0 1.23 465879 !1:5;%< = - obspm.fr

! ! " # $ % & ' ( ) #+* , # #-, . / 0

#-, . / 0 . & " 0 " *1& 2 3 " . .

4 57698: ;=< >9?A@BDCFEHGJI

KLNMOQPRK9SKUTWVYXZO[XRS=K\VYX^]N_7`Mbadce=KgfhViXZM_kjKglbe5MTmVBMnVpopcTiKUPR`XR_qMsrt]vuTw`K

x

"

! #"$ &%('*)+'*%( ,.-/ 01.23465879 !1:5;%< = >x/? x @BAC8D8EGFHEJI/DLK8MONJPRQ9ISFTP<FUEJISDLK8MONVPXWYMZQHQ9M[?\?]?\?]?]?\?]?\?]?]?]?]?]?\?]?\?]?]?\?]?O? ^x/?`_ abc9FHdZefM]K3M]Q9AghAQHMZD3iZMOFUMZQ9QHMc9FUQ9Mj?\?]?O?\?]?\?]?]?\?]?\?]?]?]?]?]?\?]?\?]?]?\?]?O? ^x/?lk abc9FHdZefM]K3M]Q9AghAQHMZD3iZM]iZAZNGMZcmFUM]iZEJD3AZe#PnFUEGop3Mq?]?]?\?]?\?]?]?]?]?]?\?]?\?]?]?\?]?O? rx/?s^ abc9FHdZefM]K3M]Q9AghAQHMZD3iZMOFUMZeftuI/QHMNv?\?]?O?\?]?\?]?]?\?]?\?]?]?]?]?]?\?]?\?]?]?\?]?O? wx yL zZ-/%n4h1$(465u,"Y 0=h20%(523(4h5u, *%(%< |%<

_z? x ~$PRQ9ISFTP<FUEJISDFUMZQ9QHMc9FUQ9MOMZc9FEJQ9QHA/p8NJEGdZQ9MS??\?]?\?]?]?\?]?\?]?]?]?]?]?\?]?\?]?]?\?]?O? _z?`_ :QHEJD3iZEJt8PSNJMcp8iFUpPnFHEJI/D3cK8M\NJPXQHISFUPnFUEGI/DFUMQHQ9MZc9FHQHMn??\?]?]?]?]?]?\?]?\?]?]?\?]?O? _z?lk :QHEJD3iZEJtuMK8MONJPRt8PSQUPSefAFHQHEGcUPnFHEJI/DK3M]NJPXQHISFUPnFUEGI/DFUMQHQ9MZc9FHQHM]MFK8MOcHPfefMZc9p8QHM0?]?O? x(__z?s^ /I/NGp3FUEGI/DLK8MZcFUMiT8D8EGop3MZcZ??\?]?]?\?]?O?\?]?\?]?]?\?]?\?]?]?]?]?]?\?]?\?]?]?\?]?O? x_z?`r MNVPnFHEJI/D3ciZEGD8AZe#PnFUEGo*p8MZc?]?\?]?]?\?]?O?\?]?\?]?]?\?]?\?]?]?]?]?]?\?]?\?]?]?\?]?O? xw

5,Y"$ z z,u"$ ='*."$ "$,$246Y "Y &=62 %(523(4h5u, *%(%< |%< x;¡k3? x ¢PSK8Q9M]D3M£FUISD8EJMDK8MONJPXQHISFUPnFUEGI/DFUMQHQHMc9FHQHM ?]?]?\?]?\?]?]?]?]?]?\?]?\?]?]?\?]?O?¤_S¥

k3? x/? x :o*pPnFHEJI/D3cD8M£FHI/D8EJMD8D8McK8pefI/p3/Me#MD¦FK3M]Q9ISFTP<FUEJISD§?\?]?\?]?]?\?]?O?¤_S¥k3?`_ :op8PnFUEGI/D8cK¨l:p8NJMQm©~EGI/p3EJNGNJM ?]?\?]?O?\?]?\?]?]?\?]?\?]?]?]?]?]?\?]?\?]?]?\?]?O?¤_x

k3?`_z? x :o*pPnFHEJI/D3cK¨`:p8NGMZQ©~EJI/pzzEGNJNGM ?\?]?\?]?]?\?]?\?]?]?]?]?]?\?]?\?]?]?\?]?O?¤_xk3?`_z?ª_ aI/NJp3FHEJI/D«/AZD8AQUPSNGMOtI/p3Qp8DefIK8dZNGMK8MOW.MQHQ9M]Q9EJ/EGK8M ?]?\?]?\?]?]?\?]?O?¤_S

k3?lk ¬PSQHEJPnFUEGI/D8c®K8MZctPSQHPSe#dFUQ9MZcK¨sI/QHEGMZD¦FTP<FUEJISDLK8MONVPXWYMZQHQ9M ?]?]?]?]?\?]?\?]?]?\?]?O?¤_S> ¯B°± ¦#"Y 0=h2²,Y5u,%<4h³46"Y4h' ;¡

^8? x @BAghISQHe#PnFUEGI/DiZMD¦FUQHE´ghp8/M ?]?\?]?]?\?]?O?\?]?\?]?]?\?]?\?]?]?]?]?]?\?]?\?]?]?\?]?O?jk/¥^8?`_ .ISFHMZD¦FUEGMZNiMZD¦FUQ9EGghp8/Mµ?]?\?]?\?]?]?\?]?O?\?]?\?]?]?\?]?\?]?]?]?]?]?\?]?\?]?]?\?]?O?jk x^8?lk ¶·EJSp8QHMefIb/MD8D8M]K8MONVPXWYMZQHQ9M ?]?\?]?O?\?]?\?]?]?\?]?\?]?]?]?]?]?\?]?\?]?]?\?]?O?jk x^8?s^ ¸MFK3M]N¹¨lANVPScmFUEGiZEGFHABc9p8QNJMZcefI/efMZD¦FUcK¨lEGD8MZQmFUEJMº?\?]?\?]?]?]?]?]?\?]?\?]?]?\?]?O?jk/k^8?`r »¼D3p8MD8iZM]K8MON½¨sAZNJPSc9FHEJiEGFUAcHp8QNGM¾e#I/pz/MZefMZD¦FK8pt¿SNJM ?]?]?]?]?]?\?]?\?]?]?\?]?O?jk¦r^8?l »¼D3p8MD8iZM]K8MON½¨sAZNJPSc9FHEJiEGFUAcHp8QNJPRNGI/D8/p3MZp8QK8pÁÀ9I/p3Q?]?\?]?]?]?]?]?\?]?\?]?]?\?]?O?jk/^8?`Â ÃBD8ANVPScmFUEGiZEGFHAÄ?]?]?]?]?]?\?]?\?]?]?\?]?O?\?]?\?]?]?\?]?\?]?]?]?]?]?\?]?\?]?]?\?]?O?jk/

Å ¯B°± ¦#"Y 0=23(!5uZ1.Æ$%( *#"$ f5-/'*2,Y >¡rz? x ·Ç3iEGFUPnFUEGI/D8c/AI/t8¦bcHEGop3M ?\?]?]?\?]?O?\?]?\?]?]?\?]?\?]?]?]?]?]?\?]?\?]?]?\?]?O?È^¦¥rz?`_ ÉBPnFHp8QHM¾K3piI/p8t8NJPS/M¾MZD¦FHQHM]p8D8MOiZI/p3iT8M]8p8EJK8M¾MFNVPvW.MQHQ9M]c9I/NJEGK8M?]?\?]?]?\?]?O?È^xrz?lk ¶I/D8iFHEJI/DOK¨sMÇziEGFTP<FUEJISDÁK¨sp8D8M®iZI/p8iT3M®p8EGK8MMF·efI/efMZD¦FYiZEGD8AFHEJo*p8MK8MiMFHFHMiI/p8iT8M^¦krz?s^ :op8PnFUEGI/DÊK¨`:p8NGMZQ©~EJI/pzzEGNJNGMtuI/p8Qp8D3M\WYMZQ9QHM]PSD8ANVPScmFUEJo*p8M«?]?]?]?\?]?\?]?]?\?]?O?È^/^rz?`r ·Ç3iEGFUPnFUEGI/DÊPnFUefI/c9t88AZQ9EJo*p8M ?]?]?\?]?O?\?]?\?]?]?\?]?\?]?]?]?]?]?\?]?\?]?]?\?]?O?È^*r

rz?`rz? x »¼Dzp8MZD3iZM]K8MZcnPSQHEJPnFUEGI/D8cK3M]t3QHMZc9cHEGI/D&P<FUefI/cHt83AZQHEGo*p8MS??\?]?\?]?]?\?]?O?È^¦

_

rz?`rz?ª_ »¼Dzp8MZD3iZM]K8MZc/MD*FHcZ?X?]?]?\?]?O?\?]?\?]?]?\?]?\?]?]?]?]?]?\?]?\?]?]?\?]?O?È^*Ârz?l ·Ç3iEGFUPnFUEGI/DLIziA|PSD3EJo*p8M¤?\?]?\?]?]?\?]?O?\?]?\?]?]?\?]?\?]?]?]?]?]?\?]?\?]?]?\?]?O?È^¦

rz?l3? x IzK8dNJM¾K¨sIiZA|PnDcmFTPnFHEJo*p8MPSQ9I/e#AFUQ9EJo*p8Mh»O?]?]?]?]?]?\?]?\?]?]?\?]?O?È^¦rz?l3?ª_ IzK8dNJM¾K¨sIiZA|PnDK3bDPne#EGop3M?O?\?]?\?]?]?\?]?\?]?]?]?]?]?\?]?\?]?]?\?]?O?¤rxrz?l3?`k Q9K8QHM¾K8MO/QHPSD8K8Mp8QK8pÊFUMZQ9e#MI/DPSNK3pefI/efMZD¦FiZEGD8AFHEJo*p8M¾IiZA|PnD8EJo*p8M#?¤rxrz?l3?l^ aAZQHEGMZcK¨sMÇziZE´FTPnFHEJI/DLIiZAZPSD8EGop3ML?\?]?\?]?]?\?]?\?]?]?]?]?]?\?]?\?]?]?\?]?O?¤r/_

rz?`Â EJNJPSDK8McM¸MFUcPnFHe#I/c9t88AQHEJo*p8McMFIziA|PSD3EJo*p8MZcc9p8QN½¨sI/QHEGMZD¦FTPnFHEJI/D«K8MONVPvW.MQHQ9M0?¤r/_rz?`Âz? x ¸MFHcc9p8QNJM¾efI/p3SMZefMZD¦FK8ptu¿/NGM?\?]?]?\?]?\?]?]?]?]?]?\?]?\?]?]?\?]?O?¤r/_rz?`Âz?ª_ ¸MFHcc9p8QNVPvNJISD8/p8Mp8QK8pÁÀ9I/p8Q§?]?\?]?]?\?]?\?]?]?]?]?]?\?]?\?]?]?\?]?O?¤rSw

,Y,Y ;¡ yL'z-/5u!1:5u|4 (4h5u,"Y!³;'*5u1:5 ,46 =$ z,!ÆY28%<!5u,Y4¹Y #Z1.ÆY'*%<4¹Y R7=¹4h ,.2u -f=6

!5u! ,(v"±´4¹,$ *%(46 uÃÁ? x¶I/QHeXp3NVPSEGQHMÊ?\?]?]?]?]?]?\?]?\?]?]?\?]?O?\?]?\?]?]?\?]?\?]?]?]?]?]?\?]?\?]?]?\?]?O?j/kÃÁ?`_ @BAZefI/D8cmFUQHPnFUEGI/DÊP8Q9AZ/AM ?]?\?]?]?\?]?O?\?]?\?]?]?\?]?\?]?]?]?]?]?\?]?\?]?]?\?]?O?j¦rÃÁ?lk§~EJMZD3cPSMZi]NJMcefI/efMZD¦FUcK¨lEGD8MZQmFUEJMBK8MONVPvW.MQHQ9M ?\?]?\?]?]?]?]?]?\?]?\?]?]?\?]?O?j¦Â

5,Y28, #Y|$ =¹=h x 4·=6465;³;%(281.Æ.4h 3>

k

u

# f B º

! #"$ &%' (!)+*, -.%"/,0"$ 1%2 (!)3*&, 45)-/-6)~$PQHISFUPnFUEGI/DK8MvNJP«W.MQHQ9MvMZc9FOK3ACD8EGMviZI/efefMÁNVPQ9ISFTP<FUEJISD&K8MvNJP«iZQ9I873FUMXFHMZQ9QHMZcmFUQ9MfISp0NJEGFH8In©

cHt38dZQ9MtPSQ]QUPSt3tI/QmFXPnpzÇAFUISEJNJMcZ?Y~MZc\I 8cHMQ9nPnFHEJI/D8cÁPSc9FHQHI/efAFHQHEGop3MZc]MFXSAZIK8AZc9EJo*p8MZc\QHA/dZNGMZD¦Fo*p8MNVPiZQHI973FUMc9MK8AghISQHefM9:<MF:o*p8MNGMZcAFUI/EGNJMZc.cHI/D¦F±NGI/EJD\K8MiZISD8c9FHEGFUp3MZQK8Mc PSNGEJcHMc·EGD8DPSefIzE 8NJMcZ?; D3MQHISFUPnFUEGI/D«D3MtISp3nPSD¦F<FHQHMiI/D8c9EJK8AQHAZM¾o*p¨sMZD¦FHQHM¾K8MpzÇcmbc9FUde#McK¨`P(Ç3McQHEG/EJK3MZc:NVP]e#McHp8Q9Mt8Q9AZiZEGcHM¾K8MBNVPÁQ9ISFTPnFHEJI/D#FUMZQ9QHMc9FUQ9M¾D8AZiMZc9cHEGFHMONVP\K3ACD8E´FUEGI/DLMFNJPÁiZISD8c9FHQHp8iFUEJISDLt8QHAZPSNVP3NJMBK3MK8MZpÇc9bcmFUdZefMZc#K8MÊiZII/QHK3I/D8D8AMZcfi|PSQmFUAZc9EJMD8D8MZc&:±p8D>=1?@=1ACB1DFEGHEJILKNMOK1ILE1PRQSE!ACE1I1ILES=1ATILERMFfp8DU=1?V=1ACB1DFEGHE2ISKNMOK1ILE1PRQSEWQSK1XYES=1ACE?¢MXtuI/EGD*FMZcmFghI/D8K8PSe#MD¦FTPSNYt8p8EGcHo*p8MXD8InFUQHM\iZI/D3DPSEJc9cUPSD3iZMXK8MÁNVP#Q9ISFTP<FUEJISDFUMQHQ9MZc9FHQHMvMc9FOK¨lPSp3FUPSD¦F¾t8NJp3cCD8MXo*p8MvNGMZcQ9AghAZQ9MZD8iMZc]iZANJMZcmFUMc¾MFFHMZQHQ9MZcmFUQHMcOcHI/D¦FOt8Q9AZiZEGcHMcZ?.PSQMÇzMe#t8NGM9:¦c9ENJMZc±tuI/EJD¦FHc:/AZIK8AZc9EJo*p8Mc®K8pfQHAghAZQ9MZD¦FUEGMZN;iZANJMZcmFUMcHISD*F®iZISD8D*p8c®c9MZp8NGMZefMZD¦F[ZO¥\: x^]t8Q9dZc&:N½¨sM¸MFK8M]NVPRD8I/DQHEJSEJK8E´FUA¾K8M]NVPRW.MQHQ9MÁcHp3QBNVPvD*p3FUPnFUEGI/D&K8M]N½¨lP<ÇzM]K8MÁQ9ISFTPnFHEJI/DÊK8Me#Mp8QHMQUPR/I/EGNJAS?~$PfefMZc9p8QHM]K8M]NVPvQHInFTPnFHEJI/DLFUMQHQ9MZc9FHQHM\D8AZiMZcHc9EGFHMXPSp8c9cHE$p8D8M]QHAghAZQ9MZD8iMÁK8MOFUMe#t8ct8NGp8cc9FTP 8NJM]o*p8MiZMNJNGM¾K8I/D8D8AMOtPSQNJM¾ibziNJMOK8EGp8QHD8Mn?

W.ISp3FUMciZMc¾QUPSEGcHI/D8cD8I/p3c¾PSefdZD8MD*F_Z«iZISD8cUPSiQHMQiZMXiT8PSt8EGFHQHM\EJD¦FUQ9IzK8p3iFUE´g±PSpzÇcmbzcmFUde#Mc¾K8MQHAghAZQ9MZD8iM\c9tPnFUEGIn©+FHMZeftISQHMZNGcZ?

L` aWbFc"$dfe )g(J)g-.ihj-.)fJkl)3"$)-/-6)fc"m-.)~Mc9bc9FHdZefM¾K8MBQ9AghAQHMZD3iZMFUMQHQ9MZc9FHQHMj:P8Q9AZ/At8PSQa3.W0:3MZcmFp8Dcmbc9FUde#M¾K¨`P<ÇzMc

(Gxyz)tPnQm©

FUEGiZEGtPSD¦FnZNVP QHInFTPnFHEJI/D[K8MNVP iZQHI973FUMÊFUMQHQHMc9FHQHM&MFKPnD8c#NGMZo*p8MNNGMefI/efMZD¦F#iZEJD3AFUEGo*p8MQ9MZNJPnFUE´gK8M\iZMZNGNJM ©¼iZE$Mc9F¾D*p8N¹?MZNJPnFUE´/Me#MD*FoZ#iMXc9bcmFUdZefM9:K8EGFK8M0pWEJc9cHMQUPSD8Km]j:NGM\iT8PSe#t&K8MZcK3AZt8NJPSiZM ©efMZD¦FUcK8pe«PSD¦FHM|PSpÊFUMQHQHMc9FHQHM]MZc9FEGQHQHInFTPnFHEJI/D8D3MZNq:i|PnQc¨lEGNiZI/D¦FHMZDPSE´Fp8D8M]QHISFUPnFUEGI/DLcHI/DefI/e#MD¦FiZEGD8AFHEJo*p8M¾Q9MZNVP<FUEGgcHMZQHPSEGFD8I/Dz©+Dp3N8rPSp3FHQHMe#MD*FK3EGFO:zEJND8M¾iZI/D¦FHEJMZD¦Fo*p8M¾K8McK8AghI/Q9e«P<FUEJISD8ct8p3QHMZc?¢MZtuMZD3KPSD¦FO:;p8DÊFUMNc9bc9FHdZefM\Mc9FK8ACD3E$Zfp8D3M]Q9ISFTP<FUEJISDLiZI/D8cmFTPSD¦FHM\t8Q9dZc?;.I/p8QNJM¾K3ACD8EGQt8QHAiZE©cHAe#MD¦FO:EJNcHp\sRFK8MOc9FHEJt8p3NJMZQNVPXtuI/cHE´FUEJISDK8pÊt¿SNJMD8ISQHK/AZI/SQUPSt83EJo*p8M0Zvp8DÊefI/e#MD¦FK8I/D8D8A¾MFNJMe#AQHEGK8EJMD«I/Q9EJ/EGD8MS?z¢B¨sMZc9FiZMo*p8M¾N¹¨lI/DP\g6PSEGF®MZDg6PnEJcUPnD*FiZI9t½D8iZEGK8MZQ®NJMt¿/NGMD3I/QHKL/AI//QHPSt88EGop3MP|/Mi«NVPLtuI/cHE´FUEGI/D0K8p!tu¿/NGMvK8M#Q9ISFTP<FUEJISD/MZQ9cÀHPSD¦EJMQ x/¥/¥3?/upPnD*F\PSp²efAZQHEGK8EJMD I/QHEG/EJD8Mj:in¨lMc9FiZMNJp8Eop3EYEGcHc9pK3ptu¿/NJMBD8I/QHKtPSc9cHM]tPSQwv¾QHMMZD¦£8EJiT?@MZt8p8EGc:NGM¾t¿/NGMK8MOQHInFTPnFHEJI/DÊPvK8AQHEGSAOK8Mt8NGp8cHEGMZp8Q9ce#dFUQHMctPSQQUPSt3tI/QmFPSpÊt¿SNJM¾D8I/Q9K?

~:¨yxOzE0GHES=|~XYES=iHKS9Ix1|~HT~ES=Gz

Mc9F®/I/EGcHEJD#K8MN½¨YxOzE0GHE/.9HILE1:o*p8EuMZcmFN¹¨`P<ÇzMK8MBcmbe#AFUQHEGMK8MÊN½¨sMZNGNJEGt8cHI9t½K8MRFUMZQ9QHMc9FUQ9MÊK8MÊQHAghAQHMD8iZMn?¢MFfMZNGNJEJt3cHI9t½K8M«Mc9Ffp8D8MLC/p3QHMLEJK3A|PSNGEJcHAMK¨sp8D8MÊWYMZQHQ9M

^

o*p8E±cHMQUPSE´F\iI/D8cmFUEGFHp8AZMfK8MfiZI/p3iT8MZc\8I/efI//dZD3MZcOMF\D8MfcHp 8EGQUPSE´FOPSp8ip8D8M#K8AghI/Q9e«P<FUEJISD?YI/p8Q]K8MNJISD8/p8Mc¾AZiT8MNJNJMc¾K8MvFUMe#t8c&:t8NGp8c¾/QUPnD8K8MZcOo*p8MRNJMc¾tAQHEGIzK8McK8MRiZISD*SMZiFUEJISDKPnD8c¾NJMve#PSD¦FUMZPSpEJN·MZc9F]iI/D8iZMnP8NJMRo*p8MfNJMc]K3AghI/Q9e«PnFHEJI/D3cBFUMQHQHMc9FHQHMZc]cZ¨lPSD8D*p8NGMZD¦F\MZD²e#Ib/MD8D8Mj:YK3Mfc9I/Q9FHMRop3M#NJPWYMZQHQ9M¾t8QHMD8D8M¾NJP\ghI/QHefMBK3M¾iZMFMZNJNGEJt8c9I9t+K3MK8M¾Q9AghAQHMZD3iZMS?8~±¨lP<ÇzM¾K8MCSp8QHMQ9MZt8Q9AZc9MZD¦FUMOK8I/D3i¾N½¨lP<ÇzMK¨sEJD8MQ9FHEJMDF?^E1PÊK8MvNVP«WYMZQ9QHMn?~:¨lAi|PSQmFOMZD¦FUQ9MfN¹¨`P(Ç3MÁK8MXC/p8Q9MvMFON¹¨`P<ÇzMXSAZI//QHPSt88EGo*p8M

GzD¨lMc9F

tPScfQHEG/I/p8Q9MZp8c9MZefMZD¦FfiZI/D3c9FTPnD*F:I/D I 8c9MZQ9SM&o*p8MN½¨lP<ÇzMÊK8MLC/p8Q9MK8AQHE´/MÊ/MZQ9c#NGMvOQ9IzMD8NVPSD3KP|/Mifp3D8MvzE´FUMcHcHMRK8MR¥z?l^ ]ncHEGdZiZNGM9:t8QHI 8P8NJMe#MD¦F ZLi|PSp8c9MvK8MRNVP«Q9MZefI/D¦FUAMfK3MZc¾cHISNJc¾D8I/Q9K8EJo*p8Mc½ai|PSD8K3EJDP|EJM ©p8cHc9EJM c9I/p8cN½¨sM¸MFK8MONJPÁghI/D¦FUMOK8MZc/NJPSiZMcPSQHiFUEJo*p8Mc ! ?

~$PQHAZPSNJEGcUPnFHEJI/D t8QHPnFUEGo*p8M#K3p[a3·W0:YNJMRQHMtdQHM#K8M«Q9AghAZQ9MZD8iM«FUMQHQ9MZc9FHQHM#I/p ·W0:$MZc9F\ghI/D8K8AMcHp3Qvp8D e#IK8dNJM«SAZI/t8¦bcHEGo*p8MLK8p[e#ISp3/Me#MD*FXK8MZcvt8NJPSo*p8MZcXFHMZiFUI/D8EGo*p8MZcvMFvcHp8Qvp3D MZD8c9MZe 8NGMK8McmFTPnFHEJI/D3cK¨sI 8c9MZQ9nPnFHEJI/D3cZÁNJP\cHp3Q9g6PSiMK8pL/NGI Mn?~$McI 8c9MZQmSP<FUEJISD8c/AIzK3AZcHEGo*p8MZctuMZQ9e#MFHFHMZD¦FK¨lPjsfD8MZQRNGMLtI/c9EGFHEJI/D8D3MZefMZD¦FvQHMNVPnFHEGgK8McfcmFTPnFHEJI/D3cZ?:~MZcRiIzI/Q9K8I/D8D3AZMZcfK¨sp8D /QHI/p3tMLK8MÊtuI/EJD¦FHc/AIzK8AcHEGop3MZc :.P<¸QHPSD8iT8EGc]K3MfNGMZp8QOefI/p3SMZefMZD¦FÁK3Mfe#PSQ9AZM9: p¼QHAZPSNJEGcHMZD¦F@]vNGMf·W¾?Y¢Mc\iIzISQHK8I/D©D8AMZcBiI/eft8QHMD8D8MZD¦FoZÈNVPXghI/EJcp8D3M\tuI/cHE´FUEGI/DÊEJD8E´FUEVPnNJM_ZRp8DEJD8cmFTPSD¦FK8I/D8D3A

t0MFNJMOK8AZt3NVPSiMZefMZD¦F

FUMiFHI/D8EJo*p8M 6iI/D8c9EJK8AQHABiI/efe#MNGEJD8AZPSEJQ9MMZD#ghISD8iFHEJI/DfK8p#FHMZeft8c ?~$M·WMZD#p8cUPn/MQ9A|PSNGEJc9Mp3D8MiZISD8K8EGFHEJI/DLK3M]WEGcHc9MZQUPnD8K&PncHcHM \SQHI/c9cHEJdQHMOtuI/p8QNVPvNGEGFU3I/cHt83dZQHMn?

~MBaMZQ9EGiZM»¼D¦FUMQHDPnFHEJI/D8PSN8K8MNJP¾ISFUPnFUEGI/DXK8MNJPBW.MQHQ9MMF±K8MZc®abcmFUdZefMK8MAghAZQ9MZD8iM h»¼D¦FUMZQ©DPnFHEJI/D8PSN;±PSQ9FHLInFTPnFHEJI/D#PSD8K«MghMZQHMD8iZM¶;QHPSefMazMQ9EJiM ±MZc9FiTPSQ9/ABK8MQHAZPSNJEGcHMZQMF®e#PSEJD¦FUMD8EJQp8DLFUMNQHMtdQHM9:;Pnt8tMNJAwp¼»¼D¦FUMZQ9DPnFHEJI/DPnNWYMZQHQ9MZcmFUQHEJPSN$MghMZQ9MZD8iM]¶;QHPSefM^]BI/pÊ»¼W¶ F#"SiT3M¾iZI/D3C8AZMZvN½¨s»¼D8c9FHEGFHp3F vOAI//QHPSt88EGop3MOÉBPnFHEJI/DPnN ?

@PSD8c·NVPFHMZQ9e#EGD8I/NJIS/EJM:PniFUp3MZNJNGM9:(I/D\K8EJcmFUEJD3/p8MNJMZc.D8ISFHEJI/D8cYK8M =1?@=1ACB1DFEfGHElILKNMOK1ISE1PRQSEMFILEC|~B1ILEGHE ILKNMOK1ILE1PRQSE?~MvcmbzcmFUde#MvK8MRQ9AghAZQ9MZD8iMRMZc9FOp3D²cmbc9FUde#MRK¨lP<ÇzMZc¾K3ACD8E:t8PSQp8D iZISD8iZMt3FO:e#PSEJcpK3AZcHEGD8i|PnQHD8A8]OtPnQI/t8tuI/cHE´FUEJISDJZRcHPfQ9A|PSNGEJc9EJI/Dt3QUPnFHEJo*p8M9:3NJM¾QHMtdQHM]K8MOQHAghAZQHMD8iZMn?

%$ aWbFc"$dfe )g(J)g-.ihj-.)fJkl) kli*1)fc"$) kl &!fe , "$ '&)(!)~MQ9AghAQHMZD¦FHEJMZNiAZNGMZc9FHMMc9FNJMghISD8K8MZefMZD¦Fe <ZefMK8MN½¨lPSc9FHQHI/D8ISe#EGM9:<i|PSQ&:¦cUPSD8cNJp3Eq:SEGN8D¨ bRPSp8QHPSEGF

tPScefIb/MZDK8MOQHMNJMSMZQNJMctI/c9EGFHEJI/D8cK8MZcPSc9FHQHMcMFK3M]iZPSK8Q9M\tuI/p8QAFUp8K8EGMZQNJMp8QHcefI/p3SMZefMZD¦FUc?»¼N¾MZDµMZcmFD8I/DµcHMZp3NJMZefMZD¦FNJMghISD8K8MZefMZD¦F:e«PSEGcÊPSp8c9cHEq:MZDµop3MZNJo*p8M²cHISQ9FUM NGM 8p3FO:iZPSQÊD¨sMZc9Fm©EJNt8PSct3QHI 8NGdZefMOt8NJp8cghI/D8K8PSe#MD¦FTPSNo*p8M\K8MÁK8AFUMQHefEJD8MQD3ISFUQ9M0p¼t8NVPSiM^]¾KPSD8cN½¨sp8D8E´/MQHc:;o*p8M\K8MK8AFUMZQ9e#EGD8MZQYD8I/cpe#PSQ9op3MZc@]±tPSQYQUPSt3tI/QmF.PSpv¢I/c9e#ISc+*a3PSD8cYD*p8NzK3I/p3FUMj:(NVPop\<FUMK8M®NJPQ9AghAQHMZD3iZMiZANJMc9FUM\P8c9I/NJp3M9:8iMZNJNGM¾o*p8EiZI/D3c9FUE´FUp8MONJPRQ9A|PSNGEGFHAp8NGFHEJefMBK8p¢I/cHefI/c&:3ghp3FN½¨sp8D8MOK8McefISFHEGnPnFUEGI/D8ct8Q9EJD8iEJtPSNGMZc.K8MN½¨lPSc9FHQHI/D3I/e#EGM®MF:K8MNJPBt8¦bcHEJo*p8M·À9p8c9o*p¨`Pnp-,.,dZefMc9EJdZiNJMj:/P|nPSD¦F±op3MNVPBe#P(À9I/Q9EGFUAK8McÁMZc9t8QHE´FUc]D8MfcHMfQUPSNGNJEJM ZNVPLiI/D8iZMt3FUEGI/DPniZMZD¦FHQHEJo*p8M#MF\QHMNVPnFHEGEJcmFUMvK8pe#I/D3K8MvghI/QHe#PSNJEGcHAvtPnQNVPÊFU8AI/QHEGM«K8M#NVPMNVPnFHEGEGFHAS?$@BdcvN½¨sÃBD¦FUEGop3EGFUAfcHM«tI/cHP&NVPo*p8MZcmFUEJISDK8p QHAghAZQ9MZD¦FUEGMZN®PSp8o*p8MZNI/DK8MSPnEGFvQHPSt8tuI/Q9FHMZQÁNGMZcvefI/p3SMZefMZD¦FUcvK8Mcvt8NVPnD8dFHMZcZ?~$ISD8SFUMe#t3cXe#EGcHM#cHI/p8cvNGM uI/EJc9cHM|Pnp tPSQXNGM/AIziMZD¦FUQ9EJcHefM¾PSQ9EJcmFUISFHAZNJEGiZEGMZD:*MZNGNJMQHA|Pnt8tPSQHP0/JFHQUPÁPnp1,B¬»¼de#M¾c9EJdiZNJMj:3MFcHM¾iQHEJcmFTPSNGNJEGcHMZQHP\KPnD8cNJMco*p8MZQ9MZNGNJMZctPncHcHEGI/D8D8AMZcK8p2,B¬B»H»¼dZefMOcHEGdZiZNGM¾I/t8tuI/cUPnD*FHcip¼8AZNGEJIiZMD*FHQHEGc9FUMc@]BMFip¼/AZIiZMD¦FUQHEGc9FHMZc@]<?$! "$ %('*)+'*%< ,Y-/ -/'=6 -¦4¹,$'!23(46$ +3 ~$Pe#PSD8EJdQHMNJP!t8NGp8cDPnFHp8QHMNJNGMMZcmFÊK8Mt8Q9MZD8K8Q9MiZI/efefM®Q9AghAZQ9MZD8iMNJMcAFHI/EJNGMZc4SNJMciG9 ILESQ1ATqP\=iILE1X x9A 59ES=YK3McHEG/DPSpzÇ\ANJMZiFUQ9I/e«Pn/D8AFHEJo*p8McEJc9E 8NGMZcISpLD8I/DghI/Q9e#MD*Fp8Dnpe#PSEGNJNVPn/M^]j:nK8I/D¦FNGMZcD8IMZp3K8cghI/p8Q9D8EJc9cHMD*FK3MZctuI/EJD¦FUc®K8MQ9MZtudZQUPn/MtuI/p8QNJMcPSc9FHQHMZcNGMZcP|/I/EGcHEJD8PSD¦F|?

6 p8cHo*p¨lPSp7,B¬B»H»¼de#Mc9EJdiZNJM®I/DviZISD8cHEGK8AZQHPSEGF·iZI/efeXp8D8Ae#MD¦Fo*p8MNJMc·AFUI/EGNJMZc.AFUPSEJMD*FPnFHFUPSiT8AMZc

r

cHISNJEJK3MZefMZD¦F/Zp8D8McHt88dQHMj:<NJPcHt88dQHM®K8MZcC3ÇzMZc&:nK3I/D¦F.NGM:iZMD*FHQHM®AFTPnEGF$NVPFHMZQ9QHMS?n¢B¨sAFUPSEGF$NJPQ9AghAQHMZD3iZMP8c9I/NJp3M9:8Q9AZtuI/D8KPSD¦FwZvN½¨sEJK3A|PSNuPSQ9e#I/D3EJMZpÇK8MONJPÁt88EGNJI/c9I/t88EGMB/Q9MZiZo*p8M]MFPnpiT3QHEJcmFUIiZMD*FHQHEGcHefMK8M¾NJP]ghI/EiT8QHAFUEJMD8D8Mn?~:¨lI/t3EJD8EGI/D8ANJEJIiZMD¦FUQHEGo*p8M9:MZDÊcHISEq:D¨lAFTPSE´FtPncK8AZ¦Pn/AZMK3pt3QHAÀ9p3/AK8M¾NJPcHt38dZQ9MK8Mc:C3ÇzMZcZ?z¢I/tuMZQ9D8EJic9MiZI/D¦FUMD¦FTPOK¨`P|nPSD8iMZQ±o*p8MNJMiMZD¦FUQ9MK8MNJPcHt88dQHMK8McC3ÇzMcD¨lAFTPSE´FtPScNJPRWYMZQ9QHM]e«PnEJcNJM¾c9I/NJMEJN¹?8~$PfK3AZiZISp3/MQ9FUM\K8p&efI/p3SMZefMZD¦Ft8QHISt8QHMOK8McAFUI/EGNJMZcPnp ,¬»H»9»¼dZefMcHEGdZiNJMPnF9FUp3F]K8ACD8EGFHEGSMZefMZD¦F]MZD 3Q<ZiT3M«iZMFHFHM#iI/D8iZMt3FUEGI/D?$~$PÊQHAghAQHMD8iZM«P8cHISNJp8MRcHMfK8ACNVPSE´F|?¢MZtuMZD3KPSD¦FO:NGMZcQ9MZNJM/AcK8MZctuI/cHE´FUEGI/D8cK3MZcAFHI/EJNGMZcc9Mg6PSEJcHPSEJMD¦FFUISp<À9I/p8Q9ct8NJp3ct8QHAiZEGcZ?3ÃpÊiZI/p8Q9cK8p-,B¬»9»¼dZefMc9EJdiZNJMj:*N½¨sEJD¦FUQ9IzK8p3iFUEGI/DRK8MZcEJD3c9FUQ9p8efMZD¦FUcK¨sI/t3FUEGo*p8M9:QHA/I/NGp3FUEGI/D8DPSE´F:N½¨lPScmFUQHISe#AFUQHEGM9:t8p8EGcHo*p8M#NVPÊt8QHAiZEJc9EJI/D²K8ptuI/EGD*FHA9:M Ç3iNJp8c9EGSMZefMZD¦FÁEJc9p8MZNÀ9p8c9op¨ Z&iMF9FUM«AtIo*p8M9:$tPncHcUPnEGF\K8ML_z¨ZefI/EJD8c\K¨sp8D8MLcHMiZI/D3K8MÊK8MLK8MZSQHAS? ¾D McHiI/e#tzFTPSE´FvtMQHiMZQviZMQ9FUPSEJD8cÁeÁbc9FUdQHMc::iZISe#efM«iMZNJp3EK8MNVP K8EJcmFTPSD3iZMK8MZcfAFHI/EJNGMZcRo*p8Ee«PSEGD¦FUMZD8PSEGFRMDPSNGMZEGD8MÊNJMZcfPScmFUQ9I/D8I/efMZc?ÃEJD8c9Eq:±PSp[ghp8QfMFFZefMZcHp3QHM]op3M\NJPRQ9AghAQHMZD3iZM]K8MZcAFHI/EJNGMZc]C3ÇzMc@]\tuMZQ9KPSEGFc9I/Di|PSQmFTPSiFUdZQ9MÁP 8cHI/NGp:cHISDEGD*FHAZQ<Ft8QUP(©FUEGo*p8M\iQHI/EGcHcHPSEGFZ?;.I/p8QefMZcHp3QHMZQNJMOefI/p3SMZefMZD¦FK8Mct3NVPSD8dFUMc:uiT8MZQ9iT8MZQNJMZctPSQHPSNJNJP<ÇzMZc&:K8AZiMZNJMQNJMc¾SPnQHEVP<FUEJISD8cBK8MfNVPQ9ISFTP<FUEJISDFUMZQ9QHMc9FUQ9M9:$EJN.g6PSNJNJPSEGFK8MZc]i|P<FTPSNGI//p8Mc¾K¨lAFUI/EGNJMc¾K8I/D8DPnD*F]NGMZp8Q¾K8A ©iZNGEJDPnEJcHISDLMFNJMp8QPScHiMZD8c9EJI/DK8Q9I/EGFHMFUI/p<À9ISp8QHct8NGp8cghI/p8Q9D8EMFt8Q9AZiEJcZ?;~MOefI/p3/Me#MD¦Ft3QHI/t8Q9MOMZDcHISED¨sMZcmFtPScp3DLI 8c9FUPSiZNGMghI/D3KPSefMZD¦FTPSN :*tI/p3Q9pLo*p¨lEGNc9I/EGFiZI/D3Dp?~$PÁiZI/D3DPSEJc9cUPSD3iZMK8MciZII/Qm©K8I/D3D8AZMccHt83AZQHEGo*p8MZcK3MZc¾PScmFUQ9MZc_Z#p8D8MÁAtIo*p8MÁK3I/D8D8AM9:MFK8M\NJMp8QefI/p3SMZefMZD¦Ft3QHI/t8Q9MÁNGM\iZPScAZiT3A|PSD¦FO:MZc9FBcHp\sfcHPSD¦FOtI/p3QghI/p3QHD8EGQp8D&e«PSEGNJNJPS/MK8M\QHAghAZQHMD8iZMWZfNVPfKPnFUM\K¨sI 8cHMQ9nPnFHEJI/D?;¬±MZQ9cx(Ân^/¥ QUPnK8NJMb«K8AiZI/pzzQ9EGFp8DLip8QHEGMZpzÇe#ISp3/Me#MD*FPSD8D*p8MZNo*p8EPn¸MZiFUPSEGFc9bc9FHAZe#PnFUEGop3MZefMZD¦FNJMcAFHI/EJNGMZc&:¦N½¨lPMQHQHPnFUEGI/D:/MFK8I/D¦F®I/D«tuI/p3nPSE´FQHMZD3K8QHMiZI/eft3FUMtPSQNVPOiZISe#tuI/cHE´FUEGI/DvK8MBNJPOE´FUMZc9cHMK8MNVPXNGp8efEJdZQ9MP|/MiONVPÁEGFHMZcHc9MOI/Q 8E´FTPSNGMBK8M¾NJPXW.MQHQ9MS?;:D xw/k/¥ McHc9MZN$e#MFHFUPSEGFMZDAEJK8MD8iZMONJPXt8QHM ©efEJdZQ9MtPSQUPnNJNVP(Ç3MPSD3Dp3MZNJNGMS?*»¼NuPSt8tPnQUPSEGcHcUPnEGFK8I/D8io*p8MBKPnD8cNGMcmbzcmFUde#M/AZIiZMD*FHQHEGop3MBNJMc®AFUI/EGNJMccHISD*F\Pn¸MZiFUAMZcOK8MvefI/p3/Me#MD¦FUcOc9bc9FHAZe#PnFUEGo*p8MZc]PSc9cHIiZEJAcZN½¨sI/Q 8E´FUMvPnD8D*p8MZNGNJMS?¢MZNGp8E´©+iZE·D¨lAFTPSE´Ft8NGp8cXNJM#i|PSK3QHMLPSK3AZo*pPnFRtuI/p8Q\iZII/QHK8ISD8D8MZQÁNJMZcÁAFUISEJNJMcZ?Y»¼NK8M/MDPSEGFRAEJK8MD*FXop3MLNJMZcÁtI/c9EGFHEJI/D8cPSt8t8PSQHMD*FHMZcK8McAFUISEJNJMcK8MSPnEJMZD¦Fi<FUQ9M¾K8I/D8D8AMZcKPSD3cp8DÊc9bc9FHdZefM]3AZNJEGIziMZD¦FUQ9EJo*p8MI tPSQUPnNJNVP(Ç3MMF]P MQHQUP<FUEJISD0PSD8D*p8MNJNJMc¾cZ¨sAnPSD8ISp8EJc9cHMZD¦FZ?/u¾p3EGFUM ZiZMvo*p8MRiZMc]tuMZQmFUp8Q PnFHEJI/D8cBcHI/EGMZD¦FOi|PSNGiZp8NGAZMcMFt8Q9EJc9MZcMZDiZI/eft3FHMOPSpefI/efMZD¦FK8MON¹¨lI 3cHMZQmnPnFUEGI/Dg6PSEGFHMOPSpÊcHI/N¹?

ÃBpÊK8A 8p3FK8p2,» ,BdZefMcHEGdZiNJM9:3PSNJISQHco*p¨sI/DPvPPSD3K8I/D8D8AFUI/p3FHM¾EJNGNJp8c9EJI/Dfo*pPSD¦FwZXNVPÁD8PnFUp8Q9MP8c9I/NJp3M\K8pQHMtdQHMÁK3MZcBAFUI/EGNJMc:I/De#MFBMD&AEGK8MZD8iMXNVPRDPnFHp8QHM]I/D8K3p8NVPnFHI/EJQ9M¾K8MÁNJPfNGp8efEJdZQ9M9:8MFtPSQNJPven<e#Mj:zFUISp3FPSpÊe#I/EGD8cNGM¾iZQHISEGF9©+I/D:zN½¨sMÇzEJcmFUMZD3iZMOK8MOcHI/DefEJNJEGMZp#K8MOt8QHI/t8PS¦PnFHEJI/D:^pN¹¨lAFU8MQNJp3e#EGD8EGghdQHM^]<?S¢MFAFU3MZQ:SiS¨sMZc9Fp8DfD8I/pz/MZN;P|nPnFUPSQKPSD3cNJPBQHMiT8MZQ9iT8MBK3pfQ9MZtudZQ9MP 8cHI/NGp?/~$P¾o*p8MZc©FUEGI/D²iZMZD¦FHQUPSNGM#K8MEJMZD¦F Yo*p8MNJNGMfMc9FÁNVPLe#ISp3/Me#MD*FÁK8MfNVPÊW.MQHQHMfKPSD3cÁiZMfefEJNJEGMZp *f~YPÊNJp3e#EGdZQHMt8Q9AZcHMD¦FTPSD¦FRp8D8M#zE´FUMcHcHM«p8D8EGghISQHefM#KPnD8cÁN¹¨lAFU8MQ:·cHPEGFHMZcHc9MMZcmFviTPSD3/AZMt8PSQÁQHPSt8tuI/Q9F ZFUI/pzFI À9MFOcZ¨ b0efI/p3nPSD¦F|? ¾D Q9A|PSNGEJcHMQUP#FHI/p3FHMZcOcHI/QmFUMc¾K¨lM ÇztAQHEJMD8iZMc\ISt3FUEGop3MZc¾tuI/p8Q¾K8AiZMZNGNJMQNJMÁg6P(©efMZpzÇ p¼/MD¦F#K¨lAFU8MQ@]KPSD8cvNJP&EGFUMcHc9MK3MLNVP&NGp8e#EGdZQ9MS?~$Pt8NGp8cXg6PSefMZp8c9MMZcmFfN½¨sMÇztAQHEGMZD8iMLK8MEGiT8MZNGcHI/DMF I/Q9NJMb xw/w/Â ? PSEJcPSp8ip8D8M]K¨sMZD¦FUQ9M\MNJNJM¾D3M\K8Ae#ISD*FHQHMQUPRp8D&o*p8MNJiZISD8o*p8M\M¸MFK8p e#ISp3/Me#MD*FfI/Q 8EGFUPSNI/p[K8MNVP&E´FUMZc9cHMiZI/c9e#EGo*p8MÊK8MÊNVP0W.MQHQ9MS?±~$P²t8PSQHMD*FH8dZc9MK3MN¹¨lAFU8MQcZ¨sMZcmF¾QHMghMZQ9e#AÁPSMZiXNJPfFH8AZI/Q9EJM]K8MÁNJP«MZNJPnFUE´zE´FUAj:K¨`Pnt8QHdcBNVPnop3MZNJNGMONVPfE´FUMZc9cHMXK3MÁNVPfNJp8efEJdQHMOMZcmFEJD¦nPSQ9EVP8NGMBK¨sp8DQHAghAZQHMD¦FUEJMN/ZRN¹¨`Pnp3FUQ9MS?

@BMZt3p8EJcNJM ,B¬B»H»H»¼de#MOc9EJdZiNJMOK8M\D8I/e 8Q9MZpzÇiZPnFTPnNJI//p3MZcK¨sAFUISEJNJMcI/D¦FpNJMÀ9I/p8Q&:uNGMOK8MZQ9D8EJMQMZD!KPnFUM#AFUPSD¦FXiZMNJp8EQHAZPSNJEGcHAR/Q "SiZM«PSpzÇI 8c9MZQ9nPnFHEJI/D3c\K8p!cUPnFHMZNJNGEGFHMEJt8t8PSQHiI/c]SMZQ9c x//¥z?·¢M ©tuMZD8KPnD*F:mZLtPSQmFUEJQK8M1x¦Ân¥\:NJP«FUMZiT3D8EJo*p8MRK8MvNJP«QUPSK3EJILEJD¦FHMZQ9ghAQHI/efAFHQHEGM Z«FUQ9dZc¾NGI/D8/p8M PScHMj:$PefEJc:p8DfFUMZQ9e#MPSpfQHd/D8McUPSD3c®tPnQ9FTPn/MK8MZc®AFHI/EJNGMZc *PSNGI/QHc:o*p8MNJMZp3Q:tI/EGD¦FUAI/t3FHEJo*p8MMZcmFQ9MZc9FHQHMEJD¦FtPSQNJPvFHp8Q 3p8NVPSD3iZM]PnFUefI/c9t88AZQ9EJo*p8Mj:NVPvQUPSK3EJIREJD¦FUMQ9ghAQHI/efAFHQHEJM¾AEGFUMOp8DÊFUMN$AZiZip8MZEGNMFNJMcQHPSK8EGIcHISp8QHiMZc«M ÇFUQUPn¦PSNVPniFUEGo*p8MZc 6o*pPScHPSQHc&:[u]a vcHISD*F#tuI/cHE´FUEJISD8D8AZMc«P|SMZi&p3D8Mt3QHAZiEJc9EJI/DEJD8A¦PSNJAM9:

iZISD3CDPSD¦FNVPOe#EGNJNJEGcHMiZI/D8K3MK8MBK3MZ/Q9AS?z±Dx/¦ÂON½¨ ; D8EGI/DRÃBcmFUQHISD8I/efEJo*p8M»¼D*FHMZQ9DPnFUEGI/DPSNGM 6»¼Ã ; PiZISD8cUPSiQHANJMQHMtdQHMK8MZcQUPnK8EJI/c9I/p8Q9iZMZcMÇFHQUPS¦PnNVPSiFUEJo*p8Mc±PSp«QHPSD8OK8MQHMtdQHMK8MQ9AghAQHMZD3iZMBiAZNGMZc9FHMEJD¦FHMZQHD8PnFUEGI/DPSN 6»m¢¶l:z»¼D*FHMZQ9DPnFUEGI/DPSN¢MZNGMZcmFUEVPnNMghMZQ9MZD8iMO¶QUPSefM ?»¼NiZI/D3cHEJcmFUM¾KPnD8cNVP\K8I/D8D8AMK8MciIzISQHK8I/D3D8AZMc:i|PSQmFUAZc9EJMD8D8MZc±K8Mo*p8MNJo*p8Mc®iMZD¦FTPSEGD8MZc:K3MQUPSK8EGI¾cHI/p3QHiZMc±MÇFUQHPS¦PSNJPSiFHEJo*p8MZc·K8I/D¦FNJMc\efI/p3SMZefMZD¦FUcÁPSD8/p3NVPSEGQHMZcOQ9MZNVP<FUEGghcOD¨sMÇzidZK8MD*FRt8PSc x¥

−6 ”/an? EJMD!MZD¦FHMZD8K8p NGM#iT3I/E´Ç²K8p

t8NJPSD0ghI/D8KPSefMZD¦FUPSNMZcmFÁiI/D¦/MD*FHEJI/D3D8MZN¹?.~:¨sMZQ9QHMZp3Q\PnD8/p8NJPSEJQ9MXK8I/D¦F]cHI/D¦F\MZD¦F#"niT8AZc\NJMZcOtuI/EJD¦FHc¾K8MQHAghAZQ9MZD8iM\Mc9FK8MON½¨sI/QHK3QHM¾K8M]¥\:l¥/¥/¥¦r\]n?

W.ISp8cÁiMZcXcmbzcmFUde#McXI/pQ9MZtudZQHMcÁI/D¦FÁiZMZiE®MDiZISe#eXp3D:$op¨lEGNJc]cHI/D¦FÁghISD8K8AZc\cHp8Q\K8MZcÁI À9MFHciZANJMc9FUMcZ?¢I/e#efMREJNGc¾D8M#ghI/D¦F\EJD¦FUMQ9SMZD8EGQÁPSp3iZp8D8MfFU8AI/QHEGM#t3*bc9EJo*p8M9:.MF\cHI/D¦FÁMZD¦FUEGdZQHMe#MD¦FÁK8A ©FUMQHefEJD8AcÁtPnQ\NGMZcÁtuI/c9EGFUEGI/D8c&:YA/MD*FHp8MZNGNJMe#MD*FXNJMZc\e#ISp3/Me#MD*FHcXQHMNVPnFHEGghcOK8MiMZcXIÀ9MFHc:·ISDNJMcD8I/efefMc9bc9FHdZefMZcI/pÊQHMZtudZQ9MZciZEGD8AZe#PnFUEGo*p8MZc?

$! L"$ %('*)+'*%( z,Y-/ L-/'=h z L"$,Y284¹Y +3 ÉISFUQ9Mt3QHAZc9MZD¦FTP<FUEJISD«K8Mcc9bcmFUdZefMZc®K8MBQ9AghA ©QHMD8iZMiAZNJMc9FHMcHMZQHPSEGF·FUI/p3F ZBg6PSEGF·EJD8iI/e#t3NJdFHMc9E8D8I/p8cg6PnEJcHEGI/D8cN¹¨lEGe#t8PScHc9McHp3Q:NJMZc·K8ASMZNJISt8tMe#MD¦FUcK8MXNJP#efAZiZPSD8EJo*p8M Z«tPSQmFUEJQK8p ,¬»H»¼de#MÁcHEJdiZNGMS?~$Mct88EGNJI/c9I/t88McBc9iZI/NJPSc9FHEJo*p8MZcBcZ¨sAFTPnEJMZD¦F¾NGI/D8n©FUMe#t3cEGD¦FUMZQ9QHI/SAZc±cHp8Q±NJPOiZPSp8c9Mo*p8Et8Q9AZc9EJK8MwZONVP¾iZI/D3cHMZQmnPnFUEGI/DRK8p#efI/p3SMZefMZD¦FK8MZciZISQHt8c?3ap8EGFHMPSpzÇ!FUQHPnPSpÇ K8M vOPSNJEGNJAM#MFR@BMZc9i|PSQmFUMc:±NVP&c9iZEGMZD8iMK3M/MDPSD¦FfMÇztuAZQHEGe#MD¦FTPSNGMMFRI/tuAZQHPnFUE´/MMFt8Q9MZDPSD¦FcHMc®K3EJc9FUPSD8iMZc®PSMZiNVPefAFUPSt8¦bcHEJo*p8MMFNJPBFU8AI/NJI/SEJM9:nNJMc:cUP|nPSD¦FUcK8MEJD3QHMZD¦F®t8NJp3c:EJD¦FUA ©QHMcHc9AZcBt8PSQNJMopiI/e#efMZD¦F@]¾o*p8M]tPSQNGM ptuI/p8QHo*p8ISEC]n?8»¼NGcQHAZp3cHcHEGQHMD*FoZRK8AZ¦Pn/MZQK8MZcNJISEJc/AD8AZQHPSNJMcK8pe#ISp3/Me#MD*F:;K8I/D¦FNVPvc9bD¦FU8dcHMXK3ACD8E´FUE´/M¾ghp3Fg6PSEGFHM¾tPSQÉM£FUI/D?~$PRt8QHMe#EGdZQ9M¾K8M\iMZcNJI/EGc:iS¨sMZcmF]iZMZNGNJMXK3p | I# PRQ1 |~E GHEWX PRE1I#A qE1:ghISQHeXp8NGAÁtPnQv]PSNGEJNGAZM]MF]@BMcHi|PnQ9FUMc p+FUI/pzF¾iZI/Q9t8cOPSp8o*p8MNI/D²PLEJeft8QHEGe#A]p8D²e#ISp3/Me#MD*F]PFHMZD8KPnD8iZM ZLNJMvtuI/p8Q9cHp8E´zQ9MvK8Mvg6PZISD²Q9MZiFUEJNGEJ/D3MÁMF'Z«EGFHMZc9cHMp8D8E´ghI/QHefM^]<?*ÉM£FHI/DnPÁPSNGI/QHct8Q9AZiZEGcHMQ ^p Z\NJP]iI/D8K8E´FUEJISD«o*p¨sEJNuD8MBc9I/EGF®cHI/p3e#EGclZXPnp8iZp8D3MghI/Q9iZM^]:MFK8pen<e#MOiZISp8t&K8ACD8E´FNJPXghI/QHiM\iI/e#efMopAFTPSD¦FNVPRi|PSp3cHM]K8p&iTPnD8/MZefMZD¦FBK8M\N¹¨lEGD¦FUMZD3cHEGFHA¾K8pefI/p3/Me#MD¦FV]n?;~:¨sMÇztAQHEGMZD8iMÁNJp3Ee#I/D¦FHQUPSD¦Fo*p¨sp8DiZISQHt8c , ghI/EJct8NGp8cNJI/p8Q9KÊMZc9FBPSiiZAZNGAZQ9A , ghI/EGcefI/EJD8ctPSQNJMen<e#MM¸I/Q9F:3EJN;tuI/cHMBop3M¾NVP]ghISQHiZMBMZc9FNJMBt3QHIK8p8EGF®K8MNJP\e#PScHc9MtPSQ®N½¨lPSiZiAZNGAZQUP<FUEJISDcHp 8EJM®tPSQYiZMiI/QHt3cZ?S¢B¨lMc9F:NJPiAZNJd 8QHM®QHMNVPnFHEJI/D¾ghI/D8K8PSe#MD¦FTPSNGMK3MNVPK3bDPSefEJo*p8Mn?n~$Pop3MZc9FHEJI/DÁop3EcHMBtI/c9M¾PSNGI/QHc&:in¨lMc9FK8MBcUP|/I/EGQtPnQQUPnt8tISQ9FiZ\op3MZNJNGMBQ9AghAZQ9MZD8iMe#PnFUAQHEJMNJNGMiMZcNGI/EJcK8I/E´/MD*F<FUQ9MghI/Q9eXp8NJAMZc?~$P«QHAtISD8cHMj:MZeft8EJQ9EJo*p8M9:uiS¨sMZcmFOo*p8MviZMvcmbzcmFUde#MvK8MvQ9AghAQHMZD3iZMvD¨sMZcmFOtPScOPSiiZMZc9cHE 8NJMj:e#PSEJc®op¨lEGNtMp3Fi<FUQHMOQ9A|PSNGEJcHABPSt8t8Q9I|Ç3EGe«P<FUEGSMZefMZD¦F|?3:Dt3QHMZefEJdQHM¾Pnt8t8QHI|ÇzEJe#PnFHEJI/D#iS¨sMZc9FNGMNVPuIn©QUP<FUI/EGQHM9:ue#PSEJctuI/p8QBtMp²o*p¨sI/D cZ¨sEJD¦FHAZQHMcHc9MFZK8McOe#I/pz/MZefMZD¦FHc Zt8NJp8c¾SQUPSD8K3MvAZiT8MNJNJM\g6PSEJcHPSD¦FEJD¦FHMZQ9SMZD8EGQK8MZcPSiiZAZNGAZQHPnFUEGI/D8cFHI/p<À9I/p8Q9ct8NJp8cg6PnE 8NGMZc:zEJNug6PSp8K8QHPRt3QHMZD3K8QHM]cHp8iiZMcHcHE´/Me#MD*FBNJM¾cmbzc©FUde#MvSAZIiZMZD¦FHQHEJo*p8MvD3I/D0FUI/p8Q9DPSD¦FO:NJMXcmbzcmFUde#Mf8AZNGEJIiZMD*FHQHEGop3M9:NGMXc9bcmFUdZefMR¦PSNJPSiFHIziMZD¦FUQ9EJo*p8M9:MFHiS?´?

