HAL Id: hal-00426015
https://hal.archives-ouvertes.fr/hal-00426015
Submitted on 23 Oct 2009
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
Law of spreading of the crest of a breaking wave
Yves Pomeau, Thimotée Jamin, Michael Le Bars, Patrice Le Gal, Basile Audoly
To cite this version:
Yves Pomeau, Thimotée Jamin, Michael Le Bars, Patrice Le Gal, Basile Audoly. Law of spreading of
the crest of a breaking wave. Proceedings of the Royal Society of London Series A Mathematical and
Physical Sciences, 2008, 464, pp.1851. �10.1098/rspa.2008.0024�. �hal-00426015�
!"$#%
&'(
)+*,.-0/21436587:9<;=>?*@A30/2BDCFEG=IHJ*IKL1M(36N:OPEQ=
,*KR1S30T
E
30CUVMW*XY5U-ZT\[^]
_a`Gbdcfeghbjikelmghnpo:nrqPs:tvuwlyx{z|nR}|ikbji~lui~lyx{z|n enregwbn}z
n{gwlknzgfna8gz|n`0seeov
a
:d.qbglup
no:n
Z¡¢g£b n¤
¥§¦
¨ui~l~i~z¨iodnr©n
sng
snuwzgLnuªqs
n«e¬n{nuª®egwuV
x{zlm¯lkcgfnL°G±(©³²
§´
rGª©ª}Yµ
¶
l·j¸k±¹bgwu{n{lm·n°0lºjngwuwl~i
nQ ´ gz|n¡»¤A¼e<lyeji~¸0zglynZ½Pq{²j§:¾^±¹bjgunlmn
no:n
jZ¡¢g£b n¤
¿ `Gb:ceghbjikelmghnpo:nr±¹eao
n<lÀu{bji~lyeÁn±
n
b|l~xznL°¢±^©
²§
°6lmºn{gulmi
nqlyn{gwgfnn{i
±¹bglknp0zglyn6qP·b n¼zuulyn{zd bvu{n":²j a $qbgwlup
nodnf A¡4ghb na¤
Â$Ã0Ä{ÅaÆvÇÈjÅ
É£Ê(Ë.ÌÍΨÏrÐËjÊÑjÏRÒjÓAÔÒ§ÊÎÍ·ÕfÍÒ§ÊÖÒÔÏËjÊ(ÌPË×jÏÖØÐÏËÙ«Ú|ÛÜÍÖÔ{ËjÊ^Ø4ÏLÖhÏ{ÏÊ^ËjÖIÕfܨÏRÝ.ËjÊÍ·ÓmÏÖ£Þ
ÕfËÕfÍ·Ò§ÊÒjÓ6ËÖfÍÊѧßàËÐÍ·ÕâáÍÊ$ÕfܨÏrΨáÊËjÝÍÔ{ÖÒjÓ0ÕfܨÏã|ßÍÎ$ÖfߨÐfÓ~ËjÔÏjäÝÒ×ÍÊÑ"ß|ÊΨÏ{ÐPÕfܨÏÏåÏÔÕ
ÒjÓ»ÕfܨÏ"ã|ßÍÎFÝÒjÕfÍ·Ò§Ê8ßÊÎÏ{ÐʨÏËÕfÜ¢Úæ%ÏÖfܨÒÌçÕfÜËÕ{äGËÕÕfܨÏ"Ò§ÊÖhÏ{ÕrÒjÓØ|ÐfÏËÙÍÀʨѨä«ÕfÜÏÌPË×jÏ
ÔÐfÏÖfÕÏèé|ËjÊ|ÎÖ"ÍÊÁÕfܨÏÖhé|ËjÊÞkÌIÍÖhÏÎÍ·ÐfÏÔÕfÍ·Ò§ÊËjÖÕfÜÏÖêdßËÐÏ$ÐÒdÒjÕÒjÓIÕfÍÝÏjÚÛÜÍÀÖÍÖëÐwÖhÕ
ΨÏ{ÐwÍ·×jÏÎìÓmÐfÒ§ÝíËÕfÜÏ{ÒjÐfÏ{ÕfÍÔ{ËjàQËjÊ|Ëjà·áÖÍÖËjÊÎìÕfܨÏÊ^ÔÒ§Ýé|ËÐfÏÎ(ÌÍ·ÕfÜÏèé4Ï{ÐÍÝÏÊdÕfËjà¢ë|ÊÎ|ÍʨѧÖ{Ú
ÛÜÏLËÑjÐfÏ{ÏÝÏÊdÕIÍÖPÏè¨ÔÏàà·ÏÊdÕ{Ú
î ïð6ñjò§óAôõ»öñj÷\óQð
øùúûaühýþûùdÿ ¢ùùûvþ^ù+ý6ûûvû ù 4ûÁû4þû !" 4ûÁþûù
#þ$!%&" 4û'()(*4þþwû)(û+%ù,-*~ùþ-./0" û-*10%2" ûWû34*¢ù"5%
"6%7þ8" 4û9%kþûû-*4þ-%\ù(vû:<;^û=> ¢ù.þû~ùû)$,$4ûvù? ¢ùúû(ý6ûû)@þû)wû)Aû$ ýA
øB ¢ùDCFEGAHI4JK> *1L IûúûþMFùdÿN4þû$(="O%7þL 4û>>$4ûP%Q 4û
þR(vþwû)S:UTM 4û?ùúûühý4þwûùÿ4Vù5*mùþW.FýQû)(vù*wûN >û=2%û3*4ù"
X$ûvþÀúû$*1$4ûvþX 4ûLù-*Y1"R" ¢ùZX" 4ûM-*4þ-%\ù(vûMO(wû#"8 1þ[)A{ù\Kdù$ý6ûü
(ù*1û>X*1"ìù%]ûvþù_^`Wû#(û# ¢ùIùúûvþS"(vù1ùû4a1~ù4û:TM O4þý1mû)
>-*$û)$^4þ-bYù5$4û)cK¢ù-*(û)$d"(ý6ûNû)ûvþ(N%7þ> M.QûP%e*mùþW.gf
h
ÔÒjÐÐfÏÖhé4Ò§ÊÎÍÊÑËjߨÕfÜÒjÐ
bl0b§o§ogfnuwu"ikj4l)mnop4qr)j`sut\nvsut\wZx5yz Ú{0Ò§ÝÏËjß|wÚ
hal-00426015, version 1 - 23 Oct 2009
Author manuscript, published in "Proceedings of the Royal Society of London Series A Mathematical and Physical Sciences 464 (2008) 1851"
