Modeling Shear Wave Propagation in Biotissue: An Internal Variable Approach to Dissipation

! "#"%$&('))+*-,/.%02143656798:"%;214<>=@?A<4BC1'D=E.CFG<>8H<>IE5J.H7#5K7ML5J.CIE56NENPO21CQR 7#S7I1T=U

79<C3WVD<>=X56<>YZ3J1 F9F9=E.H<C[X;/I.M\56NENP5JFZ<>IE5J.H7W*&]^79021T=&IE;91095J=E14[_IE5J.H7`.Cab'(=E.Cac14NPN.C=:*Z$*9L<C72d%NXeX*

$&;21<>YZ563656IgfhI.i=E143K56<>YZ3Jfh021TI14[_I[_.C=E.H79<>=Ef`<>=EI1T=Efj0956N14<CN1YZ<CNE140`.H7`IE;21<C[_.HO9NIE56[79.H56N14N

F9=E.%09O9[_140jY-f#<iNI1479.HNE56N&[T<C7kFZ=E.lB%56021<iNE56miFG3J1C-79.H7%Ug567Bn<CNE56BC1I14[X;97956o-O21ap.C=0956<>8H72.HNP56NT*(O2=E=P147qI

=E14N14<>=X[P;1_r%FZ3J.H56IENWIE;21(NE;914<>=ts@<lBC1)uZ143609NW567Yv.%02fIE56NPNEO21bI.091TI14[_I!<C790<C7Z<C3JfwT1)[_.C=E.H79<>=EfNI1472.HNE14NT*

xmh<>IE;214mh<>IE5K[T<C3Gmi.%021432.CavIE;95KNDNf%NI14mk%O2IE56365Jw45K728<C7#567I1T=P79<C39NI=X<C567iB><>=P56<>YZ3J1&<>FZF9=E.4r256mh<>IE56.H7iI.

IE;21yoO9<CNP5zUg36567214<>=B-56NP[_.1436<CNEIE56[[_.H79NIE56IEO2IE5JBC1+14o-O9<>IE5J.H7{F9=E.CFv.HN140{Yf/|9OZ728#567}z~4n€Gs<CNF9=E14N147I140

567A}ƒ‚n€*)$&;21mi1TIE;2.%09N„<C790{560214<CN„.HO2IE3K5672140`567`IE;9<>I&FG<>F…1T=<>=E11_r-FG<C7902140/O2Fv.H7k567`IE;Z56Ns).C=PdG*

N<C7{567Z5JIE56<C3W567BC14NIE5J8H<>IE5J.H7tG<M;9.Hmi.C8C14721T.HO9NIgs@.>Ug0956mi147ZNE5J.H79<C3WB%56NE[_.-1436<CNIE5K[8C1T.Hmi1TI=Ef

56N&[_.H7ZNE56021T=E140t*)[email protected]=Pm†567/‡92IE;956N&8C1T.Hmh1TI=EfkYv14;9<4BC14N<CN<M.H721:095Kmi1479NE5J.H7Z<C3…mh.-02143Z<C790

IE;21=E14NEOZ3JIEN@8C14721T=P<>I140/ap=E.Hmˆ5JI„<>=E1[_.HmiFG<>=E140`I.iIE;21.H7210956mh1479NE5J.H79<C3Z=E14NEO936IEN)ap=E.Hm‰}ƒ‚Š€*@"%1TBC1T=P<C3

B><>=P56<>IE5J.H79N&.CaRIE;91+mi.%02143W<>=E1+[_.H79NP56021T=E140W2I.j<C363J.Šs‹ac.C=095zŒv1T=E147qI<CNENEO9miFZIE5J.H79N„<>Yv.HO2I„IE;21143K<CNIE56[

=E14NFv.H79NE1C*# †NIE<>IE56NEIE56[T<C3(NE568H795JuZ[T<C79[_1iI14NEI:56N14mhFZ3J.lfC140I.091TI1T=Pmh56721h56a)IE;21#1_r-I=X</FZ<>=P<Cmh1TI1T=PN

721T1402140/ac.C=[_1T=PIE<C567kB><>=P56<>IE5J.H79N&.Ca!IE;21:mi.-09143W<>=E1+7214[_14NENP<>=Efk567kmi.%02143656728y1_Œv.C=EIENT*

apI1T=B><C365609<>IE5K728#IE;91hmi.-09143!s5JIE;ŽIE;21h[_.HmiFZ<>=X56N.H7ŽI.kF9=E1TB%5J.HO9NuG790956728HN4…mi.C=P1h[_.HmU

FZ365K[T<>I140k8C1T.Hmi1TI=P5J14N<>=E1+021TBC1436.CF…140t*"%56myO936<>IE56.H79N567qBC.H36B-56798<M;21TI1T=E.C8C14721T.HO9N8C1T.Hmi1TI=Efks5JIE;/<

O97956ac.C=Pm=P56728:=PO9797Z56728IE;2=P.HO28H;MIE;91.C=X5J8H5679<C3…mi140956OZmk<y‡021TFv147902147I)mi.%02143Gs;956[X;#[_.H79NP56021T=PN<

=P5J8H5K0h.%[T[T36O9NE5J.H7Mac.C=Xmi140`<C3J.H728yIE;215K79721T=(=X<C0956O9N(.CatIE;218C1T.Hmi1TI=EfC9<C790`<ymi.-09143Zs;Z56[P;#[_.Hm+YZ5K7214N

IE;21`=P56798‘<C790’.%[T[T36O9NE56.H7’<>=P1jFZ=E14N147I140W*“”7•<C7–<>II14miF9IiI.Ami.ŠBC1kI.ls<>=P09NiIE;21kO936IE56mh<>I1j8C.H<C3

.Ca)091TI14[_IE56728kIE;21i3J.%[T<>IE5J.H7Ž.Ca)<`NI1479.HNE56Nap=E.Hm—IE;21i09<>IE<`8H<>IE;21T=E140˜<>IIE;91[X;214NI™s@<C363<C7˜567BC1T=PN1

$&;Z56N@s).C=Edk56N„09140956[T<>I140kI.Mm:f`ap<CmM563Jf#<C7Z0`ac=P56147909NT

5K[P;2.H36<CNRO9dC1@s<CNRYv.C=P7.H7|21TY9=XO9<>=EfM~C~>Z~-567+?A<>I1T=PI.ls7W-1TsD.C=Ed…CI.FZ<>=E147IEN

&.CYv1T=EI<C790–' <>I=P56[T5K<!O2dC1C*“1`;Z<CN[email protected]=Y9=E.CIE;21T=H.H7WD<C790•fC.HO9728C1T=iYZ=E.CIE;21T=

OZNEN14363 *‘ Ni<C7 5J=i|2.C=P[_1/L@=P<>I%(;91j;9<C0’IE;21`.CF9Fv.C=EIEOZ795JIgfŽI.Ž1_r%F…1T=X5J1479[_1jIE;21j[T3K56mh<>I1k<C790

[TO93JIEO9=E1.Ca 0Z5zŒ…1T=P147qI„=E1T8H56.H79NT2Yv.CIE;`ac.C=P145J8H7/<C790/09.Hmi14NIE56[>*

S7‘~-9;956N)a^<>IE;21T==E1TIE5J=E140#ac=P.HmIE;21 5J=@|9.C=P[_1C9<C790#IE;21a^<Cmh5636fi=E143J.%[T<>I140#I.=P1T1479N”U

Yv.C=E.2(Rs;21T=E1`5K[P;2.H36<CN8C=X<C09O9<>I140•ap=E.HmL)147–(*("%mh5JIE;’568H;–"2[P;2.-.H3<CNM"%<C36O909<>I.C=X56<C7“.Ca

IE;21`[T36<CNEN.Ca+~*<lB-56798ŽNEF…147Im:O9[X;’.Ca;956N:365Jap1#<C0EO9NIE5K728{I.˜721Ts†<C790•095zŒv1T=E147I:147B%5J=E.H7%U

mi147IENT IE;21#<CO9IE;2.C=:s<CNy567“72.;O2=P=EfŽI.‘3J14<lBC1j;Z56NNEO2=P=E.HO979095K728HN567=P1T1479NYv.C=E.2b<C790“0914[T5602140

I.h<>II14790/<3J.%[T<C3W795JBC1T=PNE56IgfC*D1=E14[_145JBC140`IE;21.C=EIE;{<>=E.H3K5679<y$14<C[X;956728h|2143K3J.lsN"2[P;2.H36<>=XNE;95JFt

<C790’8C=P<C09OZ<>I140–NEO9mhmh<‘[TO9m36<CO9091Map=E.Hm .C=PIE;–„<>=E.H365679< 8C=X56[TO93JIEO2=X<C3)<C790•$!14[P;97Z56[T<C3&"-IE<>I1

795JBC1T=PNE56Igf`s5JIE;kYG<C[P;2143J.C=! N021T8C=P1T14N567{ F9FG365J140{,<>IE;214mh<>IE56[TN]ps5JIE;<Mmh5K72.C=567kFG;qf%NE56[TNXeX…<C790

,<>IE;214mh<>IE56[TN(09O9[T<>IE56.H7W*

1i=P14[_145JBC140“<kap14363J.ŠsNE;956F‘ap=E.Hm $&;91h\<lB-5K0“<C790˜!O9[T563J1i' <C[Ed><>=P0’|2.HO97909<>IE56.H7Wts;95K[P;

[email protected]<C3K3J.lsx;956mI.:FZO9=PNEO21&<y'(;W*\ <>I@;95KN([P;9.H56[_1.Cat5679NIE5JIEO9IE5J.H79Nb.Cat;9568H;21T=)3J14<>=X79567282* 1Yv1T8H<C7

;956N&8C=P<C09O9<>I1+NEIEO9095J14N&5K7/<>F9FZ3656140jmM<>IE;214mh<>IE56[TN<>I.C=EIE;‘„<>=E.H365679<h"-IE<>I1y7Z5JBC1T=PNE5JI™fj5K7kIE;21a^<C363

.Ca(""2~>v<C790/=E14[_1456BC140<j,{<CNI1T=! N.Ca("%[T561479[_1:\1T8C=E1T1567/ F9FZ3656140/,{<>IE;214mM<>IE56[TN5K7""#2*„?x5JIE;

IE;21M[_.HmhFZ3J1TIE5J.H7˜.CaIE;95KN0956NENE1T=EIE<>IE5J.H7WtIE;91M<CO2IE;2.C=s56363 ;9<4BC1#14<>=P72140;956N\.-[_I.C=y.Ca„'(;95K3J.HN.CFZ;f

021T8C=E1T1+ac=E.Hm +*…*G"-IE<>I1C*

L@1T8H56797956798{567’"%1TF9I14m+Yv1T=4D""$-(;91#s5K363bYv1M14miFG3J.lfC140’<CN<{Fv.HNI”Ug02.%[_I.C=P<C3)ac143K3J.lsˆ<>I

x

?;Z563J1IE;91[_.HmhFZ3J1TIE5J.H7j.Ca!<');W*\y*956N)<I=P14mi147902.HO9N567Z095JB%5609O9<C32<C[T[_.HmiFG3656NE;9mh147qIT25JI56N

[email protected];956798IE;9<>I)[T<C7#Yv1<>IIE<C5679140hs5JIE;9.HO2I(N.Hmi1ac.C=Xm.CaW<+NPO2F9Fv.C=EIDNI=POZ[_IEO2=E1C* ?56IE;MIE;95KND567

mh567Z0Wv 0Ž365JdC1I.k=E14[_.C8H7Z5JwT1hN1TBC1T=P<C3D5K79095JB%5609O9<C3KN„s5JIE;2.HO9Is;9.HmkWIE;956N<C[P;[email protected]Ž72.CI

;9<lBC1+Yv1T147`Fv.HNENE5JYZ361C*

| 5J=PNI.Ca<[email protected]˜3656dC1iI.{=E14[_.C8H7956wT1Mm+f˜<C[T<C0214mM56[h<C790˜IE;914NE56N<C02B%56N.C=l\=4*#:*$*

L<C72d%NT*j$;9<C72d‘fC.HO“ap.C=+fC.HO2=yNEO2F9Fv.C=EI<C7Z0˜1479[_.HO2=P<>8C14mh147qIyIE;2=E.HO28H;9.HO2I+m:f‘8C=X<C09O9<>I1#[T<>=P1T1T=4*

s5K363bap.C=E1TBC1T=iYv1M8C=P<>I1Ta^[email protected]=yfC.HO2=i[_.H72uZ091479[_1j5K7mi1Cb1TBC147•IE;9=E.HO28H;IE;21#IE5Kmi14Nys;2147mh<4f

72.CI;9<4BC1i0214NE1T=EBC140Ž5JIT*<Cm <C3KN.#IE;Z<C72da^O93I.`\=4*5J147$!=P<C7WW\=4*,{<C7ZN..C=<C56021T=4v<C790Ž\=4*

1T8H<CNE; ,{1409;9567W)<C363.Cas;Z56[P;–N1T=PBC140–.H7–m+f•[_.Hmhmh56II1T1C* $&;9<C72dAfC.HO ac.C=hfC.HO9=h5679NE5J8H;Ii<C790

<C02B%56[_1C* 0Z095JIE5J.H79<C3K3JfCZ 0Ž365JdC1+I.`IE;9<C79d{\=4* <C3JFG;Ž"%mM5JIE;WG\=4*+,56[X;9<>143D"%;214<>=E1T=4W\=4*,{1TII1

36O9apN147tR<C790•<C363).Ca&IE;21`NIEO909147qIENys;2.‘FZ<>=EIE5K[T5JFZ<>I140’567AIE;21k F9FZ3656140“,{<>IE;914mh<>IE56[TN=P<C0ZO9<>I1

"-IEO909147qID"-14mh567Z<>=4*tap1T143%IE;9<>I IE;21„ , "Z"s<CNb<[_=PO9[T56<C3FZ<>=EIb567ym:f:<C[T<C0214mh5K[@<C7Z0:FZ=E.Cac14NPNE5J.H79<C3

021TBC143J.CFGmi147qIT-<C790i ap1T1432F9=P5JB%563J1T8C140yI.y;9<4BC1&Yv1T147h<>YG3J1„I.+Yv1&<FZ<>=PIE56[T5JFZ<C7IT*! <C36N.:m:O9NEIb1_r-F9=P14NEN

m:f8C=P<>IE56IEO9021hI.{\=4*#"2;9<C7972.H7Ž?f-7Z721_UVb1T=Ed-=PO2f%NEN1Cs;2./;2143JFv140Žmi1iI=E14mi147Z02.HO9NE3Jfs5JIE;ŽdC1Tf

