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ᘮ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`,8/$&"*)+"6 +3$55"*+,$6 +&"&*6*+:M.(+`a&()& +*J +9($/&"*)+$3+$ +1)"JS")5+N$3"3 +J*%+ 7&*"/."*'(&%S+")+`6('()&$%S+-.('"3&%S=+OBP@+I6+#%(3()&(+/*)&%"V8&*+#*&%(VV(+3&"'*6$%(+"+,*/()&"+8)"2(%3"&$%"+$+2$68&$%(+ 6Q"#*&(3"+,"+$,*&&$%(+J")$6'()&(+&$6(+/*)/(&&*+5"4+$6+6"2(66*+,(66Q")3(5)$'()&*+")&%*,8&&"2*+,"+-."'"/$+]()(%$6(+#(%+"6+ /*%3*+,"+6$8%($+")+7/"()<(+-."'"/.(@+ 4./)$53''"/$'3,6"(73'+"," >*33"$'*+%$##%(3()&$%(+8)$+[8$63"$3"+%($<"*)(+/."'"/$+/*)+"6+3(58()&(+J*%'$6"3'*+ Σ+b+νb+?b+!+Σ+c+νc+?c *##8%( Σ+b+νb+?b+"+Σ+c+νc+?c ;(+3#(/"(+/."'"/.(+?b +(+?c+ %$##%(3()&$)*+"+%($5()&"+Fb+d+D0+L0+eH+(,+"+#%*,*&&"+Fc+d+D0+L0+eH+/.(0+%"3#(&&"2$'()&(0+ 3/*'#$"*)*+(+3"+J*%'$)*+)(66$+%($<"*)(+/."'"/$@+;(+[8$)&"&4+3(/*),*+/8"+6(+3#(/"(+%($5"3/*)*+3*)*+,$&(+,$"+/*(JJ"/"()&"+ 3&(/."*'(&%"/"f+[8$),*+νb+'*6"+,(6+%($5()&(+bg(3"'*+%($5"3/*)*0+(+[8"),"+3/*'#$"*)*0+3"+J*%'$)*+νc+'*6"+,"+#%*,*&&*+cg (3"'*@+ T8$),*+#(%+'(&&(%(+")+%(6$<"*)(+%($5()&"+(+#%*,*&&"+83"$'*+"6+3"'V*6*+!+2*56"$'*+%(),(%(+(3#6"/"&*+"6+J$&&*+/.(+$66$+J")(+ ,(66$+%($<"*)(0+")+,(&(%'")$&(+/*),"<"*)"+3#(%"'()&$6"0+#*33*)*+$)/*%$+(33(%(+#%(3()&"+"+%($5()&"0+*22"$'()&(+")+[8$)&"&4+ ")J(%"*%"+%"3#(&&*+$66(+[8$)&"&4+")"<"$6"+F&+d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νb+ Fb+d+D0+L0+eH@+I)+5()(%$6(+$6/8)"+%($5()&"+#*&%(VV(%*+(33(%(+")+(//(33*+(+%"'$)(%(+")$6&(%$&"+$66$+J")(+,(66$+%($<"*)(@+I + %($5()&"+6(+/8"+[8$)&"&4+")+'*6"+3"+$))866$)*0+,(&(%'")$),*+/*3h+6$+J")(+,(66$+%($<"*)(0+2()5*)*+,(&&"+-'.,'&(*#"*1*(.&(*@+ >(%+,(3/%"2(%(+[8$)&"&$&"2$'()&(+8)$+%($<"*)(+/."'"/$+/*)2"()(+8&"6"<<$%(+"6+6")58$55"*+'$&('$&"/*@+?+[8(3&*+3/*#*+ ,(J")"$'*+*"#,-.)%#)*#./.&0.1'&(%#)'"".#-'.0*%&'+0+ξ0+$6+&('#*+&+'"38%$&*+,$6+'*'()&*+")+/8"+")"<"$+6$+%($<"*)(0+/*)+6$+ 3(58()&(+([8$<"*)(+5()(%$6(f )"+d+)"C+i+ν"+ξ+ I6 + 5%$,* + ," + $2$)<$'()&* + R + *22"$'()&( + 8)$ + 5%$),(<<$ + (3&()3"2$@ + 7( + /*)3",(%"$'* + 6( + /*)/()&%$<"*)" + ,(66( + 3#(/"(+ /."'"