HAL Id: hal-00003788
https://hal.archives-ouvertes.fr/hal-00003788
Preprint submitted on 6 Jan 2005
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.
Closed form approximations for transition densities: a path integral approach
Marc Goovaerts, Ann de Schepper, Marc Decamps
To cite this version:
Marc Goovaerts, Ann de Schepper, Marc Decamps. Closed form approximations for transition densi-
ties: a path integral approach. 2003. �hal-00003788�
!#"%$ & '('*)+!#,-"/.1024365 7 88 9 , :$;,-<<,-" =>3@? !#"%$ 9 ,A$A!+B <02
CAD+EGFIH/JLKNMOFQPQR SUTV#JLWH/JLEYX[Z\JL]_^/FIW`
a
D+EGFIH/JLKNMOFQPQR SUTb`cMLPdJLKfe4g`cXPIhYJjicJkPIhYJLKO]lgEAeM
mGD+EGFIH/JLKNMOFQPQR SUT\bE-PQnJLKpo-X[qrg4skW]@PQR SUT\bo4oA]tFpJue vsNSEAS`FwsLMNXyxKOFIEYMNMLPQKfg4g/P{z/|X[Z}~44
bE-PQnJLKpo-X[Z\JL]_^/FIW`
+k G/
U uG[-*k>4%/>ful4fuYfN/Gulul4 Gu/--lul>+I/G@Gul4GuL>uf>k 4U
¡ Nf¢-uk/uY Y fN/Gulul4Gu/--lul>rI/[NuYk£/>YkN/GG@Gul4¤GuL>uf>
k/ /l>¥\*¤L¦Gu>uf> 1¥ §>/G/ -u %fk/N/w *¨Y/jfk/kN/[k/uuk/+§Y>k
/ L¦Y/L\k/kGul4 *4uul-l/Yl>/GYf /G/l¥1uk/L¦Gu>uul4GI/{uY©fN/Gulul4
Gu/--lul>£/G I/uYj§ ¦Y§cG§ Gu/--ld¥-uGk ª f>L4G -uL4Gufu/ruY
YkNlul4 /\/ /G/l¥1uk/GGu>¦Y§ ul4 I/uY fN/Gulul4 Gu/--ld¥/+{GN
GfkQG- k/f\uY-u %fk/N/*(f1L4§-lL¦ fc*\k/kGf> «Y\GGu>¦Y§ ul4
cGu>f>%kA-/f> 4 L4%/L¦ L4§¤-Gul4 /£ Yk /G/l¥1uk/#YG*k{/G lk
*4GGI/£uYfN/Gulul4Gu/--lul>k «YQ/L£uG(uYGGu>¦Y§ ul4 [/G/l¥1uk/
G/f4§j§*/uu/%/Y/%u/>kY/ _Y GI/uYj%/>ful4ul4 /+ªu/ /Gul4Gk ¨¢G/l¥/
Y>§4GffNf uY /kkYN/L¥ /\uY GGu>¦Y§ ul4 1¥ §>/G/j Ik /N-Gk/
GffNul4Gk
¬
JLR n(SKfeMk
G@Gul4 GuL>uf>kGfN/Gulul4 Gu/--ld¥A1-u %fk/N/w
L4§4Y/f4Gkld¥
xb®#¯**°4± ³² ° µ´£¥A °4± ³² ° t¶©*·¸ ¸>²1 µ¹ ° ²1 _º ° t»£¼
½ ¾¿#À/Á4Â[Ã(Ä(Å1À4ÆpÂ#¿
ÇcÈ-ÉÊ1Ë ÌIÍ Ë Î-Ï*ÐÑIÒÓÊ1É*Ï Ë ÎÔOÐ ÒOÕ#ÐÍÌyÖÍÊ1ÑIÑyÈ ÍÎÉY×LÌIÉGØ*ÎØ*ÒuÙU×LÌIË Ð Ë Î-Ï*ÐÑIÒÓÊ1ÔOÐ Ú©ÌIÏ*ÐÑyÈ
Ø*ÒOÐÏ Ê1É*Ï ÒN×LØ*Ï*ÌIÐÏ É*Î/Ú\Ê1ÏÊÈ-Ò ÌIÉ Õ*ÔOÌIÍÌIÉ*Û Ê1É*Ï ÌIÉYÜÐÒN×LË ÐÉY× ×LÝ*ÐÎÔOÌIÐÒÞß ÎÒN× Î1àj×LÝ*Ð
á
¶/uu>f*4GGY/YuY/
v` gFI]+g4e4eKuJOMNMk /G µY>uNYkG*kLâ\G µ/ _* ãQªG äåNYkG*kæN
ÒN×LÎ-ÍkÝÊ1ÒN×LÌIÍ Ï*Ì+ÐÔOÐÉY×LÌQÊ1Ñ¢ÐGØÊ%×LÌIÎÉ*ÒjÌIÉ ×LÝ*ÐàpÎÔOË
jÝ*ÌIÒ ÐGØÊ%×LÌIÎÉ Ï*ÐÖÉ*ÐÒ Ê ÒN×LÎ-ÍkÝÊ1ÒN×LÌIÍ Õ*ÔOÎ-ÍÐÒOÒ !" $## % &(')+*, ÓÔOÐ.-ÐÍ×LÌIÉ*Û
Ð1Þ³Û*Þ£×LÝ*Ð Õ*ÔOÌIÍÐ Õ*ÔOÎ-ÍÐÒOÒ ÌIÉ ×LÌIË Ð1Þ/fÉ ×LÝ*ÌIÒ ÐGØÊ%×LÌIÎÉ¢Ó !0 $## % &(')+*, ÌIÒ Ê
ÒN×kÊ1É*ÏÊ1ÔOÏ 1ÔOÎ/Ú©É*ÌQÊ1É Ë Î1×LÌIÎÉ¢Ó 324 ÌIÒc×LÝ*Ð Ï*ÔOÌyàw×Î1à{×LÝ*Ð Õ*ÔOÎ-ÍÐÒOÒ Ó[Ê1É*Ï 65" 324
ÌIÒ\×LÝ*Ð Ï*Ì+Ø*ÒOÌIÎÉ Î1à Þ1Î1×LÝ Ê1É*Ï ÍÊ1É ÍÎÉY×kÊ1ÌIÉ ÎÉ*Ð ÎÔ©Ë ÎÔOÐÕÊ1ÔLÊ1Ë Ð×LÐÔOÒÞ
/fÉ ×LÝ*ÌIÒ(ÍÎÉY×LÔOÌ87*ØA×LÌIÎÉ¢Ó/ÚÐ{Ú©ÌIÑIÑGÊ1ÒOÒOØ*Ë Ð{×LÝÊ%××LÝ*ÐÏ*ÔOÌyàw× Ê1É*Ï ×LÝ*ÐÏ*Ì+Ø*ÒOÌIÎÉ 65 Ï*ÎÉ*Î1×
Ï*ÐÕ#ÐÉ*Ï ÐAÕ*ÑIÌIÍÌy×LÑyÈ ÎÉ ×LÌIË Ð
Þ jÝGØ*ÒÓ1ÚÐjÍÎÉ*ÒOÌIÏ*ÐÔÒN×LÎ-ÍkÝÊ1ÒN×LÌIÍ\Ï*Ì+ÐÔOÐÉY×LÌQÊ1Ñ-ÐGØÊ%×LÌIÎÉ*Ò
Î1à(×LÝ*ÐàpÎÔOË
9 : ; $<
Ú©Ý*ÐÔOÐ Ê1Ò ÌIÉ ×LÝ*Ð ÛÐÉ*ÐÔLÊ1ÑÏ*Ì+Ø*ÒOÌIÎÉ Ë Î-Ï*ÐÑÓ×LÝ*Ð àpØ*É*Í×LÌIÎÉ*Ò 9 32= Ê1É*Ï : 32= ÍÊ1É
ÍÎÉY×kÊ1ÌIÉ ÕÊ1ÔLÊ1Ë Ð×LÐÔOÒÞ?>ÎÔN×LØ*ÉÊ%×LÐÑyÈÓ¢×LÝ*ÌIÒ×LÌIË Ð>ÙfÌIÉ*Ï*ÐÕ#ÐÉ*Ï*ÐÉ*ÍÐ ÌIÒ ÎÉ*ÑyÈ Ê Ë ÌIÉ*ÎÔÔOÐ>Ù
ÒN×LÔOÌIÍ×LÌIÎÉ¢ÓYÒOÌIÉ*ÍÐ¤Ë ÎÒN×{Î1à¢×LÝ*ФÍÑQÊ1ÒOÒOÌIÍÊ1ÑË Î-Ï*ÐÑIÒÐ1Þ³Û*ÞYàpÎÔÌIÉY×LÐÔOÐÒN×\ÔLÊ%×LÐÒÊ1ÔOÐ¤Ë ÐË 7#ÐÔOÒ
Î1à(×LÝ*ÌIÒjÍÑQÊ1ÒOÒ©Î1àÕ*ÔOÎ-ÍÐÒOÒOÐÒ ÒOÐÐ Ê1ÑIÒOÎ ÒOÐÍ×LÌIÎÉ @ Þ
