A mathematical model of the cell cycle and its control

(1)

HAL Id: inria-00071690

https://hal.inria.fr/inria-00071690

Submitted on 23 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.

A mathematical model of the cell cycle and its control

Jean Clairambault, Béatrice Laroche, Stéphane Mischler, Benoît Perthame

To cite this version:

Jean Clairambault, Béatrice Laroche, Stéphane Mischler, Benoît Perthame. A mathematical model

of the cell cycle and its control. [Research Report] RR-4892, INRIA. 2003. �inria-00071690�

(2)

ISRN INRIA/RR--4892--FR+ENG

a p p o r t

d e r e c h e r c h e

THÈME 4

INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE

A mathematical model of the cell cycle and its control

Jean Clairambault — Béatrice Laroche — Stéphane Mischler — Benoît Perthame

N° 4892

Juillet 2003

(3)

(4)

)+*-,+.0/213,54768,59;:<,+=>1@?BA C>D2E-,5?F6F4HGI*KJ,+6FL(GBM>*-NOCQP(?8ESR>M<,+.*TU47VFGBM17*I6FWCXD2*S.>L+YH?

Z[*I6\?8M<,59]*-^

_a`cb\def2gih-jkdlcmonBpqjsrStueprwvxpqjsdjoyzn{pzjkrwt

| eyz}-y~pzbdeyrSdvcmse\xey

Xqr{e\pqyhhch5epa[[

n{vcv+rwzp | ezeF`ce\`cet+>fSwIKg Slcjkmsmkep[wwSgBv5n{weFy

O \¡B¢c£w w¤&¥ e\rwtyzj| e\dnBpq`ce\dnBpqjkn{m¦dr | emkya§¨rSpz`eemsm(\}xmkew©cj7ªeSªXpq`ceyze«Ilce\t5er{§>e\¬Se\tIpqy

pq`nBp[mseFn | yapqrdj®pqrSyzjky©n{ppz`cemse¬we\m(r{§Xnv5rSvclcmonBpqjsrSt¯r{§Xemsmoy\ªa_a`ceFy~enwzey~pzql#pqlcqe | v5rSvclcmonBpqjsrSt

<nw~pqjknwm-°[js±+ezetSpqjknwmc²Q«Iln{pzjkrwtypq`nBp | eFyz\zjk³5epq`cee\¬Srwmklxpzjkrwt2r{§5pz`cev+rwvclmkn{pzjkrwtn{mkrwtc´enS`&vc`5nwyze

rw§xpz`ce}xmkeQnwt | pz`eXpzn{t5y~jspzjkrwtpqrpz`eQtce\Ipvc`nSy~eSª_a`ceFy~ed2r | emkyn{mkmsrBµ¶yze\¬Se\n{mBp}-v+eyr{§rStIpzqrwmoy

yzl`nwypq`ce\n{v+e\lxpqjk\rwtIpzqrwm-jkt\nwyzer{§·\n{t5e\pq`ce\n{v-}O¸Hy~rSd2e`cedr{pz`e\n{vcjkey>n{qea¹-tcrBµtpqrnw#p

rStyzv5eFjsº5´vc`nSy~eFyQrw§(pz`e\}xmke[rSrStpq`ce´pzn{tyzj®pqjsrSty³5e\pµee\tvc`nwyzey»Qrwjkqn | jon{trwtIpqzrSm5³-}

pq`ceQ\e\tIpzn{mBtcez¬Srwly·yz}xypqe\d¼¸¨jktpz`ceXyzlcvcnw`cjonwyzdnBpqjkt-lmke\j½»#ª ¥ eypql | }pq`ceXmkrwtcpqjsdeX³+e\`n8¬-jkrwlc

rw§·pz`cjoyay~}xy~pzed¼rw§(Q°[²Qyalyzjst&n{tOe\tIpzqrwv-}depz`r | n{t | ex`cjk³cj®pF©-³I}t-lcdezjo\nwm5yzjsd&lcmkn{pzjkrwty©Ipz`ce

nS#pqjsrStrw§(pz`ejkqn | jon{turStSpqzrSm

¾¯¿IÀÂÁqÃÄ ¡BÅw¤ hIpqzl5#pzlze | v+rwvclcmonBpqjsrSt | }It5n{djky\©Se\mkmc}x\mseS©wjo\nw | jon{t&n{t | pz`ceqnwv5elxpzjoarStSpqzrSmH©

etIpzqrwv-}depz`r | y\©n{t\e\adr | e\mkmsjktc

ÆÇ¨ÈÉ(Ç½ÊQË8Ì8Í@ÎÏ@ÐÒÑ<Ó8Ô<ÓFÓ8ÔË{ÕÖ×xÖIØ~Ù#ÚFËSÛÜFØ~Ú#ÝaÞ-ÐQßÂà8Ðá7â8ã~äß·Ðå8ÐÒæ´ãâ8å´Ç¨ÈÓFç+É(èçOÝ#ÚéQê3ßÂà8Í@Î#â8ÎÑ7àFë~ÍHãÌ{ÐìFÑ7íïî\ì8Ð

å8Ðáð~ãâ8ðÐÍHá¨ñÒË{ò(Î#á7Ì8íÑ7ãóx×cãì8óô¨ÕÂÍ@Î#ì8á7áHÐ#ËBõéÜ#ÙÛö>íïóïóïÐ¨Ï@ì8í÷xðÐå8ÐÒæSËÏHÐ~ãâIÖðóøãíïÍHãùúBãì8óÑ3ûíïâ8Í@íøãFÖ÷kÍ

ü

ÞcÓ8ÓwË{ý×ÂÓ8þ#ß·ÈÉÓwË8ÝÍ@ì8ÐQÿÎ#óïíïÎÑ@ô@ßÂì8Í@íïÐ#ËBõFØ#Ø~õí÷cá7ìFÍÐÒÑHÑHÐ#Ë{óøãÍHÎ\ð3à8ÐzûóïáHázÖá7ìFÌwÐóïÐð#Ö÷kÍ

Ç¨ÈÉ¦Ç½ÊËBÌ8Í@ÎÏ@ÐÒÑ>ÕÂÊÈ ËBÕÖ×xÖwØ~Ù#ÚFËwÛÜFØ~Ú#ÝaÞ-ÐQßÂà8Ðá7âBãäßÂÐå8ÐÒæwËBùíïá7ð3àFóïÐ~Í7ûå8ùãFÖÐâ8á~Ö÷kÍ

ç+È>ÓFþ>èÊË8ýèÉ¯Ü#Ú#Ú#ÝFËBéÚÍ@ì8ÐXåý(óïùË8ÛÚ#Ý#Ù×cãÍ@íïá¦ð~Ðå8ÐÒæÙ#ÚFË8Ì{ÐÍ@ÑHàBãùÐzûå8ùãFÖÐâ8ázÖ÷sÍ

(5)

!&('

¤ rwl5y<rwt5y~j| qrwt5y(lctdr | b\mkeadnBpz` dnBpqjk«Ilceav+rwlc>mkea\}xmkea\e\mkmslmknwjsqew©Bey~p| jkzemkn

y qjke | ¬ te\de\tIpqyadetn{tIpmkn2djspzrSyzew©5n{l tcjs¬Senwl | lctcev+rwvlcmkn{pzjkrwt | e\e\mkmslcmkeyªeyzrwtIp | ey

«Sl5nBpzjkrwt5yn{lxO° qjs¬ eFy<nw~pqjsemsmkey«Ilcj | qjs¬Se\tIpam ¬Srwmklxpzjkrwt | ltcev5rSvclcmonBpqjsrSt | lcn{tIp`nS«Sle

v`nwyze | l¯}xmkeepmkn2pqqnwtyzj®pqjsrSt2mkn2vc`5nwyzeyzlcjk¬Bn{tIpzeSª!eyadr | b\mkeyav+e\qdepzpze\tIp | jk¬weqyp}-v+ey | e

\rwtIpz#"wmkeyrSdd2eamkerwtIpq$"Smsepz` qnwv5elxpzjo«Ilce¸@\e\zpqn{jktceFy<`cjsdjkr{pq` n{vcjkey>yzrwtIp<rwttIleyv5rSlcXn{Sjs

yzlc | eyvc`nSy~eFy(yzv jsº5«Ilcey | l2}xmkeQemsmklcmon{jkzerwlyzlcmseFy(pqqnwtyzj®pqjsrSty¦etSpqzeQvc`nwyzey»·rSlmkerStIpz#"wmke

\js\n | jke\tuvn{mseyz}xypqb\detcez¬Se\lxue\tIpqqnwmQ¸@nwl¯tcjs¬Senwl | eytrB}Sn{lcy~lvcqnS`cjonwyzdn{pzjo«Ilcey»#ªcrwly

pzl | jsrStyamse\rwdv5rS~pqe\de\tIpnwyz}-d2vcpzr{pqjk«IlceetOpqe\dvyamkrwtcv+rwlceyz}xypqb\de | ²° etlxpqjsmkjoyznwtSp

ltced pq`cr | e | e\tIpzqrwvjsee\pQtcrwl5y<drwtIpzqrwty©{S#%Se& | eFy>pzeFypyXt-lcd qjk«IlceFy\©wm nwpzjkrwt | lrStIpz#"wmke

\js\n | jke\t¦ª

' Ä F Á £)( ¤ °}-tnwd2jo«Ilce | ev+rwvclcmonBpqjsrStyy~pzql#pqlc ey©c}xmkeemsmklcmon{jkzeS©crwtIpq$"Smsejkqn | jke\t ep

pq` n{v+e\lcpzjo«Slew©xd pq`cr | e | e\tIpzqrwvcjkew©xdr | msjoyzn{pzjkrwt | l¯\nwteª

(6)

, -

!&('>Q!

