Résolution de l'équation de Poisson sur des maillages étirés par une méthode multigrille
63
0
0
Texte intégral
(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Re´solution de l’e´quation de Poisson sur des maillages e´tire´s par une me´thode multigrille Je´roˆme FRANCESCATTO. N˚ 2712 Novembre 1995. PROGRAMME 6. ISSN 0249-6399. apport de recherche.
(3)
(4)
(5)
(6)
(7)
(8)
(9) "! # #$ % & ' (*)+, - ! % &./
(10) 0! ' & $1 2 53 46 758:9+;,<>=@?
(11) ACBDA=FEEHG I&JKMLNJPORQQTS,U,V WXOZY\[']Y_^P[a`bSdcMe`gfihj]kSmlnQKokpaYq`b^rOZe`\KMcHSaesYbKMLm`b[a`\SaY5ct]uQTp'Jv`bhj]kS IJKRwSaeyxMz{y|x }%OR~k~KNJvesouS,JS'[rkS'J[ruSc#>tt ZV {K MSdQFkJSC NMV MU#~iORLMSd^ j @ ORck^(['SJPOm~k~KMJvedlckKM]k^XpaeP]kot`\KMck^X]kcuSyQpaePkKokSQF]Yge`\LMJv`qYgYbS,OmoiOR~ePp'S~KM]kJYO#Jp'^PKRYb] e`bKNcokS'^% Iok]^PS'['KNckoKNJouJS,^P]kJXouSd^QCO `gYgYORLNS'^Xpae`bJp'^dn{%KM]k^]e`qYg`b^PKNcu^XY¡ ¢OR~k~kJK[£kSQ#]Yge`bLNJv`gYqYbS okSe¥¤~SNKRY\]uQTS'^fic`b^yORLMLmYbKNQp'Jp'^XokpaNSaYbKN~u~p'S,~KN]uJXYOJpd^¦KmYb]e`bKNcokS'^%p'hj]iOZe`\KMck^o§ ¢&]YbS'J¨© KM]e o§ ªOmKMJo§lRKNc1~kJp'^PS'cMePSs]kcuSsQpaePkKokSXokSLNp'ckp'JPOZe`\KMc«OR]ePKMQCO e`bhj]kSsokS'^&LNJv`gYgY\S'^&LNJKM^P^`b¬'JSd^~iORJORLNLRY\KR Qp'JPO e`bKNc
(12) okSNKRY\]uQTSml5OR]ePKMJv`\^£OmcMe%]uc@^¦SdQ1`g®okp'JPOZ¯CckS'QTS'cMeo`\JS'[ae`bKNckcuS¨Y¡liOR^Pp,^¦]kJsYbS'^[dKSa¯C[a`\S'cMeP^ okSY¡ °pdhj]iOZe`bKNcokS,IKR`\^¦^PKNc5i±§Sd^okp'Jv`qMp'Sd^^PS'['KNckouSd^^PKMcNeOm~k~uJK[rkp'S'^X^P]kJ[riORhj]kS,c`gNS OR]HS'c`\cMePJKR ok]`b^rORcMey]kc
(13) ²¡OR[aePS']kJ%ouS«['KMJJSd[ae`bKNcORoiOR~ePp#OR]@^¦SdQ1`g®okp'JPOZ¯CckS'QTS'cMed³%c´OR~k~Yg`bht]uS«['SaeePS#QpaePkKokS ~KN]kJJp'^PKN]uokJSY¥ °p'hj]iO e`bKMc/okS,I Km`b^P^PKMcHSaeY\S'^sp'hj]iOZe`\KMck^okS#{O'j`\S'JvxMePKNµRS'^d ¶¸·u¹ZaºP»M¼½ QpaePkKokS'^CQF]Yqe`bLMJv`qYgY\S'^CFp¨Ybp'QSdcMeP^fict`\^,MKmYb]kQS'^Cfic`b^#^PS'Q1`g®okp'JPOZ¯>cuSdQS'cMe p'hj]iO e`bKMcHSaYqYg`b~e`\hj]kS2ORciOZYq¤^PScj]kQp'Jv`bht]uS ¾\¿ À¥ÁÂÄÃÆŨÇÈÂqÉMÊMÂqË¥Ì. Unite´ de recherche INRIA Sophia-Antipolis.
(14) T C -T § ( . ! . !
(15) $1 ( ! ./ ¨¹ u»m¹N zvc eP`b^JSd~KMJvedl XS^eP]ko¤O
(16) Q#]tYqe`bLNJv`bo:QSaePkKo² KNJ1^PKRYqj`bckL^PS'['KNcuo KMJokS'JI X °^ KMc^ePJSaeP[rkS'oQSd^¦kS'^d S]k^¦S%ePuSfic`gePSNKRY\]uQTS,ORLMLmYbKNQS'JPOZe`\KMcQ#]Yge`\LMJv`bo@OR~k~kJKjOm[£okSaNSaYbKN~S'o ² KMJT^¦KmYgj`\ckL´ePkS&]Y\S'JCS'hj]iOZe`\KMck^d §`\J^edl XS~kJS'^PS'cMeHO+QSaePkKoePKLNS'ckS'JPOZePS/['KjOmJ^PSLNJv`bok^CM¤ NKRYb]kQS2ORLMLmYbKNQS'JPOZe`\KMc§l OZYgY\K `\cuL%OXot`\JS'[ae`\KMciOZYt^¦SdQ1`g®['KjOmJ^PS'c`bckLXnOm^PS'oKMcePkS(IKR`b^P^PKMc§ ^5S'hj]iOZe`\KMc ['KSa¯>[a`bS'cNeP^'1©skS^PS'['KMckoKNJouSdJouSdJv`gmOZe`qMSd^1OmJSOR~k~kJK t`bQ>OZePS'o OZe,SZOR[r@Y\SaNSaYM¤`\cMePJKok]k[a`bckL/O ['KNJJS'[ae`bKNc ²¡Om[aePKMJOmoiOR~ePS'o:ePK ^PS'Q1`g®['KtORJ^PS'c`bckLk ©kS'c§l XS+OR~k~Yg¤:eP`b^HQSaePkKo:ePK ^PKRYgNS
(17) ePkS IKR`b^P^PKMcHS'hj]iO e`bKMc/ORckoHePuS,{yO¨t`bS'Jv¦xMePKMµmS'^S'ht]nO e`bKNcu^d 5º 1· M Q#]Yge`\LMJv`boQS¨ePuKok^&_fic`gePSySaYbS'QTS'cMeP^&fic`gePSNKRY\]kQS'^& ^PS'Q1`q¥['KtORJ^PS'c`bckL SaYqYg`\~te`\[ S'hj]iO e`bKMck^Xcj]kQSdJv`b[ O Y ORciOZYq¤^`b^ . . .
(18) . . . . . . . . . . !
(19) ".
(20) .
(21)
(22) ! #"$%& '( " *)
(23) " #+,%- /.0,%1
(24) 2 3(" ' 4. +
(25) ! 5 ( 798 ¹ · »m¹:· 8 :bº #> 8 8 ¹ < = uq ?
(26) KRe`gmO e`bKNcok]^PS'Q«`g®oupdJPOZ¯CckS'QSdcMe #,,#,,#,,F,,,F,,,F,, uª xNSdQ1`g®okp'JPOZ¯CckS'QTS'cMeyOZYbLNp'kJv`bhj]kS ,,#,,#,,#,,F,,,F,,,F,, u @ AciOZYg¤u^¦Sok]HYg`b^P^PS']kJy,,#,#,,#,,#,,#,,F,,,F,,,F,, < » D u k 8 E: F_ j /H¼ G 0 F_ ¹ :· 8 JI t»R¹ :· 8 º J:LKX :· 8 @uq xm¤u^ÈeP¬dQSYg`bckp O `bJS,LMJv`qYgY\SfnckS0#,,#,,#,,#,,F,,,F,,,F,, @uª xm¤u^ÈeP¬dQSYg`bckp O `bJS,LMJv`qYgY\S'^LNJKM^P^`b¬'JSd^ #,,#,,#,,F,,,F,,,F,, Q E:¼¼ jR Q ·n'9 : S j P 8 ¹ :· 8 tOnq ALMLmYbKMQTp'JPOZe`\KMcC`b^PKRePJKN~S/#,#,,#,,#,,#,,F,,,F,,,F,, Onª ALMLmYbKMQTp'JPOZe`\KMcHORc`b^PKmePJKM~S #,,#,,#,,#,,F,,,F,,,F,, On @ nOm[aePS']kJokS['KNJJS'[ae`\KMc ,#,#,,#,,#,,#,,F,,,F,,,F,, OnV O uS'Q~Y\S'^o§ ªOmLMLmYbKMQTp'JPOZe`\KMck^y#,,#,,#,,#,,F,,,F,,,F,, OkV Onq ?OZ`qYgYORLMSd^2^ePJ]k[aeP]kJp'^#,,#,,#,,#,,F,,,F,,,F,, OkV Onª ?OZ`qYgYORLMSd^2~Y\]u^s['KNQ~YbS uSd^H,#,,#,,#,,F,,,F,,,F,, ¶¸M¹ D ·
(27) ¼b¹ : Q E:¼¼ uq ³%~kp'JPO ePS']kJ^okSePJPORck^² S'JveT#,#,,#,,#,,#,,F,,,F,,,F,, q Mq ³~kp'JPOZePS']kJsokSJS'^ePJv`b[ae`\KMc ,#,,#,,#,,F,,,F,,,F,, q Mª ³~kp'JPOZePS']kJso§ `bcNePS'J~KmYOZe`\KMc #,,#,,#,,F,,,F,,,F,, uª A~k~tYq`b[ O e`bKNcu^scj]kQp'Jv`\hj]kS'Y^ X1Y¥ °p'ht]nO e`bKNcokS#I Km`b^P^PKMc #,,F,,,F,,,F,, ªuq ?OZ`qYgYORLMSyJp'LM]Yg`\S'J ,#,,#,,#,,#,,F,,,F,,,F,, ªuª ?OZ`qYgYORLMSypae`bJp",#,#,,#,,#,,#,,F,,,F,,,F,, ªu @ ?OZ`qYgYORLMSyouSYO1~YORht]uS #,,#,,#,,#,,F,,,F,,,F,, ªuV O ?OZ`qYgYORLMSyouSYO1['KMckok]`gePS@,,#,,#,,#,,F,,,F,,,F,, ªuª ?OZ`qYgYORLMSyou]@Z{ Ay[W ABBu Z ,#,,#,,#,,F,,,F,,,F,, ªuªU ?OZ`qYgYORLMSyou]@ } A UMN ,,#,,#,,#,,F,,,F,,,F,, u @ A~k~tYq`b[ O e`bKNcu^%OR] p'ht]nO e`bKNcu^%okS,{O'j`bS'Jv¦xMePKMµmS'^ ,,#,,F,,,F,,,F,, @uq I&iOR^PSYq`bckp OZ`\JS ,#,#,,#,,#,,#,,F,,,F,,,F,, @uª I&iOR^PSckKMcHYg`\cupZOZ`bJS #,,#,,#,,#,,F,,,F,,,F,, ] · 8 »M¼ :· 8 » : 8 ¹ . 6 ;.
