• Aucun résultat trouvé

PAT- a Reliable Path Following Algorithm

N/A
N/A
Protected

Academic year: 2021

Partager "PAT- a Reliable Path Following Algorithm"

Copied!
25
0
0

Texte intégral

(1)

HAL Id: inria-00072655

https://hal.inria.fr/inria-00072655

Submitted on 24 May 2006

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from

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

PAT- a Reliable Path Following Algorithm

Dany Mezher, Bernard Philippe

To cite this version:

Dany Mezher, Bernard Philippe. PAT- a Reliable Path Following Algorithm. [Research Report]

RR-3991, INRIA. 2000. �inria-00072655�

(2)

ISRN INRIA/RR--3991--FR+ENG

a p p o r t

d e r e c h e r c h e

INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE

- a Reliable Path Following Algorithm

Dany Mezher, Bernard Philippe

N˚3991

Août 2000

THÈME 4

(3)
(4)

./1032547698;:+69<>=@?BAC69<D0E/1<GFIH:+JLKMJLN+NO6;P

QSRUTVXWYZ\[^]_Va`Ubdcfeg]ih9jkWe"hml@eg]iVX]dnocpeo]_hmj

q Wnsr@nseoTGVCWDnth9VClubiWv^WDn

wBxghpyzWe{"bdc

q

]_j

|"cmlUl1hmxoe q WxoWDt,RUWx,t,RUWja}9~mmu€&Z{Shm‚Ue"ƒm„m„9„Z\ƒU€…l†cp‡mWDn

ˆŠ‰+‹GŒfŽUpŒ9 ‘ WŠlUxgWGnoWj;e]ij’egRU]dn lucml†WGxac&jUW“”eoWDt,RUjU]d•;`UWX–—hmxegRUWŠxgWb_]_cm˜Ub_WXthmVXlU`@e,cfeg]ih9j™hm–SeoRUWŠš+›b_Wœ9Wbt`Uxoœ9W

q WžujUW q ˜^rŸ¡ 3¢M£3¤¦¥¨§>©Šª¬«­3®£+¢¯©^¤®^¥Iš±°“RUWGxoWa£²]dncŠthmVXlUb_Wv–—`ujut³eg]ih9jµ´"QSRUW lUxghml1h9noW q cmbi‡9hmxg]¶egRUV·˜U`u]ibq ncmj

hmxg˜U]ie¸hm–Oc q yscmtWGj;e¸WD•9`u]ibdcfegWx,cpb±eoxg]_cmjU‡mb_WGneohtcml@eo`uxoWeoRUWXb_Wœ9WbEt`UxgœmWCcpj q `unoWGnc˜u]_noWGteo]_hmj’cpb_‡mhmxg]ieoRUV)hmj™nsl1WGt]¶ž1t

eoxg]dcpjU‡9biWœmWGxseg]_tWGneoh¹thmVXlU`@egWºc™j;`uVCWGxo]dtcmb"cplUluxoh>v@]_VXcpeo]_hmj»eoh¹Ÿ   ¢M£3¤³´5QSRUW¼VXWeoRUh q lUxghfœ;]q WDn½c²‡9`ucpx,cpj;egWW&hp–

eoWGxoVX]_jucfeg]ih9jµ¾@Wœ9Wj&]ij&egRUWlUxgWGnoWjutW¸hm–xghm`Uj q^¿hmÀºWxgxoh9xgnG´

Á¼Â;ÃÅÄoÆaÇ fȋ9 wEcfeoRº–—hmb_bihf“]_jU‡u¾ulunsWG` q h ¿nol†WDt³egxo`UV¾1VXWxghmVXhmxglURU]dt¸–—`Ujuteo]_hmjunG¾†h9xo˜u]¶eD¾†˜U]dnoWGt³eg]ih9jµ¾†noV½cpb_biWDnze¸ns]_jU‡m`ub_cmx

œfcpb_`UWm´

ÉdÊ3ËoÌÎÍGÏSËбÑdÌMÒMÓÔ

Õ¦ÖÅ×GؗÙ1ÚÜÛ+×DÝ>Þpß3à,áâ>ãDä¡åDæsä±×Gçzèéæzê>çzæzäæìëí@æsçMî>ê>ï³ðéï³ñ³èéæzäoÞpÙÅæzèéò¯ãDësÞfó^æzôfà,ê>ï³ê;õÅֆá"à,èéðdö@å>à,ê÷õáæzøzî>æzòÎùú^õãDä_ûzõæså9õðéô;õ

ü

ؗý¡Ø¯×þÚÜؗÿý¡ØÜþÞpß3à,áâ>ã>äµå>æBÙÅæsà,ã>ðéèéæzã;Þýµæzê>ê>æzä±ß3æzå>æ mÞfòLà,ê>çzæõÅֆá"à,èéðdö@ôpæzò¯êfà,òLå9õâ>î>èéðéèéâ>âpæoù±èéòLèéäMàDõ_òzõ

Unité de recherche INRIA Rennes

(5)

‹



hm`unSlUxGnoWj;eghmjun

q

cpj†n¦tWxgcmlUl†h9xseS`Uj&cpb_‡mhmxg]ieoRUVXW…ž†cp˜Ub_W

q

Wns`U]_œ^]

q

W¸bi]_‡mjUWDn

q

WjU]iœ9WGcm`

q

žujU]_WGnSlucmx

Ÿ¡ 3¢M£3¤ ¥)§>©’ª «­¦®£+¢L©;¤G®¡¥#š±°kh¹£ q Gno]i‡9jUW½`UjUWŠ–—hmjuteo]_hmj¹th9VXlUbiWv@Wm´cpb_‡mhmxg]ieoRUVXWXlUxghml1h9nXthmVXVXWjutWŠlucmx

th9junseoxg`U]ixgW"`UjuW…no`U]¶egW q Weoxg]_cmjU‡mb_WGnG•;`U]_b_cpeGxgcm`@vCb_Wb_hmju‡ q W…Ÿ 3¢L£3¤BlU`U]dn`@eg]ib_]dnsW¸`Ujcmbi‡9hmxg]¶egRUVXW q W q ]_t,RUhmeoh9VC]_W"l1hm`Ux

tcmb_t`Ub_Wx`ujUWcplulUxoh>v@]_V½cfeo]_hmjXj^`UV xg]d•9`uW q WŸ 3¢L£3¤³´!cV eoRuh q W‡9cmxgcmj;eo]ieBb_cegWxgVX]ijucm]_nohmj½V "GVCW…WjŠcmxo]ieoRUV eo]d•9`uW

# hmesegcmj;eoWm´

ŒG‹

Ä

&%

 [^`u]iœ^]

q

W¦bi]_‡mjuW

q

W¦jU]_œmWDcp`µ¾flunoW`

q h ¿

nsl1WGteoxgWm¾D–—hmj†t³eo]_hmj†nVXWGxoh9VCh9xoluRUWGnG¾>hmxg˜U]¶egWm¾

q

]dt,RUhmeohmVX]_Wm¾flUb_`un±l1Weo]ieoW

œfcpb_W`Ux"no]_jU‡m`Ub_]_TxgW

(6)

