This content was uploaded by our users and we assume good faith they have the permission to share this book. If you own the copyright to this book and it is wrongfully on our website, we offer a simple DMCA procedure to remove your content from our site. Start by pressing the button below!
VM(V Q2--%+A/05K(@ *.V C *:t - ) t -?@ (/(t?2@ ( iVP+,5K*,*.V(G5&(*,V+.]Cr-BZ *.jV9-\DF/24--%+W/5K(@ *.V CEjCE*.Ve]G$|>V YV 24*,-%+P@\Cv* -M24-\]mX-%(Ve(*WC1--%(jVc@BD&-%(L 5 "@B05F=C -f@ (/ -\(V @BD&-%(L 99 @B05FC$mv-\*.VM*.@ *:5K*8/-VC (j-%*:3@YVa@f D-+,-%*W@B*.V/ @BLz@B5&(£@B+.-\1(/ *,fV 5)@ 5Chi 5K(*,V24-\1(*,V+A2DK-0.2 P5CEV/5&+.V 2*.5K-\.( 3 ]@B*.+,5K >:-`@B(/*. Ve( *.+W@B(C}DF@B*,V / i0 3 b 717>3]@B*,+.5& z>W$')(*.j5FCr2@%C}?V -*.V `-%+.D/ -\]m-%L\V(V-\1Cr24--%+W/5K(@ *.V *C 3 m> @B+,V:+.VeDF@B*,V /m*.-M*.V82@ ]mV+W@95K]@BL%V 24--\+A/5&(@B*,V dC 3 m> @%CZ-%D&DK- r1C s *u 3.#\$<lR > # y y y 2-C C}5K( y y y # y y PV+,V u y y # y u "GC}5K( y 24-C y y# yy y y b # y y y # # y y y # y y "F5 # y y " b y 2-C C}5K( y y # y "9 - }u y # y " u y "GCE5&( } 4 ^,5l
,$b d#$%
^y`a"b ?
CE5K]aXDK5 V /d]m-0/VeDn-BZr5&]@BL\V Z-\+.]@ *.5K-\(5C:C}- P( 5K(u
5KL%1j+.V#%$<0$@0$d')( *,5FC7CE-2e@BDKD&V /GX5K(j-%DKV 2 @ ]mV+A@r]m-0/VDA-%*.VPD&V(Cn5FC|@\C.CE1j]mV /c*.-7iV@8CE5K(jL%DKVPX-\5K(0*$|>V -\+.DF/M24--\+A/5&(@B*,V CF3j5f7:971<,>
- Z@ X-%5&(* @B+.V*.+A@ (C[Z-\+.]mV/h*.-8*.V5&]@BL\V2--%+A/05K(@ *.V [email protected]:C/>n1(/0V+XV+WCEXV 24*,5KYVPX+,-/}V 24*,5K-%( $ C.C}1]mV *.3@B*r*.V8-%+.5&L%5&(d-BZ`*,V824--%+W/5K(@ *.VMC}C}*.V]5Cv@ **.jV9D&V(Cr24V(0*.V+*3 CE-P(Gi0dq5K( u5KL\1+.VM#\$<$=@ >D@B(3/ 5C*.jVZ-02@ D?DKV(jL%*.M-BZ
*,V72@ ]mV+W@ -%*,V/05FCE*W@B(2VvZ+.-\] *,VvD&V(Cn*.-8*.V5K]@ L%VPXD@B(V$|>jV( 1C}5K(LM*.V7* -cV J15&Y\@BDKVe(*|*.+,5F@ (L%D&V C `V72@ ( P+.5&*.?V s ",C u 3.#\$<\y > 9 <# H5&(24VP*.jVv5&]@BL\V5FC|@ D P@jCZ-%+.]aV /:1XC}5F/Vr/- P.( -05K*n5C|241CE*,-%]@ +.8*.-:13CEV@ (jVL@ *.5KYVrC}5KL\(h5&( Z+,-%(0* -BZ*.j*V C 5&(*.V7@ i-BYV7V 1@ *.5K-\(?$|u+.-\] *,V7@Bi- YV7V 1@B*,5K-%( -*.j*V Ch5K]@BL%V24--\+A/5&(@B*,V CP@B+,V9L\5KYV( i0 s Cau*" < 9 3.#\$<0m# > H5&]m5KD@B+.D&? -%*,ZV @ "24--%+W/5K(3@B*.VC-BZ|*,V75K]@ L%V7@ +.V7L%5&Y# V(mi0 s @4u*" p< 5 3.#\$<\< > # >V @Bi- YV:V 1@B*,5K-\(C+,VX+,V CEV(0*P*.jV9XV+WCEXV 24*,5KYV7*.+W@B(C)Z-%+,] P5&*.*.V8-%+.5&L%5&(d@ **.jV9D&V(C$P' Zn*,V -%+,5KL\5K(m5C]m- YV /:*.-c*,V5K]@BL%V -@\CPCE- P(5K(u5KL\1+.Vc#\$<0$ .i -*,VXV+AC}XV 24*.5&YVvXj+./- }V 2*.5K-\(m5FC`/V (jV / i0m*.VZ-\DKDK- P5&(LcV 1@B*,5K-%(31C s @4u M" 5 < 3.#\$<\N > Cau " 9 < 3.#\$< S > #
#y
y (X,Y,Z)
(X,Y,Z)
y f f
O O Z
Z
u 5&L%1+,Vc#%$=< s`Un5K(-\DKV82@ ]mV+A@7]m-0/VD $$3 @ >Pqr+.5&L%5K(@ *v*,V7DKV(C$$3i >vqr+,5KL%5&(@B*P*.jV95&]@BL\VXD@B(V$ ')*c5FCc(-\*mX-C.C}5KiD&Vd*,- /Ve+.5KYV@XV+AC}XV24*.5&YVm]@B*,+.5& C}5K]m5&DF@B+8*.-*.V*.+W@B(C}DF@B*,5K-\(.-rC.2@ DK5K(jL/-`@B(/ +.-\*A@ *.5K-\(]@B*.+,5F24VCv/1jVh*,- *,Vc(@ *.1+,Vh- ZPV 1@B*,5K-\(Cc#%$<\Nd@ (/ #\$< S$ (VM(VV/d*.-5K(0*.+,-0/124VM@ ( -%*,V+P*,+A@B(3C[Z-%+,]@B*,5K-\(2@BD&DKV 4/ I0Q?SQ L pL Q lG APRJ G N&Q?P=SJ Q $n>V7-\]m-%L\V(V-\1C*,+A@ (C[Z-\+.]@ *.5K-\( 24-\(YV+,*ACP*.V J?P LRG J +Q?P :QhQ?P 0J LRG36587:9;7=<,>P5K(0*.-M*.j4V I0Q?SQ L pL Q lG +Q?P :QhQ?P /J L G 3 5f7 9;7 0<x7 />W$7')(G*.5C*,+A@B(3C[Z-%+,]@B*,5K-\(GV @%2Af 587:971<24--%+W/5K(3@B*.VM5FCP]M1DK*,5KXD&5KVe/hi@24-\(CE*W@B(0* M-
@B(3/ 5FC7@BXjXVe(/V /@%C7*.V:Z-\1+.*, 24-\]mX-%(Ve(*- ZP*,VhYV24*.-\+$hH5&]m5KD@B+,DK? -*,Vc5K(0YV+AC}V:-\]m-% L%Ve(V-%13C*.+W@B(C)Z-%+,] 24-%(0YV+,*AC*,V-\]m-%L\V(V-\1Cn5K]@ L%V24--%+W/5K(@ *.V rC 3 7 &7 h7 =>n5K(0*.-7*,V _`@B+,*.V C}5F@ (d5K]@BL%V824--\+A/5&(@B*,V zC 3 7 7 >D-i0/5&Y5/5K(LcV@%2Ad-BZ *.V8*.+,VV824-%]mX-\(V(0*AC P5K*, *.jV Z-\1+.*,G24-\]mX-%(Ve(*e$ >V7XV+AC}XV24*.5&YV]@B*,+.5&m2@ ((- 6iV:/0V (V /@\1C s # y y y u yy y# y# yy y y b # # >VcXV+WCEXV 24*,5KYVc*.+W@B(C)Z-%+,"] - P52G+,VDF@ *.V CP*.VM-\]m-%L\V(V-\1C -\+.D/24--\+A/5&(@B*,V C P5K*,G*.Vc-\ ]m-\L%V(Ve-%1C5&]@BL\V724--%+W/5K(3@B*.VC5CP/V (V/ @\1C s ?5 # y y y ?5 9 u y # y y 9 / < y y # y /< " w y y b # (V:2e@B(V @%C}5KD&/V+,5KYVr*.Vc_`@B+,*.V C}5F@ (d5K]@BL%V 24--%+W/5K(@ *.V CZ+.-\]*.jV:@ i-BYV7V 1@ *.5K-\(G@\1C s @ u M" 5 < 7 3.#\$<\; > Cau " 9 < 7 3.#\$<\g > P52@ +.VMV@\24*.D&*.VaC.@ ]mVcV 1@B*,5K-%(3C9@\CV J13@B*.5&-%(Cc#\$<%N@B(/#%$=
(a)
!
"
! " # $
#
%& $ %& $ %& $ % & % & % &
'
(
*) (
+
(
'
(
4
` ,`
#%#
dc
> VMXV+AC}XV24*.5&YVc*.+A@ (C[Z-\+.] +.VD@B*,V C*.V-\+.DF/24--\+A/5&(@B*,V C P5&*.*.VM5K]@ L%VM24--\+A/5&(@B*,V C PjV( *.jVM2@B]mVe+A@c5FCvD&-02@B*,V /G@B*7*.jVc-%+.5&L%5&(G-BZ`*.V1`-%+,DF/G24--\+A/5&(@B*,V C4$1r-`VYV+&-5K(G+.V@BDnD&5 ZV `V:(VeV / *.-G*,+A@ (CED@B*.V@ (/ +,-%*A@ *.V*.jV2@B]aV+A@5K( -\+A/V+c*,-Gi+.5&(LG*.jV -\i'}V 24*8-BZ5K(0*.V+,V CE*85K( *,V VDF/-BZ Y05KV 7$`>V+,V4Z-%+,?V -*,V824-%]aXDKV*,V72@ ]mV+A@:]a-0/VDf5&(Y-\DKYV C`CEVYVe+A@BD?-\*.Ve+v*,+A@B(3C[Z-%+,]@B*,5K-\(CiV C}5F/VC *.jV9XV+WCEXV 24*,5KYV*,+A@ (C[Z-\+.]G$ ')( -\(VCE5&]mXDKVM]m-0/Ve2D -n@\C.C}1]mV*.@ *c*.V2@ ]mV+W@ 5FC 3+ACE*M@ *c*.V-\+.5KL\5K(-BZ*.jV `-%+,DF/24--%+, /5&(@B*,V 1C -n5C *,V( *,+A@ (CED@B*.V/ i0y 365 h7D9 h7=< >o3 ]@ *.+,5K *>D-n*.V(~+.-%*W@B*,V /@B+.-\1(/ *.jV
u 24-C y y y # "*< y y # " # y y5K(0YV+WCEV:y *,+A@ # (C[Z-\+.]CZ-%+7y *.y VM*.+Wy @B(C}DF@ *.#5K-\(@B(3/+.-\*A@By *,5K-\y (C:y @ +.Vm1C}# V /GV+.Vz$m>5C v % , * h V , * B @ 8 * . * M V 5F+.Cr-\*Ai@ V*.2V @B/ 1-|C}+AVh@ *.5&*vVe5C+:*.*.3VM@B(24-*.-\+AV/5&-\('i @B}V*,Vm24*C}$C}v*.V- ] *-n@ *.*.*A@\Vd2j_`V @ /I+.*,*,V -mCE5*.@Bj(VM5K2]@B]m@ L%VeV+A@c2-*.-%+A@ /0*95K(5Cv@ *.iV VCc5K(j2L @ (*,+Ai@ V(CE24D@B-%*.]mV/GXj1@B*.(V // Z+.-\]V1@B*,5K-\(C1s
'
'
(
& c('*),+. & )0243+ b "! $ % # ! 0/ 1 % # / #65 & c('*)>;< & )92:3+ )0243;< & c('>),+?)0243@; #7"!8#%! & )0243C+ c('*),;K"/- =#%/ & c('*),+Cc('>),#A;LCB- D#DB & )92:37; HI #7"!$#J ! & )0243+?)92:3N;<- 0/1#6 / & c('*),+?)0243; CBD#A B& c('*),;<#7"!M#%! "/1#J/ #DCBD#AB
(P
` ,` `cm%Q"`d%&'
- E 5 7 #6 5 - 7O 5
f>v jGF & f>v j>h &
)' (*.V7X+,VY5&-%1CPC}V 24*,5K-%()V8/5FC,241C,CEV /m*.jV:2e@B]mV+W@9]m-0/0VD2- P52+.VeDF@B*,V C*,V-\+.DF/24--\+A/5&(@B*,V C P5K*,G*.Vc5&]@BL\V824--%+W/5K(@ *.V C$:')* @%C@\C.C}1]mV /d*,@B**,VM2@ ]mV+A@9Z-02e@BD|DKV(jL%*. -+,-%*A@ *.5&-%(~@B(L\DKV C=@B(3/*,+A@ (CED@B*.5&-%(/5CEXD@%24V]aV(*WCn@B+,V 0(-P(?$ v(@ DK*.Ve+.(@ *.5KYVr]mV*,-0/:Z-%+r24-\]mX1*,5K(L7*.jV72@B]aV+A@ ]m-0/VeD5C*,-c1CEV7*.jV72@B]aV+A@7@%CP@:]aV @%C}1+.5&(L8/VY05F24Vr*.-M/Ve*.V+,]m5K(VP*,V1( (- P(C5&(m*.jV72@B]aV+A@ ]m-0/VeD)$>5CXj+.-024V C,Cm5FCm2@ DKD&V / 2@ ]mV+W@2@ DK5&i+A@ *.5K-\(?$'[(k*,5FCm]mVe*.-0/ -r@IZV X-\5K(0*ACm5K(£N ) P5K*, 0(- P(24--\+A/5&(@B*,V CP@B(3/h*.Ve5K+`24-%+,+.V C}X-%(/5&(L:5&]@BL\V2--%+A/05K(@ *.V C`@B+.V1CEV /c*.- 2@BD&5Ki+W@B*,Vv*,V 2@ ]mV+A@0$ >VdXj+./- }V 2*.5K-\( -BZ9NB -\]m-%L\V(V-\1Ch2--%+A/05K(@ *.V Cc-%(0*.-*.V5&]@BL\VmXDF@ (V 3 Z+,-%] V 1@ *.5K-\( #%$=<JkR >P2@ (iV CE1]a]@B+,5KV /c@\1C s
#<
u
! " # $
l7
b8 bb
u
bC b b
b
C
5
3.#\$N\y > 3.#\$N0#m>
9 7 <
# PV+,V @B(3/ +.VCEXV 24*,5KYVD&M/V(-\*.V7*.V82@ ]mV+W@c@B(/ -%+,DF/m-\]m-%L\V(V-\1Cv2--%+A/05K(@ *.V C=-@B(/ u z-z/V(-\*.Vr*.Vr2@ ]mV+W@]@ *.+,5K¢$?>Vr@B5&] 5&(c*.Vr2@ ]mV+W@v2@ DK5&i+A@ *.5K-\(c5FC*,-7/V*,V+. ]m5&(V*.jV9]@B*.+,5K 1C}5K(LM*.jV 0(-P(GN ) X-\5K(0*ACr@B(/*.V5&+r24-%+,+.V C}X-%(/5&(Lm5&]@BL\V:2--%+A/05K(@ *.V C$ >V]@B*,+.5K 5C S -S0- P52@\C #egI1((-P(C$ v-VeYV+ - M5FC:(-\*h]aV @B(5&(LBZ1jD5K(*,V 5K]@BL%V 24--%+W/5K(3@B*.VC4$0V 2@ 1CEVc*,Vc5K]@ L%V85FC-%(D&d* -/5K]mVe(CE5&-%(@ 2D -*.Vc5&]@BL\VM24--%+W/5K(@ *.V C72@ ( iVm/0V*.V+,]m5K(jV /mi 1- - $c>Ve+.V4Z-\+.V?- `VM/-(-%*7(VeV /d*.-/V*,V+.]a5K(V7*.jVc*.5&+A/d+.- -BZ *.jV]@B*,+.5& - P52M5FC1C}V / Z-\+ $|v- *- `V7@B+,V7-%(D&hD&V4Z * P5K*.#e<:1'( 0(- P(C5K(m*,V]@ *.+,5K $ (V P5KD&D (/d-\1*vD@B*,V+v5&(d*,5FCrCEV 2*.5K-\(d*,@B* V 2@B( @B+.ij5K*.+W@B+, -%(jV:-BZ`*,Vm#e @B+.V7L\5KYV(i0 @4u 7 3.#\$N\< > Cu 3.#\$N\N > # u+.-\]*.V7V 1@ *.5K-\(C#%$=N#.#\$N%N V7L%V&* s u b8b 5 w b 9 w b 1
'
rb
#
!
"
$ #
! $
" $
!
b8b b! !
"
-
-
!
$
"
$
$
bC /
-
-
$
b B
-
-
b
rb ! rb !
#
f>v & >f v GF &
# / # BD# H # H = / # H B # H O b8b
'[(*.V`@Bi- YV|V 1@B*,5K-%(3Cf*.V+,V|@B+,Vr#<1'( 0(- P(C 3 7 7 >:- @ (/ YV 0(- P(;C 3j5f7D9;71
/
B
#
b8b ! b -- b / b -- b B b -- b b8b ! b / b B b
bb!
b
b- / C - - b B - - b b b b b b ! - C / - B ! / B
-
!
C
/
B
# b rb ! b # b # rb ! #
rb # H b r!b # H rb ! # ! # H
rb !
/ b # b / #
B b # b B #
# / I# BI# b # H b / b # H b B b # H b # H / # H B # H
# H
/# H
BI# H
f>v >h & f>v &
vv
f>v ]f & f>v &j & f>v &
vv
f>v
&
# N @B'[i(~- Y*.V8V CEC}jVmCE*,VV] 1@B2*,@ 5K(-\(iC:V *.PV+.5K*,CE*.1Vi(aC,245K+.(5&X]*AC:@B*,-\+.({5& 36Z58-\+.7:] 9;7=@\<,C >8Z-\@BDK(DK-/vrC=3A@Bs 7DCE>/V(j-%*.V*,VmX-%5&(*c(01]MiVe+$>V 4
b / b B b ff vv / B
! !
!
f
/ B
vv
!
!
!
b / b B b ff / B
/
f
B
b8b
# b B b # b bb # B # b b # >! # >/ # B # C # HH b ! b # HH b / b # HH b B b # HH b # ! # / # B # rb H# >! # H >/ # H B # H # b ! b # !
p '
# b / b # /
f>v & E:
vv
vv
f>v &
E
*.Pj-\V9]mVe1j-%+.('L\V V((jV--\5PCv1(3C@MC1C}-< @BC}(3*./-V] /0#<MVP*.]V+,5F]m@B2A*,M5K+.(j5Kt VP@%- *.C]MV7@M1+.VeDK5F*,]C5KX#@BD&< 5&VP(-C}5K-%(DK#9L71j*.Y15KV(-\2(*.(C4-%$`-&+ P->@B((CV/G$|+,V4pfycZV-%*5F+,CrV?-@BDCEV7-au2e@ @B#k(-#e< *.@ +.-Vei(m5*.*.+AY@ V V8+.245&*.DK@ c-\i+-X$PY52->V7cjC}-\5FCP(C}*.V75FVCr]-B@ Z 2@ ( iV8+.V P+,5K*.*,V(@\1C s
'
! b / b B b
f
f
vv
!
/
!
vv
/
f
B
B
!
!
# ! b b # !
b / b B b ff / B
f
! / B
# ! # ! # !
# b / b # /
# b B b # B
/ # B # b HH b # HH b / b # HH b B b # / # B
# ! H
# H * /
# H B
b8b b b b Cb rb
b v v H b H vv
H
f>v
f>v *F &
'[(*,V@Bi- YVCEjCE*,V]"-n*.jVm]@B*,+.5& @ (/ YV24*.-\+ @ +.V 0(-P(?$(V2@B( /V*,V+.]a5K(Vc*,V#%# 1('0(-P(C75K(GYV 24*,-%+ Qi0G1CE5&(L*.VMXC}V1/-5K(0YV+AC}V?-5lZr@ *9D&V @%C}*8; # ;-%+7]m-\+.VMNB X-%5&(*WC7@B(/ *.jV5K+824-\+.+.VCEX-%(/05K(L5K]@ L%VM24--\+A/5&(@B*,V Cc@B+,V0(-P(?$bd1D&*.5KXjDK05K(Lm*,Va@Bi- YVhV1@ *.5K-\( i0 -%(i-%*. CE5/V CP@B(3/ +.V@B+.+W@B(L\5K(LV7L\V*s u 3.#\$ Sz^ > u 3 4> b 3.#\$;\y > # qr(24V 5FCP/0V*.V+,]m5K(jV / -%*,V7]@B*,+.5K 5CP/V (V/ -'P5F2A24-\]mXD&V*.V C|*.V82@ ]mV+W@:2@ DK5Kij+A@B*,5K-\(?$
!
!
!
!
!
*#x ,$%m8i ` ,` `z` F gb
&
v(75K(0*.Ve+.V C}*.5K(jLP5K(0YV+AC}VnX+.-\iDKVe]/V @ DFC P5K*.8*.V|+,V 24- YV+.r-BZ 2@ ]mV+W@X@ +A@B]aV*.V+WCZ+.-\] *,V`2@B]aV+A@ ]@ *.+.5&f$7u-\+Vj@B]mXD&V?-L%5KYVe(G@mX-\*.-%L\+A@ X *A@V(Gi0G@B(1('0(-P(2@ ]mV+A@:Z+.-\] @B(1('0(-P(
4# S DK-02e@B*.5&-%( Pj5F2A.-%@\CiVV(a24+.-\XXV /m@ (/ -\+PV(D@B+.L\V / --k2e@B( `V/Ve*.V+,]m5K(V|*,V2e@B]mV+W@t=CX-CE5& *.5&-%(M@ (/:-%+,5KV(0*A@ *.5K-\(.-\@B(/c/Ve*.V+,]m5K(V*.V`V*,V(0**,- P5F2A7*.VPXj5F24*,1+.V P@\Cn24+,-%XXV /:-\+nV(D@B+.L\V / vXXjDK5F2e@B*.5&-%(Cn- Zn*,5FC|-02241+`5K(C}VYV+A@ D¢@B+.V@%C4$`u-%+`5K(C}*A@B(324V?-5K(@ 1*.-\(-%]a-%1C(@Y05KLz@B*.5&-%(.-j@c24+.1j5FCEV ]m5C.CE5&DKV`24-\1DF/c-%i*W@B5&(h*,Vr2@B]aV+A@v*,+A@ (C[Z-\+.]@ *.5K-\(c]@B*,+.5& Z+,-%] @*.Ve+.+A@ 5K(c]m-0/0VDCE*,-%+,V / -\(i-z@B+W/ @B(3/ *.jV( 24-%]mXj1*.Vm*,V2@B]aV+A@X@B+W@B]mV*,V+AC7*.@ *M/V (jV *,VYV524DKVt=CDK-02@ *.5K-\( @B(/V @%/05K(Lj$ vDCE/- -
@CE*W@B*,5K-%(3@B+.~2@ ]mV+A@MY5&V P5K(L@+,-%i-%* @B+,] -%+ C}X@%2Vm24-\1DF//V*,V+.]a5K(V7*.jVhX-C}5K*,5K-%(~-BZ *.jVc@B+,]G$|>V8]@B+ 5&(LC- Z`CEVYVe+A@BD?X-\5K(0*ACP-%(dX3@B+.*r-BZ *.V8]@B(5&X1D@B*.-\+ -\1DF/@BD&DK- 6*,V5K+PV@%CE V0*.+W@%24*,5K-%(MZ+.-%] @B(5K]@ L%V@B(/mX+,- Y5/VL%+,-%1(3/ *.+,1*.MZ-%+P*.jV:2e@B]mV+W@72@BD&5Ki+W@B*.5&-%(?$|>jV72@B]aV+A@ X@ +A@B]aV*.V+WC72@B(*.Ve( iVm/Ve+.5KYV/ Z+.-%] *.jVm2@ ]mV+W@h*.+W@B(C)Z-%+.]@B*.5&-%( ]@B*.+,5Kt -?@B(3/*.VaDK-02@ *.5K-\( @B(3/ -%+,5KV(0*A@ *.5&-%(-BZ*.V7]@ (5KXj1DF@ *.-%+r2e@B(iV:-%ij*A@B5&(V /m+.VeDF@B*,5KYVr*.-M*.V8C}*A@B*,5K-\(@B+,d2e@B]mV+W@$
|_ -%(3CE5F/0V+|@7NB xX-\5K(0* P5&*.M24--\+A/5&(@B*,V Cx365 #k7:9m#l7=<7#l7#h> 3)CEVeVru5KL\1+.V7#\$ S >W$n' Z 2@B]aV+A@P]@B*,+.5& 5FC (-P(V72@ (G/Ve*.V+,]m5K(VP*,V75K]@ L%V24--%+W/5K(3@B*.VC- Z`@:X-%5K(0*Pi0m1CE5&(LcV1b @B*,5K-\(#\$N\y -*.@ * 5FC"! u -#PV+.V#! u 3 7 &7 h7 =>A$|' Z`V]M1DK*,5KXD&$! P5K*. -'V CE-\1DF/mL%Ve* *.jV:-%+,5KL\5K(@ D b i@%.2 f$pfV*1CCEV* du y -f*,V%( ! u3 =7 h7Ay 7 1>W$7v- *-i@\-2 0X+,/- }V 24* ! i ! u& $ (1V P5&DKDnL\V*8@m(V NB X-%5&('* -P5F2ACE-\1DF/GDK5&V:-\( *.VMC,@B]mV DK5&( Vc2-%((V24*.5&((L @B(/G *.jVM24V(0*.V+P- ZPX+,/- }V 24*,5K-%*( ) 3 CEVVMu
5KL% 1j+.V#%$TS >W$ H5&]m5KD@B+,DK? -#Vc2e@B(*A@ V @B(j-%*.jV+|NB X-%5&(+* u3j5G< 7:9c< 71<< 7h# >:-@ (/:L%V(jV+A@ *.V f -/Pj5F2A P5&DKDD&5KV|-%(c*,VD&5K(V|X@\C.CE5&(L *.j+.-%1jL%, @ (/c*.Vr24Ve(*,V+- Z¢X+./- }V24*.5&-%(?$v- *-/V 2@B(cV @\CE5&DKc/0V*.V+,]m5K(j-V )Ii0:*,VP5K(0*.Ve+ACEV24*.5&-%( -BZ *.V C}V* -MDK5&(V C4$ ! " # $ #
/.
