HAL Id: inria-00073589
https://hal.inria.fr/inria-00073589
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.
Adaptative Multigrid and Variable Parameterization for Optical-flow Estimation
Etienne Mémin, Patrick Pérez
To cite this version:
Etienne Mémin, Patrick Pérez. Adaptative Multigrid and Variable Parameterization for Optical-flow Estimation. [Research Report] RR-3102, INRIA. 1997. �inria-00073589�
a p p o r t
d e r e c h e r c h e
Adaptative Multigrid and Variable Parameterization for Optical-flow Estimation
Etienne M´emin and Patrick P´erez
N ˚ 3102
Janvier 1997
TH `EME 3
;=< $ %>$+?
@BADCFEHGG EJILKENMOCPG#QRGS#TQUADVWCFXZY[TJKEHVDEN\
]^_
`.a`bcedgfUh`Zi jlkmhnpoqf
^
oqa8a`mrsa8jlk
^
ntfu`lv
nta8jxwl`.yZv{zuoqf|f~}`Z`.yZvkmoqf{f|jlntyyjlf{km`.y
i oH5`Zh/ /
jx{olihzu`i`.k
^
`Zi k
^
`fUbZqcqjlfUnp`Zi.lqc .|jxwl`.y
.N |¡lq¢¤£
`¥ntfUl`.yhnpwqjxh`h
^
`¦{y`?ol§jlz|jx{hjxhnpl`¥a¨¦{©phnpwli nªz«a8ntf|nta8np¬.jxhnpoqfjl©pwloli nph
^
a8y§FoliBh
^
`®`.yhnta«jxhnpoqf
ol§:h
^
`8jx{|jxi`.fUhaolhnpoqf°¯|`.©tz±
]^
`{ioloqy`.z²jx{|ioqjlk
^
{i ontzu`.yjJkmo
^
`Zi`.fUh¥jlf{z²`m³kZnp`.fUh§Pi jla`Z´oliµ§Poli
`.yhnta«jxhntfuw|np`.km`Z´/nªy`yaoRolh
^¶
o´·¯`.©tz{y§Foliz{n¹¸`Zi`.f7hB|jxiWjla`Zh`Zi np¬.jxhnpoqf|yBi`.©tjxhnpl`ho«jlz|jx{hjxhnpl`|jxihnthnpoqf{y
ol§ºh
^
`®nªa8jxwl`l±
]^
`®`Zi§Poli a8jlf{km`.yol§ºh
^
`?i `.y¦{©phntf{wjl©pwloli nth
^
a8yBjxi`zu`.aoqf{yhi jxh`.zOntfh
^
`z{n¹³kZ¦{©th~kmoqfUh`m»Rhol§
j8fuoqfkmoqf7l`m»¼wq©pol½jl©`.fu`Ziwl¾J§FoliWa¦{©ªjxhnpoqf$±
¿ÀUÁÂÃÄ
HÅl¢
ol{hntk
¶
o´¥vUiol½|¦{yh~yhjxhntyhntkZy.v7wq©pol½|jl©a8ntf{nªa8np¬.jxhnpoqf$vqjlz|jx{hjxhnpl`/wliWntz{yZv7a¨¦{©phntwli ntzjl©pwloli nth
^
a8yZv
xjxi ntjx½|©p`®|jxiWjla`Zh`Zi np¬.jxhnpoqf
ƹÇÈ
ÉËÊÍÌ.Î
È
ÉÏÐpÊsÑÓÒmÔ
Unit´e de recherche INRIA Rennes
Í
<
$ %>$+?868+ +$
À À ¢
oq¦|y®{iR}`.y`.fUhoqf{y¥¦{fu`¨§jla8nt©t©p`¨zjl©pwloli nth
^
a`.y®zu`a8ntf{nªa8ntyjxhnpoqfva¨¦{©phnpwli nª©t©p`.y`Zh¥jlz|jx{hjxhnp§yZvzu`mr
z{nD}`.y
_
j ©`.yhnªa8jxhnpoqf z{¦ k ^
jlayOzu`.yRnph`.y y`.yJjx{|jxi`.fUh`.y¼z{jlf{y¦{fu`²yR}`R¦u`.f{km` znªa8jxwl`.yZ±` yk
^ }`.a8j zu`
a8ntf|nta8ntyjxhntoqf `.yhz}`.kmi nph¨zu`«a8jlf|n
_
`Zi`8w}`.f~}`Zi jl©p`Joq¦uiz{np¸/}`Zi`.fUh`.yjxi jla#}`Zhi ntyjxhntoqf{yz{¦ k ^
jla zu`.yRnph`.y y`.yZ±
j§Poli a¦|©tjxhnpoqf¦{f{n¹¯}`Z`®jlntf{yn|ol½{h`.fR¦u`kmoqf{z{¦{nphzu`?§PjkmoqfOf{jxh¦{i`.©t©p``ZhBkmo
^ }`Zi `.f7h`
_
j¨`.yhnta8`ZiBy ¦ui¦|fu`/|jxi hnphnpoqf
jlz{jx{hR}`Z`¨zu`©nta8jxwl`¦{fOk
^
jla¼kmoqa8a`§Poqf{kmhnpoqfkmoqf7hntfR¦u`®|jxiaoliWkm`.jl¦»¼j.l`.k¥z{ntl`Zi yzu`Zwli}`.ykmoqf{kmoqa«nphhjlf7hy
zu`|jxiWjla#}`Zhi jxwl`l±
2Ä Â ¡À ¢ ¶
olh¨ol|hnU¦{`lv:yhjxhntyhnU¦u`iol½|¦|yh`lv(a8ntf{nªa8ntyjxhnpoqf[wq©pol½|jl©p`lv(wliWnt©t©p`.y¨jlz{jx{hjxhnpl`.y.v~jl©pwloli nth
^
a`.y
a¨¦{©phnpwli nª©t©p`.yZvU|jxi jla=}`Zhi nty jxhnpoqf¼xjxi ntjx½|©t`
® $+¥83 $+
f{`Ziwl¾7rͽjly`.zaozu`.©tykmoqf{yhnph¦{h`~joN´~`Zi§¦{©l´Bj.¾hokmol`:´/nth
^
©po´rs©p`Zl`.©Unªa8jxwl`:{i oRkm`.yy ntfuw{iol½©p`.a8yZ±
]/^
oqy`
a`Zh
^
oz{y'jxi`ntyy ¦u`.z`.nth
^
`Zi'§Fioqa kmoqfUhntfR¦uoq¦{y §FoliWa8jl©tntya«yy¦|k
^
jly
y oli*`.nph
^
`Zi §Pioqa z{nty kmi`Zh`a8oRzu`.©ªnp¬.jxhnpoqf
y¦{k
^
jly jxiµloNiWjlf{zuoqa ¯|`.©tz{y.±
]^
`B¦{f{zu`ZiW©p¾Rnªfuw{iol½©p`.a8y jxi`~`.jly nt©p¾¥hi jlkmhjx½©p`np§{h
^
``.fu`Ziwl¾¨ntykmoqfUl`m»±®fu`
^
jlyh
^
`.f hoJz{`.jl©º´/nth
^
§¦{f{kmhnpoqf{y
^
