• Aucun résultat trouvé

Subspace-based Fault Detection and Isolation Methods - Application to Vibration Monitoring

N/A
N/A
Protected

Academic year: 2021

Partager "Subspace-based Fault Detection and Isolation Methods - Application to Vibration Monitoring"

Copied!
33
0
0

Texte intégral

(1)

HAL Id: inria-00073389

https://hal.inria.fr/inria-00073389

Submitted on 24 May 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.

Subspace-based Fault Detection and Isolation Methods - Application to Vibration Monitoring

Michèle Basseville, Maher Abdelghani, Albert Benveniste

To cite this version:

Michèle Basseville, Maher Abdelghani, Albert Benveniste. Subspace-based Fault Detection and Iso- lation Methods - Application to Vibration Monitoring. [Research Report] RR-3299, INRIA. 1997.

�inria-00073389�

(2)

ISSN 0249-6399

a p p o r t

d e r e c h e r c h e

INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE

Subspace-based fault detection and isolation methods - Application to vibration monitoring

Mich`ele Basseville, Maher Abdelghani, Albert Benveniste

N ˚ 3299

Novembre 1997

TH `EME 4

(3)
(4)

, $-!"/.0-12 $ %!3&4!12-!5

687:9<;>=@?:ACB0DFEGEHAJIK7L?M?:AONOPQ6RD;>AJSTUV)A@?:WF;QDX)7PT?MUAJSGYBZAJXKIFAJX)7MEGY<AO[

\^]`_acbdfehgjikalnmpoOqriksutvb<qsuwnqrikafikx-oOqriksut

y bxrznxrq _acbx^{suacwnmkbH|nbx

}~rsO€b<q0gjikua‚o„ƒ

…%o†w`w2su~q y b~rb{G]`b~r{-]`b‡tˆ„ƒ†‰u‰‚e‹Š%s@Œ„ba`~rbŽ@‰u‰„ehƒ†‰cwKo†ubx

‘’“•”•–J—`˜u”u™š bo y`y ~rbx xq ]`bw`~rsunmkba›s†œ y b<q b{<qrikt`o†t y ikx-s†mpoOqrikt`‚œo†lnmžq xacs y b<mkb y o†x{-]Ko†t`ubx%iktŸq ]`b

b<ikubt`xrq ~rl`{<q l`~rbZs†œ>o0mžikt`b•o†~ y zntKo†afik{•oOmxrznxrq ba¡ ¢\^]`bw`l`~rw2sux bs†œ2q ]`bwKo†w2b~ikxq s y bx {~ik2bo†t y o†tKoOmžzn£b

t`b<¤¥œo†lnmžq y b<q b{<qriksut8o†t y ikx s†mpoOqriksut¦oOmkusu~ižq ]`acx•§>Ko†x b y sutv~rb{bt„qxrq sF{-]Ko†xrqrik{x l``x wKo†{bH¨©Ko†x-b y iy btqriª¨

« {•oOqriksut8acb<q ]`s y xo†t y q ]`bCxrq-oOqrikxrqrik{•oOmmksF{•oOm¬o†w`w`~rs„o†{-]8q s­q ]`b y bxrikut¦s†œ y b<q b{<qriksut®oOmkusu~ižq ]`acx• ‚\^]`b

o†w`wnmžik{•oOqriksutŸq sŒjik`~ oOqriksutŸacsutnižq su~ikt`fs†œQacb{-]Ko†tnik{•oOmQxrq ~rl`{<q l`~rbx^o†t y ~rs†q-oOqrikt`fa‚o†{-]nikt`bx$ikx y ikx {l`x x b y  

¯ {sut`{bwnq lKoOm¬{suacwKo†~ikx sut°ikx*a‚o y bf¤^ižq ]8o†t`s†q ]`b~ y b<q b{<qriksut±oOmkusu~ižq ]`a²Ko†x b y sutvq ]`bfikt`xrq ~rl`acbtq-oOm

Œuo†~ipo†nmkbxiy btqri« {•oOqriksut³acb<q ]`s y §o†t y w`~rb<ŒFiksul`xrmžzŸw`~rsuwsux b y „z´q©¤µss†œq ]`bo†lnq ]`su~rx• 

¶¡·¸)¹ º» –J¼“u™¾½ o†lnmžq y b<q b{<qriksut8o†t y ikx s†mpoOqriksut>§Qx l``x wKo†{bH¨©Ko†x-b y x q sj{G]Ko†xrqrik{iy bt„qri

«

{•oOqriksut8acb<q ]`s y x•§

xrq-oOqrikx qrik{•oOmQmksj{•oOmo†w`w`~rs„o†{-]>§x q ~rl`{<q l`~ oOmQŒjik`~ oOqriksut³acsutnižq su~ikt`` 

¿kÀQÁÃÂÅÄ@Æ^ÁÈÇɞÂÅʝËÌ

Í)Î@ÏÑÐÈÒ2ÓHԝÕcÏÖÐ^Ð:×OØJØuÓHÔ:ÙÅÚrۂÜÝcÞ×JԝÚÕGߨOԝÓ-àMÚáÃÙâOÓCã äGåHæcç„èÑé„êFë@ìîíjìïkð0ӕÛJÚîñÜOßHÐ:Úr۟ò„ÙÅԝ׆áÃÙÅ×JÔÅß-ñQó^ÓGâJÏôÙÅÓHÔ:ÏõâOö׆ÐMÏõâOö

÷žøùú†û ÚÔÅß-ٝÏõÓGâüýjüîÙÅÚóRÏÖÛ@ÚâٝÏõþ†áß-ٝÏõÓGâuÿ>áîÓÓHÔÅەÏõâ†ß-ÙÅÚÛZÜÝ>ìjÚ× HÚâ)Úîñõö-ÏÖ×Jó

èÑì é ì !""#$!&%$!')(+*%

,

èÑì é

è-./&0$%1(+2'3$"40$&5!6+$&5 $&5!'&7$#!&%!)(8*%

Unit´e de recherche INRIA Rennes

IRISA, Campus universitaire de Beaulieu, 35042 RENNES Cedex (France) T´el´ephone : 02 99 84 71 00 - International : +33 2 99 84 71 00

T´el´ecopie : 02 99 84 71 71 - International : +33 2 99 84 71 71

(5)

© & 2(* 1 n

, $ %!

41. - ! .* 1 $2 !

“ ™ t­{sut`xriy _~rbmkbw`~rsunmk_acb y bmpo y q b{<qriksut b<q y l y ipo†ut`suxrqrik{ y bwKo†t`t`bx%acs y mžikx bxwKo†~

y

bxZ{-]Ko†t`ubacbtq x

y

bmpo‚x q ~rl`{<q l`~rbw`~rsuw`~rb y

l`t xrznxrq _acb

y

zntKo†afiFl`bmžikt

oOik~rbu *o†t`x{b<q*o†~qrik{<mkbx-sut„q

y {~ižq xb<qo†tKoOmžznx x y b‚t`sulnŒ„b•o†lF|RoOmkusu~ižq ]`acbx y b y q b{<qriksutRb<q y ipo†ut`suxrqrik{ y b‚q b<mžmkbxwKo†t`t`bx•§¢Ko†x x

x l`~mkbxa q ]`s y bx~ {btq bx yiy bt„qri« {•oOqriksut+wKo†~x-sul`x¨©bx wKo†{bxb<qx l`~*m o†w`w`~rsF{-]`b´xrq-oOqrikxrqriFl`b‚mksF{•oOmkbu 

