMSKioAeAYzf>qX]Y[-]YTeatsS]YT’Vx]FEYK]EYKCPm’QSMSCD]YT;VYK-QSKbdra;KbT;`lKAYW QSKB;MPGU` GJILKbTrMPGjMPGjKbQfHh&O;GU`DOhRKTLAFh dra;AYMSKY{N½ KM [ 2  TV
 7 33 3 E [ 2


@pOLKbT gž

7 

]YT;I

[  2  > g´ 3 [  2


›;aLCDMPOLKCD[AYCPKYf

C @F_@2]YT;I

C X  TV
@ F \ [

7 

h&OLKCDK

  

X >  34 X 65 > 
34 T' 
5

ž 

7

[

[  2 3 š>  7—µ E [  2
 F X 



TV
\

@ 

7

[



C

X 

T V
\

@

]^CPK€CPAeAYMPQAYWZMPOLK Kbdea;]^MPGjAxT 

´ 

X [

[  O
 D
 7

ƒ





•F 7

 3

 3

”  >

[  2 3 [  2
 \

 

X   3 <¡  >  7—µ E

›LAYCXKlŒH]Y[B_jKYf g„

JV [  O  D
  Z 3 >  XAV
3 >  XJV
3 >  XJV
 E

X‰ _JMPOLAxaLVxO  @  @x]YT;I  ]^CPKTLAYMZVxGjEYKbTirmq&]Y[-]YTeatsP]YTfYMPOLKm]^CPK\VxGjEYKbTGJT²NTrMSCPm)Fƒ ™ GJGJGW GJT‹\On]^B;MSKCb‚9AYWwq&]Y[)]YTratsP]YTuvQpQPKb`lAxT;IŠTLAYMSKioAeAYz(Ÿ¶´efnB {n”^µx”¨¢£{·²yŒeBn_UGJ`GjMP_jmYf 

7 F´  TV


G)2 @ @4 @ [ 2
 

7 F´  AV


G)2A!@4T4T  @ [ 2


]YT;I 

7 F´  J V


G)2@4T  E [ 2


²Ndea;]Y_JGJM¹m gž€GUQ€Kb]YQSm(MSAB;CPAFEYKYfwiaLM€MPOLKB;CPAeAYW#QAYWMPOLK)CPKb[)]YGJT;GJTLVŠGUILKbT~MPGJMPGjKbQ€]^CPKEYKCPm I;G ¼ `a;_jM{²yŒH`lKBnMW#AYC g„œfN«eAxTҟ¶´Y´¨¢\O;]YQcWŽAxa;TnI(B;CPAeAYW#Q€AYWMPOLK-CPKb[-]YGUT;GJTLVŠ`_J]YGU[-Q{¾0GUI q&]Y[)]YTratsP]YT…O;]FEYK KlŒeBn_UGJ`GjM\GJILKbTrMPG `]^MPGjAxT;Q·W#AYCMPOLK MPOLCPKK [-GJQDQPGJTLVcKlŒeB;CDKbQPQPGjAxT;Q\GJTHg„œf;AYC I;GJIOLK[KCPKb_jm‡`lAxTtsšKb`lMPa;CPK…MPO;]^M9MPOLKCPKKlŒLGJQSMPQ9]³CPKB;CPKbQSKbTrMP]^MPGjAxTW#AYC [  O
 D
GUT7MPOLK W#AYCD[ g„ SªÑ|†M€QSKKb[-Q€MSAa;Q MPO;]^MGJW·q&]Y[)]YTratsP]YT(hRKCPK)]^in_JKMSA`lAx[Bn_jKMSK)MPO;GJQ+KbTrMSCPmYf:O;K hRAxa;_JI(O;]FEYK)TLKKbILKbI(MSAzeTLA¨h MPOLKE^]Y_JaLKAYWRMPOLK-`_J]YQPQGJT~E^]^CDGJ]YTr M ™QSKK g” 6 - Q @h&O;GJ`œO ]^B;Bn]^CDKbT~MP_jmOLK€I;GUI…TLAYMzeT;AFh€fn]YTnI…h&O;GJ`œOh·Kc]Y_JQSA-ILA-TLAYM&zeTLA¨h€{ @pOLKXBn]^BoKCDQyiem €]YTLV…Ÿ µt¢£f>Ÿ YÕ¢ ]YT;I…«eAxT³Ÿ¶´^µt¢ 2Ÿ¶´Y”¨¢>`lAxTrMP]YGJT B;CPAeAYW™QNAYW QSKEYKCœ]Y_W™aLCPMPO;KC MPOLKMP]W™a;T;`lMPGJAxT…GJILKbTrMPGjMPGjKbQ\W#CPAx[ MPOLK_JAxQSMpTLAYMSKioArAYz2{

