• Aucun résultat trouvé

Power-Law Bounds on Transfer Matrices and Quantum Dynamics in One Dimension

N/A
N/A
Protected

Academic year: 2021

Partager "Power-Law Bounds on Transfer Matrices and Quantum Dynamics in One Dimension"

Copied!
23
0
0

Texte intégral

(1)

HAL Id: hal-00080559

https://hal.archives-ouvertes.fr/hal-00080559

Submitted on 19 Jun 2006

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.

Power-Law Bounds on Transfer Matrices and Quantum Dynamics in One Dimension

David Damanik, Serguei Tcheremchantsev

To cite this version:

David Damanik, Serguei Tcheremchantsev. Power-Law Bounds on Transfer Matrices and Quantum Dynamics in One Dimension. Communications in Mathematical Physics, Springer Verlag, 2003, vol 236, pp.513-534. �hal-00080559�

(2)

* +! ,!#%'&-%./ 0+%.!#1%'

235476829237:$3<;=68>?37;729@'ACBED<F=AG6IH=JLK=ACBAC:JEK3<;H7@MAG4N

OQPSR'TVUXWZYZ[RM\]Y7^X_V`aUXYZbcR'[UXYZdfeMg<hjijkml5k5n5oqprUXstdu_8^vWZ\cdfU wx\VgyYZdzYZ{cYZRr^X_V|=R'e}bc\c^vsz^v~jvo€‚UvgZUvƒ„RM\VUVo

pr…‡†Vˆjˆhvi„o5‰Š„…

‹1‰S`aŒŽj]hXl`a…€`’‘(o„‰S\cdz“vRMW}gydzYc”RƒL•–‘WZstR'Uj\Vg'o]—1˜€<˜55nXij†co5™šœ›]ijj5n‘WZstR'Uj\Vg p”R'ƒ„RMžLo

™VWUj\Ve.R

Ÿ

š [UXdts ¡<ƒVUX[UX\cdt¢V£duY}gM˜eMUjsuYR'e}bE˜R'ƒc{Eo„gyR'WZ~v{cRMd ˜Y}e}bcRMWRM[£sfUX¤C^j[UqYbE˜{c\cdt“všœ^jWstR'UX\GgM˜_8W

hjjj(…S`Š¥Š5{V¤„¦§R'e.Y$pIstUvgZgZdz¨GeMUXYZdt^j\E¡<cˆq©(ˆ'

ª

R' «’^vWƒVgM¡QŠ„e}bcWm¬^vƒcdz\c~vRMWS‘TCRMW}UqYZ^vWg'oc©{VUX\]YZ{V[­P]\GUX[dte'gMoc™7dt¤G^v\VUje'e.dE€<^jYZRM\]YdtUjs

®7¯m°œ±m²q³X´±5µ¶(·Q¸m¹º·§» ·§¼M½7¾}¼$¾}¸¸m¹ ¿.¾}ÀœÁ½ ¿ÃÂMÄq¾}¼.½ ÄÅ9Ɓǁ¼m¾}Å ÈÉÀZ¾}ÊvÊÉ¿ZËL·§¹ÌX¿ÍÄm¼mÆm»EÎt¿Í¹

ÆmÈÉ»ºÀ§¹ ·x½ · ¿Í¼·§ÏfÆmÈÉÅ ·§¼m» Èɿͼq¾}Ê

@

ÀœÁm¹yпÍÆmÈɼmÑÍ·§¹¿Í¸j·§¹ ¾½ ¿Í¹º»ËÁmÈÉÀœÁ(ÈÉ»QÌq¾}» ·§Æҿͼ(¸X¿ZËL·§¹ºÏfʖ¾yË

ÌX¿ÍÄm¼mƁ»‚¿Í¼½º¹œ¾}¼»ºÎz·y¹=ž½ ¹ºÈÉÀ§·y»yÓ

6

½‚»ºÄÔ À§·§»7½º¿Áq¾§Õ.·r»ºÄmÀœÁÌX¿ÍÄm¼mÆm»<Îz¿Í¹<¾¼m¿Í¼m·§Å ¸½ÖÇ

»º·§½G¿}ÎX·§¼m·§¹ ÑÍÈÉ·§»Zӄ¶·¾}¸m¸mÊÇQ½ºÁmÈÉ»c¹ ·§» ÄÊ½V½º¿7Õ}¾}¹ ÈÉ¿ÍÄm»VÅ ¿'Ɓ·yÊÉ»y×}ÈɼmÀ§ÊÉÄmƁÈɼmÑ7½ºÁm·EØVÈÉÌX¿Í¼q¾}À§À§È

K ¾}Å ÈÉʽ ¿Í¼mȖ¾}¼vÓ

ˆj˜ÙÚEÛÝÜÝÞ=ßàáGÛLâ8ÞÚ

pI^j\Ggydfƒ„RMW1UgZRMsz_֚œUvƒm¦§^jdt\]Y^vTGR'WUXYZ^jWãä^j\UgyR'TVUXW}UX¤VszRåSdzst¤GR'WyYgZTVUjeMRæèçŽéM‹jêºëSìí ^jW

éM‹XêºîQí͘ï|ÃbcRƒc]\GUX[dte'UXs‚R'“j^jst{„Ydz^v\ð^j_UX\ñdz\VduYdtUjsIgyYUqYRòôóõæö÷Íò$÷çøˆjo7dfg~jdt“jR'\ð¤5

ò1ê8ùyíçúRMž5T=ê§û üœù§ãíxò˜«ðRgZbVUjszs‚ƒ„R'\c^XYRÒò1ê8ùÍöZýíç­þ8ò1ê8ùyíÍöÿ.o bcR'WZR ç ÿÒdfgYZbcR

e'UX\c^v\cdte'UXsQ¤GUjgZdtg^j_Ãæ stUj¤GR'szstR'ƒñ¤5ðýŽó9ë1ì^jWýŽó9îr˜õ‘\cR{Vgy{GUXstszYUX¢vR'gò-gy^¥YbVUqY

ò1ê cöZýíç ò1ê8ýíS¤GRIR'szs<st^„eMUXstdMR'ƒ êÖ_UjgyY1ƒcR'eMUm5dt\c~UXYdt\„¨V\cdzY§cí͘™V^jW1R.žcUX[TcstRjoÝ^j\VR(eMUj\

Y}UX¢jRò9ç ÿ O

dt\¥YZbcR(^j\cRMšœƒcdz[RM\Ggydt^j\VUjsEeMUvgyRv˜I«9bcdtstR¤GR'dz\V~ sz^„e'UXstd'R'ƒ¥UqYSùIç VocYZbVRrUm“vR

TVUve}¢jRMYSdz\’~jR'\cRMW}UXs7gyTcWR'Uvƒcg duYbaYZdt[R(^q“vRMW YbcRÒ¤VUjgZdtg1˜wœY$dtg$eM^j\5“jR'\cdzR'\]YYZ^¥e.^v\Vgydfƒ„R'W

YbcR$YZdt[R.šxUm“jRMW}UX~vR'ƒ]{VUj\]YZdzYZdtR'g

êý‚öí‚ç

ˆ

òêùÍöyýí

‹

ùÍö

ê8ý‚ö!íQç#÷.ò1÷

‹ ç ˆ$_8^jWUjszs"$# &%

êyˆí

|ÃbcR'WZR¥RMž5dfgyY¤VUjgZdfeMUXststïY'I^ïTC^vggZdz¤cdtstduYdzRgYZ^ e}bVUjWUveÍYRMWd'RYbcRgZTcWZRUjƒ„dt\c~ñ^X_1YZbVR(rUm“vR

TVUve}¢jRMY'˜Q™7dzW}gyY'oc^v\cReMUX\eM^j\VgZdtƒcRMWÃYZbVR{cTcTCRMWSUj\Vƒ+sz^)rRMW W}UqYR'g UjggZ^5eMdtUXYZRƒYZ^YbcR_Uvg§YR'gyY

ê^jWÃYZbVRgyst^)IRg§YÍíQTGUXWZYÃ^j_=YbcR*ÃUm“jR1TVUje}¢vR.Y'˜,+R.Y

-

ê/.<öí‚ç

102&23

5476

‹

ê8ý‚ö!íÍö8.(9 &%

™V^jWÃYZbVR$_UjgyYZR'gyY TVUXWZY'o„^v\cRƒ„R.¨G\cR'g

2 Ó 2

ӁËE¾}»» Ä¸m¸X¿Í¹º½º·yÆ1Èɼ¸q¾}¹½ÌMÇ

;<@

Ø D

¹œ¾}¼.½

;

¿mÓ

2<:@;:<;<>=<>=<>=

Ó

(3)

. 6

ç9gZ{cT .(9õ

stdz[õdt\„_

"!$#

st^j~

-

ê/.<öí

sz^v~

ç9&%ö ê hjí

. ! ç gy{VT . 9õ

stdt[õgZ{cT

'!$#

st^j~

- ê.7ö!í

sz^v~ ç  %

êºkví

ê duYb e.^j\5“vRM\]YZdt^j\ñst^j~çèû)( í͘…Sggy{V[ÒR YZbVUXY.* #c˜|ÃbcR'\ïduY_8^jstsz^)g$_8W^j[ YZbVdtg

ƒ„RM¨V\cdzYZdt^j\+YZbGUqYÃ_8^jWSUj\5 +-,.+ . 6

ö0/ # co

102&23

541

132

êý‚öí 954

66 ê›]í

_8^vWSUXsts 9 ˆ* duYbU{c\cdz_8^jW[ êdz\ 1í e.^v\Vg§Y}UX\]Y74Ҙ ™c^jW . !

oGUgydt[dzsfUXW ¤C^j{c\Gƒ¥bc^jsfƒcg^v\

gZ^j[R$gyR>v{VRM\VeMR1^j_Ydz[R'g &8:9<;"( ˜I‘\cRe.^j{Vstƒ YUX¢vRU(gZszdt~jb]Yszƒcd>=ÝRMWRM\]Yƒ„R.¨G\cduYdz^v\¥^X_

.&* gZ^ÒYZbVUXY^j\cR$bVUvgr_8^jWUj\]?+5,.+ . 6 o

102&23

54 1

132

êý‚öí89-4ê@,cí #  ê ijí

êºUX\VƒgZdz[dtstUjWZst_8^jW . !

