• Aucun résultat trouvé

Stochastic Localization of Instability and Deterministic Enhancement of Accuracy for Iterative Algorithms

N/A
N/A
Info
Télécharger
Protected

Academic year: 2021

Partager "Stochastic Localization of Instability and Deterministic Enhancement of Accuracy for Iterative Algorithms"

Copied!
14
0
0

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

Texte intégral

(1)Stochastic Localization of Instability and Deterministic Enhancement of Accuracy for Iterative Algorithms Philippe Langlois. To cite this version: Philippe Langlois. Stochastic Localization of Instability and Deterministic Enhancement of Accuracy for Iterative Algorithms. RR-3966, INRIA. 2000. �inria-00072682�. HAL Id: inria-00072682 https://hal.inria.fr/inria-00072682 Submitted on 24 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. Stochastic Localization of Instability and Deterministic Enhancement of Accuracy for Iterative Algorithms Philippe LANGLOIS. No 3966 May 2000. ISSN 0249-6399. ISRN INRIA/RR--3966--FR+ENG. ` THEME 2. apport de recherche.

(3)

(4) 

(5) 

(6)  

(7)   !"#%$&

(8)  ' (*)  ),+- . /102 .

(9)   )3-4) 57689 +

(10) :$ ; + < ),+ = ) 6>?

(11)  + @ - A!BCEDFCEGGIHKJML"N OPJRQ"STVU W,XZY\[^]

(12) _`badc\eZfg]!hjilkmfjnfg]\h ]oRnpqhrns<h/tvuw[xyilhjfrzms<] {}|~iq€]o33|~ce<plfg|~] ‚RpqƒZƒyil|„o3 †]|„]‡n@XZ]|@n@XZ]ˆe‰mŠl‹mŒlŒ`Žp‘u._l’l’m’!`“‡’ƒ%pqkl]‡t. ” •—\˜™;šZ›l˜lœž fge<fŸo~]ƒZ|„]‡nfrtvfjilenil[ ƒZsZo~p;o~fgime<td[p‘up;¡]\n#oo~XZ]t€o@pqxZfjhgfgo€uKiq¢fŸo~]|@p;o~fg£m]pqhjklim|„fgo„X<[ t – ple< ¤o~XZ]Kpln\nsZ|@plnu¥il¢dnil[ ƒZs†o~]\ ¦t„ilhjs†o~fgime<t§73s†o~il[p;o~fjn pqƒ<ƒZ|„i¨pln@XZ]‡tpl|„].ƒZ|~ilƒyimt„]\ ¤o~i¥nile¨o„|~ilh o~XZ]\t„]–]¡y]‡n#o@tpmt!¢©il|^]ªZpl[^ƒ<hg]m«o~XZ]"¬:­®†WR¬8pqe< o~XZ]"¬:­:¯R°[^]o„XZi† Zt\§P±¥]²¢©i†ns<tX<]|~]–ile³p nil[ ƒZhj][ ]e¨o@pq|~us<t„]3iq¢o~XZ]\t„]3o€´i![ ]o„X<iw <t}o~i

(13) hgi†n\pqhjfgµ\]3sZe<tvo~plxZhg]Rx%]\X<p‘£wfgim|}iq¢o„X<]¶pqhjklim|„fgo„X<[ «mfg[^· ƒ<|„i;£m]fgo~ttvo~pqx<fghjfŸo€u pqe% ^o„XZ]RpmnnsZ|~pmnuiq¢o„XZ]dtvimhgsZo„fjile<t\§±¥]3ƒZ|~]\t„]e¨o:nil[ ƒZs†o@p;o~fgime<pqhZ]ª†ƒ%]\|„fj[ ]e¨o~t ime.fjhjhŸ·¸nime< †fgo„fjileZ]‡ –ƒyilhjuweZil[ frpqh |~i¨ilo~tMplƒZƒZ|~i‘ªwfj[p;o~]\ ´Mfgo„XK¯3]\´,o„ime/¹ t3fŸo~]|@p;o„fjileº§ »K¼¨½¾~¿À ™;Á—lœ  fjeZfgo„]{I|„]‡nfrtvfjile/« ®¨o@pqxZfjhgfgo€ul«MnnsZ|@plnum«%¯R]´,o„ime/¹ t3ÂÃo„]\|~pqo„fjile/«%{ilhju¨e<il[ fjplhŽKs<hŸ· o~fgƒ<hg]

(14) ‚Miwilo~t\«%¬:­:®†WR¬2ŽK]o„XZi† «¬RÄd¯RˆÅºfgxZ|@pq|~ul«†Rs†o„im[ pqo„frn¬:il|~|„]‡n#o~fgime/«<¬:­I¯RÆŽK]o„XZi† . ÇrÈ É„ÊÃË\Ì,ÉMÍÎjÊÃÏEÐÑ Ò¤Ó%Ô3Õ@ÖØ×rوÚ@Û;܄Ý\ܸÞ#Þ߆àráâ~ãäÝ#å\Ü~æ~ç#ß~ã‡æè„Ý~é\å„ã<àrêë†ìîí/ï‘ÖØð"Ô3Õ@ñò‘ðEó€ôõÖØö‡÷KÖØðKÕ@×ØðFø¦Õvù#Õ@ÖØ×úÕ@û‡×ØüÕ@ðKÕ³ôFü€ðFü„Õ@ôõóÃïýôFü¸þ lö ø#ô©÷

(15) ø@ÿ÷Fï‘üwÕ@ûlø#ôFÕ~÷Fø#ÖØôFü‘ü×  ñ‡ÿgø#ôFÔ3Õ~÷FÖ\ò‡ü ‘ò ZÕ@ôFÕ@×Ø×

(16) v×ØÖØðFÔMü }Ó%ó€ø#×Øüºø#ôFñ‘Õ@×Øü\ò‘ö

(17) €ôõÖØüvò‡ôFü‘ü ø#ñ ;ôFÕ@ñ‘ó€ü Û@Þ<à ß~ã‡æè„Ý~éå„ã<àrê#ë~á „Ú‘ì. Unit´e de recherche INRIA Rhˆone-Alpes 655, avenue de l’Europe, 38330 MONTBONNOT ST MARTIN (France) T´el´ephone : 04 76 61 52 00 - International: +33 4 76 61 52 00 T´el´ecopie : 04 76 61 52 52 - International: +33 4 76 61 52 52.

(18)  

(19)    /.

(20) / 9 ) ' ) €. / !"@  ) 5 - M + 

(21) ' ),+-   / ) ' )   + M 

(22)  9 + ' ) 8

(23) ?

(24)  + @ -4) @   + ; —  œ ź]\t npqhrns<hjt ]e ƒZ|~c\nfrt„fgim 

(25) e <eZfj]ƒy]sZ£m]e¨oKp;¡]\n#o~]|"hrp¦tvo~pqx<fghjfŸo~c¥ Z]\t"pqhjklim|„fgo„XZ[ ]‡t fgo„c\|~pqo„fg¢õtM]o3hrp ƒZ|~c\nfjt„fgimeK †]\t3t„ilhjs†o~fgime<tMnplhjnsZhgc\]\t\§IĶ]\tRplƒZƒZ|~i†n@XZ]\tMpls†o„im[ pqo„frz¨sZ]\tMt„ile¨o3ƒZ|~ilƒyimt„c]‡t ƒyils<|nile¨o„| lhj]|n]\t]¡y]o~t,plnil[ [ ]Rƒ<pl|:]ªw]\[ ƒZhg]m«whg]‡t:[ co„XZi† †]‡tM¬:­®†WR¬V]oR¬:­I¯R§Z¯3ims<tIe<ils<t fje¨o„c\|„]‡t„t„ile<t frnf sZeZ]PplƒZƒZhjfjn\p;o„fjileVnil[ ƒZhjc[ ]e¨o~plfg|~]K †]Pn]\t² †]\s†ª[ co„XZi† †]‡t²ƒyilsZ|²hji†nplhgfrtv]\|hg] nil[ ƒyil|„o„][ ]\emofje<t€o@pqxZhj] †]^hF¹ pqhjklim|„fgo„XZ[ ]m«/pq[ chjfgim|„]\|dt~p t€o@pqxZfjhgfgo„c ]ohrp.ƒZ|„c‡nfrtvfjile¥ †]\t!t„ilhjs†o~fgime<t§ ¯Rils<tRƒZ|~c\t„]e¨o„ime<tR †]‡t3]ªwƒyc|~fj[^]\e¨o~p;o~fgime<t3ewsZ[ c\|„frz¨sZ]\t¶tvsZ|¶hg]^nplhjnsZhºƒ<pl|Rhrp²[ co~XZi† †] Z]¯3]\´,o„ime Z]d|@plnfge<]\t,ƒyilhju¨e<il[ fjplhg]‡t[ plhºnime< †fgo„fjileZe<c]\t\§ ›  œ {}|~c\nfjt„fjil  À ˜‡— ¾  e <eZfj]l«tvo~plxZfjhgfgo„cm«ºƒZ|~c\nfjt„fgime/«/ÂÃo~c|@p;o„fjile †]¯3]\´,o„ime/«‚3pmnfjeZ]ƒyilhju¨e<il[ fŸ· plhg].[sZhgo„fjƒZhj]l«}[ co„XZi† †]¬:­:®†WR¬¶«xZfgx<hgfjiqo~XZY\z¨sZ]K¬RÄd¯R

(26) «}nil|~|„]‡n#o~fgime³pqs†o~il[p;o~fjz¨sZ]m« [^co„XZi† †] ¬:­:¯R

(27) §.