¢MQHAghAZQ9MZD¦FUEGMZNPIScHI/NGp«D8M£FUI/D8EGMZD:zeÁb*FU8EGo*p8M9:cHMe 8NJMcZ¨sEJD8iQHEGQHMMZDtuI/Q9FHM_Z\g6PnpzÇ :ziZPSQKPnD8cN½¨sp8D8E´/MQHcÁI8cHMQ9nP8NGM9:FUI/p3cÁNJMc\iI/QHt3cÁt8Q9AZcHMD¦FUMZD¦FRK8McXefI/p3/Me#MD¦FUcÁMD PSiiZAZNGAZQHPnFUEGI/DQ9MZNJPnFUE´/MS?ÃBNGI/QHc±iI/e#efMZD¦F®EJe#PS/EGD8MZQo*p¨sEJNbfPSE´Fp8D«iI/QHt8c®I/pfK8MZc®iZI/Q9t8cMD«tPSQmg6PSEGFefI/p3SMZefMZD¦Fp3D8EGghI/Q9e#MI/pPSpQ9MZtuI/cfP8c9I/NJp *&~$P²K8AZiI/p3/MQ9FHM&K8MNVP0QHInFTPnFHEJI/D[¦PSNJPSiFHEJo*p8MJZ²k/¥/¥*e1ncfP K8AFHQHI/D3ANGMPSQmbiZMZD¦FHQHMÁK3MZce«PSc9cHMcK3p&c9bcmFUdZefM]cHI/NJPSEJQ9MMZDFTPSD¦Fo*p¨lISQHEJSEJD8M¾tuI/cHc9E 8NGM¾K8pc9bc9FHdZefM\EGD8MZQmFUEJMN½?ÃBNGI/QHcOK8M/I/D3cm©¼D3I/p8cXtuI/cHE´FUEGI/D8D8MQ]N¹¨lISQHEJSEJD8MvPnp!iZMD¦FUQHM#K8M«NJPL¦PSNVP(Ç3EGM * &PnEJc]iZMZNGNJM ©¼iZE:D¨`PSiiZANJdZQ9MF9©+MZNGNJMÁSMZQHcON¹¨`PSe#PSc/PSNVPSiFUEGop3MXK8Mv¬EGQH/I4*QHMg :NJMvt3QHI 8NGdZefM9:cHI/p8cON¹¨`PSD3/NJMXD3M£FUISD8EJMD:t8QHMD8KN½¨lPSt8t8PSQHMD8iZMOK¨sp8D8M¾EJc9cHM]KPSD8cCD?

:DÁFU8AI/QHEGM®K3MNVPMZNVP<FUEGE´FUA v¾AZD8AQUPSNGM®I/D\FUQUPnD8iT8MiMD8IMZp3KX/I/Q9K8EJMD\MDXQHM¼À9MFTPnD*F·N½¨sEJK8AM®o*p¨sEJNMÇzEGc9FUMp3DvQHMZtudZQ9MP8c9I/NJp8efMZD¦F±PnpvQHMZtuI/c:KPnD8cNJMo*p8MZN8NGMZcNGI/EJc.K8MÉM£FUISDfc9I/EJMD¦F±QHEJSI/p8QHMp8cHMe#MD¦FcHp3EGEJMcZ?~M:i|PnQUPSiFUdZQ9M:EJD8MQ9FHEJMZNnMZcmF$NJIi|PSNnMF$cZ¨lPSt8t3NJEJo*p8M ZFHI/p3FiI/QHt3cYc9I/p8efEJcRZNJPcHMp8NJM±/QHP|zE´FTPnFHEJI/D6MDiT*p3FUM&NJE 3QHM ?:ÃBEGD8cHENJMQHMtdQHM/AZIiZMD*FHQHEGop3M&D8I/DFUI/p8Q9DPSD¦FO:±iI/D8cHEGK8AZQ9APSp/I/EGcHEJD8PS/MÊK8p

Â

iZMD¦FUQHM]K8MM]NJPvW.MQHQHMj:MZcmF9©¼EGNFUISp3FPSp8c9cHE$EJD8MQ9FHEJMZNo*p8M\NGM¾QHAghAZQHMD¦FUEJMN8AZNGEJIiZMD*FHQHEGop3MS?~M¾i|PSQHPSiFHdZQHMOEGD8DPSiiZMZc9cHE 8NJM¾K8pÊcmbzcmFUde#MOEJD3MZQ9FHEJMND8M£FUI/D8EGMZDÊD8MOK8I/E´FtPnce#PSc9op3MZQcHMcQHA|P(©

NJEGcUPnFHEJI/D3c®Pnt8t8QHI|ÇzEJe#PnFHEG/Mc:*I/p ILEC|~B1ILES=0G9?jP x9D T~ES=±i|PnQUPSiFUAZQ9EJcHPSD¦Fp8DQ9AghAZQ9MZD¦FUEGMZNEJD8MQ9FUEGMZN;NJIi|PnN½?~$PBt8NGp8c·iI/D8D*p8M9:SiS¨sMZc9F±NGM®Q9AghAQHMZD¦FHEJMZN PSQmbziMZD¦FUQ9EJo*p8Mj:/K8I/D¦F:N¹¨lI/Q9EJ/EGD8M±iZI/EGD8iZEGK8M®PSMZiNGM PSQmbiZMZD¦FHQHMK8Mce«PncHcHMcK8pcmbzcmFUde#M¾c9I/NVPSEGQHMn?z:DLM¸MFN½¨lPSt8t8NGEJiZPnFUEGI/DRK8MNVP]NJI/E;K8MBNVP\SQUP|EGFTP<FUEJISD«p8D8E´/MQHcHMNJNGMtuMZQHefMFÁK8MK8AiZQ9EJQHMfCK8dNJMZefMZD¦FvNJPFHQUP(À9MiFUISEJQHM#K8MZcÁt8NVPSD3dFUMcXMFÁK8p cHISNJMZEGN±KPSD8cXiMQHAghAZQ9MZD¦FUEGMZNq:e#PSNJ/Q9ABo*p8MNJo*p8MZcNGAZ/dQHMZcMZD¦FUI/Q9cHMcQ9AZcHISNJp8MctPSQNJPXMNVPnFHEGEGFHA0v¾AZD8AQUPSNGMS?8¢MZcFUQHP(À9MZiFUI/EGQHMcQHA|P(©NJEGcHMD*FXp8D[QHMZtudZQHPS/MLtuI/p8QXFHI/p3FRPSpzFUQHMLIÀ9MFZ?:·PSQvM ÇzMZeft8NJMj:cHED8ISp8cvI 8c9MZQ9SI/D8cRFUMNJNJM#I/p FUMNJNJMiZISe#dFUM!Z&t3QHI|ÇzEJefEGFUAfK8M 6 p8t3EGFUMQ:YD8I/p8cÁcHI/efe#McXMZD efMZc9p8QHMj:.EVPNVP&iI/D8DPSEGcHcHPSD8iZMLK3MNVPÊFUQUP(©À9MZiFUI/EGQHMPSQmbiZMZD¦FHQHEJo*p8M«K8M 6 p3t8EGFHMZQ:$K8MfNVPÊtuI/cHE´FUEJISD8D8MZQ¾K8PSD8cÁNGMRc9bc9FHdZefM PSQmbiZMZD¦FHQHEJo*p8Mn? ; D8MK8MpzÇzEJdZefMBQ9A|PSNGEJcHPnFUEGI/D: uM|PSp3iZI/p8tLt3NJp8cQHAiZMZD¦FHM9:8in¨lMc9FNGMQ9AghAZQ9MZD¦FUEGMZNe«PnFHAZQ9EVPSNGEJcHAtPSQNGMZc®I/Q 8E´FUMc/AIziMZD¦FUQ9EJo*p8MZcK8MOcUP<FUMZNGNJE´FUMZcPSQ9FHEGCiEJMZNGc:FUMZNop3M\NGMZccUP<FUMZNGNJE´FUMZciv]a?

»¼NMÇzEGc9FUMvp3D8MfPSp3FUQ9Mve«PnD8EJdQHMÁK¨`PSiiZAK8MZQ]PSpzÇQHMtdQHMZcOEGD8MZQmFUEJMNJcNJIi|PSpzÇ :cUPSD8cOtPncHcHMQOtPSQNGMFUQ9p8iT8Me#MD*F®K8MNVPefAZiZPSD8EGop3MD3M£FUISD8EJMD8D8MMFK8MNVP¾NGI/E3K8MNVPSQUP|EGFTP<FUEJISDvp8D8EGSMZQ9cHMZNGNJM ¦iMc9I/D¦FNJMcnbzQ9I/cHiI/tuMZcBefAZiZPSD8EGop3MZc:;NGMZcSbQHIn©+NVPSc9MZQ&:NJMZcSbQHIScHiZIStMc_ZfPnFUI/efMZcghQHISEJK8c&:op3EYtuMZQ9e#MFHFHMZD¦FK8MvefMZc9p8QHMQNJMc¾PSiZiAZNGAZQUP<FUEJISD8cK¨sp8D c9bc9FHdZefMve#Ai|PSD3EJo*p8M9:iZI/efe#M\NVP«Q9ISFTP<FUEJISD&EJD3c9FTPnD*FUPSD8AMvK8MNVPXWYMZQ9QHM]tPSQQHPSt8tuI/Q9FPSpÊQ9MZtudZQHM]EJD3MZQ9FHEJMNNJIi|PnN½?

aWbFc"$dfe )g(J)g-.ihj-.)fJkl)3"$)fe % -6)i*~MZcXK8AFUMQHefEJDPnFHEJI/D3c\PniFUp3MZNJNGMZc\K8M«NJPQHInFTPnFHEJI/D²K8M«NJPWYMZQ9QHMc9I/D¦FXK8AK8p8EGFHMZcXK3M«efMZcHp3QHMZcÁK8M

FUMe#t3cÁMÇFHQ<ZefMZefMZD¦F\CD8MZc?·@Mt8NJp3c\NGMZcOp8iFHpPnFHEJI/D8c\KPSD8c\NVPLEGFUMcHc9M«K8M#QHISFUPnFUEGI/DD3M#ghp8Q9MZD¦FefMZcHp3QHAZMco*p¨ ZXtPSQ9FHEJQ±K8pefI/efMZD¦F®I N½¨sI/D#cHp3FQ9A|PSNGEJc9MZQ±K8MZcAZiT8MNJNJMcK8MFUMZeft8c®t8NJp8c®c9FUP8NJMo*p8MiZMNJNGMBK8AiZI/p8NJPSD¦FK8MNJPÁcHp3iZMZc9cHEGI/DÊK8MZc.À9I/p3QHcc9I/NVPSEGQHMcZ?z~YPXQ9AghAQHMZD3iZM¾K8MFHMZeft8cYÀ9I/p8MBK8I/D8ip3DLQH¿/NGMFUISp3FPSp8c9cHEghI/D8KPne#MD*FUPSNo*p8MONJMcQHAghAQHMD8iZMcc9tPnFUEJPSNJMcZ?

6 p8cHo*p¨sMZD x/Â/_ONJP\c9p8iZiMZcHc9EJI/DLK3MZc$À9ISp8QHc®cHI/NJPSEJQ9MZc±e#IbSMZD8ciI/D8cmFUEGFHpPSE´F®N¹¨lAiT8MZNGNJMK8MFUMZeft8c®K8MQHAghAZQ9MZD8iMiEGEJNGM9:NJMWYMZeft8c ; D3EG/MQHc9MZN*I/p¾W ; ?<¢MtMD8KPSD¦F:K8dZc$NJMc$PSD8D8AMZc x/kS¥K8MZc$EJQ9QHA/p8NVPnQHEGFHAZccUPnEJcHISD8D8EJdQHMcghp8QHMD*FK3AZiZMNJAMZcMZD¦FUQ9M¾NJMW ; MFNJMc8I/Q9NJI//MciZXo*pPSQmF ¾o*p8ESMZDPSEGMZD¦FK¨ <FUQ9M¾e#EGcHMcPSptI/EGD¦F|?;¢MQ9FTPnEJD8McI 3cHMZQmnPnFUEGI/D8cK8MZct8NVPnD8dFHMZcMFK8M\NJP#~p8D3MÁP|nPSEJMD¦FK3AÀZ#efEJcMD&AzEGK8MZD3iZMo*p8MRW ; D¨`P|nPSE´FOtPScOp8D8MRe#PSQHiT8MRPnp8cHc9Ep3D8EGghI/Q9e#M\o*p8M#NGMXFUMe#t8cOPncHcHIiZEGA ZÊNJPe«PnQHiT8MvK8MRiMZcPScmFUQHMc:I/p W.Me#t8cfK8Mc:t88Ae#AQHEJK3MZc:±W?®~±¨sAZiT3MZNJNGMK3MFHMZeft8cRW D¨lMc9F#D8Et8NJp8cfD8EefI/EJD8co*p8MvNVPfQHAZPSNJEGcUPnFHEJI/Dt8QUP<FUEJo*p8MÁK8pp¼FHMZeft8cBD8M£FUI/D3EJMZD²P3cHI/NGp$]j:uEJD¦FUMQ9/MDPSD¦F¾KPnD8c¾NJMcBAZo*pP<FUEJISD8cK8E´¸AQHMZD¦FHEJMZNGNJMcD8M£FHI/D8EGMZD8D8McK3pefI/p3SMZefMZD¦FK8MZct8NJPSD8dFHMZc?

ÃBp<À9ISp8QHK¨s*p8EYNJMFUMe#t3cK8M]QHAghAZQ9MZD8iMÁMZcmFfp+g6P8Q9EJo*p8A^]0ZRtPSQmFUEJQK¨l8ISQHNJIS/MZcPnFHI/e#EGo*p8MZcQHAtPSQ©FUEGMZcvc9p8QvFUI/p3FfNGML/NJI uM9:.K8I/D¦FfiZMNJNJMLK3MN¹¨ 8c9MZQmSP<FUI/EGQHMK8M.PSQHEGc ·iS¨sMZc9F#NJMLWYMZeft8cRÃFUISe#EGop3M»¼D¦FUMQHDPnFHEJI/D8PSNq:/WYÃB»S:*K8ISD*F®N½¨sp8D8E´FUAK8MFUMe#t3c®AFTPSNGI/D:¦NVP¾c9MZiZISD8K8MBWYÃB»S:*c¨`PSiiZp8eÁp8NJMK8MZt3p8EJcNJMx|MQÀHPSD¦EJMQBx/rSw3?@Bpg6PSEGFOK8pQUPSNGMZD¦FUEGcHc9MZefMZD¦FÁK3M#NJPÊQ9ISFTP<FUEJISD FHMZQ9QHMZcmFUQ9M9:YNVPÊcHMZiI/D8K8M#W ; :YiS¨sMZcmF9© Z(©K8EGQHMNJPXw/S^¦¥S¥SdZefMtPSQmFUEGMK8p\À9I/p8Qc9I/NVPnEJQHMe#IbSMZDPSp8/efMZD¦FHMMZDÊefI(bSMZD8D3M]K3M x8:`XefctPnQcHEJdiZNGM6MD g6PnEJcUPnD*FfP 8c9FHQUPSiFUEJISD K3MZcREJQ9QHAZSp8NVPSQ9EGFHAZc Z0t8NGp8cRiZI/p8QmFRFUMZQ9e#MLK3MNJP0NJI/D8Sp8MZp8QvK3p0À9I/p3Qvop3EPnF9FUMZEG/D8MD*FOr«e#EGNJNJEGcHMiZI/D8K3M]c9p8Q]ÂS¥PnD8c ?~$PcHMZiI/D8K8MRWYÃB»PAFHAviT8I/EGcHEJMÁiZI/efe#M\NVPwSS^¦¥/¥Sde#MtPSQmFUEGMK3pOÀ9I/p8QcHISNVPSEGQHMefI(bSMZD#K8MZcPSD8D8AMZc x|w¦_S¥3?¦»¼N;MZD«QHAZc9p8NGFHMo*p8MNJMWYÃB» P<FNGAZ/dQHMZefMZD¦F®t8NJp3cEGFHMXo*p8MRNJMXW ; :MF¾t8Q9AZc9MZD¦FUMfK8I/D8ivp3D²M ÇziZdZc]iZQ9I/EJc9cUPSD¦FOtPnQQUPSt3tI/QmF ZLiZMvK8MQHD8EGMZQ&:iZQ9I/EJc9cUPSD8iMcZ¨lPSiiZAZNGAZQHPSD¦FP|/Mi®N¹¨`Pnp8/efMZD¦FTPnFHEJI/D¾c9AZip8NVPSEGQHM±K8M±NVPc9MZiZISD8K8MK3MW ; i|Pnp8cHAM®tPnQYNGM±QUPSNGMZD¦FUEGcHcHMe#MD¦FK8MONVPXQ9ISFTP<FUEJISDFUMZQ9QHMc9FUQ9MS?

w

u

3 ! Êf

`W 5, -.%"/,0"$ 1%2 "$)-/-6)fc"m-.) )fc" #-.-. (J*1 1d-6)2ÃBp<À9ISp8QHK¨s*p8E$N½¨sI/QHEGMZD¦FTP<FUEJISDLK8pFHQHEGdZK8Q9MFUMZQ9QHMc9FUQ9M\t8PSQQUPSt8tuI/QmFPSpFHQHEGdZK8Q9M]iAZNGMZc9FHM\Mc9FK8AFUMZQ©

efEJD8A0ZR¥\:`_Xe#EGNJNGEJcHMiZI/D3K8MK3M]K3MZ/Q9A¾t8QHdc hD8I/p8ct8Q9AghAQHMZQ9I/D8ctPSQNJPXcHp8E´FUM¾NGMFUMZQ9e#MOPnD8/NJI<©¼cUP(Ç3ISDefEJNJNGEVPSQ9iZc9MZiZISD8K8M9:8P8QHA/A]tPSQ2]e«Pnc@]6r;p8D8M\e#EGNJNJEJPSQHicHMiZI/D8K3MMZcmFN½¨lPSD8SNJMOcHI/p3cBNJMo*p8MZNYI/DSMZQ9QUPSE´Fp8DLPnQHiBK3Mk\ieZÁNVPOcHp8Qmg6PSiZMBK8MBNJP]WYMZQ9QHM¾PSp#iZMD*FHQHMK3MiZMNJNJM ©¼iEq:^ZXSk¦Âx *e K8MK8EJcmFTPSD8iM rD8ISFUMQo*p¨sMZD xXefc:up8D0e#AQHEGK8EJMDFUMQHQ9MZc9FHQHM PnNVPSEGM]MD0e#IbSMZD8D8M

7, 29911510−8 QUPSK3EVPSD8ccHISEGF 15, 0415e#PSc ?·¢MFHFHM«t8Q9AZiZEGcHEGI/D!EGD8AZ¦PnNJAZMRK8M«¥\:`_e#PSc\Mc9FÁK8p8MLPSpÇ FUMZiT3D8EJo*p8McRPSc9FHQHIn©+/AZIK8AZc9EJo*p8Mc\K8A ©/MNJI/t3tAMZcXK8Mt8p8EGcÁp8D8M#FUQHMD¦FTPSEGD8M#K¨`PSD3D8AZM YQUPnK8EJIn©+EJD¦FUMQ9ghAQHI/efAFHQHEJM ZFUQ9dZcÁNGI/D8/p3M PncHM ¬±MZQ9b~I/D8 PSc9MZNJEGD8MR»¼D¦FUMZQmghMZQ9I/e#MFUQmb8:¬¾~ » :NVPncHMZQOcHPnFUMNJNJE´FUM ¹a3PnFHMZNJNGEGFHMv~$PScHMQÁPSD8/EGD8 :$az~Y 1:MFt8NGp8cÁQ9AZiZAe#efMZD¦FÁNJMZcÁc9bc9FHdZefMZcXK8M«tI/c9EGFHEJI/D8D3MZefMZD¦FÁSNJI PnNt8PSQÁcHPnFUMNJNJE´FUM 6NGMvOaPSefAZQHEGi|PSEGD:NJM!v]~ ¾ÉÃa8a!QHp8c9cHMj::MF 8EGMZD¦FUInFvNJMJv¾Ã~»~$ jMp8QHIStAMZD ?Ã FUEGQHMK3MLiZI/eftPSQ9EJcHISDNJMcÁFUMiTz©D8EGop3MZcOt8p8Q9MZefMZD¦FXPnc9FUQ9I/efAFUQ9EJo*p8Mc: PncHAZMfcHp3Q]NGMvQHMNJMSAZMfK8MRNVPtuI/cHE´FUEGI/D0K8MZc]AFHI/EJNGMZc&:K8I/D3D8MZD¦Fp8D8MOt8Q9AZiEJcHEGI/DÊK8MON½¨sI/QHK3QHM¾K8M\rS¥ve#PScFUI/pzFPSpt3NJp8c?

:D#N¹¨`P3cHiZMD8iZMK8MtuMZQmFUp8Q PnFUEGI/DvEJD¦FHMZQHD3MISpfM ÇFUMZQ9D8M9:*NJPW.MQHQHMFHI/p8QHD3MZQUPnEGF:p8D3EGghI/Q9e#Ae#MD*FMZD_SkSrSSefEJD8^8? x¥ScPSpzFUI/p8QBK¨lp3D P<ÇzMXEJD¦nPSQHEJP8NGM]K8PSD8c¾N½¨sMZc9tPSiM9:g6PnEJcUPnD*FBp8D PSD8SNJMÁK3MR_Sk _n3¨P|SMZiNJM¾tu¿/NGMK8MON½¨sAZiNJEJtzFUEJo*p8Mn?8~MOcHp<À9MFcHMZQHPSEGFE´FUMPSNJP|b/AS?;:DÊg6PSEGFNVPXQHInFTPnFHEJI/DLK8MONJPXW.MQHQHM]t8Q9AZcHMD¦FUMK8Mcfp3iFUp8PnFUEGI/D8cRK8I/D¦FfEJNc¨`PSSEGFRK8MÊK8EGcHiZMQHD8MQ#NGMZcRi|Pnp8cHMcZ0NVPghI/EGcvK8MD8PnFUp8Q9MPSc9FHQHI/D8ISe#EGop3MMF/AI/t8¦bcHEGop3MS?ÉI/p8cPSNGNJI/D8cK3AZiZQ9EJQ9M]c9I/efe«PSEGQHMe#MD*FiZMZcEJQ9QHA/p8NVPnQHEGFHAZcK8PSD8cp8D8M]tMQHcHtuMZiFUE´/M8EGc9FUISQHEJo*p8Mn?~$PviT8QHI/D3I/NJI/SEJMBK3M]NGMZp8Q9cK8AZiI/p3/MQ9FHMZcQHM8dFUM\PSp8c9cHENGMZct8Q9I//QHdcK8MZcFUMiT8D8EGop3MZcK8MefMZcHp3QHMZcYPScmFUQ9I/e#AFUQ9EJo*p8MZc$MF$/AZIK8AZc9EJo*p8McZ?<@PSD8c$p8D]K8MpzÇzEJdZefMFUMe#t3cYD3I/p8cYPSNJNGI/D8cu/I/EGQiZI/efe#MD¦FiZMcnPSQ9EVPnFHEJI/D3ccHISD*FefMZc9p8QHAMZc:;MFo*p8MNJNGM¾tPSQUPne#AFUQHEGcUPnFHEJI/D«MZc9Fp3FHEJNGEJcHAM0ZRiZMF9FUM¾CD?

`WL` -. Jkl ,*1)fc( k " ( ,0"$ 1%2Jc (!)+*, -.%"/,0"$ 1%2 "$)-/-6)fc"m-.)2 2 1Y%('-/ zZ|465u, 3 ~$Pt8QHMe#EGdZQ9MÁEJQ9QHA/p8NVPnQHEGFHA]ghpzF¾e#EGcHM\MZD AEJK3MZD8iMvK8dZcON½¨sÃBD¦FHEJo*p8EGFHAÁtPnQN½¨lPScm©FUQ9I/D8I/efM!v¾QHMi EGt8tPSQ9iT8M/MQHcÁ©_S¥/¥P|nPSD¦F 6 ?`¢ .NJM«tuI/EGD*FÁ/MZQ9DPSNISp NVPK3EJQHMiFHEJI/DK3p c9I/NJMEJNPSpt8Q9EJD¦FUMe#t3c 6NGM&D8IMZp3KK8MZc9iZMZD3KPSD¦FK8pt8NVPnDAZo*pPnFHI/QHEJPSNcHp8QLNGM&t8NJPSDK8MN¹¨lAiZNGEJt3FHEJo*p8M vMZcmFPSD8EGe#A#K¨sp8D[e#I/pz/MZefMZD¦FvK3MLQHAFHQHI/SQUPSKP<FUEJISD!cHp3QvNJM«t3NVPSD K8M«N½¨sAZiZNGEJt3FHEJo*p8Mj:.I/p | ILKSQSES=S=1qP0tPnQQUPnt8tISQ9FPnpzÇLAFUI/EGNJMZc 6EGNuFHI/p8QHD3MKPSD8cNJMc9MZD8cEGD8K8EJQ9MZiFKPSD3cNJMBQ9MZtudZQ9M¾AZiZNGEJt3FHEJo*p8MI/QHEGMZD¦FUAtPSQNGMtu¿/NJMXAiZNGEJt3FHEJo*p8MXD8ISQHK ?ÃBp3FHQHMe#MD*FOK3EGFONJMÁt8NVPSD0Ao*pPnFUISQHEVPnN.FUISp8QHD8MvK8PSD8cONJMXc9MZD8c]K8Mc\PnEJ/p8EGNJNGMZcK¨sp8D8MefI/D¦FUQ9MP|SMZiN¹¨lEGD8iZNGEJDPSEGcHI/D¾iI/D8cmFTPSD¦FUM_Sk

_Sz¨ hI 8NGEJo*p8EGFHA tPSQ.QUPSt3tI/QmF ZN½¨sAZiNJEJtzFUEJo*p8M /I/EGQ

¶·EG8?ª_? x ?8~$PvzE´FUMcHcHM\PSD8Sp8NVPSEGQHMMc9FK8MON½¨sI/QHK3QHM\rS¥tPSQPSD:MFNGM¾tISEJD¦F/MQHDPSNYPSiiZI/eft8NGEGFK8ISD8i

p8D0FUISp8QiZISe#t8NGMF¾c9p8Q¾NJM ZIK8EVPSiÁMZD_/rSw/¥S¥LPSD8cZ?Ã N½¨s8MZp8Q9MRPSiFHp8MZNGNJM\NJMvtuI/EJD¦FBSMZQ9DPSN:cHMvFHQHI/p3SMKPSD3cNVP]iZI/D3c9FUMNJNJPnFUEGI/D#K3MZcYI/EJc9cHI/D3c¹:EJc9iZMc 1:zMFcZ¨lPSt8t8Q9IziT8MBK8MBNJP\iZISD8c9FHMZNJNJPnFUEGI/DRK8MZc®¬±MZQHc9M|PSpÇ6Ão*pPnQHEJp3c hSI/EJQ¶·EG8?`_z? x ?

~:¨`P<ÇzM¾K8M¾Q9ISFTP<FUEJISDK8EJp3QHD8M¾Mc9FtuMZQHtuMZD3K8EJip8NVPSEGQHMBPSpLt8NVPnDLAZo*pPnFHI/QHEJPSN½?Ã i|Pnp8cHMOK8M¾NJPÁt8QHAiZMcm©cHEGI/D:N½¨lP<ÇzMBK8AiZQ9EGFp3DLiZ¿/D8MPSp3FUISp8QK8MBN½¨lP<ÇzMBK8Mct¿SNJMZc®K8MN¹¨lAiZNJEGt3FUEGo*p8MMD_/rSw/¥S¥ÁPSD8c?3Ã N½¨s8MZp8Q9MPSiFUp8MNJNJM\N½¨lP<ÇzMXK8MvQ9ISFTPnFHEJI/DtISEJD¦FUM]/MZQ9cON½¨sAFUISEJNJM]tuI/NVPSEGQHMj:ue#PSEGcBKPSD3c xk/¥/¥S¥PSD8c¾EGN.tuI/EJD¦FHMZQUP#MZDK8EGQHMZiFUEGI/DLK8M¾¬±MZ¦P hSI/EJQ¶.EJ8?`_z? x ?

_z? xÃ /PSp8iT8M t8Q9AZiMZcHc9EJI/D²K8MvN¹¨`P<ÇzMvK8MvQ9ISFTP<FUEJISD ¹ PSp3FHI/p8Q¾K8p tu¿/NJMÁK8MvN½¨sAZiNJEJtzFUEJo*p8M ?8Ã K8QHI/E´FUM78t3QHAZiMZc9cHEJISD&K8ptISEJD¦F/MQHDPnNYc9p8QNJMIzK8EJPSiS?

23465u, 3 Ã NVPt8Q9AZiMZcHc9EJI/D]EJMZD3D8MZD¦FYcHMcHp8tuMZQ9tIScHMZQYK8McYIScHiZEGNJNJPnFUEGI/D8ctuAZQ9EJIK8EJo*p8McK8MN½¨lP<ÇzM:K8MQHInFTPnFHEJI/D:NJMcDpzFTPnFHEJI/D8ct3QHAZK3EGFUMc$KPSD8c$NJMc [I1 PRQ1 | Tx x9A ~E1D x9A qQx:K8MÉM£FUI/D?<¢Mc$I/cHiEJNJNJPnFUEGI/D8ctuAZQHEGIzK3EJo*p8MZccHISD*FK8MBt3NJp8c±g6PSE 3NJMZcPSeft8NGEGFUp3K8MZc&:¦MZDK8M |PÁK3M x/¨´?z¢B¨lMc9FtuI/p8Q9op3I/E;NJMZp3Q®K8AiZI/pz/MZQmFUMD8AiZMZc9cHE´FTPN¹¨`P|9<ZD8Me#MD*FK8McFHAZNGMZcHiI/tuM²MFNJp8D8MFHFHMZcZ?:Dx(Ân^¦w:N½¨lPSc9FHQHI/D3I/e#MPSD8/NJPSEJc ®QUPSK8NGMbK8AiZI/p3Q9M#NJPDpzFTPnFHEJI/D0t8Q9EJD8iEJtPnNJM9:uMZDFxw\:lÊPSD8c&:K8MRN½¨sI/QHK3QHMXK8Mpx¥ ]j:MF]PncHcHIiZEGAZMWZLNVPQ9ISFTP<FUEJISDK8p t8NJPSDI/Q 8EGFUPSNNJp8DPnEJQHM«P|/MZiLiMF9FUMLtuAZQHEGIzK3MS?.~$McRPSp3FHQHMZc\FUMZQ9e#Mc:o*p8MNJo*p8Mcve#EGNJNJEGMZQ9c]K8PSD8cXNGMefIzK8dNJMK3M]Q9AghAQHMZD3iZM\PSiFHp8MZN :cHI/D¦FPSpÊe#ISEJD8c x|¥vghISEJct8NGp8ctMFUEGFHcZ?

~$PRiZPSp8c9M\K8M¾NJPXt8QHAiZMcHcHEGI/Dz©+DpzFTPnFHEJI/DMZcmFN¹¨`PniFUEGI/DK8McghI/QHiMZc/QUP|EGFUPnFUEGI/D8D8MNJNGMZcNGp8D8E©¼cHISNVPSEGQHMcHp3QNJM ISp8QHMNJMF®AZo*pP<FUI/Q9EVPSNuK8MBNJP\WYMZQ9QHMS?zÃ tPnQ9FUEGQ®K3MZcPSD3D8AZMc x¦ÂS¥:NGMZc®I 8cHMQ9nPnFHEJI/D8cPSc9FHQHI/efA©FUQ9EJo*p8McI/D¦Fe#EGcMZDAEJK8MD8iZM\NJM¾g6PSE´Fop3M\NGMZcDpzFTPnFHEJI/D8cD¨sAFUPSEJMD¦FBtPncFHI/p3F ZRg6PnEGFiZMNJNGMZcK¨lp3D8MWYMZQHQ9MQHEG/EJK3MS?(ÃYSMZiNVPt8QHEGcHMMDviZI/eft3FHMK8MNJPcmFUQHp3iFUp3QHMEJD¦FHMZQHD3MK8MNJPWYMZQHQ9MMF:K3McHMct8QHISt8QHEGAFUAcQH3AZI/NGI//EJo*p8Mc:zNJMZce#IK8dZNGMZcPSiFHp8MZNGctMQHefMF9FUMZD¦Fp8D3M¾K8MZc9iZQHEGt3FUEGI/D«FHQHdZcC8D8M9:~Z efI/EJD3cK¨sp8DÊe«Pnct8Q9dZcZ? 5u u ! ,#".1=h +3 :p8NGMZQK8Ae#I/D¦FHQUPXFU8AI/QHEGo*p8MZefMZD¦FMZDsx(ÂS/rÁop3M9:KPSD3cp3DMNJNGEJt8c9I9t+K8MK8M±QHA/I/NGp3FUEGI/D¾8I/efI//dD8M:MZD]QHInFTPnFHEJI/D:N½¨lP<ÇzM:K8M±QHInFTPnFHEJI/D:o*pPSD8K]EJNSD¨lMc9FYtPSc$iI/D3ghI/D8K3p\P|SMZiN½¨sp8DK8McP<ÇzMZc.t8QHEGD8iZEGtPSpzÇ¾K¨lEGD8MZQmFUEGM9:(MZcmF:PSD8EGe#A:K¨lp8D3MI/c9iZEJNGNVPnFHEJI/D¾NGE 8Q9M:tAQHEGIzK8EGo*p8M±K8I/D¦FNJPghQ9AZo*p8MZD3iZMiZQ9I/EGFYP|SMZiN¹¨lMNJNGEJt3FHEJiZE´FUAn?~$PW.MQHQ9M®AtI/p3cUPSD¦FNJPghI/QHefM:K¨sp8D\FHMZN*MZNGNJEJt3cHI9t½K8M9:I/D\iZPSNJip8NJM±o*p8McHI/DÁP<ÇzMK8MOQHInFTPnFHEJI/DtuMZpzFI/cHiEJNJNGMZQNGE 8Q9MZefMZD¦FP|SMZi]p8D8MOtAQHEGIzK8MBK8M]k/¥¦rÀ9I/p8Q9cZ?~:¨lPSc9FHQHI/D3I/e#MOPne#AQHEJiZPSEJD¢PSD3K8NJMQXPSiiZI/eft8NJE´FÁp3DtPScXK3AZiZEGcHE´gMZD K8AiZI/p3QHPSD¦FvMZD7xwS x8:YcHp8QXNJP PncHMK8McvI 8c9MZQ9nPnFHEJI/D3c

x¥

K8MNVP0NVP<FUEGFHp8K8MÊ/AI//QUPnt88EJo*p8Mj::p8D8MI/cHiEJNGNVPnFHEJI/DMD^¦kSkÀ9I/p3QHc:fXYE ACE1I#DFEGHE.\x9P G\XYE1I#::K¨lp3D8MPSeft8NJE´FUp8K3M\K8MR¥:`k x¥e ZNJP«cHp3Q9g6PSiM 1:$Z#NVPSo*p8MNJNJM\cZ¨lP(À9I/p3FHMvp8D0FUMQHefMvPSD8D*p8MNK8MXN¹¨lI/Q9K8QHMÁK8M¥\: x ¹¶·EG8?`_z?ª_?ÉI/p8c/MZQ9QHI/D3c¾op3MfN¹¨lIScHiZEGNJNJPnFUEGI/DLK8Mv^¦k/k¾À9I/p8QHcBcZ¨sMÇzt8NJEGo*p8MvtPSQp3DPnNJNJISD8/MZefMZD¦FK8M]NVPvtuAZQHEGIzK3M¾K¨`:p8NGMZQMZDQUPSEGcHI/DÊK8M]NVPvD8ISDQ9EJ/EGK8EGFHAK8MONVPvWYMZQHQ9MS?u@Á¨lPSp3FHQHM]tPSQ9FNJPRt3QHAZiMZc9cHEJISDz©D*p3FTP<FUEJISDcZ¨lPSiZiI/eftPS/D8MK¨sp8DLe#ISp3/Me#MD*FK8pLt¿SNJMK8EJp8Q9D8M9:zQHAFUQHIS/QUPSK3M 6K8PSD8cNGMBcHMD8cEGD8K8EJQ9MZiFKPSD3cNGMO.W 1:~ZRNVPXPnp3FUMp8QK8M\_S¥ve«PScPnpt8NGp8c ¹¶.EJ8?`_z?`_ ?

_z?`_ ISp3/Me#MD*FK3MN½¨lP<ÇzMBK8MBQHISFUPnFUEGI/D«c9p8QNVP\iZQHI973FUMBFHMZQ9QHMZcmFUQ9MS?8ÉISFUMQNVP]iZI/eftuI/cUPSD¦FHM0ZNJISD8#FHMZQHefM9:uiZISD8c9FHEGFUp3AXK8p&FHMZQHefMvPSD3Dp3MZN·MFK8MÁN½¨sI/cHiEJNJNJPnFUEGI/DLNJE 8QHM]K8MR¢8PSD8K8NGMZQ:PSEGD8cHEYo*p8MvNJMcuI/p8iZNGMZcK8EGp8QHD8McQHAFUQHIS/QUPSK3MZco*p8EYPSiZiI/e#t8PS/D8MD*FNJPvt8QHAiZMZc9cHEGI/Dz©¼D*p3FUPnFUEGI/D?

28%<462z(465u,Y"Y R=h2 4h | v"Y v%(523465u,5u "Y R=h2«=h5u,Y³u$ Y%O"YZ5uY% ~$PQHISFUPnFUEGI/DÁK8EGp8QHD3MPSc9cHp8QHPSEGF\NVPghI/D8iFUEGI/DK¨lp8D3M«8I/Q9NJI/SMfcHPSD8c\K8Ag6PSpzFO:3À9p8cHo*p¨ Z&iM«o*p8M#ÉM£®iZISe ::atMD8iZMQ 6 I/D8Mc x|¦_SS:K8M#azE´FHFUMQ x/_/Â BK8AiZI/p3Q9MZD¦FXp8D3MfK3AZiZANJMQUPnFHEJI/D cHAiZp8NJPSEJQ9MvK8MfNVP«EGFHMZcHc9M#K3MfQ9ISFTP<FUEJISD+1, 6

efcvtPSQRcHEGdZiZNGMLcHp8QRNJPK8p8QHAMÊK8p0À9ISp8Q:MFRK8MZcRp8iFUpP<FUEJISD8cvcHMÊK8AQHI/p8NJPSD¦FRcHp8Qpx¥ Z²ÂS¥PSD8c hK8MLN½¨sI/Q9K8QHMK3M&r&efcXc9p8QRNVP&K8p3QHAZMÊK8p&À9I/p3Q 1:.MFRK8ISD*FfNJP&i|PSp3cHM9::t3QHI P 8NJMe#MD*FXEJD¦FUMQHD8Mj:K8Me#Mp8QHM\e«PSN$iMZQHD3AZM /I/EGQB¶·EG8?u_z?lk? up8MNJo*p8MZcPSD8D8AMZct8NGp8cFTPSQ9K0aFHI(b nI x/k/Â K3AZiZISp3QUPSE´FK8McnPSQ9EVPnFHEJI/D3ccUPnEJcHISD8D8EJdQHMcK8M¾N½¨sI/QHK3QHMK8M]¥3?`rÁefc:8o*p8MON½¨sI/DLM Ç3t3NJEJo*p8MFHQHdc 3EJMZDLt8PSQN½¨sM¸MFK8Mc/MD¦FUcZ?

~MZc$I 8c9MZQ9nPnFHEJI/D3cK8M±/AZIK8AcHEJM·cHtPnFHEVPSNGM ½az~Y :@vOa tuMZQHefMF9FUMD*F$K3M:e#McHp8Q9MZQN½¨sAZiZPSQ9F∆LOD¹~ ¾@ P8QHAEVPnFHEJI/DLK8MON¹¨`PSD3/NVPSEGcp~$MD8SFH Bg·@P|b] K3M]NJPvNJI/D8Sp8MZp8QK3pvÀ9I/p3QtPSQQUPSt3tI/QmFwZvcUP

nPSNJMp8QBD3I/e#EGDPSNGM]K3MXw/S^/¥/¥#cWYÃB»T?~MZcI 3cHMZQmnPnFUEGI/D8cPnc9FUQ9I/efAFUQ9EJo*p8Mc:PSp<À9I/p8Q9K¨sp3E·NJMcBI 3cHMZQ©nPnFUEGI/D8cvK8Mc#QHPSK8EGIn©¼c9I/p8QHiMZcRMÇFHQUPS¦PnNVPSiFUEJo*p8McvtPSQRQUPnK8EJIn©+EJD¦FUMQ9ghAQHI/efAFHQHEJMFZ FHQHdcfNGI/D8/p3M 8PScHMj:K8I/D3D8MZD¦FD3I/DtPSc®PSiiZdZcZ

∆LOD:*e#PSEJc Z]N½¨lPSD8/NGMK8MBQ9ISFTPnFHEJI/DRK8MNVPOW.MQHQ9MBKPSD3cNJMt8NJPSD#Ao*pP<©

FUISQHEVPnNq:MFÁK8ISD*F\NJMc\EGQHQ9AZ/p8NJPSQ9FHEGFHAZc¾QHAcHp8N´FUMD*F\K8M#N½¨sEJD¦FUA/QUPnFHEJI/D0K3MZc\nPSQ9EVPnFHEJI/D3c¾K8M#NJPÊE´FUMZc9cHM#K8M ! "$#%&(')+*-,.0/21!'3*54-6879':;<,+7>=9'8/@?.BA'64C7*D/E%GFIH3%+JLKMON

xx

QHInFTPnFHEJI/D?;YI/cHISD8ciZMNJNGM©¼iEAZ¦PnNJM'Zω = Ω(1 + m3)

I ΩMZcmF¾NVPvEGFUMcHc9MvPSD8/p3NVPSEGQHM¾K8M\QHISFUPnFUEGI/D

D8I/efEJD8PSNJMj:nPncHcHIiZEGAZMiZNJPBNJISD8/MZp3Q·K8pÀ9I/p3QcHI/NJPSEJQ9M®efIb/MD ¯LOD = 86400c:W.Ã»YMF±I

m3Q9MdFUM

NJMcnPSQHEJPnFUEGI/D8cK8MOiMFHFHM¾zE´FUMcHcHMn?uÉI/p8cP|/ISD8c

LOD = k2π

Ω(1 +m3)

¹_z? x I

kMc9F±NJMg6PSiFHMZp8Q:tuI/p8Q·tPScHc9MZQ:K8pBÀ9I/p3QcHEGK8AZQHPSN8PSpÀ9ISp8QcHISNVPSEGQHMefIb/MD?DvQHMiZI/D8D8P0/JF

LOD =2π

Ω

NVPK8p8Q9AZMK8pBÀ9I/p8Q·K8MQHAghAQHMD8iZMj:¦AZ¦PSNGMfZ¾w/S^¦¥S¥c:W.Ã»T?*±DRD8A/NJEG/M|PnD*FNJMZcFHMZQ9e#Mc:K8pRcHMZiI/D8KI/Q9K8QHMj:N½¨sAZi|PnQ9FK8MONVPXK3p8QHAM\K8pXÀ9I/p8Q

LOD − LODMZcmF

∆LOD = −LODm3¹_z?ª_

~$PSPnQHEVP<FUEJISDÁK8MN½¨lPSD8SNJMK3MQHISFUPnFUEGI/DvK8MNVPWYMZQ9QHMMZD¦FHQHMNVPBK8PnFUMEGD8EGFHEVPSNGMt0MF±NJPKPnFUM

tcHMK8AK8p8E´F

K8MωtPSQEJD¦FHAZ/QHPnFUEGI/D

θ(t) − θ(t0) =

∫ t

t0

ωdt =

∫ t

t0

Ω(1 +m3)dt¹_z?lk

cHISEGFθ(t) − θ(t0) = Ω(t− t0) +

∫ t

t0

Ωm3dt¹_z?s^

I/pÊMZD3iZI/Q9Mθ(t) − θ(t0) = Ω(t− t0) −

∫ t

t0

∆LODΩ

2πkdt

¹_z?`r DK3EJc9FHEJD8Sp8M¾PSEGD8cHENJPXtPSQ9FHEJMnPSQ9EVPSD¦Fp8DzghI/QHefAZefMZD¦FP|/MiÁNJMFHMZeft8cK8MOiZMNJNGM©¼iEo*p8EMZcmFBEGQHQ9AZ/pz©NJEGdZQ9M9:3M Çzt8QHMcHcHEGI/D&EGD¦FUAZSQUPSNGMK8MZcMÇzidZcK8MONVPvNJI/D3/MZp8QK3pXÀ9ISp8QZ?

`W%$ -. Jkl ) (!) *&, ,0- ,e "m-. c$,0"$ &%' (!) *&, -.% "/, "$ 1%2 "$)--.)fc"m-6)3)" (!)+c$, e )fc (-6)

Ãt8Q9I/t8QHMe#MD¦FvtPSQ9NJMZQ\NJMf/MZiFUMp8QvK8MQ9ISFTPnFHEJI/DD¨sMZc9FXtPScXK8AFUMQHefEJD8AK3EJQHMiFHMZefMZD¦FXtPnQXNJMcI 8c9MZQmSP<FUEJISD8c 3QHp3FHMZcZ?·¢MZNGNJMcm©¼iEq:8PSp3FUMp8Q:.PEJeXp3FH:8Mp8QHMj:YK8PSD8cÁNGMRi|PSc]K8M«tuI/EGD*FHAZc\PSc9FHQHI/efA©FUQ9EJo*p8Mc:efMZc9p8QHMvK8MXFHMZeft8c¾tuI/p8QNGMZcFUMiT8D8EGop3MZcO/AZIK8AcHEJo*p8Mc:c9I/D¦F¾ghI/D8iFHEJI/D0K3MvN½¨sI/QHEGMZD¦FTPnFHEJI/DK8pQHAcHM|PnpK8MccmFTPnFHEJI/D3cK¨lI8cHMQ9nPnFUEGI/DÊtPSQQUPnt8tISQ9FPSpÊQHMtdQHMOK8MOQHAghAZQ9MZD8iM\iAZNJMc9FHMS?

¢NVPSc9cHEGop3MZefMZD¦FO:uN½¨sI/QHEGMZD¦FTP<FUEJISDLK¨lp3DQHMtdQHMÁefI 8EGNJMMc9FBQHMZt3QHAZc9MZD¦FUAÁtPSQNJM]t8QHIK8p8E´FK3M]FHQHI/EGcQHInFTPnFHEJI/D8c:c9p8iZiMZc9cHEGSMZc&:zFUMNJNGMop3MiTPniZp8D8MK¨sMZNJNGMZc±cZ¨sM¸MZiFUp8MBPSp3FHI/p8Q±K¨sp8DP<ÇzMK8p#QHMZtudZQ9M9:¦FUQHPSD8c©ghI/Q9e#A#I/p D8I/D:.D8MLiZIjt+D8iEJKPSD¦FÁtPScRP|/MiLiZMZNGp8EK3MLNVP&Q9ISFTPnFHEJI/Dt8QHAiZAK8MZD¦FUMj:±cHEMNJNGM«MÇzEGc9FUMn?:~$PcHp3iZiZMcHc9EJI/DK8MOiZMZcQHInFTPnFHEJI/D8cMZc9Fc9iT8AZe#PnFUEGcHAM\tPnQNVPvcHAop3MZD8iM

(Xi)Rl(αl)−→ (x

(1)i )

Rm(αm)−→ (x(2)i )

Rn(αn)−→ (xi)I Rl(αl)

:ztPnQ®M Ç3Me#t3NJM9:K8AcHEJSD8MBp8D3MQHISFUPnFUEGI/DfK¨`PnD8/NJMαlPnp3FUI/p3Q®K8MBN½¨sp8D«K8McFUQ9I/EJcP<ÇzM

xi:zMF

m 6= l:n 6= m

?¢MF9FUMXc9AZo*p8MZD3iZM9:D8ISFUAM

(lmn)tuMZp3Fo<FHQHMÁQ9A|PSNGEJc9AZM]K8M x(_vg6PZISD8cBK8E´¸AQHMD*FHMZc?~$P#t8NGp8cBpzFUEJNGE´©

cHAM#Mc9F ¹kxk?±NGNJMviI/QHQ9MZcHtuI/D8KPSpzÇ x9PH9XYES= G [XYE1IBiZNVPncHcHEGo*p8MZcα3 = ψ

:α1 = θ

MFα3 = Φ

?

x(_

_?`k X¬PnQHEVP<FUEJISD8cZ]NGI/D8OFUMQHefMK3MNJP]NGI/D8/p8Mp8Q±K8pOÀ9ISp8Q±K8Mtx|w/k¦_ Z xS¦Âz?*~$P]nPSNGMZp8Q±K8MQHA ©ghAZQ9MZD8iMMZc9FwSS^¦¥/¥c:WYÃB» 6cHAQHEGMt8QHIK8p8E´FUMt8PSQ:NJM 6 ±~ :/K8EGcHtuI/D8E 8NJM®cHp8Q±¦FHFHt n3t8EJMQHcZ?sI 8c9t8e?sghQ

~:¨`PnD8/NJMψMZcmFfPSt8tuMZNJAPSD8/NGMK8MÊt8QHAiZMcHcHEGI/D@:

θPnD8/NJM«K8MLD*p3FTPnFHEJI/DfMF

φPSD8SNJMK8MLQ9ISFTP<FUEJISD

t8Q9I/t8QHMn?~:¨lPSD8/NGMθ (OX3, Ox3)

MZc9FBI/QHEGMZD¦FUA\tPSQNJM\SMZiFUMZp3Q~x

(1)1

?¢MFHFUMÁcHAZo*p8MD8iZMRtPnQ9FK¨lI/Q9K8E´©DPSEGQHM:K¨sp8D\QHMZtudZQ9M®iAZNGMZc9FHM®AiZNGEJt3FHEJo*p8M ¹P|b/PSD¦F·tuI/p8Q$t8NJPSD]ghISD8KPSefMZD¦FTPnN/N½¨sAZiNJEJtzFUEJo*p8M:K¨lp8D3M®AtIo*p8MK8MOQHAghAZQ9MZD8iM\MFtuI/p8QISQHEJSEJD8MK8PSD8ciZMOt8NJPSDÊN½¨sAZo*p8EJD3IÇzMOefI(bSMZDK8MOiZMFHFUMOAtIo*p8M ?

:DLt8QHEGD8iZEGtMiZMZc®FUQHISEJcPnD8/NJMcc9p\sfcHMZD¦FtuI/p8QK3AFUMQHefEJD8MQ®N¹¨lISQHEJMD¦FTPnFHEJI/DfK8MN¹¨l»¼W¶!tPSQ®QUPSt©tuI/Q9F ZLN¹¨l»m¢¶? PSEJc&:PSp e#ISEJD8cN¹¨lp3D0K¨lMpzÇ :$MZD N½¨sIziiZp8Q9MZD8iM

ΦnPSQ9EJMXMD*EGQHI/D K8Mfk//¥

MD_n^

8Mp8QHMc xr¾e#PSc±tPSQ±efc ?¦»¼N;g6Pnp8K8QUPnEGF±NJMc±K8I/D8D8MQPSMZip8D«tPnc±FHMZeftISQHMZNK3MB¥\: xe#c±cHE;N¹¨lI/DRK8AcHE©QUPnEGF±p8D8Mt8Q9AZiEJcHEGI/DfK8M:xe#PSc±cHp8Q±N¹¨lI/Q9EJMD*FUPnFUEGI/DvcHt8PnFUEJPSNJMK3MNJPOWYMZQ9QHMn?»¼NMc9F®8I/Q9cK3Mo*p8Mc9FUEGI/DfK8Mt8Q9IziAZK8MQPSEGD8cHE¹?*¢I/D3ghISQHefAZefMZD¦F[Z]NJPOt8PSQUPSefAFHQHEGcUPnFHEJI/DXcmFTPSD3KPSQHK«PSK8I/tzFUAZMtPSQ±NGMazMZQmzEGiZM»¼D¦FUMZQ©DPnFHEJI/D8PSN/K8M®NVPInFTPnFHEJI/DOK8MNVPW.MQHQ9M®MF·K8Mc:abcmFUdZefMZc.K8M®AghAZQHMD8iZMj:SN¹¨lEGK8AZM±MZcmF·K3M®c9AZtPSQ9MZQ&:nKPnD8cNJMcÁPnD8/NJMcOK8M«Q9ISFTPnFHEJI/DR:NJMc\iTPnD8/MZefMZD¦FHcXe#IK8ANJEJc9AZc hQHISFUPnFUEGI/DK3EJp8Q9D8M9:$t8Q9AZiZMcHc9EJI/Dz©+D*p3FTPnFHEJI/D K8MOiZMpzÇo*p8EcHISD*FEGD8iZI/D3Dp3cZ?