Ö á

 á
         
      FÖ  ZÖ

á


  

$ :
_%+ " %F*W%<0 »Z]^VYKbQ0”YžY”e”Yžxƒ)GJTMPOLK Bna;in_JGJ`]^MPGjAxT AYW:MPOLK_jAxQPMpTLAYMSKioArAYz(Ÿ b„¨¢:`lAx[BnCDGJQSK ]-QPan[-[-]^CPm AYW+QSAx[K…AYWXqX]Y[-]YTeatsS]YT uvQ T;I;GUTLVxQc]^ioAxaLM½4]Y[ioKCPMQSKCDGJKbQ{@&OLKBn]^BoKCMPOn]^Mh·K…h&GU_J_ hpCDGJMSKW#AYC9MPOLKBnaLin_JGUQPOLKbI(B;CDAe`lKKbI;GUTLVxQAYWXMPOL K  Sij͖ÍnÎ^ É LÁ œÊ HÉ'Á^  H É DÈ >ÇHÈDÁ œÎ h&GJ_U_2`lAxTn`lKbT~MSCD]^MSKcAxTŠMPO;GUQ\WŽCD]^Vx[-KbT~M{N¦XKCPK€hRK`GjMSKAxT;_jm)M}h·AKlŒH]Y[-Bn_jKbQ{ RKVxGJT;T;GJT;V hXGjMPO’MPOLKhRAYCPzAYW&ˆ+]YanQPQf>½>KVYKbT;ILCPKYf:]YT;I ¬ ]Y`lAYiGgf>½>]Y[cioKCPM€QSKCDGJKbQ O;]bEYK ioKKbT°a;QSKW™a;_GJT®I;KCDGjEHGJTLV’WŽAYCœ[ca;_U]YQWŽAYCMPOLKŠTea;[ioKC-AYW+CPKBnCPKbQSKbTrMP]^MPGjAxT;Q-AYW ](BoAxQPGJMPGjEYK GJTrMSKVYK*C ,(iem…`lKCPMP]YGJTdea;]YILCœ]^MPGJ`+WŽAYCœ[-Q{N›LAYC0KlŒL]Y[Bn_jKYf;GjW Q , \I;KbTLAYMSKbQpMPOLKcTra;[cioKCAYW h\]bmHQNAYWCPKBnCPKbQSKbTrMPGJTLV€MPOLK&B2AxQDGjMPGjEYK&GJTrMSKVYKC ,]YQN]cQPa;[ AYW X QPdran]^CPKbQf~MPO;KbT-MPOLK0½>]Y[ci2KCDM QSKCDGJKbQpGJILKbTrMPGjM¹m 5 , L!: N [  2_7Ё 3 b„ > >  : @ I;aLK MSA ¬ ]Y`lAYinGgfLmHGjKb_JInQ\MPOLK WŽAYCœ[ca;_U]

:<; T

  , )7b„Q>c : N 

! :

> "  E

«HGJ[)GJ_J]^CD_jmYfo_jK$M #%  , 0ILKbTLAYMSK-MPOLK-Tea;[cioKC0AYWRh\]bmHQ€MPO;]^M€MPO;KB2AxQDGjMPGjEYKGJTrMSKVYKC ,®`]YT(ioK CPKB;CDKbQSKbT~MSKbI]YQ&]-QPan[ AYW X MSCœGJ]YTLVxa;_J]^CpTea;[cioKCDQ{w@pOLKbT…MPO;K€½>]Y[ci2KCDMpQSKCDGjKbQpGUILKbT~MPGJM¹m 5 5  g´ , 3  X  P X :<STU.VJX  > : g´ , 3  X  P X :<S T U.VJX N N  JVJX ^'& 2 X _7 > b„  3  X6:<S T b„  >  X :<S T  :<;= :<;= VxGjEYKbQ&MPOLK€`lAYCPAx_J_J]^CDm  N N " X >  " X E # &  , _7 • ! • ! P6:<SJU (  *P )HVJ AU

