• Aucun résultat trouvé

Delaunay Triangulation Based Surface Reconstruction : a short survey

N/A
N/A
Protected

Academic year: 2021

Partager "Delaunay Triangulation Based Surface Reconstruction : a short survey"

Copied!
16
0
0

Texte intégral

(1)Delaunay Triangulation Based Surface Reconstruction : a short survey Frédéric Cazals, Joachim Giesen, Mariette Yvinec. To cite this version: Frédéric Cazals, Joachim Giesen, Mariette Yvinec. Delaunay Triangulation Based Surface Reconstruction : a short survey. RR-5394, INRIA. 2004, pp.12. �inria-00070609�. HAL Id: inria-00070609 https://hal.inria.fr/inria-00070609 Submitted on 19 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. Delaunay Triangulation Based Surface Reconstruction : a short survey Frédéric Cazals — Joachim Giesen — Mariette Yvinec. N° 5394 Novembre 2004. N 0249-6399. ISRN INRIA/RR--5394--FR+ENG. Thème SYM. apport de recherche.

(3)

(4)  

(5)    !" $#%'&(*)+&(' ,$ &- /. 01 23 45

(6) 687:9<;9=7?>A@B"CEDFCHGAI J8KHL CH@%M>ANOP>RQ=I?Q<S J-T CH7:>RQVU?UWQ XY>ASQ<@ Z5[]\^"_'`<acx-beylpVz{df_j|h `F}cgihk~:jlpV\:^"^m~_?j|h ylruhlg<€ ^onEp=qsrut<vw_:h  €ƒ‚]‚Ep=ykj „i_y|_: [w_:y| [w_‡†Hˆ‰ƒŠ=‹ƒŒdŽ p%=_^onwyl_2ƒ‘=‘ƒŒ'd“’?'‚]€ƒ”=_:h ∗. †. ‡. •—hlvw–$ylžŸ˜:€V™š%_ª›w©œV™V[w ru [ `ir£hvw«FykžŸ†w€=p%©_ † y|_:pV†wp=q£†]g¨hkj|jl[wy|v]ylp=¡j|vwrs”Vp=[ †¢€op=¬]†]†whlrsr£jlhk_j|h"h|€ƒr£†¤^"‚wq£pVrs†]^"”]‚w­®vwZ5jlr£[w†wru”¥h„i€¦pi^mvwpi^"„i__:†<qj jl[Eruh€%j—€"€ƒhk[w‚]p=‚wykyljpW§ihlvwr£^¨yl=€%_jlg¨_?hop=†€ hl€µvwqsylp=žŸ†w€V”V_(_:y°y|_:hkv]pVyl†]=hk_jlg y|v]©¡ylj|rsrsjkp=j|†_†¶^"nF_j|g [wpi·w„wy|~:h„in]~:€Vylruhlo_:„'¸¹pV€ƒ†"º?€ƒ¯°quh°_:q£€V€V†]vw„P†]€W»Vgp<€Vj|yl ru[w€ƒr£†w^+”=vw}cqu€%r£_:jlr£hlpV_††½­,¼¾±²¸5j®}[]‘V€VŒ%h¿RnH­c_Z5_:†o[wruy|h°_©hl[wy|pVr³jlyljljª_:†hlvwž´yly|=pV_^ g ruh ÈH^"Ò¨_?Óª€ƒÅ|†<Ë j°ÇƒÈwj|pµÎ¡ÏAnEáÂ]_mËnHÏR͟_'Ç%ȗpV†]©_[]pƒr£ ž®[¶j|[wruhc_opV †w[]_m€V‚ipƒjlž®_:y°j|[wpV_¨ž$„ij|[w_q£_mr£V`F_j|y €%€ƒj|n]_'qs_?pVh ž®pƒjlž-[w_mjl[wÀ _mylÔ8jcvwy|pV_:‚E‚Hp=_:€Vykj†¶ÁH†wÂi_áj{ÄW©¹ÅpVÆ y|« ÇƒÈÊpƒž8ɰ_Ë §iÌÂi_Íuq£Î qsÍÐ_:ÏR†]͟Ç%È_ À°Ñ ±{bÖÕ`F[]€V‚E_=­ ×PØ<ÙÛÚ|Ü'Ý š%Þ$˜V `ivwykžŸ€=_y|_:p=†]hkjly|v]¡j|rsp=†,ßwhk[E€ƒ‚H_€V‚w‚wy|pW§irs^¨€%j|rsp=†,ß<yl_:V_y hl_ªr£†w”V_:†w__:ylr£†w”. ∗ † ‡. àEù áŸä{â ó%ãAì äæáŸååAéç$ä{è{öâ¡éåîÐè{ö?åAúsáŸâ¡ê¾ëláAì?é íWì|î´åAï$ê¾ûƒð,íƒîÐüEñ¦ýò:þÊâ¡ó?ÿôWWáêõ칟ê¾ë²ñ$ô öåAê¾óVâ¡÷¾ê ø àEáŸâ ãAäæåç$è{â¡éè{åAáŸê¾ëlì?íWî´ï$ð,îÐñ¦ò:â¡ó?ôWêõì¹ñ$öåAê¾óVâ¡÷¾ê ø. Unité de recherche INRIA Sophia Antipolis.

(7) )+&(  $ &8$    #%&( 2 $'  $   ' 

(8) .   $#  $4 hlvwylžŸ˜€V  _o p=†w

(9) †F vw€—_"hky|_:_:vwpVqs_:†]^"hkjl_y|†<v]j2¡j|‚]rsp=€ƒ†Êycvw„i†_"~:hkv] []ykžŸ€V€=†=j|_"rsq£q£pVpV†Ö†Ehk„wruh{_oj|_‚HpV r£†<j|€Vh:q£­"vw¸(q£__"y„ivwpi†vw^m^"pi_„i†<\:jqs_"„it<p=†wvw†wr8_m€ƒ‚]vw‚w†ylpW€V§i‚Er£_:^"y_'vÖvw†w„i__ „w¸(r_Û~„iy|pi_†<vwjl^"_?h_^"†<j8~€ªj|[w~pijl„i~5_:y|h ~:„i„wr£_”V~yl_? °p=‚E†]€ƒh{ylj|jlylr£y8vE¡„jl v]r£pV†o† ~„ij|_'€%j8hl„ivw_5ylžŸq€V €V_?ykh5j®‚wn]q£€Vv]hlh®~_?€Vh‚w‚whkv]y|y pƒž´q£pV€m†Ej|„iylrFru€ƒ~:†]y|”Vrsvwjqu‚E€%€ƒj|rsy®p=·w† y|~:„i„i_o~:¯°ylru_:q£¸¹€Vvw€ƒ†]º:€W€VgVq£h ­ _ÁHj Ï »=ϲp=Å €VÇ —[]rsÏ^ ]Ũ}cɪrsá_?Ï5hk_:Óª† Å]¼õ¸5Ç%á}Ï ª‘ƒŒVÁH¿RÂi­‡Ã¡ÄW¸(ÅÆÖ_j ǃ€ƒÈ¥‚Hɪ_yË Ìv ÂiÍu_:ΡhkÍÐj ÏR͟Ç%„iÈ _?h{j|rsÈH†]Ò ~Ó° Å Ë Ç%p=È]†]ΡhkÏAjlársÂ]jlvwË_:ÏA͟yµÇƒÈ]vwß$† ‚w y|[]pF€V„w‚wvwrsr³jljoy|_¶‚]€ƒ„iyov¤qs_µy|€Vy|‚w~:hl‚H_:pV€Vylv j Ñ „! _Ñ §i_q£qs_:†]__:vwylp=‚E~:_† À ±{bÖÕ`i[]€ƒ‚H_V­ "‡Ý ™?˜ Ú œ$#  ˜  y|_:p=†]hkjly|v]¡j|rsp=† „i_2hlvwykžŸ€=_=ßw€ƒ‚w‚wy|pW§irs^¨€ƒjlr£pV† „w_ªž´p=yl^"_=ßwrs†]”V~†]rs_:ylr£_ªr£†FV_:y|hl_.

(10) mÅ Ñ ÂiÈ Ñ Æ wÃ¡Í Ñ È VÂ Ñ ÏAÍŸÇƒÈ Ñ ÎÅ Ò"ÁHÂià  Ñ Ë ÅªÓªÅ Ë|ǃÈwΡÏRáÂ]ËÏR͟Ç%È Š o¨  &- ±æhl†"vwylj|žŸ[w€V_ª_ hlvwyl­žŸ€VZ5_[w_oyl_?j|€=pVhk†E« h{j|ruylhªv]jlp jlr£pV†"pV^"‚w‚wy|pVvinwj|q£_m_^€ hl©(vw_ªykžŸ€ƒ€=y|__ ”Vr£V_r£†=†¨j|_p=y|†w‚Eq£p=gmq£€ƒ€cjl¬]r£†w†]”µr³j|j|_ª[wh|_"€ƒ^"hl€V‚w^mq£rs‚]†wqs” r£†wS” pƒž­2€ƒ†"Z5[wvw_o†]«<y|†]_:p%pV©† † hvEkjlhky|_?v]„ jlnF_:g „½S„ihkp%vw©ylžŸ†]€Vhkjl_ y|_:S€Vˆ^3ruhm”Vp=_:^m†w‚]_y vi€ƒjlq£_:qsy gւwyly|_:pV‚w”Vy|y _:€ƒhl^¨_†<h¹jl_?ž´„p=y€Vž´Shovwˆyl€Pjl[wjl_:y|y°ru€ƒ‚w†wy|”=pivwq£_:€ƒh|jlhl_?rs„¥†w”Ehk­-vwZ5ylžŸ[w€V__µy|_:j|[]pV€%†]j¨hkSjly|€Vv]† jlnEr£pV_ † „ihkr£yl[w_?p=¡vwjlquq£„g ^¨hlvw€ƒylj|žŸ€V [ _ojly|[]_:_'pVpV†]y|r£hk”Vjlr£y|†]v]€ƒ¡qj|rshlp=vw†¶ylžŸru€Vh2_€ƒ†rs†¶rsq£jlq ²_‚Hy|^¨p=hlh _:„¶pVž8‚]”Vyl_p=p=nw^"qs_:_^ejly|ruhl2rs†]€ƒ†]_'„ j|[wj|pV_y|‚H_¨pVq£€ƒpVy|”=_mr£:hl€ƒ_q,=‚w_y y|€ƒpVq‚Hjl_y|ylr£jl€Vr£_:†wh:”Vß]v]n]q£€ƒvijljª_:„Ör£†¶hk”Vv]_:yk†wžŸ€=_y _:€ƒh q j|hl[]‚H€%_:jors¬E^mr£r³”Vj|rs[<_?j2h'ž´pVvwž qs¬]jlq£[wq8_ j|[whl_:€Vhl^"_—‚wqsy|r£†wrsjl”_y|€ƒru€w†]­ „¥b¶p=†¥__jlj|[]rs†]_ ”P‚w”Vy|_pVp=‚H^"_yl_jljlr£y|_:ruh'opƒp=ž y2j|jl[wp=_ ‚Ep=h|€ƒqsp=^"”V‚wruq£€V_:q8„½hky|vwr³j|yl_žŸy|€Vr£€ _V­„i_:±æ‚E† _:†]‚]„w€Vhykj|p=r£†¦vwq£jl€V[wy:_ ß p=hl‚]ylr£€V”Vy|¹r£hl†]_:r³j{€V:g=qۀƒßv]hlvwy|hl_:_µyl„wžŸ€Vy|vw_:†]_ª„wpV^¨€V†]†]hk€ƒjl«=y|g=_2v]ß®¡hk†wj|vwpVrsylp=ružŸ†¦hk€Vr£†wnE__?p=hlylrsh'_?quh'pƒpVž5„i†Ep%jlh{©[wj|yl_ †¦v]h|j|€ƒjlp¶r£^"pV_:† ‚whkq£j|€mrs€V†wnw ”Ê[Eq£r£pV€ƒhl[wq£y'qsr£_:†w†]†w”ÊpV”V† r£†wæp=hk”m^"†w‚w†wpFyl_?pƒp=¡j|nwjl[wr£q£pV†w_†E^ _?hhl­honH€ƒ_†]j{©¹„¥_nH_† pVv]h|†]€ƒ„w^"€ƒ‚wy|r£q£_:_:hh'pV©ž[wjlru[w [ _ j|€V€V[wylnw_m_:r£qshlrs†w_Êj{g_:h|rs”=€ƒj|[<^"p½nH‚wpVq£piy _:hc„ih¨_ pVru†Öh—j|[w€¥jl_¶[w_µ:†w€ƒ_:hl†]rsvw”=„wyl[<r£žŸ„w€VnH€ƒpVjl_Vy|_Êß,r£†w€ƒ€V”¦†Fvig¶§iyl_:rs”=q£q£ru€ƒ_€ƒjlp=y|r£^mg½pV†]_„wh¨jl€%y|r£r£j †m€¥€ƒh{p=j|†F†]ylg vEhkjl¡„iy|jlv]rsv]y|¡yl_:j|_Prsjlp=r£ž´†ÖpVp=†,yµ„iß¹_y|¬]_:j|[w†wp=_Êr£†w†]¯ª”Phkjl_y|€ quv]€ƒ¡hlvwr£j|^m†]rsp=€W‚]†,g½qs­ rujlruy|¹€ƒr£€Vq8_:†w:”V€ƒpVv]v]^"hlq£€ƒ‚w_Pjlq£r£_pƒpV§Êž2† p=rsj|r£† hh p=nFpV<vwr£y|pVr£hlvE[whk_?q£gµ„ €op%V¬]_y|y hkj°jl[w_oqu€V‚]h|h5€Vhkj €V†]ž´pV„iv]ru„wyª€%g=j|_:_V€ƒ­8y h:­¹_?±æ†¶pV†EžŸh{€Vj|¡yljªv]jljl[wr£_:pVgP† €ƒ^"y|_2_jljl[][wpF_o„]pVh†wn]q£€Vg hl_:pV„ †w_?pVh† ž´pV¯ªyª_©qu€ƒ[wvwru†] €W[¶gµpVjl†wy|_or£€V†w€ƒ”V†Êvwqu‚w€%ylj|p%rsp==† _ j|hl[wv _µp=ylr£__jl†<ruj5€VqpVyl†E_?„ihkr³vwj|qsrsj|p=h"†]hp=†d¤jly [w€%jl_¶[]t<_y-v]€Vy|_:qsrshkj{jlg½y|ru¡pVjlžªr£Vj|_=[wß<_P€Vyl†]_?„¨p=„i†]poh{j|†wylpƒvEj5¡jlt=_?vE„¢€ƒq£hlr³ž´vwgmylžŸjl€V[]_°_V­nH_[]Z5€W[wF_?r£hkpV_Pvwy(‚wy|pƒpFž pƒjlžŸ[]h"_ª[w€ƒp=q£”Vq£„ p=ylvwrsjl†E[]„i^"_yh rsž$jl[wÀ _žÐjl_pVy?†]ß„i€ rsjlr£hlpV[w†EpVhylj2€ƒy|‚w_ªy|_:†whlpV_j †<j|^"€ƒjl_r£j:pV­ †ÊpVž-j|[w_"^"€Vrs†¥pV†]_‚ij hªvEhk_?„Ör£†Öjl[w_"¬]_:q£„,ß,jl[]r£h2hl_:jlr£pV†yl_:<r£_© h _hlpV§i^"[]€ƒ_¶v]hkpVjlž2r£Vjl_=[wß<_Öjl[w^¨_2€ƒy|r£_:† €=„i¯°__:y5q£€Vruhvwyl†]_€Wž´g _y|yln]_?€V„¨hl_:j|„ pPyl¼¾¸5_?}pV€V†Ey{h{¿,j|ylž´v]p=y jl€or£pV^o† v]^" [ _j|^m[wpip=„wyl_2h­ pVZ5^"[w‚wruy|h—_[wy|__:F†]r£hk_r£©V_r£hlh vwylnF=g _g=†w­ p ^"_:€V† . .  . . P. 

