• Aucun résultat trouvé

A Fault Tolerance protocol for ASP calculus: Design and Proof

N/A
N/A
Info
Télécharger
Protected

Academic year: 2021

Partager "A Fault Tolerance protocol for ASP calculus: Design and Proof"

Copied!
41
0
0

Chargement.... (Voir le texte intégral maintenant)

Texte intégral

(1)A Fault Tolerance protocol for ASP calculus: Design and Proof Françoise Baude, Denis Caromel, Christian Delbé, Ludovic Henrio. To cite this version: Françoise Baude, Denis Caromel, Christian Delbé, Ludovic Henrio. A Fault Tolerance protocol for ASP calculus: Design and Proof. [Research Report] RR-5246, INRIA. 2004, pp.37. �inria-00070752�. HAL Id: inria-00070752 https://hal.inria.fr/inria-00070752 Submitted on 19 May 2006. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published 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..

(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. A Fault Tolerance protocol for ASP calculus: Design and Proof Françoise Baude — Denis Caromel — Christian Delbé — Ludovic Henrio. N° 5246 June 2004. ISSN 0249-6399. ISRN INRIA/RR--5246--FR+ENG. Thème COM. apport de recherche.

(3)

(4)  

(5) 

(6) 

(7) 

(8)  

(9) !#" $%&('$) * '+,-./"0

(10) 

(11)  132547698;:=<?>&@BAC47D9E9@GFIH@J69<K>ML#4N25:=OG@JPQFRLCS925<K>&T5<U476VH@JPKW9XYFIZD9E9:\[<K]B^(@J692&<?: _%`badc#efghjilknm\oqpradc#e&otsuvc#cwbxbyzsd{vx;p o |3}ru~qep€g€{voyzo ‚ƒ{„b„7u;}Qpt \e†}e5sr`be&}rs `be‡x7ˆ9‰;Š‹;ŒBilwŽxbeŠvv‹i‘n’„Ž{v“ve5o. ”•–&—d˜™bšv—v› _%`byzoƒ}re&oe&{} sr`œ}e&„7uv}ptŽ}roQp€ \edpr{yŸžzo {(su;cCcwŽxbyŸs&{pry¡u;xœyŸxŽ \wŽsde& ¢sr`Že&sr£n„7u;y¡xJpyŸxb“¥¤K{wbž¡p pruvžŸed} {xŽsdeC„b}rupru\su;ž3{v Ž{„\pre& ¢pru¦|3}ru;§s¨pyŸ©vevª{¦v{«©{ž¡yŸ¬b} {}rmMpr`Ž{py¡c#„bžŸedc#e&x;pro†pr`be¥§€k\|­c#u\ \e&ž?® _%`byzocCub \edž¯yŸo¬Ž{voe& xœ{C}e&°Jwbe5oqp±«}red„bžŸmc#e&s `Ž{xbyzoc® ²³x´u;}r \e&}puY„b}u©veMpr`beBsu;}}re&spxbe5oou¤pr`byŸo(„Ž}uvpu\sduvžUª$µe¢y¡xJp}ru\ \wŽsde¢{´¶¡·&¸ ¹¶º\¹»¨¼U½K¹¶†·»¾;¿» ¬7epqµe&edxœed©ve&x;protu\s&swb}r}yŸxb“#uvxœ{#“vyŸ©vedxM„b}ru\sde&orod®R_%`ŽyŸotuv} \e&}yŸoteÀnpe&xŽ \e5 yŸx;pru¥{#“;ž¡u;¬Ž{ž¯uv} \ed}¬nm pr`be%ÁÂ{c#„7u;}Qp5à o`Ž{„b„7e&xbe& nÄŬ7e¤Æu;}e}e&žŸ{pyŸuvx¯®ÇyŸxŽ{žŸžŸmvªµe$„b}ru«©veIpr`Ž{p¤Æ}ruvcÈ{ sw\ppr`Ž{p9yzo=Ɂsu;xŽoyŸoQpe&x;p e&xbuvwb“;`nÊ ª«{oe&sduvxŽ €edÀne5sw\pry¡u;xyzoÂsu;xŽoqpr}r{vy¡xŽe& ƒprut“vue&°JwbyŸ©{vž¡e&x;prž¡mƒpupr`be3Ž} oQp¯u;xbe3wŽx;pyŸžJ{tsuvxNoQyzoqpredxJp “;ž¡u;¬Ž{žËoQpr{peuv¤p`beN}roQpuvxŽeÌÍp`Že†`byzoqpruv}rm¥sdž¡uJoQwŽ}e«Î¨® _%`JwŽo&ª5p`be„b}rupubsuvž; \e&ors}ry¡¬7e5 y¡x†pr`byŸo}e&„7uv}p¯e&xŽoQwŽ}e5oËp`Ž{p&ª«e&©vedx†¤Æ}u;c­{y¡xNsuvxNoQyzoqpredxJpÂ}re&sdu«©ve&}m žŸy¡xŽevª{¢}redeÀ\e&sdw\pyŸuvxÏsd{vxbxbup#ž¡e5{v ÐpruÑ{xÏy¡xŽsduvxŽoyzoqpredx;poQpr{pre(pr`Ž{psduvwbžz GxbuvpCedÀ\yŸoQpCyŸxÒ{¢xbu;}c{ž edÀne5sw\pry¡u;x¯® ӜÔJÕ=ց×Ø ˜«Ù–;› ¤K{wbž¡ppu;ž¡e&}r{vxŽse;ª\s `be&s £n„7uvyŸx;pyŸxb“Nª\c#e&oor{“;e€ž¡u;“v“vyŸxb“Nªns&{wŽor{žŸy¡p³m¥}redžz{pyŸuvx. Unité de recherche INRIA Sophia Antipolis 2004, route des Lucioles, BP 93, 06902 Sophia Antipolis Cedex (France) Téléphone : +33 4 92 38 77 77 — Télécopie : +33 4 92 38 77 65.

(12)  

(13) 

(14) #$

(15)  . 

(16)  -' ¢

(17)  !" ) $

(18) (+d

(19)  $ t  –

(20)  › fe }r{v„b„7uv}p \e }re&s `bed} sr`bet¤K{y¡ppu;w\p% Ëà {¬7uv} #wbxŽeƒ„Ž} 5oQe&x;pr{pyŸuvx(  p {yŸž¡ž de€ Ëà wbx(„b}rupuvÄ sduvžŸe \e€pu;ž &}r{vxŽse{w\À(„Ž{vxbxbe&o%„Ž{v}%„7uvyŸx;p o \e}e&„b}ryŸoe yŸxŽ \wby¡p o%„Ž{v}%c#e&oro{v“ve€{; b{„bp #|3}ru;§s¨pyŸ©vevª wbxbe#žŸyŸ¬b} {yŸ}yŸe#;{5©{(yŸc#„bž dc#edxJpr{xJp†žŸe#cCub \adžŸe#§€k\|®feCc#u\ badžŸeCe&oQp†¬Ž{vo #oQwb}†wbxÑc &sd{vxbyzoQc#e# \e }re&°Jw pre&o¨±«} d„7uvxŽoe&od®  {vxŽožŸe†¬bwbp  \e†„Ž}u;wb©ved}žz{suv}r}re&s¨pry¡u;x \ese†„b}rupru\su;ž¡e;ª\xbuvwŽoty¡xJp}ru\ \wbyzoQu;xŽo%wbxY·»¾»¿ƒº\¹»¨¼?½K¿d¶ ¶¡·5¸r¹¶9e&x;p}re†žŸe&o d©va&xbedc#edxJproƒ°JwbyÂuvxJpƒž¡yŸedw¦owb}twbxœ„b}ru\se5oowŽo \u;xbx v®tfepƒuv} \}ree&oQp dpedxN \wœedxœwbx u;}r \}re“vžŸuv¬N{ž“;} ;se (žz{(}redžz{pyŸuvxÉq`Ž{v„b„7edxŽe& nÄŬ7e¤Æuv}re¨Ê \e#ÁÂ{c#„7u;}Qp5® tu;wŽo€„b}u;wb©vuvxŽoƒŽxŽ{žŸedc#e&x;p °Jw¯Ã („Ž{}pyŸ}€ ¯Ã wbxŽe#suvwb„7eɁow ¥o{vcCc#e&x;psduv` d}redxJpeÊ ª=wbxbe#oQe5su;xŽ \eeÀ &sdw\pyŸuvx¢e&oQpsduvxJp} {yŸx;peC \e oeƒ d}ruvwŽž¡e&}R \et¤K{ u;x 5°Jwby¡©{žŸedxJp!e †žŸ{†„Ž}e&cCyŸad}re9~qwNo°Jw¯Ã †wbx p {p“vžŸuv¬Ž{vžŽsu;` d}redxJpR betžz{†„b}redc#y¡a&}e ÌKžŸ{sžŸupwŽ}e† \e†ž?à `byzoqpruv}ryŸ°Jwbe«Î¨® §tyŸxŽoQyUª;žŸe„b}rupubsuvžŸe$„b} &oedxJp “;{v}r{vx;pry pI°Jwbe;ªvc dc#e „Ž{v}QpryŸ}I Ëà wbxbetž¡yŸ“vxŽe be}re&su;wb©n}e&c#edx;p3xbu;x sduv` d}redxJpe;ªwŽxbe(} dedÀ &sw\pryŸuvxÐxbe(„7e&w\pC„Ž{voc#edxbe&"} ¦wb# x dpr{py¡xNsuvxNoQyzoqpredxJpC°Jwbyxbe„7uvwb}r} {y¡p„Ž{;o edÀnyzoQped}t b{vxŽo%wbxbe†ed$À 5sw\pry¡u;xxbuv}rc{žŸev® š &  –B› pu;ž &}r{vxŽseC{w\À¦„Ž{xŽxbe&o&ª=„7u;y¡xJp† \eC}e&„b}ryŸoevªJ~quvwb}rxŽ{vž¡yzo{pyŸuvx¢ \eCc#e&oro{v“ve5odª7}redžz{pry¡u;x %ÈØ —&– Ö ' \esd{vwŽo{vž¡y¡p.

(21) ¹\¶ ¼Ž·¶¡¿»¹7¸ ¿·» 

(22) . .

(23) t'. .  "!

(24) #$%'&!

