Tải bản đầy đủ (.pdf) (545 trang)

Springer helmig r mielke a wohlmuth b (eds) multifield problems in solid and fluid mechanics (LNACM 28 springer 2006)(ISBN 3540349596)(545s)

Bạn đang xem bản rút gọn của tài liệu. Xem và tải ngay bản đầy đủ của tài liệu tại đây (17.16 MB, 545 trang )

)")! $!( $' ) "#))$#
$ *(%#($#(#
^/5F/WW/Y3 *@DbF+,
bW


FZ_@_c_/4IXLLC@/+FCgZ@ZF+cD/X@%C@DcC_@IF*F@d/XZ@_gI4
_c__;X_*45/FeC+X@F;8\*\i8]G_c__;X_*/XDFg











&
/LX_D/F_I+/
F;/F@/X._/D
_@%*%cC_++/@/F%@Z.Z@%Zg
_/D
_@%Z*F@d/XZ@+++/IF%/L%@
IF*Z@CCJ]i?*IF%/L%@
IF*>@C/







2!!+5) _>/D_@%C DI+/CZ 4IX Z/+@D/F__@IF LXI%/ZZ/Z X/ F//+/+ @F Fc?
D/XIcZ@F+cZ_X@CLLC@%_@IFZ4IX_>/+/Z%X@L_@IF*Z@DcC_@IF*+/Z@;FF+%IF_XICI4
ZIC@+?C@Rc@+Z/LX_@IFLXI%/ZZ/ZI4ZcZL/FZ@IFZP>/7XZ_Z@DLC/!c_%IDLC/_/DI+/C
+/Z%X@!@F;_>/Z/__C@F;I4 DIFI+@ZL/XZ/ ZcZL/FZ@IF I4 ZDCC X@;@+ ZL>/X/Z@Z_>/
B@F/D_@%Z/+@D/F__@IFDI+/C+c/_I
gF%>"G`#*e>@%>C/+Z_IZ%CXFIFC@F/X
%IFZ/Xd_@IFCeP>//f_/FZ@IFI4_>@ZDI+/C_I9I%%cC_/+ZcZL/FZ@IFZ*LX/ZZcX/
7C_/XZ*LICg+@ZL/XZ/ZcZL/FZ@IFZF+%IF_@FcIcZCgIL/X_/+%CX@7/X?_>@%B/F/XcF@_Z
;@d/X@Z/_IdX@/_gI4_@D/?+/L/F+/F_LX_@C+@5/X/F_@C/Rc_@IFZe@_>@F_X@;c?
@F;FIF?Z_F+X+LXIL/X_@/ZP>/Z/LXIL/X_@/Z@F%Cc+/Z_XIF;Cg+/;/F/X_/LX!IC@%
/Rc_@IFZ*4X//!IcF+XgLXI!C/DZ*Z_XIF;Cg%IcLC/+ZgZ_/DZI4%IFZ/Xd_@IFCeZ
e>@%>Dg4@C_I!/>gL/X!IC@%*F+%IFZ/Xd_@IFCeZe@_>+@Z%IF_@FcIcZ9cfP
>@Z%IF_X@!c_@IF;@d/ZFId/Xd@/eI4_>/c_>IXZWX/Z/X%>_>_>Z!//F+/dI_/+
_I_>/D_>/D_@%CDI+/C@F;I4ZIC@+?C@Rc@+Z/LX_@IF*_>//f@Z_/F%/F+cF@Rc/?
F/ZZFCgZ@ZI4_>/Z//Rc_@IFZ*_>/+/Z@;FF+%IFd/X;/F%/FCgZ@ZI4FcD/X@%C
Z%>/D/Z*F+_>/LLC@%_@IF_I/F;@F//X@F;LXI!C/DZPf_/FZ@IFZ_II_>/XLLC@%?
_@IFZF+;/F/XC%IF_X@!c_@IFZ_ID_>/D_@%CFCgZ@ZX/CZI++X/ZZ/+P


%LJ8@#A!/+@D/F^^@HF*KHCf+@YK/WY/YbYK/FY@HFY*D^>/D^@%CDH+/C*
YfY^/DH5%HFY/Wc^@HFCdY*FbD/W@%CY@DbC^@HF

, )3/+63%+)
9=9 @84%5A 8( %#15%6EE186
>/ Y/+@D/F^^@HF H5 YbYK/FY@HFY @FcHCc/Y ^>/ D/%>F@%Y* :Hd F+ ^WFYKHW^
KWHK/W^@/Y H5 D@e^bW/Y H5 :b@+Y F+ YHC@+Y* +WHKC/^Y HW !b!!C/YO bF+D/F^C
2


/Z/X%> XIA/%_ b T/+@D/F__@IF e@_> IDLX/ZZ@IFU


0

P/XX/Z*P,
cX;/X*F+P
P/F+CF+

YK/%^YH5Y/+@D/F^^@HFF+W/C^/+YHC@+?C@Qb@+Y/KW^@HFKWH%/YY/YYb%>Y
8C^W^@HF HW %/F^W@5b<^@HF @F%Cb+/ KWHK/W^@/Y H5 YbYK/FY@HFY F+ /DbCY@HFY
LW>/HCH<f*KW^@%C/Y@g/F+Y>K/*KW^@%C/?KW^@%C/@F^/W%^@HF*YbW5%/%>W?
%^/W@Y^@%Y*f@/C+Y^W/YY*%HF%/F^W^@HF*c@Y%HY@^fM*@F+@c@+bCKW^@%C/YLHW@/F^?
^@HFF+YbW5%^F^YM*F+Y/+@D/F^YF+KHWHbY%B/YLK/WD/!@C@^f*KHWHY@^f
F+%HDKW/YY@!@C@^fMO>/Y/KWH%/YY/YW/H5%W@^@%C@DKHW^F%/5HWYHC@+?C@Qb@+
Y/KW^@HFY@F^>/%>/D@%C*D@F@F<*KbCKF+KK/W*dY^/d^/W*5HH+*K>W?
D%/b^@%C*%/WD@%F+H^>/W@F+bY^W@/YO
^>/D^@%CDH+/CY5HW ^>/Y/KWH%/YY/YW/H!c@HbYCfH5^>/HW/^@%CY
d/CCYH5KW%^@%C@DKHW^F%/O>/f>c/!//Fd@+/CfYb<^>F>C5%/F^bWf*Y^W^@F<d@^>^>/%/C/!W^/+KK/W!f
fF%>"G_#*d>H
dY^>/8WY^^HKWHKHY/KW^@C+@6/W/F^@C/Qb^@HFLM*DHW/KW/%@Y/Cf*
Y%CW*8WY^?HW+/WFHFC@F/W%HFY/Wc^@HFCd*^H</^>/Wd@^>@F@^@CF+!HbF+?
Wf%HF+@^@HFYY%HDKC/^/LC!/@^Y@DKC/MDH+/C5HW^>/Y/^^C@F<H5YbYK/F?
Y@HFO
fF%>VYDH+/CdY%K!C/^H%K^bW/DHY^K>/FHD/FWF<@F<5WHD
^>/+@Cb^/C@D@^^H^>/K%B/+Y/+@D/F^OHKb^^>/b^>HWYVW/Y/W%>@F^>/
KWHK/WK/WYK/%^@c/*d//DK>Y@g/^>^^>/c@C!C/B@F/D^@%Y/+@D/F^^@HF
DH+/CW/5/WY^HYbYK/FY@HFH5/QbC?Y@g/+>W+YK>/W/Y^>^Y/^^C/@F%HCbDF
>c@F<F/@^>/W@FC/^YFHWHb^C/^YO

bWW/Y/W%>@F^>/KWHA/%^a>Y!//F+/cH^/+^H
+ ^>/D^>/D^@%CDH+/C@F<*
+ ^>/FCfY@YH5d/CC?KHY/+F/YYL/e@Y^/F%/F+bF@Qb/F/YYM*
+ ^>/+/Y@+ ^>/KKC@%^@HF^H/F<@F//W@F<KWH!C/DY
5HW Y/c/WC /e^/FY@HFY H5 ^>/ %CYY@%C B@F/D^@% DH+/C* @F%Cb+@F< YbYK/F?
Y@HFY 5HWD@F< %HDKW/YY@!C/ Y/+@D/F^Y* 8C^W^@HF +/c@%/Y* %HF^@FbHbYCf HK/W?
^/+%CW@8/W?^>@%B/F/WbF@^Y*F+KHCf+@YK/WY/YbYK/FY@HFYOC^>Hb<>CC^>/Y/
/e^/FY@HFYW/!Y/+HF/F<@F//W@F<KKC@%^@HFY*^>/f/e>@!@^cW@/^fH5@F?
^W@/Qb^@HFYd@^>Y^WHF<^fK/+/</F/W%f*%HFY/Wc^@HFCdYd@^>+@Y%HF^@FbHbY
:be*F+Y^WHF<Cf%HbKC/+YfY^/DYH5%HFY/Wc^@HFCdYd@^>W/<@HFYd>/W/
>fK/W!HC@%@^f@YCHY^O
HY^H5^>@YW/Y/W%>dYFH^KW^H5^>/HW@<@FCKWHA/%^KWHKHYC*!b^
/D/W</+@F W/YKHFY/^H%HF^@FbHbY@F^/W%^@HFd@^>%HCC/<b/Y5WHDD^>/?
D^@%YF+/F<@F//W@F<*Kb!C@%KW/Y/F^^@HFY*%HDD/F^YHFKb!C@Y>/+dHWB*
F+^>/+K^^@HFH5@+/YYB/^%>/+@FKK/WY!fH^>/WYO ^CYH^bWF/+Hb^
^>^^>/W/YbC^Y%HbC+CYH!/bY/+5HWH^>/WKKC@%^@HFY*Yb%>Y^W7%DH+?
/CY"_9*;[*;0#F+KHKbC^@HF!CF%/DH+/CYH5!CCd/W@F";a#O F++@^@HF*YHD/</F/WC%HF^W@!b^@HFY^HD^>/D^@%CFCfY@Y>c/
!//FD+/@F"_h#O


