HAL Id: inria-00073176
https://hal.inria.fr/inria-00073176
Submitted on 24 May 2006
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub-
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non,
Non-Robustness of Continuous Homogeneous Stabilizers for Affine Control Systems
David A. Lizárraga, Pascal Morin, Claude Samson
To cite this version:
David A. Lizárraga, Pascal Morin, Claude Samson. Non-Robustness of Continuous Homogeneous
Stabilizers for Affine Control Systems. RR-3508, INRIA. 1998. �inria-00073176�
a p p o r t
d e r e c h e r c h e
THÈME 4
INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE
Non-Robustness of Continuous Homogeneous Stabilizers for Affine Control Systems
David A. Lizárraga — Pascal Morin — Claude Samson
N° 3508
Octobre 1998
21436578*1,9&:*%";
<+=?>@BACEDGF@IH?JLKKM=LN=LOQPSRT=LUV?=LWYXZ[K@B\PG](WB=L^SAS_E`=LabUZ[\
cedgf-hikj(lnm?ophqgrts2uvoxwzy+i/uw|{}uvoxhot~suopw|y
i~?~ufhi~/wzh{grxi- }i~
w|i/u-s|i
%s{{wzu ividgivdiyLSz||lT/uw|iz|l({s||i~
* ¡-¢2£g¤|¡|¥ cedgot~T{s{Li-Y¦§w}/q~i~Yw|ys|~¨h{}uvwuvop{wzoxy¨u©ª~uvsoxrpox«¬s2uvoxwzyQw¦~hw?wuds2®ygi¯-w|y¨uvw|r
~}~uvi-h~°G±gw|Ys|~¨h{}uvwuvopY¦§i-i sz²~usgoprpox«i-~-³s~oxh{grpi i-´ygoxuopw|yµw¦e¶·¨¸º¹?»º¼¾½L¿/»v»ÀoÁuvdvi~{Liºu
uvwµqgyghw i-rpi  ?yshot-~ot~s w|{}uvi °+c*Àw+uvdgi-wzih~sviudgiyÃ{gw2Äzi ÀdgotdÃ~us2ui~q}®Å-oxiyzu
-w|y oÁuvoxwzy~e¦§w|%udgiŽ[·2½Æª¶·z¸/¹?»º¼B½[¿º»»Çw|¦Sdw|hw|zi-ygiw|q~e~uvsoxrpox«i-~-°0cedgi´~uudgiw|vi-h+³gÀdgotdQs{}©
{rxopi~uwk~}~uih~uds2uShsMk/wzy¨uvsopys ox¦Èuui-vh+³2oxy?Äzw|rpÄ|i~*sÉ~{i¬/ox´0/rts|~v~w|¦}¦§i-i s|²~uvsoxrpox«i-~-°
cedi~i¬/wzy w|ygiz³ÀdopdQs|{g{grpoxi¬~uw ox¦Èurpi~v~É~}~uvi-h~És|y ot~Y~uvsui opy i{iy iyzuvrx+w|¦s|y?{s|©
uvop-qgrtse~usgoprxop«-i³¨{gvw2Ä?o i¬~Çs-w|y oÁuvoxwzyvi-rts2ui uw(syÅiÄ|i-y¨uvqsrLrxw¨~~Çw¦sy²¯w|¦udgiks|/i~v~oxgoprpoÁu
op~uvoxq}uopw|yʰGYygi%w|¦[udgiT/w|y~i¬Ëzqi-y-i~Sw¦[uvdgiY~i-w|y vi~qgrÁuop~Gudsu³z¦§w|TÌ/Í?ÎÏȽL¿Ð2ÆÒÑ/·¶ºÓ »ºÔM»º¼Õ¿-Ó»º³
ywbÖI~uvs2uvop¬×-w|y¨uopy?qgw|q~kdw|hw|zi-ygiw|q~ki- ?{Lw|yi-y¨uotsr0~usgoprxop«-iÖI~w|hiw|¦eÀdopdÃdsMÄziii-yÃ{gvw©
{Lwz~i
oxyudi(rpoxui-s2uvqgvi¬×Y-syivw|gq~uToxyudgi~i-y~i
i/´yi
dgi-vi-opyʰØS gs|h({rxi¬~svi{gvw2Ä?o
i
Àdopdoxrprpq~uvvsuis(u?{got-srÊs|{g{grpops2uvoxwzyw¦Siszdvi~qgrxu°
ÙµÚ¨Û[ÜvÝÞ ¢2ß |¥ %w|gq~uÉ~uvsoxrpox«¬s2uvoxwzyʳ}dgw|hwz|i-yi-w|q~G¦§ii sz²[³}ygw|ygdw|rpw|ygwzh(otk~}~uih~°
àÇáâ¬ãåä*æçè¾âMéºê*ãåäÊä¾çMëMëéºê§è¾ìíkî/ïTðÊñSò*ó*ðLôSáõ§ök÷ªø¬ãåùéMú
1'Ê:%"#¯";"#) )57
¥ w|q~/wzy~o wzy~(rps ~uvs|goxrpot~suopw|y sz~?h{}uvwuot˨qgi i~~}~uvf-hi~ o vi-y¨uotsgrpi~
s®ygi~i-yÂrtsQ-w|hhsy iz°Ssuvs|y¨u qgygi ´yoÁuvoxwzy irps wzgq~ui~v~i{s(vs|{g{Lw|u i¬~ ¨©
yshop˨qgi¬~ygw|y hw rpot~ i~³ygwzq~ hw|y¨uvw|y~ i-q} ud w|vf-hi~˨qgo ygw|y/i-y¨u i¬~Å/wzy oxuopw|y~
~q}®Å~vsy¨ui¬~{wzqgrps9½[·2½Æª¶v·z¸/¹?»¼ª¿/»v»-¿ i¬~Å~uvsoxrpop~vs2uvi-qg~/wzyzuvoxy?q~dw|hw|zf-ygi¬~-°Êiµ{ih(opi- ©
~qgrxuvsu¯{Lw|ui~qg i~¯~}~uf-hi¬~¯-w|h{wzusy¨u Ä|i-y¨uvqgi-rprxihi-y¨uqgyÃuvi-vhi i voxÄziÅi/usµuvvs|oÁu
qygi¯-rpsz~~i~{ /ox´Ë¨qgi i(~usgoprpop~vs2uvi-qg~-°i¯~i-w|y {Lw|ui¯~qg i¬~É~?~ufhi~T~s|y~ opÄ|ii/uYi¬~u
ygw|y opy {iy shhi-y¨u q ~uvs|goxrpot~sui-qÉq}uvoxrpop~ ! opr uvs|grpoÁuTqgygi¯-w|y oÁuvoxwzy iyw|y}©Õwzgq~ui¬~~i
s{{wzu i"¯qgygi Äzi-y¨uqgirxrpiT{iuvi iTsyg iYrts op~uvoxq}uopw|y sz--i~v~opgoprxoxu °$#Éygik/w|y~ Ëzqi-y-i
i/i i-vygoxi ~qgrxuvs2ui¬~u˨qgi|³{wzqgrpi~¯~}~ufh(i¬~~w|q~ÉÑ/·2¶ºÓ¿µÌºÍ}Î&%Ƚ('¿-³Çsq/qgyÃvi/uvw|qg ) uvs2u
ÖB~us2uvop˨qgiMׯ-w|y¨uopy?qʳGdgwzhw||fygi|³Çi/uiy s|yzurwzop|opygii- }{wzygi-y¨uopi-rprpi-hi-y¨uÅ~usgrpiy i¬~uvw|gq~uvi
sy~erpi~iy~/wzy~o °+*i¬~ iq} Åud w|vf-hi¬~~wzyzuoprxrpq~u ~,(rs|o i i/ }ih({rxi¬~-°
-Þ ¡¬ Ü ¤!. ¥ m¨usgoprxot~vs2uopw|yvw|gq~uiz³}i-uwzqg uvsu%dgw|hw|zf-ygiz³}~}~uf-hi¬~eygw|y}©Õdgwzrxwzygw|hi~°
*1 + Ç/¯
Éw|hw|zi-ygioÁuds|~%{grpsMzi s|yµoxh{Lw|uvsy¨u%vw|rpiopy+udgi i-Äzi-rpw|{ghi-y¨u%w|¦Gygw|ygrpopygis|É/wzyzuvwzrudi-w|v|³
{suot/qgrtsvrx qgvopyguvdgiYrts|~u0uÀw is i¬~-³?sy uÀw¯hsw|0i¬s|~w|y~s|/w|qyzuǦ§w|eoÁu~Çoph{wzusy-i|°
ªy+uvdgi´v~uÉ{grts|-i|³dw|hw|zi-ygiw|q~s|{g{gvwM ?ophs2uvoxwzy~ei-ys|grpiudgi¯oxy?Äzi~uopzs2uvoxwzyw|¦rxw}-s|r{gvw|{Li-uopi~
w|¦ygw|ygrpopygis|Y~?~uih~udwzqg|d+uvdgi¯~uq w|¦Li/uuiYLi-dsMÄzi Ä|i¬ºuvw|%´i-r ~ u?{got-s|rxrp|³udgis{}©
{wM }ophsuopyg+Ä|i¬ºuwz´ir ~dsMÄ|i{Lw|rp?ygw|hotsrÇ-w|h{wzygi-y¨u~sy ~{s|yÃygoxrp{Lwuiy¨u¯sy w|´ygoxui-rp
zi-ygivsui Êopi0s|rxzi-gs|~³Ms%¦IszºuSÀdgopd¯i¬~qrÁu~opy(~oph({rxi-w|h{gq}us2uopw|y~-°Ø$Li¬ºuvoxÄzi0hi-udgw ~i/ }ot~u
¦§wzÉuvdgi¯-w|y~uvq/uopw|yQw|¦Gdgw|hw|zi-ygiw|q~És{g{gvwM }oxhsuopw|y~ ~i-im¨ui-¦Isygojg³[zs|y Éi-vh(i¬~p¾³
¦§wzopy~uvsy/i|°! É~¯{wzoxy¨ui w|qgu¯opyÃudgw¨~ii-¦§i-vi-y-i~³dw|hw|zi-ygiw|q~s|{g{gvwM }oxhs2uvoxwzy~-s|yÃi+~w
-w|y~uvq/ui sz~Guvw{gvi~i-vÄ|iÉs|~op%{gwz{iuvoxi¬~Çw|¦udgiYw|voxzoxysr~}~uvi-h+³?rxw}sr-w|y¨uvw|rprtsgoprxoxu(ioxyg
wzygiew¦Ludgih+°Scedi%~i¬/w|y visz~wzyot~Sudiq~i-¦§qgrpygi~v~w¦[dgwzh(wz|iygi-oxuopy~w|rpÄ?oxyYuvdgie¦§i-i sz²¯~uvs2©
oxrpox«¬s2uvoxwzy{gvw|grpi-h ¦§wz*yw|ygrpoxyis~}~uvi-h~-°*ªy
ii
³dw|hw|zi-ygioÁu-s|yLiÄ?ot~qsrpox«i
sz~SsÉysuqgsr
i- ?ui-y~opw|y¯w¦[rxopygis|oxu|³s|y
~iÄ|i-sr¨{gvw|{Li-uopi~Sw|¦rpoxygi¬s~?~uih~svi0s|rp~wYÄ2s|rxo
¦§wzdgw|hwz|i-yi-w|q~
wzygi~TÄ?otshopygw|s
q~uvhi-y¨uv~°(cedi-w|vygi-~uw|yii¬~qrÁuopy uvdgop~
oxvi/uopw|yʳ{gvw2Ä|i
?Qw¨~opi-kopy
å¾³s|~opsrprxÃ~uvsui~¯uvds2uox¦Éudi+-w|y¨uopy?qgw|q~Äziºuvw|(´ir#" ot~¯dw|hw|zi-ygiw|q~(sy udgi+wzop|opy
w|¦%$
&('
"*)
&,+