DOI : 10.1098/rspa.2008.0024
34*¢ùA"W"mû 4ûvùþP 4ûV-*~ùþ?"^û:b*4ùW " 4ûFù¢ùW-P% " 1 Y$4û)aPü
û)$'"Y$4û)Qû)$û)(û > Wþwû)-6û(24ûP-¢ù(ûP(þ-$4ùûù1$"5"^û:TM &
*Y()û)A9%7þN" 4û8ýþûùdÿ6%LþwûùLùúû)5¨úú$4û%7þ^ù"N%Rù
*4þS%\ù(vû$ù$4ûvû$Y" 4ûþû=%7þû?.#V¢ù(û (þ-$4ùû):*Sù%]ûvþLý4þûvùÿ4Y"
*4þS%\ù(vû?()*$4û)ù5(wû)$' 1~ù¢ùdþ ()*4þúû8> 4ûþû? {ùû)A>~ù4û_IúûvþS"(ùcK
" b(*4þwúû þ->5%kþ ùYgAùb 4ûNû=_%e*mùþW.:.ù5 Ag 4û(vù
þ$@" 4ûV-"*1$1%M 4û6E *4þûþû34*¢ù"@ *$ ùW,+" ûV.(vù
W"*¢ù %7þ>ªùjúûaü£ý4þûvùÿ4%ù$ 4ûP(*4þwúû-*S_(û)A"4û$d *$Áþû$*(û û%
" ù/¢ùþ5%_ A):.*4þ #þ-$uKO 4ûdªùúûýþûùdÿ@()(*4þû)ûvþ(ù
ùùgA_ù-*4þ-%\ù(vûìù1$ 4þwûù$2~ùûvþ26+ 4ûR-¢ù«ü\>û $mþwû)(Q: TM 1
¢ùQûvþ_úû2" ûP"^ûP$4û)Qû)1$4û)(û9%O" 1_-4þûvù$1:Lûù<ªùjúû)ùþwûR$4û(vþ-mýQû)$
ýA 1614ûùdþ"û)34*¢ù1?>W" *1N QûY%rùAû11(?û4ûvþùO*1u:
TM 4ûvþwû%7þwûLIûþû_$ù.ù4ùk%" 4ûý4þwûùÿ4$>P%1- N-*"u%$4û
û)34*¢ù1#> V.#9-¢ù(û8()þ$¢ùû)):." 1 Y$û)U" 4û2>$1" V%k" 4û21*~ùdþ
þûY1(vþûvùû#û4ûvþ-(vùWRÿûM" ûb-3*4ùþûþL%Q(û&$16ûvþû(vûRýQû.Iûvû) 4û
ù(*¢ùX(ûù$ " 4ûYS{ùA8> 4ûþûY" 4û5*1?ýQû)()^ûN-*~ùþ_^4þ-):TM 4û)
ªûV " 4ûþû="(vùW6" 4ù 4ûù^û^ý4þûvùÿ46þ(vû)-9(()*4þ-R¯þwûùªùûvþ
ùúûKU 4ûù4þ-1FùZ"%1RùúûKGþû)mù"ÀúûY^ù0ùYW"*$4ûù$'4ûdü
ûùý1mû9$Qûvþ-Q:./" ûmù-N¢ùþSPIûVþû)wû)Aû6ûþ(û)AùaýûþwúdùN%
" 4û&þûù$N%g" 4û>(vþwû)S#%0ý4þûvùÿ4:üªùjúû2^ù?~ùdýgþù"þ-Rwûü.*^ù>ù(ü
()*4þùû ^ûvù*4þwû)(û)A"2+- ¢ù ªùûþ)Kg b >%ùFþwû)^ùþÿ:ùýû.ùþûû)(û)A
> ' 4û8" 4ûþû="(ù4þû$(=û)$Wû= 4û4):
Aò§ó! î#" ñjó$%"'&)(+*-,.0/»ò1,#(2A÷\ð4356(7! óAô4,8
ªû) Iû^¢þ--.þû(ùO-{ù$¢ùþ-$ þû*W"N " 4û5:ü.(ùmû$ 4ûY$(û)-4ù>CSE9?J
¨ú-()$:#*4þûvþû34*¢ù"ù$ìûû)1$5 4û) "_. 8¢ù(vûM$^û>C ?J=:ZTM 4û
FùWþû)-*2%O" û; Jù4ùb& ¢ùb" 4û >$1" %O" û *mùþRþû)þ>
ÿû_" ûN-34*¢ùþû.þM%<(ûK¢ù%]ûvþ 4û8^¢þSb-*~ùþ-.:
./E9<=<?><-Yû~ù4û)$' "5Àúû8" û)@ù*( Aþýû) %7þ " 4ûû3*4ù"
A%B
ACED
B
A%B
AFHG
=JI CFEJ
TM ¢ù4ÿ4R P*1"P g-ýmûY"6- 4û (()*4þwþû(vû %>-*~ùþ-mû)
ù%]ûþù?^`1ûM(û#%7þù?>$4û>()mùa%QY 5W"~ù1$¢ùù1:ATM 4ûRû)34*¢ù+CSEJe ¢ù
" 4û?( *1"
B CF4K0C J G
BML C FONPB%C J K CJ
> 4ûvþwû BML C F J " 4û ~ù&()1$uK {ùÿdû) ùZ C G
=1:RQbû " ¢ùZC7]JVB 4û
hal-00426015, version 1 - 23 Oct 2009
*1"V%#*4þûvþrû34*¢ù"VùÿûM~ù(ûù C G
='C]" 4û2W"~ù`()$1"V 4û)
(û> ûvþûù C =AJPù$5" 4ù2CJIûb$? -6û()W%]R> ¢ùL" OW"mù($W"
NC]ªûNW4ûû)$dM"ýQûý6ûÀü ¢ù6û$¹ù$dY UJ=:
" 4ûþ ªùV%uLþ-"P L*1a"R($4ûvþL" 4ûùþ*^ûA % BML
KV 4û
þ Awü. 4ù$'$4û8%»û)34*¢ù@C JK¢ùRùR%7*(="d% B C F4K C J=f
C B C F4K0C
JJ
G
FN$B%C K C AJ
> 4ûvþwû C IJM>" 4ûP¨úûþwû %7*(="% BL C IJ=:2ùV(~ù-(ùAþwû)*12 ¢ù&%7þùA
ý6ûü. 4ù6û$%ù$'-" ~ùU$¢ùZ{ù BML K1 4û_^¢þS>*mùþW.% B CF4K0C JªùQûùdþ
