HAL Id: inria-00072589
https://hal.inria.fr/inria-00072589
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- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
On Equivalence between Timed State Machines and Time Petri Nets
Stefan Haar, Laurent Kaiser, Françoise Simonot-Lion, Joël Toussaint
To cite this version:
Stefan Haar, Laurent Kaiser, Françoise Simonot-Lion, Joël Toussaint. On Equivalence between Timed
State Machines and Time Petri Nets. [Research Report] RR-4049, INRIA. 2000. �inria-00072589�
ISRN INRIA/RR--4049--FR+ENG
a p p o r t
d e r e c h e r c h e
THÈME 1
INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE
On equivalence between Timed State Machines and Time Petri Nets
Stefan Haar, Laurent Kaiser, Françoise Simonot-Lion, and Joel Toussaint
N° 4049
November 8, 2000
Unité de recherche INRIA Lorraine
2 43, 657'-
849;:=<?>A@CB>A>ADFEHGJIK>AL%D;:H@M9NO>APRQ:HD=GTSUDF>@,VHWXPYQ;:Z8'PY[\WA@,WA9]^IPRWX@U_G`>A@%acbAW4:Hd
e WXL,QQF>APY@f9Fg
hjilk1mnoqpsrtuvnwyx{z|n}~uv{u}k1mnu
n}Khrv
rKwyA yv}nvn;in1inA%HHpsK ynmAn1Ay=&polw =nu
¡|¢%£¤1¥¦§y¤y¨ ©}iª«uwy?}ª«1¬n=f®n¯ª°{n=}ª²±³w´u?xX¬°wyuu& ±jhjªmn;µ~x{}v =m¶w}w¸·YµK¬«xw¹ª¬«¬Kº«o^»³¼^
w¬«¬n;¾½4¿ÁÀ¶ÂÃ\ÄAÅÇÆÅÇÂÈZÆ=ÉÊ{¿ÁËAÂÌwyu®nwyÍH¬«ÎnÏHxª«w¬«n1H}ЮÑ;Ñ};ÑÒu?}v y =¬Ó}vª«mnÔnilwFÕª =|} Ów
w =ª°1w¬j¬°wyuu$ ±hjª«mn,n1}vªj~n}u·YhjÖ~u¼¯ª«6}viln´uvn1u?n ±×Ðnv¬«ª«ÓwylÙØwnº«oF»ÇÚjm yn
lvn;ª°u?n¬=X}vin®nwÍ´n;Ï=xlªw¬«n1n¯i y¬°uq±³ y&A yx{n yÛÜAn hjÝÞ®ª}vißuvn1¬±ÁÛÇ1 yl1xvnloy
n1 y}vn´ohjÖÑlhKà{×Ouwylª´lwy?}ª«1x¬«wymnuuvwy yn&u?Õli ylªánv {{x^}ulw¬«¬n;hjv&à{×Zu1
wyvn$m¶wª«¬Ðxu?n;б³ yq}nu?}q =n1nw}vª« yfÚM =O}viln$ y}vinqiwlMX}in1n¯ª«u&wvª°iO¬«ª²}n1w}vxlvn¯ yZhjÝ~u
ª«´ynvªâ1w}vª« yfÑ,ãKnln =xm }ªw}ª =|} ¶ ym$ª«n&}vinu?}vn1 y}viluj y±%A }i´m¯ {{n¬«uÑUänvn;u?nH}
iln1nqwyn1zÕl¬ª°ª}~ =lu}vx^}vª« y|±³ yj}® Û®jwF}vwu?¬°w}ª =|An}®n1n1oÛ©hjÖuwlhKà{×OuÚ{ª´A }i
ªn}vª« ylu}inA ®ÝnK ±Ö1¬ {Í}vª«mª |ª«unz{¬« yª}vn;}v | ={}wyªO1 yl1ª«uvnwylÐwlwy¬Õá;w¬«nm Õn1¬°u1Ñ
hjilnhKà×åm {{n1¬Ö y{}wª«nZ±³v =mæ}vin}wyluv¬«w}vª« yZiwyuwu}w}vn¶uvn}}in¶u?ª«á1n ±Ý}vin¶nw=ilwlª¬«ª²}
=wyifÚHª²}Ý}viÕxluݪm yn;uU yç}vin&¬°wyuu =wyi¶ y{}wª«nÕ¯}vilnÂ1Ëlè{À¶ÂéÆÅR¿ÁêFÂqÀ¶ÂųÊë;úìF»ÇXº»RÑUhjin
n1z{ª«u?}vnlnj ±A}vilnj}vwluv¬«w}vª« y$v {1n{xnyy®iª«iilw=uUw¬°u? &An1n¯ª«m¬«n1mn1H}vn;¯ª¶w}v Õ y¬lv y}v y}HAny
í½AîïÄlÈÐ{m¶wÍ=nu}vilnm¯ {{n¬MnÏHxª«w¬«n1l1nqn1ðAn;^}ª=nyÑ
ñÐòHóXôõö ¥÷%£y¨ hjª«mnOµ~x{}v =mw}wlAhjª«mn,n}vª,Kn}u1Anw¬f}vª«m¯n¯u?{u?}vnmu}nu?} =n1nw}vª« yf=n1ª²Û
âA1w}ª =
ø&ùlú?û^üþýqÿ'ûüþý þýýFý'ü !"#$% &ú?ýFý(')#*+,- .;ú?ýMý þü0/1Rý(23 .456 -7%ý.&8429:4
û;1Rý=<>?1@FýBACYûý: .=DFEHGI*Yû Jýú(1LK6MNK6$OAOP6AQR*SXû.T1ú16Gfý2ýYý.FúýUAGWVOX0+EHGLYWX;SDX;Z[\X]##\4SMû;X
Yý&-û.*.^?K6*1@Fû
_
M%`BGFa]KFX;AAÿ6*AOEb!cdý:.TFýeFýUüfg+ûh(16;ýUüfi56>ý, *j:[ckQ .;ûý*d Yý+, .Fúý4
AC þü0/l8Mm ý.T1:4nU &Rýo+, .Fúû&Rý4 û.;û 1p 7%üþûf*423
q
W.dR4VXüf &RýU$% &Rú:ü0RSXüþýû.T1X]+ý .+, .Fúý4QAC þü0/m1Rû*&-&r .1r7%üYý4.*d X]<*4úüþý:û.18429
" -'$# ! 2 43% %K%'&3,-
(*)
£,+.-
) ¨
¹wylun}wv}vª°¬«nyyl yxluÖª«{nH}vªâl yluÝxnu? =xluÛ©¬°wyuuvn ymmt1n½4¿ÁÀ¶ÂÃ$ÄÅ©ÆÅ©ÂKÈZÆ=ÉÊ{¿ÁËAÂÌ
nujwx{} ym¶w}nuÝ}vnm =vª°u?t;uÝn&µ~¬xln1}K¹~ª«¬¬Uº«o»f1 ymmn~± wyª¬«n1mn=}n;Ï=xlªw¬«n1H}n¯·lwjwA yv}wyx
1 ymA yv}vn1mn=}±³ =?}n1mn1H}}n1m =vª°uvt;¼0/xln¬°wyuu?nw =ª«ÏHxnnrtuvnwyx{z{n%t1}vªM}vnm =vn¬«u
lv = Hu?t;u×Ðn1¬«ª6n1}¯Øwn|º«oF»ÇÚ,¬xut1ª«uvn1mn=};'1n}?}nç±wyª¬«n|t;ÏHxªwy¬nlnnu?}$t}w¬«ª«n|wFyn;
¬«nu&rKC}n1m =vn¬«uqA ytu%ËAëË!132%Â1ËAën}4/wyx{}v yÛÇ1 yl1xvnln65=l }vt;u&ohjÝÑ87fn;u&hKà{×ßMn}
l }wymm¯nH}4¬nxluflv {{xª}u'u?Õlilv =ª«uvtu9/jmn;uvuw =nufÏHx8: y =mm¯nÝhjv&à{×ßuv yH}4uvxv}v yx}4x{}vª«¬«ª«uvtu
A yxl ytt1n1nu}nu?}uÑ'¹nç¬;:wyx{}vnçlwy?};4ª«¬Önz{ª°u}nçxn|¬ª}?}t1w}vxlvn¶}vk;uª«inçuvx$¬<:x{}vª«¬«ª«uw}ª =
nurK¸}vn1mA yn1¬°uUn1¶=t1ª²âA1w}ª =fѹ=: ?>¯l }vnm }ªw}ª =¶{n~ =mª«nU¬«w&xlª«uuvwylnKnu{nx{z
m {{k¬n;u1Ñ
~ yxluÖm¯ =H}v yluUª°ªxnq yu}vxl}vª« ynz{¬«ª°ª}vn~ÏHxªnvmn}j{n}w={xª«vn¬«nuÝohjÝ n1|hKà×
n1}4Õª«1nUynuwÚwyluf¬«nu4{n1x{zuvn1lu yu,:wxlynUu?xl4¬°wjxª°uvuwl1n{n¬°w}vnm¯A yª°uvw}vª« y&lw4i y¬ = yn;u
A yxl y{}n1ª«{n;um {{k1¬«nu yª°un}$wylw¬«{uvwy¬«nuÑ87fnç =wyin¶9:t}w}u${x6hKà{× y}vn1Õx¸lwy¬«w
}w={xl}vª« yn}ÝnK¬«w}wª«¬«¬n~x¶ ywinK8:w}?}vnª =lwlª¬«ª²}tyÚª«¬Anu?}Ý{ yj¬xunA@çwynKÏHxn~¬nK =wyinK{n
1¬«w=uvuvnu~ y{}n1ÕxOlwy¬°wOÀB1ÅÁÊlëÃ=Â6BËè{ÀCB1évÆÅY¿Áêºì»Ç%º»RÑD7E:nz{ª°u}n1l1n${xv {1nuu?xlu{n}w={xl}vª« yf
ª«m¬°wH}vt&wx´u?nª9:xlv y}v }ÕAnq8: =x{}vª«¬Yí½îïÄlÈÐ{vnlç¬;:tÏHxª«Fwy¬nln&{n;ujm¯ {{k¬n;unðXn^}ª=nyÑ
Fö ¤;£ ô §G) £Z¨ µ~x{}v =m¶w}vn;uK}n1mA yª«uvtuMrtuvnwyx{zO{n$,t1}vª'}n1mA yn1¬°u1Muv=}k1mnu}n1mluqvtn1¬RX ytÛ
lt1w}vª« y{n&}vn;u}u1lyt1ªâ1w}vª« y
$43 &¶!Ö' A&
ä ilª¬«n}viln1nKnz{ª°u};±³ yÖ%n1}vª~n}uÖ®ª²}i yx}}vª«mª =A ®n1v±³x¬lwy?}ª«wy¬ y{n1}vnilª«ÏHxn;uUxluvªl n}
xl{±³ y¬°{ª« =u¯·±Ñ纻RUº«oF»ÇUº»Á¼~±³ =~±³ =vm¶w¬%ynvªâw}vª« y4Auvªmª«¬«wyqwy =w=inu~ilwFyn =¬«Ow笫ªmª}vn
ª«mlwy}ª}vin ym¶wª«| y±½4¿ÁÀÂÂ1ÅYé^¿$ÂÅYÌ1½ª«=}v {{xn|Õ|×Ðn1¬«ª´wlØlwyvAn1&º«oF»ÇÚ^±Ñ«
il ®Ýnyn1;74ª¬«ªxuKº»³¼^ÑUhjin~wylw¬«{u?ª°uU ±4uvxliçuv{u}n1m¶uU}in1n±³ =vn =n1nwy¬¬«n1¬«ªn;uU yO·Yu? =mn~ynuvª« y
y±¼}vinßÆyÉÉÂ^ÌÌévÆÊwÙwm =xH}u}viÕxlu}v ¸wÙwylw¬«{u?ª°u y±K}vª«mn\wx{} ym¶w}wOª«6}vilnuvn1luvn| y±
µ~¬xlqwylO¹ª¬«¬jºo1»RÑ&hjiª°u~±w=^};} y =n}viln1q®ª²}iÐ}vin¯ª«=}n1nu?}ª«Zxluvª« wylw¬«{u?ª°u} H =¬«uq{n;u?ª« yn;±³ y
=nm {{n¬'ª«O}in$1 yH}vn1zH}q ±U}in$ y}vinAm }ªw}nZxluK} |ª«Õynu?}vª« =w}vn}in¯nÏHxª«Fwy¬nln ±ÖA }i
m {{n¬f¬°wyuu?n;uwyl|}v ¬ Õ =ͱ³ yw´wx{} ym¶w}ª«}wylu?¬°w}ª =窫A }i®jwF{u1Ñ,hjinuvn =lwl|}viª«
uvn}vª« yluKvn;u?nH}K}vin}®Ý ±³ =vm¶wy¬ª°u?m¶uÑj©On1lwyvª« ¯±³ y~}vin}vwluv¬«w}vª« y´ {nxvn=®nilwFynw
1¬ Hu?n¬« H =Ͷw}Ö}ªmª« $1 ylu?}vwª«H}uwyl}ªmnu?nm¶wH}vª°1u'®nKª°{n1H}ª²±³}inuvxª}wl¬nqu?xX¬°wyuuvnu y±
}ªmn;Owx{} ym¶w}wçw´}vª«mn$ÖMwyuK®n1¬«¬,wyu}in¯v =n~ y}vª« yÐ y±U}vª«m¯n;OAn1ilwFÕª« y~}v wy¬¬« ®T}vin
1 ymlwyvª°u? =fÑhjin y}vª« y´ ±, yu?nvw}ª =lw¬Xn;Ï=xlªw¬«n1nª°uªH}v {{xl1nª«´}vin&±³ =?}i´uvn}vª« yfÚl}vin
}wyluv¬«w}vª« y|lv {n;{xn&vn;u?An}vª« yluvn1w}vª« yw¬AnÏHxª«Fwy¬nln&ª°u yª«yn|ª«OàÕn}vª« yluwyllÑ
1 !¾| & ' ! 1 !J"$'' (*,+ -
!#" $&%(')+*,$-'/.103254+67#./2+0
74n}8:9Ô()AnwOÅR¿ÁÀ¶Ã=ëÀ¶Æ¿ÁË<;yÚfuvn}8>=@?BAC8EDGFHJIK LNM^Ñ&Ø y&w|uvn} O ±Ö1¬ {Í´wª«wy¬«nuQPw
wyvª°w¬«nq®ª²}iw¬«xn;ujªROwylSª«JT 8>=jnâlnq}inu?n1}u1UWVXO MjwlZY[VO M ±,¬« {Íç yu}wyªH}u
\
w=u·³®n& ymª²}Kwn1H}vin;u?n;u¼]¼^
±³ y_UWVXO M`?
