Interfaces stationnaires pour les équations de Navier-Stokes
Texte intégral
(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Interfaces stationnaires pour les e´quations de Navier-Stokes . Fre´de´ric Abergel et Elisabeth Rouy. N 2651 septembre 1995. PROGRAMME 6. apport de recherche. ISSN 0249-6399.
(3)
(4) ! "# %$&
(5) '$&"(")*,+
(6) -
(7) . /01- -23 43"( 65 7!$ 89 "' : <;=
(8) ->,6; @?AAB*C D<&7E01$&
(9) $& F! "*9HG
(10) JIKL< M&NOPIQSR- FTP" ;-
(11) H
(12) U'VW
(13) HX5XRY*!NA?<B=Z['\S 6G.
(14)
(15)
(16) !" #%$ & (')+*,-/.0/1
(17) 1
(18) 1 2436587 593;:=<>@?BA
(19) 3DCEA9F8GHGIGIGEA9J"KLFM:=N;OP?BA
(20) JRQTS"UWVYX Z+[]\D^6[`_;a-a-b(ced. fg_;hjiHklhnmoiHpqbrtsopvuEw
(21) klb
(22) x
(23) a-\8ytzhqpjmo_Rsopq\Dr{b#s|hq\6^DpjiIpqb#hWr8kla-z#[opjw
(24) klb Z+[]\6}=b#sB~kla"_;s]. B_RlW\D[osy8b[ob;i`lb#[`i`lbr . cD. d. mb#s]b#a0l[]b #6 d. _R^Dbm. -8#/l~B\DkWml[]zmb#r8s]\6rWmkrlb z#s]kWy8b|iH\6a-lhqs]bytb;mz;w9k_Rs]p\DrWmnytbg~_#8pqb#[o
(25) so\D
(26) b;m ms_Rs]p\Drlr_Rpq[ob;m/_#
(27) b;i/iH\6rWytpqsopq\6rWmL_;klhqpa-pqsob#m(ytb-m=kl[M_6iHb-hpql[ob
(28) ~\6kWm/yt\Drrl\DrWm/y8b;m []z;m=klhqs_Rsmy¢¡£b#8pjmsob#rWiHbxHyE¡¤klrlp¥iHpqsoz+b#snytb [oz#^Dklh¥_R[opqs]z W\Dk[ ytb;m¢z;iI\Dklhb#a-b#r8s`mWytb hqp¥w9kpjytb;m tp¥m]w
(29) klb#kl{¦0mkl[=M_DiHb§hqpl[]b l¨¢b;m|s]b;i`lrlp¥w9kb;m+kls]phqpjm=z#b;mgm\Dr8s(ytz;iH[opqs]bmYb#rytz#s_Rph© ª¬«H®`¯
(30) °±²~_#8pqb#[os]\D
(31) bmHxlm=kl[M_6iHb;m³hpql[ob;mHx8\DWz#[`_;s]b#k[`m|b#hqhpqlsopjw
(32) klb;mH . ´qµ ¶©·©¸j¹±ºI»¼¸¥½9¾;¸±¿ÁÀ GGGjÂ.
(33)
(34) ! "# %$&
(35) '$&"(")*,+
(36) -
(37) . /01- -23 43"( 65 7!$ 89 "' : <;=
(38) ->,6; @?AAB*C 7E01$&
(39) $& F! "*9HG
(40) JIKL< M&NOPIQSR- FTP" ;-
(41) H
(42) U'VW
(43) HX5XRY*!NA?<B=Z['\S 6G. GGGIGjÂ. Unite´ de recherche INRIA Lorraine Technoˆpole de Nancy-Brabois, Campus scientifique, 615 rue de Jardin Botanique, BP 101, 54600 VILLERS LE` S NANCY (France) Te´le´phone : (33) 83 59 30 30 – Te´le´copie : (33) 83 27 83 19 Antenne de Metz, technopoˆle de Metz 2000, 4 rue Marconi, 55070 METZ Te´le´phone : (33) 87 20 35 00 – Te´le´copie : (33) 87 76 39 77.
(44) ,- # . R0
(45)
(46) / & !" . ' #(4* ,-+/.0. nHl¯D
(47) bl[]bmb#r8sg_/iH\Da-[]b#lbrWmp
(48) b|msokWy 0\Rnsolb§ms_Rsopq\Dr_R[
(49) {~_#8pqb#[o
(50) so\D
(51) b;m b;w
(52) kW_Rsopq\Drm| pqso±[ob#b#Mmkl[=M_DiHbBW\Dklryl_R[ "iH\Drytpqsopq\DrmH |b;mklhs`m+\Rnbtp¥ms]brWiHb
(53) x;klrlp¥w9klb rlb;mom-_RrWy [ob#^Dkhj_R[opqs. _;[]b ^6pq
(54) b#r±\D[/±[]b#b©m=kl[M_6iHbW \B mIx_;rWy s]b W_6mpji"s]\
(55) \6hjm-_;[]b b#8lhj_;pqrlb;y0pqrytb#s_RpqhM
(56) ® « D ~_#8pqb#[o
(57) so\D
(58) b;m+b;w
(59) kW_;s]pq\6rWmHxt±[ob#b mkl[=M_DiHbmHxlb#hhqpqs]pji³\6Wb#[`_;s]\D[mH .
(60)
(61) !"$#%&' (*)!+, -&./.0132. ,"65. 4. 5. . 798;:=<?>@A@CBEDGF!HICJ<KLBL>M@9JON@G>P9Q<R!J<KLBSN@UT?IWVXDYJ1ZKN@. [1\][ ®§ª¬« 8°.^± t_^Á«1` b ab;m]iI[]pqs]pq\6rytk"a-\8yt#hb b c48b#a-hqb;m ® f« R n° t_ ^Á1« ` ti hnt ti^]j¢ nOk ;«n°.l8 -¯
(62) «Wmkn° 9 [1\e g gfg_DmBytb§h©¡¤zw9klphqpl[]p b orqts b u\6[]a0klhj_;s]p\Dr"y¢¡£klr"l[]\6lhqa-ba{\8yt#hqb. d &n &n . vw8yxz<BDGI{Q<>ICJ<KLBSRI{QOQI{RR|K}QJ~I}HNpKLVXI{<BL@. . ® k e\][ g. 4. R«n°.l8 lYG^±°]^ ^ . 4. g fg_Dm|hqpqrz;_Rp[]b bc4sokWytbeytk"hqpqrz;_R[opjmz ytb g_;kls]\6kl[yE¡¤klrlb m=\Dhqks]pq\6r"W_R[os]pjiIklhqp#[]b 4R4 z;m=\Dhkls]p\Drytk []\Dhq#a-b(_Rktphqpj_;pq[ob§yl_Rrm klr"\6kl
(63) b#[]s ® i^ ti ^±« `nz k kGkY« # ; e\e 4 z;iI[]pqsokl[]b ytk"l[]\6lhq#a{b§m\6kWm krlb±\D[]a{b±\DrWiIs]pq\6rlrlb#hhqb az#[]p6_RlphqpqsozW_;[[_RlW\D[os ¦ b . . . d 1. . ` ' 9\][ ®g; 48 bc4sokWytbey¢¡¤klri#_6m³W_R[os]p¥iHklhqpb#[ 48 b a pjmoiHkWm]m=pq\6r9l \Dklsopqh¥m³rlz;iHb;mom]_;pq[]bm 48 R 4 b¼¡ r8s][o\8ytkWiHsopq\6r _;ki#_;hjiHkhytb m 8a0P\6hqb;m ¢ iÁ^ °]±^ ti±^ «1` 8/«. k t 8 ;zn k t n« £^¤g 9\e ®g-. . 48 . . . . 4_;lWb#hjm 84 gfg_RhjiIklhnytkm ta0W\Dhbl[opqrWiIpqW_;h. 1 1. . QQ. "{µ¶·[?. . . . . . '`Pi^ t°±. d d. 44. ¯±° ®9\][ ®g°±°.^]k_^Á¯^j; ®9\e ®g`n«`n¯
(64) {²£` R8#n° t³W`n l° ®9\" ®g! 8mkn°
(65) 0¯
(66) «1`P
(67) ® t´kn° 84 gfg_DmBytki 8hqprWyt[obb#r"[o\Ds`_;s]p\Dr 84 gfg_DmBy¢¡¤klrbLm=kl[M_6iHb§rl\Dr)iH\Da{W_DiHsob. . . . . ¥{8y¦~RRT<P9ICJ<KLB¨§©N@£>ªRQK«T¬bVX@G>P9KLBP9Q@YJ>. . . w8yJHNp@N@T]<B{}@GQ><<T<JDNHET<BDGI{Q<>D. . 4. n. . . n. . . . n.
(68) ' «
(69)
(70) . . #)#. ® «W '`P^ 8 90¯
(71) «1`n¯
(72) °Án&^±«1` ¤ 4 b#a R_ [`w
(73) klb^6z#rlz#[_Rhb ¤ 4 b#a R_ [`w
(74) klb§m=kl[|hqb i#_6m s0yl_RrWm . . . ®9\"®. . D D£Q@CBP9@G>. . 4 ISQP43.
(75) .
