• Aucun résultat trouvé

Closed form approximations for transition densities: a path integral approach

N/A
N/A
Protected

Academic year: 2021

Partager "Closed form approximations for transition densities: a path integral approach"

Copied!
40
0
0

Texte intégral

(1)

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�

(2)

!#"%$ & '('*)+!#,-"/.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}~€4€4€

bE-PQnJLKpo-X[Z\JL]_^/FIW`

 ‚+ƒk„…†G‡/„

ˆU‰ Šu‹GŒŽ[-*‘k’>“4”‘ŒŽ‰%•/‘>fŠuŒl–4Šf‘Šu‹Y‘Šf’N/‰GuŒlŠuŒl—4‰ G’u—/˜-˜-ŒŽ™ŽŒlŠuŒl‘>+šI—/’›GŒ@œžGuŒl—4‰G’u—ŸL‘>uf‘>k 4ˆU‰ 

¡ ’NfŠ¢-’uŠk“/”‘u‹Y—” ‹Y—” Šf’N/‰GuŒlŠuŒl—4‰G’u—/˜-˜-ŒŽ™ŽŒlŠuŒl‘>ršI—/’[’NŠu‹Y‘k’£–/‘>‰Y‘k’N/™G›GŒ@œžGuŒl—4‰¤G’u—ŸL‘>uf‘>

Ÿk/‰ /™l”>¥\˜*‘¤‘L¦G’u‘>uf‘>› ˜1¥ §‘>/‰G—/š -Šu‹ ŒŽ‰%Šf‘k–/’N/™w *¨Y—/’jf‘k•/‘k’N/™[Ÿk™Ž/uuŒŽŸk/™+§—›Y‘>™Žk“

/‰ ‘L¦Y/ŸLŠ\Ÿk/™ŽŸkG™ŽŠuŒl—4‰ ŒŽ*—4uuŒl˜-™l‘/“Y™l‘>/›GŒŽ‰Y–Šf— /‰G/™l¥1ŠuŒŽŸk/™ž‘L¦G’u‘>uuŒl—4‰GšI—/’{Šu‹Y‘©Šf’N/‰GuŒlŠuŒl—4‰

G’u—/˜-˜-ŒŽ™ŽŒlŠuŒl‘>£/‰G› šI—/’Šu‹Y‘j§ ¦YŒŽ§cG§ G’u—/˜-˜-ŒŽ™ŽŒlŠd¥-Šu‹Gk ª f‘>ŸL—4‰G› -’uŠŸL—4‰GuŒŽfŠu—/šrŠu‹Y‘

›Y‘k’NŒl•ŠuŒl—4‰ —/š\/‰ /‰G/™l¥1ŠuŒŽŸk/™GG’u—>¦YŒŽ§ ŠuŒl—4‰ šI—/’Šu‹Y‘ Šf’N/‰GuŒlŠuŒl—4‰ G’u—/˜-˜-ŒŽ™ŽŒlŠd¥/“+”{‹GŒŽŸN‹ ŒŽ

Gf‘kšQG™-ŒŽ‰ Ÿk/f‘\Šu‹Y‘-Šu‹ ŒŽ‰%Šf‘k–/’N/™*ŒŽ(Šf—1—ŸL—4§-™l‘L¦ Šf—c˜*‘\Ÿk/™ŽŸkG™ŽŠf‘>›ž «‹Y‘\GG’u—>¦YŒŽ§ ŠuŒl—4‰

”‘cG’u‘>f‘>‰%Šk“AŒŽ˜-/f‘>› —4‰  ŸL—4‰%•/‘L¦ ŸL—4§¤˜-ŒŽ‰GŠuŒl—4‰ —/𣐠‰Y‘k” /‰G/™l¥1ŠuŒŽŸk/™#YG*‘k’{/‰G› ™l—”‘k’

˜*—4G‰G›šI—/’£Šu‹Y‘Šf’N/‰GuŒlŠuŒl—4‰G’u—/˜-˜-ŒŽ™ŽŒlŠuŒl‘>k «‹Y‘šQ/ŸLŠ£Šu‹GŠ(Šu‹Y‘GG’u—>¦YŒŽ§ ŠuŒl—4‰ ŒŽ[/‰G/™l¥1ŠuŒŽŸk/™

‹G/f—4§‘jŒŽ§*—/’uŠu/‰%А/›Y•/‰%Šu–/‘>k“Y‘/ _–Y GšI—/’Šu‹Y‘jŒŽ‰%•/‘>fŠuŒl–4ŠuŒl—4‰ —/š+ªuŒŽ/‰ —/GŠuŒl—4‰Gk ¨¢ŒŽ‰G/™Ž™l¥/“