(28) 

(29)    ! " $#%&&(') *,+.-%"-!/ 0,&12 434%56/7 8!'.9:6 -!0;-%1 <. Š. y + ' 9.I

(30) .  fjeZfgo„]dƒZ|„]‡nfrtvfjile.nil|~|~sZƒ†o~t}¢©sZe< Zpl[ ]e¨o~plhyƒ<|„imƒ%]\|vo~fg]‡tIil¢ºewsZ[ ]|~fjn\pqhpqhjklil|~fgo„XZ[t o~X<p;o,XZimhj fje–]ªZpln#o pl|„fgo„X<[^]o„frnq§3hjklim|„fgo„XZ[ t€o@pqxZfjhgfgo€uple< >=‘im| nil[ ƒZsZo„]\  t„ilhjs†o„fjile pln\nsZ|@plnu![p‘u!x%]3pq¡y]‡n#o„]‡ ^fge,?<i¨p;ov· fjeZk²ƒyilfje¨o¶nim[ ƒZs†o~pqo„fjile/§,ˆ´]hjhg·@weZi;´Me ]ªZpq[ ƒZhj]

(31) frt,o„X<]nim[ ƒZs†o~pqo„fjile"´Mfgo„XP¯R]´,o„ime/¹ t3fgo„]|@p;o~fgime il¢fjhghg·¸nile% †fŸo~fgimeZ]\ .|~i¨ilo~t,il¢ƒyilhju¨e<il[ fjplhF« A&-A «3[sZhŸo~fgƒ<hg]

(32) im|,eZ]\pl|„eZ]‡t„t|~iwiqo~Ct Bj%“ DEE§ ‚MimsZe< †fjeZk2]\|„|~il|@tKpqe%pqhjuwt„frt"fjtPƒZ|„fje<nfgƒ<plhghju ƒ%]\|v¢©im|„[ ]\G Fx¨u X<pqe%H FIBKJE^x<s†opqsZo„il[pqo„frn³pqƒ†· ƒ<|„i¨pln@XZ]‡t!s<t„]o„XZ] nim[^ƒ<s†o„]\|o~iƒZ|~i;£¨fr †]²[ im|„]²km]eZ]\|~plhIpqe% ¤]\pmtvu¨·Eo„iq·Ãs<t„]pqƒZƒZhjfrnp;o~fgime<t\§Â¸e¤o„X<fjt ƒ%pqƒy]|‡«´]"¢©i†ns<t²ile7o€´:i³pls†o„im[p;o„frnKpqƒ<ƒZ|„i¨pln@XZ]‡M t Lo„X<]¥¬:­:®†WR¬°pqe< o„X<]¥¬:­I¯R*[ ]o„X<iw <t§ W,X<]¬:­:®ZWR¬Æ[^]o„XZi† « †]£m]hjilƒy]\ xwO u N%Q§ PRfjkleZ]‡tdple< XZfjtnilhjhg]‡pqkls<]\tdtvfje<n] “\S‹ R

(33) D%«%frt!p²¢©im|„´,pq|@ tvo„i†n@X<pmt€o~fjnR[ ]o„X<iwT Bg“‡

(34) Š EçÂÃo,ƒZ|~i;£wfj †]‡tIp^ †uwe<pq[ frn3]‡t€o~fg[p;o~fgime–il¢ o„XZ]dewsZ[xy]|,iq¢ºt„fjkleZf %nple¨o †fjklfgo~t il¢nil[ ƒZs†o~]\  |~]\t„sZhgo~to„X%p;o:plhghji;´3tfge%t€o@pqxZfjhgfgo€uhji†nplhgfjµ\pqo„fjile pqe<  pln\nsZ|@plnunime¨o„|~ilhE§W,XZ]3plfg[ iq¢o„XZ] ¬:­:¯R7[ ]o„X<iw fjto~i¶fj[ ƒZ|„i;£m] o„X<],pmnnsZ|~pmnudiq¢Zo~XZ],nil[ ƒZsZo„]\ |„]‡tvs<hŸUo B Œ EE§3ƒZƒ<hguwfjeZkdo„XZfrtplnnsZ|@plnu fj[ ƒZ|~i;£l][ ]\emoo~itv]\e<t„fŸo~fg£m]3fge¨o~]|~[^]‡ †frp;o„]M£;pl|„frpqxZhj]\t}[ p‘u^pqhrtvi

(35) tvo~plxZfjhgfjµ]3plhgkmil|~fŸo~XZ[t}tvsZ¡y]\|„fjeZk¢©|~il[ |~ils<e< †fjeZk]\|„|~il|@t\§ W,XZ].o€´iP[ ]o~XZi† Zt pq|~].nim[ ƒZhg]\[ ]e¨o~pl|„upqe< ³o„XZ].¢©ilhjhji;´MfgeZkt„n@XZ]\[ ]–frte%p;o„s<|~plhIo~iPfj[^ƒ<|„i;£m] o~XZ]–ewsZ[ ]\|„frnplhz¨s<plhgfgo€uil¢Rpqe¦plhgkmil|~fŸo~XZ["§W,XZ]K¬:­:®†WR¬ [ ]o~XZi† ³frt <|@tvos<t„]\ o~iPhji†npqhjfjµ]–ple s<e<t€o@pqxZhj]Rxy]X%p‘£¨fjil|:iq¢/o~XZ]¶plhgkmil|~fŸo~XZ[tIple< ²ƒZ|~i;£wfj Z]\tIp|„]\hgfrpqx<hg]3x<s†ofje<pmnns<|~pqo„]¶nil[ ƒZs†o~]\ |~]\t„sZhgo\§ W,X<]e/«ºo„XZ]²plhgkmil|~fŸo~XZ[ |~sZe<t´Mfgo„Xo„X<].¬:­I¯R8[ ]o„XZi† t€o@pq|„o„fjeZk"´MfŸo~X¥o„XZ]ƒZ|~]£wfjils<t„hjuPnim[^ƒ<s†o„]‡ |~]\t„sZhgo\W§ V3]\e<n]m«yplepln\nsZ|@p;o~] %e<pqh|„]‡tvsZhgoRfrtRnil[ ƒZs†o~]\ K´Mfgo„XZims†o3o~XZ]nil[ ƒZs†o~fgeZk–i;£l]|~XZ]‡pl ²il¢ o„XZ] nil|~|„]‡n#o~fgeZk[ ]o„XZi† Ko~X<p;ofrtRs<t„]hj]\t~t¶´MXZfghj]

(36) o~XZ] nil[ ƒZsZo~p;o~fgime|~][pqfje<tdt€o@pqxZhj]l§¶Â¸eo„X<fjtdƒ<plƒ%]\|\«y´:] ƒ<|„imƒ%i¨tv]o„i]ª†ƒ%]\|„fj[ ]e¨o}o~XZfjt:pqƒZƒ<|„i¨pln@X^´MXZ]efjhghg·¸nile% †fŸo~fgimeZ]\ ^|~iwiqo~t}iq¢ ƒ%imhguweZim[ fjplh<pq|~]3nim[^ƒ<s†o„]‡ ´Mfgo„XK¯R]´,o„ime/¹ t,fŸo~]|@p;o„fjileº§ ±¥]!xZ|~fg%] ?<u–|~]£wfj]´Vo~XZ]o€´:i [ ]o~XZi† ZtMfje®w]\no„fjileK_ pqe< –o„XZ]

(37) n@X%pq|@pln#o~]|~fjtvo„frnt:iqX¢ ?<i¨p;o„fjeZk ƒyilfjemo nil[ ƒZs†o@p;o~fgime²iq¢ºƒyilhjuweZil[ frpqhfjhghg·Ãnile< ZfŸo~fgimeZ]\ |~iwiqo@tIfje ®w]‡n#o~fgime.ŠZ§¸e"®w]\no„fjil) e D%«w´:]dfghjhjs<t€o~|~pqo„]¶o„XZ] %] Y²nfj]e<nu²iq¢o„XZfrt3plƒZƒZ|[email protected]< XZfjklXZhjfjklX¨o~t <eZfgo„]ƒZ|„]‡nfrtvfjile.]¡]\no~tM´Mfgo„X"]ª†ƒy]|~fg[ ]\emo@pqh |~]\t„sZhgo~t\§ Z. 