o†w`wnmžik{•oOqriksutCmpo´x l`~Œ„b<ižmžmpo†t`{bfŒFik`~ oOq s†ik~rb y bx*xrq ~rl`{<q l`~rbx*a {•o†tniFl`bx*b<q*a‚o†{-]nikt`bx*q sul`~rtKo†tq bxbxrq

y ikx {lnq bu Èbxa q ]`s y bxŸx sut„q´{suacwKo†~ bx´{sut`{bwnq l`b<mžmkbacbtq8l`t o†lnq ~rbvoOmkusu~ižq ]`acb°Ko†x x l`~‚mpo

a q ]`s y b yiy bt„qri« {•oOqriksut wKo†~Œ†o†~ipo†nmkbxfikt`x q ~rl`acbt„q-oOmkbx•§b<qcw`~rsuw2sux w`~ { y bacacbt„q‚wKo†~ y blF| y bx

o†lnq bl`~rx• 

Èb8q ~ oŒuoOižmbxrq b)b{<q l 8y o†t`x¡mkb8{•o y ~rb y l w`~rsO€b<q ¬l`~rb"!Oo+t`s Ž$#&%„ƒ('*),+.-/10"204365 s y b<mKo†x b y

7 q ~rl`{<q l`~ oOmKacsutnižq su~ikt`*l`xrikt`98;:>¹-»*<b~ oOqriksut “ ¸ “ q baiy bt„qri« {•oOqriksut>=H§?Flninbx q{sFsu~ y sut`t wKo†~mpo%x-sj{<i q

@BAC0„§1QblnŒ„bt>§1D$b<mk†iFl`bu 

”•“ ¹ ˜GF ™ q b{<qriksut b<q y ipo†ut`suxrqrik{ y b wKo†t`t`bx•§µa q ]`s y bx´xrq sj{G]Ko†xrqriFl`bx yiy bt„qri« {•oOqriksut wKo†~

x sul`xr¨©bx wKo†{bx•§o†w`w`~rsF{-]`bx q-oOqrikxrqrijl`bmksj{•oOmkbu§Kx-l`~Œ„b<ižmžmpo†t`{b y bxŒFik`~ oOqriksut`x• 

(6)

1 2

!12*f !

D$b<œ:su~rb*sulnqrmžiktnikt`cq ]`b*wKo†wb~§K¤µb y bx {~ik2b*sul`~^acs†qrižŒ†oOqriksut`xZo†t y ikt„q ~rs y l`{b*q ]`b*acs y b<mkx^¤]nik{-]¡¤Èbl`x b

q ]`~rsul`u]`sulnq• 

3543 687:9;+<>='9;7@?BA

\^]`b³w`~rsunmkba#s†œ0œo†lnmžq y b<q b{<qriksut o†t y ikx s†mpoOqriksut3C D.)6=fikx´o¦{~rl`{<ipoOm%ikx-x l`b¡¤]nik{-] ]Ko†xC2bbt iktŒ„bxrqriª¨

„oOq b y ¤^ižq ] y i)b~rbt„qcq©znw2bxcs†œ%o†w`w`~rs„o†{-]`bx•§$o†xc{•o†t b´x bbtRœ:~rsua q ]`bŸx l`~Œ„b<zRwKo†wb~rxFEˆ„ƒF§ÈŽHGIo†t y

q ]`b´sFs !FxJEôƒOd`§KGIÈo†acsut`vs†q ]`b~~rb<œ:b~rbt`{bx•  5³su~rbs•Œ„b~§o†t®ikt`{~rb•o†xrikt`³ikt„q b~rbxrqiktR{sut y ižqriksutF¨©Ko†x b y

a‚oOiktq btKo†t`{b]Ko†xo†w`w2b•o†~rb y iktŸompo†~rub*tjl`a2b~s†œikt y l`xrq ~ipoOmo†w`wnmžik{•oOqriksut`x@ ¬\^]`b !ub<zCiy b•oq ]`b~rb0ikx$q s

~rbwnmpo†{b´~rbulnmpo†~x zFxrq ba‚oOqrik{Cikt`x w2b{<qriksut`xz8{sut y ižqriksutF¨©Ko†x b y ikt`x wb{<qriksut`x@§iÅ bu Ÿikt`x-wb{<qriksut`x y b{<iy b y

l`w2sutCq ]`b%{sut„qriktjl`sul`xacsutnižq su~ikt`fs†œ>q ]`b{sut`xriy b~rb y xrznxrq ba 3a‚o†{G]nikt`bu§`xrq ~rl`{<q l`~rbu§nw`~rsj{bx xÈsu~¬wnmpo†tq =H§

Ko†x b

y

sut­q ]`bx bt`x su~rx

y

oOq-on§2ikt su~

y

b~%q sCw`~rb<Œ„bt„q0œ:~rsua owsux-xriknmkba‚oOmžœ:l`t`{<qriksutvsu~

y

o†a‚o†ubfb<œ:su~rbižq

]Ko†w`w2bt`xo†t y suwnqrikafik£b*q ]`b0a‚oOikt„q btKo†t`{b{suxrq• ML©q$]Ko†x^2bbt¡~rb{suutnik£b y q ]KoOqo~rb<mkb<Œuo†t„qZo†w`w`~rs„o†{-]¡q s

{sut y ižqriksutF¨©Ko†x b y a‚oOikt„q btKo†t`{b‚{sut`xrikx q x%ikt³q ]`bfb•o†~mžz y b<q b{<qriksut°s†œ N!POQ/RSRT!+%"!"#%$U ¤^ižq ]°~rbx wb{<q0q s

o 3wKo†~ o†acb<q ~ik{={-]Ko†~ o†{<q b~ik£•oOqriksut°s†œq ]`bxrznxrq ba ikt­l`x-lKoOmQ¤µsu~ !jikt`C{sut

y

ižqriksut`x•§¤^ižq ]`sulnqZo†~qri

«

{<ipoOmbH|j¨

{<ižq-oOqriksut>§x wbb y ikt` y s•¤t>§su~^x q suw> }~rsF{bx xrikt`cmksut`‚xGo†acwnmkbxs†œ¢alnmžqriª¨©x bt`x su~%sulnq w`lnqacb•o†x l`~rbacbtq x

ikxs†œMq bt­t`b{bx xGo†~zœ:su~$q ]nikxw`l`~rw2sux bu 

LÃqÈq l`~rt`xÈsulnqÈq ]KoOq•§jikta‚o†tz´o†w`wnmžik{•oOqriksut`x•§Fq ]`bVC D.)>w`~rsunmkba s†œ>ikt„q b~rbxrq$ikxµq s y b<q b{<qo†t y´y ipo†ut`sux b

{G]Ko†t`ubxiktŸq ]`b0b<ikubt`xrq ~rl`{<q l`~rbs†œ¢omžikt`b•o†~ y zFtKo†afik{•oOmQx zFxrq ba¡  ¯ t´ikacwsu~q-o†tqbH|Ko†acwnmkb*ikx^xrq ~rl`{<q l`~ oOm

