Constrained Flows of Matrix-Valued Functions: Application to

!#"%$'&()*+),-../
021,1 -34 657#89)
:;<* >=>*?:),@!A3
:
BCDB.EGFHJIK EGLNMOFQPSRUTCDV3WYX#E[ZU\^]'F`_OPFNa RcbCGTF`_OdeX#EGFfRDgfhUI,i:CGjDgNZGkfF`_lgNW
‰QŠ‹ŠŒfŽ‹‘’‹“~mSn.”‹ŠopŒ‹mr•`qt–‹—sf’u`~vNQwN˜™xz’yŽ~{Sšqp•œ|~›œ}Qx€˜~vGšœu”‹€xz‚Yž~ƒN”`„[Ÿ…†—œyQŒN|c Q‡Yš™ˆ ¡† ¢œ˜f Qš‘¡SŽ‹˜
c¼!²£‚rwf¤™ˆ#x€¯¥§€ˆ¦#}†¨#vcu½©[…ªQˆ#…¦`‚rˆ§«¬ˆY¿Q…²Nn­Ê~zx€yQu`|N…r|N¿^x€À§®x€ˆÇ|cyˆ§x€…ÁyQ¿`…'ˆ:yQv[¿`¿QyQˆ§€…ru`‚Y}»ËcxzyyÃ
~
wc¯fÉLjYx®ˆ#°U¾Äyˆ§}†…y²Nˆ§®…z|œˆ#u#}‚Y¼Åxzƒy‹‚r}†²[ˆ#uƱœ‡†wĈY²[®yx€y`Á¬}‚*x€uQxz|cu`|[yËf‚}†Ì’³µˆˆ#´·‡O|c¶¹}@u¸
‡YxǂruQºGˆ|~yQ}†…yQuQˆ»|c²c|c¯È…†‚Yu#ÂÍy¼½…rm’}¼|x®Éµxzy`}†¯f‡OwNˆY}Oxz®‚‚¾
x€ÊQ‡Y|cuQy¿%|œ€²c}†uQˆ§ˆY|įÔÎ~}#‡YÉeƒ»²Nu`¼ |[|cˆ^‡l‚’}†}…†x€vcu`y…|cx€uQ|c‚@vGˆ§u‹¯È²c‚r|[ˆ%¯N¯fyyƈ§}O…yQ¿`¿`‚ruˆ§ˆYx€uQ}O|cÁ@‚Y¿,™ˆYÓ}†u`…r…rxzˆ¬}†‡:wNÉÇu`Éeu~…†¿Q‡Yyu`²[Á@|[‚*yˆYu`3¼
²NuQy…*…|[Ï,x€¯Õ|œ}†}†‚rˆ§uvG…ˆ#ˆ#¯N‡O‚’ˆ§}}†‚’…†xzu`y¿Q|3|ЇlÑc´»u`u|[¶¹¼p‚’¸Ò}†‚…†yuQÑ[x€Ép|~u#}OÁ¼p‚Y‚Â
y}†Ã
y`…r‡lx€wcÎ~}ˆ {{
}Á‡Yx€uQu`y…|c…|Nˆ#yx®Ée‚rzu‚YvGƒfÇu`¯NyQ|c‚|c¯f¯¬³µx€Êœ|c¯Nx€¿ˆYˆY¼ vGˆ§Ê`ˆ§ˆ#|[uQ¯€¯²Ny`}uQ‚x€|u`ØD|Ö}†x€wcˆ´»ˆ!¿`¶¹|c…¸!uQy²c}†× ‚p²cvc…†‚yQy…[uQˆ…Á@ÉeuQwNˆY²c}†u`…r|cÁ@xz¯^‡§uQ‚‘¿`Ë~uˆ§¾:É'|N}†Á¬ˆ§wNu`x€ˆ²c|N‚*²cx€Á¬|c‚r¯Nvcx€À#ˆ§y`y…r‡Y}®ˆ§¾~x€‚OuQx€ºO|c|%»¿3uQsf‡YÉ»²fuQ‡Yx€|[}Ou`y‚’‚’}†ËN}.…†€yˆ@Ée²Nxz|N|~|[ˆ#²N‡l¯ {{
}†x€Á@|Öwfˆ§xÇÁ@‚…rxz‡§ˆ#}†ywc¯f'xzˆ§‡§‚uQy‡O…ÍwNˆY}ˆ§x€ÁxzÁ@‡§yyQˆ#3¿‚x€ÉÇ}†|c…†w[¿NyQyÛcÁ@} }†ˆYwcÙc¼ ˆ} u`}†……wNˆ§Ïп`ˆ.²f}†‡lzwNu`yQ…|[…ru`x€‚’À#²N}†y…†¿`}yw<x€x€uQ|~|½y,}O‚u…yÉ ˆ#…‡Y¯~ˆ¹ˆ§x®|œ°Uy}%Ç²[‚r‚’uyx€u`|[vc|%¯9…ˆ#}†‚r‡†ˆ§ˆYw[|c|~y‚r}†€u`€ˆ§ˆ§….¯'|N‹Ê`¿QÓÚuQx€|c€²cˆp¿ÈÁ@x®®vcˆ#€²[…‚3uQ‚’³µ}†ËN¶3…†€yˆ§Ã }†Á ˆ {
Ü^opm†ºOÂ
ÝNÞ­ßGàUá3â*ã*äÍßUåOápÞ
æ h,MlEGFPegfWlMIGF`XgfIUFfRÍç‹gN_Odeg~MldzLchUg~P·\:FQMlEGLGIUW¬gNhUIÄhGLchGPzdehGF`gf_è­TéK WEUg‹çfF:ê'FQFQhÄë3deIGFQPzì
ZUWOF`IÈMlLMlgfX#ícPÇF%XLN\^]UZUMOFQ_¬ç[deWOdÇLNhÔ]U_lLNêGPÇFQ\^WQRWlZUX#EÐgfWde\^g~kfF%_lFQWlMOLc_lgfMOdÇLNh<î€ïQð'RlñœòDRlñ~ó'R
ôNõ‹ö RGWOFQkN\FQhcMYg~MOdÇLNhÔî ñNñ ö RcWlMOF`_OFQL~÷êUgfWlFQI ô TÅ_OF`XLNh'WOMY_lZUXMOdÇLNhÈî€ï`ñ ö R[de\^g~kfFdÇh']Ug~dehcMOdehGkî ò'R
ó ö RGLN_¹de\gfkfF@\^g~MYX#EGdÇhUk^gNhUIÚLN]GMldÇXQg~P™ø'LœëùFQWlMOde\^g~MOdÇLNhÕî€ïfRYñURïfï ö!ú gN\:LchGk^LfMYEGFQ_¹FûGgN\:÷
]GPzF`WüYC'ýcLfPeZGMOdÇLNh'W­MlLMYEGFQWlF]'_OLcêGPzF`\^WRcëEGFMYEGFQ_.MYEGFìÖgN_OFXZU_lçfF`WRcWlZU_OHJgfXFQWQRNLc_pde\^g~kNFQWQR
gf_lF*LNêUMlg~dehGF`IÆêcìÖXLchNMldÇh[ZGLcZUWlPzìÖIGFHþLN_Y\dÇhGkgfhÆdÇhGdÇMOdeg~P‘F`WOMldÇ\^gfMOdÇLNhÖMYEU_lLNZGkcEÆgø'LœëIGF÷
ÿ hGFQI:êcì¬gèpTé*C‹V3EGF¹XLc_l_lFQWY]'LchUIGdehGk3FçNLfPeZGMOdÇLNhF [ZUg~MldzLchUW IGFQ_ldzçNFpFQdzMYEGFQ_·HJ_lLN\ WOde\^]GPÇF
PzLGXgfP!EGFQZ'_OdeWOMldÇXQWLN_HJ_OLc\ XLcWOMHJZUh'XMOdÇLNh'g~P!\dÇhUdÇ\d Qg~MldzLchUWQC æ hÈMYEGFÖXLchNMlFûGM¬L~H.dÇ\^g~kNF
gfhUII'g~Mlg_OF`WOMlLN_Yg~MldzLch‘RëEGdeX#E@deW·XLNhUWldÇIUFQ_lFQI¬deh@MlEGdeW ]Ugf]DFQ_QRQMYEGF.dÇIGF`g3deW»MlLgfX#EUdzFQçfFpgWOF÷
PzF`XMOdÇçfFWY\L[LfMlEUdÇhGk@MYEUg~M!_lFQ\LœçNFQW
hGLfdeWlF3ëEGdzPÇF]U_lFQWlFQ_lç[dÇhGk¬Pegf_lkfF¹kfPÇLNê'g~P[HþFQgfMlZU_lFQWQR~WYZUX#E
gfW!Lcê †FQXMpXLchcMOLNZ'_lW ú IGdeWlXLNhcMOdeh[ZGdzMldzF`W!LfH™MYEGFWldÇkNhUgfPJüYC~j'Lc_!MlEUdÇW.]UZU_Y]'LcWOFNRfLchGFkfF`hGFQ_Yg~PÇPÇì
ZUWOF`WgNhGdeWOLNMl_lLN]GdeXhGLchGPzdehGF`gf_*IUd ‘ZUWldzLchÄèpTé*K WQR'ëEGdeX#EÄLfHþMOFQhÈIGFQ_ldzçNFHJ_lLN\çœgf_ldÇgfMOdÇLNhUgfP
]U_OdehUXdÇ]GPÇFQW ú WYZUX#EÖgNW!MYEGF '÷’HJZUhUXMOdÇLNh^HþLc_l\:ZGPÇgfMOdÇLNhÄî [RQïQðURYñœò'RYñ õ‹ö ëEGdeX#EÖEUgfW­]U_lLœçfFQh^dÇMlW
F ÖXdÇFQhUXì%HþLN_kN_Yg‹ìN÷rçœg~PeZGFQIÖdÇ\^g~kNF@_OF`WOMlLN_Yg~MOdÇLNh‘ülC
FQhGF`_lgfPzd dehGk,MlEUFQWlF½g~PÇkfLc_OdÇMlE'\WMOLÈ\:ZGPzMld€÷rçœg~PeZGFQI<IUg~MYgfWlFMlWdÇWhGLœë g~MlMl_YgfXMldÇhUkÄg
kN_lLœë3dÇhGk<dÇhcMOF`_OF`WOMQC æ h F ™FQXMR3MlEUFÔdehUX_lFQgNWOFÈL~H:XLN\^]UZGMlFQ_Ú]'F`_†HþLc_l\^gfh'XFQWÚEUgNW½\^gfIUF
]'LcWlWldÇêUPzFMYEGF!de\]UPzF`\:F`hcMlg~MldzLch¬L~HGèpTé*K WgNXMOdehGk3LchPegf_lkfF ÿ FPeIUW‘L~HGçNFQXMlLN_YW™LN_\^gfMl_ldÇXFQWQC
bFQXFQhcM»ë.LN_Yí[W»]DLfdehNM·MOLœë¹gf_YI¬MlEGdeW
IGde_OF`XMOdÇLNhRQë3dÇMlE@MYEGF¹IGF ÿ hUdzMldzLchL~H'\FQMlEGLGIUW·HþLN_·XLNPzLc_
dÇ\^g~kNF!_OF`WOMlLN_Yg~MldzLchî ñ~ó'Rlñ 'R ô ïNR ôNõ‹ö RLc_IGde_OF`XMOdÇLNh ÿ FQPÇI@_lFkcZGPegf_ld `g~MOdÇLNh^î õ Rï [Rlñ ô RlñfðUR ôNôœö C
øDLœë LNht\ZGPÇMOdz÷rç‹gfPÇZUFQI IUg~MYgÈdeW^kfF`hGFQ_Yg~PÇPÇìÕhULfM%gÕWOMY_lgfdzkcENMOHþLN_lë.gN_lIÕkNFQhGF`_lgfPzd QgfMOdÇLNh
L~HdÇMlWÆWlXQg~Pegf_XLNZ'hNMlFQ_Y]Ugf_lMRgNhUIthUFëMlEGFQLN_lFMOdeXgfP3IGFçNFPÇLN]U\FQhcMYWgN_OFdehcçfLfPÇçfF`I‘C
j'Lc_
dÇhUWlMlgNhUXFNR!deh MlEGFÄXQgfWlF,L~H@IGdÇ_lFQXMOdÇLNh ÿ FQPÇI _lFQWlMOLN_Yg~MldzLch‘RçfF`XMlLN_YW%gf_lFXLNhUWlMl_Yg~dehGF`I<MlL
EUg‹çfFÚgÔZUhUdzMÖhGLc_l\ÚCV3EGdeWìcdÇFPeIUW^gÕWOdÇkNhUd ÿ XQgfhcM:\LGIGd ÿ XgfMOdÇLNhtL~H*MYEGF,XLc_l_lFQWY]'LchUIGdehGk
IGd ‘ZUWldzLchÚèpTé*K W3êNìÆdÇhcMl_lLGIUZUXdÇhGk%g^XLcZU]GPÇdÇhUkMlFQ_Y\ êDFMë.FF`h½çNFQXMOLN_¹XLN\^]'LchGFQhcMYWC
V3EGF@g~de\ L~H MlEGdeW3]Ugf]DFQ_¹deW¹MOL%]U_lLœç[dÇIUFWlLN\FHþLN_Y\^g~P‘gfhUIÚh[ZU\FQ_ldÇXQg~P‘MlLcLNPÇW.MlL^IUFQg~P
FÖXdÇFQhcMOPÇì ë3dÇMlEtMlEGdeW%MìG]DFÚLfH]U_lLNêGPÇFQ\^WQRë3dzMYEtgÕ]UgN_OMldÇXQZGPegf_:FQ\^]UEUgNWOdeWLNh<ø'LœëWL~H
\gfMl_ld€û[÷rçœg~PeZGFQI^HJZ'hUXMldzLchUW¹ZUhUIGF`_OkNLfdehGkLN_lMlEULfkfLchUg~PDgfhUI½Wl]DFQXMl_Yg~P™XLNh'WOMY_lgfdÇhcMlWQC[iZ'_ ÿ ÷
hUg~PLcê †FQXMOdÇçfF%XLchUXF`_lhUWMYEGFÖ_OF`WOMlLN_Yg~MldzLchÄL~H¹IGd ™ZUWldÇLNhÐMOF`hUWOLc_dÇ\^g~kNFQW¬LfH­MlEUFÖEcZ'\gNh
êU_lgfdÇh ú T¬V.÷ ,b æ üÚî ñGï ö R!\LGIGFPÇFQI gNW ÿ FPeIUW^LfH¬WlìG\\FQMl_ldÇX,]DLNWldzMldzçNF,IGF ÿ hUdzMlFÈ\^g~Ml_ldz÷
XFQW ú dSC FfC·XLNh'WOMY_lgfdÇhGF`IÄMlLE'g‹çfF^]'LcWOdÇMOdÇçfF^FdÇkfF`hcç‹gfPÇZUFQWülC ÔFÖWlMlgN_OMHJ_lLN\>MYEGFHJgfXM@MlEUgfM
\:LcWOM¬FQçfLfPeZGMldzLchÈè­TéK W@XQgfhÐê'F%ç[dÇFë.FQIÐgfWLN_YIGdehUgf_lìÄIGd ÍF`_OF`hNMldÇgfPF [ZUgfMOdÇLNhUW ú iTé*ü
LNh,gÖWYZGdÇMlgfêUPzF@HJZ'hUXMldzLchÄWl]'gfXFNC EGF`hÄhGLchGPzdehGF`gf_XLNhUWlMl_Yg~dehcMlWgN_OFdehcçfLNPzçNFQI‘RUMYEGFXLN_O÷
_OF`Wl]DLNhUIUdÇhGkÈø'LœëWêDFPÇLNhUkÈMOLÐgfh9deh ÿ hUdzMlFÚIGde\FQhUWldÇLNhUgfP.WYZUêU\^gfhUd€HþLNPÇI ÖL~HMYEGFÚdÇhGdÇMOdeg~P
WOF`gf_YX#E½WY]UgfXFfC WYZUg~PÇPzìNRUMlEUdÇWkfFQLN\FMY_OdeXçcdÇFë]DLfdehcMdeW*EGdeIUIGF`h,ê'F`EGdÇh'I,MlEGF:ZUWOFL~H ·g~÷
kN_YgfhGkNFp\ZGPÇMOde]GPÇdzF`_lW deh:XLNhUWlMl_Yg~dehGF`I@çœgf_ldÇgfMOdÇLNhUgfPc]U_ldehUXde]GPÇFQWQC æ M
g~PeWlLgf]']'F`gf_YW»de\^]GPzdeXdÇMOPÇì
dÇh½MlEGF@hGLchGPÇdÇhGF`gf_.EGFQgfM¹F [ZUg~MldzLch‘RGê'Lc_l_lLœë.FQIHJ_lLN\ EUgN_l\LNhUdÇX\^gf]ÖMYEGFLc_OìNR[ëEGdÇX#EÚEUgNW
ê'FQFQh_OF`XFQhcMlPzì]U_lLN]DLNWlFQIMOL@_OFQkNZGPegf_ld FpIGde_lFQXMldzLch ÿ FQPÇI'Wî õ Rlñ~ð ö CœV3EGF¹dehNMlFQ_lFQWlM·LfHDg*HJZGPzPÇì
kfFLc\FMl_ldeX@dÇhcMlFQ_Y]U_OFQMlgfMOdÇLNhL~HMYEGFWYZGdÇMlgNêGPzFHJZUhUXMldzLchÈWY]UgfXFdeW*Më.L~HþLNPÇI‘CDj
