Un algorithme pour trouver la permutation entre deux codes binaires équivalents
14
0
0
Texte intégral
(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Un algorithme pour trouver la permutation entre deux codes binaires e´ quivalents Nicolas Sendrier. N ˚ 2853 Avril 1996 ` THEME 2. ISSN 0249-6399. apport de recherche.
(3)
(4)
(5) ! "#$%&
(6) '%( #)%* + ,).-0/
(7) 12(
(8) 3-534 6,2
(9) 7(8%($9,:<;>=@?<A@B,CEDGF HI1:JDKI L(M&OQN PRO2S,TVUXOQW Y@Z[O,\^]`_`Z^abZ^Ob\ Obc(aQl.dem \[aQf@\"ghEPiE]`\^Z^jkf@O ]`nObcpoqsr2t.u v d`wEwx] m c(yEO m Oba M O m a M O Yz{S}|`~` TVs m Z[\3Q`` T > wEdK_`Obg k e 3(]f@gsw m ObW gOQY}c]Y@gZ[abZ"fEYdK\^_`] m Z[c M POwxO m PObccd}Y`c(yEO m Obc m ]@f@`O m \dwEO m Pf@c1d> cZ^]m YOQY`c m OyEmOQf@ab]yEObg\[ZY3OQW dKZ mm Obg2M i@ZYEdKZ m ObgObW jkf@Z^KdK\^OQY`cg>$ m dK\^_`] m Z^c M Pm O2Y@O <]@Y@abcZ^N]YEY@m Ojkm f@O \^] g8jkf@N O\^O_ ]fEwEOy ¡d}f@c]l P] m w Z[g1POyEObg2ab]@yEObgm ab]Y@gZ^y7O W ObW g Obg8cc Z^ZdK\£¢¤m a`¥Obgc d>¦yEZ O O1W m y§f@Z^c d\dgOQf@\^OZ[yEOQY}cZ^cEO`W ]@f yEOQf@ab]yEObgsi@ZYEdeZ Obg¨m ObW jEf@Z[KdKm \^OQY`c8g dK\OQW dKc8]`Z Obg(yEO\^]Y@_m f@OQf Q } ` Obc2yEOyEm ZPOQY@g8Z[]@Y©~` ` E¢\^O{cOQPªw@g2yEOaQdK\^aQf@\%Gd Z^OOQY`c O{«Obc|` gObab]Y@yEObg,gf fEY@O gc1dKcZ^]YyEO2c d>GdKZ^\&r2t.o0} ` ` `¬`} ` E ®°¯±³²´¶µb·²¸º¹²»¼. Unit´e de recherche INRIA Rocquencourt Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY Cedex (France) T´el´ephone : (33 1) 39 63 55 11 – T´el´ecopie : (33 1) 39 63 53 30.
(10) (8
(11) Q {2)
(12) 12 ¤ # "&%$
(13) / 0.p 0 .6,2
(14) 7%( /
(15) º p + ,).
(16) ` Ow m ObgOQY}c M O m Od`YdK\^_`] m Z[c M P d}i@\[Osc],ab]PwEf@cO(c M O wxO m Pf@cdKcZ^]YiEObc%ObOQY c%]Xm _`M Z^`OQY©ObjEm f@Z^GdK\^OQY}cM i@ZYEd m h©\^ZY@m OQd m ab]@yEObgQ L(Mm OdK\^_`] m M Z^c M P]m Y@\^h 7] m gZ 2M c M Od`f@c8]K P] m w Z^gP _ ]fEwXm ]em pc O{ab]Y@g8Z[yEO Oby©ab]yEObM gZ^gc Z^ZdK\£¢ c dKcZ^g Oby§f@abOby©M c]c OªZ[yEOQY}cZ^ch wxO Pf@cdKcZ^]Y& ] d`Y@yE]@Pab]@yEObg7]e \^OQY@_`c Q } ` d`Y@yyEZPOQY@gZ^]Y~} ` E¢`c O(ab]PwEf@cdecZ^]Y cZPO,Gd m Z[ObgiEObc %ObOQY«d`Y@yX|` ,gObab]Y@yEgs]Y d %] m gcdecZ^]Yr2t3o` ` ` `¬}` ` E.
(17)
(18) !
