• No results found

Implicit Runge-Kutta Methods for Stiff and Constrained Optimal Control Problems

N/A
N/A
Protected

Academic year: 2020

Share "Implicit Runge-Kutta Methods for Stiff and Constrained Optimal Control Problems"

Copied!
144
0
0

Loading.... (view fulltext now)

Full text

(1)

"!$#&%'#&(*)"+",.-0/12)3((5467-8(:9";<"=?>@;BA7(:#DC4E+3<F(54G(-H;.+"=(:A54G#&+3-8<FI"(#$J4E!

;B+(:A;B!KLA;BM3!&-'7=NOQP+"<"-8A(9"-R<"#$A-8%8(:#$;B+J;E>S(-839"-8+HTU*4E "MV-8!$!XW

*9"-J")"A:U;.=-J;E>(9"-JA-'=-N4GA%09Y"A:-8=-8+(:-8<Y#$+Z(:9"#$=(:9"-8=#$= #&=(;[MV-8((:-8A7)"+3<"-8A=:(54G+"<Y4E+"<\#& "A;E].-?<"#^/

A-'%8(?(A04E+"=:%8A#$"(:#&;.+Z

-8(9";<"=R>_;.A`=(:#DCF4G+"<Z=:(54E(:-7%8;.+"=(:A54G#&+3-8<a;B"(:#&J4E!%8;.+b(:A;.!*"A;.M"!$-87=cedY9"-'+Z=;.7-#$7"!$#$%8#$(**)"+",.-0/12)3((54 -8(9";<"=4EA:-#$73!&-'?-8+(-8<e4E=`4G""A;Ef#$g4G(#$;B+3=S(;J(93-<"h+U4G7#$%8=*;G>4E+[;B"(:#$g4E!

%8;.+b(:A;.!i3A;BM3!&-'HU4j!$;B==;G>4E%8%')"A54G%8he;%8%8)"A:=`k*9"-8+[(93-<"h+U4G7#$%8=*MV-8%8;.7-`=:(#^CZ;BA%8;B+"=:(A04E#$+"-8<Rl+"-8k

,BA:#$<eA-0mV+"-87-'+b(=(:A54E(:-8,Bhnk*9"#$%59J-8f"!$;.#&(:=(:9"-]B4GA#Q4E(:#$;B+7;G>4E%8%8)3A54E%'he#$=<"#$=%')"==:-8<+H4G<"<"#$(#$;B+o"(93-`)"=-;E>`4JA-'=#$<")U4G!*>_)"+3%8(#$;B+p#$+\"!Q4E%8- ;E>2%'!X4G==:#&%c4E!*-8A:A;BA?-'=(#$J4E(#$;.+H(:-8%09"+"#$q)"-8=7#$="A;E].-8+Z(:;Hk;BA:rpk-'!&!T>_;.A

=(:#^Cs=:hb=:(-8 =N;.7")3(54E(:#$;B+U4G!U-8fV-8A#$-8+3%8-?A-8].-N4E!$=(9"-#$7"A:;E]B-8 -8+(S#$+g-ut7%8#$-8+"%8hH4G+"<eA:-8!$#X4GM"#$!$#&(hk*9"-8+

(93-g+3-8kv=:(A04E(-',B#$-8=g4GA-J#$+"%8;.AV;BA54G(-8<Y4G=U4GA(?;G>w4n<"#$A-8%8(?(:A54G+"=%8A:#$"(#$;B+Y4G!&,.;BA:#&(:9"H[x";.A#$+"<3-8fZ(:9"A-8-<"#^Cy-8A-8+(:#X4G!^/z4G!&,.-8M"A04E#$%-8q)U4E(:#&;.+"=NV(:9"-`=;.!$)"(#$;B+3=;E>S=:;B7-#$73!&#$%8#$(**)"+3,B-0/1)"((04?7-'(9";<"=*J4ch?+";B(%8;B+/

]B-'A,B-.;Ek-8]B-8Ac"%8;.7")3(54E(:#$;B+U4G!b-'fbV-8A:#&-'+"%8-`A:-8]B-N4G!$=4E"U4GA-8+(%8;B+].-8A,.-8+"%8->@;BA(9"-=54E -*7-8(:9";<"=)"=-8<

k*9"-8+n#&+3<"-8f7(:9"A-'-=:(54E(:-`#$+"-8q)U4G!&#$(h %8;B+"=:(A04E#$+(=MV-8%8;.7-`4E%'(#$]B-B(*#$==:9";Ek*+J(9U4G((:9"-`=;.!$)"(#$;B+[{5|3}B~@~_c€0

4E!$;.+",e(93-g%';B+"=:(A54G#$+b(?MV;B)3+"<U4EA:hZ4E!$!$;Ek*#$+", >_;BAMU-'((-'Ag4E3"A;Ef#$g4G(#$;B+"=cH‚J;.A-8;E].-8AN(:9"-J%8;B+"=:#$=(-'+"%8ha;E>

(93-7+";.+"!$#&+3-N4EA"A:;B,BA04E 7#$+","A;.M"!$-8ƒ>_;BA:7-8<[Mhs4 <"#$A-'%8((:A54G+"=%8A:#$"(#$;B+a4E!$,B;.A#$(93„)"=#$+",H4G+p#$7"!$#$%8#$(

(2)

!' #(# ) & !'*+, )

&-*.&/0++1 2 !

Mh

, +435 1*,

6-798;:<:>=@?<ACBDAE8GFIH:>JKL%8MA<A<=N7OA<FAEP=QR?CBI7JSBDA<=UTVBIWXJYMA>ZOF[]\RFI?EA<P2^]BD?EFIYM8GHVB%_A`BA<=

a H8Mb=@?`:>8GA>Z8GHcVB?<AE8;BDYd[eJfYhgVYMYGL%=@H9AiF[iAEP=j?<=kJ8G?E=@L%=@H9A`:l[eFm?'A<P=onR=@pm?<=@=jF[qnRF9WrA<FI?sFD[

t P8GYMF:uFmcP9Z

tqvRw

Q

v

6yx

w

T

wstqzqv 6q{'|

w

\}_

v~z

_

z

6

v

^]

4G!&-'#&,.9

€Xr‚

6 tƒtqvRw'„…z n5†ˆ‡‰

(3)

9U4E#$A;E>S<"]#$=;.Ah7;.77#$(:(-8-g4G(#$%8=k*#$(9J4%8;B+3%8-8+(A04E(#$;.+7#$+g‚e4G+U4E,.-87-'+b(S%'#&-'+"%8-`4E+"<JIU-8A04E(:#&;.+"=**-8=:-N4EA:%59J#$+7‚e4ch ‚ o+7‚e4ch

‚

B9"-A-8%'-8#$]B-8<J9"#$=*‚pyB#$+7IV-8A54G(#$;B+"= -8=-c4EA%09Jk*#$(974`‚n4E(93-8g4G(#$%8=7#$+";BA)"+3<"-8A(9"-<"#$A-'%8(#$;B+ ;E>

ANV"4E!Q4E9J*UL!&J4E,.9"A54GMbhy-8#$!#&-'9"+e9U4G=*%8;E/4E)"(:9";BA:-8<H4+)"?MV-8A*;E>%8;B+ >_-8A-'+"%8-?"A:;b%'-8-8<"#$+",.=N0;B)3A+U4G!

4EA:(#$%8!$-8=74G+"<Z(:-8%09"+"#$%N4E!A-8V;BA:(=ca+

€rXr

S-'#&!*#$-89"+aA-'%8-8#$]B-8<a(:9"-e"4E!Q4E9a*S!$g4G,B9"A04EMhH4ck*4EA:<p>_;.A

;B)3(=(04E+"<3#&+3,w4G%09"#$-8]B-8 -8+(S#$+ 4G+"<?%8;.+b(:A#$M")"(:#$;B+(;`(:9"-mU-8!$<?;E>IU-'A54E(:#$;B+"=**-8=:-N4EA:%09S+(9U4G(S=54G7-hB-N4GAN

9"-`A:-8%8-8#$].-8<p(9"-RdY#$+b(:;B+/*;.=-A-'=-N4GA%09Z4ck4GA<J#$+H‚e4G(9"-8J4E(:#&%'=N-8#$!#&-'9"+e#$="A:-8=-'+b(:!$he-873!&;Eh.-8<7Mh

(4)

‚

‚

)"7-8A:#$%N4E!y‚J-8(:9";<"=*>_;.AIA<"#$+U4GAhg#^Cy-8A-8+(:#X4G!4E+"<

#^C -'A-8+(#Q4G!D/!$,.-8M"A54G#$%2q)U4G(#$;B+"=*``2R2``2R2``

€

‚ ‚ ‚ ;BMU4G((:;: 7-'(9";<"=>_;.A (#^Csh=(:-87= 2``2R2``

‚

‚

€

#^Cy-8A-8+(:#X4G!^/!&,.-8M"A04E#$%2q)U4G(#$;B+3= `2R2``2R2``

‚ € I"(:#& #! N4E(:#&;.+ ``2```2R2``2R2`` ‚<

‚ € ‚ ;B+"!$#$+"-N4GAKLA;B,.A54G77#$+", ``2R2``2R2`` ‚X‚

‚

€

€

I"(:#$g4E!V;B+(A:;B!l2```2R2``2R2``

‚<€

‚ € " )"7-'A#$%N4E!y‚J-8(:9";<"=*>@;BAI"(#$J4E!U;.+b(:A;.!`2``2R2`` ‚#

‚

" $;4E!$=*4E+"<J;B+(A:#&M3)"(#$;B+3=e2```2R2``2R2``

‚

% &('*)+-,/.102'345)+6879:6;&(+<=/>?)@. %:A

€ ‚ #$A-8%'(*iA04E+"=:%8A#$"(:#$;B+ `2```2R2``2R2`` €X

€

€

-'qb)3-8+(#Q4E!B)U4G<"A54G(#$%KA:;B,BA04E 7#D+3,g`2R2``2R2``

€X€

€

" -8"A-'=-8+(#$+", (9"-`;.!$)"(#$;B+ ```2R2``2R2``

€DC

€ C ‚J-'=9H -0mU+"-8 -8+(2O;B!$<UW 2```2R2``2R2`` €

€ C ‚ LAA;.A=(:#$g4E(:#$;B+eOQ;.!$<UW7``2R2``2R2`` €E#

€

C

€

‚ -8=9e;B+3=(A:)"%8(:#&;.+ZOQ;.!$<UW```2R2``2R2``

€

F 02-.GIHJ.@5)@LK;IKM,NOP45)@ F:%

"

‚

‚J-'=9H -0mU+"-8 -8+(2O+"-8kW 2```2R2``2R2``

€

3‚ ‚ LAA;.A=(:#$g4E(:#$;B+eOQ+3-8kW ``2R2``2R2`` C

3‚ € ‚ -8=9e;B+3=(A:)"%8(:#&;.+ZOQ+3-8kW„``2R2``2R2``

"

€

)"7-8A:#$%N4E!yf"4E "!$-8= `2```2R2``2R2``

C

3

€

‚

*93-2;-8#$+",?-8=( -8(F```2R2``2R2``

C

3€ € K4G(9g;.+"=(:A54G#&+3-8<HKA:;BM"!$-8 = `2R2``2R2`` CEC

3

€

" *k;E/(04E,B-* 2```2R2``2R2``

3€ C T-8+)"=xo!&hMh?`2```2R2``2R2`` E#

3€ 4E;Q=KA;.M"!$-8 2```2R2``2R2``

3

€

#

+"<"A:-8k*=OQVq)"-8-/ 8-'A ```2R2``2R2``

R 7ST.GU:.G.WVJ3)@6PX,/Y, Z@R

C ‚ P+"<"-8A:=(54G+"<"#$+",?;Ek "I*J;B+].-8A,.-8=`2R2``2R2`` #

C

‚

‚

+U4E!$h=#$=;E>S4E+J+"<"-8fW?h=(:-8 `2R2``2R2``

#

C ‚ € -8A:#$]B4E(#$;.+?;E>OC €-# W4G+"<pOC € BWT#$+\[9]

.G:.G4^F

`2R2`` C

C

‚

" )"7-'A#$%N4E!yfV-8A#$7-'+b(:= ``2R2``2R2``

C

€

P+"<"-8A:=(54G+"<"#$+",?dY9hJ"I*g;.+]B-8A:,B-8= `2R2``2R2``

C € ‚ *93-8;BA:h7;E>S;B+"=:#$=(-'+b("3A;Ef#$g4E(:#$;B+"= R2``2R2``

(5)