A
É*ÐcÎ1à¢×LÝ*ÐBGØ*ÐÒN×LÌIÎÉ*Ò\ÌIÉ ×LÝ*ÌIÒ{ÍÎÉY×LÐ-×jÌIÒ×LÎ ÖÉ*Ï Ê ÍÑIÎÒOÐÏ-ÙUàpÎÔOË ÐAÕ*ÔOÐÒOÒOÌIÎÉ àpÎÔ×LÝ*Ð
Õ*ÔOÎ7Ê07*ÌIÑIÌy×fÈ Î1à[×LÝ*ÐÕ*ÔOÎ-ÍÐÒOÒ ÔOÐÊ1ÍkÝ*ÌIÉ*Û ×LÝ*ÐÜ1Ê1ÑIØ*Ð 2"C Ê%××LÌIË Ð ÛÌyÜÐÉ ×LÝ*ÐcÜ1Ê1ÑIØ*Ð 2D
Ê%×¤Ê àpÎÔOË ÐÔ\Õ#ÎÌIÉYשÌIÉ ×LÌIË Ð # E Þ=F ÐÚ©ÌIÑIÑ¢Ø*ÒOÐ×LÝ*Ð É*Î1×kÊ%×LÌIÎÉ
G
HI20HJKI20KI
L20K"M N0O"P
&Q KI;E 20KRQ HS 20HT*
àpÎÔ ×LÝ*Ð ×LÔLÊ1É*ÒOÌy×LÌIÎÉ Ï*ÐÉ*ÒOÌy×fÈ Î1à×LÝ*Ð Õ*ÔOÎ-ÍÐÒOÒ Þ jÝ*Ð UGÉ*Î/Ú©ÑIÐÏ*ÛÐ Î1à×LÝ*ÌIÒ Ï*ÐÉ*ÒOÌy×fÈ
ÌIÒ ÌIË Õ#ÎÔN×kÊ1ÉY× àpÎÔ ÌIÉ*ÒN×kÊ1É*ÍÐ ÌIÉ ×LÝ*Ð àpÔLÊ1Ë ÐÚÎÔU Î1àcÏ*ÐÔOÌyÜ1Ê%×LÌyÜÐ Õ*ÔOÌIÍÌIÉ*Û*Ó(Ú©Ý*ÐÔOÐ ×LÝ*Ð
ÒN×LÎ-ÍkÝÊ1ÒN×LÌIÍ Õ*ÔOÎ-ÍÐÒOÒ ×LÝ*ÐÉ ÔOÐ.-ÐÍ×LÒ©×LÝ*Ð Õ*ÔOÌIÍÐÕ*ÔOÎ-ÍÐÒOÒÞ
V
ÎÉY×LÔLÊ1ÔNÈ ×LÎc×LÝ*Ð\ÔLÊ%×LÝ*ÐÔÒOÌIË Õ*ÑIÐàpÎÔOË Î1à×LÝ*Ð\Ï*Ì+Ø*ÒOÌIÎÉ ÐGØÊ%×LÌIÎÉ $< Ó%ÒOØ*ÍkÝ ÊÍÑIÎÒOÐÏ-Ù
àpÎÔOË ÌIÒ ÎÉ*ÑyÈ UGÉ*Î/Ú©É àpÎÔ Ê àpÐÚ ÍÊ1ÒOÐÒÓjÐ1Þ³Û*Þ{×LÝ*Ð F ÌIÐÉ*ÐÔ Ë Î-Ï*ÐÑÓ×LÝ*Ð ÛÐÎË Ð×LÔOÌIÍ
F ÌIÐÉ*ÐÔ©Ë Î-Ï*ÐÑÓ-×LÝ*ÐXW{Ê1ÒOÌIÍÐU Ë Î-Ï*ÐÑ[Ê1É*Ï ×LÝ*Ð V ÎYGÙ+/fÉ*ÛÐÔOÒOÎÑÙZ©ÎÒOÒ©Ë Î-Ï*ÐÑÞ
/fÉ Ê ÕÊ1Õ#ÐÔ Î1à
\[[[
ÒOÐÐ
&]*
Ó;^cÌy×NÙT_AÊ1ÝÊ1ÑIÌQÊ Õ*ÔOÐÒOÐÉY×LÐÏ Ê Ë Ð×LÝ*Î-Ï ÑIÐÊ1Ï*ÌIÉ*Û ×LÎ Ê
ÍÑIÎÒOÐÏ-ÙUàpÎÔOË Ê1Õ*Õ*ÔOÎYAÌIË Ê%×LÌIÎÉ àpÎÔ ×LÝ*Ð Ð*Ê1Í× ×LÔLÊ1É*ÒOÌy×LÌIÎÉ Ï*ÐÉ*ÒOÌy×fÈÞ`¤ÌIÒ Ê1Õ*Õ*ÔOÎYÊ1ÍkÝ ÌIÒ
7Ê1ÒOÐÏ ÎÉ Ê `¤ÐÔOË Ìy×LÐjÐÕÊ1É*ÒOÌIÎÉ Î1à+×LÝ*ЩÏ*ÐÉ*ÒOÌy×fÈ Ê1ÔOÎØ*É*Ï Ê É*ÎÔOË Ê1ÑÏ*ÐÉ*ÒOÌy×fÈ àpØ*É*Í×LÌIÎÉ¢Þ
ÇØ*Ð{×LÎc×LÝ*ÐÍÑIÎÒOÐÏ àpÎÔOË Ó/×LÝ*Ð\Ê1ÏAÜ1Ê1ÉY×kÊ1ÛÐÒàpÎÔ(Ï*ÐÔOÌyÜ1Ê%×LÌyÜÐÕ*ÔOÌIÍÌIÉ*Û¤ÔOÐË Ê1ÌIÉ¢Ó7#ÐÌy×(×LÝÊ%×
×LÝ*ÐÊ1ÍÍØ*ÔLÊ1ÍÈ Ï*ÌIË ÌIÉ*ÌIÒOÝ*ÐÒÞa jÝ*ÐÕ*ÔOÎ7*ÑIÐË Ú©Ìy×LÝ ×LÝ*ÐË Ð×LÝ*Î-Ï ^cÌy×NÙT_AÊ1ÝÊ1ÑIÌQÊÕ*ÔOÎÕ#ÎÒOÐÒÓ
ÌIÒ ×LÝÊ%× Ìy× ÍÎÉYÜÐÔOÛÐÒ àpÎÔ b Kdc H ÛÎÌIÉ*Û ×LÎ eÐÔOÎ*Ó7*ØA× Ìy× Ë ÊÈ ÑIÐÊ1Ï ×LÎ 7Ê1Ï
Ê1Õ*Õ*ÔOÎYAÌIË Ê%×LÌIÎÉ*Ò Ú©Ý*ÐÉ ×LÝ*Ð ×LÌIË Ð Ý*ÎÔOÌ8eÎÉ ÌIÉ*ÍÔOÐÊ1ÒOÐÒÞ>ÎÔ ÖÉÊ1É*ÍÌQÊ1Ñ\Ê1Õ*Õ*ÑIÌIÍÊ%×LÌIÎÉ*ÒÓ
×LÝ*Ð Ê1ØA×LÝ*ÎÔjÒLÊÈ-Ò¤×LÝÊ%×Bb ÌIÒ©É*ÐÜÐÔB7*ÌIÛÛÐÔ\×LÝÊ1É ×LÝ*ÔOÐÐ ÎÔ©ÒOÌf Ë ÎÉY×LÝ*ÒÓÒOÎ ×LÝ*ÌIÒjÚ©ÌIÑIÑ
Ë Ø*ÍkÝ ÑQÊ1ÔOÛÐÔjÝ*ÎÔOÌ8eÎÉ¢Þ
/fÉ ×LÝ*Ð Õ*ÔOÐÒOÐÉY× ÕÊ1Õ#ÐÔÓ#ÚÐ Ú\Ê1ÉY××LÎ ÛÌyÜÐ Ê1É Ê1É*ÒNÚÐÔ×LÎ/Ú\Ê1ÔOÏ*Ò×LÝ*Ð ÒOÎÑIØA×LÌIÎÉ Î1à×LÝ*Ð
Õ*ÔOÎ7*ÑIÐË Ò ÒU1Ð×LÍkÝ*ÐÏ Ê07#Î/ÜÐ1Þ>ÌIÔOÒN×ÓÚÐ ÒOÝ*Î/Ú Ý*Î/Ú àpÎÔ ÛÐÉ*ÐÔLÊ1Ñ\×fÈ-Õ#ÐÒ Î1àcÏ*Ì+Ø*ÒOÌIÎÉ
Õ*ÔOÎ-ÍÐÒOÒOÐÒÓ\Ú©Ý*Ð×LÝ*ÐÔ ×LÝ*Ð ×LÌIË Ð ÌIÉY×LÐÔNÜ1Ê1ѤÌIÒ ÒOË Ê1ÑIѤÎÔ 7*ÌIÛ*Ó×LÝ*Ð ×LÔLÊ1É*ÒOÌy×LÌIÎÉ Ï*ÐÉ*ÒOÌy×fÈ
G
HI20HJK.I20K ÍÊ1É 7#ÐÐAÕ*ÔOÐÒOÒOÐÏ 7YÈ Ë ÐÊ1É*ÒjÎ1àÊ >ÐÈ-É*Ë Ê1É ÕÊ%×LÝ ÌIÉY×LÐÛÔLÊ1ÑÞ jÝ*ÌIÒjÌIÒ
Ê Õ#Î/ÚÐÔNàpØ*Ñ{ÍÎÉ*ÍÐÕA× 7#ÎÔOÔOÎ/ÚÐÏ àpÔOÎË GØÊ1ÉY×LØ*Ë Ë ÐÍkÝÊ1É*ÌIÍÒ Ø*ÒOÐÏ ×LÎ Ï*ÐÒOÍÔOÌ87#Ð ×LÝ*Ð
Ê1Ë Õ*ÑIÌy×LØ*Ï*Щ×LÎ Ë Î/ÜÐB7#Ð×fÚÐÐÉ ×fÚÎ Õ#ÎÌIÉY×LÒÌyà[ÐÊ1ÍkÝ Õ#ÎÒOÒOÌ87*ÑIÐcÕÊ%×LÝ ÌIÒ{ÛÌyÜÐÉ Ê ÍÐÔN×kÊ1ÌIÉ
Õ*ÔOÎ7Ê07*ÌIÑIÌy×fÈÞß Ê0UGÌIÉ*Û Ø*ÒOÐ Î1à¤ÒOÕ#ÐÍÌyÖÍ Õ*ÔOÎÕ#ÐÔN×LÌIÐÒ Ê1É*Ï ÍÊ1ÑIÍØ*ÑQÊ%×LÌIÎÉ ×LÐÍkÝ*É*Ì8GØ*ÐÒ ÎÉ
ÕÊ%×LÝ ÌIÉY×LÐÛÔLÊ1ÑIÒÓ\ÚÐ ÒOÝ*Î/Ú ×LÝÊ%× Ê1É Ð*Ê1Í× ÍÊ1ÑIÍØ*ÑQÊ%×LÌIÎÉ ÌIÒ É*Î1× ÎÉ*ÑyÈ Õ#ÎÒOÒOÌ87*ÑIÐ àpÎÔ
×LÝ*Ð àpÎØ*ÔÍÑQÊ1ÒOÒOÌIÍÊ1ÑË Î-Ï*ÐÑIÒË ÐÉY×LÌIÎÉ*ÐÏ ÐÊ1ÔOÑIÌIÐÔÓ47*ØA× Ê1ÑIÒOÎ àpÎÔÒOÎË Ð Î1×LÝ*ÐÔ×fÈ-Õ#ÐÒ Î1à
Õ*ÔOÎ-ÍÐÒOÒOÐÒÞ
_-ÐÍÎÉ*Ï*ÑyÈÓGÒN×kÊ1ÔN×LÌIÉ*Û àpÔOÎË ×LÝ*ФÕÊ%×LÝ ÌIÉY×LÐÛÔLÊ1ÑÐAÕ*ÔOÐÒOÒOÌIÎÉ àpÎÔ×LÝ*Щ×LÔLÊ1É*ÒOÌy×LÌIÎÉ Ï*ÐÉ*ÒOÌy×fÈÓ
ÚÐ Õ#ÎÌIÉY×©ÎØAשÝ*Î/Ú ×LÎ ÖÉ*Ï Ê ÍÑIÎÒOÐÏ-ÙUàpÎÔOË Ê1Õ*Õ*ÔOÎYAÌIË Ê%×LÌIÎÉ àpÎÔ\×LÝ*Ð×LÔLÊ1É*ÒOÌy×LÌIÎÉ Ï*ÐÉ-Ù
