Design and Evaluation of Staggered Partitioned Procedures for Fluid-Structure Interaction Simulations

(1)

HAL Id: inria-00073448

https://hal.inria.fr/inria-00073448

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.

Design and Evaluation of Staggered Partitioned Procedures for Fluid-Structure Interaction Simulations

Serge Piperno, Charbel Farhat

To cite this version:

Serge Piperno, Charbel Farhat. Design and Evaluation of Staggered Partitioned Procedures for Fluid-

Structure Interaction Simulations. RR-3241, INRIA. 1997. �inria-00073448�

(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

Design and Evaluation of Staggered Partitioned Procedures for Fluid-Structure Interaction

Simulations

Serge Piperno, Charbel Farhat

N˚ 3241

Septembre 1997

THÈME 4

(3)

(4)

#*",+-."/0!"213)(,45 "6+7)" 985 !" !+7( :;(<=)(>

? @BACD@FEGIH7@BAJ6K LNM7OPRQSAT-@VUXW7QYAZPRQY[\LDL

]_^a`(bdc>efhgjikblamon0pqisrVt.cpr\uvpqisbdiowxnypxikr\t

z c!wx{jw|px`bdcw}rVbduamsc(~vcw

Rqryc(pqwnyikb,nyt

Xn\uauSr\xp z cxcZ}'^ac('}'^ac*tVV0eYfgjcuvpxcbaqcd\jfhyedunyVcw

) (0a\\

lbcxio}(n\mwxikblamon0pqisrVtwr\Xlatw|pxcZn

z

{r0Xwun\w|p,nc(~jikamkcw|pxql}pxlaqcqc Blaikxcpx^ac

wxikblamspqn\tac(rVlw_w|rVmslvpqisrVtr\ wpqxlY}¡pxlqn\m z {BtYnybdik}w_nyt z ry laiz)z {jtn\bdik}w-rVt z c(¢r\qb,nyamkc z {BtYnybdik}

bdcZw|^acZw(£*¤¥cFuxcZw|ctVp;^c(qcFnytc¦§n\mslYn0pxikr\tbdc(px^ar z r\w|pqn\\Vc(qc z unyxpxispxikr\tc z uaqrj}(c z lxcZwd¢r\

pqisbdc(¨©iktBpxc(VqnypxiktaXpqâcwxc¢rv}lw6}rVlauamkc z uaxrVamkc(b,w(£]_âiow6bc(pxâr z ikwnVw|c z rVtn\tcw|pxikb,n0pqisrVtryYpxâc

ctac(q\{px^nyp&iowªtjlabdc(qik}nymkms{}qcnypxc z nypªpx^ac«laizY¬ w|pxql}¡pqlaqcRistBpxc|nV}c«Sc}nylwxcRryaw|pqn\\\cxiktaY£&gjisb¨

umsis¢{jistan\wqw|lbuapxikr\tw&bdn\®\cRpq^aiow&cZwpqisb,n0pqisrVtcnVw|{¢r\niz c«nybdikms{>r\abis~vc z c(~vuamsio}isp ¬ isbduamkio}isp r\

ikbduamkik}(i¯p ¬ ikbumsio}isp°5wx{BtY}'âxrVtar\lYwr\n\wx{BtY}'âxrVtar\lYw_uaxrv}(c z laqcw£X±²twxik\^BpqwVnyiktac z ¢xrVb³pqâikwc¦§n\m¯¨

lYn0pxikr\tbdc(pxâr z n\xc}r\ta´xbdc z i¯pq^pxâcnytn\ms{vwxikwry«tjlabdc(qio}(nym xcZw|lm¯p'w¢r\pxâclvpxpxcr\Rn;Yn0p

uYnytacmYiktwxlauYcqwxr\tik}Xn\is'w|pxqcnyb,wRikt;prn\t z px^xcc z ikbdc(twxisrVtw7n\t z ¢rV7pq^acXpqqn\tw|ikc(tBp_nyc(qrjc(mon\w|pxio}

qcwxuSr\twxcr\6n\tµX¶>µX·¸eVeB¹a£ºista,ikt)px^ac>pqqn\tw|rVtaio}qc(VisbdcV£

»¼B½D¾q¿À 0Á\ÃÂ mklaiz ¨²wpqxl}pxlaqciktBpxcqnV}¡pxikr\tYw(°S}r\luamsiktanymk\r\qispx^ab.°Yw|pqn\\Vc(qc z unyxpxispxikr\tc z uaqry¨

}(c z lxcV°vc(tacxV{;}r\tYw|cx¦0n0pqisrVtª°jc(¦0nymklnypxikr\t.nyt z.z cZw|ik\t.}qi¯pqc(qisrVt

ÄoÅªÆ|ÇÉÈÊÆ_ËÌkÇÉÍ©ÎÏ

ÐÑÒIÓ'ÔÕ²Ö×ªØ'ÙÛÚXØ'Ü

Ð¡Ð ×DÕÜ(ÖIÕÒ&ÝsÓ¡ÒªÞªÕ|ÒÓ¡ß©à§Ø'á|Õâ(ÖIÒIãZáÖIã§ÒÕßxäVå Ü§ÙæÕÒß©ÙÖèçÓ'ÝY×DÓ¡éÛÓ¡Ò©Ø'êZÓXØqÖëDÓ¡ãZéÛê§ÕÒ|ä\ëDÓ¡ã§éÛêZÕ|Òä\×ªì-ä0åâÞ

Unité de recherche INRIA Sophia Antipolis

2004 route des Lucioles, BP 93, 06902 SOPHIA ANTIPOLIS Cedex (France)

Téléphone : 04 93 65 77 77 – Télécopie : 04 93 65 77 65

(5)

( (<=)(>( h x( "!+«6 ).-45 "6)+«)"

n3wxikblamon0pqisrVttjlab(qik Blac z}(r\lamkc(bdc(tBp'w)iktBpqnypxikr\tatn\isqcw.n\lvpxrVla z c wpqxl}pxlaqcw

wxr\luamscZwt}cZwxwxispxcmon)Zw|rVmslvpqisrVt w|ikblm¯p'nytc z cuaqr\amk`(bdcZw z c z {jtn\bio Blac z cw>wpqxlY}¡pxlxcZwc(p z c

z {BtYnybdik Blac z cwªlaiz cw&c(t z rVbdn\istc z ¢rVxb,n\amscV£ rVlwªuZw|ctVpqr\twDio}iBlatac7b(px^ar z c z¦0nymkln0pqisrVt

zn\msVr\qi¯pq^abdcw br z lmkn\isqcw z }nymw lvpxikmkikwwuSr\la6m iktBp(Vqnypxikr\t!ct!pqc(bduw z c_}c-p{juYc z c_uaqr\amk`(bdc\£

-c(p|pqc bpx^r z c xcuYrBw|c wxla)latac cZwpqisb,n0pqisrVt z c mctac(q\ikc }c tjlab(qik BlacbctBp! miktVpqc(xn\}(c

Ylaiz c¨²wpqxl}pxlaqc }nylwxc z l z }(n\mkn\\cV£·cw>^j{juYr\px^a`Zw|cZwwxikbumsis´Y}(nypxqik}(cwuSc(qbc(p|pqc(tBp z(¦0nymklac(

wxikbumscbctBp}(cpxpxcc(tacxViscuYrVla>latacd\'nyt z c!n\bikmkmsc znymk\r\qispx^abdcw£ cwua z io}¡pqisrVtwr\vpqc(tjlacw

uYnyd}cpxpxcbpx^r z c)rVtVpp}(r\tv´Yxb(cZwuYnymnytn\ms{vwxc z cZwwxlamspqnypqw z cwxikblamon0pqisrVtwn"(qr#(mon\w|¨

pqik BlacZw z l¥rypxpxcbctBp zlt unytatcnylwxr\labdiow$ )ltZ}rVlamscbdc(tBpw|luYcqwxr\taio Blacc(t z c(la~ cppqxrVikw

z isbdc(tYw|ikr\tw°yc(p z c_mkn(uSr\twxc_istw|pqnypxikr\tatYnyikxc zlatacXnyikmkc_µX¶>µX·eVeB¹v£ºXctd\ikbc-px'nytYwxwxr\taio Blac\£

% À Z ¾ "& ±²tBpxc('n\}pxikr\twYlaiz c¨²wpqxlvpqlaqc\°Yn\msVr\qi¯pq^abdc z c}rVlauamonyVc\°wq}'^(b,nVw z }nymw°Y}rVtwxc(x¨

¦0nypxikr\t z cm(tc(q\ikc\°v}qi¯pq`(qc z¦0nymkln0pqisrVt ¬ }(r\tw|pxql}¡pqisrVt

(6)