(19) " # $ %& &')(* %,+-. / 0.+2
(20) 1 3 / +. . $p$
(21) 2N :0ObW \OQW POQY}cgQ¢; fEY OQY}cZ^O m E gc m Z^abcOQPOQY}c{wE]`g8Z[c8Z¡ .u@]`Z^OQY}c)<>= @ u ` ] ^ Z c ) 576\^Oab] m w@g98$Y@Z d ? <A@ B C C CDB
(22) <!EF%ObH c G"= ? G&@,B C C CDB
(23) G EF%yEOQf@ ObW \1OQW PROQY`cg%yEO5 6 I l ]f m c]@f@c7OQY@g8OQPi@\^OJ8$Y@ZLK¢EY@]f@g Y@]`c8O m ]Y@gMNKOMeg]YaQd m yEZYEdK\£ g P
(24) E{\£¥OQY@g8OQPi@\^OSRB C C C0B
(25) ;UT I l ]f m c]@f@c7OQY}cZ^O m ;¨Y@]@f@g Y@]`c8O m ]Y@Q O Vsd`PPRZY@_ OQY`c m OyEOQf@ObW \OQW POQY}cg < m Obc G ? yEOO 5 6 E gO m dYX&Z ? <UB*GF = I d yEZ^gcd`Y@abOyEW M[R]\_^`P
(26) EWMa<!bd=e c G bfT¢@\^OwE]}Z[yEgyE O Vsd`PPRZY@_yEO <g8O hd gdZ <$F_=iM[Ra\_^YP
(27) EWMa<jbd=0c T \ km yESO 5m 6 E ¢"Y@]f@gY@]}cm O m ]Y@Jg khl g]@YX] m c M ]}_`]YEdK\£¢ I l ]f m c8]f@c2g]@f@g¦ObgwEdKabO}Obabc] m Z^Obd d`f@ggZ"d`wEwEOb\1OW ab]@yEO2y§fEde\ yEO k¢kwx]f \[Ow ]@y§f@Z[csgaQdK\dKZ Of@gf@Ob\£ m n (§ 2)ª + $
(28) (m ]f@gw m ]wE]}g]Y@gZ^abZ fEY dK\^_`] N m Z^c M m POwxO m PN Obcc1d`Y`cyEO m y7ObW cO m PRZY@O m mbN gZ%yEOQf@©ab]yEm Obg\^Z¡ Y3OQW dKZ Obg2g]@Y`cXObW jkf@Z^Gde\[OQY}m cgQ¢¤a`¥Obm gc dG¦yEZ O ObW _d`f@ dfEY@OwEO Pf@c1dKcZ^]Y w Obgy§fXgfEwEwx] cQ¢¤Obc y§d`Y@gsabOaQdKg(yEO,yE]YEY@O \dªwEO Pf@cdKc8Z[]@Y& 4 2
(29) $
(30) 8 2o p 4. qLrfs. u"t v_wyxz|{7}~$y!~. ObW jkf@Z^KdK\^OQY`cg. & | Ue $ k k % 'Y(
(31) %.+h%O ;_y .+(
(32) %.+ k J k + $ % + $+ |,'a +, " /
(33) " & `% P
(34) E 3 ? < b F @D!b!E ^ k" &+$& !+ k!>k k!= ? " k F . ? <j b F @D!bE ^Ok C. )_ ~$¡`¢{7! w£¢!xf¡O~!¤Y _ ~$¡O¥ xf ¦ y ~/t ¡ & | U¨§© k (* %" *1 %" ;Uª «+& |¬ +&+
(35) ®0 j+ h-, % P
(36) E| ¯ (
(37) % k $°(
(38) /1 O¬e,+, _%Q1 ± $ /!. k³´ ² =µR ? <!bF b¶·¸ ¹ ´ M ? <!bF
(39) @D!bES^OkhTB (º ,+, ®$a» ®% 0"3 h .+£!a+ !+ $%.'
(40) 1 ,+y Q¬¼+&$ _+,.º
(41) >
(42) 1 ,+ qLrq. . ½|½¿¾dÀ ÁÃÂÄÃÅ.
(43) (*& + $%& * . ¯ (
(44) % k (*(
(45) ( _ O¬,+, £%Q1 ± $ j&. k ´ = R ? <!bF b¶· ¸ ¹ ´ M ? <!bF
(46) @D!b!E)^Ok ^ ¬ B*< = T B. . (º ,+, ®$a» ®% 0³3 h$J+, $ _(
(47) j+ * £,1 +3 " ,+" +%&Y(
(48) % k %&$ £ .+(* %!®
(49) 1 ,+ /%,' *1 .+£! H¬ +,/ £$ .+ !+ .+% &')(
(50) a+ ª "$
(51) Y(
(52) %&,+, £%&h ; M ¬ M. ¬ ]`c]Y@g%jEf@O \^Obg%yEOQf@m ]w.O W m demcZ^]Y@g.ab]PªPf@c8OQY`cQ l ]@f m c8]f@g.g]@f@g¦OQY@gOQPi@¬ \^Obg(yEm Z^g£n³]}ZY}cg m ¬ Obc &yE O P
(53) E{Y@]@f@gpY@]}cO ]Y@g%dK\^] gdkh´ ² ´
(54) =>k ´
(55) ´ ² \^Oab]@yEOHk wx]`ZYab ]YEY.OW OQY Obc deabab]f abZ§OQY ¬ $ |eµ & k (
(56) %` *1 O%Y & ;Uª +& $ d¬ Q¬ %& &' +,&+*® !+, h-, ,+ % +, $ + % y+, $!