~MZcPSD8/NGMZcΨMF

θo*p8EK3I/D8D8MD*FNJPK8EJQ9MZiFHEJI/DK3M²N¹¨`P(Ç3M&K8MZcÊtu¿/NJMcL/AZI/SQUPSt83EJo*p8MZcLK8PSD8c

N½¨sMZc9tPSiMXcHI/D¦FBe#IK8AZNGEJc9AZcKPSD8cNGMZp8QnPSQHEJPnFUEGI/DZ«NJI/D3#FUMQHefM FUMZQ9e#McBK8MÁtAQHEJIK8Mcc9p8tAQHEGMZp8Q9MZcZ _ÊÀ9I/p8Q9cLKPSD8cLN¹¨lMcHtPSiM K8M ¶I/p8QHEGMZQ 1:P|SMZi p8D8M0t8Q9AZiEJcHEGI/DK8M N½¨sI/Q9K8QHMK3M x²e#PSc iS¨sMZc9FNJPt8Q9AZiZMcHc9EJI/Dz©+D*p3FTPnFHEJI/D?$~$MfefIzK8dNJMvK8Mft8Q9AZiZMcHc9EJI/Dz©+D*p3FTPnFHEJI/DK8AC8D8EGF]p8D!P<ÇzM#K8ISD*F]N¹¨lEGD*FHMZQ9cHMZiFUEGI/DP|/MiN½¨s8AZefEJc9t88dQHMD8I/Q9K«K8MNVPOcHt88dQHMiZAZNGMZcmFUMBMc9FPSt8tuMZNJAM fXYE [K1XYES=1A E#P~A E1I#DFKG9Tx9 ILE[E1XYES=ATTx9X#P~A E1I#DFEG9Tx9ACEwXYE (? ¾D#tMp3F®e#I/D¦FHQHMZQ±o*p8MNJMB¢»[c¨lAi|PSQmFUMBPSp«t8NGp8cK8M_n¥\e#PSc±K8M

8@ @ D D ! "$#8 %&D!'#8)(+* !(+*+, B D ! OI!D #LOD ' I-. ! /'-

0 1 @ -@ %2D O %3@ 94*@OD '#8)(* 3(+*!5#%6 I7@ % D 1ODI3# D98@)(+* /' I-.D ! /'-

:%; <>= & /'@? A# B# # @ @>= C ;D (MEEE%- F5#HG0@ 8 I %E9DJ G A#LK2M9NAOQP"R/NAOTSTUVOLWOHS

xk

N½¨lP<ÇzMEJD8cmFTPSD¦FUPSD8AK8MQHISFUPnFUEGI/D?/¢B¨lMc9F®tI/p3QHo*p8I/E;I/DRiZISe#t3FHMN½¨sM¸MFK8MNVP¾QHInFTPnFHEJI/DvK8EGp8QHD3MPnp3FUI/p3QK8MiMFRP(Ç3Mn?~$P&tPnQ9FUEGM#D3I/Dz©¼efIK8AZNGEJcHAM#K3MZcvPSD3/NJMc

ΨMFθMZcmFvcHiEJD8K3AZMMD K8MZpzÇ!tPSQmFUEGMZc 6E

p8D8M]iZISQHQHMiFHEJI/DcHp8QNVPRt8Q9AZiZMcHc9EJI/Dz©+D*p3FTPnFHEJI/DR:iS¨sMZc9Fm© Z<©+K8EJQ9MOcHp8QNVPvtuI/cHE´FUEJISDc9tPnFHEVPSNGM¾K8p0¢» hEJE p8DÊFUMQHefM]A/I/NGpPSD¦FBPSMZi\K8MZcghQHAop3MZD8iMZcBEGD3ghAZQ9EJMp8QHMc ZRK8MpzÇXÀ9I/p8Q9c:uPScHc9IziEJAM\PnpzÇÊp8iFUpPnFHEJI/D3c/AI/t8¦bcHEJo*p8McK8M]N½¨lP<ÇzMOK8MZct¿SNJMZc/AI//QHPSt88EGop3MZcovn?¢M]K8MQHD8EGMZQFUMZQ9e#MOD¨sMZcmFBt8PSciIzISQHK8I/D3D8AKPSD3c]NGMXQHMtdQHMRiZANJMc9FUMj:I/D NJMvtPnQUPSefAFHQHEJc9MXKPSD3c]NGMXQHMtdQHMvFUMQHQ9MZc9FHQHM#PSt8Q9dZcOP|/I/EGQOPSt8t8NGEJo*p8AvNJPe#PnFUQ9EJiZMRK8MfQHInFTPnFHEJI/D²K8EJp3QHD8Mn?.@BPSD8cÁiM«Q9MZtudZQHMj:.N¹¨lAi|PSQmFÁMD¦FUQHM#NJM#¢» MFÁN½¨lP<ÇzMv#A/I/NGp8MfNJMZD©FUMe#MD¦F|?ÉI/p8c¾PSNGNJI/D3cBK8I/D3ivK8EJcmFUEJD3/p8MZQBk«F¼btMc]K3MXtPSQHPSe#dFUQ9MZcK¨sI/Q9EJMZD¦FUPnFUEGI/D hE K3MZc¾AZiZPSQ9FHciZANJMc9FUM#tISp8Q\NJPLtI/c9EGFHEJI/D K8p[¢»/: hEJE Bp8D8MfiZI/Q9QHMZiFUEGI/D!Q9MZD8KPnD*FÁiZI/eft3FHMfK3MZcÁEGQHQ9AZ/p8NJPSQHE´FUAc¾K8MN½¨lPSD8SNJMK8MQHInFTPnFHEJI/D hEJEGE NJMciZII/Q9K8I/D8D8AMZcFHMZQHQ9MZcmFUQHMc:K8pf¢».:/PSEJD8c9E3o*p8MiMZNJPMZc9FK8AZiQHEGFiZE´©¼PSt8Q9dZcZ? 28%(2*|%< "±´5;%<4h z,u23(4h5u,&,

3,

x=6 '-/28%(21u=6 X-/'z=h +3 W.I/pzFK¨lPuI/QHK]K8MZpÇ

tuMFUE´FUc]PSD8SNJMZc&: dX, dY

BEJDzghAZQHEGMZp8Q9cZNJPÊefEJNGNJEGcHMZiI/D8K8M\K8MRK8MZSQHA9:YPSt3tMNJAZcONGMZcopAi|PSQmFUc]PSp²t¿/NGMiZANJMc9FUMj:iI/eftMD8cHMD*FBNJMcBK8Ag6PSp3FUcK8pefIK8dZNGM]K3MÁt8Q9AZiZMcHc9EJI/Dz©+D*p3FTPnFHEJI/D ZfN½¨s8MZp8Q9M\iMZNGp8EYPSK8I/t3FHAtPSQN¹¨ ; ÃB»MD_n¥/¥/¥K8M]N½¨lP<ÇzMOK8M¾C/p8Q9M\K3M]NJPvW.MQHQHMn?¢MZNJp3E´©¼iE$PvtI/p3QiIzISQHK8I/D3D8AZM]AZo*pPnFHI/QHEJPSNJMiZANJMc9FUM

X = Xmod + dX, Y = Ymod + dY?·PnQiI/D¦/MZD¦FHEJI/D:EJNGciI/D¦FUEGMZD8D8MD¦F¾K8MZcI/cHiEJNGNVPnFHEJI/D8c

K8I/D¦FNJMctAQHEGIzK8MccHI/D¦FcHp8tuAZQ9EJMp8QHMc ZRK8MpzÇÁÀ9I/p8Q9cZ? 28%(2*|%< "±5;%n4h ,23465u,Ê,

«S7 3 ~$M±o*pPSNGEGCiZPnFUE´g9pEGD*FHMZQ9e#AKPSEJQ9M .t8Q9MZD8KOFUI/pzF

cHISD0cHMZD3c:t3p8EJc9op3MXiS¨sMZcmFOPSp3FHI/p8QBK3MXN½¨lP<ÇzMÁK8p0¢»µo*p8MXN¹¨lISDiZI/eft3FHMÁNVPRQHInFTPnFHEJI/DK8EJp8Q9D8MÁMFc9MZcp8iFUpP<FUEJISD8cZ?3¢I/efe#MD8I/p3cN½¨lP|/I/D3cefMZD¦FUEGI/D8D8At8NJp3cPSpzFO:*NJMB¢» D¨lMc9Ft8PScN¹¨`P<ÇzMK8MBQ9ISFTP<FUEJISDEJD3c9FTPnD*FUPSD8D8Ae#PSEJc·I/DRtMp3Fe#I/D¦FHQHMZQ±o*p¨sEJN8MD#iI/D8cmFUEGFHp8Mp8Dfe#Ib/MD8D8MK8EGp8QHD8Mo*p8ED8Mc¨lMD«AZiZPSQ9FHMtPSc]t8NGp8c\K3M#t8NGp8c]K8M_n¥efEJNJNGEJc9MZiZISD8K8MZcBK8M«K8M/QHAn?Y~$MRFUQ9I/EJc9EJde#MvtPnQUPSefdFHQHMRK¨sI/QHEGMZD¦FTPnFHEJI/D²MZcmFPSc9cHIiZEJAXPSpzÇ&EJQHQ9AZ/p3NVPSQ9EGFUAcK3MvN½¨lPSD8/NGM\K8MÁQHISFUPnFUEGI/DK8MXNJP«WYMZQHQ9M

θPSp3FHI/p8QK3p²¢».?$¢MNJp8E©¼iZEYMZcmF

iZISD8c9FHEGFUp3AXK¨sp8D8MvtPSQmFUEGM\nPSQHEJPSD¦FNGEJD8AZPSEJQ9MZefMZD¦FP|SMZivNJM]FUMe#t8cPnFUI/efEJo*p8M\W.Ã»S:MF¾K¨sp8D8MvtPSQmFUEGMEJQ9QHA/p8NJEGdZQ9M9:

δθ

θ = θ0 + ΩTAI + δθ½_z?l

I θ0MZc9Ffp8D3MiI/D8cmFTPSD¦FUMj:

ΩMZcmFfNVP&EGFHMZcHc9MPSD8/p8NJPSEJQ9MK8MÊQHInFTPnFHEJI/D PncHcHIiZEGAZMPSp&À9I/p8Qvc9I/NVPnEJQHM

PnFHI/e#EGo*p8MOK8MXw/n^¦¥/¥#cI/p0PnpRÀ9I/p8QcHEGK8AZQHPSNYK8MXw/xS^8?l¥//w/x|c ¹k/S¥Sw/xS^8?l¥//w/x|c ?ÉI/p3cBK8AC3©

D8EGcHcHISD8c]PSNJI/Q9cNJMXFHMZeft8c¾K8MRNVPQ9ISFTP<FUEJISDFUMZQ9QHMc9FUQ9MRI/p W.Me#t8c ; D8EGSMZQHc9MZN x ; D8EGSMZQ9cUPSN:WEGe#M1x8:; Wx iZI/efefMXNJM]FUMZeft8c¾o*p8MvefMF9FUQUPnEGFNJP«WYMZQHQ9MWZLPSiZiI/eft8NJEGQN¹¨`PSD3/NJM

θZNVP#E´FUMZc9cHMRPSD3/p8NVPnEJQHM

p8D8E´ghI/QHefMΩ:c9I/EGF

UT1 = θΩ

?;~±¨sAZo*pP<FUEJISD ¹_z?lD8I/p8ctuMZQ9e#MFPSNJI/Q9cK8M¾FUEGQHMZQ

δθ = Ω(UT1 − TAI) − θ0.¹_z?ªÂ

MÇzt8Q9MZc9cHEJISDRg6PnEJcUPnD*FPSt8tPnQUP0/GFUQHMNJM®tPSQHPSe#dFUQ9MiZISQHQHMiFHEGg;K8pXFHMZeft8c:PnFHI/e#EGo*p8MUT1−TAI :SiI/D8c9E´©K8AQHAvMZD0FUPSD¦F¾o*p8MXFUMNiZI/efefMÁtPSQHPSefdFUQ9MXK¨sI/QHEGMZD¦FTP<FUEJISD&K8MvNJP«W.MQHQ9M9:t8p3EJcHo*p8Mvc9tAiZE´C;PSD¦FOtPSQ©

g6PSE´FUMZefMZD¦F\N½¨lPSD8/NGM#K3M«QHInFTPnFHEJI/D?Y:Dg6PSE´FO:$iZMD¨lMc9FvtPncXNVPK8EG¸AZQ9MZD8iMUT1 − TAI

op3EMZcmFvMZDp8cHPS/M9:3e«PSEGc

UT1− UTC:3I ; W¢ Mc9FNJMFUMe#t8cPnFUI/efEJo*p8M

TAIK8AZiZPSNJABK¨lp3DLD8I/e 8Q9MMZD¦FHEJMZQ

K8Mc9MZiI/D8K8Mj:K8M«FHMZNJNGM#c9I/Q9FHMo*p8MN¹¨lAi|PSQmF |UT1 − UTC| QHMZcmFUM«FHI/p<À9I/p3QHcÁEGD3ghAZQ9EJMp8Q Z¥z?`&c?:¢MFUMe#t3cUTC

I/pLWYMZeft8c ; D3EG/MQHc9MZN$¢II/QHK3I/D8D8AMc9FN¹¨lAiT8MZNGNJMBK3MFUMZeft8cNGAZ¦PnNJM9:*QHPSK8EJIK8E´¸p8c9AZMMFPSc9cHp8QHPSD¦Fp3DcmbzD3iT8QHI/D3EJcUP<FUEJISDefI/D8K3EVPSNGMS?z±NGNJM¾PvAFUAOEJD¦FUQ9IzK3p8EGFHMBMZDsx¦ÂS_:3tuI/p8QK8EGcHtuI/cHMQK¨lp3D8MAZiT3MZNJNGMK8MFUMZeft8cPnFHI/e#EGo*p8Mo*p8EQHMdFHMNGMFUMe#t8c±K8MNJPOQ9ISFTP<FUEJISDXFUMZQ9QHMc9FUQ9MwZ]NJPcHMZiI/D8K8Mt8Q9dZcMZDp8MK8MNVPBK8AFUMQHefEJDPnFHEJI/D]K8McNJI/D3/EGFHp8K8MZc?S@MZt8p8EGcNJM®K8A 3p3F:K8MWYÃB»S:nMZD1x/rSw\:<PSNJISQHc·A¦PSNZ ; Wx9:; WxP\t8Q9EJcp8DQHMFTPSQ9K«/ISEJcHEGD«K8M

33c6MDÊ_S¥/¥S1:¦iMo*p8MBN¹¨lI/DfFUQHPSK8p8E´F®t8PSQ

UTC−TAI = −33

RR WOHS %G D-* D022/= 6,8 02D $' %2@6* 8&* ? @6* @ < $#8 %&D58 4*@OD

x|^

cZ?;YI/p8Qe«PnEJD¦FUMD8EJQNJPviZI/D8K3EGFUEGI/D |UT1 − UTC| < 0.9s:3I/DQ9MFUPSQHK8M

UTCMZDEJD¦FUQ9IzK3p8EJcHPSD¦FO:8c9E

D8AiZMZc9cUPSEGQHMj:p8D8M\cHMiZI/D8K3MvPnFUISe#EGop3M]EGD¦FUMZQ9i|PSNGNVPSEGQHM ZfKPnFUMcC3ÇzMcZ?ÃEJD8c9E$NJM\k xÁK8AiZMe 8QHMX_S¥/¥¦rfPK8p8Q9A]w/S^¦¥ x¾cWYÃB»T? 28%(2*|%< ¾"±5u%<4h ,23(4h5u,!,

> ,

Å =6 ¾-/55;%<"Y5u,Y,Y'* ]".!1u=h

x ¦y3 ÃµN¹¨lEGcHc9p8MK8M

N½¨lPSt8t3NJEJiZPnFUEGI/D]K8MNVPQHISFUPnFUEGI/DÁK8EGp8QHD3M9:SD3I/p8c:D8Mc9I/efe#MctPSc·FHI/p3FZBg6PnEGF.KPSD8c:NGMQHMtdQHMFHMZQHQ9MZcmFUQHMn?»¼N3D3I/p8c·Q9MZcmFUMfZg6PSEGQHM PSc9iZp8NGMZQ·NGMt8NJPSDXAop8PnFUI/Q9EVPSN*K8pf¢» cHp3QNJM®t8NVPSD\AZo*pPnFHI/QHEJPSN/AZI/SQUPSt83EJo*p8M9:PSpe#Ib/MD&K8M]K8MpzÇ&PSD8/NGMZc

xMFy:D¨lM ÇziZAZK8PSD¦F¾tPSc x ]]MFBo*p8E$K8ISD8D8MZD¦FPSp8cHc9E.NGMZciZII/QHK3I/D8D8AMZc

K8p¢»[KPSD8cNGMBQ9MZtudZQHMFUMZQ9QHMc9FUQ9Mxp = x

:yp = −y

zp ≈ 1?3~YP]FUQUPÀ9MZiFHI/EJQ9MFHMZQHQ9MZcmFUQHM¾K3p¢»

MZcmFK8AZtuMZEGD*FHM¾cHp8QNJPÁC/p8Q9M]_z?`_vt8PSQNVP\FHQUP(À9MiFHI/EJQ9M¾e#Ib/MD8D8MOK8M¾N¹¨`P<ÇzM¾EGD8c9FUPSD¦FTPSD8D3A¾K8M¾QHISFUPnFUEGI/D:Pn¸QUPSD3iT8EJM¾K8MOc9MZcI/cHiEJNJNJPnFUEGI/D8c®K8EJp8Q9D8MZc?

28%(2*|%n46Z23465u,È³u=65 Y2=6 "$ º=5;%n4h ,23465u,jZ1Y23(4h2=6 "$ º=h2 *%(%( ¦ (46!23465u,ÃC8DK¨lI zFUMZD3EJQN¹¨lI/Q9EJMD*FUPnFUEGI/D«SNJI PnNJMK8pÊQHMZtudZQ9M¾K8M¾QHAghAZQ9MZD8iMOFHMZQ9QHMZcmFUQ9M9:8I/DPSt3t8NJEGop3MBcHp3iZiZMcHc9E´©/Me#MD¦F7 NVPRQHISFUPnFUEGI/D

NPPSefMZD8PSD¦FNGM\abc9FUde#M\K8MXAghAQHMD8iZMX¢AZNJMc9FHM ½az¢c9p8QNJM\abc9FHdZefMX:o*pP<©

FHI/QHEJPSN¬±QHPSE ½az:¬1:K8ISD*FN¹¨lM Ç3t3QHMZc9cHEGI/D hEJD¦/MQHc9M 1:;K8ISD8D8AZMOtPnQ

[SEV ] = NP (X + dX, Y + dY)[RRC]¹_z?lw

7 p8D8M¾Q9ISFTPnFHEJI/D«K¨`PnD8/NJMθ = ΩUTC + Ω(UT1− UTC) + θ0

Pnp3FUI/p3QK8p¢»tuI/p8QPSefMZD3MZQNGMefAZQ9EJK8EGMZDLiZANJMc9FUM]I/Q9EJ/EGD8M 6K8Me#E©¼/QHPSD8KLiMZQHiNJMÀ9I/EG/DPSD¦FNJM¾tu¿/NGM]K3p¢»MFip¼N½¨sI/QHEG/EJD3MBiZA ©NGMZc9FHMiZI/D¦/MD¦FUEJISD8D8MZNGNJM8] ·cHp8Q±NGMe#AQHEJK3EJMZDvEGcHc9pfK3p¢±MFtPncHcUPnD*FtPnQN¹¨lISQHEJSEJD8M±FUMQHQHMc9FHQHMiI/D¦/MZD¦FHEJI/D8D3MZNJNGMS?Ã N½¨sEJc9cHp8MK8MBiMF9FUMQ9ISFTPnFHEJI/D#D8I/p8ccHI/efe#Mc®K8PSD8cNGMBc9bcmFUdZefMAop8PnFUI/Q9EVPSNQUPnEFUI/p8Q9DPSD¦Fa3¬W

[SEV T ] = R3(ΩUTC + Ω(UT1 − UTC))[SEV ]¹_z?l

7 p8D8M®QHISFUPnFUEGI/DOtMQHefMFHFUPSD¦F·K3MtPSc9cHMQ·K8pXQ9MZtudZQ9MAZo*pP<FUI/Q9EVPSN/QUPnEFHI/p8QHD8PSD¦FPSpÁ.WNJp8E©¼e <ZefM riMFHFHMXQHInFTPnFHEJI/DMZc9FBghI/D8iFHEJI/DK8MXN¹¨lAi|PSQmFMZD¦FHQHMXNGMv¢» MF¾N¹¨`P<ÇzM

GzhQHAZPSNJEGcHAÁt8PSQBN¹¨`P<ÇzM

GzK8p!.W0:Yo*pPnD*FHEGCA#tPSQ]NJMc]iIzISQHK8I/D3D8AZMcÁAZo*pP<FUI/Q9EVPSNGMZc]K8p ¢»(x,−y) KPSD8c]NJM#·W¾?DP

[SRT ] = W (x,y)[SEV T ]½_z? x¥

¶·EJD8PSNJMe#MD*FN½¨sI/QHEGMZD¦FTPnFHEJI/D«K8MONVPXWYMZQHQ9M\tuMZpzF <FUQ9M]K3AZiZQ9EGFHM¾e«PnFHQHEGiZEJMNJNGMZefMZD¦Ft8PSQ

[SRT ] = W (x,y)R3(ΩUTC+Ω(UT1 − UTC))NP (X+dX, Y +dY)[SRC] = Q[SRC]½_? xx ~MZc$I 8c9MZQ9nPnFHEJI/D3c/AZIK8AcHEJo*p8Mc$K8AZtuMZD8K3MZD¦F·K3M:NVPe#PnFUQ9EJiMK¨sI/QHEGMZD¦FTPnFHEJI/DBiZE´©+K8MZc9cHp8c$MF$K¨`Pnp3FUQ9MZc

tPSQHPSefdFUQ9MZcOcHMNJI/D²K8Mc\Q9MZNVP<FUEJISD8cwpK¨lI 3cHMZQmnPnFUEGI/D$]Xt8QHISt8QHMnZNJPFUMZiT3D8EJo*p8MfMZD¦EJcHPS/AZMn?Y±D²FUI/pzFi|Pnc:3t8PSQNGEJD8AZPSQHEGcUPnFHEJI/DfK8MZcQHMZNJPnFUEGI/D8cK¨sI 8cHMQ9nPnFHEJI/DLPnp3FUI/p3QK8MBnPSNGMZp8Q9cK8Mt8PSQUPSefdFHQHMcP<©+t8QHEGI/QHE6EGcHc9p8MZcRK¨sp8D e#IK8dZNGMI/p K¨sp8D8MÊt8QHAK8EJiFUEGI/D 1:.I/D tMp3FfP(À9p8cmFUMZQRNGMZcRtPSQHPSe#dFUQ9MZcvK¨sI/QHEGMZD¦FTP<FUEJISDdX, dY, UT1 − UTC, x, y

?

x(r

`W %*'(!"$ 1%' (!)fc"$)fkJ! &-(!)fc@BdZc:xS¥/¥XK8MZcc9MZQmzEGiZMcEGD¦FUMZQ9DPnFHEJI/DPnpzÇ :3cHp3iZMZc9cHE´/MZefMZD¦FNJMOaMZQ9EGiZMO»¼D¦FUMZQ9DPnFHEJI/DPnNK8Mc~YP<FUE´©

FUp3K8MZc h»~Ya 1:<NJMazMZQmEJiZM®»¼D¦FUMZQ9DPnFHEJI/DPnNK3pI/p3SMZefMZD¦F:K8pX.I/NGM6» a 1:<NJM p8QHMZPSpX»¼D¦FUMQHDP<FUEJI<©DPSN*K8MN½¨ Mp8QHM » I/D¦F·AFUAiTPSQ9/AZcYK8MiZI/NGNJMZiFUMQYMF·K3M®iI/e 8EGD8MZQ$NJMc$e#McHp8Q9MZcPnc9FUQ9I/efAFUQ9EJo*p8McMZD²p8M#K¨lMc9FUEGe#MQ¾QHA/p8NJEGdZQ9MZefMZD¦FONJMc]iIzISQHK8I/D3D8AZMc\K8pt¿SNJMvK8MRQHInFTPnFHEJI/D?~$M » qPLK8I/D8D3A#NGMtPSQHPSefdFUQ9M ; Wx¾K¨lp8D3Mg6PZI/DLQ9I/p3FHEJD8EGdZQHMK8MZt3p8EJc x|/¦Âz?W.ISp3FUMcNJMZce#McHp8Q9MZcAFUPSEJMD¦FPSc9AZMZcc9p8QN½¨lPScmFUQHISNVPuM¾K8M\@PSD<À9I/DR:uNJPvNJp8D8MFHFHM\efAZQ9EJK8EGMZD8D8Mj:8NJM¾FHp M ZAD8EGFHPSN$I/pNJMcEGD8c9FHQHp8efMZD¦FUciZEGQHip8eR©ZAD8EGFHPSpzÇorMZNJNGMZcAFUPSEJMD*F®K8I/D3D8AZMcFUI/p3cNJMcrÀ9I/p8QHc&:ze#PSEGcN¹¨`P<FUefI/cHt83dZQHMNGEJefEGFTPnEGFNGMZp8Qt8Q9AZiZEGcHEGI/DZ¥\:l¥ x ]<?@BMt8p8EGc x¦Â/_:uN½¨sAZiNJI/c9EJI/DK8MZcFUMZiT3D8EJo*p8Mc]K3MX/AZIK8AcHEJMÁcHtPnFHEVPSNGM9: ZiZISe#efMZD8iMZQtPSQNGMFUQHPSi *EJD8R@I/t8t8NGMZQMFNJMBFHEJQNJPScHMQcHp8QNJPX~p8D8M 6~$p3DPSQ~$PScHMQPnD8/EJD3 :8az~Y 1:zt8p8EGciZvtPSQ9FHEJQ®K8Mx¦Ânw\:8NJMFHEJQNJPScHMQcHp8QcUP<FUMZNGNJE´FUM ¹a3PnFHMZNJNGEGFHM¾~$PScHMQPSD8SEJD8 :8a3~$ MFNVPXQUPnK8EJIn©+EJD¦FUMQ9ghAQHI/efAFHQHEJMoZFUQ9dZcNGI/D8/p3M PncHMc9p8Q·NGMZc·QHPSK8EGIBcHISp8QHiMZc:MÇFHQUPS¦PnNVPSiFUEJo*p8Mc ¬±MZQmbX~I/D8 PScHMNJEGD8M®»¼D¦FHMZQ9ghMQHI/efMFHQ9b9:¬¾~ » ¾PLtuMZQHefEJcBp8D uI/D8K KPnD8cONVPt8Q9AZiZEGcHEGI/D K8MZcOtPSQHPSefdFUQ9MZc¾K¨sI/Q9EJMZD¦FUPnFUEGI/D0K8MRN½¨sI/QHK3QHMvK¨sp8Dg6PSiFUMZp3QBx¥z?$~YPÊC/p8Q9M_?l^QHMdFHM«N½¨sASI/NJpzFUEJISD²K3p!tuI/EJK8cOK8Mc\FHMZiT8D8EGo*p8MZc\KPSD8c]NJMc\K8AFUMQHefEJDP<©FUEGI/DRK8MZc OY?*@BMZt3p8EJc x/w/:¦N½¨lPSc9FHQHI/efAFHQHEJMI/t3FUEGo*p8MD¨lMc9Ft8NJp8c±p3FHEJNGEJcHAMKPSD8c±NJP]K8AFUMQHefEJDPnFHEJI/DiZISp8QUPSD¦FHMÁK8Mc ¾.?uÃºtPSQmFUEGQK3M x/Sk\:NJM2v]aÊcZ¨sMZc9FEJeftI/c9AOtMp Z#tuMZpiZI/efe#M]NVPRefMZEJNGNJMp8QHMFUMiT8D8EGop3MLtI/p3QXK8AFHMZQ9e#EGD8MZQXNGM«efI/p3SMZefMZD¦FRK8p tu¿/NJM#MFRNVPNJI/D8SMZp8Q\K8pÀ9I/p8Q?:¢MZtuMZD3KPSD¦FO::NGM¬¾~ »Q9MZcmFUMÁNJPfc9MZp8NGM\FHMZiT8D8EGo*p8M Z#e <ZefMOK8M\ghISp8QHD8EGQ ; WxXMFBNGMZcBAi|PSQmFUcBPSpzÇtu¿/NJM]iZANJMZcmFUMn?@BM ©t8p8EGc x|/w/w\:¦NGM ®» P]AFUAQHMe#t3NVPSiAt8PSQ®NGMazMZQmzEGiZM»¼D*FHMZQ9DPnFUEGI/DPSNK3MBNVPOISFTP<FUEJISDfK3MBNVPOWYMZQHQ9MMFK8McabcmFUdZefMZcK8M\AghAZQHMD8iZM 6»¼D¦FUMQHDP<FUEJISDPSN$±PSQ9FHISFTP<FUEJISDÊPSD8KMghMQHMD8iZMXabc9FUMe azMZQmzEGiZMj:»±Ba ? 6 p8cHo*p¨sMZD x//Â]NJMcPniFUE´EGFUAcK8MN½¨s»±BaRAFTPnEJMZD¦Ft8QHEGD8iZEGtPSNJMe#MD¦F®iI/D8iMZD¦FUQ9AZcfZ\N¹¨ 8c9MZQ©nPnFUISEJQHMvK3M«.PSQHEGc p8QHMZPSp!¢MZD¦FUQHPSN ¾MF'ZN¹¨ ; a0ÉBP|nPSN 3cHMZQmnPnFUI/Qmb 6c9AZQHEGMZcF]QUPnt8EJK8M8]j:MZD²p8MK¨sp8D8MOp3FHEJNJEGcUPnFHEJI/DfFUMe#t8cQ9AZMN ?8~$McPSiFHEGEGFHAZcK8MON¹¨l»±aLc¨lAFTPSD¦FAFHIS¸AZMZc&:p8D8MOQHMc9FHQHp8iFUp8QHPnFUEGI/DcZ¨sMZcmFÁEGe#tuI/c9AZMS?~YPÊtPSQmFUEGMRPSK8efEJD8EGc9FUQHPnFUE´/MXMF]I/QH¦PnD8EJcHPnFUEGI/D8D8MNJNJM]MZcmFÁt8PSQ9FHEJMWZ¶;QHPSD ¦ghI/QmFO:e#PSEJcN½¨sI 8c9MZQmSP<FUI/EGQHMXK8Mf.PSQHEGc¾QHMZcmFUMRNJMviMZD¦FUQ9MRD8AQUPnNJ/EGop3MvI N½¨sI/D0ghI/p8QHD3EGF¾NJPcHAZQ9EJMXFHMZeftI/Q9MZNGNJMXK8Mc ¾op3E·PfNJMOc9FUPnFUp3FK8M]QHAghAZQHMD8iZM\EJD¦FUMQHDP<FUEJISDPSN 6c9AZQ9EJM]iZI/e 3EJD8AMÁ¢¥n^?u~$P#e#PSEJD¦FHMZDPSD3iZMOK8pQHMtdQHMÊFUMQHQHMc9FHQHM&EGD¦FUMZQ9DPnFHEJI/DPnNP²AFUAiZI/DzCAZMZ²N¹¨l» vOÉ':FUPSD8K8EGcfo*p8MN½¨ 8cHMQ9nPnFHI/EJQ9MK3M&.PSQHEGcMFXN½¨ ; a3É Èc9I/D¦FRiTPSQ9/AZcvK8M«e«PSEGD¦FUMZD3EJQ]iZI/D<À9ISEJD¦FUMe#MD*FXNJM«Q9MZtudZQ9MLiZAZNGMZcmFUMEGD*FHMZQ9DPnFUEGI/DPSN¹?Y~$Mc]p3EJK8Mc/AZISt8¦bzc9EJo*p8Mc@]¹PnFHe#IScHt88dQHMj:3IiZA|PnD8c:8D3I(b/PSpp8EGK8M9:zM|PSpÇiI/D¦FUEJD3MZD¦FTPSNGMZc&:3MFHi $À9I/p8PSD¦Fp8D QH¿/NGMÊiZMZD¦FHQUPSNKPnD8c#NGMZcREJQ9QHA/p8NVPnQHEGFHAZcXK3MNJP0QHISFUPnFUEGI/D FUMZQ9QHMc9FUQ9M9:±p8D iZMD*FHQHMK8MÊN½¨s»a NJMZp3QMZcmFRK8AZc9I/QHe#PSEGcXiZI/D3cUPSiQHAS?±@MZt8p8EGc1x/¦ÂH:·NJMcÁFUMiT8D8EGop3MZcf/AZIK8AZc9EJo*p8Mcfo*p8EAFTPnEJMZD¦FÀ9p3cHo*p¨lPSNJI/Q9ciTPStuISFHAZMZc]tPSQON¹¨l»±a I/D¦F]t8Q9EJc¾NJMp8Q]PSp3FHI/D8I/efEJMXK8PSD8c]NJMvi|PnK8QHMfK8MRD8I/p3SM|PSpÇ!c9MZQmzEGiZMc\EGD*FHMZQ©DPnFHEJI/D8PSpzÇ :3o*p8ENGMZp8Qc9I/D¦Ft8QHISt8QHMcZ?;~$PXt8QHAiZEGcHEJISDÊPSiFHp8MZNGNJMK8Mc ¾ MZc9FK3M¾N½¨sI/QHK8Q9M¾K8MO¥3?`_Áe«PnctuI/p8QNJMp8QK8AFUMZQ9e#EGDPnFHEJI/D\À9I/p3QHDPSNGEJdQHMS?

-<Æ.,Y4¹Y L³;'5"Y'|46$ zÊ!5"Y *%<,Y 3 .I/p8Q¾NGMÁ¬¾~ »NJP/QUPSD3K8MZp8QBK8M PSc9MvMZc9FONJPK8EG¸A©QHMD8iZMÊK8MLFHMZeft8cvK¨lPSQHQ9EG/AMÊK¨lp3D[ghQ9I/D¦FRK¨sI/D8K8MÊK¨sp8D8MÊcHISp8QHiMQHPSK8EGI0MZD K8MZpzÇ QUPSK8EGISFUANJMcHiZIStMcK8EGc9FTPnD*FHcÁK8Mfo*p8MZNGo*p8MZcXefEJNGNJEGMZQHcBK8M *e?.@BPSD8cÁNGM#iZPScÁEGK8A|PnNiM«K8ANVPSE±Mc9FXp3D8EJo*p8Me#MD*F]ghI/D8iFUEGI/DK8MNVP t8QHI(À9MZiFHI/DISQ9FU3I//I/DPnNJMLK8MNVP0NJEG/D8MLK8M PScHMMZD¦FHQHM&NGMZcfK8MZpÇFHAZNGMZcHiI/tuMZcfcHp8Q#NVP0K8EJQ9MZi ©FUEGI/D0K8MvNJPQUPSK8EGI/cHISp8QHiMS?~Mvi|Pnc]Q9AZMN:MZc9FOt3NJp8c¾iI/e#t3NJMÇzMj:i|PSQ¾NGMvK8AZNJPSE·EGD¦FUdZSQHMvK8Mc]M¸MFUcOD8I/D©/AI/e#AFUQ9EJo*p8MZc&:iZI/efefM0NJM0K8Ag6PSp3FK8M c9bD8iT8Q9I/D8EGcUPnFHEJI/DµK8MZc8I/Q9NJI/SMZc:NVP iZI/p3Q 8p8Q9M K8p ghQ9I/D¦FK¨sI/D8K8MÊNGI/QHcvK8McHISDtPncHcUPn/MÊKPSD8cRN½¨lPnFHe#I/c9t88dQHMS?±:D[FUI/pzFRi|PSc&:NGMZcvQ9MFTPnQHK8cR¬¾~ »S::tuMZp3SMZD¦F<FHQHM\MÇzt8NJEGiZE´FUAZcMZDghI/D8iFHEJI/DK8MctPSQHPSe#dFUQ9MZcK¨lISQHEJMD¦FTPnFHEJI/DK8pQ9AZcHMZPSpK8M\QUPSK3EJISFHAZNJMcHiI/tMcBtPnQQUPnt8tISQ9F:PnpzÇXQHPSK8EGI/cHI/p3QHiZMcMÇFHQUPS¦PnNVPSiFUEJo*p8Mc·EJc9AZMZc&:/MFK¨`Pnp3FUQ9MZctPnQUPSefdFHQHMZc·iZI/D8K3EGFUEGI/D8DPnD*F·NJMcM¸MFHcXD8I/D©¼/AI/e#AFUQ9EJo*p8MZc?Y·PSQ\EJD¦/MQHcHEGI/D:YI/DtuMZp3FÁQHMe#I/D¦FHMZQ\PSpzÇtPSQHPSe#dFUQ9MZcÁK¨lI/Q9EJMD*FUPnFUEGI/D?~MZcI 8c9MZQ9nPnFHEJI/D3c:cZ¨lPSQ9FHEJiZp3NJMZD¦F®PSp3FHI/p8Q±K8Mo*p8MZNGo*p8MZcQHAcHM|PnpzÇ#K8MQUPSK8EGISFUANJMcHiZIStMc:¦o*p8EI 8c9MZQm/MZD¦F

x

_z?s^ Ê:SI/NJpzFUEJISD&K8p0tuI/EJK3cK8McBFUMiT8D8EGop3MZc¾KPSD3cBNVPfK8AFHMZQ9e#EGDPnFUEGI/DK8MZciIzISQHK8I/D3D8AZMcK8ptu¿/NJM¾MFK8M ; Wx]K8M x¦ÂS¥WZvD8I/c·À9I/p8Q9cZ?

iZISe#eXp3D8AZefMZD¦FcHp3Q_n^v8MZp3QHMZcp8DÊiZMQ9FUPSEJDLD8ISe 8QHM¾K3M]QHPSK8EGIn©¼c9I/p8QHiMZciI/D8cmFUEGFHpPSD¦FNJMBQHMZtudZQ9MOK8MQHAghAZQ9MZD8iM«iZANJMc9FUM#EJD¦FUMQHDP<FUEJISDPSN½?~MZcÁc9MZMcHEJISD8c\K¨lI 3cHMZQmnPnFUEGI/D8c]cHI/D¦FXMcHtPniZAZMcXK8M«r Z&ÂÁÀ9ISp8QHc?D#AFTP3NJEGF±p3D8MK3EJc9FHEJD8iFUEGI/DvMZD¦FUQ9MBNGMZc±tPSQHPSe#dFUQ9MZc±K¨lPSQHiiZI/efefMNJMZc ¾.:*NJMc±iZII/QHK8ISD8D8AZMcK8McQUPnK8EJIn©+cHI/p3QHiZMc·o*p8EcHI/D¦F:iI/D8cmFTPSD¦FK3p8QUPSD¦FFHI/p3FHMNVPcHMcHc9EJI/DvK¨sI 8c9MZQmSP<FUEJISDXMF·NJMZc.tPSQHPSe#dFUQ9MZcl]NJIn©i|PnpzÇ]W:8FHMZNJco*p8M]NJMccUPSp3FHcK¨l3ISFUQ9NJI//Mc:8NGMOQHMFUPSQHKPnFHe#IScHt88AQHEGop3M9:o*p8EnPSQHEGMZD¦FiZI/D3c9FTPne#efMZD¦F|?~MZcPSQHQ9EGSAZMZcK8McghQHISD*FHcK¨lISD8K8MÁc9I/D¦FBQ9MZD8Q9MZ/EGc9FHQHAZMcK3M\e#PSD8EGdZQHM¾EGD8K8AtMD8KPSD¦FUM\MZDiTPSo*p8MÁc9EGFHMcHp3QBK8Mc PSD8K3MZce#PS/D8AFUEGop3MZcZ?¢MNJNJMcm©+iZEYcHI/D¦FMD8cHp3EGFUM\MZD¦/IbSAZMZc'Z#p3DiZMD*FHQHMj:I p3D ]iZISQHQHANVP<©FUMp8Q@]¾tuMZQHefMFK3M]K3AFUMQHefEJD8MQNJMcK8EG¸AZQ9MZD8iMZcKPSD8cNJMcFUMZeft8cK¨lPSQ9QHEGSAZMcZ?

~$PFUMiT8D8EJo*p8MK8pXFUEGQ.NJPScHMQ.c9Mg6PSEGF.cHp3Q·K8MccUPnFHMZNGNJEGFHMZc.PSQ9FHEGCiEJMNJc$I/pXc9p8Q·NJPNJp3D8MS?n~:¨lI 3cHMZQmnPnFUEGI/DK8M PScHMÁMZc9FBNJMOFUMe#t8cBPSNJNGMZQMFBQHMFUQHISp8QBK¨sp8Dt3p8NJc9MÁNVPncHMZQ&:Q9AAiT8E·t8PSQBp8D&iZI/EGD&iZp M\t8NVPSiAÁc9p8QNJMLcHPnFUMNJNGEGFUMn?±¢MÊFUMZeft8cRMZcmFPncHcHIiZEGA Z NJP0K8EJcmFTPSD8iMo*p8Ec9AZtPSQ9MNJP0c9FTP<FUEJISD K3pcHPnFUMNJNJE´FUM«EJP²NJPEGFHMZcHc9MXK8M\NVP#NGp8efEJdZQ9MS?u¢I/efefM\iMFHFHMXK8EGc9FTPnD8iZM\MZc9FMZNJNGM]ghISD8iFHEJI/DK8MÁN¹¨lI/Q9EJMD*FUPnFUEGI/DK8MÁNJP#WYMZQHQ9MKPSD3cN¹¨lMcHtPSiM9:;I/DiZI/D ZI/E´FK8I/D8i]o*p8M\N¹¨lISDt3p8EJc9cHM]QHMZefI/D¦FUMQPSpzÇ ¾tPSQiZMFHFUMOFUMiT8D8EGop3MS?;ÃN½¨s8Mp8QHMÁPSiFHp8MZNGNJM]NVP#t3QHAZiEJc9EJI/DK8MÁNJP#efMZcHp3QHMvPnF9FUMEJD¦F¾rn¥#t8c&:/ISEJQHM\e#ISEJD8c&:iS¨sMZc9Fm© Z<©+K8EJQ9M xXiejMZDK8EGc9FTPnD8iZMn?

~M«a*bzcmFUde#MRK8MRYI/cHE´FUEJISD8D8MZefMZD¦F'v¾NJI 8PSN.t8PSQ¾cUPnFHMZNGNJEGFHMÁMc9FOghI/D8K8Avc9p8Q¾p8D²MZD8c9MZe 3NJMvK8MRcUP(©FUMNJNGEGFUMÁop3E®Ae#MFHFUMD¦FÁK8Mfe#PSD8EJdQHMRtuMZQHe#PSD8MD¦FUMfK8MZc]cHEG/DPSpzÇ²QHPSK8EGIMD!K8EGQHMiFUEGI/D²K8p!c9I/Nq:KPnD8cNJMcHo*p8MNJcvcHISD*FfiIzK8AcRNJMZp3QÁFUMe#t8cRK¨sAZefEJc9cHEGI/D?~McvQHAZiMZt3FHMZp8Q9cfFHMZQ9QHMZcmFUQ9MZc:±Aop3EJtuAZcRK¨s8I/QHNGI//Mcc9bD8iT3QHI/D8EGcHAMZcOP|/MiÁiZMNJNGMZcK8MZccUPnFHMZNJNGEGFHMZc:tuMZQ9e#MFHFHMZD¦FBK3MÁefMZcHp3QHM]NJMOFUMZeft8cPSNJNGMZQK8MccHEG/DPSpÇR:MFK¨lMDÊK8AZK8p3EJQHMBNVP\K3EJc9FUPSD8iMo*p8ENJMccHAtPSQ9M¾K8pLcUPnFHMZNGNJEGFHMAe#MFHFHMZp8Q?azEp8DLQHAiZMZtzFUMZp3QMZD8Q9MZ/EGc9FUQ9McHEGeXp8N´FTPSD8Ae#MD¦FBNGMZcc9EJ/DPnpzÇK3Mvk«cUP<FUMZNGNJE´FUMZc&:NGMÁQ9AZiZMt3FUMp8Q¾MZcmFOtIScHEGFHEJI/D3D8A2ZN¹¨lEGD¦FUMZQ9cHMiFUEGI/DK8MckRcHt88dQHMcBiZMD¦FUQHAMZccHp8QNJMccUPnFHMZNJNGEGFHMZc:3MFK8MOQUP|b/ISD8cNGMZcK8EGc9FTPnD8iZMcK8AK8p8E´FUMZcK8McBkvFUMe#t3cPnNJNJMQZ?

x(Â

@BMiMF9FUMBg6PI/D:*I/DI3FUEGMZD¦FNJP\tuI/cHE´FUEJISD#K8p«QHAZiMZt3FHMZp8QKPSD8cNGMQ9MZtudZQ9MEJD8MQ9FHEJMZN;K8MccUP<FUMZNGNJE´FUMZc?¦ÃtPSQmFUEGQK3MNJP]Q9ISFTPnFHEJI/DfMZD¦FHQHMBNGMQHMZtudZQ9MBEGD8MZQmFUEJMNMFNJMQHMtdQHMFHMZQ9QHMZcmFUQ9M9:I/D«Q9MZefI/D¦FUM_ZONVPOtuI/cHE´FUEJISDK8pQ9AZiMZt3FHMZp8QKPnD8cNGMQ9MZtudZQHMFUMZQ9QHMc9FUQ9MS?8¢B¨lMc9FNGMt8Q9EJD8iEJtuMK3ptIScHEGFHEJI/D3D8MZefMZD¦F®/NJI 8PSN½?¦»¼D¦/MQHc9M©efMZD¦FO:cHEuNJMctuI/cHE´FUEJISD8c±K¨lp3DLMZD8c9MZe 8NGMBK8MQHAiZMZtzFUMZp3QHccHISD*FtPSQ9g6PnEGFUMe#MD¦F®iI/D8D*p8Mc:8NGMZcefMZc9p8QHMcD8I/p3c¾tMQHefMFHFHMZD¦F]K¨lPjsfD8MZQ¾D8InFUQHMviI/D8DPnEJcHcHPSD8iMfK3MfNJP«QHInFTPnFHEJI/DK3pQ9MZtudZQHMXFHMZQ9QHMZcmFUQ9Mft8PSQ¾QUPSt©tuI/Q9FPSpRQ9MZtudZQHMEGD8MZQmFUEJMN½?<ÃN½¨s8MZp3QHMPSiFUp8MNJNJMNGMfv¾NJI PnN8.IScHEGFHEJI/D3D8EJD8¾abc9FUMe qvOa ·K8MN½¨lPSQHefAZMPSefAZQ9EJi|PnEJD8MRt8Q9AZK8I/efEJD3MS?·azMZcXiI/D8ip8QHMD*FHcvcHI/D¦FvNGMvO~ ¾ÉÃ¾a3aQHp8c9cHMj:MFvNGM#cmbc9FUde#MLMp8QHIStAMZDv¾Ã~»~$ :8MDÊK8ASMZNJISt8tMe#MD¦FO:8K8ISD*FNGMt8Q9MZefEJMZQ®cUPnFHMZNGNJEGFHMPXAFUA¾MZD¦SI(bSAÁNGMO_SwXK8AiZMZe 8QHM]_S¥S¥¦rK8Mt8p8EJcNJP PScHM]K8M PSE SI/D3I/p8QMFK3I/D¦FNJPvt8PSc9M]IStAQUPnFHEJI/D8D3MZNJNGMBK8A 8p3FHMZQUPfMZD&_S¥/¥/wz?

5u!1.23%<284¹Z5u,"$ -nÆY,.46$ 3 ~$PFUMZiT3D8EJo*p8M¬¾~ ».MZc9F®iZMQ9FUPSEJD8Me#MD¦F®NJPt8NJp3ciI/eft8NJdFUM9:e#PSEJc]t8NJp3cXNJI/p3QHK8M#MFvNJPt8NGp8cXiZI973FUMp8cHMJZ&efMF9FUQ9MMZD IMZp3Q9MS?:¢B¨sMZcmFRNVP&c9MZp8NGMo*p8EtuMZQ9e#MFHFHMZD¦FK8MOK8AFUMZQ9e#EGD8MZQc9p8Qt8NJp3cHEJMp8QHc.À9ISp8QHcNJMcnPSQHEJPnFUEGI/D8cK8M¾N¹¨lISQHEJMD¦FTPnFHEJI/DK3M]NJPvW.MQHQHMOKPnD8cN½¨sMZcHt8PSiZMj:ZÊcUP|/I/EGQ\NJPt3QHAZiMZc9cHEJISDz©¼D*p3FUPnFUEGI/DMF ; Wx/?Y~$PQHPSEJc9I/DMD!Mc9FXo*p8MfNJMc\efMZc9p8QHMc\¬~ ®»BcHISD*FÁK8E´©QHMiFHMZefMZD¦FQUPnF9FTPSiT3AZcPSpLQHMtdQHMOiZANJMc9FUMj:8tPSQmg6PSEGFHMZefMZD¦FcmFTP3NJMS?8~$McFUMiT8D8EJo*p8MccUPnFHMZNJNGEGFUPSEJQ9MZcD8MtuMZQHefMF9FUMD*FftPncfK3MK8AFUMQHefEJD8MQvN½¨sI/QHEGMZD¦FTPnFHEJI/D K3MNJPFUMZQ9QHMÊKPSD3cfp3DQHMtdQHMPSp8c9cHEc9FUP8NGMS?±~$Po*pPSNGEGFUAvK3pQ9MZtudZQHMfPSc9cHIiZEGA#PnpzÇ cUP<FUMZNGNJE´FUMZcBMZc9F\t8Q9AZiZEGcHAe#MD*F\PSc9cHIiZEGAZM ZLNVP\À9p8c9FHMZc9cHM«K3pefIzK3dZNJMI/Q 8EGFHI//QUPnt88EJo*p8Mn? Q:(EJN¦Mc9FEGe#tuI/c9cHE 3NJM:K8M®e#IK8AZNGEJc9MZQNVPFUQHP(À9MZiFUI/EGQHMK8MZc.cUPnFHMZNGNJEGFHMZc$cHp3Q·t8NGp8cHEGMZp8Q9cÀ9I/p8Q9cP|/MiXp8D8M\t8QHAiZEGcHEJISDcHp\sfcHPSD¦FUM9:t8QHEGD8iZEGtPSNGMZefMZD¦F Z«i|PSp3cHMXK8pghQHMZEGDPS/M\PnFHe#I/c9t88AQHEJo*p8Mn?;»¼NMZcmFK3I/D8i8I/QHcK8Mo*p8MZcmFUEGI/D«o*p8MNJMc®cHPnFUMNJNJE´FUMcghI/p8QHD3EJcHc9MZD¦F®K8MZco]tuI/EJD¦FUc±K¨sMZD3iZQUPn/MiAZNGMZc9FHM^]tI/p3QK8McK8p8QHAMZcK8AtPScHcHPSD¦FNVPÁc9MZe#PSEJD3MS?3Ã p8DLe#ISe#MD*FI/pJZXp8DPSp3FHQHMj:3N½¨sI/Q 8EGFHMK8ISEGFMFUQ9M¾QHA|PÀ9p8c9FHAZMMZDghI/D8iFHEJI/D²K8McXI 8c9MZQ9nPnFHEJI/D3cZ?$Ã iI/D¦FUQHPSQHEGI :$cHENJMZcOFUMiT8D8EGop3MZcXcHPnFUMNJNJE´FTPSEGQHMc¾cHI/D¦F\EJeft8QHI/Q9MZc'ZK8I/D3D8MZQRNVPt8QHAiZMZc9cHEGI/Dz©¼D*p3FUPnFUEGI/D[MF ; WxtuI/p8QXK3MZcRK8p8Q9AZMZcfcHp3tAQHEJMp8QHMc ZÂRÀ9ISp8QHc&::MZNJNGMZcXc9I/D¦FFUQ9dZcM1sfi|PSiMZcOtISp8QBK8AFUMQHefEJD8MQBNJMciZII/Q9K8I/D8D8AMZcK3p0t¿/NGMÁMFK8MXNJP«NJISD8/MZp3QBK8p#À9I/p3QZ?±D0M¸MFNJMLefI/p3SMZefMZD¦FfK8p t¿/NGM9:K8PSD8cRNJMLQ9MZtudZQHMÊEGD*FHMZQmFUEJMNq:·PSt8tPSQHP0/JFRiI/efe#Mp3D8MÊI/cHiEJNJNJPnFUEGI/DK8EGp8QHD3MKPSD3cNJMcHMD8cFHQHEJSI/D8I/efAFHQHEJo*p8MK8MN½¨lP<ÇzMK3MZctu¿/NJM/AI//QHPSt88EGop3MS?3¢B¨lMc9FtuI/p8Q9o*p8I/EucUPÁefMZc9p8QHMD8MQHMo*p8EJMQ9FtPScNVPXcmFTP3EJNJE´FUAK8pQ9MZtudZQ9M\EGD8MZQmFUEJMNc9p8Qt8NJp8c9EJMp8QHc·À9I/p8Q9cZ?

`W )i*&,0"$ &%'Jc kl !fe ,0"$ &-(!)fcazE8NGMZciI/e#tuI/cHPSD¦FUMZc:K3pX/MZiFUMp8Q±EJD8cmFTPSD¦FTPnD8AK8MQ9ISFTPnFHEJI/DÁKPSD8c:NGMQHMtdQHMiAZNJMc9FHMI/pXFUMQHQHMc9FHQHM

D8M¾ghI/D¦FtPScN¹¨lI *À9MFK8MOK8AFUMZQ9e#EGDPnFHEJI/D8cQHI/p3FHEJD8dQHMc:8MNJNJMce#AQHE´FUMZD¦Fp8D3M\P<FHFUMD¦FUEJISDLtPSQ9FHEJip8NJEGdZQHMNJISQHcHo*p¨sI/DcZ¨lPnFHFUPSiT8M'Zfp3D8M\K3MZcHiQHEGt3FUEGI/DFH8AZISQHEJo*p8M]K8MONVPvQ9ISFTPnFHEJI/DLFHMZQHQ9MZcmFUQHMn?¢B¨lMc9FtuI/p8Q9o*p8I/EEJNMZcmFvEJeftuI/Q9FUPSD¦F\K¨lAFTP8NGEJQOK8McXQHMNVPnFHEJI/D8c]MZD¦FHQHMNGMZc]tPSQUPne#dFUQHMcÁK¨sI/Q9EJMZD¦FUPnFUEGI/D 6PSD8/NGMZc]K¨`:p8NGMZQ&:AZNGAZefMZD¦FK8MONVPve#PnFUQ9EJiMK¨sI/QHEGMZD¦FTPnFHEJI/DR:3MFHiS?´? MFNGM/MiFUMp8QEJD8cmFTPSD¦FTPnD8AOK8MOQHISFUPnFUEGI/D?

~M#/MiFHMZp8QXEGD8c9FUPSD¦FTPSD3A#K8M#QHISFUPnFUEGI/D~ωK8pa3·W tPnQ\QHPSt8tuI/Q9F\PSpa3¢ºcZ¨sMÇzt8Q9EJefM#K8PSD8cÁNGM

a3·W cHISp8c¾NVP#ghISQHefMXp8cHp3MZNJNGM~ω = Ω(m1~x1 + m2~x2 + (1 + m3)~x3)

:ΩAFUPSD¦FONVP«EGFHMZc9cHMvK8MvQ9In©

FTP<FUEJISDXK8MQHAghAZQ9MZD8iMK3MNVPBWYMZQ9QHM±MF:N¹¨lI/DvEGD¦FUQHIK8p8E´F:PSNGI/QHc.NVPBnPSQ9EVP8NGM®iI/eft8NJM Ç3Mm = m1 + im2

?

~ωMc9FvNJPQHAcHp8N´FTPSD¦FHM«K8McXQHISFUPnFUEGI/D8cOEJD3c9FTPnD*FUPSD8AMZcvPSpzFUI/p8Q]K8MiT8PSiZp8D K3MZcÁFHQHI/EGcÁP<ÇzMcÁK8MNJP

cHAo*p8MZD8iM(lmn)

:in¨lMc9FoZvK8EJQ9M7

~ω = αl~Xl + αm~x

(1)m + αn~x

(2)n

½_? x(_:DM Ç3t3QHEJe#PSD¦FNJMciZI/eftuI/cUPSD¦FHMZcK8M

~ωKPSD8cNGM]a3·W MDghISD8iFHEJI/DLK8McPSD8/NGMZc

αl:αm

MFαn:

HG5# 2 % D I O-$- KM9 HOMKMJJ J N3HEN 6 9

xw

I/D²I 3FHEJMZD¦FOK8McOQHMZNJPnFUEGI/D8c¾iEJD8Ae«PnFHEJo*p8Mc¾iZI/e 3EJDPSD¦F¾NGMZcOiZISe#tuI/cUPnD*FHMZcOK8p /MiFUMp8Q]EJD8cmFTPSD¦FTPnD8AK8MOQHInFTPnFHEJI/DLKPnD8cNJM]a3·W0:NGMZcPSD3/NJMcK¨lISQHEJMD¦FTPnFHEJI/DLK8p&a3·W MFNJMp8QK8AQHEGSAZM¾FUMe#tuI/Q9MZNJNGMS?

