Application of Genetic Algorithms to the Solution of the Space Vehicle Reentry Trajectory Optimization Problem
46
0
0
Texte intégral
(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Application of Genetic Algorithms to the Solution of the Space Vehicle Reentry Trajectory Optimization Problem Jean-Antoine Désidéri, Sergey Peigin and Sergey Timchenko. N° 3843 Décembre 1999. ISSN 0249-6399. ISRN INRIA/RR--3843--FR+ENG. THÈME 4. apport de recherche.
(3)
(4)
(5) ! "# $ %&'( ) %& *,+ ! ,-./0 $ 1 2 435* $ 1 67 8/
(6) 9 :; <>=@?>A$BDC!AFEHG5IJA =LK(MONHIQP:MORSIUTWVYX$=ORZ5=\[^]_=OI`ZFIJAba?cA:PdXe=ORZF=f[hgiIJjlkWm =OA:n5G5o p/qsrtvuwyx z|{}t~s {}fu_f{tv{} {W u@rtvuftvs}u|u uz|{}O~s _Wscf uuDqsuDqsu>bWWw\x ut¡sui¢H£f£f£x wO¤y¥¦fu §(¨ ©ªS«¬s®Wª\¯ ~{}s¦qsut&Wsqsu{}uuOvW°F
(7) ¥u/±fuqs{u_ qsu/quS²¥~|v qsu
(8) ¡c (~°JWu{}vW¦fu4q¥fuqsW vW}±Wuy±Wu!ftvs}uqsus u ³ {}f´sf¡s}ut°`fµ qusWu_±fuq{u4~s°JuW¶Y·4suW°Fqsucf{}¡su¥W{¸±fu¹ºS|* u ~su qsuqsuS_²¥~|»qsu¡c !~s°JWu{_ &f {}tv{¼uqsuuu\! u f ¥W t&u u4 tv{}s{}t&{}¼uvW°qsu0qsuS
(9) ²¥~|{}\ u¦f WJ¶p/qsuvs~scfu0W° qs{}
(10) u5f {4f¸±fu0 qsuvf| {}t&{}¼S {}f½sf¡ut¾W°Y qsu0uu\¿ u W{}\ qsu&ÀW q tvfsqsuui¹{¸ qÁu5uy qu´qsu²s~|Ã{\ u¦f º qu´ W¦f¥ {}fÄcf{}OW° fd¡s}~s\/¡5 W¶µp/qs{/f¡s}utÅ{} f¸±fu ¡\itvuSWs/°e qsu²s\ {}s¦³Æ5W{\Ç
(11) uu {} È }¦ff{¸ qt&ÉUÇ È
(12) Ê ±|{ÁS~sË {}fhW°
(13) qsu¿qsu´²¥~@hu±ff}~ {}f^W}fs¦Ã qsu¿uu|³ » Ìuf¿{L qsu0°` t&u¹ºWÍW°Y qsuvsW|³ÎuÏ@~{}{¡{}~stÐt~s¸ {}ftvcfsuO q{ ±|{}f~syqs@DÍLSfutv uÉJp Ñz|Ò Ê ¶:p/qu´W~{WÁW°ºqs{}sf¡s}utС\ÁÇ
(14) uu {} È }¦ff{¸ qt&
(15) {}{\uu{s¦!°`WtÓ¡cW q½sW{WµWs{}S{}±Wu´ t&u qs f}f¦f{}S 5f{}\ /W° ±@{u¹Ô>¡5uSW~su{}{}_0±Wu¦f@ u st&u utvfs uqsuÇ È uÕ0³ {}us°`Wqsuf}~ {}fÂW°µWÂf{tv{}¼S{fÂsW¡sut.¹{}q¿vO~st¡cuW°bftvsu sf|³Æ{}suS Ws W{}\ ¶µp/qu {|²¥~suu/W°¥qsuÇ È ¥WWtvuu ¹ºuW qsu ¡c Ö ×`Ø Ùeø ×` ÚYØ ÛÜ × ÝÝ ØÞ Û Ùe ßâàÌæÆóáQâµöÌçèãHßâö
(16) ä ø5åOçèà á æçèÛßïéèâÜ äÝÛÌÝêìÝ Ûë:íîô ï ç
(17) }ÛHôÌÝÛÌð×`äQîþUÝôܺâé ñSßòóÌçõô Ú öáUçèòWßéõç÷ä ø5ùãHâúûýüÌþÆô öæÿâ ß/ä öÌçâþÆäQç á ÛSðï ÞÝ ÝÛå@âöÌçõöô ïðÛ ß/äfÛµñHësûÞÛÌÙeàäUäJç÷ô. Unité de recherche INRIA Sophia Antipolis 2004, route des Lucioles, B.P. 93, 06902 Sophia Antipolis Cedex (France) Téléphone : 04 92 38 77 77 - International : +33 4 92 38 77 77 — Fax : 04 92 38 77 65 - International : +33 4 92 38 77 65.
(18) ¤.
(19) ! "#$&%'(")*+, ! "#$*-./10234. ¦fuftvu WÔcqsu¡5 !~°JWuSDW¸O {}yW {¸±|{¸ÎÂW uDW{}¿sq\@{}S Ws W{}\ f qsu0f| {}t~st¾f}~ {}fÃW f qsuv¦fW{¸ qstÓW{¸ qstvu {}SWbfuÕi{us½{} {\±fu{¦\ u ¶ 576489;:=< « >:©W¯ Ç È Ôºp Ñz|ÒÔºqsuS´²¥~|5Ô u WhW {}tv{¼ {}fìÔ_sf|³Æ{}suW fs W{\. ×`Ø Ùe×`Ú.