P6:<SAU ( T +P ) HKJ  U

‘(KO;]FEYK(i2KKbT anT;]^in_jKMSA T;IÒMPO;GJQ WŽAYCœ[ca;_U]‡GJT“MPOLK(`_J]YQDQPGJ`]Y_+_JGjMSKCD]^MPa;CPKY{%@pOLK nCDQPM AH``aLCPCPKbT;`lKbQ9zHTLA¨h&T¯MSAa;Q9]^CPKŠGJTCPKb`lKbTrMBn]^BoKCDQirm €]Y`…]YT;I‘]^zHGJ[AYMSAҟ¶‚¨¢&]YT;I¯iem B TLALfrqpAYinGJTnQf~]YT;I‘]YOn_>Ÿ b´¨¢£{y‘(K&O;]FEYK&W#Axa;T;I] BnCPArAYWo]Y_jAxTLVMPOLKp_JGJTLKbQZAYWqX]Y[-]YTra^sS]YTuvQ MPO;GJT;zeGJT;VL{ ( =-,
.-/W%<+%  /0/2*1- +* = (/+%2 :/W0-,3Z+ 8 %  *1!0K+ , *W( ? «eAx[K’AYW€MPOLK([AxQPM]Y[)]^¿bGJTLVWŽAYCD[a;_J]YQGJTÒMPOLK(_jAxQSMTLAYMSKioAeAYzÒGJTrEYAx_jEYK’GJT;`lAx[Bn_JKMSK Kb_J_JGJB;MPGJ`\GJTrMSKVYCD]Y_JQ{Z‘(KX`GJMSKwsPa;QSMyAxTLKXAYWQSKEYKCD]Y_KlŒH]Y[B_jKbQ{wqpKb`]Y_J_nMPO;]^M G)> YwGJQyILLK T;KbI iem g´ œ{ |}W G  >  G  >  T @  @  8Ï 7  G  >    G  >  @  MPOLKbT " #  4 X98%:1;=<08 RPWTV D @ U £ƒY5476 G)> #6 G)>#   G)>#@ G)># T @  " # 7 E ž X  ]   > D Q J G T # C 1 B U 1  1  D E B D = X98%:1;=<08 R?> @ 1 2A X@ 1FDBD ]HG A

@pO;GJQ]YTnIŠQSKEYKCD]Y_>AYMPOLKC&W#AYCD[a;_J]YQpGJTMPO;K_jAxQSM&T;AYMSKi2AeAYz AYW:MPO;KQP]Y[KQPAYCPMphRKCPK\nCDQPM B;CPA¨EYKbI³irmqX]^VxO;]bE^]YT]YT;I³q&]YT;Vx]Y`DO;]^CDGpŸ b”¨¢£{€¦XAFhRKEYKCbf MPO;KbGjCXBnCPArAYW™QXBn]^CPMPGJ]Y_J_JmI;KB2KbTnI

á




 
á   ZÖ

aLBoAxT…GJILKb]YQph&GjMPOh&O;GU`DO…q&]Y[)]YTratsP]YT…hRAxa;_JI…TLAYMXO;]bEYK€ioKKbT…W™]Y[-GJ_UGJ]^Cb{:|†T…B]^CPMPGJ`a;_J]^CFfeMSA B;CPA¨EYK#£ƒYœfnMPO;Km a;QPKbI…MPOLK€CPKb[)]^CPzt]^i_jK I;G oKCPKbT~MPGU]Y_oKbdra;]^MPGJAxT 


"

g•

  >–µ "  7 G)> Y G)>    G)>  @  G)>  T @   



>–b”  X 3

µ 

 3 

 @

h&O;GU`DOMPOLKmdeaLAYMSKcW#CPAx[˜MPOLKMSCPKb]^MPGJQSK9AYWN›LCœGJ`PzYKŠŸ¶•efoB {2¡~”Y‚¨¢£{+@&OLK]Ya;MPOLAYCbfo¦{o¦{ ‹\O;]YT f ]YT;IŠ«2{ H«2{H¦0a;]YTLVGJT ]YT…a;TLBnaLi_JGJQPOLKbI9[-]YTea;QP`lCœGjB;M·On]bEYK VxGjEYKbT…[AYCDKXKb_jKb[-KbT~MP]^CPm B;CPAeAYW™Q AYZW £Yƒ \]YT;I g• œ{ - (/+*2( < % ?“  :T=Y+!*.-/( 98 %  -,2M%0  :
W: ( < :M( qpKb`]Y_J_pMPO;]^M-MPOLKŠq&AYVYKCDQ rq&]Y[)]YTratsP]YT–`lAxTrMPGJTeaLKbI®W#CD]Y`lMPGjAxT /2GJQI;LK TLKbI¯iem #<¡ œ{ ¸0QPGJTLVMPOLK€q&AYVYKCDQ rqX]Y[-]YTra^sS]YTGJILKbTrMPGjMPGjKbQfLhRK AYi;MP]YGJT…MPO;K€ioKb]YaLMPGjW™a;_2CPKB;CPKbQSKbTrMP]^MPGjAxT 

