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Can a non chiral object be made of two identical chiral moieties?

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(1)Can a non chiral object be made of two identical chiral moieties? Jean-François Le Maréchal. To cite this version: Jean-François Le Maréchal. Can a non chiral object be made of two identical chiral moieties?. Journal of Chemical Education, American Chemical Society, Division of Chemical Education, 2008, 85 (3), pp.433-435. �hal-00267557�. HAL Id: hal-00267557 https://hal.archives-ouvertes.fr/hal-00267557 Submitted on 27 Mar 2008. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

(2)   

(3)    !#"$%& '( )  &*+(&-,/. 01 24365781:94;)<=1?>A@@CB D*EF?G'HAII J#HAICKA1 0L5-M:NO P(MNQRAS&TVUW5/XZY\[]942_^`YaU bcNSed5PfT(Shgji;5kUlRANDm]=Rno5qprR*Pj7`Mn&5%s<AtAiP(So5L<AP(5;5kU_l6RCN6D HAu`Mnvni5;'wox#gjMnoS5DCuyIuHADUzc{kprD)O'[Y]pr2_9 |~}L€oL‚ƒ€ sA5/dA5P(Mn't'5-;M„AR*„ASo=Mn R †‡5?=/g(T]=MN 5\< Tˆ5;g‰R;S&T(=L<ŠTLT4=3SoP(Mn&Shg‰l16^$5P(5-D‹$5\< Tˆ5\g‰35%=L<gRŒMNMttCn5 g‰RŽTj3R‹g‰3M/gg‰35M)TLT(RA=SoM/gjSoRN‘RŒ’S&;5N?g“So=-M:n”=3S•P(Mn–7`RASo5/gjSo5)TZ=MN‘Œ‰RP(7 M—N6R*N˜=3SvPˆM:nR †‡5=/g‡1 {=/gjM35-;P(MnA=:3S™PfMnoShg‰lrSšT!< T(5;~gjR%Œ#SoNA;›T(Shg+<M/g‰SeR*N'T5-œ)<'S•dMno5N)g g‰Rg‰35=/<gR*Œ'g‰365MttCne51 žŸ# ¢¡¤£ L¥ ¦ sA5=RN;J#zc5MP§bcN;5Pj„P(M;)<M/gj5D–x“N6R*Pj„MNS=¨2k365:7rS+T#g‰P“l6D©YNMnoR„CS5T(Dª2kRRP(;SoNMLg“SoRN 2]R*7ctAR6<AN6;TˆDC2q3SoP(Mn&Shg‰l6DC{=/gjM365;P(MnA=3SoP(Mn&Shg‰l6D69WNMN)gjSR*7$R*P“t36Dsl67›7r5/g‰P“l6D6«cSoN„ w#T=/<g  v#¬ x#gS&T”=RC7`7`RCN tCnM=5­‹`35N§gj5M=3SoN„®=:3SoP(MnShg#l¯gjR°<T(5±7rM/gj5PjS&Mn`R †‡5=/g(T8g‰R—Sonne< T‰g‰P(M/gj5©g‰365±So;5MT SoNdARCn•d5;8SoN›g‰3S+T];RC7`MSoNRCŒ=357rSšT‰g‰P“l'1A2]3SvPˆM:nShg‰lSšTqg‰365~tP(RtA5P+g+l8RŒ7`RCn5=/<n56T4R*P4R6 †(5-=/g(T_‹`3S=3 MP(5’NRN—T#<AtA5P²So7`tAR'T(M An5³RN´g‰365:S™P

(4) 7`SoP“P(RP(J#So7rM„A51qµ¯3S&n5’tAM:SoPfTRCŒ`=3SoP(Mna¶c·¸&¹º»¸¹¼’MPˆ5³=Mn&n5; 5N6M:N?g“SeRC7`5PfTˆDŠt'MS•P‡TRCŒ]=3SoP(Mn½¶¾¿v¹ÀLÁv¾A¸·AÂ&ù?º?¿•¼D_T‰< =3’M)T\=P“l'T#gjMn&TˆD_MP(5›=Mnn&5-;©5N6M:N?g“SeRC7`RP“t3CT%ĉʼnÆ'1 Y`T~ŒjMPM)Tc7`RCn5=/<n5TMP(58=RNA=5P(N65;D_=3S•PˆM:nShg‰l³n5?M;'TagjR

(5) g‰35›tP(RtA5P+g+l’RAŒk 5SoN„­Rtg‰So=MnnvlªM=Lg“S•dA5-D ‹c3S&=3®=R*NAT(S+T#g(T–SoN— 5SoN„ÇM An5´gjR—PjR)gjMÈgj5©g‰365´tAnM:NA5ZRŒ8tARCnoMP(S•É 5;—nSv„A3)g‡1csC5LdA5P(Mn`5Ê*M:7`tAn56T”RCŒ 7rM/gj5P(SoMnR †f5-=/g(Tk<!T(5-;ËgjR–35not

(6) gj5M=38g‰358=RN=5tg¤RŒ~T‰<AtA5P(Sv7`tAR'T(M AS&noShg‰l’3AMdA5› A5-5:NtP(5T(5N?gj5;–S&N g‰3S&TÌ·»Àf;A¸j1qÎV3S+Tr=R*N6=?5tgjD4‹c3So=3±S+T`tAS•dARgjM:n¤Œ‰R*P`n5MP(NSoN„Ï=:3S™PfMnoShg‰lADa36M)T 5-5:NZSoN)g‰P(RA;)<=5;³ Al M)TjÐCSoN„ÑT#g+<;5N?g(T³g‰RÒ=RNCT(Se;C5P³g‰365—tP(RtA5Pšg‰Se5)TZRCŒ–g&‹$RÓSe;5:N?g“Se=Mn