j.ntfuwjlf²¦{f{nR¦u`¥a8ntf|nta¦|a h ^
jxh®a8j.¾¼½``.yhnta8jxh`.z°´/nph
^
zu`Zh`Zi a8nªf{ntyhntk
zu`.ykm`.fUha«ntf{nta8nt¬.jxhnpoqf jl©pwloli nph
^
a8yZ±/oN´~`Zl`Zi.v´
^
`.f nth«kmoqa`.yho#zu`.y npwqfjlkZkZ¦uiWjxh`°jlf{ziol½|¦{yh8a`Zh
^
oz{yZv
jx½|©p`®ho
^
jlf|z{©p`jlf|zJho8©poRkZjxh`¥jlyB|i`.kZnty`.©p¾jlyB oqy ynp½|©p`?z{ntykmoqfUhntfR¦{nphnp`.y.v7`.fu`Ziwqnt`.yBh`.f{zJho½`?fuoqfO©ªntfu`.jxi´/nph
^
fR¦{a`Zioq¦{y*©toRkZjl©{a«ntf{nta8j±
]^
`Bol{hntkZjl©
¶
o´ `.yhnta8jxhnpoqf8nªy(fuolh(jlf`m»ukm`Z{hnpoqf«ho¥h
^
nty'i ¦|©p`RvURv|Zuv{.v7qvUͱ
l`.f¼´/nph
^
ntfjlf¼ntf{kmi `.a`.f7hjl© "!$#&%(')*+ ,')-«§Poli a¨¦{©tjxhnpoqfol§ h ^
`{iol½©p`.a/.P´
^
ntk
^
nªyjl©ªaoqyhntfu`.y kZjx|jx½|©p`®ntf
kZjly`Jol§©poqfuw i jlfuwl`Jaolhnpoqf{yho°½ ``.yhnta8jxh`.z10Wv*oqfu`
^
jlyho zu`.jl©~´/nph
^ j y`R¦u`.f{km`ol§wq©pol½|jl©~ol{hnta«np¬.jxhnpoqf
{iol½©p`.a8yB´
^
nªk
^
i`.a8jlnªfJhi ntkµR¾l±
]
o«kmol``m³kZnp`.fUh©p¾J´/nph
^
y¦|k
^
wq©pol½jl©`.fu`Ziwl¾Oa8ntf{nªa8np¬.jxhnpoqf$vR´`{ioloqy`
^
`Zi`¥j8§Pjla8nª©p¾«ol§'zu`Zh`Zi a8nªf{ntyhntk
ol{hnta«np¬.jxhnpoqf jl©pwloli nph
^
a8yZ±
]^
`.y`2 !3,4Ojl©pwloli nth
^
a8yjxi`J`m»Rh`.f|ynpoqf{yol§h
^
`Oa`Zh
^
oz {ioloqy`.z ntf5ͱ
]^
`Z¾Ojl©t©to´2ho{i ol `ZiW©p¾kmoqa½|ntfu`¨j«a¨¦{©phnpwliWntz¼a8ntf|nta8np¬.jxhnpoqfOyhi jxh`Zwl¾¼´/nph
^ h ^
`a¨¦uhnpi `.yoq©t¦uhnpoqf¼§Fi jla8`Z´~oliµ
kmoqa8aoqf|©p¾ ¦{y`.z ntf aolhnpoqf[jlf|jl©p¾Ry ntyZ±
]/^
`µl`Z¾°nªzu`.jOkmoqf{yntyhyntf²h
^
`8a8ntf|nta8np¬.jxhnpoqf ol§h
^
``.fu`Ziwl¾°§P¦|f{kmhnpoqf
h ^ ioq¦{w
^
jlf jx{{i ol{i ntjxh`
^
np`Zi jxi k
^
¾ol§y¦u½|y|jlkm`.y«ol§h
^
`°´
^
oq©p`°kmoqf¯|wq¦ui jxhntoqf y|jlkm`l±
jlk
^
y¦{½|y|jlkm`²nty
zu`m¯f{`.z¼jly/jy`Zhol§*kmoqf¯|wq¦uiWjxhnpoqf{y/kmoqf|yhi jlntfu`.z¼ho«½`|np`.km`Z´/nªy`|jxi jla`ZhiWntki`.©tjxhntl`¥hoj8km`Zi hjlntf¼|jxi hnphnpoqf
ol§'h
^
`¥nta8jxwl`l±
]^
`.y`/a¨¦{©phnpwli nªz¨a«ntf{nta8nt¬.jxhnpoqfjl©pwloli nph
^
a«y*h¦ui foq¦{h(ho¥{ioNRnªzu`jlf«jlkZkm`.©p`ZiWjxh`.zkmoqfUl`Ziwl`.f{km`?ho´Bjxi zntar
{ioNl`.z`.yhnta8jxh`.yZ±76|¦uih
^
`Zi a8oli`lvRjly yoRkZnªjxh`.zhoj¨zu`.f{y`iol½|¦{yh~ol{hntk
¶
o´ `.yhnta«jxhnpoqfa8oRzu`.©Ív7h
^
`®a¦|©phnpwli ntz
§Pi jla`Z´oliµ{i ontzu`.y?`m³kZnp`.fUhaolhnpoqf²`.yhnta«jxholi yjl©t©poN´/ntfuwho¼kmoqa½|nªfu`z{n¹¸`Zi`.f7h?|jxi jla8`Zh`Zi np¬.jxhnpoqf{y®ol§~h
^ `
l`.©pokZnphs¾¯|`.©tzh
^
i oq¦uw
^
jlf¼jlz{jx{hjxhntl`|jxihnphnpoqfol§ h ^
`¥nta8jxwl`wliWntz$±8 kmoqa8{ioqa8nty`?yoq©ª¦uhnpoqf{y½`Zhs´`Z`.f©pokZjl©
zu`.f{y`a`Zh
^
oz{y9v;:v5*ntf7loq©tRntf{w8yaolh
^
fu`.y ykmoqf{yhi jlntfUhyjlf{zwq©pol½|jl©|jxi jla`ZhiWntkjx{|ioqjlk
^
`.y?jlyy¦|a8ntfuw
©poN´ oli zu`Zioq©p¾fuoqa8nªjl©i `Z{i`.y`.fUhjxhnpoqfOol§'h
^
`l`.©pokZnph˾¯`.©tz<¹lv|v+={vºntyh
^
¦{yntfUhioz{¦{km`.z$±
]^
`Oi`.a8jlntf{z{`Zi¨ol§?h
^
`O|jx`Zi8ntyoli wqjlf{np¬Z`.z jly§Poq©t©poN´/yZ±=dgfy`.kmhnpoqfRv´~`O|i`.y`.fUhh
^
`Oiol½|¦{yha8olhnpoqf
`.yhnta«jxhnpoqf §FiWjla`Z´~oli µ ol§nªf7h`Zi`.yhZ±
]^
`J`.yhnªa8jxhnpoqf nty¨{i`.y`.f7h`.z jlyh
^
`¼nªf{kmi`.a`.fUhjl©Ba8ntf{nta«np¬.jxhnpoqf[ol§®j
wq©pol½|jl© `.fu`Zi wl¾«§¦{f{kmhnpoqf$±
]^
`ol½`.kmhnpl`§¦{f{kmhnpoqfkmoqf{ynªzu`Zi`.z
^
`Zi`lvuntfUloq©pl`.yBiol½|¦|yh~`.yhnta8jxholi yBhozu`.jl©½olh
^
´/nph
^
y|jxhntjl©z|ntykmoqfUhntfU¦|nphnp`.yol§®h
^
`l`.©toRkZnph˾=¯|`.©tz jlf{z´/nph
^
©tjxi wl` zu`Zntjxhnpoqf{y8§Fioqa h ^ ` z{jxhj#aozu`.©Ó±d5f
y`.kmhnpoqf#bRvº´`{i`.y`.fUhh