í.oj¤c{„YYZbcR[RUX\cdt\c~^X_Ý\5{c[¤CRMW}g .&* dzstsc¤CRR'ggyR'\]YZdfUXstszYbcRSgUX[Rj˜

|ÃbcRgZTcWZRUjƒ„dt\c~ÒWUXYZRgr_8^jWrYZbcRgZst^)IRg§YÃTVUXWZYÃ^X_7YZbcR ÃUm“jR1TVUje}¢vR.Y eMUX\+¤CR$ƒcR.¨V\cRƒ duYb

gZ{c[[UqYZdt^j\ñ^q“vRMW ¡ ý

BA

7C&UX\GƒðYUX¢5dt\c~dt\„_. dt\ êºhjí.orêºkvíêºgyR'R UXsfgy^EDhXGF_8^jW(U

gZszdt~jb]Ysz+ƒ„d>=ÝRMWRM\]YƒcR.¨V\cdzYZdt^j\Cí͘ wx\YbcRTcWR'gZRM\]YSTVUjTGR'W rRgybGUXsts¤CRdz\]YRMWR'gyYZR'ƒEoGbc^)rRM“vRMWo

^v\cszdz\+YZbVR$_UjgyYZR'gyY TVUXWZY ^X_7YZbcR*ÃUm“jR1TVUve}¢jR.Y˜

|=^ƒ„R.YRMW[dz\cRYZbcR\5{c[(¤GR'Wg . *

_8^vWIe.^v\Ve.WR.YR ]{VUX\]YZ{V[-gZ„g§YRM[gMov^j\cRgybc^v{csfƒ(¤CRUj¤cstR

Y^WZR'stUXYZRdzYQY^YZbVRSgyTCR'e.YZW}UXsGTcWZ^vTGR'WyYdzRgQ^j_L㠘7«9bGUqYdfgdt\_Uje.YI¢5\c^) \ UjWZRgZ^j[R~vRM\cR'WUjs

st^)IR'W¤C^j{c\VƒVg _8^jW.&*r˜S…szYZbc^v{c~jb\c^XY$g§Y}UqYZRƒ¥dz\aYZbcdfg_8^vWZ[¥oCduY_8^jstsz^)g_8WZ^v[ YbcRTVWZ^5^X_g

^j_HDh„oVhX†GFEYZbVUXY

. 6 9 ˆ

ƒcdz[JIÒêLK&MEí.ö 꺍ví

Uj\Vƒ _8W^j[ YZbcRTcW^5^X_7^X_DhjNFEYZbGUqY

. ! 9 ˆ

ƒ„dt[OSêLK&MEí êœnXí

ê duYb

9Žˆdt\YZbVRre'UjgZR^X_Pº‹jêºëìyí=UX\Gƒ

燈dt\YZbVRre'UjgZRQ^X_Pº‹XêîQíZí͘ åR'WZRQK&MdfgEYbcRrgZTCR'e͚

YWUjsV[R'Uvgy{cWRSUvgZgZ^„e.dfUqYZRƒ(YZ^YbcRgyYUXYZRò UX\GƒÒYZbcR^jTCRMW}UqYZ^vWãïo„UX\Gƒƒ„dz[JIÒêLKí.öIƒ„dt[ROêLKí

ƒ„R'\c^XYR<YZbcRê8{cTcTCRMWÍíLåUX{Vgƒ„^jW0=(Uj\Vƒ$TVUje}¢5dt\c~ ƒ„dt[ÒR'\VgZdz^v\VgE^j_vYbcRQ[R'Uvgy{cWRBK‚oWZRgyTCR'e.YZdt“jRMstj˜

™V^jW$ƒ„d>=ÝRMWRM\]Yƒ„R.¨G\cduYdz^v\VgUX\GƒaWRMsfUqYZdt^j\Gg¤CR.Y'rRMRM\’YZbVRM[¥oEgyR'RjoÝ_8^vWRMž„Uj[TcszRvoSD›Go<ˆmn]oLk]nF ˜

wx\TVUjWyYdteM{csfUXWo„YZbcRÒåSUj{VgZƒc^jW0=’ƒ„dt[ÒR'\VgZdz^v\dtgƒ„R.YRMW[Òdt\cRƒ¤5 YZbVR[^vgyYe.^v\]YZdt\]{V^j{Vg TGUXWZY

^j_YZbVR[ÒRUjgZ{cWRTK‚¡

ƒ„dt[JI(êUKíQç5KݚœR'gg§šxgZ{cTWV

6

ê@XíÍö

bcR'WZR'V

6

êUX(írdtgÃYbcRst^)IR'Wrst^„eMUjsLR.ž„TG^v\cRM\]Y ^X_YK‚o

V 6

êUX(íç stdz[õdt\„_

Z

st^j~SKQê0DX û\[„ö0X];^[F8í

st^j~B[

ö_X-ó+gZ{cTcTK,%

™V^jWÃYZbVRTVUje}¢5dt\c~҃cdz[RM\Ggydt^j\EoIR$bVUm“vR

ƒ„dt[

O

êUKíç`Kݚ RgZgyšœgZ{cTV êUXí.ö

(4)

_ "

bcR'WZR'V

!

êUXí dtgrYbcR{cTcTCRMWst^„eMUjsLR.ž„TG^v\cRM\]Y ^X_7YZbVR[ÒRUjgZ{cWRjo

V !

êUXíQç szdt[ gy{cT

Z

st^j~ KQê DX û [„ö0X`;^[NFÖí

sz^v~B[

ö X-ógy{cTVTK,%

‘\cR(eMUX\^v¤VgZRMW“jR$YZbGUqYS_8^vWåUX{Vgƒ„^jW0=ðƒcdz[RM\Ggydt^j\EoGYZbVRWR'gZ{csuY1dtggystdt~jb]YZst+gyYZW^j\V~jRMWYZbVUj\

꺍víÍo„\GUX[RMstjoê ijírbc^vstƒVg duYb . 6

ç9ƒ„dt[ I êLK M í͘

wœ_ ^j\VR ¢5\c^)g¥YZbVR e.^v\]YZdt\]{VduY§ TcWZ^vTGR'WyYdzRga^j_ÒYbcR gZTCR'eÍYWUjs[R'Uvgy{cWR êRM\VeM^5ƒcR'ƒ dt\

V 6

êUX(íyí+UX\Vƒ ^j\cRðbVUjg+UXsfgZ^ gy^v[R’dt\„_8^jW[UqYdz^v\ UX¤C^j{„YYZbcRñƒ„ReMUm ^X_YbcRð~jRM\VRMW}UXstd'R'ƒ

R'dz~vRM\„_8{c\GeÍYZdt^j\Gg M‚ê8ý‚ö XíÍocUvgZgZ^„e.dfUqYR'ƒY^(YbcR$g§Y}UqYZR$òo5YZbcR'\^v\cR1e'UX\dz[TcW^q“jRSYZbcR$st^)IR'W

¤C^j{c\Gƒð꺍ví_8^jW . 6 Dhj„oGh]n F ˜

`^vWZR(dz\5“j^vsz“vR'ƒ(]{VUj\]YZdzYZdtR'g bcdte}bðƒ„R'ge.Wdt¤GR(YZbcR(_UjgyYZRg§Y$TC^jWZYZdt^j\a^j_QYZbcRÃUm“jRTVUve}¢jRMY

UjWZRYZbcR$Ydz[RMšœUm“vRMW}UX~jRƒ[^j[RM\]Y}gÃ^X_7YZbcRTC^vgZduYdz^v\^vTGR'WUXYZ^vW'¡

þ M íQç

ˆ

ý

ò1ê8ùÍöZýí

‹ ç ý

ê8ý‚ö!íÍö #õ

꺏ví

ê bcRMWR

ý

dfg YZbVR\c^jW[ dz\aë1ì dt\¥YZbcRÒeMUjgZR^X_SPº‹jêëìZíZí͘‘\cRe'UX\aƒ„RM¨V\cRYbcR(UvgZgZ^„e.dfUqYR'ƒ

{cTVTGR'WUX\Vƒ+st^)IR'Wr~vWZ^)ÃYbRMž5TC^j\VRM\]Yg'o

6

êÝíQç szdt[ dt\„_

"!$#

st^j~þ

M í

sz^v~ ö

Uj\Vƒdt\¥UÒgZdt[ÒdtsfUXWÃ[UX\c\cR'Wr_8^jW

!