(28). . C. ".
(29) . . . M. . ".
(30). ". . . !
(31). ".
(32) . . . . " .
(33). . . \ T. .
(34). ^_^a`[bZc dec. . . ;. .
(35).
(36) . W. 6. ". . ". . B. 6NM O. U 6
(37) T U u M M U C+W @M @M @MU @MU @M nO ON@ OO OjU NO U Oj B. u . W#M #W M.
(38)
(39)
(40) ! #"$%& '( " *)
(41) " #+,%- /.0,%1
(42) 2 3(" '. . > (/
(43) 2 ³c«ot`\^e`bckLM]kSoiOmcu^ Y¡ p'['KM]Y\S'QS'cMe2ouSXY¡ ¢OZ`\JOR]ePKN]uJo§ °]kckSOZ`qYbSXo§ ªO'j`\KMcCokS'] dKMckS'^&e®¤~`bhj]kS'^d± O 'KNcuSXpaY\KR`\LMckp'S(okS2YO~iORJKR`kokSXY¡ ¢OZ`gY\SXK FY\S'^² KNJ['S'^ouSX² JKReePSdQS'cMe ^¦KNcMecupdLRYg`\LMS OmYbS'^ Sae&Y¥ °p'[dKM]YbS'QTS'cMe S'^es['KMck^`bokp'Jpy['KMQQTSS'^P^¦SdcMe`bSaYqYbS'QTS'cMesckKMcj`b^Phj]kS'] 5esYO 'KMckS~kJ¬'^sokSYO1~iORJKm`5K ^PS^`geP]kSYO ['KN]u[rkSYOmQ1`bciOZ`\JSXouSePJ¬d^²¡OZ`\YbS(p'~iOZ`\^P^¦Sd]uJ O `bck^`hj]kSokS'^ ~kkp'ckKMQ¬'ckS'^ ['KNQ~YbS uSd^ Yq`bp'^cuKmerORQQTS'cMe XYOeP]kJk]tY\S'ck['Smk³cORokKN~tePSsS'cLNp'ckp'JPOZYi]kckSQTKoup¨Yg`b^rO e`bKMc«okS2YO%eP]kJk]YbS'ck['SyOR]ePKMJv`\^rORcMe ]ucT[ OZY\[']Y ^P]kJokS'^sQCOZ`qYgYORLMSd^ fick^S¨epae`\Jp'^s^¦]`qmORcMe%YO1^PS']YbSo`\JS'[ae`bKNcerOmcuLNS'cMePS XFYO1~iORJKR`¥ ±OCJp'^PKRY\]e`bKMcct]uQTp'Jv`bhj]kSokS[dS'^p'['KN]tY\S'QS'cNeP^['KMQ~kJS'^P^`bY\S'^NS'J^,]ucp¨erOZe,^erOZe`\KMckciOZ`bJS#S'^e ^PKM]NS'cMe X[dKMcMNS'JLMSdcu[dS1YbS'cNePSSaeePJ¬'^,['KN]tePSd]u^PSmI KN]kJ,OR['['p¨Ybp'JS'JYOTt`gePS'^P^PSokS['KNcMMSdJLMS'ck['S~Y\]t ^`bS']kJ^QpaePkKokS'^C~S']MS'cN e ¨ePJS
(44) ]e`gYg`\^Pp'S'^d2±OePS'[£kc`bht]uS@S'Q~YbK ¤Np'S
(45) oiORck^['SJPOm~k~KMJveSd^ÈeiOm^¦pdS ^P]kJ]kckSCOm~u~kJK[rkSCQF]Yge`\LMJv`qYgYbSCokpaNSaY\KM~k~p'ST~KM]kJ,Jp'^PKM]kokJS1Y\S'^Fpdhj]iOZe`bKNck^o§ ¢&]YbS' J
(46) g ¡l
(47) UP&xjKMc S tePSdcu^`\KMc Om] ´ePS'JQS'^o` 5]k^`g² ^#^' ¢O'¬'JSePJ¬'^«Sa¯C[ Om['S^¦]kJ,okS'^1Q>OZ`gYqYOmLMS'^,ckKMc ^ÈePJ]k[aeP]kJp'^«Sae#`b^PKR ePJKM~S'^
(48) g ¥±OLMpdcupdJPOZe`bKNc OR]ePKMQCO e`bhj]kSCokS'^#LMJv`qYgYbSd^FLNJKM^P^`b¬'JS'^,S'^e#KMePS'ct]uS~iORJ#OmLMLRY\KMQpdJPOZe`bKNc okS'^#['SaYgY\]YbS'^,ok]Q>OZ`gYqYOmLMS1fic
(49) q ¥l
(50) U P © KM]ePSa² Km`b^['S¨eePSCQpaePkKokSCcupd['S'^P^`gePSokS'^«ORQpdcnOmLMS'QTS'cMeP^ ~KN]kJ^d ªOm~k~tYq`bhj]kS'J XokS'^sQCOZ`qYgYORLMSd^2~kJp'^PS'cNerORcMe%okSy² KNJveP^p¨e`bJS'QSdcMeP^
(51) ¡ Sd^Jp'^P]YgerO eP^KMcNepaePp#~u]kYg`\p'^oiORck^%['SaeePS#ot`\JS'[ae`\KMc
(52) ~iORJ ?O'Jv`b~Yg`\^Sa e (S'ckµ OZerOmµjJv`b^PkciOR c
(53) q O ~KN]kJJp'^PKN]uokJSY\S'^pdhj]iOZe`bKNck^okS,{O'j`bSdJvxMePKMµmS'^%S'cokS']
(54) o`bQS'ck^`bKNck^O'NS'[]kcQKok¬aY\SokSeP]kJk] YbSdcu[d S X%]uckSXp'hj]iO e`bKMc«okSxj~iOZYORJveSae AYgY\QCORJPOm^'m|ckS2S tePS'ck^`bKMc#S'c#ePJKR`b^o`bQS'ck^`bKNck^&OpaePpsOmQKMJ['pdS ~KN]kJ(Jp'^PKM]kokJSYbSd^2pdhj]iOZe`bKNck^(o5 ¢&]YbS' J
(55) q 5SaeX['S¨YgYbSd^2okS{yO¨t`bS'Jv¦xMePKMµmS' ^
(56) g @§^¦]kJ(okS'^XQCO `gYgYORLNS'^ckKMc ^ePJ]k[aeP]kJp'^Sae`b^PKRePJKN~S'^dM&cQ>OZ`gYqYOmLMSX^ePJ]u[¨eP]uJpMlmY¥ °]e`gYq`b^rOZe`\KMco§ °]kckSsQpaePkKokS2Q#]Yge`\LMJv`gYqYbS X~nOmJve`bJ o§ °]kcH^¦SdQ1`g®okp'JPOZ¯CckS'QTS'cMe%OFpaePp~kJp'^PS'cNePp'S~iORJs}OmouSd^¦~`\SaY5^P]kJYbS'^sp'hj]iO e`bKMck^XokS,{O'j`bSdJvxMePKMµmS'^XS'c okS'] >o`bQSdcu^`\KMck ^
(57) ¡u± ]te`qYg`\^£O e`bKNcCouS%YOFQTpaePkKouS%QF]Yqe`bLMJv`qYgY\S,OZYbLNp'kJv`bhj]kS^P]kJokS'^XQCO `gYgYORLNS'^ckKMc ^ePJ]k[aeP]kJp'^² KMJvePS'QSdcMeP^1Omc`b^PKRePJKN~t`\hj]kS'^,OpaePppaeP]ko`bp'SC~iOm J XORckS'µ
(58) g ^P]kJY¡ p'hj]iOZe`\KMc+SaYqYg`b~e`\hj]kSm ?
(59) KMJPOmckKkl ?O'Jv`\~Yg`b^Sa!e (S'ckµ OZerOmµjJv`b^PkciORc1KNcMe['KM#c "']#]kcOZY\LMKNJv`gePkQSXokS2^PS'Q«`g®oupdJPOZ¯CckS'QSdcMe&okS(ePJv`g ORckLN]tYOZe`\KMck$^
(60) ªM ¡W(S2okp'JPO ¯CckS'QS'cNe&Yg`\Zp XYOo`b^P['Jpae`\^£O e`bKNc1okS(Y¡ °pdhj]iOZe`bKNcokSsI Km`b^P^PKMc#S'^e(OR~k~Yg`\hj]kp X1okS'^%QCOZ`qYgYOmLMS'^XckKMcH^ePJ]k[aeP]kJp'^Sae%pae`\Jp'^d W(SaeePSXpaeP]kokSXS'^eY\S2~kJKmYbKMckLNS'QS'cMeo§ °]kcFePJPO'mO `gYiS 5Sd[aeP]kp(~nOm&J %KKNu]k'^
(61) g( k^P]uJ okS'^&Q>OZ`gYqYOmLMS'^ckKMc ^ePJ]k[aeP]kJp'^X~KM]kJYOFJp'^PKRY\]e`bKMcCokSY¥ °p'ht]nO e`bKNc>okSIKR`\^P^¦KNc~iORJYOFQpaePkKokSQ#]Yge`\LMJv`gYqYbSokSe®¤~SNKR Yb]kQSd^fnc`\^(ORLNLRYbKNQp'Jp'^dM± °]e`qYg`b^rO e`bKMcCokSs['SaeePS%QpaePkKokS^P]kJokS'^QCO `gYgYORLNS'^&`b^PKmePJKM~Sd^OokKMckckpokS KNck^Jp'^P]YgerOZeP^d&cCJSamOmcu[rkSmlMY¡ °]e`qYg`b^rO e`bKMcCokSsQCOZ`qYgYORLMSd^pae`bJpd^o`bQ1`\cj]kS^rOy~S'Jv² KMJQ>ORck['Smj± °KNwSae okSXcuKmePJSp¨eP]uokSX['KNcu^`\^ÈePS Xp¨YORKMJS'J ]kcCOZY\LMKNJv`gePkQS(~SdJQSaeerORcNe&YO[dKMck^ePJ]u[¨e`bKMcTOR]ePKMQ>OZe`bht]uSXokS'^ LMJv`qYgY\S'^LNJKM^P^`b¬'JSd^(~nOmJXoupdJPOZ¯CckS'QSdcMeo`\JS'[ae`bKNckcuS¨YgYbSMW S¨eO YbLMKNJv`gePkQSSd^Èe%Om~u~Yq`bhj]kp,~iORJ(YO#^¦]`qeP$S X Y¡ p'hj]iOZe`\KMc/ouS,IKR`\^P^¦KNcS¨eOm] pdhj]iOZe`bKNck^okS,{O'j`bSdJvxMePKMµmS'^d ±O^P]`gePS%ouSs['SsJPOR~k~KNJve(S'^eo`qj`b^Pp'SsS'cChj]iOZePJS%~iORJve`bSd^' Omcu^ YO~iORJve`\ S )lMKNc~kJp'^PS'cMePSY¥ `\cMePp'*J ae ok]
(62) ^PS'Q1`q¥okp'JPO ¯CckS'QS'cMe%Saey^¦Sd^['KNck^¦pdhj]kS'ck['S'^^P]kJXY¡ ªOm~k~tYq`b[ O e`bKNco§ °]kc
(63) [ OmJJp,]uc`qeP+p `\cu[dKMck^`b^erORck['Sml KM~e`\Q1`b^rOZe`\KMcok]+~iORJPORQT¬aePJS1okSJSaYO nO e`bKN,c P_±O>~iOmJve`b.S -CePJPOZ`qePSokS1YOo`b^P['Jpae`\^rOZe`bKNcokSFY¡ p'hj]iOZ e`bKNco5 ¢ORoNS'[ae`bKNc¥o/` §]k^È`\KMc^P]kJ(]ucHQCO `gYgYORLNS`bc`qe`OZY hj]kSaYb['KNckhj]kSmn³c~kJp'^PS'cMePSoiORck^(YO,hj]iOZePJv`\¬'QS ~iORJve`\SYO LMp'ckp'JPO e`bKMc:Om]ePKMQCO e`bhj]kS
(64) okS'^LMJv`qYgY\S'^LMJKM^P^`b¬dJS'^ok] Q>OZ`gYqYOmLMSfic:~iORJOmLMLRY\KMQpdJPOZe`bKNc o`bJS'[¨e`bKMckckSaYqYbS
(65) Sae>~uJKN~KN^¦S/]kc ²¡Om[aePS']kJokS[dKMJJS'[ae`\KMc:QCO ePJv`b[a`\SaY~KM]kJY¡ ¢OR~k~kJK[£kS/ouSHYO+['KMck^`b^ erORck['STouSd^^P[rkp'QCOR^ct]uQTp'Jv`bhj]kS'^#^P]kJ[dS'^LMJv`qYgYbSd^' ³c´QTKMcMePJSCoiORck^YO~iORJve`\+S 0okS'^#OR~k~Yg`\[ OZe`\KMck^ cj]kQp'Jv`\hj]kS'^ XFY¥ °p'ht]nO e`bKNcokS#I Km`b^P^PKMcHSae%OR] p'hj]iOZe`\KMck^souS#{O'j`\S'Jv¦xmePKNµRSd^' . . . . . . . . . . . . . ^_^a`[bZc dec.
