ISRN INRIA/RR--4739--FR+ENG
a p p o r t
d e r e c h e r c h e
THÈME 2
INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE
An Algebraic Cryptanalysis of Nonlinear Filter Generators using Gröbner bases
Jean-Charles Faugère
— Gwénolé Ars
N° 4739
Février 2003
Unité de recherche INRIA Lorraine
( $)*%),+- ( ).%/0-$
1325436-78:9;43<>=?2A@BC43DEGFH<>25IKJ
LNM/O:P 6)QG=
PSR
<T@U
VWYX>Z:[ \]_^a`>bYcd[%egfihAcgjcd[>e
[kljmneojpqesrut5Zv3fiegcowApq[
xCyzfn{|[kzr~}5xl}
~mi Y 3fiyk$Y[%y[TjWY[yjWY[b3i]`>5ycg[y~\nAi]_\Y* qmnhA[>r
>Yii VWYcgr~ qmn 3[y$ Yyz[>r[bHkr mibSmneghi[vqyzmicgj¡jyztH Ykzmnb¢mnegt5rcorfi£bqfibYegcdbq[>mny ¤qedk[>y~hi[>bY[ymkzfiyT¥
egcgbY[>miy~ruWYcd£¦klyz[hAcgruk[>y$fn£;ed[>bYhnkzWS§¨¤qe©kz[yz[>v5tmbqfib/edcgbY[Tmny$v3fHfAed[Tmny$£ªpqbqj'kzcdfAb¬«fi£)[>hiyz[[%®H¯°±²«³
cor~[TwHpYcdmied[>bAkzedt/[Trjycgv¢[T/v5tm´r[k¡fn£Cmneghi[>vYyzmicgj*[TwHpqmkzcdfAbqr¥$µSfAy[% qy[Tjcoru[>edtA¶qcd£N·¸cgr~kWY[:rucg¹[ fi£
hAcdA[bfipkz Ypk~vYcdkzr$kWY[>bº [*WqmKi[%mrt5ruk[>Z»fi£·¸mneghi[>vYyzmicgj¡[>wHpqmnkcgfibqrfi£-kzfnkzmie-[>hiyz[[*®A¯>°±²«³ cgb
§"mnyzcgmivYeg[>r>¥¼ trfieg5cdbYh½kWqcgr$rtr|kz[Z¾fn£[>wHpqmnkcgfibqr º [aj>mnby[Tjfi[>ymiedeGkzWY[* ¢fHrrcdvqed[acdbqc©kzcgmiesr|kmk[
¿
kWY[ru[Tjyz[k%Ài[>tÁafi£kzWY[´[>Hcoj[S¥^ayÂAvYbY[y%cor% Yyz[>jcgr[egtmib[ôjcg[bHk%kf5fieC£ªfiyrfieg5cdbYhSmiedhA[vYymncoj
rtr|kz[ZÄr>¥C$[>j[bHkegti¶¢i[yztÄ[ôjcd[>bAkamneghifiyzcdkWYZÄr
¿ÆÅÇÄÈ
T\TɪÁWqmKA[¡v3[[>bS YyfA ¢fHru[Tº$WqcgjWSmnyz[%ru[>i[>yzmie
fAyzY[yfi£lZÄmnhAbYc©kzpq[£Æmiruk[>y½kzWqmnbÊkWY[WYcor|kzfiyzcgj>mne¼ pqjW5v¢[>yhA[y½miedhAfiyzc©kzWYZ/¥ÌË[/rWYfºÍkWqmnk:º$cdkW
fAbYegt½m* 3fiegtHbqfiZcgmieYb5pYZv3[yfn£Gfipkz YpkNvqc©krCº [ljmib:yz[>jfi[>ycgbÄ 3fiegtHbqfiZcgmiekcgZ[$kWq[~cdbqc©kzcgmie¢rukzmkz[i¥
µfiyz[$ Yy[Tjcoru[>edt½º[~j>mnbÄrWYfºÊkzWqmkcgrN[bYfApYhiW:kfWqmKi[lαƧÏK³Cfipkz YpkNvYcdkzrNº$c©kzW´®ÄоÑÒ'ÓÔ
Õ×Ö º$Wq[yz[
Ø cgrNkWY[ab5pYZv3[y fn£Kmiycomnvqed[TrCfn£kzWY[¡¤qe©kz[yzcdbqh £ªpYbqjkcgfibs¥C}5pqy YyzcorucgbYhiegti¶A£ªfiymnege¢kWY[*r|kzy[TmnZ¾jcg YWY[>yzr
rzmkzcgru£ªt5cdbqh%^afAedc²ÙjiÚr;[TrucghibÄjycdk[>ycom*mnbq½¤qedk[>ycgbYh*£ªpYbqjkcgfibqr;£ªfipYbqcgbedcdk[>yzmnkpYyz[$º [£ªfApYbq:kzWqmk® cgr
Z½pqjW:ed[TrrkzWqmnb½kWY[$ qy[Tcgjk[T½v3fipqbqÛs£ªfAy;cdb¢r|kmnbqj[kzWY[~ÜscgegcYcgr)fi£3[>hiyz[[$ÝavYpkNm*rcdZ Yeg[~^ayÂAvYbY[y
jfiZ YpkmkzcdfAbqr rWYfº~r*kW¢mkcdkv3[WqmKA[>r%egcdÀA[´mS[hAy[>[ÄÞ/£ªpYbqjkcgfibs¥SCA[bßZfiyz[´rupqy YyzcorucgbYhiegti¶º[
rWYfºà[á 3[yzcdZ[bHkmnegedtkWqmnk~£ªfiyarufAZ[ [áYmnZ Yeg[>rlº[½jmnbSyz[>jfi[>ykWY[ cgbYcdkcomne)r|kmkz[ cdb¬ ¢fAedt5bYfAZ:comne
kzcdZ[½º$c©kzWfibYegt/§â"ãlfApk YpYk¡vYcdkzr>¥lä¡c©åG[yz[bHkamnkukmijÀr$WqmKA[%v¢[>[bcgZ Yed[>Z[bHk[T¶mnbq/º [ hicgi[ m
egcor|k~fi£-kcgZcdbqhÄ[á ¢[>ycgZ[bHk[TfAb/Zmib5t´y[Tmnercd¹>[*rcg¹[
¿
§çæéèiê:vYcdkzrÁr|kzy[TmnZ»jcd qWY[yr
ëSìHíGîzïð ñiò coY[>bcd[>eg´NwHpqmkzcdfAbqr
¿ò Á¶5µpYe©kzcdmiycomkz[~ ¢fAedt5bYfAZcgmie¢[TwAp¢mkcgfib¢r¶5^ayÂAvYbY[y
v¢mir[>r>¶5ledhA[vYymncoj yt5 kmnbqmiedtrcgr>¶qfiZ Ypkz[y~ledhA[vYymY¥
óCô5õªö3÷øzôYù)úsõ¦ûÌüýúþKøÿö üsøzõªýúsõ¦û
ö )þTönûü3þ
ô5õªö3÷û)øÿö ü-øÿ Cú
( ).%/
[kmnykcojeg[ Yyz`>r[bHk[pYbY[´jyt5 kmnbqmiedtr[Ämneghi`vqycowHpY[:Y[>r%yz[hAcgrukyz[>r¡¤qedkyz`>r% ¢mny%pYbY[
£ªfAbqj'kzcdfAb×v¢f5fAed`>[bY[bqfib egcdbq`>mncgyz[i¥¡b× 3[pkZ:f`>edcor[ypqb y[>hicor|kzy[SegcgbY`>micdyz[¬[Skmncgedeg[§¾¤qe©kzy`
¢mny~pYbq[%£ªfibqjkcgfibSv3f5fieg`[bq[½« [[>hiyz` ®A¯>°±²«³ qmiylpYbrtr|kzXZ[Ú`>wHpqmnkcgfibqr~miedhA`vYyzcowApq[>r>¥NxCegpqr
[áYmij'kz[Z[bHkT¶5rcG· [>ruked[abYfiZ½vYyz[¡[avYcdkzr[aegm:ru`TwHpY[bqj[¡[*rfiykcg[lfibfivkzcd[>bAkpYb/rutrukX>Z:[a[*·
`TwHpqmkzcdfAbqrl[:[hAy` kfnkmne)®A¯>°±²«³~[b¬§éKmiycomnvqed[Tr¥~Nby`TrufAedmibAkaj[½rtr|kzXZ[fAbSy[kyzfipYA[ e?Ú`kzmk
cgbYcdkcomnespyz[hicorukyz[¡jnÚ[>ruk½Ycdyz[*egm:jeg`%ru[Tjyz[k[A¥Ü-[>rvqmAru[Tr[ ^ayÂAvYbY[yrfibHk pqbfApkcgeGkyzX>r[ÃÄj>mij[
3fipqy~y`TrufApqyz[¡eg[>rlrutrukXZ[Tr~mneghi`>vYycowHpY[>r>¥C$`Tj[ZZ[bHkT¶qpYbmiedhAfiyzc©kzWYZ[
¿²ÅÇ
Á[j>mneojpYesY[ vqmir[>r
Y[ ^ayzÂivYbY[>yml`k` Yyzfi 3fAr`NfibHk-e?Ú[ôjmAjcdk`N[Tr|k)[N qedpqrcg[pYyr-fAyzYy[NY[Nhiymnb¢[pYyrupY 3`yzcg[pYyz[lj[eged[
Y[$e²ÚmneghifAycdkWYZ[WYcor|kzfiyzcgwHpY[~Y[~¼p¢jWHv3[yzhi[>y>¥¡bZ:fAbHkyz[wHpsÚcge¢rpÃkNÚpqbÄbYfiZ½vYy[ 3fiegt5bYfiZcomneq[
vqc©kr* ¢fApYy*y[kyzfipYA[yle?Ú`kzmnk%cdbYcdkcomne)[>b¬kz[Z qr* 3fiegtHbqfiZcgmie²¥xCedp¢r* Yy`Tjcoru`>Z[bHk>¶fAb¬ 3[pk%ZfibHkyz[y
wHpsÚcgerpÃk:[αƧ ÏK³%vYcdkzr½[rfiykcg[mKi[Tj:®"Ð ÑÒ'ÓÔ
Õ Ö
f Ø [>rukeg[bYfAZvYyz[´[´mnyzcomnvYeg[>r Y[´egm
£ªfAbqj'kzcdfAb[:¤qedkymnhA[i¥:äl[ZÄmnbYcgXyz[rupYyz Yyz[bqmibHk[i¶G 3fipYy*kzfipqraeg[>r*hA[bY[>yzmnk[pqyzrl qru[>pqfSmneg`fAcdyz[>r¡[k
rzmkzcgru£ÆmncorzmnbHkeg[>rjyzcdkXyz[>r [%^afiegcÆÙjlwHpY[abYfipqrmKAfibqrNk[Tr|kz`>r>¶HbqfipqrmKifAbqr;kzyfApYi`apYb[hAy`a®[bqjfiyz[
qedpqr* 3[kzc©kwHpY[´j[kk[v¢fAybq[iÛ* qmny%[á[Z Yeg[: 3fipqy ÜscgedczK\fibkyzfipYA[Y[>ra£ªfib¢j'kcgfib¢r%[Ä[hAy`:Þq¥
NbqjfAy[ Yedp¢rrpYyz Yyz[bqmibAkT¶KbYfipqrZfibHkyzfib¢rs[á 3`yzcdZ[>bAkmneged[>Z[bHkwHpY[ ¢fApYy)j[ykzmicdb¢r-[á5[>Z Yed[Tr-bqfipqr
3fipqifib¢r$y[kyzfipYA[y$[ÃÄj>mij[Z[bHkle?Ú`kzmnklcdbqc©kzcgmiemKA[>j*ru[>pYeg[Z[bHka§ âÊã¡vYcdkzr¡[½rfiykcg[i¥$ä¡c©åG`yz[bHk[
mnkukmiwHpY[>rNfibHk`k`¡cdZ YeomnbHkz`[>r[kbYfApqrYfibYbYfAbqrpYbY[aedcor|kz[¡[av3[bqjWYZÄmiyÀrNmKA[>j~Y[>rkzmicdeged[TrNyz`[>edeg[>r
¿
§Êæ×èAê½vqc©krzÁ¥
ð
T
î
xfAedt5b AZ[>raZpYedkcgmnyzcd`Tr¶s¼mAru[TraY[Ä^ayzÂivqbY[yT¶yt5 kmnbqmiedtr[½miedhA`vYyzcgwHpY[A¶- mneojpYe
qfiyzZ[e?¥
) *
½-) +N