^
`{ioloqy`.z a¨¦{©phntwli ntz §Fi jla8`Z´~oliµ ±>®¦ui¥jx{|ioqjlk
^
nªy®Hjl©tnªz{jxh`.z U¦|jl©tnphjxhnpl`.©p¾°jlf{z
R¦{jlf7hnthjxhnpl`.©p¾¨oqfi`.jl©u´oli ©tzjlf{z«y¾RfUh
^
`Zhntky`U¦u`.f|km`.yZ±
]^
`.y``m»`Zi nta`.fUhjl©i`.y¦{©thy*jxi`i`Zolih`.z8ntfy`.kmhnpoqf
=u±
? @
+?! < 3*$:%&:? < W%>$+
A
hjlf{z|jxi z[ol{hnªkZjl©¹r
¶
o´ `.yhnªa8jxholi yjxi`½|jly`.z#oqf#h
^
`«´`.©t©:µfuoN´/fB' C3D) 'EFCG')-H%& !ID)"-J.LKNMO10`U¦|jxhnpoqf
¹;:ͱ
]^
nªy z|n¹¸ `Zi `.f7hntjl©U`R¦{jxhnpoqf$v7nªyy¦u`.z¨§Pioqa j®©tntfu`.jxi nt¬.jxhnpoqf¨ol§|h
^
`½{iWnpw
^
hf{`.yy'kmoqf{yhjlf{km¾jlyy¦{a8{hnpoqf$vl©tntf{µRy
L#5-H- # #5- D-J4 D !& C #(!I#
h ^
`«y|jxhnpoxrÍh`.aoli jl©*wliWjlz{np`.fUhyol§Bh
^
`«©t¦{a«ntf{jlf{km`ho¼h
^
`¦{fuµfuo´/f²l`.©toRkZnph˾²l`.kmholi.±Jdgf oliWzu`Zi¥ho¼`.yhnªa8jxh`
h ^
`®hs´o8kmoqaoqfu`.fUhyol§ºh
^
`®l`.©pokZnphs¾l`.kmholi.v|j %3 ';' -1#&%3%|i npolioqfJh
^
`?yoq©t¦uhnpoqfntyB¦{y¦{jl©ª©p¾kmoqa½|nªfu`.z´/nph
^
nphh
^
i oq¦uw
^
i`Zwq¦{©ªjxi np¬.jxhnpoqf<v5=|vº;:ͱ
¦u`¨hoJh
^
`¨z|n¹¸ `Zi `.f7hntjl©f{jxh¦ui`¨ol§(h
^ ` KQM Oºvh
^
ntyyhjlf{z{jxi z°aozu`.©tntfuwzuoU`.y®fuolh
^
oq©tz§Foli©tjxi wl`¨z{nªy|©tjlkm`mr
a`.fUhyZ±
]
o°kZnpi kZ¦{al`.fUhh
^
`8|iol½|©p`.aOv´~`kmoqf{yntz{`Zijlf ntf|kmi`.a`.fUhjl©(`.yhnta«jxhnpoqf[ol§Bh
^ ` ¶
o´¯|`.©tz[kZjx{h¦{i`.z
½olh
^
½R¾8h
^
`?ol{hntkDr
¶
o´·a¦|©phnpi`.yoq©ª¦uhnpoqf8y`Zh¦{ uv llv5=$jlf{z½U¾8h
^
`?a¨¦{©phnpwliWntz8yhi jxh`Zwl¾2 %(#$4 D#GD C !I#5%5'
,')- # #5N¹;v (ͱ
]/^
`a¨¦{©phnpi`.yoq©t¦uhnpoqf§Pi jla`Z´oliµ¼ntfUloq©pRnªfuwj8R¾Ui jla«ntz{jl©zu`.kmoqa8 oqy nphnpoqfOol§'h
^
`¨nta8jxwl`
z{jxhj8nªyyhjlf{z{jxi zOjlf{z¼´~oqfh½`®`.a
^
jlynp¬Z`.z
^
`Zi`.nªf$±'dgfJh
^
`§Poq©t©poN´/ntfuwuv´`¥y
^
jl©t©jlyy ¦{a`ho´oliµjxhjwqnpl`.f
i`.yoq©ª¦uhnpoqf°ol§~h
^
nty®yhi ¦{kmh¦ui `l±9o´`Zl`Zi.v oqfu`
^
jly®ho¼µl`Z`Z nªf°a«ntf{z°h
^
jxhh
^
``m»{i`.yy npoqf²jlf{z kmoqa|¦uhjxhntoqf{y
jxi`a8`.jlf7hho«½ `i `Z{ioz{¦{km`.zOjxh`.jlk
^
i`.yoq©ª¦uhnpoqfO©p`Zl`.©jlkZkmoliWz{ntfuw8hojkmoqjxi y`ho8¯fu`¥yhi jxh`Zwl¾l±
`Zh¦{yfuoN´ jlyy ¦{a`/h
^
jxhjioq¦uw
^
`.yhnta8jxh`?ol§$h
^
`?¦{f{µRfuoN´/f8l`.©toRkZnph˾¯|`.©tznty~jHjlnª©tjx½|©p`
.P`l±wu±pv §Fioqa&jlf `.yhnta8jxhntoqf[jxh©poN´~`Zii`.yoq©t¦uhntoqf²oli¥§Fi oqa>jJ{i`Znpoq¦{y®`.yhnªa8jxhnpoqfJ0Wvoqf h ^
`i`.kmhjlfuwq¦|©tjxi|np»R`.©
©tjxhhntkm`±
`Zh. $0!"#.$%& $0'()²½` h ^ ` ©t¦{a8ntf|jlf{km`¼§¦{f{kmhnpoqf jxhJhnta`* W±,+?f{zu`ZiJh
^
`²kmoqf{yhjlf{km¾
½{i ntw
^
hfu`.y y*jlyy¦{a|hnpoqf§Pioqa hnta`- 'ho /.[xvUjy a8jl©t© -JC(!$#5>#5-J10 #5432/46587 .96:9 0<;kZjlf«½``.yhnªa8jxh`.z
½R¾a8nªf{nta8np¬.nªfuwh
^
`§P¦{f|kmhnpoqf{jl©>=@?'=BAC.EDC=GFHv{´/nph
^
Rv(IH
= A .J21*KLM 0 ?ON
&P
;Q
A SRT.$U.V & .JW0XWY2/ .G[ZI.$/& \M 0I .5W0
=]F).J21*KLM 0!? N
^
M_`bacPd
Q
F7fe .JY.E21&0Yg .J]`h.E21]`;0eI/ .Ó 0
´ ^
`Zi `VD8i2vcj nty?h
^
`8y`Zh®ol§f{`.npw
^
½oli nªfuwynth`¨jlnpi y®©p¾ntfuwoqf²wli ntzT `U¦|np{`.z´nph
^
yoqa`fu`.npw
^
½oli
^
oRoRz
y¾yh`.a(kvlROyhjlf{z|y(§Poli~h
^
`?y|jxhntjl©|wli jlz{np`.fUh:ol§m vU[Z$.$%& \&n 0 ?o.$m.p & q.#W0lg!.$/& I0~nty:h
^
`z{nªy|©tjlkm`.z
§Pi jla`z{n¹¸`Zi`.f{km`lvujlf{z§¦{f{kmhnpoqf{y
Q
Ajlf{z
Q
Fjxi`yhjlf|z{jxi z !Y'1r5 %&Cst$#&%5 " DL'!G% .P´/nph
^J^
¾R`ZirÍ|jxi jla8`Zh`Zi y-ucA
jlf{z*uvFW0W±
a½`.z{zu`.znªf7hoJj "!$#&%(')*+ ,')- CG';D)!3%(#w L'xy07- #yhi jxh`Zwl¾lv$h
^
ntynªf{kmi`.a`.fUhjl©jx|{ioqjlk
^
jl©t©to´/yho
`.yhnta«jxh` D)!