”‘ ›Y‘>§—4‰GfŠf’NŠf‘ Šu‹Y‘ /ŸkŸkY’N/ŸL¥ —/š\Šu‹Y‘ GG’u—>¦YŒŽ§ ŠuŒl—4‰ ˜1¥ §‘>/‰G—/šj šI‘k” –/’N-‹GŒŽŸk/™

ŒŽ™Ž™ŽGfŠf’NŠuŒl—4‰Gk 

¬

JLR n(SKfeMk­

›GŒ@œžGuŒl—4‰ G’u—ŸL‘>uf‘>k“GŠf’N/‰GuŒlŠuŒl—4‰ G’u—/˜-˜-ŒŽ™ŽŒlŠd¥A“1-Šu‹ ŒŽ‰%Šf‘k–/’N/™w“

ŸL—4§—4‰Y—/Šf—4‰GŒŽŸkŒlŠd¥

xžb®#¯*­*°4±  ³² °  µ´£¥A“ °4±  ³² °  t¶”©“*·¸ Ž¸>²1 µ¹“ ° ²1 _º °  t»£¼

½ ¾¿#À/Á4Â[Ã(Ä(Å1À4ÆpÂ#¿

ÇcÈ-ɞÊ1Ë ÌIÍ Ë Î-Ï*ÐÑIÒÓÊ1É*Ï Ë ÎÔOÐ ÒOÕ#ÐÍÌy֞ÍÊ1ÑIÑyÈ ÍÎÉY×LÌIÉGØ*ÎØ*ÒuÙU×LÌIË Ð Ë Î-Ï*ÐÑIÒÓÊ1ÔOÐ Ú©ÌIÏ*ÐÑyÈ

Ø*ÒOÐÏ Ê1É*Ï ÒN×LØ*Ï*ÌIÐÏ É*Î/Ú\Ê1ϞÊÈ-Ò ÌIÉ Õ*ÔOÌIÍÌIÉ*Û Ê1É*Ï ÌIÉYÜÐÒN×LË ÐÉY× ×LÝ*ÐÎÔOÌIÐÒÞß ÎÒN× Î1àj×LÝ*Ð

á

¶—/’u’u‘>f*—4‰G›GŒŽ‰Y–/YŠu‹Y—/’

v` gFI]+g4e4eKuJOMNMk­ /‰G‰ž µ›Y‘>uŸN‹Y‘kG*‘k’Lâ\G µ/Ÿ _˜*‘ ãQª‰G‰ ä‘åŸN‹Y‘kG*‘k’æN 

(3)

ÒN×LÎ-ÍkݞÊ1ÒN×LÌIÍ Ï*Ì+ÐÔOÐÉY×LÌQÊ1Ñ¢ÐG؞Ê%×LÌIÎÉ*ÒjÌIÉ ×LÝ*ÐàpÎÔOË

jÝ*ÌIÒ ÐG؞Ê%×LÌIÎÉ Ï*Ð֞É*ÐÒ Ê ÒN×LÎ-ÍkݞÊ1ÒN×LÌIÍ Õ*ÔOÎ-ÍÐÒOÒ !" $## % &(')+*, ÓÔOÐ.-žÐÍ×LÌIÉ*Û

Ð1Þ³Û*Þ£×LÝ*Ð Õ*ÔOÌIÍÐ Õ*ÔOÎ-ÍÐÒOÒ ÌIÉ ×LÌIË Ð1Þ/fÉ ×LÝ*ÌIÒ ÐG؞Ê%×LÌIÎÉ¢Ó !0 $## % &(')+*, ÌIÒ Ê

ÒN×kÊ1É*ϞÊ1ÔOÏ 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 ÎÔOÐ՞Ê1ÔLÊ1Ë Ð×LÐÔOÒÞ

/fÉ ×LÝ*ÌIÒ(ÍÎÉY×LÔOÌ87*ØA×LÌIÎÉ¢Ó/ÚÐ{Ú©ÌIÑIÑGÊ1ÒOÒOØ*Ë Ð{×LݞÊ%××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-ÍkݞÊ1ÒN×LÌIÍ\Ï*Ì+ÐÔOÐÉY×LÌQÊ1Ñ-ÐG؞Ê%×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 ÕžÊ1ÔLÊ1Ë Ð×LÐÔOÒÞ?>žÎÔN×LØ*ɞÊ%×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*ФÍÑQÊ1ÒOÒOÌIÍÊ1ÑžË 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×LΠ֞É*Ï Ê ÍÑIÎÒOÐÏ-ÙUàpÎÔOË ÐAÕ*ÔOÐÒOÒOÌIÎÉ àpÎÔ×LÝ*Ð