(76) !"$#%&' (*)!+, -&./.0132. ;n @$ . 7 7. !" # . $+ . $. 5. *. :=K!NDGT<>ICJ<KLB. r"W\Dkl[o[`_-iH\6rWmkhqs]b[ 4 © t¯3^]ki^Á«1` n « Gl8° 0®
(77) ml
(78) 8 zk£hn&^.j 8 « Gl8° [1\][1\.[. 6G^Á¯
(79) «P
(80) ^ ; bms+klr/_R[`_;a-#so[]b³W\mpqsopv w
(81) klplpqr8s]b[]8pqb#r8syl_;rWm+hj_y trW_;a-pjw
(82) klb 8y b;m Wklpjy8b;mH fB¡£b;ms(klriH\
(83) b iHpb#rts(ytb0l[]\6W\D[]sopq\6rlrW_RhpqsozW\Dk[Lklrlb/±\D[iHb0ytb/±[]\6s]s]b a{b#rtsw
(84) kW_RrWy/hqb klpjytb(mbBy8z#lhj_6iHb
(85) xDbs³y8\DrWi|klrlbBa-b;m=kl[]bytbh¥_ytp¥m]mpW_Rsopq\6r"y¢¡¤zrlb#[]^6pqb h\D[m|ytk"a-\Dkl
(86) ba-b#r8s# . 0b;msgklriH\
(87) b Hi pqbrtsgytb[]\DW\6[] sopq\6rlrW_RhpqsozBw9klpEmI¡¤\DP\mb§¦§hj_§ytzH±\6[]a"_;s]p\Dr{y¢¡¤klrbprtsob#[M_6iHb
(88) 6Z4hkWm e b;ms ^D[_RrWyExtlhkWm @¯
(89) « ¯^ `W @'`
(90) ^Á«1`#Gk +¯^ 8°Á° . . krlbLprtsob#[M_6iHb klpjytb©_;pq[#xWW_;[b#8b#a-hqb b;ms(ytp iHphqb§¦0ytzH±\6[]a-b#[|bs|lhqkWmBhj_0iH\Drtu ^6kl[`_;s]p\Dr0b;msgms_Rlhb
(91) ' ¡©hWytz#Wb#rWy0ytbBhj_s]ba-Wz#[`_;s]kl[ob³b#sgytbBhj_rW_;s]kl[obytbm klpjytbmH r rbW_;[]hb#[`_W_6m³yl_;rWm³iHb(iH\6kl[`m ytb;m b Eb#s`m ytb(mk[M_DiI b ±b Eb#s`m _R[_Rrl^6\Drlp tx8
(92) \Dpq [ £ w
(93) klpEmbBl[o\8ytklpjm=b#r8s³hq\6[`mow9klb(hqb;m+6_R[opj_Rsopq\6rWm³ytbBs]ba-Wz#[`_;s]kl[obprWytklp¥mb#r8s+klr \Ds|m=kl[³h¥_ m=kl[M_6iHb
(94) "b;msBm=kllW\
(95) m=z/iH\6rWms_Rr8s# . `n&^j;. ty k klpjytbbms |¨_²±\D[iHb ytb ^D[_8pqs_Rsopq\Dr bms " # ! \%$&# ! b;m=s \6[]pb#rtsoz#b ]
(96) b#[m³hqb§W_Dm t . . r/
(97) b#ks+W\Dkl
(98) \6pq[+b#r88pjm]_;^Db#[s]\DksYs 8Wb. «W ^]` 3^]³1^ . $³Wt«W9 3^. y8b[ob;iHplpqb#r8s \DkiH\6rtsob#rlb#kl[ . 1« ` £^ji ^±« `n l9 .° ^±´ ^ 8L ° « i^.³1^ _;[]lps][_Rpq[ob§ytb ytz#hj_DiIb#a-b#r8sgytkiH\Dr8s]b#rb#kl[# . r m=b0yt\Drrlb/klrlb/8pqsob;m]m=b. Γ. Σ n t. ')(+*-, QQ. "{µ¶·[?. . Ω.
(99) ' «
(100)
(101) . c. #)#. L® t#¯i^]k_^Á«1` n k ;«n°.l8 kGh n&^]j
(102) \Dps kr\Dkl
(103) b#[osy8b \6k ; 9_±[]\Dr8s]p#[]b b;m=s|hj_[oz#klrlp\Drytb ytb#k tWb#[mkl[=M_DiHbm|iH\Drlrb#tbm b#s y8k@s 8Wb y8bLhj_{mll[]b
(104) xEytpjmj}=\Dprtsob;m bs[oz#^Dklhpq#[ob;m
(105) LxWW_R[(b#tba-lhqb%` l¨_{mkl[=M_DiHbb;m=suW8b s_RrWy8pjm|w
(106) klz b m=b#[`_/hj_/m=kl[M_6iHb§hqpq[]b
(107) Z \6kl[|m=pqa-hqpvub#[hbs][_Rps]b#a-brtsxRrl\6kWm|mklW\
(108) mb[]\Drm|w9klb(hqb Wklpjy8bb;msgb#r{iH\Dr8s`_6iHs _#
(109) b;i0hqb-8pjytb ±\Dkb#rWiH\6[]b"h©¡ _Rp[/_Rk []b#W\m ` |f b#sos]b"hqpa-pqs_Rs]p\Dr _W\Dkl[{mb#khqb-uWr ytb m=pqa-hqpvub#[ klr Wb#krl\
(110) mi_RhjiIklhjmIxlb#s|rlbLr\DkWmba- ;i bW_6mytb§s][_Rps]b#[Bklrlb pqr8s]b#[=M_DiHb brtso[]b§ytbkl-hqp¥w9kpjytb;m+8pjmow9klbkl-W_;[|b#tba-lhqb . §®,j 8i^Á«1`nL« nt°]^Á `P§°²t¯
(111) «Wn° 8 `P ¨¢bmYpqriH\Drlr8klb;m|y8k-l[]\6lhqa-bm=\Dr8s y8zHuWrlpb;m³m=kl[ ¢f b m=\Dr8shb;mY6_R[opj_;lhqb;m. {o9 Wi`W_Ra{"ytb§
(112) b;iHsob#kl[`mIx ¢i`W_;a--moi#_Rh¥_Rp[]b
(113) x C i`W_;a-ytb0s]brWmb#k[`m§m 8a-z#so[]pjw
(114) klb;mI ¢f b;m±\DrWiIs]pq\6rWm§m]_;s]pjm©±\Dr8sLhb;mz;w
(115) kW_Rsopq\6rWm m=klpq6_;rtsob;m g«^. ¯
(116) «Wmk «#8 `W. ¡=y"£ $o$ogyl_RrWm . . ¨¢bm|iH\Da-W\m]_Rr8s]bm|ytb²m=\Dr8syt\6rWi§yt\Drrlz#b;m|W_R[. "! #$"!%"G 'o&! ) o(' ! yl_;rWm *. j. ti^±«1` {² ^]`n¯
(117) «P´k t#
(118) ^ G^Á°^j;. +(,.-. ~s0yl_Rrm */ o. . 0. \6k"b#rWiH\6[]b. 1 o / s yl_RrWm 32 4 ' . «1`n &8i^Á«1` ° j `Pi^j; «W9 8 `W o657 i6¡¤b;m=s]M¦RMytpq[ob. 1. 0. o. +(,.- 8:9 yl_;rWm ;/. 4. 0. & o' ! 1 ) ' ! < 9=! yl_RrWm * 3 2 4 <2 4 < o. 4 ISQP43.
(119)
(120) !"$#%&' (*)!+, -&./.0132. Ghn '`¯ l « 3^]³1^ . # =m kl[ ±\Dryt\6rlrlbLh¥_Ltps]b;momb§y8bLy8z#lhj_6iHb#a-brtsgytb ` o. Á . 5 ! ~s0mk[/. ©. «1` £^ji^±«`nz °?²"^.`W l¯ o. \%$o. 5 ! b;m=sh¥_Ltps]b;mombrl\6[]a"_;hqb
(121) x8b#s s]bhqhqb w9klb- ! ! . !. m=kl[. ©c. a(_RrWm|iHbs]s]bBz;w
(122) kW_Rsopq\6r-
(123) b;iHso\D[]pb#hqhb
(124) x b;msghj_LiI\Dkl[olkl[]b(a-\
(125) b#rlrlbBytb|B lZ+_;[BiH\Dr8
(126) b#rl sopq\6rx
(127) b;m=s0iH\Da{ls]z#b0W\
(128) m=pqs]p
(129) b#a-b#r8sh¥¦ \ $ _RW_R[_ qs{iH\6a-a-b0iH\6rWi#_#
(130) b
(131) xtkb"ytb hM¡¤prtsoz#[]pb#kl[ ytb . «1` £^ji^±«` # -° E«P°±n . ' Os0iH\DrWm=s`_;rtsobLy8\Drlrlzb
(132) . %. ®
(133) `P ik R
(134) t_^Á«1` 80j ti^±«1` g « ^ /¯
(135) «W´ kY«#8 '`P f b#s]sob³h\Dpi#_R[_DiHsoz#[]p¥mb³hb|iH\6a-W\D[os]b#a-brts ytb;m Wklpjy8b;m r b |s]\6rlpqb#rmYpqriH\Da-[]b;mompqhqb;mI c+hqhbbtl[opqa-bghqbBs tWb§ytb([]z;_6iHs]p\Dr{ytk-a-phqpqbk c+r-bI± ±bs#xgmpB\DrTrl\Dsob klrlb m\6kWm±W_;[]s]pbw
(136) klb#h¥iH\Drw9klb)ytb xghj_²[oz;mklhs`_;rtsobytb;m/±\D[`iIb;m btb#[iHz#b;m+W_;[|hqb klpjytb m=kl[ b;msByt\6rlrlz#b§W_;[ "! # ! %$ xl\ $ # ! b;m=s³h¥_Lrl\D[oa"_Rhbb#8s]z# [opqb#k[]b| ¦ B r/Wb#ks³y8z;iH\Da{P\mb#[nhq\8i_Rhqba-b#r8sniHb#s]sobY±\6[`iHb|b#r0klrlb³±\6[`iHbBy8b|l[]b;momp\Dr bsBytb;mY±\D[iHb;m|ytb±[o\Ds]sob#a-b#r8s# j ti ^±1« ` ²"^]`¯
(137) «W´ k 8#& ^ £^±]° ^q; f bs]s]biH\6rWytps]pq\6r b#8l[opqa-b0h©¡£pqr8D_;[]p¥_Rlphqpqsoz y8k/
(138) \Dhqka-b ytb '&`x;h©¡¤brWmb#a0lhb ytb;mW\mpqsopq\6rWmHx
(139) ¦Bh©¡¤prWms_Rr8s(&Ix
(140) y8b;mW\Dprtsm+w9kptz#s_Rpb#rts y_RrWm|kl) r +*_;k sob#a-Wm pqrlps]pj_;h© r_/yt\6rWi. . bsByt\DrWiz . QQ. "{µ¶·[?. &. . !%,.-0/. 5
(141) o ts . . ' . !%,.-0/. . 5io ' . !1,.-2/. 5 # ! %$ TiI\DrWm=s`_Rr8s]b o.