$¡*+ B± $

‘ WlUxoWDnsWGj;eS]_j&eoRU]dnlucml†WGx"cClucfegR–—h9bib_hf“]iju‡Xcmbi‡9hmxg]¶egRUV eohŠthmVXlU`@egW¸eoRUW š+›b_Wœ9Wbµt`uxoœ9W¸‡9]iœ9Wj&˜^r

Ÿ¡ Å¢L£3¤¥ §D©Xª¼«¨­†®£+¢¯©^¤®9¥ š±°

“RUWGxoW£]dnSc th9VXlUbiWvX–—`Ujut³eg]ih9j q WžujUW q hfœmWGx« “RUWxgW! ]dnOc žujU]ieoWnsWeG´EQSRUW¸š+›biWGœmWb1t`UxgœmW…]_n¦c‡9xgcmlURU]dtSeoh^hmb

eoR†cfelUxghfœ;]q WDnegRUW½`unoWx“]ieoR’]ijU–—hmxgVXcpeo]_hmj’cp˜1hm`@eegRUW½nsWGjuns]ieo]_œ^]¶ezr¬hp–egRUW#"WGxoh;n¸hp–S£±´$Îe tcmj²˜1W½`unoW q eohb_h^tGcpb_]%"GW

eoRuWnsWe hp–¦eoRUWŠcmlUlUxgh>v@]iV½cfegW q "WGxoh;nhm˜@e,cp]_jUW q ˜^r²cxgh;hmežuj q ]_jU‡¬cmbi‡9hmxg]¶egRUV ]_j™“Ru]_t,R™eoRuWŠnzeghmlUlU]_jU‡ºtxo]ieoWGxo]_hmj™]_n

®£+¢¯©^¤®'& š+´($Îe+]_n±hm–ÜeoWj`unoW q ]_jegRUWtcmnoWBhm–1£+¢¯©^¤B¥ š*) +,†¢-Š› ©.^¤³¾>“RUWxgW/- ]dn±cV½cfeoxg]ivcmj q š*) +,U¢0¤]dnµegRUWnsV½cmbib_WGnse

no]ijU‡9`UbdcpxSœfcpb_`UWhp–10¾@eoRuWš+›b_Wœ9Wbµt`Uxoœ9W…]dn32^jUhf“jkc9n¦eoRUWš+›lunoW` q h½nsl1WGteoxg`UV´ $Îe"]_nS`unoW q eohXxgWb_]_cm˜Ub_r½bih@tcpeoW¸eoRuW

W]_‡mWGj^œ>cmbi`uWGn"hm–/-546;¾+€D~@¾+€Y7δ¸QSRuWCthmVXlU`@e,cfeo]_hmj¬hp–BegRUWnoV½cpb_biWDnzens]_jU‡m`ub_cmx…œfcpb_`UW]_n¸cRu]i‡9R¬th;nzethmVXlU`Uegcfeg]ih9j983]ie

tcmjk˜1Wl1Wxo–—hmxgVCW

q

“]ieoR

q

]iÀÅWxgWj;ecpb_‡mh9xo]ieoRUV½n

q

WGl†WGj

q

]_jU‡½hmjkeoRUWV½cpeoxg]¶vknseoxg`uteo`UxgW4~u¾

¾µ€D„@¾3€Dƒ:7δ

QSRUWVXh9nse]_j;eo`U]ieo]_œmWegWGt,RUjU]d•;`UWeghŠthmVXlU`UeoWaŸ   ¢M£3¤S]dneohŠthmjuno]

q

WxcCž†jUW ‡mxg]

q&q

]_ngtxgWeg]%"G]ijU‡CegRUWath9VXlUbiWvklUbdcpjuW

cpj q eghŠthmVXlU`UeoW £+¢¯©^¤O–—hmx"cmbib3‡9xo]q juh q WGnG´+QSRu]_n]dncCRU]_‡mRUb_rWv^l1Wj†ns]_œmWcplulUxoh;cmt,Rno]_jutW]ie"xoWD•;`U]ixgWGnOegRUWWœfcpb_`ucpeo]_hmj

hp–¡£kcfeOcmbibu‡mxg]q jUh q WDn´1$ìj½hmx q Wx+egh xgW q `utWSeoRUW…thmVXlU`Uegcfeg]ih9jucpb†th9nseG¾9lucfegRX–—hmb_bihf“]_jU‡ cmbi‡9hmxg]¶egRUV½nEcpxgW¦`†nsW q eoh b_hf“OWGx

eoRuW eohmegcmbj^`UV˜†WGxhp–B]_junol†WDt³egW q jUh q WDn´<;ScmnoW q hmjºthmj;eo]_j^`ucfeg]ih9j¼“]¶egR¬cŠluxoW q ]_teoh9x…th9xoxgWGteoh9x"not,RUWGVXW4_€p¾=^¾ ¾€9€>7M¾

eoRuWCluxoh@tWDnon¸V½c>r–¯cp]_bE]_j¬egRUWŠtc9nsWChp–Ono]_jU‡m`Ubdcpxl1hm]_j;egnG´?$ìj@4ƒA7M¾1;OW2fcmncpj qB cpb_b_hml1hm`Ub_h9n q Wœ9Wb_hml¬eoRUW hm˜uxgcklucfegR

–—hmb_b_hf“]ijU‡¼cmbi‡9hmxg]¶egRUVC8cR^r^˜Uxo]q cpb_‡mhmxg]ieoRUV egRucfe `†nsWDn cthmj;eg]ij^`ucpeo]_hmj’not,RUWGVXWŠthm`ulUbiW q “]ieoR¹ckžujuWŠbih@tGcpbE‡mxg]q egh

th9VXlU`@eoWŠeoRUWŠl†nsWG` q h¬nol†WDt³egxo`UV hp–"cV½cfegxo]iv3´D$ìjE4Y7ξ `U]iesž†Wbq eCcmj q |`URUW q Wœ9Wb_hml1W q cºth9j;eo]_j;`†cfeo]_hmj’VXWegRUh q

˜uc9nsW q hmj@FB`Ub_Wx¿ W“Seghmj “RU]_t,R lUxgW q ]dt³e,n½ns]_jU‡9`Ub_cmxl1hm]_j;egn½cmbih9jU‡¬egRUWbiWGœmWGbSt`UxgœmWk–—hmxXb_cmxo‡9W q ]iVXWj†ns]_hmjucmbnsluc9tW9´

QSRUWGrk]_junoWxoe…cpj¼cp`Uv^]_b_]_cmxorklucpx,cpVXWegWx"cmj q lucmngnSegRUWno]iju‡m`Ubdcpxl1hm]_j;e…`uno]iju‡Šcpjºcp`u‡mVXWj;eoW q nsr@nseoWV´ ‘ WalUxghml1h9noWc

eoWDt,RUjU]d•;`UW˜ucmnoW q hmjcC˜U]dnsWDt³eo]_hmj&lUxgh@tWGngnG´

QSRUWcpb_‡mh9xo]ieoRuV lUxoWDnsWGj;eoW q ]_jkegRU]dnSlucpl1WxhmÀ1WGxgn¦eghpegcmb3xoWGbi]dcp˜u]ib_]¶ezrX–—h9xSeoRUW thmVXlU`@e,cfeg]ih9jkhm–±Ÿ   ¢M£3¤Scfe"cCbihf“Ith;nzeD´

