"!#$%&(')*,+)-.0/1*2+)$34/3
5$
67
,+8
9;:=<>:?A@CBED6@GF>?=HIBA@GJLK
M3HNB=OA@PDRQSTUF>VXWZYNOA[
\]@CB=^`_a@CW7[
bc@CBHITXYdcQeRHNYIYITUf>g=HNTh
"i j=kmlonqpsrtl
uwvyx#vozUvo{}|.~w"svo|Uc|.
{|#mt{=vo|U
|.svav$#~s{}}otx}~{$tsI{}vm.~s(av$s|#xs
|.
{}t}s|#.ysvmo.{vmyo=tx,vy~s|qz.vGq0svmv"av$s|#xs.va|.x#vo0o|. voXm¡
¢ svm|.c~s|qzx#vm{}|#ot{Avm|.
|.{}.v]q0o|.s{xvoz.va.svy£U
|.
#sv"vm~¤mvao|.X|.{
vms}¥Xsv>o¡uwv]~|qzUv0GqmZ
|Usvy~Cvmo}.{m.v]|.
#vma3{}svm.~s|U~Gvm
s$}|.m7£C|t
t#¦{}vmt~s]av$|x.v¦|.x#vm$|UXzUvo.vmU}(.{{Ca|.avoXo¡=uwv~s|qz}xsv§R t£s}{ yt.{#}
|.
=svavm.2|t
A£G|.2{}vmt~syavos|#xsmG.xv0o|.#¨q3sv0}a~s{$av$s|#x2}%s$|Ux#}|..{{}
.£s{}v}"vavm.y
|., t£s{}v# voym¡=©}t{}{}.v.}z.v|.avsvm|.v$o.{G.x"savoot{Gv$sta~s{}vm|
}{}{qvsv>vvms{m¡
ª «¬®A¯6°R±2²,=³$¯¬
´µ´ ¶·=¸¹»º¼s½¾¿ÀÁ½¿ÃÂ#·A¾»ÄÆÅÇ·=ÈÉ¿%ºËÊÇ7ÂsÌ%½3ÀÍ
Î voa}mt{v>.|UP#voy3s}P}z.|U{zUv"yt{}{s]£Gvm0|t
%a|.{}vmos{v>|t
%ovot}4~Gv>$}vm0yÆws|t
£Cv6Ux#vm¥Xtvo{}a|#x#vm{v>x£cx#v$voasa|.x#Gtx#§CvmvmU}.{vm¥Xt}|.ÐÏ ¢ÑÒÓ |#x#vm{N¡cÔ#voy
q]z.|U{zUvyyt{}{s]£Gvm|.
»a|U{v>$s{}vm|.
3|.avy~Gv>$}vm.xwz.vmR{t.vas]£Gvm|.
,a|U{v>$s{}vm|.
|.svm6~Gv>$}vmyyÆvo#s£6x#.a}mat6tsUv(
|.Õx#ovovRtGxL|#U }(|4$|.Xs|U"tGx
xsv$vma}s }.¡AÖ×~C|..X%v$sta~s{}vm»|.
# voy3tv{}zaovo{}{}ØÙÆÚ7Ù.ÙU7Ù.#Ûtܦ¡
Ý }{}{v>~s}vcØ Þs߯Üxsvm$£Cvm2x#ovovy|#.a}o|Xo|.~sa|#x#vm{=
|.,vo{}{× vmx# voym5tGx
.Rt{}.|UsÃot{}{}vmxcÔX|#U }0Ô#]s{}t}|.cà%{}.|UáÏIÔsÔ#à Ó
|.%v$s.$}s{q|U2c3s2vmU
voa}mt{vmU|U(vmz.voX%%]s{}tv>x7|Usvqav.¡,âc|.vvm$vmX»~Gt~Cvo0Ø ãsÙmäqÜ5|qåq.s
|.æs}çsvo=ot{}vmè%|#x#vm{X.x0y.éX}sovo..~s~s|Æ#yq|Umm|UsvyÆo.|U#=a|.vv$ê"$}voX
£#t~~s|Æ#}yqv]s{}t}|.co.{{}vmxë×ìqí#î×ïðìñZòôóXõ.3s2}%zÆ.{xsx#vm$vmt}Usa~#|Uo¡©ssvm
a|UvU#33s|q36t3sx#vm%vm¥Xsvm$v|t
=.~s}|.m3s}.vmsvot{}{}ys|.{x"3svmsvs£Cvo3|.
a|U{v>$s{}vm|t
=voz.vm~Cvmov>3%z.vm({}.Uv.soovm}z.v0vm~3|.
A.~s~s|Æ#yq|U3o.2£Gv0yUx#vGq{}vmUx
|Rc |#.yx#§CvmvmU}.{vm¥Xt}|.öÏNÔ ÑÒÓ |#x#vm{ÏI¡ v.¡|Usv"x#zUvow£ Ý tG}.3svys|.v Ó =tGx
{yqvo{}|cvy|.x#Gtx#§CvmvmU}.{vm¥Xt}|.6Ï ¢ÑÒ Ó t]tvyvm{{éX|q3|Rsvoa 0.sv
vmU|U6qvvm¥Xt}|.m¡A÷5.#¦{v>t~s}sX|..vosvm»3(és|q3av$|x,
|.%Ô ÑÒ 3tGx ¢ÑÒ m~s|qzx#vm
tavm|Ué
|U=svvm.a{v>=t~~s|Æ#}yq}|.txa|.{}#}|.a|.
5øí#ïùëNòúoûìqï}ðsvmo.{{}0vmU}svmyo
3vovsvymt{}vmtv|qz.vm6.s.v]|t
,~G|U~ss{q}|.G|.
,svmo.{~Cvm$}vm
|.üa|#x#voqv|(zUvo2{}.Uv
s]£Gvmm¡
þaÿ ÿ =ÿ
ÿ
,ÿ Aÿ
ý$ÿ þaÿ ÿ 0ÿ ÿ »ÿ %ÿþ
=ÿ ÿ Uÿ ÿ =ÿ Xÿ ÿ
=ÿ ÿ
=ÿ ÿ
A
ÿ
X
ÿ Aÿ
,ÿ Xÿ ÿ
Uÿ
öÿ Aÿ
ÿ ÿ
ÿ 3ÿ
»ÿ
=ÿ ÿ=ÿ =ÿ ÿ ÿ
ÿ
ÿ =ÿ =ÿ Xÿ
ÿ
c
ÿ
ÿ Xÿ ÿ
þ ÿ
ÿ
Uÿ ÿ ,ÿ Xÿ Gÿ ÿ 3ÿ
ÿ
"!$#
&% (' $%
)!$+*,!.-&/0/1234 5(!$#6& $-7!$8 9-:&:;!$<
": >=/@? $/BAC7DFE GH I.J$I.K$L$M/N/1
O E9: )/P!$#;*,!.):&-&Q7
&.
C!$#;* $%
#R!$& 4 $/ B' = 1S23
P83!T48 $Q-&::;!$U=/V&W* $%
#R!
X &-&U!$#W2Y5&!$%!$?$(-&&5VEZ[\]Z^Z>8 _A!&1UDQJ.I$L.I.`H I7a5H`<H Ib.bc76=/"&+d11EV: )/!$#3eS&?$(-&&5VE4fVe
8 _gA9!71hECe6H DjiVI.JH I$I.e6[V`$bMJ$I7=/k"A !. $%97
&(D!.-& !.l-7mAC7D 8 _n*32>H I`Ib$b$c$M7 l=/k&
X &-&9#o!$V*,!.%
% $=;!$ U',
!$_&!.%
!.?$9&!$-?.@?$ BEZ9ZBE+a<KH0I$JHpE9H I.I$I$MU#o!.q&Vd11&ZBUm[ _(fr)$1
s E $m291&i9
%
%:
C*,!$-%
?7* $ $
.* %#o!$ 1323&B _t!#Y&
-&!,8 $,-&::;!<u
t: v=/+BZB
,D!
fr))!#97
/w)[B 5 x&t* $%
#R! X -&u!#2j_!$%
!.?$y-&4EZ[\ZzZB8 _yA!&1"DQJ.I.L$I`<H0IaH0`H I.b.b$c
$"
G: =/{& {!$%
-% U7
& X -7C-7!./ $59A!&19`M$M/N.`$bm8> 7 uA !. $%6| $=;!$ !$
{&
EV: )/W!#6e6?]} B~/i9&!.)W!+|Y#R~m\Q!.? $"1
às|tsvovov}R3ssvma}mt{}{v>.$}s(# voy.vs{mt{}v}z.|.{}z.v>»v]3x#vzÆ.q|U
|.
vm.$}|.cqvmm¡©s|Uxsv$vma}s }#vmamGs X~Cv|t
{}o.{v]£GvmÆz|Uo|.aa|.s{}2éX|q3
U§Cvmo¡%Ö×2sv]voa}mt{5éX}svooo|.XvomZ §Zsvm%|#m$sx#v0|"sv]~sv>vm$v|.
{}|qEtx2
U
vmU|U»3svov ,|y|.3a|.v
.%v>.$}|.»sv>t{o.$vm{7vm.2|.svmm¡Ö¦%}vm{{és|q3q%}RG
t}|.mv$#~s{}}o3savo}mt{Cav$|x~Cvo
|.Ëz.vma~C||.{y$|Ua~tvmxa|]}a~s{}}o3av$s|#xsØ ÚqÜI¡A÷»sv
§Zsvmy~ssvms|.avms|.Ðo.L.{}|£Gvc|U£voz.vmx`}`svR|#.2svoao.{3|#x#vm{N¡;÷»svca~s{}$".
avos|#xØÙmÛqÜ».,~s|.~C|Uvmx6U»t2t{vot}z.v|svvo~{$»tav$s|#x6
|U3 §|#U }vmyo
.x,U,Xvmo.{{}6x#vma|.qvmx6|a|.#~Gvm
|U¨svvo~{$3.avos|#x(
|.»s|Uv#voym¡
´µ
½AÂsÉ =·Â#ɽ¿¨·A¿À ¸Z½¿Â#¼É ¾3ÂsÉ ½¿Íw½ "ÂsÌÉÍ ½¼s¹
÷»vv$#~s{}}o%t#¦{}vmt~saav$s|#xX|#x#ovmxPØ ãqÜ».»a|.}zÆtv>x(£6sv
U3qo|.X}s|.,av
.xx#ovov"qv"âRté.|qzc~|#$v>vm£CvoGÆz.va{|#mt{}{R{}}é.v" =|.|U~s|#$vmyØ ÙÆÞ>ÜI¡÷»ss|t|U}
vmo.~s{}tv>xcsv$|U$vm~#|.
Asv~s|.~Cvo 6
sG}|. UÏ Ó 3sRv$
vo3|"sv]~|U£t£s}{} 2|t
~Cv yvmU}|.|#oos}sav}vXvmzq.{Ø Ó G.}z.vm6q3sv0#vm 3ctv Rq3av
Z£Cvo}s UÏ Ó #Ï Ó . Õä¡Ö×Xs}z.vm{UZ|.sv0a}.Xvo#~Gv>tv£CvoÆz}|.s|t
v$#~s{}$.
U,vm{{7.q3|t
5a~s{}}o»t#,|.s{x6.~s~s|UUa
|.3y.{{ "q3|.
va|#x#vo{xsvm$£Cvmx6£Xasv0ÔsÔ#à
.{U|.s Ï |.v>¥Uzqt{}voX{]£Xsv%voa}mt{syU voAvm¥Xt}|.cØ qܦ.3sa}.a#Gsvvm |.
¢ÑÒ
|U,sv}avvoz.|U{s}|.6|.
v~|U£t£s}{}v> Ó ¡ |qvmz.vmm]¥X.XqzUv.t{}#|t
svvo|Uosv>x
£vv|.
Asv>vt~s~s|Æ#ytvav$s|#xsG.%|t£Cvovm~s|qz}xsvmx2}csv]{vmtsv.¡à ¥XtXq}z.v
v> ytv|t
sv{}|#o.{Gvm|..,
s|U6|.
5 vo~}¤ov (s|Us{x"£Cvv$
{G
|U,xsvoz.vm{|U~s}s]qvo.}vm
|.
.#|Uyqvo~G}¤ov0vo{}vm$}|.C.»,vo{}{.%aUsx#v2svvm.(
|.%Usvo3|Ux#vm%.m$sqvtsI{}vm.~s
avos|#xsm¡
Ö×s=~.~Gvm5,v,xsvoz.vm{|U~].]tGt{}|t
C{|#mt{Xvo|U|t
£C|tsv»v$#~s{}}oAtxa~s{}$t]vos|#xsm¡
uwv0x#|y|]£"|U£vmz}s]t,svv$sU3~s|.£.£s{} a
|.3t"UzUvo(vm¥Xsvm$v|.
5vm.$}|.||#m$s3}
Gsv}v"xsst}|. o.£Cva3vo.(vm¥Xsvm$v|t
,voqvmxR}Xvm.t{}z.|.{}z"v~|U~Gvm
|U3tx6v$#~C|.svmU}.{}|t
sv~s|.~Cvo a
|Uo¡à{s|.."svmvXvm.t{mtss|.,£Cv}a~s{}
GvmxwUvosvm.{NZsvowotw£Cvyv$#~tGx#vmx.c÷Æ{|Uvov>~C|qvm|.
7¡ }ss0.~s~s|U.v
s|q q0£C|tsvyv$#~s{}$.xa~s{}}otwav$|xtv¦|.x#vo$|UvoX} 7¡aÖ×P.xsxs|U
,v~|qzx#v0v$#~s{}$
|.{}.v0
|.sv{}vm.xss6|.x#vo{|#o.{5vm|.%voÁ|t
aÏ Ó
|.sv]avmttxRo|t
zq.tov|t
=v$#~s{}}ot¡uwvt{|y~s|qzx#vy}a{t£s#{}vm3v$#~s{}$%
|.s{
|.a~s{}}o.¡âc|Uv
}a~G|UtX{}.A|Usat~s~s|UUP~s|qzXx#v># voyq}6av$|x4
|.x#}ssv{|#mt{,vo|Uvmy]|t
.{{
a|UvmX3s~(|"."~G|q,vo»|.
7¡
Ö¦G £Cv|tv>xcqss{}}é.vat ¢ÑÒ Csvxs}$v$v|#U }]a|xsvo{Ao.£Cva}s{qvmx`ð ì.ûoëNï
}$v,zU|.{}z.vmvm¥Xsvm$v|t
x#ovovvoz.vmXmX.{£Cvo,Gt~s~Cvos}s($|.Xs|UavU¡=÷»,ta{}|mt{
vm|.5
|.{}.vqAs|U{}x]|.s{}
|.,úøyìqïôïCðoó tí.õ yÆs|tA£Cv,|.
Gvo{}vozqtG$v,ss{}vmsv».s.v,|t
Czqt{}}x#
}o{xsvm 6zq.{sv>,3s6{~s{}vv>.$}|.,tv{}éUvo{}a||#o$m¡A÷»s,,Æasv{}|#o.{Cvm|.
|.{}.v
o|.s{x£Gv]t~s~s{}}vmxRt}|.33vov|Usv0.$.{{}6,|.{}x(vsv{}vm.~s}syav$|xo¡uv0{}||.é6t3s
sva}svy$|UUv$|t
,|.avv$sta~s{}vm.xs|q qé.vmvo~s}s|.s{}2v voüv{}|#o.{Avo|U
|U»svavm.(.x6zq.tov|.
ôvo2~s|qz}xsvmv>.|..£s{vt~s~|Æ#}at}|.|v{}|#o.{Cvm|.
|. zqt{}svm
q.v{t.vvos|Us.(Gq3vv>ts£Cvo3|.
vmU}|.G{}vm.~#%|qz.vm»}»|U6sv|.x#vo3|.
Ù>ä]|U3a|.v.¡
Î |U}vm$|.
C{v>t~s}sav$|xa.{|Usv,xs|Xv>=s|tAUttXvmvo|.z.vmUvoov|qz.vmv3Xvmzq.{N¡5uv
vm|.svm{zUvm%|2#voy3{}}svm.~s|.~CvoG
s|UtGxR|q t
|U£C|tsvv$#~s{}}o
.xy}a~s{$,tyavos|#xsm#t{}{a|.avoXo|.z.vmUv|0s|Uv|.
Csvo|.v>|.{}#|Uy360U{|U£t{Gvo|U
|.
aÏ Ó ¡÷»sv}.sGo.$v|t
7}v>{,}tU|.|.{} vmv${t}tsv%t"av$s|#xs
çv>ta{}vm{}#èt|UR}U|ÔsÔsà0¡ZÖ¦
}x#vov>xctRav$s|#xsx#}z.vo.v>x2|.$|UXzUvo.v>x6|(|.av~|#$v>vm
|.svmt2ÔsÔ#àUsvo(|.sv|Us{xyÆz.v|]£Gv,.|t
5}s]z.voayt{}{ (vo~Go¡A÷»s,|.{}x".{}|tv
o|.ovo%.£G|U#s|qEy.{{5}»||6y.{{I¡ s|q3]qsvmo|.z.vmUvUsvm»%t,v0svov>x2|.s{}
o|.ovo2|.svm{zUvm»3Ro|.a~s#q}|.Gt{voê"$}voo6}Rx#vmo}x#}s"3vo2|(32
|. svtcav$s|#xs
|6ÔsÔ#à¡
uwv»t{|~s|qzx#vAv,vm~}¤ov».a~#|.t£{} vms{
|.5sv,avm.|t
s£C|t0sv,tvos|#xsm
|U# voy%3c{}vmt~s|.~Cvo 6
s$}|.m¡%÷»svmv.£s{} (vms{%o|.#Ãtv0avmtc|.