(57) #% Y PE. P E . ?k ² F l = ?k l F ² B ´ ´
(58) ´ ´
(59) ? k ´ ² ´
(60) F£= ? kF C ´ ´
(61) |z|{7¢xf{ºU¤¡. qLr. @u ]`Z^c £E \£¥OQY@gOQPi@\^OyEObg2m ab]@yEObg2m \^ZY.OQW dKZ m ObgyEO\^]Y@_f@OQf m ; gf m 576>¢&g]`Z^c µ= E !#" £E \£¥OQY@gOQPi@\^OyEObg ab]@yEObg(\^ZY.OQW dKZ Obgsgf 576Q & | U%$ ZY}Gd m Zd`Y`c +, K .+ Q$S
(62) 7 (
(63) & '& K h3 O% &'Y(
(64) %.+
(65) 1 3 / +£º $$ $ _ S) ( "h l d m ObOQPw@\^O\dª\^]Y@_f@OQf m ¢\dyEZPOQY@gZ^]Y g]Y}c(yEObg ZY}Gd m Zd}Y`cgg1f m \^ObgsOQY`cZ^O m g>$ OQW Y@fEPO1W m decOQf m yEObgwE]`Z^yEgsObgc fEYZY`Kd m Zd`Y}c g1f m \^Obg wx]`\^hkY ]* PRObg dN ab]@,O +{abZ^OQY}cg OQY}cZ^O m gQ - /.. $ > 10 # $
(66) / ª +& k #(
(67) %" *1 & "%h & ;Uª +, $ ¬ ¬ % '³+&+
(68) ®0 j+ h-, ,+ % +, $ + % _+, L /
(69) " & % . P
(70) E. P
(71) Eº. 0 ?³ k ´ ² ´
(72) F£= 0 ? ? k F ´ & ´
(73) F. 243L½265.
(74)
(75) !
(76) " # $ %& &')(* %,+-. / 0.+2
(77) 1 3 / + qLr. . . xLy{/¤ wy¢~$¡. ~. gZ^_YEdKcf m O. & | U + h !+, h-. ,+, Q /O
(78) º (*& 3 » ¯ $ £(
(79) % k %J ; ³h» Y 1 a 1 $ \ % P
(80) E a+*+, ( © 1 a 1 $ ? k"B*\fF % h 3 # ` *" e % P
(81) E & # & \ %&!+ P
(82) E!ª ? ? kFÃB ? \fFDF|=
(83) ? k"B*\F ! k +$ _,'a +, \ %&!+ P
(84) E [+ ¯ L/S+ [ / 0 ,+, % ? ? 3 k"B*\fFd
(85) = c kB F & k +, & Q \ ¯ L/Q+, [ $& .+ % ? ? #% + $( +%&!+ P E ª k"B*\F
(86) = c k"B F,. Ey Z^ga m ZPZYEd`Y}cO c]`cdK\^OQPOQY}c"yEZ[g8a m ZPZYEd`Y`c8O. $ . |¨§ & k (
(87) %O%&Y ; +, % +,(
(88) " $/ Q! khª & & D+. H ,!"%L & " $ +,S% k .+ y * ª h+, $ .+ _ & " / %& +,(
(89) " $/ d! J (
(90) %& kJ
(91) 1 3 $ S» kO. . /O+, $ O " / . t3Y wEd m cZ^aQf@\^Z^O m ¢ m Z^\.Y&¥Ob@Z^gcO{d}f@aQfEY@m OM gZ^_YEdKcf m Oc8]`m cdK\^OQPOQY}cyEZ^ga m ZPZYEd`Y}cO{wE]@f m fEY ab]yEO wx]`ggEObW y§d`Y`c(fEY_ ]fEwxO2y ¡d`f@c8]P] w Z^gPRO Y@]Yc Z^@Zde\< °A 0 | K Q u@]}Z[OQY}c yEOQf@gZ^_YEdecf m Obggf m KOb) b O c c K m ObgwEObabcZ^`O1 ¢.y%
(92) O W 8$Y@Z^O¨wEd m ? k"B*\fFh= P? OQ? Y}cQ¢3\d gZ^?_YEdecf m O¨w m ]y§f@Z^cyEO Obc ¢%Y@]`cEm ObW O m = k"B*\F.B _ k"B*\fFDF Obg8c(Ob\^\[O1³P OQ* POfEY@O2gZ^_YEdKc1f Ogf K KJJ , L ¨ a 7 u@]`Z^c 0 fEY ZY}Gd m Zd`Y}cgf m K¢E\^Obg2d`wEw@\^Z[aQdecZ^]Y@g ² UObc K g >f m K §>y7
(93) O W 8$Y@Z^Owx]f m c]f@c%ab]yEJ O k yEO,\[]@Y@_f@OQf m ; Obc(c8]f@Hc \"y§d`Y@g P
(94) E{wEd m ² ? kB
(95) \F|= 0 ? k F%Obc ? k"B*\fF|= 0 ? k F.B b b g]@Y`cyEObggZ^_YEm decf m Obg2g1f m K{&² dgZ^_YEdecf m Ogf m K ,dKgg]@abZObW O dN 0 gO m d\^O{w m ]y§f@Z^c2yEOªabObg yEOQf@gZ^_YEdecf ObgQ¢§Y@]}ckO W = U §Q, @ 0 $© | K > X a u@]`Z^c 0fEY@OgZ^_YEdKc1f m Ogf m K¢ g]}Z[c k fEYab]@yEO2\^ZY3OQW deZ m O2yEO2m \^]Y@_@f@OQf m ;"§]f@g PfEY@Z^gm g]Y@g Km y fEY] m y m Oc]}cdK\ Y@]`cEO W (]f@gy7
(96) O W 8$Y@Z^gg]Y@gfEY@O Ob\dKcZ^]Yy ObW jEf@Z^GdK\^OQY@abOgf P E wEd . . . . . . . . . #. . . . . . . "!. #. #. %$ & '. #. & '. )(. #. #. #. . *. . . +. -,. \/.. ½|½¿¾dÀ ÁÃÂÄÃÅ. "0 ? k"B*\F7=
(97) ? k"B F,C.