! "
$
1023-34
> V-\+.5&V(*W@B*,5K-%(a-BZ@c2@ ]mV+A@5C/V3(V /m@\C*.jV-%+,5KV(0*A@ *.5K-\(m-BZ*.jV5K]@ L%VPXD@B(Vz$|'[*`5FC`24DKV @ +nZ+.-%] u5&L%1+,V:#\$;:*.3@B*P@\C*.Vr-%i'}V24*]m- YV C24DK-zCEV+|*.-8*.VDKV(C|5K*WC 5&]@BL\Vv]a-BYVC Z @B+,*.V+ @ P@:Z+.-\] *,V 5K]@BL%V 24V(0*.V+ @BDK-\(L*.V 9 "@B05FC$z(kV(*.Vc-\i'}V 24*75FC@B*7*.VMDKVe(C1-f*,VM5K]@ L%V P5&DKD
iV Z-\+.]mV / @B*85K( 3(5K*}$a>Vm-%(jDK P@G*.VM5K]@BL%VM-BZ@ (5&*.V -%+,DF/X-\5K(0*:2e@B( iVhZ-\+.]mV /@B*85K( 3(5K*}d5C95lZ *.jVZ-\1+.*,24-%]aX-\(V(0*n-BZ *.Vr-\]m-%L\V(V-\1Cn5K]@ L%Vr24--\+A/5&(@B*,V C5C eV+.-j$nu+.-\]QV J13@B*.5&-%(G#\$N\y `V @YV
! " #
u
5
9 7 <
3.#\$;0#m>
y # P52L%5&YV C*,VZ-%D&DK-P5K(LM2-%(C}*.+A@ 5K(0*P-%(*.V82@ ]mV+A@7-%+,5KV(0*A@ *.5K-\(.s 3.#\$;\< > rb 5 w 9 w 1
#;
4
Y
θ
X
φ
u
5KL%1j+.Vc#\$N sP_`@B]aV+A@hqr+.5&V(0*A@B*,5K-\(?$
Z
u @ +A24*W@B(
"
3.#\$;\N >
7
u @ +A2C}5K( rb w " r b w 3.#\$; S > # ')*5C|@BDFC}-:X-C,CE5&iDKVr*.- 24-%]mXj1*.V`*.VPZ-02@BD¢DKV(jL%*. - C,2@BD&5K(L8@ (/h-%*,V+`2@ ]mV+A@rX@B+W@B]mV*,V+AC?Z+.-%] *.jVM2@B]mVe+A@:]@ *.+.5&f$ v-`VYV+-*,VM/V+,5KY\@B*,5K-\(C@B+,V:Z @B5&+.DK5&(Y-\DKYV / 0- *.Ve+.V4Z-\+.V `VM/-m(-\*724- YV+
.* jV] 5&(:*.j5FC5&(*,+.-0/12*.-%+,:i--/¢$`>VP5K(0*.V+,V CE*,V /9+,V @%/0V+|CEj-%1D/ D&--/c@ * <%N 5K(c*,Vij5KiD&5K-%L\+A@ X Z-%+r*.jV:/0V*A@ 5KDFC$
8g%&i'! b f !"c&`
C,CE1]mVc*,@B1 * `V @B(0*:*,-G+.-%*W@B*,VmYV 24*,-%+ @ +.-\1(/ YV 24*,-%+ i0@B(L\DKV 0$f(V2@B( /V 24-\]mX-CEV YV 24*,-%+I5&(*,-G* `-GX@B+,*AC=--\(V24-%D&DK5K(jV @B+8*.- -`@B(3/ -\*.Ve+cXVe+.XV(/5241D@B+c*.- k@\C Z-\DKD&-rC=-x3)C}VV u5&L%1+,Vh#\$?g >:s u3 .> wv3 " 3 .> .> 3.#\$;\; > # # # >V 3+ACE*24-\]mX-%(V(0*P5FCP5K(0Y\@B+,5F@B(0*P1(/0V+v+,-%*W@B*.5&-%.( - PV+,V @%CP*.jVcCEV24-%(/24-%]aX-\(V(0* -1(3/V+. L%-VCv@cXDF@ (@B+r+.-\*A@ *.5K-\(d*,+.-\1L% @B(L\DKV Pj5F2Am]@hiV P+.5&*.*,V.( s 24-C 3." 3 # B> B>twCE5&( 3 -3 "v3 # B> .>R> # 3.#\$;\g > >5CL%5KYVC1s ux24-C dw CE5&( -,wv3,# "2-C ?>:3 .> O7 3.#\$;lR > #
#g
X1
X11
y U1
L U2
X21 X2
u5&L%1+,Vd#\$ S/s7rV*.V+,]m5K(j5K(LM*.VMDK-02e@B*.5&-%(-BZ2@B]mVe+A@$8>VM5K]@ L%Vc- ZrNB QX-\5K(0*AC*5 #M@B(/5 #%#M5FC Z-%+,]mV /m@ * #k-f@ (/ 5&]@BL\V-BZX-%5K(0*ACx5G<M@B(3/ 5G<0#:5FCZ-\+.]mV/m@B* <$`>V75K(0*.V+WCEV 24*,5K-\(m-BZ`@cDK5&(V X@\C.CE5&(Lm*,+.-\1L%85 #c@ (/ 5~#%# P5&*.*.V7D&5K(V7X@\C.CE5&(LM*.+,-%1L\"5G<M@B(/5G<#85FC)x-'P5F2A5FCP*.V DK-02e@B*.5&-%(-BZ`2@ ]mV+W@$ x
-%+
3.#\$;\s >
2 @ ( u )dw CE5&( 5 3 .>w 3.# "24-zC >A5 3 .> 7 3.#\$;\^ > PV+,V*5 3 .>5C-\XV+A@ *.-%+ P5F2A5FC*.jV:YV 24*,-%+`X+.-0/1324*i0 -*,@B*r5FCP*.V8@ (*,5FCE0]m]mVe*.+.5&2P]@B*,+.5& Z-%+,]mV / Z+,-%]*,V824-%]aX-\(V(0*AC- Z @%CZ-\DKDK-r=C s y " y " # 5 3 .>u 3.#\$g\y > " y >V+,V4Z-%+,V:*.-a+.VX+,V CEVe(*r*.V8+.-\*A@B*,5K-\.( -V:(jVV / YV24*.-\+ O-f@ (/I*,Vc@ (L%D&V r$ (VM2@ ( Z1+,*.Ve+ CE5&]mXD&5 Zc*.j5FC1-j@B(/+.VXj+.V C}V(*`*.V7+,-%*A@ *.5&-%(di0m-\(DK@cYV 24*,-%&+ - ?-CE12A*.@ * s u 3.#\$g0m# > du # >VP]@ L%(5&*.1/0V-BZ 5C*.jVr@B]m-\1(*-BZ¢+.-\*A@B*,5K-\.( -0@B(/c*.Vr/05K+.V24*.5&-%(:- Z¢-BZ P5FC
*.Vr@ 5C-BZ +.-%*W@B*,5K-%( $ u5&(@BD&DK?-*.jV9+,-%*W@B*.5&-%(]@B*,+.5Ka2@ ( iV P+.5K*,*.V(@%1C s 5 3 l > 5 9 3 >
ru u )dwC}5K( wv3,# "24-C > 7 3.#\$g\< > PV+,* V 5 3l>`5FCL\5KYV(mi0t s y " y "
5 39l>;u 3.#\$g\N > " y#
PV+,V -3 -/>;u iV P+.5K*,*.V(@\C1s
u d w CE5&( -,wv3,#"2-C ?> -"3 -/>:7 3 B> " $|v-*-Z+.-\]*.V8@ i- YV7V1@B*,5K-\(d*.jV9+,-%*W@B*.5&-%(]@B*,+.5K
#
#BR
4
OBJECT
OBJECT IMAGE
IMAGE
LENS
LENS
OBJECT
IMAGE
LENS
u5&L%1+,V#%$; s7vV*,V+.]m5&(5K(jLc*.Vc-\+.5KVe(*W@B*.5&-%(-BZr2e@B]mV+W@$Cr*.Vc-\i'}V 24*r]m- YV Cv2DK-C}V+r*.-*.VcD&V(C 5K*WC5&]@BL\V7]m- YV CZ @B+.*,V+@ P@mZ+.-%] *,V75K]@ L%V824V(0*.V+ @BD&-%(Lm*,V9"@ 5C4$$(kVe(d*.jV9-\i'}V 24*r5FC @B*r*.jV9D&V(=C -*.jV95&]@BL\V P5KD&DfiV9Z-\+.]mV/m@B*P5&( (5&*Ez$
#s
v’
(v.n)n n θ
v
v-(v.n)n
u5&L%1+,VM#%$gs|O-\*A@ *.5K-\(d- Z|YV 24*,-%+Nc@ +.-\1(/ YV24*.-\+ Gi@ (L%D&V $
!8`d ,$"%&'"b J13@B*.Ve+.(5&-%(d5CP@ X3@B5K+ zu 3 ?7 ,>:-'PjV+.V 95[email protected]@BDF@ +r@B(/d5CP24-%]a]m-%(D&M2@BD&DKV /M+.V @ D?X@B+,*v- Z @B(3/ k5FC`@cNB 6YV 24*.-\+0- @B(3/h5FC`2@BD&DKV /c5K]@ L%5&(@B+,cX@B+,*P-BZ $|> `-11@B*,V+.(j5K-%(3CP2@B(miV7@\//V /mD&5V @B(0mS\)YV 24*.-\+AC$ v-VYV+&- ]h1D&*.5&XDK5&2@ *.5K-\(h- Zn* `-J1@ *.V+,(5K-\(CP5FCL%5&YV(mi0 s 3 ?7 ,> r3 7 >u}3 " 7 - w w ,>:7 3.#\$g S >
#
PV+,V - M@B(3/ # h/0V(-%*,V7*.V71C}1@BD
YV 24*,-%+r@B(3/d/-\*vX+,-0/124*WC4$`>Vc2-%(/}1Lz@B*,Vc@B(3/ *.jV9(j-%+.] -BZ@1J1@ *.V+,(5K-\(@B+.V /V(jV /@%C1s u 3 7 " ,>:7 3.#\$g\; > u du w 3.#\$g\g > u-%+c@ (~+.-%*W@B*,5K-%( - Z7@NB YV 24*.-\+ - -n*.jV+.VmVe5CE*7* -d# -\XX-C}5K*.V 1@B*,V+.(j5K-%(3C d@ ( / " P52C,@B*,5FC[Z u '3 5FCP2-%(0YV+.*,V /h*.-M@ 1@B*,V+.(5&-%(i0@%C,CE1]m5&(LcV+,-:+,V @BD?X@ +.&* -@B(/ CE5&]m5KD@B+,DKc*.jV:+.V@BD
X@B+,*-BZ|*,V:+,V CE1jDK*A@ (* 1@B*,V+.(5&-%(G-\(d*.jV:+.5&L%0*v5CvC}V*r*.-mVe+.-M*.-M]@B*W2 P5K*, *.jVc+.-%*W@B*,V /dYV 24*,-%+r-%(G*.jVcDKV4Z*CE5/lV >A$7>jV J1@ *.V+,(5K-\( h5Cv2-%]mX1j*.V /mZ+.-%] *.V81(5&*7/5K+,V 24*,5K-%( YV 24*,-%+ I- Zn*,V8@B05FC-BZ +.-%*W@B*,5K-%( @B(/5K*WCP@B(L\DKV :ia*.VZ-%+,]h1jDF@ s du3 24-=C 3 < >D7ACE5&.( 3 < > B> 3.#\$glR > # H5&]m5KD@B+.D&? -4*,-vV@%2A:X@ 5K+
-BZ¢1(5&* 1@B*,V+.(j5K-%(3;C 3 7 " >*.jV+.V|5FC
@@\C.CE-025F@B*,V /:1(5 J1jV+.-\*A@ *.5K-\(c]@B*,+.5&
"
!
# ! $
%
&
#^
4
z
w " "yn <3 ;w n > < 3 D'n " >
}u
PV+,V du3 7 &7 h7:n >A$
< 3 " n > <3Dnw > w yn < 3=n. " => < 3=nw => yw n " " " "
3.#\$g\s >
'b b.;% `*;%&' ')(X-zCEVV CE*,5K]@ *.5&-%(.?- *.jVhX+,-%iD&V]o5FC7*.- /V*.Ve+.]m5&(V:*,Vh-\+.5&V(*W@B*,5K-%( @B(/X-zCE5K*,5K-\( -BZ@ ( -\i'}V 24* 3)2e@B]mV+W@ > P52 `-%1D/ +.VCE1D&*h5&( *,VdXj+.-/}V 2*.5K-\( - Z8@IL\5KYV( C}V*h- Z8*.+,VV /5K]mVe(CE5&-%(@ DX-%5&(*WC
5K(0*.-M@cL%5&YV(CEV*r-BZ 5K]@ L%VX-%5&(*WC4$vqr(V7- Z|*.V75&]mX-%+.*W@B(0*r@BXXjDK5F2e@B*.5&-%(C- Z|X-C}VcV CE*,5K]@ *.5K-\(m5FC5&( *.jVm]m-0/VDi@%C}V / -%'i }V 24*7+,V 24-%L\(5K*,5K-\(?$d')(< )*,-GNB ]m-0/VDi@%C}V / -%'i }V 24*7+,V 24-%L\(5K*,5K-\(@dN ) ]m-0/VeD- Zn*,V-\'i }V 24* -j@B(/m5&*AC< )X+.- }V 24*.5&-%(hZ+,-%] @:X@B+,*.5241DF@ +Y\@B(0*A@ L%V7X-%5&(*P- Zn*,V72@ ]mV+A@5C L%5&YV.( -f*,VM@B5&]5Cv*.-/0V*.V+,]m5K(jV9*,+.VeVc+.-%*W@B*,5K-%(3C9@ (/G*.+,VVc*.+W@B(C}DF@B*,5K-\(C+.VD@B*.5&YV:*,-CE-\]mVci@%C}V 24--\+A/5&(@B*,VcCEjCE*,V]G$ pfV4* 3j5 7D9 71< >iV*,VmN )]m-0/0VD`24--%+W/5K(@ *.V C:- Z@ X-%5&(&* -|@B(v/ 3A@ 7:C >iVm*.VaX+./- }V24*.V / 5K]@BL%VM2--%+A/05K(@ *.V C$ C,CE1]mV8*.@ *:*,Vh-\'i }V 24* 3 2@B]aV+A?@ >P5FCv+,-%*W@B*.V/ +AC}*7iy 3 7 7 >:-
*.@ * ]@ X$C 365 7:9 71< >
*.- 36587:971<,>A$|rV&* -%*.jVP-%'i }V 24*|5C*.+W@B(C}DF@B*,V /hi04 3 7 7 >:-0@B(3/ (3@BDKD&:*,V 5K]@BL%V75CvX+.-0/0124V /d1C}5K(LaXVe+ACEXV 2*.5KYV8*.+W@B(C)Z-%+.]@B*.5&-%(1CE5&(LmDKVe(Cv2V(*,V+.V/d24--\+A/5&(@B*,VMCEjCE*.Ve"] @B(3/*W@ 05K(L8X-CE5&*.5&YVvY\@BD&1Vr-BZ $|>V5&]@BL\Vr24--%+W/5K(3@B*.VCP@Z*.Ve+XV+AC}XV 24*.5&YVvXj+./- }V 2*.5K-\(m@ +.VL\5KYV( i0 s 32@ 7DC >u3 O36
<%y > VMX@B+,*.5@BDP/0V+.5& Y% @ *.5&YV Cv5K(*.jVm @ i- YVmV J1@ *.b 5&-%(~2@B( i VMV @%C}5KD&24-%]mXj1*.V / Z+,-%]oV1 @ *.5K-\(k#%$lR y0$ u-%+rVj@B]mXD&?V - u k# -f@ (/ u " $$ (V82@B( 24-%]aX1*.V @B(/ Z+.-\]*.jV9+,-%*W@B*.5&-%(]@B*,+.5Kt - $ C `V (- £5 gZ 365 7:9 71< >|5FC+.-\*A@ *.V /@B+.-\1(/89:)@ 5Ci@ (L%D&V -*,V7(V 24--%+W/5K(3@B*.VdC 3j5f7:971<,> @B+,V7L%5KYVe( i0t s 5 u 5 24-zC w <CE5&( 7 3.#\$ R< > 9 u 9 7 3.#\$ RN > < u "F5 C}5K( w < 24-C 3.#\$ ReS > # >V( 3.#\$ R; > 5 u "r5 C}5K( w < CE5K( u
(
"
!
!
<#
4
@
#
C
y
" 5 " 5"9
h3 < w:5 > " = 9
"
"
y
#
9
h3
u 5&L%1+,Vh#\$ R sP>V7X@B+,*.5@BD/V+.5&Y\@B*.5&YV C- Zn5&]@BL\V824--%+W/5K(@ *.V CP5K*,+.V C}XV24*v*,-cV @%2Ad- Zn*,Vc2e@B]mV+W@ X@ +A@B]aV*.V+WC4$
%# $H*W@B+,* P5K*,@B(~5K(5&*.5F@ D|V CE*,5K]@ *.Vc-BZC}5KGX@ +A@ ]mV*.Ve+AC1-3 7 7 7 7 >A$' Z -%1/0(-\* 0(-*-@%C,CE1]aV7@BD&D?X@B+W@B]mV*,V+AC|*.-MiV9eV+.-j$ <$ vXjXDK*.+W@B(C)Z-%+,]@B*,5K-%( *.- *,Vd]a-0/VD2- @B(/ X+,-/}V 24*M*.jVd]m-0/VeDP-%(k*.jVd5K]@BL%VXDF@ (Vdi0 24-\]mX1*,5K(L 32@ 7:C >A$ N$_|-\]mX1*,V9*,V7V+.+,-%+WC -@B(3/ $|' Zn*,V7V+.+,-%+ACP@ +.V @%224VeX*A@ iDK?V -J1j5K*$ S$ru5&(/M2@ (L%VP5&(mC}5K8X@B+W@B]mV*,V+A=C - 3 7 7 7 7 7 >
-BZ *.+A@ (C[Z-\+.]@ *.5&-%.( i0m1C}5K(LMDKV @\CE*rC J1@ +.V C 3*$Pv-\*.-aCE*,VX 3)< >W$ u5KL\1+.VM#\$s s|U
-CEV8V CE*,5K]@ *.5&-%(@ DKL%-\+.5&*.]G$
<%<
3@ >
3i >
3)2m> 3)/p> 3 Vk> u5&L%1+,Vm#%$=^ s,3 @ r> >jVcN'" ]m-0/VeD?-BZ`@m/0+.5KD&D)$,3i > >V:X+,-/}V 24*,5K-\( - Z`*.V8V /L%VC1- PV(d*,Vc/0+.5KD&D 5FC5&(1((-P(X-CEVz$f)3 2h>>jVhX-C}5K*,5K-%(~-BZr/0+.5KD&D|@Z*,V+7-%(VM5K*,V+A@ *.5&-%(?$3)/M>>jVhX-C}5K*,5K-%(-BZ/0+.5KD&D @Z*,V+P* -85K*.Ve+A@B*,5K-\(C4$x3 Vl>>V7X-zCE5&*.5K-\(-BZ/+,5KDKD¢@Z*.V+P*,+.VVr5K*,V+A@ *.5&-%(C=- P52m5C*,V724-\+.+.V24*X-C}V
-BZ *.V8/+,5KDKD $
<%N
4 4
,$#r%mb db #%$x(k@ *v 5C*,V:+,-%*W@B*.5&-%(G]@ *.+,5KcZ-%+@B(G-%i'}V24*P+.-\*A@B*,5K-\(G-BZ`N\y @ +.-% 1j(/d*.Vk@ 5C1-Z-%D&DK-V / i0Gg\y @ +.-\1(/*,V @ 5C1
- @B(3/ Z-\DKDK-`V /di @m+.-%*W@B*,5K-%(~-BZr^\y @B+.-\1(/*,V @B05FC4$ vDKD +,-%*A@ *.5&-%(Cr@B+,V:2-%1(0*.V+r2DK-02. P5CEV$ <$xk( @ *5C *,Vr+.-%*W@B*,5K-%(a]@B*,+.5KZ-\+P@B(a-%i'}V 24*+.-%*W@B*,5K-%(a-BZ@ +.-\1(/m*.V @B05FC1-%Z-\DKDK-`V / i0 @B+,-%1(3/*,V @B05FC=- @B(3/ Z-%D&DK-V /ci0m@7+.-%*W@B*,5K-%(a-BZ £@B+,-%1(/m*,V @ 5C4$ vD&D+.-\*A@ *.5K-\(C @ +.V824-%1j(*,V+A24D&-02-#P5FC}V$ N$_|-\(CE5/V+P@:YV24*.-\+F}3 R?A7 NA7 < > Pj5F2Ah5C+.-\*A@ *.V /m@ +.-\1(/m*.V @B05FC|ia^%y - @ (/m*.V(a+.-%*W@B*,V / @ +.-%1j(/ *,V @B05FC
i8^%y @ (/ (@ DKDK8*.+W@B(C}DF@B*,V /:i0'3 S/7 "N 47 RkA> $|u5&(/:*.jV(V 24--\+A/5&(@B*,V C
- Zn*,V7YV 24*.-\+$ vD&Df+,-%*A@ *.5&-%(Cr@B+,V:2DK-02. P5CEV$ S$Hj- *.@ *Z-%DKD&-P5K(Lc5/V(0*.5K*,5KV C`@B+,V9*,+.1Vz$ u - b u b b u b - b u b $ ;$rvVe+.5KYVV J13@B*.5&-%(C#\$<\sh@ (/#\$<%^0$ g$_|-\(CE5/V+|*.VZ-\DKD&- P5&(L82@B]aV+A@P]m-0/VD $ C.C}1]mV*,@B*+WCE*|*.jV2@ ]mV+W@L\5K]Mi@BDj24V(0*.V+
5FC|@ * *,Vv-\+.5&L%5K(M-BZ
*,V -%+,DF/M24--%+W/5K(3@B*.VC4$|vV0* -*,V2e@B]mV+W@v5FCn*,+A@B(3CEDF@ *.V /ci0M@B]m-\1(*r3 y 7A<7A< >D@ (/d5K*r5FCP+.-\*A@B*,V /di0d@ (L%D&Vc^\y @B+,-%1(/ <@ 5dC -Z-%DKD&- V /mi0 +,-%*W@B*.5&-%(G- Z#eN%; @ +.-\1("/ 5 @ 5C4$ 0-%*,+.-%*W@B*,5K-%(3Ch@ +.V5K(*.jV24DK-0.2 #P5FCEV/5K+,V 24*.5&-%(C$ Z*,V+:*,@B*M*.jVd2e@B]mV+W"@ 3 5K]@BL%V XD@B(kV >5FC7*.+W@B(C}DF@B*,V /i0 @ ]m-%1j(* 3 # y%< 7 # y0l# 7 # y%N >P5&*. +,V CEXV 2*:*.-L%5&]hi@ D|24V(0*.Ve+$u5K(@ DKD&? 5&]@BL\V5FCZ-%+,]mV /h1C}5K(LMXV+AC}XV 24*.5&YV*.+W@B(C)Z-%+,]G$ C.CE1j]mV7*.@ *Z-02@ D?DKV(jL%*.-BZ|*,V82@B]aV+A@ 5C # y\N%y$|u
5K(/:*,VP5K]@ L%V 24--%+W/5K(@ *.V Cn- Z?*.jVPX-\5K(0 * P5F2A:@\C -%+,DF/M24--%+W/5K(3@B*.V|C 3,l# 7k# 7Ay # < >W$ R$Hj- - @ (75&]@BL\VX-\5K(0$* 3A@ &7:C >¢5FC?]@ XXV /*.-*,V `-%+.D/:24--\+A/5&(@B*,V C?1CE5&(L*.jV5K(0YV+WCEV XV+WCEXV 24*,5KYV]@ *.+,5Kt -JYVe+.5 Zc*,@B*r*.jV9V J1@ *.5&-%(C7#%$=<%;M@B(/G#%$=<%gM@B+,VcC.@ *.5C V /¢$ s$rvVe+.5KYVV J13@B*.5&-%(C#\$;\Nh@ (/#\$;BSj$ ^x$ )|V+,5 ZMV J13@B*.5&-%(C#\$;\g -?#%$=g%yM@B(/#%$=g%<$ !#" N -%N $'&)(+*,( & ".- *(/$ 021 143 & - 56 ( 7" (98 ;: &2<=$ >=6!/?A@CB &2$ - 6#D * #%#\F$ )|V+,5 ZMV J13@B*.5&-%(#%$=g%s0$ #<0$9r5KYVe(N -N +,-%*W@B*.5&-%(]@B*,+.5Kt - z-24-\]mX1*,V J13@B*.Ve+.(5&-%( 0$
%
EGFH655 & ?IGJGJ * " ((& -K7"#L-M NA (98 ?PO=6 *#$ < ?6- & B < ? (+* "!3/?RQ# ( J#" * ?P (& B5 & L" ( ? TSU* " < (98 V $$'(+*( < ! $ ?9 & "? S u 2S WF 8& J (98!*,( -ML"#7-K N!L">X3 $ ( $ & " uZY S S " TS 7 3.#\$s0#m> 3 * "Q#KJ $ (( #" * ? }u[Y S S ]\ S u \ ^Y S \S S 7 3.#\$s\< > J 8 $ S ? * S -cS - *(9$ 0 < #5)#" < L"> & " 2SU* " < S `_ 8 G? & DL6 ( & "a ?b>2 !)";Q9c (98 M6"# ( V >d#" !A3 (&T$e* ?+? & 3V *( < J (98K(98 ?A- * D^Df/? ( V >)"M * DL6! & B (98 - *(9$ 0g u[h S \S S
"
"
#4Sj$ C,CE1]aV - c@ (/6:iV 1@B*,V+.(j5K-%(3C4$PH-6*.3@B*s
3
3.#\$s\N >
> u "Z3 D> 7 3 ?> 3 > u 3 p> 3 D> 7 3 ?> # 3 @ >Uu 3 # p> # 3 # l>:7 $
! !
3.#\$s S >
$!
$!