=

8D ",.+7

]_^ctjlabdcxio}(n\mjwxikblamon0pqisrVtr\laizY¬ wpqxl}pxlaqc_istBpqc('n\}¡pqisrVtua^c(tarVbctn>nyqikwxcw iktb,n\tB{!n\c(qrVwxun\}(c

cta\iktacc(qistanyuauamkio}(n0pqisrVtw7wxl}'^nVw-n\isx¢r\ikmrBwx}(ismkmon0pxikr\tYw(°Vlvpxpxc(uaqc z io}¡pqisrVtw°\´V^Bpxc(-pqn\ismSal3>Dcpqist°

n\t z nXmonyq\c«}(mknVwxw&ryar\pxâc nycxrjcmknVwpqik}6iktw|pqnyismki¯p{>uaqr\mscbdw£ µm¯pqâr\l\^}(msrBw|c z Ï¢rVxb w|rVmslapxikr\tw nyqc

n§¦0n\ismonyamkc¢rV-nycxrjcmknVwpqik}X}(r\bdualvp'n0pqisrVtw«^act;r0Xw-nyqcXtar\pikt,px^cpqqn\tw|rVtaio}xc\ikbdc\°j}r\bdualapqn0¨

pqisrVtnymSbdcpq^ar z w«¢rV}(r\bduamkc~,tarVtamsiktacZny«Yr0Xw7^n§¦VcXSc(c(tlat z c z c(¦\cmsrVuabdc(tBp«¢rVn\msbdrVw|p7pc(tBp{

{Vcn\qw6?Û2@©£«]_^acZw|cbdcpq^ar z ww|^r\lamz Scn\wcA;}(isctVpXnVw-uSrVwqwxisamkc0B¢b,n0~vikbdn\mSpxikbc!w|pxcu¢rVpx'nytwxisctBp

n\tnymk{vw|iowC¡£EDXr0c(¦\c°Bpqâc({wxârVlamz nymowxruaqc z ik}pnV}(}(laqnypxcms{,wx{jw|pxcb,w_istw|pqn\aikmsispxikcw9B¢pxâctjlabdc(qio}(nym

z i>DlwxisrVt;¨Rnyt z pq^ac(t)px^cpqisbdc>wpqc(u,¨«wx^ar\lamz Scwxb,nymkmFC°vw|l}'^;px^nyp_n\is'}'n0èp z cwxisVtac(}(n\t;xcms{drVt

tjlabdcxio}(n\m6wxikblamon0pqisrVtw(£n\|pqi¯pqisrVtac z uaqrj}(c z lxcZw¢rVpx^acpx'nytYw|ikc(tBpnytn\ms{vwxikwry-laizY¬ w|pxql}¡pqlaqc

iktBpxcqnV}¡pxikr\t.^n§¦Vc>YcZ}r\bdc!¦Vc(q{uSr\ualmkn\nyt z °bdr\qcuaqc}iowxc(mk{\°Yw|pqn\\Vc(qc z uaxrv}(c z laqcw°v¢rVX^aio}'^

Â

mklai

z

·{jtnybdio}(wnyt

z

gBpqxl}pxla'nymR·{jtnybdio}(wnyqcpxikbcdiktBpxc(Vqnypxc

z

wxc(un\qnypxc(mk{nyt

z

w|lY}(}cZwxwxik¦\c(mk{\£

]_^ikw>®jikt

z

r\w|px'n0pqc(\{ n\msmkr0Xwbdr

z

lamkn\xisp{ nyt

z

}(r\bdualvp'n0pxikr\tYnymRcA;}(isct}{pq^aqr\laV^FuSrVwqw|ikamkciktv¨

pqc(x´c(m

z

uny'nymkmscmsiowxbG?¹@©£

±²t.pq^ac!unVwp{Vcn\qw°vua^j{vw|io}(n\m&n\}}la'n\}({;ry6px'nytYw|ikc(tBpXtjlabdc(qik}nym&wxikblamon0pqisrVtw_n\wXnV}'^aisc¦\c z j{

qc z l}ikta>px^cpxikbdcw|pxc(u;n\t z n\w7n!w|iz c(¨©c&>ScZ}¡p«pq^ac}rVbdualvpqnypxikr\tn\macA;}(isct}{V£6]_^cXistY}qcn\wxcry5b,n0¨

}'îstacuYc|¢rVxb,n\t}cZwRnVw-n!unyxpxionymDw|rVmslapxikr\tdpxrpxâiowuaqr\amkc(b.£6µp-pqâcwqnybdcXpqisbdcV°jwxr\bdcXuxrV\qcwqw

^Yn\wSc(ct z r\tac!pxr0_ny z w-px^ac}r\tYwpqxl}pxikr\try«n\}}la'n0pqcnyt z c&A,}(isctBpbdcpx^r z wH?kZ2@É£]_^c!xrVmscr\

ctac(q\{n\t z bdr\bdctVpqlab c~a}'^n\ta\cZwXpq^aqr\laV^px^aclizY¬ wpqxlY}¡pxlxcistBpqc(xn\}c^n\wSc(ct cbu^n\wxi¯¨

I c z £ Â r\!c(~anybduamkc\°px^ac)istY}r\t z i¯pqisrVtnym-wp'nyaikmsisp{¥ryXw|rVbdc;unyxpxio}lmkn\!msiktacZny}(r\laumsc z w|{vw|pxc(b n\w

c(mkmªn\wpxqlacwp'ny\Vc(qc z uaxrv}(c z laqc¢r\_pqâcwxc!w|{vw|pxcbdwX^n\w_Sc(ctcZwp'nyamkiow|âc z °aâctw|rVbc>ctac(q\{

}(r\twxc(q¦0n0pqisrVtuxrVuYc|p{._n\wnVwxwxlabdc z ?k@©£ Â l|pq^ac(qbdr\qc\°Ypx^acZw|ciz cZn\w-cxc!px'nytwxmknypxc z pxrtr\tv¨

mkiktacn\7}rVtv´\lqnypxikr\tw°\mkis®Vcpx^cXistj¦jiowx}(iz Yr0 unVwp_n>c(~jikamkcw|pxql}¡pqlaxcV°\pqr!ikbuxr0¦Vc_px^acn\}(}(la'n\}{

n\t z wp'nyaikmsisp{;uaqr\uSc(xpxikcw_r\6wxr\bdcunyxpxispxikr\tc z uaqrj}(c z lxcZw6?k\@©£

]_^acXn\isb ryYpx^aiowRun\uYc«ikwpqr!}rVtwpqxlY}¡p«n}qi¯pqc(qisrVt!¢rV«unyxpxispxikr\tc z uaxrv}(c z laqcwVis¦jiktanytdc(¦0n0¨

mklnypxikr\t>ryBpx^ac7c(tacxV{px^nyp&iowªnyxpxis´Y}ionymkmk{}qcnypxc

z

nyp5px^ac«iktBpxc|nV}cRSc}(n\lwxcRryvwp'ny\Vc(qist£5±²t>r\

z

c(

pqr.bdn\®\cpx^aiowc¦§n\mslYn0pxikr\t cnVw|{V°Dpx^aiowc(tc(q\{iow>cw|pxikbdnypxc

z

lat

z

c(!wxisbduamkis¢{Biktan\wqwxlabduvpxikr\twpq^n0p

bdik\^BpRYc z xrVuauYc z ikt¢laxpx^ac z c(¦Vc(mkr\uSc(bdc(tBp'w(£µXtdc(¦0nymklnypxikr\tuny'nybdcpqc(6iow6uaxrVuYrBw|c z ¢rV«niz c

n\bdismk{;ryRw|pqnyV\cxc z un\|pqi¯pqisrVtac z uaqrj}(c z lxcZw!B©gjc}pxikr\t C£«]_^acwxcJLK%+%+5cw|pxikb,n0pqisrVtwnyqcpq^ac(t

}(r\bdun\xc z ispx^ tBlbcxio}(n\m7qcwxlamspqw!r\nycxrjc(mon\w|pxio},wxisblamknypxikr\tw!ist pry¨>nyt z pq^aqc(c¨z ikbdc(twxisrVtnym