ŒFik`~ oOqriksut acsutnižq su~ikt``§¤]nik{-] ¤µbvo y`y ~rbx xCikt x b{<qriksut(%n  \^]`b !ub<z ikx x l`b q ]`b~rb­ikxq s8iy bt„qrižœMz o†t y

acsutnižq su~cŒFik`~ oOqrikt`8{G]Ko†~ o†{<q b~ikxrqrik{x3acs

y

bxCo†t

y

acs

y

oOmx ]Ko†w2bx =s†œ%acb{-]Ko†tnik{•oOmZxrq ~rl`{<q l`~rbxCx-l`F€b{<q

q s $,. W o†t y $'#$X%"!+#$'%WY tKoOq l`~ oOmbH|`{<ižq-oOqriksut> *\znwnik{•oOmbH|`o†acwnmkbxo†~rbfs&)x ]`su~rbxrq ~rl`{<q l`~rbx

x l`F€rb{<q¬q sxr¤Èb<mžmŧj`lnižmy ikt`ux$x l`F€rb{<q¬q s¤^ikt y su~µb•o†~q ]jlKo&!ubu§n`~iy ubx•§ y o†acx•§j¤^ikt`uxÈx-l`F€b{<qµq sZKlnqrq b~

ikt[Z`iku]q•§`o†t y q l`~rnikt`bxµx-l`F€b{<qq sxrq b•o†a q l`~r`lnmkbt`{bu§FœM~ik{<qriksut‚ikt‚b•o†~ikt`ux@§jo†t y ikacw2b~œ:b{<q¬KoOmpo†t`{<ikt`` 

¯

~rb<mkb<Œuo†t„qo†w`w`~rs„o†{G]q sq ]`b%Œjik`~ oOqriksut´acsutnižq su~ikt`fw`~rsunmkba ]Ko†x$2bbtCx ]`s@¤tCq sb%Ko†x b y sut‚q ]`b

acs y b<mžikt`s†œ>acs y bxµo†t y acs y oOm2x ]Ko†wbx¬q ]`~rsul`u]Cxrq-oOq b%x wKo†{b~rbw`~rbx btq-oOqriksut`xEôƒ #QIŧq ]`bl`x bs†œ #*\"

#$'NY

o†t

y #TW!+$']W!0T$

iy btqri

«

{•oOqriksut+acb<q ]`s

y x 3x l`{-] o†xikt`xrq ~rl`acbt„q-oOm$Œuo†~ipo†nmkbxsu~KoOmpo†t`{b

y

~rb•oOmžik£•oOqriksut­oOmkusu~ižq ]`acx =^EюuŽIŧ`o†t y q ]`b0{suacw`lnq-oOqriksut¡s†œQx wb{<i« {`_baH¨ÅqÃzFw2b%q bxrq x$Ko†x b y sutq ]`b0x sO¨©{•oOmžmkb y

ikt`xrq ~rl`acbtq-oOmxrq-oOqrikxrqrik{x[E‰IÅ C5³su~rbs•Œ„b~§)q ]`b y bxrikutvs†œq ]nikx^_ a ¨Åq bxrqZikxZowKo†~qrik{lnmpo†~0{•o†x bs†œ¬oubt`b~ oOm

o†w`w`~rs„o†{G] q s.CD )¤]nik{G]­`lnižm

y

x%o

y

b<q b{<q su~œM~rsua oc{sutŒ„btnikbt„q0bxrqrika‚oOqrikt`cœ:l`t`{<qriksutcEюJƒn§Kˆuˆn§1%IÅ 

tq ]`bÈs†q ]`b~]Ko†t y § y l`~ikt`%q ]`bµmpo†xrq y b{•o y bÈq ]`b~rbÈ]Ko†x2bbtfou~rs@¤^ikt`%iktq b~rbxrq¢iktx-l``x wKo†{bH¨©Ko†x b y

mžikt`b•o†~xrzFx q ba iy bt„qri« {•oOqriksutfacb<q ]`s y xdEôƒGn§@ˆ%eK§Jƒ†‰Ijo†t y q ]`b<ik~~rb<mpoOqriksut`x ]nikw¤^ižq ]ikt`xrq ~rl`acbtq-oOmjŒuo†~ipo†nmkbx

EˆFŽIÅ  D$b{•o†l`x b0s†œ>¤]KoOq$]Ko†xȍ2bbtŸo†~rul`b y o†2s•Œ„bu§Fq ]`b jl`bx qriksut´o†~ikx bxÈq s y bxrikutFC D.)>oOmkusu~ižq ]`acx^Ko†x b y

sut´q ]nikx${<mpo†x x$s†œQiy bt„qri

«

{•oOqriksut acb<q ]`s y x•§Fq sikt„Œ„bx qrik„oOq b0q ]`b<ik~µq ]`bsu~rb<qrik{•oOmQw`~rsuw2b~qrikbxo†t y {-]`b{ !q ]`b<ik~

~rb<mkb<Œuo†t`{bœ:su~^q ]`b*ŒFik`~ oOqriksut­acsutnižq su~ikt`´w`~rsunmkba¡ fLÃq^ikx^q ]`bw`l`~rw2sux bs†œq ]nikxwKo†w2b~^q sCo y`y ~rbx-x^q ]`bx b

q ]`~rbb*ikx-x l`bx• 

354+g hjikAH9%l\m mn7Mokl\pA.=:?Borqf=>s=:mnlU9%lsA

š b{sut`x iy b~^mžikt`b•o†~alnmžqriª¨ÅŒuo†~ipo†nmkbxrzFx q bacx y bx {~ikb y „z­o y ikx {~rb<q bH¨Åqrikacbx q-oOq b*x wKo†{bacs y b<mBt

uwv(xybz|{ }Vv(x~€Hxybz

‚ x { ƒ„v(x

3Ž$=

¤]`b~rb‚x q-oOq b

v

o†t y su`x-b~Œ„b y sulnq w`lnq…‚/]KoŒ„b y ikacbt`xriksut`x…†"o†t yˆ‡ ~rbx wb{<qrižŒ„b<mžz„ C\^]`bcxrq-oOq bct`s†ikx b

w`~rsF{bx xJ‰

€QxŠ]x

ikxo†t

$,. W Œ‹

o†l`x xripo†t¦¤]nižq bt`s†ikx bCx-b"jl`bt`{bc¤^ižq ]®£b~rs acb•o†t±o†t y {s•Œuo†~ipo†t`{b

a‚oOq ~iª|t ŽQ

‰

€Hx%Šk{’‘n“€Hx^€”

x5•—–˜+™

{›š

(7)

¤]`b~rb

‘

‰

Š y bt`s†q bx*q ]`bfbH|`wb{<q-oOqriksut¦suw2b~ oOq su~  ½ su~0q ]`b y sul`nmkbcxGo&!ubcs†œ¬xrikacwnmžik{<ižq©z8o†t y ŒuoOmžiy ižq©z°s†œ

q ]`bo†~rul`acbtq x¬¤Èbl`x bu§u¤Èbo†x x l`acbt`s†ikx b

€Hx

q s*2b^xrq-oOqriksutKo†~z„§q ]KoOq¬ikx{sut`xrq-o†t„qÈ{s•Œuo†~ipo†t`{ba‚oOq ~iª|

š  

š bo y`y ~rbx-x^q ]`b*ikx x l`b*s†œ¢~rsu`l`xrq t`bx x¤^ižq ]¡~rbx w2b{<qq sct`sutF¨©xrq-oOqriksutKo†~z­bH|`{<ižq-oOqriksut¡ikt­x b{<qriksut #F 

b<q

–˜+™

{ ‘n“v(x

‚ ” x •

2bZq ]`b*{~rsux x¨©{su~r~rb<mpoOqriksut­2b<q©¤Èbbt­xrq-oOq b v(x

o†t y su`x-b~Œ†oOqriksutŒ‚

x

§`o†t y mkb<qt

{ ƒƒ }

   

ƒ }

z

o†t y

{8“

}

}

z •

3©ƒ =

2bŸq ]`b q ]F¨©su~ y b~‚su`x b~Œuo†nižmžižq©z+a‚oOq ~iª|+s†œZx zFxrq ba 3Ž$=fo†t y {sutq ~rs†mžmpo†nižmžižq©z a‚oOq ~iª|+s†œZwKoOik~F‰

}!