_>/D_@%C I+/CZ 4IX _>/ /+@D/F__@IF I4 cZL/FZ@IFZ

G

9=G /1A 86E@1HE186
F /%^O a* d/ !W@/:f Hb^C@F/ ^>/ B@F/D^@% Y/+@D/F^^@HF DH+/C* ^>/ HW@<@FC
W/Y/W%> KWH!C/D* /FbD/W^/ YHD/ H5 ^>/ Qb/Y^@HFY Y^^/+ DHW/ ^>F  +/%+/

<H* F+ W/c@/d ^>/ FYd/WY 5HbF+ +bW@F< W/%/F^ f/WYO
 YfY^/D^@% W/c@/d H5 ^>/ W/Y/W%> K/W5HWD/+ 5HWDY ^>/ %HW/ H5 ^>@Y KK/W*
F+ @Y Hb^C@F/+ @F /%^YO _2\O %> H5 ^>/Y/ Y/%^@HFY +/CY d@^> HF/ KW^@%bCW
D^>/D^@%C HW /F<@F//W@F< YK/%^O
5 KW^@%bCW @F^/W/Y^ @Y ^>/ %Y/ H5  DHFH+@YK/WY/ YbYK/FY@HF d@^> HF/
Y@F<C/ KW^@%C/ YK/%@/YO F /%^O _ d/ 5H%bY HF ^>/ HF/?+@D/FY@HFC :Hd H5
Yb%> D@e^bW/Y @F Y/c/WC +/c@%/Y* @F%Cb+@F< %CW@8/W?^>@%B/F/W bF@^Y L/%^O _OIM
F+ KW/YYbW/ 8C^W^@HF L/%^O _OaMO / @CCbY^W^/ ^>/ FHF?Y^F+W+ 5/^bW/Y H5
/%> H5 ^>/Y/ DH+/CYZ FD/Cf*  +@Y%HF^@FbHbY :be F+  +@6bY@HF ^/WD @F ^>/
5HWD/W F+  5W// !HbF+Wf @F ^>/ C^^/WO
HFY@+/W@F< DH+/CY W/KW/Y/F^@F< Yb%> YK/%@C %Y/Y Y  <@c/F @FKb^* d/
YbDDW@g/ @F ^>/ Yb!Y/Qb/F^ Y/%^@HFY ^>/ D^>/D^@%C FCfY@Y ^>^ >Y !//F
KKC@/+ ^H YHD/ H5 ^>/DO CC DH+/CY %HFY@+/W/+ <@c/ W@Y/ ^H ^@D/?+/K/F+/F^
KW^@C +@6/W/F^@C /Qb^@HFY ^>^ >c/ %/W^@F FHF?Y^F+W+ 5/^bW/YO F KW?
^@%bCW* d/ W/c@/d W/YbC^Y 5HW ^>/ 5HCCHd@F< ^fK/Y H5 /Qb^@HFY) Y^WHF^/* FHF?C@F/W KW!HC@%?>fK/W!HC@% %HFc/%^@HF?+@6bY@HF /Qb^@HFY L/%^O _O_MZ
%HFY/Wc^@HF CdY* @F KW^ d@^> +@Y%HF^@FbHbY %H/7%@/F^Y L/%^O _O;MZ %HbKC/+
YfY^/DY H5 Y%CW /Qb^@HFY H5 ^>@Y B@F+ d@^> ++@^@HFC /Qb^@HFY H5 DH^@HF
L!/@F< Y@D@CW ^H c@/W?^HB/Y /Qb^@HFYM* L/%^O _O9MO
F /%^O ; KHCf+@YK/WY/ YbYK/FY@HFY W/ %HFY@+/W/+O F /%^O ;OI  D^>/D^@%C DH+/C H5 YbYK/FY@HFY @Y Hb^C@F/+* d>@%> !/fHF+ ^>/ B@F/D^@%
KKWH%> 5/^bW/Y !H^> F /e^/FY@HF ^H KW^@%C/Y d@^>  Y@g/ HW +/FY@^f +@Y^W@?
!b^@HF LYH?%CC/+ KHCf+@YK/WY/ YbYK/FY@HFYM F+ ^>/ 5HWD^@HF H5 %HDKW/YY@!C/
Y/+@D/F^YO >/ +/W@c^@HF H5 ^>/ DH+/C Df Y//D 5@WCf %HDKC/e* !b^ ^>/ 8?
FC /Qb^@HFY >c/ ^>/ +cF^</ ^>^ d/ Df %HFc/F@/F^Cf W/5/W ^H CC YK/%@C
DH+/CY LYf* 5HW DHFH+@YK/WY/ HW KHCf+@YK/WY/ YbYK/FY@HFY* d@^> HW d@^>Hb^
Y/+@D/F^ %HDKW/YY@!@C@^fM Y YK/%@C %Y/YO >/W/5^/W* W/YbC^Y 5HW YfY^/DY H5
%HFY/Wc^@HF CdY H5 D@e/+ >fK/W!HC@%?/CC@K^@% ^fK/ L/%^O ;OaM F+ QbY@C@F/W
KW!HC@% YfY^/DY L/%^O ;O_M W/ W/c@/d/+O
F /%^O 9* d/ ^bWF ^H ^>/ +/Y@<F F+ FCfY@Y H5 FbD/W@%C Y%>/D/Y 5HW ^>/

+@6/W/F^ DH+/CYO >/Y/ Y%>/D/Y @F%Cb+/ 8F@^/ +@6/W/F%/* 5WHF^ ^W%B@F< F+
W/Ce^@HF D/^>H+Y* F+  c/Wf W/%/F^ DbC^@W/YHCb^@HF ^/%>F@Qb/ 5HW /7%@/F^
%HDKb^^@HF H5 +@Y%HF^@FbHbY YHCb^@HFYO
HD/ W^>/W Y@DKC/ Y/+@D/F^^@HF F+ W/C^/+ DH+/CY 5HW Y@DbC^@HFY F+
KKC@%^@HFY >c/ !//F @DKC/D/F^/+ 5HW KW%^@^@HF/WY @F HW+/W ^H /F!C/ ^>/D
^H K/W5HWD Y@DbC^@HFY d@^>  bY/W?5W@/F+Cf ^HHCO >@Y %^@c@^f @Y !W@/:f YbD?
DW@g/+ @F /%^O \O
Hd/c/W* CC DH+/CY W/Qb@W/ ^>^ %/W^@F %HF%/F^W^@HF?
+/K/F+/F^ D^/W@C?YK/%@8%* /DK@W@%C DH+/C 5bF%^@HFY W/ BFHdFO C/WCf*
^>@Y @F5HWD^@HF >Y ^H !/ H!^@F/+ 5WHD /eK/W@D/F^^@HF* d>@%> C/+Y ^H
^>/ KWH!C/D H5 KWD/^/W @+/F^@8%^@HFO /%/F^ %HF^W@!b^@HFY HF ^>/ FbD/W?
@%C YHCb^@HF H5 ^>@Y @CC?KHY/+ @Fc/WY/ KWH!C/D W/ /QbCCf W/KHW^/+ @F /%^O \O


Ji

P/XX/Z*P,
cX;/X*F+P
P/F+CF+

@FCCf*/%^O\KW/Y/F^Y!W@/5+@Y%bYY@HFH5KKC@%^@HFYH5^>/D^>/D^@?
%CF+FbD/W@%C^/%>F@Qb/Y</F/W^/+d>@C/Y^b+f@F<Y/+@D/F^^@HFDH+/CY
^HW/C^/+DH+/CY@FC^/WF^@c/KKC@%^@HFYL/O!CF%/DH+/CYMO
/C/%^/+HK/FKWH!C/DYW/++W/YY/+@F/%^O[O