g‚





2 34 @ 65 2 $Y34 @ 65 E 2 X 34 @ 65 2   34 @ 65

 O TV @ /2_7

\aLMB2KCœO;]^BnQ€MPO;K [AxQPMGJ[-B2AYCDMP]YT~M]YTnI‡a;QPKW#a;_NMPOLKAYCPKb[ ]^ioAxaLM/2YGJQVxGjEYKbTirm(MPOLK W#AYCD[can_J]  >–> /2Y)7 G)>  TV @  @ šµ h&OLKCDK

/2

G)> RGJQILKLTLKbIiem?g´œ{N@pOLK€`lAYCDAx_J_J]^CPmYf



šY

>–Y>W/ @ 2Y 7

/ @ 2

 TV @ G)>  @ 

G & > Y  @ YG &  >  @ 

JG Q ]Y_JQPA EYKCDm³a;QPKW#a;_£{c@pOLKbQPKCDKbQPa;_jMPQ ]^CPKW#Axa;T;I’GJT’qX]Y[-]YTra^sS]YTuvQQSKb`lAxT;ITLAYMSKioAeAYzŸ l¡Lf B;B {´Y„Yže´Y„xƒF¢·]YT;I³hRKCPK nCDQSM0B;CPA¨EYKbI³irm‘]^MPQSAxT°Ÿ¶´t¡^¢yWŽAYC+MPOLK9Bna;CPBoAxQSKAYWyKbQPMP]^in_JGJQPOnGJTLV QSAx[K+AYWZq&]Y[-]YTeatsP]YTuvQ\`_J]YGJ[-Q\]^ioAxaLM /2·[-]YILK GJTO;GJQ nCDQPM·M}h·A-_jKMSMSKCœQMSA¦X]^CDI;m’Ÿ bžef B;B {ŒeŒeEHGJGgf2ŒeŒeEHGJGJG ¢£{c@pOLKmŠhRKCPK-]Y_JQSA…`lCDan`GJ]Y_J_jmanQSKbI³irmMPOLK-]YaLMPOLAYCbf4‹O;]YTf ]YT;? I "oO;]YT;V Ÿ¶ž¨¢:GUTŠILKCDGjEHGJTLV9VYKbTLKCœ]Y_ W#AYCD[can_J]YQpW#AYC&MPOLKKlŒeBn_UGJ`GjMKE^]Y_Ja;]^MPGjAxTAYW /2AE2‰XQ&h·KQPO;]Y_J_QSKK GJT’MPOLK-T;KlŒeM€B]^CD]^VYCD]^BnO;Qbf q&]Y[-]YTeatsP]YT(CPKb`lAYCDILKbIM¹hR!A ~Et]^CDGU]^in_jK-VYKbTLKCœ]Y_JGj¿b]^MPGjAxT;Q€AYW šµ  ]YT;I šY pGJT…O;GJQ_JAxQSMpTLAYMSKioArAYz2{ B T…Bn]^VYK´^µ~ƒ9GJT…O;GJQ_JAxQSM&TLAYMSKioAeAYzf;qX]Y[-]YTra^sS]YTŠ_UGJQSMSKbIMPOLCPKKcGJILKbTrMPGjMPGjKbQf šb´ 