.I/p3QNJPRc9AZo*p8MD8iZMXMp8NJAQHEGMZD8D8M]iZNJPScHc9EJo*p8M ¹kxk1:D3I/p8cI 3FUMD8I/D8cNJMcQHMZNJPnFUEGI/D8ciEJD8Ae«PnFHEJo*p8McK8E´FUMZcK¨l:p8NJMQ

θ + iΨ sin θ = ΩmeiΦ

Φ − Ψ cos θ = Ω(1 +m3)

½_? xk :D#M Çzt8QHEGe«PSD¦F±NGMZc±iZI/eftuI/cUPSD¦FHMZc±K8M

ωK8PSD8c±NJMa3¢D8I/p8c±I zFUMZD3I/D8c±NJMcQ9MZNJPnFUEGI/D8ciEJD8Ae«PnFHEJo*p8Mc

QHMNJEJPSD¦FNJMciI/eftI/cHPSD¦FUMciAZNGMZc9FHMZcK8pÊ/MiFUMp8QBEGD8c9FUPSD¦FTPSD3A¾K8MOQHISFUPnFUEGI/DLMFNJMcPSD8/NGMZcK¨l:p8NJMQ

ωX + iωY = θeiΨ + iΦ sin θ eiΨ ½_? x|^ωZ = Ψ + Φ cos θ

¹_z? x(r

x

u

! 9[ f

$n ,(!-.)3J)"$%'J 1)f (!)+*, -.%"/,0"$ 1%2 "$)-/-6)fc"m-.) !#"$%&!!('*)+,!-)+!%('!/.00&

.I/p3Q·AZiQHEGQHM±NJMc.Aop8PnFUEGI/D8cYD8M£FHI/D8EJMD8D8Mc·K8MNVPQHISFUPnFUEGI/D¾FUMQHQHMc9FHQHM9:<N½¨s¦btISFH8dZc9Mc9p8Q.N¹¨lISQHEJSEJD8MK8pQHMtdQHMOEJD8MQ9FHEJMZND¨lEGD¦FUMZQmEJMZD¦FtPSc?;:DM¸MFNGMZcAop8PnFUEGI/D8cK8M]ÉM£FUI/DtMQHefMF9FUMZD¦FK¨sI/tuAZQHMQp8DK3AZiZISp8t8NVPn/MÁiI/e#t3NJMFMD*FHQHMXNGM\efI/p3SMZefMZD¦FISQ 8E´FTPSNK8M\NVPfW.MQHQHM\MFBcHI/DefI/p3SMZefMZD¦FK3MÁQHI<©FTP<FUEJISDÊPSp3FUISp8QK8MOcHI/DiZMD¦FUQHM]K8MOe#PScHc9M9:iZISe#efM¾D8I/p8cPSNGNJI/D3cNJM¾QHPSt8tuMZNJMQiZE©¼K8McHcHISp8c

¢I/D8c9EJK8AQHI/D8cNJP\Q9MZNVP<FUEJISD#ghI/D8K8PSe#MD¦FTPSNGMBK8MNJP\K3bDPne#EGop3M9:3M Çzt8QHEGe#AMKPSD8cp8DLQHMtdQHMEGD8MZQ©FUEGMZNK3I/D¦FN¹¨lISQHEJSEJD8MD¨lMc9FtPScc9tAiZEGC8AZM-

dmd2 ~R

dt2= d~F

6k3? x I ~R

tuI/c9EGFUEGI/D8D8MOp8D3MXe«PncHcHM\AZNGAZefMZD¦FTPSEGQHMdm

K8MÁNJP#WYMZQ9QHMXKPnD8cBp8D0Q9MZtudZQ9MÁEJD3MZQ9FHEJMNq:D8I/D&cHtuA©iZE´CA9:MF

d~FMZcmFNJPvcHI/efe#MBK8MZcghI/QHiMZcPSt8t3NJEJo*p8AMZccHp3Q

dm?

~MFUMe#t8c·MZDRe#Ai|PSD3EJo*p8MK3MD8M£FHI/DvMZcmF±cHp8t8tuI/c9AcZ¨sAZiZISp8NJMQK8MNJPBen<e#Mg6PZISDvMZDXFUISp3FNGEJMZp0rEJN¦Mc9F.K8I/D8ituI/cHc9E 8NGM:K8M®iIzISQHK8I/D3D8MZQYN½¨sMZD8c9MZe 3NJM±K8MZcYefMZcHp3QHMZc.K8M±K8p8Q9AZMt8PSQ$p8DÁc9MZp8N*tPSQHPSefdFUQ9M

t?

azI/E´F ~R0NJMQUP|b/I/D#/MZiFUMp8QK8pSAZIiZMZD¦FHQHMhNJMiZMZD¦FHQHMBK3MZce#PScHc9MZc®K8MBNJP]WYMZQ9QHM KPSD8c®NJMQHMZtudZQ9M

EJD3MZQ9FHEJMNiZI/D3cHEJK3AZQHAOMF~rNVPXtuI/cHE´FUEGI/DLK8M

dm:8QUPnt8tISQ9FUAM]PSpÊQHMZtudZQ9M\SAZIiZMZD¦FHQHEJo*p8Mn?;ÉI/p3cP|SI/D8c

dmd2 ~R0

dt2+ dm

d2~r

dt2= d~F

6k3?ª_:D0EJD¦FUA/QUPnD*FBiZMFHFUMÁQHMZNJPnFUEGI/D&c9p8QN¹¨lMD8cHMe 8NJM\K8MXNJP#e#PnFUEGdZQHMOFUMQHQ9MZc9FHQHMj:I/DK8Ae#ISD*FHQHMvPnEJcHAe#MD¦FNJMFH8AZISQHdZefMOK8pÊiZMD*FHQHM]K8MOe«PncHcHMj:iS¨sMZcmF9© Z(©¼K8EGQHM7

Md2 ~R0

dt2= ~F ext 6k3?`k

_S¥

I ~F ext Mc9FXNJPQ9AZc9p8NGFUPSD¦FUMfK8MZc]ghI/QHiMZc]MÇFUAQHEJMp8QHMcÁc¨lM Ç3MQZPSD¦FvcHp8Q\NVPÊW.MQHQ9M9:$QHAK8p8EGFHMZc\t8QHMcHo*p8MMÇzNGp8cHE´/MZefMZD¦F ZRNVPX/QHPE´FTPnFHEJI/DNGp8D8E©¼cHISNVPSEGQHMS?»¼NMZDQHAcHp8N´FUMOo*p8M

dmd2~r

dt2= d~F − dm

M~F ext 6k3?l^

¢MF9FUMLAZo*pP<FUEJISD i|PSQHPSiFHAZQHEGcHMLNGM«efI/p3/Me#MD¦FRK8MN½¨sAZNGAZefMZD¦FXK3MLe«PSc9cHMdm

KPSD3cXp8D[QHMtdQHM/AIziMZD¦FUQ9EJo*p8MvK8I/D¦F¾NGMZc¾P(Ç3Mc¾¦PSQ9K8MZD¦F¾p8D3MvI/QHEGMZD¦FTPnFHEJI/DC3ÇzMvKPSD8c¾p3D0QHMZtudZQ9MvEJD8MQ9FHEJMZN.Z#ghI/QmFUEGI/QHEEJD3K8ACD3E½?¢M²QHMZtudZQ9M 8PSQ9biZMD¦FUQHEGo*p8Mt3QHI/t8Q9MISp Q9MZtudZQHM²/AIziMZD¦FUQ9EJo*p8M²K3bDPSefEJo*p8MZefMZD¦FD8I/D©FUISp8QHDPnD*F:*K8p#tuI/EGD*FK8Mp8MD8M£FHI/D8EJMD:*D¨sMZc9FtPScEJD8MQ9FHEJMZN¹?`ÉI/p8cSI(bSI/D8c®op3MNGMefI/p3SMZefMZD¦F®K8MN½¨sAZNGAZefMZD¦FK8M]e#PScHc9M¾MZc9FiZISD8K8EGFHEJI/D3D8AtPSQNJPoMOISQSEGHED x9ISKSE ~F K3I/D8D8AM\tPnQ

~F = d~F − dm

M~F ext 6k3?ªr

~M#Q9MZtudZQ9M#/AIziMZD¦FUQ9EJo*p8MfK3bDPSefEJo*p8Me#MD*F\D8I/D©+FUISp8QHDPnD*F]tuMZp3F'<FHQHM#PScHc9EJefEJNGAoMOI#DFE1X XYE1DFE1P~A Zp8D Q9MZtudZQHM«EJD8MQ9FUEGMZND8M£FHI/D8EGMZD Z&iI/D8K8E´FUEJISD!K8MLiI/D8cHEGK8AZQ9MZQXNJPghI/Q9iZMK3Me«PnQHAZMj:.o*p8MLD3I/p8cXI ©FUMD8I/D8cvMD[QHMFHEJQHPSD¦FWZNVPghISQHiZM#FUISFUPSNJM#cZ¨sMÇzMZQ |PSD¦F#cHp8QvN¹¨lANJAZefMZD¦F

dm:d~F:.NJM«FHMZQHefM dm

M~F ext

:iS¨sMZcmF Z&K8EGQHM9:·PSpiIzM1s#iEJMD*F

dmt3QHdZc&:N½¨lPSiiZAZNGAZQHPnFUEGI/D!K8p SAZIiZMZD¦FHQHMLKPSD3cXp8D QHMtdQHMEGD8MZQmFUEGMZN½?

~$P²ghI/Q9iZMK¨sEJD¦FUMQUPSiFUEJISD/QHP|zE´FTPnFHEJI/D3D8MZNGNJMMD*FHQHMNVP0W.MQHQ9M&MF#NJMc#iI/QHt3c«iZANJMc9FUMc«D8MtMp3Fn<FUQ9MefMZcHp3QHAZMj:PSNGI/QHc®op3M]NGMZcghISQHiZMcK8Me#PSQHAMZc hI/pLNJMp8QEGD3p8MD8iZM¾c9p8QN½¨lPSiZiAZNGAZQUP<FUEJISDK8MtuMZcHPSD¦FUMZp3Q cHISD*FK8AFUMiFTP 8NJMctPnQNJMZcSQUP|EJefdFUQ9MZc?;±NGNJMccHMp8NJMct8Q9AZc9MZD¦FUMD*FBp8D8MOQHAZPSNJE´FUAc9MZD8c9E 8NGMS?

ÃBEGD8cHEFUI/p8c\NJMcXK8ASMZNGI/t8tuMZefMZD¦FUcvK8M#NVP&efAZiZPSD8EGop3M«D8M£FUI/D8EGMZD8D3MtMp3/MD¦Fn<FUQ9MLPSt8t8NGEJo*p8AcKPSD3ciMOQHMZtudZQ9M\tuI/p8Qmpo*p8MON½¨sI/DÊD¨ bLiZISD8cHEGK8dZQ9M]o*p8M]NJMcghI/QHiMZcK8MOe#PSQHAM ~F ?

@PSD8cNJM]i|PSK3QHMÁK3M\NJPfefAZiZPSD8EJo*p8M]D8M£FUI/D8EGMZD8D3M9:uI/D&tuMZp3FBK8I/D8i]MZD¦EJcHPS/MQBK8MpzÇK8AZe#PSQHiT3MZctuI/p8Q®FHQUPSE´FUMQNJMt8QHI8NJde#MK8MNVP\QHISFUPnFUEGI/D«K¨sp8DLiI/QHt8c?~$PÁt8NGp8ciZISe#eXp3D8MBiI/D8cHEGc9FHM ZXPSt8t8NGEJo*p8MQNJMFU3AZI/Q9dZefMK8p«e#I/efMZD¦F®iZEGD8AFHEJo*p8MPSpiZISQHt8c®iZI/D8c9EJK8AQHAKPSD8c®NJMQHMZtudZQ9M PnQ9biZMD*FHQHEGop3Mt8QHISt8QHMn?~$PXcHMiZI/D8K3M¾e#AFU8IK8MMc9FghI/D3K8AZM¾c9p8QN½¨lPSt8t3NJEJiZPnFUEGI/DfK8EJQ9MZiFHMK8MNJPÁQHMNVPnFHEJI/DfghI/D8KPne#MD*FUPSNJMK8M¾NJPK3bDPSefEJo*p8M ZXN¹¨lMD8cHMe 8NGM¾K8MZcANJAZefMZD¦FHcK8M/I/NGp8efM¾op3EiZI/eftuI/cHMD*FNGMiZISQHt8cMFMZDEJD¦FUMQUPSiFUEJISDeXp3FHp8MZNGNJM r8PSt8QHdcEJD¦FUA/QUPnFHEJI/DLK3M\iMZcAZo*pPnFHEJI/D8cK3EG¸AZQHMD¦FUEJMNJNGMZcI/pK¨sp8DvÀ9MpQ9AZK8p3EGFI 3FHMZD*p8cBPSpefI(bSMZDÊK¨lPSt8t8Q9I|Ç3EGe«P<FUEJISD8c:*I/DÊI 3FHEJMD*FNJMBiT8PSe#tLK3MZcK8AZt3NVPSiMZefMZD¦FUcK3M¾iZMZcANJAZefMZD¦FHc:3K3I/D¦FI/DMÇFHEJQHtuMPSNJISQHcNVPt8PSQ9FHEJM±PSc9cHIiZEJAMPSp\efI/p3SMZefMZD¦FYK8M±QHISFUPnFUEGI/D?|»¼N/nPcUPnD8c.K3EJQHM:o*p8MiZMFHFHM®efAFH8IzK3MMZcmFM ÇFUQ<e#Me#MD¦FiI/e#t3NJMÇzM Z]efMF9FUQ9MMD«IMZp3Q9MMFo*p¨sI/D«NGp8Et8Q9AghdZQ9MBNJPOt3QHMZefEJdQHMj:¦t8p8EJc9o*p¨lMNJNGMcZ¨lPnF9FTPSiT8MLK¨lMe 8NJAMLK8M]À9MpZK3MZcvo*pPSD¦FUE´FUAcv/NJI 8PSNJMc:YiZI/efe#M#NJMcXe#ISe#MD*FHcXK¨sEJD8MQ9FHEJM9:YMFRc9MghI/Q9eXp8NJMLMD ghISD8iFHEJI/D[K8Mc#/QHPSD8K8Mp8QHcfQHMiT8MZQ9iT8AZMc:®iS¨sMZc9Fm© Z<©+K8EJQ9MÊNJMZcRiI/e#tuI/cHPSD¦FUMZcRK8p /MiFUMp8QEJD3c9FTPnD*FUPSD8AOK8MOQHInFTPnFHEJI/D?

ÉI/p3cOPSNJNGI/D8cK8I/D8iXK3A/MNJI/t3tMQ¾NVPfFH8AZISQHEJMÁK8MXNVP#QHISFUPnFUEGI/DFHMZQHQ9MZcmFUQHMvMD0D8I/p8c PScUPnD*FOc9p8QNGMFU3AZI/Q9dZefM]K3pefI/efMZD¦FiZEGD8AFHEJo*p8Mn?

$nL` &-( ,0"$ 1%2Jc ( (!*1)- 5 1%( &*1*1) ' !#. &, &!

@PSD8cNJM¾FUQHPSEGFHMZefMZD¦Fo*p8E$cHp8E´FO:NGM]cmbc9FUde#M\e#Ai|PSD3EJo*p8MOEJD8iNJp3FPSpefI/EJD8cNJPvW.MQHQHM\QHMc9FUQ9MZEGD*FHMZÊcUPt8PSQ9FHEJMvcHISNJEJK3M9:mZÊNVPSo*p8MNJNGMvI/DtuMZpzFÁc9p8QHEGe#tuI/cHMQON½¨lPnFUefI/cHt38dZQ9MvMF\NJMZcOIiZAZPSD8cZ?.¢MtMD8KPSD¦F

_x

D8I/p3c]c9I/efe#Mc¾NJE 3QHMZc¾K3MvQHMÀ9MFUMQ\iMZcOiZI/p3iT8MZcOp8EGK8MZcOcHp3tMQ9CiEJMZNGNJMc¾KPSD8cOp8D²c9bc9FHdZefM#M ÇFUMZQ9D8MMZDEJD¦FUMQUPSiFUEGI/D PSMZiNVP0W.MQHQ9M&cHISNJEJK3MS?:~MÊFU8AI/QHde#MÊK8pe#I/efMZD¦FRiEJD8AFUEJo*p8MD8I/p3c#K8E´FRo*p8M&NJPnPSQHEJPnFUEGI/DXK8pRefI/efMZD¦F:iZEGD8AFHEJo*p8M ~H K8MNVPWYMZQ9QHMMZcmFAZ¦PSNGMPSpRefI/e#MD¦F ~Γ K8Mc:ghI/QHiMZc±MÇFUAQHEGMZp8Q9MZco*p8ENJp3EcHI/D¦FPSt8t3NJEJo*p8AMZc2

d ~H

dt= ~Γ

6k3?`

»¼N®Mc9FÁP|SPnD*FUPS/MpzÇK¨lM Çzt8QHEGe#MQ\NGMRFH8AZISQHdZefMfK8p!efI/efMZD¦F]iZEJD3AFUEGo*p8M#t8PSQ\QHPSt8tuI/Q9F\PSpa3·WtuI/p8QK8MZpzÇ&QUPnEJcHISD8cZ?u@Á¨sp8D8MXt8PSQ9FD8ISFHQHMÁtuI/EGD*FK8M]p8MXMZcmFiMZNJp3E.K8p/AZISt8¦bzc9EJiEJMZDR:PnF9FTPSiT3A Z«NJPiZQ9I873FHM«FUMQHQHMc9FHQHM9:.o*p8EefMZc9p8QHM#K8MZcXSQUPSD8K3MZp8Q9cvPSpc9I/Nhe«PSQ9AZMf/QUP|EJefAFHQHEGop3M9:$t8QHMcHc9EJI/D:Y/MD*F:MFHiS? ?@Á¨lPSp3FHQHMtPSQ9FfD8ISp8cfg6PnEJcHISD8cREJD¦FUMQ9/MD8EJQRNJP e#PnFHQHEJiMLK¨sEJD8MQ9FUEGMÊMF#NJM/MiFHMZp8Q#EJD8cmFTPSD¦FTPnD8AK8MQ9ISFTP<FUEJISDo*p8Eq:YKPSD8cvNGM«Q9MZtudZQHMFHMZQ9QHMZcmFUQ9M9:c9I/D¦FvcHAtPSQUP 8NJMcvMZD p8D8M«iZI/eftIScUPSD¦FUM«t8QHEGD8iZEGtPSNJMiZISD8D*p8MRMFOK8Mc¾tMQ9FUp3Q PnFHEJI/D3co*p¨lEGNQHMc9FHMWZK8AFHMZQHefEJD3MZQZ?~:¨lAop8PnFUEGI/D ¹k3?lFHQUPSD8c9iZQ9EGFUMÁKPSD8c¾NGMQHMtdQHM¾FUMQHQ9MZc9FHQHM]cZ¨sAZiQHEGF

(

d[H]

dt

)

SRT

+ [ω] ∧ [H] = [L]¹k3?`Â

I[H]

:[ω]:[L]

c9I/D¦F\NGMZcOe#PnFUQ9EJiZMc¾iZI/NGI/D8D8Mc¾K8MZc]iZISe#tuI/cUPnD*FHMZc&:MÇzt8QHEGe#AMZc]KPSD8cONGMfa3·W0:K8pefI/e#MD¦FiZEGD8AFHEJo*p8Mj:K8p0/MiFHMZp8QOEJD3c9FTPnD*FUPSD8AXK3MXQHISFUPnFUEGI/DK8p0Q9MZtudZQ9MXFUMZQ9QHMc9FUQ9MvtPSQQHPSt8tuI/Q9F¾PSpQHMtdQHMOiZANJMc9FUMj:;MFK8pÊe#ISe#MD*FK3MOghISQHiZMOQ9MZcHtuMZiFUE´/MZefMZD¦FZ?

~M®efI/efMZD¦F$iZEGD8AFHEJo*p8M±K8MNVPW.MQHQ9M®Q9AZcHp3NGFUM±K8MNVPc9I/e#efM:K8Mc.efI/efMZD¦FUc$iZEGD8AFHEJo*p8Mc.K8M±iTPniZp8DK8McAZNJAe#MD¦FUcK8M¾e#PSc9cHM

dm:ztI/c9EGFHEJI/D8D3AZct8PSQNJMQUP|b/ISDÊSMZiFUMZp3Q

~rK8Mt8p8EJcNJMBiMZD¦FUQ9MOK8MZce#PScHc9MZc

K8MNVP W.MQHQ9MS?azE~vK8AZc9EJ/D3MNJP EGFHMZc9cHM&K¨lp8DAZNGAZefMZD¦F«K3Me#PScHc9M&o*p8MNJiZISD8o*p8M&KPnD8c#NGMcmb*FUdZefM

iZANJMc9FUMO/AIziMZD¦FUQ9EJo*p8Mj:uD3I/p8cI 3FHMZD8I/D3cN¹¨lM Çzt8QHMcHcHEGI/DEJD¦FUA/QUPSNGM

~H =

∫

Terre

~r ∧ ~vdm ¹k3?lw¢B¨lMc9F ZiMfcmFTPSK3M#o*p8MfD8I/p8c]EJD¦FHQHIK8p8EJc9I/D8c¾NGMRSMZiFUMZp3QÁEJD3c9FTPnD*FUPSD8ARK8MfQHISFUPnFUEGI/D0K8MfNVPLWYMZQHQ9M

6t3NJp8cM Ç8PniFUMe#MD¦FK3pe#PSD¦FUMZPSpÊI/pÊK8pQHMZtudZQ9MFUMQHQHMc9FHQHM tPnQQUPSt8tuI/QmFPSpÊc9bc9FHdZefM]iAZNGMZc9FHMS?;:DM¸MFNGM/MZiFUMp8QE´FUMZc9cHM

~vMc9FK8AiZI/eftIScHAOMZD

~v = ~ω ∧ ~r + ~vr6k3?`

I ~vrMZc9FNJPBzE´FUMcHcHMQHMNVPnFHEGSMiZ¾NVPiZQ9I873FHMS?¢MF9FUMK8AiZI/eftIScHEGFHEJI/DÁD¨lMc9FtPSc±/QHPnFUp3EGFUM /MZNGNJMQ9MdFUM

NJM±g6PSE´F·o*p8MNJPEGFHMZc9cHMK¨sp8DXANJAe#MD*F·K8Me#PScHc9MMc9F:K8p3MMZc9cHMD*FHEJMNJNJMe#MD¦F ZBNJPQHInFTPnFHEJI/D]K8MNJPWYMZQHQ9M¹kn^¦¥Áe ncZÁN¹¨lAo*pPnFUMp8Q MFKPnD8cp8D8M3EJMZD«e#I/EGD8K8Q9MBefMZcHp3QHM¾PSpÇK8At8NVPniZMZefMZD¦FHctPSQQHPSt8tuI/Q9FZNVPXK3EJc9FHQHE 8p3FUEGI/D«efIb/MD8D8MOK8MZce#PScHc9MZcKPnD8cNJMe#PSD¦FUMZPSp?8:DM¸MF:8tISp8QNJMcAZiT8MNJNGMZcK8MFHMZeft8co*p8MD8I/p3c:PSNJNGI/D8cYMÇzt8NGI/QHMQ:<cHp8tuAZQ9EJMZp3QHMZcZop3MZNJo*p8Mc:8MZp3QHMZc&:¦NJMc·cHMp8NJc·K8AZt8NJPSiZMe#MD¦FUcc9EJ/D8E´Ci|P<FUEGghcPnF9FUMZEG/D8MD*FPSpt8NGp8c¾k/¥#e1nc ]¼À9MF9©+c9FUQ9M|PSe]]K8PSD8cNJP#c9FHQUPnFHI/cHt38dZQ9MX/MZQ9c x¥<© x(_ *e¤K¨lPSNGFHEGFUp3K8M rNJMcPSpzFUQHMcK8At8NVPSiMZefMZD¦FUc«t8QHIK8p8EGcUPSD¦FK3MZcLQHMK8EJcmFUQ9E 8p3FHEJI/D3c#K8M&e«PSc9cHMZ!N½¨sAZiT8MNJNGM&t8NJPSD8AFUPSEJQ9M9:iZISe#efMNJMce«PnQHAZMcNJp8D8E©¼c9I/NVPSEGQHMKPSD3cNGM¾e«PnD*FHM|PSpLMFNJMZcIiZAZPSD8c&:NJMZce#PSQ9AZMZc] FU8MQHefEJo*p8MZcO]K8M

TG*$+* (* D J8 D @ I8 I 9D % 8 F(+* % B *- #/6 -B % $ B#/D T8' # )(* I 8 (* @D J8 %> 3 % D I @ > J8 % @ ' O$# % * - @ #O- D 9 &#%H# I

_/_

N½¨lPnFHe#I/c9t88dQHMPSiFHEG/AMtPSQNJMiTPSp3¸PS/McHI/NJPSEJQ9M9:*cHISD*FMÇFUQ9dZefMZefMZD¦FNGMZD¦FUc&:zK8MN½¨sI/QHK3QHMK8pLe#dFUQ9MtPSQ.À9ISp8QZ?;:DQHMZtuI/QmFTPSD¦FN½¨sMÇzt8Q9MZc9cHEJISD 6k3?` KPSD8c ¹kz?`w#:8D8I/p3cI3FUMD8I/D8c

~H =

∫

Terre

[r2~ω − (~r.~ω)~r]dm +

∫

Terre

~r ∧ ~vrdm6k3? x|¥

~$P«t8QHMe#EGdZQ9MÁEJD¦FHAZ/QHPSNJMj:PncHcHIiZEGAZM Z#NVP#Q9ISFTP<FUEJISD&/NGI PSNGM]K3p0c9bc9FHdZefM9:Mc9F¾NGMÁefI/e#MD¦FBiEJD8A ©FUEGo*p8MK8MQHISFUPnFUEGI/DvI/pRNJMFHMZQ9e#M0D x9ATqB1ILERr¦NJPcHMiZI/D8K3MEGD*FHAZ/QHPSNJMj:/PSc9cHIiZEGAZMPSpRiTPSeft#K3MZc:EGFUMcHc9MZc~vrMD iTPSo*p8MftI/EGD¦FOK8MRNVPWYMZQHQ9M9:$MZcmF]NJMvefI/e#MD¦F¾iZEGD8AFHEJo*p8MRQHMNVPnFHEGg±I/p NJMXFHMZQ9e#M!DF 59E1DFE1P~A¹?

~:¨lAo*pPnFUEGI/D²t8QHAiZAZK3MZD¦FUMLtuMZp3F'<FHQHMRghI/QHeÁp8NJAMfe#PnFHQHEJiEJMNJNJMe#MD¦FKPSD3c\p8Dc9bc9FHdZefM«K¨lP<ÇzMZc\o*p8MZN©iZISD8o*p8M\t8PSQ

[H] = I(t)[ω] + [h]6k3? xx

I I(t)

Mc9FNVPve#PnFUQ9EJiZMBK¨lEGD8MZQmFUEGMK8pc9bc9FHdZefM\efAZiZPSD8EJo*p8MOc¨lM Ç3t3QHEJe#PSD¦FtPSQ

Iij =

∫

Terre

(r2δij − xixj)dm6k3? x_

I δij

MZc9FNGM¾c9be uI/NJM¾K8M ¾QHISD8MZi nMZQZ?:DXe#IbSMZD8D8Mj:ntuI/p8Q$K8Mc·K8p3QHAZMc·c9p8tAQHEGMZp8Q9MZc Zo*p8MZNGop3MZcPnD8D8AZMc:<NVPW.MQHQ9M®t8Q9AZc9MZD¦FUMFHQHI/EGc$e#In©

efMZD¦FUc®K¨lEGD8MZQmFUEGMt8Q9EJD8iEJtPnpzÇA < B < C

iZISD8c9FUPSD¦FUc:3PSK8efMF9FTPSD¦FNGMZc±nPSNJMp8QHc.A = 8.0101 1037

*ve 2 : B = 8.0103 1037 *ve 2 : C = 8.0365 1037 *ve 2 ?3ÉISFHI/D8co*p8M (A−B)/A ≈ 2, 5 10−5FTPnD8K8EJcBop3M(A − C)/A ≈ (B − C)/B ≈ 3 10−3 ?~Mc¾K8MZpzÇ0t8QHMe#EGMZQHc¾efI/efMZD¦FUc A MF

BI/D¦F

NJMp8QHcP(Ç3MccHEGFHp8AZcK8PSD8cNJMt3NVPSDLAop8PnFUI/Q9EVPSN/AZIS/QUPSt38EJo*p8M ZvefI/EJD8c®K8M x ]Bt8Q9dZcZ?Ãp3FUQ9MZefMZD¦FK8E´FN½¨lP<ÇzMK¨sEJD3MZQ9FHEJMt3QHEJD3iZEJt8PSN

ICMZc9FSI/EJc9EJDLK8M¾N¹¨`P(Ç3MBK8MZctu¿/NJMc/AZIS/QUPSt38EJo*p8MciZ1x ]Bt8QHdcZ?~McP<ÇzMZc

IAMFIB

D8MiZIjt+D8iEJK8MD*FXtPScvP|/MiLNJMcvP<ÇzMZcGx

MFGy

K8p a3.W¾?:D M¸MFvN¹¨`P(Ç3MIA

t8Q9AZcHMD¦FUMp8D8MRNGI/D8/E´FUp8K8M\K8M

λA = −14, 9291 ± 0, 0010|?$¢MNVPLD8I/p3c\Pne#dD8M ZLK8AC8D8EJQ¾NGMvc9bc9FHdZefMRFHMZQ©

QHMc9FHQHMEGD*FHMZQ9e#AK8EVPSEGQHMGx′y′z′

op3Ezc9MK8AK8p8EGF·K8pRa3.WGxyz

tPnQ.p8D3MQHInFTPnFHEJI/D]iZI/D3c9FTPnD*FHMK¨lPSD8SNJMλA = −14, 9291 ± 0, 0010

PSp3FHI/p8QK8MXN¹¨`P<ÇzM2vn?@BPSD8cGx′y′z′

:/ISEJcHEGD&K8p&c9bc9FHdZefMvK8MZcBP<ÇzMZct8Q9EJD8iEJtPSpÇLK¨sEJD8MQ9FHEJM9:3NVPXe#PnFUQ9EJiZMBK¨lEGD8MZQmFUEGM¾EJD8cmFTPSD¦FTPnD8AZM t8QHMD8Kp3D8M¾ghI/QHefM¾o*pPScHE©¼K8EJPS/I/D8PSNJM

I(t) =

A + c11 c12 c13c21 B + c22 c23c31 c32 C + c33

¹kz? xk

I NJMccij

c9I/D¦FBNGMZcEJD3iZQHAe#MD¦FUcK¨sEJD8MQ9FUEGM¾cHp8t3tI/c9AZctMFUEGFHcK 78cPSpzÇK8AghI/QHe#PnFHEJI/D8cI/p&PnpzÇPSD8I<©e#PSNJEGMZc·K3Me#PSc9cHMS?*~McQ9MZK8EGc9FHQHE 3p3FUEGI/D8c/NGI PSNGMZc.K8Me«PSc9cHMc®Pnpfc9MZEGD#K8MNJPW.MQHQHM he«PSQ9AZMc:cHI/NGEJK8McMF±IiZAZPSD8EGop3MZc:¦t3QHIiZMZc9cHp8c±FU3MZQHefEJo*p8Mc:KPSD8c±N¹¨`PnFHe#IScHt88dQHM .t8QHIK8p8EGcHMD*FK8Mc:SPnQHEVP<FUEJISD8c·K8Mc±e#In©efMZD¦FUcK¨lEGD8MZQmFUEJM]FUI/pzF¾PSpt3NJp8cK3MXN½¨sI/QHK3QHMÁK3p0e#EGNJNJEGI/D8EGdZefMBK8Mce#ISe#MD*FHcBK¨sEJD3MZQ9FHEJM\t8QHEGD8iZEGtPSpzÇcij ≤ 10−8A

6K8AghI/QHe#PnFUEGI/D8c ZI/DPnNJMZcK8M¾NVPÁWYMZQ9QHM¾c9I/p8cN½¨lPSiFHEJI/D#K8M¾N½¨lPnF9FUQUPniFUEGI/D«NGp8D8E©¼cHISNVPSEGQHM ?~MZcK3p8QHAMZc¾MZD#À9Mp&nPSNJMD¦F¾PSp0efI/EJD3co*p8MNJo*p8MZc¾3MZp8Q9MZc:cHE 8EJMDo*p8M

cij ≤ 10−8AΩ?~$McFUQ9MZev©

8NGMZefMZD¦FUc®K8MBFUMQHQ9MBi|Pnp8cHMD*FK8MZcQ9MZK8EGc9FHQHE 3p3FUEGI/D8cK8Me#PScHc9MBNJIi|PnNJMZc±c9p8Qo*p8MZNGo*p8MZcefEJD*p3FHMZc:*c¨`PSi ©iZISe#tPn¦PSD¦FtPSQK8McnPSQ9EVPnFHEJI/D3c

cijK8MON½¨sI/Q9K8QHM¾K8M

10−11Acij ≤ 10−7AΩ

?~Mfcmbc9FUde#M

G′y′z′AFUPSD¦F]p8Dcmbc9FUde#MfK¨lP<ÇzMRK8MRWEJcHc9MZQHPSD8K:NJPÊiI/D¦FUQ9E 8p3FHEJI/D0K3pe#PSD¦FUMZPSp

KPSD3c[h]

Mc9F\D*p8NJNGMS?NJMcOiZI/eftIScUPSD¦FUMchiK8I/E´/MZD¦F'<FHQHMfQHMZiT3MZQHiT3AZMZcvK8PSD8c]NJMZcOefI/p3SMZefMZD¦FUc]K8p

; $5 DOD D 9D <@ # 55#%D %EJLKKK04'#8)(+* <O #HGD

_Sk

D8Ib¦Pnp I/p K8MZcÁiZI/p8iT3MZcRPnFHe#I/c9t88AQHEJo*p8M«MFXIiZAZPSD8EGop3McHE®iZMZNGNJMcm©¼iE®c9I/D¦FvEJD3iZNJp3cHMZcÁKPSD8cXNGM«cmbzc©FUde#Me#Ai|PSD3EJo*p8MS?z~MefI/e#MD¦FiEJD8AFUEJo*p8MQHMNVPnFHEGgMc9Fc9p8Q9FHI/p3Ft3QHIK8p8EGF®tPSQ®NJMc®/MD¦FUcPnFHe#I/c9t88A ©QHEGo*p8MZc&:MFPnFHFHMZEGD*Fp8D8M¾nPSNJMp8QK8MON½¨sI/QHK3QHM¾K8M

1026 *fe 2 c −1 tuI/p8QcUPRiZISe#tuI/cUPnD*FHMOP<ÇzEVPSNGM9:zcHI/E´Fhi ≤ 10−8AΩ

AΩ ≈ CΩ ≈ 6 1033 *e 2 c −1 #:ISpMZD3iZI/Q9M&p8De#EGNJNJEGI/D8EGdZefMfK3pefI/e#MD¦FiZEGD8AFHEJo*p8Mt3QHI/t8Q9MK8M¾NJP\WYMZQHQ9MS?;¢ISe#t3FHMBFUMD*p8MOop3MNJMciTPSD8SMZefMZD¦FUcK8MiEJQ9iZp8NJPnFUEGI/D«/NGI PSNGMc9M

K8AQHI/p8NGMZD¦FPSpÊe#ISEJD8cc9p8Qp8DÁÀ9I/p8Qhi ≤ 10−8AΩ2 ?

:D EJD¦FUA/QUPnD*FN½¨sMÇzt8Q9MZc9cHEJISD ¹k3? x¥LKPSD3c&N½¨sAZo*pP<FUEJISD 6k3?ªÂÊD8ISp8c&I zFUMZD3I/D8c&NGMZc K x9ATqP\=G [XYE1I9.q 5@ X XYEc9I/p8cghI/QHefM¾e#PnFUQ9EJiZEGMZNGNJM

dI

dt[ω] + I

d[ω]

dt+d[h]

dt+W

(

I[ω] + [h])

= [L]6k3? xZ^

I W MZcmFNVPXe#PnFUQ9EJiZMPSD¦FUEJcmbe#AFUQHEGo*p8MOK8pL/MZiFUMp8QBEGD8c9FUPSD¦FTPSD8A¾K3M\Q9ISFTPnFHEJI/DR:zin¨lMc9F9©CZ<©¼K3EJQHM7

W =

0 −ωz ωy

ωz 0 −ωx

−ωy ωx 0

¹kz? x(r·PSQQUPSt3tI/QmF0ZfiZMXcmbzcmFUde#MXNJPfWYMZQ9QHMXMc9FOPnD8EJefAZMOK¨sp8D8MXQ9ISFTP<FUEJISD&PSpzFUI/p8QK¨sp8D0P<ÇzMXQ9MZc9FUPSD¦F

ZRt8QHI|ÇzEJefEGFHAK8M]N½¨lP<ÇzMGz = Gz′

K8pQHMtdQHMOFUMZQ9QHMc9FUQ9M hAZiZPSQ9FEJDzghAZQHEGMZp8QfZpx ] #:P|/MiÁp8D8M¾EGFHMZc9cHMt8Q9MZcHo*p8M\p8D8E´ghI/QHefMS?3±DiZISD8cHAop3MZD8iM9:NGM/MiFUMp8QBEGD8c9FUPSD¦FTPSD3A]K3M]Q9ISFTP<FUEJISD

~ωc¨lM Çzt8QHEGe#MOKPSD3cNGM

QHMtdQHMGx′y′z′

tPSQ

~ω = Ω

m1

m2

1 +m3

¹kz? x I

Ω = 7.2921151467064 × 10−5 QUPnK+ncfMZc9F#NVPEGFHMZc9cHMK8MQ9ISFTP<FUEJISD D8I/efEJDPSNGMK8MNVP0WYMZQHQ9MMFNJMZc#AZiZPSQ9FHcmi

6cHPSD8cK3EJefMZD8c9EJI/D vcHISD*F«tMFUE´FUc«K3MnPSD¦FLN½¨sp8D8E´FUA 6N½¨sI 8c9MZQmSP<FUEJISDefI/D¦FUQHMo*p8Mm1 ∼ m2 ∼ 10−6 MF m3 ∼ 10−8 MF m1 ∼ m2 ∼ 10−6Ω

MFm3 ∼ 10−8Ω

?3»¼iEMFKPSD3cNVPOcHp8E´FUMj:NJMcEJD8K3EJiZMc:x8:;_XMFkvcHI/D¦FefEJctuI/p8QNJMciZI/eftuI/cUPSD¦FHMZc

x:yMFzQHMcHtuMZiFUEGSMZefMZD¦F|?

MtISQ9FUISD8cNGMZcMÇzt8Q9MZc9cHEJISD8cK3M\NJPRe#PnFHQHEJiM¾K¨sEJD8MQ9FUEGM ¹k3? xkMFK3MZciZI/eftIScUPSD¦FUMcFHMZQ9QHMZcmFUQ9MZcK8pSMZiFHMZp8QOK¨sEJD3c9FTPnD*FUPSD8AvK8MÁQHISFUPnFUEGI/D ¹kz? x(rH:`k3? xKPSD3c¾N½¨sAZo*pPnFHEJI/DK¨`:p8NGMZQ¾~EJISp3EJNJNGMS?;~MXK8A ©/MNJI/t3tMe#MD*Fg6PSEGFPSt3tPSQUP /JFUQ9M\K3MZcFHMZQ9e#McBK8M\N½¨sI/QHK8Q9M\K3M

10−6AΩ2 Ωcij

:AΩmi

:hi:AΩ2mi

:Ωhi

:8MFK3MZcFUMZQ9e#McK¨sI/QHK8Q9MOcHp8tuAZQ9EJMZp3Qt8PSQQUPSt8tuI/QmFwZRiMZco*pPSD¦FUE´FUAc

Ωcijmk ≤ 10−14AΩ2 :AΩcijmk ≤ 10−14AΩ2 :(C − A)Ω2m3m1/2, (B − A)Ω2m1m2 ≤ 10−16AΩ2 :Ω2cijmk ≤ 10−14AΩ2 :Ω2cijmkml ≤ 10−20AΩ2 :Ωhimj ≤ 10−13AΩ2 :: /6 % IOJ@ I 8 ' I D '/' &' L-!*@ *@ L 4' L@ 83$@ # <# 58 I)(+* !

$' A /6 ' ) Q#/36 - O 3* # O /6 &586# * ADA6@ D-5# $' 9? D % E 8 D @ /3D I2* ' )8 @ 9

_n^

FUISp3FPSpÊt8NGp8cPnF9FUMZEG/DPSD¦F10−12AΩ2 6Mc9FHEJe#PnFUEGI/D8cM¸MiFHp8AZMcK¨lPSt8Q9dZcNGMZcuI/QHD8MccHp8QNGMZco*pPnDz©

FUE´FUAcmi:cij:hiMFONGMZp8Q9c¾K8AZQ9EG/AMZc¾FUMe#tuI/Q9MZNJNGMZct8QHAiZEJc9AZMc]t3NJp8c¾Pnp3F ?ÉISp8cOD8MvQHMFUMZD3I/D8cOo*p8M

NJMc®FHMZQHefMZc®K8p x|MQI/Q9K8QHMMFD3I/p8cI zFUMZD3I/D8cPSNGI/QHcNJMcAop8PnFUEGI/D8cK¨`:p8NGMZQm©¼~EJI/p3EGNJNJMNGEJD8AZPSQHEGcHAMZc

m1 −B

(C − A)Ωm2 =

Ωc13 + h1

Ω(C − A)+

Ωc23 + h2

Ω2(C − A)− L2

Ω2(C − A)

¹kz? x(Â

m2 +A

(C −B)Ωm1 =

Ωc23 + h2

Ω(C − B)− Ωc13 + h1

Ω2(C − B)+

L1

Ω2(C − B)

¹kz? xw

m3 = − c33C

− h3

CΩ+

L3

CΩ

¹kz? x ~:¨lMQHQ9MZp8Q:EGD*FHQHIK8p8E´FUMtPSQNJPBcHp8t3t8QHMcHcHEGI/DfK8MZcFHMZQHefMZc·K8pRcHMZiI/D8KRI/Q9K8QHMAo*p8EGnPSp3F ZD8AZ/NGEJ/MQ·KPnD8cm1:m2

MFm3

K8MZcnPSQ9EVPnFHEJI/D8cK¨lPSp t8NJp8c x¥−11 :iMvo*p8EMZcmF¾FUI/pzFZ«g6PSEGFBD8AZ/NGEJ/MZP8NGMÁPSp Q9MZ¦PSQ9KK8MNVPOt8QHAiZEGcHEJISD«K8Mc®K8AFUMQHefEJDPnFHEJI/D3cK3MN¹¨lI/Q9EJMD*FUPnFUEGI/DRcHtP<FUEVPnNJMK8MNVP¾W.MQHQ9M ¹Pnp«efEJMZpÇpx¥/¥

µPSc:

r x¥−10 QUPSK3EVPSD8c ?¢MZcOAZo*pP<FUEJISD8c¾QHA/EJc9cHMZD¦F]N½¨sASI/NJpzFUEJISD&FUMe#tuI/QHMNJNGMÁK8Mc]iI/eftI/cHPSD¦FUMcFUMZQ9QHMc9FUQ9MZc]K8p0/MiFUMp8Q

EJD3c9FTPnD*FUPSD8ARK8MfQHISFUPnFUEGI/D?~Mc]c9MZiI/D8K!FHMZQHefMZc&:$PSt8tuMZNGAZMZcOghI/D8iFUEGI/D8cOK¨sMÇziZE´FTPnFHEJI/D MF]D8InFUAZMcΨi:

QHM/QHISp8tMD¦FK8McBFUMQHefMZcPnK8EJefMZD8c9EJI/D3AZc:;PncHcHIiZEGAZcBPSpzÇe#ISe#MD*FHcBK8M]ghI/QHiM\M ÇFUAZQ9EJMp8QHcLi1:uPSpzÇ

K8At8NVPSiMZefMZD¦FUcOK8MRe#PScHc9MRcHp8Qmg6PSiZEGop3MfISpEGD*FHMZQ9D8M 6efI/e#MD¦F¾iZEGD8AFHEJo*p8MRQHMNVPnFHEGghi#:I/p MZD8iI/QHMnZ

K8McQ9MZK8EGc9FUQ9E 8pzFUEJISD8ce#PScHc9EJo*p8MZc FUMZQ9e#Mccij

K8pLFUMZD3cHMZp3QK¨sEJD3MZQ9FHEJM ?ÉI/p8ctIScHI/D8c

ψ1 =Ωc13 + h1

Ω(C − A)+

Ωc23 + h2

Ω2(C − A)− L2

Ω2(C − A)

¹kz?ª_S¥

ψ2 =Ωc23 + h2

Ω(C −B)− Ωc13 + h1

Ω2(C − B)+

L1

Ω2(C −B)

¹kz?ª_x

ψ3 = − c33C

− h3

CΩ+

L3

CΩ

¹kz?ª_/_~M¾c9bc9FHdZefM]K¨lAop8PnFUEGI/D ¹k3? x(Â:lk3? xw\:lk3? x|I/tudZQ9MZD¦Fp8DÊK8AiZI/p8t3NVPS/M¾MD¦FUQHM¾NGMZcK8E´¸AQHMD*FHct8QHI<©

iZMcHc9p8cÁc9p8cHiMZt3FHE 8NGMZc]K¨`P<¸MiFUMQONVPLQHISFUPnFUEGI/DFUMQHQ9MZc9FHQHMn?$·PSQOMÇzMe#t8NGMRD8I/p8cOtuI/p3/ISD8c\iZPSNJip8NJMQ ZtPSQmFN½¨sM¸MFPnFHe#I/c9t88AQHEJo*p8Mj:8cUPnD8ciZI/D8c9EJK8AQHMQN¹¨lEGD3p8MD8iZM¾K8Mce#PSQ9AZMZcNGp8D8E©¼cHISNVPSEGQHMZc?

~MZcK8MpzÇ«e#I/efMZD¦FHc®K¨sEJD3MZQ9FHEJMAZo*pPnFHI/QHEJPSpzÇ MFÃ t8QHAcHMZD¦FHMZD¦Fp8DAi|PSQmFQHMNVPnFHEGgK8M¥3?l¥/¥¦_!:t8Q9MZcHo*p8Mbx¥/¥ghI/EGcvEJD3ghAQHEJMp8QWZ0iZMNJp8Eo*p¨sEJNGcfM Çz8E uMZD¦F#P|/MZiNJMLefI/efMZD¦FRK¨sEJD8MQ9FUEGMÊP<ÇzEVPSN

C?±:D

t8Q9MZefEJdZQ9MBPnt8t8QHI|ÇzEJe#PnFHEJI/DRiZMFAi|PSQmFtuMZp3F[<FHQHMBD3AZ/NGEJ/AtuI/p8Q9po*p8MNJMcM¸MFHciI/D8cHEGK8AZQ9AZc®cHI/EGMZD¦F8EGMZDt8NJp8c/QHPSD8Ko*p8M\NGMZcefIzK8E´Ci|P<FUEJISD8cEJD3K8p8EGFHMZctPnQNJPXFUQHEJP<Ç3PSNJE´FUAn?azED8ISp8ct3QHMZD3I/D8cp8DMNJNGEJtz©cHIjt+K8M#K8MQHA/I/NGp3FUEGI/D²8I/efI//dZD3M 6iI/QHt3cp8EJP<ÇzEVPSN ]\FUMN®o*p8M

A = B1:YN½¨lP<ÇzM

IAtuMZp3FXt8QHAcHMZD¦FHMZQ

D¨sEJeftISQ9FUMvo*p8MNJNGM#K8EGQHMiFUEGI/D KPSD8c\NJMRt8NJPSDAo*pPnFUISQHEVPnNq:MF\D8I/p3c\tuI/p3SI/D8cÁK3I/D8i#PSK8I/t3FHMZQ]NJMfQHM ©tudZQHMFUMQHQ9MZc9FHQHM

GxyztuI/p8Q±AZiQHEGQHMNJMZcAZo*pP<FUEJISD8c®K¨`:p8NGMZQm©¼~EJI/pzzEGNJNGMS?/:DLPnK8I/t3FUPSD¦FNGMZc±D8ISFUPnFUEGI/D8c

iZISe#t8NGMÇzMZcm = m1 + im2

:L = L1 + iL2

:h = h1 + ih2

:c = c13 + ic23

:8MFψ = ψ1 + iψ2

NJMciZISe#tuI/cUPnD*FHMZcAZo*pP<FUI/Q9EVPSNGMZctuMZp3SMZD¦Fo<FUQ9M]QHPSe#PScHc9AZMZcKPnD8cN¹¨lM Çzt8QHMcHcHEGI/D

m+i

σe

m = ψ =c

C − A+

h

(C − A)Ω− i

Ω

(

c

C − A+

h

(C − A)Ω

)

+iL

(C − A)Ω2

¹kz?ª_Sk

I σe = C−A

AΩMZcmFNVPXt8p8NGcUPnFHEJI/DLK3EGFUM¾K¨`:p8NGMZQ 6tuAZQ9EJIK8M¾K8M]k/¥/k3?lÀ9I/p8Q9c ?

_/r

:DPSt8t8PSQHMD8iZM]FUI/p3FHMZcNJMcAo*pPnFUEGI/D8ccHI/D¦FtIScHAZMcMFBNGMOt8QHI 3NJdZefM¾MZcmFFHISFTPnNJMZefMZD¦FiZMQHD8An?;»¼NcHps#QHPSEGF]K8Mfi|PnQUPSiFUAZQ9EJc9MZQ]NJMZc]QHMK8EJcmFUQ9E 8p3FHEJI/D3c¾K8M#e#PSc9cHM#PnFUefI/cHt38AZQ9EJo*p8MZc&:$IziA|PSD8EGo*p8MZc&:Y¦bK8Q9In©NJIS/EJo*p8Mc:uI/p0iZMNJNJMcBt8Q9I/Iop3AZMZcOtPnQBNJMce#PSQHAMZcNGp8D8E´©+cHI/NJPSEJQ9MZctuI/p8QBK3EJcHtuI/c9MZQK8Mcp8iFUpPnFHEJI/D3cK8pL/MiFHMZp8QEJD8cmFTPSD¦FUPSD8A¾K8MOQHInFTPnFHEJI/DMFMZDQHMiZI/D8cmFUE´FUp8MQN½¨sM¸MFcHp3QN½¨sI/QHEGMZD¦FTPnFHEJI/D«cHtPnFHEVPSNGMBK8MONJPWYMZQHQ9MS?:DQHAZPSNJE´FUAj:/iZMcHMQUPSE´F®EG/D8I/Q9MZQ:o*p8MNJMZc:p3iFUp8PnFUEGI/D8cK8MNJP¾QHISFUPnFUEGI/DvFUMZQ9QHMc9FUQ9MBMD8/MZD3K8QHMD*F:tPSQ±efIzK3EGCiZPnFUEGI/DvK8MN½¨sM¸MFiZMD*FHQHE´ghp8/M9:¦K3MZcK8AghI/Q9e«P<FUEJISD8c:K8p«e#PSD¦FUMZPSpfMFMZD#iZI/D8c9AZo*p8MD8iZM¾K8McnPSQHEJPnFUEGI/D8c±K8Mc®FUMD8cHMp8QHcK¨lEGD8MZQmFUEJM

cij?8¢McHMZQHPSEGFPSp8c9cHEuEJ/D8ISQHMZQo*p8MBN¹¨`P<FUefI/cHt83dZQHMMFNJMcIiZA|PnD8c

t8Q9I(SIzo*p8MD¦F\K3MZcK8AghI/QHe#PnFHEJI/D8cK8MXNJP«W.MQHQ9MXcHI/NGEJK8Mj:Q9MZc9tI/D3cUP8NGMZc¾K8M\SPnQHEVP<FUEJISD8cBPnK8K8EGFHEGSMZcK8Mccij?¾DRtuI/p8Q9QUPSE´FtuMZD8c9MZQ±o*p8MiZMZcM¸MFHcPScHc9IziEJAZcZ¾NJPD8I/Dz©+QHEJSEJK8E´FUAK8MNVPBWYMZQ9QHMcHI/D¦F±FUQ9I/tvg6PSE 3NJMZc

tuI/p8Qo<FUQ9MXK8AFHMZiFUAZc&:e«PnEJcEJN$D¨sMZD D¨sMZc9FQHEJMD:uMF¾in¨lMc9FOtuI/p8QHo*p8ISEq:uKPSD8cNGMZciTPSt8E´FUQHMccHp3EGnPSD¦FUc&:D8I/p3c±PSNJNGI/D8c·FHMZD8EGQiZI/eft3FHMK8MZc:t8Q9I/t8Q9EJAFHAZc:Q98AZI/NGI//EGop3MZc:K8MNJPW.MQHQHMMF±K8McUP¾c9FHQHp8iFUp8Q9MEJD¦FUMQHD8Mn?¢MZtuMZD3KPSD¦FO:3PSpfp8MK8MBNJP¾iZI/eft8NJM ÇzEGFUAK8p#t8QHI8NJde#MMFKPSD8cp8D#cHI/p8iEK3EJKPSiFUEGop3M9:*D8I/p8c®PSNGNJI/D8ciZISe#efMZD8iMZQtPnQM ÇztI/c9MZQNJM¾iZPScK¨sp8D&efIzK3dZNJMBK8MOW.MQHQHMOQ9EJ/EGK8MS?

& &%#.0 &! . )+ ' &! '! !#.. ! . &'!¢MBo*p8MN½¨sI/D«MD*FHMZD8K«P8E´FUp8MNJNJMe#MD¦F®t8PSQ DFGHB1XYEoGHE E1I#ILE I# 9TGHE1:¦iS¨sMZc9FNVPOW.MQHQHMQHMc9FUQ9MZEGD*FHM

Z¾cUPOtPSQmFUEJMEGD¦FUMZQ9D8M 6iQHI87zFUM9:¦e#PSD¦FUMZPSp:/D3I(b/PSp#8p8EJK8Mj://QHPSEJD8Mc9I/NJEGK8M YiZI/D8c9EJK8AQHAMiI/e#efMQ9EJ/EGK8MS?@PSD3c#p8D FUMNiZPSK8Q9M9:±NJMcRghISD8iFHEJI/D8cRK¨sMÇziEGFTP<FUEJISD D3Mc9I/D¦F«tPnc#EGD3p8MD8iZAMZc«t8PSQRNJMZcvnPSQ9EVPnFHEJI/D8cmi

K8pÊ/MZiFUMp8QBEGD8c9FUPSD¦FTPSD8AOK8MOQ9ISFTPnFHEJI/D hcHI/p3cN¹¨`PSiFUEGI/DLK8MON½¨sM¸MFiMZD¦FUQ9EGghp8/M 1:K8M]cHISQ9FUMOo*p8M]NJMcAZo*pP<FUEJISD8cK8M¾~EGI/p3EJNGNJMNJEGD8A|PnQHEJc9AZMcIS¸QHMD*Fp8DLK8AZiI/p8t8NJPS/Mt8PSQ9g6PSE´FMD¦FUQHMBQHISFUPnFUEGI/D«EGD8c9FUPSD¦FTPSD8AMMFM Ç3iEGFUPnFUEGI/D?

¯¾=6=¹4h1.Z5 "$ "$ %('5u=6$465u, 3 azED3I/p8cRPSc9cHEJefEJNGI/D8c\NVPWYMZQHQ9M Z p3DMNJNJEGt8cHIjt+K8M#K8MLQHA/I/NGp3FUEGI/D8I/efI//dD8M9:SN½¨sAZo*pPnFHEJI/DRK8E´¸AQHMZD¦FHEJMZNGNJMo*p8E;Q9AZ/E´F:NJMK8At8NVPSiMZefMZD¦FK8MN½¨lP<ÇzMK8MQHISFUPnFUEGI/DvMZcmF 6k3?`_Sk?:DN½¨lP8c9MZD8iMBK¨sMÇziEGFTP<FUEJISD#NJP]c9I/NJp3FHEJI/DfK8MN½¨sAZo*pPnFHEJI/D ¹k3?`_Sk#:*PSNJISQHccUPSD8c®cHMiZI/D8K«e#Me 8QHMMZcmFNGMFUMQHefM¾iZEGQHiZp3NVPSEGQHM

m = m0ei(σet+φ0) ¹kz?ª_n^

I m0

MFφ0

QHMZt3QHAZc9MZD¦FUMN½¨lPSeft8NJE´FUp8K8M#MFRNJP t3PScHMj:P<©¼t8Q9EJI/Q9EEGD8K8AC8D8EJMcZ?±¢MNVP cHEJSD8EGCM«op3MNGMtu¿/NJMK8MBQ9ISFTP<FUEJISD#tuMZp3FK8AZiQHEGQHMNJE 3QHMZefMZD¦F®cHp8Q®NVPOiZQ9I873FUMFUMQHQHMc9FHQHMp8D«iZMZQ9iZNGMBMZD«p8D8MBtuAZQ9EJIK8MK8Mk/¥/kz?`À9I/p8Q9cZ?¢B¨sMZc9FNJMOefI/p3SMZefMZD¦FBNGE 8Q9MK¨l:p8NJMQ:;K8pD8I/eÈK8pe«P<FU8Ae«PnFHEJiEJMZDLc9p8EJc9cHM\~AZI/DPnQHK:p8NJMQ\o*p8E±N¹¨`PÊK8AZefI/D¦FUQ9AfFH8AZISQHEJo*p8Me#MD¦F xÂ/rSwl_¹?Y»¼N±EGe#t8NGEJo*p8Mvo*p8M#N½¨lPSD8/NGMvMZD¦FUQ9M«NJMAZD8E´FUK¨sp8DNGEJMZpRK8ISD8D8ABMFN¹¨`P<ÇzMK8MQHISFUPnFUEGI/D:/in¨lMc9F9©CZ<©¼K3EJQHMNVPONVP<FUEGFHp8K8MPScmFUQ9I/D8I/efEJo*p8Mj:*8p8iFHp8MBtuAZQ9EJIK8E´©o*p8MZefMZD¦FPSpiZISp8QHc®K8p#FHMZeft8cZ?z~$P\QHMiT8MZQ9iT8M¾K8MnPSQHEJPnFUEGI/D8c±K8MZc®NVPnFHEGFHp8K8MZcP]AFUAMZD¦FUQ9MZt8Q9EJc9MBFUI/pzFPSp NGI/D8K8p[K8EÇ*©¼D8Mp3EJdZefMc9EJdZiNJMn?:¢MZNGNJMcm©¼iEI/D¦FvAFUALM¸MiFUE´/Me#MD*Ffc9p8cHtuMZiFUAZMc#t3p8EJcXK3AZiZMNJAMZcZN½¨ 8cHMQ9nPnFHI/EJQ9MÁK8Mv:p8N SI/I 6p8c9cHEGM BK8M x|wS^¦kZ xw/ÂSk«tPSQ.MFHMZQ9c:$ÉbQ9AZD:MF'v¾bNGK8AZD:t8p8EGctPSQ 3D8c9FHD8MZQZ MQHNJEGDMZD xwSw¦r mre#PSEJciS¨sMZc9FZLN¹¨`PScmFUQ9I/D8I/efMXPSefAZQ9EJiZPSEJD¢PSD8K8NGMZQ&:MZD xwS x xq:3op¨lEGNQHMzEGMZD8K3QUPRK8M¾K8AZiI/p3QHEGQNVPXtuAZQHEGIzK3Mt8QHEGD8iZEGtPSNGMK8M¾iZMcIScHiZEGNJNJPnFUEGI/D8c:*^¦kS¥BÀ9ISp8QHcMFD8I/Dk/¥/kÀ9I/p3QHcZ?u¢ISe#efM¾D8I/p8cNJMSMZQ9QHI/D8c&:iMF9FUM]K8EG¸AZQ9MZD8iM]Mc9FMÇzt8NGEJo*p8AZM]tPSQNJPvD8I/Dz©+QHEJSEJK8E´FUABK3M\NJPWYMZQHQ9M9:MFMDt8PSQ9FHEJiZp3NJEJMQcHISDANVPScmFUEJiEGFHAS?