5
%)(3%
+' +
+)+%0-/0 60-)0%+)0


@Y^HW@%CCf* ^>/ D^>/D^@%C FCfY@Y H5 Y/+@D/F^^@HF KWH%/YY/Y !/<F
d@^> ^>/ YK^@CCf HF/?+@D/FY@HFC B@F/D^@% Y/+@D/F^^@HF DH+/C +b/ ^H
fF%> "G_#* d>@%> C/+Y ^H  Y%CW FHF?C@F/W %HFY/Wc^@HF Cd d@^>  FHF?
%HFc/e* YDHH^> :be?+/FY@^f 5bF%^@HFO Y @Y d/CC BFHdF* YHCb^@HFY H5 Yb%> /Qb?
^@HFY W/ +@Y%HF^@FbHbY @F F ++@^@HF*  Y/C/%^@HF %W@^/W@HF* @O/O*  YH?%CC/+ /F^WHKf %HF+@^@HF* F//+Y ^H
!/ KHY^bC^/+ @F HW+/W ^H Y@F<C/ Hb^ ^>/ K>fY@%CCf W/C/cF^ DHF< KHYY@!Cf
Y/c/WC d/B YHCb^@HFYO L %HDKW/>/FY@c/ ^W/^D/F^ H5 ^>/ B@F/D^@% Y/+@D/F?
^^@HF DH+/C @Y <@c/F @F ^>/ DHFH<WK>  .2 3@@.53 3 ,.0 3.3* "90#*
d>@C/ ^>/ W^@%C/Y "9;* \;* \9# H6/W >@Y^HW@%C W/c@/dY HF Y/+@D/F^^@HF F+
^>@%B/F@F< W/Y/W%>OM
/ FHd W/Y^^/ ^>/ !Y@% KWHK/W^@/Y H5 ^>/ B@F/D^@% Y/+@D/F^^@HF DH+/C*
d>@%> W/KW/Y/F^ ^>/ Y^^/ H5 BFHdC/+</ ^ ^>/ !/<@FF@F< H5 HbW W/Y/W%>O >/
L@+/C@g/+M YbYK/FY@HF @Y %HFY@+/W/+ Y  %HF^@FbbD F+ ^>/ Y/+@D/F^^@HF
KWH%/YY @Y W/KW/Y/F^/+ !f ^>/ %HF^@Fb@^f /Qb^@HF H5 ^>/ YHC@+ K>Y/)
FL H P FU 2, LHM 3 h +

h 6 ] 6 + S 5 h +

LIM

d>/W/ H @Y ^>/ CH%C cHCbD/ 5W%^@HF H5 YHC@+Y Y  5bF%^@HF H5 >/@<>^ ] F+
^@D/ S* F+ 2, LHM 3 HX: @Y ^>/ G3, @, (CF  3=.@G #C3@.53* d>/W/ X: @Y
^>/ YHC@+Y K>Y/ c/CH%@^fO >/ !Y@% YYbDK^@HF @Y ^>^ ^>/ CH%C YHC@+?C@Qb@+
W/C^@c/ c/CH%@^f @Y  5bF%^@HF H5 ^>/ YHC@+Y cHCbD/^W@% %HF%/F^W^@HF H HFCf*
d>@%> 5HW !^%> Y/+@D/F^^@HF @F  %CHY/+ %HCbDF @Y /Qb@cC/F^ ^H Y^^@F< ^>^
X: 3 X: LHMO HW ^>/ Y/+@D/F^^@HF H5 F @F@^@CCf >HDH%HF%/F^W^@HF HG * LIM @Y %HFY@+/W/+ ^H</^>/W d@^> ^>/ @F@^@C %HF+@^@HF



5HW ] 3  +
h
HL]+ hM 3 HG
LaM
5HW h = ] =  +



H.D 5HW ] 3 h +
d>/W/ @^ @Y YYbD/+ ^>^ ^>/ 5bF%^@HF 2, Y^@Y8/Y 2, LHM 3 h 5HW H 6 h HW
H 2 H.D F+ 2, LHM = h 5HW h = H = H.D * d>/W/ H.D @Y ^>/ De@DbD YHC@+Y
%HF%/F^W^@HFO >/ BFHdC/+ <@c/F @F@^@C %HF%/F^W^@HF HG * F+ ^>/ YHCb^@HF %F !/ %HFY^Wb%^/+ !f ^>/
D/^>H+ H5 %>W%^/W@Y^@%YO H +/Y%W@!/ ^>/ !^%> Y/^^C@F< c/CH%@^@/Y H5 KW^@%C/Y
@F W/C YbYK/FY@HFY H5 YDCC KW^@%C/Y* FbD/WHbY D^/W@C YK/%@8% %HFY^@^b^@c/


_>/D_@%C I+/CZ 4IX _>/ /+@D/F__@IF I4 cZL/FZ@IFZ
 




























✵✶











✶✵








JJ


































































































































❪❫











❫❪
































































P






















































































q

❺❻







❻❺





s

t






r




























































































q



) %) I+/Z I4 Z/+@D/F__@IF ?J _I ?` "8J#P XID _>/ C/4_ _I _>/ X@;>_* _>/ 9cf
LCI_* _>/ Z/__C@F; LCI_ Z>Ie@F; %>X%_/X@Z_@%Z F+ Z>I%B C@F/Z* F+ IF/ %IF%/F_X_@IF
LXI7C/ M4IX I 3 I N X/ Z>IeF 4IX /%> DI+/P >IX+Z @F _>/ 9cf LCI_Z F+ Z>I%BZ @F
_>/ Z/__C@F; LCI_Z >d@F; _>/ ZD/ ZCIL/Z X/ DXB/+ !g _>/ ZD/ ZgD!ICZ

/Qb^@HFY 5HW X: 3 X: LHM HW 2, LHM 3 HX: LHM d/W/ KWHKHY/+ LY// CYH "a_* [[*
[0#MO >/ DHY^ 5W/Qb/F^Cf bY/+ @Y ^>/ /Qb^@HF +b/ ^H @%>W+YHF F+ B@
"Ih[#)


W HLI : HM: 5HW h 6 H 6 I +
2, LHM 3
A5I+
L_M
h
5HW H = h F+ H 5 I +
d>/W/ W @Y ^>/ ^HB/Y c/CH%@^f* @O/O* ^>/ Y/^^C@F< c/CH%@^f H5  Y@F@F F bF!HbF+/+ :b@+O >@Y /Qb^@HF >Y ^>/ @F%HFc/F@/F%/ ^>^ ^>/ Y/^^C@F<
c/CH%@^f !/%HD/Y g/WH ^ ^>/ YHC@+Y %HF%/F^W^@HF H 3 I* d>@C/ /eK/W@D/F^CCf
^>@Y H%%bWY ^  De@DbD %HF%/F^W^@HF H.D !/^d//F hG\ F+ hG[O >bY
>@F+/W/+ Y/^^C@F< 5bF%^@HFY ^>^ W/ +/Y@Y>HbC+ !/ KW/5/WW/+ d>/F/c/W c@C!C/O
H %HFY^Wb%^ ^>/ YHCb^@HF H5 ^>/ @F@^@C cCb/ KWH!C/D LIM* LaM* ^>/ D/^>H+
H5 %>W%^/W@Y^@%Y @Y /DKCHf/+O >@Y D/^>H+ @Y !Y/+ HF ^>/ KWHK<^@HF H5
*
LHG L]G MM
HG L]G M* ^>/ @F@^@C cCb/ KW/Y%W@!/+ ^ ] 3 ]G * ^ %HFY^F^ YK//+ 2,


Jb

P/XX/Z*P,
cX;/X*F+P
P/F+CF+

@F]c/WYbYS+@<WDO>/Y/Y^W@<>^C@F/Y*^>/,<@ <.=@.=*D@<>^@F^/W?
Y/%^*d>@%>DB/YYHCb^@HFYH5LIM+@Y%HF^@FbHbY@F</F/WCO>@Y@Y+b/^H^>/
FHFC@F/W@^fH5^>/:be+/FY@^f5bF%^@HF2, O F5%^*/c/F5HWYDHH^>@F@^@C
+^* Y%CW%HFY/Wc^@HFCdd@^> FHFC@F/W:be +/FY@^f 5bF%^@HFDf
KWH+b%/+@Y%HF^@FbHbYYHCb^@HFYOHHb^C@F/YHD/D@FKWHK/W^@/YH5+@Y%HF?

