27 Mar 2012 ... cle boundaries, we rely on two preprocessing stages. First, we apply an
anisotropic filter that reduces image noise. This 4D filter takes into ...
Anisotropic Filtering for Model Based Segmentation of 4D Cylindrical Echocardiographic Images Johan Montagnat, Maxime Sermesant, Hervé Delingette, Grégoire Malandain, Nicholas Ayache
To cite this version: Johan Montagnat, Maxime Sermesant, Hervé Delingette, Grégoire Malandain, Nicholas Ayache. Anisotropic Filtering for Model Based Segmentation of 4D Cylindrical Echocardiographic Images. Pattern Recognition Letters, Elsevier, 2003, 24 (4-5), pp.815-828. .
HAL Id: inria-00615640 https://hal.archives-ouvertes.fr/inria-00615640v2 Submitted on 27 Mar 2012
HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
!" #$"% & '( ) *,+.- /1023! 4 6578)*9 8 5;:@?BADCFEHGJIFCGKEHLHM6?N>@OQPSRUTVPXWYGJCh?iGe_bGeC jGe`bC3M k\> l2mQGenHo'P prqhsprt,uwvexXy{zU|}~rQHd~
}"zUhD}cy
D'd'dY)*X
xXUy{|t@S{yx
y 8¡3,a6 "[,-!\6$5"|%$;-&#$*B0! ,:"+T+6`#$,!\&1#J, !5,-; &1#$*0,-;A@"@$,:1"#$*0 ,n3"&"#) &!-NPp@$,! ,j&()*,-!k ,;-.]$!5,-%B" ,;-"#$!/5$;D @$,S@$,-5 (8" &1"#:T^ "(¡,-;A@$"=;V+ %$&"*+6$@$&1;G&1(8*,!q¢S,-5*,-,sNQ tuuuznQ[K(8"!5K"Th@,-(£5,-.8"#0A+**,-% '¤ qe\ ()#0,nReN>QUtVuu$w ¤ ,n.|#$ % ,2sNQtuuJ¥|w=¦k"$#$*4,RsNQUtuuJ¥|w 5x],2sNQtuuw$j,-;-,-5;Ax],2sNQ§tVuuyJzN ¤ ,;-,#Pk(4, @$"|%!EK@$,-5,K6$ "6"!5,-%9&1#g @$,p1&>,+ $ ,kT^"@,p ,-;"#$!/ ;&"#9"T;VmH %$&`+;k;n.=;-1,!&#Cd$>+! "$#%g&1(8*,!-NVI#]q 6L%$,(8,n5&1!h,eN>QM¨¨|t znQV[&1"(4,-%$&;V (8"=%$,1!~ ,8$! ,%T^"~@,V/a(4"&"#+#L.=!5&1!-Nhp@$,)! ,-*(8,#P+&"#!/A*,]&1!C! ,(8&WH
"()M&1;)#$% ! &(86$&L,%[J.$!5&1#$*c"6,-#$,%d;A@,-!54%$"*@,V/8&()+*,-!N $/T;-,H [L!5,-%)(4, @$"=%$!D@LV3,R[,,-#46$ "6"!5,-%9T^"D1,nTiD3,#P &;-1,K!5,-*(4,-#JAM&1"#§Q,-&>@$,D ,.JH &1#$*\"#f ,-*&1"#a;1$!/, &1#*4q #;A@$, Hj5 & ,k+eN>Q¨¨¨Jz"6$ &"!5@L6,K#$%9(8"+&1"# ;-"#!5 &1#J !)q "#JA+*#L+~#$%j,-&1#$*, ,Q§¨¨¨Jz2 "B()x+,f@$,9! ,*(4,-#JA+ &1"#c5"+H [$$!/"2$ !5"$#$%~#$"&! ,N ""xP#$"EK1,%$*,+Q+#$"2"@,-EG"5xC%,VJEK& @~ @$,S#LM&3, *,-"(8,n5.)"TD ! "$#$%?&1(8*,-!;-,-5#L+ &3,.Q! ,n3,- @$" !6$5"6"! ,%4 "C5,-%$;-,R! 6,-;AxP1,K1,n3,[J.f!56L+ &`$;"(fH 6"$#$%$&#$*}q ¤ "@$1&#$*,7sNQjtVuuJvz]"] "d%$,n,; ["$#%L &,-!B&1# { &1(8*,!0[J. (8"=%$,1&1#*!56,;AxP1, #$"&1! ,qer ,-5EK&#$! xP&sQ2tuuyJznN ,*(4,-#JA+ &1"#¡6$6$5"J;A@$,!][L!5,-% "#c3"V|,-1!:;1$!/,-5&1#$*7+Ti ,-\#$"&! ,f;" 5,-; &1"#@LV3,4[,-,-#! "B6$ "6"!5,-%¡qs¢S"$x,/H "&,RsNQ§tVuuuw ,5,#'#% & ,-Q¨¨¨JzN I#¡@&1!96L6,-QkEG,'6$5"6"! ,'(4"|%$,>H [L! ,%d!5,-*(4,-#J+&"#d6 "=;-,-%$ ,+N &"f" 1,nTiG3,-#J5&1;-,2!5,-*(4,-#J+&"#§QJ@$,2&1(8*,K&1!L>,-5,-%4"g5,-%$;-,j!56,;Ax=,j#$"&! ,+N= J #$&! " "6$&;a%$& U$!5&1"#'6$ "=;-,%$$ ,9[,-#$,n$!:T^ "( @$,fES,-x ;-" ,`+ &1"#'"Tk! 6,-;AxP1, @$5"$*@8&1(4,NPI(8*,R["$#$%L5&1,!5,2@,-#0,n= ;n,-%B$!5&1#$*gg%$& U, ,-#J &`o"6,- MH "G! 6,-;&`& ,%)T^"k@$,j;n.=1&1#%$ &;Vo*,"(8,n/.)"T @$,j$> ! "#$%]&1(8*,!S+;-Q§tuuJ|w$23+ , ,~sNQ tVuuJ|w ,- "#L7+#$% +1&1xoQ tVuu¨Jz@L+!C[,-,#%$,n3,1"6,-%"?! (4"|" @#&(9H *,+Q§@P$!C ,-(4"3=&1#$*B@$&*@XT^ ,-@^FX@$,]*%$&,-#Ja @$ ,! @$"% q^ @$,)3+1,0[" 3,]EK@$&1;A@ @$, *+%$&1,#P&!D;-"#! &1%,- ,%)@$&*@9,-#$"$*@9T^"j3"V|,-o":[,R\["$#$%L+5.96"&1#JzN G;n! !9#b,-%*,nH ,-#$@L+#$;-&#$*$, EK@$,-5,? @$,0&1(8*,]*%$&,-#Jf&!f@$&1*@UQ@,?%& $! &"# &1!a@&1*@&#@$,0%$& ,;&"#6L+1,-" @$,0["$#$%L+5.+#$%b#$,-*JM&3,]&1# @$,0%$& ,-;H &"#"/@$"*"#L "7 @$,)["$#$%$5.Np@$, ,nT^" ,+Q@,)&1#J ,-#$!5&I.*J6&1#$; ,V+! ,-!a#$% @$&!S6$5"|;,-!5!1,-%$!G "f#],#$@L#;-,-(4,-#Jp"+Th["#$%L5&1,-!N|p@,\#$&! " "6$&;2%& $! &"# ,#$! "K&!EK &5,#'! 8 5 8 5 8 5 8 5 I.0"T&1(8*,j5,-*&"#$!K&1#$; ,-! ,!2+#$%? @$, "|;;-$5 ,#$;-,"+T$@$&*@g* %$&,-#Jh3"V|,-1!%$,-; ,V+! ,-!Np@P$! @$,@$5,-! @"1%a(g$!5%$,-; ,-! , EK& @b &1(4,N 9(a$!54+1! "c[,0%$&,-5,-#JfT^"f,-;A@d%&1(4,-#$!5&1"#§Q!a@,?&#T^"5()+ &1"# %$,-#! &I.?+#$%03+ &`M&1"#]&1!K%$& U, ,-#J-N