šb” šl¡<

G)>  T V @ K@ >M XJV @  > 7 3 @  TV @ ) G > T =  @ @K> T @  T = 



@ > @ 7 3

G)>@K>T A   ) G > XK@K> KYX  @ G X > T =  @ @K> T @  T = 

7>



ž



3

ž



X

G)> @K> @  X  G @  > X <@K>   X  @ )G & > T =  @ K@ > T @  T = 

X 3

h&GjMPO;AxaLM€QSBoKb`GjW#meGJT;VMPOLK)W#a;Tn`lMPGjAxT;Q ]YTnI 9{ «HAxT–Ÿ b‚¨¢RO;]YQioKKbT]^in_jKMSAInGJQP`lKCDT’MPOLK GJILKbTrMPGjMPGjKbQ\AYW @ @;]YT;0 I / @;]YT;IQSA-B;CPA¨EYK€MPOLK€W#Ax_J_jA¨h&GJTLVMPOLKAYCPKb[Š{N|†W 



šbž šb„





G)> T = 
K@ > T @     TV @ G)>  G) >  @ $F@K >  X4=KT4T 7  O TV @ G) >  7





3 MFG)> @ T =  @ @K> T @    > NKYG)> >  T@ T =  @ @K

 X @K> 4X =  T   @ T=  @K> X @  T' @ T=

Ö á  á
         
      FÖ  ZÖ á
   MPOLKbT šb´ /šl¡<XOLAx_UI{ RmQPKMSMPGJTLV 7 F @GJT?šbž]YT;I šb„œfanQPGJTLV9MPOLKdea;GJTrMPaLBn_JKXB;CDAeI;an`lM\GUILKbT~MPGJM¹m 

G)> X   @K>  &  3 

G)>@K> X

 

G)>

_7



!X @K>   G)>    @ G)>  @K>  X 

h&GjMPO   @  7 2@4 X X]YT;I 2 X @4 O T œfCPKbQPB2Kb`lMPGJEYKb_jmYfKb[Bn_jA¨meGUTLV ¬ ]Y`lAYinGguvQ+MSCDGJBn_jKBnCPAeIna;`lM GJILKbTrMPGjM}mYfn]YT;I…aLMPGJ_UGj¿bGJTLV&g‚œfnhRK€QSKK€MPO;]^M G)> 
@K>    3 YG)>  X @K>  T   G)>  X @K>     @ šFƒY 7 7 7 



šb•

/2  T V @ G)>  @   TV @ G)>  @K>    G)>   K@ >  T4T  > FG)> < @K>  T    TV @ G)> K@ >    7 7 7 /2AE Y G >  X @K>    )  O T V @ G)>  @ 

«HGJTn`lK 7 ^f:WŽCDAx[ šFƒYœf šb•œfw]YT;I g´œfZh·KQSKK)MPO;]^M šb´ ]YT;I šl¡< CPKbIna;`lK-MSAŠMPOLK M¹hRA[)]YGJT…GJILKbTrMPGjMPGjKbQf šµp]YT;I šYœfnCDKbQSBoKb`lMPGjEYKb_jmY{ ‘(K(`_jAxQSKhXGjMPO–]‡ioKb]YaLMPGjW™a;_MSCD]YT;QPWŽAYCD[)]^MPGjAxT–W#AYC]VYKbTLKCD]Y_UGj¿b]^MPGjAxT“AYW MPOLK’qpAYVYKCDQ q&]Y[)]YTratsP]YTŠ`lAxTrMPGJTeaLKbI…W#CD]Y`lMPGjAxT…W#Axa;T;IAxTBn]^VYK€¡~„9AYWZMPOLK€_jAxQPMpTLAYMSKioArAYz2{ ½ KM X
µ @ C 7 š 3 +  3 ¡ X ^´ @ ]YT;I F 7 >c 3 +  3 ¡ X ^´ E @&OLKbTf2WŽAY# C B CB/D% ]YT;IŠq&K 9)–µ @ šFYƒ   X 3  X 3 X X 3     X   7  3  3  3  37666 C 3 C 3 F  3 C 3 F  X 3 C 3 F   37666 E |šT-Bn]^CPMPGU`a;_J]^Cbf~GJW X 7 ´ @rh·KXAYi;MP]YGJT)MPOLK&W#Ax_J_jA¨h&GJTLV Kb_jKVx]YTrM\`lAYCPAx_J_J]^CPmYfe]Y_JQSA€W#Axa;T;I)AxT-Bn]^VYK ¡~„ef;ina;Mh&GjMPO…]-QP_UGjVxO~M[-GUQSB;CDGJTrM{w›LAYC B CB
 Ù >Ú !#"%$#&')(+*#,-*#"/.*#10 24356#2//789#':;/!=<> ? Ù  
A@ CÛ B
EDF CÛ B%G I × HKJ L ã MF#MFN/ OPM! %Qx ã PO 
Y F
2Ù Û R(S*#,T*#".*#U0 2VW#':;C==<>2CX Y+*#Z[Z[ZCAbØ \6

] Ù  Q_^Ù  G @>] F>Ù a` DPb ~ã MPM¨ã  
Y F
2Ù  % Û R(S*#,T*#".*#U0 2VW#':;C==<>2CX Y+*#dce$FØ \6 f] Ù  Q_^nÙ  G @#] !4Ù a` DPb rã MPMF !
  
