Some Remarks on the Optimization of Hölder Functions with Genetic Algorithms
Texte intégral
(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Some remarks on the optimization of Ho¨lder functions with Genetic Algorithms Evelyne LUTTON, Jacques LEVY VEHEL. N˚ 2627 Juillet 1995. PROGRAMME 5. ISSN 0249-6399. apport de recherche.
(3)
(4)
(5) ! "#%$'&)( *+ ,$.-/102 "14356 78 0:9;*"<6 1) ?= >A@CBEDGFG@H IJKJLM/[email protected]=?YZ[Y=]\=!H ^_a`Cbc_6dfeKeKgih!jkA_ldfmonagpeqgpr.n2sutvamwbcrSdfxzySdft{n|`Ced}n|m~tg?gpn _a`.stupn|m~tg ^_a`f gpni kA?A Xdf`C_nXsg _ag"lg"_algr]{fC?j)ftmwxxgpnch!jCh]Sd}bCg"v. 6 ¡}¢S£f C¤¦¥ gmr§g"v|n|mb.d}n|g
(6) n|ug%_a`c¨uxg"e5`c©ª]`C« xsg"_ ©Etrpn|mw`cruv`c{nameKm¬d}n|mw`crtvamrbig"rgpn|mw%ixbC`c_amn|eKv!®¯i°l± ¥ g ²u_avnsg"_amo§g?d]_ag"x³d}n|m`Crq¨gpn¯´2g"g"rn|g!ª]`C« xsg"_gpµ¶`crg"r.n·`f©Vn|g ©Etrpn|mw`crAynag?vldfeKxmwrb_6dnagCyudfrsqn|g!dfp"tu_ldfp¸ `f©Gnag!`C{n|mwe%te¹x`d}xwm¬d}n|m`CrºyS¨`fnamwrqnag!su`cedfmrdfrsnag!_6d}rubcg]`f©n|g?©Etrpnam`crA±·kmvX_ag"x³dnam`Cr»`Cxsv·©E`c_?dfr¸ `c{nameKm¬d}n|mw`creKgpn|`s´ m6q´`c_a¼K`Cr»v6d}eKuxg"sKvagd}_al»vaSdf"g"v± ¥ g n|g"r_ag"v|g"r.nXd?²Srg"_ d}rd}x¸vamvmrqn|g?d}vagi`c©An|ug tuv|gi`c©GdX%y´ mwlqmwv2¨d}vag"sq`Crd!sg""g"{n|m§mon¯¸»dfrSdfxo¸{v|mwv± ½ t_Xdf_a`.d}ltvag"v d]sg""`CeK`cvamonam`Crq`Crn|ug]ªidcdf_·¨Sdfvamvy.´Xml_agp¾ug"pn|vXmrd%rSd}n|t_6d}xQ´ d"¸Kn|g]ª]`C« xsugp_ vna_|tupn|t_ag `f©¿n|ugi©Etrpnam`Crº± ÀÁnXd}xwx`´ v2n|`_ag"x³d}n|gXn|gsug""gpn|mo§{mon¯¸yn|g?gpµ`Crg"r.nidfrsv|`CeKgiSdf_6d}eKgpnag"_|v`c©An|ug
(7) i®Ãmru"xtsumrb n|g?vldfeKxwmrb_ag""mvam`Cr°6±kg"vagi_|g"vatxn|vu_|`§{msgiva`CeKg mwrsmwdn|mw`cruv´Xmled"¸g"xwKn|`%edf¼Cg·nag "`Cr§g"_abcg"r"g?`c© diÄgd}vamg"_± Å»Æ.ÇQÈaÉ!Ê ¡fË¿c¤ .n|`.ld}v|n|mw ½ {n|meKmw¬dnam`Crºyig"rugpn|mixwbc`C_amon|eqvy"ª
(8) `c« xsug"_Q©³turpn|m`CrvyCÌXg""g"n|mo§{monÁ¸ rSd}x¸vamvy}_ldfpnldfxv±. ͳÎ
(9) ÐÏ ÑÁÒÓ Ð Ï AÔ ÕÑÁÖÁ×"Ø Unite´ de recherche INRIA Rocquencourt Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY Cedex (France) Te´le´phone : (33 1) 39 63 55 11 – Te´le´copie : (33 1) 39 63 53 30.
(10) 5- *q- , ? %q-?5G-1,*» )¿ ! "#+$10 " &)( *+ "?1 * %+ + %*<%6 1 . < - ¤ `Ct
(11) Æ Æ v gp natsm`Crvxwg]u_|`C¨x g" eKg]sug%x `c{nameKmv6d}n|m`Cr»sg%©³`Crpnam`cruv
(12) ª]`C« xs g" _amg"rurg"vdq x dfmsg]s dfxbC`c_amonaeKg"v bg" r gp nam~.tug"v± `Ctv gp nld}¨uxmvava`cruv¿n|`Ct{ns d}¨`C_as%trg_ag"x³d}n|m`Cr%g"r.n|_ag·x gpµ`Cvldfrnsg ª]`C« xsugp_ sg x³d ©E`Crpn|mw`crAyCxEd ©E_ g" ~.tg"r"g s g" ld}r.n|mxwx`CrrSdfbcggpnx³d _ g" "mvam`Cr
(13) sg·xw`.dfxmv6d}n|m`Cr
(14) sgx `C{name%tey"g"r%`Cvamon|mw`cr%gpn§cdfxg"t_±gpn|n|g·_ag"x³d}n|m`Cr%g"v|nG§Cd}xEd}¨xwg `ctu_Qn|`ctn|gxg"vV! e gp n|`sgGs `cn|meKmwvld}n|m`CrX~.tm.`cr.n¿d}"" g" vAturm~tg"eKg"rn d2 t r g" ld}r.n|mxwx`CrrSdfbcg sgx g"vaSd}"gsg_ag"lg"_algC± `ctv
(15) _a`C`cva`Crv
(16) g"rvatmonagCyVsSdfrv%xwgKd}v
(17) sgx gpeKux`CmG s tr dfxbC`c_amonaeKgb g" r gp nam~.tugCy¿turgdfrSdfxo¸vagKxwtv]²urgCy¿~.tm g"vn©E`cru#s g" g vat_x³d ru`fn|mw`cr sug/s g" "g"{namo§{mo$n gC ± `fn|_ag df_a`lg gpµux`cmn|g trg #s g" "`ceq`cvamonam`cr sg x³d ©E`cru6nam`C& r %'d `c{nameKmvag"_?v|tu_x³d¨SdfvagsugKªidCdf_yº~.tum_|gp¾ g6 nagsum_ag"pn|g"eKg"rn!x³dvna_|tupn|t_agKª
(18) `c« xw#s g" _|mwg"rrg%su(g %V± `Ctv`c¨n|g"r`Crvdfmrvam trg_ag"x³d}n|m`Crq~tmºxmwg xEd]#s g" "g"{n|m§m$n gC yx gpµ{`cv6dfrn·sg %»gpnX"g"_nldfmruv·Sdf_6d}) e gp n|_ag"vsg?x dfxbC`C_|mn|eKgXb gp r gp n|m~tg®Ãs`Cr.n x³d ²urg"vav|g s g" ld}r.n|mxwx`crurSdfbcg}°l±2g"v2_ g" vatxon6dnav©E`Ct_armvavag"rnsg"vmrsumdnam`Crv~.tum¶`Ct_a_ldfmg"r.n2sSdfrv"g"_|nldfmrvdfv2© df"mxwmon|g"_ x³d]"`Cr§g"_|bCg"r"g!sugx dfxbC`C_|mn|eKg·b g" #r gp n|mw~.tugc± £ + Æ ¤Â½ n|meKmwvld}n|mw`cr n|`lSdfvnam~tgCyQixwbc`C_amon|ueKg"v *¦Ê } È , g" r gp nam~.tug"vyV`cru6nam`Crv
(19) ª]`C« xs g" _|mwg"rrg"vyirSdfxo¸vag
(20) sgq.Ì 0g / "gpn|mo§{mon gC y¶{_6dfpnldfxv±.