(20)
(21) ÿ " i'" Æ "$ ! $ 435* $ : !, v $
(22) / Î' ! '!,"e © ¯ 4Ws0»sqsWu uu\ u!tvfsq {}ÏO~su ~s ±f q{~su!¥ {WJÔ {tvcf Wsu ~L W°`u
(23) qsutv{}Ï@~ui¥{} Dbu uW{ui f}~ {}f ~ sf¡rt&u´ftvs}u|u uiË»Wu{WÁ qsutv{ÏO~su¶ tvHfu ¥W{¸° u( ~s{}u u4²¥~@ u
(24) Dq¥u~s/¥W{ DW5fs{ u yf{tv{}u_}u/sW Wtvr u u
(25) Ìuf{}u ¥ ut&{}s{}tv{uº {\ ¦f u_u& utvs ~v²¥~| u_Dq¥W}u~¶Òeu¡s~ u_u W5f u u& f~ u&u&sW¡srtvu u& f{tv{} {W u&Ë u f{}u u&uO u(³ t&Wsqs {}ÏO~su±@{
(26) ±|{} u {}\ ¦f W}u ~i²¥~@(~icf{}O W ~s´fs*Wf { { {}tvus{fsuJ"¶ !ºu
(27) f¡s}rtvu
(28) u f}~¥Wº~sW¦Wf{¸ qstvu4¦W s {}Ï@~u´É È Ç Ê u W¦fu( u ¥W0}u¡s{W{ ~ W}~s u ±Wf~| {}f ~l²s~|Áqsut&{}ÏO~suÂW~ f~ uËy u f{}uu°JW{} O_ q\@cW qsru ~Â f~s}utvuO u
(29) ²¥~s{ u W{}° qsfÿ³ ÏO~s{}{}¡suDqs{}t&{}ÏO~suyu uW~sDqsu uDqs@±|{}ÏO~su~su0tv{}su(ÉJtv r}up Ñ
(30) zÒµ.Ô
(31) 2 # 0 %$ 2 03'& $4 Ê ¶´Ò f}~ {}f uiuif¡s}rtvui¥WW¦Wf{¸ qstvuv¦f s {ÏO~su s u\uL~ {}\ ( ÂWs{}S {¸°t&W{}!W~s{
(32) tv qs f}f¦f{}Ï@~uWÔW({}4 W¦f{¸ ~s r¡cf¿u utvsu tvfs {¸° u uÕ&SW{} uy È )Ç ´ f~ uy~s¿sf¡s}rtvu W {}tv{ {}f W~stv{* u(sft¡su~suvf\ W{}Ou0sWs{}s W{u¶½Ò {}²¥~susu u¥WWtvru u ¥s{¸ {}f u È Ç {s{ìÏO~suË0¦f ftv {}u ~!fsÔ¥}u u¦W {¸±@{} ÂD}O {}ÏO~su u½~s°JWu!uiu W{u&f\ W{}Ou&sq\@{}Ï@~u(~si f}~ {}ff{t&W}uu}u, + u W}¦ff{}qstvuu_ ±W~s uW¶ È ÇvÔp ÑzÒµÔ4²¥~|d qsutv{ÏO~suÔvf {}tv{ {}f uÁ u f{}uÔ - < ªÌ© 9 /® . © ¯ f\ W{}Ou_sfs}{}s SW{}u.
(33) w.
(34) ! "#$&%'(")*+, ! "#$*-./10234. v $0 " .
(35) . . . . . -. . -. . . § -. . . ". !. § w¶¢ /p qsu{}²¥~usuW° quÇ È ¥WWtvuu¶ ¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶ ¢ w¶÷¤ /p qsu*{}²¥~usuºW°@ qsuYsf¡s}utd¥ Wtvuu:f quYW {}t&Wf u ff¶v¢H£ 2 - 6 2 6 Æ0{¹ºu ³ÎÍOsH¹l q¥ ~s{}s¦¿qsu(sWu(±Wuqs{}}u!uu\ Ä{\¿ qsu!ÀW qlt&³ sqsuu(qsuqsuSy²¥~| y qu(¡5 Ã~s°JWu{}0W¦fu´ qs0fsu´q¥Wy f¸±fu! ±fu(ftvsu !qsu/sW u {}f!sf¡s}ut#°`Wº qsu±fuq{u~s°JWu¶Y·4su
(36) W°$ qsu5fÿ³ {}¡suv¥{¸±fu&¹ S@ !u ~suv qu&quS²¥~|½
(37) qsuv¡c ¿~°JWui{}
(38) !f{tv{}¼u qsu0uu\ u f¿¥ Wtvuu!t&{}s{}tv{¼uvqsuvqsuS
(39) ²¥~|½{}\ u¦W WJ¶ Î qs{} SWuqsu»f~| {}f)W° qsuÂqsuS&²s~| f {}tv{¼ {}f)Wuf¥u u{}¦fhf¡s}ut {} suu\u {}! qs{}ucfS¶ p/q{isf¡ut {v qsusf¡s}ut W° qsuuu\ uflf| {}t&{}¼S {}f){}\ qsuLÀWq tvfqsuuL¹{¸ q u5u l qsu½{}\ u¦W W
(40) W° qsu½qsu!²¥~| qsu D¦f¥{fvcf{}O°ìf ¡s}~s\*¡c f¶bp/q{f{tv{}¼S{Wisf¡s}ut {}f¸±fu ¹{¸ q qsusq\@{}SW Ws W{}\ Wqsu¡5 !Wuu {f»W}fs¦v ÌufW fqsu tiÌ{}t~t ±W}~su*W°suÏ@~{}{¡{}~st utvcu ~suºW°sqsuY¡5 ~°JWuY³5 qsuYt&|{t~st uÏO~s{}{}¡s{}~st utvcu ~su0W° qsu¡5 Â~s°JWu ÁWss
(41) u|uu ´suSW{}¦fsu {}tv{}±W}~su ¶ È 4WÂf¡|u {¸±fuy°`~s{fFÔcqsu{}\ u¦W W f\±Wu{}±Wu0qsuS²¥~| e_ qu¡c ~s°JWuWWs¦qsu°`~¥ u f&{*fs{ uu W qsu_±W~su s{}ºWt&~ u f qsu¡¥W{YW°5 qsuO~stvu{W>f}~ {}fiW°5qsu_t~s¸ {}ftvcfsuO*sfuÏO~s{}{}¡s{}~st q{ ±|{}f~s_qs@DÍHWu_uÏO~¥{WsÉJp Ñz|Ò Ê ¶ p ´f¸±fuqs{sW¡sut &±W{W\W°b quf¡s~s²¥\ {}s¦³Îcf{}\
(42) Ç
(43) usu {} È ¦f³ {¸ qstv4{}4~su ¹{¸ q¿ quyW{}qstvu {}S fH±fu
(44) W5u f4W ¹{}q¿ qsusfO~ss{ ³ °`ft {DWu³ ucu u\4t~D {}fÂW5u f¶ #!$
(45) . . +. ,.-. . . %. 0/21%. & ' . ,. . ( *). -. 3. 43. &5.6. 7596 8':<;. =7> ?=7>. ×`Ø Ùe×`Ú.