êCí͘I|ÃbcR$\]{V[¤CRMW}g

*êÝírƒ„RMTCRM\VƒEocdz\+~jR'\cRMW}UXs o5^j\YZbcR

gyYUXYZR$òSoc¤V{„Y IR dtszsszRUm“jRYZbcRƒ„R'TGR'\Vƒ„R'\Ve.Rdt[Tcszdfe.dzY'˜wœYdtgeMszRUXWrYZbGUqYê8›5írdz[TcstdtR'g

þ M

1í89-4

C 1 6

66

_8^vWUX\5., # cö0/ # {c\cdz_8^jW[szdz\ 9 ˆUj\VƒYZb5{Vg

6

êÝí 9&.

6

˜I|=^j~jRMYZbcR'W duYbïêví

YbcdtgÃ5dtRMsfƒcg

6

êCí 9

ƒcdz[JIÒêLK&MEí.ö 꺆ví

YbcR’¤C^j{V\Vƒ [^]g§Y+^X_ÖYZR'\ {GgyRƒ9YZ^õ¤C^j{c\Vƒ _8WZ^v[ ¤GR'sz^)øYZbcRð[^j[RM\]Yg+^j_YZbcRñTC^vgZduYdz^v\

^vTGR'WUXYZ^jW˜‚Š5dz[dtstUjWZstjo„^v\cRUXsrUm„grbVUvg

!

êÝí 9.

! 9 ì

ƒ„dt[ROêLK&MEí.˜

wœYdfgdt[ÒTC^jWZYUj\]YYZ^^j¤GgyR'WZ“vR(YbVUqYÒg§YWZdfeÍYdt\cR]{VUjszdzYZdtR'g

6

êÝí#.

6 ö !

êÝí#&.

!

[Um¥^„eMe.{VW'˜$|ÃbcdfgSdfg1TG^]gZgZdz¤VszR(du_QYbcRrUm“vRTVUje}¢vR.Y1bVUjgTG^vsz5\c^v[dtUjszstƒ„R'e'Um]dt\c~Y}UXdtstg$UXY

dt\„¨V\cdzY§j˜Q…gZgZ{c[Rjoc_8^jW R.žcUj[ÒTVszRvo5YZbVUXY _8^jWgZ^j[R . #.

6

UX\Vƒ+gy^v[R #õco

0223

54

ê8ý‚ö1í 954 6 êyˆ'ví

{c\Vdu_8^vWZ[st(dt\$9 ˆv˜7|ÃbcR'\

6

êCí89&.ûL˜‚|Ãbcdfg¤C^j{c\GƒdtgI¤CR.YyYRMWIYZbVUj\

6

êCí89&.

6

_8^vW+sfUXW~jR1RM\V^j{c~vbE˜

RM\VRMW}UXs‚st^)IR'W¤G^v{c\Vƒcg$_8^vW$YZbcRYdz[RMšœUm“vRMW}UX~jRƒ[^j[RM\]Y}g* bcdfe}b’Y}UX¢vRÒdt\]YZ^Uje'e.^v{c\]Y

êdz\ïUgZ^j[R bVUXYbcdtƒVƒ„RM\ñ_8^vWZ[ í1TC^jst]\V^j[dtUjs<YUjdzsfgMo<UXWR^j¤„Y}UXdt\cR'ƒðdt\5Dk FIUX\Vƒ-Dk]n Fœ˜|ÃbcR

TcW^5^X_gïUjWZR ¤VUvgyRƒú^v\)YbcR gZTGReÍYWUjsYZbcR'^jWRM[/Uj\Vƒ-ƒ„RM“vRMst^jT-YZbcR9dfƒ„RUjgï^j_ {VUjWZ\cR'WZd

Dzˆ'†NFœ˜ |ÃbcRõ^j¤„Y}UXdt\cR'ƒúsz^)rRMWð¤C^j{c\VƒVgðUjWZR R.ž„TcWR'ggyRƒ‡dt\#YZR'WZ[gð^X_+gyTCR'e.YZW}UXs[R'UjgZ{cWR

K&M DkcoÃk]n F$^jWdz\ YZR'WZ[g^X_¤C^XYZb gyTCR'e.YZW}UXs1[ÒRUjgZ{cWRUX\Vƒ ~jRM\VRMW}UXstd'R'ƒ RMdt~jR'\„_8{c\Ve.YZdt^j\Vg

M<ê8ý‚ö0X(í Dk5n F ˜ |=^ñUjTcTcstïYZbVRM[äY^ñeM^j\VeMWZRMYZR ]{VUX\]Y{c[ gZ5gyYZR'[gMoI^j\cR¥gybV^j{csfƒ bGUm“jR¥U

~v^]^„ƒ ¢5\c^) szRƒ„~jR¥^j_TK&M‚ê0DX û-[5ö X ;][NFÖí.öJX óúgZ{cTcTK&MêUj\Vƒ UXsfgy^ñ^j_YbcR¥_8{c\Ve.YZdt^j\Vg

-!

êUXíç#"

102&2$ !

M<ê8ý‚ö ‹dt\YbcR eMUvgyR^X_IYZbcR[dzž„R'ƒ’sz^)rRMW$¤C^j{c\VƒVg$_8WZ^v[ Dk]n F8í͘

(5)

Š5{Ge}b U$¢]dt\Vƒ^j_Ýdt\„_8^vWZ[UqYdz^v\dtgIƒ„d eM{csuYIYZ^^v¤„YUjdz\dt\YZbcR[{cszYZdfƒ„dt[RM\VgZdz^v\VUXsCeMUvgyRv˜=å^)Ú

R'“jRMWo5dz\¥^v\cRƒ„dz[R'\Vgydt^j\+_8^vW ^jTCRMW}UqYZ^vWgrã0^X_=YZbcR$_8^vWZ[

ãò1ê8ýíç9òê8ý¥ûõˆí&; òê ýJ; ˆí&; êýíxò1ê8ýíÍö êyˆjˆí

YbcRMWRRMž5dfgyYW}UqYZbVRMW1R=ÝR'eÍYdz“vR[R.Ybc^„ƒcg1¤VUjgZR'ƒa^j\YbcRÒgyYZ{Gƒ„^X_gZ^jst{„YZdt^j\GgY^ YZbVR_8^vWZ[UXs

R'dz~vRM\„_8{c\GeÍYZdt^j\R]{VUqYdz^v\㠒ç X =öTX ór˜wx\aTVUjWyYdteM{csfUXWoVYbcR(~vWZ^)ÃYbTcW^jTCRMWZYZdtR'g^X_

YbcRYWUj\Vgy_8RMW1[UXYZWduž êý‚ö0XíSUjggy^„eMdtUXYZR'ƒ( duYbaYZbVdtg1R]{VUXYZdt^j\UjWZRÒe.st^vgZRMst¥WZR'stUXYZR'ƒ( duYb

YbcRgyTCR'e.YZW}UXsLTcW^jTCRMWZYZdtR'gr^X_7^jTCRMW}UqY^jW ã™c^vWgydt[Tcszdfe.dzY§jo5_8W^j[ \c^) ^v\ rRgybVUjszsLUjsÃUm„g

Y}UX¢jR1òõç ÿ O

UX\Gƒ rR* WZdzYZRgZdz[Tcst K’dz\Gg§YR'Ujƒ+^j_K m˜

‘{cWQTV{cWZTC^vgZR dfgQ\c^jY‚YZ^~vdz“vRÃUƒcR.YUjdzstR'ƒstdfg§Y^j_CWR'gZ{cszYg‚^v¤„YUjdz\VR'ƒdt\YZbcdfg<¨VR'stƒL˜<«ðR dtszs

[UXdt\cst¤CRdt\vYRMWR'gyYZRƒdt\[^„ƒ„RMsfg dzYZbTC^)IR'WyšœstU ~jW^)ÃYZb+^X_7YZbcR\V^jW[ ^X_<YbcR$YZW}UX\Vgy_8RMW

[UqYWZdzžL˜ Œ ^v{c~jbcst gZTGRUX¢5dz\V~Vo‚YbcRgyst^)IR'WYbcR¥~jW^)ÃYZb ^j_÷ ê8ý‚ö XíM÷Xo<_8^jWRX ó Uj\Vƒ

Uvg

ý 9 ( o<YZbcR+[^jWRe.^v\]YZdt\]{V^j{Vg(dtgYZbVRWR'gyYZWdte.YZdt^j\ï^j_WK9^j\˜ð«9bGUqY dtstsr¤CR+^X_

TVUjWyYdteM{csfUXWÃdz\]YRMWR'gyY _8^jW {Vg dt\+YZbcRTcWZRgyR'\]YÃTGUXTCRMWoVUXWR1YZbcR$Y'r^Ò_8^jstsz^) dt\c~WZRgy{VsuY}gM˜™7dtWgyY'o

dz_$÷ ê8ý‚ö XíM÷

A

4êUXí

ý 6

_8^jW"KݚxUc˜Rj˜&Xøóö"KQê1í ## dzYZb / ó DVöMˆjhjíUX\Vƒ¨V\cdzYZR

4ê@XíÍo„YbcRM\^DhXk„oChq›GF

KQê0DX û\[„ö0X`; [NF8í

A

êUXí[ O 6 ‹ 6

öWX-óö

gZ^ÒYZbVUXYrYbcR[R'Uvgy{cWR$dtgêyˆûïhG/c휚xe.^v\vYdz\5{c^v{Vgr^j\˜‚wx\¥TVUjWyYdteM{cstUjW'o