(98) . (*& + $%& * . @u ]`? Z^cSR @ B C m C CDBÃT= m ? k"B*m P E Fd>`l Oba m @ ¿C C C >¢ \£¥OQY@gOQPi@\^OyEObgGdKm \^OQf m g{¬ w m Z[g8ObgRwEd m kB
(99) \Fs\^] g8jkf@OY\,wEd ab]f chP
(100) E§ ]f c]f@c ¢(
(101) `¢ Y@]f@g{Y@]}cO ]Y@g \dXab\dKggO m m ¬ ¬ y m ObW jkm f@Z^KdK\^OQY@abOyE]@Y`c(\^ObgObmW \1OQW PRm OQY`cg%]Y}c(wE]f ZPdK_`O § dm wEd cZ^cZ^]Y ? @ B C C CDB ¢Ey§d`m Y@gabObc ] y O`¢EyEOP
(102) EªZY@y§f@Z^cOwEd \d m Ob\dKcZ^]Yy ObW jEm f@Z^GdK\^OQY@abO gO dd`wEwEOb\1ObW NO _BÃm km B QF ³wEd c8Z[m c8Z[]@Y yE¬ )O P
(103) E& ¬ ]`c]Y@gjEf@OabObccOwEmd cZ^cZ^]YXObgc] yE]YEY.ObW O`¢y§d`Y@g2\^Og8OQY@g2] f \£¥] y OyEObgwEd cZ^Obg @ B C C CÃB Y&¥Obg8c wEdKg(ZY@yEZ O W OQY}cQ $ |%$ & k_= ? kF (
(104) %©
(105) 1 3 / » k³ª ? _BDkJB QF ®
(106) % .+ ? ¬ ?¬ . ,. -,. . ).. P
(107) E. @DF,B C C CDB. . . . ,. F . ,. &km >b ¶L&{ U K > u@]`Z^OQY`c m XObc yEOQm f@gZ^_YEdKc? f m Obg3gf m K Obc£m K ¢K\dgZ^_YEdKc1f m O gO dªyEZ^cOw@\f@g 8$Y@OjEf@O2\dªgZ^_YEdKcf O « wE]f k gZ\d _BÃkB LF ³wEd c8Z[c8Z[]@YyEOhP
(108) E{Obg8c w@\f@Jg 8$Y@Ojkf@O\d ? BÃkB m
(109) F ³wEd m cZ^cZ^]Y yEO)P
(110) E ? \[Obg] m y m Obg m ObgwxObabcZ <g Obc
(111) gf m K ObHc KJ&Y@O(n]f@OQY`cZ[abZ"d`f@aQfEY ]}* \[O F 5Q. . . . . . /. . . ,. ,. ,. ,. w£}f} wy _ ~ }fx ~/t {7x¢~ & | U © %L (
(112) %&)
(113) 1 k .+ % 1 ±d$ d(*&"S+, / Ã+
(114) ( # *( +,% +/ j+! ? kFy=>k "Sk³l« qLr. . . M @f \^\ $ ,|+, _ /&
(115) 0i &$ /
(116) &$ d k ? ?. 0. kFDF. . (
(117) %³
(118) 1 A
(119) º (*& 0$#&% k('&. . (8
(120) { § ° 0 "&%$
(121) p(§ ).! + 2).-'34 6,
(122) 7(p($u@]`Z^OQY``c k ObOc k yEOQf@m ab]@yEObgyEO P OQ* Pm OX\[]@Y@_f@OQm f m ]f@g`]@f@\[]@Y@ggd>`]`Z m gQ¥ Z^\? g]Y}c ObW jkf@Z^Gde\[OQY}cgsObcQ¢Ey§d`Y@g\<d + PdecZ^`O`¢@aQdK\^aQf@\[O fEY@OwEO Pf@cdecZ^]Y cOb\^\^Ojkf@O kJ= kFb r2d`Y@m g2\^OaQdKg,] #f N k#Ob"c km g]@Y`c ObW jEf@Z[KdK\^m OQY`c8gQ¢"Obc2jEf@O{yEOw@\f@g{Y@]f@gm ab]M YEYEdKZ^gg]@Y@gRm fEY@O gZ^_YEdecf Om c]`cdK\^mOQPOQY}c2yEZ^ga ZPRZYEd}Y`cOXwE]f k¢ \£¡f@cZ^\^Z^gdKcZ^]Y yEO{\£¥s\^_`] Z^c POXwEO PRObc y ¥]@i@cOQY@Z \dwxO Pf@cdKcZ^]Y . $ ] +*"¨ 0u@]`Z^OQY`c k ObHc k yEOQf@ab]yEObgXObW jkf@Z^KdK\^OQY`cgyEO,\^]Y@_f@OQf m ; Obc g]}Z[c fEY@O gZ^_YEdecf m O2c8]`cdK\^OQPOQY}c%yEZ[g8a m ZPZYEd`Y`c8ORwx]f m k{ ° >wEO m Pf@cdecZ^]Y / E % ab]yEJ O k{N¢ k -, g8Z[_@YEdKcf m O h\ 7 " PE ). . . . +. . 243L½265.