C

€

C

;.+]B-8A:,B-8+"%'-`;E>(9"-`"#$,.A54E39"=7`2R2``2R2``

‚<

C

€

*93;B)",.9b(:=;.+e;B+]B-8A:,B-8+3%8-``2R2``2R2``

‚X‚r‚

7S6P,/P:, )@ *3. 79:,N.G)@*, F

‚

;.+"%8!$)"=#$;.+"=F``2```2R2``2R2``

‚X‚

€ x3)"()3A-`;B+"=:#$<"-8A54G(#$;B+3= 2```2R2``2R2`` ‚X‚/C

V VJ3)@6PX(OY)+6;&(:6P3OP:1 [ .@,N936.G4 F @%:%

)+U:)@3U. *6P'36P.G-, @%

2‚ +U4E!$h=#$=;E>S2oK ;B!$)"(#$;.+ ```2R2``2R2`` ‚<€

(6)

"

‚

;.!$)"(#$;B+3=(:;7y#$+"-N4GA+"<3-8f ""KA:;BM"!$-8

‚

`2R2``2R2``

CG#

"€ ;.!$)"(#$;B+3=(:;?A:hb=:;B+Q=KA:;BM"!$-8 ``2R2``2R2`` C

"" (04E(:-w ;B!$)"(#$;.+"=(:;7y#$+"-N4GA*+"<"-8fW""KA:;BM"!$-8 € R2``2R2`` C

"C ;.+b(:A;.!;B!$)"(:#&;.+"=(;7y#$+"-c4EA*+"<"-'f\""KLA;BM3!&-' € 2``2R2`` X

" ;.+"=(:A54E#$+(*)"A>4E%8-`-8#$,B9(>_;.A!&e #&<3-8A `2R2``2R2`` X€

"

#

(04E(:-w ;B!$)"(#$;.+"=S>@;BA*!$J*#$<"-8A ``2R2``2R2``

"" ;.+b(:A;.!;B!$)"(:#&;.+"=T>_;BA*!&J*#$<"-8Ap``2R2``2R2``

" (04E(:-w ;B!$)"(#$;.+"=(:;7* 2```2R2``2R2``

"

;.+b(:A;.!;B!$)"(:#&;.+"=(;7* ```2R2``2R2``

"‚E ;.+b(:A;.!AA:;BA= >_;BA**R2"I*J]=NSI"I* 2``2R2``

"‚r‚ KA:-8]#$;B)"=:!&hJ*4E!$%8)"!Q4G(-8<J;B+(A:;B!KA:;EmU!$->_;BA*T-8+)"=xo!&hMh `2R2``

"

‚E€

"A;E].-8<7;B+(A:;B! >_;BAS-8+)"=xo!$hMbh `2R2``2R2``

"

‚

a(04E(:-w4G+"<eIA<"-8A*-8<3)"%8(#$;.+7>@;BA*4E;Q=KA:;BM"!$-8[(-8A04E(:#&;.+

C

`2R2``

#X

"‚/C (04E(:-w4G+"<eIA<"-8A*-8<3)"%8(#$;.+7>@;BA*4E;Q=KA:;BM"!$-8[(-8A04E(:#&;.+ `2R2`` #X

"

‚

;.7")"(:-8<g;.+(A;.!bI"I*„```2R2``2R2``

#X€

"‚O# ;.!$)"(#$;B+3=(:;?+"<"A:-8k*=OQVq)"-8-/ '-8ANy"I* `2R2``2R2`` #

C ‚ !$;B=:-PJ;E>)" -8A#$%N4G!;B!$)"(:#&;.+>_A;.e4G+"<JA)"-`;.!&)3(#$;B+ 2R2`` #

C

€

;.+b(:A;.!y,B#$]B-8+ Mhg"I* 4E+"< (9"-R(A)3-`=;.!&)3(#$;B+

‚<

`2R2``

#

C " ;.+b(:A;.!y,B#$]B-8+ Mh7*1 F4G+"<J(9"-(:A)"-`=:;B!$)"(:#&;.+ ‚< `2R2`` #

C C ;.+b(:A;.!y,B#$]B-8+ Mh7*1 F4G+"<J(9"-(:A)"-`=:;B!$)"(:#&;.+ #DC `2R2`` #

C

;.+b(:A;.!y,B#$]B-8+ Mh7*1 2J4E+3<7(93-`(A:)"-`=;.!$)"(#$;B+o

#DC

`2R2``

#

C # ;B+J(93-w 2\k*#$(9JV-8A(:)"AMU4G(#$;B+ `2R2``2R2`` D‚

C

" Ko-8A:()"A:MU4E(:#&;.+e#! 8-]B-8A:=)"=`(:-8e#! 8- `2R2``2R2``

C

(04E(:-w4G+"<e;B+(A:;B!;.!$)"(#$;B+3=;G>O

C

"-BW `2R2``2R2``

C 9U4G((:-8A*!$;B+3, ;.+"=(:A54E#$+(N39 ‚ ``2R2``2R2``

C ‚E 9U4G((:-8A*!$;B+3, ;.+"=(:A54E#$+(N3 #‚ ``2R2``2R2`` DC

C

‚r‚

‚J)3!&(:#$"!$#&-'A=:(#$g4G(-8=T>_A:;B ``2R2``2R2``

C ‚E€ 3#&,.A54G"97;G>T4x3)"+"%8(:#&;.+e2```2R2``2R2``

C

‚

\ =:#& "!$-*9U4E(>@)"+"%8(:#&;.+ 2```2R2``2R2``

‚

+U4E!$h(#$%=:;B!$)"(:#&;.+"=*(;(-'=(3A;BM3!&-' `2R2``2R2``

‚<€-#

2‚ ‚J)3!&(:#$"!$#&-'A4G""A;Ef#$g4G(#$;B+3=>@A;Bn)"=:#&+3,? ``2R2`` ‚<€

2

€

]B-8A04E,B-'<g?)3!&(:#$"!$#&-'A=a`2```2R2``2R2``

‚<€

(7)

"‚ (:-8A54G(#$;B+e(04E(#$=:(#$%8=>_;.A*i-'=(KA:;BM"!$-8 O3‚ Wl2R2``2R2`` E

"

€

"I*7]=cSI23I2* ;B+e"K ``2R2``2R2``

CEC

"" (:-8A54G(#$;B+e(04E(#$=:(#$%8=>_;.Ay#$+"-N4GA+"<3-8f ""KA:;BM"!$-8 ‚ ``2R2`` CG#

"C (:-8A54G(#$;B+e(04E(#$=:(#$%8=>_;.A*A:hb=:;B+Q=KA:;BM"!$-8 `2R2``2R2`` C

"

(:-8A54G(#$;B+J=(04E(:#&=:(#$%8=>_;.Ay#$+"-N4GA*+"<"-8fW""KA:;BM"!$-8

€

``2R2``

"# (:-8A54G(#$;B+e(04E(#$=:(#$%8=>_;.A*2"I* ;B+J!$J*#$<"-8A2R2``2R2`` X€

"" "I*7]=cSI23I2*g>_;BA** KA:;BM"!$-8 `2R2``2R2`` E#

"

(:-8A54G(#$;B+e(04E(#$=:(#$%8=>_;.A*+"<"A:-8k*=OQVq)"-8-/ '-8ANy"I* ``2R2``

#X€

C ‚ -8!Q4E(#$].-2A:A;BA:=#$+g;.+(A;.!yP=:#&+3, [4E(*-8A:7#$+U4G(#$;B+e`2R2`` #

C

€

M"=;.!&)3(-`#DCy-8A:-8+"%8-`;G>;B!$)"(:#&;.+"=``2R2``2R2``

C

" KA:-8<"#$%8(:-8<H4E+3<gM"=;.!$)"(-`#^C -8A:-8+"%8-'=2;G>L;.!$)"(#$;B+3=e2``2R2``

C C KA:-8<"#$%8(:-8<H4E+3<gM"=;.!$)"(-`#^C -8A:-8+"%8-'=2;G>L;.!$)"(#$;B+3=N2 ``2R2`` DC

C #$=%8A:-8(#! N4G(#$;B+J;G>LI"(#$J4E!y;B+(A:;B!KA:;BM"!$-8 2R2``2R2``

‚

;-0t7%8#$-8+(:=*;E>;B!$)"(:#$;B+7x3;BA =g``2R2``2R2``

(8)

*9"-g4E(:-8A#Q4G!"A:-8=-8+(:-8<p#$+e(9"#$=(93-8=#$=#$=2(:9"-A-8=:)"!$(2;G>?h7V4E=((:9"A-8-?h.-N4EA:=`4E=24 K9 =(:)"<"-8+(4G(

;.A(:9H*4EA:;B!$#$+U4 (54E(:-`P+3#&].-8A=:#$(hbT*9"-A-8=:-N4EA:%59pk*4E=*=:)""V;BA:(-8<[Mh7(93-`24G(#$;B+U4G!%8#$-8+"%'- x3;B)"+3<U4E(:#&;.+

*4E #&+ <"-8-8n,BA54G(#$()3<"-`(;?(:9"-2"xa4G=*k-8!$!4E=*?h?4E<"]#$=;.AAc(:-8"9"-'+HSV*4E73MU-8!$!y4E+"<J(:9"-`;b-'#&+3,

;B U4E+hR>_;BA*4E!$!y;G>i(93-mU+U4G+"%8#Q4E!y=:)""V;BA(S9U4c].-2A:-8%8-8#$].-8<

*9"-e;.A#$,B#$+U4G!*"A;u-8%8(7MV-8,4E+ak*9"-8+Y?k;BA:rB-8<ak*#$(9YAN ;.9"+Y-8((:= 4G(?(9"-n;-8#$+",Z;.7U4G+bh[#$+

(93-?=)" 7-8A*;G> ‚ Rdp-`)"=:-8<p(9"-7 U4EA:=-7I"(#$J4E!i;.+(A;.!S;E>_(k*4EA:-

[(:;7mV+"<p7#$+"#$)"l(#$7-=;.!$)"(#$;B+3=>@;BA(:9"-*g4G%09"#$+"-S(;;.!&#$+",;E>U%';B73!&-'f2V4EA(:=N(k*4E=;E>U,.A-N4G(S#$+(-8A:-8=(S(:;(9"-*=:%8#$-8+(#$=(:=4E(;b-'#&+3,

(;?)3+"<"-8A:=(54G+"<e(:9"-U-8Az>_;BA:g4G+"%8-;E> Jk*9"-8+n%8;B+"=:(A04E#$+(=*MV-8%N4E -`4E%8(:#&].-B

AN-8((:=NANS*4G7"MV-8!$!*4E+"<a`MV-8,b4G+ak;.Ar#$+",H;.+Z#$73A;E]#$+",J(9"-eV-8Az>_;BA:g4E+3%8-7;G> \k*9"-8+

%8;.+"=(:A54E#$+(=MV-8%N4E -24G%8(#$]B-.dY9"-8+?%8;.+"=(:A54G#&+(:=4EA-4E%8(:#$]B-B.(9"-A-8=:)"!$(#$+",=;.!&)3(#$;B+?#$=*4E!$=;4w=;B!$)"(:#$;B+?(;4

9"#$,B93-8AS#$+"<"-8f?**E!&(:9";B)3,B9

?=:-8-87-'<7(;k;BA:rk-8!$!>_;.AS#$+"<"-8f2w#&+3-8q)U4E!$#$(#$-8=cEk-*+3;B(#$%8-'<?(9U4G(S(9"-+)"7-'A#$%N4E!V7-'(9";<"=)"=-'<g<3;?+";B(%8;B+].-8A,.->@;BA*(93-2=04E -*#&+3<"-8f\R"A:;BM"!$-8 =S(A:-N4E(:-8<H4E=*-'qb)V4E!$#$(#$-8=No*>@(-8A

#$7"A:;E]#&+3,(:9"-V-8Az>_;BA:g4E+3%8-;G> 7V;.)"A>_;%8)"=()"A:+"-8<p(:;g)3+"<"-8A:=(54G+"<"#$+",e4E+3<e"A;E]#$+",

%8;B+]B-'A,B-'+"%8-;E> >_;.A*=(04E(-%8;.+"=(:A54G#&+3-8<e;B3(#$g4G!"%8;B+(:A;B!o"A;.M"!$-87=c

7

]

)@'3.G2

#$+b(:A;<")"%'-8=S(93-*g4E(:9"-8J4E(#$%N4G!b4G+"<!$#$(-'A54E(:)"A-*A:-8]#$-8ka;E>y#& U;.A(04E+(%8;.+"%8-83(=k*9"#$%59>@;BA

4RMU4E=:#&=>@;BA(9"-%8-8+(:A54E!ok;.Ar?;G>(9"#$=*(93-8=#$=NT!$(93;B)",.97(93-2J4E(:9"-8g4G(#$%N4G!bA:-8]#$-8kF#$=+";B(%8;.7"A:-89"-8+"=:#$]B-B

4J%8;.+"=#$<"-'A54EM3!&-74G((:-87"(R9U4E=`MV-8-8+\g4G<"-(:;e%8#$(-?J4E+hJk;.Ar=`k*9"#$%09p%N4G+pMU-

)"=-8<6>_;BARA-0>_-'A-8+"%'-B[*9"-A-c4E<"-8An=9";.)"!$<YMU-n> 4G7#$!$#X4cAk*#$(9Y+)" -8A#$%N4G! -8(9";<"=j>_;BAJ;.A<"#$+U4GAha<"#^C -'A-8+(#Q4G!2-'qb)V4E(#$;.+"=N+";B+3!&#$+"-c4EA

"A:;B,BA04E 7#$+",24G+"<7;."(#$J4E!"%8;.+(A;.!+g-'fb%'-8!$!&-'+b(*MV4E%0r,BA;.)"+"< ;E>i(:9"-8=:-`(;."#$%8=*%N4E+ MU->_;.)"+"< #&+ A:h=;B+

4E+3<g;‚ z-8(:(= z-8A:(=-'rB4E= i4E+"<J=:%09"-8A24G+"<eKo-8(= 8;.!$<" z

7

]

)@'3.G %

,B#$].-8=(:9"-JA-N4G<"-8A74G+Z#$+p<"-8"(:9a!&;;.rs4G((:9"-7#$+"<")3=(A:#Q4E!%8;<"-eU4EA:=-eI"(#$J4E!;.+b(:A;.!