FG1
" $ # !#/), . -@A,(IH"1 "J,2$gA@
#$&! " "6&1;C%$&$! &"#'&!!5$& ,-% "8L ,- $ !5"$#$%'&1(8*,-!No :1"EK!2$!2" %$+!5&;V.g ,-%$;-,R@$,R! 6,-;AxP1,2#$"&! ,KEK@$&1,R,#$@L#;-&1#*~@,2!/ ; ,["$#%L &,-!N
¥
k &1!kC6 ,nH ! ,*(8,#JA+ &1"#9"=" @L+k;V#8#$" &1;-,-[$>.a&1(46$5" 3,p@$,RI.f"T(8"=%$, [L!5,-%'5,-;"#$!5 $;n&"#§N &1#;-,$ !5"$#$%:&()*,-!§!56,;Ax=,G&!#$"h#$,;-,! !+ &1>.\;-" ,`+ ,-%:&1#\ &1(4,Q-&>h6$6,V+ ! !Rf@$&1*@]T^5,-@$"*@0@$,\!56,;Ax=,~(8x+,-! ! "(4,f6L/!:"Tk@$,9["$#$%$ &,-!:%$&1! 6$6,VQU@,9 &1(4,a%$&U$!5&1"#c+11"EK!j "?5,-;" 3,- ! "(4,C"TD@$,(7Nop@P$!QU&2! ,,-(4!(4,V#&1#$*T^§"]6,-/T^" ( #&1! "+ "6$&1;:%$& U$!5&1"#7"# J£&1(8*,!0q1V.J%$&sQGtVuuJv|w #$;A@, H j5& ,feN>QGtVuuuJzN¢S #$%a,9sNqmtuuuz ! &(8&`5.4$! ,:&(8,:+#$%'!56L;-,C&1#|T^" (8+&"#]T^"K4[,n ,K%$, ,-; &1"#7"T ! "$#$% &1(8*,j["$#%L &,-!N
'?,2$g.,2"Y
p@$,RJ#$&1!5"5"6$&;%$&$!5&1"#9&1!+6$6$1&,-%f"#9@,p&1(8*,!5,-,- +&"#0#%B @$ ,! @$"1%$!R5,\! &1*#$&L;-#J>.)%$&U, ,#PK;1,- >.)!5@$"EK&1#$* @$,:%LMA9#$&! " "6J.N
DÛ¯Á(¯ÊÆ²ÒÆ½H³ÒÒ ¹dí º³¶·U²¸r·c³µ¶¯Ç°rûĸ¤¸r®µ¤³ÖıS½¯ºÃ6ÅcÅc¯ ¯ ßß×c×c°¤°r¯Ê³¶ÄdÅÚ·(¯¯Á·Ú²×SÆÉʳ¸rµ¢Ò ²î °rÄd¯ÊÆd×c®Y·S¸Å(ûH¸¤¯®Á³@²¹dƺ³¶°ÅcįÕJ´¸¤×c®°¤³h³¶ÅÚ®c³¶¯²Á(µ¤¸²ÒƳ"ü³»{Õâ°¤¸²ûYÁ¸¤®³@³hÅSį ´µ¢¯Ê×SÆd°¤¯Ç·c¯ÊÄd²· É ±S²µ²Á³¸r³µ¢°ÂÒ
,g;V#X"[! ,-/3,9"#XO&1*$5,a8 @L+j @$,f#&1! "+ "6$&1;:L ,-5&1#$*8! (4"|" @$! @$,a#$"&! ,+Q [$2x,,-6$!R@$,C! @L+ 6$#$,! !j"+T ["$#$%L+ &1,!-QL,n3,-#',-#$@L+#$;-&#$*)&>R+R! "(4,~6`;,-!-N$, ;V#¡1!5""[$! ,53,7@L+4@,7J %$& $! &"#b&1!4[,n ,-4&1#d$, &#$*c#$"&1!5,7&#d@"(8"MH *,-#,-"$! "#$,-!4#% ,-#$%$!f "X6$ "=%$$;,?(4"5,0;-"#J&#P$"$!f["$#$%$ &,-!-QEK@$&1;A@ &1!Q &1#$%,-,-%UQh3,-/.&#J,-5,-!/&1#*?T^":(4"|%,-D[L!5,-%! ,-*(8,#P+&"#§Nhj& U$!5&1"#c&!~+#, U,;nH &>3,C6$ ,6$ "=;-,! ! &#$*)[R&R ,()&#$!p;-"(86$|A+ &1"#L+1.8,n|6,-#$!5&3,NI# f&1(4,\! , &,-! ;-"(46"! ,%4"+T$3,R &()+*,-!EK@"! ,K%$&(8,#$! &"#$!D5,R¥ g¥ 8tv|Q@,R%& $! &"# 6$ "=;-,! !\A+x,-!C¨0(4&1#P ,-!EK@$&1,g @$,f%$,nT^" (8+&"# "Tk@,f(8"=%$,-&1#c&()*,g"T @$,:!5,-. &#P3"3,-!C*+%$&1,#P:;"(46$AM&1"#cT^5"( @$,9&1#$6C&1(8*,-!NUI# &()+*,-!K[L!5,-% "# 85,-*`K`M &;-,4qsr5 ,-! &1#'&()+*,-!znQ$@,g;-"(86$|A+ &1"#B"T *+%$&1,#P93,-; " !4&1!9(4"!5 .[L! ,%¡"# ! ,6L [$1,0L>, !7q , @11Q "[,p"6,+ " !z "p ,;-$5! &>3,:L ,- &#$*?q , @11QLr#$#J.JHmj,-5&1;A@$,\L>, !Cq "#$*Jf,2sNQtuutz znN|@$,-# ;-"#! &1%,- &#$*\&1(8*,!"+T;n.=1&1#%$ &;V=*,-"(8,n5.Q;`!5! &1;-|6$6$5"J;A@$,!k;-#f[,$! ,%9&1# ,V;A@7! &1;-,+Q$;-"(86$|&1#*4 *%$&,-#J!R#%7#$,*1,; &1#$*a @$,\A#$*,-#J&1;-"(46"#$,-#J-N S&!S+1! "C6"! !5&1[$,R "~&#P ,-56"1+,p @$,&()*,p"#]C ,-*$`1+ &1;-,K[,T^"5,+6$6$.=&#$* "6,- +"5!-NU{2#T^"/$#$+,.Qo@&1!\66$ "J+;A@X&1!@"6,1,! !j%$,a") @$,f&1(46"5A+#P #$*`f5,-! "1 &1"#d#$%b@$,?1"E ! &1*#L>He"+H #$"&! ,] +&"¡q^! ,,7,Ti4"T$*$ ,?cT^" ] ,!(46$1&#$*],$+(86$,a"#] ,-1&!5 &1;C,-;A@$"=;V5%$&1"*6@$&1;a&()+*,g;"(86"!5,-%X[J.cu 6$`+#$,-!znNPI#$!5 ,V%UQ=EG,;"(86,2g *+%$&1,#P3,-; "GT^"k,-;A@]&()*,3"V|,-U @$, ;.=1&#$%$5&1;V+*,"(4,/.Xq^! ,,4q 2, &1#0#%02.J+;A@$,QtuuJzT^"a! &(8&`k66$ "J+;A@0&1# :znN
Image plane M r z
x y θ
ÛDŵ¯ÊƯÃÒ)²¹É´Ò Æü³³ÄdÕâÁ¸û³³¶¸rõ¤®ÑÄHÒ Ã²µÅc¯ÊÄÆµ¢²±S®S¯Ãw¯ÇÁ²Æ³¯Ç·U¸r³µ¤±´Ädɲ¸¤¯Äd·3Äd·"² í ²µ¤¸r³¶°¤¯²·ËƵ¢¯ÅüÒ î ¯Æd®U¸ûÃÑHÉǯ·Í
n, :[,f06"&#Jj&1#cD$;1&%$,V#X!56L;,aEK&@r+5,! &1#c;-"=" %$&#L+ ,-!9qD E e E i nz #$%a;n.=1&1#%$ &;VP;-"="5%$&1#LM,-!q E cE i nzGq! ,, &*@J"+TLL*$5,SPzNn, 5:[,k@$,;n.=1&1#=H %$ &;V&1(8*,C%$,$#$,-%! 5 ¤ ¤ QUEK@$, , b&1! @$,f%$&! ;-5, ,f;.=1&#$%$ &;V
v
* &%~"3,-EK@&1;A@g @$,G* ,.JH 1 ,3,-P3+1$,!+ ,kx=#" EK#UNp@$,G;-"#J3"1 &1"#~"TL2d!5&1*#L+ [J.?aL ,- X+R6"&1#J 2&1!p%$,nL#$,%'&1#7r/,! &`+#?!56L;,g!