(25) ()*$%. ”.- ”#šv—0/21 Ô43 •"5 Ô š— %ÈØ Ù Ô & fuvc#cwbxbyzsd{pyŸuvx ®®†®®†®®†®®†®®†®®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®® 7 ®7 ‚edxŽ \e08ÄÅ©vuvwŽo€®®†®®†®®†®®†®®†®®†®®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®® 7 ®Š |3}u;„7ed}pyŸe&o{xŽ § oowbc#„\pry¡u;xŽo¥®†®®†®®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®® 7 ® ®7 ‹ kJpr{v¬bž¡ekJp {pe5o ®†®®†®®†®®†®®†®®†®®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®® :<; ™b–=/ƚ?> & Ô Ô -=—&– ØA@ —=B ÔDC ˜ Ø — Ø š Ø & Š\® 7 f`be&s £n„7uvyŸx;proM®®†®®†®®†®®†®®†®®†®®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®® Š\® Š |3}u;c#yŸoe& ‚e5°;wŽe&oqp o ®®†®®†®®†®®†®®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®® Š\®  §Â©vuvyz œg }r„b`Ž{xœhMe&oro{v“ve&o ®†®®†®®†®®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®® Š\® b® 7 ‚e5°Jwbe&oQp Qi,j ®†®®†®®†®®†®®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®® Š\® b® Š ‚e&„bžŸm ®†®®†®®†®®†®®†®®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®® Š\® ‹ §Â©vuvyz ²³x\ÄUp} {xŽoRy¡pti,jhœe&oro{v“ve&o ®®†®®†®®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®® Š\® ‰ fuvxŽoe&sdw\pyŸ©ve{vxŽ ²³c#„7u;oroy¡¬bžŸef`be&s £n„7uvyŸx;p o(®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®® () Ô I Ô –&— Ô š )Ô J 0— / Ø -K?/K–d— Ø ˜ Õ H b® 7 |3}u;¬bžŸedco ®†®®†®®†®®†®®†®®†®®†®®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®® b® 7 ® 7  wb„bžŸyŸs&{pre& M‚e&„bž¡yŸe&o ®®†®®†®®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®® b® 7 ® Š f${vwŽo{vž  ed„7e&xŽ \edxNsyŸe&o®†®®†®®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®® b® Š knuvžŸw\pyŸuvMx L3‚e5°Jwbe&oQpt‚e5sed„bpyŸuvO x NƒyŸoQpruv}rm®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®® b®  fž¡uJoQyŸxb“#‚e5°Jwbe&oQpt‚e5se&„\pyŸuvO x Nƒyzoqpruv}rm®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®® (Ô š Ø 1 Ô ˜ Õ P ‹Ž® 7 ²³xŽsd{v}xŽ{pyŸuvx twbc¬7e&}ro#®†®®†®®†®®†®®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®® ” &SR Ø T˜ /ÍU— B 4/K? š V Ô –5šT˜ / J 0— / Ø Q ‰\® 7 |3}yŸxŽsdy¡„bžŸe&o ®†®®†®®†®®†®®†®®†®®†®®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®® ‰\® Š §tžŸ“vuv}ry¡p`bco‘®®†®®†®®†®®†®®†®®†®®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®®. + 6. ,. X 6. YZ(!

(26) !

(27) M$[

(28) #M\)\^]_!`a( d™ –5™&S/͗ Õ ˜ Ô &ƙ\—0/ Ø - @ÅØ ˜(™b– Õ -šTB˜ Ø - Ø –#˜ Ô)I Ô –&—#– Ô ˜=1"/Kš Ô – Œb® 7gf ž¡e&c#edx;p ouv¤ed©ve&x;pQÄŬŽ{;oQe5 {xŽ{vžŸmnoyzo!®®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®® Œb® 7 ® 7 f`Ž{v}r{;s¨pred}ryh8&y¡xb“ f Àne5sw\pry¡u;xŽo®®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®® Œb® 7 ® Š |9{}pyz{ž¯ÁÂu\sd{vžÂg } \ed} ®†®®†®®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®® Œb® 7 ®  fw\p oG®®†®®†®®†®®†®®†®®†®®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®® uv„7e&}r{puv} ®®†®®†®®†®®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®®®†® Œb® 7 ® ‹ Œb® Š f${wŽor{žŸy ⊕pqm¥y¡xœ§ kb| ®†®®†®®†®®†®®†®®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®®. ijilkm`npoqsr. Œ ’ ’ 9 E F F. 7. . 7.  . 7. 7G7 7 7 G ,

(29) : 7 7 7 7 7 , 6 7. Š Š. ‹.  ‰ Œ. ,

(30) W 7 7. ’ ’. bc :Ae. Š. 7. Š 7. Š Š. 7. ŠvŠ Š. 7.

(31) ‹. C¿¶ ¿ Ž»¨½K· I¹»· ¿d¶ . E. W. . Œb® Š\® 7 ÁÂu\sd{vžËsd{vwŽor{žŸy pqm¥}e&žŸ{pyŸuvx(¤Æu;}t§ k\| ®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®® Š‹ Œb® Š\® Š |Iy¡e5sedµyzoQe  epe&}c#yŸxbyzoQc ®®†®®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®® ŠŒ Œb® Š\®  fu;xŽoQyzoQpedxJp f xŽuvwb“;`¦fw\pro¢®†®®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®® ŠŒ C ˜ Ø 1"/ -jRК Ø ˜«˜ Ô š—U- Ô –5– ØA@ —=B ÔDJ ˜ Ø — Ø š Ø & : 6 ’n® 7 |3}u;c#yŸoe& ‚e5sed„\pry¡u;xŽoЮ†®®†®®†®®†®®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®® Š;’ ’n® Š P ijsw\p/®†®®†®®†®®†®®†®®†®®†®®†®®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®® Š;’ ’n®  fuvxŽoyŸoQpe&x;p ÄÅsdw\prot{xŽ MsuvxNoqpr}r{vy¡xbe5 (eÀ\e&swbpyŸuvx ®®†®®†®®†®®†®®†®®†®®†®®†®® ŠF ’n® ‹ ‚e&sdu«©ve&}m¥{vxŽP œfuv}r}re&s¨prxbe&oro ®®†®®†®®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®®jv ’n® ‹Ž® 7 ‚e5su©ved}rmfw\pG®†®®†®®†®®†®®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®®jv ’n® ‹Ž® Š ÁÂuv“v“;e& hMe&oror{“ve5oÒ®†®®†®®†®®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®®j 7 ’n® ‹Ž®  fu;}}re&spxbe5oo$u¤pr`be†„b}uvpu\sduvž ®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®®†®®j 7 — / Ø -´• Ô — ×ÔnÔ -Ҕ C C ˜ Ø ”š0— /S1 Ô `™ -Ù U— BM/K– ×Ø ˜ (Ô &ƙ\= H[H

(32) . . . . i.

(33) ¹\¶ ¼Ž·¶¡¿»¹7¸ ¿·» 

(34) . ‰. " Â. .  