²Q¬we\t pq`crwlcS`uenw`p}-v5er{§<\n{t5e\joylctjk«Ilce³+en{lyzer{§pz`ce&rwdvcmkexjsp}jktu§@nw#pqrwyar{§ | e\¬Se\mkrwv

detSpyzl` nSy´pz`ce¬Bn{qjkep}¯r{§pzjoyzyzlceFy\©·pq`cet-lcde\qrwlyrSd³cjktn{pzjkrwty[r{§we\tepzjon{mspzeqn{pzjkrwty©Âpz`ce

yzleyqyzjsrStOr{§>e\¬Se\tIpqyanSya¬8nSyz\lcmkrwwetceyzjoynwt | n{tcSjsrSwe\teyzjky´¸.ï0/3©1.k82/¨»#©yze\¬Se\n{mÂqj®pqjkn{m·e¬we\tIpyn{qe

`rBµe¬we\[rwddrwtupqrpq`ce&e¬wrSmslxpqjsrSt¯r{§XeFnw`Kn{t\e\µ`jk`Knwzepqn{qwe\pqy§¨rwv+r{pqe\tIpzjon{mpz`e\n{v+e\l

pqjk&nwpzjkrwtyª[d2rStcpq`ce\d joypq`cey~lcvvczeFyzyzjkrwt¯r{§Qnwv5rSvxpzrIy~joy¸@vcqrwwn{dde | \e\mkmslcmon{ | eFnBpz`+»n{t |

| e\qe\wlmkn{pzjkrwt¯r{§Q\e\mkmvzrSmsjs§¨e\nBpqjsrSt¦©µeqe§¨epqr3.kw4/§¨rwnqe\¬-jke\µr{§<pq`cjkynSy~v+epª[_a`jky[mseFn | ypzr

pqz}pzrlct | e\ypn{t | pq`cepzld2rSlc | e¬wemsrSvcde\tIpXnBpXpq`cemse¬wemcr{§¦nv+rwvclcmonBpqjsrStr{§·e\mkmoy<µ`cjkmse)5dnw\zr)

yqrSvcjodr | emky§¨rwpz`ce&tce\rSvcmknSypqjkvczrSwqeyqy~jkrwt `n8¬Se³5ee\t µj| ems}uvcqrwv+rSyze | nwt | ¬Bn{mkj| n{pze | ¸.ø/

nwt | pq`ce2ze\§¨e\qe\t\eypz`cezejst5»ª2[tce2\n{t `crwv+e&pz`n{pn³5e\p~pqe\lct | e\ypn{t | jktc n{t | rwtIpqzrSmrw§Xpz`ce

\e\mkm\}xmke\nwt³+elyze | vcqnS#pqjkn{mkms}jst \nwtepz`e\n{v-}wª¶[lc2nwjsdjoypqrKjktmkl | e jktrwlc2dr | e\m

pµr;¹we}¶§¨en{pzlcqeyrw§´yze\¬Se\n{mn{tIpqjÒ\nwte

|

zlcIy\ª _a`euºqy~prwte joypq`nBppq`ce\} nw#prSt y~v+e\j®º5

v`nwyzeyrw§[pq`ceKemsm[}xmkew©§¨rwjkty~pqnwteu³-}vcqrwdrwpzjktc;rwjktc`cjk³cj®pqjst¶pzn{tyzjspzjkrwt]§¨zrSd n;wjk¬wet

v`nwyzepqr nwtcr{pq`ce\F©Ârw[pzrun{v+rwvxpqrSyzjkyª_a`cey~eFrwt

|

rwtce2joypq`nBp

|

qlcSy[e6\jset} nwt

|87

rSpqr8xjk\j®p}

yze\edy(pqr³5ey~pzqrwtcSms}qe\monBpqe | pzrnBf´`crwlc>q`-}Spq`cd jkdv5rIy~e | ³-}pq`cejkqn | jon{t2e\tIpqqnwm-\msrx¹&.k29/7ª

h-e¬weqnwm5dnBpq`ce\dn{pzjo\n{m·nwvcvcqrSnw`eyXnwze´vcqrwv+rSyze | pqr&dr | e\m+pq`ce´\e\mkm¦}xmke | e\v+e\t | jktcrwtOpz`ce

e\xv5eF#pze | rSlxpzvlxprwtce´µjkyz`ceFyQpqrnw`cjke\¬Sewª>°eFyz\zjkvxpzjkrwtr{§>n&yzjstwmke´\e\mkm·³I}nyz}xypqe\d r{§X[ | jstnwz}

°[js±+ezetSpqjknwm·²Q«IlnBpqjsrStyadr | e\mkmsjktc2pz`eyze«Ilceterw§³cjkrwdrwmke\lcmon{ae\¬Se\tIpqy`nSya³5ee\t vczrSv5rIy~e | ³-}

yze\¬Se\n{m·n{lcpz`crSqyan{t | yzv+ejsº5n{mkms}pq`cejk\n | jknwtq`-}Spq`cd%joyapzqen{pze | jkt:.{f/7ª ¥ `ce\t¯n2v5rSvclcmonBpqjsrSt

rw§Qemsmoyjoy[\rwtyzj| e\qe | rStcejoymken | pzry~pzqlpzlcqepz`ev+rwvclcmonBpqjsrSt ³-};5nwwe)jstKpz`ce&vc`nwyzenwt | pz`jky

joy[pz`cev+rwjktIp´rw§Q¬-jseµ µe&lyze2`ce\qewª_a`cednBpq`ce\dn{pzjo\n{m§¨rwqdn{mkjkyzd §¨rw´pq`cjky´vclzv+rSyze&etIpze\y[pz`ce

\mknSyzyr{§X<n{zpzjon{m°js±Âe\qe\tIpzjon{m²Q«IlnBpqjsrStyª´_a`ce2y~jkdvcmkey~p[µan8}Opqr | r y~rjoy[zemkn{pze | pzrpq`ce§@nwdrwly

<K=e\t | zjo¹ ><rSt@?rIeqy~pzead2r | emH©5n{moy~r\nwmsmke | qe\tceµnwm+eF«IlnBpqjsrSt¸Hy~ee ./3©1.k0/·§¨rSjst5ypn{t\eF»

A

ACBEDGF B4H+IJ1K

A

A%ILDGF B4HMIJNKPO

F

IJ

DGF

B4H+IJRQTSHUBWVXSHIYVZSH

¸wªkF»

DGF

B4H+I Q[S\JGQ^]`_a%bc

F

IJ

DGF

B4H+IJOdICH ¸wªïw»

DGF

BGQ[SH+IJGQ

D b F

I`J4e ¸wªS»

fe\qe

DGF

B4H+IJ | etcr{pqeypq`ce | etyzj®p} r{§e\mkmoynBppzjkde B n{t | n{Se I © O F

IJ pz`e | en{pz`;qn{pzeS©n{t |

c F

IJ pz`ce³cjkzpz`uqn{pzeSª>_a`jkySe\tceqnwmÂd2r | em¦dn8}³+eyzv+ejon{mkjhg\e | pqr&pq`ce\nSy~e

c F IJGQjik

F

IQmlonJ4H

pq`-lye\-vzeFyzyzjstpq`nBp&d2jspzrIy~joy¸| rwlc³msjktc rw§pq`ceO\e\mkmo»nwzjoyzeynBp&wjk¬we\t¶nwwe I;Qpl n ª¯_a`cjoyp}-v5e

rw§Qdr | e\m<`nSy´³5ee\tKl5y~e | ³cqrSn | mk}unwt | \rwdvnwze | pzr $rq(*+ e\-v+e\qjkd2etIpqy´jsts.ï{0/3©G./Xn{t | pz`ce

qe§¨ezeteFyapz`e\qe\jkt¦ª_a`cedr | e\mµevczrSv5rIy~e³+e\mkrBµjky[nwetce\n{mkjhgnBpqjsrStrw§<pz`cjoy¹-jkt | rw§ | eyqqjsv

pqjsrSt¦ªut(eply[v5rSjstIp[rSlxppq`nBp[pz`ceyzjsdvcmkjk\j®p}urw§<pz`ce2³cjkrwmkrwwjo\nwm | eFyz\zjkvxpzjkrwtKjstKyzl`KnOdr | e\mmse |

yze\¬Se\n{mÂn{lxpq`crwypzr2jsdvcqrB¬wede\tIpqyan{t | ¬Bn{qjknwtIpqyª!?rwajktypn{t\e | j®±Âe\qe\tIpjst | js¬-j| lnwm¦e\mkmoy\©xlct | e\

\rwty~pqnwtIpe\t-¬-jkzrStcde\tIpqnwm5rSt | jspzjkrwty©-`n8¬we³5ee\t vczrB¬Se | pqr&e\-`js³cjspa`cjsS`cmk}2¬Bnwzjon{³cmkejktIpzezdjspzr{pqjk

jktIpzez¬Bn{moy¸t(e\³+rBµj®pMg2nwt | lc³cjktcrBµv.kw/Qnwt | pq`ceze\§¨e\qe\t\ey[pz`cezejst+»nwt | pq`cjoyrw³yze\q¬BnBpzjkrwtKmse |

(7)

pq`crSyzen{lxpq`crwy[pzruv+rSy~pzlcmonBpqen{tjsdvcqrB¬we

|

dnBpq`ce\dnBpqjkn{m<dr

|

e\m<µ`e\qe&pq`cev+rwvclcmonBpqjsrSt joyn{moyzr

y~pzqlpzlcqe

|

jktpqe\qdyrw§nSe\tceqn{pzjkrwtpqjsde·©-pz`-lymken

|

jstcpzr&pz`ce´e\¬Srwmklxpzjkrwt§¨rwpz`ceemsm

|

ety~jsp}

DGF B4H+ICH

JA

ACB DGF B4H+ICH J1K

A

A%I DGF

B4HMICH JK

F

I8H J

DGF

B4HMICH JRQTSHUB VsSHI&VXSH VsSH

DGF

B4HMI QTSH JGQ^] c F ICH H J

DGF

B4HMI8H JO\IYO

DGF

BRQ[SH+ICH

JGQ

D b F ICH

Je

¸wªfI»

yzrwde\µ`n{p´qe\monBpqe | ³clxpdrwqe&Se\tceqnwmdr | e\m<joy[pz`n{pr{§rwpzetI³+e\q;.c4/7ª2_a`ce\t(©·pz`ce³cjkr

mkrwSjkn{m·`cj|c| et ¬Bn{qjknw³cmke´joyndn{pzlcnBpqjsrSt ¬Se\mkrxjsp} "!SH$#&% ©n{t | pq`cerS³y~ez¬Bnw³cmsey~pqn{pze I jkypz`ce