;G>_(k4GA-7O WT<"-8].-8!$;BV-8<s4G((:9"-;-8#$+",g;.7U4G+hb [)"=-'=w4j<"#$A-8%'(`(A04E+"=:%8A#$"(:#&;.+e%8;.!&!$;%N4G(#$;B+

(9)

g4ch,b4G#$+7-8].-8+J7;BA:-#$+"=:#&,.9(#$+(;?(:9"-#&+3+"-8A*k;BAr#$+",.=*;E> >_A;. -8((:=

7

]

)@'3.G F

<"-8=:%8A#$MV-8=#& "A;E].-87-'+b(:=J4E<"-(:;g(:9"- p4G!$,B;BA:#$(9"[LfbV-8A:#&-'+"%8-79V4E==:9";Ek*+[(9U4G(

p<"#$<[+";B(V-8A>@;BAƒk-'!&!L>_;BA=(#^CY4E+"<[%8;B+3=(A04E#$+"-8<p3A;BM3!&-'7=NRl+"-8k-'AA;.A-'=(#$J4E(#$;.+g3A;%8-8<")3A-#$=24G+U4E!$hG 8-8<e(:9"-8;.A-8(:#&%c4E!$!$h 4G+"<e-8 "#$A#$%N4G!&!$hk*9"#$%09e#$7"A:;E]B-8=*-8A:A;.A23A-8<"#$%8(:#$;B+J>_;.A=:(#^Cs3A;BM3!&-'7=N (9U4G=

MV-8-8+7=:9";Ek*+?#$+?(9"-!$#&(:-8A54G()"A:-*(9U4G(S=(:#^Cn4G+"<%8;B+"=:(A04E#$+"-8< "A;.M"!$-87=g4chR%59V4E+",.-*(9"-;BA<3-8AS;E>i4G+?#$7"!$#$%8#$(

*)3+",B-0/1)"((04`#$+(-',BA54G(;.AN +"-8kF4G""A;4E%097(:; 4G""A:;Efb#$J4E(-(93- €Bc€€{c~ ;G>i4E+ #& "!$#$%8#$(i*)3+",B-0/

1)"((04<"#$=%8A:-8(#! N4G(#$;B+n7-8(:9";<7#$=4G+U4E!$hG 8-8<o

7

]

)@'3.GSR

-'f 4G7#$+"-8=o%8;B+].-8A,.-8+"%8-;E> >_;BA#$+"-8q)U4G!$#&(h=:(54E(:-*%8;B+3=(A04E#$+"-8<?;."(#$J4E!B%';B+(A:;B!""A:;BM/

!$-87=cy!$(:9";B)",.9?(9"-#$73!&#$%8#$(*)"+",.-0/12)3((54w7-8(:9";<"=S)"=:-8<JMbh Jg4ch+";.(%';B+]B-8A:,B-k*9"-8+7)3=-8<e4E=4

+)"7-'A#$%N4E!3#&+(:-8,BA04E(;.AS>@;BAS9"#$,.9?#&+3<"-8f?<"#^Cy-8A-8+(:#X4G!^/z4G!&,.-8M"A04E#$%*-8q)U4E(:#$;B+"=cB%8;.+]B-8A:,B-8+"%'-2#$=;E>_(:-8+7;.M"=-'A]B-'<7#$+

ek*93-8+J#&+3-8q)U4E!$#$(h?%8;B+3=(A04E#$+(=MU-8%';B7-`4G%8(#$]B-.*9"-mUA=:(U4GA(*;E>9U4G"(-'A C -8f"4E7#$+"-'=|

#$=4EM"!$-(;%8;.+b].-8A,.->_;.A*9"#$,B97#$+"<3-8f7#$+"-8q)U4G!$#&(h%8;.+"=(:A54E#$+(=Mh7#$+(A;<")3%8#$+",(:9"-`%8;.+"%8-83(;E>{0|"}.~_~@N€'*9"-=-'%8;B+"<nU4EA:(*=9";Ek*=

| e%';B+]B-8A:,B-8=)"=#$+",(93-`(9"-';BAh ;E>%8;B+"=:#$=(-'+b(4E"3A;Ef#$g4E(:#$;B+"=c

7

]

)@'3.G

%8;B+3%8!$)"<"-8=(9"-(9"-'=#$=4G+"<<"-8=%'A#$MU-'=*A-8=:-N4EA:%59Jq)"-8=:(#$;B+3=Sk*9"#$%09?9U4c]B-*h.-8(S(;RMU-4G+"=k-8A-'<

-8].-8A54G!V-8;B"!$-e9V4c]B-JMU-'-8+F4E+a#$7V;BA:(54G+b(R#&+U)"-8+"%'-e;B+a7-J4E+"<a;.+ (:9"-Jg4G(-8A:#X4G!3A-8=:-8+(-8< 9"-8A:-B

AN[*4E73MU-8!$!S9V4E=`MV-8-8+Y4E+p#$+"=:"#$A54G(#$;B+p(:9"A;.)",B9";.)"(?h KL9 %N4E+"<3#&<V4E%8hJ`9U4c].-74E!$k4ch=`-'+0;EhB-'<Z4

,B;;<[!X4G(-?4c>_(:-8A+3;b;.+H<3-8MU4E(:-?#$+H9"#$=;Et7%'-B7‚e4G+bhJ;G>(:9"-?(9"-';BA#$-8=R"A-8=:-8+(-8<\9"-8A:-79U4c].-=:(-8 7-8<J>@A;B

(93;B=-%8;B+].-8A=04E(#$;.+"=N*9"-'A-9U4c]B-4G!$=;`MV-8-8+e4+)"?MV-8AS;G>(#$7-8=Tk*9"-8A-9"#$=J4E(:9"-8g4G(#$%N4G!B,B-'+"#$)"=!$-0>@(S7-=V-8-8%09"!$-8=:=N

`k;B)"!$<Z4E!$=:;H!$#$rB-?(:;H(:9U4E+"rZAc ;B9"+a-8((:=74E+"<\;B(93-8A?=%8#$-8+(:#&=:(=74G((:9"-7;-8#$+",Z;B

U4E+hJ*9"-=)377-'ASk;BA:rB-8<J#$+e-N4G((!$-B3de k*#$(9eAN-8((:=k4G=*;B+"-k*#&!$!V+"-8].-8A*>_;.A,.-8(NAc-'((=%8;B+3=#$=(:-8+(!$h

%09U4E!$!$-8+",.-8<J7-B.!$-8((:#$+", -=:9U4EA:-`#$+79"#$=*,B;4E!$=T>_;BA U9U4c].-2-'+0;EhB-'<7%8;.!&!Q4GMU;.A54E(:#$+",k*#$(:9gAN-8((:=

>_;.A*;E]B-8A € hB-N4GA=4G+"<J9";BV-(;?%8;.+b(:#$+b)3-2k;BA:r#&+3,k*#$(9J9"#$v4 >_(-'A*,BA54G<")U4G(#$;B+

S?)"=:(4E!$=;R(9U4G+"r Ac ;b-'="9e)"+"+"AcB*#$7;.(9h1-8!$!&-'hbAN"K#$-8A:A-S$wA-8J4E)"<AN.#$!$!$h(:-8k4GA(

4E+3< Ac""4E!Q4E9J!$g4G,B9"A04EMhboS4E%09J;E>S(93-8=-`3A;E>@-8==:;BA=9U4G<g4=:(A;.+",7#$+V)"-8+"%8-R;B+7 -k*9"#$!$-4G((:-8+"<"-8<

2* P-8=V-8%8#Q4E!$!$hZk*4E+((;[(9U4G+"r AcS!$g4E,.9"A54GMhJ>_;BA#$+(A;<")3%8#$+",H -7(:;H=:%8#$-8+(#^mU%eA:-8=-N4GA%09F4G+"<

(10)

xo#&+V4E!$!$hb0Vk4G+(y(;(:9U4E+3r+3+`#$-893+EAc8dY#$!$!$#Q4EZ#$-89"+4G+"<`1-8A:=(-'+ 4E%8;.M"=;.+>_;BAy(:9"-8#$A)3+bk*4c]B-'A#$+",

=)3"U;.A(;E>i?h?4E%c4E<"-8 #$%-8+"<3-N4c]B;.A=N

+J(9"->_;.!&!$;Ek*#$+",`!$#$=(cBk-`4EA:-`-8#$(9"-'A*#& "A;E]#$+",;BA*)3+"<"-8A:=(54G+"<"#$+",?(:9"-`+)"7-'A#$%N4E!V=;.!$)"(#$;B+3=;.M"(54G#&+3-8<

Mh7(:9"-`U4EA:=-I"(:#$g4E!y;B+(:A;B! ;E>_(k*4EA:-OSWo<"-8]B-'!&;.U-'< 4G(**9"-;-8#$+",7;.7U4G+hb

K;IKM,N45)@P:

)"7-8A:#$%N4E!4E!$,B;.A#$(9" =S>@;BAIA<"#$+U4GAhe#^C -8A:-8+(#Q4E!Sq)U4G(#$;B+3=O_I=0W;G>_(-'+H4E!$!$;Ek

)"=-8A(;`3A-8=:%8A#$MV-`!$-8].-8!y;E>i4G%8%8)"A04E%8hj>_;BAk*9"#$%097(93-+)"7-'A#$%N4E!V=;.!$)"(#$;B+?#$=%8!$;B=:-2(:;`(93-2(:A)"-4E+U4G!&h(:#&%c4E!=;.!&)3(#$;B+ *9"-J4E%8%8)3A54E%'hp;E>* +b)37-8A:#&%c4E!S=:;B!$)"(#$;.+H#$=`;G>_(-8+p%09"-'%5r.-8<aMhH9U4G!$]b#$+",

(9"-=(-'H=:# '-?;BA%';B7V4EA#$+",?(:;g4 9"#$,B93-8A;.A<"-8A -8(9";<*93#&=(9"-'=#$=`,B#$].-8=24j+"-8k 4G""A:;b4E%09[k*9"#$%09e#$=

=9";Ek*+e(:;79U4c].-`=-']B-8A04E!rB-8he4G<"]B4E+(54G,B-8=k*9"-8+H4G""!$#$-8<e(:;7;B3(#$g4G!U%8;.+(A;.!"A;.M"!$-87=c (9"-';BA-'

#&=*3A;E]B-'<gk*93#&%09J,B#$].-8=4E+ )""V-8AMV;B)"+3<e;B+ (9"-`=:#! 8-`;E>(9"-R(A)3-`-8AA:;BAcS*9"-`MV;B)3+"<Jg4chMU-=9V4EA

>_;BA=(:#DCe"A:;BM"!$-8

=;.+7%8;4EA:=-,BA:#&<3=N)37-8A:#&%c4E!V-8fU-8A:#$-8+"%8-`=:9";Ek*=*(9V4E(MU-8(:(-8A=;.!&)3(#$;B+"=*4E+3<77;.A-4E%8%8)3A54E(:-`-8=:(#$g4G(-8=*%N4G+JMU-;BM3(54E#$+"-'<

02-.G 9.@YP: ‚e4G+h2+)" -8A#$%N4G!B -8(9";<"= >_;BAS#^C -'A-8+(#Q4G!D/!$,.-8M"A54G#$%q)U4E(:#$;B+"=O_*=5WL;BAiI=

)"+"<"-8A:,B;J4A-8<")3%8(#$;B+[;E>S;.A<"-8A;.+g=:(#^CZ4E+"<G;BA*%8;.+"=(:A54G#&+3-8<H3A;BM3!&-'7=N*9"-R7-8(:9";<"=*-8f"!$;BA:-8<e#$+

(9"#$=(9"-8=:#$=N(9"-JA54GU-N 8;B#$<FOW4E+"<\-8A:7#$(-u/z#$ "=;.+ O2"W -8(9";<"=cS4EA:-gr+";Ek*+p(:;HMV-J!$-8==