Õ*ÔOÎ7žÊ07*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-ÍkݞÊ1ÒN×LÌIÍ Õ*ÔOÎ-ÍÐÒOÒ ×LÝ*ÐÉ ÔOÐ.-žÐÍ×LÒ©×LÝ*Ð Õ*ÔOÌIÍÐÕ*ÔOÎ-ÍÐÒOÒÞ

V

ÎÉY×LÔLÊ1ÔNÈ ×LÎc×LÝ*Ð\ÔLÊ%×LÝ*ÐÔÒOÌIË Õ*ÑIÐàpÎÔOË Î1àž×LÝ*Ð\Ï*Ì+Ø*ÒOÌIÎÉ ÐG؞Ê%×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*ÛÐÔOÒOÎюÙZ©ÎÒOÒ©Ë Î-Ï*ÐÑÞ

/fÉ Ê ÕžÊ1Õ#ÐÔ Î1à

\[[[

ÒOÐÐ

&]*

Ó;^cÌy×NÙT_AÊ1ݞÊ1ÑIÌQÊ 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

7žÊ1ÒOÐÏ ÎÉ Ê `¤ÐÔOË Ìy×LÐjÐ՞Ê1É*ÒOÌIÎÉ Î1à+×LÝ*ЩÏ*ÐÉ*ÒOÌy×fÈ Ê1ÔOÎØ*É*Ï Ê É*ÎÔOË Ê1ўÏ*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×(×LݞÊ%×

×LÝ*ÐÊ1ÍÍØ*ÔLÊ1ÍÈ Ï*ÌIË ÌIÉ*ÌIÒOÝ*ÐÒÞa jÝ*ÐÕ*ÔOÎ7*ÑIÐË Ú©Ìy×LÝ ×LÝ*ÐË Ð×LÝ*Î-Ï ^cÌy×NÙT_AÊ1ݞÊ1ÑIÌQÊÕ*ÔOÎÕ#ÎÒOÐÒÓ

ÌIÒ ×LݞÊ%× Ìy× ÍÎÉYÜÐÔOÛÐÒ àpÎÔ b Kdc H ÛÎÌIÉ*Û ×LÎ eÐÔOÎ*Ó7*ØA× Ìy× Ë ÊÈ ÑIÐÊ1Ï ×LÎ 7žÊ1Ï

Ê1Õ*Õ*ÔOÎYAÌIË Ê%×LÌIÎÉ*Ò Ú©Ý*ÐÉ ×LÝ*Ð ×LÌIË Ð Ý*ÎÔOÌ8eÎÉ ÌIÉ*ÍÔOÐÊ1ÒOÐÒÞ>žÎÔ ÖžÉžÊ1É*ÍÌQÊ1Ñ\Ê1Õ*Õ*ÑIÌIÍÊ%×LÌIÎÉ*ÒÓ

×LÝ*Ð Ê1ØA×LÝ*ÎÔjÒLÊÈ-Ò¤×LݞÊ%×Bb ÌIÒ©É*ÐÜÐÔB7*ÌIÛÛÐÔ\×LݞÊ1É ×LÝ*ÔOÐÐ ÎÔ©ÒOÌf Ë ÎÉY×LÝ*ÒӞÒOÎ ×LÝ*ÌIÒjÚ©ÌIÑIÑ

(4)

Ë Ø*ÍkÝ ÑQÊ1ÔOÛÐÔjÝ*ÎÔOÌ8eÎÉ¢Þ

/fÉ ×LÝ*Ð Õ*ÔOÐÒOÐÉY× ÕžÊ1Õ#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 >žÐÈ-É*Ë Ê1É ÕžÊ%×LÝ ÌIÉY×LÐÛÔLÊ1ÑÞ jÝ*ÌIÒjÌIÒ

Ê Õ#Î/ÚÐÔNàpØ*Ñ{ÍÎÉ*ÍÐÕA× 7#ÎÔOÔOÎ/ÚÐÏ àpÔOÎË G؞Ê1ÉY×LØ*Ë Ë ÐÍkݞÊ1É*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*ÑIÐc՞Ê%×LÝ ÌIÒ{ÛÌyÜÐÉ Ê ÍÐÔN×kÊ1ÌIÉ