Š §

~rbx w2b{<qrižŒ„b<mžz„ 

š

bZo†x x l`acb%q ]KoOq•§œ:su~"Ÿmpo†~rub%bt`sul`u]>§n2s†q ]su`x-b~Œ†o†nižmžižqÃzo†t

y

{sutq ~rs†mžmpo†nižmžižq©zŸa‚oOq ~ik{bx

o†~rb*œ:lnmžmQ~ o†t! †8 

¯ xacbtqriksut`b y o†2s•Œ„bu§o†t y o†x-x l`afikt`cq ]`bsu`x b~ŒuoOqriksut­a‚oOq ~iª|

ƒ

q scb*†ižŒ„bt>§`q ]`bw`~rsunmkba ikx^q s

iy btqrižœLzŸo†t y acsutnižq su~$q ]`bZsu`x b~Œ„b y xrznxrq ba b<ikubt`xrq ~rl`{<q l`~rbu µ\^]`b%su`x-b~Œ„b y x zFxrq ba b<ikubt`xrq ~rl`{<q l`~rb0ikx

q ]`b‚{s†mžmkb{<qriksut±s†œf† wKoOik~rx.‰$#

!%'& Š

§>¤]`b~rb(#±~ o†t`ubxs@Œ„b~*q ]`bcx b<qs†œ$b<ikubt„ŒuoOmkl`bxs†œ$xrq-oOq bfq ~ o†t`xrižqriksut

a‚oOq ~iª|

} §

%'& { ƒ*)+&

o†t y )+&

ikx0q ]`bf{su~r~rbx wsut y ikt` b<ikubt„Œ„b{<q su~ —LÃt¦oOmžm¢¤]KoOq*œ:s†mžmks•¤x•§>¤Èb‚o†x x l`acb

q ]KoOqq ]`bCxrznxrq ba']Ko†xt`s alnmžqrikwnmkbŸb<ikubt„ŒuoOmkl`bx•  š bCx q ~rbx xq ]KoOqq ]`bC{s†mžmkb{<qriksutRs†œ…‰$#

!%'&RŠ

w`~rs•ŒFiy bx

l`x*¤^ižq ]8o´{•o†t`sutnik{•oOm¬wKo†~ o†acb<q b~ik£•oOqriksut®s†œ¬q ]`bcw2s†mkbcwKo†~qs†œµxrznxrq ba 3Ž$=H  LÃt°wKo†~qrik{lnmpo†~§ižq y sFbx*t`s†q

y bw2bt y sutCq ]`bxrq-oOq b%x wKo†{bKo†xrikx^EюuŽIÅ KLÃt‚q ]`bx b"Fl`b<mŧ~rb<œ:b~r~ikt`q sŒjik`~ oOqriksutacsutnižq su~ikt``§nx l`{-]Ÿo*wKoOik~

‰$#

!%'& Š

ikx{•oOmžmkb y o‚acs y bu \^]`bx-b<qs†œq ]`bV†'acs y bx^ikx{sut`x iy b~rb y o†x^q ]`bxrznxrq ba wKo†~ o†acb<q b~-,Œt

,

–˜+™

{/. 0

21Ž+354

3ň =

Lît 3ň =H§

0

ikx$q ]`b0Œ„b{<q su~¤]`sux b*b<mkbacbt„q xZo†~rb*q ]`b*b<ikubt„ŒuoOmkl`bx#§

3

ikx$q ]`b*a‚oOq ~iª|¡¤]`sux b*{s†mkl`act`xo†~rb

q ]`b

%'&

x•§Ko†t

y

21Ž

ikx$q ]`b{s†mkl`act­xrq-o†{ !ikt`Csuwb~ oOq su~ }¢o†~ o†acb<q b~6,c]Ko†xxrik£b(‰

‡

~87HŠ

†8§K`lnqxrikt`{b0q ]`b

b<ikubtŒ„b{<q su~rx )9&

§o†t y q ]jl`xq ]`b

%'&

§o†~rb y b « t`b y l`w­q s´oc{sut`xrq-o†tqZ{suacwnmkbH| tjl`a2b~§q ]`bwKo†~ o†acb<q b~

x wKo†{b;:

{=<?>A@2B

,Ÿ]Ko†x y ikacbt`xriksutDC

{ ‡ †8 \^]`b(C D.)¬w`~rsunmkba ikx0q s y b<q b{<qo†t y ikx s†mpoOq bc{G]Ko†t`ubxikt

wKo†~ o†acb<q b~Œ„b{<q su~,K  DÈzikx-s†mpoOqriksut>§`¤µbacb•o†t

y

b{<i

y

ikt`‚¤]nik{-] acs

y b 3x =^]Ko†x 3:Œ„b=${-]Ko†t`ub y  

\^]nikxdC D.)Kw`~rsunmkba {•o†t‚oOmkx s02b^o y`y ~rbx x b y l`xrikt`*o†tfikt`w`lnq¨©sulnq w`lnqFEHG.A6E¡~rbH¨Å¤~ižqrikt`*s†œ2xrq-oOq b$x wKo†{b

acs y b<m 3Ž$= t ‚ x {

IJLK

zM

J ‚ x J ~

z

I

N

KPORQ

NTS x N

3d =

¤]`b~rb.‰

S

xŠ]x

ikxo ‹ o†l`x xripo†tŸ¤]nižq b*t`s†ikx-b*x b"jl`bt`{b0¤^ižq ]¡£b~rscacb•o†t³o†t y iy bt„qrižq©z¡{s@Œ†o†~ipo†t`{ba‚oOq ~iª|>§

o†t y ¤]`b~rbq ]`bTEHG°{sFbVU‚{<ikbt„q x

M J

o†~rb~rb<mpoOq b y q sfq ]`bwKoOik~…‰

ƒW! } Š

s†œacs y b<m 3Ž$=ȌFipo t

ƒ } {

IJLK

z M J

ƒ-}

J 3 # =

\^]`b[CD )¢w`~rsunmkba ikxq ]`bt³q s y b<q b{<qZo†t y ikx s†mpoOq b{-]Ko†t`ubxZikt­q ]`ba‚oOq ~iª|XEHG8wKo†~ o†acb<q b~rx0s†œo‚alnmžqriª¨

Œuo†~ipo†nmkbTEHG.A6E8w`~rsF{bx x^¤^ižq ] l`t!jt`s@¤t A6E¦wKo†~q• 

354ZY [W\k9%p;?Blc7^]V9`_Bl qf= q l\s

š b « ~rxrq~rb{•oOmžm¬q ]`bCq©¤Ès Ko†xrik{{sut`{bwnq x¤]nik{G]8¤µbl`x bcœ:su~ y bxrikutnikt` q ]`bCt`b<¤ x l``x-wKo†{bH¨©Ko†x b y CD.)

oOmkusu~ižq ]`acx^w`~rsuw2sux b y iktCq ]nikx$wKo†wb~ gFb{<qriksut­ƒ*x l`aca‚o†~ik£bxÈq ]`b%Ko†xrik{%w`~ikt`{<ikwnmkbx^o†t y {suacw`lnq-oOqriksutKoOm

