• Aucun résultat trouvé

On the Number of Cylindrical Shells

N/A
N/A
Protected

Academic year: 2021

Partager "On the Number of Cylindrical Shells"

Copied!
12
0
0

Texte intégral

(1)On the Number of Cylindrical Shells Olivier Devillers. To cite this version: Olivier Devillers. On the Number of Cylindrical Shells. RR-4234, INRIA. 2001. �inria-00072353�. HAL Id: inria-00072353 https://hal.inria.fr/inria-00072353 Submitted on 23 May 2006. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. On the number of cylindrical shells Olivier Devillers. N° 4234 Juillet 2001. ISSN 0249-6399. ISRN INRIA/RR--4234--FR+ENG. THÈME 2. apport de recherche.

(3)

(4)  

(5)  !#"$%&" )' (+*+,-*+.0/1 .2,-*+(3(+.0/4 57698:<;=?>A@CBD9EF;HGJILK2EJMEF;G ;NOMPQGRMTSUGWVYXZ:?[\ILGJER]2SU; ^`_aIQbc;NaV^`_aEJVd: ; eOPQf9f\IL_dN&gh;H_d;iMj69;_jMj69;kD\l$mZ=QnLmo>qpQSUEFGJGF;Nr=Qs2s9t>qu!fvPQKL;iV. w%x$yz{}|9~LzL @CEF€2;D PCVd;TN‚ƒIQ„\ %f\ILEJD0NaV†EJD!Na69_a;;ghEJ:<;DUVdEFI2DUV‡2PCMXZGFEJDUgh_aEJMPQG9Vd69;GJGhIL_`ˆILD9;7MTXZGJEFDvgh;_ RE V‰„ŠI2_d: ;ig‹[0XrNcŒIOMTXZGJEFDUg9_dERMPLGLMTXZGJEFDUg9;_jVWŒEFNd6HNa69;VaPQ: ;ŽP}hERV-VdSUMj6‹Nd6vP}NPLGFG2fvI2EFD0NjVWIQ„9PL_d;`[\;TNcŒ;;D Na69;`NcŒIOMTXZGJEFDvgh;_jV‘-’“;f9_dI}€2;Nd6UPQN-Nd6U;ŽDZS9:?[\;_$IQ„9MTXZGJEFDUg9_dERMPLG2Vd69;GJGJVW;DUMGFI0VYEJD9KO”fUP2VdVdEFDUK7Nd69_aILS9K26 MIL:![9EFDvP}NdI2_dERPQGJGJXghE–•—;_a;D0NVdS9[UVd;TNjVŽIL„—˜6UP2VŽVYEJˆ;C™Cš+ W›}œPQDUg<š3 ‰žLœŸ+f9_a;€ZEFI2SUV` ZD9I}ŒD [\ILS9DUg Œ7PLV <š3 W¡Qœ£¢¤‘ ¥§¦0¨—©aª?« {}¬yL®­ I2: f9ShNaPQNdEJILDUPLG‰KL;IL: ;TNa_dX2‡h:<;Nd_aILGJILK2XL‡hMTI2D0€2;T6ZS9GJG. 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.

(6)   T &%?

(7) %&

(8) &?  " ?T" %  %%" T!   y

(9)  NaPLD0N)ghI2D9D9BoS9D˜;DUVd;:![9GF; gh;o f\ILEJD0NaV ;D ghEJ:<;DUVdEFI2D Nd_aILERV‡OILD Mj69;_jMj69; g9BD9I2:?[9_aBGJ;%D9I2:?[9_a;%g9;fUPLEF_a;%gh;)MTXZGJEFDvgh_d;iV?MI2P}hERPQShoNd;GFGJ;)]2SU;NdI2SUV<GF;iV?f\ILEJD0NaV<gh;) VYI2EF;D0N MIL: f9_aEJV;D0Nd_a;GJ;V?g9;Sh MTXZGJEFDvgh_d;iV‘OILSUV!ghB: ILD0Na_dI2DUV]0S9;GJ;D9I2:?[9_a;gh;%fUPQEJ_d;iVgh; MTXZGFEJDUgh_a;V MI2PQZERPQS9?MTILD0Na;DUPLD2NŽ ;VYNŽ[vI2_dDUBfUPQ_‚™Cš3 › œ-;N<š+ ž œ‚ŸŠGRP‹:<;EFGJGJ;S9_a;[vI2_dDU;&MTILDUD0SU;BNaPLE–N<š3 W¡Qœ£¢¤‘  « ziy © ~  y  @CBI2: BTNd_aEJ;‹PLGFK2IL_aE–Na69: EJ]0S9;2‡Z:<BNd_aILGJILK2EF;2‡0;DZ€L;GJILfUfv;HMTI2DZ€L;Th;.