3.#\$s\; >
# # # PVe+.V # 5FC*,V8/-%*PX+,-0/124*e$ # #;0$ +.-\*A@ *.5K-\( ]@ *.+,5K Z-\+h+,-%*W@B*.5&-%( @B+.-\1(/ @B(k@ +.i5&*.+W@B+.~YV 24*.-\+ci CE-%]aV@B(L\DKV2@ ( iV V0X+,V C.C}V /G@%C7*.VcX+,-0/124*8-BZ *.+,VVc+.-\*A@B*,5K-\(C'3 { 1jDKV+etC@ (L%D&V C >Ds+.-%*W@B*,5K-%( @B+.-\1(/5 @ 5C i0 @ (L%D&V -Z-%D&DK- V /i*.Va+.-%*W@B*,5K-%( @ +.-%1j(/ 9 @B05FC:i0 @ (L%D&V ¡@ (/Z-%D&DK-V /Gi0*,V +,-%*A@ *.5&-%(@ +.-%1j(/ < @B05FCni @B(L\DKV $ rDKD*,Vv+,-%*W@B*.5&-%(C`@B+,V24-\1(0*.V+|2DK-0.2 P5CEV$|H- *,@B*&s 24-zC 824-C 2-C cC}5K( :C}5K( "CE5K( c2-C 24-zC :CE5&( 724-zC wC}5K( cC}5K( u CE5&( c24-C C}5K( cC}5K( :C}5K( w24-zC 824-C C}5K( cCE5&( 724-C "2-C cC}5K( # "GCE5&( 24-C :CE5&( 24-C 724-zC #g0$u-%+ CE]@ DKD+.-\*A@ *.5K-\(C V72@ (@%C,CE1]aV7CE5&( ou -@ (/24-C zu #%$PH5K]mXjDK5 Z7*,V7@Bi- YV7]@B*,+.5& @\C.CE1j]m5K(LMC}]@BD&D+.-%*W@B*,5K-%(3C4$P'}C*.jV9+,-%*W@B*.5&-%(]@B*,+.5Kc(j- DK5K(jV @B+`5K( ;7 @B(/ !#" N -%N $'&)(+*,( & ".- *(/$ 021 143 & - 56 ( 6#D $ @ ? * ">TD /? 1 * " < #s0$vVe+.5KYV8*.VMV0X+.VC.CE5&-%(CPZ-%+:*,VcX@ +.*.5@BD`/V+,5KY\@B*,5KYV CPL%5&YV(G5K(G*,Va>@ iDKVaCE- P(5K(u5&L%1+,V #\$ R$ #^0$ 01C}5K(LV 1@B*,5K-\(#%$s\y24-%]mXj1*.V8*.VcXV+,XVe(/5F21DF@ +7/5FC}*A@ (24Vc-BZ @mX-%5&(* 3A@ 7:C >Z+,-%]@ D&5K(V$
k
]4
"!"#$%&'
|{ /L%V/V*.V24*.5&-%( P5F2AG@%Cc@ *.*,+A@%2*.V /G*.V@B*.*,V(0*.5K-\(- Zr]@B(0d+,V CEV@B+A2AV+WC b 5FC7-%(Va-BZP*,Vm]m-zCE* 5K]aX-\+.*W@B(0*m@ +.V @\C5&(kDK-Ve+mDKVYVeDr24-%]mXj1*.V+MY05FCE5&-%(?$ v-VeYV+-5&*mC}VV]Cc*.3@B**.VGXj+.-%ijDKV] -BZ /V*,V 24*,5K(L7V /L\V C5&(h+,V @BD C.24Ve(V Cn5FC`CE*.5&DKD¢@B(a1(CE-\DKYV /cX+,-%iD&V] 5&(m@7L%V(jV+A@ D?CEVe(CEV$|{|/L\V7/V*,V 24*,5K-%( 5FCc5K]aX-\+.*W@B(0*hiV 2@ 1CEVG*,VGC}1224VC.Ch- Z:j5KL%jV+hD&VYVDPX+,-024V C,CE5K(jL +.VD&5KV CcV @Y05KD& -%(kL\--0/xV /0L%V C$ r+A@DKVYVD
5K]@BL%VC24-%(0*A@ 5K(@ ( V(-\+.]m-\1C7@B]m-\1(0*9- Z/@B*W@ -
]h12AG-BZ Pj5F2AG5FC95&+.+,VDKVY\@ (*&-fV$ Lj$ *.jVi@%.2 0L%+.-\1(/h- Z
*.V C.24V(jV$H- @B*`*.V5&(5K*,5F@ DCE*W@BL%V -*.jVV4¢-%+,*5FC|]@%/0VP*.-:+,V /12VC}-%]mVr-BZ
*,V /@ *A@ n*,VM-%'i }V 24*WC7@B+.VaCEVeX@B+W@B*.V/IZ+.-\]o*.VMi@%.2 0L%+.-\1(/@B(/V(*,5K*,5KV CC}12A@%C9V/L%V C P5F2A@B+,V X0C}5F2@ DKD&mC}5KL%(j5 ¢2@ (* @B+,V:5F/0V(*,5 V/f$ ')(¡*,V C}*.V+,V-*.V 2A(5 J1jV 1C -Z-%+5&(CE*W@B(24V -5K]@ L%V Cc*A@ V(xZ+,-%] * - /5l¢V+.V(0*mD&-02@B*,5K-%(3Cd@B+,V 1*,5KDK5&V /:*,-cL%V*`*.V/VX*,m5K(0Z-%+.]@B*.5&-%(?$ vDKD¢C}*.V+,V-:*,V 2j(5 1V Cn/0V @BD P5K*.a*.V W24-%+,+.V C}X-%(/Ve(24V PV+,Vm*.jVm*.- V(CvZ+.-\] *,Vm+.5&L%0*c@ (/DKVZ*:5K]@BL%VM@ +.Vm]@B*A2AV /G5K(-%+W/V+8*.-GL%Ve*:*.jV/5FC}X@B+,5K*} -BZ`* -M5K]@BL%VC4$P>V8V /L\V:5K(0Z-%+.]@B*.5&-%(XDF@jCv@ (d5K]aX-\+.*W@B(0*v+,-%DKV85K(*.V CEVD&V 24*.5&-%(-BZ *./- Ve(C4$r')( ]m-\*.5K-\.( -*.VM/Ve*.V 24*,5K-\(G-BZP]a-BY05K(jLc-%'i }V 24*WCv5FC/-%(VMi0d5F/0V(*,5 Z05K(Lc*,Vc*.5&]mV:Y\@ +.05K(LmV/L%V C@B(/ 24-\+.(V+WC4$>V@ XX+.-z@%2AV Cc*.-C}*.+.1324*.1+,VmZ+.-%] ]m-%*,5K-%( -n*.+,-%1L\ P52 *,V*.+,VV/5K]aV(CE5&-%(@ D CE*,+.12*.1+,V9- Z|-%'i }V24*ACP5FCP24-\]mX1*,V / -j@BDFC}-h+,V 15K+,V:2-%+.+,V CEX-\(/V(2V9- Z|*.- V(C$vqr'i }V 24*+,V 24-\L%(5&*.5K-\( ]mV*,-0/C?i@%C}V /9-\(c-%(D&7*.V`* `-/05K]mV(3CE5K-\(@BDzCE@ XVP1CEVP*,VV /0L%V5&(Z-%+,]@B*,5K-\(?$?bd-C}*|@BD&L%-\+.5K*,]C Z-%+r+.V24-%L\(5K5&(L:*,V7X@B+,*.5@BDKD&m-0224D&1/V /m-\'i }V 24*AC`@%C,CE1]mV7*,V7X+.V C}V(24V-BZ|L\--0/dV /L%VC4$
]4:]
^ db d8i db
H 5&(24Vm*,VL%+A@DKVeYVDnZ1(24*,5K-%( 2A@B(jL%V CcC}5KL%(j5 ¢2@ (*,DK@ *c*.VV /0L%V C:- Z7-%i'}V 2*AC1-|*.jV 5/V @ DV /L\V 2@ (iVM]m-0/VD&V / i0d*,VMCE*,VXIZ1j(24*.5&-%(?$ '[(G+,V @BD|5&]@BL\V C1--VYVe+-f*,VcL%+W@GD&VYVD@B*7*.jVcV /L%VC -BZ @ (G-%i'}V 24*r/0-V C(-%*72A@ (L%V @Bi+,1X*.D&?-i1*5&(CE*,V @%/ -¢2A@B(L\V CvL\+A@%/01@BD&DK$r>V C}VcV /L\V Cv2e@B(GiV ]m-0/VeDKV /i*.Vc+W@B]mXdZ1(324*.5&-%(?$hHz-%]mV*,5K]mVeC* -C}*.VX3C9@ (/ -%+:+W@B]mX3C@BXXV @ +824DK-zCEVc*.-\L%V*,V + *.jV CEV8@B+,V:+,V CEXV 24*,5KYVD&M2@BD&DKV /aCEX5 V:@ (/ +,--BZ|V/L%V C$P>V7X-C,CE5KijDKV:*}0XV C-BZ|V/L%V Cr@B+,V8CE- P(d5&( u5&L%1+,V:<0$K#\$ ~t R=1 ,m
k:2: k: <%;
<%g
(a)
(b)
(c)
(d)
]4
u5KL\1+.V <$K#ks>|XV C- Z`{|/L%VC4$r3)@ >PHz*.VX.-.3i >`Or@B]mX.-t3)2m>PHzX5V?-0@ (/3 /p>POP--BZ,$
b.`zi db %h d8i F *#$%&' bd-C}*PV /L\V7/V*,V 24*.5&-%(aC.2AV]mVC2-%(C}5FCE*`-BZ*.+,VVCE*A@ L%V C=s L P *L=P:L J Q -j@B(/ L L Q $ ')(h*,V D&*.V+,5K(L8CE*W@BL\V?- *.Vr5K]@ L%VP5C X3@%C.C}V /c*.+,-%1L\@ D&*.V+5K(M-%+A/0V+|*.-7+.V]a-BYV|*,Vv(j-%5FC}V$|v-\5FCEV 2@ (kiV/01VG*.- *,Vd1j(/V C}5K+A@ iDKVGVfV24*ACc5K(0*.+,-0/124V / 5&( *,VC.@ ]mXDK5&(L/- J1@ (*,5K @ *.5&-%(.- ijDK1+,+.5K(jL @B(3/¡/VZ-0241CE5&(L - Zc*,V2@B]aV+A@v- @ (/k5K+.+,VL%1jDF@B+,5K*,5KV Ch- Zc*,VCE1+}Z @%24V~CE*,+.12*.1+,VG-BZc*,V-%i'}V 24*WC4$ >Va/5 ¢V+,V(0*.5F@ *.5&-%(CE*W@BL\Vh5&L%D&5KL\*WCv*.VMDK-02e@B*.5&-%(C5&(*,Vc5K]@ L%V1PVe+.Vc5K(0*.Ve(CE5&*E2A@B(jL%V C7@B+,V CE5&L%(5 ¢2@ (*e$¡u
5K(@ DKDK - 5&( *.jV/V*.V24*.5&-%( CE*W@BL%V - *,-C}VGX-%5K(0*ACPV+.V*.V5K(0*.V(3CE5K*}~23@B(L\V Cm@B+,V CE5&L%(5 ¢2@ (*r@ +.V7DK-02@ DK5&V /f$ ')( *,VV @ +.D&5KV+ @BXX+,-@\2VC*,V DK*,V+.5&(LcC}*.VX P@\CPC 05KXXV /t- *.V7/05 ¢V+.Ve(*,5F@B*,5K-\(CE*,VX P@%CPXV+. Z-%+,]mV /mi0d1C}5K(Lm*,V 3(5K*,V)/05 ¢V+.Ve(24V8@BXXj+.-@\2 - @ (/d*.jVc/V*,V 24*,5K-%(P@\C/-%(jVciDK-02e@B*.5&(Lm*,V XV @jC5K(M*.jVL%+W@%/5&V(*`-BZ
*,V5K(0*.Ve(CE5&*E7Z1(24*,5K-\(m1CE5&(Lc@:*,+.VCE-\DF/f$|')(M*.V C}V7@BXjX+.-z@%2AV C1- DK*,V+. 5K(jL P@\C (j-%*824+.13245F@ DnC}5K(24Vc-\(DK CE0(*,V*,5F295&]@BL\V Cr@B(/G*.Vc5&(/1C}*.+,5F@BDC.2V(V C P5&*.@24-\(*,+.-%D&DKV / V(0Y5&+.-\(]mV(0* `V+.V 24-%(C}5F/Ve+.V /f$rp?@ *.V+&- H-%iVD5K(0*.+.-0/0124V /*.VM@YV+W@BL%5&(LaCE*.VeXGiVZ-%+.Vc*,Vc/05 ¢V+. V(0*.5@B*.5&-%(C}*.VX $ H5K(2Vd@YV+W@BL\5K(LG5C:@5&(/ -BZ DK*,V+.5&(L/n- iV*,*.V+c+,V CE1D&*AC `V+.Vm-\i*A@ 5K(V/ i0*,V
^8
H-\iVeD-\XV+A@ *.-%+e$mvVe*.V+,]m5K(@ *.5&-%(d- ZP*,Vh*,+.VCE-\DF//VXV(/C-\(*,Vm/0-%]@ 5K(G-BZ *.VM@ XXD&5F2@ *.5K-\( B@ (3/hY\@B+.5&V C Z+,-%] 5K]@ L%VP*,-c5K]@ L%V$v1*,-%]@ *.52PCEVD&V 24*.5&-%(M-BZ
*,+.V C}-%D/5K(jL:5FC`CE*,5KDKD3@:@B+W/hX+.-\iDKVe]G$ @B+W@BD&5F2. S ¢XV+EZ-\+.]C|*.V7/05 ¢V+.Ve(*,5F@B*,5K-\(CE*,VXmi0 +WCE* *,*.5&(Lc@:X5&V 24V P5CEV24-%(0*.5&(1j-%1CX-%D& (-\]m5F@ Df*.-M*.jV9L\+A@mD&VYVD(V5&L%0i-\+.--0/G-BZ @cX5K0VD2-j@B(/*.Ve( 3(/5K(jLc*.V8X@B+,*.5F@ D
/V+,5KY\@B*,5KYV C|-BZ *.jVX-%DK0(-\]m5F@ D)$n')(m*,5FC`@BXXj+.-@\2 -*.V 3DK*.Ve+.5K(jLcCE*,VXm5C(-\*PVXjDK5F25K*-\i1**,V *,*.5&(LcV C.C}V(0*.5F@ DKD& CE]a--%*.3C*,V:L\+A@DKVYVD¢5K]@ L%V8@B(3/ *.01CPXV+EZ-\+.]CP@ 3DK*.Ve+.5K(jLMCE*.VeX?$P')(*,15K*,5KYVD&?-*.V8V+.+,-%+r-BZ3* 24-\(*,+.-%DC*,V7/VL\+.VV-BZCE]a--%*.j5K(Lj$_`@B((0 ?N -j< 13CEV Cv@B13C.CE5@B(5K(a*.V 3DK*.Ve+.5K(jL:C}*A@ L%V8@B(/24-\]m X1*,V C*.V 3+ACE*8/5&+.V 2*.5K-\(@BD/V+,5KY\@B*,5KYV @BDK-\(Ld*,VcL%+W@%/5&V(0*7/5K+,V 24*,5K-%(/01+.5&(L*.VM/5l¢V+.V(0*.5@B*,5K-%(
J< R CE*W@BL\V$|')(c*.V /V*.V24*.5&-%(cC}*A@ L%V7_`@B((0?-0/V*,V 24*AC?XV @jC5&(c*.Vr/Ve+.5KY\@ *.5KYV|-\1*.X1j**,-DK-02e@B*.VP*,VPV /L\V X-%5&(*WC4$MbG@B+,+:@ (/ v5&DF/+,V*. @BDCE-d13CEVm@B1C,CE5@B( @%C7@DK*,V+ l#N )$ >VGXV+EZ-\+.] /5l¢V+.V(0*.5@B*,5K-%( CE*,VXGi0d*.jVMp?@BXD@%245@B(.-P52G5Cv*.VMC}1]- ZP*,VMCEV 2-%(/dX@ +.*,5F@BD /V+.5&Y\@B*.5&YV Cr@BDK-\(L*.V@ @B(/ C)@ 5C4$
]4
}%hc=
,$%h8i e4`zi
VX>D&5&V]mVcVD V]m$
(0>-z*,CE3*75FXC C}5K05KP]mV@D6Xjc>`DK5FV*.CrVr+.D&V*.+AXV@ D+(@%5F/24CvV-\/d]*,iVc(-\]m5F*.C}VV@ Vc(5FC|]m@VD&Y*.@BVV(d+A+e@ $7- L%ZP'[V (/cL\+A*.-%@1jdVc*D&$|]aVpfYV VV@BDF* CP( d5K(/DK*,V@V(j+ C}-%-f]*.*,Vr@B*.D&VcD?jL%(Vv+WV5&@5K]L\d@BDKiL\VeV-\Y+.VPD
-@B-05F*2A/V@%@B`2A+,VG-%1 X(3@B5F/I24(0*,**,1*,+.-VV D&*.V+&- /V(-\*.V7*.jV DK*,V+.V/ 5&]@BL\V?-0@B(/24-\(CE5/V+r@cN-aN:(Ve5KL%0i-%+,--0/d@ +.-%1j(/d@:X5&VeD)$
>V(
EH & EH &
EH & EH &
f E H # f & hf - # f E H & hf - # f E H - f & hf - E H # f & hf & h f - H - f & h f - - f H f & h f - - f H & h f - - f H - f & h f 3j v f & f E H # f & E # f E# f & - # fE E H # & # f E & - #E f E H - f & # f E E f & f& E# f& - EH & E & - EH - f& Ef& #f 3j v j & S b bE H # f & f E# f & f E H & f E & f E H f & f E f & 3j v & SY b Y b - E H - & E & 3j v & EH & EH &O # EH # EH
vVe+.V /0V(-%*,V7*. V DK*,V+ -j@B(/ M/V(-\*.V C*,Vc2-%(0Y-%DK1j*.5K-\(-%XV+A@ *.5&-%(?$P>jV 3DK*.Ve+P5K(*.5Cv2e@%CEV75C N -N-@B(/mV @\2X5&VeD5&(*.V 3DK*.Ve+P5FCC}V*P*.- b $|>V D&*.V+ m5CP24-%(0Y-%D&YV 1/ P5K*.*,V75K]@ L%V G@B(/ *.jVP+.V C}1DK*n5Cn@ D&*.V+,V /95&]@BL\V $|>Vr24-\(Y-\DK1*,5K-\(:-%XV+W@B*,5K-%(M5FCP5F/VD&71CEV /c5K(M_|-%]mXj1*.V+)5FC}5K-%( @B(3/c'[]@BL%V`Un+.-02V C.C}5K(Lj$|>VP24-\(Y-\DK1*,5K-\(:-%XV+W@B*,5K-%(M2e@B(ciVPY5CE1@ DK5&V /7@%CX3@%C.C}5K(L @B+.-\1(/M@ D&*.V+ ]@\C 3 ]@\C M> 5K(d*,V:5&]@BL\VZ+.-%] DKV4Z*r*.-a+.5KL\&* -*,-%XG*,-hi-%*,*.-\] @%CC}- P(G5K(Gu
5KL%1j+.VM<$=<$>V ]@\C m5Cv24Ve(*,V+.V /@ *V @%2AX5K0VD?5&(d5K]@BL%V O-f@ (/d*.V CE1] - Z*,Vc2-%+.+,V CEX-\(/5K(jLmX5K0VD& i0X5&VD X+,-0/124*r5FCP24-\]mX1*,V /f$ >V]mV@B( D&*.V+|XV+}Z-%+.]CV 1@BD¢@YV+W@BL%5&(L V@%2AhX5&VeDY\@ DK1V7@ +.-\1(/d@8CE]@ DKD(V5&L%0i-%+.j--0/ 5FC|@\C.CE5&L%(V/V J1@ D V5&L%0*$ v(-\*.V+`1CEVZ1'D DK*,V+|5FC|2@BD&DKV /h@ 1C.C}5F@B( $')(m*,V9@ 1C.C}5F@B( D&*.V+|V @\2 X5&VD tC Ve5KL%0*5C5&(YV+WCEVD&:X+,-%X-%+,*.5&-%(@ D?*.-c*.jV7/5FC}*A@ (24VZ+.-\] *,V724V(0*.+W@BD¢X5K0VD)$
>Vc@B13C.CE5@B( 5FCP/0V (V /@\1C s %
[email protected]:C/>+u
" " ! " "
3)<0$;?>
7
PV+,V 65C*,V~CE*A@ (/@ +A/6/VeY5@B*.5&-%(k- Z@ 1C.C}5F@ (.-7@B(/ 24-%(0*.+,-%DFCm*,VG]@%C kC}5KV$ >V]@\C -BZ t3A@B7DCE> 2@B( iVGL%V(Ve+A@B*,V / Z-\+@L\5KYV( Y%@ DK1V-BZ ¡i0*A@05K(jL Y\@B+.5&-%1CMY%@ DK1V[email protected]@B(3/vCp@B(3/ C}1iC}*.5K*,1*.5&(LG5K(~*.V@ i-BYVmZ-\+.]M1DF@0$Gu-%+:Ve@ ]mXDKV - P5&*. @ u ":#k7+C u ":#l7@B(/ }uo#k Z3 "8l# 7 "8m# >u uy N%g?R -PC}5K]m5&DF@B+,DK Z3)y 7m# >uy g%y$£')*c5FCc2-%]m]m-\( *.-~C.2e@BDKV*,V 24-V 245&V(*WC:5K( *.V@ 1C.C}5F@ ( D&*.V# +c*,- *.jVd(V @ +.V C}*h5&(*,VL%Ve+AC4$ # 0V 2e@B1C}V *,VG5K]@BL%VaL%+A@ DKVYVDC @B+,VG5K(0*.VL\V+A=C -P5K*M5FCmC}5K]mXD&V+c*.-~XVe+EZ-%+,] 5&(*,VL%V+M]M1DK*,5KXD&5F2@ *.5K-\(@%C24-\]mX@ +.V /*.- +,V @BD(01]MiV+ ]M1DK*,5KXD&5F2@B*.5&-%(C$
>Vv]@%C c- Z
*.V7@B1C,CE5@B( DK*,V+nZ-%+ Xu < -0]h1jDK*.5&XDK5&V /iM<\;%; -@B(/h*,+.1(32@B*,V / *.-a*.V8(V @B+,V CE*5K(0*.VL\V+P5FCrCE- P(G5&(Gu5&L%1+,Vc<$=N$7v-\*.V8*.@ **.5C5Cv@#N -#eN]@%C ¢$Pu-%+Y%@ DK1VC
#"
$
%"
' (
+*
&"
! " ! )" " ! " (
,"
<%s
f
f(x-1,y+1) f(x-1,y)
h
f(x,y+1) f(x,y)
f(x+1,y+1)
f(x-1,y-1)
1/9
f(x,y-1)
f(x+1,y)
1/9
f(x+1,y-1)
1/9
1/9 1/9 1/9
1/9 1/9
h(x,y)
1/9
u 5KL%1j+.V7<0$< sP_|-%(0Y-%D&1*.5&-%(-%XV+W@B*,5K-%( $ @.7:C g -*.VL [email protected]:C/>5CnYV+. CE]@ DKD)$
>Ve+.V4Z-\+.V?-%*,-C}VY\@BD&1V Cn@YVviVVe(h5&L%(-\+.V /f$ v-VYVe+-BZ-\+ *.jV5KL\V+`Y%@ DK1VC-BZ +-*,V]@\C MC}5KV3@%C*.-8iV9ij5KL%L\V+$Hz5K(24Vr*.jV @ 1C.C}5F@B(mZ1(324*.5&-%(miV 24-\]mV C DKVC.CP*.@ (# - Z|5K*WCv]@ 5&]c1]QY\@BDK1jV:Z-%+ @B7DC N +-5K*r5FC@ XX+.-\X+.5@B*,Vc*.-M1CEVM@h]@%C CE5KeV:-BZ @ * DKV@%CE*rg Hw #%$ "
"
"
]4
% , d;%&`d%&' e4+`Zi
>V8/V+,5KY\@B*,5KYV- Z|@M24-\(*,5K(01-%1CZ1j(24*.5&-%( G5FCP/V3(V /@%C=s u n?n @ u DK5K] 3A@ >" 3A@ @ " @ > 3)<0$g?> H5&(24Vd5&]@BL\V Cc@B+,V/5FC,24+.Ve*.?V -|*.VG]a5K(5&]c1]oY\@BDK1jVd-BZ @k2@B(ki# V#\$6v- *.V @Bi- YV Z-\+.]M1DF@ +.V/124V C*,/- s u n?n @ u 32@ >" O32@ "kh# > 3)<0$ Rk> # >5C5FC|2@ DKD&V /c@:/5C.24+,V*.Vr@ XX+,-B05K]@B*.5&-%(c- Z@:/V+,5KY\@B*,5KYV$n_|-\(CE5/V+P@+,- kXj+.-3DKVPZ+.-%] @ (m5K]@BL%V @%CrCEj- P(5K(u5&L%1+,V:<0$ Sj$@$|')*WCP/V+.5&Y\@B*.5&YVi0m1CE5&(Lc*.jV:@ i-BYVZ-\+.]M1DF@75FCL%5&YV(5K(u5&L%1+,V7<$TS$ i $
<%^
0
y y y y y # y # S y N #%# # g <%y < ^ N%y < #\# NBS < ^ N%y # g <%y y N #%# y # S y y # y y y
y # < < < # y y y y N g ^ #%# ^ g N # y y #\# <%y N%y NBS N\y <\y #%# S # y <\g ;%y R N s%< RN ;\y <%g #%# N y ;\y ^%N #N%g #e;BS #eN%g ^\N ;%y <%y g # RN #N\g #^%s <\<%; #e^%s #N\g R N N%y ^ < s\< #; S <%<%; <\;%; <\<%; #; S s%< NBS #%# < RN #N\g #^%s <\<%; #e^%s #N\g R N N%y ^ < ;\y ^%N #N%g #e;BS #eN%g ^\N ;%y <%y g # <\g ;%y R N s%< RN ;\y <%g #%# N y #\# <%y N%y NBS N\y <\y #%# S # y N g ^ #%# ^ g N # y y y # < < < # y y y y u
5KL%1j+.V8<$=N s@B1C,CE5@B(G]@\C P5K*. fu£<0$ v-\*.Vc*.3@B*7*.VM/0V+.5&Y%@ *.5&YV:2e@B(iVM2-%]mX1j*.V /i @BXXD&5&(L@m]@\C *.- O-
CE5K]a5KDF@ +P*.- D&*.V+,5K(L@ ( 5K]@BL%Vz$')(M*.5C|2@%C}Vv*,VP]@%C cC}5K]mXD&824-%(C}5FC}*ACn-BZ
* -7VD&V]mV(0*,C@\C|CE- P(m5&(mu5&L%1+,Vr<$TS$/¢$ 5C|@ CE*,VXV /L\V?-@ (/m5K*ACP/0V+.5&Y%@ *.5&YVvL\5KYV C`@:5KL\ Y\@ DK1V8@B*P*,VD&-02@B*,5K-%(-BZ @B(V /L\V$|>V+,V7@B+,V8CEVYV+W@BD -%*,V+P]@\C jC P5F/VeDKM1CEV /hZ-\+24-\]mX1*,5K(L8*.V +WCE*/V+,5KY\@B*,5KYV@%CrCE- P(d5&(u5KL\1+.V8<$TS$TV %Z,$ ')]@BL\V Cc@B+,VG* `- /05K]mV(3CE5K-\(@BD $ L%+W@%/5&V(*MYV 24*,-%+M-BZ [email protected]:C/>:5C 3 7 >:- PVe+.V 5C *,V /V+,5KY\@B*,5KYV85K(G*.j4V @/5K+,V 24*,5K-%( -?@B(/ 5C*.VM/Ve+.5KY\@ *.5KYV85K(*.V C/5K+,V 24*,5K-%( $c>VML%+A@\/5KVe(*3@%C ]@ L%(5&*.1/V -@B(//5K+,V 24*,5K-%( h@\Cv/V (V /miVDK- *s u @ +A24*W@B( 7 3)<0$?s > u w 3)<0$?^ > # >V8/5&+.V 24*,5K-\(@BD /V+.5&Y\@B*.5&YV5K(*,V8/5K+,V 24*.5&-%( :5Cv/0V (V t/ s u @ Fw C CE5&( # >V+,V8@B+.V8C}VYV+A@ Df]@\C jCZ-%+r24-\]mX1*,5K(LcL\+A@\/5KV(0** 3 7 >:-CE-\]mV7@ +.V8CE- P(5K(u5KL\1+.V8<0$g$ "
]4(P .
F *#$%&' e4`zi
-
4 /
pfV* [email protected]:C/>$u [email protected]:CE>tw [email protected]:C/>|iVM@cL%+W@%/5&V(0*v]@ L%(5&*.1/0Vc@B*rX5&VD[email protected]:CE>W$rvV(V 3A@B7DCE> @%CP*.jV9(j-%+.]@BDK5&V /cL%+W@%/5&V(*P]@BL%(j5K*.13/V7C.2e@BDKV/iV* `VV(y:*.-#y\yh@\C Z-\DKDK-rC=s [email protected]:C/>+u @CS b [email protected]:C/> 3 R7 /> - #y%y 3)0< $K#ey > #
!