4E%8%8)3A54E(:-`>@;BA%'-8A(04E#$+H%'!X4G==:-8=;E>=:(#^C64G+"<e%8;.+"=(:A54G#&+3-8<H3A;BM3!&-'7=N he<3hb+V4E7#$%N4G!$!&h"A:-8<"#$%8(#$+",

(9"-;BA<3-8A?;E]B-8A?]B4GA#$;B)3=`#$+b(:-8A]B4G!$=NSk-e4EA:- 4GM"!$-7(:;H-0t7%'#&-'+b(:!$hZ=;.!$]B-7=:(#^C 4G+"<Z%8;.+"=(:A54G#&+3-8<a"A;.M"!$-87=c

)" -8A#$%N4G!U-8fV-8A#$-8+3%8-=:)"M"=:(54E+(:#X4G(-8=(9"#$=4G""A;4E%09

345. Y)+68.GU:)+OP:5+T:.GW79:,NO)@P, ‚n4E+h;B"(:#&J4E!c%8;B+(:A;B!"A:;BM"!$-8

=y%8;B+(04E#$+`=(04E(:]B4GA#Q4EM"!$#&+38q)U4E!$#$(hJ%8;B+"=:(A04E#$+(=`k*9"#$%09p<";J+";.(`<"8V8+"<\;B+[(9" %8;B+(A:;B!?dY938+p(9"'=7%';B+"=:(A54G#$+b(:=`MV8%8;B

-4E%8(:#&].-BE(:9"-*;B"(:#$g4E!.%8;B+(:A;B!3=;E>@(k4GA-?)"=(omU+"<(93-*=;B!$)"(:#$;B+`(:;4*2 N(T9U4E=;E>@(-8+?MV-8-8+?(:9";B)",.9(

(9U4G((93-+)" -8A#$%N4G!B7-'(9";<`)"=:-8<??)"=:(yMU-*4EM"!$-S(:;=;B!$].-S(9"-)"+"<3-8A!$h#$+",2 2*c(#$==93;Ek*+(:9U4E(o

(11)

k*9"#$%59A-'!X4G(-8=\k*9"-8+?)"=:-8<?#$+ 74E+3<\)"=:-8<g4G=4E+*1Y -8(93;b<;B+(93-*)"+"<"-8A:!$hb#$+",*2

(#$==9";Ek*+[(9U4G((:9"-?(k; 7-8(:9";<"=%c4E+[<"#^C -8A`4G=2?)3%59e4G= OEW*#$+e(93-?%8;B+(A:;B!he%09U4E(:(-8A:#&+3,

;B+Z4E+3<p;ECY(9"-

%8;B+3=(A04E#$+(N(:9"-J+b)37-8A:#&%c4E!S;."(#$g4G!%8;B+(A:;B!=;.!&)3(#$;B+p%N4G+Z4E"3A;Ef#$g4E(:-(:9"-7(:A)"-=;B!$)"(:#$;B+7k*93#&!$-(9"-` 1 >_;BA:?)"!Q4E(:#&;.+;G>i <";-8=*+3;B(N

79:T:.GU. D.I+<S ] . [ )+'.- .G ] *9"-8A:-9U4G=MV-8-8+e4%';B+"=:#&<3-8A54GM"!$-24E ;B)"+(;E>A:-8=-c4EA%09J<"#$=/

%8)"==:#$+",?(9"-%8;.+]B-8A:,B-8+"%'-`;E><"#$=:%8A-8(:-4E3"A;Ef#$g4G(#$;B+"=(:;%8;.+(#$+)";B)"=%8;.+b(:A;.!y"A;.M"!$-87=c!&!y;G>(9"-"A-8]#$;B)3=ik;BA:rrb+3;Ek*+`(;(9"-*4E)"(:9";BA<";-8=+";.(S4E%8%8;.)"+(o>_;BAok*9U4E(o#&=o9U4E3U-8+3#&+3,2#$+R x3;BA4*%8-'A/

(54E#$+ %8!Q4E==*;G>i"A:;BM"!$-8 =N.#$(#$==9";Ek*+J(9V4E(*Mh?<"#$=%8A:-8(#! 8#$+",?(:9"-;B"(:#$g4E!3%8;B+(A:;B!y"A:;BM"!$-8 )"=:#&+3,R

(9"-`K k*9"#$%09e#$=>_;BA:7-8<J%8;.+"=#$=(:-8+(!$hH4G""A;Ef#$g4G(-8=(93-%8;.+(#$+)";B)"=;B"(:#$g4E!V%8;.+b(:A;.!i3A;BM3!&-'H

24E -8!$hbG#D>(9"-R;B"(:#&J4E!V=;.!&)3(#$;B+"=;E>S(:9"-`4E""A:;Ef#&J4E(:#&+3,2K=4EA:-2%';B+]B-8A:,B#$+",V"(93-8h7%8;.+]B-8A:,B-`(:;

(9"-`%';BAA:-8%8(=;.!$)"(#$;B+oS*9"-`%';B+]B-8A:,B-8+3%8-3A;;E>S<";-8=+";.(4E==:)"7-;.A"A:;E]B-(9"-R%8;B+]B-'A,B-'+"%8-;E>S(9"-4E==:;%8#Q4E(-'<so4E,BA04E+",.-?)3!&(:#$"!$#&-'A=N +e> 4G%8(N +b)37-8A:#&%c4E!-'fbV-8A:#&-'+"%8-7=:9";Ek*=(9U4G((9"-??)"!$(:#&3!&#^-8A=*<3;

+";B(*%8;.+]B-8A:,B->_;BA*93#&,.97#$+"<"-'f G;BA:<"-8A*%8;.+"=(:A54E#$+(=c

*9"->_;.!$!&;Ek*#$+",")3M"!$#&%c4E(#$;.+"=#$+"=:"#$A-8<e4G+"<E;.A*A-8=:)"!$(-8< >_A;. (9"-k;BA:r7;E>(9"#$=*(:9"-8=#$=c

‚ *(-839"-8+gTb*4G7"MV-8!$!E-'#&!V#&-'9"+4E)3A-8+( 4chb4G+"<?A54E%'hdp-8=:(M"A:;;Bry

`{



.}B

~&|3 € € €

N~$| E*}

~@€}80{N~ €

~

N}.~

B;B ""!$#$-8<?‚e4E(:9

‚<€r

€rrX

‚E

/

‚

‚

€

;B93+`E-8(:(=N-8#$!"#&-'9"+(-839"-8+gTB*4E "MV-8!$! 'dY#$!$!&#Q4G Kc) C J4E+



8}.~

€ € .N€

}.€ Q}B~

8|\€





~ € Q€:5{c~~@€}

8{N€

~

c~&| Gu ;B e3"!$#&-'<Z‚e4E(:9

‚<€

€rrX ‚/C c/ ‚

3-8#$!S#$-89"+S(:-8"9"-'+ T*4E "MV-8!$! ;B93+p`y-'((=c4G+"<pdY#$!$!&#Q4G Ko)Cyg4G+

! c€



{0

{

! c€



~ Q€ $8{c€c~N}.~



~

}#"i{

~_€ "

€

$ "$

8"KA;%`;G>i(93-`+(-8A:+U4E(:#&;.+U4E!o=:=;E/

%8#Q4E(#$;.+?>_;.A‚e4G(9"-'g4E(:#$%8=4E+"<J;B ")"(-'A=*#$+g#$?)"!Q4G(#$;B+ €rXr 4G)"=54G+"-BoO_**I‚eW'

C ;B93+g`-8(:(=N3-8#$!y#$-89"+V(-839"-8+HT"*4E73MU-8!$!EdY#$!$!$#Q4E K)Cyg4E+o% b~@}B~ }&"('

c€ *)



{0

Q~&|J('

" Q~

€ Bc€

}.€ Q}.~

+ '|e€





~ € €0{N~~@€}

8{N€

~

+

(12)

O_* *I‚eW8

;B93+H`V-8((:=NodY#$!&!$#Q4E KU)Cyg4E+oU-8#$!S#&-'9"+4G+"<s (-8"93-8+ZSy*4E "MV-8!$! '

" Q~

€ .N€

}.€ Q}B~

'z|J€:





~ € Q€0{c~S~@€}

u{c€

~

c~&| Gu*IS$ -8%09g -8V;BA(‚2/

S*/

/

X€r€

‚

#

;B93+e`V-8(:(=cydY#$!$!&#Q4GvK")C J4E+3-8#$!#&-'9"+y4E+"<[(-839"-8+pSy*4E "MU-'!&!['|*





~

|"}B~ '

" Q~ *€.N€"}.€ Q}.~ BKA:;%B"I"(#$g4G!$=(-')"-8A)3+",B=:"A;.M"!$-87-#$+<"-'A )>_(/)"+"<74E)"j>4E93A(N

P+"#$]B-'A=#$(04E(M$A:-8#^>_=k*4E!$<K)"M"!$#$=93-8<JMbh #$-8A:;B+h?)"=N‚J)"+"%09"-'+ €Xrr ‚ / ‚E€

3 ;B93+p`-8((:=N-8#$!#$-89"+S(:-8"9"-'+ S*4E "MV-8!$!y4G+"<pdY#$!$!&#Q4G Ko)Cyg4G+

! c€



{0

{

! c€



~ Xu{c€c~c}B~



~

}&"{

~@€ "

€

$ "&

u"KLA-8"A:#$+b(c €Xrr

;B93+H`V-8((:=No-8#$!S#$-89"+ (-8"93-8+ZS*4G7"MV-8!$!"4E+"<[dY#$!$!$#X4GvKV)Cyg4G+ '

" Q~

€ .N€

}.€ Q}B~

'z| €





~ € Q€:0{N~~@€}

u{c€

~

c~$| E{

~@}B~

}#"2('

c€ Q

{0N

(13)

*9"->_;.!$!&;Ek*#$+",?=:-8%8(:#&;.+"=`k*#$!$!#&+(:A;<")"%8-?(:9"-?A-c4E<"-8A(;J(:9"-?=V-8%8#^mU%

g4E(:9"-8J4E(#$%N4G!y(;."#$%8=`k*9"#$%09Hk*#$!$!MU-)"=:-8<J(9"A:;B)",.9";B)"(*(:9"-A-8=:(;G>i(93-2(:9"-8=:#&=cS(*k*#$!$!UMV-`4E=:=)" -8<7(:9U4E(*(:9"-A-N4G<"-8Ar+";Ek*=(93-`MU4E=:#$%%8;.+"%8-8"(:=

MV-89"#$+"<e<"#^Cy-8A-'+b(:#Q4E!-'qb)V4E(#$;.+"=N3+";B+"!$#$+"-N4GA*;B"(:#$7#! N4E(:#$;B+74E+3<g;."(#$J4E!V%8;B+(A:;B! -N4E<3-8A=)"+> 4G7#$!$#X4GAk*#&(:9

=;.7-;E>i(:9"-8=:- 4GA-N4G=4EA-A:-0>_-8A:A-8<[(; " C € " ‚ i4E+3<

x";.A-N4E=:#&-'A2A:-N4E<3#&+3,UVk-#$+(A;<")3%8-?(9"-R>_;.!&!$;Ek*#$+",+";B(04E(:#&;.+!$!]B-8%8(:;BA`]B4GA#Q4EM3!&-'=24E+3<e]B-8%'(;BAR]B4E!$)"-8<

>_)"+3%8(#$;B+3=4EA-%8;.+"=#$<"-'A-8<[%8;B!$)" +?]B-8%'(;BA:=24G+"<Jk*#&!$!VMU-k*A:#&(:(-8+n#&+ MU;.!$<>4E%'-BSx";.A*-8f"4E "!$-B

O5W =#$+O5WoO5W ! #"$

‚ 3 &%"#r€

k*9"-8A:-(' <"-8+";.(-8=R(9"-(A04E+"=:U;.=-?;E>*4?]B-'%8(;.AN`+[4E<"<"#$(:#&;.+"k*93-8+H#$(#&=%8!$-N4GA>_A;.v(:9"-?%8;B+(:-8f(Nyk-`k*#$!$!

#$+"=(:-N4E<J;G>

O5W8

$#$]B-8+J4A-N4G!].-8%8(;.A

;E>!&-'+",B(:9*)k-k*#$!&!y)3=-(9"-R+";BA:7=N

+

+

-,/. 01324

1$56

7

+

+8

YJ4Ef 1:9

1

9

k*9"-8A:-;

1

#$=*(:9"-;<(9J%8;B U;.+"-8+(;E>i(:9"-`].-8%8(;.A

+*)>=?)ng4G(A:#&fA@ 9U4G=*(9"-`#$+"<3)"%8-8<J+";.A7=c

+ @ +

=)3

BDC 2FE

+ @

+

+

+

+

@

+8

=)"

BDC 2FE

+

@

+ 8

+

+!8

(14)

+

oO5W

+

=)"

" oO5W

4E+3<7>@;BA]B-8%8(:;BA]B4E!$)"-8<j>_)"+"%8(:#$;B+"=c

+

O5W + =)"

"

+

O5W + 8

%

! #"

%$& ' !