(142) ' «
(143)
(144) . d. #)#. «1`n &8i^Á«1` "° j `P_^ ; -«WY 8 '`P fB¡£b;ms h©¡£b#8l[]b;momp\Dr{ytbh¥_ [ob#hj_;s]p\Dr±\6rWyl_Ra{b#rts_Rhb§ytb§hj_/y 8rW_;a-pjw
(145) klb§yl_;rWm W¨+¡ _DiiHz#hqz[`_Rsopq\6r-b;msBy8\Drlrlzb_R[ o y o57 o o9 'Y '& / & / & & bs|hj_/ytz#[opq
(146) z#bBb#r"s]ba-Wm³y8b o"b;ms|r8klhhqb§yl_;rWm|hqb§i#_6mm=s`_;s]pq\6rlrW_;pq[]b ¨¢b;m±\6[`iHb;m _;llhqp¥w9kz#b;m+m=\Dr8s|y¢¡£klrlb|W_;[]s³hb;m±\6[`iHb;m+b#8s]z[]pqbkl[]b;m%9 ÁW_;[³b#8b#a-hqb ^6[`_#8pqs`_;s]p\DrxD±\D[iHb;mgy¢¡¤b#r8s][_ rlb#a-b#r
(147) sx±\6[`iHbm³ytb§f \D[opq\DhpjmIx9bs`iD q b#s|y¢¡ _Rklso[]bBW_R[os|hqb;m ±\6[`iHbmytklb;m(_Rkl)iH\Dr8s][_Rpqr8s]bm¦h©¡£pqr8s]z#[opqb#k[|ytk Wklp¥ytb
(148) xEm\Dps +(,.- + c+rb Eb#s#xEW_R[h¥_ ±\6[]a0klhqb(ytb []b#brxt\6r_ . !. # ! %$ . !. . + , - £ '=. Ghn '`¯ « i^.³1^ f \Dr8s][_Rp[]b#a-brtsE_Rk Wklp¥ytb;m¢W_;[M_Rps`mIx#klr W klpjy8b 8pjmow9kb#klrlb"^6hqpjmombW_Dmhb"hq\Dr^y¢¡¤kr W\D[y []pq^6pjytb+pqh|b;m=sb#r8s][_ rlz"W_R[-h¥_ _R[]\6p h\D[m]w
(149) klb iHb#hqhb#MiHplb;m=s|b#r"a-\Dkl
(150) ba-b#r8s# . 1« ` £^ji ^±« `ny T?° ²"^.`W l¯ ¨_ l[]b#a{pq#[ob/iH\6rWytpqsopq\6r o 5 ! s/mklg [ -b;m=s i_R[`_6iHs]z[]pjm=s]p¥w9klbytkei#_Dmm=s`_Rsopq\6rlrW_Rp[]b
(151) ;¨+¡£pqr8s]b#[=M_DiHb4yt\Dps#s][obYprWytz#Wb#ryl_Rr8s]b y8kLs]ba-Wm _;hq\6[`mBw9klb hqb Wklp¥ytbLbmsBb#r"a-\Dkl
(152) ba-b#r8s# a\6rWiLpqhrbLWb#kls _
(153) \6pq[Bm=kl[hbLW\D[yw9kb y8b;m³tps]b;momb;m s`_;rl^Db#r8s]pb#hqhb;mH ¨_§mbiH\DrWy8biH\6rWytps]pq\6rso[`_6ytklpqs hM¡¤z;w
(154) klpqhpql[obgyt b Bx
(155) b#r0i#_Rh¥iHklh¥_Rr8s+hj_[]zmklhs`_Rr8s]bBy8b;m y8b#rWmps]z;mgytb±\D[iHb;m³_;llhpjw
(156) klz#b;mgr ¦ B W
(157) p\Dr"l[o\D}=b#s]so b - ! mkpq6_Rr8s ! y¢¡¤krlbW_;[]s|b#s|hb hj_Rr{s`_Rr^Db#r8sB6 ¦ y¢¡ _;kls][ob§W_R[os#xt\6r"\Dlsopqb#r8s³hb§m mso#a-bBy¢¡£z;w9k_Rs]p\DrWmIxtz;w
(158) klpD_;hqb#r8sg¦ Mc xWmklpD_;rt
(159) s . ?. ?. - ! 5 ! - ! 5 & ! s &+! s`_;rl^Db#r8s(¦r. d. w
(160) klp m \Dr8sBhqb;m³z;w
(161) kW_;s]pq\6rWm|y¢¡£z;w9kpqhqpl[]b ¨¢bg
(162) b;iHs]bkl[- ! b;msnhj_BiH\6rtso[`_Rprtsob b#tb[`iHz#bW_R[nhqb Wklp¥ytb³brkr/P\6pqr8s+y8bYh¥_m=kl[M_6iHb hpql[oby_RrWm³h¥_/ytpq[ob;iHs]p\Dr{ytk"
(163) b;iHsob#kl[ rl\D[oa"_RhM 8¨+¡¤z;w
(164) kW_Rsopq\6r d;Ápp m=pq^6rlpvuWb yt\DrWi§w
(165) k¡¤br i`W_6w9klb(P\6pqr8sBytbLh¥_/mkl[=M_DiHb§hpql[obhqb
(166) biHs]b#k[|iH\6rtso[`_Rprtsobb;m=s|rl\D[oa"_RhM a_;rWmhM¡¤z;w
(167) kW_Rsopq\6r dR±p x []b#l[oz;mbrtsobh¥_e±\6[`iHbe¦b#8b#[`iIb#[³W\Dk[Ly8zH±\D[oa-b#[³h¥_ m=kl[M_6iHb
(168) n¨+¡¤prtsob#rWm=pqs]z{ytb-h¥_iH\Dr8s][_Rprtsobb#8b#[iHz#b/W_;[/hqb Wkpjytb"m=kl6 [ b;m=sLhj_"6_Rhqbkl[ moi#_Rh¥_Rp[] b - ! 5 ! ¢¨_0iH\6rWms_Rr8s]b []bl[]z;m=b#r8s]b§hj_/l[]bm]mp\DrxEmklW\
(169) mzb0iH\DrWm=s`_;rtsob
(170) xWytb hM¡ _;kls][ob§ i Dsoz ytb§h©¡¤prtsob#[M_6iHb
(171) . 8´k° t 0®g¯
(172) «W° 8 ' `P " Gk
(173) B«^± 8£^±°±°
(174) ®
(175) # t°j Ápjytpa-b#rWm=pq\Drrlb#h ¨+¡£z;iH\Dkhqb#a-brtsBytb0W_6mb-b;m=s§klr \DsLh¥_Ra-prW_Rp[]b hqb0hq\Dr^ yE¡¤klrhj_Rr pqriHhqprlz/y¢¡£klr [1\][1\ e. !. _;rl^Dhb ;¨¢b|yt\6a"_Rprlb b;msniI\DrWm=pjytz#[oz|iH\6a-a-bprtuWrlp8b#shqb l[o\RuWhytkei W_;a-§ytbgtps]b;momb;m 4 ISQP43.
(176) .