"= ) D @ @ F5# * B5*' * /' I * ID @@ OOD O- D $ % ! 9 &# BO D 8 % 5*86D4(+* D ; C JHF@D DB% ) 6 9$- $8D IAGB? D /' L#O% % I >) +%! 6 #" O O-%$ D ,* /* 'D% ; &" @ 3 %(' M9EF

_S

~$POc9I/NJpzFUEJISDv/AZD8AQUPSNGMK8MN½¨sAZo*pP<FUEJISD ¹k3?`_Sk.tuMZpzF®c¨lI3FUMD8EJQ:tPnQFUQUPnD8c9ghI/Q9e«P<FUEJISDXK8M¶I/p8Q9EJMZQI/p[MZD PSt3t8NJEGop8PSD¦FRNVP&efAFH8IzK3MLK8MÊNVP&nPSQHEJPnFUEGI/D!K3MNJP&iZISD8c9FUPSD¦FUM9:±o*p8EiI/D8c9EJc9FHM Z0FHQHI/pz/MZQRNJPghI/D8iFUEGI/D

C(t)FHMZNGNJM¾o*p8M

C(t)eiσe(t−t0) /AZQ9EGCM]N½¨sAZo*pP<FUEJISDK3EG¸AZQHMD¦FUEJMNJNGMiZI/D3cHEJK3AZQHAMS? DFHQHI/p3SMPSEGcHAZefMZD¦F

m(t) = −iσeeiσet

∫ t

−∞

ψ(τ)e−iσeτdτ = m(t0)eiσe(t−t0) − iσee

iσet

∫ t

t0

ψ(τ)e−iσeτdτ6k3?ª_Sr

~MZcnPSQHEJPnFUEGI/D8cK3M]NJPÁEGFUMcHc9M\K8MOQ9ISFTPnFHEJI/DLc9I/D¦FFUQHISp3/AMZcMZDEJD¦FUA/QUPSD¦FN¹¨lAop8PnFUEGI/D ¹k3? x.

m3(t) −m3(t0) = ψ3(t) − ψ3(t0)¹kz?ª_S

¯¾=6=¹4h1.Z5 "$ ²%<4h2 $4h2=B%<4h³46"$ 3 ~$PÊFHQHEJP<Ç3PSNJE´FUAÁK3EJefEJD*p8MvNJA/dZQ9MZefMZD¦F]NVPghQHAo*p8MZD8iM«K8pe#ISp3/M ©efMZD¦FNGE 8Q9MK¨`:p8NGMZQMF®NJMQHMD8K«MNJNJEGt3FUEGo*p8MS?¦:DM¸MFFHQUPSD8c9tIScHI/D8cNJMc®Ao*pPnFUEGI/D8c ¹k3? x(Â MF ¹kz? xw cUPnD8ccHMiZI/D3K0e#Me 8QHM¾©QUPSt8tuI/QmFUAZMc¾PSpQHMZtudZQ9MÁFUMQHQ9MZc9FHQHMXEGD¦FUMZQ9e#AK8EVPnEJQHM

Gx′y′z′:;SI/EJc9EJDK3pQHM ©

tudZQHM(IA, IB, IC)

©KPSD8cN¹¨lMcHtPSiMOK8MZct8p8NGcUPnFHEJI/D3c

m1(σ) − B

(C − A)Ωiσm2(σ) = 0

6k3?`_/Â

m2(σ) +A

(C −B)Ωiσm1(σ) = 0

6k3?`_Sw

:DANJEGe#EGDPSD¦FtPnQMÇzMZeft8NJMm1(σ)

MZD¦FHQHMOiZMcK8MpzÇAZo*pP<FUEJISD8c:I/DPuI/p3FHEGFfZvNJPRiI/D8K8E´FUEGI/D

σ = ±σ′e avec σ′

e =

√

(C − A)(C − B)

ABΩ

¹kz?ª_S ~MÊe#I/pz/MZefMZD¦F#NJE 8QHMMc9F#K8I/D8iÊNJP iI/eftI/c9EGFHEJI/D K8MÊK8MpzÇ efI/p3/Me#MD¦FUcfiZEJQ9iZp8NJPSEJQ9MZcvI/t3tI/c9AZc?ÃBpzFUQHMe#MD¦F¾K8EGFBEJNYMZcmF¾MZNGNJEJtzFUEJo*p8Mn?u~$MÁQUPSt8tuI/QmFK8MXNJP#t8p3NJcUP<FUEJISDK8MXiMXe#ISp3/Me#MD*FMZNJNGEJt3FHEJo*p8M'ZiZMNJNGM¾K¨`:p8NGMZQMc9F

σ′e

σe

=

√

(C −B)A

(C − A)B= 0.9962

¹k3?lk/¥

m(σ) = σe

ψ(σ)

σe − σ= −σeψ(σ)Fσ [iH(t)eσet]

H(t)

% -8DQ!= LI)6@ DE *t < 0

J *t ≥ 0

8 #%(* I

m(t) = −iσeψ(t) ∗H(t)eiσet

∗5#62D <55*0@ 4A*D 3 2 5 D)8OI2D 55*0@ 4A*@ 8V@ $&*- %@63D I

m(t) = −iσe

∫

∞

−∞

ψ(τ)H(t− τ)eiσe(t−τ)dτ

DH(t − τ)

,= # OI! 8 4* 6 (+* G*t − τ ≥ 0

% τ ≤ t

DI!$ J%+* ?@ G ' I

m(t) = −iσeeiσet

∫ t

−∞

ψ(τ)e−iσeτdτ = m(t0)eiσe(t−t0) − iσee

iσet

∫ t

t0

ψ(τ)e−iσeτdτ

_/Â

~$PXFUQHEJP<Ç3PSNJE´FUAK8EJefEJD*p8MNJPXghQHAZo*p8MD8iZM]K8M]¥3?s^ qMFPSp8/efMZD¦FUMONJPXtAQHEJIK8M¾K¨l:p8NJMQK¨lp3DtuMZpt8NJp3cK¨sp8DXÀ9I/p8QZ?:p8EJc9o*p8M\D3I/p8cP|/I/D8cPn¸PSEGQHM Zvp8De#I/pz/MZefMZD¦FMZNGNJEGt3FUEGop3M9:NVPvcHI/NGp3FUEGI/DNGE 8Q9M¾cZ¨sAZiZQ9EGF

m1(t) = m0 cos(σ′et+ φ0)

¹kz?`k x m2(t) = rm0 sin(σ′

et+ φ0)¹kz?`k¦_

I rMZcmFK8AFHMZQHefEJD3A¾tPSQN½¨sAZo*pP<FUEJISD

m2(t) + A(C−B)Ω

m1(t) = 0

r =

√

(C − A)A

(C − B)B= 1.00379

¹k3?lk/k

DXMZDÁiZI/D8iNJp3F·o*p8MNJMK8Me#E©¼/QHPSD8K\P<ÇzM9:<K8EJQ9EJ/A±/MQHc0y′ = IB

:nMc9FMD¦zEGQHI/DX¥3?l^ t3NJp8c./QUPSD3KXo*p8MNJM®K8MZefE´©+tMFUE´F·P(Ç3McHEGFHp8AKPnD8cNJM®t8NVPnDXe#AQHEGK8EJMDÁI/Q9EJ/EGD8M®t8PScHcHPSD¦F±tPSQ

0x′ = IA?¦azE :<F¼bt8EGop3MZefMZD¦F

m0nPSpzF_n¥/¥]e#PSc&:¦N½¨sAZi|PnQ9FPnF9FUMZEGD8K8QHP\¥3?lw¾e«Pnc:¦iZMo*p8E;MZcmF®FHI/p3F[ZOg6PnEGF±cHEG/D8E´Ci|PnFHEGg?S~YP¾FUQ9EVP<ÇzEJPSNJE´FUA

EJD3K8p8EGFp8D8MÁtI/NJPSQHEGcUPnFHEJI/DÊK8p&e#I/pz/MZefMZD¦F¾K3pt¿SNJMO/MZQ9cλA + 90 = 75

azW K8MÁN½¨sI/QHK8Q9M\K3M xe#PScZ?Ã t3QHAZc9MZD¦FÊK8AFUMZQ9e#EGD8I/D8c#NVP ghI/QHefM&/AD8AZQHPSNJMK8pefI/p3/Me#MD¦FK8ptu¿/NJMK8MQ9ISFTP<FUEJISD:±MZDcHISp8cN½¨sEJDzp8MZD3iZMRK¨sp8D8MfMÇziZE´FTPnFHEJI/D AZo*pP<FUI/Q9EVPSNGMS?~MZc]AZo*pP<FUEJISD8c ¹k3? x(Â BMF 6k3? x|wBKPSD8c]N½¨sMZc9tPSiM#K8Mct8p8NGcUPnFHEJI/D3ccZ¨sAZiZQ9EGSMZD¦F

m1(σ) − B

(C − A)Ωiσm2(σ) = ψ1(σ)

6k3?`kn^

m2(σ) +A

(C − B)Ωiσm1(σ) = ψ2(σ)

6k3?`k/r ¹kz?`k/

~$PvcHI/NGp3FUEGI/D:8Pnt8QHdcK3AZiZISe#tuI/cHE´FUEGI/DLMZDÊghQUPSiFUEGI/DLcHEGe#t8NGM9:zMZc9F

m1(σ) = σ′e

irψ2(σ) + ψ1(σ)

2(σ′e − σ)

+ σ′e

−irψ2(σ) + ψ1(σ)

2(σ′e + σ)

¹kz?`k¦Â

m2(σ) = σ′e

−irψ1(σ) + ψ2(σ)

2(σ′e − σ)

+ σ′e

irψ1(σ) + ψ2(σ)

2(σ′e + σ)

¹kz?`k/w :DtPSc9cUPSD¦FJZ!NJP²FHQUPSD8cmghI/QHe#PnFHEJI/D K8M0¶I/p8Q9EJMQ#EGD*SMZQ9cHM9:PSDPSNGI//p8MZ!iZMNJNGMM Ç3t3NJEJiEGFHAZM&K8PSD8cNJPD8ISFHM]\:8I/DPuI/p3FUE´FfZ2

m1(t) =

∫ t

−∞

σ′e

rψ2(τ) cos[σ′

e(t− τ)] + σ′eψ1(τ) sin[σ′

e(t− τ)]dτ ¹k3?lk/

m2(t) =

∫ t

−∞

−σ′erψ1(τ) cos[σ′


e(t− τ)]dτ ¹k3?s^¦¥¹kz?l^x

~MZcK3MZpzÇiZI/eftIScUPSD¦FUMco*p8Ec9I/D¦F¾QUPSt3tI/QmFUAMZc¾PSpÇ P<ÇzMZcGx′ = IA

MFGy′ = IB

tuMZp3SMZD¦F<FUQ9MQHM/QHISp8tAMZc

m(t) =

∫ t

−∞

−iσ′eψ1(τ)r + i

ψ2(τ)

r cos[σ′


e(t− τ)]dτ6k3?s^*_

_Sw

$n%$ , -. ,0"$ 1%2Jc (J)fc ,0-6,'e d"m-.)fc (C% -6 1)fW"/,0"$ 1%2 (J) *, 45)-/-6)¢I/efe#MOD8I/p3cBN½¨lP|/I/D3cp&K8PSD8cBNGMOiTPSt8E´FUQHMÁ_:N¹¨lI/Q9EJMD*FUPnFUEGI/DLK8M\NVPvW.MQHQ9MÁtuMZp3F <FHQHM]K8AZiQHEGFHM

Z#N¹¨`PnEJK8MOK8McBFUQ9I/EJcPSD8/NGMZcK¨l±p3NJMZQ&:;QHMZNGEJAcBPSpÇ&iI/eftI/cHPSD¦FUMcFUMQHQ9MZc9FHQHMcK8p&SMZiFHMZp8QBEJD8cmFTPSD¦FTPnD8AK8MLQ9ISFTPnFHEJI/DtPSQXNGMZcXQ9MZNJPnFUEGI/D8cÁiEJD8Ae«P<FUEJo*p8McXK¨l:p8NJMQ ½_z? xk ?~:¨sEJD¦FUA/QUPnFHEJI/DK8MLiZMcvQHMNVPnFHEJI/D8ctuMZQHefMFÁK¨sI 3FUMD8EJQ\N½¨sI/QHEGMZD¦FTP<FUEJISD? &PSEGcÁNJM#t8QHIiZAK8AMc9FvQ9MZD8K8p iI/eft8NJEGop3A#tPnQÁNJMfg6PSEGF\o*p8MiMZcQHMNVPnFHEJI/D3cD3Mc9I/D¦FtPSc®NJEGD8A|PSEGQHMcZ?¦@PnD8cNJP]efMZc9p8QHMI

θcZ¨sAZiZPSQ9FHMBtuMZpK¨sp8D8MnPSNJMp8Q±e#Ib/MD8D8M

θ0:

I/DÊtuMZp3FFUISp<À9I/p8Q9c:MZDt8Q9MZefEJdZQ9MOPSt8t8Q9I|Ç3EGe«P<FUEJISD:zNGMZcQHAcHI/p3K8QHMOMZD

[θ]tt0 + i [ψ]tt0 sin θ0 = Ω∫ t

t0meiΦdτ

Φ = Φ(t0) + [ψ]tt0 cos θ0 − Ω∫ t

t0(1 +m3)dτ

¹kz?l^¦k

_S

u

&º u

! ihj% - e ,0"$ 1%2 k[)fW"m-. &h0( ')¢I/efe#MNJPBFUMQHQHMD¨lMc9F±tPSc:p3DfiI/QHt3cQ9EJ/EGK8M9:<MZNGNJM®MZc9FK8AghI/QHefAZMtPSQ 6E YNJPiTPSQHSMSPnQHEVP 8NJM®K8M

N½¨lPnFHe#I/c9t88dQHMBMFK8MZcIiZAZPSD8chEJE ±NGMiTPSD8SMZefMZD¦FK8MNJP\ghI/QHiMiZMD¦FUQHE´ghp8/M¾t8Q9IzK3p8EGFtPSQNGMZcnPSQ9EVP<©FUEGI/D8cK8M]NVPvQHInFTPnFHEJI/D hEJEJE ®NJMcghI/QHiMZcK8M\e#PSQ9AZMZcNGp8D8E´©+cHI/NJPSEJQ9MZc?8~MZcK8AghISQHe#PnFUEGI/D8cIiZi|PncHEJISD8D8AZMcI/D¦F±K8Mc®Q9AZtuMZQHip8cHc9EJI/D3cc9p8Q±NJMSMZiFHMZp8QK8MQHInFTPnFHEJI/D?n·PnQHefE3FUI/pzFUMZc±NGMZc:K8AghI/QHe#PnFUEGI/D8cMD¦zEGcUPSSAZMZc&:EJNMZDMZc9Fp8D3M]o*p8EK3AZtuMZD8KK8pSMZiFUMZp3QEGD8c9FUPSD¦FTPSD8AOK8MOQ9ISFTPnFHEJI/D 3NVPvK8AghISQHe#PnFUEGI/DiZMD¦FUQHE´ghp8/Mn?

»¼Ng6Pnp3FÁK3EJc9FHEJD8Sp8MZQ]NVPÊK8AghISQHe#PnFUEGI/D EJD¦nPSQHEJP8NJMRK8M#NVPÊW.MQHQ9M«K8p8MFZNJPtPSQmFUEGMfiI/D8cmFTPSD¦FUM«K8MN½¨sM¸MFiZMZD¦FHQHEGghp3/M&©WZN¹¨lI/Q9EJ/EGD8MK8p I/p3QHQHMNJMFLAZo*pPnFHI/QHEJPSN©RK8M0iZMNJNGM&o*p8E¾MZcmFÊi|PSp3cHAZM0t8PSQLNJMctuMZQ9FHp8Q 8PnFUEGI/D8c

mMFm3

c9p8QNJM/MiFHMZp8QK8MOQHISFUPnFUEGI/D?.I/p3QiMop3E8MZcmF®K3MNJPtPSQmFUEJMiZI/D8cmFTPSD¦FHM9:¦N½¨sAZiT3MZNJNGMK8MFUMe#t3co*p8E8POt3QHAZc9EJK8AwZ¾NVPK3AghI/Q9e«PnFHEJI/D

MZcmF±EJD8K3ACD8EGM9:nMZDvFUI/pzF±i|PSc:c9AZiZp3NVPSEGQHMS? ; D8MghISEJcNJPBK8AghISQHe#PnFUEGI/DvPSiT8M/AM9:¦FUI/pzF:AZNGAZefMZD¦F:K8Me#PScHc9MK8MLNJPW.MQHQHMLMc9FfMZD[Aop3EJNJE 8QHM#cHI/p3cfN¹¨`PniFUEGI/DiI/D<À9p8/AMLK8MZcvghI/Q9iZMcv/QUP|EGFUPnFUEGI/D8D8MNJNJMcÁEGD*FHMZQ9D8MZc&:iZMD¦FUQHE´ghp8/Mj:MFÊK8McLghI/QHiMZcÊK8M0t8Q9MZcHc9EJI/D?~YPWYMZQ9QHM cHM iI/e#tuI/QmFUM0PSNGI/QHc«iZI/efe#M&p8Dp8EJK3M0MZDAZo*p8EGNJE 8QHM]¦bzK3QHI/cmFTPnFHEJo*p8M9:K8I/D¦F¾EJNYQHMc9FHMWZ«K8AFHMZQ9e#EGD8MZQNVP#CSp8QHMn?~MXt8Q9I 8NJde#M\K8MXNJPfghI/Q9e#M\K8MNVPWYMZQ9QHMRe#PSEJD¦FUEGMZD8K3QUP«MDPnNJMZEGD8MXNGMZc¾cUP|nPSD¦FUcOK8p ,B¬B»H»9»¼dZefMvcHEJdiZNGM2EJN.I/t8tuI/cHMQUPLNJMcFUMZD8PSD¦FUcK8M]NVPvefAZi|PnD8EJo*p8M]D8M£FHI/D8EGMZD8D8Mj:;K¨`Pnt8QHdcBNVPnop3MZNJNGM¾NVPvWYMZQHQ9M\c¨lAFUEGQHM]KPSD8cNJMOt8NJPSDÊAZo*pPnFHI/QHEJPSNq:8MFN½¨sAZiI/NJMvK3M 6 MZPSDz©¼@BI/efEJD8EGop3MR¢PScHc9EJD8E:o*p8E:SI(b/PSEGF]N¹¨lAFUEJQ9MZefMZD¦F¾KPnD8cONVPLK8EJQ9MZiFUEJISD0K8MZc]t¿SNJMZc?~MQHMD3Me#MD*F#AZo*pP<FUI/Q9EVPSNghp3F p¼MZD¦FUMQHQHEGD8D8A8]ÊtPnQfNGMZcRcUP|nPSD¦FUcfK8MiZMFHFUMAZtuIop3Mo*pPSD3K: Z²N¹¨lEGcHcHp3MK¨sMÇztuAZK8E´FUEJISD8cc9iZEJMD¦FUEGC8op3MZcCD8PSD8iZAMZct8PSQNGMBI/E;K8M¶QHPSD8iZMj:zISD«MZpzFI 8c9MZQm/A¾o*p¨sp8DLen<e#MPSQ9iK8M\e#AQHEJK3EJMZDR:K8MÁN¹¨lI/Q9K8QHM]K8MBxÁK8M/QHA hK8EG¸AZQ9MZD8iMÁK8M\NVPnFHEGFHp8K8M]PSc9FHQHI/D3I/e#EGo*p8M MZcmF¾t8NGp8cNGI/D8«PSpcHMt3FUMD¦FUQHEGI/Dop¨ ZRN½¨sAZo*pPnFHMZp8Q?

azI/p8c¾N¹¨lM¸MFOK8MZc¾tuMZQmFUp8Q PnFHEJI/D8cBK8MvNVP«Q9ISFTP<FUEJISDt8QHISt8QHMe#MD*FHc¾K8EGFHMZc&:NJMcAZiT8MNJNGMZc¾K8MXFHMZeft8ccHISD*F·FUQHIStXiZI/p3Q9FUMctuI/p8Q·o*p8MNGMZc.AZNJAe#MD¦FUc·K3Me«PncHcHMK8MNVPW.MQHQ9MPSK8I/tzFUMZD¦F:N¹¨lAo*p8EJNGE 8Q9M¦bK8Q9I/c9FUP<©FUEGo*p8MS?~I/QHc9o*p8MN½¨sM¸MF®iZMD¦FUQHE´ghp8/MFUEJQ9M/MZQ9cp8D8MK8EJQ9MZiFUEJISD#NGAZ/dQHMZefMZD¦FK8EG¸AZQ9MZD¦FUMj:FHI/p3F®AZNJAe#MD¦FK8M®e«PSc9cHM®MZc9F·cHI/p3e#EGc6Zp8D8MghI/Q9iZMK8MQHPSt8tuMZN*K8MNJPtPnQ9F.K8MZcANJAe#MD*FHc·MD*EGQHI/DPnD*FHc:<o*p8E3c¨lI/t3tI/c9MPSp²K8AZt3NVPSiMZefMZD¦FÁiMZD¦FUQ9EGghp8SMS?Y:D!t8Q9MZefEJdZQ9MfPSt8t8Q9IÇzEGe«PnFHEJI/D0iMF\M¸MFÁtPSQOp8D8MRghI/QHiM#ANVPScmFUEGop3MhghISQHiZMt8Q9I/tuI/Q9FHEJI/D8D3MZNJNGMPSpRK8At8NVPniZMZefMZD¦F :ISp#PnD8AZNJPSc9FHEJo*p8M 6K8At8PScHPS/MMZD¦FHQHMNVPBghI/Q9iZMPSt8t8NGEJo*p8AMMFXNJMK8At8NVPniZMZefMZD¦F ?~McvK8AZt8NJPSiZMe#MD¦FUcvAFUPSD¦FvefI/EJD8c\/QUPnD8K8cXo*p8MLiMZpzÇop3EcHMLt8Q9IzK3p8EJQHPSEJMD*FKPSD3cNGM¾i|PScK¨sp8DÊp8EGK8M9:NGMZcEJD3iZQHAe#MD¦FUcK¨sEJD8MQ9FUEGM¾cHI/D¦FK8EGe#EGDp3AZctPSQN¹¨lANVPScmFUEGiZEGFHAS?

:DFUI/p3F#i|PncD8I/p8c#D8I/p8cPnFHFHMZD8K8ISD8cZ!iM&o*p8MiMZcEGD8iZQ9AZefMZD¦FUc«K¨lEGD8MZQmFUEGMc9I/EJMD*FfghI/D8iFUEGI/DK8Mc¾tMQ9FUp3Q PnFHEJI/D3c

mMFm3

cHp3QNJM]/MZiFUMp8QOEJD8cmFTPSD¦FTPnD8AXK8MvQ9ISFTPnFHEJI/D?~Mc¾AZo*pPnFHEJI/D8cBK¨`:p8NGMZQ©~EJI/pzzEGNJNGMBcHMQHI/D¦FefIzK8E´CAZMcMZDiZI/D3cHAZo*p8MD8iZMn?

k/¥

!L` >% "$)fW"$ 1)i* kl)f "m-6 1h ( ):D0p8D0tISEJD¦FBK3MXNVPfW.MQHQHMj:K8MÁQUP|b/I/DSMZiFUMZp3Q

~r:uNJM\tInFUMZD¦FHEJMZNYK¨lPSiZiAZNGAZQUP<FUEJISD&iZMD¦FUQHE´ghp8/M

UcMZcmFK8ACD3EYt8PSQ

~∇Uc = −~ω ∧ (~ω ∧ ~r) = ω2~r − (~ω.~r)~ω6^3? x

cHISEGFO:MD&EGD*FHQHIK8p8EGcUPSD¦FNJMciIzI/Q9K8I/D8D3AZMZcω1, ω2, ω3

K8p&/MiFHMZp8QK8MÁQ9ISFTPnFHEJI/DÊMFBNGMZciZII/QHK8ISD8D8AZMci|PnQ9FUAcHEGMZD8D8Mc VÇ :sb9: K8M

~r

~∇Uc = Ω2

(ω22 + ω2

3)x− ω2ω1y − ω3ω1z

(ω21 + ω2

3)y − ω1ω2x− ω3ω2z

(ω21 + ω2

2)z − ω1ω3x− ω2ω3y

h^8?ª_

ÉISp8c/Ib/I/D3cBEJefefAZK8EJPnFUMe#MD*F®o*p8MUc

cZ¨sMÇzt8Q9EJefMOcHI/p8cNJPvghISQHefM

Uc = ω21

y2 + z2

2+ ω2

2

x2 + z2

2+ ω2

3

x2 + y2

2− (ω1ω2xy + ω1ω3xz + ω2ω3yz)

h^8?lkcHISEGFBPSt8QHdcBANJEJefEJD8PnFUEGI/DK8McFUMQHefMZcK8pcHMiZI/D3K0I/QHK8Q9M\MFEGD*FHQHIK8p8iFUEJISDK8McBiIzI/Q9K8I/D8D3AZMZcBcHt88A ©QHEGo*p8MZc

Uc = Ω2(1 + 2m3)r2 cos2 φ

2− Ω2(m1 cosλ+m2 sin λ)r2 cos Φ sin Φ

6^8?s^MZD

ΦMc9F«NVPNJPnFUE´FUp8K3MMF

λNVP NJI/D3/EGFHp8K8MS?®¢MtISFHMZD¦FUEGMZNiZMD¦FUQHE´ghp8/MtMp3F<FUQHMK8ASMZNGI/t8tuAMZD

PSQ9e#ISD8EJo*p8MccHt88AQHEGop3MZcK8MOK8MZ/Q9A\_

Uc = −Ω2

3(1 + 2m3)r

2(P20(sin Φ) − 1) − Ω2

3(m1 cosλ+m2 sin λ)r2P21(sin Φ)

h^8?`r

P|/MiÁNJMct¿/N´bD8I/efMZcK8M]~MZ/MD8K8QHM)P20(sin Φ) = 3 sin2 φ−1

2

MFP21(sin Φ) = 3 sin Φ cos Φ

hSI/EJQÃBD3D8MÇzMÃÁ? x ?S~$PBSPnQHEVP<FUEJISDÁK8MtuISFUMD¦FUEJMN3iMZD¦FUQ9EGghp8/MEGD8K8p8E´FtPnQNJMcEJQ9QHAZSp8NVPSQ9EGFHAZcYK8MNVPBQ9ISFTP<FUEJISDFUMQHQ9MZc9FHQHM]MZcmF

∆Uc = −Ω2

32m3r

2(P20(sin Φ) − 1) − Ω2

3(m1 cosλ+m2 sinλ)r2P21(sin Φ)

h^8?l

¢I/efe#Mm3 ≤ 10−8 MF m1, m2 ≤ 10−6 :$iS¨sMZcmFvN½¨sPSQ9e#ISD8EJo*p8Mvc9t88AZQ9EJo*p8M ¹_: x OiZPSp8c9AZM«t8PSQÁNJP

tuI/88IK8EJM¾o*p8Et3QHAZK3I/e#EGD8M¾KPSD3cp3DQHPSt8tuI/Q9F:x¥S¥3?!%$ (-.) e % b2)fJJ)+(!)+*, 45)-/-.)

:D#efIb/MZD3D8MNJPW.MQHQ9Mt3QHAZc9MZD¦FUMp8D8MQ9ISFTPnFHEJI/Dvp3D8EGghI/Q9e#Mn?/~:¨sM¸MF±iZMD¦FUQHE´ghp8/MAFUPSD¦FiZI/D8cmFTPSD¦F:e#PSNJ/Q9AN½¨sAZNJPSc9FHEJiZE´FUAK3Mc9MZce#PnFHAZQHEJPSpzÇ :/NJPOWYMZQ9QHMcHMK8AghI/Q9e#MiI/D¦FUEJD 78efMZD¦FÀ9p8cHo*p¨ ZÁiMo*p8McZ¨sAFUP<©8NGEJcHc9MN½¨sAZo*p8EGNJE 8QHMf¦bzK3QHI/cmFTPnFHEJo*p8M ·MD FUI/p3FXtI/EGD¦FXNVPghI/QHiM«FUISFUPSNJM#QHAcHp8N´FTPnFvK3MLNVP&/QHP|zE´FTPnFHEJI/D6iMZNGNJM/AD8AZQ9AZM0tPnQLNVP!WYMZQ9QHM #:K8M0N¹¨`PSiiZANJAZQHPnFUEGI/DiMZD¦FUQ9EGghp8/M&MFÊK8M0NJP!t8QHMcHc9EJI/Dµ Mc9FÊD*p8NGNJMS?

k x

:NJNGMXt8QHMD8K²PSNJISQHcp8D3MXghI/QHefMXI/p0C/p3QHMvEJD¦nPSQ9EVP8NGMS?u~:¨lAo*p8EJNGE 8Q9MX¦bzK3QHI/cmFTPnFHEJo*p8MvcHMvFHQUPSK8p3EGF¾tPnQN½¨sAZo*pP<FUEJISDLNJIi|PSNGM

~∇P + ρ~∇W = 0h^8?`Â

I ρMc9FNVPXe#PScHc9M]SI/NJp3e#EGop3M9:

PNJPvt8QHMcHcHEGI/DQHdZSDPSD¦FPSptuI/EGD*FiI/D8c9EJK8AQHA9:;MF

WNJMOtuISFUMD*FHEJMN

K8M#tMcUPSD¦FUMp8QXA¦PSN ZNJPc9I/e#efMfK8p/AI/tInFUMZD¦FHEJMZNUMF\K8ptuISFHMZD¦FUEGMZN±iZMD*FHQHE´ghp8/M

Uc?Y@Á¨lPSt8Q9dZc

iZMFHFHMAo*pPnFUEGI/D FUI/pzFUMLcHp3Q9g6PSiMAop3EJtuISFUMD*FHEJMNJNJM#K8MW

Mc9FftMQHtuMZD8K3EJiZp3NVPSEGQHMD8ISD c9MZp8NGMZefMZD¦FnZ~∇W e«PSEGc:PSp8c9cHE Z ~∇P ?¦~:¨lAop3EJNJE 8QHM¦bK8Q9I/c9FUPnFUEGop3MEGe#t8NGEJo*p8MK3I/D8io*p8MNGMZc±AZo*p8EGtInFUMZD¦FHEJMZNGNJMc:K8MtuMZcUPnD*FHMZp8QBcHI/E´FBPnp8cHc9E·K8McBcHp3Q9g6PSiMZcEGcHI PnQHQHMcZ?;ÃºNJPfc9p8Q9g6PniZMÁK3MÁNVPfW.MQHQ9M9:uNVPRt8QHMcHcHEGI/DMc9FA¦PSNGMZPS = 105 .P 1

PnFUe :P|/Mi«K8Mc¾SPnQHEVP<FUEJISD8cQHMNVPnFHEGSMZc¾K8MRN½¨sI/Q9K8QHMvK8Mpx¥ L?Ã p3D x *eK8Mt8Q9ISghI/D8K8Mp8QNVPXt8Q9MZc9cHEJISD&PnF9FUMEJD¦FK8A¼ÀZ«_n^¦r\ghI/EJcNJPXt8QHMcHcHEGI/DPnFUefI/cHt38AZQ9EJo*p8MS?8@PSD8cNVPvK8ACD8E´FUEJISDK8MONVPvc9p8Q9g6PSiMOEJcHIPSQHQ9M¾e#IbSMZD8D8Mj:;NJMZcnPSQ9EVPnFHEJI/D8c®K8MONVPvt8Q9MZcHc9EJI/DPnFHe#I/c9t88AQHEJo*p8M¾MD&c9p8Q9g6PSiMOD8McHISD*Ft8PSct8Q9EJcHMcMZDLiI/e#tzFUM9:zMFN¹¨lISDtMp3FK8I/D3iiZI/D3cHEJK3AZQHMQo*p8M¾NVP\C8/p8QHMBe#Ib/MD8D8M¾K8M¾NJPÁWYMZQHQ9MiZIjt+D8iEJK8M ZNJP#ghI/EGc¾P|/MZiRp8D3MvcHp8Qmg6PSiZMvEGcHI PnQHQHM

P = PSISp

P = 0cHEN¹¨lI/D&MZD MZD8SNJI uMXN½¨lPnFHe#In©

cHt38dZQ9MvKPSD8cNJMÁcmbc9FUde#MÁW.MQHQHMn?@BISD8iXNVPRC/p8Q9MÁK8MÁNVP#WYMZQ9QHMXMc9FOPnp8cHc9E·p8D8MÁAZo*p8EJtuISFHMZD¦FUEGMZNJNGMOK8MNVPXtuMZcHPSD¦FUMp8Q

W0?

¢M&K8MQHD8EGMZQRtuI/EJD¦FfMZcmF«ghI/D8K8PSe#MD¦FTPSNiZPSQ#EGNnP²D8ISp8c#tuMZQ9e#MFHFHQHMK¨lAFTP3NJEJQvNJP ghISQHefMLK8M&NJPWYMZQHQ9MS?3@Á¨`Pnt8QHdcN½¨sÃBD8D3MÇzMBÃ ¹:o;? 1:NJM/AI/tInFUMZD¦FHEJMZN

UcZ¨sAZiZPSQ9FHMK8MiMZNJp3EuK¨lp8DLiI/QHt3ccHt38AZQ9EJo*p8M

8I/efI//dD8MLMZc9cHMD*FHEJMNJNJMe#MD¦F#t8PSQRp8D8MÊPSQ9e#I/D3EJo*p8MLcHt38AZQ9EJo*p8MK8MÊK8MZ/Q9A_::t8QHIStI/QmFUEGI/D8D8MNJNJMFZJ2 = −C20 = (C − A)/(MeR

2e)I

MeMc9FNVPXe#PSc9cHMOK8MONVPXWYMZQ9QHM-

U =GMe

r

(

1 + (Re

r)2C20P20(sin(Φ)

)

:D²t3QHMZD8PSD¦FOp8D8MvQHInFTPnFHEJI/Dp8D8EGghISQHefM Z«NJP#EGFUMcHc9MRPSD8/p8NJPSEJQ9MΩ:NJMXtuISFUMD¦FUEJMN·K8MÁtMcUPSD¦FUMp8Q

hSI/EJQ:o;?^8?`rRtuI/p8QNGM¾tInFUMZD¦FHEJMZNiZMZD¦FHQHEGghp3/M MZcmFK8I/D8i

W =GMe

r

(

1 + (Re

r)2C20P20(sin(Φ)

)

− Ω2

3r2(P20(sin Φ) − 1)

6^8?lw

ÉISp8cÁA¦PSNJISD8c\iM«tuISFUMD¦FUEJMNlZN½¨sAZo*pPnFHMZp8Q 6QHPbSI/DRe

OMFvPSpt¿SNJMfD8I/QHK 6QUP|bSI/DRp:YtInFUMZD¦FHEJMZN

iZMD¦FUQHE´ghp8/MOD*p8N

GMe

Re(1 − C20

2) +

Ω2

2R2

e =GMe

Rp(1 + (

Re

Rp)2C20)

h^8?` ~:¨`Pnt8NVPnFHEJc9cHMZefMZD¦FY/AI/e#AFUQ9EJo*p8M

αMZc9F.K8ACD8EtPSQ

α = Re−Rp

Re

c9I/EGFRp = Re(1−α)

?n:D\D8AZ/NGEJ/MZPSD¦FNJMcFUMQHefMZcMZD

α2 6K8MON¹¨lI/Q9K8QHM¾K3M]K3M(1/300)2 1:8EGNEJMZD¦F

−C20

2+

Ω2R2e

2GMe= α + C20

6^3? x¥ K¨sI N½¨sI/DFUEGQHM7

α = −3

2C20 +

q

2

6^3? xx I N½¨sI/DPvK8AghD3EGFNVPvo*pPSD¦FHEGFUA

q

q =Ω2R2

e

GMe

6^3? x(_

k¦_

iZISe#efM®NGM®QHPSt8tuI/Q9F.K8M®N½¨lPSiZiAZNJAQUPnFHEJI/D]iZMD¦FUQHE´ghp8/MlZN½¨lPSiiZAZNGAZQHPnFUEGI/D\SQUP|EGFTP<FUEJISD8D8MZNGNJMZN½¨sAZo*pPnFHMZp8Q?@BMcnPSNGMZp8Q9cK3MZciZI/D8cmFTPSD¦FHMZc

Ω:Re:GMe

FUEGQHAMZcK8MN½¨sÃBD8D8M ÇzM o:¦D3I/p8cP|/I/D8cq = 3, 46110−3 ≈

1/289?

·PSQPSEGNJNGMZp8Q9cNJMFHMZQHefM¾K8MOK8M/QHA\_XK8p/AZI/tuISFHD8MFHEJMZNMZc9FK8ISD8D8A]tPSQ

U20 =GMe

r(Re

r)2C20P20(sin(Φ)

h^8? x|kcHISEGFO:3AFTPnD*FK8ISD8D8AOo*p8M

C20 = −(C − A)/(MeR2e)

U20 =G

r(1

r)2(C − A)

3

Ω2r2U c

20

6^3? x|^I

U c20 = −Ω2

3r2P20(sin Φ)

MZcmFXNGM#K8M/QHA_K8M#NVPÊtPSQmFUEJMfiZISD8c9FUPSD¦FUM«K3ptInFUMZD¦FHEJMZN±iMZD¦FUQ9EGghp8/Mn?¶·EGDPSNJMe#MD¦F

U20 =3G(C − A)

Ω2r5U c

20

6^3? x(rÃ NVPXc9p8Q9g6PSiMOK8MONVPvW.MQHQ9M9:I/DtIScHM

U20 = ksUc20

6^3? x I

kSMc9FK8I/D8D8AOtPnQ

ks =3G(C − A)

Ω2R5e

≈ 0.9426^8? x(Â

MZcmF¾PSt3tMNJAÁD3I/e 8Q9M\K8MÁ~I(SMXcHAiZp8NJPSEJQ9MS?u~:¨lM¸MFiMZD¦FUQ9EGghp8/M0pc9AZiZp3NVPSEGQHM^]¾cHp3QBNJM]/AI/tInFUMZD¦FHEJMZNYMZcmFkS

ghI/EGcNJM¾tuISFUMD¦FUEJMNiZMD¦FUQHE´ghp8/MOiZISD8c9FUPSD¦FK3M]K3MZ/Q9AÁ_?:D\Q9MZtuI/Q9FUPSD¦FN½¨sMÇzt8Q9MZcHc9EJI/DOK8M

C20KPSD3c 6^8? xx #:ZN½¨lPSt8NJPnFUEGcHc9MZefMZD¦F/AI/t8efAFHQHEJo*p8M¹PSpOtu¿/NJM mtuMZp3F

MZD3iZI/Q9M]c¨lM Çzt8QHEGe#MQt8PSQ

α =q

2(1 + ks) ≈

1

297, 5

6^3? xw ¢MF9FUMOQHMNVPnFHEJI/DLc¨`Pnt8tMNJNGM¾N½¨sAZo*pPnFHEJI/DLK8M\¢NJPSEJQHPSp3F|?

~$PvghISQHefMB/AI/e#AFUQ9EJo*p8MK8M¾NJPÁWYMZQHQ9M9:K8ISD8D8AZM¾t8PSQNJMQHP|b/I/DL/MiFHMZp8QrtuMZpzFf<FUQ9M¾K8AZK3p8EGFHM¾K8M

N½¨sAZo*p8EGtInFUMZD¦FHEJMZNGNJMK8MOtMcUPSD¦FUMp8QW

ZvNVPvcHp3Q9g6PSiM :A¦PSNGM0ZW (Re)

GMe

r

(

1 + (Re

r)2C20P20(sin(Φ)

)

−Ω2

3r2(P20(sin Φ)−1) =

GMe

Re(1−C20

2)+

Ω2

2R2

e

6^3? x »¼N¦PSt3tPSQUP /JFo*p8M

rD3M:K8AZtuMZD8K]o*p8M±K8M:NVPNJPnFUE´FUp8K3M9:MF$o*p8M±NVPWYMZQ9QHM±t8Q9MZD8K]NVP®ghISQHefMK¨sp8D\c9t88AQHI9t½K8M

K8M QHA/I/NGp3FUEGI/DµPSp3FHI/p8QÊK8M N½¨lP<ÇzM K8MZct¿SNJMZc?:D tuI/cUPnD*FPSNGI/QHcr = Re(1 + δr)

?~:¨lAop8PnFUEGI/Dt8Q9AZiZAK8MZD¦FHMtMp3F9© <FHQHMQHAZc9I/NJp3MBPSEGcHAe#MD*FtPnQQHPSt8tuI/Q9F[Z

δrMZDD3AZ/NGEJ/MZPSD¦F±NJMZc:FHMZQHefMZcK8p#cHMZiI/D8K

I/Q9K8QHMOtPSQQHPSt8tuI/Q9FwZvN¹¨`PSt3NVPnFHEJcHc9MZefMZD¦FαI/p

δr?¶·EGDPSNJMe#MD¦F

r = Re(1 − α sin2 Φ)h^8?ª_n¥

! )" (!)3* Ci*&,'c"$ &kl #"$ c (- *1)fc e %2e )f "/c (C &J)-/"$ 1)~:¨lI 3cHMZQmnPnFUEGI/DRe#I/D¦FHQHMo*p8MNVPWYMZQHQ9McHI/NGEJK8Mj:/cHI/p3cN¹¨`PniFUEGI/DvK8MghI/Q9iZMcnPSQ9EVP8NGMZc p8iFUpPnFHEJI/D3c

cHMRK8AQHI/p3NVPSD¦F]K8MRo*p8MZNGop3MZc]8MZp8Q9MZc'ZLt8NJp8c9EJMp8QHc]PSD8D3AZMZc 1:$D8MRcHp3EGFOt8NGp8cONJMviZISe#tuI/Q9FHMZefMZD¦FOK¨sp8Dp8EGK8M9:e#PSEJcLt3NJp3FH¿SFÊiZMNJp8EOK¨sp8D c9I/NJEGK8M0AZNJPSc9FHEJo*p8Mn?~I/MPPnNJI/Q9cLK8AZefI/D¦FUQ9Ao*p8M²cHEONVP[WYMZQHQ9M

k/k

MZcmFvcHISp8e#EGcHMFZ&p8D tuISFUMD*FHEJMNK8MfghI/QHiMMÇFUMQHD8MW2

nPSQHEJP8NGM9:YP|b¦PSD¦FvNJPghI/QHefMfK¨lp3D8M«ghI/D8iFUEGI/DPSQ9e#ISD8EJo*p8MK8MK8MZSQHAB_ 6NGMtISFHMZD¦FUEGMZNK8Me«PnQHAZMNGp8D8E´©+cHI/NJPSEJQ9MI/p#NJMtuISFUMD*FHEJMNuiMZD¦FUQ9EGghp8SM 1:PSNGI/QHcNJMc±K8AghI/Q9e«P<FUEJISD8cEJD3K8p8EGFHMZc±t8Q9I(SIzo*p8MD¦Fp8D#EJD8iQHAe#MD*FK8pftuISFUMD*FHEJMN/QUP|EGFUPnFUEGI/D8D8MN3K8MNVP¾WYMZQHQ9MK8I/D3D8A0tPSQ

δU = (Re/r)3k2W2

ZN½¨sMÇFUAQHEJMp8QI/p ZNVP!c9p8Q9g6PSiM0K8MNJP!W.MQHQ9M r = Re

?~MiZIM&sfiEJMZD¦F

k2:PSt8tuMZNGAÁD8I/e 8QHM\K8Mv~I/M9:MZc9FiZI/D8cmFTPSD¦FZ«NJP#c9p8Q9g6PSiMvK8MXNJP#WYMZQHQ9MXMFBSPnp3F

0, 29hSI/EJQÃD8D8M Ç3M ?~M¾t88AZD3I/e#dD8M]cZ¨sMÇzt8NJEGiZE´FUMK8MOe#PSD8EGdZQHMPSDPSNGI//p8M0ZviMZNJp3Eop3Ei|PSQHPSiFHAZQHEGcHM¾NGMiZISe#tuI/Q9FHMZefMZD¦FK8MONVPXWYMZQ9QHM]cHI/p3cN¹¨`PniFUEGI/DLiZISD8c9FUPSD¦FUMOK8MON½¨lPSiZiAZNGAZQUP<FUEJISDLiZMZD¦FHQHEGghp3/M ¹:o;?^8? x|?

~$POtuMZQmFUp8Q PnFHEJI/DvK8pRtuISFUMD¦FUEJMN3iMZD¦FUQ9EGghp8/MMc9FcHp3cHiZMt3FUE 8NJMK3Mt8QHI/Io*p8MZQ±K8Mc±K8AghI/Q9e«P<FUEJISD8cZ?¢MZNGNJMK3M0K8MZ/Q9A ¥\:t8Q9I/tuI/Q9FHEJI/D8D3MZNJNGMZ

m3t8Q9I(SIzo*p8M p8D3MFUMZD3cHEJISDµp3D8EGghI/Q9e#Mj:®QHPSK8EJPSNJMj:®MFÊMZD

iZISD8cHAop3MZD8iMfD3MXtMp3FÀ9ISp8MZQop3MXcHp8QBNJMOFUMZQ9e#M\K8MXK8M/QHAÁ¥«K8p0/AI/tuISFUMD*FHEJMN½?u~$P#tuMZQ9FHp8Q 8PnFUEGI/DK8MOK8M/QHA\_XcZ¨sAZiQHEGF

δU c20 = −Ω2

3r22m3(P20(sin Φ) + (m1 cosλ+m2 sinλ)P21(sin Φ) h^8?`_x

MFiZPSp8cHMOK8ISD8iONVPXnPSQHEJPnFUEGI/D

∆U = k2(Re

r)3δU c

20 = −k2(Re

r)3 Ω2

3r22m3(P20(sin Φ) + (m1 cosλ+m2 sinλ)P21(sin Φ)

6^3?ª_/_K8p/AZIStISFHMZD¦FUEGMZN¹?ÉI/p3ctuI/p3SI/D8ce#MFHFHQHM¾iZMFBEGD8iZQ9AZefMZD¦FcHISp8cNJPXghI/QHefM¾p8cHp3MZNJNGM¾K8pK8ASMZNJISt8tM ©efMZD¦FMZDPSQHefI/D8EGo*p8MZcc9t88AZQ9EJo*p8McK8p/AI/tInFUMZD¦FHEJMZN

∆U =GM

r(Re

r)2C20P20 + (sin Φ)(Cc

21 cosλ+ Sc21 sinλ)P21(sin Φ) h^8?`_Sk

P|/Mi

Cc20 = −k2

2Re

3GMr2Ω2m3

6^3?ª_n^

Cc21 = −k2

Re

3GMr2Ω2m1

6^3?ª_/r

Sc21 = −k2

Re

3GMr2Ω2m2

6^3?ª_S ¢MZcEGD8iZQ9AZefMZD¦FUcK8pL/AZIStISFHMZD¦FUEGMZNucHp\sfc9MZD¦FwZXMZcmFUEJefMZQ®N½¨sM¸MFK8MNVP]K8AghISQHe#PnFUEGI/D?:DLM¸MFKPnD8cN½¨sÃBD3D8MÇzMvÃÁ?lk\:D8I/p8c¾K8Ae#ISD*FHQHI/D3co*p8MvNJMce#ISe#MD*FHcK¨sEJD8MQ9FHEJMÁK3MXNVP«WYMZQ9QHMvc9MvK8AZK8p3EJcHMD¦FOEJD¦FUA ©/QHPSNJMe#MD*FK8MZcFUMQHefMZcK8MOK8MZSQHA\_XK8pSAZI/tuISFUMD¦FUEJMNt8Q9EJcfZRNVPXcHp3Q9g6PSiM]K3M]NJPvW.MQHQHMOc9MZNJISD

I12 = −2MR2eS22

6^3?ª_/ÂI13 = −MR2

eC216^3?ª_Sw

I23 = −MR2eS21

6^3?ª_S

I11 =1

3Tr(I) − 1

3MR2

eC206^3?`k/¥

I22 =1

3Tr(I) +

1

3MR2

eC206^3?`k x

I33 =1

3Tr(I) − 2

3MR2

eC206^3?`k¦_

azENJMc9bc9FHdZefMefAZiZPSD8EJo*p8M 6WYMZQ9QHMPnFHe#IScHt88dQHMIziA|PSD8c.tPSQYMÇzMZeft8NGM /I/E´F·cHPBe«PncHcHM®iZI/D3cHMZQ©/AM9:uI/DK8AZefI/D¦FUQ9M]o*p8M\NVPXFUQHPSiZMOK8pFUMD8cHMp8QBK¨sEJD3MZQ9FHEJM¾Mc9FEJD¦nPSQHEJP8NJM ?¢B¨lMc9FN½¨s*btuISFU3dZcHM\o*p8M

5 D% - 4'4D % %J K3HG% % D2 8 O "O,= > D #O% 9 5 % D%5 K IF8 K @J

kS^

D8I/p3c]ghMQHI/D8c]tPSQONJPÊc9p8EGFHMS?$~MZc\iZIM&sfiZEGMZD¦FUc]K8p/AZI/tuISFHMZD¦FUEGMZN±PSK8K3EGFUE´gk2Uc

cHI/D¦FÁPSiZiI/eftPS/D8ActPSQNGMZcnPSQHEJPnFUEGI/D8c

Icij

K3MZce#I/efMZD¦FHcK¨lEGD8MZQmFUEGM9:8K8ISD8D8AZMct8PSQ

Ic13 = k2

R5e

3GΩ2m1

Ic23 = k2

R5e

3GΩ2m2

Ic11 = k2

2R5e

9GΩ2m3

Ic22 = −k2

2R5e

9GΩ2m3

Ic33 = k2

4R5e

9GΩ2m3

6^3?`k/k

:DEGD¦FUQHIK8p8EGcUPSD¦FNGMD8I/e 3QHMOK8M]~I(SM\c9AZip8NVPSEGQHMks

6±o;?^8? x(Â #:8N½¨sEJD3iZQHAe#MD¦FK¨sEJD8MQ9FUEGM¾K¨sI/QHEG/EJD8MiZMD¦FUQHE´ghp8/M

Ic = Ic13 + iIc

23

c¨lAiZQ9EGF

Ic =k2

ks

(C − A)mh^8?lkS^

! (J)fJkl)+(!)+* i*,c"$ kl #"$ c (!- *&) e %( )fe )f "( ( *1)ÉI/p3c.iI/D8cHEGK8AZQ9I/D8cYNJM:iZPSc.K¨lp8D3M®WYMZQ9QHMAZNVPnc9FUEGo*p8M 8E´©¼P<ÇzEVPSNGMS?|@BPSD8cYN½¨sAZo*pPnFHEJI/D ¹kz?ª_Sk QHAZSEJcHcHPSD¦F

NJMefI/p3/Me#MD¦FK8pt¿/NGM9:±NVP0ghI/D8iFUEGI/DK¨lM Ç3iEGFUPnFUEGI/DiI/e#tuI/QmFUMNJMLFUMQHefM&K¨sI/QHEG/EJD3MLiZMZD¦FHQHEGghp3/MIc/(C − A) =

k2

ks

(C − A)mK¨`Pnt8QHdcN¹¨`:o;? 6^8?lkS^#:8ghI/D8iFHEJI/DÊK8pe#ISp3/Me#MD*FK8pt¿/NGM

m? ¾D

tuMZp3FNGMg6PSiFUI/Q9EJcHMQP|/Mi¾e 6MFmtI/p3QcUPvK8AQHE´/AZMFHMZeftISQHMZNGNJM ±KPnD8cNJMe#Me 8QHMBK8M¾¦PSp8iT3M¾K8M

N½¨sAZo*pP<FUEJISD ¹k3?`_SkMFI3FUMD8EJQPSNGI/QHc

m(1 − k2

ks) +

i

σe(1 +

C − A

A

k2

ks)m = ψpure 6^3?`k¦r

I ψpure MZcmFON½¨sMÇziZE´FTPnFHEJI/DJpt8p8Q9EGCAM^]ÁK8p efI/p3SMZefMZD¦FOK8p0tu¿/NJMn?~:¨lAo*pPnFUEGI/D0t8Q9AZiZAK8MZD¦FHM#c¨lAiZQHE´FMZD3iZI/Q9M-

m+i

σcm =

ψpure

1 − k2

ks

6^3?`k/

I σc = σe

1 − k2

ks

1 + C−AA

k2

ks

?(@PnD8c$NJM:i|PncK¨lp3D8M®WYMZQ9QHM±AZNJPSc9FHEJo*p8M:NJPghQHAZo*p8MD8iZMK¨l:p8NJMQYMc9FYeXp8N´FUEGt8NJEGAZM

tPSQNJM¾g6PSiFUMp8Q 1 − k2

ks

1 + C−AA

k2

ks

≈ 1 − k2

ks≈ 0.7

:;MFNVPRtAQHEJIK8M]PSp8SMZefMZD¦FUM\KPSD8cNJM]QUPSt3tI/QmF x/?l^¦rz?DcZ¨lPnF9FUMZD3KK8I/D8i_Z\I 8c9MZQm/MZQN¹¨lIScHiZEGNJNJPnFUEGI/DXNJE 8QHM/MQHc^S^¦¥À9I/p3QHct3NJp3FH¿SFo*p8MBk/¥/kÀ9I/p8QHc&:zMFin¨lMc9FM¸MZiEGF9/MZefMZD¦FNGMi|PSct3p8EJc9op3MBNVPOiZISe#tuI/cUPnD*FHMBt8Q9EJD8iEJtPnNJMK8p«efI/p3SMZefMZD¦FK3pt¿SNJM9:*NGMFHMZQHefMK8M¢PSD3K8NJMQ:t8Q9AZcHMD¦FUM]p8D8MOtAQHEGIzK8M¾K3M

433 ± 2À9I/p8Q9cZ?

