B-splines pour l'optimisation de forme
Texte intégral
(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. B-splines pour l’optimisation de forme Mehmet Celikbas. N° 4968 Octobre 2003. ISSN 0249-6399. ISRN INRIA/RR--4968--FR. THÈME 2. apport de recherche.
(3)
(4)
(5)
(6)
(7) ! "# %$ '&()* -+ ,/.102,/34#,6587:9<;=> ?A@CDFB E#DHGJILKNDFM OQPRD!SRTU/PRV
(8) PWD S D XbdV
(9) c Y(SZV
(10) [\S<]^QE`_TSRPZa6[\D T(efD
(11) XK!ghgigij k YlmlmT c AX nQD c D V @ D c V @ DoOp q/r/st#ILu!V
(12) XT6_ c DvG(w/wxJIyxx#l\YUD ]. |z }{ ~F }|{ D c YlmlmT c X`n D M V c PRXJE#T/OX c YY(PRSnQD]XYUDn\T/O6XJS T6_efD V
(13) XPWD
(14) M XYPWX`S: PRElQS
(15) DFM EDFO6XY(XPWT6O n< [\O\c DH_\PR_QSRPRTX @CD B c a[QD!][ c c SRD ]V
(16) T/[ c _mDF] c D
(17) X][ c 8YV
(18) D ] ]lQSRPRO\D ] c D
(19) XSB [QXPWSRPZ]YXPRT/On\DHV
(20) D
(21) XXDv_QPZ_QSWPRTX @Cc DFB a6[\D lT/[ EYOQPZl\[QSRD SRD ]V"T/[ _D ]<a[QPPRO6XD PRD O\O\D O6X<n\YOm]<nQD ]l T6_QS D E#D ]Cn< T6lQXPZE#PR]Y(XPWT6OUD
(22) M T6E2D
(23) M X PZa[QD m { c c b c c YE«D M ~"X c PR] Y(}X~¡PWT6OC£6T/lQT6X[ PRE#_PZD ]]`YXD
(24) PRT/X`O][ UD M 8T/YE2V
(25) D D
(26) M]vX c PZa¢][QlQD SRPZOQD£ A¤v¤ £¥/¦§!g ¥¨£Y/l\l T©QPREY(XPWT6Oª ¢]l\SWPZOQD£l\Y. ¬C1®:¯°f±²°³µ´Q°f¶ ® ¶ ¯ ¶ °´µ³µ· 1¶ ¸°¹·´µº°¸¯¸´»°¬¼1½¼1¾¿ÀÁ²¯ÂA. 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.
(27) 1
(28) '&(`J '
(29) "!1 "# ~ ?A@ PZ] c D lT c X2nQD ]V c PR_D ]2X @ D T c
(30) nQT6OQD n\[ c PZOQUEJ^oPRO6XD c O\] @ PRl PZO X @ D-l c TefD V
(31) X K!gih ggj# ?A@ DA@ ][m_c efD V
(32) X Y/] X @ DPREc lQSRD E#DFO/XY(XPWT6O`T¨YH@ E#Tnm[QSWD T c d¢]lQSWPZOQDc V
(33) [ c DF]1YO\n#][ c 8Y/V"D ] Y/O\nPWX][\]D!PZO X DvX DFY(XEDFO6XAT(V [ D ] £QPZO//TSRDFn PZO ] Y/lmDHT/l\XPZEPZ]Y(XPRT/O l T/_QSRD E] }
(34) ~ ¢]lQSRPZOQDV
(35) [ c /DYO\nv][ c 8YV
(36) D£ A¤v¤ £¥6¦§g b ¥¨£Y/l\l c T©PZEY(XPWT6OC£ l\Y c Y/E#D
(37) XD c PZ]Y(XPRT/O<£ ] @ Y/lmDHT/l\XPZEPZ]Y(XPRT/O.
(38)
(39) !!" $#
(40) &%'(
(41). *" ) . x. $ !1 , + -/. }~} ~ 10 /}~32v~54 76!8 }~ 9 : :<; O6X c TQn\[\V
(42) XPRT/OvvHvHvHvvHv!vHvvHvHvHvv!vHvHvvHvHv!v q : G>=T/O\V
(43) XPRT/O\]An\DJ_\Y]D ]AnQDF] ]lQSRPROQDF] vHvvHvHvHvv!vHvHvvHvHv!v q : G\ : jND M ?OQPRXPRT/OvHvHvvHv!vHvvHvHvHvv!vHvHvvHvHv!v q : G\ G bdc T/l c P"D
(44) M XQD M ] vHvHvvHv!vHvvHvHvHvv!vHvHvvHvHv!v @ : G\ x @ TPW©n\[ DFV"XD [ c OQTQn\YS!vHvvHvHvHvv!vHvHvvHvHv!v @ : G\ q A)©QD ElQSRD ]vHvHvvHv!vHvvHvHvHvv!vHvHvvHvHv!v @ : x T6[ c _mDF]d¢]lQSWPZOQDF] HvHvvHv!vHvvHvHvHvv!vHvHvvHvHv!v s : xm : jND M ?OQPRXPRT/OvHvHvvHv!vHvvHvHvHvv!vHvHvvHvHv!v s : xm G bdc T/l c P"D
(45) M XQD M ] vHvHvvHv!vHvvHvHvHvv!vHvHvvHvHv!v B : xm x A)©QD ElQSRD ]vHvHvvHv!vHvvHvHvHvv!vHvHvvHvHv!v t : xm q gSRUT c PRX @ E#D ]An\DH_mY]D ]A][ c SWDF]V"T6[ c _mDF]d ¢]l\SWPZOQD ] vHvHvvHvHv!v t : q ¥Q[ c 8Y/V"DF]d¢]lQSWPZOQDF] HvHvvHv!vHvvHvHvHvv!vHvHvvHvHv!v : s : q : jND M ?OQPRXPRT/OvHvHvvHv!vHvvHvHvHvv!vHvHvvHvHv!v : s : q G bdc T/l c P"D
(46) M XQD M ] vHvHvvHv!vHvvHvHvHvv!vHvHvvHvHv!v : s : q x A)©QD ElQSRDHvHvHvvHv!vHvvHvHvHvv!vHvHvvHvHv!v : B : q q gSRUT c PRX @ E#D ]An\DH_mY]D ]A][ c SWDF]][ c 8Y/V"DF]d ¢]l\SWPZOQD ] vHvHvvHvHv!v : B CED F CHG 4 }Q{ } 8 Q 6 8 G\ :<; O6XQD M c D
(47) I Xb n\[ A¤v¤ HvHvHvvHv!vHvvHvHvHvv!vHvHvvHvHv!v Gw: G\ G ¥6¦§: g bd¥ c !vvHvHvHvvHv!vHvvHvHvHvv!vHvHvvHvHv!v G : G\ G\ c D M ]@ D O6XYXPRT/c O vHvvHb v!vHvvHvHvHvv!vHvHvvHvHv!v G : G\ G\ G g V PWXD V
(48) X[ DvnQD¥/¦§!g ¥*vHvvHvHvHvv!vHvHvvHvHv!v G G\ x JNPR]Dv: D OTD [Q c D HvLc HKMv H v
(49) 1vN N OHvPQ!
(50) vHvvHvHvHvv!vHvHvvHvHv!v G/G G\ xm hDvV"T6O/XD OQDF[ Lc KM
(51) 1N NR7%' OS
(52) HvvHvHvHvv!vHvHvvHvHv!v G/G G\ xm G hDvV"T6O/XD OQDF[ vvHvHvHvv!vHvHvvHvHv!v G/G G\ xm x A)©QD ElQSRD ]AnC [QXPWSRPR]Y(XPWT6O v!vHvvHvHvHvv!vHvHvvHvHv!v Gx T 4U4 76 Q 6 8W V YX 4 6:F6 ~ \ 6 8[Z } { } { 67\< } CH] b c : xm D M ]D O6XYXPRT/O vvHvHB vHvvHv!vHvvHvHc vHvcv!vHvHvvHvHvc !v Gs xm G u!l\XPZEPZ]Y(c`XPR_:T/k OV"T6[\lQS"D
(53) M D Y[\OQDYn\Y/lQXYXPRT/OJn\DdSZYil\Y Y/E2D
(54) M X PZ]YXPRT/OHYDFV)nQDF]V
(55) T/[ _D ] n\DvD M ^
(56) PRD Yl\lD
(57) SZ] a vHvvHv!vHvvHvHvHvv!vHvHvvHvHv!v Gs xm x gn\Yl\XY(XPWT6OnQDHSRY l\Y c Y/B E2D
(58) M X c PZ]YXPRT/O Y/D V!nQD ]V
(59) T/[ c c _D ] c ]lQSRPRO\D ] vvHvHvc !v G,B xm q u!l\XPZEPZ]Y(XPRT/OV"T6[\lQS"D
(60) M D Y[\OQDYn\Y/lQXYXPRT/OJn\DdSZYil\Y Y/E2D
(61) M X PZ]YXPRT/OHYDFV)nQDF]V
(62) T/[ _D ] ¢]l\: SWPZOQD v!vvHvHvHc vvB c Hv!vHvvHvHvHvv!vHvHvvHvHv!v Gr xm q ku!lQXPZE#PR]Y(XPWT6On\[V PRX D cD b vHvvHvHvHvv!vHvHvvHvHv!v Gr xm q G D M ][QSRXYX] vHvHvvHv!vHvvHvHvHvv!vHvHvvHvHv!vx/w. ¾ ¾ ¹de'fgh.