(7) ARAR*Ð'T’g‰3MLg­=-MN¨no5?M;Ôg‰RÔg‰35 =RN=nh<!T(SoRCN›g‰36M/gVg‰35~ ARARÐ'T¤MP(5DSoN;55-;Dg‰35›TˆM:7r5›ÄÖÕ²Æ'1{kg‰35P¤5/Ê*M7tAn5)T¤RŒ_tA5;AM„AR„S=MngjRRn+T¤MP(5 tAnoMSvN’S;A5:N?g‰S=Mn;*S+T(3A5)Tag‰36M/g¤3M/d58Mn+T(R– A55N

(8) < T‡5;

(9) g‰R–SoN)g‰P(RA;)<=5%g‰35›NR)g‰SeR*N’RŒT#<At5P(So7tAR'T(M ASon&S×g#l1 ÎV35S•P`T#gjM=ÐASoN„ª7›MÐA5)T`T#<AtA5P(So7`tARTˆM- ASnoShg#l©Mtt'MP(5N)gØMN6;

(10) g‰35lª=MN– A58;S&Œ‰Œ“5P(5N)gjSoM/gj5;

(11) lª7rMP“ÐASvN„ g‰357¨Ä+ٓÆ1ÎV35%T(M7r5$TˆR6<APˆ=5MnšTˆR$< Tˆ56TN6M/<g“Son•<!TqT(3A5nvn‰TqT“tAn&S×gVSoN›3AMnoŒgjR›Son&n•< T‰g‰P(M/gj55N6M:N?g“SeRC7`RP“t3CTÈ1)x(N g‰3S&TcMP#gjSo=n5D½‹$5‹$S&non_<!T(5›g‰355-Ê*M7tAn5

(12) RAŒ=/<g+g‰SoN„ÚMttCno5TcM)TcM

(13) 7r5/gjMt36R*PcŒ‰R*Pag‰365

(14) M)T‡T(RA=S&MLg‰SoR*NªRCŒ =3SoP(MnA=?5N)gj5PfTÈ1 ÎV35›=3SoP(Mn&S×g#lÛR*Œ¤MN”R6 †‡5=/gk=MN

(15) A5›S;5N)gjSoŒ“S5;

(16) l’=R7`tAMP(SoN„©S×gq‹`Shgj3–Shg(T7rSoP“P(RP(J#So7rM„A5

(17) Ä&F(Æ6D <g¤M 7`RP(5´T‰g‰P(MS•„A3)gjŒ‰RP#‹`MP(;´‹$M/l§S+T`gjR´< T(5­T“l7r7›5Lg‰PˆlÏ=-R*NAT(So;C5P(M/g‰SoRN'TL1_X´R*no5-=/<'n5T`g‰3M/g`36M/dA5’tCnMN5TˆD =5N?gj5PfTˆDkRP`Mn×gj5P“NMLg“SoN„ZMÊ*56T$=MNNRg A5–=3SoP(Mn~ÄÜ(ÆD]MN6;±7`R'T#gcRŒag‰35ËgjSo7›5-DkRNnvlªg‰35©T“lA7r7r5/g‰P“l tAnoMN5R*tA5PˆM/g‰SoRN›S+TW=R*NAT(S;5P(5;'1x‰g=MNrMn&TˆR A5~365:notAŒ#<n'Œ‰R*P]T#g+<;5N)g(TŠgšR›no5MP(N›36R6‹g‰R›P(5-=R„NS•É?5ag‰35 tAR'TfT(S• An5=:3S™P(Mn'=5N?gj5PfTRŒŠ7`RAno5=/<n56TÈ1 Yag]T(=36RCRnoD =3SoP(Mn&Shg‰lS+T]RCŒ&gj5N8SvN?g‰P(RA;)<=5;‹`Shg‰3MT“l7›7r5/g‰P(So=-M:n!=MPˆ *R*NM/gjR7›T(DC‹`3S=38MPˆ5c *MT(S&=cM:NA; Œ+P(5œ)<5N)g‰n•lÏRA==/<AP“P(SoN„Ï=3S•P‡M:nØ=5N)gj5P‡T(D4 <g%7$M:NlÏRg+365P8T(Shg+<M/gjSoRNCTr7›MlÏMP(S+T(5 1qÎV3A5Ût36RTjtC36R*PjR< T M/gšR*7¨SoN›tA3R'T“t3SoNA5%7rM-l8 *5%M%=3SoP(Mn!=5N)gj5P]MN;87`RCn5=L<'no5T]7rMlrtP(5)T‡5N)gWM%=3S•P(Mn MÊAS+T(DŠT#<=38MT]SoN Mnon&5N656TˆD

(18) ASvtA35NlAn5T¯RP°TjtCS™P(MN5)TÈ1X´RCno5=L<'n5T±‹`S×g‰3ÑMÔ3A5noS=)Mn­T#g‰P‰<=Èg+<AP(5˜Mn&T(RÝ5/ÊAS+T#gjD³T‰<=3ÑMT Þ N6ß#35n&S=?5N5à“N~á’uâWRPq7`RCno5-=/<'n5TWRCŒV3So„C365PW=RC7%tAn5-ÊAS×g#l”T#<=3rM6T]T‰gjMP(=3Ä#ã‰ÆDäp›Y®R*PtP(R)gj5SoNATL1x(N SoNRP“„AMNS=