~:¨lANVPScmFUEJiEGFHAK3MBNVP]W.MQHQ9MPXPSp3cHcHEutuI/p8QiZI/D8c9AZo*p8MD8iZMOK¨lPSeft8NJE´CMZQ±N½¨sM¸MF®K8MNVP¾ghI/D8iFHEJI/D#K¨sMÇ*©iZE´FTPnFHEJI/DR:t3p8EJc9op3M¾iZMZNGNJM ©¼iZE;Mc9FeXp8NGEJt8NGEJAMt8PSQ

1/(1− k2

ks) = 1.43

? PSEJc®iZI/efe#MD8I/p8cNJMSMZQ9QHI/D8ctPSQNJPXcHp8E´FUM9:NGMZcQHMK8EJcmFUQ9E 8p3FHEJI/D3cK8M]e«PSc9cHMcK8PSD8cN½¨lPnFUefI/cHt38dZQ9M¾I/pNGMZcIiZAZPSD8c ¹PSc9cHIiZEJAMZcPSpzÇnPSQHEJPnFUEGI/D8c±K8Mt3QHMZc9cHEGI/DLPnFHe#I/c9t88AQHEJo*p8MI/pK8MBPSp3FHMZp8QK¨lMZPSp IiZiZPScHEGI/D8D8MD¦Fp8D8MK3AghI/Q9e«PnFHEJI/DK8M¾NJPXiZQHI973FUMFHMZQHQ9MZcmFUQHMOMFMZDÊiZI/D3cHAZo*p8MD8iZM\iZQ9AZMZD¦FK8McEGD8iZQ9AZefMZD¦FUcK¨lEGD8MZQmFUEJMBK8M¾NVPXWYMZQ9QHMOcHI/NGEJK8M/MDPSD¦FMZDtPSQ9FHEJM¾iI/e#tuMZD3cHMZQN¹¨lM Ç3iEGFUPnFUEGI/DK8p8M'ZviZMciI/p8iT8Mcp3EJK8McZ?

k¦r

! (J)fJkl)+(!)+* i*,c"$ kl #"$ c (!- *, *1%2 (!) (!-( ( R% (!-~$PvE´FUMZc9cHM¾K8M¾Q9ISFTP<FUEJISDK8M¾NVPÁFHMZQ9QHM

Ω(1 +m3)MZc9FQ9AZ/EGMtPSQN¹¨lAo*pPnFUEGI/D ¹kz? x 1:I N½¨sEJD8iQHA©

efMZD¦F±K¨sEJD8MQ9FUEGMP<ÇzEVPSNc33

iZI/D¦FHEJMZD¦Fp8D8MtPnQ9FUEGMK¨sI/QHEG/EJD3MiZMD*FHQHE´ghp8/MIc33

EJD8K3p8EGFHMtPSQ±NVPBnPSQ9EVPnFHEJI/DK8MBE´FUMZc9cHM¾K8M¾NJPÁQHInFTPnFHEJI/D:*MFK8I/D8D3A¾tPSQN¹¨lAo*pPnFUEGI/D h^8?`kSk?z:DQ9MZtuI/Q9FUPSD¦F

Ic33

K8PSD8cN½¨sAZo*pP<FUEJISD¹kz? x 1:8D8ISp8cI 3FUMD8I/D8c

m3 = −k24R5

e

9GΩ2m3

C− cpure

33

C− h3

CΩ+

L3

CΩ

6^3?`k¦ÂI

cpure33

Mc9FN½¨sEJD8iQHAZefMZD¦FK¨sEJD8MQ9FHEJMOK8M]NVPvW.MQHQ9MÁPn¸QUPnD8iT8E$K8MÁN¹¨lM¸MFiZMZD¦FHQHEGghp3/MS?u~$PRFHQUPSiM\K3M\NJPe#PnFUQ9EJiZMBK¨lEGD8MZQmFUEGM¾MZc9FiI/D8c9FUPSD¦FUMn?¶.EJDPSNGMZefMZD¦FN¹¨lAop8PnFUEGI/DLt8QHAiZAK8MZD¦FUM\cHMOQHAK8p8E´FwZ

m3(1 +4k2R5

e

9GΩ2

C) = − c

pure33

C− h3

CΩ+

L3

CΩ= ψpure

3

6^3?`k/w

I NJMFHMZQ9e#M 4k2R5e

9G

tMp3Fw<FUQ9MOQHAZAiZQ9EGF 43

k2

ks(C − A)

MFN¹¨lI/DÊP

m3 =ψpure

3

1 + 4(C−A)k2

3Cks

6^3?`k/

·PnQEGD¦FUAZSQUPnFHEJI/D:zD8I/p8cI zFUMZD3I/D8c

m3 =ψpure

3

1 + 4(C−A)k2

3Cks

+ Cte 6^3?l^¦¥

~$PghI/D8iFHEJI/DRK¨sMÇziEGFTP<FUEJISD p¼t8p8Q9M^]MZc9FK8E´EJcHAMtPSQ x/?l¥/¥ xk¾MFSI/EGF±cHPOnPSNGMZp8Q:K3EJefEJD*p8AZMK3M¥z? x(r!:iZM\o*p8E$MZc9FBD8AZSNJEJSM|P8NGMOPSp&Q9MZ¦PnQHK&K3M\NJPfefAZK8EGIziQHMOt8Q9AZiZEGcHEGI/D hcHp8tuAZQ9EJMp8QHM2Zx PSMZi\NVPSo*p8MNJNJMI/DÊK8AFUMZQ9e#EGD8MOI/pÊe#IK8ANJEJc9MNJMciZI/eftuI/cUPSD¦FHMZcK8MONVPXghI/D8iFUEGI/DLK¨sMÇziZE´FTPnFHEJI/DP<ÇzEVPnNJMS?

! !i*,c"$ k[ 1"$azE$NVPvWYMZQHQ9M\AFTPSE´FtPSQmg6PSEGFHMZefMZD¦FAZNJPSc9FHEJo*p8M9:EGND¨ bPSp8QUPnEGFPSp8ip8D8M]K8EJc9cHEGtPnFUEGI/D:zMFNJMOe#ISp3/M ©

efMZD¦FÁK3pt¿SNJMRtISp8QHQHPSEGFOMD*FHQHMQÁMZD!QHAZc9I/DPSD3iZMLP|/Mi«NJPefI/EJD3K8QHMRMÇziEGFTP<FUEJISD/AI/t8¦bcHEGop3M!ZNJPtuAZQHEGIzK3M¾K8M]¢PSD8K3NJMZQ? QNJMFUMQHefM¾K8M\¢PSD8K3NJMZQ/PSQHK8MOp8D3M\Pne#t8NGEGFHp8K8MBefIK8AZQ9AZM¾EJDzghAZQHEGMZp8Q9M Z¥3?`r ]n?;@BMt8p8EGctxS¥/¥vI/D&PRI 8c9MZQm/AÁcHPfK3AZiZQ9I/EJc9cUPSD3iZMO/I/EGQHMOcUPfop8PScHE©¼K8EGcHtPSQ9EGFHEJI/D«SMZQ9c x¦_Sr(©;xSk/¥\:t8p8EGccUPvQ9MZt8Q9EJcHM ZXt8PSQ9FHEJQK3MZcPSD8D3AZMZc:xn^¦¥3?3¢MZNVPXc9EJ/D3EGCMo*p8Mj: 8EGMZDÊo*p¨lEGNPSt3tPSQUPnEJcHMBiZI/efe#Mp8DefIzK8MNJE 8QHMK8MQHInFTPnFHEJI/D:*EGNMZcmFPSefI/Q9FHE zEJNuD8MtuI/p8Q9QUPSE´FcHMBe«PSEGD¦FUMZD3EJQMFPSp8Se#MD*FHMZQc¨lEGND¨lAFTPSE´FMÇziEGFUAt8PSQo*p8MZNGo*p8Mt8QHIiZMcHcHp3c±nPSQ9EVP3NJMS?<@BMN¹¨lM Ç3EGc9FHMZD8iMK¨lp3D#Pne#I/QmFUEGcHcHMe#MD¦FD8I/p3c:iZI/D8iNJp8ISD8cZp8D8M¾tuMZQmFUMK¨lAD8MZQ9/EJMn?3»¼Ng6Pnp3FK8I/D3io*p8M¾NJMcK8AghISQHe#PnFUEGI/D8ciMZD¦FUQ9EGghp8SMZcMD8/MZD3K8QHAMZctPSQNGMBefIzK3MNJE 8QHMvD3M#c9I/EJMD*F]tPnc\EGK8A|PSNGMZefMZD¦FOAZNJPSc9FHEJo*p8Mc:e#PSEJc¾c9I/EJMD*F\PSiiZI/eftPSSD8AZMc\tPnQ]p3D8M#K3EJcHc9EJtP<FUEJISDcHISp8c:ghI/QHefMK8MiTPnNJMZp3Q:KPSD8c±NJMc:K8EG¸AZQ9MZD¦FUMc±iZI/p8iT3MZcK8MNVPWYMZQ9QHMS?¢MFHFHM2x9PRK1X x=1ATqQ1 ACK·c9MFUQUPnK8p8EGFtPSQNJMBg6PSE´Fo*p8MONJMcnPSQHEJPnFUEGI/D8c®iZMZD¦FHQHEGghp3/MZcK8Mce#ISe#MD*FHcK¨sEJD8MQ9FHEJM

cMFc33

c9M¾t8QHIK8p8EGcHMD*FP|SMZip8DÊiZMQ9FUPSEJDÊQHMFTPSQ9K

δτt8PSQQUPnt8tISQ9FwZXNVPXtuI/NG8IzK3EJMS?z~$PXiZI/eftuI/cUPSD¦FHM¾AZo*pPnFHI/QHEJPSNJMK8MONVP\ghI/D3iFUEGI/D

K¨sMÇziZE´FTPnFHEJI/DÊiMZD¦FUQ9EGghp8/M¾c¨lAiZQ9EGFPSNJISQHc

Ψc(t) =k2

ksm(t− δτ)

h^8?s^x k/

cHISEGFKPSD3cNGM¾K8I/e#PSEJD3MK8M]¶I/p8QHEGMZQ

Ψc(σ) =k2

kse−iσδτm(σ)

h^8?l^¦_ @BI/D3i#NJPÊtuI/NG8IzK3EJMWZÊNVPghQHAop3MZD8iM

σ6t8Q9EJD8iEJtPSNGMZefMZD¦FZÊNVPghQHAop3MZD8iM«K8M«¢PSD8K3NJMZQ Ot3QHIK8p8EGF

N½¨sMÇziEGFTP<FUEJISD

Ψcσ(t) =

k2

kse−iσδτmσ(t)

h^8?l^/kÉISp8cEJD¦FUQ9IzK8p3EJcHISD8cPSNJISQHcNGM¾D8I/e 8Q9MOK8M]~$ISM]iI/eft8NJM Ç3M

k∗2 = k2e−iσδτ 6^3?l^/^

ÉISp8c:cUP|/ISD8c±op3M90

K8MZcp3iFUp8PnFUEGI/D8cK8pRtu¿/NJM®cHMFHQHI/p3SMZD¦F[Z432

MF365

À9I/p8Q9c:ncHI/E´Fσ ≈ Ω

432

:KPSD3cfiMZcfiZI/D3K8EGFHEJI/D8cvNJP0K8AghI/Q9e«P<FUEJISD QHMFUPSQHK3MPnpt8NGp8cRK8MÊo*p8MZNGop3MZcÀ9I/p8QRcHp8QRcHP²iZPSp8cHMj:±cHI/E´Fδτ ≈ 2π/Ω

? DÊPÁK8ISD8iσδτ ≈ 2π/432

:MFin¨lMc9FtuI/p8QHo*p8ISEk∗2 ≈ k2(1− iσδτ)

?8ÉI/p8ctuI/p3SI/D8cK8I/D3i]AiZQ9EJQHM7

k∗2 = k2(1 + κ)h^8?s^*r

I κ ≤ 0

K8AZtuMZD3K Zt8Q9EJI/Q9EK8MÊNJPghQHAop3MZD8iMMD*EGcUPS/AMÊKPSD8cRNJM«e#I/pz/MZefMZD¦FRK8p tu¿/NJMn?:azENGMQHMFTPSQ9K«Mc9FK3MN¹¨lI/Q9K8QHMK8p¾À9I/p8Q:*NGMiIzM1sfiZEJMD¦Fo*p8EuQHMZD3K8QUP]iZI/eft3FUMK8MNVPOK8AghISQHe#PnFUEGI/DRt8QHEGD8iZEGtPSNJMMZcmF

κ = −k2σδτ ≈ −2π/432 k2 ≈ −4 10−3.6^3?l^¦

~MZcvK8A/MZNGI/t8tuMZefMZD¦FUcRK8p[tPnQUPS/QHPSt88M«^8?ªriZI/D8cHPSiZQ9AZcfPSp iZPScvt8p8Q9MZefMZD¦FRAZNJPSc9FHEJo*p8MQ9MZc9FHMZD¦FnPSNJEGK8MZcLtuI/p8Qmp K8M Q9MZeft8NVPSiMZQNGM0D8I/e 3QHM K8M²~I(SMQ9AZMN

k2tPSQLNGM0iZI/eft8NGMÇzM

k∗2?ÉISp8cÊMZD

iZISD8iZNGp8I/D8co*p8MONVPvtuI/88IK8EJMj:3tuI/p8Qp8D8MOWYMZQ9QHM]PSD8ANVPScmFUEJo*p8Mj:8cHp3EGFN½¨sAZo*pPnFHEJI/DLK3EG¸AZQHMD¦FUEJMNJNGM

m +i

σ∗c

m =ψpure

1 − k∗2ks

6^3?l^*Â

I σ∗

c

MZcmFBNJPXt8p8NJcHPnFUEGI/DLiZISe#t8NGMÇzM σ∗

c = σc + iαh^8?l^/w

P|/Miα = −σe

κ

ks(1 +

C − A

A)

6^3?l^¦ ÉISp8c/Ib/I/D3co*p8M

αMZcmFtIScHEGFHEGg :ziZM¾o*p8EEJeft8NGEJo*p8MBo*p8MONGM¾e#I/pz/MZefMZD¦FNGE 8Q9M9:3c¨lM Çzt8QHEGe«PSD¦FKPnD8c

NJM¾t3NVPSDÊiZISe#t8NGMÇzM¾tPSQ

m(t) = m0eiσ∗

c (t−t0) = m0eiσc(t−t0)e−α(t−t0) 6^3?ªrS¥

MZcmFPSefI/Q9FHE½?azEuD8I/p3cPSK8I/tzFUI/D8c®NVPOSPnNJMZp3QK8MκiE´©+K8MZc9cHp8c&:

α = 10−9 c:zMFN¹¨`Pne#t8NGEGFHp8K8MK8pefIzK3MNJE 8QHMBMZc9FK8E´EJcHAMOtPSQePnp uI/p3FK8pÊFUMe#t3c 6K8E´FK8MOQHMZNJP<Ç3PnFUEGI/D

1/α ≈ 30PnD8cZ?

@PSD8cNJM¾iZPScPSD8ANVPScmFUEJo*p8Mj:8NVPÁghISD8iFHEJI/DÊK¨sMÇziZE´FTPnFHEJI/DÊ/AI/t8¦bcHEGop3M\M¸MiFUE´/MOMZcmF

Ψgeoph. =ψpure

1 − k2

ks

(1 + iκ

ks

)6^3?ªrx

MF.iZISe#efMκ ≤ 0

:(MZNGNJM±cHMFUQ9I/p3/M®K8I/D8iNJA/dZQ9MZefMZD¦F.K8AZiZPSNJAM®K8M®N½¨lPSD8/NGM:tIScHEGFHEGg − κ

ks≈ 1

KPSD3c.NGMt8NJPSDAZo*pP<FUI/Q9EVPSNtPSQQHPSt8tuI/Q9FZXN½¨sMÇziZE´FTPnFHEJI/D#I/QHEG/EJD8MNJNGMS?*:DLg6PSEGF:zN¹¨lI 3cHMZQmnPnFUEGI/DK8pLefI/p3SMZefMZD¦F

k¦Â

K8p t¿SNJMLtuMZQHefMFRK3MK3AFUMQHefEJD8MQvNJMLtPnQUPSefdFHQHMαtuI/p8QvNVPghQ9AZo*p8MZD3iZMK8M¢PSD8K8NGMZQ?±ÉI/p8cRNGM

efI/D¦FUQHISD8ciZE©PSt8Q9dZc?azE8NGMe#IK8MMc9F®PSefI/Q9FHEzMF±cHp8E´F:NVPNGI/E

m(t) = Y (t−t0)m0eiσc(t−t0)e−α(t−t0) :SI Y (t−t0)

MZcmFNVP¾ghI/D8iFUEGI/D M|P|EJcHEGK8MK8A 8pzFTPSD¦FMD

t0:zPSNJI/Q9c±I/DefI/D¦FUQHMPSEGcHAZefMZD¦F®o*p8MBcHPÁt8p8EGcHcUPnD8iZMcHtuMZiFHQUPSNGM

MZcmF

|m(σ)|2 =4π2m2

0

α2 + (σ − σc)2

6^3?ªr/_

.ISp8Q±NVP¾t8p8NGcUPnFHEJI/DvK8M¢PnD8K8NJMQ±I/D#I3FUEGMZD¦F |m(σc)|2 =4π2m2

0

α2

?¦ÉI/p8c±/Ib/ISD8c®o*p¨sp8DfFUMZNc9tMiFHQHMMZcmFc9befAFUQ9EJo*p8M¾Pnp3FUI/p3QK8M¾NJP]ghQHAo*p8MZD8iMOK8MQHAcHI/D8PSD8iZMn? DtMp3Fc¨lEGD*FHAZQ9MZcHc9MZQPSpzÇ«K8MpzÇLt8p3NJcUP(©FUEGI/D8c

σ− = σc− ∆σ2

MFσ+ = σc +

∆σ2

tISp8Q:NJMcHo*p8MZNGNJMc:NVPBt8p3EJcHcHPSD8iMc9tMiFHQUPSNGMD8MnPSp3F±t8NGp8c:o*p8MNVPe#I/E´FUEGAK3McUPt8p3EJcHcHPSD8iMiZMZD¦FHQUPSNGMS?/:DXFHQUPSK8p3EJcUPnD*F·iZMFHFUMiI/D8K8E´FUEGI/D:(I/DXFUQ9I/p3SMop3MNVP ]NVPSQ9/MZp8QZK3MZefE´©¼8PSp3FUMp8Q@]XnPSp3F

∆σ = 2αMFÁop3M«NJMft8EGi#c9tMiFUQHPSNMZc9FÁK8I/D8i#K¨lPSp3FTPnD*FÁt8NJp3c\NJPSQH/Mfo*p8M

N½¨lPSefI/Q9FHEJc9cHMZefMZD¦FMZcmF¾AZNGMSAS? D0K8ACD8E´Fp8c9p8MZNGNJMZefMZD¦FNJM]g6PSiFHMZp8QK8MXo*pPSNGEGFUAQK8pt8EGiÁcHtuMZiFUQHPSN

tPSQNGM¾QUPSt3tI/QmFK8MONVPvt8p8NGcUPnFHEJI/DLiMZD¦FUQHPSNJMZvNVPXNJPSQHSMZp8QfZvefE´©¼8PSp3FUMp8Q:zcHI/E´FQ = σc

∆σ= σc

2α

~I/QHc9op3M¾I/DMÇ3PSefEJD3MBNJMcHtuMZiFUQHMBK8Mt8p8EGcHcHPSD8iZMBK8pLe#ISp3/Me#MD*FK8ptu¿/NJMj:zI/D#/I/E´Fo*p8MNGMBt8EGi

Z&NJPghQHAop3MZD8iMLK8MÊ¢PSD3K8NJMQ:·NJPSQHSMZefMZD¦FÁt3QHAZK3I/e#EGDPSD¦FO:YMZcmFvAZNJPSQHSEMFvc9befAFHQHEJo*p8M h/ISEJQX¶.EJ8?^8? x ?YÉI/p8c]cHI/efe#McOK8I/D8i#MZD!K3QHI/E´F\K¨`PSc9cHEGe#EGNJMZQ¾NGMRe#IK8MRNJE 8QHM ZÊp8D8M«IScHiZEGNJNJPnFUEGI/DcHEGD*p8cHI9t½KPSNGMPSefI/Q9FHEJMj:¦MFK3MBK8AK8p8EJQ9MBNGMiIzM1s#iEJMD*FK¨`Pne#I/QmFUEGcHcHMe#MD¦FI/p«NJMg6PSiFHMZp8Q®K8MBo*pPSNGEGFHAK8MNVP]NVPSQ9/MZp8QZefE´©+PSp3FHMZp8QOK8p!t8EJifcHtuMZiFUQUPnN½?YW.I/pzFUMZc\NJMc\AFUp8K8McXcZ¨lPSiiZI/Q9K8MZD¦FvtuI/p8Q\K8EJQ9M#o*p8M#NJMRg6PSiFHMZp8Q\K8Mo*pPSNGEGFUA\K8p0FUMQHefMXK8Mf¢PSD3NJK8MQcZ¨sAZiT8MNJI/D3D8MRMZD¦FUQ9M«Ân¥MF xwS¥3?azE.D8I/p8c¾t3QHMZD3I/D8c

Q = 100:K8M

N½¨sMÇzt8Q9MZc9cHEJISDα = σc

2Q= −σe

κks

(1 + C−AA

)D8ISp8cFHEJQ9I/D8c

κ = − ks

2Q

σc

σe

6^3?ªrSk

cHISEGF −4, 710−3 ≤ κ ≤ −1, 6510−3 ?*~$P]tI/NG8IK8EJMiT8PSD8K8NGAZQHEGMZD8D3Mt8Q9AZiAZK8MQUPSE´FK8ISD8iNJP]K3AghI/Q9e«P<©FUEGI/DLiZMD¦FUQHE´ghp8/MOK¨sp8D8M]K8p8Q9AZMδτ = |κ|/(k2σc)

iZI/eft8QHEGcHM¾MD*FHQHM1MF

0.37À9I/p3QZ?

Q5#/GD 6D /6 5*(- *B@ L(+*&#L= * A9 *-@98 # 5@)(+* 1Q

= 12π

∆EE

∆EE L@)&AGD / 6 = # $D 9* 8*J2!= * 5HD 9O QD 2 6, ' /D DD

E8%' I O) #' I"(* Q = σc

2α

Q % 3!= 9*OI" 6*--(* . @)&6 # $D -O6? D %

*29* /' I@(* = 9' )$ ' I % 6#/

k/w

^8? x ]aztuMZiFHQHMK3Mt8p8EGcHcHPSD8iZM®K8pXefI/p3SMZefMZD¦FK8pÁt¿/NGMPnp3FUI/p3Q.K8M®NVPghQHAZo*p8MD8iZMK8M¢PnD8K8NJMQ0.845

ibiZNGMOtPSQPSD ?

k/

u

/ [

W kl 1"/,0"$ 1%2Jc i% bcm '&)(!)ÉI/p3cPSI/D8cpÊiZISe#efMZD¦FNGMZc®t8QHI/t3QHEJAFUAct8¦bcHEJo*p8McK8MNVP\W.MQHQHMBK8EJefEJD*pPSEGMZD¦F®NVP\ghQ9AZo*p8MZD3iZM

K8p efIzK3M«NJE 8QHMj:$MFvN¹¨`PSefI/QmFUEJc9cUPSEGMZD¦F|? PSEJc\N½¨sMÇziZE´FTPnFHEJI/D²/AZISt8¦bzc9EJo*p8MÊMZcmFvQHMc9FHAZMLEJD3K8ACD3EJMS?.~$Pt8NGp8ct8p3EJcHcHPSD¦FUMMc9FiMZNGNJMt8QHIK8p8E´FUMtPSQNGMZc®QHMZK3EJc9FHQHE 8p3FUEGI/D8cK8MBe#PSc9cHMZcKPSD8cNGMZc QS QS~ES=lHTGHES==1@|~E1INQ1qE1X XYES=1:¦N¹¨`P<FUefI/cHt83dZQHMMFNJMZcIiZA|PnD8cZ?8¢B¨lMc9Ft8Q9AZiEJcHAe#MD¦FN½¨sI À9MFK8p«t8QHAcHMZD¦FiT8PSt8EGFHQHMK8Mi|PnQUPSiFUAZQ9EJc9MZQ¾NJMp8QEGe#tPniFc9p8Q¾NVPQ9ISFTP<FUEJISD&FUMQHQHMc9FHQHMS?Ãºt8QHI/t3QHMZefMZD¦FOtPnQHNJMQiZMcOK8MZpzÇ0iZI/p8iT3MZccHISD*F·iZI/p3t8NJAMZc:<i|PnQ·NVPcHp3Q9g6PSiMIiZA|PnD8EJo*p8M®MZc9F·K8AghISQHefAZMcHI/p8c·N½¨lPSiFHEJI/DOK8Mc·nPSQHEJPnFUEGI/D8cK8M®t8QHMcHcHEGI/DPnFHe#I/c9t88AQHEJo*p8McZ?±YI/p8QvFUQHPSEGFHMZQXN¹¨lM¸MFRK¨lp3Dt8Q9IziMZc9cHp8cf/AZISt8¦bzc9EJo*p8Mj:K3EG/MQHcRc9bcmFUdZefMZcfefAZi|P(©D8EGop3MZctuMZpz/MZD¦Fi<FUQ9MBMZD¦EJcHPS/Ac x :W.MQHQ9MBcHISNJEJK3M r ½_ :W.MQHQ9MBcHISNJEJK3M IiZAZPSD8c P<FUefI/cHt83dZQHM6r¹k Áe«PSD¦FHM|PSp ¤NGEGFHI/cHt83dZQHM6r 6^Áe#PSD¦FUMZPSp NJE´FU8IScHt88dQHM ¤PnFUefI/cHt38dZQ9M IziA|PSD3cr ½r ÁNGE´©FU3I/cHt83dZQHMn?;azMNJI/DLNGMBc9bcmFUdZefMOMZD¦EJcHPS/A9:zp8DÊt8QHIiZMcHc9p8cMÇziZE´FTPnFHEGg$c9M¾e«PSD3EGghMZcmFUMKPSD8cNJP]ghI/D8iFUEGI/DK¨sMÇziZE´FTPnFHEJI/DÊc9I/p8cFUQ9I/EJcghI/Q9e#MctIScHcHE 8NJMc

EGD8iZQ9AZefMZD¦FUcK8McefI/efMZD¦FUcK¨lEGD8MZQmFUEJM¾K3pcmbzcmFUde#MI13

MFI23?

µPSt3tPSQHE´FUEGI/DK¨sp8De#I/efMZD¦FiEJD8AFUEJo*p8M¾Q9MZNJPnFUE´g(h1, h2, h3) efI/efMZD¦FK8M¾ghI/Q9iZMOMÇFUMQHD8M

(Γ1,Γ2,Γ3).ISp8Q#FHQUPSE´FUMZQfN½¨sM¸MF«PnFHe#I/c9t88AQHEJo*p8MI/pIiZAZPSD8EJo*p8Mj:®ISDt8QHAghdZQ9M&/AD8AZQHPSNJMe#MD*F«iZI/D3cHEJK3AZQHMQ«NGMc9bcmFUdZefM ½_ ÁI/p 6^ÁEJD8iNJpPSD¦FRNJP iI/p8iT8MÊp8EGK8MÊiZI/D3cHEJK3AZQHAM9::o*p8EcHMÊe#PSD8E´ghMZc9FHMÊPSNJISQHcvtPSQRK8McEJD3iZQHAe#MD¦FUcK¨sEJD3MZQ9FHEJMMFLK8McLe#ISe#MD*FHc«iEJD8AFUEJo*p8McQHMNVPnFHEGghc?®~:¨lP|SPnD*FUPS/MK3MiZMFHFUM Pnt8t8QHIiT8Mj:iS¨sMZcmFo*p¨sMZNGNJMcHM&ghI/D3K8MMcHc9MZD¦FUEGMZNJNGMZefMZD¦F#cHp8Q#N½¨sI 8cHMQ9nPnFHEJI/D K8MZc«QHMZK3EJc9FHQHE 8p3FUEGI/D8cRK8Me«PSc9cHMj:MFAE´FUMNJPÁe#IK8ANJEJcHPnFUEGI/DfK8MZcghI/Q9iZMcK¨lEGD¦FUMZQHPSiFHEJI/D«MZD¦FUQ9M¾NJMcmbzcmFUde#M¾efAZiZPSD8EJo*p8M hW.MQHQ9M¾cHI/NGEJK8MI/pN½¨sp8D8MK8McHMc®t8PSQ9FHEJMZc MFNVP¾iZISp8iT8MBc9p8tuMZQ9C8iZEJMNJNGMS?¦~MiZI/p8t3NVPS/MMc9FPSNJISQHc±MZD¦EJcHPS/AcHI/p3c®NJP¾ghISQHefMK¨sp8D!AiTPSD8SM#K8MRefI/efMZD¦F]iZEJD3AFUEGo*p8MREJD¦FUMQHD8Mj:MF]D8I/D²tPSc]cHI/p3c\iMZNJNGMvK¨sp8D!efI/efMZD¦FOK8MvghI/QHiMMÇFHMZQHD3MS?

~MZcPSp3FUQ9MZct88AD8I/efdZD8MccHp8c9iZMZtzFUE 3NJMZcK¨sEJD38p8MZD8iMZQNVPXQ9ISFTPnFHEJI/DFHMZQ9QHMZcmFUQ9M\c9I/D¦F NGM¾ibiZNGM]cHPSEJc9I/D8D8EGMZQKPnD8cNJM¾iZISD*FHMZD*p&MDMZPSpzÇÊK3I/p8iZMOK8MciI/D¦FUEGD8MZD¦FUc N¹¨lEGD*FHMZQHPSiFHEJI/DD3I(b/PSpz©+e«PSD¦FHM|PSp NGMZcnPSQHEJPnFUEGI/D8cK3pD8E´/MZPSpK3MZc/NVPniZMZciI/D¦FUEGD8MZD¦FTPnNJMZc NGMZcFUQ9MZe 3NJMZefMZD¦FK8MOWYMZQ9QHM]K8MOe«PSSD8EGFHp8K8M¾vMFt8NGp8c»¼NzM ÇzEJc9FHM 8EGMZD\K¨`Pnp3FUQ9MZct8Q9IziMZc9cHp8cK¨`PSeft8NGMZp8QYt8NVPnD8AFUPSEJQ9MZc nNJPt3QHMZc9cHEGI/DXK8M®QUPSK8EJPnFUEGI/DOcHI/NJPSEJQ9M9:

NJMcFHMZeftdFUMcB/AI/e«Pn/D8AFHEJo*p8Mc:;NJM]K8AZ/PS/MZefMZD¦FtMQHe#PSD8MD*FBK8MÁiT8PSNJMp8Qt8PSQNGM\D3I(b/PSp?´?G?&re#PSEJcEJNGc:cHI/D¦FcHISEGF±FUQ9I/tRtMp«AZD3MZQHSAFUEGo*p8MZcI/pRFUQHISt#tuMZpfM&sfi|PniZMZc®K¨sp8D«tuI/EJD¦F±K8Mp8Me#Ai|PSD8EGo*p8MtI/p3QEJDzp8MZD3iZMZQK8MOe#PSD8EGdZQHM¾K3AZiZMNVP3NJM¾NVPXQ9ISFTP<FUEJISDFUMZQ9QHMc9FUQ9MS?

^¦¥

~MZcK8AZt8NJPSiZMe#MD¦FUcK8Me«PSc9cHMc®K¨lPSEGQ:I/pRK¨lMZPSp«D3MtuI/p8Q9QUPSE´FP|/I/EGQ:NJEJMpRcUPSD8c±N¹¨`PSiFUEGI/DvK8p«c9I/NJMEJNI/pÊK8MONVPvNGp8D8MS?3»¼Ng6PSp3FK8EGc9FUEGD8/p8MQ

N¹¨lM¸MFK8MNJP 0' 0 @:¦Q9MZc9tI/D3cUP8NGMK8MNJPnD x9ILKSE2@QSKx9P~T~E hK8MN¹¨lI/Q9K8QHM\K8p0efdFUQ9MÁMD²t3NJMZEGD8M]e#MQ MFK8MvNJPD x9ILKSE Sx9ILDFK1ATI#T E1:ucHI/E´FMD*EGQHI/D x¥ jK8Mcp3iFUp8PnFUEGI/D8cK8MOt8Q9MZcHc9EJI/D©PnFHe#I/c9t88AQHEJo*p8Mn?

N¹¨lM¸MFK3p + NGMZcÊiZISD*FHQUPScmFUMcFU3MZQHefEJo*p8Mc:t8Q9EJD8iEJtPSNGMZefMZD¦FLK8EGp8QHD3M²MFcHPSEJc9I/D8D8EGMZQ:nMZD8SMZD8K8Q9MZD¦FK8MZc±Q9MZK8EGc9FUQ9E 8pzFUEJISD8c·K¨sM|PnpfMF±K¨lPSEJQ&:ScHMc9p8tMQHtuI/cUPnD*FPnpzÇve#PSQHAMZc?

ÉI/p3c\D¨lPuI/QHK3I/D8cOtPScON½¨sEJDzp8MZD3iZMRK8MZc]e#PSQHAMZcOIziA|PSD3EJo*p8MZc&:$NVPSo*p8MNJNJMÁtMp3F<FUQ9M#K3AZiZISp8t8NJAMK8Mce#I/pz/MZefMZD¦FHcK¨lISQHEJSD8MFH8MZQ9e#EGop3MMFMc9FHEJefAZM0ZXtPnQ9F|? DLcUPSE´Fo*p8M¾NJMce#PSQHAMZcIiZAZPSD8EJo*p8MccHMOK8At8NJISEJMZD¦FP|nPSD¦FFUI/p3FwZRK8McghQ9AZo*p8MD8iZMcBK8EGp8QHD8McMFcHMe#E©¼K8EGp8QHD8Mc:zMZDi|PSp8cHPSD¦F

K8McBtuMZQmFUp8Q PnFUEGI/D8ccHp8QNVPRDpzFTPnFHEJI/D ≈ 1e#PSc 6tPnQ9FUEGM\Q9AFHQHI//QHPSK8M]K8EJp3QHD8M\K8MÁNJPRghI/D3iFUEGI/D

K¨sMÇziEGFTP<FUEJISD r K8McI/cHiEJNJNJPnFUEGI/D8c®K8EJp8Q9D8MZcMFc9MZefE´©+K8EJp8Q9D8MZccHp8QNJM¾efI/p3SMZefMZD¦FK8pt¿/NGM7¥3?`_Xe«PScRr c9p8QI/cHiEJNJNJPnFUEGI/D8c®K8EJp8Q9D8MZcMFcHMZefE´©+K8EJp3QHD8McK8MONVPXNJISD8/p8Mp8QK8pXÀ9I/p8Q x¥

µc

ÃiZISD*FHQUPSQ9EJIEGNzMc9FghISQ9Fe#PSNJPSEJc9A®K¨sMZcmFUEGe#MQ·N½¨sM¸MFK8MNVPe«PnQHAZM PSQHISe#AFUQHEGo*p8M9:<MF:NGMZcefMZc9p8QHMcK8MXNJP#t8Q9MZc9cHEJISD PnFUefI/cHt38AZQ9EJo*p8MXPnp0cHI/NYMZD8SNJI uMZD¦F¾NJPfFUInFTPSNGEGFUAOK8McBp8iFUpP<FUEJISD8c PSQ9I/efAFUQ9EJo*p8Mco*p¨sMZNJNGMZcc9I/EJMD¦FFU3MZQHefEJo*p8McI/pL/QHP|zEGe#AFUQ9EJo*p8MZc?3@BPSD8cNVP]t8QUP<FUEJo*p8MBNJMZc®K8MZpÇLM¸MFHccHI/D¦FFHQUPSE´FUAciZISD<À9I/EJD¦FHMZefMZD¦F|?

WL` g,0" (-6) ( ( kl% ( J*, ') )fW"m-.) (J!) kl% ( k!) (! (!) )" *&,45)-/-.) cm%*& &(!)

~M\efI/efMZD¦FK8M¾ghI/QHiMONJp8D8E©¼c9I/NVPSEGQHMcHp8QNJMuI/p8Q9MZNJMFAZo*pPnFHI/QHEJPSNK8M]NVPvWYMZQ9QHM9:1023 É eKPnD8c

cUPt8PSQ9FHEJMe#Ib/MD8D8Mj:MZcmFLQHA/NJAtPSQ«NGMZcefI/p3SMZefMZD¦FUc«I/Q 8E´FTPSpÇR:o*p8MN¹¨lI/DiZI/D3DP0/JF:®efIK8AZNGEJcHMMFÁt8QHAK8EGF\P|/Mip8D8M#t8QHAiZEGcHEJISD!K¨s8I/Q9NJI//MQZ?Y¢B¨sMZcmFvtISp8QHo*p8I/E±NJPt8Q9AZiMZcHc9EJI/D©¼D*p3FTP<FUEJISD: 8EJMDo*p8MNJA/dZQ9MZefMZD¦F·Pn¸MiFHAZMtPSQYNVPc9FUQ9p3FUp3QHMEJD¦FUMQHD8MK8MNJPW.MQHQHM®MF.cUPQH8AI/NJI/SEJM9:ZMZc9FYFUQ9dZc 8EJMD\iMZQHD3AZM9:9Zp8D8MefEJNJNGEJc9MZiZISD8K8MK8MK8M/QHAt8QHdctPnQNGMe#IK8dZNGMiZI/D¦SMZD¦FUEGI/D8D8MN»¼Ã ; _S¥/¥/¥ ¹PnK8I/t3FHAtPnQN¹¨ ; D8EJISDÃBcmFUQ9I/D8I/efEJo*p8M»¼D¦FUMQHDPnFHEJI/D8PSNMZD_S¥/¥/¥ ?*~MiI/p8t8NJPS/M9:¦K3Mc9p8QHiQHI /GFO:*MZcmF®SI/NJp8efEJo*p8Mj:¦MF®cUPOi|PSp3cHMMZcmFt8p8QHMe#MD¦FSQUP|EGFUEGI/D8D8MNJNGMS?

~M«iZISp8t8NVPn/M#MD¦FUQHM#p8D8M#iZI/p8iT3M«p8EGK8M#c9p8tuMZQ9C8iZEJMNJNGM#MFÁNJPWYMZQ9QHM«c9I/NJEGK8MfcZ¨lPSdZQ9M MZPSp8iI/p8tt8NGp8cK8ANJEGi|PnF[ZÁK8AFUMQHefEJD8MQZ?@Bp«g6PSE´Fe <ZefMop3MBN½¨lPnFHe#I/c9t88dQHMI/pNJMcIiZAZPSD8cD3MBcHMBiZI/eftISQ9FUMD¦FtPSc.K8Me#PSD8EGdZQ9Mt3QHAZK3EJiFHE 8NGMPSpÁK8MNyZK8Mo*p8MNJo*p8MZcÀ9I/p8Q9c:<EJN¦MZcmFEGe#tuI/cHc9E 8NGM:K8MK3QHMZc9cHMQp8DXefIzK3dZNJMt8Q9AZK8EGiFUE´gK8MZcghI/Q9iZMc]o*p8MviMZcOiZISp8iT8MZc]MÇzMQHiZMD¦F\c9p8QONVP«WYMZQ9QHMRcHISNJEJK3MS?@BMRt8NJp8c¾NGMXiZISp8t8NVPn/MXMZcmFP|nPSD¦FFHI/p3Fc9p8Q9g6PSiEJo*p8M 8NGMZcghI/Q9iZMZcK8MOt8Q9MZc9cHEJISDo*p8ED8MOtPncHcHMD¦FBtPnQNJMiMZD¦FUQ9M\K8MO/QHP|zE´FUA¾K8MONJPWYMZQHQ9M9:iQHAMZD¦F]MZD iTPSo*p8MRtuI/EJD¦F¾K8MÁNVPcHp3Q9g6PSiMvp8D e#I/efMZD¦FBK8MXghI/QHiM9:MF¾iZISe#efMXNJMÁiTPSeft0K8Mt8Q9MZcHc9EJI/D D¨lMc9FvtPncXp8D8E´ghI/QHefMRN½¨sMZD8c9MZe 8NGM«K8M«iZMZcÁe#I/efMZD¦FHcÁAZNGAZefMZD¦FTPnEJQHMcÁI/D¦FÁp8D8MQ9AZcHp3NGFTPnD*FHMD8I/DD*p8NJNGMS?Y~:¨`PSp3/e#MD¦FTPnFHEJI/D K8M#NVPÊt8QHMcHcHEGI/D!MDp8DtI/EGD¦FÁK8ISD8D8AfK8M«NJPc9p8Q9g6PSiM hK8p!t8NJPSD8iT8MQIiZA|PnD8EJo*p8M OiI/QHQ9MZcHtuI/D8K Zp8D8M#PSiiZp8eXp3NVPnFHEJI/D K8M#e«PSc9cHMfK¨lPSEJQ 6K¨lMZPSp 1:Yo*p8E±MÇzMZQ9iZMMD!Q9MFUISp8Qp8D8MvghI/Q9iZMvK8MR/QHP|zE´FTPnFHEJI/DPSiZiQHp8MRcHp3Q]NJPW.MQHQ9Mfc9I/NJEGK8M9:cZ¨sI/t8tuI/cUPSD¦F'ZLN½¨sEJD8iQHAe#MD*FK8MvghI/QHiMvK8Mt8Q9MZcHc9EJI/D?3ÉI/p8ct3QHASIb/I/D8cK8I/D8iN½¨sMÇzEJcmFUMZD3iZMBK¨lp8D«iZI/p8t3NVPS/M/QHPE´FUEJISD8D8MZNMD¦FUQHMNVPOW.MQHQ9McHI/NGEJK8MMFN½¨lPnFUefI/cHt38dZQ9M6NGMZcIiZAZPSD8c ®SMZDPnD*FiI/e#tuMZD3cHMZQNJMZcM¸MFUcK8MBNVPÁt8Q9MZc9cHEJISD?~$PÁFUQ9I/EJc9EJdZefMF¼btuMK¨sEJD¦FUMQUPSiFUEGI/DMZcmFvNVPÊghQHEGiFUEGI/D hEJc9iZI/c9EGFUA 1: MZPSp8iZISp8t t8NJp3cÁK8E s#iEJNGMFZ&efIK8AZNGEJcHMQ\o*p8M«NJMZc\K8MZpÇt8Q9AZiZAK8MZD¦FHMZcZ?

:DQHAcHp8efAÁNGM]efI/efMZD¦FK8M\ghISQHiZM]K¨sEJD¦FUMQUPSiFUEGI/DK3MZciI/p8iT8McBp8EGK8MZccHp8QNVPRW.MQHQ9MÁcHISNJEJK3M]c9MK8AiZI/eftIScHMOMZDÊFUQ9I/EJcFHMZQHefMZc

^x

• p3DFHMZQHefMOK8MOt8QHMcHc9EJI/Dt8QHIEJMD¦FBK8ptuI/EJK8cK3M\NJPXiZI/NGI/D8D8M¾/MQ9FHEJi|PnNJM¾K¨lPSEJQISpK¨sM|Pnpc9p8QNJPcHp3Q9g6PSiM]K3M]NJPvW.MQHQHMOc9I/NJEGK8M r

• p8DLFUMZQ9e#MBK8M¾/QUP|EGFUPnFUEGI/D«Mc9FK 7 ZXN½¨lPnF9FUQUPniFUEGI/D«M ÇzMZQHiAZM]tPSQNGMZce#PScHc9MZcPnFHe#IScHt88AQHEGop3MZcI/pÊIiZA|PnD8EJo*p8Mcc9p8QNJMZce#PSc9cHMZcc9I/NJEGK8MZcK8MONJPRWYMZQ9QHM r

• p8DFHMZQHefMBK3MBghQHEGiFUEGI/DfMZc9FPScHc9IziEJAPnpzÇ«ghQ9ISFHFHMZefMZD¦FUc®t8QHIK8p8E´FUc®tPSQNGMZc/MZD¦FHcMZDLcHp3Q9g6PSiMI/ptPSQNGMZciZISp8QUPSD¦FHce#PSQ9EJD8cc9p8QNJM¾t8NJPSD8iT8MQIziA|PSD8EGo*p8MS?~MZcefI/efMZD¦FUcK8M\ghISQHiZM\K8MÁt3QHMZc9cHEGI/DMFBK8MX/QHP|zE´FTPnFHEJI/DÊc9MXi|PSNGiZp8NGMZD¦FtPSQK8MZcEGD¦FUAZSQUPSNGMZcK8M

cHp3Q9g6PSiM9:YD8AZiMZcHc9EGFUPSD¦FXK8MfiZI/D3DP0/JFHQHMRNVPÊt8Q9MZcHc9EJI/D!PSp²cHI/N±I/p!PSpghI/D3KK8McÁIiZAZPSD8cZ?Y~:¨sMÇzt8QHMcHc9EJI/DPSDPnNGb*FUEGop3M¾K8pFHMZQ9e#M¾K8MOt8Q9MZc9cHEJISDMc9F

~Γp = −∫

surface

~r × PsndS¹rz? x

I ~rMZc9FfNGMQUP|b/ISD:

Ps:NVPt3QHMZc9cHEGI/D ZNVPcHp3Q9g6PSiMK3MLNVPWYMZQHQ9MLcHI/NGEJK8Mj:

n:NJM#/MZiFUMp8Q#p3D8EGFUPSEJQ9M

D8I/Q9e«PnNcHI/QmFTPSD¦FwZRNVPXc9p8Q9g6PSiMOK8MONVPvW.MQHQ9M9:cHISEGF

~Γp =

∫ π2

−π2

∫ 2π

0

R2eh

∂Ps

∂λ

cos θ cosλcos θ sin λ− sin θ

+∂Ps

∂θ

sin θ sin λ− sin θ cosλ

0

dθ dλ¹rz?`_

I hMZcmFRNVP&Pnp3FUMp8QvK8p[QHMNJEJMgtPSQÁQUPSt8tuI/QmFRPSp QUP|bSI/D[AZo*pPnFHI/QHEJPSN

Re:θMFλ:·NVPiZI/NJPnFUE´FUp8K3M

MFONJP«NJISD8/EGFHp8K8Mj:g:N¹¨`PniZiZANJAQUPnFHEJI/DefIb/MD8D8MRK8MvNVP#tMcUPSD¦FUMp8Q&:

Φ:NJMXtuISFHMZD¦FUEGMZN·K3MfSQUP|EGFTP<FUEJISD

FUMQHQ9MZc9FHQHMn?~M¾FUMQHefM¾K8MO/QUP|EGFUPnFUEGI/Dc¨lAiZQHE´F

~Γg =

∫

volume de fluide

~r × ~∇Φρ dV¹rz?lk

I ρMc9F®NVPOK8MZD8c9EGFHAK8pfp8EGK8M9:¦c9I/EGF:*PSt8QHdc®N¹¨`Pnt8t8QHI|ÇzEJe#PnFHEJI/DvK8E´FUMK8M2]iZISp8iT8Me#EGD8iZM8]MFK¨sAZo*p8E©

NJE 8QHMB*bK8Q9I/c9FUPnFUEGo*p8M)

~Γg =a2

g

∫ π2

−π2

∫ 2π

0

Φ

∂Ps

∂λ

cos θ cosλcos θ sinλ− sin θ

+∂Ps

∂θ

sin θ sinλ− sin θ cosλ

0

dθ dλ¹rz?s^

upPSD¦FPSpÊe#I/efMZD¦FK8M¾ghQ9EJiFHEJI/DR:3EJNcZ¨sAZiZQ9EGF

~Γf =

∫

surface

~rηn.∇~vsdS¹rz?ªr

I ηMZcmFp8Dt8PSQUPSefdFHQHM¾K8M¾EJc9iZIScHEGFHAOMF

~vsMc9FNVPÁEGFHMZc9cHM]QHMZNJPnFUE´/M¾K8pÊp8EGK8M ZRNVPXcHp3Q9g6PSiM\K8MONJP

WYMZQHQ9MOI/pc9p8QNJM¾t8NJPSD8iT8MQIziA|PSD8EGo*p8MS?;¢McM Çzt8QHMcHcHEGI/D8ccHI/D¦FK8AZefI/D¦FUQ9AZMcK8PSD8c s^ ½?^*_

¢MF9FUM#PSDPSN´bzc9MRPLAFUARK8A/MNJI/t8tuAZMRKPnD8cONVPK8AiZMZD3D8EJM x//¥:K8Mc]c9AZQ9EJMZc¾FHMZeftI/Q9MZNGNJMZcBK8MRe#In©efMZD¦FUcXK3MghI/QHiMZcvPnFHe#IScHt88AQHEGop3MZcXI/D¦FvAFUALiZPSNJip8NJAMZcZ? &PSEGcXNVPghI/QHiMK8M«ghQ9EJiFHEJI/DQHMc9FTPnD*FXe«PSNK8AFUMZQ9e#EGD8AZMj:3iMFHFHM¾e#AFU8IK8MMc9FQ9MZc9FHAZMOPSiZPSK8Ae#EGop3M9:3MFD¨sMZc9Ft8PScPSt8t3NJEJo*p8AMtuI/p8QK8AFUMQHefEJD8MQK8Me«PSD3EJdZQ9MQ9I/p3FHEJD8EGdZQHMN½¨sEJeftPSiF±K8MN¹¨`PnFHe#IScHt88dQHMI/pK8McIiZAZPSD8cc9p8QNJP\QHInFTPnFHEJI/DRFUMQHQHMc9FHQHMhMZDcHMghI/D3KPSD¦F±cHp8Q:NGMZc:Aop8PnFUEGI/D8c:K¨l:p8NJMQm©~EGI/p3EJNGNJM±QHMc9FUQ9MZEGD*FHMZc Z¾NVPtPnQ9FUEGMcHISNJEJK3MK8MNVPWYMZQ9QHM ?Dt8Q9AghdZQ9MRNVPefAFU3IzK8MvK3EGFUMÁK8pefI/efMZD¦F¾iEJD8AFUEJo*p8MvI NJPiZI/p3iT8Mf8p8EJK8MXg6PnEGFt8PSQ9FHEJMvK8p c9bcmFUdZefMefAZi|PnD8EJo*p8Mj:MFOMÇziEGFUMfNVPQ9ISFTP<FUEJISDFUMZQ9QHMc9FUQ9M#t8PSQ¾N½¨sEJD¦FUMQHefAZK8EJPSEJQ9MÁK8MRiMZcOEJD8iQHAe#MD*FHcOK¨lEGD8MZQmFUEGMIij

MFK8Mce#ISe#MD*FHciEJD8AFUEJo*p8McQ9MZNVP<FUEGghchi:o*p8MN½¨sI/D#i|PSNGiZp8NGM_Z\t8PSQ9FHEJQK8MZcI8cHMQ9nPnFUEGI/D8c®e#AFUAZI<©

QHISNJI//EGo*p8MZcISpIiZAZPSD8I/SQUPSt83EJo*p8MZc&:8cUPnD8ctI/p3QPSp3FUPSD¦FK8AFHMZQHefEJD3MZQNJMcghI/Q9iZMZco*p8ENGMZcEGD8K8p8EGcHMZD¦FZ?