(123)
(124) !
(125) " # $ %& &')(* %,+-. / 0.+2
(126) 1 3 / +. «. 7 ? P E ? k"B F7= k B*\F \ > ,¤ && ? F u@Z2Y@]mf@g M `]f@\^]Y@g\^OP OQ* Pm O m ObW gf@? \^cdKcgd`Y@g d©N w m Z[] m Zgf ? m k{¢yk Obc (¢3Z^\s d}f@cP]yEZ[8§O m \£¡dK\^_`] Z^c PO`&(]f@gsY@]`cO ]Y@g k"B*P
(127) EaF.\£¥OQY@g8OQPi@\^OSR kB
(128) \F,BD\7^`P
(129) E$T . $ ] +*"¨#§ u@]`Z^OQY`c kObQc k yEOQf@ab]@yEObg yEO\^]Y@_@f@OQf m ;XObcg]`Z^c ©fEY@O2g8Z[_@YEdKcf m O` ° > ObW jEf@Z^GdK\^OQY}c / E % ab]yEJ O k{N¢ kJ , g8? Z[_@YEdKcf m O ? kB
(130) P
(131) E]F_= k B
(132) P
(133) E F dM ? kB
(134) P
(135) E]F Ma=e; wEO m Pf@cdecZ^]Y ? k{¢ k ¢ £F Uk!= ? k"F > , &$ ? F ºU > , &$ ?
(136) F ºU > ,¤ && ? F ºU > ,¤ && ? F ? \^_`] m Z[c M PO S ab]Y@ab\f m dc]f>m n]f m g>¢(gm d`f} y§d`Y@g \^O©aQdKgX] f N ? k"B*P
(137) EaF= ? kB
(138) P
(139) E F Obc M k"B*P
(140) E]F M ;"(o%Ob\d gZ^_Y@[Z 8§O d©_ OQW Y3O W dK\^OQPOQY`cjEf@O k ObO c k g]@Y`c ObW jEf@Z^GdK\^OQY}cgQ¢ PªdKZ^g jEf@O2\dgZ^_YEdecf m OY& Obgc wEdKg degg O yEZ^ga m ZPd`Y}cOwE]f m \^O,aQdK\^aQf@\yEO,\dªwEO m Pf@cdKc8Z[]@Y& . . .
(141) . . . . . . . +. .
(142) . . . . . . ,. _rfs. {!e£~!"e~$U¤ wy£~ ¡]x L£{/¤w£¢&~ x¡a!¢x#"x£{7U¤~. @u ]`Z^c km fEYªab]yEOm \^ZY.OQW dKZ m O`¢@g]}Z[c%fEY@OgZ^_YEdKcf m O m gf m m K yEZ^ga m ZPRZYEd}Y`cOwE]f m k{¢}Obc7g8]`Z^c fEYZY}G¬d Zd}Y`csg¬ f §? ]f@g PfEY@Z^gg]@m Y@gK y ¡fEY] yl Oc]`cde\$Y@]`cEO W ( m u@]`Z^c @ B C C CB m \d _m BDk"B F ³wEd cZ^cm Z^]Y yEO)P
(143) E f@Z^gjEf@O m Obg8cyEZ[g8a ZPZYEd`Y`c8O`¢ Y@]@f@g d>`]Y@g %m$ `¢Ky ¡d`f@c m O wEd m c g$Z H=;¢@dKl \^] g m XObc.c]}cdK\^OQm POQY}c.yEZ^ga ZPZYEd`Y}cOObc.Z^\&Y&¥Obgc7m wEdeg Y3(*ObW ) abObggdKZ O) yE¬ O + wx]f gf@Z^m O\^O{aQde\[aQf@\£ ]@f c]f@c8O wEd cZ^'O & yEOYR@B CC BaT@¢$Y@]f@gY@]`cO ]@Y@g = ,+ ¶ ¢@Obc wE]@f c]@f@c \y^YP
(144) E§¢ . 0 ? ) ? / 021 k 35476 b F,B 0 ? k 3 4 b F,B 0 ? k 354 b F.B 0 ? k 354 6 b F98 g8LZ \_^YP
(145) E;: (*) - k"B*\FU= < g8ZY@]@Y . 0. -,. . ,. . . . ½|½¿¾dÀ ÁÃÂÄÃÅ. & '. $. & '. $ & '. & '.