(10)  

(11)  !#"%$#&'$. n. ? $ ) ‚T! @CEJ€L;DoP)Vd;TN IL„ ”fvI2EFD0NjV‹EFD“Nd69_a;; ghEJ: ;DUVdEJILDUV‘+* MXZGFEJDUgh_aEJMPQGŽVd69;GJG`ERVC„ŠIL_a:<;ig[ZX§Na69;VdfUPLM; [\;TNcŒ;;D)NcŒI%MTI2PQhEJPLG-MTEJ_aMS9GRPQ_rMXZGFEJDUgh;_aVOEFDn-,?‘\5769;!Vd69;GFGEJVrVdPLEJg§NdI;DUMTGJI2Vd;? ‡\E–„ŽNa69;!Vd;TNC EJV [\;TNcŒ;;D?Na69;7NcŒI‹MXZGFEJDUgh;_aV‘576U;7g9E–•—;_a;DUM;[v;NcŒ;;D!Nd69;_jPLg9EFEhIL„vNa69;7NcŒIHMX0GJEJDUgh;_jV†ERVNd69;ŒERgZNd6 IL„-Na69;VY6U;GJG3‘ .EJDUghEJD9KNa69;?: EJD9EF:!S9: ŒERgZNd6Vd69;GFG;DUMGFI0VYEJD9K ERVrPLD§EF: f\IL_dNaPLD2NC: ;TNd_aILGJILK2Xf9_aIL[UGF;: ‡vNd6UEJV ŒERgZNa6MPQDH[\;Ž€ZEJ;Œ;gHPLV-P7:<;iPLVdS9_a;`IQ„ZNd69;]2SvPQGJE–NcXCIQ„9MTXZGJEFDvgh_dERMPLGQIL[9bc;M¤Ni/‘ ,r;€ZEFGJGJ;_jV-PQDvgH^`_d;fUPQ_jP}NjP _a;g9SUMT;%Nd69; f9_aIL[9GJ;: NaI“GJEJD9;PL_<fU_dI2KL_jPQ: : EFD9KEFDNd69;§Vdfv;iMTERPQGMP2VY;%IQ„rVd: PQGJG7ŒEJgZNa6”PLDU1g 0UDUg P fU_dI}€}PQ[UGFX K2IZIZgoPQfUf9_dI hEJ: P}NdEJIL3D 2 ,r^Žs2s 4 5‘ *OK2PQ_aŒ7PQG /‡ *&_aILD9I}€“PQDU7g 6Z6UPL_dEJ_MTI2: f9ShNd; EJD ]0SUPLg9_aPQNdERM NaEF: ; P MTI2DUVcNjPQD0N„+P2M¤NdI2_?PQfUf9_dI hEJ: P}NdEJILD IL„Na69;ŒERgZNa86 2 *9*96hs2s 4 ;‘ :OPL_ <£^;GJ;g PQDv7g =ŽPQ_jPLg9PL_aPQbYPQD fU_dI2fvI0VY;‚NdI‹MTIL: f9S9Nd;7PQ?D >A@CB†PQfUf9_dI hEJ: P}NdEJILDHEJD!NdEJ:<;7GJEFDU;PQ_EJD! PLDUg;hfvI2D9;D0NdERPQGZEJED DFG2 :OH^ =Cs9&t 4 ‘ 5769;_d; ERV‹„Š;Œ ŒI2_d hV‹PQ[\ILS9N‹;9PLM¤NPLGFK2IL_aE–Na69: VONaI MTI2:<fUShNd;<Nd6U; ŒEJgZNa6W/‡ I£D K2;D9;_aPLGf\I2VdEFNdEJILDW‡ J fvI2EFD0NaVrgh; 0vD9;g PMTILDvVcNjPQD0NODZS9:?[\;_rIQ„‚Vd69;GJGRV?ŸŠGJ;VaVNa6UPQD Lt KQs0¢6UP €ZEFDUK Nd69;iVY; J fvI2EFD0NjVOI2D)Nd69;EF_ [\ILSUDUg9PQ_aMX 2 ,ON§^‚5s9t 4 ‡ZNd6ZSUVP<DUPLEF€2;CPLGFK2IL_aE–Na69: ŒEJGFG‰6UP €2;‹<š3/ P}œŽMIL: f9GJ;ThE–NcX2H‘ *&K2PL_dŒ7PQG ‡ *&_aILD9I}€ PLDUQg 6h6UPQ_aEFR_ 2 *S*969sLTs 496UP €2;‚f9_aILf\I2Vd;g?P&_a;ghSUMTNdEJILD?NdI‹PrMILDZ€L;‹6ZS9GJGZEFD%tsrghEF: ;DUVYEJILDvV$Œ6UEJMj6!X0EJ;GRg9V NaI P <š3 W¡Qœ‚MIL: f9GJ;ThEFNcXPQGJKLI2_dEFNd69:)‘ I£D§Na69ERV&fUPLfv;_‡vŒ;ŒEJGJG$f9_aI}€L;‹S9fUfv;_CPLDUg)GFI}Œ;_[\ILSUDUg9VO„ŠIL_Na69;?DZS9:![v;_OIQ„ŽMIL:?[UEFDUPQNdI2_dERPQGJGFX g9E–•—;_a;D0NO;DUMTGJI2VdEFDUK MXZGFEJDUgh_aEJMPQG-Vd69;GFGRV7„ŠIL_CP VY;N&IQ„` fvI2EFD0NjVEFD)Na69_a;;?ghEJ: ;DUVdEJILDUPLG-VYfvPLMT;2‘5769;iVY; [\ILSUDUg9VŽXZEJ;GRg9V‚NdI?P?<š3 ž œ†MTI2:<fUGF;ZEFNcX!„ŠIL_ŽNa69;O;9PLM¤NPQGJKLIL_aEFNd69: IQU„ *&K0PQ_aŒPLG3V‡ *&_aILD9I}€<PQDUg 6h6UPQ_aEF_ MIL: f9ShNaEFDUK!Na69;Vd: PLGFGJ;VYNŒEJghNd6);DUMGFI0VYEJD9K Vd69;GJG3‘  Y  ?   ?