GU`uxsegRUWxgVXhmxgWm¾B]ie½lUxohfœ^]q WGnCc²‡m`ucmxgcmj9egWWkhp–"egWxgVC]_jucpeo]_hmj»WGœmWGj»]_j»egRUWlUxoWDnsWGjutW&hp–…xoh9`Uj q^¿hpÀ Wxgxghmx,n´¹QSRUW&V½cp]_j

]q WGc¼hm–SeoRUWklUxoh9l†h;nsW q cpb_‡mhmxg]ieoRUV ]_n eohºb_]ijuW`Ul¹cºnoWehp–"WG•;`U]_bdcfeoWGxgcmbEeoxg]dcpjU‡9biWDn cpb_hmjU‡egRUWŠb_Wœ9WbOt`UxgœmWŠcpj q `unsWkc

˜U]dnsWDt³eg]ih9jºcpb_‡mhmxg]ieoRUVH4i€ 7hfœ9WxegRUW egxo]dcpju‡mb_WœmWxoeo]dtWDneghth9VClu`@eoWCŸ   ¢L£3¤´{"bieoRUh9`U‡mRºeoRU]dn…cmlUlUxgh9c9t,Rkh9jUbir&xgWG•;`U]_xoWDn

eoRuW thmj;eg]ij^`U]iezrŠlUxghml1Wxoezr½hp–B£¼]_j&eoRUW q h9V½cp]_jkhm–]_j9egWxgWGnseG¾U“¦Wbi]_VX]¶e"h9`Ux"nseo` q reohCeoRuWez“OhC–—hmb_b_hf“]ijU‡Xtc9nsWDn

€9´£+¢¯©^¤+¥5šI) +,U¢J- ›™©.^¤SthmxgxgWGnol†h9j q ]_jU‡ eghegRUWlunoW` q h ¿nsl1WGteoxg`UV q WeoWxgVX]ij†cfeo]_hmj¡¾

ƒU´£¼]dncVXWGxoh9VCh9xoluRU]_t…–—`Uj†t³eo]_hmjK4A7Ruc>œ^]ijU‡LNM%OQPRAPSUTI®£+¢¯©^¤®p¥WVX ´

$ìj’eoRuWGnoWŠtcmnoWGnG¾Ÿ   ¢L£3¤]dneoRuWŠ`UjU]_hmj’hp–c&žujU]ieoWj;`uVa˜1Wx hm–tbih;nsW q t`UxgœmWGn q WjUhmeoW q ˜^r™Ÿ Y%ZN[  ¢L£3¤no`Uxgxoh9`Uj q ]_jU‡&eoRuW

"WGxoh;n¦hp–B£ ´

QSRUW&lucpl1WxC]dnh9xo‡;cpjU]N"W q cmna–—hmb_b_hf“"n\8eoRUWV½cfegRUWV½cfeg]_tGcpb¦˜ucmnoWGnXcmxoW q Wxg]iœ9W q ]_j noWGteo]_hmj ƒ]8OeoRUWcpb_‡mh9xo]ieoRUV egh

th9VXlU`@eoWŠcno]iju‡mb_WXthmVXl1hmjUWGj9e Ÿ^Y%Z%[  ¢L£3¤…]_n lUxoWDnsWGj;eoW q ]_j’noWGteo]_hmj’~U¾µ“Ru]ib_W½]¶e,n th9VXlUbiWv@]¶ezrº]dnWGnseo]_V½cfegW q ]ij noWGteo]_hmj

~U´_€m´a[@WGt³eg]ih9j™~u´ƒŠlUxghfœ;]q WDn…ck˜ucmt_2^“Scpx q Wxgxoh9x¸cmjucpb_r@ns]dn¸cpj q c‡9`ucpx,cpj;eoWGW hp–eoWxgVX]ij†cfeo]_hmj¡´[^WGteo]_hmj²YkxgWl1hmxoegn…eoRuW

eoWDt,RUjU]d•;`UW½`unoW q eohºthmVXlU`@egWŠcpb_bth9jUjUWGteoW q thmVXl†h9jUWj;e,nhp–¦eoRUW½b_Wœ9Wbt`UxgœmWm´#$ìj noWGteo]_hmj ¾j;`uVCWGxo]dtcmb+eoWDnze,n cpxgW

q WDnotxo]_˜†W qkq WVXhmjunseox,cfeg]iju‡egRUWxgWb_]_cm˜U]ib_]iezrŠcpj q Wa`Št]iWGjutrŠhm–egRUWlUxghml1h9noW q cpb_‡mhmxg]ieoRUV´

b c

k"- ¦ ’& ¡

‘ WalUxgWGnoWj;e]_j¼eoRu]_n¸nsWDt³eg]ih9jeoRUWVXcpeoRUWGV½cfeo]dtcmb˜†cmnoWGnhm–EeoRUWCcpb_‡mhmxg]ieoRUV `unoW q eoh&tcml@eo`UxgWegRUWalucpesegWxgjºhp–Bcno]_jU‡mb_W

th9jUjUWDt³eoW q thmVXl1hmjUWGj;eBhp–ÅeoRUWbiWGœmWb†t`UxgœmWŸ  YNZ%[ ¢M£3¤³´ ‘ W"nze,cpxoeB˜;r q WžujU]_jU‡ cb_cpeseg]_tW"hp–Å`UjU]i–—hmxgVXbir q ]_nseoxg]_˜U`@eoW q jUh q WGn

cpj q egRUW th9xoxgWGnol†h9j q ]_jU‡ egxo]dcpju‡m`UbdcpxSVXWGnoRµ¾Ucpj q egRUWj¼th9juno]q WGxcCno`U˜unoWeed]f²hp–eoRUWVXWGnoRkeoxg]_cmjU‡mb_WGn¦“RU]dt,R&thmj;egcm]ij†n

eoRuWlucpeoR²hp–OŸ 1¢M£3¤>8µ“¦Waluxohfœ9WeoRucpegd]f¹]_n…žujU]ieoWXnoWecpj q thmjunseoxg`utecŠeox,cpjuns–—hmxgV½cfeo]_hmjeghk‡9WjUWGxgcpeoWano`U˜unoWe,nhm–/d]f

–—xghmV cpj^rC‡m]_œmWj½WGbiWGVXWj;ehIªCd]f+´+QSRuW…noWeid]f“]ib_b†luxohfœ^]q WeoRuWW q ‡mWGn–—xghmV “RU]dt,RŠl†h9]ij;e,nhm–¡Ÿ¡ Å¢L£3¤OcpxgWth9VXlU`@eoW q

`uno]iju‡XcC˜U]dnoWGt³eg]ih9j¼cpb_‡mhmxg]ieoRUV´

j& —ŒÇ lk mlnKoprqs t švu@w]x^y{zI|r}sI~ }| o€ Ÿ   ¢L£3¤U}~ y‚z*| ~ |\y

ƒ

 3¢L£3¤B¥§D©X­†®£+¢¯©^¤®& š±°„

(7)

zI|oA~]p |  3¢L£3¤ o€  3¢L£3¤}~_o ]s |_ qs  y‚z*| o y~ }| o€ Ÿ¡ Å¢L£3¤?| s |_ at

 3¢L£3¤B¥§D©C­Å®£+¢L©;¤G®u š±°

}~rqs]s_o ]s |_ o | s ~ |ay

QSRUW&–¯cmte½eoRucpe L%MNOQPRAPSUTI®£+¢L©;¤G®O¥ VX]_VClubi]_WGnXegRucfe½–—h9x½Wœ9Wxgr5u wu¾egRUWxgWWv@]_nsegn¨ª)no`ut,R eoRucpe