ot~ks|~?h({guwuvopsrprxµ~uvs|grxiz³Ludgiy uvdgi-vii- ?ot~uv~ks~q}®Å/opi-y¨urp oLiiy¨uotsgrpiÍ}·2Ó·-¨¿-Æ
½[¿·2¹?»+Êzs|{gqgygw2Ħ§qgy/uopw|yʰ. q~i-¦§qgrL-w|vw|rprps|z³ i-vopÄ|i ?w|hi/uesy m}s|h~wzyoxy/å102¾³¨i/ ?uiy ~
%wz~oxi ~i¬~qgrxuuwTuvdgi%-sz~ieÀdgii " i-{Li-y ~{iopw ot-srprpw|y¯uophi|°ÇYygi w|hs|oxy(oxyÀdgotd(udgi¬~i
{wz{iuvoxi¬~Ésvi¦§vqgoxu¦§qgrSot~%uvdgi¯~?yzuvdgi~ot~Éw|¦¦§i-i s|²+~usgoprpox«i-~¦§w|(½L·½gÍ}·x·½L·2Ó(ÏIÌ(»ºÔM»º¼Õ¿-Ó¯»ÖIoxy
wzqg%/wzy¨ui/ ?u¬³}udgi¬~is|i vox¦Èurpi~v~%~}~uih~%ÀoÁuvdµrxi¬~~-w|y¨uvw|ropyg{gq}u~uvdsyµ~uvs2uviÄ2svops|grxi¬~v×/°3 É~%op~
{i¬~iyzuvrx(À0i-rpr²?ygw2Àyʳ?~qd~?~uih~ w¯ygwue~suot~¦§540vw?²zi/uu ~ygi-i~v~s|/wzy oxuopw|y¦§wzTÌ·2½¼BÏȽÆ
¹·¹?»É{gqgvi~us2uvi¯¦§ii s|² ~uvs|goxrpop«s2uvoxwzy9ÖBº¦°640vw?²zi/uuÕ³m?wzy¨uvs7z2§×º°Åc*w+i-rpq iuvdgiq~i(w|¦
op~v/wzyzuvoxy?qgwzq~Ç~uvs|goprxop«-iv~³zwzygiÉi Li¬ºuvoxÄziYs{{gw¨s|dÅ-w|y~op~uv~Çoxyq~oxyg(~hw?wuvdQ¼¾ÏÈÓ¿-Æ98MζºÔ2ÏȽY¦§ii ©
s|²ÅrtsMÀ%~-°cedgop~%ui¬dgygotËzqiÀ0sz~~q/i¬~~¦§qgrprxoxy¨uvw q-i ?m}s|h~w|y+opy7|uvwÅs|~¨h{}uvwuvopsrprx
~uvs|goprxop«-i/wzy}´|qvsuopw|y~¯Ö§o¾°iz°{wzoxy¨uv~Topy uvdgi~us2ui-©Õ~{sz/i¬×%w¦s-s|u©¾rpop²|i|³Lygwzygdgw|rpw|yw|hophw|goprxi
vw|Lwu¬°Sm}w¨wzys¦Èui-¬³ *w|vw|y/j:Ê~dgw2À0i
uvds2u%sy?~h(w?w|ud
ox¦Èurpi~v~e~}~ui-h'syik~usgoprpox«i
uvw(s
{Lw|opy¨u¨Å~hw?wuduophi/©Õ{iopw
ot%¦§ii
sz²[° *wzy~uvqºuvoxÄziTs|{g{gvwzs|di~GÀ0i-viT{gwz{w¨~i
?w|hi/u
å:;Ǧ§w|¯sQ/rts|~v~kw¦ voÁ¦Èuvrxi¬~~¯~}~uih~³Ssy ? *wzwzyÃsy w|hi/u<;:Ǧ§w|¯/w|y¨uvwzrxrtsgrpi voÁ¦Èuvrxi¬~~
~}~uvi-h~°*Éw2ÀiÄ|i-¬³syoph{wzusy¨uÇ~dgw|uv-w|hoxyTw|¦Ê~hw?wuvd¯uvoxhi-©¾{Li-voxw ot%~uvs|goxrpop«-i-~Sot~uds2u³|¦§w|
hw¨~uÉopygoxuotsr/w|y oÁuvoxwzy~³uvdgis2uiw¦G/wzy¨Äzi-v|iy/ikot~%ygw|uÉi/ }{Lw|ygiyzuvops|rB³[s|~%À0sz~e´~uT{wzoxy¨ui w|q}u
opyQm}sh~w|y+sy ÉoÁu©= É isdoxh>?¾°A@+qgvvsMi-uÉsr¾°B|*~dgw2Ài uvds2uÉ~hw?wud³}uophi/©Õ{iopw op
¦§ii s|²+-syygwuÉi- }{wzygi-y¨uotsrprp~uvs|goxrpop«-iyw|ygdgwzrxwzygw|hot~}~uih~%uws{wzoxy¨u¬³LÀdi-vis|~CTqgÄ?oxuv~
s|y ÊoD:*{gvw2Ä|i udsuFEzr iY-w|y¨uopy?qgoÁuw¦uvdgi/wzy¨uvw|rÊrtsMÀ%~Àes|~uvdgidgop|di~uÉi|qgrtsvoxuÅw|ygi
-w|qgr soph su%oxy+w| ieuwÅs|doxiÄ|iki/ }{Lw|ygiyzuvops|rÊ/wzy¨Äzi-v|iy/iz°.@ *rpwz~²|isy @+qsM-s|i-¦§qgrprx
~uq oxi udiY/wzy?Ä|i-v|iy/is2uvi%w¦~w|rpq}uvoxwzy~-³¨sy oxy/p¬}³2;uvdgi-{gvw|{Lwz~i sGFEzr i-w|y¨uopy?qgw|q~
~uvs|goprxop«-i¦§w|%rpw2Àe© oxhiy~opw|ysr~}~uih~%oxyµ{Lw2Ài©¾¦§w|vh+°Çcedgiox¦§ii s|²ÖIygw|yg©ox{~vdgoxu«su%udgi
wzop|opyµgq}u~h(w?w|udQirp~i-ÀdgiiM×evi-y ii udgi/rpwz~i ©¾rpw?w|{Q~?~uih dw|hw|zi-ygiw|q~Éw¦ i|vi-i«i-vw
s|y uvdgiÉwzop|opyÀ0sz~G~dgw2ÀyuwiTrxw}srprxIH|©Õi/ }{Lw|ygiy¨uotsrprx~usgrpi|°Scedgi¬~iYi¬~qgrxuv~~{qgvi ¦§quvdgi-
i-Ä|irxwz{ghi-y¨u¯w|¦Y/wzy¨uopy¨qw|q~¯ygw|yg©Õ~hw¨w|ud dgw|hw|zi-ygiw|q~¯~usgoprpox«i-~¯s|y ³uvw suiz³udgiii/ }ot~u
~i-Äzi-sr¦§ii s|²+/w|y¨uvwzrp~Àdopdµ¦§wzrxrpw2À irpsui {gvoxy-ox{rxi¬~Ésy i-y~qgviJHz©¾i- ?{Lw|yi-y¨uotsr~usgoprxoxu
ÖBº¦°S¦§wzoxy~uvs|y/i5p0?³10¨³Ê¬}³Ê¬}³§×º°
YygiËzqi~uopw|y Àdgotd udgiy svot~i¬~op~(·Â¼IÍ}¿º»-¿EÌv·½¼¾ÏȽ¹·¹?»Õ¼¾ÏÈÓ¿-Æ982Î2¶ºÔ2ÏȽÃÍ?·Ó·¨¿/½[¿v·¹?»
Ñ/¿¿Ðz¸vÎz̬»¶v¿º»-¿-¶?8M¿DHLÆ¿g·2½L¿-½¼¾ÏIλº¼ÕΨ¸ºÏÒÏȼ¾ÔSÍ}¿/½¼BÍ?¿TÎ|Ì-¼B¹Î:g»ºÔM»º¼Õ¿-Ó»F82¿Ì/¼ª·2¶¿xÐM»YÐÏÉ¿/¶É»?ÒÏ2ͨ¼ÁÔ
Ѷv·2Ó#¼BÍ?·M»-¿E¹?»-¿Ðb¼ª·9Ð|¿/»Ï|½¼BÍ?¿(Ñ/¿¿vШ¸vÎ|Ì xÎ! cedgiE{gvi~i-y¨u{s|{is
g
vi~v~i¬~udop~op~v~qgi ?
´v~u%{gvw|{Lwz~oxygs i-´ygoxuopw|y+w¦Swzgq~uygi¬~~ew|¦Ss(¦§ii s|²~uvs|goxrpop«-i-Àoxudµvi~{Liºuuvw+¹}½Ó·Ðz¿ x¿Ð
ÐÔ2½LÎÓ¯ÏIÌ/»º³*sy uvdgi-yE{gvw2ĨopyguÀwudgiw|vi-h~°¯wzqg|dgrpQ~uvs2uvi ³Êudgi¬~i(udi-w|vi-h~Ti~uvs|grpop~d uvds2u
¦§wz~wzh(iT/rts|~v~i¬~0w¦*~}~uvi-h~0ÀoÁuvdygwzy}©ª/w|y¨uvwzrxrtsgrpi%rpoxyises{{gwM }ophs2uopw|y~-³¨wzgq~u0i- }{wzygi-y¨uotsr
~uvs|goprxop«suopw|y -syygwuÅLi s|doxiÄ|i ? hi¬sy~w|¦k-w|y¨uopy?qgw|q~dgw|hw|zi-ygiw|q~(¦§ii s|²[° Y~Ài
~ds|rxr~i-i|³wzqgTi¬~qgrxuv~k-w|y-i-vy ~}~uih~TÀoxud voÁ¦ÈuÅÖ§iz°°udi(qy i-©ªs|ºuvqs2uvi ~vs2uvi-rprxoxuiM×Ts|~YÀirxr
sz~~}~uih~eÀoxudw|q}u vox¦ÈuÖ§i|°°S²?opygi-hs2uvopkhw irp~ew|¦hw|oxrpikwzw|uv~׺°
cedgiwzq}urpoxyi(w|¦Gudi({s{Li-kop~ksz~ɦ§wzrxrpw2À%~°ªy m}iºuvoxwzyEÀivisrpr*sz~ot(/w|y/i-{guv~Tirpsui uw
dw|hw|zi-ygioÁuz°Êªym}iºuvoxwzy(YÀ0i i/´ygi0ÀdsuSÀoprpr}iehis|yzu?vw|gq~uyi~v~Àoxudvi~{i¬ºuuwsY-rpsz~~
w|¦h(w ir*{Li-uqsuopw|y~°Ém?i¬ºuopw|y j/wzyzusopy~euvdgihsopyQvi~qgrxuv~És|y udi-opY{gvw?w¦I~°ªym?i¬ºuopw|y
À0i ot~v/q~v~uÀ0wi/ gs|h({rxi¬~w|yÅdw2ÀÂuvdgi~iÉvi~qgrxuv~Çs|ieu?{got-s|rxrps{g{grpopi °Gm?i¬ºuopw|y6;{gvw2Ĩo i¬~G~wzhi
-w|y-rxq oxy(vi-hs|²}~°
c*w~oxh{grpox¦§uvdgiywuvsuopw|yÃÀ0iÅrpi/u#"$%'&
'
"(%()+*,.-sy hs|²|iq~iw|¦F40szdghsygyg©*sy s|q ~
ywuvsuopw|y s|~¯¦§w|rprpw2À%~-° CToxÄzi-y ¦§qgy/uopw|y~ "0/21!3 )"$%546"87"
+
sy :9;/<1!3 )"(%7"
+
~qdÂuvds2u
9)
&,+*' ,(o
& '
,g³}À0ikÀoxuiF " ot~>= )?9
+ Ö§wz " ' = )@9
+
×eox¦¦§w|%srprA / "
BDCFE
GH 3 I"*)
&KJ A + I
I9 )& + I ' ,.L
m}oxhoprps|rp|³ " ot~M )@9
+ ÖIw| " ' M )?9
+
×his|y~kuds2u¦§wzsy?NA / " uvdgi-vii/ }ot~u¯s+vis|ry?qghLi-
OQPR,sy sygi-op|d?Lw|vdgw?w TS w¦*udgiwzop|opy+~qduds2u
I
"*)
&J A + I
I
9)
&,+
I0U
O
¦§wzi-Äzi-v
&
/VS )+*,W-z°
X Y
1*%,-";)1:;6,)¯,-,/
cedi¦§w|ud-w|hopygi¬-s|rxrt~%svirpoxhoxui uwuvdgisz~ot i-´ygoxuopw|y~Ysy {gvw|{Li-uopi~%w¦dgw|hwz|i-yi-w|q~
~}~uvi-h~°k±w|khw|vi i-uvs|oxrpi op~v/q~~oxwzy~³uvdgi(i¬s iYot~Ti-¦§i-vi uwi|°°J%ihi¬~pÕ³KZsMÀ%~²?o
p||³Ê¬2ÊwzYYrxÄzi- å|2Õ°
[]\_^ `;acbdaefg>fachji6kmlonpnrq_gpeci
Éyts[©Buvqg{grpiw¦%~uvop/urp {Lwz~oÁuvoxÄziÅi¬srt~!u
' )uv
J
LLL
Ju % +
op~¯-srprpi s+ÝÚxwzy|{ ¡N} Ú ¤|¡ Þ ¢ °/CTopÄ|iy s
À0i-op|d¨uÄ|i¬ºuvw|~u¯s|y s¯vis|rPR,g³?udihs|{g{gopyg# &"o%"o% i/´yi ?
