Segmentation interactive d'images fixes et de séquences vidéo basée sur des hiérarchies de partitions
214
0
0
Texte intégral
(2)
(3) .
(4) .
(5)
(6)
(7) .
(8) .
(9)
(10) . .
(11)
(12) .
(13)
(14)
(15)
(16) !"#" $
(17) # %&' (!"#)* , - # . #/ "0 $
(18) #1 2
(19) * # *.
(20)
(21) +
(22)
(23) +
(24)
(25) +
(26)
(27) +
(28)
(29) .
(30)
(31) .
(32)
(33)
(34) ! " # $% & # " " ! $% !! $ ' ( " # " ' $% ' " ) ! ! " ' * + ) ' ( ! ! ', ' - . ) $ !( . ) $ ! )" $ # $ " ,! , ! # ( ' ) $ ' # / 0 # " 1 " % %% $' 2 % ( 0 " ) , % $ , ( 0 1 )!" ) $ *! '' ( 0 3" ) # !! ! ! ' ! ( 0 4 5 " ) $ ! ! '' " ) ! ! ', ' $ $ ( 0 # 4 5 " $ '' ) $ ) $' !( 0 4 " ' % , ' ,# * ) % ' , " . ' 6 ' ) ( 0 ' " ) ! ' ' 2 1 , $ '&! % ( 0 ! ) % ! ! ' !, " ) , % * 7 5 !* .( 0 8 ) " ) ! ! ' 6 2 $ ! ' ,# ( 0 3 " ' , ( 0 4 " ) ! ' ' % 9( 0 # " % ) $ ' ! , ' * / +:!# " ;!
(35) " < 8 " = " :, " ' 4 ( ( ( 0 $ ! ) $ ! ' " % ) $ '! # , ( # * * " ) 2 ' ( 1 " % . # '! 2 ' ' (. %.
(36)
(37) % ! ! !) %! ! ! ' ) . 6 ' . ( '' 2 , > ' . $ $ (. ' ? ., ! ' !' ' " !) ' ! ! * ' ,@ ! ( < ', $ ! !" % ) * ( $! ' ' + ' A 2 $ % ! ! & ) ! + $ ! ( ' ', ' ! ! ) " ! % . ( ' '" A! ! ! . ') ! ! " ) ' ! ' $ ' ) ', ( .# '" ' ! ! ' &. ! . !) %! '' B+ ! % ( " ) ! ! 2 !) %! '# ! ( $ ' '! ' 2 $ ' ! # % ( 3 - . ' ! * $ , ! " ' ! * % # *, C ! $ ' 7 ' $ ! ! (. %.
(38)
(39)
(40) '' " % * D + % > ( '' , ) , * ( % ? ., * ' " % ) ' * ' ( ', " * ' ( < % ' ' , * ( " ' ', & ( " % ' ? " A * ' D D %, ( " ' * 5 * % ) ( ' % ) ( % ' ' " ' % ( < ' * > ' * * " * ' % , , (. ..
(41)
(42) . E(E % ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( E(F $'' ! % ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( E(B # ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( (
(43) . F(E F(F F(B F(J F(G. ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ! $ ( ( ( ( ( ( ( ' ' $ . $, %! ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( (. ( ( ( ( (. ( ( ( ( (. ( ( ( ( (. ( ( ( ( (. ( ( ( ( (. ( ( ( ( (. ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( $ , ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ! ' $ , ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( :! ! ) ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( B(J(E ' ! ! ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( B(J(F M ! ) @ ' ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( B(J(B M ! ) ! ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( B(J(J #, $ ! ) ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( B(J(G $ ! ) 2 ' $ ( B(J(G(E $'' ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( B(J(G(F $'' ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( B(J(H ! ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( (
(44) ' ! ! ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( B(G(E O ) !& ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( B(G(F ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( B(G(B , . 6 %! , ' ( ( ( ( ( ( :! ' ,@ ! $ ( ( ( ( ( ( ( ( ( ( ( ( ( ! ' $ ( ( ( ( ( ( ( ( ( ( B(I(E '' ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( B(I(F '' ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( (. ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( (. ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( (. ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( (. ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( (. ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( (. . B(E B(F B(B B(J. B(G. B(H B(I B(K. .. ( ( ( ( (. ( ( ( ( (. ( ( ( ( (. ( ( ( ( (. ( ( ( ( (. ( ( ( ( (. ( ( ( ( (. ( ( ( ( (. ( ( ( ( (. ( ( ( ( (. ( ( ( ( (. ( ( ( ( (. ( ( ( ( (. ( ( ( ( (. ( ( ( ( (. E F B . G H I K L. EE EE EF EJ EJ EG EG EH EI EK FN FF FJ FJ FG FH BN BF BF BB BJ.