}5kyz[>mnZ jcd qWY[yr¡miy[:hi[>bY[ymnegegt£ÆmAr|kz[yakWqmib¬vYegfjÀjcg YWY[>yzracgb¬Wqmiyzºmnyz[i¶Gmnb¢bY[>[> megfº ¢fº [y
jfibqrpYZ kzcdfAbs¥CYpYykWq[yzZ:fAy[A¶5vYpåG[yzcdbYhÄcoregcdZcdk[>/mibqcdbSrc©kzpqmkzcdfAbqrº$WY[yz[akymnbqrZcgrzrcdfAb[yzyzfiyr
j>mnb/fjjpYykWY[[yzyfAy qyfA qmnhHmkcgfibcgr~edcgZc©kz[>¥~fibqrco[y~mÄrt5bqjWYyzfibYfApqrr|kzy[TmnZ0jcd qWY[y~cgb/º$WYcojW
kzWY[Ài[>trukyz[>mnZ/¶TkWq[ qegmicdb ?k[á5k>¶imibq%kzWY[$jcg YWY[y ?k[á5kCmnyz[r[>wHpY[>bqj[Trfn£¢vqcdbqmiyt YcdhAc©krÛkzWY[fipkz Ypk
r[>wHpY[>bqj[fn£$kWq[ÀA[t rukyz[>miZ hA[bY[>yzmnkfiyT¶±,+-?³.-0/1cor½mAY[TÌvYcdk|º$cgr[Äkf¬kWY[ Yeomncgb ?k[á5kru[TwApq[bqj[
±23-³!-/41H¶Y YyzfpqjcdbYhkzWY[ jcg YWY[>y ?k[á5k±5 -³!-/41H¥VWY[%ÀA[t r|kzy[TmnZ¾hi[>bY[ymkzfiycor$cdbqc©kzcgmiedcg¹[TkWYyzfipYhAW
m/r[>jy[k*ÀA[t76ʶ-mnb¢Wq[bqj[i¶s[TmijW Ài[t86 º$cgegeNjfAyyz[>r ¢fAbqSkzfSmnb fipkz Ypk½r[>wHpY[>bqj[A¥Ä}cdbqj[kWY[
ÀA[tcgr~rWqmiy[Tv3[k|º [[>bkWY[%kzyzmibqrZ:cdkukz[ylmibqkWY[y[Tj[cgi[>y>¶5kzWY[ yz[>j[cgi[y~j>mnbS[TjyztH Yk~vHtmiYYcdbYh
kzWY[%fipYk Ypk~fi£-kzWY[%Ài[>trukyz[>mnZ¾hA[bY[>yzmnkfAyNkzfkWY[ jcd YWq[y ²kz[á5k>¶fAvkzmicdbYcgbYh:kWq[%Z:[TrrzmnhA[ar[>wHpY[>bqj[A¥
VWY[ÄhAfAmiecorakf/[ÃÄjcd[>bHkegt¬ Yyzfpqj[:ymnbqfAZ ?egf5fiÀ5cdbqhr[>wHpY[b¢j[>rakzWqmk miy[Ämir:9ucdb¢cgrukcgbYhApYcgrW
mivYeg[; mir$ 3fArzrucgvYeg[%£ªyzfiZ,kzypqedtyzmibqfAZ0r[>wHpY[b¢j[>r>¥~eoruf¢¶£ªyfAZmÄjyt5 kmnbqmiedtrcgr 3ficgbHklfn£;5cg[º%¶¢m
hAf5f5rukyz[>miZ jcg YWY[>yNrWYfipYeo:v¢[ly[Trucor|kmnbHkNmnhHmncgbqruk;Yc©åG[yz[bHkNÀ5cgbqfn£mkkzmijÀrCmArCm=<
>&4?@ABCDFE
,DG
<n¥ qfiyÄmßrut5bqjWqyfAbYfipqr:rukyz[>mnZjcd qWY[yT¶m À5bYfº$b Yeomncgb ²kz[á5kÄmkukmijÀÌcor[>wHpYcgmneg[bHkkf kWY[
qyfAvYed[>Z fn£C¤¢bqcgbYhkWY[:Ài[>tH6kzWqmk% Yyzfpqj[mhicgi[b¬fipkz Ypk%Ài[>trukyz[>mnZI+1GJ+
Ô
JLKMKLKLJ+NPO
Ô
¥½
jfiZZfibßZ[kzWYffiegfihAt¬£ªfAy Yyzf5YpqjcgbYhymnbqYfiZ ?egcgÀi[Äru[TwHpY[bqj[>rcgr kfpqr[´egcdbq[>mny£ª[[TvqmijÀ ruWqc©£¦k
yz[hAcgruk[>yzr>¶iÜ)}Y~r¶5º$cdkW´eg[bqhnkW´§"mirNvYpYcgegcgbYh vqedfjÀrCcgbcdå3[>y[>bHkºmKt5rNmnbqÄm*¤¢e©kz[yzcdbYh£ªpYbqjkcgfibqr
«"kzf¬vYyz[>miÀ kWY[edcgbY[Tmnyzc©k|tßfn£lÜ;}~r>¥ßqpYykWY[>yZfiyz[i¶kzWY[r[>jy[k½ÀA[tQ6 cor:fn£¦k[>b"jWYfHru[>bßkf v¢[
kzWY[ÄcgbYc©kzcgmieNrukzmkz[Äfn£ kWY[y[>hicor|kz[yr¥Ë [´jmnbÌ[Trjycgv3[Äfn£$rupqjWßmSjyzt5 kfHrutruk[>Z º$WY[bÌ· vYcdkzr%fi£
kzWY[´yzpYbYbYcgbYh?ÀA[tcor hAcdA[bßv5t mibçmneghi[vqyzmicgjrt5ruk[>Z fi£$· [TwHpqmkzcdfAbqr%fn£~[>hiyz[[´®H¯>°G±?«³'¥3RbÌkWY[
yz[>ruk~fn£kWq[ qmn 3[yTS¡±²«Jz·¬³$[>bYfnkz[*kWYcorlmiedhA[vYymncoj¡rtr|kz[Z/¥¤qyzruklmnb¢fAv5Hcgfip¢ry[TrupYedklcorkW¢mk~cd£
· æ §ÏUVW@XY¶KkWq[b kzWY[ y[TrufAedpkzcdfAb%fn£YkzWY[jyt5 kzfArtr|kz[Z cgr 3fiegtHbqfiZcgmieAcgb½§ ÏUVW@XY
¿
Zfiyz[N qy[Tjcoru[>edt
αƧ[ZYÏUVW@XY|³ º$WY[yz[]\¨Ð_^:cgr kzWY[%[á 3fibY[>bAk~fi£-kzWY[ jfAZ: qed[á5cdk|t´fi£egcdbq[>mny$miedhA[vYymAÁ¥
VWY[*ZÄmncgb/mkukmijÀr fibr|kzy[TmnZ»jcd YWq[y$mnyz[%fAyyz[eomkzcdfAbmnb¢¢miruklfAyyz[eomkzcdfAb´mkkzmijÀr È`
¶
`
É?¥
VWq[l[>rzr[bHkcomne¢ Yycgbqjcd Yeg[~fi£kWY[*mkkzmijÀ:v5t:jfiyzy[>egmnkcgfibcorCkzf½mirzrcdZcgegmnk[$kzWY[lyz[>r[>miyzjWfn£GkzWY[¡cgbYcdkcomne
rukzmnk[¡fn£-m yz[hAcgruk[>yCkzf:m YyfAvYeg[ZÍfn£-jfiyzy[Tj'kcgfibÄfi£s[yzyfAyzr>¥
ò
[bqj[¡º [lcgZÄmnhAcdbY[lkWqmnkNkzWY[¡fApk qpk fi£
kzWY[~bYfAbYegcdbY[Tmny)¤qedk[>yNhA[bY[>yzmnkfiy;yz[>rpYedkzr)£ªyzfiZ kWY[~kymnbqrZcgrzrucgfib: Yyzfpqj[Tv5t½m*yz[hicoruk[y)kzWYyzfipYhAWm
bqficorutjW¢mnbYbY[>e²¥;VWY[%[>yyzfiyrº$WYcgjW/fjjpYy~pYyzcgbYh:kWYcorkymnb¢ruZcorrcdfAbjfiZ[*cdb£Æmijk$£ªyfAZ¾kWq[*¤qe©kz[y
£ªpqbqj'kzcdfAbs¥VWY[: YyzfivqmivYcdegcdk|tfi£N[yzyzfiylcor¡kW5pqraWYcghiWY[>y¡cd£NkzWY[½k|ºfru[TwApq[bqj[>r>¶GkWY[:fipkz Ypk*fibY[mnb¢
kzWY[:y[>hicor|kz[ylfAbY[i¶smiy[:ruegcghiWHkegtSjfiyzyz[eomk[T¥*lr¡kWY[r[>wHpY[b¢j[:hi[bq[ymk[T/v5tSfibYegt/fibY[:y[>hicor|kz[y¡cgr
rukyzfibqhiegty[TpYbqqmnbHk>¶º[´j>mnbÌyz[>jfibqrukcdkpkz[Äc©k½pqrucgbYh¬mibÌmneghifiyzcdkWYZ fn£~[>jfcdbqhSº$WYcgjWçjfiyzy[Tj'kr
kzWY[%[yzyzfiyrNfi£kzyzmibqruZcorrcgfibfi£mjf[ba;¥
k;kzWYcgr;kcgZ:[A¶nkzf*kWY[$v3[>rukCfn£3kWY[~mipkWqfiyrÚrÀHbqfº[>eghA[i¶KkzWY[$fibYegt fikWY[>y; YpYvYegcgrWY[T:mibqrucgZcdeomny
mnkukmij˼mir~ Yy[Tru[>bHk[>/v5tSfipYykfAcgr
È
É¥~VWY[ co[TmÄcgr~kf cGFLEBdeD ¶Gº$cdkW¬mhAfHf/ Yyzfiv¢mnvYcgedcdk|ti¶
kzWY[´¤¢e©kz[yzcdbYh£ªpYbqj'kzcdfAbÌpqr[>ÌcgbçV-ftAfjyztH Yk vHtßmSegfº¾[hAy[>[Ä ¢ft5bYfAZ:comnemnbqßkzf¬mn q YedtkWq[gf¡Ü
miedhAfiyzc©kzWYZ
È
KÉs£ªfAylrufAed5cgbYh:kWY[ miedhA[vYymncojarutruk[Z/¥NVWq[%Z:[kWYf Yyz[>r[bHk[Tcdb
È
É-cor$º [egesmiYmi k[T
£ªfAykWY[ Vftifjyt5 k[áYmnZ Yeg[*vYpklf5[TrbYfnklr[[>Z¾kfv3[ mhi[bq[ymneGZ[kWqf5s¥
R b kWqcgr% ¢mn 3[y º [ Yy[Tru[>bHk%m/hA[bY[>yzmie;mnbq [ôjcd[>bAk Z[kWYfkf/¤qb¢¬kzWY[ÄcgbYc©kzcgmieNrukzmkz[Äfn£ kWY[
yz[hAcgruk[>y>ÛNº[ rcdZ Yegt/jfiZ YpYk[m^ayzÂivqbY[y~v¢mircgr$fi£Cmneghi[vqyzmicgj*rt5ruk[>ZhS¡±?«J·¬³¥~VWY[cdôjpYedk|tcgr
kzWY[bkzf:[>mnegpqmkz[¡kzWY[ jfAZ Yed[ác©k|t´fi£kzWYcor~jfAZ: qpkzmnkcgfibs¥
¡rZmib5t fikWY[>yÄmneghifiyzcdkWYZÄr>¶N^ayÂAvYbY[y:vqmAru[Tr½miedhAfiyzc©kzWYZÄrv3[WqmKA[Z½pqjWÊv3[kk[>y:cgb¨ YyzmAj'kzcgj[
kzWqmnb×cgb×kzWY[º fiyr|kj>mir[i¥~eghi[>vYymncojSrutruk[ZÄrjfiZcgbYhߣªyzfiZ bYfib×egcdbq[>mny¤qedk[yhi[>bY[ymkzfiyrÄmnyz[
k|t5 Ycojmie~[áYmiZ: qed[TrÛSkzWY[¬jfiZ Ypkmkcgfib fi£ ^ayzÂivqbY[yÄvqmAru[TrÄfi[>y
Õ
¶WqmAr´mnb mArut5Z kzfnkcoj/º fiyr|k
j>mir[:kcgZ:[v¢fApYbq º$WYcojW cor%[á5 3fibq[bHkcomne?¶-º$WYcgeg[Äc©kr yzpYbYbYcgbYh/kcgZ[Äcgr v¢fApYbq[TßvHtm/edfº [hAy[>[
3fiegt5bYfiZcomneAcdb%kzWY[C qmiyukzcgjpYeomnyj>mir[;fn£qrukyz[>miZ hA[bY[>yzmnkfiyT¥
ò