)& + ' )
& v J LLL
J
& % +
ot~%srprxi s ß w.§£g¡ w§Þ| Þ%ÝÚxwzy|{ ¡ u?°0cedi~s|h(ikuvi-vh4ot~w¦Èuvi-yµq~i uvwi-¦§i-uvwµ¼IÍ}¿SÍ}·x¿eÑ/ÎÓ¯ÏÒÔ
w|¦ oxrts2uvoxwzy~oxy i/ }i ?0P,g° oxrts2uvoxwzy w¦kÀioxzdzuuEÀoxrpr%Li i-ywui s|~T#° Y~iÄzi
uvds2u%Àdi-y u ' ) J J LLL
J +
³gw|yiTvi-w2Ä|iv~Çudgi-rpsz~~ot-srÊ-w|y-i-{}uw|¦dgwzhw||iygi-oxu|³¨uvdgi
oprpsuopw|y~
Li-w|hidgwzhwudi/uopi~³s|y
opy+udgot~T-s|~ikudi
oprpsuopw|yµot~%vi/¦§ivi
uvws|~euvdgi ¡£
ߣ}¢2ßß
w
.§£g¡
w§Þ|
g°
*wzy~o is oprts2uopw|y |° ¦§qyºuvoxwzy " &p"o% 4 "m "6ot~~vso uw i{Þ ÞyÚW*Ú¨Þ *
Þ ß Úxy ¢ Ú?Ú EÝ w¡ { ¢ Ú Ú ¤|¡¡ Þ6#ÅÖ§wzgvoxi|³.u¬©Õdgw|hwz|i-yi-w|q~ew¦ i-zii×oÁ¦ "*)# )
&J
A
++ '
"*)
&KJ A +
¦§wzsy? )
&J
A + / "o%4p"0°B 9Ä|i/uwz´ir & )
&KJ
A
+
,)
&KJ A + '
) v )
&J A + J
LLL
J % )
&J
A
+-+
ot~%~vso uvwi{*Þ Þ yLÚWÚ?Þ Þ ß Úxy ¢ Ú?Ú Ýw¡ { ¢ Ú Ú ¤¡¡ Þ6#Ö§wz%gvoxi|³Wu¬©Õdgw|hw|zi-ygiw|q~
w|¦ i-ziiÊ×ox¦³S¦§w|i¬s|d
' J LLL
J
s³udiŦ§qgy/uopw|y ot~u¬©Õdgw|hwz|i-yi-w|q~w¦ i|vi-i 5u °
{*Þ ÞyÚW*Ú?Þ * *Þ ¢& £g ¬ Þ ¤ w£}¡ Ú ß Ý w¡ { £ß w.§£}¡ w§Þ 9Ö§wzopiz³Ys|y u¬©¾yw|vh×ot~s
-w|y¨uopy?qgw|q~{Lwz~oxuopÄ|i/© i-´ygoxuikhs{g{gopyg5H& "(%"Àdgotdot~]u¬©Õdgw|hw|zi-ygiw|q~0w|¦ i|vi-ikw|ygiz°
wuiÉudsuG¦§w| P,³zsk¦§qgyºuopw|y " Àdopdot~cu¬©Õdgw|hwz|i-yi-w|q~w¦ i|vi-i ot~!xu¬©Õdgw|hwz|i-yi-w|q~
w|¦ i-zii"# udgot~oph{grpoxi¬~uvds2u¯udgiÀioxzd¨uv~syÂs|rxÀesM}~Liygwzhs|rxop«-i ~w sz~uvw dsMÄziuv
'
°% %rt~w³*?Ei-Ä|iy¨uqs|rxrp vi-ys|hoxyg+uvdgi-w¨wz oxysui¬~-³*ÀisyÃsvsygzi¯uvdgi-w|h{wzygi-y¨u~w¦]u+opy
yw|y i¬/visz~opygwz i°ced?q~³?ÀoÁuvdgw|q}urpwz~v~0w¦*zi-ygivs|rxoxu|³¨À0iksz~~qghiYudgvw|qgzdgw|qguÇuds2u ' uv
U
u$
U&%%%.U u % °
Y~~qghi uvdgi /w|h{Lw|ygiy¨uv~w¦uvdgiÀ0i-op|d¨uÄ|i/uwzTu
' )uv
J
LLL
Ju % +
us²|i('*) ot~uopyºu
Ä2s|rxqgi¬~-³ i-ygw|ui s|~ru v J
LLL
J
u,+ ÀoÁuvd
' u
v.-
%%%
-
u,+
' u %
°±w|sy?"o%[©ÕÄMs|rxqi hs|{ " ³0/
Àoprprvi-{i¬~iyzuTudi u¬Ü£}¢M¡ w¡ w§Þ| Þ " ³Àdgotd/wzy~op~uv~Tw¦!'8~qg}©ÕÄ|i¬ºuwzv~1/
v J LLL
J / +
~qdQuvds2u
" ' )/ v J LLL
J / + +
³[sy ~qd+uds2u ",2 ) / * J LLL
J
so-
+
op~Ysyµi-y¨uvw¦3/4 )65 / * J LLL
J
'-
+
o
u 2 ' u 4
°±gwzoxy~usy-i|³?oÁ¦ou
' ) J87 J87.J97 +
sy " ' )" v J " $ J
";:
J
"=<
+
³?udgiy>'
'@?
³xu
v ' J u $
'A7
³
s|y / ' )/ v J/ $ +
Àoxud/ v ' )=" v +
³B/ $ ' )" $ J
";:
J
"C<
+
°cedgiq~iw¦Lw|r ~?hLw|rt~Ö§iz°°/
JED
×Éuw
i-ygw|uik{suoxuopw|y~ew¦SÄ|i/uwzv~0ÀoprxrLi/wzy~ot~ui-y¨uvrx-w|y~i-vÄ|i dgii¬s2¦Èuvi-¬°
[]\?[ [email protected] f0HKJWq_fKiaMLV` acbdaecfKg>fa hpiONNfBPQJxa3HSRqfBTEUpi
i/u#GLi0s
oxrts2uvoxwzy¯s|y
WV
&
&"
V )& +
sÉ~hw¨w|ud u©Õdgwzh(wz|iygi-wzq~ÊÄziºuvw|´i-r
w|¦
i-zii3X?°$Êi/u
Y ' )Y v J LLL
J Y + + sy
D!' )D v J
LLL
JED
+ +
iygwuviudgiu©Õ{s|uvoÁuvoxwzy~%w|¦
V
s|y
&
³Li¬~{Li/uopÄ|i-rp|°
cedi-y
Z[Q\^]Î|Ì/͵̷Ópg·2½[¿/½¼0·Ñ V Ït»Î }·:ÒÔ2½L·Ó¯ÏIÎ:¨Ñ¹}½[Ì/¼¾ÏI·2½°
Z`_0\Wa§ÑG¼BÍ?¿Ç»ºÓ··¼IÍ 82¿vÌ-¼ª·2¶ 0¿ xÐ Vcb
Ït»Ku?ÆÕÍ}·2Ó·-¨¿/½[¿·2¹?»0·Ñ0Ðz¿ |¶¿¿dX
b
L¼BÍ?¿-½e V J
Vcbgf
Õ¼BÍ?¿ SÏI¿%¸/¶Î|Ì¿/¼D
Ït»]u¨ÆÕÍ}·2Ó·-¨¿-½L¿·2¹?»¯·ÑÐ|¿=|¶¿¿hX iX b °
Z^jk\^l·¶¿vÎzÌºÍ 5/ * J LLL
J
'- G¼IÍ}¿Ì·2Ójg·2½L¿-½¼B»·ÑmY 4 Î2¶¿
s¨×ÉÏIÐz¿/½¼BÏIÌÎ:ÒÔ¬¿-¶·ÏÑ]u 4 -on
X?³
×Ì·½g»º¼Õν¼ÏÑ~up4
' n X?³
¬×Sѹ}½LÌ-¼BÏI·½g»k¼IÍ}Î2¼A8MνÏt»ÍµÎ¼Ç¼BÍ?¿(·2¶ºÏ|ÏȽÏÑ>up4 P n X?°
ZWqB\Ir*½Pp¿º»» Vts ,WGÏȼB»Ðz¿=¶¿¿XÍ?Î2»¯Î5x· Ç¿/¶(¸v·¹}½LÐ,uvX)
n
u,+°
Z`w0\Wa§Ñ~u
' ) J LLL
J + νLÐ^X
-
,WG¼BÍ?¿-½ V Ït»Ìv·½g»º¼ªÎ2½¼¾°
Z^xk\Wa§Ñ X
-
,µ¼BÍ?¿-½.Ñ/·¶¿Î|Ì/Í 5/ * J LLL
J
'-Ç·2½ ÒÔ
D v J LLL
JED
4y v ÓÎ2ÔÎg¿Î2¶¯¿ ÒÏIÌ-ÏȼÁÔÅÏȽ"Y.4
[]\ `;acbdaefg>fachjiRnpn1H.a]qbdlBJ.q_acgpi
i/u
$
J'
" 3 ) +
2 v " 2 ) +
2 Ö¬×
vi-{i¬~iyzuTsy s®yi¯/wzy¨uvw|r*~}~uvi-h i-´ygi oxy"o%³ÀoÁuvd rpw}-sr/w?w| opys2uvi~
6' ) v J
LLL
J
% + ³
-w|y¨uvw|rÄzi/uw|
%' ) v J
LLL
J
+ / "
sy %"
3 J LLL
J "
~h(w?w|udµÄ|i¬ºuvw|e´ir ~°,#%ygrpi~v~%w|udgi©
Àot~i~us2ui ³À0is|~v~qghiYuvds2u " 3 ),
+.'
,°±gwzÉ~oxh{grpop-oÁuw¦Si/ }{Lwz~oÁuvoxwzyʳÀ0i~dsrpr~rpop|d¨urps|gq~i
ywuvsuopw|y?~w|hi/uvoxhi~srprxopyg%82¿Ì/¼ª·2¶0¿ xÐsy+s{g{grpot-s2uvoxwzy " &+"(%4"5p"o%Ehs{g{gopyg ) JA +
uvw "*)
J A +
oxy~uvis w|¦*Ä?oxiÀoxy(oxuÉs|~s¯¦Is|h(oprpw¦Ä|i¬ºuwze´i-r ~eopy i- ?i ¨ A°
ªy+w|qe¦§vs|h(iÀwz²[³}syVu¬Ü {*Þ ÞyLÚx*Ú?Þ * (£KB*¢ Þw £}¡ w§Þ Þ Û ¡ Ú [Ýw¡ { ¤ ÞÊÞ ¢2ß wtÜ
£}¡ Ú ¤ { £ yLÚ
& '
) + £ ß ÝÚxwzy|{ ¡ } Ú ¤¡ Þ ¢ u¯ot~s~}~ui-h
$
&<'
3 )& +
2
v 2 )& + 2 J
ÖB|×
Àoxud
3 J LLL
J
~hw?wuvdÄzi/uw|0´ir ~-³~qdudsu
3
ot~~u©Õdgwzh(wz|iygi-wzq~0w¦ i-ziir,³gsy ¦§w|h
' J LLL
J!