\
?aA SRbcP[d5PebfSgd+h
\ d
\Jijk\<lnm
±³ y_Y[VXO M`?
\
?aA SRbcP[d5PebfSgd
\ i jo\ lp
U\®jwyuÝ{nâlln¶ª«Oº«o»ÇÑ,~ }n}vilw}Y[VXO Mq9rUWVXO M^Õ®ª}viç yAn1ݪ¬«xlu?ª« y'nª²}in1 yAn1|ªH}vn?Û
wy¬«u% =,ª«uxl}vª« yluUwyvn yH}wª«nªoY[VO MÑ'änjilwFynÝ}vin±³ =¬¬« ®ªl ~nÏHxª«w¬«n1H}Uvnnuvn1H}w}vª« y
y±Y[VXO MjwlEUWVO M]7fn1}
s ?BA t<FuQIwvxXIFuQI^LgM`?uQIwv_yZ8>=qIuobrv{z
|
s ?BA t<FuQIwv}M^IV~uQIwvwxIV~uQIv]M^I V~uQI^LgMq?uQIwv1yZ8Iuobrv{z
hjiln1f®ª}viRPqwyuwy =nqwylZ
i
}wyÍHª« w¬«xnujª«
|
sÎwl
l
ª«s
±³ y_UWVXO Mq?
\ A P_yZ
i d \ i jk\ l d \ i \ l
±³ y_Y[VXO Mq?
\ A P_yZ
l d \ i jk\ lp
K'üL .HP6þüþü+jN@:dý> - 2«û1ý:&Rý(TFý.Fúý&B .W Ia 2ûfú?üþû1úKúû.&1 .T1&
a].ûLû Fýü&:*.Fûú?üþû1úFþüþü=ý(dýWý: Hc.Fý^\1dýU1-ý &Rû?üþüo.Fý^\1-dýU1ý6düFý&4ú: .=<ýU&Rú: Fý
! W._72+7(' . 'r0&6. "! 0
ä ª}vi}vilnqwy =nyH®Ýnq{nâllnyÕ±³ y¬«¬« ®ª ¯µK¬«xwl|¹~ª«¬¬;:u&ºo^»4nâlª}vª« y ±ÖÅR¿ÁÀ¶ÂïÅRévÆËÌ^¿ÁÅY¿ëËÐÅÇÆ3]«Â^Ì^
#ò%$'&'(
¤ (ö&*)+-,.(
- ò
÷Ó¡$+'¤
ö
-6¦{¤
ö/&-01,
¡2
¿°Ì$ƶÅRè{QÂ43 AeV5I7698nIOWI;: M<>'ÊÂ1évÂ
=?>
5A@AAB´¿°ÌÆ4CËl¿ÁÅ©Â&Ì1Â1Åjë;u}w}nuD
E%> 698y5TųÊÂ~ª«ª²}ª«wy¬4u?}w}nF
GH>
OI@ABZÆ4CË¿ÁÅÇÂÌÂ1Åë;K¬« {Í{u<ÖÆ'¿ÁËl¿ÁÅR¿ÆKJçÌÂ1ÅÆÅ H
L/> :ÔÆÌ1Â1Åjë;wy}vª« ylu&ÊÆê;¿ÁË Å³ÊÂMëé^ÀONWAeVQPFRwVN M]I1SVNM^IUTVVNM^IURVWQVVNM#M<>'ÊÂ1évÂYX
ÆPFR VN My5T¿°ÌųÊÂ~u? =x1nu}w}vnë1ZNH
([SVVNMÆ4CËl¿ÁÅ©ÂÌèJÌ1ÂÅjë11UWVXO M
É\TVVNM`9rO¾ÅÁÊlÂÌ1Â1Åë1É}ë;É7]ÌÅ©ëkÂKnuvn}Kw}HÆÅÅÁÊlÂ$Â1ËAÃë1"NHÝÆËXÃ
Ã^RW VN MÅÁÊlÂ}w yn1}u?}w}vnë;ZN
>
µ~|wy}vª« y_Nqm¶wFAn~nz{n;x{}nª«|u}w}nMP`RVVNMUw}Ö}vª«mnZaUªð%{w}Ö}vª«m¯na^XÆy =lu?}vwª«=}uUª«_SVVNMÖwn
uw}ª«u?âln;MÑK }n}ilw}q}vin¬« {Í{u~nnZ }u?il ®Ô}in¯ y¬« ylwy¬4}ªmn´·³nuvn}ucbþ¼^Ñ.dnuvª«nu~}vilw}fwÕ
1¬ {Í[Pm¶wF.e¯uwFyHw}}ªmnafe$lwyuuU}in~ª« yiH}ilw¶¬ª«mª²}v ±HnyÑ lÑ«Huv ymn1PnFuQIwvxª«gSVVNMÖ®ª²}i yx{}
ëévÉ1¿ÁË $}viln¯n1z{nx}vª« yZ y±MNçw}ha^Ú4w}ha^iNmwFxu}wyu®n1¬«¬,uvª«m¯l¬O¬« Õ =uvnnlw¬«ª« ®ª}vil yx{}wÕ
w=^}ª =Ù·(ÖÂÆ9]´ÅY¿ÁÀ¯¿ÁË ;¼^Ñhjiª°u1 yH}vwyu?}u~®ª²}iO}inâvª« | =¬«ª Hw}vª« yeÌ^ÅYévëË ÅR¿ÁÀ$¿ÁË<.eª«ZhjÖ~uÑ
än¶®ª«¬¬ª«H}v {{xlnçwm ynvn;u}vª°^}ª=n }ª = y±x±³ y&}ªmnßwyx{}v =m¶w}wl41wy¬¬«nÙÌ^ÅYéëË Zé^è{Ël
®ilª«iZª«u1wyuu?n;ÏHxn1l1nu¬« ÕÍ=n´Õ´ª«¬ª« ´wlÐAn1mª²}uK}in ymlwyvª°uv yЮª}vihjÝ~uÑqµ~¬«uv l
=x =lu}vx^}vª« yn¬ ®Ô¬n;wFyn;uÖ}ini yª°nq} ¯m {{n¬Mn1yn|}in&®Ýn;wÍÕ¬«}vª«m¯n;´hKà{× An1iwFHª« yjÕ
u?}v yl y¬«}vª«m¯n;oÛ©hjÖ~uÑ
#ò%$'&'(
¤ (ö&jk0;,.(
- ò
÷mlf¤¦{¤
ò F
¦§on
(V&%ò
2
'ÂÅp3 ÂÆÅY¿ÁÀ¶ÂÃÆè{Å©ëÀ¶ÆÅ©ëË > îV7%ëé~Â1êÂéqJ4N yr:
SVVNM>A t`spt{zkU¿ÁųÊuspt_yEYvUųÊÂ1Ër3 ¿°Ì$ÉÆÂÃÆ.,.( - ò ÷wlf¤¦¤ ò F ¦l§Yn (V&%òx0;, l F 2 >
~ }nÖ}ilw}%}vinvnnz{ª°u}h%µ~u'}viw}UwnÝ y},whKà{×¾wl$1wl },nm {{n1¬«n$Õ&âlª}vnjhKà{×OuÚ=Ø%ª =xn
¯uvi ®Kujw´nzwym¯l¬n=Ñ
!y z|{ 6. 2+7 ) 0&'r 7;{}|M~032|{ 0
74n}0nçwyßw¬«ilwAn}®ª}vi6uvAnª°w¬uvÕmA y¬MrywÚ,®Ýn¶®ª«¬«¬xluvnßwyuw¬°wAn1¬U±³ =}vwu?ª}vª« ylu
®ª}vil yx{}Öu?}w}vnKilwy yn;u1Ñ'än~n1 y}vnj}vilnKu?n1} ±X y{ÛÇn1m{}âlª}vn® yu, ynUw¶w¬«ilwyn1}ÖwyuM
=
wylu"W?BA
=v
t H5zH®in1nHu?}wylu,±³ =U}vin~n1m{}® yMÚy}vin~uvn}Ý ±,¿ÁË9CË¿ÁÅÇÂ®Ý =lu,ª«uMz Ð=w
M ?aA* Ñ 7fn1}?%MfVf to z M1|An}vinnzÕ}vnluvª =¶ ±X}vin{Û©{n¬n1}vª« i =m¯ =m yiª°u?m
="ªRÑn=Ñ,}vinxlª«ÏHxnm¶wyª« ¶u?xli}viw}±³ yKwy¬¬
i
y["
l
y wlGy[xgt` zH
V
i
l M AwV
i
M1VV
l
Mwyl V
i
i
l
M>AV
i
MiVV
l M p
Øl yqw¶®Ý =X{n }nª}uK¬«n1l }viwyu dd²ÑØ =4Gy A®vª}vnVu M±³ =K}vilnnâz
ip}pp
/ y±
wrVf MÖ±³ yj}in Hu}vâz =ª=n1ÕZAAV<M1Vfv<M^Ñ
#ò%$'&'(
¤ (ö&0?ò
+
(
¦G
ò&
¤¤
ö
¡*G+'¥ç¦
& ÷
#r(
GG
)
2
îV Zy8 Ì1ÆÅR¿°ÌCÂ^Ì
=?> F0ö&'ö
¤
ö&i(
§ (¤
óXz'ëéÆ5F= i
;ÝÆËAÃ
E%>
¥
ö
¥ ò
£;£
Xjîdd3A:LwųÊÂ1Ë
Lm
Z¿°ÌKÆ ¤ (- ò ÷Z£ ò + ò& § ò > + ¤ (- ò ÷ õö ¥÷ ëêÂ1éÆË´ÆlÊÆnÂ1ÅiÔ¿°Ì~ÆqlÆ¿ÁéRA VVIQMU¿ÁÅÁÊv y^
ÆËAà ÙƶÅR¿ÁÀÂÌ1Âw1èlÂ1ËAÉÂ
>
ÄXÂ1ÅYÌë;&ÅY¿ÁÀ¶ÂÃÖëévÃFÌëêÂ1éh Æév¯ÉÆÂà ¤ (- ò ÷ GY¦ & +%¦ ò £ ëêFÂ1éh
>
hjilnnz{n;x{}ª =Zu?n;ÏHxn1l1nu~±³ y&h'µÞwn}® Û©{ª«m¯nluvª =lw¬4uvª«ln$}vin¯u?{u?}vnm mwF´wyFwyln$ªZ}vin
¬« y =ª«w¬M{ =mwyª¸·³Õwy^}ª =lu¼Ö =}vin&}ªmn{ =mwyªß·Hç}vª«m¯nu?}vnlu¼^Ñ
#ò%$'&'(¤ (ö&-'Â1Åp3 ACVf5I76 8 IwOWI;: M Â&Æн%+ > + ¤ (- ò ÷£¤¦{¤ òZë1M3 ¿°ÌÆÆ¿ÁéACVf63I +M~Ì^èlÉÊ