}(r\tv´Y\la'n0pqisrVtw6B©gjc}pxikr\tMC£

N

#*" +_ . &+"6 $! PO _()>(

±²tpxâiow.w|cZ}¡pqisrVtª°XcFuaqcwxc(tBppqâc¥c(¦0nymkln0pqisrVt%bdcpqâr

z

¢r\.w|pqnyV\cxc

z

unyxpxispxikr\tac

z

uaqrv}c

z

laxcZw(£

]_^cwxcbc(px^ar z w^n§¦\c.Sc(ctistBpxqr z l}(c z pxr uSc(x¢r\qb ikt%n w|ikbduamkc n§{ tBlbcxio}(n\mwxisblamknypxikr\tw

r\}(r\lauamkc z uaqr\amkc(b,w£]_^c({F}(r\bdualvp'n0pxikr\tYnymkms{F}(r\laumscdtjlabdc(qik}nym6bdcpq^ar z w>¢r\pq^ac,istBpqc('n\}¡pqist

wxlawx{vwpqc(b,w£QDXr0c(¦Vc(Z°6px^acw|pqn\aismkisp{ nyt z n\}}la'n\}({rywxikbumsc}rVlauamkist¥n\msVr\qi¯pq^ab,wn\xc¦\cx{

z i>Dc(qc(tBp¢qr\b/pqârVwxc>ry6tjlabdc(qik}nym5bdcpqâr z wXlwxc z ikt.cn\}'^ z cZ}r\luamsc z ć(mz £7±²t.Vc(tacqn\mI°anblY}'^

w|pxqr\t\c(}r\t z i¯pqisrVt r\t px^acpxikbdcw|pxcu ikwqc Blaikxc z £]_^aiowc~vuamonyiktw^j{wxl}'^F}rVbdualvpqnypxikr\tw}(n\t

Sc¦\cx{,c(~vuYctw|ik¦\cV£

RSR

ÜUT#V+WXY

(7)

±Ép>^n\wSc(ct wx^ar0tpx^Yn0ppx^acmsrBwxwikt n\}}la'n\}({n\t

z

w|pqn\aikmsisp{ikw

z

lacpxr.w|pqnyV\cxikta°YYcZ}(n\lw|c

pq^ac¢rVq}(cw,nyt

z

ctac(q\ikcwdc(~a}'^nytaVc

z

n0p,pq^aclai zY¬

wpqxl}pxlaqciktVpqc(xn\}(c.n\xctryp;n\mkn\t}c

z

?k\@©£

Â

laxpx^acxbdr\qc\°RnFVnyikt ikt nV}(}lqnV}{nyt

z

w|pqn\aikmsisp{ }(nyt Ycr\apqnyiktac

z

i¯px^ac

z

i<>Scxct}cZwScpc(ct

c(~a}'^nytaVc z c(tc(q\ikcw!iow}r\tBpqxrVmsmkc z ?k\+@É£¥¤ c)uaxrVuYrBw|c^ac(qc;pqr }rVtw|pxql}¡pn\t c(¦0n\mslnypxikr\t r\px^ac

ctac(q\{dpq^n0pXiown\}pxln\msmk{}(xcZn0pxc z nyppq^aciktVpqc(xn\}(cSc}nylwxc>ry6wp'ny\Vc(qist£¤ c´'wp}(r\bdun\xcpx^ac

nV}(}(lablamon0pqc z c(tc(q\ikcw>c~a}'^n\ta\c z Scpc(ct¥pxâc,Ylaiz n\t z pxâc)wpqxl}pxlaqcd¢r\w|{jt}'âqr\tr\lw>nyt z

nVw|{jt}'^xrVtar\lw wp'nyV\c(qc z uaxrv}(c z laqcw£ ]_^c(qcn0èpqc(Z°0-c z iowx}(lwqw&pq^acqc(mon0pxik¦\c-bdc(qi¯p'w6ryYcZn\}'^nybdismk{

r\ uaqrv}c z laqcwn\wuaqc z ik}pxc z j{,pq^acc(tacxVcpqik}c(¦0n\mslnypxikr\tª£

¤¥c´Yqw|p´~Fw|rVbctaryp'n0pqisrVtª£>±²t px^c¢rVmsmkr0ist° z ctarypqcw>wpqxlY}¡pxlqn\m z iowxuamknV}cbctBpqwnyt z n

z ryp|pqc z wx{jbSr\mwp'nyt z wX¢r\px^acpxikbc(¨ z c(qis¦0n0pqis¦Vc!ry«n) VlYnytBpxisp{\£¤¥c}(r\twxiz c(n;\c(tc(qik}>uSr\iktBpn0p

pqâclaizY¬ w|pxql}pxlaqciktBpxc(xn\}(c\°an\t z pqâc}r\qqcwxuYrVt z ikta!Sr\lat z nyq{,c(mkc(bdc(tBp£R¤¥cr\bdi¯p_pqâc>msctaypq^

rVwxlaxn\}cryRpq^aikw>wxb,nymkm cmscbctBp>n\t z px^cwx{jbSr\m GBè¢rVuaqcwqwxlaxcCw|pqnyt z wX¢rVn¢r\'}cn\w-cmsm

BistFpxâc,}n\wxcryn;¦jikwq}rVlwr0°Spxâclaiz ¢rVq}(ciowtaryp>msikbdi¯pqc z pxr)pxâcuaqcwqw|lxc¢rVq}(c2C£ Â iktn\msmk{\°

wxlauSc('wx}(xikuvp'w«nyqcXnymkn§{vw6qc(mon0pqc z pxrpqâcpqisbdc\°jnyt z pxâcpqisbdcwpqc(uikw«pxâcw|pxql}pxla'nymvpqisbdcwpqc(uª£

"!$#%'&(*)+,-,./#0,21!3)543&/!3/3,6,789'9':&:;<,-)543:=>:,

¤¥c´'w|p-}rVtw|iz cRpx^ac}r\tj¦Vc(tBpxikr\tn\maw|cxionymYwp'ny\Vc(qc z uaqrj}(c z lxc9B©_gg C«nVwRistBpqxr z l}(c z j{ Â nyq^nyp

&!S?e@É£,]_âiow>uaxrv}(c z laqcikwwx{jt}'âqr\tarVlw(°5i©£c\£pxâcliz nyt z pqâc;wpqxlY}¡pxlxcdnyqc,}r\bdualapxc z n0p

pqâcdwxn\bcpxikbdcw£±²tFpxâc¢r\mkmkr0istaY°Ycdw|^n\msm6nymowxr)}rVtwxiz cXpqâcmkcn\uv¨©¢xrV,p{juYcisbduaqr0¦\c z w|cxionym

w|pqn\\Vc(qc z uaxrv}(c z laqcJB¢±|gg Cr\ ?e@É°Sâik}'îow}(mscZnyqms{n\wx{jt}'âqr\tarVlw(£]&rbdn\®\c>pqâc z cZwx}(xikuvpqisrVt.n

mkisp|pxmkc;wxâr\xpxc°Dctr0¸\ik¦\cpxâc z cpqn\ismow>ry_nVc(tacxio}wp'ny\Vc(qc z n\msVr\qi¯pqâb.£ Â r\>px^cdw|pqn\\Vc(qc z

iktBpxc\'n0pxikr\t¢xrVb$@?pxrA@?7BCDE@?GFH'°vpq^ac_gag)uaqr z c}lxcxcZn z w

\£_b,ny®\c_nuaxc z io}¡pxikr\tIJ?7BKC6¢rV pq^acwpqxlY}¡pxlqn\m z ikwxuamon\}cbdc(tBp6nyp6pxikbc@?7BKC§£±²tb,nytj{!w|pxl z iscZw(°

px^aiowuaqc z io}¡pqisrVtikw}rVbumsc(pxc(mk{.r\lvp z n0pqc z n\t z qcn z wIJ?7BKCLD*M?D£¤¥c}(r\twxiz c(px^acbdr\qc

\ctac('nymDuaqc z io}¡pqisrVt.ist)¢lat}pxikr\tryuny'nybdc(pxc('wONKPn\t z N C °

I

?7BC

DQ

?

FHN P "R ? FHN

C

'STR

?U

R

?-V+CXW

B2C

v£}rVbulvpxc¥n tac( liz Vxiz n0ppxikbcY@?7BCb,nypq}'^aikta pq^aikw)uaqc z io}¡pqc zz iowxuamknV}cbctBp°Xnyt z

n z ¦0n\t}cpx^cYlaiz ry'°&uSrVwqw|ikamk{istn.w|laD}{v}(msc z _n§{ B¢ispx^n\w>b,nytj{.liz pxikbdc,wpqc(uw

n\wtacZ}cwqwqnyq{3C£ Â r\dwxlaS}({v}mkistaY°«c)^n§¦Vcmkisbdispxc z r\liktj¦\cZwpqisBn0pxikr\tYwpxrnymk\rVxispx^bdw!¢r\

âio}'^ pqâc.bcZw|^ wxuYcc z ikw,}(r\tw|pqn\tVp z laqikta n }(r\lauamkc z pxikbdc wpqc(uª£3±Ép,ikwpqâc(t3\ik¦\ct j{

Z

?7BC\[^]_Da`bIJ?7BC

U

IJ?dc ef'£]_^ikw>iowpx^ac,}n\wxc¢rV>n\msmRuxrv}c z laqcw}rVtw|iz cxc z iktQ?e@É°ªikt