^@FbHbYYHCb^@HFYH5 LIM*d/%HFY@+/W^>/. 2337<51 2*d>/W/F@F@^@C
5bF%^@HF

H8
5HW]5h +
G
HG L]M3
L;M
"
HG 5HW]=h
%HFY@Y^@F<AbY^H5^dH%HFY^F^Y@YKW/Y%W@!/+O!c@HbYCf*^>/@F@^@C?cCb/KWH!?
C/DLIM*LaM%HFY@Y^YH5^dH+A%/F^@/DFFKWH!C/DYKWH+b%@F<^dHU5FYV
H5%>W%^/W@Y^@%YF++@Y%HF^@Fb@^@/Y*d>@%>@F^>@Y%Y/Y^W^^H@F^/W%^5^/W
8F@^/^@D/ S3 O^+@Y%HF^@Fb@^@/Y*LIM@YFH^Y^@Y8/+F+@YW/KC%/+!f^>/
30.3 -C*53.5@53.@.53*d>@%>%HWW/YKHF+Y^H^>/HW@<@FC%HFY/Wc^@HF
CdF+Y^^/Y^>^^>/CH%CKWHK<^@HFc/CH%@^fQLH8 +H" MH5+@Y%HF^@Fb@^f
!/^d//F^>/YHCb^@HFcCb/YH8 !Hc/F+H" !/CHd^>/+@Y%HF^@Fb@^f@Y<@c/F
!f
2, LH8 M : 2, LH" M
QLH8+H" M3
G
L9M
H8 : H"

Hd/c/W* +@Y%HF^@FbHbY YHCb^@HFY Y^@Y5f@F< LIM ^ KH@F^Y H5 %HF^@Fb@^f F+ ^>/
FB@F/?
bHW ^>@Y W/YHF* F ++@^@HFC +D@YY@!@C@^f %W@^/W@HF @Y F/%/YYWf ^H Y/C/%^
^>/ K>fY@%CCf W/C/cF^ +@Y%HF^@FbHbY YHCb^@HFO F/ H5 ^>/Y/ /F^WHKf %W@^/W@*
d>@%> +/^/WD@F/ ^>/ bF@Qb/ d/B YHCb^@HF F+ %>W%^/W@g/ @WW/c/WY@!@C@^f* @Y

C/$.F@BVY AbDK %HF+@^@HF W/Qb@W@F< ^>^
QLH+ H" M 2 QLH8 + H" M 2 QLH+ H8 M

5HW CC H !/^d//F H" F+ H8 O

L\M

>@Y %HF+@^@HF @Y Y^@Y8/+ @5 F+ HFCf @5* @F F 2, c/WYbY H KCH^* ^>/ %>HW+
AH@F@F< ^>/ KH@F^Y LH8 + 2, LH8 MM F+ LH" + 2, LH" MM W/D@FY !Hc/ ^>/ <WK>
H5 2, 5HW H8 = H" F+ !/CHd ^>/ <WK> 5HW H8 5 H" O
@Y%HF^@Fb@^@/Y Y^@Y5f@F< !H^> L9M F+ L\M W/ %CC/+ =,50=O 5* @F ++@^@HF*
*
*
LH" M 3 QLH8 + H" M HW 2,
LH8 M 3 QLH8 + H" M +
2,

L[M

^>/ Y>H%B @Y %CC/+  53@@ .=53@.3C.@GO F ^>^ %Y/ ^>/ %>HW+ @Y ^F8
^H ^>/ <WK> H5 2, @F ^ C/Y^ HF/ H5 @^Y /F+KH@F^YO 5 d/ YYbD/ ^>^ H"
G = HG
"
8
*
F+ ^>^ 2, LHM 5 h 5HW HG 6 H 6 HG * @^ 5HCCHdY ^>^ FH Y>H%B %F !/
8
%HFY^Wb%^/+ !/^d//F H"
G F+ HG O F ^>^ %Y/* ^>/ @/DFF KWH!C/D LIM* L;M

>Y  %HF^@FbHbY YHCb^@HF

8
*

LH8
5HW ] 5 2,
HG
G MS *
"
*
"3
*
*
L0M
HL]+ SM 3 L2, M L]RSM 5HW 2, LHG MS 6 ] 6 2,
LH8
G MS *


"
"
*
HG
5HW ] = 2, LHG MS *


_>/D_@%C I+/CZ 4IX _>/ /+@D/F__@IF I4 cZL/FZ@IFZ

J`


8
*
* "3
d>/W/ L2,
M @Y ^>/ @Fc/WY/ H5 2,
W/Y^W@%^/+ ^H ^>/ @F^/WcC "H"
G + HG #O >@Y YH?
Cb^@HF @Y %CC/+  << #@.53 ED F+ @Y ^>/ bF@Qb/ K>fY@%CCf W/C/cF^ d/B
YHCb^@HF H5 ^>/ @/DFF KWH!C/DO  K@/%/d@Y/ %HF^@FbHbY 5bF%^@HF Y^@Y5f@F<
^>/ %HFY/Wc^@HF Cd LIM ^ KH@F^Y H5 %HF^@Fb@^f F+ L9M F+ L\M ^ +@Y%HF^@Fb?
@^@/Y @Y bF@Qb/O HW ^>/ KWH!C/D H5 Y/+@D/F^^@HF H5 F @F@^@CCf >HDH
YbYK/FY@HF* <@c@F< W@Y/ ^H ^dH +A%/F^ @/DFF KWH!C/DY HFCf* Yb%>  YHCb^@HF
%F !/ /eKC@%@^Cf %HFY^Wb%^/+ !f ^>/ D/^>H+ H5 %>W%^/W@Y^@%YO HW /eDKC/*
5HW  :be +/FY@^f 5bF%^@HF 2, d@^> bK ^H ^dH @F:/%^@HF KH@F^Y* ^>/W/ W/ Y/c/F
QbC@^^@c/Cf +@6/W/F^ YHCb^@HFY* +/FH^/+ %%HW+@F< ^H "G_# Y
5 = 5#  .2 3@@.53O HW ^>/ Y@DKC/Y^ %Y/ H5  5bF%^@HF 2, d@^> /e%^Cf HF/ @F:/%^@HF
KH@F^* ^>W// H+/Y H5 /+@D/F^^@HF H%%bW* Y// @>/ 5HWDbC^@HF H5 +D@YY@!@C@^f %HF+@^@HFY 5HW DHW/ YHCb^@HFY LFH^ F/%/YYW@Cf K@/%/d@Y/ +@6/W/F^@!C/ HF/YM C/+ ^H ^>/ %HF%/K^ H5
3@<57G E 0 =51C@.53=O
Wb&gBHc KW/Y/F^/+ @F "GI#  bF@Qb/F/YY W/YbC^O
F IG0;* OO bY^HY "9[# /D!/++/+
fF%>VY ^>/HWf @F^H ^>/ Y^^/ H5 ^>/
W^ H5 D^>/D^@%C FCfY@YO F  Y/W@/Y H5 KK/WY* YbDDW@g/+ @F >KO [ H5
"90#* @^ dY %HF8WD/+ ^>^ ^>/ BFHdF YHCb^@HFY %HFY^Wb%^/+ @F "0_* II0# W/
@F+//+ YK/%@C %Y/Y H5 /F^WHKf d/B YHCb^@HFYO ^@C@g@F< ^>/ D/^>H+ H5 %>W%?
^/W@Y^@%Y* @^ dY KHYY@!C/ ^H /e^/F+ ^>/ %HFY^Wb%^@HF H5 DH+/Y H5 Y/+@D/F^^@HF
^H

fF%> !^%> :be +/FY@^f 5bF%^@HFY d@^> ^dH F+ DHW/ @F:/%^@HF KH@F^YO
F IG[9 /^^f "Ih9# D+/ F ^^/DK^ ^H /e^/F+
fF%>VY ^>/HWf ^H %HF^@Fb?
HbY Y/+@D/F^^@HFO >/ !Y@% +@6/W/F%/ ^H !^%> Y/^^C@F< @F  %fC@F+W@%C c/YY/C
H5 >/@<>^  @Y ^>^ ^>/ bKK/W /F+ ] 3  @Y @+/F^@8/+ d@^>  5//+ @FC/^ F+ ^>/
CHd/W ] 3 h d@^>  +@Y%>W</ Hb^C/^O >/ c/YY/C @Y 5/+ %HF^@FbHbYCf d@^> 5//+
YbYK/FY@HF ^ ^>/ @FC/^ LYbW5%/ YHbW%/M F+ +@Y%>W</+ %HF^@FbHbYCf ^>WHb<>
^>/ Hb^C/^ LYbW5%/ Y@FBMO >/ Hc/W:Hd H5 %C/W C@Qb@+ @Y FH^ /eKC@%@^Cf DH+/C/+O
5 L 3 LLSM @Y +/8F/+ Y ^>/ cHCbD/ :Hd W^/ H5 ^>/ D@e^bW/ K/W bF@^ W/*
d>@%> %F !/ KW/Y%W@!/+* ^>/F
fF%>VY /Qb^@HF 5HW %HF^@FbHbY Y/+@D/F^^@HF
%F !/ dW@^^/F Y
2
+
FL H P FU LLSMH P 2, LHM 3 h G
LGM