ÒOÌy×fÈÓØ*ÒLÊ07*ÑIÐàpÎÔÊ1ÉYÈ Ï*Ì+Ø*ÒOÌIÎÉ Õ*ÔOÎ-ÍÐÒOÒÓÚ©Ìy×LÝ ÜÐÔNÈ Ý*ÌIÛÝ Ê1ÍÍØ*ÔLÊ1ÍÈÞL/fÉ ÍÎÉY×LÔLÊ1ÒN×Ú©Ìy×LÝ
×LÝ*Ð©Ë Ð×LÝ*Î-Ï Ï*ÐÜÐÑIÎÕ*Õ#ÐÏ ÌIÉ
&]*
Ó×LÝ*ÌIÒÊ1Õ*Õ*ÔOÎYAÌIË Ê%×LÌIÎÉ ÍÊ1É 7#ЩØ*ÒOÐÏ àpÎÔ{ÊÒOÝ*ÎÔN××LÌIË Ð
ÒOÕÊ1É Ê1ÒjÚÐÑIÑ£Ê1ÒjàpÎÔ©Ê ÑQÊ1ÔOÛÐÔ\Ý*ÎÔOÌ8eÎÉ¢Þ
jÝ*Ð ÕÊ1Õ#ÐÔ ÌIÒ ÎÔOÛYÊ1É*Ì8eÐÏ Ê1Ò àpÎÑIÑIÎ/Ú©ÒÞ F Ð ÒN×kÊ1ÔN× Ú©Ìy×LÝ Ê 7*ÔOÌIÐàcÏ*ÐÒOÍÔOÌIÕA×LÌIÎÉ Î1à¤×LÝ*Ð
ÍÎÉ*ÍÐÕA×LÒ Ê1É*Ï É*Î1×kÊ%×LÌIÎÉ*Ò Ê07#ÎØA× ÒN×LÎ-ÍkÝÊ1ÒN×LÌIÍ Ï*Ì+ÐÔOÐÉY×LÌQÊ1ÑÐGØÊ%×LÌIÎÉ*Ò Ê1É*Ï >ÐÈ-É*Ë Ê1É
ÕÊ%×LÝ ÌIÉY×LÐÛÔLÊ1ÑIÒÌIÉ ÒOÐÍ×LÌIÎÉ < Þ _-ÐÍ×LÌIÎÉ ÍÎÉY×kÊ1ÌIÉ*Ò×LÝ*Ð ÖÔOÒN× ÌIË Õ#ÎÔN×kÊ1ÉY×ÔOÐÒOØ*Ñy×Ó¢ÐGÙ
Õ*ÔOÐÒOÒOÌIÉ*Û ×LÝ*Ð ×LÔLÊ1É*ÒOÌy×LÌIÎÉ Ï*ÐÉ*ÒOÌy×LÌIÐÒ©àpÎÔ©ÛÐÉ*ÐÔLÊ1Ñ£Ï*Ì+Ø*ÒOÌIÎÉ Õ*ÔOÎ-ÍÐÒOÒOÐÒB7YÈ Ë ÐÊ1É*Ò©Î1àÊ
ÕÊ%×LÝ ÌIÉY×LÐÛÔLÊ1ÑÞ/fÉ ÒOÐÍ×LÌIÎÉ *ÓrÚÐ ÒOÝ*Î/Ú Ý*Î/Ú ×LÝ*Ð Ë Î-ÏÊ1Ñ(ÕÊ%×LÝ ÎÔË ÊAÌIË Ø*Ë Õ*ÔOÎ7-Ù
Ê07*ÌIÑIÌy×fÈ ÕÊ%×LÝ ÍÊ1É 7#Ð Ï*Ð×LÐÔOË ÌIÉ*ÐÏ¢Þ_-ÐÍ×LÌIÎÉ ÌIÒcË ÐÊ1ÉY××LÎ Õ*ÔOÎ/ÜÐ Ý*Î/Ú ×LÝ*Ð àdÊ1Ë ÎØ*Ò
/U×Î ÑIÐË Ë Ê ÍÊ1É 7#Ð ×LÔLÊ1É*ÒOÑQÊ%×LÐÏ ÌIÉY×LÎ ×LÝ*Ð ÕÊ%×LÝ ÌIÉY×LÐÛÔLÊ1Ñ£àpÎÔOË Ê1ÑIÌIÒOË Þ=^¤àw×LÐÔNÚ\Ê1ÔOÏ*ÒÌIÉ
ÒOÐÍ×LÌIÎÉ AÓ¢ÚÐ Ë ÐÉY×LÌIÎÉ ×LÝ*Ð ÑIÌIË Ìy×LÌIÉ*Û ÍÊ1ÒOÐ Î1à\ÑIÎÉ*Û ×LÐÔOË Õ*ÔOÎ7Ê07*ÌIÑIÌy×LÌIÐÒÞ6_-ÐÍ×LÌIÎÉ @
×LÎÛÐ×LÝ*ÐÔÚ©Ìy×LÝ ÒOÐÍ×LÌIÎÉ
Î1à¢ÍÎØ*ÔOÒOÐ
ÍÎÉ*ÒN×LÌy×LØA×LÐÒ{×LÝ*Ð T7#Î-ÏAÈ Î1à¢×LÝ*ÌIÒÕÊ1Õ#ÐÔÞ)`¤ÐÔOÐ
ÚÐcÒOÝ*Î/Ú Óa7Ê1ÒOÐÏ ÎÉ ×LÝ*ФÕÊ%×LÝ ÌIÉY×LÐÛÔLÊ1ÑÐAÕ*ÔOÐÒOÒOÌIÎÉ¢Ó-Ý*Î/Ú ×LÝ*Щ×LÔLÊ1É*ÒOÌy×LÌIÎÉ Ï*ÐÉ*ÒOÌy×fÈ àpÎÔ
ÛÐÉ*ÐÔLÊ1ÑÏ*Ì+Ø*ÒOÌIÎÉ Õ*ÔOÎ-ÍÐÒOÒOÐÒ ÍÊ1É 7#Ð Ê1Õ*Õ*ÔOÎYAÌIË Ê%×LÐÏ Ú©Ìy×LÝ Ê ÍÑIÎÒOÐÏ-ÙUàpÎÔOË àpÎÔOË Ø*ÑQÊAÞ
/fÉ ÒOÐÍ×LÌIÎÉ ÚÐ Õ*ÔOÐÒOÐÉY× Ð*Ê1Ë Õ*ÑIÐÒcÎ1à×LÝ*Ð Ë Ð×LÝ*Î-Ï*ÎÑIÎÛ1ÈÓàpÎÔ¤ÍÎË Ë ÎÉ Ë Î-Ï*ÐÑIÒ©ÌIÉ
×LÝ*Ð ÖÉÊ1É*ÍÌQÊ1Ñ×LÝ*ÐÎÔNÈÞ F Ð ÛÌyÜÐ Ê1É ÐAÕ*ÔOÐÒOÒOÌIÎÉ àpÎÔ ×LÝ*Ð ×LÔLÊ1É*ÒOÌy×LÌIÎÉ Õ*ÔOÎ7Ê07*ÌIÑIÌy×fÈ ÌIÉ
ÐÊ1ÍkÝ ÍÊ1ÒOÐ1Ó#×LÎÛÐ×LÝ*ÐÔcÚ©Ìy×LÝ Ê1É ÐAÕ*ÑIÌIÍÌy×cÍÊ1ÑIÍØ*ÑQÊ%×LÌIÎÉ ÌyàÕ#ÎÒOÒOÌ87*ÑIÐ1Þ6_-ÐÍ×LÌIÎÉ [ Ï*ÐË ÎÉ-Ù
ÒN×LÔLÊ%×LÐÒ ×LÝ*Ð Ê1ÍÍØ*ÔLÊ1ÍÈ Î1à\ÎØ*Ô É*ÐÚ Ê1Õ*Õ*ÔOÎYAÌIË Ê%×LÌIÎÉ 7YÈ Ë ÐÊ1É*Ò Î1àjÊ àpÐÚ ÛÔLÊ1Õ*Ý*ÌIÍÊ1Ñ
ÌIÑIÑIØ*ÒN×LÔLÊ%×LÌIÎÉ*ÒÞ
jÝ*Ð Õ*ÔOÎ-Î1àpÒ Î1à×LÝ*Ð ×LÝ*ÐÎÔOÐË Ò Ê1É*Ï ÒOÎË Ð ÐAÕ*ÑIÌIÍÌy× ÍÎË Õ*ØA×kÊ%×LÌIÎÉÊ1Ñ\ÔOÐÒOØ*Ñy×LÒ Ê07#ÎØA×
ÕÊ%×LÝ ÌIÉY×LÐÛÔLÊ1ÑIÒjÊ1ÔOÐ 7*ÔOÎØ*ÛÝYש×LÎÛÐ×LÝ*ÐÔjÌIÉ ×LÝ*Ð Ê1Õ*Õ#ÐÉ*Ï*Ìf+Þ
"!#$!%&'!$(*)+%,
/fÉ ÎÔOÏ*ÐÔ ×LÎ ÐAÕ*ÑQÊ1ÌIÉ ×LÝ*Ð ÒOÌIË ÌIÑQÊ1ÔOÌy×LÌIÐÒ Ê1É*Ï Ï*ÌIÒOÒOÌIË ÌIÑQÊ1ÔOÌy×LÌIÐÒ 7#Ð×fÚÐÐÉ /U×Î ÌIÉY×LÐÛÔLÊ1ÑIÒ
Ê1É*Ï ÕÊ%×LÝ ÌIÉY×LÐÛÔLÊ1ÑIÒÓ(ÚÐ 7*ÔOÌIÐ.-*È ÌIÉY×LÔOÎ-Ï*Ø*ÍÐ ×LÝ*Ð ÍÎÉ*ÍÐÕA× Î1àcÊ ÛÐÉ*ÐÔLÊ1Ñ\ÒN×LÎ-ÍkÝÊ1ÒN×LÌIÍ
Ï*Ì+ÐÔOÐÉY×LÌQÊ1Ñ¢ÐGØÊ%×LÌIÎÉ¢Þ
^ -/ÙfÒN×LÎ-ÍkÝÊ1ÒN×LÌIÍÏ*Ì+ÐÔOÐÉY×LÌQÊ1Ñ¢ÐGØÊ%×LÌIÎÉ ÌIÒjÏ*ÐÖÉ*ÐÏ Ê1Ò
.4 T
P
0/
Ú©Ìy×LÝ ÒOÎÑIØA×LÌIÎÉ
'L
C
12
.4 $##T# C
12
P
$##0/ $#
Ú©Ý*ÐÔOÐ ÌIÒ©Ê ÒN×kÊ1É*ÏÊ1ÔOÏ 1ÔOÎ/Ú©É*ÌQÊ1É Ë Î1×LÌIÎÉ¢Þ
jÝ*ЩÖÔOÒN×ÌIÉY×LÐÛÔLÊ1ÑÌIÉ ÌIÒÊ Z©ÌIÐË Ê1É*É-ÙfÌIÉY×LÐÛÔLÊ1ÑÓ4×LÝ*ЩÒOÐÍÎÉ*Ï ÎÉ*ФÌIÒ{Ê -/ÙfÒN×LÎ-ÍkÝÊ1ÒN×LÌIÍ
ÌIÉY×LÐÛÔLÊ1ÑÞ
/Uà43
! 3
$## % &(')+*,
ÌIÒcÊ Õ*ÔOÎ-ÍÐÒOÒÊ1ÏÊ1ÕA×LÐÏ ×LÎ ×LÝ*Ð ÉÊ%×LØ*ÔLÊ1Ñ?1ÔOÎ/Ú©É*ÌQÊ1É ÖÑy×LÔLÊ4Ù
×LÌIÎÉ¢ÓA×LÝ*Ð -/ÙfÒN×LÎ-ÍkÝÊ1ÒN×LÌIÍÌIÉY×LÐÛÔLÊ1Ñ
56 /07
C 3
C
12 3 $#0/ $#
ÌIÒjÏ*ÐÖÉ*ÐÏ 7YÈ
5 6 /07
C 3 ÑIÌIË
89;:
8+<&=
>?A@BDC EF0G
?H
EI EF
?AJLK
HNM
I EF
?