(45) . ! "!# $ %&!#. ' . J(E ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( J(F $ . ! ( ( ( ( ( ( ( ( ( ( ( ( J(F(E ' ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( J(F(F ! ,! * ' ,@ ! ( J(F(F(E , ) ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( J(F(F(F ' ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( J(F(F(B ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( J(F(B . ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( J(B % * $ ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( J(B(E ! $ % ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( J(B(F ' A! % . ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( J(B(B ' ( ( ( J(J ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( (. ( . G(E 2 % . ( ( ( ( ( ( ( ( ( ( ( ( ( ( G(F 1 2 % . ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( G(F(E P ' '! . ( ( ( ( ( ( ( ( ( ( ( ( ( G(F(F % ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( G(F(F(E !& ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( G(F(F(F ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( G(F(B % ! ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( G(B < %. ! % ( ( ( ( ( ( ( ( ( ( ( G(B(E % ' ' ' ( ( ( ( ( ( ( ( ( ( G(B(F % ' + ) ( ( ( ( ( ( ( ( ( G(B(B 1 !' $ ' % ( ( ( ( ( ( ( ( ( G(B(J
(46) ) ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( G(J % '' ' % % ( ( ( ( ( ( ( ( ( ( G(J(E 3!! ( ( ( ( ( ( ( ( ( ( ( G(J(F 3!! % ( ( ( ( ( ( ( ( ( ( ( G(J(B A! . !! ( ( ( ( ( ( ( ( ( ( ( G(J(J ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( G(J(G ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( G(J(G(E ! ! ' $ ' G(J(G(F ' . $ ( ( ( ( ( ( ( ( ( ( G(J(G(B ' ! ! ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( G(J(H
(47) ! ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( G(J(H(E . ) ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( G(J(H(F O ) . ' % ) ' G(G 5 ' ' 2 % . ( ( ( ( ( ( ( ( ( ( G(G(E P ' ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( G(G(F 5 )+' ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( G(G(F(E P )+' ! . % ( ( ( G(H < %. ! 5 ' ( ( ( ( ( ( ( ( ( ( ( ( G(I 5 )+' ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( G(I(E . $ ' ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( (. ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( (. ( ( ( ( ( ( ( ( ( ( ( ( (. ( ( ( ( ( ( ( ( ( ( ( ( (. ( ( ( ( ( ( ( ( ( ( ( ( (. ( ( ( ( ( ( ( ( ( ( ( ( (. ( ( ( ( ( ( ( ( ( ( ( ( (. ( ( ( ( ( ( ( ( ( ( ( ( (. ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( (. ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( (. ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( (. ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( (. ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( (. ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( (. . BG BG BH BI BI BI BK BL JN JN JE JF JB. '. JH JH JH JL JL GN GE GF GF GB GB GH GH GH GI GK HN HN HE HF HB HB HB HB HK HK HK HL HL IN IE.
(48) ! "!# $ %&!#. . G(K P ' ! . % ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( IB G(L ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( IB ) # * . H(E ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( H(F :! ! 2 '' ( ( ( ( ( ( ( ( ( ( ( ( ( H(F(E :! 5 ' ( ( ( ( ( ( ( ( ( ( H(F(F :! % ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( H(F(B :! ! ' ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( H(F(B(E " , % ! ( ( ( H(F(B(F $ ! ) $ ( ( ( ( ( ( ( ( ( ( ( ( ( H(F(B(B ! ! ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( H(F(J ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( H(B :! ! ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( H(B(E ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( H(B(F $ ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( H(B(F(E !& ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( H(B(F(F M ! ) ! ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( H(B(F(B $ ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( H(B(B ! ) ! , ( ( ( ( ( ( ( ( ( ( ( ( H(B(J
(49) ' ! ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( H(B(J(E $ , ) ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( H(B(J(F , . 6 %! ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( H(B(J(B ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( H(B(G ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( H(B(H
(50) '' % % $ . ( ( ( ( ( ( ( ( ( ( ( ( ( ( H(J :! ' ) ) ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( H(J(E 3 ' % ! 2 ' ( ( ( ( ( ( ( ( ( ( H(J(F $ ! ) ' ( ( ( ( ( ( ( ( ( ( ( ( ( H(J(B ' & ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( H(J(J
(51) ! ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( H(G % ' , ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( H(G(E ! % ! ( ( ( ( ( ( ( ( ( ( ( ( ( H(G(F :! , ' #, $ ! ) ( ( ( ( ( ( ( H(G(F(E ! ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( H(G(F(F ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( H(G(F(B . ' $'' ! ( ( ( ( ( ( ( ( ( ( H(H $* ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( H(H(E :! . . ') H(H(F ) ? ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( H(H(F(E !& ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( H(H(F(F ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( H(H(F(B . ' $'' ( ( ( ( ( ( ( ( ( ( ( ( ( ( H(I ! $ ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( H(I(E # 2 % ! ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( H(I(F ! ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( H(I(F(E
(52) ! $ , ( ( ( ( ( ( ( ( ( ( (. ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( (. ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( (. ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( (. ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( (. ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( (. ++. ( II ( IK ( IK ( IK ( IL ( KE ( KE ( KF ( KF ( KJ ( KG ( KH ( KH ( KI ( KK ( KK ( KL ( LG ( LG ( LH ( LI ( LL ( ENE ( ENF ( ENB ( ENJ ( ENI ( ENI ( ENI ( EEE ( EEB ( EEJ ( EEG ( EEI ( EEK ( EFN ( EFN ( EFE ( EFB ( EFJ ( EFJ ( EFI ( EFI.