^W^@F< 5WHD /^^fVY DH+/C "Ih9#* bY^HY* HF%> F+ /F+CF+ "9G# Y^b+@/+
 c/Wf Y@DKC/ DH+/C 5HW %HF^@FbHbY Y/+@D/F^^@HF* @F d>@%> LGM @Y W/Y^W@%^/+ ^H
 YK%/ @F^/WcC "h+ # d@^> @W@%>C/^ !HbF+Wf %HF+@^@HFY ^ ] 3 h F+ ] 3 O
>/ KWH!C/D @Y d/CC KHY/+ @5 ^>/ !HbF+Wf %HF+@^@HFY W/ W/?@F^/WKW/^/+ Y
Y/^?cCb/+ /F^WHKf !HbF+Wf %HF+@^@HFY "\I#O
eK/W@D/F^C /c@+/F%/ +/DHFY^W^/+ ^>^ d>@C/
fF%>VY ^>/HWf %%bW^/Cf
KW/+@%^Y ^>/ Y/+@D/F^^@HF !/>c@HW H5 YbYK/FY@HFY H5 /QbCCf Y@g/+ YDCC W@<@+
YK>/W@%C KW^@%C/Y* ^>@Y @Y FH^ ^>/ %Y/ 5HW :H%%bC/F^ YbYK/FY@HFY 5HWD@F<
%HDKW/YY@!C/ Y/+@D/F^YO HW Yb%> D@e^bW/Y*  B@F/D^@% DH+/C @Y FH CHFYb7%@/F^ F+ HF/ F//+Y ^H ^B/ @F^H %%HbF^ +fFD@% /6/%^Y* @F KW^@%bCW
^>/ %HF%/K^ H5 /6/%^@c/ YHC@+ Y^W/YYO F/ ^>/F H!^@FY  Y^WHF%HFc/%^@HF?+@6bY@HF /Qb^@HFO >/ YbKKC/D/F^ ^H LIM !f F ++@^@HFC +/?

fF%>VY


J:

P/XX/Z*P,
cX;/X*F+P
P/F+CF+

^>/HWf"9\#O>/W/YbC^@F</Qb^@HFLW/KC%@F<LGMM%F!/Y^^/+Y
+
2
@
FHPF
L
U L LSMHP 2
, LHM 3 FU LHM +
d@^>

'
LHM)3

A

$LPM +P+ $LHM)3:
G

2, LHMQLHM


+
O3H

LIhM

LIIM

d>/W/ O 5 h @Y ^>/ YHC@+?:b@+ +/FY@^f +@6/W/F%/* 3 @Y ^>/ %%/C/W^@HF H5
<Wc@^f* F+ Q @Y ^>/ /6/%^@c/ YHC@+ Y^W/YY 5bF%^@HFO ^ @Y YYbD/+ ^>^ ^>/
KW^@%C/Y ^Hb%> /%> H^>/W ^  %W@^@%C %HF%/F^W^@HF H . "h+ H.D #* F+ ^>^
^>/ /6/%^@c/ YHC@+ Y^W/YY Q F+ @^Y +/W@c^@c/ Q* Y^@Y5f

3 h 5HW H 6 H *
*
Q LHM + Q LHM
LIaM
5 h 5HW H 5 H O
F+/W ^>/ YYbDK^@HFY LIIM F+ LIaM* F+ d>/F L_M @Y bY/+* LIhM @Y  Y/%HF+?
HW+/W KW!HC@%  ^>^ +/</F/W^/Y @F^H 8WY^?HW+/W >fK/W!HC@% ^fK/ 5HW H 6
H O @F%/ ^>/ ^fK/ +/%CC/+ Y^WHFH5 ^>/ ^fK/?%>F</ @F^/W5%/* d>/W/ H 3 H * @Y FH^ BFHdF !/5HW/>F+O
^WHF^ ^>/ ^@D/ H5 ^>/ @F@^@C KWHA/%^ KWHKHYC* F+ ^>/ D@F DH^@c^@HF H5 HbW
W/Y/W%> dY ^H KWHc@+/  d/CC?KHY/+F/YY FCfY@Y 5HW ^>@Y /Qb^@HF* ^H +/Y@FbD/W@%C D/^>H+Y 5HW @^Y YHCb^@HF* F+ ^H KKCf ^>/D ^H KW%^@%C Y@DbC^@HFYO
/5HW/ 5HWDbC^@F< YHD/ YK/%@8% KWH!C/DY +bW@F< ^>/ @F@^@C Y^</Y H5 ^>/
KWHA/%^ C/^ bY KH@F^ Hb^ ^>^ LIhM dY W/Y^W@%^/+ ^H  8F@^/ C/F<^> @F^/WcC
"h+ #* %HWW/YKHF+@F< ^H ^>/ YH?%CC/+ @+/C %HF^@FbHbY ^>@%B/F/WO ^ ] 3 * @^
dY KW/YbD/+ ^>^ ^>/ %HF%/F^W^@HF %F !/ /eKC@%@^Cf KW/Y%W@!/+ Y

HL+ SM 3 H LSM +

S . Lh+  # +

LI_M

d>@C/ ^ ] 3 h* ^>/ ^H^C :be @Y W/+b%/+ ^H @^Y %HFc/%^@c/ KW^* @O/O
LLSMH P 2, LHM : FU LHM 3 LLSMH

^

]3h*

d>@%> W/+b%/Y ^H ^>/ !HbF+Wf %HF+@^@HF
2, LHM : FU LHM 3 h ^

]3hO

LI;M

^ @Y 5bW^>/WDHW/ YYbD/+ ^>^ F @F@^@C %HF%/F^W^@HF @Y <@c/F)
HL]+ hM 3 HG L]M +

] . "h+ # G

LI9M

Qb^@HFY LIhM F+ LI_M2LI9M 5HWD F @F@^@C?!HbF+Wf cCb/ KWH!C/D L M
5HW %HF^@FbHbY Y/+@D/F^^@HF H5  :H%%bC^/+ YbYK/FY@HF* d>@%> 5HWDY %HD?
KW/YY@!C/ Y/+@D/F^YZ @F Y>HW^* ^>@Y  DH+/CY = .2 3@@.53 E.@, 527< ==.53O H^/ ^>^ @^ @F%Cb+/Y ^>/ KWH!C/D H5 !^%> Y/^^C@F< H5  YbYK/FY@HF d>/F?

/c/W d/ Y/^ L 0 h F+ H 0 h* F+ ^>^ ^>/ %HFc/F^@HFC
fF%> FCfY@Y @Y
@F%Cb+/+ 5HW  0 hO >@Y KWH!C/D 5HWD/+ ^>/ Y^W^@F< KH@F^ H5 HbW W/Y/W%>*
d>@%> dY 5H%bY/+ HF ^>/ 5HCCHd@F< Qb/Y^@HFY)


_>/D_@%C I+/CZ 4IX _>/ /+@D/F__@IF I4 cZL/FZ@IFZ

J8

M Y @^ KHYY@!C/ ^H /e^/F+ /e@Y^@F< FCfY/Y H5 @F@^@C?!HbF+Wf cCb/ KWH!C/DY
5HW %HFY/Wc^@HF CdY "a* [h# Y d/CC Y /WCf KKWH%>/Y ^H ^>/ /e@Y^/F%/
F+ bF@Qb/F/YY FCfY@Y H5 Y^WHFII[* Iah* Iaa# ^H KWHc@+/ d/CC?KHY/+F/YY L/e@Y^/F%/ F+ bF@Qb/F/YYM 5HW ^>/
 LIhM* LI_M2LI9MR
Hd +H/Y ^>/ %HF%/K^ H5 /F^WHKf YHCb^@HFY CHHB C@B/
>/W/R F KW^@%bCW* >Hd +H/Y ^>/ %HF%/K^ H5 /F^WHKf !HbF+Wf %HF+@^@HFY
KKCf >/W/R
!M F HF/ +/Y@<F F /7%@/F^ FbD/W@%C Y%>/D/ 5HW ^>/  F+ KWHc/ @^Y
%HFc/W%M Y @^ KHYY@!C/ ^H bY/ ^>/ W/YbC^Y H5 LM F+ L!M ^H 5HWDbC^/  %HF^WHC KWH!?
C/DR
+M F ^>/ DH+/C F+ @^Y FCfY@Y !/ /e^/F+/+ ^H Y/c/WC YK%/ +@D/FY@HFYR
bW@F< ^>/ %HbWY/ H5 ^>/ KWHA/%^* ^>/Y/ Qb/Y^@HFY >c/ !//F +/C^ d@^> @F
^>/ 5HCCHd@F< dfO
M FCfY/Y H5 Y^WHF<@FF@F< H5 ^>/ b^>HWYV W/Y/W%> @F%Cb+/+ ^>/ KK/WY !f HCK/W^ "II\# F+
HCK/W^ F+
b+A/c "II[# Kb!C@Y>/+ @F ^>/ C^/ IG\hY* F+ %HF^W@!b^@HFY
!f b >bHQbF F+ >@Y %HCC!HW^HWY 5WHD ^>/ IG0hY "Iah* IaI* Iaa* Ia_#O