³ 2 ot~]u¬©¾dgwzhw||iygi-wzq~0w¦ i-zii
X 2 - ,
oxy
&
©Õ-w¨wz
oxysui¬~Çuvdgi~?~uihÖ¬×op~%|opÄ|i-y?
$
&<'
3 )
&,+
3 )& +
2" v ) 2)
& + Q2 )
&,+ + 2 J
ÖIz×
ÀoÁuvd 4# ' = )Hx%$&(')
+ Ö5 ' , J LLL
J!
³B
' J LLL
J
s×Y¦§w|s|y?u¬©¾ygwzh>HÂÖ 4!# ot~kuvdgi.¾©Buvd
/wzh({Lw|yi-y¨u%w¦*udgiÄziºuvw|0´ir 4¬×
udgi oxiJ Érxzi-gs(%syg² *w|y oxuopw|yÃÖ, É*e×0dgwzr ~s2ueudgiwzop|opy
*+-,/.
* V ), + & V /10KC32 ) 3 J LLL
J
+- ' " % L Ö§j¨×
Ú £}¢54
cedgot~
i/´yoÁuvoxwzy¯s{{grxopi~i¬ËzqsrprxÀ0i-rpr¨uw
ox¦Èurpi~v~S~}~uih~eÖIoxy(Àdgotd¯-sz~i
" 3
'
3 ' ,¨×º°
±w|kÖI~?h(hi-uvop¬×
voÁ¦Èuvrxi¬~~e~}~uvi-h~-³[Ö§j?×Got~0s¯~q}®Å/opi-y¨u0-w|y
oÁuvoxwzy¦§w|0rxw}sr[/w|y¨uvwzrxrtsgoprpoÁus2u0udgi
wzop|opyʰ±w|~}~uih~YÀoxud
ox¦Èukuih+³dgw2À0i-Äzi-¬³uvdgot~
i/´ygoxuopw|yEot~YywuÄ|i
ihs|y
opygoxyudgi
~i-y~iuvds2uÖ§j¨×op~Ài¬s²zi-ÖBsy i¬s|~oxiuwQiÄ2srpqs2uvi¬×kuvdsyÂm}q~~hsygy ~¯~q}®Å-oxiyzu(/w|y oÁuvoxwzy ¦§w|
m}hs|rxrx©ªceoxhi Êw}-s|r *w|y¨uvw|rprtsgoprxoxuQÖBmgc,*e׺°
6 Y
1*,-%" &(*)k*%";%
ªyrxopygi¬sk~}~ui-h~Yudi-w|vÃÖI~i-i(i|°°±i-opyzuvqd 02Gs|y uvdgi¯vi/¦§iiy/i¬~%uvdgi-vi-opy×/³wzgq~uygi¬~~Yw¦s
¦§ii s|²rpsMÀ Ö§Àoxud i¬~{Li/u%uwqgyghw i-rpi Q ¨yshop~v×hsMLi i-´ygi oxyµuvi-vh~%w¦Çs~{sz/iw|¦
wz{ivsuwzv~iy
w2À0i
ÀoxudEs~qgoÁusgrpiuvw|{Lw|rpw|zwzYhi/uvot° ~}~ui-h ot~Évi-{i¬~iyzuvi
?bÎ }·ÏȽ¼
opy uds2u¯~{s|-i|³Ssy
s+¦§ii
s|² rtsMÀ ÀdgopdÃ~uvs|goxrpop«-i~¯s+ygw|hopysr~}~ui-h!ot~-s|rxrpi
vw|gq~uox¦%oÁu
~uvs|goprxop«-i¬~iÄ|i-v~}~uih rpw}-sui
»º¹9Ì-ÏI¿/½¼ÁÔY½[¿vζÇÖ§o¾°i|°oxy(sY~hsrprzygioxzd?wzdgw?w
w|¦v×uvdgi0ygw|hopysr
~}~uvi-h+° dgii¬s|~ÊsÉ~ophoxrtsÊzi-ygivs|rs{g{w¨s|dk-sys|rp~weiq~i oxyudgiÇs|~iw¦}ygwzygrxopygi¬sÊ~?~uih~-³
À0is wz{}uÉsys|vw2Ài{Li-~{i¬ºuopÄ|ik?-w|y~o i-voxys(ygwzhoxys|r~?~uih ~qg}i¬ºuuw{Li-uqsuopw|y~
Àdopdʳzs|~ot-srprp|³svis g oÁuvoxÄzieui-vh~SÀoÁuvd~q}®Å-oxiyzuGvi-zqgrtsvoÁuz°*ØG~v~iy¨uotsrprxz³2udgot~Ä?opi-À{Lw|opyzuGÀes|~
s|rp~ws wz{}ui opyudgi i-´ygoxuopw|y+w¦Svw|gq~uyi~v~zoxÄzi-yoxy%40i-yysygoÊs|y w|qdw|y(2Õ°
Úow¡ w§Þ [ Y½ £gß$ w ¬ w.Ú Ú ¢¬¡ Ê¢2£}¡ wIÞ Ït»kλºÓ··¼IÍÓÎ ÏȽ
9) J %+
»º¹ÌºÍ¼IÍ}Î2¼gÑ/·¶
¿82¿/¶ºÔ / " 9) J %+
Ït»Î»Ó·¬·2¼BÍ<82¿vÌ-¼ª·2¶¿xÐÏȽT"o% Î2½[Ð 9), J& +.'
,Ñ/·¶¯Î
& / "o%3
Úow
¡
w§Þ@_ *¿-¼ t& "o%N4T"Rm"
¸v¿Î%Ñ/¿¿Ðz¸vÎzÌxÎ9»º¹Ì/ͼIÍ}Î2¼¼IÍ}¿·2¶ºÏ|ÏȽ·Ñk¼IÍ}¿§½L·Ó¯ÏȽ[Î
»ºÔM»º¼ª¿/Ó >ÏȼBÍ
' )
.J A +
Ït»Ip·ÌÎÁÔ ÎM»ºÔ2ÓpL¼Õ·¼BÏIÌÎ:ÒÔµ»º¼ÕΨ¸?p¿ ÊÍ?¿YÑ/¿¿Ðz¸vÎ|Ì <Ï0¸v¿ÅÌÎx¿Ð
¢ Þ * ¡ ÏÑ Ï82¿-½+νÔÇÑ/ÎÓ¯ÏÒÔ·ÑTÎ|ÐÓ¯Ït»»ºÏB¸?p¿8}¿-¶º¼¾¹}¶¸Î¼BÏI·½g» 9 3 J LLL
J9
»-Î2¼¾Ït»ÈÑÔ2ÏȽ 9 3 ) J ,
+*' ,ÉÑ/·¶
¿82¿/¶ºÔ / " Y¼BÍ?¿-¶¿¯¿zÏt»º¼I»
3
P:,Q»º¹ÌºÍ¼BÍ?μ¼BÍ?¿(·2¶ºÏ|ÏȽ÷Ñk¼BÍ?¿}¿-¶º¼B¹}¶¸v¿Ð%»ÔM»º¼ª¿/Ó
$
'
" 3 ) + 9 3 )
J +
2
v )",2 ) + 9,2 ) J ++
2)
.J A +
ÖB|×
Ït» x·¬ÌÎÒÔÎM»ºÔ2ÓpL¼Õ·¼BÏIÌÎ:ÒÔÅ»º¼ªÎz¸ x¿ÇÑ/·¶¯¿8M¿-¶ºÔ / en 3 J 3 f
Y~ i-´ygi sLw2Ä|i|³¨s hot~~opgrxiÉ{iuvqgs2uopw|y~hsMLiÉÄ?oxiÀi s|~GÄzi/uw|G´i-r ~GÀdwz~i{iuvqgoxyg
i Li¬ºu-s|y Li¯hs i(sz~~hs|rxr s|~ i¬~opi ?udgidgwzop-iw|¦s~hsrprSi-ygwzqg|d¨°Õ¦Ëzqsy¨uox´i~
uvdgiqgy-i-uvsopy¨u opy+udgi²?ygw2Àrpi |iw¦Suvdgivisr*~}~ui-h ÀoÁuvdQvi~{i¬ºuuwÅudgiyw|hoxysrwzygi|³udgi
¦§wzi|wzoxyg i-´ygoxuopw|y~Gs|ivisz~wzysrxiuwhw i-rÄMs|opw|q~~wzqgv-i~Sw|¦Livw|opyi¬sr-w|y¨uvw|r}~?~uih~-°
w|ygi-udgirxi¬~~³}s g oÁuvoxÄziY{Li-uqgvsuopw|y~Gl opy-rxq oxyg(hw|viYzi-ygivs|rL-rpsz~~i~³?~qds|~ ot~-w|y¨uopy?qgw|q~
wzygi~l svi(¦Isk¦§vw|h Li-opygµi- ?dsq~uopÄ|i(uwµhw irGsrprG{w¨~~opgrxiivw|~Ö§{s|vs|h(i-uiTivw|~³Ê~us2ui
hi¬s|~qgihi-y¨u0ivw|~³zuvoxhopygi-vvw|~-³¨i/u°å׺°
*wzy/iygopyguvdgi¦§ii sz²rtsMÀ%~³À0i~dsrprʦ§w}/q~Yw|qÉs2uui-y¨uvoxwzyµw|y Ì·2½¼BÏȽ¹·2¹?»kÍ?·Ó·¨¿/½[¿v·¹?»
HLÆ¿ g·2½[¿/½¼BÏIÎ:}~usgoprxop«-iv~°Çvopw|uvw|opĨopygs{gvi-op~i i/´ygoÁuvoxwzy+w¦G~qd¦§ii sz²}~-³grpi/uYq~vi-s|rxr
~w|hikygw|uopw|y~evi-rts2uvi uw~usgoprpoÁuz°*w|y~o i-s/w|y¨uvoxy?qgwzq~~}~uih
)
+ & $
& '
"*)
&KJ A +
¦§wzÀdopduvdgiTw|voxzoxy
&<'
,ot~esyÅi¬Ë¨qgoxrpopgopqgh+°cedgiTw|voxzoxyot~e~s|o uvw¯Li -¡¬£g .ÚµÖ§opyÅudiT~i-y~iÉw|¦
zs|{gqgygw2Äg×ÇoÁ¦¦§w|%s|y¨ A3 / "sy s|y¨VP:,³?udgiii- }op~uv~ X P,~qdudsu
& 3 - X
'
& )A J A 3 J & 3 + -
J A3):A
3 J
Àdi-vi
& ) %J A 3 J-&
3 +
vi-{gvi~i-y¨uv~*s%~w|rpq}uopw|yuvw )!