q
§zq nzG; qDuH K
K
DE e
H
e E i mH
i z
qYDE e E i zC*:D2* e
i = *
qmt z
K
"9EK &>,j @$&1!K,-3,p;"+H ,Y4 W ;-&,-#J!k,-.];-"! ,\ "9 @$, "+&"#BM|&1!EK@,- ,C%$,#$! ,C%L+9&!R3+&`[1,N
Z
[
V\
# | ^
#J.9%$,nT^" (8[$,! $/T;-,K5,-6$5,-! ,#JA+ &1"#$!k@LV3,R[,-,-#86$ "6"!5,-%9T^"D(4"|%$,>H [L! ,% ! ,*(8,#JA+ &1"#0"T (4,-%$&;V&1(8*,!\q ;-I#$, #$,n.?#$%B, "6"$1"!QUtuuJznN|p@$,:1,nTi 3,#P &;-1,pES!L !/G(4"=%$,-,-%9$! &#$*:6L (8,n, & ,-%9 ,6$ ,! ,#P+&"#)!5$;A@]+!k!5$5T+;-, @L5(8"#&1;-!\q ;A@P$%.0#$%?¢`5%§QtVuJvuJzQ|!5$6, QUtuuJznQ
y
D±SÛ ²¯ÊƵ¯Ò °róÄd·ÒJKÄÄÕJ±äÞHĵ¤Î´ÄªÙ3³¶ÉSûJÄñZÑH³Éµ¯Ç·c²¸rÅĵ¢µ¢¯°hò»{ÉJɳÆÕ µ¢¸²ÂI.f"f%$,nL#$,\!5@L6,\;-"#$!/ &1#J!S&1#0a;"(86A+ &1"#$1>.f, 4;-&,-#J ()+#$#$,-N
YW
o
)
! .
!#"%+!#
H ! &1(46$,n?(4,-! @X&!j]%$&! ; , ,a#$"#=HI6L (4,5&1;C ,6$ ,! ,-#J+&"#c"Tk]! $/T;-,g&1# s s ¤ %,L#$,%d[J.bX!5,9"TR3,5&;-,! +#$%@$,&1a;"#$#$,;&>3=&I.ND 9&!fX ,*$`+ MHI;"#$#$,; ,-%)(4,-!5@§NP !D"6""*.g&1!%$L$ "g\5&`#*$`M&1"#§Q+#$%8&>;V#8 ,6$ ,! ,-#J ! $/T;-,!2"+T #J.] "6"1"*+.N=p@$,~*,-"(4, 5.]"+T!5&1(46$1,](4,-!5@$,-!R1"EK!p$!"9%$,nL#$, %$&1!5;-5,,?&,-!4! $;A@+!8(4,V# ;-53++ ,7+4,V;A@¡3,-/,n}q^! ,-,qsj,1&1#*,5,Q tuuuzT^"G%$,&1!AznN=3,-/&1;,-!pT^"1"EaR,Ep"#$&`#01VEZ"+Th(8" s &1"#UN=p@ ,-,\xP&#$%$! s s 9 "TT^" ;,-!G ,K;-"(86$|,-%8+,-;A@83,-5 ,n NJp@$,K&1#J ,- #$$T^" ;, ,-#|T^" ;,-!k! "(4, s a 9 ,*$`+ & +&"#[,@LV3|&"-Np@$,B,n=, #L+ST^" ;, 6$$1!~ @$,0(8"=%$,k " ES5%b @$, s 3,#P &;-1,9["$#$%$ &,-!-NUp@$,9*1"[$%$&! 6$1;-,(8,#J\T^" ;, &!j;-"(46$ ,-%cT^ "( a*1"[L #!5T^"5()+ &1"#4EK& @BT^,nE %,-*5,-,-!K"ThT^5,-,-%"(£%$,! &1*#$,-%0"f;"#$!/+&1#?1 3,5&;-,!k%&1! 6`;,-(4,-#J!Np@$,p`VE "T(4"&"#a&1!%$&1!5;- ,n& ,-%9$!5&1#$*j$#$& ,%$& ,-5,-#$;,-! #$%7#B,n|6$&1;-&>p& ,- +&>3,\! ;A@,-(4, s 9s ; 9s 9s 9s ; s s 9 s a 9 ; Zq/t0 H Uz-q H z
q z Zq/t0 H z qJz K
2D F
Q
2
Q
ON
Q )
Q
s 9s EK@$,-5, %$,#$",! @$,p6"!5&&"#g"+T3,-/,n M &(8, l Q]&! j%L+(86$&#$*j;"|, 8;&1,#P-Q c#$%X ,K@,R&#J,-5#Lo#%),n= ,- #$LT^" ;,REG,-&*@J!-Q=#%]&1!:1"=;V+1&I.CEG,-&1*@P-N p@$,%$&! ; , ,G &1(4,G!/,-6g&1!@&1%$%$,#g&#g@$, GQ?#$% 8;"|, 4;-&1,#J!-NM,G$! ,;-"J+ ! ,H
N
XW
6N u
XW
"+HeL#$,:66$ "J+;A@§Q$1&(8&>&#$*:(8"=%$,-%$,T^" (8+&"#];V+6L[$&1& &1,!G[J.0!5, &1#$*B" , " +C@$,4[,*&1##$&1#$*B"TS@$,4%$,T^" (8+&"#c6$ "=;-,! !-Qh@,-#* %$L+1.'&1#$; ,-! &#$*7&>:" 1"EZ(4"5,\1"=;V%$,T^"5()M&1"#$!-N$p@, ;"|, 8;&1,#PK3+$,\&1!p!5,R"Bt\@P$!R@LV3|&#$* ¡3+ &1+&"#$!jEG,-&*@Jg@,85,-! 6,-;n&>3,)L$,#$;-,8"TS @$,)&#J,-5#L#%@,),n= ,- #$ T^" ;,-!Np@$, ?;-"=, 4;-&,-#JD3+ &,-!T^5"(
t":¨=>tK! 9&1#$; ,V+! ,-!Np@$,K%L(46$&#$*23+$, &!2|,%c "0¨= J¥8[L+! ,-%c"#'! "(4,a,-(46$& &1;-h ,! $>!j!5@$"EK&1#$*] @$&1!R3+1$,~$! L+1. 6$ "3=&1%,-!9'T!/f;-"#J3,- *,-#$;,7!56,,-%§N 2# "()+ &1;81*" &>@$(T^"g*"3,-5#$&1#* ,3"1 &1"#0ES!K6$ "6"!5,-%?&1#q "#JA*#$+2#$%?j,-&1#$*,n ,Q§tuuyJznN
N
XW
YW