(53) . ! "!# $ %&!#. H(I(F(F $ , ( ( ( ( ( ( ( ( ( H(I(F(B ! # ( H(I(B % ) ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( H(I(B(E % ) ( ( ( ( ( H(I(B(F % ) ( ( ( ( ( ( ( ( ( H(I(J , ) ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( H(I(G ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( H(K ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( (. ( ( ( ( ( ( ( (. ( ( ( ( ( ( ( (. ( ( ( ( ( ( ( (. ( ( ( ( ( ( ( (. ( ( ( ( ( ( ( (. ( EFI ( EFK ( EFL ( EFL ( EBF ( EBJ ( EBJ ( EBH. I(E ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( I(F $'' ' % ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( I(F(E ' ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( I(F(F ,# ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( I(F(F(E > ! 2 ( ( ( ( ( ( ( ( ( ( ( ( ( I(F(F(F ) ? ., ! ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( I(B :! ! 2 !) %! ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( I(J $'' B ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( I(G ' '! ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( I(G(E ' ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( I(G(F $! ' $ ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( I(G(B $! ' ' ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( I(G(B(E ' & ( ( ( ( ( ( ( ( ( ( ( ( ( ( I(G(B(F ! ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( I(H
(54) ! ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( I(I ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( I(I(E Q% , R ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( I(I(F
(55) ! . $ ' ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( I(I(F(E ' ' % ' & ( I(I(F(F 1 % ! ( ( ( ( ( ( ( ( ( ( ( ( I(I(B '! ' % ( ( ( ( ( ( ( ( ( ( ( ( ( I(K % $ ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( I(L ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( (. ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( (. ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( (. ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( (. ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( (. ( EBL ( EJN ( EJN ( EJN ( EJN ( EJE ( EJE ( EJB ( EJL ( EJL ( EGN ( EGN ( EGN ( EGE ( EGH ( EHH ( EHH ( EHK ( EHL ( EHL ( EIE ( EIE ( EIF. ( ( ( ( ( ( (. ( ( ( ( ( ( (. ( ( ( ( ( ( (. ( ( ( ( ( ( (. ( EII ( EIK ( EIK ( EIK ( EKE ( EKE ( EKF. + # , . . ( . K(E ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( K(F ;3M ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( K(F(E $ * ') ( ( ( ( ( ( ( ( ( ( ( K(F(F % $ &. K(F(B % $, ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( K(F(J ! % ( ( ( ( ( ( ( ( K(B $! # 3+J ( ( ( ( ( (. - / . ( ( ( ( ( ( (. ( ( ( ( ( ( (. ( ( ( ( ( ( (. ( ( ( ( ( ( (. ( ( ( ( ( ( (. ( ( ( ( ( ( (. ( ( ( ( ( ( (. ( ( ( ( ( ( (. ( ( ( ( ( ( (. ( ( ( ( ( ( (. ( ( ( ( ( ( (. ( ( ( ( ( ( (. ( ( ( ( ( ( (. -. ++. .. L(E '' # ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( EKB L(F ' % ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( EKG.
(56) ! "!# $ %&!#. . . .+. (E !& ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( EKI (F '' 2 ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( EKI (F(E ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( EKK. . .-.
(57) . ! "!# $ %&!#.
(58) .