œ:su~racx$s†œQq ]`b%x q sj{G]Ko†xrqrik{Z¤µb<iku]„q b

y

x-l``x wKo†{bH¨©Ko†x b y iy

bt„qri

«

{•oOqriksut­acb<q ]`s

y

x$sut´q ]`b%Ko†xrikx$s†œQ¤]nik{G]´¤µb

w`~rsuw2sux b*q s y bxrikut CD )¢oOmkusu~ižq ]`acx• Lît­wKo†~qrik{lnmpo†~§K¤Èb y ikx {l`x x%l`x b<œ:lnmQxrzFx q ba wKo†~ o†acb<q b~{G]Ko†~ o†{<q b~iª¨

£•oOqriksut`x•§Qo†t y q ]`bf~rs†mkbfs†œ¤Èb<iku]„qrikt`¡ikt°acs y b<m¢~rb y l`{<qriksut> fgFb{<qriksut8ˆCx-l`aca‚o†~ik£bxoCubt`b~ oOmacb<q ]`s y

(8)

œ:su~ y bxrikutnikt` y b<q b{<qriksutCoOmkusu~ižq ]`acx@§Ko†x b y sutcbxrqrika‚oOqrikt`œMl`t`{<qriksut`x¬o†t y o0x q-oOqrikxrqrik{•oOm`mksj{•oOmo†w`w`~rs„o†{G]

3Åo†x x-l`acwnqriksut¡s†œo†xrznacwnq s†qrik{•oOmžmžz´{<mksux-b*]„znws†q ]`bx bx =H \^]`btŸ¤µb0q l`~rt´q sfq ]`b0w`~rsuwsux b y x-l``x wKo†{bH¨©Ko†x b y

CD )ÈoOmkusu~ižq ]`acx• fgFb{<qriksut8d´ikx y b<Œ„s†q b y q sŸq ]`b<ik~ y bxrikut8o†t y o†tKoOmžznxrikx•  LÃtvwKo†~qrik{lnmpo†~§Q¤ÈbcbH|n]niknižqo†t

iktŒ†o†~ipo†t`{bfw`~rsuw2b~q©z³s†œq ]`b _baG¨Åq bxrq x@  ÈsuacwKo†~ikx sutvikxZa‚o y b¤^ižq ]³q ]`bikt`x q ~rl`acbt„q-oOmŒuo†~ipo†nmkbx¨©Ko†x b y

y

b<q b{<qriksut±oOmkusu~ižq ]`a4w`~rsuwsux b

y

ikt E‰%IÅ \^]`bc{•o†x bcs†œÈt`sutF¨©xrq-oOqriksutKo†~z¦bH|n{<ižq-oOqriksut8ikxo y`y

~rbx x b

y

ikt¦x b{H¨

qriksut #F °\^]`bx q ~rl`{<q l`~ oOmȌFik`~ oOqriksut acsutnižq su~ikt`¦w`~rsunmkba ikxo y`y ~rbx-x b y ikt®x b{<qriksut %n  ½ iktKoOmžmžz„§x suacb

{sut`{<mkl`xriksut`xZo†~rb y ~ o¤t ikt¡x b{<qriksut³F 

* " ! $ %!#&42(*

š bc2b†ikt°q ]nikx*x b{<qriksut°¤^ižq ]8oŸx l`aca‚o†~z°s†œ¬q ]`bcKo†xrik{fw`~ikt`{<ikwnmkbxo†t y {suacw`lnq-oOqriksutKoOmœMsu~racxs†œµxrq sO¨

{G]Ko†xrqrik{fx l``x wKo†{bH¨©Ko†x b y iy

bt„qri

«

{•oOqriksut¦acb<q ]`s

y

x•§)o†x x l`afikt` !jt`s@¤t³xrznxrq ba su~

y

b~ \^]`bt³¤µb

y

ikx {l`x x

q ]`b~rs†mkbCs†œ^¤µb<iku]qrikt`vœMsu~acs y b<mµ~rb y l`{<qriksut>  š bCsulnqrmžikt`bŸo¡xrznxrq ba4wKo†~ o†acb<q b~{-]Ko†~ o†{<q b~ik£•oOqriksut ikt

q b~racx%s†œ¢o†t¡bxrqrika‚oOqrikt`CœMl`t`{<qriksut>§K¤]nik{-]­¤Èbl`x b0œ:su~ y bxrikutnikt`cq ]`b*q bx qxrq-oOqrikxrqrik{x• 

gb43 =:A;qBs;?U;XqdpXl\A ?k7 ? AQikAH9%l\m 75sokl\s

¯

xbH|`wnmpoOikt`b y ikt°q ]`bcikt„q ~rs y l`{<qriksut>§b{•o†l`x bcs†œÈq ]`b.CD )Èw`~rsunmkba²¤ÈbCo y`y ~rbx x•§¤µb‚o†~rbciktq b~rbxrq b y ikt

sulnq w`lnq¨©sutnmžz o†t y {s@Œ†o†~ipo†t`{bH¨y ~ižŒ„bt°oOmkusu~ižq ]`acx•  š bo†~rb*q ]l`x%†ižŒ„bt ofx b"Fl`bt`{bs†œ{s@Œ†o†~ipo†t`{bx t

J

–˜+™

{ ‘|“

‚ x ‚ ” x J •

36% =

s†œ¢sulnq w`lnqS‚

x

s†œ¢ocxrq-oOq b*x wKo†{b*acs y b<m 3Ž$=H  š b*2b†iktŸ¤^ižq ]­x b<Œ„b~ oOmw2sux xriknmkb*{G]Ko†~ o†{<q b~ik£•oOqriksut`x0s†œq ]`b

xrznxrq ba/wKo†~ o†acb<q b~, 3ň =H 0\^]`btv¤µbx l`aca‚o†~ik£bq ]`bfbxrqrika‚oOqriksut°w`~rsj{b y l`~rbx•§>o†t y l`x b<œ:lnmiktq b~rw`~rb<q-oJ¨

qriksut`x• 

½ su~ ~ 7

§`mkb<q

ybz

b0q ]`bnmksF{ !¨0o†t!ub<ma‚oOq ~iª|t

ybz { O z

z

z a

                 

y

z

3© =

¡» ”•—n” 8M»*:

¯

q%q ]nikxZws†iktq•§2oCt`s†q-oOqriksutKoOm{sut„Œ„bt„qriksut¦x-]`sulnmy 2bxrq ~rbx x-b y §K¤]nik{-]°]`s†my x%q ]`~rsul`u]`sulnq

q ]`b´wKo†wb~  ¯ xsu„ŒFiksul`xœM~rsua 3© =o†t y 36% =H§¢t`s†q-oOqriksut ikxl`x-b y œ:su~q ~rl`b nmksj{ !„¨0o†t!ub<m^a‚oOq ~ik{bx•§

¤]`b~rb•o†xÈt`s†q-oOqriksut‡ikx¬l`x-b y œMsu~¬bacwnik~ik{•oOm2nmksF{ !¨Zo†t!ub<m2a‚oOq ~ik{bx « mžmkb y ¤^ižq ]Cbacwnik~ik{•oOm2{s•Œuo†~ipo†t`{bx• 

"!#!