³jsrSmsrSwjo\n{mn{weS©drwqeqe\mke\¬Bn{tIppq`n{tupq`cev`I}xyzjkn{mn{weS©jkt r{pq`ce\[µrS | y\©pz`ce | e\Szeer{§<dnBpqlczjsp}

¸Hn{t | pq`ce\t I'

jkypq`cevc`-}xy~jo\nwm¦n{wejkt pz`cevcqe\¬-jkrwlydr | e\moy»#ªX_a`cet¦©xpz`e | e\tyzjsp}Or{§v5rSvclcmonBpqjsrSt

DGF B4H+ICH

J

yqnBpqjky~ºeFyQpq`cepzn{t5y~v+rwzpe«IlnBpqjsrSt

A

ACBuDGF B4H+ICH

J1K

A

A%I DGF B4HMICH

J1K

F

ICH

J

DGF B4HMICH

JGQ ])(

F

ICH

H J

DGF B4H+ICH

JO H

¸wªww»

µjspz`¯nwSn{jktO³+rwlt | n{q}O\rwt | jspzjkrwt5ynBp I QTS

©cnwt | jstcjspzjon{m | nBpqnn{p BGQTS

©

DGF

B4H+IQmSH JGQ^]vc

FI H H J DGF

B4HMI H JO OdI H

DGF

BRQTSH+ICH JQ

D b F ICH Je

_a`cjoyadr | e\mÂe\t`n{t\eypz`ey~pzrx`nSypqjk\j®p}jktOpq`ce[pzjkd2ee¬wrwmklxpqjsrStOr{§(pz`cev+rwvclcmonBpqjsrStpq`n{tc¹xypzr

pq`ce¹Se\qtce\m ( µ`cjk` nwmsmkrBµynn{t | rwd `5n{tcSer{§>pz`cedn{pzlcnBpqjsrStu¬we\mkrxjsp}w©+n{t | nwmkyzr©nSyjkt¯pz`ce

vze¬Ijkrwl5y<dr | e\moy\©-jktpz`ce[³cjk~pq`vcqr-\eyqy\ª ¥ e[n{moyzrze\§¨e\QpzrY.k/5§¨rSrwpz`ceQdr | e\moyQµjspz`pz`ce[tcr{pqjsrSt

rw§dn{pzlcqj®p}Sª@<¯rSzeqe\e\tIpzmk} §¨n{Sde\tIpqn{pzjkrwtd2r | emky`n8¬we³+e\e\t¶vzrSv5rIy~e | pqr¯denwyzlcqee\mkmoyjkt

pqe\qdyXr{§Âpq`ce\jk°´ rwtIpqe\tIp*Omken | jstpzr5ïy~jhg\e[ypqzl\lxpzqe | {dr | e\moy¸.f/¨»#ª<_a`cjoyXjoyXqe\monBpqe | pqrpz`ce

qe\e\tIp&n8¬Bn{jkmon{³cjkmsjsp}Krw§,+rBµ }IpzrSd2e\pzq} µ`jk`nwmsmkrBµyrwt 7mkjstedenwyzlcqe\de\tIpyr{§°´ rwtIpqe\tIpª

_a`e´dr | em·pz`cetujky³5nwyze | rwtpz`ceeF«Sl5nBpzjkrwt

A

A8B DGF B4H * J1K

A

A * DGF B4H * J1KZO

F* J DGF

B4H * J Q.-

DGF B4HMi * J0/

DGF

B* J4e ¸wª9S»

_a`ceqjkw`Ip`n{t

|

yzj

|

ee\-vzeFyzyzey[pz`5nBpnB§½pqe\djspzrSyzjoy\©·pq`ce°´%\rwtIpzetSp

i

*joyyzvcmkj®pjkt pµjoe

* 3°´\rwtIpzetIp§¨rwenS`\e\mkmHª

1Òtpq`cjkyQvn{v+e\Qµe¹Se\e\v2pq`ceqe\tceµnwmxd2r | emc§¨rSQemsm\}xmken{t | µeaºypXvcqeyze\tIpQndr | e\m5µ`cjo`

nwmsmkrBµypzr¹wee\vudrwqe[³jsrSmsrSwjo\n{mkmk}³nwyze | nwyqy~ld2vcpzjkrwtypq`n{t pz`ed2ezeeF«Sl5nBpzjkrwt;¸Sªs8»#¸SªS»#ª ¥ e

qe§¨eyzv+ejsº5n{mkms}´pzr[pz`etcrwpzjkrwt&r{§vc`5nwyzeyjstpz`cea}xmkeµ`cjk`2n{mkmsrBµ;pqrjktIpzqr | learStSpqzrSmkyy~l5`&nwy

pq`cee±Âepr{§>n2\js\n | jon{t\msrx¹µ`jk` ³cmkr-¹xyav+e\qjsr | jo\nwmsmk}pz`evc`nwyze´pzn{tyzjspzjkrwt¦ª ¥ ewjk¬wey~rSde

dn{pz`cedn{pzjo\nwm<zeFy~lcmspqyrwt5e\qtcjktc pz`ceyzrwmklxpqjsrStyn{t | eFy~v+e\jknwmsmk}¯pq`ceexjoypqe\t\er{§n¶¸< nwm®pq`-lyq»

v5n{n{depqe\§¨rSpz`e pzrwpqnwmwqrBµapz` rw§pz`ce v5rSvclcmonBpzjkrwt(ª _a`ce\t µe vcqrwv+rSyze t-lcde\qjo\n{mpzey~pqyOpzr

deFnwyzlcze[pz`ee±Âe#prw§pq`cejk\n | jknwtmkrx¹rwtpz`epzr{pn{m·SzrBµapq`¦ª

(8)

;B'%

#

i S

?jsSlcze<Xzjkt\jsvcmker{§pz`ce\e\mkm(}x\msen{t | jspqyv`nwyzeyª

_a`ce emsm | jk¬IjoyzjsrStU¸¨djspzrSyzjoyq»jkypz`ce zeFy~lm®prw§n¯§¨lcmkma}xmkepq`nBpn emsmay~`rwlcm| lct | e\qwr yzl

\eyqy§¨lmsmk}]¸ .sf/½»ª 13p&jkyl5y~lnwmsmk} nS\\e\vxpqe | pz`n{ppz`ce}xmkerSty~joy~pqyjkt§¨rwlcv`nwyzey©¸@jo»nuSzrBµapq`

v`nwyzew© | e\tr{pze | 2S©Sµ`ceze[drSy~pzmk}&pq`cee\mkm | rwl³cmseFyQjspqyayzj#gew©Â¸¨jkjo»n2y~}-tIpz`ceFy~joyXv`nwyzew© | etcr{pqe | ³-}

h·©+µè\qepzè2°´¼joy | lcvcmkjknBpze | ©X¸¨jkjkjo»ńqey~pvc`nwyzew© | etcr{pqe | ³I} c©·µ`cjk` jky[lyze | pzru`ce¹

nwt | zevn{jkapz`ee\qzrSqyjktKhOv`nwyzew©(¸@js¬c»pq`cedj®pqrSyzjky©cvc`5nwyze <¶©jspqyze\ms§µ`e\qepz`cepµr°[[§¨rwm| y

yze\v5n{nBpze ¸@nwtn{vc`5nwyzeF»[n{t | pz`ceemsm | js¬-j| ey´ºt5n{mkms}Sª&_a`ce2jsdv+rwzpqnwtSp§¨eFnBpzlze&§¨rwrwl´vlczv+rSyze2jky

pq`nBppz`ceemsmÂ}x\mse[vczrSwqeyqy~jkrwt2joy\rwtIpzqrwmkmse | ³-}2vzrwpze\jkty´¸ }xmkjktO°ev5et | etSp =jktnwyzey©°o=jkt

yz`crS~pF©Iyze\e .ïw0/½»n{t | pq`-lyQµeµjoyz`pzr&¹we\evpz`cjoytcr{pqjsrStjstOpz`ce[dnBpz`e\dnBpqjkn{mdr | emHªXmkyzrdl5`

rw§Qpq`ceemsmoyypn8} nBpqey~pjst;nu«SljseFyz\e\tIpvc`nwyze\nwmsmke | c©·p}-vcjo\nwmsmk}w©y~¹-jkt\e\mkmkynwzerSty~pqn{tIpqms}

jkt pq`ce}xmkew©·et

|

r{pq`ce\mkjon{m<emsmoy[nwze&¹-tcrBµt pqr y~pqn8}¯nBpqey~p´n{t

|

dn8}u³5enwpzjk¬BnBpze

|

³-} >Xnwyqlcmon{

²Qt

|

r{pq`ce\mkjon{m´qrBµapz`P?5nwpzrwyµ`cetn{tcSjsrSwetceyzjkyrxlcy\ªK[t;pq`cer{pq`ce\&`n{t

|

©pz`ceO\e\mkm\}-\mse

|

lcqn{pzjkrwtjoyQn{moyzre-pzqe\de\mk}2¬8nwzjon{³msea§¨rSX`-lcdn{temsmoy©w§¨qrwd¼y~e¬we\n{md2jkt-lxpzeFy<pqry~e¬weqnwm

|

n8}xy¸¨lcv

pqry~e¬we\n{mÂ}Sen{y§¨rw\e\mkmkyaµjspz`umkrBµUqe\tceµnwm+nBpqey»#© | ev5et | jktcrwtpz`ee\mkmoy).sf/3©N.sF/3ª

[lc\e\mkm·v5rSvclcmonBpqjsrStOdr | e\m·lyzeypq`ce | e\t5y~jsp}r{§>emsmoyajstpz`e´v`nwyzeq© | e\tcrwpze | ³-}