8 @$,'[,-*&1#$#$&#$*"T @$,'%$,nT^" (8+ &1"#b6$5"|;,-! !Q ; ¨+#$%§Qk%$$,7 " @$,';"(fH s 6$+&"#7"+T q "#JA+*#L+2#$%'j,-&1#$*,n ,Q§tuuyJznQL,.,2"J,2$&nQ# &! a;-$/3++$5,\ ,`+ ,-%B#$*1,;-1,-% 2.A'21, CA@>1,nQ$+#$%$&1!S#0,-,3++&"#)T^$#;&"# s [" 3% , q! ,,?qsj,1&1#*,5,QtVuuuJzT^"%,A+&11!znNo j;-# [,a! @" EK# @L+j)! &(86$,n (8,! @9! @$6,p&! %$,nL#$,-%4$6f":j!5&1(4&11 &>I.\+#$!5T^"5()M&1"#g[J.g @$,p! ,nG"+T&>! (4, &; s s s; s 6L (8,n, !R#$%B! &(861,n0#$*,-! & E E N
F
D
s s s s ;A@?3,-/,n &1!pM ; ,-%B"ES %?f6"&1#J(' "#7f!5(8"="@,-(4,-!5@§Nn, ' Q ' #$% ' s) %$,s #$",9@,8(4, &1;f6$(4, ,-5!-Q§@,4!5&1(46$1,c#*1,9#% @$,86 "Ml5,;&"# s "T ' "* # 5,-! 6,-;n&>3,->.Nop@$,~&1#J, #L§T^" ;-,:;-#'[,:%$,-;"(86"!5,-% +!R @$,~!5$( "T aA#$*,-#J&1#$%?#$"5()+§;-"(46"#$,-#J
+-, /.q
s
z ;q
' s) H
s) z QZq0q
!
s$#
t¨
E1
s;
E
s
E2
s
z H3q
!
s# E
' s E ' s E ' ;
s
z z
s =
p@$,G#$*,#J&`+J;-"(46"#$,-#J "T$ @$,G&#J,-5#LT^"5;-,k;-"#J "! @$,k3,-/,n~!56L;-&#$*"3,- @$,R! 5T;,N="C,-#$!5$ ,$#$&T^" (4.~! 6$5,V%)3,-/&1;,-!Q|(4, &1;p6$(4, ,-5!S5,R1L!5, s; s ; ,-I.4&1!K(a$;A@?@$&1*@$,-NLI#? @$,:;V!5,~"TJ &1(8*,5.Q|!5+&!5&;V3+ &1+&"#](4"|%$,!pES"1%B"#$>.][,C5,-,3+#JpT^"@,C!5,-*(4,-#JMH &"#7"+TD"#$,+Q! .?@,~L5!5VQ&1(8*,+No;A@'T^"1"EK&1#$*9&()*,C"+T @$,~! ,+! "$#%[,V+( ,23L,-;n,-%M4 @$,'" *J# &1#J ,-5T+;-,-!)#$% @$,7 &1[ "=;-;-$! &"#$!Qk(8x+,? @$,?3,-#J5&1;1, ;-"#J "$ !C@L5%X"?%$, ,-;)qiT1!5,f#$,-*JM&3,-!znN,95,-.'"#c@$,9(4"|%$, ,*$1 & &1#* [,@LV3=&1"C#$%X @$,85"[$$!/:T^" ;,4,|6$ ,! ! &"#$!C6$ "6"!5,-%[,1"E "7%,V EK&>@XT1!5, 6"! & &3,-!K#$%BT! ,\#$,*J+&>3,!-N
W
tt
o*d
1
?0
!#$g"
,
1 @
A.
r 1"!5,-!/2["$#%L5.83"V|,-!2+ ,\;-"(86$|,-%0T^"p,-;A@03,5,?[J.0! ;-#$#$&#$*f@$,\&()*, S 1"#$*j@$,p3,-5 ,n4#$" (8%$& ,;&"#9$#J&L\["#$%L/.a3"V|,-o&1!D5,V;A@,-%§NPI#$%$,,-%§QP&> @L!K[,-,-#7! @$"EK#7&1#q &1(4&`~,2eN>Q§tuuJzk @L+K@$,:;`!5!R"+T!5$5T;,~%,T^"5()+ &1"#! &1!j#"\ ,!5 &1;n,%[J.X"#$.7;-"#! &1%,- &#$*0%$&! 6$1;-,(8,#P\1"#*],V;A@X3,-5 ,n#$" (8eN p@P$!-QEG,85,-!5 &;:@$,9!5,V5;A@T^"\["$#$%$5.X6"&#P !:1"#$*]@$,9#$" (8 %$& ,-;n&"# s s N "T,V+;A@73,5 ,n
,f6 "=;-,-,%[J.X!5;V##$&1#$*?;n.|&1#$% &1;-h3"V|,-1!:&#P ,-5! ,-;n,%[J. @,f#$" (81&1#, s s q E z&1#8 @$,&()+*,R3"1(8,KEK& @$&1#)~|,-%B+#$*,;,-#J, ,%?"#],V;A@]3,-/,ncq!5,-, 1,nTi:"TSL*$ ,8JznNp@,8&()*,a&1#J,#$! &>I.65q z:Mg+#P.c#" (8 &1#$,f6"&1#J &1!j &WH 1&#$,V5.~&1#J, 6"`M,-%aT^5"( @$,K,-&*@J;-1"! ,-!/k&1(8*,S3"|,&#J,-#! & &1,!G5 " 5 2q!5,-, ;-,#P ,-j"+TL* ,aznNop@$&1!2*" &>@$( " 6$!8&1!5R"T3"V|,-!T^"pEK@$&1;A@7ES,~!5" , s @$,&1:&1#J ,- 6"1+,%X&1#J,#$! &>I.X3+1$,9#% @$,-&~D$;1&%$,V#c%$&!5#$;-,fT^5"( Np@$, ! ;-#|HI&1#$,R+#$*,j&!k|,%7+!g6,-5;-,-#J*,\"T @$,j&1(8*,K!5& ,+N|,$!5,-%?~ ,-#|He3"V|,- 1,#$*@B!5;V#|H 1&#$,\&1#B"$p,|6, &1(4,-#J !-N
I5 I7
I4 I1
P
I6
I3 I0
Vi
ni
ÓÛDĪ¯ÊÆÔHÒc³¶É ÷H´½Òò^º ĵÅcÁ¯°r²±Xɴɲ¶É¯Ñ·³^ÄÕD²¸¤·S®Åڳ˸¤°¤®có@²·c°¢Ã·²³¶·cÅ!·Ó³¶ÄªÅ8ÔHÓ³¶ÉͰ¶ÔÒ ³¶É° Jµ¢¯àÍɯ·c³¶²µw¯·Y¸r³µ¤±´Ädɲ¸¤¯ÊÄd·ÚÄd·!²ÐÃÑɯ·Sŵ¢¯Ã²É I2
1
$ 1, 2, " q!#$ .