+
ot~~qgi ¦§wzh
& 3 su(A
' A3
°cediÇw|vop|opyTot~ -¡¬£g.Ú
ox¦S¦§w|T~wzh(ii¬srt~>A
3
sy P ,g³s|y ~w|hi~i˨qgi-y/i )& 3 #2 +
2#"%$ ÀdgopdQ-w|y?Ä|izi~0uvwÅ«-iw³}udgii
i- }op~uv~%s~i¬Ëzqi-y-i )A 2 +
2#"%$ ~qdudsu
& )A 2 J A3 J& 3 #2 +
)& Ö§Àoxud
& 3 #2/ " % J A2 ) A3 J'
/( ׺°
±opysrprp|³}|opÄ|iys oprpsuopw|y#³}uvdgikw|voxzoxyop~ot~~vso uwLiÖ§rpw}-srprp}×DHzÜvÚ Þ|ÚW ¡ w£ ..Û ¡£g.Úox¦³
¦§wzsy?u¬©¾ygwzh HL³uvdgi-viÅi/ }ot~u¯i¬srGy?qgh¯iv~X P ,g³ O P ,Qsy *) P ,Q~qduvds2u¯¦§w|iÄ|i
A 3 )R,
H )& 3 + - X
'
H )& )A J A 3 J & 3
+-+
U O H )& 3 +,+
y.-0/21y31465
J A3)A
3 L
Úow
¡
w§Þ&j L¹g·M»-¿¼IÍ}Î2¼rÏt»¯Î2½Tu?ÆÕÍ}·2Ó·-¨¿/½[¿·2¹?»¯Î ¶·zÏÈÓμBÏI·½Ã·Ñk»ºÔM»º¼Õ¿-Ó cÏȼBÍQÌv·Æ
·¶Ð2ÏȽ[Î2¼ª¿ÌºÍ}Î2½ z¿
&!' ) + ÊÍ?¿Ñ/¿¿Ðz¸vÎ|Ì xÎ ' ) v J LLL
J + /1!3 )
"o%t4"87"
+
ÏG¸v¿
ÌÎ:x¿ÐÎ
¤
Þ|
¡
w@
Þ
*
{*Þ
ÞyLÚx*Ú?Þ
*
HzÜvÚ Þ|*Úx
¡ w£ .e ¡£g
w. wzÚ
¢
ÕÞ
¢
[-ÏÑ
¾Ï 2 Ït»]u?ÆÕÍ?·2Ó·z¿-½L¿·2¹?»¯·ÑÐ|¿=|¶¿¿
n X 2 ) ' J
LLL
J !+
¾ÏÈÏżBÍ?¿(·2¶ºÏ|ÏȽ÷Ñk¼BÍ?¿(Î L¶·zÏÈÓÎ2¼¾ÏȽ»ºÔM»º¼Õ¿-Ó ÏȼBÍ
' )
&J A +
Ït»HLÆ¿ g·2½[¿/½¼BÏIÎ:ÒÔ»º¼ªÎz¸ x¿
Y~iÄziudsu³}Àdgiyi- ?{i¬~~i opyuvdgiTw|voxzoxys|r-w¨wz oxysui¬~
J' y v )& +
³s¦§ii sz² h(ii/uvoxyg
uvdgivi˨qgopih(iy¨uv~0w¦*udgirts|~u i/´yoÁuvoxwzyÀoprprsrt~w+Ö§rpw}-s|rxrpg×AH|©Õi/ }{Lw|ygiyzuvops|rxrpÅ~uvsoxrpox«iTudgiwzop|opy
w|¦Ö¬×/° ªy i-i ³0udgii/ }op~uiy/iµw|¦syRu¬©¾dgwzhw||iygi-wzq~ ʨs{gqygw2Äæ§qgy/uopw|y ot~Åzqssy¨uii ³0opy
uvds2u-sz~iz³? s uvopĨotsr0i/ ?uvi-y~oxwzybw¦Twz{w¨~oxuopw|yÂjopy w|hi-us|y m}s|h~w|y 0 ¾°bcedi-vi/¦§w|vi|³
uvdgirpw}-s|r,Hz©¾i- ?{Lw|yi-y¨uotsr~usgoprxoxui-y~qgvi ? Âot~É{i¬~iÄzi s2¦Èuvi-%uvdgi¯s g oxuopw|yQw|¦{iuvqgoxyg
uvi-vh~SÀdgopd³|opyÅ/rpwz~i ©Õrxw?wz{ʳ2i¬~qrÁuGopy~qgh~w|¦u¬©Õdgw|hwz|i-yi-w|q~*Äzi/uw|S´i-r ~w¦~uvop/urp{w¨~oxuopÄ|i
i-|vi-i¬~-°ªyQudsuT~i-y~i 9op~Avw|q~u uwuvdgi(s g oxuopw|yµw|¦Ç~qdµ{Li-uqsuopw|y~° i-Ä|iuvdgi-rpi~v~³.
hsM¦Is|oxrÊuwiwzgq~ueopyudgi~i-y~ikw¦Yi/´ygoxuopw|yQg³sy uvdgihsopy+-w|y¨uvopgq}uopw|yw¦*udgi{gi¬~iy¨u
{s{Li-%/wzy~op~uv~e{gvi-op~i-rpopy{Lw|opy¨uopygw|q}uÉ-w|y oÁuvoxwzy~eqgy iÀdgotd Ït»k½[·2¼vw|gq~u¬°
)- ,º*
p\_^ F!JWlBJWfKbdfKgvJ
Ei´~u~us2uiÅcedi-w|vi-h~s|y
}³*udgihs|oxyÃvi~qgrxuv~opyEudgiÅ{s{Li-¬³s|y
hs|²|iÅ~w|hivi-hsv²}~
Li/¦§wzik{gvw}/ii opyg(uw(udi-op%{gvw¨w|¦I~-°
{Ú?Þ ¢ Ú [ k»v»º¹}Ó¿ ¼BÍ?Î2¼N! Í}ÎM»bÎ2½5u?ÆÕÍ?·Ó·¨¿/½[¿v·¹?»ÂÎ L¶·zÏÈÓÎ2¼¾ÏI·2½ ÏȼBÍ Ì·¬·2¶ÐÏȽLÎ2¼ª¿
Ì/Í?ν¨¿
&M'
) + *¿/¼ !¸v¿ÂÎ Ì·½¼¾ÏȽ¹·2¹?» Í?·2Ó·z¿-½L¿·2¹?»%HLÆ¿g·2½[¿/½¼BÏIÎ:Y»º¼ªÎz¸/ÏÒϬ¿/¶ÅÑ/·¶5
ÌBÑ N(¿@ǽÏȼ¾ÏI·2½ ¹g·M»-¿¼BÍ?Î2¼Ñ/·¶»-·2Ó¿ A
3 / " Î2½[е»-·Ó¿ÏȽ¼ª¿=z¿-¶» / * J LLL
J - νLÐ
/ * J
LLL
J
so-
)2
J A3 +'
, Î2½[Ð
n
X - u J
Ö;z×
SÍ}¿/¶v¿ 2 / "o%9Í?Î2»Î2¼G¼BÍ?¿
ƪ¼BÍ¿/½¼B¶ºÔÅÎ2½[л¿å»-¿SÍ}¿/¶v¿ ÊÍ?¿-½.Ñ/·¶Î2½Ô P:,.S¼BÍ?¿ÇÑ/Î2Ó(ÏÒÔ·Ñ
ÎzÐ2Ó(Ït»»ÏB¸ x¿jg¿/¶º¼¾¹}¶¸vÎ2¼¾ÏI·2½» 9 2 ) ' , J J LLL
J! +
Ð|¿?G½L¿Ð¸ºÔ
9,2) J & + &'
0~zy ) )2 JA 3
+-+
2 J ÏÑ ' J
, J
·2¼BÍ?¿-¶Ït»/¿
J Ö 0×
Óο/»k¼BÍ?¿(·2¶ºÏ|ÏȽ÷Ñk¼BÍ?¿>}¿-¶º¼B¹}¶¸v¿ÐÌx·2»/¿ÐÆ9x··»ºÔM»º¼ª¿/Ó SÍzÏIÌ/͵ÏȽ
&
ÆÌ·¬·2¶ÐÏȽLμտ/»Ït»
$
& ' 3 )
&,+
3 )& + 9 3 )& +
2" v ) 2 )& + 2 )& + 9 2 ) J & +-+
)
&J
A
+J
ÖIz×
¹}½»º¼ÕΨ¸?x¿2Í}¿/¶v¿IÑ/·¶¿ Ït»½[·2¼0¶·z¸/¹?»º¼ÇÏȽ ¼BÍ?¿»-¿/½»/¿(·Ñj¯¿?G½ÏȼBÏI·½
cediTyi/ ?u%i¬~qrÁue¦§w|rprpw2À%~0¦§wzh4cedgi-wzih koxyuvdgi~{Li-oÁ´LTs|~ikw¦
ox¦Èurpi~v~~?~uih~-°
{Ú?Þ ¢ Ú _ G·2½»ºÏIÐ|¿-¶¯Î»ºÔM»º¼ª¿/Ó ·Ñ¼BÍ?¿Ñ/·2¶ºÓQ ÏȼIÍ " 3 '
,tÕÏÈ¿ ÎÐ2¶ºÏѼx¿º»»»ºÔM»º¼Õ¿-Ój;u
$
J'
2" v " 2 ) +
2 L ÖIz×
L¹g·M»-¿¼IÍ}Î2¼r»/μBÏt»z0¿º»k¼IÍ}¿rFG Î2½LÐÎM»»º¹}Ó¿¼BÍ?Î2¼[Ñ/·2¶(¿ 82¿/¶ºÔ / * J LLL
J
-
WCFE
*+-,/.
* V ), + & V/ 0C21)" v J LLL
J " y v J
"
& v J LLL
J " +- - s n Öz×
ÕÏÈ¿2DT¸ºÔ¶¿-Ó·:8ÏȽ " ¼IÍ}¿Î|ÌÌ¿º»»ºÏB¸ºÏÁÏȼBÔ ÐÏt»¼¾¶ºÏB¸/¹}¼BÏI·½ Î2¼D¬¿-¶· x·M»-¿/»(Ó·2¶v¿¼IÍ}Î2½b·2½[¿ÅÐ2ÏÈÓ¿-½g»ºÏI·2½:
ÊÍ}¿/½ e½[·+Ìv·½¼¾ÏȽ¹·¹?»Í?·Ó·z¿-½L¿·¹?»HLÆ¿g·2½L¿-½¼¾ÏIÎ*»º¼ÕΨ¸ºÏÁÏ¿-¶Ñ/·2¶VÏt»¯¶·z¸/¹?»º¼ÏȽE¼BÍ?¿»/¿-½g»-¿·Ñ
(¿?G½Ïȼ¾ÏI·2½
Ú £}¢54Ê
[-Y~iÄzikudsuÉudii-Ä2s|rxqsuopw|yQw|¦udgi sy²z©Õrpwz~v~ /w|y oÁuvoxwzybÖ¬z× w¨i¬~ÉywuYvi˨qgopvikudgi/wzh¯©
{q}uvsuopw|yw¦Ês|y¨¯dgw|hwz|i-yi-w|q~s{g{gvwM }oxhsuopw|yʰcedgop~Gop~/w|y?Äzi-ygopi-y¨uÇ~oxy-iudi%rpsuuvi-Çot~Çsk{w}/i¬~~
Àdopdw¦Èuvi-y+i¬Ë¨qgoxvi~e~oxzygox´-s|yzui Lwzu¬°
_ Y~uwcedi-w|vi-h}³¨oÁuop~ÇÀirxr²¨yw2Ày¯uvds2uÀdgi-yuvdgi%rpoxygi¬s0s{g{gvwM }oxhsuopw|y $
& '
2
v 2),
+
2
w|¦udgi(ygwzh(opys|r0Ö ox¦Èurpi~v~×É~}~uvi-h op~k-w|y¨uvw|rprps|grpi|³wzygi¯syµ´y rpoxyisY¦§i-i sz²+-w|y¨uvw|rt~uvds2u
iy~qgirpw}-s|rB³sz~?h{}uvwuot~uvsoxrpoÁuw¦udgiw|voxzoxyʰA@+w|vi-w2Äzi-¬³¨oxuÉot~%i¬s|~uwÅdgi¬²Åuvds2uYs|y?~qd
-w|y¨uvw|rLot~vw|q~ueopyuvdgi~iy~i i-´ygi sLw2Ä|iz°±w|ew|q0vi~qgrxuv~uwLikw¦Ä2srpqgiz³?udgis|~v~qgh{}uopw|y~
h¯q~uÉudi-vi/¦§w|vii- }-rxq iuvdgot~Y-rpsz~~Yw¦Ç~}~uvi-h~-°Tcedgot~Éot~ w|ygi¯Ä?opsuvdgi(i¬Ëzqoxvi-hi-y¨u¯Ö¨×º³[Àdgotd
oph{grpoxi¬~uvds2u(udirpoxyiss{{gwM }ophs2uopw|y ot~(ygwu/wzyzuvwzrxrtsrxiz° ªy ii ³ÇoÁ¦ToÁuÀii/wzyzuvwzrxrtsrxiz³
,/.