ù2 4ûR¢û)(="+ A2%O" 4ûN%7*(="
BML
6" û$þ A_%O 4ûR^ùZR*1 > 4û)
BML Mg-úûYC7ûû?^*4þû5EJ:
.$4ûû)$uK 4û#-*~ùþ-.8 4ùQû)X> 4ûR" 4û *1" B CF4K0C J=KdùeúûýA$û34*¢ù"
CAJKý6û()(û) R*údù*4û)$uK" ¢ù a> 4û4ûúûvþ
G
=1K 4û&$4ûvþ-údù"ÀúûRý6ûN{ùÿdû)
t
initial condition breaking
-0.8 -0.4 0 0.4 0.8
-0.8 -0.4 0 0.4 0.8
t>0
x
u
-0.8 -0.4 0 0.4 0.8
-0.8 -0.4 0 0.4 0.8
t<0
x
u
-0.8 -0.4 0 0.4 0.8
-0.8 -0.4 0 0.4 0.8
t=0
x
u
zoom (a)
(b)
ZͷѨÚÚ yËZ|ÙjÏ{ÕfÔÜ ÒjÓrÕfܨÏÕ\áé|ÍÔ{ËjàÕfÍÝÏÏ{×jÒ§àÀߨÕfÍ·Ò§Ê?ÒjÓrË JØÐfÏËÙÍʨÑ%ÌPË×jÏjäÖhÕfËÐfÕfÍÀʨÑ
ÓmÒjÐÍÊ|ÖhÕfËjÊÔÏÓmÐfÒ§Ý ËìѧËjß|ÖfÖfÍËjÊ%é|ÐfÒjë|à·ÏjÚGÛÜÏ.ÖhÕfËÐÍÀÊÎÍÔ{ËÕhÏÖrÕfÜÏ.ÍʨãÏÔÕfÍÒ§Ê8éÒ§ÍÀÊ:ÕrÌÜÏ{ÐfÏ
ÕfܨÏÖfÍʨѧßàÀËÐÍ·Õ\ápëÐÖhÕËé|éÏËÐwÖ{Ú yØ1|ÏÖhÒ§àߨÕfÍ·Ò§ÊìËÕIÕfܨÐfÏ{ÏRÎ|ÍåÏ{ÐÏÊ:ÕÕfÍÝÏLÒjÓ6ÕfÜÏRßÊÍ·×jÏ{ÐwÖfËjà
ÏêßËÕfÍ·Ò§ÊÓmÒjÐÕfܨÏÌPË×jÏÞkØÐÏËÙÍÊÑ y |wä×ËjàÍÎËÕëÐÖhÕ"ÒjÐÎÏ{ÐÓÒjÐ.ËjÊdáÁØÏàÀàÞ\ÖfÜËé4ÏÎWËjÊ|Î
ÖfÝÒdÒjÕfÜ8ÍÊÍÕfÍËjàGÔÒ§ÊÎÍÕfͷҧʢä«ÔÒ§Ê|ÖfÍΨÏ{ÐÍÀʨÑÕfÜËÕªÕfܨÏ"ëÐÖhÕªÖfÍʨѧß|àËÐÍ·Õâá$ÕfËÙjÏÖé«àËjÔÏËÕ
ËjÊÎ !YÌÍ·ÕfÜ#" ! yËÓÕhÏ{ÐìÔwÜËjʨѧÍʨÑYÕfܨÏ(ÒjÐwͷѧÍÊÖ.ÒjÓrÕfÍÝÏ^ËjÊ|Î Öhé«ËjÔÏFËjÊÎ ËÓÕhÏ{Ð
$ ËjàÀÍà·ÏËjÊÕhÐËjÊÖfÓÒjÐÝ |wÚ
hal-00426015, version 1 - 23 Oct 2009
ù>()-ùA :`TM mû)$
C D $
$ B G
=I C7I4J
`þLùYúû C B
J=K 4û?^ùû)-M(û2> 4ûû)34*¢ù/C7I4J ¢ùù5-*"dM> 4û)
" 5*1" 5-ù"¢ùþS> þwû)Qû)(=V C KO" 4ùY9> 4û) $ C G
=1K C ù$ B
ý6ûYþû~ùû)$ýACI4J:<TM Pmû$)=
G $ C G N $ B
Kþ -Y
G
=1: Aû
*M ÿ^ùZ " 4û8T»ùþû¢ù-'%
C B
Jùþ*1$ " gA:@#-ùAù$
4ûùþ5ûþYV(vù ýQûÁû)Y¢ùZû)$+ýA ( 4ù@" û+þ-%_"^ûYù$-¢ù(ûK
ù$?ýAùmûvùdþù1-%7þ- Cc:¯û:g 4û ^¢þ--?*mùþW.'{ùÿdû)?~ù(vûìù C G
=¹ù$
F G = >W"
B G
=AJ=:OTM ûvþû=%7þûKO" 4û'T»ùþìû=¢ù1 % C B
J$þwûù$1
C B J G
N B
D B
D IIIKM" û/(«û (mû4%
B
ý6û 4û¨ùúû "! ¢ùúû ù!-*~ùþ-.
ùQûùþ- %7þ-ªùþ$ "^û):_(û*A"?û)34*¢ù CJP" Yúû(ùYªûþ
þ$ûvþa" 4ûb*úûvþ-ùQû)34*¢ùY%7þa" 4û ªùúûaü£ý4þûvùÿ4K|úù$9%7þIùA(ý6ûü. 4ù6û$
ù$dY" 1"mù ()$1"¹ù C L
=1f
= G B D
FONPB%C I CJ
`þ> þS>"(û)PC7\:û:Gùþ-*$'" 4û.ý4þwûùÿ41Y(û C G
=AJ=K B (ùmû)&ÿû C ù$ F
ÿû C
K" MFùdÿ5%" 4ûNù(û?þ$ûvþ)K C
KGùQûvþY>'" 4û.þ Awü. 4ù$'$4û
%»û)34*¢ù/CJ=:
Qbû#" 4ùX" ûþû*W B C F J%XCJXûaü£údù*4û)$N%7þ C 4û¨ùúûù$Rþ-ûaüDúù*4û$
%7þ
C
gúû?CwûvûM^`*4þwû?EJ=: %Zù_-Fù1$-¢ùúû#ûþ ù$$4û$9"8" 4ûrû34*¢ù"
CSEJ 5Fùÿdû?rþwû)ûýû? 4û QùúmûþüS;4"ÿdû)Lû)34*¢ùQK`4û8ý1ù1 " 4û?:ü.(ùmû$
#*4þ-ûvþ-Rû34*¢ù"uf
A%B
ACED
B
A%B
AFHG A B
A%F
K CAJ
> 4ûvþwû
(ù/-Fùrù$ gúûd(«û Y()mûA:LTM 4ûù$1$ %b" Y$1-¢ùZ"úû
ûþ 8ù,ù%þû)*~ùþ-[ " 4û+*1"V%CSEJKL 4û6R*W"ü£údù*û)$ þû*W"
ý6û þwû)mù(vû$ ý4çù -* ùdþ*1$ F G
=K#" ¢ùZ%þû4þûû)AÁù0 1({ÿ %7þV"
$4û\:
TM 4û8júû.V%*4þ S"*$1V()(û) %kþ " 4ûûû)1 %" -ù$¢ùþ-$¹ù4þ-¨ù(