(177) !"$#%&' (*)!+, -&./.0132. e2. e1. α. ')(+*-, . . bms m=b#a-pq±W_;[`_RW\6hqpjw
(178) klb
(179) ¨_ 8pqsob;m]m=bob#s hj_Bl[]b;momp\Dr"mo_Rs]p¥m¼±\6rts hqbBm lm=s]#a{b|ytb§
(180) s]\6
(181) b;m . 6o: ,
(182) a(_RrWmhqb{m mso#a-beytb0iH\
(183) \D[yt\Drrlz#b;m' / ,
(184) C /& ,
(185) / b8xpqh+b#8pjm=s]b klrlb m=\Dhkls]p\Dr _R[]sopjiHkhqpq[]b§pqr86_R[]p¥_Rr8s]b o ! o9 / s(`xlW\6kl[hj_6w9kb#hqhbhbLsob#[]a-b ytbLso[`_Rrm W\6[]s o ! 57" o@! b;m=s|pjytb#r8s]p¥w9kb#a-bIrts+r8klhM . ¨¢\6[`m]w
(186) klb h©¡£\DrTPb[]s]k[]Wbhqb ±\6rWy¢x|\Dr Pbkls"a-\Dr8s][ob#[ ±
(187) \Dp[ 4 +`x³W_;[ytb;m@a{z# sol\8ytb;mh\8i#_Rhb;mHxh©¡£b#8pjmsob#rWiHb§b#s§hM¡¤klrlp¥iHpqsoz/y¢¡£klrlb0m=\Dhqks]pq\6rms_Rsopq\DrrW_Rp[]b{¦@iI\DrWytps]p\Dr w
(188) klb§h©¡ _Rrl^6hqb m\6pqs§m=k "mo_Ra-a{b#rts Wb#sopqs# ¢f bs]s]b iH\6rWytps]pq\6rxW_l[opq\6[]p[]bms][opjiHsopq
(189) b
(190) x
(191) b;m=s br M_;pqs/rW_;s]kl[ob#hqhb ³brD}o_Ra-pr_a-\6rtso[]z"yl_;rWm 1 Bw9k ¡¤pqhgb#8pjmsob-klr *0s]b#hw9kb m=p *;xlhM¡¤z;iI\Dklhb#a-b#r
(192) sgytb W_Dm=bLb;m=shpqrlz;_;pq[ob#a-b#r8s ms_Rlhb/_;hq\D[mw
(193) k¡¤ph¢b;m=sprWms_RlhbLm=p *Áhb;m¢Wb#[]sokl[]W_;s]p\DrWm+iI[]\Dp¥m]m=b#rtsbtW\Drb#rtsopqb#hhqb#a{bHr8s a_Rrm+iHbgi#_DmIxRhM¡¤b#8pjm=s]b#riHb yE¡¤klrlb(m\6hqklsopq\6r-m=s`_Rsopq\6rlrW_Rp[]br ¡¤b;m=sY_DmYztp¥ytb#r8s]b
(194) x;b#s b#hqhb|[]p¥m]w
(195) klby8b[ob#l[]zmb#r8s]b#[klrlb iI\DrtuW^6kl[`_;s]p\Dr prW_DiIb;m]m=pqlhbl lm=pjw
(196) klb#a-b#r8s# L®8/°±° `n²G` ¯ n°.^]` ´h«i^
(197) «`Wl° _;kls]\6kl[(ytb m\Dr)_R8b ω. _;rlpqa-z0yE¡¤klrlb"8pqsob;m]m=b-ytb{[]\Ds_Rsopq\Dr. Γ. Γ e2 Ω. Σ. ω=0. Σ e1 Ω. ' (+* , 4 . _1,). . 3 ). r_0ytb#k"iH\Dr8uW^Dkl[_Rsopq\Drms][o;m|ytpEz#[ob#r8s]b;m|m=b#hq\6r hj_L8pqsob;m]m=b _Rrl^6klhj_;pq[]b unpq^l 4 QQ. "{µ¶·[?. . ±
(198) \Dpq[.
(199) ' «
(200)
(201) . #)#.
(202) n.
(203) p8hj_B^D[`_#8pqsoz|b;msnrlz#^6hqpq^6b;_Rhqb³_R[ [`_;lW\D[]sg_;kl/_;kls][ob;m+W_R[_Ra-#so[]b;mÁ\6k0ytb³M_I\Dr zw9klp6_Rhqbrtsob
(204) x
(205) mpEhj_§tps]b;momb(_Rrl^6klhj_;pq[]b§b;m=s³^6[`_Rryt b `x8hj_ mkl[=M_DiHb§hqpl[]b(ms_Rsopq\DrrW_Rp[]bb;m=s kr"i 8hqpqryt[]b(iH\
(206) _;tp¥_RhM a_;rWm³hqb;mgi#_Dm³prtsob#[]a{z;ytp_Rp[]b;mIxR%\ $@hb;mY6_;hqb#kl[m³ytb(hj_L^D[_#tps]zb#s y8 b m\6rtsiH\Da{W_R[_Rlhb;mHx8ytb;m z#s]kytb;mYbtWz#[opqa-b#r8s`_;hqb;mnytb ³brD}o_Ra-pr/b#s|Z_Rs]_R \6rtsga-\Dr8s][ozw
(207) k¡£pqhWWb#kls|b#8pjm=s]b#[gytb;mgm\6hqklsopq\Drm|ms`_;s]p\DrlrW_;pq[ob;m³akhqs]plhqbm ±\6[]a-z#bm+ytb hqkWm=pqb#kl[mYlkhqhqbm³W_R[|b#8b#a-hq b
(208) p h¥_@^D[_#tps]z0b;ms l[]z#W\6rWytz#[_Rr8s]b ±rl\Ds_Ra-a-brts(m
(209) p Xs xhbl[o\Dlh#a-b/r¡£b;ms hqkWm¦{m 8a-z#s][opqb mlz#[]p¥w9kbLb#sphr ¡ _-lhqkWm(ytb0m\6hqklsopq\Dr i thpqrWyt[opjw
(210) klb
(211) W¨¢b/s 8Pbeytb h¥_²m=kl[M_6iHb i`W_Rrl^6b Mytb;m-iH\6pqrWm0_RW_R[_Rpjmomb#r8s r r¡¤zs]kWytpb#[`_ _Dm-pjiHpBiIbi#_6mHx³b#s \6r [ob#rt
(212) \6pqb ¦ £ Mx ©x 4 d W\Dkl[§hqbm³l[]\6lhq#a{b;m³ \ $h©¡¤prtsob#[M_6iHb[ob#rWiH\6rtso[]bLh¥__R[]\6p [opq^6pjytb
(213) . §®)ª l# £^ «Pn´^Á O° = «R¯ {² l«³G^jti^±«1`. ¨ _²a"_6m]m=b r ¡¤b;m=s|m\6kla-p¥mbBrlp¦Lh¥_L^D[`_#8pqsozrlp¦/y8b;m4±\6[`iHb;m³btsoz#[]pb#kl[]bmH t
(214) bklhjm h©¡¤b ¢bs|ytb§m=kl[M_6iHb bsYhM¡ _;s]s][_DiHsopq\6r-ytbmYW_;[]s]p¥iHklhb;mb#r8s][obb#hhqb;m m=\Dr8s³¦L[]b#rWy8[]bBb#r-iI\Da-lsob
(215) r0b#8b#a-lhb W\6kl[][_Rpqs #so[]bBiHbhqklpy¢¡¤krlb|lhj_;rl#sob
(216) x
(217) mpiHb|r¡¤bms w
(218) klb|hqb|a{\8yt#hqbgr¡¤bms+W_6mYprWiH\Da{l[]b;m= m=pqlhbb#sByt\6pqs|sob#rlpq[BiI\Da-lsoby8b;m lz#rl\6a-#rlb;m+a"_;^Drlzs]\D± lyt[o\8 y 8rW_Ra-p¥w9kb;mH a_;rWm§iHb/i_DmHxphr¡ _ _Dm§ytb/W\D[y [opq^Dp¥ytb MiD¡¤bms]M¦RMytp[]b/W_6my8b0iH\Dr8s][_Rpqr8s]beytk s 8Wb o s gb#s|hb;m³pjm=\Da-z#so[]pb;m ytk"lhj_;r l[oz;mb#[o
(219) b#r8sYhb;m|m\6hqklsopq\6rWm ±
(220) \Dp [ ©x +` . . K}QV. 7 v [1\e\.[. HTICJ<K±B. VWICJ1ZDCV©ICJ<?F!HL@. l °²jG^Á°]^ o. NHERQK«T¬bVX@. P9K±VXRT@YJ. q~s. r 6_-y8\Drlrlb[#xEyl_RrWm(iHb i#_DmIxPh¥_ }=kWm=s]p uEi#_Rsopq\6ry¢¡£klrlbL_R[]sopqbeytk a-\8y8#hqb
(221) x¦s]ps][ob yE¡¤b#8b#a-lhb Á\6r@[ob#r8
(222) \Dpqb ¦ W\6kl[krlb§z#s]kWy8bLy8z#s`_;pqhqhz#b rmb§lh¥_DiHb yl_;rWm h¥_/iH\Dr8uW^Dkl[_Rsopq\Dr)yt\Drrlz#bzunpq^Dk[]b . ry8zHuWrlpsBy¢¡ _;P\6[`y hM¡¤z#rlb[]^Dpb§y¢¡£klrlb iH\Dr8uW^Dkl[_Rsopq\Dr ¨+¡¤z#rb#[]^6pqb _6m]m=\8iHpqz#be¦h¥_. m=kl[M_6iHbBb;msghj_Lm=\Da-a{bBytbso[]\6pjmYsob#[]a{b;m DhM¡¤z#rb#[]^6pqb|W\Dsob#rtsopqb#hhqbBytb(Pbm]_Rr8s]bkl[ (w9kb hM¡¤\6r yt\Dps§ytz#Wb#rWm=b#[W\Dk[Ly8z#lhj_6iHb#[h¥_a"_6m]mb0y8b Wklpjy8b PhM¡¤z#rb#[]^6pqb/y8b0mkl[=M_DiHb/hpql[ob
(223) /l[]\6P\6[]sopq\Drrlb#hqhb ¦²hj_ s`_Rphqhbytbh©¡¤prtsob#[M_6iHb"hqp¥w9klp¥ytb#M_Rp[ +b#s0b#rtuWr hM¡¤z#rb#[]^6pqbytb oa-\Dkpqhqh¥_R^6b l[o\DW\D[os]p\Drlrlbhqhqb ¦/hj_Ls_Rpqhhqb§y8bhM¡¤prtsob#[M_6iHbhpjw
(224) klpjy8b#Á[oz;iHplpqb#r
(225) s r"6_klsopqhpjmb[³klrl[]prWiHpqWb6_;[]pj_;s]p\DrlrlbhP\6kl[(i#_Rh¥iHklhqb[³hj_/m=kl[M_6iHbLhpql[ob
(226) PfB¡£b;ms h¥_±[]\6rtsopq#[ob§ytb§h©¡£b#rWmbalh b w
(227) klpa-prlpqa0pjm= b m\6kWm h¥_/iH\Dr8s][_RprtsobLy8b
(228) \6hqkla{ b ` . 4 ISQP43.