(38) /1

(39) .' ( )  ),+ -   \[ )  '. ±¥]hjfj[^fgo¶imsZ|Rƒ<|„]‡tv]\emo@p;o~fgime il¢o„XZ]‡tv][^]o„XZi† Zt3o„i–o„XZ][ plfgeple< "XZ]\|„]‡p;¢ o„]\|Rs<t„]¢©s<hpmtvƒy]\no~t\§3‚M]¢ · ]\|„]\e<n]‡t3pq|~]!ƒZ|~ilƒyimt„]\ fjeKo„XZ]xZfjxZhgfjilkm|~plƒZXwul§­ ªZn]\ƒ†o„]‡ K´MXZ]eKfje< †frnpqo„]‡ «ynil[ ƒZs†o~]\ "£;pqhjsZ]‡t3´]\pq| p^X<pqoMfge o„X<]

(40) tv]‡zms<]hE§ ]W^`_. acbedgfihijWa,klfnmodqp6b rWs. W,X<]:¬:­:®†WR¬[^]o„XZi† !t„fg[sZhrp;o„]‡t/tvo„i†n@X<pltvo„frnpq|~fŸo~XZ[ ]o~fjno~i3ƒZ|~i;£wfj †] pled]‡t€o~fg[pqo„fjile!iq¢¨o„X<]}ewsZ[xy]| il¢dt„fgkmeZf %nplemo †fjklfgo~t fje¦o~XZ]Knim[^ƒ<s†o„]‡ ¦|~]\t„sZhgo\§ W,XZfjt ]‡t€o~fg[pqo„fjileplhghji;´3to„XZ]K †] <eZfgo„fjile iq¢¶o„XZ] t„ƒy]\nf %n £;pqhjsZO ] t †]‡t„n|„fjxZfjeZk¤p¥µ]|~i¥£‘plhgs<] im|²p¥eZile†·¸t„fgkmeZf ynpqe¨onim[^ƒ<s†o„]‡ ¦£;pqhjsZ]m§IuRe< †]\|„hjuwfgeZk Xwuwƒyiqo„X<]\t„fjtnile<n]|~e<t^o„XZ]PƒZ|„imx<pqx<fghjfjtvo„frn" †frt€o~|„fjxZs†o~fgimeViq¢do„XZ]]\hg]\[ ]e¨o~pl|„u³|~ils<e< †fjeZk]|~|„im|~t pqe% o~XZ]"ƒZ|~]\ †im[^fje<ple<n] iq¢¶o„XZ]\fg| <|@tvo im|~ Z]| ƒZ|~ilƒ<plkmp;o~fgime/§¦W,XZ]P¬¶Ä¶¯¶ hgfjxZ|@pq|~u¤fg[ ƒZhj][ ]e¨o@t o„XZ] ¬:­®†WR¬V[ ]o„X<iw pqe% –nime<t„fjtvo~tfje nil[ ƒZs†o~fgeZk^´Mfgo„X" †fŸ¡]|~]e¨oM|~ilsZe< ZfgeZk^[ i† †]\t,t„]£l]\|~plhyt~pq[ ƒZhj]\t il¢dfje¨o„]\|„[ ]\ Zfjpqo„]Pple< <e<pqh¶£;pqhjsZ]\t\§ W,XZ]\|„]¢©il|~]l«,xZ|@pqe<n@X<fgeZk¥o~]\tvo~t–ple< 7£;pqhjfj †fgo€u7X¨uwƒyiqo~XZ]\t„fjt–pq|~]. vv. ñxwzy { | |.

(41) 6& 1- H3   D. Zu¨e%pq[ fjn\pqhjhgunile¨o„|~ilhjhg]‡ §¯3sZ[ ]|~ils%tI]ª†pl[ ƒZhg]‡tiq¢ºfje<tvo~pqx<fghjfŸo€u hji†npqhjfjµ\p;o~fgime–pqe% –pln\nsZ|@plnu^nile¨o„|~ilh fjhjhgs<tvo„|@p;o~]do„XZ]!ƒZ|@plno„frnplhy]%Y²nfj]e<nu–iq¢o„XZ]![ ]o„XZi† «<t„]] Bj“!E/¢©im|M]ªZpq[ ƒZhj]!pqe< .]e¨o~|„fj]\t\§ ]W^(]. acbedgfih k. mod p b rUs. W,X<],¬:­I¯¶³[ ]o~XZi†

(42) |~]hjfg]‡t/ile

(43) p <|@t€oºim|~ Z]|nil|~|„]‡n#o~fgimedƒy]|„¢©il|~[ ]\ ´Mfgo„Xpls†o„im[p;o„frn} †fg¡]|~]e¨o„frp;o~fgime ple< "o~XZ]nil[ ƒZs†o@p;o„fjilePiq¢}]hj][ ]\emo@pq|~u.plx<tvimhgsZo„]|~ils<e< †fjeZk²]|~|~il|@t§MÂÃodfjtdp¢©im|„´,pq|@ " †]o~]|~[^fjeZfrt€o~fjn plƒZƒZ|~impmn@X/§adfj£l]\e p nil[ ƒZs†o~]\

(44) «†o~XZ]![ ]o„X<iw uwfj]hr ZtMp nil|~|~]\n#o~]\ Z]<eZ]‡ "plt .  .    . W,X<] nil|~|„]‡n#o„fjeZkP¢õpln#o~il|    frto~XZ]Knim[^ƒ<s†o„]‡ ³hjfgeZ]‡pq|~fgµ‡p;o~fgime³iq¢3o~XZ]"klhjilx<plh:]\|„|~il|fge ´Mfgo„X |~]\t„ƒy]\n#oMo~io„X<]

(45) ]hj][ ]e¨o@pq|~u–]|~|~il|@t« A&-A «¶|~ils<e< †fjeZk]|~|„im|~tfje¨o„|~iw Zs<n]‡ "fge"o~XZ]

(46) fjemo~]|~[ ]\ †frp;o~]nim[· ƒ<s†o~pqo„fjile<t!il ¢ § ¶t!o~XZ]²nim|„|~]\no„]\ ¢õpmn#o„im|   ple< o„XZ]–nil|~|„]‡n#o~fgime¥plhjt„iKtvs†¡]|¢©|„im[*|~ilsZe% †fge<k ]\|„|~il|@t\«qp¶£;plhgfr †fgo€uxyilsZe<  "!"iq¢yo„XZ]3nil|~|„]‡n#o~]\ |„]‡tvsZhgo fjtInil[ ƒZsZo„]\ /§W,X<]|~]¢©il|~]l«‘o~XZ]3]ª†pmn#o |~]\t„sZhŸo „ t q p „ o r f t <  ‡ ] t  "  !(   "!*)ypmt„t„sZ[ fjeZko„X<pqoIo~XZ] <|@t€o:il|@ †]|IplƒZƒZ|~i‘ª†fg[p;o~fgimeil¢o„XZ]3kmhgimx<pqh. #%$ '& ]\|„|~il|Ifjt£;pqhjfj /§W,X<fjt:Xwu¨ƒyiqo~XZ]\t„frtIfrt:t~p;o~fjt <]‡  ¢©il|hgfjeZ]‡pq|,pqhjklil|~fgo„XZ[t}´]¶ Z] <eZ]‡ ²fjT e BRzE,+†ƒ%imhguweZim[^frpqh ]\£;pqhjs<p;o~fgime²xwu V3il|~eZ]\|\¹ t:t~n@XZ]\[^]dfrt:imeZ]diq¢/o~XZ]["§ ±¥]plƒZƒZhju o„XZ]¬:­I¯¶ [^]o„XZi† –o„i^fg[ ƒZ|~i;£l]Ro„XZ] pmnnsZ|~pmnuiq¢%o„XZ] <e%pqh†|~]\t„sZhŸo}ple<> =‘im|t„]e%tvfgo„fj£l]fge¨o~]|~[^]‡ †frp;o„],£;pq|~frpqxZhj]\tºo„i!tvo~pqx<fghjfgµ\]o„XZ]Mpqhjklim|„fgo„X<[ § Ænil[ ƒZhj]o~] Z]\t~n|~fgƒ†o~fgime.il¢o~XZ]![ ]o~XZi† .frt,klfj£l]\e.xwO u B Œ Eç -. ..  - "  9².?40/ .. 

(47)  '.#

(48)  ) '21> 843ý

(49) #$. - 

(50) .  fjeZfgo„]ƒZ|~]\nfrt„fgime–]¡]\no~t,ime–o~XZ]!nil[ ƒZsZo~p;o~fgime–il¢fjhghg·Ãnile< ZfŸo~fgimeZ]\ –|„iwiqo@tiq¢ƒyilhjuweZil[ frpqhX<p‘£m]¶xy]]\e ewsZ[ ]\|„ims<tvhju.ple<pqhjuwµ]‡ "fgeKo~XZ]ƒ%pltvo\« -zA65 A «!tv]\] B 7E¢©im|R]\emo~|„fj]\t\§M±¥]ƒZ|~]\t„]e¨o¶X<]|~]!o„XZ][pqfjes<t„]¢©sZh ƒ<|„imƒ%]\|vo~fg]‡tI¢©im|MilsZ|Mƒ<sZ|„ƒyimt„]l§ 8W^`_. 9;:<:>=$fir@?4sApBA`r@?DC? s. kpSpBCEAF?GCEHI:`d kKJ"J"LMNCJO. ¸hjhg·Ãnile< †fgo„fjile<]\ |~iwiqo~t:pq|~]Rt„]e<t„fŸo~fg£m]3o~it„[ plhghyƒy]|„o„sZ|~x<p;o~fgime²iq¢ o~XZ]dƒ%imhguweZim[^frpqhyniw]!Y²nfg]\emo@t§}®ws%n@X niw!] Y²nfj]e¨o!ƒ%]\|vo~sZ|~x<p;o~fgime[p‘uxy]² Zp;o@p ]|~|„im|~t\« |„]\ƒZ|~]\t„]e¨o~pqo„fjile]\|„|~il|@t« -A65 A « †]‡nfj[ plho„iKxZfje<pl|„u nilew£l]\|~t„fjile/«†pqe%> =‘im|[p‘u nil[ ]¢©|~il[5o„XZ]!x<pmn @w´pl|~ .]¡]\no3iq¢ |„imsZe< †fjeZk ]|~|~il|@t:fje"o„X<]