ųÊÆÅ'6y5T¿°ÌƶÌÅ©Æũ¯ÆËAÃ!yZ8 =#"$%" ¿°ÌÆçêFÂÉ1ÅÇëéë1É}ë;É7] lëFÌ^¿ÁÅY¿ëËÌ
>
hjiÕxlu$u}v = Ðn1w¬«ªl { Õnu }¯w¬«¬ ®.w´}wylu?ª}vª« y¸} OAn =mn{ª°uvwy¬«n¸®ª}vi =x{}}inuv{u}n1m
iw =ª |ª²}u~¬« y =ª«w¬'u?}w}vn=Ñhjiª°u~ª°uqw|u?}v y =n1KnÏHxª«vnmn1H}~}ilwZµ~¬xlqwylO¹ª¬«¬<:u& =lu?n;x{}ª =
±³ =q}vª«m¯n;uvnÏHxnln;u1fuvn1n¯An1¬« ®Ñ¯àÕª«ln$}vª«mnÖ~uiwFyn$u?}v yl ç}vª«mªl lf®n¶1w y¬«Ði =n$±³ y
n;ÏHxªwy¬nlnª²±f®n{ª°u1w¶ ={Û©u}v = y¬«}ªmn|nilwFÕª =ÚHAnuvª«{n;u}ilw};Õ®Ýnn¬ª«n1=nK}viw}}vinvnª«u
w¬«wyv =n1¬«w=uvuÝ ±'wy¬«ª«w}ª =lu®in1n~ª°{¬«ª wyujwy =n~1wy|An&1 yluvª°{n1nçw=u±wyx¬}¶ yªl1 yvn;^}¬
m {{n¬n;|An1ilwFÕª« y;Ñ
#ò%$'&'(¤ (ö&'&ÔîVZR/A VVIM$¿°ÌÆÅY¿ÁÀ¶ÂÃÖëévÃU¿ÁųÊrgy MiÆ ¥ + &Þë1h3 ëêÂ1éR&¿°ÌÆ|Ì1ÂèlÂ1ËAÉÂ
( A ( i ( lp}pp U¿ÁųÊ
( ACV6#I )XMq
( ? Vf6983I*o8{M,+.-*/0 12+.-43 V6
i
I
i M +65/075
Vf6
l
I
l M +89/078
/
pp}p
I
'ÊlÂé 6-A 6 8 6 i pp}p
¿°Ì´Æ¸ÌÂ1èlÂËXÉÂOë1Ì^ÅÇÆÅÇÂÌ$ÆËXà rA:
8 i pp}p
ÆÌ1ÂèlÂ1ËAÉÂOë;ÐÉ]ë;É]¸êÂÉ1Å©ëéÌ
Ì1ÆÅY¿°ÌJ¿ÁË %X
=?>; &'(
¤ (
¦G
(=<
¦{¤
(ö& X 6 8 y[5
8
ÝÆËAÃ>
8 VSM A H.ëé$ÆJSRyEO!?
E%>A@ ö/& £ ò §?+4¤ (ö& XMëé¶ÆB 5F':ÉëËlÅ©Æ¿ÁËÌÌëÀÂ.NA VP`RVVNM^IDC-I;SVVNM^I7TkVN M]I;RW VVNM M'ÊÂ1évÂ
V= E
i VSM KF G E
i
M7H I
$
ÌÆÅY¿°ÌCÂ^ÌzSVN MqÆËXÃ
. V~SQM A J H ? SRyTkVVNM
KE
i
V~SQMKF V~u M G V~u E
i M ? S@yTkVVNM
L¯Â1ËAëÅ©ÂųÊÂÅR¿ÁÀÂëÆË yèlÆ}HÂë1"3 ÆFÌMWVV3 M$ÆËAÃçÅÁÊlÂÌ1Â1Åë;é^è{ËÌ ëéZ3 ÆÌ#NDOQP?P5V3 M >
hjin;u?n¶{n1âlª}vª« ylu&n1ðAn;^}ª=n1¬«Ðnz¬«xl{n 2%Â1ËAë$An1ilwFÕª« y;MªYÑnyÑu?xiO}viw} ´ y ynuuKª°u&m¶wy{n
ª«|uvª}vnq ±4w|ª{⪲}nÕxm$nÝ y±f}vª«mnu?}vnlu®ª²}iç Hu?ª}vª«ynq{xw}ª =fÑ dÝx}Ý®ª}viµ~¬xlwyl繪¬«¬<:u
nâlª}vª« y4M}vinçh%µ ª«uu?}vª«¬«¬w¬«¬ ®nO}v Ðu}wFЪ¸uv ymn¯u?}w}vnu6¶wylO} ´¬n1}q}ªmn¶lw=uvuqAn1= ylZ}vin
nwy¬ª«nu ±}wylu?ª}vª« yu¬«nwyª yx{}$ ±6=ÚÝuv Ð}vilnuv{u}n1m ®Ý =x¬°SR?wyxluvnUTç ±Kª}u$®Ýn;wÍ}vª«mª
} |An1ilwF=n${ªðXn1n1H}v¬«´±³v =m)w|u?}v y =¬}ªmnZ yn$®ª²}i yx}wyÕ´ª²ðXn1n1l1nª«Z}inVRnw=u? =lw¬«nUT
An1iwFHª« y;Ñ,h4 ¶w¬«¬« ® ±³ ymn;wª« ±³xl¬f ymlwyvª°uv yluÕ®Ýn&ª«=}v {{xnn
W
DL@Fý Fý4X,.1þû.û 2CK%üW .HPWþüþüQj]6Y+ûWüþüZ\[ 1-@;ý:ýý(' &1&6&Yûý^]B_a` &Fúr@1@,\1,bQcedfhg_iZkj(Fú?û:dý&
û.Fü>1-@FýUú: &YýUû 2.6X,.1YýU&Rý( ;ý:.;ú?ý&ml,1-@FýU;ý7X.1-þû.=&FûTXý1Rûi Fü>1Rûc<yû 1@AX,.*1Rý ..X,.1YýMû&84
#ò%$'&'(
¤ (ö& 'Â1Å
(
U¿ÁųÊ
(
_A V6#I*.MÂÆOé^è{ËÎëêÂé.RA VImJM´ë1c3 A V5I6
8
IwOWIU: M > ½XÊÂ
£
ò Gò ¤ ö/&QV
(
Më1
(
¿°Ì¯Å³Ê¶Ì^ÅYè{ÅRÅÇÂ1é^¿ÁË .év¶êÂéÌ^¿ëËÎë1 6 > (
¿°Ì¶Æ
£1¤¥
ö&
¥+
& ¿¶Â¿ÁųÊÂ1é|ë1ųÊÂ
ëëU¿ÁË<çÊëÃFÌDX
=?>
d VV M}d<A L VV
(
Md A:L&oëé
E%>
d VV M}d+A? yO jÆËAÃU¿ÁųÊ
( A Vf6 Im MųÊÂ$Ì^ÅÇÆÅÇÂévÂÆyÉÊÂÃZDJ|ųÊÂÆFÌ^ÅjËAëË 1V\ÅRévÆËlÌ¿ÁÅR¿ëË
ë1"RU
( ÌÆÅY¿°ÌCÂ^ÌDXiëé$ÆË J.N|ÌèlÉʴųÊÆÅpPFR VN M/A6 ÆËXÃ|ÆË Jvs ySVNM
FPR Vs M' VVsM#Mx D FHJILNM A B+I ·o;¼
'ÊÂ1évÂ$ÅÁÊlÂs ÆévÂÅÁÊlÂ$Â}Â1ÀÂ1ËlÅ©ÆéqJÉ]ÆèÕÌ1Â^Ì 'ÊëÌ1¯ÉëË^è{ËAÉ1ÅR¿ëËO¿°Ì4s
>
½XÊlÂ&Ì1ÂÅÖë;ÌÅRévëË é^è{ËlÌ~¿°Ì&Ã=ÂËXëÅ©ÂÃ"P.NmO P?PÖÆËXïÅÁÊlÂÆË<èlÆ=Â$ë1ÆyÉ1ÅR¿ëË´Ì1ÂèlÂ1ËAÉÂÌ&Éëé^évÂÌXëËAÿÁË
Å©ë¯Ì^ÅRévëË<çé^è{ËlÌq¿°ÌM
>
=l{ª}vª« yÓ·o;¼qu?}w}vnuq}ilw}w}q}in¯}vª«mn¯ª«lu?}wy=}w}&®ilª«i
(
nwyilnu±³ yq}viln¯¬°wyu?}&}vª«mn¯ª}uqâlw¬
u?}w}vnc6oзf6om¶wFilwF=nnn1OÕª°u?ª}vn;ÐAn±³ yn;¼Awy¬¬,¬« {Í1 ylu?}vwª«H}uj±³ =wyH´wy}vª« yЬ«nw={ªl ç yx{}
y± 6oilwF=n´wy¬nw={6n1zÕlªnMÑcàÕª«lnÐ \¬« ÕÍÙª«u¶nuvn}ç®ilª¬«nÐ}vilnOu?{u?}vn1m uvª²}u¶ª wßu?}w}vnyj
±³x}vxnª«lu}wH}~®ª«¬¬'n1lwy¬«nwÕw=^}ª =fuv 3 ª«uK±³ yn;|} |u?}wF|ª«\6oHÑÇ}~ª°u~1¬n;w}ilw}q®ª²}i yx{}
nÏHxª«ª ç·?o;¼HxluÝwnKAn1m¯ª}?}n} $uvªm¬«¬n1}wy¬¬X{nw={¬«ªn;ulw=uvuÝwl窫{¬«n~xln1nuuvwyvª«¬« ÑàÕ
n;ÏHxªwy¬nln®ÑÑ}Ñ,u?}v y &xluUª°u,âlnU}viw}ÖxnÏHxª«w¬«n1l1ny=wylwlv =vª°w}nÖ±³ =Ö =mlwª«uv yu
®ª}vi\u}v = y¬«O}ªmnÙu?{u?}vn1m¶uÚ,}vinuvwymnçi y¬°u±³ y®nwyÍZn;Ï=xlªw¬«n1ny,ªRÑn=ÑÐxß} Z{n1¬«n}ªl Z y
ª«luvn1v}vª« uÐu?}vn1u1Ñ
!! #"%$w"! 0'&^! 0<0 6)(C0H~._)+*14+' .17-, 6 257#' .,6.4 032+0
µ hjv&à× ª°uwy$n1zH}n1luvª« y ±MhKà{× }vilw}nvmª}uUmn;uvuw =nuvÕli yª«áw}vª« y®ª}vi¶ y}vinhjv&à{×
·Y =m¯wn$ÅR¿ÁÀÂÃÉë;ëwlÂ1évÆÅR¿ÁË ´Æè{Å©ëÀ¶ÆũƯº«o{;»³¼^Ñ