N%y
Z 3 M> # y #y # y #ey # y <\y %< y \< y %< y %< y Zet 3p > y y y y y e# y y y y y > y y y y y e# y .e# y y y y Z 3p
,# #
.# y # .# y y # u5&L%1+,Vc<$TS/srv5lfVe+.(0*.5F@ *.5&-%(?,$ 3 @ > -%(V /5K]aV(CE5&-%(@ DfZ1(24*,5K-\( 3A@ >A$*3 i > vV+,5KY\@B*,5KYV 32@ >13CE5K(jL *.jVc/5C.24+,V*.V8@BXjX+.- 05K]@ *.5K-\(?,$ 3 2m>vHzV 24-%(3/d/V+,5KY\@B*,5KYV 32@ >A$,3 /p>rvVe+.5KY\@ *.5KYV]@%C f$,3Vl> E3 Z=>r> `@%/j/5K*,5K-%(3@BD/V+.5&Y\@B*.5&YVv]@%C jC4$ >V(cV/L%V C2@B(ciVP/0V*.V 2*.V /7i8@BXjXDK05K(L @v*.+,V CEj-%DF0/ -\(c*.VP(-\+.]@ DK5&V /L%+W@%/5&V(*
]@ L%(5&*.1/V $ '[email protected]:CE>u y# 5-%Z *,V3A+ @BP7D5CECEV > 3)<0$K#\#m> PV+, V '[email protected]:C/>n5CP@B( V L%V7]@ X?$
. /.
4
')(*,Va@Bi- YV V*, V 4*.5&-%(G]mVe*.- -`Vh-\(DKG1C}V *,VhL\+A@ 5KV(0*7]@BL\(5K*,1 V V 5 G(-\*:1C}Vh*,V L%+W@ 5&V(0* 5K+,V 4*,5K-%( $>VGL%+W@ 5&V(* 5K+,V 4*.5&-%( 5FCM@BD @ChXV+,XV( 5!41DF@ +m*.-*,VdV 0L%V?-@B( *,V L%+W@ D&VYVD"C A@B(L\Vc*.V7]m-zCE*r5K(*.@ * 5&+.V *.5K-\(?$P' Z @#4V+,*A@B5&(X5K0VD)t=CL%+W@D&VYVDf5C(j-%*$A@B(jL%5K(jL CE5&L%(5 %@ (*,DKm5&( *,&V 5K+, V 4*,5K-%(- Z|L%+W@ 5&V(*&-*.Ve( *,@B*rX5&VD?Xj+.-%i3@BiD& 5C(-%*@B(V L\V:X-%5&(*e$;(V (V'V *,-mC}1XX+,V C.CP*.3@BZ* 3 (-\(d]@ 5&]@ >
X-%5&(*e$|bG@B*.jV]@B*,5 @ DKD&c*.V7(-\( ]@B05K]@8CE1XXj+.V C,CE5K-\(d5C V 3( V @%=C s
[email protected]:C/>+u
* ()
[email protected]:CE>-,/. [email protected]:C/> ,/. [email protected]:C/>
32@027:C106>32 4 32@ 050A7:6C 0706>
3CBD5E>B >
9:;<>=?,@A< )+ 8 2H4I 2H=G<J:G;
32@ 7DC >
3A@ 7:C >
3A@B7DCE>
.-
7 7 7 7 7
~E
M(x’, y’)
M(x’’, y’’)
s C2h94jN2Hl,5N 2
@AP^^=G< @@A,594`DQ,7K;:^9 @@A,5Q_7<
K=g2 ,5
(b)
Yz,5KPa=<&BD[
]";<#<' K<
65
@?
<
7
[Z
65
87
:9 ;7"< 7= >7 A7 B C DB 1E GFH7IC JE KFH7 LC MBIN E GF 7 1O O B B PC ;7 RQ R7 TSU?V= JEXW YF
\^]1!*L0#$2_-a`cb # ]1-.%(] d 4PNUQ<>=9H.O~LR5 ~Z2H4 S[eS5 [< K<9^
U
YW ~
8 E
8
E
E
jE j E j E
8
8 Gj E
8
jGE
8
>W
E 8
E
8
E
E
8 j E
E
8 j E
E
8 Gj E
jGE j
8
U ;
W 8
E
W 8 jHW
E
E
8 jGE
E
8 j E 8
8 jE
jE
8 Gj E 8
|
jE
(W o = HN
O : h< 9Q
Qt5
& 687:9<; 6# 7 = . ; 6+ 7 2 ; 6 ; 6
]";,!@T,@2 4Z9=G,5
& 6 7 >#1'?+9@(EA7VB#C.dE)'?+5.D7 >#,@ EE '?+1.D7 >#1'F+G. EG1.D7VB#1'+H@
B
,W po
KHFI.S|J7 >#1'?+?2 E
7
] ;<eV94o19_5P:G,594SN2@ X.9=L:;a,@b9^
DBI7
35 Q
7
7 ;7
R,!/#-TS
h?
65
A7
% *,#$
65
DB (C
B
fC
MBJE F 1B
7
B
MB
]";
O
~~
.P4 :,594@".9_5_79 ?"< Qt#:G;4:M@x9 .$:;a
hE KF>7 B T5 C DBnE F
e9
9
C
d 7 @ C DB 7 > #1'?+ 9 . 6 # . /+G. /#6 . ?# +. /+$6 . ?# . /# 6?+ . /# + 6 . /+ 2 HWD5E>~ ]";<$K=M2 ,7
Qt#:;<.9_5_59 ?,74KL< u1P2H:G,594I@VD
; 7# @ ,74 . ; 7+ 91@!$' HWD5Eo ; 67 ; 67 7 " >#1'?+ 9 ; # @A,54 6# .=; + V91@86$ . W ; # 6 7 + V9 @%@A,54& 2 HWD5E'Y 6 6 ; ; ; ; N@A,54K#:G;<VPQ,!
^9_7t49N#,2 _{2H^a^=9 l,5N2 :,594X9 .F7 K,7o1
7 ?;
,
9 , . , )G., 6 ) 6 . , )' +) -
' , 9 6 @A,54. V9 @$' , 6 9 @ ,54 6 . @ ,74 91@! . V91@ 6 $' , 9 @ ,54 . @ ,74 6 { V9 @!. @ ,74V9 @ 6 . 0 V9 @ $2 wT,lQy<>=
HWD5E/.
9
HWD5E>} HW DpW 8 HW DpW EK
U
~H|
"" + ) o3,5) 7 C MBIN
7
fo4, 7 , 7 ) W
U ;
Y=9N :G;
" +) PW4,
B
(
B C
0
2
7
7VB#-' + 9* . 6 #. + 2
3R<X?2 4:U:9
HWDpW W L5
V9N#^aP:< ' 6 ' P@ ,74K _5<'2@ :@u1P2 =< @bv:FD 3f<e?,5_7_V94@A, <>=#2 ~ ~f?,74 9 ? 2H=G9P4I <'2g; ^,5l
W '7
:W '
?
7
7E9 . 7W
9 .
HWDpW~ HW Dp W |
6 #. /+ ' . /+ 6 ' 6# 6 D DD
HWDpW[ HW DpW o
. 6 #!. /+ 2
7y} 9
9H.{<'u6P2 :,794@F2 4XQ<$?=,7::<>4X2@
]";,!@@ ta@ :<>N
7E
DD
D 7} y
E
9
7 9
# + #6 +6
E
7W
7
A7 _
E
DD D
2
#
+
6
'
HWDpW3'Y HWDpW .
hT9 ? o1< V:G9= #>2H4XQ<&V9N#^P:G< JP@A,54KU:;<$^@A
7
7 9
9
' '
HWDpW} HW D\~8
O
~[
f -1,1
-1,0 -1,-1
K1
LW '
1,1
0,1 0,0
1,0
0,-1
1,-1
f1
f2
f3
b
11
b
12
b
13
f4
f5
f6
b
14
b
15
b
16
f7
f8
f9
b
17
b
18
b
N
19
B
Y,7KP=G< D JeY2V
?;
9q
T5
35
,!@2J~ e}LN2H:G=,7lyDz]";
7zE 7IW
7|
$ 6 $0 $0 0 $ $0 $0 ##6 %6 66 %6 %6 ##6 #6 %#6 %6 %6
7 ' 6 'z2H4I U>2H4 !7 ,@"K,7o1
h 9 ? T
Q<eV9N^P:<' .=G9N
7%~
7%[
7Io
7
7
9
.
'
7%}
E
W ~
HWD\~EK 2
:;<2HQ9 o1<< u6PI2H:,794 QtZP@A,54KRV94o19_5P:G,594`DXY9=
6 7W . $0/7y~ . $0/7|. 87y[. 0?7o. 7 ' . $0?7 . . $0 7y} ' HWD\~ W 9 7 ' ?;
9
$ 87E
. ?;,!c;,@ 94o19_5Pa:,5941
9H.2r. 2V
U
Yo ~
W
' W jE>~ E' WYW E ' W W W W4' WYW ' E' WYW E ' W W ' W jE>~
jGEF~
W'
W
jGEF~
~E j[ jGE j[ ~E
j||
8
' >j>oYo W. 6 j>oYW
W W
W
8
0 >8 W W
HW jHW jHW jHW jHW W
j
|
8
j
j|
8
E
8 Gj E
>W j
W 8 j>W
W W
j|
E
8 j E
HW j
8
jGE
jGE
jGE
jE
j|
HW 8 W
j
8 8 8
|
MBIN
B
8 8 8 8
W
8
W
8
jk|
W
|
W 8
HW jHW jHW jHW jHW 8
Y,7KP=G< D $ 2H=M2H_5,! \@{N2@ @.9=OV9N^P:,74K 6@VD
' 6 ' ' 2 2 2 ' 0P@A,54KU_5< 2@ :@Gu6P2 =<v:79=N2@B@{K,5o1<>4p,74eY,5KP=<WD .D WD{9N#^P:G< $ '@ ,74 'V9 @! D ~D{9N#^P:G< , 6 ', D |Dqk.2, 8J2 4 % % ) :;
W
,C
DBN
Y,7KP=G< D\}${]";<&@ :G
HW 8 W j
j 8
W
>W
W | jGE jHW j>W jk| jGE jHW W | 8
W
jGE Gj E Gj E Gj E Gj E
[
jGE 8 E
j
jk|
:W . 1C
'
j 8
>W W8 W8 W8 W8 W8 |W WE j>W j>W j>W j>W jHW W E E E E E E j| j>W
W W
E
j[
>oYW j>o . j>oYW 8 8 8 oYW o . oYW j
jGE
W
|
[
'
6
W
jGE Gj E Gj E Gj E Gj E
jGE
jGE
'
||
6
j[
W W W W W | W jGE jGE jGE jE W 0 >j W j>W j>W j>W jHW 8 8E jGE jGE jGE jGE jE j>W jGE W W W W W j| j>W
j ~E [ E [ j ~E
oYW o. oYW
8
j||
jE j E j E j E j E
0 WW
||
j
~ E j|| 8 || j ~E
U ;
E
E
E
E
E
~ E j|| 8 || j ~E
11
W
0 O.$ O1 O
2
4' ~
L
Y ,7KP=G< D7EF8 2 gD ]";<#Q9:G:_5
)
O WD d
7
,
B
ED
B
'
?VO
kQ C
DB
:G;< 2 =g2H_7, X< K< <>:< V:G9=
,W
.9=2LK,7o1
^a^_5t#N 2@ U:9U:;a<
,7N2HK<1D
~DwT<>:< V:<>=9V=G91@@A,54K @VD
C26=F2 4e2H_594KU< 2g;=9 ?7=< 9= 2 4X< K<$^9,54:2H::;<$_79F2H:G,5949 .{nF
~
U
.
W ;W h
O
h I O
O
U ;
PW K
Y,7KP=G< D7E C2 E jCw 2 P@@A,2 4 Iv _5:<>="?,5:G;:9 ED kQ EVj w O2HP@G@ ,2 4pv_7:
O
=
7 7
]";<2 42H_7t:G,F2 _<>l^=G< @@A,594@9H.:;a<J9^<>=g2H:G9=L,74f94<2H4 f:A?"9 ,5N#
>#
&,6 B #-' +
GE 9
@ # 6
6 '
; #6 = . ; 6+ 9 >W@ # 6 . + 6 6 ; 6 ; 6
9
' 94 > #1'?+gD
HWD\~~ HW D\~ |
?;
hO DW W ;W W W 7 6W W
W W Y7 1O
7
?VO ,?VO
hO
DW
7
11
0 O.$ O1 O
(W W jCw OO2HPI@@ ,!2H4Xv_7:
Y ,7KP=G< D7EF~$ C2 ?,5:G; :9 ED
~}
9
$ WHj w OO2HP@G@ ,!2H4Xv_7:
ED Q
9
WD K?VO
U
|18
2
U ;
kQ
W C2gD{]";<Q9::G_5<,5N2 K<1D1QgD ]";
Y,7KP=G< D5EV|
7
7
7
] ;
KB
A7
W
?VO
W
]1%(b # ] -10#$ %(' \ L..0!2 ]";<_ O 2 P@@A,2 4Z;2@4, <
^a=9^
O
.7
7
O
]";< O2HPI@@ ,!2H4U9H.%@A:g2 4 2H=
2 | D#]";,!@
^=G9 P V< @&2X@A,5K4a, v F2 4:$=G< P V:G,594 ,54 V9N^P:g2 :,794@_5, 1
W
7
fW 1C
W
O
;7
R7
O
7
?
O
7
,O
,C
!O
3O
;7
B
W
W
R7
W .7
:41n 0 O.$
|E
8Q
:;a,@@ F2H_7,54K#^a=9^
O
O
O
W
O
"! #$% '& B# )(*+,-./0 1+, 32/465 87%-019:#+, ;)( + 5 < ! #$% >=?@+ 5 @+ %9 (BACD%9:EB-1+ 5 F! #1% G 'H 6 & GI=?@+ 5 +,-J"0 1+, W2
KMLON & > #
& > # 9 PRQ Q
S
S
TU P"Q 9
P"Q 9
Y
9
S S TU
Q Q
W
V X V
X
TU
HWD\~[ HW D\~ o HW D\~3'Y HW D\~ . HW D\~}
Z H 6 & B#
\[] *^J7%-_`a 01+, 0E )(b! #$% dc ># )(I+e-J0 1+, ! - f! #$% dg B# )(+,-."`0 1+e C2"465 /7%-019h#+, i)(/+ 5 ./+e=?j(#'-7a+, k`J#9l+ B mJ7%-n 01+, 0E/)(k! #$% & 6 H c po g B# )(^+,-J"0 1+, ! 6 . 6 2 KMLON "t
Y
U
W |
! 9
qC:G
W
Y7 E
ED | ED D\8 D D | D D ~D\8 ~D5E ~D\~ ~D\[
W
|
~
W pW W W po
o
[
.
9
E
Y7 9 W W pW po po
! 9
'
E D ~D\8 ~D |aD5E |aD [D\8 [D | [D D\8 D | D
W. '
} E>8 E E
! 9
o
~
! 9PW7 49d~
. .
po ' po
~ D |aD [D D\~ D\8 D D D }D }D EF8D
o
o.
o'
W =
~ D5E |D\~ [D\~ D\8 D 1D | D\8 D\[ }D\8 }D\[ E>8D8
o
'
o
Y7 49 E
U ;
'
'
' po
. pW
.'
pW
'
pW
$= E 7 O9d~ 2[ [ o
Y,7KP=G< D5E>[ 1P < @@A,5o1<^
W
! 9
|
|
~
Y7 9 W 2 W W E
! 9
~
.
[
'
} >E 8
o
W o =1P < @@A,5o1<^
Y,7KP=G< D5E
7
Cq 4#2$^2H=G:, P_2 =,7N#^_7
W
_W ;o7
d
W
7
;7
7
O
O 7 O VO
R7
A: ?39j ,5N#<>4@ ,7942 _ O2HP@G@ ,!2H4 v_5:G
W
R7
TW /.
C 7
.O
7
:41n 0 O.$
|1~
7
?VO
4
87
O
(?
7 .?VO 7 h?VO
7
465 9h7 & 6 B #-' +
)(R! #1% f7%a/=?@++) E?(19W9:=
>+
;+
9
; 6
K-L%N
B#r
>+
.
;#
; 6
>#?2
HWD | [
1?
]";<&2HQ9 o1<F2 4Q<&@A;9 ?4X< 2@ ,5_7t#Qt#P@ ,74KUY9P=G,5
:= d
>#
vu?'
qFs
LW
O
7
>#
R
B+
;+
; 6
7
qRs q s R q s R
O
vu RF2 8@^tvu 6 6 vu 6 ?'
vu 'pu 6 F2 @^t u 6 6 ' 8@^tvu 6 6 2 : u ')u 6 ?'
?;
HWD |Ao HW D | 'Y HW D | .
B#1'?+ MDbh9H?7%Qte:g2KB,54aKp:G;
>#1'?+ qFs @8tvu 6 6 2 u ')u 6 2 "tV9N#^2 =,54aKb^2 ,5=g@WD | .J2 4 6WD5EEDpL W ?"<$;2Fo1<7 ; + B + 9 ; + >#1'?+?2 > # ; 6 ; 6 =1,7N#,5_!2H=_7t7Qt#=<>^_2#V,54KC#pQtM+ 7 2H4 +JQtM#p,74:;<&2HQ9 o1<$< u1P2H:G,594?3<
;I2'o1< ; # > # 9 ; # B #-' + 2 > + 6 6 ;+
; 6
;
Y,742H_7_5t@ PN#N,54K$:;a
>#
;
>+5. B+ ; # 6 >#9 ; + 6 >#1'?+1. ; # 6 >#1'?+9 & 6 B#-' + 2 ; ; ; 3 ;,%c;#,!@"
;+
; 6
U
||
(O
U ;
B B+ &2H_594K < 2#c; WD{94o19_5o1<:;a
g(x)
gyy(y)
2
g(x,y) * I(x,y)
I(x,y)
+
Image g(y)
gxx(x) (a)
I(x,y) * g(x,y)
I(x,y) g(x)
g(y)
Image
W . = IW
UW
(b)
?VO
Y,7KP=G< D5E $ 1
O
$
_
O
|1[
O "!$# #$% & !
'%(# *)(* 7 ,+ + 7 ># 9 @#.- %(# /M#0+ 1 #% 1 "#! "23 !$%4#$ !$
/ 53 6#7% -5 8 ! 91&896 ! % (7- % 8*8 %2: d $ !$ !;!
<% 1 "# !%(# % -=9> '? !$% 3 21 1 8* !$%5!$ & * 1 ! 2@ j ' j 6 ' j 'j )'j ' j 'A+*+9+9+ 7 j
% ! 1& ! 2@ k ' k ' k '0+*+9+*+.E %(# * ! 7 !$ & ; F@ ! % G- %(#D!$
% G1& ! ! % % kH k9 I Dj D. I j 6 . I 6 j . I Dj . I j 2 J D!$%!$
/G 6!$# A 72I 9KI GI 9KI 2+
% /L % 8* ! % 2@ M ! % "53 *G1 8*ON (/ k9 I G j . j R1.PI 8 j 6 . j ;1.PI 6 j 2 N ! *89*>"9 )Q/G "!# 7 : R# ;!
/ 53 "#% -S&8 ! *1 89% T ! % .- #$% ? !%4U !$% % 1 !$ 8*8 !
k V 8 ! 8 7 :
"# W !$
!$%(! 8X 53 "#'% - 8 ! Y+4Z,[) "# 2H8 7 : & P* ) !
1 #% 1 "#$! % -\/G "!# 7 : % 8* "L !% 1 "# - %C# c ]_^ 7I t `ab(c W . Kd e5 8 ! 91&89 Y ! % : % <9)C ON 6 !#$ ! % G- #$% a ]_^ 7fI t `/ab g+
m #-"#$/ -.%(] X&JE U 7WYF (71 #% 1 % f ) R% 1 6# !%(#: !$ & & % -S- % # % 1 8 "n "n 1 % ! 28 "2o3 1 1 #$%2n *4 ! p3/ !$ & N # ! "# *L( ! *L e% -q O2$20+C C$ ! !4 ) "! ! % 41 6# - %(# G3/ % /L % 8*L* ) !
% G9r) : !$ Q-s& ! % 7utB#wv2 x3/G4 # B/9 ) ) !;!
r n 94R* !$
<% ! 1 !% - !$ % /L % 8* ! % 0+X2 /1 YON !$
# " 1 "# - %(# r # !$ 6# % !$
'% ! 1 !D% - !$ % 1 "# !%(# + d(+ O %y% "!$ ! % 0+ & "#$
% &8 3 ;8 %: 1 #$% 3M3 *89 ! % -0-z2989* ) !% 4 # B /) 1 % * ! R7& 8 %: 1 #$% 33 *89 ! % -.-z28 8944 # B* )< % { ) 1 % 9 ! Y$+ =y* 3 %(!$ !
1 #% 323 98* ! # -s ! % % - !
'% ! 1 ! *)(28 !% % R# ! % 7 !$ $ # !$ "# % %C#$# 1 % !$% 4 n *G|>"9 ) 9)(M8 !$% % '# ! % + W + O %y% 8 % "2899>F ! % 0+
1 % 9 ! D4 # B 4( /) 3 !
R% 1 6# !%(#
% &8 e3 ( Y8 % ( 1 % *3 8 '!$%5!$ & ! "#% - !$ & ;!# ) + U + D 8* % #$ 1 %
!:% # 3/ % 1 "# !$%C# #$ 1 % !%!
/) 7 % '% - !
_ ! 3 % M "#$ 4R-z8 ' ) + E %(#G!
8 % "289*>2 ! % # !$ "# K X /WM !
9/L "# 4% - !$ & ! 3 "!: " !$
}!$# ) 2 !$
) 4 # B G3/ !$
% 1 "# !$%C# +'E %(#D!$ & ! 2 ( #$ '
!$
! # L/ ! % 59 !$ & 1 % ! % % - !
4 n 95 % - !$ & 7% 1 6# !%(#% ! 1 ! 1 + C - % % !S!$ ! t$d2v~ Ht Wyv~ #$ % % ! * )'2 ! !S!
"#$ . !$# { % Q %C# & "#! * ! '1 # 9 T*1 8 3 "!: 6 !$
+ #$% # % 1 "# !%(# FL R) %y% 49)(M89{ !$% { % '# ! % 3 ! 1 %y%C# 8 % "8*9>2 ! % G2 L/ {L "# $/+ X&5 !$ & 1 #$% / !% - !:% # ! "# !$% % 53 9 !
*4; * )-s 8 : "y1+ C D!$
N O 7uBt #v 7 : %
4 n *G9> ! 1 #% ! + X / #$# 9L !R!
% 8* ! % - %(# 7u>t #wv 7 : !
m Q "# { % -s{s3 %2n % 1 6# !%(#<: %
: CH1 #$% 1 % 43f < % /- 8 4 # !$% E W;d F,+~ "n/!
!$ & ;! # # !$ "# % !$%< 8*9G* ! !$ & 5 8 ! 91 8 # 1 % M Y1+ C # !
7# 2@ # !u! !X!$
-s ! % 7 : 98*8 %(! FL D!$%y% 4/ #$ 1 % !% }9&)(8 ! 1 ) 9 !$ & L/ T* ! % - !
!$ 10+ C 89*G ! !
53 "#% -D1 K B& 9 !
R# 1 % M %! !D!$ & "#$ : 9898
3 <8 %2: 1 #$% 3M3 *89 ! % - Y8 # 9 )< %(#$ !$ 2 % ' ) + C h
(2L2Gi[j[lk*,+(#
o
d(+ % G1 ! x!
) # !5% - 942) 7gt>#1'?+ v'3 % /L % 89L/9&) !<: ! W!
N # ! 6 # 9LC ! 9L % OM$* #} + / #$ ! % Y+ 7 t>#1'?+ v9 7gt>#1'?+ v t @ # v
' 6 @ 7 t>#1'?+ v9 7gt>#1'?+ v t + v 2 6
tHW+ yv tHW+ ? v
W+h9 6# - %(# % {r n 94'&1 1 #$ $ % % !
) # ! r)(& ! + U + d 1&1 89 !$ "# !$
#
% 8 * ) !%[!$
% &{4 n *4&1 1 #$ $ W4)C ! +)= "2 !$
*4) - #$% 8 - ! { # 9) ! 7 !% 1 {s3 %(!!$% +Z- !$ & ) # # ! 42)( ! !!$ & 1 n/ 8
3 % L '!$
*) f!$
# &% 8 I7 T8 # R!$ ! (2 ) 1 % * ! + & #$ Y # 9L 8*G8 %y% B ! ! 7 9) 3 %(# t % !$ I7 %C# . % ! v +'Zz- !$
) # / ! 42)( ! D3 % L
8 %2: !
#$
% 8 7
T8 #$ '!$ ! (D ) 1 % * ! +
Eu9)C #$ W +*d
$ = ! 1*:X2 /N ) " ! !$%C# + !$# !$% 4GB 7!
! 2 3 "!: 6 G1 KB&9 !
% # 1 % M 21 1 #%n 9r !$ D!$%
': ! 4% !$ & ;# 1 % <% - !$
'% 1 6# !%(#!% 5* )(8 !$ 10+ : ! 3 % !!$
$2 ( !$ & R% 1 "# !%(# : !$ + % !$
"# *L( ! % % -H L Y8 % e- %(# PQ- %C# 2 % 1 ! 9428 ) 6!$ !%(# 7 X / ('8 % !$ & = !$% C ! %"D1 ! *G9>F ! % 6!$
% !$% "# *L !
G% 1 ! *48 ) G% 1 "# !$%(# +
G% 1 ! 9{ G*>2 ! % }289) %C# !$ ! 8*894 *8989{ T8*9<3 * )< # % L "#D!$
1 <% -X1 % $93 8 N8 ! "# Y+'Z ! 1 #% " 3/ % ! 9/ % M89 !$ 6# ! 9 ) !$
#% ) !$
- % 898 %2: * )5 ! 1 d(+ # ! % ) 3 /9 6 ) O2$ # 2 % / 3 "# !%G!$ & $2G1 8 xLC8* % - ! $ 1 ) + W+ % L % 89L !
N8 ! "#: !$ e! ) 7& LC8* ! ;!
'#$ 1 % + U h+ 9 6#$! # 3 !$
N8 !$ "# %y !T ! =3/448*8
% ! +
+ % L % 89L ! 6: N8 !$ "#: !$ 4!$ & ; ) 72 LC8* ! ;!
": # 1 % + ? + 2 ) !$
N8 !$ "# 3M( % !
' Q ! % - !$ & 1 "#! # 3 ! % x*ft U v +
*G1 8 ! ! % % - X2 / N % 1 "# !$%C# *L % 89L !$
- % 898 %2: * )4 ! 1Y+ d - ! "#D!$
*4) ; ( 3 " % L % 89L : !$ /G "!# .O 7 !$
X ) / #$ ! % R ! *4 ! 7- #$% !$ & ) # ! % - !$
%y%(!$ & G942) * ! ! G # -z# +
) # # ! 4)C ! !$
e % {r n 94'&1 { 1 # $ e9 ! ! #$ ! % 0+
8*) %C# ! "! !$
#
% 8 3C % 8 % "8 ! 94 !$ % -X9r) % +SZ ! rK B S '% - !:%5!$
# &% 8 & !$% 8 : !$ 4!$ & 1 #$% 3&8 % -X !$# K B/9 )&+
9 1 8 ! ! % % F- X / N % 1 "# !%(# D
%2: f9 Eu9)C #$ W+9d +
R# &8 ! % 3 ! 9 : ! 4!$ % 1 "# !$%C# #
%2: e*eEg9)( #$ W+ W +
$
'
zt v t3wv Eu9)C $# W+ W 7tz v + & 3 C% !$! 8 * 4) + ts3wv +
' /) 41G- #% !
X / ) " !$ !$%C# +
6/!# Lb !/#
= % -z #D: ' "L C$& !$
LC8* R% -9 !