(11). P.

(12). 

(13). . . . . Vp·$žr£”Vj|vw[wy|__ ’ vwy| V_ _žÐj € h|€ƒ^"‚wq£_:„2vwy|V_V­$r£”V[<j ,¯ª_qu€ƒvw†E€WgcpV†<j|€Vrs†]h€‚wr£_:_ ²©r£hl_8q£rs†w_?€ƒy$€ƒ‚w‚wy|pW§irs^¨€ƒjlr£pV† $ w "   . . . . . . 

(14). .  !#"$#%'&(%*),+ !).-0/. Z5_[]q£q]_ ž´p=®y5pVy|_:pV€V†] [¨pVr‚H„ipVrur£€ƒ†<”=j¹y|r£€V† ^ V (S8­ Z5[w)_ªpƒž-_q£€µq h|€ƒ^"‚wq£pƒr£†wž” jl[wS_c‚Ep=ruhcrs†<€µj _:ruqsh(q£vwjlqu[w€ƒ_cyªqspipV^"v]‚wh-q£pV_ž§¶‚HpVp%r£=†=_j y|h-rs†]©” []r£R [ ßۀƒ©y|_°r³j|[¶q£p=pVhl†w__y S V (p) p 21. P. P. ðð+ö. 43658789;:. P. 3.

(15) Ñ :Ñ ¾Î 5͟šÎÅÈ Ä?ÍÐÈHÅ Ë Œ. .  . . j|p p jl[]€V†—j|pµ€ƒ†Fgµpƒj|[w_y‚HpVr£†<jpƒž S ­ P. Z5Ë Å []¾_5Î _ q£q£Ë h8ÅpƒÏŸÎž (VÅ (SÒ <ÅÎ ) €ƒÈHy|_¹ÒµÄWpVņFáVÏR͟_Ë|§ÅΡ‚E­ p=qsg<jlp=‚E_?h­Z5[w_5žŸ€=_:hpVž V (S ) €Vyl_:€ƒq£qs_?„'y|_:hl‚E_?¡j|rs=_q£g EÇ%ÃlǃÈHÇƒÍ Ñ Ñ V (p) = {x ∈ R3 : ∀q ∈ SP. kx − pk ≤ kx − qk}..  . P. . P.

(16) *)$"$)6% )." +*)!%*#". ),"(&. )(6%

(17)  / % -  %"!#

(18) /. 5Z¯ª[]_qu_€ƒv]¯ª†]_€Wqu€ƒg¥v]†]pV€W^"g—‚wq£p=_^"§¢‚wrsqs†]_§—qsvEpƒ„iž$_:jlh"[]_€ÊhlžŸ€V€V^m_ ‚]qsž´r£p=†wym” _?S€V [½r£h¹hlvwj|[wn]_hl_„ij v]€Vq pƒž$jl[w_ ß-®hlv]p= yl[½p=†wj|pV[]r €%„ijmru€ƒjl”=[]y|_ €V^ r£†<jlV_:y|(Shl_:jl)r£­8pV†½Z5[wpV_ ž j|¯ª[w__ qu€ƒ®v]pV†]y|€WpVgµ†wp=p=r^m_:‚]qsquqsh_§—∩p%V_:Vy|h-(p)jl[]_r£hªpV†w†Fp=V†Ê_§µ_^"[F‚ivwj{qsqg=­2pVž Z5[wr£hª­®žŸ±²€=žjl_mT[w_2r£h°∈h|jl€ƒ[w^"S_¨‚wq£pVrs†]†F” V_§ [Fruvwh5q£q †wconv(T pVy|ž €ƒTjl_V­2ßFrRZ5­®[w_V_ ­ ) V p. † i „  _ = ”  _ w † : _ r£:†]€ƒq£qsqs_?v]„¨„w_:j|h[w_2†wpP¯°_:hlvwq£€Vn]vwhl†]_€Wjg"pƒjlž(y|¬]ru€ƒV†w_¨”=vwp=q£€ƒhl‚Ejlr£_:pVyl† rupƒ€Vž q$‚HpVr£†<€ƒj|†]h:„ ß Sjl†w[]pV_µjl_:¯°„ _:q£€Vvw†]€Wg¶­®±²p=ž^"„i_‚w”=qsS__§Ê†w_:ruy|h2€=€ r£_:hlh(r£^mpF‚]:qsruvwy5ru€ƒr£q8† pV^"ßF‚wjlq£[w_§ _ ¯ª:€ƒ_†—qu€ƒhkv]jl†]r£q£€WqHgnH_p=pV^mnij ‚]€ƒqs_r£†w§'_:^¨„µ€Wn<g2g"[]j|€WylruV€ƒ_†]”V_:vwqsququ€%h$j|©rs†w[w”'ruS rs["† €V€ƒyl†F_¹g"†w©¹pVj®€Wgmhlr£^mjl[]‚]D(S q_ªsru†wp=ru€ƒ† qR)­$hlrsÀ¤^"¯ª‚wq£_ruqu€ƒru€ƒv]qۆ]€W_gq£qujlhy|ßFr£nw€V†wvi”Vjv]rsj¹q£€ƒrujlh¹r£pV†w† p'SD(S ) £ q V p ] † V ”  _ v]†wr£t<±²j vw_:ž´p=qsg qsq£p%„i© _¬]h¹†]ž´_:y|pV„ ^ ­ jl[w_„i_¬]†wrsjlr£pV† j|[]€%j j|[w_'¯ª_qu€ƒvw†E€Wg¨žŸ€V_:h 8_q£q£h:ßižŸ€=_j hßE_:„i”=_:h €V†]„ V_:ykj|r£_:h y ‚j|H€V[wylpV_ _2r£†<h{ j|j|[]h¹yl€ƒp=[]y †w€W€V”VF_:r£jl†wy5_:”yl‚wr£ºylj|_?p=[w„¦‚E__:Vn<yk_j{gg"yljlj|ruj|[w[]_?_ €%h-j5Å pVj|ž[wHj|_[wÏRr£Æy°_°hlžŸ€=^"Ñ €V_qsÛq£pV_:Ãl† hkÇj]r³j Åh¹r£Ã¡y|ÏAnEÆ vwp=vw^¨hl€W†]hlgF„wr£€Vyl†wr£yl”¶nwg=r£­†wj|[]¯ª”o€%_nEjmqu€ƒ€ƒjlq£v][wq †]_:r£h5€Wyl_ g"_:^mžŸruhm€V‚w€Êj{_g—j|n]h5pƒ€ƒ€Vžq£†]q5hl„µ€V_^"^"_?„i‚w‚i”Vqsj{__?g¥h-‚HpVj|pVžª[]r£†<€%hlj|j5€Vh:^"[]ßw€W€ƒ‚w=y|qs___ :€ƒq£qs_?Z5„—[w_2y|_:hlpV‚H^'_:¡n]j|rsrs†]=€ƒ_q£jlg p=yl}ru€ƒ€ƒqÛn]€ƒyl†]r£_„ qH€ƒžŸ€Vq£”Vp=_j ylh rsjl[w€ƒ†]^"„ ru°}©¹€ƒpVn]y ylhkr£j¹_q _?€=„ihk_”V_?hp=­ ^"‚wqs_§ir³j{g¨pVž,jl[w_2¯ª_qu€ƒvw†E€Wg"jly|r£€V†w”Vvwqu€%j|rsp=† pVpVpVž]žž n‚Hj|[wpV‚E_q£g<p=hk[]rsv]†<_:ykj|„ižŸhy €=r£€ƒ† q<_2pVRhly®€Vhl^"ru^mh ‚wpFΘ(n pqsr£V†wjl”<[oh)hl­ vw­ yl žŸ€Vp%©¹_:_h(=¼ À_y¹jl‘<[wFruh߃©¹À pVy h{j®‘VŠW¿w€=hk€ƒ_5†E„2p=jl^m[]_5‚]qs_pV§F^"rsj{‚wg2q£ru_h®§ihkrsj{vwg2nÛr£t<h$v]r£€V†„wžŸy|€V€ƒjlj®ru8qsr£ž´†wp=_:y8€Vhly€Vž´^mp=y‚]^mqsr£†wp<”=h{jh 1. P. P. P. 1. p∈T. P. P. P. P. P. P. %$. )(. 3. ,-