[>bqj[A¶K[i[>b%c©£YA[yzt¡[ôjcg[bHkmneghifAycdkWqZr
£ªfAyjfAZ YpkcgbYh¬^ayzÂivYbq[y vqmAru[Tr mnyz[bYfºÍmKKmicdeomnvqed[
¿²Å
Ç È
T\KɦÁ¶kzWY[ymKº$vqmAjÀfn£~^ayÂAvYbY[>y vqmir[>r
miedhAfiyzc©kzWYZÄr cgr kzWqmk$kzWY[ jfAZ: qed[á5cdk|t´cor _( D CDCcFL,cB ¥
Ë [W¢mKi[r[[>b%kW¢mnb kzWY[ Yy[>5cdfApqrskzycg5cgmieAv3fipqbq:αƧ[ZÏUDVMWXMY|³[> ¢[>bqYr)r|kzyfAbYhiegt*fib%kzWY[[hAy[>[
fi£skWq[*miedhA[vYymncoj$bYfAyZÄmieq£ªfAyZ¾fi£)«¥;¼ pk º [*jmnbmneoruf½y[> Yyz[>r[bHkNkzWY[*v¢f5fieg[>mib´£ªpYb¢j'kcgfib/«/v5tÄfibY[
fAy%ru[>i[ymne F,4 d « N
º$WY[yz[Ä·
X
¶mnb¢
X
mnyz[½ 3fiegt5bYfiZcomneorafn£ Y[hiyz[[®/eg[>rzrakWqmib
®H¯>°G±?«³'¥çµSfAy[ Yyz[>jcor[egti¶Cº [ qyfA[ÄkWqmnk´® Ð Ñ ÒÓÔ
Õ Ö
º$WY[>y[ Ø cor½kWY[b5pYZv3[yfi£lmnyzcgmivYed[Trfi£
kzWY[¤qedk[>ycgbYh£ªpYbqjkcgfibs¥qyfAZ kWqcgr>¶cd£º[WqmKA[· æͧÏÄfipkz Ypk vYcdkzr>¶-kzWY[b kzWY[^ayÂAvYbY[>y%vqmircgr
jfiZ YpkmkzcdfAbyz[>p¢j[>r kzfÄrucgZ Yed[%egcgbY[>miy~mneghi[vqyzmq¶Hrfº[*¤qb¢mjfiZ Yeg[ác©k|tfn£;αƧ[ZYÏT³¥
Ë [WqmKA[kzfçZÄmnÀA[/mÌj>mnyz[£ªpYe¡cgrukcgbqjkcgfib×v3[k|º [[b¨kzWY[^ayzÂivYbY[>yjfAZ Ypkzmnkcgfib fn£]S¡±?«J·¬³
mibqkWY[´jfiZ YpkmkzcdfAb fi£kzWY[Äyz[ Yyz[>r[bHkzmnkcgfibß«
N
º$WYfHru[Ä qycgZÄmnyztS YpYyz ¢fHru[Äcor*kf/[>Kmiedp¢mk[
qy[Tjcoru[>edtÄ®
¿
mibqkW5pqr$·¬ÁC£ªfiy$m: qmnykcojpqegmiy«¥;VWYcor Z:cghiWHk$v3[*jfib£ªp¢rucgbYhrucgbqj[¡kWq[*jfiZ YpkmkzcdfAb
fi£-·
X
mnbq
X
cormiegrf%kzWY[¡yz[>rpYedkfi£
C
^ayÂAvYbY[yvqmircorjfiZ Ypkmkcgfib-¥
ò
fº[>i[>y;kWYcorru[TjfAbq
^ayzÂivqbY[y*vqmArucor%jfAZ: qpkzmnkcgfib
¿
kz[>jWYbYcojmiedegt¬m/vqmArucor*fn£kWY[cg[Tmne;fi£ yz[eomkzcdfAbqrafn£~«Áacgr*A[yzt[>mArut
mibq/WqmAr$kfv¢[:fibY[fibYegtfAbqj[ £ªfiylmÄhAcdA[b¬«¥~VWY[ ¤qyzruk¡jfiZ Ypkmkcgfib¬^ayzÂivqbY[y~cor$kzWY[½Yc©Ã´jpqe©k
¢mnyk$mibqZpqruk~v¢[ YfibY[a£ªfiy$[>i[>ytÄhAcdA[b/ru[TwApq[bqj[afi£fApk qpk~vYcdkzr>¥
l£-jfipYyru[$º [$WqmKA[kfZÄmiÀi[~r[i[>yzmieYjfAZ: qpk[>yrcdZ½pYegmnkcgfibqrCkf D kWY[l Yy[>5cdfApqrC[Tr|kzcdZÄm
kzcdfAbs¥cgyr|k%º [:W¢mKi[jfiegeg[>j'kz[> megcor|k fi£ rukyz[>mnZ jcd qWY[yr%rmnkcor|£ªt5cgbYhS^afiegcÆÙjiÚr*[Trucghib jyzc©kz[yzcgmmnb¢
¤¢e©kz[yzcdbYh£ªpYbqj'kzcdfAbqr%£ªfApYbqÌcgbÌegc©kz[ymkpqy[
È
¶N>Y¶¶;5¶
`
¶N>É¥Yfiy:mnegeCkzWY[´[áYmiZ: qed[Tr º [Ä£ªfipYb¢
kzWqmkkWY[*[>hiyz[[¡®½corZ½pqjW´eg[>rzrCkzWqmnb´kWY[¡kWY[>fiyz[kzcgj>mneqv3fipqbq
¿
mnbqmnegº mKtr;eg[>rzrCkzWqmnbÞ £ªfAymnege3kWY[
[áYmnZ Yeg[>rÁ'¥)VWHp¢rCº [l[>rukzmivYegcgrWkWqmnkC£ªfiy m yz[>mArufAbqmnvYeg[b5pYZv3[yfn£shicgi[>bfipkz Ypkvqc©kr
¿
rmKtru[>i[>yzmie
À5v5tHk[TrzÁº [ jmnbyz[>jfA[y [ôjcg[bHkzedtkWY[ r[>jy[kÀA[tÄ£ªfAy$y[Tmnesrcd¹>[%r|kzy[TmnZ»jcd YWq[yr
¿
i:vYcdkzrÁ'¥NCi[>b
ZfAy[~rpYyz YycorcdbYhAedtA¶iº [lrWYfº [á ¢[>ycgZ[bHkzmiedegt½kWqmnkC£ªfiy rufAZ:[lfn£kWq[l[áYmiZ: qed[Tr;º[¡jmnby[Tjfi[>y)kWY[
cgbYcdkcomne-rukzmnk[*cgb 3fiegt5bYfiZcomneGkzcdZ[%º$cdkW/fibYegt§¬âÊã$fipYk Ypk~vqc©kr¥
VWYcor ¢mn 3[y cor%fiyzhAmibYcg¹[> mir%£ªfiegedfº~r>¥}5[Tj'kzcdfAbÌ\/Y[>rzjyzcdv3[>r%bqfibYegcdbq[>mny ¤qe©kz[y hA[bY[>yzmnkfAyzr*mnb¢
kzWY[cgy) Yyzfi 3[ykcg[>r>¥}5[Tj'kcgfib:lcgbHkyzfpqj[Tr^ayzÂivqbY[yvqmir[>r)mibq vqmArucojC qyfA ¢[>yukzcd[Tr¥)}5[>jkcgfiba Yyz[>r[bHkzr
kzWY[Äymkcgfib¢mne)y[> Yyz[>r[bHkzmnkcgfibfi£ v3f5fieg[>mnb£ªpYbqjkcgfibqr%mibq£ªfjpqr[>r*fAb jfiZ Ypkmkcgfib¢mneCjfAZ Yed[ác©k|t
v3fipqbq:fn£GkWY[~mnkukmijÀG¥)}[>j'kzcdfAbahicgi[>r;m*[kzmicdeg[>egcgrukCfn£GyzpYbYbYcgbYh?kcgZ[>r)£ªfAyCZÄmnb5trukyz[>miZ jcg YWY[>yzr
º$WqcgjW jfAb¤qyzZ¸kWY[/kzWY[fAy[kcojmne$mi Y YyzfAmijW-¥"}5[>jkcgfib jfiZ qmiy[TrfApYyÄmkkzmijÀʺ$c©kzW¨jfiyzy[>egmnkcgfib
mnkukmijÀr¥;}5[Tj'kcgfib ½ YyfA ¢fHru[TrmibYfnkzWY[y$rukymkz[hitGÛ£ªfiy$m¤Yá[>r|kzy[TmnZ,jcg YWY[>y$jfiZ YpYk[%mrut5Zv3fiegcoj
^ayzÂivqbY[yCv¢mircgr;cgbm* Yyz[>jfiZ YpkmkzcdfAbÄ YWqmir[AkWq[bkWq[lcgbYc©kzcgmie¢rukzmnk[lj>mnbÄv3[~£ªfipqbqi[>yt½[ôjcg[bHkegt
v5trpYvqrukcdkpYkcgbYh´mijkpqmieKmiedpq[>rfn£kWq[%ypYbqbYcdbqhÀi[tÄcgbkWY[%hA[bY[>ycoj*^ayÂAvYbY[y$v¢mircgr>¥
! $%&" ( $%%"! $-'
Ë [*[>rzjyzcdv3[avYycg[#¢t´mbYfAbYegcdbY[Tmny¤qedk[yhA[bY[>yzmnkfiyT¥ Rk$corjfiZ 3fAr[>£ªyzfiZ,m:Ü-;}àmnb¢m%¤¢e©kz[yzcdbYh
£ªpqbqj'kzcdfAbs¥;Ë[%yz[£ª[>ykf
È
i¶¢\TÉ-£ªfiy£ªpYykWY[>y~[kmncgegr>¥
!"#$% #'&()*+-,
Ü-[k/.v3[Smnb¨cdbHkz[hi[>y>¶Nº[/[¤¢bY[SÜ-;}fibÊkWY[/¤qbqc©kz[¤¢[eo10Y¥¨egcdbY[Tmny£ª[>[>vqmAjÀçruWqc©£¦kÄyz[h
coruk[y½ Yyzf5Ypqj[Trm¬r[>wHpY[>bqj[A¶32 54 1 J4
Ô
JLKLKMK¶Crzmkcoru£ªtHcgbYhSkzWY[egcgbY[>miyyz[>jpqyyz[bqj[´yz[eomkcgfib-¶6487
9':
;<
Ô 5 ; 4=7 O ;
J+>@?§ º$WY[>y[§ cor:kWq[eg[bYhikW¨fn£~kzWY[SÜ-;}%¶&5
;BA
C0¬£ªfAyED GFJLKLKMK J§l¶Nmnb¢
4-
A 0 JHI?¨êq¥
VWY[ §×rukzmihi[Tr¶J 7 ±K4 7 J4 7
ÓÔ
JLKLKMK J4 7 Ó : O Ô
³¶qcor$jmnegeg[>/m cDD
fi£kzWY[ ruWqc©£¦k~yz[hAcgruk[>y~mnbqº[
bqfnk[ML ±NJ 7 ³O7
< 1
kzWY[Är|kmkz[r[>wHpY[>bqj[A¥Ë [´[¤¢bY[:kWY[
c
cG
<
Cd
kzf/v¢[/PRQ$±KS³
F3T 5 Ô
SUT 5 Õ S Õ
TWVXVYVZT 5 : O
Ô\[
: O Ô T35
: S :
¥;VWY[l¤qyr|k§Ìfipkz Ypkrut5Zv3fieor>¶$41GJ4
Ô
JLKLKMK J4
: O Ô
¶mnyz[
cgbYcdkcomnegedtedfHmi[T¬cgbHkfkWq[´Ü-;}%¶-kWY[Tru[ÄrtHZ½v¢fAegr%miy[Äj>mneged[TkzWY[
BCB cDD
¥VWYcor*cgr miegrfkWY[
r[>jy[k$Ài[tfn£-kzWY[ Ü-;} ¥
VWY[ÄegcgbY[>miy%y[TjpYyzy[>bqj[:v3[k|º [[b kzWY[´r|kmnhA[>r*cgZ: qedcg[>r myz[eomkzcdfAbv3[k|º [[>b jfibqr[>jpkcgi[Ärukzmkz[iÛ
J 7
ÓÔ ']^J
7
º$Wq[yz[_] cor kWq[ jfiZ qmibYcgfibZmnkyzc©áfn£`PRQ¥
VWY[:ru[TwHpY[bqj[>rL aJ 1 JbJ
Ô
JMKLKMKl Yyz[fpqj[>v5t/edcgbY[>miy$£ª[[TvqmAjÀyz[hAcgruk[>yzr$W¢mKi[%ZÄmnb5tcdbHk[>y
[Tr|kzcdbqh½ Yyzfi 3[ykcg[>rrpqjWmArmA[yzt:egfibqh½ 3[yzcdfcojcdk|ti¥ R £kWY[a£ª[[TvqmAjÀÄ ¢fAedt5bYfAZ:comnecP
X
cgr YyzcgZ:cdkcgi[
kzWY[% 3[yzcdfcgr.