(59) . . 2 % ! * # " & ! ! ! A! $'' ( . ' " # % ' ' , ! ' . ! ' ,# $ " ) '' " ! ' ! !, (. '!" %! , ' $'' . !.( ' $'' " ! ' ! ) ) ' % 6 .' ! ' ' $ ) ' * ( + " ' ) '' 0 ' . ' ' $ ' '" $ '# " $ ' ' 0" )$ !& ' ! ) $ 2 (. ! " % !% '' % $* ', ! $ ' ' " ) $'' $'' $)+ $ %! ! ) " % . , !% ''!( % '' $ ' S % $! !( ) ) . ' / 0 ', ! $'' ' ' %! ! ) !! ' '' ! 2 $! ' ! ( S # ' ' ' % # 2 ' ' ( '' $* ' ', ! $A ) . 6 !! " $ ! # % - # ( 0 3+J TBHU" TIIU % * ! ,! !' #
(60) ( M , % !& ! ! ) # ( 3+J '!& ' ) 2 ' ! !' ( $ ! ' + ) * ! !' ! ', ! $ ' * ( 0 D ! ) ) ! $* , $ . $ ' ! 2 . ( 3+I THKU ' !" ) * ' ! ( E.
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
(62) % $ ! ! ' ( $ +2+ )$ % ) ' ! 2 " * ' ,@ ! ) ' ! $ 2 A! % . ! (.
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
(64) '. . ! ' ! ! * $ , . 6 %! " ) ' # # ' . A! % . ! ( 1 " ' I ' ' ! ! ' &. ' % 6 ! $ * ' + ,@ ! ! 2 !) %! '# ( ' ! ! ! # . 6 > " ) ' 2 $ !) %! '# % # ' $ A ( ' K # ' ' % + ' ) ' ! ! # " ' L ' ' ) ) ' * ( $! ' * ! % ' ! ) ' % !*! ' TKKU" TKLU" TLHU(.
(65) .
(66) . . . , $ ! ! !, ! ! !* ( + ' " . $'' ) !" % ! ! ! )$ ' ) ', % !% '' ' ! 2 '' 2 ' $ ( ' $'+ ' . ,W ! ) $, $ ! 6 (
(67) ' . ' # & F(E( . " $, $ ! 6 ' 6 $ " * . *! ( " '' !! ) $ $ ' ! ! , ' ! ) $! ) ! % ) ' ( !% '' % '' ! * %! A ' $ % ( ) ! $ # % ! ! ' . ' ' + '.( ' ) ! $ , ( ! " % '# ) " % % ) # > ' % ( .# ' ' $ ' !% ( ' % !! ' ! # ' $ ! ' ) # *( ! %%." ? ., ' ! ' # $ # % ( # % ' % 6 ! . ' ' % A! / 0 $ , V 0 # $ $ # ' ( . ' !! ' '# ! " # % " $+ , ! ! ! $ ( F(F ' ! ) ) + ! ) $ % )$ , # *( F(B # * . ' % ! $ ( F(J * !% # * $ . $, G.
(68) ).
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
(70) 0 . +. ! ,! 2 ! 5 $ ( ' $ " * [ D \ TBJU !& $, * $! , ( * '! $ $! ) *% ! ! * $ ) ' ! * . !& ' $ ( ! $% ' # ! " $%! !' ' ' # ) $ $ ( TEHU ! ' $ * C ) !' !! % 2 ) ' ( ] A! *" # ' ! ) , ( ' ' " ! ! ( $ ) ,! ' # ! 5 TLU" ' '') * ( 4 C ) ' ! ' % 6 ,! % ! ! & $! ' * ' % TIHU" TJFU(.
(71) # % ' '! % ,! ) ) . ) ! ' $ X ! ( $ )$ ) ) ! ) ! ! * ) " $ '' ) ' )$ % ! # $ .' ' ', ! $ 7 ' 6 *( A! *7 $ ! ! ' '! ! " ) '')! ( 2 ' $ ' 2 ' # TLIU" 2 ) # , $ ! 6 TIFU" TEEEU" TFGU 2 ) ! $ ! ) ) ,, 2 ! ' $, TEEU( $ % .! ' ? ., " ') $ ' ' ' !% !' $ 2 ( !' $ ' * " ! # !, ( ( 2 $ % $!% $ ( '' ,! " $ ' 2 2 $ 2 ' $ ' THBU" TEHU ( ! ' !' ' ( ) " $ % ' $ ' % ( '' ,! !" $ ' % ! ) A! ! $ TIKU" TENKU" TENLU" TJJU( M % ' ' 2 ' % ! # " ! ' !, ' $ " ) $, $ ! 6 TENU( $ ' $ .! ' ? ., ' ) $ @ ! " ) '! 7 ' $ % !( 1 2 2 ' $ " ) ' & ! " + ) TEGU( " $ $ ' @ $!% ! )$% $ .
(72) ..
(73) . ' .! (.