âio}'^)pqâiowX}'âr\io}c_n\wn\}pxln\msmk{n z ¦\rv}(nypxc z £

a£}rVbulvpxc7n z ikw|pxqislvpxikr\tr\Vpqqn\tw¢cxqc z laiz uaqcwqw|lxc¢r\'}cZwg

?7BC

h

nyuauamkikc z pxrpq^ac7w|pxql}¡pqlaqc

B¢ispx^,pqâcXpqisbdc(¨Én§¦Vc('ny\iktar\Rpqisbdcwx}'âcbdcXry5{\rVla7}'ârVik}(c2C£]_âiowR¢rVq}(c}(n\tdYcw|cc(t;n\w«pxâc

uaqcwqw|laqc¢r\'}c>c~vc(xpxc z j{px^ac>liz r\t)px^c!wpqxl}pxlaqcn0p_pxikbdcG@?7BCy£

e£n

z

¦0n\t}cpx^c!wpqxl}pxlaqc>ry'«ispx^px^acuxc¦Bikr\lYw|mk{}rVbdualvpxc

z

¢rVq}(c\£

ikjPRgi

Þ

(8)

]_^c)uaqc

z

ik}pxikr\t B|2Cikw´'w|p|¨Ér\

z

c(n\}(}(la'n0pxc)i¯LN

P

D)nyt

z

wxc}rVt

z

¨Ér\

z

c(n\}}la'n0pqclat

z

c(px^ac

n

zaz

ispxikr\tn\m&}rVt

z

ispxikr\tpx^Yn0p N C

D ev£7]_^c>lai

z

pxikbc(¨©iktBpxc\'n0pxikr\try«w|pxcua£-}nyt.Yc

z

r\tacispx^

c(~vuamsio}isp>r\>isbduamkio}isp°5´'w|p|¨_r\w|cZ}rVt

z

¨Ér\

z

c(n\}(}(la'n0pxcpxikbdcwq}'^ac(bdcZw(£!±²t¥nymkmR}(n\wxcw°D-cd}(n\tFVis¦Vc

n\t cw|pxikb,n0pqc¢rVpqâcpqqn\tw|¢c(qxc z c(tacxV{pqâxrVla\^ nyt cmscbctBpr\«pxâclaizY¬ wpqxl}pxlaqciktBpxc|nV}c\£

]_^ikw_cZwpqisb,n0pqc^n\wpq^ac\ctac('nymS¢rVxb

YD U

I

?7BC U

I

? ?

BIC

^c(qc I z c(trypxc)w|l}}cZwxwxis¦Vc z iow|uamon\}(c(bdc(tBp'w!rypq^ac;Ylaiz \qiz Sr\lat z nyq{QBI}r\ikt}(iz ikta i¯pq^ px^ac

uxc z ik}pxikr\tr\px^ac¥wpqxl}pxla'nym z ikwxuamon\}(c(bdc(tBpqwC;n\t z T?

iow,px^c laiz uaqcwqwxlaxcFistj¦\rVms¦Vc z iktpx^ac

Sr\lt z nyq{.lv~ ¢r\>pq^ac,}laqxctBppqisbdc(¨Éw|pxcuª£,]_^aikw¢r\qblamoniow>c~anV}¡pistrVtac¨z ikbctwxisrVtª£ T?

}(n\t

p'ny®VcrVtac>ry px^ac>¢rVmsmkr0ist¦0n\mslacZw

?

DE ? BI\nMC

?

DQ

?7BC

BIy:C

?

T?MFH T?7BC

BI\}#C

?

_`\c BI z C

Â r\ c(~anybduamkc\°>¢r\ n3´qw|p|¨Ér\ z c.¢r\qn\ z ¨! Rlamkc(wq}'âc(bdcV°pxâc ctac(q\{lv~ pxâqr\l\^Npxâc Ylaiz

iow }(r\bdualvpqc z lwxista Ylaiz ¦0nymklacZw n0ppqisbdcH? £ ¤ cpq^ac(t*^n§¦Vc D U

Z

?7BC\[^]

? D

IJ?7BC U

IJ?

? £ ]_^ac(t T?

iow,\ik¦\ct3j{ B\n$C¡£ Â r\)nyt isbduamkio}ispn\}'®j_ny z ¨! Rlamkc(,wx}'^c(bdc\°

T?

iow\ik¦\c(tFB{BIy:C£]_^aiowc Blnypxikr\tiowrVtams{.c(~vnV}¡p¢r\pxqlaclata¨©mkistcnyqi

I c z ikbduamkik}(i¯p¦\cqwxikr\twr\

pq^acdn\}'®j_ny

z

¨! Rlamkc(>wx}'^acbdc\£

Â

r\!wxc}(r\t

z

¨©rV

z

cXpqisbdc;wq}'^ac(bdcw°ªn\rjr

z

n\uauaqr§~visb,n0pqisrVt ryO T?

iowVis¦Vc(tB{BV}#C¡£

Â

iktn\msmk{\°ac>^n§¦\c}(r\twxi

z

c(qc

z

px^acuSrVwqw|ikaikmsisp{r\ Ylai

z

wxlaD}{v}mkikta£R¤¥cn\wqwxlabdc

pq^ac!Ylai

z

\qi

z

iow}r\tYwp'nytBp

z

laqikta)n\msm&lai

z

wxlaS}({v}mkcwry7n;}(r\lauamkc

z

pxikbc(¨Éw|pxcuª£¤^ac(tpq^ac!Ylai

z

pqisbdc(¨Éw|pxcu iowwxl3A;}ikc(tBpxmk{ wxbdn\msm_}rVbdunyqc z ispx^ px^ac.w|pxql}¡pqlaqn\m«pqisbdc¨²w|pxc(u '°7nFwxc}(r\t z ¨Ér\ z c

cZwpqisb,nypxc>ry T?

iow\ik¦\ct)j{ BI z C£

Â iktnymkms{V°\iktw|pxcude£k°y-cnVwxwxlabdcpx^acw|pxql}¡pqlaxc_iow6msiktacZny«nyt zz iowq}qcpxi

I c z lYw|iktan´taispxcc(mkc(bdctVp

bdr z cm«{jiscmz iktab,n\wqw° z n\buista nyt z w|pxi<>StacZwxw!bdnypxqik}(cw#"%$Z°'&($Z°6nyt z) $ Bn\msm«px^aqc(c;n\xc,wx{Bb¨

bdc(pxqik}uSrVwxispxik¦\c\°*"$nyt z+) $Ycist z c´Ytai¯pqcuSrVwxi¯pqis¦Vc2C£±Épiowpxikbdc¨²n z ¦0n\t}c z lw|ikta,pq^acikbduamkik}(i¯p

pqqn\uYc

I

rViz n\mRxlmscV° qi¯pxpxct¥ikt¢lat}pxikr\t r\w|pxql}pxla'nym z iowxuamknV}cbctBpqw °¦\cmsrv}(i¯pqiscZw#,<D 2nytR z

nV}(}(c(mkc('n0pxikr\tYw.- D0/°nVw213

435

M?2BCDQM?GF676

B 6 87

]

,T?2BCD9, ?GFH;:

B : 87

]

" $ -3?7BKC'F& $ ,G?7BKC'F )<$ M?7BKCDE

?7BKC

h

B¢e$C

= tc_¢lat z n\bctBpqnymYuaqr\uSc(xp{!ryDpx^cXuaqc}c z iktapx'nyuSc

I

rViz nymaqlamkcX}r\tY}c(qtwpq^acXc(tc(q\{qc}(c(ik¦\c z j{

pq^ac!w|pxql}¡pqlaxc z lxiktadr\tacpqisbdc!w|pxc(u&£R¤ c!}(r\twxiz c(px^ac!w|pxql}pxla'nym5ctac(q\{

h D

,>" $ ,EF

)?$

BI¹C

RSR

ÜUT#V+WXY

(9)

pq^ac(tpq^ac!wpqxlY}¡pxlqn\mSctac(q\{¦§n\xion0pqisrVt

z

lxikta,npxikbc!w|pxcu.ikw

?7BC

h U ?h D

?7BKC

U ?

T?

h F

?7BKC

h

U

,

?7BC\[^]

&($,

?7BC\[]

^c(qc?,G?7BC\[^]0D `,G?AF9, ?7BC c@e;a£)¤¥c}nyt b,ny®Vc;n z ikw|pxikt}pxikr\t Scpc(c(tpq^ac;ctac(q\{ msrBwp!j{

iktBpxcxtn\m z nybduaikta B¢tc(Vnypxik¦\cpxcxb

U

,G?2BC^[^]8&($ ,G?7BC\[^] C6nyt z pq^acc(tacxV{px'nytYw¢cxqc z B{px^ac

Ylaiz

h D

?7BC U ?

T?

h

FH

?7BC

h

BºMC

-mkcn\xmk{\°ypx^acXc(~a}'^nytaVc z c(tacxViscZw*Bº$C6nyt z B©Cispx^ T?