dÇ_YWOMQRDdÇM]'_OLf÷
çcdeIGF`W»gWldÇ\^]GPÇFpgNhUI@ZUhGd ÿ FQI@HJ_lgN\:FQë­Lc_lí*MOL*ê'ZGdzPeIXLNhUWlMl_Yg~dehGFQIø'LœëW‘HþLN_»\^gfMl_ld€û[÷rç‹gfPÇZUFQI
HJZUhUXMldzLchUWQRfëEGFQMlEGF`_!LN_phGLfM!MYEGFì^IGF`_OdÇçfF¹HJ_lLN\ çœgf_ldÇgfMOdÇLNhUgfPU]U_OdehUXdÇ]GPÇFQWQC[ý[FQXLchUI‘RNdzMph'g~M†÷
ZU_lgfPzPÇìì[dzFQPÇIUWQRÍMlEU_lLNZGkcE,MlEUF:ZUWlF:LfH!FûU]DLNhGF`hNMldÇgfP \^gN]UWR™WYZGdzMYgfêGPÇF:h[ZU\F`_OdeXgfP WYX#EGFQ\F`W
MlEUgfMgf_lF¬gfPÇWlL^XLNh'WOMY_lgfdÇhcM¹]U_OF`WOF`_Oç[dehGk'C
V3EGdÇW»gf]U]U_lLNgNX#E*deW»]'_OF`WOF`hNMlFQI¬gfW‘HþLfPÇPzLœëWQC`ýcF`XMOdÇLNh^ïdehcMl_lLGIUZUXF`Wg¹kfFQLN\FMY_OdeXWlFMOMldÇhUk
MOL:IUF ÿ hGFXLNh'WOMY_lgfdÇhGF`Iø'LœëWpgNhUI^MlEUFde_­]U_lLN]DFQ_­h[ZU\FQ_ldÇXQg~PUde\^]GPzF`\FQhcMlgfMOdÇLNhUWQCGý[FQXMldzLch
ñÖIGdeWlXQZUWYWOF`WMlEUFgN]U]GPÇdÇXQg~MOdÇLNhLfH!MlEGF`WOF\FMlEUL[I'WMlLÆMYEGF:IGF ÿ hGdÇMOdÇLNhÈL~H!MlE'_OFQF:IGd ÍF`_OF`hcM
_OFQkNZGPegf_ld `g~MldzLch*MlFQX#EUhGd [ZGFQWHþLN_»TV.÷ ,b æ IUgfMlgNWOFQMlWQCj
dÇh'g~PÇPzìNRQWlFQXMldzLch ô ]U_lFQWlFQhcMlW·_OF`WlZUPzMYW
L~H·h[ZU\FQ_ldeXg~P™FûG]DFQ_lde\:F`hcMlW.LNh½g:_lFQgfPDT¬V.÷ Äb æ çNLfPeZU\FLfH»MlEGF@êU_Yg~deh‘R[PÇFQgfIUdÇhGk:MOL^MlEUF
XLNh'WOMY_lZUXMOdÇLNh½L~H
_OFQkNZGPegf_.MOdeWYWlZGF ÿ ê'F`_3\gN]UW3dehÆMYEGF@ëEGdÇMOF\^g~MlMOF`_C
á ßGà'ålä ÝNÞ­ß à *à ß ·ßUåOápÞ á ÔápÞ NßGà åOÞ­ß Ôà à åOÞ
Oá
! #"$
%&'%
(*),+.-0/0+13254176,8
+),9
»FMZUWXLNhUWldeIGFQ_ MlEUFWl\L[LfMYEMY_lg†FQXMlLN_lì ú YüLfHÍg]'LNdÇhcM\LœçcdehGk¬LNh:gfhgf_YêGdÇMl_Ygf_lì
\gNhGdzHþLfPeI 7C hcì^WYZUX#E%MY_lg†FQXMOLN_lì:XQgfhÖêDFIUF ÿ hGF`I‘RGg~M!PÇFQgNWOM­PzLGXQg~PÇPzìNRNgfW­MlEUF*dehNMlFkc_lgfP
XZU_lçfF¬L~H
g^Wl\L[LfMYE½çNFQXMOLN_ ÿ FQPÇI ÖR'gfhUIÚWYg~MOdeW ÿ FQW¹MYEGF@FçNLfPeZGMOdÇLNh½F[ZUgfMOdÇLNh
ú Yü ú ú YüOü
ú ëEUFQ_lF ú ü ü
ú ïfü
bFQXQg~PÇP­MYEUg~MWOdehUXF >deW:gÈçfFQXMOLc_ ÿ FPeI‘R ë­FÚEUg‹çfF
7R ú ‘ü 7R ëEGFQ_lF
IGFQhULfMOF`W
»C hFûUgN\]UPzFÄLfHWlZUX#E gfh dehNMlFkc_lgfP
XZU_lçfFNRGdÇhUI'ZUXF`IÚêcìÆgçNFQXMlLN_ ÿ FQPÇI½LNhg^WY]UEGFQ_lFfRGdeW¹dÇPzPeZUWlMl_Yg~MOF`IÚdÇhÚj
dzkDC‘ïQg'C
¿`Ã
…wcuQuQ²c²cv¿`wN}†wNu`ˆ§²fu`}…r¾œ}†Â~wfÓxz‚ˆ.vc…yQˆYvGÉeˆ§ˆ§…§…!ƒ}†¼u ˆÆËG~ƒuQ……u#ͼÉeuQ…‚ruQ}†Á@wcˆ3ˆ‡Y}†uQuœ…uQ…ˆ#z‚@‚rvGÉeu`…uQ|cÁ2¯fx€|c¯~¿@x®°UËcˆ§y`…‡†ˆ§Ï~|œ¿`}…xzyu`­²N|[¿`¯Uˆ§uQ Á@ˆY}†…r¾ÔyQ|[¯ÈØDx€ˆ
;:=<>@?
:
!A
CB
D ?
:
D :FE
B
?
:
G? IH JCA
MB
QSTA
0NO?JA
VUXW.YOU
ZT[.\]Y^[U`_
aZ]bcYdfe!A
i
0j kml Lnporq
ZgUh?
B
LK
? PJRQSTA
TF`Wl]GdÇMOF@dÇMlW*WOde\^]GPzdeXdÇMìfRGF ÍC ú ïfüpXLNhcMYg~dehUW.MlEGFífFìÖFQPzF`\:F`hcMlW3MlL^ê'ZGdzPeIg~PÇPMlEUFXLNhG÷
WOMY_lgfdÇhGF`I,ø'LœëW¬]U_lFQWlFQhcMlFQIÈêDFPÇLœë@C »FQM¬Z'WgNWlWYZU\FMlEUgfM dÇW¬gÚWlZ'êU\^gfhGdzHþLfPeIÔXLN_Y_OF÷
Wl]DLNhUIUdÇhGkMOLWlLN\FhGLchGPzdehGF`gf_!XLNhUWlMl_Yg~dehcMlWLch:dÇMlWpFQ\:ê'F`IUIGdehGk:WY]UgfXF CNV3EGF`h‘Rfë.FXgNh
Wlg‹ìÄMYEUg~M:gÆøDLœë deW
ÐdzH¹dÇM@deW@MlgNhGkfF`hNM@MlL 7C æ MlW@HþLN_Y\>HþLfPÇPÇLœëW
_OF`gfIGdÇPzìHJ_lLN\ MYEGF­FûU]U_OF`WlWldÇLNh@LfH'MlEGF.MlgNhGkfF`hcM WY]UgfXF­gfM gNhNì]DLfdehcM :L~HDMlEGF¹XLchUWOMY_lgfdÇhUFQI
WOFQMC~V3EGdeW
gf_lkNZU\FQhcM dÇW çœg~PÇdeIHþLc_ êDLfMYE ÿ hGdzMlF3gfhUI:dÇh ÿ hGdÇMOF3IGde\:F`hUWldzLchUg~PG\^gfhGdzHþLfPeIUWQCœj'Lc_
LNZU_gN]U]GPÇdÇXQg~MldzLch‘R»ë.F%ë3dzPÇP¹XLNh'WOdeIGFQ_\gNhGdzHþLfPeIUWLfH¹MYEGF%HþLc_l\
ú ülR ëEGFQ_lF
RIGF ÿ hGFQIÔLNhÔgfhÈLN]DFQhÈWYZUêUWlFM LfH­MlEUF
ú ü3dÇW¬gÚWOFQMLfHpHJZUh'XMOdÇLNh'W
é­ZUXPzdeIGFQgNh<WY]UgfXFfRgfh'I<ëEGdeX#E MYgfífF½çœg~PeZGF`W^dÇh gÔXLNhUWlMl_Yg~dehGF`I<\^g~MY_Odzû<\^gfhGdzHþLfPeI C
V3EGdÇW^deh ÿ hUdzMlFIUdÇ\FQh'WOdÇLNhUgfP\^gfhGdzHþLfPeI LfH\^gf]U]UdÇhGkcW^XLNZUPÇI ê'F,IGF ÿ hGFLNh gÐWlZGdÇMlgNêGPÇF
gNhUgfX#E^Lc_ dzPeêDFQ_lM.WY]UgfXFî€ïQó'Rï 'Rlñ ~ö CNj'LN_.gkNdzçNFQhÖ]DLfdehcM
ú ülRGdÇMlW­MlgNhGkfF`hcM
Wl]UgNXF¬deW¹dÇIGF`hcMOd ÿ FQIÚMOL%MYEGFWlFM3L~H·HJZUhUXMOdÇLNhUW
ú ü
ú ü WlZ'X#EÆMYEUg~M ú ü
ëEGFQ_lF
deW3MYEGF@MlgNhGkfF`hNM3WY]UgfXF¬MOL gfM ú ülC
æ h MlEGFÈHþLfPÇPzLœë3dehGk'R deWÖç[dÇFë.FQIÒgNWÆg WYZUêU\^gfhUd€HþLNPÇI LfH¬MYEGFÈPÇdehGFQgN_ÆWY]UgfXF
ülRœëEGF`_OF IGFQhGLNMOF`W·MYEGF3WOFQM
L~H Æ_OF`g~P[\^g~Ml_ldeXFQW œC LfMOF.MlE'g~M
dÇh:MlEUF
ú
IGF ÿ hUdzMldzLchL~HDMlEGF.MlgNhGkfF`hNM Wl]'gfXFNRQë.F­gNWlWYZU\FQIMlEUgfM ú ü™dehUEGF`_OdÇMlW·dÇMlW
XLchUWOMY_lgfdÇhUFQI
kfFLc\FMl_lì¬IGdÇ_lFQXMOPÇìHJ_OLc\ùdÇMlW
XL[IULN\^g~deh C ÔF¹IGLhULfM
XLNh'WOdeIGFQ_·gfIUIUdzMldzLchUg~P[WOMY_lZ'XMlZ'_lgfP
XLNhcMY_lgfdÇhcMlWQR­WYZUX#EùgfW½dÇhcçfF`_OMldÇêUdzPÇdzMìNR¹ëEGdÇX#Eë­LcZGPÇI ì[dzFQPÇIù\:Lc_OFÐXLc\]UPzFû HJgN\dzPÇdzF`WÚL~H
\gN]U]GdehGkNW ú WlFF,HþLc_%dehUWOMYgfhUXFÄMlEUFÈkN_lLNZ']UW^L~HIGd ÍFQLN\LN_Y]UEGdeWY\W½ZUWlFQI deh MlEGFÔdÇ\^g~kNF
\gfMlX#EGdehGkÖXLNhcMOFû[Mî ô ~ö üYC æ hMlEGdeWWlFMlMOdehGk'R'gNhÚFçfLNPÇZUMOdÇLNh½F [ZUg~MldzLchÚLNh ú ü­\:ZUWlM
WlgfMOdeW†Hþì
ú ü ë3dÇMlE ú ü
ú ñGü
ú ü
æ h¬LN_YIGFQ_‘MlLWY]'F`Xdeg~PÇd QF!MlEUdÇW»F [ZUg~MldzLch¬MOLMlEGFp]'_lgNXMOdeXgfPNXQgfWlFQWWlMlZUIUdzF`I@dÇhMlEGdeW»]UgN]'F`_R
ë­FXgfhÈg~PeWOLÆhULfMOdeXF:MlEUgfMgÆë3dÇIGF_lgNhGkfFL~H!LN_lMlEULfkfLchUg~P·gfhUIÄWY]DFQXMY_lgfP XLNhUWlMl_Yg~dehcMlW3Lch
\gfMl_ldÇXFQW¬IGF ÿ hGF
ÖgNhUI
#C»V3EGFQìÈgf_lFWYZUêU\^gNhGd€HþLNPÇI'W¬L~H
ëEGdeX#EÕ]U_OF`WOF`hcMWOLc\:FÖhUdÇXFÖg~PÇkfFQê'_lgfdÇX^]U_lLN]DFQ_lMOdÇFQWQC æ hÕ]Ugf_lMOdeXZUPÇgN_RMYEGF%MlgNhGkfF`hcM
Wl]UgNXFg~M¬gfhcìkfdÇçfFQhÈ]'LNdÇhcM*LfH­gÚ\gfMl_ld€û ·dzF:kN_lLNZU],deWFQgNWOdÇPzì,IGF ÿ hGF`IÄdehÄMOF`_l\^WL~HpdÇMlW
MlgfhUkfFQhcMWY]UgNXFÖg~MdÇIGF`hcMOdÇMì ú dzMYW ·dzFÆgfPzkNFQêU_YgGüî€ï ö C V3EGdÇWdÇW:]Ugf_lMOdeXZUPÇgN_OPÇìÄde\]DLN_lMlgNhcM
WOdehUXF.F [ZUgfMOdÇLNh ú ñ[üYR`MlLfkNFMlEUFQ_·ë3dzMYEMYEGF­FûU]U_OF`WlWldÇLNh@LfH'MlEGF.MlgNhGkfF`hcM WY]UgfXF­gfM gNhNì@]DLfdehcM
LNh RUë3dÇPzPì[dÇFPeIIGdÇ_lFQXMOPÇìÖMlEUFXLNh'WOMY_lgfdÇhGF`IÖøDLœëW¹ë­F@gf_lF¬PzL[LcíNdehGkHþLN_QCGbFQkNgf_YIGPÇFQWYW.L~H
MlEGF!MìG]DF!L~HGXLchUWlMl_Yg~dehNMYW‘IGdeWlXQZUWlWlFQI¬dehMlEGF­WOF`XMOdÇLNh@ñURë.Fë3dzPÇPNIGF`WlXQ_OdeêDFFQgfX#E¬]DLfdehcM‘LNh
dÇhÆMOFQ_Y\^WpLfHdzMYW.FûGMl_ldÇh'WOdeX*XLcLc_lIUdÇhUgfMOF`W!deh CcV3EGF¬\^g~dehÖ_lFQgfWlLNh^deW­MlEUgfM.g:WlZGdÇMlgNêGPÇF
]Ugf_Ygf\FMY_Od QgfMOdÇLNhÕLfH*gÔXLNhUWlMl_Yg~dehGFQI9WlFMdeWkNFQhGF`_lgfPzPÇìÐIUd ÖXZUPzMQR!WOdehUXFÚWOFQçfF`_lgfP­X#EUgN_OMYW
gf_lFÖL~HþMlFQh<hUFQXF`WlWYgf_lìÈMlLÔXLœçfFQ_MlEGFÚZUhUIGF`_OPÇì[dÇhUkÔ\^gfhGdzHþLfPeI‘C
V3EGF½XLNhUWlMl_Yg~dehcMWlFM^\g‹ì
FçfF`hEUg‹çfF@WlFçfF`_lgfPXLchUhGFQXMOF`IÚXLN\^]DLNhGF`hNMYW ú MYEGFkc_OLcZU]ÆLfHLN_lMlEGLNkfLNh'g~P‘\^g~Ml_ldeXFQWQRGHþLc_
ӈt|[y}†²N…†y®®:¾(³ ˆYÎ~}†ˆ§|[¯ ºO}†ƒu }†wNˆ ³ ˆYÎfvc…ˆ#‚D‚’x€ºÔu`| y®Æ}†wcˆ uQvGˆ§…†y}†‡YuQu`…†…‚Õ…ˆ#‚rˆYvGÎ~uQxz‚’|[}¯Nxz|N‚È¿ }†u uQ| }†wcˆ9ˆ§±~ͲcÂ:y®ØDx®}’ˆY¾ }
³ Uº Ú³ Uº ³ Uº
³µvN…u~¯N²c‡l}!uQɑÁy}†…rxz‡Yˆ#‚OºOÂ
A
b dT[_mULZ [UaLYr_rY
[ \
A
?