OM$}3( /) "!$ !$%(# B/ %2: 0+
9 1 %C#$! ! 1 #$% 3 8
%2: !% "! "# 9 '!$ & 21 1 #$% 1 # ! LC89 % - p*[G)C9L *4) +
M : 6#7!%! @ ! % 4 %(! !# *) /! - %C#$: # w+ C73 " }5 ! 9L #$ % - # # 7& !$ & 1 #$% 3&8 4 #$ r9 !$% 3 M % 8*L * !
) "# 28g + 3
## nC7*8 # "!$ N # ! 1 #$% 1 % !
?VO % 1 "# !$%C# 7 !$
)C) !$ e- % # /mQ "#$ ! LC8* % $- .7 : #$ 9_)d 'DW ' '$.+
#D ) "! !$%C#: C7 %C! 9LC !$ 43 !$
#$% 1 &{ % 8 % )( 680N * )y23 % !'!$ & R 4}L % 0+DZ ! C73 " # 1 %(#!$ ! ! * 42eL/ % 7 - % # *> % - 898g*G98 #0!% ?VO % 1 "# !$%C# "n ! +
# *> "2<3 21 1 #$%2n 94 !$ '3 !$
23 % L - % # ALC8* Y + S ?VO % 1 "# !$%(# "23 % 6#$ }3 e1(NM8 !$ 6#7! !$% % - #$ 2@ Yy+
R !% - % # N8 ! "# !% % L "#!
':
% 8 1 !# % -.- #$ F@ T T+ d %y% PC !
5 8 ! 91 8 LC289 % - P #$ * ) "!$ ! % 7 !
9 1 %C#$! !@ ! % #
%2: % % % 53 9 - % #< ) r1 ## C7*8 # "!$ 1 ! - %C#$: # !$
d1+, 19 L
> "#$% #$% * )y !$ ! % 9 T % L 6# L "# 28 68 7% -7 `-7afE%# +, 7 : ! !$ : # 1 "28989 9)(&ON "2 ! (+ P C %:X L "# 7 !$ # !$ 6# % 7 : : CG L "# ! ON 7 # G* !% 1 #% 3 8 L "# C*89y+ Z,[ d . U 7-3 ! B/9g EXW ? F :#%(! L "# 9 ! 28u121 "# 7w* : % }
* !#$% e "8 1 + =y* '!$
70 68 1 < (73 "
%C!!$% 1 '9e8 %2: "# 8 L 8 % G1 ! "# L % 0+ 3 ! B*} # )C !$ ! * D!$
6#$ = %<# ! % 28 !% 8 ! /
% 8 1 !# % - % 1 "# !$%C# 9> Y1+ 3
<> "#% #$% $9 ) \* !$
dY{ J -s ! % "! ! !!$
% ! 9/ % - "8 ' #$ 1 8 %C!$!$ *K # @ W1M 7 !$
e- %(# & % !$% # T+ # @G1 : ( ! "# ; "8 1# +
9 !$ "# ! 9 ) !$ 9 )'23 % ! "28 1M !$ ! 9 !$ # % !$# ! 9 )5R> "#$% #% 9&)G !% 68 C9 )C8 1 % * ! 7 %2:o:X " !$# ! G ) 1 % 9 ! (D % !% # 9 !
68 1# +
% !% # 9 !$
"8 1M FL % % 1 #$% 1 6#$! T+SE %C# 9M ! 2 7 !$
% !% # # 8 : " % 1 !!
3 %(!$!% ts8 %2: uDv 7 "T8 % } !'!$ & R!$% 1Wt 9)
3.
uDv 7y8* B #
Y+
6#$ - %C#$ 7/95) % * )R- #$% !
8 %: "8 t uv !%
9) "28 7 $!
> "#% $# % $* ) 4" 1 1 # 7 3 !D!$ & 4 # L "# #$ !$
+
k ,# ]/h0K #$ d(+ % % "#!
942) 7 )C9L }9 !
- % 8*8 %2: 9 )&+ d $ !$ ! ! !$% 3 % L % 89L : !
!
4( B L7 !$ & ;# &8 ! !$% 3 1& ! * !% 942) +
>- W - U - - ? ->o - ' -+. - -d -dCd -d;W -d U -d - d ? - d;o -d' -d/. -d
->W ->Wd d TW U ->W W >- W U ->W ->W ? ->WYo ->W3' ->W . ? o ->W - U - U d - U W - U(U - U - U(? ' . - U o - U ' - U . - U - -&d -W - U - - ? -Ao - ' - . - )&d )W ) U ) ) ? )Ao ) ' ) . ) ) d ) d(d )&d;W )&d U ) d )&d ? ) do ) d' ) d . )&d
)AW )W/d A) WYW ) W U )W )W ? )AWYo )AW4' )W . A) W ) U ) U d ) U W ) U(U ) U ) UC? ) U o ) U ' ) U . ) U ) ) d )AW ) U ) ) ? )o ) ' ) 3. ) % G1 ! !$
- % 898 %2: * )I
7 d 7 U W7w2 AW+ W+ 3 # !$ % - %C# % L % 89L/9 )C7 : ! +1C7* ! % " % ! 3/<- % # 8 %y% 1Y+ U + J7 6# 9L "n 1 #$ % G- %(#D!$
?021 8#T2 % - O & 6 )C9L G* 2@ M ! % ,W+ U &+
+ O 6# ! !$
4C B;- %C# W ?(? 5 & 6 7 : & :9 dC+ 0# " ! 28984(B'L(289 !%'!$
#$ ! * ! ) "# T+ ? + O 6# ! 4!$
r( Bf- %(# W ?C? 5 & 6 7 :
09 Ed 2 ? + 0# " ! 28984C BfLC89 !$%!
#$ ! 9 !$ ) "# T+ o + = &%:_!$ ! ?01&8 Y & 6 79 7 .D7 R28 % )(9L [3 & 6 79 7 " . 7 B " 7 :
"#$ 7 " N 4(D % "# 9LC ! 9L % - 79 !$ & #$ ! % 72 7 B " !
% "# *LC ! *L * !
# ! % G1 "# 1 % T 8 #!$% + 'y+ % % "# <3 9{ T 3 % 71 % 8* % G28 N G9 2@ ! % , W+9d U + t,yv JD "# *L 2@ ! % M W+9d G2 6W/+9d ? + t3
v d 1 1 89 !$ & 3M ! ! ! % % -DLC # 3 8 # 9 )S* 7+ 9 ) % x9 2@ M ! % W/+9d U !% 2 ) 7uBt #1'?+MvS* !% 7 +t )Dv 7 x
%2: !$ ! 7 +t )v)(*L G3/ 2@ ! % , W/+9d ./+ .+ % % "# 5 % %C# 6# 1 % 89/ % B8 7g>t #1'?+ v 9 . 6 # . /+. /# 6 . ?+ 6 . # + 2 -d
?
% G1 ! r( B& - %C# '5 ' ' ' ' 59 )f8 C ! @ # ;N ! + % " U 5 U : * %2: #$% # 1& n/ 68w* !
942) +
+ = &%: ! ! ) # # ! 4)C ! #%(! ! % *LC # 2 ! + ? "!D!$ ! ) # ! ! 1 % 9 ! Bt #-' +Mv )(9L x3/tB7 '?7 v + d $ ! !D!$ & R% 3 ! #%(! !$ } #% n R7 !$ & 1 % 9 ! Bt #-' +Mv % L !% 1 % * ! tB# '?+ v +
76 . 7 6 9
7 6 .D7 6
d + 3 ! !
% G1& ! ! % 8 % G1&8 "n ! % - X&IN ) "! !%(# 2 )?01&8Y % OM$ ) "! !%(# +~Eu # ! ! O-s4*G !$ 1S9 /) 6!$ !%(# 7 !
% 1 !$ !
% G1&8 "n ! ;- %C# 9 /9L/ 280 !$ 10+
?d
d(dC+G % G1 8 6!$ D!$
- % 8*8 %2: 9&) ! 3&8 '#$ 8 ! !$%5!$
# " ) " !$ !$%C# : ' "L / Y$ w+
Eu*8 ! "# * )
J lQ "#$ ! ! %
J7 6!$ ! %
% G1 8 6n !
% G !
I
-L
R '
R
?W
V2_-"] * L /-10 32
"!
m$#&% 2L08-
Z, $! 21 !$ 6#<: 4: 98*88 # 3 % !!
)( ! ! % % -*4) R9 !$%# )( % + R5 % G1 8 ! # 1 1 #$% # !%G!$ & < ) "! ! % } "!$ &% :X 8 # x9 !$
8C ! 1 !$ "# +Z, ) "!$ ! % : )( ! 2R*4) 3'% ! O-s/9&) !
3 % # % - % 3 ! T+
3 % & # # e!
8 % " ! % :
"#$ 4!
9 !$ ! f )C9 )&+WZ, !$ & e#$ )( % P3( W21 1 #$% 7 :X x: *898 ! O-s # )( % % T 1& A3/ !
4% 3 ! T+JC "#$ 7 : G: *898) #$% 1W1 n 8 : # 9G*8 # * % R# )( % 1 #% 1 "#! +
N # ! 1 #$!% - ! 21 !$ 6# 28 : !$ " )( ! ! % 0+Z, 6 )( ! ! % 5 # )C ! ! % % -g9r) % 3 ! 29 53( % !
) # "58 L 8 !$# 93 ! % % ! *L ! % -1 n 8T+ C %2: L "# 7 " )( ! ! % PG*) /!<#$ 8 ! * !%y% r/W48*8 #$ )( % 5!$% % %C!$
6# -z# !$%C# Y+GZ, !
% 1 #!R% - !$ 21 !$ 6# 7 : 5: 98*8 T % "!
% R- %(#G# )( % W) #$%2: 9&) + & "!$ &% : *8983 !% "# ) 48*8D # ! #$ )( % 9 !$% 8 # ) "#D% !$ !7# 1 #$ !!
'% 3 ! %(# T8 % 89y+
d
0 32 (' # +34 #$2_-*)- 0 32
)( ! ! % % -D2A*4) 7utB#1'?+MvX'1M #$! ! % % - 7gt>#1'?+ v't,C;
%2: A*fEu9)C #$ 5U +9dGv* !% &3e9r) ,+ '"+ 6 ' 2 2 2 '"+7BQ e! !!
- % 898 %2: 9 ) % !# 29 ! D #$ ! N 5 d(+.- BV0/ + V 9 7ut>#1'?+ v?2
W+.+7V213+54 79 6r7 t&9:8 9+
3&942) $ ! ,N <1 #$ " !$ %C# "!% -~1 # 6 !$ T+= % "n G1&8 S # d 898w1& n/ 8S9}/4&3 942) + V 5 !X "L !$ & ) #$ G8 L 8z+ d 898w1& n/ 8S9}/4&3 942) + V 5 ! %(! lQ 6# 35 %(# !$ &(j ) # 48 L 8T+ d 898g1 n/ 8*2 3 *4) + V ! %(! mQ "# 3/4 %(# '!$ 2 &!j - #% !$
) #$ 8 L 8 % - !$
'# )( % 0+ { & ! & # L/ ! % % -~) # "48 L 8.9}24 3 *4) + V ! 3 42898z+
U + S
{ { {
;=>< ?A@B@DCFEHGJILK"MNK"OQPSRLK"R
?(U
?
O
R1 R0
R3
R2
Eu*)( # RU +9d)SZr) )C ! ! % 0+
60G4 b # # +34 #$2_-*)- 0 32
,Z !$ & *G1 8 6( :
"#$ 7utB#1'?+Mv % ! 29 % % 3 ! 7 !
) # G8 L 8 *4) "2G3 % L "#!$ 9 !$% %C#$# 1 % 9 )<3&9 # 5942) t>#1'?+ v +~Z, ! S3 9 # 5942) !
% 3 ! 1 n/ 8 : *8983 dYN !$
3MDB) #$% & A1 n 8 : 98*8.3 N Y+ 0% "! "# 9 x3&9 # 9r) : " !$% % !$ $
% 8% 7(=- % 898 %: / tB#1'?+Mv9 d |C% -1!$7g
"t>#1#: '?+ v t U +9d2v = % LC # ! % % - !$
3 % L "C 9 T89 ;!
M R% - !:X%!
#$
% 8 87 2 6 C% # L # &) '% - !
#$
% 8 87 9 ' 6 ' 2 2 2 ' y+ t>#1'?+ v 9 d |%C - !$
6 #$: 7u Bt #1'?+Mv 6 t U +pWyv >t #1'?+ v 9 d |%C- !$7u
6>t #1#$: '?+ v t U +U v
,
!# 93& ! % % -) # F<8 L 8 "53 !$% 6 !$ "# G 9 S!
!$
# &% 8 < R9<3 * # <942) Y+ d !$% ) # ) # 1 !
/ 3 "#5% -1 n 8<9 9 r) }: ! A1 #! %T 8 # ) # " 8 L 8DC4
?(?
W ?C? W ?C? W ?(? W ?(? W ?(? W ?C? W ?C? W ?(? W ?(? W ?(? W ?C? W ?C? d d d W ?C? W ?C? d d d W ?C? W ?C? d d d W ?C? W ?C? W ?(? W ?(? W ?(?
W ?C? W ?C? W ?C? W ?C? W ?C? W ?C?
30 25 20
15 10 5 0 0
50
100
150
200
250
Eu*)( # 5U +pW$tz v=y*G1 8 !$
6! '942) : !$ f% <% 3 ! +Gt3
v CD !% ) # % - 942)
%2: [9 t,yv + -s ! % % - !$
942) S% -M) # "'8 L 8Y+0E %(# / !
"! .942) .! !$% ) # : *898 % ! * ! * ! 1& B Y+.Z,}Eu9)C #$ 'U +pW/+ 5<9 1 8 o!5,oR*4) : ! G% '% 3 !
%2: 0+
1 n 8
) # F 8 L 8 %C#$#$ 1 % /9 ) !$%'!
% 3 ! #$ d 7& !$
1& n/ 8 %(##$ 1 % * ) !$%!
3#MB/) #% 5 # W ?C? +
!% ) # % - !$ u*4) ~
%2: 595Eu*)( # U + W+ 30+ "2 X!$ !$% ) # 2 ( !:% 1 B R7 ! 6898 G3 9 % 8z+
' !% ) # % -X #$ 280942) 4"5 %(! % ! 29 T8 # 1 B R7 * ! G ! 4" % !'% -D1 K B&R ALC898 &;CR
%2: [9Eu9)C #$ U + U + < 8S*4) # #$ 8*" % ! 29 ! 1 ) T+ & ) # "G8 L 8S !!$
' ) 2 ) ) # M898*- #$% 3MDB) #$% & !% - %(#$ ) #$% w+ #$ 8 ! 941 G B D GLC8*8 &9 !
' !$% ) # 2+ D3 ! : !$ 21 1 #%n 9r !$ 89 !
$2 R# ) % -) # "8 L 8=- %C# T8(T+
< !$% ) # 2 % -;W*4) G: 98*8 "L 1 G B - %C#< Y8( % - % 3 ! 2 % 8 # ) 1 K B %(##$ 1 % * ) !$%4!
3 DB/) #$% w+ 0% / ! 9 )C 3 "!: " / ! 9 ! T8( % - % 3 ! 8 7 : M !
%y% !$ $
% %8 R 7 # 89/9 )G3 "!:X " !:X% 1 K B&T+Eu9)C #$ 5U + &+ G
%2: ;2A*4) % ! 9 ) % - !
#$ "
(a)
(b)
Eu*)( # RU + U t, vz{$ts3wv n 1 8 % -~3 9 % 8 !% ) # 4Y+
?o
W ?C? W ?(? W ?C? W ?(? W ?C? W ?(? W ?C? W ?(? W ?C? W ?(? W ?C? W ?(? d ? d ? d ? d ?
W ?(? W ?(? W ?C? W ?C? W ?(? d d W ?C? W ?(? d d W ?C? W ?(? d d W ?C? W ?(? W ?(? W ?C? W ?C? W ?(? W ?(? W ?C? W ?C? W ?(? W ?(? W ?C? W ?C? W ?(? W ?(? W ?C? W ?C?
W ?(? W W W W
W W W W W
W ?(? W ?(? W ?(? W ?(? W ?(? W ?(?
O
40
35 30 25 20
15 10 5 0 0
20
50
T1
100
150
T2
200
T3
Eg9)( #$ U + IDt, vXZ,42) % ! 9 ) % - !$ $ " '% 3 ! Y+t3wv C7 !% ) # % -S9r)
%2: e*ft, v + % 3 ! 87u2 !$
%(##$ 1 % * ) !% ) #
%2: [*[Eu*)( # 5U + + 3+ & "#$ # - % # 1 B R7 !$ $ " %C#$#$ 1 % /9 ) !%A% 3 ! R7X % %(##$ 1 % * ) !$%f!$ & M3 DB) #$% & w+
# " 3 9M # 9r) "2e3 ) 6# ! G* ) !$
#
% 8 C - % 898 %: / d O- 7utB#-' +Mv "tB#-' +Mv9 %(!$ & "#$: d | - 7uBt #1'?+Mv 6 t>#1'?+ v9 6 %C!$
6#$:
2t>#1'?+ v9 d |C% - !$
66 #$: u7 tB#1'?+Mv
D 9 1 %C#$! !.!$ * ) !% %C!$ 23 % !!
7 !% ) # _ !$ ! ! 6 % 89 ! 9 )C 3 "!: " T8($ % - % 3 ! Y+RZ ! %y %(! % ! *f/1M ! 8.*- %(# 4 ! % 0+ & "#$ - %C#$ 8O-X3 8DB}
28O- : !$ *4) 7
$S3 % # G942) D: !$ 8 ! "# M !$ 3 8DB5 : !$ 3 8 % MB& % - 2@ 8/ 3 "# 7 x9r) % - # % 3 8DBG2 : !$ %C! % - 2@ 28 !$# 93 ! % "L ;!
$2 !$% ) # +
, C7 !$% ) # 4 % - #$ 8*4) rF" % ! *Pr898S1 GB G!$% % +
"# - %(# 7. %C! 8*8 !
1 K B& "f3 *f )C ! ! % 0+ - %C#$ < !% ) # 1 KB& "f3 9 )C ! ! % 7 : " !$% "!$ 6# G* ) &9 1 KB& : % %C#$#$ 1 % !%e!$ & G% 3 !;# )( % Y+"3 5: 9898S !$ & 1 K B/9 $ ! ! - %(#D!$ ! 1& # 1 % + d 1 KB4) %y% 1 KB4O-~ ! 7 # 12 " 1+ d 1 KB4 # 1}O- !
#$ q "# ! 48*8,+ 3 : *898wM '!$
'# ! %<% -X #$ % -X #$ ! 2 )(8 ; T8 % * ) !
250
2 K 4 OF &
?
'
W N
P Vb Va
Eu*)( # 5U + ? :9 KB/9 $ ! ! + 7 #$ 5!$
< & 9) ! % - L(2898 87 : ! A% -X1 KBI7_ !$
*) /!% -S1 GB7 !$
/ 53 c 6#% g -~1 n 8=3 "!: 6 c g +
1 KB !%!
53 "#% -S1 n 8 6# <1 KB}( !$ & # 1 % -\1 KBft,C7
%2: e9}Eu*)( # U + ? v +
1 ! 4% -S1 GBx !$
'# 8 ! 9L
9) !% -.1 GBw+XZ, ! ! !:X ;: *8980 '!$
- % 8*8 %2: 9&) 9/- %(# r ! % 423 % ! R1 GB5 d(+ 3 9 : ! 4% - !$
1 KB4*x) #$ 8 L 8 # ) - #$% LC8*8 !$% LC898 y+ Wh+ 9 9
9) !X% - !
1 KB
+ U + c ' g 9 !
'!:X% LC898 51 % 9 ! !$%< # '% -~1 KB
+
+D 9 !
&3 "#S% -\1 n/ 8S9 !$ & *4) % L "# 3/ !
1 KB
+
# 1 % -HG1 K Be N ( !$
<# ! % w
+
:%C# ! 1 % $93 8 "C # ! 2 )(8 +
r898 "#! # ! { % 7 !
# 1 6#!$
1 KB
+
# ! % % !$ & R
*) /!% - !
LC2898 !%G!$
*) /!% - !
1 G Bx w z 6 o } { +
! 8g1 KB/9 $ !$ !7: *898 3 '!$
1 #% !D% - !
;# ! % / t c . g v 5 d @ ! 't b2b 9 d @ 2 W t 5Rv Z- !
1 K B/9 ) #$ !$ "#D!$ 2} % ;!
#$
% 8 7 !$
! ! 1 K B : 98*8w3 r- %(# )( { ! ! % 0+
h32L23# # h b3#! " (]#$&%' ( = % -z #R: "L G% 8*AM !
) # "[8 L 8.9/- %(# r ! % - %(# )( ! ! % 0+M3 G "L %(! / 1 ! 8D9- %C# 4 ! % % - #$ )C % T+ d q %(!$ # 89 "#*)S !$% ) # 4 % %C! )(*L /W1 ! 28 9/- %(# r ! % 0+PZ, %(# "#
?.
. . . . . . . . 8
O
o
o o
o
o o
Eu9)C #$ U +po 19. n 8 % & ! T+tz v({ % !$ w+t3wv2.2{ % !$
+t v o2{ % !$ w+ (d + = 6 !
3 9M # 942) 8 - !!%# 9) /!*)/!$% 1 !$% 3 %(!!$% + W+DZ- !$
"# } 83 8 1 n/ 8 : !$
DB !$ & *) 3 %C# % - !$ & 1 n 8 9 ! 1 WR2 GC$*)( !$ & 823 8|- !
#$ & 823 8 : !$ RL(289 '% - d N9+
+ = !% 1 :
}8*8 !$
1 n 8 % -SLC89 dYN "L 3 " x83 8 w+ Eu*)( # 'U + 'J < T # 9L % !$ : % 1 % ! d *8 ) %C# ! + % ! % 1 % ! 289) %C# !$ +
6#$ # x!
#$ 6 1 % $93 8 ) # " % - % !$ $ ) ( &%: }9}Eu*)( # RU +po/+Z,G- % # % ! $ ) q1& n/ 8w$ % 6#$ !$% 3 % !$ !% - % #D% ! w9G !$ 9) 3 %(# =ts8 - !)"# 9) !) &1 ) 2 %:
v ) 3 "2 X!$
1 n/ 8w # ! ! 2 S% + Z, .2{ % !$ $ !$
2) % 8 8 ! #$ 8 % % % "#$ w+
"#$ - %(#$ ) 71& n/ 8y % M "#$ !$% 3 % & ! !% 2898 ! 9) /! *) 3 %C# C &%: 94Eu*)( # U +po/+ 30+~Z !$
#$ 6!$ % 429< ! . %C! 1 1 #% 1 # !$ !% M D!$
.T89% 2 ! + & .T8* ! 3 "!: " !$ & !$ "# 1 n 8X2 ) % 81& n/ 8S W +}Z942) )u% &899 !$ ) "# 1 n 8' #$ L(289% w+
"# - %(# )u%C!$
6# ! 2 ) 8* B D!$
$3 % # ! 2 ) #$ w+
& $3 % # ! 2 $ N 4C t$t>#/'?+ Tv t># 6 '?+ 6 vv 9 "!$#0t% #@D# 6 %(')%*+ @K+ 6 % v 2 t U + /v d %(# /9 ) !$%'!$ ! 8*8 *) /! *) 3 %(# % - !$
!# 281 n 8/ #$ ! ! 2 dC+
"# - %(# !$ & f # % % "# % !$
+ 3 "P28 % o2{ % !$ f(
%2: [*[Eu*)( # GU +po/+ (+5Z, o{ % ! 4/ !:% 2) % 8 8 ! . #$ % M "#$ % !$ w+ 3 D: 98*8 # 93 * !
"n/!.!:% 3M ! % !:X% 289) %C# !$ 4/ #$ T # *L 2@ ! 8- %C# N /9 ) % & ! % G1 % ! *}4942) +
S#$ T # 9L 289) %(# !$ )(9L 9Eu*)( # SU + ' :X%(# B& : 898y2 ; ( !$% *G1 8 ! +
1 #% 3 8 !$ ! ! # T # 9L + 8*) %C# ! ) :
# & % 42898 % G1 ! "#: ! <899 !$ G ! DB ) 4" (98* # &<9 !$% ! DB % L "# %: )C: R:X% 8% "L !% 3 7! KB " #$ % -03/ !$ & 1 #$% ) # 2G "# + E %(# ? ;d W ? d WR942) : !$ @ #!$ "# 9898* % ;1& n/ 8 )(!$
# T # *L 289) %(# !$ rF "L L "# 8 !$ &% # T # 9L "2898Y+
?
(d + = 6 !
3 9M # 942) 8 - !!%# 9) /!*)/!$% 1 !$% 3 %(!!$% + W+DZ-M< 83 8 1 n/ 8 (.LC89 =% - N9d N ) (9)C< ": 83 8 !% ! %C# * ) !$%D!$
- % 898 %2: 9 ) # 8 / s d
?
d s
?
?
s d
? ?
?
d s
? ?
? t = "! ?
9 v +
U + J7 6!$ "# G9 D 2@ 9LC28 T8C$ % -~823 8T+
+DZ, !$
% x1C$ ) C$9)( !
$ 2 8 23 8 !$% 2898 8 ! u*} F@ *LC8 T 8(T+ Eg9)( #$ U + . = 2@ ! 8 % !$ % G1 % ! d *8 ) %(# ! + (d + % G1 ! ;!
' !$% ) # 2 % -\q)C9L G*4) + W+ =y %y%(!$ }!$
' !% ) # 3/4"L "# )(* ) !$%5#$ % L 48*81 GB Y+ U +DZ ! |-s6 % ! 1 KB&72 xLC8*8 &=* !$
' !$% ) # +
+ J7 6!$ ! ) %y% e1 K B&H3/421 1 89/9&)<1 KB/9 !$ ! + ? + = )( !!
942) M9&) !$
#
% 8 D !!
LC898 &T+ o+ d 1&1 89 % !$ % G1 % ! 89) %(# !$ + Eu9)C #$ U + = !$ 19} )( ! ! % G9 ) !% ) # +
2@ ! 8'289) %(# !$ G !:X% 1(e289) %C# !$ : % 823 8 !
f#$ )C % Mx# %C# * ) !% 1 YON 1M !$! "# MGt, 6 Eg9)( #$ 4U + . v +
N # ! 1C$5"2 !$ & 3&9 # f942) 2 P($9)C2 83 8 o1 n 8P ": 823 8,+ Z, !
C$*)( !4% - !$
823 8 !$
83 8 % -5 9) 3 %(# { 9&) 1 n/ 8} # % M "#$
+ J # 9 ) !
% 1C$ !$
83 8 % - 1 n/ 8} # 2 ) !% !$ & 823 8 % - !
#< 2@ &9LC8 Y8(T+ d $& G!$ ! !!
4 % - !$ & N # ! 1( : 4 1 : ! 83 8 N !$ $% &) H8 N ) !
- % 8*8 %2: 9 )83 8 : "# "! "# 9 PC !% 3 F@ 28> >t ! ' Y?v '<t >' &?v '< t '?70?v '5>t ! ' ?v '5t ' 2v?'
: 5: 98*8 "L
- % 8*8 %2: 9&) 2@ 9LC28 T8($ 5>t ! ' ' )' ?v '6 t '?75' ` ?v '6et t' 9 v + J # * ) !$
% 1C$ !$
823 8 ' )'w2 : 98*803 ) !% !+ =y9 98 # 8* !$
83 8 7f ` : 989803 2 ) !$% ) 4823 8 9 : *89803 ) !$% t$+
#Q# #
"
#*)
2% :W:X 64 G4 # 9> LC # % M ! 1S9 $!