\ik¦\ctj{ BIMCR}nytatryp7}rVbduYctwxnypxcc(~vnV}¡pqms{

Sc}nylwxc>px^c!uaqc z io}¡pqisrVt B|2C_iowXtrypXc~anV}¡p£_]_^jlw°c(tc(q\{;iown\|pqi¯´Y}(ikn\msmk{}(xcZn0pxc z r\ z iowqw|ikun0pqc z n0p

pq^aclaiz c ¬ wpqxl}pxlaqciktBpxc|nV}c\£6]_^aiow_}r\lmz uSr\mkmklvpxctjlabdc(qik}nymSxcZw|lamspqw-ry&lvp|pqc(wxisblamknypxikr\tw«¢r\

c(~anybduamkc\°anyt z {jikc(mz nuSrjr\Xn\}}la'n\}({,istpq^ac z cpqc(qbdistnypxikr\try lvp|pqc(Xmkikbispqw£

±²tpx^cXw|cZ Vlc(m©°\ciktBpxct z pxr\ik¦\cn\tc¦§n\mslYn0pxikr\trySpx^cXnyxpxis´Y}ionymvctac(q\{!}(xcZn0pxikr\tATF

h

ikt%pqâc¥unyxpxio}lamony.}(nVw|c âc(qc pxâcwpqxlY}¡pxlxc¥ikw)rVwq}ikmkmknypxikta ispx^ n }(r\tw|pqn\tVpnybduamkispxl z cnyt z

ulamkwqn0pqisrVt

£¤ c.nymowxr n\wqwxlabdc;px^Yn0ppxâc)laiz uaqcwqwxlaxcr\t pqâc.wpqxl}pxlaqcrBwx}(ismkmon0pxcZw!ispx^ pxâc

wqnybdc>ualamowqn0pxikr\t&£ Â r\c(~vn\bduamscV°jpx^ac>pr¢r\mkmsr0iktad}rVlauamkc z ^nyqbdr\taio}c(¦\rVmslapxikr\twn\xcuYrBwxwxikamsc

` \cD `

\c

_`\cDX`

+F/c

_`b\cD `

\c

_` \cD " / `\c F%& `b\c+FR ) `b\c

B©C

±²t B©C¡°5pqâc´'wp!wxcpryc Bln0pqisrVtwxcuaqcwxc(tBpqwn.w|ikbduamscdua^Yn\wxcwxâisèp>Scpc(ctFpqâclaiz nyt z pxâc

w|pxql}pxlaqc\£%±²t pqâc wxc}rVt z w|c(p;ry>c Blnypxikr\tw°n\c(qr z {jtnybdio})mkrVn z wdr\t3pqâcFw|pxql}¡pqlaxc^Yn§¦\cpxâc

c&>ScZ}¡pr\Xn zaz c z b,n\wqw(° z nybduaiktaFn\t z w|pxi<>StacZwxwb,n0pxqio}cw B¢qcwxuYcZ}¡pxik¦\cms{ z ctarypqc z j{ " ° & nyt z

) C¡£rypq^;w|c(pqw7n\xcc Blaik¦§n\msctBp-is ) U ] "

2nyt z

& £ cplw z c´tac

prduny'nybdc(pxc('w"!)n\t z ,j{

!D

) U ] "

#

$%

_D `&

c#

$&'

B)(MC

¤¥c.n\wqw|labdc.w|{vw|pxcbdwnyqc)n z ¦0nyt}(c z ist pxikbc.lwxikta¥n }rVtwp'nytBppxikbc.w|pxc(u nyt z wxl}(}(cwqw|ik¦\cZw

¦0n\mslacZw_¢r\MM?)n\t z T?nyqc>px^act nyuauaqr§~visb,nypxikr\twry/`@?dc-nyt z _`@?dc7ispx^ *3? D+'£ c(plw

iktBpxqr z l}cpx^c z ikwq}qcpqi

I

n0pxikr\t)uny'nybdc(pxc(,D

'£-cZ}(nylYw|cry w|pqn\\Vc(qistaY°Vc(~a}'^nytaVc z ctac(q\ikcw

pqâqr\laV^ pqâcistBpqc(xn\}c n\xc.tar\p;c~an\}pxmk{ r\uuYrBw|ispxcnytj{jbdr\qc\£%]_âccxqr\dikt c(tacxV{ c~a}'^n\ta\cZw

z

c(uSc(t

z

w7r\t,pq^acXVmsrVnym}(r\laumsiktan\msVr\qi¯pq^ab.£

Â

r\«c(~vn\bduamscV°Vmkcplw7nVwxwxlabdccXlwxcXpx^cXuaqc

z

io}¡pqisrVt

B|2C«i¯pq^N

P

DEN

C

D.nyt

z

n\t;c~vuamkio}isp7¢r\q_ny

z ¨ «lamsc7wq}'^ac(bdcX¢rV«pq^acXli

z

i¯pq^;tarwxlaD}{v}mkikta°

{jikc(mz ikta,nYlaiz ctac(q\{;¦0n\xion0pqisrVt\ik¦\ct)j{ B©C_n\t z BI\n$C¡£«]_^act¢rVcn\}'^)pxikbdc!wpqc(uª°

D U ? U ?-V+C ?

D /!0 `

? c U 1g`

? c32 ` ?-VgC c U X`

? c

ikjPRgi

Þ

(10)

]_^cuxcZ}c

z

ista ¢r\qblmkn ikw,wxlabdbdc

z

lau r0¦\ch}rVlauamkc

z

uYcxikr

z w * D Ke

r\rBwx}(ismkmknypxikr\tª£

w|iktapx^cmscbb,nVw(°

1

45

X`

@?GF c `

@?dc

` c

&'+`

@?TF c'+`

@?dc

` c

+`

@?GF c `

@?dc

'+` c

BMC

pq^acc(tc(q\{dpx'nytYw¢cxqc

z

pxrdpx^c>lai

z

wxlab,w_laupxr

ispx^ D , /!L`3X`,+c

U

fc

U

1'+` ,gc)2

]_^ikwpqc(qb2}(n\t)Sc z c¦\c(mkr\uuYc z nVwxwxlabdist ,

>n\t z pqn\®\cw-pq^ac>¢r\qb

D U

! , U

,

!

U

"

U , ]

#

F%$`,'&7c

gjikbdismony7c(mkc(bdc(tBpqn\x{!}nymo}lamon0pqisrVtwR}(n\tSc z rVtac_i¯pq^dpx^acctac(q\{¦0n\xion0pqisrVt_

h

ryEBºMC ¢rV7nytj{

®jikt z r\&wx}'^c(bdc\£ Â rV-c(~anybduamkc\°ji¯ -cn\}¡pqlnymkmk{dn z ¦0nyt}(cXpq^acw|pxql}pxlaqcSc¢rVxcpx^aclaiz °ji©£cV£ispx^

?2BC

h

DE ? °apxâct-c´t z pq^n0pXpqâcc(tc(q\{dpx'nytYw¢cxqc z j{,pxâc>Ylaiz pqrdpxâc!w|pxql}pxlaqcw|lab,wlu

pqr

h

i¯pq^ h D ,

0&'+`,gcD U ,5]

#

F$` , & c

]_^jlw°0¢rVRpxâiowRun\|pqik}(lamony«}rVlauamkist>n\msVr\qi¯pqâb.°0px^cpxr\pqnymvctac(q\{nyxpxisÝ}ionymkms{}qcn0pqc z pxâqr\l\^pxâc

Ylaiz c ¬ w|pxql}pxlaqc>istBpxc|nV}c>w|lbdwXlaupxr

`

F6

h c

i¯pq^

U ! ,

]_^c7un\qn\bc(pxc( ) F*

h

\ik¦\cZw n\t!c(¦0n\mslnypxikr\t!r\vpx^ac_n\}}la'n\}({r\vpx^ac_}rVlauamkistnymk\rVxispx^b£

·c(uSc(t z istrVt!pqâcw|ik\try ! Bn\t z n\mkwxrXpqâc_r\ z c(ryYbdn\\taispxl z c_ry !D°\âik}'^ z c(uSc(t z w6r\tpxâc¢r\qb

r\ªnyc(qr z {jtnybdio}mkrVn z wRr\t,pqâcw|pxql}pxlaqc2C°\pqâikw-un\qn\bc(pxc7}(n\t,âc(mku;uaqc z io}¡pqist!px^cSc(^n§¦jikr\la«r\

pqâc!wq}'âc(bdc Bn\|pqi¯Ý}(ikn\m5uYrBw|ispxik¦\c>rVtc(Vnypxik¦\c z n\buista8C7¢r\Xwxbdn\msmªpxikbc!w|pxcuw9B3,

+ 2C£

cpdlwcbdua^n\wxi

I

c;pq^ac;nV}¡ppx^nypc¦§n\mslYn0pxikr\t uny'nybdcpqc('w,*nyt z h

}(nyt Yc.}rVbulvpxc z

wxc(uYny'n0pxcms{¢r\ z i>Dc(qc(tBp laiz nyt z wpqxl}pxla'nymVunyxpqw&ryvpqâc}(r\laumsiktan\msVr\qi¯pqâb,w(£ª±²t!pxâc7¢r\mkmsr0ikta°

cd\ik¦\cdpqâc;}rVbulvpxc z uYny'nybdcpqc('w¢r\ z i<>ScxctBpwx}'âcbdcw!n\t z z ikwq}lwqw>pqâc,bdc(qi¯p'wry_uYrBwxwxikamsc

}(r\laumsiktan\msVr\qi¯pqâb,wRist)msik\^Bp7r\5pxâcuny'nybdc(pxc(-,£6±²t,pqâcwxc BlacmI°B-cw|^YnymkmYwqn§{pq^n0p_n}rVlauamkist

n\msVr\qi¯pq^ab iow+

¨Ér\ z c-ctac(q\{B¨²n\}(}(la'n0pxci¯+

.