Õ*ÔOÎ7žÊ07*ÌIÑIÌy×fÈÞß Ê0UGÌIÉ*Û Ø*ÒOÐ Î1à¤ÒOÕ#ÐÍÌyÖžÍ Õ*ÔOÎÕ#ÐÔN×LÌIÐÒ Ê1É*Ï ÍÊ1ÑIÍØ*ÑQÊ%×LÌIÎÉ ×LÐÍkÝ*É*Ì8GØ*ÐÒ ÎÉ

՞Ê%×LÝ ÌIÉY×LÐÛÔLÊ1ÑIÒÓ\ÚÐ ÒOÝ*Î/Ú ×LݞÊ%× 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*Ф՞Ê%×LÝ ÌIÉY×LÐÛÔLÊ1ўÐAÕ*ÔOÐÒOÒOÌIÎÉ àpÎÔ×LÝ*Щ×LÔLÊ1É*ÒOÌy×LÌIÎÉ Ï*ÐÉ*ÒOÌy×fÈÓ

ÚÐ Õ#ÎÌIÉY×©ÎØAשÝ*Î/Ú ×LΠ֞É*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

ÒO՞Ê1É Ê1ÒjÚÐÑIÑ£Ê1ÒjàpÎÔ©Ê ÑQÊ1ÔOÛÐÔ\Ý*ÎÔOÌ8eÎÉ¢Þ

jÝ*Р՞Ê1Õ#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-ÍkݞÊ1ÒN×LÌIÍ Ï*Ì+ÐÔOÐÉY×LÌQÊ1ÑÐG؞Ê%×LÌIÎÉ*Ò Ê1É*Ï >žÐÈ-É*Ë Ê1É

՞Ê%×LÝ ÌIÉY×LÐÛÔLÊ1ÑIÒÌIÉ ÒOÐÍ×LÌIÎÉ < Þ _-ÐÍ×LÌIÎÉ ÍÎÉY×kÊ1ÌIÉ*Ò×LÝ*Р֞ÔOÒN× 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

՞Ê%×LÝ ÌIÉY×LÐÛÔLÊ1ÑÞ/fÉ ÒOÐÍ×LÌIÎÉ *ÓrÚÐ ÒOÝ*Î/Ú Ý*Î/Ú ×LÝ*Ð Ë Î-ϞÊ1Ñ(՞Ê%×LÝ ÎÔË ÊAÌIË Ø*Ë Õ*ÔOÎ7-Ù

Ê07*ÌIÑIÌy×fÈ ÕžÊ%×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*Р՞Ê%×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*ÔOÎ7žÊ07*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*ÌIÒ՞Ê1Õ#ÐÔÞ)`¤ÐÔOÐ

ÚÐcÒOÝ*Î/Ú Óa7žÊ1ÒOÐÏ ÎÉ ×LÝ*Ф՞Ê%×LÝ ÌIÉY×LÐÛÔLÊ1ўÐAÕ*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*ÎÑIÎÛ1ÈӞàpÎÔ¤ÍÎË Ë ÎÉ Ë Î-Ï*ÐÑIÒ©ÌIÉ

×LÝ*Р֞ɞÊ1É*ÍÌQÊ1Ñ×LÝ*ÐÎÔNÈÞ F Ð ÛÌyÜÐ Ê1É ÐAÕ*ÔOÐÒOÒOÌIÎÉ àpÎÔ ×LÝ*Ð ×LÔLÊ1É*ÒOÌy×LÌIÎÉ Õ*ÔOÎ7žÊ07*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%×LÌIÎɞÊ1Ñ\ÔOÐÒOØ*Ñy×LÒ Ê07#ÎØA×

՞Ê%×LÝ ÌIÉY×LÐÛÔLÊ1ÑIÒjÊ1ÔOÐ 7*ÔOÎØ*ÛÝYש×LÎÛÐ×LÝ*ÐÔjÌIÉ ×LÝ*Ð Ê1Õ*Õ#ÐÉ*Ï*Ìf+Þ

(5)

"!#$!%&'!$(*)+%,

/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 ÕžÊ%×LÝ ÌIÉY×LÐÛÔLÊ1ÑIÒÓ(ÚÐ 7*ÔOÌIÐ.-*È ÌIÉY×LÔOÎ-Ï*Ø*ÍÐ ×LÝ*Ð ÍÎÉ*ÍÐÕA× Î1àcÊ ÛÐÉ*ÐÔLÊ1Ñ\ÒN×LÎ-ÍkݞÊ1ÒN×LÌIÍ