D F B4H+IJ ©nBp

pqjsde B nwt | µj®pq`nwwe I jst pz`e\e\mkmH©n{t | yzn8} Q S §¨rwpz`e2qey~pvc`nwyzec©¦nwt | Q #dHMi e2ee%H

µjspz` &Q - jst¯pq`cenw³5rB¬Seyz\e\tnwzjkrª ¥ e2\nwmsm (

F

IJ VTS pq`cepzn{t5y~jspzjkrwt¯nBpqe§¨zrSd v`nwyze

pqrvc`nwyze K.# | e\v+e\t | jktcrwt pq`cen{Se I jst pz`evc`nwyze¸(

ypn{t | yyzrwde\pzjkd2eFy§¨rw (

jkturw | e\pqryzjkd2vmsjs§¨}yzrwdetcr{pnBpqjsrStyq»ªXynyzjsdvcmkedr | e\m¦µe\n{t `n8¬Se[jktud2jkt | joy

(

F

IJRQ _aN_

!#"

H

%$

SH

¸HxªkF»

n\rwty~pqnwtSpnBpqenB§½pzeyzrwden{we I

joynBpzpqnwjstce | ªQ_a`ceFy~epqqnwtyzj®pqjsrStnBpqeyrSlcm| ³+erStIpzqrwmkmse | ³-}

| zlcIyrw³-}pz`ejkqn | jon{tumkrx¹nwyade\tIpzjkrwte | jst pq`cejstIpqzr | lpzjkrwt¦©-pq`-lyamseFn | jktc2pzrn2¬Bn{qjon{tIp

(

F B4HMIJGQ

F

B+J

&

_0a%_

!" H ¸Hxªïw»

(9)

pq`ce\t F

B+J

jkynuyzµj®p`nS#pqjs¬BnBpqe

|

v5ezjkr

|

jkn{mkms} nBpe~pn{jkt pzjkdeyjktpz`cejk\n

|

jknwt rStIpzqrwm7©·³I} n

pq`ce\n{v-}jkt¯\nwyzer{§pz`ceqnwv5elxpzjorStSpqzrSmHª

_a`cetpz`ee¬wrwmklxpqjsrStr{§xpz`e | ety~jsp}jstpz`cevc`nwyzeQjoyd2r | emsmke | ¬Ijonnu< =et | qjk¹ ><rwt)?cr-e\y~pze\

eF«IlnBpqjsrStnSyvczeFy~etIpze | jkt pq`cejktSpqzr | l5#pzjkrwt(ª >Xnwzjon{³mse O $ S jky´pq`ce | en{pz`;nBpzejktKpq`cevc`5nwyze

nSyde\tIpqjsrStce | jkt rSlc[jktIpzqr | l#pqjsrSt¦©+j®prSlcm| n{moy~r³+erwtIpqzrSmsmke | ³-} | zlSy[µj®pq`KnO\js\n | jknwt

q`-}Ipz`cd

+F IJ

$ S jky>pq`cee\¬Srwmklxpzjkrwt2y~v+e\e | jst2pz`evc`nwyzeaµ`cjo`\rwlcm| n{moy~r³+erwtIpqzrSmsmke | ³I}2y~rSde

t-lxpqzjke\tIpy§¨rwjktypn{t\ejstuvc`nSy~e2SªRfe\t5ew©-§¨rS # © B VZS n{t | IYVZS ©µe`n8¬Se

A ACBuD F

B4HMI`JK

A

A%I

! F IJ

D F

B4H+IJ%`K O F IJ

D F B4HMIJ1K (

F

IJ

D F

B4HMIJGQ[SH

+F S\J

D F

B4H+I QTS\JGQ^] _aCb (

+F I J

D 0F B4H+I

JOdI

e

¸HxªS»

?rw Q # ©Ipz`ceqe\tceµnwm5\rwt | jspzjkrwt | r-eytcr{padn{¹Se[yze\tyze[³+en{lyzepq`ce´vc`nwyze / # | r-eytcr{paexjoyp

nwt | µeqe\vcmonw\e´jsp³-}

F S\J

D F

B4HMI QTS\JGQji ] _ aCb (

FI J D F

B4H+I J!OdI H ¸HxªfI»

µ`e\qe S

#

jky[pz`e&nBpqe&rw§emsmoyµ`jk`rwtIpqjst-lcepz`ce}x\mse2nB§½pzed2jspzrIy~joyª ?crw[pz`e2yqn{¹Se

rw§(y~jkdvcmkjk\j®p}µe`n8¬Setcr{p

|

eFyz\zjk³5e

|

pz`evc`nSy~e S

µ`cjo`Oqe\e\jk¬weFy>pz`ce´e-pqqn\e\mkmkynB§½pqe\dj®pqrSyzjky

nwt

|

v+rSyqyzjs³cmk} \nwt jktIpzqr

|

le2tceµ emsmoy´jst pz`e\}xmkewª§arSlcqyzerSlcdr

|

e\m<joy´\rwdvcmkepqe

|

³I} n

nwl`-}

|

nBpny~e\p

D +F

BRQ[SH+IJ!Q

D b F

IJ VZSH Q #dHe2eeNHCH%I

$

Se ¸Hxªww»

_a`cjoydr | e\mpz`-ly2qepn{jktyy~rSd2e nwyzv5eF#py&rw§[rwpze\t-³+e\q .ïx/adr | em¸Hy~eeOpq`ceujstIpqzr | lpzjkrwt5»

µjspz` n |

jkyqqepqey~e\pr{§<dnBpzlqn{pzjkrwt¯ypnBpqey¸ jkt¶¸SªwS»rSzqeyzv5rSt

|

ypzrQjkt¸HxªS»z»µ`cjkmse¹Se\evcjst

pq`cedn{jktu§ën{pzlcqepq`nBpé\tcrSlcwùvc`nSy~evczrSwqeyqy~jkrwtjkytce\e

| e |

§¨rSpqqnwty~jspzjkrwtupqrpz`etce-pv`nwyzewª

13pnwmkyzr`nwypq`cen

|

¬Bn{tIpn{we´r{§jst

|

jknBpqjstc\mseFn{qms}v+rSyqyzjs³cmkerStSpqzrSmÂv5rSjstIpqy§¨rSa§¨lczpz`ced2r

|

emsmkjktcª

_a`jky¹Ijkt | rw§<yz}xypqe\d \n{t¯ej®pq`ce\´qen{pzeexv+rwtcetIpzjon{m¦SzrBµapq` rSexv+rwtcetIpzjon{m | eF\n8}r{§>pz`cepzr{pn{m

v+rwvlcmkn{pzjkrwtOyzjhg\e | e\v+e\t | jktc&rwtpq`ce | enBpq`On{t | pzn{tyzjspzjkrwtvnwqnwdepzeqyQn{t | rw§rSlcy~epq`ce[\rwtIpzqrwm

v5n{n{depqe\y\ª>_a`cjoy§¨enBpqlcqejkynwtn{mk}xy~e | jktpq`cetce\Ipyzepzjkrwt¦ª

;'>$ $

_a`eQn{³+rB¬we<yz}-y~pzedUrw§Ipqqnwtyzv5rS~p¦eF«Sl5nBpzjkrwt5yÂjky(e\t | rBµe | µjspz`natn{pzlcn{mwdn{xjsd&lcdUvcqjktjkvcmkeXµ`cjo`

vzeFy~ez¬Sey>pq`ce[trwtctceSn{pzjk¬Ijsp}r{§

D

n{t | r{§ntnBpqlcn{m

pz`cerwq}2µ`jk`qe&+5e#pyXpq`cerSty~ez¬Bn{pzjkrwt

rw§ | etyzj®pqjseFy>³I}pq`ce | qj®§½p>pqe\qd ª>_a`ceFy~ean{qel5y~lnwmxvcqrwv+e\zpzjkeypz`n{pX\n{t2³+e`5n{t | mke | ³-}¬Bn{qjsrSlyµemsm

lt | e\y~pzr-r | dnBpz`e\dnBpqjkn{mÂdepz`r | ynwt | µeypnBpzen{texjoypqe\t\e[qeyzlcmsp§¨rS\rwdvcmkepzetceyqyª!< rwqe

jktIpzezeFypqjstc jky&pq`ceumknwzSepzjkde nSy~}-dvxpqr{pzjo n{tnwms}xyzjky&µ`cjo`]\nwt`nw | ms};³+e v+e\z§¨rwqde | `ce\qeO³-}

y~pqnwt | nw | d2e\pz`cr | y³nwyze | rwt t(nwvcmknSe´pzn{t5y§¨rSzduª ¥ enBpq`ce\lyzee\tIpzqrwv-}de\pz`cr | yajktIpzqr | le |

(10)

jkt pz`cjoyrStIpze-pjkt .ï{/7©yze\enwmkyzr .sF0/7©.dw/7ª

¥ e nwmsµan8}xynwyqy~ld2eK³5emsrBµ pq`nBpun{mkmpz`e ¸@tcrwtcte\Sn{pzjk¬we8»r-e6\jsetSpyK¸

O © © (

»On{qe

\rwtIpzjkt-lcrwl5ynwt | $ V F

IJ V $

SH F

J B

D B D

e ¸@cªkF»

( F

IJ ( H ¸@cªïw»

O F IJ

I H ( F

IJ

$ S II e ¸@cªS»

¿-Ä ¡ ¿

"!$#&%

'4 $C ('*) 0'' ` %($'

!+-,.

'0/

!1+2,3+

' $C

D b

F54

J4H

*+ L

% '4'L `$$6 L'*4 `($C '`$

D 87

F94

;:

F54 J J

D

V S ; '4"0'4

!1<,3+

'0=

!1<2,>

'

,@?