ƒ„dt[RI(êUKí 9 ˆ ûïhG/Ýö

6

êÝí89 7꧈ ûïhG/cí;%

êyˆhjí

`^vWZR~jR'\cRMW}UXststjoUvgZgZ{c[RÒYZbVUXYRM“jR'WZagZ^jst{„Ydz^v\’^j_IYbcRR]{VUXYZdt^j\ñã ç X 7ö'Xøó

^v¤GR'5g

4 O ê@Xí

‹

A

102&2$

<ê8ý‚ö0X(í

‹ A 4 ‹ ê@Xí

‹

êyˆ'kví

dzYZbïTC^vgZduYdz“vR¨V\cdzYZR 4 O êUXí.ö 4 ‹

êUXíUX\Vƒï +

O A ‹ + ;"( ˜¥|ÃbVRM\ñYZbVR [R'UjgZ{cWRdtg

h

O

O

;

‹

휚xe.^v\]YZdt\]{V^j{Vg^j\ Duˆ'›coQhq›GFœ˜wx\ TGUXWZYZdfe.{csfUXWo‚ƒ„dz[ I êLKí 9 h

O

„ê

O

;!

‹

í͘

‘\cR e'UX\^j¤VgZRMW“jRrYbVUqY‚YbcRSe.^v\Vƒ„dzYZdt^j\a÷;(ê8ý‚ö0X(íM÷

A

4ê@Xí

ý "

duYb gy^v[ÒR$# 9õ1dt[ÒTVszdtR'g

‹ A

#.; ˆjh„˜

|ÃbcRTC^jst5\c^j[dfUXs {cTcTCRMW¤C^j{V\Vƒõ^j\õYZbcR¥\c^vWZ[ ^X_1YZbcR¥YWUj\Vg§_8R'W[UXYZWdužõUXsfgy^ïUXstst^)g

^v\cRY^¤C^j{c\Gƒa_8W^j[&%('*),+.- KQê0DX)û [„ö0X ; [NF8í͘Š5{Ge}b’U¤G^v{c\Vƒe'UX\’¤GR{VgZR'ƒLoÝ_8^vszst^) dt\c~

~vRM\cR'WUjsLWZRgy{cszYgS^X_WDkcoGk5n FœoVY^ ^j¤„Y}UXdt\\c^j\cšºYWZdt“5dtUjsƒ„5\VUX[dfeMUjs¤C^j{c\VƒVg _8^jWSYZbcR([^j[RM\]Yg

ê 6

êÝí #ôví$_8^jW(gZ^j[RgZ„g§YRM[g* dzYZb TV{cWZRTG^vdz\]YÒgZTCR'eÍYWZ{V[ Dzˆ'NFœ˜’Š5dt\VeMR dz\ YZbcdfge'UjgZR

ƒ„dt[RI(êUKíç co<YZbVR'gZR¤C^j{c\VƒVgÒe'UX\c\V^XY(¤CR^v¤„YUjdz\VR'ƒ ¤5ñ{VgZ{VUXsr[R.Ybc^„ƒcg¤GUjgZR'ƒï^v\ïYZbcR

eM^j\]YZdt\5{cduY§’TcW^jTCRMWZYZdtR'g^j_rYbcR [R'Uvgy{VWZRv˜ñ꺅\c^jYZbcR'WRMž„Uj[TcszR^j_ÃYZbcdfg¢5dt\VƒLo‚g§Y{Vƒ„dtR'ƒï¤5

/

duY^j[dtWgZ¢qUmvURMYSUXs ˜„dz\^DhjiFœo& dtszsL¤CRƒ„dfgZeM{VggyRƒsfUqYRMW ^v\Gí͘

…Sg ÃUjggUXdfƒ Uj¤G^q“vRjoXYbcRS~vRM\cR'WUjsVWR'gZ{cszYgQ^j_ Dkco]k5nF IR'WZR^v¤„YUjdz\VR'ƒ{VgZdz\V~YZbVRgZTGReÍYZW}UXs

YbcRM^vWZR'[ _8^jW7YZbcR ^vTGR'WUXYZ^vW7ã UX\VƒYZb5{Vg<¤5WRMTcWR'gZRM\]Ydz\c~1UXsts5YZbcR ]{VUj\vYduYdzRg<^X_Cdz\]YZR'WZRg§Y‚Ujg

gZ^j[RSdt\]YZR'~jW}UXsfgQ^q“jR'WYbcR$gyTCR'e.YZW}UXsC[ÒRUjgZ{cWRj˜<wx\ YbcRTVWZRgyR'\vYÃTVUjTGR'W rRTVWZ^vTG^]gyRSUj\c^XYbcRMW

[R.Ybc^„ƒ¤GUjgZR'ƒ’^j\ðdz\]YZR'~jW}UXsfgS^q“vRMW*+ER'¤GRgy~v{cRÒ[ÒRUjgZ{cWRÒW}UqYbcRMW1YbVUX\ð^q“jR'W)K M ˜‘\cReMUj\

¤C^j{c\Gƒ_8W^j[ ¤GR'sz^)-W}UqYZbVRMWƒ„dtWR'eÍYszYZbcR gZ{c[g "

102&230

ê8ý‚ö!íêUj\Vƒ’YZb5{VgYbcRYZdt[R.š

Um“vRMW}UX~jRƒñ[^j[RM\]Yg¥þ

1íyí({VgZdz\c~’YZbVR¥€‚UjWgZRM“qUjsIR>v{GUXstduY§`DkvhFœ˜1UX[RMstjo_8^jWUX\5

ò9óæo

ˆ

!#

2

‹34

òêùÍöyýí

‹ ùQç

ˆ

h5" 76

ê 8Òê@X];ïü)íxòÃí.ê8ýí

‹ X % êyˆM›]í

(6)

_ "

åSRMWRjo ý ó-ëSì^jWý óôîroUX\Gƒ8ê5í¥ç êã û]í

6

O+dfgYbcRWR'gZ^jst“jR'\]Y ^X_ãï˜#|ÃbcR

dt\]YZRM~vWUjs ^j\ YZbcRsº˜bE˜gM˜Qdt\#꧈'›]íÒdfg“jR'WZ e.st^vgZRY^ñYZbcRñpIR'gUXW^Ydz[R.šxUm“jR'WUj~jRƒ ]{VUX\]YduY§

ê8ý‚ö!í͘|ÃbcR'WZRM_8^jWR rR[^5ƒcdu_8YZbcR ƒ„RM¨V\cdzYZdt^j\ñ^X_

ê8ý‚ö1íSdt\9꧈mí$UX\Vƒ’^X_þ

ídt\

꺏vírUje'e.^jW}ƒ„dt\c~jstaêÖYbcdfg dtgSƒ„^j\cR$dt\+YZbcdfg ÃUm¤][Uj\5UX{„Ybc^jW}g}íÍo

êý‚öí‚ç

ˆ

!$#

2 6 ‹ 34

òê8ùÍöZýí

‹ ùÍöþ

M

1íQç ý êý‚öí.ö êyˆijí

Uj\Vƒ I^vWZ¢ duYb¥YZbcRgyRƒcR.¨V\cdzYZdt^j\Ggdt\ bVUqY_8^vszst^)g'˜Ã‘\cRe'UX\¥R'UvgydtstgZRMRYbVUqYYbcdfgSƒ„^5R'g

\c^jYe}bVUX\V~jRYZbVR \5{c[¤CRMW}g

*

êCí.o<TcWZ^q“5dfƒ„R'ƒ’YbVUqYYbcR [^j[R'\vY}g

M êùy탄^\V^XY~vWZ^) _Uvg§YRMW YbVUX\aTC^jst5\c^j[dfUXstszñê bVdte}bdfg YWZ{cR(dz\[^]g§Y$UXTcTcstdfeMUqYdz^v\VgUj\VƒLoCdz\aTGUXWZYZdfe.{csfUXWocdt\

UjszsEUjTcTcstdte'UqYZdt^j\Gg e.^j\Ggydfƒ„RMWR'ƒdz\+YbcRTcWR'gZRM\]Y TVUXTCRMWÍí͘

|=^^j¤cYUXdt\ U\c^j\„š YZWdt“]dfUXsrƒ„5\VUX[dfeMUjsIst^)IR'W¤C^j{c\GƒLo‚duYdfg(gZ{ e.dtRM\]YÒYZ^¤C^j{V\Vƒï_8W^j[

¤CRMst^)

"

102&23 4

8êUX 1íxòêýí

‹ _8^vWrgZ^j[R . #õ_8^jWX‡_8W^j[ôgy^v[RgZR.YI^j_TC^vgZduYdz“vR

+RM¤CR'gZ~j{cR[R'Uvgy{VWZRv˜wx\^j{VW^j\cRMšœƒcdz[RM\Ggydt^j\VUjsEeMUvgyR* dzYZbaò9ç ÿ O

oVYZbcR(WZRgy^vsz“vRM\]Y 8êUX];