) v ) ,
+J LLL
J
), + +
Àwzqgr LiVs s|y ³? ihw2ĨopygQs|y¨ Äziºuvw|´i-r ³Sudgis|/i~v~oxgoprpoÁu
op~uvoxq}uopw|y+s2u%«i-vw¯À0w|qgr rxw¨~is2u%hw¨~uw|yi oxhi-y~opw|yʰ
p\?[ GIH.a~aMLi
²|iYirxih(iy¨u*opyudgi0{gvw?w¦}w¦gwzqgÊ´~ui¬~qrÁuop~vw|{Lwz~oÁuvoxwzyGirxw2À³2ÀdopdhsMTi0Ä?oxiÀi s|~s
hw ox´i Äzi-~opw|y¯w¦[w|ygiew¦Ludieudgiw|vi-h~Sq~qsrprxi-¦§i-vi uvws|~cSÔ|ι}½[·8¬Æ?*Í}¿/¼ªÎ|¿8|»YÏȽg»º¼ªÎz¸/ÏÒÏȼ¾Ô
¼BÍ?¿·¶¿/Ó¯»ÖI~i-i¯i|°° Ésdy ³Êm?i/u°|Õ³Éo zsz~s|zs ;SwzjZkds|rxoprAx¬È×/°Yªyw| i-%uw+~oph{grxox¦§
uvdgiY¦§w|ud-w|hoxy ot~-q~v~opw|yʳ?À0iÉq~iYudgiY¦§w|rprxw2Àopyg¯ygwus2uopw|ysr[/w|y?Äzi-y¨uopw|y~°.CToxÄzi-ys¯i¬sr P:,
s|y s¯{Lw|opy¨u / "o%³Ài~i/u
S ) + &' * & / " % & & n U -
ÖIoB°i|° S ) +
op~Éudi(-rxw¨~i srprw¦Gs opq~ -i-y¨uii s2u ׺° Érp~w³[|opÄ|iy s~i/u "o%³À0iÀoprxr
i-ygw|uikoÁu~opyzuvi-voxwzs|~
. )!
+
sy oxuv~eLw|qgy svs|~ °
Z ¢ Þ Þ w¡ w§Þ|o[ G·½g»ºÏIÐ|¿-¶¼BÍ?¿»ÔM»º¼ª¿/Ó
$
&<'
"*)
&J
A
+J
Ö|¬×
SÍ}¿/¶v¿ "N/1!3 )"(%4" 7 " +
Î2½LÐ "*), J A
+*'
,ÉÑ/·¶T¿8M¿-¶ºÔpA / "B!T»»º¹}ӿɼBÍ?Î2¼S¼BÍ?¿-¶¿k¿zÏt»º¼GÎÇѹ}½[Ì/¼¾ÏI·2½
/:1 v )
"o% 7 " +
Î2½[Ð Î2½9· g¿/½Â»/¿-¼
"o%opÏȼBÍ , /
»º¹Ì/Í ¼BÍ?Î2¼
)& +
P<,ÃÏÑ & / νLÐ
)
&,+ ' , ÏÑ & /
I~k»»¹}Ó¿SÓ·2¶v¿v·:8M¿-¶ ǼBÍ?μ¼BÍ?¿-¶¿¿ zÏt»º¼
Î2½ · g¿/½ÏȽ¼ª¿/¶?82Î "
¶¿Î*Ì·½g»º¼Õν¼B»~OP,W )/"f, J
eµÎ2½[Ð PR,W
»º¹Ì/ͼBÍ?μ u )
&J
A + / e S ), +f 4 & ) + )
&J A +
)ROSe )& +f- L Ö¬|×
ÊÍ}¿/½¼IÍ}¿¯·¶ºÏÏȽ
&<'
,·Ñ0Ït»k¹}½»º¼ÕΨ¸?x¿2
Z ¢
ÞÊÞ9\ Êi-u#A
3 / sy
dgw?wz~i P ,~qd uvds2u
b &' eA3 JA 3
A f
Ű Ei{w}/ii
?
-w|y¨us
op/uopw|yÃsy
s|~v~qghiuvds2u¯udgiw|voxzoxy w|¦Ö|M×kot~¯~uvs|grxiz° cedgot~¯sz~~qgh{}uvoxwzyÃoxh{grpoxi¬~uvds2u
¦§wzTs|y?
& 3 /
S P)
, + Àoxud
& 3
~qg®-oxiy¨urpQ~hsrpr¾³uvdgi~wzrxqguopw|y
& )A +
uw Öz¬×º³ot~v~qgi
¦§vw|h
& 3 s2uA
' A3
³op~ i/´ygi ¦§wzA / eA3
J
eSsy ~vs2uot~´i~
& )A +
/'S ), +
¦§w|i-Äzi-vA>) A3 ° Êi/u
)A + &' )& )A + +
~wuvds2u )A 3
+*' )& 3 +
P,¯sy ) A + )A + '
) + )& )A
+J
A + ° EiT-rps|oxhuvds2u
& )A +
-s|ygygwuTi¬s|d ¦§w|Ys|y? A / b°kªy i-i ³[sz~~qghi A_v / b ot~Y~qdµuvds2u
& )A_v
+ / sy
& )A + / S ), +
¦§w|¯i-Äzi-v A / eA 3 J
A_v e°(%iy/i )A_v
+ ' , - )A 3 +
³SÀdgotdbhisy~uds2u
i/visz~i¬~ÇÀdoxrpi )& )A
+J
A + / e S ), +f 4Ű 40q}ueudgot~ot~s/w|y¨uvvs op/uopw|yuvwµÖ¬z׺³g~w(udgi/rtsoph
¦§wzrxrpw2À%~°Scedi-vi/¦§w|vi|³?uvdgi~w|rpq}uopw|y
& )A +
vi-hsopy~eopy S ), +
¦§wz%srprKA / b°±gvw|h Ö¬|×/³gÀ0ik~i-i
uvds2u ) A +) A +
):O e )A +f-
sy ³g? opi¬ºu%opy¨ui-zvsuopw|yʳ
)A +
)O ) n ) + )A n A 3 +
&e )A 3 +fv y.-
L
40ÅiÄ2srpqs2uvoxygsu]A
' A 3
+sy q~opygce )A3 +fv y3-
P,³}Àikzi/u
)A3
+ P eO ) n ) + f
P, L Öz×
cedi¯/wzy¨uopy¨qoÁu+w¦ ³Ludgis|~v~qgh{}uopw|y ),
+A'
,g³s|y udi¯opygi˨qs|rxoxuÃÖ¬z×oph{grp+udsuYuvdgi(~i/u
1 ' * & / '& )& +.'
eO ) n ) + f
-ot~ygw|yg©¾ih({gusy /rpwz~i ³g~ww|yiis|~oprxÅdgi¬²}~ÖIs¨sopy
?-w|y¨uopy?qgoxuÅw¦ ×uds2u
&' C
.
G
"!
&
i- }op~uv~³2sy uvds2u PR,g° wuviGuvds2u T w¨i¬~ywu i-{Li-y w|yuvdgidgwzop-iÇw|¦
& 3
°S±gvw|h Àdsu*{gvi-i i¬~-³
wzygi/w|y/rpq i~Yuvds2ukudi(wzop|opy ot~Tqgy~uvs|grxi~oxy/i¯udgiygwzh w|¦Çudi~w|rpq}uvoxwzy opy¨Ä2s|otsgrpµs2uuvsopy~
uvdgi~uvop/urpÅ{w¨~oxuopÄ|ikÄ2srpqgi °Gcedgot~/w|y¨uvvs op/uv~udis|~v~qgh{}uvoxwzyuvds2uuvdgiw|vop|opyot~~usgrpi|°
Ú £}¢54 ªy~uis w|¦Ys|~v~qgh{}uopw|y Ö¬z׺³w|ygiw¦ zs|{gqgygw2Ĩ© *dgi/usi-Ä ~uvdgi-wzih~(vi˨qgopi¬~uvds2u
uvdgi-viÇi- }op~uSsY/rts|~v~#" ¦§qyºuvoxwzy ~qduds2u ) + )
&KJ
A + ) ) & +
¦§wzs|rxr )
&KJ
A + / e S ), +f 4>"0°
Éw2ÀiÄ|i³¬qgy iudgis|~v~qgh{}uopw|y~*w¦Lcedgi-wzih udop~ygii ygwuSiudies|~i~oxy/iudgi/rpwz~i ©¾rpw?w|{
~}~uvi-h i{iy ~kwzyQudi¯uvoxhi-©¾Ä2sv?oxy¦§ii sz² dz*sy udgirts2uuvi-khsMµÄ2sygot~doxy i-{Li-y i-y¨urp
w|¦uvdgihszygoÁuvq ikw¦
&
°Gcedgi{w?w¦w¦Swz{w¨~oxuopw|yEw|yrxÅvi˨qgopvi~udgii- }op~uiy/iw|¦sy+wz{iy
uvoxhi-©¾opy¨ui-vÄ2srwzyÀdgotd ) + ) %J A +
ot~eygw|u"Êop{~doÁuv«ksuudgiwzop|opyʰ
qB\_0\[ Z ¢
ÞÞ %Þ {*Ú?Þ
¢ Ú [
ªy
&
©Õ-w¨wz oxysui¬~-³¨udi{iuvqgLi -rxw¨~i ©¾rpw?w|{~}~ui-h4ds|~0uvdgik¦§w|vh
$
& '
"*)
&KJ
A + 9 3 ) J &,+
2 v
9,2) J &,+
2 )
&J A + J
Ö-j¨×
Àoxud
"*)
&J A + &
'
3 )
&,+
3 )& +
2 v ) 2 )& + 2 )& +-+
2 )
&KJ A +
i-ygw|uopygudgiqgyg{Li-uqgvLi /rpwz~i ©Õrxw?wz{ Ä|i¬ºuvw|T´i-r °m?opy-i¯uvdgivoxzdzu©¾dsy hi-hLi-w|¦TÖ-j¨×
ot~/wzyzuvoxy?qgwzq~Ö§gq}uygw|u(yi/i¬~~vsvoprx Êop{~vdgoxu«¬×/³udii- }op~uiy/iw¦Y~w|rpq}uvoxwzy~ot~(|qs|vs|y¨ui-i ¦§w|
s~q}®Å/opi-y¨urp ~hs|rxrSygwzy}©Õi-h{}uµuvoxhi/©Õopyzuvi-vÄ2srmeA 3 J
A_v,eÒ° #%ygot˨qgi-yi~v~kw¦0~w|rpq}uvoxwzy~-³ÀdopdEoxyudop~
s|~iÅygii ywu¯dw|r ³Got~ygw|u¯vi˨qgopi uw{gvw2Ä|iÅopy~uvsoxrpoÁu w|¦udgiw|voxzoxy°! %rt~w³?Ãq~oxyg udgi
dw|hw|zi-ygioÁus|~v~qgh{}uvoxwzy~³À0i~i-iuvds2uTis|dQ-w|h{Lw|ygiyzu "C w|¦ " op~!M )Hx%$
+
¦§w|Ys|y? u¬©Õygw|vh H°
Yq%soph ot~euw{w2ÄziYuvds2uÉs hop~v~oxgrpi{Li-uqgvs2uvoxwzy~ 9 3 J LLL
J9
³s|~ i/´yi opy Ö=0×/³-s|y+iy i-
uvdgi+w|voxzoxy w¦¯Ö-j?×qy~usgrpi|°9cedgot~Àoxrpriµsz-/wzh{grxot~dgi
¨ ~dgw2Àopyg udsuµÖ-j?×Äzi-voÁ´i~¯udgi
sz~~qgh{}uvoxwzy~%w|¦Gwz{w¨~oxuopw|yæ§w|Ys|y?dgwzop-iw¦ P;,g°Éc*wudop~Y{gqgv{w¨~iz³À0iÀoprxrS/wzy~uvqºuYs
¦§qyºuvoxwzy d& "(%" sy s~i/u s|~evi˨qgopvi opyudgi{wz{w¨~oxuopw|yʰ+i/u
H )
&,+ ' %
3 v
&
$
J
Àoxud ' %
v u J
Ö¬|×
s|y i/´yikudgis|q} }oxrpops|hs|{g{gopyg5&"o%N"o%?