(51) pqhjklil|~fgo„XZ[ ƒ<|„i;£wfr †]\ xwuo„X<]x<pln @w´,pq|@ Ppqe%pqhjuwt„frt§¸exyiqo„X³n\plt„]\t\« o„X<]–nim[^ƒ<s†o~pqo„fjile[p‘uuwfg]\hj ¥fje<pln\nsZ|@p;o~] |~iwiqo@tple<> =;il|Mp^´M|„imeZk e¨s<[xy]|Miq¢nim[^ƒ<s†o„]‡ .|~iwiqo@tMpqe< .XZ]e%n]!´Mfgo„XKpq|~xZfgo„|@pq|~u^im|~ Z]|‡§ W,XZ]^¢©imhghji;´Mfge<k.ƒZ|~ilƒy]|„o€u"XZfjklXZhjfgkmX¨o~tdo„X<] t„]e%tvfgo„fj£wfŸo€uKil¢:ƒyilhju¨e<il[ fjplh|„iwiqo@, t Bg“m “ EE§ Å/]o *P xy] p |~iwiqo iq¢ [sZhŸo~fgƒ<hgfrnfgo€u Q5iq¢ ƒ%imhguweZim[ fjplSh R  @UT;VW V YXZX[X>\T;] §2|„]\hjpqo„fj£l],]|~|„im_| ^

(52) il¢ TW` ƒy]|„o„sZ|~x<t o~XZ]!|~i¨ilo "P o~i "P  ^  t„s<[email protected]„X<pqoMo„XZ]¢©im|„´,pq|@ ²]\|„|~il|,t~p;o„frt <]\to~i²p %|~tvoMil|@ †]|,iq¢ pqƒ<ƒZ|„i‘ª†fj[p;o„fjile P  ^ E&Y P . Qfe TW`g "P ` a<b0c ^aFbFcKd &  Rih cj  P lk. VR]e<n]l« [sZhŸo~fgƒ<hg] |~i¨ilo~tdpq|~]^plhg´,p‘u†t3fjhghg·¸nile% †fŸo~fgimeZ]\ pqe< o„XZ]^¢©im|„´,pq|@ "]|~|„im|Rfrtqp |~iwiqo@tpl|„]!plhjt„ifjhjhŸ·¸nime< †fgo„fjileZ]‡ –´MXZ]\esrr T ` "P `,t Rvu  *Po rrWw ^ . “. m on  ^ a<b0c . §®†fgeZkmhg].  v y x.

(53) 

(54)    ! " $#%&&(') *,+.-%"-!/ 0,&12 434%56/7 8!'.9:6 -!0;-%1 J. ź]o s<t|„]\[pq| @¶o~X<p;o |~]hrp;o~fgime m l“ nºuwfj]hr Zto„XZ]Mpqovo~plfge%pqxZhj]pmnnsZ|~pmnum« A&-A « o~XZ]:xy]\tvo¢©il|~´pl|~

(55) ]|~|„im| xyils<e< ²´]dn\pqe.]ª†ƒ%]‡n#oM´MXZ]\e²o„X<]d|~iwiqo <e< †fjeZk [ ]o„X<iw –]£;pqhjs<pqo„]\t R   « -zA65 A «3¯3]\´,o„ime/¹ t[ ]o~XZi† § ź]o B R (  x%]–o„XZ] pqx<t„ilhjs†o„]–|„imsZe< †fjeZkK]|~|~il|

(56) fje R   ]£;pqhjs<p;o~fgime/«R  * R  @ B R ( * «}pqe%  tvs%n@XPo~X<p;o  B R (   rr T ` "P `  rr    W,X<]x%]‡t€o

(57) nim[ ƒZs†o„]‡ pqƒZƒZ|~i‘ª†fg[pqo„fjile * P iq¢ *P t~p;o~fjt <]\t R  * P[@ tZ§  |~il[5|„]\hjpqo„fjile m o“ n«†o„XZ]

(58) pqovo@pqfje<pqxZhj]!pln\nsZ|@plnufjt. < . P &f P. . Qfe. . aFb0c.

(59) . r R h cj  P  r r r. . _. m n. ¶ t fje B DE먴:]M|~][pq|@!o~X<p;o}|~]hrp;o~fgime m _nfrt}p[ ]o~XZi† w·Efje< †]\ƒ%]\e< †]\emo]|~|„im|]\tvo„fj[ pqo„]m§W,XZ]¶plnnsZ|@plnu il¢Io~XZ]ƒ%imhguweZim[ fjplh ]£;pqhjs<p;o~fgime¥nile¨o„|~ilhrt¶o„XZ].plnnsZ|@plnu"il¢:o~XZ]²nim[^ƒ<s†o„]‡ |~iwiqo‡§^±¥]² †frt„ns<t~to„XZ] ƒ<|~pmn#o„frnplhs<tv]!il¢ºo~XZfjtRp;ovo@pqfje<pqx<hg]!pln\nsZ|@plnufge o~XZ]!eZ]ªwoMƒ<pl|~plkl|@pqƒZX/§ 8W^(]. ¶t„t„sZ[ fjeZk. d p6r@?

(60)  9$pSd MNCXpBA`r@?A<?IA"p6dYM d J"AWA`r@? C?4s\j p6r A<? fYMvA"p6diM A<C t . fjtRnhjimt„]d]\eZils<klX²o~i o„XZ]!|~iwiqo. . *P. «Z´]!nil[ ƒZsZo„]o„X<]

(61) ¯3]´,o~ile fŸo~]|@p;o~fgime. l_s  . ! !. R $   ) R u $   ) . Š ¸e]ªZpln#opq|~fŸo~XZ[ ]o„frnq«¨fgo„]|@p;o~fgime m Š;n nime¨£m]|~kl]‡t zms%pl †|@p;o~fjn\pqhjhguo„ip

(62) t„fjeZklhj]3|~i¨ilo}xZs†oileZhjukm]im[^]o„|~fŸ· n\pqhjhgud´Mfgo„X|@p;o~fgiQ t  Q &"o o„i¶p3|„iwiqoiq¢Z[sZhŸo~fgƒ<hgfrnfgo€u'Q Bj“\’

(63) Eç¸e <eZfgo„]:ƒZ|„]‡nfrtvfjileº«\o~XZ]:nilew£l]\|„km]e<n] il¢/fŸo~]|@p;o~fgime m Š;n [p‘utvs†¡]|:¢©|~il[ o„XZ]R¢©ilhjhgi;´MfjeZkhgfj[ fŸo@p;o„fjile%t m nil[ ƒZsZo„]\ .z¨s<pqe¨o„fgo„fj]\tIX<p‘£l]¶hgi¨t€o:o„XZ] X%p;oMXZ]|~]\pq¢ o„]\| n§ # Rvu $ !  )  t^xZs†_o R $   )% $ t<« #   l_ !  xZsZ@o R $   ) $ tZ§ # R $   )  Ru $   )  t^xZs†o !  frtMeZilo3pqeKpln\nsZ|@p;o~]dplƒZƒZ|~i‘ªwfj[p;o~fgime–iq¢ *P « VR]e<n]l«¨pqe !] Y²nfj]e¨o:tvo„imƒZƒZfjeZk!n|~fŸo~]|~fgime iq¢fŸo~]|@p;o„fjile m ;Š nX<pmto„i

(64) p‘£milfr t„s<n@Xnpmtv]‡t§W,XZ]MƒZ|~]£wfgims<t„hgu Zfjt~ns<t~t„]\ "p;o„o~pqfje<plxZhg]!pmnns<|~pmnu–t„XZils<hj xy]

(65) s<t„]¢©sZhºo„i² †] <eZ]t„s<n@XKpn|~fŸo~]|~fgime/§IRhjpmt«Z|~]hrp;o~fgime m _ n frt}e<iqo:nil[ ƒZs†o@pqxZhj]RpltIhgimeZk

(66) plt}o„XZ]R[sZhgo„fjƒZhjfjnfŸo€u iq¢o~XZ]R|~iwiqo}|~][pqfje<t}s< e @weZi;´Me/«mple< ^o„X%p;o:frt}il¢ o„]\e o~XZ]

(67) npmtv]m§ W,XZ]¢©imhghji;´MfjeZk^n|„fgo„]\|„frp pq|~]¶´]hjhg· @weZi;´Me–¢©il|,o„]\|„[ fje<p;o~fge<kfŸo~]|@p;o„fjile m ;Š n#§ & e n4L ! 'o&Y !  ( ^u    m ‚M]\hjpqo„fj£l]­}£limhgsZo„fjilv ” m 3x<t„ilhjs†o~]

(68) ‚M]\t„fj Zs<pqyh n4L R $ ! 'o ))+*"u W,X<] '/ /  |~]hrp;o~fg£m]dxyils<e< ^u  p  ^  hgfj[ fŸo@t,o„XZ]

(69) tvo~plkle<pqo„fjile.iq¢ºo~XZ]!fgo„]|@p;o~]xZs†o3frtMkl]\eZ]|@pqhjhgu fjeZ%] Ynfg]\e¨o!¢©il|

(70) fjhghg·¸nile% †fŸo~fgimeZ]\ |~i¨ilo~t\§.¬:XZiwimt„fge<, k *"u  p  *  ´MXZ]|~] *7fjto~XZ]²t„[ plhghj]\tvo

(71) eZime†·Eµ\]|~i ƒyimt„fgo„fj£l] ?<i¨p;o~fgeZk–ƒ%imfge¨o¶ewsZ[x%]\| m */. ^n3´:imsZhr Kx%]ƒ%i¨t„t„fjxZhg]fŸ¢}o~XZ]nil[ ƒZs†o@p;o~fgimeKiq¢ o„X<]|~]\t„fj w· s%pqh R $ ! 0l )Mfjt^]\|„|~il|¢©|„]\]l§¬:ile%tvfr †]|~fjeZk|~]hrp;o„fjile m _ n%« *"u,t„XZilsZhr ¦ Zu¨e%pq[ fjV n\pqhjhgu¤nile¨o„|~ilh:o„XZ] fje<pmnns<|~pmnuiq¢o„X<]!ƒ%imhguweZim[^frpqh ]\£;pqhjs<p;o~fgime/«Zn@XZiwimt„fge<k¢©im|3]ªZpq[ ƒZhj1] *"u  ^3254 `6"]  TW`   l `  7 B

(72) ‹ Eç ±Vfgo„Xtvo„i†n@X<pmt€o~fjndpq|~fŸo~XZ[ ]o~fjnl«ZfŸo3frt,´]hjhŸ· @weZi;´Me²o~X<p;oRplhŸo~]|~e<p;o~fg£m]n|„fgo„]\|„frp^pq|~]dp‘£;pqfjhrpqxZhj] Bg“‡

(73) Š EE§ . vv. ñxwzy { | |. . &. m n.