(21) K +1-10 " k´2`ed}mwr»©Ãdfpn|`C_|vedf¼Cgn|g`cn|meKmw¬dn|mw`cr`c©"g"_nldfmr1©³turpn|m`Crvsum?>KptuxonA@¶x`d}xm_a_|g"bCtxEd}_amon¯¸/®Ã©E`c_mruvn6d}rupgCyQr`cr sm?B¶g"_ag"rnam³df¨mxwmonÁ¸S°_ag"vatxon|mwrb
(22) mr´ mwxsK`Cv|"mwxx³d}n|mw`crvy{dfrsnag gpµ{mv|n|g"r"g`c©Vvagp§Cg"_6dfxºx`.dfx¶gpµn|_ag"ed±Sn|`lSdfv|n|m?`cn|meKm / ¬dn|mw`cr eKgpn|`sv ´2g"_ag
(23) sgp§Cg"xw`cg"s na`qn6d}l¼xg
(24) nag"vag%s?m >K"txn|mg"Av @Q`crg`f©nag"m_lSdf_6d}pnagp_amwvn|mw]©³gd}n|t_ag"v!mwvXn|Sd}n!r`d _am`C_|mQ¸{`fnag"v|g"v df_|g?edfsgi`Crn|g ©Etrpn|mw`crn|`¨g`cn|meKmw¬"gp8s Cr`"`cr.n|mrtmon¯¸yr`C_·sg"_amo§Cd}¨umxmnÁ¸Kmv·_ag"~tm_ag"sºyud}rs n|gX©Etrupn|m`Crmvr`cn·dfvav|tueKg"s%n|`
(25) Sd"§g `Crx¸`crugix`d}xed}µmwe%te ®z`c_eKmrume%tue°l±}k2mwvedf¼cg"vv|n|`lSdfv|n|mieKgpna`.sv tvagp©³tuxmrr.teKg"_a`Ctv Ds*m >"tuxoFn E%d}uxmd}n|mw`crv ®z`f©A"`Ct_av|gX`c©³n|g"rd}nn|gXgpµ¶g"rv|g `f©ºmbCK"`CeKt{nld}n|mw`crn|meKg"vp°ly.d}v©³`C_ gpµdfeKxgi`Cr»mwr§g"_|vag?_|`C¨xwg"eKvdfgdf_|mwrb%mwred}n|g"_am³dfx¶`C{nameKm¬d}n|m`Crºy.mwed}bCg!d}rSdfxo¸{vamvy.`c_X_a`."g"vav·"`Crn|_a`Cxz± À r d}susmon|mw`cr na`»nag"`c_agpn|mwd}x2mr§g"v|n|mb.dnam`Crvd}¨`Ct{n]n|g"mw_!"`cr.§gp_abCg"r"gqu_|`Cg"_|n|mg"vyºn|gKed}mr lSdfxxwg"rbCgKmr n|g ²ug"xs`f©v|n|`.6Sd}v|n|mw
(26) `c{nameKm¬d}n|mw`cr»mwv n|`qvagpnin|ug]d}_6dfeKg6nag"_|v `f© n|g
(27) eKgpn|u`.sv v|`naSdn n|gp¸1df_agn|ug]eK`Cv|n Gg >"mwg"rn± k2mwv _a`C¨xg"e4mvi`c©`C¨§{m`Ctvi_6dfpn|mdfx¿mrnag"_|g"v|ni¨t{nimon?d}xwv|`¸{mg"xwsvXv|`CeKg?n|g"`C_agpn|mdfxVmwrvambCni`crn|ug!¨g"Sd"§{m`Ct_i`c© n|g"vag`cn|meKmw¬dn|mw`crqn|g"lrum~.tug"v± À¯n!mv?s?m >K"txon?n|`sg"_amo§g%_atxwgpv ©E`c_?natrmrubn|gSdf_ldfeKgpn|g"_avi´Xmon|u`ct{nedf¼.mrubd}r.¸ d}vavateK{nam`Cr`Cr/n|gvnatsmwgps ©³turpn|m`Crº± ½ r
(28) n|g`cn|g"_ SdfrsºyCmo©´g d}_ag2n|` ed}¼Cg_ag"v|n|_|mwpn|mo§gdfvav|tueK{n|mw`crvy"n|ugp¸
(29) va`Ctxws]ru`fn_atxg2`ctn D mwrn|g"_ag"v|n|mru(b E ©³turpn|m`Crvy¿dfv©E`c_]mrv|nldfr"gKr`Cr s*m B¶g"_|g"r.n|m³df¨xwg
(30) ©Etrpn|mw`cruv!´Xmon| edfr¸1x`d}x gpµ.na_|g"ed{±¶À r namv?´`c_a¼yQ´2g"`Crvamsg"_ d"xEd}vav
(31) `f© ©³turpn|m`Crv%´ m6 mv
(32) ¨`cn| ~.tumon|gKbCg"rg"_6d}xÁyGdfv]mn]mru"xtsug"v]vaeK`.`cn| ©³turpn|mw`crvdfv
(33) ´gpxwx2d}v]§g"_¸ mw_|_ag"bCtx³df_ `crg"vyud}rusqva.t >Kpmwg"rn|x¸"`Crv|n|_ldfmrug"sqva`d}v2n|`
(34) `C¨{nldfmrtvagp©³tux¶_ag"v|tuxon|v±{k2umv"xEd}vav2mvnaSdn·`c©Gª]`C« xsug"_©Etrpnam`cruvy´ u`cvag sgp²urmn|m`Crmv·_ag"dfxxg"smrvag"pn|mw`cr1± vavag"rn|mEd}xwxo¸y ª]`C« xsg"_
(35) ©Etrupn|m`Crvqd}_ag"`cr.n|mwr.t`Ctv©Etrpn|mw`cruv´ m6 ed"¸ Sd"§gCyt na` d1"g"_n6d}mwr d}eK`Ctr.ny¿´ mwxs §cdf_am³d}n|m`Crv±SÀ¯r Sd}_|n|mw"tx³df_ySedfr¸»ru`cr1su?m B¶g"_ag"rn|mEd}¨uxg
(36) "`cr.n|mrt`Ctv?©Etrpn|mw`cruvyºdfv?x`Crbdfv?n|g"mw_ mw_|_ag"bctux³df_|mnÁ¸d}r ¨g ¨`ctursg"s1mwr1dK"g"_n6d}mwrvag"rvagCy¨g"x`CrbKna`Kn|umvi"x³dfvav±¶ª]`c« xwsg"_X©Etrpnam`cruv dfr1r`cn mrbCg"rg"_ldfx¿¨g
(37) `cn|meKmw¬"gps»n|_a`Ctbc tvatSd}xÁyfgC± bu±}bC_6d}sumg"rn¨d}vag"sºyfeKgpn|u`.sv±.`CeKg D ©E_ldfpnldf*x E ©³turpn|m`Crvydfv©³`C_ mrv|nldfr"g2n|g ¥ g"mg"_avna_ldfvavG`crug ®Ãv|g"g v|g"pnam`cr c°d}_agª]`C« xsg"_
(38) ©Eturpn|m`Crv´Xml ¶`cvavag"v|v%mwr{²urumon|g"xo¸ ed}r.¸ x`d}x g6µn|_ag"ed± .t6 ©Etrpnam`CrvKeK`cn|mo§Cd}n|gKnag»tvag`c© vna`.lSdfv|n|m`C{n|mweKm¬d}n|m`CrqeKgpna`.suv·dfrs1d}_agina.tv d%bc``.s»n|g"vn n|`qd}vavagpvav2n|ug"m_·Gg >K"mg"rp¸± kg²u_av|nSdf_ldfeKgpn|g"_]´ mwl Sdfv%n|` ¨gvagpnyG©E`c_gp§g"_¸ smva"_agpn|gq`C{n|mweKm¬d}n|m`Cr eKgpna`.s na_¸{mrb1n|`/xw`.d}n|gn|g `c{name%tue8`f©d1"`Crn|mwr.t`Ctv©Etru6nam`Crºymv
(39) n|ug»v6d}eKuxmrub d}""tu_ldfpI ¸ H"± ¥ g´Xmxxvag"gmr vag"pn|m`Cr 1n|Sd}nnagª]`C« xsugp_ ©³_6dfeKgp´2`C_|¼g"xwvn|`²µd]"`c_a_ag"pnidf"ptu_ldfp¸± ¥ gXn|ug"rK©E`."tv`Crig"rgpn|mwiixbC`c_amonaeKv2® X!°ly´ umlK¨g"x`Crb!n|`]n|gi¶`.`Cxu`c©¿d}_|n|m²u"m³dfxSg6§`Cxt{nam`CrKeKgpn|`svyCmÁ± gC± eKgpn|`sv mwrvam_ag"s©³_a`Ce,rSdnat_6d}x gp§C`Cxtn|m`Cr/u_|mwr"muxg"vydfrs v|u`´ n|Sd}nn|gª
(40) `c« xwsg"_i©E_6d}eKgp´`c_a¼dfxxw`´XvXn|`»`C¨{n6d}mr eK`c_agqvag""mo²S_|g"vatxonav± G§`Cxt{n|mw`crd}_|¸ eKgpn|`svmr bCgprug"_ldfx·dp§g»¨g"g"r tvag"s vamr"gdf¨`ctnnam_|nÁ¸ ¸Cgdf_|vydfrs d}_ag ¼.r`´ rdfvd}_|n|mw"tx³df_axo¸%Gg >"mg"r.nmrKrteKg"_a`ctuvdfxwmd}n|m`CrvX®zv|g"g JoL Kuycyy KSyS M{y{{y{O Nðl±k2gp¸KSd"§CgX¨g"g"rq´ msg"x¸ vnatsmg"s
(41) mwr!§Cdf_|mw`ctuvVsu`cedfmruvy"©E_a`ce d·n|ug"`c_agpn|mdfxSdfv¿´gpxwx{dfvV©³_a`CeÂd _6df6namdfx¶`cmwrnG`f©S§mwgp´!± vA´gdf_agsgdfxmwrbig"_ag ´ mona1smva"_ag6nag
(42) `c{nameKm¬d}n|mw`creKgpn|`svyS´2gdf_ag]mwrn|g"_ag"v|n|g"s/mwr iivyu´X`Cv|g%6Sd}_6dfpn|g"_amv|n|m]©Egdnat_agcyºmr/p`CeKSdf_amva`cr ´ mona`cn|ugp_ gp§C`Cxtn|m`CrSdf_¸Knag"lrmw~.tg"vyumwvnaSd}n·n|gp¸´2`C_a¼`Cr»smwv|"_agpn|g?v|gdf_alv|d}"g"v±Sk2g"`C_ag6namdfxVd}rSdfxo¸{v|g"v`c©i d}_ag ¨d}vag"s»`Crn¯´2`%s*m B¶g"_ag"rnidf_a`.d}lug"Pv @ r Rd}_a¼C`§lSdfmreK`.sg"xwmrTb @{©E`c_ gpµdfeKxgCyuÌ d"§mwUv J O NºSd}vXva`´ rn|dnid
(43) §g"_¸ Q _a`.`c©Ev·`c©¿"`Cr§g"_abcg"rupg]¨Sdfv|g"s`cS x`´ sg""_|gdfvamrb?`f©un|ge%tnldnam`Cr]u_|`C¨Sdf¨mxwmon¯T¸ V1W d}xw`crubXn|gbCg"rg"_6dn|mw`cruvGmruv|t_ag"vVn|g2nag"`c_agpn|mwd}x"`Cr§g"_abcg"r"g `Crn|`qd]bCx`C¨Sdfxº`c{name%tuey s v `C_ambCmrSdfxºnag"`c_|X ¸ Jo}hyVO Yy¿Ccy¿} N¯y Q sg""g"{namo§g!©Etrupn|m`Crv!d}rd}x¸vamvy¨Sdfv|g"s1`Cr .lg"edKdfrSdfxo¸{v|mwvidfrs/ª `Cxx³dfr ´ umllSdf_6d}pn|g"_am¬"g"v n|ug?Gg >K"mg"ru6¸q`c© di%ySd}rsdfxxw`´Xvn|`v|ug"sxmbCn·`Cr1i /zs?m >K"txn2©Etrupn|m`Crv± Ìig"pg"n|mo§{mon¯¸?Sdfv¿¨g"g"r]mwrnatmon|m§Cg"x¸ _|g"xEdnag"sn|` n|g2¨mw`cx`CbCmdfxr`fnam`Cr!`c©ug"mv|nldfvamZv J NÁy"´Xml]d}r
(44) ¨gtrusg"_avna`.`.s dfvXd%v|`C_|n`c[© D ru`cr /Ãxwmrgdf_|mnÁ.¸ E%sg"bC_|g"gC±¶ÌXg""g"{n|m§mnÁ¸sug"g"rsv `cr @ \ nagSdf_ldfeKgpn|g"_·vagpnnamrb%`c©Gnag
(45) i
(46) y \ nagvaSd}g`c©¿n|g?©Etrupn|m`Crn|`¨g`C{n|mweKm¬"g"sºy g Ec´·d".¸ E%`f©Gvad}rurmrub%n|ugv|gdf_alv|d}"gC± \ nag"`.smwrb`f©¿n|ugv|`Cxtn|m`CrvymÁ± gC±{n| <. =. ]P]_^a`Ob cb d.