(46) &. &. 0
(47)
(48) 0 "#
(49) 2/ ). 9 -6
(50) % 2 2
(51) 2 Ò$u~sµWs{ uµqsu/¥u/±fuqs{u_tvH±|{}s¦W}fs¦4 u W0{}\
(52) qsuÀW q&t&³ sqsuu¶
(53) p/qsu±fuqs{}}u&uuO»{4¡cu¦W{s{s¦i°`ft qu0W¸ {¸ ~ u ¾¹{¸ q qsu&±fu}@{¸Î !#"%$&fÔ qu´¡cu¦f{}ss{}s¦Wuu {f {}y¡suOÔb qsui±fuq{u ti{/fsDW\S(¶ 'ÃuW~stvuq¥/ quÀY q!{}_vsqsuuWÔ¥{¸ ¹{{}s¦&{_W¡su\ W qsu¦fS±|{¸Î0°`fu @usW u5u Wi}{}~ *u )#+-,U¶bp/qu us{}Î {}{}¡s~ {}f {/ qu°`W}H¹{s¦v°`~ss {}fW°:qsuW¸ {¸ ~ *u ./%0 Éÿ¢ Ê 1 1 325467.98:$; 03< = !>;-?! p °`Wt~uv qsuif{tv{}¼S{fÃsW¡sut!Ô }u~s~sscfu& q¥A @ {}qsu&WD ²¥{¦WqOv{tvuW°qsu±Wuqs{}}u»tvH±@{¦ÁW}fs¦½ qs{}&qs{¦Wq)¥W&W°qsu ÌufW¶ Î qs{}SWuWÔ\ qsu WDsf\±Wu{}±Wuqsu²¥~|&b qsuDW¦fs {}fv5W{\W°c qsu_f ¡s}~s\ ¡5 ~s°JWu OW}fs¦ ÌufSW0¡cu W~s u ~s{}s¦
(54) qsu*°`f}H¹{¦
(55) u{fC B Ê ./ (DEFDG@ 0HJM ILK P./O.Q@R0SDT :.Q@R03DTUWV5D3XD3 ZY[0]\@3! Q É ¤ ON ^uu H._.Q@R03D3 `.Q@R0SDEU D3aD3 ZY[04{ qu&quS²¥~|ÃqsuiDW¦W¥ {}fL5W{\W°*qsu ¥WuN ±fuq{uÂf ¡s}~s\V i¡c Á~s°JWuWbÔ :.c@R0{0 qu(²¥{¦WqO0±Wu}|{}ÎWÔ .c@R0{yqsu ²¥{¦WqO
(56) W}{}~ udÔ Â{}
(57) uÏO~¥W ´qsuy {}(W° qsu¡5 ~s°JWu0t&W{}¿~s±~su qsu(DW¦W¥ {}fÁcf{}\S(Ô U V {} qu(Dq¥WWu0}{suW{¼uW°/ qu(sW¡sut!eÔ Y/Wu qsu_ÍOsH¹(¥WWtvu uYW°Fqsu_qsuuW¦fusuf~s*Dqsutv{}SWcuW{f*@~s{}s¦yYqsu ¡5 (~s°JuW¶ Òeu:~ fs{ ue qsuµ°`f}H¹{}s¦±W{ {}f¥WWsf¡u%t B ¥ qsuµtv@W q°`~ss {}fs :.Q@R0/W .c@R0
(58) /É gfh@fh@ Ê ¹qs{}Dq»q¥S±fu
(59) qsu
(60) °`f}H¹{¦&ι*ifcu {}u5 B ¢W¶µp/qsu±W}~su 5{}tv{s{}t~%t i ¤@¶ p/qsu uÏO~s{}{}¡s{}~st utv5u ~suºW°¥ qsuº¡5 ~s°JWu/ qu W¦f¥{W05f{}\ P.Q@R0 @usu|uu qsusuW{¦fu }{}t&{¸±W~u ¶ p/q{_sW¡sut.{}_f¸±fu ¹{}qqsu
(61) °`f}H¹{}s¦ifs {\ j B :./0Hk l5D ._0P=g< m.Q@ 0(= V D .c@ 0H= V ÉJ Ê n; :o .Q@R0 nqphrs D n o n ft V 1qu .Q@R0G wvx.Q@R0 É`w Ê y . -. 8. 8. 8. =7>. 3. = >. 6. 6. 8. 6. 6. 6. =7>. 8. 5 6. 8. 5 6 8': ;. Ù Ù ö;zsïj{ Þï. 8.
(62)
(63) ! "#$&%'(")*+, ! "#$*-./10234. uu t V {u°`uusuWuS!Dq¥W u{{¦» qsui¡5 ~s°JuWÔ { quit&WW° qsu
(64) ±fuqs{}}uW¶ p/qu uË{Ws {}ÉQ Ê tvuSWyq¥ qsu* Ìuf¡cu¦f{}s °`ftd qu 5W{\ ./ l5DTg30 W ss{qsu4qsucf{}\0É/ V DT V 0¶p/qsu ¥u {}f¿{} É`w Ê {}_fsuu ¹{¸ q qsut&u {}SW:u { {}fs´ qsu²¥{}¦fq\4W {¸ {}fs¶p/qsuyuW f {}{W ÉJw Ê )#+-, { qsuf¡\±|{}f~s°`ftsq\@{}S 5W{\y° ±@{u¹ {}Ä°JW{¸ytvuSWÔb qsqsu uu}u {}f WWs¦» u fÄWss0u|uu qu(t&|{t~st W¦ uu}u {}f ucu {s¦_°`ft _t&|{}t~st W¦/°`fuµ°`fì qu*¦f{¸±fu¡c fÔÌ°`fì quY¦W{}±Wuy}{}~ u W °`f qu¦W{}±Wu²s{¦fq\±fu@{¸Îf¶ È 0{{}{ËWºti qsuti {}SW/tv uº°`WySW}~Ë{¦Lqsu{\u¦fW {} ÉQ¤ Ê ¹*u¹{} ~suyqsu q{ É`qO@cufs{} Ê ±@{}W~sqs@DÍ»Sfu
(65) uÏO~¥ {}fs¶p/quuvuÏ@~s {}fsWu qsuW@tvW {}_°`Wt W°5 qsu S±@{}u³ÿz@ WÍWu*uÏO~¥{Ws W cut&{¸*~sYfu ¸ u{}¡cu_qsu ²¥H¹h ~ ~u_¡5uιºuuiqsu¡5 ~s°JWu_W qu_qs@D͹ S±Wu{¸°5qsu °`f}H¹{¦if {¸ {}fs_WuuSW}{}¼u B ^. 8 h DUW2 D UW2
(66) m.]x0S! . p/qsuW¥W¸@{} utvfs u q¥/ qs{}t& ueq¥W_0¦f| W~sW°`f/W~s/ W¦fu WH° W ¾°`fW}ìcf{¡u u f{uw) w;,Q¶ È _ quDW¦fs {}f»cf{}\_qs{}uÏO~¥ {}fs_@ut { qsuf {{±W{W¡s}u q¥W/ qsu
(67) °`f}}̹{}s¦0°`fJ t ) -, B D y D ÉÊ .].q0 0 wk .q0 v D 1 ). > >. ). 1o(#D > ' & % > % ! *( )"+ (-,.( ! 0/ ( 1 2 D y D!>! ! D43 8 D . +657+ v 5 v 0 9\ \ 8 D U;.: 5C > y=< v .q0 v 1! v D u 27 D y D5!>! !>D*3 8hD , YC> Y? >Y @ Y TY D. >$# "! 1oYD > > 8 Y Y , 1 6:. >. ÉÊ É/+ Ê ÉJ Ê ÉJ£ Ê. ×`Ø Ùe×`Ú.