<CNFv14[_IEN&.CaRIE;956NFZ=E.”14[_IT*

,/fy8C=P<C09OZ<>I1&[T<>=E1T1T=(s<CNDa^O97902140yY-fy<ap14363J.ŠsNE;956F:ap=E.Hm IE;21&\<lB-560M<C790iO9[T5K3J1„'R<C[Pdn<>=X0

|2.HO97Z09<>IE5J.H7WZ<C7Z0/N.hm:OZNI<C[Ed%72.Šs3J14028C1:IE;2.HN1s;9.h<C363J.ls@140{mh1I.MFZ<lf`m:f`YZ56363KN(ap.C=IE;21+FZ<CNI

u9BC1fC14<>=PNT*$!.jIE;21i 02B%56N.C=Pf/'R<C79143 W\=l*.C=Pmh<C7Ž|2=X<C79[T56NTW\=4*+"%;95J=X3J1Tf/,{<C36[_.Hm/t\=l*?A<C36I1T=

,<CNEN1TfC„<C790–\=4* H<Cmi14N#"%IE5JIE;WDIE;9<C79dfC.HO–ap.C=h<C363J.Šs56728˜mi1`I.AYv1k<ŽFZ<>=EIi.CaIE;21 =P<C0ZO9<>I1

"%[X;2.H36<>=PN#F9=E.C8C=P<Cm/* $&;21{5K7qI1T=P<C[_IE56.H79NjIE;9<>IMh;9<lBC1˜;9<C0 s56IE; fC.HOx<C790m+f–ap14363J.Šs =P<C0ZO9<>I1

"%[X;2.H36<>=PNap.C=IE;21iFG<CNI:‚`fC14<>=PN:;9<4BC1#O97902.HO2YZI14093Jf{;21436F…140Žmi1MI./Yv1h<`Y…1TII1T=ymh<>IE;214mh<>IE5K[T56<C7W

<C790ks56363…N1T=EBC1:mh1s)14363W<CN)a^O2=EIE;91T=&m+fk[T<>=E1T1T=4*

&.CYv1T=EID,{1T=PNTq\=4* 5K3JYv1T=EI <CNEI1T=P3J.ls+ C=4\=l*!?x563JYZO9=b"%mM5JIE;<C790IE;21=E14NIb.CaGIE;21„ap<C[TOZ3JIgf567yIE;21

mh<>IE;214mM<>IE56[TNi021TFZ<>=EIEmh147qIi<>Ih.C=EIE; <>=E.H36567Z<{ 8C=P56[TO93JIEO9=P<C3)<C7Z0’$!14[P;Z7956[T<C3&"-IE<>I1/795JBC1T=PNE56IgfC*

#361TacIjfC.HO2=/5679NEIE5JIEO2IE5J.H7 s5JIE;<•YZ<C[P;9143J.C= Nk021T8C=E1T1Cmi.CIE5JB><>I140xI. [_.H7IE567O91Žm:f NEIEO9095J14NT<C790

FZO2=XNEO21+<C7Ž<C02B><C79[_140Ž021T8C=E1T1567‘mh<>IE;214mh<>IE56[TN4*?x5JIE;2.HO2IfC.HO2=NEO2F9Fv.C=EI<C790{147Z[_.HO2=P<>8C14mi147I<CN

<C7jO979021T=E8C=X<C09O9<>I1CHD02.H7 ƒI(Yv14365J1TBC1„IE;9<>I@ s).HOZ360M;9<lBC1mh<C0915JIDIE;Z56NDa^<>=)567#m+fh<C[T<C0914mh56[[T<>=P1T1T=4*

,/fi<>F9FZ=E14[T56<>IE5J.H7M8C.14N(I.ym:fac.C=Pmh1T=(.M[_1mh<>I14NT C.C=P09<C7j,{<CNPNE<C0W+<>IE5J1<lBn<C7Z<>8H;W

=P5KNIgf/@.>Œv1TfC <C[P;2143Rt1TB-fC q56363 &1T14NE1CG<C790L)=X56<C7/ 09<CmhNT*$&;9<C72dk<C363t.CaRfC.HOap.C=;2143JFG56728imi1

8C1TIh<C0EO9NI140•I.˜8C=P<C0ZO9<>I1kNE[P;2.-.H3 )Y….CIE;•<C[T<C0214mM56[T<C363Jf’<C790•N.-[T5K<C363JfC*“$!.AL@=P56<C7Wq56363bL@=P<C7909f

L@1472140956[_IT <C790H<CN.H7•NYv.C=P721C!IE;9<C72d%Nap.C=+IE;21”ap<Cmh5K3Jf {095679721T=XNT ”ap<CmM563Jf /0956NE[TOZNENE5J.H79N4<C790

”a^<Cmh563Jf h.HO2IE5K728HNT*SI N7956[_1+I.k3656BC1+s5JIE;<M8C=P.HO2F.Ca(F…1T.CFG3J1s;2.j<>=E1y8C.H56728jIE;2=E.HO28H;IE;21NE<Cmi1

I=P56<C3KN&<C790/I=X5JYZO936<>IE56.H79NT*D ƒBC1+=E14<C3K3Jf`147”.ŠfC140{IE;91:36<CNI ifC14<>=PNT…365JB%56728.H7 3J14728H<>=E=PfCGmi.C=E1+IE;9<C7

fC.HO{[T<C7{56mh<>8H56721C*

?;Z563J1567`8C=P<C09OZ<>I1:NE[X;2..H3Z5JI&56N&5KmiFv.C=EIE<C7qII.jmh<C567IE<C567k<iYZ<C36<C7Z[_1Yv1TIgs@1T147/YZO9NP567214NEN

<C790ŽFZ3614<CNEO2=E1C*+$;21iNE<4f%56728 363Rs).C=EdŽ<C790Ž72.`FZ36<lfC*J*J* ;9<CNN.Hmi1imi1T=P56II./56IT*"-Fv14[T56<C3!IE;9<C72d%N

8C. .HO2IkI. $!1T=E14NE<"[email protected]=E1Tf?567I.H7W"-I1TBC1“<C790!567909NP<4f,<4fC:"%I1TBC1’"-IE<C7956NP36<4B… fH<C7

"%56NEd-567Z0W…"%<>=P<C; =P.lBC1C!!<CO2=P<j(3636s)14567tG<C790‘1TBC1T=Ef-Yv.-02f{1436N1ys;2.`;9<CNFZ36<4fC140Žap.-.CIYZ<C363!s5JIE;ŽO9N

.H7k"%O97909<lf-N4*R 36N.2-IE;9<C72d%N(I.y1TBC1T=Ef-Yv.-02fi567MIE;21021TFZ<>=EIEmi147I(s;2.:;9<CN)FZ<>=EIE5K[T5JFZ<>I140hs5JIE;Mmi1567

IE;21567I=P<CmyO2=P<C3vNFv.C=EIEN@F9=E.C8C=P<Cm/*D ƒBC1Yv1T147`<FZ<>[email protected][P;9<CmhFZ5J.H79NE;Z5JFMI14<CmhNNE5679[_1(NIE<>=PI140

FZ36<lf-5K728“m:f–u9=PNIhfC14<>=k;21T=P1]ph;9<4BC1ŽIE;21I”UgNE;95J=PIENhI.“FZ=E.lBC1Ž5JIXeX* .-.-036O9[Pd•s5JIE; IE;91{a^O2IEO2=E1

N14<CN.H7ZNT*

t<C36N.m:OZNIR<C[Pd-79.ls3J14098C1m:fa^<Cmh563JfC*R$.m:fFZ<>=E147IENTCWI=PO936f[_.HO9360y72.CIR;Z<4BC1„02.H721<C7qf

.Ca IE;956N„s5JIE;2.HO2I„fC.HOW*$&;9<C79dMfC.HOac.C=&fC.HO9=3J.ŠBC1C…NEO9F9Fv.C=EIT%ac=E1T1+ac.-.-0tZ<C790k8C14721T=X<C363Jfj1TBC1T=EfIE;Z56728

IE;9<>IifC.HO ;Z<4BC1{02.H791kac.C=Mmh1j.ŠBC1T=#IE;91jFG<CNIM‘fC14<>=PNT* H.H7–<C790 OZNEN14363 bIE;Z<C72d-Nhac.C=hNE;Z<>=P56728

m:fA.-0Z0N147ZN1#.Ca;O9mh.C=4 ac.C=FZ36<lf-5K728/B%56021T.‘8H<Cmi14NiO97IE563(567ZNE<C721#;9.HO2=PN+5K7“IE;21`mi.C=P7Z567282b<C790

567{8C14721T=P<C3 v;2143JFZ5K728hmi1+I.`=E14mh14m+Yv1T=79.CII.`NFv14790/<C363.Ca(m:[email protected]=Ed%567282* 36N.2… 03656dC1I.

IE;9<C72dh$!.Hmˆ<C790`<>IE5J1?563Kmi.CIE;W%<C790 1TYv14[T[T< .-0Z5J.2*!?x;21TIE;21T=s@1s@1T=E18C.H56728:I.IE;21mh.lB%5J14N

]p8C.-.-0/<C7Z0kYZ<C0GeX2IE<>d%56728h<i=P.H<C0kI=P5JF`I.h?x5636365K<CmhNYZO2=P82q.C= EO9NI„FZ3K<4f%56728Yv.H<>=P0`8H<Cmi14N<>I;2.Hmi1C

5JIEN&<C36s@<lf-NY…1T147k<C7<C02BC147IEO2=E1C* D.HO<>=E1IE;21Yv14NIT*

| 5679<C363JfC-m:O9NEI@=P14[_.C8H795JwT1+<>=P147 D.Cd-3J1TfC*)$&;9<C72d#fC.HOkac.C=fC.HO2=„1479[_.HO2=P<>8C14mh147qITGfC.HO2=

3J.ŠBC1Ct<C790{1TBC1T=PfIE;95K728#IE;Z<>IfC.HOŽ02.2*$&;21yFZ<CNI MfC14<>=PN;9<4BC1Yv1T147s).H79091T=EapOZ3 G<C790;2.CFv1:IE;9<>I

x

! "

# $% &')(*+,' % #

- .

)(! 0/1 2

% 3

-*6~ '(;f%NE56[T<C3 1T.Hmh1TI=Ef`.CaRIE;91:,/.%02143 *****+*******+*******+***** #

-* $&;21)oOZ<>IE5J.H79N„.Cab,/.CIE56.H7 *+********+*******+*******+***** ‚

-*-*6~ $&;91:@.H7qIE5K7O956Igf`(o-O9<>IE5J.H7 *****+*******+*******+***** ‚

-*-* $&;91+,/.Hmi147IEO9m (o-O9<>IE5J.H7ˆ*****+*******+*******+*****

-*-* 7/ 3JI1T=P79<>IE5JBC1:|2.C=PmyO936<>IE5J.H7k.Ca IE;21+,{.Hmi147IEO9m )oOZ<>IE5J.H79N‰*+***** ~

-*-*# $&;91(o-O9<>IE5J.H79N„.Cab,{.CIE5J.H7 *****+*******+*******+***** ~4‚

-* |2.C=PmyO936<>IE56.H7/.CaRIE;[email protected](o-O9<>IE5J.H7ZN*******+*******+***** ~$

-*-*6~ )36<CNIE56[ 14NFv.H79N1 **+********+*******+*******+***** ~!

-*-* $&;91 &1409O9[_140 &1436<nr2<>IE5J.H7{|ZO979[_IE5J.H7 *******+*******+***** "

-*-* $&;91S7I1T=P79<C3WVD<>=X56<>YZ3J1+,{.-09143t FZF9=E.4r256mh<>IE56.H7#**+*******+***** "

-*# 14721T=P5K[$&;21T.C=E1TIE56[T<C3!,/.%02143 *******+*******+*******+***** %~

-*‚ @.HmiFGO2IE<>IE5J.H79<C3,{.%021436N`***+********+*******+*******+***** C

-*‚-*6~ +~ UP~_E"-V ******+********+*******+*******+***** 

-*‚-* ŠUP~_E"-V ******+********+*******+*******+***** #

-*‚-* ŠUP~_E"-V ******+********+*******+*******+***** C‚

-*‚-*# +~ U™nE"-V ******+********+*******+*******+***** $

4 5

!6

%

7'8

.

)(!9 ;:<='8?>

%

A@B/C

%

&

%

EDF&! =

-6G

-*6~ @.HmiFGO2IE<>IE5J.H79<C3,{1TIE;2.%09N–**+********+*******+*******+***** 

-*6~>*6~ "%<CmiFG3J1 =P560 1TuZ7214mi147I"-IEO909fy*+*******+*******+***** C

-* @.HmiFGO2IE<>IE5J.H79<C3 14NEO93JIEN:***+********+*******+*******+***** #

-* "-IE<>IE56NEIE56[T<C3,{[email protected]<>=P5KN.H7 *******+*******+*******+*****

3 H

/1 2

%

$% I

%

.

'

5

/KJ! L"NMOLI/CL&0L

#2*6~>*6~ Dr%<Cmh5K7956728IE;21DŒ…14[_I.CaR\1479NE56Igf`?56IE;9567jIE;21:,{.-09143h*****+***** #

#2*6~>* $&;91SmiFv.C=EIE<C7Z[_1.CaRV56NE[_.-1436<CNIE5K[T5JIgf`567/,{.-02143K56728ibŒv.C=EIEN†***+***** #

#2*6~>* ”miF9=E.ŠBC14mi147I.CaRIE;21+1TI1T=E.C8C14721T.HO9N,/.%02143Ž***+*******+***** ‚

#2* ”79[_.C=EFv.C=P<>IE56728h<i‡M\1TFv1479091479[_f#”7I.hIE;21+,{.-02143*****+*******+***** "

#2* @.Hm:YZ56795K728IE;21 56798C140 1T.Hmi1TI=Ef{,{.-09143t<C790kIE;21‡M\1TFv1479091479[_f`,{.%02143–*** #

$%

IL' ! 9/

.