"@ 4û64þ-ýû) %_%7þ-FùZ" %?- ({ÿ -*11V%?4ûùþ5 A6ûþý (
û)34*¢ù1_>" YþûP" ¢ù û9¢ù(ûìúùdþ~ùdýmû: @#1$ûvþ_%7þ_-ù(ûR" 4û5(ùû
%2. -¢ù(vûWúdùþmùýmû)K
F
ù$! Kù$ mû B C
F4K K0C
Jù$!"gC F4K K0C
JýQûd 4û'.#
@ùþ-û)-~ù9( 4ûA"O%` 4ûúû().?^¢û$u:TM 4ûMû4ûvþù[ùP%U" 4û 14ûùdþ
û)34*¢ù/CFEJþûù$
A%B
ACED
B
A%B
AF D "
A%B
A G = K CcHJ
hal-00426015, version 1 - 23 Oct 2009
A "
AC D B A "
AF D " A "
A G
=I C <AJ
TM þû4þûû4#" û `*$(û)( ¢ù( û)34*¢ù1L%7þù?¨ùa> *1L4þwû)-*4þûK 4û
þ %#> ( @(ù ýQû5þù(û)$ ý¢ù({ÿ6"'" û >þ()~ùK;( * ù?" 4û(û)1$@%
>þ W" RK4þýmû 0 K #ÿ K> 4ûþû QRûM $4ûþÀúû)" 4ûL34*¢ù$4þù"( mù%
$4þùP%7þý $û)Ljú1N8ù `*$ ú$V%gû)4ù()W.-5" û& þ$1 %Q 4ûO-
þùmù"ýAdû_C]" 4ûL4ûIûvþþùmù"ýA:@# 4û)$ù$pøB 1"^ù?þùmùû
" 4ûMþ¢ù4mù" A;mù({ÿ4_ìþ$W.J:ZTM 1Oû=a%Qû)34*¢ù1O ¢ùPýQûvûY*1û)$
ýA0û $jú( CFEGAH =AJ#Fû=mùd" 4ûN%7þ^ù'%OmùþûP-(ùûPSþ*1("*þû)2 4û
bÀúûþûK4ù-*Y1ù ûA"~ù ?:|ø ûb *û)-#" ¢ù 4þ-§ú$4û)rùN$4û
%7þ_" û9(()*4þwþû)1(vûY%L1*~ùdþmûb%7þ2(ûaü$4û)Qû)$û)A8%7*(="8%L.#d¢ù(vû
()þ$1¢ùû)NC F4K
J:
;YmùþW9"9" ûYE9 (vùûK¢û)34*¢ùPCcHJù$@C<AJù$WLùR%7þ^ùg*1"
FON C B CF4K K C J
G
C B4K "J K CGAJ
ù$
NPC
"gC F4K K0C
J
G
C
B4K
"J
K
CSE9=AJ
> 4ûvþwû
CB4K "JRù1$
C B4K "JRùþwûR$4û=^`4û)$?ýAd" 4ûR~ùk($W"): (þ*(~ùþûü
Fùdþÿ %7þO 4û&%7>8O" 4ù 4û&mû%]ü. ¢ù$5$û)L%u" ûû3*4ù"bCcGAJù$+CSE9=AJ
ùþûd¨údùþ-~ùA5*$ûvþYû)4ûþùMþùS%7þ^ù9%2" ûd4ûvùþ9þ-*u: Aû ýQû
" 4û8û)4ûþùu. ý4V.#YFùZþ %< #þ*1uK1> '«ü[vûvþ-5$4ûûvþY4ùA:>
ý¨ú*L" ¢ùZ?CBK "1J
G C B4K "Jù$ CF4K J
G C F4K 1Jùþû&*1"L%Aû3*4ù"
%L" 4û9ù^ûR%7þ ù_" 4û9û%]wü ¢ù$ -$4û9%û3*4ù"YCcGJ"ù$ CSE=J=:uTM 8 $
þ-*4û_> ' 4û8^ùþW ù(9@C
B4K
"JIù$/C F4K
J:2%<()*4þ-û8" û8ù(û
û)ûvþùQ4ûùdþ ^ùV> ( ¢ùû2û4ûvþùg 4û2%7*1("
CB4K "Jù$
CB4K "JO
ùWþù" ûvþ?()Y(ùZû)$ ªù: #*1KAýQû)(vù*wû" ûY^ù,?4ûùdþ_?>XN( ¢ùû
" 4û'$4ûþûû%"ù gY~ùL
B
ù$ " :OTM 4ù4ÿ4Y " (þwû)^ùþÿ,ªûd 4ùýQû
ùýû& 1?K4> *1 (ù()*1~ùuK" ¢ù *mùþW"û)Xmû$P$1(A"*1"û)a%
$4ûvþ-údùúû&>W" Yþû)-6û(_
F
^ù'4þwûù$6ùAd$þû)(="uK" ûù¢ùRýQû)
Fù$4ûýAWù-*R^¢þ--&" ¢ùM 4û?*mùþW.V-4þûvù$&þ^ù "
F :
`þOY" 91"mù$¢ù{ùK
ù$
ùþwûM*( Y" ¢ùZO" 4û>1"mùFù1_%kþ- CB4K "J
"'C F4K
1JO#ûb"P4û:1TM 4ûb*1"L%û)34*¢ù18C\HJù1$ C<AJýQû)()^ûb1*~ùdþ
> 4û)ûúûþ" 4û'"^û'$4û6û$4û4 ù()ý1~ùaC C J9%_ 4ûdFù1 %kþ C B4K "J "
CF4K 1JªýQû)()^û&-*~ùþùRù9(vûvþS{ù "(û C :`TM ù()ý1~ù¹þûvù$f
aCC J G A
A " D C
A
A%B D
C N A
AMB A
A " I CSEEJ
hal-00426015, version 1 - 23 Oct 2009
AûM*ªù-*(û2" ¢ùZ#" û_*mùþW.5(()*4þ-#^¢þSrù
G
=$ù$%ù
G G
=P>W"
B G " G
=5": _d 4ûE (ùwûKg &~ù-þû)Sþ-(&"ù2 þ-ùARù
4û5()*$ý6ûûúûR^4þ-)fk" 4û5þ-¢ùû34*¢ù".ùþwû ùmûvù+¨úùdþ~ù4)Ku'" 4ù
4û&(ùFùªùIý4þ-?"