74n}c3 A Vf5 I76
8
IO I;: M^ WA 53I
p}pp
I- U%nçhKà×Ouuvxli}vilw}\_@A/.Zªm¬«ª«nuv5 D\510oAIB{
O DqO20WABFwyl : DM:301AB{Ñ.7fn1}54ÐAnÝwKâlª}vnÝuvn}, ±
- ò
£;£;¦
ò
£
wylVC ?F:\ t6z
V(t37I98nz;:<4>M
m¶wyª« =u4±³ y A 5nI
pp}p
I= UÑ%ã~n1nykC wVVNM>A6¶mnwu4}ilw} Nnz{n1x{}vn;u'wyª«H}vn1lwy¬=wy}vª« y$®ª²}i yx{}
1 ymmxlª«w}ª =fÚ17u¶u?}wuU±³ =Ö}inÌ1Â1ËAÿÁË mnuuvwy yn1uky>4ß®iln1rNq {11xu1Õwl?8{vj±³ yqévÂÉÂ1¿Áê;¿ÁË
mn;uvuw =nvky@4jÑhjinçw=^}vª« y¸x¬«nuwn}viln1ß =m¯l¬nm¯nH}vn¸ÕÐ}in|1 yl{ª}vª« y}ilw}$wyßwy^}ª =
Ny:),®ª}vi C AA8{uç1wy {11x yl¬çª±
oyÑ"3 ,ª«uKªÐu?}w}nZP`RVNM^
{ÑZs VVNMjª°uuvw}vª°uâln;Mw
ìÑu?ª«mxl¬²}wn yxluv¬=u? =mnN0 yr:30&®ª²}i "@AB.çwl CC01AD7u¶ {11xu
E
1@FýUFüþýû., & &L.T1Yý.Fý4
l¬xlu¯}inЪ«H=n1u?nvn;u}vª°^}ª =Ù±³ = C 0
AD7uÚª«Îlwv}vª°xl¬«wyÖw=^}ª =luu?Õli ylªáª Õ6mnuuvwy yn;u
wyvn yH}v =¬¬«n¸Õ¸m ynç}vnm =wy¬Ý =lu?}vwª«=}u}ilw\ªH}vnvw¬Ýw=^}ª =lu$uvª«lnw¬«¬1 ylu?}vwª«H}u y±
}in1ª« =m¯m$xª°1w}vª« yZwv}vnqw=^}vª« yilwFyn}v n¯±³x¬âl¬«¬n;¸wyu®Ýn¬¬RÑhjiª°uu?Õlilv =ªá;w}ª =Ð =¬²Û
ª°Zvnln}u1ë¿ÁËlÅÅÇë lë¿ÁËŲ۩u?Õlilv =ªá;w}ª =fÚM }in1A y¬«ª«1ªn;u}vwluv¬«w}vn¯ªH} ´ª²ðXn1n1H}vxl¬n;uqwylM
1 yluvnÏHxnH}v¬«yÕªH} çw¯ª²ðXn1n1H}~uvªm$x¬«w}vª« yÕç,n}vªfKn1}uKw=ujn¬ ®Ñ
x$ªH}n1nu?}ª\hjv&à{×Ou$in1n窰um }ªw}nßÕ}vinªwl¬ª°1w}vª« y¸} O}vn;u}ªl O ±Knwy¬²ÛR}vª«mn
wy¬«ª«w}ª =lu1%xluvn¸ª«wª°uvn1n1}¯w¬RÑߺ«oìF»ÇjºoF;»jwyl yt|wyl wyu?}wyn}ºo»RÑOhjiln1n|wn¶}®
m¶w yjwlin;u ±Uw¬«ª°1w}ª =lu
Ø%ªu};Hw& =ª=n1¶uvn;ªâ1w}vª« yu5/N Pª°uUm Õn1¬«n¶wyuÖwhjv&à{×ßÚ =n~wyuuv Õ1ª«w}vn;uUwÅÇÂÌ^Å+Xè{éXëÌÂ1
ªYÑnyÑjw¶uvn =l´hjv&à{× }vilw}~n1nuvn1H}u}in yAn1v}rsO}v ¶An}vn;u}nMl}v = yn}in1®ª}viOw
yÛRnm¯}Ou?n1}_P]P<N a]VQMW9-5VQM y±Ýwyn{}vª« ´u}w}vn;u1Ñ&©}vinuvHiv = yxuK {{xl^}
hjv&à{× ±5N PÖw' ynÝ}vin¯w}?}n1m{}u%} qw¬°x¬°w}nÝ ={ÛR}vin1Ûlwqu?x1n;uvu%lw}vi·ªYÑnyÑ
¬n;wy{ª« ¯ªH} _P]P<N a]VQMM=n1ª²±³Õª« s'ÑUDZ% ¶u?xliZª°uݱ³ yxlf{}vin& yAn1v}ª«uª«uv ynfÚ
wOuvxl11nuulw}viUUÕªn®Ýn;¸wyuwZhjv&à{× ª²}u?n¬²±UÕª«n1¬°uw6ÅÇÂÌ^ÅÇÂ1é~±³ =s'ÑZhjinç}vnu?}vnu}viÕxlu
y{}wª«n´wyvn}vin}v ¶Anªm¬«n1mn1H}nª}inw¬«ª°1w}ª =f{nyÑ lÑ«lwyn¬nFw}v =j1 yH}v y¬RÑ
×Ðx¬}vªÛÇ1 ymA yn=}|uv{u}n1m¶u1wy\AnÐm Õn1¬«n\H\hjv&à{×Ou¶ =m =n1H}u®ilª«iÎwn|}in1
u?Õlilv =ªánZHZm¯n;wluq y±Ýmnuuvwy yn¯nzilwy yn=Ú4 =m¯wn}vilnç Õ yAn1w}ª =O ±Ý}vª«m¯n;¸µKx{Û
}v =mw}wª«Óº«o{F»RѶh' y yn1}vin&®ª²}i}inç =lu?}vxl^}ª =Z ±j®nwÍÕ¬«ÐnÏHxª«w¬«n1H}hjÖ.{nuª«n;
n¬ ®}viª°ujÕªn¬«u~w¯u?}vxl}vxnm Õx¬«wyKhjªmn,n}vªf~n}Km {{n1¬«ª« }vn;iª°Ï=xlnyÑ
hjinm$x{}vxw¬fuvHiv =ª«áw}ª =ç ±%}® $m¶wyilªn;ujª}nu?}vª« m¯ y}vª«w}vn;uj yxKil yª°nq ±'mn;uvuw =n
uvÕli yª«áw}vª« y¶}nilª«ÏHxn=Ñ
1 2 43, 657'-
2 5-.! 5 2 57-
xl%ª«H}vnvn;u}Uª«¯hjÖuUª°u,m¯ y}vª«w}vn;Õ}inu}v = qvn;u?x¬}uUw=iª«n1yn;xluvª« ~}iª°u,±³ ym¶w¬«ª«uvmª¯yn?Û
ªâw}vª« y4Hª«lwv}vª°x¬°wÝ}viln¶Â1Ëlè{À¶Â1évÆÅR¿ÁêFÂÀÂ1ųÊë;Ã~ y±'dn1v}vil ymªnxwyl|¹ª«wyáº;»4wyl¶}inwlwy¬{uvª«u
wy¬ = yª²}im.nuvn1H}vn;|ª«¸ºo;F»ÇÑ
#ò%$'&'(¤ (ö&*+ ò ¤1¥ (Ðò ¤ 0 2 ¿°ÌƶÅRè{QÂV qI"!I
(
N3I $#F69a^I%8 M>'ÊÂ1évÂ& A' V M¿°Ì
ÆZCËl¿ÁÅ©ÂqÌ1Â1Åë1)( G¦l§ ò £ ! A*! V M¿°ÌÆ"CË¿ÁÅÇÂÌ1ÂÅÝë; ¤1¥¦ & £ (¤ (Yö/& £ ÖÆËAÃ$
(
N?+ /:,!A ÆËAÃ
$#F69a?-! :. ÆévÂh(&/(
+4¤10
ö
+'¤
(
+4¤ç¦{¥§323+
&
§y¤
(Yö/&
£
évÂÌlÂÉÅR¿ÁêÂ]KJk?Æ -6¦{¥
(V& \ë;
¿°Ì$Æ
è{ËXÉÅR¿ëË3% ?4 :! ÆËAÃ5%8´¿°Ì¯ÆÐÿ°Ì^ÅY¿ÁË<è{¿°ÌvÊÂÃÀ¶ÆéU]¿ÁË OÉÆÂÃÅÁÊl (V&'(
¤ (
¦G0-6¦¥
(&
ë; >
+ÞÅRévÆËlÌ^¿ÁÅY¿ëË6¿°Ì -6¦{¥ (V& ôò& ¦{¢ Gò ÷ ¿ÁË7% ÃyÂ1ËAëÅ©ÂÃ% pwU¿8 9:
( N V;I6M)<=% ëéÆ
Ry> ?ųÊÂ4$ ¥ (V& \ë;?6ÅÁÊlÂËÅYéÆËÌëé^ÀÌ@% ¿ÁËlÅ©ëA%CBVÝÃyÂ1ËAëÅÇÂÃA% D%CBV>'ÊÂ1évÂ8
% B A F% E IGF
8 (
N<V;IH6Mx5KwE I 8 F $#F69a]V6<IQM
p
·Yy¼
ÄMÂÅ'/VI% Mq?BA tJ6y! ?% /cz8 >
©T×Ðn1¬ª«CwylCØwnº«oF»3:u|m {{n1¬R~,n1}vª&~n}}vwluvª}vª« yluwnwyuuv Õ1ª«w}vn;ήª²}iÔwß}ªmn
ª«H}vnvw¬}viw}{nuªAnuÖ}viln~An1ª {窫|®ilª«i|wy|nlw¬«n¶}vwluvª²}ª =çm¶wF¯âlvn=Ñ%µÔx¬«¬«n}?K~An±³ =vn
=w±Á}vn~wn1¬«n1mn=}~n1 y}vnujª}uKª{Û = yx{}x{}~{ =m¶wª«f{vn;u?An}vª«yn¬
Zy ? K R?aA tJ6 y! ?5 $#F69a]V6<IQM H5z I K ?BA tJ6y! ?5
(
N<V;IH6MNH5z
6y ! ? K 6 ?BA tZy ?5