(146) |. (*& + $%& * . >d `mOba\d ab]@Y``OQY}cZ^]Y m ¬ + =g8Zm ³^ec R&B C C CBaT@¢ \£¡d`wEw@\^Z^aQdKcZ^]Y -) y%O
(147) W 8$m Y@Z^cfEmY@OgZ^_YEdKc1f m O gf m mR N < TwE]@f c8]f@cOwEd cZ^OS8$Y@m Z^O & yEO m m > ObW \1OQW POQY`c < gO dXwEd ab]Y}`OQY}cZ^]Y gfEw3OlW Z^OQf m dRc]f@c{ObW \1OQW PROQY`c%yEO wx]f c]f@c%] y O` ]f % c]f@c 2wx]`gZ^cZ ¢&Y@]f@g PfEY@Z^gg]@Y@g(\£¥OQY@gOQPi@\^O2yEObg wEd m cZ^Obg(yEOhR&B CCB aT(yEO\£¥] m y m O gf@Z^Kd`Y`c . M &HM M & M / &
(148) & " 0 ]f M &HMa=iM & MkObc +¶ ) +¶ )
(149) l ]f m fEY ab]yEO k yE]YEY.O W yE]Y`c\d ? _BDk"B LF³³wEd m cZ^cZ^]Y ab]PwE] m cO XwEd )m cZ^ObgQ¢7Y@]@f@g Y@]`m c8O m ]Y@g & \^O w@\f@gwEObcZ^cObW \OQW POQY}c{wE]f m m cOb\(jEf@OX\d gZ^_YEdecm f m O m = - m g8]`Z^c g? c Z^abcOQPOQY}cRmw@\f@Jg 8$Y@ON jkf@O ( d gZ^_m YEm decf O dKZm Y@gZ% y7
(150) O W 8$Y@Z^O wxO PObcc dyEOy7
(151) O W 8$Y@m Z fEY@O BDk"B QF ³wEd cZ^cZ^]Y&¢E] f Obgc2fEY ] y Oc]`cde\gf #K¢ w@\f@gJ8$Y@Ojkf@Oª\dXwEd cZ^cZ^]Y ¬ @ B CCB ¬ o M dKjEf@O £]`Z^g{m jEf@O¨Y@]f@gwE]@f m mm ]Y@g]i@cm OQY@Z m OQY©Z^cEO W m N d`Y}cabO¨w m ]abObgg1f@g m fEM Y@OXgZ^_YEdKc1m f m O c]}cdK\^OQM POQY}cyEZ^ga ZPm ZYEd`Y}m cO¨wx]f k¢"Z[\gO d wx]`ggZi@\^O dX\£¡deZ[yEO N yEObg{dK\^_`] Z[c PObgy%ObW a Z[c8mg w@\f@g m d`f@c%yEOsy7ObW cO Pm ZY@O g8Z$fEYªab]yEOsyE]YEY3O W kEObg8cObW jEf@Z^GdK\^OQY}c d k¢`Obc%gZ]f@Z£¢yEOsyE]YEY@O \dwEO Pf@cdKc8Z[]@YOQY`c OabObg yEOQf@ab]yEObg> _rq £~ £y~ ¡ax Ly{$¤wy¢~ (]f@gm d>`]Y@g(EfjEf&¡m fEY@OgmZ^_YEdKc1f m OwxOQm f@c Ob* c m Oab]@Y@gc m m f@Z^cO d{N m wEd m cZ m yEO,c]f@csZY}Gd m Zd`Y`c> o%ObcªZY}Gd Zd`Y`cªyE]`Z^c wxO PObcc O{y ¥]@i@cOQY@Z fEY@OgZ^_YEdecf OyEZ^ga ZPZYEd`Y}cO`¢%abOjEf@Z(Obab\f@g \^ObgZY`Kd m Zd`Y}cgcOb\^gjEf@O\d\^]Y@_f@OQf m m ]f \d yEZPm OQY@gZ^]Y&"r¡d}f@c m OZY}Gd m Zd`Y}cgQ¢¤cm Ob\^gjkf@m O\d yEZ^gcd}Y@m abOPZY@ZPdK\^O`¢&]fPm Z^OQf@OQY@m ab] O`¢E\dyEZ^gc ZiEf@cZ^]Y yEObgm wE]`Z^yEgwEOQf@`OQY}c wxO PObcc O\d ab]Y@g8c f@abcZ^]Y yEOm gZ^_YEdKc1f ObgyEZ[g8a ZPZmYEd`m Y`c8ObgQ¢"m c]f@cO1 £]`Z^gQ¢ \^] gjkf@OªN\d cdeZ[\^\^Om y§fXab]@yEO d}f@_K POQY}cO`¢EabObgsZY`Kd Zd`m Y}cg wxOQf@`OQY`csgQ¡md>.O W m O Obl.c m OQ* POQPROQY`c%yEZ +{abZ^\^Obg d,aQdK\^m aQf@\^O m M f@\^\< ¢"¥w@Z^y7\f@ObW g2Ow ObmgObcW abdeZ^gE\[OQ] W PgOQY`yEcO{\gQdd`yEwEZ^wEgc f@m h`ZiEO f@cg1Z^]f YX\yEd ObgwE]]`wxZ^yE]`gQg Z^c&Z^]O Y m ObW gf@Obc2\^cdKy c(¡f@g1cf@Z^\^Z[Z^Kgd`O Y}c2fEwEY OQf@ZY`c2KdKd Z^yEZd`O Y}mcdªN y§gf O ab]Y}GdeN ZY@a m O2jEf&m ¡fEYc8Ob\§ZY`Kd m Zd`Y}c wE]@f mm d Ob* c m O7yEZ^ga m ZPRZYEd}Y`csc]f@c3OQY m Obgcd`Y}c m Ob\decZ^`OQPOQY}c dKZ^gEO W daQdK\^aQf@\^O $ | H h%& " j+ O"a /$ %S 7%L (* % *1 & %J & ; +, 576 $%" D+ /(
(152) !+, $ Ã+3 ; $%a+ Ã+HD .± $ ª (* (*&!+, $ ,+, W1 » b!#" : b . ,. ,. . ,. . . . ,. ,. . . . . . 243L½265.