(12) )T W X Z b d $e3f;

(13) + $ !A$#gO! h

(14) +&C?#

(15)  "i !"jk l9m& nho [Q\ ¦Z« { ¦

(16) ^]`_ a c &p$#q?$ $nr$ ™Cš3 › œ s t { «Wv« u  ’o;MTI2DUVdEJgh;_Nd69_a;;Vd;TNjV7IQ„† f\ILEJD2Nj&V w xhy{z vš G | }m~ }m~ œ } >G | ” € y z vš | }m~ } œ } >G |  ‚Ly{z š ƒ y } | }~ œ } >G | ” VdSUMj6Nd6UPQNrNa69; ‚ y [v;GFI2D9K2VrNaINa69;<MEF_jMTGJQ; „ EFD“f9GJPLD9+; z ~ IL„MT;D2Na;G_ † z š ‡ } ˆD }~ œPQDUg_aP2ghEJSU9V ‰ PLDUg  EJV&VdIL: ;‹f\I2VdE–NaEF€2;CfvPQ_jPQ: ;TNa;_NdI [\;Mj69I2Vd;D GJPQNd;_Ÿ+Vd;G; .EFK2S9_d; t ¢¤‘ 5769;D)„ŠIL_&PLD0XNd_aEFf9GJ;š œ`Na69;PQEJ:ERV7NdIg9; 0UD9;!P<Vd69;GFG-VdSUMj6 Nd6vP}N&Na69;HEFD0Na;_aDUPQGWMX0GJEJDUgh;_OEJV NjPQD9K2;D0N&NaIGJEFD9Q;  z z | ~ }‹Š-PQ}N Œ x y PQDUg§NdIGJEJD9;  z Ž z ~ P}N €# PLDUg§VYSvMj6§Nd6UPQNONa69;?;0Na;_aDUPQG MXZGFEJDUgh;_EJVNjPQD9K2;D0NŸŠILS9NaVdEJgh; ¢NdI ­ EJ_aMGFO; „“PQN ‚L ‘ 5769;NcŒ‘I 0U_jVYNHNaPQDUKL;DvMTEJ;VPL_d; K2_aPLD2Na;g“f9_aI}€0ERgh;igNa6UP}N?Nd69;PQhEJVHIL„Na69;Vd69;GJG‚ERV?g9EF_a;MTNd;go[ZX €2;MTNdIL_ x y’€# PLDUg fvPLVaVY;iVNd6U_dI2S9KL6P%f\ILEJD2N‹IQ„GFEJD9; x y —‡—Na6UP}N‹fvI2EFD0N‹EJV‹Mj69I0VY;DP}NCNd6U;!EJD0Nd;_jVd;M¤NaEFI2D (. ). “%“•”–A—˜ ™#—.