=sv
}a~s{}}otc3sG$|.Gx#|Ut{}{}.£s{v
=sv|.U.{vm Ua~#|.o.{{}6t£{vU3s}{vv$#~s{}}o
t4vm¥Xs}vm0{}}t}|.]|.Pavm~}¤ov"|vmsv t£s}{} U¡÷»svmv6vms{]tv"z.vm}a{t|sv
!
"$# %
&
'
)(
*
+ -,
*
+.
!0/
1
32
76
98
:
; /
:
<.
>=
7
>?
@
54
§4 t£s}{} cvms{
|.v$#~s{}}otxRa~s{}}o Ò {vmav$s|#xst~s~{}vmxR| ¢ÑÒ m¡÷»s}.{}|"v$#~s{t}
3ysv}~{$3.(av$s|#x~Gvm
|Uy,£Gvovo3
|U% §# voyØÙmÛqܦ¡Auvs|.vGq]|Uvs|.|.sU
.t{}#%|.
§P.£s}{ 2z.|U{zUvm3{}||.é}s(ts|. svv>tZ£sssv]£CvoGÆzX}|.|t
Usvo|.x#vo
a|UvmX0Ø Ü¦¡
´µ 4¾%ÂsÅÉ¿Çå½ "Â#ÌÇEÈ·=ÈǼ
Ö×4Ôv>|UPÚ(,vy£sv x#v>o}£Gvasv"|#.asvoao.{A|#x#vm{tGxsva.#¦{v>t~s}s2svmavmm¡yuv
.{}|x#o ,|}vmGq}~G.|UstGt{} tGtavo{}0v$vo|U]|.
sv3~s|.~Cvo 0
s|U|v>t{
tv>.x£G|Usx#}s(svas£Cvo|.
vm.$}|.Rvmz.vmU|2Æz.|.xcsvmUt}z.va qv>.vm{{U.£st}{
{t.vs£Cvo,|t
G}sUm¡Ö×Ôv>}|. ,v~svmvoXsv{}|mt{Cvo|UtGt{}|.
sv.#¦{v>t~s}s0av$s|#xs
.x~s|qz.vasvo}0¦|.x#vo0o|.}vm$U¡(Ö×Ô#vm|U4Ûc,vy
|#$|.4vmy34{}sv>t0~|U~Gvm
|U6.xL~s|qzUvcäq× t£s}{ .xö$|.zUvo.voG$v|t
t{}{a|.avoXo
|."£C|tö.#I{}vm.~s}svos|#xsm¡
©ssvma|.v.v~s|qz}xsvsvvm~}¤ov0Ua~#|tt£{} t.{#}%|t
sv0av>t2
|.£G|.2v.
avos|#xsm¡5Ö×aÔvm$}|.aÞ%,v~svmvoXA|Uavv$s.~{v>5.x0~s|qz}xsv£C|tsvm|.v$}mt{txXvmo.{Uvms{
s|q3}sa I|Uxsvo%$|Uz.vo.vm$v|t
=sv.cav$|xoC.3,vo{}{5U»svvm.}|.2|t
Azqt{}}xs (|t
=sv]v>$|.Gx
|Uxsvo{|#o.{5vm|.
|.s{tvU¡©5}.{{}.Z,v]ytéUv]|.av]o|.o{Gx#(voyté#.xs.Uvm}|.%
|.
#v
,|.éZ¡
=¯"² =³o² ²
³o²
¯"° 0¬2° 0±
c³m¬ ²
Ö×s}Avm$}|.v3x#v>o}£Cvsv3x#ovov3 qv..o|.X}s|.5av%âR.éU|qz~|#$v>a|#x#vo{
|UAvm{{× v>x
voa}mt{AvmU}|.w#vmam.,vo{}{A..vo#U}{}t}|.t{}.|.s
|.s|#x#vm{Aés|q3wUsv
ë >û sìÆúëIò û òôøí#ïìqëIò qó ï õ òôë ø ÏNÔsÔ#à Ó Ø Þ»ßÆÜI¡Euwv.{}|4x#vm$}£Gv2svRt#¦{v>t~s}s4svoav>o»£C|t
vo#~s{$tGxR}~{$m53s}w,vovx#v>}.vmx
|.v$ê"$}voX.x.~s~s|Æ}yqv]s{q}|.|t
sa|xsvo{
Ø ãsÙmäs5ÙmÛqÜI¡÷»s|.sUs|.s%s~t~Cvo> x#vos|.v>%svv$|t
s|UssvmUqzUv0}UvoUvotGx Esvvo|.
|.ssvmUt}z.vv>t{Zs£Cvom¡
uwvo{}{¦}vmxwsvmo.{vm.$}|.#vmaot£Cv".m$sqvo{}x#vm$}£Gv>x£wc$|.Xs|U}av6x#
ovov qvâRté.|qz(~s|ovmØ ÞÆÜ¦¡à#vmÁo|. s6|t
a|.{}vmos{t~Cvm$}vmUtv `Ï Ó
3vov Ï Ó 0svX£Cvo|.
%a|.{}vm${v>|.
3sv I~Gv>$}vmq]}v ¡Ô#s~s~C|Uv"Gq voa}mt{
Ó yÆ|#o$ta|Usyvmv]~Gv>$}vmm¡à|o}tv>x23vmUcv>.$}|. }
vmU|U Ï ËÙ
s|UssvmUqzUv0ñ ñðoósúòôë í#óZû$ëIò qó
Gqvy~s|U£t£{} 2qvmU}|. 3{}{
Gt~s~CvoP}Pv"sv$]yt{}{A}av6}Xvozqt{Ø Ó } UÏ Ï ÓÓ #Ï Ó U ä¡ ¢ m$svm$va|.
3
vmU|U {}vm.x»|66tsUvRtv0|.
¡%÷»sv .v0x#vovma}svmxc£(sv0 X~Cv|.
Av>.|U
.ZtxR.v}x#vm~Gvmx#vmU|t
Asv]tvU%,vo{}{5.3}vU¡÷»sa|#x#vm{{}vm.x3|6sv~s|U£t£{} 2x#vm
|U XÏ Ó
|.»svav (
|U3vsv$vmU}|.#3svov R»sv0tv0t3}v GtGx
XÏ Ó
.Ï Ó ¡à{}|ssv~s|.£.£s}{ yGq»svv$3v>.|U( 3.}z.vm6£ ¡ s|q3
svmv% ,|~s|.£.£s}{ ]x#vmv>A
|.svsv$vmU|U]avtx ~Cv.Xvmt"]s{qv»sv# vo|.sv
vmU|Ucvoz.vmXqy}vU¡Ô}$vsvx#voG 6
|UGÆz.v0a~s{}v0
|Uymsv]]s{}t}|.c~s|#$v>}
v>..¡=÷»s=vos|#xa=és|q3Usv ë >û sìÆúëIò û òôøí#ïìqëIò qó ï õ òôë ø Ø ßqܦ¡ Ý }z.vmy# vo |.
Zvoa}mt{
vmU|Uo5v"
|.á|t
»sv(~s|.~Cvov> Ï Ó yÆw£Gvx#vozUvmx
|.
sxs.vmXt{,~sG$}~s{v>0sGx#vo
ovo.a.~s}|.m.tGxsv sa|U#A|£Cv3~G|U{s|Ut{3Ø ÞÆÜ¦¡ |tv»qAsv%x#.o=|.
Z# vo
%o|.a~s{}v$vm{(t.$vo}¤ovmx6£ P .x
|U EÙ ¡
=
$
6
$
8
!6 &%
6('
!" #
8
*)+
-,+
.
/54 !
:
;
)+3
98
-:
4@
!6 A )3+
%#, +
:
=<<< >8
?'6
:
21
0/
76
1
D B:
C/
)3
-
# !
%
D FE HGFI?JLKMONQPSR
TE ;VUVY
W X[Z :
$
6
$
8
!6 ^%
6('
J \MON=P ?
]
JLKMONQP
8
`_
.
a8
bD ;
<=<< ]8
p#n ©s|.t6vm.{svmo.{vm .yRas|UssvmUqzUv0 qv.G"v>.|U(vmz.vmUs|Us{x
|t3{v>.x"|yvoUt}z.v qv.sov|.ssvmUt}z.v qv>»tvs|.,~X#}mt{}{yav>ts}st
{N¡÷»sv
|U{{}|q3
o|.xs|U4|. 6tGx 6sv>$v>t.x4#ê"$}voX|voGsvys}m¡÷»v($|Ux#}|.4t
|.t
svo UÏ Ó åäs¡ %|tvt%vmv0$|.Gx#|U%.vts|.ytot{}{}6o.~#svmx£
sv~C|.{}X|.a}.{7~s|.~Cvov>,t$|Uv
|. Ý {}{v>~v »a|#x#vo{I¡
i(kmk l
÷»s|.sUs|.ss~t~Cvo,v,t{}{.savt5.}z.vmt}s}.{# qv Ï ä Ó
svov»}A£C|.sGx#vmx£vo
]tsv3#vm vmyt}
|.t{}{}av»3~|U£t£s}{}
ih&j
cedgf
1
)+3
;lD em1
kD )3+
;
n_
Fo
Qp frq QsCtuwv
x/
y
N9z
)
3+
{
5y
N
;
1
)3+
ÙU¡AÖ×2|tvo3,|.xso
Ï Ó
/
x1
y
`ä
7
N
Ù
2;
ÏÙ Ó
<
3µ´ ÌÇ;Ç 3ÈÅɸ7É ÂP·=¿ÀüÉÊÈÅɸ7É ÂÂ#·A¾üÊ1ÇÂ#̽3ÀÍ
÷»vð $ñCïùò ûoòôëë¦ìtí#î×ïðìñCòôóõ,av$|x]U5£Cvovm]x#v>o}£Cvmx0}2Ø ãXÙ>äÆÜ#|U.vosvm53a$vmt}]vo~G}¤ov»vm{v>|U
ovms¡÷»s|..s|U#s}~Gt~CvovaGt{}{v$
vm|6svy qvs~Zxsqvavos|#x|£Gvax#v>o}£Gv>xR£Cvo{}|q
Usvyvo#~s{$.avos|#xtx}voas|U{|U.Rt{}{t~~s{vmUtx#{}vm|.
3t vo~}¤ovyvm{v>|U
ovm}|.»v>x7¡
Ô#s~s~C|Uv Ï Ó 2}vosvoX» qvaÏôsv~Gvms4çv$ètGxs
|.,v$#~s{}}o». Ó ¡A÷»svm"
|U»
av0vm~|.
öäsv0 qv0t }»UzUvo£X
Ï Ó
Ï Ó
ÏIÚ Ó
32
MSP 2/
;
1
> MSP /
;
W
;
MSP D <
YX`Z
vov. Ï Ó UÏ UÏ Ó Ó G
|. Ù stv}x#vm~Gvmx#vmU =|.|.(.x#|.Ëzq.t£s{}vm»3
av>tctx(zqt}.$v UÏ Ó 7¡
÷»va~s{}}o3tPÏs|Usx#v>xz.vo|U Ó vos|#x~s|.~C|Uvmx(PØÙoÛqÜ5~s|#ovovmx3.,
|.{}{}|q%o¡ Ý }z.vm6q
Ï Ó },sv0$svoX% qvUsv0tv0t,av wÏ öä Ó ».é.vm6|£Cv
Ï Ó
UÏ Ï ÓÓ
Ï UÏ UÏ Ó Ó UÏ Ó Ó
vov.#sv0s~GvmçèatGxs,
|.3}a~s{$%t¡
÷»vcss|.sxsvmx`a~s{}}o6tLUasvRxs}.x#zq.UtUv6q""{v>.xs|4 qvzq.{sv>aGq6tv2s|t
}Xvm.vom¡]Ö×w|.x#vo|2o$z.vmXs}~|U£s{vm27sva|.sGx#vmxa~s{}$tw».~s|.~C|UvmxR}ÐØÙmÛqܦ¡]Ö¦
yÆ"£Cv0x#v>o}£Gv>x2.
|.{}{|q%m¡
Ô#s~s~C|Uvqq}av %,vGÆz.v0sva qv
Ï Ó LÏsvys~CvosÐçè6tGxs
|.|Usx#v>x
}a~s{}}o%t Ó ¡© >s$|U~#vsvXvov>x#qvtvzqt{}sv 7.m$|Ux#}s]|RÏ Ó
Ï Ó
Ï Ï Ï Ó Ó Ï Ó Ó
ÏÛ Ó
÷»vo6.~s~s|Æ}yqv»sv.t{Gs£Cvo,|t
ZU Ï Ó |.
v>.$}|.ytsvo{ }yv%}av}Xvozqt{
Ï Ü£"vyòôóë×ðIõXð î Æìtïùíð .x#|.Ëzq.t£s{}v
Ï Ó x#vosvmx£
Ï Ó Ø UÏ Ó UÏ UÏ Ó Ó UÏ Ó Ü
ÏIÞ Ó
vovsv Ï Ï Ó Ó
|. Ù .vsvaúoìtøað0óí#ø ð úvmx(vm¥Xt}|.ÏÛ Ó stGxØ tÜx#vms|tvm
svsv>tvm»|.ssvmUt}z.vXvm.vm»| ¡
©}t{}{}..é.vv0 qv0t»}v 6|y£Gv
Ï Ó
Ï Ó
ÏNß Ó
MSP ! (
;+ ! !
4
M S P !
/
;
9;
<=<< ]8
/
4
M S P ;
W
;
4
M S P D S/
!
;
YX[Z
W
D !
<
YX[Z
(
4
M >P /
;
/
/
;
;
W
D S/
YX[Z
W
' "!
& ! (
!
4
M >P #
4
M >P ;
<
YX`Z
! ! D ;
S/
$
:
%
(' '
=<<< >8
<
)
()
/
4
M >P ;
;
W
4
M >P D YX`Z
<
Ö¦
Ï Ó c}%.(}Xvm.vo3zUvm$|.>Xsvmc|a Ï Ó ¡
÷»|Us.s|U#%sv]vm|.
s~t~Cvo>Za~s{}}o.t{}{5av>tcsv]s|Usx#v>xc}~{$tZs{v>
~Cvm$v>x(|.svm3v.¡
/
4
M >P ;
4
M YP ! /
*
3µ »Â#Ç¿ÍXɽ¿Ã½ 6ȼs½ÈÇ¿ÍXÉ Â ¾¿¸CÂsÉ ½¿ÃÂ#½1¼Ç·AÅÍUÂ#·Â#ÇÍ
©|.3sv~ss~C|Uv|t
.t{}#3.»,vo{}{U3~s.}mt{o|.a~s#q}|.|t
v0a~s{}$3t%}3}a~G|UtX3|
vovoGxRsvyx#v$|U|.
~s|.~Cvo 2
|U|~C|U}z.vv>t{= qv>o¡]÷»svaa~s{}}otwvos|#xwo.
~|#x#ov qv>t3.v} #£s#%tvs|t»svmovm.}{}}Xvm.vom¡ Ò z.vm"|.sU6~s#o.{{}a}»»s|t
av>ts}st
{N,svmz.vmsvo{}vmvms{6yqvoyq}mt{}{a,vo{}{Cx#vosv>x"~s|#$vm£Cvmmtv%sv~|U~Gvm
|U UÏ Ó tv0~G|U{s|Ua}.{}txcvoovÆzUvytst{5v$vm}|.R|"vm.{s£Cvom¡ %|q,vozUvo>
|Usv3|.Aa|Uv3|.
Gsv%~s|.~Cvo
s$}|.£Gv>$|.av3svmUt}z.v,svmsv%~|#$v>=£Cvmo|.avm{}{×x#vosvmx¡=÷»}
3v>.{}ys#vmx(£6v$a|y¤ovm|at"~|U~Gvm y
sG}|. UÏ Ó t%vozqt{}tvm,|y£GvmvoUt}z.vU¡
Î |U}x#vm,svvo#.a~s{v|.
asU{vvmU}|.s}s.{}v~Cvmov>3oUv
ä
÷»v~s|.~Cvo 6
sG}|. ZÏ Ó Ï Ù Ó 3}{}{5£CvsvmUt}z.v0
ä Ù.¡ Ò z.vmc3svocsv]tv]}
~C|U}z.v.sv~|U~Gvm (mt2£Cv0svoX qzUv.¡÷»s%x#|v>3s|tt~s~Cvo23c}XvoUvotv>o¡uÐsvo R%.
}Xvm.vo> ZÏ Ó 1äy
|.£C|t ätx ËÙUtx ZÏ Ó Eä6
|. Ú#¡0÷»y.é.vmvov|v$
ZÏ Ó ;ä
|U%ä EÙ.¡uÐsvmPÙ ÐÚ# ZÏ Ó Ðäss|qvmz.vmsv0|#oosvm$v|t
v>.$}|.3{}{{}vmUx
|6t2sv>t{}}svoXqzUv0 qv Ú#¡»÷»s}%aÆ(£Gv]Æz.|.x#v>x6£2x#v$s CÏ Ó æä
|.0Ù åÚa.
,vo{}{I¡ ssvos{v>.xs|(x#}$|UX}X|.~s|.~Cvo
sG}|. ZÏ Ó ¡©|UÃsva~G|UX|t
z}vo |.
|Us%tGt{}o»,
t3a|Uv$|Uz.vovmU,|aÆzUvo|.X}s y|t
CÏ Ó |vmsvo|.}vm$yvms{m¡=uv
.{{Ux#|.~#3sv
|.{}{}|q3sv$vo|U(|.