(47) . . . À rn|umviSdfg"_y´2g]"`cru"gpr.n|_6dnag%`Cr»nag
(48) sg""g"{n|m§mon¯¸1df_a`.d}lAyu´XmlAydfvX´2g´Xmxxºva`´!ySmvX´g"xxAvatmn|g"sn|`n|g }d rSdfxo¸{vamv`f© ª]`C« xsugp_·©³turpn|mw`crv± g"pn|m`Cr K%_ag"d}xwxvva`ceKgX¨Sdfvami©Ãdfpn|vXdf¨`Ct{n sugp"g"n|mo§{monÁ¸dfrSdfxo¸{v|mwv±À¯rvag"pn|m`Crhyud
(49) sg""g"{n|m§mon¯¸dfrSd}x¸vamvmvedfsg ©³`C_Xª]`C« xsug"_©Etrupn|m`Crv±Sk2mwv d}rSdfxo¸{vamv_a`§{msugpv d
(50) eKgd}rqn|`%gG>K"mg"rnaxo¸Kn|trug va`CeKgi`f©Vn|g
(51) i'd}_6dfeKgpn|g"_|vy´Xmlmv sg"_amo§Cg"smwrvag"pn|mw`cr1±SkAg"v|n|v·`Cr D ©³_6dfpnld}x E%©Etrupn|m`Crv d}_ag_ag"vag"rn|g"smrvag"pn|mw`cr1± &)( *+ $.-1101 Æ EÊ "!$#&%$Ê ' +ÃË Æ ¡)( £f EÊ* Ê ( Æ+-, Ê AÆ. 0/ 1 0G 3® 2547698?° 0) ;® :4<6=°> $42TU /$ +/ @?7 ! -:0/ BA @C2EDF: / (''? ) ª]`C« xsug"_ ©³turpn|mw`crK`c©Qgpµ{`crug"rn /HG YI4mo©¿©E`C_·gd}6H JK4MLONH2 vat6n|Sd}nP6Q8]®RJ4Lu°S'Cy{´2g?Sd"§CgZ@ 6I=® A R® JQ7° 4 A 3® L° ° TVUW698!R® J4LuY° X ®RJ4L0NH2/° ®|}° ©³`C_Xv|`CeKgi"`Crv|nldfrPn U G Y± kg?©E`cxwx`´ mrub%_ag"v|txn|v df_|g"x³dfvav|mwd}x(@ Z ¡ [Ê , Ê E*Ê \!^] ! A_ #&(% '?); 234 _G 0 1`/a,4$#&(% '?)+G234 _G 0 1`/[a1!U (''b/[a NN4YI4 / N ? Z ¡ [Ê , Ê E*Ê ^c 0GdA > #&(% '?)+GZ! -.0/ *?e A GfA /F11--.@? xon|`CtbC d ª]`C« xsugp_q©Etrpn|mw`cr mwvdfxo´·d"¸{vq"`Crn|mwr.t`Ctvymonrug"g"svr`cn¨g1su?m B¶g"_ag"rn|mEd}¨xwg ®Ãvag"gn|g gpµdfeKxwg»`c© ¥ g"mg"_av|n|_6d}vav©Etrupn|m`CrvX¨g"x`´ °l± À rnatmon|m§Cg"x¸®Ãvag"gi²ubCt_ag"v KdfrshC°lyud%ª]`C« xsg"_2©Etrpn|mw`cr´Xmon|d!x`´ §Cdfxtg?`c© / x`.`C¼.vetlKeK`C_|gimw_|_ag"bCtx³df_ n|Sdfr d]ª
(52) `c« xsug"_2©³turpn|m`Cr´ mn|d]umbCK§Cdfxtgi`c© / ®Ãmrq© dfpny{n|umvv|nldnag"eKg"rn·`Crxo¸Ked}¼Cg"vvag"rvagimo©V´2gi"`Crvamsg"_2nag umbCg"vn §cdfxtug`f© / ©³`C_´Xml/®|}°`Cxsvp°l± . 1. 0.8. 0.6. 0.4. 0.2. 0. 0. 0.2. 0.4. 0.6. 0.8. 1. ¿mbCt_ag% @ ¥ g"mg"_av|n|_6d}vav©Etrupn|m`Cr»`c©¿sumeKg"rvam`CrC± h± gih ]gkj.
(53) kg©E_6d}eqg`c©ª]`C« xsg"_V©Etrpnam`Crvy´XmxwgmweK`cvamrub d "`crsumon|mw`cr!n|Sd}n¿´ mxwx_a`§gtuv|gp©Etx.©E`c_¿natrmrub·nagd}_6dfeKgpn|g"_|v `f©Vn|g
(54) i
(55) yud}xwx`´ v2n|`%"`Crvamsg"_2§g"_|¸qm_a_|g"bCtx³df_©Eturpn|m`CrvySd}v·n|g ¥ g"mwg"_|v|n|_6dfv|v2©Etrpnam`Cr»smvaxEd"¸Cg"s`cr²ubCt_ag%!d}rs sgp²urg"s¨8¸ @. . vamr¶® JQ° ´ mon| G dfrs S S ®¯C°
(56) kmv%©³turpn|m`Cr mv
(57) r`´ g"_agsm?BQg"_|g"r.n|m³df¨xgCyG`Cvav|g"vavag"v%mr{²Srmonag"xo¸ ed}r.¸ xw`.dfx`cn|med{yGdfrs ed"¸ ¨gv|u`´Xr n|` vld}n|mwv©³¸dKª]`C« xsg"_X"`crusmonam`Cr»´Xmon| / J MNÁ±`C_ vatl DeK`cru`f©E_6d}pnldfx*E©Etrupn|m`Crv]®zmz± gC±u©³turpn|m`Crv?Sd"§mwrbn|ug!v6d}eKg m_a_|g"bCtx³df_amon¯¸Kdn·gdfl»`Cmr.n6°ly{mon·mv`c©³n|g"r»"`Cr§g"rmg"r.n·n|`
(58) n6d}xw¼KmrKnag"_|eKv2`f©G¨`µqsmweKg"rvam`CrO6®Ãva`CeKgpn|meKg"v_agp©Eg"_|_ag"sn|` d}vD ©E_6d}pnldfx*EsmweKg"rv|mw`cr¶°ly´ m6ºymwrn|mv v|mweKxgXdfv|gCySmvX / ± ª
(59) `c« xsug"_%©Etrupn|m`Crvdfgdf_rdn|tu_ldfxx¸ mr va`ceqgq_6df6namdfx·vamon|tdn|mw`cruv%´Xg"_|gru`/vaeK`.`cn|rug"v|vdfr ¨gd}vavateKg"s d}rs `C_ ´ ug"_|gXdi©E_6d}pn6d}x¨¶gpdp§{m`Ct_2df_|mwvagpv·®Ádfv ©E`c_gpµud}eKuxg2n|`]v|`Cxo§gn|ug mwr§g"_|vag_a`c¨uxg"e©E`c_ À| J N¯ycmr"`cruvna_ldfm / ®RJQ° . r g"sedn|g"_am³dfxº`C{n|meKmw¬dnam`CrXJ cNÁyS`c_imwr»medfbCg]d}rd}xo¸{vamv nldfv|¼v Joy1KNðl±À¯n mv n|tvimeK`C_|nldfrn·na`K`c¨nld}mwrgp§g"r§g"_¸ _ag"xmeKmwrSd}_|¸!"xtug"vnaSd}n·dfxx`´ n|`]natrgXn|ugiSdf_ldfeKgpn|g"_av`c©Vd!v|n|`lSdfvnami`C{n|mweKm¬dnam`CrKdfxbC`c_amonae xwm¼Cgii
(60) y.mwrK`c_asg"_ n|`¶g"_©E`C_|ed}rgG>Kpmwg"rn `C{nameKm¬d}n|mw`cr`cr»vat6q©Etrupn|m`Crv±. 9 <%? %* G-1*6, G
(61) )1*<1 0XG ¥ g?²u_av|nidfss_ag"v|v·n|gu_|`C¨xg"e `f©¿n|ug natrmwrb`f©¿n|g]_agpva`Cxt{nam`Cr1®z`c_ vldfeKxwmrb
(62) _ag""mvam`Cr°mrn|ugbcg"rg"_6dfxAdfv|gCymÁ± gC± ´ mona`ctnXd}vavateK{n|mw`cr`crnagsmva"_agpn|g `C{nameKm¬d}n|m`CreKg6na`.stuv|g"sA±ukmvmwv2mwrsg"g"s1d]"_|tu"m³d}xºu_|`C¨xwg"e vamru"g mo©Vn|g vldfeKxwmrb_ag"pmwvam`cr mvmwrSdfsg"~.tSd}n|gCyd}r.¸ `C{n|mweKm¬d}n|m`Crn|g"lurm~tg®Ãgp§g"r gpµ{Sd}tuvnamo§gKv|gdf_al° ed"¸1bc_a`Cv|vaxo¸©Ãdfmx n|` g"vn|mwednaginag_|mwbc.n·`cvamonam`Cr`f©¿n|gbCx`C¨Sdfxº`cn|mete4®Ãvag"g?²ubCt_ag
(63) c°6± Detected maximum. Real maximum. VmbCt_ag!:@irmrd}sg"~tSd}n|g!v6dfeKxmwrb!u_|g""mvamw`credp¸KeKmvaxgdfsKnag`C{n|meKmw¬dnam`Crq_a`."g"vav± À rn|ug]dfvag!`c©dKª]`C« xsugp_i©³turpn|m`CrºyQd%§g"_¸v|mweKxgi_ag"edf_|¼»d}xwx`´ vX`Crgn|`q§gp_amo©³¸ U G naSdn n|g!6`cvag"r _|g"va`Cxt{n|mw`cr HSdfv·xg"sna`Kd%"`c_a_ag"png"v|n|mwednagC±ukg?¸¶`fn|ug"v|g"v df_|g n|g!©³`Cxxw`´ mrb
(64) `Crg"v @. ]P]_^a`Ob cb d.