L8)(I

%

( DF&! &

# #

‚-*6~ ”7qBC1T=PNE1+'D=E.CYG3J14m ,/1TIE;9.-02.H36.C8Cf*******+*******+*******+***** ~ "2~

‚-* ”7qBC1T=PNE1+'D=E.CYG3J14m &14NEOZ3JIEN‹**+********+*******+*******+***** ~ "

‚-*-*6~ 7k”795JIE56<C3v”7qBC14NEIE5J8H<>IE5J.H7k.Ca IE;21”7BC1T=PN1'D=P.CYZ3J14m *******+***** ~ "

‚-*-* 1TuZ7956728IE;21y,/14NE;/ac.C=&IE;91S7BC1T=PN1:'D=E.CYZ3614m***+*******+***** ~ "#

‚-*-* ”79[_=E14<CNE5K728iIE;21+O9m:Y…1T=„.Ca \<>IE<M.-0914N567`IE;21”7BC1T=PN1+'(=E.CYZ3J14m **** ~ "H‚

‚-*-*# 1TB-56NP5JIE56728IE;21”7qBC1T=XN1+'D=P.CYZ3J14mˆ.H7{<M.H<>=PN1T=,{14NE; *****+***** ~ "$

‚-* ”7qBC14NIE568H<>IE56728hIE;21:bŒv14[_IEN&.Ca IE;21+,<>I1T=P56<C3' <>=P<Cmh1TI1T=PN&.H7kIE;91S7BC1T=PN1:'D=E.CYZ3614m ~ "

5

%

+L &

% ##

~>*6~ $RO2=EYZO936147qIYZ3J.-.%0Z.ls 8C14791T=P<>I140/Y-fk<iNI1472.HNE56N *****+*******+***** 

-*6~ ”3636O9NI=X<>IE5J.H7j.CaRIE;91FZ;f-NE5K[T<C3v8C1T.Hmi1TI=Efk[_.H79NE56091T=E140k567k.HO2=&mh.-02143K567281_Œ….C=PIENT* ** ‚

-* 7/<>=EYZ5JI=X<>=Ef#143614mi147qI&5K7k<iFv.H36<>=&[_..C=X095679<>I1+NEf-NI14m **+*******+***** $

-* ”3636O9NI=X<>IE5J.H7j.CaRIE;91Bn<>=X5J.HO9N„O97956I@BC14[_I.C=XNO9NE140k567`.HO2=021T=X5JBn<>IE56.H7W*“***+*****

-*# "-I=E14NPN14N&1_r%1T=EI140/.H7{<C7/<>=EYZ5JI=X<>=EfMFv.H36<>=„143J14mh147qI*****+*******+***** ~C~

-*6~ .C=Pmh<C365JwT140{ [T[_143J1T=X<>IE5J.H7{09<>IE<hF9=E14N147I140/567A}ƒ‚n€* ****+*******+***** "

-* 'R.HNE5JIE5JBC1:<C790/721T8H<>IE5JBC1:[P;9<>=P<C[_I1T=X56NIE56[TN567qI1T=X<C[_IE56728hs56IE;k02.Hmh<C567`Yv.HO9790Z<>=P5J14N** %~

-* 56miFGO936N109<>IE<hO9NE140/<CN„Yv.HO97909<>=Pf#09<>IE<h5K7A}ƒ‚n€“*****+*******+***** C

-*# @.HmiFG<>=P56N.H7`.Cab :~ UP~_"%V=P14NEO93JIENI.M0Z<>IE<%* *******+*******+***** C‚

-*‚ @.HmiFG<>=P56N.H7`.Cab ŠUP~_"%V=P14NEO93JIENI.M0Z<>IE<%* *******+*******+***** C‚

-*$ @.HmiFG<>=P56N.H7`.Cab ŠUP~_"%V=P14NEO93JIENI.M0Z<>IE<%* *******+*******+***** $

-* @.HmiFG<>=P56N.H7`.Cab :~ U™n"%V=P14NEO93JIENI.M0Z<>IE<%* *******+*******+***** $

-* @.HmiFG<>=P56N.H7.Ca`~T\ <C[T[_14361T=P<>IE5J.H7‹09<>IE<•I. >\<>F9FZ=E.4r256mh<>IE5J.H7.Cay<C[T[_143J1T=P<>IE5J.H7

[_.HmiFZO9I140{O9NE5K728imi.-09143W ŠU™nE"-Vy* ****+*******+*******+***** #"

#2*6~ ,{.-02143 1T.Hmi1TI=Efks56IE;k<hO9795Jap.C=Pm =P56798y.Ca <h095JŒ…1T=E147I&mh<>I1T=P5K<C3A****+***** #

#2* ,{.-0956u9140k5672FZO9I@a^O979[_IE56.H7`s5JIE;`wT1T=E.MNEI14<C02fkNIE<>I1 ****+*******+***** ##

#2* Vb143J.%[T5JIgf`=E14NPO93JIEN„ap.C=&IE;21B><>=P5J.HO9N;21TI1T=E.C8C14721T.HO9N8C1T.Hmi1TI=P5J14N<>I&I "%*""2~C‚ *** #q‚

#2*# Vb143J.%[T5JIgf`=E14NPO93JIEN„ap.C=&IE;21B><>=P5J.HO9N;21TI1T=E.C8C14721T.HO9N8C1T.Hmi1TI=P5J14N<>I&I "%*"" *** #q‚

#2*‚ Vb143J.%[T5JIgf`=E14NPO93JIEN„ap.C=&IE;21B><>=P5J.HO9N;21TI1T=E.C8C14721T.HO9N8C1T.Hmi1TI=P5J14N<>I&I "%*""$"H *** # $

#2*$ Vb143J.%[T5JIgf`=E14NPO93JIEN„ap.C=&IE;21B><>=P5J.HO9N;21TI1T=E.C8C14721T.HO9N8C1T.Hmi1TI=P5J14N<>I&I "%*"" "$ *** # $

#2* Vb143J.%[T5JIgf`=E14NPO93JIEN„ap.C=&IE;21B><>=P5J.HO9N;21TI1T=E.C8C14721T.HO9N8C1T.Hmi1TI=P5J14N<>I&I "%*"2~4%~ *** #

#2* Vb143J.%[T5JIgf`=E14NPO93JIEN„ap.C=&IE;21B><>=P5J.HO9N;21TI1T=E.C8C14721T.HO9N8C1T.Hmi1TI=P5J14N<>I&I "%*"H# *** #

#2* &14NPO93JIEN„ap.C= ap.C=&Bn<>=Pf-56798iBn<C36O914N.CaRIE;91=E1436<nr2<>IE5J.H7kFZ<>=P<Cmh1TI1T=4k<>II "%*""2~4‚ #

#2*6~ " &14NPO93JIEN„ap.C= &ap.C=&Bn<>=Pf-56798iBn<C36O914N.CaRIE;91=E1436<nr2<>IE5J.H7kFZ<>=P<Cmh1TI1T=4k<>II "%*"" ‚"

#2*6~C~ &14NPO93JIEN„ap.C= &ap.C=&Bn<>=Pf-56798iBn<C36O914N.CaRIE;91=E1436<nr2<>IE5J.H7kFZ<>=P<Cmh1TI1T=4k<>II "%*"2~4%~ ‚"

#2*6~4 &14NPO93JIEN„ap.C= &ap.C=&Bn<>=Pf-56798iBn<C36O914N.CaRIE;91=E1436<nr2<>IE5J.H7kFZ<>=P<Cmh1TI1T=4k<>II "%*"2~ C ‚%~

#2*6~ &14NPO93JIEN„ap.C= &ap.C=&Bn<>=Pf-56798iBn<C36O914N.CaRIE;91=E1436<nr2<>IE5J.H7kFZ<>=P<Cmh1TI1T=4k<>II "%*"H# ‚%~

#2*6~ # &14NPO93JIEN„ap.C= &ap.C=&Bn<>=Pf-56798iBn<C36O914N.CaRIE;91=E1436<nr2<>IE5J.H7kFZ<>=P<Cmh1TI1T=4k<>II "%*""# ‚C

#2*6~$ &14NPO93JIEN„ap.C= &ap.C=&Bn<>=Pf-56798iBn<C36O914N.CaRIE;91=E1436<nr2<>IE5J.H7kFZ<>=P<Cmh1TI1T=4k<>II "%*"# ‚

#2*6~! &14NPO93JIEN„ap.C= &ap.C=&Bn<>=Pf-56798iBn<C36O914N.CaRIE;91=E1436<nr2<>IE5J.H7kFZ<>=P<Cmh1TI1T=4k<>II "%*"$" ‚

#2*6~ &14NPO93JIEN„ap.C= &ac.C=Bn<>=Ef%56728B><C36O214N„.Ca IE;21=P1436<nr%<>IE56.H7kFZ<>=P<Cmi1TI1T=lk<>II "%*""" ‚#

#2*6~ &14NPO93JIEN„ap.C= &ac.C=Bn<>=Ef%56728B><C36O214N„.Ca IE;21=P1436<nr%<>IE56.H7kFZ<>=P<Cmi1TI1T=lk<>II "%*""C ‚#

#2*" &14NPO93JIEN„ap.C= &ac.C=Bn<>=Ef%56728B><C36O214N„.Ca IE;21=P1436<nr%<>IE56.H7kFZ<>=P<Cmi1TI1T=lk<>II "%*"" ‚C‚

#2*%~ &14NPO93JIEN„ap.C= ac.C=Bn<>=Ef%56728B><C36O214N„.Ca IE;21=P1436<nr%<>IE56.H7kFZ<>=P<Cmi1TI1T=lk<>II "%*"2~ # $ ‚C‚

#2*C &14NPO93JIEN„ap.C= &ac.C=Bn<>=Ef%56728B><C36O214N„.Ca IE;21=P1436<nr%<>IE56.H7kFZ<>=P<Cmi1TI1T=lk<>II "%*"2~# ‚$

#2* &14NPO93JIEN„ap.C= &ac.C=Bn<>=Ef%56728B><C36O214N„.Ca IE;21=P1436<nr%<>IE56.H7kFZ<>=P<Cmi1TI1T=lk<>II "%*"H# ‚$

#2*# &14NPO93JIEN„ap.C= &ac.C=Bn<>=Ef%56728B><C36O214N„.Ca IE;21=P1436<nr%<>IE56.H7kFZ<>=P<Cmi1TI1T=lk<>II "%*"CC‚ ‚

#2*C‚ &14NPO93JIEN„ap.C= &ac.C=Bn<>=Ef%56728B><C36O214N„.Ca IE;21=P1436<nr%<>IE56.H7kFZ<>=P<Cmi1TI1T=lk<>II "%*"H‚"# ‚

#2*$ &14NPO93JIEN„ap.C= ac.C=Bn<>=Ef%56728B><C36O214N„.Ca IE;21=P1436<nr%<>IE56.H7kFZ<>=P<Cmi1TI1T=lk<>II "%*"$# ‚

#2* &14NPO93JIEN„ap.C= &ac.C=IE;218C1T.Hmi1TI=Efk[_.HmiFZ=P56N140`.Cab095zŒv1T=E147I&mh<>I1T=P56<C3KNT2I "%*""2~C‚ $%~

#2* &14NPO93JIEN„ap.C= ac.C=IE;218C1T.Hmi1TI=Efk[_.HmiFZ=P56N140`.Cab095zŒv1T=E147I&mh<>I1T=P56<C3KNT2I "%*""* $%~

#2* &14NPO93JIEN„ap.C= &ac.C=IE;218C1T.Hmi1TI=Efk[_.HmiFZ=P56N140`.Cab095zŒv1T=E147I&mh<>I1T=P56<C3KNT2I "%*""$"H $C

#2*" &14NPO93JIEN„ap.C= &ac.C=IE;218C1T.Hmi1TI=Efk[_.HmiFZ=P56N140`.Cab095zŒv1T=E147I&mh<>I1T=P56<C3KNT2I "%*"" "$ $C

#2*%~ &14NPO93JIEN„ap.C= &ac.C=IE;218C1T.Hmi1TI=Efk[_.HmiFZ=P56N140`.Cab095zŒv1T=E147I&mh<>I1T=P56<C3KNT2I "%*"2~4%~ * $

#2*C &14NPO93JIEN„ap.C= &ac.C=IE;218C1T.Hmi1TI=Efk[_.HmiFZ=P56N140`.Cab095zŒv1T=E147I&mh<>I1T=P56<C3KNT2I "%*"H# * $

#2* &14NPO93JIEN„ap.C= ac.C=IE;218C1T.Hmi1TI=Efk[_.HmiFZ=P56N140`.Cab095zŒv1T=E147I&mh<>I1T=P56<C3KNT2I "%*""# * $#

#2*# &14NPO93JIEN„ap.C= &ac.C=IE;218C1T.Hmi1TI=Efk[_.HmiFZ=P56N140`.Cab095zŒv1T=E147I&mh<>I1T=P56<C3KNT2I "%*"$C‚* $#

#2*C‚ &14NPO93JIEN„ap.C= &ac.C=IE;218C1T.Hmi1TI=Efk[_.HmiFZ=P56N140`.Cab095zŒv1T=E147I&mh<>I1T=P56<C3KNT2I "%*"# * $C‚

#2*$ ”miF9=E.ŠBC140/=E14NEOZ3JIENac.C= &ap.C=&IE;21+=P56728C140`8C1T.Hmi1TI=PfCZI "%*""-******+***** $

#2* ”miF9=E.ŠBC140/=E14NEOZ3JIENac.C= &ap.C=&IE;21+=P56728C140`8C1T.Hmi1TI=PfCZI "%*"" %~>******+***** $

#2* ”miF9=E.ŠBC140/=E14NEOZ3JIENac.C= ap.C=&IE;21+=P56728C140`8C1T.Hmi1TI=PfCZI "%*"2~4%~>******+***** $

#2* ”miF9=E.ŠBC140/=E14NEOZ3JIENac.C= &ap.C=&IE;21+=P56728C140`8C1T.Hmi1TI=PfCZI "%*"2~ C-******+***** $

#2*#"”miF9=E.ŠBC140/=E14NEOZ3JIENac.C= ap.C=&IE;21+=P56728C140`8C1T.Hmi1TI=PfCZI "%*"HC-******+***** $

#2*#9~’”miF9=E.ŠBC140/=E14NEOZ3JIENac.C= &ap.C=&IE;21+=P56728C140`8C1T.Hmi1TI=PfCZI "%*"$C‚-******+***** $

#2*#q 1T.Hmi1TI=Pfks5JIE;`.%[T[T36O9NE5J.H7k<C36.H728h5679721T=„=X<C0956O9N ******+*******+***** "

#2*# &14NPO93JIEN„ap.C= &ac.C=IE;218C1T.Hmi1TI=Ef`s56IE;k<C7/.%[T[T36O902140k567Z721T==P<C0956O9N4-I "%*""2~4 ** >

#2*## &14NPO93JIEN„ap.C= &ac.C=IE;218C1T.Hmi1TI=Ef`s56IE;k<C7/.%[T[T36O902140k567Z721T==P<C0956O9N4-I "%*"" ** >

#2*#q‚ &14NPO93JIEN„ap.C= ac.C=IE;218C1T.Hmi1TI=Ef`s56IE;k<C7/.%[T[T36O902140k567Z721T==P<C0956O9N4-I "%*"2~4%~‰**