(74) Œ. 6& 1- H3  . º” & m ®¨o„i†n@X<pmt€o~fjn3x%tvimhgs†o~]!­}£limhgsZo„fjilevnL   l &Y !    t º” m ®wo„i†n@X<pltvo„frn3x<t„ilhjs†o~]

(75) ‚M]\t„fj Zs<pqhyn4L"R $ ! 'o )  t ,W X<]\t„],n|„fgo„]\|„frp¶s<tv]o~XZ]3tvƒy]\nf yn,£‘plhgs<]Ut §±¥]M|„]‡npqhjhwfŸoI Z]\t~n|~fgxy]\t pdµ]\|„id£;pqhjsZ]Mil| pdeZime†·Ãt„fjkleZf %nple¨o nil[ ƒZs†o~]\ ¦£‘plhgs<c ] Bj“‡_†«Š EE§¦±VXZ]e   o t„pqo„frt <]‡to„XZ]®†R­ o~]\tvo\«:nil[ ƒZs†o~fge<kR $ !  o )Mfjt e<]\n]‡t„t~pq|~u o„i †]‡nfr †]!fg¢ ! 'o fjtRpqe"plnn]ƒ†o@pqxZhj]!pqƒZƒ<|„i‘ª†fj[ pqo„fjile²il¢o~XZ]!|~i¨ilo\§ 0. . . ),+  -4) 

(76)  1. ) º9 @.  t iq¢ƒ%imhguweZim[^frpqh    @'

(77)  &  S  t  . ź]oMs<t3nile<t„fr †]|o„X<]

(78) nil[ ƒZsZo~p;o~fgime"iq¢ºo~XZ]

(79) †imsZxZhj]!|„iwiqo R   . *PI. o~XZ]}ilo„XZ]\|/|„iwilo/fjt P & t  Bg“%EE§¯3sZ[ ]|~frnpqhl]ª†ƒ%]\|„fj[ ]e¨o~tpq|~] ƒ%]\|v¢©im|„[ ]‡ ¶s%tvfjeZkM¸­}­}­}·R$JD3xZfje<pl|„u ?%imp;o~fge<kƒyilfjemo3pl|„fgo„XZ[ ]o„frnRime.p ®wsZe u3hgo„|@p8J´:im|7@†tvo~p;o~fgime m ®ws<e® JZ§KR†«Z®wilhrpq|~fjt¶“l§ Š n«  d‚WM‚3R¯ ‹m’ m ±im7| @Z®wXZimƒ¬:im[^ƒ<fghj]|@tJZ§ ’<«  d‚WM‚3R¯ ‹m’._†§ ’ nRpqe< ¬RÄd¯R hjfgx<|~pl|„u"£Z_†§Ø_†§±¥]^hjfj[^fgoo„XZ] ¢©imhghji;´MfjeZk,ƒZ|„]‡tv]\e¨o~p;o~fgimeRo~iM¸­}­}­ `· RJD3tvfjeZkmhg] ƒZ|~]\nfjt„fjile|„]‡tvs<hŸo@t« A&-zA «^ B   t "!\«‡]ªZn]ƒ†o~]\ fje o~XZ],eZ]ªwo ƒ<pl|~plkl|@pqƒZX!´MXZ]\|„],pq|~],pqhrtvidƒZ|~ilƒyimt„]\

(80) †imsZxZhj],ƒZ|„]‡nfrtvfjile|„]‡tvsZhgo~t\« A&-A «@^#$  %  t  a'& . (. ^`_. )+*%(Gfir-, . acbed 98hMh h=. LWpBCXpNAr@?. ±¥]nil[ ƒZs†o~]

(81) ¯3]´,o~ileKfgo„]\|~pqo„fjile m Š nMfgeK¸­}­I­ ·R$JD²t„fge<klhj]

(82) pqe< " †imsZxZhj]!ƒZ|„]‡nfrtvfjile%t,s<tvfjeZk VRil|~eZ]|‡¹ t t~n@XZ]\[^]¶¢©il|o~XZ]!ƒ%imhguweZim[ fjplhy]\£;pqhjs<p;o~fgime<tR" pqe% R u §}W,XZ]¶o€´:i tvo„ilƒ<ƒZfge<k n|„fgo„]\|„frp‚3­ ple< R‚ pq|~] fj[ ƒZhj][ ]e¨o„]‡

(83) |~]\t„ƒ%]‡n#o~fg£m]hju¶´Mfgo„ X ^ u  ^¶ilG| ^#pqe% * u 3 t   t  !  ®wo~pq|„o„fjeZk¶´MfŸo~X  t @ t . « xyiqo~XPnim[ ƒZs†o~pqo„fjile<t¶uwfg]\hj !  t~p;o~fjtv¢©uwfgeZk–o„XZ]^t€o~ilƒZƒ<fgeZk n|~fŸo~]|~fgimeR‚ m t„]]e<]ªwoRo@pqxZhj]on§/Ro~XZ]| pmnn]ƒ†o@pqxZhj]!n@XZilfrn]‡t:il¢  t  klfj£l]tvfj[ fghrpq|M|~]\t„sZhgo~t\§ ¸eZfgo„frpqhqP}plhgs<]  t     R $   ) Ru $   )  *P &Y !   t  "P  ^ ’Z§KJ “‡Œ t  01+  2 ’Z§ ’ ·¸ŒZ§ ŠZ“­}·"J _Z§ Šm‹q­ ·J ^# ’Z§KJ _8J t  01  3415% t 1 ’Z§ ’ ŠZ§ ’lŒl­ ·,7 “m§ ŒSR‘­ ·¸‹ W,XZ]¤plx<tvimhgsZo„]P]\|„|~il|.x%imsZe< ý¢©il|"ƒyilhju¨e<il[ fjplh R ]£;plhgs<pqo„]‡ 2xwu V3im|„eZ]\|\¹ t t„n@XZ]\[ ]Pfje p|„iwilo e<]fjklXwx%im|„X<i¨i† t„pqo„frt <]‡t   ^ u § VR]e<n]nil[ ƒ<pl|„fjeZk ´MfŸo~X P  t  6051  360+ «Zo~XZ]²nim[^ƒ<s†o„]‡ |~iwiqo   pqkm|„]\]\t:o„X<]!ƒZ|„]‡ †frn#o„]‡ .pmnnsZ|~pmnukmfg£m]e x¨u–|„]\hjpqo„fjile m _n§ {I|„]‡nfrtvfjile. (. ^(]. 7. '8 . r J*CE:FA iAF?. p b d

(84) AF?8pBC H A<:FA"pSO. A"p b. p bedgfihijUa kIf. mod p berWs. ±¥]

(85) s<t„]o„X<] ¬RÄd¯R hgfjxZ|@pq|~uo„i²nil[ ƒZs†o~]

(86) fgo„]|@p;o~fgime m Š nM´MfŸo~Xn|~fŸo~]|~fjp²®†R­ýpqe% "®ZR‚!§ ®¨o~pl|vo~fge<k plkmplfge.´MfŸo~X  t @ t   «†x%ilo„X®†3­2ple< "®†R‚ n|~fgo„]|~frp^pl|„]t~p;o„frt <]\ –¢©il|,o~XZ]¢©ilhjhgi;´MfjeZk £;pqhjsZ]l§ {}|~]\nfjt„fjile ¸eZfgo„frpqhqP}plhgs<]  t   R $ !  ) Rvu $ !  ) !  ^ ’<§ J “‡’ 9  :<;>="? t ’<§ ‹mŒq­ ·¸Š.  v y x.