(66) . 0" %-J
(67)
(68) . ! 5
(69) % ( y! y> ± KMwSae%okS1['S#~iORJPORLNJPOR~kkS,S'^eokSF~kJp'^PS'cMePSdJ¨l XePJPO'MSdJ^Y¡ °p¨eP]uokS«o5 ]kcQKok¬aYbS#^`bQ~YbS«Saeo§ °]kc QCO `gYgYORLNS[ ORJvePpd^È`\S'c§luY¡ `bcMePp'*J ¨eok]^PS'Q1`q¥okp'JPO ¯CckS'QS'cNeS¨e^PS'^s['KMck^Pp'hj]kS'ck['Sd^' . . . . . . !#"$% !# &('*),+.-/0213'54768$:90&5-/;-& . ³c['KNcu^`\ou¬dJSY¡ °pdhj]iOZe`bKNcokS,IKR`\^¦^PKNc>^P]kJX]kc[ OmJJp]uc`qePp,O¨NS'[okS'^s['KMcko`ge`\KMck^%OR] >Yg`\Q1`gePS'^sokS e¥¤u~S `bJv`\[£YbS¨e`\Q~KN^¦pdS'^Om] HKMJok^sou]/okKMQCO `bckSmlu^PKR`qe. ¦ |ckS+QpaePkKokSokS´o` 5p'JS'ck['Sd^>fic`bS'^/S'^e]e`qYg`b^Pp'S~KM]kJHJp'^PKM]kokJS´[dSaeePS+p'hj]iOZe`\KMc§±_S+ouKNQCOZ`\ckS o§ °paeP]kokS Sd^ÈeXo`\^¦[dJpae`b^Pp^P]`gmORcNe2Y\S[ruKm` okSokS'] S'cMe`\S'J^ Sae JSd~uJpd^¦SdcMerORcMeP^XYbSckKNQFkJSokS okS'LMJpd^okSYg`\S'JvePp%JS'^P~S'[¨e`gNS'QS'cMeX^P]`gmOmcMe Sae ij± Ocj]kQpdJKRerOZe`\KMcCokS'^^PKNQQSaeP^(S'^e ot`\Jv`bLNp'S ^P]`gmORcNe i±_S'^X~iOR^souS,['S,QCO `gYqYORLNS^P]`gmORcNe Sae >^PKNcMe . . =<. >@?*ACBEDGF3HJIKBML NODQPSR!HTFVU7WXPSR!HTFVU BZYS[\D]R!H_^`D]abNdc. N. . ji*k ji*l *i*k i*l. *i*l. F. m f D. F. enfpo ts. u\v. D@w kyx H lTzK{ D@w}| m f H~ m h{. ebh. =<. m h D. qr. SaesYbS'^s['KKNJouKNckcupdS'^XouS,[riORhj]kS,^PKMQQS¨e H^PKMcMe. egf. F F. ebho. H. =<. BMLw2| H2~ {. PSR!H egfo. FUWPSR!H eho. ±O1o`b^P['Jpae`\^rOZe`bKNcokSY¡ p'hj]iOZe`\KMc ¦ (^P]uJs['SQCO `gYqYORLNS^d °p'['Jv`qe. FVU. s DO| w ebho. qr. ).{
(70) o. ~ o. F3c. =<. . ?. . B xM# z ?. )B. x z:o. B xb# z ?. B x z8 ?. )B. x z:o. B x zb. w m f3{2 w m h{2 B8 z DB D B O D B ] D R # z x x b . ¥ . DF. ~KN]kJ Sae ±§Sd^>`\cu[dKMckcj]kS'^
(71) ^PKMcMe/okS'^e`bckp'S'^ X Om~u~kJK[rkS'J>Y\S Q1`\S'] ~KM^P^`bY\SFYbSd^ymO YbS']kJ^#okS1YOH^¦KmYb]e`bKNcS nOm[aePSCOR] ~KR`bcNeP^ok]+QCO `gYgYORLNSm ³c+^PKM]kiOZ`qePSCO'MKm`bJ P2±_S^P[rkp'QCO ¥ FS'^e['KNcu^`\^ÈerOmcMeCSae~kJp'[¨`bR^ X´Y¥ °KNJouJS@~KM]kJ1Y¡ ¢OR~k~kJK t`bQCO e`bKNc ok] ~kJKMYb¬dQS,['KMcMe`\cj]§ IKM]kJQKMcMePJSdJ&Y¡ `bcMePp'*J ¨eXou]T^¦SdQ1`g®okp'JPOZ¯CckS'QTS'cMedljKMc^d `\cMePp'JS'^P^PS X%YOJp'^PKRYb]e`\KMcok]^P[rupdQCO ¥ ~iORJ ]kcuSXQp¨ePuKokSXQ#]tYqe`bLNJv`gYgY\S XouSd] 1c`gNS Om] §txjKm`ge XYO%ot`\^P['Jpae`b^rO e`bKMc«]kct`q² KMJQSXok]1[ZORJJpX]kct`qePp Sae YOo`b^P['Jpae`\^rOZe`bKNc~Y\]u^sLMJKN^P^È`\¬'JSePSaYqYbShj]kS ~. B x z¤£. N. . . B
(72) w. P F\HK¡K¡K¡H eh U. |. . P¢F3HK¡T¡K¡H enf U. B x z. . . . u v { ¥. . . p¦§ ©<. d¦*¨. ¦5§ D@ª«w kx H lKzK{. Sae ±_S^¤^eP¬'QS,QCOZePJv`\[a`bS¨YouS ¥ ^P]kJ #^d °p'[dJv`ge. N. ¦*¨. D@ª¥w kx H lKzK{. r ¬. N. d¦§. r ¬. kyx D| m f H kyx D. ). | m f H. @ . lTz D~ m h\® lKz D. )~. m h3® c. ¯. =<. O . §3°5§ D²± §. ^. ³µ´
(73) ³µ¶.
(74)
(75)
(76) ! #"$%& '( " *)
(77) " #+,%- /.0,%1
(78) 2 3(" ' @. K SQ.'QTS^P]kJXYO1LNJv`gYgY\S. . ° § D@w ° § H ° § K H ¡K¡T¡H ° § T H ¡K¡K¡H ° § 2 { v ¦d¨ <. ¨°*¨. ¯. ¥ . ± ¨ c. D. jx Km`geY¥ °KN~updJPOZePS']kJokS1~kJKmYbKMckLNS'QS'cMe okpafic`geokS MS'J^ S¨eY¡ KM~kp'JPOZePSd]uJyouS«JS'^ePJv`b[ae`\KMc okpafic`geokS ,MS'J^ s ±_S[¨¤[aYbSTQF]Yge`\LMJv`qYgYbS['KNck^È`\^ePS-XOm~k~tYq`bhj]kS'J,]kckSCKM]+hj]kSaY\hj]kS'^`qePp'JPOZe`\KMck^#o5 ]kc^P[rupdQCOokSJSa YO nOZe`\KMc NOR['KN`¡l yOm]k^¦^¦xjSa`bokSaY §^P]kJ&YbS%^¤^eP¬'QSQ>OZePJv`b[¨`bSaY O Plj^P]`gj`\S'^(o§ °]kckS['KNJJS'[ae`bKNcokSLNJv`gYgY\S LMJKN^P^È`\¬'JS tKNcKN~u¬dJS]ucHePJPORck^² S'Jve%^¦]kJ okSY¡ p'hj]iOZe`\KMc/ou]HJp'^`bok]. ¥U K S'^eXYO^PKmYb]e`bKNcJSaYO updS^¦]kJXYO1LNJv`gYqYbS N ±_SX[ OZY\[']YnS nOR[aeokS2YO^PKRYb]e`\KMc1ok]^¤^eP¬'QT S ¥U ^P]`gj`iokSX^¦KNcFePJPOmcu^² S'Jve ~iORJ okKMckckSs]uckSs^PKRYb]e`\KMc ['KNJJv`bLMpdSouS cuKmePp'S. v xjKR`qedl §. . ¨. . ¨. ¦5§. . . §. ¦d¨. ¦5§. ¦*¨. . ¦*¨. . ¯. B §. ¨. q. <. ¨. ¨. D. §. . . B §. . § B <. § B . D. §. B § o ¨ §. §. ¨ ¯.
(79). M. § . ¨. ± § ? ¯. § B §
(80). 5¦5§ =<. ° § ?B §. § D. ¨. B § o ¨ § ¨ c q. D. K #okp'ckKRePSY¡ KM~kp'JPO ePS']kJ2`\ouSdcMe`gePp,^P]kJ N &c/~KM^rOmcMe lnKNcKNe`bS'cMe q. § B §
(81). ¯. ¦5§. § B . §. ± § ?. O'MSd[. § q. . § D. §. ?. §. D. §. ¨. ¯. ¨. U §. q.