5sv~s|.~Cvo y
s$}|.¡
n
k l rtl `l Ck l n "p !kol>p#l k Ý }z.vo~C|.{}s|.at{
l 7l k
~|U~Gvm 2
s$}|.
,voXvo}|.
E|.X2s|UssvmUqzUvvm.{5zUvm|. }
xsv$sv>xR.3
|.{}{|q%m¡»Ö¦
svzq.{sv|t
UÏ Ó .m$|.x#}s|ysvçqst{voXvo}|.èa%s|UssvmUqzUv.#svo
UÏ Ó ».}z.vm(£ysvqst{7v$vo|U¡ ¢ vo3}v UÏ Ó åäs¡
÷»v
|U{{}|q3}s #voay}%vm.a|y~|qzUv.¡
p % Ö¦
7sv|.UGt{s~s|.~CvoG
|U
$
Ð.v3~C|.{}s|.at{oUvoysvo}voXvo}|.
1U0x#v$Gsvmxw£ Ñ v$|U .v #~s¤"o|.X}s|.|U.R£G|Usx#v>xP£Cx#|Uyt}w|.
¡
p#n '& %|.v(|.
%svco|.}vm$P.xo|.z.vmUvoovyv>s{~s|qz.vmP`}~.~Gvmvm¥Xs}v 6|
£Cvy~C|.{}X|.a}.{}m¡ ,#svyv>{
|Ua~s{}$t.vsvoü|2£G(v #~s¤y$|UX}X|.|.wt
£C|.x#vmx2s£Zx#|.yt}2|t
¡
3µ ¶½¾¿ÀÉ¿º1½ "ÂsÌ%*Ç )2½ÉÍÍX½¿ ¼s·A¿À½Ê =·¼GÉ · ÅÇÍ
à{{ssv,.#¦{v>t~s}svos|#xstv£Uv>x0|U]Uvosvmt}s =|U}|U0tx#|U s£Cvo3a.}z.vo]avmtatGx
zq.tov.¡6÷»v =|.|.wx# }£s#|UP3Ps|.s¤mvo|2v>tP.Us|.¤ovo|2~s|.£.£s{} c|R.£st}{
{t.vs£Cvom¡÷»s}3mtco.v|.av~s.}mt{U»vm{{U,svm|.v$o.{7~s|.£s{}voym¡
¢ v~|U£s{vmü}q0yÆR~s|xs$vasvmUqzUvtvazqt{}svmm73sPtv]s|U#¦~sot{I¡]÷»vosv
~|U~Gvm}vmyƣCvm$|Uav"svoXqzUv]
|UsvmUt}z.vy qvmm¡2÷»}]ot{}vmUxw|Rc~s|#$v>3}0£C|t
ytsvmato.{{}.xc$|Ua~s#t}|..{{}6}{}{×x#v$Gsvmx7Zov0~s|.£.£s}{}vm%.x2svm$v0~|U~Gvm}vmo.ss|t
£CvsvmUqzUv.¡A©s|U3G tov.s$|U}x#vm»sv|.avo¤>q|U6vm.$}|.
ä
÷»v~|U~Gvm c
sG}|.w CÏ Ó 53svmv ä(}|.avy$|UtX>¡ÔXt}scq0tst{ qv
UGvov0}ys|Us¤ovm|y~s|.£Gt£s}{ (t%sv vm~R|t
Avo~{$tcyÆ(~|#x#ov0ysvmUqzUvqv.¡
Ö¦
As%.~s~Gvm3svoRsv0vo#~s{$tcav$s|#x2£Gv>$|Uv>%}{{×x#v$vmx7¡3Ö×c|Ux#vm3|(Æz.|.x6st}|.
3vosvmz.vo%svmUt}z.v qv»vm.vmx(vt{}{7vm~s{.$v%3c]|.ssvmUt}z.v qv0U,
|.{}{|q%m¡
7,+3
!
(
Z
!
;
;
Z
;
Z
%
<
/
;
B;
* !
;
!
u`s QsCtu
7d
d u =stbult
A )3+
q (t qd u =s
%
p`u
,
=stbu
*
=t
t =s =s
q
A ,3+
%
d
d
d
,
!
!
xdgf
f
+
A ,`3+
%
,
A )3+
%
;
,
,3+
cedgf
ih
_
,`+3
)
-
Z>%
!
;
<
bE
+
!"$# Ôs~s~C|Uvsva qv]£Gvo
|.vsv]tsI{}vm.~R}
Ï s|.svoXq}z.v Ó .xavtvvmUsvmxa£v{}vm.~ y% »0svmUt}z.vtv.xysvs]£Gvm»|t
vm.$}|.
|#m$sv>x(Uoo|.x#|]sv{}vmt~
|U Ù
|.& »Ù |
;
*;
¡A÷»svo
=<<< >8
8
(') ( '
*
* }3|.ssvmUt}z.vsvm£v>té
Z(
I
W
;
D ; YX`Z
ov x
÷»vv>s{}syqv * ,.é.vm6|£Cvvsvoæs~Zxsqvmx2 qv.¡
÷»vvm$|Ux~s|.£s{}voEqvozUvo
ssvsv# vo qvm5àsa~#|U]Ú#>svt0avos|#xs5s
=|U}|.w.x#|.ás£Cvo3}{{.vmsvoqv"t£s.}{}R{}.Uvys£Cvo03Ps|Us¤ovm|c~|U£t£s}{} U¡2÷»}
X£C|.x#vmxssvm3{}vm.x,|yx#êyos{}vm33va~s{}}otav$s|#x2£Gv>otGvv.s.v|t
zq.{sv>,
|.
3}]sv»}a~s{$Aav$|xvm{{sx#vosv>x]o|.s{x0~C|U}£s{}.voA.£.}{{}y.{{I¡Ö×|.x#vo|ÆzU|.xs
~|U£s{vm2Us|.sUs|.#svv> |t
sv~.~Gvm,v.{{Z.v%tsv%
|U{{}|q3£C|.sxss$ +>sGoq
~|#$v>x#sv}»vmx¡
,-,./0.,.1
23425.1,6789/:.;<=.15>?$# uwvas||Uv
6~svmx#vosvmxRzÆ.{v0
|. (@7ACBacq3svosvmz.vm
6Ï Ó v$sovovmx (@7ACByvv$
(@7ADB¡
Ö×
Ums."~s.}mt{Zsavo}mt{7svoav
|.»~s|#x#$}s =|.|U".x#|UËX£Cvo3t{},Æ#~s|#x#G$vm3
£C|.x#vmx2x#£ss}|.(|aÆz.|.x"|qzUvo |q¡Ô#||.av$s}syté6|}»£C|.sGx#3ts|.ytot{}{}"x#|.sv
£t =|.|.(s£Cvo3Uvosvmt|.,q%|Usv|Us{}x(v2~s.$$v.¡
p#n FE uv0|U£voz.vt t}syqt"|.ssvmUt}z.vXvm.vm% qv Rsv£C|.sGx#y~s|#ovmx#svm
xsvm$£Cvmx}P}v>|U4x#|Rs|.]t{vm0v"~s|.£.£s{} |.
»vmz.vmUq}z.|U{zUvy¤ovo|c|.]|.sv6v>.|U
G}scÏ Usa (@7ADB ;Ù Ó ¡÷»s3»£Gv>otGv£H G3vmytéRÙ
sv0osvmU%tv
%G6q
sv|#oosvoG$v|t
|.svvmU}|. {}vm.x,|"svoXqzUvtv.ssv~s|.~CvoG y
s$}|.2,|.s{x£Gv¤mvo|
.xsvoG$vs33}{{s|t%.~s~Cvo¡
I J4¯"² %®A®A¯® 0¬ LK ³
Ö×.vmsvot{ICsvvozU|.{}#}|.Rv>¥Xq|U%
|U~|U£t£s}{} cx#vm}vm|.
$|UUs|U}vaâR.éU|qz.G|U
."}#sv{}t$v%
|.-.yssv# vo-|t
¢ÑÒ 3s}yéX|q3".=svsvma}mt{yU vov>¥Xq|U
}(sv0m.v|.
v|#U }svmo.{7ésvo|#x#vm{Ø ßqÜI¡AÖ×(s3vm|U(,vx#vo}z.vv>$s}z.vXvo.t{
|Uy,
|Usv0|.{}#}|.(|t
svmvvm¥Xt}|.».x6{}|#o.{Z÷Æ{|U»v$#~tG}|.|t
5sv>v}XvoU.{}m¡A÷»s».}z.vm
G%£.},
|U%t.{¤ms]v{|#o.{7vo|U,}$vmx(£ysvt#¦{}vmt~sav$s|#xso¡
#v$sv3{¦Gx#v$=
M Ï M NMO' Ó 3svo:v M Ù
x#vms|tv%v>¥Xsvoov3|t
7vm.$}|.vozUvoX
QP Gt~s~Cvos}s(t|Ux#vmmZtGxR{}v$= R M5R &svs£Cvo|t
vmU|URvozUvoXm¡ #v$0 S5Ï M Ó x#vo|tv
sv~s|.£.£s}{ yGq3v0v>¥Uvoov|t
5vmU|U,t%|#o$vmx6vXvmzq.{Ï Ü53~svmo}vo{}T MZ
o|.xs|Usvmx|.£Cvo}s"q%qv Rq»}av ¡÷»svo23
|.{}{|q%,q
SÏÏ Ó Ó
3vovwÏ Ó .xs
|U|vmU}|.G.~s~Cvos}söÏôvcvoa~# 4vm¥XsvoG$v Ó tGx Ï Ó
Ï Ó ¡Ö×
Uxsx#}|.U S5ÏÏ M VM ' Ó Ó yÆ"£Gv3vm2v>$s}z.vm{a}voy3|t"
S5ÏÏ M VM ' Ó Ó £X
S5ÏÏ M
VM' Ó Ó W S5ÏÏ M
VM' Ó NX Ó
ÏÓ
,
d
f
g
e
g
e
e
,
d
\
Z
h
j
i
X
Y P[Z Ï D\ ^]_]`] aZcb \ Ó
Ö¦
|.{}{}|q%%£2xs|URGPq
|Uv>. wtxkMZlS5ÏM Ó }t.t{}X
sG}|.|t
c
|U.{{ ,
.x(tm S5Ï M Ó aÏ 5n n Ó U äs¡
&
1
&
;0;
! ;;
"
Y
cedgf
ih
k
5;
:
1
7:
)3+
TZ <=<< =<<=< >8
1
b;
\
? < < G I?JKLMONQPSR ;
$ E !
Z =<<=< gZ =<<< Z =<<< ;
R
gZ =<<=< E
;
Z
I
D ;
.
* :-%
o
;
W X`Z Y
U
Z
\ P MOR I
P
I
? < 9
D HG I*J K MON
+
\
+
+
<
1
1
,
uwva3{}{o|.a~s#v SÏ M Ó
|.vmys~w| R M5R -ÚwÏI¡ vU¡voy|t
,s~w| aÏ ÓÓ
|U.vovot{
. x P¡Aà savmo.{voav%G GÆz.v%0÷Æ{|Uv$#~.}|.a} a
|.sv%t|Uy~s|.£.£s{}}vm=q
ytsv>,t%|t
svsv~s|#$v>3x#v>o}£Cvmxt£C|qz.v
|.»vmy3~(| aÏ Ó G
|.»G¦|.x#vo».m$s.o.¡
}sRÏ Ó |.G$v.#,v|.£#t}
,d h ji X EÙ
h Ï Ó
S5ÏÏ Ó Ó W
à~s~s{}sÏ Ó |U$v.Ut}#,v|.£#t}
,d \ ,d ,d \ ,d hNi X
S5ÏÏ Ó Ó W S5ÏÏ Ó VX Ó Ï
\Ó
3vov
Ù ¡
uwvyÆ"÷5Æ{}|.vo#~tx"svv>¥UGq}|.G
|Uf S5ÏÏ Ó Ó .x SÏÏ Ó Ó |]|U£#.(sv
|U{{}|q3
vms{m¡
UÏ Ó \ Ï Ó \ Ï Ó aÏ Ó
S5ÏÏ Ó Ó UÏ Ó ÚÙ
\
ÏÓ
Ù
S5ÏÏ Ó Ó Ú \ Ï Ó Ï
\ Ó aÏ Ó
3vov
Ù ¡
3µ´ 0½3¸Z·AÅ · %޼ÍPÍXǼÉÇÍ ½¼LÂsÌ%ÇæÇ ½Å¾3ÂsÉ ½¿Ã½ 6Â#ÌÇæÊ½ÊÇ¿ÂsÍ
uwvo|.}xsvoAsv%a|.avoXA|t
Zv%G$voavoX Ï Ó Ï Ó ¡÷»sv$|.Gx#|Ut{sa|.avmU 6Ï Ï
Ó `Ï Ó R Ï Ó Ó 3.}z.vm(£
'
Ó `Ï Ó R Ï Ó Ó ' "Ï Ï
SÏ M Ó ÏNã Ó
P
P
n P n '
âR|.vUvosvm.{{}.Xsv0$|Ux#}|..{ mca|.avoX "ÏÏ Ï Ó Ï ÓÓ R Ï Ó Ó 3.}z.vm(£
'
Ó Ï ÓÓ R Ï Ó Ó ' "ÏÏ Ï
S5Ï M Ó OP ÏÙmä Ó
P P '
? *;
.
5.
/
8
.
,
R
;
G I?J K MONQP
E
+
G I?J K MON
\YP MOR I
P
;
<=<< ]8
<
(Z > iZ ;
/
/
R
;
(Z
E
<
;
!
(Z ;
/
/ ;
H/
+
PSR G J K MON
\
+
\
P
iZ !;kD9
< /
:$.
X[Z
'
;
D $.
/
/
\
=<<< >8
%
< W
/
/
+
\
=<<< >8
> Z +
G I*J K M N
kD ;
! /
!
S/
! C/
%
/
H/
;
;
S/
? X`Z
D
!
<
X[Z
X
/
H/
;
S/
! /
!
/
!
;
;
X[Z
nn
* X
D
<
X[Z
uwvGÆz.vUx#|.~#vmxLsvw}~{vR|tt}|.Ðq(
|.Pz.v>|U x#vms|tvm"svmI
|.{xövo|.
~|#x#$m»3sö}ywvo|.y|.
tsé } x#}avo}|.m¡ Ö×ö~t${}.]svÚqGx`a|UvmX"aÆ£Gv
voXtx#vmx.t Y Ãat7¡=à%|t
Csv.£G|qzUv»|UavoXAvo#}%Ï }sv Ó |.s{}
Zsv$|.vm~G|Ux#}s
}#vvov>6ÏÙmä Ó $|.zUvo.vmm¡RÔ}$v6
|.].v>x L.;x MZ SÏ M Ó ].t{}Xa
|.t{}{ 7.xP
sv6}#v(vov>$|Uz.vo.v>ss
|.a{
|. Ø ä #Ï Ó Ü¦=
|.tv>x =svo4sv$|.a~C|.svmX0|.
Ó Ï ÓÓ R Ï Ó Ó 3}{{7£Cvt.{X
s|U»|t
"
|U Ø ä #Ï Ó Ü7
|.3|Uav #Ï Ó öäs¡
6ÏÏ `Ï
àsa}s0q,sva|.avoXvomXv3{}{7$|.a~ssv%svoË~"|vmyo{Gx# aÏ Ó ¡©s|.s,v
vovmx|Us{"|"sËvmy33 & Ù.x & åÚ]}ÏNã Ó tGxwÏÙmä Ó ¡÷»3,vUv$
Ó Ï Ó R Ï Ó Ó
"Ï Ï
DSÏÏ Ó Ó
Ï \ Ó SÏÏ Ó Ó aÏ Ó
\ .x
Ó Ï ÓÓ R Ï Ó Ó
6ÏÏ `Ï
S5ÏÏ Ó Ó
Ï \ Ó SÏÏ Ó Ó aÏ Ó
\
1
,3
w.
5.
.
1
S/
&
/
H/
;
? +
1
1
0
!
;
S/
!
/
!
/
!
;
/
!
/
!
;
;
/
;
W
D ;
W
W
YX[Z
S/
!
;.
D < YX[Z
D X[Z W
W
W
X[Z D iZ X`Z
D X`Z
D9
< /
(Z /
< .
.
!
!
<
Ô#s£#swÏ Ó t x}a~s{}
}syv|U£#.
Ó Ï Ó R Ï Ó Ó
"Ï Ï
UÏ Ó
ÏÙ.Ù Ó
Ù
Ú \ D\ Ï Ó D\ Ï Ó a\ Ï Ó aÏ Ó
|U»svav>tctx
Ó Ï ÓÓ R Ï Ó Ó
"ÏÏ Ï
UÏ Ó
Ù
Ú \ \ a\ Ï Ó Ï Ó
ÏÙ>Ú Ó
Ù
Ó
Ó
Ï
Ï
\
\
\
Ú \ Ù
Ú \ Ï a\ Ó D\ Ï Ó Ï a\ Ó
aÏ Ó
|U»svUvosvm.{ >2a|.avoXm¡
÷»vo|.xs|Ut{o|qzÆ.tG$vs~| aÏ Ó yÆ"£Cv0$|.a~ssvmx2.{}|]G}sÏ Ó ¡ }sv
.3q
Î |qzZÏ Ï Ó R Ï Ó Ó Î |qzCÏ Ï Ó Ï Ó R Ï Ó Ó
Ó Ï ÓÓ R Ï Ó Ó Ï "Ï Ï Ó Ï Ó R Ï Ó ÓÓ
"ÏÏ Ï
,vyÆ"|.£#t}
Î |qzZÏ Ï Ó R Ï Ó Ó
Ï Ó
Ù
Ú \ \ Ï Ó \Ï Ó \Ï Ó
ÏÙ Ó
Ù
Ú \ a\ a\ Ï Ó Ï a\ Ó Ï Ó
Ù
Ú \ \ Ï Ó \ Ï Ó \ Ï Ó aÏ Ó
3vov,vÆzUvs|.|q3"v0x#v$t}{}3|.