(
N<V;IH6MNH5z I6
K
?aA tHZy ?5 $#F69a]V6<IQMcH5z
#ò%$'&'(¤ (ö& +m,.(- ò ò ¤1¥ (5Ðò ¤ 01,
2 ÉëËlÌ¿°Ì^ÅYÌë;~Æ_> ÆËXÃÀ¶ÆwnX¿ÁË ÌNa ? !A 8>=
ÆËAÃa ??! V8>=
tLczMçųÊÆÅÆFÌÌ^¿ËÎÅ©ëÂÆ=ÉÊ\ÅRévÆËlÌ^¿ÁÅY¿ëË\¿ÁÅYÌ$ò ¦{¥ G(Yò £¤ ÆËAà G¦¤ ò £1¤ $ ¥ (&
¤ (- ò £ ? ÖÂévÂ1è{¿ÁévÂ4Na]V6M<a]V6MëéÆ 6y ! > + £1¤;¦{¤ òßë; ¿°Ì$ÆWlÆ¿Áé6WACVI% I;a#M U¿ÁÅÁÊ7%
Æ|À¶ÆéU]¿ÁË ´ÆËXÃvaqy 8 =0ÆçÅR¿ÁÀÂ$¿ÁËlÌÅ©ÆËÅ
>
4Â1Å 6-ÂÉëÀ¶Â$ÀÆéU]¿ÁË<1?Â1ËAÆ3]«ÂôÆÅÝÅR¿ÁÀ 8 >
½XÊÂ1Ë.6´¿°Ì
ò& ¦{¢ Gò ÷ ¿ÁËZÌÅ©ÆÅ©Â46WACVI% ImJMq 8 ¿9
=?>
VK_G 8 My FNa]V6M^Ia]V6Mx·¤ (- ò´ò%& ¦{¢ Gò ÷ ¼ÝÆËXÃ
E%>
6ZÖÆFÌËAÂ1êÂéÀ¶ÆéU]¿ÁË 1?ÿ°Ì1Æn}ÂÃZÂÅXÖÂÂËi 8 ÆËAÃV
>
$é^¿ÁÅÇÂ % p¿8 /0 96´¿°ÌÂ1ËAÆn}ÂÃ|¿ÁË6_ACV% IDJMYÆËXÃ% 8 /0 %CB¿9'% /ÆËAÃ%8 /0 8 %CB
hjiln±³ =¬¬« ®ª« ®ª¬«¬4w¬«¬« ®Cu?nm¶wH}vª°& ymlwyvª°uv y| y±%hjÖwlh'µÑÑ
#ò%$'&'(¤ (ö& 'Â1ÅiRA6
i 6 l>p}p}p
y!4
>
ο°ÌÆ $ ¥ (V& £ ò + ò& § ò¸ë1 ¿9ųÊÂ1évÂ$Â=¿°Ì^ÅÖÀ¶ÆéU]¿ÁË Ì
% -y\ë1 Ì^èlÉʴųÊÆÅ % 8 -D%
i 85 % lp}pp
> î ß¿°ÌÆ|ÅY¿ÁÀ¶ÂÃÌ1ÂèlÂ1ËAÉÂųÊÆÅÌ1ÆÅR¿°ÌCÝÂÌ
% 18 - /0 -3
% i 8/5 /05 %
lpp}p
Ö¶ÉÆVVI QM$Æ
¤ (- ò ÷ $ ¥
(V& £ ò
+
ò&
§ ò > ë1
> ½XÊlÂÌ1Â1ÅKë1ÅR¿ÁÀ¶ÂÃ
CÖé^¿ÁË ¶ÌÂ1èlÂËXÉÂ^Ìëé
¿°Ì MWV M >
µuvuv {ª°w}ª ´w´¬« {Í PV6M} Ðnw=iZ}wylu?ª}vª« y 6Õ4®n¶1wß{n1âln¯}vª«mn¸u?}w}nu4xluwylu?}v yl
xluw=uwA yn&w¬°u? $±³ yKhjÝÚuv ymnuvx{}v¬«n}ªn;u®ª}vi}viª°u®ª«¬¬MAn{ª°uv1xluu?n;|An1¬« ®Ñ
!
Ø%ª« yxnso3 "Ö{±³ yª« u?n¬²±ÁÛ
1 yl1xvn1ç{n yn1n5 µuu}w}nª}in¶ªH}v {{xl}vª« yf4®Ýn®ª«¬¬U±³ {1xlu y
=
1½
}ilw}¶ª°u1ÝhjÖ~u®ª}viÔÌ1Â] 1?ÉëËAÉ1è{é^évÂËXÉ<J6Ã=ÂXyév 5yÑkdݸ}iª°u®Ýn
mn;w}viw}ÝwyH$ yª«yn$}wyluvª²}ª =6qª«|wÕ$vn;wyilwy¬nu?}w}vn~w{Û
l }Öu?}wv}Um ynÝ}ilw =njâlª w}Öw~}ªmn=HwylMy®ª}vi =njâlª
xll{n1®jwFy'1w y}u}wv}wy }in1&An±³ =vnâllª«uviª« }vinâlu?}Ñ
©ªl1ªl¬n==}in~n;ÏHxªwy¬nln;uÝuvi ®çAn1¬« ® 1wyv$ =n1Ö}v $}vin
A yxll{n1w=u?n=Úf}in¶ y¬«n1m)ª°uq}viw}mx¬}vª«¬«nâlª Hu& ±Ý}vw{Û
uvª}vª« ylu~ yª«ynª«uvn} w¶wª«n} ±{ª°u}ªl}âvª« |uvn1m¶wH}ª«u1l±³ y
®ilª«i´}inwylw{}w}vª« y´ y±%}in Õ ±u~n1nuu?ª}w}vnxlmAn1u? =m¯n
wyl¬«n1 y}viÕ¯wyuvn~{ª°u}ª^}vª« yu1ÚÕu?nnºaF»l±³ =Ýwª«uxluuvª =¶ ±Mmx¬Û
}ªl¬nÖâlvª« qu?nmwyH}vª°1ufª«$hjÝÑFDZ}vilnÝ1w=u?nÝ ±m$x¬²}ªl¬nn1lwy¬«ª
ln1yn {xu1M®n¶1wy¬¬ w = 1½ uvª«ln¯ª²}u&m¶wz{ªm¶wy¬,n1 yn1n
y±,uvn1¬±ÁÛ© yxvnl¶ª°u 5=ÑU©wv}vª°x¬°w;95ÛÇ =xl{n;hjÝ~u~wyvn
o1ÛÇhjÝ~u4x{}}iª°u{Õlwym¯ª°1wy¬Uvn;u}vª°^}ª =ª°u y}n1nuuvwyvXÚ%u?n¬²±ÁÛ© =lxn1l1O{n1 =vnn*5çw¸n
u?}vxl}vxw¬«¬¯n1±³ ynÕ¶wyl{ªl w¬« Õ y¶®ª}vi| =nK¬°wy1n
8
w}nwyi 6wyl¶ =n}v =Íynç y¶n;wyi$
8
ª«O}in¯ªª}vª°w¬Um¶wyvÍÕª« lÑq©O±w=^}f1 yluvª°{n1&Ø%ª =xvnonw}u? =m¯n}vª«mn¯An}®n1nS yrFuQIvwxR-6çâlvn;u1Ú
uvª«ln}iª°uâlªl çvnm ynu}in} yÍ=n1±³v =m O±³ y~ =noëwy¿ÉÆlª«lu?}wH}"e>6 :uKâlvª« ¶ y}q1 yluvxmªl
wyÕ|}ªmnyMª}lx{}u&wçln1®c}v =ÍynO yH}v Aw}}vinuwmn lÊJFÌ^¿ÉÆAªlu?}wyH}ZeAA}in$1¬ {ͱ³ y6 :un1zH}
âvª« ª«ujnuvn}Kw}1Hwç}innzÕ}âlª« ®ª¬«¬fAnn1}®Ýnn1 Kgu|wyliKNvFlwylu? ¯±³ yv}vi4Ñ
×Ð =vn yn®n´®ª¬«¬KilwF=n}v ¸vn;ÏHxªn¸ËAëË 132%Â1ËAë1~ÂÌ̱³ yçhjÖuçwyu®nO{ª°Ù±³ =çh'µÚÖ1wy¬¬Kw
l y{Û?ÜAn1l o1ÛÇhjÖwy>), ¸Ñ
.-'j3'q&' A&ß ^1 & "¶( !/5
2 57-
©}vilª«uuvn}vª« yfM®n$ª«H}v {{xln¶w }ª =Z y±Ý yu?nvw}ª =lw¬%nÏHxª«w¬«n1l1n±³ =q}vª«m¯n;uv{u}n1m¶uÚf}vilª«u
lvnlwnuÝ}vilnnz{¬«ª«1ª²}j}vwu?¬°w}ª =lu
±³ yw yª«yn$}ªmn;çu}w}nmw=iª«nyHªH} w yu?nvw}ª =lw¬«¬«nÏHxª«w¬«n1H}~oÛ©hjÖ ®ª}vi|n1m{}
}vwluvª}vª« yluwl
±³ y~w¯ =ª=n1´ohjÝ ªH} çw yluvn1w}vª« yw¬«¬¶n;Ï=xlªw¬«n1H}KhKà{×7®iª°i´ª«u y±4}inuvªánq y±
:u~wy11nuu ywif
®ilª«i®ª¬«¬fAnnuvn1H}vn;|ª«}vinn1zÕ}}® ¶u?n;^}ª =lu1Ñ
74n}wçn1} y&h%µ0An$ =ª=n1fXwlO¬n1}hR i A VV
i I i
M^IUR l A VV
l I l
MWy 8 An}® ¶}vª«mnZ®Ý =u
wyl
( i A V6
i
I
i
M^
( l A V6
l
I*
l
MKvxlluK =n1ZRwlR
l
Avn;u?An}vª«yn¬=Ñän¯uvwF|}vilw}
( i
ª°u § ö ¦¥F£ ò ¥
}ilw
( l
{n1 y}vn;
(
i
( l
ªð\·ª°¼V
( i M>AV
( l
M^lwyl·³ª«ª°¼ i
b l
±³ =Kw¬«¬ -y´¸Ñ
àÕ ´w =wyuvn1vxl R?¬xmluq} y =n}viln1mT$u? =m¯n¯ =lu?n;x{}ª=n}ªmnu}n1luq}ilw}{ }ilwy yn$}vin
¬« y =ª«w¬Xu}w}nq y±f}viln&uv{u}n1m´ÑUK y}vnq}vilw}j}viª°u{n⪲}ª =wy¬¬« ®Ku
( i
} $Anu}vª°^}¬ =wyuvn1Ö}vilwy
( l