%$&

()

+*

!

‚e4G+bhJ"9h=#$%N4G!"A;%8-8=:=-8=%N4G+HMV-<3-8=%8A:#$MU-8<Z4G%8%8)"A04E(:-8!$heMhg;.A<"#$+U4GAhJ<"#^Cy-8A-8+(:#X4G!-8q)U4E(:#&;.+"=?O_I=5W;.A

<"#^Cy-8A-8+(:#X4G!^/z4G!&,.-8M"A04E#$%-'qb)V4E(#$;.+"=*O_*=5W'dp-%';B+"%8-'A+7;.)"A=:-8!$]B-8=Tk*#&(:9(:9"-*>@;B!$!$;Ek*#&+3,In>_;BA:?)"!Q4E(:#&;.+"=N

(93-2#$+"#$(:#X4G!U]B4G!$)"-"A;.M"!$-8 OQKSW*k*#$(:9?)n%8;B U;.+"-8+(=c

-, O5W < O

O5W 5W /. 0 21

O0NW

0 O‚ ‚ W

4E+3<g(:9"-MU;.)"+"<U4GAh ]B4E!$)"-3A;BM3!&-' OKSW8

-, O5W < O

O5W$ 5W$*3. 0 21 5460

O0NW87941

O21 W

k*9"-8A:-54 0 4G+"<:4 1 4EA:-7J4E(A:#$%8-8=?4E+"<

#&=74n]B-'%8(;.A?;E>2!$-8+3,B(9 )ak*9"#$%09a"A;E]#$<"-?)

%8;B+"<3#&(:#$;B+"=?4E((9"-MV;B)"+"<V4EA#$-8=c?*9"-8;.A-8 =;B+[-8f#&=:(-8+3%8-g4G+"<H)3+"#$qb)3-8+"-8=:=`;E>*=;.!&)3(#$;B+"=cy=(04EM"#$!$#$(hJ"A;.U-8A:(#$-8=cS4E+"<[=;.!&)3(#$;B+

>_;.A7=Tk*#&!$!"+3;B(*MV-,B#$].-8+79"-'A-B3M")"(%N4E+JMV-*>_;.)"+"<7#$+

€

CI‚ i4E+"<

C@€

i].-8+J#^>i4E+gIp#$=r+";Ek*+7(:;

9U4c].-w4)3+"#$qb)3-2=:;B!$)"(:#&;.+#$+J7;B=:(%c4E=-'=NV(9"-R-8q)U4E(:#&;.+"=4EA:-`(;;?%8;.7"!$-8f?(:;mU+"<e4E+e4G+U4E!$h(#$%N4G!y;B+"-BTdp-4EA:-;E>_(:-8+J#&+J+"-'-8<e;E>+)"7-8A:#$%N4E!V=#$?)"!Q4E(:#$;B+"=S(:;;.M"(54G#$+g4E+e4G""A;Ef#$g4G(-*=:;B!$)"(#$;.+

*9"-8A:-`-8f#$=(49";.=(*;E>+)"7-8A:#$%N4E!V7-8(:9";<"=*k*9"#$%09g4G""A;Ef#$g4G(-*(:9"-=;B!$)"(:#$;B+"=*;G>L4R<"#^C -8A:-8+(#Q4E!o-8q)U4c/

(#$;.+`*9"-'=-7#$+"%'!&)3<"- Lfb3!&#$%8#$(*)"+",.-0/12)3((543 "!$#$%8#$(*)"+",.-0/12)3((543y<V4E7=cV<U4G7=/‚J;.)"!$(;B+o"*2x

xo#$+"#$(-!$-8 -8+(4E+"< 7;.A-Bo24G#&A:-8AN.;.A=:-8((4G+"<7dZ4G+"+"-8A "

€

4G+"<74E#$A-8A*4E+3<?dZ4E+"+"-'A "-y,B#$].-4%8;Bj/

"A:-89"-8+"=:#$]B-7=:()"<3hH;G>(:9"-8=- 7-8(:9";<"=`4E+"<[;B(:9"-8A:=N +H(:9"#$=`<";%8)" -8+(Nyk-?%8;B+3%8-8+(A04E(- ;B+[(k;J "!$#&%'#&(

*)3+",B-0/1)"((04aOQ 1wWR7-'(9";<"=<;A04EV-/ 8;B#$<Y4E+3<Z-'A7#$(:-0/z #& "=;.+pI]B-8AJ4eU4GA(:#&(:#$;B+Z;G>2(:9"-J#&+(:-8A]B4G!

0 1

06=

4

= %%!% = 2>@?

4

(15)

, 1 < . ? 4 7 . ? 4 0 24 1 , . ? 4 7 1 . ? 4 ‚ < . . ? 4 7 . ? 4 0124 1 , 1 k*9"-8A:-, 1 #$=4G+g4E3"A;Ef#$g4G(#$;B+(; , O . ? 4 7 1 . ? 4 W'! . ? 4 . . ? 4 "4E+"< . #$=(:9"-`4E"3A;Ef#$g4E(:#$+", =;.!$)"(#$;B+ (; O .

W8dp-g4chA-8"A:-8=-'+b(`4? )"+",B-u/1)"(:(547-'(9";<7)3+"#$qb)3-8!$h?Mbh (9"-R)"(:%09"-8A(04EM"!$-N4G)

@

k*9"-8A:-(:9"-%8;B U;.+"-8+(=;E> @

4GA-1 y4E+"< 4EA:-1 >_;.A ‚ < #$=%c4E!$!$-8<

(93-?=(54G,B- +b)3?MU-8A;G>(:9"-g )"+",B-u/ 1)"(:(54J

€ 4E+"< j>_;.A`(9"-?A04EV-/ 8;B#$<Z4G+"<

-'A7#$(:-0/z #& "=;.+?7-8(:9";<"=A-8=:U-8%'(#$]B-8!$hS*9"-'#&A*(04EM"!$-N4G)

  

‚ ‚X€ ‚r€

‚X€ ‚r€

2

   

‚X€ r€DC ‚

‚r€DC

‚ ‚E# €

‚-#

‚E# € ‚-#

%

*9"-8#$A*J4E(93-8g4G(#$%N4E!$!^h`-8q)"#$]B4E!$-8+(%8;B!$!$;%N4E(:#&;.+?>_;.A =4GA-‚

. . ? 4 7 . ? 4 € O < . 7 < . ? 4 W . . ? 4 7 . ? 4 # O < . 7 C! < . 7 < . ? 4 W k*#$(9 < . < O . . W*4G+"< < . <#" . ‚ € O . 7 . ? 4 W$ . ‚ € O . 7 . ? 4 W-7 . ? 4 O < . ? 4 < . W %

%'&(%'& % )+*',.-0/!/1*321212465879/1:*<;=?>*'@BAC/1DEFACG=/17058=

*9"- iA04EV-/ 8;.#&<a4E+"<p-8A #$(-0/#$7"=:;B+[7-8(:9";<"=`MV-8!$;B+",[(;n(9"-J=54G7-> 4G7#$!$h7;G>*1„7-'(9";<"=`%c4E!$!$-8<

(16)

V;B#$+(

O

.

W*4E+"<J(:9"-`+)"7-'A#$%N4E!V=;.!$)"(#$;B+

(9"-'A-BV(93-2,.!$;BMU4G!U-8A:A;.A#$=*<"-0mU+3-8<e(;?MV-.

.

.+

O

.

W %

*9"-!$;b%c4E!-8AA:;BA

.

#$=(:9"-<3#DCy-8A:-8+"%8- MU-8(k-8-8+

.

4E+"<e(:9"--8f"4E%8(`=:;B!$)"(:#&;.+e4E(

.

k*9"#$%09eU4G==-'=`(9"A:;B)",.9

(93-2V;B#$+(

.

?

4

dp-+";EkY<"-umU+"-`(:9"-`;BA:<"-8A*;G>L4+)"7-'A#$%N4E!V7-'(9";<

. 3POP@L

c€ Q{0}#"

~@

€}.~

€

"&} ${

c€



~ J;BA<3-8A €~$|" €}&""

)S~&|3

"

$

}&"ic€8€ €8}B~$S8

+

.

.

+8

O‚ € W

|3N€: YJ4Ef

.

.

$}?{ 8~_}

~

| Q{0| B



$

G €~&|3 .N€

}.~

'

O5WR}

}.€8~}&"

Bc€

}B~

8

<

Q~$|J€'

0{c~~ }

x";.A`=) t7%8#$-8+(!$hH=:7;;B(:9H=:;B!$)"(:#&;.+"=No7-'(9";<"=`#$+p(:9"-g ;BMU4G((;J: >4E #&!$h 9U4c]B-?;.A<"-8A €

€

*-'%N4E!$!y(9V4E(

#$=*(9"-+)"?MV-8A;G>i=:(54E,.-8=*#$+7(:9"-`*)"+",.-0/12)3((54R>@;BA?)3!X4G(#$;B+oU*9)"=cY9V4E=

€

4E+3<g

9U4G=

C

+e4G<"<"#$(#$;B+oB(:9"-`!$;%N4E!y-8A:A;.A>_;BA*(:9"-8=-R7-8(:9";<"=*=54G(#$=>_h

.

O

4

W

%

+";.(9"-'A#$7V;BA:(54E+("A:;BV-8A(hJ;E>(9"- 4E+"< 2 7-'(9";<"=#$=**/=(54GM"#$!$#&(h "-o*9"#$=*7-N4G+"=(:9U4E(T>_;.A

=;.7-*"A:;BM"!$-8 =N.(9"-=(04EM"#$!$#$(h;G>(9"-+)"7-'A#$%N4E!37-8(:9";<"= #$7#D%T(9";.=-;E>(:9"-<"#^C -8A:-8+(#Q4E!y-'qb)V4E(#$;.+?-8]B-8+

;B+n%8;b4GA=-?,.A#$<"=c+e,B-8+3-8A54G!o4?+)"7-'A#$%N4E!o7-8(:9";<e#$=%N4G!$!&-'<H /=:(54EM3!&-#^>S(9"-+)"7-8A:#$%N4E!o7-8(:9";<e#$=w4G!$=;

=(04EM"!$-B3A-8,4EA:<"!$-8==;E>i(:9"-`,.A#$<7=:# '-B";.+g(:9"-"A;.M"!$-8

,

O5W FoO5W

k*9"-8A:-*-.OVW =



dp-k*#$!$! 4G!$=;`MV-#&+(:-8A-8=:(-8<n#&+ (9"-MV-89U4c]#$;BAS;G>i(:9"-+b)37-8A:#&%c4E!V7-8(:9";<?k*9"-8+e4E+JI26#&=8~*$#$]B-8+

#$+()"#$(#$].-8!$h#$+ "z"4G+eI2\#$=<3-8-87-'<H8~„;E].-8A4E+ #&+(:-8A]B4G!

4

#^>

&$$(9"-T=(-'7=#! 8-*+3-8-8<"-8< (;`J4E#$+(54G#&+=(04EM"#$!$#$(h`;E>y(9"->@;BAk*4EA:< L)"!$-8AS7-'(9";<#&=?)"%09=J4E!$!$-8A

(17)

-'-8<"!$-8==(;R=54chN(:9"-*>@;BAk*4EA:< L)"!$-8AS7-'(9";<

.

.

? 7

.

?

<

O

.

?

.

? W'B<";-8=T+";B(9U4c].-*]B-8A:h`,B;;<

=(04EM"#$!$#$(hJ"A;.U-8A:(#$-8=c7=4 7;BA:-q)U4G+(#$(54G(#$]B-`<3-0mU+"#$(#$;.+yk-?k*#&!$!%8;.+"=#$<"-8AR(9"-7IlO ‚ ‚ W(;JMU-J8~

;E]B-'A*(9"-#$+(-8A:]B4E!

4

. 0 21 #D>(9"-R-8#$,B-8+]B4E!$)"-'=

;E>i(:9"- 4E%8;.M"#Q4E+

<

B

O

O5W$5W=54G(#$=>@h

O

4

W #&+

*-.O

W ==

‚ %

xo#&A:=(<"#$=%8;E].-8A-'< MhpKA;.(9"-'A;Z4E+3< *;.M"#$+"=;.+

C

z(:9"-g4G%8%8)"A04E%8h\;E>(:9"-J=;B!$)"(:#$;B+"=`;.M"(54G#$+"-8<p)"=:#&+3,

=-']B-8A04E!y*1 7-'(9";<"=Sk*4E=T+";B(SA:-8!Q4E(:-8<7(:;`(9"-%8!Q4E=:=#$%N4E!V;BA:<"-8A;E>y(9"-7-8(:9";<4E=S<"-umU+"-8< #&+7-0mV+"#$(#$;B+ ‚

KA:;B(93-8A;J4E+"<J*;BM3#&+3=;B+ C -'f 4G7#$+"-8< (9"-(:-8=("A;.M"!$-8

,

O5W oOoO5W

O5WW87

,

O5W$oO 0 W O 0 W O‚ "BW

k*9";.=-[=;B!$)"(:#$;B+a#$= O5W O5W';B(-n(9U4G(HO ‚ "BW?#$=746!&#$+"-c4EA#! N4G(#$;B+a;G>

,

O 5W8 k*#&(:9 4E=g4G+

4E3"A;Ef#$g4G(#$;B+(;VO O5W$ 5W8

dp-4EA:-S%8)"A:#$;B)"=4EMV;B)"(o(9"-SMV-89U4c]#$;BAo;E>"p4E+3<`2k*93-8+`2KL=L4GA-*8~

*y@>Uk-S<"-umU+"-.