/.(+,(J")"$'*+"6+5%$,*+,"+$2$)<$'()&*+#(%+8)"&4+,"+2*68'(0+8)$+5%$),(<<$+")&()3"2$f /"+d+/"C+i+ν"+ξ2 -*)3",(%$),*+6$+3#(/"(+"g(3"'$+/*'(+%($5()&(+6"'"&$)&(+F/')*#*&4-.H0+"6+2$6*%(+'$33"'*+,(6+5%$,*+,"+$2$)<$'()&*+)(6+ /$3*+,"+%($<"*)"+"%%(2(%3"V"6"+F)"+"+C+0+/"+"CH+2$6(+ ξ+d+g+)"Cjν" ξ2+d+g+/"Cjν" ?338'(),* + 8)$ + /*'#*3"<"*)( + 3&(/."*'(&%"/$ + ,(" + %($5()&" + "6 + /$6/*6* + ,(6 + 5%$,* + ," + $2$)<$'()&* + ,(66$ + %($<"*)( + ,4+ *22"$'()&(+6*+3&(33*+2$6*%(+$+#%(3/"),(%(+,$6+%($5()&(+/*)3",(%$&*@ k(6+/$3*+,"+%($<"*)"+6"'"&$&(+,$66Q([8"6"V%"*+/."'"/*+#*33"$'*+3/%"2(%( ξ2+d+F/"([g+/"CH+jν" >(%+*5)"+3#(/"(+/."'"/$+"g(3"'$+F%($5()&"+(+#%*,*&&"H+) "+%$##%(3()&$+6(+'*6"+#%(3()&"+)(6+3"3&('$+,"+%($<"*)(+$6+&('#*+&0+ )"C+3*)*+6(+'*6"+")"<"$6"+F&+d+CH0+(+ν"+R+"6+/*(JJ"/"()&(+3&(/."*'(&%"/*+/*)+/8"+6$+3#(/"(+/*'#$%(+)(66Q([8$<"*)(+/."'"/$+ V"6$)/"$&$@+`Q+)$&8%$6(+,(J")"%(+ν"+l+C+#(%+"+#%*,*&&"+(+ν"+m+C+#(%+"+%($5()&"+(+%"/*)*3/(%(+/.(+6Q([8$<"*)(+/*)+/8"+$VV"$'*+ ")&%*,*&&*+"6+5%$,*+,"+$2$)<$'()&*+,(66$+%($<"*)(+%$##%(3()&$+"6+V"6$)/"*+,(66(+'*6"+#(%+*5)"+3#(/"(+/*")2*6&$+)(66$+ %($<"*)(+/."'"/$@+ !*#*+/.(+6$+%($<"*)(+$6+6"2(66*+'"/%*3/*#"/*+,(56"+$&*'"+(+,(66(+'*6(/*6(+3"+R+%"#(&8&$0+$%;R#$%1'#/*'&'#;$-*((.0+#(%+8)+ )8'(%*,"+2*6&(+#$%"+$66$+/*3&$)&(+,"+?2*5$,%*0+,"/"$'*+/.(+"6+5%$,*+,"+$2$)<$'()&*+,(66$+%($<"*)(+2$6(+ξ+d+D+'*6%a)+@+ k(6+&('#*+)(/(33$%"*+#(%+%$55"8)5(%(+[8(3&*+2$6*%(+6(+'*6"+,("+%($5()&"+3*)*+,"'")8"&(+,(66$+[8$)&"&4+νb+Fb+d+D0+L0+eH+(+ 6(+'*6"+,("+#%*,*&&"+3*)*+$8'()&$&(+,"+νc+Fc+d+D0+L0+eH@+ I6+5%$,*+,"+$2$)<$'()&*+ξ+3"+(3#%"'(+")+'*6"+F'*6%a)H+(,+R+3('#%(+n+C0+")J$&&"+F) "+g+)"CH+j+ν"+n+C+W+(33*+,"#(),(+,$6+&('#*+ (+%$55"8)5(+8)+2$6*%(+'$33"'*+3"$+#(%+6(+%($<"*)"+/.(+%$55"8)5*)*+6Q([8"6"V%"*+/."'"/*0+3"$+#(%+6(+%($<"*)"+/."'"/.(+ "%%(2(%3"V"6"+F6"'"&$&(+3*6*+,$66(+[8$)&"&4+,("+%($5()&"H@+I+/*(JJ"/"()&"+3&(/."