(65) K. . n|g©Etrupn|m`Cr A @
(66) D
(67) :mvª]`C« xsg"_]´ mona gpµ{`crugpr.n /"G Y1dfrs "`Crvn6d}r.nOU ®Ádfxx_ag"vatxonav]mwr n|umv vag"pn|m`Cr_ag"ed}mwrKn|_atgm© A bC`.g"v ©E_a`ce
(68) Kna`
(69) /y N}°ly i 1 n|ugKsmva"_agpn|g%`C{n|mweKm¬dnam`Cr/eKgpn|u`.s Sdfv
(70) dqv6d}eKxwmrb_ag""mvam`Cr/`c©6HBS ®Ã©³`C_
(71) mrv|nldfr"gCy H ©³`C_ di´ g"_ag mvin|g%lu_|`CeK`Cv|`CeKg xwg"rbcn|°l± R»`c_ag
(72) _ag""mvag"xo¸ ySn|g% tursg"_axo¸{mrbK"`Crnamr.tu`ctuv?vagdf_|l vaSdf"gmvv6d}eKuxg"sd}n _ag"bctux³df_|x¸vaSdf"g"s»`Cmrnav?R® J °6y{´ mon|
(73) J J
(74) H2©E`c_ dfxxºmzy iR 1 n|gsmwvap_agpn|g`C{n|mweKm¬d}n|m`CrqeKgpna`.sdfxo´ dp¸{v·bCmo§g"vn|g]_ambc.nXd}ruv´g"_·`C rn|gsumva"_|gpnag sSd}nld @m`© J W mwv ©E`Ctrs¨¸n|g!dfxbC`c_amon|ueycnag"r»mnmwv2n|_atginaSd}n @M 4 A R® J W ° A R® J ° ®Ãmwrdfvag?´2g!d}_agix``c¼mrub
(75) ©³`C_ d]ed}µ{me%te°6± kmvxEd}v|n ¸{`cn|g"vamvmeKuxmg"vin|Sd}n n|ugeKgpna`.s1mwv]d}xwv|`»d}¨uxg
(76) na`»x`dn|g%n|X g D¯na_|tuLg E»vagp"`Crs edµ{me%tue mwrn|g smva"_ag6nag vaSdf"gCyumz± gC±.nag`cmwrn J Wa vatlnaSdn @. M 4 A R® J Wa ° A R® J ° `crusmonam`C)r iR 1 eKmwbc.n vag"g"en|`
(77) ¨g?d!xwmonn|xwg·na`.`
(78) e%t6n|`d}va¼±{ªX`´gp§Cg"_y.`Ct__amedf_¸
(79) "`cru"g"_|rg"_agimvr`cnn|`d}vavag"v|v n|g~.td}xwmonÁ¸ `c©in|g`C{n|mweKm¬d}n|m`Cr eKgpn|`s monav|g"x©¯± ½ r n|g"`cr.n|_6d}_|¸ydfvav|tueKmrbnaSd}nKn|geKgpn|`s mvK¶g"_©Eg"pnq`cr smva"_ag6nag·sSd}nld{yc´g ´·dfrn n|`²Srs`ct{n´Xgpn|g"_mn mwv`Cvav|mw¨xg2na`!mruv|tu_|g2n|dnd v6d}eqxmwrbi_ag""mvam`Cr%d}rK¨¶g·vagpnyc´Xml d}xwx`´ v n|`]x`.d}n|gXnagied}µmeteÄmrn|ugi"`cr.n|mrt`Ctvsu`cedfmr´ monamrqd?bCmo§g"rd}""tu_ldfp¸± R»`C_|g"`§g"_y.mnmv¼r`´ rn|Sd}n v|`CeKgiv|n|`.6Sd}v|n|mw`cn|meKmw¬dn|mw`creKgpn|u`.svy{v|tuld}v ©E`c_Xmruvn6d}r"g].mwe%tx³d}n|g"sirrugd}xwmrb J NA`c_?i J O NÁy{s`"`cr.§Cg"_abcg ´ mona»_a`c¨d}¨umxmnÁ¸`Crg?na`n|g]bcx`C¨SdfxA`C{n|mwe%te mwrn|ug!smwv|"_agpn|g]v|d}"gtrusg"_i"g"_n6d}mwr»¸{`cn|g"vag"v±Q_|`Ce5d
(80) bCg"rg"_6d}x `cmwrn`f©V§mgp´]y´2giSd"§gX©E`ctursn|Sd}nii `f©³n|g"r©Etxo²SxxQv|tuld!"`crusmonam`Crºy{dfrsdf_agigp§Cg"rdf¨xg n|`%xw`.d}n|gi_ag""mvag"xo¸ JW d}r0s J Wa tv|mwrb]d?vaSdf_amrb?nagp6rm~tg J NÁ±¿mrSdfxx¸yCvamrupg·´2g d}_ag ´2`C_a¼.mrub`crd?²urmn|gXv|Sdf"gi`c©Qv6dfeKxg"vycmonmv2dfxo´ d"¸v n|g"`C_|gpnamd}xwxo¸q`Cvav|mw¨xg n|`qd}vavateKgXn|dn iR 1 mwv·eKgpn± 1. e. f(xm’) f(xm). k.e. h. xm xm’. VmbCt_ag?.@{dfeKxmwrb
(81) _ag"pmwv|mw`crmr¾utg"r"gC± kg"`crusmonam`Cr`CrHmv·n|g"r»gdfv|¸Kn|` sg"_amo§CgC ±g"dftvag`f©¿n|ug!ª
(82) `c« xwsg"_· _a`Cg"_n¯¸q`f© A {y ´gSd"§Cga@ M 4JfN0N J 4MJ J
(83) A R® JQ° A R® J °
(84) TVUH7X n|tv @ A R® JQ° T A R® J °"! UH<X. gih ]gkj.