ü 1í§ÿ

O êýí dfgSeMsz^]gyR'sz+WZR'stUXYZRƒY^YZbVR(e.^vWZWR'gZTC^j\Vƒ„dt\c~ÒYZW}UX\Gg§_8R'WS[UqYWZdzž (ê8ý‚öMˆ0X`; ü í.o

bcdfe}bðdtgdt\ðYZ{cW\ïe.st^vgZRÒYZ^ ê8ý‚ö'ˆ Xídu_ )dfgsfUXW~jRUX\Vƒðý dtg\V^XYYZ^5^¥sfUXW~jRj˜Œ ^v{c~jbVsz

gZTGRUX¢5dt\c~VoXdz_÷;êý‚öMˆ0Xí'÷Qdfg‚¤C^j{c\VƒcR'ƒ(_8WZ^v[)Uj¤G^q“vRrTC^jst5\c^j[dfUXstszdz\ý_8^jWQgZ^j[RWXojYZbcR'\

8êUX ;+ü íyÿ

O êýíQƒ„ReMUm„g<\c^_Uvg§YRMW‚YbVUX\TC^jst5\c^j[dfUXstsz_8^jWý¥\c^jYQYZ^5^sfUXW~jR꺃„RMTCRM\Vƒcdz\c~

^v\ í.˜‚|ÃbcR$_8^jstsz^) dt\c~ÒWZRgy{VsuY dtszs¤GRTcW^q“jRƒ dt\¥Š„R'eÍYdz^v\ah„¡

' ' + '! "+"Iã$#&%ÒéM‹vêëSí +éM‹jêî‚í %('('"#&).'% %*a꧈vˆíê-+#&-,#&.#/ )'

%(+01%32 ".*4/+"%2"#&5#+"%768 $9#&%: ';7 )<=)>#&%0'?/ @6 'íACBD0E +6 'F7 "G<*+";6*+"H 'JI #ø7K

4 #õ7K## 7KL& 'M<*+))+.-+#&%'N/(+%2"#&5#+"%N +.)O26P

Q

+R "%*S #  )O "5'7' '%0+"0'EKM& 'T' 'VU#W656X Y%+%'THZ[*R\ +" ' )]6 'T ê5Sí_^ `6.0/V

7 " ê5Sí(^ DuûaIö!I FG %32

÷ ê8ý‚ö!bc XíM÷

A

4dS

"fe

Xúóê5SíÍö

e

ý‚ögbø¡

ý A

b A

S

êyˆ'ví

êg '.6[]AOK -+#&&ˆ

A ý A Saöˆ

A b A

Sh#&%c& 'R/ @6 ' +i<réM‹vêîQíyíjA

'T]S êí‚ç $O4

O! "

%32 )'T]kêí %('d '1ˆ. =l%'T#m'@ %(+! + +E2 +i<n 'o6 'T(êS êíyíjP

1íQç NX)ó ¡pXqó (êS êíyí.ö

X û Xq

A

ˆ)*1%

r '%-<*+"X .))5 #Žˆ )O "5'7' '%0+"0'EKL& 'M<*+))+.-+#&%' %+"01%2- +.)s2@6P

2&23 !

ê8ý‚ö!í89ut 4

í

S O 6 ‹ " ê1íÍö êyˆmnXí

-v 'T ' t

4w#W6R6*+"H 'x01%#<*+.Hy +6#&[#&).'z/(+%6l %DZ %32

k

2'%0+"'T6R ' ' %'T6g'"0 'xH ' @6.01 '

+g<d& '6 'k{A

|

%J .[#/T0 )s K]<*+} %* # 1K +%'7 @6R& '(<*+.))+-+#&%'%+"01%2o<*+-& '-5#&H '=g ).'T! j'7'2

H +H 'T%D6 +i<& 'G +@6.#&5#+"% + '! "+"P

þ M

1í89 t 4

S ! O 6 ‹ " ê1íÍö êyˆ'ví

-v 'T '(þ

M

í#W6X2'5~L%'2z @6#&% ꧈mijíA

wx\ YbcRïg§Y}UqYRM[RM\]Y¥^X_(|ÃbcR'^jWRM[ ˆðduY¥dtg+dt[TG^vWyY}UX\]YYbVUqY+YZbVRñeM^j\VgyYUj\]Y 4 dt\-êyˆ']í

¤CRdz\Gƒ„RMTCRM\VƒcRM\]Y ^X_dS"Uj\Vƒ ^X_"X ó êS’í͘ wœ_ ê5Síe.^v\VgydfgyYg^X_$Uñgydt\c~jstR¥TG^vdz\]Y X

(7)

&RD@1 ꠑ\VR.š

Ÿ

\cR'WZ~v |ÃbcRM^vWZR'[í

n|

<

÷;(ê8ý‚ögb 0X

íM÷

A

4êUX

í.ê

ý ; b í"

êyˆ'†ví

<*+"d6*+"H ')X

KL01%#<*+".H )>*z#&%ý‚ögbcK+& 'T%

6 êCí 9

ûõˆ û’› #

ˆQ;#

%

wœ_<^j\cR$^j\Vsz ¢5\c^)gIYbVUqY÷;(ê8ý‚öMˆ0X

íM÷

A

4ê@X

í ý 6

ocYZbcR'\+^v\cR$eMUX\YUj¢jR #’ç hG/ÝocgZ^

YbVUqY

6 êCí89

ûõˆ ûð /

ˆQ; hG/

%

ê hXví

wœYdfgdt\]YZR'WZRg§Ydz\c~aYZ^eM^j[TVUXWRYZbVdtg(¤G^v{c\Vƒ dzYZb êyˆhvíÍo‚g§Y}UqYdz\c~a_8^jW(

A

/-+ ˆjh„oEYbVUqY

6

êCí89=êyˆQûhG/cí.˜Q‘\VRS^j¤GgyR'WZ“vR'g‚YbVUqYêºhjví5dzR'stƒcgrU¤CR.YZYZR'W WZRgy{cszY_8^vW +sfUXW~jRR'\c^j{c~vb

êºUX\Vƒ(^j\cRr\cR'R'ƒcg7YbcRÃTG^vsz5\c^v[ÒdfUXs„{VTcTGR'W‚¤G^v{c\Vƒ_8^jW<YbcRrYZW}UX\Vgy_8RMW<[UqYWZdzž^j\cst_8^vW<U$gZdz\V~jstR

TC^jdt\]Y(UX\Vƒð\c^jY^j\ïgZ^j[R gZR.Y^j_ÃTC^vgZdzYZdt“jR[R'Uvgy{cWRí.˜+`a^jWRM^q“jR'W'oLdt\ñYZbVReMUvgyR/ 9­ˆ.Xhco

YbcR¤G^v{c\VƒõêºhX]ídfg$UXsrUm„g\c^j\cšºYWZdt“5dtUjs_8^vW ñsfUXW~jR(RM\c^v{c~jbEo" bVdzstR꧈hví~vdz“vR'g1\c^jYZbcdt\c~V˜

wx\ YbcdtgeMUvgyR¥YbcRgZTGReÍYZW{c[ ^X_ã"[Um ¤CRaTc{cWRTC^jdt\vY duYb TG^vsz5\c^v[dtUjszst ƒ„ReMUm5dt\c~

R'dz~vRM\„_8{c\GeÍYZdt^j\GgM˜

…\V^XYZbVRMWdt\]YZRMWR'gyYZdt\c~e.^v\VgZR]{cRM\Ge.R1^X_‚|ÃbcRM^vWZR'[ˆdtgrYbcR$_8^jstsz^) dt\c~G¡

&RD@1 ]n|

<d& 'T' 'VU#W6Y4 # cö)X

óIö 9 ˆY60/;7 "

÷;êý‚öMˆ XíM÷

A 4

<*+"X .))Vý‚ö X 6.0/V;&

ý

X û X A

ˆ"KL '%

6

êÝí89 ûõˆ&%

|7UX¢5dz\V~ç h(dz\pI^jW^jstsfUXW+ˆv˜hco IR$^v¤„YUjdz\YZbcR[Ujdz\ƒ„5\VUj[ÒdfeMUjsLWZRgy{VsuY ^X_DhjiFœ˜

™7dz\GUXstszvorR\c^XYRYZbGUqYUjszsLYbcRWR'gZ{cszYg [R'\vYdz^v\cR'ƒUj¤G^q“vRUXWRg§Y}UX¤cstR dzYZbWR'gZTGReÍYY^

¨V\VduYRMstgy{VTcTG^vWyYR'ƒTGR'WyY{cWZ¤GUqYZdt^j\GgM˜7|Ãbcdtg<dfg7^X_Cdz\]YZR'WZRg§Y‚gZdz\VeMRrUjszs5YbcRÃTcWRM“5dz^v{Vg7ƒ„5\VUX[dfeMUXs

st^)IR'W¤C^j{c\VƒVgrRMWR¤VUvgyRƒ^j\’ƒ„dz[R'\Vgydt^j\GUXstduY§¥TcW^jTCRMWZYZdtR'gS^X_IgZTGReÍYWUjs[R'Uvgy{cWR'g bcdfe}b

UjWZR1“jR'WZgZRM\GgydzYZdt“jR1YZ^gZ{Ve}b+TGR'WyY{cWZ¤GUqYZdt^j\GgM˜

&RD@1

B0E +@6 '( 'v +'%[# .)