.{Uvo£ss¡
3µ ÌÇ;Ç 3ÈÅɸ7É Â·A¾üÊÇ7ÂsÌ%½3À
©|.svv$#~s{}$t"av$s|#x7Xsv >a|.avoX|.
v}$voavoX3$|Ux#}|.sv>xy|. Ï Ó }.}z.vm
£
Ï
Ï Ó
Ï ÓÓ R Ï Ó Ï Ï Ó Ó ÏÙoÛ Ó
©|.6o|.z.vms}voovcvRsayt¤mvRvm{{éX|q3`
U(.£G|U#"svRa|.avoX"|t
=|U}|U`tGx#|.
zq.t£s{}v32v>t ¡
!'
S/
!
/
!
/
!
;
;
W
D YX[Z
W
/
S/
! /
H/
W
D X[Z ;
D !
!
D !
!;
D kD :$.
X[Z
;
W
D YX`Z
W
/
X[Z X[Z W
/
S/
;
S/
!
S/
! ! H/
H/
;
/
;
/
W
D ;
/
W
;
'
,
!;kD C/
!
!
X[Z
/
;
X[Z D X[Z
.
W
$.
X[Z
W
/
W
D /
S/
/
! H/
/
;
!
/
!
;
/ <
D / YX`Z
W
/
X[Z X[Z /
W
W
!;
D D D !
!
D D D !
!
D :$.
X[Z
X[Z !
X[Z
W
/
W
W
X[Z
MSP ^/
S/
MSP /
MSP !
/
MSP ;
-;
W
D !
<
YX[Z
;
p Ôs~s~C|Uv }y =|U}|Utxs|. qz tt£s{}v(3Ðav>tötxLzqt}.$v ¡å÷»svm`
|U"t
$
}Xvm.vo LÚ
6Ï Ó
aÏ Ó ä
ÏÙ>Þ Ó
xdgf
f
;
/
$.
%
<
÷»vAvm;x#vAvv$#~Cvmq|U|.~Cvoq|U7|.svUUGtx}x#v|t
Ï ÙmÛ Ó yÆ£Gvvo#~txsvmx.sy
|.
vmym#vm.(|t
3s}3t>I
|.{x(voG|U,~|#x#$m¡=Ö¦33£Gv|tv>xyq3svvoG|U,~|#x#$
xs||t$|Ua#v}.vmsvot{I¡©|.}tG$v 3}yÆR£Cv}Xvm~sv$vmxw.svyyq 5}
|tv>¥UGt{| Æ3sPaÆ£Gv(Xvo~svov>xwUv6yq ¡cÔ#ovyv 6.vy}x#vm~Gvmx#voX
=|U}|.m7|t
sv>v vmym7s|Xva3szU|.{}z.v0 ,|2|.a|.vyx#§ZvovoXzqt{}svm|.
4Ïô ,||U|Uv
xs§ZvovoXv>.|URtsvo{ Ó 3}{{Æz.v]v$#~Cvmq|U%qtv aÏ Ó |.s}.svmm¡©{}v$$|.Gx#vo
svvmy»q3}z.|.{}z.v|.{(|.svvm.$}|.tsvo{I¡÷»svovtv |t
5sv>v0.x"svotv|t
sv
|.
Ï UÏ Ó Ó
Ù
÷té}sav$#~Cvmq|U3txv$t}s]|Us{6vmy»s~| aÏ Ó Cv|.£st}
6Ï
Ï UÏ Ó ÓÓ
UÏ Ó aÏ Ó
3vov,vÆzUvvmx #voay #¡A÷»XG3vo|.o{xsvq
Ï
Ï Ó
Ï ÓÓ R Ï Ó Ï Ó aÏ Ó
ÏÙmß Ó
p#n Ò ¥Xq|UcÏ Ùmß Ó {}{|.{xs
Zsv =|U}|.X£Cvotv3£G|Usx#v>xy.m$|.x#}ssv~s|#ovmx#svm
}`Ôv>|U`Ú#¡ =£Cvmo.v"£ G3vmytéwß4Ï ~s|qzXx#v>x ].PXvm.vm]qv Ó s£C|.x#}sR|.{Pq§Zvm$
vmz.vmU»32~s|U£t£{} aÏ Ó ¡
Î |Ua~tÏÙmß Ó 3öÏÙ>Ú Ó txt{|o|.}xsvos G3vmyté ~s|qzx#vmsvy~s||t
|.
svy
|U{{}|q3
svo|Uvm2¡
l ÷»sv(v$#~s{}}o.4av$s|#x4],vm.é{
Gn p 1r 5k kml r ! r ll>p
o|. voXy|PG¦|.x#vo>}öv2
|.{}{|q3}s4vov.¡ Î |.}xsvo".}z.vmöst{ qv
|."sv
vo#~s{$3.¡÷»svm(
|U3vmU åÙvovv$#} LäatGx Lä2Ï xsvo~Cvox#}sy|U Ó G6q
6ÏÏ Ï Ó
Ï ÓÓ R Ï Ó Ó "ÏÏ Ï Ó Ï ÓÓ R Ï Ó Ó Ø ä Ü ÏÙ Ó
vov0sv]|.Ã.2s.£s{v]s|.Á.3svxs$v>xÚÆ¦s|.Ã
|.svvoG|Um¡÷»s}vms{s|.{xs
voXtx#{}vm|.
3svosvm3v =|U}|.6s]£Gvm3.v£C|.sGx#vmx|.»s|.m¡
Ô#ovsv]o|.a~C|.svmU|t
Av]a|.avmUvm|.tvvo#~Gv>t}|.|t
o.{}.zqt{}sv>xR~C|.{}X|.a}.{}
`Ï Ó |U Ï Ó o|.x#}|.vmx|. Ï Ó
Ï Ó 5=÷»vo|.voáãc{}vm.x|2sv"
|U{{}|q3
o|.|.{}{}.U¡
Gn ! ! p#n ©s|.]t]s{}zÆ.qvy~G|U{s|Ua}.{A
s$}|.
,%.x}.{qv
svovv$# Läa.x Läy(Gq
7Ï Ï ÓÓ ZÏ Ï ÓÓ R Ï Ó `Ï Ó Ø ä >Ü ÏÙ Ó
8
^D ZD
D
/
BD ZD
/
D Z
D
/
^8
.
/
( D Z
! /
8
D ! ;
<=<< ]8
.
D ! !
MSP !
aD ;
<
! /
.
"
MSP ! C/
/
H/
MSP ;
;
W
D ! /
.
<
YX[Z
ih
cedgf
.
/
'
d t
dgf
h
d
tu Qs
d u
t
q s
d
s
p
f
t
d
1
S/
MSP MSP !
/
MSP /
;
S/
! )3+
/
/
!
;
/ 7
1
0
<
(
/
)
t (t
MSP !
/
/
!
;
MSP /
;
j
A ,3
%
,
1
)3+
MSP S/
C/
H/
MSP !
;
/
;
/ &
1
<
'
|qå,v3{}{7xvo~v>|U
|.»v0$|v$ê"$}voX»|t
sv aÏ Ó vm|.,vmy,
|U»svavm..x6sv
o|qzqt}.$vyqZ¡A©|.»vv>tvUv$
Ï Ó
Ï Ó R Ï Ó Ï Ï Ó Ó
_
/
.
MSP !
/
MSP H/
MSP !
;
;
/
W
YX[Z
D ! 3}2.}z.v>
Ï Ó
ÏÓR ÏÓ UÏ Ó
ÏÙmã Ó
Ò ¥Xq|UÏ Ù>ã Ó txwÏ ÙUÙ Ó |..vosvm»~s|qzx#vsv{}|#o.{7vo|U}svavm.
|.»vv$#~s{}}o3tvos|#x7¡
MSP ! /
MSP !
/
MSP !
/
;
;
W
D9 !
<
YX[Z
7>?,2Q".1..k<C,.l8^2^<D. 1 98", < 2
> , #
Ó Ï
Ï
MSP /
%
/
!
ÓR
H/
MSP
`Ï Ó
;w/
Ù
;
Ï Ó \ Ï Ó \ Ï Ó aÏ Ó ÏIÚtä Ó
Ô#ovsv =|U}|."s]£Gvm Ï Ï Ó Ó tvxsvo~Cvox#vmXm,v.vo
Î |qzCÏ Ï Ó R Ï Ó Ó
ÏÓ
ÏIÚ#Ù Ó
3vovsvvo|. mt]£Gv,vm~svmvoXv>x£sv,yq$vm ¡5÷»vv>¥UGq}|.GÏIÚ#Ù Ó tGx6Ï Ù Ó |.Uv$svo
~|qzx#v»3sv{}|#ot{7vm|.»}sv0o|qzÆ.tG$v%
|U3v$#~s{}}o3t¡
Ú
;
W
X[Z \
D X[Z
;
D :.
!
!
<
MSP ! C/
a\
! W
/
MSP !
H/
;
;
W
D / YX[Z
D /
D D 7>?,2Q".1..k<C,.l8^2^<D. 1 >?"5.1,>?9,< 02
> ,:#
Î |qzCÏ Ï Ó R Ï Ó Ó 4Î |qzCÏ Ï Ó R Ï Ó Ó
Ù
Ú \ \ Ï Ó \ Ï Ó \ Ï Ó Ù
Ú \ a\ D\ Ï Ó Ï a\ Ó Ï Ó Ù
Ú \ \ Ï Ó \ Ï Ó \ Ï Ó M SP ! C/
M SP !
H/
;
W
/
;
W
X[Z W
D /
X[Z W
X[Z /
!
;
;
D !
D D "kD D9
D9
"kD9
ÏIÚ.Ú Ó
X[Z
W
/
X[Z
W
/
C/
aÏ Ó
:$.
X[Z
p#n |tvt6sv aÏ Ó {}|mt{vo|Uyvmyx#vozUvmxL
|U"vavm.åtxå$|qzqt}.$vc|.{x
voXtx#{}vm|t
»3sv$svosv =|U}|.wX£Cvo0tvasmqv>xPq (@7ACB(|U0s|.mA}ovas0|Us{q§Zvm$
vmz.vmU3~s|.£.£s{} aÏ Ó ¡ %|q,voz.vmmsv>v
|.s{tvx#|6|t|.{xc
|UsvvmU|UÆ,Æ
|. tva3q0{}vm.|.sva¤ovm|2$|Ua~G|UsvoXm¡a÷»s£Gv>otGv]svy~|U£t£s}{}v>|.
,|2v>.|U
vmz.vmUcÏ3sL} aÏ ÓÓ 3{}{%£Cvct{vovmx`£Pvc£G|Usx#}s~s|ovmx#v|t
Ôvm$}|. Ú#¡ 3}öÆz.|U}xs
voUt}z.vqvmm¡
3µ ÌÇæÉÊ1ÈÅɸ7É×ÂÂ#·A¾üÊÇ7ÂsÌ%½3À
Ý }z.vm"q Ï Ó
|U,vo~}¤ov Läsv}~{$»t(av$|x(}XzU|.{}z.v>Axss Ï Ó
3}Rsv]ss¥Uv]|.{}#}|.R|.
]Ï Ó ¡u Ï Ó 5.xR$|Ua~tÏ Ó 3`ÏIÚ Ó s|q%
q ZaÆ6£Gv3vm2U,svs}¥Xsv0|.{}#|U(|.
UÏ Ó UÏ Ó
ÏIÚ Ó
3vov
Ï Ó
ih&jj
cedgf
_
.
!0/
-
.
.
!
(
+
! /
/
4
M S P ;
/
M SP 1
/
/
4
;
/
4
M S P &
/
;
/
/
;
W
D S/
YX[Z
;
W
D YX[Z
MSP < <
»÷ .}z.vmRtR}st{= qv
vo.2s}séc|t
=sv]}a~s{}}otvos|#x.%}z.|U{z}sy sv
o|.a~s#q|U|.
t2Xvov>x#qv0tv .m$|Ux#}s]|"vo#~s{$%t.xvoR|.{}zX}s
|. 7}2sv
}a~s{}}ov>¥Xq|UwÏIÚ Ó ¡÷»XG 3yx#v$vo}s }
sG}|.2|.
¡
uwvvo3vaÏIÚ Ó
|U%$|UXzUvos}voG$v.
Ó åä
yÏ
ÏIÚqÛ Ó
Ó Y Y Y
3vovsv ×a||t6
|U yÏ
¨».}z.vm(£
Ó
yÏ
UÏ Ó UÏ Ó
ÏIÚ.Þ Ó
Ö×ö|Ux#vm|vosvt »}a,vo{}{%x#vosvmx`
|U L#ê"$}voX{}yt{}{N,v2vsvc}a~s{}}oy
sG}|.
svo|Uvm2¡Auvs|.vGq
yÏ
ä Ó åä
÷»v UU$|.£}.
}3UzUvo(£X
Ï Ó
ÏIÚtß Ó
3vov 0=sv Y }x#vmX yq7¡÷»t äsv X.$|U£st}=sv%x#voX ]at7Xtxasvm$v
s{}{CtéC¡=÷»svmvo
|.v.X£Xsv}a~s{}}o»
s$}|.6svm|.vosvmvv$# `ä#0vo.}|. #tGx
×||.(
s|U Y Ø ä >Ü
(Gq 3.}z.vm(£
yÏ Ó =Ï Ó Y Ø ä >Ü
ÏIÚ Ó
|tv]q yÏ ä Ó ¡Ï ÷»sv
s$}|. .{}|(x#vm~Gvmxs|U 5£s#0ov],vÆz.vs#vmxsv v
xs|6s|.|q;svax#vo~Cvoxsvoov|.cvo#~s{${} Ó ¡à o.vo
s{{||.é2qsv]~s||.
|t
=sv]a~s{}$
sG}|.
svo|UvmÃÏNvmvØÙ Ü
|U} tov Ó vo{}{}Aq,}$v»sv X.o|.£st}Gx#vo~CvoxsvoX|.
Uv%yÆs||Uv
|y£Cv0t£st{}"{t.v£s#£C|.x#vmx¡ %|q,vozUvo>sv0}¤ov|t
]aÆ(£Gv0yt{}{vm3v{}.Uvo Uv$o¡
Ô#ov6£sv(£G|Usx#}s~|#$v>x#svy|t
=|U}|UtGx#|.ás£Cvo .é.v>0£C|.sxsvmxPzqt{}sv>o=,v6o.
|X|Xv |"£Cv]y£C|.sGx#vmxcvoU|U2to|.X.t{}{5~C|U}£s{}v0zqt{}svm|t
¡©|.%ss|U}ov.Gvtv
}{}{.v>x6|.
vv$#}vm$v|.
Läa(tÏNÚ Ó s|.{xsm¡
p#n uÐs}{}vsvsvm|.v$}mt{o|.}xsvoq}|.avoX}|.vmxct£C|qz.v}x#otvm%t%v0{}.Uvo (@7ACB
mGsvayt{}{}vo ayÆ2£Cv.Z~sU}ov,vÆzUv0svozUvovoo|.sXvmv>x2~s|.£s{}voy%}RGx#}s((|U{#|Uc|
sv}~{$3vm¥Xq|U6}ssv %vm»|U(vmt}|.#3svm(G}s~sU}mt{7 vo~}¤ovmm¡=Ö¦33£Gvs|.v>x
q0}a{tsvo|Uvoot{Ao|.ovoRv$# }svyt~~s{ot}|.|t
svaa~s{}}o Ò s{}vovos|#x|RÔ ÑÒ
xs}z.vm(£ Ý .t3svs|.v.¡
uwv"3}{{,$|U~#vasv"zqt{}svm0|t
tx £wx#§ZvovoX}t}s`ÏIÚqÛ Ó ¡ Ñ §ZvovoX}t}s`ÏIÚqÛ Ó 3
vm~Cvm3| 7,v|U£#.
åä
3}2s~C|.2]svv$#~svm|UÏNÚUÞ Ó
|. 1vm{}x
Ï Ó .Ï Ó UÏ Ó åä
ÏIÚ Ó
1
,3+
/
/
/
`/
/
C/
C/ / < /
< ;&/
/
^/
0
,3
W
,3
,
S/
D %
,3
<
YX[Z
"
C/
/
;
/
2.
;
A ,`3
S/
< <
W
;
<
D .
S/
YX[Z
^;
A
;
/
C/ _
;/
, 3
7%
S/
C/
/
1
0
,`3
<
/
+(
/
cedgf
z
/
ih&j v
_
R
R
/
W
D YX[Z
Ô#s£#s
-^;
C/
W
;
0
D C/
äPÏNÚ Ó .x(.{}|}sÏIÚ Ó .x(sv
U»GqyÏ ä Ó
Ï åä Ó
Ï Ó ÏÓ
'
;
;
S/
W
;
<
'
YX[Z
D S/
YX[Z
F<
;&/
}vo{xs
ÏIÚtã Ó
Ñ §CvmvmU}t}sÏIÚ Ó 32vm~Gv>3| 7Gv|.£st}
'
Ðä
|tsaq åäss.x6t%3svo Ðä äa.x v|.£st}
Ï åä Ó \ \ Ï Ó Ï Ó Ï Ó D\ 3vov,vÆz.vv>xysv
.»q q ÐätGxÏIÚtã Ó ¡ÔG$v |.}U{ /
/
_
/
;
R
/
/
/
;
/
;
/
/
W
HX`Z S/
X[Z
;
a<
!