(85) h k2mwv2ed"¸q¨g?_ag6´X_|mnn|g"rdfvP@ k2.tuvym©;@ ´2g?bcgpn. . mo© 4. 4J W J . J4 J N0 N J W. A R® J1W!°. A R® JQ°T A R® J Wa A 3® J¶°eT A R® J Wa. °"!. UH7X. °"!. U1H7X. A R® J Wa ° VUH7X. ®Á°. @. J4^J N0 N J1W 4J1W J A ®3J¶° T A ®RJ1W]° kmveKgdfrv2n|Sd}n·mo©®Á° mwv2§Cg"_amo²ug"sAy.´g dfrr`cn·¨g mwrn|g?v|mn|tSd}n|m`Cr`f©¿²ubCt_ag.ySdfrsn|tv2n|dn·nag?`cvamonam`Crq`c© n|g]edµ{me%te mv·xw`.dfxm¬"g"s»´ monan|g]¨g"vnX`cvavam¨xwg u_|g""mwv|mw`crºymÁ± gC± H?®Ãvag"g?²ubCt_ag
(86) °l±kg_agpvatxn mv·n|g"rgpµu_|g"vavagps mrn|g?©E`Cxx`´ mwrb Z ¡ Ê[, Ê EÊ 0)+ / )1 1 R 1 0) iR 1 > <Z2Z[ A R® J1W]° A R® J Wa. ° VUH7X . 4J1W J ®3J °N0N A ®RJ1W]° UH X 4 A ®RJ1W°"!. JBNN JW. . A. UH X J. ®K.°. 23 J $4 ( 4 &"![4 U _(4-. 4S4 / 141-1-.$ +/ ?. k mv
(87) _ag"x³d}n|m`Cr ~.td}r.n|mo²Sgpv]nagqmwrn|tumon|m§CgKbCtg"vav!naSd}n
(88) m© / mwv
(89) x`´4®Ãmz± gC±Amo©n|gq©Etrpn|mw`cr mv!§Cg"_|¸ m_a_|g"bCtx³df_p°lyQn|g"r °d}rus A ®RJ Wa °¿v|u`ctxws"xwgd}_axo¸
(90) sm?B¶g"_mwr`C_asg"_Gna`¸{mg"xs%_ag"xmEd}¨uxgmr{©E`C_|edn|mw`crA± ½ n|g"_|´ mwv|gCyf¨g"dftvag A Sdfvx³df_|bCg `cva"mxwx³dnam`Crvy.n|ug]d}¨uv|`Cxt{nag ed}µmwe%te`c© A p`Ctxws¨gmrn|grug"mbc¨`C_|u`.`.s`c©dJ Wa mrv|n|gdfs»`c©¿mwrn|Sd}n `c©`J W ± ^_6dfpn|mdfxºmeKxwmd}n|m`Crv`c©An|ug u_|`C`Cv|mn|m`Crdf_ag _ag"vag"rn|g"smrvag"6nam`Cr±{À rqnag?dfvag `c©i'`C{n|meKmw¬dnam`Crºy.mon·mv `cvavam¨xwgXn|`bc`d%xmnn|xwgX©Et_|n|g"_ d}rusqna`%²Srsd}r [ G §Cd}xmwsSd}n|m`Cr_|tuxg?r`cn`Crx¸K©³`C_ n|gv6d}eqxmwrb_ag""mvam`Crºy ¨t{nidfxva`
(91) ©E`C_n|g`cn|ug"_ Sdf_6d}eKgpnag"_|v`c©¿n|geKgpn|u`.sº±Sk2umvmv·´ Sd}n·´2g?_ag"vag"rn mwrqnagrgpµn vag"6nam`Crv± A R® J W. 0 »
(92) p #9; %* » ½ t_ df_a`dfl
(93) mv¨Sd}vag"s
(94) `crqi`cxws¨g"_ab v¿sugp"g"n|mo§{monÁ¸d}rd}x¸vamv JY.y{CGNÁy}´ mwl
(95) tvagpvd sg""`CeK`cvamonam`Cr!`f©Sn|ug2©³turpn|m`Cr n|`¨gq`C{n|mweKm¬"g"sºy %AyA`Cr ¥ d}xwva `Cxo¸ru`ceKmEd}xwv±ºkmv]sg""`CeK`cvamonam`Cr dfxxw`´ v?n|`1sgp²Srgd»rgp´ ©Etrupn|m`Cr % a yº´Xml d}r ¨g%trusg"_|v|n|``.s d}v!dqva`c_|n `c© D _agp©Eg"_|g"ru"gLE»bcm§Cg"r ¨¸n|giÂn|`n|g`cmwrn|v`c©n|gv|gdf_al1vaSd}"gst_amrbqn|g v|gdf_alº±kmv ©Etrpn|mw`cr % a mvXmrv|`CeKgvag"rv|g]dvamweKxm²ug"sK§g"_|vam`Cr»`c#© %Vyug"_a"g"mo§g"s¨.¸qn|ugi%±k2g
(96) iÂmvXv6d}mwsn|` ¨gisg""g"{n|m§Cg?´Xg"rKnag bCx`C¨Sdfx¶ed}µmwedX`c© %dfr) s % a s`
(97) r`cn·"`c_a_ag"v|`Crsqn|`]n|g?vldfeKgX`Cmrnav2`c©Anag?v|gdf_|6qvaSdfpgC±. . "!$#&%. R`C_ag_ag""mvag"xo¸yn|mvdf_a`.d}l
(98) mwvG¨Sdfv|g"s
(99) `Cr]valg"ed2n|g"`C_|¸ J .y{}hN¯± valugped_ag"_ag"v|g"r.n|v d vat¨ /ÃvaSdf"g`c©unagvagdf_|l v|d}"gCydfrs~.td}r.n|mo²Sg"v·nag!_ag"vagpe¨x³dfr"g?¨gpnÁ´gpg"rmonav _ag"_ag"vag"rn|mwrbp`sg"v @{©E`c_igpµud}eKuxginag!valg"ed('!*)+)[![!*)&'/mv d
(100) vat¨ /zvaSdf"g`f©¿n|gvaSdf"g`f©G"`sg"v·`c,© M]¨mn|v·xwg"rbfna ®,)K_|g"_ag"vag"rn|vid&D ´ mxws/zd}_as Euy{´ mwld}r»¨¶gY%`c_!°6± kgKieK`sg"xxg"smr1valg"ed%nag"`c_|¸1mv?dKd}r`Crmwd}x2i´ mwl df6nav `Cr1¨mwrSdf_¸v|n|_amrubcvyQd}rus©E`c_?´ umln|g "_|gd}n|m`Cr»`c© d]rgp´ bCg"rg"_6dnam`Cr»mv¨Sdfvag"s»`Crn|_ag"g?`cg"_6dna`c_av @ ]P]_^a`Ob cb d.
(101) . . . dfr1g"xmonamv|n G'? / yQ´ g"_agn|ug
(102) ²n|rug"v|v ©Etrpn|mw`cr v|n|g"vm[r @nag
(103) _a`c¨d}¨mwxmon¯¸»n|dn]dva`Cxt{n|mw`cr`c©n|gptu_|_ag"rn `CtxEdnam`crmwv·vag"xg"pn|g"s»mwv·_a`C`c_|n|mw`crSdfx¶n|`mn|v²un|rg"vavy Q n|ug 9; 0 / @u`Crg`cmwrnXp_a`Cv|va`§gp_ dfrs»¨umon /þume%t{nld}n|mw`crAy_ldfrs`CeKxo¸dfuxmg"sºy{´Xmon|_a`c¨Sdf¨mwxmonamg"v V·dfrs V W ± lg"ed}nldd}xwx`´ n|`_ag"_ag"vag"rn bCx`C¨Sdfxºmr{©E`C_|ed}n|mw`crdf¨`ctn·n|g!²n|rug"v|v·©³turpn|m`Crº±SÀ¯n Sdfv·na`¨gtursg"_avna`.`sn|Sd}n v|lug"edn6d%d}_ag2¯tuvn n|`.`Cxv·´ m6»g"xn|`trusg"_avn6d}rsnag"`.sg"vXv|n|_atpn|t_agC±ÂiÄn|tv´`c_a¼.v `crd%`cutx³d}n|m`Cr`c© ,"`sg"vySd}rsmeKxwm"monaxo¸%tvag"v·mr©³`C_aednam`cruv`crd%"g"_n6d}mwr»dfeK`Ctrn·`c©Gv|lug"edn6d± ¥ g%_ag"d}xwxG¨g"x`´¦n|ug
(104) v|`dfxxg"s Dvalg"ed%n|ug"`c_ag"e E´ mwl1mv?¨Sdfv|g"s1`Cr/n|g
(105) `C¨vagp_|§Cd}n|m`Cr1naSdn?n|ug%gp§cdfxtdnam`cr `f© d%v|mwrbCxgi"`.sug]d}xwx`´ vna`sg"sut"gv|`CeKgi¼r`´ xg"subcg]df¨`ctn·n|ug?valugpednld]n|`%´Xm6qnaSd}n "`.sg¨¶gpxw`crubcv± Q. ! # £ Æ /¢/ ÆÊ Æ.Ê ¡ Æ $ Z'?G
(106) U 9( L / . ¡Æ . 1 #(''* ). /® 4|° > U L'? T! G-G/ "![ L/ G 6 - '? "!$4 4 9; 0 b Q %A® °B> U a40 "!$4 G'* 1"! Q ® °B> U4 U1-. > "!`_:F) > 8 4 UL/ / (''? ) `C_asg"_ "!84 L/ G Q ® ° > 4 )4 0/ > 42T X4 3G () '? `_; ) > 46"!4 UL/ 6/ (''*F) sgp²Srmon|mw`crxg"rubfn| Q. "!$4 UL/ Q?. > U4 / L > > 4' i Q V1W > U-. 4 F > > 4' R "!U 9; 0 " !8 / )+< Q%V > U4 UF 30 "![4 /G-. 1P - ?' ? Q V. 0 G . /® 4"! }° /® 4|° %º® % ° oJ . ® V . ° ® °*V W N. kg
(107) ~.tSdfr.n|mon|mwg"v ® ° dfrs ® °Xg"xna`qeK`sg"xVn|g
(108) mr{¾Stg"r"g
(109) `c©n|g%bCg"rgpn|mw
(110) `cg"_6dna`c_av?`crnag%valg"ed @ n|gixw`crbCg"_nagXsgp²urmn|m`Crxg"rbcn|K`c©ºn|givalg"ed mwvyCn|g eK`c_ag©E_ag"~.tg"r.n|xo¸Kmonmwv¨_a`c¼Cg"rK¨¸d?"_a`cvava`§Cg"_i® n|g v|lug"ed n|g"`C_¸ Sdfv!¨g"g"r sgp§g"x`Cg"s ©E`c_%d»`crgK¶`cmwrn]"_a`Cv|va`§Cg"_p°l±ºÀ r n|ugKvldfeKg
(111) ´ dp¸yVn|gK¨umbCbcg"_nagK`C_|sug"_!`c© mwvyQn|g eK`c_agX©E_agp~tg"r.n|xo¸ mwv¨_a`c¼Cg"r»¨¸d]e%tnldnam`Crº± _a`ce dK~.td}xwmonld}n|mo§g§{mgp´¦`Cmrnyunamv ©E`c_ae%txEd]eKgd}ruvXn|Sd}nin|u g DbC`.`s Eqvalg"ed}nld{ySd"§mrubdva`C_nisgp²Srmonam`cr xg"rbcn| dfrs dx`´¦`c_asg"_ynagprusn|`bC_|`´¦§g"_¸_ldfmwsxo¸»mrn|ug%`CtxEdn|mw`crA±¶kg"vag%Sdf_nam"txEd}_ivalg"ed}nldKdf_ag]dfxxwgps > -.4'*);9 > '*/
(112) ± kgqtuv|gp©Etxwrg"vav!`c©·n|gvalg"edqn|ug"`c_|¸ mvn¯´2`c©³`Cxs @º²u_av|ny¿mon!vatxwmg"v!va`CeKg%na`.`Cxv]n|`lg"l¼ ´ ugpn|g"_d»bCmo§gpr _|g"u_|g"vag"rnld}n|mw`crmv2´2g"xwx /Ãvatmn|g"s©E`c_XdKi
(113) ±S.g""`crusºynag]d}rd}x¸vamv`c©VnagrSd}n|t_ag`c©VnaS g D bC``.s Evalg"ed}nldy{tvamrb%©³`C_ mrv|nldfr"g ¥ dfxva©Etrupn|m`Crv J yV NÁydfrbCmo§gva`ceKg?msgdfvX`crnag%i¦Gg >K"mg"ru6¸ J NÁy{§{m³d
(114) n|g]r`fnam`Cr»`c©sg""g"{n|m§mon¯¸ n|Sd}n·´2gsug"v|"_am¨g?¨g"x`´!±. gih ]gkj.