#W6 6.0/R& ] ' + '! "+"<ã

-+#&Z +'T%D5# )

6 [#W6~ 'T6R 'R1*V +"& '.6.#W6 +i<

r '+" 'HA

' ¡Cë]9 êi'T6[ AOK ¡Ýî 9 ‚í %('

o~L%D#&' )>*Y6.0E +".'2 '.501 % "5#+"% "%2(ã0çŽã

;yA

r '%?& ' + '! "+"ãh6 "5#W6~ 'T6

êyˆmnXíX %2 ꧈']íTA

r 'X6 H '"#&%2 +i<d6.l %#)>#&5*} +.)s2@6M<*+ +" +.))s .#'T6A{ %32AA

«ðR gybVUjszsQUjTcTcstYZbVRÒWR'gZ{cszYgUj¤G^q“vRY^+“qUjWZdt^j{Vg1[^„ƒ„RMsfg1_8W^j[ø^v\cR.šxƒ„dt[ÒR'\VgZdz^v\VUXs,]{VUqš

gZdteMWZ„gyYUjsLYZbcR'^jWðêºeÍ_§˜YDuˆmhF8íÍ¡rYZbcRҙ7dz¤C^j\VUveMeMd7åUX[dzszYZ^v\cdfUX\EoGYZbcR(TGR'WZdt^„ƒƒ„^j{V¤cszdt\c~+åSUX[dtsuš

Y^j\cdfUX\Eo„Uj\VƒYbcR1|Ãb5{cRMšœ`a^jW}gyR1åSUX[dtsuY^j\cdfUX\˜<`a^jWRUXTVTcszdfeMUXYZdt^j\Vg8 dtszsݤCRƒ„dtge.{GgZgZR'ƒdt\¥U

_8^vWyYbVe.^v[Òdt\c~ÒTc{c¤cstdfeMUqYdz^v\^DuˆmiF ˜

|ÃbcR™7dt¤G^v\VUje'e.dLTC^XYZR'\]YZdfUXs -¡jë^9 dtgÃ~vdz“vRM\+¤5

ê8ýíQç V

O 6

!#"

O

ê8ý%$ [^„ƒˆmí;%

ê h„ˆí

åSRMWRjoV(# Uj\Vƒ&$õdfgÃYbcRdt\]“vRMW}gyR$^j_=YbcR~j^vstƒcRM\+[ÒRUX\EocYZbVUXYSdtg'o'$ ç)ê)( i$ûõˆíXh„˜I™c^jW

UÒ~jdt“jR'\ VocstR.Y

4+*(ç hW;-, 7; V %

ê hjhjí

(8)

_ "

«ðRgybVUjszsLTVWZ^q“vR

] êºUví

Q

+" 'T).'T.* K - 'n ).'

6 êCí 9

ûõˆ û’› #

ˆQ;#

ö

-+#&

#ðç #rê@VCíIç

h<st^j~Gê 4 * ê h 4 * ; ˆíy‹'í

st^j~ $ 6 O %

ê hXkví

ê¤Gí

Q

+ ')'.* "%2 'T).'T.* V # ›K - 'n ).'

6 êÝí89

û .ûñk#

ˆQ;#

ö

-v 'T ' # #W6 6#&% ê hXk]í %32

.+ç .<êVGíIç

st^j~Gê h V ; hvhjí

st^j~ $ 6 O

ûõˆT+ŽˆQ;# %

ê hq›]í

+ERMY({VgÒe.^v[TVUXWRYZbcRWZRgy{VsuYÒ^X_|ÃbcRM^vWZR'[ h( duYb TcWRM“5dt^j{VgZsz’¢5\c^) \ïsz^)rRMW¤G^v{c\Vƒcg

_8^vWÃYZbcR[^j[R'\vY}gM˜<wx\+_Uje.Y'oVUjszsÝYbcR'gZR$¤G^v{c\VƒcgSUXWR1¤GUjgZR'ƒ^j\ñê†ví.˜Q|ÃbcR$sz^)rRMWäC^j{c\GƒcgÃ_8^jW

YbcRåUX{Vgƒ„^jW0=+ƒcdz[RM\Ggydt^j\_8^vWYbcR™7dt¤G^v\VUje'e.dGåUX[dtsuY^j\cdfUX\ Dzˆ'co5hX›co5hjNFGdt\Y{cWZ\bVUm“jRSUjszs

¤CRMR'\+TVWZ^q“vR'ƒ {Ggydt\c~a꧈kví.˜Q™c^jW RMžcUX[TcstRjo„dt\ DhXGFduY ÃUjgrTcW^q“jRƒYbVUqY

ƒ„dt[JIêUKí 99h„ê';# ; ˆjhjí.ö

ê hjijí

bcR'WZR

ç

st^j~Gê ( ˆmnq›]í

i<sz^v~Gê$ 6 O í

&%cˆhj

Uj\Vƒ #dfgQ~vdz“vRM\¤5aêºhjkví}˜‚™c^vWsfUXW~jR=ojYbcRSƒ„^v[Òdt\VUj\vYIR.ž„TcWR'ggydt^j\dt\YZbcRsz^)rRMW‚¤C^j{V\Vƒ_8^jW

6

êCí‚dz\ |ÃbcR'^jWRM[h1dtg „êyˆ; #<í bcdfe}bdtgQeMszRUXWsz(¤GRMYyYRMWQYbVUX\ h „ê; #';’ˆjhjí͘=«’R

YbcRMWR._8^vWZRgZRMRYbVUqY^j{cWWZRgy{cszYSdt[TcWZ^q“vR'grYbcRTcWRM“5dt^j{VgZst¢5\c^) \¥sz^)rRMWS¤G^v{c\Vƒ+_8^jWstUjWZ~vR

«ðRÒUjstgZ^\c^jYZRYZbVUXYpI^vWZ^vszsfUXWˆv˜kdtg1TVUjWyYdteM{cstUjWZst+dz\]YZR'WZRg§Ydz\V~dt\aYZbVdtg$e.^v\]YZR.ž5Y˜1|ÃbcR

™7dt¤G^v\VUje'e.dVåUX[dzszYZ^v\cdfUX\bVUvgQgyTCR'e.YZW{c[^j_"MRMW^*+ER'¤GRgy~v{cR[R'Uvgy{cWR"Dn„ovkvNFCUj\VƒÒbcRM\VeMRjo

¤5 UïgZ{cdzYUj¤cszRaUjTcTcstdte'UqYdz^v\õ^j_YbcR’Š5dt[^j\„šœ«ð^js=ŽUXW~j{V[ÒR'\]Y DkX› F o Uñ~jR'\cRMWdfe¥WUj\c¢ïY'r^

TCRMWZYZ{cW¤VUXYZdt^j\ êUXY(Y'r^eM^j\VgZR'eM{„YZdt“jRgZdzYZR'g}í dzstsITVWZ^„ƒ„{VeMRU’gyTCR'e.YZW}UXs[RUjgZ{cWZR bcdte}b dtg

R'\vYdzWRMstgy{VTcTG^vWyYR'ƒ’U rUm+_8W^j[ <˜(`^vWZR(TcWR'e.dfgZRMstjoÝYZbVRÒgZTGReÍYWUjs7[RUjgZ{cWZR(^X_QYbcRTGR'Wyš

Y{cWZ¤CR'ƒ^jTCRMW}UqY^jW dtsts]¤CRÃgy{cTVTG^vWyYR'ƒ^v\(USeM^j{c\]Y}UX¤cstRIgZR.Y<^X_cR'dz~vRM\5“qUXst{cR'g duYb¤CRMdt\c~YZbcR

gZR.Y$^X_IUveMeM{c[{csfUqYdz^v\TC^jdt\]Yg1^X_IYZbcRgyRÒRMdt~jR'\]“qUjsz{cRgM˜wx\ðTVUjWyYdteM{cstUjW'oLU~jR'\cRMWdte(W}UX\c¢+Y'r^

TCRMWZYZ{cW¤VUXYZdt^j\a[Um+YZ{cW\YbcRÒgZTCR'eÍYWUjs<[ÒRUjgZ{cWR^X_QYbcR™=dt¤C^j\VUveMe.d<åSUj[dzszYZ^v\cdtUj\Eo" bcdfe}b

dfg$¢5\c^) \Y^¤GR #šxe.^j\]Ydz\5{c^v{Vg1_8^jWgZ^j[R # #úVodt\vY^aU+Tc{cWRTG^vdz\]Y[R'Uvgy{cWRj˜wx\ðYZbVdtg

gZduY{VUqYdz^v\EoVTVWZR'“]dt^j{Gg ¤G^v{c\Vƒcgƒ„^\c^jYS~jdt“jRUj\]]Ybcdz\V~_8^jW YbcRTCRMWZYZ{cW¤CR'ƒ^vTGR'WUXYZ^jWo bcdtszR

^v{cWäG^v{c\Vƒ_8^jW

6

êÝírdtg gyYUj¤cszR* dzYZb¥WR'gZTGReÍYÃYZ^ gZ{Ve}b¥UÒTGR'WyY{cWZ¤GUqYZdt^j\˜

‘{cW$\cRMž]YUjTcTcstdte'UqYZdt^j\’dtg1Y^+YZbcRTCRMWdz^„ƒðƒ„^j{c¤Vszdt\c~¥åSUX[dtsuY^j\cdfUX\ bcdfe}b ÃUjg$e.^v\VgZdtƒ5š

R'WZRƒLo_8^jW7R.žcUX[TcstRjoqdt\.Dcomco5ˆjˆjo]ˆk„oqh„ˆ Fœ˜ +R.Y¤GRIYZbVR1ê8Y'I^jšœgZdtƒcR'ƒVígy{c¤Ggybcdz_ÖY‚~jR'\cRMW}UqYR'ƒ

¤5YbcRgy{V¤Vg§YduY{„YZdt^j\9 VˆjoLˆ9 vÒUj\Vƒ¥ƒ„R.¨G\cRjo5_8^vWSgy^v[R $õóUX\GƒUÒ~jdt“jR'\+eM^j{„š

Tcstdt\c~e.^v\VgyYUX\]YTVoGYZbcR(TG^jYZRM\]YdtUjs *

"!