W%$ n%2Jk["$ 1%2 ( ) kl #"/,0"$ &%' ( (JJ) kl% (JkJ) (J &(!) )" e % e )f "kl &!"$ &-(!) (!) kl)"m"$)3kl% (JkJ)

@Á¨lPSt8QHdcBNGM\iTPnt8EGFHQHM]k\:u:ou? ¹kz? xx 1:NJMOefI/efMZD¦FiZEJD3AFUEGo*p8MOK¨lp3D8MÁiI/p8iT8M\op3MZNJiI/D8o*p8M\K8MÁNJPWYMZQHQ9MOI/pK3M]iMZNGNJM©+iZEt3QHEJc9M¾KPSD8ccHPf/NGI PSNGEGFHA9:tMp3FFUI/p(À9I/p8QHcf<FUQHMOc9AZtPSQ9AOMZD&K3MZpzÇLFHMZQ9e#Mc

NGMBt8Q9MZefEJMZQMZcmFPSc9cHIiZEJAoZÁNVP\QHISFUPnFUEGI/D#Q9EJ/EGK8MK8MNVP(©¼K8E´FUMiZI/p3iT8MOP|/MZi¾NJP\WYMZQ9QHM0ZÁNJP]EGFHMZc9cHMK8M#QHISFUPnFUEGI/D

~ω:$MFÁcZ¨sMÇzt8QHEGe#M#iZI/efefMfNGM#t3QHIK8p8EGF]K8pFUMZD3cHMZp3QXK¨sEJD8MQ9FUEGMRK8M«iMFHFHM«tPnQ9FUEGM

P|/Mi\NGM/MiFUMp8QEJD8cmFTPSD¦FTPnD8AOK8MOQHISFUPnFUEGI/DLK8MONVPXWYMZQ9QHM r;I/DÊN½¨lPSt8tuMZNGNJM/AZD8AQUPSNGMZefMZD¦FFUMQHefMK8Mop¼e«PnFHEJdQHM^]6r

NGMLcHMZiI/D8K FUMZQ9e#MLMc9FfNJMLefI/efMZD¦FRiZEGD8AFHEJo*p8MLQ9MZNVP<FUEGgK8MÊiMFHFHMÊiZI/p8iT3MtPnQvQUPSt8tuI/QmF Z²NJPiQHI873FHM¾FUMZQ9QHMc9FUQ9M r;I/DÊN½¨lPSt8tuMZNGNJMBFHMZQHefM¾K8MopefI/p3SMZefMZD¦FV] ~hf ?

azI/EGMZD¦FI

f NJPXe«PnFHQHEGiZM¾K¨sEJD8MQ9FHEJMK8MOiMFHFHM\t8PSQ9FHEJMiI/p8iT8Mj:uNGMFUMQHefM]K3M]e#PnFHEJdZQ9McZ¨sAZiQHE´F

[Hf ] = If[ω]

cHISEGF

[Hf ] = Ω

If11m1 + If

12m2 + If13(1 +m3)

If12m1 + If

22m2 + If23(1 +m3)

If13m1 + If

13m2 + If33(1 +m3)

¹rz?`

azENGMZcefI/efMZD¦FUcK¨sEJD3MZQ9FHEJMK3M]NJPÁiZISp8iT8M]cHI/D¦FtMFUE´FUctPnQQUPSt8tuI/QmFUcfZviZMpzÇÊK8MONVPXWYMZQ9QHM¾/NGI PSNGM9:iZM¾o*p8EMZc9FNGMi|PncK8MN½¨lPnFHe#I/c9t88dQHMMFK8MZcIiZAZPSD8c 6p3DLe#EGNJNJEGI/D8EGdZefMPSpLt8NGp8c #:8I/DLI 3FHEJMD*FPSt8QHdccHp3t8t8QHMcHc9EJI/DK8MZcFUMQHefMZcK8pcHMiZI/D8KI/QHK3QHM7

[Hf ] ≈ Ω

If13

If23

If33

¹rz?ªÂ

.ISp8Q$p8D8M:iZISp8iT8M±p8EJK3M9:|Q9MZt8Q9AZcHMD¦FTPSD¦F.p8D8M:;PSE 8NJMt3QHI/tuI/Q9FHEJI/DBK8M±NVPe#PScHc9M±K8M:NVPWYMZQ9QHM9:NGM:i|PSNGiZp8NK8Mce#ISe#MD*FHcK¨sEJD8MQ9FHEJM8I/QHc©¼K8EJPS/I/D8PSpzÇ

If13

:If23

MF:K8pvefI/e#MD¦F·K¨sEJD3MZQ9FHEJMP<ÇzEVPSNIf33

c¨`PSt3tPSQHMD¦FUMK8I/D3i Z[iMZNGp8EK8pFUMQHefM0e«P<FUEJdQHMK8p e#I/efMZD¦FLiEJD8AFUEGop3M0K8M0iZM0p8EGK8MS?@PSD8cÊNJMcAZo*pP<FUEJISD8cK¨l:p8NJMQm©~EGI/p3EJNGNJMvEJD¦FHMZQ9EGMZD8D8MD¦FXt8NGp8cÁM Ç3t3QHMZc9cHAe#MD*FfNGMZc MOPRQ1ATqP\=FGHEFDFDFE1P~AQ1 PRK1ATT EGHED x9ATqB1ISE

χmat =If13 + iIf

23

C − A=

If

C − A

¹rz?`w

χmat3 =

I33

C

¹rz?`

^¦k

MFNGMZc MOPRQ1ATqP\='GHE DFDFE1P~AQ1 PRK1A T~E2GHE DF 59E1DFE1P~A

χmv =hf

(C − A)Ω

½r? x¥

χmv3 =

h3

CΩ

½r? xx W &-( ,0"$ 1%2 ( (!*1)- 5 1% ( 1*&*1) %(- (J!) 45)-.-.) ,!i*,c

"$ '&-(J)~M\cmbzcmFUde#M]e#Ai|PSD3EJo*p8MOo*p8M\D3I/p8cMZD¦EJcHPS/MZISD8ciI/eft8QHMD8KNJPvW.MQHQHM]MFc9MZciZI/p8iT3MZc8p8EJK8Mc

cHp3tMQ9CiEJMZNGNJMcZ?Y:D!iZISD8cHEGK8AZQHPSD¦FXo*p8M«NJPt8PSQ9FHEJMRcHI/NGEJK8MRK8M#NVPLWYMZQHQ9M«Mc9FvPnD8AZNJPSc9FHEJo*p8M9:$N¹¨lM¸MFÁK8McMÇziEGFTP<FUEJISD8cp8EGK8MZccHp3QNGM¾e#ISp3/Me#MD*FK8ptu¿/NJMc9M]FHQUPSK3p8EGFPnNJI/Q9ctPSQN½¨sAZo*pP<FUEJISD 6^8?s^*Â

m +i

σ∗c

m =Ψf

1 − k∗2ks

½r? x(_

P|/Miσ∗

c = σc[1 + i/(2Q)]MF

Ψf NVPÁghI/D3iFUEGI/DÊK¨sMÇziZE´FTPnFHEJI/DÊK8I/D3D8AZMOtPSQ

Ψf = χmat + χmv − i

Ω(χmat + χmv)

½r? xk ~MZcghI/D8iFUEGI/D8c$K8M±e#ISe#MD*F$iEJD8AFUEGop3M:e«PnFHEJdQHM:I/pONJMc$e#I/efMZD¦FHcK¨lEGD8MZQmFUEGM:iZI/Q9QHMZc9tISD8KPSD¦F.I/D¦F.p3D8MefI(bSMZD8D3MÁD8I/D©¼D*p8NJNGM9:iI/QHQ9MZcHtuI/D8K8PSD¦F_ZfNVPRK8EJcmFUQHE 8p3FHEJp8I/DÊefIb/MZD3D8M\K3p&p8EGK8MS?¢MF9FUM]e#IbSMZD8D8Mj:K8I/D¦F¾ISD0tMp3F¾cHp3t8tIScHMZQOo*p¨sMZNGNJMÁM ÇzEJc9FHMvK8MZt3p8EJcK3MZcFUMe#t3cEJefe#Ae#ISQUP8NGMZc&:I/pFUI/pzFOPSp0efI/EJD8cK8Mt8p8EJcBt8NJp8c9EJMp8QHc¾PnD8D8AZMc:P#MZDg6PSE´FBp8D0EGe#t8PSiFBK8ACD3EGg±cHp3QNJM\e#I/pz/MZefMZD¦F¾K3p0t¿/NGM hK8AZiZPSNVPSSMiZISD8c9FUPSD¦FRMFviI/D¦FUQHE 8p3FHEJI/Dc9p8QvNJMfFUMQHefMK8MÊ¢PnD8K8NJMQvPSefI/Q9FHEJMnZN½¨s8MZp3QHMLPSiFUp8MNJNGM ?azMZp3NJMNJPtPSQmFUEGMSPnQHEVP 8NJMj:·cHp3cHiZMt3FUE 8NJMK8MÊt8Q9I(SIzo*p8MQ#p3DefI/p3SMZefMZD¦F#PSiFHp8MZNMZcmFfK¨lEGD¦FUAZQ<FZ? yL2,Y-/ Y4|Y4 Y=6 X)+5u,Y-S(465u,Yv" $-¦4 23(4h5u,.\5"Y !5u! ,R-¦46,Y'¦(46$ XZ5u,#-/5u,.|46"$'%('* Y,.46$ z z,u«"$2,Y#=h Y%#1.23%(46 828%<4h2 ·=h +3

~I/QHc9op3MNJPt8QHMcHc9EJI/D]K8p¾p8EGK8M:MZD]cHp8Qmg6PSiZMPSp3/e#MD¦FUM 6K3EJefEJD*p8M ;MZD]p8D8M ZISD8D8M±K8I/D8D3AZM9:iMZNGNJM©iZEc9M\iQHMp8cHM uI/e uM #:8iZM]o*p8EK8I/D8D3M\NGEJMZpJZRp8D8MOK8EGe#EGD*p3FTPnFHEJI/D ¹PSp8Se#MD*FUPnFUEGI/D ®K3MZce#I/efMZD¦FHcK¨sEJD8MQ9FHEJMRK8MfNVPÊW.MQHQHM#cHI/NGEJK8Mn?$@BMfe«PSD3EJdZQ9MR/AZD8AQUPSNGM9:FUISp3FUMRnPSQHEJPnFUEGI/D0K8MZc\e#ISe#MD*FHcOK¨lEGD8MZQmFUEGMK8M NVP iI/p8iT8M²p8EJK3M

δIf htPSQÊQUPSt3tI/QmF Z cHP[nPSNGMZp8QLefIb/MD8D8M LMZcmFPniZiZISe#tPn/D8AZM tPnQp3D8MnPSQHEJPnFUEGI/D I/t8tuI/cHAM

Icharge K8MZc«e#I/efMZD¦FHc«K¨sEJD8MQ9FHEJMK8MNVP WYMZQHQ9McHISNJEJK3Mc9MZNJISDNVP²QHMZNJPnFUEGI/D K8Mt8Q9I/tISQ9FUEGI/D8DPnNJEGFHA Icharge = k′2δI

f ½r? x|^I

k′2 ≈ −0.3MZc9FNGMD3I/e 8Q9MK3M~I/MK8E´F±K8MK8AghI/Q9e«P<FUEJISD?/ÉI/p8c®PSK8efMFHFHI/D8c:iMFHFHMM Çzt8QHMcHcHEGI/D:

o*p8EMZcmFPSDPSNGI//p8MZOiMZNGNJMK8ISD8DPSD¦FN½¨sEJD8iQHAe#MD*FK¨lEGD8MZQmFUEGMcHI/p3cN¹¨`PniFUEGI/DXK8pRtuISFUMD¦FUEJMN8iZMD¦FUQHE´ghp8/Mn?~:¨lM¸MF:K8MK8AghI/QHe#PnFHEJI/D]iZI/eftuMZD8c9MtPSQ9FHEJMNJNJMe#MD¦F.N¹¨lEGD8iZQ9AZefMZD¦FK3Me#ISe#MD*F·K¨sEJD8MQ9FUEGMo*p8EzN½¨lPg6PSEGFDP0/GFUQ9MS?~$PXghI/D8iFUEJISDK¨lM Ç3iEGFUPnFUEGI/D 6tPnQ9FUEGMnPSQHEJP8NJM ®cHMOQ9AZAZiQHE´FK8I/D8i

Ψf = (1 + k′2)χmat + χmv − i

Ω[(1 + k′2)χ

mat + χmv]½r? x(r

MFNJPXtPSQ9FHEJM¾Aop8PnFUI/Q9EVPSNGMK8MON½¨sAZo*pP<FUEJISDK¨`:p8NGMZQm©¼~EJI/p3EGNJNJMK8MzEGMZD¦F

m+i

σ∗c

m = χmat eff + χmv eff − i

Ω(χmat eff + χmv eff)

½r? x ^/^

ghI/D8K3AZMOcHp8QNGMZc MOPRQ1A qP\='E_ESQ1A 59ES=GHEDFDFE1P~AiQ1 PRK1ATT~E K x9ACI#Tx9X

χmat eff =1 + k′2

1 − k2/ks

χmat χmv eff =1

1 − k2/ks

χmv ½r? x(Â@Á¨lPSt8Q9dZcNJMcSPnNJMZp3QHcK8McD8I/e 8Q9MZcK8MO~I/MOK8ISD8D8AZcMDÃD8D8M Ç3M\_

(k2 = 0.3, ks = 0.9883, k′2 =−0.3075)

:8ISDI3FUEGMZD¦F

χmat eff ≈ 1, 02 χmat ½r? xw χmv eff ≈ 1, 47 χmv ½r? x

:D[QHA|PnNJEGFHA«N¹¨lAop8PnFUEGI/D ½r? x ]QHA/EJc9cUPSD¦FRNGM«efI/p3/Me#MD¦FRK8p[t¿/NGM«c9I/p8cvN½¨lPSiFUEJISDK¨sp8D8MLiZISp8iT8Mp8EGK8M¾MZcmFEJeft8QHI/t3QHMBtuI/p8Qp3D8M¾MÇziZE´FTPnFHEJI/DLK3EJp8Q9D8M¾I/pÊcHp uK8EGp8QHD8M ?8±DÊM¸MFoZXiMF9FUMOAZiT8MNJNGM¾K8MFUMe#t3c:*NJMD8Ib/PSp#p3EJK8Mt8QHISIzo*p8Mp8D8MI/cHiEJNGNVPnFHEJI/DXNGE 8Q9MQHAFUQHIS/QUPSK3M9:¦o*pPSc9E´©¼K3EJp8Q9D8M −1−1/433ibiNJMRtPSQ®À9I/p3Q K8MRN¹¨`P<ÇzMvK8MvQ9ISFTP<FUEJISD0K8p e«PSD¦FHM|PSp?ÃBp3FHQHMZefMZD¦F]K8E´F¾EJNM ÇzEJc9FHMvp8D8MRQHAcHI/D8PSD8iZMj:o*p8E:PSeft8NGEGCM]N½¨sM¸MF¾K3MXFUI/p3FHMXMÇziEGFTP<FUEJISD0K8I/D¦F¾NVPfghQHAZo*p8MD8iZM#PSt8t3QHIiT8M −1 − 1/433

ibiNJMvtPSQÀ9I/p8Q? *1: ,Y"Y2,u Y"Y2,YÁ-/ .4:Z.4 ,$5u.\,Y %(24 *%(5u,.O$ Ê=m´46!1Y2-S]"Y ]%< "Y4¹%<4 7.$(4h5u,.f"$ !2|Z #Z 0"$'%(5uY=62,u|$%L1.=¹Y|4h z$%< 5$%< :1:5uY%=6 |$ =¹=h R=m'$23(4h5, Å 36 \ R5u²)+24 R2"$'Y2z +3.ISp8QNJMcnPSQ9EVPnFHEJI/D8cK8M\NVPRzE´FUMcHcHMXP<ÇzEVPSNGM9:;D8I/p8cPSI/D8cBpo*p8MvNGMZcM¸MFHc¾K8MÁK8AghI/QHe#PnFHEJI/DiZMDz©FUQ9EGghp8SMAFTPSEGMZD¦FtuMFHEGFUc ¹¥: x(r EJNJctuMZp3SMZD¦Ff<FHQHMBD3AZ/NGEJ/AcPSp«QHMZ/PSQHK#K8MNVPOt8Q9AZiZEGcHEGI/D:cHI/p3SMZD¦FEJD3K8AFHMZQHefEJD3AZM9:;K8McghI/D3iFUEGI/D8cK¨sMÇziZE´FTPnFHEJI/DPnFUefI/c9t88AZQ9EJo*p8M\MFIziA|PSD8EGo*p8MS?:D ISD8D8M\PSt8t8Q9IÇzE©e#PnFUEGI/D:3NJPÁEGFUMcHc9M\K8MOQ9ISFTPnFHEJI/D«MZc9FBPSNGI/QHcQ9AZ/NGAZMOiZISe#efMiZMNJNGM¾K¨lp3DiI/QHt8cQ9EJ/EGK8McHMNJI/D

m3 = −Ψf3

½r?ª_S¥ P|/Mi

Ψf = χmat3 +χmv

3

?8¢MtMD8KPSD¦FO:zN½¨sAZNJPSc9FHEJiZE´FUAMZD¦FHQUPSEGD8Mp3D8M¾PSp3FHQHMK8AghI/Q9e«P<FUEJISD:/iZMNJNGMK8p3M0ZNVP]iTPSQ9/MnPSQHEJP8NJMK8p«8p8EJK8Mj:8P(À9ISp3FTPSD¦FfZ\N½¨sMÇziZE´FTPnFHEJI/D#NJMFHMZQ9e#M

k′2χmat3

?zÃp ISp3FK8pLiI/e#tzFUM9:I/DP

m3 = −χmat eff3 − χmv eff

3 + Cte¹rz?`_x

P|/Mi\NGMZcghI/D8iFUEGI/D8cM¸MZiFUE´/MZc

χmat eff3 = (1 + k′2)χmat

3 ≈ 0, 70 χmat3

½r?ª_/_χmv eff

3 = χmv ½r?ª_Sk ~:¨lAi|PSQmFK8M\NVPRNJI/D3/p8MZp3QK8pRÀ9I/p8QBMc9FBp8D8MÁo*pPnD*FHEGFHAÁt8NGp8cBPnt8t8QHA8MZD3cHE 3NJM9:uMFBK¨lPSt8QHdcN½¨sAZo*pP<FUEJISD½_?ª_ NGMZciI/p8iT8Mcp8EGK8MZcNJPXe#IK8EGC8MZD¦FcHMNJI/DÊN½¨sAZo*pP<FUEJISD

∆LOD

LOD= χmat eff

3 + χmv eff3 + Cte

¹rz?`_n^

W kl 1"/,0"$ 1%2 ,0"/e %'c !-. &-(!)~M\efI/efMZD¦FiZEJD3AFUEGo*p8MÁP<FUefI/cHt83AZQHEGo*p8M

[HA] + [hA] = [ΩIA13,ΩI

A23,ΩI

A33] + [hA]

:;g6PnEGFN½¨sI z©À9MFfK8MÊK8AFUMQHefEJDPnFHEJI/D3cÀ9I/p8Q9DPSNJEGdZQ9MZcZ?~$McRI 8cHMQ9nPnFHEJI/D8cRefAFHAZI/Q9I/NJI/SEJo*p8MZc 6t8Q9MZcHc9EJI/D©+/MD¦F vD8MQHMD8K8MD*FfiI/e#tzFUMK8MLNJPQHAtPSQ9FHEGFHEJI/DK8MZcRe#PScHc9MZcvK¨lPSEJQÁMFRK8MLNGMZp8QXefI/p3SMZefMZD¦FRo*p8MLtPSQmFUEGMZNJNGM©efMZD¦F|?u.ISp8QBiZPSNJip8NJMQp3D8MÁo*pPSD¦FHEGFUA]/NGI PSNGM¾iZI/efe#MOp8D&e#I/efMZD¦FiZEGD8AFHEJo*p8Mj:uEGNg6PSp3Fe#MFHFHQHM]MZDIMZp3QHMvp3D0e#IK8dZNGM\D*p8efAZQ9EJo*p8MXtuI/p8Q ]EJD¦FUMQHtuI/NJMQ@]ON½¨sAFTP<FK8MvN¹¨`PnFHe#IScHt88dQHM\NyZ#I D8MvN½¨sI 8c9MZQ9SMtPSc?

# ) ' <6 GGI2 # D5@ !@ # D /* M * %

^*r

! ! '!(, . & '!.0! & 0)+ #. &!DM Ç3t3NJEJiEGFHMXNJMc¾e#I/efMZD¦FHc¾K¨lEGD8MZQmFUEGM

IA13

MFIA23

KPSD3c]NGMvQHMtdQHMvFUMQHQHMc9FHQHMfMZD²iZII/QHK8ISD8D8AZMccHt38AZQ9EJo*p8MZc

r, λ, θ hQUP|b/ISD:$NJI/D8SEGFUp3K8M9:iZI/NJPnFUE´FUp8K8M BMZD²g6PSEJcHPSD¦FOK8MZpzÇ!PSt3t8QHI|ÇzEJe#PnFUEGI/D8ciI/D8c9A©

iZpzFUEGSMZc

• FUISp3FANJAZefMZD¦FK8MÁSI/NJp8efM]K8MÁN¹¨`PnFHe#IScHt88dQHM]MZcmF¾MZDAo*p8EJNGE 8Q9M\¦bK8QHISc9FTP<FUEJo*p8Mj:iMÁo*p8E·tuMZQ©efMFO:K8PSD8c·NGMZc$EJD¦FHAZ/QHPSNJMc$SI/NJp3e#EGop3MZc:(K8McHp 8c9FHEGFUp3MZQ.ZN½¨sAZNGAZefMZD¦F$K8E´¸AQHMZD¦FHEJMZNdrNJPK3EG¸AZQHMD¦FUEJMNJNGM

K8MOt8Q9MZcHc9EJI/DR:t8p8EJc9o*p8Mdp = −ρgdr

ρMZcmFNJPve«PSc9cHM¾/ISNJp8efEJo*p8Mj:3fNJM¾iTPne#tÊK8MOtuMZcUPnD*FHMZp8Q r

• N½¨sAZt8PSEJc9cHMZp3QBK8MXNJP#iI/p8iT8MXp3EJK8M\AFTPnD*FFUQ9dZcEGD3ghAZQ9EJMZp3QHM\PSpQUP|bSI/DFUMQHQHMc9FHQHM9:MZNJNGM\Mc9F¾t3QHEJc9MiZISe#efM¾iZI/D3c9FTPnD*FHMOAZ¦PSNGMOPSpÊQUP|b/ISD&AZo*pP<FUI/Q9EVPSNGMS?D&PuI/p3FHEGFPnpzÇÊMÇzt8Q9MZc9cHEJISD8cc9p8EGnPSD¦FHMZctISp8QNJMFHMZQHefM¾K8MOe#PnFUEGdZQHMj:8QHM PSt3FHEJc9AOPSNJI/Q9cFUMQHefM

K8MOt8Q9MZcHc9EJI/D[Hp]

:KPSD8cNJM¾Q9MZtudZQ9MOFHMZQ9QHMZcmFUQ9M)

[Hp] = −R4e

gΩ

∫ π2

−π2

∫ 2π

0

Ps sin2 θ

cos θ cosλcos θ sin λ

sin θ

dθ dλ¹rz?ª_Sr

I Re

MZcmF:NJMQUP|bSI/DvAZo*pPnFHI/QHEJPSNK8MNVPW.MQHQ9M9:Ω:nNVPzE´FUMcHcHMPSD8/p8NJPSEJQ9M±K8MNVPW.MQHQ9M9:

g:<NVPtMcUPSD¦FHMZp8Q

efI(bSMZD8D3MXMFPs:uNVPft8QHMcHc9EJI/D0K8MÁN½¨lPSEJQPSpc9I/N½?~MZcefI/efMZD¦FUcK¨sEJD8MQ9FUEGM\c9MXQHMFUQ9I/p3/MD¦FOQHAZK3p8EGFHc0Z

K8McEGD*FHAZ/QHPSNJMccHp3Q9g6PSiEJo*p8MZcK¨sp8D8M¾ghI/D8iFUEGI/DÊK8AFHMZQHefEJD3AZM¾tPSQNJPXt8QHMcHcHEGI/DPnFUefI/cHt38AZQ9EJo*p8MS?~:¨`PnFHe#IScHt88dQHM:Q9MZt8Q9AZcHMD¦FUMMD¦zEGQHI/DOp8DOefEJNGNJEJISD8EJde#MK8M:NJPe«PncHcHM:K3MNJPWYMZQHQ9M

MA ≈ 5, 2 1018

*1:.I/QHK3QHMLK8MSQUPSD8K3MZp8Qvo*p8MLN¹¨lI/D!I 3FUEGMZD¦FXg6PSiEJNGMZefMZD¦F ZtPnQ9FUEGQÁK8M«NVP&t8Q9MZc9cHEJISD efIb/MD8D8MÊPnFm©efI/cHt83AZQHEGo*p8MPSp[cHI/N :

105 .P²K3I/D8DPSD¦FfNVPe#PSc9cHMÊK¨sp8D8MiZI/NGI/D8D8MLK¨lPSEGQvtPSQvefdFUQ9MLi|PSQ9QHAj::cHI/E´Fdm = 105/g ≈ 104 3?±~$Mc#efI/efMZD¦FUcvK¨lEGD8MZQmFUEJMLK3MN¹¨`P<FUefI/cHt83dZQHMLQ9MZt8Q9AZc9MZD¦FUMK8I/D8iPSp t8NJp3cx¥

−6A?

@PSD8c·N½¨lPnFUefI/cHt38dZQ9M®NGMZc.nPSQ9EVPnFHEJI/D3cYK3MNVPt8QHMcHc9EJI/DvP<FUefI/cHt83AZQHEGo*p8MefIb/MZD3D8MMZDÁcHp8Qmg6PSiZMc9I/D¦FcUPnEJcHISD8D8EJdQHMcZ?¦ap8QNVPt8NVPSD3EJcHt38dZQ9MK8MNJP¶·EJ3?Sr? xc9I/D¦F:QHMtI/QmFUAMZc:SMZDRnie 2 hI/p1x¥ *<e 2 :nAZo*p8E©nPSNVPnD*F Z x|¥/¥O·P#:¦NJMZcnPSQ9EVPnFHEJI/D3c·K8Mce#PSc9cHMZc±K¨lPSEGQK8M·À9p8EJNGNJMF Z®ÀHPSD¦EJMZQ?*azMc±nPSNGMZp8Q9c±MÇFUQ9AZe#PSNJMccHISD*F\PnF9FUMEJD¦FUMc]c9p8Q]NJMZc¾iI/D¦FUEGD8MZD¦FUc&:$cHI/E´F\_S¥LniZe 2 :ISp_ ¤K8MRNVPLt8QHMcHc9EJI/DPnFUefI/c9t88AZQ9EJo*p8Mn?ÃiZISD*FHQUPSQ9EJINJP#t8Q9MZc9cHEJISD0D8MÁnPSQHEGMÁt8QHPnFUEGo*p8MZefMZD¦F¾tPnccHp8QBNJMZcIziA|PSD3cZ? DD8InFUMZQHPo*p8MXN½¨lPSiiZp8eXp©NVP<FUEJISD#K8MBe«PSc9cHMK¨`PSEGQ®c9p8QN¹¨l8Ae#EGcHt83dZQHMD8I/Q9KMZDL8E´/MQMZcmFPSiiZI/eftPS/D3AZMtPnQK8McK8AZt3QHMZc9cHEGI/D8cKPSD3cN¹¨l3AZefEJcHt38dZQ9M¾cHp8K?u~M¾t88AD8I/efdZD8M]cZ¨sEJD¦SMZQHc9M\MDAFUAn?

~MZc#nPSQ9EVPnFHEJI/D3cXQHMNVPnFHEG/Mc#K3MZcfe#I/efMZD¦FHcfK¨lEGD8MZQmFUEJMPnFHe#IScHt88AQHEGop3Mc9I/D¦F«K8ISD8i&Pnpt8NGp8cfK8Mo*p8MZNGo*p8MZc 8NGMZp8QtPSQmFUEGMBnPSQHEJP8NJM

cAijPnFHFHMZEJD¦FK8ISD8i

0, 01 10−6A = 10−8A ≤ 1030 fe 2 ?@PSD8cLN¹¨lAo*pPnFUEGI/DK¨`:p8NGMZQm©¼~EJI/p3EGNJNJMLEGD¦FUMZQmEJMZD¦FLK3I/D8ip8D3M&ghI/D8iFUEJISDK¨sMÇziZE´FTPnFHEJI/DAo*pPnFUI<©QHEJPSNJMj:cHPSEJc9I/D8D8EGdZQ9M9:K8MRN¹¨lI/Q9K8QHMÁK8M

10−8A/(C − A) = 3 10−6 QUPSK MFOD8I/p8cOt8Q9A/IbSI/D8cÁp3D²M¸MFiZISe#tPnQUP8NGMcHp3QNGM¾t¿SNJM9:3iZI/D3C8DPSD¦F x ]= 5 10−6 QHPSK ?~$PfghI/D8iFUEGI/DK¨lM Ç3iEGFUPnFUEGI/DP<ÇzEVPSNGM

c33/C:FUISp3FPSp&t8NGp8c

10−8A/C = 10−8 QHPSK:;EJD38p8MZD8iMÁNJPNJISD8/p8Mp8Q\K3pÀ9I/p8Q'Z&NVPPSp3FHMZp8Q\K8M10−8 ∗ 86400 = 0.001

c x«efcXPSp!t8NJp8c\K¨lPSt8QHdcÁN¹¨`:o;?½r?ª_n^?

¢MZcfI/QHK3QHMZcfK8MÊ/QHPSD8K8Mp8QRcHI/D¦FfiZI/DzCQHefAZcftPSQvNGMZcRi|PSNGiZp8NGcve#AFUAI/QHI/NGI//EGop3MZcXK8M[Hp]

::op3EcZ¨lPSt8t3p8EJMD*Fc9p8QN½¨sMÇzt8QHMcHc9EJI/D ½rz?`_/r ?8Ã tPSQmFUEGQK¨lp3D8MOQHA|PnDPSNGbc9M]SNJI PnNJMBK3MZcK8I/D8D8AMZce#AFUAI/QHIn©NJIS/EJo*p8Mc]K3M x|S^¦w Z&_S¥S¥¦r:NGM#ÉB¢± 6ÉBPnFHEJI/D8PSN±¢MZD¦FHMZQOghI/Q]±D¦EJQ9I/D8efMZD¦FTPnN®:Q9I/cHtuMZiFO: ; azÃ MFÁNJM#É¢ÃB 6ÉBPnFHEJI/DPnN¢MZD¦FUMQÁghI/QÁÃFHe#IScHt88MQHEGi«MZc9M|PSQ9iT: ; azÃOI/D¦FXi|PnNJiZp3NJAZc]NJMfefI/e#MD¦F

^¦

rz? x &¬PSQHEJPnFUEGI/D8cK8MZc]e«PncHcHMc\K¨`PSEGQ¾K8MBÀ9p8EJNGNJMF0ZÁÀHPSD¦zEGMZQ¾tPnQ]p3D8EGFHAvK8M#c9p8Q9g6PniZMvFUMQHQHMc9FHQHMMZD <iZe 2 6I/p x¥ *ne 2 :AZo*p8EGnPSNJPSD¦F Z x¥/¥L.P?~$McnPSNJMp8QHcM ÇFUQHAe«PnNJMZc¾c9I/D¦F]PnFHFHMZEGD*FHMZc¾c9p8QNJMciZISD*FHEJD8MD¦FUc¾MFOiI/QHQ9MZc9tI/D3K8MZD¦FZo*p8MZNGo*p8MZc ÈK8MvNVP«t3QHMZc9cHEGI/D PnFUefI/c9t88AZQ9EJo*p8M ¹azEJK8ISQHMZD SI :_S¥/¥/_:8t?dx| x&lr iZEGD8AFHEJo*p8M]PnFHe#I/c9t88AQHEJo*p8MOFUISp3FUMcNGMZc#8Mp8QHMc 6¥S8W ; :uS3W ; : x(_n8W ; : xwS8W ; ?;ÉISp8cBP|SI/D8cC/p3QHAiZMZc®K8I/D8D3AZMZc®cHp8QNVP]¶·EG/p8QHMr?l^\K8M_n¥/¥¦_ ZÁ_S¥S¥S^)¦D3ISFUI/D3c®KPnD8cNGMZc:FUQ9I/EJc±iZISe#tuI/cUPnD*FHMZcK8pFUMQHefMRK8MRt8QHMcHcHEGI/D hMZD *&e 2 c −1 NVPLtPSQmg6PSEGFHMXzEGcHE 8EJNGEGFUA\K8p²ibiZNGM#cHPSEJc9I/D8D8EGMZQ¾tuI/p8QOiTPSip8D8MK8Mc¾iZI/eftIScUPSD¦FUMc¾K8pFUMQHefMXK8Mvt8Q9MZc9cHEJISD:K8MXN¹¨lISQHK8Q9MXK8M

5 1024 *Êe 2 c −1 :PnEJD8c9E·o*p8MvtuI/p8QNJPiZISe#tuI/cUPnD*FHM]P<ÇzEVPSNGMK8pLFUMQHefMOSMZD¦F 50 1024 *Re 2 c −1 ?

! ! '!(,!%0 .I/p3Q¾NJMXefI/efMZD¦FiEJD8AFUEJo*p8MvQ9MZNJPnFUE´g:i|PSp3cHAvtPSQBNJMZcSMZD¦FUc&:$PSt8tuMZNGAvPSNJISQHc2ACE1I#DFE759E1P~A 6EJD3K8EJiM

v1:8N¹¨`Pnt8t8QHI|ÇzEJe#PnFHEJI/DfK8MOiZI/p3iT8MOe#EGD8iZMK3MZefMZp8Q9M9:8e#PSEJcNVPXQHAK8p8iFUEJISDLK8MON½¨sEJD¦FUA/QUPnNJM/I/NGp8e#EGo*p8MZvp8D8MOEJD¦FHAZ/QHPSNJM¾K8MOc9p8Q9g6PSiMOD¨lMc9Ft8NJp3ctI/c9cHE 8NJMn? DI zFUEJMD¦F

[hA] = R3e

∫ ∞

h=0

∫ π2

−π2

∫ 2π

0

sin θ

vθ sinλ+ vλ cos θ cosλ−vθ cos λ+ vλ cos θ sinλ

−vλ sin θ

ρ dh dθ dλ¹rz?ª_n

I vλMFvθcHI/D¦FÁNJMZc]EGFUMcHc9MZcXQ9MZNVP<FUEGSMZc]QHMcHtuMZiFHEGSMZefMZD¦FRNJI/D3/EGFHp8K8EJD8PSNJMcMFÁe#AQHEJK3EJI/DPnNJMZc hK8p

D8I/Q9K /MZQ9c#NGMLcHp8K 1::i|PnNJiZp3NJAZMcvtISp8QRiTPSo*p8MÊcHp8Qmg6PSiZMEJc9I PSQ9MPS?±~:¨s*btuISFU3dZcHMK8MÊN½¨sAZo*p8EGNJE 8QHM

¦bK8QHI/cmFTPnFHEJo*p8M]iZI/D3K8p8EGFwZvN¹¨lM Ç3t3QHMZc9cHEGI/D

[hA] =−R3

e

g

∫ PS

0

∫ π2

−π2

∫ 2π

0

sin θ

vθ sinλ+ vλ cos θ cos λ−vθ cosλ+ vλ cos θ sinλ

−vλ sin θ

dP dθ dλ¹rz?ª_SÂ

~:¨lp8D3MK3MZc±i|PSQHPSiFHAZQ9EJc9FHEJo*p8Mc:t8QHEGD8iZEGtPSNJMcK8Mc/MZD¦FHc:*iS¨sMZcmF®NJPt8QHAcHMD8iZMK¨sp8D8MiZEGQHiZp3NVPnFHEJI/D\/NJIn©PSNGM\K3M\N¹¨lI/p3MZc9F/MQHcBN¹¨lMc9F:e#P<ÇzEJe#PSNJMBKPSD8cNJMZc ZISD8MZcBFHMZeftAQHAMZcBMFBt3QUPnFHEJo*p8MZefMZD¦FD*p8NJNGM\KPnD8c

^*Â

NJMcZI/D3MZc]tI/NJPSEJQ9MZcMF]AZo*pPnFHI/QHEJPSNJMn?¢MZcO/MD¦FUc_pZISDPSpzÇ]vcHI/D¦F]o*pPScHE©¼EGD8MÇzEJcmFTPSD¦FHc ZÊNJPLcHp8Qmg6PSiZMj:e#PSEJcK3MEJMD8D8MZD¦FcHEG/D8EGC8i|PnFHEGghcKPnD8cNGMZcI/D8MZcFUMe#tuAZQ9AZMc ZRtPSQmFUEGQK8M x¥ e K¨`PnNGFUE´FUp8K3MMFPnFm©FUMEJ/D3MZD¦FNJMZp3Q:e«P<ÇzEGeXp8e : À9p8c9op¨ Z

30e1<c://MQHc x(_ eºK¨`PnNGFUE´FUp8K3M h/ISEJQ±¶·EG8?*rz?`_ ?/~$Mc®iI/p8NGI/EJQ9c

PSAQHEJMD8cÁMe#t3QHp8D¦FUMD¦FviZMc ZI/D8McXK8M ]+À9MF9©+c9FHQHM|Pne ]RtI/p3Q\NGMZc\SI/NJc\/MZQ9cXN½¨sMZcmF hNJM«/PSEJDK8M#FHMZeft8cPnF9FUMZEGD¦Fop3MZNJo*p8Mc3MZp8Q9MZctI/p3Qp8DSI/NNJISD8n©¼iI/p8Q9QHEJMQ ?

rz?`_XazMiFUEGI/DXefAZQ9EJK8EGMZD8D8M®K8MNJPBe#IbSMZD8D8MPnD8D*p8MZNGNJMK3MZcEGFHMZcHc9MZc:K8Mc/MD*FHc ZI/DPnpzÇ he1<c ?ÃBN´FUE´FUp8K8MOMD *e:ucHp8Qmg6PSiZM\EJc9I PSQ9QHM]MZDe 8PSQZ?¬PSNGMZp8Q9ctuI/cHE´FUE´/MZc/MQHcN¹¨lMc9F ½azEGK8I/QHMD SI :_S¥/¥¦_:t?x/Â lr ?

rz?`k aMZiFHEJI/D²efAZQHEGK8EJMD8D8MvK8MfN½¨sI/c9iZEJNGNVPnFHEJI/D&PSD8D*p8MNJNJMRKPnD8c\NJPÊE´FUMZc9cHMfK8MZcO/MD¦FUc I/DPSpzÇ6e nc ?8ÃNGFUE´FUp8K3MMZD *e:c9p8Q9g6PSiMOEJcHIPSQHQ9M¾MZDe PSQ ¹azEJK3I/QHMD SI :u_S¥/¥¦_H:8t?x¦Â lr ?

:DefI(bSMZD8D3M&N½¨lPnFHe#I/c9t88dQHMLt8Q9AZcHMD¦FUMp8D AFUPnF#K8Mc9p8tuMZQfQHISFUPnFUEGI/D:MF#N¹¨lISDtuMZp3FfiZPSNJip8NJMQo*p8MBNGMefI/efMZD¦F®iZEJD3AFUEGo*p8MQ9MZNJPnFUE´gK8MN½¨lPnFUefI/c9t88dZQ9MtuI/c9cHdZK3Mp8D8MiZI/eftIScUPSD¦FUMP<ÇzEVPnNJMe#IbSMZD8D8Mj:K8M#N½¨sI/QHK8Q9M#K3M

h3 ≈ 144 1024 *&e 2 c −1 6K¨lPSt8Q9dZcRazEGK8I/Q9MZD nI( :·_S¥/¥¦_H:sSI/EJQ]PSp8c9cHE®¶·EJ3?Yrz?l^?$Ã^¦w

FUE´FUQ9MvK8MRiZI/eftPSQHPSEJc9I/DNJMvefI/efMZD¦FOiZEGD8AFHEJo*p8MvK8MRN¹¨`PnFHe#IScHt88dQHMj:K8p5ZÊcHPQ9ISFTP<FUEJISDMZD 8NJIivMZcmF10−6CΩ ≈ 6 1027 fe 2 c −1 ?~$P[c9p8tuMZQm©+QHISFUPnFUEGI/DefIb/MZD3D8MMD cHI/ED¨lMc9Fo*p8M K8M0tMp K¨lEGe#tuI/Q9FUPSD8iM&tuI/p8QLNJM 8p3Fo*p8MD8I/p3cLtI/p3QHcHp3EG/ISD8c c9MZp8NGMZcLNJMc«nPSQHEJPnFUEGI/D8cfK8M0efI/e#MD¦FUciEJD8AFUEJo*p8MccHISD*FÊc9p8cHiMZt3FHE 8NGMZcLK¨sEJD©K8p8EGQHM]p8DM¸MFBc9p8QBNJPfQ9ISFTPnFHEJI/D? ¾QNJMcSMZD¦FUcI/DPSpÇ&t3QHAZc9MZD¦FUMD¦F¾p8D8M]SPnQHEVP<FUEJISDPnD8D*p8MZNGNJMOFUQHdct8Q9I/D8I/D8iAZMj:zÀ9p8cHo*p¨ Zsx|¥e1nc&:iI/e#efMXN¹¨lEGNJNJp3c9FUQ9M\NJP¶·EG8?rz?lk\:MFONVPiI/eftI/cHPSD¦FUMRP<ÇzEJPSNJM\K8p e#In©efMZD¦FÊiZEGD8AFHEJo*p8M0QHMNVPnFHEGg¾t3QHAZc9MZD¦FUM²p8D8M0p3iFUp8PnFUEGI/D PSD8D*p8MNJNJM0K3M

∆hsaison.3 ≈ 20 1024 [e 2c

−1 /I/EGQ¶·EG8?r?l^#:c9I/EGF¾r ÈK8MvcUPefIb/MZD3D8MS?»¼N·MZD0QHAcHp8N´FUMXp3D8MXghI/D8iFUEJISDK¨sMÇziZE´FTPnFHEJI/D0P(Ç3EJPSNJM∆hsaison.

3 /CΩ ≈ 4 10−9 : ZNJPSo*p8MZNGNJMfiZI/Q9QHMcHtuI/D8K[p8D8MnPSQ9EVPnFHEJI/DPSD8D*p8MNJNJM#K8MLNVPNJI/D8Sp8MZp8Q\K8pÀ9I/p8QA¦PSNGM Z3 10−9 ∗ 86400

c ≈ 0, 3efc

0, 6e#ct8EGi Zvt8EJi ?

~MZc&SMZD¦FUc EJD3K8p8EGFHct8PSQ&NGM!ibiNJM!FH8MZQ9e#EGop3M!K8EGp8QHD8MD8Mc9MiZI/eftuMZD8c9MZD¦F tPScZN½¨sAZiT8MNJNGMt8NJPSD8AFUPSEJQ9MMFK8ISD8D8MZD¦FDPSEGcHcHPSD8iZM Z p8D8M²I/c9iZEJNGNVPnFHEJI/DK8EJp3QHD8M0K8pµefI/e#MD¦FLiZEGD8AFHEJo*p8M0QHMNVPnFHEGg :Pn¸MZiFTPSD¦FÊK8E´¸AQHMZefefMZD¦FLiZISe#tuI/cUPnD*FHMZcÊP<ÇzEJPSNJMMFÊAZo*pP<FUI/Q9EVPSNGMS?YI/p8QLNJP!tPSQmFUEJM&AZo*pPnFHI/QHEJPSNJM ∆hdiurne ≈ 5 1024 *Re 2 c −1 :8MFtuI/p8QNVPXiZISe#tuI/cUPnD*FHM¾P<ÇzEVPnNJM ∆hdiurne

3 ≈ 0, 5 1024 *Re 2 c −1 ?

W kl 1"/,0"$ 1%2 % klf,! &-(!) ' &!/' % &! . %) . &!

D D8MtuMZp3FÁtPScXiI/D8cHEGK8AZQ9MZQXN¹¨lEGD3p8MD8iZM#K8MN¹¨`PnFHe#IScHt88dQHM#cHp8QXNJPWYMZQ9QHMc9I/NJEGK8M«cHPSD8cÁFHMZD8EGQiZISe#t3FHMÁK8M\NVPfQHA|PniFUEGI/D&K3MZcIiZAZPSD8c¾PSpÇnPSQ9EVPnFHEJI/D3cK3MXt8QHMcHc9EJI/D0P<FUefI/cHt83AZQHEGo*p8MÁMF¾PSpzÇ/MD¦FUcMZDcHp3Q9g6PSiMS?;:DÊM¸MFO:N¹¨`P<FUefI/cHt83dZQHMBEJD8K8p3EGFK8MciZI/p8QHPSD¦FUce#PSQHEGD8cMFK3MZciTPSD8/Me#MD¦FUcKPSD8cNJPPSpzFUMZp3QK¨lMZPSp?

; DLIiZAZPSDc9FUPnFUEGo*p8MBMc9Fp8DLIiZAZPSDK8ISD*FNJMcM|PnpzÇD¨lI/D¦FPnp8iZp8DLefI/p3SMZefMZD¦FSNJI PnNuQ9MZNJPnFUE´/M©efMZD¦F0ZNJP#WYMZQHQ9MXcHISNJEJK3MS?~$MÁe#I/efMZD¦FiZEGD8AFHEJo*p8MXIiZAZPSD8EJo*p8M\EJD8K3p8EGFtPSQN¹¨`P<FUefI/cHt83dZQHM\D8MXiI/eR©tuI/Q9FHMo*p8MNJMFUMQHefMK8Mt3QHMZc9cHEGI/D ht8QHMcHcHEGI/D«K3MN¹¨lMZPSp#c9p8QNJMt8NVPnD8iT8MZQIiZA|PnD8EJo*p8M ? D#EGe#tuI/cHMNYZp8D8MiZI/D3K8EGFHEJI/DRQHAK8p8iFUQHEGiZMj:e#PSEGc±ghISQ9FEJD¦FUAQHMcHcUPnD*FHMBtPnQ®NGMZccHEJeft8NGEGCiZPnFUEGI/D8c·o*p¨sMZNGNJMPSt8tuI/Q9FHMS? DcHp3t8tIScHMRPSNGI/QHco*p8MvNJMcBIiZA|PnD8cD8MXtuMZpz/MZD¦FOt8Q9AZc9MZD¦FUMQ]o*p8MÁK8MZpzÇQHAZPSiFHEJI/D8ctIScHcHE 8NJMcg6PSiMvPSpzÇnPSQHEJPnFUEGI/D8cK8M\t8QHMcHc9EJI/D&PnFUefI/cHt38AZQ9EJo*p8MS? ; D8MÁt8Q9MZefEJdQHM]*btuISFU3dZcHMÁc9FUEGt8p8NGM]o*p8M\N½¨sIziA|PSDQHAZPS/EGFiZISe#efMp3D PSQ9I/e#dFUQ9MEGD*SMZQ9cHAhMZDLPSD3/NVPSEGc±»¼D*SMZQmFUMZK PnQHI/efMFHMZQ #:*iS¨sMZc9FiZÁK8EJQ9Mo*p8MBNVPOt8QHMcHcHEGI/DFUInFTPSNGM 6PSEJQ MZPSp ±cHp8QNJMt8NVPnD8iT8MZQIiZA|PnD8EJo*p8MQHMc9FUMEJD¦nPSQHEJPSD¦FUMn?azE;NVPOt8QHMcHcHEGI/DLPnFHe#IScHt88AQHEGop3MZXNVPXc9p8Q9g6PniZMOPSp8Se#MD*FHM9:8in¨lMc9FNVP\PSp3FHMZp8QK¨sM|Pnpo*p8EK3EJefEJD*p8MBtuI/p8QiZI/eftMD8cHMQiZMFEGD8iZQ9AZefMZD¦F|?DfPSK8efMFPSNGI/QHco*p8MN½¨sM|PnpvK8AZt8NJPSiZAMcHMQHAtPSQ9FHEGF±c9p8Q:FUI/p3FHMNVPc9p8Q9g6PSiMEJefe#MQH/AMK8pf/NJI uMe#PSEJcK8Mfg6PZI/D²cHENJMD¦FUMfop3M«NJMfefI/e#MD¦F\iEJD8AFUEGop3M#Q9MZNVP<FUEGgPSc9cHIiZEJAnZiMF9FUM«Q9MZK8EGc9FHQHE 3p3FUEGI/D K8MZefMZp8Q9MD8A/NJEG/M|P3NJMS?SÃBp3FHQHMZefMZD¦FK8EGF:tuI/p8Qo*p8MBNGMe#IK8dZNGM»cHI/E´F±SPnNJEJK3M9:¦NVPOQHMK8EJcmFUQ9E 8p3FHEJI/DfK¨sM|PSp«K8I/EGF<FHQHMNJMD*FHMS?:D«M¸MFN¹¨lI 3cHMZQmnPnFUEGI/DfP]efI/D¦FUQ9Ao*p8MNVP¾QHAZPSiFHEJI/Df»iI/D8cmFUEGFHp8Mp8D8MPSt8t8Q9IÇzEGe«PnFHEJI/D8I/D3I/QUP3NJM«tuI/p8QÁK8MZcvtuAZQ9EJIK8MZc\cHp8tuAZQ9EJMZp3QHMZcWZ9x|¥RÀ9I/p8Q9cZ?~:¨s¦bztuISFH8dZc9M» Ao*p8EGnPSp3F ZQHAZK3p8EJQ9MN½¨sEJD¦FHAZ/QHPSNJMÊK8McHp8Qmg6PSiZM ¹rz?`_/r vK8I/D8DPnD*F«NJMÊFUMQHefM&K8Mt8QHMcHcHEGI/D PSpzÇiI/D¦FUEJD3MZD¦FUc?»¼NcHMQ9AZAZiQHE´FiZISe#efM7

[HA] = −R4e

gΩ

∫ π2

−π2

∫ 2π

0

f(λ, θ)Ps sin2 θ

cos θ cosλcos θ sinλ

sin θ

dθ dλ¹rz?ª_nw

I f(λ, θ)

MZcmFBNJPÁghI/D8iFUEGI/DÊK8EGFHM¾K8M'vOQ9MZMZDLnPSNJPSD¦F:x]c9p8QNJMciI/D¦FUEGD8MZD¦FUcMFB¥vc9p8QNJMZcIiZAZPSD8cZ?

^¦

2002 2002.2 2002.4 2002.6 2002.8 2003 2003.2 2003.4 2003.6 2003.8 2004−8

−4

0

4

8

x 1e24 H1 − pression

2002 2002.2 2002.4 2002.6 2002.8 2003 2003.2 2003.4 2003.6 2003.8 200416

20

24

28

32

x 1

e2

4

H2 − pression

2002 2002.2 2002.4 2002.6 2002.8 2003 2003.2 2003.4 2003.6 2003.8 2004

10160

10170

10180

x 1e24

H3 − pression

2002 2002.2 2002.4 2002.6 2002.8 2003 2003.2 2003.4 2003.6 2003.8 2004

−4

−2

0

2

4

x 1

e2

4

H1 − vents

2002 2002.2 2002.4 2002.6 2002.8 2003 2003.2 2003.4 2003.6 2003.8 2004−4

−2

0

2

4

x 1e24

H2 − vents

2002 2002.2 2002.4 2002.6 2002.8 2003 2003.2 2003.4 2003.6 2003.8 200480

100120140160180200

x 1

e2

4

H3 − vents

r?l^ ÊWYMZQ9e#McBK8M]t8QHMcHc9EJI/DMFK3M]SMZD¦FK8p&e#I/efMZD¦FiZEGD8AFHEJo*p8M\PnFUefI/c9t88AZQ9EJo*p8MOK8MX_S¥/¥¦_WZ_S¥/¥n^¾MZD *]e 2 c −1 ghI/p3QHD8E~Z¾¥n:¦S: x(_n:xwSvtPSQ:NGMÉ¢±4SÉB¢Ã ; azÃ ?¦~:¨lM¸MF±cUPSEGcHI/D3D8EJMQt8Q9AZK8I/efEJD3MBcUPnp3gYtI/p3QNJMciZISe#tuI/cUPnD*FHMZcAo*pPnFUISQHEVPnNJMZc®K8pFUMQHefMB/MD¦FQHAZSp8NJAMZcMZc9cHMD*FHEJMNJNJMe#MD¦FtPSQNGM¾ibiZNGM¾FU8MQHefEJo*p8MOK8EJp3QHD8Mn?

rS¥

.I/p3Q®K8Mc®AiT8MZNGNJMc®K8MFUMe#t3ct3NJp8c±iZISp8Q9FHMZc:*MFD8InFTPSefe#MD¦F±NVPPSD8K3MK8EGp8QHD3M hK8I/D¦FNVP¾tPSQmFUEGMQHAFUQ9I//QUPnK8M¾À9ISp8MZQHPtuI/p8QONVPÊD*p3FTP<FUEJISD 1:NJPÊQ9A|PSiFUEGI/DK3M«N½¨sIiZA|PnD5ZN½¨sMÇziZE´FTPnFHEJI/D²PnFHe#IScHt88AQHEGop3MQHMc9FHMfEGD8iZISD8D*p8MS? D tMp3FOg6PSEJQ9MXN½¨s¦btISFH8dZc9MRQUPSK8EGi|PSNGMZefMZD¦F¾I/t3tI/c9AZMj:$ZÊcHP|/I/EGQ]o*p8MRNGMZc¾IiZA|PnD8cMF®N½¨lPnFHe#I/c9t88dQHMcHI/D¦FK3AZiZISp8t8NJActuI/p8QiZMc®ghQHAo*p8MZD8iMZc?:DN½¨sIziiZp8Q9QHMD8iZMj:zN¹¨lIiZAZPSD#D3MBQHAZPS/E´F®t8PScPSpzÇSPnQHEVP<FUEJISD8cK8MOt8Q9MZcHc9EJI/DPnFHe#I/c9t88AQHEJo*p8M¾MFiZMZcnPSQHEJPnFUEGI/D8c®cHI/D¦FFUQHPSD8cHefEJc9MZcEJD¦FHAZ/QHPSNJMe#MD*FPSpt8NJPSD8iT8MQLIziA|PSD3EJo*p8MMFLK8I/D8i ZNJP!WYMZQHQ9M0cHI/NGEJK8Mn?¢B¨sMZcmFN½¨s*btuISFU3dZcHM0K3EGFUM&K8p PSQ9I/e#dFUQ9MD8I/D©¼EJD¦SMZQHc9A hMZDPSD8/NJPSEJc&:3ÉI/Dz©+»¼D*SMZQmFUMZK PSQ9I/e#MFUMQ:É»?

@PSD8cNVPt3QUPnFHEJo*p8MiTPSo*p8McHAQHEJMFHMZeftISQHMZNGNJMK3MefI/efMZD¦F±iZEGD8AFHEJo*p8MPnFHe#IScHt88AQHEGop3MMc9FK8I/D©D8AM]K8PSD8cp8D8MO/MQHcHEGI/D»µMFp8D8MO/MZQ9cHEGI/D&É»B?

' &!/' % ' %)+&!¢MZtuMZD8K8PSD¦F·I/D]tuMZp3FFHQUPSE´FUMZQN¹¨lEGD3p8MD8iZM:K3MZc$IziA|PSD3cYK3Me#PSD8EGdZQ9M:t8NJp8cQ9A|PSNGEJcmFUMMD\iI/D8cHEGK8AZQHPSD¦F

NJMcBAop8PnFUEGI/D8cNJIi|PSNGMZcop3E.NGM\Q9AZ/EGcHcHMD¦F¹ÉP|zEGMZQ©maFHI SMc:iI/D8c9MZQ9nPnFHEJI/DK8MXNJPfe#PScHc9M9:uMFHiS?´? ? DPuI/p3FHEGFPSNGI/QHcZOp8Dfe#IK8dZNGMK8MiZEGQHiZp3NVPnFHEJI/DvIiZAZPSD8EJo*p8Mj:¦iZI/D¦FHQUPSEGD*FtPnQNGMZc±I 8c9MZQmSP<FUEJISD8c±IziA|PSD8I<©/QHPSt88EGop3MZc:zo*p8EtuMZQ9e#MFK8MiZPSNJip8NJMQiZISp8QUPSD¦FHc:znPSQ9EVPnFHEJI/D3c®K8MBPSp3FHMZp8QK¨lMZPSpLMZDLiTPnop3M¾tI/EGD¦FK¨sp8D8Me«PnEJNJNGM#NGMLiZI/pzzQHPSD¦F|?@Á¨sI N½¨sI/D AnPSNGp8MÊK8MZcfcHAQHEJMcvFUMZeftuI/QHMNJNJMcXK8p e#ISe#MD*FRiEJD8AFUEGop3MIiZA|PnD8EJo*p8Mn?

~MÁFUMQHefMXe«P<FUEJdQHM]MZcmF]PSNJI/Q9ciI/D8K8E´FUEGI/D8D8A\tPSQNJP#t8Q9MZcHc9EJI/D c9p8QNJM\t8NVPnD8iT8MZQBIziA|PSD8EGo*p8MPO?

DfPK8I/D8ip8D3MMÇzt8QHMcHc9EJI/Dfc9FHQHEJiFUMe#MD*FEJK8MD*FHEJo*p8MfZ¹rz?ª_Sr 1:ntI/p3Q9pRK¨sbÁQHMe#t8NJPSiZMQNVPt8QHMcHcHEGI/DiZISD*FHEJD8MD¦FTPSNGMXtPSQ

PO:PO

c¨`PSD3Dp3NVPSD¦FOcHp3Q¾NJMZcBiZI/D¦FUEGD8MZD¦FHcZ?YazE.NJMÁp3EJK8MvMc9FOEJD3iZI/eft8QHMcHc9E 8NGM9:ucUPK8MD8cHE´FUA

ρex¥/¥/¥ ne 3 ®MZcmFp8D8EGghISQHefMS?z±DLp3DtuI/EGD*FK8pÊt8NVPnD8iT8MZQIziA|PSD8EGo*p8M9:8K3Mt8QHInghI/D8K8Mp8Q

hP (λ, θ)hP ≥ 0

1:;NVPft8QHMcHc9EJI/Dc¨lM Çzt8QHEGe#M\tPSQPO = ρegh

:;c9E 8EGMZD&o*p8MÁNJMOFUMZQ9e#M\e«P<FUEJdQHMOK8pefI/e#MD¦FiZEJD3AFUEGo*p8M¾IziA|PSD3EJo*p8MOcZ¨sAZiQHEGF

[HO] = −R4e

∫ π2

−π2

∫ 2π

0

(1 − f(λ, θ))ρwh(λ, θ) sin2 θ

cos θ cosλcos θ sinλ

sin θ

dθ dλ¹rz?ª_n

~MFUMZQ9e#MK8MZciI/p8QHPSD¦FUcIiZA|PnD8EJo*p8Mc:8K8MzE´FUMcHcHMc~v:8cZ¨sAZiQHE´FK8Me#PSD8EGdZQHMBPSDPSNGI//p8MBPSpFUMQHefM

K8M¾/MD¦F ¹rz?ª_n

[hO] = R3eρe

∫ hP

h=0

∫ π2

−π2

∫ 2π

0

sin θ

vθ sinλ+ vλ cos θ cosλ−vθ cos λ+ vλ cos θ sinλ

−vλ sin θ

dh dθ dλ¹rz?`kS¥

. ' . ! '! .0%'! . ' 0!#. )+! (' )+ )+!% & &! &!

~MZc±IziA|PSD3cQ9MZt8Q9AZc9MZD¦FUMN½¨sAZo*p8EGnPSNGMZD¦F:K¨sp8D8MiIzo*p8EGNJNJM®K8M_/rS¥/¥eºK¨lAtPSEGcHcHMp8Q±iZI/pzzQHPSD¦F±FUI/p3FHMNVPRcHp3Q9g6PSiMÁFUMQHQHMc9FHQHMS? D&MZDFUEJQ9M\NJP#e#PScHc9M\IiZAZPSD8EGop3M

MO ≈ 1, 3 1021 *8?¢B¨sMZcmFMD*EGQHI/D _SrS¥ghI/EGcNVPXe#PScHc9M]K3M]N¹¨`P<FUefI/cHt83dZQHMn?Ã iI/D¦FUQUPnQHEJINVPÊzE´FUMcHcHM«e#Ib/MD8D8MK3MZcXiI/p8QUPnD*FHcÁMc9FvK8M#N½¨sI/QHK3QHMfK8M

vO = 1iZe nc&:·PSp!NJEJMp

K8MvA = 10

e1<ctISp8QNJMc/MD*FHcZ?Y~MZc¾iI/p8QUPnD*FHcZI/DPnpzÇ0D8Mvc9MRK8ASMZNJISt8tMD¦F\t8PSc¾cHp8QFHI/p3FHMvNVPcHp3Q9g6PSiM#K8Mc\IiZAZPSD8c&:Ye#PSEGc¾cHMZp3NJMZefMZD¦F\KPSD8c]N½¨s8Ae#EGcHt88dQHMRcHp3K!I NJMc\iI/D¦FUEJD3MZD¦FUc]D8MRghI/D¦F\t8PSc

rx

I 8cmFTPSiNJMc2ZÊiZMc\iI/p8QUPnD*FHc hKPSD8c]NVP PSD3K8M#K3M#NJPnFUE´FUp8K8MRk/r©mÂn¥

ap8K:$cHI/E´F\_S¥ K8MRNJPc9p8Q9g6PSiM

FUMQHQ9MZc9FHQHM\PSpÊt8NJp3cZ?~MefI/efMZD¦FiZEJD3AFUEGo*p8MQHMZNJPnFUE´gP(Ç3EJPSN8o*p8EuMZD#QHAZc9p8NGFHMSPnp3FPnp#t8NGp8c

MO/MA vO/vA 0.2 r

K8M¾iMZNJp3EK¨sI/QHEG/EJD3MPnFHe#I/c9t88AQHEJo*p8M 6cHISEGFMD¦zEGQHI/Dr x|¥ 24 ve 2 c −1 ?8@BM¾NJPÁtPSQmFK8McIziA|PSD8c&:8EJND¨ bÊPRK8I/D8iOtPScNGEJMpK3M]c¨`P<FHFUMD8K8Q9M'ZRp8DÊM¸MFEJeftuI/Q9FUPSD¦FKPSD3cNJPvNJI/D8SMZp8QK3pvÀ9I/p3QZ? #. &!(' ! &% &!