ª«Zª«{âllª²}n1¬«Om¶wÕOu?n ymn1H}u y±Ö uvª«mx¬}wyn1 =xlu?¬«yMuv |}ilw}&}in}® ´u?n;Ï=xln1l1nuqwn R?ªâlª}vn1¬«
±wyqwylwv}7T^Ñ.dÐ yH}w=u};Al y{Û?ÜAn1l Û©KnuuKnluvxvn;uK}ilw}&}in1n$ª°uq ª{⪲}n¯u?}vn}iZ y±ÖªH}n1 ynu
FI
p}p}p
Mݱ³ y®iª°i l
A
l
]=
±³ yKw¬«¬ UÑhjinvn1±³ yny
?aA V E i M ·ì=¼
nâln;u$wyÙn;Ï=xlªw¬«n1n|n1¬°w}ª =ß yÙ}vinu?n1}u!NmO P?POw\PkNDOQP?PÕÖ®iª«iÙ®Ýn1w¬«¬ö ¢,£ ò ¥ ¦{¤ (ö& ¦ G
ò + (K ¦Gò& § òÑ
3 & "( & 2 57-
hjilª«uª«u}vinm ynç ym¬«ª°1w}nß y±j}vin|}®Ý Ð}wyluv¬«w}vª« yluAn}®n1n6h·³v&¼và{×Ou¯wlßhjÖu1Ñän
iwFyn}v lwF¸u?An1ª«wy¬Ýw}v}vn=}ª =ß}v O}vinxlu?nwl¸nuvn}$ ±~¬« {Í{u1,ª«6lwv}vª°xl¬«wy}vinªH}n1wy^}ª =
y±juvn1=n1w¬1¬ {Í1 ylu?}vwª«H}u& y±jwÐhKà{×6'w¸ Huvuvªl¬nç1 ymmxlª«w}vª« yu&n1}®Ýnn1}®Ý Ohjv&à×
1 ymA yn=}u1Ñ
!#" *Z&6)+* ' .4A 2
74n}3 AeV5I6D83IwOWIU: MKAnwçhKà×ßÑ©O}vinâu?} yx y±U}vin¯ =lu}vx^}vª« y4l®nª = ynw¬«¬'1¬ {Í
1 ylu?}vwª«H}uÚH}vin;u?n&®ª«¬¬fAnwyl{n¬°w}vn yfÑ
oyÑØ =n1ynvu}w}vn.6y5jnw}nqw¯¬°wy1n Vf6{MÚ Z?aA tH V6 M`?_6 y[5`z=Ñ
{ÑØ =|n1=n1Ów=^}ª =N@y}:0±³ ym u}w}vn 6O} 6 B~nw}vnOw6ln}|}wyluvª²}ª =6cA 65VVNM^Ñ àÕn}
!e?aA tJ65VN M-? Nry :zw V65VVNM#M ?BA NÓ·wy¬¬~}vwluvª²}ª =lu¶An1¬« ® ®ª«¬«¬AnO¬°wAn1¬«nA¼^
Na]V6M1AeHwyl a]V6M1A L Úf}vin¬« {Í´1 ylu?}vwª«H}u~±³v =mÔ®ª«¬¬,Anm¯ {{n¬n;OÕÐwyª
u?xln}u1Ýu?nn|An1¬« ®ÑØlx?}in1;®nw=6w1u±³ ym Vf6{M}v 6Ow¸±³v =mD6´}v V6JBM^U®ª}vi
( N V; Vf6{M]IH6M A' $#F69a]V6<I V6JBM#M>A 5ÑÖàÕ }inu?Í=n1¬«n} y ±, yxjn1}Kª«uKwy´àÕÛRn1}
A V IJ!I MÑ
ìÑ?%
8
V;QMª°uKuvn}j}v 5q±³ y A Vf6
8
Mwl} H¯ y}vinv®ª°u?n=Ñ
E
51
t
/
-3
E
1t /7-73
t
15 I =
3
1 - I
=
3
E 1 3 E - 1t
/
-3
8 - 1t
/7-43
E
891
t
/ 5D3
E
- 1
t
/ 5 3 8 1
t3
E 1 3 E 5 1t
/ 53
88 1t /7-43
8 8 E 1
3 88 1t
/5m3
t E 1t
/ 5D3
8 1t3
85 1t /
-3 8 3
8 - 1t
/5 3E 8 1t
/ 5 3
8 8
8 5 1t /5m3
Ø%ª« yxn&+
¬ {Í|1 ylu?}vwª«H}uª«m¯l¬nm¯nH}vnÕçn1}Km Õx¬n;u1Ñ
! [4+6._0 %#6 257 . ( $ %(')+* )' .103254+67#./2+0
än ®ÔilwFyn}v ª«l¬«xl{nª«H}v ¯}vinhjÝm Õn1¬f¬« {Í| =lu?}vwª«=}u ±%}vinq±³ ymks'®invn&nw=i
sЪ«uwyn¬nm¯nH}w笰wxu?n& ±'}vinq±³ =vm PWy Fu IvwxM yPWy&FuQILNM^ÑØl yjnw=iuvxlin1¬«n1mn1H}wyvs4w
uvxln} n1nuvn1H}vª« w$nluvxvª« .s¶®ª«¬«¬n~ªl1¬x{n¯ª«=} ÑUhjinuvn&Àë;Ãè5ÂÌ^Hª«uv¬°wFyn$ª«
Ø%ª« yxn$ =luvª«u?}~ ±,±³ =x~¬°wy1nuwl}ivnn}vwu?ª}vª« ylu~nw=ifÚ±³ =~nw=iOu?xiÐm¯ {{xl¬n}vwluvª²}ª =
6Õ QV6M A 4ÑçDZaA L 4}vin¶m {{x¬«nuu?ª«m¬ª±³©ßØ%ª =xvnçf}viln¶lwv}u&ª«ßwyuvinA Fz{nu&ª«
n;wyim {{x¬«n®Ý =vÍ$nz¬«xluvª=n1¬«}v nluvxvnKwq⪲}nK¬°w}vn;u}Öâlvª« &}ªmn1u KRvÚyu? ±³ =Öw&vª« yiH}vÛRª«{âlª}vn
ª«H}vnvw¬f·¬n1±Á}?ÛǪâlª}vn~ =lnKwAnª = yn¯u?ª«l1nKu?{u?}vn1mÞvxlluu?}wv}Öw}U}ªmn1HH¼qFuQI^LgM=ª}Öu?x@¶1nu
} i =çwF®wF}vinqwyuvinA Fz ±M}viln =vnuvA yl{ª« &m {{x¬«nyÑUK y}vnK}ilw}Ý}vinm Õx¬n;u®ª«¬¬AilwF=n
} n1 ym¬«n1mn1H}vn;}v ¶wy yxl=}j±³ =K¬« ÕÍ|vn;u?n1}uÕuvn1nAn1¬« ®Ñ
µuvuvxmn¯âlu?}q}vilw} RA FuQIvwxRMªRÑnyÑ[vA a]V6M"! L ÑÖ¬«w=n&
i
ª«uqª«ª}vª°w¬«¬Om¶wyvÍ=n6·Yu?ª«ln$#
ª°u~w}WHH¼^Ú l
wl&%A }viZvn;n1ª«yn$w}v =Íyn1Ow}~}iniÕ{uvª«w¬4ª«lu?}wy=}®in1Ð}in$1 ylu?}vwª«H}~ª°uâlu}
uw}ª«u?âln;MÚ4uv 6wZâlvnwyuquv H =w=uqw|}v =Íynwª=nu~w} V6M^Ñhjinf4w}}ªmnovF ('ª°uqmwyvÍ=nM
wyl
l
ªmmnª«w}vn1¬«O¬« =uvnuqª}uq}v =ÍynfÚ/6jª°u& ®0l¬ {Íyn;Z®ª}vinuvn;^}&}v }viln1¬ {ÍO1 ylu?}vwª«H}
P y@FuQIwvwxÇÑDZa]V6M1A L Mvnm yn}in¯}vwluvª²}ª =lu&6
l
0
wyl 6 %
0
w=u~®n1¬«¬Uwyu}vin¬°wy1nu % w ('
·³}vilw}¯ª°u,}vinlwv}u$ª«\uvmwy¬¬jw=u?in;ßA FzÕn;uª«\Ø%ª« yxn=¼^ÚÖ}vinvn;wyuv yª« Oª°u¯wlwy¬ = y yxu&}v }vin
wy =nyÑ
~ }vn$}viw}q}vin¯m Õx¬n;uqªZ}viª°u& yu}vxl}vª« yZwyvn$¬ª«Í=nOª«uvxliZw®jwF|}ilw}& }vwluvª²}ª =
±³ ym !ߪ°u$±³ yn6}v âln®iª«¬«nspt|ª«uuw}ª«u?âlnfÚÖ}iHxu¯}vin®Ýn;w͸}ªmª« ¸ ±hKà{×sª°u$m {{n¬n;
®ª}vilª¸w´u}v = ç}ªmª« Ðm Õn1¬RM}vilw} ±hjÝÑ'àÕª«l1n¯ª}1wyZAnç{nuvªwl¬n$±³ yq}vn;u}xlvA =uvnu}v
n{±³ ynu?}v y }vª«mª fª}u?i =x¬°ZAn }nZ}vilw}w={ª« ´ª =vª}vª«nuqª°uu?x @ç1ªn=}&±³ =}iª°u}w±Á}n1
uv¬«ª =i=}m¯ {{ªâw}vª« yu ±U}inm {{x¬«nª«=}n1¬°wFy =ª=niª« yin;u}~lvª« yª²}ªOwyÕu?}vxl^}xw¬41 y lª°^}
} }viln}vwluvª}vª« y4·Yu¼'±³ ym !XÚ=}viln1¶âlª« vn;w¬{}wyluvª²}ª =luUª°uª =vª}vª«á1n;¯ yn1Uª°{¬«ªl ny =l¯}vin