HOH
EP
H
QSRUTVWXZY&VT\[$]^[$]_RUW ` a F Bcb
F
Kdb e^e^e&b
Ff+g Kdb
Ff
a F
QSRUTih;j]_kj l Vm
EF
?AJLK
M F ? Hon
`,p
VWq h;]^[$j
F G
?sr*tvu
Vwi[$R
F G? a F
?,x y
EF
?AJLK
M F ? H{z
| r
hdVW[;[$R qT$V}h V+[O[
r
W[$]_RUW [$R [$jT r*r ~ Y r
k*]VwDkjRU]_k r*~
RQ y z
| j r W y ]
~;r*tvu
VwD[$R r TORp&[$j
r
Vw ur*~
RQ
C
VT
r
kjR
~Or
W V+[c[$j
r wr
Q[;YLRU]_W[
~
pLVWq
[$j
r
y
~
[$R kj&V
~
[$]_k ]_W[
r*
T$Vw4k*RU]_Wk*]_q r*~
h;]^[$j VW [+R ~ [$R kj&V
~
[$]_k ]_W[
r*
T$Vw
z | r
h;]_w_w
[$j WR[V+[$]_RUW
B
C
E EI
HOH
a C
B EI E
H ,H
I E
H
E
H
h;j
r W h r u~Or
[$j]
~
[X Y
r
RQ ]_W[
r*
T$V+[$]_RUW z
j r l R ~ [ ]_l YLRUT\[VW[ Vq
VW[V
Ur
RQ
[$j]
~
kjRU]_k r ]~
[$j
r
QVk[ [$j&V+[ [+R ~ [$R kj&V
~
[$]_k ]_W[
r*
T$Vw
~ ~
V+[$]
~
QX [$j
r l VT\[$]_W
Vw
r
YTORUY
r
T\[X z
q]
~
Vq
VW[V
Ur
jRh rUr
Td]
~
[$j&V+[ [$j
r
kj&V]_W T u wr RQDk*wV
~O~
]_k}Vw&k}Vw_k u w
u~
]~ WR[
Vw_]_q
z
| j r W y ]
~;r*tvu
Vw [$R p&[$j
r
Vw ur*~
RQ
C
VT
r
kjR
~Or
W V+[c[$j
r l ]_q YLRU]_W[
~
pLVWq
[$j
r
y
~
[$R kj&V
~
[$]_k ]_W[
r*
T$Vw T r q u k r*~
[$R V v[$T$V+[$RUWR
]_kj
~
[$R kj&V
~
[$]_k ]_W[
r*
T$Vw
z | r
h;]_w_w u~Or
[$j
r
WR[V+[$]_RUW
K
C
E EI
HOH
a C
B EI E
HOH
I E
H
E
H
E
h;]^[$jR
u
[]_Wq r m H
h;j
r W h r u~Or
[$j]
~
[X Y
r
RQ]_W[
r*
T$V+[$]_RUW z
j r ~ [$R kj&V
~
[$]_k ]_W[
r*
T$Vw
WR w_RUW
Ur
T ~ V+[$]
~&r*~
[$j
r l VT\[$]_W
Vw
r
YTORUY
r
T\[XUp
u [ WRh [$j
r
k*wV
~O~
]_k}Vw kj&V]_W T u w r
]~
QSRUTOl Vw_w^X
~
V+[$]
~&r
qipRUT
C
B
! SEI E
HOH
G
@LK
I E
H a EI EF
HOHNM
EI E `
HOH
e
E"
H
]_Wk rZ~
[$R kj&V
~
[$]_kZ]_W[
r*
T$Vw
~
h;]^[$j
y a r
j&V
Ur
w_]$#
r&%
]r l VWW ]_W[
r*
T$Vw
~ E
[$R V
k r T\[V]_W
r
m [
r
W[
H
p&[$j
r
RUl ]^[O[VWk
r
RQ VW ]_Wq
r m
~Or*r
l ~ Vk*k
r
Y,[V'w rz
j
rs~
]^[
u
V+[$]_RUW h;]^[$j
y
r*tvu
VwL[$R sk*RUTOT
r*~
YLRUWq
~
[$R V kjRU]_k
r
QSRUT4[$j
r
TO]
j[ YLRU]_W[
~*z
| r
h;]_w_w q r WR[
r
[$j]
~
#v]_Wq RQN]_W[
r*
T$V+[$]_RUW V ~
K
C
E EI
HOH
a C
B EI E
H( H
I E
H e E
`
H
j r
QSRUw_w_Rh;]_W
T r
wV+[$]_RUW r [h
r*r
W
Ur
W r T$Vw
y
~
[$R kj&V
~
[$]_k ]_W[
r*
T$Vw
~
VWq v[$T$V+[$RUWR
]_kj
~
[$R kj&V
~
[$]_k ]_W[
r*
T$Vw
~
h;]_w_w) r Ur
T\X j r w_Y,Q
u
w]_W [$j r q
rUr
w_RUYl
r
W[ZRQ4R
u
Tsl
r
[$jR qRUw
R X * C
B EI E
H G H
I E
H a C
B EI E
HOH+
I E
H x E y M
H C
B
! SEI E
HOH
e E
H
YTOR RQk}VW r
QSR
u
Wq ]_W VW
r V ~ X hdV}X u~
]_W
V}X w_RUT
r
m,Y&VW
~
]_RUW
~*z
r
X Wl VW Y&V+[$j ]_W[
r*
T$Vw
~
RUTO]
]_W&V+[
r
QSTORUl tvu
VW[
u l l r
kj&VW]_k
~
ph;j r T r
[$j
r X VT
r
u~Or
q [$R q
r*~
k*TO]$
r
[$j
r
Vl Yw_]^[
u q r
[$R
R QSTORUl RUW
r
YLRU]_W[;[$R VWR[$j
r
TcYLRU]_W[}ph;j r T r
r
Vkj YLR
~O~
]$w
r
[$T$V
r
k[$RUT\X ]~ ]
Ur
W V k r
T\[V]_W YTOR&V']_w_]^[X
z s~ ~Ou
kjip [$j r X YTOR
]_q r V
Ur
T\X r
k*]
r
W[o[$R RUw]_W [$j r q r
TO]
V+[$]_RUW RQL[$T$VW
~
]^[$]_RUW YTOR&V']_w_]^[$]
r*~*z
R[
r
[$j&V+[ ]_W [$j
r
RUTO]
]_W&VwNVYYTORVkjip
r
X Wl VW
u~Or
q VW ]_l V
]_W&VT\X VT
Uu
l r
W[ RQ [$j
r r
m,YLRUW
r
W[$]Vw
Q u
Wk[$]_RUWip,h;j
r T r V ~ h r u~Or
V T r VwDVT
Uu
l r
W[ u [ #
r*r
Y [$j
r
QSRUTOl Vw_]
~ l z
r
X Wl VW Y&V+[$j ]_W[
r*
T$Vw
EF "!#$&%OF '!#$'
H a
C)(+*-,(
C/.0*-,0.
1
#NE H 2
g4365
(
5.
87 , D
*-,
D *D :9
D E
H
h;j r T r ;
E=<# E
H
!#NE H ! H ]~
k}Vw_w r q [$j
r > V
T$VW
]VWip,]
~ q r W r q X
EF "!#$&%OF '!#$' H a ?@BA
fCED
EF
:GIH
H f # K #
e^e^e
#&f+g
K
J 2 M H
f+g
K
>?A@B
; K #
?AJLK
M # ?
H ! #
?,x
#
?AJLK
! F
?,x
F
?AJLK
L E
M
H
QSRUTV;Y&VT\[$]^[$]_RUW F
a F
Bcb
F K b e^e^e&b Ff
a
F '
h;j r T r H a
EF '
M
F
H
ON VWq
F
?AJLK
a F
?x
H
VWq h;j
r T r h r u~Or
q [$j
r
WR[V+[$]_RUW
# ? a
#NEF
?
H{z
[ ]~
]_l YLRUT\[VW[ [$R WR[
r
[$j&V+[ ]_W QVk[ [$j]
~ q r
W]^[$]_RUW l V'#
r*~ u~Or
RQcV l ]_qYLRU]_W[
kjRU]_k r V ~
]^[ hdV
~
[$j
r
k}V
~Or
QSRUTN[$j
r
Y&VT\[$]^[$]_RUW ]_W V v[$T$V+[$RUWR
]_kj
~
[$R kj&V
~
[$]_k ]_W[
r*
T$Vw
z
s~
V k*RUW
~Or*tvur
Wk r p RUW
r
j&V
~
[$R r Ur
T\X k}VT r Q u
wNh;j
r W k*RUl Y&VTO]_W
RUT"l ]Am,]_W
[+R
k}Vw_k u w
u~
VWq
r
X Wl VW Y&V+[$j ]_W[
r*
T$Vw
~*z
s~
VW
r
mVl Yw
r
p&h
r
k*RUW
~
]_q
r
T"V P TORh;W]VW l R[$]_RUWip,QSRUT;h;j]_kj [$j
r > V
T$VW
]VW ]~
r*tvu
Vw[$R
;
E6<#Q!#R! H a 7 ,S
z
W [$j&V+[Zk}V
~Or
[$j
r l u
w^[$]_Yw
r
]_W[
r*
T$V+[$]_RUW k}VW r h RUT # r q
R u
[;]_W V ~
[$T$V]
j[OQSRUT\hdVTOq hdV}XUp&T r*~Ou
w^[$]_W
]_W
C)(+*-,(
C/.8*-,0.
1
#NE
H 2 M
C)(
C/.
<
# E
H
a ?@BA fCED
EF
:GIH
H f #
Ke^e^e
#&f+g
K 2 M H
f+g
K
>?A@B K #
?AJLK
M # ?