(87) 

(88)    ! " $#%&&(') *,+.-%"-!/ 0,&12 434%56/7 8!'.9:6 -!0;-%1 R. W,X<] ¬:­:®†WR¬ [ ]o„XZi† |~]\ Zs<n]‡t3o~XZ]ewsZ[x%]\|¶il¢Ifgo„]|@p;o~fgimepqe< PƒZ|~i;£¨fr †]‡tRŠ²kms<pq|@pqe¨o~]]\ K Z]\nfj[pqh ZfgkmfŸo@t m ¬¶Ä¶¯¶5imeZhju¥ †frt„ƒZhjp‘u†t

(89) t„fjkleZf %nple¨o †fgkmfŸo@tple< ¤ †iw]\teZiqokls<pl|~plemo~]]^o„X<]–hrpltvo †frtvƒZhrp‘ul]‡ Z]\nfj[pqh} †fjklfgo BØ_

(90) Egn#§–Wipqe<plhguwµ\]o~XZ]¢©il|~´,pq|@ ]|~|~il|‡« ´:] |~][pq|@Ko„X%p;o!o„X<]kls<pl|~plemo~]]‡ P †fjklfgo~t!il¢ o~XZ] ¬¶Ä¶¯¶ˆ|~]\t„sZhgodpq|~]!]ªZpmn#o¶nil[ ƒ<pq|~fjeZk o„i "P §RW,XZ]

(91) ewsZ[x%]\|Riq¢It„fjkleZf %nple¨o¶ †fjklfgo~tRplkl|~]]‡t,o„XZ] ƒ<|„]‡ †fjno„]‡ .pmnns<|~pmnul§. (. , M rGA<? . ^8. 9. p bed kKJ"J"LGM CEJO. A"p b. p6b dgfih k. W,X<]nil|~|„]‡n#o~]\ .fŸo~]|@p;o„fjile m Š;n´MfŸo~X.o~XZ]¬:­I¯¶Æ[ ]o„X<iw frt. ! '  o_ ! . . &. m. d p berWs. ! . R $   )  R u $   ). m D;n. ´MX<]|~] R  R     R  ple< R u  R u     Rvu  pq|~]Ro~XZ]!nil|~|~]\n#o~]\ ]\£;pqhjs<p;o~fgime<tiq¢ºƒyilhjuweZil[ frpqhrt R ple< RvuF§ ÂÃo„]|@p;o~fgime m D;nfrtMnimemo~|„imhghj]\ –´MfŸo~X o„XZ]

(92) tvo„imƒZƒZfjeZkn|~fŸo~]|~fjp ‚M­Vpqe% .¶‚!§ u¶tvfjeZk.¬RÄd¯R |„]‡tvs<hŸo‡«<pqeKimƒ†o„fj[pqh/fjeZfgo„frpqh/£;pqhjsZ]  t  t„pqo„frt %]\t  t    t    t  ´Mfgo„X o~XZ] ¸­}­}­ `· RJDt„fgeZkmhg].ƒZ|~]\nfrt„fgime³£;pqhjsZ]\t  t    t  605 t t$t8t$t pqe<  t  D t  0 4 1   §K±] nil[ ƒZs†o~]Pfgo„]\|~pqo„fjile m DWns<t„fjeZk¤o„X<]o€´i³fge<fŸo~fjplh¶£;pqhjsZ]‡t  t   pqe%  t  +do~XZ]|~]\t„sZhgo~t.pq|~]Ko„XZ] ¢©imhghji;´MfjeZk<§ {I|„]‡nfrtvfjile.  ^. ¸eZfgo„frpqhqP}plhgs<]. t . . .   D S7$D 8J D D S7 xD. !. R $   ).   . . &f .   t     . & l. I"!. R ’Z§ ¨_ I‹ l‹ ŠZ§R;’q­}·~“‘_ ’Z§ ’ _†§ Œl’l­ ~· “zD Œ ’Z§ ¨_ mŒ mŒm‹m_ D<§ 7lŠq­}·~“‘_ ’Z§ ’ ‹Z§j“\‹l­ ~· “

(93) J ilo„Xfgo„]\|~pqo„fjile<t3o„]|~[ fge%p;o„]^t„pqo„frt€¢©uwfjeZko~XZ]^‚3­ n|~fgo„]|~fjile/§¶®†i–eZi.[^im|„]plnnsZ|@p;o„]pqƒZƒZ|~i‘ª†fg[pqo„fjile il¢Ro~XZ]|~i¨ilo²nils<hj x%]nil[ ƒZs†o~]\ 7fje7¸­I­}­ ·¸tvfjeZklhj]KƒZ|~]\nfjt„fgime7tvo~pl|vo~fge<k¥´Mfgo„XVn@XZi¨tv]\e  t  §ýW,XZ] o€´i.nil[ ƒZs†o~]\ ¥pqƒZƒ<|„i‘ª†fj[ pqo„fjile<t P  t  05 5 5 ple< P  t  0+ 0 pl|„]^ †fg¡y]\|„]\emo!p;¢ o~]| o~XZ]²o~XZfj|~ ¤ †fjklfgo\§Rto„XZ]   !VxyilsZ e% ¤£;pqhjsZ]²£;pqhjfj <p;o„]‡t!o~XZ ] 7 %klsZ|~]\tiq¢Mx%ilo„X¦plƒZƒZ|~i‘ª†fg[p;o~fgime<t\« ƒyilhjuweZil[ frpqh  R X<plt¶o€´i"t„]ƒ%pq|@p;o„]|„iwilo~tdfge¥o~XZ] eZ]fjklXwxyil|~XZiwiw Piq¢ *P pqƒ<ƒZ|„i‘ª†fj[p;o„]‡ xwu P pqe%  P § Ro„XZ]\|:n@XZimfjn]\t}il¢  t  «  t     t    t   «muwfj]hr ²t„fg[ fjhjpl|:nimew£l]|~kl]\e<n]o~i

(94) o„X<]¶t~pq[ ]Mo€´i %eZfŸo~]!ƒZ|~]\nfrt„fgime–hjfg[ fgo~t P ple< P §  ^. ( ^(. t   t . . acbed h CJplfir. , ILep6dHs. j:r@:FLWpNAr@?. W,X<]\t„]M]ª†ƒ%]\|„fj[ ]e¨o~t}fghjhgs%t€o~|~pqo„]3p´]hjhŸ·@weZi;´Me]¡y]‡n#oIil¢ %eZfŸo~]3ƒZ|~]\nfjt„fgime ´MXZ]enim[ ƒZs†o„fjeZk![sZhŸo~fgƒ<hg] ƒyilhjuweZil[ frpqh |~iwiqo~t\§–W,XZ]² ZilsZxZhj]|~i¨ilo *P « A&-A «o„XZ]²]ªZpln#opl|„fgo„X<[^]o„frntvimhgsZo„fjile/«fjto~|~ple<tv¢©il|~[^]‡ fje¨o„i^o€´i t„]ƒ%pq|@p;o„]t„fgeZkmhg]d|~i¨ilo~t P ple< P fje <eZfgo„]!ƒZ|~]\nfjt„fgime/§¯3]£m]|„o„XZ]\hg]‡t„t\«wo„X<]nilew£l]\|„km]e<n] |@p;o~]!pqe< –o„XZ]

(95) pqovo@pqfje<pqxZhj]!pln\nsZ|@plnu²pq|~]dnile¨o„|~ilhj]\ –x¨u–o„XZ]!im|~ Z]|3_iq¢o„XZ]!]ª†pmn#oMƒZ|~ilxZhj][5|„iwiqo‡§ ¸­}­I­ · R$JDnil[ ƒZs†o@p;o„fjilet„s†¡y]\|~td¢©|~il[ o„XZ]fje<pln\nsZ|@p;o~]ƒyilhjuweZil[ frpqh ]\£‘plhgs%p;o„fjilD e R  * pqe% PeZi kms<pq|@pqe¨o~]]nils<hj "xy]

(96) klfj£l]\e o„i² †fjklfgo~t3pq¢ o„]\|¶pqxyilsZo3X<pqhg¢o„XZ]

(97) ƒ<|„]‡nfrtvfjile m pmt3|~]hrp;o„fjile m _ n,fje< †frnp;o~]\t n#§ W,X<]¬:­:®†WR¬V[ ]o~XZi† "hgi†n\pqhjfgµ\]\to„X<fjtMfje<tvo~plxZfghjfgo€u.pqe% –|~]o~sZ|„e%t,o„XZ]‡tv]

(98) t„fjkleZf %nple¨oM ZfgkmfŸo@t§ ¸eKxyiqo~X n\plt„]\t\«lo~XZ]p;ovo@pqfje<pqx<hg]dplnnsZ|@plnu^xyilsZe< .ƒZ|~]£m]e¨o~t}o„i  †fjtvo„fjeZkmsZfjt„X²o~XZ]\t„]tv]\ƒ<pq|@p;o~]3|„iwilo~t\§ ¬:im[^ƒ<s†ov· fjeZk–nil|~|„]‡n#o~]\ R«Zo~XZ] ¬:­I¯¶ˆ[ ]o~XZi† "fg[ ƒZ|~i;£l]‡to„XZ]^pln\nsZ|@plnu²iq¢o„X<]

(99) ƒ%imhguweZim[ fjplh/]£;pqhjs<pqo„fjileKfje. vv. ñxwzy { | |.