2Ù 

Û   SB @P   Q  g @P f]   QF`   @P f]    D B  @P %   DF hUi:j(SCk_:/2l (S*#,-*#"/.*#I$C#":CmC*F$# L Û DT@ بØYÙ @# N  
 
2Ù 

Û   SB @P  @P % C Q9n1B @P

] Ropq95 $:r>*P5 "*##2smWi:t(SCk_:/2lP(+*#,-*#"/.*# $/#%"K:m*F$uv#A! Ù \6 Ù  f] Ù _
A@ CÛ B w1Hx L ã MPM PN/rZã ^/ã Qxã >M 
  K
2Ù  % Û  Q Y g @P

]   D B  @P %   DF  y9#,z:{i:#C:,j2{#zvi:|(SCk_:/2lP(+*#,-*#"/.*# $/#%"K:m

 *F$@#uv %# I}(S*#,T*#@# %"b_.\6 *#U0 2~56#2C+9#':;/!=< L Û D-@ ØtØYÙ @# N  
<
2Ù Û _  (S*#,-*#%".*#9t€U:':28*#9 #,j,z:‚*#ƒ> ? Ù  
„@ CÛ B  D_… 6 † [D=‡ \6\6 …/Ùb

… >Ù Hã MPMfˆ  DF

DF
A@ CÛ B  D_… 6A DF % fDF rã MPM O_  #Ù@#9…‰~@P

:~ oŠ
55  qK@P2b_$/i\6?j:D ‹K" D  <>#1:E"f9tŒifC:{%S:9#"ffk_:XŽ{_KZ[ZCFÖHÙ g Ü Ù   rÙ \ Ø  \‘] rã MKL M+^ ;   #’ Û  ZC%“:uk#*F;5Œ:|ifŒk=i:2/+:6k>ife,T=#" 5Œ:2~#r#:*”41:2/"=q%:*P5 k_:!;*#2*#9 " ,T;@#:… ji :#ƒ# \‘\ b Ùp|Ö@ B¨Ù DP  × @PD % DF ZÙ DF? Ù†Û  × L  Q;M
 × G \6 Ú b_\ C_
 × G \6 Ú b_\ e^   g \ G6G¶Ù ?T\6  @# % ^   ^Ù Ú  N/
BR• g ÚgÙ 
Ú™Û rã MPMK 



O




á

 
á   ZÖ

ã E QF`  @P

] WyK#,z:}i:C#:,82A# i:}(+Ckf:/2lP(+*#,-*#"/.*# $/#%"K:)m*F$uv#*#9 *#2/2!$*#':C vi:‚*~m" 9$#A_:u:2~}(S*#,T*#".*#U0 2W56#2/ 9#':;/!=< L Û DT@ ØtØYÙ @# N  ãlã E QF`  @P

] %(S*#,-*#"/.*#10 2Um#/,j" 56*#2m/#i:W:pq95 v$  :r>*P5 "%*##„m{i:(+/k_:2/lP(S*#,T*#".*#E$C# u "K:~m*F$uv#&*#Kzi:'*PlCm" 9$#2 L Û D-@ بØYÙ @# N  ã4 

D A D Ü \Œ Ú  @P

† ^Ö %’ @ B%G
S&i:tC:'qKC:2:‚*#uv#mW':‚k_:2s*#2d2C" ,828mW*#fk#" 56*# " ,T;:2C  Ù  g @ 
„@ CÛ Bx L ã MPM PN/%K=Q_MK! ãE @>] B @!‡#@# j@P % Y  @#

]F@#… B @>\ 
S„(S*#,-*#"/.*#10 2~:55  qK$W':‚k#*P5 2*#9j,-!#" 56*#_:u:2C  g ? ÜYÙ  | Ö B¨Ù DP × @P