(68) &. &. 0
(69)
(70) 0 "#
(71) 2/. uu. +. ^. ; ; 8 < M 1 \4xD 5 > D < M 1 \q4xD . Y UW 2 <1 D 6 D. >
(72) D , YC< D 8 v V + Y Y YC 8 r Y Y D Y@ C r Y Y + & ' . r YV , > 03D )"+ ) Y t & t & r Y 8 r YV 3Y D EY r YV & t Y 8 t Y & D 8 3 V TY D .! 2 # " 03D t t & & + + 8 D mY ' ' r r V V Y C Y D EY Y t & & Y )"+ ) Y V ! & t & )"+ $) Y & ^uuqsu|W {}¥uU V 4 {}DWÍuW}fs¦ qsusfti>qsu¡c v~s°JWu i U V 4 . = 4 D. Wuyqsu0@f {¥ u
(73) u}u u W}fs¦( qu&t&W{} {}u {}fLf¿ qsuv¡c ¿~°JWuv qsuÂD¦f¥{f 5W{\SÔ U U V $ uÂqsu»t&W{}h {}{W° qsu¡5 ~s°JWuÔ u V . D y 03D u Wu¿sq\@{}SW
(74) ftv5fu\ W°qsu»±fuf(±fu@{¸Î WWs¦ 4 4 {u{Ws¶ v &Ô Ô Ô¥Wu
(75) u5u{}±Wu¸Âu~suWÔ u|³ {¸ÎfÔ utv cu ~suW°_¦\W0tv{ |u ~s1quu ÔY¹q1q{Du q 1 f! {} &W°3 Wt&cfsu\ ¶ . T0 Ô u % $ . y E0"Ô w x$ $aÔ UW2* 1qu u U V $ . T0ÔXWu±@{}W{¸ÎfÔì5u{ ¥yqsu _fsDW\su~uWÔ5µ W $O~st¡cuÔìu@sf @~t¡cuÔctvf}u~ËW¹*u{}¦fq\4W° qsutv{¸@ ~uu5u {¸±fu}W;¶ TYÆXÔ mYÆaÔ u v / YQ$ y aÔ u v TY[$ . y T0 Ô u1qu YÆCÔ u1qu 1 o YQ$ U V Ô Y ut&W
(76) fu\ {fFÔìtvfu~sW¹*u{}¦fq\SÔe5u{ ¥0u\q¥W}OWÔìcu{ s&quSÔ st ft&Wftv5fu\(W°
(77) { F~s{W)²¥~| ±fufÔð`Wt& {}f ±fu}@{¸Î)W° 2G8 q cu{}uW ¡s{}¥Wz|qstv{ _@~t¡cu¶ p/qu(¡5W~s WÄf {¸ {}fs°`fqsu(| ut W°uÏ@~s {}fs!É Ê ³ ÉQ£ Ê Wui qu´°`f ³ H¹{}s¦s¶ È 0qsu!qs@DÍĹºS±fuÄÉ 8 Ê quqO@cufs{}ÂWssH|{}t& {}f W°_¦fusu W}{}¼u WÍ@{}su4³ ^~¦ffs{}WW {¸ {}fsWu
(78) ~su B < . 0 D . ? D y 03D É¢ Ê < . + 57+ v 5 v 0( ;D . 5&%. . 5&%. . )(. . . 5'%. 5&%. . 5'%. . . +*. ). >. < > ' & . 8 ! ") + u / / u 0( ;D. Ù Ù ö;zsïj{ Þï. ,. 6 D. 8 yD.
(79) .
(80) ! "#$&%'(")*+, ! "#$*-./10234. .2 D y D! !>! D43 8h-0 < , Y TY u 8 TYC ZD È 4 qsu0¡c »~s°JuÉ8F Ê qsuuW¦fusuf~sDqsut&{}SµuS {}fsu WÍWuÃ{}\ Wf~s\W qsuS {Dq¥W¦Wu{}\¹ W W°:¡c ({su¦fuu B. uu. ZD , Y 5o Y < + D 2 D! ! !>D43 8 , 8 < !. ^. D. É¢W¢ Ê. % > ' & y V 5 ! D , 8 , ! )"+ / 1qu u 3Îl q{vSuWÔY qsu±W}~su 6P./.c@R0SD3 `.Q@R03DTU V D3a DT 6Y 00W ¡5uW~s u N °`f}H¹{¦&¹ºSaB. {}lqsu P./O.Q@R0SDT .c@R0SDTUWVD3XD3 ZY[0H=Z! 1qu u , ./.c@R0SD3 .Q@R03DTUWV5D3aDT Yc0 É¢H¤ Ê N p/qsu , ±W}~suy{}
(81) SW}~su °ý uf~| {}fW° qsu¡5f~ W±W}~suysf¡s}ut É Ê ³ É¢f¢ Ê ¶
(82) :{¥¸}u_~ssWuq¥/°`f/¡cf~s W(f {}{fÉÿ¢f¢ Ê qsu{\ u¦f . HDT%DG@ 0H @ M ILK ./O.Q@R0SDT :.Q@R03DTUWV5D3XD3 ZY[0]\@3! É¢S Ê N W qsu{\ u¦f ÉJuuÉQ¤ ÊÊ WDqs{}u±Wu qu{}tv{}s{t~stv4{}t~¸DWuf~s}ÁÉ`°`Wqsu Wtvu
(83) u f Ê ¶ %6 2 6
(84) 2 6.
(85) >W¿f}~{f W°& qsul¡5H±fulf| {}t&{}¼S {}f f¡s}ut ±W{ËO½°iqsu ²¥\{s¦³ 5f{}\/Ç
(86) uu {} È ¦Wf{¸ qstv*{*~su ¶
(87) }\ {}s¦³Æ5W{\ºÇusu{ È }¦ff{}qstvºuW}{u4 ftvsftv{uy¡5uιºuu½¡s{}¥WO³Æ u Çusu{ È }¦ff{¸ qt&4W Àb±Wf~| {}fLz@ u ³ ¦f{u` )è ,QÔ {}suv qsu½~su&tvfW°* qsuvËW{}SWºÇ
(88) usu {} È ¦fW{¸ qstvtvuDq¥W{t& ¹qsuuSW qsu(¹*fÍ {}u}!_qsusqsusWÎ@s{}}u±Wu${}ÍWuÀb±ff}~{f¿z@ u¦f{}u¶ 'Ãu»~u f {}¥W {}s¦f}u»cf{\Ô ~ss{¸°`ft f&W{}qstvu{WfH±fufcu ̳ f¶#ÒeuÂ~Â~sscfu½ q¥Â{} {¸±@{ ~¥W} . r + D! !>! D r Y D r Y + D!>! ! D r 0W 6. 6. 6. . ). =. 8. 5 8': ; 8 6. 6. %. 6. 1. '= >. ,. -. 0/. ×`Ø Ùe×`Ú.