:
TFi¥
VWY[ZÄmncgbßyzmKº$v¢mijÀº$c©kzW Ü)}Y r[>wHpY[>bqj[Tr¡corakW¢mk%c©£ º[mnyz[:hicgi[bmr[>wHpY[>bqj[:fn£ §àjfib
r[>jpkcgi[½fipkz Ypk%rut5Z½v¢fAegr>¶3kWY[>bs¶spY[½kfkWY[:edcgbY[Tmnyzc©k|tA¶3º [º fipqegj>mneojpYeomkz[ kzWY[½fApk qpk*rt5Zv3fie
mnkmnbÌmnyzvYcdkymnyztkcgZ:[cdbqrukzmibqj[A¥}5f¢¶-fibq[´jmnbqbYfnk pqr[´mZÄmácdZ½pYZ ?eg[bqhnkWÌÜ)}YYcdyz[>jkegtmir%m
ÀA[t r|kzy[TmnZÍhi[>bY[ymkzfiyT¥
d e-f"hg Efifjgk 3hbl=%f"
mlfibedcgbY[>miy¡v3f5fieg[>mibS£ªpYbqjkcgfibqr>ÚG YpYyz ¢fHru[:cdbÀi[>trukyz[>mnZhi[>bY[ymkzfiyr$corlkzfWqcg[½kWq[½egcdbq[>mnyzcdk|tcgb
kzyfp¢j[>v5tÄkWq[ Ü-;}~r>¥C v¢f5fAed[Tmnb£ªpYbqj'kzcdfAb/cgr~m½£ªpYb¢j'kcgfib«on
Ò
Õ/p Õ ¥
qyfAZ0mnbmiedhA[vYymncoj¡ ¢fAcdbHklfi£5cg[º%¶¢mv3f5fieg[>mib£ªpqbqj'kzcdfAb¬«¬j>mnb/v¢[½[>rzjyzcdv3[>v5tcdkzr F
deG d
¿
ml;Á'¥3Üs[kq1Jq
Ô
JMKLKMKLJq
Ò
Jrq
Ô\s
Õ
JMKLKMKLJq
Ôbs
Õ
sutututsÒ
v¢[ rfiZ[*[eg[Z[>bAkrcdb Õ
rpqjWkWqmnk>Û
«)±
[ Ô JLKLKMK J
[ Ò ³ vq 1 â Ò
w
x < Ô w Ô\y
-{z
su|u|u|}s -~
yÒ q -z
su|u|u|}s
-~ [ -z&KLKMK
[ -~
º$Wq[yz[~miYcdkcgfib´mibq:ZpYedkcg Yegcgj>mkzcdfAb´mnyz[$cdb
Õ
¥;VWY[l[>hiyz[[fn£GkWq[lm¡fi£-«´corNj>mneged[TkzWY[ GFc
fi£)«
¿
mibqY[bYfik[>v5t®H¯>°G±?«³uÁ'¥
¡r$º[%ºmnbHkT¶fibfipkz Ypk>¶¢yzmibqfAZ egfHfAÀ5cdbYh:ru[TwHpY[bqj[>r>¶º[*bY[>[>kfÄyz[>rukyzcoj'kkWY[ jWqficoj[*fn£kWY[
v3f5fieg[>mibS£ªpYbqjkcgfibs¥* Ø Kmiycomnvqed[Tr~v3fHfAed[TmnbS£ªpqbqj'kzcdfAb « cor c@c ½c©£j±²«)±`-³ êA³ ±?«)±K-³
FK³ Ô
Õ
¶Yº$WY[>b cor$jWYfAr[bpYbYcd£ªfiyzZedt´cgb ÒÕ ¥
d W e-f"g Mgk% 6%fI1#
VWq[SbYfibYegcgbY[>miy¤qe©kz[y´hA[bY[>yzmnkfAyÄcgrkzWY[jfAZvYcgbqmnkcgfib fn£akWY[Ü-;}º$c©kzW mßv¢f5fAed[Tmnb"£ªpYbqj'kzcdfAbs¥
lhAmicdbs¶lc©£ kzWY[¬v3f5fieg[>mib×£ªpYbqjkcgfibs¶lkWY[£ª[[TvqmijÀ 3fiegt5bYfiZcomnelfAykzWY[ßjfibqbY[>jkcgfib×v3[k|º [[békWY[
£ªpqbqj'kzcdfAb´mnbq½kWq[lÜ-;}×miy[$bYfikjWYfHru[>b½ Yyzfi 3[yzegt kWq[bkWq[~º$WYfieg[~rt5ruk[>Z ZÄmKt cgbqjy[Tmir[kWY[~yzcoruÀ
fi£v3[cgbYh´mkkzmAjÀi[>s¥
#$GLF c
¡rkWY[ed[>bYhnkzW§
¿
rmKt§Êæ F èAÁfn£kWq[ Ü-;} mnbqkzWY[%b5pYZv3[y Ø ¿
rmKt
Ø æ F>êHÁNfi£miycomnvYeg[>r
fi£¢kzWY[~v3f5fieg[>mnb½£ªpYbqjkcgfib«mnyz[pqrup¢mnegedt:c©åG[yz[bHkT¶iº [$bY[[Tkzf cgbAkzyfp¢j[ kWY[¡jfibqbY[ácgfibqr)v3[k|º [[>b
kzWY[*k|º f:[>ed[>Z[bHkzr>¥
Ü-[k ± -³
Ò-
< Ô
v3[mibcgbqjyz[>mArucgbYhSr[>wHpY[b¢j[fn£bYfibqbY[hHmkcgi[cgbHk[hA[yr%rufkzWqmk
Ô
ÍêSmnb¢
Ò
Ð"§T/Fi¥)VWY[>b kWq[ fApk qpkCru[TwApq[bqj[ ±+ 7Y³O
7 < 1
fn£YkzWY[bYfibqedcgbY[>miy-¤¢e©kz[y;hi[>bY[ymkzfiycgr;[¤qbY[T
v5t3+(7 «)±`4=7
Ó
zJLKMKLK J4=7
Ó
³J>B? êq¥ VWY[½ru[TwApq[bqj[corljmiedeg[>kzWY[ DGB LCLc fn£)kWY[
Ü;}%¥
VfmKAficoYc©åG[yz[bHkamnkukmijÀr¶G^afiegcgj
È
>KÉ qyfA ¢fHru[Trl[Trucghibjycdk[>ycom:£ªfiy¡bYfibYegcgbY[>miy~¤qedk[>y¡hA[bY[>yzm
kzfiyr¥
) ! $%&"' ( $*%
g!I C3 f g
Ë [$ZÄmKt½rpY Y 3fAr[kWqmnk«´corCm*v3f5fieg[>mnb½£ªpYbqjkcgfibÄfAb§ßmiycomnvYeg[>r>¥-Ë×cdkWkzWYcor;bYfnkmkzcdfAbs¶nkzWY[$fipkz Ypk
r[>wHpY[>bqj[jmibçv¢[º$yzc©kk[b"º$c©kzWçkzWY[Ü;}»rukzmnk[[á Yyz[>rzrucgfib L ¸±J37q³O7
< 1
Ûg+ 7 «)±J37³
«)±d]
7 J 1 ³J >o? ê
lb:miedhA[vYymncojNmnkukzmAjÀ%fn£¢kWY[bYfAbYedcgbY[Tmny¤qedk[y)hA[bY[>yzmnkfiyT¶Kc©£3º[À5bYfºç·0vYcdkzr)fn£¢kWY[ÀA[t rukyz[>miZ/¶
cor kf´rfiegi[¡kWq[ rutruk[Z Û
+1 «)±NJ 1T³JF+
Ô
é«)±`]=KuJ&1T³JYVXVYV JF+NO
Ô
é«)±`]
NO
Ô KJ 1T³
¿
TÁ
^ayzÂivYbq[y´vqmArucor´ qyf5co[>rÄmib×[ôjcg[bHk´kzfHfAe~£ªfAyrfiegHcgbYhçrtr|kz[ZÄrÄfn£% 3fiegt5bYfiZcomnel[TwHpqmkzcdfAbqr¥
Ë [Ämirzrufjcgmnk[½kf
¿
KÁ~kzWY[cgY[>mne N¾ru qmibYbY[T¬v5tN +1 TÊ«)±`S³J+
Ô
T"«)±d] KS³JMKLKMK JF+NO
Ô T
«)±d]
NO
Ô KS ³ º$WY[>y[ES¸kzWY[A[>j'kzfiy±
[ 1 JLKMKLK J [ : O Ô
³'¥¡VWY[½^ayzÂivYbY[>ylvqmArucor~jfiZ YpkmkcgfibShAcdA[>r~m
rcgZ: qed[>y$edcor|k~fi£hA[bY[>yzmnkfiyrfn£kWY[%co[>mieN½¥
VWY[^ayzÂivqbY[y$vqmArucor$fi£
¿
TÁ hicgi[akzWY[rfiegpkcgfibqrfi£kzWYcorlrt5ruk[>Z»cgbkWY[miedhA[vYymncojajegfArpYy[ Õ fi£
Õ
¥ }cdbqj[%º[%fAbYegtºmnbHk~rufAedpkzcdfAbqr$cgb Õ
¶¢º[%miqkzWY[%¤q[>eg[TwAp¢mkcgfib¢r
[ Õ- â [ - £ªfiyH FGJLKMKLK Jz§~¥
ò [bqj[i¶Yº [*WqmKi[¡kf´jfiZ Ypkz[akWY[^ayzÂivYbq[y$vqmArucor fn£
LN
[ Õ1 â [ 1JMKLKMK J
[ Õ: O Ô â [ : O Ô
J+M1cTÄ«)±
[
1GJMKLKLKMJ
[ : O Ô
³JLKMKLKMJF+NO
Ô
T«)±d]
NO
Ô ±[ 1 JLKMKLKMJ
[ : O Ô
³³
lb½[TwApqcdmneg[bHk;Z[kzWYfcorkfaºfAyÀ%cgb½kWY[yzcdbYh
Õ
[ 1 JMKLKMK J [ : O
Ô ! [ Õ
1 â [ 1 JMKLKLKLJ
[ Õ: O Ô â
[ : O Ô
%¶YmibqÄkzfÄjfib¢ruco[y kzWY[*cg[Tmne"
N
cgb# ¿cdb#¶qmnegeG ¢fAedt5bYfAZcgmieWqmKi[a[hAy[>[¡fAbY[¡cgb/cdb[>mAjW
miycomnvYeg[TÁÛ
N +1Tß«)±
[ 1 JLKLKMKLJ [ : O Ô
³JMKLKMKLJF+NO
Ô
TÌ«)±`]
NPO
Ô ±[ 1JMKLKMKLJ
[ : O Ô
³u³ ¿\iÁ
R b/kzWY[ yz[>ruk~fn£)kWY[ qmn 3[y:Sa±²«J·³~[>bYfnkz[*kWYcorlmiedhA[vYymncoj*rutruk[Z/¥ Ë[½jmnb/bYfikcoj[*kzWqmklcd£;º[
kmnÀA[:·$§l¶GkWY[Ämneghi[>vYymncojrt5ruk[>ZIS¡±²«Jz·¬³
¿
\AÁlcor L? &% nÛ¡cdk%WqmiraZfiyz[½[TwHpqmkzcdfAbqr¡kWqmib
miycomnvYeg[>r>¥
d ' }Ckf"# fI I 3# #
cgyzruk*º[:cdbHkzyfpqj[½rfiZ[[¤qbqc©kzcdfAbqrafib ^ayzÂivqbY[yavqmir[>r>¥ YfAy¡ZfAy[[kmncgegr>¶º [yz[£ª[yakzf
È
nÉ;fiy
È
>É?¥CÜ-[k~pqr$jfibqrcgY[y~m½¤q[eol¥
ì Æð ZfibqfiZcgmieifAyz[>ycgbYh
[GÔ JLKLKMKLJ
[ :
:]F @ ek LL ! dd
[
±
)Ô JLKLKMKLJ
: ³ A
:
L0 cB
=eDD$
LB
B 0
[
[
A
: kL
[ Ó
[ Ó"
BB =e>[LB?.
B
B dP C L :! bk=ded LL kdeBA
LA deLC (
L!"
#%$
'&
ì(*)
k!+]'P"
L + ]'P cL"$EGc (e
,-
"$L
[
[ >[ dd.0/ L
[
[ 1
1
9v:
-< Ô - 1231
9':
-< Ô 2 -
1 1 1231 "4 H
A65
FGJMKLKLKJz§87 .@9
- 2 - !:=H BDÄШ§TJ
; 2 ;
GL,c
"+]'P"; =< =c Ac P D =cdP (D
) k LBd B, L
[ 1 JLKMKLK J
[ : O Ô
+M1JLKMKLKLJ+NPO
Ô
>[T>&BB LT LTB LL ?>@
#$ C dd 2 >[ >&BD 2 2BA&2C > C 2A
FD 2BC DkL CH
[ -
F + ;
-E/L3C 2 2BA 2CGF 2H 2BH
A
2H
C e Cg 2BA 2BH
A
2BA 2BH
A
2BC 2 HC
-
Ü-[k« 9 q
[
v¢[mSbYfAbY¹[>yfS 3fiegt5bYfiZcomneCcgbI
[ Ô JMKLKMKLJ
[ :
¶kzWY[eg[>mAcdbqhZfibYfAZ:comneNcgr
§KJͱ²«³ 2q
[DL
5
[
7 mnbqkWq[%ed[TmicgbYhÄjf5[ôjcd[>bAk$cor$§3M±?«³ 'q
rf½kzWqmkl§KJͱ²«³
[
¥
ì ÆðON
"$L %$EQ8dd:
LB '" %[CBDg C L 8P
5 ° Ô
JMKLKMKLJ|°RQ 7
!
c
bL
c
^ayzÂivYbq[y$vqmArucor
:s«
A
4H°
A P C 3k
§3Jͱª°³
§3Jͱ?«³
S ð & ð ÆðT
%GkcLVU-:"$ WP c:"; =<GLL c4 [k LBdBg
L
[ 1 JLKMKLK J
[ : O Ô
+1GJMKLKLKLJF+NO
Ô
:>[P C ,B(D BXP k A ±,+-?³
NO
Ô
-< 1
>&BgE LB C
>[TBBk Y+]'P"Q L
; =< =cc=. C cV
S ð & ð ÆðZN #$ C3dd B k
Cc 6; =< c ! N %[ L
,[
: =CL% =LCLc ±+ -³ N-< 1 .