*'(&%"/"+3*)*+[8$)&"&4+$,"'()3"*)$6"+(33(),*+ ν"+d+OF)"+g+)"C+H+j+ξP+d+∂)"j∂ξ0+/"*R+%$##%(3()&$)*+6(+'*6"+,"+3#(/"(+%($&&"2$+/.(+3/*'#$%(+F%($5()&(H+*+3"+J*%'$+F#%*,*&&*H+ #(%+'*6(+,"+5%$,*+,"+$2$)<$'()&*+,(66$+%($<"*)(+F'*6"j'*6%a)H@+ I)+8)$+%($<"*)(+/."'"/$+6$+3(58()&(+%(6$<"*)(+3&(/."*'(&%"/$+5()(%$6(+&%$+,8(+%($5()&"0+b+d+D+(+b+d+L0+2"()(+/*'8)('()&(+ $##6"/$&$+)("+#%*V6('"+3&(/."*'(&%"/"+ ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++F)D+o+)DCH+j+νD+d+F)L+o+)LCH+j+νL+ Δ)D+d+FνDjνLH+Δ)L+ T8(3&$ +([8$<"*)(+R+8)$ +,"%(&&$+/*)3(58()<$+,(6 +J$&&*+/.(+")+8)$ +%($<"*)(+/."'"/$ +6(+[8$)&"&4+,(" +%($5()&" +/.(+3"+ &%$3J*%'$)*+)("+#%*,*&&"+R+,(&(%'")$&*+,$6+5%$,*+,"+$2$)<$'()&*+,(66$+%($<"*)(+ξ@ ?VV"$'*+[8"),"+8)+3('#6"/(+/%"&(%"*+#(%+3&$V"6"%(+3(+")+8)$+%($<"*)(+/."'"/$+R+#%(3()&(+8)+%($5()&(+6"'"&$)&(@+I)J$&&"+"6+ -'.,'&('#"*1*(.&('+#(%+)b+"+C+#%(3()&$+"6+2$6*%(+'")"'*+#(%+5%$,*+,"+$2$)<$'()&*+,(66$+%($<"*)(+,$&*+,$+ξ+"+g+)bCjνb+@ -*'(+#%"'$+$##6"/$<"*)(+/*)3",(%"$'*+6$+3(58()&(+%($<"*)(+OpP \+?5F3H+i+L+qL7F5H+i+rLF5H+"+L+?5L7F3H+i+L+qLrF6H ,(&(%'")"$'*+"6+%($5()&(+6"'"&$)&(+)(66$+%($<"*)(+,"+C@KBC+5+,"+?5+FC@CCEED+'*6H0+/*)+C@D\C+5+,"+q L7+FC@CC\DD+'*6H+(+ C@CECC+5+,"+rL+FC@CCLBC+'*6H0+(+/$6/*6"$'*+6(+[8$)&"&4+,"+?5L7+(+,"+qLr+/.(+3"+J*%'$)*@+7"+)*&"+/.(+"6+'*&*,*+%"3*68&"g+ !& 012',+!"!3$44'/!5677!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!''#$%'"!#$!%&'(')$!*+,,$!-)./,$ 82$:/!:'!$;$*<$(+*9/ 2*+V$3$&*+386+/*)/(&&*+,"+5%$,*+,"+$2$)<$'()&*+,(66$+%($<"*)(+R+)*&(2*6'()&(+#"U+3('#6"/(+(+,"%(&&*+%"3#(&&*+$+&8&&" + [8(66"+J")*+$,+*55"+#%*#*3&"+O2(,"+9"J@p+(+%"J(%"'()&"+"2"+/"&$&"P@ -$6/*6"$'*+6(+[8$)&"&4+g+)bCjνb+#(%+&8&&"+"+%($5()&" C+j+ν qL7+H+d+C@CCLCp+'*6%a)+ L7 C gF)?5 +j+ν?5H+d+C@CCLLC+'*6%a)+ gF)r C+j+νr +H+d+C@CCLBC+'*6%a)+ L L gF)q "+,"JJ(%()&"+2$6*%"+"),"/$)*+/.(+"+%($5()&"+)*)+3*)*+")+%$##*%&*+3&(/."*'(&%"/*+(,+"6+2$6*%(+'")"'*+C@CCLCp+'*6%a)+"),"/$+ /.