(89) &. £. &. 0
(90)
(91) 0 "#
(92) 2/. Wu&DqsfuÁ°`Wtu}u {}f s|uyWsWuO¶p/qsu´W { ³ ¥WÂ{}s¦f}u0cf{\
(93) fH±fuf5u f4s r ~suyqsur °`f}H¹{}s¦(ι*Dq{ u YW Z . + D! !>! D EY D Y + D5!>! !>D 0_É`¹qsuu 2:{/ W ft7~³ ucf{\ Ê ¶ Æ° 5Y{}v W ft O~st¡5ui{} qsu{}\ u±W Z< * qsu!~s{}°`ft fH±fu&W|³ u fy ~suy qsu(°`W}H¹{s¦¿Î¹*½Dqs{} u b . r + D!>! ! D r Y D! !>! D r 0 YW . + D! !>! D Y D! ! !>D 0º¹qsuu . + D ! !>! D EY D EY + D!>! ! D 0 . r + D! !>! D r Y D TY + D!>! ! D 0. >. >. . 3. . ?>. >. >. >. >. <>. >. >. r >Y r EY Y jj YYfhZ!! . Y . > . r Y j Y Z!. EY j Ydf ! .
(94) ¥f/qsu{¸ qstvu{W$f̱Wuf5u f/ qsu±W}~su r Y W Y W uSW}~Ëu ~s{}s¦v qsu
(95) °`f}H¹{}s¦v°`ft~sË >. r >Y .9 8 r 0 r Y r E Y D r 8! ;! . >. Y .] 8 r 0 EY rqr Y. >. ¹qsuu @Ô¥W y{}_0 W ft.O~st¡cu_{}qsu{\ u±W Z< Q¶ È qsuit~D {}fÄfcu WÔ$¹ºui~su& qsuisfO~ss{¸°`ftt~D {}fÁfcu f u ³ ¥su ¡\ {Dq¥u¹{¼ )è£ ,U¶ Æ°bi¦fusu Y { it~ uÔ¥ qsusu¹±W}~su Y {}DqsWu W ft ¹{¸ qs{}{\ u±W 2 XY9D r 4 Y $¡\(qsu
(96) °`f}H¹{¦&°`ft~sZ B s É¢w Ê Y Y &q. YX8 Yc0 8 # &{}µ4 ft O~st¡cub°`ft ZD5 UÔ s {}b qu ¦fuu {}f0O~st¡cuÔ {}b qsu t&|{}t&W ¦fusu {W&O~sr t¡5uÔ *{}b qu/u ssutvu\Y¥WWtvuuÔ Y>{}µ ftv¸yDqsfuv°`ft 2 XYbW 4 Y ÉJ}H¹ºu ~s5u¡5f~ W° qsu
(97) ±W{W¡s}u Y Ê ¶ ·4su*W°¥ quºt&W{}ysW¡sutv q¥µW{ub{}vÇ È {} ut&~suºf\±fu¦fusu¶
(98) >W f}~ {}fÂW°b q{_sW¡sut ¹ºu~su qsu{}Dsu ³ÿu5u u\ Â~|D{f»Wss\WDq )}¢ -,U¶&p/qs{}ssfWDqÃfs{ {Ã~s{}s¦! qsu {} Wsu&¡cuι*uuà qsuvιºt& u{} f uYftvs~u qut~|D{fi ;u B qsu_t~ {}f´ u_{}ºsWs¦fu*fsDW\ ¥W t&u uÔì{¸4{} @¥Wtv{}SW}¸¿Wt&~ u °`W¡cW q¿Dq{ uLW u5u
(99) f»qsu ¥Wu\ ¶Àb±Wu& {}tvuW~ss}uW°F{ {}±@{ ~¥W} {}*DqsWui°`f*t&{¦sÔ\ qsu_t~ {}f uy{
(100) ftvs~u W ¹{}b¡cuvWs{}u (qsu{}
(101) Dqs{} uðýu4fH±fu@~s¶ Æ° qsui¥Wu\ 0u´ÏO~s{¸ ui}fuÉJ{J¶èu¶qsu{}t&{s¦»{{}ÍWu}L ¡5uifs{ uu W {su Ê Ô qsy¹*f~s }uS ½¿qs{}¦fqlt~ {}fl u´°`f qsu{yDq{ uìÔ¹qsuuSW t~ {}f u¹{}}F¡cu4t&W}u {¸° qsu´Wu {}DO¶ È / {DW\{¸ u{˹*u|fÍ. 3. . . . . .
(102) >. . .
(103) >
(104) .
(105) . . .
(106). . .
(107). . ,. 3. Ù Ù ö;zsïj{ Þï. .
(108) ¢.
(109) ! "#$&%'(")*+, ! "#$*-./10234 ,. i uË {¸±fu {} Wsuy r q¥_Dr ÍWu{\r (Wf~s\4 qu¡cf~s W°µuSDq¿±W{W¡s}uW°bqsu { {}±@{ ~¥WJ¶ Æ° . + D! ! !>D Y D!>! ! D 0W . + D! !>! D EY D! !>! D 0¡cu_qsuι*yt&u 3. r aY 8 TY ' \92 &5@j. wD 0( Y )"+ r 4 XY 8 2 aY. Â{} {}Dsuv¥WWtvuu4 qs
(110) SL¡cuy~su ! ~s
(111) qsuy¹ S¿qsu {} Wsu0{} ftvs~u ¶ Òeu . D 0y¡5u! qsuÂt~ {}f uÁÉ . D 0 8\ 2 &5@j. D 0 Ê ¶ Æ° W Wu´{ u\{WQÔµ¹*u(q¥S±fu . wD W0 Ji¹qs{DqltvuSsy q¥ quui¹{}º¡cu Äftvs~f t~ {}f f)uSWDqh±W{ËW¡uÂW°
(112) qsu»Dqs{ uì¶p/q¥({}(}uSW}) @ Ws¦ t~D {}fìÔW { f u )H±Wf{ qsSÔ4¹*uÃ{}\ ~u ¹qs{Dq fu5W 0 qsut&|{}t~st t~D{W u4q¥_{_W}}̹*u ¶ \. . . . . . . 3. . . D 0H :\Z! y. .. . 8. 8. .] 8O\92 &5@j. wD 0R0. ÎÂf~/SW}~s{f_¹*u
(113) @fÍ ¶ z@sÔ¥f~s/f| {}t&{}¼S {}fÂtvu qs {}\±ff¸±fu qu°`W}H¹{s¦&su~ & u B @ # {s{¸ cfs~Ë{W .Q@R0
(114) ;+ / ;+ /
(115) & %& $
(116)
(117) ¹qs{}usW fu :.c@R0 B u}u ¥Wu\ ; 3. >. %$. &.
(118)
(119) # +/1
(120) 0
(121)
(122) . uft¡s{u. . ,&. 7>Q.c@R0. $.
(123) "
(124) /. t~ u . . $. Q.c@R0. 7>.
(125) /. u±W}~¥u. 7>[.Q@R0 .c@ - 0 B 7 : >Q.Q@R0 . . . &.
(126)
(127) /
(128) .
(129) 2/1
(130) 0. &. #. 0
(131) . *$.
(132) 0 +
(133) /
(134)
(135)
(136) . ¡cuÌÉ Ê. @ # @ . ×`Ø Ùe×`Ú.