(35)        . _%`byzo€Ž}roQp„N{}p„b}re&oedx;p o{(¤K{vwbž p†puvžŸed} {xNse„b}rupru\su;ž¤Æuv}† byŸoQp}ry¡¬Žw\pe5 Buv¬\~qe&s¨p†c#yz b \žŸedµ${v}e;®_%`ŽyŸo „b}rupru\su;ž9`Ž{vo¬7ede&xÑyŸc#„bž¡e&c#edx;pre& ѵy¡pr`by¡xÐ|I}uJ§%spyŸ©ve ŒŪ{vxÑuv„7edx ouvwb} se;{«©{cCyz b \žŸedµ%{}re¤Æu;} {;oQmnxŽs `b}ruvxbuvwŽo{vxŽ  byŸoQp}ryŸ¬bw\pe5 uv¬\~qe&sproyŸc#„bžŸedc#edx;pryŸxb“ pr`be§ k\|ÒÌ?§ƒomJxNsr`b}ruvxbu;wŽo9kne&°Jwbe&x;pryŸ{vž\|3}ruÄ sde&ooe&o Îc#u\ \edž  !’ Å® hœ{xnm´¤K{wŽž pœpruvžŸed} {xŽsdeфb}rupru\su;žŸo¤Æuv}¦ byŸoQp}ry¡¬Žw\pe5 Vom\oqpredcoM`Ž{«©veÐ{žŸ}re&{v bm´¬7ededx­„b}ruv„7uJoQe5 Ë® _%`b}redec{vy¡x {„b„Ž}uJ{vs `be&oCsd{vxϬ7eMyz \edx;pry¡Že& ϤÆuv}}u;ž¡žŸ¬Ž{vs £JÄU}e5su«©ved}mѤK{wbž¡p#pruvžŸed} {xŽsd" e  7 ‹  Lœsunu;}QÄ \yŸxŽ{pe& Gs `be&s £n„Nu;yŸx;pyŸxb# “  Fbª 7 $ Ū3sduvc#cwbxbyzsd{pryŸuvx\ÄÅy¡xŽ bwŽse5 Ðsr`be5sr£n„7uvyŸx;pry¡xŽ“YÌUf²f%%Î  ‰\ª9Š 7 ª 7 ’Jª9Š;Šnª Š F\ª 7 $Œ Ū7{vxŽ Mc#e&oror{“ve†žŸuv“;“vyŸxb G “  Š 9bª 7 ªN&‹ Å®²³xœp`byzoƒµuv}r£=ªŽµe{}re†yŸx;pe&}e5oqpre& MyŸx¢{„b„bžŸyzsd{pryŸuvxŽot}wŽx\Ä xbyŸxb“uvxM`bedped}ruv“;edxbe&uvwŽo%om\oqpredcoµy pr`MžŸu«µ ¤K{yŸž¡wŽ}e†}r{p(e 'npr`JwŽotµe†Ž}roQpƒsd{vcCepu¥{(f²f {„b„b}ru;{;sr` ¬7e&s&{wŽoey ptyzo%wNoQwŽ{vž¡žŸm(s `Ž{} {vspe&}y 8de5 ¥¬Jm{C} {p`Žed}%žŸuµ u©ved}r`be&{; ¤Æu;}%¤K{wbž¡p¤Æ}e&eedÀne5sw\pry¡u;xŽod® f²f „b}rupru\su;žŸowNoQwŽ{vž¡žŸmGc{£vep`be¦{voroQwbc#„\pry¡u;xYp`N{pe&©ved}rmЄb}ru\se5ooCu¤ p`Žeœom\oqpredc sd{vxϬ7e s `be&s £n„7uvyŸx;pe5 M{pƒ{vxJm¥pry¡c#evªŽpuedxNoQwb}resuvxNoQyzoqpredxŽsdm¥uv¤}re&sdu«©ve&}m¥ž¡yŸxbe&o&® )$w\ptp`byzoƒ{voroQwbc#„\pryŸuvxMs&{x ¤K{vy¡žË¤Æu;}tsduvc#„bžŸeÀuv}t„Ž{}pyzswbžz{}toQm\oQpe&co%µ`be&}ep`be„b}ubse&oroQe5odÃboqp {pe†yzoxbupƒ{vž¡µ%{5m\o{5©{vyŸžŸ{v¬bž¡e;®9²³x pr`be€suvxJpedÀnpu¤;{«©{†c#yŸ b bž¡e&µ${}re&oRžŸy¡£ve€|3}uJ§%spyŸ©vevªJ„7e&}royzoqpredxŽse sd{vx¥¬7eƒu;¬\pr{vy¡xŽe& yŸx({sduvxJ©;edxbyŸedx;p {vxŽ „7u;}Qp {¬bžŸeµ${5m(¬Jmoqp {xŽ Ž{} ;{5©{CoQe&}yz{žŸy 8&{pry¡u;x¯® Ntuµe&©ved}5ªb{vo$pr`b}re&{v Žosd{vxbxbupt¬7eoQe&}yz{žŸy 8de& ¯ª {vxyŸc#„7uv}pr{vx;p„Ž{v}Qpuv¤p`be{;s¨pyŸ©ny pry¡e5+o *«ª\pr`beoQpr{vs £\odªbsd{vxbxbup¬7es `be&s £n„Nu;yŸx;pe5 Ë® _%`b}e5{v bo„7e&}royŸoQpe&xŽse€s&{x¬Ne†{vs `by¡e&©ve& ¥¬nmc#u\ \y¡¤Æmny¡xb“pr`be€edÀne5sw\pry¡u;x(edxn©ny¡}ruvxbc#e&x;p{p$p`begk žŸed©ve&ž  Š‹ Žuv}3{p9p`Že%©nyŸ}QprwŽ{ž\c{vs `byŸxbe%ž¡e&©vedž  7 9\ª Å®9§txbuvp`be&}IoQu;ž¡wbpyŸuvxyzopruwŽoe{€o„7e&sdy 7s%suvc#„byŸžŸed} µ`byzs `M{; b bosdu\ \e€prusd{v„\pwŽ}ee&xbuvwb“;`yŸx\¤Æu;}c{pry¡u;xŽo$pu¥sr`Ž{v}r{;s¨pred}rhy 8&eƒp`Žeoqp {pe†u¤9{#„b}ubse&or,o  Šv!‰ Ū u;}%wNoQesuvc#„byŸžŸeÄUpyŸcCe†}r.e -Že&spyŸuvxpu„b}ru«©nyz \e„7ed} oQyzoqpredxŽsde€¤ÍwŽxŽs¨pry¡u;xŽ/o  Š$Œ Å0® )wbpp`buJoQepunu;žŸo%wŽowŽ{žŸžŸm yŸxJ©vu;ž¡©vet{žŸu;oro9uv¤=„7uv}pr{v¬by¡žŸy¡p³m{vxŽ N±uv}3e ¥syŸedxŽsdmv®²³x#p`be suvxJpedÀJpRu¤¯;{5©{bªy¡pRyzo3} {pr`bed}Iwbx\¤Æuv}pwbxN{pe pru#ž¡uJoQe„7uv}pr{v¬byŸž¡y¡pqmv® §‡„7uv}pr{¬Žž¡e{xŽ ¢suvxn©vedxbyŸedxJp€ouvžŸw\pyŸuvxœ¤Æuv} pr{v£JyŸxb“{v b©{xJpr{“;e†uv¤$f²f „b}rupru\su;žŸotµ`be&x¢s `be&s £JÄ „7u;y¡xJpro9s&{xuvxbžŸm†¬7e$pr{v£vedxC{p3ouvc#e$„b}ruv“v} {c­„7uvyŸx;pro9yzo„b}re&oedx;pre& yŸxpr`byŸo9„N{„7ed}5®Â²³xCuvwb}3{„Ž„b}uJ{vs `¯ª µe€sduvwbxJped}r¬Ž{vžŸ{vxŽsetp`be€wbxŽoed}ryŸ{vž¡yzor{¬byŸž¡y¡pqmCu¤¯p`b}re&{v ŽoR¬nmCp`Žeƒ¤K{;s¨ppr`Ž{p5ª\{p%ouvc#eƒ„b}ruv“;}r{c „7uvyŸx;p odª pr`beoqp {pe†uv¤p`be{vspyŸ©ny pqm(yzo%¤ÆwbžŸž¡mMsr`N{} {vs¨pred}rhy 8&e& (µy¡p`bu;w\p {xJm£JxŽu«µžŸe& \“;e†{¬7u;w\pp`beoqp {pre†u¤9y¡pro pr`b}e5{v Ë®9§ oµy¡žŸž7¬7e o`bu«µxª;u;wb}cCub \edž={žŸž¡uµtoIwŽoRpuyz \e&x;py¡¤Æm¥oQwNsr`¥„Ž}u;“v} {c „7u;y¡xJpro&ªnsd{žŸžŸe& 1¨¼Å¹ ¨¶¡¿ 1¨¼Å¹¼Å.¿ 1y¡xœpr`be¤ÆuvžŸž¡uµyŸxb“Ž®ƒ§ƒoƒp`be5oQeCoqp {¬bžŸeoqp {pe5oƒu\sdswŽ}ƒyŸx¢{}re&oQp}ryzs¨pe5 œ{xN MwbxŽ„b}e5 \yzs¨pr{v¬bžŸeµ${5m;ª µe  be&oQyŸ“;xbe& {v x 243 ¨»¨½K¾ 65 87 .¿ 191d;¹ :;¿¶Ÿ<· :!:2½ =:#„Ž}uvpu\sduvž\pr`Ž{p%{žŸž¡uµtoI}e5su©ved}rm¤Æ}u;c “vžŸuv¬Ž{vžNoqp {pe5o c{v beu¤R}e5oqpr}yzs¨pryŸ©vedžŸm„ŽžŸ{;se& ¢sr`be5sr£n„7u;y¡xJpro&®hMuv}re“ve&xbed} {žŸž¡m;ªNuvwŽ} „b}rupubsuvž„b}u©nyŸ be&of²fRÄU¬Ž{;oQe5 ¤K{vwbž p$pruvžŸed} {xŽseƒyŸx(c#yz b \ž¡e&µ${}re&oµ`bed}reƒp`bes `be&s £J„7u;y¡xJpr{v¬bž¡e „b}ruv“;}r{c „7uvyŸx;p o${}re oQ„7e5sy¡Že& ¥e&y pr`bed} edÀn„Žž¡yzsy¡pe&ž¡m(¬Jm¥pr`be†eÀ\e&sdw\pe5 „b}ruv“;}r{c u;}%yŸcC„Žž¡yzsy¡pe&ž¡m \wbepu#p`be†c#yz b \žŸedµ${v}ec#u\ \edžU® kJpr{v}Qpry¡xb“еy¡p` {Gf²f „b}rupru\su;ž?ªc#e&oro{v“veMž¡u;“v“vyŸxb“Ñc#e5sr`Ž{vxbyzoQco`Ž{«©veM¬7e&edx´{; b \e& ÏpruG \e&{vž µy¡p`(wbxb„b}re& byŸspr{¬Žž¡e s `be&s £n„7uvyŸx;pžŸu\s&{pyŸu;xŽod®3g€©ved} {žŸž?ªvp`be€su;x;p}ryŸ¬bw\pyŸu;xyzo{xbe&µ´c#y À\e& ({„b„b}ru;{;sr` ¬7epqµe&edx0f²fj{xŽ oedžŸe&spyŸ©veBc#e&oror{“veBž¡u;“v“vyŸxb“N® _%`be „b}u;„7u;oe& ´„Ž}uvpu\sduvž€ \e&žŸ{«m\os `be&s £n„7uvyŸx;p o \wb}ryŸxb“p`be†eÀ\e&swbpyŸuvx¯ª\c{yŸxbž¡mpr`Ž{xb£\o$pu#{»+¿ >sŽ.¿ 1¨¼R»¿r¸ ¿³º7¼?½K· ?2J@½ 1 ¼³·A» 3® $»· @½ 1d¿ ¾¥»9¿ > ŽA¿ 1¨B¼ 1{žŸž¡uµ pruϞŸuv“ÏuvxbžŸm }re&°Jwbe&oQpMoQe&xŽ \e&}royz \edxJpy¡Žed} o{vxŽ ´pruτ7ed}¤Æuv}rc ¤ÆwbžŸž¡m {vomnxŽsr`Ž}u;xbuvwŽo(}e&sdu«©;ed}m;® §tx . . . . CEDGFIH$JKFMLNFMJPOBQ$FROSFMJKTVU+WEOBX Y!X O[Z\JBU9OSQ!F]JPOBQU k H!JB^_WMFM`S`POS^aXcb$F k OSX LdZeOBQ$F JKf k OSXcTgFRF k OBX O[Z_h. ijilkm`npoqsr.

(36) Œ. C¿¶ ¿ Ž»¨½K· I¹»· ¿d¶ . . yŸc#„bž¡e&c#edx;p {pry¡u;x`Ž{vo¬7ede&x{vsr`Žy¡e&©ve& †µy¡p`byŸxC|3}uJ§%spyŸ©vev®²Åp9{vž¡žŸuµtoÂwŽoÂpu „b}re&oedxJpŽ} oQp¬7e&xŽsr`Žc#{v}£\o ou#{;o$pu#e&©{vž¡wŽ{peu«©ve&}`be5{v (y¡xŽ bwŽse& ¬nm(uvwb}„b}rupru\su;ž?® _%`byŸo$„Ž{v}Qp$yzou;}“J{xby 8de5 {voR¤Æu;ž¡žŸuµtod®3k\e&s¨pry¡u;x 7 „b}re&oedxJproRpr`be{vspyŸ©ve uv¬\~qe&s¨p%c#u\ \e&ž7¬7e&y¡xb“CwŽoe& Ë® kne5s¨pyŸu;xŠoQwbc#c{}ry 8de&oRp`be€c{yŸx(„b}ry¡xNsyŸ„bž¡e5ou¤¯pr`be€„b}uvpu\sduvžU®9kne5s¨pyŸuvxyŸxJp}ru\ \wŽse5o${xŽ ¥}re&ouvžŸ©ve&o pr`be„b}ruv¬bžŸedc u¤$e5°Jwby¡©{žŸedxŽsdeC¬7edp³µ$ededxÐ \y =ed}e&x;pedÀ\e&swbpyŸuvxŽo&®(kne&spyŸuvxы¦ \e&ors}ry¡¬7e5o€p`be}re&sdu«©ve&}m „b}rupru\su;ž?®3kne5s¨pry¡u;xœ‰“vyŸ©ve&o$p`Že†{vž¡“;uv}ry¡p`bco$u¤pr`be†„b}uvpu\sduvžU® . j I+ ËR

(37) .t g wb}R„b}rupru\su;žb`Ž{voI¬7e&edx( \ed©ve&ž¡u;„7e& #yŸx#pr`be su;x;preÀnpRuv¤=p`be §€k\|Guv¬\~qe&s¨p$s&{žzswbžŸwŽoR{vxŽ #c#uv}reto„7e&sdy ¤ÍÄ yzsd{vž¡žŸm#¤Æuv}$p`be†|3}ru;§s¨pyŸ©ve€ž¡yŸ¬b} {}rmCp`Ž{p%yŸcC„Žž¡e&cCe&x;p o$p`byzosd{žzswbžŸwŽo&®3§ k\|Ïu;¬n~qe5s¨ps&{žzswbžŸwŽo$yŸo%¬Ž{voe& u;xœsu;xŽswb}r}redx;pƒ{vspyŸ©ny pry¡e5od®tfuvc#cwbxbyzsd{pyŸuvxŽoƒ{}re†{;oQmnxŽs `b}ruvxbuvwNo$c#edp`bu\ œs&{žŸžŸoµy¡pr`Mp} {xŽo„Ž{v}e&x;p ¤Æw\prwb}e5odªI¬Ž{voe& ÐuvxY{¦c#e5oor{“;e„N{voroQyŸxb“¦c#e&s `Ž{xŽyŸocµy pr`G}re&°Jwbe5oqp o{vxŽ Ð}red„bžŸyŸe&o&® f {vs `Y{;s¨pry¡©ny¡p³m sduvxŽoyŸoQprouv¤ƒ{¦„Ž}u\sde&orodª3{¢oepCuv¤tuv¬\~qe&sproÌKµ`byŸs `Yµ$es&{žŸžy¡proœ¹ ºvº7¶ ½K¸ ¹¼?½  ¿ 1¨¼³¹¼³¿«Î¨ªR{xŽ Y{¦}re&°Jwbe&oQp °Jwbe&wbev®3_%`be&}eƒyzo${c{;oqpred}u;¬n~qe5s¨p%{vcCu;xb“p`be{„b„bžŸyzsd{pry¡©ve oQp {peƒp`N{p$yzo$sd{žŸžŸe& #pr`be#¹;¸¼U½ ¿· d¿r¸d.¼ ' c#uv}re€„b}e5syzoQe&ž¡me&©ved}rm}e&°Jwbe5oqpoedxJp$pru#{vx{vspyŸ©ny pqmyzo{vspwŽ{vž¡žŸm¥{x{;oQmnxŽs `b}ruvxbu;wŽoRc#epr`bu\ sd{vž¡ž=u;x pr`byŸot{;s¨pry¡©veu;¬n~qe5s¨p&® . .