YJ4Ef

.

.

k-2<3-8=#$A-R(;)"+"<"-8A:=(04E+"<ek*9V4E(*9U4G"U-'+"=*k*9"-8+e 4E+3<72J4GA-`4E"3!&#$-8< (;eO

‚

c€ R8~ "

Q~;

.

4E=Rg4Ef

.

.

 7(R()"A:+"=`;B)3(`(9U4G(`7-'(9";<"=`=04E(:#&=z>_h#$+",

,.#$]B-?4E+Z4E=:h7"(:;B(#$%N4G!$!&h

-8f"4E%'(`A-8=:)"!$(`#$+H(:9"#$=%N4E=:- E )"%09p7-8(:9";<"=24GA-?%N4G!&!$-8<\8~ J}.{5{ €}.~_c*9"-8=-?#$+"%'!&)3<"-74G<U4E)e:

y;.MU4E(:(;: 4E+3<gy;.MU4E(:(;?:

(9V4E=SMV-8-8+ =9";Ek*+?(:9U4E((9"- ;BMU4G((:;`:F -8(9";<"=9U4c].-*;BA:<"-8A

?

4

#D>yk-<"-0mV+"- *7#$+

1

1

>_;.A

O

‚

"BW "Ez *9"#$="9"-'+";B -8+";B+n#&=%N4E!$!$-8< € .N€€{c~

*9"-8A:-0>_;BA:-By;.+"- #$,B9(+3;B(-'fbV-8%8(R(9"-,B!$;BMV4E!

-8A:A;BA;E>Y;.A*2 (;?!$;;Br?!$#$rB- 7O

?

WT>_;.A*=(#^CH3A;BM3!&-'7=N

(#&=(:9"-8+[+U4E(:)"A54G!S(; =9";Ek %8;B+]B-'A,B-'+"%8-7;G>4?+)" -8A#$%N4G!7-8(:9";<ek*#$(9";.)"((:9"-?%8;B+3=(54G+(

#&+aO

‚

€

W

<"-8V-8+"<3#&+3,?;B+J(9"-RU4EA:(#Q4E!y<"-'A#$]B4E(:#&].- <

B

Sy-8()"=*<"-0mU+3-`(9"->_;.!$!&;Ek*#$+",R;B+"-0/=#$<"-'< #$"=%09"#$(= %8;.+"<"#$(#$;.+s

. 3POP@ %

{N~

< O

5W X*u} ~ 8}B~$ }

 ) B

u{0| ~{

Q~

}

" *~$|"c€

('$8~ `}

~_{

8~@}

~[ {5|[~$|"}B~

X

<

O

5W

<

O

X

5W

+

X

+

€`}&""

X

~&|3?{

Q~

| "E

" €

X



8N~

€8c€`~ ~$|"  ) B

u{0| ~

{

Q~

(18)

-'A-B

#$=*(9"-?)"%'!&#$<"-c4E+e#$+"+"-'A"A:;b<3)"%8(k*9"-8A:-+ +

*dY#$(9J(93#&=<"-0mU+3#&(:#$;B+3(9"-%8;B+3%8-8"(

;E>S/%8;.+b].-8A,.-8+"%8-%N4G+gMV-`,.#&].-8+ € z

. 3POP@ F |3

c€ Q{0}#"

N~$| €}

$2{0}&""&){

! N€



~ € .N€

+

.

O

.

W

+

|3N€: € "Q'

" ~$|"  ) .

u{0| ~{

u~@}

~

$

~$|" .N€

}.~

'

}

}.€8~}&"

Bc€

}B~

8 < S('B{ "

<

B

(?%N4G+ MV-e=:9";Ek*+a(9U4G(?(9"-J>4E7#$!$he;G>wy;.MU4E(:(;p:„7-'(9";<"=74GA-J+";B(?#$+a,B-'+"-8A54G!T/%';B+]B-8A:,B-8+(

€

;Ek-8].-8ANT(9"-JA54GU-/ ';B#$<ZA:)"!$-g#$=S/%8;.+b].-8A,.-8+(

€

p+\1A54B4G#0-8]B4E+3,B-8A "

#$==9";Ek*+\(;[MU-T/ %8;.+]B-8A:,B-8+(;G>i;.A<"-8A € k*#$(:9g]B4GA#Q4EM3!&-=(:-8e=#! 8-`4G+"<

+

,,,

+

MV;B)"+"<3-8<

xo#&+V4E!$!$hb.k-+";.(-`(:9U4E(*(:9"- € Bc€€{c~

39"-8+";.7-8+";.+7#$=*+";.(*!&#$ #&(:-8<?(;?=:(#^Cp"A;.M"!$-87=c+gJ4E+h

%N4G=-8=c"(#$ -<"-8A:#$]B4E(#$].-8=;G>

<

O

5WJ4ch+3;B(MU-%8;.+b(:#$+b)3;B)"=4G+"<E;.AMV;B)3+"<"-8<+J,.-8+"-8A04E!#^>

<

O

5W9U4G=

MV;B)"+"<3-8<?<"-8A:#&]B4G(#$]B-'=NE(:9"-S>@)"+"%8(:#&;.+

k*#$!&!9U4c].-#7

‚

,

<

O

5W'yh"#$%N4G!$!&h

(93-*;BA<3-8A;G> 4w+b)37-8A:#&%c4E!7-8(:9";< j#&=T<"-8(-'A7#$+"-'<?MbhRg4E(:%09"#$+",k*#$(9?(:9"-mUA:=( /7

‚

(-'A7=T;E>y(9"-*S4ch!$;BA

-8fU4G+"=#$;B+o*9"-8A-u>_;BA:-B"#^>i;.+"!$h 7

‚

<"-8A#$]B4G(#$]B-8=*;G>

-'fb#$=:(4E+"<e4EA:-MU;.)"+"<"-8<o"k-2=:9";B)3!&< ;B+"!$h?-8fV-8%8(4

+)"7-'A#$%N4E!V7-'(9";<7(:;?9U4c]B-;.A<"-8A

*9"A;.)",B93;B)"((9"-A:-8g4G#&+3<"-8AS;G>i(93#&=(93-8=#$=N3k-k*#$!&!V4E==:)"7-(9U4G((:9"->_)"+"%'(#$;B+

<

O

5W#$=4G(!$-N4G=(%8;B+/

(#$+)";.)"=No*9"#$=#$=%8;B+3=#$=(:-8+(*k*#&(:97(:9"-=:;E>_(k*4EA:- k*9"#$%097k-)"=:-(;=;B!$].-*;B"(:#&J4E!"%';B+(A:;B!V"A;.M"!$-87=c

+p=;.7-;B"(:#$g4E!%8;.+(A;.!3A;BM3!&-'7=No(93-?;B"(:#&J4E!=;.!$)"(#$;B+[#$=`<"#$=%';B+(#$+)";B)3=NJ;Ek-8].-8AN#$(`#$=`%8;.7 ;B+

"A04E%8(:#&%'-`>_;.A*=%8#$-8+(:#&=:(=)"=#$+", n(;[€

"$}B€ N(:9"-`%8;.=( >_)"+"%8(:#$;B+3hb#$-8!$<"#$+",?=:;B!$)"(:#&;.+"=*k*9"#$%09e4EA-R%8;B+/

(#$+)";.)"=4G""A:;Efb#$J4E(#$;.+"=(:;(:9"-<"#$=:%8;B+(#$+)";.)"==:;B!$)"(:#&;.+x";.AS-8f"4E "!$-BB(:9"-;."(#$J4E!%8;B+(:A;B!

oO5WL>_;.AS(9"-"A:;BM"!$-8 ;E]B-8A 0 21

7#$+ 21 O‚ C W

=N(c

,

O5W O5W O

‚

W

9

O5W

9

‚

O

‚

#

W

(19)

$ $

7#$+ 21 7 "

"

O5W O‚ W

=N(c

,

O5W O5W O‚ W

9

9

‚ O ‚ ‚< W

O 0 W 0 O

‚

‚X‚

W

k*#$(9



= =-=

‚

k*#&!$!VMU-4`%8;.+(#$+)";B)"=4G""A:;Efb#$J4E(#$;.+(:;?(9"-<"#$=%';B+(#$+)";B)3=*=;B!$)"(:#$;B+

%'&(%'& BDE 7 @17 /1D -4C7 ,@1- D- /1D *.=

;B+3=#$<"-8A*(:9"-`,B-'+"-8A54G!%8!Q4G==*;E>-8q)U4E(:#$;B+"=

O

-, 5W

A

O0NW

0

%

O

‚

‚<€

W

@>

B

#$=4R+";B+3=#$+",B)3!X4GASg4G(A:#&fyE(:9"-8+J(93-=h=:(-8„4EMV;E]B-#&=%N4G!&!$-8<J4E+ #& "!$#$%8#$(iI*"I(9"-8A:k*#$=-`k-A:-0>_-8A

(; O ‚ ‚<€ W4E=4<"#^Cy-8A-'+b(:#Q4E!y4E!$,B-8M3A54E#$%-8q)U4E(:#$;B+?;BAS 2**=4EA:#$=-*+U4G()"A04E!$!$h`#$+J4E+h`4E""!$#$%N4G(#$;B+"=S4G+"<

9U4c].-2MV-8%8;.7-(9"-`=:)"M0-8%'(;E>S?)"%09?A:-8=-N4GA%09[;E]B-8A*(:9"-U4E=:( €r hB-c4EA=c ‚ ‚ ‚# @-3@ ‚

+J(9"#$=*<";%8)" -8+(N(:9"-`"A:#&J4EA:h`>_;%8)3=*#&=*;.+e8

*)('

"{ Q~*=

-,

<

O

5W O‚ ‚ .4BW

A

U

O

5W O

‚

‚

GMUW

O0cW

0 O

‚

‚

E%cW

O0 W 0 O ‚ ‚ G<UW

,

O5Wo<";-8=+";.(i4G"U-c4EA;.+`(93-!$-0>_(y9V4E+"<`=:#$<"-;G>O‚ ‚ EMUW'

*=`4EA:-`<"#^C -'A-8+(>_A;. I2L=2#$+H4j+)"?MU-'A*;E>k*4ch=N;B(:-`(9V4E(`4EA:M"#$(A54GAhJ#$+"#$(#Q4E!y%';B+"<"#$(:#&;.+"=<3;7+";.(

g4GrB-`=:-8+"=:-Bedp-??)"=:(9U4c].-?(9U4G(

U

O

0

0 0 W

A

j+"#$(#Q4E!S%';B+"<"#$(:#&;.+"=k*9"#$%09p=54E(:#$=>_h[(9"-74G==:;b%'#X4G(-8<

4E!$,.-8M"A54G#$%%8;.+"=(:A54G#&+(:=gO

‚

‚

GMUW4EA-?%c4E!$!$-8< {  $8~_

(20)

,

4

O‚ ‚/C 4BW

,

O

‚

‚/C MUW



4

O5W O ‚ ‚/C %cW

k*9"-8A:-,,,

O5Wj-8f#&=:(=74G+"<a#&=?%';B+(#$+)";B)3=NF!$-N4GA!$hSk-g+3-8-8<

4

O 0 W O 0 W8 ;Ek-8]B-'ANk-[4E!$=;[+"-8-8<

O0cW

,

O08W*4G+"< O08W

,,

O0cW8;=:-8-(9"#$=N!$-8(*)3=*<"#^C -8A:-8+(#Q4E(:-`(93-`%8;B+3=(A04E#$+(`O

‚

‚NC %NW'



O

4

O5WW

,

4

,

O5W

,

O5W

%

+3;B(93-8A<"#^Cy-8A-'+b(:#Q4E(#$;.+7h#$-8!$<"=



O

,

O5W:W

,

,,

O5W

,, O5W %

S4Er#$+",`;.+"-7;BA:-<"#^Cy-8A-'+b(:#Q4E(#$;.+g,.#$]B-8=

,

O5W

,,, O5W %

I+"-`J4ch(:9"-8+J%8;B+3=#$<"-8A=;B!$]#$+",(9"-=h=:(-8„;G>LI=N

,

4

,

,

,,,

O5W O

‚

‚

W

k*#$(9`(:9"-*4E==:;%8#Q4E(-'<g{

 Xu~@

~#$+"#$(:#X4G!E%8;B+3<"#$(#$;B+"=cy*9"#$==h=(:-8;G> I=9U4G=(9"-=54G7-S4E+U4G!$hb(:#$%S=;.!&)3(#$;B+