, ?^c(t ,"/ . Bn\t z .

iowXnd}rVtwp'nytBpC£

b "!$'#1032"4 #%'& ; 35G:g&:K!/76M3^; 8^=>:Q,-)54:K=*:K,

¤¥c_tar0 Vis¦Vc«px^c¦0n\mslacZwry¢rV pq^ac_\ctac('nymjuaqc z io}¡pqisrVt B|2C nyt zz i<>ScxctVp6liz pxikbdc_wq}'^acbcZw(°

ikt}(msl z ista)px^rVwxc}(r\twxiz c(qc z n\Yr0¦Vcnyt z {jiscmz ista)laiz c(tacxV{¦0n\xion0pqisrVt BIMCispx^Y T?

Vis¦Vc(t j{

RSR

ÜUT#V+WXY

(11)

BIMC£«]_^acwxc>¦§n\mslcwnyqc>\ik¦\ctj{

/` 7c^` c)2 D !@`bNP U c, FE`

U N P

#

FHN

C c,

F U "FE`

# U NKP

FHN

C c, ]

F%$`,'&7c B \n$C

$/` fc\` c)2 D !@`bNP

U c, FE`

U N P

# F fN

C c,

F U

"FE`

# U 7NP

F N C c, ]

F%$`,'&7c B y:C

/` fc\` c)2 D !@`bNP

U

7c, FE`

U

fN P F

7N

C

c,

F U

"FE`

U N P FHN

C c , ]

F%$`,'&7c B \}#C

/` fc^`5c)2 D !

`bNP

U

7c, FE`

U N P

8

F

7N

C

c,

F U "FE`

8

U N P F N C c, ]

F%$`,'&7c B z C

"!$'#1032 #%'& ;335G:&:!" 8&!3, #%:g&&:K; #\/&5) :,

¤¥ctr0 Vis¦Vc!c(¦0n\mslnypxikr\twryRpq^ac}(rBc&A;}ikc(tBp

h z cxik¦jist,¢xrVb BºMCnyt z }(r\qxcZw|uSr\t z istdpxr z i¯è¨

¢cxctBp}'^r\io}cw¢rV>px^ac,iktaualap!¢r\'}cZwL

?2BC

h

ist¥pq^acdpx'nyuSc

I

r\i

z

nymRqlamkc Be$C£;¤ c;}(r\twxi

z

c(px^cd¢r\la

¢rVmsmkr0ikta}'^r\io}cw

?7BC

h

DQ ? BVn$C

?7BKC

h

DE

?7BKC

BV(:C

?7BC

h D

T?TF T?7BKC

BV}#C

?7BC

h D

87

_`b\c BV z C

Â r\-cn\}'^)}'^ar\io}cXr\5px^ac¢r\qb V°jc}nyt}(r\bdualvpqcn z i>Dc(qc(tBp-iktaualapuaqcwqwxlaxcX¢r\'}cXj{ z cpqc(qbdi¯¨

tista>pq^acpqqn\tw¢cxqc z ¢r\'}c

?2BC

h

¦\cxis¢{jista

T?

h

FH

?7BC

h

DQ

£6]_^aiow«®jist z r\ªnymk\r\qispx^ab¸Vis¦VcwRn\t

c(~an\}¡p}rVtBpxqr\mSryªpqâc>brVbdc(tBpxlab/px'nytw|¢c(qxc z j{dpxâcliz pxrpxâcw|pxql}¡pqlaqcnyt z un\|pqikn\mS}(r\tBpxqr\m

ikjPRgi

Þ

(12)

¢rV_px^acctac(q\{dpq^aqr\laV^BIºMC¡£«]_^cwxc>n zaz

ispxikr\tn\mª}'^ar\io}cZw}rVxqcwxuYrVt

z

pqr

?7BC

h

D9_

? U ?

h

B§yn$C

?7BKC

h

D9_ ?7BC U ?

h

B§0:C

?7BKC

h

DE

?7BKC

B§y}#C

?7BC

h D

87

_` \c U ?

h

B§ z C

]_^cqcn z c(}nyttarypqik}(cpx^nyp}'^ar\io}cZwB|\:C>nyt z B§y}2Cn\xc,w|pxqik}pxmk{ c Blaik¦0nymkc(tBp£d¤¥c,\ik¦\c z c¦\c¨

mkr\ubctBpqw-ry5px^cun\qn\bdcpxc

h

ikt,¢latY}¡pxikr\t)ry ,;¢r\-px^cwxcc(ik\^BpLBn\}pxln\msmk{,w|c¦\ct:C6¢rVq}(cXistualvpqw£

] c z isrVlw}(n\mk}(lamknypxikr\tw{jikc(mz

h /` c32 D !

U , F ,'

F% U

,5]

F%$`,'&7c BZ\n$C

h /` e8 c)2 D

U , ]

#

F%$`,'&2c BZy:C

h /` c32 D !

U , F ,'

#

F% U

,5]

8

F%$`, & c BZ\}#C

h /` 5c)2 D ! U , F

,'

F% U , ]

F%$`,'&7c BZ z C

h /` 8 c32 D ! U , F ,

F%

U , ]

#

F%$`, & c BZyc2C

h /` c32 D !

, U ,'

F% !

U

,5]

#

F%$`, & c BZ0/C

h /` 8;5c)2 D U , ]

F%$`,'&2c BZy8C

Q,-)+3,-,- /!a/! 032 #%'& ,21!3)543&/!3/3,3&8@/!:;3&) :; &:K,

¤¥c´'wp«}rVtwxi

z

c«nymk\rVxispx^ab,wispx^_N

P

D.>nyt

z N C D .istpq^acXwpqxlY}¡pxlqn\mBuxc

z

ik}pxikr\t BC¡£±²tpq^n0p

}n\wxc\°Bpx^cuxc z ik}pxikr\tikw_rVtamk{}rVtw|iow|pqnytBpZ£]_^aiow_®jist z r\nymk\rVxispx^b ikw´'w|p|¨Ér\ z c(c(tacxV{B¨ÉnV}(}lqnypxc

¢rV7nymkmaun\isRr\ªwx}'âcbdcw°yc~a}cuvpxc z ¢r\6pqâc´'wpx¨©rV z c(Rc~vuamkio}isp«tarypx¨ÉwxlaD}{v}mkc z laiz wq}'âc(bdc\ik¦jist

BI\n$C}rVlauamkc z ispx^ B|Z\}#C¡£F±²t px^nyp}n\wxc\°px^ac)c(qxrV!iown\msbdrVw|p

I

c(qrFw|ikt}(c0 `?-V+C / ? cGD

U

h `@? / @?7BC cq£ lvppx^aiowXwq}'^ac(bdc>iow_r\j¦jisrVlw|mk{,tar\pX\c(tc('nym©£

¤¥ctar0N}(r\twxiz c(_´'w|pXr\ z c(_uaqc z io}¡pqisrVtw9BCi¯pq^ NKP D nyt z N C

D.£7gjc(¦Vc('nym5nymk\rVxispx^bdw

ikt!pqâiowR}mon\wqw n\xcw|cZ}r\t z ¨©rV z c(ªctac(q\{B¨²n\}(}(la'n0pxcV£&¶c(tacqn\msmk{\°§pqâc_w|b,nymkmkcw|pcxqr\ ikwr\apqnyiktac z âct

c(~an\}¡pc~a}'^n\ta\cry7bdr\bdctVpqlab px^xrVla\^pqâclaizY¬ w|pxql}pxlaqciktBpxc(xn\}(ciown\}'âikc(¦Vc z °5i©£cV£!âct

pqâc>¢r\'}cpqc(qb/istB|ZC}(r\qxcZw|uSr\t z istapxrpqâc>laiz wx}'âcbdciowX}'ârBw|ctª£¤ cVcp

`fc

C

C U

`\c

U ` \cGD

U ,5]

F%$`, c D

B|(e$C

RSR

ÜUT#V+WXY

(13)

Dr0-c¦\c°\px^acr\uvpqisb,nym5wq}'^ac(bdcwxc(cb,w«pqrScVis¦Vc(t,j{ BV}#C-nyt

z

§

z

CR¢r\^aio}'^,px^acc(tc(q\{c(qxrV

iowwxmsik\^Bpxmk{wxb,nymkmscHB D U , ] e F$`,'7c"C£

Â

iktnymkms{V°Xpq^ac¥wxc}(r\t

z

r\

z

c()uaxc

z

io}¡pxikr\t B2Cispx^ N P D nyt

z N C D e; {Bikc(m

z

wn pq^ais

z ¨

rV z c(!ctac(q\{B¨²n\}(}(la'n0pxc,n\msVr\qi¯pqâb isnyt z r\tamk{ isXc~anV}¡pc(~v}'^YnytaVc,ryXbdr\bdc(tBpqlab9pxâqr\laV^pxâc

YlaizS¬ w|pxql}¡pqlaxc>iktBpxc(xn\}(c>ikwnV}'^aisc¦\c z £6¤ cVcp

`fc

C\[^]

C U

`\c

U ` 8\c

D!