(38) .

(39) . YZ. . . # $% #. ´`be&xM{x{vspyŸ©Jy¡pqm¥sd{vžŸžŸo%{c#ep`Žu\ (u;x{vx{vs¨pryŸ©ve u;¬n~qe5s¨p5ªb{xbedµ }re&°Jwbe5oqp%yŸo{v b be& ¥prup`be}re&°Jwbe&oQp °Jwbe&wbe uv¤¯p`Že€}e5se&y¡©ve&}&® ´`bedx(pr`beoy¡“;xŽ{prwb}reƒu¤Âp`bes&{žŸž¡e5 ¥c#ep`Žu\ ¥`N{vo${}edpwb}rx(©{žŸwbe;ªn{¤Æw\pwb}re yzoCs}re&{pre& ÐuvxGp`beMoQe&xŽ \ed}#oQyz \e L#pr`byŸo¤Æw\pwŽ}e}red„Ž}e5oQe&x;propr`be}re&owbž pCu¤tp`be}e5°Jwbe&oQpp`N{pCyzoxbup £nxbuµxmvedp&®Iǎw\pwb}re&ot{}re€“ve&xbed} {žŸhy 8&e& ¥}re¤Æe&}e&xŽse5op`Ž{pts&{x¬7ec{xŽy¡„bwŽžŸ{pe& {;osžz{voroQyzsd{vž7u;¬n~qe5s¨pro&® Nƒu«µe&©ved}5ªtoQu;c#e¦u;„7ed} {pyŸu;xŽo¦ÌKev® “Ž®ÈŽe&žŸ {vs&se&oro Î#xbe&e& {G}re&{vžƒuv¬\~qe&sp©{žŸwbe¦puY¬7eB„7ed}¤Æuv}rcCe5 Ë® |ed}¤Æuv}rcCyŸxb“towŽs `†uv„7ed} {pry¡u;xŽo=u;x€¤Æw\prwb}reIu;¬n~qe5s¨p o¯ž¡e5{v boËpuƒ{¬bžŸu\s £ve& oQp {peRs&{žŸž¡e5 R¹½ÍS¼ 7 .377¿ ¸r.¿ 191¨½ÍS¼ 3® ´`be&xBpr`be#}re&sdedyŸ©ved}edxŽ bop`be¥oQe&}©nyzseCu¤%{}e5°;wŽe&oQp&ªËp`Že{;oou\syz{pre& œ¤Æw\pwŽ}e¥sd{vxB¬7e#wb„= b{pe5 Ly¡p oedxŽ bot{C}e&„bžŸmp`Ž{ptµy¡žŸžËpr{v£ve€p`be†„bžz{vsdeu¤pr`be¤Æw\pwb}rev® Be†wŽoe€pr`be¤ÆuvžŸž¡uµyŸxb“Cxbuvpr{pyŸuvxŽo0L {C}re&°Jwbe&oQp%¤Æ}u;c i pu j ª Qi,j {C}e&„bžŸm¤Æ}ruvc i pu j ª Ri,j {Cc#e&oro{v“ve ¤Æ}u;c i pu j ªÂÌ Mi,j yzo Qi,j u;} Ri,j Ψª Mi,j p`Že}re&°Jwbe5oqpt°Jwbe&wbeuv¤ i ª Qrcv i p`beoed}r©nyŸsde€u¤pr`be†}e5°Jwbe&oQp Qi,j ® X(Qi,j ) _%`be€{vspyŸ©ny pqm#yz \edxJpy¡pyŸe&o {xN sd{x(¬7e uvc#y¡pQpre& ¥µ`Žedx¥p`Žed}reƒyzoxbuC{vc¬by¡“;wby¡p³m;ªn{vxŽ ¥{}re&°Jwbe&oQp u;}{C}red„bžŸm(s&{x¬7eyz \edxJpy¡Že& Mi µy pr`œj{xyŸxŽ \eÀÑÌ Qn u;} Rn Ψ® ÇyŸ“vwŽ}e 7 o`buµtopqµu {vspyŸ©ny pry¡e5o i {xŽ j ® j sd{žŸžzoC{Bc#ep`Žu\ Yuvx i LM{B}e&°Jwbe5oqp#yzo#oQe&x;p¦Ì Q Ψ® Ì Î%{xŽ {C}red„bžŸm¢Ì Ψªb}re&owbž¡pu¤p`Že†oed}r©nyŸsdevªnyzooedxJp f ©ve&x;prwŽ{žŸž¡m;ª\p`byzo}e5°Jwbe&oQp%yzooed}r©ve& (u;x ¤Æ}ruvc i pru j ®g xNse}e5se&y¡©ve5 ˪np`byzo}e5oQwŽž ip%prX(Q) }r{vxŽo„Ž{}redxJpžŸmwb„= b{pre&Ro%p`be¤Æw\prwb}re†uv¬\~qe&s¨p5® . . . . . . . . . . . . i.

(40) ¹\¶ ¼Ž·¶¡¿»¹7¸ ¿·» 

(41) . ’ X(Q) i. R. Q (stable state). j (service). Çy¡“;wb}re 7 LRfuvc#cwbxŽyŸs&{pyŸxb“{;s¨pyŸ©ny pry¡e5o _%`beMy¡c#„Ž{;s¨pu¤{Bc#e&oror{“ve}e&sded„\pry¡u;xÏuvx {xÒ{;s¨pyŸ©ny pqmGyzo \y =ed}redxJp¥ \e&„7edxŽ \yŸxb“ uvxÏp`beœ£ny¡xŽ uv¤p`Žec#e&oro{v“ve;®(g xÑu;xbe#`Ž{vxŽ ˪{}re&°Jwbe5oqp}e5sed„\pryŸuvxÑc#u\ \y¡Že&o†uvxŽž¡m¦p`Že}re&°Jwbe&oQp°JwbedwŽe#uv¤pr`be }re&se&y¡©;ed}wbxJpyŸž$y p#oQe&}©ve5opr`be(}re&°Jwbe5oq=p Lpr`be{v„b„bžŸyŸs&{pyŸ©ve(oQpr{pe¥yzoxbuvp{vž pred}re& µ`byŸžŸe¥p`byzo}re&°Jwbe&oQp yzo„7edxŽ \yŸxb“Ž®¦g x p`be(up`Žed}`Ž{vxŽ ˪9{M}red„Žž¡mB}e5sed„bpyŸuvxÐsd{vxÐsr`N{xb“;eCpr`be({v„b„bžŸyŸs&{pyŸ©ve¥oQpr{pe¥u¤$pr`be }re&se&y¡©;ed}†ÌKcCub \y Ns&{pry¡u;xµ`byŸs `MyŸoc#uv}redu©ved}%y¡}r}red©ved} oQyŸ¬bžŸe5ή9_%`byzot \y 7e&}e&xŽse†}e&“;{} \yŸxb“pr`be†y¡c#„Ž{;s¨p uv¤pr`be}e5sed„bpyŸuvxuv¤9{#c#e&oror{“veyŸoƒoQ`buµxMuvxœÇy¡“;wb}e 7 p`b}ruvwb“;`p`bee&xŽ \„7uvyŸx;p ouv¤pr`be{}r}uµtod®I§ }re&°Jwbe&oQpt \une5o$xŽupƒsuvc#e€p`Ž}u;wb“v`M \uppe& žŸy¡xbe5o%}re&spr{vxb“vžŸe&o&ªn¬bw\pƒ{C}red„bžŸm( bune&o&® . . b. . M#*  \. ²³xGu;wb}cCub \edžUª3sduvc#cwbxbyzsd{pyŸuvxŽo{}re({;oQmnxŽs `b}ruvxbuvwŽo&ª¬Žw\pp`Žed}re(yŸoC{¦o`bu;}Qp»¿s=¾v¿ .7 ·=1{ppr`be ¬7ed“;yŸxbxby¡xŽ“Cuv¤Âpr`be†sduvc#cwbxbyzsd{pyŸuvx¯® ´`be&xM{vx{;s¨pyŸ©ny¡p³m(oedxŽ Žo{c#e&oro{v“ve pu{xbuvp`be&}&ª\y pƒoqpruv„Žo%y¡pro edÀne5sw\pry¡u;x¢wŽx;pyŸž9pr`be#c#e&oro{v“veyŸoy¡xBp`besu;x;preÀnpu¤Rpr`be#}e5sedyŸ©ved}5®_%`beC}redxN \e 8ÄÅ©vuvwNoƒyŸc#„bžŸy¡e5o pr`be pqµuC¤Æu;ž¡žŸu«µyŸxb“#„b}ruv„7ed}pyŸe&0o L sduvc#cwbxbyzsd{pyŸuvxŽo{}reDzqÇg0„7u;y¡xJpQÄUpuÄń7uvyŸx;p5ª sduvc#cwbxbyzsd{pyŸuvxŽo{}re{;sr£nxbuµž¡e5 \“ve5 Ë®. .  . ] !

(42) (&M!X M\4#.

(43). . . \)\). & # \. . ²³x ’!Ū\p`be§€k\| s&{žzswbžŸwŽo{žŸžŸu«µe5 ¥pru#„b}ru«©ve€p`bepqµuC¤Æu;ž¡žŸu«µyŸxb“#c{yŸx„b}ruv„7ed}pyŸe&o0L C ˜ [ Ø J3Ô ˜«— Õ , , 2\¿·»¾v¿d»#· »¿ ¸r¿qºN¼U½K·TG· »¿³º7¶ ½K¿.1C¾\»¨½24:M¹¾½@1¨¼?»¨½ s\¼Å¿ ¾M¿n¿r¸ \¼U½K·T 2\¹$1 =·¸ ·T 7 1d9¿ > Ž¿ 7¸ ¿· YB¼ 2n¿ ¿.2n¹ 5½Æ·»M· ¼B2n¿ºN»·<:v»¹ ¹$1+1p ½2=:¦¼B2n¹¼ =·¢¾;¿r¹v¾\¶¡·5¸¢½@1(¸r¹=1¿ ¾ .3 R¹½Í¼B7 .37 =¿r¸ A¿ 1+1¨½ÍB¼ 3 C ˜ [ Ø J3Ô ˜«— Õ , :  ¿n¿ ¸s\¼U½K·T ¸r¹ r¿¢¸.2n¹»¹v¸d¼Å¿d»¨½ 5¿r¾Ò·Ž¶ 3 A3мK2\¿¢·»¾;¿»¿ ¾G¶ ½@1¨¼K1q·T=¿ ·»¦¿ ¹v¸.2 ¹;¸¼U½ &½ÍS¼ 3 · †»9¿ > ŽA¿ 1¨0¼ 1ds¿ =¾v¿d»†½K¾v¿ Ž¼U½ ¿d+» 1 Be{žzouCc{£ve€p`Že€¤Æu;ž¡žŸuµy¡xb“{vorowbc#„\pyŸuvxŽo%}red“;{v}r \yŸxb“pr`beoQm\oQpe&c {vxŽ (p`be{;s¨pry¡©ny¡pyŸe&0o L . . .