''BAW ') C*4*4 M `$C

C

3DFEHGHGHG(E

]JIb D F

B4H+IJ O\I LKM3NPOPQ

PRST&U(VXWYSZ\[

e ¸@cªfI»

_a`ce n;vzjkrwqj³5rSlct | `ceze¯joy¬wez}]ql | e¯n{t | | r-eFytcr{pl5y~eupq`ce¯vcqejoyzeuy~pzqlpzlcqe¯r{§´pz`ce

rSv5eqn{pzrSqyajkt-¬wrwmk¬we | jst¯pq`ce | }It5n{djky\ª 13p´jky[n{jkde | pqrOy~`rBµ µ`-}

pq`ce\rSz} joytn{pzlcn{m(pz`cqrwlcS`

jspqy[y~jkdvcmkjk\j®p}Sª rwt\e\qtcjstpz`cepzjkd2e&³5e`n8¬-jsrSlcF©cj®p[pzlcqtyrwlxppq`nBp[pz`cev5rSvclcmonBpzjkrwt¯SzrBµyaµjspz`

nwte\xv5rStce\tIpzjon{m·nBpqer{§v5n{n{depqe\^]¦ªd2rSzenwlcnBpqezeFy~lcmspjkyajkt | ee |

¿-Ä

¡ ¿ 3_

! $2`Y Mq`*1'a) L '' ` C$' cb% *+

+2,.

W *+

% '4(')

`$8$6& *+ *

] 4

$C`$8$6&

! Y `Cq u$'4$d'

7 `$%$'&e

+F IJ

$

S

e F IJ

S;0' I ' M

C

fDFEHGHGHG(E

]gIb D F B4H+IJe

F I`J`OdIQ

0hiK

C

3DFEHGHGHG(E

]JIb D b F I`Je

F

IJ OdI %B VXSe

¸@cªww»

te\xvcmsjojspa§¨rwqdlcmon§¨rwpz`ce)< nwm®pq`-lyavn{n{de\pze\@] joyawjk¬we\t³5emsrBµ©-eF«Sl5nBpzjkrwt;¸@ªI»#©Ipz`5nBpn{mkmsrBµy

pqr´`e¹µ`cepq`ce\pq`ce\qejoye-pzjktpzjkrwt2jHªewª&] XS rSSzrBµapq`jHªewª&]

$ S ª013p<n{t³+ey~ee\t2nwypz`ceºyp

ejsSe\t-¬Bn{mklce´§¨rwpq`celct | e\qms}-jktcrwv+e\nBpqrwpz`cee\xjky~pzeterw§µ`cjo` §¨rwmkmsrBµya³-}Opz`ce =qe\jktÒlxpqdnwt

pq`ce\rSzed ¸./¨»#©³clxp&³5emsrBµ¼µeSjs¬Sen | jsqepn{t | rSty~pzql#pqjs¬Se2vzr-r{§ª ¥ en{t¶n{moy~ruSr§¨l~pq`ce\

nwt | dnw¹wedrwqevczeFjoy~e[pz`emsrStc2pzjkd2enSy~}-dvxpqr{pzjo\ynSy§¨rwmkmsrBµy

(11)

¿-Ä

¡ ¿ f

!

b 0'4" C4'1' )@s L'M' ` C$' $C;$C($'Lab% *M

+-,f<

*+

% '4(') `$$6 0'4(q '`$

! :@ `Cq $'4$d'

A A%I

! F IJ F

I`J%`K !O F IJ1K (

F

IJNK ] % F IJRQTSH

FS J F

IQ[S JGQ ] _ a%b (

FI J FI

J!O\I

H

¸@cª9S»

$C@$C '

] I_ D b

D F B4H+IJ

hLK

/ b

+F IJ O\I

SH I B H ¸@cªø{»

b

$'4$ '

C

3D EHGHGHGE

] Ib D b F IJ O\I Q

b C

3DFEHGHGHG(E

] Ib F IJ O\I8e

_a`ceFy~e2pq`ce\rSzedy[§¨rSmsmkrBµ§¨qrwd monwyqyzjkn{m>depz`r

|

yµ`cjk`µ`ceze2e-pzet

| e |

pqrpq`cer{pqe\t-³+e\q

dr | em¦jst:.ï{0/3ªXrwpzjoepq`nBppq`cerStI¬Se\qwete[qn{pzejst¶¸Hcªø{»\nwt ³+evcqrB¬we | pzr³+eexv+rwtcetIpzjon{m·jkt

yzjkd2vmseyzj®pqlnBpqjsrSty©¦³clxpµe | rutcr{p¹-tcrBµ r{§y~jkdvcmke§¨rwqdlcmonwy´jktI¬Srwmk¬-jstcpz`eOr-e6\jsetSpyr{§pz`ce

eF«IlnBpqjsrStKjspqyze\ms§¸O © (

pq`nBp\nwt ³+e§¨rwlt | jkt nOd2rSze2y~rSvc`cjoypqjknBpqe | §¨rSzd jktP.w/<n{t | µe2rwtcmk}¯y~¹Sep`upz`ce2dn{jkt n{qwl

detSpy\ª

¡ Ä¦ÄÄ ¿-Ä ¡ ¿

¥ e | rtr{pawjk¬wen&vcqrIrw§¦r{§·pq`cjky¬Se\q}\mknSyzyzjo\n{m5zeFy~lm®pµ`cjk`jky³nSy~e |

rSt2pz`cean{t5nw`3Xjo\n{ | º-e | v5rSjstIp<pq`ce\rSzed ©In{t | µerwtcmk}de\tIpqjsrSt2³zjke&+}pz`ce | e\qjs¬Bn{pzjkrwt2r{§Âpz`ce

nOvcqjsrSzj³5rSlct | ¸HcªfI»#ª_a`ce&v5rIy~jspzjk¬-j®p}ur{§<pq`cey~rSmslxpqjsrSt¯jky[rw³-¬-jkrwly³5eF\n{l5y~e

FD J

¸¨pz`ce2tce\InBpqjs¬Se

v5n{zpjoy | eº5tce | ³-}

I

Q I * F SH / IJ

»joyn&yzlc³yzrwmklxpqjsrStµjspz`¯n&¬8nwtcjoy~`cjktcjktcj®pqjknwm | nBpnn{t | pz`-ly

qe\dnwjstyate\Sn{pzjk¬we¸½pq`ce\qe§¨rSzege\qrI»Q§¨rwnwmsm·pqjsdeFy\ªQ_a`e

³+rwlct | joyrw³cpqn{jktce | ³-}jktIpzewnBpzjkrwt jkt

nwweS©Il5y~jktcpz`ev5rIy~jspzjk¬-j®p}rw§(pq`ce O

O

OdB

C

3DFEHGHGHG(E ] I

b D F

B4H+IJ O\IK

C

3DEHGHGHGE ] I

b (

F

IJ

D F

B4HMIJO\I C

fDFEHGHGHG(E F

S\J

D F B4HMS\J4H

pq`ce\qe§¨rSzeS©Bpz`e³+rwlct | n{q}+lxxeFy<ecnwpzmk}2\rwdv+e\tyqnBpqe¸@nwyQexv+e#pqe | jktpz`ced2r | emo»>pz`cepzn{tyzj®pqjsrSt

nBpqeyan{t | jspqe\dn{jkty

O

OdB

C

fD EHGHGHGE

]gIb D F

B4HMI`J`OdI Fi

/"#J ]JIb (

F

I`J

D F B4H+IJ O\I

Fi /"#J (

[ ] Ib D F B4H+IJ O\I

Fi

/"#J (

[ C

3DFEHGHGHG(E ] I

b D F B4H+IJ O\I8H

(12)

nwt

|

pz`ceqeyzlcmsp§¨rSmsmkrBµyª

¡

Ä¦ÄÄ ¿-Ä

¡ ¿ _

_a`ce&ypnBpzjkrwt5n{q}

|

lnwm¦vcqrw³cmke\d pzrK¸HcªkF»·¸@ªS»QjoySjs¬Se\tu³-}n{t¯ejsSe\t

¬Bnwmslcevcqrw³msed ºt | ]Ky~l5`Opq`nBppq`ce\qejkynyzrwmklxpzjkrwtpzr

F

IJ

A

A%I e F

IJ/

!O F

IJ1K ( F

I`JK

]

%e

F

IJRQ / e

FS J

( F

IJH

e

+F IJ

S I I e

¸@cªS»

fe\qeµe]`n8¬we¶l5y~e |

(

F

IJXQ ( F

IJ

§¨rS Q #H2ee2eNH / #

n{t | ( 0F

IJsQ

i (

0F I`J

ª

1Òtr{pq`ce\µrw | y\©·d&lcmspzjkvcms}-jktc¶¸@ªs8»Â¸Hcªïw»³I}

e

+F IJ

©¦dlcmspzjkvcmk}-jstcueF«Sl5nBpzjkrwt ¸@ªI»³-}

D +F B4HMI`J

nwt

|

jstIpzewnBpqjstc

O\I

n{t

|

yzlcddjstclv jkt©xµen{qqjs¬Se´n{p

O

OB

hLK

C

fD EHGHGHG(E ] I

b e F IJ

D F

B4HMI`J`OdI / hK

C

3D EHGHGHGE F

IQmS\J

D F

B4H+IQmS\Je

F IQ[S\J

Q /

hLK

C

fDFEHGHGHGE e

FS J ] b I

( F

IJ

D F B4HMI`J`OdICH

¸¨pz`cjoylyzeyQpz`ce´rwt | j®pqjsrStOnBpjstcºtcjsp}§¨rwpz`ce | lnwm5vcqrw³msed ï»#ª<§½pze\qen{qn{tcSjstc´pq`ce´yzlcd rStpz`ce

qjkwÌpn{t | pqnw¹IjktcjktSpqrnw\\rwlctIpapzèzetce\µan{m·rSt | jspzjkrwt;¸@ªS»#©xpq`cen{³+rB¬weé«Iln{pzjkrwt ze | leFypzr

O

OdB

hLK

C

3DFEHGHGHGE

]JIb e F IJ

D F

B4H+IJ O\I Q[Se

_a`ceze\§¨rwqe´pz`ceqeyzlcmspr{§<_a`ce\rSzed ª&joyqe | l\e | pzrvzrB¬-jktcpq`cee\-joy~pze\t5er{§<nyzrwmklxpzjkrwt pzr

pq`ce | lnwm+vzrS³cmsed µj®pq`Opq`cen{tctrwlct\e | vczrSv5e~pqjseFy\ª>_r | r2yzr©-µe[µqj®pqepq`cey~rSmslcpzjkrwtOµ`e\t ] jky

Sjs¬Se\tKnwt | yz`crBµpz`5nBpnyzjstwmke] jky´v+rSyqy~jk³cmke&jktKrS | e\pqr yqnBpqjky~§¨} pz`cerSt | jspzjkrwtnBpjstxº5tcj®p}Sª ¥ e

`5n8¬we

e F I`JGQ

!M_ R

!