®£+¢¯©^¤®'u “RUWjuWœmWGxa®©Å®u µ´BQSRUW nsl1WGt]_cmbµtc9nsWhp–!™¥š¬b_WGc

q

n¦eoh

ƒ  3¢M£3¤#" 0&¢w%$… @¤

“RUWGxoW 0¢Jw%$… U¤¦]dn¦eoRUW tbih;nsW qkq ]_n 2Š“]ieoR¼tWGj9egWx"cpe wCcmj q xgc q ]i`†n&… Å´

j&Â

—Œ

Ç lk

k')(

o

}

~ y}s

\y Io

}s y

~&*Bqs

,+

qp

|

~aq

} y o-

|š!.

~ |

*qpq y|_ }€ x qs



os

t }€ x

§ * $+D°0/ ƒ   ¢L£3¤21¥43 qs  § * $+>°5/   ¢L£3¤21¥43]„

6 s y‚z]}~ q~ |ax y{zI| ~ |87:9#| s y<;* $=+>/}~g~\q } yo- |š!.~ |Iqp q y|_:

1 1.5 2 2.5 3 3.5 4

1.5 2 2.5 3 3.5

Skl

Sk+1,l−1

Sk,l+1

Sk+1,l

Tkl

Tkl

~

k k+1 k+2

l−1 l l+1

G±]_‡m`UxgWX€:?EQSRUWbdcfeseg]_tW¸–—hmx"©

Z

¥EwXcmj q ©A@S¥B

C }EDA| s ¢L©

Z

$g©A@³¤¦ª¼«!F ~= _zCy{z q

Z

1¥©A@x

G

¢¯©

Z

$g©A@³¤B¥§

G)H=I

¥ © Z

VKJ3¢¯© @O›™©

Z

¤KVLo¢¯© @›™©

Z

¤NM

ZPOQ

$D¢JR$LL¤¦ªTS F °

}~ y‚z*| ]s }€aop9'q y y}U|-V~ | |<W7YX=Z o€Us o | ~<~\q yJ}~{€_t }s 7

®G[HA\I

W]

› G[H^\I®9¥¨®G[H

W]

\I › G)H^\I ®m¥ ®© Z

›’© @f®

qs  |U s }s 7 q yp }qs 7 qp 9#|~ z _

¢L©

Z

$o© @³¤B¥a`C¢¯©

Z

$g© @³¤[bac`C¢L©

Z

$g©A@³¤

((zI| p|

`I¥I§h H=I ¥ § G H^\I $ G H

W]

\I$ G H^\I

W]

° ­u¢8JR$PLM¤ªdS F °

qs  `5¥§c hc

H=I

¥ § G[H^\I$

G)H

W]

\I $ G[H

W]

\Ife

]

°­†¢JR$LL¤¦ªTS F °

( |g qs | qA~ }Et ~ |_|Uy‚z q y1h HI qs  ch H=I qp |?|=h }Eq y | p q Kyp }qs 7N| ~

(8)

$ìjŠegRUW¸–—hmb_bihf“]_jU‡†¾;“¦W q WjUhmeoW˜^r d]f¼egRUW¸no`U˜unoWehm– ¢¯©

Z

$o© @³¤O“RUWxgW!hIªQd]f¼]i–z¾ucpj q hmjUb_r½]i–z¾IhRuc9n¦cpebiWDcmnseOez“¦h

š ¿ nsWGlucpx,cfegW q œ9Wxoeo]dtWDn´

 ÇOÇ ‹:—Œ:Ç k m n(opUq E1©

Z

© @x(d]f@}~rq s }‚y| ~ |ay

 ÇµÇ GUh9x¦cmj^regxo]dcpju‡mb_Weh7ªQd]f+¾;eoRuWxgWWv@]dnze,nSc œmWGxsegWv

G

Z ª ƒ

 Å¢L£3¤´[^]ij†tW

ƒ

 3¢M£3¤E]dn¦˜†h9`Uj q W q eoRuWj

G

¢¯©

Z

$g© @³¤ /

ƒ

 3¢L£3¤¦]dncžujU]ieoW noWecpj

q *

¢d]f¡¤

*

¢G

¢L©

Z

$g© @³¤[/

ƒ

 Å¢M£3¤s¤³´

‘ W"tcpjCWGc9ns]_b_ransRuhf“ eoRucpeB]¶–h»]dnBcmjWGbiWGVCWGj;eBhp– d f eoRUWGjh Ruc9n±ez“Oh†¾mcpj q h9jUbir ez“Oh†¾mš ¿ noWl†cpx,cfeoW q W q ‡mWDn´±QSRUWxgW–—h9xoW9¾

j& —ŒÇ lk zI| o 9g9 os D| p y| y o y{zI|…š!.~ |*qp q y|_ ~ }| ~ }~ q E%|_ y‚z*| }ED o y o € h qs  | so y| ¢h…¤

j&Â

—Œ

Ç lk

| |

s

|y{zI|ry p qsI~{€aop

9 q y} os

V~

|_|<W7 ]p

|"!Z

¢{h…¤E¥ X¢¢h…¤$$#&%'B¢Lš› ®£+¢(¢h…¤s¤G®¤)*+¤¢h…¤

((zI|

p |

#&%,'B¢.-ŤB¥0/

B }€ -21 w

› B }€ - & w

qs C¢L© $39¤g}~ y{zI| p o yq y}os | s y| p |_ q y+©Xª¼« ( }‚y{z qs 7:%|3

9 q ~ | D| p>t yp }qs 7:%|eh o€ d f }s yo q yp }qs 7:%| ¢{h…¤

G±]i‡9`UxgWSƒ¸noRUhf“"neoRUWS–—h9`UxEtcmnoWGn+hm–uegRUW egxgcmjunz–—h9xoV½cpeo]_hmjµ¾>“RU]_biWSe,cp˜Ub_W"4z€65¡luxoWDnsWGj9e,neoRUW"thmxgxoWDnsl1hmj q ]ijU‡…xohmegcpeo]_hmj

cpju‡mb_WGnG´

Q¡x,cpj†nz–—h9xoV½cfeg]ih9j h

¢{h…¤ ¢{h¸¤ ¢

¢{h…¤o¤ 3

QOr;l1W Qr^l1W QOr;l1W

$$ $ $ ª ƒ   ¢M£3¤ ª ƒ   ¢M£3¤ 78

F^$ F $ ª  3¢L£3¤ ª ƒ  3¢M£3¤ › 78

F F F F ª  3¢L£3¤ ª  3¢M£3¤ › 78

$ F $ F ª ƒ   ¢M£3¤ ª   ¢M£3¤ 78

Q±cp˜ubiWX€:?BQSRuW–—hm`Uxl1h9ngns]_˜U]_bi]ieo]_WGn¦–—h9xihIcmj q9 ¢{h…¤

 ÇOÇ ‹:—Œ:Ç k k n(opUqs t | N| 9#| s yKhIªQd

f

x5( |,q }E9 y{z q y

X: ¢{h…¤ ¥lhx1

! :¢{h¸¤g}~rq D| p y| o € ¢{h…¤>x

; h qs  ¢{h…¤ qp | q =< q _| s yx

>

T z*|,o 9,9 os |  7|?yo h qs  ¢h…¤g}~ š!.~ |*qp q y | x y{zI| p |€aop | ¢{h…¤¦ªCd

f x

?