#2*# $ &14NPO93JIEN„ap.C= &ac.C=IE;218C1T.Hmi1TI=Ef`s56IE;k<C7/.%[T[T36O902140k567Z721T==P<C0956O9N4-I "%*"2~$C **

#2*# &14NPO93JIEN„ap.C= &ac.C=IE;218C1T.Hmi1TI=Ef`s56IE;k<C7/.%[T[T36O902140k567Z721T==P<C0956O9N4-I "%*"HC ** #

#2*# &14NPO93JIEN„ap.C= &ac.C=IE;218C1T.Hmi1TI=Ef`s56IE;k<C7/.%[T[T36O902140k567Z721T==P<C0956O9N4-I "%*"#" ** #

#2*# &14NPO93JIEN„ap.C=ac.C=IE;218C1T.Hmi1TI=Ef`s56IE;k<C7/.%[T[T36O902140k567Z721T==P<C0956O9N4-I "%*""2~4 ** >‚

#2*‚" &14NPO93JIEN„ap.C=ac.C=IE;218C1T.Hmi1TI=Ef`s56IE;k<C7/.%[T[T36O902140k567Z721T==P<C0956O9N4-I "%*"" ** >‚

#2*‚%~ &14NPO93JIEN„ap.C=ac.C=IE;218C1T.Hmi1TI=Ef`s56IE;k<C7/.%[T[T36O902140k567Z721T==P<C0956O9N4-I "%*"2~4%~‰** $

#2*‚C &14NPO93JIEN„ap.C= ac.C=IE;218C1T.Hmi1TI=Ef`s56IE;k<C7/.%[T[T36O902140k567Z721T==P<C0956O9N4-I "%*"2~$C ** $

#2*‚ &14NPO93JIEN„ap.C=ac.C=IE;218C1T.Hmi1TI=Ef`s56IE;k<C7/.%[T[T36O902140k567Z721T==P<C0956O9N4-I "%*"HC **

#2*‚# &14NPO93JIEN„ap.C=ac.C=IE;218C1T.Hmi1TI=Ef`s56IE;k<C7/.%[T[T36O902140k567Z721T==P<C0956O9N4-I "%*"#" **

#2*‚C‚"%mh<C3K3J1T=NP[T<C3J1:=P14NEO93JIENac.C= ap.C=IE;21y8C1T.Hmi1TI=Ef{s5JIE;<C7‘.%[T[T36O902140‘5679791T==P<C095KO9NT

I "%*""2~4#****+*******+********+*******+*******+*****

#2*‚$"%mh<C3K3J1T=NP[T<C3J1:=P14NEO93JIENac.C= ap.C=IE;21y8C1T.Hmi1TI=Ef{s5JIE;<C7‘.%[T[T36O902140‘5679791T==P<C095KO9NT

#2*‚x"%mh<C3K3J1T=NP[T<C3J1:=P14NEO93JIENac.C= ap.C=IE;21y8C1T.Hmi1TI=Ef{s5JIE;<C7‘.%[T[T36O902140‘5679791T==P<C095KO9NT

I "%*"2~4%~y****+*******+********+*******+*******+*****

#2*‚ "%mh<C3K3J1T=NP[T<C3J1:=P14NEO93JIENac.C= ap.C=IE;21y8C1T.Hmi1TI=Ef{s5JIE;<C7‘.%[T[T36O902140‘5679791T==P<C095KO9NT

I "%*"2~$C#****+*******+********+*******+*******+*****

#2*‚"%mh<C3K3J1T=NP[T<C3J1:=P14NEO93JIENac.C= ap.C=IE;21y8C1T.Hmi1TI=Ef{s5JIE;<C7‘.%[T[T36O902140‘5679791T==P<C095KO9NT

I "%*"HC#****+*******+********+*******+*******+***** "

#2*$"‹"%mh<C3K3J1T=NP[T<C3J1:=P14NEO93JIENac.C= ap.C=IE;21y8C1T.Hmi1TI=Ef{s5JIE;<C7‘.%[T[T36O902140‘5679791T==P<C095KO9NT

I "%*"#" M****+*******+********+*******+*******+***** "

#2*$%~ "%mh<C3K3J1T=NP[T<C3J1:=P14NEO93JIENac.C=+ap.C=IE;21y8C1T.Hmi1TI=Ef{s5JIE;<C7‘.%[T[T36O902140‘5679791T==P<C095KO9NT

I "%*""2~4#****+*******+********+*******+*******+***** %~

#2*$C"%mh<C3K3J1T=NP[T<C3J1:=P14NEO93JIENac.C= ap.C=IE;21y8C1T.Hmi1TI=Ef{s5JIE;<C7‘.%[T[T36O902140‘5679791T==P<C095KO9NT

I "%*""#****+*******+********+*******+*******+***** %~

#2*$"%mh<C3K3J1T=NP[T<C3J1:=P14NEO93JIENac.C= ap.C=IE;21y8C1T.Hmi1TI=Ef{s5JIE;<C7‘.%[T[T36O902140‘5679791T==P<C095KO9NT

I "%*"2~4%~y****+*******+********+*******+*******+***** C

#2*$# "%mh<C3K3J1T=NP[T<C3J1:=P14NEO93JIENac.C=+ap.C=IE;21y8C1T.Hmi1TI=Ef{s5JIE;<C7‘.%[T[T36O902140‘5679791T==P<C095KO9NT

I "%*"2~$C#****+*******+********+*******+*******+***** C

#2*$C‚"%mh<C3K3J1T=NP[T<C3J1:=P14NEO93JIENac.C=+ap.C=IE;21y8C1T.Hmi1TI=Ef{s5JIE;<C7‘.%[T[T36O902140‘5679791T==P<C095KO9NT

I "%*"HC#****+*******+********+*******+*******+*****

#2*$$"%mh<C3K3J1T=NP[T<C3J1:=P14NEO93JIENac.C=+ap.C=IE;21y8C1T.Hmi1TI=Ef{s5JIE;<C7‘.%[T[T36O902140‘5679791T==P<C095KO9NT

I "%*"#" M****+*******+********+*******+*******+*****

#2*$ 'D=P.CFZ<>8H<>IE5J.H7.Ca=P<C0956<C3BC143J.%[T5JIgf #s<4BC1ŽIE;2=P.HO28H; <8C1T.Hmi1TI=Ef s5JIE; <;95J8H;93Jf

021479NE1C9FZO2=E1436fh1436<CNIE56[+mh<>I1T=P56<C3W<C790{<C7k.-[T[T3KO9NE5J.H7`.H7{IE;215679721T=„=X<C0956O9NT-I "%*"" C‚

#2*$ 'D=P.CFZ<>8H<>IE5J.H7.Ca=P<C0956<C3BC143J.%[T5JIgf s<4BC1ŽIE;2=P.HO28H; <8C1T.Hmi1TI=Ef s5JIE; <;95J8H;93Jf

021479NE1C9FZO2=E1436fh1436<CNIE56[+mh<>I1T=P56<C3W<C790{<C7k.-[T[T3KO9NE5J.H7`.H7{IE;215679721T=„=X<C0956O9NT-I "%*"" %~ C‚

#2*$'D=P.CFZ<>8H<>IE5J.H7.Ca=P<C0956<C3BC143J.%[T5JIgf s<4BC1ŽIE;2=P.HO28H; <8C1T.Hmi1TI=Ef s5JIE; <;95J8H;93Jf

021479NE1C9FZO2=E1436fh1436<CNIE56[+mh<>I1T=P56<C3W<C790{<C7k.-[T[T3KO9NE5J.H7`.H7{IE;215679721T=„=X<C0956O9NT-I "%*"2~4%~ $

#2*"x'D=P.CFZ<>8H<>IE5J.H7.Ca=P<C0956<C3BC143J.%[T5JIgf #s<4BC1ŽIE;2=P.HO28H; <8C1T.Hmi1TI=Ef s5JIE; <;95J8H;93Jf

021479NE1C9FZO2=E1436fh1436<CNIE56[+mh<>I1T=P56<C3W<C790{<C7k.-[T[T3KO9NE5J.H7`.H7{IE;215679721T=„=X<C0956O9NT-I "%*"HC $

#2*-~•'D=P.CFZ<>8H<>IE5J.H7.Ca=P<C0956<C3BC143J.%[T5JIgf #s<4BC1ŽIE;2=P.HO28H; <8C1T.Hmi1TI=Ef s5JIE; <;95J8H;93Jf

021479NE1C9FZO2=E1436fh1436<CNIE56[+mh<>I1T=P56<C3W<C790{<C7k.-[T[T3KO9NE5J.H7`.H7{IE;215679721T=„=X<C0956O9NT-I "%*"H #

#2*>'D=P.CFZ<>8H<>IE5J.H7.Ca=P<C0956<C3BC143J.%[T5JIgf #s<4BC1ŽIE;2=P.HO28H; <8C1T.Hmi1TI=Ef s5JIE; <;95J8H;93Jf

021479NE1C9FZO2=E1436fh1436<CNIE56[+mh<>I1T=P56<C3W<C790{<C7k.-[T[T3KO9NE5J.H7`.H7{IE;215679721T=„=X<C0956O9NT-I "%*"#"$

#2*'D=P.CFZ<>8H<>IE5J.H7#.CaWIE<C728C147qIE5K<C3ZBC143J.%[T5JI™f „s@<lBC1IE;9=E.HO28H;M<:8C1T.Hmi1TI=EfMs5JIE;h<:;95J8H;93Jf

021479NE1C9FZO2=E1436fh1436<CNIE56[+mh<>I1T=P56<C3W<C790{<C7k.-[T[T3KO9NE5J.H7`.H7{IE;215679721T=„=X<C0956O9NT-I "%*""

#2* #'D=P.CFZ<>8H<>IE5J.H7#.CaWIE<C728C147qIE5K<C3ZBC143J.%[T5JI™f „s@<lBC1IE;9=E.HO28H;M<:8C1T.Hmi1TI=EfMs5JIE;h<:;95J8H;93Jf

021479NE1C9FZO2=E1436fh1436<CNIE56[+mh<>I1T=P56<C3W<C790{<C7k.-[T[T3KO9NE5J.H7`.H7{IE;215679721T=„=X<C0956O9NT-I "%*"" %~

#2*>‚'D=P.CFZ<>8H<>IE5J.H7#.CaWIE<C728C147qIE5K<C3ZBC143J.%[T5JI™f s@<lBC1IE;9=E.HO28H;M<:8C1T.Hmi1TI=EfMs5JIE;h<:;95J8H;93Jf

021479NE1C9FZO2=E1436fh1436<CNIE56[+mh<>I1T=P56<C3W<C790{<C7k.-[T[T3KO9NE5J.H7`.H7{IE;215679721T=„=X<C0956O9NT-I "%*"2~4%~

#2*$'D=P.CFZ<>8H<>IE5J.H7#.CaWIE<C728C147qIE5K<C3ZBC143J.%[T5JI™f „s@<lBC1IE;9=E.HO28H;M<:8C1T.Hmi1TI=EfMs5JIE;h<:;95J8H;93Jf

021479NE1C9FZO2=E1436fh1436<CNIE56[+mh<>I1T=P56<C3W<C790{<C7k.-[T[T3KO9NE5J.H7`.H7{IE;215679721T=„=X<C0956O9NT-I "%*"HC

#2* 'D=P.CFZ<>8H<>IE5J.H7#.CaWIE<C728C147qIE5K<C3ZBC143J.%[T5JI™f „s@<lBC1IE;9=E.HO28H;M<:8C1T.Hmi1TI=EfMs5JIE;h<:;95J8H;93Jf

021479NE1C9FZO2=E1436fh1436<CNIE56[+mh<>I1T=P56<C3W<C790{<C7k.-[T[T3KO9NE5J.H7`.H7{IE;215679721T=„=X<C0956O9NT-I "%*"H # "

#2* 'D=P.CFZ<>8H<>IE5J.H7#.CaWIE<C728C147qIE5K<C3ZBC143J.%[T5JI™f „s@<lBC1IE;9=E.HO28H;M<:8C1T.Hmi1TI=EfMs5JIE;h<:;95J8H;93Jf

#2* <C0Z56<C3DBC143J.%[T5JI™f–] e=E14NEO93JIENac.C=y</8C1T.Hmi1TI=Ef˜s5JIE;A<{NP365J8H;IE3Jf‘mh.C=E1M021479NE1CR3J14NPN

B%56NE[_.-1436<CNIE56[=P5K728i<C790/<C7k.%[T[T36O9NE56.H7W2I "%*"" %~ ******+*******+***** C

#2*" <C0Z56<C3DBC143J.%[T5JI™f–] e=E14NEO93JIENac.C=y</8C1T.Hmi1TI=Ef˜s5JIE;A<{NP365J8H;IE3Jf‘mh.C=E1M021479NE1CR3J14NPN

B%56NE[_.-1436<CNIE56[=P5K728i<C790/<C7k.%[T[T36O9NE56.H7W2I "%*"2~4%~ ******+*******+***** C

#2*%~ <C0Z56<C3DBC143J.%[T5JI™f–] e=E14NEO93JIENac.C=y</8C1T.Hmi1TI=Ef˜s5JIE;A<{NP365J8H;IE3Jf‘mh.C=E1M021479NE1CR3J14NPN

B%56NE[_.-1436<CNIE56[=P5K728i<C790/<C7k.%[T[T36O9NE56.H7W2I "%*"2~$C ******+*******+*****

#2*C <C0Z56<C3DBC143J.%[T5JI™f–] e=E14NEO93JIENac.C=y</8C1T.Hmi1TI=Ef˜s5JIE;A<{NP365J8H;IE3Jf‘mh.C=E1M021479NE1CR3J14NPN

B%56NE[_.-1436<CNIE56[=P5K728i<C790/<C7k.%[T[T36O9NE56.H7W2I "%*"HC ******+*******+*****

#2*$R<C728C147qIE5K<C3)BC1436.-[T5JI™f ]le=P14NEO93JIEN:ac.C=<8C1T.Hmi1TI=Ef“s5JIE;“<‘NE365J8H;IE3Jf˜mi.C=E1`021479NE1C

3J14NEN&B-56NP[_.1436<CNEIE56[=P56728i<C790{<C7k.-[T[T3KO9NE5J.H7W%I "%*"" %~#****+*******+***** #

#2*#$R<C728C147qIE5K<C3)BC1436.-[T5JI™f ] e=P14NEO93JIEN:ac.C=<8C1T.Hmi1TI=Ef“s5JIE;“<‘NE365J8H;IE3Jf˜mi.C=E1`021479NE1C