7

·%$·

–J—1Fȓ

¸

“”

· <

—`–J—1

· ” ·

–‚˜'&—`–O—`˜u”

· – 8"(

—n”

8M»*:

“

Zik~rb{<q¡{suacw`lnq-oOqriksut`x¡s†œq ]`b) J

xœM~rsua#q ]`b³acs

y

b<m0b"jlKoOqriksut`xŸmkb•o

y

q s±q ]`b³œ:s†mžmks•¤^ikt`R¤µb<mžm9!Ft`s•¤t

œo†{<q su~ik£•oOqriksut w`~rsuw2b~q©zEôƒuIkt

ybz {

ybz

3XG =

È]`sFsuxrikt`°q ]`b¡b<ikubt„Œ„b{<q su~rxs†œ

}

o†x‚ovKo†xrikxfœ:su~fq ]`b¡xrq-oOq bŸx wKo†{b+*czFikb<my xcq ]`b´œMs†mžmks@¤^ikt`8wKo†~qrik{lnmpo†~

~rbw`~rbx btq-oOqriksut³s†œq ]`bsu`x b~Œuo†nižmžižq©z¡a‚oOq ~iª|cE‰Ikt

ybz

‰e,

ŠM{

33 ,

   3 ,

3ʼn =

-

Í)ÎJÏÖÐ)ÏÖÐQáß-ñôñõÚrÛZÙÅÎOÚó^ӕÛOß-ñÜOßHÐMÏÖÐQÏõâÙÅÎOÚÏõÜOÔÅß-ٝÏõÓGâZó^ÓHâ@ÏôÙÅÓHÔ:ÏõâOö^ß-ØOØ@ñõÏÖáß ÙÏõÓHâ*Ó/.`Ð:ÚráÃٝÏõÓHâå$

(9)

¤]`b~rb y ipo†usutKoOma‚oOq ~iª| , ikx y b « t`b y o†x ,

{L@

‰0 Š

§Qo†t y 0 o†t y 3

o†~rbo†xZikt 3ň =H  ½ su~0o†tz s†q ]`b~

xrq-oOq bKo†xrikx•§nq ]`bsu`x b~Œuo†nižmžižq©z¡a‚oOq ~iª|

ybz

{•o†t b0¤~ižqrq bt o†x…t

ybz {

ybz

‰e,

Š

3ŽHe =

œ:su~ocx lnižq-o†nmkbV† F†²ikt„Œ„b~qriknmkba‚oOq ~iª|

 

ŠZs•¤¥¤Èbfo†~rb†ižŒ„bt>§)sutvq ]`bsut`b]Ko†t y §QoCx zFxrq ba wKo†~ o†acb<q b~,K§2o†t y sut³q ]`bs†q ]`b~0]Ko†t y oCnmksF{

0o†t!ub<ma‚oOq ~iª|

ybz

§Jo†t

y

¤µb¤^ikx ]q s{-]Ko†~ o†{<q b~ik£bµ¤]`b<q ]`b~

ybz

{•o†t{su~r~rbx-wsut

y

q s^wKo†~ o†acb<q b~9,K 

½ ~rsua 3XG =H§3ʼn =o†t y 3ŽHe =H§2¤µbfub<qq ]`bœ:s†mžmks•¤^ikt``  š ]`b<q ]`b~

ybz

{su~r~rbx wsut y xZq s ,C{•o†tvb{-]`b{ !ub y

ikt¡q ]`bœMs†mžmks@¤^ikt`cœMsul`~b"jlnižŒuoOmkbt„q¤$oznx…t

Ž„ 

ybz

ikx0q ]`bcsu`x b~Œuo†nižmžižq©z¦a‚oOq ~iª|

ybz

‰

ƒX! } Š

œ:su~Zx-suacbcwKoOik~(‰

ƒW! } Š

¤^ižq ]¦b<ikubt`xrq ~rl`{<q l`~rb;,K§

o†t y ybz

o†t y ybz

]KoŒ„b*q ]`bxGo†acb*~ o†t`ubx wKo†{bu 

ƒF 

ybz

ikx0q ]`bcsu`x b~Œuo†nižmžižq©z¦a‚oOq ~iª|

ybz

‰

ƒX! } Š

œ:su~Zx-suacbcwKoOik~(‰

ƒW! } Š

¤^ižq ]¦b<ikubt`xrq ~rl`{<q l`~rb;,K§

o†t

y

ybz

o†t

y

ybz

]KoŒ„b*q ]`bxGo†acb0mkb<œLq !ub~rt`b<mx wKo†{b† 

ˆn 

ybz

‰e,

Š

ikx y b « t`b y „z 3ʼn =H§o†t y ybz

o†t y

ybz

‰e,

Š

]Ko•Œ„b*q ]`bx-o†acb*~ o†t`ubx-wKo†{bu 

d` 

ybz

‰e,

Š

ikx y b « t`b y z 3ʼn =H§uo†t y ybz

o†t y ybz

‰e,

Š

]Ko•Œ„bÈq ]`bµx-o†acb¬mkb<œLq !ub~rt`b<mnx wKo†{bu§ux wKo†t`t`b y §

x-oz„§`zŸq ]`b{s†mkl`act`xs†œofa‚oOq ~iª|

M  

}s†ikt„q¢s†œFŒjikb<¤ Ž„ †ižŒ„bx~ikx bq s^q ]`bl`x lKoOm„xrq sF{-]Ko†x qrik{¬~rb•oOmžik£•oOqriksutacb<q ]`s y xo†xQ¤µb~rb{•oOmžmFt`bH|Fq• DÈlnq•§†o†x

y ikx {l`x-x b y œ:l`~q ]`b~b<mks@¤§w2s†ikt„qÈs†œŒFikb<¤ d` ¢w`~rs•ŒFiy bxµl`x¤^ižq ]o*al`{G]Cacsu~rb y ik~rb{<q¬{G]Ko†~ o†{<q b~ik£•oOqriksutŸs†œ

wKo†~ o†acb<q b~,K§@¤]nik{-]ikxq ]`bµKo†xrikxQœ:su~sul`~o†w`w`~rs„o†{-]q sq ]`b y bxrikuts†œKxrq-oOqrikx qrik{•oOmq bxrq xœMsu~b<ikubt`xrq ~rl`{<q l`~rb

acsutnižq su~ikt`` 

– 8;: ˜ 8< F·+» ” & · < – »*<» “ · ¼ — << – » —`˜'& D$b<œ:su~rbw`~rsF{bb y ikt``§¤µbŸxrq ~rbx-xq ]KoOqcsul`~co†w`w`~rs„o†{-] q s

ŒFik`~ oOqriksut acsutnižq su~ikt`Rw`~rsj{bb y xŸo†x‚œ:s†mžmks•¤x-E‰n§ŽHeIÅ 

‹

ižŒ„bt y oOq-o±{s†mžmkb{<q b y œ:~rsua q ]`b­x-oOœ:b­xrznxrq ba¡§

`lnižmy q ]`b°bacwnik~ik{•oOmnmksj{ !„¨0o†t!ub<ma‚oOq ~iª| o†t y bH|nq ~ o†{<q­o®acs y oOm*wKo†~ o†acb<q b~¡bxrqrika‚oOq b , O

l`xrikt`±sut`b­s†œ%q ]`b x l``x wKo†{bH¨©Ko†x b y iy bt„qri« {•oOqriksut acb<q ]`s y x y bx {~ikb y b<mks@¤  \^]`bt>§${suacw`lnq b¡q ]`b

su`x b~Œuo†nižmžižq©z¦a‚oOq ~iª|

‰e, O Š

iktvq ]nikxacs

y

oOmKo†xrikx•§Qo†x y b «

t`b

y

ikt 3ʼn =H§o†t

y

{suacw`lnq boa‚oOq ~iª|

M

‰e, O Š

¤]`sux b{s†mkl`act`x%x-wKo†t¡q ]`bmkb<œMq !ub~rt`b<mx-wKo†{bs†œ ‰e, O Š

 $\^]`bt>§†ižŒ„bt³t`b<¤^mžz¡{s†mžmkb{<q b y³y oOq-on§`lnižmy q ]`b

bacwnik~ik{•oOmnmksF{ !¨0o†t!ub<ma‚oOq ~iª| /o†t y {G]`b{ !´¤]`b<q ]`b~

M ”