\ [
1 â q1JLKMKLKLJ
[ : O Ô â q : O Ô ±`q 1GJMKLKMKLJq
: O Ô ³ k 4eL(
\
-F bkLF=bL(,
lbYfnkzWY[yi[yztlp¢ru[£ªpYeA qyfA ¢[>yuk|t¡fn£q^ayÂAvYbY[>ysvqmir[>rscgrskWqmnk-c©kcgr- ¢fHrrcgvYed[)kzf$¤qbq
B
kzWY[miedhA[vYymncoj
yz[eomkzcdfAbqrlmiZfibYhr[A[ymne ¢fAedt5bYfAZ:comneor¡«
Ô
JLKMKLK«
x ¿ ru[>[
È
>KÉ; qmihi[:iÄ£ªfiy*m´ Yyz[>jcgr[[¤qbYcdkcgfib¬fi£
kzWY[cgY[>mne5fi£¢yz[eomkcgfib¢rzÁ¥sË[º$cgedep¢ru[ kWqcgr Yyzfi 3fArc©kzcdfAb kzfajfiZ Ypkz[m 9uyzmnkcgfibqmiei£ªfAyZ;fi£¢mav¢f5fieg[>mib
£ªpqbqj'kzcdfAbs¥
S ð & ð Æð
kM P# E]ddC
B
[Ô JMKLKLKMJ
[ 7 J
Ô
JLKLKMKLJ
x > C T4
ded B MB . ]C
[GÔ JLKMKLKLJ
[ 7 GFcDLk8B ded bB Ø Ô
JMKLKLKMJ
x
LBd B,
B
ALP c k!; =< :c :
B R
)
kL P Ø Ô
JLKLKMK J
x
LLc B k F @kd « Ô
JMKLKMK Jz«
x
VWY[½ Yyz[5cdfApqr~[¤qbYcdkcgfib\´f5[>r~bqfnk¡[> ¢[>bqSfAbmnb5tmiedhAfiyzc©kzWYZ/¥$VWY[ ¤qyruklWYcgyzrukfAycojmie-mneghif
yzcdkWYZ#£ªfiy:jfAZ: qpkcgbYh^ayzÂivYbq[y vqmAru[Tr ºmir*kzWY[¼ pqjW5v3[yzhi[>ymneghifAycdkWYZ
È
T¶É?¥µSfiyz[´[ôjcd[>bAk
miedhAfiyzc©kzWYZÄr~mnyz[%bYfºmKmncgegmivYeg[ rupqjWmAr$kzWY[½miedhAfiyzc©kzWYZ ÅÈ
i'É)º$WYcojWScdbHkzyfpqj[>rledcgbY[>miy¡miedhA[vYym
cgbßkWq[jfAZ Ypkzmnkcgfibs¥µfiyz[Äy[Tj[bHkzedtA¶-kzWY[miedhAfiyzc©kzWYZ Å Ç È
T\TÉ º$WYcojWÊmKifAcgYr*yz[>Ypqj'kzcdfAbßkf¹>[yzf
£ªfAy¡hA[bY[>ycojrtr|kz[ZÄr>¥aË×cdkW mhAf5f5cdZ Yeg[Z[bHkmkcgfibfn£;kzWYcgr%miedhAfiyzc©kzWYZ/¶¢º [½j>mnb rufAedA[ y[Tmne)rucg¹[
rukyz[>miZ»jcg YWY[>y
¿
r[[%r[>j'kzcdfAb AÁ'¥
d 6kf"BfI % #$% c8f"! %f C 'e l E Bf"+lRCkfj#
VWq[´£ªfiegegfº$cdbYhS qyfA ¢fHrucdkcgfibÌ Yyzfi[Tr*kW¢mk:mAr egfibYhmir½º[Yf¬bYfikWqmKi[´kWY[rufAedpkzcdfAbs¶)[A[yztbY[>º
[TwHpqmkzcdfAbhAcdA[>r pqr[£ªpYescgb£ªfAyZÄmkzcdfAbqr>¥
S ð & ð Æð
"$L %$Eg8( ([L CLc
±,+-?³O-
< 1
cd eCBc % L LLFD.:"$
LN c
&%
,[ -
4· 1
A
C B · ?¨· 1 N N =B êÐ"· ¨· 1 N"! N
ÓÔ
S ðsð$#! %4BcPkT"$# % ' kL >&B3:CL &%
+(' O Ô T/«)±`]
' O Ô
Lg1³ +M1RT«)±dLg1K³ >&B
L 1 ±
[ 1 JLKMKLKMJ
[ : O Ô ³ P% )' )' O Ô
"$ k L · 1 2HN>
5 · @@9 N N
ÓÔ
7 # =B ê:Ð · "· 1 N*! N
ÓÔ
%Bc N N
ÓÔ + N Tß«)±d]
N KL 1 ³ A N :% 4%P bkd C k,
+N Tß«)±d]
N
L 1K³ vPı+1TÌ«)±`L 1K³ JLKLKMKLJ+N O Ô Tß«)±d]
N O
Ô L 1K³ J
[ Õ1 â [ 1JMKLKLKLJ
[ Õ: O Ô â [ : O Ô ³
/3B k C ! A L 1&+
p
]L 1 ±
[ Ô JMKLKMKLJ
[ : O Ô J[ 1 â 9v:
O Ô
-< Ô -[ -³
+ N TÌ«)±`]
N
ÓÔ L 1 ³ Pı,+ 1 TÌ«)±`]L 1 ³JMKLKMKLJF+ N O
Ô
Tß«)±d]
N L 1 ³J
[ ÕÔ â [ Ô JLKMKLKMJ
[ Õ: O Ô â [ : O Ô J
±[ 1 â
: O Ô
w-< Ô -[ -³Õ â [
1$â : O Ô
w-< Ô -[
-?³
+N
ÓÔ TÌ«)±`]
N
ÓÔ L 1³ Pı,+,
Ô
TÌ«)±`]Lg1³JMKLKMKLJF+N Tß«)±d]
N L 1T³J
[ Õ
1 â [ 1 JLKMKLKMJ
[ Õ: O Ô â [ : O Ô ³
% + N
ÓÔ TÌ«)±`]
N
ÓÔ Ko±
[ 1 JMKLKLKMJ [ : O Ô
³u³
A N
B N
Ó Õ N
ÓÔ
N
- BD F,
>[ Cck :G· ?¨·=1
N N
. 0/ /21´¢ ( .%/43 -$ 5/ +*
6 C3g 6# lg}
~[>j[>bHkamneghifAycdkWqZr$£ªfiy*jfiZ YpYkcgbYh^ayzÂivYbq[ylv¢mir[>r
¿²Å ¶ ÅÇ
Á$cgbqjy[>Z:[>bHkzmnegegtjfibqrukyzpqj'kaZÄmkyzcoj[>r
cgbS[hAy[>[ ¶k^Y¶s¥>¥¥ SÛ
]
222 ®H¯>° ¯K¯Ð H> [ Ô JLKLKMKLJ
[ :
2
Ô
«-{z KLKMK
2 Õ «
-
KLKMK
2
« -
KLKMK
VYVXV VXVXV
º$WY[>y[ 2 Ô JF2
Õ
JLKMKLKNmiy[SZfibqfiZcgmiegrÄrpqjW¨kW¢mkÄkWq[Skfikzmne¡[hAy[>[fi£]2
;
«-/cgrÄeg[>rzr:kW¢mnb S¥
VWq[bq[á5kr|kz[ ¨cdb¨kzWY[mneghifAycdkWYZ cor:kfçjfiZ Ypkz[Smyzfº,[TjWY[egfib¨fn£_]
pqrucgbYhßegcdbY[Tmny´miedhA[vYym
kz[>jWYbqcgwHpY[Tr¥&Rk~Z½pqr|k~v3[%[Z YW¢mircd¹>[>kWqmnk$kWY[%yzfº~r fn£3]
cgr~m deB C L fi£)miedeGkzWY[% ¢fHrrcgvYed[
yzfº~r
5
2S« - KMKF%Ð HNÐ · 2 "!$#&%'(%#*)+ , KMKY®H¯>°G±2/³ Ð T ®H¯>°G±?« -³ 7A¥
fAbqru[TwHpY[bHkegti¶Nkfß[>rukcgZÄmkz[kzWY[SjfAZ: qed[á5cdk|tÌfn£¡kWY[jfiZ YpkmkzcdfAbÊfn£*mÌ^ayÂAvYbY[yvqmArucor>¶Cº[
bq[[>Ìkf¬À5bYfºkzWY[ZÄmácgZÄmne[hAy[>[´fn£$kzWY[ 3fiegt5bYfiZcomneor fjjpYyyzcgbYhScdbÊkWY[jfAZ: qpkzmnkcgfibs¥ Üs[k
®
x.-
A v¢[kzWYcor%ZÄmácdZÄmieC[hAy[>[½kzWY[b kzWY[ĺ$WYfieg[ÄjfAZ: qed[á5cdk|tfi£kzWY[´mneghifAycdkWYZ cor%[TwApqcdmneg[bHk*kf
jfiZ Ypkz[%yfºà[>jWq[egfib£ªfiyzZ»fi£]
Ï
~0/21rfkWqmnk~kWq[jfAZ: qed[á5cdk|tcor ± 9 Ï
~0/31
-< 1 ±:-
³³DZº$WY[yz[b\ Ð ^cgr
kzWY[ jfAZ Yed[ác©k|t´fi£egcdbq[>mny~miedhA[vYymY¥
¡rº[aºfAyÀ:cgbkzWY[*ycgbYh ¶Ymiede3kzWY[*Z:fAbYfiZcomne3WqmKi[am½Y[hiyz[[F¡cgb[>mijWKmiycomnvqed[Tr¶HWY[b¢j[akWY[
kzfnkmne;[hAy[>[½fi£ mZfibYfAZcgmiecoraed[TrrakzWqmnbߧ~¥Rk%cgrakzWY[yz[£ªfAy[jeg[>miy¡kzWqmk*kzWY[ÄjfiZ Yeg[ácdk|tfn£kWY[
^ayzÂivqbY[y)vqmArucor;jfAZ: qpkzmnkcgfibjmnb:v3[~fibY[cgb
¿
rcdbYhAed[KÁ[á 3fibY[>bAkzcgmie5kcgZ[i¥ l£GjfipYyru[kWqcgr;cor)fibqedtm
yzfipqhiW´pY q ¢[>y v3fipqbqmibq´Z½pqr|kv3[*jfiZ qmiy[Tkf½kWY[*jfAZ Yed[ác©k|tÄfi£-[áWqmipqr|kzcdA[¡r[>miyzjWαƧ
:
³'¥
R k*cgrli[>yt/cdÃÄjpYedk¡kzf´[mnegpqmnk[ZfAy[mAjjpYyzmnk[>edtkWY[:jfiZ Yeg[ácdk|t/fn£^ayzÂivYbY[>y~vqmArucorljfiZ Yp
kmkzcdfAbmnbq[>r 3[>jcomnegegtcgb/kWY[½jmir[%fn£;fA[yl[k[>yZcgbY[>Srtr|kz[ZÄr$fn£; 3fiegt5bYfiZcomnes[TwAp¢mkcgfib¢r
¿
kzWqmk
corkzfrmKtº$WY[b· F §×º$WY[>y[ ·¸corkzWY[ b5pYZv3[y¡fn£;[>wHpqmnkcgfibqrÁ'¥Ë[½[á5kymijk$£ªyfAZ
È
KÉ
¿
ru[>[mneorf
È
KɪÁkWYcor$pqr[£ªpqesy[Trupqe©kTÛ
ì ª "$L S c MLF D d ! · é§4,%'5
Õ
±Æ§³~yzmibqfAZ C,k B § GLA
kL8 ; <GLLc= c=cdT ( B7 C ?.E kLC Bd δ±²¯7698:<;>=?8:<;3=?6A@B@
8:C;2=B6A@
³-
R bSfikWY[>ylº fiy¶£ªfiy¡mÄbYfibqedcgbY[>miy$¤qedk[>ylhi[>bY[ymkzfiyº$cdkW¬Ü)}Y ed[>bYhnkzW§~¶qcd£)kWY[½b5pYZv3[yl·¸fi£
À5bYfº$b +-qcor)WYcghiWY[>ykzWqmnb:§4,D%5
Õ
±Æ§ ³skzWY[b:º [ j>mnb[á ¢[Tj'k)kf¡¤qbqkWY[cgbYcdkcomneYrukzmkz[fi£YkWq[ hA[bY[>yzmnkfAy
cgb¬rpYv [á 3fibY[>bAkzcgmieskzcdZ[:cdb¬§l¥Rb¬Hcg[ºfi£;kWY[½£ÆmijklkzWqmkaº[½WqmKi[ F! kWqmnklkWq[:miedhA[vYymncoj
[TwHpqmkzcdfAbqr*fivkmncgbY[>£ªyzfiZ#m/bYfibßegcdbY[Tmny*¤qedk[>y hi[>bY[ymkzfiy%mnyz[ F d kzWYcgr y[TrupYedk Zp¢r|kmiegrfSv¢[
miedcoYmkz[>ÊvHtÊy[Tmne$jfAZ: qpk[>yrcgZpYeomkzcdfAbqr¥¨µSfiyz[fA[yT¶;rupYv ?[á5 3fibq[bHkcomne kcgZ[/cgrA[yztßjedfHru[kf
[á ¢fAbY[bHkcomnesrf:kWYcor$yz[>rpYedklf5[>rbYfik$k[egespqr~WYfº kzWY[ mneghi[>vYyzmicgjamkkzmAjÀrucgZ Yegc©¤q[TrkWq[%y[TrufAedpkzcdfAb
BHF c ¥ ¡bßkzWY[´fikWY[>y Wqmnb¢¶kWYcor yz[>rpYedkjeg[>mnyzegt¬cgbqcojmkz[>r*kzWqmk½kWY[Z:fAy[Ä[TwHpqmkzcdfAbqr%tifAp
W¢mKi[ kWY[lZ:fAy[~mivYeg[~tifApmiy[ kzfjfAZ: qpk[$kzWY[¡^ayzÂivYbq[y;vqmArucorCmnb¢:kW5pqr;kzf%y[TjfA[ykWY[aru[Tjyz[kCÀA[ti¥
6d g!IfIkC EGF^ fIH !IC - g6Cf"#
Ë [:WqmKi[½bYfnkzcgj[>v5tjfiZ Ypkz[y%rucgZpqegmnkcgfibSkzWqmk*kWq[^ayzÂivYbq[yavqmircgr*jfiZ Ypkmkcgfibfn£CkzWY[:cg[Tmne
¿
\iÁv3[WqmKA[>rmircd£-kzWY[*£ªpYbqjkcgfib«SWqmAm½egfº[>yY[hiyz[[*®ÄÐ ®A¯>°±²«³¥)VfpYbq[>yzrukzmibqkWYcor¶qº[*jmib
[áYmnZcdbq[acgb/Zfiyz[a[kzmicdekzWY[ mneghifAycdkWqZ ÅÇ
¥
VWY[´miedhAfiyzc©kzWYZ ÅÇiÈ
T\TÉcgr%mib cgbqjy[>Z:[>bHkzmneCmiedhAfiyzc©kzWYZ fibkWq[Ä[eg[Z[bHkzr fn£NkzWY[Äco[>mie N
+ 1 Té«)±
[ 1 JLKLKMKLJ [ : O Ô
³JMKLKMKLJF+ NO
Ô
T׫)±d]
NO
Ô ±[ 1 JLKMKLKMJ
[ : O Ô
³³ %ÛkWY[SmiedhAfiyzc©kzWYZjfAZ: qpk[¤qyr|k
kzWY[ä¡~Ü×^ayzÂivYbq[yavqmircgrafi£ +M1 TÊ«)±
[
1JMKLKMK J
[ : O Ô
³%¶smnb¢SkWq[bßm^ayzÂivYbq[yavqmircgr¡fn£ +M1T
«)±
[
1JLKLKMKLJ
[ : O Ô
³J+
Ô
Tß«)±d]ç±
[
1JMKLKLKMJ
[ : O Ô
³u³%¶Ymibqrffibߥ¥>¥
}5f¢¶cdb/fAyz[>yNkzfÄ[mnegpqmnk[¡kWY[ jfiZ Yeg[ác©k|tA¶5º[*bY[>[>kfÄ[>rukcgZÄmkz[¡¤¢yzrukkzWY[ [>hiyz[[afn£[>ed[>Z[bHkzr
cgbkWY[%co[Tmnefn£y[>egmnkcgfib
¿
r[[* Yyzfi 3fArc©kzcdfAbHÁ + 1 TÌ«)±
[ 1 JLKMKLK J [ : O Ô
³%¥
S ð & ð Æð "$L q gB Õ ) Cg Cc ; <GLLg . -
«)±
[Ô JLKMKLKMJ
[3Ò
³)â'q
B C%+]'P" CDBC 8B DkL 4 Bc ! B kFLA ° A >&B
d BCBde ® gk9
:)±
[ Ô JLKLKMKLJ
[ Ò ³ A ÒÕ J«)±
[ Ô JLKMKLK J
[ Ò ³ 'q °G±
[ Ô JLKLKMKLJ
[ Ò ³ éê
¿
AÁ
/ D
· Ï k
Bde CQ! bk cLb,CGc ! A,k
°
.