(17) m. a !&. €. . . ƒ. aLp&#$. „ „. xhy. . Vyr. . ‚L †. ƒ. xy. ‚L. EJKLS9_a; t w‚™Cš3 › œŽGJI}Œ;_[\ILSUDUg ;T9PQ: f9GJ;L‘ f\ILEJD0N IQ„ † ŒEFNd6 \‘‹5769;D Nd6U;<MX0GJEJDUgh;_CŒEFNd6§Na6UP}NHP}hERVOfUP2VdVdEJD9K Nd6U_dI2S9KL6 PLGJVdIfUP2VdVd;V Na69_aILS9K26 y  €# PLDU‚Lg  ERVNaPQDUKLx ;y D0NNdI<f9GJPLD9;CO ƒ <VYI?Nd6UPQNf\ILEJD0NaV x }z  | PQDvg €  } z  Š PQ_a;Oxhy I2ShNaVdERgh;ONa6UP}N MXZGFEJDUgh;_‘ ’o;H6UP €L;rD9I}Œ NaI MTILDvVYERgh;_D9I}ŒƒNd69;HMTXZGJEFDvgh;_ŒEFNd6%Nd69;HVaPQ: ;HP}hERVfvPLVaVYEJD9K!Nd69_aILS9K26 ‘ .EF_jVcN Œ;7MPQD!_d;: PQ_a rNa6UP}NNd6U;7MEF_jMTGJ;IQ„vM;D0Nd;_  yr fUP2VdVdEJD9K&Na69_dI2S9KL6 ‚  EJVNjPQD9K2;D0N$;0Na;_aDUPQGJGJX‹Nd‚T9I  „VYEJDUMT; EFNaVC_jPLghEJSUVrEJVC[9EJKLK2;_ONd6UPLD Nd6U;!_jPLghEJSUVrIQ„ „` ‘ 6ZEJDUM;?Na69;<MXZGFEJDUgh;_CERVrD9IQN‹€L;_YNaEJMPQG ‡\EFNaVCEJD0Nd;_jVd;M¤NaEFI2D ŒEFNd6Nd69;r69IL_aEFˆILD0NaPLG9f9GRPQD9;OEJVD9IQNP?MTEJ_jMTGJ;&[9ShN7PQD ;GJGJEFfUVd;L‡ZPQGFNd6UILS9K26W‡2[ZX Mj69IZI2VdEFDUK  GRPQ_aKL;&;D9ILS9K26 EFN!ERV!fvI0VdVdEF[UGF; NaI: PQ 2; Nd6UEJV!;GJGFEJfUVd;%MGFI0VY; NaI“P“MTEJ_aMGF;PLDUg NaI f9_a;Vd;_a€L; Nd6U;%f9_aILf\;_dNcX Na6UP}eN „ EJV NjPQD9K2;D0NEFDvVYERgh;CNdI Na69;MTXZGJEFDUg9;_i‘ .. $  ‰‚T?%$&

(18) ’o;HŒEJGFGWfU_dI}€2;rEJD)Nd69ERV&Vd;MTNdEJILDW‡ZNa6UP}N&Na69;MTI2DZ€L;T6ZS9GJGWIL„†M;_dNaPQEJD)VYf\;MEJPLG-MTI2D 0UKLSU_aPQNdEJILDIL„f\ILEJD0NaV EJDghEJ: ;DUVdEFI2DUVŽMPQD9D9ILN`_d;iPLMj6Na69;&ŒIL_jVcN`MP2VY;MIL: f9GJ;ThE–NcX!IQ„‰<š+ }œa‘ N§IL_a;fU_d;iMTERVY;GFXEF„—Nd69;&Vd;TN IL„} fvI2EFD0NjV&ERV&IL[9NaPQEJD9;ig)[0X%NaPL ZEFD9K #f\ILEJD0NaVOEFD PLD§60XZf\;_af9GRPQD9;?PLDUg) IQNa69;_rfvI2EFD0NaVOŒ69ERMj6 PQ_a; Na69;‹f9_aIQbc;MTNdEJILDIL„WNd6U9; 0v_aVYN “fvI2EFD0NjVEJD)PQD9ILNd69;_6ZXZfv;_dfUGJPLD9;rŒ6UEJMj6 ghI!DUIQNEFD0Na;_jVY;iM¤NNd69;‹MTI2D0€2;T 6ZS9GJG‰IQ„$Nd69;H “fvI2EFD0NjV‡ZNa69;D Nd6U;‹MILDZ€L;6ZS9GFG‰EJD  ghEJ:<;DUVdEFI2D%ERV7Nd6U;C;ZNd_aSUVYEJILD%IQ„Nd69;HMILDZ€L;60SUGFG EJD Nd69;H6ZXZf\;_af9GJPLD9;V7PLDUg6vPLVMTI2: f9GF;hE–NcX%<š3    œd‘.

(19). ! " “ $#.

(20)  

(21)  !#"%$#&'$ K. .  . ƒ  . . ƒ. . EFK2S9_d;=Aw .9IL_7Na69;Hf9_aIZIQ„$IL„5769;IL_a;: =9‘ .. ¦Z« { ¦.

(22)   g  5

(23) ;- b & b p"dv$5  "v   M" aT#&‹d5   -!  L $? [Q\ &pqe‹ nm#&!dA$O   s &  Gvn 9"d ZV b & b  "vQ   &

(24) e‹#  s "   i $&H  ‘b h!$9"dv    9!  b m&#&!d  d  " VqCdm#’! &   n   z  !  # s "   #d a%$- '&    ( "$+! +$&"