#l`.©pokZnphnp`.y.± 6{¦|f{kmhnpoqf{y
Q
Ajlf{z
Q
F«`.f{jl©ªnp¬Z`8h
^ ` 4 # D ')-H%§Fi oqa&h
^
`Jz{jxhj²aozu`.© .nͱ`l±pv(h
^ `
KQM O 0jlf{z²§Fi oqa¤h
^
`¯|i yh®oli z{`Zi¥yaoRolh
^
ntfuw{i npoliv$´
^
ntk
^
jxi `l`Zi¾°©ªnpµl`.©p¾¼hoOokZkZ¦ui .P`l±wu±pv`.y`.kZntjl©t©p¾jxi oq¦{f{z
';C3C( %& '-+%I0W±
oq¦uw
^
©p¾y `.jxµntfuwuv?j=iol½|¦{yhs rÍ`.yhnta8jxholi§P¦{f|kmhnpoqf
Q
ntyOjlf·ntf{kmi`.jly ntfuw#kmoqyhO´
^
ntk
^
`.f{jl©ªnp¬Z`.yJ©tjxiwl`
z
i`.ynªz{¦{jl©b{Oxjl©t¦u`.y©p`.y yzuiWjlyhntkZjl©t©p¾²h
^
jlf R¦{jlzui jxhntk§¦{f{kmhnpoqf{yzuo :Rv.v}|ͱ°dËhkZjlf=½`y
^
oN´/f#h
^
jxh¨¦|f{zu`Zi
km`Zihjlntfynta|©t`?kmoqf{z|nphnpoqf{y .a8jlntf|©p¾kmoqf{kZjRnths¾Jol§~.+0? Q
. 0I0Wv|jlfU¾Ja¦{©thntz{nta`.f|ynpoqf{jl©a8ntf{nta«np¬.jxhnpoqf{ioxr
½|©p`.a ol§?h
^
`¼§FoliWa
z
¯f{z jxi w~a8ntfUh '
Q
. 0{#kZjlf½`Oh¦ui f{`.z ntfUho j[z{¦{jl©/a8ntf{nta«np¬.jxhnpoqf={iol½|©t`.a
z
¯f{z
jxiwa8ntfq_ ' !
. 0 F . .J
0 {#ntfUloq©pRnªfuw D)% D)!\ D)!& D1r5#&%2.Poli E#5 %$0
ykmoqf7hntfR¦uoq¦{y ©p¾ ©p¾Rnªfuw[ntf
.U.&˱ nty¥j¼kmoqfUhntfR¦uoq¦{y©p¾²z{n¹¸`Zi`.fUhntjx½|©p`§¦{f{kmhnpoqfvºzu`Z`.f{z{ntf{woqf
Q v jlf{z ?1©tntaM~vL.+0W±
]^
`8fu`Z´
a8ntf|nta8np¬.jxhnpoqfntyh
^
`.f¼©t`.jlz<D) #(!3-1D f #5´/nph
^
i`.y`.kmhho°jlf{zJhoh
^
`
yZ±*dg§
yjxi`¥jH³fu`§Poli a8y.va«ntf{nta8npr
¬.jxhnpoqf²´¥±i±hZ±[ntyjJyhjlf|z{jxi z E#5 #G4 #$D%5 %w(HD)!$#&%/{i ol½|©p`.aO±?dgf°h¦uiWf6[½`.ntf{w«§Piol¬Z`.f$vh
^
`½`.yh´`.npw
^
hy
^
jl`h
^
`§Poq©t©poN´/ntfuwkZ©poqy`.z¼§Foli a!H
. 0h
Q
. 0
[B
. 0
~ . 0 F
I .Ób 0
d5foq¦ui:kZjly`h
^
`´`.npw
^
hy~jxi`ol§ hs´of{jxh¦{i`.ywH .j 0 4 DLD ' L#5!3% E#5
%B.Pi `.©tjxh`.z8ho¥h
^
`z{¦{jl©§Poli a¦|©tjxhnpoqf
ol§}=BA30Wv|jlf{z .P½ 0 4)"%5CG'- "- J E#5 % ©t¾Rntf{w¨oqfh
^
`z{¦|jl©wli ntzOol§ .P{i ontzu`.zO½R¾h
^
`z{¦{jl©§Poli a¨¦{©tjxhnpoqfOol§
=GF;0W±
]^
`B¯|iWyh*y`Zh(ol§ ´~`.npw
^
hyZvRzu`.fuolh`.z½R¾
w pqvUjl©ª©po´/y(hojxhh`.fU¦|jxh`/h
^
``m¸`.kmh:ol§z{jxhj§Poli(´
^
nªk
^
h ^
`>KQM O nªy®Rnpoq©ªjxh`.z$±
]^
`y`.kmoqf{z[oqfu`lvzu`.fuolh`.z²½R¾ X` /[ijC7v${i`Zl`.fUhy§Pioqa ol`Zirsya8oUolh
^
nªfuw
ntf©poRkZjxhntoqf{y(ol½RRntoq¦{y©p¾`m»
^
np½|nphnªfuwynpwqf{n¹¯ kZjlf7h(l`.©toRkZnph˾8z{ntykmoqfUhntfR¦{nphnp`.y.±
]^
``.yhnta8jxhntoqf«nty~fuo´ `m»R|i`.yy`.zjly
h ^
`¥wq©tol½|jl©$a8ntf{nªa8np¬.jxhnpoqfJntf<.J216
0ol§ ? !AC.D F®´
^
`Zi`xH
6AW.J2/p
KL&n 0 N
MP
;
A
R.$q.w& .JW0W 21. Z .$%& \MB30
F
.)A;.