A
>
E
H
J
Q
E
<>
B
B
Q "!$#&%)
J
Q "!$#&%$'(
"
A
+*-,/.0,
214351
*-,/.0,
gH
:
N
:;
H< N
J
=
> ?A@
"!$#&%
ED
IH-XYP\cd9J a_
B
E
@B
E
B
D %
!
J
BGF
Wd9K0dL\ Yr[Y d9J._
E
76 98
J
Q "!$#&%$C
cK
_
aZ]bcYr_
*L,.0,
C
`
*-,/.0,
M
ON
Z[R]\^R`_bacN
_
ih ejZ
ih \
QPSRT UdV(U
ih `RLk0hga[P
QPSRTLUWVXU
YTLUWVXU
Y_fefZg\
dÇhUWlMlgNhUXFNRfEUgNWMë­LXLNhUhUFQXMlFQI^XLc\^]'LchGFQhcMlW ~MYEGF*WlFMlW!L~H_OLNMlgfMOdÇLNhUWgNhUI^gfhcMOdz÷r_lLfMYg~MldzLchUW
ú ë.FXg~PÇP lgNhcMOdz÷r_lLfMYg~MOdÇLNh g^_OFø'FQXMOdÇLNhÚXLc\êGdehGFQI½ë3dÇMlEg^_OLNMlg~MldzLch™üOüYC
%&
`+ / 0(71
49 6 1
(*),+.-0/04179
6,+1#4)X/
ihGF¬ë.g‹ìÖLfH êUZUdzPeIGdehGkÖg^XLNh'WOMY_lgfdÇhcM3]U_lFQWlFQ_lçcdehGk:ø'Lœë ú ñ[üHþLc_3gWY]DFQXd ÿ X@]UZ'_l]DLNWlF¬dÇW¹MlL
\:dehGde\dQFÆgXLNWlM¬HJZUhUXMOdÇLNhUgfP CV3EGFÖXLN_Y_OF`Wl]DLNhUIUdÇhGkÚFçNLfPeZGMOdÇLNhÔF[ZUgfMOdÇLNhÐdeW@ZUWlZ'g~PÇPzì
IGF ÿ hUFQI@gfW·g¹kN_YgfIGdÇFQhcM™ø'LœëÐMlE'g~MHþLNPzPÇLœëW‘MYEGFpIGde_OF`XMldzLchLfHUWOMlFFQ]DFQWlM·IUFQWYXFQhcM‘MlLœë.gN_lIMlEUF
hGFQgN_OF`WOMX_ldzMldÇXQg~P]'LNdÇhcMQC™V·LêUZGdÇPÇIÔWlZUX#EÔgÖøDLœë@R deWFQhUIULœë­F`I,ë3dzMYEÔg ëEUdÇX#E IGF ÿ hGFQW%HþLN_%g~PÇP
g9WYXg~Pegf_^]U_lLGIUZUXMÖê'FQMë­FQFQh gfhcì Më.L
çfFQXMOLc_lWL~H¹MlEUFÖMlgNhGkfF`hNM@WY]UgfXF 7CbF`XgfPzP!MYEUg~M@MYEGF%kN_YgfIUdzF`hNM¬deW@MlEUFQhÕIGF ÿ hGFQI9gNW
MlEGFZUhUd [ZGF@çNFQXMlLN_ ÿ FQPÇI ÄWYZUX#EÚMlEUgfM
!
" ú Dü # ú ü $
ëEGFQ_lF " ú DüpIGF`hGLfMlFQW.MlEGF %
'&@L~(H Äg~M Ædeh½MlEGF¬IGde_OF`XMOdÇLN)
h ÍC[V3EUF¬XLN_Y_OF÷
Wl]DLNhUIUdÇhGk%\dehGdÇ\d dehGk^ø'LœëùdÇW3kNdzçNFQhÚêcì
ú Yü ú ú YüOü
úúü ü
+*
EGFQh deWÆg9PÇdehGFQgN_%HJZUhUXMOdÇLNhWY]UgNXF,F [ZGde]U]DFQIÒë3dÇMlEMlEG-F , #÷\FMY_OdeXÄIGF ÿ hGFQIÒêcì
/. ú ü .ú ü " R.MlEUFÈF [ZUgfMOdÇLN4h ú ü XLc_l_lFQWY]'LchUIUW%MlL MlEUFÔZUWYZUg~P
é­ZGPÇFQ_O÷ 1g~kc032_lgNhGkfFF [ZUg~MldzLchÆLfH çœgf_ldeg~MOdÇLNh'g~P‘XgfPÇXQZGPÇZ'WC
æ h LNZU_HJ_Ygf\FQë­Lc_líÍR3ë.F<X#EGL[LNWlF9MOLF`hUIGLœë
ú üÚë3dzMYEÅMlEUF<\FMl_ldeX
65 7 8032 95 ú ü ú ü ;:
F < : IGF`hGLfMlFQW½g9WlZGdÇMlgNêGPÇFÄbdÇFQ\^gfh[÷
" R­ëEGF`_O
hGdÇgNhÕ\:FQMl_ldÇX^Lch R·ZUWYZUg~PÇPÇìÔgfh
¬Lc_@g >= ^dehÕMlEGFÖXQgfWlF%L~H »dÇF
kN_lLNZU]UW
gNhUI:EULN\LfkNFQhGFQLNZUW
WY]UgfXFQWî€ï õ‹ö C æ h^]U_lgNXMldÇXFfRœëEGF`h:MYEG?F , #÷’kc_lgNIGdzF`hcM·deW!í[hGLœëh
HþLN_gNh9gf_YêGdzMY_lgN_OìÄXLNWlM¬HJZUhUXMOdÇLNhUgf@P <LNh ú
ülR·ë­F%ë3dÇPÇP­êDFÆgfêGPÇF%MOLÔ_OF`ZUWOF%dÇMlW
FûU]U_lFQWYWOdÇLNh9MlLÐIUF ÿ hGFMYEGFkN_YgfIGdÇFQhcMLfHMYEGFÚ_lFQWlMl_ldeXMOdÇLNh<L~AH ÒMOL ú üYC ]tMOLÕg
X#EUgfhGkNF¬L~H!\FMl_ldeX~RUMYEGFXLc_l_lFQWY]DLNhUIGdehGk^Ml_Ygfh'W†HþLc_l\^g~MldzLchÖdeW*gNh½Lc_OMYEGLfkNLNhUgfP‘]U_OL †FQXMOdÇLNh
LNh½MlEGFWYZGdÇMlgfêUPzF@MYgfhGkNFQhcM3Wl]UgNXFNC
A
YpUGXb
K
?
S
J
5XY K0ZT[[2XZ [
A
Q S A
N
!JMQSTA
S
_mU
D ?
?
E
ZXZ UXdT[
:
D :
S
?
E
S ?
:
? IH J
A
LK
A
6
?
E
I
E
A
B
B
E
"!$#&%
[/ ZXZT[U
H
S
[ dK
E
Z
K0Y^UXb
*
6
+* ,/.<,
CB
%&
DFEHG+1I1p6X4)
$G
254
J(KLM 6 g4)?NIPOIQKL./
/
41#9
ýcMlgNhUIUgf_YIÈh[ZU\F`_OdeXgfP!\:FQMlEGLGIUWHþLc_¬IGd™FQ_lFQhcMldÇgfPF[ZUg~MldzLchUW¬gf_lF%ZUWlZ'g~PÇPzìÄhGLNM@WlZGdÇMlgNêGPÇF
HþLN_ÚXLNh'WOMY_lgfdÇhGF`I ø'LœëWQC LfMOFÔMlEUgfM½ë3dÇMlEùg<WldÇ\^]GPÇFÈé.ZGPÇFQ_Ú\:FQMlEGLGI‘R¹MYEGFÐh[ZU\F`_OdeXgfP
dÇhcMOFQkN_Yg~MldzLchÖL~H
F [ZUgfMOdÇLNh ú ïfü!ìcdÇFPeIUW¹MYEGF@FûU]GPÇdÇXdzMWYX#EGF`\:F
ëEGF`_OF
T ú ü "
úSô ü
;RHS
ëEGFQ_lF " XLc_l_lFQWY]DLNhUIUWMlLÚMYEGF^dÇhcMlFkN_Yg~MldzLchÈWlMOF`]‘C·ýcdehUXF%ë.F%gf_lFZUWldehGkFûGMl_ldÇh'WOdeX
XL[LN_YIGdehUg~MlFQWQRGMlEGF`_OF@deW*g%_ldÇWYíÖLfH
WlMOF`]U]GdehGk%LNZUM3HJ_OLc\ HþLN_3F`gfX#E ú hULNhÚdÇh ÿ hGdÇMOFQWlde\gfPJü
IGdÇWY]GPegfXFQ\FQhcMC æ h<HJgNXMQRpêcì ë_OdÇMOdehGk ú’ô üë.FÚde\^]GPÇdÇXdzMlPzì gfWYWlZ'\:F`I<MYEUg~M%MYEGF,dehNMlFkc_lgfP
U „[u`….yQ|ÆyQ…Ëfx®}†…†yQ…r¾Æ‡Y²N…ʋWˆ VMX­uQZ
| Y ƒU‚r²c‡Ow%}†w[y[} V]\ LV½y|[+¯ ^`^ _bXda cc X;e$\ gf[ƒUu`|Nˆ‡YuQÁ@vc²f}†ˆ#‚
}†wcˆ.Ùc…†‚’}pÊ`y…rxÇy}x€u`|^u(É hÉDžu`Á }†wNˆ3¯NˆYÙc|Nx®}x€u`| i9h _ ³ fNº ^j3^ k _bX a6l ccc X#e$\ Â
8
:
? !
;
H
%
B
7B
E
? ! %
B
B
? ! %
:
? D
B
E
? !
JCA
D %
BGF
A
e
e
e
Tp M
t+dt
p(0)
T
M
p(0)
dtV(pt )
M
Tp M
t
pt
p = exp dtV(pt )
pt
t+dt
dtV(p )
t+dt
pt+2.dt
p(t)
T
p(t)
M
M
!7%
!
%
o!x€ˆ§DÁ« [yQ«»|N|N³þyœxzyQº
|:m’|œÁ}†ˆ§yQ¿`|f…†x€yÉÇuQ‘z‡Y¯'²N …ʋˆ3uQÉ·y¬Ê‹ˆ§‡l}†u`…!Ù[ˆYz¯uQ|Öy¬ÁyQ|fx€ÉÇuQz¯Y ƒ,³µËUº .ˆ§u~¯Nˆ§‚’xLJ*‚’}†ˆ§vc‚puQ|Öy
XZU_lçfFPÇdzF`W%dÇh gÕPÇdÇhUFQgf_ÆWl]UgNXFNC æ htLcZU_ÖWldzMYZUg~MldzLch‘R!ë.F,\ZUWlMÆgfIOZUWOM%MYEGF,dehNMlFkc_lgfMOdÇLNh
\:FQMlEGLGIMOL¬gfXXLN\^\LGIUg~MlFpMlEUF­MY_lZGF.XLchUWOMY_lgfdÇhUFQI@kNFLN\FQMl_lìLfH 7CœV3EGF ÿ _lWlM»deIGFQg*dÇW MlL
]U_OL †FQXM!gœHþMOF`_!F`gfX#E^WOMlFQ]%MYEGF*]DLfdehcM
Lch^MlEGFZUhUIGF`_OPÇì[dÇhGk:\gNhGdzHþLfPeI‘C ÐF*]U_lLN]DLNWlF
EGFQ_lFÈMlLtg‹çfLNdÇI MYEGdeW½]DLNWlM†÷]U_lL[XFQWYWOdehGk<;RIZ'S WOdehGktg kfFLc\FMl_ldeXÄdehNMlFkc_lgfMOdÇLNhÒWlMOFQ] _OFQPzì[dehGk
LNh
>=
§RDHþLfPÇPÇLœë3dÇhGkÖIUdÇ_lFQXMOPÇì½g%kNFLGIGFQWldeX@]Ug~MYE,ê'FQMë­FQFQhFQgNX#EÚdzMlFQ_Yg~MOdÇLNhC
V3EGdÇWÆMOF`X#EUhGd cZUFÄdÇW½ê'Lc_l_lLœë.FQI<HJ_OLc\ Fû[deWlMOdehGk<h[ZU\FQ_ldÇXQg~P*\FQMlEGLGIUWÆLNh bdÇFQ\^gfh'hGdÇgNh
\gNhGdzHþLfPeIUWî®ï õ Rlñ ö C æ MXLchUWOdeWlMlW¹L~H_lFQ]GPegfXdÇhGk úSô üpêcì
FûU] 6ú " ú üOü
ú ò'ü
ëEGFQ_lF3FûU] IGFQhGLNMOF`WMlEG;RHF*S FûU]'LchGFQhcMldÇgfPD\^gf]^g~M 7C~b*FQXgfPzPDMlEUgfMHþLN_pg¬kfdÇçfFQh^]DLfdehcM
ÄLNhÈg ú ÿ hUdzMlFIGde\FQhUWldÇLNhUgfPJü¹\gNhGdzHþLfPeI 7RÍgNhUIÄgÆçfFQXMOLc_
7R'MYEGFQ_lFFûGdÇWlMlWg
ZUhGd cZUF@kfFLGIGF`WOdeX
ú YüpWYZUX#EÚMlE'g~M
gfh'I ú ü
úü
V3EGFÖFûU]DLNhGF`hcMOdeg~Pp\^gf]ÐFûG]
deWMlEUFQh9IGF ÿ hGFQI9êcìÔFûU] ú Dü ú ïfü
ú -WYZUX#E,MlE'g~M ú ïfü­Fû[deWlMlWülCÍj'LN_ " 3* WlZ ÖXdzF`hNMlPzì,WY\^g~PÇPSRÍF [ZUgfMOdÇLNh ú òUü.XLN_Y_OF`Wl]DLNh'IUW
MOLÖgkfFQL[IUFQWldÇXWOMlFQ]ÚL~H
PÇFQhGkNMlE
" ú ü
" ú ü " ú ü
dÇhÚMlEUFIGdÇ_lFQXMOdÇLNh½L~H ú ü ú WOFQFj
dÇk'Cï`ê™ülC
æ h,kfF`hGFQ_Yg~P’RUMlEUF:F cZ'g~MOdÇLNhLfH!gÖkfFQLGIGFQWldÇXWlgfMOdeW ÿ F`W*gÖWlFQXLNhUILc_lIUFQ_IGd ™FQ_lFQhcMOdeg~P F [ZUg~÷
MOdÇLNh‘C æ h^MlEGdeWp]UgN]'F`_Rfë­FZUWlFMYEGF3HJgfXM!MlE'g~MHþLc_!WOde\^]GPÇF*\^g~Ml_ldzû\^gfhGdzHþLfPeIUWQRfXPÇLNWlFQI:HþLc_l\
WOLNPÇZGMldzLchUWgf_lF¹L~HþMlFQh^g‹çœg~dÇPÇgNêGPzF ú gNhUIMlE[ZUWMYEGF3FûU]DLNhGF`hcMOdeg~PU\^gf]™üYC *LNMOF3MYEUg~MLch:PÇdehGFQgN_
\gNhGdzHþLfPeIUWFQhUIGLœë.FQIÄë3dzMYEÄMlEUF:é.ZUXPÇdÇIUFQgfhÔ\FMl_ldeX~RÍkfFLGIGF`WOdeXWgf_lF:WlMl_Yg~dÇkNEcMPzdehGFQWQC™j'Lc_
dÇhUWlMlgNhUXFNR»MYEGFÖMlgNhGkfF`hcMWl]'gfXFÖgfM dÇh
deWIGF ÿ hGFQI9êcì
gNhUI
ë­F%EUg‹çNF
FûU]
T ÖCV3EGFQh‘R‘F [ZUg~MldzLch ú òUü_OF`IUZUXFQWMOLMlEUF
LN_ldzkNdÇhUgfP™é­ZGPÇFQ_¹dehcMOFkc_lgfMOdÇLNh½\:FQMlEGLGI‘C
æ h¬LNZU_™HJ_Ygf\FQë­Lc_líÍR#MlEUFQWlF!dÇIUFQgfWFûGMOF`hUI@hUg~MYZU_Yg~PÇPzìMOLMYEGFpIGF ÿ hGdÇMOdÇLNh@LfH[gh[ZU\F`_OdeXgfP
dÇhcMOFQkN_Yg~MldzLch:WYX#EGFQ\F3Lch ú ülC dzçNFQhFûU]
MlEGFFûU]'LchGFQhcMOdeg~PU\^gN]:Lch
A
#? !
g
%
B
7B
YradT[Yr[ UGXZ K0Z a_
? !
%
B
S
7B
:B
S
E
? ! %
? D
B
7?
?
J
J
Q ?A
:
'H
?