:"
$&,/. /A.
,$ !5! ,p@$,p,=+;,%8!5;V#41&#$,S&#f" %,- "j$#$%f@$,K* %$&1,#JD#$"5( ,n= ,-(8 1"#$*X@$,?#$"5()p%&1 ,; &1"#§NDI#d6$+;&;-,+Q @$,?#$" (8p%$& ,;&"# +)* %$&,-#J 3,5,~3,23"V,1! EK& @$&1#CK*&3,-#C&1#J,#$! &>I.\#*,k#$%g"+T,-#$* @~* ,VM,- @L#~R(4&1#$&(a$(@ ,-!5@$"%§N j#$;-,f@,f[,*&1#$#&1#$*]"+TS05,-*&"#X@L!\[,-,#cT^"$#$%§QUEG,9! ,- ;A@cT^" @$,fL !/\3"V|,- 3+1$,f @L+C%$"=,-!g#"C[,1"#$*B"B@,85,-*&"#&#J,-#! &I.c #$*,f @=!g;-" ,! 6"#$%$&#$* "c@$,?,-#%¡"T2@$,? ,*&1"#UN:&>3,# @L+4! $;A@Fc3"|,2@L+!8[,-,#dT^"$#%dEG,? @$,-# 1"="x~T^":3"|,oEK@"! ,R*+%$&1,#Pk#$" ( &!["3,\*&>3,-#9@ ,-!5@$"%8	 @$,K3|&;-&#$&I. "Tp@,0 ,-*&1"#,#$%§Np@$&1!f+1*"5& @$( ,&`+1& ,-%X+!~+#,-1&6$! "&% "$*@$>.X;-,#P ,-5,-%&#$! &%$, @$,?3,#P &;-1,+NkO&1* ,7v!5@$"EK!)@$,? ,;-"#!55$; ,-%!5$5T;,-!cqi"6d "E2z9#$%d @$, &1#J, !5,-; &1"#X"+TG,-;A@c! $/T;-,aEK&>@ "#$,f"T@$,g&1(8*,C6$`#,-!4q["5"( "E2zN§p@$, ,(86$1+,&1(8*,@$( q(4&1%$%$,z 6$5" 3=&%$,-![,5, ,! $>! T^"["+@9@$,R*+%$&1,#Pk,| ,(a$(
#$%9@$,R&1##$,-%L5xf ,*&1"#!k!5,V5;A@§N=p@$,5,-*&"# 6$6$5"J;A@ q &*@Jz [, ,-k! (4"|"+@$!@$,R["$#$%L+5.4#$%8&1!k(8" ,R;-;$M,2!G;-#)[, ;-,V5.]!5,-,#'&1#] @$,:(8&> 3+>3,C ,-?q1"EG,-K6L/K"T&1(8*,zN
! *d$ ,+!
0*
$d2' +*/. -@A,( @
p@$,:,-(46",3"1 &1"#B"T@$,:;- %$&1;\1,nTip3,#P &;-1,:&!p,n= ; ,-%7T^5"( f! , &,-! "T,-&1*@PG,-;A@"|;- %$&"* 6$@$&;p&1(8*,-!;-"3, &1#*~@,R@,V/G!/.=!5"1,~q;"#J+;&"#ozN p@$,:" &*&1#$U&()*,-!+! "$#%X[,-( [P.' &[$!-N ,*&1"# [L!5,-%c6$6 "J;A@X&! $! ,%?T^";-"(46$ &1#$*a @$,\,n= ,- #$&1(8*,+ ;n&1"#],-5(7N|I#7" %$,"f!5 $%.] @$, [,#$,9"TR#$&! " "6$&;)%$&U! &1"#§Q @$,]! (8,)J£&1(8*,4&1!~! ,-*(8,#P ,-%b["@EK&>@ #$%BEK& @$"K6$5&1"S%$& $! &"#§N p@$,\(4"|%$,U[$&1G&1#8@$,\6$5,3=&1"$!,n|6,-5&1(4,-#JK&1!G$! ,%7+!Kg,-(46$1+,RT^"G @$,\! ,*+H (8,#JA+ &1"#0"Th @$,\L !/p3"$(8,&1#0&(8,+N|K,-;A@?T^"11"EK&#$*~ &1(4,j!5 ,-6§Q$ @$,\(8"=%$, &1! &#$& &`& ,-%:T^ "( & ! 6"! & &1"#a+ @,p6$ ,n3|&"$! &1(4,S&1#!5A+#P-Np@$,K! (8,S%$,T^"5() H &"#f6L (8,n, !D@LV3,K[,-,#8$!5,-%9T^" "5&1*&#L|#$%9%$& U$!5,-%9&1(8*,! ! ,*(4,-#JA+ &1"#UN ES"8%$,T^" (8+&"#B!5A+*,-!R"|;;-$pT^"K,-;A@'&(8,\&#$!5#J o9*1"[L§5,-! ;-1&#$*9"T @$, (8"=%$,$$! &#$*~:*1"[L+L 4#$,K;-"#!5 &1#Jq ;tQ 7; t ¨ ]Q! ;-#)&1#$,S#$*, q; t¨ 3"V|,-!Az2T^"1"ES,% [J. ]"|;-h%$,T^" (8+&"#'!/A*,~@L+;-"(46,-#$! +,!jT^"#$"#|HI5&1*&% %$,T^" (8+&"#$!:q >; ¨= |Q 7;Zv ¨ ]Q ;}¥g3"|,1!AzN
-W
LV volume
ÛD»{°r¯ÊÄdÆÉÇÒ¯Å(HÒ É¯ÇK·³³Õ ÂD¸ûH¯ÁÓÄd²ÉÆ×c³¶Á°¶Ò ³^î Ó)¯Ê²Ædµ¢®U¯Ç²¸û¸¤¯Ê°¤Äd×·(µ¢Õâ³²Ôør³hµ¢²ÁÃÄH¸r³¶ÅcÅ8³¶ÉÕâ°I.!5(8"=" @$&1#$*7;V! ,-% [J. @$,]%$& U$!5&1"#6$ "=;-,! !Q@,]&1#J,#$! &>I.c@$5,-! @"1%%,L#$&#$* 5[ &1*@Pg ,*&1"#! '&! %$& ,-5,-#Jj @$,g"5&1*&#Lh#%'@$,~%$& $!5,-% %LMANp@$,a%$,nL#$&>&1"#'"T @$,~3,-#J5&1;1, ["$#$%L5&1,!8&!8!5,-#$!5&&>3,?" @$&1!9@ ,-!5@$"%F#$% @$&!85,-!5$ !)&1#d%&1! 6`;,-(4,-#J "T @$,g+6$6L5,-#Jj["$#$%$ &,-!K@L+2,n|6$1&1#!R @$,~%& ,- ,#$;-,~&1#B3"$(4,~,!5&()M&1"# [,nIES,,-#b@$,)" &*&1#L+G+#$%%$& $!5,-%%L+q!5,-,0,Tia"+TR$*$ ,]yJznNI#@$,0+[$! ,#$;-, "T* "$#%5@! ,*(8,#JA+ &1"#§Q&>C&1!\3,5.%$& 4;-:"?! ,n~ @$,)5,-*&"# @$ ,! @$"1% ! " @L+g @$,]5,-;-"#$!5 $;n,-% ! 5T;,0;-"5 ,-!56"#$%$!a"7@$,]6@P.=!5&1;V+["$#$%L5&1,!g"T @$,g@$,V/j3,#J &;-,f#$% @L+j @$,a;-"(86$|,-% 3"1(8,~;-"5 ,-!56"#$%$!j"8@$,9;nL+ 3"$(4,N
W