(44) . . ijilkm`npoqsr. . . . .

(45) C¿¶ ¿ Ž»¨½K· I¹»· ¿d¶ 9. . . ;{ s¨pyŸ©ny pryŸe&o{}re ¤K{vy¡ž¡Ä³oqpruv„" Š;’!Uª ¤K{vy¡žŸwb}re&o{}re \edpe&spe5 y¡xœ{xM{}r¬by¡p} {}rm#¬bwbpŽxby¡pepry¡c#e  9Uª {vxM{5©{vy¡žz{v¬bž¡e€`buJoqpt{vž¡µ%{5m\o$eÀ\yzoqp o&ª\y¡xMuv} \ed}%pu#}re&oQpr{v}Qp{¤K{vy¡žŸe& M{vs¨pryŸ©Jy¡pqmvª {#oQpr{v¬bž¡eoqpruv} {“ve;ªJ£nxbuµx¬nm(e&{;sr`M{vspyŸ©ny pqmvªbeÀ\yzoqp o%y¡xMuv} \ed}%puor{5©;esr`Že&s £J„7u;y¡xJpro&ª pr`bed}reyŸo#{¦„b}ru\sde&orodª3s&{žŸž¡e5 pr`beB»¿ ¸r· «¿dA» 3º7»·&¸r.¿ 1+1 ªµ`byzsr`Ï`Ž{voC{vs&se&oro{p#{vxJmÑpry¡c#epu¢pr`be oQpr{v¬bž¡e†oQpu;}r{v“ve€{vxŽ £nxbuµtopr`be†xJwŽc¬7ed}tu¤9{vspyŸ©ny pry¡e5o%u¤pr`beomnoQpe&cM®    . . . . X  . . X XM\. ²³xM§ k\|ªŽ{x{;s¨pry¡©ny¡p³m¥yzo$yŸx{ 1¨¼³¹ ¶¡/¿ 1¨¼Å¹¼Å¿µ`be&xy¡pt \une5o$xbuptoQe&}©ve€{vxJm¥}e5°;wŽe&oQp&®9²³xŽ \ede5 ˪\¬7edp³µe&edx pqµuM}e5°Jwbe&oQp†oed}r©Jyzse5odªËp`be¥{„b„bžŸyzsd{pyŸ©ve#oqp {pre#{vxŽ ¢p`be„7edxŽ \yŸxb“M}re&°Jwbe5oqp°Jwbedwbe{v}e#ow¥syŸedx;p†pu ¤ÆwbžŸžŸmYs `Ž{v}r{;s¨pe&}y 8de(pr`beœoQpr{peMu¤ p`be¦{vs¨pry¡©ny¡pqmv® fuvxNoQe5°;wŽedx;prž¡m;ªIpr`beœoQpr{v¬bžŸeMoQpr{peMu¤{xÒ{;s¨pry¡©ny¡p³m s&{x¥¬7e }re&sduv} \e& Cpr`b}ruvwb“;`(oqp {xŽ b{v}r (v{«©{oQe&}yz{žŸy 8&{pry¡u;x#uv¤Ëpr`be€{v„b„bžŸyŸs&{pry¡©ve€oqp {peCÌ?oqp {}pyŸxb“{ppr`be {;s¨pyŸ©veuv¬\~qe&sp Î3{vxŽ Cu¤=p`bet„7edxN \y¡xŽ“†}re&°Jwbe5oqpR°Jwbedwb(e 'vpr`bed}reyzo3xŽu†xbede5 pruoed}ryŸ{vž¡y 8de$pr`bep`b}re&{; ˪;{vxŽ {#s `be&s £n„7uvyŸx;pts&{xp`nwŽo¬7epr{v£vedx¯® g xœÇyŸ“vwb}re 7 ªN{}re&s¨p {xb“;ž¡e \} {«µxMwŽoy¡xb“( bupQpre& œž¡yŸxbe&o os `bedc{py 8de&opr`be„7e&}yŸu\ M bwb}yŸxb“¥µ`byzsr` pr`beM{vspyŸ©ny pqmÐyŸo#oed}r©ny¡xŽ“B{¢}re&°Jwbe5oqp5ªR{xŽ Gp`JwNoCyzoCxbup#yŸxÒ{BoQpr{¬Žž¡eMoqp {prev®ÒfuvxJ©ve&}roedžŸm;ª3{B„7ed}ry¡u\ \wb}ryŸxb“#µ`byzsr`p`be{;s¨pry¡©ny¡p³m(yŸoyŸxM{#oQpr{v¬bž¡e†oQpr{peyzo}e&„b}e5oQe&x;pe5 (¬Jm{oQyŸc#„bž¡e†žŸy¡xbe;® .  '+  t'

(46) Ï  "0

(47) 

(48) $

(49)  _%`be#„b}ruv„7uJoQe5 œ„Ž}uvpu\sduvžyzo€¬Ž{;oQe5 ¢uvx ‰$R{xŽ  Š 7 Å®g xÑ{vxÑ{vspyŸ©Jy¡pqmvª¯e5{vsr`Ñs `be&s £n„7uvyŸx;p†yŸoyz \edxJpy¡Ä Že5 ¢¬nm¢{oe&°Jwbe&xŽseCxnwbc¬7ed}5ª¯µ`byzs `Ñy¡xŽsd}e5{voe&o c#uvxŽupu;xbuvwNoQžŸmv® Ñe \edxbuvpe N current pr`be#žz{pre&oQp s `be&s £n„7uvyŸx;p$xnwbc¬7ed}%uv¤¯p`be†{vs¨pry¡©ny¡p³m i ®I_%`be }re&sdedyŸ©ved}uv¤{c#e&oro{v“ve Mi,j 1+2n·T\¶Ÿ¾ i r¿·»¸r¿ ¾¼³·C¼³¹ ¿ ¹M.¸ 2n¿r¸ rº\·S½ Ž¼ƒy¡¤3pr`beoedxŽ bed}5à otžz{pre&oQp€sr`be5sr£n„7uvyŸx;p xnwbc¬7ed} „Žy¡“;“vmn¬Ž{vs £ve& ¬nm i,j ª= \edxbuvpe& N ª yzot“v}re&{pe&}%p`Ž{vxMp`N{pƒuv¤9p`be}re&se&y¡©ve&}&®$²Å¤9¤Æuv} se5 Ms `be&s £n„7uvyŸx;proƒsduvwbžz M¬7e†pr{v£vM edx¦{p {vxJm(pry¡c#evªNp`Žedx {“;ž¡u;¬Ž{ž3oQpr{pre#sduvc#„7u;oe& ¢u¤$s `be5sr£n„7uvyŸx;p o€µy¡p`Bpr`beor{c#eCxJwŽc¬7ed}†yzo€“;wŽ{} {xJpe&e& œpuM¬7esu;xŽoQyzoQÄ predx;p5®†kny¡xNseCsr`Že&s £J„7u;y¡xJpro€sd{x¦u;xbž¡mMu\sdsdwb} µ`bedx¦p`be#{vs¨pry¡©ny¡p³mMyzoƒyŸxB{(oqp {¬bžŸeoQpr{pe{vxŽ ¦oy¡xNsepr`be u\s&swb}r}e&xŽse5ouv¤9oqp {¬bžŸe†oQpr{pre&o{v}ewbxb„b}re& \yzs¨p {¬bžŸevªŽ{xM{v Ž \y pry¡u;xŽ{žËc#e5sr`Ž{vxbyzoQc yŸoxbe&sde&oro{v}m;® ª;µ`byŸs `{vžŸž¡uµtop`Žet{;s¨pry¡©ny¡p³m f {vs `{;s¨pyŸ©ny pqm`N{voI{†sr`Že&sr£n„7u;y¡xJpyŸxb“pyŸc#etsduvwbxJpe&}&ª; \e&xbupre& pru„7e&}yŸu\ \yzsd{vž¡žŸmCpr{v£ve€{Csr`Že&s £J„7u;y¡xJp&ª\y¡xuv} \ed}puCedxNoQwb}reƒpr`be}e&“vwbTžzT{}RC¤Æiu;}c{pryŸuvx(u¤}e5su©ved}rmCž¡yŸxbe5od® _%`byzopyŸc#eMsduvwbx;pred}#yŸoCyŸxby¡pyz{žŸhy 8&e& V¿r¹;A¸ 2Y¼U½ ¿œ¹GA¸ 2\¿r¸ ºb·S½ Ž¼@½ 1¼Å¹ ¿ ´µy pr`Ò{¢©{žŸwbe \edxŽupe5 G¬nm ® T T C IN IT ²³x p`byzo(„Ž{„7e&}&ª{Ðc#e&oro{v“veœž¡u;“v“vyŸxb“ c#e5sr`Ž{vxbyzoQc yŸo({; b \e5 ÏpruÐpu;ž¡e&}r{peœ}re&oQp}ryŸspyŸ©vedžŸmY„bžz{vsde& s `be&s £n„7uvyŸx;pro&®IhMuv}redu©ved}5ªvp`be„b}u;„7u;oe& „b}rupru\su;ž7 \y 7e&}ro¤Æ}ruvc  $‰ ¯{vxŽ?  Š 7 ˬJm#pr`be€žŸu;oQp$uv¤¯ºN»·5¸r.¿ 191 ¹ \¼Å· 7· 3ªR{vo beŽxbe5 Gy¡x  $Š  L({xÏ{vs¨pry¡©ny¡p³m xbe&©ved}C be&syz \e5oy¡proedž¡¤tpu¢pr{v£ve{¢s `be5sr£n„7uvyŸx;p5® ´`be&x  {oQpr{v¬bžŸe#oqp {preCyzo€}re&{;sr`Že& ˪=pr`be#„b}rupru\su;ž9sd{x¢pr}yŸ“v“;ed}{s `be&s £n„7uvyŸx;p \wbeCpruM{„b}red©nyŸuvwŽo€c#e&oro{v“ve }re&se&„\pyŸuvxªJuv}% \wbeƒpruedžz{„Žoe& (sr`be5sr£n„7uvyŸx;pryŸxb“pry¡c#ed}su;wbx;pred}&® Ñe µyŸž¡žËoedeƒp`Ž{pp`ŽyŸo%or{vs}ry¡Nseƒu¤{ sded}Qp {yŸx¢ \ed“;}e&euv¤I„b}ru\sde&oroƒ{w\pruvxbu;cmyŸxŽ \wŽsde&o€{suvxNoQe5°;wŽedx;p€}e5 \wŽs¨pry¡u;x¦u¤Ip`Žepuvpr{vžxnwbc¬7ed}€uv¤ s `be&s £n„7uvyŸx;pro&® . . . . . . − −− → Mi,j. .

(50). . . . . i.