(82). 8 . ¥ . ¨ § § ¯ c. ± O² KNck[ae`bKNcokS>YO
(83) LMJv`qYgYbS S'^e«okS~S'JQSaeePJSHYbSCYg`\^¦^rOmLMSCokS>ePKN]ePS'^1YbSd^1iOR^P^PS'^,² Jp'hj]kS'ck['S'^ okSFY¥ °S'JJS']kJ~kJK MSdcnOmcMe,okSFYOTQ>OZ`gYqYOmLMS,fnc N_±_S'^iOR]ePS'^² Jp'ht]uSdcu[dS'^^PKMcMe^P]k~k~KN^¦pdS'^O'NKR`bJypaePp Yg`\^P^¦pdS'^~iORJ%YbS1^P[rkp'QCOCokSFJSaYO nO e`bKNc
(84) ^P]uJ N _`bciOZY\S'QS'cMe& # 2 3(" '- ^PSFokp'['KNQ~KN^PS S'c/ouSd] ~kiOR^PS'^ D k Q E:¼¼ 8 % ±5`\^¦^rOmLMSokS'^iOR]ePS'^² Jpdhj]kS'ck['S'^okSFY¥ °S'JJSd]uJyouS#YOC^PKRY\]te`\KMc
(85) ok]^¤^eP¬'Q S O X~nOmJYbS«^P[£kp'QCO okSJSaYO nO e`bKNcSae%JS'^ePJv`b[¨e`bKMc/ok]Jp'^`bok]/^¦]kJXYO1LNJv`gYqYbS s D k Q E:¼¼ Q ·i' : S F WXOZY\[']YokSYO[dKMJJS'[ae`\KMc X#OZwKN]tePSd*J XyYO^PKmYb]e`bKNcCouS%YOF~kiOR^PS%LMJv`gYqYbSsfnckSokKNcuckp'Sy~nOmJ&Y¡ p'hj]iOZ e`\KMc U P ¦*¨. ¦ § 5 ¦§ . . . !#". %$. .
(86). %&. . . !#". . =<. %$. ^_^a`[bZc dec. ¦*¨. .
(87). .
(88).
(89) . .
(90) O. 0" %-J
(91)
(92) . H 8 :b¹:· 8. ; 6 + f =h #+ ("! '= "! / #" ! )
(93) " %- " ! )
(94) " D 7h f "
(95) fV =h Y " )
(96)
(97) " )
(98) / E%& /" !)
(99) ! Y
(100) '%-+ Z! ) " .# " )
(101) / E%& 2 &. W(KMQTQS
(102) Y¡ ¢O QKMcMePJp+Jp'[dS'QQS'cNe %KKMk]k^
(103) g ¥l['SaeePS+QpaePkKokS+~iORJHoupdJPOZ¯CckS'QSdcMe`\^¦KmePJKM~S ko KMckckSokSKMck^Jp'^P]YgerO eP^C~KN]uJ«okS'^CQCOZ`qYgYORLMSd^F`b^PKmePJKM~SM I ORJ[dKMcMePJSmlSaYqYbS^PSHokpaePp'Jv`bKNJSYbKNJ^okS Y¡ ]e`gYg`\^rOZe`bKNcokSQCO `gYgYORLNS'^Xpae`bJp'^ ¥ORc`b^PKmePJKM~Sd^P IKM]kJsJS'Qp'o`\S'ZJ X«['S~kJKMYb¬'QTS~Y\]u^`\S']kJ^ePJPOZ`qePS'QS'cNeP^~Sd]tNS'cMe aePJS,S'cMj`\^rORLMpd^ 8 T¼ D k Q E:¼¼ 8 % z®Y&[dKMck^`b^eP-S XCQKo`gfiS'JYO>QTpaePkKouS«okS1JSaYO nO e`bKMc+O ficouS#Yg`\^¦^PS'J%YbS'^iOR]ePS'^² Jpdhj]kS'ck['S'^okS Q>ORc`b¬'JS(~iOmJv²¡OZ`gePS(oiOmcu^_YOo`bJS'[ae`\KMc«~S'J~S'ckot`\[']YO `bJS XY¥ °pae`\JS'QS'cMedW(S'[a`~S']!e aePJSXS 5S'[¨eP]upMl ~iOmJS uS'QT~tY\SmluS'c]e`gYq`b^rORcNe(YOFQTpaePkKouS%okS OR]k^P^ȦxjSa`bokSaY~iORJYq`bLMckS'^(okKNcMeX[£iOmhj]kSckKS']ko>ok] Q>OZ`gYqYOmLMSS'^e%~kJv`b^sS'c['KNQ~ePS,~nOmJX]uckSYg`\LMckSSae%]kcuS,^PS']YbS
(104) q U
(105) g R P 8 T¼ D k Q E:¼¼ Q ·i' : S F z®Y[dKMck^`b^ePZS X,JS'~kJS'ckokJS^P]kJ&YO,LMJv`qYgYbS%LMJKN^¦^`\¬'JSmlMoiORck^YbS%[ OR^K YO,~knOm^PS~kJp'['pdouSdcMePSc§ ªO,~iOR^ p¨ePpQKo`gfip'SmljYbS'^XiOR]ePS'^(² Jp'ht]uSdcu[dS'^XQCOZYYg`b^P^Pp'S'^(^P]kJYO#LMJv`qYgYbS%fnckSmW S'[¨`5~Sd]t'e ¨ePJSS 5S'[¨eP]upMl ~iOmJ(S uS'Q~Y\SmltS'cokp'JPO ¯CciORcMes]kc`bhj]kS'QSdcMes^¦]`qmORcMe >ht]nOmcko^PS']YbS%YbS'^² Jp'ht]uSdcu[dS'^X^¦]`qmORcMe C^PKMcMeXYq`b^P^Pp'S'^sSae~iOm^['S¨YgYbSd^^P]`gmOmcMe Omck^['SXJPOm~u~KMJvedlRKNc1paeP]ko`bSXY¡ ¢ORQpaYq`bKNJPOZe`bKNc1okS(YO~kiOR^PSXLMJv`qYgYbSXLNJKM^P^`b¬'JS(~iORJ]kc1okp'JPOZ¯>cuSdQS'cMe o`bJS'[¨e`bKMckckSaYOR]ePKNQCOZe`\hj]kSmM±_S'^ fiLN]uJSd^ XSae QKMcNePJS'cMe&Y\S'^&okS'] 1e¥¤~S'^&okSXokp'JPOZ¯>cuSdQS'cMe ^¦]`qmORcMe YbS,QCO `gYqYORLNS`bc`qe`OZY¥
(106) <. . !. . . $.
(107). . . &. . !. . . . . $. .
(108). .
(109).
(110) . . di*k. i*l. *i*k. . H Ih. Ih H. _`bLN]uJSC ," . M∆ x,∆ y. M2 ∆ x,2 ∆ y. +%-+ ! # E+ 7idk idl " !)
(111) . ^. ³µ´
(112) ³µ¶.
(113)
(114)
(115) ! #"$%& '( " *)
(116) " #+,%- /.0,%1
(117) 2 3(" '. . H Ih. Ih H. _`bLN]kJSF M∆ x,∆ y. . . . -/. 13'54=6M$:90&5-/. ," . M ∆ x,2 ∆ y. . %& ! # E+ 7i*l " )
(118) . 4*68 j)5-. -& `$. _± S okp'JPOZ¯CckS'QTS'cMeOZY\LMp'kJv`bht]uS['KMck^`b^ePS X2LNp'ckp'JS'J_]kckS&^Pp'Jv`\Sfic`bSokSLNJv`gYgY\S'^_LMJKN^P^È`\¬'JS'^['KMck^ePJ]`gePS'^ ~iORJ,OmLMLRY\KMQpdJPOZe`bKNc
(119) okS'^,['SaYqYb]YbS'^,okSC['KNcMePJ RY\S MKm`bJfiLM]kJS @ ouS«YOLNJv`gYqYbS1fickSm±_S'^['S¨YgYb]Y\S'^,^¦KNcMe ² KMJQTp'S'^1X~iORJve`bJ«okS'^FQTp'o`ORckS'^«okS'^ePJv`ORckLRY\S'^d A [£iOmhj]kS>^PKNQQSae. S'^e YbS/ckKMQ#uJS/ePKRerOZY%okSckKS']kok^Cok] Q>OZ`gYqYOmLMS Pl&KMc:Om^P^¦K[¨`bS]kcuS@['SaYgY\]Yb
(120) S [dKMck^ePJ]t`qePSS'c+wKm`bLMciOmcMe ^P]k['['S'^P^`gNS'QS'cNeYbSd^['S'cMePJSd^ouS#LMJPO'j`qePpFokS'^%ePJv`ORckLmYbS'^[dKMcMePS'ciOmcMeY\SFckKS']ko Sae%YbS'^Q«`gYg`\S'] @okS'^ ^PS'LMQTS'cMeP^X`b^P^P]u^sokS ¡ ¯ x H %x. |D. F\HK¡K¡K¡ H e I. }e I. . ¯ x. ¯ x. noeud A i. noeud Aj. Volume de controle (ou cellule) C i. _`bLM]kJS @ /"! / _ #+
(121) 2 " ' ±O#ot`\^P['Jpae`b^rO e`bKMcHok]
(122) ±OR~YOR[a`\S'c^P]kJXYO1LNJv`gYgY\SfnckS,S'^esKMePS'cj]kS,~iORJXYO1QTpaePkKouSokS'^%paYbpdQS'cMeP^ fic`b^d ]F²¡OZ`qeokSXY¡ ªOmk^¦Sdcu[dS2okSXePJv`OmcuLmYbS'^^P]uJ YbS'^LMJv`qYgYbSd^LMJKN^¦^`\¬'JS'^dlZKMc«S5Sd[aeP]kS]kckSOm~k~uJK t`\QCOZe`\KMc okSY¡ °KN~kp'JPOZePS']kJy± Om~YOR[¨`bS'cH^P]uJ%[£iOm[']kcuS,okS#['S'^sLMJv`gYqYbS'^%~iORJ]kckS,QpaePkKokSFokSe¥¤u~S yO YbS'JµN`bc§_W S'[¨` JSaj`\S'cMe[Xokpafic`bJ¨lR~iORJ5Y¥ `\cMePS'JQp'o`OZ`bJSXok]#oupdJPOZ¯CckS'QSdcMedlRokS'] FKM~kp'JPOZePSd]uJ^ okS&ePJPORck^² S'Jve o§ °KNJouJS ·i¼· 8 Q u 8 ¹ ¹ z®YS'^esoup¨fnc`okS NS'J^ #~iORJX]kcuS`\cZwSd[ae`bKNcciOZeP]kJSaYqYbS . . . . . V. . . . !. $.
(123) .
(124) ". $
(125). ¦*¨. . w. {. *¦5§. dB. ^_^a`[bZc dec. . ©<. ¨. ©<. DOB §. q u. B ¨ . ¦*¨. qr. B § ¤¦§ c.