,

F%$`,'&7c

D

B|Z¹C

Â r\pxâc,wxc}(r\t z ¨Ér\ z cuaqc z io}¡pqisrVtª°Spxâcdctac(q\{nyxpxisÝ}(ikn\msmk{}qcn0pqc z YcZ}(nylYw|cry-w|pqn\\Vc(qistaikw

rVuvpxikb,nymkms{qc z l}c z âc(t px^c¢rVq}(cwc~a}'^n\ta\c z Yc(p-cc(t pqâclaiz n\t z pqâcdwpqxl}pxlaqcdn0ppxâcis

iktBpxc|nV}cn\xc,c(~vnV}¡pqms{r\uuYrBw|c z °n\t z }(r\twxc(q¦0n0pxikr\tr\XbrVbdc(tBpxlab iownV}'^aisc¦\c z £ ]_^aiow^n\uauSc(tw

^c(t T?

n\t z

?7BC

h

xcZw|uSc}pxik¦\cms{;iktj¦\rVms¦Vc z iktBIMC_nyt z Bº$C¦\c(qis¢{

?

D T?

h

FH

?7BC

h

B|ºMC

"!$#%'&(!<,71! )54&5/!/ , &8 /!3:; &) :;33&:

5S% * ?e@ª^n§¦Vc>n z ¦\rv}n0pxc z pqâclwxcr\&pqâc±|gagn\wx{jt}'âqr\tarVlw7uxrv}c z laqc\£±ÉpXikw_laismspnVwn

mkcn\uv¨©¢xrV;wx}'^acbdc BèYlaiz ¦0nymklacwnyqc}rVbdualvpxc z nyppxikbdcwL@?7BC\[^]n\t z w|pxql}¡pqlaqn\mw|pqnypxcZwnyppxikbdcw

@? C£«]_^ac!nymk\rVxispx^b xcZn z w

\£}rVbulvpxcpx^cuaxc z io}¡pxikr\t IJ?7BC\[^]3D T?F

] RT? Bw|pxql}pxla'nym z iow|umknV}c(bdctVp«nyppqisbdc@?7BC\[^]2C

v£}rVbulvpxcn tac( lai

z

\qi

z

nyp!pxikbdc@?7BC\[^];b,n0p'}'^aikta.px^aiow!uxc

z

ik}pxc z z

ikwxuamon\}(c(bdc(tBp°6nyt

z

n z

¦0n\t}cpx^c>lai

z

r\'°auSrVwqwxisamk{;iktnwxlaD}{v}mkc

z

_n§{\£

a£}rVbulvpxc!npx'nytYw¢cxqc

z

lai

z

uxcZwxwxlaqc

z

iow|pxqisalapxikr\t

?7BC

h

n\uauamkisc

z

pqrdpx^ac!w|pxql}¡pqlaqc\£

e£n z ¦0n\t}cpx^c!wpqxl}pxlaqc>ry'«ispx^px^ac>pqqn\uYc

I

rViz n\m5xlmsc B¢e8C¡£

]_îkwuxrv}c z laqcwxnypxiowćZw_px^c¶c(r\bdc(pxqik}-rVtw|cx¦0nypxikr\t n§ B©¶! CL?k(e@ ispxârVlvpX¦jisrVmknypxiktadpxâc

iktBpxc|nV}c}(r\tBpxiktjlai¯p{}rVt z ispxikr\t rVt ¦\cmsrv}ispxikcw£F]_^aiowuaxrVuYc|p{¥iow z lc;pxr px^ac)px'nyuSc

I

r\iz nym«qlamkc\°

wxikt}c

R

Z ? `bIJ?7BC\[^]

U

IJ?-V+C\[^] c efD `M?

U

M?8V+C c ef5FH`RM?

U RM?-VgC c e; RT?D£«]_^acctac(q\{

pqqn\tw|¢c(qxc z pxrpq^ac>laiz }(nyt.nyBnyikt)Scqi¯pxpxc(tnVwO YD

U

IJ?2BC^[^]

U

IJ?-VgC^[^]

T?

^ac(qc

?

D B|§C

n\t z

¸p'ny®\cZwr\tac>rypx^c>¢r\mkmsr0ikta¦§n\mslcw

DE ?8V+C\[] B (\n$C

D

?2BC^[^]

B (y:C

?-VgC^[^] FH ?7BC\[^]

B (\}#C

_`\c B ( z C

ikjPRgi

Þ

(14)

}(r\qxcZw|uSr\t

z

ist xcZw|uSc}pxik¦\cms{¥pxrnF¢r\qn\

z

¨! Rlamkc(Z°«n Yn\}'®jn\

z ¨ Rlmsc°«n w|cZ}r\t

z

¨©rV

z

c(ikbduamkik}(i¯p

n\t

z

n^aik\^ms{B¨²w|laD}{v}(msc

z

lai

z

wx}'^acbdc\£

Â

rV_pxâcZw|c>}'âr\io}cZw(°Bpqâc>uny'nybdcpqc(

ikwpq^ac(t\ik¦\ctj{

/`

e

c)2 D ! , U

,

F U

"F , ]

F$`, & c BZ\n$C

/`

e

c32 D ! U , U

,

#

F U 'F

, ]

F%$` ,'&2c BZy:C

/`

e c)2 D ! U

,'

F U

"F , ]

F$`, &2c BZ\}#C

/`

e

5c)2 D !U

,'

F U U , ]

F$`, &2c BZ z C

cZ}ikuaqrj}nymkms{V°j¢r\XcZn\}'^uYrBwxwxikaismkisp{,¢r\ ikt B| ($C¡°vpq^acistualvpX¢rVq}(cM

?2BC

h

¢r\pq^ac>px'nyuSc

I

r\iz nym

qlamkc B¢e$C_}nytYc!}'^rVwxc(t)nV}(}(r\ z istpqr,r\tac>ry px^ac>pr¢r\mkmsr0ikta,}'^arVik}(cw

?7BC

h D B© MC

?7BC

h D U ?

h

B©v2C

¤¥ctar0N\ik¦\cpx^ac!}(r\qxcZw|uSr\t z istaun\qn\bc(pxc h

¢r\Xn\msmDpqâcwxcuaqcwqw|lxc>}'âr\io}cZw(£R]_âc{;qcn z

h /` . e

c)2 D ! U

,

F

,

#

F U

,5]

F%$`,'&7c BIVyn$C

h /` .-e c32 D ! U , F ,

F%

U , ]

F%$` , & c BIV0:C

h /` .-e

c)2 D ! U

,GF ,

F% U ,5]

F$`, & c BIVy}#C

h /` . e

5c)2 D ! U , U

,'

F% ! U , ]

F%$`,'&2c BIV z C

h /` e 5c32 D ! U , F

,

F% U

,5]

F$`, &2c BI\\n$C

h /` e

c32 D U

,5]

F%$`,'&2c BI\y:C

h /` e c32 D ! U , F

,

F% !