(74)
(75) ! $ ' ' % ' % ! ! $'' 3+J THGU" THJU 3+I THIU" THHU( . " !+ ' ' ! ! !% ''! ) ' , $ . " % ) " $, %! 2 ' !) ' 6 # % !( ) $* + * ) '' % ' # , ' ! ( ! % ) ) + '' % . " '' # ! % # ( . ' $'' ) ! TJLU TENFU( '' # *" $ ' # !) " & !& $, $ ! 6 ( " , ) % !) ( !! " ' ! 2 $ $+ ' $ .! ' * & ) ! , ' * ( TEEU" % ! ) ! ' ! ) '. $ ( $ ' $'' ' # !) ' $ * ! ' ,, ! ! $, ( '. ,! 2 ! ' ) ' ,, ! $'' # ' ( ! , ' ! . ( 4 ) ! ! ! ' # ' '! ' % " $ ) ' $ $ ' # % " $ 6 ', ' , ' ' ! *" ! ' !% ' ! ' * ( M # % ', ! $ ! . ! ! ! ! ' '! TIFU( TENU" % ! ) ! ! ' ! '. $ ( M ' [ *55 + \ % . ! '. !( $ !) " $ .! ! ' " $ ' t − 1 % $ 2 $ ' $ ' t( $ % $ $ )$2 &" ) $ " ' ! %! " $, ( $'' ' ! ! TFGU 2 $ '' . * $, ' # !) ( % ! ! ! 2 $ ! 2 $ . ! ! ) $ & % . $, ' # !) ( " $, % ) '' ' % % $ ' . ' ) 0 6 # ) ' # 0 % ! ! ! 2 $ ! 2 $ . ! ' !( $ ! ! . ! 2 $, ) ' ! ! ! ' '! ' ) # # TENIU" TENHU( ) ' '! TEEEU ' 6 ' $ ( '' . * ' $ ! $ *.
(76) 0 " . -. & % . $, ( $ ! ! ! # ) !( $! ' %" ! ' ! % ! ) ' % ! $ % ( ! TFHU " $ ', ! $) ! ) ! ) $, ) !( ! ' ! ! ' $, !& ' $ ' # ( % 6 * ' %" ! ' % * (. " # 4 ' ! % ! ! !% ''! 2 ' $ + ) ) ! ' $ ! ! ! " $ ' # $ " ) , ! ( ! $ + ' ! % ' ,# / 0 , @ * $ + Y ' ' $ ' # Z V 0 ' !%, ! ! V 0 ) ? ., !" ) , 2 * ! ' * (. !) %!" % % ) $'' ' % ' * !+ ) ( M %! $ ' ) # ' ! 2 ! * ) $ ,! ' % $ ' $ .! Y) ' 6 # Z( ! & '% $ 6 $ ' * ( " ', ' $ ' ' ! + * 2 ' ' # , ( ! $ ) ' ! # 2 '' 2 ' ,# (.
(77) 3.
(78) .
(79) .
(80) ! . . ' ' ! , ! ) % ! ' $ , ( ! ' ,@ ! $ 0 ) # % ,! 0 ' ( ' ' ' " ' H I" ! '!&) ' ! ' ! !) %!( ! ) ' $ , I % ! !!+ i ∈ I ( 7 ' " B(F" $ , ( " B(B ' ! ! ' $ , ( B(J $!)% ! ! ) " ) ' *7 * + ! ! ) ( ' ! ! " B(G" . # ' ! ! 2 $ ' / $ , . 6 %! ( B(H ! ' ! ! ' ! ' ,@ ! $ ( 1 " ! % B(I ) ) + ) ! ! + (.
(81) ' * ! ' 4 5! TBU ' !& $ , ! ( ) ' $'! ∧ $ ) ' $'! ∨( $ . !! % , '! $!! *! $!! '! ( a b b
(82) a a b( $ . ' $! !( " ' ≺ , . $! !" a ≺ b ( "* 0 A A 4 ∀a, b, c ∈ A. ab ∧ bc ⇒ ac. ∀a ∈ A. aa. EE. YB(EZ YB(FZ.
(83) . . "* 0 A A . . ∀a ∈ A. aa. ∀a, b, c ∈ A. ab ∧ bc ⇒ ac. ∀a, b ∈ A. ab ∧ ba ⇔ a=b. YB(BZ YB(JZ YB(GZ. ∀a, b ∈ A. YB(HZ. ab ∨ ba.
(84)
(85) . $ +2+ " , $ " ' $!! $ , ' 6 ' ! ( "* 0 A
(86)
(87)
(88) .