/
;
D /
;
W
;
/
/
D S/
Ï äÓ
¦a|X|.(
.x 7s,v|U£#.2}sy÷5Æ{}|.
|.{}txÏIÚtã Ó .xÏ ä Ó
UÏ Ó UÏ Ó Ú \
\ \ Ï Ó Ï Ó Ï Ó aÏ Ó 0Ï Ù Ó
÷5|(s|qEsvo|. voo|.
Asva}a~s{$tav$|xv]svov>xovot}R{}voay.3stv]tv>x
.x~s|qz.vo(sv0à%~s~CvoGx#2à0¡
÷»v2
|.{}{|q3}sP{}voay4.vmt"
|.(#ê"ovmU{Ly.{{vm~¤mvmasvR|.sxsvmxöz.vm}|.L|t
sv
}a~s{}}o%t2$|Uo}xsvm»32v$#~s{}}o3t¡
p àsa}sasv]£G|Usx#}s"~|#$v>x#svm»|.
Ô#vm|UÚ#¡ #
|Ut(.}z.vo2}st{5tv
$
svovwv$#} ä` q
Ï Ó
Ï Ó 3;~|U£t£s}{} EÙ.$|Ux#}|.sv>x |U
ÏÓ
Ï Ó #
|U%t{}{ Ø ä >ÜI¡
n Ö¦a
|.{}{|q%
|. ÏNÞ Ó .x #voayPÚ ty
|. üäyt{}{3vo|.sU
Ï3
~|U£t£s}{} RÙ Ó ¡
/
;&/
/
xdgf
/
>;
W
D C/
YX[Z
W
M >P 1
X[Z W
;
MSP :
/
'
j
tbu =s
dgf
d u
t
(tbp`u
d rs frq Cs
4
M YP ! %
S/
(t t
.
<
1
)3+
/
4
M >P
;
MSP
%
,
;&/
1
-
;
/ 7
3+
)
1
0
<
d t
dgf
j
tbu =s
d u
S/
4
M S P ! %
S/
Nr llmp àsa£C|.sxss]~s|ovmx#v>A|t
5Ôv>
,txy}st{7qv
svmvv$#
Ï Ó Ï Ó Ø ä >Ü Ï Ó
d ks frq C! s
t xp`u (tp[u
/
4
M S P !
s
ap
A ,3
;w/
%
,
!
1
;
/ 7
1
)3+
s© |U{{}|q%
|U #vmy"Ú 0.x Î |.|.{}{}.2Ùmä¡
âR|.vo|qz.vmmX,vmt2x#vo}z.vsv
|U]s{0
|U3sv{}|#o.{7vo|U|.
5sva~s{}$3t2av$s|#x7¡
(t t
ap
4
M >P & k Nkol 5r n
Gn
|UÚs¡ .
|U,.Xa]s{zq.qv~C|.{}X|.a}.{
|U
Lä.x öäaG6q
7Ï Ï ÓÓ 7Ï `Ï ÓÓ n
S/
©s|U{{}|q%
|U # vmy2Ù .x Î |.|.{}{}.2Ùmä¡
n
D llmp àsas£G|Usx#}s~s|#$vmxssv>A|t
Ôv>|U
,%tx}st{, qv
svov"v$#
Ï Ó Ï Ó Ø ä >Ü Ï Ú Ó
s
A , 3
C/
S/
X[Z
! Nr
Gn % k Nkol 5r n Ús¡
|U].Xs{}zqt}tvy~C|.{}s|.at{
|U Lä.x öäaG6q
Z Ï
Ï ÓÓ 7 Ï `Ï ÓÓ D 0
(t t
d t
4
/
;
/
MSP ;&/
7/
<=
rj
f
4
M >P /
b;
Qo
@
<
7>?,2:.1.1,. <C,.l8^25 <C,. 8 2
> T, # uvs|.vtsvvoË3(x#|Us£s{}vsayq|U"
Ï Ù Ó aÏ Ó ¡0÷»s
|.{}{|q%
|U #vmyÚ.Þ#¡ voovsv
|U{{}|q3}s6v>¥UGq}|.aÆ2£Cvav>xc|6vo{qv
{}|#o.{7vo|U,}2a~s{}$3t|]q%|.
vo#~s{$3.
Ï Ó
Ï Ó
UÏ Ï ÓÓ UÏ Ó aÏ Ó
Ï ÛÓ
|tv0Gq%s}vm¥Xt}|.RUsavm Ï Ó
Ï Ó ¡3Ö×R|Ux#vm3|($|.a~ssv0sv >Ra|.avoX|.
Ï Ó Z|.sv].3|6tvsv>¥Xq|U2|ysv~C|qvm "tGxtéUv0v$#~Cvm$q|U%|.
A£G|.}xsvmm¡3Ö¦
sv tv~C|.{}X|.a}.{}mssvvo#~Gv>t}|.c|U2sv]}.X%.xR}x#v3{}{}z.|.{}z.vté}s"v$#~Cvm$q|U%|.
zq.}|.»~C|q,vo|.
=|U}|U6txs|.¨zqtt£s{}vmv
|.s{tv
|.33sctvvm{{7és|q3¡
c³ o³ K 0¬2° ²3¯]
¬ %® ¬2² t¯]® K Á³ m³o¬ ® 2®A¯ ¬
=³ K
U±c¬2²,=³$¯¬
Ö×2svm|Ucv3}{}{}XzUvm}Utvv t£s}{} (~s|U~Gvmv>3|t
=sv0v$#~s{}$tx2}a~s{}}o%tcav$s|#xs
|Uvmy=3{}}svm.A~s|U~Gvm
|U.x~|qzUvqsvo$|UXzUvo.v3]G¦|.x#voAUo$U$.¡
uwv
|o|U6svmo.{vmU}|."# voy3svov .x tvt£st.t£#sv~|U~Gvm ]
s|U
UÏ Ó té.vsv
|.
Ï Ó EÙ
Ï ÞÓ
3vov tv3$|U tX=z.vm$|Um¡5à}a~G|UtX=
|. |t
7t£{} vm{vmzÆ.X
|U$|UXzUvo.vm$v}q
|.
,ät¦.£s{} 4Ø ÚqÜI¡y÷»sv
|.{}{}|q3s2x#vos}|.w}.vmsvot{}}¤mq|UR|t
ss|.}|.|c|#.#voy
q%%Ux#vm¥Xtv
|.%|Us»~ss~G|Xv|t
=vm.£s{}}s}ssv0o|.z.vmUvoov|t
At{}{7a|.avoXo¡
lE ä kol>p#j ! l Ñ vms|tv3£X
l
¨ v%x#}$v$vav3savoot{#.~s~s|Æ}yq|U|t
Z|#U }
~|#$v>m¡uwvyGt{}{=Æ2Gqsvasavoot{=av$s|#xäq×t£{v]s~w| 6a|.avoX
,
|."v>xRav
}Xvmzqt{Ø ä 3ܦsvmvv$# `äa.x ' `ä
|. & Ù Ù C&=G6q
'
"ÏÏ qÏ ÓÓ ' Ó "ÏÏ Ï ÓÓ ' Ó (' "ÏÏ .Ï ä ÓÓ Ó "ÏÏ ÏNä ÓÓ Ó %
03svm
|Ut{}m{ & ÁÙ =tx
v L}0.£.Uä 6
|. ÁÙ A5tGx
o|.v>~C|.Gxv>~Cvm$}z.vo{}|sv,savo}mt{|U{s}|.5|.£#t}svmx
|U t~t}5|.
Gt£st}st{
o|.xs|U qÏ ä Ó Ï ä Ó 3s}c.v.x#|U¨zqt}.£s{v>».sav>x"|yÆz.vsva|.avmUo¡
©|.%# voy»32{}svm.3~s|.~Cvov>»|t
5sv
|UáÏ Þ Ó #svv$#~s{}}o3t2av$s|#x(».}z.vm(£
Ï Ó
ÏÓ
UÏ Ï Ó Ó
Ï ßÓ
÷té}sav$#~Cvmq|U3$|Ux#}|.sv>x(|U Ï Ó s,v|U£#.
"Ï
Ï Ó R Ï ÓÓ
ÏÓ
ÏÓ
3}2yÆ"£Cv3voc.
"Ï
Ï Ó R Ï ÓÓ
Ï Ó Ï Ó
Ï Ó
3vovsv Y yq E».}z.vm(£
Ï Ó
.
(
A
4
M S P /
;
MSP /
W
MSP !
D C/
%
>.
!
!
<
YX[Z
_
4
M S P !
/
4
MSP !
;V/
;
M SP !<
/
1
`
=
!
`#
B
.
^8
!
7d
1
u`s QsCtu
j
`s Cs
=<<=< /
, 3
1
;
=<<=< >8
/
/Z
*
/
/Z ;
<
,3
0
/Z /
;
/
U
;
;
/
=<<< g ;
=<<< /Z
/
YX`Z
4 X[Z 4
/
4
62;
<=<< /
/
MSP ! ;
MSP !
/
W
D9 MSP /
<
YX[Z
C/
MSP ! e/
MSP /
MSP MSP !
;&/
W
D /
MSP !
YX[Z
C/
.
MSP ! /
MSP ;w/
MSP /
MSP !
.
;
W
D YX[Z
{
<
'
p#n uwvcvmytéP
|.asvcs#
.}{}}."v>.x#vmt"
tx tv2.x#|. zÆ.t£{v>svo
6ÏTR Ó }%sv$|.Gx#|Ut{5v$#~Cvmq|UR|t
o|.xs|Usvmx2|U 4G.xc6.x#|.Ãzqt}.£s{v3s}}
2x#vovma}s}]
s$}|.w|t
t.é.vmvyzÆ.{v "ÏTR Ó 3svm .é.v>svazqt{}sv ¡
÷»vo
|U{{}|q%3q "Ï "ÏR ÓÓ "Ï Ó ¡uwvÆzUv0vmx2svmva$|.G$vo~s%}Rsvat£C|qz.v0x#vm}zqq}|.Go¡
©|.%£UvmqavoX%|t
5s3s|.}|.cvmvyØÙÆÞ>Ü
|.3}.$vU¡
÷té}ssvvo#~Gv>t}|.|t
0Ï Ó sv|U£#.
"Ï
Ï ÓÓ Ï Ó "Ï Ï ÓÓ
Ï ãÓ
Ô#a}{}.{}",v|U£#.(v
|.{}{|q3}s
|.3}a~s{$3.
Ï Ó
ÏÓ
Ï Ó
Ï Ï Ó Ó
Ï Ó 0Ï ÛUä Ó
3}2{}vm.x,|
"Ï
Ï ÓÓ Ï Ó "Ï Ï ÓÓ
Ï ÛÙ Ó
3vov E»sv0.avyt6UzUvo£Ï Ó ¡
µ´ ÐÍ %ÊÈ%Â#½AÂsɸÐÍ.Â#· ÉÅÉ Â Ë½ yÂsÌ%Ç ÊÇ·A¿
©|.%a$|UtX%vo~G}¤ov 7
"Ï
Ï ÓÓ Ï Ó % "Ï Ï ÓÓ
Ï ÛXÚ Ó
.x
"Ï
Ï ÓÓ Ï Ó % 6Ï Ï ÓÓ
ÏÛ Ó
÷»sv]av>t|.
v]vo~{$t}s{q|Uvmz.|.{}z.v>%}(.vm|.av$0~s|.Uv>}|. svy.v.
sv6vo#~s{$ Ò s{}vo]s{q}|.P|.
»sv#voá|t
3v>¥UGq}|.G 3s}{v"sv(v>tP|.
»}a~s{}}o.
vmz.|U{zUvm 0sv(tav".0sv6a~s{}}o Ò s{}vo]}s{q|U¡c÷»sv"avm.PzÆ.{v"|t
»v"v$#~s{}}o].
}s{q|U(%.a~#|.ot{}{}" t£s{}v
RùÙ Ï Ó ,R ;Ù EÙ
Ï Û.Û Ó
3{}vsvav>tzÆ.{v|t
sv}~{$%.}s{q|U(%.a~#|.ot{}{}6 t£s{}v
Ù ?RÙ Ï Ó ,R æÙ
Ù
Ï ÛXÞ Ó
3vov Ï Ó },sv I2{}.Uvm,vmUvozqt{}sv|t
p#n |tv]Gq}a~s{}}o.R$|Ux#}|..{{}c t£s{}v}Rsv]av>tc
|U.£s{v#vmaÏI¡ v.¡
# voy%3|Uv yqc.t{}{vmUvozqt{}svmcsv{}v$
ô$|U~{vo.{
~{}.sv Ó ¡÷»so{v>t{$|.sy
.x#zqtXt.v»|qzUvo=v$#~s{}}ot
|U §2#voym..|.£voz.v>x0}RØÙmÛqÜI¡ %|q,vozUvoAx#vot}{}vmxa x#]|t
Csv
Ua~#|t]£GvmÆz|Us|.
Asvyo|qzÆ.tG$v.xRs}.vo|.x#voa|.avoXvm$v>tw|.x#vo|2.v>
sv0st£s}{} (|t
5}a~s{}}o%t(
|.%§w# voyØ ÜI¡
µ sÄqÍU· ÉÅÉ Â Ë½ yÂsÌ%Ç ÊÇ·A¿
p ,|.(svvo~{$tx(}~{$%.(avos|#xs%.vät¦.£s{v}(svavm.¡
$
n ÷»sv>v
|U{{}|q;
|UÃtGxstx~s|#ovmx#svm»és|q32}2Xvmo.{tGt{}»|t
¢ÑÒ o¡ Ò vmXt{}{
|U{{}|q%
|Uü£G|Usx#}s
|.v$#~s{}}ot.xcsva£G|Usx 3s
|.{xs»
|.%#ê"$}voX{6yt{}{ 7¡ %vmv á%t"s]£Gvm3.vmqvo,Gt ¡
ih&j
cedgf
/
/
-/
x/
/
/
;
/
9/
;
;
MSP ! C/
;
MSP S/
<
A
4
M S P 7*
/
;
/
4
M S P !
*
W
D 4
M S P 7*
/
W
YX[Z
D /
4
M S P YX[Z
4
M S P S/
;
W
D /
4
M S P !
YX[Z
Z
I
S/
4
M S P !
C/
MSP '
)
S/
C/
MSP 4
M S P ;
;
I
S/
4
M S P <
;=
w;
:=
4
+
(m
b4
6;
6`;
<=<< >.
=<<< Y.
6
ih&j
cedgf
4
_
)(
xdgf
f
)
rj
(t t
G R
$
(
#
*
G
R
µ
Ç ·=¹ ¸Z½¿ ǼsºÇ¿¸ZÇ
uwv"3}{{x#vozUvavm¥Xq|U
|.svyvozU|.{}#}|.w|t
,v mPa|.avoX "ÏÏ Ï ÓÓ Ó ¡6©s|.ÕÏ ß Ó
|U{{}|q%,Gq
"ÏÏ
Ï ÓÓ R Ï ÓÓ Ï Ï ÓÓ
P
P
Ó
Ó
Ï
Ï
Ï Ó aÏ Ó
Ó
P MÏ M 3vov,vÆzUvvmx #voay #¡=uvvo3vs3vm¥Xt}|.2.
"ÏÏ
Ï ÓÓ R Ï ÓÓ Ï Ï ÓÓ
P PÏ
Ó
Ó
Ï
Ï
Ï ÓÓ Ï ÛUß Ó
Ó
M}Ï M P
aÏ Ó
÷»v
|.{}{|q3}s #voaya»vo
s{I¡
p Ö¦
(svm4vo|.a~G|UsvoX|.
3sv.sé 2vmP |U P P Ï Ó tv"{}sv>t
$
o|.]£sGq}|.G»|t
sv0$|Ua~G|UsvoX»|.
5svtséÏ M ÐÙ Ó vm|U
¡
P P Ï Ó Ï3}cU o|.a~G|UsvoX Ó a{}vmt$|.
n Ò .2$|.a~C|.svmX|t
sv0voG|U
£t}|.2|t
A]s{zq.qv|Us|.at{» y3Rxsvo. vov M ÙU¡÷»svvo|. P $|U3|.
=.{{
sv{zqtqva|.|.a}.{}»} a|t
=x#voUvmv M Ù.¡
Î |U£s}s}s #vmyyÚtä3PÏÛXß Ó voGt£s{}vm»3|a3v
"ÏÏ
Ï ÓÓ R Ï ÓÓ
Ï Ó Ï Ï ÓÓ ' :' Ï Ï ÓÓ ' aÏ Ó
3vovsv0{}}svm.%|.~Cvoq|. :' y.~Raav$voG|U»|.
=tTé &=}U|"aav$vm|U%|t
=.sé ¡
÷té}sav$#~Cvmq|U»|t
=£G|.c}x#v>o#,v|.£#t}
"ÏÏ
Ï ÓÓ Ó Ï Ó 6ÏÏ Ï ÓÓ Ó ' ' 6ÏÏ Ï ÓÓ ' Ó aÏ Ó Ï Û Ó
Ô#a}{}.{},v6t{}{xsvozUvyvm¥Xq|U
|U0sv"vozU|.{}#}|.P|.