50 .= 0
F.J2/p
KL&n 0 N
^
M_`bacP#d
!F X`/e .J[.V2/B30#g .J`%.V2/`(0e
F
.VF .LI`;0 ., 0
o´`Zl`Zi.v*h
^
`«¦{f|zu`Zi ©p¾ntfuwJ`.fu`Ziwl¾²§¦{f{kmhnpoqf= ½`.ntf{w¼fuoqfrskmoqfUl`m» ´/nph
^
i `.y`.kmh¥hoh
^
`¦{fuµfuo´f²Hjxi nªjx½|©p`.y
ol§Bntf7h`Zi `.yhZv´`8yhnt©t©
^
j.l`«hozu`.jl©'´/nph
^
jJhoq¦uw
^
ol{hnta8np¬.jxhntoqf |iol½|©p`.aOvnªf°y|nph`ol§~h
^
`¨i `Z§Foli a¨¦{©tjxhntoqf$±d5f
|jxihnªkZ¦{©tjxi.v h ^
`Jjl©ph`Zi f{jxh`Ja8ntf{nªa8np¬.jxhnpoqf |ioRkm`.z|¦ui`«nty¨fuolh¨wq¦{jxi jlfUh`Z`.z ho i `.jlk
^
jwq©tol½|jl©~a«ntf{nta¨¦{aOv`Zl`.f
h ^ oq¦uw
^
`.jlk
^
yh`Z8nty'kmoqf{yhnph¦uh`.zol§jlf`m»ujlkmh(a8ntf|nta8np¬.jxhnpoqf .P½|¦uh ´/nph
^
i`.y `.kmh'hooqf{©t¾j®y¦u½|y`Zh'ol§Hjxi nªjx½|©p`.y30W±
5$%&W % )* +
]
o°`m³kZnp`.f7h©t¾#kmol`J´/nph
^
oq¦uiwq©pol½|jl©ol{hnta8nt¬.jxhnpoqf={iol½|©p`.a¼v ´`¼zu`.yntwqf#j
^
np`ZiWjxi k
^
nªkZjl©
z
kmoqf{yhi jlntfu`.z {°`m»Rr
|©poliWjxhnpoqf ol§¥h
^ ` kmoqf¯|wq¦{i jxhnpoqf y|jlkm`5H²h
^ ` ol|hnta8np¬.jxhnpoqf nty©p`.jlzh
^
ioq¦uw
^ j y`R¦u`.f{km`°ol§kmoqf{yhiWjlntfu`.z
kmoqf¯|wq¦{i jxhnpoqf¼y¦{½|y|jlkm`.yBol§*ntf{kmi `.jlyntfuwynp¬Z`
z{nªa .$510z|nta .$5
A
0z{nªa .$5
0´/nph
^ 5
o5 .,: 0
jlf{zO´
^
`Zi`5ntyBh
^
`y`Zhol§*ntf|kmi`.a`.fUhB¯|`.©tz{y´
^
nªk
^
jxi`kmoqf|yhi jlntfu`.zJho«½ `np`.km`Z´/nty`®|jxiWjla`Zhi ntkjlkZkmoli z|ntfuw
hoj|jxihnphntoqf«ol§wli ntz±
`Zh ! ?" !
#
$p wwwm&%
z{`.fuolh`.yBh
^
nty|jxihnthnpoqfjlf|zh
^
`®l`Zihntkm`.yBol§h
^ `
jlyyokZntjxh`.z kmoqf{fu`.kmhnpnphs¾wli jx
^ A ±
jlk
^
|jxhk
^
ol§'h
^
`¥ntf{kmi`.a8`.f7hjl©¯`.©tzOntyzu`m¯f{`.zOy¦{k
^
jlywH
'
$p '
(
# 2/B*)
#
.+
#
0 .Í0
´ ^
`Zi `,+
#
nty/j|jxi jla`Zh`Zi/l`.kmholi.±
]/^
`´
^
oq©p`ntf|kmi`.a`.fUhkZjlf¼h
^
`.fO½``m»{i`.yy`.zcH
21) .+ 0 .$| 0
´/nph
^ + -+ #
$.J©t¾Rntf{wntf#h
^
`i `.z{¦{km`.z#|jxi jla`Zh`Zi8yjlkm`0/1m±
]^
`§P¦{©ª©¹rÍi jlfuµ²§¦{f{kmhnpoqf2)3¨ntyh
^ `
- #5! ')D ,')- ' #5!IDL')!®½`Zhs´`Z`.fh
^
`i`.z|¦{km`.zy¦{½|y|jlkm`4/ jlf{zh
^
`§¦{©t©oliWnpwqntf{jl©kmoqf¯|wq¦ui jxhntoqfy|jlkm`5®±dgh
ntyjoqf{`mrÍhoxrÍoqfu`¨a«jx{|ntfuw¨§Pioqa5/6ntfUho5 d5a7)3m±
8:9<;>=.?A@
RCB
=:;D=:EGF&=IH
RKJ FL@M;
BON
FP:;RQL?ASTFOP@:U?GFOP:;WVAS
BJXY F&PM=:HZ=:H
B3RK[\O]
=:EA;WQLPF
Y
E_^
\
H`@WFa
\Mb
@MHZ=:;DP:;
J
=F
R
Q?CSTFOPQLP:HTc<d
: L#5-H- # #5- D-J4 D !& C #(!I#
!"#$%&'()+*','-
d5fOh
^
ntyB´oliµ´~`¥§PokZ¦{yoqf¼©tnªfu`.jxi§FoliWa8yol§ h ^
`ntfUh`Zioq©tjxhnpoqfJol`Zi jxholiH
'
$ '
#
M2/B).
#
.$)0O+ # .Ó 0
´ ^
`Zi `/.
#
.$)0~nty½R¾10
#
a8jxhiWn¹» ± ]^
`?kmolii `.yoqf{z{ntfuw|jxi jla`Zh`Ziyjlkm`.yjxi`?nªf«h
^
`.y`®kZjly`.y/ '932
8
:(q:
9
254
\ ± ]^
`8yhjlf{z{jxi z jxi jla`Zhi ntka8oRzu`.©ªy¥¦{y`.z[nªf aolhnpoqf jlf|jl©p¾Ry ntykmolii`.yoqf{z[ho60
#
¥RvQ=uv:Joli|<¹qvN=ͱ
d5f[h
^
nty¥´~oliµ²´`«´/nª©t©*kmoqf{yntz{`Zi¥h
^
i`Z`«z|n¹¸ `Zi `.f7h¥jxi jla`Zh`Zi np¬.jxhntoqf{y¥ol§h
^
`kmoqf¯|wq¦ui jxhntoqf y¦u½y|jlkm`.y>.ntf h ^ `
§Poq©t©po´ntfuw yhjlf{z{yB§PoliBh
^
`l`ZihntkZjl©$jH»unty´
^
`Zi`.jly87zu`.fuolh`.yBh
^ ` ^
oliWnp¬Zoqf7hjl©oqf{`lvuh
^
`®oli npwqntfoqntf7h½`.ntfuw¨h
^ `
¦u{`Zi©p`Z§Phkmoli fu`Ziol§wli nªz6v|ntfJh
^
nªyB§Foli a¼vlLjlf|z97/jxi`h
^
`¥kmoUoliWz{ntf{jxh`.yol§*ynth`.y 0W±
:6;=<?>@BA1C,DE>F<HGDJILKHGMIONP<?Q3EJ;
`Zi`lv|h
^
`kmoqf¯|wq¦ui jxhntoqfOol§ 5 jxi`kmoqf{yhiWjlntfu`.zOho½ `np`.km`Z´/nty`¥kmoqf|yhjlf7hol`Zi?`.jlk
^
|jxhk
^
ol§'h
^
`¥|jxi hnphnpoqf
!\H
'
$*
'
#
R.