" )( ! ! % 5289) %C# !$ (X
%2: G*GEu*)( # U + +5Z, !$
N # ! !$ 1 !$
< !% ) # % - 2[ 942) % G1 ! w+
5 !$% ) # 2 4" % ! *
o
O
% 48*8(1 KB& X!$% % 2 ;& L *898* G9M ! % 0+ J # 9 ) !$ & % ' !$ 1 !
S !$% ) # 2 %y%C!$
!$%}#$ % L
42898.1 GB Y+AZ,[1 # 9T91 8 ) 2 % - !$
N8 ! "# T f9 !
8C ! 1 ! "# " 3 & "#$ +_Z, % ! 6( ) *G1 8 "L "# 2)(* ) % L 6#4U[ 8 ! % - !
!$% ) # :%(# B #$ C % 3 8* :X 898z+= % 6! 9 ) %C#$ % !% ) # 4 "2[3 %y%(!
A3/ %y%(!$ 9 ) L "# 28 ! * T+gZ, !$
D!$ # 5 ! 1 ) " !$ 1 KB&2 LC8*8 &. # % ! |N <*G1 8* 3/ 6!$ ! 9 )8 % "2804 n 9r GG* 9r79 !
' !$% ) # 2+. "n!X!$
) %y% e1 KB& # "!$ !$ 3/9 ) !
1 G B* $ !$ ! +SZ, !
N - ! !$ 1 !$
*4) )C !$ RM9&) !$
#
% 8 !!
LC8*8 &=3 "!: 6 G1 K B&T+
8C ! !$ 14M !$% "! "# 9 < "!% - % !$ % G1 % ! =* !$ & *4) + & ;# &8 ! =- %C#7# )( % } )( ! ! % 4 #$
%2: }9}Eu9)C #$ U +9d +
= )C
# " # \ ]
# "
! ! % M9&)R) # "8 L 8 !# 93& ! % 42 % ! 9L/ ! % -.1& n/ 8 643 % M "#$ 5 6 )( ! ! % 0+ )( ! ! % " !$% 3 e# N [9 )f9/- %(# r ! % 3 % !G!$ & 1 % - !$
<# )( % '2 !$ & 42 ! " % - #$ )C % T+ ; )( ! ! % }G9) ! 8 % / 8% !$%y% 4/ r898 #$ )C % M )u: 6 !% 3 "# ) : ! 9) 3 %(# 9 ) #$ )C % T+ 3 : *898 T' L "# 8 8*) %C# ! 4.- %(#D#$ )C % 4) #$%2: 9 )&+ q !
% ! *G1 8 89) %(# !$ - %C#G#$ )( % W) #$%2: 9 )&+ Z, ! 58*) %C# ! !$
}#$ )C % G # F@ ! 8*8951 89 ! x "# ) <9 ) % 1 # 6 !$ ! 98 %C!$ * )643 "# ) %(# 1 89 ! tz( &%: 9PEg9)( #$ }U +*d(dv +
289) %C# !$ % ! 89* A*WEg9)( #$ 4U +9d U + <289) %(# !$ "P3 % !$# !$ 43}5*G1 8 *4)
%2: 9 Eu9)C #$ QU +9dW+Z !$ "n G1&8 )/: R: *8980 L 6# *G1 8 1 #$ / " !$ + 5 .A_9@`0E%9 B)( O9 B ;k` n` + 5 j F + 0% ! #!: !$ )!$ & :
% 8 9r) % % "#$ AC % G# )( % 0 + =y* 8*8 !$
1 n 87* !
*4) % %(!' "L
) # "8 L 8 )(!$ & 942) X1 8* ! * !% @ # # 2 ! ) C
%2: 49 Eu9)C #$ U +9dW+ +X "n/!*) 4 !$! G1 ! S4 !$% "# ) / !:% # !X#$ )C % MT+ ! % % - !
'@ # ! X$ ! ,-s !
1 #$ /" !$ ) !$ & "#$ - %C#$ 5!$
6#$ % "# ) +5 "n/*! ) 8*8 !
#$ 6 G@ # ! "n 1 !!
1&1 6# 8 - !@ M # ! # 1&89 !!$ <9 !$% - % # 48*8 "#.# )( % t, 6 Eu*)( # U +9d W+ 3
v + d !=! S ! ) '!$
# " 3 { @ M # ! "2p3 "# ) 9 !$%% 8 # ) 4#$ )C % 0+ :% 3&{ @ # ! 5 !5!$ & 8 %2: 6# 1 #!<% - !
9r) # -s #!$
"# 1 89 ! (< &%: P*PEu9)C #$ rU +9d W+ (+fEu92898* ) # 9&) !$ & "n/! 6# ) 5% 1 "# ! % !
#$ 4* 9 )5 3 { @ M # ! #$ "# ) : !$ }!$
8 # ) #$ )C % 0+ d !! D ! ) 2898 #$ )C % 7 ! -s !$ & 1 #$ % " ! 2 x % -s #$!
"# "# )(* ) %C# 1 89 !$! * )<$ % + G8*) %(# ! 58 % "2898 p3 % # W 8 ! * ) + & !$%#$ % L ts 8 ! v !
e:X KB 3 % # R3 "!: 6 !:X% # !#$ )C % )g
"# )C9 ) !$
G!:X%x# )( % Y+ & 1 2) % T !$
# ! % \u - %C#.!$
3 % & # <3 "!:X " !
!:X%7# )( % Y+SZ !$ u289) %(# !$ )!
# DB ) 3 "!: " !:X%'#$ )C % M(S
%2: G9 Eu9)C #$ U +*d ? + ' # w+
D ) " (9893 7# 1 #$ !$ 9 ) !
1 "# ) # tHt W . d2v tHW . dv$v (
%2: e*4Eu9)C #$ U +9d ? + 30+ & !$# ) ! 4% - !
) 3 "!: " e1 % * ! 9 # )( % + ' e1 % 9 ! 9 #$ )C % + 6 7)(*L e3/ !$
23 % 89 ! mQ "# % -\) # "G8 L 8 t ' v 9 %*7gt>#'?+ Tv@D7utB# '?+ v % 6 6
od
O O
tz v
t3wv
t 2v
t v
t v
t-Tv
ts)v
t v
tsv
Eu*)( # 4U +*d _C7 !% ) # %y%(! 9&)e1 #% $RM9&)e1 KB/9 $ !$
#
% 8 9 +9d ) "L *> 9 ? + t,yv # *)(9M8g942) +'t3
vhC7 !$% ) # 2 - %(# *4) *Pt,yv ) 1 KB&C9 U ) 1 GB F- !$ 6# 1 KB/9 $ ! ! 9 d .+5t 2vC7 !% ) # F- !$ 6#% %y%(! 9&) ) 1 GB G9 ? ) 1 KB&F- ! "# 1 KB/9 $ ! ! 9 'y+
#$ 6 %y%C!$ * )y ) 1 GB 9 d(d ) 1 KB&"- !$ "# 1 KB/9 ! ! 9 +t-Yv )( % =- #% _1 }d t +9 + v +7ts)v )( % - #$% 1 ,Wxt +9+9dCd;oyv +t v )( % - #$% 1 U td(do+9+ W U v +tv )C % M - #$% 1 }tHW U +*p+ W ?(? v +
oYW
O
R1
R2
P(R) = false
R
R4 R3
(a)
R1
R2
P(R1 U R2) = true
Eu*)( #
(a)
(b)
(c) (d)
Eg9)( #$ U +*d J7 % !$# ! % % -\1 8* ! 2 x 6# ) 8*) %C# ! +
O O
(d + &1 89 !# )( % 3+ * !% - % # # !D#$ )( % t @ # # 2 ! vXO- T t /! a CtN+'v9 57 ! b C+ + " # ) / !:% # !# )( % .+ D 3+ 6 O- T t /! a CtN+& 3+ 6 v9 a C+ U + !% 1 :
4 % -s #$!
"# "# )(* )<2 e1 89 !$! * )5 # 1 % $93 8 + Eu*)( # U +9d U 1 8* ! 2 d(+ " # ) '!:%<# )( % O-
oU
6# ) d *8 ) %C# ! +
t % # v d 6 6 ;t ut ' 6 v :
6#$ D !$ & 1 "# 9 6!$ "#S% - #$ )( % 3 + ) 6 !
1 "# * "!$ 6#=% - $# () % 3+ 6 + + "# ) '#$ )( % O t % & # v %C! 280 53 "#% -.1 % 9 ! % !
3 %(# "# d
Eu*)( # U +9d I ) % T ! d *8 ) %C# ! +
' ) $ Y8 # : GO- !
t ' vS3 8 %2: % !$
# &% 8
+ t ' v9 d |%C- !$
"t # : ' v
': / $ % - !$ & ;: &% 8 3 % & # e !$
& % - :X / % -S289803 % & # 41 % 9 ! Y+ t ^ T ! + v 9 t ' v
8*) %(# ! % ! 89* 9 Eu9)C #$ U +*d &+ :%P
# ! 6x #$
6#$ = J CJ% 5 7A+) +
<:X / & # ! D !# *) /! - %C#$: # w+Z- !
R# ! %G% - : x3 % # 1 % * ! !$%!
4!$%C! 8/ 53 "#'% -3 % # P1 % * ! R3 6!:X " P2 !:X% # !R# )( % <3 % L % !$ $
% %8 )y!$
!:%'#$ )( % #$ "# ) w+ %2:X L "*# )C!$ & # ! !$ & !%R% L "# "# ) # )( % Y+
"# - %(# )(:X " R71 ) % Y ! 7
# ! % )": %
X#$ 8 ! ! #$ )( % 0+
'# 8 ! =- %C#7# )( % } )C ! ! % 4 #
%2: e*}Eu9)C #$ U +*;d o/+ , Z, !$ "!$ &% :X ) # "x8 L 8 !$# 93 ! % % - #$ )C % M !% T O- !$
r
% 8 43 6# ) w+ "!$ &% r1 #$% 33&989 ! 7*xM ! #$ +3 % % "#!:%< /1 %C!$
D 6 +
"# #$ !:%<#$ )( % T+ 6
"# % R#$ )( % 0+ 3 : 98*8g($ !$ ! 9 # }#$ )C % )!
) # "e8 L 8 / !# *3 ! % "}3 21 1 #%n 9r !$ r3/ !$# 93 ! % 0+ ! ) O-gR1& n/ 8 8 !$ 5 !# % )y!$ & 1 #$% 33&989 ! ! ! ! ( ) # "G8 L 8 j )C9L 43/
o
A
.
O
. B
+
R2
R1
+
+ +
+
+
+ +
+
+ +
+ +
+
+
+ +
+
+
+
8
+
+
+
+
+ +
+
+ +
+
+
Eu*)( # 5U +9d ? )( % f "# )(9&)9 ) ) % Y ! 8*) %(# ! +
zt v t 3wv t 2v Eu9)C #$ U +*d;o$7tz v +
3 %(!! 8 *4) +ts3wv + 6 )( ! ! % +t 2v + d - ! "## )( % 4 "# )(9&) +
o?
O O
R2
R1
m2
m1 _ X1
_ X2
σ1
σ2
Eu*)( # RU +9d'J )C % x "# )C9 )* ) 89
%y% # ! % 289) %(# !$ +
d
Y
'
:
"# #4 !
) # "48 L 8
!$ & ! 2 # L/ ! % 0+ d $ 4!$ !G# )( % + % ! *, 1 n/ 8 ) # #$ # 1 ! 9L 89 !$
p ! 2 # L/ ! % % - #$ )C % + (<
%2: p*[Eg9)( #$ 4U +9d ' + d 8 % ( !$ !R!$ & ) # F 8 L 8D # 9 1 !% - # %C!$
6# +
!
1 #$% 33&989 ! % - # )( % :+ "L* )G) # "8 L 8 >t #/'?# 6 ' 2 2 2/'?# vS)(*L G3/5
t dY
v
t U +? v 2
9 9 8 # 8* ) :X 6 % G1 !
1 #% 323 98* ! 7- %(##$ )C % :+ 6 ) # )( % - % 8*8 %2:
qtB# o '?# o 6 ' 2 2 2 '?# o
v 9 t
d
Y 6
d
Y
! v
v
+ 9 + +
o
6 (
t U +poyv t U + 'Cv
oYo
O
%2: ) !$ & 1 #$% 3M3 *89 ! .- %(# 7 2 6 # )(9L eC
Tv
d v ft d v t U + . v v9 t Y Y 6 d v o
9
v 9
8*
%y% # ! %
t Tv 9 t Yv o 9 < < t 6 v t v t 6 v
'#$ )C % 7 #$ "# ) 5O- #
'+
) 5#' i \^] ) b % )( % P# T) # 1 Gt d v # L "# } -s 8$ ! !$# ! # 7- %(#<# )( % f
# " #
"# )C9 )}289) % { # !$ rT+Z, ! ) # 1 ) # )( % D # <#$ 1 #$ ! 4(7 % 2 # !#$ )( % D #$ % !$ 3/fP # 3 "!: 6 !
% Y+ % 6# e9G1&8 *4) % ! 9 ) % -NL # )( % 5dE' $' U ' I' ? (R
%2: [9Eu*)( # GU +9d ./+ /+
1& n/ 8 %(#$# 1 % 9&) !$% # )( % #$ %(!$ A3} ! #$ )( % 4 53 "# Y+ d $ D!$ ! % 1 # %" ! !% "# ) 7# )( % Y+Eu # !*) #$ )( % 5 U #$ "# ) w+
*4) <: ! 1 ! #$ )C % ;R &%: 9PEu*)( # GU +9d/.+ 3+ "n/!'#$ )C % U D "# ) : ! #$ )C % 4C;
%2: 9fEu*)( # 5U +*d .+ (+'Eu*8*89 )#$ )C % rH "# ) : !$ #$ )( % d(+ Z !$ ;1 #% $ ).!$
#$ )C % 83 8R #$ &) A5 8 ! 91&8 R! 9 T+4E %(# 9 ! G
83 8 % 1 n 8=3 8 % )C9 ) !%<#$ )C % <\N # ! ) !$%5UR!
!$% ) rN2898* !% d(+SZ, !$ "n G1&8 !$ & 9r) L "# 442898 ) # 4#$ )( % % ! % -=- 6: 1 n 8T+ !) ! %C! % G % !%
"L 5!$
% $2 % -D1& n/ 89 # f#$ )C % 0+4Z, !$ "( )u!
)C9 ) % -D83 8 # 2@ & #$ %(#$ % L "#$ & w+ & "#$ - %C#$ ) * ! % - )C9 ) #$ )C % x83 8 % - # 1 n 8 # 9 ) !$ & "# )C9 ) ) :X : 98*8g1 1&89 !$
6# ) '% 1 6# ! % % f d +
d $ %(##$ 1 % * ) !$% Eu9)C #$ U +*d ./+ { # &%: 595Eg9)( #$ DU +*d ./+ { + 3
#$ )( % 'u 6# ) : ! !
#$ )( % U )y!$
% '9 !
d # % L ) !$
# "D #$ # ! !%<#$ !!$ & ": *4) (
%2: e*eEg9)( #$ U +*d .+ -+SZ ! 8 %G#$ %(# !$ !!
1 n 8u83 8 U } #$ < 2@ 9LC28 ! +
6# ) '% 1 6# ! % 7- %(#!
9r)
%2: 9}Eu9)C #$ QU +*d .+ G #
%2: e9 U +*d .+ : ! e!$ & ; F@ *LC8 ! 83 8D !$
9& ! 8 9r)
%2: [*fEu9)C #$ 5U +9/d .+ "2A3 !% ) "!!
NM8S )( ! x*4) 9G*8 #D!$%4% &%: }9}Eu*)( # RU +9/d .+
+
( ( 3#(
#
# " # \^]
# "
d(+
&3 "#% - !$
# &% 8 &q p* !
289) %C# !$ + % 89) %(# !$ 4R }% %C#!:X% !
#$
% 8% ) 3& !%(!
"# L "# 8 !
#$
% 8 Y+ +
5%(# "#'% - "# )(9&) L 6# 49G1 %C#$! 2 ! +
N28 )( ! ! % : 98*8 1
"L/98* % !$ & ;%C# 6# 9 : G# )( % D # "# ) w+ U + 6 e )( ! ! % 48 % 9 1 %C#$! ! +DZ- !$
)( ! ! % !% ! #$!: !$ # ( % 23 8 ) !
#$ )C % ) #$%2: 9 ) : *898/9G1 #% L ! -s #!$
"# 3* ) !$ & 1 5 r ! .*- %(# 4 ! %
0 O O
2
2
2
2
4
2
2
2
2
3
1
1
2
2
4
1
1
2
2
3
1
1
2
4
4
1
1
2
3
3
2
2
2
4
3
2
2
2
3
3
5
5
5
4
3
5
5
5
3
3
4 -> 3
3 -> 2
(b)
(a)
2
2
2
2
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
2
2
2
2
1
1
1
1
1
5
5
5
2
2
5
5
5
1
1
2 -> 1
(c) (d)
1
2
3
4
1
2
4 -> 3
3 -> 2 3
5
5 (f)
(e)
1
2
1 2 -> 1
5 (g)
5
Eg9)( #$ U +*d . )( % } # YG) # 1 't d v + (h)
o4'
o.
O
% - $# )( % T+ %2:X L "#*) O- !
* ! 28. )( ! ! % 7L "# }1 %y%(#*)g!$
5#$ )( % A) #$%2: 9&) : *898 %C! *G1 #% L ! + d :X R "L $2 )w ) 6!$ ! % e2 #$ )C % )C ! ! % #$ % G1 8 ! # 1 #% Y+ Z,G1 # 9 T*1 8 )(: 6 "! "# G* #$ )( % \- #% !
/) % - !$
% 3 !) 2 ) =- #$% # )( % Y+ %2: L "*# )y!$ & "#$ # L "# 8 "# S3 "!: " !
'!:%
3 % & # % 3 ! 29 3/ /) "! ! % 4 #$ %(! $ # 989 T8 % w+ + ) "! ! % % ! 8*8 % "8z + )( % } )C ! ! % G %C#$ )C8 % 38z+ U + )( % f )( ! ! % " "23 *G1 #$% L G3/e9 ) 8 ! *{,1 !$# 809r) Rt + )
+ % 8 %(# 9 { 2) v )
%2: L "#X!$
6#$ %(! 5 # LC ! 2) 949 )55 8 ! 9{z1 !# 8*4) 9 ) 6!$ ! % 0+
+
1 % ! % % - <3 % & # Pt ) vX8 % "289*> x* /) "!$ ! % ) 3 ! %C! $$ # *89 * # )( % } )( ! ! % 0+
Q
\ #H # . ]# )
](b# ] # # ( ( '
" # '(
D
)C !$ 49 !$%5#$ )C % )0: 6" "! "# 9 '!$ & ) "% "!$# "2801 #$% 1 "#$! <% #$ )( % : "2[3 A9 !$
5% 3 !;# % )( ! % 0+}Z !$ R ! % )u: 5: 98*8 # 93 - ": 9 1 %C#$! ! 1 #$% 1 6#$! T+D3 e: 98*8C$& 4!$ !!
e# )( % P #$ 1 #$ ! A3/P 3 9M # 9r) ) tB#1'?+Mv + " N d #$ %(# 9> <% - !$
<# )( % 7 !$%C! 8~ 53 "#D% -X1 n/ 8 % Y 1 e3 !$
#$ )C % +RZ ! )C9L G3/ B
09 t U +9d v Bt #-' +Mv
! % # N'1 #$
! !
!$ # %8 % <".! 89% % !$-X &
1N
N # !
)C9L 4C
/ /
! "#.% - 4 # 3 # !# # 5 21 #$ )( % ) 2 < ! " 3 #$ )C % 0+4 !$#$% ) t #1 ' + vX)C9L G3/ / B / # tB#-' +Mv ' 9 #" t U +9dCdv
B / + >t #1'?+ v / + 9 2 t U +9d v
% !)
) ) !$ & % R % ! )
9 B # Bt #1'?+Mv / / 9 B + Bt #1'?+Mv / /
6
) 6)
#$ #$ 1 ! 9L 8* t U +9d U v t U +9d v
2
4
2D O
o
B # 6 >t #1'?+ v / / B 6 9 + 6 >t #1'?+ v
6 9
t U +9d ? v t U +9do v
/ /
'N
1 6# 9 "!$ "#0% -g #$ )( % S % -0 ! .3 (% # "# 1 n/ 8T+ d 1 n/ 8 : < (S ! 8 ( ! % 1 n/ 8w*4 ! 9) 3 %(#
%y% x- #$% !$
3# / ) #% G$"8*8 4R3 %(# "# 1 n/ 8,+ I ' % G1# ! $ ) , ) $ N 4(- % 8*8 %2:
,09
t U +9d'(v :
6#$ P !$
# % - #$ )C % ) W !
1 "# 9 "! "#w% - !$ & #$ )( % 0+ & % ! % G1M ! # )( % 4XT # T8 )C: !$ % G1# ! $ F@ 28 !% d
#$ % -SY # Y8 D% - # /95+ Y + 6 2 !
1 6# 9 "!$ "# Y +;v +
% G1# ! $ % -S5 @ #$ 21 + N
%C# ! ! % ) )w% -D #$ )( % ""f3 % 1 !$ x3/ "! "# 9 * ) !$
n % R % e % !% -* "#! 4t, " Eu*)( # 5U +9d v +
- % 898 %2: * ) "n 1 #$ % 1 9 P\P >t #D9& @D+ % . )v 6 >t #1'?+ v T # T + t U +9/d . v Y 6 '
Z ! " 2x3
%2: [tz " /n "# T v ! ! G* 9 >T* )3 % L ; 6n 1 # $ % # &8 ! * !% 9 9
:
6#$
% 9
t U +9d v
' 6 . Bt !@ F v 6 !H@ ' . t>!H@ F v 6 6 K
t U + v
)
! 9 9
9
P\P # 6 >t #1'?+ v T # T + ' P\P # + >t #1'?+ v T # T + ' P\P +3 6 t>#1'? + v T #! T +4 '
# 9 #,@ # ) + 9 +G@ + +SE (% #!$ & / #$ "! ! 9 # 6 9 #+ 9 + 6
t U + /dv t U + v t U + U v % r9 ) ! ' ) ' #$ )C9L 4C - % 898 %: / tB#1'?+Mv @ # 6 ' t U + v t>#1'?+ v1@ # +I ' t U + ? v tB#-' M+ v @ + 6 2 t U + o v
'
O
(X,Y) r (Xo, Yo) s θ
θ
ρ
Eu*)( # RU +9d J7 "!$ 6# G* 9 ) %C# ! ! % % -\ # 3 !# # #$ )( % 0+
k 3# ] # ( #( d(+D ! 899 !$
#-+, 19 289) %C# !$ 9 ) 5 + 7%-J7a+pJ.% + + J7 L 289) %C# !$ - %(# "!$ "# G9&9 ) 2@ 9LC28 T8( Y+ U + J7 6# 9L 2@ M ! % / U + ? )U + o ) 2 U + 'y+
+ J7 6!$ "# G9 '!
% G1 ! ! % 8 % G1 8 "n ! % -H 2@ ! 8~ #$ T # *L % !$ % G{ 1 % ! 8*) %C# ! 4Y+ ? + &%: !$ !!$
' 2@ ! % % -X<899
%2: }9}Eu9)C #$ U +9d q)(*L 43 #D9 @D+ % . ) 9 2 t U + 3'(v S "# O-s !$ !!$ & Y8 % ! 1 % 9 !% !
899 7!%
'%(# 9)C94X ! t @&)S9& '/. ) % ! v ) !
1 # 2 "!$# F@ ! % G- %(# <1 % 9 ! >t #! '?+Tv % !$ & 8*9 )(*L G3/5 #! 9 @ )S* . b % ' t U + . v + 9.&) % . b * ' t U + v :
6#$ b (D
%2: e*}Eu9)C #$ U +* d /+ o+
! ) ) 3 "!:X " 4<1 % 9 ! >t #1'?+ vS2 !
89* )(*L G3/ t U +U v 6 9 >t # @D#!Yv 6 . >t + @D+ Tv 6 2 &3 ! ! !$ #!2 M+ - #$% 2@ M ! % U + .5 U + <9 !
3 % L ; F@ ! % ) 2 "# { ! ! 7!
# 8 ! 2 !X 2@ M ! % : !$ 5#$ 1 !!% b ) 2 4 "!X!$
D 2@ ! % !$% > 6#$% +
%2: !$ ! %2: b )C9L G3/ t U + U dv b 9 # % . +* 2
'yd
'y+ &3 ! ! !$ U + U d'9 2@ ! % M U + .2 U + ) 4 &%: !$ ! @D+ % ! . )v 6 2 6 9 tB#79 .+ &%: !$ ! "# ! ! 9 ) 2@ ! % U +9d . : !$ <#$ 1 !.!% );2 2@ M ! * ) !$
# &8 !.!% > "#% # 8 ! /
Rt #7 9@ + % . )v9 ' t U +U v :
6#$ t #1 ' + vS !$
!$# % ) # +
+FN9 ),# 9 #,@ # ) + 9 +G@ + ) &%: !$ ! 9 2@ ! % U +*d .R %2: )(9L G3 9 !9 6G@ * % . % 86 ' t U + UCU v :
6#$ ! ) ) #$ C N G* 2@ ! % U + d U + U + d x
%2: !$ ! "228 % 3 :# !$! C 9 d Bt !G. "v @ d Bt !G@ "v % H@ d 9 2 t U + U v
d + "# ! ! * ) F@ ! % U + U : !$ G# 1 !=!% R 2 2@ M ! * ) !
# 8 !S!$% > "#% ) &%: ! ! ! 2 9 !@ ' t U + CU ? v
) L "# |-s 2@ M ! % U +*d
5 U + +
'
O
' #
"!
,Z ! 21 !$ 6#;:X <: 98*8 T; L "# 8 ! @ - %(#'#$ 1 #$ ! 9&) !$
1 G% - 3 % & # # )( % 9r< )C !$ <942) + & '#$ 1 #$ ! ! % #$ '!$
23 !# ! % % - ) #$ )( % 9}53 % 8*- %(# ): % 4: 98*803 M -s 80* % 3 !#$ % )C ! % + "#$ ) : ': 98*8w429 8* 3 8*9 ) : ! ) #% 1 * ) % 1 "# ! % Y+E %(# 9 ! 2 )/!$
) #$% 1 9&) % - /) 1 % * ! 9 !$% !$# *) /! 89* ) T # T8 )2 898*91 )( 6! (+gE %(#S#$ 1 #$ ! 9&) #$ )C % : : 98*8 T !$
28 n !# 2- %C# ) 1/ # G ) @ !#$ " T+.E %C#=# 1 # ! * )3 % & # : D: 98*8 T !
% ) G!# 2- %C# ) ) "# 289*> % ) P!$# 2- %C# ) 9 % ) P 1 53 "# + %y% W 1 4#$ 1 #$ ! ! % &% 8 x3 % G1M ! ) % G1 8 6!$ ) &53 9)C % M ) e ! 3 8 +
" %
)
'(
'
% ) R!# M- %(# "3 !%7# 1 # ! 1 8 T # L )" + ) + ) 8*9 ) T # T8 ) R1 # 23 % 8C ) NM G3r289 ! 68 "n 1 #$ $ % Y+
"# #$ % ! % 3 "!:X " !
% ) 4!# M- %(# !$ & 8 ( ! @ M #$ N ! +Z, !$ & 8 ( ! @ M #$ H 6!$
% ) % L "# { % !# 29 ! & ! % - 2@ ! % MH !$% % G1 ! 7!