(25) + "T$ 

(26) b ‹d! #

(27) b p)$-;"$   s & &   g ! " r$    #s. . š œ š œ <š3 œ t { «W«vu  5769;%VdfUPLM;ERV!g9EF€ZERgh;g EFD „ŠILS9_ ]0SUPLgh_jPQD0NjV[ZXoNd69; 6ZX0f\;_af9GRPQD9;iV PLDUg  Ÿ+Vd;;‘.EFK2S9_a; =2¢¤‘5769_a;; IL„Na69;Vd; ]2SvPLgh_jPQD0NaVHPL_d;<IL[Z€ZEJILSUVdGFX Vd;fvPQ_jP}Nd;ig „Š_aIL:  [ZX I2_ PQDvgNa6ZSUVHMPLD9D9IQN EJD0Nd;_aVd;MTN & #š  œa‘ ­ ILDUVdEJg9;_7P„+P2MT;*kIQ„ &  š  œ†EJDNa69;C„ŠILS9_dNd6 ]0SUPLgh_jPQD0Ni‡2Œ;S0v_aVYN7MGJPLEF: Na6UP}N   [\;GJILDUK2VNdI Na69;?ghEJ_a;M¤NaEFI2D%IL„+ ‘ I£DUgh;;g‰‡vE–„†Œ;g9;D9ILNd;, PQD)6ZXZfv;_df9GRPQDU;‹VdS9f9f\IL_dNdEJD9K! PQDUg 'Na69;CD9IL_a: PQG9Na.I  V‡ ƒ)P€2;_dNd;<IL'„ kEJD PQDvg ƒ  EFNaVf9_aIQbc;iM¤NdEJILD I2D  ‡   P?€L;_dNd; IQ„kEJD  PQDvg E–NjVHf9_aIQbc;MTNdEJILDoILD ? ‘ 6ZEJDUMT!;  ERVHP VdS9f9f\IL_dNdEJD9K§6ZXZfv;_dfUGJPLD9;!Œ; :?SvVcNH6UP €2;eƒ PQDvg ILDoNd69; VaPQ: ;‹VYERgh;CIQ'„  Nd6UPQNEJV7VdEFK2DWš ƒhƒ / ' -‹œ z VdEFK2DWš    / ' -‹œd‡9[UShN&VYEJDUMT; ƒ ƒ  PQDUg   PL _d;CMTI2GFGJEFDU;PQ_NdI I #‘   PQDUg%EFD)I2f9fvI0VYEFNd;HghEJ_a;M¤NaEFI2DUV‡hŒ;‹KL;N7Nd6UPQN   [v;GFI2D9K2VNa! I£D)„+P2M¤NOŒ;H6UP €L;‹Na6UP}NONd69;H„+P2MT;iVIQ„ & #š  œPL_d;H;E–Na69;_&„+PLMT;iVIQ„ & #š  œd‡v„+PLM;VIL„ &  š   œ‚IL_ „+P2MT& ;iVGFEJD9  ZEJD9KP „+P2MT;IL„ &  š  œ‚NaIEFNaV&fU_dILbc;M¤NaEFI2D)EF& D & # š   œd‘&576ZSUV7Na69;NaIQNaPLG-DZS9:![v;_&IQ„†„+PLM;V IL„ #š œŽERV7Na69_d;;CNdEJ:<;iV7Nd6U;HD0SU:?[\;_IQ„„+PLM;V7IL„ #š œd‘ “%“•”–A—˜ ™#—.

(28) a !& J. . aLp&#$. ODh„ŠIL_dNdS9DvP}Nd;GFX2‡Œ;§6vP €L;)D9IQN „ŠI2S9DUgPLD0X”VYSUE–NjPQ[9GJ;§KL;D9;_jPQGJEFˆiP}NaEFI2DIL„‹5769;IL_a;: =oŒ69;_a; LP DUg  PL_d; Œ < vPQNaVHŒEFˆ Nd6 Œ   Ž 9‘ .UIL_;hPL: f9GF; ˆ EF„  z #x ySz š | } | ˆ }~A}~ œ >5 |  PQDvg  Rz x y z š œ &>M |  Nd6U;D Nd6U;<š+ œrVYEJ: f9GJEJM;V š x y } x y  D } x } x  D œrPQ_a; MTI2D0€2;T 6ZS9GJG—„+PLM;V‘ ~A}m~ } | } |  