_ !e F

S\J0/ e

F S J]

_

b

(

F

J

F I`J

M !M

R

!

RO

H

µjspz`

F

I`JGQ ] _ b O F

J1K ( F

J

+F IJ

O e

en{lyzepz`ce¯vcqrw³msed jky | e\ºtce | lvpqr;nd&lcm®pqjsvmsjo\n{pzjk¬we¯rStypn{tIp¯¸¨µe mkr-rw¹;§¨rSpz`ce ºyp

ejsSe\t-¬Bn{mklcer{§Xnv+rSyzj®pqjs¬Serwv+e\nBpzrS»µedn8}`cr-rSyze e F

S\JRQ # ªa_a`cet¦©xpz`e¬Bn{tcjoy~`jstc\rwt | j®pqjsrSt

n{pjstxº5tcj®p}O§¨rw

e

Sjs¬Sey

e N FS JGQ(] I

b

( N

F

J

F IJ

M W M

R

! R O

e

(13)

r{pqjk\epz`n{pQrwlQnwyqy~ld2vcpzjkrwtyXyz`crBµ]pz`n{pXpz`jkyQjstIpzewn{mcjoyXµe\mkm

|

e\ºtce

|

§¨rw ] $ O '

2nBpQmkenSypFª_a`ce

¬Bnwtcjkyz`cjktcrSt

|

jspzjkrwtunBpjktxºtcjsp}§¨rw

e N

pq`ce\tuSjs¬Sey

e

FS JRQ e N FS J (] Ib

( N F

J

F I`J

M

R

! R O

e

§½pzenrwdvcmkepqe}xmkew©cµen{qzjk¬we´nBppq`cerSt | jspzjkrwt

#uQ e FS JGQ e FS J ] I

b

(

F

J

F IJ

M U M

R

!

R O H

jktur{pq`ce\µrw | ypz`ce¬Bnwmslcerw§&]ujoyawjk¬wet³-}pq`ce§¨rwqdlmkn

#uQ

3D

] Ib

( F

J

+F IJ

M !M

R

! R O e

¸@cªS»

0rSt

|

jspzjkrwtOpz`n{pjoyX§¨lmsmsºmkmse

|

³-}nyzjktcwmke¬Bn{mklce´r{§ ]³+en{lyzepq`cjoyvzr

|

lp

|

e\ºtceFyn

|

eFqenwyzjktc

nwt

| 7

§¨lct#pqjsrSt¦©(jsp¬Bn{tcjoyz`cey´§¨rS]

nwt

|

j®ppqe\t

|

y´pzr

§¨rw]

/

ª_a`cjkyrwt5mkl

|

ey

pq`cevcqr-r{§>r{§pz`cee\-joy~pze\t5er{§<nyzrwmklxpzjkrwt e

pzrpq`ce | lnwm¦vcqrw³cmke\d ¸¨tcrwpzjoepq`nBp[nwmsmÂpq`ceqe«Ilcjkze |

vzrSv5e~pqjseFynwzejkt | ee | yzn{pzjoyº5e | »n{t | pq`-lypz`ce_a`e\rwqe\d cªïjoyvcqrB¬we | ª

¡ Ä¦ÄÄ

¿-Ä ¡ ¿ 3 ¥ eqe§¨epzrL.ï{/(§¨rw[nvcqrIrw§>nwt | µelyp[jst | jknBpze³czjke&+5}pz`e¬wez}

qenSy~rSt³5e`cjkt | pq`cjky<\rwt-¬wezSe\t\ewª1?jkqy~prw§5n{mkmH©Btr{pzjoepz`5nBppz`ceexjoypqe\t\eQr{§+y~rSmslxpqjsrSty(pzr´e«IlnBpqjsrSt

¸Hcª9S»§¨rS

§¨rSmsmkrBµy¸@³I}ue\xnS#p§¨rSzd&lcmonwy»§¨zrSd pz`ce2yznwd2e&`crwjoenSynw³5rB¬Ser{§<pq`cevnwqnwdepze ]

¸@jstr{pq`ce\µrS | yXpz`ce´vcqjsdnwm+nwt || lnwm5vzrS³cmsedyQ`n8¬Sepz`e´yqn{deº5qy~pejsSe\t-¬Bn{mklcenwyqyzr-\jkn{pze | pzr&n

v+rSyzjspzjk¬wee\jkwetI¬Sepzrw ï»#ª>e-pF©cµe`n8¬Se

A ACB

F hLK

D F B4HMIJJ1K

A

A%I

! hK F

IJ

D F B4HMIJ%`K

!O F

IJ1K (

F

I`JK

] %D F

B4HMIJGQ[SH

F S\J

hLK

D +F

B4HMI Q[S\JGQ^] _a%b

(

+F

I J hLK

D F

B4HMI JO\I e

h-l³ypqqnS#pqjstceF«Sl5nBpzjkrwt¯¸Hcª9S»(§¨rw

©In{t | dlm®pqjsvcmk}-jst³I}

F hLK

D F

B4H+IJ / J

¸½pq`cjoy<jkyXµemsm

l5ypqj®ºe | e\¬wetOpq`crwlw`pz`ce O§¨lctpzjkrwt¯joyatcr{pyzdrIrwpz`5»µen{qzjk¬wenBp

A ACB

hLK

D F

B4H+IJ/ F IJ K A

A%I

!

+F IJ

hLK

D F B4H+IJ/

F IJ %

K !O F IJ1K

(

F IJ1K ] %

D F B4H+IJ/

F

IJ Q[SH

FS J hLK

D F

B4HMI QTS\J0/

F I QTS\J

] _ aCb

!(

FI J hLK

D F

B4HMI

J/

FI J%8O\I e

(14)

_a`e\qe§¨rwqew©+nB§½pqe\´jstIpzewnBpqjsrSt n{Snwjst5yppq`ce

|

ln{m>y~rSmslcpzjkrwt e F

IJ

©·n{t

|

y~ld2dn{pzjkrwt rw§<pz`ceFy~e&e«Iln

pqjsrStyaµenwzqjk¬wenBp

O

OdB

C

3D EHGHGHGE

]

_a%b hK

D F

B4HMI`J / F IJOdI

e F I`J

C

3DFEHGHGHG(E

e FS J ] _a%b

(

F

IJ

! hLK

D F B4H+IJ/

F IJ%OdI

/3]

_a%b

(

+F

IJ

hLK

D F B4H+IJ/

F IJ

OdI

sSe

_a`cjoyvcqrB¬weyXpz`n{papz`ce«Iln{tIpzjsp} | en8}xyQ³clcpnwmkyzrpq`nBpapz`e´«IlnwtSpqj®p}jktOpq`ce´zjkw`Ip`5n{t | y~j| e´jky

] I

KD b ] _aCb (

F

IJ ! hLK

D F

B4H+IJ / F

IJ%O\I / ] _aCb (

F

IJ hLK

D F

B4H+IJ / F

IJ OdI H

µ`jk` jsdvcmkjkeyapq`nBp

hLK

D F B4H+IJ0/

F IJ

SH I B H

rSt pz`ceyzlcvcv+rwzpr{§

(

FP

J

pq`ceQ°[² n{In{jktn{t

|

\rwdvnwpztceFyzynwzSlcde\tIpqypq`nBpnwze

|

e\pqn{jkmke

|

jst:.ï{0/3ª

ua'> ! u $(

t-lcdezjo\nwmdepq`cr | l5y~e | `cezeSª13pjky³nSy~e | rSt n{t lcv-µjst | yq`ce\de§¨rw´pz`ce2pqqnwty~v+rwzpe«IlnBpqjsrSt

¸ .s8/¨»>jstpq`ceºtj®pqe¬wrSmslcdeyzvcjsqjspª<_a`ceyzedepq`cr | yQnwzea¹-tcrBµt2pzr³+ejktnwlcnBpqee\ce\vcpQµ`ce\tnwt

pq`cjoyjkyav+rSyqyzjs³cmkelct | epz`ezeFypqzjo#pqjsrStpz`5nBp

F IJRQ

7;

B4H Q #dHe2eeNHCH

n\rwt | j®pqjsrStupz`n{pµe&nwyqy~lcde§¨qrwd tcrBµrwtuµj®pq` F IJWQ #

©j7ªeSª BWQ

I

µ`ce\qepz`eyzen{qepz`ce

¸@lctcjs§¨rwqd» | jkyqqepqj#gFnBpzjkrwtOvn{n{depqe\yQjktpz`ce´pµr&¬Bn{qjon{³cmkey

B

n{t | I

ª<e\mkrBµ µe | etcr{pqe[³-}

D FJ

pq`cen8¬weqnwwe¬Bnwmslcerw§

D FB HMI`J

rStOpq`ce / B

B Q D B ª

1ÒtrS

|

e\pzr n8¬wrwj

|

e\nwt¶jsdvcmkjk\j®pyz`e\de§¨rwpz`ce

| enBpq`nBpqeynwt | pqqnwtyzj®pqjsrStnBpqeyª ¥ en{qqjs¬Se´n{ppq`cen{mkwrSzjspz`d

D

F

JGQ

B C

D N

EHGHGHG(E (

+F

JD

F / #0J4H

(15)

D

F J !