(229)
(230) !"$#%&' (*)!+, -&./.0132. 1. Σ. z. Ω. Γ. x=(x 1 ,x 2 ). U. ')(+*-,P0 r"m=kllW\
(231) m=b/w
(232) klbg b;m=s³hb^6[`_Rlb y¢¡¤klrb±\DrWiI. i^ t_^Á«1` "°²q'` i³1^ /;«ll° . . sopq\6ry8zHuWrlpb§mkl[Bklr"b#rWm=b#a0lhqb Bhq\D[m. . . . \%$. Os8xlb#s. . . . . 6 . . 9 . #!.
(233) . . . #!. 1« ` £^ji ^±1« ``nt¯ 8# ^ # iI\Dr8s][`_;pqr8s]b§y8b
(234) \6hqkla{b phyt\6pqs|b#8pjm=s]b#[.-. QQ. "{µ¶·[?. . . . . ' ' . 9 ' ' . . ¨_/6_R[opj_Rsopq\6r y8bhM¡¤z#rb#[]^6pqb§mI¡¤z;iH[opqs. .-#,!" * 6 6 %& $L& 6 . # !
(235) %$ 9 $ %$ . 9 . $ %$. 9 . . 57'$ ' + ' & $! ' ' ( 7)* . f \6a-a-b/ph³mI¡ _;^Dpqs0y8b-a-pqrpqa-pmb[. ,$. . . $! $ %$ . 6 L§m=\DkWmLh¥_. $ ' ' / sob#hw
(236) klb
(237) xlW\6kl[so\Dkls/$ ¦0mklW\D[]s(iH\6a-W_DiIs|yl_;rWm00xl\Dr)_Rps $ 2- $ ' s(/ 1 .
(238) ' «
(239)
(240) . #)#. =. i6¡¤b;m=s]M¦RMytpq[ob. . 7 $ ' ' ~s( Bkls][ob#a-b#r8s ytps#xl\Dryt\6pqsB_#
(241) \Dp[|b#r"s]\6klsW\6pqr8s' ytb.0x . 6- . # ! 5. -)/ 2 "# ! 9 ' 5 )* . %\ $"hqb§a-b#a/l[obBytb§^
(242) _;kWi bbms|hj_L[]b;mompq\6r" yt[]\ms_Rs]p¥w9kbbr@kr@W\6pqr8sBmpqsoklz mkl[|h¥_ ±[o\Dr8s]p#[]bhpql[obb#s|hbsob#[]a{bb#r-M_6iHs]b#k[Bytb -bms|hj_0iH\6kl[]lk[]b§a-\
(243) b#rlrlb(ytbzB [ h¥_-l[]b;momp\Dr ¦ hM¡¤z;w
(244) klphqpq[]b§b;msx_Rk mpq^6rlb0l[];mIx¢hqb/sob#rWm=b#kl[ ytb;m§iH\6rtso[`_Rprtsob;mb#s yt\6rWi \6r_[ob#s][o\Dkl
(245) zhM¡¤z;w
(246) kW_;s]pq\6r dR±p r\Ds]pqbrWyt[`_;pqs§y8ba a-bklrlb0iI\DrWytps]p\Dr _Rkhqpqa{pqs]bm|mkl [ b#r b#rlhb#6_Rr8sh¥_ [ob;mso[]p¥iHs]p\Dr"m=kl[|hqb mklW\D[]s(yt+ b $ ;²n° 8i^Á«1` {²qG`Ok ;«n°.l8 -« £l8°
(247) p1 b;msyt\6rlrlz#b
(248) x;hqbm mso#a-b±\6[]a-zgytb;mnz;w9k_Rs]p\DrWm n¦ r¡ _ _Dm ytb|m=\Dhkls]p\Dr _0l[]p\D[]p PbrbE b#s#xWhqb;m|z;w
(249) kW_Rsopq\6rWm© | b#sM c xw9kp+ytzIuWrlpjmomb#r8sBhqb;miI\DrWytps]p\DrWmm=kl[ m=\Dr8s0iH\Da{P\mz#bmHxnmpob;ms klr
(250) b;iHs]bkl[ ¦
(251) iH\6a-W\
(252) mo_Rr8s]b;mIx+ytb iH\6rWytpqsopq\6rWm moi#_Rh¥_Rp[]b;mbs-hqb ml m=s]#a-bb;ms mkl[ytz#s]b[]a-prlz
(253) {c+r [ob#6_RrWi`lb
(254) xgm\6kWm"ytb;m- t W\Dsol;m=b;m [_Rp¥m\Dr_Rlhb;mHx¢hb/ml m=s]#a-b±\6[]a-ze ytb;m z;w
(255) kW_;s]pq\6rWm B ¦ M x %|b#s dR±pqp _Dyta-bs|klrlb [1\e\ e. f«. m=\Dhkls]p\Drxw9klp ytz#Wb#rWy"ytbzBx o / / ` W~\6kWmY±b#[]\6rWm|yt\6[]z#rW_#6_Rr8s|[]zI±z#[]b#riHb¦/iIb m lm=s]#a{biH\6a-a-b|z#s_Rr8s|hqb m mso#a-b(_Rkl8pqhpj_;pq[]b* ¨¢bl[]\6lhq#a{b-a"_Rsolz#a"_;s]p¥w9klb{¦²[oz;m\6kWyt[]bWb#kls{_Rhq\6[`m-m=b@±\6[]a0klhqb#[eiH\Da{a-bh¥_ [ob;i`lb#[`i`lb(y¢¡¤krlb§mk[M_DiI6 b m]_Rsopjm©M_Rpjmo_Rr8shM¡¤z;w
(256) kW_;s]pq\6r. \%$ bsg o. ±. iH\6rWms_Rr8s]b /. . ?± ! 5 ! . . / / g m\Dhkls]p\Dr)ytkm ms]a-b. ` . r Wb#ks_;hq\D[m [ob;i`lb#[`i`lb#[ W_;[klr a{z#s]l\8y8bLy8bW\6pqr8s uW8b l\6r mb/y8\Drlrlb klr *;x8\Dr"[]zm\Dkshbl[]\6lhqa-b_;kl8pqhqp¥_Rp[]b
(257) lklp¥m³\Dri#_;hjiHklhbhj_§6_Rhqbkl[Bytb W\6kl[iIb#s]sob m=kl[M_6iHb§b#s|\Dr"ps]#[ob§yl_Rrmhj_/ytp[]b;iIs]pq\6r"ytb . ¡©hiH\Dr8tpb#r8s+yt\6rWiB_6_;rts+so\DklsgytbBm=bByt\Drrlb#[ klr{i#_Dyt[ob³±\DrWiIs]pq\6rlrlb#h_Dytz;w
(258) kW_;s+W\Dkl[. y8zHuWrlp[|iH\6[][]biHs]b#a{b#rts bs³[]zm\Dkyt[]b hqbl[o\Dlh#a-b§_;kl8pqhqp¥_Rp[]b
(259) t ij [ . . (p
(260) ' . . . . '
(261) !1 ± , & . . 3i. 4 ISQP43.
(262)
(263) !"$#%&' (*)!+, -&./.0132. ; L³;n . v 7. L /4 . $65. 4. ;. . xz@URQK«T¬bVX@. I}H <T<I{<?Q1@. 0 r [`_RPbhqhqb(w
(264) klb#hjw
(265) klb;m+[oz;mklhs`_;s`m³iI\Drlr8kWm³iI\DrWiHb[]rW_;rts hqb(m mso#a-b|b#hhqpls]p¥w9klbp ±
(266) \Dp[ * Mx 4D . l0°.^]`n ^ r{mbByt\6rlrlb" b#s}Bx8ytb#kl0m=kl[M_6iHb;m+[]z^Dklhpq#[ob;mH a_Rrm³iHbBi#_6mHx nWb#klsgmH¡£z;iH[]p[]b +(,.- o ~ s0yl_;rWm +(,.- 9 ~ o # m=kl[* s0yl_;rWm o5 ! s/mkl[g ! 5 &! ~ s0mkl[/ &+! s_Rrl^6b#rts(¦6. e\][1\.[. \6kxllhkWm|mpa-lhqbab#r8s _#
(267) b;iy8b;m|iH\Drytpqsopq\Drmytb|ap[]p¥i lhb#s l\Da{\D^Drlb;mHx. +(,.-. + , - o ~ s0yl9 _Rrylm _;rW m o ~s/m=kl[ o 5 ! ~s0mk[ ! !. - ! 5 & s m=kl[/ &+s`_;rl^Dbrts(¦6. r"a-\Dr8s][obhM¡¤b#8pjm=s]b#riHbBy¢¡¤krlb§m\6hqklsopq\6r@_R[|klrlb§a-zs]l\8ytbB6_R[opj_Rsopq\6rlrlb#hhqbb#sgb#r ks]pqhpjmo_Rr8s³h©¡£pqrlz^
(268) _Rhpqsozytb\D[or ±
(269) \Dpq[xtW_;[|b#8b#a-lhb
(270) x ©x D w
(271) klb#hhqb w9kb0m\Dp s []z#^6klhqp#[]b
(272) xE¦6_Rhb#kl[m
(273) biHs]\6[]pqbhqhqbmYb#s§mo_Rsopjm¼M_;pjmo_Rr8s s"m=kl[ krlb§W_R[os]pqb yt b ) ±W_R[|b#8b#a-hqbBmk* [ xl\Dr_ .