(29) %

(30) Y †  %%†T? "& ? ?¤%

(31) @CEJ€L;D PVd;TN IQ„Ž #n , fvI2EFD0Nj9V *OK2PQ_aŒ7PQG ‡ *&_aILD9I}€ PQDUg6h6UPQ_aEF_Q2 *9*96hs2s9‡\fUPQK2;QKht2tMTI2G3‘ =T4;Th69EJ[9E–N P“Na_aPLDUVc„ŠI2_d: PQNdEJILD : PLf9f9EJD9K P#n , f\ILEJD0N x z !š ƒ }  } 9œEJDNcŒI#6UPLG–„HVYfvPLMT;iV  PQDUg  EFD tis g9EF: ;DvVYEJILDUnV w   š ƒ ˆ @  ˆ œ @ ƒ D @ d ˆ @  › Ž dƒ  ž Ž dƒv ¡ Ž d @!š! ˆ @ ˆ œ P @ š!ƒ ˆ @1 ˆ œ  š ƒ ˆ @  ˆ œ @ ƒ D @ d ˆ @  › Ž dƒ  ž Ž dƒv ¡ Ž d D @!š! ˆ @ ˆ œ P @ š!ƒ ˆ @1 ˆ œ Œ6U;_a; D } D PQ_a;rNa69;MTIZI2_aghEJDUPQNd;VEJD ts<ghEF: ;DUVYEJILDvV‘ *OK2PQ_aŒ7PQG ‡ *&_aILD9I}€PLDU g 6Z6UPL_dEJ_`f9_aI}€L;iV-Na6UP}N‚Nd69;OMIL: f9GJ;ThEFNcXIQ„—Nd6U;EFD0Nd;_aVd;MTNdEJILD IQ„\Nd6U;O OPQDvg  ‹[vI2S9DUg9VCNa69; MTIL: f9GJ;ThEFNcX§IQ„Nd69; ;DvMTGJI2VdEFD9K VY6U;GJGJV‡-PQDvgVdEFDUM; Œ;<6UP €L; PQD“EFD0Na;_jVY;iM¤NdEJILD“IQ„ } 6vPQGF„VdfUPLM;V7EJDotis ghEF: ;DUVYEJILDvV7KL;TN&PLD)<š3 ¡ œŽ[\ILS9Dvg‰‘ *ODEJD0Nd;_jVd;M¤NaEFI2D IQ„r6UPQGF„rVdfUPLM;V!f9_dI2[9GJ;: MPLD [\;Na_aPLDUVc„ŠI2_d: ;ig#EFD”P“MILDZ€L;o6ZS9GJG7IQ„Of\ILEJD0NaV fU_dI2[9GF;: Na69_dI2S9KL6 g9SUPQGJE–NcX“E–„&Œ; ZD9I}Œ P§f\ILEJD2N!EFDUVdERgh; Nd6U;EJD2Na;_jVY;iM¤NaEFI2DW‘ :O;_a;Œ;MPLDo_a;: PL_d  Na6UP}NH„ŠI2_?VdIL: ; GRPQ_aKL; ;D9I2S9KL6Ÿ+GJPL_dK2;_CNd6UPLD Nd69;Va]0SUPQ_a; ghERVcNjPQDUM; [v;NcŒ;;DoNd69;IL_aEFK2EFD PQDUgoEFNaV „+PL_YNa69;VYND9;EJKL6Z[\IL_7EJD ¢T‡9f\ILEJD2NHš ~A}m~ }m~ }m~A}~A}~A}m~ }m~ }m~A} ŽœWERVMT;_YNjPQEJD9GJXEFDvVYERgh;CNd69;‹6UPLG–„`VdfUPLM;V‘ X P!Na_aPLDUVYGRP}NaEFI2DIL„$Na6UP}N&€2;M¤NaIL_i‡0Nd69;H6ZXZfv;_dfUGJPLD9; . . . . . . . .

(32). . . . . . . . . . . . . . "!"!#!. . . . . . . . . . . . . . . %$. &. $. D + *)  @ z ) y  y ~ -y , D. ERVR0U_jVcNNa_aPLDUVY„ŠIL_a: EFD Nd6U;H60XZf\;_af9GRPQD9; z ~. ) . ('. @.  +. y y @ ). y., D. D ). š . D Ž $. Žœ. @/$. D š @ Ž  œ @ y vy D ~ y D Œ6U;_a; vy PL_d;HNa69;!MIZIL_jghEFDvP}Nd;iVEJD§Nd69;!D9;Œ „Š_jPQ: ;2‘O5769ERV&;]0SUPQNdEJILD§ERVODUIL_a: PLGFEJˆ;ig [0X§ghEJ€ZEJg9EFD9K%E–N Z[ X PLDUg[ZX ghSUPQGJEFNcXŒ;‹K2;TNNd6U;Cf\ILEJD0N š @ D } D} ˆ} ›} ž} ¡} } P} } D œ z. ) . ). +. 0. $. . ) 1. -,. 1. ) . ) . ). ) . 0. $. ). ). ). ). ). ) . ). ) . ) . ) . ) . ) . ) . ) . ) . ) . ). 0 ) . ! " “ $#.

(33)  