Ï*Ì+ÐÔOÐÉY×LÌQÊ1Ñ¢ÐG؞Ê%×LÌIÎÉ¢Þ

^ -/ÙfÒN×LÎ-ÍkݞÊ1ÒN×LÌIÍÏ*Ì+ÐÔOÐÉY×LÌQÊ1Ñ¢ÐG؞Ê%×LÌIÎÉ ÌIÒjÏ*Ð֞É*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*ϞÊ1ÔOÏ 1ÔOÎ/Ú©É*ÌQÊ1É Ë Î1×LÌIÎÉ¢Þ

jÝ*Щ֞ÔOÒN×ÌIÉY×LÐÛÔLÊ1ўÌIÉ ÌIÒÊ Z©ÌIÐË Ê1É*É-ÙfÌIÉY×LÐÛÔLÊ1ÑÓ4×LÝ*ЩÒOÐÍÎÉ*Ï ÎÉ*ФÌIÒ{Ê -/ÙfÒN×LÎ-ÍkݞÊ1ÒN×LÌIÍ

ÌIÉY×LÐÛÔLÊ1ÑÞ

/Uà43

! 3

$## % &(')+*,

ÌIÒcÊ Õ*ÔOÎ-ÍÐÒOÒÊ1ϞÊ1ÕA×LÐÏ ×LÎ ×LÝ*РɞÊ%×LØ*ÔLÊ1Ñ?1ÔOÎ/Ú©É*ÌQÊ1É ÖžÑy×LÔLÊ4Ù

×LÌIÎÉ¢ÓA×LÝ*Ð -/ÙfÒN×LÎ-ÍkݞÊ1ÒN×LÌIÍÌIÉY×LÐÛÔLÊ1Ñ

56 /07

C 3

C

12 3 $#0/ $#

ÌIÒjÏ*Ð֞É*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

~

[$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

(6)

[$j WR[V+[$]_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 r‚Ur

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

~

[$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

~

[$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

r‚Ur

w_RUYl

r

W[ZRQ4R

u

Tsl

r

[$jR qRUw

ƒ

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

(7)

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

(8)

a

:G EF '

M

F H 2 M

E#$'

M

#$

H

EF '

M

F

H e E ˆ 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 r‚Ur

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

rz„z

]_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

(9)

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

ƒ

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 rz„z

ˆ 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

(10)

]~ [$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

ƒ

]$#R q,X l w_]$#

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

rz„z

` 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 ˆ 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:

(11)

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

(12)

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

rz„z

` 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

ˆ H % jRh

r‚Ur

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 ƒ

~

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

ƒ

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

rz„z

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

(13)

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 ˆ 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

(14)

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 ˆ ` 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

(15)

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 ˆ 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 ˆ H

RUT

I EF

H a

! SEC EF

H H

C EF

H e E ˆ 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

ˆUˆ

H

h;j]_kj W]_k

r

w^X [ ~

h;]^[$j Eˆ M

H{z

(16)

/ 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 r‚Ur

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 ˆ , 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 ,

&)(

(17)

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{}|

= ??

(18)

! 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

(19)

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

(20)

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

Références

Documents relatifs

To test whether the vesicular pool of Atat1 promotes the acetyl- ation of -tubulin in MTs, we isolated subcellular fractions from newborn mouse cortices and then assessed

Néanmoins, la dualité des acides (Lewis et Bronsted) est un système dispendieux, dont le recyclage est une opération complexe et par conséquent difficilement applicable à

Cette mutation familiale du gène MME est une substitution d’une base guanine par une base adenine sur le chromosome 3q25.2, ce qui induit un remplacement d’un acide aminé cystéine

En ouvrant cette page avec Netscape composer, vous verrez que le cadre prévu pour accueillir le panoramique a une taille déterminée, choisie par les concepteurs des hyperpaysages

Chaque séance durera deux heures, mais dans la seconde, seule la première heure sera consacrée à l'expérimentation décrite ici ; durant la seconde, les élèves travailleront sur

A time-varying respiratory elastance model is developed with a negative elastic component (E demand ), to describe the driving pressure generated during a patient initiated

The aim of this study was to assess, in three experimental fields representative of the various topoclimatological zones of Luxembourg, the impact of timing of fungicide

Attention to a relation ontology [...] refocuses security discourses to better reflect and appreciate three forms of interconnection that are not sufficiently attended to