(274) ' . . ' . f bs]s]b(pqrlz#^_Rhpqs]zg}=\Dklb hqba a-b|[ 6 hqb w9kbhM¡¤prlz#^
(275) _;hqps]z(ytb Z\DprWi#_R[oz
(276) .
(277) \6pqs 4 ! 5 ~s / ~s / 5 ! ~ s0mkl[W ul\6[]a-b#hhqb#a0b#r8s#x \6r"a-pqrlpa-pmbBhj_±\6rWiHs]p\Drlrb#hqhbm=s][]p¥iHs]ba-b#r8s³iI\Dr8
(278) b#tb ty zHuWrpqb§W_R[. . { ' 9 5 ' m=kl[ 0 ¨+¡¤prlz#^
(279) _;hqps]z0ytb \D[or²pa-lhpjw
(280) klb§w
(281) klbb;ms Hi \
(282) b#[`iIpq
(283) bLbs§yt\Dri/w9klb _6yta-b#s kr@W\6pqr8sBytb§a-pqrlpaka krlpjw
(284) klb yl_Rrm 0 1c4sBw
(285) klb#hhqb;mgw9kbLm=\Dpb#rts b#s¬ yl_;rWm 0x 5 . QQ. "{µ¶·[?. ) : ) +(,.- . . . . 5 :: ' 9 5 ' 5 9 5 '"! # : % ! $5 ) .
(286) ' «
(287)
(288) . . #)#. [. "! # 1% ! 5 . . : % ! 5 &! 5 &! /. bs|yt\6rWiDxlb#riH\6a-a-b#r _Rr8s+W_R[Bl[ob#rWyt[ob§ytb;m¬¦/mklW\D[]s(iH\6a-W_DiIs#xtph¢8pqb#r8s|w
(289) klb§m=p 5 ~sW\6kl[so\Dkls§xW_Rh\D[m ph¢b#8pjm=s]b sob#hnw9kb. +(,.- : 9 *. klpjm³\6r s][o\Dkl
(290) b. . : % ! 5 &! (s . aB\DrWiDxt±\6[]a-bhqhqbab#r
(291) sxDklrlb m=\Dhqks]pq\6rytkl[]\6lhqa-b_;kl8pqhqp¥_Rp[]bb;m=s|klr. y8b )b#s|[]z;iIpql[o\8w9klba-b#r8s# . ;«W {²qG` #«W°Ái^±«1`Mk #i^Á¯
(292) n°]^.l r 6_mbhj_DiIb#[-y_RrWm-hqbmb;m=W_DiIb;m-ytbDh¥ytb#[# |
(293) \6pqb#r8s §x-
(294) b#s s(/
(295)
(296) \Dps} *+klrlbBm=kl[M_6iHb*
(297) L r0mkllW\mb Á t. W\Dsol;m=b w
(298) klb³hb³l[o\Dlh#a-b. e\][1\ e. ;. n °.^]` i^±# . W\6pqr8sBiH[]ps]pjw
(299) klb. . _;kl8pqhqp¥_Rp[]b+hpqrlz;_;[]p¥mz } _Rk
(300) \Dpjm=pqrW_;^Dbytb±o *;x;m\6hqklsopq\6r0ytkLl[o\Dlh#a-b _;kl8pqhqp¥_Rp[]b y_RrW m *i . 5 y_RrWm* mkl[ 5 ! (mkl[g * O o * 57 O 57o * 4 : ! 5 & ! . . yl_Rrm. *. bms|klr"l[o\Dlh#a-bBb#hqhpqlsopjw
(301) klbpqb#r"W\
(302) m=z
(303) xlW\Dkl[. 4 . . . . . " " . 4. !4 " . * . " * £ ? * " ? *&. . . i6¡¤b;m=s]M¦RMytpq[ob-w
(304) k¡¤ph+b#8pjm=s]b/klrlb iH\DrWm=s`_;rtsob$# s@sob#hqhb0w9kbW\Dk[/s]\Dks]b;m±\DrWiHsopq\6rWm 4$/ . ./%|yl_;rWm|hqb;m³b;m=W_DiIb;m|iHpqMytb;momkWm|mo_Rsopjm¼M_;pjmo_Rr8sh¥_/iH\DrWy8pqs]p\Drytb iH\6a-W_Rsopqlphqps]z. & ' %$ # 5 ! %$ / . ' . " *&gm=\Dhkls]p\Dry8k@[]\Dhq#a-b* }+sob#hnw
(305) klb & ( (*),+.- / , / # ( 4 / . %/ 0 ( . &. ph¢b#8pjm=s]bkr@krlpjw
(306) klb. . . 4 ISQP43.
(307) .
(308) !"$#%&' (*)!+, -&./.0132. Hi \Drrtk Á
(309) \6pq[ 1 Mx 46 Mx 4 d b#s 4 +Bw
(310) klbhM¡¤ tW\6s]l;m=b |b;m=s[_Rp Eb#sxDhqbBm lm=s]#a-bp }n
(311) z#[opvuWbgh©¡ _;hqsob#[]rW_;s]p
(312) b³y8bul[]bytl\Dhax;i#_;[YhM¡¤\6Pz [_Rsob#kl[0b;ms0b#hqhpqlsopjw
(313) klb-b#s0hqbm/iH\DrWy8pqs]p\DrWm0_Rk hqpa-pqsob;m
(314) z#[]p uWb#r8sLhb;miI\DrWytps]p\DrWm0ytb [ob;iH\6klt[ob#a-b#r8s#
(315) p \6r _"klrlb-krlpjw
(316) klb{m\Dhkls]p\DrW\6kl [ 4 / . /%0 E s(/ ./s((_;hq\D[mhM¡¤ tW\Dsol;m=b +bmsBm]_;s]p¥m¼M_Rps]b
(317) ¡©h+b;m=slpb#r m=\Drlr_Rlhb
(318) '4 c r0b. 8#«W°Ái^±«1` nOk R«n°.l8 l9G^Á°]^ ^ `0G` «P9 # r mklW\
(319) mb{w
(320) klbLhbLW\D[y [opq^Dp¥ytb6b;ms
(321) b#s§w
(322) klbLh¥_±[]\6rtsopq#[obLhqpl[]bz b;ms(ytb iIhj_Dmomb6 " W\Dk [ t riH\6rWmp¥yt#[obhqb m mso#a-b +(, - o57 o 9 yl_;rWm +(,.- o sy_RrWm o # mkl[ o5 ! ~s0mkl[ ! - ! 5 & ~s/mk [ \%$ # 5 ! ~s0mkl [ + |h8«ilt [ 0 L *)1# !
(323) {o *z
(324) ) 0&3
(325) ( e\][1\ . . . . . .
(326) « G |-&
(327) |) o *6«' -&
(328) |) (i *)
(329) ± *
(330) E«%&
(331) )#z
(332) p
(333) . ) ( i )z-&
(334) b L ) 6{'p%&
(335) ) ( ,-&
(336) p)«o *. . . . #. . . 8«`nHt_^Á«1`. ¨+¡£b#tp¥msob#rWiHb b#snh©¡£klrlpjiIpqs]z4y¢¡¤klrb³m=\Dhkls]p\Dr/l[o\8i lby¢¡¤kz r o * yt\6rlrlz m=\Dr8s|\Dlsob#r8klb;m³W_;[klrs]lz\D[]a-by8b;mY±\DrWiIs]pq\6rWm|pqa-lhpjiHp sob;m w9klpEkls]phqp¥mbhM¡¤ tW\Dsol;m=b M_;pqsob[]z;iHzytb#a-a0b#r8s# t ij e
(337) (6o 6' ) #p)# #p)z(,%& ,) z .//)p%&±. . . *5%! . g C #%& 6o s6
(338) } p%&±o 3 ±1 *# g%&g * !y z . t ij . . v v. . . . . . . . . {1. . z
(339) ´g)# «.y' ( g) ( g 6. I{Q<ICJ<K±B>ORI{QOQI{RR K«QJO§"!. -8¯i^ ; ªk ;«°]l8 "#«WnG` =«; ¼«`n¯Di^±«1`£` t°±° f«; ° ti ^±1« ` n k ;«°]l8 ¬¯
(340) «W´k°
(341) r¬`i lb#[`i`lb ¦ []z;m=\DkWy8[]bhM¡¤z;w
(342) kW_Rsopq\6r ?± $#% %\ $ b;ms(ytzHuWrpqbW_;[ e\e\.[. ?± - ! 5 ! . bsg /o/ 1+b;m=sm=\Dhkls]p\Drytk"l[]\6lhqa-b§_Rktphqpj_;pq[ob
(343) r mb{yt\6rlrl b * kryt\6a"_RprlbLW\6[]rlz0W_R [ * b#sz * []z#^6klhqp#[]bmH r6_"i`l\Dp¥mpq[ krlb iHhj_6m]mb ytb m=kl[M_6iHb;m|w
(344) klpnm\6rtsByl_;rWm|klr
(345) \6pjmprW_R^6b ytbz * QQ. "{µ¶·[?. .