#
.$)0}
ST
e
UV ?WFnÓ±`l±pvL2/B/ + # ST 2X
#
2%
# UV
.5Z 0
]^
nªy(µntf{z8ol§kmoqf{yhi jlntfUh
^
jly:½`Z`.f`m»Rh`.f|ynpl`.©p¾«¦|y`.z«ntfji`Zwq¦{©tjxi nt¬.jxhnpoqfrͧPi`Z`kmoqfUh`m»Rhol§kmoqf7l`.fUhnpoqf{jl© ½|©pokµUr
a8jxhk
^
ntfuw²h`.k
^
f{nR¦u`.y¨§Folintzu`Zo²kmoRz{nªfuwu±²dËh
^
jlyjl©tyo²½`Z`.f=y¦{kZkm`.yy§¦{©t©t¾[¦{y`.z=§Folih
^
`Jzu`.yntwqf#ol§?a¦|©phnpwli ntz
aozu`.©ty´nph
^
i`Zwq¦|©tjxi np¬.jxhnpoqfv{§Foli®aolhnpoqf`.yhnta8jxhntoqf jlf{z y`Zwqa`.fUhjxhnpoqf .P½olh
^
ntf aolhnpoqfjlf|jl©p¾Ry nty ('jlf{z
ntzu`Zo8kmoz{ntfuw lb0W±
`.y|nph`¥nphyy nta|©tnªkZnphs¾lvRh
^
ntykmoqf|yhi jlntfUhwqnpl`.y§jlyh/jlf|zJ`m»km`.©t©t`.f7hi `.y¦{©phylv =ͱ
YOCREZ>EA1CDE(DJCN\[;]C_^`E5QaKFbcGEdNP<?Q3E;
d5fh
^
nªyºy`.kmoqf{zaozu`.©7h
^
`~|ioH5`.kmhntoqf½`Zhs´`Z`.f¨h
^
`By¦u½|yjlkm`.y/1jlf{zh
^
`~kmoqf¯|wq¦{i jxhnpoqf¨y|jlkm`-5nty zu`.ykmi np½`.z
½R¾j§Poq¦uijxi jla`Zh`Zi yhiWjlf{y§Poli a8jxhnpoqfcH
'
$*
'
#
e.
#
.$0}
ST
- 7
7/ g L
UV
jlf{z + # #
f7
# gh
# i X Jj# W .5lW0
]^
nªyaoRz{`.©kmoqfH`.kmh¦ui`.yh
^
jxh«h
^
`|jxihnphnpoqf |jxhk
^
`.ykmolii`.y oqf|z ho h ^
`{ioH`.kmhnpoqf ol§¥b
|©ªjlf{jxi8§jlkm`Zhy
|jxi jl©ª©p`.©ho«h
^
`nta8jxwl`©tjlfu`´/nph
^
jx{|jxi`.fUh/aolhnpoqfi`.yhi nªkmh`.zOho«hi jlf|y©tjxhnpoqf$vz{npl`Ziwl`.f{km`jlf{z¼iolhjxhntoqf$±~dgh
ntyBµfuo´f¼jlyh
^
`¥y nta|©tnp¯|`.zjH³fu`¥aozu`.©Ó±
YOCREZ>EA1CDEkKFbcGEdNP<?Q3EJ;
+?y¦{jl©t©p¾ j=aoli`²kmoqa|©p`Zh`²jH³fu`°aozu`.©/nty{i`Z§P`Zii`.z± /`Zi ` h ^ ` b
©tjlf{jxi«jxhk
^
`.yJol§¥y¦{i§Pjlkm`²jxi`²fuolh
jlfU¾Raoli `®y ¦u{oqy`.z8ho½`?|jxi jl©t©p`.©|hoh
^
`?nªa8jxwl`®|©tjlfu`?jlf{zh
^
`.npiBaolhnpoqf{yBjxi`®kmoqf¯fu`.zhoiolhjxhnpoqf|yjxi oq¦{f{z
h ^
`ol{hntkZjl©ºjH»untyjlf{z¼hohi jlf{y©tjxhntoqf¼ntf¼h
^
`¥§Pjlkm`Zh y?|©ªjlf$±
]/^
`kmoqf{yhiWjlntf7h?ntyzu`.y kmi np½`.zO½R¾Jjyn¹»O|jxi jla8`Zh`Zi y
l`.kmholiH
'
$* ' # . #
.$0}
ST 7
> 7/
UV
jlf{z + # # # i # g # #
# W
.5. 0
]^
`?jH³f{`?aozu`.©
^
jly½`Z`.f´ntzu`.©p¾¦{y`.z§PoliBa8olhnpoqfrͽ|jly`.zJy`Zwqa8`.f7hjxhnpoqf ¹lvRv|W$oliB§FoliBh
^
`?`.yhnta«jxhnpoqf
ol§zuoqa8ntf|jlf7h8aolhntoqf ol`Zih
^
`¼`.fUhnpi`nªa8jxwl` Rv/Rvlͱdgh8nty8kmoqf{y ntzu`Zi`.z jlyj wloRoRz hiWjlzu`¼ox¸·½`Zhs´`Z`.f
aozu`.©'kmoqa|©p`m»unph˾ jlf{z²aozu`.© `m³kZnp`.f{km¾ ͱd5f²y`Zwqa`.fUhjxhnpoqf[jx{©tntkZjxhnpoqf{y.vh
^
`8jH³fu`aoRz{`.© z{`m¯fu`.y?h
^ `
{iox¯ ©p`Jol§h
^ ` ¶
o´ nªf{yntzu``.jlk
^
y`Zwqa`.fUh8ol§?h
^
`jlyyoRkZntjxh`.z nta8jxwl`O|jxi hnphnpoqf$±
]^
`¼jlkZkZ¦{i jlkm¾ ol§?h
^
`J¯|`.©tz
`.yhnta«jxhnpoqf zu`Z`.f{z{yol½Rnpoq¦{y©p¾#oqf h ^ ` R¦{jl©tnths¾=ol§h
^ ` y`Zwqa`.fUhjxhnpoqf$±dg§?h
^
`kmoqf{ynªzu`Zi`.z i`Zwqnpoqf|y8jxi`¼hoRo
©tjxiwl`h
^
`.f=j y ntfuwq©p`jH³fu`JaoRz{`.©:a8j¾ ½|jlz{©t¾°i `Z{i`.y`.fUhy¨h
^
`a8olhnpoqf ol§/h
^
`jly yoRkZnªjxh`.z b
y¦ui §Pjlkm`l±
]^
`
|©tjlf|jxi nphs¾
^
¾Uolh
^
`.y nty:jxi`?ntf{zu`Z`.z«l`Zi¾8©tnpµl`.©t¾¨ho½`/npoq©tjxh`.zntfh
^
nty~kZjly`l± ®f«h
^
`?ol{oqynph`lvUy ntf{km`/¦{y ¦{jl©t©p¾fuo
z
kmoqfUhntfU¦|nphs¾U{¥½`Zhs´`Z`.f|jxhk
^
`.yBnty:a8jlntfUhjlntfu`.z8oqf«h
^