¤5*

"!

ê8ýí ç V'$ ˜ w§gdfg¢5\c^) \¥YbVUqY_8^jWRM“jR'WZ

Vç ’UX\Vƒ RM“jR'WZ $ óco<YbcR+^jTCRMW}UqYZ^vW dzYZb TG^jYZRM\]YdtUjs *

"!

bVUjg(Tc{cWRMstïgydt\c~j{VstUjW

eM^j\]YZdt\5{c^j{Vg(gyTCR'e.YZW{c[ êgZRMR DuˆkNFr_8^jW(YZbcdfgÒWZRgy{cszYÒUj\Vƒ`Dco<corˆjˆXoQhcˆ FÃ_8^jWRUXWszdtRMW(TVUXWZYZdfUXs

(9)

Q

+ ').'T.* V %32 ')'.* $ ó K - 'd7 ")'

6 êCí 9

ûñi

h %

|ÃbcdfgWR'gZ{cszY=dfgE^j_cdz\]YZR'WZRg§Y_8^jW7“mUjWZdt^j{GgLWZRUjgZ^j\Vg'˜™7dtWgyY=^j_„Ujszs oYZbcdfg7dtgEYZbcRI¨VW}g§Y7ƒ„5\VUX[dfeMUXs

WR'gZ{cszY_8^jWYZbVdtg[Ò^„ƒ„R's YZbGUqY~v^]Rg¤GR'j^v\Vƒ YZbcRŒS…

Ÿ

YZbcR'^jWRM[ êdº˜Rj˜torYZbcR’ƒ„5\VUX[dfeMUXs

WR'gZ{cszY YZbVUXY_8^jstsz^)gr_8W^j[ Tc{cWRMsteM^j\]YZdt\5{c^j{Gg gyTCR'e.YZW{c[ í͘Ãwx\Vƒ„R'R'ƒLoCUXTVUjWyYÃ_8W^j[ gydt\c~j{VstUjW

eM^j\]YZdt\5{cduY§vo'\V^XYZbVdz\c~^j\R'duYbcRMW7ƒ„dz[R'\Vgydt^j\GUXstduY§1^jWƒc]\GUX[dte'gÃUjg¢]\V^) \WZdt~j^vWZ^v{Vgystj˜L|ÃbcR

ƒ„d=ÝRMWRM\VeMR$YZ^YZbVR™7dz¤C^j\VUveMeMdeMUvgyRvo& bcRMWRjoGUjgƒ„dfge.{VggyRƒ¥UX¤C^q“jRjo„RUXWszdtRMW WR'gZ{cszYg dt\+YZbcRgyR

ƒ„dtWR'eÍYdz^v\VgIR'WZR¢5\c^) \oÝgyYZR'[gS_8W^j[ YbcRÒUj¤VgZRM\VeMR^X_rUX\adt\5“mUjWZdfUX\]Y_8^vW1YZbcR(YZW}UjeMR[UXTE˜

`^vWZReM^j\VeMWZRMYZRMstjo„dzYeM^j{csfƒ+\c^XY¤CRgybV^) \YbVUqY YbcRYWUve.R$[UXT¥^jW¤cdzYg WRM[UXdt\+¤G^v{c\Vƒ„Rƒ

_8^vWêgZ{ e.dtRM\]Ysz[UX\5cí<RM\VRMW~jdtR'g<_8W^j[-YZbVRgZTGReÍYZW{c[¥˜<«9duYbUWR'gZ{cszYstdz¢vR1pI^jW^jststUjWZˆj˜tˆ

UXYr^v{cWrƒcdtgZTG^]gZUjsºo]“jR'WZ rR'Uj¢ÒWR'gZ{cszYgr^j\YZbcR1TCRMWdz^„ƒƒc^j{c¤cstdt\c~YWUve.R[UjTgZ{ e.R$UXstWZRUjƒ„

Y^ðUjszst^)ô{VgÒYZ^ðR'gyYUj¤cstdtgZb YbcR¥WZRgy{cszYUX¤C^q“jRj˜ Š„R'e.^v\Vƒ„stjoI^j¤VgZRMW“jRYZbVUXY(YbcRƒ„5\VUX[dfeMUXs

¤C^j{c\Gƒ rR$^j¤„Y}UXdt\¥dz\|ÃbcR'^jWRM[ kÒdfg dz\Gƒ„RMTCRM\VƒcRM\]Y^X_7YZbcReM^j{cTVszdt\c~e.^v\Vg§Y}UX\]Y'˜Q|ÃbVdtg dfgÃdt\

gZbVUXWTe.^j\]YWUvg§Y‚Y^$YZbcRS™7dt¤G^v\VUje'e.dCeMUjgZR bcR'WZR ^v{cWQ¤C^j{c\VƒêºUX\VƒTVWZR'“]dt^j{Gg<^j\cRgí<¤CR'eM^j[R'g

r^jW}gyR$UjgrYbcRe.^v{cTcstdz\V~eM^j\VgyYUj\]Yrdfg dt\Ve.WR'UvgyRƒL˜

™7dz\GUXstszvo IRaeM^j\VgZdtƒcRMWYZbVR’|Ãb5{cR.šx`^vWgZR+åUX[dtsuY^j\cdfUX\ bcdfe}b rUvg gyYZ{Vƒ„dtR'ƒEoÃ_8^jW RMž]š

Uj[ÒTVszRvodt\-Dzˆjo7i5ocoˆ'„o=hcˆ Fœ˜ +ERMY

¤CRYZbcR’êÖY'r^Xšxgydfƒ„R'ƒGígZ{c¤VgZbcdz_ÖY~jR'\cRMW}UqYR'ƒ¤]YZbcR

gZ{c¤VgyYZdzYZ{„Ydz^v\ð 9 Vˆjo‚ˆ 9 ˆUj\Vƒ’ƒcR.¨V\cRUvg1Uj¤G^q“vRjoÝ_8^vW$gZ^j[R $#ó

Uj\Vƒ’U~jdt“jR'\

eM^j{cTcstdt\c~ e.^v\Vg§Y}UX\]Y.VoÃYZbcRaTC^XYRM\]YZdfUXs #*

"!

¤5 *

"! êýí¥ç<V'$ ˜ «ðR’gZbVUjszsSgZbc^)­YZbcR

_8^vszst^) dz\V~V¡

vQ

+ ').'T.* V %32 ')'.* $ ó K - 'd7 ")'

6

êCí 9 û ˆ1%

…Sgrdt\YZbVRTcWRM“5dt^j{VgQYZbcR'^jWRM[¥o]YZbcR1¤C^j{c\Vƒ dtgVcš dt\Vƒ„R'TGR'\Vƒ„RM\]Y UX\VƒYZbcR¨VW}g§YÄ5\VUX[dfeMUXs

WR'gZ{cszYQ_8^jW‚Ybcdfg[^„ƒ„RMs ˜‚™c{cWZYZbVRMW[Ò^vWZRvojdt\YZbcdfge'UjgZR YZbVRSgyTCR'e.YZW}UXsVY§]TCRbVUvgQ\c^jYRM“vRM\¤CRMR'\

dfƒ„RM\]Ydu¨VRƒñdz\ïUjszsreMUjgZR'g'˜ wœYdfg¢5\c^) \ðYZbGUqY_8^vWRM“vRMW\V ç UX\VƒðRM“vRMW $-ó o=YZbcR

Uj¤Vgy^vsz{cYZRMstae.^v\]YZdt\]{V^j{Vg$gZTGReÍYZW{c[ dtg$R'[ÒTcY§ êÖYbcdtg_8^jstsz^)g_8W^j[øWR'gZ{cszYg$^X_

ª

^XY}UX\cdDhXNF

Uj\Vƒ +=UjgyY<Uj\Vƒ(Š5dt[^j\ DkvNF8íÍoX¤c{cY‚Uj¤VgZRM\VeMRI^j_VRMdt~jR'\]“qUjsz{cRg7dtg7^j\Vsz¢5\c^) \(~jRM\VRMWdte'UXstszvo'YbVUqY

dfgMo5_8^vWUƒ„RM\VgZR $gyRMY^X_ $õó

ê8YZbcdfg ÃUjg gZbc^) \¤5+PSR'szv^j\¥UX\Vƒ+€<RM5Wd R'WZR DuˆNF=Uj\Vƒ

åS^X_IRMYUXs ˜SDhcˆ F o{Vgydt\c~ƒ„d=CR'WZR'\]Y$[RMYZbc^„ƒcg}í͘|Ãbcdfg$dzstst{Vg§YWUXYZRg1YZbcRÒYZbVRM[R^X_IYZbcdfg$TVUXTCRMW

dt\U\cdteMRÃUmC¡‚«9bVdzstRrReMUX\V\c^XYSgUmUj\]]Ybcdz\V~ UX¤C^j{„Y YbcRƒ„dt[RM\VgZdz^v\VUXstdzY§^X_‚gZTGReÍYZW}UXs