(34)  !#"%$#&'$. 5769_aILSUKL6%Nd69ERVf9_aIhMT;VaV‡0Œ;‹KL;NNdI fvI2EFD0NjV x ?PLDUg . x. . ƒ ˆ @ ˆ dƒ d  ƒ ˆ @1 ˆ } ƒ ˆ @ ˆ } ƒ ˆ @1 ˆ } ƒ ˆ @ ˆ } ˆ ˆ > Žƒ ˆ  @ ƒ  ˆ } ƒ Ž ˆ d@ ƒv ˆ } ƒ Ž ˆ d@  ˆ } ƒ ˆ @1 @ ˆ } ƒ ˆ @ ˆ m} ~  ƒ ˆ @  ˆ $ ƒ  - ƒ ˆ @1 ˆ @ ƒ ˆ @3 ˆ } ƒ ˆ @1 ˆ } ƒ ˆ @ ˆ } ƒ ˆ @1 ˆ } ƒ  dƒv d  ˆ @1 ˆ > ƒ Ž ˆ @ ˆ } ƒ Ž ˆ @ ˆ } ƒ Ž ˆ @ ˆ } ƒ ˆ @ ˆ }~A} ƒ ˆ @ ˆ  > x  @ ƒ ˆ @ ˆ $ }m~ }m~A}~A}~A}m~ }m~ }m~A} Ž > } > . z . x. x. z . š. z. Qœ. ’o; _d;: PL_d Nd6vP}N #[\;GJILD9K0VNaI Na69;“6vPQGF„ < 6ZXZfv;_dfUGJPLD9; ERV%Nd69; Uf _dILbc;M¤NaEFI2DIQ„ x I2D  x z ~ PQGJILD9K‹ghEJ_d;iM¤NdEJILD e z š }m~A}~A}~A}m ~ }m~ }m~AD }~A} z Ž > ~ } }>Lœ3‘†5769;7~ 6ZX0x f\IQNa69;Vd;V „ŠI2_r5769;IL_a;: =PL_d;€2;_aEj0v;g§PQDvg§Œ;!MTILDvMTGJSUgh;Na6UP}NrNd69;<MTI2:<fUGF;ZEFNcX)IQ„`Na69;?EJD0Nd;_jVd;M¤NaEFI2DUV&IL„`Nd69;  rPQDUg  OŸ ¢`MPQD [v;O_d;ighSUMT;ig!NdI?<š+ ž œd‘†’o;OMPLD VcNjP}Nd;7Na69;7„ŠILGJGJI}ŒEFD9K‹Na69;I2_d;:)‡QEF: f9_aI}€ZEFDUK Na69;Hf9_a;€ZEJILSUVx_a; VdS9G–N[ZX%P!„+P2M¤NdI2_IQ„ w b d $S! › g "e

(35) e 

(36) e

(37) Qo H!d!?&vd !"d $#&Ud i"hVq [Q\ ¦Z« { ¦

(38)  _ a;"Q$&&  ; "dEed

(39) b ‹#C <š+ ž œ ’

(40) C s  ?% "T?!  &  $? &

(41) " ’o;<6UP €L;!f9_dI}€2;D§Na6UP}NCNd6U;!DZS9:![v;_CIL„MTI2:?[9EJDUPQNdIL_aERPQGJGFX)ghEF•\;_d;D2NHMTXZGJEFDvgh_dERMPLG`VY69;GFGRVr;DUMGFI0VYEJD9K%P Vd;TN&IL„ of\ILEJD2NjVERVO™Cš+ › œd‘5769EJV&_d;iVYS9GFNOPQfUf9GFXNdI Na69;HDZS9:?[\;_&IL„†PLGFG$VY69;GFGRV ‘ O„`MTILSU_aVd;‹EFD)KL;D9;_jPQG f\I2VdEFNdEJILDW‡—Na69; :<EJD9EJ:?S9: ŒEJgZNa6#VY69;GFG†ERV‹S9D9ER]0S9;L‡WŒ;<: P X P2VY §Œ6vP}N‹EJVCNa69; : PQhEF: PQG†DZS9:![v;_CIL„ : EJD9EJ:?S9:kŒERgZNd6 Vd69;GJGJVEJD!PLD0XHf\I2VdEFNdEJILD?PLDUgŒ6UPQNERV$Nd69;7: P}hEJ: PQG0D0SU:?[\;_†IQ„vVd69;GFGRVŒ69I2Vd;‚ŒERgZNd6 ERV7GJIZMPQGJGFX:<EJD9EJ: PQGWEJD)KL;DU;_jPQG—fvI0VYEFNdEJILD-‘ ’o;6UP €2;PQGRVYI f9_aI}€L;DNa6UP}N&Na69;DZS9:![v;_&IQ„ŽMTI2:?[9EJDUPQNdIL_aERPQGJGFXg9E–•—;_a;D0NOVd69;GJGJVOEJVr<š+ ž œ‚Œ69ERMj6 _a;g9SUMT;iV-Na69;MTI2:<fUGF;ZEFNcXHIQ„ *&K0PQ_aŒPLG3‡ *&_aILDUI}€‹PLDUCg 6Z6UPQ_aEJ_PLGFK2IL_aE–Na69: NdICNd6vP}NŽMTI2:<fUGF;ZEFNcXL‘ * MTGJ;PQ_ I2fv;D%fU_dI2[9GF;: ERV7NdI _a;ghSUM;CNd69;HK0PQf [v;NcŒ;;D Nd69;iVY;‹GJI}Œ;_PQDUg%S9f9f\;_&[\ILSUDUg9V‘

(42) }&" 2 *S*O6hsLds 4 ^PLD9 }P}b ‘ *OK2PQ_aŒ7PQG ‡ IL_aEJRV *&_aILDUI}€\‡ZPQDv? g N)ERMj6UeP 6h6UPQ_aEF_i‘ †9P2M¤NPQDUg%PQf9f9_aI hEF: PQNdEJILD PQGJKLIL_aEFNd69: V„ŠIL_): EFD9EJ:?SUQ: < ŒERgZNd6˜MTXZGFEJDUgh_aERMPQGHVd69;GJGRV‘ I£D  mL s !Mo  h

(43) b $ s  r$&&mi!9 q-d !V

(44) $ ‡UfvPQKL;iZ V Kht#s " K9t ‡Z=Qs2sLs Ÿ NdIPLf9f\;PQZ_ , ­ @H¢¤‘ . .  1 . . . . $. . . . '. “%“•”–A—˜ ™#—. 1 . 1 . .