#WK

B

FO F J1K (

F J%1Q

D F

J4H

QTiHe2eeNHH

¸@ecevxp<§¨rw Q #

µ`cezepz`ee\mkm

|

jk¬-jkyzjkrwt&§@nw#pqrw

i jkyQn

|c|

e |

»#ª!fezeaµe`n8¬wejkt2djkt

|

pz`n{p<pz`ce

º5qy~pv5rSjstIpjkt I zevcqeyze\tIpqypz`e+lx rwtpz`ce³+rwlct | n{q}On{t | tr{pn{tun8¬weqnwwe[jst¯nemsm7ªX_a`ceze\§¨rwqe

pq`cev+rwjktSp

D

FJ joye\x\msl | e | §¨zrSd%pq`ce | jkyqqepqezetce\µan{m·¹Se\qtce\m7ª

0 0.5 1 1.5 2 2.5 3

0.7 0.71 0.72 0.73 0.74 0.75 0.76 0.77 0.78 0.79 0.8

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

0 0.2 0.4 0.6 0.8 1 1.2 1.4

?jkwlcqe h-rwmklxpzjkrwt r{§pz`ceqe\tceµnwmeF«Sl5nBpzjkrwt ¸¨rStcevc`nwyzeF»[jktnwyzeO¯¸¨v+enw¹we | qe\tceµnwm¹Se\qtce\m½»#ª

t(e§½p pq`cepzrwpqn{m·v+rwvlcmkn{pzjkrwt | ety~jsp}OnSyn§¨lt#pqjsrSt rw§pqjsdeSªXjsS`Ip >pz`eypqen | }OypnBpqe F IJ ª

0 0.5 1 1.5 2 2.5 3

0.66 0.67 0.68 0.69 0.7 0.71 0.72 0.73 0.74 0.75 0.76

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

0 0.2 0.4 0.6 0.8 1 1.2 1.4

?jkwlcqe ah-rSmslcpzjkrwt rw§pq`ceqe\te\µan{m¦eF«Sl5nBpzjkrwt¸@rwtce&vc`nSy~e8»ajst \nwyze ¸@lctcjs§¨rwqd qe\te\µan{m(¹Se\qtce\m½»#ª

t(e§½p >pz`cepqr{pqnwm·v5rSvclcmonBpqjsrSt | e\tyzj®p}nwyn&§¨lctpzjkrwtur{§pzjkdewªXjkw`Ip >pq`cey~pzen | }Oy~pqn{pze F IJ ª

?rw·pq`ceQyqn{¹we>rw§-\rwdvcmkepzetceyqy©µe<tcrBµKvzeFy~etSp¦qeyzlcmspqyÂ§¨rS·pz`eX\nwyze<r{§-rwte<vc`nwyze¸<K=e\t | zjo¹

><rSt ?cr-eqy~pze(e«Iln{pzjkrwt5»ª_a`ce}n{qeXrw³cpqn{jktce

|

µj®pq`

3Q[i`iS

¸

iS

joy¦pq`cet-lcd&³5erw§

|

joyz\ze\pzjhgnBpqjsrSt

v+rwjktIpqyX§¨rwQnltcj®pan{Seapzjkd2eµ`cjk`joy<pq`cedn{-jkdn{mnwwea§¨rSQqe\tceµnwmxjstpq`ce`crSjk\eµednw¹we³+e\mkrBµ

§¨rS

(

j7ªeSª

I Q #

jkt pq`ce2pµr \nSy~eFy³+e\mkrBµ»#ª1Òt r{pq`ce\´µrS

|

yrSlcy~jkdlcmonBpqjsrSty´n{qe&rSt

|

lpze

|

(16)

§¨rS

S vI pi oI

n{t

|

lcv¶pzrKpz`ceOºtnwmQpqjsde B _

Q oI

ªKmkyzrKµeOlyzeOn

|

en{pz`nBpqe

O F

IJ Q i`e oI'I

Kª [ye\xvczeFyzyze

|

hK ©

pq`ceyzrwmklxpzjkrwturSt-¬we\qweFypzrny~pzen

|

}y~pqn{pze³lxpµjspz`¯n{t¯rIyz\jsmkmkn{pzrSz}³+e\`n8¬-jkrwlcFª

¥

eex`cjk³cjsppz`jky

v`ce\tcrSde\tcrStjkt pz`cet-lcde\qjo\n{m+pqey~pqy³+e\mkrBµ nwt | zemkn{pzej®ppqr2pz`ce§¨rSzd%rw§pq`ce¹wezte\m ( F I`J l5y~e |

§¨rSpq`ce2zetce\µan{m(pze\qduª ¥ erSty~j| e[jkt pq`cjkynwyzenOqe\te\µan{m(¹Se\qtce\m ( µjspz` ³5rSlct | e | yzlcvcv+rwzpª

¥ e[yz`crBµ pq`nBppz`ce´drwqe)5v+enw¹we | SjoyQpz`ce[¹we\qtcem ( ©wpq`cedrwqerIyz\jsmkmonBpzjkrwt5y<pz`e[yzrwmklxpzjkrwte\x`cjs³j®py\ª

?jsypnwyzewª ( F

IJGQ.-

&

_

Q

N _ _ Q "

h-e\rwt | nwyzewª ( F

I`JGQTi

_a`cjoy¹-jst | r{§(³+e\`5n8¬Ijkrwl`nSy³5ee\t\rwtxº5zde | n{t | dn{pq`ce | pqr&e\-v+e\qjkd2etIpqyrwtO¬BnwzjkrwlyQp}-v5e

rw§Xe\mkmoyjktmkl | jktcOn{t\e\qrwlye\mkmoy¸@yze\e@.w0/3© ./3© .f/¨»#ª[²Qy~v+e\jknwmsmk}pz`ce&jsdv+rwzpqn{t5erw§<pzn{tyzj®pqjsrSt

pqjsdeFy`nwya³+e\etuµemsm·qe\v+rwzpze | jktOpq`cen{³+rB¬weqe§¨ezeteFynwt | d2rSzee\-v+e\qjkd2etIpqn{m·µrwq¹xy¸.9/¨»#ª

ua'>'>$ $! #' ! !&('>w u $($

¥ e tcrBµ rwdeOpzr pz`ce \nwyzeOrw§pµr vc`nSy~eFyjkt¶pz`edr | e\m¸7xªS»·¸HcªwS»´§¨rw&pz`ce emsm}x\mseSª_a`ce

|

le

|

t-lcd³+e\rw§

v5n{n{depqe\yjst pz`ce2dr

|

e\mµ`cjsmke

|

en{mkjktcµjspz` nd2rSzezeFn{mkjky~pzjoy~pzql#pqlczeSª´hIpqjsmkm<nwyqy~ld2jktcpq`nBp

pq`ce}xmkey~v+e\e

|

yn{qerwt5ypn{tIp´jktpz`ce2pµruvc`nwyzey¸@r{§eF«Iln{m<mke\tcwpz`e\¬Se\t pz`crSlcw`¶2&v`nwyzejky

l5y~lnwmsmk}¯qe\v+rwzpze | nwy[pz`e2mkrwtwey~pn{t | pz`cedrSy~p +l#pqlnBpqjstI»#©j®pn{tK³+e | joyz\ze\pzjhg\e | ecnS#pzmk} nwy

e\xvcmknwjste | vcze¬-jsrSly~mk}jktqfn{t | µe | r2tr{pwjk¬wen || j®pqjsrStn{m | epqnwjsmoyª

0 5 10 15

67 68 69 70 71 72 73 74 75 76

0 0.5 1 1.5 2 2.5 3 3.5 4

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

?jkwlcqef 2h-rwmklxpzjkrwt;rw§pq`ceOemsm}xmkee«Iln{pzjkrwt ¸½pµr¯vc`nSy~eFyq»´µjspz`crSlxpv+e\qjsr | jorStIpzqrwm7ªYt¦e\§½p

pq`cepqr{pn{mÂv5rSvclcmonBpqjsrSt | e\t5y~jsp}jstpq`ce[ºqy~pv`nwyze[nSyn§¨lt#pqjsrStOr{§(pzjkd2eSª<jsS`Ip pz`ce´ypqen | }ypnBpze

F I`J ª

¥ eºyp\rwtyzj| e\pq`celct5rwtIpqzrSmsmke | \nSy~eS©cµenwzejktupz`ce&y~jspzln{pzjkrwtur{§>pqqnwty~jspzjkrwt nBpzeFywjk¬wet

(17)

n{§½pzeQtcrSzdn{mkjhg\jktcpz`e[yzrwmklxpzjkrwt³-}2pz`ewqrBµapz`§@nS#pqrw hLK ©-µj®pq`c]Opz`ceºqy~pejsSe\t-¬Bn{mklce¸(< n{mspz`-ly

v5n{n{depqe\#»Xµ`cjo`u`nwya³+e\et¯n{tnwms}xyze

|

jkt qª

e-p©Iµe`5n8¬weajst-¬Sey~pzjkSnBpqe | pz`cee±Âe#pXrw§¦n´\js\n | jon{trStSpqzrSmIpz`n{p\nwtn{±+eF#p<pq`cepzn{t5y~jspzjkrwty

nSydrwpzjk¬8n{pze | jstKpz`ce2jktSpqzr | l5#pzjkrwt(ª13pjky[¹-tcrBµt¯pq`nBp`cenwm®pq`-}u\e\mkmky´n{qe`jsS`cms}¯n{±+eF#pze | ³-}upz`ce

pqqnwtyzj®pqjsrSty\©+n{t | e\jspz`ce´y~pzrSvcvcjktcpz`epqqnwty~jspzjkrwt5y | lcqjstn\e\zpqn{jkt¯pqjsderw§<pz`ce | n8} rwF©5rSt¯pz`ce

\rwtIpzn{q}w©wjstOnwmsmkrBµjktcvc`nSy~epqqnwtyzj®pqjsrSty | lzjktcn&e\zpqnwjstpqjsde[jstIpzez¬BnwmHª1ÒtenS`r{§Âpz`eyze[\nSy~eFy\©

nSy>msrStcnwypz`jkyX\js\n | jon{t&\rwtIpzqrwmxjoy>r{§Ây~dnwmsmnwdvcmsjspzl | ew©Sµea`n8¬SerS³y~ez¬Se | pz`n{pXj®pQ\zeFnBpzeFya¸@nB§½pqe\

yzrwdepqqnwty~jspzjkrwt+»anjkqn | jon{tuv+e\qjsr | jktupz`ce\e\mkm | }-tnwd2jo\yª 1ÒtL?jkwlze wc©µey~`crBµn{tue\xnwdvcmse