(126) U. 0" %-J
(127)
(128) . ¹ ta¹ E:»R¹:· 8 z®YsS'^eC okpafict`sokS HM S'J^ s(W(SaeCKM~p'JPOZePSd]uJ«S'^e1Y¥ ªORo wKm`bcMeTouSHY¡ KM~pdJPOZePS']kJ1okSH~kJKRYbKNckLMSa QTS'cMe. !.
(129) . $.
(130) ".
(131) . w {.
(132). `¦5§. ¦*¨. <. Tc. ²D. ±O1QCO ePJv`b['S,SaeXYbS,^PS'['KNckoQSdQFkJS,ok]^¤^eP¬'QSYg`\ckp OZ`\JS ¥ (ouSYO1LMJv`qYgYbS ^PKMcMe%okKMckckp'^~iOmJ ¦*¨. > ¯. ¨. ± ¨. D ¯ § D ± § c. n<. . ±_S^P[£kp'QCO ¥ (S'^e['Sd~S'ckoiORcMeX`\cu[dKMck^`b^erORcMes~iORJsJPOR~k~KMJveyOR]H~uJKNYb¬'QS,['KNcMe`bct][ OmJ. ¦ B . n<.
(133) w ¯ ¨ { 8 ± ¨ DO B ¨ . K S'^eXYO^PKmYb]e`bKNcS iOR[aePSok]~kJKNtY\¬'QS ¦ P |%cuSHS u~Yq`b[ O e`bKMc X@[dS'[a`sS'^e1² KN]uJc`\S~iORJ#Y¡ ¢ORciOZYq¤^PSokSYO~kJp'[a`b^`\KMc okS'^1ePJPOmck^Ȳ SdJveP^' ¢OR~kJ¬'^ Om[£µjk]k^P[£
(134) g U ¥ltYO['KNckot`qe`bKNcckp'['Sd^¦^rO `bJS~KN]kJOm^P^¦]kJS'JX]kckS,KMckckS,Sa¯C[ Om[a`gePp`\LMJv`gYqYbS,S'^esokKMckckp'S ~iORJ. ¦ N K S¨e ^PKNcMe(JS'^P~Sd[ae`gNS'QS'cNe2Y¥ °KNJouJSyouS%~kJp'[a`b^`\KMcCokS Sae ljSae YbSokS'LNJpokSY¡ p'hj]iOZe`\KMc OR] oupdJv`gp'Sd^C~nOmJve`bSaYqYbS'R^ XJp'^PKN]uokJSm(± °KN~updJPOZePS']kJokSY¥ °p'ht]nO e`bKNcouS@I Km`b^P^PKMc p¨erORcMeCokS/ouSdLMJp/ SaeY¡ KMJokJS
(135) okS'^KM~kp'JPO ePS']kJ^ouS/ePJPORck^² S'JveHouS@ouSdLMJp MlY¡ `bckp'LtOZYg`qePp ¦ M 1c§ °S'^e~iOR^Cp'Jv`qfip'SmIKM]kJ ['KNJJv`bLMSdJ2[dSaeePS`bck['KMck^`b^erOmcu[dSmlt]kckSQpaePkKokS,['KMck^`b^ePS XOm~k~tYq`bhj]kS'J%OR] >ePS'JQTS'^okSYO«QCOZePJv`\['S ]kc['KSa¯C[¨`bS'cMe>QF]e`b~Yq`b[ O e`g² 2W(S[dKSa¯C[a`\S'cMeCS'^eCokpaePSdJQ1`bckp X+~iORJve`bJOm] ^¤^eP¬'QS ¦ 1S'c]kckS o`bQSdcu^`\KMcHSaeSdc['KNQ ~iORJPORcNe2YO1^PKRY\]te`\KMcHcj]kQp'Jv`\hj]kSFSaesYO«^¦KmYb]e`bKNcS nOR[aePSM ± °p'ht]nO e`bKNc ¦ S'c a ^d °p'['Jv`qe. ¦ Z ±O1^PKRY\]te`\KMcHS nOm[aePSokS[dS^Ȥu^ÈeP¬dQS,S'^e. ¦ @ ) ³c/['KMck^`bok¬'JS,okS'] /o`\^¦[dJpae`b^rOZe`\KMck^o` 5p'JS'cNePS'^okS,Y¡ `\cMePS'JvmO YgYbS
(136) Bulq okKNcMeY¥ °]kckSSd^ÈeyokS'] H² Km`b^ ~Yb]k^LNJKM^P^`b¬'JSM P :¼¼ 8 A"~iORJve`\JokSYOo`b^P['Jp¨e`b^rOZe`\KMc okSY¥ `\cMePS'JvmOZYqYb S
(137) Blb s['KMck^e`geP]kpHokS `bcNePS'JvmOZYqYbS'^O'NS'[ ) ltY\S,^¦[rkp'QCO1ct]uQTp'Jv`bhj]kS#ok]~kJKMYb¬dQS ¦ ^d °pd['Jv`ge B. . . . g<. o. . . . . . . . ¯. ¨. s. . =<. . . ?tB w kg{ DF. . . H k. B
(138) w2R { DB=w F { D. P RHTFU. . R!c.
(139) <. B=w kn{ D. k w Fj?. kg{. c. .
(140). !. . D. . . &. v ?. . F. ,o. F. =<. ^. ³µ´
(141) ³µ¶.
(142) .
(143)
(144) ! #"$%& '( " *)
(145) " #+,%- /.0,%1
(146) 2 3(" '. ). B xM ? ?. B x8o. B x. . m . ±O#^¦KmYb]e`bKNcS nOR[aePS,ok]^¤^eP¬'QTS ¦ O (S'^e . F D. m. u. F o. . ¦ 9O c. =<. B. K. v. s m w Ft? D. s m {. ). H. B. § . !. q . DF3HX|©DF3HT¡K¡K¡ H . s D. RHK¡K¡K¡ . F\c o. DB
(147) w kg{ c. v. ±_S^P[rupdQCO ¦ O S'^eokKMck[['KNck^È`\^erORcMe%OR]H~kJKMYb¬dQS ¦ P P :¼¼ Q ·nd : S , ³c ['KMck^`bok¬'JSCQ>OZ`bcNePS'ciORcMe#Y¡ `bcMePS'JvmO YgY\S ['KMck^e`geP]kpokS `\cMePS'JvmO YgYbSd^O'MSd[ ) n±_S^Ȥu^ÈeP¬dQSYg`bckp O `bJS['KNck^ÈePJ]`qYe X1~iOmJve`bJsou]H^P[£kp'Q>O ¦ O S¨eokS'^sKM~kp'JPO ePS']kJ^ aS e ^d °p'[dJv`ge ) ). ¦ Z ±O#^¦KmYb]e`bKNcS nOR[aePS,ok]^¤^eP¬'QTS ¦ (S'^e
(148). . !
(149).
(150) . PSR!HTFVU. v 8 ?. . . F. F. o. . . D. =<. °. ?. °. xM ?. °. x8o. xb. D. m. . H¤|:DGF3HK¡K¡T¡ H . . c. =<. °. K. v. D. <. ). F W. s. . w F?. ). s Z{. ¨. s D. . ° v. RHK¡K¡K¡ H . D. ). F. . o. F3H. q u. D. ). m c. WCB=w kn{ c. _± S^P[rupdQCO ¦ S'^eokKMck[`\cu[dKMck^`b^erORcMe%Om]~kJKMY\¬'QS ¦ P ³c
(151) MKm`ge²¡Om[a`gY\S'QS'cMehj]kS1YOCQ#]tYqe`b~Yg`\[ OZe`\KMc+ok]+QS'Q#uJSTouS«LjOm]u[rkS1ok]^¤^eP¬'QS ¦ Z X~nOmJ ~SdJQSae X okS['KMcMNS'JLNS'J2NS'J^sYO1^PKRY\]e`bKMcHS nOm[aePS ¦ @ ok]/~uJKNYb¬'QS,['KNcMe`bct]uS ¦ Z P ³c
(152) JS¨j`bS'cNeQCOZ`\cMePS'ciORcNe,OR]
(153) ~kJKNtY\¬'Q S ¦ O ficouS#okpaePS'JQ1`\ckS'JYbS'^y['KSa¯C[a`\S'cMeP^Q#]Yge`\~tYq`b[ O e`g² ^ ^P]`gmORcNeY\S'^o`\JS'[ae`bKNck^okSokp'JPOZ¯>cuSdQS'cMe/]e`gYg`\^Pp'S'^d³c ]te`qYg`\^¦SYOLMJv`qYgY\S
(154) fnckS +oupd['Jv`gePS+oiORck^ Y¡ S u~kJS'^P^`bKNcokS @ P xjKR`qeY\S'^,QCOZePJv`\['S'^ Sae ['KNcu^e`qeP]nOmcMe,YbSC^¤^eP¬'QSYq`bckp O `bJS^P]kJ,['SaeePSCLMJv`qYgY\SCKMePS'cj]kSC~iORJYO QpaePkKokSokS'^p¨Ybp'QSdcMeP^fic`b^d A`\ck^È`_Y\S^¤^eP¬'QS O (okSaj`bSdcMe °. s. . v. ¦5§. . ¯. § . ¯. § . . ^_^a`[bZc dec. F. . ¯. § o. ¯. . § . =<. B § D²± §. D. . .
(155) U. 0" %-J
(156)
(157) . K !. § B § H B § T H ¡K¡K¡H B x§ HK¡K¡K¡ H B # . ± § D !. <. m h. B § D !. n['KSa¯C[a`\S'cMeso§ °pae`\JS'QS'cNe. m f D.
(158). ± § H ± § K H ¡T¡K¡H± x § HK¡K¡T¡HV± § # § ¯ x x D. !. § ¯ x x D !. § ¯ x x D. O'MS'[
(159). ± x§ D. m f m h. ). § ¯ x x D. § ¯ x x D. § ¯ x xM D? F3c. ³c['KMck^`bok¬'JSQCOZ`\cMePS'ciORcNe_YOXLMJv`gYqYbSLMJKM^P^`b¬dJS
(160) ['KNcu^ePJ]`gePS ~nOmJ5okp'JPOZ¯>cuSdQS'cMeokS %¦*¨. Dª\w kx H lTz {. ¦*¨. K. . ¦. kyx D|. r ¬. . F. f D. F. fo. . . ¦5§ #¦*¨. qr. . f H F. h D. . lKz D~. h®. c. F. dhpo. ¦5§ M<. _± Se®¤~S,okS,oupdJPOZ¯CckS'QSdcMe]e`gYq`b^Pp,S'^es['KMcMePJ mYbp,^P]`gmORcNeYbSd^2mO YbS']kJ^okS ,Sae JS'~kJp'^PS'cNerORcMe YbSycuKNQFkJSokSokS'LNJp'^(okSYg`\S'JvePpyJS'^P~S'[ae`qMSdQS'cMes ^P]`gmORcNe Sae iu±_S^¤^eP¬'QTSYg`\cupZOZ`bJSy^¦]kJ ['KNcu^ePJ]`ge%~iORJ(YbSd^KM~kp'JPO ePS']kJ^okSePJPORck^² S'Jve Sae ^d °p'['Jv`qe^PKN]u^(YOF² KMJQS,^P]`gmOmcMePS enf. 5i*k. . K. F. . o. . B ¨ D. D. ³ cHo`b^e`bckLM]kS$@[ Om^ 6 » k ORck^XYOQSd^¦]kJS,K FS'^ey]uc`q² KMJQS okS'] ot`\JS'[ae`\KMck^ Sae iluKMc/O. enf D. . ebh D. . ± ¨ !. !. ¯. D ¨ D . . D m H f h ¯. . B ¨. . . . . § H. . ¯
(161). m. f D m h D m 8 *h D . H. . ± ¨ H ± ¨ K H ¡K¡K¡H± ¨ HT¡K¡K¡H± ¨ . f D . j¦*¨. D²± ¨. ¨ D ¯. e. Z¦5§ *i*k i*l. . . ¨ . i*l. ©<. B ¨ H B ¨ K H ¡K¡K¡H B ¨ .