(89) . YB(IZ $ +2+ )$ , $ $ , ' !! " $ , ' !! !( ∀ a, u, v ∈ A. au ∧ av ⇒ uv ∨ vu. 0
(90)
(91) !
(92) " . #
(93)
(94) .
(95) . " A " ! . ' !! u v $ !! a ∈ A( . !& B(B ') ) u v" v u" $ ' !# * ! $ ( . %! &! ! " Y. B(G $ Z u = v ' !! * ! ) (. "* 0' $
(96) A
(97)
(98)
(99)
(100) !
(101)
(102)
(103) A Som(A) = {a | (a ∈ A) ∧ (∀b ∈ A : a b ⇒ a = b)}. "* 0 %
(104)
(105) &
(106) ! T er(A) = {a | (a ∈ A) ∧ (∀b ∈ A : b a ⇒ a = b)}. "* 0) .
(107) "* 0+ A ⊂ P (I)
(108)
(109)
(110) I I ! 2
(111)
(112) &
(113)
(114) . ∀ a, b ∈ A,. a ∩ b ∈ {a, b, ∅}. YB(KZ. 2
(115) &
(116) .
(117)
(118)
(119) ∀ a ∈ A,. ∪ {b | (b ∈ A) ∧ (b = a) ∧ (b ⊂ a)} ∈ {a, ∅}. YB(LZ.
(120) 0 . . "* 0. '
(121) A
(122) . . support(A) = ∪{a | a ∈ A}. '' A I " ) A I ( M ! ' * !! . , 2 !! ( ! & ) {i} ∈ A(
(123) ) ) {i} ∈ A" $. ! Y. B(LZ % ' ?" !! A ' 6 , ' !! ! {i} ( ) ! . ! & I Y I ∈ AZ( M ! & I ! ( ! " I ∈ A ∀i ∈ I : {i} ∈ A( 0
(124)
(125) A
(126)
(127)
(128)
(129) . ⊆ . " A " $ # . ' !! u v ) ) $ !! . a ∈ A". % ')$ a Ya ⊆ u" a ⊆ vZ( " ' $. B(K u ∩ v ∈ {u, v} Y ! ' ' .Z ' , ' " $ +2+ " u ⊆ v v ⊆ u" ) ' 2 !& B(B( "* 0- * A
(130)
(131)
(132) ∀ a, b ∈ A. a ≺ b ⇒ ab. YB(ENZ. $ +2+ " a b ' $ ! ) " a + b ' $ & ( $ , A '' ! *( $ & ' 6 !& ' '' A R" '' ! * " ) ∀ a, b ∈ A. a ≺ b ⇒ f (a) < f (b). YB(EEZ. $ & % ! 2 ) % ! + ( O A ! ' I " ' ' ''!+ 2 * f / f (I) ≤ 1. . f ( {i} | i ∈ I) = 0. YB(EFZ. " ) f 1( M # ' % N E" % N ' . !! !(.
(133) '. . $ % "* 0 3 d I , . ∀ i, i ∈ I. i = i ⇒ d(i, i ) > 0. ∀i ∈ I. d(i, i) = 0. . ∀ i, i ∈ I. d(i, i ) = d(i , i). ∀ i, i , i ∈ I. d(i, i ) ≤ sup(d(i, i ), d(i , i ) ). YB(EBZ YB(EJZ YB(EGZ YB(EHZ.
(134) ) ) $. B(EH ' * ) $! ! ( ] ' ! ) " '% !& , Bo Y, % Z Bf Y, * ! Z c ρ / Bo (c, ρ) = {i | (i ∈ I) ∧ (d(c, i) < ρ)} Bf (c, ρ) = {i | (i ∈ I) ∧ (d(c, i) ≤ ρ)}. YB(EIZ YB(EKZ. 0 %
(135)
(136) # " . (. A " ! . ' i, i ) ) '' 2 , * ! Y '( % Z ρ c( " $. B(EH" ) . ' 2 $ ! , " / " . d(i, i ) ≤ sup d(i, c), d(c, i ) ≤ ρ. ) & ) . ' ) ) '' 2 , ' % 6 " '" !! . $ ! ( " . ' ' !! Y!& # Z . 2 ! ( 0' )
(137) #
(138) " B(c, ρ) , * ! i ' ) ) , ( ) i ! B(c, ρ)( % B(B ) ' '' 2 B(c, ρ) 2 *! ! 2 ρ i( " B(c, ρ) ⊆ B(i, ρ)( 2 ' ! $ % B(i, ρ) ⊆ B(c, ρ)( i ∈ B(i, ρ) ) i ∈ B(c, ρ)( ] ' $! ! ! ) " / d(i , c) ≤ sup{d(i , i), d(i, c)} ≤ ρ. ⇔. i ∈ B(c, ρ). 0 * .