(51) ¹\¶ ¼Ž·¶¡¿»¹7¸ ¿·» 

(52) b. F.  . Y *M$ &  # 

(53) \. . ÇyŸ“vwb}reMŠBoQ`buµtoC{Ñsr`Že&s £J„7u;y¡xJp uvxÒ{xÒ{vspyŸ©Jy¡pqm ®Ï_%`be“v} {„Ž`byŸs&{ž$}e&„b}e5oQe&x;p {pyŸuvxGyŸxŽsdž¡wŽ be&o ¡y proƒoQe5°JwbedxŽsdexnwbc¬7ed}Ì nΨªŽp`besdCwbi}n}redxJp}re&°Jwbe5oqpƒ°Jwbedwbie Qrcv Ì Q1, Q3, Q4  ΪN{xN {vxM{; b \y¡pyŸuvxŽ{vž °Jwbe&wbe sd{vž¡žŸe& #p`be»¿A1d¿ 7¾ > Ž¿ Ž¿Ì  Q2, R5 ¡ÎƒÌKoede€kne5s¨pry¡u;x(Šbi® ‹nΨ®²Å¤{°Jwbe&wbeƒyŸoedc#„\pqmvªny p$yŸo$ \edxbuvpe& ¬nm [∅] u;} ]∅[ ® tuvpep`Ž{pty¡xNsuvc#yŸxb“#c#e&oror{“ve5o%{}re€¬bžŸu\s £ve&  \wb}ryŸxb“{#s `be&s £n„7uvyŸx;p;'\pr`bedyŸ}t}e5sed„bpyŸuvx yzo%„7uJoqpr„7uvxbe5 ѹ  ¼Å¿d»p`bes `be&s £n„7uvyŸx;p&® Q1. Q4. ⇑{Q2 ,R5 } [Q1 ,Q3 ,Q4 ]. i. R5. Q3. Q2.         . Cn. ÇyŸ“vwŽ}eŠXLf`be&s £n„7uvyŸx;pu;xM{xM{vspyŸ©ny pqm Be xbuµ sd{vž¡ž I»+1¨¼I¿ n¿r¸ \¼U½K·T  »· yŸo%pr{v£vedx¯ªŽ{xŽ B»¿ ¿ J¿ ¸s\¼U½K·T   »· Cn. . i. b. . b. ] !

(54)  \ .  .   p`be edÀ\e&swbpyŸuvx¥uv¤Â{x({vspyŸ©ny pqm {¤Íped}p`besr`be5sr£n„7uvyŸx;p †p`be†edÀne5sw\pry¡u;xu¤ i {¤Ípe&}t{C}re&sui©ved}rmC¤Æ}ruvc C n ®. Cin  Cin.  a*M\ 

(55) \. i. § „b}u;c#yŸoe& }re&°Jwbe&oQp9yzo3{ žŸu\s&{ ž

(56) $oQwŽ¬Žoqpry prw\pe%¤Æu;}3{€}e5°Jwbe&oQpp`N{p3yzo9xbuvp9m;ep3}re&se&y¡©ve5 y¡xpr`be%}rededÀ\e&sw\Ä pry¡u;x6'y¡puvxbžŸmsuvxJpr{vy¡xŽoËpr`beRyz \edxJpy¡p³muv¤np`Že{vspyŸ©Jy¡pqmƒ¤Æ}ruvcVµ`byzsr`{}re&°Jwbe5oqpÂyzo{5µ${vy¡pe& ˮ²Åp{vž¡žŸuµto=pr`be „b}rupru\su;žbpru„7ed}¤Æuv}rc {; b \y¡pyŸuvxŽ{vžNžz{ 8&moQmnxŽs `b}ruvxby 8&{pyŸuvxyŸxsd{;oQe u¤Â}e5su©ved}rmv®§ „b}u;cCyzoe& }re&°Jwbe&oQp {«µ${y¡pe5 #¤Æ}ruvc yŸx¥pr`be€}e&°Jwbe5oqp%°Jwbedwbe€u¤ yzo$ \e&xbupre& ¥¬Jm promised ®3_%`Že€oQe&}©nyzseƒu¤{„b}ruvc#yzoQe5 }re&°Jwbe&oQpƒyzo oQwŽ¬ni~qe5s¨p puomJxNsr`b}ruvxby 8&{pyŸuvxp`Žj }u;wb“v`¦{¥µ${y¡pQÄŬJQmJÄÅi,jxbe&se5ooy¡p³mc#e&s `Ž{xbyzoc L%µ`be&x¢{x¦{;s¨Ä pry¡©ny¡p³m j p}ryŸe&oRpuCoQe&}©ve {„b}ruvc#yzoQe5 #}re&°Jwbe5oqp Qpromised ªJy¡p$yzo¬bžŸu\sr£ve5 wbx;pry¡ž7pr`byzo„b}ruvc#yŸoe& }re&°Jwbe&oQp yzo%wb„= Ž{pe5 Ë®RknuNª\µ`be&xM{vxM{vs¨pry¡©ny¡p³m j }e5se&y¡©ve5o%i,j{C}e5°Jwbe&oQp Qi,j ¤Æ}ruvc i L y¡¤ j yzo¬bžŸu\s £ve& Ðu;xY{¦„Ž}u;cCyzoe& Ð}e5°Jwbe&oQpÌƵy¡p`Yp`Žeor{c#eoedxŽ \e&} iÎ Qpromised ª3p`ŽedxGpr`be i,j µ${vy pÄU¬nmJÄUxbe5se&oroy pqmu;x j yzo}edžŸe&{;oQe5 {xŽ j oed}r©ve&o Qi,j ª y¡¤ j yzoxbuvpt¬bžŸu\s £ve& ˪Ž¬bw\ptpr`bed}re†yzou;xbe†uv}tcCu;}e†„b}ruvc#yŸoe& }e5°;wŽe&oQproÌƵy¡p`Mp`Žeo{vcCeoedxŽ \e&} Î y¡xMy¡pro}e5°Jwbe&oQp°Jwbe&wbevª\p`Žedxp`Žeu;žŸ be&oQp Qpromised yzo%wb„= b{pe5 µy¡p` Qi,j ª i Qpromised i,j i,j e&žŸoe Qi,j yŸoedxŽ°Jwbe&wbe& y¡xp`Že}re&°Jwbe5oqpt°Jwbe&wbeu¤ j ® _uÏoQwbc#c{}ry 8devªƒ{ЄŽ}u;cCyzoe& }re&°Jwbe&oQpyŸo{ЄŽžŸ{;se¢`buvžz \e&}¥¤Æu;}{G}re&°Jwbe5oqp(p`Ž{pµyŸžŸž ¬7eB}e5sedyŸ©ve5 {¤Íped}{(}re&sdu«©ve&}mM{xŽ ¦`N{vo€{žŸ}re&{v bm¬7ededxB}e5sedyŸ©ve& ¦y¡x¢p`beŽ} oQp€eÀ\e&sdw\pyŸuvx®knwŽs `¢}re&°Jwbe5oqp oƒe&y pr`bed} sduv}r}e&o„7uvxŽ ¥pu#žŸuv“;“ve& (}re&°Jwbe&oQpro%u;}$pru#}e5°Jwbe&oQprooQe&x;pƒ \wb}ry¡xŽ“Cp`be†}redeÀ\e5sw\pry¡u;x¯® . . . . . H$JK^ATgXc`SFMb\JKF;f$FM`KO8Xc`0`BF k O &FMOFMF k U+WEOSX Y;X OSXcFM`]h. ijilkm`npoqsr.

(57) 7. . C¿¶ ¿ Ž»¨½K· I¹»· ¿d¶ .

(58). b. . . . .  . . !

(59) & *#. . . M\)\  M\. §ƒx#{vspyŸ©Jy¡pqm¸r¹`7·¼ ¿j·»¸ ¿r¾pu€pr{v£ve%{sr`be5sr£n„7uvyŸx;p!'vy¡p3cwŽoQp3µ%{y¡p¤Æu;}pr`be%xbedÀnpIoqp {¬bžŸeoqp {pe;ªp`Žedx s&{xuvxbžŸm}re&{vsp ¹ƒº\·$1¨¼³¿»¨½K·»¨½Í®R_%`JwŽo&ª;µeƒ©ny¡}pwŽ{vž¡žŸmCoQ`by¡¤Íp}re&sded„\pry¡u;xŽo3uv¤=c#e5oor{“;e&opr`Ž{p$o`buvwbžz C¤Æuv} se {¥s `be5sr£n„7uvyŸx;p5ªŽprupr`bec#uvc#edxJp µ`bedxœpr`be}re&se&y¡©ve&}ƒ{;s¨pwŽ{vžŸž¡m(p {£ve5oƒ{¥s `be&s £n„7uvyŸx;p&®€fuvxŽoe&°Jwbe&x;prž¡m;ª pr`be}e5sed„\pryŸuvxœuv¤RoQwNsr`¦c#e5oor{“;evªNc#uv}re„b}re&syzoedžŸm{¥c#e&oror{“veyŸxŽ \yzsd{pyŸxb“¥p`N{p N > N current ª j pr}yŸ“v“;ed} o${xM{;s¨pyŸuvxM \e&„7edxŽ \yŸxb“uvxy¡pro£ny¡xN ˪b}e5°;wŽe&oQp%u;}%}red„Žž¡m;® () Ô I Ô –d— Qi,j : H  , ²Å¤Rpr`beC}re&se&y¡©ve5 ¦cCe5oor{“;eyŸo{}e5°Jwbe&oQp&ª=p`byzo€}re&°Jwbe5oqp€µyŸž¡ž3¬7eC}e&„bžŸ{;se5 œµy¡p`Ñ{„b}ruvc#yŸoe& ¦}re&°Jwbe&oQp yŸxMpr`be}e5°Jwbe&oQpƒ°Jwbe&wbeuv¤9p`bexbedÀJp€s `be&s £n„7uvyŸx;ptp {£vedxœ¬nm ®  uvyŸxb“p`byzodª7µe©JyŸ}pwŽ{vž¡žŸm Qpromised „7uJi,joqpr„7uvxbe†pr`be}e5sed„\pryŸuvxœuv¤ Qi,j y¡xBsd{voeu¤I}re&su©ved}rmvªŽžŸyŸ£ve Q yŸx¢sd{;oQej uv¤I}e5su©ved}rm¥¤Æ}u;c n + 1 yŸx ÇyŸ“vwb}retb®9_%`be&}etyŸoIxŽu†„b}ruvc#yzoQe5 C}e5°;wŽe&oqpRy¡x#pr`bet}re&°Jwbe5oqp°;wŽedwbeƒ \wb}ryŸxb“pr`beŽ} oQpIedÀ\e&sw\pry¡u;x¯ªJoQyŸxŽsde pr`be†}e5°;wŽe&oQp%yzo%}red„ŽžŸ{;se& µy pr`M{#„b}u;c#yŸoe& (}re&°Jwbe5oqpT· N¶ 3¥y¡xp`Žesr`be5sr£n„7uvyŸx;p5® _%`Ž{xb£\o3pu„b}ruvc#yzoQe5 }re&°Jwbe5oqp odªvp`beƒ}e&žŸ{pyŸ©veuv} \ed}Iu¤Ë}re&°Jwbe&oQpI}re&sded„\pry¡u;xŽo3yzoI„b}re&oed}r©ve& yŸx¥sd{;oQe uv¤}e5su©ved}rmv® . − −− → Mi,j.     . . C n+1. ⇑{∅} [∅]. i Q.         .      Q. ÇyŸ“vwb}re†