(153)
(154) !
(155) " # $ %& &')(* %,+-. / 0.+2
(156) 1 3 / +. . . ` º + º
(157) ! * ©% (
(158) %.+ *1 & ,+Y%& & ; + 5 6 ]&$ S % % " j+ Y%&$*1 ,+, W1 " / L$J(*&!+, $ Ã+3 ; /%a+H Ã+D .± $ "f1 ». . "Q= b 7@ : b C r2d`Y@g2\^OaQdKgi@ZYEdKZ m O ? :)= S&Fb¢&\dyEZPOQY@gZ^]Y©P]Kh`OQYEY@Oªy§f M f@\^\%ObgcOQY}Z m ]@YObW _dK\^O dN !C«` ¢@Obc "Q= @ 0 !C >E¢ !C x¢ 0! C¡ }S` >bb ¡m dK\^_`] m Z[c M PO.y%ObW a m Z^cmy§m d`Y@g"\m d(g8ObabcZ^]Y(Y@N O(wEOQf@c d`iE]f@c8Z m wE]@f m m c]f@c ab]@yEO`Gt3YO m ObM cQ¢QwEd m ab]Y@g8c f@abcZ^m ]Y&¢Z^\Y@N Owx]f d Ob* c m Od`wEw@\^Z^jkf3O W dªfEYab]yEO,yE]Y`c\[O_ ]fEwEOy ¡d}f@m c]P] w Z[g1PO Y&¥Obg8cpwEdeg ObW y§f@Z[c d,\d,gOQf@\^OwEO Pf@cdecZ^]YZ^yEOQY}cZ^cEO`W ¢@wEf@Z^gjkf&d`f@aQfEY@O2gZ^_YEdecf Osc]`cdK\^OQPOQY}c yEZ^ga m ZPZYEd`Y}cOY@Owxm OQf@M c de\[] m g(m Ob@Z[g8cO m m ? a1 l.m ]wEM ]`g8Z[c8Z[]@YS Fb M m md`f drO7fEY@w@O\f@yEgQZ¢>P\<dKOQY@\^_`g8] Z[]@Z^Y c cPOb\^O3\^OgOjEf@dOZPgdw yEdKZ^gcc Z^aQm Zd`iEi@f@\^O%cZ^a]YXdKyEjkObf@g2O° <wx]}]`Z[Z^g"yEjEgf@Y@O7O\^O wEOQf@f@\^c \EyEOb* cObm g"Oab]]i@yEcObOQg"Y@abf@]O{Y@abwEO d mY3Ob\[W O g aQdK\^aQf@\ ? yEZPOQY@gZ^]Y gfEw3O W m Z^OQf m O dN y§m d}Y@g(\^O2aQdKg i@ZYEdKZ m O F m o%OQwEOQY@y§d`Y}cQ¢&gZ.Y@]@f@g2Y@Oab]@Y@gZ^y7O W ]Y@gjEf@OyEObg2ab]@yEObg2dK\OQW dKc8]`Z ObgQ¢&d`f@aQfEYXyEOabObgyEOQf@ ZY@ab]Y}.OQmW Y@Z^OQY`cgY& ZY}cO m @Z^OQY`cOQYw m decZ^jkf@O`%r¡d}iE] m y ¢°m y7ObW gjkf@OX\d yEZPm OQY@M g8Z[]@Y0y ¡fEY m ab]yEO dK\1OQW dKc]`Z Oy%mbOQW N wEdKggm Osjkf@Ob\^jEf@m OyEZ QdeZY@Obgy fEY@Z[cEm ObW gQ¢Eg8]m Y_ ]l.fEmwxOy ¡d`f@c]@P] w Z^gPOObg8m c(c Z^@Zde\ d>`ObafEY@Oc Obg(_ d`Y@yEOw ]iEd`i@Z^\^Z^ckO`W &r¡d}f@c OwEd cQ¢\d ]@wE]`gZ^cZ^]YX~Y@]f@g2deggf OjEf&¡fEY ab]@yEO2a M ]`Z^gZ dK\OQW dKc]}Z m OQPOQY`c(Y&¡dªw m ObgjEf@Od`f@aQfEY@O,a M d`Y@abO,yEOwx]`ggObyEO m fEY M f@\^\"yEO2_ m d`Y@yEO cdeZ[\^\^O` . . _r. . . + @ +: . + =. . . . .