>/ FCfY@Y H5 ^>/  LIhM* LI_M2LI9M dY ^>/ ^HK@% H5 ^>/ Y/%HF+
b^>HWVY +H%^HWC dHWB "I9#* 8F@Y>/+ @F IGG\* d>@%> <c/ W@Y/ ^H ^>/ K?
K/WY "9a* 9_#O >/ /e@Y^/F%/ KWHH5 5HW  5f@F< F /F^WHKf %HF+@^@HF L@F Y>HW^* /F^WHKf YHCb^@HFM* %>W%^/W@g/+ !f
Wb&gBHc /F^WHKf 5bF%^@HFY* dY !Y/+ HF ^>/ cF@Y>@F< c@Y%HY@^f D/^>H+O
>/ bF@Qb/F/YY KWHH5 5HW ^>@Y KWH!C/D @Y !Y/+ HF ^>/ AbDK %HF+@^@HF
/Y^!C@Y>/+ @F "Ia_# F+ W/C@/Y HF ^>/ YYbDK^@HF H5  YDHH^> +@6bY@HF
%H/7%@/F^O  %HWW/%^ 5HWDbC^@HF H5 ^>/ !HbF+Wf %HF+@^@HFY C/+Y ^H Y/^?
cCb/+ YH?%CC/+ /F^WHKf !HbF+Wf %HF+@^@HFY "9a#O
F5HW^bF^/Cf* DHY^ +@6bY@HF %H/7%@/F^Y $LHM 5HW ^>/ Y/+@D/F^^@HF?
%HFYHC@+^@HF DH+/C +H FH^ Y^@Y5f ^>/Y/ YDHH^>F/YY YYbDK^@HFYO F "a[#
F @DKWHc/+ c/WY@HF H5 ^>/ FCfY@Y H5 "9_# @Y KW/Y/F^/+* F+ @^ @Y Y>HdF
^>^ ^>/ c@Y%HY@^f D/^>H+ CYH >F+C/Y /c/F +@Y%HF^@FbHbY +@6bY@HF %H/5?
8%@/F^Y F+ +H/Y FH^ C/+ ^H F/d Y@FK/WD@^Y ^H KWHc/ ^>/ bF@Qb/F/YY H5 ^>/ Wb&gBHcVY
S+Hb!C@F< H5 cW@!C/YT ^/%>F@Qb/O
>/ %>H@%/ H5 ^>/ YHCb^@HF YK%/  * d>@%> 5HWD/+ ^>/ !Y@Y H5 ^>/ d/CC?
KHY/+F/YY FCfY/Y @F "a[* 9_#* ^bWF/+ Hb^ ^H !/  Y/c/W/ W/Y^W@%^@HF 5HW ^>/
^^/DK^ ^H </F/WC@g/ ^>/ W/YbC^Y H5 ^>/Y/ KK/WY ^H H^>/W @F@^@C?!HbF+Wf
cCb/ KWH!C/DY* @F%Cb+@F< YK^@CCf DbC^@?+@D/FY@HFC KWH!C/DYO F KW^ @F?
YK@W/+ !f "IhI#* d/ b^@C@g/+ ^>/ DHW/ 8/C+Y "\_# 5HW ^>/ FCfY@Y H5  5W// !HbF+Wf 5HW  KWH!C/D H5 KW/YYbW/ 8C?
^W^@HF "_I#* Y// CYH /%^O _O_O ^ Y//DY +@7%bC^ ^H /e^/F+ ^>@Y KKWH%> ^H
DbC^@?+@D/FY@HFC +/</F/W^/ KW!HC@% /Qb^@HFY d@^> g/WH :be !HbF+Wf
%HF+@^@HFY* !b^ Y// "_h# 5HW  KW^@C W/YbC^O


J]


P/XX/Z*P,
cX;/X*F+P
P/F+CF+

>Hb<>/F^WHKf!HbF+Wf%HF+@^@HFY/FYbW/d/CC?KHY/+F/YYH5^>/@F@^@C?
!HbF+WfcCb/KWH!C/DLIhM*LI_M2LI9M"9a#*@^^bWF/+Hb^^>^^>/Y/%HF?
+@^@HFYW/bFK>fY@%C+b/^H^>/c@HC^@HFH5%HFY/Wc^@HFH5DYY*F+
Y>HbC+!/W/KC%/+!fg/WH?:beHW:be?^fK/!HbF+Wf%HF+@^@HFYOHW^>@Y
W/YHF*d/FCfg/+@F"a[#@FKWCC/CY/%HF+ *@Fd>@%>^>/!HbF+?
Wf%HF+@^@HFLI_M@YW/KC%/+!f
LLSMHP2, LHM: FU LHM3 LM
S ^ ]3+

LI\M

d>/W/ LSM@Y!HbF+Wf5//+:beO/CC?KHY/+F/YYH5^>/ LIhM*LI;M*
LI9M*LI\M@YY>HdF@F"a[#Z^>@Y@F%Cb+/Y^>/g/WH?:be@F@^@C?!HbF+WfcCb/
KWH!C/D5HW!^%>Y/^^C@F<^^@F/+!fY/^^@F<L 0 hF+0 hO
^Y>HbC+!//DK>Y@g/+^>^5HW^>/ LIhM*LI;M*LI9M*LI\Md@^>:be?
cCb/+!HbF+Wf%HF+@^@HFY*^>/!HbF+Wf%HF+@^@HFYW/CDHY^CdfY
Y^@Y8/+@FKH@F^d@Y/Y/FY/*d>@%>DB/Y/F^WHKf!HbF+Wf%HF+@^@HFY
bFF/%/YYWfO@FCCf*C/^bY%HDD/F^^>^^>/Qb/Y^@HFH5!HbF+Wf%HF+@?
^@HFY/eK/W@/F%/+FH^>/W^bWF@FW/%/F^f/WYO@F%/DH+/C@F<%HF^@FbHbY
Y/+@D/F^^@HF^>WHb<>5//+F++@Y%>WbC^/+ @F ^>/ /^^f?bY^HYDH+/C "9G* \I* Ih9#M @Y bFK>fY@%C* 5//+ F+
+@Y%>W</D/%>F@YDYY>HbC+!//eKW/YY/+!fY@F:be+@Y%HF^@Fb@^@/Y*Y///%^O_OIO
!M 5^/W ^>/ d/CC?KHY/+F/YY FCfY@Y >+ !//F %HDKC/^/+ "I9* 9a* 9_#* HbW
/6HW^Yd/W/ +@W/%^/+^H ^>/ +/c/CHKD/F^H5FbD/W@%C Y%>/D/Y5HW LIhM*
LI_M2LI9MLF+@^YcW@F^YMO F^>/KK/WY"I[*I0*a0#*HK/W^HW?YKC@^^@F<

8F@^/+@6/W/F%/Y%>/D/Yd/W/bY/+5HWFbD/W@%CY@DbC^@HFYH5^>/KWH!?
C/D*!b^^>/fd/W/Y^@CCC%B@F<W@<HWHbYFbD/W@%CFCfY@YO>/FCfY@Y
H5 8F@^/ +@6/W/F%/ Y%>/D/Y 5HW Y^WHFdY<W/^Cf+cF%/+!f^>/KK/W!fcA/F+
WCY/F"[a#*d>HKWHc/+
%HFc/W</F%/H5DHFH^HF/8F@^/+@6/W/F%/Y%>/D/^HF/F^WHKfYHCb^@HF
5HW^>/@F@^@C?!HbF+WfcCb/KWH!C/DH5Y^WHF+@6bY@HF /Qb^@HFYO>Hb<>^>@Y Y%>/D/%HbC+!/ /Y@Cf+K^/+ ^H^>/
LIhM*LI;M*LI9M*LI\M*Y//"_;#*@^dYFH^H!c@HbY>Hd^H+/Cd@^>
!HbF+Wf%HF+@^@HFYO>@YKWH!C/DdYYHCc/+c/WfW/%/F^Cf@F"a;*a9#*
d>/W/%HFc/W</F%/H5/eKC@%@^F+Y/D@?@DKC@%@^DHFH^HF/+@6/W/F%/D/^>?
H+Y^HF/F^WHKfYHCb^@HF@YKWHc/+O///%^O9OI5HW+/^@CYO
%M b/^H@^Y@FcHCc/+FHFC@F/WF+Y^WHF^>/  LIhM* LI_M2LI9M F+ @^Y cW@F^Y +H FH^ +D@^ /e%^ YHCb^@HF
%HFY^Wb%^@HFYO ^Y//DY^>/W/5HW/@DKHYY@!C/^HKW/%@Y/CfKW/+@%^^>//6/%^
H5%HF^WHC%^@HFY*Yb%>Y%>F</YH5^>/5//+:be*Y@YKHYY@!C/5HW^>/
B@F/D^@%Y/+@D/F^^@HFDH+/C"\h#O
Hd/c/W*^>//6/%^H5%HF^WHC%^@HFY*
@FKW^@%bCW%>F"I[*I0*a[*a0#*F+C^/W*5HW^>/%CW@8/W?^>@%B/F/WDH+/C*@F"aa*;I*;9#O
>/KWH!C/DH5HK^@DC%HF^WHC*5HW/eDKC/d@^>^>/@D^HDe@D@g/
^>/ YHC@+Y^>WHb<>Kb^HW^H D@F@D@g/ ^>/ 8CC?bK^@D/* >YFH^f/^!//F
^W/^/+O