(63) q.
(64) 5 "K # * i & A
(65) .
(66) . A O gJ»u _ T/OmV"D l\XPRT/Ogi]]PR]XQD M D!lmY c u c nQPZO\Y(XD [ c aSWDF]AT/_efD X][\XPRSWPZ]QD M ]A]T/O6X]T6[QDFO6Xn\D ]lT( SR^QO T/I E#DF]!V"T/c [ cc _D ]lmT/SW^QOQT6E#PRYSWDF]D X1][ c 8YV
(67) D ]@lmT/SW^QOQT6EPZY(SRD ]#"E#YX @ D M EY(XPRa[Qc DFEDFO6X
(68) £V"D B ]1lTSR^QO T/I E#c D ] n\Tc PRD O6X] fDFM V P DdnmYc O\][\O\D_mY]cDn\T/O\O D
(69) M Dh DV TPW©`c nQDV"D XXD_\Y]DD ]XPZElmT XYO6X1c PR] Y(PZ]1nQD ]c l _ T( l P"D
(70) M XQD M ]An\DV"DF]iV
(71) T/[ _mDF]T6[N][ 8Y/V"D ] H A O%D $ D
(72) X £ l DFOQT/O\]S: D"©QD ElQSRDn< [\O\DV"T6[ _mD#nQD`5D M ^
(73) PRD P D DFM V c PWXDvn\YO\]SZY_\Y]DvnQDvD c O\]XD
(74) PZO a. . . & _(' a*),- . + _3' a & /!021 + T [B . . . .=<?>*@ <BA . _3' a4)65 ' _ :87 ' a ; & ; ' w ; :%C + : + 9 giPRO\]P & _3' a D ]XV
(75) T/O\]XPRX1 [ D
(76) M D nC [mOQD + ]D [\SWD c V"IGT/[ c _DdlTSR^QOQT/E#PZY(SRDd]P6_Qc PRD Oa[QD &c _(' a Y[\OQDV"T6O/XPRO[QPRXQD M n\D V
(77) SRY/]]D=DFEjHYO\]1V"c DF]1V"T/OmnQPWXPWT6O\] £ PRS\l\Y Y Xn\c PIH V"PRSRDn\D E#TQn D M SWPZ]D n\D ]1V"T6[ _D ]Y^/0Y/O6X nQDF]lTPZO6X] Y/OQU/[\SWDF[©PRD6nQD ]dV"T/[ _D ])n\T/O6X)[\OT/[ l\SR[\]PRD [ ])lTPZO/X]OC T/O6Xa[C [\OQDV"T/O6XPRO[QPRXQDJM D /§iT6[\]YSWSRT/O\]. /TP cc n\Y/O\]<SZYcv]B[QPWXDda[Qc D)S PRB O6X c TQn\[\V
(78) XPRT/OJnQDSRY_\Y]DnQDF]< ]lQSRPRO\D ] _ D OJY/OQUSZY(PZ]C n\D D E«DFM nQPRD YV"DJl T/_QS DFED/
(79) LK M NBOQPR4NSOFNT8OFNTUWV2NXZY[[O\N -]C^]!- _ }{ ` 8 6 6 8 u!On DM ?OQPRXSWDF] T/O\V
(80) XPRT/O\]n\DH_mY]D ]AnQDvSZY. 8YV"a T6O][QPRYO6XD= c nQDfe ¤ : c D M D
(81) SZ. ]Jg OQT6On D M V c T/PR]]Y/O6X]g 0h b l\Y c [mODFO\]D E`_\SWDdo c D ]XY/l\lD
(82) S"DHM D V
(83) XDF[ c OQTQn\Y(S£QSRD ]pg ]T6O/XAY/l\lmD S"D M ]AOQTD [mn\]
(84) b l\Y c [mO n\D
(85) U c DfM mq hc YP cD Bc E#D T/OmV"XPRT/O nQDN_\Y/]DF] ]lQSRPROQDF] nQDNnQD U c D?M q _ T/[ nC T c n c Drq ¤ DFM V
(86) [ DFO\V"Ds <BA . .k A . : # g ;g i tu0 _ Ug av) w4x y2z|{ y2zk}~. x) w # L ^ 2 k . . . 7 t _ Ug av) g .kg 7 g g . t i _ g a ¤ g .kg i i7 7 g .g i t 9 . Q ¢]lQSWPZOQDF]'a. lmD c E#D
(87) X. g^i h6jkjljmh gon` : aJDF]X. YSWT c ] n D'M ?OQPRDl\Y c. .k i i _ Ug a 9. _:a. ¾ .
(88)
(89) !!" $#
(90) &%'(
(91) @. } { } { ~ A . .k b t . _ gUa)D ]XA[\OlmT/SW^QO T6I EDvnQDJn\D
(92) U c DfM q Y B ][ml\lmT c XAV
(93) T/El\YV
(94) X
(95) £\nQDJ][\l\lT c X g ; g i C b t _ gUaYlmT6[ c n D M c PRD
(96) M Ds . i . . t . i _ . t i _ gUa . . q t _ gUas) q ga 7 _G a 9 qg g 7 g g i9 7 g i . b ¥6PS T/O c D U c T/[\lDHSWDF]OQTD [mn\8] g l\Y c l\Ya[QD X]nQD`YSWDF[ c ]PR nQDFO6XPZa6[\D ] i jljkj Q£. V @ Y/a6[\D
(97) D M XYO6X c DFM ldD
(98) M XQD
(99) M D e A TPZ]dn\Y/O\]dSWD/D V
(100) XD [ c OQTQn\Y!S c Y/D V - e ) e ¤ : 6giSWT c ] t _ gUa DFO V @ Ya[QDJlTPZO6X D ]XV"T6O6XPZO6[\DJnQD`V"SZY]]D D 9 n D V"P Y lm/!T60 [ c V
(101) T/O\]QD M a[QDFO\V"DHa[C Y[QU6EDFO6XD c SRY E[QSRXPZlQSWPZV"PRXQZD M e nC [mO O\T6DF[\nC£mn\PRE#PZO6[\D!SZY V"T6O6XPZO6[\PWXQDM DFOV"DvlmT/PRO6X b ¥6P<S T6O/c D [QXn 'D M : ?O\P c c ¤ : T/OmV"XPRc T/Om]Ac nQDv_\Y]D ]Ac nQDvnQD U c fD M q YB l\Y c XP c nC [mO/D V
(102) XD [ c OQTQn\Y(S<nQD SWT6OQU/[\D [ e ¤ Y(SRT ] nQT/PWXAdD M RP ?mD SZYV"T/O6X YPRO6XD! T6O\n\YE#DFO/XY(SRDv][QPRYO6X4D _ x a e ) ¤ q ¤ : A AdO D $¨D X
(103) £iSZY nQD c OQP D B c D ]lQSRPRO\D t _ gUaY lmT6[ c ][\l\lT c X g ; g i C £V
(104) T/EE#D«V( D ]XSRY nQD c OQP DB c D!d¢]lQSWPZOQD/£:g inQTPRX D
(105) I X c c + DªD M U/Y(SRDHY[ nQD c OQPRD c c OQTD [mn + : gonJ+ gPZO\]P:£ ]P S: T/On\ PR]lmT6: ]+DnC [mODFV"XDF[ OQTQn\YS nQD` SWT6OQU/[QDF[ 7 e 7 ¤ : D
(106) Xin< [\OªnQD
(107) U c D M q Y(SRT c ]APRS^ YD"©\YV
(108) XDFEDFO6X ¤ T6O\V"XPWT6O\]AnQDJ_\Y/]DF]AYDFV ) e q -]C^] T . 6 } }Q 8 h DV @ Tc PW©ªn\[i D V
(109) XDF[ c c OQTQn\Y(SDF]XHI V"T6O\nQPRXPRT/O\O D#M l\Y c xD Xvl\Y c SRD#8Y(PRXHa[C PRS)nQTPRX D
(110) I X c DV c TPZ]]YO6X jHYOm]SRYl Y(XPRa[QD £\T6Ol DFO\nlQSR[\X T\X _ q a g 0 ) jkjkj ) g g i jkjlj g i g ) jkjkj ) g i + P DvT6O c DFM l D
(111) B XZD q ¤ : TPZ]ASRD ]Y(SRD [ c ]D
(112) ©X c D I E#D ] +9 + -]C^] 9 <}QF 4 }~ b c DFOQT/O\]SRDvDFV"XD [ c OQTQn\Y!S g 0 )6g i ) g @ ) g) w ; g) : ; g)-G ; g) g) g) g!)|x D XAV"T/Om]X c [QPZ]T/O\] SRD ] T/OmV"XPRb T/Om]c nQDv_\Y]D c ]An\DHn\D
(113) U c D!M x\£QT/OYnQT6O\V ) e 7 q 7 : c ) r 7 x :7 : ) @Q£ P Ds` T/O\V
(114) XPRT/O\] nQD_mY]D ] T6[ T6_QXDFOQP V"DF]) T6O\V"XPWT6O\]nQD_mY]D ]dT/O Y/l\lQSRPRa[QDSRY D SRYXPRT/O £6V
(115) D!a[QP O\T/[\]AnQT6O\OQDHSRD ] T6O\V"XPWT6O\]A][\PWYO6XD #] · &(´ %·´µÁ²³µ)¹ &$Á %F+¯ *,%Á²³ # "$# $Á %·±"f¯:¯Á²¹' -]C^]C. .. ¾ ¾ ¹de'fgh. 4 6.