(139) .
(140) " . , % " * ! ' . $ . , " !) ) (.
(141) 0' 5 ,. . ! . ' $ ! ) d @ ' i0 , i1 , . . . , in ( % %! &! / d(i0 , in ) ≤ sup { d(ih−1 , ih ) | h = 1, . . . , n }. YB(ELZ. $ +2+ ) . . ! ! $ @ . ! ' @ ( ! ! ' * ) $! ! " ! ' ! n Yn = 2 ' 2 $. B(EHZ(. . ! ! &! A ' $ , I $ # f ( ' !& d . !! i, i I ' ' f ! ' ) . !! i i '' 6 !! A" a(i, i )( '' !! a ∈ A . ! ( ' ' i i a(i, i ) = inf {a | (a ∈ A) ∧ (i ∈ a) ∧ (i ∈ a)}. YB(FNZ. ' $ & !! ! / d(i, i ) = f (a(i, i )). YB(FEZ. $ . $!! a(i, i ) I ∈ A Y$ , ' ! ' $ , Z( $!! a(i, i ) , ' + i i ( $!! a(i, i ) $ . ' Yi ∈ A i" i '' 2 A! Z" i i !& ! & ( !& ! ) ( %! & " > %! & ) ∀ i, i , i ∈ A. d(i , i ) ≤ sup { d(i , i), d(i, i ) }. YB(FFZ. A " a(i, i ) a(i, i ) . $!! i" ) ') ) $ . , $ Y. B(K ! Z !) !! i" i i ( ! ) %! &! " ' 6 !! /.
(142)
(143)
(144) i i . "
(145)
(146) i i i . (
(147) !' ) " ! ! , & I $ ! ) d" ' !& ! ! ' A ' !! . ! , ! ) 2 ) !! , ' ' ) ( A " $ , , $ ! ) %! & . B(K B(L( $. B(K * ') . , $ ! ) $ $ " !) ' ' . $ , % ( $. B(L * / $ ' , ) ) r" Br " # $ , , ' $.
(148) ). . ' , *! 2 r" " ' ' ' ! ! $ ! ) % ' !! " ) , , !' ( !) " ' )$ , ! ) ' $ ' Y , % * ! ' ' % d = 0Z" $ , , !' Br (. , * I * 4 * ,( !& $ ! ) 2 ' . ! > ' ! ) . !! $+ & ' ' . !! " ' !& ! &! 2 ' ! ) > ' , ! & ( ! ! 2 d * ! & " $. B(EB $ ! ) $' Yi = i ⇒ d(i, i ) > 0" ) ') ) , !! !Z( ' . ' $! ! Yi = i ⇒ d(i, i ) ≥ 0Z" ', ! $% , Y% ' & ! Z ' $ !! I " ) ' % % ! A ) ' & (. " # $ % . A! ! ) dk ' % 6 !& 6 , ! I ( ' $ *7 , ' , % ! ) " ) 2 % ! ( # , * %! & ) !& d(i, i ) = sup{dk (i, i )}. ∀ i, i ∈ I. k. YB(FBZ. ! ) " ) ' , ' ! ) ( ' ! / ' $ ! ) # . !! A! !' % ! A! ( " . !! ! ! ! ' $ ( 6 , " ! ) d(i, i ) = inf {dk (i, i )} k. ∀ i, i ∈ I. YB(FJZ. $ ' ! ) , !& ' ! ( ] $ . ' " ! , A * ! ' ' a, b, c" ) . ! ) d1 d2 ! ! !& / d1. d2. dinf. " , E F E " B F F ," B E E 4 ) d1 d2 %! & ! ) " $ ' ' dinf " ') dinf (a, c) sup{dinf (a, b), dinf (b, c)}( ' " % B(J(G ! ) 2 ' $ ( " 6 ! ) !& ' inf .