~MZcc9AZQHEGMZc®K8MBefI/efMZD¦FiZEJD3AFUEGo*p8MBIiZAZPSD8EJo*p8McHISD*FtMpD8I/e 8QHMp8cHMcZ?8@BPSD8ciMo*p8EucHp8E´FD8ISp8ciZISD8cHEGK8AZQ9I/D8c¾iZMNJNGMXK8MR.ISD*FHMfPnF]PSN½? x|//wo*p8E·iZI/p3Q9MfNJPtAQHEGIzK8MBx/w¦r©;x/SP|/MZiRp8D tPnc¾K8MrfÀ9I/p8Q9cfMF#P AFUAÊMZcmFUEGe#AMÊPSpefIb/MDK¨sp8D e#IK8dNJMK8MiZEGQHip8NVPnFHEJI/D!IziA|PSD8EGo*p8MLiZI/D¦FHQUPSEGD*FftPnQNJMc#K3I/D8D8AMZcP<FUefI/cHt83AZQHEGo*p8MZc#K8pt8Q9I<À9MF#K8MQHA|PnDPSNGbc9M/NGI PSNGMLK8pÉB¢± nÉ¢ÃO?»¼ND¨ bPtPScLK¨`PSc9cHEGe#EGNVPnFHEJI/D[K8M0K8ISD8D8AZMcÊIziA|PSD8EGo*p8MZc&:iS¨sMZcmF ZK8EJQ9Mo*p¨`Pnp8iZp8D3M²I8cHMQ9nPnFUEGI/DD8MEGMZD¦FiZISD*FHQUPSEGD8K8Q9M0NJMefIzK3dZNJM&K8M0iZEGQHiZp3NVPnFHEJI/D TZNVPK8E´¸AQHMD8iZM K8McLe#IK8dZNGMZcLP<FUefI/cHt83AZQHEGo*p8MZcÊo*p8Eq:MZpÇR:cHI/D¦FOiZISD*FHQUPSEGD¦FUc¾tPSQBK8MZc¾/Q9EJNGNJMZcK¨sI 8c9MZQ9nPnFHEJI/D3c ?~$Mc¾e#ISe#MD*FHciZEGD8AFHEJo*p8Mc 6t8Q9MZcHc9EJI/D0MFiZISp8QUPSD¦FHc ®c9I/D¦FQHMZt3QHAZc9MZD¦FUAccHp8QNJPX¶·EG8?zrz?ªr]K8M x/Sk Z x//rz?3~$P\nPSQ9EVPnFHEJI/D#cUPSEGcHI/D3D8EJdQHMBK8PSD8cNGMFUMQHefM¾K8M]t8QHMcHcHEGI/DiZI/efe#MBKPSD8cNJM¾FHMZQHefM/MD¦FBMc9FK8M]N½¨sI/QHK8Q9M¾K8M

0, 3 1024 *fe 2 c −1 :cHI/E´F:x¥ghI/EGce#I/EGD8co*p8MOKPSD3cNGMe#ISe#MD*FiEJD8AFUEGop3M\P<FUefI/cHt83AZQHEGo*p8MS?

W 1*&,' (!)fc ) )"/c , "/e %'c !-. &-(!)fc )" % klf,'! '&)(!)fc c (-* C% -. &)f "/, "$ 1%' (!)+*, 45)-/-6)

! . &! )+,!-)+!%(' &!ÉI/p3cD8I/p8cBEJD¦FUAQHMZc9cHI/D3cOPSpzÇp8iFHpPnFHEJI/D8cPSpefI/EJD8ccHp8tuAZQ9EJMp8QHMc0Z¥OÀ9I/p3QHcZ?@PSD3c¾iZMXK8I<©

e#PSEJD8MBNJMZcK3AZQHE´/AMZcFUMe#tuI/QHMNJNGMZcK3MZcghI/D8iFUEJISD8cK8MOe#ISe#MD*FiZEJD3AFUEGo*p8M¾tMp3/MD¦F <FUQ9M]D3AZ/NGEJ/AMZc:MFN¹¨lAop8PnFUEGI/DLK8pe#I/pz/MZefMZD¦FK8pt¿SNJM¹rz? |cZ¨sAZiQHEGF

m +i

σ∗c

m = χmat eff + χmv eff = χeff ½r?`k

~MfefMZe 8QHMvK8MR¦Pnp8iT8MfK8MRiZMF9FUMRAZo*pP<FUEJISDiI/D8c9FHEGFHp8MvN½¨sMÇziZE´FTPnFHEJI/D0Ao*pPnFUISQHEVPnNJMÁFHISFTPSNGMvo*p8MN½¨sI/DÊtuMZp3FK8AK8p8EGQHMOK8MZcI 8c9MZQmSP<FUEJISD8c/AZIK8AcHEJo*p8Mc 3iS¨sMZc9FN½¨ + 1 #%

χG = m+i

σ∗c

m½r?`k¦_

o*p8MN½¨sI/D SP0iI/e#t8PSQHMQWZ²N¹¨lM Ç3iEGFUPnFUEGI/D /AZISt8¦bzc9EJo*p8MAZo*pPnFHI/QHEJPSNJMj:I/p[MÇziEGFTP<FUEJISD K3MZcfiZI/p8iT3MZcp8EGK8MZc

χFhe#Me 8Q9MÁK8MXK3QHI/E´FUM iZI/eft8Q9MZDPSD¦F¾N¹¨lM ÇziZEGFUPnFUEGI/DP<FUefI/cHt83AZQHEGo*p8M

χAMF¾N½¨sMÇziEGFTP<FUEJISD

IiZA|PnD8EJo*p8MχO?

~MfiZPSNJip8NK8MRN¹¨lM Ç3iEGFUPnFUEGI/D0/AZISt8¦bzc9EJo*p8MfKPSD8cONGMvK8I/e#PSEJD8MÁK8p²FHMZeft8cZLtPSQ9FHEJQK3MfK3I/D8D8AMZcK8EGcHiZQ9dFHMZcQ9MZtuI/cHMc9p8Q·p3D8Me#PSD8EJt3p8NVPnFHEJI/D¾D*p8efAZQ9EJo*p8M 6K8AQHEGSAZMFHMZeftISQHMZNGNJM MFc9p8Q·NGMiT8I/EÇ\K¨lp3D8MnPSNJMp8QK8MvNJP#ghQHAo*p8MZD8iM#K3Mf¢PSD8K8NGMZQ

σ∗c

?$¢B¨lMc9FOiMZNJNGMXK¨sp8D I/cHiEJNGNVPnFHMZp8QBPSe#ISQ9FUEYMFOc¨lAiZQ9EGFOcHISp8cghI/Q9e#M¾iI/e#t3NJMÇzM /I/EGQtPSQUPn/QUPSt38M¾^8?`Â

r/_

1993 1993.2 1993.4 1993.6 1993.8 1994 1994.2 1994.4 1994.6 1994.8 1995

0.2

0.4

0.6

x1

e2

4

H1 − pression

1993 1993.2 1993.4 1993.6 1993.8 1994 1994.2 1994.4 1994.6 1994.8 1995

−0.4

−0.2

0

0.2

0.4

x1

e2

4

H2 − pression

1993 1993.2 1993.4 1993.6 1993.8 1994 1994.2 1994.4 1994.6 1994.8 1995

−1.5

−0.5

0.5

1.5

x1

e2

4

H3 − pression

1993 1993.2 1993.4 1993.6 1993.8 1994 1994.2 1994.4 1994.6 1994.8 1995−0.4

0

0.4

x1

e2

4

h1 − courants

1993 1993.2 1993.4 1993.6 1993.8 1994 1994.2 1994.4 1994.6 1994.8 1995

−0.2

0

0.2

0.4

x1

e2

4

h2 − courants

1993 1993.2 1993.4 1993.6 1993.8 1994 1994.2 1994.4 1994.6 1994.8 1995−0.4

0

0.4

0.8

x1

e2

4

h3 − courants

rz?`r WYMZQ9e#McK8MXt8Q9MZc9cHEJISD0MF¾K8MÁiZI/p8Q9QUPSD¦F¾K3p0e#I/efMZD¦FBiZEJD3AFUEGo*p8MÁIiZAZPSD8EJo*p8MÁK8M /SkZ//rvMD *Re 2 c −1 ghI/p3QHD8EFHI/p8cNJMcrÀ9ISp8QHctPSQYI/D¦FUM]MFPSN¹? //w

rSk

σ∗c = σc(1 + i/2Q)

½rz?lk/k~MZcSPnNJMZp3QHcK8M

σcMFQnPSQ9EJMZD¦F®K¨sp8D8MBAFUp8K3M0Z\N¹¨`PSpzFUQHMn?*~$P\tuAZQHEGIzK3MK8M¢PSD8K3NJMZQMZcmF^¦k/_À9I/p3QHc

Z .À9I/p8Q:t8Q9dZc&:/MF±c9I/Dfg6PniFUMp8Q:K8Mo*pPSNGEGFHAI/cHiEJNGNJMMD¦FUQHMQ = 50

MFQ = 180

?/ÉI/p8c±P|/ISD8cPSK8I/t3FHANVPÁnPSNGMZp8QANJM/AZM

Q = 179iI/QHQ9MZc9tI/D3KPSD¦F ZRN¹¨lMc9FHEJe#PnFUEGI/D«K8M EGNJcHISDLMF¬EGiZMD*FHM /S¥?3ÉI/p8c

P|/I/D3c\t8Q9EJc¾p8D3MRghQ9AZo*p8MD8iZMfK8M#¢PSD8K3NJMZQ¾K3M#¥z?`wS^/k¦r«iZtP 6ibiZNJMvt8PSQ]PSD 1:cHI/E´F¾p8D8MRtuAZQHEGIzK3MvK8M^¦k/kÀ9I/p3QHcZ?

ÉI/p3cP|/I/D8cK8AZQ9EG/ABN½¨sMÇziZE´FTPnFHEJI/Df/AZIK8AcHEJo*p8M_ZÁtPSQmFUEJQ±K8McK8I/D8D3AZMZcK8MefI/p3/Me#MD¦FK8ptu¿/NGMK8M®N½¨s»a hcHAQHEJMiZISe 8EJD3AZM$À9ISp8QHDPnNJEJdQHM:»±aX¢¥S^ ?n~:¨sMÇziZE´FTPnFHEJI/DÁPnFUefI/c9t88AZQ9EJo*p8Mp3FUEGNJEGcHAZM±KPnD8cN½¨sAFHp8K8MMc9FiMZNJNGMBK8pÊÉB¢± nÉ¢Ã :K8A¼ÀZXK8AZiQHEGFHMt8NGp8cPSpzF|?8ÉI/p8cpzFUEJNGEJc9I/D8cN¹¨`Pnt8t8QHI|ÇzEJe#PnFHEJI/DK8E´FUMK8p PnQHI/efdFHQHMEJD¦/MQHcHM 6» ?®~$P²cHAZQ9EJMK8M&efI/efMZD¦FfiZEGD8AFHEJo*p8MIziA|PSD8EGo*p8M9:iZI/D¦SMZQ9FHEJMMZDghI/D8iFUEGI/DÊK¨lM ÇziZEGFUPnFUEGI/D:zMZc9FiZMNJNGMK8M].I/D¦FHM\MFBPnN½? //w iZI/p3QHPSD¦FNJPXtAQHEGIzK8M |/w¦rz?l¥<© |//3?lk3?

~:¨lAiTPSD¦FUEGNJNJISD8DPS/MK8MccHAQHEGMZcK¨lM Ç3iEGFUPnFUEGI/D#SAZIK8AZc9EJo*p8MBMFPnFHe#IScHt88AQHEGop3MBP]AFUAi|PSNGo*p8ABc9p8QiZMNJp8E$K8M]NVPRcHAQHEGM\IiZAZPSD8EJo*p8Mn?u~$MOCN´FUQUPn/M¾MFN½¨sEJD¦FUMQHtuI/NVP<FUEJISDD8AZiMZc9cUPSEGQHMZc_ZfiMFHFHMÁI/tuAZQHPnFUEGI/DÊI/D¦FAFHARQHA|PnNJEJc9AZct8PSQOPSt8t8NGEJiZPnFUEGI/D&K¨sp8D CNGFHQHMX/PSp8cHc9EJMD²K3MftuAZQ9EJIK8MXK8MvK3MZefE´©¼iI/p8t8p3QHMXK8M¥]À9ISp8QHc&:AZNGEJefEJDPnD*FONGMZc\PSp3FHMZcÁghQ9AZo*p8MZD3iZMZc&::MFÁEJD¦FUMQHtuI/NVPnFHEJI/D²tPSQ\tISNGbD8¿/efMZc]K8ML~$PS/QHPSD8/MfK¨sI/QHK3QHM^8?~MZcc9AZQ9EJMZcBI 3FUMD*p8MZc¾c9I/D¦FFUQHPSiZAMZcOP|/MiXNJMp8QBc9tMiFUQ9MvK8Mv¶I/p8Q9EJMQc9p8QNJMcCSp8QHMcOrz?l

χG1:rz?`Â

χA

®MFr?`w χO

?~$PÁC/p8Q9M]rz?lXe#I/D¦FHQHMNJPÁiZI/e 8EJDPnEJcHISDK8M¾N½¨sMÇziEGFTP<FUEJISDLPnFUefI/c9t88AZQ9EJo*p8M¾P|SMZiN½¨sMÇziEGFTP<FUEJISD#IiZAZPSD8EJo*p8Mn? DD8InFUMo*p8MNGMZct3EJiZc®cUPSEGcHI/D3D8EJMQHcc9I/D¦FuM|PSp8iI/p8tLt8NGp8ce#PSQ9op3AZcKPnD8cNJMcMÇziZE´FTPnFHEJI/D3cp8EJK3MZco*p8M\K8PSD8cN½¨sMÇziZE´FTPnFHEJI/D«I 8cHMQ9SAZMS?

~MZciZI/eftPSQHPSEJc9I/D8cKPnD8cNJMK8ISe«PSEGD8MK8pÊFUMe#t3cMD¦FUQHMON¹¨lM Ç3iEGFUPnFUEGI/D/AIzK8AcHEGop3M]MFiZMZNGNJM¾K8MciZISp8iT8MZcÊp8EGK8MZcLc9I/D¦FQHMZt3QHAZc9MZD¦FUAMZccHp8QÊNVP!C8/p8QHM²r? ¥:PSt8Q9dZcÊP|/I/EGQLQHMFUEJQ9A0p8D8MFHMZD8KPnD8iZM5ZiTPSip8D8M]K8MZccHAQHEGMZctPSQCN´FUQHPS/M¾¦PSp3cHcHEGMZDP|/Mi\p8D3M\tuAZQ9EJIK8MK8M]K8MZefE´©+iZI/p3t8p8QHMBK8M]/¥/¥À9I/p8Q9cZ?

1985 1990 1995

-400

-300

-200

-100

0

100

chi_G composante 1chi_G composante 2

r?` ! "#$ %'&χG (*) ,+.-0/21 34506 78#"'9;:=<=>@?A1BC9;:=:=D@?AE@?F G 6IH%.@JHK#"L"GM6 GN%2OP#"GBQ@%NH! #R &PH!4S?

TVU W7XZY[U s X \]UZ^_W5`KUaXZY@bSbdc e]f_\gY@^0U ^_bdUCe]UZWhWSc bd\]UZW7`ijUlk[X \$_f_S\]Y@^0m@cZY[`nc WS\gopKUCUl_7m@cZY@qKrs!WS\go!pnU WWSY^_5X fe]XZpKe]cZWLWSU egY@^tePfCuvY@bdwxpKe]U7m@c ^KcZbfegU : q*Y@pKbL`KUZp[ktWScZbS\gU WL_UZwyq*Y@bSUZe]egU W

XUZ_Y

C(X, Y ) =σ2

XY

σXXσY Y

z|!~Y ePfMXZYfbd\Pf^nX U

σ2 U W_

1985 1990 1995-100

0

100

200

300

400

chi_A composante 1chi_A composante 2

[ a 6 =H# ! "#$ %5&χA ( / /.+ +G; ! %Q@H#"d4 6 8#"I9;:=<=>@?A1 9;:=:=D@?AE@? F G 6IH% @BHK#" "8 M6 N2% OP#"8 MQ@%2H! #G

&PH!4S?

1985 1990 1995-40

-20

0

20

40

chi_O composante 1chi_O composante 2

! ; 8B! "#$ %&χO ( 8"JC %v? 9;:=:=<4I6 a8#"9;:=<=>@?A1 9;:=:=D@?AE@? F . 6IH%G@J"Hn#"L"GB6 G%2O]#" JQ@%NH! #G &PH!4S?

1985 1990 1995-100

0

100

200

300

400

chi_F composante 1chi_F composante 2

[ 0V@ " % 6 =H#8 ; ! "#$ %M&χF4 y6 8#"C9;:=<=>@?A1

h9;:=:=D@?AE@? F G 6IH%R@B"Hn#"h8GM6 RN%2O]#"GBQ@%NH! #R &PH!4S?

@

1985 1986 1987 1988 1989 1990-100

-50

0

50

100m

aschi_Gchi_A+chi_Ochi_A

1991 1992 1993 1994 1995 1996-100

-50

0

50

100

mas

X

1985 1986 1987 1988 1989 1990-100

-50

0

50

100

mas

chi_Gchi_A+chi_Ochi_A

1991 1992 1993 1994 1995 1996-100

-50

0

50

100

mas

Y

[ / 6IH! # " %76 @'"6IH5L"#L S@ ( 6 H# ; 8h. 6 =H#85"%LHK#N%$I6IHn=d 8"x&P ! d42

y&P!d4S?

[ Y!UJX \gU ^_W `KUMXZY@bSbdc ePf8_\]Y^ U ^_SbSUMe|ijUlk[XZ\g_f8_\]Y^ m@c Y!`KcZWS\]opKUMUl_Ie]UZWIUlk[X \$_f_S\]Y@^nW f_wJY@WSqKrnc bS\gopKU z Ul_hY[XZcf^K\gopKU

[ n ~(χG, χA) (χG, χF )

@

σ2XY =

1

N

N∑

i=1

(Xi − X)(Yi − Y )z|!~

XUZ_Y`KcZWS\]m^ f^_ e]UZW2fe]U pnbSWNwJYsU ^K^nU WG`KUhWSc bd\]UZW

XUl_Y TVU W X YbSbScZePf_S\]Y@^nW2`KU @ n ~

WSY^_RbSUZq Ybd_cZWR`Kf^KW ePf _fKe]U [ ^y^nY_UhpK^KU fwJc eg\]Y@bSf_\gY@^C\gwyq*Y@bd_f^_UL`KUhe]f XZY@bSbdc e]f_\gY@^Bo!pn\uvbf^KXrK\g_5f\]^KWd\ePf! fbSbSUI`nU W Wd\Ve|ijY@^0f#"dY@pn_SU e]U WLU%$ Ul_WhY!X cf^K\]opKUZW TNi U%$ Ul_5U Wd_5Wdq UZXZ_fX pKe]f\]bdUWSpnb ePf X Y@wJq YWf^_U

xq Y@pnbRe]fopKU ege]U5e|i fwycZe]\gY@bf_S\]Y@^CU Wd_ qKb'&ZW `KU e]egU UZWd_L`KU ~ q YpKb.e]f

X Ywyq*Y@Wf^_SUy

Y@pnbxop f^_\)( U bae|ijU$ UZ_xwJY=s@UZ^+* WdpKbxpK^ \]^_UZbdfe]egUB`KU'_UZwyqnWC`KY@^n^Kc,* `KU'e if_SwyYWSqKr-&ZbSUyY@p`KU e i Y!X c f^ WdpKb egU wJY@pn@UZwyUZ^_ `Kp q/.@e]U* ^KY@pKW fY@^KW U W_\gwyctq fbywyY@\g^K`KbdU W'X fbSbdc W egU W'fw0qKeg\g_pn`KU W `KUZW _U bdwyUZW qKbS\g^KX \gq fp[k ` f^KW0egU W uvY@^KXl_\gY@^KW ìjUlk[X \$_f_S\]Y@^21hf^K^pKU egW3* WdU wJ\)"f^K^pKU egWUZ_a_UZb"f^K^pKU egW3* qKbSY@mbf`KUZWCUl_xbScl_bdY@m@bf`KU W TVU'wJY!`-& egUJopKU'^KY@pKWCf#"dpKWd_SY@^KWxWdpKbCegU W uvY@^KXZ_S\]Y@^nWìjUlk[X \$_f_S\]Y@^

χX Y@wJqKe]U;k[U WhX Y@wJq*Y@bd_SU fpKWSWd\VpK^KU q UZ^_U

atUl_ pn^4K\]f\]W

b1

χ = χ1 + iχ2

z|!~ @=

∑

j

Cjeiωj(t−t0) + at+ b

=∑

j

Ajei(ωj (t−t0)+φj) + at + b

Y65Cj

UZWd_te|i fwJqKe]\$_pK`KUtX YwyqKegUlk[U q*Y@pKb0e]U _SU bdwyU `KU uvbdc opKU ^nX Uωj

T,f `KY@^K^nc U`KUCj

U W_c opK\$fe]UZ^_SU e]f `nY@^K^KcZU ìjpK^KUIfwJqKeg\g_pn`KUhbSc UZe]egU

Aj

Ul_ ìjpK^KU qnr fWSUφj

bfqnq Y@b_cZU pK^nU7` f_SU(nk[U ^tqKbf_S\]opKU*Ke]U _SU bSwJUIq*c bS\gY[`n\]opKU

jWZi cZX bd\g_71

χ1 = A(ip) cos(ωt) − A(op) sin(ωt)z [~ @

χ2 = A(ip) sin(ωt) + A(op) cos(ωt)

Y65 egU WxfwyqKeg\g_SpK`KU WAWdY@^_x_Y@p[_U WCbSc UZe]egU WCUl_Me]UZWxUlk[q*Y@Wf^_SW z

ip WdY@^_MwJ\]WCq*Y@pKb98Z\]^ qKr fWSU,*:8

`KcZWS\]m^ f^_ egU _SU bSwJU U ^ qKrKfWSU z \]XZ\;* egU _SU bSwJU U ^ XZY@WS\g^!pnW `KUCe]fJqnbSU wJ\:&ZbSU X Y@wJq*Y@Wf^_SU UZ_ zop

WSY^_JwJ\]Wxq*Y@pKb<8lY@pn_= Yu>qnr fWSU*>8'_SU bSwJU rKY@bdW qKr fWdU3? z \]XZ\;* e]U _UZbSwJU U ^ WS\g^!pnWJ`nUte]f qKbSUZwy\@& bdUX Ywyq*Y@Wf^_SU ; T,UZW U Wd_S\]wyf_\gY@^KW*U$ U Xl_pKcZU WRWSpKb ePf q*c bd\]Y!`KU @[ n~ *WdY@^_RbdU q*Y@bd_Sc UZWR` f^KW

AB%CD#EFCHG+IKJ#LMONI=PIQ3NRIQTS3CHL%UWVXLYN;C#V;IZUWI[DH\HL%GI%]

! 6 N "#6 8% ( "6I % "# % 2% OP2 S ( 6 ="H#8ya; 8 6IH%x6 C H!" # HHn#"% HK=1=1=1@?A1@? # 9;:=<=>@?A1 9;:=:=D@?AE ( "#5 6 =H# / /R+ ( "#h; h 8"5. %v? & 9;:=:=<4S?

χG χA χO χFXZq f w'fW wyfW w'fW wyfW ~[6 [

nj [

n

nj

n ~ [

Kj~

n [

[ @~n

[ ~ [

[ nj

[ [

[j Kj

n ~ !

K @~ j

[~ @

~n ~

~ [ !

[F

[

[ [

~ ~n nj@

~ n

~ ~ [

[ K

ePf _f,Ke]U ![ ^KUbSUZqKbScZWSU ^_f_\gY@^ m@bSfqKrK\gopKUWSY@pKW0uvY@bdwyU `KU U XZ_SU pKbdW ` f^nWtegU qKePf^ XZY@w0qKegUlk[U z \gm [ q*U bdwyUl_GìfqKqKbScZX \gU b e]U K\gePf^M`nU5wJY@wJU ^_ X \g^KcZ_S\]opKUh`KpJWds!Wd_'& wJU U bdbSU5WSY@eg\]`KU f8_wJY@WSqKr & bSU Y[XZcf^KW TVU W fe]UZpKbSWRY6n_SU ^pKU WL^nU bSU &Z_SU ^_hq fW e]faq*Y@WS\$_\gY@^y_SU bSbdU W_bSUI`np q .@egU `nU bSY_f_\gY@^ U ege]U X \

q*U pn_Z_SbSU `Kcl_U bdwy\g^Kc UIUZ^\g^@U bdWf^_ e|ijc op f_S\]Y@^ z [~ ` f^nW5egUI`KY@wyf\]^nU `KU WhuvbScZopKU ^KXZU W 1

m(σ)

(

1 − σ

σ∗c

)

= χeff(σ)z [~

f^nW7ePfM_fKe]U [ ~ ^KY@pnW7bSUZq Ybd_Y^KW egU W U$ UZ_W Wf\gWSY@^n^K\]UZbSW f_wJY@WSqnrKc bd\]opKU UZ_ Y!X c f^K\go!pnUaWdpKb7egUwJY@pn@UZwyUZ^_ `Kp q/.@egUx`KUMbSY_f_S\]Y@^ Ul_ e]U W fbd\Pf_S\]Y@^nW7Y6KWdU b@c UZW YpKW X Y@^KW_f_SY@^KW opKUMe|i f#"dY@p[_`KUZW Y!X c f^KWhbSUZ^K`wJ\]UZp[k XZY@wJqn_UI`KptXZs!XZe]U Wf\gWSY@^n^K\]UZb

! "#%$'&($')+*-,+"-."#0/"213)+"#TVU WhfbS\Pf8_\]Y^KW.`KU e]fBegY@^Km@pnU pKb `np "dY@pnb5WdY@^_5`Kc `Kpn\g_UZWh`KU e|ijc op f_S\]Y@^ z [8 1

∆LOD

LOD= χmat eff

3 + χmv eff3

Y@pnbxX Y@wJq fbdU b e|ijUlk[X \$_f_S\]Y@^ m@c YqKrs[Wd\]opKU fp[k4KpKXZ_Sp f_\gY@^KWaY6KWSUZbdc U WM`nU ePfte]Y@^KmU pKb `Kp"dY@pKb*\ge!u fpn_2qKbdcfe]f,KegU wJU ^_ bdUZ_S\]bSUZb `KU.X U ege]UZWXZ\[egU W U$ UZ_W cZ_bSf^Km@UZbSWNfp[kxU;k[X \g_f_\gY@^KW `KU WKpK\]`KUZWWSpnq UZb=( XZ\]U egW

CijpK^KU q fbd_5^KYpKWhWf@Y@^nW7opKU WSY@pnW e ifXl_\gY@^ `KU W5wyfbScZU W5 Y@^Kfe]UZW z `KcZq UZ^K` f^KXZUCUZê]f_\$_pK`KUWSUZpKe]U *!e]U wyY@wJU ^_Gìj\]^KUZbd_S\]U f8k[\Pfe `KU e]f6 U bdbSU WdY@e]\g`KUhfbS\]U*UZ_ \g^K`KpK\$_.`nU WRfbd\Pf_S\]Y@^nW _Sb'&ZWK\]UZ^wJY[`KcZe]\gWSc UZWa`nU'ePf0e]Y^Km@pKUZpKba`np<"dY@pKb* `nU'e|ijY@bd`KbSUJ`KU wyW Ul_xU%$ Ul_x`KUyw'fbdc U75 Y@^Kfe]UZWCU W_\]ege]pKW_bdc WSpKbhe]f \]m@pnbSU [ ~n

Ci fpn_bdUBq fbd_3* qKbdY6 f,ne]U wJU ^_ X fpKWSUB`KUMe i \g^_U bSfXZ_S\]Y@^ U ^_bdUJegUx^KY=sfp Ul_ e]Uxwyf^_U fp+*e]fe]Y^Km@pKUZpKbR`np7"dY@pKb8 pKXZ_SpKU7`nU wJWRUZ^[\gbSY@^ f=U XI`KUZW.q*c bd\]Y!`KU WRXfbSfXZ_Sc bS\gWd_S\]opKU5`KU ~ * ~ UZ_

[ %$ 0I6 6 85 #"B9;:=<=>@?A1M 9;:=:=D@?AEM"LOP#6 I"#" L%H%$ J6IH%S=? # RH% χG ( "6I vH% χA ( Hn%% χO& 8"7G %v? 9;:=:=<4S?

[ ~ ,6 R "#6 G % ( "6I %RN"# % N% 6 6 8 @H % 6IH%h 6 H!" # HHK#" % HK8 =1=1=1@?A1@? #M9;:=<=>@?A1 9;:=:=D@?AE ( "# 6 =H#/

/R+ ( "#h; 85 " G %v?*& 9;:=:=<4S?

pG pA pO pFXZq f wyfW wyfW w'fW wyfW [j

n n

~ [

!@ [

~[ ~ n

n

~n n

~[ @~n

~[@~ @~nj@

[ , n

~

@ @[F

[ ~

~ ~

~ 6[ @~

~K

6[

~ n ~

~ [

~ ~ [@~

Kj@

[j W_\gw'f_S\]Y@^nW `KU W _UZbSwJU W f^K^pKUZe]W3*,WdU wJ\)"f^K^pKU egW Ul_a_SU bK"f^K^pKUZe]W ` f^nWae i U;knX& Wa`KUePf `KpnbSc U0`Kp"dY@pKb z T *2e|ijU$ UZ_J`KUZWywyfbdc U W 5ZY@^ fegU WBUZ_Je]f _U ^n` f^KXZU fsf^_ycZ_Sc0qKbSc fePf,ne]U%wJU ^_IbSUl_\gbSc UZW Ul_Ie|ijUlk[XZ\g_f8_\]Y^ f_SwyY@WdqKrKcZbS\]opKUC`KU qKpn\]W [ 1fwJqKeg\g_pn`KU W5U ^ wJW UZ_ qKr fWdU WbfqKq Ybd_cZU W e|ijc q*Y[opKU

∆LOD χ3 × LODXZq f wJW wyW ~ ~

~ ~KF

F [

~ ~ [F

~[

f^KW i UZWd_7ìf\]e]egU pKbdW e|ij\]bdbScZm@pKePfbS\g_Sc qnbS\]^nX \]qKfe]U* ( m@pnbSc U ` f^nW5egU r fqK\$_bSU 0z \]m !~ Ul_5`KY@^_e|ij\]wJq fXl_ WdpKbho!pnU e]opKUZW7f^K^Kc UZW7fqKq fbSf]_LWdpKbhePf \gm@pKbSU [ z m@bfqKrK\]opKU `KbdY@\g_SU l

^tbdUZ_S\]bf^_ `KU ePfae]Y@^KmU pKb `np "dY@pKb e i U%$ Ul_LqKbScZ`K\]Xl_\@Ke]U `KUIePfCwyfbdc U-5ZY@^ fegU UZ_hUZ^ c eg\]wJ\]^ f^_e]UZWI_U bdwyUZW `Kc XZc ^ fp!k qKfbT( eg_Sbfm@U*^KY@pnWaq*Y@pnY@^KW X Y@wJq fbdU bIePf uvY@^nXZ_\gY@^ìjUlk[X \$_f_S\]Y@^ f_SwyYWSqnrKc bd\]opKU

χ3

UZ_5e]UZWLfbS\Pf8_\]Y^KWL`KpT bScZWS\]`npKU ege]U WhopK\,WSY^_ \]wJqKpn_Sc UZW e|i f_SwyY@WdqKr-&ZbSU z \]m [ @; Y@pKWGu f\]WdY@^KWGX UZ_d_U X Y@wJq fbSf\]WdY@^yWdpKb.e]f _SY_fe]\g_ScL`KU W.`KY@^K^KcZU W `n\]WSq*Y@^K\@Ke]UZW q Y@pnbRe]f Wdc bS\gU *XijU W_ `K\]bdU5`nU qKpK\gW [ TVU XZY[U%JX \]UZ^_ `KU5X Y@bdbScZePf_S\]Y@^BU ^_SbSU7egU W `KUZp[kyWSc bd\]UZW.U W__b=& W5c egUZ@c* ~ *KX U opK\,\]^K`n\]opKU opKUae if8_wJY@WSqKr & bSUIUZWd_ qKbSUZWSopKUaU ^_\@& bSUZwyUZ^_7bdU WSq*Y@^KWSf,KegUa`KUZW pKXl_p f8_\]Y^KW `np T * rKY@bSwJ\]WhegU W5U$ UZ_W qKbScZ`K\]Xl_\@Ke]UZW5`nU W7wyfbdc U W5 Y^ fe]UZW Ul_7egU W pKXl_p f_S\]Y@^nW`KcZX U ^n^ fe]UZW ^ pn_S\]eg\]Wf^_ pn^KUywJcZ_SrKY!`KUBì UZWd_S\]wyf_\gY@^ q fb wJY@\]^K`nbSU W X fbSbdc W WS\]wJ\]e]f\]bdU X UZe]egUpn_S\]e]\gWScZUIq Y@pnb5e i cl_pK`nU `nU W _SU bdwyUZW5WSf\]WdY@^K^K\gU bdW5`np wJY@pn@UZwyUZ^_7`Kptq/.@e]U z \gX \*n^KY_SbSU wyY!`-&Ze]UIU W_WSYpKW ePf7uvY@bdwyU

A cos(σt+φ) *^KY@pKW f@Y^KWRUZWd_S\]wJc e]UZW fwyqne]\g_SpK`KUZW `KUZW _SU bdwyUZWNWf\gWSY@^K^n\]U bdWN` f^KW

e|ijUlk[XZ\g_f8_\]Y^Bf_wJY@WSqnrKc bd\]opKU5UZ_Gm@c Y!`KcZWS\]opKU T,UZWRfegU pKbdWGWdY@^_.bdU q*Y@bd_Sc UZWR` f^KWRe]f _f,KegU [ n T,UZW`K\)$ cZbSU ^nX U W5\]^nUlk[qKe]\gopKc UZWL^KU `Kc q fWSWSUZ^_ q fW wJW

1985 1990 1995 2000

-1

-0,5

0

0,5

1

ms

LODAAM

[ / 6IH! # 8#"M%= #$ I@ F &P 6 #";! % " #"#"d4 %$'O S 6 =H#yZ@$ %JHy9;:=< 3?A1@? F A#" H#""H! # Ov ;?

1985 1990 1995 2000-1

0

1

2

3

4

ms

LOD

DS99

1994 1995 1996-1

0

1

2

3

4

ms

LOD

DS99

[ ~ #$ yL%$ @#"h@ # &P"# ) ,+.-M/21 34NGK G6 #";! % H! ##@B6 %L SO]# =5R-6I"59;:=:=:B& -@:=:4S? @#"" ( ;6 #N% = #$ G #";?

1985 1990 1995 2000-1

-0,5

0

0,5

1

ms

1985 1990 1995 2000

0

1

2

3

ms

[ 8 ( #$ 7,% S 7 6 =H#2Z$ %.& / /.+ +G; ! %Q@d4 (% h"%$ #"B&]"#6 I 8 L%; #"l4LQ8 5" #"#"=? @#"" ( = #$ t7%$x@#"I@#C&P"# ) +.-t/21 34L#"@%%M H# 7 # #"#"a% 6 #" ;! %M&]6 %a SO]# =C-6I"59;:=:=:4NN% S@ 6 =H#8 %$7" 5! % 6 #"

"! $# % ! $# & ' ( ) ! (

*,+.- /103254 67.8:9;2=<TNifXZX cZe]c bSf_\gY@^0m@bf!\g_f_\gY@^K^KUZe]egU5_SU bSbdU W_bSU

~g`Kc bd\g@U `Kptq*Y_UZ^_S\]UZem@bf!\g_f_\gY@^K^KUZe

U1

∇U = ~gz ?>

^ `Kc wJY@^_bdUIopKUIX UI`KUZbS^K\gU bLUZWd_h`KcZX Y@wJq YWf,KegU U ^0pK^nUIWSY@wJwyU ìjr fbSwJY@^K\gopKU W WdqKrKcZbS\]opKUZW1

U(r, φ, λ) =GM

r

+∞∑

n=0

n∑

m=0

(

Re

r

)n

(Cnm cosmλ + Snm sinmλ) Pnm(sin φ)z F@

YA@rU Wd_0e]f `K\gWd_f^KX U m@cZY[XZU ^_bd\]opKU*

φe]f ePf_S\g_SpK`KU Ul_

λe]f e]Y^Km@\g_SpK`KU`Kp q Y@\g^_ fpKopKUZeIY@^

`Kcl_U bdwy\g^KUIe]UIq*Y_SU ^_\gU eABGU W_ e]fxX Y@^nWd_f^_SU m@bf!\g_f_\gY@^K^KUZe]e]U*

Ree]UIbfsY@^cZop f_YbS\PfewyY=sU ^

_UZbSbdU Wd_SbSUIUl_MePfCwyfWSWdU `KUIe]f U bSbdUCB

CnmUZ_Snm

WSY@^_he]UZW X Y!UJXZ\]U ^_SWL`KU _SYADUZW3* `Kc%( ^K\]W.`KUePfxwyf^K\@& bdUIWSpK\$f^_SU01

Cnm =1

MRen (2 − δ0m)

(n−m)!

(n+m)!

∫

M

rnPnm(sinφ) cos(mλ)`M

z ~

Snm =1

MRen (2 − δ0m)

(n−m)!

(n+m)!

∫

M

rnPnm(sinφ) sin(mλ)`M

Y65(r, φ, λ)

WSY^_7e]UZW XZY[Y@bd`KY@^K^nc U W `KUCe i cZe]cZwyUZ^_5`MUl_7egU W

Pnm(sin φ)WSY@^_ egU WFEHGJILK;MONPGJIRQTSVU

WXUPYVU;IS[Z\U]SVU_^Z\U;àNPb;Z\UTUcQdêbcKcU z @Y@\gb fKe]U f> 1

Pnm(x) = (1 − x2)m/2dmPn(x)

dtmz

Y650e]UZWPn(x)

WSY^_5egU WgêGJhjiJILkJ`1UcQ]SVUlWXUPYVU;IS[Z\U1

Pn(x) =1

2nn!

dn(x2 − 1)n

dxn

z Y_Y@^KWhopKU

Pn(x) = Pn0(x)

@~

Y@wJwyUhe]UZWRq*Y@e$s[^ .@wyUZWPnm(sin φ)

fpKm@wJU ^_UZ^_._b=& WRbfqK\g`KU wJU ^_GU ^yfe]U pnbRfKWSY@egpKU f=U Xe]Ua`KU mbSc

n* UZ^ qKbf_S\]opKUaY@^ qKbdcZu & bdUxpn_S\]e]\gWSUZb5egU pKb5uvY@bSwJU ^KY@bSwyfeg\]WScZU 1

Pnm(sin φ) = βnmPnmf@UZXβnm

e]UIXZY[U%yXZ\]UZ^_5`KU ^KYbSwyfe]\gWf_S\]Y@^y`KY@^K^Kc q fb z @Y\]b f,Ke]U @ 1

β2nm = (2 − δ0m)(2n+ 1)

(n−m)!

(n+m)!

z @TVU WhX Y!UJXZ\]U ^_SW `KU _SYADUZW WdY@^_ fe]Y@bdWL^KY@bdw'feg\]Wdc W.WdU egY@^ 1

Cnm = 1/βnmCnm Snm = 1/βnmSnm

z

f> Y@^KXZ_S\]Y@^nWLr fbSwJY@^K\gopKU WLWdqKrKc bd\]opKUZW z WdY@pKbdX U ;

^ q*U p[_ u f\]bdU `K\)$ cZbSU ^_SU W bSUZw'fbSopKU W op f^_tfp[k q fbd_\gX pKe]fbS\$_cZWy`KU XZU W0X Y!UJXZ\]U ^_SW `KU _SYADUZW 1

\5e|ijY@bd\]m@\g^KU `Kp bSUZq &ZbSUX Y@^KWd\]`KcZbSc UZWd_'qKbS\gWSU fp X UZ^_SbSU `nU w'fWSWSU`KU e]f U bdbSU,*RY@^ f 1C00 = 1

UZ_C10 = C11 = S11 = 0

z @Y\]bLq fbSfm@bSfqKrKU WSpn\gf^_ ; TVY@bdWSopKU m = 0

*2egU WCn0

WdY@^_'fqKq UZe]cZWMX Y!UJX \gU ^_W75 Y@^Kfp[k * fpKWdWS\L^KY_Sc W −Jn

UZ_Jq fb`Kc%( ^K\$_\]Y^ 1

Sn0 = 0

?> Y@^nXZ_\gY@^KWL`KU TVU mU ^K`KbdUPnm(sin φ)

`KU `KU mbScnUZ_5`ijY@bS`KbdU

m

7UZm@bScm = 0 m = 1 m = 2 m = 3

n = 0>

n = 1 sin φ cosφ

n = 23 sin2 φ− 1

23 sin φ cosφ 3 cos2 φ

n = 35 sin3 φ− 3 sin φ

2cosφ

15 sin2 φ− 3

215 cos2 φ sinφ 15 cos3 φ

Y!UJX \gU ^_WM`KU ^nY@bSwyfe]\gWf_S\]Y@^ q*Y@pKbxegU WxXZY[U%yXZ\]UZ^_SWB`KU _SYADUZWJ`nU `KU m@bdc `Kpq*Y_UZ^_S\]UZem@bf!\g_f_\gY@^K^KUZe _SU bSbdU W_bSU 1

Cnm = βnm Cnm

Ul_Snm = βnm Snm

bS`KbdUm β2m

√5> √

53

12

√

53

TVY@bdWSopKU n = m* e]UZWLX Y!UJX \gU ^_W5`KU _SYADUZW WdY@^_ `n\g_WLWdU Xl_Y@bd\Pfp[k

TVY@bdWSopKU n > mUl_m ≥ 1

*Cnm

UZ_Snm

WSY@^_7fqKq*U egc WLX Y!UJXZ\]U ^_SW5_SU WSWdc bSfp[k

*,+ 4 0$258X9;0 8 2 < Ypn_Nc egc wJU ^_2`nU w'fWSWSUR_U bdbSUZWd_bdU

dm*`KU.bfs@Y@^xU Xl_U pnb

r′*qKbSY!`KpK\$_2UZ^MpK^Mq Y\]^_ U;k!_U bd^KU

e]f UZbSbdU LWd\g_pnc ePfJ`K\]W_f^nX Ur`Kp X UZ^_bSUM`nU W wyfWSWdU WIUl_ ePfJ`K\]W_f^nX U

δ = |~r − ~r′| `KUxe]fwyfWSWdU e]Y_Udm

GePfMX Y@^_SbS\:npn_\gY@^ 1`U = G

m`m

δWSpnb e]Um@c Y@q*Y_SU ^_\gU eUz Y@\]b \]m @; ^ ^KY_f^_ V e]Ut@Y@egpKwJU Y!X XZpKq c q fb e]f U bSbdU,* egU

q*Y_UZ^_S\]UZem@bf!\g_f_\gY@^K^KUZe _SY_fe U Wd_ 1

U(~r) = G

∫∫∫

~r′∈V

`m

|~r − ~r′| = G

∫∫∫

~r′∈V

`m

δ

z @

^yq*U pn_ `ncZ!e]Y@qnq UZb 1

δ

m@bX Uhfp[kBq*Y@egs!^-.@wJU W `KU5T,UZm@U ^n`KbSU 7f^KW e]U _SbS\Pf^Km@e]UO− ` m)−S *Y@^tf 1

δ2 = r2 + r′2 − 2 r r′ cos θz

1

δ=

1

r

(

1 − 2r′

rcos θ +

r′2

r2

)−1/2

O

Sδ

(m)

dm

z

y

x

θ

r

χ

λ

ϕ

β

ρ

TVUJm@c Yq Y_SU ^_\gU e bScZm@^ f^_Cfp q*Y@\g^_ S bdc WSpneg_UJ`KUJe|i fXZ_S\]Y@^XZY@w!K\g^Kc UJ`KUB_Y@pKWae]UZWc egc wJU ^_Wh`KU wyfWSWdU

dm

T,fyuvY@^KXl_\gY@^f( r′

r) =

(

1 − 2r′

rcos θ +

r′2

r2

)−1/2 UZWd_I`ncZ@UZe]Y@qnq f,KegUCU ^ Wdc bd\]UCUZ^_\:&ZbSUx`nU r′r

z Ul_U W_5X Y@^@UZbSm@UZ^_UCq*Y@pKb

r′ ≤ r q fb1

f

(

r′

r

)

=∑

n≥0

(

r′

r

)n

Pn(cos θ)z ?>

Y65θU W_he|i f^Km@egU7UZ^_SbSU e]UZW @UZXZ_UZpKbSW

~r′UZ_~r*KUl_

PnWSY^_hegU WLq*Y@egs!^-.wyUZW `KU TVU m@UZ^K`KbdU _SU egWLo!pnU 1

Pn(x) =

n∑

2k=0

(−1)k (2n− 2k)!

2n (n− k)! (n− 2k)! k!xn−2k

z f>A>=

^'q*U pn_.wyY^_SbSUZbGopKU X UZW `KU bd^K\]UZbSWGWSY@^_.WSY@egpn_\gY@^y`nU e i cZo!pKf_\gY@^y`nU TVU m@UZ^K`KbdU7WSpn\gf^_U z cZo!pKfH_\gY@^ `K\)$ cZbSU ^_S\]U ege]U `np`KUZp[k[\:&ZwyU Y@bd`KbSU 1

(1 − x2)d2Pn

dx2− 2x

dPn

dx+ n(n− 1)Pn = 0

z f>W@opK\V^KY@pnW5q*U bdwyUl_ fe]Y@bdW `ijcZ_f,Ke]\gb q fbhbdc X pnbSbSUZ^KX U* o!pnU 1

Pn(x) =1

2nn!

` n

`xn

[

(x2 − 1)n] z f>=~@

fb5XZY@^KWdc opKU ^_3* Y@^0q*U pn_5cZX bS\gbSU01

1

δ=

1

r

∑

n≥0

(

r′

r

)n

Pn(cos θ)z ?>

^Wdp-KW_\g_Sp f^_5e|ijUlk[qKbdU WSWd\]Y@^tqKbdc X cZ`KU ^_SUC`KU 1δ

`Kf^KWhe|ijc op f_S\]Y@^ z * Y^f 1

U(~r) =G

r

+∞∑

n=0

1

rn

∫∫∫

V

r′n Pn(cos θ)`m

z ?>@ ^q*Y@WdU

U(~r) = U0 +∑

n≥1

Un

z f>@f@UZX

U0 =GMe

rUn =

G

r

∫∫∫

V

(

r′

r

)n

Pn(cos θ)`m

z ?> @ ^ ^KY_f^_

(r, λ, φ)egU W X Y!Y@bS`nY@^K^KcZU WCWdqKrKcZbS\]opKUZWx`KU

S*VUZ_

(r′, λ′, φ′)X UZe]e]UZW3*VfbS\]f,KegU W3* `KU'e]f

wyfWSWdUdm

*n^KY@pKW f@Y@^KW1

cos θ = sinφ sinφ′ + cos φ cosφ′ cos(λ′ − λ)z f>

7U XZUZ_S_SU uvY@bSwCpKe]U*RY@^ `KcZ`KpK\$_0fp wJYsU ^ `ijpK^ XfegX pKe ePf,*Y@bd\]U p!k *Ge|ijUlk[qKbdU WdWS\]Y^ WdpK\gf^_SU `Kpq*Y@egs!^-.@wJU `KU TVU mU ^K`KbdU

Pn(cos θ)1

Pn(cos θ) =n∑

m=0

(2 − δm0)(n−m)!

(n+m)!Pnm(sinφ)Pnm(sinφ′) cos(λ′ − λ)

z f>

Y65ye]U WPnm

WSY@^_LegU W uvY@^KXZ_S\]Y@^nWR`KU7TVU m@UZ^K`KbSU `Kc(K^K\]UZW q fbGe|ijc op f_S\]Y@^ z l ^yU ^ `nc `KpK\$_.opKU*q*Y@pKb

n ≥ 11

Un =G

r

∫∫∫

V

(

r′

r

)n n∑

m=0

(2− δm0)(n−m)!

(n+m)!Pnm(sinφ)Pnm(cosφ′) cos(λ′ − λ)

`mz

WSY\g_Un =

GMe

r

(

Re

r

)n n∑

m=0

[Cnm cos(λ) + Snm sin(λ)]Pnm(sinφ)z V>

f@UZX

Cnm =1

MeRne

(2 − δm0)(n−m)!

(n+m)!

∫∫∫

V

r′nPnm(sin φ′) cos(λ′)`m

z 6

bnm =1

MeRne

(2 − δm0)(n−m)!

(n+m)!

∫∫∫

V

r′nPnm(sin φ′) sin(λ′)`m

z ~@

*,+ 9;< 8T<7;< 4 0]4 < d9 <_2X9;<< 7.8 <_2 25< /&! #"%$ 5 '&( )*+,.-0/1*,*23 -&,546 " ,*78

9 4: *);-6*< =87: 1

I =

I11 I12 I13I12 I22 I23I13 I23 I33

=

A+ c11 c12 c13c12 B + c22 c23c13 c23 C + c33

?> )@BA

765(A,B,C)

78B,C&(7&(,DE*F+*F: 4 " -0/1*,*&7 $ 63*:+7 B-: EF,&( >:G *6+H,&(,B-0/1*,*

cijI7846

i, j = 1, 2, 37KJ%*,BML! NO78*(--*F*:4P*72-

&( O: *J )*< A -4!-6H )*=&B -6 " , -4 , &,2 J8+F " *+,*: 4 " - / *F* > 784 4!+7 )*F&(*FH 46 F*7 -6-6.H J878F46*F78+* 78!+,78*F--&9 4 1

A = B>/ +43-+,7P%(+,*,D - / *F* ,-H%(:* - < &( *@&#4* J )D01

I11 =

∫

(y2 + z2)-M I12 = −

∫

xy-m

I22 =

∫

(x2 + z2)-M I23 = −

∫

yz-m

?> 8A

I33 =

∫

(x2 + y2)-M I13 = −

∫

xz-m

) )*F4 FE+7%+,*B - 7AD,- -=8H -4 " -643=8H,78 7,D*,;* 9 4* -H-46*,B#-, " *7 > 68A > BA *:78B 1

C20 =1

2 MeRe2

∫

r2 (3 sin2 φ− 1)-m

=1

2 MeRe2

∫

(

3(r sinφ)2 − r2) -

m

=1

2 MeRe2

∫

(

3z2 − r2) -

m

=1

2 MeRe2

∫

(

2z2 − x2 − y2) -

m

=1

2 MeRe2 [−I33 + (I11 + I22 − I33)]

=1

MeRe2

[

−I33 +I11 + I22

2

] ?> 8A

=C − A

MeR2e

pour une Terre biaxiale ?> A

C21 =1

MeR2e

∫

r2 sin φ cos φ cos λ-m

> BA

=1

MeR2e

∫

(r cosφ cosλ)(r sinφ)-m

?> 8A

=1

MeR2e

∫

xz-m

?> A

= − I13MeR2

e

?> R>KA

S21 =1

MeRe2

∫

r2 sinφ cosφ sinλ-m

> 8A

=1

MeRe2

∫

(r cosφ sinλ)(r sinφ)-m

> BA

=1

MeRe2

∫

yz-m

?> )@DA

= − I23

MeRe2

?> A

C22 =1

4 MeRe2

∫

r2 cos2 φ cos(2λ)-m

=1

4 MRe2

∫

(r cosφ)2 (cos2 λ− sin2 λ)-M

=1

4 MRe2

∫

[

(r cosφ cosλ)2 − (r cosφ sinλ)2]

=1

4 MRe2

∫

(x2 − y2)-M

=I22 − I11

4 MRe2

?> 8A

S22 =1

4 MRe2

∫

r2 cos2 φ sin(2λ)-M

=1

4 MRe2

∫

(r cos φ)2 (2 sinλ cos λ)-M

=1

2 MRe2

∫

(r cos φ cos λ)(r cosφ sin λ)-M

=1

2 MRe2

∫

xy-M

= − I12

2 MRe2

?> A

7846 I784PJ8785-7+ " *& F +7%+,*B -< &( )*+,2-0/1*,*., NO7+,*78 -,+7%+,*B )&78* 9 4,E H* 9 4- -=H -43=H78 7,B*, 1

I12 = −2 M Re2 S22

J878*F 9 > > 8AA ?> 8A

= −√

5

3M Re

2 S22 J878*F ,6 > 8A

I13 = −M Re2 C21

J87* 9 > > R> A ?> 8A

= −√

5

3M Re

2 C21 J878*F > 8A

I23 = −M Re2 S21

J87* 9 > > 8A ?> @ A

= −√

5

3M Re

2 S21 J878*F ,6 > 8A

# F43*:78M 1

I22 − I11 = 4 M Re2 C22

> A J78* 9 > > BA

I33 −I11 + I22

2= −M Re

2 C20

8A J78* 9 > > BA

I11 + I22 + I33 = Tr(I) BA

r

z

λ

φ

S

x

yO

> 7P7-786H, H,* 9 465-4 I7*B -: 6 2/& " * $ * 5 A > ,5+7%78-7H, 78< *F, 78B )781

x = r cosφ cosλ*y = r cos φ sinλ

*z = r sinφ

* , -78+r2 = x2+y2+z2 >

$ '&&?- / H 9 4 )*F78H 9 4* J )46 1

I11 = I22 − 4 M Re2 C22

> A

I33 = I22 − 2 M Re2 C22 −M Re

2 C20 8A

2 I22 − 4 M Re2 C22 + I22 − 2 M Re

2 C22 −M Re2 C20 = Tr(I)

BA

*F**78766*,D1

I11 =1

3Tr(I) − 2 M Re

2 C22 +1

3M Re

2 C20

> A

=1

3Tr(I) −

√

5

3M Re

2 C22 +

√5

3M Re

2 C20

I22 =1

3Tr(I) + 2 M Re

2 C22 +1

3M Re

2 C20

BA

=1

3Tr(I) +

√

5

3M Re

2 C22 +

√5

3M Re

2 C20

I33 =1

3Tr(I) − 2

3M Re

2 C20

8A

=1

3Tr(I) − 2

3

√5 M Re

2 C20

>

> > 78 B46*F*H,E-: + H 4-6 >

×10−6

! "#$&%%')()* Cm 7, 0400 1037 +$, " 2 -/.10324 4 45 )(6"7$! "#$&%%')()* Am 7, 0165 1037 +$, " 2 -/.10324 4 489 :(;"7<! "#$&%%')()* C 8, 0365 1037 +$, " 2 -/.10324 4 45 )(= ?>:! "#$&%%')()* A 8, 0101 1037 +$, " 2 -/.10324 4 489 :(= ?>:@ , ((=A* 5=()* λA −14, 9291 ± 0, 0010 -/.10324 4 4%%' AB "# 9 =C%D 8 9 ( J2

2 E F ? G H I 4J2KL2 E −3 E E 4 -/.10324 4 4( , 8 ? ('C , 8 %M$ J2 = −(A + B − 2C)/(2MR2)N O< 89 ' P(= Q>: Re

G?H<R F 2 H G G J2K " E E 2 I -/.10324 4 4S "UTC&( @ V< k2EW H -/.10324 4 4

(=( , 8 ?S "UTX( @ V<QC 8 k0

EW 4 H F H -/.10324 4 4S "UTX( @ V< ∗ k′

2 Y EW H E RI -Z N ? E E H(=( 8\[ "7 ;(=( , 8 ?X CC=(= Ω 7, 292115 10−5 (]C −1 -/.10324 4 4"#O<=(= U>:^ 8 $((Q_`D'( T0 a H H W 2 J2 W R K b C a E E E X$cedfC 24 4 Rg 89 Q(Q_`D'( fC

EW F a H H J H E K \O%' a E E E (_` C< , 8 < 9 GMe

H 4 F G E E aha 2 F J F K 1014 " 3 C −2 E E E ? -/.10U24 4 4(= , V

JAi K S "?TC( @ V<"# 8 C`j?&%' 8

!(

> 6-, > > * >R> * ! #"$%&;*('*) * > * > @+c> > ,.- 4,3* > $ *0/213546798:4:;03<4=?>@%AB+*C'*) * > )@+c> ED *F+,D,* > > *GF *F78 >$ * > > * #4IH7>JCK$LG 40MN>@ 4)* D 78 > '9O:P+* * $Q@,+Q@8@*R @$ - D *78 > *? * 5,784: - 0> * )*F > - # B D > 1 >$ *(S &(7 ,*F+ 78 9 4

78! - 6- +78&: *7UT*F )&(7 ,*F+. =4< &78&(,B4& J) *< )*78,/@*WVGXY UcGc^&ZVi QX![ UcQX:*'#O&) *0\ 7 > * @*$RR> @* >

, *F-78, D7KJ]\ > I> * $QQ * * 5*fD ?, * / 7 $ JP * _^ &* a` $ * 9 4 -6C*F ,* +* H,E- < 7) )*78., A * - - > * 5&( )*F3*6b378+,784 >

)@

0 1.23 465879 !1:5;%< = - obspm.fr

Documents