(115) . 0.8 0.74 0.72. 0.7. 0.7 0.6 0.68 0.5. 0.66 0.64. 0.4. 0.62 0.3 0.6 0.2. 0.58 0.56. 0.1. 0.54 0 0. 50. 100. 150. 200. 250. 300. 60. 70. 80. 90. 100. 110. 120. 130. 140. 150. 160. VmbCt_ag K @ A4! & % ®z"`cr.n|mrt`Ctvp°
(116) d}rus % a ®Ãs`cnnagps¶°!©E`C_%d ¥ g"mg"_av|n|_6d}vav]©Etrpn|mw`cr `c© sumeKg"rvam`Cr c± »v6d}eKuxg"s c` r M ¨mon|v± *9; ¬"`.`Ce`Cr n|g_ag"bcm`Cr `f©?n|g²u_av|nn¯´2` edµ{med3@ n|ug»©Etrupn|m`Cr mvKru`fn Y /Ãsug""g"{n|mo§g dfxon|u`ctubc om nqmv Y± Yc /Ãsug""gpn|mo§gC±. 1.7. 2. 1.6 1.5. 1.5 1. 1.4. 0.5. 1.3. 1.2. 0. 1.1 −0.5 0. 50. 100. 150. 200. 250. 300. 60. 65. 70. 75. 80. 85. 90. 95. 100. VmbCt_agh;@ A4! & % ®z"`cr.n|mrt`Ctvp°
(117) d}rus % a ®Ãs`cnnagps¶°!©E`C_%d ¥ g"mg"_av|n|_6d}vav]©Etrpn|mw`cr `c© sumeKg"rvam`Cr c ± »v6d}eKuxg"s `cr M ¨mon|v± *9; ¬"`.`Ce`Cr n|g_ag"bcm`Cr `f©?n|g²u_av|nn¯´2` edµ{med3@ n|ug»©Etrupn|m`Cr mv Y /zsg""g"{n|mo§g dfox n|u`ctubc mnmwvr`cn Y± YCh /Ãsug""gpn|mo§gC± ]P]_^a`Ob cb d.
(118) M. . . ! % !$
(119) "
(120)
(121) % ,# , "#
(122)
(123) !. . À r%`C_|sug"_Ana`Xn|g"v|nmo©dXbcm§Cg"r]©Etrpn|mw`cr(%]mv¿gdfv¸
(124) `c_¿sum?>"tuxonAna` `C{n|mweKm¬"g©³`C_ d i
(125) y}`crug"`ctxws]§Cg"_amo©³¸ nag D ¨utmxwsmrub ¨x`l¼.v E%.¸`cn|g"vamv @ C±·msug"rn|m©w¸ nag ¨tmxwsmrub ¨xw`.l¼vP@mz± gC±"`ceKut{n|g d}xwxXn|g eKgdfr ²n|rug"v|vag"v»`c©!n|ug/va`C_n»valg"ed}nld ´ uml'd}_ag _ag"_ag"v|g"r.n|g"s]´ monamr%d bcg"rg"_6d}n|m`CrºyCdfrs%msug"rn|m©w¸
(126) dfvG¨utmxsumrbX¨xw`.l¼v¿n|g2`crug"v¿´ `Cvag_ag"_ag"v|g"r.nld}n|m`Cr%mru"_|gdfvagpv dfx`Crb
(127) n|uggp§C`Cxt{nam`Crºy ±§g"_|m©w¸/´ gpn|ugp_!n|gK`C{namedfxva`cxwt{n|mw`cr ¨g"xw`crubcv!n|`n|ug"v|gK¨utmxwsmrb¨ux`.l¼vyºn|`¼.r`´ mo©2n|gK¨utmxwsmrub¨ux`l¼.v ed"¸"`Cr{©Etvag?n|ug]i%y{`C_·ru`fn± ªX`´gp§Cg"_yfn|umv _a`."g"stu_|gmv `C¨§{m`ctuv|x¸]"`CeKt{n6dn|mw`crd}xwxo¸!mr.n|_6d}pnldf¨xwgC±fÀ¯ruvnagd}sºy{i`Cxs¨g"_ab?Sd}v vatbCbcg"v|n|g"sn|`tvag deKgpn|`s/¨d}vag"s `cr dsug"p`CeK`Cv|mn|m`Cr1`c© % `Cr n|ug`C_na`Cbc`CrSdfx¨Sdfv|mwv`f© ¥ dfxva1©Etrupn|m`Crv
(128) `Cr J Y W W G NÁyQ´ g"_ag J Y W W G NAsg"r`cn|g"vXn|ugv|gpn·`c©mr.n|g"bcg"_av·`c©¿n|gmwrn|g"_|§Cd}, x J YI4p G NÁ± ½ r»n|gvagd}_alvaSdf"g J YIW W G NÁy{´2g?d}rsgp²urg
(129) ¥ dfxva»`Cxo¸{r`CeKm³dfxvdfAv @ .®RJQ° ® }° ® }° *JK4 NXJ Y W W GN . . . . . . . . #"%$ $.
(130). )(+* " $ $ $-,+. /. '&. . 0. !. dfrs d}_ag?n|g?§Cdfxtg"v `f©¿n|ug n| ¨mn·`f©¿n|ug¨mrSdf_|¸qsg""`ceq`cvamonam`cr`c©`J/dfrs ± À¯n?mwvi´g"xx¿¼.ru`´Xr1n|dn?n|g"vag ¥ dfx va / ¶`cx¸r`CeKm³dfxv©E`C_ae,dfr/`C_na`Cbc`CrSdfxG¨Sdfv|mwvi`c©n|g%vagpn?`c© ©³turpn|mw`crvsugp²urg"s `cr J YIW W G NÁySd}rus´2gxgpn %AR® JQ°
(131) C®RJQ°¨g?n|ug?sug""`ceK`Cvamon|mw`cr`f©¿n|ug?©³turpn|m`Cr%V± kgsg""g"{namo§mnÁ¸`f© %mvlSdf_ldfpn|g"_am¬"g"sna_a`ctbCnag?©Etrpn|mw`cr % a JoYyºcLNAsgp²Srg"sdfv©E`cxwx`´ vA@ J. . 10. 20. . . &. a ®3J¶° .