(162) <.
(163). ¯. ¨ D § H ¯ ¯. ± ¨. ¨ ¯. ebh.
(164). c. XSae%KY\S,oupdJPOZ¯CckS'QSdcMe^d °S5S'[aeP]kS,oiORck^XYbS'^. f D h D ) m P K <. P F3HT¡K¡K¡ H f dh U. ¨ D. ^. ³µ´
(165) ³µ¶.
(166) .
(167)
(168) ! #"$%& '( " *)
(169) " #+,%- /.0,%1
(170) 2 3(" ' ¨ . . ¯. !. D. ¨ . . ¯. D. ¨ D. . ¯. ¯. ¨ M D?. . )j. ± O,['KMQT~nOmJPOZ`\^¦KNcCokS['S^¤^eP¬'QS,O'NS'[Y\S^P[£kp'QCO#['KMck^`b^erOmcMeXQKMcNePJShj]§ `gY ^¦]¯eXokSQ#]Yge`b~Yq`bS'J YbSd^&['KSa¯>[a`bS'cNeP^&okS2YOQCOZePJv`\['S ~iORJ ]uc«²¡OR[aePS']kJouSs['KNJJS'[ae`bKNc sSae ~iORJ X~KN]kJYbSXJS'ckokJS ['KNcu^`\^ÈerOmcMed ¨ . ¯. . ; : S. F. . s\f ¯. ¨ . sh o. . ¨ ¯. B ¨. D²± ¨ H. » k ]²¡OZ`gesokSY¡ pae`bJSdQS'cMeyouSd^['S¨YgYb]Y\S'^^P]`gmOmcMe QS'cNeCoiORck^1YOo`bJSd[ae`bKNc ³cOokKMck[ °K . . enf. ebh. *<. . ± ¨ ! !. ¯ !. ¯. D ¨ D . f. ¨ . h D. ). ¯ D. ¯. ). m f m h H. ¨ D?. . 5s3h. qr. ¯. ¨ b D. . f D. . m f. enf . h D. . qr. sh D. ). F. c. 8 . f. D. m f. h. D. m h. c. E¦5§ ©<. s\f D. H 8 :b¹:· 8. D. ebh {. m h. ). F. )t. ¨ 8 D?. ¯. » k zvcNMS'J^PS'QTS'cMedl YbSToupdJPOZ¯CckS'QSdcMe1okS oiORck^YOHo`bJS'[ae`\KMc. ) ,Sae P5³%c/O1okKMck[ . sh D. ©sh. ©< s\f DF. C : S. s¥f D. ¨ . P F\HK¡K¡K¡ H f *h U . ±_S'^XmOZYbSd]uJ^%okS ,Sae ^PKMcMe%okKMck[ s\f. m h{ h d. ¨ D. F. ¯. PluKMcHS§S'[aeP]kS]kcokp'JPOZ¯>cuSdQS'cMe%^PS']YbSa Sae. Sae ) P. didk w m f f D enf. idl. q u. s\f. ). F qr. idk. S'cMePJPO `bckS. f. D. 8 . Sae. *h. D. ebh. sh DQF3c. & ; ; R ))
(171) '& ²¡Om[aePS']kJokSX['KNJJS'[ae`bKNc # E Mi*k + %s\f " )
(172) E%-+
(173) # E = s3h ' ! + !))
(174) ' %& " ! ¯ ¨ " )
(175) E%-+ ¯ ¨ )
(176) #"-" #" " ' ! ! %& #"¦*¨ #" # %& '(!" R " /.0!( 2 E2 #"! s\f sh !"!" 3(!+ ' " ; 6 ! ! .#%- # " ¦*¨ . ! » k-: '·k¹
(177) · $ F. i*l. s\f D. ^_^a`[bZc dec. sh D. ). F.
(178) B. 0" %-J
(179)
(180) . » k 8 :'·k¹ · , !. .
(181). . $. / "%-+ ! # E+ 7idk s¥f DF. qr. / "%-+ ! # E+ 7idl s\f D. . . ]&5$ +.-. ). s3h D. F. ). F. sh DF3c. qr. +!+.-)56. '*). ± O['KNcMMSdJLMS'ck['S%ouSsY¡ ¢OZYbLNKMJv`qePuQTSQ#]Yge`bLNJv`gYqYbSokp'~S'cko² KMJvePS'QSdcMeXokSYOQp¨ePuKokS%ouS%JSaYO nOZe`\KMc. Yg`\^P^¦Sd]uJ(5]e`gYq`b^Pp'Sm {KM]k^ O'MKNck^ [rkKR`\^È`mYbSd^Qp¨ePuKokS'^5`qePp'JPOZe`qMSd^^erORckoiORJo,okS OR]k^P^xjSa`\ouS¨YMSae NOR['KNt` ~iORJPOmQ¬aePJp'S'^%~KN]uJXYbSd]uJ%~kJKM~kJv`bpaePp#okS,KMck^XYg`\^¦^PS']kJ^%nOm]ePS'^² Jp'ht]uSdcu[dS'^d|ckSFOmciOZYg¤u^¦S,cj]kQpdJv`bhj]kS okS'^QKokS'^%YbK[ O YbS'^%ouS kKM]kJv`bS'J
(182) u( ^¦]kJsY¡ °pdhj]iOZe`bKNcokS1IKR`\^¦^PKNc
(183) S'^eS §S'[aeP]kp'S«OZfic
(184) okS1okpaePSdJQ1`bckS'J YbSy~nOmJPORQ¬¨ePJSokSJSaYO nOZe`\KMc &~S'JQS¨eerORcMeso§ °KNtePSdct`\J(]kcuSt`gePS'^P^PSokS['KNcMMSdJLMS'ck['S%KM~e`bQ#]kQH xjKm`ge YOLMJv`gYqYbS%oupd['Jv`gePS%onOmck^&Y¡ S u~kJS'^P^`bKMc @ ~iORJPOmQpaePJp'Ss~iORJ Sae YOQCOZePJv`\['S ok]^¤^eP¬'QSYq`bckp O `bJS,^P]uJ FokSo`bQTS'ck^È`\KMc RluePSaYgY\Sht]uS . . . w
(185) {. . enf W. d¦5§. ¯. K. D. F w m f{2. ebh. f ¯. o. F w m h\{2. ). O'MSd[ Sae &c/~KM^rOmcMe . D. q. D. h ¯ x x8 DG? F\c. ?. <. . B b DB o. YbS^¤^eP¬'QS ¦ ZU okSaj`bSdcMe. M D 8 ± b DB ?XB . ¯. §. h ¯. ± OQp¨ePuKokS`qePp'JPOZe`qMS~KM]kJCYO Jp'^PKRYb]e`\KMc:ok] ^¤^eP¬'QS/Yg`bckp O `bJS okp'['KNQ~KN^È`qe`bKNc>okSYO«QCOZePJv`\['S,^¦KN]k^2YOF² KMJQS + K ¯. D. H. h ¯ x x D. f ¯ x x D. ¯. ©<. h ¯ x x D. f ¯ x x D f ¯ x x D. § § . D. . ¦5§. . =<. ¯ B. D. ±. S'^eKMePS'cj]kS~iORJYO. ¦ ZU . ¦ R. D c M q q D?X? . n~ OmJve`bJokSsYOokp'['KMQT~KM^`qe`bKMc K l Sae ^PKNcMeJS'^P~S'[ae`gNS'QSdcMe(YOo`OmLMKMciO YbSml YO~iORJve`\SFePJv`OmckLM]YO `bJS1^ePJv`\[aePS'QS'cNe`bc² p'Jv`bSd]uJSTSaeYO~iORJve`\SFePJv`OmckLM]YO `bJS1^ePJv`\[aePS'QS'cNeF^P]k~kp'Jv`bSd]uJSMl KMcHS'c/oupdou]`qeY\S'^okS'] QpaePkKokS'^souS,JSaYO nO e`bKNc^P]`gmOmcMePS'^ A. . ¯. . . =<. ^. ³µ´
(186) ³µ¶.
(187)
(188)
(189) ! #"$%& '( " *)
(190) " #+,%- /.0,%1
(191) 2 3(" ' M . ¶¸M¹D · !. D D . . . D. . . !. u»N· J:i. . " " ?. ¶¸M¹D · . D. . #. D. . ¯. ?. . M. . " " ?. .
(192). . ¯. . " .
(193). . o. n'aº < N: j¼i. P. ± `\cMePJKok]u[¨e`bKMc/oiORck^2Y¥ °p'ht]nO e`bKNc ¦ R(ouSd^QKokS'^sokS uKN]uJv`\S'JX^d °p'['Jv`qmORcMey^PKM]k^(YO1² KMJQTS D. . . . ?.
(194). . M. #. . . o. .