(60) L3_%`be†}re&°Jwbe&oQp. j. ⇑{∅} C n+1 [Qpmd ] i,j. ⇑{∅} C n [∅]. Q. yŸo}e&„bžz{vse5 (¬Jm{C„b}ruvc#yzoQe5 (}re&°Jwbe&oQpy¡x. Cjn+1. (Ô)J & Õ Ri,j ²Å¤p`be†}re&sdedyŸ©ve& (c#e5oor{“;e yzot{C}e&„bž¡m;ª\y¡ptyŸoy¡c#„7uJooy¡¬Žž¡e€pru#„7u;oQp„7u;xbe€p`byzo}e5sed„bpyŸuvx¯®3§ oµ}y¡pQpredxMy¡x kne5s¨pyŸu;x 7 ® 7 ªvp`Žeƒ}re&sded„\pry¡u;xuv¤¯{}red„bžŸmCc{5msd{wŽoe {x({ž¡ped} {pryŸuvx#uv¤Ëp`be µ`bu;ž¡e {vspyŸ©ny pqm#oQpr{petp`N{p yzoyŸ}r}e&©ved} oQyŸ¬bž¡e;®#_%`JwŽo&ª{}red„Žž¡m¦p`Ž{po`bu;wbžŸ ¢¤Æu;}rsde#{œsr`be5sr£n„7uvyŸx;puvxBpr`be}re&se&y¡©ve&}yŸo \edŽxby¡pyŸ©vedžŸm {vxMu;}„b`Ž{vxMcCe5oor{“;ev®fu;xŽoQe5°JwbedxJpžŸmvªN{¤Íped} {}re&su©ved}rmvª\p`Že}re&sdedyŸ©ved}tc#{«m}re&se&y¡©ve{}red„bžŸmy¡pƒ`Ž{; {vž¡}re&{; \mÑ}re&se&y¡©ve5 Ë® Ntu;„7e¤ÆwbžŸž¡m;ªIp`beMcCe5sr`Ž{vxbyzoQc uv¤t¤Æw\prwb}e5oCedxŽowb}re&opr`Ž{p{BowŽs `Ï{MÉQ \wŽ„bž¡yzsd{pe5 }red„bžŸm;ʃyŸo†T¹ \¼³· ¹¼U½K¸r¹¶Í¶ 3yŸ“vxŽuv}re& Ë®9_%`bed}re yŸo$xbe&©ved}p`be&ž¡e5oouvxbe€sduvxŽoQp} {yŸx;=p Ls¿  1\»¿B¼ 2n¹¼T¾ «º7¶ ½K¸r¹¼Å¿ ¾ »¿qºN¶ ½K.¿ 1(¹»¿¥½K¾v¿ Ž¼U½K¸r¹¶I¼³·B¼ 2n¿·»¨d½ :v2½ 7¹¶R»¿qºN¶ ½K.¿ 1 Ñe#µyŸž¡ž9¤ÆwŽ}Qpr`bed} \yzosdwŽoo†{¬7uvwbp€p`byzoxbe5se&oroy pqmœuv¤ e5°;wŽy¡©{vžŸedxŽseu¤edÀne5sw\pry¡u;xŽo%yŸxœkne5s¨pry¡u;xMb® |3}u©nyŸ be& pr`Ž{p bwb„bžŸyŸs&{pe5 #}e&„bžŸy¡e5oI{}reyŸ \e&x;pryŸs&{žbprupr`betu;}yŸ“vyŸxŽ{vž\uvxbe5odªvp`buJoQep³µuc#e&s `Ž{xŽyŸoco {«©vuvyz (yŸxŽsu;xŽoQyzoQpedxŽsdm( \wbepru#uv}r„b`Ž{vxcCe5oor{“;e&o$y¡xœsd{;oQeu¤}re&sdu«©ve&}m;® : H  :. . . . i.

(61) ¹\¶ ¼Ž·¶¡¿»¹7¸ ¿·» 

(62) b. . . . 7G7.  l   # = )!` # \  . . . M\)\  (M\. ǎuv}te&{vs `Mc#e&oor{“;e ªN{xœ{vs £nxbuµž¡e5 \“vc#edxJpc#e&oro{v“ve„by¡“;“vmn¬Ž{;sr£\o ªbpr`bežŸ{pe5oqpƒs `be&s £JÄ „7u;y¡xJpxnwbc¬7ed}$uv¤Ëp`bMe i,j}re&sdedyŸ©ved} j 'Jp`byzo„byŸ“v“;mn¬Ž{vs £ve& #©{žŸwbeƒyzo \e&xbupre& (N \jedcurrent xbuvpe& N ®3_%`bed}re¤Æu;}e;ª µ`be&x N > N current ª{xÒ{vspyŸ©Jy¡pqmÐyŸo¤Æu;}rsde& Ðpu s `be&s £n„7uvyŸx;p{voCy ¤€y p`Ž{v Yxbup#mvedpoQe&x;pCpr`be {v„b„bžŸyŸs&{pyŸ©ve€c#e&oor{i“;e Mi,j ÌK}e5°Jwbe&oQp%uv}%}red„bžŸmbΨ®3_%`be†oedxŽ \yŸxb“#{;s¨pry¡©ny¡p³m¥yŸo%yŸxbed©ny¡pr{¬Žž¡m(oQe&}©nyŸxb“C{}reÄ °Jwbe5oqpµ`by¡žŸe†oQe&xŽ \yŸxb“pr`becCe5oor{“;evª;pr`JwŽoy pyzo%xbupy¡xMoQpr{¬Žž¡eoQpr{pe;®3_%`byzo¤Æu;}rsde& sr`be5sr£n„7u;y¡xJp%cwŽoQp pr`bedxM¬Ne†„NuJoqpr„7uvxbe5 ¥puCpr`bexbedÀnptoqp {¬bžŸeoQpr{pe;®RfuvxNoQe5°;wŽedx;prž¡m;ªnp`beoQedxJpc#e&oro{v“ve yzo{xyŸx\Ä?pr}r{vxŽoQy¡p c#e&oror{“ve LCy¡pCµyŸžŸž$¬7ež¡uJoqpCy¡xÏs&{voe¥uv¤t}re&sdu«©ve&}m;®Ñg wb}#oQu;ž¡w\pry¡u;xGyŸopru¢žŸuv“¦p`ŽyŸoCcCe5oor{“;e(oQuB{;opu }re&oedxŽ (y pyŸxs&{voe uv¤Â}re&sdu«©ve&}m;®_%`byzo$c#e&oror{“ve€sd{vx¬7e€žŸuv“;“ve& ¥yŸx©vuvžz{pryŸž¡e c#e&cCu;}mµ`Žy¡žŸe pr`bexbeÀnp s `be&s £n„7uvyŸx;ptyzotxbuptpr{v£ved"x LRž¡u;“v“vyŸxb“#uvxœ{oQpr{v¬bž¡eoQpu;}r{v“ve€u\s&swb} o \wŽ}yŸxb“#p`Žesr`be5sr£n„7uvyŸx;p5ªN{žŸž¡uµyŸxb“ u;xbž¡mu;xbe{;sdse5oopu¥pr`beoQpr{v¬bžŸeoQpuv} {“;ev® ÑeµyŸž¡žxbupre Mresend(n) pr`be(».¿ 1ds¿ =¾ > Ž¿ Ž¿#·  i ·» n yU® e;®9pr`be†uv} \ed}re& (žŸyŸoQptu¤c#e5oor{“;e&op`Ž{pt`Ž{«©ve€pu#¬7eoe&°Jwbe&x;i pyz{žŸžŸm(oedx;p¤Æ}ruvc i yŸxœsd{;oQeu¤}re&sdu«©ve&}m ¤Æ}ruvc p`bes `be&s £n„7uvyŸx;p n ® ÇyŸ“vwŽ}e‹o`bu«µto$p`ŽežŸuv“;“vyŸxb“Cu¤ Q ÌÆxŽupe5  Q ¡Î$y¡xp`bes `be&s £n„7uvyŸx;p n ® ← −− − Mi,j. ← −− − Mi,j. .    . C n-1.   . ⇑{∅} [∅]. Cn. ⇑{Q} [∅]. Q. i Q.    . j. ⇑{∅} C n [∅]. ÇyŸ“vwŽ}e‹`LI_%`be}re&°Jwbe5oqp. Q. yzo%žŸuv“;“ve& ¥¤Æuv}}re&oedxJpy¡xp`Že†s `be5sr£n„7uvyŸx;p n u¤ i ®. _%`Ž{xb£\oIpup`byzož¡u;“v“vyŸxb“cCe5sr`Ž{vxbyzoQcMªJxbuc#e&oror{“vetyzoRžŸu;oQp${¤Ípe&}${}e5su©ved}rm¤Æ}ruvc {vxJmC}re&sdu«©ve&}m žŸy¡xŽev® b. . YZ#\ M$ *   . +. #. . . & \ \. . .  . . Y *M$ a&. . # 

(63) \. § oM{x {vspyŸ©ny pqm sd{p sr`Že&owb„ pruYpr`beўz{pe5oqpœsr`Že&s £J„7u;y¡xJpxnwbc¬7ed}Muv¤upr`bed}M{;s¨pyŸ©ny¡pyŸe&o&ªƒy¡pMc#y¡“;`;p ¬7e¢¬7ed`byŸxŽ ´¬JmÒc#uv}reœp`Ž{vx´uvxŽe¢sr`be5sr£n„7uvyŸx;p5®­²³x´p`ŽyŸos&{voevª%y¡pcwŽoQp(pr{£ve¢oed©ve&}r{vžƒsuvxNoQe5sw\pyŸ©ve s `be&s £n„7uvyŸx;pro&ª 3½ÍB¼ 2nT· \R¼ 1d¿d» &2½ =:T¹  3»+¿ >sŽ.¿ 1¨¼ ¿d¼ R¿r¿ B¼ 2n.¿ 1d¿†A¸ 2\¿r¸ ºb·S½ ŽB¼ 1 ®I_%`be5oQe sr`be5sr£n„7u;y¡xJproR \y =ed} u;xbž¡m(y¡xpr`bedyŸ}ƒ{voroQu\sdyŸ{pe& °Jwbedwbe5odªŽoy¡xNse€pr`be{„Ž„bž¡yzsd{pyŸ©ve†oqp {pre† \une5o%xbupƒs `Ž{xb“;ev®9²³xM„b} {vspyzsevªb{vx {;s¨pyŸ©ny pqmCp`Ž{p$yŸoc#uv}retp`Ž{vx¥u;xbe s `be&s £J„7u;y¡xJp¬7e&`by¡xN pr{v£ve&o€T· =¿A¸ 2\¿r¸ rº\·S½ Ž¼ 3½ÍB¼ 2 1d¿ ¿d»¹¶ 1+¿ >sŽ¿ 7¸ ¿ A r¿+» 1¨ªn{xN ¥oed©ved} {ž7 \y =ed}redxJp$}re&oedxŽ ¥{vxŽ }re&°Jwbe5oqp$°Jwbe&wbe&o&®9ǎuv}edÀ\{vc#„bž¡e;ªJuvxÇyŸ“vwŽ}e€‰bª cwŽoQp p {£ve€pqµus `be&s £n„7uvyŸx;prot \y =ed}ryŸxb“#uvxŽž¡m(¬Jm¥p`be†}re&oedxN °Jwbe&wbeÌK`bed}re  Q1, Q2 ={xN  Q2 ¡Î¨® j txŽ \e&}9pr`bet \e¤K{vwbž¡pIoed}r©nyzse$„7uvžŸyzsmu¤7u;wb}3c#u\ \edžUªvy?® ev®9DzqÇg oed}©nyŸxb“Nª{x#{vspyŸ©ny pqmyzo3y¡x{oqp {¬bžŸe oQpr{pe¬7e¤Æu;}ee&{;sr`}re&°Jwbe&oQptoQe&}©nyzsev®9²Åpƒsd{xpr`JwŽo%p {£ve†{#sr`Že&s £J„7u;y¡xJp¬7e¤Æu;}ee&{;sr`}re&°Jwbe&oQptoQe&}©nyzsev® . . . . . . ijilkm`npoqsr.