4E=(:9"-7*lO

‚

‚NC

W8R(#&=R#& U;.A(04E+(*(;J+";.(-?(9V4E((9"-?+)" -8A#$%N4G!#&+(:-8,BA04E(#$;.+H;G>wO

‚

‚

W*%8;.)"!$<H!$-N4G<H(:;

=;.!$)"(#$;B+3=k*9"#$%09J<"A#^>_(*;GCH;E>(9"-%8;.+"=(:A54G#&+(`O

‚

‚/C %NW8

*9"-4GMU;E].-24E+V4E!$h=#$=,.#$]B-8=*)"=*=:;B -#$+()"#$(#$;.+g4EMV;B)3(*(9"-

.'n;E>S4 2*

. 3POP@5R

€~&|3 cu~@

~&|37#$+"<"-'fZ}&"

}J "~

O

O5W$

O5WW $~$|" "$0}E8~

$

c€

*N€:

~Q}.~ 

0B *~$|"}&"



$

€:}Q{{

8~@€}

~

$

~

,

O5W

b "

~@N€



O5W

O5W

}

*9"- #&+3<"-8f[%N4E+Z4G!&=:;JMU- %59V4EA54G%8(-'A#! 8-8<Y4E=R(9"- +b)3?MU-8A;G><"#^C -8A:-8+(#Q4E(:#$;B+"=`+3-8-8<"-8<a)"+(:#&!4E+ZI k*#&(:9

%8;.+"=#$=(:-8+(?#$+"#$(#Q4E!S%';B+"<"#$(:#&;.+"=`#$=>_;.A -8<pk*9"-8A:-g#$(:=`=;.!&)3(#$;B+p#$=)"+"#$q)"-8!$hH<3-8(-8A:7#$+"-8<oe+Z(:9"-7-'f

4G7"!$-O ‚ ‚/C W (9"- #$+"<"-8fek*4E=?3=:#&+3%8-?#$(2(:;;Bre(:9"A-8- (#$7-R<"-8A#$]B4G(#$]B-8=(:;g,.-8(

,

,,,

(21)

U

,

+"<"-'f ‚ 2=4EA:-4*=:U-8%'#X4G!%8!Q4E==o;E>""A:;BM"!$-8 =">_;.Ak*9"#$%09-8f(-8+3=#$]B-A-8=:-N4EA:%099U4G=MV-8-8+<";B+3- " ‚O# OEO ‚

;.(-(9V4E(4E!$!I=4EA:-`#$+"<"-8f



2=c

#$+"%8-?(:9"-<3#DCy-8A:-8+(#Q4E!S]B4GA#Q4EM3!&-'=

,

?)"=(MU-#$+(-8,.A54E(:-8<ok-!$;;BrJ(; +b)37-8A:#&%c4E!7-8(:9";<"=*>@;BA2I=

(;=;.!$]B-`*=N;Ek-8].-8AN+3;B(4E!$!yI2\#$+(-8,.A54G(;BA:=4GA-`4E3"A;."A#Q4E(:-BSI+"-7#$,B9(S-'f 4G7#$+"-*(:9"-A-8,.)"!Q4EA/

#! N4E(:#$;B+7;G>O ‚ ‚ .W

-,

oO

5W O‚ ‚O# 4BW

,

O

5W O

‚

‚O# MUW

k*9"-8A:-

= = =

‚

(#$=*+";B(A-'%8;B

7-8+"<3-8<79"-'A-(;(A:hg4E+3<7=;.!$]B-(9"#$="A;.M"!$-8H.M")"(*#$(<";-8=*,B#$].-=;.7-#$+"=#$,.9b(#$+b(:;7k*9U4G(+b)37-8A:#&%c4E!7-8(:9";<"=%c4E+[MU-?)"=:-8<?#$+"%8-(93-?A-8=:)"!$(#$+",J=-8(R;E>I=k*#$!&!MV-=:(#^CZ#$+

(93#&=%N4G=-B #&(g4GrB-8=*=:-8+"=- (;

%8;B+"=:#$<"-8A+)"7-8A:#$%N4E!o7-8(:9";<"=k*9"#$%09[k;.ArJk-'!&!;.+e=(:#DCZ3A;BM3!&-'7=N=k-=54ck MV-0>_;BA:-B"(:9"-`y;.MU4E(:(;?: 7-8(:9";<"=4EA:-=(#7h74G%8%8)"A04E(-4E+"<J%8;.+b].-8A,.-`#$+7(:9"-`]B-'Ah7=:(#^CH!$#$7#$(N

+(-8A:-8=(:#&+3,B!$hb (9"-;BA:<"-8A;E>4j+)"7-8A:#$%N4E!o7-8(:9";<eg4ch?MV-MV-8(:(-8A>@;BA(:9"-?*2 (9V4E+e(:9"- 4G==:;b%'#X4G(-8<

=(:#^CH"A;.M"!$-8 ,B#$]B-8+ #$+HO

‚

‚O#

W'Sx";.A(:9"-`#$+"<"-'f

‚

*2

,

<

O

5W O

‚

‚

BW

A

U

O

5W O ‚ ‚ W

k*9"-8A:-U

9U4E=*4MV;B)"+"<3-8<J#&+].-8A=:-24E+3<7(93-#$+"#$(#Q4E!3%8;B+"<3#&(:#$;B+"=4GA-%8;.+"=#$=(:-8+(N(:9"-`y;BMV4E((:;`:F -8(93;b<3=

A-'(54E#$+J(93-8#$A>_)"!$!y;BA:<"-8AN €

€ E ‚O#

zo==-8-'+e#$+7(93-`"A-']b#$;.)"=*=-8%'(#$;B+3(9"#$=*#$=*+";.(*(A)3->@;BA*=;.7-=(:#^CsI2L=N

‚e4E+h 9"#$,B9"-8A#$+"<"-8fJ*=*%N4E+JMV--8f"A-8=:=-8<[#$+R808

$ c€

>_;.A[y+J#$+"<"-8f

€

26#&+J-8==:-8+MU-8A:,

>_;.A

!$;;Br=!&#$r.--,

< O

5W O‚ ‚ 4BW

A

U

O

5W O

‚

‚ MUW

k*#$(9

U

B

<

#$+]B-8A:(#$M"!$-Bo+?(9"#$=%N4E=:-B(93-y;BMV4E((:;`:Y7-'(9";<"=SA:-8(54G#$+?(9"-8#$AT>_)"!$!";.A<"-8A#$+(:9"-<3#DCy-8A:-8+(#Q4E!

]B4EA:#Q4EM"!$-8=

(22)

"A:;BM"!$-8 = " #

x";.A#&+3<"-8f *2L=2#$+[-8=:=-8+MV-8A,n>_;.AH3(9"-?y;.MU4E(:(;J:l7-8(:9";<"=24GA-+";B(]#Q4EM"!$-B*9"-#$+"<"-8f1

=h=:(-8„!$;;Br=!&#$r.-B

,

<

O

X

5W O

‚

€X

W

X

,

SO

X

5W O ‚ €D‚ W

A U O

5W O ‚ €X€ W

k*9"-8A:- U

B

< #$=#&+].-8A(:#&M3!&-.+[(93#&=%N4G=- (9"-8A:-?#$=`+";J,B-8+3-8A54G!S%8;B+].-8A,.-8+"%8-j>_;BA(93-?iA04EV-/ 8;.#&<p4E+3<E;.A

-'A7#$(:-0/z #& "=;.+`7-'(9";<"=c@>SO

X 5W

4

O

X W 7 4

4

B(:9"-8+ k-*9U4c].-(:9U4E(S?,.#&].-8=4G+?;BA<3-8A*;E>

€ € 4G+"<  >_;.A

X

4E+"<

A-8=:U-8%'(#$]B-8!$h ‚ -8+"%'-By;B+3-`%N4E+3+";B(-8fU-8%'(2%';B+]B-8A:,B-8+3%8-?#$+g(:9"-4G!&,.-8M"A04E#$%

]B4EA:#Q4EM"!$-8=T>_;BA*y"#$7#$!Q4EAA:-8=)"!$(:=9";.!&< >_;.AR

=Jk-Hk*#$!$!=:-8-B`(:9"-[%8;B+]B-'A,B-'+"%8-pA-'=)"!$(= >_;BA -8=:=-8+MV-8A, =h=(:-87=J;G>#$+"<"-8f

‚

€

4E+"< Z<3;Z+";.(

+"-8%'-8==04EA#$!$h74E3"!$h(:;`(A04 0-8%8(:;BA:h?;B"(:#& #! N4E(:#&;.+=)"M0-'%8(*(;`#$+"-'qb)V4E!$#$(h`%8;B+3=(A04E#$+(=c*9"#$=Sk*#$!&!3MU-*<"#$=:%8)"==:-8<

#$+7<"-'(54E#$!o#&+J9U4E3(-8A C

<

*9"-<"-8=#$,.+7;E>J4E+h"9h=#$%N4E!V=h=:(-8 =#$+]B;.!&].-8=7#$+"#$7# 8#$+",*;BAg4Gf#&?#! 8#$+",4G+?;BM0-'%8(#$]B-=)"%09e4E=T"A;GmU(N

>_)"-'!(:#$7-(:;?%8;B "!$-8(#$;.+E%8;.=(NV-8+3-8A,.hb-8(:%B*IU-8A04E(:#&;.+"=*-'=-N4GA%09e#$=4RmU-8!$<J;E>=()3<"hJk*9"#$%59J#$=<"-8]B;.(-8<

4E!$ ;B=(-8+(#$A:-8!$he(; (9"-`=:()"<3he;E>;."(#$ # c4E(#$;.+?(-8%09"+"#$q)"-8=4E+"<e3A54E%'(#$%8-8=c-8%c4E)"=:-?;E>(:9"-8#$A]B4G=(24G""!$#^/

%N4GM"#$!&#$(hV;B"(:#& #! N4E(:#&;.+J"A;.M"!$-87=%8;.7-`#$+pg4G+h?>_;.A7=`4G+"< y4c]B;BA:=N?*93-?;B"(:#& #! N4E(:#&;.+J]B4EA#Q4GM"!$-8=g4ch

MV-g#$+(-',B-8A:=NA-N4G!$=NS%';B73!&-'fH+)"?MV-8A=?4E+3<E;.A>_)"+"%'(#$;B+"=cZ+\,B-8+3-8A54G!*k-Jg4chnk*A#$(-e4E+\;B"(:#$7#! N4E(:#$;B+

"A:;BM"!$-8[

#&+ O

W

=)3M0-8%8((;

.

k*9"-8A:- n#$=%N4G!$!&-'<g(:9"-;BM0-8%'(#$]B->@)"+"%8(:#&;.+e4E+"< (9"-R%8;B+"=:(A04E#$+(=-'(N*9"-`(;."#$%8==:()"<3#&-'<e#$+g(:9"#$=(:9"-8=#$=

(23)

dp-k*#$!$!y%8;.+"=#$<"-8A(9"-mU+3#&(:-<"#$7-8+"=:#$;B+U4G!U+";.+"!$#$+"-N4EA"A:;B,BA04E 7#$+",3A;BM3!&-'

#$+ O

W O‚ € .4BW

=)3M0-8%8((;eOQ=c(NW



1

O

W$< ‚ %%!% O ‚ € GMUW

 O W$ ‚ %%!% O ‚ € E%cW #&=4G+?) = ‚ A-N4G!]B-'%8(;.A4E+"< . @>S(:9"-U;.#&+( =04E(:#&=zmU-8= oO W oO W . 4O W 9 + + =

A U

O W$ A ]O W k-2%c4E!$!