H L
a
:G EF '
M
F H 2 M
E#$'
M
#$
H
EF '
M
F
H e E H
j]
~ h r
w_w#vWRh;W T
r*~Ou
w^[4k}VW r T r
Vq V ~
[$j
r
[$T$VW
~
]^[$]_RUW YTOR&V']_w_]^[XZ[$R
R"QSTORUl [$j
r
~
[VT\[$]_W
YLRU]_W[
#$
V+[ [$]_l
r
F
[$R"[$j r
W&Vw,YLRU]_W[
#$'
V+[N[$]_l
r
F '
h;j r W [$j
rdu
Wq
r
TOw^X ]_W
YTOR k r*~O~
]~ V ~
[VWq&VTOq P TORh;W]VW l R[$]_RUW
z
j&VWq
~
RUl r T
r*~Ou
w^[4V'LR
u [ r
X Wl VW Y&V+[$j ]_W[
r*
T$Vw
~
k}VW r
QSR
u
Wq ]_W [$j
rd~
R"k}Vw_w r q
RUw_l R
RUTOR
YTORUY
r
T\[X
z
[
~
jRh
~
jRh [$R h;TO]^[
r V Y&V+[$j ]_W[
r*
T$Vw V ~ V k*RUl ]_W&V+[$]_RUW
RQ
~Ou
k*k r*~O~
]
Ur rUr
W[
~ *
EF &!#$"%OF '!#$'
H a J D
g=D
# D
EF "!#$&%OF
D
!#
D H J EF
D
!#
D
%OF '!#$'
H ! E , H
h;j
r T r F D ]~
VWX [$]_l
r r
[h r*r
W
F
VWq F '
z
TOR RQ
~
pVYYw_]_k}V+[$]_RUW
~
VWq l RUT
r q r
[V]_w
~
V'LR
u
[D[$j]
~
YLRh
r
T\Q
u
wvk*RUWk
r
Y,[Nk}VW r
QSR
u
Wq
rzz
]_W M,p P p
,
z
l YLRUT\[VW[ k*RUl Y u
[V+[$]_RUW&VwNT r*~Ou
w^[
~
VT r ~Ou
l l VTO]_
r q ]_W VYY
r
Wq]Am
z
W [$j]
~ ~Or
k[$]_RUWiph r ~
jRh jRh [$j
r
[$T$VW
~
]^[$]_RUW YTOR&V']_w_]^[X QSRUT
~
[$R kj&V
~
[$]_k YTOR k r*~O~Or*~
q r W r q X l r
VW
~
RQ"V
~
[$R kj&V
~
[$]_k q]
r T r
W[$]Vw r*tvu
V+[$]_RUWip k}VW r r
m,YT r*~O~Or
q X
l r VW
~
RQ;V r
X Wl VW Y&V+[$j ]_W[
r*
T$Vw
z | r ~
[VT\[ h;]^[$j V q]
u~
]_RUW r*tvu
V+[$]_RUW h;]^[$j
u
W]^[Zq]
u~
]_RUWip VWq h r Ur
W r T$Vw_]_
r
[$j r T
r*~Ou
w^["QSRUT r*tvu
V+[$]_RUW
~
h;j r T r
[$j
r
q]
u~
]_RUW
]~ V Q u
Wk[$]_RUW RQN[$j
r ~
[$R kj&V
~
[$]_kZYTOR k r*~O~*z
TOR RQ
~
VT
r
YTOR
]_q
r q ]_W VYY
r
Wq]Am P z
!"#$ &%' (*) =,+-
y.
)0/ 6:+ / -1+32 8+Q54766+ )
8
EF
H a 9 E 8
EF HOH
F x I EF
H E P H
:
8
I EF
H
+ - ;- <E
) :
+ = )
+
)
> =,++ ) ? )A@ @ +B+CED ) )0/ 6:+ / ? )0/ 00
8 a F 8
E
H ! G `
!OF
H /
@ :
I+
@ C = 8=
) D ?6 +Q:
J E`
!5K
B
%OF!5K
C H a
K
CIL M1NPO 8
EF HRQ
K
C5S
8 E` H a K B E H
a C* 5
B
*
1
KiE
H 2 M C
B <K M C
B 9
EK
H x 9
K
x C
B 9
EK H
K e
>
+ 80,6/ + +- ?- ) D / ) + / ) D y
+ - ++ ) ) D )0/ 6:+ /
+
> )
I= ?
)A@
@ +B+CED
) R?
)0/
00
8 /
@ /
/
65- :
J EK H a w_]_l
C
CED J E `
!5K
B
%OF! K H a EK
B H 2 9
E H
! E H
:
8
/ )
= EK
B H
+ - I= + 5-
@ C / )
-1++
) ) D )
&= :0 54766
) ) "
$ &%'
Qo[$j
r
qRUl V]_W RQ4[$j
r ~
[$R kj&V
~
[$]_k YTOR k
r*~O~ 8 ]~ E ` ! x H
]_W
~ [ r
Vq
RQ
E M ! x H
p,[$j
r
q]
r T r
W[$]VwiY&VT\[ 1 KiE
H
j&V
~
[$R r T r
YwVk
r q X 1 J
KiE H{z
$ &%
j r
wV
~
[;]_W[
r*
T$VwD]_W [$j r r
m,YLRUW
r
W[sRQ
E H r
j&V
Ur*~
V ~ V v[$T$V+[$R
WR
]_kj ]_W[
r*
T$Vw z)
[$T$VW
~
QSRUTOl V+[$]_RUW ]_W[$R VW [+R ]_W[
r*
T$Vw V ~ l r
W[$]_RUW r q ]_W
E
H p
r
W&V'w r*~;u~
[$R h;TO]^[
r
[$j r ~
jRUT\[;[$]_l
r
[$T$VW
~
]^[$]_RUW YTOR&V']_w_]^[X V ~
J E`
!5K
B
% F!5K
H
a
F
:G
F 2 M
EK
M K B H
F M F
9
EK
B H x 9
EK B H
EK M K B H
a
F
:G
F 2 M
EK
M K B M F 9
EK
B
HOH
F ! E " H
h;j]_kj k*RU]_Wk*]_q
r*~
h;]^[$j [$j
r
k*wV
~O~
]_k}Vw
r
m,YT r*~O~
]_RUW QSRUT l r V
~Ou
T
r*~
V
~O~
R k*]V+[
r q h;]^[$j
q]
u~
]_RUW YTOR k r*~O~Or*~
h;]^[$j
u
W]^[
RUwV+[$]_w_]^[X
z
$ &% j r
k*RUW
~
[$]^[
u
[$]_RUW RQc[$j
r
Y&V+[$j ]_W[
r*
T$Vw E H
W]_k
r
w^X ]_w_w u~
[$T$V+[
r*~
Z]_T
~
VWR
~
[$j
r
RUT
r l E
~Or*r rzz
H{z
Wq r*r
qip&[$j
r
YTOR k r*~O~
EF
H a r
m,Y
C
B 9
EI E
H H
I E
HM
C
B 9
EI E
HOH
! E
`
H
]~ [$j
r %
VqRUW
]$#R q,X l q r
TO]
V+[$]
Ur
RQ4[$j
r l r V
~Ou
T r ]_W
E H
[$R [$j
r | ]r W r
T"l r V
~Ou
T
rz+s~
V k*RUW
~Or*tvur
Wk r p [$j
r
q]
u~
]_RUW YTOR k r*~O~
q r W r q X
E P H ]~ V P TORh;W]VW
l R[$]_RUW h;]^[$j T
r*~
Y r
k[ [$R [$j
r l r V
~Ou
T r q r W r q X [$j
r
[$T$VW
~
]^[$]_RUW YTOR&V']_w_]^[X ]_W
E H{z
R[
r
[$j&V+[ ]_W k}V
~Or
[$j r ~
[$R kj&V
~
[$]_k YTOR k r*~O~ 8
j&V
~
qRUl V]_W
E ` ! x H
]_W
~ [ r
Vq RQ
E M ! x H
p[$j
r
YTOR k r*~O~
EF
H
RQ
E
` H ]~
[$j
r %
VqRUW
]$#R q,X l w_]$#
r q r
TO]
V+[$]
Ur
h;]^[$j T r*~
Y r
k[c[$R V P TORh;W]VW l R[$]_RUW #v]_w_w
r q V+[c
r
TOR
z
$ &%
j r
[$T$VW
~
]^[$]_RUW YTOR&V']_w_]^[X ]_W E H
Vw
~ R ~
V+[$]
~&r*~
[$j
r
QSRUT\hdVTOq
R##
r T
wVWk # r*tvu
V+[$]_RUW
J
F a
J
K
C M
K C E 9 EK
C H J J H ! E H
h;j
r T r J ]
~cu~Or
q V ~ V ~
jRUT\[sj&VWq WR[V+[$]_RUW QSRUT [$j
r
YTOR&V']_w_]^[X
J E `
!5K
B
%OF!5K
CH p
~Or*r
rzz
` z
!"#$ &% (*) =,+-
y.
)0/ 6:+ / -1+32 8+Q54766+ )
8
EF
H a 9 E 8
EF HOH
F x E 8
EF HOH
G I EF
H E
H
:
8
I EF
H
+ - ;- <E ) :
+ = ) + )
/ 6 ) D OI+ @ 0
C EF
H a 3 C
B
8
E
H
E 8 E
HOH
G
@LK
a E8
EF HOH
80,6/ + :
)0/ 6:+ / -1+32 8+Q54766+ )
C EF
H a 9 E g K
EC EF
HOHOH
E g K
EC EF
HOHOH
x Ey M
H
K E g K
EC EF
HOHOH
F x I EF
H e E
M
H
> + 80,6/E+ - ?- ) / ) + / ) D y
+ - ++ ) ) D )0/ 6:+ /
+
!"#$ &% (*) =,+- ) )0/ 6:+ / -1+32 8+ Q54766+ )
8
EF
H a 9 E 8
EF HOH
F x E 8
EF H H
I EF
H E H
:
8
I EF
H
+ - ;- <E ) :
+ = ) + ) -
:
8
EK
H a 3
E
H - 0
) . - / 88:,+ DI6 / + )
> =,++ ) ? )A@ @ +B+CED ) )0/ 6:+ / ? )0/ 00
8 a F 8
E
H ! G `
!OF
H /
@ :
I+ @ C = 8= ) D ?6 +Q:
J E`
!5K
B
%OF!5K
C H a K C L M1NPO
8 EF
HRQ
K
C5S
8 E` H a K B E , H
a
EK
CH J C* 5
B
*
1
KiE
H 2 M C
B <K
J 2 M
C
B
EK
H x
K x
B
EK H
K !