(100) 6& 1- H3   7. 6e-08 Computed polynomial Corrected polynomial and its bound. 4e-08. 2e-08. 0. -2e-08. -4e-08. -6e-08 0.42845. 0.4285. 0.42855. 0.4286. 0.42865. 0.4287.  fgkmsZ|~]^“8L W,XZ]o€´:it„]ƒ<pl|~pqo„]d|„iwilo~tiq¢R" R § plƒZƒy]\pq|3nil[ ƒZs†o~fge<k  o~XZ]d|„iwiqoeZ]fjklXwxyil|~XZiwi† §W,X<]|~]¢©il|~]l«mo„X<]plx<t„ilhjs†o„]¶|„]‡tvfr †s<plhy †iw]‡t:e<iqo:?<s<t„X²o„i^µ]\|„i^pqe< ²ƒZ|„i;£wfr †]\t p t„]\z¨sZ]\e<n]diq¢fŸo~]|@p;o~]\t   o„X<pqoRnime¨£m]|~kl]‡t o„i P im| P ´MXZfjhj]o„XZ]ƒZ|~]\nfjt„fgim\ e ^fjtMt„6s Y²nfj]e¨o,o„i fj[ ƒZ|~i;£l]¶o„XZ]

(101) pmnns<|~pmnuiq¢   « A&-zA «3´MX<fghj]o„XZ]!‚M­2n|„fgo„]\|„fjile.fjt3eZiqo3t~p;o„frt <]\ § ÂÃo3¢©imhghji;´3t:o„X<pqoMo„XZ]tvƒZhjfgovo„fjeZkil¢o~XZ]

(102) †ils<xZhg]!|~iwiqoMfjemo~i^o€´:it„fgeZkmhg]!|~iwiqo@tM †iw]\t,eZiloRnil[ ]d¢©|~il[ o~XZ]!|~ilsZe< ZfgeZk]\|„|~il|@t:iq¢ fŸo~]|@p;o~fgime m D;n#§:±]!ƒ<|„i;£m]¶o~X<p;oMo~XZ]

(103) †]‡nfj[ plh o„ix<fge<pl|„u nime¨£m]|@tvfjile–iq¢o„XZ] niw!] Y²nfj]e¨o~t:iq¢ƒ%imhguweZim[^frpq;h R fjttvs%n@X²o„X%p;. o R. X<pltIo€´it„]ƒ<pl|~pqo„]¶t„fjeZklhj]R|~iwiqo~t:fje–]ªZpmn#opl|„fgo„X<[^]o„frnq§ W,X<],¢©ilhjhgi;´MfjeZk|„]‡tvs<hŸo@t}nim[^],¢©|~il[ tvuw[x%imhgfrnMnim[^ƒ<s†o~pqo„fjile ´MfŸo~X²Žpqƒ<hg]m§±¥]3|~]ƒZ|~]\t„]e¨o}nim[^ƒ<s†o„]‡ ƒyilhjuweZil[ frpqh  R plt R    T  T  T a  T; ] «<´MX<]|~] TW ` frt,o„X<]!]ªZplno m |@p;o„fjile%pqyh nI£;plhgsZ]!il¢ ¸­I­}­ `· RJD tvfjeZkmhg]^ƒZ|~]\nfrt„fgimeKxZfge%pq|~u £;plhgsZ]^iq¢Io„XZ] TW` ni¨%] Y²nfj]e¨odil¢ R m t   n#§ u¶tvfjeZkK®¨o„sZ|~[ t„]\z¨sZ]\e<n]‡t«wfje¨o„]|~£;pqhrt  pqe<   fge<nhgs% †]do„XZ]

(104) nile<t„fj Z]|~]\ ²]ªZpln#o,|~i¨ilo~tiq¢ R ´Mfgo„Xº«Zhgfj[ fŸo~fge<k o„i^o„XZ] [pqªwfj[s<[ 7 tvfjkleZf %n\pqe¨ o3 †fgkmfŸo@t,iq¢¸­}­}­ `· RJDtvfjeZklhj]ƒZ|~]\nfrt„fgime/«    $ t  05 5 1 t  6054 1  ) ple<    $ t  6051+11  t  0%1 10 )  ±¥]nil[ ]Ix%pln @do„i¶ƒZ|„]\£wfgims<qt ?%imp;o~fge<k3ƒ%imfge¨o nim[^ƒ<s†o~pqo„fjile<teZiqo~fge<k3o„X%p;ox%ilo„X|~]\t„sZhgo~tnim[^ƒ<s†o„]‡ ´Mfgo„Xo„XZ]ƒZ|~]\t„]e¨o„]‡

(105) pqƒ<ƒZ|„i¨pln@X

(106) t~p;o~fjt <]\t P #   ple< P #   §  fjkls<|„] m o“ nº|~]ƒZ|~]\t„]e¨o~tnim[^ƒ<s†o„]‡  R «‡nil|~|„]‡n#o~]\ Rpqe<'  *!x%imsZe< Ztºfge "P eZ]\fgkmX¨xyil|~XZiwi† §/ÂÃo/]ªwX<fgxZfgo~t/o„X<pqo R!X<plt/o€´:iMt„fge<klhj]}tv]\ƒ<pq|@p;o~] |~iwiqo@t,fgeKfje¨o„]|~£;pqhrt   pqe%   t„s<n@X o„X<pqo     ple<      §  hjimpqo„fjeZkƒyilfjemo3]ª†ƒ%]\|„fj[ ]e¨o~t plkl|~]]¶o„XZ]!|~]\t„sZhgo~t,il¢ºo„X<]

(107) tvuw[xyilhjfrndnil[ ƒZs†o@p;o~fgime/§.  v y x.

(108) 

(109)    ! " $#%&&(') *,+.-%"-!/ 0,&12 434%56/7 8!'.9:6 -!0;-%1 .. ‹. 

(110)  :9 º

(111) .  fjeZfgo„]ƒZ|~]\nfrt„fgime.nim[ ƒZs†o~pqo„fjile.fjteZilo,|~]hjfrpqxZhj]¶´MX<]e²o~XZ]ƒZ|~ilxZhj][ o~i t„ilhj£l]¶fjt,fjhjhŸ·¸nime< †fgo„fjileZ]‡ §¸e o~XZfrtn\plt„]l« ?<i¨p;o„fjeZkƒ%imfge¨o,|„]‡tvsZhgo~tpq|~]RX%pq|@ o„ifge¨o~]|~ƒZ|„]o,ple< ²[p‘u ]£m]e²uwfj]hr ²´M|~ileZk^nime<nhjs<t„fgime<t§ Rs†o„im[p;o„frnplƒZƒZ|~impmn@XZ]\t¶pq|~]

(112) ]!Y²nfj]e¨odo„iwilhrtRo„X<pqonil[ ƒZhj][ ]e¨oRo~XZ]im|„]o„frnplhple<pqhju†tvfrt§  fgeZfgo„] ƒZ|~]· nfjt„fjile]¡]\no~t

(113) pl|„]il¢ o„]e¤t„sZx†o~hg]–ple< ¥[ ]|~kl]\ ¥´Mfgo„X¤ewsZ[ ]|~ils%t!pqe< ¤ †fY²nsZhgoilo„XZ]\|plt„ƒ%]‡n#o@t§ Å/]o s%tnfŸo~]do„XZ]]¡]\no~t,il¢nime< †fgo„fjile/«wo~XZ]sZe< †]\|„hjfjeZ]\ .ƒZ|~]\t„]e<n]¶il¢tvfjeZkmsZhjpl|„fgo„fj]\t\«† Zp;o@p]\|„|~il|@t\«lo~|„sZe%np;· o~fgime²]|~|~il|@t«¨pqhjklil|~fgo„XZ[ t€o@pqxZfjhjfŸo€um«mƒZ|~ilƒy]|„o„fj]\t:iq¢ ?%imp;o~fge<k

(114) ƒ%imfge¨oMpq|~fŸo~XZ[ ]o~fjnl«m]\hg]\[^]\e¨o~pq|~u^¢©sZe<no„fjile<t ¢õplfŸo~X†¢©sZhjeZ]\t~t\«lhjfgxZ|@pq|~u

(115) ]\£lilhjs†o~fgime<t«mnil[ ƒZfjhj]|@t ilƒ†o~fgime<t\«q´:iwimhghjut„ƒ%]‡nf %npqo„fjile<til¢yƒ<|„imkl|@pq[ [ fgeZkhrpqe†· kms<pqkm]\t\«§§§~W,XZ]|~]¢©im|„]m«/pqs†o~il[p;o~fjn plƒZƒZ|~impln@X<]\tdnpqeeZiqople<t„´:]\|¶sZe<fg£m]|@t„plhghjul§ÂÃo †i"eZiqo!|~]ƒZhrpln] o~XZ] @weZi;´Mhj]\ †km]¶il¢ewsZ[ ]|~fjn\pqh/t„iq¢ o€´,pq|~]¶]ª†ƒ%]\|voMxZs†o3X<]hjƒ X<fg[5o„i²nime <|~[ XZfrt,fge¨o~sZfŸo~fgime/§ ” ›  Àw¿  ¼ Á  ¼ ˜\—mœ W,XZ]3pqsZo„XZim| o„X<pl e @†t Nm]\pqeZ·ÃŽpl|„fj]3¬:XZ]\t„eZ]\pls†ª

(116) ¢©im| o„XZ]¬RÄd¯RVhjfgx<|~pl|„u ple< ¤XZfrt^XZ]hjƒ ZsZ|„fjeZkfŸo@ts%tv]m«IŽpq|@n–Ädpqs<[ pmtple< ¬:hrpqfj|„]  fgeZilo¢©im|£;plhgs<plxZhj] †frt~ns<t~tvfjile%tpqe% ŽPpqƒZhj]s<tv]m§ )  ),+) . ) 1. Bg“%E Nm]\ple†·¸Žpq|~fg].¬:X<]\t„eZ]\pls†ª § >"1