GFc
®
S ðsð$# N
"$
°
c dB4Bd
GFc=F @HL,0 cB -
%
± - ³ 5 2 A ÒÕ
Jz«)±`2)³ -q 7
±ª°³
5 A Õ Ò J|°±
³ êW7
> C
Õ
k F
LA (.
Õ
PPcc
B Dek (BcDLBA CLU kcF d
Ec,
2 A
L k
° x A -
° x
F
C
°
L
5 [ ÕÔ â
[Ô JLKMKLKMJ
[ ÕÒ â [3Ò
7 L
°
LA bD
-
"$
±²«
Ô
JLKLKMK Jz«
x ³
c k
Cc
; =< Hc .
-
k +'P"
L. # Bc
HB
H A 5
FGJMKLKMKJ.267
«-
L% -
° A -
e% 4 H1
A 5
FGJMKLKMK J.267
@@9
§KJͱ²«- ³ M
§3Jͱª°³
b >[=>[
<
>&BHC!+'P"
>[ k
GFc
«- Ð GFc ° g
°
gdB4Bd
GFc
A,HL 0 cB GFc
« - GFc ° -
C3Lde >[
>[Hck C ±`H1 JLKMKLKMJH³ @@9 §3Jͱ¦°*T׫ - T VYVXV1T׫ - z³§3Jͱª° T
« - TvVYVXV%T « - ³ Fc
« - GFc
° - ] ° A LCLcg% CBD Q ?4
A
LgC ° « - â'VYVXVâ"« - b% k?; =<GLL cccCDBk Bc cc. B$kFLA C
° >&BQdB4Bd GFceL,0 cB - ]B Cc c
C E,GL]ceeBc
B DkL 4,
VWYcor: Yyzfi 3fArc©kzcdfAbÊ Yyzfi[Tr%kW¢mk:kWY[Säa~Üà^ayzÂivqbY[yvqmArucor½jfibHkzmicdb¢r½miede kWq[ZcgbYcgZmie$[hAy[>[
yz[eomkzcdfAbqr-rzmkzcgru¤q[T%v5t¡kzWY[ [eg[Z[bHkzr ±
[Ô JMKLKMK J
[GÒ
³ A ÒÕ
rfiegpkcgfibqrfn£kzWY[ [>wHpqmkzcdfAb½«)±
[Ô JMKLKLKMJ
[GÒ
³
q3¥N}5fº [%jmnb[>rukcgZÄmkz[ m½v3fipqbqfn£jfiZ Yeg[ácdk|t´cdbSrfiZ[%jmAru[Tr¥
ì ç
C dcCB F (&BCDLFL,Q k CB, gG 0F"!=F?
LLCD8. CcAc (
« « N
> kLF
· X
X
F Cd !
GFc
®
Ac C
®H¯°±²«³
#$ BkDeC cMAc (L L
B8"DF" [ > $# F
( H. GFc Ý B F>ê GLA ( kX; =< c]. Pk] ! FLAC Å
T/«
cCDBk F>Þ F @k. GFc Þ #$ BCcDc
±?«â
[&%
â [ Þ [ èlâ
[ Þ [('
â [ [ Ý¡â
[ [*)
â [ Ýlâ
[+' â [
FTêA³
[ F [
^ éê
kL FLA, c =>&BL8=P cFGL,
« -,/.0,/12,34,$5
â
,$6,$72,$10,3
â
,$6,/.0,34,$5
â
,86,$12,39,$5
â
,8:,$12,/.0,86
â
,8;,$12,/.<,3 â'VXVYV
, . , 1 , 3 â , 6 , 1 , 3 â , . , 6 , 1 â , 6 , . , 3 â , 6 , . â , 1 , . â , 6 , 3 â , 6 , 1
6d Ef"lhfIWf gk k
Ü-[kKJͱ²§TJz®H³v3[~kzWY[~b5pYZv3[yNfn£ZfibYfAZ:comneor;fi£G[>hiyz[[~rZÄmneged[>y;kWqmib´®q¶WJͱƧPJ®5³ 9 Ï-< 1 ±:-
³'¥)Ë[
j>mnb[>mircgedt[miedpqmnk[¡kWY[%jfiZ Yeg[ác©k|tÄfi£jfAZ YpkcgbYhÄm^ayÂAvYbY[y vqmArucor fn£· ?ZJͱƧTJz®H³N[>wHpqmnkcgfibqr
fi£[>hiyz[[%®´rcdb¢j[akWY[ jfiZ YpkmkzcdfAbcor$fibqedt´egcgbY[>miy~mneghi[vqyzmfibSmnegeGkWY[%ZfAbYfiZcomneorÛ
ì5ð ì · ?
W: sÏcY
N
kLQC; =<GLLcc c c cdP (D
B
δ±±Jͱ²§TJ®5³u³!Zs³
αƧ ÏZG³
ì ç N C FM gCcFLd >[3c L ® k CGL_L7k cdP (D
. gk3 cT! FLAC3! C cMAcH (L L LgFckcB
# #$gBCc
"F"
[ >
$#
>[c L ® Þ BkDc . Ý ·
F>Þ
66 E Ef"l \fI
ì5ð ì N "$ « cCgcMAc (L,7>&B Ø B (,
Ø A ,-
) kLF EB= cCcD4 q A Õ k kd BCBde GFc ® ! k +]'P" ; <GLL c
LALdLC,! -
à«)±
[GÔ JLKMKLK J
[3Ò
³âq =A>[ C ÑÒÓÔ
Õ Ö > C F Ñ Ö
=k > CAe (deL
C !
S
ðsð$# ) M. :(:CFLd
>[ CPD %[
U Cd
P A
L k
P A -
"$L ck c Dkc ±kFJ
[Ô JLKMKLKMJ
[3Ò
J
[GÔZ[
Õ
JLKMKLKLJ
[GÔ VYVXV
[3Ò
³ eHc. %
Bd
/
Ò
\
]c (dB ek
Ø
=L B Ø
>[ cCc
k d B
5 2 J.2S«
A 1 2
ded
±02S³ÐÍÑ Ø âF
Ö 7K
w-< 1 ±Ò
- ³
w-< 1 ±Ò-
³â
w-< Ò ±-³ Ò
âé±
Ò
³
% kT d B Bc CL LC9 ]
5 2 1 2 ded GFc ±2/³ Ð ÑÒ'ÓÔ
Õ Ö 7
cFc
4CP J
A
>&B P ê Fc
P Fc
ÐÍÑ>Ò'ÓÔ
Õ Ö
Lek P «â éê
\
]c (dB C
Ø
Ø !âF
«)±
[ Ô JLKMKLKLJ
[ Ò ³ « Ô ±[ Ô JLKMKLKMJ
[ Ò O Ô ³ [ Ò â*«
Õ ±[ Ô JLKLKMK J
[ Ò O Ô ³
%
±[ Ò â FT³«)±
[ Ô JMKLKLKLJ
[ Ò ³ ±
[ Ò â FT³«
Õ ±[ Ô JLKLKMK J
[ Ò O Ô ³
g] Ø
T'F
L
4%P HJ" H
A#
>&B P H$0ê GFc
P H
H Ð¸Ñ WÒ O ÔY
ÓÔ
Õ Ö L7C P Hg«
Õ
â% H ,ê 7#
P ±
[GÒ âvFT³kP H
& ±
[GÒ
âvFT³' H
>[ C
GFc P Ð âvF Ñ ÒÓÔ
Õ Ö
ccc L
Ø
8 HC Ld=>[
Fc
ÐÍÑ Ò'ÓÔ
Õ Ö
/ k k>&7C
4±dP
;
J
;
³ J"D
A
>&B
GFc P ;
;
ÐÑ>Ò'ÓÔ
Õ×Ö
Lk
P ;
×ê
EP
;
« â(
; ê 3
:%D
A ;
éê
kL
q F P ; A&)
-
P ; ê
+* L
4
Ô
L
k
:CD
A Ô J$
;
ê
q-,
; A -
ì
ç / c %
cAc ( C=k L%
(=kcFLd
q
(
q
q*âF
"$ k
L k cMAc (
«)±
[Ô
J [ Õ ³ Fâ
[GÔ â [ Õ â
[Ô\[
Õ )
kY+'P" ; <GLL
c =! ׫)±
[ Ô J[ Õ
³â q B [ Ô J [ Õ qF «)±
[ Ô J [ Õ
³ q ê
ð ð Æ íO >[ k JͱƧPJHÑ Ò'ÓÔ
Õ Ö ³ ( (: ALde 4
kL C cdTAFEB3. C?; <GLL
cc=cdP (D8 δ±±9
z
-< 1 ±-:
³u³!Z³ δ±²§
z
Zs³
S ðsð$# # Fd CbF ]FM.
kLF @] C >&B Ñ ÒÓÔ
Õ Ö ) C
k:M. bcBd BA eC FM. =! CFLd
ì ç ) F (b3 BdeV*/ Cb GL=k « c@c B k
deC,F,
L >[ c E kcL cL,D =F ( BgF c
Lc CFEK-#$BkDc
k cMAc (L, ±
,86 JMKLKMKLJ
,86
³ +p
,/.0,/12,34,$5
â
,.0,$1
â
,86
L% ® ^ ·
Ï
%Bc "DF"
[ >
/#
3@e (L,7B F>ê A Ø FTê >[FE Cc % GFc
%
F @k. GL >[ (
MF>Þ
FLAC .