(137) &. ¢f¢. &. 0
(138)
(139) 0 "#
(140) 2/. u s
(141) ¥f_WsS|{t&{W¿W°bqsu uf!¹*u~su u¼{}u
(142) z@s{}suuuu\D {}fì¶ È ${}${}$ÍOY sH¹y u¼{u:~s±Wu*°f u 3{} u ¥u ¡\4qsu usu{}cf¸|ftv{ËW} Y*É ³Y¡{sWt&{We|uÕi{u\ Ê & & ./&-0H ' & Y d Y D YC Y & Y .9 8 &-0 & Y D Y 2 .3 38 2 0 D É¢ Ê Y) & & & & ¹qsuOu & usWu qsu½¥WWtvuuW°qsu½~s±fuà WÍO{¦ ±W}~suÂ{ ZD QÔ 7 YWu qsu0f\ Wµ5f{}\ ¶vz|sÔ W
(143) {¸{
(144) uuð`Wt É¢ Ê qu u¼{}u~s±Wu&{}ftvs}uu¸ uutv{}su ¡\ qsu
(145) Wu{WÂ@f {}¥uW° qsuf\ We5f{}\ ¶
(146) ¥f$f~:f| {}t&{}¼S {}fsf¡s}ut!ÔWqsu*sW Wtvu u &º{}:uÏ@~sW@qsu {tvu{}fs}u {}t& u @R$ @
(147) u¼{}u0WsS|{t&{W W° qu´ u fÃ{} u utv{u ¡\ @f {}¥uw . Y D Y[0 W° qsuWOfecf{}\ 7Ye¹qsuu . . . . ). . . ). 8. 8 D 8 8 g V 8 l V `J./DT0 8 ]. D5-0 . r + D r v D5!>! !>D r + D r D5!>! !>D r v v 0 t %B & & & r YC Y D Af 2(f .3 8 -0 r C Y . Y D J 3 f 2(f . y 3 8 y 0 t + & k 3 8 y y rY 2XY t r 4 Y. p/qsu ¥ W qsu´W 45f{}\ 0u |u Ôb¹qs{}Dq Wu ³ cf ì_f {¸ {}fsYÉJ Ê ¶ p/qs{}$t&uWsìq¥$f~sF {¦ q¥W/ qsu
(148) °`f}}̹{}s¦0°`ft z|sÔO
(149) {}s¦ WO W{}s ±W}~suW°5f\fscf{}\ ¶ p/qsuu_±W}~suYWu ±W{}u °`ft : ¹qs{}Dq¿WuH¹*uW ~sscu¡cf~s W° qu±W{Ë¡su ζ uS~su qsuµfs {\ $°`fFqsuf{tv{}¼S{fsf¡s}utuµ{}suÏO~¥W}{¸ {}u ~s{}s¦ uS{}¼S{W(W°ìqsuuW¦Wf{¸ qstvY¹ºu4tv { ¥u qsuf¡@u{}±Wu4°`~ss {}fì¶ Î(f~ºSu ¹ºu~su qsu
(150) °`f}H¹{}s¦itv { ¥u f¡|u {¸±fu°`~ss {}f V B . 3. =. ¹qsuu. V . . . =. . +N N v . n :o .c@R0 n $ s 8 r 03D . 56 8 5.6 0R$ 5 6 D N N . n :o .c@R0 n $ s 8 Q. @R0R$ s 0 N = D N . Ù Ù ö;zsïj{ Þï. É¢ Ê. YW N eY Wu_ qsu4f¡s}ut ucu u ¥WWtvuu¶. g.Q@R0H t V 1 .Q@R0G v .Q@R0G$Z. y %0. n o .Q@R0 n rqs D 5 6 5 6 D n o .Q@R0 n g.Q@R03D " !$#&%')( *,+ -&.(/..
(151) ¢Ì¤.
(152) ! "#$&%'(")*+, ! "#$*-./10234. ΰJWÔ>qs{}4Ws\WDqÂu¥¡su4fsu iu@ u quuSWDq¥WuyW iu±W ³ ~¥ u{} utv suiqsu{ {}±@{ ~¥W}Ô/ qs Äs´ {}°ýl ½ qu»Ws W{}\ W°b quyf{tv{}¼S{ff¡s}ut!¶ Æ{±fu»{}tv5WDO (W uq¥ { Fu{}s¦(°`ft f~¦\ u/¦W {}u\Yf{tv{}¼S{Witvuqs *Ç È tvuqs YWu/sYW\0u { {}fs fvtv|Wqssu°:qs{u |us{Wì¶ - % 2 % % %!% 6 % p/qsuf~| {}f¿W°bqs{}±W{{fsW$sf¡ut ¹ºWW¡DW{}su °`f qsu°`f}H¹{¦( W¦fu W° f¡s}ut.W Ç È ¥ Wtvuu5 B 3. 3. 1. -. /. +*. /. 1. ,. ,. t V y ! x v $ <. -. r Z! Z<. ;;7 D y ;;7 O< ` Z!
(153) D! Z< UWV Z! ? D! ;?! lb= ! " $ .D V y ! $ .D g x D bV ; D 8 : ; 5 6'. Z!
(154) f f ;!#Z<=Z! wf 8
(155) !Z< t y ZD ;ZD5xZD y Z< xZD y Z< y ;ZD ; ZDWZ<="gf3 f . ¹qsuu {ºfH±fuºsf¡sW¡s{}{¸ÎfÔ {ºt&|{}t~st#W}H¹*u t~|D{fisW¡|³ W¡s{}{¸ÎfÔ t {05f~sË {}f!{}¼uW¶ Æ({~s u @ q¥´ qsuW~s {}f^W°
(156) qu{\ u¦f 0É¢S Ê ±@{ËÄqsu {}u @~t&u{}SW
(157) f}~ {}f W° qsu½p Ñz|Ò uÏO~¥ {}fs@ut uWDq^ Ìufh5f{}\ uÏO~s{}u&±Wu ˦fuftvs~ uvuf~suW¶
(158) ¥f qs{}0uWfFÔY¹*u!q¥S±fu!~su qsu °`f}H¹{¦ÂssS|{}ti uvWs\WDqF¶ È
(159) qsu s u½qsuv{{}{ËW:¡5W~s W»±W}~su sf¡ut É Ê ³Éÿ¢f¢ Ê ¹ºW
(160) f}±Wu °`f4¦f{¸±fuL±W}~su* U V 7Ô c7Ô Yµf½¦f{ y yy ¹{¸ q u < u Z! y %$;&Éý°`f:±Wu}|{}Î Ws¦Wuº°`ft +|¶è4ÍOt ¤@¶õÍOt Ê W ¹{¸ q u < J y ! ; É`°`WW¸ {¸ ~ uWs¦fu°`ft¢ &ÍOt iÍOt Ê ¶ È qsuuf u&¹*uSW}~Ëu qsu/W¡|u {¸±fu°`~ss{W¿Éÿ¢H Ê ±@{{}\ ucfË {}fvW°5qsu/f¡ W{}su u~s¸ _f qsu
(161) ±fu@{¸ÎWf qsuW¸ {¸ ~ u~s{}s¦ ³Î{}suusuu\ {}fì¶ p/qu(ftv¥{}fs utvfs u q¥qsu { 5uusu¡cuι*uul{\ u¦f ºqsu ²¥~|ÃW}fs¦ { Fuu\ Ìuf{}uÔ W~s u f½ qsu&¡¥W{uWW qsuiW¡cH±fu {}u ι*³Æ uWsS|{t&uyWs\WDq { su uu ZD (Ô¥¹qs{}Dq¿cutv{¸ _~s v~su
(162) qs{_tvuqs °`f/u{WeW~s {}fs¶ . 8. 3. ). 6. ) ,. ,),. +*. +*. ×`Ø Ùe×`Ú.