 Ù G @ Û£Ù Ö D Ø \‘… Ú A  D# 

\‘‡ Ù  Ú \ Û#× †  ٚÚgÚ Y
DF? Ü @ 9× xã MPO#M FØt<Ø rãlã M!Qxã FM ã !E/ @P?T@# g @P V~#“:;C!=<#2 r>P5 "f,z:2! Ö @ Û @ ' Ú™Û \ Û g Û£Ù D  g % %@#? Ù Û @ G>نÚgÙ @#[… B1
DF? Ü @ 1×  ã M P ã EY @P?T@P g @P RŠP5 5Œ:C$':CTYS*q%:2CF|BFÙ G¶ÚgÙ @ F4Ù a` D#b ~ã M K ã EY @P?T@P g @P ehRi:d€1#2/ VW#':;/!=< *#9
Si:UPqK"%;!5  2i:-Y+*q%:/2/ @#[D Ú @ !4Ù  :Ù G6B \ eã MPOPO ã!_  F @P

b_\Œ :C#uk_:sVW:r=55Œ:}*#2# $ DF % fDF
„@ CÛ BA D_… %w L ã M FN/¨ãCQ  ãO_    @P %b_\6 d(S*#,T*#".*#U0 2E,-*#"f2$/ qK2}*#949#':;C==<>2CXtZ[ZC
g G6G E DF

DF 0
„@ CÛ BE Df…  L ã MPOPMFN/  Fã/Q;  ãME V DF _y9#,z:+i:'* mC"f9$#T_:u:2Š:56*#':~'~i:+(SCk_:/2lP(+*#,-*#"/.*#-$C#":C mC[*F$#% † [D_…  ? Ù  
„@ CÛ B$ D_…  L Û D-@ ØtØYÙ @# N  K E A DF "%;v$t_:u:2dm~vi:‚*mC" K$#%2/t| Ö B¨)Ù  @P?T@P g @P  L Û DT@ بØYÙ @# N  ¨ã E   DP y9#,-:':‚k#*P5 2mSvi:‚*|mC"f9$#2SE(+*#,-*#"/.*#10 2|56#2Ce9#':!;C!=<> † [D_… ٚ٠%\6

] Ú D ^CÛ B¨Ù  \ CÛ B @# %@P \Œ@#  g ? ÜYÙ  | Ö B¨Ù DP ×  ÚgÚ D_…\6@ Û \‘DF
ÙšÙ†Û \6

] L )T g ØFÛ @E@P %  TYU’ \ G6G \6@P? Ú nÙ Ú  N/ ? Ù \‘…@P
A@ CÛ B¨Ù ?T@ Û \‘…@ G  Df…\ Ù}Û#9×  † [D>‡f\6 Ù

… #Ù F  L Û D-@ ØtØYÙ @# N  LE A DF 9y1:'qK$ti:‚*m" 9$#A_:u:2WA(S*#,T*#".*#U0 2W56#2/Š9#':!;C!=< L Û DT@ ØtØYÙ @# N  KE A DF  hŠzi:'*mC"f9$#Iv_:%u u:2I(+*#,-*#"/.*#10 2~56#2C+9#':;C==< L Û D-@ بØYÙ @# N  V!E  U’ @ Û£Ú DF WhUi:#C:,j2T2/‚*#':I;ƒA(S*#,-*#%".*#cRZ[Z#dhUi:#C:,j2z# $/#%"K:8m*F$uv#2/T  DF

DF
A@ CÛ B$ D_…  w L ã MK#MFN/ PM=QFO  á x Ö %’ B \ ÛgÛ @Pb Ù @P %  F ’ @ Û£Ú DF 1 h%C:*#2:j#&i:EhUi:C#/ƒEmWŽ:2C2:5U‹K" 9$#2CX F9A:C_6  @#? Ü \6 f] ) Ù 

\‘‡ Ù  Ú \ Û#× †  ٚÚgÚ Y @#? Ü \6 f] #Ù rã M   





!#"$ %'&)(+*,"-+(/.'0213%4(65+"7*,%4(68:96;=@-+8BAC"&+;D8E(FG.C0IHKJ=JL8E-'.'8:;=&+[7%+-'%<H\JLJL8E-'.C8E;X]'M^Q'M<_>#Y+` o ,-*#v5U*FF#C:2C2La,b4cdLe)f=g)hiRjLgLk lnm7oDmRplc fLm