(116) s.
(117) 5 "K . 1. 0.9. N35. N30 0.8. 0.7 N31. 0.6. N32. N34. N33. 0.5. 0.4. 0.3. 0.2. 0.1. 0. 0. 0.5. 1. 1.5. : b O! HL#
(118) K
(119)
(120) LPQ
(121) SO5M
(122) 1# .
(123) 8P OFNTUWV2NXZY[[O\N -] T\]!- _ }{ ` 8 6 6 8
(124). A. 2. 2.5. 3. w ;w ;w ;w ;: ;G ;x ;x ;x ;x C. OQDJV"T6[ c _D!d¢]lQSWPZOQDvnQDvnQD U c DM q _ /T [ nC T c n c DZq ¤ : aDF]XSZY#V
(125) T/[ c _D!l\Y c Y/E2D
(126) M X c D M Din DM ?OQPRD!lmY c. .4<r>. . . . & _ g as) + t _ g a & /!0. _@ a. . T [ B & b c £ _ q c )-c GT/[rq )|xc a TcQ6I [ V"T/Om]X [QP D[\. OQDvV
(127) T/[ _mD!c ]lQSRPRO\: DHn\DHn\D
(128) U c DM B q YB l\Y c XP c Qn D : ¤ : lc TPZO6X] & nQPRXlTPZO6Xc ]AnQD V
(129) T/O6X TSRD£mPWS 8Y[QX!nQT/OmVJ]D#nQT/OmOQD e ¤ OQTDF[\n\]T [re ) ¤ q ¤ £lD E#D
(130) XXYO6X!nQDn D'M ?OQP SRD ] T6O\V"XPWT6O\]AnQDJ_\Y/]DF] t _ gUa. ¾ .
(131)
(132) !!" $#
(133) &%'(
(134) -] T\]C. b b b. b b. b. B. } { A }{ ~ @ c Ya@[QD & _ g c ; g i C aCn c DM ?OQ&PRD_ [\O`Y c VnQD V
(135) T/[ c _Ddn D M SWPZE#PWXQD)M l\c Y c SRD ]lmT/PRO6X] & _ g a¨D
(136) X & _ g i a ¥[ V Ya[QDvY Vn\DJV"T/[ _D gUa1DF]XlTSR^QOQT/E#PZY(SRDvnQDJnQD
(137) U DM q AdO[\OlTPZO68 X gªnQPZ]XPROmV"Xi& nC_ [\OOQTDF[\nC£ & _ g a)DF] XnQnD`V"SZY]]DDFE _ lmT/SW^QO T6I ED aD
(138) XADFO[\OOQTD [mn g nQDJE[QSWXPRl\SWPZV"PRXQ D M e 6£ g a)DF]XAnQDJV
(139) SRY/]]DD 9 jND M c PWdD M D!nC [\OQDJV
(140) T/[ c _D! ¢]l\SWPZOQ4D . i . . i t _ s a &_ gUa*) q +:-. 9 g . i9 i 7 _ gUg a . i _(& i 7 & a /!0 h Yn D M c PRD
(141) M D!nC [\OQDJV"T6[ c _mDH ]lQSRPRO\DvD ]Xn\T/O\VHY[m]]P<[\OQDJV
(142) T/[ c _mDH ¢]lQSRPZOQD b T/[ c [\?O gNnQT6O\O D/M £ & _ gUaYl\lmY c XPRD O6X YB S D O6D SWT6l\lmDvV
(143) T/O6D
(144) ©DHnQ< DF]AA lmT/PRO6X ] & 0 ; jkjlj ; & T/ElQXDXD O[ nQD ] ][\l\lT c X] n\D ]# T/OmV"XPRT/Om] nQD_\Y]D ] £]P g g ; g i C YSWT c ]+ SRD ] ]D [QSRD ] T/O\V
(145) XPRT/O\]inQDv_\Y]D ]AOQT6OO[QSRSRD ]]T/O6X t £<WRR£ t Qj!T/O\=V < A .9 .. . & _ gUas) tW _ g a & ; lT/[ c g g ; g i C / D
(146) X & _ g aY/l\l\Y c XPRD O6X Y#B S: D O6/D
(147) SRT/l\lDv9 V"T/O6/D"©QD!n\D ]AlTPZO/X] & ; jljkj ; & j b T/[ c Y/]][ c D c SZYvV"T G O\V
(148) PRn\D O\V
(149) Dn\DASRYvV
(150) T/[ c _mDAY/D V SWDF])lTPZO/X])nQ9 DV
(151) T/O6X Qc TI SRDD"©QX c D I E#DF]
(152) £T/Ol c D Omn SWDv/D V
(153) XD [ c OQTQn\Y(S<][QPRY/O6^X 4 6. g 0 ) kj jlj ) g g i jljkj g i g ) jkjlj ) g i . +:9 + + : # AdOvD $¨D X
(154) £T/O`YiY(SRT c ] t _ g 0 as) w #L^) 2 w nQT/ O\V & _ g 0 a*)|wD X & _ g 0 as) y }~ y ~ (_ & i 7 & 0 a "nQDJE D I E#DHlmT6[ c8& _ g i5as) & D
(155) X & _ g iQas) y } y _(& 7 & iQa 9 + + + 9 + +9. ¾ ¾ ¹de'fgh.
(156) t.
(157) 5 "K -] T\] T. <}QF4 }~. . 0.8. 0.9 P3 P1. 0.8. P3. P1. 0.7 0.7. P(u4). P(u5). P(u4). P4. 0.6. P(u3). 0.6. P4. P(u5). P2. P(u6). 0.5 0.5. P2. 0.4 P0. P(u2) 0.4. P(u7). P5. 0.3. 0.2 0.3 P0=P(u0)=P(u1)=P(u2)=P(u3). 0.2 0.5. 1. P5=P(u6)=P(u7)=P(u8)=P(u9). 1.5. 0.1 P(u ) 0. 2. 0. P(u1). P(u8). P(u9) 0. A. 0.2. G b 5K
(158) A
(159) #
(160) #
(161)
(162) P
(163) SO
(164) 3PQ
(165) SO5M
(166) c 1# " "PQ
(167) SO
(168) LPQ
(169) SO5M
(170) 1# w ; : ; G ; x ; q ; @ ; s ; B ; t ; r C # "7M
(171) . 0.4. 0.6. 0.8. w ;w ;w ;w ;: ;G ;x ;x ;x ;x C. 1. 1.2. ,HO
(172) .
(173). hY ?U/[ c DAnQDn c TPRXDAE#c T/O6X c DA[\OlmT/PRO6XPZE#lT c XY/O6X^c ]PQS: T/OBYHl\Yc]n\D ])OQTDF[\n\]1D"©QX cDFI E#D ]1nQcDI E`[\S XPRl\SWPZV"PRXQDFM ]AEY©QPREYSWDF]AY(SRT ]dSZY# ]lQSRPROQDv] Y/O\O[QSRD T V D M E#DFO/X Y#S: T PRUPZOQDHD OSWDF]OQTD [\nm]D"©QX D E#DF]
(174) -] T\] 9 7 Z 6 }6~ } ~ }~~ 8}6~ }~32v~54. 76!8 }~ . . 8/ ~ }~ 0 8 6 8 ~ } ~ }~ ] b T/[ c V
(175) Y(SZV
(176) [\SWD c SWDF] t _ gUa £FT/OHY[QXPRSWPZ]D c SZY c D
(177) SZY(XPWT6O ! / 0 c c c _ c @ : n\D DFM V
(178) [ DFO\V"D a "QDFO Y/l\lQSRPRa[\Y/O6XV
(179) D
(180) XXD D
(181) SZY(XPRT/OT/OT/_\XPRD O6XASWDv]V DFM E#+ Y#][QPWY/O/X\ . . . ¾ . 1.4. 1.6. 1.8. 2.