(163) &. ¢H. &. 0
(164)
(165) 0 "#
(166) 2/. p f¦fu qsub¹{}qy qsuº{s{¸ {Wsf¡s}ut W~{Wv¹*u/Ws{ uu qu/f}~ {}f0W°¥qsu °`f}H¹{¦{}O±Wuuºf¡s}ut B ¥ qsuYuu\ uf
(167) ¹{¸ q¦f{}±Wu { {}¡s~{WW° qsuqsu²¥~|iµqsuDW¦W¥ {}fvcf{\YW°5 qsu_f^¡s}~s\º¡c vW}fs¦
(168) u ff¶ Î qs{}eSWuµ°`fì qsuµ¦W{}±Wu Ìuf4f4 qsu¡¥uµW°@ qsuµp Ñ
(169) zÒ´uÏ@~s {}fs$W~{Wqsu { {¡s~| {}f° qsu
(170) qsu/²¥~|f¦y qsu¦f{¸±fu u W´¹ºW u utv{su ¶ È °ý u q¥Ô qutv{}s{}t&{}¼S {}f»sf¡s}ut.°:qsu
(171) °`f}H¹{¦if°`~ss {}f!¹ Wf}±Wu B ' P.Q@ Yc0 8 V .Q@ Yc0 v Éx¢ + Ê V ./0 Y )"+ N N N N ¹qsuu {} qsu
(172) ¦f{ O~st¡5uf¦&|W {}¥u @ Ô N V .Q@ Yc0º{ qsuÍOsH¹±W}~su
(173) W° vquS²¥~|( &&¡c (~s°JWu{Âv{tvucf{\ @H@ Yƶ p/qu»W~{WhW°qs{}´{}O±Wuusf¡s}ut {v±fu {tvcf W\i°`ft tvuqs {W 5f{}\W°F±@{}u¹¶ Æ°c¹ºuW~stvu qsuWucf usu¡5uιºuu& qsuuu\ 0 u f W qsu {}{}¡s~{f»W°µ qsuqsuS²¥~|»W}fs¦´{}yÉ`°`f_Wqsu |u ¥WWtvuuW° sf¡ut Ê {}/fsu ³Æ³ÎfuWÔ|qsu
(174) W~{W° qs{}/sf¡ut W°:f{tv{}¼S{f{}/ÍOsH¹ B vtv{}s{}t~st.±W}~su N {}/uÏO~¥We0¼u´ qsuuu\ u f(f¡ W{}su °`ft f}~ {}fLW° W~sf {}tv{¼ {}fLsW¡sutqsW~s f{}s{ uv¹{¸ qÃqsuv¦f{¸±fuÃfsu¶ Î s {¸ {}fìÔ>¡cuS~su{! qs{}_SWu¹*uÍOsH¹ quf~| {}f»W°: qsusf¡s}ut.¹*uq¥S±Wuy ¦f| ¹ºH´ 0±fu{¸°ý( qsu¦fW{¸ qst W~s W!W 0u{t&u{¸ f¡s~s suW {}_uÕ&{}usf¶ ·4suuWtvs}uyW°: qs{}{}\±fuusf¡ut f}~ {}f¿{}uu\ u { ¥¦s¶4¢fÔ>¹qsuu qsu {}{}¡s~{f b$ _W m$ /±Wu~s/ {}tvu ÃÉ ¥¦s¶/¢S Ê W Ó±Wu~s É ¥¦¶ ¢S¡ Ê Wu H¹FO¶ ^uu}{u&³
(175) ¦f{¸±fu ufWÔY}{}suv¡Ä³
(176) qsuf}~{flW°/qsu {\±fuusf¡s}ut!¶ Òeu4~s W¿{ qsu¡5u¦f{}ss{}s¦(fÂftvuyf~| Wt&uW°µiO~stvu{W f~| {}f¿W° W½{\±fuuisf¡s}ut!¶0p/qsuvu~s¸ W°Y qu0@ut& {}´W}~s {}fs utvfs u q¥qsu~s¦f¦fuu W}¦ff{}qst.{}ÏO~s{¸ uf¡s~SÔ>q¥4v¦f| W~s WW iqs{}¦fq u±fu>W°ìW{¸ qt&u {}SW¥fYuÕi{usX Bµ°`f t ;Ô 3 x
(177) qu±W}~suW° N °`f W°Y~ss @u
(178) Wu|uu x °ýu0¢ ´¦fuu {}fsiÉ`qsu0f¡ W{u u f ¹{}qi¦fWsqs{}y~ WÂf{}s{ u ¹{¸ q qsu¦f{}±Wufu Ê W qs*u ! {tvu°`f fsu
(179) ±W{W\/¹ uÏ@~sWì &³ 0tv{}ÁÉ`f0ftvs~uz ; z5¢ |¢Swf Ê ¶ 3. . . . . 6. . . . 6. 6. . 6. 3. 3. ),. . <). Ù Ù ö;zsïj{ Þï. ,), ,.
(180) ¢Sw.
(181) ! "#$&%'(")*+, ! "#$*-./10234 1 line line line line. a) 0.9 V/V_0. 1a 1b 2a 2b. 0.8 0.7 H/H_0. 0.6 0.5 0.4 0.3. t/t_m 0.2 0.0. 0.2. 0.4. 0.6. 0.8. 1.0. 100 H (km). line 1a line 1b. b). 95 90 85 80 75 70 65 60 55. V (km/sec) 50 2.0. 3.0. 4.0. 5.0. JÉ }{}su Ê ¶ 2 :¶Òe{su µ¦f{}±Wu ÌufW¶.
(182) {¦W~su¢B0z@f~| {}fs°º qu´{}O±Wuu(sf¡s}ut Z! x. . Ô@. 8. ;. 6.0. . r B. Ô. 7.0. Ô. 8.0. t ; 3 N . ×`Ø Ùe×`Ú. a) V/V_0 H/H_0 t/t_m.
(183) &. ¢. &. 0
(184)
(185) 0 "#
(186) 2/. . *).