E
Q S A
S
N
JMA
A
:<>
A
>
'H
K
E
A
S
:
: B
? ! %
S B
B
: B
E
? ! %
: B
? ! %
B
E
6
S !+
B
? ! %
B
8
4
;N
B@J
*-,/.<,
B
OQ E
*-,/.<,
B
S
gQ S <>
*-,/.0,#"
*-,/.0,
ü3gÚWlMOFQ]G÷SHþLc_Oë¹gf_YILN]DFQ_Yg~MlLN_ EHG
ú ü
ú9 EHG ^ü ú ü FûU]
ú ü
ihGFÖXgNhÔF`gfWldzPÇìÈX#EGF`X#í,MlE'g~M ]EHG ì[dÇFPeIUWgXLchUWOdeWlMOFQhcMh[ZU\FQ_ldeXg~PdehcMOFQkN_Yg~MOLc_ ú deh
MOde\:FfüHþLN_3MYEGF@XLchNMldÇh[ZGLcZUW¹F[ZUgfMOdÇLNh ú ñGülR'WYZUX#E½MlEUgfM
lú ü ]EHG " ú ü FûU] " Yú ü
ú’õ ü
;RHS
ë3dzMYE §ú ü
gNhUI
ú ülC
bFkcgf_YIGdÇhUk@MlEGFIGdÇWYX_lFMld `g~MldzLch^dÇhÖWY]UgNXFLfH .ú LNh üYR ÿ hGdÇMOFIUd ™FQ_lFQhUXFWYX#EGFQ\F`W
IGFçNFPÇLN]DFQIÔHþLN_@ZUh'XLNh'WOMY_lgfdÇhGF`IÈF [ZUg~MldzLchUWWlMOdÇPzPpgN]U]GPÇìfC XMYZUg~PÇPzìNR»XLchUWlMl_Yg~dehNMYW¬LNhÐMlEUF
XLGIGLN\^gfdÇh LfH ú ü­LchGPÇìÚX#EUgNhGkfF@MYEGFMldÇ\FIGdÇWYX_lFMld `g~MldzLch,WlX#EGF`\FfC æ H!ë.FEUgNI
MOL IGF`g~P3ë3dÇMlE HJZUhUXMOdÇLNhUW
ëEULNWlFWY]UgfMOdeg~PIGLc\gfdÇh ë.gNW%gfh gf_YêGdÇMl_Ygf_lì
\gNhGdzHþLfPeI ú HþLc_dehUWlMlgfh'XF½gNh9de\]UPzdeXdÇMWYZU_OHJgfXF½IGF ÿ hGFQI<êNì9gÈPzFQçfFP¹WlFMHJZ'hUXMldzLch™ülR
ë.F
XLNZUPÇIÚXLc\êGdehGF@MlEUdÇW¹MlFQX#EUhGd [ZGF@ë3dÇMlEÚMlEGF¬HJ_Ygf\FQë­Lc_lí^dehcMl_lL[I'ZUXF`IÆdeh9î ô~ö C
Oålä ßGåOápÞ á ÔápÞ fßGà ålÞpß Èà à 3ålÞ †á ßGáùå
ã [åOápÞ
Þ Nápà ­ã à'å ßGåOápÞ
ú
R‘ë­FdÇhcMY_OLGIUZUXF:Lch ú
üpIGF ÿ hGFQIêcì
N
J
<>
!
%
B
B ! %
"!$#&% B
E
:=B ! %
E
7B
B
J
D
B
E
B
JMQ !$#&%)
Q
<>
LK
B
B
:hB ! %
!i#
%
B
7B ! %
B
*-,/.<,
P+1]E 041#94J
&'%
>
V
G! 7"$
$
+ p4 p6,+1#/
ÔF¹]U_lLN]DLNWlF­hGLœë9MlLZUWlF­MYEGF¹]U_OFQç[dzLcZUWMlLcLNPÇW·MOL¬gfI'IU_OF`WlW»MlEGF¹]U_lLNêGPÇFQ\ LfHDIGd™ZUWldÇLNhMlFQh[÷
WOLc_­_lFkcZGPÇgN_OdQgfMOdÇLNh‘C »FQM.è ú ügfhUIi ú ü!IGF`hGLfMlF_lFQWY]'F`XMldzçNFPÇì[email protected]~H WOìG\^\FMl_ldeX
]'LcWOdÇMOdÇçfF@IGF ÿ hGdÇMOFfRDgfhUIÚLN_lMlEULfkfLchUg~P™_lFQg~P\^gfMl_ldÇXFQW¹L~H
WOdF CGbFQXQg~PÇPMlEUgfM
Úè ú ü 6gfhUI ú óUü
Äi ú ü
ú deW3MlEUF@dÇIGF`hcMOdÇMìÆ\^g~Ml_ldzûÍü ú [ü
ÔFgf_lF½\^g~dehGPÇì9dÇhcMlFQ_lFQWlMOFQI<dÇht_OFQkNZGPegf_ld dehGk ÿ FQPÇIUW
4è úSô ü¬L~HIGd ‘ZUWldzLch
MOFQh'WOLc_lWXLN\dÇhUk¬HJ_OLc\ T¬V.÷ ,b æ de\^g~kfdehGkDCfV3EGdeW!_OF`XF`hNMgNhUI^hGLNh[÷rdehNçœgNWOdÇçfF ô Tù\:F`IGdeXg~P
dÇ\^g~kNdÇhUk:\LGIUg~PÇdzMìÖXLNhUWldeWOMYWpdehÆ\FQgNWlZ'_OdehGkMYEGFë.gfMOFQ_.\LfPÇFQXQZGPzF¬\LfMldzLch%dÇh½MlEUFMldÇWYWlZUF
ÿ ê'F`_lWQR­Z'WOdehGk<\^g~kchGFMldÇXÈ_OF`WOLchUgfhUXF,MOF`X#EUhGd cZUFQWQCpé­gNX#E çfL‹ûGFP ú ü è úSô ü:L~HMlEUF
gfX [ZGde_lFQIde\gfkfF deW*IUF ÿ hGF`IÄêcì,gÖWOìG\^\FMY_OdeXgfh'IÄ]'LcWOdÇMOdÇçfF:IGF ÿ hUdzMlF ô ô \gfMl_ld€û
MlEUgfM¬IUF ÿ hGF`WMlEGF^PÇL[XQg~P
ë¹g~MOF`_¬\:LNPzF`XZGPÇF^\:LNMOdÇLNh ú d’C FNC‘MlEGF ÿ êDFQ_¬Lc_OdÇFQhcMlgfMOdÇLNhUWü¬î ðURQï R
ñGïfRïò'R ô ò ö CUV3EGF`WOF ÿ êDFQ_WlMl_YZUXMlZU_lFQW3gN_OF¬hGLfM3FûU]GPzdeXdÇMOPÇìÆkNdzçNFQh½êNì½MlEGF\^gfMl_ldÇXFQW ú ülR
êUZGM3XgNhÆêDF¬_lFMY_OdÇFçNFQI½êNìÖWY]DFQXMY_lgfP‘IGFQXLN\^]'LcWOdÇMOdÇLNh ú ü 5 ú ü! ú ü 5 ú ü RGëEGFQ_lF
5
i úSô ü*deWMYEGF ÿ FQPÇI L~H ô ô
=
½XLN\^]DLNWlFQI9LfH¹MYEGF½Z'hGdzM
FdÇkfFQhcçNFQXMlLN_YWLfH Rœgfh'I! dÇW
MYEGF ÿ FPeI:L~H'MYEGF ô ô \^gfMl_ldÇXFQW"! ú ü IUdÇgfk ú$# %# # & ü
XLN_Y_lFQWY]'LchUIGdehGkMOL,dÇMlW
>= #C XMlZUgfPzPÇìfR·MlEGFÆWY]DFQXMY_lgfP­IGF`XLc\]DLNWldÇMOdÇLNh
Wl]GPÇdÇMlW.MlEGF¬IGd ™Z'WOdÇLNhÆMOFQh'WOLc_ ÿ FQPÇI dehcMOL:gNh
5 ú \gfdÇh½IGde_OF`XMOdÇLNh'W
L~H·MYEGF@ë¹g~MOF`_3\LfMOdÇLNh‘ügNhUIÚg'& ( *) +! ú çfFPÇLGXdÇMìÖL~H
MlEUF@ë.gfMOFQ_¹\LfMldzLch™ülC
h'g~MlZ'_lgfP¬_lFQ]'_OF`WOF`hNMYg~MldzLch L~H 4dÇWÚMYEGFQh ]U_lL[I'ZUXF`I ZUWldÇhUktFQPzPÇdÇ]'WOLNdÇIUWÚëEGLcWOFÕgœûGF`W
gfhUIÚ_lgNIGdÇdgf_lF_lFQWY]'F`XMldzçNFPÇì%kfdÇçfFQhÚêcì%MlEGF@FQdzkNFQhcçfF`XMlLN_YWpdeh 5(gfh'IÆMYEGFXLc_l_lFQWY]'LchUIGdehGk
]
1
1
1
N
J
N
J
1
1
N
E
E
!J
E
* ,
3
[b
1
H0'(
H<
E;
cK
>
J
5
4
3
H
>
3
E
d9rUXW.dc\]d [ Z SK0Z UXb Ym_
/
3
;ad _,Ui YCY \ Yr[/ Z
JYm_
VdXYr[ UIZgUGXd [`erY Z UJ0LY
"J._i,U erY Z UJ0LY
A
E
6
[2]
λ2u
[1]
λ1u
[3]
λ3u
O
Í«'«­x€ˆY¼<uÉ»yQ¶¯~x€°U²c‚’x€u`|:}†ˆY|[‚ru`…ÙcˆYz¯ Û ´p³œºOÂ
]'LcWOdÇMOdÇçfF¬FdÇkfF`hcç‹gfPÇZUFQW # # # ú WlFF@j
dzkDC'ñ[üYC
æ hÔMYEGFHþLfPÇPzLœë3dehGkDR‘MlEGFÖ\^g~MYEGFQ\^& gfMOdeXg~P!_lFQgNWOLchGdehGk½IGFQçfFQPzLc]'F`IÈdehÕWOF`XMOdÇLNhtï^dÇW@gN]U]GPÇdzF`I
MlEU_lLNZGkcE:g¬]U_lLfkc_OF`WlWldÇçfF­gNhUg~PÇìGWOdeW L~H™MlEGFIUd ‘ZUWldzLch:MlFQhUWlLN__lFkcZGPegf_ld`g~MOdÇLNh]U_OLcêGPÇFQ\ÚC ÐF
_OFHþFQ_3MlLÖMlEGF:_OF`WOF`gf_YX#E½_lFQ]DLN_lM3çfF`_lWldzLchÚL~HMlEGdeW*]'gf]DFQ_î ö HþLN_gÖIUFMlgfdzPÇFQI,IUFQ_ldzçœg~MldzLchÚL~H
MlEGF_OF`WlZUPzMYW]U_lFQWlFQhcMOF`I êDFPÇLœë@C *LNMOFÚMlEUgfMMYEGdÇW:HJ_Ygf\Fë.LN_YíÈgfPzPÇLœëWZUWMlLÈkfF`hGFQ_Yg~PÇd F
]U_OFQç[dzLcZUW3_OFQkNZGPegf_ld Qg~MldzLchÖ\FMYEGLGIUWgfXMOdehGk%IGde_OF`XMOPÇìÖLch½MYEGF\^g~MY_Odzû½_lFQ]U_lFQWlFQhcMlgfMOdÇLNhÆL~H
TV.÷ ,b æ IUg~MYg,î ð'Rï R ô ñ ö C
gZ
9P
6
8
& H
N
IK KL] 6 )=176 N7P+ 17/ 46X1
+ /p6 p6
ì½gfhUgfPzLNkfìë3dzMYEÚWYXgfPÇgN_pde\^g~kNF_lFkcZGPÇgN_OdQgfMOdÇLNh%\FMYEGLGIUWQRGMlEGF ÿ _YWlM­deIGFQgMlL_lFQWlMOLc_OFg
TV.÷ ,b æ ÿ FQPÇIÈdÇW*MOL ÿ hUIÈgÆ\gfMl_ld€û[÷rçœg~PeZGFQIÚø'LœëÅ\dehGdÇ\ddehGkgÖ_OFQkNZGPegf_ldQg~MldzLch½HJZUhUX#÷
MOdÇLNhUgfIP R
\
Ç
d
h
ü
ú !
ú Uü
ú
ü T#" ú
ñ * œü "%$
2 &
2
ü deW3MYEGF = .ú ëEGF`_OF ! '& ( ! gNhUI ! ú
& deh $ üYRNëEUdzPÇF*]U_lFQWlFQ_lç[dÇhGk¬MYEGFWlìG\\FQMl_ldÇX3]DLNWldzMldzçNF*IG*F ) ÿ hG,dÇ+MOFXLNhUWlMl_Yg~dehcM ú óUülCNV3EUF
ÿ ûGFQIÐ]Ugf_Ygf\FMlFQ_ " ]U_lFçfF`hcMlWMlEGF^FûU]DFQXMOFQIÐWlLfPeZGMOdÇLNhÄHJ_OLc\>ê'FQdÇhGkMlLcLIGd ÍF`_OF`hcM
HJ_OLc\ MYEGFkfdÇçfF`h,hGLfdeWlì ÿ FQPÇI RÍëEGdÇPzF deW
ÈëEGdeX#E
XLNhcMY_OLNPÇWpMlEGF@_lFkNZUPÇgN_Od QgfMOdÇLNh^ê'F`EUg‹ç[dzLc_ ú MlEGdeW '÷SHJZ'hUXMldzLch%HþLN_Y\ZUPÇgfMOdÇLNh%ë¹gfW ÿ _YWOM.dÇhcMY_OLf÷
IUZUXF`I^dÇh^MYEGF*XLNhcMOFû[MLfH™WYXgfPÇgN_
dÇ\^gfkfF_lFkNZUPÇgN_Od QgfMOdÇLNhë3dÇMlE^F`IGkfF]'_OF`WOF`_Oçœg~MldzLchÚî [RQïQð'R
ñœò ö ülC *LfMlFMlE'g~M3MlEUF@HJZUhUXMOdÇLNhUgfP ú Uü!dÇW*dÇhcçœgf_ldegfhcM3êNìÚ\^g~Ml_ldzû½Ml_Ygfh'Wl]DLNWldzMldzLchgfhUIÚMlE[ZUW
MlgfífFQW¹dehcMOL%gfXQXLNZ'hNM¹de\^]GPzdeXdÇMOPÇìÆMYEGFWlì[\^\FMY_Oì½]U_OLc]'F`_OMìÆL~H·MYEGF@FçNLfPÇç[dÇhGk^\^g~MY_OdeXF`WC
3 ?G 3]* /10 32 V3EGF­WOde\^]GPzF`WOM‘ë¹g‹ìMlL3dÇhcMl_lLGIUZUXF
ø'LœëW‘LNh ú è ú ülü
dÇW¹MlLXLNhUWldÇIUFQ_.MlEGFHJgNXMOLc_Od QgfMOdÇLNh%LfH gNhNìÖWlìG\^\:FQMl_ldÇX]DLNWldzMldzçNF¬IUF ÿ hGdÇMOF@\^g~MY_Odz5û 4 dÇhcMlL
g]'_OLGIUZUX7M 6 6ÅëEGF`_OF 6 ú üYR»MYEGF »dÇF@kN_lLNZU]ÆL~H
dÇhcçNFQ_lMOdeêGPzF Õ_lFQg~P\^g~÷
Ml_ldÇXFQWQC æ MlW »dÇFg~PÇkfFQê'_l9g 8;: ú ü·dÇWMYEGF*WlFMLfH™_lFQgfPUçœg~PeZGFQI^\^g~MY_OdeXF`WRfgNhUIë­FXQgfhdeIGFQhcMOdzHþì
gfhcìÆMYgfhGkNFQhcMçfF`XMlLN_ < g~M]'LNdÇhcM 6 ú üë3dÇMlEÄg%çNFQXMOLN_ L~=H 8;: ú ü.MlEU_lLNZUkNE
<
6 ^C'V3EGdeW3PÇFQgfI'W¹MOLø'LœëW¹LNh
ú ú ülüpëEGdeX#E½gN_OF¬kfdÇçfF`hÆêcì
6
6
ëEGF`_OF
ü gfhUI 6
6
ú
ú ú üOü
-
9XY^[U
!
!
%Q%
-
E
;
-
E
6
E
@
@
6
# ED
@
@
@
[
_IaZ UXZ
@
\cZ
H
D
>
*
*
PZT[
[ bLY Z _ [.\
e J[ bpUGXd [
28
`+17/
46X1
./
6X1
+.-
J
1
;
7*
J
E
D :
E
3I1
1
;B
D
1
1
B
B
J
7* ,.0,
1
B
7*
1
1
D %
!