(45) u. a !& . aLp&#$. §^Ž5s9t&4 rGFEJ€ZEF;_ ,O;€0EJGJGF;_aV‡ ;_aDUPQ_jgQN§ILS9_a_aPLEFD-‡d.9_jPQDUMIC^`_a;fvPQ_jP}NaPU‡QPQDUg ^`6UEFGJEFfUfv;&5$_d;[9SUMj69;N‘. rDMTEJ_aMS9GJPL_‚MTXZGJEFDvgh;_jVŽ[ZX!„ŠILS9_ILH _ 0U€2;&f\ILEJD2NjVŽEJDVdfUPLM;L‘—e&PQf9f\IL_dNgh;O_d;iMj69;_jMj69;mUt -K9‡ I OZ e I *?‡\=Qs2s9t2‘ 2 ,C^ŽsLds 4. rGFEJ€ZEF;_ ,r;€ZEFGJGJ;_jVŽPQDU+ g .U_aPLDUMTI^‘Z^`_a;fUPL_aPQNaP9‘ `€}PQGJSUPQNdEJD9KHNd6U;rMTXZGJEFDvgh_dERMTEFNcX?IL„-P‹D9ILe: < EFDUPLGFGJXMX0GJEJDUgh_aEJMPQG`f\ILEJD2NVd;TNie‘ I£D    s  !  Mo    h

(46) b T$ s  r$&&m&‹9 q-do  !V

(47) $ ‡9fUPLKL;iV Kht#u " K2= ‡Z=Qs2sLs9‘ 2 :O^ =rs9&t 4 6hPQ_aEF;%G :rPQm_ < ^;GJ;g)PLDUg HPLVYNdS9_aE-eHv‘ =ŽPQ_jPLgUPQ_jP}bYPQD-‘@C;I2:<;Nd_aEJM?VY6UPLfv;!PQf9f9_aI hEF: PQNdEJILD €0ERP<GFEJD9;iPQ_aEFˆiP}NdEJILD-‡U=QsLsUtL‘$: PLDZSUVdM_dEJfhNi‘ 2 ,nN. '. . ! " “ $#.

(48) Unité de recherche INRIA Sophia Antipolis 2004, route des Lucioles - BP 93 - 06902 Sophia Antipolis Cedex (France) Unité de recherche INRIA Lorraine : LORIA, Technopôle de Nancy-Brabois - Campus scientifique 615, rue du Jardin Botanique - BP 101 - 54602 Villers-lès-Nancy Cedex (France) Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu - 35042 Rennes Cedex (France) Unité de recherche INRIA Rhône-Alpes : 655, avenue de l’Europe - 38330 Montbonnot-St-Martin (France) Unité de recherche INRIA Rocquencourt : Domaine de Voluceau - Rocquencourt - BP 105 - 78153 Le Chesnay Cedex (France). Éditeur INRIA - Domaine de Voluceau - Rocquencourt, BP 105 - 78153 Le Chesnay Cedex (France).   

(49).   . ISSN 0249-6399.

(50)

Références

Documents relatifs

AMC PAPI : Spécificités du contexte torrentiel – Rapport de Phase 1 Page 18 sur 46 Dans le cas des laves torrentielles, on peut résumer les conditions nécessaires au

Gillard, “Combinaison de la DG-FDTD avec un mod` ele de substitution pour un calcul de dosim´ etrie locale dans un probl` eme variable et fortement multi-´ echelle”, dans 18`

Le jugement porté par les femmes lettrées sur leurs soigneurs doit donc être nuancé en fonction de la personnalité de chacune, de la gravité de la maladie,

3.3 Processus d’alimentation d'entrepôt de données : Nous devons extraire, transformer et charger les données à partir des sources précédemment citées, dans l'entrepôt de

« La prophétie, ou interprétation et conférence des Écritures se fera par les ministres du Colloque, en l’assemblée où chacun dira la tête découverte ce que Dieu lui

Pendant six ans, jusqu’au premier janvier 1568, le clergé de France doit fournir chaque année au roi l’équivalent de quatre décimes, un million six cent mille livres tournois,

« On ne fait pas que des psychothérapies en clinique/…/On en parlait encore ce matin : est-ce qu’on a le temps de faire des psychothérapies, parce qu’on voit les gens

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des