»sv ma|.avmU "ÏÏ Ï ÓÓ Ó ¡
©|U ÏÛXä Ó 3
|.{}{|q%q
Ï Ó
Ï Ó Ï Ó 6Ï Ï Ó Ó
voov3
|U{{}|q%,Gq
"ÏÏ
Ï ÓÓ R Ï ÓÓ Ï Ï ÓÓ
P P
Ï
Ó
Ó
Ó
Ï
Ï
Ï Ó aÏ Ó
P MÏ M Ó 3vovyvyÆzUv]Gv>x #voay ¡6÷Æ{|Uv$#~tGx#4Ï Ó tGxvm.tsU"vmym5,vavm3v
s3vm¥Xt}|.2.
6ÏÏ
Ï ÓÓ R Ï ÓÓ Ï Ï ÓÓ
ÏÛ Ó
P PÏ
Ó
Ó
Ó
Ó
Ó
Ï
Ï
Ï
a
Ï
MÏ M Ó P
+
MSP S/
MSP S/
MSP /
;
MSP S/
LX`Z
MSP S/
P M I
W
D MSP !
/
! /
.
YX[Z
"
MSP ! C/
H/
MSP !
;
MSP S/
W
/
$.
xdgf
&) ]D v
f
1
,3
) MI
(t t
)
P D
MSP /
MSP ;w/
P D MSP /
) M I
)
P D
P
.
)
L+[Z
) MI
)
MSP M I
<
S/
MSP !
C/
LX[Z YX`Z
) M I
L+`Z
P
MSP S/
Z
I
MSP S/
OX[Z
$.
/
! /
<
MSP ! C/
;
MSP !
S/
Z
I
S/
X[Z
MSP !
.
C/
4
M S P /
4
M S P !
;w/
W
I
Z
D 4
M S P /
4
M S P <
YX[Z
(
S/
4
M S P !
H/
4
M S P ;
4
M S P C/
LX`Z
4
M S P !
S/
MI
4
M S P H/
4
M S P ;
4
M S P C/
I
Z
D9
/
4
M S P ! /
.
]I
Z
W
X[Z YX[Z
W
YX`Z
S/
P S/
+
4
M S P !
MI
P D /
4
M S P $.
/
<
'
÷»},vm¥Xt}|."»}a{t|2ÏÛXß Ó s~"| aÏ Ó voyo¡ %vm$v.,£Cv$
|Uv$|.]£s}s#vmaaaÚtä3Ï Û Ó
vmt£{v>»»|a3v
6ÏÏ
Ï ÓÓ Ó "ÏÏ Ï ÓÓ Ó "ÏÏ Ï ÓÓ Ó
Ï ÛUã Ó
' Ó aÏ Ó
Ó
Ó
' "ÏÏ
Ï
'
3vovsv{}sv>t3|U~Gvmt|. ' tvx#vosv>xU»sv0oUv|t
v$#~s{}}o3t¡
p ,|.ysvvo#~s{$t6.xy}a~s{$»."av$|x.väq× t£s{}v%s~y|sv >(a|.avmU
|.
$
.{{Xvm.vm `äs¡
n ÷»s3{vmaaa,sv
|U Ù£
#vmy2Ù>ãs¡A÷»sv~s||t
|U{{}|q%»£6}x#$}|.¡ vv>¥Xq|U
Ï Û Ó |.ÏÛXã Ó tGx(.~s~s{}6 txtx6£C|.sGx#avms}¥Xsv>Ï vov #vmaa #¡ Ús¡ Ús¡ Ú|t
»ØÙ>߯Ü
|U3.$v Ó ¡
.
4
M S P ! S/
!
)(
;
4
M S P !
S/
'
Z
I
X[Z
4
M S P !
S/
4
M S P !
S/
4
M S P
$.
/
xdgf
v j
f
(t t
;
,
-
p#n ÷»svc£C|.x#}s~s|#ovmx#svm|.
Ôv>}|. Ús¡ x#|s|t6t§Cv>avRäq× t£s}{ P|t
a|.avoXo
}$v]£G|Usx#}s|.s{}cq§Zvmvmz.vmU%|.
aÏ Ó ¡0©s|.v$#~s{}$.tGxR|.sxsvmx2}~{$tC£Cvmmtv|.
}Xvm.vo%tv>%3}{{7|Us{(q§Zvm aÏ Ó voy3.oo|.x#}s0|UG%voyté6ßs¡A©|.»vaÏ ss|.sGx#vmx Ó }a~s{}}o
t7G$v0s|U#¦Xvm.vm qvm%|#m$ssv aÏ Ó vmÁyÆ(£Cva|#x#vmx¡÷»}.XvozUvoXmG£G|Usx#}s
.a|.sX|(a|#x#
s2svayq -.vm{{Usvavo|. ' }LÏ Û Ó .xLÏÛUã Ó £#svms|Uy
3}{}{ {}{£Cvsv0G$vvo6.vsv0xsavoG}|..{N¡
p Ër n r ! Nr lPl>p Î |U}x#vm6Pvm 3Ð{}vmty~|U~Gvm
Gn
|Uo¡`©s|.y.XUzUvo}s t{3qv `Ï Ó
{}v$sv2vo~{$]t`vo% s|#x`£Gvc.~s~s{}v>x
3`v}st{%tv Ï Ó ö.x43`}avc vo~
`%Z3vov
ÃtGx
Ãat X¡÷»svmP
|.]vm.~G|X}z.v"}Xvm.vo Asvmv(v$# a$|.G tX ¨äRtGx ¨ä4Ï 3s}
xsvo~Cvox2|U R.x Ó }x#vm~Gvmx#vmU|t
tGx 2G(q
"ÏÏ Ï ÓÓ Ó "ÏÏ Ï ÓÓ Ó
|.%.{{ Ï ä Ó
ihlvv
cedgf
.
.
! /
".
d t
v
dgf
h
tu
d
d u
d
t
d
e/
7/
MSP ! E
;
q Cs
d
s
E
p
;
1
)3+
; Z w;
<=<< /
YX[Z U
;
$
-
MSP E
S/
S/
! E
0
1
<
n ÷»svy~s||t
,
|.{}{|q%
|.á|#x#Gmq}|.|.
».xstxvms}¥Xsv>}wsavmo.{t.{#}q
s|qåt$|.G voo6tGx(ät¦.£s{} "a~s{}(o|.z.vmUvoov.¡=Ôvov0à~s~Gvmx# ¡
(t t
Î |.}xsvoy#vo 3L{}}svm.~|U~Gvm
! Nr llmp
Gn "% p -r n r
|Uo¡4©|.at.}z.vmPs t{3tv Ï Ó
{}v$v(}a~s{$a.4av$% |x`£Cv.~s~s{}v>x
% 3svov
3ösvR}st{tv Ï Ó åtxL3öavRvo~G
ütGx
yq X¡=àsav£G|Usx#}s~s|#ovmx#svm|t
Ô#vm|UÚs¡ tvvmx7¡A÷»svm"
|Uv>."~C|UzUv}XvoUvo
Gsvmvvo#}$|U tX öäy.x äcÏ3scx#vo~Cvox2|U Rtx Ó }x#vm~Gvmx#vmU|t
w.x cG
q
"Ï Ï Ó Ó 6Ï Ï Ó Ó
|U%t{}{ ÏNä Ó
d t
v
dgf
d
h
tu
/
d u
d
t es frq Cs
d
7/
4
M SP E
;
1
)3+
"QZ C/
(t t
p
n
s
;
;
E
4
M S P E
/
<<=< U
YX[Z r;
S/
! E
0
1
0
<
à%~s~CvoGx# ¡
7#
Ö×Rsv>}|.c,v]o|.x#vovozUvot{5v$sta~s{}vmmG.xc}{{}qv]z}asvo|U2tGxcsavo}mt{vo#~Gvm}avoX
q3sv{|#mt{7vo|.
|.s{tvtx6v{}svm.3$|.zUvo.voG$v£CvoGÆzX}|.,yÆy£Cv|.£voz.v>xa
|.%tsUv|.
vm~¤mv$ Rzqt{}svm3s}Rsv]v$#~Gv>vmxRs]£Gvm|.
v>.$}|.|m$ssy$|Ux#vm.£s{({}.Uvo3t
ÙU¡
Oo
3µ´ 3·AÊÈÅÇ1´XÍX½ÊǼÉ7·ÂsÉ ½¿¨¼sÇ·A¸CÂsÉ ½¿
Î |U}x#vm»sv|.avo¤>q|U6vm.$}|.
ÏIÞtä Ó
32~s|.~CvoG y
s$}|. ZÏ Ó ÏNä Ó }svav}Xvozqt{Ø ä 3ÜI¡
Q
"5. >?.1, >? ,<F8 ", , 5.l,>?,# ©s|Uy}(~s|.£s{}voÕvot xsvozUvcv$#~s{}}o
.t{}Xo.{|U{s}|. `Ï Ó
|Usv6v>t4.xwzÆ.tG$vy|t
»sv"v$sU0~s|#$vm"ÏN.oo|.x#}s|ÔsÔsà Ó .
,vo{}{=.3
|Usvvo#~s{$.xc}a~s{$tvos|#x4Ï ss|.sGx#vmx Ó 3o|..U vo~¤mv 7¡Ö¦yÆ£Gv
s|q3yq Ï Ó ,£s}s|.at{C.x#|.zqt}.£s{}v36~Gttav$vo5 S tGx
]Ø ãqܦ¡ %vm$v
svv$#~Cvm$vmxzqt{}sv0.x6zq.tov.vUzUvo£X
"Ï Ï ÓÓ
ÏIÞ#Ù Ó
.x
Ù
tÆÏ `Ï ÓÓ
ÏIÞ.Ú Ó
|tvqÏNÞsÙ Ó svtavUsv|.{}#|U"|t
svx#v$vo}s } ¢ÑÒ a|#x#vo{ ü3 Ï ä Ó
¡,÷»s%%x#v|asv0{}sv>t (|t
sv~s|U~Gvm 6
s|U}c.vmsvot{Zsvsvv>t2|t
v0a|xsvo{
xs|Xv>3s|.»vmz.|U{zUvsv0.av»Æ6Usv ¢ÑÒ |#x#vm{N¡
Ö¦3
|U{{}|q%
|U¨svv>{»|t
=Ô#vm|U2Û]q
"Ï
Ï ÓÓ ÏÙ Ó "Ï Ï ÓÓ
.x
.mÏ
Ï ÓÓ Ï Ù Ó .mÏ Ï Ó "Ï Ï ÓÓ
©|UËvmvv>$s}z.vvo{q}|.Gs}~,,v|.£#t} "Ï Ï Ó tx .mÏ Ï ÓÓ
"Ï
Ï ÓÓ Ï Ù Ó %
ÏIÞ Ó
.x
tÆÏ
Ï ÓÓ ÏÙ Ó % ÏÙ ÏÙ Ó % Ó
ÏIÞqÛ Ó
uwv0|U%svx#vot}{%|t
=svx#vm}zqq}|.¡uwvÆzUvUsavmx Ï ä Ó |y£Cvx#vovma}s}t¡3÷»
.>Ï Ó ;ä¡ %|.vqsvvmz.|.{}#|U|.
=svavm.c}3svtav0U»
|.3sv0vo~{$ Ò s{}vot~s~s{}}vmx|
sv ¢ÑÒ a|#x#vm{ á3 Ï ä Ó "Ï .Ut}(xssv|a{}sv>t 6|t
sv~s|.~CvoG y
s$}|. Ó ¡
Ö¦3
|U{{}|q%
|U¨svv>{»|t
=Ô#vm|U2Û]q
"Ï
Ï ÓÓ "Ï Ï Ù Ï Ó ÓÓ
.x
t>Ï
Ï ÓÓ .Ï>Ù Ï Ó Ï ÓÓ 6ÏÙ Ï Ó Ï ÓÓ
©|UËvmvv>$s}z.vvo{q}|.Gs}~,,v|.£#t} "Ï Ï ÓÓ tx tÆÏ Ï ÓÓ
"Ï
Ï ÓÓ Ï Ù Ó %
ÏIÞ.Þ Ó
.x
tÆÏ
Ï ÓÓ ÏÙ ÏÙ Ó % Ó
ÏIÞtß Ó
uwvÆzUvUsavmx Ï ä Ó |y£Cv0x#vovoa}t¡÷» .mÏ Ó ä¡
©|.s}v$sta~s{}vav"s|q1£G|.Psavo}mt{Av> yqvm0U,vo{}{.svo|Uvoot{o|.a~s#q|Uo¡6uv
|Uvsv0~Gv>$Gzqt{}svm ÏNä Ó Ùmä.ä#tx Ðä ÙU#32]av}Uvozqt{Ø ä oÙ>äqܦ¡
%
/
/
;
/
;
/
E
0
/
GFI
;
S/
/
;&/9E G I
G I
/9E
(
<
_
/
;
E G I
;
S/
^.
/
;
/
e/
;
E
MSP C/
MSP S/
;
;
/
MSP
MSP
S/
MSP !
;
Z
I
MSP S/
MSP
S/
<
A
/9E
/
MSP
7/
C/9E
MSP
;
;
MSP C/
C/
C/
C/
E <
;V/9E
x_
/
;
/
/
;&/9E
4
M S P !
S/
S/
4
M S P !
+
S/
e/
4
M S P
4
M S P
;
+
/
+
M
+
a<
<
/
4
M S P
A
E
ZH+
Z
R
P
/
EF<
S/9E
;
4
M S P !
S/
S/
;
;w/9E
/
/
;
4
M S P
4
M S P
C/
S/
+
4
M S P C/
;
MSP C/
;
;
0
©}{},v%v$
vmA|©}.svÙ.U3svov3vm}yqvmxavo|.=asv%avm.y|t
7v$#~s{}}ot.}~{$t"tGx
sva|Usx#v>xR}a~s{$.tv]s|q3¡0÷»v]{}vmto|.z.vmUvoov|t
vo#~s{$tx`Ïss|.x#vmx Ó }a~s{}}o
t}${}vm.%
|.Ásv]U.~sm¡Ö×s~s{|.mZ
|Usv]{t.v> zÆ.{v ¨Ù.7 t}s(t ÏNä Ó ¨ÙmäUäyv
vo#~Gv>Ù>ä.ä Y ä Ù Y Ù ÙmävmU}|.G=|0|#m$s|."Æz.vm..v»~Cvovm~¡A÷»sv{}}svm.$|Uz.vo.vm$v»£CvoÆz}|.s
t~s~.vmX0Rvm.}|.|t
Pzqt{}sv>0}43s4s~|`Ùmäcvo#~Gv>v>xs£Cvo|t
3vm.$}|.0|m$s>¡R÷»sv
xsvoz}t}|.,
|.¨sv{}vmt%osz.vtvxssv|asvv$§Zvm$3|.
sv0ta~s{}v}¤ov|.
Ù>ä t¡
÷»v3vo|U5|.
Gsv3|Usx#v>xa~s{}}oAtaA|Uo|.aavoX}s|.¡©|.A{t.votazqt{}svm=A}a{t
|6svass|.sGx#vmxa~s{}}ot¡÷»}}Xs}z.vm{v$#~Gv>vmx7G$v]
|.{}.Uv zÆ.{vmsvv$#~Cvm$vmx
s]£Gvm|t
,v>.|U.oo|.x#}s"|Ï ss|.sGx#vmx Ó }a~s{$.{t.v].x|Usx#}s26{t.vs£Cvo
~|#x#ovmsvm.{}U£{v3.s.vU¡ %|q,vozUvo
|.yt{}{ azqt{}svmmUU=~G|UXv>x|.#} #voayaÙ qv3|Usx#v>x
}a~s{}}o%tcs|.s{x~s|xs$vsv0.avv>s{3U3v$#~s{}$3t¡÷»s%£CvoÆz}|.s»3|.£voz.v>x6}c©Usv
ÙU¡
©}.svÚs|q%Asvvo|UA}ysvzqttov3
|.svv$#~s{}}o»txÏss|.x#vmx Ó }~{$t"av$s|#xs
Uo|.a~s#vmxR
|U ÏIÞ.Ú Ó AÏNÞtÛ Ó .x4ÏIÞtß Ó ¡ %|tv0qsva$zUvm.vt{}a|U{}sv>ts~R| ËÙ]3s
.U.w$|.vm~G|Uxs3|Ùmä"vmU|U%G}s|.ÆzUvotUv03svot}sq
Ùmä.ä¡©Gt{}{R©}.sv
s|q%,svvo|U}2zqt}.$v|t
a~s{}$%.6
|U%]{t.vm».s.v|t
(zq.{sv>o¡
a<
;
2/
;
;
<(
_
-
/
;
;
E
)
signed errors of mean for rounded (red) and unrounded (blue) imp tau and exp tau (green)
2
1.5
1
signed errors for mean
0.5
0
−0.5
−1
−1.5
−2
−2.5
0.1
0.2
0.3
0.4
0.5
0.6
stepsize
0.7
0.8
0.9
1
"!#%$&' ())*+,-/.10
!2*43 " )56!)"7%8 9 !2*435"' )35:7;35:#
*+3<8= ?> > 5@:2*4355A5B!DC
8 :3= E74! "7?355#
8= GF H/> 5@-IJ#J7J"7K:2*4355A5B!DC
!#J7L E7
NMO7J! 355#
8= PFRQ> 5<S0T*+355A@!D'
">?F.". 27>?,2"..1,. <D.18^25,# Ö×svosta~s{}v}5t{|3~C|U£s{}vA|$|U~Gtv=svUt{
{}|#o.{Cvm|.3(».~s~s|Æ}yq|Uy£Xasv aÏ Ó vo2#}$vv
|Uavm,mt6£Cvx#vozUvmx(t.{Xo.{{}.¡
÷»}»vovmo}v},qvo»ss}Xvovm}s(v0o.v|.
svv>t2}ovsv£GvmÆz|Us,}3a}{}.,|a3q
|Usv0vo~Cvm$%
|U v$#~s{}$tx2}a~s{}}o Ò s{}vo%{}|#o.{vo|U»
|.s{tv
|U3v ¢ÑÒ 4¡,Ö× vmUx
,vs|q ~s{|.,|.