`/l`.©toRkZnph˾¨¯|`.©tz$vRya8jl©t©p`Zi:i`Zwqnpoqf{y(a«j.¾8©p`.jlz«ho¨ntf|jlkZkZ¦ui jxh`
aolhnpoqf `.yhnta8jxhntoqf$±
]^
nty¥nªf{jlkZkZ¦ui jlkm¾ okZkZ¦ui ynp§Bh
^
`«©tntf{`.jxiy¾yh`.a&ho ½`«yoq©pl`.z=nty¥½jlz{©p¾²kmoqf{z{nphnpoqf{`.z .ntf
i`Zwqnpoqf|y
^
jRntf{w«¦{f{np§Poli a ©ª¦{a8ntf{jlf|km`?§Poli/`m»ujla|©t`olinªfjxi`.jlyZv y¦{k
^
jlyoRkZkZ©ª¦{ynpoqfOi `Zwqnpoqf{yZv{´
^
`Zi`¥h
^ ` KNMO°nty
fuolh¥xjl©tntz jxhjl©t©"0W±
`.km`.f7h©p¾lv'jO½|©toRk µU´/nªy`yaoRolh
^
|jxi jla`ZhiWntk8aozu`.©*ntfUloq©pntfuwOntfUh`Zirͽ|©pokµ°i`Zwq¦{©tjxiWnp¬.jxhnpoqf
^
jly/½ `Z`.f kmoqf{yntz{`Zi`.z ¹|ͱd5f¼h
^
nty´oliµv h
^
`¯`.©tznty/kmoqf{yhi jlntf{`.z¼ho½ `©poRkZjl©ª©p¾jH³fu`oqf j8½|©pokµJ|jxi hnphnpoqf
jlf{zj?i`Zwq¦{©tjxiWnp¬.jxhnpoqf¨h`Zi a ntfh
^
`B|jxi jla`Zh`Zi(y|jlkm`nty'jlz{zu`.zntfoli zu`Zi'ho`.fu§Poli km`yaoRolh
^
fu`.yy'jlkmioqy y*|jxhk
^
`.yZ±
o´`Zl`Zi.v7h
^
`Bi`Zwq¦|©tjxi np¬.jxhnpoqf¨{iWnpoli kmoqf|yntzu`Zi`.z¨zuoR`.y*fuolh*jl©t©poN´=ho®`.jlynª©p¾y¦u| oli hz{n¹¸`Zi`.fUhjxi jla`Zh`Zi np¬.jxhntoqf{y
ol§*h
^ ` ¶
o´2¯|`.©tz± 6|¦uih
^
`Zi a8oli`lvh
^
ntyjx{{i oqjlk
^
nty/f{olhzu`m¯f{`.z
^
np`ZiWjxi k
^
nªkZjl©t©p¾Jjlf{z¼h
^
¦{y?nta|©tnt`.yBhokmoqf{y ntzu`Zi
a8n¹»h¦ui`®ol§*aozu`.©tyB´
^
`.fJh
^
`¥½|©pokµJntfUloq©pl`.y/y`Zl`Zi jl©aolhnpoqf|yolij8kmoqa8|©p`m»OaolhnpoqfO{i ox¯©p`l±
]^
`¥¦{f{µRfuoN´/f
fR¦{a½`Zi~ol§a8n¹»h¦ui`.y(kmoqaoqfu`.fUhy
^
jly:ho¨½``.yhnta«jxh`.z«´/nth
^
jlf
rÍhs¾R `?jl©pwloli nph
^
aLoliByoqa`?ol§nphy(xjxi ntjlfUhy
ͱ
+ -3$ H'-%$' !
`ZhJ¦{yJfuoN´¤y`Z`°aoli ` {i `.kZnty`.©p¾
^
oN´¤h
^
`.y`²z{n¹¸`Zi`.f7h|jxi jla8`Zhi ntka8oRzu`.©ªya8j¾ ½` `.a½`.z{zu`.z ´/nph
^
nªf jlf
¦{f{np¯|`.z
^
np`ZiWjxi k
^
nªkZjl©ºa8ntf|nta8np¬.jxhnpoqfOy k
^
`.a`¨ol`Zi¥kmoqf|yhi jlntfu`.z°kmoqf¯|wq¦{i jxhnpoqf{yy¦u½|yjlkm`.y 5Z±
`.kZjl©t©tntfuw«h
^
jxh
oq¦ui |¦uioqy`(nªyºho½|¦{nt©tzj
^
np`ZiWjxi k
^
¾ol§|y¦{k
^
y¦{½|y|jlkm`.yh
^
`:jxihnphnpoqf{y
^
j.l`Bho®yjxhnty§P¾®h
^
`§Foq©t©to´/ntf{w{iol`Zihs¾LH
'
$* $*
YA
H7 # 7
YA
#
.5.b 0
´ ^ nªk
^
`m»{i`.y y`.y/h
^
jxh !kmolii`.yoqf{z|yhoJj«y¦u½$z{ntRnty npoqfol§(`.©p`.a`.fUhy/ol§
YA
±
]^
nªyntf{z{¦|km`.y/jf{jxh¦ui jl©ºhi`Z`
yhi ¦|kmh¦ui`§Poli´
^
ntk
^ $[ntyBh
^
`¥jxi`.f7h/ol§$*±
]^
`kmoqf{yhi jlnªfu`.zOol{hnta«np¬.jxhnpoqf¼ntfp5 d5a ) ntyol½RRntoq¦{y©p¾`U¦|npHjl©t`.f7hhoh
^
`a8nªf{nta8np¬.jxhntoqfol§'h
^
`fu`Z´
`.fu`Ziwl¾J§¦{f{kmhnpoqfH
.+
hKLM 0 ? .:)
.+
0
KLM 0
| L#5-H- # #5- D-J4 D !& C #(!I#
zu`m¯f{`.z8ol`Zi /1Dv´
^
`Zi `.jly:h
^
`´~`.ntw
^
hyZvh
^
`?z{jxhjvujlf{zh
^
`¯|`.©ªz8ho¨½ `i`m¯fu`.z«i`.a8jlntf«h
^
`®yjla` .nÓ±`l±pvRz{`m¯fu`.z
oqfh
^
`Boli npwqnªf{jl©7wliWntzG70W±6uioqa h ^
nªy§jla8nt©t¾ol§|`.fu`Ziwl¾¨§¦{f{kmhnpoqf{y.vH´`jxi`fuoN´ jx½|©p`ho¥zu`m¯fu`oq¦ui(a8ntf|nta8np¬.jxhnpoqf
yk
^
`.a`jlyjkZjlykZjlzu` .P§Pioqa3ho 0ol§'ol{hnta8nt¬.jxhnpoqfJ{iol½|©t`.a8yBol§i `.z{¦{km`.z¼kmoqa©p`m»nths¾LH
. +
0 jxiw'a8ntf
\ _ _ .+
hKLM
YA
. )
YA
. +
YA
0
\
0 wwwmU .55= 0
´/nph
^
+
YA
±
]^
`B¯|`.©tz + / ©tnp`.y'oqf«h
^
`i`.z{¦|km`.zwli ntz ´ ^
`Zi`.jly(h
^
`/´~`.npw
^
hy:jlf|z8h
^