GFc
Þ
1Ä)/ $½ $-+
qfiyNkWY[ljfiZ Ypkz[y rucgZpYeomkzcdfAbqr~¶Hº [~pqr[$kWY[amneghifAycdkWYZ ÅÇH¿|È
T\KɦÁCZ:fcd¤q[Tkf cgbqjedpqY[~kWq[¡Yyzfiv3[
bqcdpqr¡ZÄmn
Õ -¥¡VWY[:mneghifAycdkWYZcorlcgZ Yed[>Z[bHk[Tcgb cdbkWY[: YyzfihiymnZ^av
¿
kWY[>y[:mnyz[mneorf
r 3[>jcd¤¢jedcgbY[TmnyÄmneghi[>vYyzmcdZ Yeg[Z[bHkmkcgfibÊ£ªfiy:kWq[¤¢[eo Õ
Á'¥"qpYykWY[>yZfiyz[i¶C^avÊcgbHk[hAyzmnk[kWY[
hA[bY[>yzmnkcgfib´fi£-kzWY[%mneghi[vqyzmicgj¡rutruk[ZhS¡±²«Jz·¬³'¥;Ë×cdkWYfApkljmiy[A¶HkWYcor qmnyk~jfApYegv¢[*kzWY[*ZfAruk$jfib
rpYZcgbYhÄ qmnyklfi£kzWY[½jfiZ Ypkmkcgfib
¿
c©kaº mAr kWY[:jmir[%cgbSfipYy$¤¢yzruk~cdZ Yeg[Z[>bAkmkzcdfAbScdb/kzWY[ hi[>bY[ymne
jfiZ Ypkz[y~miedhA[vYym½rtr|kz[Z»µ¬mn Yeg[TÁ¥
Ë [ [>rzjyzcgv¢[%mÄrcdZ Yeg[*Z:[kWYfkfÄhA[bY[>yzmnk[a[ôjcg[bHkzedtkWY[*[>wHpqmnkcgfibqr>Û
S ð & ð Æð "$L °±
[
1JMKLKMK J
[ : O Ô ³ ¨°
Ô ±[ 1 JLKMKLKMJ [ : O Õ
³â
[ : O Ô ° Õ ±[ 1 JLKLKMKLJ
[ : O Õ ³ c]C 2
C LLFD
FE[k ±02ÍâFK³
C8P B
+ x T + x O Ô âÌ°
Ô ± [Ô
JMKLKMKLJ
[ : O Ô
³u³-â : O Ô
w
;<
1
6 [ ; ° Õ ± [Ô
JMKLKMKLJ
[ : O Ô
³u³
>&B 5 1 T 5 Ô
ST 5 Õ S Õ
TVYVXV T 5 : O Ô [ : O Ô T 5 : S :
@P Q ±`S³ k: c cG < kd
kFc < bdeV
cdPAEB, ( ! PC:LLF ! ] CCT ±½±`PRQN³Hâ FT³± : O Ô
: Ó ÏUVW@XY
O Õ
³5âß±
ÏUDVMWXMY
: O Ô ³
>&B ® k ! «
*° -
Ë [~yz[ZÄmnyzÀ%kW¢mkCkzWY[ljfAZ Yed[ác©k|t½fn£3kWY[~hA[bY[>yzmnkcgfib:fn£GkWq[~[>wHpqmnkcgfibqrCY[ 3[bqYrCfibkWq[~º[>cdhAWHk
fi£ P6Q
¿
kWY[b5pYZ½v¢[>yfi£*bqfibY¹>[yzfçjf5[ôjcg[bHkcgb kWq[£ª[[TvqmAjÀÊ 3fiegtHbqfiZcgmiePRQCÁ'¶~º$Wq[yz[>mir>¶ kWY[
jfiZ YpkmkzcdfAbÌfn£l^ayÂAvYbY[>y vqmircor [ 3[b¢Yr C
fAbßkWY[[hAy[>[Äfn£kWY[v¢f5fAed[Tmnb £ªpYbqjkcgfib"«
¿
r[[
r[>jkcgfibq¥AÁ¥
Ë [ Yyz[>r[bHk~rufAZ[ rucgZpYeomkzcdfAbyz[>rpYedkzr £ªfAylru[>i[>yzmieGÜ;} fn£)mnyzcdfApqrrucg¹[MF è ?ק?¨ÞHêY¥CVWY[
yzpYbYbqcdbYh²kzcdZ[Trlmnyz[%hicgi[>b£ªfiy¡m ò x º fiyzÀr|kmkcgfib/º$cdkW¬mibmneg YWqmÄ
`
´ Yyfj[>rzrufAy~mkTiiĵWY¹i¥
ledejfAbqrcg[>y[T ¤qedk[yz[>磪pYbqjkcgfibqr:mnyz[´vqmiegmibqj[TçmnbqÊjmnbÌv3[£ªfipYbqçcdbÊkWY[edcdk[>yzmnkpYyz[iÛ´miedekWY[
v3f5fieg[>mib½£ªpqbqj'kzcdfAbÄ[áYmnZ Yeg[>rCmiy[kmnÀA[b:£ªyfAZ
È
¶H¶
`
É¢£ªfiy;kzWY[a mibqcde¢[áYmnZ Yeg[>rCmibq½£ªyfAZ
È
KTÉY£ªfiy
kzWY[ Ü-¼$^[áYmnZ Yeg[>r>¥)Ë[ j>mnb¤qbqkWq[cgy~mneghi[vqyzmicgj¡bYfiyzZÄmne3£ªfiyzZ»mibqkWY[>cdy$ZcgbYcdZ½pYZ0Y[hiyz[[%®
cgbS~bYbq[á¥
;áYmiZ: qed[ § · ±dP6Q³ fiZ Yeg[ácdk|t }5fiegi[
ܼ$^Ì A >55 § Z ½r
ܼ$^Ì i nq § Z *WSA\Z
ܼ$^Ì i iK i § Z
W\½Z
ܼ$^¬\ A ` § Z >q¥:r
ܼ$^¬\ i \n ` A § Z *W/iÄr
ܼ$^¬\ i iYTi i § Z WSA\Z
mibqcdeC i
`
iH\ A § Õ Z i¥g%r
mibqcdeC T\ T\nn
` § Õ Z >q¥\½r
mibqcde\ i
`
iH\ A § Õ Z i¥g%r
mibqcde\ T\ T\nn
` § Õ Z >q¥:r
mibqcde- i HAK A § Õ Z i¥r
mibqcde- T\ T\nn
` § Õ Z T\Y¥r
mibqcdes i
`
iH\ A § Õ Z %r
mibqcdes T\ T\nn
` § Õ Z Y¥:r
;áYmnZ Yeg[ Ü m º ¿
xÁ fiZ Yeg[ácdk|t }5fiegi[
mnbqcge i `
\A\ § Õ Z Y¥g%r
mnbqcge T\ qT\i
` § Õ Z Y¥g%r
mnbqcge
`
i `
\Y i § Õ Z Y¥r
mnbqcge
`
T\ qT\i
` § Õ Z Y¥r
mnbqcge i >q i § Õ Z Y¥Hr
mnbqcge T\ \A i
` § Õ Z >r
mnbqcge A >H K § Z Y¥g*r
mnbqcge i Y § Z *W/Z
mnbqcge i \i Y A § Z WS Z
mnbqcges A THnA\ K § Z \i¥\½r
mnbqcges Hn\A\A H § Z AZ\%r
mnbqcgeC> A >H K § Z ` ¥½r
mnbqcgeC> i AKA n § Z W\aZ
VmnvYeg[iÛSð ì Æ ì ì ì ð ð N*
ledey[Trupqe©kr~ Yyz[>r[bHk[T/cdbkWY[:mnv3fi[*kzmivYeg[½jfAb¤qyzZ,kzWY[mnegcoc©k|t/fi£kzWY[ qy[>Hcgfip¢rljfAZ Yed[ác©k|t
[Tr|kzcdZÄmnkcgfibfn£kWY[>fiyz[Z A¥
s $ + / ×/ +
/
Ë×W¢mk~corkWY[%ZcgbYcgZpYZ0bHpqZv3[y~fi£vYcdkzr$fi£kzWY[%yzpYbYbYcgbYhÀi[>t´yz[>wHpYcgy[TÄkf¤¢bq/mpYbYcowApq[ rufAedpkzcdfAb
kzf:kWY[ rtr|kz[Z S¡±?«J·¬³ S i[>yt´jfAmnyr[¡pY q ¢[>y~v¢fApYbqcorÛ
S ð & ð Æð
"$L= 4Bc % DL F >&B_8dMEBd (d ?DAL G " # %(' AL G
§ e U gcAc cAc (L «
4 ( ( LCLc
±+-³Õ 6 O Õ
-< 1
k:de
fibY[
BCB > ( G= = C c
k ( ( ! k=CB % DL: LLFD.
VW5pqr>¶kWq[rutruk[>Z,Wqmir~fibYegtmrfiegpkcgfib/cd£º [%WqmKi[%· ? :
T F%[>ed[>Z[bHkzr>¥NVWYcor$ Yyzfi 3fArc©kzcdfAb
YfH[TrbYfnk$kz[egepqrkzWY[%ZcdbYcgZcgmiesb5pYZv3[y~·ç¥C~hAmicdb-¶º[%mnyz[%ficgbYhÄjfAZ Ypk[>y~rucgZpqegmnkcgfibqr>¥
VWY[:¤qhApYyz[:y[> Yy[Tru[>bHkzr>¶¢£ªfAy%mymkzcdffn£CkzWY[bHpqZv3[y*fn£ hicgi[b¬fipkz Ypkzr%· v5t/kWY[eg[bYhikW¬fi£
kzWY[ r[>jyz[k$ÀA[t´§~¶YkWY[*£ªyz[>wHpY[>bqjt´fi£[ámiZ Yed[Trº$WY[yz[*º[a¤qb¢kzWY[ rfiegpkcgfibs¥
$j>jfiycgbYh%kzf%kWYcor hiymn YW-¶icdk r[[ZÄrCkWqmnkº [lfibqedt:bY[[T´· §â¬ã;kzf ¤qb¢kWY[¡cdbqc©kzcgmie3rukzmnk[lfi£
kzWY[:bYfibYegcgbY[>miy~¤qedk[>yahA[bY[>yzmnkfAy>¥*}5fº [½bq[[>¬mb5pYZ½v¢[>y¡fi£Nfipkz Ypkr¡ qyfA ¢fAyukzcdfAbqmnekzfkzWY[:ed[>bYhnkzW
fi£)kWY[ cgbYcdkcomner|kmk[ kfĤqb¢SmÄpYbYcowHpY[rfiegpkcgfibs¥mlfnk[ kWqmnkl[A[bScd£;·¸corlrZÄmneged[>y$kW¢mnb§×º [ jmib
jfiZ Ypkz[:kWY[´^ayzÂivYbY[>y*vqmircgrafi£[S¡±?«J·¬³amnb¢£ªfApYbq mnege)kWY[ 3fArzrucgvYeg[rfiegpkzcdfAbqr
¿
kWqcgr*cor%rucgZcdeomny
kzf¬kzWY[edcor|kÄ[TjfcgbYhjfibqj[ kcdb"CyzyfAyÄfAyyz[>jkcgbYh f[>rÁ'¥ ò fº[>i[>y>¶)º$WY[>b"· corruZÄmnege kWY[
jfiZ YpkmkzcdfAbfn£kWY[%^ayzÂivYbY[>ycgr Zp¢jWZfiyz[*c©Ã´jpYe©k~mibq´cdk$cgrbYfik [>i[>bjeg[>miyc©£c©k~jmibv3[%fibY[
cgb/ ¢fAedt5bYfAZcgmie¢kzcdZ[A¥
;[>ytrupYyz YyzcgrcgbYhiegti¶5º [¡£ªfApYbqkW¢mk~rufAZ[a[áYmnZ Yeg[>rcgbkzWY[% Yyz[5cgfipqrkzmivYeg[Ä*j>mnbv¢[ mnkukmijÀi[T
A[yzt%[ôjcg[bHkzedt½[i[>b½º$Wq[b·0cor;rZmiede?¥;}5[[kmnvYeg[~\lv3[egfº%¥)VWYcgr)corCmib½fA ¢[>b:corzrupY[ kzfapqbq[yrukzmnb¢
mibq¡kf~v3[NmivYed[)kzf$ Yyz[>coj'krpqjW%mv3[WqmK5cgfiyG£ªyzfiZ kWY[Cv3f5fieg[>mib¡£ªpqbqj'kzcdfAb mnbq¡kWq[;kzmi Y YcgbYh~ru[TwHpY[bqj[i¥
0 20 40 60 80 100
0,7 0,8 0,9 1,0 1,1
P e rc e n ta g e
cdhApYy[A¥;;á ¢[>ycgZ[bHkzmiesmnbqmiedtrcgr fn£kWq[%Z:cgbYcgZÄmnesb5pYZ½v¢[>y$fn£fApk qpk~vYcdkzr
;áYmiZ: qed[ ed[>bYhnkzWS§ b5pYZv3[y~· ^ayzÂivqbY[y
fn£;Ü-;} fi£fApk YpYkzr
mibqcde H A \A\¥r
mibqcde i n ` ¥r
mibqcde `
``
AY¥r
mibqcde n A \A\A¥:r
VmnvYeg[ \¥C^ayÂAvYbY[>y~mkukmijÀĺ$WY[>bS· æ駨fib ò x×ä*}Y\Tii½µSWY¹
& s %)$* s Ä 0/ /%)-
VWq[ [Trr[bHkzcgmieH qycgbqjcg Yeg[fn£3mnkukmijÀrvHt½jfiyzyz[eomkcgfibcgrkzf*jfiZ qmiy[kWY[yz[>r[>miyzjW fi£qkzWY[$cdbqc©kzcgmieYr|kmk[