¬°w}nu?}K{nw={¬ª«n=Ñ
!y $&%(')+* 4 0H 250
hjiln¶vn;u?n1}?}vª« Ð y±1¬ {Í{u&m¶wÍ=nu&ª}n1nuuvwyvO}v Oilwy yn}inçn1¬«ªmª«lwOn1}$u?}vxl^}xvn=Ñ~ }vn
}ilw};{ªÐw¯hjv&à{×ß1¬ {Í{ujwnnuvn}Æ1Å©Â1éÖ}inq}vwluvª²}ª = 66%}vilw}vn;Ï=xlnu?}uÝ}vinnuvn};Õx{}ÂVëévÂ
nw=iª« q}vin}w yn1}Öu}w}vn~ ± 6ÕÑ,än}in1n±³ =vnª«H}v {{xln=±³ =Ýw&nuvn}Ö y±X1¬ {Í P=wl¬«w=n t t V~P}M
w±Á}vn?65V6 M^w¬« y ¯®ª²}iÐwn1®C}vwluvª²}ª = 6 t t V6 MAn}®n1n V6 0{MjwylA t 8 E t t V6 I PM^Ñ
Ølx?}in1;®nq1 ym¬«n1mn1H}}in¬« ÕÍ yu}wyªH}jm¯ {{xl¬n;u±³v =mÒwA yn&wyu±³ =¬¬« ®Ku&·uvn1nØ%ª =xn
ìH¼_
yn&¬°wy1n
E t t
V6 IwP}MÖ±³ ynw=im {{x¬«nVC }ilw}K{nnlu =´1¬ {ÍoPÚl®Ýnuvn}
$#F69a]V6 I
E t t
VP}M#M/A 5={ }viln1Kw1ujwyvn&nn{n;MÚ
±³ y%nw=i¬« ÕÍP1 yl1n1nMF =n¬°wy1n/t E t t]V6 I P}Mf®ª²}iA
(
N<Vt E t tV6 IPM^IH65V6M>A
®in1nA
ª°uj}vin&Õxm$nK ±%m¯ {{xl¬n;uKnw}vn|±³ yK1¬ {ÍoPÑ
ªnw=içm {{x¬«nAC¾}ilw}K{nnluj y¬« {Í PÕ}vin1n}vwluvª}vª« ylu65V66#IwP]u
M465V6 I Pv
Mw
65V66#IwP]P
M,}v $ªm¬«n1mn=}Ý}vinvn;u?n1}Öª«¶}vin~}vin1nq{ªðAnvn=} Huvuvª«¬n1wyuvnu4nÏHxn;u}Ývn;n1ª«yn;
®in1Ð1 ylu?}vwª«H}ª°u
ËXëÅMJyÂÅÝÌ1ÆÅR¿°ÌCÂ÷ i
m¶wyvÍ=nl¼ P]u
Ì1ÆÅY¿°ÌCÝÂ÷;
l
wA&%&mwyvÍ=nl¼ Pv
=
ËXëëË HÂé&Ì1ÆÅY¿°ÌCÝÂ÷;('m¶wÍyn;l¼ P]P
Ñ
DZ a]V6MAeL A}vwluvª²}ª =[a
ª«uq y}nn{n;MMwl^a
iwyu y¬«´ yn$ª = yª« wyu?ª«ln
}vinvnª°uj % Úl{n¬n1}vn&}vilnlwv}ujª«ÐwyuvinA FzÕn;uªÐØ%ª =xnÑ
~ }n}ilw}Kl n1¬°wF¶®ª¬«¬fAn&wxluvnÕ¶}vilnvn;u?n1}m {{x¬«nyÚm =vn yn1; ª°u&oÛ©uvw±³nqwyl|}vinvn1±³ yn
wo1ÛÇhjÖTÕ1 ylu?}vxl}vª« yfÑ
Ø%ª« yxnçìÐu?il ®Ku~}® O¬« {ÍZ =lu?}vwª«=}u&®ª²}i¸ yn¶nuvn};Ñ|K y}vn}viw}}in1nçwn >VP}M&w1u
¬«nwFÕª« On;wyi6¬°wy1nA E t t]V6<I P}M$wl >V~PMwyun1H}n1ª nw=i߬«w=n E t t]V6<IPM^
1¬ {Í Pjiwyu,} nKnuvn}U®invnynUª²}Öª°uUnuvn1H};yªRÑn=Ñ'ª«¶nw=i$m {{x¬«nKn1nuvn1H}vª« w PÛ© =lu}wyªH};
l }n1nuuvwyvª«¬«ç yn1ª« $}vinuwmnwy}vª« yfÑ
$[0;0]$
$[u,u]$
$[0;0]$
$[0,0]$ $[v,v]$
$[0;0]$
8 1t 3 81t
/7-73 E
1 3
E
1t
/7-43
8 8 8 88 8
8 1t /
^3 8 1t
/
3 - 8 1t
/ 3
E
1t
/ - 3 E
1t
/7-43
/
8 3 8 3
`
- I /
=
t
t
t t
1- 3 t
5 I / =
8 3 8 8
E 1
3 8 1t 3 E 1 3 E 1 38
Ø%ª« yxnqìJ ym$ªlª ¶1¬ {Íçnuvn}uwyl´ =lu}wyªH}jm Õx¬n;u1Ñ
!! 17! 6%;.1)p:'o2 *Z 2k! '"Z %
hjiln ymlwyvª°uv y ± 3 wyl VV3 Mjilw=uj}v }wÍ=nªH}v çw=11 yxH}j}vilw}~ yl¬|}vin&}wylu?ª}vª« yuª !
1 yvn;u?A yç} çwy^}ª =luª«:ÚXw¬«¬4 }in1un¬ = yª« } 笫 ÕÍ =lu}wyªH}Km {{x¬«nuwyvn¬°wAn1¬«n
wyl$mxlu?} }AnKn1 Hw{n$wyuUilwy yª« }vinK¬« y =ª«w¬{u?}w}n ±A}vinln}ÑàÕ ®n¬xmn1}mwyvÍÕª« =u
} y =n}viln1jªH} ¶nÏHxª«Fwy¬nln1¬«w=uvuvnu%Øl ym¶wÍÕªl =u%
i % l ±
uvn}
% i % l
?#" % i
V;QM>A % l
V;QM Zy. p
hjiln1
ª«uwyn;ÏHxªwy¬nln&n1¬°w}vª« y4Ñ,×O yn1 yn
$Ýò - -6¦ )A4ëéÆË/J&% ACVV wIDXM`y M_V M$ÆËAÃçé^è{Ë N1yiNmO PFPJV M$ëêÂé'%_X
=?>
î VI% #I*.M
V%F= i I .= i
MųÊÂ1ËZųÊÂMëëU¿ÁË çÊlëÃÌ<X
% % = i
" 6 @y. I
ÆËXÃëųÊç¿ÁÀKJųÊÆÅ = i
A'. > îË|ųÊÕ¿°ÌÉÆFÌ1Â< U¿ÁųÊ%e?aA % VKi M% V VKnK'5{Mi MU?'ųÊÂ1Ë% %
E%> 4ëéÆË J % yGM_V3 M¶ÆËXÃÐÆé^è{ËiNyaNDOQP?P+V3 MųÊÂ1évÂçÂy¿°Ì^Å % yGMWV MçÆËAà % yGMWV M
Ì^èlÉÊÐÅÁÊlÆÅ % % ÆËXÃ N ACVI% VK(M^I*.Mq 'ÊÂ1évÂ&% #V;QM A E /E 1 3 >
~ }n}ilw}
6ÛRn;ÏHxªwy¬n=}m¶wÍÕªl =uj =vnuv =l¶} ¯}vinuwmnu}w}nqª«3 Ñ
~ ®{¬n1}43 wyl V3 Mnª«Ðu}w}nV ACV63I +MÑ
, n òÕö
¥ ò -
)A'ëéÂêÂéqJ
( i A V
i
ID
i
M1yrP.NmO PFP+VV3 MÆËXÃ
( l A VV
l
Im
l
MyPkNmO P?P+V
MųÊÂ1évÂÂy¿°Ì^Å
( i
ACV i I i
Mqy_PkNmO P?P5V
M¯ÆËXÃ
( l
AeV l I l
M`yuPkNmO P?P5VV3 MÌ^èlÉÊÐÅÁÊlÆÅ
( i
( i ÆËAÃ
( l ( l p
¥ öfö 2¨
( i ( i
UàÕxA =uvn3 ª°uª«|u?}w}n A Vf6nI*+MÝwl V3 MUª«|wu?}w}n V% I*+MÝu?xli}ilw}
% E /E 1 3 ÑUDZ,
t /0
p wl B AeVRWQVN M M^®ª}vn pt /0 BRÑÖàÕn}
#F6o6 VKnM ?BA tYN y:&?.P`R VNM>AA63I
QI
1t 3 sz3I
wl±³ y a`y FH+ID<xRyuvn} `?aA KZVVa^I
pp}p
I;a#M%wyl\ ACVf63I (M^Ñ,hjin±³ y¬«¬« ®ª ~±wy}u,wnÖª«mm¯n;{ª°w}vn
±³ yj}inªlª²}ª«wy¬4u}w}nwnzÕ}vnlH|ªlxl^}ª = =n1jxlu
o=ÑDZֱ³ y&w¬«¬ia_y FH+ID<xR #F6Y6 VnMA: #F6o6 VK #M^A}vin wOnw=iOw|u?}w}vnVI%CB~I* (M~uvxliÐ}ilw}
%CB
%/wylâlvª« yl¬rÛǬ«wyn¬n;|}wyluvª²}ª =lu1ÕªRÑn=Ñwu?n;Ï=xln1l1n y!