% 8* ! % 0+ & "#$ - %C#$ )/!$
/ 53 6#=% - F@ ! % = %C#$ ! !$ & / 53 "# % -X %2: Y+RZ, !
% &) f!$# 2- %C# ) f "# { % M !$# * ! !$ 7 !$% % 1 !$ '!
% 89 ! % 0+
"# - %(# )w!
&3 "#% - 2@ ! % 7D8 !$ 2 !
/ 3 "#D% -X %2: Y+
"# # 5 8 ! 91 8 % 89 ! % q* ! 6( +oZ,P-z !) 9 4/ "C ) * % ) !# 2- %C# 9&)(8 % !# * ! M !$% % G1& !$ 898S1 % *3 8 % 89 ! % MT+ !R: " % M !$# * ! L %(!$ H- %(# 6!7% -S1 % $93 8 % 89 ! % T+
% 89 ! % : e ( !$
4 %(# ! % -SL %C!$ D 8 ! w+
"#$ !$ # G1 % $93 *89 ! ) 9 : % 4!
53 "#% - % !# * ! H 2@ 8 !%!
53 "#% -S / %2: Y+ = "!
% < 6898 !$
t D % G1 8*9 ) % M vS "!$
%
+
r9 ! 1* #$ '!$
- % 898 %2: * ) ! d(+ D % G8*G 8 !!$ & 9 *< / 53 6#% - % !# * ! !%< ! 94 !$ !
% 89 ! % + +DEu* !
R 6#$#$%C# 3 "!:X " !$
! 94 !$ % 8* ! % f2 8*"8 ! 1 % 9 ! Y+Z- !$
"#$#%(# 8 ! !$
'!$% 8 "# )!
@ & *! )/ 8 ) %5!$% t$d2v +
;=>< ?A@B@DCFEHGJILK"MNK"OQPSRLK"R
#U
#
4
5
3 5
y
4 3 2
c
2 1
1
x
m
Eu*)( # +*d !Eg !$! 9 )<8*9 9 ) $!
% ) !# M- %(# +tz v % * ! H*41 +;ts3wv 9 9 1# %C#$# 1 % 9 ) !$% 1 % 9 ! 9G1# +
89* =* ! "# ! ! <9&)(8 1 % * ! + (a)
(b)
!#"$&% '$)(+* ,-/.0#1 2243 .51768-/9:3;9<17=>=@?A243B.50#3 6C?!DC0.5E)FG-A2HI6CEJK.56'LA..0#3;3NMO?AFP.51>6C-/6PH:FQ2&.5ERFP17D80S.=>17-#3T.6.0#3 3 D83TUV6817- .R2XWY0#3T3PM?AFP.51768-Z6GH:F;=>17-#31[2DC1>\3]-Z^S_ ! `aZ;b Pc dfe W7gPh 9<0#3]E3 FG- FPE53:.50#3:24=>6CUA3
#
S q : gCW ?AFP-S.17]3T.50!3UtFGERFPJQ3].3]E<2&UAF 3 ~ c]p]p]p]pip]pwc c) ~ c]p]pip]p]p]pXcR W W{#6CE3PF 0Q3 DC3BUV6817- . d@cR h 6 HI68E dy `a ~ cR c) bsb h 6 q`md h ob ) PcR ` GcR b g p SW{l1>- .50#3T=>6 FG=@JZFPS1>JZF17-Z.50!3UtFGERFPJQ3].3]E<2&UAF 3kW { 17DC?!E53 e W ! 68?#DC0.5ERFP-A2 HI68E5J FG=>DC68E517.0#J HI68ELA.5.17-#D24.ERFG1>DC0 .<=71>-#3P2wW
Y p
Θ
{l1>DC?#E3 e W ! 6C= FPEHI6CEJ 6GH3NMO?AFP.51>6C-Z6GH
24.ERFG1>DC0 .q=>17-#3kW X
gCW ?AFP-S.17]3T.50!3UtFGERFPJQ3].3]E<2&UAF 3 ~ c]p]p]pip]p]pXc c ~!c]p]p]pXp]p]p]c W W{#6CE3PF 0Q3 DC3BUV6817- . d@cR h 6 ` 62A b 241>- ) c @` c Sb g8W SW{l1>- .50#3T=>6 FG=@JZFPS1>JZF17-Z.50!3UtFGERFPJQ3].3]E<2&UAF 3kW { 17DC?!E53 e W e! 6C?#D80Z.5ERFP-A2 HI68E5J FG=>DC68E517.0#J ?A2&17-#DrUA6C=[FGE
#
gCW ?AFP-S.17]3T.50!3UtFGERFPJQ3].3]E<2&UAF 3 ~ c]p]p]picR cR ~ cip]p]pXcR c ~#cip]p]pXc yp W{#6CE3PF 0Q3 DC3BUV6817- . d@cR h 6 HI68E dy <`a ~ cR cR bsb h HI68E dy <`a | ~ cR | cR | jbzb h 6 dr h b dy h ` W cR c ` cR c #b g p SW{l1>- .50#3T=>6 FG=@JZFPS1>JZF17-Z.50!3UtFGERFPJQ3].3]E<2&UAF 3kW {l17D8?#E53 e W ! 68?#DC0.5E)FG-A2HI6CE5J FP=7DC68E51>.50#J HI68E+Lt.5.51>-#D >1 E =>3W gCW ?AFP-S.17]3T.50!3UtFGERFPJQ3].3]E<2&UAF 3 ~ c]p]p]picR cR ~ cip]p]pXcR c ~#cip]p]pXc yp W{#6CE3PF 0Q3 DC3BUV6817- . d@cR h 6 {#6CE d ` ~ c c bsb h q` 62# q` ; 241>- PcR ]c ` ]cR Pc #b g p SW{l1>- .50#3T=>6 FG=@JZFPS1>JZF17-Z.50!3UtFGERFPJQ3].3]E<2&UAF 3kW {l1>DC?#E3 e W 1>E =>3W
!
6C?#D80.5E)FG-A2HI6CEJFG=7D86CE17.50!J HI68E Lt.5.51>-#D 71 E =73'?t2417-!D UA68= FGETHI6CEJ 6PH<3PM?AFG.1768-6PHnF
$& &*
Y0#3T3PM?AFG.1768- 6PH:F 71 E =73 ]3 - .53]E3 PF . dPcR h9<17.0 E)F >1 ?A2 1 2DC1>\3]-Q^ _ dy h | b dT h | | `Sp
! dfe Wh
,-s.0#1 2 F824393Z0AF]\3Z.50#E3]3/?#- -#6P9<-A2 !]cPc WaY0#3iE53wHI68E53Z.50#3ZUAFPERFPJQ3].53iEr24UAF 3/1[2.0#E53] 3 1>JQ3]-A2&176C-tFG=WY0#3rFP=7D86CE51>.50#J HI68EqLA.5.17-#D 17E =73T?A2&17-#D 6C?#D80.5ERFP-A2 HI68E5J 1 2qD817\3]-17-{ 17DC?!E53 e W W Y0#3TDCE)F 1>3]- .FG-#D8=73T17-SHI68E5JZFP.51>6C- FP-Z^V3T?A2&3 .56'E3 ? 3n.50#3 68JQU#?#.)FG.51>6C-AFP= 68JQU#=>3]S1>.&_;17-.50#1[2 F8243BFG=[246#W -#68.50#3iE
dfe W e h fd e W h
9<0#3]E3B;1 2.50!3DCE)F 1>3]-S.FP-#DC=>3WY0#3B241>JQU#=>1 LA3 FG=>DC68E517.0#J HI68ELA.5.17-#DrF 17E =731 2D817\3]-17-Z{l1>DC?#E3 eW W
##
: :
) '( ' 6'HyFGE)V.0#3 68?#DC0.5E)FG-A2HI6CE5J 0AFC2<^A3]3]-?A243 .56 3].3 .240tFGUA3'9<0#1 0 FG-^A3;3] U#E53N25243 FG-tFG=7_ . 1 FG=7=>_W 6P93]\3]E)VJ FG- _/2&0AFGUA3P2T17-.0#3E3PFG=96CE= " FG-!-#6C.T^A33iSU#E3P252&3 FG-tFG=7_ .51 FG=>=7_WB,-.0#62&3 F 8243P2$)S.50!3qD83]-#3]E)FG=71>]3 6C?!DC0Q.ERFG-t2 HI6CEJ FG-Q^A33]JU#=76P_3 .56 3].53 .FP-S_FGE^#17.ERFPE5_r240tFGUA3W:Y0#3 17- HI6CE5J FG.51>6C- 68-S.)FG1>-#3 17-'.50!3q3PM?AFP.51768-6PHFT240AFPUV3 FG-r^A3 FPU#.5?!E53 17-F.)FG^#=>3 FG=>=73 ( +; YlFP^#=73kW Y0#3QLAE)24.r24.3]Us1>-.50!3 D83]-#3]E)FG=>17]3 6C?#D80s.ERFG-t2 HI6CEJ 1 2;.6 3]\3]=768U.50!1 2 +; YlFP^#=73W{ 17ER2&.;.0#3 3]- .5E6C1 6GH.0#3T6C^ 3 .<1 2 3].3]E5J17-#3 F82HI68=7=>6G92 ! // ~ // ~ dy@cR h ` dfe W h dy c) h // ~ // ~ dy c) h ` dfe W # h d@cR h c 9<0#3]E3 d@cR h1 2
#3# ) # .#
" %
C6 .0#3]E59<1[243 #e W W qFOh:3] 24? .*)C 0HI6CE:.50A3PFPF . ! 0r3 DC3nUV6817- . yd )c h )O.0#3\3 .56CE ` d 7c) h 1[2 ]3 .53]EJQ17-!3 Qd F82240!6G9<-Z1>-Q{l1>DC?#E3 `ab dfe W h `ab dfe W7g h Y0#3Z17-SHI68E5JZFP.51>6C-FG^A6C?#.r.50!3 \3 .6CER2T1 2 6C=>=73 .3 17-.0#3 Y FG^#=>3 d FC2'2&0#6P9<-17-{l1>DC?#E3 e W # W ^ h9<0#1 0r1 217- 3]S3 ^S_r.50#3DCE)F 1>3]- .
!
#"
$
'
&%
'
' '
#
g
g
y’
φ x’
(x,y)
g
g " " " " g " g "
"
(xc , yc )
g
g
"
g "
d FOh
d^ h {l1>DC?#E3 e W # ! 3]-!3]ERFP=717i3 6C?#D80.5E)FG-A2HI6CE5J W d Fh - FGE^#17.ERFGE_240AFPUV3'9<1>.50 3]- .5E5681 FG. d cR 4hRW Y0#3'.)FG-#D83]-S.nFG-!DC=73rFP.UA6C1>-S. d@cR h1[2 ) FP- FP- FGE3;E53N24UA3 .17\3]=>_.0#3 1[24.)FG- 3'1>- FP- 17E3 .176C-t2jHIE56CJ d@cR hUV6817- .q.6.0#3 3]-S.E5681 6GH.0#3T6C^ 3 .]W d ^ h Y FG^!=73W
Cg W ?AFP-S.17]3T.50!3UtFGERFPJQ3].3]E<2&UAF 3 ~ c]p]p]pXp]p]pXcR cR ~ c]pip]pwpip]p]cR p SW{#6CE3PF 0Q3 DC3BUV6817- . d@cR h 6 68JQU#?#.3 dy@cR h HI68Eq3PF 0Z.)FG^#=>33i-S.E5_'HI6CE 6 `a;b ` b c) @` cR #b g p SW{l1>- .50#3T=>6 FG=@JZFPS1>JZF17-Z.50!3UtFGERFPJQ3].3]E<2&UAF 3kW "
{l1>DC?#E3 e W ! 3]-!3]ERFP=717i3 6C?#D80/.5E)FG-A2HI6CEJKFP=7D86CE51>.50#J W
dfe >W g]h fd e >W g e h
#
O j 1>JQ17=[FGE5=>_ )C.0#3B2 FP=73 GF - 5E 68.RFP.53 \ 3]E)241768-Z6GH d cR h1[2DC1>\3]-Q^ _ ! ` d 6k2# b 241>-Oh ` d 2&17- b 6k2Vh ?#^t24.51>.5?#.17-#D'.0#3BFG^A6P\3;3PM?AFP.51768-A217-Z3PM?AFP.51768-A2 e W Ie W>g 9:3D83]. ! ` b kd 62! b 2417-h ` b d5n 241>- b 62AOh q6P9 )C1 H .0#3<3PM?AFG.1768-A2 e W>g] fe W7g e FGE3<E53]U#=[F 3 ^S_T.50!3FG^A6P\3<3PMO?tFG.51>6C-A21>-'.50#3
'
'
dfe 7W g # h fd e 7W g Oh #
dfe 7W g Oh fd e W h 68?#DC0 FP-s^A3 #
"
%
0AFP17- 6 3/1[2'F\3]E5_241>JQU#=>3Q.53 0#-#1[MO?!3HI6CE'E3]U#E53N243]- .51>-#Dv240AFPUA36GH 68-S.6C?#EiW ,- 0AFP17- 6 3 3PF 0 17E53 .53 =>17-#3243iDCJQ3]- .53 1[2F8252&17DC-!3 F 6 3WY9:6/UA62241>^#=73 6 3P2'FGE3Z240!6G9<-1>-{l1>DC?#E3 e W SW F ^@W ,-z# {l17D8?#E53 e W WF.50#3 1>E53 .51768-A2'FGE3M?AFG- .51>]3 1>-S.6 HI68?#ErUV6k252&17^#=>3 17E53 .51>6C-A2 ! g @FP- 3]D8E53]3N2wW
"
"
2 3
1
2
0
1
0
4
5
3
7 6
(a)
0
(b)
0
1 0
chain code
3
001003333212322111
0
1
3
1 3
1 2
1
2
first difference 3 0 1 3 0 3 0 0 0 3 3 1 1 3 0 3 0 0
3
2
shape number 0 0 0 3 3 1 1 3 0 3 0 0 3 0 1 3 0 3
3 2
{l1>DC?#E3 e W ! 0AFPUA3Q-S?!J^A3]EiW d Fh d ^ h Y96/UA6k25241>^#=73 A0 FG1>- 6 P3 2XW d h 0 FPUV3B-S?!J^A3]E:6GH 6C- .568?#E2&0#6P9<-/1>- d h)W 6 3kW d h A (c)
(d)
68-S.6C?#ET9<17.0F t0 FG17-
_SE)FGJQ1 1 2q\3iE5_/?t243wHI?#= FP.RF24.5E? .?#E53'HI6CETE53iU#E53P2&3]- .517-!DQ17JZFPDC3'E3]DC1>6C-A2XW _SE)FGJQ1 1[2 ^!?#17=>.^ _ ?A2&17-#DBJ?#=>.51>U#=73 6CU#1>3P2j6PH.0#317JZFPDC3WjF 0=73]\3]=!17-Q.0#3U _SE)FGJQ1 1 2 6GH.50#3T2&17]36GH .0#3U#E3]\ 176C?t2 =73i\3]=W Y0#3=>6P93P2&.=73i\3]=#17-.50#3U _ ERFGJ1 1 2j6PH.0#30#1>DC0#3N24.<E53N246C=>?#.51>6C-!FG- .0#30#1>DC0#3P2&.=>3]\3]=#1[26GH .50!3=>6P93P2&.<E53P2&6C=7?!.51768-@W
3]3B{l1>DC?#E3 e W7g HI68EFG-/3i#FPJQU#=73kW
#"
a"#$&"(!" $ , - FP?A252&1 FP-/U _SE)FGJQ1 .50#3T=>6G9:3P24.:=73]\3i= ! #1 2.50!368E5 1>DC17-t FG=@17J FGDC3#"VWY0#3;=>3]\3]= $&% S1[2 6CJQU!?#.53 ^ _Q93]1>DC0 .53 FN\3iERFGD817-#D'6PH\8FG=>?#3P217-Z=>3]\3]='%)( 17-F 9<1>- 6P9mF82jHI6C=7=>6P92 ! | | , , '% d *5c + h ` dc 1h '%)( d * bc +b h p dfe W gGh ( | ~ ( | 0 -/. . Y0#1 21[22&0#6P9<- D8ERFPU#0#1 FG=7=>_1>-Z{l1>DC?#E3 e W>g];HI6CE68-#3 17J3]-A241>6C-AFP= FC2&3W q6C.3.50tFG.<.50!3 3]-A2&17.&_ 6GH-#6 3N217-Z=73]\3i3= 2 1>-Z6C-#3 17JQ3]-t241768- d .&96 1>JQ3]-A2&176C-t2 h 1 20AFG= H d 68-#3qHI6C?!E5.50uh.50#3T-#6 3N2
"
"
"
" "
0
"
Sg
0
0 1
3
0 3
1 2
2
2
chain code
0123
chain code
003221
first different
1111
first different
303303
shape number
1111
shape number
033033
(a)
0
(b)
0
1 1 2
0 3
1
3
1
3 0 3 2
2
2
chain code
00332211
chain code
03032211
first different
30303030
first different
33133030
shape number
03030303
shape number
03033133
l{ 1>DC?#E3 e W7g ! 68JQ3<3]!FGJQU!=73P2@6GH 240AFPUV3- ?#J^A3]EiW d FOh # E 3]E e 2&0AFGUA3-S?!J^A3]EiW d ^ h # E 3]E 240tFGUA3 - ?#J^A3]EiW d h d h #E 3]E r240AFPUV3B-S?!J^A3]EiW (c)
(d)
!
gCW{l1>- 3 3i-S.E51 17.&_ ! d FhZ{l1>- .&96TUA6C17- .R2FP.j.0#3<JZFPS1>J?#J 1[24.RFP- 3
{l1>DC?#E3 e W7g8g
!
=7D86CE17.50!J HI68E 86 JQU#?#.17-#D240AFPUA3;- ?#J^A3]E:6GH
FG- FGE5^!17.5E)FGE_Q6C^ 3 ]. W
"
Level 1: 1x1
Level 2: 2x2
Level 3: 4x4
i
j
2i Level 4: 8x8 2i+1
2j
2j+1
Level 10: 512x512
!
{l17D8?#E53 e W7g
"
_ ERFPJQ1 W
Gaussian Pyramid
g2
c
b
a
b
c
g1
c
b
a
b
c
g0
g0 = IMAGE
{l1>DC?#E3 e W7gi ! 68-#3 17JQ3i-A241>6C-AFP=qD8ERFGU!0#1 E3]U#E53N243]- .RFP.51768- 6GHB.50!3U#E56 N3 252Q9<0#1 0 DC3i-#3]ERFP.53P2F nFG?A2241[FG-U _SE)FGJQ1 W g1 = REDUCE[g0]
C
gCWY0#3TJZF82 ;240#68?#= ^A3'24_ JQJQ3i.5E&1 8.50AFP.<1 2 d * h ` d5* h HI6CE l* `Sc g c 0
0
"
SWY0#3 24?#J 6GHJZFC2;r240#68?#= ^A3'g8W 3]. d h ` d gPh ` d gGh ` !FG0 0 0 WY0#3]b b ` g p "
"
dfe W e h
"
"
0
d h ` d Oh ` "
0
"
dfe W h "
SW >= = -#6 3P2FG.nF'DC17\3i-Q=73]\3i= Jr?A24. C6 - .5E17^#?#.3T.50#3B25FPJQ3T.568.RFG= 93i17DC0 .<.56r-#6 N3 2qFP.q.0#3;-#3iS. 0#1>DC0#3iE<=73]\3]= b ` ip dfe W h "
241>-#D'.50!3;FP^A6G\3T.0#E53]3 86 -A24.ERFP17- .R2"#9:3T0AF]\3
"
"
!
d h `Ac dfe W # h 0 d gGh ` d gPh ` e g c dfe W Oh 0 0 d h ` d Oh ` e g p dfe W Oh 0 0 Y0#3 4 6K68UV3iERFG.1768-3P252&3]-S.1 FP=7=7_3]SUtFG- 2nFG-17J GF DC3T6PH<2&17]3 b g;1>-S.6QFP-17JZFPDC3B6GH 241>]3 b g ! % ~'` 4 6 % ~ ( yc dfe W h 9<0#1 0 FP- ^A3 68JQU#?#.3 ?A2&17-#Dr.50#3HI68E5Jr?#= FB2417J17= FPE.56 e W SgBFC2HI6C=>=76P92 ! | . | . hc , % ~ d*c+ h ` , d c h p % ~ ( d * c +; dfe W gGh ( | ( | 0 . . 9<0#3]E5 3 % ~ 1 2.50!3 1>( JZFGD83BFG. =7( 3]~\3]= 2 6C^!.RFG1>-#3 ^S_ZFPU#U#=>_S1>-#D 4 6.6 % .51>JQ3P2wW3]E5368-#=7_ .53iE5JZ2lHI6CE:9<0#1 0 | - #FP- | FPE531>-S.3]DC3]E)2FPE531>- =7? 3 W #q-!3.51>JQ3<3] UAFG-A2&1768- 6PH.0#31>JZFGD83FP. =73i\3]= 2 FG-Z^A3;68^#.RFP17-#3 F82 ! | . | . hc , , % d *5c+ h ` d c h p % d * c +' dfe W Oh ( | ( | 0 . . nFG?A2241 FP-US_ ERFPJQ1 HI6C E FPJ^#?!E5D;.)FG 1@17JZFPDC31 2240#6P9<-Z17-{l1>DC?#E3 e W7g e W Y0# 3 @FPU#= F 1 FP-US_ ERFPJQ1 V1[2+D83]-#3]E)FG.3 ^ _ 6CJQU!?#.51>-#D'.50#3 1 u3]E53]- 3T^V3i.49:3]3]-17JZFPDC3P2
"
"
"
"
"
"
"
"
"
"
"
"
e
{ 17DC?!E53 e W>g e! n FG?A2241[FG-U _SE)FGJQ1 HI68Eq.)FG 1@17JZFPDC39<17.50 ` p e W
g3 c
c b
a
b
g2 c
b
a
b
c
g1
c
{ 17DC?!E53 e W>g
!
b a
b c
6C-#3 1>JQ3]-A2&1768-AFG=uDCERFPU#0#1 E3]U#E3P243]- .RFP.51>6C-Z6GH.50#3$
g0
U#E56 P3 252XW
C
Cg W52 ` =>6CD - ~ W SW <3wH 17- 6P9 `a B 9<1>- 6P9 HIE6CJE53XHI3]E53]- 3U _SE)FGJQ1 3i-S.3]E53 FG..50!3HI3PFG.?#E53
"
$
$
"
"
$
"
$
$
"
$
{l17D8?#E53 e W7g
!
=7DC68E51>.50#JHI6CE 86 E5E3]= FP.51768-Z?A241>-#DU _ ERFGJ1 2XW
:##* &"
!$ +( #$5(% !" $5
_SE)FGJQ1 2 FP- ^A3?A243 HI6CE243]\3iERFG=3]-S.=7_ 68JQU#?#.17-#DT.50!3 6CE5E3]= FP.51>6C-@W 6CE5E3]= FP.51>6C-Z1 2?A243 1>-Q.53]JU#= FP.53JZFG. 0#1>-#D89<0#3]E53 F;DC17\3i-QUAFG..53]E6GH F/DCE)F]_=>3]\3]=9<17- 6G91[2;UAFC2243 .0#E568?#DC0.50!3 1>JZFGD83.6 LA- .0#3Q^A3P2&.'JZFG. 0@W Y0#1 2 FG-^A3 F 0#1>3]\ 3 9<17.0# 6C?!.j?t2417-!D;U _SE)FGJQ1 2wW 224?#JQ3<. 0AFG.:93 0AF]\3<.5 6TLA- FJZFP. 0'6GHFg g 9<1>- 6P9 17-vF 17J FGDC3kWT{t68E.50!1 2q9:3'-#3]3 d B g h d g h ` c g.3P24.)2w$ W q6P93]\3]E 17. FG-^A3;2&0#6P9<-Z.50AFP.q?A2&17-#D'U _ ERFGJ1 .50#3T.53N24.R2 FG-Z^A3E3 ? 3 .56r6C-!=7_ e vd g qb gGh | ` g c g 9<0#1 0Z1 2
"
"
"
!"
"
"
"
"
?AF .E53]3Q1[2;F/?A2&3wHI?#= FG.)F24.5E ?#.?#E53Q.6E53]U!E53P2&3]-S.BF/E3]DC1>6C-@W .3i\3]E5_-#6 3 6PHTFM?AF .E53]3 .50!3]E53 FG-Q^A3JZFPS1>J?!J 6PHlHI68?#E 3P2 3i- FG- .R2XWY0#3]E3TFGE3.50#E3]3.&_ UV3N2j6GH 3P2 3i- FG- .R2 ! ,&Y<mFG- WY0#3 -#6 3 68E5E53N24UA6C- .56 F/E53]D8176C-9<0#1 01 2?!-#1 HI68E5JQ=>_/^#=[F FG- .50#3 ,&Y<s-#68.53 6CE5E3P24UA68- .56ZF'E53iDC1768-9<0#1 0Z1 2#-#1 HI6CE5J=7_r9<0#17.3W 0#1>=73 -#6 3 68E5E53N24UA6C- 2+.6QF'E53]D81768- 9<0!1 0 1[2
:
$
"!
;
$
$
;
#!
gCW,fH.4_ UA3T6GH
_ ERFPJQ1 1 2 3]=[243 d Fh <3 ?#E)2417\3i=7_Lt- d ^uh <3 ?#E)2417\3i=7_Lt- d h <3 ?#E)2417\3i=7_Lt- d h <3 ?#E)2417\3i=7_Lt- SW <3].5E?#-@W
"
6CE n,4Y<.50#3i-/E53i.5?#E-@W
.0#3BMO?AF .0#3BMO?AF .0#3BMO?AF .0#3BMO?AF
$
.5E53i36PH:2468?#.50 .5E53i36PH:2468?#.50 .5E53i36PH-#68E5.50 .5E53i36PH-#68E5.50
3PF824.nMO?tF E)FG- .]W 9:3P24.nMO?tF E)FG- .]W 3PF824.nMO?tF E)FG- .]W 9:3P24.M?AF ERFG- .]W
{l1>DC?#E3 e 7W g
# !
=>DC6CE17.0#J HI6CE 6CJQU#?!.517-!DrMO?AF .5E53i3?t2417-!D'US_ ERFPJQ1 W
g
g g
g WHITE
g g g
GRAY
BLACK Level 3
Level 2
{ 17DC?!E53 e W7g
Level 1
!