(19) =RA7%tCn5ÊA5?T(D_µ¯5P“NA5Pc;5:7$R*NAT#g‰P(M/gj5-;”g‰36M/g¤RA=ÈgjM35;P(MnW=RC7%tAn5ÊA5Tc=R6<Ane;© A5=:3SoP(MnaĈåæ“ç(Æ l”P(5)T(RAnedASoN„’2]RAà&p%^%è“âˆà“2qn•â(àš^cé+pr2W^cé(2_^cé+p$^cé“â“é]g‰35N6D½nM/gj5P(DV2qRê“à“{a^câ“ë(à&p%^%è‰âLì&é‡1C^$5›5/d*5:NtP(RdA5; ‹`Shg‰3g‰35noM/g+gj5P'g‰3MLgV5NMN?g“SoRA7`5P“l`=-R6<no;`RC=-=/<APVSoN›T“tA5?=So5TŠg‰3MLgV=RN)gjMSoN%N6R›=MP‰ ARN`M/g‰R78TL1 ÎV35M)TLT(RA=SoM/gjSoR*NrRŒg+‹$R8=3S•P(Mn =-5:N?gj5PfTV‹`Shg‰3SoNR*N65~78Rno5=/<n5~=?MN›n5M-;$gjR›S•N?gj5P(5)T‰g“SoN„=M)Tˆ56TÈ1µ¯35N g+‹cR­Œ+P(M„A7›5N?g(T`RŒMÛ7$RCn5=/<n&5’MPˆ5” *R6g‰3Ú=3S•P‡Mn¤M:N6;±7`SoP“P(RP%So7›M„A56TˆDkŒ‰RP`5/Ê*M:7`tAn5˶%¹¼È·æ#gjMP+gjMP“So=.

(20) M=So;Dg‰35k‹c3RCne5\7`RAn&5-=/<'n5S+TVNRg =3S•P(Mn+1 ν365\Œ‰SoPfT#g!tAMP+gR*Œ'g‰3S+TVtAMtA5Pœ)<5?T#g‰SoRN'TŠg‰35=-R*N?dA5PfTˆ5RCŒ'g‰35 tP(5/dASeR6< T¤T#gjM/gj57$5:N?gjD'S+1×51×DS×gM)TjÐ'T(D'SoŒqM~N6R*N=3S•P(Mn 7`RCn5=/<n5$S+TW7›M-;C5RCŒg+‹$R8=3S•PˆM:n=)5N?gj5PfT(D;RC5)TShg Œ‰RCnonoR*‹¨g‰36M/g_g‰365)T(5r=5N?gj5PfT7~< T‰gq A5›7`SoP“P(RP]So7›M„'5)TØRŒ]5?M=3–R)g‰365P  x“N”R6g‰365Pk‹cRP(;CT(D'‹`5%‹%SonnVnoRCRÐ Œ‰RPM=R6<AN?gj5P(5/Ê*M7%tCn5kg‰36M/gT“3R‹rTV3R‹ MaN6R*N`=3S•P‡M:nR †(5=/gT#<=3`MTMN`MttAn5=MN% A5~T“tAn&S×gVSoN)gjR~g+‹cR S;5N)gjSo=Mn'=3SoP(MnR6 †‡5=/g(TÈ1ÎV35N6DCSoN$g‰365~T(5?=RN;%tAMP#gR*Œ g‰35atAMtA5PˆD6‹$5k‹`Son&n=RC7%tAMP(5kg‰35atMP#g(TRŒ'g‰35 MttAno5k‹`Shgj3`RA=ÈgjM35;P(MnA=RA7%tCn5ÊA5TÈ1  ž

(21) ]ƒ € Y7`RCN„%g‰365k‹`Ml'TWSoN$‹$3S&=3%tA5-R*tAno5=/<g g‰35S•PMttCn5)TˆD'R*N65;5)T(5Pˆd*5)T]T“tA5=SMn'MLg+gj5N)g‰SoRNDAM)TShg n&5-M;CTŠgjR g+‹cR³5no5„AMN)g¤tRP+g‰SoR*NATag‰3MLgaŒ‰Shg]g‰R„A5fg‰35PM)TSoN’Mg‰3 P(558;Sv7r5NCT(SeRCNMnt<AÉÉ?n&5 1§ÎV3SšT¤‹`MlÛRCŒ¤=/<g&g‰SoN„ MttAno5TaS+T¤NM7r5;›g‰35ÁvÍ ¼º»A¿V;)<5~gjR›g‰35`no5„A5N;Ëg‰36M/gWShg_‹$M)T]tP(5?T(5N)gj5;gšR–M~«%SoN „–SoN–M%P(57`Rgj5 =R<AN)g‰P#l1Î_R–=-MP“P#lËR6<g4M~«%SoN„ w#T¤=/<gjDVT#gjMP+g l”=/<g+g‰SoN„–M%dA5P#g‰S=Mn œ)<MP#gj5P¤;R‹%NŒ+P(R7Óg‰35›T‰gjM:n™Ð’R*Œ g‰35`MttAno5DŠ7$MP“ÐA5;`pÑSvNŒ‰Sv„<APˆ5Û?1×M`à“MnoRN„8g‰35`nvSoNA5pYâ(D'g‰35N=L<g]M%3RP“S•É:R*N?gjM:n 3AMnoŒ]à“noSvNA5`Y2qâ(D g‰35N–Md*5P#gjSo=Mnœ)<MP#gj5PØà#noSoNA5›2sâ;R‹%N8g‰RËg‰365$ *R6gg+R7ÑRŒ_g‰365›Œ+P#<'S×gjDg‰35N–M›neM6T‰g]3MnoŒ¤à“n&SoNA5