BGF
E
D
J
1
cK
ihGFWldÇ\^]GPÇì%XLc\êGdehGFQW­MlEUdÇW­FûU]U_lFQWYWOdÇLNh^ë3dÇMlEÆMlEGF*HJgfXMOLN_ldQg~MldzLch^L~H MlLLcêGMlgfdÇh^øDLœëW
MlEUgfMgfXM3IGde_lFQXMlPzì½LNh ú è ú üOüYC
50 32 *Lœë@RUdzHë­F¬PÇFMIGF`hGLfMlFQW¹MlEUF , ÷’kc_lgNIGdzF`hcM­LfH ÄLNh ú & &DülC
ÔFWlEGLœëÒdehÈî ö MlEUgfMpMYEGFhUgfMlZU_Yg~PDkN_YgfIGdÇFQhcMøDLœëXLN_Y_lFQWY]'LchUIGdehGk@MOL:MlEGF_OF`WOMY_OdeXMldzLch^L~H
,MOL ú è ú’ô üOü ú FQhUIGLœë.FQI½ë3dÇMlEÚdzMYWhGLc_l\^g~P\FQMl_ldÇX~üpWlgfMOdeW ÿ F`W
T
ú ðUü
* T T æ h½LcZU_3XgNWOFNR[MlEGF\^g~MY_Odzû ú ü!dÇWIUF ÿ hGF`IXLN\^]DLNhGF`hcM¹êcìÆXLN\^]DLNhGF`hNM3ë3dÇMlE
" ú * ~ü * IGdÇç ú ü ! úï ü
*LfMlF½MYEUg~MMlEUF½è­Té ú ðGü@g~PÇPÇLœëWMlLÈFçNLfPÇçfFÚIGdÇ_lFQXMOPÇìÕMlEGF\^g~Ml_ldzû9XL[F ÖXdÇFQhcMlWëEGdÇPÇF
]U_OF`WOF`_Oç[dehGkMlEGFWlìG\\FQMl_ldÇX¬]DLNWldzMldzçNF¬IUF ÿ hGdÇMOF`hGFQWYWQC
JKLM 3 OQKL 2 j'Lc_ F [ZUg~MldzLch ú ðGülR~WldehUXF.MlEGF3ZUh'IGFQ_lPzì[dehGk¬\gNhGdzHþLfPeIdeWgfhLc]'F`h
_OFQkfdÇLNhÚL~H!g%PÇdÇhUFQgf_*Wl]UgNXFNRDgÖWldÇ\^]GPÇFé.ZGPzF`_*WlMOF`],XLNZUPÇI,êDF:ZUWlFQIRD]U_lLœç[dÇIGF`IÚMlEGF:dÇhGdÇMOdeg~P
HJZUhUXMldzLch deW*HJgN_FQhGLcZGkNEÄHJ_OLc\ MlEGF%XLchUWlMl_Yg~dehNMWOFQM@ê'LcZUhUIUgN_OdÇFQWQC WOdehGkMlEUFFûU]'Lf÷
hGFQhcMOdeg~P\^gN]½MYEGFLc_Oì½]U_OF`WOF`hcMOFQIÚêDFHþLN_lFfRGë.F@XgNh½dehcMl_lLGIUZUXF@g^\LN_lF@WlZGdÇMlgNêGPÇF¬WYX#EGF`\:F
FûU] ú * Yú T !ü " Yü$ FûU] ú * Yú T pü " Yü ú ïfïfü
>= R­h[ZU\FQ_ldeXg~PÇPÇì dÇ\^]GPÇF÷
ëEGFQ_lF,FûU;RH] S ú ü ( IGF`hGLfMlFQW
\:F`hcMOFQI:ZUWldÇhGkgè!gNI­F!a gf]']U_OL‹ûGde\^g~MOdÇLNhRgfW IGFQWYX_ldeê'F`I@dÇhÚî®ï ôœö C‹ihGF.XgNh@FQgNWOdÇPzì@X#EGF`X#íêcì
dÇhUI'ZUXMldzLchÖMlE'g~M.MlEGdeW­WYX#EGF`\:FWlgfMOdeW ÿ FQW­MlEGF¬XLchUWOMY_lgfdÇhcMQC »FQM FûU] ú * Yú QT
ú è ú üOülR¹ë.FÔEUg‹çNF
ü " YülC æ Hë.FÕgfWYWlZU\F
ü
6
U
C
3
V
[
E
U
Z
Q
W
R
.
Yú
. lú ü . . ú ü Yú ü §ú ü .
;RHS
ú Yú ü . ü$ Yú ü ú §ú ü . ü
D?EHG M ;KL OI] Q 2 hÔgN]U]GPÇdÇXQg~MldzLchÄL~H.MlEGFÖWlìG\^\:FQMl_ldÇX]DLNWldzMldzçNF
IGF ÿ hUdzMlF^_lFkcZGPegf_ld QdÇhGkÖø'Lœë ú ðUü.LchÈgÆhULfdeWOìNR™WlìGhcMlEGFQMOdeX ô TMlFQhUWlLN_ ÿ FQPÇIÈdÇWdÇPzPeZUWlMl_Yg~MOF`I
dÇh,j
dÇk'C ô CDV3EUFMOF`hUWOLc_ ÿ FQPÇI,deW [ZGdÇMOF:ë­FQPzP _OF`WOMlLN_lFQI‘RDêUZGMWYZ ™FQ_YW¹HJ_lLN\
=
== *( JRpIUFQWY]GdzMlFÄMlEUFÄgfhGdeWOLNMl_lLN]GdeXIGd ™ZUWldÇLNh LNêUMlg~dehGF`Itë3dÇMlE MYEGF '÷SHJZ'hUXMldzLch
HþLN_Y\ZGPeg~MldzLch‘C XMlZUgfPzPÇìfR'ëEGFQhMYEGFhGLNdÇWlFIGL[FQWhULfM*g ÍF`XM3MlEUFMOF`hUWOLc_3LN_ldÇFQhcMlgfMOdÇLNhUW3gNW
\ZUX#E½gfW.MlEGF@IGd ‘ZUWOdÇç[dzMldzF`W ú ëEGdeX#E½dÇW.MlEUF¬XQgfWlFEUFQ_lF~ülRGg:kfPÇLNêUgfPÍ\^gfMl_ld€ûÆ_lFkcZGPÇgN_Od QgfMOdÇLNh
]U_OLGXFQWYW [ZGdeX#ícPzìÔWl\L[LfMYEGFQW¬MYEGFÖIGd ™ZUWldÇçcdÇMOdÇFQWdÇhÐ_lFkNgN_lIÈL~H¹MlEGF%Lc_OdÇFQhcMYg~MOdÇLNh'WC‘V3EGF`_OF÷
HþLN_lFfR™MOL,g‹çfLNdÇIÈMlEGdeW¬FdÇkfF`hcç‹gfPÇZUFWY\LcLNMlEGdehGkDR‘ë­F^EUg‹çfFMOL,WY]GPÇdzM¬MlEUF^_lFkcZGPegf_ld `g~MOdÇLNhÄL~H
MlEGFÚMOF`hUWOLc_Lc_OdÇFQhcMlgfMOdÇLNhUW:gfhUItIGd ™ZUWldÇçcdÇMOdÇFQWQC *LNMOFÆMYEUg~MMlEUFÚWYgf\FÆícdehUI LfH*ê'F`EUg‹ç[dzLc_
gf]U]DFQgN_lWdÇhÔXLNPzLc_*de\^g~kfF_OF`WOMlLN_Yg~MldzLch‘R'ëEGF`_OFWOFQçfF`_lgfP \FMYEGLGIUW¬]U_lLN]DLNWlFMOLÚWOF`]Ugf_Yg~MlF
MlEGF*X#E'_OLc\gfMOdeXdÇMì:gNhUI^MlEGFêU_OdÇkNEcMYhGFQWYWdeh[HþLN_Y\^g~MOdÇLNh:HJ_lLN\ gXLNPzLc_
çfFQXMOLc_RfgNhUI%_lFQWlMOLN_lF
MlEGF`\ ë3dÇMlEIGd ÍF`_OF`hNM3F [ZUg~MldzLchUWî õ Rï GRlñ~ð'R ô ï ö C
4976 1
=+.-
1
8
6
+*
.
D 6
D :RE
6
K
E
E
ED
K
L
H
8
6 g4)#/
D
(
!
%
B
7B
E
:
! %
B
Y ^adT[Yr[ UGXZ
F
g
:
! %
B H0'd
B
^
J
! %
BN
H
;
! %
!
J
%
B
1 p/C+1
/ #1
! %
6
! %
! %
N
1
N
E
7B
E
6
J
B
! %
L
B
*L,
B
B
E
J
N
[.\
! %
! %
B J
*-B ,
H0'd
! %
! %
B
B
! %
;
H K
B
9 4 p4
ZT[
_ Y
B
ZgUG K
:
! %
B
UXW.Y
D
E
! %
Y Y bpU
-8
Y \ Y^[2TZ
JY
& !" #
! %
$ % !" & (
' *) ,! +7%
!
%
! `%
D4« 35-'«0 4s~¾f6 Á@‹Á@ºO ˆY}†…rxz‡ÆvGu`‚’x®}xzÊ`ˆÔ¯fˆYÙ[|fx®}†ˆÑ[u#¼ u`|Òy9‚’¾f|œ}†wcˆY}xz‡½}†ˆY|[‚ru`…ÖÙ[ˆlÇ¯ù³e¼x€}†w/.‘³0º
e
n21
M
k
C& B
n
O#+
7
/ + 174)*(*),+.-
épdÇkfFQhcçœg~PeZGF:LœçfFQ_O÷Wl\L[LfMYEGdÇhUkÖXgfhÔê'F^g‹çfLNdÇIUFQIÄêcì,_OFQkNZGPegf_lddehGkÖMlEUFLc_OdÇFQhcMYg~MOdÇLNh,]'gf_lM
5gfhUIÕMYEGF½IGd ‘ZUWOdÇç[dzMì9]UgN_OM ! L~HgÄIGd ™Z'WOdÇLNh9MlFQhUWlLN_ ÿ FPeI Rë3dÇMlE<IGd ™FQ_lFQhcMXLNZG÷
]GPzF`IÚF [ZUg~MldzLchUWQCUV3EGdÇW*]U_OLcêGPÇFQ\ EUgNW3ê'FQFQhg~Pe_lFQgfIUìÖXLNh'WOdeIGFQ_lFQI½dehÕî€ï R ô ñ ö C LfMlF@MlEUgfM
MlEGFÖ_lFkcZGPÇgN_Od QgfMOdÇLNhÈL~H¹MlEGFÖIGd ‘ZUWOdÇç[dzMì ÿ FQPÇI !7XgNhÔêDFÆEUgNhUIGPÇFQIÐë3dzMYEÕXPegfWYWOdeXçfFQXMOLc_
_OFQkNZGPegf_ld `g~MldzLchèpTé*K W^î ñ~ó'Rlñ 'R ô ïNR ôNõœö R™ëEGdeX#EÐ\ZUWlMEULœë­FQçfFQ_WYg~MOdeWOHþì,MlEGF%\^gœûGde\ZU\
]U_OdehUXdÇ]GPÇF,dehtLc_lIUFQ_^MOL9]U_lFQWlFQ_lçfFÚMlEUFÄFdÇkfF`hNçœgfPÇZGF,]DLNWldzMldzçNFQhGF`WlWQC ÐFÄXgfh MYEGFQhtHþLGXZUW
LNhÚMlEGF:_OFQkNZGPegf_ld `g~MldzLchÖL~H
MlEUF@LN_ldzF`hNMYg~MldzLchÖHþF`g~MlZ'_OFNRUdSC FfCDMlEGF_lFkcZGPegf_ld `g~MOdÇLNhÖø'Lœë MlEUgfM
\:dehGde\d QFQW3MYEGF¬HþLfPÇPzLœë3dehGk '÷SHJZUh'XMOdÇLNh'g~P
\
Ç
d
h
ú 5:ü ú 5 ü T " ñ ú 5 * 5 ü ";$
9
8
2 &
2
3 AG( M* / 0 32 ìIUF ÿ hGdÇMOdÇLNhRNi ú ü
ú ;ü : C æ MYW¹MlgNhGkfF`hNM¹WY]UgfXFg~M deW i ú ü =<?> ú ü R[ëEGF`_O@F <A> ú üIUFQhGLNMOFQW
dzMYW »dÇF@g~PÇkfFQê'_lg'RcMYEGF@çfF`XMlLN_¹Wl]'gfXF¬LfH B - )
#C'V3E[ZUWRDgfhcì^ø'Lœë Lch
ú i ú ülüpWlgfMOdeW ÿ FQW3gfh½F [ZUgfMOdÇLNh½L~H
MlEGF¬HþLc_l\
ëEGF`_OF C ú <A> ú üOü ú i ú ülü
ú ï`ñGü
30 2 V3EGFkc_lgNIGdÇFQhcMø'Lœë HþLc_*MYEGF_lFQWlMl_ldeXMOdÇLNhÄL~H ÐMOL ú i ú üOü.ë3dzMYE
_OF`Wl]DFQXM.MlL%dzMYWêGdz÷’dehcçœgf_ldÇgNhNM¹\FMY_OdeX D@deW¹kfdÇçfF`h½êcì ú WOFQFÆî ö ü
*
* *
ëEGFQ_lF FE E * E IGFQhULfMOF`WMYEGFÚkfFQhUFQ_Yg~PÇd QFQI »dÇF½ê'_lgNX#í~FMYWR gfhUI
ú ü!dÇW¹MYEGFZUWYZUg~P‘kc_lgNIGdÇFQhcM
ú 5 5 ‹ü IGdÇç ú 5 ü 5 j
H
08
!
`+17/
46X1
!
./
%Q%
D
E
6X1
=+.-
1
E
J
4
EC
_ TY
_ 9KAK0YpUGXb
1
*Q
'
6
J
K
1
1 +*
E
1
'
ZgUGXb Yr_
K
1
D D :
4976 1
E
J
E
1
D %
!
J
BGF
D :
4
'
LK
1
=+.-
D D
E
E
'
E
E
E
E
GIH Z=J5R L
6LQR
Z KNMPOje
"
*
Ãͅ#³J³ 'ºK@³ 'ººIi
ih
ih
*
D
!