(346) ' «
(347)
(348) . c. #)#. = «1`n¯Di^Á«1`G` 8° rLz;iH[opq[_³klrlb|m=kl[M_6iHb! _Dm]m=b³[]\8i`lb|ytb * m\6kWmh¥_±\6[]a-b. yE¡¤klrlb(D_;[]p¥_Rs]p\Drrl\D[oa"_Rhb§ytbz. *i . . ~ * . !. . *. \%$y/b;msBklrlb±\6rWiHs]p\DrytzHurlpqb mk[ *(¦r\D[]a{b
(349) Wb#s]ps]bb#s ! *Bb;m=s|hj_/rl\D[oa"_Rhb§¦ *; f bgi`l\DpmI¡¤b#8lhqp¥w9kblbkl[]p¥ms]p¥w9kb#a-b#r8slW_;[hj_|l[]\6P\mps]pq\6r/iHp©y8b;m]m=\DkWm ±
(350) \Dpq[n_;kWm]m=p # ` .
(351) ;«1k «P
(352) ^ i^±«1`. . %&('. . [ 9 g' -
(353)
(354) g)± **-ib) ( )| |-&
(355) g # &-3|) z |'%&. . . . 8«`nHt_^Á«1`. - ! * *. . . * .
(356) n . r¬ytzIuWrlpqs"hM¡¤\D[opq^6pqrlb y¢¡£klr[ob#W#[]b b#rTklrW\Dprts)ytbm ;* r. \6[]pb#rtsobiHb"[]b#W#[obytb)m\D[os]b)w9klb *"_Rps-iI\Da-a-b0lh¥_Rr s_Rrl^6b#r8s-hqb"lh¥_Rr
(357) ~s²b#s m=\Dpshb/^D[_Rllb{y¢¡£klrlb/±\DrWiHsopq\6r +
(358) \Dps _Rhq\6[`m klr²W\6pqr8sLy8b-iH\
(359) \6[`yt\6rlrlz#bm6 '/
(360) y_RrWm§iHb []b#W#[ob/s]b#hw9k b '²m=\Dpqs yl_;rWmhqbeyt\Da"_;pqrlbeytb0ytzHurlpqsopq\Dr y8b' r i`lb#[`i`lb krW\Dpqr8. s * ' * / ' *§ytb * b#sLkr[]z#bh - sob#hjm w9kl b mo_Rs]p¥m¼M_6m]mb"hM¡¤z#^_Rhqps]z &n ` h\D[`
(361) m *b;m=s|hqb§W\DprtsBw
(362) klpnm]_;s]p¥m¼M_Rps . /. . *i. . . . / *& - . c+r§ b Eb# s ±
(363) \Dpq[EW_R[nb#8b#a-lhb 4 ©x% d `xI\Dr a-pqrlpap¥mbh¥_|w9kW_;rtsopqsoz '
(364) 9 br@h¥_L6_R[]p¥_Rlhb -mkl[|hb yt\Da"_;pqrlb ytb ytzHuWrlps]p\Dr"ytb W¨¢ba{pqrlpakla yt\6pqs(m]_;s]pjm©M_Rp[]b. '6;:9
(365) s(/ i6¡¤b;m=s]M¦RMytpq[ob§w9kbhb
(366) b;iHsob#kl[p ' /
(367) y8\Dpqs#so[]brl\6[]a"_;h¦$ *; r W\
(368) m=b / ' 8 9
(369) 9 ³_;hq\6[`m s(/s( sb#s{\Dr 6_-klsopqhqp¥mb#[Bhqb0s]z#\D[o#a-b/y8b;m±\DrWiHsopq\6rWmpqa-lhpjiHp sob;m³W\Dkl[ a-\Dr8s][ob#[w
(370) k¡£pqh+b#8pjm=s]b klrlb m=\Dhkls]p\Dr"klrlp¥w9klb ytb
(371) / t sw
(372) kW_;rWy b;m=s_;k
(373) \Dp¥mprW_R^6bLy8b s8x¢i6¡¤b;m=s]M¦RMytpq[ob§ytb h¥_/iH\Dk[]Wb
(374) r_ . + O
(375) . M ) . 9 . f b#sb#rWyt\6a-\D[ollpjm=a-b+b;m=s+pqr8
(376) b#[mpqhqbgmplhM¡¤\6r/b;ms _6m]m=b|l[]\8i`lbBytbg s(/s` c+r0bEb#s#x. phWPbkls|mI¡¤z;iH[opq[obBiH\Da-a{b³hj_§m=\Da-a-bByE¡¤klr-sob#[]a{b|yt\6a-pqrW_;rtsx +
(377) 9 nb#sgy¢¡£klr sob#[]a{b/w
(378) klp+rlb{ytz#Wb#rWy w
(379) klb-y8bh¥_ s_Rphqhqbeytk
(380) \6pjmprW_R^6b0ytb w9klb/hM¡¤\6riH\6rWmp¥yt#[obb#s w
(381) klb/hM¡¤\DrWb#ksLy8\DrWi[ob#rWyt[ob0_R[olpqso[`_Rp[]b#a{b#rts|Wb#sopqs ¨¢b-y8z#s]b#[oa-pqr_Rr8sytb0iIb#s§b#rWyt\6 a{\D[]lpjm=a-b|mI¡¤z;iH[opqs iI\Da-a-bghj_ m\Da{a-bBytb
(382) 9 nb#sytbsob#[]a-bmWb#s]ps` m
(383) hb []b#a-pb#[+sob#[]a-b mb#[_Lrl\Drrtklhnm=p.
(384) 9 . . . . 4 ISQP43.
(385)
(386) !"$#%&' (*)!+, -&./.0132. \%$ b;m=s/hj_ iI\Dkl[olkl[]b"a-\
(387) b#rrlb
(388) f \Da-a-b$ *0b;m=s/ytb"iIhj_Dmomb " P\6kl[ x mo_-iH\6kl[]lk[]b/b;m=sklrlp ±\D[]a{z#a-bIrtsgP\6[]rlzb P\6r_{yt\DrWiLkrlb0m\6hqklsopq\Drkrlpjw
(389) klb/¦0rl\Dso[]b []\Dhq#a-b Z\6kl[g_Dm]m=b/Wb#s]ps#xW\Dr 6_@iI\DrWm=s][]kpq[]b klr ytpEz#\6a-\D[ollpjm=a-b§_;kWmp []z^Dklhpqb#[(w9kb mk[hqb yt\6a"_RprlbuWtb*±
(390) \Dp[ 4 ©x b#s 4 +` r hbLi`l\6pjmpsBytb sob#hqhb m\D[os]b0w
(391) k¡¤phb#r8
(392) \Dpqz b * mk[ xEw
(393) k¡¤phnm\Dpsz#^_Rh ¦hM¡¤p¥ytb#r8s]pqsozhq\6pqr ytb *§b#s
(394) \D[`mBy¢¡£klr"
(395) \Dpjm=pqrW_;^Db§y86 b *# r)mb yt\Drrlb yt\DrWi§hqb;m s][o\Dpjm|b#rWm=b#a0lhqb;m m=klpq6_Rr8s`m {w9klpbrt
(396) \6pqb. \%$. . OsLb;m=si`l\Dp¥mp. 4 . . . /. * . 0 0 . . . ytb§s]b#hhqb§m=\D[]sob w9klbz. * / -1. . . /. . 0 . . . . . . . * . /. /. . . *i. . . . *3 . 4|b#s *
(397) sob#hw
(398) klb . . . *. - ! * . y8pEz#\Da{\D[]lpjm=a-b-W\
(399) mompqhqb bms{_Rhq\6[`m/hj_ ±\DrWiIs]pq\6r y8zHuWrlpb iI\Da-a-b{mkpqs& m=p ' xE_Rh\D[`m ' ' WW\Dkl[(hqb;mB_Rklso[]b;mBP\6pqr8s`mIxP\6r ytzHuWrlps#xWyl_;rWm§i _Dw
(400) klb/i#_;[]sob h\8i#_Rhb
(401) x hj_²so[`_Rrm¼±\D[oa"_Rsopq\6r w9klpBb#r8
(402) \Dpb hj_ iH\Dkl[oWb
(403) ' mkl["h¥_yt[]\6pqsob
(404) ts /b#sBhj_Rp¥m]m=bprt6_;[]pj_;rtsob§hqb;mByt[]\6pqsob;m
(405) /b#s
(406) 8 fB¡£b;mso©¦;©y8pq[]bew9kb hM¡¤\6r"ytzHuWrpqsByl_;rWmi`W_6w9klb i#_;[]sobkr m lm=s]#a{bytb rl\D k
(407) b#hqhb;m iH\
(408) \D [yt\Drlrz#b;m ' /
(409) W_;[ Br. \%$. . / / / #( mo_Rsopjm¼M_;pqs. ' '
(410)
(411)
(412) : #. # G ' Os :#. f bm lm=s]#a-b{_Dy8a-b#s/y8b;m/m\6hqklsopq\Drm +\DrWb#kls{i`l\Dp¥mpq[xW_R[0b#8b#a-lhb
(413) x x p ' b#sb#r0ytz;ytkpq[]b b#s #8 r{__RprWmpEytzIuWrlp8klrlbBs][`_;rWm¼±\6[]a"_;s]p\D r '/
(414) ') /
(415) _;kWm]m=p[]z#^6klhqp#[]b w9kl| b l h\D[mHxtW\6kl* [ ' x. ' } '/ *& ' O } '/ *& ' %\ $ "b;msnklrlb ±\DrWiHsopq\6r/ytb
(416) z
(417) E¦6_;hqb#kl[my_RrWm
(418)
(419) w klp
(420) 6_Rkls b#r8s][ob}s|b#s b#s s _RklMytb#h¥¦Lytb 'upqrW_;hqb#a{b#rtsx b;msgklr"ytp ¢z\Da-\6[]llp¥ma-bgytb(a #a-b []z^Dklh¥_R[]ps]z(w9kb lxiD¡¤bms]M¦RMytp[]b. b | s © h ¡ ; _ l l h j p # i ; _ s]pq\6r b;m=sBytb iHhj_6m]m=b 4 _;pqrWm=pnw9kbg 4 " . ±
(421) \Dp[4 . QQ. "{µ¶·[?. . . . .