?aA*!m !h
Ú
Ѫ±) t /0
p B®ª}vi\ BQACVf6 BI 4BM;}vin w&nwyi&wKu?}w}vnV%CBI 4BMfu?xliq}ilw} %CB
E /E 1
3
wyl|âlvª« ¶uv ymn RAA
6`
®ª}vi
i
IU
l
y!h
wl>6w¯}wyluvª²}ª =|¬°wAn1¬«n®ª²}iN=Ñ
©¯±wy^};lo±³ y¬«¬« ®Ku,HªluvAn^}ª = ±l}inK¬« {Ím {{x¬«nuy y}vª« q}vilw} &vn;u?n1}Uw {11xU{xª
}vin}vª«m¯nª«H}vnvw¬f1 yluvª°{n1nwyuj¬« y ¶w=uj uNâlnuÑØ =~{{ y}vn&âlu?}}vilw}@65VVNMª«uKn1lwy¬n;|ªð
Nª°uÑjhjilnvn;u?n1}uj}vª« y =n1nÕN}vwlu?±³ ym¶u ªH}v BRÚl}innuvn}~{nHª°nª V3 MAn1v±³ ymu
}vinnuvn}ujª´án1 $iÕ{uvª«w¬X}vª«mny®iw}vnynÝ}inxlvn1H}Ku}w}nq y±'}in¬« {Íçm {{x¬«nuÑ
yÕynuvn1¬«yÕ =n y{}wª«luw¯w¬«ª«x
( l
±³v =m
( l
Õ| y yxlªl } y yn1}vinnÏHxª«w¬«n1H}mwyvÍÕª« =u
wl}wyluvª²}ª =lu'w=u4wy =nª}vinݪÕ=n1u?nÖªn}vª« yfÚwy =wª«f;}vilnuvÍyn¬n1}v yuf ±A }ixlu% =lu?ª°u?}
u? =¬n¬| ± :¸wyl ! }vwluvª²}ª =lu{vn;u?An}vª«yn1¬«yÑ
µuw¶ =lu?n;ÏHxn1l1ny ªiln1ª²}uKw¬°u? ¯ ={ÛÜXn1 yÛÇ~nuuÖ±³ ym 3 Úu? VV3 Mª°uKwo;hjÖÑ
! ! 'z4%#7 . ( $-'{O{ _.17#)6 2+7('/. & q2._0 7#' . 25'}#"%$wz! 0
©Ù y{n1} Zn1zH}n1lß}vinwA yn|1 ylu?}vxl^}ª =¸}v Zhjv&à×Ou1U®nçilwF=n¶}v wy11 yxH}±³ =$mn;uvuw =nuÑ
à{xA =uvn´uv ymnÐmnuuw yn C ª°u¶xluvnÓÕß}®Ý ß1 ym =n1H}u i
wl l
ju?xi\}ilw}76
i
y-: V i M
wF®jwª}u$}ilw}|mn;uvuw =n·Y{n1 y}vn;8Cм^ÑÔhjin1f6
i
1wyÙâlnÐ yl¬Z yª«=}¬\®ª²}i wß ynuv =l{ª«
}wyluvª²}ª =6
l
±³ ym l
}vilw}uvn1u C/·{n }n7Cм^Ýwyl\Hª°nynuwÑßhjinvn1±³ ynyÖuvxli\lwª«u
y±}vwluvª}vª« ylu®ª¬«¬jnvnnuvn1H}vn;¸HßwOuvª« y¬«n|n1}$}wyluvª²}ª =f%}vin±³xluvª =6 ±K}in1 ymA yn=}
}wyluvª²}ª =lu1,m {{n1¬«ª« Ð}vilnuvÕli yª«áw}vª« y¸Õ CÑØl y¯xª°Ï=xln1n;uvu,®Ýn|}viÕxlu$n1n;¸}v n1luvxn
}ilw}~w}m¯ Hu} =nwy}vª« ynK ymA ynH}jnmª²}u 7C ª²±,C V6M AA86Cæ±³ yKwyH6ª«wyÕ| =m¯A yln1H}Ñ
hjilª«u¯±³xluvª« y =lu}vx^}vª« yÓ =vnuv =lu$}v -lë¿ÁËÅ<1©Å©ë 1lë¿ÁËÅ<1?ÉëÀ¯À¯è{Ël¿ÉÆÅR¿ëËÚ±³ y¶ y}vin}HAnu y±
1 ymmxlª«w}ª =fÖ}inÐn1}¶}vwluv¬«w}vª« yÓilwyu¶}v ljwÓwfAnOm Õª²âln;MÚK®nЮª¬«¬K y}ji ®n1=n1;
n1yn¬ =|}iª°uj =ªH}Kinvn=Ñ
3 & 2 5?- & "¶( -
änÐ ® yª«ynOw¸ =lu}vx^}vª« yÓ ±wÎn;Ï=xlªw¬«n1H}çhKà{×ßÝ yª«ynÓwÎo1ÛÇhjÖÚU}vilnO{ª²ðXn1n1nu®ª}vi
dn?}i ymª«n1x´wl×Ðn1wyuin:u&ºì»Rfºþ;»Â1Ëlè{À¶Â1évÆÅR¿ÁêF¯Æw3Aévë;ÆyÉʶuvi =x¬«An }nMÑ
74n} A V qIJ! IH
( N IH $#F69a^I% 8 M,An~wA yxll{n¶hjÝ wl&A Vf5I;: MUª}unw=ilwlª¬«ª²} ywifÑ
ã~n1nyy}vin¬«wyn¬ª« &±³xl}vª« y J?F:^ !ά°wAn1¬°un;{ yn;uU ± 3 Õ}in~ =vnuvA yl{ª« &n1}Ö}vwu?ª}vª« yfÑ
3 ==}wª«lu}vin¶nw=ilwl¬n$mwyvÍÕª« =uq y± Ñ|àÕn1}c5 ?aA,to6 ? % yx3 zHf®in1n %6 ª«u
ª«n;^}vª«yn=/6_?aA % 8 w:&?BA !Ñ
änÖwyuuv Õ1ª«w}vnUª«n}vª«yn¬ ynÖ1¬ {ÍWP
8
}v Knynv}wyluvª²}ª =6 y± ÚnO VqM`?BA t{P
8
??6y!V M^z=Ñ
hjiÕxluÕn1=n1$ {11xvnln4N& y± 6®ª«¬¬XAn = ynvn;¯H}in&uvwym¯nq¬« {Í P 8
ÑUµ11 y{ªl }v $}vin&hjÖ
uvn1m¶wy=}ª«u1f}vinç1¬ {Í P 8
ilw=uq}v ÐAn¶vn;u?n1}w}á1nv ´nzw=^}v¬«Zw}q}i =uvn¶iÕ{u?ª°1wy¬,ªlu?}wyH}u }vilw}A6
An1 ymnun1w¬«nÐwylOuvxliÐ}viw}$6®w=u~{ª°uvwy¬«n´±³ =qw}¬«nwyu?}~ =n¬« y =ª«w¬4ª«lu?}wy=}qªmmnª«w}vn1¬«
An±³ =vn¯ yw} MÚ4}viª°u1wy y}qAn¶{n1ª«{n;Z¬« {1wy¬¬«Ð®ª²}iw´1¬ {ÍEPDt;ÑhjiÕxlu1f1 yluvª°{n1% 8 %CBÑ
hjiln1f{±³ =46
t
6
TkVVNM ?BA t{P
8
?"Zy> ?
F% VM'
(
N<V IH6M ! ( N<VI
|
6Mx
j FV% VM'
(
N<V IH6M#M K $#F69a]V6<IQM (
N<VI 6MxXz|
m
}ilw}Uª°u1=nzwy}v¬«&}vinK1¬ {Í{u, =vnuv =l{ª« }v &n},}wylu?ª}vª« yu%}vilw}Uwyvnjnlw¬«n¯w±Á}n16¯ÉëÀÂ1ÅÇÂÌ
ª}uÖâlªl wl®n1n$ÿ°Ì©wy¬«nçw±Á}vn1)6$Ì^ÅÇÆé^ÅÇÂê}uÖâlªl ilwFynj} An~nuvn}Ö =| =m¬n1}vª« A6 :uâvª« lÑ
~ }nnhjiª«u¯{n1âlª}vª« y6ª°ulwy?}$ ±}vil =uvn¶}vilw}ilwF=n¶}v OAn|m {{ªâln6ª²±}inw=uvuvxm{}vª« yß y±Ku?n¬²±ÁÛ
1 yl1xvnl´{n1 =vnn$5¯ª«u&{ yln;MÑ©Ø%ª« yxn$X}vin =lu?}vxl^}ª =Oª«u&uvi ®Oª«Z}in yH}nzÕ}q y±
}in|o1ÛÇuw±³n¯hjÖÞ ±U}viln$¬«n±Á}&ilwOu?ª°{n=Ñq×OwyvÍÕª« =uwn yª«ynOwyumx¬}vªÛ©u?n1}u ±¬°wy1nuÚXuvª«ln$}vin
ln}Kª°u&oÛ©uvw±³nyÕ}vilnuvnqm$x¬}vªÛÇuvn}uwnÝxu}~uvn}u1Ñ
än1wy ®Ô{n1ª=nq}vin¬« {Í| =lu?}vwª«=}uݱ³v =mINaÖwla^ÑUØl yKwÕ7% y3 46[y/VI% M#M
wylNy E i V6M^luvn}
SVN M ?aA
P
1t3 y FNa]V VVNM#M]Ia]V-VNM#Mx
j
8 I 1 1 3
E 1t
3D3
P 8 y FH+Ia]V6
B
Mx p
l
%
P 8 -
y&FN m x P 88 y&F m
#+x
(
N`6YN9a]VP
8 8 M
P 85 y&FP
m
x
' FQI#5x
N il P 8 -
y&FN m x
j P 85 y FH m
x j P 8 -
y&FH m x
j P 8 8 y&FH m
#+x P 85 y FP
m
x
(
N`6YNYa]V~PI6<8M
(
N`6YNYa]V~P
8- IP 85 M
j P 8- y FH m x
N 8l
N 8i N ii N 8%
6 % 6 l 6 8
Fu Ivwx 8
FN I x i
tHz FPI
x
6 i P
8 y FuQIwvwx N 88
t 8 z
t
i
I
l z
tH
l
I('nz t
i
I % z
tH % I('nz
Ø'ª« yxlvn&J =lu?}vxl^}ª =| ±Uwhjv&à{× ±³v =m whjÖ
hjiÕxlu 6Z?BA VN Mª}uvn1¬±ÝÕª«n1¬°uwn1¬«n1mn1H}wyvO1¬«wyxluvn$ =-P
8
±³ ynyn1Ðu?xi\NHÚf}in }viln1¬°wxluvnu
1 ymnq±³v =m}invnm¶wª«ªl ¯n;{ yn;uj¬n;wFÕª %wln ln;^}}viln&±wy^}}ilw} ¯}vwluvª²}ª =´ª«uwy¬¬« ®Ýn;
} n1¬°wFª}uqâvª« |An1= ylO}vin¬°w}nu?}âlª« |}ªmn¯ ±jw| = lª°^}ª ylnyÑ~ }vn$}viw} yn¯1wy }
mnv =n~}inuvn =lu}wyªH}uݪ«H}v ¶w¶uvª =¬n& =n&n;1wxu?n& ±% Huvuvª«¬n1¬ {Ͷnuvn}u1Ñ
ä ª}vi3 V MÖ}inwx{} ym¶w} y¶}iHxuj y{}wª«nMÕ®n ={}wyªª«l{xl}vª«yn1¬«}viln±³ =¬¬« ®ª« $1 yxH}vn?Û
wv}j y±%hjin yn1m)o3
, n òÕö ¥ ò - j 'ëé¶ÂêÂ1éqJ
( i A V
i
ID
i
M_yPkNDOQP?P+V VV3 V M#M¶ÆËXÃ
( l A VV
l
Im
l
MWyP.NmO P?P+V M¯Å³ÊÂ1évÂ
Â=¿°Ì^Å
( i
AeV i I i
M`ygP.NmO PFPJV M$ÆËAÃ
( l A V l I l
MygP.NmO PFP+V#VV3 V M#MÌ^èlÉÊ´ÅÁÊlÆÅ
( i
( i ÆËAÃ
( l ( l p
~ }nZw Hwª«\}ilw}}viª°uçnuvx¬}1wy }nZnzÕ}vnl{n }v 6xlu| ±.3 xl{n|®nwyÍ6}vª«mªl lÚq}vin
w=uvuvxm{}ª = y±%u?}v y ¯}vª«mªl ¯ª°un;uvuvn1H}vª°w¬RÑ
Ç}Ýuvi =x¬«¶wy¬«uv AnK }n$}viw}}iª«u}vwluv¬°w}vª« yª°uÖ{ªðXn1n1H}U±³v =m´Hwyl¯m¯ =vnK1 yl1ª«uvnj}viwf=}vin
Â1Ëlè{À¶Â1évÆÅR¿ÁêFÂ$À¶ÂųÊë;Ã|ºìF»Ç,ºF»RÑK©O}vilw}qwlv Hwyifl yn1 yluvª°{n1u}in =wyi´ ±Ö¬°wyuuvnu y±Uu?}w}vn;u1
®iln1n}viln¯u?}w}vn¬°wyuu?n;u~wn$nâln;OÕ6·³xl=}ªmn;l¼~âlvª« u?n;Ï=xln1l1nu¬n;wy{ª« ç} wu}w}nyÑàÕª«ln
}in~uwmnu}w}nmwF$n~vn;wyin;Õ}® yUm =vnK{ªðXn1n1H}Öu?xiuvnÏHxnln;u1y}vinK1¬«w=uvu ywi$}viÕxlu
={}wyªlnª«uªß =n1nwy¬Umxli߬°w yn}ilw¸}inçnw=ilwª«¬«ª²}O =wyifÑdÝ ==}w=u};4 =xmn}vil Õ
lvn;u?n=}n´invn e®iª°iO1wÐAn$w¬«¬n;}vin´É]«ëÉ] 1?ëé^¿ÂËÅÇÂÃÀ¶ÂųÊë;Ãhe´w¬«®wF{uÕª«n1¬°uKn1z{w=^}¬}vin
nw=ilwlª¬«ª²}| ywi´wyuj}inx{n1¬Õª« çu?}w}n ywli y±,w¶}vª«m¯n;Ðwx{} ym¶w} yfÚ}viª°uKª°u~w=iªnyn;|Õ