(22) säØpâ AM-=ЛgjRg‰35T‰gjMn•Ð 1Aν3S+T¤=/<gV‹`Sonon 5c=R*NAT(S;5P(5;85Shgj3A5P]M)Tg‰35T(S•Ê”MPˆ=6T p›YDYØDØ2]D2sADVsä¨MN; äØp›DAR*PM?T½g‰365kp`YØ2s6äØp¨n&SoNA5~SoN%g‰35~Œ‰RCnonoR‹`SoN„ 1prR*N65~RŒg‰365)T(5=/<g(T]T“36R6<no;r=P(R'TfTW5M=3rRg‰35PÈ1)x“Œ g‰35k AnM;5RŒg‰365\ÐANSoŒ“5=/<g(TŠg‰365MttAn&5M?Tq;5-5tCnolrMTŠg‰357›S;;n5M-ÊAS+TWRCŒ'g‰35Œ+P#<ShgjD* <gŠN6R6g!7`RP(5D)g‰365 g+‹cRtSe5=5T=MN% 5~T(5tAMP(M/gj5;'1Ø5„CSoNN65PLT_7`So„A3)g P(5-M:Ð%g‰365MttCne5R*PV„A5/g!N6R*N%tA5P“tA5N;S=/<n&MPVtCS5=5TˆD <g!tP(M-=Èg‰So=?5~TˆRCRN%7`MÐA5TVtA5P²Œ‰5-=/g‡1 N. N. C. C D. B. B A. A. àjMâ. D. S. S. OŠSo„ 1 OP“R7—g‰35~TjtC365P(5kg‰Rg‰35=/<g!tSo5=-5)TRCŒ'g‰35MttCno5 1. àš â. a{ T(5P#dASoN„ÚR*N65

(23) RCŒ]g‰358tCSe5)=-5)T›T(36R6<Ano;±T(36R6‹Òg‰3M/gØShgS+Tc=3SoP(MnoDq5d5N³M?TLT#<7SoN„’g‰35MttCn5›gjR© A5M tA5P“Œj5=/g’Tjt3A5P(51x#g36M)T’NR‘T“l7r7r5/g‰P“l—tAnMN5D`NRÔSo7`tP(RtA5P’M/ÊAS+T(D`MN;°g‰365P(5§S+T³N6R6g”5LdA5N MNl T“l7r7r5/g‰P“l8RtA5P(MLg‰SoR*NR)g‰35PVg‰3MNM%2q>M/ÊAS+TL1AÎ_35c24>”M/ÊAS+TqtAMT‡T‡5)T]Œ+P(RC7Ôg‰365%7S;;n5%RCŒŠg‰35%noSoNA5apr2 g‰3PˆR6<A„3`g‰35`=5N)g‰P(5-DŠMN6;

(24) R<g4M„AMSoNM/gg‰35`7S;;n5RAŒknoSoNA58sCY`1ν365P(5Œ‰R*Pˆ5Shg A5noRCN „'TqgjRg‰365`=3SoP(Mn tARSvN?g„PjR6<AtÚ2qéL1V{a 'T(5P#dASoN„³ ARg‰3©tASo5=-56TtP(RdA5?T\g‰3AMLgkg‰365lªMP(5

(25) S;5N)gjSo=MnD_tP(RdASo;5;–g‰35–MttCn5

(26) S+T M)T‡T#<7›5-;ËgjRË A58T“t3A5P(So=?MnoDVMN;8g‰35ÁoÍ ¼%º-»A¿ ‹$M)T¤tP(R*tA5LP“n•lÛ=MP“P(S5;–R<g‡1 R)g‰3”MP(5`7`M;5rR*Œ_g+‹$R œ)<MP#gj5PfT RŒ MN MttAn5 t'5P“tA5N;S=/<n&MP²nol MTfTˆ5:7` An5; SoN g‰35 TˆM:7r5 ‹$Ml à#OŠS™„ 1šL âÈ1ŽÎV35 5N6M:N?g“SeRC7`RP“t3R< T’tCSe5=5Tª=R<'no; 3MdA5§ A55NÇtP(RA;)<=5;— l tA5P(Œ‰R*P(7`SoN„ g‰365¯R6g‰365P~ÁoÍ ¼Zº»A¿ ¦ p`Yaär2sWp˜àšO!Sv„ 1 >âL1. >.

(27) O!So„ 1)> rÎV35aP(5?T#<nhg!RŒg‰365kg+‹cRt6RT‡T“S• An5Ø«cSoN„Šw+T=/<g(TÈ1ÎV35kg+‹cR%tSo5=?5)T½R*Œ'g‰35alA5nonoR‹ MttAn5MP(5 =3SoP(MnAMN;`S;5:N?g“Se=Mn&DAMN6;7›S™P“P(RPVSv7rM„A5TRŒ'g‰35atASo5=5TRŒ'g‰35aP(5-;Mttno51 ÎV35³Œ‰MT(=SoNAM/gjSvN „±g‰3SoN„¯M *R6<gg‰35~ÁoÍ ¼”º»A¿\S+T`g‰3M/g$Shg`S+Tg‰365³=R<AN)gj5P(5/ÊAM7%tAn5ۋ$5³7r5:N?g“SeR*N65); 5MP(noS5P(D!M)TaS×g]MPjS&T‡5)T¤Œ+P(RC7‘g‰35`Œ‰M=/gVg‰3MLg]MNM-=3SoP(MnŠR †‡5=/g4àÖg‰365`MttCne5â¤=MN› 5$tAMP#g‰Shg‰SoRNA5;