B G " G
=8" 4ûLúû()W.9^¢û)$Fù ^û> AL%Q(ûRù$
¢ù(vû:aTM 4ûd()$ û34*údùû)A5" " 4ûd(ù(vû~ù0%b" 4û'wû)()$ $4ûþÀúùZ"úû
% C B Jù B G = 4ûvþwû'R" ûdþQûvþS.0" ¢ù)KX4ûvùþ C G B G " G
=1K<" 4û ^¢þ--
«üDúdù- 1Rûvþ->" 4û?T»ùþLû=¢ù-d%" 4û ù(ýmù aC
C
Jªþwûù$
aCC J G C D B
D
" D
B " D IIIK CSEJ
> 4ûvþwû
K K
ù$%ùdþûN()S{ùA_$4ûvþ-úû)$+%kþ- W"mùu()$1):UT<úûN 4û
34*¢ù$4þù"(Pûþ C B
D
" D
B
"J d" 4û:ù()ý1~ùuK
C B4K
"Jrù$
C B4K
"J ¢ùúû
"^ý6ûpû=¢ù$û)$ Tùþbwûvþû)&"V mþ-$+þ-$4ûvþKU> 1( 6$4û6û$8d.#Vû_%
û()|û Y()û)A": *1 4û"ùûý4þù?Lþûvù"W91^4û)$ýAY_4û)wû)%Q"P 4û
mûvù$1Pþ-$4ûvþLûþY 4ûvùþ 4û2-*~ùþ-.:+.$4ûvû$uK4ùZ C G
=N 4û ù(ýmùV^ùþ-W
¢ùrùR[ûvþ-ìû)û)¨údù*4û&" ¢ùZM(ù%ýQûù-()mùû$"ìù%ûû¨úû)(="þM 4PV 4û
F $mþwû)(="u:`TM 4ûvþwû%7þwû " û ()|û Y(mû)A_%X 4ûPT»ùþû=¢ù-+%
C B4K "Jrù$
C B4K
"JùþwûR*( ¢ù
G
=1K
G
=Fù$
G
=%ù
B G " G
=1:gTM bû)$
" ¢ùZKûùþe 4û -*1~ùþ-.K 4ûMmûvù$12þ-$4ûvþeûvþ-
C BK
"1Jù$
C B4K
"J *1$
ý6û
CB4K "J
G
" D B
D
B " D B " ù$
C B4K "J G
" K CSE9AJ
> 4ûvþwû 4ûúdùþ-*1(«û Y()mûA"e(vù$ýQûûù-"þû)mùû$N
K K K
b 4þ* $û34*¢ù"
CSE1J=:TM 4ûuKQù>mûvù$9þ$ûvþ)K¢û34*¢ù"PCcGJù$@CSE=AJªýQû)((û
FONPB%C
G
" D B
D
B " D B " K CSE)I4J
G
" K CSE J
" 4û9ûvþ
C
"+ CFE=AJýQû) 4û)mýûP(4ùþû$
" : U*þ-" ûvþ?^`(vù"
%û3*4ù" CSE)I4JRùdþû 1 -mý1mû:eþSKU4ûP(ù61"(vûP ¢ù&" 4ûNûþ " G
C
J ( ¢ùû " 4û2* þS>%k" 4û21*~ùdþ.9%kþ- ùR-þù A 4û>"ù$ýQû)A
4û > *1?1~ùWùA 4ûvþ8-1^`(vùAþûfu4ûvùþ_" ûY-*~ùþ-.4û5^ù
ùªùù4þ^ùû2" 4û84û2%e-*~ùþ-.(ýA¹ù9-þù AM4û:;«û)($uK`û8(ù
ù-bû)û)( 4ûLûvþ-
B " G C J B K(vûL(vù$ýQûIùýþýQû)$ A"ù&( ¢ùû
%
B
A"
B
D gK
ý6û.ù?()1-{ù4):
%]ûþþû)-(ù1Kû)34*¢ù+CSE)I4J<^`¢ù mûù$
"ù2*1úûvþù4û3*4ù"R%7þ< 4û ùúûaühýþûùdÿA? RK§úù$N%7þPù4$ý6ûü. 4ù6û$
ù$dY" A~ùg()$1"f
= G B D FONPB
CC N J I CSE AJ
QbûL ¢ùùûvþ-.û)34*¢ùZ" CSE AJAùþûL%þ$4ûþC 4ûvùþ" 4ûL*mùþW.K)>W"
C K B C ù$ F C :QTM _ >8*þ_Fù+ 4)Kg4ù^û'" 4ù
hal-00426015, version 1 - 23 Oct 2009
ùúûaühýþûùdÿ4Jk4þwûù$1<mÿû C ùZ%]ûvþu 4ûa(û)1?%" ûL-*~ùþ-.K)^û="
" ¢ùZMªû?>Q úûvþW%]Yùþûvù `*$(û)( ¢ù( `()1^`*4þù"u:
Aû&*Lû)$'" 1Mû('> ' 4þûûpþwû)^ùþÿ4:
Q&û ¢ù F ù$ @$1,15 ¢ùúû'"ýQû ()þ$1¢ùû)ù þS" ¢ùªùZK
ý6û(ù*1û " 4û ù(ýmùBFùþ %þû)$1*(vû$ !W" $mù4ùb%7þ- ýA ù0û4ûvþù
( ¢ùû%M(þ-$4ùûN ¢ùRP1 û)(vûùþ ùYþ{ùuKu 4û ù()ýmù ýQû)
LþwûùkSY(ûþ-(8dû)4ûþùc:
;*1g-Y" ¢ùZ B C
F4K K0C
JýQû) ¢ùúû)_" ûPù^û?ªùÁù>" 4û.úûþ-"(ù W"
C F4K K0C J G B C F4K K0C J&, 4û5*4þS%\ù(vû5%ªù%ý4þûvùÿ4'ªùjúû6C]> ( ,_ 4û5(ùwû5
¢ù ªùûþ)Kgûvû9û=?û("UJKQ4ûP^`$2 4û9()%L A2%úûvþ-(vùe-Qû
V 4û2-*4þ-%\ù(û5C7 4û_(A"*4þ %k" û2*þ-%\ù(ûJIýA$4ûvþ-úN%kþ û3*4ù" CSE AJO 4û
()þ$1¢ùû)<%`" 4û gA"> 4ûvþwû $ G
=1:TM û 4þ1wû)( " û þ-[)4ù4~ù4û
%" M()*4þúûN ¢ù @ùþ-û)-~ùWû)34*¢ù
H F G
IUCC N J K
ù * " 4û
(þ-$4ùû X-*( Y ¢ù
G
K 4û $4û=ûvþ-¢ù
G
ý6û/{ùÿdû) > 4û)
F
g-úûù$
G N
>
F
4û)¨ùZ"úûKªù>"