2"EG,3,-QJ@,p;-"(46$+&"#a"To@,p@$,V/D1,nTi 3,#J &;-,p,ml5,-;n&"#aT^;n&"#a&TLT+ 1,! ! ! ,#$! &>&3,C "4 @$,C&1#J,#$! &>I.0@$5,-! @"1%7! &1#;-,C&K&1!R9+ &1"96L (4,,-NLp@$,~,ml5,;&"# T^;n&"#¡,nT](4,V!5$ ,!)@$,7T^;n&1"#F"T:[$"|"=%¡,Il5,-; ,-%[J.¡ @$,'3,-#J5&1;-,X+),V;A@ , Vz , 5,2@,j() &()+o#$% @$,V+5;n.=;-1, ,nTu; q IH KEK@$,-5, #% (8&#$&1(83,-#J5&1;1,83"1(8,4 ,! 6,-; &3,-.NI# @$,8$ !5g,n|6,- &(8,#Ja! @" EK#b+["3,+Q ES,f(4,V+! $5,-%X,ml5,; &1"#'T^ ; &1"#?3+1$,!"Tt  @$,a"5&1*&#Lh%L+]#$% £&1# @$,%$& $! ,%]%L+N=p@$&1!S3+$,-!G;-"(46L5,2 "g@$,2P ¥ ,ml5,; &1"#)T^ ; &1"#8,-!/&1(8+ ,-% T^ "( @L+#$%|HI(8%$,4! ,*(4,-#JA+ &1"#"T@,)&1(8*,4[J.?;V5%$&1"1"*&!5-N§p@$,-!5,0 ,! $>! ,f3,-5.c! +&!5Ti.=&1#*?!5&1#$;,4 @$,9&1#J,/H "6,+ "j3+ &1[$&1&I.B&#X@$,4;-"(46$+&"#X"T @$,:,Il5,-; &1"#0T^ ; &1"#B"#0@$+Rx=&#$%B"T&1(8*,-!p&!p&1#] @$,:" %$,K"T fT^,E 6, ;,-#J!N
p@$,(4"|%,-P! @L+6,;"#$!/+&1#J! ,-*$`5& ,k @$,S!5$5T;,%$,nT^" (8+&"#§Np@$&!&!3=&1!5&1[$, &1# @$,]!5,-;-"#$%d,|6, &1(4,-#J0q^L* ,Xtt z\EK@$,-5,0! @L+6,];"#$!/+&1#J!9+5,#=$+,) @$, , ,-;n2"+T@,C[ ,VM@$&#$*45 &T;np"#0@$,:!5$5T;,~5,-;"#$!5 $;n&"#§N
~1 \V
I#]@$&!S6L+6,GEG,j@LV3,\%$,(8"#$!5 + ,-%]@$+!5,-*(4,-#JAM&1"#]"T;n.|&1#$% &1;-o,-;A@$"=;V+/H %$&1"*6@$&1;B&1(8*,!f;V#¡[,?6,5T^"5(8,%¡$!5&1#$*%$,T^" (8[$1,B!5$5T;,-!NGp@$,7(8"=%$, 6$ "3=&1%,-!k,-#$"*@8&#J &#$! &;Cq!5@L6,zD#$%4,n=5&1#$!5&1;~q* ,.JH 1,3,-L #$*,VzD6 &1"Dx=#" EKWH ,-%$*,"#) @$,%$+AQP"~;-"#!5 &1#8@$,2%$,T^"5()M&1"#$!6$ "6,-5.4,3,-#0@,6$5,-! ,#$;-, "T§3,-5.8! 6$ !5,j#$%)#$"&1!/.9%L+NJ, ,R#$"ET^"|;$! &#$*g"#)&1#J "=%$$;-&#$*C(8"5,26 &1" xP#$"EK1,-%*,:&1#]@,\%$,T^"5()M&1"#)6$5"|;,-! !K$!5&1#$*f ,-(46" ;-"#J&#P$&I.)&1#]@,\%$,T^"mH ()M&1"#06$ "=;-,! !~q "#P*#LM+#$%'j,1&#$*,5,+QL¨¨¨JznN &1"8L>,-5&1#$*"T\@$,'&1(8*,'5,-%$;-,-!] @$,X! 6,-;AxP,X1,3,-#$%&1(46$5" 3,-!] @$,
t v
,H
*&1"#%$, ,-; &1"#UNDp@$,7 #&1! "+ "6$&1;]%&$! &"#6$ ,6$ "=;-,! !5&1#$*&1(46$ "3,!f! 6LM&`+ #$%,-(46";"#$! &!5 ,-#$;n."TS@$,9&(8,9! , &,-!g"+Tp&1(8*,!-Np@$,8&1(8*,9*,-"(8,n5. &1!R! "fAx+,-#7&1#J"4;;-"$#JRT^"R4[,5,R%,,; &1"#7"T!/5$; $ ,~["#$%L5&1,-!NLp@$, (8"=%$,>HI[$! ,%8!5,-*(4,-#JAM&1"#8,#L[$,-!G#];;-$ +,2;-"(46$+&"#9"TU @$,,Ti3,#J &WH ;-,,ml5,;&"#fT^;n&"#gEK@$,#8;"(86$ ,%9 "\@L#$%9(8%$,!5,-*(4,-#J+&"#f[J.9#9,n|6,-5-N p
§ Y= )=
\
,c+ , * +,nT^$2 "D0n {R ! "$#$%§QS @&11&6$! ,-%$&;V .=!5,(8!?rS"(86L+#P.Q 5&1,nH j%$&1,g¢S, *,\T^ "( ,! ,- ;A@§Q n"5&`Q#$%j n, @$"Qhr {¢S ["&1!-Q T^"p6$5" 3=&%$&1#$*f @$,C $ !5"$#$%?&1(8*,!$! ,%'&#B @$&1!p6$6,-N
N + P
G\
| :
>3+ , Q nDN>Q n&"#$!-Q N HWnDN>Q+#$% "5,-sQ N H NSq/tVuuJzN7I(8*,4! ,1,-;n&>3,]!5(8"="@=H &#$*?#$%,-%$*,9%$,n,;&"#[P.c#"#$1&#$,V+\%$&$! &"#§N /A.,2$g+*d>1 A)>1 2 nQ u$qsJz yJ ¥ |y|N ¢5%$&1#$,nVQJpN>QPrS"@$,#§QknDNQ#$%92.;A@$,QPCNoq/tVuuJzNL ;AxP&1#$*C#$%9(4"&"#f#$.=! &! "T @$,91,Ti3,-#J &1;1,fEK& @c%$,T^"5()+[$1,a!5$6,- 1 2 nQ tPqsz >t u tVJuN ¢S,-5*,-Q N H aNQ&1#J ,-5T^,1%-Q 9N>Q #$%nh,n@$"-QN H NkqmtuuuJzN0rS"#J "$C ;AxP&1#$* &#fD;A@$"|;- %&1"* 6$@$&; , 1 2 -) , 6* , gJ" ,/11 @A,2 * ,nQtVoqez u ¥N ¢S"$x+,-5 "$&sQLaN>QL¢!5! ,-Q aNQL¢S! xP$/VQLgN>QL#%7R"[$,Q$~Nhq/tuuuJznN ,-*(4,-#J+&"# "TD;A@$"=;V5%$&1"*6@$&1;S\+AN $>& ,-!5"1|&1"#f#$%921*" & @$( ¢!5,-%9"# \ ,n. n,n3,- AM&1!/&;-!-N=I # (,d,1 . @A, u! .A')/ "%A @-) , u! .A')/J" ,2$ 0 A(2 2J" ,d, 2? 0 " ,2$ =>,2" +!# ! " MQV3"1$(4,KtJvuK"T oQM6$*,-! ¥|t |¥Q r+(a[$ &%$*,+Q { N 6$ &#$*,-N ¢S+#$%VQopN>Q$&1*!/$ "# (7QnDNQL+#$%?+#$#$,Qo¢2N q/tuuuJznN ,-*(4,-#JAM&1"#0"T D;A@$"=;V+/H %$&"* @$&1;?I(8*, ,QOL,1%$(8-QNQ+#$%~2.J+;A@$,Q~N|q/tuuyJznN=j,nL#$& &1"#C"ToKJ¡;"#J&#="$!