[R'Uvgy{VWZRgMo rR$e'UX\+\cRM“vRMWZYZbcR'szRgZgÃTVWZ^q“vR“vRMW g§YWZ^v\c~ƒ„5\VUX[dfeMUXsݤC^j{c\GƒcgM˜

|ÃbcR^vWZ~]UX\cd'UXYZdt^j\^X_7YZbcRUjWyYdteMszRdfgUvgÃ_8^jstsz^)g'¡Q|ÃbcR'^jWRM[èˆUj\VƒapI^jW^jststUjWZdtR'g1ˆv˜zˆ.lCˆj˜k

dtszsS¤GRaTVWZ^q“vR'ƒ dz\ Š5ReÍYdz^v\ h„˜ wx\ Š„R'eÍYdz^v\Vg kql„i IR’gybVUjszsYZbcR'\ UXTcTcst YbcR'gZReMWZdzYZR'WZdfU

Y^YZbcR™=dt¤C^j\VUveMe.dI[^5ƒcRMs o=YbcR TCRMWdz^„ƒïƒ„^v{c¤cstdz\V~a[^5ƒcRMs o<Uj\Vƒ’YZbcR+|Ãb5{cR.šx`^jW}gZRÒ[^„ƒ„R'sºo

WR'gZTGReÍYdz“vRMstj˜

hc˜ÜLâfÛcÜLâ8Þ=Ú]ÞÜ(àÚLÛLà7Ú Sâ8á! "$#IÞ%&VÜ('ÞàÚEß*)

+ERMYÃãøç‡û,+-;#¤GR$UgZRMsz_֚œUvƒm¦§^jdt\]YI^vTGR'WUXYZ^jWI^j\éM‹Xêë1íL^jWr^j\ éM‹jêî‚íÒê dzYZb+PSdtWdte}bcstR.Y

¤C^j{c\GƒcUXW1eM^j\VƒcduYdz^v\dz\YZbcRIstUXYyYRMW<eMUjgZRí.˜ dt“jR'\gy^v[RQWZRUXsv_8{c\Ve.YZdt^j\ ê8ýíÍojduY7dtg_8^jW[UXstsz

ƒ„RM¨V\cRƒ¤5

ãò1ê8ýíç9òê8ý¥ûõˆí&; òêýJ; ˆí&; êýíxò1ê8ýíÍö ý’ó¥ë

Uj\Vƒ¤5

ãò1ê8ýíç9òêý+ûõˆí&; òêý ;9ˆmí&;ê8ýíxò1ê8ýí.öý # ˆjö

(10)

_ "

WR'gZTGReÍYdz“vRMstj˜ +ER.Y(¤CRgZ^j[R1e.^j[TcstR.ž^vWWR'UXsG\5{c[¤CRMW˜<«’R$ƒ„R.¨G\cRYbcRSYWUj\Vgy_8RMW[UXYZWduž

UvgZgZ^„e.dfUqYZRƒY^(YbcR^jTCRMW}UqY^jW ã Ujgr_8^vszst^)gM¡

ê8ý‚ö!bcV]í‚ç

ê8ý‚öV]íêýûõˆjöV]í

%%%

(êb ; ˆjöV]í du_<ý # bðö

du_<ýaç9bðö

6

Oqêbðöyý+!5í du_<ý + bðö

ê hXví

bcR'WZR

êý‚ö!5í<ç

ê8ýí ûˆ

ˆ 

%

™V^jWaó dzYZb¥wx[ ç Vocƒ„R.¨V\VR

ç8ê5í§ÿ

O

ç#êºã û

6 O ÿ O %

—rYbcRƒ„R.¨G\cduYdz^v\¥^X_YbcRWR'gZ^jst“jRM\]YÃ^X_7YZbcR^vTGR'WUXYZ^vWÃã o IR$bVUm“vR

êý¥û ˆmí$;

êýJ; ˆí&; ê ê8ýí<û?5í

ê8ýíç cö ý 燈jö

ê hvnXí

꺝ví$;

êºhví$; ê êyˆí7û?]í

êyˆíç ˆ

ê hXví

dt\YbcReMUvgyR$^j_=éM‹vêëSí7UX\Gƒ

êý¥û ˆmí$;

êýJ; ˆí&; ê ê8ýí<û?5í

ê8ýíç cö ý # ˆjö

ê hX†ví

êºhví$; ê êyˆí7û?]í

êyˆíç ˆ

êºkjví

dt\YZbcR1eMUvgyR ^j_CéM‹vê î‚í͘pI^v\VgZdtƒ„R'W‚YZbVRS“jReÍY^jW}g1ê8ýíç#ê

ê8ý";ñˆí.ö

ê8ýíZí

˜‘\cRSeMUj\R'UjgZdtsz

gZRMR1YZbGUqY1ê8ýíQç!êý‚ö!5í1êýûõˆíI_8^vW ý 燈j˜Q|ÃbcR'WZRM_8^jWRjo

ýíç êý‚öMˆ!5í1꧈míÍö ý # ˆ êºkcˆí

dt\¤C^XYbeMUjgZR'g'˜‚`^jWRM^q“vRMWovdt\+YZbcRe'UjgZR$^X_éM‹vêë1íÍoq^j\VR1bGUjgrYZbVRdtƒ„R'\]YZdzY§

1ê8ýíQç êý‚öZ7V]í1ê]íÍö9ý +õ%

êºkvhjí

Š5dt\VeMR+ƒ„RMY êý‚ö!5íÒçäˆjo<YbcRgZUj[ÒRdtg(YWZ{cR_8^jW êý‚ögb !5íÍo‚gy^YZbVUXY÷ 6 O ê8ý‚ögb !5íM÷¥ç

÷ ê8ý‚ö!bcV]í'÷Ã_8^jWUjszsLý‚ö!b’öVV˜‚|ÃbcR'WZRM_8^jWRjoLêkVˆíÃUj\Vƒ’êºkvhvídt[Tcst

÷1ê8ýí'÷ 9Ž÷;(ê8ý‚öMˆ!5íM÷

6 O

÷1êyˆíM÷Xö ý # ˆ êºkjkví

dt\¤C^XYbeMUjgZR'g Uj\Vƒ

÷1êýíM÷9 ÷ ê8ý‚ö7V]í'÷

6 O

÷1êví'÷qö ý + cö êºkX›]í

dt\ YbcR+e'UjgZR^j_ éM‹jêë1í͘+wœYÒdfge.stR'UjWYbVUqYÒYZ^’~jR.YUast^)rRMW¤C^j{V\Vƒï_8^vW(YbcR+WZRgy^vsz“vRM\]Y'o rR

\cR'R'ƒUj\{cTcTCRMWS¤C^j{V\Vƒ¥_8^jWSYZbcR\c^jW[­^j_<YZbcRYZW}UX\Vgy_8RMW[UXYZWduž+_8^jWSeM^j[TcstR.ž¥“qUXst{cR'gS^X_LV˜

‰gy{VUjszstjoS^j\cR’bVUjg+gy{Ge}b ¤C^j{c\VƒVg^v\csz _8^vWWR'UjsS“qUXst{cRg^j_XVogy^ IRðgybc^v{csfƒ R'gyYUj¤cstdtgZb

WRMsfUqYdz^v\Vgr¤GRMY'IR'RM\+YZbcRgyR1Y'r^eMUjgZR'g'˜

4 5D

'Xórö!S#õDAG, '5~L%'

I êSíQç gy{VT

2&2$ ! 2 2$ !

÷;ê ý‚ögb 0Xí'÷

Références

Documents relatifs

To test whether the vesicular pool of Atat1 promotes the acetyl- ation of -tubulin in MTs, we isolated subcellular fractions from newborn mouse cortices and then assessed

Néanmoins, la dualité des acides (Lewis et Bronsted) est un système dispendieux, dont le recyclage est une opération complexe et par conséquent difficilement applicable à

Cette mutation familiale du gène MME est une substitution d’une base guanine par une base adenine sur le chromosome 3q25.2, ce qui induit un remplacement d’un acide aminé cystéine

En ouvrant cette page avec Netscape composer, vous verrez que le cadre prévu pour accueillir le panoramique a une taille déterminée, choisie par les concepteurs des hyperpaysages

Chaque séance durera deux heures, mais dans la seconde, seule la première heure sera consacrée à l'expérimentation décrite ici ; durant la seconde, les élèves travailleront sur

A time-varying respiratory elastance model is developed with a negative elastic component (E demand ), to describe the driving pressure generated during a patient initiated

The aim of this study was to assess, in three experimental fields representative of the various topoclimatological zones of Luxembourg, the impact of timing of fungicide

Attention to a relation ontology [...] refocuses security discourses to better reflect and appreciate three forms of interconnection that are not sufficiently attended to