3J14NEN&B-56NP[_.1436<CNEIE56[=P56728i<C790{<C7k.-[T[T3KO9NE5J.H7W%I "%*"2~4%~#****+*******+***** #

#2*C‚$R<C728C147qIE5K<C3)BC1436.-[T5JI™f ] e=P14NEO93JIEN:ac.C=<8C1T.Hmi1TI=Ef“s5JIE;“<‘NE365J8H;IE3Jf˜mi.C=E1`021479NE1C

3J14NEN&B-56NP[_.1436<CNEIE56[=P56728i<C790{<C7k.-[T[T3KO9NE5J.H7W%I "%*"2~$C{****+*******+***** C‚

#2*$$R<C728C147qIE5K<C3)BC1436.-[T5JI™f ]le=P14NEO93JIEN:ac.C=<8C1T.Hmi1TI=Ef“s5JIE;“<‘NE365J8H;IE3Jf˜mi.C=E1`021479NE1C

3J14NEN&B-56NP[_.1436<CNEIE56[=P56728i<C790{<C7k.-[T[T3KO9NE5J.H7W%I "%*"HC{****+*******+***** C‚

#2* <C0Z56<C3qBC1436.-[T5JI™fj] e=E14NEO936IENap.C=b<8C1T.Hmi1TI=Pf:s56IE;:<3J14NEN 021479NE1C>mh.C=E1B-56NP[_.1436<CNEIE56[

=P56798h<C790k<C7/.%[T[T36O9NE56.H7W%I "%*"" %~Ž******+*******+*******+***** $

#2* <C0Z56<C3qBC1436.-[T5JI™fj] e=E14NEO936IENap.C=b<8C1T.Hmi1TI=Pf:s56IE;:<3J14NEN 021479NE1C>mh.C=E1B-56NP[_.1436<CNEIE56[

=P56798h<C790k<C7/.%[T[T36O9NE56.H7W%I "%*"2~4%~Ž******+*******+*******+*****

#2* <C0Z56<C3qBC1436.-[T5JI™fj] e=E14NEO936IENap.C=b<8C1T.Hmi1TI=Pf:s56IE;:<3J14NEN 021479NE1C>mh.C=E1B-56NP[_.1436<CNEIE56[

=P56798h<C790k<C7/.%[T[T36O9NE56.H7W%I "%*"2~$C’******+*******+*******+*****

#2*" <C0Z56<C3qBC1436.-[T5JI™fj] e=E14NEO936IENap.C=b<8C1T.Hmi1TI=Pf:s56IE;:<3J14NEN 021479NE1C>mh.C=E1B-56NP[_.1436<CNEIE56[

=P56798h<C790k<C7/.%[T[T36O9NE56.H7W%I "%*"HC’******+*******+*******+*****

#2*%~•$R<C728C147qIE5K<C3DBC143J.%[T5JIgf ] e=E14NEOZ3JIENap.C=+<`8C1T.Hmi1TI=Ef˜s56IE;˜</3J14NEN091479N1Cmi.C=P1hB-5KN”U

[_.-1436<CNIE56[=X56728i<C790/<C7k.%[T[T36O9NP5J.H7W%I "%*"" %~*+*******+*******+*****

#2*C$R<C728C147qIE5K<C3DBC143J.%[T5JIgf ]le=E14NEOZ3JIENap.C=+<`8C1T.Hmi1TI=Ef˜s56IE;˜</3J14NEN091479N1Cmi.C=P1hB-5KN”U

[_.-1436<CNIE56[=X56728i<C790/<C7k.%[T[T36O9NP5J.H7W%I "%*"2~4%~*+*******+*******+*****

#2*$R<C728C147qIE5K<C3DBC143J.%[T5JIgf ]le=E14NEOZ3JIENap.C=+<`8C1T.Hmi1TI=Ef˜s56IE;˜</3J14NEN091479N1Cmi.C=P1hB-5KN”U

[_.-1436<CNIE56[=X56728i<C790/<C7k.%[T[T36O9NP5J.H7W%I "%*"2~$Ci*+*******+*******+*****

#2*#$R<C728C147qIE5K<C3DBC143J.%[T5JIgf ]le=E14NEOZ3JIENap.C=+<`8C1T.Hmi1TI=Ef˜s56IE;˜</3J14NEN091479N1Cmi.C=P1hB-5KN”U

-*6~ =P5K0 &1TuZ7214mh147qI&ap.C= <C790 O9NP56728i :~ UP~_"-V ****+*******+*****

-* =P5K0 &1TuZ7214mh147qI&ap.C= <C790 O9NP56728 +~ UP~_E"-V ****+*******+*****

-* =P5K0 &1TuZ7214mh147qI&ap.C= O9NP56728i :~ UP~_"-V *+*******+*******+***** #

-*# F9IE5Kmh<C3vFZ<>=P<Cmi1TI1T=XN&ap.C=mi.%02143W :~ UP~_"-V *******+*******+***** C‚

-*‚ F9IE5Kmh<C3vFZ<>=P<Cmi1TI1T=XN&ap.C=mi.%02143W ŠUP~_"-V *******+*******+***** C‚

-*$ F9IE5Kmh<C3vFZ<>=P<Cmi1TI1T=XN&ap.C=mi.%02143W ŠUP~_"-V *******+*******+***** $

-* F9IE5Kmh<C3vFZ<>=P<Cmi1TI1T=XN&ap.C=mi.%02143W :~ U™n"-V *******+*******+***** $

-* \<>IE<[email protected]<>=P56N.H7˜~T\†~_E"-V B%NT*&~T\ n"%V *+*******+*******+*****

-*

B><C36O214N ***+*******+********+*******+*******+*****

-*6~ "x\<>IE<[email protected]<>=P56N.H7/>\ +~ UP~_E"-V B-N4*)>\ :~ U™n"-V **+*******+*****

-*6~C~•\<>IE<[email protected]<>=P56N.H7/>\ +~ UP~_E"-V B-N4*)>\ ŠUP~_"-V **+*******+*****

-*6~4\<>IE<[email protected]<>=P56N.H7/>\ +~ UP~_E"-V B-N4*)>\ ŠUP~_"-V **+*******+***** #"

-*6~\<>IE<[email protected]<>=P56N.H7k+~ U™nE"-V B-N4*( ŠU™n"-V ******+*******+***** #9~

-*6~ #\<>IE<[email protected]<>=P56N.H7k ŠUP~_E"-V B-N4*( ŠU™n"-V ******+*******+***** #9~

#2*6~ ' <>=P<Cmi1TI1T=Bn<C3KO214N&O9N140k5K7k56miF9=E.ŠBC140/;21TI1T=E.C8C14791T.HO9Nmh.-02143+******+***** $"

‚-*6~ F9IE5Kmh5Jw4<>IE5J.H7Ž=E14NPO93JIENap.C=+IE;21#mi.-09143 s5JIE; $#/IE<C798C147qIE56<C3@72.%0214N<C790 ~4kN1479N.C=

Fv.H567IENT******+*******+********+*******+*******+***** ~ "

‚-* F9IE5Kmh5Jw4<>IE5J.H7k=P14NEO93JIENac.C=IE;21:mi.%02143s5JIE;A~4 MIE<C728C147IE56<C3!79.-0214N<C790“~4MN1479N.C=

Fv.H567IENT******+*******+********+*******+*******+***** ~ "#

‚-* F9IE5Kmh5Jw4<>IE5J.H7k=P14NEO93JIENac.C=IE;21:mi.%02143s5JIE;A~4 MIE<C728C147IE56<C3!79.-0214N<C790 $#jN1479N.C=

Fv.H567IENT******+*******+********+*******+*******+***** ~ "$

‚-*# F9IE5Kmh5Jw4<>IE5J.H7Ž=E14NPO93JIENap.C=+IE;21#mi.-09143 s5JIE; $#/IE<C798C147qIE56<C3@72.%0214N<C790CkN1479N.C=

Fv.H567IENT******+*******+********+*******+*******+***** ~ "

‚-*‚ ,<>I1T=P56<C3tFG<>=P<Cmi1TI1T=NE1TIEN&O9N140/5K7k567qBC1T=XN1F9=E.CYZ3614m ***+*******+***** ~ "

@.C=E.H79<>=Pf{<>=EI1T=Ef‘0956N14<CN1/] \eXt<C36N.`d%72.ls7˜<CN[_.C=P.H79<>=Ef;914<>=EI0956N14<CN1/]\eXt56N

IE;21hmi.HNEI[_.Hmhmi.H7˜ap.C=Pm—.Ca;214<>=EI0956NE14<CN1C*i$&;21i<>IE56.H79<C3b”79NIE5JIEO2I1.Ca14<C36IE;˜14NIE56mh<>I14NIE;9<>I

<>F9F9=P.4r256mh<>I143JfhN1TBC147`mh5K36365J.H7i mi1T=P56[T<C7ZN(NEO%Œv1T=@ac=E.Hm IE;210956N14<CN1C%<C790#=E.HO28H;936fi‚""%"""i0914<>IE;9N

Fv1T=fC14<>=[T<C7{Yv1y<>II=P5JYZO2I140/I.j5JIy}ƒn€*„™I56N[T<COZN140{Y-fk<>IE;21T=E.HNE[T361T=E.HNE56NTGIE;21+8C=X<C09O9<C3tYGO9563609O9Fj.Ca

FZ36<Co-O21]^[P;2.H3J14NEI1T=E.H32[T<C36[T56O9m/-<C790#FZ36<>I14361TIENXebs5JIE;9567iIE;91<>=EI1T=PfC*D$&;956N)<C[T[TO9m:OZ36<>IE5J.H7j.CatFZ36<Co-O21C

d%72.ls7{<CN&<hNI1472.HNP56NT2=E14NI=X56[_IEN„IE;21 Z.ls‹.CaRYZ3J.-.-0t%3614<C0956728I.M<h0914[_=E14<CN1+567`IE;91.4r%f8C147NEO2F9FG3Jf

I.˜IE;21k;214<>=EIhmyO9NE[T361C*$&;21`14790’=E14NPO93JI.Ca<C7–<>=EI1T=X56<C3„NI1472.HNE5KNy5KNF…1T=Xmh<C72147Iy09<CmM<>8C1/I.˜IE;21

;214<>=EI)m:O9NP[T3J1CqFv.HNENE56YZ3Jf+3J14<C0Z56728I.:0214<>IE;t* L@14[T<CO9NE1 \<nŒ…14[_IENN.:mh<C7qfyFv1T.CFZ3J1&567hIE;21795JI140

"-IE<>I14NTG<[email protected]=P3602s5K021C25JIEN„021TI14[_IE5J.H7<C790kI=E14<>IEmi147I5KN„<hmh<>II1T=.Cab;9568H;`F9=P5J.C=P56IgfC*

O2=E=P147qID021TI14[_IE56.H7MI14[X;97956o-O214N(5K79[T36O9021IE;21<C728H5J.C8C=P<Cms;956[X;h56N)<=E143656<>YG3J1CHfC1TI(1_r%Fv147%U

NE5JBC1C%567Bn<CNP5JBC1&I14[P;Z7956o-O21<C790MF9=E.H721I.y567I1T=E.CYZNE1T=EBC1T=(B><>=P56<>YZ5K365JIgfk]^N1T11C*ƒ82*JW}z~C€K}n€peX*D3JI=P<nUa^<CNI

$I14[P;Z7956o-O214N<>=E1i<C36N.j14miFZ3J.ŠfC140WIE;956N56N<`72.H7%Ug567Bn<CNP5JBC1y5Kmh<>8H56728#I14[P;9795KoO211_Œv14[_IE5JBC1h567‘021_U

I14[_IE56728y<C790MNP[_.C=P56728IE;91N1TBC1T=P56Igfi.Cat[T<C36[T56OZm 021TFv.HNE5JIEN)567iIE;21[_.C=E.H79<>=Efh<>=EI1T=X5J14NT*b79ac.C=EIEOZ79<>I143JfC

$I14NIE56798#14o-O95JFZmh147qI56NBC1T=Ef{1_r%Fv1479NE5JBC1CW<C790Ž5JI.H793Jf/021TI14[_IEN+[T<C36[T56O9m 021TFv.HNE5JIEN<C790Ž72.CIIE;21

N.CapI&FZ36<Co-O214NIE;9<>Imh<>dC1+O2F{mM<C7qfj.Ca IE;21mi.HNI0Z<C728C1T=E.HO9N&3614NE5J.H79NT*

†FZ36<COZNE5JYZ3J1h<C36I1T=P79<>IE5JBC1`I.ŽIE;21`<C728H5J.C8C=P<Cm <C790–$ˆNE[T<C7’ap.C=091TI14[_IE5J.H7•.CaNI1472.HNE14N

O2IE563K5JwT14NbIE;21021TI14[_IE5J.H7j.Cat<C[_.HO9NIE56[s<4BC14N@F9=E.CFZ<>8H<>IE5K728+ap=E.Hm IE;21NI1479.HNE56NT* SI)56N(s)14363Zd-79.ls7MIE;9<>I

<>=EI1T=P5K<C3WNI1472.HN14N„FZ=E.-0ZO9[[email protected].Šs 567`FZ<>=EIE5K<C363Jfi.%[T[T36O902140k<>=EI1T=X5J14NT*

| 5J8HO9=E1h~>*6~>Q)[email protected].%0 9.ls‹8C14791T=P<>I140/Y-fk<iNI1472.HNE56N

s;95K[P;IE;2147[T<COZN14Ni<NPmh<C363@0956NFZ3K<C[_14mi147qIy567AIE;91`NPO2=E=E.HO97Z0956728`Yv.-09f˜IE56NENEO21Ž]^N1T1k| 5J8HO2=E1‘~>*6~leX*

$&;21B%5JY9=P<>[email protected];21NEO9=E=E.HO9790Z56728Yv.%02fhIE56NENPO214NT%s;956[X;j.-[T[TO2=&5K7#I™s).Mac.C=PmMNT2<i[_.HmiF9=E14NENP5J.H79<C3

s<4BC1:<C7Z0k<iNE;214<>=„s<4BC1CZFZ=E.-0ZO9[_1N.HO97909N}n€*(S7k36<>=P8C1T=&<>=EI1T=P5J14N&NPO9[P;k<CN„IE;91[T<>=E.CIE560/<>=EI1T=X5J14NT

IE;214N1<C[_.HO9NIE5K[)N.HOZ7909N[T<C7:Yv1)021TI14[_I140Y-fFZ;f-NP56[T56<C79NtOZNE56728<NI1TIE;2.HNP[_.CF…1C*b.ls@1TBC1T=4q021TI14[_IE5K728