(19) /.6%/!01

(20) &. . 2. '&. *  . +. (. $.  6#" #% &$% ),+ !).-. )."$&. 2

(21) /36%/!04

(22) &5

(23) *)$"$)6% )." +*)!%*#"76. |y® _:_p=hkj yljlp=y|Cru†w¡pVjlnErr£pV_P„i†—ru€€ƒpƒ”=žhky|v]F€Vn]^ hkjl_p yljm_?Ch{pVj|­®ž ylZ5ruR¡[wj|_:_2­ „—hl·w_jlj5pp=ympƒž$€Vßw†w†<†wpVg¦pƒ† j|žŸ_:€=_„ ^"_ ‚iFj{gµpƒy|_:ž hkVjl­ y|(Sr£jlr£pV)† ß-Fjl[w∩_ Crs†<j|pƒ_žy žŸhk€V_?¡_:jlr£h pVF† FpVž ∩V (SC ruh") ž´€Vp=qsylq£^¨_:„ h(jljl[w[w__ C V (S ) 5 Z w [  _ w „ ] v ƒ € , q V p  ž | j w [ 2 _ | y : _ k h l j | y £ r   l j : _ „ ® V p | y V p ] † V p r i „ rup=€ƒri”VžŸy €V€ƒ^ _:h(V[]€W(SV_ €) †wr£h5pV†µj|[w_:_^"hl‚ivwj{nHg"rspV†<^"jl_:‚wy|q£hl__:§ jlpƒr£pVž †"D(S©rsjl[ ) ž´p=­ylZ5^"[]_?r£„ h nFhlvwgonÛjl[wp=_°^mžŸ‚]€Vqs__:§—h8pVr£h°ž D(S  © w [ < p k h ª _ i „ ] v ƒ € q ® V p | y V p w † ) S ƒ € £ q £ q : _ — „ l j w [  _ ª ¯  _ u q ƒ € w v E † W € " g l j | y £ r V € w † V ” w v u q % € | j s r = p. † | y : _ k h l j | y u r ¡  l j ? _ µ „ | j p ƒ €. † w † ƒ p | j : _ „ ­ C D (S ) €·$Vylr£_'”]­8Z5rs^"o[w_‚Hž´pVpV®y ylpVj|€Vy|€ƒpV† †<†wjr£p=q£qsrƒv]pV„ihk†Er£jl€Vy ”V_€%‚wy j|€ƒrsj|p=^h°†,ž´­ €VpV†]yª„cjl[wjl[w_m_8yl_?¯ª_p=qu†]€ƒh{v]j|†]yl€WvEg ¡jlj|r£ylpVru†P€ƒ†wpV”=ž8vwjlqu[]€%jl_or£pVhl†cvwyky|žŸ_:€=hkjl_ y|r£Sjl_:ž´„°y|pVjl^+p Sjl[wß V_"h|(S€ƒ^"‚w)q£rs€ƒ†w†]” „ SD ­(S`F__ ) ß 3. P. P. 1. 1. C. P. C. 1. P. P. P. C. #1. S. P. P. S. P. P. 8 :9;

(24) . &$% ),+ !).-. 2

(25) + ) <6%*)."$+ ):!% #"%6. )."$&. VpZ5ž[]©¹_"_r£pV”V†][<jl_?_„µ‚ij ‚HhcpVpƒr£†<ž j|®h:­p=ylÀ p=†w-pVÅr®Í „iiru€ƒÏ²”=Å Òy|€Vw^"ǃhcÍÐÈ]€ƒÏ †Ep„Êrs† ¯ªR_qu€ƒvwruh¹†]€W€mg ‚]j|€Vylrsruy €ƒ†](z,”Vvwr)qu€%j|©rsp=[w†]_:hªyl_ :€ƒz†Ö∈nER_"”V_:„i†w__†wy pV€ƒjlq£_?r£ºh¹_:jl„¶[w_jlp ‚HpVhk_r£†=j|jh #1. =. . 3. 3. î´ï$ð,îÐñ.

(26) mÅ Ñ ÂiÈ Ñ Æ wÃ¡Í Ñ È VÂ Ñ ÏAÍŸÇƒÈ Ñ ÎÅ Ò"ÁHÂià  Ñ Ë ÅªÓªÅ Ë|ǃÈwΡÏRáÂ]ËÏR͟Ç%È . .  . ‰. . ·$rs”=vwyl_ 8_:hkjly|r£jl_?„ ¯ª_qu€ƒvw†E€Wg¨jly|r£€V†w”Vq£_:h(ž´p=y €mhlvwylžŸ€V_cr£† 3D j|rsj|[whl_ _qs]ž-Ç €ƒ-†EÅ„ Ã'rÒ%Íu∈Î¡Ï RÑ ÈHrsË j|Å hª ©¹ÂiÈH_r£Ë”VÏA[<͟ǃj:È]­ ß Ô-V_y|g ©(_:rs”=[=j|_:„ ‚HpVr£†<jª”Vr£V_?hy|r£hl_j|p—€—„iruhkj|€ƒ†E_2ž´vw†E¡jlr£pV†ßH†E€ƒ^"_q£g !. =. πp : R3 → R, x 7→ kx − zk2 − r2 .. =””= y|vw_€Vqu‚w€%^ qujl€Vr£pV€ƒrs††]†w„"­ ”—j|jl[w[w__mylÔ8_:”Vv]vwquqs€ƒru„iy-_?jl€ƒy|†Ör£€V„w†wr£”Vhkv]j|€Vq£€ƒ†]jlr£pV_m†¨nFr£g †]h{jlj|[w_:_m€=„µ‚Ep%pƒ©¹ž_jly[w_ „iru®h{j pV€ƒy|†]pV†w_'p=rHy|„w_:hlr£€V‚E”V_?y ¡€ƒj|rs^ =_€ƒq£g †]„µgFr£jl_[wqu„w_2hª¯ªjl_[wqu_m€ƒvw‚H†]p%€W©(gm_:j|ycylru„i€ƒru†€. 4

(27) 

(28). 1. .

(29) &$% ) ) % / /

(30) 

(31) #". )."$&. -

(32) &(%*)') % /!)."$/ ; 6-. H‚pVZ5ž pV[]r£_ª†<j|^"h(ru_:h rs†„whlr£rsR€V^"qH‚w€ƒ\Sq£§Fg¨ruh []jl[]M€WF_2r£A(S) †vww†w”2r£j{pV©¹† pVpžjl[wpV€o_y(^"®qsp<p=pVhkyly|_?p=_ „µ†w†wpVhl_:vwrH€Vn]žŸyl€=hl_?_h{j_:j(h5S‚EpVp=ž$pƒrsž†<„ij|Rr£h(^"r£_† ru†]h(Shljlr£pV[w­8†¶_Z5hl[wmvw_ª€ƒn]^m†]hl_„ _?j5„iqspƒ_?ru€ƒžhlh:qÛR­ €%§i\Sr£h-pƒjlž[E€€%j¬E†wpVr³j|†E_ªhkru‚Hh{j pVh-r£†<pVj¹žhl€ƒ_q£j q R pVr£†]ž jlqs[wZ5v]_chl[wr£_2pV_:†¶^"†=j|€ƒ_?_^"„iy r£h-p=€V†wpVq”µž,€%^¨§ihkru‚]€%h5[w§ipƒ_rsž®y|^¨_:€"€Vh:­qEhkvwhl·w‚wylpVžŸ[w€Vyc_€µy|_ _:hlh-S^mrs†ErupFh pVq£jlv]qs[¶„ip<hk_:hl_:„—vwqsgµykrsžŸ† €=y|_R_qu€%j|\S_:„—j|­ [wjl°_op"_j|y|qs[wp<_ _hk^¨vwhky|«=€%_2_§iq£rspƒ_^¨žj|pV€Vj|† [wqE_'rupƒh-ž^"^"R_:_?„w€ƒ\Sr£†<€Vj(qßi€%©©§irsjlru[]h[µr£ ruy|[Phª_:€=hl‚H¡p=jl_:†]vE¡hlj(€ƒr£hkq£jlqsj|gp h _?t<v]À°€ƒqۆ<j|gpohlj|^m[wpF_pVhljl«V[2_q£hk_v]j|ykpVžŸ† €=pƒ_ ž R€V\S†nE­ _8y|_:p%V_:yl_?„°€Vh jl[w_8S_:†FV_q£pV‚H_®pƒž<jl[]_8^¨€%§irs^¨€VqVhk‚][w_y|_:h r£†]qsv]„w_:„r£† p=†w_ pVžHj|[w_ j{©¹p'pV^"‚Ep=†w_S†<j-pVž ­Z5[wruh8j|y|€V†]hkž´pVy|^"€ƒjlr£pV†mr£h(€Vqsq£_:„mj|[w_°^"_:„wr£€VqH€ƒ§Fruhj|y|€V†]h{ž´p=yl^ ­ 3. 3. 3. 1. 3. 3. 3. R3 \S. ðð+ö. 43658789;:. +. 3.

(33) Ñ :Ñ ¾Î 5͟šÎÅÈ Ä?ÍÐÈHÅ Ë  . . . . .    

(34)      . q£$·€ƒ_§Fr£j”Vruh vwnEy|_:_qsp=Š †w”µZ5j|[]pµ_(j|j|[w[w_my|_hl_«V_:‚Hqs_pVjlr£†=p=j †¶hnw^¨vi€ƒjy|«V†w_:pƒ„'jª©jl[wr³j|_m[¨^"€ª_:n]„ivwru€ƒq q ·$rs”=vwy|_cŒ 8Z5[w_cž´_:€ƒjlvwy|_2hkr£º_2ruh’ r£‚]h| [wr³j|º   

(35)        . !.

(36). . 8 "

(37) /  ! ) '

(38) )4$2

(39). / %

(40). ),"(&. 

(41). /).- % " +. 8À pV_:=r³y8j|_[wrsylj-_jlruy°_h®§µr³jlj []pƒruž$_ h¹jlVjl[w[w_:_ yk_2j|®_=§ p=_ylylp=jl_†w§ pVpVr žv_:pƒqsqž VV (p(pj|[]€%))j(pVj|r£[]žh8€%€"jlj [wh|ru_€ƒh¹^"žŸjl€V[]‚wyk_j|q£_c[wžŸ_:€ƒ‚HhkylpVj®jlr£[wž´†<y|_?j pVh{^r£jhž´:y|pV€ƒ^q£r£qs†m_?„ pjl[w€m_ª‚H[]pV€ƒq£_2qsžŸhkr³‚Ež €V_ ß<hl_j8pVžÛ‚HpVr£†<j|h p H hlv]Z5 [w[ _Pjl[]q£pi€ƒj €V(vq5ž´_:−€%j|pvwwy|)_ · hl(xr£º_ V−(pr£pi)h¨€Ö) ≤ž´vw0†E­ ¡jlr£pV† x „j|w[]r£hk€%j|j¹€V†]jl[]_c_"q£j|pipP€Vjlq][wž´_—_?€%^mjlv]_?„iyl_ru€ƒhkq(r£º€ƒ_c§ir£pƒh2ž$pVhk^"ž SpFpƒ­ j|[—À°†¥hkv]ykrs^"žŸ€=lf^"_°s_:ru„w:h r£€ƒS jlr£_—‚]→h| pV[w†]Rr³j|hl_:ºcj|t<[]vwpV€%_:†<jµ†]jl€=r£†F_¨hlvwhlpVrspV”=ž¹vE†]j|h-ho[w©_¨jlp¥rsjlj|[ yl_?ru€V€ƒ  †wr£[½‚]”=qsh|_¨‚H [wpVr£r£r³†wj|†<_?ºcjµt=vErspV† €ƒ†]q£r³Shkj{j|gրVr³†<j r£hhj ’=ßwhkZ5_:_2[w·_(r£ž´”Vvwv]†]yl_jlr£ŒmpV† ž´pVy €V† :€ƒr£†2q£qsv]nHhk_¹jly hl€%_j|_:rs†'p=†,€V­h$€^"_:€=hkv]yl_(pƒžijl[]_-q£pF:€ƒq=jl[wru «F†w_:h|hpƒž]€ƒ†'pVniz{_?¡j:­$À ^onwrs”=vwrsjlr£_:h €j|Vp ylruhljl_°[w_ r£† qspiy|_::€ƒpVq®†]ž´_?hkjl€%y|jlv]v]lf¡ylj|_µsrsp=hl†µrsº:‚w_µy|pƒpiž¹_:jlh|[]hl_—_:h¹hk[E€Vh5€ƒ‚HhkpF_V­Pp=†]Z5h5[w€V_"h(jlž´pV[wq£_2q£p%h|©€ƒrs^"†w”¶‚wq£_:„wh5_¬]€ƒ†wy|_°rsjl†]r£pVpƒ†j ß„i„w_vw†E_¨hk_cjlp¶_†wÀ°p=vw^"”V_[ †<j|©€¶r³j|€V[ †]y|„ _:hl¹‚H__:y|¡† j q£¼ piÀ 5€V‹=qsg—‹W¿R„wß,_:†]€ƒhl‚i_j|vw_†wy|_:p=hªvw”V_§w[ €Vjlq£g j|[wruhªr£†<jlvwrsjlr£pV†¦€ƒ†E„P‚wy|p%<ru„i_?hª€—©¹€Wg jlp hl‚E_?rsž´gP©[w_j|[w_y2h|€ƒ^"‚wq£_:hc€ƒy|_ Ñ Î¡Âià   Ã|Ñ Ç Ë Å SÑ ÍuÎ Î'Ñ Ë Ñ  £sÅ ÅÒ ]ÑÇ%ÍÐÈ ÈEεÏ Î Ñ  õÍÐÈ Ç S Í ÅÄ%ÅÃ¡Æ ] Ç%Ø ÍÐÈEÏ x™ ŸÇ%Ý È S ÍuÎ ÑÇ%Ïà εÑ >Ò%ÍuΡ0Ï Ñ Ñ ÈÛË|Î Å Ñ sÅ Î ÎõÍÐÈ Ï  Ñ SÈ ε Ç lf s(x) _j Z5S[w_8nEž´pV_q£qs€Vp%†©r£ε†wæ”=h|hۀƒ^"y|_:‚whlvwq£_ªqsj|pVhž¼ À €"5hl^m‹V‹ƒpF¿=pV€ƒjly|[ _®hkvwp=ylylžŸ†w€V_:y,_ h{j|SpV†w_?h۞´pVy¯°_:q£€Vvw†]€Wg n]€=hk_?„cyl_?pV†Eh{j|ylv]jlr£pV†c^"_jl[]pF„,­ ”=pF_:h¹pVjlž p"º:­8_y|·]p]vwß<yljljl[w[w_2_:yl‚H^"pVpVq£_:y|h5_VßFpVrsžž j|[w_ r£h®pV€oy|‚EpV†wp=qsp=_r pV„iž$r£€Vh|”V€ƒy ^"€ƒ^‚wq£_cV‚H(SpVr£†<j) pVßF†FjlV[w_:_yl”=V_ _?¡jlj|pmpVj|y [w_2^"_:„iru€ƒr£h q €%q£§ip=[wruhlh __cM† jlp"εA(S) p v −p jl[]_c†]pVy|S^"€Vq pƒž S €%j p ­ v qs·wr£†wp=y_?€ƒhky v ¨hlvwykrsžŸ_:€=†<jl_q£gc[whlp=^¨^m€ƒ_:q£pVq ^"ε ß:pVj|y|[w‚w_8[wy|ru_:chk€ƒjly|†]r£„ jl__?=„ª_¯ª† _€ƒqu€ƒ^'vwn]†Ers€W_:g †=j jly|ruruhl€ƒpƒ†wjl”=p=vw‚wq£ru€ƒ'jl¼r£À pV† x-D°‘VŠ%(S¿jlp ) ž´p=­ yl^¨h,€5‚wr£_:_©ruhk_ ε!. 1. . i.