)
&,+ ' H )
&,+
)& +
' )H v y )
&,+& v J LLL
J H v y
)
&,+& % + )& '
,
+J
s|y ) ,
+3'
,g°0ÕuÉop~Y~oph{grpiuw~dgw2Àudsu ot~Ésdw|hi-wzh(wz{dgop~h4s|y udsuÉoxuÉop~Y/wzyzuvoxy?qgwzq~rx
o[i-vi-y¨uotsrxi(oxy"$%°±gwzTudgi(¦§w|ud/w|hopyg-w|h{gq}us2uvoxwzy~-³oxuop~k-w|y?Ä|iygoxiy¨uÉuw+opy¨uvw
q/i¯udgi
dsygzi(w|¦%/w?w|
opys2uvi~
' )& +
°+±w|s¦§qyºuvoxwzy
"
&(" $% " Ö§vi~{LiºuvoxÄzi-rps+Äziºuvw|´i-r
V
&"
$%
4j" p"
%
×|opÄ|iyopy
&
©Õ-w?w|
oxys2ui¬~-³MÀ0iÀoprpr
i-ygw|ui0oÁu~Si/ }{gvi~v~opw|yoxyz©ª/w?wz
opysui~s|~
$ " Ö§vi~{i¬ºuvoxÄzi-rp
$ V ׺° w|uiÉudsuox¦ " op~ u¬©¾dgwzhw||iygi-wzq~w|¦ i-zii ³¨uvdgi-y
$ " '
" y v op~
dw|hw|zi-ygiw|q~w¦*~vshi i-zii ³}gq}u%Àoxudvi~{i¬ºu0uw(udgi(»º¼ªÎ2½LÐzÎ2¶Ð oprts2uopw|y
° Érp~w³?ox¦ " '
= )H +
Ö§vi~{i¬ºuvoxÄzi-rp " ' M )H#
+
×*udgiy
$ " ' = ) % +
ÖIi¬~{Li/uopÄ|i-rp
$ " ' M ) % +
×/°Sm}oxhoprps|rp|³
ox¦*s¯/w|y¨uvoxy?qgwzq~GÄziºuvw|Ç´i-rV ot~ u©Õdgwzh(wz|iygi-wzq~Gw|¦ i-zii ³zuvdgi-y
$ V op~~
©Õdgw|hwz|i-yi-w|q~
w|¦ i-zii °Õ¦ÊudiYÄziºuvw|Ç´i-rV
'
)V v J LLL
J V % +
op~e/wzy¨uopy¨qw|q~0sy ~suot~´i¬~ V ' = )H & $ +
ÖIi¬~{Li/uopÄ|irx V ' M )H & $ +
×(¦§w|"
' J
LLL
J
s³euvdgi-y!
$ V ' ) $ V v J LLL
J $ V % +
~vs2uvop~´i~
$ V ' = ) % & v +
Ö§vi~{i¬ºuvoxÄzi-rp"
$ V ' M ) % & v +
׺°cedgiÄ|i-vox´-suopw|yQw|¦Çudi~isz~~i-uopw|y~
vi-{i¬~iyzu~ygwk{suot/qgrts ox®Å/qgrxu|°Sªy¯udgi%~i˨qgirB³|ÀiÀoprxrg~oph({rx¯Àoxui dgw|hw|zi-ygiw|q~ opy~uvis
w|¦ dgw|hwz|i-yi-w|q~Àoxud+vi~{i¬ºueuw °
Éy¨µ~w|rpq}uopw|y w¦ÉÖj¨×/³ÀoxudoxygoxuotsrS/wzy
oxuopw|y
& )A3 + '
,g³[~vs2uot~´i~%udgi¦§w|rprxw2Àopyg
o[i-vi-y¨uotsr
i¬Ë¨qs2uvoxwzyopy z©ª/w?wz
opysui~
$
' ) J A +
& ) y v ) + + 9 3 ) J &,+
2"
v 9 2 ) J & + 2 )
&J
A
+
G
+
/ 5
Ö ;z×
Àoxud
) J A + &'
& ) y v ) +-+
"*) y v )
+J A + L
40 uvdgiQsv|qghiyzu~opy udgi+{gvi-Ä?opw|q~({s|vs||s{gdʳSuvdgiµ/wzh({Lw|yi-y¨uv~(w¦ Äzi-voÁ¦§
' M ) % +
) ' J
LLL
J s + °
m?opy-ihs{~
+ uwµoxuv~i-rx¦³SÀiÅdsMÄ|i <&
' ) y v )2 +J
A3 + '
)2 J A3 +
°/4Es|~v~qh({guopw|yʳ
'
,sy op~(/wzy¨uopy¨qw|q~°ced?q~³S¨Ã-w|y¨uopy?qgoÁu w|¦ y v
³GÀ0iÅoxyg¦§i-(udgii/ }ot~uvi-y-iw¦%vis|rp~
P ,g³ OVvrP ,g³s|y w¦Gsy+opy¨ui-vÄ2sr &' eA 3 J A 3
f ³LÀoÁuvdA
3 - A 3 -
A_vM³L~qduvds2u%¦§wzÉsy?
) J A + / S )2 + 4
I
) y v ) + J A + I '
* . ) + ) y v )
+J A +
P:OVvL Ö0×
w2À³}{got²sy?Åopy¨ui-zi-PR,~qduvds2u
?
P X
tu
P,(s|y
dgw?wz~i P,~qdudsu¦§w|%sy?
/ " %
³Àoxud
' ³wzygids|~
n 2 U
Àdi-ygiÄ|i-
n 2
$
U Ö§udgot~sy srpÀ0sM}~Ti
szdgopi-Ä|i ~oxy/iTudgi
?
z©¾ygwzh % $s|y udgiØq/rpo i¬sy
?
©Õygwzh % s|iki˨qgopÄ2srpi-y¨u×/° Éi-´ygi
)
+*'
?
$
$
n %
v #
$
J
Öz×
s|y &' * / "
$%
&
P:,
J
$
$
P %
v #
$
-+L
Õu%ot~eisz~Åuwdgi²Åudsu
ot~syw|{Li-yµ~i/uÉs|y uvds2u%oxuv~%wzqgy s|ot~|opÄ|iy?
' * / " $% & P,
J
$
$
' %
v #
$
-"!*,.- L
ØGĨo iyzuvrxz³ op~~uvop/urpµ{w¨~oxuopÄ|i¯oxy
³Àdgii¬s|~YoÁuÄ2syop~dgi~Topy
°Õuvi-hsopy~Éuw{gvw2Ä|iuvds2u
uvdgis|~v~qgh{}uopw|y ÖM|×w¦Swz{w¨~oxuopw|yEkop~Ésrt~w(Ä|iox´i °
ªyÅÄ?opi-À w|¦udgiTdgw|ot/iYw¦ [³zuvdgiToxygi¬Ë¨qsrpoÁu(opy Ö0×dw|r ~G¦§wz A / sy ¯opyÅuvdgiÉopy¨ui-~iºuvoxwzy
w|¦
Àoxud uvdgi d??{i©Õ{grtsygi i/uvi-vh(opygi ? ' ° ±gqgudi-vh(wziz³0udgiEhs{g{gopyg ) J A +
) y v )
+J A +
ot~edgwzh(wz|iygi-wzq~0w¦ i-zii
n X ¨³~w
) J A + /
4 & I ) y v ) + J A + I
P, L Öz×
Yi-ywui(?6udgi(Ä|i¬ºuwzÉ´i-r
wzyµudgivoxzd¨u©Õdsy
h(ihLi-kw¦TÖ ;¨×º°J40
opi¼u
o[i-vi-y¨uvopsuopw|yʳ
s|y
q~opygµÖ0|×esy
Ö¬z×/³gÀi~i-iTuds2u¦§w|iÄ|i
) J A + /
4
) + ) J A
+*'
) + ) J A +
& ) y v ) ++ I ) y v ) + J A + I2 L
cedi ) J5 +
©¾ud+i-y¨uvÅw|¦*uvdgivi˨qgopi s|/wzgotsyhsuvoÁ )
&,+
)
&,+
ot~e|opÄ|i-y?|
& 4 ) y v ) ++.' H v y
%$
)
&,+
n u
u4 H y $
)
&,+& &
) y v
4 X 4 G
+
/ 5 J
Ö¾z×
Àdi-vi X 4 ' ox¦
' 5 sy
X 4 '
,ox¦d
' 5 °
)
+ ) J A +
-s|ys|rp~wiÀvoÁuuiysz~
) + ) J A
+*'
v ) J A + $ ) J A
+J
Àoxud
v ) J A + &' %
3 v
) + -) J A + J
0$ ) J A + &' I ) y v ) + JA + Ie ) +
) +fJ
s|y ) + &'
) + %
& ) y v ) +-+
'
$
$ y v
H v y
)& + n u
u &
H )& +
$
G
+
/ 5 J
Ö¾}¬×
) + &' %
3 v #
) + %
& ) y v ) ++
' n %
v #
$ y v
H v y
%$
)
&,+
n u
u &
H )
&,+
$
&
&
G
+
/ 5 L Ö¾||×
wuviudsu ) ' J
LLL
Js +
op~dgw|hw|zi-ygiw|q~w¦ i|vi-i
? n ³ud?q~ v ' M ) %
$
+ °
±qgudgihw|vi|³}~oxy/i
I n u I
u -
sy &
H )& + G
+
/ 5 U )
' , + J
uvdgiuvi-vh ÀoxudoxyQvsz²|i/u~opybÖB}M׺³[sy
di-y-i ) +
³s|i~uvop/urp{Lwz~oxuopÄ|i|°YYy+uvdgiw|udgiÉds|y
³
¦§wz
' J LLL
J
s³gÀikdsMÄziju
) ³g~w n u ' n Iu n I
°cedgi-vi/¦§wziz³}Àdgi-yi-Ä|i
'
,
)
+.'
%
v #
~|y ) +
~zy )& +
~zy )& + I I
$
y v H v y $ )
&,+
Iu n I
u &
H )& +
$
&
& G
+
/ 5 L
40q}u b{gvi~i-vÄ|i¬~SudgiT~op|yÅ-w|h{Lw|ygiyzu©¾Àot~i|³|o¾°i|°~|y ) + '
~|y ) )
&,+ +.'
~zy )& +
³¨uvd¨q~ ) + )
,°*±wzh Öz×/³¬s|y ~oxy/i ) +
PR,%s|y ) +
P,³À0iÇ/wzy/rpq iÇudsu 0$ ) J A +
P,e¦§w|*i-Äzi-v ) J A + / 4 ° 4oxy~{Liºuvoxwzyw|¦0Ö¾}¬×sy Ö¾||×/³}ÀiY¦§qgudgi i q/iTuds2u ¯s|y s|iTdgwzh(wz|iygi-wzq~Çw|¦
i-|vi-i
? n u °ªyµ/wzy~i˨qgi-y/i|³ $
ot~dgwzhw||iygi-wzq~w¦ i-zii
&
'&?
n X n u
PR,.L
i/u
% y v &' * /
"(%&
' -¯s|y
&' ! ° #Y~opygÅuvdgi(dgw|hw|zi-ygioÁuw¦"0$³L¦§w|ksy?
) J A + /
4
$ ) J A +
' I ) y v ) + JA + Ie ) +
) +fJ
Àoxud &' / % y v
°(Yygii¬s|~oxrpµÄ|iox´i¬~%uvds2u ) % y v + S :)2 +
³Ê~wEÖ0×%dgw|r ~
s|y
I ) y v ) + J A + I
)<O v ° %rt~w³ s|y
s|i/wzy¨uopy¨qw|q~ksMÀesM¦§vw|h udgiwzop|opyʳdgiy/i(udi-
suusopy uvdgi-opkh(opygophs+w|yQuvdgiÅ/wzh{s|/uk~i/u
% y v
°cedgi~i(h(opygophss|i~uvop/urpQ{w¨~oxuopÄ|iz³s|~
¦§wzrxrpw2À%~e¦§vw|h udgidgw|hw|zi-ygioÁuw¦ sy sy ¦§vw|h4udgi¦Is|/u%udsuÉLwudQ¦§qgyºuvoxwzy~És|i~uvotºurp
{Lwz~oxuopÄ|ikoxy
°Yyiksyud?q~ i/´ygi
O $ &' O
v
E#C
.