(28) SoN)gjR›g+‹cR Á  ¹Í¿vÁ&º¾A¸a=3SvPˆM:nWtCS5=5TÈ1½Y¨< T#<Mn]MN;­5-M)T“lªt'MP‰g‰Shg“SeR*NªRCŒØM:NªM=3SoP(Mn]R †‡5=/gà(T(MlÚM

(29) 3)<7rM:N’ ARA;6l â n5M;'TVg‰R8Mno5Œ&gMN;rM\P(S•„A3)g tAMP#g(1¤R)g‰3r=3SoP(MnŠT(3MPˆ56TWMP(55NMN?g“SoRA7`R*Pjt3CTL1 x“N%g‰35=M)T‡5R*Œ g‰35~ÁoÍ ¼ º»A¿D6g‰365atCSo5-=5TMP(5kg‰365$TˆM:7r51?x“N~g‰365k‹`RP(no;`RCŒŠ7$RCn5=<'no5TˆDCMk¶c¹¼L·T#gj5Pˆ5R*ST(RC7`5PqT#<=3rM)TŠg‰35k¶$¹¼L·AJ gjMP+gjM/PjS&=rM=S;ÛS+T7rM;5rRCŒ]MN8[˜=:3SoP(Mn=5N?gj5PMN6;–MN­s’RN5 !NRg_g+‹cRªs–RN5)TÈ1­Î½365ÁvÍ ¼%º»A¿S#T g‰35P(5Œ‰R*P(5a3S™„C3nol`SoN)g‰P(S•„<SvN„ 1   'C¤  +v#¬ $ž 

(30) ]ƒ '€ {=/gjM35-;P(Mn =RC7%tAn5ÊA5)T]36M-d*5%M~Œj5/‹˜Œ“5MLg+<AP(5)TqSoN=RC7`7`RCN%‹`Shgj38MÁvÍ ¼Øº»A¿#162kRA7%tCn5ÊA5?T]7›M-;5~RCŒ g‰3Pˆ55=3A5nM/g‰SoN„8;So3AMtgjRnoSo„AMN;'T(D'T#<=3rM)TW5/g‰3ln5N;SM)7rSvNA5àj5:N â(DAMP(5RCŒ&gj5N`Œ‰R<'N6;SoN%<'N6;5P“„P(M-;)<M/gj5 gj5/Ê g+ ARRÐ'TL1^cR6‹$5/dA5P(D6g‰365P(5MPˆ5~Mn+T(RrR)g‰35PVÐASoNA;CTqRŒ=3SoP(MnRC=/gjM35;P(Mn=RC7%tAn5ÊA5T(D'T(RC7$5~RŒ‹`3S=3 MP(5;S+Tˆ=/<ŠT‡T(5;% A5noR‹81 ÎV35S•PVP(5noM/gjSoRN~gjR\g‰365 ~ÁoÍ ¼]º»A¿ASšT½5/ÊM7SoNA5?;'1 . VÎ 35T(S7tAn5)T#gWRN5?T]MP(5XZà“5N â è RP_X´à“2_^ è {~2_^ é 2_^ é {~2_^ è â è D M)TWSoNO!So„ 1hI'1AÎV35S•P]=3S•PˆM:nShg‰lMn•‹`Ml T gjMÐA5)TWT(R7`5kg“So7r5kgjR$ *55/dAS;5N)g g‰R8Tšg+<;5N)g(T(DAMN6;Shg S&TWR*Œ&gj5N`N65=5TfTˆMP“l%gjR%P(5tP(5)Tˆ5N)g g‰365:7 MnoRAN„%g‰35 2 è M/ÊAS+TRCŒqg‰358=-R*7%tAn5ÊA5TL1s<=3’=RC7ctCn5ÊA5)T *5:neRCN„–g‰R–tRSoN)g¤„P“R<At–ä è DM)Tkg‰3658R*Nn•l­T“lA7r7r5/g‰P“l RtA5P(Mfg‰SoR*NAT`MPˆ5g‰3 P(552 é MÊ5)Tt'5P“tA5N;S=/<n&MP\gjR–g‰35–7`MSoNZ2 è MÊAS+TL1VÎ_365

(31) NRA7`5N=nM/g+<AP(5R*Œ]g‰35T(5 =R7%tAn&5Ê*56T¯< T(5T¯g‰35 ∆  Λ NR)gjMfg‰SoR*NAT‘ĉ Å ‰Æ'1 x‰N g‰365 T(M7r5ŽŒjM:7`SnvlAD­=-RC7%tAn&5Ê*5)TÔT‰< =3 M)T XZàj2W^cè({2_^%é(2_^cé+prà“2_^%è“âjé“â“èWMP(5=3S•P(Mn' <g!‹`Shg‰3rMN85/d*5:NrnoR‹r5P]T“lA7›7r5/g‰P#l6D'MTVg‰35Pˆ5~S+TqRNnvlM%2qè M/ÊAS+TL1AY‘=-RC7%tAn&5ÊËR*ŒVg‰3S+TT(RPšgV *5:neR*N „TgjR˄PjR6<At8t6R*SoN?gW24èÈ1CÎV35`T(S&7›SnMP(Shg#lRCŒW=3S•P(MnV=-R*7%tAn5Ê5)T]RCŒ g‰3S&TÐASvNA;±‹`S×g“3±g‰365±MttCn5­tCS5=5?T–=-M:N¯ A5§T(55NŒ+P(R*7 g‰35ZN)<7$ 5PRCŒr=RC7`7`RCNÇT“tA35P²S=Mn`MP(=)T SoNdARCn•d5; ¦ prYD 2ÇMN6;©säÒà#O!So„ 1šLâÈ1'ÎV35)Tˆ5›MP(=?T7rM-gj=3›g‰3P(55`RŒ_g‰358T(S•Ê’RCŒVg‰35«cSoN„ w#T¤=/<g4à&p›YD YØDØ2]DA2\sAD sä`DMN6;~äp`âL1aµ¯5noRAR*ÐA5-;$Œ‰RP!R)g‰35PnoSo„AMN;'TŠg‰3MLgV=R<Ano;Œ‰ShgV7$R*P(5 1. I.