³ TUœ³WVͺºSX
(J SR KOaAN
9h/Rk
5
QPSR
1
K
ýcdehUXF ú i ú üOüYR­ë.FÈEUg‹çNF R.ë3dzMYE ú <A> ú üOüYCDV3EGFWYí~FQë¹÷rWlìG\^\:FQMl_ldÇX\^g~MY_OdzûÆHJZUh'XMOdÇLNh deW3MYEGFQhÚdeIGFQhcMOd ÿ F`IÚHJ_OLc\ MlEUF
IGd™FQ_lFQhcM3FûG]'_OF`WlWldzLchUW.L~H MlEGF ÿ _YWlM.çœgN_Odeg~MldzLch ú IGFMYg~dÇPÇW3dehÕî ö üYC
¬
i
ü
F
U
û
]
JKLM 3 OQKL 2 ihi ú ülR‹ë.F.EUg‹çNF
ú
ëEGdeX#EÚìcdÇFPeIUW3IGde_lFQXMlPzì½MlEGFHþLNPzPÇLœë3dÇhUkde\^]GPÇFQ\FQhcMlgfMOdÇLNhÚL~H FÍC ú ï`ñ[ü
FûG] * " úïô ü
;RHS
QK $=2 *LNMOFMlEUgfMpdeh%MlEGdeW¹XgNWOFNR~HþLN_ ô ô WlífFë¹÷WOìG\^\FMl_ldeX\^g~Ml_ldeXFQWQRfMYEGF¬\gfMl_ld€û
FûU]'LchGFQhcMldÇgfPXgfhÚêDF@FûU]U_lFQWYWOF`IÆë3dÇMl!E & $=
* & & * ú =<?> úSô üOü
FûU] ú ü T WldÇh T ï * X LNW ëEGF`_OF * gfhUI î ö CV3EGdÇW¬F [ZUg~MldzLchÈXgNhÈêDF%ZUWOF`IÄMlLÚde\^]U_lLœçfFMYEGF%XLc\]'ZGMlgfMOdÇLNhUgfP
FÖXdÇFQhUXìÖL~H
MlEUFhc& Z'\:F`_OdeXgfP‘dÇ\^]GPÇFQ\F`hNMYg~MldzLchÆLfH F DC ú ï ô ülC
D?EHG M ;KL OI] ;
Q 2 V3EGFpHJZGPzPU_lFkcZGPegf_ld `g~MOdÇLNh¬]U_lLGXF`WlW»L~HDgIGd ‘ZUWldzLch
MOFQh'WOLc_ ÿ FPeI RUZUWldÇhGk%gNhÆLc_OMYEGLfkNLNhUgfPDøDLœëù_lFQgfI'W.gNW.HþLfPÇPzLœëW
ïfC¹bFMY_OdÇFçNFMYEGF:Lc_OdÇFQhcMYg~MOdÇLNh ÿ FPeI 5 gNhUI,MlEUFIGd ‘ZUWOdÇç[dzMì ÿ FQPÇI ! LfHpgÖMOF`hUWlLN_ ÿ FPeI
ñGC¹è­_lRGLGd’XC FQFNWYC W­MlEGF¬LN$ _ldÇFQhcMlgfú MOdÇLNü h ÿ 5FQPÇI ú 5 ü$! ë3ú dzMYü EÆ5 Lcú ZU_.ü LNC _lMlEGLNkfLNh'g~Pz÷rXLNhUWlMl_Yg~dehGFQI^\^g~MY_Odzû%ø'Lœë
ú ï‹ñ[ülC *LNMOFMYEUg~M­LNhGFEUgNW!MlLMlgNí~F*XQgf_lF3L~H‘MlEGFhGLNh[÷ZUhGd [ZGFQhUFQWYW!L~H‘MYEGFLN_ldÇFQhcMlgfMOdÇLNh
ÿ FPeZI 5RfgNW!\FQhcMOdÇLNhUFQIdÇhÄî€ï ROðUR ô ñ ö C~j
PÇdÇ]U]UdÇhGkLNhGF3FQdzkNFQhcçfF`XMOLc_ " ! ú gXLfPeZU\^hL~H
5:ü IULcF`WphGLNM­X#EUgNhGkfF3MYEGF*MlFQhUWlLN_QRNê'ZGM.\^g‹ìg ™FQXM­MlEGFgfhGdeWlLfMl_lLN]UdÇX3_lFkcZGPÇgN_Od QgfMOdÇLNh
]U_lL[XFQWYWCDV»L%LœçNFQ_YXLN\FMlEGdeW*]'_OLcêGPzF`\ÚR'g^PzLGXQg~P‘FdÇkfF`hcçfFQXMOLc_3g~PÇdzkchU\FQhcM]U_lL[XFQWYW¹dÇW
\^gfIGFpêDFHþLc_OF­gf]U]GPÇì[dÇhUkMlEGF­èpTéÄLNh¬F`gfX#E¬MlFQhUWlLN_‘LfHUMlEGF ÿ FPeI C`V3EGFphGFQdzkcEcêDLN_ldehGk
FdÇkfF`hNçNFQXMOLN_¹IGde_lFQXMldzLchUWgN_OFgfPzdÇkNhGF`IÆë3dÇMlEMYEGFXQZU_l_lFQhcM3LchGFfR'êcìÚXLNh'WOMY_lgfdÇhGdehGk^MlEUF
IGLfM]'_OLGIUZUXM3ê'FQMë­FQFQhÚMlEGF`\ MlLÖê'F]DLNWldzMldzçNF
$# &% ú ü " ! ú #Íü WOdÇkNh " ! ú ü ' ( ! ú #Íü " ! ú #Dü
ëEGFQ_l)F % ú ü.deW¬gÆhGFQdzkcE[ê'Lc_lEGL[LGIL~H C‘V3EGdeW*PÇLGXg~P LN]DFQ_Yg~MldzLchÄg~PÇPÇLœëWMOLÚgfXM*LNhUPzì
LNhMYEGFLc_OdÇFQhcMlgfMOdÇLNhÆHþFQgfMlZU_lFL~HMYEGFMlFQhUWlLN_YWCDV3EGFde\]DLN_lMlgNhUXFL~HMlEGdeW*gfPzdÇkNh'\:F`hcM
WOMlFQ]ÚdeW3WlEGLœëh½LNhÚj
dÇk'CGòNXfC
ô C¹j
dÇhUgfPzPÇìfR]U_lLGXF`WlW:MlEGF,IGd ‘ZUWOdÇç[dzMì ÿ FPeI ! ë3dzMYEtgÔXPegfWYWOdeXÆçNFQXMOLN_WYX#EGFQ\FfR
gfWdeh
î ôcõ‹ö
# ú# # Oü T IGdzç +ú * ! # Oü
*
ëEGFQ_lF * dÇWg%\gfMl_ld€ûÚMlEUgfMIU" _ldzçNF@MlEGFIUd ‘ZUWldzLchÚ]'_OLGXF`WlW*gfhUI\^g‹ì½XLNhcMlgfdÇhWlLN\F
.¹]UEcì[WldÇLfPÇLfkfdeXgfP™dÇh[HþLc_l\^gfMOdÇLNh‘C
Wë­FXQgfh,WlFFdeh,j
dÇk'C'òDR'MYEGFMlFQhUWlLN_ ÿ FPeIÄWlFFQ\^W*ë­FQPzP _OF`WOMlLN_lFQI‘C'V3EUF ÿ hUgfP·_lFQWYZGPÇMdÇW
XPÇLNWlFQ_3MlLÖMlEGF:LN_ldzkNdÇh'g~Pde\^g~kfFNRDgNhUI,IGL[FQWhGLfMWlZ ™FQ_HJ_OLc\ FQdzkNFQhcçœg~PeZGFWlë­FQPzPÇdÇhUk'C LfMlF
MlEUgfMMYEGFÄ_lFQWlMOLN_Yg~MldzLch9L~HMOF`hUWOLc_LN_ldzF`hNMYg~MldzLchUWë.gNW:dehGdÇMOdeg~PÇPzìt]U_OLc]'LcWOF`I deh î ðURQï R ô ñ ö
ZUWOdehGk%WldÇ\dÇPÇgN_3XLNhcMldÇh[ZGLcZUW.ø'LœëW¹êUZGM*IUd ™FQ_lFQhcM3h[ZU\FQ_ldÇXQg~P‘dehNMlFkc_lgfMOdÇLNhÆ\FQMlEGLGIUWQC
B
Y^U
bmWd e
SLd d e
J
Q
1
6 g4)#/
1
N!B
1
J
Q
1
J
E
B
!
%
B
4
7B
E
:
! %
B
(
K
! %7
3
d 9 \XJYr_ merdKAJ
E
Z<
H
6
6
+ 1
/ #1
J
p6 `9 4 p4
.N
H
6
1 p/
6
H
E
6
6
E
7
B
8
E
E
J
A
E
(8
H
X
N !J
E
cK
D
Z
D :
E
D
aXd9
28
H
! %
F& !
% ! W !$`% 9 W!FF ' ) ! `6 % !$! &% %")9 W !F FS F !F' )
) S F !F `
6 Í« D« .…r}†wNu`¿Qu`|[yDÑcu#¼tuQ|%y¬‚’¾f|œ}†wcˆY}xz‡ ¶ }†ˆ§|c‚ru`…Ù[ˆYz¯UÂ
G M>
&
r/ + /
0 +.-
4)
»V Lg‹çNLfdeIMlEUFFdÇkfF`hNçNFQXMOLN_ g~PÇdÇkNhU\FQhcM!WlMOF`]hUFFQIUFQI^êcìMlEUF]U_OFQç[dzLcZUW\FMlEUL[I ú ï`ñGülRœë.F
]U_OLc]'LcWOF3EGF`_OFg@Wlde\]UPzF3ë¹g‹ìL~H_lFkcZGPÇgN_OddehGk¬IGde_OF`XMOPÇìMlFQhUWlLN_
Lc_OdÇFQhcMYg~MOdÇLNh'WC æ MpXLNhUWldeWOMYW
dÇhgf]']GPzì[dehGk%LNhÚMYEGF@dÇhUdzMldÇgfP»MOF`hUWlLN_ ÿ FQPÇI,gNh
>= RDdSC FfC'g%_lFkcZGPegf_ldQdÇhGk:ø'Lœë
MlEUgfM­]U_lFQWlFQ_lçfF`W!MlEUF*MOF`hUWlLN_.IGd ‘ZUWldzç[dÇMOdÇFQWQRNëEUdzPÇF_lFkcZGPegf_ld QdÇhGk@MYEGF*MlFQhUWlLN_­LN_ldÇFQhcMlgfMOdÇLNhUWQC
3 ?G 3]* /10 32 ÐF ÿ _YWOMXLNhUWldeIGFQ_™MYEGFpEGLc\:LNkfF`hGFLcZUW‘Wl]'gfXF ú ü
Èi ú ü L~H»gfPzPÍMlEUF\^g~MY_OdeXF`WpLc_OMYEGLfkNLNhUgfPzPÇìF [ZGdÇçœg~PÇFQhcMpMlLgWOìG\^\FMl_ldeX
\gfMl_ld€û C æ Hg~PÇP¹MlEGFçœg~PeZGF`W^L~H EUgfI<MlEGFÄWYgf\FÚFdÇkfF`hNçœgfPÇZGF`W ú MlEGF,WYgf\F,gfWMlEUF
\gfMl_ld€û ülR'ë­FXLNZGPeI½\LGIGFQP»LNZ'_3XLNh ÿ kNZU_Yg~MldzLch½WY]UgNXF@gfW ú ú ülülC *Lœë.FçfF`_R[dzH
ë­F¬g~PÇPzLœë MlEGF¬FdÇkfF`hcç‹gfPÇZUFQW.L~H MOL^çœgf_lìÖWY]Ug~MldÇgfPzPÇìfR[ë.FhGFQFQI½MOL^dehNMY_OLGIUZ'XF¬gWlPÇdzkcENMlPzì
\:Lc_OF¬kNFQhGF`_OdeX\^gNhGd€HþLNPÇI
ú ü ú ü
ú i ú üOü CUjÍ_OLc\ MlEGF@Fû[÷
]U_OF`WlWldÇLNh%LfHdzMYW­MYgfhGkNFQhcM­WY]UgNXF
ú ü î 3ö ú <A> ú üOü ^ú MYEGF »dÇF
êU_lgNX#í~FQMlW@î ö XLN_Y_OF`Wl]DLNhUI'W­MlL%MlEGFXLN\^\ZUMlg~MlLN_î E@ö E * E ülR'MlEGFFûU]'F`XMOF`I
>=øDLœëW3\ZUWlMWlgfMOdeW†Hþì
ú Yü î ú Yü ö ú Yü ú <A> ú üOü
_^dT_IaY b^ULZ `+17/
46X1
./
J
6X1
1
d
+.-
E
'
D
5
"! D % E
Q
'H
"! D % EC
J
:
D :
E
:
: J
J
/
1
4
'
1
'
E
_rdT_
aY bpUGLZ
D D
cK
1
ü ú IGF ÿ hGF`I½êcì ú ï ülülR[ë.F
0 32 dÇçfFQh½MlEUF , §÷rkN_YgfIGdÇFQhcM ÅLNh ú
WlEGLœëùdÇh9î ö MYEUg~Mg^hUgfMlZU_Yg~P\dehGdÇ\ddehGk^ø'Lœë HþLN_?,Lch ú ü!deWIGF ÿ hGF`IÚêcì
ú ïò'ü
* ú T ü
ihGFXQgfh½g~PeWOLLNêGMYg~dehÆgWlZUdzMYgfêGPÇFdehcMOFQkN_Yg~MOdÇLNhÆWlX#EGF`\F*HþLc_­F ÍC ú ïò'ülRGIGF`_OdÇçfF`I^HJ_OLc\ MlEUF
FûU]U_lFQWYWOdÇLNhÆL~H
MlEGF@FûG]DLNhUFQhcMOdeg~P\^gf]½LNhÚMYEGF@LN_lMlEGLNkfLchUg~PÍkN_lLNZU]R[gNhUIWlZ'X#EÆMYEUg~M
Oú ü §ú ü$ Yú ü #ú ü ë3dÇMlE
ö úïõ ü
;RIS
§ú ü S î R
4976 1
=+.-
6
D N
D :
J
!
B
%
7B
E
E
^
B
! %
B
"! D % =K
! %
H
+*-,/.<,
! %
E
B
! %
B <!$#&%
7B
!$#
% !$#&%
K
& !" #
! %
!
%
!$`
% WF S ) F
' ) ! D %
D«'«Umr‚ru`‚rvGˆ#‡l}†…†yDÑ[u#¼<u`|%y‚’¾N|œ}†wNˆY}xz‡ *}†ˆ§|[‚ruQ…!ÙcˆYz¯'Â
D?EHG M ;KL I 3 2 é [ZUg~MldzLch ú ïòUü™ë¹gfW gf]U]GPÇdÇFQI:MOL¬MlEGF3ZUWYZUgfP[hULfdeWOìNR‹WlìGhcMlEGFQMOdeX
MOFQh'WOLc_ ÿ FPeI‘C'V3EGdeW¹FûU]DFQ_ldÇ\F`hNM3deW¹dÇPzPeZUWlMl_Yg~MOF`IÚdÇh½j
dzkDC õ C
W¹FûU]DFQXMOFQIRUMlEGF@_lFQWYZGPÇMlW3gf_lF¬WOde\dzPegf_¹[email protected]êGMYg~dehGFQI½ë3dÇMlEÚMlEGFIUFQXLc\^]'Lf÷
WOdÇMOdÇLNhÔgfhUI,MYEGFLN_lMlEGLNkfLNh'g~P»XLNhUWlMl_Yg~dehcMlWQC Lœë­FQçfFQ_QRUMYEGFXLN\^]UZGMYg~MldzLchÈXLcWOMdÇWWldzkchGd€Hµ÷
dÇXQgfhcMOPÇìÚ_lFQI'ZUXF`I ú hGL½PzLGXQg~P·gfPzdÇkNhUFQ\FQhcM*WlMOF`]UWgN_OF:hGFF`IGFQIÄgNhcì[\Lc_OF¬HþLc_*_lFkNZUPÇgN_Od dehGk
MOFQh'WOLc_­Lc_OdÇFQhcMYg~MOdÇLNh'WüYC[V3EUFè­Té ú ïQòUü!gf]']GPzdÇFQW3IUdÇ_lFQXMOPÇì%LNh½MlEGF¬LN_ldÇkfdehUg~P‘\^g~MY_OdzûÆXL[FHµ÷
ÿ XdÇFQhcMlW C
[ã †ß 9ápÞ Ý ·ß ß
ÔFÈE'g‹çfFMOF`WOMlFQI MlEUFÄ]U_OLc]'LcWOF`I IGd ‘ZUWldzLch MOFQh'WOLc_Ö_OFQkNZGPegf_ld Qg~MldzLch è­TéK W ú ðGüYR ú ï‹ñ[ülR
ú ïò'ülR·LNh9gÄ_lFQgfPï`ñ tï`ñ õ ó,T¬V.÷ ,b æ IUg~MYgfWlFM %L~H3MlEUF½êU_Yg~deh ú j
dÇk'C·óNgUR ê™ülCih
MlEGFPzFHþM.WldeIGFLfHFQgNX#E ÿ kNZ'_OFNRNë.F_lFQ]U_lFQWlFQhcM­MlEGFMOFQh'WOLc_lW.gfW­FPÇPzde]UWlLfdeIUWQRNëEGdÇPÇFMYEGF_ldÇkNEcM
WOdeIGF:WYEGLœëWMlEGFXLc_l_lFQWY]'LchUIGdehGk ÿ êDFQ_YWQRDMY_lgNX#í~FQI,êcìÚHþLfPÇPÇLœë3dÇhGkÆMlEGF^\^g~dehÄIGde_OF`XMOdÇLNhÄL~H