:
8 DI6 / +) + - 5- @ C
E
H a 9 E g K
E HOH
E g K
E HOH
M
K E g K
E HOH
e E P H
> ) I= ? )A@ @ +B+CED ) R? )0/ 00
8 / @ / / 65- :
J E K H a w_]_l
CED J E`
!5K
B
%OF! K H a EK
B H
E K H 2
E H
! E H
:
8 / ) =
EK B H
+ - I= + 5- @ C / ) -1++ ) ) D ) &= :0 54766
) ) "
$ &%
Q[$j
r
qRUl V]_W RQ [$j
rZ~
[$R kj&V
~
[$]_kZYTOR k r*~O~
E 8 H a F E 8
E HOH
! G
`
!OF
H
] ~ E ` ! x H
]_W
~ [ r
Vq RQ
E M ! x H
p&[$j
r
q]
r T r
W[$]VwY&VT\[
1
KiE
H V ~ r
QSRUT
r
j&V
~
[$R r T r
YwVk
r q X 1 J
KiE H{z
$ &%
RUT [$j
r ~
[$R kj&V
~
[$]_k YTOR k r*~O~
RQ [$j
r
RUT
r l M z
M,pd[$j
r ~
jRUT\[ [$]_l
r
[$T$VW
~
]^[$]_RUW YTOR&V']_w_]^[X ]~ r*tvu Vwi[$R
J E`
!5K
B
% F!5K
H a
EK
H
F
:G
F 2 M E
EK
H M
EK
B
HNM
F E
EK
B
HOHOH
F e E H
]_Wk
r h r
VT r q r
Vw_]_W
h;]^[$j ]_W
W]^[
r*~
]_l Vw[$]_l r Y r
TO]_R q
~
p,h
r
k}VW h;TO]^[
r
EK HNM
EK B H a
EK
M K B H J
EK B H a
EK
M K B H J
EK
B H ! E " H
VWq h;]^[$j VW m,Yw_]_k*]^[V+[$]_RUW RQ
ph R,[V]_W [$j k*wV ]_k}Vw m,YT ]_RUW
J E `
!5K
B
% F!5K
H a
:G
F
EK B H 2 M
EK
M K B M F 9
EK
B
HOH
F
EK
B H e E
MU`
H
$ &%
j r
[$T$VW
~
]^[$]_RUW YTOR&V']_w_]^[X ]_W E , H
WRh
~
V+[$]
~&r*~
[$j
r
QSRUT\hdVTOq
R##
r T
wVWk # r*tvu
V+[$]_RUW
J
F a
K
EK
H J J
M
K E 9
EK
H J J H ! E M H
h;j
r T r J ]
~cu~Or
q V ~ V ~
jRUT\[sj&VWq WR[V+[$]_RUW QSRUT [$j
r
YTOR&V']_w_]^[X
J E `
!5K
B
%OF!5K
H p
~Or*r
rzz
` z
RUT
y a `,po[$j
r
YT r
]_R u~
T
r*~Ou
w^[
~ h r T r
Vw_T
r
Vq,X q r
TO]
Ur
q X [$j
r ~
Vl r V u
[$jRUT
~
r
VTOw_]
r T E
~Or*r
H % jRh
rUr
T*pi]_W [$j&V+[sk*RUW[$TO]$
u
[$]_RUW [$j
r
Y&V+[$j ]_W[
r*
T$Vw
~ h r T r
QSR
u
Wq
]_W V k*RUl Yw
r [ r
w^X q]
r T r
W[shdV}XUpLh;]^[$jR
u
[sl V'#v]_W
u~Or
RQ4 [+R k}Vw_k u w
u~*z!
j r T r*~Ou
w^[
RQ[$j
r
RUT
r l M z QSRUT
y a ` ]~
Vw
~ R l r
W[$]_RUW
r q ]_W z
"$ !
s~
l r W[$]_RUW
r q r
QSRUT
r
piV
r
X Wl VW Y&V+[$j ]_W[
r*
T$Vw
EF &!#$"%OF '!#$' H V ~
]_W
E
H q r
~
k*TO]$
r*~
[$j
r
Vl Yw_]^[
u q r
[$R
R QSTORUl [$j
r
YLRU]_W[
#$
V+[ [$]_l
r
F
[$R [$j
r
YLRU]_W[
#$'
V+[
[$]_l
r
F '
ph;j r T r r
Vkj [$T$V
r
k[$RUT\X ]
~c
]
Ur
W V k r
T\[V]_W YTOR&V']_w_]^[X Vk*k*RUTOq]_W
[$R [$j
r
~
[$R kj&V
~
[$]_k YTOR k r*~O~
T r wV+[
r q [$R [$j r > V
T$VW
]VW
z
W QVk[}pL]_W [$j
r
h;jRUw r ~Or
["RQ4[$T$V
r k[$RUTO]
r*~
k*RUWW
r
k[$]_W
[$j
r
[h R YLRU]_W[
~
p&RUWw^X Y&V+[$j
~
]_W [$j r
]_k*]_W]^[X RQN[$j
r
k*wV
~O~
]_k}Vw
RUT l R q&Vw&Y&V+[$j YTOR
]_q
r
]_l YLRUT\[VW[ k*RUW[$TO]$
u
[$]_RUW
~
[$R
EF "!#$&%OF '!#$' H{z
Wq r*r
qip QSRUT
R[$j
r
TZY&V+[$j
~ p [$j r T r
VT
r
Vw^hdV}X
~ W r ]
jLR
u
TO]_W
[$T$V
r
k[$RUTO]
r*~
[$j&V+[Zk}VWk
r
w4R
u
["[$j
r
]_T
k*RUW[$TO]$
u
[$]_RUW
z
j]
~ l R q&Vw Y&V+[$jipZRUT l Vm,]_l
u l YTOR&V']_w_]^[X Y&V+[$jipZk}VW r q r [ r
TOl ]_W
r q E
~Or*r
rzz
P H V ~ [$j
r ~
RUw
u
[$]_RUW RQ[$j
r
RUTOq]_W&VT\X
~Or
k*RUWq RUTOq
r
T;q]
r T r
W[$]Vw r*tvu
V+[$]_RUW
F ;
<# a ;
# E M H
~Ou
r
k[c[$R [$j
r
LR
u
Wq&VT\X k*RUWq]^[$]_RUW
~
#NEF H a
#$
VWq
#NEF ' H a
#$'
z
VW mVl Yw p]^Q&h k*RUW ]_q T [$j P TORh;W]VW l R[$]_RUWip[$j l Vm,]_l l YTOR&V']_w_]^[X
Y&V+[$j ] ~ ]
Ur
W X
# 9
E
S
F &!#$"%OF '!#$' H a
F '
M
F '
M
F
#$
x M
F
F '
M
F
#$'
e E M M H
>
R R#v]_W
QSRUT [$j
r l R q&Vw"Y&V+[$j QSRUT
~
[$R kj&V
~
[$]_k YTOR k r*~O~Or*~
q r W r q X
~
[$R kj&V
~
[$]_k
q]
r T r
W[$]Vw r*tvu
V+[$]_RUW
~
]_W V QSRUTOl V ~ ]_W
~Or
k[$]_RUW M,p*[$j
r
QSRUw_w_Rh;]_W
W]_k r T
r*~Ou
w^[VYY
r
VT
~*z
!"#$ "%' (*) =,+- )0/ 6:+ / ? )0/ 00
8 a F 8
E
H ! G `
!OF
H - 5-
@ C -1+32E6 ,+ ) 54766+ ) :
+ 6+ -1+32E6 ,+ ) > = A+= #? )A@ @ +B+C ?6
K 9
E
H D ) + ? )0/ 00
:
+ ? ) +
K B
+= - I+0+
K
+= F / @ - I= + 5- += ? B+ / + BC @ C
.
K
9
EK
H x
x
EK
B
!5K
HZa ! E M H
:
8 EK
B
!5K
H
+ 5- @ C / ) -1++ )
K 9
EF
H a K >
,+ + I+:
6- ,+- + 54766 ) ,+ ) D -1+32 8 /
K 9
E HNM
K B
!"#$ "% (*) =,+- )0/ 6:+ / ? )0/ 00
8 a F 8
E
H ! G `
!OF
H - 5-
@ C -1+32E6 ,+ ) 54766+ ) :
+ 6+ -1+32E6 ,+ ) > = A+= #? )A@ @ +B+C ?6
K 9
E
H D ) + ? )0/ 00
:
+ ? ) +
K B
+= - I+0+
K
+= F / @ - I= + 5- += ? B+ / + BC @ C
.