(42). i.

(43). i. i. i. i. i. − i. i. i. . $. ". . $#%&. ( 2. & '%)(+*.  . (. P. (.  . -. (. ,.  . $.

(44). P. 1. .0/. P. i. i. i. i. .. i. !. S. P. S. î´ï$ð,îÐñ.

(45) mÅ Ñ ÂiÈ Ñ Æ wÃ¡Í Ñ È VÂ Ñ ÏAÍŸÇƒÈ Ñ ÎÅ Ò"ÁHÂià  Ñ Ë ÅªÓªÅ Ë|ǃÈwΡÏRáÂ]ËÏR͟Ç%È . .  . . =·$€ƒ§i_r£”Vylr£h:jlvwru­ y|_ _?h8‰ ^¨¨€W±ægo† nH2D_ žŸ€Vß®y-€Vž´qsy|q pV®^pVy|jlpV[]†]_ªpV^"r-=_:„w_ylr£€VjlruqH€ƒ_?§Fh'ruh8p=n]†FviVj(_y|‚H”VpV_"q£_:j|h¹p¶€ƒy|j|_ [w_ ”VvE^"€ƒ_?y €ƒ„i†<r£€Vjlq¹_:_:€ƒ„o§ir£jlh:pm­Ê±æpV† †F=3D_y|”Vß8_5hljlpVp'^"jl_[w_ª®^"p=yl_:p=„i†wru€ƒpVqr !. 1. 1. 4 54¨ #  

(46)  &¹ , &-  ¹1 ¨  ‚]©ªyl[Ehkp<r£€%†w€Vj  ” [w©¹¯°_?_h_:jlq£€VpVpmvw†Ehk†]hkp=ru€Wqs„i=g __yªj|jlyl€V[wru€ƒh¹_c†wjly|”=[]_:vw_'qup=€%„i†]jlpVr£hk^"pVjl†Êy|r£v]†]pV¡€ƒj|y †<rsp=j ®†mpVru„iy|‚]_:pVyl€µ†wp=p=nwnErqs_:_:„w[w^ r£rs€V†E­”V„PZ5y €ƒ€ƒ[]^¨†P_ªh°€ƒquq£hk€V”Vjlh|p=r£qshlylq®r³rs¬Ejlq£_:[w:€W€%^ =j|rs_:ß]p=hª€V†¨q³ylj|‚wpF[wylp=pVp=^ v]‚E”Vp<ž´[ hkp=_?y2hk„"v]t= nEv][P_:r³j|qs€¨p%_"©¤„wq£rru€=Ûh(hl_hln]y|r³€V¬H_hl†<_:€%j„"j|€ƒrsp=p=‚ †† ruh„ir µvwqsj°nH_:€Vv]hl_c^¨€V†<g €ƒq£”VpVy|rsjl[w^ pV^'n]rs†w_2„ir Û_y|_†<j°€ƒ‚w‚]ylp<€V [w_?h­ . . 1. 

(47). . ·$r£”Vvwy|_ ®Z5[w_ ®p=ylp=†wpVr _:qsquh5pƒž”VpFpi„ hl€V^m‚]qsr£†w”¨€ƒy|_ª_:qsp=†w”=€ƒjl_?„—r£† jl[w_2†wp=yl^¨€Vqۄwrsy|_:jlr£pV†,­ . . )." +

(48) " . 1.  ),"

(49). -.

(50)  $&$/. ²±€ ž‚HpVpV†]r£_†<jpVrs†E† hkru„i_y hhl[w€"pVvwhk^"qu„pF†wpƒj|pƒ[Pj'hk„wvw_ylFžŸr£€V€ƒjl_ _mSjlpF©pPr³j|^o[¶v]€m [hlv ž´ylµp=^ r£_†<jl[wj|qs_"g j „i€ƒ_†w†]”=hl__†<jh|€ƒ‚w^"qu€ƒ‚w†wq£rs_¨†w” pVž-Sj|[wßi_—jl[whlvw_—ykžŸÈH€=ÅÍ _¨ €%|j2ǃà j|ι[]€%pVj ž ‚j|H[]pV€%r£†<j5j:j|­®[w±²_ j®j|vwp=Sylyl†Ep=†wh5pVpVrÛvij_:qsj|q []pV€%ž,j5jljl[][]_r£h5h|j €ƒ€ƒ^"†w‚w”=q£__c†<‚Ejp=‚wrsqu†<€ƒj†wr£_2h¹_:€Vqsp=† †wnE”=_2€ƒjl©¹_:„—_q£q,rs†—€ƒ‚wjl[w‚]_2ylpW„i§ir£r£y|^"_:¡€ƒj|jlrs_?p=„µ†—nFpVgµžjl_[]§i_c‚wq£hlpVvwrsyljlžŸr£€V†w”m_cjl†w[]p=_ylžŸ^¨€V¡€ƒj q €ƒ„wj-_y|j|rs[w=_c_ch|€"€ƒq£^"pi‚w€ƒq£_ qÛj|‚HylpVru€ƒr£†<†]j:”V­8vwZ5qu€%[wj|rursh-p=† †]pV€ƒy|y|^"pVv]€V†]q]„µp=y-_?€Vj €ƒ †w[ ”=‚E_p=†<rsj-†<‚wj:­qu€ƒ†w_ªrs†wž´pVy|^"€ƒjlr£pV†,ß<y|_:hl‚E_?¡jlr£V_:qsg=ß<:€ƒ†µnH_cv]hk_?„"jlp ·$r£y|hkZ5j:ß[w_2rsj €Vqs”=pVpV^"y|r³‚wj|vi[wj|^ _:h¨‚wž´ylp=p=yµ‚Ep<_:hk€=_? „µ[¤nFhlg—€V^m}c‚]pVqs‚]_¶rA

(51) ß ‚H pVy|r£†<rs[Ej:hkß †]€V€V† † €ƒ€V‚w†]‚w„ y|`FpW§ir£q£rsW^¨€ €ƒkjl¼ r£ } pV† `ipƒ‘=ž‘Wjl¿ ¡[wßi_¶[]j|€=€ƒh-†]j|”V[w_y|†<_j—_‚]^¨q£€V€%†wz{pV_Êy5€ƒhk†Ejl_„ ‚Eh€ ­ . . P. P. (1. $. ðð+ö. 43658789;:. &. *.

(52) Ñ :Ñ ¾Î 5͟šÎÅÈ Ä?ÍÐÈHÅ Ë .  . . j‚]hl€ƒ_ylq£†wpV_:”=z{_:_jl¡†<r£pVj|j°rs†¤p=‚w† pVqu€ƒž2pƒ†]žch|_V€ƒßÛr³j ^"€ hm‚w †wq£æ_¶_„ir£”Vr£‚H^"[FpVnH_r£†<†]pVj|y hlhµhorsp=©†]ruh"€ƒ[]qr£ p=¯°[ ^m_:q£€V‚]€Vylvivw_Pjl†]_?†w€W„ g _:­¢rs”=jlZ5[Fy|r£nE[w€VpF†w_ pV”Vjly|vw[]r£qu†wrs€%y ”¥j|„¢rsp=‚Ehk†Pp=jlrs_:rs†<†E‚¢j hq£ru­‡v]h"„i€Ö`Fr£†w_?hk”µjlp=rsj|j|†][w „ []_oßrs†wh|r£€ƒ”¦†¤^"hk_:‚wjl€V_q£ _'‚ [ ‚Hr£€V†¢pV‚wr£†<©‚wjcy|[wpW€ƒru§i †E[rs„ ^¨jl€%[wj|__ r^ouhmvihkjl_:vEqs_?€ƒ¡qwjl†w_?_:„ rs”=€V[FhmnEp=€Py|j|hylr£ru†"€ƒ†]jl”V[wq£_°_µqspipƒž €Vj|qE[wƒ_ „oylj|_?ylrupV€ƒ†E†wh{”=j|vwylquv]€%jljlr£pV_?„¥†Ehhk­$vwZ5ylžŸ[w€V__µjly|rru €ƒ†w‚H”=pVqs_?r£h†<j|pVh vij|p,‚wviq,j-rnFg∈j|[wS_°€Vqs”=p=pVyly|y|r³_:j|hl[w‚E^ p=†]ž´„pVpqry|jl^ p €"hlvwÀ°ylžŸq£€Vhlp_yl_:[wq£p=€ƒ^"jl_:_„'pVjl^"pcp=j yl€ƒ‚w†w[]”=r£_°†<jlj®p ‚wSq£€V†w‚w_:y|h:p%ß%<j|ru[w„i__?„ ”Vy|€o__?jl„i[Eg€%j°€ƒq£hl”VpVp=^"ylrs_2jl[whl^3€V^m¼¾‚]¸5qs`ir£†w¯c”¨‘ƒŒƒp=¿]†]”V„iy|p%rsjl© r£pVh† €V[w†opVp=quyl„wr£h:_­ †<j|_:„o^"€V†wrsž´pVqu„ S €ž´2ˆp=hlylnF_^ gµ_?„ohk©_:jlrsqsy|jl_?r£[¢¡€Vjl†wr£€V”V†wqsq£”'y|__:jl€=€ƒy|„i†]r£€Vg¦„"†wruhk”Vh®_:q£qs_:”V_?h(v]¡r£jlpV„i_?vi_?„ j5„mpƒ€Vn<ž„%g'zkjl€V[wjl_[w_:_ª†<¯°j_:r£q£y|jl€Vy|vwvwr£€V†]^"†w€W”Vy|gm€=q£_:jl„ih:y|rs­ruri€ƒpV†w¹žÛ”=g¥jlvw[wq£_5€ƒp=jlj|†]r£ylpVh{ru†€ƒj|yl†wD(S ”vE=¡qsjl_?r£h8pV€ƒ†¦)†E­8j|„'[wZ5j|_—[w[w_cp=_°vihl„ijl_r£‚]q£[w_:vi_?jm„ijlr£y|rupV€Vhm†—qw€ƒ€ƒhk† †wj|€V”=p=ykqsj _?ylh-r£h_©jl†<[]jlrs_?_jl[g„ j|hlylvwruyl€ƒžŸ†]€V”V_(vwqu_?€%hlj|hl_:_„¨†<jlhlruvw€ƒykq£q£žŸg'€=„i_ vwn]_¹vijlj(prsj|j([w^¨_€W‚Hgop=h|žŸ€ƒhkr£r£nwq]q£j|_¹p'‚]r£yl†=_?j|hk__:y|†]‚Ep=_¹q£€ƒpƒjlž _°hk€Vq£r£qsVqE_jly []h:_ª­ h| €ƒ_:^"vw‚wy|r£q£hk_ jlru‚E5p=€ƒrs†<y|_¹j h-‚]p=ylp%y8Fjlrupo„i_:‚w„y|p%jl<pru„ip%_ V_:€oy|pVq£p=^"hl__ j|[wruh „ir ¨vwqsj{g—€ƒ†]„ €Vq£hlp'j|p¨[]€ƒ†E„iqs_nHpVvw†E„w€ƒy|rs_?h5pVy hl[]€ƒy|‚µž´_?€%j|vwyl_?h­

(53). P. P. . :+. . ,-

(54) /.6%/!01

(55) &.