U , ]

F%$` ,'&2c BI\\}#C

h /` e

c32 D ! U , F ,

#

F% ! U , ]

F%$`, & c BI\ z C

µbdr\taBwp_nymkmYuSrVwqw|ikamkc}(r\bistnypxikr\tw°B¦\c(q{¢c(%Vis¦Vcw|cZ}rVt z ¨6r\«pq^aik z ¨Ér\z c7c(tc(q\{dn\}(}(la'n\}{V£µ

wxc}(r\t z ¨©rV z c_c(tacxV{V¨²n\}}la'n0pqcn\msVr\qi¯pq^ab/iowr\apqnyiktac z ¢r\pq^aclaiz ¢r\'}cJB|§ ¬ (VnMC7i¯pq^r\tacr\

RSR

ÜUT#V+WXY

(15)

pq^ac,iktaualvp!¢rVq}(cw0BI

¬ (yC¡°ªrVJBIv

¬ ( z

C&n\tarypq^ac(uSrVwqwxisaikmki¯p{ ikwpq^ac>r\iktBp!lw|c,r\

n^aik\^amk{w|laD}{v}(msc

z

lai

z

{jikc(m

z

ist B0

¬ ( z

Cnyt

z

¬ (\:C¡£±²t px^Yn0p>mknVwp>}(n\wxc\°

D U , ]

e8LF $` ,

cq£;]_^ac,r\tms{pq^aik

z

¨Ér\

z

cctac(q\{B¨²n\}}la'n0pqc}rVbaiktn0pqisrVt iow

z

c(´tac

z

j{

B|§ ¬ (V}#C7nyt z BIa ¬ (yCji¯p z rBcZw_tarypXn\msmkr0NwxlaD}{v}mkistdnypnymkmI£

:!3:g&_) /= 3&5, /! '# 3&8@/!:;3&) :; &:K,

]_^cd}(mknVwxwr\wx{BtY}'âxrVtar\lYww|pqn\\\cxc z wq}'âc(bdcwr\wxc}¡pqisrVta£sdwxc(c(bpxr.Ycd¦Vc(q{ n\}(}(la'n0pxcâct

n,wxc}(r\t

z

¨©rV

z

c_uaxc

z

io}¡pxikr\t¢rVpx^acwpqxl}pxla'nym

z

ikwxuamon\}(c(bdc(tBpqwXikwlYw|c

z BNPLD nyt

z N C D e;ikt

B|2C'C¡£X]_^ac¢lt

z

nybdctVp'nymxcZw|lm¯pXr\Rpxâc!c¦0nymkln0pqisrVtry6pxâcZw|cbc(pxâr

z

wiowpx^Yn0p°Y¢r\nytj{Ylai

z

pqisbdc

wq}'âcbcV°jpxâcxc>iownn§{dpqrdnV}'âikc(¦\câik\^.c(tc(q\{;n\}}la'n\}({\£.r\qcuaxcZ}iow|cms{V°vuaqr0¦Bi z c z

px^c>¢r\'}cw

c(~a}'^nytaVc z Scpc(ct px^cliz nyt z pq^acdwpqxl}pxlaqcnyppq^ac(ik>istBpqc(xn\}cnyqc!c~anV}¡pxmk{.r\uauSrVwxc z Bº$C¡°

pqâc}(r\lauamkiktaFnymk\rVxispx^b iownypmscZn\w|p!pxîs z ¨Ér\z c(ctac(q\{B¨²n\}(}(la'n0pxcV£)]_âiowikw¦§n\msiz ¢r\nytj{ pqisbdc

wq}'^acbc Bc~vuamkik}(i¯p ¬ ikbumsio}isp°v´Yqw|p|¨«rVXw|cZ}r\t z ¨©rVz c(-pxikbc(¨ÉnV}(}(laqnypxcV°jwxlaD}{v}mkc z rVtaryp+C¡£

= tpqâc}(r\tBpx'nyq{\°apxâcuaxrVuYrBw|c z n\wx{jt}'âqr\tarVlwwp'nyV\c(qc z bdcpqâr z z cZwx}(xikYc z iktFw|cZ}¡pqisrVtFv£Û¹

}nyt¥mscZn z pxr n)pq^ais z ¨Ér\ z c(ctac(q\{cxqr\Z°ªalap¢r\!wxr\bdc,unyxpxio}lmkn\>wq}'^acbc;}(r\baistYn0pxikr\t&£,±Ép!ikw

n\mkwxr z iA;}lm¯pdpxr ´t z n \c(tc('nymuaxikt}(isuamkc.n\wdnySr0¦\cV°Rc~vuamonyiktaist ^j{ wxr\bdc)wq}'^ac(bdc.}rVbaiktn0¨

pqisrVtw>w|^r\lamz {jikc(mz mkcwqw>nyxpxisÝ}ionym6c(tc(q\{.uaqr z l}¡pqisrVtª£)Dr0-c¦\c(Z°Ypxâiown\wx{jt}'âqr\tarVlwXuaqrv}c z laqc

}(r\twxc(q¦\cZw6¦\cmsrv}isp{}(r\tBpxiktjlaisp{nyp«px^acistBpqc(xn\}cV°VnuxrVuYc|p{px^nyp-_n\wRtar\p«pqn\®\ct,istBpxrn\}(}(r\latBp«j{

pq^acc(¦0n\mslnypxikr\tistBpqxr z l}(c z istpq^aikwXunyuSc(Z£

±²t)pxâcwxc BlacmI°jc z iowq}lwqwr\t)p-r\¨6n\t z pqâxcc¨ z ikbctwxisrVtnymDqcwxlam¯p'w-pxâc>¦0nymkiz i¯p{,r\ªpxâcn\Yr0¦Vc

c¦0nymkln0pqisrVtw(£¤¥c!}r\bdun\xcV°B¢r\_bdrVw|p_ctac(q\{B¨²n\}}la'n0pqc}rVlauamkista,wq}'^ac(bdcZw(°Bpx^c!n\}¡pqlnymDSc(^n§¦jikr\la

r\}(r\lauamkikta,nymk\r\qispxâb,wi¯pq^pxâcSc(^n§¦jikr\lauxc z ik}pxc z lwxiktadr\lac¦§n\mslYn0pxikr\tbdcpqâr z £

< "6+ 2)¡

T:g& ,2"!3) 3!3:*6L-8:g& Y ;3^=>:!3,- "!

¤¥c}(r\twxiz c(Rpq^acn\c(qrjc(mon\w|pxio}-qcwxuSr\twxcXryªn>Sn0p7un\tac(mSispx^,iktv´taispxc>n\wxuYcZ}¡p7'n0pqisriktn!wxlauSc('w|rVtaio}

n\is'w|pxqcnyb ?ky°7¹@É£ ]_^ac.ua^j{jwxio}(nym_uaqr\mscb ikwdrVtams{pry¨z ikbdc(twxisrVtnym©£ ]_^ac.un\tac(mHBÂ isY£2C^n\w

rVtacFwxiz cFc~vuSrVwxc z pqr nytNnyikqw|pxqcn\b=nyt z pxâc¥rypqâc(w|iz c pqr w|pxikmsmnyikZ£ ]_âc un\tac(m>}rVtwxiz cxc z

^c(qc)^nVw,n¥msctaypq^aD .

°n¥latais¢r\qb px^aio}'®jtacwqw , D0

. V

°-n«r\lat¥bdr z lamklw

D . CP

Ae

]y°«n r\iowxwxr\t'n0pxikrHD#.

n\t z n z c(twxi¯p{

h D . ) e

0£±Épikw

}(mkn\bduYc z n0p>Srypx^¥c(t z w0BYD .nyt z YD C¡£!]_^cuxcZwxwxlaqc!ry«pq^ac,wpqismkmRnyik>lat z cpq^acunytacm6ikw

Bèlaiz uaqcwqw|laqcn0piktv´taisp{ C¡£

]_âcdYlaiz iowiktj¦Biowq}iz £;]_âc,Sr\lat z nyq{F}rVt z ispxikr\t n0ppqâcdlaizY¬ w|pxql}pxlaqcdistBpxc|nV}c,iownw|mkiku

}(r\t z i¯pqisrVtª°V^ismkcnyp-iktv´taisp{\°jpq^acXliz ikwn\wqw|lbc z }rVtwp'nytBp!Buaqcwqw|laqc3 D

G Y° z ctw|isp{

D . )

Vy°RlYw|c|¨²w|c(p!nV}'^ tBlbSc((" C¡£¥]_âc)wxisbduamkisć z n\tnymk{Bpxio}(n\m-w|pxl z {rVt pxâc

mkiktacn\iktwp'nyaikmki¯p{¥rypqâcun\tac(m!?k+@iown\wxc z lauSr\t pxâcw|^n\msmkr0 w|âcmsm-px^c(r\q{nyt z n´qw|p|¨Ér\ z c

n\uauaqr§~visb,n0pqisrVt;rypx^c!nyc(qr z {jtnybdio}Xpqâc(rVx{âc(qcpxâciktvlact}cr\ pqâqc(c¨z ikbdc(twxisrVtnymªn\c(qr z {B¨

tYnybdik}c&>ScZ}¡pqwXikwtc(\mkc}pxc z B¢px^aiown\uauaqr§~jikb,n0pqisrVtiow_¦§n\msiz ¢r\ " #"

# C£¤^c(t.px^c!wpqxl}pxla'nym

¦Vc(xpxio}(n\m

z

uaqcwqwxlaxc_¢rVq}(cw7r\t,pq^acuYnytacmY}(n\t;Scn\uauaqr§~jikb,n0pqc

z

ikjPRgi

Þ