#
E#
H x
, x
EK
B
!5K
H a ! E M , H
:
8 + - 5- + ) 8,= + - 5- + 4-
:
8 EK
B
!5K
H +
5- @ C / ) -1++ )
K 9
EF
H a K > ,+ + I+: 6- ,+- + 54766I )
,+ ) D -1+32 8 /
EK 9
E HOHNM
EK B H
!" I $ $ !" ! 0!#" P$ $
$ RUW
~
]_q r T V
V]_W V ~
[$R kj&V
~
[$]_k YTOR k
r*~O~ 8 a F 8
E
H ! G `
!OF
H q r [ r
TOl ]_W
r q X
[$j r ~
[$R kj&V
~
[$]_k q]
r T r
W[$]Vw r*tvu
V+[$]_RUW E P H
p&h;j
r T r I EF
H ]~ V ~
[VWq&VTOq P TORh;W]VW
l R[$]_RUW z
TORUl [$j
r
RUT
r l M z
UpNh
r
#vWRh [$j&V+[ [$j
r
[$T$VW
~
]^[$]_RUW YTOR&V']_w_]^[X k}VW r
h;TO]^[O[
r W X l r
VW
~
RQ[$j
r
Y&V+[$j ]_W[
r*
T$Vw
J%
E`
!5K
B
%OF!5K
H
a
*
5
B
*
1
KiE
H 2 M
B <K M
B 9
EK
H x 9
K
x
B 9
EK H
K e E M P H
RUw_w_Rh;]_W
[+R ~ wr l l V,p}[$j r ~
[$R kj&V
~
[$]_kdq]
r T r
W[$]Vw r*tvu
V+[$]_RUW QSRUTN[$j
r
YTOR k r*~O~
C a
F C E
H ! G `
!OF
H h;j
r W 8
EF
H a EC EF
HOH
p&]
~ ]
Ur
W X
C EF
H a
K g K E 8
EF H &H
F x
K g K E 8
EF H H
8
EF
H
a M
E8
EF H &H
E 8 EF
H H
F x
E 8
EF H H
8
EF
H ! E M H
RUT ]_W [$j
r
R[$j
r
T;q]_T
r
k[$]_RUW
8
EF
H a EC EF
H H
EC EF
H H
F x
! SEC EF
H H
C EF
H e E M H
j r tvur*~
[$]_RUW [$j&V+[ VTO]
~Or*~
]~ * jRh k}VW [$j]
~
[$T$VW
~
QSRUTOl V+[$]_RUW r r
m [
r
Wq
r q ]_W[$R
[$j
r
Y&V+[$j ]_W[
r*
T$Vw
E M P H
R[
r
[$j&V+[ h r j&V
Ur
[$R [V'#
r
]_W[$R Vk*k*R
u
W[c[$j
r
q]
k u
w^[X
[$j&V+[}pDk*RUW[$T$VT\X [$R [$j
r
[+R wr l l V,p[$j
r
]_W[
r*
T$V+[$]_RUW
~
]_W [$j
r
Y&V+[$j ]_W[
r*
T$Vw4VT
r
RQ
[$j
r
v[$T$V+[$RUWR
]_kj [X Y rz
V'#v]_W
"u~Or
RQV
~
[$R kj&V
~
[$]_k [$]_l
r
kj&VW
Ur
]_W [$j
r
Y&V+[$j ]_W[
r*
T$Vw EM P H
p+RUW
r
k}VW YTOR
Ur
[$j
r
QSRUw_w_Rh;]_W
T r*~Ou
w^[
E
~Or*r
VYY
r
Wq]Am P H *
!"#$ &%' (*) =,+- )0/ 6:+ / -1+32 8+Q54766+ )
8
EF
H a 9 E 8
EF HOH
F x I EF
H E M " H
:
8
I EF
H
+ - ;- <E ) :
+ = ) +) - =D ) I= + ) 8
EF
H a
EC EF
HOH
D ) :
+ / + 8 DI6 / +) +
:
. - 5-
+ D ) = ?6 + ,? 800,+ ) D ) =,++) ? )A@ @ +B+C D )
? )0/ 00
8 a F 8
E
H ! G `
!OF
H =,++) ? )A@ @ +B+C D ) ? )0/ 00
C a F C E
H ! G `
!OF
H / @ D ) 6- :
J E `
!#
B a g K
EK B H
%OF!#
a g K
EK
HOH
E ` H
a
E
g K
EK
B
HOH
J E
g K
EK
HOH
J J D
g=D
2 @ F J D
B
F
J
*
5
B *
1
#NE
H 2 M
B <# M @
B
! SE#
H
J 2 M
B 9 E#
H x 9
K E#
H
! SE#
H
J 2 x
B 9 E#
H E#
H
# M
B M E#
H
E#
H M E#
H
E#
H
e
s~
VW
r
mVl Yw
r p k*RUW
~
]_q r T [$j
r
[$T$VW
~
QSRUTOl V+[$]_RUW
8
EF
H a EC EF
HOH
a g K
EC EF
HOH
h;j r T r
[$j r Q u
Wk[$]_RUW ]~
kjR
~Or
W ]_W
~Ou
kj V hdV}X [$j&V+[
EK
H a 2 M 9
E
H e E H
RUw_w_Rh;]_W
[+R ~ wr l l V,pvQSRUTd[$j]
~
kjRU]_k
r h r
#vWRh [$j&V+[
C EF
H a
SE
8
EF H H
I EF
H a
EC EF
H H
I EF
H ! E H
RUT
I EF
H a
! SEC EF
H H
C EF
H e E M H
YYw^X ]_W
[$j
r
RUT
r l , z
Up&V
~
[$T$V]
j[OQSRUT\hdVTOq k}Vw_k
u
wV+[$]_RUW wr Vq
~
[$R [$j r T
r*~Ou
w^[
J E`
!#
B
%OF!#
H a J D
B F F M
B
! SE#
H
J
*-,
5
B
*-,
1
#NE H 2 g S
35
7
, S
9
E
U
H
h;j]_kj W]_k
r
w^X [ ~
h;]^[$j E M
H{z
/ 80,6/ D ) R?6 +
W [$j
r
YT r
]_R u~d~Or
k[$]_RUW
~
p,h rZ~
jRh
r q jRh [$R
Wq VW&Vw^Xv[$]_k}Vw
r
m,YT r*~O~
]_RUW
~
QSRUT [$j
r
[$T$VW
~
]^[$]_RUW YTOR&V']_w_]^[X RQ;q]
u~
]_RUW YTOR k r*~O~Or*~
X l r
VW
~
RQ;Y&V+[$j ]_W[
r*
T$Vw
~*z
RUT
[$j
r
k*RUl Y u
[V+[$]_RUW RQ[$j r*~Or
Q u
Wk[$]_RUW&Vwv]_W[
r*
T$V+[$]_RUW
~
ph
r
k}VW T r w^X RUW
~
RUl
r l r
[$jR q
~
VWq k}Vw_k
u
wV+[$]_RUW
~
QSTORUl tvu
VW[
u l l r
kj&VW]_k
~*z
W VYY
r
Wq]Am
h r ~Ou
l l VTO]_
r
VcQ r h
]_l YLRUT\[VW[ VWq
u~Or
Q u w r
mVk[;k*RUl Y u
[V+[$]_RUW&VwLT r*~Ou
w^[
~
QSRUTdk*RUl l RUW k*wV
~O~Or*~
RQY&V+[$j
]_W[
r*
T$Vw
~ p ~
RUl
r
RQNh;j]_kj h r T r q r
TO]
Ur
q ]_W [$j
r
QST$Vl
r h RUT # RQ
r
VTOw_]
r T T r*~Or
VTOkj RUW
VWW
u
]^[$]
r*~
h;]^[$j
~
[$R kj&V
~
[$]_k ]_W[
r T r*~
[cT$V+[
r*~*z
Rh rUr
T*p4h;j r W [$j
r > V
T$VW
]VW VYY
r
VTO]_W
]_W [$j
r
Y&V+[$j ]_W[
r*
T$Vw r
k*RUl r*~
[$R R
k*RUl Yw_]_k}V+[
r
qipLh
r
h;]_w_w j&V
Ur
[$R u~Or
VYYTOR}m,]_l V+[$]_RUW
~
]_W
~ [ r
Vq RQ
r
mVk[ T
r*~Ou
w^[
~*z
W
[$j
r
QSRUw_w_Rh;]_W
~Ou
~Or
k[$]_RUW
~ p h r
h;]_w_w
~
jRh jRh [$R
Wq VW VYYTOR}m,]_l V+[$]_RUW &V
~Or
q
RUW YTORUY
r
T\[$]
r*~
[$j&V+[;jRUw_q QSRUT
Ur
W r
T$VwDY&V+[$j ]_W[
r*
T$Vw
~*z
W RUTOq
r T [$R l V'#
r
[$j]_W
U~
k*w
r
VT*poh
r
h;]_w_w u~Or
[$j
r
WR[V+[$]_RUW
EF "!#$&%OF '!#$'
H
QSRUT
| ]r W r T;]_W[
r*
T$Vw
~
EF "!#$&%OF '!#$'
H a
(+*-,(
.8*-,0.
1
#NE
H 2 g S 3 5(
5. 7
,
S 9
4a
:G EF '
M
F H 2
g (
.
S
S 5( 5 .
E , H
VWq [$j
r
WR[V+[$]_RUW
EF "!#$&%OF '!#$'
H
QSRUT Y&V+[$j ]_W[
r*
T$Vw
~
h;j]_kj VT
r T r
wV+[
r q u
[;l RUT
r
Ur
W r
T$Vwi[$j&VW | ]r W r T ]_W[
r*
T$Vw
~ *
EF "!#$&%OF '!#$'
H a
(+*-,(
.8*-,0.
1
#NE
H 2 M
(
. <#NE
H M (
.
#
! "$#
%'&)( &)*
+!,
&
,- . *
/0+/,-1-,
&
,- 32
* &
4
(
+
&
,- . *
4 !! +65
7
*
,98 5 ,- !
&
,-
M
:+ /; 6 =<>.
*
!! 5 +
J
@?A:B!CDAE!?FGB!CDF)IH @?AB!CDA:E!?FGB!CDF)
JKJ
@?AB!CDAE!?FGB!CDF)=B $L
2
*
+5 "$#0
& (
,- 3+2
&)(
62#
&
,-
M
N #
*&)( *!O
* %>P P
,-1-1
O
+Q+ #! +2
&)(
=<>.;
&
5 8++1-# K8
*3R ,-
*
.0
&)(
P ,
&)(
P & *& & P
&:%4P3( ( P3* &!&
H J
@?AB!CDA:E!?FGB!CDF)
@?A:B!CDAE!?FGB!CDF)
! 2 P *
5 :+1-,-
P ,
&)( &)(
+/!
*
/; 5
R
,-
* . *
4 !65#
&
&)( * &)*
,-
&
,- +2
&)(
5," #!,- . *
4 !
&
&)(
5
O
+,-
$#>B&% ' %
,- :+
(
+2
&)(
"$#0
&
,-
T
+5
% &)(
5,"
* & , +1 .0
*& ( C)
(
+
& /;
*
.1 + 5 / *
( + C)
M-, *
!.; ,
:+1-1*
%
"$#0
&
,-
T ( +
& /; (
+ 5 ,-
&
! .
S0/1
@?A:B!CDAE!?FGB!CDF)
H
2
4365&
7
2
83658
( +
C)
:9 S; 2
7
2 <
C)>=@?A)
/
H S
B
;DC
@?F
9
?A=
9
@CDF
9
CDA =
;
@?F
9
?A 9 S
B
;DC
@?F
9
?A=
9
@CDFE% CDA=
=
;
@?F
9
?A=
F & &)(
&&)(
=<>.;
& &
,- ,- :+ +1-! :+!,-1* /; =<
&
5 5 2
*
.0
&)(
,-
&
G
*
+1-
5,"
* & 2* O R
,-
*
.0
&)(
,-
&
G
*
+1-
M
N
,-0+1-1*
%'P
,
&)( &)(
)
O
& &
,-
%P P
,-1-1
P3*
,& &)(
5,-
&)*
,-/#
&
,- 2
* R ,-
*
.0
&)(
P ,
&)(
<> 5 &
*&
,- +5
0+1 .;,-
&
3+
HJI
@C IH K LNMO
.QP
)@R C S P
@?A IH CDA:B
P
@?F!IH CDF
1 T
#
+5
T I
@C IH
?
?C HJI
@C IH
@?AB!CDA:E&)B!C JU
)B!C'E!?FGB!CDF)
@?AB!CDA:E!?FGB!CDF)
T4S
V
&)*
+,W
(&
2
*P
* 5 :+1-#1 &
,- 1- :+5
&
HJI
@C IH X YZ ] [\\
@?F
9
?A
)
9
?A @?F
9
) ^ C _ `
?Fa_ )Db CDAJ%
`
)c_ ?A&b CDF
?Fa_ ?A dfeg
B `
T:;
b
P3(h*4h X `
Cib
5
hGjkNlmh
lmnh
l8oNj
5
oNp
5
jk:p!O o 1fqGr
O
r1
olms
8 h tp4k
/ o / s1
sl
*:u
k:p X `
Cib H
v
w
=x 5
zy
2{}|
= ??