FQgfX#EtMOF`hUWlLN_QC
V3EUFQWlF ÿ ê'F`_lW%WYEGLœë MYEGFÄ]Ug~MYE HþLNPzPÇLœë.FQI êNì<MlEGFë¹g~MOF`_%\LfPÇFQXZUPzF`WCV·L
\gNí~F¬ç[dÇWYZUgfPzd QgfMOdÇLNhÖF`gfWldzF`_R[LchGPzìÆLNhGF@WlPzdeXF¬L~H MlEGF]'_OLGXF`WlWlFQIÆçfLNPÇZU\F¬deW3_OF`]U_OF`WOF`hcMOFQIC
V3EGFXLN\^]UZGMYg~MldzLchUW¬EUg‹çfFê'FQFQhÈXQgf_Y_OdÇFQIÄLNZGMë3dzMYEÔgÆèFQhcMOdeZU\7ï E ]'_OLGXF`WlWlLN_QR»ï L
b 9R gfhUIÔMlEUFÆXLc_l_lFQWY]'LchUIGdehGkXLN\^]UZUMlg~MldzLchÈMldÇ\F`Wgf_lF^kfdÇçfFQhÈHþLN_MlEGF^HJZGPÇPpçNLfPeZU\F
_OF`WOMlLN_Yg~MOdÇLNh ]U_lLGXF`WlWQC ÐFÐhULfMOdeXF`IÒMlE'g~MÆMYEGFÈkNFLGIGF`WOdeXÄWlMOFQ]ùgf]U]'_OLcgfX#E g~PÇPzLœëWÖMOde\:F
WOMlFQ]UWMOLÚê'F^_OFQPÇgfMOdÇçfFQPzìEGdÇkNE‘R™gfhUIÄçfFQ_lì½HþFëÅdÇMOFQ_Yg~MldzLchUW*gN_OFhGFF`IGFQIÄdÇhÄ]'_lgNXMOdeXFNCÍV3EUF
U÷’HJZUhUXMOdÇLNh ZUWlFQI<HþLN_^MYEGFQWlFFûU]'F`_Ode\FQhcMlW^deW^MlEUF lEcìG]'F`_lWYZU_OHJgfX3
F HJZUhUXMOdÇLNh‘R ú ü
ñ ï T * ñÕ]U_lLN]DLNWlFQI deh(î ö C­V3EGFÈ_lFQWYZGPzMYWÖë.FÄLNêUMlg~dehGF`I XPzF`gf_lPzìtdzPÇPeZUWOMY_lgfMOF`WÖMlEUF
ê'F`EUg‹ç[dzLc_­LfH MYEGFIGd ÍF`_OF`hcM\:FQMlEGLGIUW
V3EGFWlì[\^\FMY_OdeX¬]'LcWOdÇMOdÇçfF@IGF ÿ hGdÇMOF¬ø'Lœë ú ðUü!MOFQh'IUW3MOLÖWlë.FPÇP‘FdÇkfFQhcçœg~PeZGF`WC
V3EGF*Lc_OMYEGLfkNLNhUgfP'XLchUWlMl_Yg~dehGFQIø'Lœë ú ï`ñ[ü ë­Lc_lí[Wë.FPÇPÍë3dzMYEÖgPÇLGXg~PÍg~PÇdzkchU\FQhcM­WlMOF`]
ú j
dÇk'C'ófF~ülRUê'ZGM3HJg~dÇPeW¹LfMlEUFQ_lë3dÇWlF ú j
dzkDCUófI™üYC
V 3EGFdÇWlLNWY]'F`XMY_lgfP»ø'Lœë ú ïò'ü¹EUgNWg [ZGdzMlFWlde\:dÇPegf_¬ê'F`EUg‹ç[dzLc_RÍêUZGM¬deW\LN_lF:XLN\^]UZ[÷
MlgfMOdÇLNhUgfPzPÇìÖF ÖXdzF`hNMQC
Ã
wcˆyQ²N}†wNu`…†‚¼
u`²fz¯Ä®x€Ï‹ˆ:}†u%}†wcyQ|c
vc܅uʜ‹xzºO¯fÂNx€|cӿƈ3²[y‚Ç‚r¼u¬x€}†}†wcwÄyQ}†|Nwcψ:o¶3ÂNà „[{Su`Ü^²N…o­|Nm*x€ˆ§Ï …
¯NyÉefuQ}O yÄ{S…­„
wf³e»xz}†‚!wNÜ%xzʜ‚*yxz|c‚r¼ ²[¿u`yxz|ԅ®xzÏÀ§yQy¼|c}x€¯ yQu`‚¬|^fv[Â}†{ uœy­…ru}·xÇ´‘yOÁ®Du€¾Ô®ˆ§xz|[|N‚r‚ˆÚ²Npvc³JxzvGs ˆl¼.u`…r!f„ }†Âˆ§¯Ä{ ˜¸·¾q3q­º3o ÉÇu` …
6
1 p4)
./ 7) p/
/
R I3
I3
E
6
n
épçfF`h d€HMYEGFÈ]UEcìGWldzLNPzLNkfdeXg~P*ç‹gfPzdeIUgfMOdÇLNh L~H@MYEGFQWlFÔ_lFQWYZGPÇMlWÆ_lFQ\^gfdÇhUWÖMOLtêDFÈIGLchGFfR.LNZ'_
\:FQMlEGLGIUW@WlFF`\>MOLÄXLN_Y_OF`XM\:LcWOM@gN_OMld€HJgNXMlW ú IUZGF^MOLMYEGF%dÇ\^gfkfF^gfX [ZGdeWldzMldzLchÔ]U_lLGXF`WlWü
gfhUIÄ_lFMY_OdÇFçNF@MlEGF\^g~deh,kfPÇLNêUgfP·WlMl_YZUXMYZU_lFQWLfHMlEGF ÿ êDFQ_*hUFMë.LN_YíDC æ M*Lc]'F`hUWhUFëÅ]'F`_†÷
Wl]DFQXMOdÇçfFQW¹MlLÖXLchUWOMY_lZ'XM3gfhÚgfXQXZU_Yg~MlF ÿ êDFQ_*\gN]½\LGIGFQPL~H
MlEGFê'_lgfdÇh‘C
ÔápÞ*ä lã [å†á­Þ
æ hÖMlEUdÇW3]UgN]'F`_Rcë.F]U_lLN]DLNWlFQIÆgkNFLN\FQMl_ldÇXgf]U]U_lLNgNX#E^MOL^XLchUWOMY_lZ'XM.kfFQhUFQ_Yg~PUøDLœëW.gNXMO÷
dÇhGk@Lch%XLchUWOMY_lgfdÇhUFQI\gfMl_ld€û[÷rçœg~PeZGFQIde\gfkfF`WC ÐF*g~PeWlL@dÇhcMl_lLGIUZUXFQI^h[ZU\FQ_ldÇXQg~P'WYX#EGFQ\F`W
MlEUgfM
h'g~MlZ'_lgfPzPÇì ÿ M
dÇhcMOLMlEUdÇW·HJ_Ygf\Fë.LN_YíMlEUgNhUí[W·MlLMYEGF3ZUWlF­LfH'FûU]DLNhGF`hNMldÇgfPG\gN]UWQC‹V3EUF
FÖXdÇFQhUXìÖgfhUIÆçfF`_lWYg~MldzPÇdzMì^LfH»MlEGdeW¹WOFQMOMldÇhGk^EUgNW.êDFF`hÖdÇPzPeZUWlMl_Yg~MlFQIÖë3dÇMlE½MlEUF]U_lLNêUPzF`\ L~H
IGd ‘ZUWldzLchMlFQhUWlLN_·_OFQkNZGPegf_ld `g~MldzLch‘CV3EU_lFF.IGd ™FQ_lFQhcM
_OFQkNZGPegf_ld dehGk¹ø'LœëW·ë­F`_OF!dehcMl_lLGIUZUXF`I
ú Wlì[\^\FMY_OdeX^]'LcWOdÇMOdÇçfF^IGF ÿ hGdÇMOFfR»LN_lMlEGLNkfLNh'g~P’R'deWOLcWl]DFQXMl_Yg~PSülC»ýcLN\FL~H.MlEGF`\ kfF`hGFQ_Yg~PÇd F
gfhUI<FûGMOF`hUI ]U_lFç[dÇLNZUW:ë­Lc_lí[WdÇh<MlEGdeW ÿ FPeI‘C ZU\F`_OdeXgfP­FûG]DFQ_lde\:F`hcMlWWlEGLœë ]'_OLc\:deWO÷
dÇhGkÕ_lFQWYZGPzMYWFQçfF`h9d€H†RgfM:MYEGdÇWMldÇ\FfRhGLÕ]UEcìGWOdÇLfPÇLfkNdÇXQg~Ppg~÷r]'_OdÇLN_ld­í[hGLœë3PÇFQIGkNFÆEUgNWêDFF`h
MlgfífFQh,dehcMOLgfXQXLNZ'hNM ú HþLc_dehUWlMlgNhUXF:dÇhÈMlEGF%X#EGLNdÇXFL~H.gÆWYZGdzMYgfêGPÇF U÷’HJZUhUXMOdÇLNh™üYC‘jDZGMYZU_lF
IGFçNFPÇLN]U\FQhcMYW¹ë3dzPÇPdehUXPeZUIGFgN]U]GPÇdÇXQg~MOdÇLNh'W­MlL%LfMYEGFQ_3XLN\^]UZGMlFQ_¹ç[dÇWldÇLNhÚ]U_OLcêGPÇFQ\^WC
T
-8
! % =
,% S 5! F !$&
% ! F @) W!F S
' ) %! ! `6 %( ! D )% F F !F <& F
F*
FW 2! %!$) & F
`%
!
%
!$`
% ! F ) IF!FF
' * ) %/
! L! ]6 %5! )D % F F ! 6m &
!$`
% ! F =) W F ' )(
X!,+7%:! 6 D D %
!%
! S I) F
' )(
! D %/! 6 D %
‡lu`|[D‚’« }†'…†y«
x€|copˆ#ˆ#¯y­Á@¯~ˆlx€}†°Uwc²cu~‚’¯cx€u`‚¹|ijez}†yQˆ§‚’|[}­‚r|~uQ²N…@Á¯cËGyˆ§}Oy`…†‚ ‚rˆY…}ֈYvc³µ…¶3ˆ#Ârˆ§{S|œÜ^}!op}†wcm†ˆ¹º3‡Y…u`ˆ§¿`Á@²fvNÇy²N…r}Ox€yÀ#}yx€}uQx€|:u`|'}ƒ x€Á@²cˆ‚’x€ºO|c ¿½}†wN…ˆ§ˆ:¯fx®°Uˆ§…ˆ§|œ}
à Þ*ä
`Â3Ø»ÁÂy}qpx€u`€ÊQ|%yQ……ˆ§ˆ#ÀQ‚rvGƒ‘ˆ#o*‡O}™xz¶¹|N¿@ˆ§…rxzxzÁ‡OwNyˆ`¿`ƒˆf¯f‘xz‚ÓڇYuQˆY|~xz‡O}Ï`x€|~ˆ§²N…r}#x®}ƒx€ˆ#yQ‚Y|cÛ'¯q f´»Â·¶¹sy¸ |[‡†yQwc|cˆ§¯%À`½‚‡§¶¹y€ˆ§ˆY|c{S‚r‚rvcˆy`¯~‡Yˆ¬xz‚rv[ËcyQy`…r‚rx®ˆ#}S¯%¾,yÁvcyQvNv,…u‹ˆ#y`‚’‡†}wDx®{ Â
"!#%$&'(')*+,-./)'02143576,
!8
cƒ fÂ
~Â49:+8Â[qp
Á¬ @Ax®}#+BÂ
q $&|N';u`6|f€x€|Nˆ#yQ1Q…pƒ 2Ê`Cfy³ …rxzyºO}ƒ x€`u`yQ|c|~y²c‘yQvN…r…¾ u`ËN2€Dˆ§DÁÅEN ÉÇu`…!xzÁy¿`ˆÁy}O‡†wNx€|N¿N; :*=<4>?*%
fÂÜÚ ˆ§…r}Oy€Á¬x€uNƒ»Ø·Â Ã. wcˆY|c¿Nƒ·sG ¹‚rwcˆ§…§ƒ»y|[¯  sNyvNx€…uN ·yQ…rxzy}x€uQ|[ypvN…u`ËN€ˆ§Á‚yQ|c¯
x€vcÁyQ…ry}¿`xzˆ3yDvc¯~…x€u~°U‡lˆYˆ#…‚ˆ§‚’|œx€|c}xÇ¿y'yQˆ#|c±œ¯:²[vcyy}x€}uQ}†|[ˆ§…‚
|u`|Éeu`…x€Á@ÁvNy®}xzx€‡lu`x®|D}!ÂG‚r²cF&…rÉe$y`HI‡Yˆ§<J‚YÛG35Ã
wc!8ˆp,Ée=…†+8yKLÁ@35ˆY¼
76uQ…
Ï:eƒ yQ|[²N¯|cˆYˆ ÎNyQÁ@vf~zˆ§‚·x€|
ENÂÜÚ ˆ§…r}Oy€Á¬x€uNƒ ÂNsNyvNx€…uNƒ  yQ‚rˆY®€ˆ#‚YƒGy|[¯ ­Â y®€ˆ#‚’}†ˆ§…§Â‘mSÁyQ¿`ˆpx€|cv[yx€|~}x€|N¿N™mSN
qps~m ϋˆY€.ˆY¾œo­ƒfq­ˆ#¯~´x€}†uQƒf…§q­Pƒ O&¯c¯f=2xz‚r+uQ,|=/Ó*1ˆ#!)‚’€ˆY¾QØDKu`R|c:*¿QÁS4yQS5|'35ƒ <4O&~Tp ƒ[v[y¿`ˆ#‚ E 2U2VWE EfÂ'q Ü ´»…ˆ#‚‚Y|ƒUq M3
²NÜ …r}
C~ÂÃ. w[yQ|Æy|[
y'0|[
¯yA€¿`4uQ…r'0x€}†wN¯ ÁK
f‚Y'[PÂÂ'35s~wc
ˆ§!8+8|',!\ H]=+8 K0!^y…r35<_xzy7*6}1x€u`88|c`
yXY!†ƒ $&…ˆ#²c';‚’|c}†6uQˆ #…†yaD}x€Du`Df|ÆÂuQÉ»|cuQ/R|N{þ
ÑG6Wy6}­ x€=Á/Ry'0¿`ˆ3ÉeKˆ#
y'0}†²c…ˆ#-‚*+8!ÛUXÜ^/7u~6¯NˆY
z-‚ Z
b ÂÃ. w[yQ|Èy|[¯ f·s~wcˆ§|'ÂÆÜ%y}†wcˆYÁy}xz‡§y
Á@u~¯NˆYz‚*ÉÇu`…*zu~‡Yy­¯NˆY}†ˆY…Á¬xz|fxz‚’}xLJ¬x€|cvcyx€|œ}x€|c¿‹‚YÂ
ÃDˆ#‡OfwNÂ|Nxz‡§yDopˆ§vGuQ…r} { `ƒN¶¹ˆ§v[y…r}†Á@ˆ§|œ}
uÉÜ%y}†wNˆ§Áy}xz‡§‚Y#ƒ c ØÍq*ƒ~ØÍu`‚!q­|c¿QˆY€ˆ#‚YƒNÜ%yQ…†‡†w
U~Â3´‘ wcyQ…ËGuQ|c|Nx€ˆ§…§ƒ œq­²cËGˆY…r}#ƒœÜÚ zyQ|c‡l{J(
wcK*y5®ÉÇ{S±œ²[
yQ¯N…†y}xLJ…ˆ§P¿Q$&²NzyQ2…rax€
À#,y
}xzuQ+|;y0z¿Qu`'[…rx®}†2wc1Á„ O&‚!ˆ§…†=ÉeyQuQ2²c+…¹
¯'‡Y!,ƒfuQ!,yÁ@*|[1Qvc¯ƒ‹²NʋÜÚ}†uQˆ§€¯Â ²cÁ@xzÁyˆ·…ryÇmy¿Qml²[x€ƒ|c¯Uv[¿f™yÂ.¿`à mSˆ#¼ d| ‚ uOY¯feˆY2V }†+ˆ§e…U=Á¬/œ"ƒ x€*|N21xzD!)‚’D}Efxz‡ Â
f }­x€uQ |@ uQwcÉ ˆlɵ ¯'u`× wN|cuQ‚’}†}†ˆY…†yþƒ[x€|œ¶}
Âc´»Ã…‚ˆ#‡†‚rw~ˆ§…²cʜÁ@x€|cvG¿ˆ§…r„™8 ˆ`€u#ƒ ¼p‚ ÂfyQ„G|cyQ¯@²N¿`q­ˆ§vN…†yQvN‚­®xz‡§yy|[}¯x€u`o*|c‚Âf}†¶¹u3ˆ§mS…rÁxz‡†wcyQˆ`¿Qˆp .´»…ˆYu~u`‡YÁ@ˆ#b‚ˆY‚’}†x€…r|Nxz‡¹¿N m’|œ}†f^ˆ§35¿Q…†=y< {
35
!8==+8KN3g76
eƒ[}†u@yvcvGˆ#y…§ƒ ~Â
Df  u`²fzuQ|Dƒ!¶Â ­Â!q!€ˆYÎNyQ|[¯fˆ§…§ƒy|[¯<sU oÂqp……rxǯf¿`ˆ`Âùq ¿Qˆ§u`Á@ˆY}†…rxz‡§yyQvNvc…u`y`‡†w }†u Q¯
vc¯~x®yQ°U…r²[}†Á@‚’x€u`ˆ§|œ|Æ}}†uˆ§É|[‚r uQu`…*Á@ÁvNy²N¿`}†|Nˆ§…pˆY}sfxz‡‡lx€…ˆ§ˆ#|[‚r‡lu`ˆ`|cƒyQc­|c|N‡Yˆ¬x€Ê‹ˆ§x€Á…†‚’yQx®}S¿`¾ ˆ@ …ˆYu¿`®z²NˆYz¿`yˆ*…rxÇØÍ‚yu`}|cx€u`¯N|DuQ|D®ƒÃ͈#‡†wc|f`Âxz‡§y·o­ˆYvGu`…r}#ƒD¶¹ˆY{
f ÉDz[‚’x€u`|½u`²f}†zˆ§uQ|[|D‚rƒuQ…*¶Á ­y¿`q!|NˆY€ˆY}ÎNxz‡¬yQ|[…ˆ#¯f‚rˆ§u`…§|cƒyQy|[|[‡l¯ÄˆsUx€Á oy‘¿`ˆ#qp‚Y……rxÇm’¯fi| ¿`ˆ`h½q =
…Kjˆ§¿Q²NzyQ
…rx€À#y}x€u`|Ղ_‡†wc$&ˆYÁ@22ˆ¬
=Ée
u`…¬+¯f=x®ÉÇ {
aa'0-jOY2+
!!,1Nj>k=/+,'0a1*1Qƒ `Â
`Â3x€o|NÂ~¿Ö¶¹x®}Oˆ§‚…rxz‡†¯fwcxz‚ˆ`‡Yƒfu`´‘|œ*Â}x€M3|~²Nu`…x®}|Nx€vcˆ#‚Y…Û»uQË[q ‚’}#ÊQƒNyQyQ…r|cxzy¯ }x€u`|cÂNyq­p²NyËGvcˆ§vc…r…}#u` y`.‡†wDvfÂÆ}xz‡§m’yl| UÑ[O&u#=¼92+,ˆ§=‚’/}xzÁ1y!j}x€u`G|:¼!KNwfx®zmWˆ.vc/n…ˆ#<4‚r!,ˆ§…ʜ {
$&22
=
+do$&';6#
pI!,cƒ
ʋuQ€²cÁ@ˆ œƒ!v[y¿`ˆ#‚LU V ~ƒ¹sœx€|c¿‹yvGu`…ˆ`ƒ!¶.ˆ#‡Yˆ§ÁËGˆ§…
aDDC~Â
~ ‚rˆl}@ÂQ„GÁ@y²cˆY}†¿`wcˆY…†u~y`¯N‚ ‚¬yyQ|[|c¯¯Äo}†W wNM3ˆ^ˆY‚’…r}†xzˆ§Ê`…ˆ§ˆY|Du vc…yuQ…rËNxÇy€}ˆ§x€Á^u`|[ÂlyGvcqY…rq&x€|cqs‡lx€vNr€=ˆ#‚Y#ƒœ!