(117) ( 34/ & S0;-%( *H3e+ 43 !` /7- §cV¶pqxZfjhgfgo~pqo„fjile  Ķfj|„fjkl]\| †]‡t:‚3]\n@XZ]\|~n@XZ]‡t}W,XZ]‡tvfrt«6Ru eZfg£m]|@tvfgo„cR{}fg]\|„|~]R]o,ŽPpq|~fg]d¬:s<|„fj]l«¨{ pq|~fjt\«  |~ple<n]m«¨¯Ri;£l]\[· xy]|“\‹l‹ †J § m ¸e  |~]e%n@Xvn#§. B _E Nm]\ple†·¸Žpq|~fg]¬:X<]\t„eZ]\pls†ª «y®¨o~cƒZX<pleZ]^ads<fghrpqfje/«pqe< Nm]\ple PRfjkleZ]‡t§3ÅpxZfjxZhgfjiqo~XZY\z¨sZ]¬RÄd¯R †L ƒ<|„c‡tv]\emo@p;o~fgime²]o,s†o„fjhjfjt~p;o~fgime/§ŽPpqews<pqhE«63u eZfj£l]\|~t„fgo„cR{§†]oMŽ³§Z¬:s<|„fj]l«w{ pq|~fjt\«†¯3i;£m][xy]|d“\‹m‹lŒ<§ £;pqfjhjplxZhj]pqo Ru ‚3Å

(118)  !#"$&%(')*+(,(#<« m fje  |~]e<n@Xvn§ B ŠE Nm]\ple†·¸Žpq|~fg]:¬:X<]\t„eZ]\pls†ªple< Nm]\pqe P¶fgkmeZ]\t\§lź]\t ¢©ime< †]\[^]\e¨o~t †]}hE¹ pl|„fgo„XZ[ co„frzms<]:tvo„i†n@X<pltvo„frz¨sZ]l§   A - Aq3  $*8AQ%A / 2 .!/%A 0/T   A «%Š<“J m “\Š;n Lj“%D¨Š8J1“%D8Dm’Z«w“‡‹l‹m_Z§  /T-!  *

(119) B D$E

(120) ad]\|„[sZe< ³ÄdpqX<hjz¨sZfrt€o^pqe< 32 @l] 54l|@n@§  560 -%/  6 ¬:hjfg¡t\«<¯ %N «1du ®†

(121) «/“‡‹ R<D §Wº|@pqe<t„hrp;o„]‡ –xwu–¯R]\ "3e% †]|@tvime/§ B JE!¯Rfjn@X<ilhrplt N<§WVRfgkmX<pq["§. §{}|~]eZo„frn]·"VRplhghE«­}eZklhj]´iwi† . 34%56/7 8!'l Q* >" $#%&&('l 560;-%/   34 58/ &&60 §°®†iwnfg]o€u ¢©il| ¸e% †s<tvo„|~fjplhºpqe< 3ƒ<ƒZhgfj]\ "Žpqo„XZ]\[p;o„frnt\«†{}XZfjhrpl †]\hgƒZX<fjp<«Z{ 

(122) «>ud®†

(123) «º“\‹l‹mŒZ§ B ŒE{IXZfghjfjƒZƒ%]źpqe<klhjilfrt§3s†o~il[p;o~fjndhjfgeZ]‡pq|3nil|~|„]‡n#o„fjile–iq¢|~ils<e< †fjeZk]\|„|~il|@t\§¯3s<[^]\|„frnplh/3e<plhgu†t„fjt ‚3]ƒyil|„o Š J$JZ«qŽpqe<n@X<]\tvo„]|I¬:]\emo~|„]:¢©il|:¬:im[ ƒZs†o~pqo„fjile<plh†Žp;o~XZ][p;o~fjn\t«mŽpqe<n@X<]\tvo„]|‡«;­}eZkmhjple< « ¯Ri;£l]\[xy]|“‡‹l‹m‹Z§33hrt„i.p‘£;pqfjhjplxZhj]pltR€¯R‚M€ ‚M]\t„]\pl|~n@X‚3]ƒyil|„od‚37‚ 1†Š 7¨S_ 7Z«%ÄR]‡nq§“\‹m‹l‹Z§y®wsZx†· [ fgovo~]\ o„i €W§ BKR

(124) E{IXZfghjfjƒZƒ%]ÅpqeZkmhgimfjt¶pqe<  pqxZ|~frn]¯¶p;o„fj£l]\hF§d±VXZ]\epqsZo„il[pqo„frn

(125) hjfgeZ]‡pq|dnil|~|~]\n#o~fgimeKiq¢}|~ilsZe% †fge<k ]\|„|~il|@t frtI]ªZpln#o‡§  A8- AQ3  $*8A !A / 2 :9X.!/ -<; «†Šm_ 7 LKJDmŠ 16JD 7Z«w“‡‹l‹l‹<§­}|„|@p;o~sZ[ fge Šm_ 7 L 7m_q‹<« “‡‹l‹m‹Z§. vv. ñxwzy { | |.

(126) “‡’. 6& 1- H3   B 7E NmilX<eŽfjn@X<pl]hIŽPn¯Rpl[ ]]l§"8xZfjxZhjfgimkl|@pqƒZXwuime|„iwiqo@tiq¢Mƒyilhju¨e<il[ fjplhjt\§ A  056"A 3  A /T &1A « DSR m Š n!L Šm‹Z“ 1†Šl‹$< D «“\‹m‹lŠZ§ m ®wsZƒZƒ<hg]\[^]\e¨o~pq|~u ±V±V±&xZfjxZhgfjilkm|~plƒZXwu.pqo4uR‚3Å .   ! ('7   )*( #*

(127) /§6n#§.  . B ‹E

(128) a^§¨{]o~]|@t}pqe< ;N%§$V§m±Vfjh@wfje<t„ile/§y{}|@pln#o~fjn\pqh%ƒZ|„imxZhj][t}pq|~frtvfjeZkfge o~XZ]Rt„ilhjs†o„fjileil¢ ƒ%imhguweZim[^frpqh ]‡z¨s<p;o~fgime<t§ A  1 A /T   3   «v71gL “‡Œ 1†Š8†J «y“\‹SwR “m§. /   A « Bj“\’EźilsZfrt d§q‚3plhghE§¬:ime¨£m]|~kl]\e<n]:iq¢yo„XZ]3¯R]´,o„ime ƒZ|„i†n]\t~tºo~i![sZhgo„fjƒZhj]3tvimhgsZo„fjile<t\§  560;-%/%A T ‹1L _8J 1†Š Rw«y“\‹mŒlŒ<§. Bj“l“%ECN%§®wo„iw]|ple< ¤‚!§ :s<hgfj|~t~n@X/§  1/7*51%( "  560 -%/   34Q '

(129) 2 }im|7@ «Zt„]\nile< .]\ †fgo„fjileº«/“\‹m‹lŠZ§. §K®wƒZ|~fgeZkm]|„·P ]\|„hrpqk%«º¯3]\´. Bj“‡_ECNm]\ple;PRfjkleZ]‡t§yc\|„i![p;o~XZc[pqo„frzms<]3]oµc|~ifgeZ¢©il|~[ pqo„frz¨sZ]l§  - *$-! e !-%-! !A / 2 «1D m “ln jL “ 1y“‡ŠZ«y“\‹ 7 wR § m ¸e  |„]\e<n@Xvn#§. 9 8A -. A>34 $*8A. / &1A4 * Bj“\ŠECNm]\ple P¶fgkmeZ]\t\§¤>tvo„i†n@X<pmt€o~fjn.pq|~fŸo~XZ[ ]o~fjn–¢©il|^|„]\hgfrpqx<hg] t„nfg]\emo~f yn.nil[ ƒZs†o@p;o„fjileº§ O  G 0 qAx& &0 A «yŠ8J6LØ_qŠmŠ 1Z_qŒZ“m«Z“\‹m‹lŠ<§. Bj“%D$ECN¨pq[ ]‡tXV§;±Vfgh @wfge%tvime/§ - 56*&W 549:/ // W&,34 5 -z#%/7  /z-!  %-! §<¯3ilo„]\time^RƒZƒZhjfg]‡ ^®†nfg]\e<n] ¯Ri<§;Šm_Z«3V ]\|Žpq€]\tvo€u¹ t®¨o~pqo„fjileZ]\|„u Y²n]m«qÅ/ime< †ileº«†“\‹lŒmŠZ§¨3hrtvi¶ƒZsZxZhjfjt„XZ]‡ xwu{}|~]e¨o„frn]·V¶pqhjhF« ­IeZklhj]´iwiw K¬:hjfŸ¡ t«%¯ %N «1¶u ®†§<‚M]\ƒZ|„fje¨o„]‡ .xwu–Ķi;£l]\|\«†¯R]´}il|@y« “‡‹l‹$D<§. .  v y x.

(130) Unit´e de recherche INRIA Lorraine, Technopˆole de Nancy-Brabois, Campus scientifique, ` NANCY 615 rue du Jardin Botanique, BP 101, 54600 VILLERS LES Unit´e de recherche INRIA Rennes, Irisa, Campus universitaire de Beaulieu, 35042 RENNES Cedex Unit´e de recherche INRIA Rhˆone-Alpes, 655, avenue de l’Europe, 38330 MONTBONNOT ST MARTIN Unit´e de recherche INRIA Rocquencourt, Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY Cedex Unit´e de recherche INRIA Sophia-Antipolis, 2004 route des Lucioles, BP 93, 06902 SOPHIA-ANTIPOLIS Cedex. ´ Editeur INRIA, Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY Cedex (France)   

(131).    ISSN 0249-6399.

(132)

Références

Télécharger maintenant ( PDF - 14 Page - 387.98 KB )

Documents relatifs