(64) 7. Š. C¿¶ ¿ Ž»¨½K· I¹»· ¿d¶ .  . C n+2. ⇑{∅} [∅]. i. Q2.    . Cn. . ⇑{∅} [∅].

(65) 

(66) 

(67) 

(68)

(69)

(70) 

(71)

(72) . C n+1.    . ⇑{Q1 ,Q2 } n+2 ⇑{Q2 } C [∅] [∅]. j. Q1.      .    .  . ⇑{∅} C n+1 [∅]. C n+2. ⇑{∅} [Q1 ]. k. ÇyŸ“;wb}e‰XLI_%`be†{;s¨pry¡©ny¡p³m j cwŽoqptpr{£ve€pqµusduvxŽoe&sdw\pyŸ©ve†sr`be5sr£n„7u;y¡xJpro ƒu«µe&©ved}5ªIy pyzoC„7uJooy¡¬Žž¡epuфb}ruv“J{c {Ñ \y 7e&}e&x;p¥oQe&}©nyzse„7u;ž¡yzsmG{vxŽ Ïsu;xŽoQe5°Jwbedx;pržŸm „Ž}e&©vedx;p{vx {;s¨pyŸ©ny pqmpu(s `be5sr£n„7uvyŸx;p ¬7e¤Æu;}e¿ «¿d»A3oQe&}©nyzse;®$²Å¤R{vx¦{vs¨pry¡©ny¡p³mMoed}r©ve&ot{}re&°Jwbe5oqp p`N{p€oQ`Žuvwbžz ¤Æu;}rse{¢sr`be5sr£n„7uvyŸx;p5ª9¬bwbp#sd{xŽxbupC{vspwŽ{vž¡žŸmBpr{£ve¥pr`byŸoCs `be&s £J„7u;y¡xJp¬7e¤Æu;}e¥p`beoedQ}©ni,jyzse;ªp`ŽedxGp`byzo s `be&s £n„7uvyŸx;p ¬7e&su;c#eyŸcC„7uJooyŸ¬bž¡e;®²Åp µyŸžŸžxbuvpƒ¬7ep {£ve&x¦{xnmJc#u;}e†¬7e5sd{vwŽoQe yŸoƒ}redc#u«©ve5 ¤Æ}ruvc pr`be}e&°Jwbe5oqp°JwbedwŽe#ÌÆyŸxŽ \e&e& y¡p`Ž{vo$¬7ede&xoed}r©ve& ŽÎ{xŽ ¥pr`JwŽos&{xbxŽup%¬7e€}red„bžz{vQsdi,je& ¥µy¡p`M{„b}ruvc#yzoQe5 }re&°Jwbe&oQp5® ²³xBuv} \ed} puc#u\ \edžIsuvxŽoe&sdw\pyŸ©veC{vxŽ ¦yŸc#„7u;oroQyŸ¬bžŸeCs `be&s £n„7uvyŸx;p odªËµeCyŸx;pr}u\ bwŽsep³µu©{žŸwbe&oƒ¤Æu;} e5{vs `Ð{vs¨pryŸ©Jy¡pq[m L N min {xŽ N max ®M_%`be¥xbedÀnppyŸc#e i yzoyŸxGoqp {¬bžŸe¥oQpr{pe;ªy¡pcwŽoqpp`be&x p {£ve¥{vžŸž s `be&s £n„7uvyŸx;pro%¤Æ}u;c i C N pu iC N ®3²Å¤9{vž¡ž¯s `be5sr£n„7uvyŸx;p o{}re€„7uJooy¡¬Žž¡e;ª N min = N current + 1 ® N. . min i. i. max i. i. i. i.  'Ë  $¥9+

(73) +'¯

(74) . _%`byzo$kne&spyŸuvx(oQ`Žu«µto3Ž} oQpIpr`Ž{pRpr`beƒwŽor{“;euv¤Ëc#e&oro{v“vežŸuv“;“vyŸxb“†cCe5sr`N{xbyzoQcosd{x¥ž¡e5{v Cpru„7uvpedxJpyz{ž yŸxŽsu;xŽoQyzoQpe&xŽsm{¤Íped}I{ }re&su©ved}rm¬7e&sd{vwŽoeuv¤7 \wb„bžŸyzsd{pre& }red„bžŸy¡e5o9{xŽ Csd{wNo{vžn \e&„7edxŽ \e&xŽsyŸe&o9¬7edp³µe&edx c#e&oror{“ve5od® Ñep`be&x„Ž}u;„7u;oe u;wb}toQu;ž¡w\pry¡u;x(pru{«©vuvyz ¥p`ŽyŸoyŸxŽsu;xŽoyŸoQpe&xŽsm;® .

(75). . ] !

(76)    . . \. ƚ;™\— Ô Ù Ô J &S/ Ô – § o{C \wŽ„bž¡yzsd{pe5 }e&„bž¡m¥yzo%y¡“;xbuv}re& (¬Jm¥p`be†}e&sdedyŸ©ved}5ªJp`byzo%}red„bžŸm¥cwŽoQp¬7eyz \edxJpyzsd{žËpuCp`Žeuv}ryŸ“vyŸxŽ{ž u;xbev®9_%`beN}roQpsuvxŽoe&°Jwbe&xŽseyzo3pr`Ž{pRp`be {vs¨pry¡©ny¡pyŸe&oIcwŽoQp¬7eºN½K¿ ¸r¿ 3@½ 1d¿¾;¿¼³¿d» 2½ N@½ 1 ¼U½K¸  Š 9$ L9{vo3p³µ$u }red„bžŸyŸe&o%cwŽoqpt¬7e†yŸ bedx;pryŸs&{ž¯y¡xœ{C“vyŸ©vedxMsuvxJpedÀJp5ªnpr`bedms&{xbxbuvp¬7e€pr`be†}e&owbž¡pu¤9{vxyŸxŽ \edped}rc#yŸxbyŸoQpyzs u;„7ed}r{pyŸuvx® H  , ,. V J &S/. . . i.

(77) ¹\¶ ¼Ž·¶¡¿»¹7¸ ¿·» 

(78) 7. . |3}u©nyŸ be& (p`N{pƒ{vspyŸ©ny pry¡e5o{v}e„by¡e5se&µyŸoe† \edped}rc#y¡xŽyŸoQpyzs†{xŽ p`Ž{vxb£\o$pruCpr`be|3}ruv„7ed}pqm 7 ® 7 ªnpr`be ds uvx;predx;p3uv¤7{ }red„bžŸm;ª{vxŽ yŸxC„Ž{}pyzswbžz{}9u¤7{ \wb„bžŸyŸs&{pe5 }e&„bž¡m;ªyŸop`Žesu;xŽoQe5°;wŽedxŽsdeuv¤Žp`be`byŸoQpu;}m†uv¤ }re&°Jwbe&oQptoed}©nyzse5o$u¤p`beoedxŽ \e&}u¤p`byzo}red„bžŸmv®I_%`JwNodªbyŸxMuv} \ed}$pru#e&xŽoQwŽ}e€p`N{pƒ \wb„Žž¡yzsd{pe& }red„bžŸyŸe&o {v}e#yŸ \e&x;pryŸs&{ž3puMp`Žeuv}ry¡“;y¡xN{ž9uvxbe;ªÂµecwŽoQpedxŽowb}reCp`Ž{p†p`be¥`byŸoQpu;}yŸe&ou¤%}e5°;wŽe&oQpoQed}r©nyzse&o†{}e yz \edxJpyzsd{vžÂ¤Æ}ruvc u;xbeeÀ\e&sdw\pyŸuvxœpu{vxbupr`bed}5® knuNª7µecwŽoQp€edxŽowb}ep`Že¤Æu;ž¡žŸuµy¡xb“(}e5°Jwby¡}redc#edxJpt¤Æu;} e5{vs `s `be&s £n„7uvyŸx;p C n L i Lt_%`be`byŸoQpu;}yŸe&oƒu¤I}re&°Jwbe5oqp }re&se&„\pyŸuvxŽo {v}eyz \e&x;pyzsd{vž9 \wb}ry¡xb“¥pr`beŽ} oqp€eÀ\e&swbpyŸuvx¢{xN R1 pr`be#}rededÀne5sw\pry¡u;x¯ªÂ{vož¡u;xb“M{vo€p`Žed}reCc#yŸ“v`Jp†eÀ\yzoqp†yŸxBpr`beCN}roQp†eÀ\e&swbpyŸuvxÑ}e&„bž¡yŸe&o€p`N{p {v}e† \wb„bžŸyŸs&{pe5 yŸxp`be†}redeÀ\e5sw\pry¡u;x¯®.  . C n+1. ⇑{∅} [∅]. i Q1.    . ⇑{∅} C n+1 [∅]. X(Q1 ) X(Q2 ) j. Q2.     . ⇑{∅} C n [∅]. R2.    . C n+1. ÇyŸ“vwb}re†Œ

Références

Télécharger maintenant ( PDF - 41 Page - 649.51 KB )

Documents relatifs

Long-term neurologic and cardiac correction by intrathecal gene therapy in Pompe disease

In infantile Pompe disease patients, the glycogen storage diffusely affects brainstem motor and sensory neurons, and the whole spinal cord sensory neurons, interneurons, and

ANRU : Mission accomplie ?

De ce point de vue, il est possible d’affirmer que la mission est accomplie : les projets de renouvellement urbain (GPV et ORU) élaborés depuis 1998 dans une centaine de villes

Étude et optimisation de l'utilisation de détecteurs à gouttelettes surchauffées pour la détection de la matière sombre

cosinus (en bleu à gauche) et d’une droite (en noir à droite) sur les données simulées pour 4 années à une température de 45°C, avec un bruit de fond interne réduit de 100,

Réoccupations funéraires de séputures collectives néolithiques dans la boucle du Vaudreuil (Eure)

Florence CARRÉ ~ Réoccupations funéraires de sépultures collectives néolithiques dans la boucle du

Étude numérique des premières étapes d'agrégation du peptide amyloïde GNNQQNY, impliqué dans une maladie à prion

2 Vue plus en détails dans le chapitre 1... 2 phénomène d’agrégation des protéines amyloïdes en fibres et d’autres facteurs impor- tants doivent être pris en compte comme

The Maximum Norm Analysis of a Nonmatching Grids Method for Nonlinear Parabolic PDES

In this chapter, we prove an a posteriori error estimates for the generalized overlapping domain decomposition method with Dirichlet boundary conditions on the boundaries for

La dame et l'écureuil. Le sceau allusif de Nicole de Nouvion (1300)

Revue française d’héraldique et de sigillographie – Études en ligne – 2020-10 © Société française d’héraldique et de sigillographie, Paris,

Cirque de Mafate

Dans ce cas, comme les coulées du Bras de Sainte-Suzanne appartiennent au massif de La Montagne daté à plus de 2 Ma (McDougall, 1971), l’ensemble des coulées pahoehoe