<C[_.HO9NIE5K[NE5J8H7Z<C36Nb567hNEmM<C363J1T=(<>=EI1T=X5J14N(021T1TF#5679NE56091@IE;91Yv.-09f:;9<CN(F9=E.lBC140#095M[TOZ3JI ac.C=)Igs@.:=E14<CNE.H79NTQ

IE;214N1y<C[_.HO9NIE56[:72.H56N14N<>II147OZ<>I1NP5J8H795JuZ[T<C7IE3Jf`<CNIE;91TfkI=P<4BC143!IE;2=E.HO28H;{IE;21:5K7qI1T=EBC147Z56728hIE56NPNEO214NT

<C790kmh<C7f`[_.HmiFZ3J1_rkN.HO9790ZN)s5JIE;9567jIE;21Yv.%02fM[T<C7k.ŠBC1T=Es;21436m [_.H7qBC147IE5J.H79<C3!<C[_.HO9NIE56[021TI14[_IE56.H7

Nf%NI14mhNT*

\O2=P56728jIE;21h36<>I1/~" N4 ,{1409 [_.HO9NIE56[TN”79[>*Jt<k[_.HmiFG<C7qfŽuZ79<C7Z[_140Y-f‘BC147qIEO2=P1h[T<>FZ5zU

IE<C3R021TBC143J.CFv140˜<C790˜FZ<>I147I140“</F….H36fB%567f-360Z5ZO2.C=P5K0%1M]^'DV\|De<>=E=P<4f‘.CaFZ5J1TwT.-143J14[_I=P56[IE;Z567‘uZ36m

<C[T[_143J1T=E.Hmh1TI1T=N1479N.C=143J14mh147qIENT*D$;214N1N1479N.C=PN@<>=E1YZ<C7902Ug3656mh5JI140tqN.<CN)I.uZ36I1T=).HO2I„5J=P=E143J1TB><C7qI

NE5J8H7Z<C36Nk]p1C*ƒ82*J@;214<>=PIY…14<>IXey<C7Z0’NE.2(s;2147’FZ3K<C[_140.H7–<‘Fv1T=PN.H7 Ny<C[_.HOZNIE56[`s567Z02.ls ]^3J.%[T<>I140–.H7

IE;21i[P;914NINEO2=Ea^<C[_1ŠeXWIE;21i<>=E=P<lf;9<CNIE;21i<>YZ5K365JIgfkI.k021TI14[_I<C[_.HOZNIE56[NE;214<>=s<4BC14N0ZO21:I./<>=PI1T=P56<C3

NI1472.HNE14NT*kIE563K5Jw456728`IE;956NI14[P;972.H36.C8CfC 09.-[_I.C=PN+s).HOZ360A;9<lBC1#<C7“5K721_r-Fv1479NP5JBC1imi14<C79N.Ca&0914[T560956728

s;21TIE;91T=.C=79.CI<C7˜<C728H5J.C8C=P<>FZ;f5KN791T1402140W*+ NIE;21h;9<>=P09s@<>=E1ys<CN0214NE5J8H79140{I./[_.H363614[_I<C[T[_143zU

1T=P<>IE5J.H7˜0Z<>IE<#ap=E.Hm—IE;21ys<4BC1hF9=P.CFZ<>8H<>IE5J.H7˜<>IIE;21i[P;214NEIs@<C363v56I095K072.CI8H5JBC1i<C7f‘5K79NE5J8H;I567I.

;2.Šs IE;21s@<lBC14N)I=X<4BC143J140#IE;2=E.HO28H;hIE;21[P;914NI@[T<lB-56IgfC*( xmh<>IE;214mM<>IE56[T<C39ap=P<[email protected]=Edis<CN(721T1402140MI.

mi.%02143tIE;91+s<4BC1F9=E.CFZ<>8H<>IE56.H7/ap=E.Hm IE;91:NI1472.HNP56N&I.jIE;21:[X;214NI™s@<C363…<C790<C363J.Šs ap.C=IE;21:1TBC147qIEOZ<C3

021TI14[_IE5J.H7`.Ca!NI1472.HN14NT*b”795JIE5K<C3Z021TBC143J.CFGmi147qI.CatIE;91mh<>IE;914mh<>IE56[T<C3Wmi.%02143Gs)1T=E1F9=E14NE147qI140`567Ž}ƒ‚Š€

.Ca s;956[X;`IE;956N„095KNEN1T=EIE<>IE5J.H7k5KN„<C7/1_r%I1479NE5J.H7W*

$&;21560214<j.Ca)O9IE56365Jw456798M<C[_.HO9NIE56[s<4BC14N:567‘YZ5J.H3J.C8H5K[T<C3R<C7Z0‘mh140956[T<C3 <>F9FZ365K[T<>IE5J.H79N56N72.CI

1C*ƒ82*J(}z~C~_€K}z~$C€K} >€peX*S7•}n€ IE;21<CO2IE;2.C=PN0956NP[TO9NEN&IE;91y<>YZ5K365JIgf`I.k021TI14[_IIEO9mi.C=XN5K7/Y9=E14<CNEIIE5KNENEO21C*

"%56mM5636<>=P3Jfh}#qn€Z[_.H7ZNE56021T=PN IEOZmi.C=D021TI14[_IE<>YZ563K5JIgf567365JBC1T=bIE56NPNEO21C* 7i567BC1T=PN1„FZ=E.CYZ3J14m mi1TIE;2.%02.H3J.C8Cf

567BC.H3JB%56728i09<>IE<iap=E.Hm†I=P<C7ZNE5J147I„1436<CNI.C8C=P<>FZ;fk56NF9=E14NE147qI140567A}ƒ">€!}ƒ%~_€G<C790A}ƒ>€*

095M[TO93JI™f–IE;9<>Ik<>=P56N14Njs;2147x[_.H79NP56021T=P56798“YZ5J.H36.C8H56[T<C3IE5KNENEO21Ž<CNk<•mi140956O9m/56NjIE;21

ap.C=Pm:OZ36<>IE5J.H7•.Ca[_.H79NIE5JIEO9IE5JBC1k14oOZ<>IE5J.H79Nhap.C=MNEOZ[P;–IE56NPNEO21C*–SIM56Ns@14363&<C[T[_1TF9I140 IE;9<>IhYv.%02fN.CapI

IE56NENPO21{mi14095KO9m Yv14;9<4BC14Nj365JdC1<AB%56NE[_.-1436<CNIE56[/mh140956O9m }z~4C€K}ƒ$n€K}#H€K}##q€*‹.Šs)1TBC1T=lIE;21T=E1‘<>=E1

N1TBC1T=P<C3I14[P;97Z56oO914N&<4B><C5636<>YZ361I.M5679[_.C=EFv.C=P<>I1B%56NE[_.-1436<CNIE5K[T5JIgf`567I.h<hmi.%02143 *b”7A}#C€!<C790“}ƒ#H€9IE;21

<CO2IE;2.C=XN+F9=P.CF….HNE1MIE;9<>I<>F9FZ365K[T<>IE5J.H79N.Ca„ap=P<C[_IE5J.H7Z<C3)[T<C36[TOZ36O9NYv1jO9N140’567AB%56NE[_.-1436<CNIE56[#mi.%021436567282*

mh<>IE;214mM<>IE56[T<C3Rac=P<Cmh1Ts).C=EdkIE;Z<>I1_r2<Cmh567214NN1TBC1T=P<C3Rmi1TIE;2.%09Nac.C=0214<C365K728hs5JIE;/B-56NP[_.1436<CNEIE56[T5JIgf

]^567–36OZ728ŽIE56NENEO21Še:56NFZ=E14N147I140 567}#9~T€*–| 5679<C3636fC(|9O9728A5K7qI=E.%09O9[_140–<˜o-O9<CNE5JUg36567214<>=B%56NE[_.-1436<CNIE56[

[_.H79NIE56IEO2IE5JBC136<ls‹567A}z~4n€*D?x;9563J1IE;21T=E1<>=P1mh<C7qfjs<4f%N„I.h=E1TF9=P14N147qI„IE;91=P1436<nr%<>IE56.H7kapOZ79[_IE5J.H7`567

|9O9798 N@3K<4s%IE;21s).C=PdhF9=E14N147I140`567hIE;Z56N)09.-[TO9mh147qI56N)YZ<CN140#.H7#IE;91567I1T=P79<C3GB><>=P56<>YZ3J1<>F9F9=E.H<C[X;

0956NP[TO9NEN140`567“}ƒ‚Š€

$&;21)=E14mh<C5679091T=!.Ca9IE;Z56N!0Z56NEN1T=EIE<>IE56.H7:56NR.C=E8H<C7Z5JwT140<CN!ap.H363J.ŠsNT*RS7i;9<>FZI1T=b-Cs@1F9=E14N147I

<h021T=X5JBn<>IE56.H7k.Ca IE;21+mi.%02143*D?˜1yYv1T8H567`s5JIE;/IE;2114o-O9<>IE5J.H79N.Ca mh.CIE5J.H7WZ<C790/F9=E14N147I&IE;21ap.C=PmyO%U

36<>IE5J.H7]^5679[T36O90Z56728:0Z5zŒ…1T=P147qI„B><>=P56<>IE5J.H7ZNXe(.CaRIE;91+[_.H79NIE5JIEO9IE5JBC114oOZ<>IE5J.H79NT*

?˜1#1_r2<Cmh56791MIE;21#Bn<C365K095JIgfŽ.Ca„.HO2=mi.%02143(5K7’;9<>FZI1T= {YfA[_.HmiFG<>=P56728{56IEN+8C14721T=X<>I140

=E14NEOZ3JIENWI.0Z<>IE<&8C14721T=P<>I140yap.C=!<.H721(0956mh1479NE5J.H79<C3>8C1T.Hmh1TI=EfC* ?˜1)F9=P14N147qI!<[_.HmiFZ<>=X56N.H7.Ca%=E14NPO93JIEN

8C14721T=P<>I140“Yf‘14<C[P;“Bn<>=X56<>IE5J.H7Ž.Ca.HO2=mi.%02143 s5JIE;ŽIE;91i.H721h0956mi147ZNE5J.H79<C3R09<>IE<kF9=P14N147qI140“567 }ƒ‚Š€*

NIE<>IE56NIE56[T<C3bNP5J8H795JuZ[T<C7Z[_1yI14NEI+56N14miFZ36.lfC140˜I.k1_r2<Cmh56721IE;21hNP5J8H795JuZ[T<C7Z[_1y.Ca@1_r%I=P<kFZ<>=P<Cmh1TI1T=PN

567BC.H3JBC140/567`IE;91+mi.C=E1[_.HmiFG3656[T<>I140/mi.%021436N4*

S7Ž;9<>F9I1T= #2Gs@1+FZ=E14N147IN1TBC1T=P<C3RNE56myO936<>IE56.H79N„F9=E.%09O9[_140{O9NE56728iIE;91:mi.%02143 *?˜1[_.H7%U

NE56091T=R;21TI1T=P.C8C1472145JIE5J14NbY-f:5K7qI=E.%09O9[T5K728<O9795Jap.C=Pm =P56728=PO97Z7956728&IE;9=E.HO28H;yIE;21„mh56090Z3J1(.CaGIE;218C1T.HmU

1TI=EfC*b\1TFv1479021479[_1„.H7i‡56Nb5K7qI=E.%09O9[_140yY-f:[_.H79NP56021T=P56798<=P5J8H5K0:.%[T[T36O9NP5J.H73J.-[T<>I140M<C3J.H728<Fv.C=EIE5J.H7

.CaRIE;215679721T==P<C0Z56O9NT*b| 5679<C3636fCs@11_r%<CmM56721<8C1T.Hmi1TI=Ef`s;Z56[P;k[_.Hm:YZ567214NIE;91;21TI1T=E.C8C1472145JI™f/<C790

5679791T=„.-[T[T36OZNE5J.H7W*

?56IE;AIE;21MOZ3JIE56mh<>I1h8C.H<C3).Ca„IE;956NF9=E.14[_I+Yv1456728/021TI14[_IE56.H7“.Ca&NI1479.HN14NTRs)1#.CYB%5J.HO9NE36f

myO9NI1_r%<CmM56721h567BC1T=PN1F9=E.CYG3J14mhNO2IE563656w456728MIE;91mh.-02143*i;Z<>F9I1T=+‚j[_.H7qIE<C567ZN<`F9=E14N147IE<>IE5J.H7˜.Ca

.HO2=&567Z5JIE56<C3G1_Œ….C=EIEN567qBC.H36B-56798y567BC1T=PN1FZ=E.CYZ3J14mˆmi1TIE;2.%02.H3J.C8CfC*(?˜1O9N1<C7k567BC1T=PN1F9=P.CYZ3J14mˆ567`<C7

<>II14miF9II.juZ790{IE;21y36.-[T<>IE5J.H7.CaD<jNE56myO936<>I140.-[T[T36OZNE5J.H7W…<C790/s@1y<C3KN.#1_r2<Cmh56791+IE;21y=E.H3J1:.CaDIE;21

mh<>I1T=P5K<C3WFZ<>=P<Cmi1TI1T=XN&.H7kIE;21NPO9[T[_14NENa^O93WI1T=PmM5679<>IE5J.H7`.CaRIE;21+567BC1T=PN1FZ=E.CYZ3J14mk*

!#"$%&(' *)+,

36IE;2.HO28H;jIE;21mi.CIE5JB><>IE5J.H7`.Ca!IE;956N@F9=E.CYZ3614m 5K7qBC.H3JBC14N&IE;21021TI14[_IE5J.H7k.Ca NI1472.HN14Ns5JIE;9567

IE;21+;-O9mh<C7`Yv.%02fC9N1TBC1T=P<C3![_.HmiFZ3J1_r25JIE5J14N1_r256NI„s5JIE;`IE;21+[_.H79NP56021T=P<>IE5J.H7`.Ca IE;21[X;214NI[T<4B%5JIgfC*@$&;21

mi14095KO9m†s5JIE;Z567`IE;21+[X;214NI[T<4B%5JIgf{5KN&;21TI1T=E.C8C14721T.HOZN<C7Z0{72.CIO9795Jap.C=Pmk*@$&;21+NE;Z<>F…1+.CaRIE;91:[P;914NI

[T<4B%5JI™fA56N8C14721T=P<C3K3Jf{14363K5JF9IE56[T<C3 WYGO2IBn<>=X5J14NYv1TIgs@1T147“NEO9Y ”14[_IEN4*M|2.C=+IE;914N1h=E14<CN.H7ZNT!s@1M[_.H79NP56021T=4

ap.C=&.HO2=567Z5JIE56<C3…1_Œ….C=PIENTZ<hmi.C=P1NE56miFZ3K56NIE56[8C1T.Hmi1TI=EfC*