(56)  )$" ) 6%*)."$+ ):!% #".

(57) . -

(58)  $ &(/. |_hZ5€ƒ§F[]^"jl_2y ‚w€Vyl¡q£_?r£j †wh{j|”oylruru¡h5j|_:„i„ _†E¯°hkž´__:y|q£pV_€V^†]vwpV†]vw€W”=g¨[,j|­ylru°€ƒ­®†wžZ5”=vwp=[wvwqu_€%y|jl^¨hlr£_VpV€ƒßF† r£nH†oD_:ru:„i€ƒ_?(Sv]€hl_°nE)_:j|[w[wruh5rs_2†E«Fhk„mv]†w€Vykp%žŸqs©”=€=pV† _y|jlr³j|Sp"[w^¨nHruh5_hvw[wrs†w†mpV«F^"j|†w[w_:p%r£pV©h-‚w†,[w€%ßFp=j|rs_ylj^”=r£pVh5y|j|†wgcp"pVrujlj5h[whlj|_ pmp2S__:§F€Vrshljlžg"y jl€V[wjlp_j D (S ) D(S ) ž´€Vy|‚wpV‚w^ y|pWD(S ¨ € l h w v Û n   V p " ^ ) §irs^¨€%j|rsp=† S ­ ‚wq£_§ ©[wru [ jl[w_oyl_?h{j|ylru¡j|rsp=† pƒž D(S ) jlp €¨hkvwnEhk_j°pƒž R j|[]€%jªr£hª€¨”VpFpi„ ”=€V'qsv]”=š €ƒpV$y y|˜€ƒr³™j|†<[w j|_^ _:Z5h8[]ž´pVpV_o^"y(‚wjly|[wvwv]_cjlhk_:jcy|h_:€Vjlqsp=”=[w†]pV_ hky|jlr³¯ªj|y|[wv]_^qu¡€ƒj|vwrsp=‚]†]†µyl€Wp=gւw‚Ey|p<jlp%y|hk<ru_?€ƒru„ „i†w_?”=n<„µvwg q£hk€ƒ¹p=jl^"_r£pVy|_ †¶† 倃²†Eh|€ƒ„¶^"À ‚w^"q£r£pV†w_ž”o†<j jl€¶[wpV_ †]¼ À „ih|5rs€ƒjl^"r£‹VpV‹W‚w†—¿®q£_Vr£©5h(ß$€Vž´jlh vw[wqs_ jl¬][wq£hk_'qs_?_j„¬]­8y|hkZ5j°[wpƒj|p—_ž ‚HgFy|pVr£v]_q£_:quh{„ jh Q r£hl† _j j|[w_ ®pVy|pV­Ö†wp=Z5r([w„i_ ru€ƒ€ƒ”=q£y|”V€VpV^ y|rsjlV[w^ (Syl_)j|€V€ƒrs†E†]„¦ho€V¬]ho†]€Vqs€ƒq£†Eg¦„ijlr£[w„]_ €%jl¯ª_µD(S _ž´pVqu€ƒyvwj|†][w)€W_—gy|j|_:ylrupV€ƒ†w†]”=hkjlvwy|quv]€%jljlr£pV_:†„¥D(S pVžŸ€Vž jl_[wj|_h ∪ Q) l h w v l y Ÿ ž V €   V _  ß l j w [ — _ S ∪Q pj|Vylž ru€ƒD(S ©[]p=hlnF_ go=jl_[wyl_°jlruhlvw_?n]hmhl€V_jyl_ hlpƒ€Vž ^"‚wqs_ ©‚H[wpVru r£["†=j r£hh®­ jl[wZ5_ [wv]ruh¨†wrs€ƒp=^"†¨pVpƒv]žH†=jl[wj ho_ªjlp¦_q£quylh8_?pƒh{j|žHyljlru[]¡jm_°hljl€V[]^"_¶‚w¯°qs__:q£‚H€VvwpVr£†]†<€Wj|g h ∪rsp=Q) ] † V ” w v u q % € | j o † V p ž r£† jl±²[wj2_ ®€Vp=†Pylp=nE†w_mpVhkr [w„ip%Sru©€ƒ”=†¶y|€Vjl[]^ €ƒj°Vž´(SpVyc€—∪qsQ)p<Chk_?­ „PhkR^"pFpƒj|[Êhkv]ykžŸ€=_ €V†]„¶€ hkv µrs_:†=j|qsg „i_:†]hk_ æh|€ƒ^"‚wq£rs†w” S jly|r£€V†w”Vq£_:h°pƒž®jl[]_oy|_:hkjly|r£jl_?„¶ ε ¯°_:q£€Vvw†]€Wg ƒ p ž l j w [ " _ k h  _ ª j V p ( ž   V € ] † i „ u r w „ % € | j  _ l j | y u r ƒ € w † = ” s q ? _ ° h   = p < † | j ƒ € £ r ] † c h ƒ € £ q  q | j w [ o _ S S j|”=ylqs_?ru€ƒh-†]€V”V†]vw„¨qu€%_j|§Frsp=j|†y|€=D¡j¹€'(S^¨€ƒ)†w­$rsZ5ž´pV[wqu„"_€Vž´y|qspV”=^pVy|r³jlj|[w[w_c^ hk_rs†]j¹pVqsvEž„i_:€Vh®†]„i€ªru‚E„wp<€%h{j|j®_ ‚wjly|y|rupi€ƒ†w_?”=hlqshl_?rs†]h­” Ô®jlp§Fjl_:_qs†Er£^"hkr£rspV†]†]€ƒh(jl_pƒž„wjl€V[w†w_c”Vq£€ƒrs†]q£”V”°pVj|y|ylrsjlru€ƒ[w†^ €Vyl_c‚wy|p%Fr£„i_?„µj|p¨„i_:€Vq ©r³j|[PnEp=vw†]„w€Vylr£_:h5€ƒ†E„ €"_ylj|€ƒr£† €ƒ^"pVvw†<jpƒžhk[E€ƒy|‚—ž´_?€%jlv]yl_?h­ €p=V †]†2Ý „jlœ []r£Ý ^"_-$ru‚w؄iy|_:p%€°V_pƒZ5^"žE[w_:_mpV†=^"j$pipƒ‚wžwvipVj|j|†][wrs†w_o_”°€ƒž´q£y|yl”Vv]p=p=hk^ yljrsjl€V[]qs”=^+pV€ y|©5r³j|hl€V[wvwhc^ n]hl„i­__?j Z5hkr£[w”V†w_5_?„¶pinFp=g¶©†w_5[wÀ ru€ƒ^" q£[”V_:pVru†=hy|j rs€ €—jl[wjl_^ [wjru nw€V«VqAvw_:­r£†wqu¼ „wÀ°_:h®„¸¹€VV¯ h_ y jlhl[w‘Vrs_p=‘W¿-†2yl€=pƒv]hªž hkj®€ €ƒhlhlq£v]v]”V pV[2y|_:rsj|jlh|[][whkp=€%^ jy j|ruh¹[w_5„i_¯°¬]_:†]q£_:€V„µvw†]€=€Wh8gž´p=jly|qsq£rup%€ƒ© †w”=h­vwq£·w€ƒp=jly-r£pV_:† VD_y|g"S(Shl€V^m)‚]y|qs_:_ªhkjl‚Ey|p=r£rs†<jlC_?j „2⊂jlRp C €Vß=†'jl[]nH_ª_¹†wp=pVyl^"^¨‚w€Vviq]j|pƒ_:ž„ ­$±æ†m€%j pipVru†]h(_V€Vß?‚wjlS‚w[wy|_pWhl§Fvwr£^¨n]hl€%_j|j _:C„ vEhkr£†w” p=†w_-pVž<j|[w_¹‚Ep=qs_?h,pƒž p ­Z5[w_¹pip=†w_-€ƒj p ruhp†wp%∈©¥S„i_¬]†w_?„€Vh,jl[w_(rs†<jl_:y|Shl_:jlr£pVp†2pVž V (p) ©rsjl[j|[w_ S. S. P. P. P. P. 3. P. . $.

(59). P. 1. P. P. P. P. 3. P. 1. P. .

(60). P. 

(61). S. P. %. P. C. 3. P. P. P. î´ï$ð,îÐñ.