¢h…¤s¤}~Uq DA| p y | o€ hUx

@ Fm¢{h¸¤ 1¥lhx

A r}€ h7ª `C¢¯©

Z

$o© @³¤y{zI| sB ¢{h¸¤¦ª `C¢L©c

Z

$o© @³¤ qs  }€ hIª `C¢L©c

Z

$o© @³¤y{zI| s ¢h…¤Oª `C¢¯©

Z

$g©A@³¤

 ǵÇ

€9´eGUhmb_b_hf“"n–—xghmV#eoRUW q WžujU]ieo]_hmjhp– ´

ƒU´C¢{h¸¤]dn¦eoRuW tWj;egWxhp–eoRUWxghpe,cfeg]ih9jµ¾@RUWj†tW]ij^œfcpxg]dcpj;e˜;r ´

(9)

0.5 1 1.5 2 2.5 3 3.5 2

2.5 3 3.5 4

Ti

Γσ(f)

σ(f) Λσ(f)

Ti+1=F(T

i)

p(Ti+1)=p(T

i)

Qxgcmjuns–—hmxgVXcpeo]_hmjkhp–±QOr^l†W$ $³´

0 0.5 1 1.5 2 2.5 3

0.5 1 1.5 2 2.5 3

Ti Γσ(f)

σ(f) Λσ(f)

Ti+1=F(T

i) p(Ti)

p(Ti+1)

Qxgcmjunz–—h9xoV½cpeo]_hmjhm–+QOr^l†WgF^$³´

−4 −3.5 −3 −2.5 −2 −1.5 −1

−4

−3.5

−3

−2.5

−2

p(Ti+1)=p(T

i) Γσ(f)

σ(f) Λσ(f)

Ti+1=F(Ti) Ti

Qxgcmjuns–—hmxgVXcpeo]_hmjkhp–±QOr^l†WF F"´

0 0.5 1 1.5 2 2.5 3

0.5 1 1.5 2 2.5 3

Γσ(f)

σ(f) Λσ(f)

Ti+1=F(Ti) Ti

p(Ti) p(Ti+1)

Qxgcmjunz–—h9xoV½cpeo]_hmjhm–+QOr^l†Wg$ F"´

G]_‡m`uxoW ƒ ?EQSRUWegxgcmjuns–—hmxgVXcpeo]_hmj

(10)

¢{h…¤¦cpxgWc q ysc9tWj;eD´

Y†´C¢{h¸¤E]dn¦eoRUWth9VCVXh9jœmWGxsegWv½eghaegRUWš+›"nsWGlucpx,cfegW

q

no]

q

WGn¦hp–Kh7cpj

q

¢h…¤Oª

¢h…¤>8^egRUW¸–¯cmt³e¦eoR†cfeih5cpj qB

¢{h¸¤

cpxgW¸c q yscmtWj;ebiWDc q n¦eghXeoRUWxgWGno`Ub¶eD´

´eGUhmb_b_hf“"n–—xghmV#eoRUW q WžujU]ieo]_hmjhp– ¢ ¢{h…¤o¤¦cpj q Yu´

´ ‘ W2^jUhf“5eoRucpe hIcmj q ¢{h…¤ScmxoWc q yscmtWj;e8@–—`uxsegRUWxgVXhmxgW)±¢{h…¤ª h/ ¢{h¸¤Scpj q ¢ ¢{h…¤o¤SªQh / ¢{h…¤´µWe

`unth9juns]q WGxSeoRUW¸ez“¦hCl1h9ngno]i˜U]_b_]¶eg]iWDn?

FB]ieoRUWGx ¢h…¤B¥ ±¢ ¢{h¸¤s¤ F9¢{h…¤B¥ X¢¢h…¤$

F 78 ¤¢{h…¤21¥lh

hmxC±¢{h…¤ ¢ ¢h…¤s¤a8@]ij&egRU]_ntcmnoW

F

¢h…¤ ¥ X¢(¢ ¢h…¤s¤ 39¤#C¢(¢h…¤$39¤¢h…¤

¥ g;_¢±¢ ¢h…¤s¤+›9¢h…¤s¤¢NB› M e

Z

¤>ì¢{h¸¤

1

¥ h

“RUWGxoWg; >ì¢.-Ť¥ - V¼]dnSeoRUWegxgcmjunob_cpeo]_hmjhm–±œ9WGteohmx±´

@´i$ìVCVXW q ]_cpeoW9´

 ÇOÇ ‹:—Œ: Ç k }~rq- }<\|\y}os€_p o 9 d]f os y o d]f5

 ÇµÇ WlUxghfœmWaeoRucpe ]_ncŠh9jUW ¿eoh ¿h9jUW V½cplulU]iju‡u´µWe¸`†n…c9nono`UVXWaegRucfe¸eoRuWxgWaWv@]dnze¸ez“¦hŠeoxg]dcpjU‡9biWDn h¨cmj q h

no`ut,RegRucfe

¢{h¸¤B¥ ¢h

¤Scmj q h 1¥Eh „

‘ W 2^jUhf“”–—xoh9V lUxghml1h9no]¶eg]ih9j¹ƒ@´éƒkeoRucpe ¢ ¢{h…¤o¤Xª h ¾¢ ¢h…¤s¤Cª ¢h…¤³¾¢ ¢{h…¤o¤Xª Fm¢h…¤cpj q ¢ ¢h…¤s¤CªEh

eoRuWxgW–—hmxgW

¢ ¢h…¤s¤¦ª h/ ¢{h…¤ / F

¢h…¤ /Dh

GU`uxsegRUWxgVXhmxgWm¾Å“OW 2^jUhf“ eoR†cfegh ¾

Fm¢h…¤cmj

q

hcmxoWCc

q

ysc9tWj;e¸eoh

¢{h…¤´ QSRU]dn¸tGcpj²hmjUb_r¼˜†Weoxg`UWX]i– h±¥

Fm¢h…¤>8

eoRuWxgW–—hmxgWm¾

¢{h ¤ ¥ ¢ F ¢{h…¤o¤

¥ F ¢ ¢{h…¤o¤

cpj q no]_jutW F

¢{h…¤21¥lh $h5ªQd]f+¾@egRUWj ¢h

¤ 1¥ ¢h…¤³´BQSRU]dnlUxghfœmWDnOeoRucpe ­d]f d]f¬]dn"cChmjuW ¿eoh ¿ hmjuW…V½cplulU]iju‡

cpj q egRUWxgW–—h9xoWcC˜U]yzWGt³eg]ih9jhmj;eohCeoRuWžujU]ieoW noWeed

f ´

j& —ŒÇ lk WnKop3qs*t 7}ED| s hIªQd]f ( |i|U s |3y{zI| › op }‚y o€ h yo |3y{zI| ~ |\yX¢{h…¤B¥§hC¥