`/a«jlntfl`.©pokZnphs¾
kmoqaoqfu`.fUhyZvm ?,
YA
. )3
YA
. +
YA
0Wvjxi`8jxhhjlk
^
`.z hopv$´
^
jxh`Zl`Zih
^
`wli ntz²©p`Zl`.©x±
]^
`nªf{nphntjl©¯|`.©tz
h8
YA
8kmoqa8`.y/§Pioqa jlf¼`.yhnta8jxhnpoqf¼jxhj8kmoqjxi y`Zii`.yoq©t¦uhntoqfJoli§Fi oqa jwqnpl`.f¼nªf{nphntjl©tnt¬.jxhnpoqf$±
jlk
^
ol§$h
^
`.y`?y¦{kZkm`.yyntl`?a8nªf{nta8np¬.jxhntoqf{y*jxi`/|ioRkm`.y y`.z«ntf«h`Zi a8y~ol§nph`Zi jxhnpl`.©t¾i`Z´~`.ntw
^
h`.z©p`.jlyhyU¦|jxi`.y
jlf{z ja¨¦{©phnpwli nªz kmoqjxiWy`mrÍhoxrÓ¯fu` yhi jxh`Zwl¾ nty¼zu`Zl`.©pol`.zcH h ^
`#nªf{kmi`.a`.fUhO¯|`.©tz `.yhnta8jxh`.z2jxh ©p`Zl`.© . xv
)3
YA
.J2/
YA
0:ntyjlz{zu`.zho
YA
ho§Poli ah
^
`?fu`Z´ a8jlntfkmoqaoqfu`.fUh~ol§h
^
`l`.©pokZnph˾¯|`.©tz Zv . I0(nty:´Bjxi`.z
jlkZkmoli z{nªfuwq©p¾§Poli¥h
^
`kmoqa|¦uhjxhnpoqf[ol§~h
^
`y|jxhntjl©*jlf{z²h`.a8 oliWjl©(zu`Zi npxjxhnpl`.yjlf{z j¼fu`Z´Lntf{kmi `.a`.f7h¥nªy®h
^
`.f
`.yhnta«jxh`.zjxh/©p`Zl`.©H±
]^
ntyB{iokm`.z{¦ui`ntyi`Z`.jxh`.z¼¦{fUhnt©h
^
`®¯fu`.yh©p`Zl`.© 8ntyi `.jlk
^
`.z$±
]^
`8fu`Z´a¨¦{©phnpwli nªz `.f{`Ziwl¾²§P¦{f|kmhnpoqf{y
F a8j¾°½``.jlynª©p¾°z{`Zi npl`.z²§Pioqa h ^
`8oliWnpwqntf{jl©'oqfu` .=xr 0W±
]^
`Z¾
jxi`jl©ªyo8kmoqaoqy`.zOol§'hs´o«h`ZiWa8y 7h 7A .ED. 7F ´ ^
`Zi` 7A jlf{z 7F jxi `i`.y`.kmhnpl`.©p¾LH
A N
# P ; \ N MP
\
A
RT.$ .E
& c.·W0XW.
#
.$0O+ # . Z
.$/& M 0
F
.)A .
50 .5; 0
jlf{z
F N
^ # _ acPd
\ N
^
M_`\acPd
\
!FLLI`
.J . . # .$)0O+ #
0g .J ` . .. 0O+
0
F
.}F . X`(0m.
N
# P ; \ N
^
M_`acP#d
\
LLI`
.J
. . #
.$)0O+
#
0g .J
` . . #
. 0O+
#
0
F
.}F . X`(0
.5;: 0
´ ^
`Zi `Gj
#
? /ci jHV%ci7
#
Jntyh
^
`y`Zh¨ol§fu`.npw
^
½oli ntfuw¼ynth`«|jlnpiWyntf{kZ©ª¦{zu`.z ntf |jxhk
^ #
jlf{z
j #
? / i'jH T !
#
! Oh
^
`Oy`Zhol§/f{`.npw
^
½oli nªfuw ynth`|jlnti yyhi jlz{z{©tnªfuw !
#
jlf{z2 ! ±<8?©t©
oqyynp½©p` j
#
jlf{zBj
#
ynph`¥y`Zhy§FoliWa j|jxihnthnpoqfJol§Cj ±
`.z{¦{km`.zynph`y`Zh.h¦ui f{yBoq¦uh/ho«½``U¦|np{`.z´/nph
^
jf{`Z´1fu`.ntw
^
½oli
^
oRoz y¾Ryh`.a k ± ]^
`kmolii`.y oqf|z{ntfuwOfu`.npw
^
½oli ntfuwOjlnpiy`Zh´/nt©t©'½`zu`.fuolh`.z#½U¾*j ±Od5f
FHvu´`kmoqf{ynªzu`Ziz{n¹¸`Zi`.fUh
^
¾R `ZirÍ|jxi jla`Zh`Zixjl©t¦u`.y.vl!F?jlf|zBNv{z{`Z `.f|z{ntfuw¨oqfO´
^
`Zh
^
`Zih
^
`¥ynph`|jlnti yjxi`
ntf{y ntzu`j|jxhk
^
oli¥yhi jlz{z|©tntfuwnphy?½ oliWzu`Zi.±8©to´ xjl©t¦u`¨ol§:h
^
nty
^
¾U`ZirÍjxi jla`Zh`Zi¥ntf{y ntzu`¥`.jlk
^
|jxhk
^
.nÓ±`l±pvºj
i`.z{¦|km`.z8i`Zwq¦{©ªjxi np¬.jxhnpoqfJ0´nt©t©ujl©t©poN´ ¦{y:ho§j.loliBj©tjxi wl`Zi~kZ©tjlyy~ol§$jH³fu`?aolhnpoqf«nªf{kmi`.a`.fUhy:ntf|yntzu`B`.jlk
^
½|©pokµ
yntf|km`¥jl©t©h
^
`¥xjxi ntjx½|©t`.yjxi`h
^
`.f¼jl©ta8oqyh/zu`.kmolii `.©tjxh`.z$±
]^
`¥©tjlyhh`Zi a ol§D F kZjlfh
^
¦|y½`¥a8jlzu`¥fu`Zwq©tntwqnp½|©p`l±
"! ; ?A@M;DEC;>P:;D=:EA;DcC?GFOS
NB P$#
BON&%
b
;R@ =:H'# FO=
B
P:@Rd&(6EAH`@
JRB
?CSc FL@)6;RS`S V-; cC;R@
J
P:HTV-;Rc HR
=:EA;RHZP.H
R
HZ=:HTFLS
NB P$# ?ASTF&=:H
B3R
d
*
"RKJ FO@M;
BON P:;RQ?CSTFOP
Y
FOPM=:HZ=:H
B&R )IHZ=:E
Z\+ Z&\
VAS
BJX
@
]-,"\
=:?CP
R @ B
?C=.=
B
V-;D=:EC; @:F.#;
R
;>HTQLEV
B
P:E
BB
cK@0/"@ =:;1# FO@.=:EC;
B
P:H`QH
R
FOS
B&R
;
,32
@M;>;4
V6587:9
d