(62) mÅ Ñ ÂiÈ Ñ Æ wÃ¡Í Ñ È VÂ Ñ ÏAÍŸÇƒÈ Ñ ÎÅ Ò"ÁHÂià  Ñ Ë ÅªÓªÅ Ë|ǃÈwΡÏRáÂ]ËÏR͟Ç%È . .  . ‹. . $· r£”Vvwy|_ 8Z5[w_2hlvwn]hl_j C pVžj|[w_2y|v]h{j°€Vqs”=pVy|r³j|[w^ ruh€mjl[wru «V_:†wrs†]”opVžj|[w_hkv]ykžŸ€=_ S ­ ¬]€¨pV§Fhl^"_?_„jª‚wq£p=pƒ_‚Ež®^"_:†w_€ƒ†<rs†E†]j„i”cpƒr£„]žÛ€V€%†w€ªjl”V„i_?q£h_Vp=­vw©nwZ5[wq£[]_ru _¹[PpVhl_r£†]h j _(C«<©†]r£rsp%hjl©["jl[]† €ƒ_(‚Hj|vwpµ_†]§ r£rs†]pp=†'ßVq£€%v]pƒ§i„ižHru_ h€ƒq£‚EqF€ƒhly v]€ƒ q£[mqs_:qVpij|pªž´pVp=j|y°†w[w_:hl_h:v ­€ƒµ‚wZ5‚][wr£yl__(pW†<§ijlj|y|qsr£g ^"r£€V†w€ƒ„ijl”V__8†Eq£_:†]hkh_pVr£y|† h|^"€ƒD^"€Vqi‚w(S€%q£_Vj ­¹p)±æ€V† ž´†]pVjl„'y|[w^ €_ qj|u€V[whk_j-h|hk€ƒjl_^"‚"_j|”V[wv]_°€V€Vy|qs€V”=†=pVj|y|_r³j|_?[wh(^‡€=h¹_jl§<[wj|_y|€=¡ylj v]h®hk€2j ^¨r£†—€ƒj|†w[wrs_'ž´pVh|qu„¨€ƒ^"hkv]_2ykžŸD€=pV†E_5„i(SpVr³j|virsp=j()†]pƒh:žÛ­jl¯ª[w_?_hkg _ª€ƒ†]€ƒ†E„ „i}cr£„]p=€%hljl©5_?€ƒh­®^"¸(r®pi¼ ¯pV}†]‘V_Šw‚wß]yl¯cp%F}ru„i‘V_:Œƒh ¿ „w€V†w_:hlpƒrsj|”=[w†w__:y5„ p=€ƒ†w† __§F€Vj|qsq£__:†]„ÖhlrsÃlp=Ç † ÂF:Ρ€ƒÏ¹q£qs_?Ë Ç?„ÊË|ǃÏRÍÈHŹFÏj|p¨Ë|Ç?„iË _:Ç%€VÈÛq Ź©jlr³p¨j|[P‚wy|†wp%pVFrur£hk„wgµ_h|€m€ƒ^"©5‚w€%q£j|r£_†wyl”=jlh:r£”V­ [<jyl_?pV†Eh{j|ylv]jl_?„—hlvwykžŸ€=_2€ƒ†E„ hlZ5^" []pF_P pƒ# ^"jl[¥œ €Vrs™ hl† vwyl ružŸ„i€V_:œV€¦_¨™ Ÿpi[]Ý :_y|_ vwš y Ø ruh2h"œ €VÝ j|hp ˜:j|„i™[wš__µ¬]$º:†]œƒ__ ™ y|Ap Ý ž´ylq£p=_^“=_±²q-j8jl[]hlr£_h®_¶j ©¹hlf€V_q£^mqi«F‚](0)†wqsr£p%†w©” pƒ† ž hlÐjlpV[]^"€¥r£h-_µhkr£hhl^"^mpFpFpƒ[]pVj|r³jl[½j|[†wž´_v]ž´gvw†]†]h¡j|jljlrs[wp=r£pV_:† † pVy|f_^ ©: [wRjlp<[Ehk€%_ 7→j-º:€ƒ_†FRy|gp ­ qj|£_[w=__q5¯ªhk__qujm€ƒvw€V†]‚w€W‚wg—y|pWjl§Fy|r£r£€V^¨†w€%”Vj|v]_ q£€ƒSjlr£­¥pV† Z5jl[wp"_†¥jl[]j|_2[wº_ _y|ylp¨_?q£pV_†EVh{_:j|q,ylhkv]_j°jlr£pƒpVž †¥ru­8h S±æz{† vEh{j|jm[w_2jl[w†]_ €%j|y|vw_:y hkjl€ƒy|q,r£†wjl_:r£rspV”=† [FnEDp=yfrs†<jl_:yl‚H(SpVqu€%j|)rsp=pV† ž ^"p=yl_r£_jl†<[wj|pi_:„¦„¦¼ †wp=¸¹yl‘=^¨‘F€ƒß qu h:­Ê¸¹Z5‘w’[w¿R_µßij|ž´[wv]_2†]¡j j|€ƒrs†wp=”=† _†<j r£‚whmqu€ƒ„i†w__¬]†w€ƒ_:j„¥jl[wž´yl_'p=h|^ €ƒ^"fj|[w‚w_ q£_2„w‚Hr£pVhkj|r£†=€Vj †]h _—€ƒy|ž´_2vw†<_:hkjljlr£pVr£^¨†]h'€%j|jl_:pʄ jljl[wp=p<”Vhk__µj|[w†]_pVyy|^"©rs€Vjlq£[ h ‚j|][wq£€V_†whk_¨r£”Vjl†w[]_?yl„¨p=vw„i”Vruh{[ j €ƒ†E†]€%jl_ v]jly|po€Vq-jl[]†w_°_:rs_:”=hk[<jlnHr£^¨pVyo€%j|rsf†<_:„¨j|_j y|€ƒ‚E†wp=”=q£€ƒ_jl†<r£j(pV†,‚]ßq£€Vjl†w[]_ª€ƒjm€ƒj(ruh ‚HpVfr£(x)†=j = Σ λ (x)f ©[w_y|_ f€Vyl(x)_°jl[wr£_h (x) V € ] † „ †EnH€%_j{jl©¹v]y|_€V_:qH† p<p=y|„wrs†]€ƒ€ƒjl_?†]h-„ pVž x”VpFrs†_:h¹Sj|p"­®º±æ_†—y|p"jl[w©ru[wh_hk† _jkj|j|[wrs†w_2”Ehlßi€Vr³^mj :‚]€ƒqsr£†—†w”¨nH_2„i_hk†E[]hkp%prs©j{g—†µ∈r£jl†]S[E€%y|j5_:€=jlhk[w_?_ h­lambda ª€ƒv]h|„ipVy (x)P„ir£hkj|€V†]_ . C. . S. P. P. . 3*. &. &. %. & '%. '%. &. $. %. &. /. 3. −1. P. P. (f −1 (0)). . . i i. i. i. i. +. P. i. P. f −1 (0). "$/ % &

(63)  .  !/ % &

(64). S.  )

(65) " % " +. V€Z5†][]­8„P_¹Z5j|^¨[wp _2€Vrsyl†mq£_?€=r£hl„wp=hl_:†]r³ž´€ch{g j|pƒylj|žEvE[wjl¡_m[wjl_?ruylh8„—_:”Vhlr£quvwpV€V†]ylh|žŸh$hª€VpƒpƒžH_ ž8^mj|[w_jlruruhch5[wpijlhl[wvw„w_:nÛh† „iruh$r£jl<jl[wrup2hl_2rsn]p=nHvw†ÖpVrsvwqu€V„'†Ehª„wž´ylr£€ƒ†]p=y|hk^ g¨ru„ipƒjl_m[wž$pV_ jlyc[wh|_2€ƒpV^"viv]j †w‚whkrsq£rup=r£„i†w† _o” pVjlS[wž$_"r£†]€„ihlr£p=hl„w^"‚]_c€%€Vy|j|rs_r£†Ö€V”=qFrsnEp=hlp=†]vwvwnÛh:†]­ „i„ir£<_?ru„¶hlrsp=nF†g P. Sˆ. S. ðð+ö. 43658789;:.

(66) Ñ :Ñ ¾Î 5͟šÎÅÈ Ä?ÍÐÈHÅ Ë. ’?‘. .  . . œ$ # $™ ™  #Ÿ›  › ™š ›  #A›i™ j|j|[wrsp=ru†h-ru„i_:€'pV †"€Vj|†][w؄'_cy| ¯ª__^"Ø qu€ƒp%v]=†]_:€Whg'rs†oÙ j|yljlruvw€ƒy|†]†m”Vjlvw_ qujl€%y j|€ƒrsp=[w†,_?A„i­$Ý y|Z5€ []jl_ª[]±æ€ƒ€ƒ†—j-q£”V€'€ƒp=y|hlyl_(_rsjl^"q£[]r£«V^r£†]_q£€ƒghkqEj|jl€ƒ‚]pyl€ƒj|‚HnHh8__ž´ycylpVp=¼ vi¹^ j p=hkrujlr „i[wŒW__c¿Rhlß ¯°p°¹_:j|pVq£[]€Vru€%hlvwhlj8†]pV_:€W†]Vgm†]_€%jly|y|j-g2r£€V€Vhl†w‚w€V”V^"‚wv]q£‚wrsq£_?€ qs„ _ ‚žŸH€=pVr£_°†<j(D(S €ž´ylƒp=‚]^‡‚E_?j|)€ƒ[wy _ªhy|pV_†"^"jlp%[]%_ €ƒq]nEpƒp=žvw€2†]„wj|€V_j|yly|g=€V­®[w¸¹_:„i€Vyly _€w­ruh±æ†Êj €ƒ¼«VÀª_:`i†"‘=jl‘W[]¿²€ƒßFj-À¹†wjljlp_:hl†wrs_ª†]”V€Vvw†]qu„—€ƒy|`Fr³j{‚]gm€V”V€ƒ†Fy|r£vwhlp=_5qspVp†"ž´vwj|yl[wjl_ []_nHy5pVvwpV†]†E„]h{€ƒj|y|y|go€Vrshl†wvw_?y „ j|hl[w‚]_¹€V†wyl†w_:^mr£†wp%”%j|€VylqV_:‚w_:y|h pi-€V_:‚wh|‚Eh$_?hk€ƒp°y¹jl[]pV†¨€ƒj®j|}[w_€VnwnEylp=r£vw_q<†]žŸ„w€=€Vyl_g=j ­$hZ5€V†][]„_gµÔ(bʀƒquhl`ip'Z¥v]_?hl„i_:„—”V_?Ô-h bʟ_:„i`i”=Z¤_:h$_?„ipƒ”Vžw_?j|h8[w_¹j|po_v]”=vwqsruru„i„i_°_:€Vj|†[w_^"rsy|†]_:rs^o€%j|vwrsp=^ † pV‚]ž®ylp=[w‚EpVp<q£_:hk_?hª„Ê€ƒ†]nF„ g¦nH¸(_'[E€ƒ€ƒn]r£†wqs_2_ j|¼¾¸(pµ[]y|€=_:‘Vp=ŠW†]¿(hk^"jly|€Wv]g¡j°€ƒhlquhkvwp ylžŸnH€V_¨_?Fhrs©_:© rsjl[ʀ=h€¨€ †]pVhl†¶vw‘"qs‚w”Vjlr£_:†w†F”¶v]h‚w­y|piZ5[w_:_oh|h:­µpV†FZ5=[w_:r£¡h'j|rs€ƒp=q£†P”VpV€ƒy|q£rs”Vjl[wpVy|^rsjl[wy|^_ ^"p=ylp%r£_=†<_:j|h_:„Êr£†¦}jlvw€Vnwy|†¦ylr£_jlq$_jl‚wy y|€ƒpV[w‚H_?_„iyly|j{€ gV­2[EZ5€W<[wr£_m†w”PpVy|€ rs_:†<žŸ€=jl_:_„Öj}p=†¦€ƒnwjly|[wrs_:_ q‚wvwyly|p=yl‚E_:_:†<ykjj{gPnEp=vwpV†]†]„whlr£€V„wyl_gÊy hjl[]jl[]€ƒ_mjor£„i†<pFjl_:_:h2y|hl†]_:pƒjlj'r£pV[]†¶€W=pV_"ž8jljl[w[w__ j|hl[w^¨_2€ƒr£q£†wqs_?†wh{_jy hlr£y|ru„ivw_^¨€ƒ†]hl„ ylr£y|nw_:r£t<†wvw” r£ylhl_?‚wh-[wj|_:[]yl€%_ojpƒj|ž([w€µruhžŸrs€V†Eh{_j|j_y ©hk_?r³j|¡[Êjlr£pVj|[w† _oruh5[E_€ƒ^"qsž ²‚ihl‚]j{g—€VpV_'ž$nHh|€ƒpV^"vw†E‚w„iq£__:„Ê‚Ep=n<rsg †<j|j|h:[w­ _mžŸ€V_j€V†]„Pp=† ªÝFÜ'Ø šÖœVš $˜:™ Z5[w_"‚Ep%©¹_y2y|v]hkj€ƒq£”VpVy|rsjl[w^ ©5€Vhªrs†<j|ylpi„iv]_:„ÖnFgÊÀ ^"_†<j € _j€ƒqR­ rs† ¼ À°¸ 2‘]’n ß j8jl[w_°^m_?_„i†<rujl€ƒ_:q]yl€ƒ_?§F„PruhpVj|†Py|€Vj|†][w_'h{ž´p=‚HylpV^‡q£_:h°pƒž jlS[E€%j2€V€ƒ†my|_nH_°rs†<€Vj|‚w_‚wy|†]y|pW€ƒ§Fqr£jl^¨p €%j|_:­ „¹nFy|gors_ jl[wgV_ ß vj|]À°[w†w¸ _µrsp= 2€ƒ†¶‘]q£”V’:pƒp=€?ž®yl¿²j|rs­$jl[w[]Z5_"^e[]¯°_ _:^¨p=q£€V^m€ƒvwr£‚]†]†mvi€Wrujlg „i_?_?hn]€2߀ƒjlr£q£h®q[wpV_ jl[]ž ¯°€ƒD(S ) S : _ £ q V € w v ] † W € P g | j l y u r ƒ € w † = ” w v u q % € l j £ r V p † ƒ € E † Ê „ | j w [ µ _ H ‚ V p £ q : _ 2 h V p ¹ ž ? _ V € D(S ) ‚ž´Hy|pVpVr£^‡†<j:‚E­8p=Z5qs_?[wh_2pƒ‚HžHpVh|q£€ƒ_:^"h‚w€Vylq£_5_c‚Ej €ƒp=”Vrs†<”=j _:h®„ pV€V†oh5jl_[wrs_5jl[]nH_pVy vwr£†E†]„ihlr£rs†]„i_2”2p=nEy5pW§opVvi€Vj †]hk„oru„iv]_hkjlr£†w[]”cylp=jlvw[]”V_5[ žŸ€V€m¡j”Vy|j|_[]_:€%„wj8gµn]€ƒ€Vq£qs”VquhpVpƒy|rsžHjl†w[w_^3 r£[¦”Vhk[Fj|hlnH€V€VpVyk^"j|y|rsrs‚w†]†]qs””_ ‚Hp=† pVq£_:pVhc‚w‚Hr£†<p=jlhl_r³j|y _hl_:hk¡ruj2„i_?„ih_:­-_‚wZ5q£[]gP_'r³ž(€ƒq£jl”V[wp=_mylrsj{jl©¹[wp ^ ‚HpVpVq£^"_:h‚w€Vvwyljl_o_pVjl[]†Ö_jl‚E[w_"p%©¹hl_€Vy ^"„w_mr£€Vhl”Vr£„wy _m€ƒ^ pVž pVSžj|€ƒ[w†]_„Ö‚HhkpV[]q£_:€Vhqsq£p%©¹©_r£q£”Vg [<rsjlž-_?„ j|[wn<_g—gÖjl€ƒ[wy|__ pVrsžy j|Z5[wv]_2^m[w_2vwy €V†wy|„w_:r£pVrsrH† pVpƒ†]pƒžhkžjljly|jl[wv][w__jl_:p=„ _ylq£y|q£hl_:h vwhlpƒ‚EykžŸžp=€=†]r£†w„i_c†wr£†wr£_:h y”o©¹‚E¯ª€ƒp=_jlqsqu_?_€ƒhylv]jlr£r£†]† ”V€W[<j|g"j[wn]nw_2€ƒvi‚Hq£j qAp%­8†]©(Z5__:_:[]y5„ _c„w†wr£hl€VvwpV”Vj yly žŸnE€V€ƒ^ _2_ ^¨­ Sˆ€V†wr£h¹r³ž´pVp=nwq£„,j|€ƒ­8r£Z5†w_?[w„—_2€V^"h(_j|jl[w[]_pF„ nEp=ruvwh†]‚w„wy|€Vp%yl g nH€VnwpVq£v]g¥†]„w”V€ƒpFy|pir£„¥_:h:­ž´pVy¨„i_:†]hl_ h|€ƒ^"‚wq£_ €V†]„ €ƒ†¢nE_ _§<j|_†]„w_:„¥j|p¥„i_j|_:¡jµhl[]€ƒy|‚ _?„i”V_?hm€V†]„½€=pV^"pi„w€%j|_ j|® p¦p=# ÝFyljlp=Ü [w†w_¶pV r®h|€ƒ=Ø ^"_™ yl‚wjlq£ruÝ r£†wÞ_?” h2˜ pƒSž Z5­[w_ Z5[wp%_P© ­ q£piZ5^m[w€ƒ__qjl[w^¨pip%„w€ƒ©§Fh r£^¨^"p=€¦_†]j|hl[wpƒr£žªpi„i„w_:jly¨h[w_Pjly|[]_:ž´_ v]pV†]†]¡hkp%j|jl© rsy|p=v]† „ijcru„w€ƒj|r£”=hk[wy|j|_ €V€V^†]€V‚w_ r£‚w†]y|j|„ipWp v]§iSrs^¨_:„¤€%j|€VnF_:ylg¢„_ jlhkhl[wv]pV_yk^"žŸ€=„i_Pr£_ hkpƒj|žc€V†]jl[w€V__h j|€V[wqs”=_ pVy|nEr³p=j|[wvw^†]„w‚w€Vylylg¥p=‚EpVp<ž hk_?jl„"[]_ VnFgm(Sv]†wÔ(rs„ip=)_†¢quhkpVn]ž°ylvwj|†][w†w_P_h{ycj €ƒ¼ Ô(nw„iq£_ _:‘V^¨Œƒ¿ €V€ƒ†w†]r³ž´„"p=q£j|„][wh"_† pƒžª^¨hl€ƒpVy|^"«V_ _j|pƒ_:„"ž°j|nF[wg"p=[whl_ ruh(^"pV€ƒ^"§irs‚]^¨€ƒ€w†F­gmnEZ5_:[wqsp=_ †w©”=Sˆh-y|€Vjl‚p j|:[w€Vruhlhc_Vßi:†w€%j|p"_”V”=p=v]yl€ƒg=y ߀ƒ†<€Vjlhc_:©(_°_:ruhqsq®”V€=r£h°V_:j|† [w_ _§wp%_©‡‚wj¹j|p=[]^"€%j‚wqsj|_[w§Ê_2€ƒy|q£_:”Vp=p=yl†]rsjlhk[wjly|^ v]¡pVj|ž5_:„—}chlr£_:vwhlyl_žŸ†Ö€V€V_†]€V„Êqs©5»=€WpVgi[]h¹†½nE¼¾p=}vw»=†]‘<„ ?¿R€"­ohk±æp=†Êqsru„ _:r³­ j|[w_y &%. ". %. &. %. &. . %. .