(159) . (. . ~ "¥£¡ ~ !{7}!wy}. ¡dK\^_`] m Z[c m M POy7ObW a m Z^c w@\f@g M d`f@c d ObW cEO W w m ]}_ m d`PP O(W OQY\d`Y@_de_`O2oObc(Ob.ObW aQf@cEO(W gf m fEY@O m gc1dKcZ^m ]Y yEO{c dQKdKZ^\.r2t3o L ` ` } `¬`` ` x &ObgcOQPw@gyEO{aQde\[aQf@\^g]@i@cOQYf@gg]@Y`c,yE]YEY.ObW gwE]@f yEZ^`O g8Obg cdeZ[\^\^Obgy§d`Y@g(\d d}i@\[O` 4 % 4 % + 3 &7Ob 0]&Y!+,? ( ¡ u& F ! + I o% ]Pª ,wEf@
(160) cZY@&_R d}f@ c]P*] m w M Z[g1P_ m ]@fEw@g7]e O m8m ] m ¦ab] m8m ObabcZY@_2ab]@yEObgQ ¢E`]`\£§S}|E¢EY z E¢EPdKZ.>`|`SE¢EwEw& } I ~E`} S u@OQ Y@ y m Z^%&O ,m + ? 2 L.1 [ +Fb I¨q1 Y c M O%gc m f@abc1f m O ]K $d m d}Y@yE]Pm \^hM wxO m m Pf@c? Obl y2ab]Y@aQdev cOQYEdKcOby,ab]yEO` x¢.ObW y EwEd o d w@ZY Fb ¦ £¢§wEw&&Q` I Q«`E I iEiEd>h`OyEO,\d %f@¯ ggZ ON m O,gf m qf@a M O`¢ m d`Y@abO`¢E]@abc]i m OQ} . . . . . . . . '&. ½|½¿¾dÀ ÁÃÂÄÃÅ. . . "!#. %$. $.
(161) Q . (*& + $%& * . @Y ]Pi m O y ¥Obgg1dKZ^g QS` Q ` Q ` Q ` Q ` Q ` Q ` . ;. > ` ` ~` ` > ` ` S` ` ~` ` S`~` ~` ` Q ` S`~` QS`~ S`~` ~` Q ` ~` L d}i@\[Os. cOQPªw@g ? OQYg8Obab]Y@yEObg*F P]Kh`OQY PZY@ZPfEP PdeZPfEP >!C¡S !« C «}! C¡ S}«!C¡S !« C¡ «} `! C¡ !S C¡ C >! C¡S !S C¡« C¡ x C¡« j C¡~` ! C` C¡ j C ! CE !S C¡« j CQ ! C Q j C . 7 $+%&(
(162) ( ! J%,+(
(163) %&,+-, $ ,+
(164) ¾ ¾ ! " # $%&' )(  &!+* ) !), .Ä - / 0 ¾ "1! #2*43$ ¾ ¾ !5 Å-NÁ 0 ¾ . u@OQY@v y m Z^O m ? , Fb m I Y J% !+, &Y J I v d`wEwx] m c(yEO v Oba M O m a M O2Y z S`|}`SE¢ ¦ £¢§]@abc]i OQ``~E u@OQY@y m Z^O m ? , Fb I # h+, *( h hY /%" !
(165) "
(166) %Y(
(167) $(
(168) $
(169) %)(
(170) %& I v d`wEwE] m c(yEO v Oba M O m a M OY z S } E¢ v ¢}nd`Y`@Z^O m >``~E $. . $. $. . $. 243L½265.
(171) Unit´e de recherche INRIA Lorraine, Technopˆole de Nancy-Brabois, Campus scientifique, ` NANCY 615 rue du Jardin Botanique, BP 101, 54600 VILLERS LES Unit´e de recherche INRIA Rennes, Irisa, Campus universitaire de Beaulieu, 35042 RENNES Cedex Unit´e de recherche INRIA Rhˆone-Alpes, 46 avenue F´elix Viallet, 38031 GRENOBLE Cedex 1 Unit´e de recherche INRIA Rocquencourt, Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY Cedex Unit´e de recherche INRIA Sophia-Antipolis, 2004 route des Lucioles, BP 93, 06902 SOPHIA-ANTIPOLIS Cedex. ´ Editeur INRIA, Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY Cedex (France) ISSN 0249-6399.
(172)
Documents relatifs
Dans chaque ville et pour toutes les lignes de tramway considérées, il faudrait disposer des trafics avant et après ouverture d’une ligne et de plusieurs projections d’évolution
Le fait d’écrire à partir d’une oeuvre d’art visuelle ressemble à une forme de contrainte; nous croyons par ailleurs que cette pratique a eu un effet durable sur l’écriture
variables d'ordre psychologique: soit f.amiliale ou personnelle, soit so- ciale, soit professionnelle, soit une combinaison de ces facteurs. Ce patient a récupéré
For the two coolest objects in Figure 3.6, HD 4539 and PG 1716+426, both at Ta < 27, 000 K, there is a good match between the predicted synthetic spectra and the FUSE data: the
lui inculquer le registre li'lquistioue, les l1abitudes alimen- taires et vestimentaires ainsi que le comportement des bour- geois de Québec. Pierrette Paul doit
La conciliation emploi-famille : des mesures à développer dans les milieux de travail Tableau 4 : Les dispositions favorisant la conciliation travailfamille dans les
Figure 2.4 Predicted (continuous lines) and observed values (filled circles: stands aged from trees with root collar; open circles: stands aged from trees without root collar)
Cette posture permet de dégager deux idées centrales : le poids des milieux professionnels locaux dans l’intermédiation et le transit des idées, modèles et pratiques