(182) r.
(183) !!" $#
(184) &%'(
(185) Ndk−d (u). 0 ailleurs Ndk−d+1 (u) N2k−2 (u) Ndk−d+2 (u). N1k−1(u). N0k (u)=χ[u ,u k. N2k−1 (u). [. k+1. N1k (u). Ndk−2 (u) N2k (u). 0 ailleurs. Ndk−1 (u). Ndk (u). . ¾ ¾ ¹de'fgh. xb. OS"RO' L#
(186) M
(187) '#
(188) K Q
(189) '.
(190) :. w.
(191) 5 "K . JD a[QPO\T/[\]AnQT6O\OQDHS YSWU/T c PWX @ E#DH][QPRYO6X! 7Z 6 - V
(192) YSRV [QA SR]An\D ] ]lQSRPRO\D ]AnQDJ_\Y/]DF] A O6X c D
(193) M D q£ g m£ A c ) g 0 ; jkjlj ; gon C ¥T c XPRD t ) t _ gUa t _ gUa C giSWU/T c PWX @ E#D 0 ; jljkj ; +
(194) !#"$" %'( & ) . g?) g 0 ) g 0. )+ . ) . g?) g n ) gon. ) . * + +, .- /0 $1
(195) * ! %
(196) 32 * , 4 2 ) * + +, .- + /0 $1
(197) *+5# %6
(198) 32 * , 4 2 ) 7 $ * , 8 49: <; , =9 % 6
(199) > * , 4=9 . g h g T g i . (
(200) & : ? ~ y y } $% y }~ y A@9 }~ #9 $1
(201) .%B - 6 y y }~ y A@y 9A@ } ~ }~ 9. > * , C #A #A 2 >*, 2 . . =9 % 6 >*, . 9. 9 1
(202) DD < & 9 E
(203) F? %6 y - Gy2zl}A~ %B - 6 y zl} }~ y2zl}~ %6 A %$9 1I9 H
(204) -JG #A 1
(205) .%I . y y} 9 y y 9. 9 %K. k DFEY c a6[\D D
(206) XvY(SRUT c PRX @ ED#D ]Xv[QXPRSRPR]QD M lmT6[ cHc DFElQSWP c SRD ]vEY(X c PZV"DF]!a[QPPRO6XD c PRD O\O\D O6X!nmYO\] n\D ]Ac l c T/_QS DFB EDF]nC PZO6XD c lTSZY(XPWT6O\]T/[ nC Yl\l c T©QPREcs&YX_PRT/O\]EY(PZ]T/O OQDvS I [QXPWSRPZ]DJl\c Y/]A@ lmT6[ c D M YSR[\D c SRY c V
(207) _ T/[ _DdDFO[\O#lTPZO/X1nQT6O\O D/M (¥PQS: T/O`D [\X`D
(208) M Y(SZ[QD c gUa T/O#[QXPRSWPZ]Dl\SR[QX TX1S YI SWU/T PWX E#DdnQDc j!D TT V"PWn\D ]]T6[\'] a)a[QPCDF]X_D Y/[\V"T6[\ll\SR[\]i]XY_QSRDvO6[mE2D M PRa[QDFEDFO6XdD XET/PROm]V"T [QXDF[©D O T6ldD M Y(XPWT6O\] ¾ .
(209)
(210) !!" $#
(211) &%'(
(212). ::. A. C A C } X } c { 8 Q 6 8 } c _ } 2 < ] DO\Dn DFM E#T/O6X c D c Y(PZ]Al\Y]!V"D XYSWU/T c PWX @ E#D _ "V f %: C T6[ G T6[ x ml T6[ [\OQDJn D M E#T/O\]X Y(XPWT6O a 7Z 6 C gSRUT A c PRX @ E#DvnQDvj! A DvT6T c A O6X c D
(213) M D q£ g m£ c ) g 0 ; jkjlj ; g n C £ & 0 ; jljkj ; & C ¥T c XPRD & _ gUa + giSWU/T c PWX @ E#D 7Z A 6 . g h g T g i. 7 $* ,8 49: <; , . & 9 ? + > * , C . <9 . < & 0 ) & 2 >*, . . >*,. 2 . . (
(214) & :? . <9 D >*,C & y29 zk}~ $1 -+<-++ E
(215) ? $ y. . ) y zl} }~ @ . y2. z . . & ) _ p: 7 9 a 9 & i i ¤ & i 9 9 2 >*, 9 >*, . . * , . . & . . . . k DFEY c a6[\D b ; SD ]c X!_\PWDFO ]c [ c lmT6]]PZ_QSWDnCc T/lQXPRE#PZB ]D c @ V"D X!YSWU/T c PWX @ E#D`D OOQD ]XTQV YO6X!B lmY]XT/[m]Hc SWDF]!lTPZO6X] PRO6XD E2D M nQPZY(P DF] EYPR]1DFO¡DFM V Y]YO6X YHV Y/a[QD D
(216) M XY/lmDSRD ]lTPZO6X]1<BT/A _\XD O[\] Y!SfD
(217) M XY/lmDl D M V D M n\D O6XD/ b D
(218) X)YSWU/T c PWX @ E#D][\l\lT/]DAa[QD h q a6[\PdD M a[QPRY[QX YfB g g ; g C £/V"DAa[QP\D ]XD OUD M O D M c YS SWDV
(219) Y]vlT/[ c nQD ]JD V
(220) XDF[ c @ ]vO\TnmY[ ©n\[X¢^QBlmD _ q a b T/[ c n\D ]v/D V"XD [ + c ]vOQTQn\Y/[©a[QPO\D ]T6O/X l\Y]An\DJV"DvX¢^QlmD/£\[\OQDvXD V OQPZa[QDJV"T6O\]PR]XD Y b Y(efT/[QXD c Y[ c DFV"XDF[ c OQTQn\Y(SY[\XYO6XvnQD 1c g I 0 lT/[ c SRD c D Omn c DnQDE`[QSRXPZlQSRPRV
(221) PWXQD M q ¤ : D X Y B DFOYefQc T6I [QXD Y[QXYO6XinQDJlTPZO6X]in\D`V"T6O/X T/SWDvO[QSRSWDY[©ndD M _m[QXnQDJSZYSWPZ]XD`nQDF]lTPZO/X]inQD V
(222) T/O6X TSRD ] b PZnQDFE lT/[ c g n A A A©QD ElQSR4D ]P q )A x\£ & c ) @ & 0 ; & i ; & @ ; & C c ; c ) w ; : A ; G ; x ; q ; @ ; s ; s C Y(SRT c ]JYYO6XJnC PZOefD V
(223) XD c cD
(224) X & nmYO\]S YSWU/T PWX : E#DvnQDHjDvTT C £QT/O& 8Y(PR^X & & & @ & C c ) w ; w ; w ; w ; ; G ; x ; q ; @ ; s ; s ; s ; s D X ) w ; w ; w ; 0 ; i ; ; ; w ; w ¾ ¾ ¹de'fgh.
(225) :. G.
(226) 5 "K .. hc DF@]#lTPZO6X] PZO6XD c E«DFM nQPRYP c D ]UD M O D M c D M ]vl\Y c V
(227) D
(228) XY(SRUT c PRX @ E#DlmD c E#D XXDFO6Xn\D8YP c DS Y(SRUT( PRX EDJn\DJ][\_¨nQPRPR]PWT6OV
(229) P ¢nQDF]]T/[\] 6 6 5~ 6 8 ] h Y(SRUT c PRX @ Ec D nQD jDTT c T/l DB c D]D SWT6OJSRDA]V @ D M EYi][QPRY/O6X _ SWDF] D B V @ D ] PRO\n\PRa[QDFO/X [mOQDJV"T6E`_QPZO\Y(PZ]T/OY H OQDHD O6X DJGlTPZO6X] a &. b. P0 . . . Pk−d−1 Pk−d. = P0k−d. Pk−d+1 = P0k−d+1 d+1. Pk−d+2 = P0k−d+2 . . . Pk−1. = P0k−1. Pk. = P0k. P1k−d+1 P1k−d+2. P2k−d+2 Pdk P2 k. P1k. Pk+1 . . . Pn. q b O
(230) ' ( #
(231) c " ,7 (
(232) (#
(233)
(234) ` 5". hdc Y_SWIU/& T c PWX @ E#& D nQD][\& _0 n\PWPZ& ]PRi T/O ]XTQV &D SRD ]JlTPZO6X]`D"©Qc X cD I E#I& DF ]H& UDF M OdD iM c DFM ]i& l\Y 0 c & S: Y( SRUT c PRX& @ ED n\D jc D Tc T 0 c ; jljkj ; c c i ; c ; c i ; jkjlj ; nC [\OQDl\Y I X
(235) £ ; c 9 ; jkjkj ; ; c i ; jkjlj ; nC Y[QX D lmY X'aClmT6[ V
(236) T/O6X [QP DGiY/[QX D ]V"T6[ _mDF] ¢]lQSRPZOQD ]1nQDE D E#Ddn\D
(237) U DM a[QD SZYV
(238) T/[ _mDd ]lQSRPROQD PZOQPWXPRYSWD PZ_ O\n D M lD O\n\Y/O6XD ] S 9[\O\9 Dn\D S9 Y[QX c D 9 D
(239) XV"DF]GiV
(240) T/[ c _mDF]1EPZ]D ]1_mT6[QXf YB ¢_T/[QX c DFnQT/OmOQD O6XSRY!V"T6[ + c _D PROQPRXYSWD V²1S: D"©QDFE#c l\SWDJ@ V
(241) P ¢nQD ]]T/[\]a hdb YSWU/c T PWX E#D!DF]XSRDJc ][\PWcYO6X! c @ T6[ EPRD [Q© V"T6El DFO\n DHS: Y(SRUT PRX E#DHnQDJ][\_n\PWPZ]PRT/OC£\Y/l\lQSRPRa[QT6O\]SRDv][ c [mOD
(242) ©QD ElQSRD4. ¾ .