"
+ * ) + ) + -
uvw/w|y/rpq iTudsu¦§w|iÄ|i-v ) J A + / 4
k$ ) J A +
)O$!P,
J
Ö¾z×
s|y
)
+ ) J A + '
$ y v
) J A +
$
0$
) J A +
)
$ y v ) J A +
$
O$
L Ö¾2j¨×
ªy s oÁuvoxwzy uvw+ioxygM ) %
$
+ ³ v¯ot~Tudgi~qgh w|¦dgwzhw||iygi-wzq~ɦ§qgyºuvoxwzy~kw¦ i-zii
?
Qsy
doxzdgi-0w| i-uih~kÖÈuvdgot~0syik~ii-y¦§wzh oÁu~ i/´ygoxuopw|y+sy ¦§vw|h udgiT¦Iszºu0udsu ot~udgi~qgh
w|¦sdw|hw|zi-ygiw|q~ÇÄ|i/uwzG´ir w¦ i|vi-ir,sy dgop|dgiwz i-ÇÄzi/uw|Ç´i-r ~׺°Õu0¦§w|rprxw2À%~Çuds2u³??
Ä?opuvqgikw¦
? n P,g³}uvdgikuih
) J A + &'
$ y I v ) J A + I
$
Ö¾||×
uvi-y
~uw¯«-iwsz~
w?i~³|qgygox¦§w|vhrx(¦§wzcASoxy Űcedgi-yʳzudi-vi%i/ }ot~u b P,sy
O : />f
, J
O$,e|~qd
uvds2u
) J A + / e S 9), +f 4 & ) J A + - O : sy ) "
+ ) J A + P:, L
w2À³?{gop² ) J A + / e S ), +f 4 svgoxusvoxrp|°$#É~oxyuvdgiYopygi¬ËzqsrpoÁuvoxi¬~" ) +
PR,s|y
$
)
$
³zs|y
srt~wTudi
i/´ygoÁuvoxwzyQÖ¬z×w¦ Y³|À0i|i/u
) )?
$
+
e ) +f
P:,sy
³z~oxy/i
P,g³
) ?
$
e ) +f
P, L
cedop~rts|~u*opygi˨qs|rxoxu|³-w|hoxygi Àoxud+ÖBj¨×º³2Àdwz~iÇvoxzdzu©¾dsy hihLi-Sop~S~uvop/urpk{w¨~oxuopÄ|iz³2¨opi-r ~
) + ) J A + ) ?
$
$ y
v ) J A +
$
6O $ e ) +f
L
m}i/uuvoxy
OQ&
' ?
$
)O $ n O : + P:,
J
À0iT´ys|rxrpÅw|guvsopy
) J A + / e S ), +f 4 & ) + ) J A +
):O e ) +f
L
ªy+wz i0uwi-uqgvyuw
&
©ª/w?wz opysui~³?rxi-u
)& + &' ) )
&,+ +J
sy &' y v )
+J
s|y rxi-u " i-ygw|uikudiÄ|i/uwze´i-r oxy+uvdgiop|d¨u©¾ds|y h(ihLi-%w|¦eÖ-j?׺°GÕu%ot~%~usop|d¨u¦§wzÀes uw
di²uds2uudii¬sry?qghLi-
V&
' E C.
"
# y v ) +
i- }op~uv~³zs|y udsu ) + )
&KJ A +
)O e )& +f
¦§wzÇi-Äzi-v )
&J
A + / e ! S ), +f 4 °m}oxy-i ) &'
$
/
f, J
e¨³}uvdgis|~v~qgh{}uopw|y ÖM|×w¦Swz{w¨~oxuopw|yEkop~ud?q~eÄ|iox´i s|y uvdgi{gvw?w¦*ot~%-w|h{grpi/uiz°
qB\_0\_ Z ¢ ÞÞ %Þ {*Ú?Þ ¢ Ú _
i/u
$
& '
2 v 2 )& +
2
Ö¾:;z×
LiYs|y? u¬©Õdgw|hw|zi-ygiw|q~Çs{g{gvwM }oxhsuopw|yw¦~}~uvi-h ÖIz×GÀoÁuvd-w¨wz
oxysui%ds|yg|i
&<' ) +
°. Érp~w³
-w|y~o
i-Gs|y¨(/wzyzuvoxy?qgwzq~Sdgwzh(wz|iygi-wzq~ H|©Õi/ }{Lw|ygiy¨uotsrg~uvsoxrpox«i- Q¦§w|ÉÖBz×hi-i-uopyguvdgii¬Ë¨qgoxvi/©
hiyzu~Çw|¦ Éi-´ygoxuopw|yg°±gvw|h udgiT{gvi-Ä?opw|q~
i/´yoÁuvoxwzy~-³¨uvdgiÉÄziºuvw|Ç´i-r
~ 2
svi>u¬©Õdgw|hw|zi-ygiw|q~
w|¦ i-ziicX 2 -
,g³Àdgii¬s|~uvdgiQ¦§ii s|² ¦§qgyºuvoxwzy~ 2 s|iu¬©Õdgw|hwz|i-yi-w|q~w¦ i|vi-i n X 2
) ' J
LLL
J !+
° i/u &' * v v J LLL
J
-sy * &' * v J LLL
J
- i-ygw|ui¯udgi~i-uv~
w|¦Ä|i/uwz´i-r ~¯Ö§i/ }{gvi~v~i opy
&
©ª/w?w| opys2uvi~×0Àdgotd i/´yiudiygw|hopysr~}~uih6s|y dgwzh(wz|i-©
yi-w|q~s{g{gvwM }oxhsuopw|y ÖB:;¨×º³*i¬~{Li/uopÄ|i-rp|°Êi/u 0KC32:) )x*
- +
iÅudgi oxiÅs|rxzi-gs~{s|ygygi
?udgi¯i-rpi-hi-y¨u~Éw|¦ s2¦ÈuiYvi-hw2Ä?opygudgi }©¾udQÄzi/uw|%´i-r
h ?³[sy Q i/´ygi 0KC32 )! )+*
-
+
sz--w| oxy|rp|°.CToxÄzi-y+s(~i/u w|¦*Ä|i¬ºuvw|e´ir ~³}À0iTrpi/u ), + &'
*!+ ,/.
* V ), + & V/ V-z°
cedgi¦§w|rprxw2Àopyguvidgygot-s|rrpi-hhs~uvsui~%udsuYox¦udgi syg²¨©Õrxw¨~~ {wz{iuEÖ¨×edgwzr ~ɦ§w|Éudgi
yw|hoxysrÊ~?~uih+³?udgiy+s~oph(oprtse{gvw|{Li-uÅdgw|r ~0¦§wzeudgis|{g{gvwM ?ophs2uvoxwzy ÖB ;z׺°
Ú £ [ r*½[Ð|¿-¶¼IÍ}¿¯Î2»v»º¹}Ój¼¾ÏI·2½»·Ñ ÊÍ?¿·2¶¿-Ó 0·½L¿Í?Î2»
/ * J
LLL
J
- & WCFE0C21) )x*
- + ), + - s n L Ö¾10×
Ö 0¶·¬·ÑÏȽ¼IÍ}¿r~g¿/½[Ð2ÏM׺°
Ei/rtsoph udsuYuvdgiÀioxzdzu~pu
sviygw|us|rxri˨qs|rB³Ê~w ' ) ?
°cw{gvw2Ä|iuvdgot~-³Ê~qg{g{Lwz~iuvds2u
u ' ) J LLL
J +
°ÕuǦ§w|rprxw2À%~S¦§vw|hÇTuvds2u
v J LLL
J
svi%/w|y~usy¨uÇ~wkuvds2uesy?vsz²|i/uopy?Ä|w|rpÄ?oxy
wzygi(w|khw|vi¯w|¦Çudi~i(Äzi/uw|T´ir ~kop~ko i-y¨uvopsrprxµ«i-vw°G40q}ukuvdgis{g{gvwM }oxhsuopw|yÂÖ¾:;z×T~vs2uvop~´i~
uvdgi É*Y³[~wuvdgi¦Is|hoxrp ) v ), + J LLL
J
), + +
~{sy~j"(%Âsy ) s°Ycedgi-vi/¦§wziz³ox¦GÀi¯ih(w2Äzi
s|y?
2 ³uvdgiÅs|/i~v~oxgoprpoÁu ot~uvoxgqguopw|yEw¦ÇuvdgiÅs{{gwM }ophs2uopw|y rxw¨~i¬~Tsuh(w¨~uwzygi oxhiy~opw|y s2u
uvdgiw|vop|opyʰ*ªy+w|udgiÀwz ~ WCFE0KC32 ) )+*
2 - + ), + )s
n
³}Àdgotdµ/wzyzuvvs otºuv~kÖ¾10×/°
w2À rxi-u
D
LiYudgiru¬©¾{s|uvoÁuvoxwzyw|¦udgik/w?w| opys2uvi%Ä|i¬ºuvw|
&
°+#É~oxy¯{gvw|{Li-uopi~G(sy 3;g³?Ài
syÀoxuiTuvdgis{g{wM }ophsuopw|yEÖB:;¨×oxyudik¦§w|vh
D v ' v
D $ ' $ )D v
+
°°°
D + ' + )D v J
LLL
J8D
+ y v +
Àoxud v vi-{gvi~i-y¨uvoxyg s -w|y~uvs|yzuµhs2uvox ³ $ J LLL
J +
hsuvoÁ ?©ÕÄ2srpqgi
¦§qgy/uopw|y~³sy
'
) v J
LLL
J
+
udi/w|y¨uvwzrLÄzi/uw|¬°
Ei~ds|rxrSygw2À{gw2Äziuvds2u + ),
+B'
,?Q/w|y¨uvvs
op/uopw|yʰm}qg{g{Lwz~i¯uvds2u + ), + '
,°cedgiy
uvdgi-vii/ }ot~u~s2urpisz~uwzygiÄ|i¬ºuvw|k´ir 4 /& ~qdEudsu 4#
+ ) , +
ot~ygwzyg«-iwÃÖIi¬-srprSuds2u 4
i-ygw|ui~uvdgi!u©Õ{s|uvoÁuvoxwzyw|¦
4 ׺°Gcedik-w|h{Lw|ygiyzu~0w¦ 4!#
+
s|iYud?q~~u¬©Õdgw|hwz|i-yi-w|q~Çw|¦ i|vi-ij,
s|y 4 ot~ u¬©Õdgw|hw|zi-ygiw|q~w|¦ i|vi-i X 4 ' n u % ' n
u,+°±wzh GkÀ0ieoxy}¦§iuds2u 4!#v J LLL
J 4!#
+ y v
s|i(o i-y¨uot-s|rxrp «i-vw³~w
4 ot~s+/wzy~uvsy¨uÄ|i¬ºuvw|T´i-r °m?opy-ii-Ä|i Ä|i/uwzY´i-r opy 0KC32 )!
+
op~
u¬©Õdgw|hwz|i-yi-w|q~Éw|¦ygizs2uvoxÄzi i-|vi-iz³oÁu¦§wzrxrpw2À%~Y¦§wzh Çsy juds2usy?Qgs|²zi/uk/w|y¨usopygoxy
4 ot~«i-vw°<Éi-y-i|³ihw2Ĩopyg
4 shwzqgy¨uv~kuvwµih(w2Ä?opyg+w|ygrpEw|ygiÄziºuvw|k¦§vw|h 0KC32 )!
+ ), +
³~w
.CE0KC32 )! )+*
4 - + ), + ) s n
³}opyµ/w|y¨uvvs op/uopw|yÀoÁuvd Ö¾10|׺°
±opysrprxz³À0iÅ~dw2À uds2uudiygw|hopysrG~}~uvi-h Äzi-voÁ´i~TudiÅs|~v~qgh{}uvoxwzy~kw¦ecedgi-wzih |°±gw|
uvdgot~%oxuÉ~q}®Å-i~uvw{gvw2Ä|iTudsu%udik¦§i-i s|² bot~É~qdudsu%¦§w|É~w|hi / * J LLL
J!
-s|y ~wzhi