(32) NH2 NH2 H2 N. H2N. H2 N. N H2. H 2N. H 2N. NH2. N H2. NH2. N H2. !O So„ 1IrÎV35RA=fgjM35;PˆM:n'T‰g‰P#<=/g+<6P(5aRŒ'XZà“5N â“èMN6;Shg(TVdAS5/‹ Œ+P(RC7—g‰3652qèM/ÊAS+TL1 Î ‹$R~ ARN;CTMPˆ5 5NnMP“„A5-;Œ‰RPg‰35~TˆMÐA5RŒŠ=nMP(Shg‰l6D6 <g'g‰35RA=ÈgjM35;P(RN%S+TVP(5„<'nMPL1 ÎV35qp%^%éVŒ+P(M„C7r5N)g(TVtPˆ5)T(5N?gj5;%SoN ARAno;Œ‰M=?5=RP“P(5?T“tRN;`SoN~g‰35kg+‹cR`;P(M/‹cSoN„'TÈ1 ÎV35–2]Mà“5-;)gjMâ é =R*7ctCn5ÊZS+T`7`R*Pˆ5یjM7`R< T`Œ‰R*P`Shg(TrMN6Mnvl?g“S=Ë<!T(58g‰3MN­Œ‰R*P`Shg(T$=3S•P‡M:n]tP(RtA5P+g+l1½x‰g ;SvŒ‰Œj5PfT]Œ+P(RC7Çg‰35XZà“5Nâjèq=3S•P‡MnoShg#lSoNgj35agjR*t6R*noR„lrR*ŒŠg‰365~n&So„AMN;

(33) T(SoNA=5cR*Nnol8RN5n&So„AMN;‹cP(Mt'TV<'t g‰357`5/gjMn =M/gjSoRN'1ÎV35`T#g‰P#<=fg+<AP(5R*ŒT#<=38M=RC7%tAn5ʛ‹$M)TWR6 gjM:SoN65;›Œ#PˆRC7‘2]M Þ 2kM-à“5;)gjMâ(߇1 )^cé({ÔĉÅÅ‰Æ MN6;

(34) =RA7%tAMP(5;›‹`Shg‰3Rg‰35PfTÄ#Å?Ü(Æ1'ÎV35`MN„An5)T¤RCŒVg‰35~ ARN;SoN„–MP(R6<AN6;g‰365`2kM`=MLg‰SoR*NMP(5Œ‰MP¤Œ+P(RC7 g‰35y@ qSoN%g‰3A5=P“l'T‰gjM:neD* <g SvNg‰35atP(Rt*l6n5:N6;*SM7›SoNA5/gj5Lg‰P(MM=5fgjMfgj5à#tA;:gjMâVSeR*N6D6g‰365~T#g‰P#<=/g+<APˆ5aS&TWM:n7`R'T#g RA=ÈgjM365;P(MnAàšO!So„ 1)HâÈ1:µ¯S×g‰3~g‰35aN6R6gjMfg‰SoRN`RCŒ'g‰35k«cSoN„Šw+TW=/<g‰D)g‰365=R*7ctCn5Êr=MN% A5aP(5tP(5)T(5N?gj5;~ l~g‰3A5 p`YD½ä`YD_YØD Ø2kDWM:N6; ]ä MP(=?T%RAŒkg‰35–T“tA3A5P(5 1ŠY~n×g“36R6<A„3–g‰35P(5

(35) MP(5

(36) 7`RP(5MP(=)Tg‰3MN–‹`Shgj3–g‰35 XZàj5Nâ“è=-R*7%tAn5ÊADg‰35kg‰RtRnoR„*l$RŒg‰365=R7%tCn5ÊrS+TqT#g‰Son&nA;S&Œ‰Œj5P(5N)g Œ+P(R*7—g‰365k«%SoN„!wšT½=/<g‡1 O. O C. O. H2C O O. O Mg. C H2. N. C H2. C H2 C. CH2 N C H2 CH2. C O. O!So„ 1 H äcP(M/‹$SvN „rR*Œ'X­„Aà‰tA;)gjMâVŒ+P(R7 MN`{a[Ί9–P(5tP“5)Tˆ5ON)gjM/g‰SoRN›Ä‰Å?Ü(ƛT“36R6‹`SoN „›MaPˆ5M)T(RNM An5 RA=ÈgjM365;P(MnA=3S•P‡MnA=RC7%tAn5-Êc‹`Shg‰3`M~T(SoN„An&5noSo„'MN;~‹cP(MttASoN„%<At%g‰35=M/g‰SeR*N1 VÎ 35n&M?T#g =R7%tCn5Ê%gjR~ A55Ê*M:7rSoNA5;365P(57So„A3)g A55ÊAtA5=Lgj5;\g‰R% A5kg‰365=:neRTˆ5)T#g g‰Rg‰35 ÁvÍ ¼4º»A¿eGM)T g‰35~gšR*t6R*noR„lRAŒ½g‰365noSo„AM:N6;