(67). P.

(68). $. '&. 

(69).

(70). . . P. P. 

(71). . . . P. 1. P. P. . .

(72) 

(73) &$/. $)./

(74) &. #". !).&$% %2.

(75) - 3$)" /. "^Z5¯ª[]__qujl_ €ƒ[wv]‚wpi†]y|„wpƒ€Whmjlg—pVj{j|€VgF_†½‚Ej|y|_nH€VpV[w_ žH_:F„ij|[wr£y _€"_:©¹hlpV_ _:†¶„ ^"jl€V_[wylj|_o_µ[wpiy|r£†]„w€=„ih-hlr£rs„w€Vryl_pƒ_5Wž®p=j|j|vi[w[wj|_°_hlr£€Vruyª„iqs‚w_—[Ers^"y €_vwhkj|[E^¨[w€ƒpih|‚H„w_y|horsyln]_?n]rs†w€VpV” hl†Ers†]hkh{‚w”¶j|yl[]v]jl_[]y|jl_ _:r£h:pVr£­ †"†]Zhl^"r£p „i__ €Vj|W[wp=pivipV„wj|vwh hl†<r£¼„wjÔ-_—ž´b¶p=quyc€ƒ‹VnHŒ%h|_¿R€ƒ­®q£^"qsr£Z5†w‚w[w”Êq£rs_?†]hkpV”_ ž ©rsjl[P†]pV† vw†wrsž´pVy|^+„w_†]hlr³j{g=ßwj|[w_©¹_r£”V[<jl_?„ €Vqs‚][]€¨hk[E€ƒ‚H_2^m_jl[wpi„whª€ Û_:j|h©¹_r£”V[<j|hjlp"jl[]_'hl€V^"‚wqs_ î´ï$ð,îÐñ.

(76) mÅ Ñ ÂiÈ Ñ Æ wÃ¡Í Ñ È VÂ Ñ ÏAÍŸÇƒÈ Ñ ÎÅ Ò"ÁHÂià  Ñ Ë ÅªÓªÅ Ë|ǃÈwΡÏRáÂ]ËÏR͟Ç%È . .  . ’=’. . H‚€=pVr£†<pVj|y h:„iß,rs†]nw”ovwr£j|qupµ„¶j|j|[w[w__"y yl€V_:„i”Vr£vwrqupV€ƒž$ycj|jl[wy|_ru€ƒr£yc†w”=pVvwyljlq£€ƒ[wjlp=r£”VpVpV†¶†EpV€ƒž-q,j|hl[w‚w_:[whl__"y|_:©(h:­_:rs¹”=[=_j|y|_:†]„Ö€ƒy hl„i€Vr£^m†wr,‚]_qs_?jhc€ƒ€Vq †]„Ö¼ 5q£b¶€VnE _:q‹=jl[w‹W¿_m‚]jlyl_p=jly ‚E€ƒp<[whk_?_?„i„ y €€ nE€ƒq£q x‚w_rsj|=r³jApƒz{j|_:rs€V†w†m”¨€V€V†]qs”=„ pV¹y|r³p%j|[wgV^_:y-jl¼ x pµ5‘wpV†]’¡¿ihkjlr£†=y|v]j|yl¡pij„i_ vE¨_8rsj|_:[w†<_¹jlq£†wg¨pƒjlj|[wrsp=_2†]nHhpVpVv]ž]†]r£†=„wj|€ƒ_y|y|gµ‚Ep=pVq£ž$€V€ƒ†<†Pj|h$€V€ƒqs†]‚w„2[E€my|_hl”=[]vw€Vqu‚E€ƒy_=­ r£†<jl_:yl‚HpVqu€ƒ†<j|h pV€Vž$^"€mpVvwhl€V†<^"jjl‚wp¨qsr£†wn]” vwrsSqu„ €V†]ž´y|„ pV^3‚wylp=€¨‚Ehlp<_hkq£_c_:€mjl_:yl„P_?hlpVvw†En]h{hlj|_ylv]j pVjlž®r£pV}†µ€V^"nwy|_rsjl_:[wq pižŸ€V„ n]_j|€Vh hl_:rs†„ pV† rs†<jl_:yl©‚HpV[wqu_:€ƒyl†<_j j|h[w­®_Z5hl[w__cq£_:^"¡j|_rsp=jl[]† pFr£„ h nEn]vw€Vhlrsqu_:„w„¶h'p=jl†Ê[w_ j|[whk_"v]yky|žŸ€=€=„iS_µr£ˆv]r£hc†]pƒy|ž-_j|^"[w__:r£†=y2j €ƒhkq£^¨qsg¦€Vqshkq£j|_:€ƒhkjyljlr£†wr£y|”Pvwž´y|^¨pV^*y|rsnw€Ör£†whk” _:_:hk„‚][wjly|_ruy|€ƒ_:†wh:”=­'qs_µZ5D(S [wpV_¨ž p=)yly|_:hl‚H­pV†]À¹„ijor£†w_:” €= €ƒ[ q£”Vh{pVj|y|_rs‚,jl[wß8^ € nHnFg—pVv]€=†]„w„w„i€ƒr£y|†wg”m_?jl„i[w”V_2_5r£pƒ†]žHr£jl„i[]_:_ †<jªvw}y|yl€ƒ_:nw†<y|jrs_:y|qÛ_:žŸ€VpV†]_hkjjly|©v]r³j|jl[ _:„mjl[whl_vwyk^"žŸ€=r£†w_5rs^oruh®vw^ pV†Ehkr£ruy|„i_vwy|^¨_:„mhl€ƒyl†Er£D(S „nw'r£†wj|[w”o_ y )hl€Vvw„wykrsžŸv]€=h:­ _5ruh®_§Fjl_:†]„i_?„ . . +. . . #. P. P. P. )+#%5 &¹ ¼ À 5‹=‹%¿  Ír£u†]ÎË€¶ÃlÅÀ ÏæÅ^"®Ç_:†=j €PۀƒÂi†]Ï „¥bÊŠǀƒy hk[]£ßE€V=qsq Ÿ¹Œ _:ylŒ †,­ ’ w‰`Fƒvw‘ƒylŒEžŸ€Vßw’:_¨‹=‹Vy|_:‹]­ pV†]hkjly|v]jlr£pV†n<g ®pVy|pV†wp=r¬]qsjl_y|r£†w”]­ ¼ À 5‘<W¿ jl¯°y|p=r£€V^m†wr£”V†wvwruqut<€%vwj|_rsp=†"À¹jlpƒj|ž €V‚Eqsr2p=rs€ƒ†<†Ej h8„ pV»V†¨_?€ƒ‚H† pVæq£gF¯c[w€ƒ_:†w„wr£y|_€Vq q](hkv]p=ykr£h|žŸhl€=pV†w_:h:†]­]€ƒ±æj:† ­ 5¸(ÃlÇ:pVË ^"‚wq£Ï _o§iÉr³j{g pVž2ÁHjlÆ [w_¦]¯°ÇWΡ_:ÍÐq£Â €V3vw†]€WÇ%gÈ ÁÛÇ ³ÍŸÒ ÊÇ?ÒVÅ õÍÐÈ Ñ ÈHÒoÉ $ õÍŸË Ñ ÏR͟Ç%ÈwΡßېƒ‘V‘<i­ ¼ À ‘VŠ%¿ ¯'€ƒ†w­”=À¹vwq£jk€ƒj jl€ƒr£q£pVrAß®†¦»Epƒ­ æž5¯'‚H­ pV¹r£†=pVj ruh2hlhlpVpV†¥†w†Ehlvw€%j:ylžŸß€V€ƒ†E_?hc„¥jlÀ[w_µ­ hl^"rs_:vipFpƒjlr£jl_[¥y?­Ê:€V¸(hl_VpV­µ^"‚w±æ†½q£_§iÉ rsj{gÖpVž¹ÁÛj|Ç [w_—5„iß$_:`wq£€V€ƒvw†¥†]€W¯°gÊr£_jl”=y|p]r ß ƒ‘V‘=Šw­ ¼ À°¸¹¯ ‘V‘ƒ¿ pV^"­ pVÀ y|^"‚w[w_ru†<oj €whlvwß yl`۞Ÿ­€V¸(_m[]y|pV_:rRßHpVZ†]­ hkjl "y|v]­H¯ªjlr£_pVg=†,ßH­€V†]±æ† „¶¹'Ãl­ Ç? Ë __«FW[]Ï ʀ]­°ÉªÀ‡ÈEÈ]hlÂr£^m$‚]É qs_m€ƒq£”VÁHpVÆy|rsjl[w]^3ÇWÎ ž´pV8Çyc[wpVH^"Âi_ Ï Å Ç £ßE‚]€ƒ”=_:h i’?Š wVVwß<V‘V‘V‘]­ ¼ À°¸ 2‘w’?€%¿ ƒ‘V­]‘]À°’V­^m_:†<j|€wßH`Û­E¸([wpVrRß]€V†]„ 