‰e,

O Š ›ikx^x ikutni« {•o†t„qrmžz y i2b~rbtq

œ:~rsua £b~rs` 

"! 72” » ˜'&—`“” 8˜­– · —1F 8( —n” 8L» : — : ¼ ’—1FM— : ˜ 8;:

gjq sF{-]Ko†xrqrik{*sulnq w`lnq¨©sutnmžzŸo†t y {s@Œ†o†~ipo†t`{bH¨y ~ižŒ„bt x l``x wKo†{bH¨©Ko†x b y iy bt„qri

«

{•oOqriksut acb<q ]`s y x${•o†tŸb y bx¨

{~ik2b y ikt¡q ]`b0œ:s†mžmks•¤^ikt`a‚o†t`t`b~.Eôƒ†‰n§ƒjŽIÅ 

b<q

z

o†t y a

2bCqäµs°l`x b~î¨ y b « t`b y ikt„Œ„b~qriknmkbŸ¤Èb<iku]„qrikt`8a‚oOq ~ik{bxfs†œx ik£b-‰

~7HŠ

‡ o†t y ‡ §

~rbx w2b{<qrižŒ„b<mžz„ ¬…%b„o†~ y ikt`cq ]`b*¤Èb<iku]„q b y nmksF{ !¨0o†t!ub<ma‚oOq ~iª|>§nq ]`bx b{sut y ižqriksut`xikacwnmžzŸq ]KoOq…t

@2B! (“

z

ybz ”

a • {

@2B!

‰#

ybz Š ‰{ † Š

3ŽuŽ$=

œ0{sul`~rx bu§ÈœMsu~ !Ft`s•¤t xrzFx q ba su~ y b~§$~rb"Flnik~ikt`±o°x FlKo†~rb¡ikt„Œ„b~qriknmkb ¤µb<iku]qrikt`±a‚oOq ~iª|"

a

ikx‚t`s†q

t`b{bx xGo†~z´œ:su~93ŽuŽ$=Èq sc]`s†my  \^]`bœMs†mžmks@¤^ikt`‚¤µb•o&!ub~{sut y ižqriksutct

a$#&%('*) ,+

!

@2B! —“

ybz ”

a • {

@2B-

‰#

ybz Š ‰ { † Š

.

Í)ÎOÚñÖÚ .ÑÙÕ<ÚԝâOÚÃñFÐ:ØOßHáîÚÓ .Kóß-ÙÅÔ:Ï0/21 ÏÖÐ)ÙÅÎOÚÕHÚԝâOÚîñjÐ:ØOßHáîÚÓ .Kóß-ÙÅÔ:Ï0/2143

5

Í)ÎOÚØOԝÚrÐ:ÚâÙ©ß ÙÏÖÓGâ0ÎOÚîԝڢÏÑÐQÐ:ÓGó^ÚîÒQ렧 Ù×Jâ•׆Ð:×†ß ñRaLÙ>ÏÖÐ>ó^ÓGٝÏHß ÙÅÚrÛ%ÜÝÓG×OÔQÓHÜ@àMÚrá©ÙÏ-HÚÓ/.ÛJÚÐMÏÖöGâJÏõâOö7698jèFß ñõöHÓHÔ:ÏôÙÅÎJóÐ

(10)

¤^ižq ] ‡ §ikxcx l?U‚{<ikbtqCœ:su~q ]nikx‚w`l`~rwsux-bu Zs•¤Èb<Œ„b~§$xrikt`{bŸikt w`~ o†{<qrik{b¡q ]`b­o†{<q lKoOm~ o†t!Rs†œq ]`b

bacwnik~ik{•oOm0o†t!ub<ma‚oOq ~iª|®ikxcl`t!Ft`s•¤t>§µq ]`bŸsutnmžz±¤$ozRq s8o†{-]nikb<Œ„b 3ŽuŽ$=ikxfq svikacwsux-bŸo†t iktŒ„b~qriknmkb

¤Èb<iku]„qrikt`´a‚oOq ~iª|4

a

oOmkx-s` 

Zi)b~rbt„q{-]`s†ik{bxs†œnq ]`b¢¤Èb<iku]„qrikt`Za‚oOq ~ik{bxQmkb•o y q s y i)b~rbt„qiy bt„qri« {•oOqriksutacb<q ]`s y x 3bu ` ž§'G)o†t y

E.=o†t

y

§œMsu~sul`~w`l`~rw2sux bu§q s

y i)b~rbt„q

y

b<q b{<qriksut®acb<q ]`s

y

x• ¡\^]`bCtKoOq l`~rbŸo†t

y

iktZKl`bt`{b´s†œ$q ]`bx b

{G]`s†ik{bx%sutŸiy btqri

«

{•oOqriksutvo†t y CD.)Qikx y ikx-{l`x x b y iktŸq ]nikxx-b{<qriksut o†t y ikt­x b{<qriksut¡d`§~rbx wb{<qrižŒ„b<mžz„ 

b<q…t

z

ybz ”

a { “

•

.

4

”

3ŽJƒ =

2b*q ]`bxrikt`ulnmpo†~Œ†oOmkl`b y b{suacwsuxrižqriksut 3 0

D.=^s†œq ]nikxa‚oOq ~iª|>§K¤]`b~rb

{ -L@

‰ z !

!

Š

{sutq-oOikt`x

q ]`b† t`sutF¨©£b~rsxrikt`ulnmpo†~ŒuoOmkl`bx¢ikt y b{~rb•o†x ikt`su~ y b~§uq ]`bd† {s†mkl`act`xs†œa‚oOq ~iª|

o†~rb$q ]`b${su~r~rbx w2sutF¨

y

ikt`´mkb<œMqZxrikt`ulnmpo†~%Œ„b{<q su~rx•§Qo†t

y

q ]`b ‰#

‡

† Š

{s†mkl`act`xZs†œµa‚oOq ~iª|

o†~rbq ]`bmkb<œLqZxrikt`ulnmpo†~ZŒ„b{<q su~rx

o†x x-sj{<ipoOq b y ¤^ižq ] x ikt`ulnmpo†~cŒ†oOmkl`b

  ŠZs†q bŸq ]KoOq

ikxfœ:lnmžm{s†mkl`act ~ o†t! 3:œî {u =H +\^]`bŸœo†{<q su~ik£•oOqriksut

w`~rsuw2b~q©z¡s†œq ]`b Zo†t!ub<ma‚oOq ~iª|¡~rbx-lnmžq x^iktt

z

ybz ”

a { z

ybz

”

a

3Ž@ˆ =

¤^ižq ]>§`œ:su~bH|Ko†acwnmkb(t

z

ybz {

z

a

3ޕd =

”

a { z

z

a ”