$&;21MNP56miFZ3656u9140‘FZ;qf%NE56[T<C3D8C1T.Hmi1TI=Ef“56N:<[_f%36567Z02=P56[T<[email protected]*k$&;21#Nf-7IE;21TIE56[M8C143(.Ca

s;95K[P;#IE;218C1T.Hmh1TI=Efj5KN)[_.HmiFZ=P56N140W%;9<CNmh<>I1T=P5K<C3GFZ=E.CFv1T=EIE5J14N(NP56mh5636<>=)I.IE;2.HN1.CaN.CapIIE56NENEO214N4*

NEO2=P8H56[T<C3…IEO2Yv1s;956[P;`mh5Kmh56[TN<C7k<>=EI1T=P56<C3vBC145K7`s5JIE;`NI1472.HNE5KNT2FZ<CNEN14N„<nr256Nf%mhmi1TI=X56[T<C363JfhIE;9=E.HO28H;

IE;21y[_147qI1T=.CabIE;21ymi.H360W*„ N.HO2=X[_1:0956NEIEO2=EYZ<C79[_1j]p=E1TF9=E14N147IE<>IE5JBC1y.CabIE;21:0Z56NIEO2=EYG<C79[_1[T<CO9N140Yf

NI1472.HNP56NXe:56Ny8C14721T=P<>I140–s5JIE;9567IE;21`IEO2Yv1C*•"%;914<>=ys<4BC14NMF9=E.CFZ<>8H<>I1{IE;2=E.HO28H;’IE;21`8C143 @<C790•IE;21

NE;214<>=<C[T[_143J1T=P<>IE5J.H756N&mi14<CNEO9=E140“]pY-fjN147ZN.C=PNXe@<>IIE;21.HO2I1T=NPO2=Ea^<C[_1.CaRIE;918C143 *

t1TI.- <C790/- Y…1bIE;91(5679721T=t<C7Z0.HO2I1T=!=P<C0956O9Nv.Ca%IE;21(8C143Š=P14NFv14[_IE5JBC143Jfi]^N1T1)| 5J8HO2=P1(-*6~leX*

?˜1`<CNENEO9mi1#IE;9<>IyIE;21#N.HO9=P[_1#095KNIEO2=EYZ<C7Z[_1M56NIE5Kmi1M021TFv147902147IT ;9<CN+.H7Z3Jf˜<{=P<C0Z56<C3D[_.HmiFv.H72147IT

<C790`IE;21095KNIEO2=EYZ<C7Z[_156N<FZO9=E1NP;214<>=„ac.C=X[_1C*($&;21.HO2I1T=&NEO9=Eap<C[_1.Ca!IE;218C143W56N<ap=E1T1NEO2=Ea^<C[_1<C790

IE;218C14356N„56795JIE5K<C363Jfh<>I&=E14NEIT*

"%5679[_1is@1M<>=E1#567qI1T=P14NI140“567“mi.-09143656728`IE;21hs<4BC1jF9=E.CFG<>8H<>IE5J.H7Aap=E.Hm IE;21j5679721T==X<C0956O9N

| 5J8HO2=E1-*6~>Q(”3636OZNI=P<>IE5J.H7j.Ca IE;21FZ;f-NP56[T<C3v8C1T.Hmi1TI=Ef/[_.H79NP56021T=E140k567`.HO9=mi.%021436567281_Œv.C=EIENT*

.CaRIE;21[_f-3K567902=P5K[T<C3Zmi.H360t*D$&;956N[_=E.HNEN„NE14[_IE5J.H79<C3t<>=E14<hIE<>dC14N&IE;21NE;Z<>F…1.CaR<h[T5J=P[T3J1C%IE;-O9N„5JI„s5K363ZYv1

Yv14721TuZ[T56<C3vI.#021T=P5JBC1.HO2=&mh.-02143O9NE56728Fv.H36<>=&[_.-.C=P09567Z<>I14NT*

&& & #" '

|

3" )H+ " ƒ +!" &3

?˜1Yv1T8H567 IE;21{ap.C=PmyO936<>IE5J.H7 .Ca.HO2=jmi.-09143&Y-f 021T=P5JB%56728˜IE;91[_.H7IE567OZ5JIgf–14o-O9<>IE5J.H7567

Fv.H36<>=[_..C=P0Z5679<>I14NT*A$&;91j[_.H7IE567-O95JIgf“14oO9<>IE56.H7’5KNy<‘mh<>IE;214mM<>IE56[T<C31_r-FZ=E14NENE5J.H7.CaIE;91#FZ;f%NE56[T<C3

F9=E.CFv1T=EI™fk.Ca)mh<CNPN[_.H7ZN1T=EB><>IE5J.H7W*™INIE<>I14NIE;9<>IIE;21=P<>I1y.Ca)[X;9<C728C1.Ca(mh<CNPN5K7<C7f{FZ<>=PIE56[TO936<>=

143J14mi147I56N+14o-O9<C3)I.IE;91j095JŒ…1T=E147Z[_1MYv1TIgs@1T147’IE;21Z.lsˆ.Camh<CNENy[_.H7BC14[_I140 567“<C7Z0“IE;21 9.Šs .Ca

mh<CNEN[_.H7BC14[_I140˜.HO2IT*?˜1i[_.H79NE56021T=<C7Ž<>=EYZ5JI=X<>=Ef`143J14mi147I567‘<#F….H3K<>=[_.-.C=P09567Z<>I1:Nf%NI14mkWNEO9[X;

<CN:IE;21M.H721`021TFZ5K[_I140“567A| 5J8HO9=E1j-*-* 14[T<C363]}z~ #C€peXbIE;9<>I+IE;91#<>=E14<.Ca„IE;21#NE14[_I.C=y.Ca&<‘[T5J=P[T361M56N

8H5JBC147jY-fMIE;21ac.C=Xm:O93K<

‡2-<C7Z0#IE;-O9NT%IE;21<>=E14<y.Ca!<C7`<>=EYG5JI=P<>=P5636fyNEmM<C363Z143614mi147qIs5K363Z;9<lBC1

IE;21ap.C=Pm

~



]

e

‡

~



‡

]

e_] ‡e

~



]

e

] ‡e

36N.2R=E14[T<C363bIE;Z<>I+IE;21h14o-O9<>IE5J.H7“ac.C=ymh<CNEN 9.ls—]}z~!Š€peIE<>dC14NyIE;21hap.C=Pm! #" :!s;21T=E1$"Ž56N

IE;21+091479NE5JI™fj.Ca IE;21+143J14mi147IT k56N„BC143J.%[T5JI™fCG<C790 56N&IE;91+<>=E14<h.Ca IE;21:ap<C[_1:.Ca IE;21143J14mi147IT*?˜1

021TI1T=PmM56721IE;21Mmh<CNPN=P<>I1h[P;Z<C728C1MY-f‘myO93JIE56FZ3Jf%56728hIE;21#021T=P5JB><>IE5JBC1.Ca)IE;91M021479NE56Igf{s5JIE;Ž=E14NFv14[_I

I.MIE5Kmi1Yf`IE;21:<>=E14<h.Ca IE;21143614mi147qIT*@?x;2147/s@11_r2<Cmh56721IE;91 9.ls .Cabmh<CNEN&[_.H7BC14[_I140˜567I.i.HO2=

143J14mi147ITts@1im:O9NEI1_r2<Cmh56791yIE;91 9.ls 567Yv.CIE;ŽIE;21

[_.H7BC14[_I140‘5K7qI.iIE;21+143J14mi147I„s56363…IE<>dC1+IE;91ac.C=Xm

"

] ‡e

"

"%56mM5636<>=P3JfCIE;21 9.Šs [_.H7BC14[_I140.HO9I[T<C7kYv11_r-FZ=E14NEN140/<CN

" ]

e_] ‡e

" "-.29IE;911_r-F9=P14NENE5J.H7`ap.C=&IE;21+[_.H7ZN1T=EB><>IE5J.H7k.Cabmh<CNEN„s56363…Yv1 " ]

e_] ‡e

~  " ] e

] ‡e ]"

] ‡e

"

e ]" ]

e

] ‡e

" e ]" " e

] ‡e " ]

e_] ‡e

] "

" e

\5JB%560956728yIE;2=E.HO98H;kYfjIE;21o-O9<C7IE5JIgf ]

e_] ‡-eX9s)1:;9<4BC1

" ~  " ]" " e " ]" " e

] ‡e

"%567Z[_1.HO9=&143J14mi147IT :Z56N<>=EYZ5JI=P<>=X563JfhNEmh<C3K32s)1<C3K3J.ls ‡ "%Zf-5J143K0956728 " " ~ " ‡ " "-.29IE;91[_.H7qIE567-O95JI™f#14o-O9<>IE5J.H7{IE<>dC14N&IE;21+ac.C=Pm " " ~ " ‡ " " ]-*6~le

(r+dr)d

θ

r d

θ

dr

dr

3} "+ } H+!"4

?˜1i72.ls s56NP;{I.k021T=P56BC1+IE;21imi.Hmi147IEO9m 14o-O9<>IE5J.H79N567Fv.H36<>=[_.-.C=P095K79<>I14NYf{[_.H7ZNE560%U

1T=P56798iIE;21[_.H79N1T=EB><>IE5J.H7{.CaRmi.Hmh147qIEO9m/9s;956[X;k[T<C7kYv11_r-FZ=E14NEN140kY-f

!#"$ %& (')*,+-.

]-*He

!/0#"1 %2, (')3)+4 56

780 9 887:;*<>=? @7AB78C

[email protected]=P1apO9=EIE;21T=„1_r2<Cmh567956798:IE;21:[_.H79N1T=EB><>IE5J.H7k.Ca mi.Hmi147IEO9mk2s@1+myO9NI&<C0902=P14NEN„<iNEmh<C363W[_.HmhFZ365zU [T<>IE5J.H7i567:IE;218C1T.Hmi1TI=Efy.CaZ.HO9= <>=PYZ5JI=P<>=Ef143614mi147qIT*b$&;91@021T=X5JBn<>IE56.H7+.CaGIE;21„mi.Hmi147IEO9m14oO9<>IE56.H79N =E14365614N.H7kBC143J.%[T5JIE5J14N&567`Yv.CIE;kIE;91IE<C728C147qIE5K<C3<C790`=P<C0Z56<C3W095J=E14[_IE56.H79NT*b79ac.C=EIEOZ79<>I143JfC9IE;21IE<C798C147%U IE56<C3<C790’=P<C095K<C3@0Z5J=E14[_IE5J.H79Ny<>Ih<‘Fv.H567qIy.H7•145JIE;21T=iNE5K021#.Ca.HO2=i143J14mi147Ii02.˜72.CIi;9<4BC1kIE;91/NE<Cmi1 .C=P5J147IE<>IE5J.H7’<CN+IE;9.HN1#<>I</Fv.H567I+567˜IE;91#[_147I1T=y.Ca„.HO9=+143J14mi147IT*{$!.{=E14[_IE56acf˜IE;95KNF9=E.CYZ3614mks@1 567I=E.%09O9[_1@IE;21„O9795JI!BC14[_I.C=PND EFHG/I JD EF I KD EF.G/I q<C790LD EF I qs;21T=E1@IE;21„NEO2YZNP[_=P5JF9IEN <C790‡=E1Tap1T=bI.IE;21 =P<C095K<C3…<C7Z0`IE<C728C147qIE5K<C3095J=P14[_IE5J.H79N@=E14NFv14[_IE5JBC143JfC9<C7Z0`IE;21NEO2Fv1T=PNE[_=X5JF9IEN] e@<C790A] [email protected];9<>I IE;21:BC14[_I.C=PN.C=P5J8H567Z<>I1ac=P.Hm <MF….H5K7qI&.H7IE;21y=P5J8H;I<C790‘3J1TapI;9<C790NE56021.CabIE;91y<>=EYG5JI=P<>=Efj143J14mi147I

]^<CN5K3636O9NI=X<>I140#567k| 5J8HO9=E1-*HeX*)$&;214NE1O9795JIBC14[_I.C=PN;9<4BC1Yv1T147k021TuG72140kNEO9[X;kIE;9<>I„IE;21ap.H363J.Šs56728

=E1436<>IE56.H79N„<>=E1I=PO91CQ D E F.G/I M D E [_.HN ‡ ON ~ D EFHG/I M D E xNE5K7 ‡ PN ‡  D E F.G/I M D E /NE567 ‡ PN ‡  D E FHG/I M D E x[_.HN ‡ PN ~ D E F I M D E [_.HN ‡  N ~ D E F I M D E /NP567 ‡  N ‡  D E F I M D E xNE5K7 ‡  N ‡  D E F I M D E x[_.HN ‡  N ~ $&;214NE1=E1436<>IE5J.H79NFG36<4fj<C7/56miFv.C=EIE<C7I=E.H3J1567jIE;21ap.H363J.Šs56728FZ<>8C14N&<CN&s)1+091T=P5JBC1IE;2114o-O9<>IE5J.H79N„.Ca mi.Hmi147IEO9mk*

Q8 SRTU CVW !PXY0Z

?˜1@Yv1T8H567IE;91)021T=P56Bn<>IE5J.H7+.Ca2IE;21)mh.Hmi147qIEOZm 14o-O9<>IE5J.H79NYf1_r2<Cmh567Z56728„IE;21@3J1TacIR;9<C790:NE56021D.Ca

] -*HeT*b$&;21=P<>I1„.Cavmi.Hmi147IEO9m <C[T[TO9myO936<>IE5J.H7i56N NE5KmiFZ3JfIE;21„=X<>I1„.Ca…[X;9<C728C1„.Cavmi.Hmi147IEO9m

s5JIE;9567+IE;21)143614mi147qI s56IE;+=E14NEF…14[_IRI.IE56mi1CK[

F6\^]

_

I

[`

* |2=E.Hm IE;21021TuZ7Z5JIE5J.H7.CaG021479NE5JI™fCCs)1„;9<lBC1

IE;Z<>Iba "c—]ps;91T=E1da 56NmM<CNENTv<C790ec 5KNBC.H36OZmi1ŠeX…<C7Z0O9NP56728hIE;95KN567{.HO2=1_r%F9=E14NPNE5J.H7W

s@1+;9<lBC1

]"cfD9e

$;21BC.H3KO9mi1•ac.C=˜<C7 <>=EYG5JI=P<>=P5636fNEmM<C363y143J14mi147I‘IE<>dC14NAIE;21•ac.C=Pm c ]

]

e_] ‡e

]

e

]