(243)
(244) !!" $#
(245) &%'(
(246). A. x :. A. A O6X c D
(247) M D q£g £mc ) g 0 ; jkjlj ; gon C £ & ) & 0 ; jljkj ; & C ¥T c X& PRD cc + c @i £ @i V"T D ]lT/O\n\Y/O6X Y#B SRY : DB c DV
(248) T/[ c _D " c £ & V"T cc D ]lT/O\n\Y/O6X Y#B SRY G D B E#DHV"T6[ c _D giSWU/T c PWX @ E#D . g h g T g i. 7 $* ,8 49: <; , . . A c i A
(249) c i A w jlj C ) c w jlj C c i ¤ : jkj ¤ q ¤ :%C ) g @ A c
(250) @ A c @ A w jlj q C ) c q ¤ : jlj ¤ G q 7 C )Qc ¤ : jkj e C A & i
(251) A & i A w jkj 7 q 7 :%C ) & A w jkj 7 q 7 :%C & i 7 q ¤ : jkj C ) & 0 ; & i i ; jkjlj ; & C @ 9 9 A & @& A C A & &
(252) i & !0 C A w q ) & @ q jk¤ j : jkj ?7 ; ¤ q 9 7 ; jkjk:%j C ; ) & ¤ : jlj oC . @. ,7 (
(253) c#
(254) K # P1!
(255) 'LO "5K
(256) . b#". 1. 1 P4. 0.9. P2. 0.8 P1. P3. 0.7. P5. P3. 0.7. P(2.5). 0.6. P3. 0.6. 0.5. P4. P0. P5. P5. P3. 0.5. 0.4. P6. P2. 0.3. P2. P0 P8. 0.1. 0.4. 0.6. 0.8. 1. 1.2. 1.4. P4. 0.2. P7. P1. P0. P6. P2. 0.3. 0.2. 0 0.2. P4. 0.9. 0.8. 0.4.
(257) '. 1.6. 1.8. s b "5K
(258)
(259) 3"
(260) P
(261) SO
(262) 5# " ¾,¾ HO¹ d
(263) ce'f
(264) 5g h K # P1!
(265) ' g ) G j @ # "7M
(266) . A. 0.1. 2. 0 0.2. P7. P1. 0.4. 0.6. 0.8. w ;w ;w ;w ;: ;G ;x ;q ;@ ;s ;s ;s ;s C. P8. P5. P1. P0. . 1. 1.2. 1.4. OS5K
(267) H7!"R
(268) . P6 1.6. 1.8. 2.
(269) :. q.
(270) 5 "K . c c c c cV
(271) D X¥Y[ PRO\]SZY`lTV
(272) PZT/O6[ X]_nQDDJnQV
(273) DHT/n O6X TcQTPRI XSRDDHO\]T6T/O/[\X ]dc D T]^/XQT/DFM ] O\])PRO\_\V PW@ DFOYOQaU[QD M Di] Sl\ T/Y OcAc Y#YlmGJlmV
(274) T T/c [ X _mYB DFSR]Y ?m¢U6][ l\c SWD!PZOQPZD OQ]dPRXnQPZPZY(]SRXDPR O\V
(275) XDF]dD X a[QD D 8~F} 6 8 XR 8 8 }Q ] hD_\[\X`nQDV
(276) D
(277) X`YSWU/T c PWX @ E#D D ]X`nC PRO\]\D M c D c [\O¡OQT/[\D Y/[OQTD [\n¡]YO\] V @ YOQU/D c SRYc T c E#DOQP\SRDnQD U c DdM nQDASZYvV"T6[ c _mD ]lQSRPRO\D c " YvB V
(278) Y/[\@ ]Dn\DASRYHV"c T6O6X c Y(PZO/XD T/cO\n\Y/E#D O6XYSWD _ xac £ ]P\S T6OPROm]QD M DA[\O O\T/[Q/D Y[#OQcQTI D [mnD OSZY(PZ]]YO6XSRDnQD
(279) U DM PZO\V c Y/OQUDAM YSWc T ]1T6O#n\TPRX T V DFM E#D O6XcQI YefT/[\XD [mO O\T/c [Q/D Y[ lc TPZO/XAnQDJV
(280) T/O6X c TSRD A O c 8YPWX £mOQT6[\]Y(SRSRT/O\c]/c TP a[QDJV
(281) D XYPRO\]AlTPZO6X]AnQDJV
(282) T/O6X TSRDH]T6O/X ][\l\c l PZE2B D c M ]CD X _ D ElQSZYV D M ]l\Y c1nCI Y/[QX D ] FhD)8YPWXnC PRO\]\D M D [\O`O\T/[Q/D Y[vO\T6DF[\nJY(B efT/[QXDc nQD ]OQT6c [QDF_Y[© lmY YE D
(283) X DF] lmT/PRO6c X`n\DV"T6O/cX T/SWD ¤ OQTD [\n ca D X`nQT/OmV YefT/[\XD nQD SZY AD
(284) M ©PZ_QPRSWPRXQD M YO\TX D V"T6[ _mD P D Y/[QU/E#DFO/XDHSWDvnQD U D!M n\DvSWPZ_mD XQDHM nQDvSRYV
(285) T/[ _mD a 7 Z 6 T ; O\]D A c XPRT/O nC [mO O\T6DF[\n A lmT6[ c SRD ]AV"T6[ c _mDF]d¢]lQSWPZOQDF] A O6X c D
(286) M D q£ g m£ c ) g 0 ; jkjlj ; g n C £ & ) & 0 ; jljkj ; & C ¥T c XPRD c£ & V"T cc D ]lmT6O\n\YO6X YB SZY OQT6[QD SWSRDvV"+ T/[ c _D " giSWU/T c PWX @ E#D 7 $ * , 8 49: <; , . g h g Tg i. A c A
(287) c A w jkj C ) c w jlj C A c A ¤ :%C ) g c ¤ G jkj e ¤ : C ) c ¤ : jlj e &
(288) > * , C
(289) ( & 1
(290) ? + . : z y y ) . . y . zk} 9 y2z . . w9 & ) & ¤ _ :p7 a & . . C. . . 2 . . >*, . . 9. i. 7 q 7 q h¤ : h h ¤ : . . A©DFElQSWD. { } { Q 6 8 c } } Z c 1} { ] hD ]c YSWU/T c PWX @ E#D ]cn\D][\_n\PWPZ]PRT/O
(291) D
(292) Xdn< PZcO\]D c XPRT/O nQDHOQTD cc[mn\]dc lD c E#D
(293) XXD O6X n< Y/c [QU/E#D O6c XD @ SWDnQD
(294) U DdM nQD SWPZ_D XQD M nC [mc OQDAV"T/[ _Dd ¢]l\SWPZOQD O#c Y[\@ X D E#Tc^DFOJnC ^JY PRD DF]X1nC [QXc PRSWPW ]D S: Y(SRUT PRX EDdnCfD
(295) M S"D
(296) M Y(XPWT6On\DdnQD U D)M a[QP:£V"T6EEDdSWDF] GiY(SRUT PRX E#D ]l D M V D M nQDFO/X]
(297) £²SZY(PZ]]D)SZYV
(298) T/[ _mD PZO\V @ Y/OQUD
(299) M DvEY(PZ]iYefT6[QXDnQD ]l\Y c YE D B Xc c D ]A][\l\lQS"D M E#c DFO/XY(P c DF]
(300) c b @ SR[m]il c D M V
(301) PR]\DFM EDFO6X
(302) £\]TPRX c SWD#OQT/E_ c D n\D#OQTDF[\n\]HnQPZ]XPRO\V
(303) c X]vn\Y/O\]!_ SWD#DFV"XD [ OQTQn\YS:£CY(SRT ]S Y(SRUT PRX E#@ DnCfD
(304) M S"D
(305) M Y(XPWT6OnQDnQD
(306) 7 U : DM YefT/[\XD O\T6DF[\Qc n\I ]dY[ /D V"XD [ OQTQn\c Y(S DFO Y[QU6E#D O6XY/c O/XSRYE`[QSRXPZlQSRPRV
(307) PWXQDiM nQD!V Yac [QDi@ O\T6DF[\n aD
(308) X A lmT/PRO6X]dnQD V
(309) T/O6X TSRD D OQD nQT/O\O\D Y(PZ]!lmY]vnQD nQDF]V PZlQXPRT/On D M XYPWSRS"D
(310) M Dn\D S: Y(SRUT PRX E#Da[QD!e" YPPRElQS"D M E#DFO/XQDM h DHSWDFV"XDF[ c X c T6[QD c YV"D
(311) XYSWU/T c PWX @ E#D!YPROm]P<a[QDvSZYl c DF[QDvnQDJV
(312) D
(313) XAY(SRUT c PRX @ EDvn\Y/O\] q C . ¾ .