(422) ' «
(423)
(424) . d. #)#. i^ G^Á°]^j;6k kGk «y. e\e\ e. r 6_²a"_;pqr8s]b#rW_;rts0z#sokWytpqb[hM¡ _Rlhqp¥i#_Rsopq\Dr w9kp¦´ y8zHuWrlpbW_R[. ! 5 ! . L U . . . .
(425) z *&0_Dmom\8iHpbL . . \%$ /o/ 1bms|m=\Dhkls]p\Dr{ytk-l[o\Dlh#a-b|_;kl8pqhqp¥_Rp[]bBmk[Yhby8\Da"_;pqrlb m=kl[M_6iHb;m²bs * ´ ! *; . hpqa-ps]z W_R[ghqb;m. {³Wn° i^j; Zn\Dkl[§s]\6kls
(426) tx b;ms§y8zHuWrlpb/y¢¡£klr²
(427) \6pjm=pqrW_;^Db0ytbs-y_RrWm. " ? *&¦ 6_Rhb#kl[yl_Rrm ! " ? *& rT6_a-\Dr8s][ob#["w
(428) klb b;m=s iI\Dr8s]pqr8klbb#s y8p Ez#[]brtsopj_Rhqb
(429) 'c m]m=b#rtsopqb#hhqb#a0b#r8s#x;\DrD_L[]\Dk
(430) b#[|hj_/ytp Ez#[]b#r8s]p¥_Rlphqps]zBytks]b#[oa-br\Dr h\8i#_Rh. - ! 5 ! * . h¥_/ytpEz#[ob#r8s]pj_;lpqhpqsoz§ytb§hj_0iH\Dk[]lkl[obLrlb§W\
(431) m=b/W_DmBytb l[]\6lhq#a{ba"_R}=b#k[# 8Z\Dk[iHbhj_tx \6r±b#[_txt_R[³krlbl[ob#a-pq[]b³a{z#s]l\8y8b
(432) x
(433) hj_[]b#kl
(434) bBy8bhj_ ytp Ez#[ob#rtsopj_;lpqhpqs]zBy8 b * lkpjmHx _R[|klrlb m=b;iH\Drytb§a-z#s]\8ytb
(435) xt\6ri#_;hjiHkhqb#[_Lm]_0ytp ¢z[]b#r8s]pb#hqhb
(436) * §Wb#klsemH¡£b#t[]pqa{b#[b#r²±\6rWiHsopq\Dr ytb-hj_m=\Dhkls]p\Dry¢¡£klr ¨+¡ _Rllhpji#_;s]p\D´ r []\Dhq#a-b(_Rktphqpj_;pq[obs][_RrWm=P\6[]soz/mk[**; r"6_so\DklsBy¢¡ _RW\D[y s][_RrWm=P\6[]sob#[hbl[o\D hq#a-b _;kltphqp¥_Rpq[ob/m=kl [ *br²klsopqhpjm]_;rtsBhqb0y8pEz#\Da{\D[]lpjm=a-b§l[]z;iIz;ytb#a-a0b#r8s|ytzIuWrlp© rytzHurlpqs|hb;m4±\6rWiHs]p\DrWm o@ bs - W_R[Bhqb;m³p¥ytb#r8s]ps]z;m. . ' ' ' : ' o9 ~o9 . f bmY±\DrWiHsopq\6rWmm=\Dr8sBm\6hqklsopq\Drmy¢¡£klr"l[]\6lhqa-b_;kl"hqpa-pqsob;m+yl_;rWm. / o / $ . \%$. / o / 1 b;msBhqbso[`_;rWmW\D[os]zeytb . _R[. *i . . 6o. o. 5 o6)/ 5io/o / o5 ! / - ! 5 & ! . b#s
(437) $ b;msBhqbso[`_;rWmW\D[os]zeytb;mBmb;iH\6rWylm³a-bal[ob;mH . -'³W° i^j; t0¯
(438) « ¯^ '`P k k£k «#$ |b#a"_R[w9k\DrWmBw9kb s(/ ./ gb;m=shqbem ms]a-b ytb0~_#tpb#[]=
(439) so\D
(440) b;m|_;kltphqp¥_Rpq[obL\6[]pq^6pqrlbh© rWb#ksa-\Dr8s][ob#[ w
(441) klb§h©¡ _Rlhqpji_Rs]p\Drw
(442) klp+ ¦ -_Dmom\8iHpb/hqb;mBiH\
(443) b iHpqbrtsm³ytb h©¡¤\6Wz#[`_;s]b#kl[ / / b;ms(ytb 4 iIhj_Dmomb ytb " ? *&§¦"6_Rhqbkl[`m§yl_;rWm ! " *. 4 " *&. " £. 4 " ? *&. 4 " *&` ;¨¢b;miH\
(444) b "iHpb#r8s`mWytb Em=\Dr8snytb+hj_Y±\6[]a-b £ / $ / \%$ -b;ms+krlb ±\6rWiHsopq\Dr
(445) DphlmI¡ _;^Dpqsgytb|a{\Dr8s][]b[nw9k¡£pqh¥m+m\6rts y8p Ez#[]brtsopj_Rhqb;mniH\Da{a-b ±\6rWiHsopq\Dryt| b Á
(446) \6pq [ 4 ©x ©x 44 b s 4R% 4 ISQP43.
(447) #.
(448) !"$#%&' (*)!+, -&./.0132. 3^ G^±°.^j; o= / g#«W°±i^±«1` . / o) / $ r-kls]phqp¥mb³hbsolz#\6 [o#a-bytb;m¢±\DrWiIs]pq\6rWmpqa-lhpjiHps]b;mlW\Dk[hM¡¤z;w
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,
L’étude du lien entre changement du contenu du travail et transformations de la division du travail au sein de l’institution, montre que les restauratrices issues des
Pour modéliser l’écoulement de l’air dans les voies aériennes le plus précisément possible, on peut penser à considérer une géométrie 3D de l’ensemble de l’arbre
Dans la suite de ce paragraphe, par l’exploitation de l’outil Réseaux de Petri P-temporels, nous prospecterons à proposer une modélisation qui permet la génération de la
- L’ethnographie suppose un recours à des sources de données qui sont multiples et un intérêt porté à d’autres domaines de recherche en sciences sociales
Au regard du score de chaque groupe Véhicule sur le critère de réussite et le nombre de rats trouvant le bras plateforme en une visite lors du test de rétention, la réussite lors
Le choix est fait au niveau industriel de considérer le réseau électrique comme un accès de télécommunication lorsque le modem émet volontairement des
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
We …nd that the normal forest à la Faustmann is the optimal form of management when costs and amenity values do not depend on the proportion of trees allowed to grow over a
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
La possibilité que Bcl-2, PP1 α et Bad s’associent pour former un complexe dont l’activité Bad phosphatase est accrue pendant l’apoptose permet d’envisager que cette
Development; Economic Development; Political Stability; Transfer Of Power; Economic Growth; Algeria.. 973 10 01 972 985 2019 ّ دقم ةم :ّ دح ىلع
« Et encore […] que je ne tienne pour indifférent (comme quelques-uns des principaux de cette Église m’ont voulu faire croire) et de le recevoir sous une espèce ou sous les deux,
hommes de Dieu dans l’islam et le christianisme, sous la direction du même et de Gilles Veinstein, Paris, 2003, p.. commence aux XIe et XIIe siècles à être progressivement imposé
Les recherches que je mène depuis trois ans sur ce que j'appelle les langues ignorées de l'espace littéraire bulgare témoignent de ce manque de volonté de mémoire des textes
These narratives are very interesting from a research standpoint in that they provide a great deal of insight into how the research participants account for the emotional
We adapted shape topological description techniques to the segmenta- tion problem, using a curvature constrained geodesic based mapping function and identifying constrictions
Cette étude avait pour but d’expliquer la transformation du rôle de représentante chez des aidantes familiales dont le parent atteint de démence vit dans un centre d’hébergement