(187) !" !#$%"&"'%. qsu{}²¥~susuW°ì qu
(188) Ç È ¥ Wtvuuºf´qsu_f}~ {}f W~s W( f´qsu4W}¦ff{}qst7uÕ&{}uf¶ È }5qsuu4{}O±Wu {}¦\ {}fs/¹*uu4SW{}u f~_°`fsfsDW¸O {}¡c Â~s°Juy °`f qu°`f}}̹{}s¦´±W}~suW°: qsusf¡ut ¥W t&u u5 B
(189) {*W°$W}>¹ºu{\±fu{¦\ u . t V y ! 5 6 8':<;. . v $ < r Z! Z< @ 8 2 <. ;7 O< ` ! Z< UWVb ! ;?!. È qsu ¡cu¦W{s{}s¦4qsu u5u uuW°¥ qu f{t&W|f}~ {}fy°`ft qsu W u 3 W° qsu u¼{}u/s{}su
(190) ¹ºW/~ {}u ¶ºz|ftvu4u~}_° qs{}/{\±fu{¦\ {}f»u
(191) suu\ u {Âp W¡Q¶4¢WÔ>¹quuff~ÂSWÂuu qu¡cu s±Wu±W}~su_W°bqsuW¡|u {¸±fu°`~s{f É`°`Wt ¤ 0~s Ê °`f { 5uu\ 3L¶ p W¡uv¢ 3 " 3 3 x 3 y 3 ¢f¶ f¤W ¢f¶}¢H¢ ¢W¶¢Ì¤W¤w ¢f¶}¢Ì¤|¢Ì¤ ¢f¶¢H¤|¢f¢ ¢f¶ W¢S ¢f¶}¢H ¢ ¢W¶¢Ì¤ ¢f¶}¢Ì¤f¤|¢ ¢f¶¢H¤|¢H£ ¢f¶ W +£ ¢f¶}¢H ¤ ¢W¶¢Ì¤f£ ¢f¶}¢Ì¤f¤W ¢f¶¢H¤W\¤ ¢f¶ Wf + ¢f¶}¢Hf¢ ¢W¶¢Ì¤qw + ¢f¶}¢Ì¤Wf ¢f¶¢H¤WWw ¢f¶ ws¢ ¢f¶}¢Hf ¢W¶¢Ì¤Ww ¢f¶}¢Ì¤ |¢ ¢f¶¢H¤qw + Ƶ¹ºWµuD¡s{}qu q¥µqsu/tv{{t&Ws~Õ&{}u\±W~u/W°c¥W t&u u 3.{µuÏ@~sW Ä¢ ¶ Âu qs {}SWYS~sË {}fsyq¥S±WuqsH¹ìÔbq¥y{u»sW Wtvu u 3 x °`~sqsu/{}suSW{¦iW° 3¾±W}~su { Ws ~suW!{tvsH±futvuOW° Wf¡ W{}su f}~ {}f³*Wssfs{Ëu
(192) Ìuf{}u_W{s{ u ¹{¸ q»0¦f Wqs{u s {¸ ~ uW¶*p/q@~Ô qsuu{}¥°ý u_We¡sW{}SW}~s{f¹*uuW{u W~ 3 x¶ Æ_{}/suu WvsW uÔs q¥~s{}s¦&u}{}{tvuDq¥Ws{}tv4 t~D {}fÂf¡¥Ì³ ¡s{}{¸Î ucu usu0W¿ {DWsuy¡cuι*uu¿qsusWuOuSW}}{}tvsH±fu quW|³ ±fu¦fuu/W qsu*W~sWW¶bp/qsuu°`fu ¡cW q qsuuºtvuDq¥Ws{}tvµq¥S±fu W}¹ºS@b¡5uu ~su {}»eW~s {}fs¶ È sWqsu ±fu{tvcf W\ ¥ Wtvuu °`f:Ç È W}¦ff{¸ qt& {}: quºcfs~s {}f{}¼u ¶t È {}*{}YÍOsH¹´°`ft qsu_qsuWfÔO{}suSW{¦ qs{}µ±W~uWÔ@u~s¸º{}( {}t&{}O~ {}f W°ì qu4O~st¡cu/W°ì{}u {}fsÔ|¹qs{Dq!uuuW(°`WºWO±Wu¦fusuWÔ¥¡s~| @u W =. ,. +*. ). ). ). ). ) ) ). 3 ,. 3. Ù Ù ö;zsïj{ Þï. ). ).
(193) ¢.
(194) ! "#$&%'(")*+, ! "#$*-./10234. u~s¸v{ W uu\ {W {}t&{}O~ {}f W°_u|cu u ! {tvuW¶ Æ0tvuSWy q¥°`f qs{¦WqsuW}¦ff{}qst uÕ&{}us&¹*uq¥S±fu/ uuSWu_qsu5f~sË {}fv{}¼u/¹{}qiS±|{}s¦ Wssfs{u&f}~ {}fÃW~s Wf¶ Æ{}W} qsuf¡\±@{W~sq¥ qui{}²¥~susu&W° qsu
Documents relatifs
28 The original version is based on the Dijkstra’s algorithm for the computation of the shortest path between two nodes; however, different algorithms can be used within Yen’s
This has also led to the formulation of algorithms that can efficiently verify robots stability in multi-contact scenarios [7], [8]. Such approaches however still fail to capture
Most applied work of the IFP is concerned with protein design. Since the first de- sign of a peptide by Gutte et al. [27] using secondary structure rules, numerous works have
Intermediate MAP Score Curated Gene Hit Rate Curated Chemical Hit Rate Curated Disease Hit Rate Curated Action Hit Rate Text Mined Genes Curated Genes Gene Match Explanation Text
0 Problem is the instance treated. 0 UB is the upper bound obtained for the Make- span in single-objective studies. 0 M I and TI are the best Makespan and Tardi-
PRICIPAL AXIS FACTORING ( ﻙـﺤﻤ ﻡﺩﺨﺘـﺴﺍﻭ ﺜﻜﺃ ﻥﻤﺎﻜﻟﺍ ﺭﺫﺠﻟﺍ ﺔـﻘﻴﺭﻁﺒ ﺩـﻤﺎﻌﺘﻤ ﺭﻴﻭﺩـﺘ ﻙـﻟﺫ ﺏـﻘﻋﺃﻭ ،ﺎﻬﺠﺍﺭﺨﺘـﺴﺍ ﻡـﺘ ﻲـﺘﻟﺍ لـﻤﺍﻭﻌﻠﻟ ﺢﻴﺤـﺼ ﺩﺤﺍﻭ ﻥﻤ ﺭ ﺱﻜﺎﻤﺭﻓ .) VARIMAX (
We reduce the problem to the null obstacle case and we compute the solutions using the duality method (Merlu¸sc˘ a [9])1. In Merlu¸sc˘ a [10], the case of the fourth order
Roughly, three main components need to be addressed: (i) the way uncertain data is modeled (e.g., with the use of scenarios), (ii) the selection of an appropriate robust