¢{h¸¤$ '²ªdS°

 ÇOÇ ‹:—Œ: Ç k |ayX¢{h…¤ |ry{zI| › op }‚y €aop q 7}EDA| s yp }qs 7%|!h

X:X¢{h…¤U}~Uq s }‚y| ~ |\y

! 6€ 'º¥ * ¢ X¢{h…¤o¤?y‚z*| s 'E}~ |DA| s qs  }~ y{zI| ~ 9 q E%| ~ y *oA~ }‚yJ}ED|?}s y| 7| pg~ zQy‚z q yKh½¥Ehg

; "!

e ]

Z$#%

3 Z

¥lw ¢ &

* ¤ ((zI|

p | 3 Z }~

y‚z*|

p o y q

yJ}

os qs

7:%|

o € €aop

yp } qs

7N| h Z

>

6€ X¢{h_¤U}~ y{zI| › op }‚y €aoprq yp }qs 7N| h^y{zI| s X¢{h…¤O¥'X¢{hd¤ op X¢h…¤ /X¢{hd¤¥ 3

 ǵÇ

€9´X¢{h…¤#" d]f¬cmj q d]f²]dn"cžujU]ieoW noWeG´

(11)

h e ]

¥Eh

e ]

QSRU]_nS]dnh9jUbirŠeoxg`UW]¶–

¥ wU¾@hmeoRUWGxo“]dnsW * ¢X¢{h¸¤s¤3&'E´

QSRUW–¯c9t³e¦eoRucpe 'º]_n¦WGœmWj–—hmb_bihf“"nO˜1WGtcm`unoW!h5cmj qB ¢h…¤˜†WGbih9jU‡aeghaez“¦h q ]_n¯yzhm]_j;eSnoWe,n&`C¢L©

Z

$g© @ ¤Ocpj q4c`C¢¯©

Z

$o© @ ¤³´

~u´ µWeX¢h

%

¤B¥§h

%

$h

]

$„%„N„$h e ]

°˜†WegRUW ›hmxg˜U]¶eShp–1h

%

8U]_jegRUW–—hmb_b_hf“]ijU‡†¾1§:

Z $ G Z

$

Z° q WGjUhpegWGn¦egRUW¸eoxg]_cmjU‡mb_W

h Z

no`ut,R egRucfe^

Z

]dneoRUWSlU]_œmhmehm– h

Z

cmj q ¢ e S ZG Z $ e S

Z Z

¤¥ 3 Z ¢& *

¤¡no`ut,R egRucfe ¢h

Z

¤B¥ X¢J

Z $ 3 Z

¤¢{h

Z

¤³´+QSRUWxgW–—h9xoW9¾

“OWtcmj&ngc>r

h Z /Dh

Z

W]

¥ ; Z

$

Z

>Å¥ ; Z

]

$ G Z

]

>

‘ WCRuc>œmWajUhf“ ez“Oh&tc9nsWDn\83WG]¶egRUWx<h

Z

cmj q h Z

W]

cmxoWhp–BegRUWXnocmVCWaezr^l†W 4.&hmx½¾µnoWWCQcm˜UbiW&€ 5cpj q eoRUWGxoW–—hmxgW

Z

W]

¥l

Z

cmj q G Z

]

¥

Z

biWDc q ]_jU‡eoh

e S

Z

W]

G Z

W]

¥ e S Z Z

hmx3h

Z

cpj q h Z

W]

cmxoWhm– q ]iÀ1WGxoWGj;eezr;l1Wm¾†cpj q eoRUWGxoW–—hmxgW

Z

W]

¥

Z

cmj q G Z

W]

¥E

Z

cpj q

e S

Z

W]

G Z

W]

¥›

e S

Z Z

4z€65

µWe`unthmj†ns]q Wx¦egRUW ns`uV

e ]

Z$#%

3 Z ¥ e ]

Z$#%

¢ e S

ZG Z$ Z Z

¤¨¢ &

* ¤

¥ ¢ e S

% G % $ e S % G %

¤KVKJ

* ¢& * ¤

“RUWxgW-J’]dneoRuWj^`UVa˜1Wxhp–Seoxg]dcpjU‡9biWDn nocpeo]dnz–—r^]_jU‡ 4s€ 5³´¬[@]ijutW ¢{h

%

¤C¥ h %

¾±“¦WtGcpj¹tbdcp]_V eoRucpeJ™]dnaWGœmWjK8

žujucpb_b_r

e ]

Z#%

3 Z

¥lw ¢& * ¤

Y†´ µWeih˜1W cpjWb_WVXWj;ehp– X¢{h¸¤[/ X¢hܤ>8@egRUWxgWWv@]dnze,n¦ez“OhX]_j9egW‡9Wx,n=$ ns`†t,RkegRucfe

h ¥ Z

¢{h…¤B¥

¢h

¤B¥

¢h

¤h ¥ e Z

¢{h ¤

“RUWxgW * 6 ¢X¢hܤs¤¾ub_WGc q ]ijU‡Cegh X¢h…¤#" X¢{hd¤³´ $ìj&eoRuW nocmVCW“Sc>r½“OW tGcpj&lUxghfœmW…eoRucpe X¢hܤ#" X¢h…¤³´

kfa"!#$k%(a% *+,-

$ìj²eoRU]dnnsWDt³eg]ih9jµ¾3“OW½cmjucpb_r'"W egRUWX]iVXlUb_WVXWGj9e,cfeg]ih9j²hm–BeoRUW½l†cfeoR¬–—hmb_bihf“]_jU‡cpb_‡mh9xo]ieoRUV)lUxgWGnoWj;egW

q

]_j²žu‡m`UxgWX~U´QSRuW

‡mh;cpbÅhp–±eoRu]_n"cmbi‡9hmxg]¶egRUV ]dn¦ez“Ohm–—hmb q ?

€9´eG]_j

q

cns`U]iegcm˜Ub_Wabdcfeseg]_tWacpj

q

eoRUWCth9xoxgWGnol†h9j

q

]_jU‡

›hmxg˜U]ie eoh&tcplUeo`UxgWeoRuWalucpeseoWGxoj¼hm–cŠth9jUjUWDt³eoW

q

th9V

¿

l†h9jUWj;e…hm–EeoRUWCb_WœmWGb±t`UxgœmWm´ ‘ WXnsegcpxoe…˜^r q WeoWxgVX]iju]ijU‡ez“Ohkl†h9]ij;e,n…©

Z ª ƒ  3¢M£3¤cmj q © @aª  Å¢L£3¤…ns`ut,RºeoRucpe

®© Z

›k©A@f®9¥X“RUWGxoW q WžujUWDn+eoRUWxoWDnsh9bi`@eg]ih9jXhp–1eoRUW"bdcfeoeo]dtW9´+QSRuWez“Ohl1hm]_j;egnB©

Z

cmj q © @¦cpxgW¦`†nsW q eoh‡mWGjUWx,cfegW

eoRUWbdcfeoeo]dtW G ¢¯©

Z

$o© @ ¤O“RUWxgWgh

% ¥ § G % % $ G ]% $ G % ]

°]_ncpj&Wb_WVXWj;e"hp– d f “Ru]_t,R&‡mWGjUWx,cfegWGnOeoRUW ›h9xo˜u]¶eD´

$ìjkh9`Ux]iVXlUb_WVXWGj9e,cfeg]ih9jµ¾@eoRuWeoWGt,RujU]_•;`UW`unoW q eghXthmVXlU`@egW ©

Z

cpj q © @"]dn?