fi£m:yz[hicoruk[ykzfÄm½ qyfAvYed[>Z,fn£;jfAyyz[>jkcgfib´fi£[>yyzfiyrfibSmjf[]a;¥
VWY[Tru[%mnkukzmAjÀrNcgZ YedtjWqmnbYhA[¡cgbkWY[%[Trucghib/jyzc©kz[yzcgmfn£bYfibYegcgbY[>miy¤¢e©kz[yy[>hicor|kz[yT¥Vf Yyz[i[>bHk
£ªyzfiZ £Æmiruk jfiyzy[>egmnkcgfibs¶nkWY[¡v¢f5fieg[>mib£ªpYbqjkcgfib«Z½pqr|k v¢[2 ?DBLC¶c?¥[i¥)c©£-£ªfiy[2mnyzcgmivYeg[>r)¤Yá[T
cgb Õ
¶5kzWY[ Ø T 2 Kmiycomnvqed[Trv3f5fieg[>mib£ªpYb¢j'kcgfib «[>Ypqj[T´£ªyzfiZ«Scor$r|kzcdegesvqmiegmibqj[T¥,
VWY[Tru[ qmiyukzcgjpYegmiyv3f5fieg[>mib £ªpYbqjkcgfibqr)W¢mKi[mibcgZ ¢fAyukmnbHk qyfA Yycg[k|t%[>Zfibqrukymkz[> v5t}5cg[hA[b
kzWqmneg[y
È
É?ÛCm 2?yz[>rcdegcg[bHk£ªpYbqj'kzcdfAb«Sfi[>y ÒÕ
rzmkzcgru¤q[Tr kWY[%yz[eomkzcdfAb®H¯°±²«³ Ð Ø T82 T FA¥
}5f/kzWY[´jWYfAcgj[:fi£m 2y[Trucgedcg[bHk*£ªpYbqjkcgfibÌ[Tjyz[>mir[>rakzWY[´[>hiyz[[fn£~«¥VWY[>bs¶-cdkcor*[>mircg[y*kf
rfiegi[ kWY[rutruk[>Zº$cdkW mnb¬miedhA[vYymncoj%mkkzmAjÀº$WqcgjW¬Y[ 3[bqYrafAbSkWY[[>hiyz[[i¥Rb¬fikWY[>y¡ºmKti¶¢kWY[
£ªpqbqj'kzcdfAbqr$«/º$WYcojWmnyz[*r|kzyfAbYhiegtÄru[TjpYyz[~£ªfAymiedhA[vYymncoj~mnkukzmAjÀÄWqmKi[amWqcdhAW[>hiyz[[¡mibqÄkzWY[bkWq[t
miy[*jfAyyz[eomkz[i¥;}5fÄcdk~cgr[TmirtÄkfÄrfiegi[¡kWY[>Z»º$cdkWSjfAyyz[eomkzcdfAbmkkzmAjÀ5r>¥)Ë[%j>mnbSrmKtkzWqmk$kzWY[*k|º f
mnkukmijÀrmnyz[*jfiZ Yeg[Z[bHkmnyzti¥
R b È`
É?¶5kzWY[*v¢f5fieg[>mib´£ªpYb¢j'kcgfibcor mi Y YyzfKácdZÄmkz[>v5t´m½edcgbY[>miy £ªpYbqj'kzcdfAb
[ +p K[ ¶ A :Õ
¥CVWqcgr
mi Y YyzfKácdZÄmkzcdfAbçhicgi[/m edcgbY[TmnyÄyz[eomkcgfibÊ£ªfiy´mibÊfipYk YpkT¥ qmAr|k´jfAyyz[eomkzcdfAbÊmkkzmAjÀ5r[>ycgi[£ªyzfiZ
aàmbq[º0jf[3aHW¢mKHcgbYhÌmedfº [yÄcgZ[bqrcdfAb §l¶C£ªfAyĺ$WYcgjW m£Æmiruk´[>jf5YcdbYhßZ[kzWYf¨cgr
£ª[Tmircdvqed[A¥VWY[>bkWY[>t¤¢bq:kWY[½¤qyzrukC[eg[Z[>bAkr;fn£GkzWY[~cgbYc©kzcgmie¢rukzmnk[i¥}5pqjWÄm%jf5Y[:a H cgrNfivkmncgbY[>:v5t
jfiZ Ypkzcdbqhmnege-egcdbq[>mnyajfAZvYcgbqmkzcdfAbSfn£
yz[eomkcgfib¢r$º$WYcojWmnbYcoruWSfAb/kWY[½egmAr|k:±Æ§ TY³~ ¢fHrucdkcgfib¢r¥
x;miyzmiZ:[k[>y
f5[>rp¢rupqmiedegt´bYfik$[áYj[>[>fiy ¥
VWY[*£ÆmAr|k~jfiyzy[>egmnkcgfibmiedhAfiyzc©kzWYZ¾WqmKA[¡k|º f: qmnykzr>Û
qy[TjfiZ YpYkzmkzcdfAbS qmnyk>¶3cgb¬º$WYcojWº [ ¤qbq¬mnege-kzWY[
yz[eomkzcdfAbqr~º$WqcgjWmibYcgrWfAbSkWY[½egmAr|k
±Æ§BTY³ 3fArc©kzcdfAbqrcd£kzWY[tmnyz[ajfiZvqcdbY[T¥
[>jfcdbqh: ¢mnyk>¶Ycgbº$WqcgjW/º [¡¤¢bqkWY[¤qyr|k$[>ed[>Z:[>bHkzr$fi£-kWq[%cdbYcdkcomner|kmk[A¥
VWY[%ZcgbYcgZpYZ0bHpqZv3[y$fn£)fipYk Ypkr$yz[>wHpYcgy[T´v5t´kzWY[%mkukmijÀ´cor$hAcdA[bv5tGÛ
± Y³ z 6
"·
x -7 Ð ±>C± ³ Y³ z 6
}5f:£ÆmAr|kljfiyzy[>egmnkcgfibmnkukzmAjÀr ¤qbq[>ed[>Z[bHkzr$fi£-kzWY[%cdbqc©kzcgmiesr|kmk[%º$Wq[yz[%^ayzÂivqbY[yvqmArucor$jfAZ
qpkzmnkcgfibS¤qb¢SkWq[½º$WYfAed[rukzmkz[i¥*YpYykWq[yzZ:fAy[A¶jfiyzyz[eomkcgfibSmnkukzmAjÀ/WqmKi[m YyzfivqmivYcdegcor|kzcgjyzmnk[fi£
rpqj>j[>rzr º$WY[yz[>mAr~^ayÂAvYbY[>y v¢mircgr$jfiZ Ypkmkcgfib/mnegºmKt5r¤qb¢kzWY[%yz[>rpYe©kT¥
VWY[ZfAruk*cdZ 3fiykzmnbHk* ¢fAcdbHk%corlkzWqmk%b5pYZ½v¢[>yafi£[TwAp¢mkcgfibbY[[T[>¬v5tjfiyzyz[eomkcgfibmkukmijÀr¡cgr
E kLC º$WY[>y[TmirC^ayzÂivYbY[>y;vqmircor;mkukmijÀr)bY[>[>:fibYegt 3fiegt5bYfiZcomneb5pYZ½v¢[>yCfn£Gfipkz Ypkr¥¡b:kWY[
#$GLF c
fikWY[>y~WqmibqSm´ymKº$vqmijÀfn£)kWY[:^ayÂAvYbY[y¡mkukmijÀcgr~kWqmnklkWqcgrlbHpqZv3[y¡Y[ 3[bqYr¡r|kzyfAbYhiegtfAb/kWY[
jWqficoj[fi£CkWq[½v3f5fieg[>mnb¬£ªpYbqjkcgfibqr%«¥}5fcdbhi[>bY[ymne?¶s^ayÂAvYbY[yavqmArucor¡jfiZ YpkmkzcdfAb¬bY[>[>¬megfº[>y
b5pYZ½v¢[>y$fn£)fipkz Ypkr$mircor$ZÄmi[%jeg[>miy$v5tÄkWY[*kmnvYeg[%Y¥
Ë [% Yyz[>r[bHkkzWY[%b5pYZv3[yfi£fipYk Ypkr$bY[>[>[T´£ªfAyÜ;}àfn£eg[bqhnkWA½º$cdkW
mnbq ê
mAjjfiycdbqh/kf [áYmnZ Yeg[>r½ Yyzfi 3fAr[>ßcgb È`
É?¥ßË [j>mnbçyz[ZÄmiyÀkWqmnk½£ªfAykzWY[[áYmnZ Yeg[q¶N^ayÂAvYbY[y
v¢mircgr Z[kzWYfbq[[>qrZ:fAy[afipYk YpkrkW¢mnbfiyzy[>egmnkcgfibmnkukzmAjÀr¥ RkljfAZ:[Tr£ªyfAZ¾kWY[*£ÆmAj'kkW¢mk£ªfiy
m¬ruZÄmnege§l¶kWY[b5pYZv3[y:§ÏcgrWYcdhAWY[ykWqmib : ¥ ¼pYk£ªfiy½y[Tmne rucg¹[§l¶C^ayÂAvYbY[y½vqmircor%Z[kWqf5
º fipqegbY[[Ted[TrrfApk YpYkzr kWq[b¬fiyzy[>egmnkcgfibmkukmijÀr>¥
;áYmnZ Yeg[ \ ` >
^ayzÂivqbY[yvqmArucor H\ H\ A\ qT\ qT\fiy$A ¢T\ \HK TH5 THnY >55
fiyzy[>egmnkcgfib `
\ `
\ ` \ ` \ `
\ `
\ `
\ `
\ ` \ `
\
Vmnvqed[%Y¥ImlpYZv3[y$fi£yz[>wHpYcgyz[>´fApk qpklvYcdkzr
(
).%/*s , )$5/ +* -
qfiy$bYfº%¶qº[%WqmKA[ajfiZ Ypkz[>Smäa~ÜÊ^ayzÂivYbY[>y$vqmircor £ªfiylmib[á Yedcojcdk~fipYk Ypkaru[TwApq[bqj[±,+ -³ NPO
Ô
-< 1 ¥
VW5pqr>¶£ªfiymibYfnkzWY[y [á Yedcojcdk½fApk qpk½r[>wHpY[b¢j[i¶º [´bY[[T kfjfiZ Ypkz[
L B
kWY[^ayÂAvYbY[yvqmircgr
º$Wq[yz[>mir fAbYedt´kWY[ jfibqrukzmibAkrcdb[>wHpqmnkcgfibqr Sa±²«J·³ WqmKi[*v3[[b/Zfcd¤q[>¥
lbYfnkzWY[y*rufAedpYkcgfibcor~kzfmAYSbY[>ºmnyzcgmivYed[Tr ±+ -³ NO
Ô
-< 1
mnb¢/kfjfiZ YpYk[½m 9urt5Zv3fiegcgj½^ayÂAvYbY[y
v¢mircgr!;¥VWY[bÊ£ªfiy½miede [á Yegcojcdk:r[>wHpY[b¢j[>r½º [´bY[[TçfAbYedtkf rupqvqr|kzc©kzpk[kWq[mnegpY[Trfi£P+ - cdbÊkWY[
^ayzÂivqbY[yvqmArucor¥
µSfAy[ Yyz[>jcgr[egti¶iº[$WqmKA[Nkzf jfAZ: qpk[~m%^ayzÂivYbY[>y;vqmircor£ªfiy)kWq[~[egcdZcgbqmkzcdfAb½fAyzY[yzcdbYh
cdbHkyzf
Ypqj[Tcgb r[>jkcgfib¬q¥\Y¥ VWY[ ¢fAedt5bYfAZ:comneyzcdbYhcor¡bqfº HN Õ [ 1 JLKMKLKMJ
[ : O Ô
J+1GJLKMKLK J+NPO
Ô !
[ Õ1 â [ 1 JLKLKMK J
[ Õ: O Ô â [ : O Ô JF+
Õ
1 â +1GJMKLKMK JF+
Õ
NO
Ô â +NPO Ô
qyfAZ Yyzfi 3fArcdkcgfib¨i¶º[´À5bYfº kW¢mkcd£$º[rpYvqrukcdkpYk[ÄkzWY[´mnyzcgmivYeg[>r´±,+-?³ NO
Ô
-< 1
º$c©kzWç[á Yegcgjc©k
miedpY[Tr¶Hº [lr|kzcdegeGWqmKi[~m:^ayÂAvYbY[>yNvqmArucorCfi£kWY[¡cg[Tmne N ¿
vYpkbYfikbY[Tj[>rzrzmnyzcdegt½mZ:cgbYcgZÄmne^ayÂAvYbY[y
v¢mircgrÁ'¥
}5fkf[mnegpqmkz[%kWq[½jfAZ Yed[ác©k|t/º [ WqmKi[ kfv3fipqbq/kWq[½jfAZ Yed[ác©k|t/fn£;kzWY[ qy[TjfiZ YpYkzmkzcdfAb
qWqmir[%mnbqkWY[ jfiZ Yeg[ácdk|t´fn£kWY[ rpYvqrukcdkpYkcgfibSr|kmnhA[i¥
ì5ð
ì >[e
< ·
C,k >&B
· L G8Dk 4 L(, B
CcLAe( (,b C c
>[%
B8CdT ( ; =<GLLc
Ck >&B8 GFc
k GLA
[ ;
êÐBDÄШ§ T F ) k LBc CC c c >&BD
M S
> C M de b>&B kd$cM LLC,@ M ! bF <%§ L ( (
±,+-²³ NO
Ô
-< 1
S ðsð$#
& cDL C C B( B CB; <GLL c
>[cBB k 6; =< @]=>[
CgCHL(, CLd
k L> cc c4Bk CC.
Fc B