(37) S+T¤MnoSoNA5?MP¤=3MSoN%†“< T#g]noSoÐA5~g‰35\g‰PˆM=5%RŒ½g‰365~ An&M-;C5`RŒ½g‰365$ÐNSŒ“5`RN›g‰35 T“ÐASoN RCŒ8g‰35¯MttAn&5 1%ÎV35°noSo„AMN;ÔS+Tª=?Mnon&5-; tA5N)gjM„Cn•lA7r5D›2_^ è à“{2_^ é 2_^ é â “{2_^ è DŒ+P(R7‹`3S=)3 =Mno=S•<'7ÝMN6;ÛT‰g‰P(R*N?g‰Sh<7Ñ=RC7ctCn5ÊA5)T]‹$5P(5%tP(5tAMPˆ5;–MN6 ; cJ#P(Ml”=3AMP(M=Lgj5P“S•É 5;–Ä#ŠՓÆ1COŠS•d5%tAR'TfT(S• An+5 „A5R7`5/g‰P(So5)T¤=-M:NM~tP(SoRP²S' 5%=-R*NAT(S&;5P(5;8Œ‰R*P]M%365-ÊM-;C5N?gjM/gj5~noSoNA5?MP]nvSo„AMN;›‹cP(MttASvN „›<At–Mc=M/gjSoR*NM/g g‰35`prD_YD ØDq2]D½ä$DqMN;Zs­RA=/gjM35-;P(Mn_tAR'T(ShgjSoR*N'TcRN–g‰35©TjtC365P(5àš< T(SoN„©g‰35NRgjMÈg‰SoRNªR*ŒaO!So„ 1 LâL1 ÎV35)Tˆ5$„A5-RC7`5/g‰P(So5)T¤=-M:N8 A5`5N=-RC;5;M)Tp›YØ2_äs Ap`YØ2sä p›YcsA2_ä prY%sär2 6p›Y`s 2_ä àšO!S•„ 1•K?âL1 ν3655NMN)gjSoRC7`5P²S=~T‰g‰P#<=/g+<Pˆ5)T=MNrMn+T(R% A5=RNCT(S;A5P(5;'1?Y~n×g“36R6<A„3~g‰365)T(5Œ“S•d5%T#g‰P#<=fg+<AP(5)TMP(5 P(5noM/gjS•dA5nvlË5M)T“lrgjRËSo;5N?g‰SvŒ‰lAD'tP(RdASvN „›g‰3M/g!g‰35Pˆ5%MP(5RNnvlŒ‰S•d5%RCŒŠg‰357¨S+T];S&Œ‰Œ“S=/<nhg‡1b%NŒ‰RP#g+<ANMLgj5:n•l*D g‰35

(38) g‰3 SoRC=l*M:N6M/gj5’=R<AN)gj5P`MNSoR*N'TrMn+T(RÏ=RRP(;SoNAM/gj5ËgÖ35’=Mn=:S•<7 =MLg“SoRNZM)T8T(36R6‹cN´ l­g‰365’=P“l'T#gjMn T#g‰P‰<=Èg+<AP(5?1ªÎ½365Ñ2kM-à#tA5N)gjM„An•lA7›5â(à&pr2\sâ é =-R*7%tAn5Ê „A5/g(T— *R6g‰3Ýg‰3SoRC=l*M:N6M/gjR noSo„AMN;CT˜SvN g‰P(MNCT tAR'T“ShgjSoRN'T]à²T‰<=:3M)TVpÒMN;–sSvN›O!So„ 1VLâL1ÎV35%=-R*7%tAn5ʖT#g‰P‰<=/g+<P(5SšT4=noRTˆ5\gjRM%;S&T#gjRP+gj5;~p`YØ2WäËs H.