µ`e\qe&pq`ceO\js\n | jknwt \rwtIpzqrwm<³cmkrx¹xy´pz`cepqqnwtyzj®pqjsrStK§¨qrwd vc`nwyzeupzr¯vc`5nwyze v+e\qjkr | jkn{mkms}S©nwy

vzrSv5rIy~e | jkt]¸7xªïw»ª_a`ce§¨lt#pqjsrSt F

B+J

joypn{¹wet¯e«Ilnwm¦pzrrwtceecevxppq`nBp´jky | qrwvypzr

#'i

rSt

v+e\qjkr | jk[jstIpqe\q¬8nwmkyr{§msetc{pq`

F ,#ei`H

#eiWK eidJ

jst emsm·}x\mse´lctcjspqyªX_a`ce´rSyqjkmsmonBpqjsrSty<pq`nBp\nwt

³+eyze\et jktL?jsSlcqe w2ex`cjk³cj®p[¬8nwzjon{³msevyze\l | rwv+e\qjsr | ¸¨j½»pz`ce | rwlc³mserw§pq`ce\e\mkm(}xmkev+e\qjsr | nBp

0 10 20 30 40 50 60

100 105 110 115 120 125 130 135

?jkwlcqe)w Xh-rwmklxpqjsrStrw§(pzè\e\mkm¦}xmkeé«IlnBpqjsrSt¸¨pµr2vc`nSy~eFyq»Qµjspzùv5ezjkr | jo[³msrx¹-jstª>_a`ce´pzr{pn{m

v+rwvlcmkn{pzjkrwt | e\t5y~jsp}jktpq`ceºypv`nwyzenwyan2§¨lctpzjkrwtur{§pzjkd2e¸@lctcjsp´\e\mkm(}xmkeF»ª

(18)

0 5 10 15 100

105 110 115 120 125 130 135

45 50 55 60

108 110 112 114 116 118 120 122

! $(\!

< r{pzjk¬BnBpqe | ³I}lct | eqy~pqnwt | jktcpz`ceuqrwmkerw§\e\mkm}xmkeujst]pzlcdrSlc | e\¬Se\mkrwvcdetSpyµeu`n8¬Se \rwt

yzj| e\qe | nudnBpq`ce\dn{pzjo\n{mdr | e\mpzr | eFyz\zjk³+eOn emsmv5rSvclcmonBpqjsrStypqzlpzlcqe | ³-}j®py&nwwejktenS`

v`nwyzewª_a`cjoydr | em(joyeFy~v+e\jknwmsmk} | eyzjsStce | pqrjst5rwqv+rwnBpze\rwtIpzqrwmvn{n{depqe\ynBp[yze\¬Se\n{m7©³cjkr

mkrwSjkn{mkms}&³nwyze | ©wv+rwjktSpy[¸| en{pz`nBpqew©wpzn{tyzj®pqjsrStqn{pzeFyq»>jktrw | e<pzrpqn{¹SejktSpqrnwrSlctIp<pz`ceqnwvI}2rw

\js\n | jon{tK\msrx¹Âª dn{pz`cedn{pzjo\nwmpq`ce\rSz}u§¨rS[e\xjky~pzeten{t | msrStcpzjkd2enwyz}-dvxpzrwpzjo\y´`nwy´³+e\et

| e\¬wemsrSv5e | µ`cjo`Kl5y~eFy´nwtKetSpqzrSv-} de\pz`cr | jstIpzqr | l\e | qe\e\tIpzmk}¯jkt pz`jkyyzlc³xeF#pª&_a`cetIld2e

jo\nwmQpqey~pqy2n{qeOjktnwrS | nwteOµj®pq`pz`jkypz`cerwq}¶n{t | µjspz` y~e¬weqnwmQvcqe\¬-jkrwly&rwdvnwzjoyzrwtyµjspz`

e\xv5ezjkde\tIpqyª[lcde\qjkn{mzeFy~lcmspqy[n{qen{moyzrwjk¬wet rwtupq`ce&e\±+eF#pr{§Qn\js\n | jon{t rStIpzqrwmyz`crBµjktc©

nwSnwjst¦©8nwy(zev5rS~pqe | jktexv+e\qjsdetSpn{mSµrSz¹xy©\pq`nBpj®p>jsdv+rSyzeynjkqn | jon{tq`-}Ipz`cd0pzrpz`cee\mkm-}xmkewª

£

Ä-Ã (¿

Å !

¿

Â

_a`cen{lcpz`crSqyµjoy~`pzr2pz`5n{tc¹Xqr{§¨eFyzyzrwy ?cn{t\jky t

¬-j·n{t

|

°[nwtcjke\m mon{l

| e

§¨rS§¨ql#pz§¨lcm | joyz\lyzyzjkrwty©§¨rS[jkt | jo\n{pzjkrwtyrwt¯pq`ce&pz`ceqnwv5elxpzjo\rwtIpzqrwmn{t | §¨rSv+rwjktIpzjktcOrSlxp[t-l

dezrSlyze\§¨e\qe\t\eyarwtpz`ey~lc³ce#pFª

Ba'>!$

'" C q2 `* ;'4$2` `#* (*M$'*4

6 $ $2` q'4$

( *& %#*4"

$%

*?> *4($s$s ' $C $% M %*+ *+($

¸~Sdww»ª

(19)

.f/ 22 % /7 <= - 12 9: < < , /6 ! 2 % ;'9 = 1 :(

%+ 6+& < <©

M8 2*o$C"0'4'o o C"h E$ 8$C '

d *4q o*+v `$ `*'

!*+$Lq*4($ C*M *+$;$C 1"#

%*+ $

%

%*+ 4''4$3$ $o$81 C($'

,

g

|

jspzrSqyª8=mkl-µe\n

|

3 $@ `"# 'W$% M E

u*+$Cd

*+$'4($'

0=0'

)'Y`*^`*+

ªcQzevczjktIp{wwª

*M $r `#($'5o $` $C

%

'4* `*+ 2d `#($s"$% 4'

?P?,

rª5c©wdw xIBª

*+ *+($ "# $%; C0'4'@$[$% *

©

` *4` C*M

%

($3?B)" * 8"0'4 '

R$' *4q$

'

QzeFyzyFwIxª

.k29/( F! 7©

G$C *) *M$C *M &`4'

Fc©crª¦S©{wIxª

.k80/( !22 7©

h$'

(20)

$ o' (" `d $C ' u3$$3 6&($

©

tct¦ª 1ÒtypFªfªc>rSjstn{

tnwmHªcrwt t¦jkt

Fw©·c +Fwcª

%

( 'E$Y d q h C $RE"$ = d $% $>$C0' u$ `*

8h %")'443 E$8(*+ uM 8q2'4$ "#

©S5ªB_a`ce\rSª

^' Ch E 8 *+$

*+`"` '0' &$3 *443$r$% C*+ "0''

#

$C b ?

{fB¸~wSS»ª

(21)

Unité de recherche INRIA Rocquencourt

Domaine de Voluceau - Rocquencourt - BP 105 - 78153 Le Chesnay Cedex (France)

Unité de recherche INRIA Lorraine : LORIA, Technopôle de Nancy-Brabois - Campus scientifique 615, rue du Jardin Botanique - BP 101 - 54602 Villers-lès-Nancy Cedex (France)

Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu - 35042 Rennes Cedex (France) Unité de recherche INRIA Rhône-Alpes : 655, avenue de l’Europe - 38330 Montbonnot-St-Martin (France) Unité de recherche INRIA Sophia Antipolis : 2004, route des Lucioles - BP 93 - 06902 Sophia Antipolis Cedex (France)

A mathematical model of the cell cycle and its control

HAL Id: inria-00071690

https://hal.inria.fr/inria-00071690

Submitted on 23 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.

A mathematical model of the cell cycle and its control

Jean Clairambault, Béatrice Laroche, Stéphane Mischler, Benoît Perthame

To cite this version:

Jean Clairambault, Béatrice Laroche, Stéphane Mischler, Benoît Perthame. A mathematical model

of the cell cycle and its control. [Research Report] RR-4892, INRIA. 2003. �inria-00071690�

ISRN INRIA/RR--4892--FR+ENG

a p p o r t

d e r e c h e r c h e

THÈME 4

INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE

A mathematical model of the cell cycle and its control

Jean Clairambault — Béatrice Laroche — Stéphane Mischler — Benoît Perthame

N° 4892

Juillet 2003

0 0.5 1 1.5 2 2.5 3

0.7 0.71 0.72 0.73 0.74 0.75 0.76 0.77 0.78 0.79 0.8

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

0 0.2 0.4 0.6 0.8 1 1.2 1.4

0 0.5 1 1.5 2 2.5 3

0.66 0.67 0.68 0.69 0.7 0.71 0.72 0.73 0.74 0.75 0.76

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

0 0.2 0.4 0.6 0.8 1 1.2 1.4

0 5 10 15

67 68 69 70 71 72 73 74 75 76

0 0.5 1 1.5 2 2.5 3 3.5 4

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

0 10 20 30 40 50 60

100 105 110 115 120 125 130 135

0 5 10 15 100

105 110 115 120 125 130 135

45 50 55 60

108 110 112 114 116 118 120 122

Unité de recherche INRIA Rocquencourt

Domaine de Voluceau - Rocquencourt - BP 105 - 78153 Le Chesnay Cedex (France)

Unité de recherche INRIA Lorraine : LORIA, Technopôle de Nancy-Brabois - Campus scientifique 615, rue du Jardin Botanique - BP 101 - 54602 Villers-lès-Nancy Cedex (France)

Éditeur

INRIA - Domaine de Voluceau - Rocquencourt, BP 105 - 78153 Le Chesnay Cedex (France)

ISSN 0249-6399