(132). . !43. 5. 6® 0° V W 6® 0°° ®¯hC°. ! kg?~.tSdfrnamon|mwgpv d}rs df_|gisugp²urg"s©E`C_·gp§g"_¸70Kmr»d]v|mweKmx³df_´·d"¸dfv©E`c_nag?v|lug"ednld @ ®60°mv2n|gsumv|nldfr"g ¨gpnÁ´gpg"r n|ug²u_avn
(133) dfrs n|gKxEd}v|n!r`Cr/z¬"gp_a`1¨umon|v]`f©n|ugq¨mwrSd}_|¸/sug"p`CeK`Cv|mn|m`Cr `f © 0y¿d}rus ®80{°?mvnagKr.tue%¨g"_`c© r`cr /ì"g"_a`¨mon|v `f©0± `C_8H Y
(134) xgpPn @ 29 ;: J5NXJ Y W W GN=<
(135) %A®RJQ° %
(136) T H/> dfrs 9 a ;:@J5N J Y W W N?<
(137) % a ®RJQ° % a
(138) TIH a % % a 3 H%> 3 ´ g"_ag % ®z_|g"vaº± % a °·mv n|g
(139) bCx`C¨SdfxA`C{n|mete4`f#© % ®z_|g"vaº± % a °l±Q·g"dfxxAn|Sd}n 3 mv n|g
(140) eKgdfr§Cd}xwtg!`c©¨`fna % d}rs % a± Æ EÊ c # H È Ë Æ £ Æ , -@ Ç 1 % [L ) > H È Ë Æ £ IÆ , -@Æ ! A9 B 9 a ? ¡ CK¤ H /zsg""g"{n|m§mnÁ¸mwvr`cneK`Cr`cn|`Crm3 @.©E`C_·va`ceK8g Y /Ãsug""gpn|mo§g?©Etrpn|mw`cruvySdfr Hed"¸¨¶gi©E`ctursvatln|Sd}nn|g
(141) qÆ 1¢uD ©Etrpnam`Cr»mvr`c$n H /Ãsug""g"{n|mo§gC±·gp§g"_|vag"xo¸y©³`C_·va`CeKg ru`cr / Y /Ãsug"pg"n|mo§g©Etrupn|m`Crvy{´2g?edp¸dfxva`
(142) ²ursdfr H a vatl n|dnXn|g]©Etru6nam`Cr1m[v H a /zsg""g"{n|mo§gC±ºkmv ©Ãd}pn mwv d}_|n|m"tux³df_|x¸q`c¨.§mw`ctv `cr²ubCt_ag"6v Kdfrs h±uÀ rn|g]©E`cxwx`´ mrub ´gi´ mwxxQ`crx¸q"`cruv|mwsg"_ Y /Ãsug""gpn|mo§{mon¯¸dfv·`Ct_·sug""g"{n|mo§{mon¯¸»p_amn|g"_|mw`crA±. %. 3. a. . . ®RJQ°. ´ mona. 3. . a. . 3. . ®| . V . gih ]gkj.
(143) & ] % * »)" %*5$ + 0 » 6 % %* G4%$'&)( *+ ,$.-1/0 1 À¯r
(144) `c_asg"_Vn|`i¶g"_©E`C_|eÂd§Cd}xwtSdf¨xg2sg""g"{n|m§mnÁ¸
(145) dfrSd}x¸vamvV©E`c_ª]`c« xwsg"_V©³turpn|mw`crvy´2gdp§gn|`i_ag"x³df"gn|ugsg""`CeK`Cv|mn|m`Cr `cr n|ug ¥ dfxva/¨d}vamv]¨¸ deK`c_ag
(146) v|tumon|g"s `CrgC±¿k2umvrgp´ ¨Sdfvamvva`Ctxs dfxx`´tv?n|`_ag"x³d}n|g%nagsg""g"{n|m§mon¯¸/na`n|g m_a_|g"bCtx³df_amon¯¸]`c©¶n|ug?ª]`c« xwsg"_ ©Etrpnam`Crºy.mz± gC±cn|`]mon|v2ª
(147) `c« xwsg"_gpµ`Crg"r.n±.À rsg"g"sºymonmvmwrn|tumon|m§Cg"x¸
(148) `C¨§{m`Ctv n|dn2n|gieK`C_ag m_a_|g"bCtx³df_?n|ugK©Etrpnam`Cr mwv®ÃmÁ± gC±ºn|gx`´gp_!n|gª
(149) `c« xsug"_]gpµ{`Crg"rn%mvp°lyºnagKeK`C_|gsg""g"{namo§Cgmon
(150) mv!xwm¼Cg"xo¸1n|`1¨¶gc± ½ r ²ubctu_|g"v K dfrs hd}_agKs_6d"´ ! r % dfrs % a ©³`C_ ¥ g"mg"_avna_ldfvav©Etrpnam`cruv%`c© smeqgpruv|mw`cr C± dfrs C± yV¨`cn| v6d}eKuxg"s `cr M¨mn|A v @¿n|ug ¥ g"mg"_av|n|_6d}vav
(151) ©Etrpnam`Cr `f©ismweKg"rvam`Cr C± »mvg"_agqr`cnsg""g"{namo§g´ umxgnag ¥ g"mwgp_av|n|_6d}vav
(152) ©Etrupn|m`Cr `c© smeKg"rvamw`crC±
(153) mvsg""g"{namo§gc± kg"_agg6µ{mv|n·vameKxwg ¨d}vag"v´ uml»g"_aeKmonna`ld}_6dfpn|g"_|mw¬"gmrd%pg"_|nldfmrvag"rvag?n|gmw_|_ag"bctux³df_|mnÁ¸`c©d!©Etrupn|m`Cr»mr n|g"_|eqv2`c©Gmon|v sg""`ceK¶`cvamon|mw`cr"`.Gg >K"mg"rnav± ¥ d"§Cg"xwgpnX¨d}vag"v·`Cv|vag"vav·vatld%_a`cg"_|nÁ¸± kg´ dp§g"xgpnKn|_6dfrv|©³`C_ae ® ¥ kX°%`f©
(154) d ©Etrpn|mw`cr % "`Crv|mwv|n|vqmwr sg""`CeK`Cv|mwrb monqmwrn|` g"xg"eKg"rn6d}_|¸ v|d}"0g /zvadfxg "`cr.n|_am¨t{nam`Crvycdfvav|`"m³d}n|g"s
(155) n|` n|ug2va` /Ãdfxxwgps 2Z G'* 4 ´ m6%df_ag2"`Crv|n|_atpn|g"s%©³_a`Ced vamrubcxwg©Etrpn|mw`crAyfn|ug 0 (' :9 2Z G'?G y¨¸eKgd}rv`c©¿n|_6d}ruv|xEdn|mw`cruv d}rssmxEdnam`Crv±k2ug ¥ k `c©¿n|g?©Etrupn|m`C r %mv·sugp²urg"sdfAv @ 1J %Nz® 4 {°
(156) J %A®RJQ°&69J. . . . . ´ g"_ag N
(157) mv]dv|dfxg%d}_6dfeKgpn|g"_dfrs N
(158) ;mv]dq vaSd}"gSdf_6d}eKgpn|g"_±ºkgdfrSdfxo¸¬"mwrb´ dp§g"xgpn mv]dqva~.td}_ag mrnag"bc_6d}¨uxg ©³turpn|mw`cr`f©G¬"g"_a`%eKgdfrºybCg"rg"_6d}xwxo ¸qlu`cvag"rn|`¨g?´2g"xwx¶xw`.dfxm¬"g"smr¨`cn|v|Sdf"g]dfrs©E_ag"~.tg"rp¸± ½ tu_?d}u_a`dflmvX¨Sdfv|g"s`Crn|g]tv|g]`f© n|ug!vameKxwg"vn´ dp§g"xgpn|vymz± gC±ªidCd}_ ´·d"§g"xgpn|vyS´ mwl1df_ag!sgp²Srg"s`crn|g smva"_ag6nag vaSdf"g J Y W W N¿dfAv @ . T J5S ® ! }° 4 ® ° T J5S ®¯ ! C° W ®3J¶° %4® ! }° Y / J YIW W GN ´Xmon| Y 494 W W WM4 ?dfrs YI4C4 W W WM46 @?mwvn|ug sugpbC_ag"gi`f©Vn|g?ª dcdf_2©³turpn|m`Crºy{_ag"x³dnag"sKn|`%n|givad}xwg `f©¿n|ug ´ d"§Cg"xwgpnid}rus 5"`C_a_|g"va`Crsv·n|`mn|v·xw`.dfxm¬d}n|mw`cr/®Ãvag"g?²ubCt_ag°l± kg"vagi©Etrpnam`Crv©E`C_|e4dfr`C_n|u`cbC`CrSd}xº¨d}vamv`c©An|ug vagpn·`f©¿©Etrpnam`Crv·sgp²Srg"s`cr J YIW W N¯±.ir¸q©³turpn|m`C r %`c© J Y W W GNAd}r»¨¶gsg""`ceK`Cvag"sd}A v@ / R® JQ° / %AR® JQ° R® JQ° %º3® J¶° .
(159) . . %. . . . . . 3. . . . .
(160). . . . !. . ,,# ! !
(161) ! " !$#. . . . " !. . .t¶`cvag?n|Sd}nXn|g!©³turpn|m`Cr » % na`K¨g`cn|meKmw¬pg"smwvn|g]vldfeKxwmrbuy´ mn|»u_|g""mvamw`cr H yS`f© dKª]`C« xsg"_·©³turpn|mw`cr sgp²urg"s`crXJ YI4 N @ JHNXJ Y W W G N 4 %AR® JQ° A ® J ° %Xv|mwrb
(162) n|ugsgp²urmn|m`Cr»`c©¿n|g]ªidCd}_·©³tur pn|mw`crv 4 ! y.´g?´ _amon|g3@ "W "W . . / J %AR® JQ° %A®RJQ°N
(163) W
(164) "W . . . . ]P]_^a`Ob cb d. . ". 0. )(. (+*. )(. (+*. ". 6(. (+*. )(. (+*. A.