7sv{}|mt{Cvo|U}"vzqttovtx",.~s~s|Æ#yq|Uy£]sv aÏ Ó vo¡A©}.svm
Û]txyÞs|q`sv>v%~{|.A
|U Ùmä.ä¡5©|U svmv%~s{}|tA,}t~s~.vmXAtsvv>$|Ux|.x#voA
|U]s{
]zÆ.{xPs~| Ùy
|.v$#~s{}$.tGxPs~P| ä Þ
|U]}a~s{}}o.¡Ö×P
U>=sv.t~sG
©}.svm,ÛytGxÞ]mt{}v~|U~G|U|Ut{G| Ï (v U×q# Ó v$.s]vtavGt~Cv.¡÷»,vvoU|U
|.
%zqt{}}x# |t
3sv6{}|#ot{,vo|.
|U]s{}Rs|.{xs]s~P| ä Þ
|U]}a~s{$tAvoXtx#{}vm|t
5¡÷»sv
vo#~Gv>v>xs£Cvo]|t
»v>.|U{}vm.~#0|qz.vm3{}{£Cv".}z.vm£X ä Ù ä Þ .Útäs¡©s|U0v$sta~s{}v.
sv0$voX3 qv Ù>ä.äUä0a|.{}vmos{v>o#,vaÆ6{v>t~6|qzUvo3ÞtäY vm.$}|.Y ,tGx(}{{7Gvv0.v{}|mt{
vm|.,
|U]s{}¡=Ö¦
ÙmVä qs,vot{}vmt~2|qzUvo%ÞtäUä.ä0vmU|U»|.2Æz.vm..v.¡5Ö×s%oUvsv0#vm¨3{}{
£Cv£CvoÆz}sasvm.{}6x#vovoa}o.{{}.s.xa~s{}}o3t23}{{7~s.$o.{{}"£Cva~s{}}o Ò s{}vo>¡
U
.
/
/
.
;
/
/
e;
;
l;
a<
/
*l;
<
*
:e;
17;
a<
a< ;
?m
Theoretical error in variance at final state X(T) vs stepsize tau
2
Explicit tau
Implicit tau
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
@TB - =$!5!#JAS$T'1 ))*4,=- .B0&!2*+3 SA 2*4
)"7;J5#
' )3557
355#J*+3I8= PRF Q> :I=S0T*43:5A<!DC
8 :3/ E7J! "7 355#
/8= PF > 5 I- J#
4#J7
"7 5 2*43:5A@!D'
3µ 3·AÊÈÅÇ Ç¸Z· %É¿º=ÄÆÀÉÊÇ¼É É¿%º ¼sÇ·A¸CÂsÉ ½¿ ÍXÇ7Â
÷»}vm.$}|.R# voü».Gx#v>x}Ø ãqÜtGx4ØÙmÛqܦ¡Ö¦o|.}|t
~Gv>$}vmsx#vmU|.}s
xs§ZvovoX3 ~Gv>3|t
=svoao.{7v>.|Um¡
\ ä
x.
Z
%
Z
%
%
%
/
uwv0s|Xvzqt{}svm,
|U»sv~Gttav$vo
Z
/
;
78
ÏIÞ Ó
/
Z Û
;
Z
<
Ù Ùmä EÙ>ä.ä.ä Ðä Ù
voovsv~|U~Gvm y
sG}|.G%tvUzUvo£
;Þ Ï Ù Ó ÙmäUä.ä Ðä Ù
£Gvmssvs£Cvo|t
~Cvm$}vm ¡uwv2s|Uvyv(}st{3$|Ux#}|. Ï ä Ó ÃÛXä.ä Ï ä Ó tã s
Ï ä Ó ä6tGx2sv.{av ä ÚRÏôvtavU}ØÙoÛqÜ Ó ¡uv$|U~#v>xcv]vm$|Ux2|.x#vm{}|mt{
vm|.
|.{}6
|.vyzÆ.tG$v|.
Ï Ó t
ôvo06}avy vo~w|t
7 t}s2q qÏ ä Ó 1ÛXä.äs¡ s
ÏIÚ.Ú Ó vx(q3sv{|#mt{7vo|.,}
t>Ï
Ï ÓÓ .>Ï qÏ ÓÓÓ åÞ ÛUä Y Ùmä
uwvv> ytvmxsv%{}|#ot{vo|UAasv%zqt}.$vU.£ssyÙmä ta~s{}vm|t
Z3"£C|t6ÔÔ#àå.xv$#~s{}}o
t¡©Usv(ßs|q%0t]sv(vmo|.xP|Uxsvo{}|#o.{vm|.
|U ]s{c}vmU|Ut£s{}vys~P|w vo~}¤ov6|.
Ùmä q¡à,3svst{tv qÏNä Ó ÛUä.ä Ï ä Ó qã ].x Ï ä Ó äsv|tt{Z~s|.~Cvo 6}
Ù ßUä Y Y Ù>ä t¡ voovsvs]£Gvm%|t
v>.|U,{v>t~#%|qzUvo,
|.
Ù>ä %t£C|.s»Û |.2Æz.votUv.¡
÷5|y$|U~#vv{|#o.{7vo|U}2a~s{}$3t,vGvv
|.s{Y (Ï Û Ó ¡Ôs£G #}s"t{}{Zv0t~s~s|t
~qvzq.{sv>3}U|s3vm¥Xt}|..}z.v>
ÏÓ
Ï Ó ã Ï Ó PÛXä.ä Ùmä Ï Ï ÓÓ `ÚtäUä.ä Ï Ó aÏ Ó
÷té}svo#~Gv>t}|.x#}v>{|.£G|.`x#vm]|t
3s}]
|U]s{}A.]vm{{».¥X.}scsv"
|U]s{tGx
svo.éX}s"vo#~Gv>t}|.mZ.}z.v>3svzqt{}svm|t
"Ï Ï ÓÓ .x "ÏÏ Ï ÓÓ Ó .3
|U|t
7¡
Z;
;
/
;
;
a< F<
(
Z
;
Z ;
/
4
Z Z
;
/
;
4
/
;
;
S/
/
Z MSP Z MSP I
F<
a<
/
;
Z
`/
+
%
/Z
C/Z ;
g/
;
;
/
(
/Z
ZHE
< '
>;
e/
;
/
a<
x/
;
;
'
,
/ <
;
I
'
/
4
Z M S P ;w/
Z MSP /
Z MSP S/
C/
Z MSP !
4
Z M S P /
/
S/
4
Z M S P !
/
MSP /
$.
<
Theoretical value: Var(Xit(T))−Var(Xssa(T)) vs tau
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0
1
2
3
4
5
6
7
8
9
10
$T' )*4,( .B0&!2*+3 AS2*+
)"7
T
{ = / $!5!#JAS( :2*4355A5!
'
÷5|aé.vmvo~sv~v>vmUq|U(s|.3vx#|as|.s|qåsv0xsv$.{»|t
5sv0o|.a~s#q|U»svov.¡Auwv|.£st}sv>x
3 svtx"|t
=âRà # Ò sv
|U{{}|q3}s
|U]s{
|.»sv aÏ Ó vo|UvoË
|.,svzÆ.tG$v|t
5}a~s{}}o
tPÏô
|U% qv Ó
.mÏ
Ï ÓÓ .>Ï qÏ ÓÓ
Ù qÛ Y Ùmä
à»svo.v|t
5vo#~s{$».(,vvm}atv>x"sv{|#o.{7vo|Usavo}mt{}{U#}saa.~{v¤mv|.
Ùmä ¡
©}.sv |q%q3sv0vm$|Ux(|.x#vo3{}|#ot{7vm|.
|.{}%.||#x(.~s~s|Æ}yq|U6s~|"avm~}¤ov
|.
Y Ù>ä >¡ %vm$vvs£Cvo,|t
vmU|U{}vm.~#|qzUvoA
|U Y Ù>ä »},t£C|.#,Û |U6Æz.vm..vU¡
3µ 3·AÊÈÅÇ 3¸ÌÅ ½ ºÅ]¼sÇ·A¸CÂsÉ ½¿
÷»vaÔ#{ |U .{vmU|UØ >Ü=y
ta|Uv$sta~s{}v|.
"vm.$|U36£s}|#xs.{t}|..2x# }£s#|U¡
|tv»t~s|U£t£{} ]x#vo 0
s$}|.yA£s}a|xt{s
CU |a|#x#v>o¡»Ï âc|#x#v>tv»zqt{}svmt3s
~s|.£Gt£s}{ 6x#vm y
|Uc.3{}|mt{7yq#}s Ó ¡
`Ú
)
ÏIÞ Ó
)
.x x#vms|tv£ss§Cvmv>x"~Cvmov>3|Uv%a|.{}vm${}.~C|.~ss{q|U
.x tv.savmx|]vmyt}
v>voX}.{{}6$|UtX3|qz.vm,svav}Uvozqt{7|t
Xvovmm¡ #vo
Ï Ó Ðs]£Gvm3|t
a|U{v>$s{}vm»}sv0# vo t,av
÷»v~s|U~Gvm y
|U%tv
qÏ Ó 5Ï Ù Ó
Ï Ó Ï Ù Ó Ï Ú Ó
ÏIÞtã Ó
Ï Ó Ï Ó
÷»v]qv.s.vzUvm|.%tv
Ù.
Ù.¡ |tv0t}v>.|URx#|vms|tq}
sv0àsa~#}|.RÚ#¡
©|.,|Uv~ttav$vozÆ.{vmm.sv~s|.£Gt£s}{ ax#}}£s#}|.6|t
7}v>.$}|.y£s}a|#xst{I¡A÷»sv~Gv>$t{
~Gttav$vo3vo3t%vvmx}2|.s3]s{}t}|.}
Ù Y Ùmä
Ú Y Ùmä ÏNß.ä Ó
Y Ù>ä EÙ>ä Ùmä Þ
/^Z
.
A
C/
4
Z M S P %
C/Z /
<
;
Z E
/ <
;
I
(
I
+;
'
_
Z
(/
/
Z
;%
/
;%
/-<
'
n.
/
/
!
;
Z
^.
/
/
Z ;
;
;
;
/
0D Z
;
L<
D
;
ZL.9Z !
/
.
[<
?D
;
/
/
D
;
_
A
Z;
I
/
;
I
;
I
@
;
<
.
Z;
.
/
;
<
J5#
Local error in explicit−tau vs stepsize
0.07
Exact
2nd order approx
0.06
0.05
0.04
0.03
0.02
0.01
0
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
* T
A!3 <-I $!5!#JAS S0T*+355A@!L$&'1 E))*4, .B0&! *43 C4AS2*4J)"7LJ5#
' E) 35:7L355#
5< S0&!AS=35TA!3D"' E74! "7 35:#
5< I!*J*J0&56!#D'
uwvt(sv0]s{q}|.(
|. ä32}s}.{qv 5ÏNä Ó ;Ú.Þtä|av öÛG¡
÷»v,x#£ss}|.|.
svGt{# qv5~{|.v>x0}©}.sv ¡Ô}ovsv»Ôss{|U .{|U{s}|.G.£s}a|#xst{
xs}£#}|.Gvavm.Rtxczq.tov0t{}|.sv]x#|"s|.~s|qzXx#v0yU||x2av>.sv|t
Av>té$|.zUvo.voG$v|.
o|.z.vmUvoov}cx# }£s#|U¡ %vm$v,vv0.(v> ytv|t
v|tt{zq.q|U(x# tov£Gvo vmvo( |
xs}£#}|.6
s|U3.|.avmUv|t
vm|.>¡=Ô#s~s~C|Uv .x tvo.{}.txs|.-zqt}.£s{v>3
~|U£t£s}{} 6xsvo "
s|U7 S tx S%¡÷»sv|..{7zÆ.q|U(£Cv$ ,vovm tGx %x#vosvmx2U
i Ï Ó 6W R S Ï X Ó SÏ X Ó R i X
ÏNßsÙ Ó
Ö×sv}{}t}|.=sv(x#tG$vÏNßsÙ Ó o.4£Cv(t~~s|Æ#}yqv>x`t4voêyovmX]»Æ.¡wÔ#s~s~C|Uv6,v6ÆzUv
vm.{}¤mt}|.
|U tGx
|. "3£C|tå£G|Usx#v>xöÐsv}Xvmzqt{ 8Ø ä Ó ¡
Ñ }zXx#vasvaXvmzq.{ 2X| s£s}Uvozqt{.xwx#vos|.vv"s£Xvmzq.{}. Ø Ó ¡ |q
xsv$sv
]
Ï Ó
ÏNßUÚ Ó
] Ï Ó
÷»}3}vo{xs3t2v> yqv Ï Ó |.
i Ï Ó UzUvo(£X
Ï Ó R Ï Ó Ï ÓR
ÏNß Ó
©}.svãas|q%,sv0x# }£s#|U2vo|Uz#m¡=sv0vm~}¤ovU¡Aà%U.,v0vmv{}}svm.%$|.zUvo.voG$v£CvoGÆzX}|.m¡
¯¬2² o± =³$¯]¬ 0¬2
° c±(=±2® ¯® uwvÆz.v%~v>vmUvmx"o|. voo]vms{
|.svv$#~s{}}o3tGxya~s{}$t"{}vm.~sav$s|#xs
|.}s{q
|Uc|t
|#.0svma}mt{vmU}|.c# voyo¡ ¢ sv>s{|qåq£C|tcv0v$#~s{}}otx2}a~s{}}o
t2av$s|#xs%tv¦|.x#vm»o|. voXm¡ ¢ s3{}|#ot{7vm|.»tGt{}~|qzx#vm»yvmyq,Æa|y$|.
~#v»sv3{|#mt{#vo|.=y.{{sv3a|.avoX=~]|0t0~C|qvm=|t
7¡uwv3ÆzUvvo~{${}~s|qz}xsvmxsv aÏ Ó
vm|.
|U]s{}.v
|.vyv>tPtGxo|qzÆ.tG$v|t
»v$#~s{}}otP.,vo{}{.}a~s{}}ot¡6÷»vmvvms{
|.{x
|.Uvosvm.{vmysxsvo~X#}mt{}{vm.|.Gt£s{}v3.sa~#|Um¡5uwvÆzUv%t{|zUvoGvmx
|.vmz.vot{
vosta~s{}vmtsvtsUv0|t
zÆ.{x# 2|t
A}
|.{}y{}.Uv0vo|.sU2|£Gv]~sU}mt{}{2t~s~{o.£s{v]
t#¦{}vmt~syq|Um¡
;
;
&;
+'
(
2/
e/
S/
?Z =<<=< ^/
3
;
TZ =<<< W
C/
)i4
;
) 4
;
#)i4;
A 3
S/
A
1
1
4 Z
M I P
V;
4
0
9_
)i4 ) 4 F<
;
N
4 X[Z
W
C/
F<
) 4
) 4
<
@
&
.
/
Local error in implicit−tau vs stepsize
0
Exact
2nd order approx
−0.005
−0.01
−0.015
−0.02
−0.025
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
T
A!3 -= E$!5!#4ASEB52*43:5A@! $&' ())*45,E.10
!2*43 C+AS2*4
)"7%J5#
+ &
' E) 35:7L355#
5< S0&!AS=35TA!3D"' E74! "7 35:#
5< I!*J*J0&56!#D'
uwv6s|q,vmx¦|.x#vm0$|.zUvo.voG$v|t
3t{}{v"a|.avoX0|t
ȣG|..Pav$|x
|.]#voy3
{}}svm.~s|.~Cvo 6
sG}|.Go¡÷»vv$vo|Uc|t
=}v>{|"Uvosvm.{s|.{}svm.# voy%"s£ v>
|.
|Us.|U]vmvm.¡
Ö×L.xsxs|U,v(GÆz.v6UzUvo.`Ua~#|.(.£s}{ 4t.{#}
|.]vav>t|.
£C|t`.av$#
|#xsm¡÷»ss|q%%t}a~s{$tRs$|Ux#}|..{{}2.Xa~#|t}mt{}{2 t£s{}v0~s|qz}xsvmxv]vmÁ}
Ua~#|to.{{}"t£{vUX3{}vv$#~s{}}o,.(Uvm}|.G|U6»vo~G}¤ovU¡=÷»vmvvms{,tvx#vmU}mt{
|as|Xv
|U3v$#~s{}}o.x6}a~s{}}o Ò s{}vo3av$s|#xs3t~s~{}vmx(| ¢ÑÒ m¡
%® ¬2²
ØÙoÜ !#"$%&'q ë mû sìqúëIò )û (qòôóZð$ëIò ûìqóZìqï Æúòú .ð Æðoï ñZøaðoóë×ìqï.ñìqë +*ì
oò í ûìqëIò qówòôóañ sìoõXð î×òôó $ðû$ë×ð vU¡$|U{»ûðoïôï ú Ý vmsv$}mo7ÙmÛUã2Ï àscÙmãUã Ó ~s~¡Ù>ß -, Ù>ßtÛ s¡
Ø ÚqÜ .