(77) ­ °p=qsq£vwy|rA­Z5[w_2‚Hp%©(_:y5ylvEh{j?­$±æ†¶É ÁÛÇ ³ÍŸÒ ÊÇ?ÒVÅ õÍÐÈ Vß ¼ À°¸ 2‘w’:ni¿¤jl[w­,_2À ^"^"_:_:„w†=r£€Vj q€w߀%§i` ru­,h¹¸(jly []€ƒpV†]rRhkß,ž´€ƒpV†]y|^ „­ 28Ç­ "­ H °Âip=Ï qsq£vw y|Å rAÇ­Z5[w_"w‚HÅ p%Ç%©(áÆm_:ycÉ $yl vEh{£ßj?ß ’?vw‹ †w£’?r£ pV†]H’hcWpƒ‰ƒž(ŠwßFn]ƒ€ƒ‘=q£q£‘wh:’Vß,­ €ƒ†E„ ¼ À x( ‘VŠƒ¿ r£hlpƒ­8j|À pV‚w^"ruP_:†=€ƒj ‚w€w‚]ß8ylZpW§i­®r£»E^"­$€ƒxjlr£_pVjl†¢_y pƒh:ß8ž€ƒ †]²^"„ €VÀ'†w­®rsž´pVquv]„whh|hk­ _:qsqR­½]Å ¸(Ç%pVÃl^"ÅÏA͟‚wË vij €%jl8Çr£pV†E€ƒHq(ÂijlÏæpVÅ‚HàpVÁ q£pVË”=͟Åg ÈHµË ÅÀ ß^'ŠV‘=n]‰rs_:{†=’ j Ñ Š Š ے?‰wßiV‘V‘=Šw­ ¼ Àª`w‘V‘%¿ rsb¥†P­whlÀ¹‚]€Vjkj|__V†w­ _8ǀƒ†]„ Hb¥ÂiÏæ­wÅÃ`F‚]5€Và ”V†F vwFpV͟q£Ëp]Î ­,À°Ç%viájl p=m^¨ß €%’:jl‹ rucŸŠ hkvw¾¸(ylžŸŒF€V‰ _°w¸y|(_:Œ pV†]‰ihkßFjlƒy|v]‘V‘=¡j|‘wrs­p=†¨ž´y|pV^ ‚Ep=rs†<jhk_j|h Ñ ¼ ¸¹‘V‘ƒ¿ †]»V_?€%€ƒj|vw† y|毪€Vqw€V†w†w_:r£_rs”=q [<¹nHpVpVruv]hlhly®pVrs†w†<†Ejl_:€%ylj(‚H€VpV†]qu€%„—j|rs·]p=yl†o~?„ipVžÛ~y|„wr£2r£hkj|¸¹€V€ƒ†]º?€ƒ_¹quhž´vw­$†]`F^"jlr£p<pVpV†]jlh:[ ­H±æhk† vwyl5žŸ€VÃlÇ:_ªË y|_:WpVÏ o†]hkɪjly|ÈEv]È] jlr£ipVÉ †¨Fr£€ ÁEÆ wÇ%Î ®Ç ÛÂiÏ Å Ç £ß]‚E€ƒ”V_?hVƒŠ iVŠ=ißiƒ‘=‘V‘]­ $. (. . -. (. -. $.  2$ 8& . 1. . 

(78). . . 4 .  . $.

(79). -.

(80). . (. 4(. . 4 . . . (. . . -

(81). (. . -. -. 

(82). (. -. . -. 4 . . . (. -. . (. -. . -. !.  . . .

(83). 7. . .&8 . (. . 

(84). . *. 4(. $ .&. (. . . . (. ðð+ö. 43658789;:. $ 

(85). -. (. -. . (. -. . - 

(86). -. .

(87) Ñ :Ñ ¾Î 5͟šÎÅÈ Ä?ÍÐÈHÅ Ë. ’W.  . . . ¼ ¸¹‘w’¿ jlV» £r _?pV€ƒ† † 橯ªr³€Vj|[†wr£_”Vq _:¹pV^"pVru_hlj|hlylpVru†]¶†]”=€%v]j€ƒ€ƒy †E€ƒ„Ö†<j|·]__:ylh:~?­„i~y|±ær£† —À'¸¹€V­ º:¸(€Vq£[Eh:€ƒ­—q£^m¸(_:p=y|€ƒh y hl€ƒ_ †ERjl„ p RZ¬]†w­ ²_mb¥hk­v]ykžŸ€=[FgF_µ†w_=hlrsߪ^"_?‚w„iq£r³r³j|¬HpVy € hß ¹ÂiÃlÇ ƒÃ Ñ  i͟ˡÎ  ƒß b¶€ƒ†] []_:hkjl_y?ß]ƒ‘=‘w’=­ ¹qu€V «F©(_:qsqR­ ¼ 5b¶ ‹=‹%¿2‚w·(rs­ =¹pƒj|_rsy|†w†]”¨€ƒy €V„iqs”=r£†wpVrAy|ßwr³j|»E[w­E^ b¶ž´r³pVjly jlq£_hlvw^¨yl€ƒžŸ€V†,ß _cy|­]_: p=v]†]hkhk[]jly|^mv]_:¡rsj|_:rsy:p=ß †,¸ª­­E`Fr£qs%€]ß]w€ƒÃ †]„¶ÈwÎ }mË­EÏA͟Zǃ€VÈwvwÎ'nwÇ%r£†,È ­(Z5Íu[wΡ _2nEõÍ €ƒq£q Ñ ?Ñ ÏAÍŸÇƒÈ Ñ ÈÛÒ 8Ç ÛÂiϲÅà 5Ã Ñ  F͟ËÎ ß ‰ ŠƒŒ<‹ iŠ=‰ƒ‹]ß cj’?‹V‹=‹w­ Ñ Ñ ¼ ¹pVr ŒV¿ yl»V_?_?hk€ƒ_:† †=æj ¯ª€%j|€Vrs†wp=r£†,_­-q ¹É pVruh|hkp=†ww†]à €%È]j?έ(}c¹_Ãp=^" _jl£ßEy|ruŠ 2´Œh{j|ylv]jlvwiy|_:hž´ßEpV’:y‹ j|[wŒ]yl­ _:_ æ„ir£^m_:†]hlrsp=†]€ƒq,hl[]€ƒ‚H_y|_‚ Ñ Ñ ¼õ¸5}‘ƒŒV¿ ·wpVy|†E~:„ih{j|~:ylylv]ru"jl¸¹r£pV€V† º:€V®q£hc±{„i€ƒ_:†]€=„Öh€ƒ»V†]p<„ €V €ƒ[wq£r£”V^p=yl}crsjl[]rs_?^"hk_:h:†,­®­ ¯ª€ƒ‚]_qu‚E€ƒp=vwyk†]j €W„ig _j|y|yl_:ru€ƒ †][w”V_:y|vw qu[w€%j|_=rsßFp=±{†¶°n]€V±{hlÀ'_:„ÊßEƒhk‘=vw‘ƒylŒ]žŸ€V­ _oy|_ ¼õ¸5}€ƒyl¿ x8·(yl­ _ ¸¹Ry|€ƒ_:º?t<€ƒvwquruh—hlr³j|€V_:†]h„¤€ƒ†E»]„—­5}cr£†]rshl_?rshk”=_:[=†,j ­‡h­¯ª±æ† _quª€ƒvwÇ:†EÇ  €Wg¢Ë n]€=HhkÏæ_?Å„¤Ã¡­HhkZv]p¨ykžŸ€=€V‚w_P‚E_?y|€ƒ_:y?­ p=†]hkjly|v]¡j|rsp=† €Vqs”=pVy|r³j|[w^¨h Ñ ¼õ¸([]€=‘VŠ%¿ 2ÁE ­F¸(o[]ÍЀVÏRrsϲ†]Š҃_Vß]­ ƒÀ ‘V‘=Šwp=­†FV_:jlr£pV†m”V_:pV^"_j|ylru ²n]€Vhl_:„m€ƒ‚]‚wylp<€V ['jlp'hlvwylžŸ€V_y|_:pV†]hkjly|v]jlr£pV†,­E±æ† ¼õ¸5`i¯c‘ƒŒV¿ ¯'€ƒq£”V­®pV¸(y|pVrsjl[w[w_:^ † æ­ `Fjl_wr£†wÅ _:yÍu€ƒÎ¡Â†]„¦·¹®Ç­¯cۀw­—ÂiϲÀÅáßE”VVy|‘V__:‘ƒ„wŒEgÊ­$Z„ip¨_qu€ƒ€ƒ‚wv]‚H†]_:€W€Vg¶y:n]­ €=hk_?„ÖhlvwylžŸ€V_"y|_:pV†]hkjly|v]¡j|rsp=† Ñ ¼ ¯}‘VŠ%¿ Z Fǃ­ Âi "Ã¡È ­w¯ªE_Çg  €ƒ8dž]„ Û`ÛÂi­HÏA}cÍÐÈ p<hk©5€ƒÈH^"Ò rR¡­8ÈZ5ǃrsà ”=[<jÏA͟piǃȗpVÁ†]Ë_ ͟8ÅÈHÀ Ë Å°©5ÍЀ%È

(88) jl_:¹Èy Rjlƒr£”VÍÐÈÛ[<Å j ÅhlávwÍÐÈ ykƒžŸ€=ß<Š _ŠVy|‘=_: FŠp==†]‘ hkjlFßy|%v]ƒ¡‘=j|‘VpVŠ]y?­­ Ñ Ñ Ñ ¼ ¯}‘ƒŒƒ¿ ±æZ† ­ 5 "Ãl­=Ç:¯ªË _g" %€ƒÏ †E—„"ɪ` È]­<ÈE}c p=hlÉ ©5€ƒ^"rA­EÁHx8Æ y|p%]WÇW€VÎ nwq£_ 8ÇhkvwylžŸH€VÂiÏ _yl _?Å p=Ç †]h{£j|ß]ylvE‚]¡€Vjl”Vr£_:pVh5†oŠ=ž´ŠVy|pV‘ ^iŠVŠ=†w‹wpVß<ruhkVgm‘Vhl‘V€VŒ]^"­ ‚wqs_?h­ ¼ Ô-„i_?‘ƒŒV¿ ±æ† ­]cÔ(„i­ _À quhky|n]pVyl†]vwp%†]H†wß_` y?­­¹¹`Fv]€=hkykvžŸ€=ß,»]_­ ylx®_?€Vp= †][h{ß,j|yl€ƒvE†]¡„jlr£b¥pV† ­nF`Fg—[]€V©yly r£y?€ƒß ‚w_:‚]„irs†wrsjl”mp=y|¬]h:†]ßr³Óªj|_͟Ë‚Eƒp=Æ rs†<j°Ç hl_j hË rs†¶ÈHhl‚]Ò€=_V³Í­ Ç?Ç?Ò Ñ È ÅΡϟÎËFÃ¡Í  ÏRßw‚]€ƒ”=_:hŠ %‹ FŒ=‘VŒ]­<`i‚wylr£†w”=_y ®_:ylqu€ƒ”EßFV‘V‘ƒŒ  ¡­ Ñ Ñ ¼ Ô-b¶‹VŒƒ¿ ¹­%à Ô- „i _:£q£ßhlnw’?Šy|vwk’ †w†wŒ=_:Šy$

Références

Documents relatifs

cosinus (en bleu à gauche) et d’une droite (en noir à droite) sur les données simulées pour 4 années à une température de 45°C, avec un bruit de fond interne réduit de 100,

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

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