‚rW²N+a…rɵyQ‡Y#ˆ­!nˆYʋuQt€²N}'[x€uQ2|D1ƒ‹L´»OY¶¹¸!2+
× ‚Y
ƒ‹!,!,€ˆ§Ê‹1QˆYƒ
U~³ œºOÛ * b V.EEfƒ'Ü%yQ…†‡†w 2DD ~Â
f  .uQ€²cËÆyQ|c¯ ­Â y|ÖØÍu‹y|DR
´»…ˆ#‚‚Yƒ y®}x€Á@u`…ˆ`ƒcÜ%yQ…r¾~zyQ|c¯'ƒ[‚r>nˆ#‡Yu`|c¯`uˆ#+,¯~x€';}x€uQ6|D#ƒ2D Df!†Â ÂÃ
wNˆ QuQwc| .uQvcϜx€|[‚ c.|fxzÊ`ˆ§…†‚’x®}’¾
8EN  .…†yQ|f€²c|[¯½yQ|c¯  M3|~²N}O‚‚ruQ|D
q­‡§y`¯fˆ§Á¬xz‡.´»²cËN®xz‚rwcˆY…†‚Yƒ aDDWCœÂ  :#`1%O&=2+
!,!"*1)a$&';6#
iI!,NG M¹€²~¼ ˆ§…
2C~\
 c* .ˆY€Á@ϋˆ.yQ|[¯ fÂ[Ü^uœuQ…ˆ`R v6'(xwa./Gy^z')+,]:z!
')!†Â
sfvc…rx€|N¿`ˆ§…§ƒ 2DDENÂ
b  ** My`‡QƒNˆ#¯~x€}†uQ…§A 2@%-4y;'0
!,HP[S5e6!4{%-K[<566 +,#!†Â»Ü%y}†wcˆYÁy}xz‡§y
sf‡lx€ˆ§|[‡lˆ#‚o­ˆ#‚rˆ§yQ…†‡†w^m’|c‚’}x€}†²f}†ˆ¹´»²cËN®xz‡§y}xzuQ|[‚ENÂ[sfvN…rxz|N¿`ˆ§…§ƒ 2D WCœÂ
2U~Â3o M¹x€Á@Á@ˆY!y|[¯Än»s~u~‡OwNˆ§|D .…rx€ˆ§|œ}Oy}xzuQ|Õ¯~x€°U²c‚’x€u`|Èu`…¬wNu¼ }†uڇYuQÁËÈy½vGuQ…†‡Y²cvfx€|cˆ`Â
´»|fÃDxzˆ#…‡§u~‡OywN‡Y}ˆ#|Nx€u`‚xz‚’‡§|^x€y|NUyQ¿N|[o­ƒ¯ˆ§ vGm’u`ÁuQÁ@…ry} vN¿`²Nˆ3}†ˆ§op… ˆ§{ ­vc…~xzˆ#‚’ƒ x€‚ru`ˆY|'|~mƒ~}OsGyyQƒ }|cx€¯u`|D ƒfu`‘Á@q.vN‡§~²N‡Y ˆY}†ˆ§vN… }†ˆ#.¯¬…†}†yQuvNwN‚rvGxz‡§ˆ#‚Y‡lƒxzQyUuQ²cxz‚…‚r|c²cyˆ¹GuQu|É;p´·xz¶¹‚r²[¸·y‚  x€ |u`m’Á@ÁÁyQ¿Q²fˆ {
k
n^o opo
n
k
k
k
n^o o o
]k
Tn
n^o o o
k
o o
kpk
n^o opo
k
l
l
k
n .k
n^o o n
n^o o k
k o
.npopogk
kpk
n
k Tl o
k
kmn
Mk
k
k
l
k
l
k
k
k
k
k pl
k
npopo o Io n
gnpopo o
.npopo o
f¹ÓÓyÂP®M¹}†ˆ§®…px€|c¯N¿Qˆ ˆ§|~.ËG…ˆ§²N…¾~¿N}†Âkˆ§…§35ƒ 2
D '[~Â# S_='08
zÂÖ¯Nˆ .…²f¾~}†ˆ§…*s~}†²c¯fx€ˆ#‚¹x€|,Ü%y}†wNˆ§Áy}xz‡§‚ `Â
aDfÂ3´‘Â#M3u`…|Nvc…u`Ëc‚’}#ƒcoÂf¶¹ˆ§…rxz‡†wcˆ`ƒcyQ|c¯ Â[qp²cËGˆ§…r}#»n­u`|N®x€|cˆ§yQ…!u`vGˆ§…†y}†u`…†‚x€|x€ÁyQ¿`ˆ3…ˆ§‚’}†u`…†y{
}x€
uQ|DLÂU35m’|N=+,OY,12-+
,=/cƒœvc1!\yQ¿`ˆ§_‚ KC2V.* `ƒf´·²Nˆ§…r}†u¹%o!$&xz‡Y2uN2ƒ =²c
|c+ˆ \aD.DU~$&œmS¸·';¸»6¸
Lu`Á@IvN!,²N}†Lˆ§…·s~u~/(‡lO5x€ˆY}’¾œ-Z ƒ
f`Â*Â3¶mSsG¸·Âf¸»Ø™ØÍ¸!yQˆ |N ¿N Âx€wcy;yQ |D ÂÐ
=
Ü^ˆY}†wNIu~>n¯c‚@#yQ|ca¯Ô /y!†vc·vfs~€xzvc‡§…ryx€}|cx€¿Qu`ˆ§|[…§‚@ƒ uaÉD ¯fC~x®Â°U²[‚’x€uQ|ÐÜ^opmlÂÔm’|Èml o 9 uQ²c|c¿fƒˆ#¯fx®{
}†ÓÐuQ…§x€€ƒ ˆY>n¾2yQ1|c¯^8s~u`+4|[3g‚Yƒ
!
~Â +_'0a1*1[/(:6#=+a!
+6z0L>n,/+8]^/5- ,1zQÂ Qu`wN|
~Â3}¶x€uQ |[Ü^‚.²NyÁ¬|[¯%ÉeuQyQ…†‚¯Ð‚ru~yQ‡l|cxzy¯ }†ˆ#f¯ÖÂ
Ê`sfywc…ryQxzyw'} x€u`|c.yvN}vcx€Á…uQyËN­€ˆ§yÁvcvc‚Y[…u#$&Î~x€Á')y')}x€*u`#|c‚¬+,˜¾Ä#vN!)x€ˆ#‡YˆY.¼O&xz‚r*ˆÆ,[‚rÁ@uœuQ/G}†<5wÈ6Ée6²N |[=‡l/ {
>jK
'0+8!†ƒE œÛ CUUaV b ENƒ aD D~Â
fÂ3´‘Â3´‘ˆY…u`|[y~ .…rx€ˆ§|œ}Oy}x€uQ|ù¯~x®°U²[‚’x€u`|c‚Y q&qYq r!
W+a-!t '021 OY2+
!,!,1Qƒ
U~³ œºOÛ ECU2VWE b Uœƒ'Ü%yQ…†‡†w 2DD ~Â
eENÂ3´‘ÂQ´‘ˆ§…u`|cy3yQ|c¯ fœÜ%y®xzÏGÂ'sf‡§y€ˆY{S‚rvcy`‡YˆpyQ|c¯ˆ#¯f¿`ˆp¯NˆY}†ˆ§‡l}x€u`|¬²c‚’xz|N¿yQ|fxǂru}†…u`vfxLJ!¯~x€°U²c‚’x€u`|DÂ
q&q&qJr=!
W+a#!(nO5-
j<_ z!,!Q/G>n+8KW];8 1
+lƒ f³ U‹ºOÛ b DeV b Dfƒ
²N®¾ 2DD fÂ
C~Â3Ø»Âcop²[¯~x€|DƒcsU ¹‚rwcˆY…§ƒ[y|[¯¸!Âc„[y}†ˆ§Á¬xþÂn.uQ|N®x€|cˆ#y…}†uQ}OyÍÊ`y…rxzy}x€u`|^Ëcy`‚rˆ#¯:|cuQxz‚rˆ3…ˆ§Á@uÊQy
y€¿`u`…rx®}†wNÁ‚Y _ S_O&=KWz'G!,8+,Gy­+Lƒ OAb f8Û -CDeYV y^b ~ƒ =a
DD ~ÂYq8!N/'[21[<_ z!"!O yQÁ¬{
b  ‘sNyvNx€…uNt
ËN…rxz¯N¿`ˆ\c­|N x€Ê‹vˆ§6…†‚’x®"}S')¾xwa´·…ˆ#‚‚Y ƒ r=+8`KWÂ8
!Gd35
'[#i>n# a /!O ¹yÁ¬x®€}†uQ|NxzyQ|ÚyQ|c¯
U~Â*sGÂÍsfÁ¬x®}†wDn
.x€…†ˆYyQz¯N¯f‚!x€ˆ§mS|œ|[}‚’}„™x®€}†u#²N¼p}†ˆ­‚Yƒ‘Éeu`qp…p€¿Qopu`ˆ#…r‚rx®}†ˆ#wcyQ…†Á‡†w‚3yx€|^|[¯ Ü% y}†uQwc|œˆ§}†Á…uQyþ}™xzqp‡§yÁ@‘ˆ§sN…r‡lxzx€‡§ˆ§yQ|c|ڇYˆ#Ü%‚Yƒcyq*}†wNˆ§ Á€u~y‡O}w^xz‡§yˆ§¯fx®s~}†u~u`‡l…§x€ƒ ˆY2}’¾œDƒDEN2 DDEfƒ
™
„
fÂ3n*ʜxz»‚’x€u`sf|'u~‡†P wcˆYqY|Dq&ƒ‘q oÂr*=M¹x€#Á@!8Á@+aˆYþƒ‘ny|[¯,Go'0Â2Ü%1y®OYzy`¯~2xJ+
Â,
!,!,q ¿`1ˆ§XuQ:Á@6#=ˆY+8}†…rxz‡§#y!,!,ÉDž†yQQÁ@ˆYN¼ O&u`y;…ÏqÉeuQ,…!8€,u#/R¼ '[€ˆ§2ʋ1ˆY 
O&=2+
!,!,*1Qƒ]Uf³œºOÛ eV. fƒ 2DD ~Â
Df ­Â`ÃÍyQ|c¿fƒ ‹sfyQvfxz…ufƒQyQ|[7
ʜ 0xzy­$&wcyQ';…Á@6uQ|N
xzn‡·Á "y!v[-‚Dc}†ƒ wN ˆ§¯ bu`…r³ ‹¾@ºO ÛQÛ aÃ
EyQwcDe‚rVˆ
ˆY®¯fzbˆ§x€‚Y…QÂcˆ#ƒ'‡l¶.„[}x€ˆ§x®u`°UËc|¬²c…²c‚’¯fxzyQuQx®°U…r|¾ ²[u‚’É[x€u`¿`|ˆY~|c‡§Â ˆ§y`…†‚ryˆQ[5 ¯Nr yK*}O5y!u`|
|Nu`|f{JÑ[y}ÍÁyQ|Nx®*ÉÇuQz¯c‚ fÂqÂGÃͅuQ²cA
Ê ˆ`Âp¶.x®°Uˆ§uQÁ@u`…vcwfxz‚rÁ‚!¿Q…u`²Nv[‚.y|[¯^vcy}}†ˆ§…|%Áy}O‡Owfxz|N¿¬x€|^xzÁy¿`ˆyQ|cy®¾N‚’xǂY\ Z
*
0$&';6
n "!-cƒ f³ œºOÛ eV `ƒ aDD ~Â
`Â3¶Â~‡Ow~²NÁ@vGˆ§…raˆ¹yQ|c¯@o*Â~¶¹ˆY…rxLJ†wcˆQ u`|c‚’}†…†yx€|cˆ§¯:y|[¯²c|[‡lu`|[‚’}†…†yx€|cˆ#¯´·¶.¸p× ‚·ÉÇu`…Ê‹ˆ#‡O}†u`…
x€$&Áy2¿`2ˆ
=…
ˆ§‚’+}†)u`…†yL}x€uQ'[|DÂ*21m’4|Ö<_m’ÊQyQ…. zq­!,²c!†‚’ƒN}†v[ʋyuQ¿`®þˆ#ƒU‚ ˆ#e¯fC x®}†euQV …§&ƒ b O&~ƒ=2
+,ˆ§=…/¿`ˆY|D1ƒN!0n.u`)…r¼
K*y§
¾œƒ Q²NKn|cˆ :+,/Q 2-
~Â3¶Â'‡Ow~²cÁ@vGˆY…raˆyQ|c¯ÆoÂG¶¹ˆY…rxLJ†wcˆQ¶­x€°U²c‚’x€u`|Ö}†ˆ§|[‚ruQ…¹…ˆ§¿`²fzyQ…rx€À#y}x€uQ|Ú¼x®}†wڇYuQ|[‚’}†…†yxz|œ}O‚
vN…ˆ#‚rˆ§…ÊQy}x€u`|'¹mS| O&=2+,=/1!0)K*(q&q&q $&'^6
):2+88z $&a2
,
+Gl$&`'[Â Z
6#
nI!,k/GOA-
.35=+,,1-cƒ My²[yx‘Ü%yQ……rx€u}}#ƒ ¹y§¼
yx®xþƒ[¶¹ˆ#‡lˆ§ÁËGˆ§…
fÂ3¶ÂG‡†wf²NÁ@vGˆ§…raˆ*yQ|[¯%oÂ[¶¹ˆY…rxLJ†wcˆQ­opˆ§¿Q²NzyQ…rx€À#y}xzuQ|ÚuÉ·uQ…r}†wcuQ|cu`…Áy‘Ê‹ˆ#‡O}†u`…­‚rˆY}O‚.²[‚’x€|N¿
‡l:u`8²cYvf>k€ˆ#8¯K´»2¶¹/!¸!× ‚Y ÂcH m’B| :>OY 2+
,#=ƒ /Q²f€1¾ !^gKQÂ!Iq&qYq2!,K*
6n #-/\HI8
EN ­Â;»ˆ§Á²c…rxþƒ9 wcˆ§|'ƒÍÜÚÂUo­yQufƒDÃ.ÂÍÜ%‡ .…†y#¼3ƒÍÃ.ÂDÜ%yQ…ˆ#‡OxJƒÍyQ|c¯™ÂGÓ,y|c¿f„™x€ËGˆ§…¹}†…†yQ‡l}
Á#yvcvfxz|N-¿*ÉDžPu`Á/0¯~x€HI°U²c‚’8x€u`I|::]8}†YˆY|[>n‚ru`8…!K*Ü^2/op!\ml™im’n| $&OY'^26+
,=
/n 1!(!,4KIHPe!
:#>qY q&qƒ QL²N®¾ 2!,K*
6iQ C~ ~ÂÓڈYxz‡OÏ`ˆ§…r}#Â#<_"!8=
6-+_y; *!,["('0215O&=2+
!,!"*1QÂcÃ͈§²cËN|cˆ§…r{ »ˆ§…rzyQ¿fƒQs~}†²N}}†¿`yQ…r}#ƒ
aDD fÂ
b  ­Â {J„
ÂGӈ§‚’}xz|'ƒDsUÂ'Ü%yxzˆY…§ƒ ­Â M3wfxz¯NwNx€…§ƒG´‘ÂU¸»Ê‹ˆ§…ˆY}}#ƒU„
 uQ€ˆ#‚rÀ`ƒÍyQ|c¯Æo
vNK*…4u~‡Y:ˆ#=‚+‚’x€|c¿/RÉÇu`…:
¯fx®°U²[‚’x€uQ|Ô&}†$&ˆ§|c‚rau`2…
,Á
yQ+¿`Q|NˆY}xz‡>k…=ˆ#/‚ruQ+,|[#yQ|c'[‡Yˆ%21x€Á(yQ$&¿Qx€';|N¿N6Â<#"m’*| 10 M¹O&x€=Ϝ/B2xz|f+$&,xz=‚Y/Â';m’6Á1!kyQ
¿Q
ˆ Z
<;!,!,!,/[
7>N$g$P<_ #ƒcsfvN…rx€|c¿`ˆY…r{ »ˆ§…rzyQ¿fƒ aDDDfÂ
k l
k
k pl n
k
n
k
*k
n^o
n k
T
k
l
.npopo o
npn
Tn
n
l
k
l
Mk
l
n
kmn
!k
n
po
n
o
n
n
gn
l #k
n
npopogk
n
k
k
n^l
kmo
n
gk l
k
l
Xn
k
k
k
npopo o
po
.npl
n k
gnTk
k
l
k
k
.k
o
n^o ogk
n
n^o o k
n^o ogk
k
npopogk
pl
k