!/
0"123546
7%8'2:9;<= > qøñCí#ë×ð 6?ðoë qú @ qòôóZì A0ò Bð ðoóëIò ìqï C)DoíìqëIò qóú
ìtó $A0ò Bð ðoóëIò ìqïùî ï õUð ìqò û C)DoíìqëIò qósúZÔÖ àâPÙmã.ã s¡
Ø Ü EFG6H
4I8'2:9;<=J
!/
:9
1
&K%5LMN=O=2QPR27T S sðóí#øyð ò ûìqïGúë¦ì $òôïòôë ïðìñCòôóõ
øyðoë qú úë mû sìqúëIò ûúòôø]í#ïìtëNò tó û sðoø]ò ûìqïôï ðìUû$ëIòôóXõ"ú Æúë×ðoøúG÷5|"t~~Gv>t> ¡ Î vo2¡ #m¡
ÏIÚtäUätÛ Ó ¡
Ø Û.Ü U'VW2X+XY[Z\]VJ
9
A øyìqïôïóGí#ø ð ú $òõø qïðûoí#ïðú%Ô#ovm$vU3Ú.ã `Ï Ù>ßPà%s
Ú.ä.äXÚ Ó ~s~¡Ù.ÙÆÚtã , Ù.Ù Ù.¡
Ø ÞqÜ LMT^JN=O=O2QP2Z 1õXð$óZð ìtï5øyðoë óí#øyð ò ûìtïôï "úòôøí#ïìqëIòôóXõë sð]úë mû sìqúëNò ûëIòôøaðyð qïùí#ëIò qó
0û qí>ñCï}ð û sðoø]ò ûìqï ðì.ûoëIò qósú G¡ Î |.a~¡ #o¡}sÚ.ÚÏ Ù>ã qß Ó ~s~¡ÛUä _, Û Û¡
Ø ßtÜ C ì.ûoë%úë mû sìqúëIò û"úòôøí#ïìtëNò tó yû qí>ñZïð û sðoø]ò ûìtï ðì.ûoëIò qósú ¡ X#m¡ Î svo2¡} sÙ2Ï Ù>ã Ó
~~¡GÚ ÛUä , Ú ßsÙU¡
Ø ÆÜ ?ì `( Ka >ûðúúoðQú b dó c$óë tíû$ëIò qó 'a Æúò ûìtï û$ò ðoóëIòúë úsào.xsvoa} v>mZÙmãUãUÚ#¡
Ø tÜ W S sðû ð$øò ûìqï eìqóõUð >òôówfð D$íìtëNò tó G¡ Î svm2¡ #o¡}ZÙ.Ù ÏIÚtäUä.ä Ó ~s~¡GÚ.ã , äUßs¡
Ø ãtÜ ,ñ.ñ Uòôøyìqë×ðì.ûûðoïð ìqë×ð aúë >û ìÆúëNò ûúòôø]í#ïìtëNò tó û sðoø]ò ûìtïôï ðì.ûoëIòôóXõú Æúë¦ðoø]ú G¡ Î svo2¡
m¡}7Ù.Ù>Þ(ÏNÚ.ä.äÙ Ó ~s~¡Ù #Ùmß , Ù ¡
ØÙmätÜ LMI^N=O=O2QP2/g4668I2:9;=OAJ c$ø%ñ qð PïðìñCî¦úiò h>ð2úoð$ï}ðûoëIò qó cìUûûðoïð ìqë×ð úë mû sìqúëIò û
úòôøí#ïìqëIò qóG G¡ Î svo2¡ m¡}CÙUÙmãÏNÚ.ä.ä Ó #~s~¡ UÚUÚtã , ÛG¡
ØÙ.ÙoÜ T!j"%&Ikl$
= ë mû sìqúëIò û]øaðû sìtóòúøú]òôó2õXð$óZðað $ñ ðúúò qóG |#t¡ q{N¡Càm.x7¡
Ôs$I¡ Ô#àãtÛcÏÙmã.ã Ó X~~¡ sÙmÛ , sÙmã¡
=
$ 6
' @
'
!6
8
8
'
''
%
8 6! `@ 6('
'
!6
' !
8
8
('4
4
'
F
&8
6
6
'
!6
'
8 6! @ 6('
!
6H@
'
6
!
4
"!
=@
!6 6 @
8
54e'
' '
$
'
'
4"6H@
4
6 @'
"6
*%
6 @
!
6
8
2
6
8 6!
'
`'
@ 6('
!6
'
8
!6
6H@
6
8
"!
8
'
6
8
6
!6
!6
<'
('
'
&8
%
6
n'6
'6!
%
38
!6 @ 6('
?'6 2
'
!
6 38
!6 *6H@
8
4^'
4
"!
'
$ 6
?'6
!6
$
8 4
!6
,
4
'
8
8
'
@ @
!6
@ 6 '
'
"!
2 '
!6
7
b_
6
8
Local error in variance for explicit−tau vs stepsize
300
Numerical estimate
Theory (2nd order)
250
200
150
100
50
0
1
2
3
4
5
6
7
−5
x 10
o
T TA!3 $!5!#4ASE1S0T*+355AI!%$T"'@ ))*4,-.B0&!2*+3 @ C AS2*4
)"7%J5#
!#J%
7 #TJ2 5A!3 "5 !#D' ()3557%355#
5= (#TJ2:A!3 "): !# J5#
!2*43"' 7J! "7 355#
/
5I @ 5A!3 !*J*J"0
5 !#D'
ØÙ>ÚqÜ cë úì"ó tòú $íúòôóCð$úú}÷voGxs» Ý vmsv$}moÙÆÞÏ ©svm£Ùmã.ãUã Ó X~~¡ßUÞ , ßUãs¡
ØÙ ÜdG$G$81=
ðìtï%?ìqë sðoøaìtëNò ûìqï óCìtï ÆúòúGÔ~s.vo Avm{t Ùm»v>x#}|.GÚ.ä.äXÚ#¡
ØÙoÛ.Ü7!Y:9
1&K46
8'2:9;<=J%EMlG6
JjLMN=O=O2QP2Z ëIò B3óCð$úúòôó2úë mû sìqúëIò ûû ð$øò ûìqïôï
ðìUû$ëIòôóXõyú Æúë×ðoøQú b0S ð0òôøñCïò û$òôë»ë×ìqí#î×ïðìñZòôóXõ"øaðoë t G¡ Î vo2¡ #o¡}ZÙ.Ù>ã(ÏIÚtä.ä Ó U~s~¡7Ù>Ú tÛ , ãtÛG¡
ØÙ>ÞqÜ l t cóGë qíûoëIò qóRë $a ì oòôïùòôë 7? Uð$ïùúCàm.x#vm vm tvmx#}|.CÚtä.äXÚ#¡
ØÙmßtÜ 92R 7=O"1=) cóGë qíûoëIò qó ë í#øyð ò ûìtï óCìtï Æúòú3Ô#~s}sUvo Avo{t3Úvmx7¡}
Ù>ã.ã ¡
¬2°R³ ¯
ü® 0¬ t¯]®Á 0¬ [K =³ Á¯ æ³
m³$²%³Ã 0±
p & àsa}sasv£G|Usx#v>x =|.|.s£Cvo%tvvmx7
|.."
s$}|. $
q
#}~s¤]o|.X}s|.|..£C|.x#vmxx#|.y.R|.
.xc}st{A qv Zsvovvo#} Eä6tGx
öä(t
7Ï Ï ÓÓ ZÏ Ó R Ï Ó Ø ä >Ü
76
4'
8
%
4
A
$
'
4
8 6!
78
'6 !
!6
n'36 '
6
'
6!
4
'6 !
!6
6
8
0
6
38
4
'
A '
'
n%
4
B
xdgf
#
##
v
f
A ,3
,3
&
%
,
MSP S/
!
MSP H/
;
&
0
1
<
n Ý }z.vowt2}.{=tv Ï Ó 5Zsv~C|U}£s{}v]zqt{}sv>%
|U Ï Ó {}v}"£C|.x#vmx
s£Zx#|.y.2|t
¡ ,6svqvmx #}~s¤~s|.~Cvo "|t
C#svovv$# Läa(t
R 7Ï Ï Ó Ó 7Ï Ó R UR Ï Ó R
|tvt
R Ï Ó R R 1R .Ï UÏ Ó Ó
3vo(v R 1R#xsvos|.vm,sv0t£G|U{#vzÆ.{v|t
5v>.2$|U~C|.voX3|t
=z.vm$|U .¡÷»XG
R
Ï Ó R Ï Ó R R Ï Ó
(t t
MSP !
/
;
MSP 1$
2/
, 3
MSP S/
MSP !
/
<
_
/
MSP W
D !
YX[Z
D /
D9
MSP !
/
MSP ;
W
YX[Z
@ {
D <
Local error in variance fir implicit−tau vs stepsize
0
Numerical estimate
Theory (2nd order)
−20
−40
−60
−80
−100
−120
−140
−160
−180
1
2
3
4
5
6
7
−5
x 10
&A!3 -= E
$!5!#4ASEB52*43:5A@! &
$ ' ())*45,E.10
!2*43 @ C+AS2*4
)"7%J5#
!J
# 7%#TJ2 5A!3 "5 ! #D' ()3557%355#
5= (
#TJ2:A!3 "): !# J5#
!2*43"' 7J! "7 355
# /5I @ 5A!3 !*J*J"0
5 !#D'
,6svvmU|Us}G%voyté s#,v$|U${}x#vq
"ÏVR
Ï Ó R Ï Ó Ó UÏ Ó
|U%t{}{ Läa#ê"$}voX{}(yt{}{N#3svmv .Ï Ó `äa3o|..X»}x#vm~Gvmx#vmU|t
7¡÷»XG
ZÏ Ï ÓÓ 7Ï Ó Ï Ó R ZÏ
Ï ÓÓ ZÏ Ó R Ï Ó R
Ï Ó fR Ï Ó Ï Ó
|U c#ê"ovmU{(yt{}{I¡
-'
MSP /
MSP %
;
Z Z C/
MSP !
/
<
MSP /
;
C/
MSP ! /
MSP Z /
MSP MSP ;
!
/
;
>
$xdgf
p
f
E
v
©|.%.X6~G|X}z.v}UvoUvo &=tx}s}.{qv 2svmvvo Läatx Läa6q
Ó' R '
R Ï
Ø ä >Ü
C/
n
(t t
/
+[Z
7
1
©s|. Ï Ù Ó 3
|.{}{}|q%,t
Ï
C/
/
Ó'
;
'
Ï Ó
W
D YX`Z
Ï Ó
C/
0
'
<
'
O+[Z
Ï
S/
Ó
3vov }£G|Usx#v>xa
|.£G|Usx#v>xyzqt{}svm|t
¡=÷té}sv$#~Cvm$q|U.xa #vmyÚUÞaÏ .x"t{|
G}sav
U3q tv #~s¤|U.X6£G|Usx#v>xxs|.yt}(£#voayaÛ Ó #v|.£st}
*/
R
Ï
C/
/
Ó'
R '
W
YX`Z
R R
D @ *
'
+`Z
"ÏVR Ï
S/
Ó RÓ
Distribution Plot for Schlogl Reaction
0.14
0.12
Probability Density
0.1
0.08
0.06
0.04
0.02
0
J T
5))!
0
100
200
300
400
X
500
600
700
800
7J5)) 4
#6 &A 3 3 "!AS#%!
8 *
!2*435"'
Convergence Curve for Schlogl Model
0.35
0.3
Distribution Error
0.25
0.2
0.15
0.1
0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
Stepsize
0.35
0.4
0.45
0.5
T /7J5)) 4
# <$T"'1 )*4,/-<.B0&! 4
* 3 { 8=5 !2*+3"' /)3557;355#
*43
8= L>TQ> 5<-S0T*+355A<!DCJ8 53 7J! "7L355#
/8=5 L> > 5 <-=52*+355A@!D'
3 vov tv%vo|..X #voayaÚ.Þ]$|.vm~G|Ux#}s|]v
|U .¡Ô#ov téUvmzqt{}svm
}(£C|.x#vmxwx#|Ua.3~|U£t£s}{} PÙU7vayÆc£G|Usx "ÏCR Ï Ó R Ó Ï Ó 53svov Ï Ó }
svyq#}sÃzÆ.{v|.
|.(}%xs|.yt}¡÷»s»~s|qz.vmsvv>{>¡
&;
: C/ p © |..6{zqtqv~C|.{}s|.at{7
|U Lä.x öaä G6q
R "Ï 7Ï Ó ZÏ ÓÓ R $xdgf
f
v
A ,3
S/
C/
7
/ 1
E ,.x}.{5qv csvov0v$#
%
2/
E ,
Ø ä >Ü
<
n ÷»s,}»t(aavmxs}tv$|.Gv>¥Uvoov|t
#voay]Ú.ßs¡A÷ÆX{}|.v$#~.x#}s].xysvo(.éX}s]v$#~Gv>
q|Uov|.£st}
i ' Ï Ó Ï
'
Ó
"Ï ZÏ Ó 7Ï ÓÓ
'
i
'
(t t
C/
S/
;
OX[Z
@
+
C/
S/
/
3vov i } »sv0x#vm.vov|t
C¡Ô}$v
.é.vm»zq.{sv>»|.2a£G|Usx#v>x2x#|.yt}#,v|.£#t}6sv£G|Usx
'
ii ' Ï Ó Ï
Ó ' ' "ÏÏ
Ó ' Ó 3vov 'Ztv~s~Gvm£C|.sx
|.sv%.£|.{}#v»zqt{}svm|.
v%x#vozqt}z.vm|Usv3£G|Usx#v>x]xs|.yt}¡ s
#voay"Útß]v|U£#.(vv>s{m¡
/
C/
S/
/
C/
/
),
p ©|.3ta
sG}|. Ðq3 #}~s¤$|.Xs|U,|.(."£G|Usx#v>x(xs|.yt}(|.
Ãtx(}.{ qv #svovv$#} Läa.x öäGq
R ÐÏ 7Ï Ó 7 Ï ÓÓ R"
Ø ä >Ü
$xdgf
v
f
A ,`3
,3
%
n
(t t
S/
/
,
7
1
0
<
÷»s]
|.{}{|q%x#}v>{w
|. # vmaaUÚUÞR.xÚ #¡ %|tv6qa£Px#v$|U$|Ux#}|.sv>x4|U
Ï Ó Ï Ó ¡
r_
MSP ;
MSP !
b/
;&/
¬2°R³ ®A¯"¯ ¯ ;²3¯]¬ %® ¬2²
Ó x#vms|tvsv3vms{A|.
G|.v»vm~]|.
C¤mv ]|.
GvovoA|t
Cvt#¦{}vmt~ssvoavmA.~s~s{}v>x0|sv
#v$ Ï
}st{=$|Ux#}|. (Ï 3sR}"txs|. zÆ.t£{v0Usavmx2|"ÆzUvsv]|UavoX Ó ¡ #v$ x#vo|tv
% .]q
svsavo}mt{7|U{s}|.6|U£#.vmx"£asvtsI{}vm.~6av$s|#x632 vo~}¤ovm
|qzUvo.2Xvmzq.{|t
A{}voX ]`]_] % ¡ #v$
]`]`] GtGx2{vo ;yq ¡ #v$
£Cvvsv0|U{s}|.~s|#ovmo¡A÷»svm
6Ï 4 Ï Ó Ó "Ï `Ï Ó Ó %
"ÏÏ b \ Ï Ï ÓÓÓ 6ÏÏ b \ \ Ï Ï ÓÓÓ Ó %
"ÏÏ Ï Ï ÓÓÓ Ó "ÏÏ Ï ÓÓ Ó R
B
C/9E
!0
:
-/9E
/
QZ <=<< ;
/
E:
S/
QZ
E
R
4 X[Z
%
4 X[Z YX[Z
YX[Z
<<<
R
4 X[Z YX[Z
>
4
E:QZ+
;
4
7;
E
2/
;
4 ;
n4 4 /
%
4
4 X[Z
YX[Z
4
C/
R
! 4
S/
R
C/
%
n4 4
4 X[Z
R
4
<<=<
R
4
C/
R
<
vov],vÆz.v0Gv>xäq×t£{} cU,vo{}{A.$|.G voo.¡ Î |U tX vm{}tv|2äq× t£s}{ .7.x vo{qv=|o|. voo.¡÷»sv¥UGtX Lä»yt{}{tvo|.sU
|U£C|t0|3s|U{}x~s|qz}xsvmx ¡Ö×a~C|..U
~C|.}X»|as|tv},q»vo|. vooy}»|Us{yvovmxsvmx6
|.3}s}.{ qvm Ï Ó
|U Ø
%ÜI¡AÔ}$v
svsv~s|#$v>,»Xvm.vm3zÆ.{vmx7#%}.x#v>¥UGqv|~|qzUvo|.}vm$a
|U3Xvo.vm3}.{ qvmm¡=©|.
ät¦.£s}{ Rs|q,vozUvos|UsXvo.vm0 qvmsvmvmx|c£Cv6o|.}xsvovmxw.,vo{}{ov Ï `Ï ÓÓ svmvmxs|.0£Gv
}Xvm.vo3zq.{sv>x(
|.0Ïs|Usx#v>x Ó }~{$3.¡
&
(
4
n/
R
$o
@
1
S/
E E
H4
© Copyright 2026 Paperzz