4!$;%N4E!y #&+3#&)" ;E>O ‚ € .W8

y-8()"=*<"-0mV+"-`(93-wo4E,.A54E+3,B#Q4E+*

O

W oO

W#7 01324 1 1 O W87 0 24 O

W oO

W 7 ]*O

W-7 U O

W O ‚ €DC W

k*9"-8A:- #&=4 = ‚ ].-8%8(:;BA?4E+"< #$= = ‚ ndp-?k*#$!&!TA-0>_-'A(:;4G+"<l4E=`(:9"-go4E,BA04E+",.-??)"!$(#$"!$#$-8A=

4E=:=;%8#Q4E(:-8<Zk*#$(:9H(:9"-?-8q)U4E!$#$(hH4G+"<p#$+"-8q)U4E!$#$(hJ%8;B+3=(A04E#$+(=A-8=:U-'%8(#$]B-'!&h @O

W#$=`<"-0mV+"-8< 4G=(9"- =-8(;E>

4E%'(#$]B-#$+"-8q)U4G!&#$(h%8;B+3=(A04E#$+(=c @O W 9 O W  % *9"->_;.!&!$;Ek*#$+",?(:9"-8;BA:-8 ,B#$]B-'=`+"-8%8-'==54GAhp%8;.+"<"#$(#$;.+"=>_;.A 4E+"<[#$=%8A-8<3#&(:-8<Z(:;e1`4EA:)"=9o1)"9"+Z4G+"< )"%0rB-8A [9] .G:.G4 8 1 } }B€{ ~

.(" *N€:

~Q}

$

"$

$} " {5}#"

} ~$|"}B{c~ { 8~_€:} ~ €} Q

~ 3]Z}

U }B€" 5}.€(" .  B ~}B~ i~$|" ~$|"c€*('$8~  "$~

"N€0

 {0|[~&|3}B~ ! B *O

W A O‚ € 4BW

#"  $1 O ‚ € MUW

 1 . @O

(24)

A

O

W  1. @O

W O ‚ € -cW

[9]

.G:.G4^%

${

('

~&|

1

}

"

5}.€`}

8}B~$S8~&|3?{ ~  *~&|3

}

"

$ }&"

cc€

*9"-[-8q)U4E(:#&;.+"=HO ‚ € W8*<3-8+";B(:-8< 4E=J(9"-[11„%8;B+"<3#&(:#$;B+"=c,.#&].-J+"-8%8-8=:=54GAh %8;.+"<"#$(#$;B+3=?>_;.Ag4p!$;%N4G!

;B3(#$g4G!y=;B!$)"(:#$;B+

J$#$]B-'+H4 %N4E+"<3#&<V4E(-;B3(#$g4G!=;.!$)"(#$;B+oU;.+"-?g4ch )"=-eO

‚

€

W*(:;g%09"-'%5r[;B3(#$g4G!&#$(hB

‚J;<"-8A:+H<V4ch7;B3(#$7#! N4G(#$;B+?=:;E>_(k*4EA:-`)"=)V4E!$!$h7#$+"%8!$)"<"-'==;.7->_;.A ;E>S(9"-R121

%8;B+"<3#&(:#$;B+"=*(:;7%09"-8%0rJ(9"-;B3(#$g4G!&#$(h`;G>L4,.#&].-8+7=:;B!$)"(:#&;.+

$#$]B-8+?(:9"-*;B3(#$7#! N4G(#$;B+"A:;BM"!$-8„O ‚ € BW'E(93-8A-4EA-=-8].-8A54G!U+)" -8A#$%N4G!"(-'%593+"#$qb)3-8=(:;mU+"<74G+?;B"(:#$g4E!

=;.!$)"(#$;B+oy*9"-8=:-#$+"%8!$)"<"-*#$+(-'A#$;BAV;B#$+(i -8(93;b<3=NEV-8+U4G!&(hR7-8(:9";<"=NB4G+"<=-8q)"-8+(:#X4G!"q)U4E<3A54E(:#$%*"A;.,BA54G?/

7#$+",V+e(9"-w>_;B!$!$;Ek*#$+",%09U4G"(-'A2k-`k*#$!$!<"#$=:%8)"==`4j=-8q)"-8+(:#X4G!qb)V4E<"A04E(#$%`3A;B,.A54G77#$+",`4G!&,.;BA:#&(:9" (9U4G(

)"(:#&!$#! 8-8=*=:U4EA:=-`J4E(:A#$f;.U-'A54E(:#$;B+"=c

%'& C& / D(58- * /1@1*

‚e4G+bh"A:;BM"!$-8 =i(:9U4E(%8;.7-T>_A;. (:9"--'+",B#$+"-8-'A#$+",`<"#$=:%8#$"!$#&+3-8=4GA-*+U4G()"A04E!$!$h ;<"-8!$-8<?4E=;B"(:#&J4E!.%8;B+(A:;B!

"A:;BM"!$-8 =No+g(:9"-8=:-`%N4E=:-8=N3(9"-R<"-8%8#$=#$;.+7;BA*%';B+(A:;B!]B4GA#Q4EM3!&-'=4EA:->_)"+"%'(#$;B+"=cP+"!$#$rB-+";B+3!&#$+"-c4EA"A;.,BA54G?/

7#$+",Vk*9"-8A:-(:9"-<3-8%8#$=#$;B+[]B-'%8(;.A2!$#$-8=#&+e4 mU+"#$(-<"#$7-8+3=#$;B+U4G!y=U4G%8-By%';B+(#$+)";B)3=(#$ -2;."(#$J4E!V%8;B+(A:;B!

"A:;BM"!$-8 =4GA-#$+"9"-8A:-8+(!$h7#$+mU+3#&(:-<"#$7-8+"=:#$;B+U4G!

y-8(

O5W4E+"<

O5WoMV-)

4E+3< )<"#$7-'+"=#$;B+V4E!B].-8%8(:;BAS]B4G!&)3-8<>_)"+3%8(#$;B+3=Nodp-<"-'=#$A-*(:;mV+"<(:9"-%8;B+(A:;B!

O5W*4E+"<

O5W*k*9"#$%097 #&+3#& # 8-'=4E+J;BMu-8%8(#$].->@)"+"%8(:#&;.+U4E!

7#$+ SO

O5W$

O5W

O21W$

O21BW$ 21

O0cW$

O08W 08W % O ‚ €E# W

hb3#&%c4E!$!$hbE(:9"-`;.M0-8%8(:#&].-#&=*#$+J‚e4chB-8A>@;BA

O

O21"W$21bW O

‚

€

BW

4G,BA04E+",.->@;BA

"

"

*O

O5W$

O5W$ 5W O

‚

€

(25)

4

O

O 1 W$ 1 W87

O

O0 W 0 W-7 "

" *O

O5W$

O5W 5W % O ‚ € W

*9"-;BMu-8%8(#$].-`#$= #&+3#& # 8-'<?;E]B-8A*(:9"-`<"h+U4G7#$%*%8;B+3=(A04E#$+(=c

-, O5W < O

O5W$ O5W$5W O ‚ "  W

(93-2MV;B)3+"<U4EA:h7%8;.+"<"#$(#$;.+"=

0

0

O

O0cW$ O08W$ 08W

0

O ‚ " ‚ W

1

1

O

O1 W$

O 1 W 1 W

1

O ‚ " € W

U4G(9J%8;B+3=(A04E#$+(=

U

U

O

O5W$

O5W$5W

U

O ‚ "EBW

4E+3<g=:#$7"!$-*MV;B)"+"<3=

O5W

O ‚ " C W

O5W

%

O

‚

"

W

q)U4G!&#$(h %8;B+"=:(A04E#$+(=%c4E+eMV-`-N4G=#$!$h7#$7V;B=:-8<JMbh =-8(:(#$+",

(9"-)""V-8A!$#$7#$(S-'qb)V4E!(;?(:9"-`!$;Ek-'A!$#$7#$(Nodp-k*#$!$!4E=:=)" -(:9"-7-8f#$=(:-8+"%8-J;G> 4G(`!$-N4E=:(;.+"-?;B"(:#$g4E!o=;.!&)3(#$;B+YO

O5W$

O5WW'ex";.A`-8f#$=(:-8+"%8-JA-'=)"!$(=R>_;.A

;B3(#$g4G!"%8;B+(:A;B!o"A;.M"!$-87=cB=:-8- "

*9"-J-8q)U4E(:#$;B+"=eO ‚ "-.Wk*#$(9

U

U

Z4E!$;B+3,ek*#$(9 O ‚  W>@;BA 4e=:-87#^/-8f"!$#&%'#&(*2 =h=(:-8H\x";.A

=h=:(-8 =Sk*9"#$%0974EA-#$+"<"-8f

‚

.(9"-'A--'fb#$=:(==;E>@(k4GA-*k*9"#$%09?#$=Sr+";Ek*+?(;`k;BA:r`k-8!$!

‚

C

o+?7;.=(;E>y(9"-

A-'g4E#$+"<3-8A*;E>(:9"#$=<";%8)37-8+(N3k-Rk*#&!$!4E==:)"7-U

=

U

*;Ek-8].-8ANV(:9"#$=<";-8=+";.(-8f%8!$)"<"-(93-`"A-'=-8+"%'-;E>**2L=

@>(:9"-?#$+"-8q)U4G!&#$(h %8;B+"=:(A04E#$+(`MU-'%8;B -8=`4E%8(:#&].-B

U

O

5W

U

y;E]B-'A2=:;B -`(#$7-R#&+(:-8A]B4G!

(93-2=:;B!$)"(:#&;.+HO

W#$=*4=;B!$)"(:#$;B+7(:;?(9"-` 2

,

<

O

5W

A

U

O

5W

U

;B+].-8A,.-8+"%8-R>_;BA4+)" -8A#$%N4G!y7-8(:9";<Jk*9"-8+e#$+"-8q)U4G!$#&(h %8;B+3=(A04E#$+(=4EA-R"A-8=:-8+(k*#&!$!yMV-4?J4 0;.AS>_;%8)3=

(26)

%8;.+"<"#$(#$;B+3=24EA:-<3-8A#$]B-'<e)"=#$+", (9"-%N4G!&%')"!$)"=;E>S]B4EA:#X4G(#$;B+3=N*!&(:9";B)3,B9e;.+"!$hg=:(54G(-8<[9"-8A:-By<"-8A:#$]B4E(#$;.+"=%N4G+

MV->_;B)3+"<7#$+

‚

z

y-8()"=mUA:=(-'f 4G7#$+"-*(:9"-`=#$ "!$-8AS"A:;BM"!$-8

7#$+ O

O 1 WW-7

"

"

*O

5W O

‚

"

#

4BW

=N(c

-,

<

O

5W O

‚

"

#

MUW

A

O

O21"W 21W O

‚

"

#

%cW

O0cW

0 % O ‚ " # <UW

*9"-24G7#$!$(;.+"#Q4E+#&=*<3-0mU+"-8<n(;MU-B

*O

5W 7

<

O

5W

k*9"-8A:-`(93->_)"+"%'(#$;B+"= *O5W*4EA-4E,.A54G+",B-?)"!$(#$"!$#$-8A=cy*9"-`+"-'%8-8==04EA:hg%';B+"<"#$(:#&;.+"=>_;.A`O‚ " #

WS4GA--,

<

O

5W O

‚

"-.4BW

,

?

B

B

7 <

B

O ‚ "-GMUW

A ?

7 <

O ‚ "-E%cW

0

O0NW O

‚

"-G<UW

A

O

B

7

B

SW

9

"

% O ‚ "-E-cW

4E=4RA-N4G!]B4G!&)3-8<7].-8%8(;.ANT*9"--8q)U4E(:#&;.+"=O ‚ "EBWL>_;BA:v4`<3#DCy-8A:-8+(#Q4E!^/4E!$,B-8M3A54E#$%KUI

>_(-'+(9"-4E!$,.-8M"A54G#$%]B4EA:#Q4EM"!$-8=

%N4G+JMU-`-'!&#$ #&+V4E(-'<)"=:#$+",eO ‚ EE%NWTA-'=)"!$(#$+",?#$+e4R;BA<3#&+V4EAh <"#^C -'A-8+(#Q4G!2K

y-8()"=*+";EkY#$+"%'!&)3<"-(9"-`#$+"-'qb)V4E!$#$(h%8;.+"=(:A54G#&+(

U

O

5W

A

#$+ZO

‚

"

#

W'**9"-`=:#$7"!$-`4E<"<3#&(:#$;B+J;E>(:9"#$=%8;.+"=(:A54G#&+(,BA-c4E(!$hJ%8;.7"!$#$%N4E(:-8=(:9"-`+"-'%8-8==04EA:hp%8;B+"<3#&(:#$;B+"=c*dp-g4chRmUA:=(24G<0;.#&+?(:9"-`%8;.+"=(:A54G#&+(*(:;?(9"-24G7#$!$(;.+"#Q4E+?4E=*#$+ "

*O

5W 7 < O

5W 7 U O

References

Related documents

System is simulated with OQPSK modulation scheme which when compared with conventional Binary Phase Shift Keying (BPSK) gives improved performance in terms of

For a supply shock, interest rates do too much if interest rates would have to fall following a positive shock (for example, in the case of an inflation targeter) or too little

The biological plausibility of NMDR relationships re- ported as significant, or scored to have sufficient strength, is evaluated by considering whether mechanistic explana- tions

In this initial test, we tested the effect of the standoff distance between the sintering optics and the Tephra surface (heat flux intensity), rastering speed (total thermal power)

This paper aims at analyzing politeness strategies including negative politeness, positive politeness, bald on-record, and bald-off record strategies in posts written

Esherwood &amp; Hoy (1973) presented a four-fold typology of bureaucratic structures, based on these two general factors –control and expertise-. They calculated the means of

Table 1 Non- accidental injury syndrome types and affected areas 18 Table 2 The standard radiological procedure for children of suspected non-accidental injury 26 Table 3 Criteria

Over a half-century of studies on carcinogenicity of wood dust and the progression of regulatory permissive level of exposure to wood dust have left two key issues unanswered,