ty
6$1#$&! 6$@$, &;K #!5T^"5()+ &1"#9T^"@$,R ;AxP&1#$*g#$%) @$,j#$.=! &!G"+Tn }(4"&"#§N (,d,1 /. -@A, A)>1 2 nQoqez tuv|t|N j,-&1#$*,n ,Q CN)qmtuuuznN :,#$,- \[Pl5,-; ¤ ,;-"#!55$; &1"#[L!5,-% "# &(86$,n ,! @$,!-N 2"B1 m! u! .A')/ " ,2$)+ 2+!#LQ$J$qez >tttt-JN j,-5&1;A@$,+Q ¤ NLq/tVuyJvzNL{2!5&1#$*Cr##P. !;- &>, &`K"\%$, &>3,Kj ,;-$5! &>3,->.a&(86$,-(4,-#J,% "6|&1(8,-%$*,C%,,; "-N 2B" 1 ! u! .A')/ " ,2$ + 2+!#LQ§tPqez >tJvtVyJv|N D`V.J%&eQ Nq/tuuvzn N /"%+!# / , ,2 $g = ,- ,( '$2"% ,/11,( ,2" $ ,( -,d/ ,A,- ,2/ $&!# ,( '!#/$ 1, "%$ J" ,/.,2" , . @A,(nN @L} @$,-!5&1!-Q{2#$&>3, ! &> ,: "! ,-6@7OL" &1,-Q|\ ,-#"+H [$,QLOL #$;-,+N :, &*$Q fNQ $ # [$,--Q fN>Q &1xP&1#$&!-Q ¤ N>Q #$%f"1,-! Q OSN=qmtuuJznNP2"#$1&#$,V2#$&1!5"5"6$&; O& ,- &#$*g"+T '¤ \MA N $d G!#) ,d,+*d> 1 . @A @QUttJqez =t J=N :&1;A@$,n &sQLgNq/tuuyJznN j#|H 1&#$,C#L>.|!5&1!R"TD,;A@$"|;- %&1"* 6$@$&;~&()+*,\! , 1 2 nQoqsJz |t yN :| (8#§Q N>Q &#$;-,+QLN>Q$#% ; ,&1*@UQ$pNqmtuuPzNh*9+#$%];-"#P "$p%$,n,;&"# &#gA**,-% '¤ &1(8*,-!"To@$,p,Ti 3,-#J5&1;1,N $d o!# (,d,+*d> 1 /. @A @Q t$q/t z v+ |yyN 2, 1&#§Q AND#$%R.J;A@$,+Q~Nq/tuuznNOL,V+ $ ,),n= ; &1"#b#%b#L>.|!5&1!a(4, @$"=%$! T^"B!5,-QUR"[$1,+QogN>Q 1,/H %$Q NQ#$%X¢G`x+,QgNDqmtuuuznNR 3+1L+ &1#$*8 5"[$$!/p;-"#J "$S ;Ax+,-p"#],;A@$"=;V5%$&1"*6$@&1;!5,- 1 2 nQ Lqmt z |v¥|N ! !Q N>Q&>xP&1#§Q gN>Q +#$% ,- "6"$1"!-Q aNSq/tVuyyJzN #L+x,-! ;n&>3,BrS"#J "$ "=%$,1!- N g" 1 ! u! .A')/" ,2$ + 2+!#LQt J|t |tN &1(4&`Q ¢N>Q#$#$,#P[L$(?QgN>QJ#( % U$;Ax,-Q N$q/tuuznN j#f@,,3"1 &1"#f"+T;$53,-! 3=&`7'T^$#$;n&1"#"TK;-53++ ,]&sNh @$,];`!5! &1;-k;V!5,N !#/ $g)> 1 ! >" ?,/. " +*d> 1 A)> 1 2 -), '12 ' 1 +*d" +!#nQUt J y PP¥yN ;V;A@,-#§QoN|#$%)j$#$;-#§QN§qmtuuJvzN @L+6,%|HI[L+! , ;AxP&1#*g"T,Tik3,#P &;-$1 ES1U(8" &1"#UN $ m!#) (,d,+*d> 1 . @A @QUtLqJz v ¨ yN ;-I#,- #,.Q:\N\+#$% , "6"1"!Q\aNfqmtuuJ¥zN_ O&1#$&>,,-(4,-#J "=%$,-~T^" @L6, ¤ ,-;"#$!/ ;&"#X#% 2"#$ &*&1% " &1"#? ;AxP&1#$*NRI# 2" ,2$2)"%+!#)> 1 u!# ,2&$ ,2 * , !# u! .A')/J" ,2) $ + 2+!# + $g" /> 1 ,d> 1 " 7), 0! 2!#"%+*(- ,d,+*2 ,
+ ,d, MQ3"1(8,:u¨¥f"+T oQ$6L*,!2¥|ty ¥N 6$ &#$*,-m(H , `+*$N ;-I#,- #,.QS\NS#%¡ ,- "6"$1"!-QGaNqmtuuznNj,nT^" (8[$,?(4"=%$,-!4&#¡(4,-%$&;V &()*,j#L+.=! &! L9! $/3,n. N (,d,1 /. @A, A)> 1 2 nQ§tPqsz ut tV¨yN "#$*Q aNQj, &;A@$,Q ¤ NQ `#%L&1#UQfNQ #%arS"=;-3, L>, &1#*f#$%B,-%*,\+;Ax=&#$* IEG"96$ &()+5.4"="1!ST^"p%B,-%$*,\%$, ,-; &1"#U N /. @A, ), + 2+!# u! .A')/" A @Q$uLqPz +¨ |t-$N "#JA+*#L+-QSN+#$%Fj,1&1#*,5,QI~NRq/tVuuyJzNF\1"[$1>.;"#$!/+&1#$,%¡%$,nT^" (8[$, (4"|%,-1!GT^"K "[=l5,-;nR ,-;"#$!/ ;&"#§N @)> 1 u$&! * ,((2A @Qov|tPqsz >t v tyN "#JA+*#L+-QN|#$%)j,-&1#$*,n ,Qk~NUqe+¨¨¨JzN 6L;,j#%)p&1(4, @L6,jrS"#$!5 &#$,-% j,nT^" (8[$, $/T;-,!?T^"]J ,-%$&;V\I(8*, ,-*(4,-#JAM&1"#§N I# ,d,1 /. 0 @A, u! .A')/ "%A @C), u! .A')/ " ,2$ 0 (2 2" ,d, gJ" ,2$ =>,2"%+!# ! " MQJ3"1$(4, tuJ¥g"T oQL6L*,-!:tu |¨J¥|Q &> ! [$$5*@§Qo{ gN 6 &1#*,-N !/AQ rN #$%:R.J;A@$,+QM~NPqmtuuJzNOL5,-t¨Jvot¨JvuN 6$%$,-(4, &!- Q gNQ &1#PL!QgN>Qj&"#$,+QaN>QS#%Zj#$;V#UQpN:qs¨¨t zN D!5&() H &1"#8"T}1,nTiS3,#J &;-$1S%,T^"5()+ &1"#4T^ "(