(314)
(315) !!" $#
(316) &%'(
(317). :@. 1. 1 P4. 0.9. P4. 0.9. 0.8. P5. 0.8 P3. 0.7. P5. 0.7 P6. P(2.5). 0.6. 0.5. 0.4. P3. 0.6. 0.5. 0.4. P6. P2. P7. P2. 0.3. 0.3. 0.2. 0.2. P7. P1. P0. P0 P8. 0.1. P8. P1. 0.1. P9 0 0.2. 0.4. 0.6. 0.8. 1. 1.2. 1.4. 1.6. b
(318) '!!". B. 1.8. 2. 0 0.2. 0.4. 0.8. 1. 1.2. 1.4. 1.6. A©DFElQSWD P4. P7. 0.9. 0.8. P6. 0.8 P3. 0.7. P5. P8. 0.7 P9. P5 P(2.5). 0.6. 0.6. 0.5. P11. 0.4. P6. P2. P3. 0.3. 0.2. P0. P8. 0.1. P12. P2. 0.2. P7. P1. P0. P10. P4. 0.5. 0.3. 0.1. P13. P1 0 0.2. 2. 1. 0.9. 0.4. 1.8. g ) G j@. # . 1
(319) 'H#
(320) '. 1. 0.6. 0.4. . tb. ¾ ¾ ¹de'fgh. 0.6. 0.8. 1. 1.2. 1.4. 1.6. 1.8. 0 0.2. 2. 0.4. 0.6. 0.8. 1. 1.2.
(321) 'P"! #
(322) c#
(323)
(324) UN OS5K
(325) L H7!"
(326) "HO
(327) #
(328)
(329) 3
(330) #
(331) c#
(332)
(333) #" 7
(334) . . . . . . . . 1.4. P14 1.6. 1.8. 2.
(335) s :.
(336) 5 "K . k FD EY c a6[\D^a[C Y/l c
(337) D B ]«D M S"D M Y(XPRT/O nQDNnQD U c DM SRDNlTSR^6U/T/OQDnQDNV
(338) T/O6X cQTI SRD]
(339) D ]X c Yl\l c TQV @ D M nQDSRY V
(340) T/[ c _DAdO c D M l D
(341) M XY/O6XS T6ldD M c Y(XPWT6OC£6T/O T/_QXPWDFO6XYPROm]P[mOQD_T/O\OQDYl\l c T©QPREYXPRT/On\D!SZY V"T6[ c _mD4 1. 0.9. 0.8. P12. P13. P14. P15. P16. P17. P18. P19 P20. P11. 0.7. P21. P10 0.6. P22. P9. P23. P8. 0.5. P24. P7. P25. 0.4 P6. P26. 0.3. P5. P0. P1. P29. P3. P27 P30. P31. P32. P2. 0.1. 0 0.2. . P28. P4. 0.2. rb. 0.4. 0.6. 0.8. 1. 1.2. 1.4. 1.6. 1.8. 2.
(342) '(
(343) OS"5K
(344) cS
(345)
(346)
(347) 'P"! H#
(348) c#
(349) "
(350) OS5K
(351) L#
(352) #
(353) "
(354) . . . .
(355) p 8
(356) R4oO\N UWV2NXY [O\N -] 9 ]!- _ }{ ` 8 6 6 8. OQc D ][ c 8Y/V"D ]lQSRPROQD nQD nQD U c D M ] _ q i ; q @ aDF]XvSZY][ c 8YV
(357) D#lmY c YE2D
(358) M X c D
(359) M D`n D'M ?OQPRD l\Y c SRD l c Tnm[QPWX XD O\]T PRD
(360) S<][QPWY/O/X! . ~ . & _ g ; as) -. + - + t ~ _ gUa t _ a & _ B,a . /!0 /^0 . <r> BT [ & £ ._ q ) GT/?[ q )|x a b T6[ c V"T6O\]X c [\P c D [mOQD][ c 8Y/V"D ]lQSRPROQDn\DnQD
(361) U c DFM ] _ qi ; @q @ a YHB l\Y c XP c nQD ] _ i ¤ : a _ @ ¤ : aClTPZO6X] n\DJ@ V"T/O6 X 1c@ T/I SWD & @ £\PR: S<8Y/[Qc XnQT6O\Vv]DJn\T/O\OQD c _ c e i)¤ : a ¤ _ e ¤ : aOQTDFt [\n\. ]~ _ T [?B e i t ) _ i)¤ q i)¤ : D
(362) X e ) ¤ q ¤ £\lD ED XXYO6XnQDJn D M ?OQP SWDF] T/O\V
(363) XPRT/O\]An\DJ_\Y]D ] g a)D X a 4 6 } { }{ ~ -] 9 ]C A O c D EY c a[\Y/O/X a[QD & _ g ; alD [QX] fD M V c P c *D
(364). ¾ .
(365)
(366) !!" $#
(367) &%'(
(368). ~ . & _ g ; 4a ) -. + t ~ _ g /!0. a. . :B. - + t _ a & /^0. .. . ~ .~ . . ) + t _ gUa& _ /^0. a. _ ta. ? T/[QXD ] SRD ] l c T6l c P
(369) D M XQDFM ]`][ c SRD ] V"T6[ c _mDF]d¢]lQSWPZOQDF] ]
(370) Yl\l\SWPZa[QD O6X Y[© ][ c 8YV
(371) D ] ¢]lQSRPZOQD ]DFO V @ Ya[QDvnQP c DFV"XPRT/O gD
(372) X -] 9 ] T <}QF 4 }. w b ,
(373)
(374) #
(375) 7%' OS
(376)
(377) -] 9 ] 9 7Z 6 }6~ } ~ }~~ 8}6~ ~ 10 /}~32v~54 76!8 }~ 7Z 6 } X } { : Q 6 8 ] j!DvSZY c D
(378) SZY(XPWT6O _ ta£\T/OD On DFM n\[QPRXS: Y(SRUT c PRX @ E#DH][\PWYO6X^ :. ¾ ¾ ¹de'fgh.
(379) :. t.
(380) 5 "K . 9 AM Y(SZ[\YXPRT/On< [\O\DJ][ c 8YV
(381) DHD O[\OlmT/PRO6X _ g ; a & A A 0 0 @ A O6X c D
(382) M D q i £q £ _ g ; a£c ) g 0 ; jljkj ; g n ~ C £ ) 0 ; jljkj ; n C £ & ) & ~ 0 ¥T c XPRc D @ & _ g ; a + giSWU/T PWX E#D . @ 0 8 , : + ¤ : -+* E & _ a4) . 7Z 6 . - + t _ a & ( & : *E +*$* /^0 . ~ . 0 8 , & _ g ; as) - . + t ~ _ gUa & _ a ( & + ( *E 0 9. &0 . +. & ~ + +. .
(383). +** . jHYO\]JSRY][QPRXD£mefDOQD nQT6O\OQD c YPR]va[QD nQDF]vD"©QDFE#l\SWDF] "lT/[ c T/_QXD OQP c SRD ]JYSWU/T c PWX @ E#D ] £CPWS ][:HX n< Y/l\lQSRPRa[QD c SWDF]AY(SRUT c PRX @ E#D ]nQDJ_mY]D ]A][ c SWDF]AV"T6[ c _D ] ¢]l\SWPZOQD ]A][ c V @ Y/a[QDvnQP c D V
(384) XPRT/O gD
(385) X 6 6 5~ 6 8 ] A)©QDFE#l\SWDF]!. : :. ) w js |. b # "
(386) '7 M
(387)
(388). . #
(389) K # P1S!"
(390) S7%' OS
(391) 3
(392) ' N`
(393) . . D 8~F} 6 8 XZU8 8. g6)w j r. "HO
(394) F
(395) '. . }Q ] )A ©QD ElQSRD ]! ¾ .