‡ee

*D.Šs)1TBC1T=l%NP5679[_1s)1&<>=P1„[email protected]=Ed%56728567yIgs@.+095Kmi1479NE5J.H7ZNT>s)1&mh<lfy791T8H3J14[_I

IE;91

I1T=Pmk9<C790k.HO9=&1_r-FZ=E14NENE5J.H7`Yv14[_.Hmi14N

] " 9eD

]

]

e_] ‡-e

~



]

e

] ‡ee

?˜1y095JB%56021IE;2=E.HO28H;/Yf

]

e_] ‡eXZf-5J143K0956728

]" 2eD

~



]" D2e

363J.Šs56728

‡ "%>s@1(.CY9IE<C5K7IE;21)1_r-F9=P14NENE5J.H7ap.C=RIE;21D=P<>[email protected] <C[T[TOZm:O93K<>IE5J.H7W

s;956[P;`IE<>dC14NIE;21ap.C=Pm

]" 9eD

]-*He

Q LVW ! Z %9 (')3)+ VS %9 (',*)+$5

?˜1hNP;9<C36379.ls 1_r%<CmM56721yIE;21y[X;9<C728C1i567‘mi.Hmi147IEO9m 9.ls+*,{.Hmi147IEO9m 9.Šs 5KN[_.HmiFGO2I140

Y-fhmyO93JIE5JFZ36f-56798IE;21mh<CNEN 9.lsx<>I@<+8H5JBC147hFv.H567IDY-fiIE;21&BC143J.%[T5JI™fM<>I(IE;21NE<Cmi1F….H5K7qIT*b,{<CNPN

Z.lss@<CN0956NE[TOZNEN140ks;9147/s@1:021T=P56BC140/IE;21y[_.H7qIE567-O95JI™fk14oOZ<>IE5J.H7WG<C7Z0{IE;21:BC143J.%[T5JIgf/<>I<C7qf

8H56BC147`F….H5K7qI@s56363ZIE<>dC1IE;21ap.C=Pm‰] D

E

5D

E

s@1„m:OZNIR<C[T[_.HOZ7qIbap.C=bmi.Hmi147IEO9m 9.ls–567:IE;21=P<C095K<C3q095J=P14[_IE5J.H7WC<CN s)143K3<CNbmi.Hmh147qIEO9m 9.Šs

5K7IE;21&IE<C728C147IE56<C390956=E14[_IE5J.H7W* $.:[_.HmiFZO2I1„IE;21&mh.Hmi147qIEOZm 9.Šs 567i<NFv14[T5JuZ[0956=E14[_IE5J.H7WCs@1

IE<>dC1IE;2109.CI(F9=E.%09O9[_Ib.CavIE;21mi.Hmi147IEO9m Z.ls <C7Z0hIE;21OZ795JIbBC14[_I.C=ac.C=)IE;21[_.C=E=P14NFv.H790956728

0Z5J=E14[_IE5J.H7W*b?˜1+s56363v72.Šs 021T=P5JBC1IE;91+mi.Hmi147IEO9m 9.Šs 567`IE;91=P<C0956<C3W0956=E14[_IE5J.H7W*

]" ]

‡-ee_] ;D

E 5D E e M D E

]" Š]

e

‡-e_] >D

E D E e M D E

]" C]

ee_] >D

E FHG/I D EFHG/I e M D E

]" H]

ee_]] >D

E F I D EF I e M D E ]" ] ‡e D E M D E " ] ‡e D E M D E e ]" ] e_] ‡e D E M D E " C]

e_] ‡-e D

E M D E e

]" l]

e D E FHG/I M D E " ] e D EF.G/I M D E e

+]" Š]

e D E F I M D E " ] e D E F I M D E e NE56798iIE;21F9=E1TB%5J.HO9NE36fMNIE<>I140‘O9795JIBC14[_I.C==E1436<>IE5J.H79N4-.HO9=&1_r-FZ=E14NENE5J.H7kNP56miFZ3656u914N(I. "

] ‡e "

]

e ‡

" l]

e " ‡  ] e

" l]

e " ] ‡  ] e e ]" " e

] ‡e "

]

e_] ‡e

] " " e " ‡  ] e " ‡  ] e ?˜1y095JB%56021IE;2=E.HO28H;/Yf ]

e_] ‡eXZf-5J143K0956728

" " " " " ‡ "  "  1TI

‡ "%Z<C790/s)1+;Z<4BC1

" " " ‡ " ?˜1091T=P5JBC1IE;21mi.Hmi147IEO9m 9.ls567#IE;21IE<C728C147IE56<C3W095J=P14[_IE5J.H7#5K7j<NE5Kmh5636<>=@mh<C79721T=4-Yv1T8H567%U 7Z56728s5JIE;`IE;21:02.CI&F9=E.%09O9[_I.CaRIE;21+mi.Hmh147qIEO9m 9.ls‹s5JIE;kIE;21O97Z5JIBC14[_I.C=4D E ]"

] ‡ee_] D

E D E e M D E

]" l]

e ‡e_] ;D

E D E e M D E

]" >]

ee_] 0D

E FHG/I D EF.G/I e M D E

]" H]

ee_]] ;D

E F I D EF I e M D E ]"

] ‡eBD

E M D E "

] ‡e D

E M D E e ]" ]

e_] ‡eBD

E M D E " C]

e_] ‡e D

E M D E e

]" 4]

e D E FHG/I M D E " ] e D EFHG/I M D E e

+]" Š]

)miFZ3J.Šf-5K728IE;21+O97956I@BC14[_I.C==E1436<>IE56.H79NE;95JFGN)<>8H<C567tZ3J14<C09N&OZNI. "

] ‡e " ]

e_] ‡e

" ] e ‡  " " ] e ‡  " ]"

" e

] ‡e " ]

e_] ‡e

]" " e " ] e ‡  " ] e ‡  ?˜1y095JB%56021Yf ]

e_] ‡-eXZ3J14<C0956798yI.

" " " " " ‡ "  "  363J.Šs56728

‡ "%„s)1/uG790–IE;21/1_r%F9=E14NPNE5J.H7–ap.C=#mi.Hmh147qIEO9m9.ls 567–IE;21IE<C728C147IE56<C3

0Z5J=E14[_IE5J.H7`s5K363…Y…1 " " " ‡ " "%.29IE;21mi.Hmi147IEO9m 9.ls‹Fv.C=EIE56.H7`.CaRIE;91mi.Hmi147IEO9m†14o-O9<>IE5J.H79N„IE<>dC14NIE;21ap.C=Pm " ~ " ‡ ~ ]" "

e ]-*#e

" ~ " ‡ ~ ]"

" e

]-*‚He

Q 0 J 887 Xb*<>=4 (AB78

.ls+9s)1IEO9=P7`.HO2=„1_Œv.C=EIEN„I.hIE;21NPO9mhmh<>IE5J.H7j.CaRIE;21ap.C=P[_14N&<C[_IE56728hO9F….H7jIE;21NEf-NI14m/*D?˜1

1_r2<Cmh56791h<C7A<>=EYZ5JI=X<>=Ef143614mi147qITRNEO9[X;A<CNIE;21h.H791h021TFZ56[_I140A5K7˜|R568HO2=E1M-*#2*#)<C[P;˜a^<C[_1M.Ca

IE;91+143J14mi147IOZ79021T=E8C.-14N<hNEI=E14NEN [_.HmiFv.HN140.Cab<C7<nr256<C3tNI=P14NEN<C7Z0{<MNP;214<>=NI=P14NENT*?˜1

(r+dr)d

θ

r d

θ

t

_A

t

B

t

C

t

D

dr

dr

| 5J8HO2=E1+-*#2Q„"-I=E14NENE14N„1_r-1T=PI140/.H7/<C7/<>=PYZ5JI=P<>=Ef#Fv.H36<>=„143J14mi147I

?˜1d-72.Šs–ac=P.Hm YZ<CNE56[)FZ;f-NE5K[TN!IE;Z<>IDNI=E14NEN ac.C=P[_1

<>=E14<

CIE;O9N4Cs)1&721T140I.myO93JIE56FZ3JfIE;21&NI=E14NPN14N

Y-fMIE;91<>=P14<CN&O2Fv.H7Ms;956[P;jIE;21Tfj<C[_I&567j.C=P021T=„I.8C1TI„.HO2=„ap.C=P[_14NT*@"256mh5636<>=X3Jf:I.iIE;91mh.Hmi147%U

IEOZm 9.Šs 021T=P5JB><>IE5J.H79N4Hs)1m:O9NEIDIE<>dC1IE;2102.CIDF9=E.%09O9[_Ib.Cav.HO2=(ac.C=P[_14N)s5JIE;IE;91O9795JI BC14[_I.C=PN

D E <C7Z0 D E I./091T=P5JBC1IE;21iNEO9m .Ca(IE;91yap.C=P[_14N5K7{IE;21i=X<C0956<C3R<C790ŽIE<C728C147IE56<C3b095J=E14[_IE56.H79NTv=E1_U NEF…14[_IE56BC143JfC* ?˜1„Y…1T8H5K7:Y-f+1_r2<Cmh567Z56728IE;21„NEO9mhmh<>IE56.H7:.CaGIE;21„ap.C=P[_14Nb567yIE;21=P<C0956<C3%0956=E14[_IE5J.H7W* M D E ]

e ‡

M

D

E

] ‡-e

M D E M D E

] D

E D E e M D E ]

e ‡ ]

D E D E e M D E

] ‡e

] D E F I D E F I e M D E ] D E F.G/I D E FHG/I e M D E "256miFZ3656acf%56728IE;91+02.CI„F9=E.%09O9[_IEN42s)172.Šs ;9<lBC1

] ‡e

]

e_] ‡e

] ‡e

‡  ‡  ] e

] ‡e

]

e_] ‡e

?˜1y095JB%56021Yf

]

e_] ‡-e<[email protected]<C567

] ‡e

  ?˜1y<C363J.Šs

<C790 ‡I.MI14790/I.hwT1T=E.29f%5J1436095K728

~ ‡ ~

] e

"256mh5636<>=X3JfCGIE;91hNEO9mhmh<>IE56.H7Ž.Ca)ap.C=P[_14N567ŽIE;91iIE<C728C147qIE5K<C3D095J=E14[_IE56.H7˜[T<C7˜Yv1h021T=P5JBC140ŽY-f{1_r-U <CmM567956728IE;21ap.H363J.Šs567282* M D E ]

e ‡

M

D

E

] ‡e

M D E M D E

] D

E D E e M D E ]

e ‡ ]

D E D E e M D E

] ‡-e

] D E F I D E F I e M D E ] D E F.G/I D E F.G/I e M D E IE563656w456728y.HO2=O97956I@BC14[_I.C==E1436<>IE56.H79NE;95JFGNTs@1uZ7Z0

] ‡-e

]

e_] ‡-e

] ‡e

] e ‡  ] e ‡  ] e

] ‡e

]

e_] ‡e

] e ] e ‡  ] e ‡  ?˜1y095JB%56021Yf ]

e_] ‡-e

] ‡e

  N ‡ "%ZIE;956N„NE56mhFZ365Ju914N)I. ~ ‡ ~ ] Pe $;O9N42IE;2114oOZ<>IE5J.H79N„=E1TFZ=E14N147IE56728iIE;21+NPO9mˆ.Ca IE;21ac.C=X[_14N567`Yv.CIE;/0956=E14[_IE5J.H7k<>=E1 ~ ‡ ~

] e ]-*$He

~ ‡ ~ ]

| 5679<C3636fCWI./.CY9IE<C567ŽIE;21#mi.Hmi147IEO9m 14o-O9<>IE5J.H79NTs)1i=E1TIEO9=P7ŽI./IE;21M[_.H7ZN1T=EB><>IE5J.H7˜.Cami.Hmi147IEO9m

[_.H79[_1TF9I/5K3636O9NI=X<>I140 567 ]-*He_* ?˜1˜O9NE1–]-*He#ap.C=kIE;21

W @ ! ;,

s@1

=E1TFZ3K<C[_1

!/0 "$ %#, (')3)+?< C ! "1 % (',*,+f 5

s5JIE;•]-*#e<C790•]-*‚He

<C790

780 K 887b3.0=: 45Y7AB78

5KN =E1TF9=E14N147I140Y-fk]-*$Heb<C790/] -*Ce_* '(O2IIE5K7281TBC1T=EfIE;Z56728

I.C8C1TIE;21T=4Gs)1:<>=E=P5JBC1<>I&IE;91ac.H3K3J.ls5K728imi.Hmi147IEO9m†14o-O9<>IE5J.H79N " " ~ " ‡ ~ ]" " e ~ ‡ ~

] le ]-*He

" " ~ " ‡ ~ ]"

" Xe

~ ‡ ~ ]

Xe]-*He

.0K.0&"45!" 35} +&!" &3n"4FO}@I3"4+ } +!" & (

$&;21iap.H363J.Šs56728`8C14721T=P5K[BC1T=PNE5J.H7˜.CaIE;21#mi.Hmi147IEO9m 14o-O9<>IE5J.H79N5K7ŽBC14[_I.C=yap.C=Pm‰5KNF9=E1_U N147I140{567A}>€ "JD D M

" D #D

D M D D D " D

]-*6~ "qe

s;21T=P1 " WDD 56N IE;21„02fH<C0956[)F9=E.%09O9[_IR.Ca "JD+<C790LD

D

D

56N IE;21„NI=E14NEN I147ZN.C=4

D

M56NRIE;21„FZ=E14NENEO2=P1(ap.C=P[_1

Fv1T=&O9795JIBC.H36OZmi1C9<C790 " D

56NIE;218C=P<lB-56IE<>IE5J.H79<C3Wap.C=P[_1.H7kIE;91 ZO9560j143J14mi147I„Fv1T=&O9795JIBC.H36OZmi1C*ƒ?˜1

s563K3GO9NE1M] -*6~ "qe„I.h021T=X5JBC1IE;21mi.Hmi147IEO9m†14o-O9<>IE5J.H7{567`Fv.H36<>=&[_..C=X095679<>I14NT*D.ls@1TBC1T=4…Yv1Tac.C=E1s@1

Yv1T8H567/IE;91y021T=X5JBn<>IE56.H7WZs@1ymyO9NI1_r2<Cmh56721y<#[_.HO2FG3J1:.CaD[_.H7Z[_1TF9IENIE;9<>Is56363WYv1y56miFv.C=EIE<C7II.j.HO2=

021T=P56Bn<>IE5J.H7t*

| 5J=PNITNE5679[_1Žs@1A<>=E1˜s).C=Pd-56798•5K7 Fv.H36<>=k[_.-.C=P09567Z<>I14NTs@1AmyO9NI`=E14[T<C363IE;21Žap.H363J.Šs56728