(149) 0' 5 ,. +. ! ) $ ' ! ) +6 " ' 6 * ! ! ) ' ' $ ! &! ( ' ! ' . ' $ ! ) *! . 0 '' ! ! ! ) + 0" $ +2+ ' ! ) ' ' ) dk ( A " * ! ) *! . dk $ ' % " ')$ $ ! ) ( ' $ ! ) + ! ) " ) ' " ' ! ) *! . dk " ' ( , M . ') ! , , . $!! 2 ) !! dm % !& # % / dj ≤ dk. ⇔. ⎧. j k ⎪ < d d ⎪ 1 ⎪ ⎪ 1 ⎪ ⎪ ⎨ dj = dk 1 1. (( ⎪ ⎪ ( ⎪ ⎪ ⎪ ⎪ ⎩ dj = dk 1 1. m m (dm 1 , d2 , . . . , dn )(. $ . . dj2 ≤ dk2 . dj2 = dk2. .... . djn ≤ dkn. 4 " ' '% !& . ') ! )$ $ ! ! !& dk ( ' ' ' ,# " ') dk ! ) " , ! ( $ . ') ' 2 $ / ' ' . !! ' A " $ ! ! .# " ( . ' $ ! ) $ ' ! ) " $ . ' % / " , " ," . d1. B B F. d2. dlex. B YB" BZ F YB" FZ B YF" BZ $ % ) dlex(a, b) sup{dlex (a, c), dlex (c, b)}( 6 # ) ' $* $ ! ) " B(J(G ', ! . ' , ) ! " ! ) " ' 6 (. & ' % ( % . % " ! ! , I % ! !! " ' ' $ ! ) " ' Y !Z s !! ( "* 0. $
(150) I
(151)
(152)
(153) s
(154) I I × I ∀ i, i ∈ I. i = i ⇒ s(i, i ) > 0. ∀i ∈ I. s(i, i) = 0. . ∀ i, i ∈ I. s(i, i ) = s(i , i). YB(FGZ YB(FHZ YB(FIZ.
(155) .. . ' $ *7 ! ) d 2 ' $ s( Q ! s" ', ! ) d 2 % $!)% ! ) ! &! ( 4. , * , 7 / d(i, i ) = f (a(i, i ))" f (a(i, i )) $ . & a(i, i ) ! " a(i, i ) ' ' i i ( . . ) ' ' ' ! 2 ' $ s / ! Y[ , +' \ Z ! + Y[ '+ \Z( ! ' ! ' % + !! 6 $ s( ! ' $'' " ! $, ' % % )$2 , # ' !! !( ' ! * 6 ', ! . a, a ∈ A 2 ' $ ! s(i, i ) !! ! i, i ∈ I ( " $ ! " ) '' r(a, a ) *+ $ ! !! s(i, i )( A! !& * # 2 ! A! 2 ! ) A! ( O * r(a, a ) Ya, a ⊂ b ⇒ r(a, a ) ≤ r(b, b )Z * ' 6 ! & f ! ) Y '' ) $ & 6 * % ! Z( O r(a, a ) $ ' * " & 6 !&( , " > ' $ * & " $' ) * " ) ' , ' * ! $ %( Q ! !! ! s(i, i ) r(a, a )" ' ! , ' , 6 ) , ' , ( !' 2 ) " % ' ( 0'00. . $'' ! ' $ B(E( M !&" 2 ) ! . ' ' '! ( ) ) . ' * ! ' !& ! " r(a, a )" 2 ' $ ! !! I ( 8 , 4 M ', ! ' !& $ . 2 ' $ !! ! 2 ' $ !! ' ' ( $ +2+ / r(a, a ) = inf {s(i, i ) | (i ∈ a) ∧ (i ∈ a )}. a, a ∈ A i, i ∈ I. !& " * / ∀ a, b, c ∈ A. (a ⊆ c) ∧ (b c) ⇒ r(a, c) < r(b, c).
(156) 0' 5 ,. -. 0 $ ! . , $!! T ableDissimilarit´ es ← ! ' $!! n←. 9 n > 1 ai " aj ←. < % YT ableDissimilarit´esZ
(157) ' Yai " aj Z ^
Documents relatifs
To test whether the vesicular pool of Atat1 promotes the acetyl- ation of -tubulin in MTs, we isolated subcellular fractions from newborn mouse cortices and then assessed
Néanmoins, la dualité des acides (Lewis et Bronsted) est un système dispendieux, dont le recyclage est une opération complexe et par conséquent difficilement applicable à
Cette mutation familiale du gène MME est une substitution d’une base guanine par une base adenine sur le chromosome 3q25.2, ce qui induit un remplacement d’un acide aminé cystéine
En ouvrant cette page avec Netscape composer, vous verrez que le cadre prévu pour accueillir le panoramique a une taille déterminée, choisie par les concepteurs des hyperpaysages
Chaque séance durera deux heures, mais dans la seconde, seule la première heure sera consacrée à l'expérimentation décrite ici ; durant la seconde, les élèves travailleront sur
A time-varying respiratory elastance model is developed with a negative elastic component (E demand ), to describe the driving pressure generated during a patient initiated
The aim of this study was to assess, in three experimental fields representative of the various topoclimatological zones of Luxembourg, the impact of timing of fungicide
Attention to a relation ontology [...] refocuses security discourses to better reflect and appreciate three forms of interconnection that are not sufficiently attended to