(12)

]_œmWGj&š+¾¼cpj q c

© %

ns`†t,RegRucfe®£+¢

c

© %

¤G®, š

ÎÇ



2€m¾éƒ@¾_´_´i´

c

© H ¥ c

© % V &

HAe

]%M

Z

…®£+¢

c

© H

¤®Iu š

‰

Â

Ž

Â' È 

…nsWcC˜U]dnsWDt³eg]ih9jcmbi‡9hmxg]¶egRUV hfœmWGx

c

© % cmj q c

© H ¾

eghŠth9VClu`@eoW ©

Z

cpj q © @“RUWxgW

®£+¢¯©

Z

¤®, šv& ®£+¢¯© @³¤®Ucpj q ®© Z

›’© @f®9¥

¡Weih

% ¥ §>©

Z

$o© @^$g©

Z

V5¢¯© @O›’©

Z

¤NM

OQ

°ªQd]f¬˜†W cmj&]_jU]ieo]dcpbÅegxo]dcpjU‡9biW

‰ ˜u`U]ibq ]_jU‡CeoRUW ›h9xo˜u]¶ehp–1h

%

ÎÇ  ±¥ w%$ B:$ & $\„N„N„

h Z

W]

¥ ¢{h

Z¤

^h

Z

W]

¥Eh

%

‰±  Ž

Â' È 

G±]_‡m`UxgW~%?+wEcfeoRQGuhmb_bihf“]_jU‡Xcpb_‡mhmxg]ieoRUV

]_œmWj

c

© %

ns`†t,RegRucfe®£+¢

c

© %

¤G®, š+¾uth9juns]q WGxSeoRUW thmVXlUb_WvknoWG•;`UWGjutW q WžujUW q ˜^r

c

© H

W]

¥ c

© % V & H

%M

Z$

“RUWGxoW 3X]_ncx,cpj

q

hmV#cmjU‡mb_W8@]_j&eoRU]dn"tc9nsW9¾

LNM%O

H S T ®£+¢

c

© H

¤G®m¥ VXl„

µWe2J

%

ªX˜1W cCœfcpb_`UWhp–5Jno`ut,RkeoRucpe®£+¢

c

©

H

¤®'u š

`unoW cC˜U]_noWGteo]_hmjcpb_‡mh9xo]ieoRUV¾@nsegcpxoeo]_jU‡C–—xghmV

c

© % cpj

q c

© H

¾^eghŠth9VClu`@eoW¸eoRuWez“OhXl1hm]_j9e,n"©

Z

cpj q © @ ´

QSRUW ›hmxg˜U]¶e]dnS˜U`U]_b¶e…˜;rkns`utGtWDnono]iœ9Wb_rŠcplUlubir^]_jU‡ –—xghmV#egRUW]iju]¶eg]_cmb3eoxg]_cmjU‡mb_Wgh

% ´

ƒU´eG]_j q cmjcmlUlUxgh>v@]iV½cfeg]ih9jŠeghŸ  Y%ZN[ ¢L£3¤a8uegRU]dn]_n…cmt,RU]_Wœ9W q ˜^rl1Wxo–—hmxgVC]_jU‡†¾UhfœmWGxWGcmt,RWGbiWGVCWGj;e"hp– C¾†cX˜U]dnoWGt³eg]ih9j

cpb_‡mhmxg]ieoRUV nze,cpxoeo]_jU‡½–—xghmV eoRUWCš ¿noWl†cpx,cfeoW q œmWGxseg]_tWGnG´QSRUWt,Ruhm]dtW hm–EeoRUW˜U]_noWGteo]_hmj¬cmbi‡9hmxg]¶egRUV¾†luxoWDnsWGj9egW q ]_j

žu‡m`UxgW¸Yu¾U]dn q `UWeghC]iegn"xoWGbi]dcp˜U]_b_]¶ezr9´

! #"%$'&)(

µWeX¢{h…¤˜†WegRUW

›hmxg˜U]iehp– h7˜u`U]ibie"eghŠthmVXlU`UeoW cXj^`UVXWxg]_tGcpbµcmlUlUxgh>v^]_V½cfeg]ih9jhp–BcXth9jUjUWDt³eoW

q

thmVXl1hmjUWGj;e"hp–Ec

b_WœmWGbµt`UxgœmWŸ   ¢M£3¤>8U“¦Wbi]_VX]¶e…hm`Uxnseo`

q

reohXegRUWtcmnoW+*“RUWGxoW

*

¢X¢{h¸¤s¤iu



ÇOÇ

‹:—Œ:

Ç Km

zI|

s 9 | p ' o € yp } qs

7:%|

~s

|_| |_y o

q

y

]p

|ey‚z*|

*q

yy| p>sDo€eq

%| D|

]p

D|

o€

%|

s

7y‚zL

~aq

yJ}

~

|

~

L

'

B:w:L

, + „

-

Ødëèéäµï³ô/.Dèéï³ãDä¡ëLîfàgë¡ëMî>æBäLá"à,ðéðéæsä¯ë3ï³ò¯ô>èë±î>à,ä10OæsðéæzáæzêëMäsõ

(13)

Æ %

º®-Š›3®]u3®-+®

¥

F

®£+¢

¤G®'u š Œ Â'

 %¯‹ Â

-k¥

Â' È@

Â' È Æ %Â

G±]i‡9`UxgW…Y ?BQSRUW˜U]_noWGteo]_hmj¼cpb_‡mh9xo]ieoRuV

 ÇµÇ Guhmx¡cmj^r‡m]_œmWGj…WGbiWGVXWj;e ¨ª X¢h…¤³¾GeoRuWxgWEWv@]_nsegn¡cpj]_j9egW‡9Wx9wJD&Sns`†t,R…egRucfe ±¢ H ¢¤s¤1¥ ¢ H

W] ¢¤o¤³¾

hpegRUWxg“]dnsW ¢ ¤B¥cmj q * 6 ¢X¢h…¤s¤O¥

$ìj¹egRUW&–—hmb_bihf“]_jU‡†¾B“OW q WGjUhpegWk˜^r ¥ H ¢ ¤³¾ ¥ ¢¤cmj q ;-)$ /”´ ‘ WVXc>r¹c9nono`UVXWkeoRucpe

-¹¥ ¢¤cpj q ²¥ ¢¤³´ µWe¼˜1WXeoRuWegRU]_xq œmWGxsegWvºhp– cpj q eoRUWXegRU]ix q œmWxoeoWvºhp–8µeoRuWXez“OhnsWG‡mVXWj;e,n