3Ž$# =

¤]`b~rb

ikxo´t`sutF¨©xrikt`ulnmpo†~0q ~ o†t`xrœ:su~ra‚oOqriksut> f\^]`bfsu`x b~Œ†o†nižmžižqÃz¦a‚oOq ~iª|v{•o†t°q ]`bt°bf~rb{s@Œ„b~rb y §l`w

q sCof{G]Ko†t`ubs†œ¢Ko†xrikxsu~^b"FlnižŒ†oOmkbtqrmžz¡œMsu~^x-suacb*wKoOik~…‰

ƒW! } Š

§o†xt

ybz

‰

ƒW! } ŠB{

z

z

z

a

3Ž% =

\^]`b¦wKo†~qrik{lnmpo†~¡{G]`s†ik{b8s†œœo†{<q su~

z

a §q suub<q ]`b~Ÿ¤^ižq ]

iy bt„qrižq©z„§0{su~r~rbx w2sut y x¡q sRq ]`b°KoOmpo†t`{b y

~rb•oOmžik£•oOqriksut 3 G={•o†x b*¤]`bt ¤µb<iku]qrikt`´a‚oOq ~ik{bx z

o†t y a

o†~rbiy btqrižq©z„  ¯ t„z¡s†q ]`b~%t`sutF¨©xrikt`ulnmpo†~

œo†{<q su~a‚oz¡2b*l`x b y  

\^]`b³wKoOik~ ‰

ƒX! } Š

ikxC~rb{s•Œ„b~rb y œM~rsua ybz

‰

ƒX! } Š

ikt+q ]`b œMs†mžmks@¤^ikt`8¤$oz„  ½ ~rsua"q ]`b y b « tnižqriksut

o†t y q ]`bx ]nižœMq¨Åikt„Œuo†~ipo†t„q0xrq ~rl`{<q l`~rbs†œ ikt3©ƒ =H§¤Èb y b y l`{bq ]KoOqq ]`bsu`x b~ŒuoOqriksut³a‚oOq ~iª|

ƒ

{•o†t³b

~rb{s@Œ„b~rb

y

o†x%q ]`b

«

~rx q%nmksF{ !¨©~rs•¤¥s†œ

ybz

§o†t

y

q ]`bx q-oOq bq ~ o†t`xrižqriksutva‚oOq ~iª|

}

{•o†tv2b~rb{s•Œ„b~rb

y

o†x

q ]`bG0*x s†mklnqriksut s†œdt

}r{

ybz

3ŽJ =

Lît±b"FlKoOqriksut 3ŽJ =H§a‚oOq ~ik{bx

ybz

o†t y o†~rbCsunq-oOikt`b y „z y b<mkb<qrikt`³q ]`b « ~rxrqco†t y mpo†xrqnmksj{ !„¨©~rs@¤

ikt

ybz

§u~rbx-wb{<qrižŒ„b<mžz„ ¢\^]`bÈb<ikubt`xrq ~rl`{<q l`~rb^s†œKq ]`b$xrq-oOq bµq ~ o†t`xrižqriksutca‚oOq ~iª|

}

ikxq ]`bt~rb{s@Œ„b~rb y œM~rsua t

} {

, z

3ŽHG =

¤]`b~rb

ikx$q ]`b*a‚oOq ~iª|´¤]`sux b*{s†mkl`act`xo†~rb0q ]`b )+&

x• \^]nikx$ikx^sunq-oOikt`b y §Kbu ` ž§`z´b<ikubtŒ†oOmkl`bx-s†mžŒjikt`` 

\sx l`aca‚o†~ik£bu§Jq ]Ko†t!FxQq s$q ]`b y b «

tnižqriksuts†œjq ]`bwKo†~ o†acb<q b~Œ„b{<q su~H,$ikt 3ň =>o†t y s†œFq ]`bsu`x b~Œuo†nižmžižq©z

a‚oOq ~iª|

ybz

‰e,

Š

ikt­acs y oOmKo†xrikx^ikt 3ʼn =H§`¤Èba‚oz¡~rbH¨Å¤~ižq b 3Ž@ˆ =^o†x…t

z

ybz ”

a { z

ybz

‰e,

Š ”

a

3Ž@‰ =

"! 8– · ˜u” < —`–O—1 · ” · –˜+&—`–O—`˜u” · – 8"( —n” 8M»*:

ŠZs•¤§Qw2s†ikt„qs†œ¬Œjikb<¤ d` w`~rs@Œjiy bxl`x%¤^ižq ]8o´al`{-]8acsu~rb y ik~rb{<q{-]Ko†~ o†{<q b~ik£•oOqriksut®s†œµwKo†~ o†acb<q b~ ,´ikt

q b~racx%s†œx l``x-wKo†{bx•§`tKo†acb<mžz&t

ybz

o†t y ybz

‰e,

Š

]KoŒ„bq ]`b*x-o†acb*mkb<œMq!ub~rt`b<mx wKo†{b*¤^ižq ] {sO¨©~ o†t!J† 3©ƒe =

\^]nikxµw`~rsuwb~qÃzikxq ~rl`bsutnmžzœ:su~o0xrznxrq ba su~ y b~ !Ft`s•¤t‚b"FlKoOmKq s †8 KLÃq{•o†tcb^l`x b y œMsu~{G]Ko†~ o†{<q b~ik£<ikt`

wKo†~ o†acb<q b~-,Co†x^œ:s†mžmks•¤x• 

Références

Documents relatifs

Unit´e de recherche INRIA Rennes, Irisa, Campus universitaire de Beaulieu, 35042 RENNES Cedex Unit´e de recherche INRIA Rhˆone-Alpes, 655, avenue de l’Europe, 38330 MONTBONNOT ST

Unit´e de recherche INRIA Rennes, Irisa, Campus universitaire de Beaulieu, 35042 RENNES Cedex Unit´e de recherche INRIA Rhˆone-Alpes, 655, avenue de l’Europe, 38330 MONTBONNOT ST

Unit´e de recherche INRIA Rennes, Irisa, Campus universitaire de Beaulieu, 35042 RENNES Cedex Unit´e de recherche INRIA Rhˆone-Alpes, 655, avenue de l’Europe, 38330 MONTBONNOT ST

Unit´e de recherche INRIA Rennes, Irisa, Campus universitaire de Beaulieu, 35042 RENNES Cedex Unit´e de recherche INRIA Rhˆone-Alpes, 655, avenue de l’Europe, 38330 MONTBONNOT ST

Unit´e de recherche INRIA Rennes, Irisa, Campus universitaire de Beaulieu, 35042 RENNES Cedex Unit´e de recherche INRIA Rhˆone-Alpes, 655, avenue de l’Europe, 38330 MONTBONNOT ST

Unit´e de recherche INRIA Rennes, Irisa, Campus universitaire de Beaulieu, 35042 RENNES Cedex Unit´e de recherche INRIA Rhˆone-Alpes, 655, avenue de l’Europe, 38330 MONTBONNOT ST

Unit´e de recherche INRIA Rennes, Irisa, Campus universitaire de Beaulieu, 35042 RENNES Cedex Unit´e de recherche INRIA Rhˆone-Alpes, 655, avenue de l’Europe, 38330 MONTBONNOT ST

Unit´e de recherche INRIA Rennes, Irisa, Campus universitaire de Beaulieu, 35042 RENNES Cedex Unit´e de recherche INRIA Rhˆone-Alpes, 655, avenue de l’Europe, 38330 MONTBONNOT ST