,-;A@"|;- %$&"* 6$@J.* N ,d,1 /. -@A, A)> 1 2 nQo¥$qmt z >t v +yN 5xoQN>Q ,nAM!Q|aN>QP#$%4R|,eQknDNq/tuuJznN#$.=! &!"T§,TiD3,#J &;-$1(8"+&1"# [L+! ,-%¡"#¡3"1$(4, &1;B%$,nT^" (8[$,B(8"=%$,-!)+#$% '¤ eH N (,d,1 /. @A, A)> 1 2 nQ§tPqmt z ¥ v=tN , "#L|Q N#% &1xoQRN~q/tuu¨JznN ;V,nH 6L;,#%}D%$*,j,,; &1"# {2! &#$* 2#$&1!5"5"6$&1;gj& $! &"#§N $ !# " " ,2$g A)> 1 2 4), 6* , 2? 0 " ,/11 @A,2 * ,nQUt J+ u |u|N ¤ ,n.=#L %UQ§aN>Q¢G`x+,QU~NQ VEK&eQgN>Q I.|,-!Q NQU#$% ¤ %$%L|Q§fNq/tuu¥znNrS"(fH ; 6$|,-h ;AxP&1#$*2"T$**,% '¤ &1(8*,-!T^" (4"&"#C#L>.|!5&1!N=I# 2" ,2$2)"%+!#)> 1 u!# ,2&$ ,2 * , !# u! .A')/J" ,2) $ + 2+!# + $g" /> 1 ,d> 1 " 7), 0! 2!#"%+*(- ,d,+*2 ,
+ ,d, MQ3"1(8,:u¨¥f"+T oQ$6L*,!2v vN 6$ &#$*,-m(H , `+*$N ¤ "@$1&#$*$Q ¤ NQ|\,-,Q=gN>Q|#$%0¢S, (8#§QnDN§qmtuuJvznNp@$5,-,nH %$&1(4,-#! &1"#Lo! 6LM&`+;"(fH 6"$#$%&1#$*f"T$ !5"$#$%B&()*,-!-N ,d,1 . @A, A)> 1 2 nQ§tPqsz >t v v tVuN ¤ "#T %UQ ¤ NDq/tVuuPzN ¤ ,*&1"#|HI[L+! ,-%X!/ +,*&1,!T^"\;n&>3,a;"#J"$(8"=%$,-!-N g" 1 ! u! .A')/J" ,2) $ + 2+!#LQ§tLqsz u ¥|tN #$;A@, H j5& QofN>Qj,;-1, ;AxoQoN>Q $,/H +%L|Q N>QL#%B2"[$,Q$Nqe+¨¨¨JzN2|H "()M&1#*\ ;A@"|;- %$&"* 6$@$&;pI()*,p#L>.=! &1!NUI& # ,d,1 . @A, u! .A')/" A @ ), u! .A')/J" ,2$ 0 A(2 2J" ,d, gJ" ,2$ =>,2"%+!# MQ3"1$(4,8tVuJ¥a"T oQ 6L+*,-!RyJ$ v |uQ & ! [$ *@§Q${ ~N 6$ &#$*,-N #$;A@, H j5& Q fNUAN>Q ¤ $,-;Ax+,-5-Q aNQ+#$%¢S" *,--Q NqmtuuuJzN #$"EK1,%$*,HI[L!5,-% ,-#$!5"0#$&! " "6&1;?%$& $! &"#¡"+T~;- %&`;7()*#$, &1;? ,-!5"#L#;-,X&1(8*,!-N ,d,1 . - @A, A)> 1 2 nQLLq/tz vv t¨|tN ;A@P$%.Q ¤ No#$%7¢11 %UQLaN q/tuvuJznN ;-"(46$ ,-K(4"|%$,§T^"K,n= ; &1#$*4(4" 3=&#$* @$,-5:!5$5T+;-,-!:T^ "( T^"$mHI%$&(8,#$! &"#L ;V+ %$&1;f$ !5"$#$%c&()*,-!-N~I# gJ" ,2$ 0 )"%+!#)> 1 u!# ,2&$ ,2 * , !# u! .A')/J" ,2$ + 2+!# ! +MQ6$*,-!R |Jv|N ,n ,-#§QKfN+#$% & ,-Q N:qe¨¨¨JznN ,-%$&1>Hm:$&%$,-%FOo . ,-*(8,#P+&"#§N I# (,d,1 /. - @A, u! .A')/ "%A @ ) , u! .A')/" ,2/$ 0 A(2 2" ,d, 2" ,2$ =>,2" +!# ! " MQ 3"1$(4,ftu¥g"T oQL6L*,!2 +J¥|Q &> !5[$$5*@§Qo{ gN 6$5&1#$*,--N 5,-,;-,Q9N>Q *,-Q ¤ NQG\,-,QkgN>Qk#$%¢G,- (8#§QmnDNq/tuuyJznNFO+!58! $/T;-,'#$% 3"1$(4,g,!5 &1(8+&"#?T^5"(#$"#|H 6L+11,;-5"! !mHI! ,; &1"#$!QUT^"T^5,-,@L#$%cMH % $> H !5"$#$%§N',;A@$#$&1;- ¤ ,-6"/fJ|Qr+(a[$ &%$*,){2#$&>3,-5! &>I.D#$*&#$,-, &#$*Xj,-6$5/H (4,-#JVN ,&1;Ax+,-5-Q+N=q/tuuyJznN A !#"%$&!(')+* , .0/k2+!# 4 . @A, ')$&! * ,((2A @N ,-[$#$,- ,-5`*$N &1#J,5T^,1%-QfN>Q+¢G,- *,--Q N>Qn,n@$"Q+NQ+#$% 2#$%$!5;A@P$@$(8;A@$,-Q N|q/tVuuJvzN|PH 6,-/ "=%$,¢+! ,-% ¤ ,-;-"#$!5 $;n&1"# "T @$,g,Ti ,-#J5&1;1,~{2! &#$*] #!5@"+H ! &;:;A@"*+6$@$&1;:I(8*,!-NDI # u! .A')/ " ,2$& m$ ,+! 1 ! @ +N ¦k"$#$*QG~NQ &>;A@$(8#§QaN>Qkj"$*@$,5I.Q nDN>QS#%FR|,-sQ nDN2q/tVuuJ¥zN ;AxP&1#$* #%BO&1#$&>,,-(4,-#Jp2#L.=!5&1!"T &6,jj,T^"5()+ &1"#8&1# *#$,n&1; ¤ ,! "#L+#$;-, **&#$*$N $ m!#) (,d,+*d> 1 /. @A @QUt-oqsJz t =P=tN U@L#$*Q NqmtuuPzN§ ,+ &3,26"&1#JG()M;A@$&#$*CT^"k5,-*&!5 + &1"#4"T§T^5,-,nHeT^" ( ;$53,-! #%?!5$5T+;-,-!N g" 1 ! u! .A')/" ,2$ + 2+!#LQt$qez ttV u t ¥=N
¨