(39) «cSvN„!w+T=/<gjD'‹%S×g‰3Ëg‰365Œ“S•PLT‰g]MN6;©T(S•Êgj3R6Êl6„A5N–M/gjR7›TØR*ŒVg‰35r=3MSoN–=noRTˆ5`à“M ARdA5›MN8 A5noR‹%âqgjR›g‰35 Y2_ä®tCnoMN6DCMN;~g‰365a>AJ²KRÊl„A5N`SoN~g‰3S+TVtAn&MN1 N. N. D. N. D. B. B. D. B. S. S. S. N. D. N. B. S. D. B. S. O!So„ 1•K ! R'TfT(S• An5~T#g‰P‰<=Èg+<AP(5?TVŒ‰R*PMN`RC=fgjM365;P(MnA=R7%tCnÖ5/Ê%‹`S×g“3`MnoSoNA5MPV35Ê*M;C5N?gjM/gj5knoSo„AMN;'1 ν365 tARSoN)g(TVYà“Œ+P(RN)g‰â MN;`2Zàš AM=ÐâMP(5aNR)g!SoN;S=M/gj5;%Œ‰RPg‰365~T(MÐA5RŒ!=:neMP(Shg#l1 {a<AP±SoNShgjSM:n’SoN)gj5N?g“SoRN‘‹`M?T´gjRќ)<5?Tšg‰SeR*N‘g‰35 =RNd5PfTˆ5 tP(RtR'T“S×g“SoRNÒM==RP(;SoN„ÓgjR‘‹%3S=3‘g‰35 M)T‡T(RA=:SeM/g“SeR*NÏRCŒ~g+‹cR¯5N6M:N?g‰SoRC7`5P²S=³7`RAS&5Lg“So5?T–T(3R<Ano;°ne5M;´gjR¯MNÏM=3S•P‡Mn7`RCn5?=/<n5DM)T8SoN§7r5T(RAJ gjMP+gjM/PjS&=M=S;'1µ5؋$5P(5%SoN'T“tASoP(5; l`gj355-ÊM7%tAn5%RCŒŠg‰365\«%SoN„ w#TW=/<g!gjR›Œ#SoNA;›7`RAn&5-=/<'nMPVgjRtRnoR*„ASo5T T(So7›Sn&MP4gjRShg‡1CY7`RN„8g‰35~g+l tARCnoR„*lËRCŒq=3S•P‡MnV=-5:N?gj5PfT¤àšgj5fg‰P(M365;P(MnoD!=3SoP(MnVMÊAS+T(DŠ5Lgj=1 â(D‹$5%Œ‰RC=/< Tˆ5; RNRC=fgjM35-;P(MnŠ=3SoP(Mn&S×g#l6D‹$3S&=3noRAR*Ð'T¤=noR'T(5~gjR›g‰35`MttCno5`=/<g‡1µ¯5`5ÊAM7rSvNA5-;g‰3 P(55~gjR*t6R*neR*„ASo5T¤R*Œ n&So„AMN;CTÈ1)94M=3rRCŒg‰3657‘n5;$gjRrM~=3S™P(Mn =RC7%tAn5Êg‰36M/g ‹`M?T½gšRR8;S&TLT(S&7`Sn&MPqŒ+P(RC7Çg‰35a«%SoN„!wšTW=/<g‡1?µ¯5 MP(5ag‰35P(5Œ‰R*P(5no5;gjR A5noS5d5Øg‰36M/gŠg‰365P(5MP(5~N6RË7`RAn&5?=/<noMP45-Ê*M7tAn5)T]MN6M:neR*„AR< TVgjR$g‰35«%SoN„ w#TW=/<gjD ‹c3S&=3~‹$S&nonCtPˆR6 *M- Anol%Pˆ5:7rMSoNrMk<ANS&œ)<5=-R6<AN?gj5P(5/Ê*M:7rtCne51 2_<g&g‰SoN„rMN`MttAno5M;Ml`7rMl`ÐA55t8T“lA7r7›5Lg‰Pˆl$M/‹$Ml'1 xVg‰3MN Ð

(40) YNN5  M/<AtA5cMN;[ØR ASvN›XZSn&nMP]Œ‰RPqSo7tPˆR6dASoN„›g‰365%7`MN)<!T(=P(S•tgWRŒŠg‰3S&T]MP#g‰So=n5%MN;8Œ‰R*PVg‰35 Œ+P#<ShgjŒš<nA;*S+T‡=/< TLT(SeR*N1 v (- ! -v( ?19WnoS&5noDV91U¤1 Vµ¯Sn&5N6Das 1^81¿v¹Àȹ·ºA¹¶cÁv¼/¿eÀÏ· aÀ '¾ÍAÁº

(41) q·¶ ]·»Í  ¼ q0ÈR*3N6D_µ¯S&n5l sARNCTˆD x+pr21pr5/‹$J#zR*Pj Ð Dt 1+yCB1 > 1?Á+ÂÁ  1)t1•KBA1 I'1UV<† N6Jšb%tgšR*N6D6^1fÌ  A¹ ¶   »º "!$##%-DŠåE6D*H CK6H '1 H 1^`MP+g‰D^r1LÌ $ A¹ ¶   »º !$##%& åEGuI> uIH 1 KA1 2qR*nonSvN'TˆD6X 1)0-1/'Ì % A¹( ¶   »º $!$##%&!åE)GWLH'B?H fH'BKA1 . K.

(42) u'1^`MN6=RA=ÐAD6[\1:ä1fÌ$ A¹¶(  »º$!$### &!ååÈGyCBByy> 1 '1^~<A3655lD01 9Ø1  ÍA·À '¾ÍAÁ&º A¹¶cÁv¼/¿eÀ 1I94;C1^$MP“t5P  [ØR‹`Dpr5/‹$J#zR*PjÐD Dt'1 HAyI'1 BA1µ¯5PjN5P(DY` 1 a¹À  %?DÙÙDŠBB JB yCB1 y'1µ¯5PjN5P(DY` 1 a¹À  %!ADÙFADŠL>VJI@C1 @'1^`5PjP(5/PjRAD's1 ?b›TˆR*N6D6X 1 Y`1/Ì % A¹( ¶   »º 

(43) &'åÜGW@uCK@uuC1 ?1MP“N5/ggjD c1 U¤1 ?b`=3)g‰7rMND ›1 Y`1  ÍA·À   A¹( ¶   DÅ?E›Ä‰ Å ‰ÆD>Au H'1 L> 1[M-;MNRdAS D6ä1ä81 ?[alA=3n5/‹rT“ÐAMkb1 ?ä]†“<AP(MN6D6X 1)xL1 ?µ¯MP ?M“†#gjSšTˆDc1 ?ä%P( M jÐAR6dAS D?p

(44) 1As 1 a<AP(5(S-D ä1:X 1 ]·¸ %A¹  ÀL·ÍD !$##DÜAÕD>VB IJ‰>Vy> 1 I'1'µ¯5SoDVz›1 zr1  Î_SoNMN?gjD c1 ä$5=no5Pˆ=œD½0-1×J W1  cMN

(45) XZ5-5PfTfT‡=365D X 1 ä$Mn&5-D½0- 1 º?¿e¾ _À ¼¿ D  & ]ÙÕD½L> @JL> H'1. u.

(46)

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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