_>/D_@%C I+/CZ 4IX _>/ /+@D/F__@IF I4 cZL/FZ@IFZ

J\

+M H Hc/W%HD/ ^>/ %HF%/K^bC HF/?+@D/FY@HFC@^f H5 ^>/

fF%> DH+/C* d/
5HWDbC^/+ @F "I\* 99* 9\#  </F/WC %HF^@FbbD D/%>F@%C ^>/HWf H5
Y/+@D/F^^@HF?%HFYHC@+^@HF KWH%/YY/Y H5 YbYK/FY@HFY H5 8F/* :H%%bC^/+
KW^@%C/Y @F  c@Y%HbY :b@+O %%HW+@F< ^H ^>/ ^>/HWf H5 D@e^bW/Y* ^>/ DH+/C
5HWDbC^@HF @Y !Y/+ HF ^>/ DYY F+ C@F/W DHD/F^bD !CF%/Y H5 ^>/
YHC@+ F+ ^>/ :b@+ %HDKHF/F^YO >/F* 5HW %CHY@F< ^>/ YfY^/D* %HFY^@^b^@c/
YYbDK^@HFY W/ @F^WH+b%/+* F+ ^>/ /Qb^@HFY W/ Y@DKC@8/+ 5HCCHd@F< 
+@D/FY@HFC FCfY@YO >/ W/YbC^@F< DH+/C @Y  ^HB/Y? HW c@/W?^HB/Y?
C@B/ YfY^/D H5 /Qb^@HFY 5HW ^>/ L@F%HDKW/YY@!C/M :Hd H5 ^>/ D@e^bW/*
d>@%> @Y %HbKC/+ ^H  Y^WHF/W %HFc/%^@HF?+@6bY@HF /Qb^@HF 5HW ^>/ CH%C YHC@+Y cHCbD/ 5W%^@HFO >@Y
DH+/C dY C^/W /e^/F+/+ ^H KHCf+@YK/WY/ YbYK/FY@HFY @F "II#O F /%^O ;OI
d/ !W@/:f Hb^C@F/ ^>/ </F/WC +/W@c^@HF 5HW ^>/ KHCf+@YK/WY/ %Y/* F+ ^>/F
W/5/W ^H DHFH+@YK/WY/ YbYK/FY@HFY Y  YK/%@C %Y/O

4 +'%$ %.6% -/3%+)
F ^>@Y Y/%^@HF C/^ bY %HFY@+/W HF/ YK%/ +@D/FY@HF* 5HW d>@%> L_;M @Y ^>/
/Qb^@HF @Y LIhM* d>/W/ ^>/ +@6bY@HF 5bF%^@HF L@M @Y <@c/F !f LIIM F+ LIaMO
5 W/+b%/+ ^H HF/ YK%/ +@D/FY@HF HFCf* ^>/ D@e^bW/ :Hd @Y %HDKC/^/Cf +/^/W?
D@F/+ !f !HbF+Wf %HF+@^@HFYO >/ FHF?Y^F+W+ KWHK/W^f H5 ^>@Y /Qb^@HF
@Y ^>/ YHCb^@HF?+/K/F+/F^ KW!HC@%?>fK/W!HC@% ^fK/ +/>@Y YK^@CCf HF/?+@D/FY@HFC DH+/C C/+Y ^H @F@^@C HW @F@^@C?!HbF+Wf
cCb/ KWH!C/DY 5HW Y^WHF@CW DH+/CY W/ CYH H!^@F/+ 5HW ^>/ %/F^W@5b<^@HF "IG# F+ KW/YYbW/ 8C^W^@HF
"aI# H5 :H%%bC^/+ YbYK/FY@HFYO >/ C^^/W %Y/ @FcHCc/Y  5W// !HbF+Wf KWH!?
C/DO >/Y/ DH+/CY W/ @CCbY^W^/+ @F "I0* IG* aI# !f FbD/W@%C Y@DbC^@HFY* @F
KW^ ^B@F< @F^H %%HbF^ Kb!C@Y>/+ /eK/W@D/F^C +^O  YbDDW@g@F< ^>/HWf
H5 ^>/ YHC@+?C@Qb@+ Y/KW^@HF H5 YbYK/FY@HFY %F !/ 5HbF+ @F "0I#O >@Y DH+/C
%F !/ /e^/F+/+ ^H c/YY/CY d@^> cWf@F< %WHYY?Y/%^@HFC W/ "a\#* d>@%> HK/FY

F/d +/Y@F=9 4@1+%@0/13%6%@ 8#%4A
/^ bY 5HW  DHD/F^ YYbD/ ^>^  0 hO >/ HF/?+@D/FY@HFC Y/+@D/F^^@HF
DH+/C !f
fF%> "G_# W@Y/Y Y  YK/%@C %Y/ H5 ^>/
%HFYHC@+^@HF ^>/HWfO HW ^>/ %HF^@FbHbY Y/^^C@F< H5 F @+/C YbYK/FY@HF @^
C/+Y ^H ^>/ %HFY/Wc^@HF Cd
+
2
LI[M
FL W P FR LLZ+ SMW P 6LWM 3 h +
d>/W/ ^>/ YHC@+Y %HF%/F^W^@HF W cW@/Y d@^> +/K^> Z F+ ^@D/ S* F+ LLZ+ SM @Y
^>/ CH%C D@e^bW/ c/CH%@^fO H !/ %HFY@Y^/F^ d@^> QbH^/+ Kb!C@%^@HFY* ^>/ YfD?
!HC H 5HW ^>/ CH%C YHC@+Y %HF%/F^W^@HF @Y W/KC%/+ !f W F+ 2, LHM !f :6LWMO


J0

P/XX/Z*P,
cX;/X*F+P
P/F+CF+


































































































P








































































































































































































































































































































































































☛☞

























P















P
















P








































































































r
































 










































































 






s





t

 


P














 


) 1) M( CX@7/X?_>@%B/F/X e@_> dX@!C/ %IF_@F/X %XIZZ Z/%_@IF "`G#* '( @+/C
%CX@7/X?_>@%B/F/X e@_> %IFZ_F_ %XIZZ Z/%_@IF ":J#

>/ Y@DKC/ DH+/C 5HW %HF^@FbHbY Y/+@D/F^^@HF H5 "9G# W/+b%/Y LI[M ^H F
@F^/WcC* Yf Z . "h+ #* %HWW/YKHF+@F< ^H  %fC@F+W@%C %HF^@F/WO ^ ^>/ ^HK
Z 3 h ^>/W/ @Y F @F:Hd F+ ^ ^>/ !H^^HD Z 3  ^>/W/ @Y  +@Y%>W^>/ ^>@%B/F/+ Y/+@D/F^O ^ @Y YYbD/+ ^>^ ^>/ ^>@%B/F/W @Y 5/+ %HF^@FbHbYCf
!f ^>/ @F:Hd F+ +@Y%>W</+ %HF^@FbHbYCf ^>WHb<> ^>/ KCb<>HC/O >/ D@e^bW/
c/CH%@^f L 3 L LSM @Y  5bF%^@HF H5 ^@D/ HFCf* d>/W/ L %F !/ %HF^WHCC/+ ^ ^>/
!H^^HD +@Y%>W
%HF+@^@HFY* d>/W/ YH?%CC/+ /F^WHKf !HbF+Wf %HF+@^@HFY W/ bY/+ @F HW+/W ^H
Y>Hd /e@Y^/F%/ F+ bF@Qb/F/YY H5 /F^WHKf YHCb^@HFYO >@Y DH+/C* d>@%> %F
!/ ^W%/+ !%B ^H /^^f "Ih9#* >Y YHD/ DAHW +@Y+cF^</Y C@B/ ^>/ C%B
H5  <CH!C %HFY/Wc^@HF KW@F%@KC/O F ++@^@HF* @^ >Y !//F W/%H<F@g/+ ^>^
@W@%>C/^ !HbF+Wf %HF+@^@HFY W/ K>fY@%CCf bFW/C@Y^@%* /c/F ^>Hb<> ^>/f
C/+ ^H  D^>/D^@%CCf d/CC?KHY/+ KWH!C/DO >/f Y>HbC+ !/ W/KC%/+ !f ^>/