! j q o h lmnh t olmn sWj lmh pmo#
q
oNj jkNl%$ h q
o#
qGr
#olmh& sWj oNj h('o
q
l*) o *
)cslmn o
@q
#Wk
h&
+
k:p,
u o , hGj lmsWk:jh& $ h +
k:p4h lmnh k:j#
*
o#lmhGp4j olms.-:h
q
k:j
s l k +
oNj oNttp4k/'zs, olmsWk:j10
,
o2 sWj r
h k + lmh
q
njs3
r h +
p4k, 3 r
oNj l
r , , h q n oNjs
q
k:j lmnh k:jh n oNj& oNj& k +
lmnh tp4k:t hGp lmsWh
k + q
k:j4-:h(' k:p&hGp4h& p4s
2
k:j lmnh kNlmnhGpcn oNj&
u
)@h
q
oNj
j& o #Wk5)@hGp
oNj&
r
tt hGp $ k r
j&
+
k:p lmnh t olmn sWj lmh pmo#
0 V q
k, $sWj olmsWk:j k + $ kNlmn h('ztp4h
!
sWk:j
lmk hlmnhGp6)cslmn o q
k:p4p4h q l
4q
o#WsWj )cs##JhGj o$#Wh
r
lmk
j& oNj oNttp4k/'zs, olmsWk:j lmn ol
hGh,
lmk $ h6-:hGp
* o
qGqGr
pmolmh0
7
nh8, k
ls, t k:p l8oNj lo&9-NoNj l8o::h-k + k r
p;, hlmnk<&k#Wk:
* n o
lmk6$ h +k r
j& sWj lmnh + o q l
lmn olslp4h
4r
#l
sWj oNj oNj o#
*
lms
q
o#Ah('ztp4h
!
sWk:j
+
k:pJlmnhcoNttp4k/'zs, olmsWk:j
u
)cnhGp4h o , k l
lmh
q
njs3 r h
lmn ol oNp4h tp4h
hGj lmh& sWj lmnh #WslmhGpmol
r
p4h #Wh o& lmk h(' q #
r
s.-:h#
* j r , hGp4s
q
o#
oNttp4k/'zs, olmsWk:j
0=@k:j
h3
r
hGj l #
*:u
lmns
jh>) , hlmnk<&k#Wk:
* s
-:hGp
*
sWj lmhGp4h
lmsWj: sWj lmnh
+
pmo, h>)@k:p2 k +
lmnh tp4s
q
sWj: k + V soNj k:tzlmsWk:j 0
<? @? ?>A(B<C
7
nhD, hlmnk<& )@htp4k:t k
h-lmk
j& o qGqGr
pmolmh
r
tt hGp$ k r
j&
+
k:plmnh-lmpmoNj
slmsWk:j tp4k$<E
o$s#WslmsWh Gu
, o2Nh
r
h k + q
k:j4-:h(' k:p&hGp0%F h $p4sWh>G
*
p4h
q
o## lmnh , k l s, t k:p l8oNj l
q
k:j
q
hGtzl
oNj& jh q h
!
oNp
*
p4h 4r
#l
H
)@h p4h
+
hGp@lmk ./
u.I
;D1
+
k:p@tp4kAk +
oNj& , k:p4hJ&hl8oNs#
0
V
-NoNp4s o$#Wh6K s
3
oNs& lmk $ h , o##WhGp lmn oNj L sWj
q
k:j4-:h(' k:p&hGp4sWj:
u K
RDM
5 L u s
+N+
k:p
h o q n q k:j4-:h('
+r j q
lmsWk:j O PRQ S Q PUT VS O ` T b
lmnh h('zt h q
lmh& -No#
r h `
tp4k5-As&h&
lmnh
*
h('zs l b
oNp4h k:p&hGp4h& o .O `K b 1 R .O ` L b 1 0
V o q
k:j
h3
r
hGj
q h u .K
1XW
.L 1
oNj&
.`K _ Yb
+ 1 R .` L _ Yb
+ 1 + k:po##
Y u
)cslmn
`T b + W , oZ'
`
#9[
T b 0
\ j q h oNj h('ztp4h
!
sWk:j s 2 jk5)cj
+
k:p lmnh
lmk:t<E#Wk
!
tp4h, sr , .`L _ Yb
+ 1 u lmnh
&s
lmp4s$
r
lmsWk:j k +
lmnh -NoNp4s o$#Wh L q
oNj $ h h o
s#
* + k r
j&10
!
j&hGh&
u
lmnhGp4h s o )@h##]E
2 jk5)cj #WsWj2 $ hl)@hGhGj
lmk:t<E, k
!
tp4h, sr ,
oNj& lmnh &s
lmp4s$
r
lmsWk:j u
l8olmsWj: lmn ol
lmnh p4s::n l^E}n oNj& &hGp4s.-Nolms.-:h k + o lmk:t<E#Wk
!
tp4h, sr , .` L _ Yb
+ 1
)cslmn p4h t h q
lclmk
Y
h3
r
o#
K LNMO
.L R Y 1 _ I 0
7
nh jkNlmsWk:j k + q
k:j4-:h(' k:p&hGp4sWj:
q
oNj $ h h('AlmhGj&h&
+
p4k, l)@k
sWj:#Wh -NoNp4so$#Wh
lmk
l)@k 4r
, k +
-NoNp4so$#Wh Gu
&s 4q
p4hlmh k:p
q
k:j lmsWj r k
r
0 7
nh p4h
4r
#l
oNp4h 4r
, , oNp4s_Gh& sWj
lmnh
+
k##Wk5)csWj: l)@k tp4k:t k
slmsWk:j ` +
k:p o tp4kAk
+
hGh ./
u.I
;D1
b
0U` k:p lmnh &s
lmp4s$
r
lmsWk:j Gu
)@h , o2Nh
r
h k +
lmnh jkNl8olmsWk:j
HUa
`T b W K LNMO
.QP
R T 1 H
`bc
b
IZd
lmnh sWj4-:hGp h &s lmp4s$ lmsWk:j oNp4h &h jh& sWj lmnh #o s o#X) o o
H v
a
` b W
sWj +
T Q P
HUa
`T b
`b b
9!>C > !>B< ;(B< >9! 6C !(4A !
K W " v `P v b%
" = `P = b%
99
%
"$#
`P # b
`bb
b
C%/&% A' C !(4A !6B</( ' C!>(AB< C
.
#9[
I
1(
C ) X > . C !>* Z!>+ ,B'
L W H - v
.0/21
a
/+3
` % b % H - v
. { 1a { 3 ` % b % 99
% H - v
.24*1
a
43
` % b
`b b
5 >
K
RDM
5 L
6 798 :;< 7
nh
q
k:p4p4h
t k:j&sWj: lmhGp,
sWj lmnh 4r
, K oNj& L oNp4hco##<,
r l r
o##
*
s&hGj lms
q
o##
*
&s
lmp4s$
r
lmh&
u
k:p
"=
`P = b >
W H - v
.?@1
a
?03
` % b 0
BA 9!>C > D(B< > 1
K W
2DC
7
2E
" ` P `
)Db4b ?A)6[
`b d b
C%/&% A' C !(4A !6B</( ' C!>(AB< C
.
#9[
I
1(
C ) X > . C !>* Z!>+ ,B'
L W
2DC
7
2E H - v
.F1 a 1I
3G3
` % b4b ?A)
`b b
5 >
K
RDM
5 L
V j oNtt#Ws
q
olmsWk:j k +
lmnh , hlmnk<& k + q k:j4-:h('
r
tt hGp$ k r
j&
lmk lmnh lmpmoNj
slmsWk:j tp4k$<E
o$s#WslmsWh k +
&s
"ir
sWk:j tp4k q h
!
h
Gu
$p4sWj:
-r
lmk lmnh
+
k##Wk5)csWj: p4h 4r
#l P
H I 7J798 K L NM !>(BO>B< Z! >X C @,BQP
RTSXFU*(* B*LVL>A(B<C A( /B<C Z!
W
`XZY [ T Y H
XZ[
[ T [ b R
WV\^]Z]
`XZY [ T Y H
XZ[
[ T [ b
`b / b
MR>
WV\^]Z]
`XZY [ T Y H
XZ[
[ T [ b W
`XZY [ T Y H
XZ[
[ T [
bJU_a` bGc
-d;e
C
e
Egf h
/
iJjlk jnmZopo 1`
3>2qr [ `
:# b
I
M % B</( ' C!>(AB< C
#9[
1
5
LF> "!5 A( M (> Z!
WV\^]Z]
`XZY [ T Y H
XZ[
[ T [ b W
`XZY [ T Y H
XZ[
[ T [ bJU
+ y
7
- y c
- =
Y
=
`Y S XZY
[ T Y H
XZ[
[ T [ b ?<Y
` I b
M
` Y S
XZY [ T Y H
XZ[
[ T [ b W _a`
YZ
2DC
7
2E H - v
1a 1q3G3
` %
b? _ Y eg +
` ; b
< U$M*>A(B<C
! j k:p&hGp lmk s, tp4k5-:h lmnh
r
tt hGp$ k r
j&
u
)@h o#
k jhGh& lmk &hGp4s.-:h o #Wk5)@hGp$ k r
j&
+
k:pflmnh lmpmoNj
slmsWk:j tp4k$ o$s#Wsl
* k +
&s
"ir
sWk:j tp4k q h
!
h 0 7
nh tp4h
hGj lcp4h 4r
#l%, oNsWj#
*
k:p4s::sWj olmh +
p4k, oNj oNtt#Ws
q
olmsWk:j k +
lmnh6)@h##]E2 jk5)cj sWjh3
r
o#Wsl
* k
+
hGj
hGj10
H I 7J798 BA K L NM !>(BO>B< Z! >X C @,BQP
RTSXFU*(* $M*> A(B<C A( /B<C Z!
W
`XZY [ T Y H
XZ[
[ T [ b
W Y
`XZY [ T Y H
XZ[
[ T [ b ` c b
MR>
W Y
`XZY [ T Y H
XZ[
[ T [ b `
+ b
W
`XZY [ T Y H
XZ[
[ T [ bJU_
a 1
2
3
bGc
- d;e
e
E
1a 1q3G3>2qcUc
- d;e
C
e
1a 1q3G3>2q r [
M
X I O'NL A(>M* >
XZY C
XZ[
6 798 :;< BA 7
nh jkNl8olmsWk:j
_ ..
99 11
, h oNj
oNj h('zt h q
l8olmsWk:j k5-:hGp*F sWhGjhGp@t olmn
`
k:p@o$
k:p$ h& F sWhGjhGpt olmn s+
lmnhJ&k, oNsWj k + lmnh
lmk q n o
lms
q
tp4k q h
!
s `
#9[&% ' b4b
$ hl)@hGhGj lmnh l)@k $ k r
j& oNp
*
lms, h t k:sWj l 0
<"! LVL
=@k:j
s&hGp o lmk
q n o
lms
q
tp4k q h
! # W # `
)Db([&)
.
#9[
X 1 +
k:pJ)cns
q n lmnh lmpmoNj
slmsWk:j
tp4k$ o$s#Wsl
* q
oNj $ h h('ztp4h
!
h& o sWj
` d b 0
I