(396)
(397) !!" $#
(398) &%'(
(399). G b H'
(400) '#" !7
(401) # . 5
(402) H# N OS"5K
(403) w js { } { Q 6 8 } } Z 1} { ] A)©QD ElQSRD ]! :
(404) ). : x c7 !
(405) . . . b
(406) 5
(407)
(408) PQPQ !!!!"" # #
(409) (
(410) c# #
(411)
(412) . . ¾ ¾ ¹de'fgh. . . . . r :. H7!"R
(413) ,HO
(414)
(415) '!!"
(416) . g ) w jr . 3c7 !
(417) . U
(418) N&OS5K
(419) c H7!"
(420) ,HO
(421)
(422)
(423) P"! (#
(424) (#
(425)
(426)
(427) R.
(428) L '
(429) 5 " # "7M
(430) . g . ". .
(431) Gw.
(432) 5 "K . i * i !1
(433) h D!SZYO\U/Y(U/D YB [QXPWSRPR]D c lT/[ c S PRElQS"D M E#DFO/XY(XPWT6O _ A¤v¤ a1YPRO\]P<a[QDHSWDv]V @ DFM E#YnQDvV"TQnQD YB ][\PW c D _ ¥/¦§!g b ¥ a D M XYPWDFO/XiPRElT/]QD M ]lmY c SRD`][efD
(434) X!nQD]XYUDmhTPZOnC D
(435) I X c DJ[mO c D PRO<£¨OQT6[\]iYSWSRT/Om]AT/P c a[QD V
(436) D ]AV @ T/P ©T/O6XD
(437) M XQDHM nC [mOQDvU c YO\n\DHYPRn\DHlT/[ c c SWDJn D
(438) M /D
(439) SRT/l\lD E#D O6XnC [\OQDJ_QPZ_QSRPWT/X @CDFB a[QDva6[\PnQTPRX D I X c D 8Y/V"PRSWDFE#D O6XA[QXPRSWPZ]Y_QSRDJn\YOm]AnQD ]V
(440) TQnQD ]D
(441) ©XD OQD ] . KJ
(442) . O\ O! . . h. h D`SZYOQU6Y(UD A¤v¤ DF]Xin\DlQSZ[\]D ONlQSZ[\]![QXPRSRPR]QD`M lT/[ c S:DFM V c PWX[ c DJn\D`SRPR_ c Y(P c PWDF]EY(X @ D M EY(XPRa[QDF]
(443) £ O\T/c O@ l\Yc ]vlT/[ c ]T6O c V Y c YV
(444) c X DB c Dc T c PWDFO/XQD#M T/_cefD XJE#YPR]`lmc T6[ c SRc YUD M O D M c PRV
(445) PWcXQD`M @ a[C PWSdT $ c D/Ch Y 8Y/V"PRSWPRXQD M nQD ][ V Y UDnQD ]HT6ldD M Y(XD [ ]il DFM n DM ?OQPZ]lD _ E#D
(446) XvnQDX Yn\[\P D#[mO YSWU/T PWX E#DDFOªSZYOQc U6Y(U/D A¤v¤ DFO [\XPRSWc PZ]Y/O6X c nQDF]dO\TXYXPRT/O\] c Y]]D^iPZO6c X[QPRXPRDF] c V( fQSc D
(447) ©DFEB clQSWD!V"PWc n\D ]]T6[\]'a£6V
(448) D!a[QPCY`SWD!U YO\nYY/O6XY(U/Dc n\D DFO\n D SWDV
(449) TQnQD V"SZY(P D
(450) X`n\D DFlmT6[\]]D SRY T/O6XP D D#D O6X D SRD ]JX¢^QlD ]vD Xv T/OmV"XPRT/Om]Jn D M ?OQPZ]Jl\Y S [Qc XPRSWPZ]Y(XDF[ c D XV"DF[c © @ l c D M n D M ?OQPZ]1n\[ SZYOQU6Y(UD/@ jDlQSR[m]c SRD A¤vc ¤ D OXY/O6Xa[QDSZYOQU6Y(UDT c PRD O6XQD M T6_efD
(451) Xc lD E#D
(452) XdSWD!lmT/SW^QcE#T l PZ]E#D/£/EY(PZ]PRS Y D
(453) M XQcDiM V T/PR]P£/lT/[ nQD ] YPR]T/Om]nC D%H V
(454) Y/V"cPRXQDM @ nQDOQD!l\Y]d[QXPRSRPR]D n\DiV"SZY]]DF]Y/_\]X YPWXD ])O\P¨nQDi T/O\V
(455) XPRT/O\]P X[QD SWSRD ]da[QP¨n 'D M ?O\PR]]DFO6X)[\O lTSR^E#T l PR]E#DinQ^QO\YE#PZa[QD A O%D $ D
(456) X £/S Y/l\lD
(457) Sn< [\O\D T/OmV"XPRT/OP c X[QD
(458) SRSRDiD ]X[\O\Dn DFM V"PZ]PRT/O#l c PR]DilD O\nmYO6XS D
(459) ©dD M V [QXPRT/OC£D
(460) XdE DFI E#D ]P[\O_mT6O V
(461) T/ElQPRSRYXD [ c E#PZOQc PRE#PZ]D c Y Y[\XYO6XHa[QD lmT6]]PR_\SWD#SWD V
(462) T [QI XHnC [\OQDXD SWcSRD# T/O\V
(463) XPRT/OC£CV"D SR[\P ¢V"P n\D
(464) PWDFO6XJOQT/O¢O D M USRPWU/D Y/_QSWD#SRT ]JnC Yl\lD
(465) SZ]vPZO/XD O\]PW8]
(466) jDl\SR[\][\OQD T6O\V"XPWT6O6P X[QD SWSRD OQDlD [QXl\Y] D I X c Dn c DFM V"SZY c D
(467) M DdD OSRPWU6OQD£c lm[Qc PR]a[QDSRDX¢b ^QlmDA n\C DS: T/_QefD
(468) X)OC D ]Xl\Y/])V"T6O\O[ YH@B SZYJV
(469) T/ElQPRSRYXPRc T/OC D ]X)l? T/[ c V
(470) D
(471) XXD Y@CPRB ]T/OJa[QD SZYic SRPR_ YP PWDAB ¥/¦§!g c ¥ @ [QXPRSRPR]D O6X1nQc DAOQT/[Q/D
(472) SRSWDFB ]XD V O\PRa[Q
(473) DF ] PZO\ "]lQ
(474) P D M D ] nQDdSZYv¥ c h£ _\PR_QSRPRTX D a[Qc DA@Ylml\Y XDFO\YO6X YHSZYvnQPR]X PZ_\[QXPRT/O]XY/O\n\Y n A¤vc ¤ £ Yv_\c Y]DnQD £6V"Da[QP¨lmD E#D
(475) X [mO lTSR^QE#T l PZ]E#D ]XYXPZa[QD m ASRSWDF]A@ ]T6O/X[\XPRSWPZ]QD
(476) M D ]AlT/[ M
(477) U/ [Q PZnQ D"
(478) FSRY
(479) V
(480) T/E
(481) SlQPR!SRY HXPR T/OY ?c OnC T/_\XD O\P c [mO V"TQA c nQDNc D H V YV
(482) Dc c DF] OQT/[\D
(483) SRSRD ] XD V OQPZa[Qc D ] £dY/l\lD
(484) c S"D
(485) M DFc ] £dlD ED XXD O6XnQD V
(486) _ T/O\]X [QC P D#b nQD A c ]!l TU Y/E#E#DF] A¤v¤ E#D
(487) PRSWSRD [ ]!D @ O lmD T EY/O\c V"D#c a6[\DSRD [ c ]!YO\YSWT/U/[QD=1u k?k g§ V( f s a T/[ [\OQDYO\YSW^Q]DdlT/[\]]QD
(488) M D nQD V
(489) D ]XDFV OQPZa[QD ]1nQDl TU YEEY(XPWT6OHD OV
(490) Y(SZV
(491) [\S]V"PRD O6XP ?a[QD T6OlD [\XASWP c D B C A©DFElQSWDvnQDJV
(492) TQnQD A¤v¤ XDFElQSRYXQDvM ][ c V @ Y c UDFYO6XS T6l D M c YXD [ c
(493) - / + +/ -+ +/ 8 , -+D*-+ *G H /* +/ 8
(494) /* +/ 8 J - +/ 8 , -+<+ , "! ? * H 8
(495) " !$ H J 1$1 J , 1$<8
(496) % G 8 A %B , + , " DV"TQnQD V"PWn\D ]][\] n DM ? OQPRX [\OQDdPRElQS
(497) DFM EDFO6XY(XPWT6Ovn\[Jl c TQn\[QPRX ]V
(498) YSRYP c DD O6X c DdGD V
(499) XDF[ c ]E#YPR] SRDX¢^QlmD. n\DHV
(500) D ]A/D V
(501) XD [ c ]Y(PZO\]P<c a[QDvSWDHX¢^QlDJnQD c D XT6[ c c A OQDJ]T6O6XV
(502) T/O\c O[\]AlmY c V"D XXDH T6O\c V"XPWT6Oa6[< Y/c [E#T/E#DFO/X n\D]T/O[QXPWSRPR]Y(XPWT6O V Y c PRSR]Jc ]T/O6XHnQT/Omc OdD M ]Hl\c Y S:C [QXPWSRPR]Y(XD [ ChDF]v]DF[QSRD ]vV"T6O6X Y(PZO/cXD ]!][ _ V"D ]HX¢^QlD ] ]T/O6X a6[< PRSR]nQT/PW/D O6X) T6[ OQP SRD ]dT/l D M Y(XDF[ ] JD
(503) X ¤ ) JD
(504) XSRYJ T/O\V
(505) XPRT/OEDFE`_ D ]PR^ D a `V
(506) D!a[QP DF]XSRDJV
(507) Y/]Al\Y c D
(508) ©DFElQSWDvlT/[ c SRD ]X¢^lD ] '# N N P
(509) SO$## K
(510) &% D
(511) X '# N N P
(512) SO$## K
(513) &% N N PQ H
(514) ('S
(515) ¾ .