(165) Y. . H0. . H1. 1. 1. 0. 0 2l−1. 2l. 2l−1. −1. 2l. −1. degree 0. H3. H2 1. 1. 0. 0 2l−1. 2l. 2l−1. −1. 2l. −1. degree 1. degree 1. H5. H4 1. 1. 0. 0 2l−1. 2l. 2l−1. −1. 2l. −1. degree 2. degree 2. H7. H6 1. 1. 0. 0 2l−1. 2l. 2l−1. −1. 2l. −1. degree 2. degree 2. VmbCt_ag.@SªidCd}_·©³turpn|mw`crv ©E`c_ ±. . /. . nag"r. @. )(. (+*. )(. (+*. °N J %º®RJQ° %A®RJ !
(166) " W " W J J J A ® ° A ® ! °N / .
(167) " W *LON J Y 4+J 4 L !) N J Y 4+J 4
(168) A ®RLu° A ®3L !S°
(169) 0T U
(170)
(171) X J J *JfNXJ YIW W N N J YIW W N 4
(172) A ® ° A ® ! °
(173) TVUu X . ·g"dfxxQn|Sd}n. " W . . . . ". . (5*. )(. (+*. ". )(. . . . . . ¥ g?²urd}xwxo¸q`C¨{nldfmrnag?´2g"xwx /z¼.r`´ r¨`Ctrs©E`C_·nag]ªidCd}_ p`gG>"mw g"rn|vX`c©dª]`c« xwsg"_©Etru6nam`CrU@ 4
(174) /
(175) T U X 0. . gih ]gkj.
(176) c kmv2mrg"~tSdfxmon¯¸mwvmwed}bCg"sK`crq²ubCt_ag.±uk2gi©³`Cxxw`´Xmrb]_|g"edf_a¼]mwv_|g"xwgp§cdfrn2©E`c__6dfpn|mdfx¶mweKxg"eKg"r.nld}n|m`Cr @n|g `c{namedfxS§Cd}xwtg `c©dU®zmz± gC±n|g?x`´2g"v|n·`crug}°sg"g"rsuv·`Crqnag?vldfeKxmwrb!u_|g""mwv|mw`crA±{k2g?"t_|§Cg"v `f©A²Sbctu_|g]
(177) df_|gisu_ld"´ r ´ mona U W h©³`C_d ¥ g"mg"_avna_ldfvavi©Etru6nam`Cr vldfeKxwg"s`Cr }K¨mn|vyAd}rus1´ mn| U K©E`c_]dfr R vldfeKxwg"s`Cr Y ¨mon|v± Weierstrass 1.7. FBM 1.45. 1.4. 1.2. 1.2. 1. 1. 0.8. 0.8. 0.6 hj. hj. 0.6 0.4. 0.4 0.2. 0.2. 0. 0. -0.2. -0.2 -0.4. -0.4 0. 500. 1000. 1500. 2000 2500 j on 12 bits. 3000. 3500. 4000. 4500. 0. 200. 400. 600 j on 10 bits. 800. 1000. 1200. VmbCt_ag; @2ªidCd}_"`.Gg >K"mg"rnav®Ã"`Crn|mwr.t`Ctvp°dfrs ¨¶`ctrus ®zs`fn|n|g"s°©³`C_d ¥ g"mg"_avn|_6dfv|v%©³turpn|mw`cr `c©?sumeKg"rvam`Cr C± vldfeKxwgps`Cr/}
(178) ¨monav?®Ãxgp©³n6° dfrsdfr R `f©GsmweKg"rv|mw`crC± Kh!v6dfeKxg"s`cr OY%¨monav?®Ã_ambCnp°l± . " . . ! # ! "# #.
(179)
(180) %. . #.
(181) !. . . k2gtvag`c©·dªidCd}_sug""`ceK`Cvamon|mw`cr/©³`C_!sug""g"{n|mo§{mon¯¸ d}rd}x¸vamvSdfv
(182) dfx_agd}s¸/¨g"g"r _a`c`Cvag"s mrIJo}LNÁyº¨tn]monvag"gpeKv n|Sd}n nag
(183) "`ceKxwgpn|g!"`CeKtnldnam`Cr`c©n|ug%dfsf tv|n|g"s "`.gG>K"mg"rnav
(184) ®ÃmÁ± gC±Sn|g
(185) "`.gG>K"mg"r.n|v `c© n|g
(186) ©Etrupn|m`Cr % a °´·dfvir`cn gpµxwm"mon± ¥ gn|tvGtvag2g"_|g·d·n|_6dfrv|©³`C_aedn|mw`cr]¨gpnÁ´g"g"r ¥ dfxva
(187) dfrsªidCd}_¨Sd}vag"v¿na`igpµxwm"monaxo¸?"`CeKtn|g n|g dfsf tv|n|g"s ªidcdf_X"`.Gg >K"mg"rnav±¶ÌXgpnldfmxwv `c©Gn|ug!"`CeKt{nld}n|mw`cruvXd}_ag!bCmo§g"r»mwrd}ug"rsmw"g"viÄn|`Ì
(188) ySd}rs`Crxo¸n|g]ed}mwrvnag"v d}_ag _ag"v|g"r.n|g"s»¨g"x`´]± ¥ gSd"§g®Ãvag"g]d}ug"rsmµq° @. . ®3J¶° ® ® ° . )(+*. &.
(189). !. $ ,+.. W $. . $ . . )(. (+* . . )(. R® JQ°°. ´ mona 0. ! . d}rsU _ag"_agpvag"r.nAn|g n| ¨mon¿`f©{nag¨mrd}_|¸ sg""`CeK`Cv|mn|m`Cr `c©dfrs 2`cr.§Cg"_avag"xo¸®Ãvag"g]d}ug"rsmµ ·°@. C®RJQ° ® }°. . W.
(190). !. &. . (+* W $ $ W%®RJQ° . $ ,+.. ´ mona 0. ' ®|! CUu°<4. ¥ g?n|tvX`c¨{n6d}mwrn|ug?gpµ{_ag"v|vam`Cr`c©ªidCdf_Xdfsf tv|n|g"s. . / a. 4 U[@. N JY WW. &. U0NXJ YIW W . GNdfrs . dfrs^U
(191). !. . . GN:d}rus. N J YIW W &. NXJ Y W W. "`gG>"mwgpr.n|v?®zv|g"g]dfg"rsumoµ dfrs1Ì?°@. GN. U ±
(192). !. . . GN. ; !<I + ^
(193) ^+ W+>5 = ^b(/ ?A!@B )C^ j ) <X C 5YD,+ +1 ^ ^ 1!H!"
(194) # Z;D%$$
(195) ^ ^&50 ^ ^OQ % '!P E /,((+ 5^*+. F[,) /G !^H +"
(196) ,^ +. K-\>^ 6 5!IJ
(197) ^ UM K^[00 D, / &I +1 LM+"/2^ 9#+ 3N + ^Q+
(198) &+%L'] 4D>OQ5 2+ P bK+ ^/ \ ) ^ /2!+ " 1#RLSEM%$ 5 ^ + 1^ +. 0T D,& ^7BLV6 U 8+ :^T 9# 5 +.++ ]P]_^a`Ob cb d.
(199) . . . / a ®3J¶° % a ®3J¶° .
(200) / a W / W Jo V ®a! ! ® c° ° VW%®|! °N. ® V ° ®| ° / W W
(201)
(202) V W / W " W
(203) ¥ g]df_|gr`´'_agd}s¸qn|`"`ceqt{n|g!d}rtug"_X¨`cturs©E`c_ n|g~tSdfrn|mnÁ¸
(204) %A®RJ¶° % a ®RJ¶°
(205) @
(206) %A®RJQ° % a ®RJQ°
(207)
(208) ® / / a ° ®RJQ°
(209)
(210) T
(211) / / a
(212)
(213) C®3J¶°
(214)
(215) `fn|mw"g?n|Sd}n·©E`c_J5N J Y W W GN;@ ®RJQ° YI4 ! ' %® J ° %® J ° ! . . . !. (. !. (. !. $-,+.. $. *. $. $. $. !. (+*. &. . . . . . . . . . . 0. . . ´ g"_ag ®¯°_ag"_ag"v|g"r.n|vnag!mwrn|g"bCg"_·Sdf_|n `c©`JV± `C_id]²µg"s JAySdfrs©E`C_·gdfl y.n|ug"_|ggpµ{mv|n|vXd%v|mwrbCxg §cdfxtug f` © 5vat6qnaSd}n
Documents relatifs
Chez l’Homme, les segments de gène V H ont été classés en sept familles (la famille 7 n’est pas représentée ici car aucun segment fonctionnel n’y a été décrit) qui ont
Le Négus consacra une énergie considérable en vue de gagner cet appui international, mais, malgré la force de son discours prononcé en juin 1936 devant ses pairs à la tribune de la
In this paper, we propose a novel approach based on the barycentric coordinates of automatically tracked 2D facial landmarks from videos to objectively evaluate the facial
Dirk Obbink (dir.), Doctrine and Doxography. Studies on Heraclitus and Pythagoras, Berlin / Boston, De Gruyter, 2013, p.. et le logos auquel les hommes devraient accorder
Les exorcismes ne sont pas publics, les sœurs noires elles-mêmes sont tenues le plus possible à l’écart, et c’est chaque fois Jeanne qui force les choses pour que, finalement,
Toute- fois, d’autres marqueurs des cellules POMC tels que NeuroD1 n’ont pas été induits dans cette expérience, ce qui indique que Tpit suffit in vivo pour provoquer la
Mais elle y occupait une place modeste : il faudra la liberté et le goût de la transgression du roman en langue vulgaire pour que la situation soit renversée :
Les thèmes majeurs (tab.5.4) abordés par les îliens interrogés sont, pour la grande majorité, les mêmes sur toutes les îles : ils concernent les usages anciens