ý6û(ù*1û
F G
C C N Jrù$
C :
. 4ûþ9¢ù(û'$(û)-1)KX4þù((vùW/HRKe 4û%þûvù1ùý júû'-
#þÿ4)K¢ùZMmûvù-M#û4ûvþùQ4û):TM 4û2^¢þ--Rù$ YS ý¨ú*1 W"*¢ùV 4û
wûX%1%7þ-Fù8%Gù&- ({ÿ?ªùúû $ù&()Y4þwû)-mýûa¨ù#C7" 1 ({ÿ8ùúû ()*1$
ý6û>û4ûvþùû$^ýA91* NY*-úû)pù?¢ùþùýg( ^û={ù1 4ûû"L(ù8¨ùKmûvù$
"8" û&%7þ-FùZ"R%0ùN- ({ÿRªùúûb4ûùþO 4ûM%7(* JKA* -N4ûLû1-IýQû%7þwû
" 4ûN(vþ-(ùu"(û C G
=1: Yû.ûû)1+%X 4ûpùþ*1^û4bþû)wû)Aû$ >
" ¢ùZ " 4ûb^¢û)$ B C F4K K
K0C JK-*1%" 4û24þû*þûaümû ªûvþ-*Qû)34*¢ù1ý6ûü
()(û)e1*~ùdþùX4û Ae 4ûRû(ûþ-(vù-¢ù(ûLù$ùPù_$4û^`1û "(ûK
{ùÿdû)ÁùM[vûþ:k(ùY" ^¢û)$Múû)Wý4%ùþ->%< 4ûû)34*¢ùQf
= G B D FONPB
CC N N J I CSEHJ
. û3*4ù" ù$
ùþwûb(þ-$4ùûO^ù?S-û%Qý134*4ûRùZO$4û)Qû)$1
4ûNW"~ùu()1$:%. 4ûP1 4-(ù ¢ù(vû >W" '" 4ûpþû)*~ùþ-[vù"%ýA
$g*-d" 4ûP1*~ùdþ.'b-* þ-û)$ýAÁùû)û.û=¢ù1$V Y" 4û="(ù
> %ù [vûb(þûù1ù
C
:TM 1 *$8ýQû2" 4ûb(ùwûù " 4û_û= %k%7þ-FùZ"
%ùRû)4ûþ(8 ({ÿùúûNWùR()Y4þû-mýû8¨ù):#*1M" ûvþû? þû_" 4ù " ¢ù
" 4ûùdýgjúûù¢ù-): _4û8(ù¹ù-R-*$1 4û_(ùû_> 4ûþû8" 4û2()|û Y()û)A>% B ¢ù
&$6ûvþwû)A2%kþ- " 4ûP4û2Yû)34*¢ùCSEHJ=:-@#-$4ûþb> ¢ùb ¢ù16û_%<"
()|û Y()û)AO>CC N D JSûù$9%<C C N N
J=: UþùApúù*4û % C " 4ûû34*¢ù"
%7þ B K¢ù(û)W;=
G B D F N B CCN D JX ¢ùL 4þûû&-*")KùaûùSL5(vûþ-{ù
hal-00426015, version 1 - 23 Oct 2009
$^ù1N% " 4û6C
J84ù(vûKe$^ù8" ¢ùP()~ùû9"ù*þ-%\ù(ûV*$ûvþP 4û
ÁùZIû)<()1-þ-*(QK0ùV-*4þ-%\ù(vûR^ùÿ4Y" 4û ({ÿüªùjúû:2^ûvùb ¢ùb" 4ûþû
pù- ({ÿü\ùúû -* þ-û)$ýA ù-*4þ-%\ù(vûFýQû%7þû^ù$ùZ%]ûvþ C G
=1:TM 4û^û)$ûV%
" 4ûP ({ÿüªùúû9*þ-%\ù(ûR>> 4ûvþwûìù$> 4û)6 4û («û (mû42%
B
2[vûþKU" 4ù2
ù+" û 4Qûvþwýgmù C G N : C G
=+" 1R A6ûþý ~ù6$û)û4ûvþùûYA"
_.#d-þù A.ù-Y1"û)K
G
: _ ù ~ùþ-ûvþ8-(ùûR" 4ûþû(ùþû5ûYþ_.#
({ÿV-*4þ-%\ù(vû) ¢ùM^ùFû 4ûvþ ^ûþû2ù û2 A þý4þûvùÿYV. 5mû(vû)K
$4û)Qû)1$N9> ¢ùa-$4û>% " ûM 4Qûvþwýgmùû>û)e 4û> ({ÿU:ATM 4ûb(vù1 AQûvþý mùû
ùþû8 4ûû)$ûb%< 4û? ({ÿ *4þS%\ù(vûK`" 4û -*YÁù(vþM" 4û?- ({ÿû)$15"5[vûþ
ù>4û8Yjúû)ùR" ûN- ({ÿ*4þS%\ù(vû?"ªùþ$'" 1rû)$1û:
¢ùdþ$'"þûvù$4ù6ûþ
ýA þ-$¹û=Rù\:CFEGG=J $4ûù > Wùþwû)mùû$'(K1 4ûý%7*þ(ùZ"M%»ù9 ({ÿ
*4þS%\ù(vû:
(+*-, /»ò1,#(2A÷\ð3 ÷âð(88kóJ& &:(ñ9,|ò
TM 4û?ù¢ùV4þwû)ûAû)$ýQû%7þwû6$|û)%ù1 $mþwû)( "/" 4û6(vùû %?¯þwûù
ùZûvþLùúû))Ký6û(ù*wû2" û^ùþûb $4û)-(vþ-mýQû)$^ù" û)^ù"(ùpý4Y" ûû3*4ù"
%7þù `*$^ú$%kû¢ù(.Kþ 4þû*þûaümû): bªûaúûþ&W#(vù%ýQû2 1>QK¢ù#$14û
ý6û?Ke ¢ùK< ù6Iû)ü.$4û=^`4û$!Y)Ku" R" 4ûþ-@ìþûmûaúù4 %7þR" 4û%ýþûùdÿ
%#ªùúûR, ¢ù ùûvþ:<TM ?N$4û(ýA?û)-^ù" " 4û5.(vùa34*¢ùA"W"mû
$4û)-(vþ-mýY 4û8ùúûaühýþûùdÿVÁùRªù1mþû$¹ý4 4ûN4þû*þûaümû2(vùûKQù$
ýA5 >1N ¢ùKA(ùþwû%kûþû)1(vûb%kþù(ûMjúùZL 4û>Qûvû$V%Qûùþeªùúû)K4û
þû()júûþb 4ûû)34*¢ù1&%< 4û?4þû*þûaümû `*$'4ûvùþM" 4û?-*1~ùþ-.:
TM 4û?$1¢ùY( %1Rùúûb¹ùR~ùûþM%¨ú-()$ *$'%$4û1" 'R*( d^ùmûvþ
" ¢ù " û,.(ùþùû,%$údùþ-~ù % " 4û?údùþ*'34*¢ùA"W"mû'¨úÀúû$ Cwûvû