(516) G:.
(517) !!" $#
(518) &%'(
(519). JK
(520) LK . }6{ ~F}8 Q 6 C^]C^]!-. 8. @. ¥/¦!§g c b ¥ _ ¥/¦!E_mT/SWPZVY/O\n¡§[m@ ED c PZV g b lQSRPRV Y(XPWT6O¥ a D c ]X`[\O\D_QPZ_QSRPWT/X @CDFB a[QDn D M D SWT6l\l D M D#; Y/[ k]D
(521) ; PZg2O n\h[T cl c Y(TPZOQefD
(522) D Xh K!; gb hs\gAdgSWSRj D) n\T6DJ[ c ¥O\T/PWXl nQPZD Y] ¢T/gi[QO6XXPWPRSZl]TlmSRT6PR] [ cDFOEV
(523) Y/TOQSRPRSRlmY/_m[QSWT D c Yn\XPRD T/] O YD /V
(524) XD DFV[ Sc f] D M £ aE[QPZYlmX D`c PR¥V
(525) lmD ] Y£FV"lDFT]SRnQ^QDHO T/I S:E#§D ] Y B [\OQD#T/@C[ B lQSZ[\]PRD [ c ]!Y c PRY/_QSRD ] £D XV(RRB ¥/¦§!g b ¥ Y B D
(526) M XQDM n D M D SWT6l\l D M D`YDFVJSRD#]T/c [\V
(527) PR]!nC c D Oª8Y(P c D[\OQD _\PR_QSRPRTX D a[QD!YV"XPW/Dn\Y/O\] SWDH]D O\] T [c S: T/OYAeY/E#YPR]]l DFM V"PR?DM SRDX¢^QlD!n\D ]nQPl$iD Mc DFO6c X] Y U/[\E#D O6X]dnQD V
(528) D ] T/OmV"XPRT/Om]
(529) D ]XSRD V"T/ElQPRSZY(XDF[ a[QP1PRO\]XY/O\V"PRD#SWDF]i T6O\V"XPWT6O\]vnQT6O/X!SRD#l TU Y/EED#YD $¨DFV"XP /D E#D c O6Xc _D ]TPZO D
(530) XOQT6OSRDJl c TU c Y/E#E#c DF[ c h DJ@ l c c T/U c c YEE#D [ c ]DJV"T6cO/XD O6XDvnQDJb n\T/O\OQD c c nQDF]V
(531) Y/OQD
(532) Y] n\Dl TU YEE#D a[QDSRDV"T6ElQPWSZY(XD [ Yª]DV Y UD n\DV"T6ElQS"D
(533) M XD ¥6¦§g ¥ T6[ OQPWDnQT/O\VnQD ] T6O\V"XPWT6O\] ]T6[\] B T c E#Dn< [\O\DPZElQS" D M E#D O6XYXPRT/O UD M O D M c PRa[QDD X c [\O\DEJ^ c PRY/nQDn\D]b ldD M V
(534) PRYSWPZ]Y(XPRT/Om])V @ Yc V [\OQDY/n\YlQXQD
(535) M DF] Yv[\OX¢^QlmDn\Di]XTQV YUDA]ldD M V
(536) P ?¨a6[\Dh YHUD M O D M PRV
(537) PWXQDdM nmYO\]d¥6¦§g ¥DF]X)T6_QXDFO[QDl\Y SRD c _QPZY(PZ]vnC [mO [\]Y(U/DD
(538) ©QX cD I E#D E#DFO/X!PZO/XD O\]PWn\[E2D M V YOQPZ]EDnQD
(539) ' M
(540) n DFM V c PWXHn\YOm]HSRY ]DFV"XPWT6O l DFM V DFM nQD O6XD C^]C^]C 6 } } }
(541) } 8U6} 8} 4 :~ ~ 1 8}6 ~ } }~ !"#%$&'!
(542) O OS
(543)
(544) n\Y/O\]#¥6¦§g b ¥¡D ]XJSRY n D M ?OQPRXPRT/O¡nQD SZY c D l c DFM ]DFO6XY(XPWT6OªPZO6XD c OQDnC [mO¡T/_efD X
(545) £ SRD c OS c
(546) c
(547) T/[ c c OQPRX SWDF] T/OmV"XPRT/Om] nQDN_\Y]DnQT/O6X [\OQDNY/OS_\ ]X Mc
(548) Y V"
(549) XPWT6S O«Y/[ c Y_D ]TPZOC£)]DNV c D
(550) M D c £1]D lmY V"O5T/ [ QSP £YV
(551) V D M n\D Yc nQD ]!nQcT/OmOdD
(552) M DF]ic V
(553) T/O6XDFO6[\D ]D XVWR hD ] ]T6O6XiPZE#l\S"DFM E#D O6XQDFM ]DFOXY/O/X ac [QD : ]T/[\D O6X1l\Y YE«D M X D
(554) M DF]Cl\Y SRDdX¢^QlDn\D ]V"T%D H V"PRD O6X]a[C D
(555) SRSRD nQD c T6O/XV"T6O/XD OQP c _ D"©QD ElQSR=D D l nCRWRa
(556) O # (
(557) D ]Xd[\O (
(558) 'M OS
(559) Y/[\a[QD
(560) S ]T6O6XdY(XXY/V @ D M ]nQD ] OS M
(561)
(562) S ; S PRElQS
(563) DFM EDFO6XDiY/[\]]P nQD ] YSWU/T c PWX @ E#D ]]ldD M V
(564) PRYSWPZ]QD M ]dlmT6[ c V"DF] OS
(565)
(566) S _ D
(567) ©DFElQSW D \SWPZO\YSWUWR a } 8U6} }~F~F ~ 1 } ~ ()* h D ] P1H
(568) ]T/O6XSRD ]PZO6XD c l c D
(569) M XY(XPWT6O\] a[QDAS T/OlmDF[QXnQT6O\OQD ciYvB [\O OS
(570)
(571) " ASRSWDF]n D M ?OQPZ]]D O6X1SRY ]\I DFM cE#Y/O6XPZa6c [\DHc EYX @ DFM EY(XPZa[QDvn\[ OSI M
(572)
(573) b c Y c _ D"-/©Q. DFE# l\SW'D/
(574) £m#[\# "O OSK'R
(575) &M
(576)
(577) " N N
(578)
(579) ,,+ + # # #lm# DF[Q XK
(580) &Y/% [\]% ]P_\PWDFO D X DPZO6XD l D M XQDM V
(581) T/Ec E#D![\O B lTc SR^O T/E#D!c [mOQ_PW0 Y
(582) SOP"D M '
(583) ## " K'R
(584) " ,N N
(585) ,+ # ## " K'R
(586) &% % a£\a[QD V
(587) T/EE#Dv[\O D V
(588) XDF[ D OY(SRU D _ DiSRPRO D M YP D a }1 ~ #%)!324H h D ] (5#"
(589) ' ]T6O/XJn\D ]JV
(590) TSRSWDFV"XPRT/Om]vnQD T/OmV"XPRT/Om]Ja[QP] Y/l\lQSRPRa[QDFO/X YB n\D ]vT6_efD
(591) X]Jl\Y c XYUDFYO6X n\D ]Al c T/l c P"D
Documents relatifs
Florence CARRÉ ~ Réoccupations funéraires de sépultures collectives néolithiques dans la boucle du
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
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
Revue française d’héraldique et de sigillographie – Études en ligne – 2020-10 © Société française d’héraldique et de sigillographie, Paris,
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
Cette approche a l’avantage d’induire directement, et de façon transitoire (pendant 7 à 10 jours), l’expression dans l’épithé- lium pulmonaire et alvéolaire de cette
In infantile Pompe disease patients, the glycogen storage diffusely affects brainstem motor and sensory neurons, and the whole spinal cord sensory neurons, interneurons, and
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