;-)$ >cmj q ;R$ >cpxgW¸š ¿ noWlucmxgcpeoW q cpj q lucmxgcmbib_WbM´ $Ζ+©

Y>[

ª ;-)$:> / cŸ   ¢L£3¤Scmj q ©

Y =[

ª ;R$ > / cŸ   ¢L£3¤OegRUWj

®©

Y>[

›™©

Y =[

®,1 ¢P;-W$ >8$^;R$:>—¤B¥

,

+

& „

QSRUWGxoW–—hmxgWm¾u“¦WacmxoW‡9`ucpx,cpj;eoWGW q eohklUxoh9‡mxgWGngnS˜^r&c q ]_nsegcmjutW juhpe…noV½cpb_biWGxeoRucmj"!$#

8

F

–—hmxžuœmWathmjunoWGt`@eo]_œmWegxo]dcpju‡mb_WGnG´

% & ('*),+.-+0/ 211 315460)*+ & 21 $)*6 &$()

{nnsRUhf“jC]_j½lUxoh9l†h;ns]ieo]_hmj½ƒ@´Yu¾peoRUWlUxgh@tWDnon±egWxgVC]_jucpeoWGnB“RUWj ¢{h H ¤¥Eh

%

´EQ¡h‡9`ucpx,cpj;eoWGWegRUW"lUxgh@tWDnon±egWxgVC]_jucpeo]_hmj

Wœ9Wj]_jkegRUWlUxgWGnoWjutWhp–+xoh9`Uj q^¿hpÀºWGxoxghmx,n¾^“¦W`unoW]ij;eoWG‡mWGx"th^hmx q ]_jucfegWGnOeoh½]q Wj;eg]¶–—rkeoRUWbdcfeoeo]dtWjUh q WDn´OQSRUWxgW–—h9xoW9¾

eoRuW¸juh q W G)H=I ]dnS]q Wj;eo]ižuW q ˜^r½egRUW¸ez“OhC]ij;egW‡mWGxgn&Jcpj q Lcmj q eoRUWWœfcmbi`ucpeo]_hmjkhp–+£+¢G[H=I ¤OxgWG•;`U]_xoWDnOeoRUWWœfcmbi`ucpeo]_hmjkhp–

£+¢¯©

Z

VKJ3¢¯© @O›™©

Z

¤KVLo¢¯© @O›™©

Z

¤NM QO

¤a„

Kk m 7CŽU Æ Ž@fÈ Â > Ç Ž Ž %à ‹:¯‹

µWe¸`†n…juhf“¨th9juns]q WGxegRUWWÀ1WDt³ehp–Oxoh9`Uj q hmÀ™WGxoxghmx,n"h9jºeoRuWCWGœfcpb_`ucfeg]ih9jºhp–¦£+¢G[H=I ¤…“RUWGxoW G[H=I ]_nckVCWDnsR²jUh q Wm´r$Îe

VX]i‡9R;e˜1WXl†h;nono]_˜UbiWCegRucfe]_j™nohmVXWXtcmnoWGn…egRUW½thmVXlU`UeoW q œfcpb_`UW½£RLs¢g®£+¢G[H=I¤G®¤¸cpj q egRUWXWvUcmteœfcmbi`UWº®£+¢G[HI¤®1WGjutb_h9noW

eoRuWCš+›b_Wœ9Wb+t`UxgœmWCcpj q egRUWxgW–—h9xoW9¾1eoRUWCthmj†nzegxo`uteoW q hmxg˜U]ie q ]iÀÅWx,n"–—xghmV eoRuWWv@c9t³e¸hmjUW9´ ‘ WXnsRucmbib±lUxghfœmWegRucfe¸eoRuW

th9VXlU`@eoW q h9xo˜u]¶eS]_n¦egRUWWvUcmte¦h9xo˜u]¶ehp–±ca–—`ujut³eg]ih9jB%ŠcplulUxoh>v@]_V½cfeo]_jU‡X£¼“]ieoRU]_j&clUxgWGt]_no]ih9j q WžujUW q ˜^r½egRUW

#

h9cpeo]_jU‡

l1hm]_j9ecmxo]ieoRuVCWeo]dt¸lUxoWDt]dns]_hmj¡´

$ìjkeoRUW–—h9bib_hf“]iju‡u¾@“¦W q WžujUWegRUW €aop ( qp  | p>p op M H=I

hm–¡eoRuWWœfcpb_`ucfeg]ih9jkhm–+£+¢

G[H=I

¤¦˜^r

£RLo¢L£+¢G)H=I¤s¤¥5£+¢ G[HI¤KV M HI

–—`UxoeoRUWGxoVXh9xoW9¾1“¦W½cmngns`uVCWaeoRucpeeoRUWXWœfcmbi`ucpeo]_hmj²hp–¦£’]dnl1Wxo–—hmxgVCW q ˜^rºckxoWGbi]dcp˜Ub_WXcpj q nze,cp˜Ub_WCthmVXlU`@e,cfeg]ih9j¬“RU]dt,R

VXWGcmjun¦eoRucpe ? ®M H=I®;¥'X¢98;: HI¤

“RUWGxoW8]dnSeoRuWVXc9t,RU]_jUWlUxoWDt]dns]_hmjklucpx,cpVXWeoWxcmj q :=<?>@¥EOA$B3¢98^$>®£+¢G H=I¤G®¤a8UeoRu]_n]_VXlUb_]iWDn¦eoRucpe

OA?B

RDC

< YR \ RE

[ ®M R ® : R ¥ X¢98³¤

Références

Documents relatifs

Unité de recherche INRIA Rennes, Irisa, Campus universitaire de Beaulieu, 35042 RENNES Cedex Unité de recherche INRIA Rhône-Alpes, 655, avenue de l’Europe, 38330 MONTBONNOT ST

Unité de recherche INRIA Rennes, Irisa, Campus universitaire de Beaulieu, 35042 RENNES Cedex Unité de recherche INRIA Rhône-Alpes, 655, avenue de l’Europe, 38330 MONTBONNOT ST

Unité de recherche INRIA Rennes, Irisa, Campus universitaire de Beaulieu, 35042 RENNES Cedex Unité de recherche INRIA Rhône-Alpes, 655, avenue de l’Europe, 38330 MONTBONNOT ST

Unité de recherche INRIA Rennes, Irisa, Campus universitaire de Beaulieu, 35042 RENNES Cedex Unité de recherche INRIA Rhône-Alpes, 655, avenue de l’Europe, 38330 MONTBONNOT ST

Unité de recherche INRIA Rennes, Irisa, Campus universitaire de Beaulieu, 35042 RENNES Cedex Unité de recherche INRIA Rhône-Alpes, 655, avenue de l’Europe, 38330 MONTBONNOT ST

Unité de recherche INRIA Rennes, Irisa, Campus universitaire de Beaulieu, 35042 RENNES Cedex Unité de recherche INRIA Rhône-Alpes, 655, avenue de l’Europe, 38330 MONTBONNOT ST

Unité de recherche INRIA Rennes, Irisa, Campus universitaire de Beaulieu, 35042 RENNES Cedex Unité de recherche INRIA Rhône-Alpes, 655, avenue de l’Europe, 38330 MONTBONNOT ST

Unité de recherche INRIA Rennes, Irisa, Campus universitaire de Beaulieu, 35042 RENNES Cedex Unité de recherche INRIA Rhône-Alpes, 655, avenue de l’Europe, 38330 MONTBONNOT ST