%>F</ H5 ^>/ ^WFYKHW^ :be LLZ+ SMW F+ ^>/ %HDKHY@^/ :be LLZ+ SMW P 6LWM*
d>@%> C/+Y ^H  KbW/ @F@^@C cCb/ KWH!C/DO
HW/Hc/W* ^>/ 5//+ YbYK/FY@HF Y>HbC+ !/ 5/+  @E 3 ^>/ +@Y%>W^ ^>/ Y/+@D/F^ +@Y%>W</ ^ ^>/ !H^^HD F+ ^>/ Hc/W:Hd ^ ^>/ ^HK H5 ^>/
%HF^@F/WO >/F ^>/ HF/?+@D/FY@HFC DH+/C@F< C/+Y ^H F bKdW+?+@W/%^/+
D@e^bW/ c/CH%@^f L
6 h !Hc/ F+  +HdFdW+?+@W/%^/+ c/CH%@^f L 2 h !/CHd
^>/ 5//+ C/c/CO >/ 5//+ YHbW%/ @^Y/C5 @Y +/Y%W@!/+ !f  Y@Fb%> S%CW@8/W?^>@%B/F/WYT >c/ !//F KWHKHY/+ !f Y/c/WC b^>HWY @F%Cb+@F<
"\a* G9# F+ >c/ !//F FCfg/+ ^>HWHb<>Cf @F KW^@%bCW !f @/>C LY// "\0* \G#
F+ ^>/ W/5/W/F%/Y ^>/W/@FMO H YB/^%> ^>/ D^>/D^@%C DH+/CY d/ %HFY@+/W
 %CW@8/W?^>@%B/F/W d@^>  LW/ h = .+0 6 LZM 6 .D * Y// @<O a LMO >/ DH+/C @Y ^>/F <@c/F !f ^>/


_>/D_@%C I+/CZ 4IX _>/ /+@D/F__@IF I4 cZL/FZ@IFZ


€























































JG
































































 

 

 







 

 





 

 















 

 

 

 


 

 

 







































































































































































































































































) 0) X/ZZcX/ 7C_X_@IF I4  9I%%cC_/+ ZcZL/FZ@IF "bJ#

@F@^@C cCb/ KWH!C/D
LZMFL W P FR 3LW+ ZM 3 h + Z .  + S 5 h Z

5,
bW


LW : W M


 LW : W M P LZM6LWM 5,
b
W



3LW+ ZM )3
 LW : W M P LZM6LWM 5,
bW




 LW : W M
5,
bW

WLZ+ hM 3 WG LZM . "h+ I# + Z .  Z
Z = :I *
:I = Z = h *
h=Z=I*
Z5I*
LI0M

d>/W/  2 h F+  2 h W/ ^>/ KW/Y%W@!/+ cHCbD/ :be/Y H5 ^>/ YbYK/F?
Y@HF* d>@%> C/c/ ^>/ %HF^@F/W ^ ^>/ !H^^HD HW W/ 5/+ @F^H ^>/ %HF^@F/W*
W/YK/%^@c/Cf* 
3  :  @Y ^>/ W/YbC^@F< cHCbD/ :be ^ ^>/ Hc/W:Hd* F+
W @Y ^>/ YHC@+Y 5//+ %HF%/F^W^@HFO HW Y@DKC@%@^f* ^/DKHWCCf %HFY^F^ %HF?

^WHC 5bF%^@HFY 
*  F+ W W/ YYbD/+O >/ DHY^ W/KHW^/+ W/YbC^Y +/C
@F ^>/ 8WY^ @FY^F%/ d@^> ^>/ %Y/ H5 %HFY^F^ %WHYY Y/%^@HF  0 %HFY^G d@^>
L
3 
R F+ L 3  R L@>/ FCfY@Y H5 %CW@8/W?^>@%B/F/W DH+/CY* @F%Cb+@F< d/CC?KHY/+F/YY* %HF?
c/W</F%/ H5 FbD/W@%C D/^>H+Y F+ /e^/FY@HFY ^H :H%%bC^/+ F+ KHCf+@YK/WY/
YbYK/FY@HFY* >Y HK/F/+  F/d C@F/ H5 W/Y/W%> d@^>@F ^>/ KWHA/%^ ^>^ ^/+  Y/W@/Y H5 KK/WY "Ih* aa* _a* __* _\* _[* _G* ;h* ;I* ;_* ;;* ;9#O ^>/D^?
@%C F+ FbD/W@%C YK/%^Y H5 %CW@8/W?^>@%B/F/W DH+/CY W/ 5bW^>/W +@Y%bYY/+
@F /%^YO _O; F+ 9Oa* W/YK/%^@c/CfO


bi

P/XX/Z*P,
cX;/X*F+P
P/F+CF+

F=G @%AAH@%14E@E1868(48H4E%#HA:%6A186A
>/Y/+@D/F^^@HF?%HFYHC@+^@HF^>/HWfdYCYH/e^/F+/+^HKW/YYbW/8C^W?
^@HFH5:H%%bC^/+YbYK/FY@HFYO8C^W^@HF+/c@%/@YYB/^%>/+@F@>/YbYK/FY@HF@Y%HF^@F/+@F%fC@F+W@%CcHCbD/*d>@%>@Y!HbF+/+^
^>/^HK^>/@<>^ 636LSM!fDHc!C/K@Y^HFF+^^>/!H^^HD!f8e/+
8C^/WLHWSD/D!WF/TMO>@YD/D!WF/@YK/WD/!C/5HW^>/:b@+HFCfO>/F
^>/KW/YYbW/ QLSM@YKKC@/+^H^>/K@Y^HF*^>/:b@+@YYQb//g/+^>WHb<>^>/
8C^/W/C/D/F^OF^>/D/D!WF/YH?%CC/+8C^/W%B/!b@C+YbKO>/8C^/W
%B/ <WHdY %HF^@FbHbYCf F+ @^Y >f+WbC@% W/Y@Y^F%/ @F%W/Y/Y %%HW+@Fd>@%>>@F+/WY^>/DHc/D/F^H5^>/K@Y^HFO

>@Y8C^W^@HFKWH%/YYLY/+@D/F^^@HFF+%B/5HWD^@HFMd@^>^>/D@e?
^bW/ :Hd %bY/+ !f ^>/ K@Y^HF DHc/D/F^ %F CYH !/ +/Y%W@!/+ !f ^>/
Y/+@D/F^^@HF?%HFYHC@+^@HFDH+/C@FHF/YK%/+@D/FY@HFO>//YY/F^@C@+/
@Y^>^%HDKC/^/D^>/D^@%CDH+/C%F!/H!^@F/+F+FbD/W@%CCfY@D?
bC^/+!f^>/%>H@%/H5KKWHKW@^/!HbF+Wf%HF+@^@HFYF+^>/%HbKC@F<H5
KKC@/+KW/YYbW/ QLSMF+K@Y^HF>/@<>^ 6LSMO
/W/^>/Y/+@D/F^^@HFH5^>/
YbYK/FY@HF@FY@+/^>/%HF^@F/W@YCYH@F%Cb+/+O
>/W/YbC^@F<KW/YYbW/8C^W^@HFDH+/C%F!/Y^^/+Y5HCCHdYO>/8/C+
/Qb^@HF5HW^>/%HF%/F^W^@HFHY5bF%^@HFH5^@D/SF+>/@<>^ ]@Y
+ *
2
@
FHPF
L M + h=]=6SM
L + S5 h G
LIGM
L
U 6LSMHP2
, LHM 3 FU H
>/KHW/KW/YYbW/ E*d>@%>@YCYHYHb<>^*%F!/%C%bC^/+5WHD HL]+SM!f
FU E3:OLHM3 : FU Q LHM +

h =]=6LM+
S S5h +

LahM

d>/W/OLHM3HO: PLI : HMO# @Y^>/CH%C+/FY@^fH5^>/D@e^bW/*@5O: F+ O#
W/^>/+/FY@^@/YH5^>/YHC@+F+^>/C@Qb@+*W/YK/%^@c/CfO

Qb^@HFYLIGMF+LahMW/YbKKC@/+d@^>^>/@F@^@C%HF+@^@HFY
6LhM36G Z HLh+]M3HG L] M +

h 6 ] 6 6G +

LaIM

L6G @Y^>/@F@^@C>/@<>^F+HG @Y^>/@F@^@C%HF%/F^W^@HFMF+^>/B@F/D^@%
!HbF+Wf%HF+@^@HFY
2
+
LaaM
2, LHM : FU LHM Lh+ SM 3 :6* LSMHLh+ SM + S 5 h +
2+
2
+
La_M
2, LHM : FU LHM 6LSM+ S 3 h + S 5 h G
HF+@^@HFY LaaM F+ La_M Y^^/ ^>^ ^>/ YHC@+ K>Y/ @Y >/C+ bK ^ ] 3 h F+
^WFYKHW^/+ ^ ] 3 6LSM d@^> ^>/ K@Y^HF c/CH%@^f 6* LSMO >/ %HbKC@F< !/^d//F
QLSM F+ 6LSM @Y +/Y%W@!/+ !f ^>/ +fFD@% !HbF+Wf %HF+@^@HF
2
+
2
+
La;M
QLSM 3 Q HLh+ SM : 3 ?G P O# L6LSM : 6G M : @# . 6* LSM G

/W/ ?G @Y ^>/ @F@^@C DYY H5 ^>/ YbYK/FY@HF* +@c@+/+ !f ^>/ %HF^@F/W %WHYY
Y/%^@HF* @# @Y ^>/ +fFD@%C c@Y%HY@^f H5 ^>/ KbW/ :b@+* F+ . @Y ^>/ >f+WbC@%



×