(195). . ©<. q v
(196) x x \z . D q xz. K. v. ! ! qr | D? ~SdJQSae%o5 KMePS'c`bJXY¡ p'hj]iOZe`\KMc/ouSd^['KS¨¯C[a`bSdcMeP^ q v < D#"dw v H$ H { q v. q v. Kt l PSR!HTFVU Sae " YbS,QKok]YbSo§ ªOmQ~Yg`qfn[ZOZe`bKNc
(197) Om~u~iOmJvePS'ciORcMe X& «% w. D. D m h3{p . s m f H. DQP ? H bU:WXP ? H bU. F\H. ±_S['Jv`qeP¬'JSokS^erOR`gYq`gePp~KN]kJYOFJpd^¦KmYb]e`bKNccj]kQp'Jv`bht]uSSd^ÈeXp¨erORYg`_^P]kJYO#['KMcko`ge`\KMc^ePJv`b[aePSokS 2 KMc {S']kQCOmckc . *<. " v H$ {. Y dw. Y. (' w) v H {p* F. c. ± S'JJS']kJ(S'^eXokp'['KMQT~KM^Pp'S%S'c]kcuSy^¦KNQQSokSiOm]tePSd^ ² Jpdhj]kS'ck['S'^! SaesiOR^P^PS'^&² Jp'hj]kS'ck['Sd^+ -,£ xj]`gmORcNe(YbSe®¤~S%okSokp'JPOZ¯>cuSdQS'cMe(okS %YbS'^okKNQCOZ`\cuSd^. Sae/ -,^PKMcMe JS'~kJp'^PS'cMePp'^(^P]kJ&Y\S'^&fiLM]kJS'^ O#Saes±_SYg`\^¦^PS']kJokKm`ge'aePJSKN~e`bQ1`\^¦p%~KN]uJXO eePp'cj]kS'J(KN~te`\QCOZY\S'QS'cNe(ePKM]ePS'^YbSd^2iOm]tePSd^² Jp'hj]kS'ck['S'^ okSY¡ S'JJS']kJC~kJK MS'ciOmcMeok] Q>OZ`gYqYOmLMSfnc§XI KN]uJ CokKMckckpml&YO+okpaePS'JQ1`\cnO e`bKNc ok]:~iORJPOmQ¬aePJS. erORY\S OR]+ ,Sae% (^d °S §S'[aeP]k$S X1~iORJve`\Jok]~kJKMY\¬'QS[aYOR^P^`bhj]kSok]Q1`\c¥QCO 5§. ¦§. 5§.
(198). *<. "108w
(199) {. ^_^a`[bZc dec. D . 32 6 5 4 87: <9 ;= Y d" w v H H . {. Yc.
(200) . 0" %-J
(201)
(202) θl. θl. π. π. HAUTES. π. π 2. −π. HAUTES. 2. BASSES θk. π 2. −π 2. θk. −π. π. π. −π 2. −. −π. _`bLM]kJS. ¶¸M¹D ·. π 2. −π. §`\LM]kJS. O )
(203) " / 1.#
(204) "
(205) ! ) " Z # " %& J /" !)
(206) . )
(207) " / 1.0
(208) ! " !
(209) !) " Z # " +%-+ ! # E+ 7i*l . . !. BASSES. . u»N· J:i. . " " . . "5w v H H . {. DF?. ," . . o. . w F o. /" )
(210) . "10. ," . w. {
(211) o. . . I:w v {.
(212). c. /" )
(213) . "10. BuªUB BÄ BuVO0@ F R 8 BªUt Bu @ O F R B ª N U U Bu @@ F R BªUNU Bu @@ ©ORYbS "% " " 2 ) % #% #" " /
(214) ) #" 2 %& .# N ! # E+ *' )
(215) 1" +%-+ *%Z) 2 !. m B UB BuªUB B¢ Bª k Bu UM BªN Buª M
(216) m BB M BB
(217) m BB M BB. . V{. ¶¸M¹D · K. " " . P.
(218). B UB.
(219). n'aº < N: j¼i . " . "dw v H H . { D. ". "3 . ^. ³µ´
(220) ³µ¶.
(221)
(222)
(223) ! #"$%& '( " *)
(224) " #+,%- /.0,%1
(225) 2 3(" ' @. "3jDF? ". . DF?. . . x x o < . . { .x .x c o . <. { . o. w F o . w F o. " " )
(226) . "10. M M BB Buª M BB M BB M BB M BB. ," . " )
(227) . "10. BuªB m BB BªB BuªUU B UU BVOO FR M BuªU B U@ BVOi FR M . B B B U @ BVOi FR M BB B U@ BVOi © ORYbS+ "% " " 2 ) % #% #" " /
(228) ) #" 2 %& .# #! J! # E+ *' )
(229) 1" +%-+ % ) '
(230).
(231). _`bciO YbS'QSdcMeY\S+~nOmJPORQ¬¨ePJS´okS+JSaYO nO e`bKMc mOmJv`bSml~KM]kJ>Y\S'^okS'] QpaePkKokS'^H`gePp'JPO e`gNS'^dl ^P]`gmORcNeYO1mOZYbSd]uJsokS ¨ H #> 8 8 ,¹ :d·u¹ · , ±_S²¡Om[aePS']kJokSJp'ok]k[ae`\KMc "10 Sd^Èe%KM~e`\QF]kQ ~KN]uJ S¨eePS'ckoNS'J^ ok¬'^ht]uS ORck^ Y\S[ OR^sokS,QCOZ`qYgYOmLMS'^Xpae`\Jp'^dltYbS,okp'JPO ¯CckS'QS'cMes`b^PKmePJKM~SSd^Èe%QCO YORoiOR~ePpm IKM]kJXYbS'^sokS'] QpaePkKokS'^okS,JSaYO nO e`bKMc§luKNcO .
(232). .
(233) . !. . .
(234). . . $. DF. . . F. <. "10 @F3c R\R '. R!c \R. !. F. . H #> 8 8 ¹ 8 :'·k¹ · F IKM]kJ2ht]uS¨Yb['KNcuht]uS,oiORck^ ln'[ S'^sQpaePkKokS'^JSd^ÈePSdcMeokS,KNck^2Yq`b^P^PS']kJ^ ?
(235) paePkKokSokS NOR['KN`
(236) . . . .
(237). $. . U RHTFU. ¥<. . . ?
(238) paePkKokSokS.
(239) <. . Om]u^P^¦xNS¨`bokSaY. R!c. -- "10
(240) ORc ¥R. ¥<. "10
(241) ORc 0 R. R!c MF. c['KNcu[¨Yb]k^`bKMcYbS,QS¨`gYgY\S']kJ2²¡Om[aePS']kJsouS,Jp'ok]k[ae`\KMc~KM]kJXYbS'^%ouSd] Qp¨ePuKokS'^s`gePp'JPO e`gNS'^Sd^Èe%KM ePS'cj]Cht]nOmckoYbS^PS'Q«`g®oupdJPOZ¯CckS'QSdcMe(S'^e(]e`gYq`b^PpmkxM`nY\S['Ke(ok]ePJPORck^² S'Jve(S'^e(ckp'LmYg`bLNpmlZYO,['KNQ~Yb S t`qePp ORJv`qePkQpae`bht]uSH~KN]kJ]kc y¥[a¤u[aYbSO'NS'[]uc iOZYO'¤tORLN SokS NOR['KN`X^¦]kJ,[rnOmhj]kS ct`qMSZOR]Sd^Èe«okS ~iORJ ^PKMQQTSae#~KM]kJYbSCokp'JPO ¯CckS'QS'cNeF`\^¦KmePJKM~SCSae#ouS ~KM]kJY¡ ¢ORc`b^PKmePJKM~S
(242) U ¥ ORck^,['S[ Om^'l5YO[dKMQ1 ~YbS `gePpePKRerO YbSQ1`\ct`\QF]kQ"~KN]uJXokp'['JK qePJSY¡ S'JJS']kJso5 ]kcuS,okp'[ OmokS^¦]kJs]kcQCO `gYgYORLNS`b^PKRePJKN~SS'^esokS Uu BBF~iORJX^PKMQQTSaeS¨e^P]kJX]uc/QCOZ`qYgYORLMS² KNJvePS'QS'cNeOmct`\^PKRePJKM~SokSC OjUu . . . . ^_^a`[bZc dec.
(243) O. 0" %-J
(244)
(245) . .! 1H ! (
(246) > , « C X & §
(247) + ³cH^PS~uJKN~KN^¦SokSo`b^P['Jp¨e`b^PS'Js^¦]kJ YbS,^¤^eP¬'QS^P]`gmOmcMe . ¦ U paerOmcMeYOF² JKMcNe`b¬'JS,ok]okKMQ>OZ`bckS S¨e ]kcHMS'[¨ePS']kJ2j`qePS'^P^PSokS~kJKM~iOmLjOZe`\KMc§ . . . N. >. ^. +. /. . . B. . . . . &547$%#6M- 6M#-. -. . C. =<. cKwB { DF\H. ? ACB o B`YS[.D R. N. . . . . . &5-. ± OCQpaePkKokS]e`gYq`b^Pp'S~KM]kJo`b^P['Jpae`\^PS'JYbSd^pdhj]iOZe`bKNck^ ¦ U sS'^e,]uckSQTpaePkKouSTQ1` tePS«MKmYb]kQS'^ fic`b^1S¨epaY\p'QS'cMeP^#fict`\^d&±§S~kJKMY\¬'QS['KMcNe`bcj] ¦ U S'^eOm~k~uJK[rkp~nOmJF]kc ~uJKNYb¬'QSHo`b^P['JSae«S'c ]e`gYq`b^rORcMesYO#² KMJQ#]tYOZe`\KMcmOmJv`O e`bKMckckSaYqYbS^P]`gmORcNePS nKMc[rkS'J[ruS (ePSaYhj]kS . B. ©<. «w
(248). w}B
(249) H
(250) { D u. K. . w}B=H
(251) { Dw ? u. Sae. b BML {. .w
(252). r. BgI
(253). . . w2N {. . ©<. 2w N {. cTwB { {
(254) k l. ACB o. ±
(255) k l c. { D. _± SokKMQCO `bckS,o5 paeP]kokS S'^eOm~u~kJK[rkp~nOmJokS'^%~KmYg¤LNKMckS'^du±O1o`b^P['Jp¨e`b^rOZe`\KMc^P~iOZe`OZY\SJS'~KN^¦S^P]kJ ]kckSyePJv`ORckLM]YOZe`bKNc Fok]/ouKNQCOZ`\ckS N. N §. V§.
(256). N § D. z H z !. z*" V§ D@ª. x HX|©DF3HK¡T¡K¡ H e r. ®. c. ³cOm^P^¦K[¨`bSX #]uckS,~iORJve`qe`bKMcHok]iOZYbSMln['KMck^e`geP]kp'SokS,['SaYqYb]YbS'^sokS,['KMcMePJ mYbS NKR`\JfiLM]kJS$@ N §. M<. #. N § D. %x c x$ b. I KM^PKMck^ MlZY¥ °S'^P~iOR[dS2okS'^ ² KMck[ae`\KMck^ `\ck[aYb]kS'^ oiORck^ P5xjKR`geXYO1^P]t`qePS ['KNcu^e`qeP]nOmcMe%]uckS,iOR^PSokSY¡ S'^P~nOm['S · m ¼ ¹:· 8 I : ¹:· 8J8 j¼¼ 1 © JKM]NS'J ePS¨Yhj]kS~KM]kJXePKM]k^ KNc
(257) OZ`qe. ¦ Z = = &. § D ª%
(258) w#N §3{.
(259). . e. r. | e B. B.
(260) . . q. H | e }| L L u q u q ª%
(261) x® x. .
(262) x:. w ?. Vq u. B
(263) H.
(264) ]Y [.D]R ®. r ¬. §. . §. '. L. ACB. o(. §. =<. cKwB { {
(265) x k l D. '.
(266) x k l c. ^. ³µ´
(267) ³µ¶.