û("RI&%7þùb$-()*-R% 4û#þ-$4ûvþ<%`^ùW"*$û)¨úÀúû$UJ(vùýQû#$4û(vþ-mýQû)$
ýAV" û2%7>Nû=>%û)34*¢ù1#%7þ 4ûý¢ù-(b3*4ùA"mû ()þwþû $R" 4û
`*$,$û)1 C F4K K0C
J"ù$ " " 4û9. @ùdþ-ûmù/(Ygû)A"?%a" ûY 1þ[)A{ù
`*$(úû)()W.K B C F4K K0C JPù$ "gC F4K K C J=f 4ûb($W"5%u^ùa(ûþwúdù(þûvù$
A
AC
D A C B UJ AF
D A C"UJ A G = K
CSE9<AJ
" 4û?($W" %eY(û)A"*1 ()ûþwúdù"d " 4û F ü$mþwû)(%þwûù$1
A%B
AC D B A%B
AF D "
A%B
A D
A
AF G = K CSEGAJ
ù$d " û ¨ü.$1mþû(
A "
AC)D B A "
AF D " A "
A D A A G
=I C =AJ
hal-00426015, version 1 - 23 Oct 2009
%Rû)34*¢ù1ìù$Y |üþ-ú~ùL-Ymû5ªùjúû'*1" > 4û4ûúûvþ56%7*1("
$4û)Qû)1$O VC7%7þ<S{ù1(vûJ:Q&«üþÀúmùA*11()*1$ýg" ìù2$û)Qû)$4û(vû
F K Yù$
C
$_ûû)D"8û1-):QRûúûþ- 4û)û)?W22 -mýûN%ù¢ùW[vûP 4û
(()*4þwþû(vûN%<1*~ùdþmûªýA'ÀúR Mwûb¹ù5()¨úûmûA2Y:
Aû*1$W^¢þ--%7þV-*11$4û6û$ F 1:ø ûù-*(û+ ¢ù G
L D
<C F4K0C J&> 4ûþû L b" 4ûR(S{ùACâù$ gúûJ&$û)1 uKuR*( mùþûþb ¢ù
" 4ûN^ùQQûvþ-*4þý4ù"
C F4K0C
J=:`TM Rù>MYû)û)(&ûvþ->%eþ$4ûþ
C F4K0C
J B
> Wþwû)-6û(&" L B C F4K0C J=:1TM 4ûPû wûb%»û)34*¢ùrþwûù$1)f
A
AC D B A
AF D L A%B
AF G = K C EJ
ù$uf
A%B
AC D B A%B
AF D A
AF G
=I C J
Qb(ûN ¢ùKGù" 1*
+ ¢ùý6ûû)64ûmû(û)$>W" Yþû)-6û(b" L
'%kþAb% K
B
4ùFýQûvû ÿû1KIý6û(ù*wû6^ù@4þ-þ-MV^ùûvþR" 4ùçùA!" ûvþûvþ-
LþWû8û=("WRFû)34*¢ùZ" C EJbC7Y¢ùþ-(*~ùþKù# 4û2-*~ùþ-.Kªûû=6û(
" 4û
F
$4ûvþ-údù"Àúû_Y51^`W.1J=:
Tùdÿû_ L
ù *W %7þ
uKAþ$*(û6-*( " ¢ùZ
G L
C7 4û2-*4ý(þ1
>"^þû)(vù" 4ùb Lúû()W.dªùb$4ûvþ-úû$6^¢þS"ýA ªûvþ-*]JK1{ùdÿû ù2*W
%7þ B ù$6( ûR4û= *W"b%7þ C ù$ F *1( 6" ¢ù&" û)mþþùY&4û?> 4û)6 4û)þ
þù9d1 4-(ùk*> XK" û.û34*¢ù"M%7þ
Wù$ B ýQû)()^ûf
A
ACED B A
AF D A%B
AF G = K C AJ
ù$uf
A%B
AC
D B A%B
AF
D A A%F
G
=I C ZI4J
TM wû$û)34*¢ùZ"ýQû)(^ûN$û)A"(ùkW% B G
k:UTM b(þþwû)-g1$2"Y" 4ûN:ü.(ùmû$
ûªùúû: Aû
B G
G
Ke" û.#?û)34*¢ùZ"dC J$ù$ C ZI4JpýQû)()^ûV 4û
mû84ûf
A
AC D A
A%F D A AF G
=JI C J
hal-00426015, version 1 - 23 Oct 2009
ýA " û6( ¢ùû6%?*4ÿ4>B%7*(=" %kþ
"BC
D
EJ=: > ¢ùV 4û
*mùþW./R" 4û ù(û¹ùR" 4û 4û%7*$ ýQû%7þwûKX%2(*4þwû'ù 4û= þû*W
ùùcK¢ý6û(ù*wûR%O 4û -mýW. %O-ú1" ûP%7*wû9CSE<AJKXCFEGAJLù$ C =AJrýA
&û)^ù M(û" 1$ > " G
=ù$d5$4û6û$4û)1(vû :
AûM*M1 ÿ(ù#" 4û_$1(û)-û)-ªû)34*¢ùZ"#%7þ# 4û_4ûùþaªùjúû?4þ4ù:ü
¨ù 4ù ªùûvþM RK1*-P" 4û8ù^û2(ù1:TM û8Fù- ()ûþwúdù"
mû)$)f
A
AC D A%B
AF D A "
A D B A
A%F D " A
A G = K C AJ
TM 4ûN()$1" %eY(û)A"*()1ûvþúdù"Áù
F
ù$ Fþwûù$uf
A%B
AC D B A%B
AF D "
A%B
A D A
AF G = K C HJ
ù$
A "
AC D B A "
AF D " A "
A D A
A G
=I C <AJ
Aû_*1"ù-*(û ^¢þ--2 ¢ù&" 4ûP(vùVmù>&%7þ gK F K C
ù$
B
ùþwûP 4û ù^ûpùb
" 4û>û4ûvþ-(M-*1~ùþ-.N% " 4û #*4þ-ûvþ-û)34*¢ùuK" ¢ùa C K F C
ù$ B "C :QTM 4û û3*4ù"!C J=K C 2$Y¢ùA2()Y¢ùþwû)$
"
C L
:`TM 4ûvþwû%7þwû$ùZ>mûù$9þ$4ûþRû34*¢ù"/C Jªý6û()(û)f
A
A%C D A%B
AF D B A
AF D " A
A G
=I
;YmùþW " " 4û ED(ùwûKOIû(vù! 4û) ÿ/%7þù,-YmûVªùúû*1"uKXc:¯û:
G B
:QT»ùÿ4
G B D
Eù_4û *4ÿ4> %7*(="uKg4û ^`$1_" ¢ù5C AJù$
C HJªþû)$1*(vû?"(ù9mûû34*¢ù" %7þ
A
AC D A
AF D " A A G
=JI
Aû&*> Lþ-ûû3*4ù"/C <AJ >W" " 1M4û= %7*(="
f
A "
A%C)D A "
AF D " A "
A N A "
A%FD A
A G
=I
TM 4û>^¢þS 4þûû&ûvþYa()þwþû $V? 4û #*þûþû)34*¢ùuK> ûvþûvù 4û>~ùS
.#>ûþY()þwþû)-g$NM" 4ûúûþ-(ùúþS"(.: Aû*ÿùk" 4ûmþk(Aþý*1uK
hal-00426015, version 1 - 23 Oct 2009
$1*(vû¹ù4û)ûvùýû(þþwû)( "!%Pþ$4ûþ
C
:#TM ^ûvùV ¢ù S{ùþS"
%kþ ù þþ-{ù4ù ~ù ()1$ C\ù,-" 0ªùúû+þ¢ù¨ù" " û F
$mþwû)(="'>W" d $4û)Qû)1$4û)(ûJKgúþ-"()W. û)ûvþùZ"dM"(ý6ûû=Qû)(=û)$ù
" 4û ^4þ-Xþ$4ûþPþûmûaúù4e"8*4þ<" 4ûþ-:QbûM IûúûþO" ¢ùe" X$|û)XO4þû()*$4û
úþS"(). û)ûvþùZ"ùa 4ûvþOþ-$4ûvþùZO" 4ûrû$û>% " 4ûrý4þwûùÿ4?[)4ûKùO 1>
%7þ -ù(û8ýA$>»ûþûþ4û CSEGGGAJ.ù 4û8û)$1û %Lý þû):eTM 1$úûvþ-@Aûþû-"
34*4û)S"!$ýQû$ " 4û-()Qû %>" û4þûû4Y¢ù6ûþ)KPý*R>IýQûV" û%7(*R%
%7*1"*þû8" 4ûþû="(ùAù$Yû6ûþ(û)Aùk-*$mû):
Qûmû("P 4ûLúþS"(.K4 4û2S-û$ýQû2úû$a" ûbù^ûùa" 4ûb4û2-úû)$
%7þa" 4û&4þû-*4þû_û)- `*1$u:4TM 4þ-júû)#*4þLgAKA¢ù(û)W9" ¢ùZªùZ#ûù$Nþ$4ûþ
" 4ûV1*~ùdþ *1/P%7þ B C IJCâù$6%7þ
UJ?" û ù(û8ùP%7þ " û4þû-*4þû
mû>(ùwûK *'"5" 4û.ù$$1"'%" 4ûN()1-{ù4bQûvû$+4û(vûùdþ-'"YûRþ-$d%< 4û
.ùûùd( ¢ù1û9%O%kþù^ûP%þû%kûþû(vûKu" 4û *$úû)()W. "YýQû) -*S?4þ þfü
"¢ùQ :.d¢ùþS"(*~ùdþ)K1 4û8>$4ûY%" 4û?ªùjúûaü£ý4þûvùÿ4$^ù' 4û
$mþwû)(="d-(ùû)>ÿû2 4û?34*¢ùþwûpþ->%<(û:
TM 4û>(ù()*mù"ùdýgjúûM-*û-a ¢ùO PýQû) 4ùjú*4þO *1úûþù Z%7þO«ü4ûùþ
«ü$-6ûþ-úûbùúû): 2" 4ûþÿ4$ %ªùúûùdþûÿ4> "ìý4þwûùÿUKmÿû&" 4û8(vûvù
ùúû)5$4ûû)0ªùûþ'C7>W" uK4þù("(ùKk1^`1û$4û)" UJPþP" ûþùú. ªùúû)
4û¹ù"Y- 4ûvþwû:_|û) 4û)þ94þwûù$1 " 4û @$1mþû(@%7 " û ù(û
34*¢ùþwû8þN~ùVTM 4û8ù-IûvþN"d" P34*4û-"$4û6û$R@¢ùdþ-"()*mùþ?@ 1
4þû()û?(ùWýQûNwû>" ûN-ùA&%<(û_%" 4ûý4þwûùÿ454þ(vû):
(+*-,.0/»ò1,#(2A÷\ð43 ÷âð+ñ , î#" ö( ,M5ðóQð 8\÷âð4,#(4ò:÷kñP* ^ô÷ 6,|ò ÷kóQð
TM &û(dM"Yÿþwû?()û)W¹ù>" ûNªùúûaü£ý4þûvùÿ4,ER: þûNQû)()W%~ü
(vùW ªû5^ùÿûR 4ûR()4û)(="?ý6û=.ªûû)/ 4û9*16%L 4ûìû)34*¢ùZ"5CSE9<:ü =J
ù$6 4û ¯þwûù ªùúûühý4þwûùÿ41:uTM 4û94ûû)$ " $1" "ùþ-û_%kþ 4û9ûPý«ü
ûþwúdù" " ¢ùZN 4û51düªùúûû)34*¢ù1pùdþû5()ûùþ-6¨úù$ù8" 4û5"^û % 4û
ý4þûvùÿü.* ù$uKL4þû*^ùýW!(ûd(û¹ý6û=%7þûYý6û(ù*wû+" û+Qû
" 4û$ü
úûþû)K6ù * 4û.û)34*¢ùRùþwû?$4ûvþ-úû$+*1$4ûvþM" û$ù-*Y1'%ùY-*4þ-%\ù(vû
> Yù9-FùQ-Qû:TM 1>W"*¢ù þùZ" 4ûþ&(Y Fù44þý1mû)Y#> 4ûþû
" 4ûVû=9%M-*~ùþ-. R-*Sù>W"4û ¢ùR-(û> 4ûþû%ù1$0(û(û^ù«ü
" ûvþIù4þ-FùdC7þIù 4ûvþa(û" 1$UJX ¢ùL$ýQûb*wû)$Y" -úû& 4û&4þý1mû)
ùN ¢ù$QK»ù ù14þ^ù" $0ûþû)AN%kþ " 4ûY4û5" ¢ùZPûù$1?d 4ûY1*~ùdþ
ý6û ¢ùú*4þ:
2ÿ4>6 ¢ùb$-6ûþÁû 0û(2()()*þþ8ùZb 4û 4û_þ-$4ûvþ&d" 4ûP ¢ù
ùZûvþù4þ-1FùZ",C7" û ^ùu¢ùþù^û=ûþýQû)Y 4û `*$$4û)" uKU" 4ûNmûvù$
þ$ûvþý6û?" ûû3*4ù"a%Q 4û&4þûaú*aû(UJXmû$9" 4û8þ-ûIû)dü$4û þmû
C 8$ 8JIû)34*¢ùVV 4û8()YjúN%kþù(û:TM 4û8$ û3*4ù" ¢ù 1R^`ûb(û