Level 0
?AF .E53]3TDC3i-#3]ERFP.51>6C-@W
& v :
#
{l1>DC?#E3 e W>g ! 3 1 FG=
FG 1 2.ERFP-A2 HI68E5JWZY0#3UV6817- .R2T6C-.50#3rJQ3 1 FG=
FG 1 2TFGE3Q.50#3 3]- .53]E)2 6PH.50#3 JZFPS1>JZFG= 17E ?#=[FGE-#3]1>DC0 ^V68E50#66 2.56C.)FG=>=7_ 6C- .RFP17-#3 17-r.50!3T240AFPUA3W q6C.3q.0AFG.<.0#3 3]- .53]E)2
6PH .50#3 24J FG=7=>3]E 17E =73P2 d 2&0#6P9<- 68.5.3 h 6'-#6C. 68-A24.17.5?!.53T.50#3TJQ3 1 FP= FPS1[2jHI6.0#1 2<2&0AFGUA3W
gCW,.53iERFG.17\3]=>_ C6 JU#?#.53 FC2HI6C=>=76P92 ! d@cR h ` d@cR h b J17- d ( d c hh d c h2&? 0 .0AFG. * dd@cR h c]d c h5h g8W SW 3 1 FG= FPS1[21 2D817\3]-Q^ _ZFP=7=@UA6C1>-S.)2 d@cR h:24? 0Z.50AFP. ! dy@cR h d c h c d c h2&? 0 .0AFG. * dd@cR h c]d c h5h g8W
dfe W e h
"
dfe W h
{l1>DC?#E3 e W ! , .53iERFG.17\3TFP=7D86CE51>.50#J HI6CE 86 JQU#?#.17-#D'JQ3 1 FP= FPS1[2.5E)FG-A2HI6CE5J W "
$
Y0#3JQ3 1[FG= FPS1[2
.ERFP-A2 HI68E5J1 2?A2&3 .56BE53]U!E53P2&3]-S. .50!32&0AFGUA36GH@E3]DC1>6C-A2XWY0#1 21[2l^AFC2&1 FP=7=>_'FT2 ;3]=>3 .568-/6PH.50#3TE3]DC1>6C-@W #-#3T9
"
" "
" "
" "
" "
"
" "
"
gCW,.53iERFG.17\3]=>_ C6 JU#?#.53 F82jHI6C=>=76P92 ! ( ( d@cR h ` JZ FG( Sc]d JZFG/ d c hh g 168H .50#3i 5E 9< 1 ` 2&3 d c h2&? 0 .0AFG. * dd@cR h c]d c h5h g8W
dfe W h
{l17D8?#E53 e W Sg ! , .53iERFG.17\3TFP=7D86CE51>.50#J HI6CE<17- \3]E)243JQ3 1 FP= FPS1[2.5E)FG-A2HI6CE5J W "
g
g g
g
g g g g g g g g g g g g g g g
g
g g g
g g
g
g g g
g g g "
"
"
"
"
"
"
"
"
"
"
"
g
g
g
g
g
g g
g g
g g g
g "
g
g
g
g
g g
g
g
g
"
"
"
"
g
g
g
g
"
g
g g g
l{ 1>DC?#E3 e W ! 3 1 FP=FPS1[2.ERFP-A2 HI68E5JW d FOh <3 .)FG-#D8?#= FPEZ240AFPUA3 d d @cR h5h)W Y 0#3| ^tF ;SD8E56C?!- U#1>S3]=[2"#9<0#1 0 FGE3'-#6C.n240#6P9<-xFGE53rFP=7= W d ^ h:17- .53]EJQ3 1[FG.53n24.3]U d d @cR h5h)W d h d@cR hRWY0#3 UA6C1>-S.)2+1>- 3 1 FP=@FG 1 2<2&0#6P9<-/1>- ^A68= HyF 3W
" "
g
g
g
"
"
g
"
g
"
g
" "
g
g
g
g
g
g
g
"
g
"
"
g
" "
g
"
g
g
g
g g
g
{l1>DC?#E3 e W C ! , - \3]ER2&3<JQ3 1[FG=!FG 1 2| .5ERFP-A2 HI68E5JW d Fh 3 [1 FG=uFG 1 2 d d@cR h5hRW d ^ h
,-S.3]E5JQ3 1 FP.53:24.3]U d dy@cR hhRW d h #E51>DC1>-AFG= 2&0AFGUA3 d d@cR h5h)W "
{l17D8?#E53 e W e "
!
68JQ33]!FGJU#=73P26PHJQ3 1 FP=@FG 1 2.ERFP-A2 HI68E5JW
: :
:
6CE)F]\3 2T17- .53]E3P24.B6CUA3]E)FG.568E1[2'F \3iE5_v?A243wHI?!=HI3PFG.?#E53QUA6817- . 3i.53 .6CEFG- 1 2;9<1 3]=7_v?A243 1>JQ68.51768-'FP- 24.3]E53]6!WY0#1[2 68UA3]ERFP.56CE1 3]- .51 Lt3P2 UA6C17- .R2 d 17-THyF .24J FG=7=9<1>- 6P92 hx17-;.0#3<17J FGDC39<0#1 0 FGE3 ! ;17-/.0#3TDCE)FN_Z=>3]\3]= 2XW{l17E)24.SHI6CE3PF 0 e Ze 6P\3]E= FPU#U#17-!D'9<17- 6P9 #HI6C?#E 1>E53 .1768-AFG= \8FGE1 FG- 3P2j1>-D8ERF]_r=73]\3]=[2 d 0!6CE51>]6C- .RFP= \3]E5.1 FP= 1 FPDC6C-t FG= AFP- FP-S.1 1 FPDC6C-tFG=fh 3]-#6C.3 ^ _ FG- FGE3 3i.53]EJQ17-#3 FC2HI6C=7=>6P9 d 243]3B{l1>DC?#E3 e W WF h ! } | , , h d@cR ` d d'b *5cR b + h d'b * b g cRb + hh | dfe W # h . . | } d@cR h ` , , d d'b *5cR b + h d'b *5c) b +b gPh5h | dfe W Oh . . | | d@cR h ` , , d d'b *5cR b + h d'b * b g cRb +b gPh5h | dfe W Oh . . | } , , Pd@cR h ` d d'b *5cR b + h d'b *@ g cRb +b gPh5h | p dfe W e h
"!
$#&% '#)(
#&*
#
"
#&%
+
#)(
+
#&*
+
#
+
.
.
dy@cR h1[2 6CJU#?#.53 FC2HI6C=>=76P92 ! d@cR h ` JQ17- d dy@cR h c d@cR h c yd c) h c d@cR h5h p dfe W e gGh oe/e 9<17- 6G9 3]- .53]E3 FP.TU#17 3]= dy c) h<1[2 3 = FGE3 ! r1 H<1>.1 2TFQ=76 FG=JZFG 17J F;17-F g g r-#3]17D80S^A68E50#66 d 2&3]3B{l17D8?#E53 e W W 3ChRW:Y0#3'FPE5E)FN_ " d @cR h:24.6CE53N2+.0#3;1>-S.3]E53P2&.51>-#D;UA6C1>-S.)2+1>.50!31>JZFGD83 ! g 1 H dy@cR h d c h c d c h d@cR h " dy@cR h ` dfe W e Oh 68.50#3]E9<1 2&3 p q3] .!FGEERF]_
,#
#
#
%
#
(
#
*
#
"
"
- !
"
.#
/#
10
"
Y0#3TE53P2&?#= 2&.HI6CE 6CE)FN\3 2 17- .53]E3P24.:6CUA3]ERFP.568EFPE53'2&0#6P9<-/1>-Z{l17D8?#E53 e W W
"
P 0,0
P 0,1
P 0,2
P 0,3
P 0,0
P 0,1
P 0,2
P 0,3
P 1,0
P 1,1
P 1,2
P 1,3
P 1,0
P 1,1
P 1,2
P 1,3
P 2,0
P 2,1
P 2,2
P 2,3
P 2,0
P 2,1
P 2,2
P 2,3
P 3,0
P 3,1
P 3,2
P 3,3
P 3,0
P 3,1
P 3,2
P 3,3
(b)
(a)
P 0,0
P 0,1
P 0,2
P 0,3
P 0,0
P 0,1
P 0,2
P 0,3
P 1,0
P 1,1
P 1,2
P 1,3
P 1,0
P 1,1
P 1,2
P 1,3
P 2,0
P 2,1
P 2,2
P 2,3
P 2,0
P 2,1
P 2,2
P 2,3
P 3,0
P 3,1
P 3,2
P 3,3
P 3,0
P 3,1
P 3,2
P 3,3
(c)
(d)
d 3Ch {l1>DC?#E3 e W ! 6CE)F]\3 2T17- .53]E3P24.B6CUA3]E)FG.568E]W d FOh qE)F]_=73]\3i=j\8FPE51 FP- 3Q1>-0#6CE17]68-S.)FG= 1>E53 . 1768-@W d ^uh E)FN_=>3]\3]= \8FGE51[FG- 3'17-v\3]E5.1 FP= 1>E53 .51768-@W d 5h ERF]_=7 3i\3]=l\8FPE51 FP- 3r17- 1[FGD86C-AFP= 1>E53 . 1768-@W d h5ERF]_Z=73]\3]=u\8FGE51[FG- 3;17- FG- .51 1[FGD86C-AFP= 17E3 .176C-xW d 3Ch 6G\3iE5= FPU#U#1>-#D'9<17- 6G9217-Fg g -#3]1>DC0 ^A6CE50!66 W "
"
"
#"
C
Sg
d FOh d^ h {l1>DC?#E3 e W ! +3P2&?#=7.)2 HI68E 6CE)F]\3 1>-S.3]E53P2&.'6CUA3]E)FG.568E]W d FhERF]_s=>3]\3]=1>JZFGD83W d ^ h 68ERF]\3 17- .53iE53P2&.UA6C1>-S.)2 d .56C.)FG= 'UA6C17- .R2Rh:24?#UA3]E17JQUA6k243 6C- d FhRW
"
"
gCW q3i\S1[243TF'2 0#3iJQ3+HI68E 3].3 w.51>-#D T+` Vdy h | w3]- .53iE53 FG. dy icR h?t2417-!D ;W 2&3.0#3D8ERF 173]- .<17-SHI68E5JZFP.51>6C-Q.6'E53 ? w3.50!3 w6CJU#?#.RFP.51>6C-A2XW 0AFG.<1[2 .0#3 w6CJQU!?#.RFP.51768-AFG= w6CJU#=73] 17.&_B6GH_68?#EFG=>DC6CE17.0#J SW q3i\S1[243FT2 R0#3]JQ3HI68E 3].53 X.517-!D .0AFG.:FPE53 ;S-#6P9<-r.56T^A3q68E51>3]-S.3 2&6;.0AFG.:FU#E51>- w1>UAFG= FPS1[2+1[2UAFGE)FG=7=>3][email protected]!3;ZFPS1[2+?A2&17-#D ;W 243B.50#3TDCE)F 1>3]- .q1>-SHI6CEJZFG.176C-Z.6 E3 ? w3n.50#3 w68JQU#?#.)FG.51>6C-A2XW 0AFG.1 2.0#3 w6CJU#?#.RFP.51>6C-AFP= w68JQU#=73iS1>.4_B6GH_68?#EFG=>DC68E517.0#J SW,fH<.0#3 ! o1[2 ?t243 HI6CE 3].53 w.51>-#D 0#6P9 .50#3 9<1>=7= =>6!6 ;Z=71 ;3 e W q6P9a968?#= _68? 1 2&.517-!DC?#1[240FG- jHIE6CJF w1>E w=>3q?A2&17-#Dr.50!3 ! .ERFG-t2 HI6CEJ W 68-A241 3]E
!
!
"
!
!
!%&
!%
'
$
*)
$
!" # $
(
+
-, ,
$.0/12
3 ,
, 4
5
!
$6
*)
7
!%
8
e
g
" "
gi
g g
d Fh E3]UAFGE3'.50#3 HI68E5JW
;.0/12
"
# # # "
g g
:
g]
9
" "
"
# # "
"
+HI68E.50#1[2+68^ 3 w..56Q^A3'?A2&3 17-.50#33]-!3]ERFP=717i3 q 6C?#D80vY )E FG-A2
"
d ^uh
2524?!JQ3-#[email protected]#3:2468JQ31>JZFGD83l0AF82 ^A3]3i-DC1>\3]-.56_6C? ]9<0#62&3jD8ERF 173]- .@JZFPDC-#1>.5? 3 1[2;DC1>\3]-17-.0#3FG^A6P\3/.RFP^#=73kW #-s.0#E568?#DC0z.50#3Z\8FGE176C?t22&.53]UA2;1>-.50#3 ! 1 3i-S.1 HI_Z.50#3'=>6 ]FG.1768-6PH<.50!3'6C^ 3 w. d c 4h?A241>-#DQ.0#3 _68?ZDC3]-#3iERFG.3 1>-Q.50!3UtFGE5. d FhRW
!%
6
'
*)
.
/
WY0#1[2U#E568^#=73]J9<1>=7=#D817\3<_68?Q2&6CJQ3<3] UA3]E51>3]- w3<9<1>.50 w6CEE53]=[FG.176C-rJZFP. R0#17-#D?A2&17-#DBUS_ ERFPJQ1 2XW 3]=>6P9 FGE53ZD817\3]-v.&96U _SE)FGJQ1 2 ! E53XHI3]E53]- w3QFP- 17-#U!?#.]W{t68Er241>JQU#=71 w1 .&_ .50!3P243ZU _SE)FGJQ1 2 0AF]\3B6C-#=>_ .&9:6=>3]\3]= 2XWjF 0=73]\3i=@6GH.0#3'US_ ERFPJQ1 1 2q^#?!17=7.<^ _/.)F; 17-#DFG=>.53]E-AFG.3;E6G92nFG- w68=7?#J-A2lHIE56CJ .50!3U#E53i\S1>6C?A2=73i\3]=W ;UAFP.5.3]E5- X6C-A2&1 24.17-#DB6GH 21 2j.6'^A31 3i-S.1 LA3 1>.0#3T17-#U#?!.q1>JZFGD83W 252&?#JQ3.0AFG..50!3 X3]-S.3]E6PH:FG-3]\3]- 241>]3 9<1>- 6P9 1[2qFP.q.0#3T?#U#UA3]E=73wHI. w68E5-#3iEU#1>S3]=yW = 2&6 FC224?#JQ3n.50AFP.3PF 0 ;^#=>6 ;FG.FD817\3]-r=73]\3i=#6GH U _SE)FGJQ1 1 2JZFGU#UA3 .6Zg g^#=76 ;ZFG.<.0#3T-#3] .<=73]\3i= C1>- 68E 3iE<.56rJZFGUQ.0#3T=76 ]FP.51>6C-Z6GH:F;9<1>- 6P9 FG.6C-#3T=73i\3]= .6.0#3 w6CEE53P2&UV68- 1>-#D=>6 ]FG.1768- 1>-Z.50#3T-#3] .<=73i\3]=W
!
"
$
"
"
"
F
F
F F
F
F
F F
F
F
d Fh 6G9zJZFG- _ X6CJQUAFPE51[246C-t2jFPE53-#3]3 3 .6T=76 ]FP.53.0#3qUtFG.5.3]E5-r17-r.50!3q1>-#U#?#.17J FGDC3<9<1>.50 68?#.?A241>-#DU _ ERFGJ1 d ^uh #-.50#E6C?#D80/\8FGE176C?t224.3]UA2<17-Z.50#3 w68E5E3]= FP.51768-ZJZFG. 0#1>-#D;?t2417-!DU _SE)FGJQ1 2wW{#68Eq3PF 0 =>3]\3]=A1 3]-S.1 HI_r.50#3T9<1>- 6P9 ^A3]1>-#D243PFPE R0#3 !FG- .50#3T=76 iFG.51>6C-Z6GH
.50#3 w68E5E53 w.<JZFG. 0xW d Ph 6G9zJZFG- _ X6CJQUAFPE51[246C-t2jFPE53-#3]3 3 .6T=76 ]FP.53.0#3qUtFG.5.3]E5-r17-r.50!3q1>-#U#?#.17J FGDC3.5ERFPE5_'=>6 ]FG.176C- 9<1>=7=u_6C?2&.51>=7= ^A3BFG^!=73T.56r=76 ]FP.53T.50!3UtFG.5.3]E5-Z1>- .0#3T17-#U!?#.<17JZFPDC3?t2417-!DQ2&.53]UA21>- d ^ h)W d 38hQ,fH.50#3QUtFG.5.3]E5-v17-v.50!3Q17-#U!?#.T17JZFPDC3'1 2 1 2&U#= F w3 .562468JQ3r6C.50!3]E'FPE5^#1>.5ERFPE5_=>6 ]FG.176C- 9<1>=7=u_6C?2&.51>=7= ^A3BFG^!=73T.56r=76 ]FP.53T.50!3UtFG.5.3]E5-Z1>- .0#3T17-#U!?#.<17JZFPDC3?t2417-!DQ2&.53]UA21>- d ^ h)W d HXh FP-Z_6C?QD83]-#3]E)FG =71>]3<.50!3E53P2&?#=7.1>- d Fh w68-A241 3]E51>-#D r UtFG.5.3]E5- #FG- 1>JZFGD83 9<0!3]E53T^A6C.0 c FGE3T3]\3]-Z-S?!J^A3]E)2wW
!
+
C
C
d D h
PF -Z_6C?QD83]-#3]E)FG =71>]3.50#3E53P2&?#=7.:17- d Gh w6C-t241 3]E51>-#D r UAFG..53]E-#FP- 9<0!3]E53T^A6C.0 c FGE3T3]\3]-Z-S?!J^A3]E)2wW
>1 JZFGD83
# W #?#.=717-!3E53 X?#ER2&17\3TFP=7DC68E51>.50#J HI68E w6CJU#?#.51>-#D'FP- q6GH:F;E3]DC1>6C- HIE6CJ .0#3BMO?tF .E53]3kW SW 68JQU#?#.3'.50#3 T6GH<.0#3;HI6C=>=76P9<17-!D/2&0AFGUA3Q?t2417-!D -!3]17D80S^A6CE0#66 W =73PF8243r240!6G9
[email protected]!3-!3 w3P225FGE_Z24.3]UA2XW
g
g
g
g
g
g
g g g g g g g g g g g g g g g g g g g g g g g g
g g g g g g
SW 2&17-#DT.0#3qJ3 1 FP=#FPS1[2 w68JQU#?#.3 FG^A6P\3E53 w6P\3]E.50#36CE17DC1>-AFG=u2&0AFGUA3^AF ;'^ _rFGU!U#=7_ 17-#DT.0#3 1>-S\3]E)243JQ3 1[FG=xFG 1 2.5E)FG-A2HI6CEJW g W 224?#J3.50AFP.FP-/68^ 3 w.0tFC2q.0#3HI6C=7=>6P9<17-#D RA0 FG1>- w6 3 d w68-#-#3 X.53 h w6CJ#U ?#.53n17.R2<2&0AFGUA3 - ?#Jr^V3iE]W
;
e
#
6 HyFGE93<0AF]\3^A3]3i- 3NFG=71>-#D9<1>.50rF2&17-#D8=73<17J FGDC3:6GHxFT24.)FG.51 <2 w3i-#3<.RF$;3]-;^ _'FqLA 3 ]FPJQ3]ERF W, .50!1 2 0AFPU#.53iE#93T9<1>=7=@^A3 3NFG=71>-#Dr9<17.50 F2&3PM?#3]- w3T6PH17JZFPDC3P2.)F;3]-FP. 1#u3]E3]- .<.517J3q1>-S.3]E5\8FG=[2wW Y0#3rJQ6C.1768-/6GH6C^ 3 X.R217-v 17- ? w3P2q.0#3 JQ68.51>6C-17-.0#3r17JZFPDC3;U!= FG-!3W'Y0AFP.;JQ68.51768-/1[2 ]FP=7=73 6CU#.1 ]FP= t6G9TW,-.0#1 2 R0AFGU#.3]E @9:3'9<17=7= 1 2 w?A252T2&3]\3]ERFP=JQ3].0#6 2qHI6CE w68JQU#?#.17-#D6CU#.1 ]FP= A6P9TWY0#3<68U#.51 ]FG= A6P9 iFG-'^A3q?t243 .56 w68JQU#?#.3< JQ68.51>6C- P1W 3Wl.ERFG-t24= FP.51>6C-FG- E568.RFG.1768- FG- 240AFPUV3kW 3'9<1>=7=FG=[246 3P2 wE51>^V3B6C-#3rDC3i-#3]ERFP=JQ3].0#6 HI68E w6CJQU!?#.51>-#DQ 17- HI6CE5J FG.51>6C-ZHIE56CJ 6CU!.51 iFG= A6P9TW
"
$
,
#
V( "( n( *"! 3].n HI?#- w.51>6C- d$# c&%Vc h S9<0#3]E3 # % FGE53T.0#3B24UAFP.51 FP= X66CE' 17-AFP.53P2! FP-' 1 2.51>JQ3('S3]-!6C.53T.0#3 17J FGDC3r2&3PM?#3]- w3kWQY0#3]- d)#*]c%+*wc ,* h1 2.50!3D8ERF]_=>3]\3]=FG.B=76 ]FP.51768- #*]c%+* FP..17JQ3 ,* W.-252&?#JQ3 .50tFG.9<17.50 F2&JZFG=>= R0AFG-!DC3 # % uFG-' 1>- # % !FG-' .50#3iE53T1 2-#6 R0AFG-#D83;1>- .0#3;D8ERF]_Q=>3]\3]= 2! .50tFG.1 02 /
(
$d # c&%Vc h ` d)#'b #@c%b %Vc b h p _LA-1'S17-#D'.0#3BYlF]_ =768E243]E173P23] UAFP-A241>6C-FGE6C?#-' #@c%Ac 6GH.50!3E17D80S.<0AFP-'/2&12'S3T9:3D83].3/
d W7gPh
# b 4 % % b54 Xp d W h d)#@c%Ac h b54 # ' 4 4 4 Y0#3BFG^A6P\3T3PM?AFG.176C- ]FG-Z^A3B241>JQU#=71 LA63 'rFC72 / #'b %b ` Sc d Wh 9<0#3]E3 `980: `;87: #FG-1' `87: WY0#3P2&<3 'S3iE517\8FP.517\3N2 ]FG-r^A3 w68JQU#?#.36';^S_rFPU#U#=>_S1>-#DTJZFC2;#2 240!6G9<-17-{l1>DC8 ?#E3 W7g.8 6.0#3T17JZFPDC3T2&8 3PMO?!3]- w3 )d #@c %Ac hRW d)#@c%Ac h `
=?@ > BA7A DC<EGF+HI)HJLKNM+HM
"
-1
1
-1
1
-1
1
-1
1
-1
-1
1
-1
1
-1
1
(a)
1
-1
-1
1
-1
-1
1
(b)
1 1
(c)
l{ 1>DC?#E3 W>g / FC2 ;!2HI6CE w68JQU#?#.17-#D24UtFG.51[FG=FG-'/.3]JQUA6CE)FG= 'S3]E17\8FG.17\3P2XW q6C.3'.50AFP..50!3 w3]- .53iE<6GH JZF82 ;Q1[2
q17\ 12' 17-#D'3PF 0.53]EJ 17-Z.50!3;FP^A6G\3T3PM?AFP.51768-Z^S_ 93TDC3i.3/ b b ` c d We h 9<0#3]E3 ` FG- ' ` 1[2
.0#3<6CU!.51 iFG= A6P9TWY0#3]E3FGE53.&96T?#-; -#6P9<-A2! FG-' C1>-'.50#3nFG^A6P\3 3PM?AFG.1768- #93 ]FP-#-#6C.2&6C=>\3.0#1 23NMO?AFP.51>6C-Z3PFC2&17=>_WY0#3FG^A6P\3T3PMO?tFG.51>6C- ]FP-/^A3TE53]9<E17.5.3]-ZF820/
*
*
*
*
`
d W h
p
Y 0#1[21 2.50!33PM?AFG.176C-Z6PHF'2&.5ERFP17D80S.<=>17-#31>- 2&UAF X3WY0#3]E3;FPE53B243i\3]ERFP=VUA6k25 241>^#=73B2&6C=7?!.51768-A2<6GH .50!1 2<3PMO?tFG.51>6C-A.50!3'2468=7?#.1768-A2 iFG-=71>3BFG- _S9<0#3iE53T6C-.0#3;=>17-#3B240!6G9<-1>-{l1>DC?#E3 W W 3]. dC c h:^A3 .50!3 w68E5E3 w.:2468=7?#.176C-xWY0#1[2j\3 w.6CE iFG-r^V3 'S17\ 21 'SN3 ';17- .56T.&96 w6CJUV68-#3]- .R!2 C6C-#3 FG=768-#D;.0#3n24.5E)FG1>DC0 . =71>-#L3 'S3]-#68.563 '^ _ #FP- 'ZFG-#68.50#3iEUA3]E5UA3]1- 'S1 w?!= FGE:.56B.50#3=>17-#L3 'S3]-!6C.5N3 '^S_ #W,.1 2j3NFC24_r.56r2&0#6P9 ^ _ ?A2&17-#DQ.E51>DC6C-!6CJQ3].E51 q21 'S3i-S.17.51>3P2.50tFG. ` : WY0#3]E3wHI6CE3 ;S-#6P9<1>-#D.0#3 ' 3]E51>\CFP.51>\3P2 FG-1' @9:3 ]FP-Q6C-!=7_ w6CJQU!?#.53<.0#3-#68E5JZFP= w6C:J UV68:-# 3]- . S6PH 6CU#.1 ]FP=A6P9TW q6P9:3]\3]EP.50!3UAFGE)FG=>=73]= w68JQUA6C-#3]- . ]FP-/-#68.<^A3 w68JQU#?#.63 ' 'S1>E53 w.=7_;HIE6CJ .0#3 'S3]E51>\8FG.51>\3P2wW #-#36PH .0#3jLtER24.
FGU#U#E6F 0#3N2 HI6CE w6CJU#?#.51>-#D<6CU!.51 iFG= A6P9 9FC2lU!E56CUA6k2463 ';^ $_ q6CE-rFG- ' R0 ?#- ; W q68E5-FP- ' R0S?!- ;U#E568UV6k2463 '/.6Q3P2&.517J FG.53 d c h:24? R0/.0AFG.qHI68=7=>6G9<1>-#Dr3]E5E6CE-#17Jr17]3 '/
4
0
"
0
)d #@c% h `md b b fh | bud | b | b | b | h c d W h 9<0#3]E3.0#3;LAE)24.;.3]E5J 1 2.50!3'6CU#.1 ]FP=t6G9 w6C-t24.5E)FG1>-S.HIE568J3PM?AFG.176C- W e FG-1'.50#3243 w6C-'.53iE5J w68E5E53N24UA6C-'!2.56Z.0#3r24JQ668.50#-!3P2526GH6CU#.1 ]FP= A6P9TW'{#6CET.50#3 w68E5E53 w. d .E5?#38h<6CU#.1 ]FP= A6P9o.0#3'LAER2&. .53iE5J 240#68?#=2';^A3 w=>62&3.56n]3]E56 G68E.50!325M?AFGE3<6GHA.0#3LAER2&..53iE5J 240#68?#=2';^A324JZFP=7=W 1>- w3:.50#3:JQ6C.176C6GHJQ62&.E53NFG=9:6CE5= '/6C^&3 X.R2q1[22&JQ66C.0 .0#3Q2&3 w68- '/.53]EJK3]- HI6CE X3P2q.50!3Q2&JQ66C.0#-#3P22 w6C-t24.5E)FG1>-S.iW q1 3iE53]- .51[FG.51>-#D 49<17.0ZE53P2&UV3 w.<.56 FG- ' !FG- 'Z3PMO?tFG.51>-#D'17.<.6i3]E56'9:3D83]3. / 4
+
+
!
0
4
+
4 `md b 4 4 `md b 4
` Sc b h < b d +b h b ud :b h ` Sp b h
4
d W8h d W h
v -
^^ (u,v)
ft fy
p ρ
d α
β
-
ft fx
u
l{ 1>DC?#E3 W / #U#.51 ]FG=A6P9 w6C-t24.5E)FG1>-S.:=717-!3q1>- 2&UAF w3kW '1 2j.0#3=>3]-#DC.06PHUA3]EUA3]-'S1 w?#= FPEHIE56CJ .50!3'6CE51>DC1>-/.56.50#3B=717-!3 1[2+.0#3'FP-#DC=>3'.50#3BUV3iE5UA3]-'S1 w?#=[FGEJZF;3P29<1>.50.50#3 #t FG 1 2XW dC cS h1[2+68-#3 UA622417^!=73246C=>?#.51>6C-@WY0#1 268U#.51 ]FG= t6G9 \3 w.6CE dC cS h ]FG-v^A3 ' 17\ 12'S36'Z17- .56Z.&96 w68JQUA6C-#3]- .R27/ 9<0#1 0Z1 2