(268)
(269)
(270) ! #"$%& '( " *)
(271) " #+,%- /.0,%1
(272) 2 3(" ' . jx Km`ge Y\S^P]u~k~KMJve,okS1YO² KMck[ae`\KMc
(273) ePS'^ePS ® ±OC² KMJQ#]tYOZe`\KMc+Q1` ePSC^¦S«ePJPORok]`ge#~iORJYbST[£kKR` okS'^X² KMck[ae`bKNck^2ePS'^ePS'^ ^P]`gmOmcMesYbS'^sePS'JQS'^s`bcMePp'LNJp'^ IKM]kJY\SFePS'JQTSokS1o/` §]u^`\KMc§lKMc ]e`gYq`b^PS1]kckS1² KMJQ#]YO e`bKMc@paYbp'QTS'cMeP^fict`\^dlokKMcNeYOC² KMck[ae`\KMc ePSd^ÈePSSd^Èe%]kckSy² KNck[ae`bKNcokSiOR^PS 2ok]^PKMQTQSae 8x.
(274) x.
(275) x. . =<. !. . u x«<. .
(276) x D !. . x H. 8x D . H. . 7. I KM]kJYbSXePS'JQSso§ ªORoNS'[ae`\KMc1S¨e&YbS(ePS'JQTSok]1^PS'[dKMcko1QSdQFkJSmlMKMc«]e`gYg`\^PS]kckS(² KMJQ#]tYOZe`\KMcFNKR Y\]kQS'^fic`b^dlRokKMcNeYO² KMck[ae`bKNcFePS'^eS'^eYO² KMck[ae`\KMc1[ZORJPOR[¨ePp'Jv`b^e`bht]uSXokS(YO['S¨YgYb]Y\S2okSX['KNcMePJ RY\S w © x}{.
(277) x D. ± °p'ht]nO e`bKNc (^d °p'['Jv`qeO YbKNJ^ w F. {. . ?. . . ACB.
(278)
(279). . x k l²o. cKw B {. . . . . . . )7. H. 8x D. %x. c.
(280) <. &c/]te`qYg`\^£OmcMesY¡ `\cMePp'LNJPOZe`bKNcokS JS'S'c§luY¡ p'hj]iOZe`\KMc ?. ©<. z# 7. |}L u. w q. . { B z . x . z c. "$#&%( ' )*#,+`. w © x { k l D w %x { . ¥B S'^eyOR~k~kJK[£kp'S~iOmJV< $- . B c ? / e z7 v x 2 "$354678#,+` . o. !. . 10. xSz . D. !. u. k l c. | L q. w %xµ{. ¥B . ¥k . K NKR`bJsfiLM]kJS,U Y¥ °S'ck^PS'Q#YbS,okS'^^PKNQQSaeP^XMKm`b^`bck^%ou]HckKS']ko vl <;. :9 l / / / S'^eYO1ckKMJQCO YbSS ePp'Jv`bS']kJ1 S X 0 ±_S(ePS'JQS%ORoMSd[ae`g²§O'MS'[ ['KNck^ÈerOmcMeonOmck^ ePKN]teYbSXokKMQCO `bckS s^d °S k~uJv`\QSs^¦KN]k^ YO² KMJQSX^P]`gmORcNePS M<. w}| {. . ! !. a ©xSz D. u x. !. ?. e xSz D. ?. a %x. eC7o. ?. a z DQP ¦# xSz H Sx z U ¤P x z H ¦ e. xSz U. . . . $- . . K. . B. /. ©xSz. =0. >. %c ? e xSz ²D. > . . . . x z. /. $- . D. ). F. B x o. w F?. xSz {Co. F { c. . xSzK{. ©<. B z{. 10. c ? e xSz . . xSz D. xSz. xSz w. N §. )" ?>. wIK| e w. _`bciO YbS'QSdcMe~KN]uJ CSae okKMckckp'^dl KMcKNe`bS'cMeH]kc:^¤^eP¬'QS
(281) QCO ePJv`b[a`\SaYokKNcMeCYO QCOZePJv`\['S
(282) S'^e ePJv`bo`ORLMKNciOZYbSM ±_S'^CQp¨ePuKokS'^Y\S'^~Yb]k^C[aYOm^P^È`\hj]kS'^C~KN]kJCJp'^PKM]kokJS['Se®¤~S@ouS@^Ȥu^ÈeP¬dQS
(283) ^PKMcMeTYbS'^ QpaePkKokS'^o`\JS'[aePS'^ePSaYqYbS«hj]kS1YOCQpaePkKokS1okS yOm]k^¦^ySaeYbSd^QpaePkKokS'^`gePpdJPOZe`gNS'^d_&cLMp'ckp'JPO YYbS'^ p'hj]iO e`bKMck^,hj]kSCY¡ KMc+Jp'^PKM]e#^PKMcMe#['KNQ~YbS uSd.^ Æpdhj]iOZe`bKNck^FokS{O'j`\S'JvxMePKNµRS'^ P Omck^[dS[ OR^dl_^¦Sd]tY\S YbSd^Qp¨ePuKokS'^X`gePpdJPOZe`gNS'^~S']MSdcMe ¨ePJS]e`qYg`b^Pp'Sd^' . . . . ^_^a`[bZc dec.
(284) U. 0" %-J
(285)
(286) ¦ . xSz. . /e. ?. . xSz ? e |. ~. /. ¦# xSz. §`\LM]kJS#U . . +. /. " (" + " , !
(287) ' . . &547$%#6M- 6M#-+ 68 +!+.76M-+. -. ± paYOmKMJPO e`bKNco5 ]kc^P[rupdQCOcj]kQp'Jv`\hj]kSml^P]kJF]kckSCLMJv`qYgYbSCLNJKM^P^`b¬'JSMl§JS'~KM^PS^P]kJ]kckSOR~k~kJK t`g QCO e`bKMcH~iORJXYO1QTpaePkKouS,okSe¥¤u~S yO YbS'JµN`bc§ ³c:['KNcu^`\ou¬dJS YOLNJv`gYqYbS
(288) ok] ct`qMSZOR] okKMcNe>Y\S
(289) JS'['KN]JS'QS'cNeS'^e['KNck^Èe`qeP]kpouS@['SaYgY\]YbS'^ ORLNLRY\KMQp'JpdS'^okSYO#LMJv`qYgYbS%fnckS u±_S^¤^eP¬'QS%Yg`bckp O `bJSokSY¥ °p'ht]nO e`bKNc ¦ &^¦]kJYOFLMJv`qYgY\S ^d °p'['Jv`qe. ¥N ± °S'ck^PS'Q#YbSokS'^`\ckot`\['S'^ okS'^ ['SaYqYb]YbS'^%^P]uJ S'^escuKmePp . . ¦ v. ¦. ]s. . ¦ v. ¯ v B v D. |. ± v c. ¦ v. je v. =<. ©<. v D@ª«F\HK¡K¡K¡ H| HK¡T¡K¡H e ® c v. . ³ c,oup¨fnc`qe YO2^P]`gePS ouSd^ ^PKN]u^®S'ck^PS'QFY\S'^5['KNcMePS'ciORcMeY\S'^_cj]kQp'JKN^ okS'^['S¨YgYb]Y\S'^S'QFKR`qePp'S'^ okSYO1LNJv`gYgY\S ~KM]kJ(YO['KNck^ÈePJ]k[ae`\KMcHokSyYO1LMJv`qYgY\SLNJKM^P^`b¬'JS luePS¨YgYbS,hj]kS <9
(290) w xµ{ $x b ¦ v. ¦ v. . v D. . ;. . . ;. 1;. Z¡K¡K¡ je v . . H. . e v . . e v c. SQ.'QTSmluY¡ S'ck^¦SdQFYbS,okS'^X`bcko`b['Sd^ okS'^ 2['SaYqYb]YbSd^okSYO1LNJv`gYqYbS,LMJKN^¦^`\¬'JS |. ±O1['SaYqYb]YbSokSYO«LMJv`gYqYbS A%`bck^`¡ljouSd]. . b ¦ v. x. b ¦ v. z.
(291) @w}| D ~ {. D. S'^e.
(292) <. v D@ª«F\HK¡K¡K¡ H| HK¡T¡K¡H e ® c v. S'^eO YbKNJ^okpafic`bS,~iORJ. g<. xv. D. . 7 z. zv c. KM~kp'JPOZePSd]uJ^(okSePJPOmck^Ȳ SdJveX~S']NS'cMe'aePJSokpaePS'JQ«`bckp' ^ Y¥ °KM~kp'JPO ePS']kJ(okSJS'^ePJv`b[ae`\KMc ~KN]kJ2Y\SyePJPOmck^Ȳ SdJveok]Jpd^È`\ok]okSYO1LNJv`gYgY\S XFYOLMJv`qYgYbS Sae Y¥ °KM~kp'JPO ePS']kJokS,~kJKRY\KMckLMS'QTS'cMe ~KN]kJFY¡ `bcMePSdJ~KRYOZe`\KMcokS>YO^¦KmYb]e`bKNc okS MS'J^ (W(S'^KN~updJPOZePS']kJ^^PKMcNeCORo wKm`bcMeP^1Y¥ °]kcokS Y¡ ¢OR]ePJSm . ¦ v `¦ v. ¦ v. ¦ v. =<. ^. ³µ´
(293) ³µ¶.
(294)
(295)
(296) ! #"$%& '( " *)
(297) " #+,%- /.0,%1
(298) 2 3(" ' . ±OFokpafic`ge`\KMcokSY¥ °KM~kp'JPO ePS']kJo§ `bc wS'[ae`\KMcHcnO eP]kJSaYgY\S S'^esokp'ok]`gePSok]okp'JPO ¯CckS'QS'cMe%okS ~nOmJ ¦ v. D@w xSzK{ x z HX| . O'MSd[. >. . F. xSz D. v b. IV| ~ I | e
Documents relatifs
Chez l’Homme, les segments de gène V H ont été classés en sept familles (la famille 7 n’est pas représentée ici car aucun segment fonctionnel n’y a été décrit) qui ont
Le Négus consacra une énergie considérable en vue de gagner cet appui international, mais, malgré la force de son discours prononcé en juin 1936 devant ses pairs à la tribune de la
In this paper, we propose a novel approach based on the barycentric coordinates of automatically tracked 2D facial landmarks from videos to objectively evaluate the facial
Dirk Obbink (dir.), Doctrine and Doxography. Studies on Heraclitus and Pythagoras, Berlin / Boston, De Gruyter, 2013, p.. et le logos auquel les hommes devraient accorder
Les exorcismes ne sont pas publics, les sœurs noires elles-mêmes sont tenues le plus possible à l’écart, et c’est chaque fois Jeanne qui force les choses pour que, finalement,
Toute- fois, d’autres marqueurs des cellules POMC tels que NeuroD1 n’ont pas été induits dans cette expérience, ce qui indique que Tpit suffit in vivo pour provoquer la
Mais elle y occupait une place modeste : il faudra la liberté et le goût de la transgression du roman en langue vulgaire pour que la situation soit renversée :
Les thèmes majeurs (tab.5.4) abordés par les îliens interrogés sont, pour la grande majorité, les mêmes sur toutes les îles : ils concernent les usages anciens