(+qL7+R+"6+%($5()&(+6"'"&$)&(@ I6+5%$,*+,"+$2$)<$'()&*+,(66$+%($<"*)(+2$6(+[8"),"+ ξ+d+g+)q L7 Cjν qL7+d+C@CCLCp+'*6%a) ,$+/8"+*&&()"$'*+6(+[8$)&"&4+,("+#%*,*&&"+%"/."(3&(f+ )?5 7+d+L+ξ+d+L+a+C@CCLCp+d+C@CC\DL+'*6+#$%"+$+D@CL+5+,"+?5L7+ L )q r+d+L+ξ+d+L+a+C@CCLCp+d+C@CC\DL+'*6+#$%"+$+C@C^\L+5+,"+qLr@ L -*'(+3(/*),$+$##6"/$<"*)(+/*)3",(%"$'*+6$+3(58()&(+([8$<"*)(+OBP L+kLq\F5H+i+kLr\F5H+"+Z+kLF5H+i+\+qLrF5H (+,(&(%'")"$'*+"6+%($5()&(+6"'"&$)&(+)(66$+%($<"*)(+,"+DC@C+5+,"+kLq\+FC@ZDLD+'*6H+/*)+DC@C+5+,"+kLr\+FC@DCE^+'*6H@ -$6/*6"$'*+6(+[8$)&"&4+g+)bCjνb+#(%+"+%($5()&" C+j+ν kLq\+H+d+C@DBpD+'*6%a)+ gF)k r C+j+νk r +H+d+C@DCE^+'*6%a)+ L \ L \ gF)k Lq\ I6+%($5()&(+6"'"&$)&(+R+kLr\+(,+"6+5%$,*+,"+$2$)<$'()&*+,(66$+%($<"*)(+2$6(+ξ+d+C@DCE^+'*6%a)@ ;(+[8$)&"&4+,(66(+3#(/"(+#%(3()&"+$66$+J")(+,(66$+%($<"*)(+3*)* )k Lr\+ d+C )k Lq\++ d+C@ZDLD+o+L+a+C@DCE^+d+C@CK\^+'*6+F+Z@CZ+5H )k +d+Z+a+C@DCE^+d+C@ZLpD+'*6+F+K@D\+5H L )q Lr+ d+\+a+C@DCE^+d+C@\Z\E+'*6+F+^@EZ+5H@ r6&%(+$,+$2(%+'"56"*%$&*+6Q$##%*//"*+,"+]$%3&+)(66Q(3('#"*+3&(/."*'(&%"/*+3*#%$+%"#*%&$&*+OBP0+/*%%(55"$'*+8)+(%%*%(+)(6+ [8$6(+(56"+R+")/*%3*+$##6"/$),*+"6+/*)/(&&*+,"+5%$,*+,"+$2$)<$'()&*+,"+8)$+%($<"*)(+$66*+3&8,"*+,"+([8"6"V%"+/."'"/"+")+ 3*68<"*)(+$/[8*3$@ -*)3",(%"$'*+D+;+,(66$+3(58()&(+3*68<"*)(+#%(#$%$&$+$55"8)5(),*+C@DCC+'*6+,"+?/rk$+(+C@DCC+'*6+,"+?/rq ?+&$6(+3*68<"*)(+3"+$55"8)5*)*+38//(33"2$'()&(+C@CDC+'*6+,"+k$rq@+T8$6+R+"6+#q+#%"'$+(+,*#*+6Q$55"8)&$+,"+k$rqs ;Q$##%*//"* + %"3*68&"2* + V$3$&* + 386 + 5%$,* + ," + $2$)<$'()&* + ,(66$ + %($<"*)( + #%(2(,( + 6$ + ,(J")"<"*)( + ,(66( + %($<"*)" + ")+ 3*68<"*)(f ?/rk$+"+?/rg+i+k$i++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++FDH ?/rq+!+?/rg+i+qi++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++FLH qLr+!+rqg+i+qi+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++FZH k$rq+"+rqg+i+k$i++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++F\H rqg+i+?/rq+"+?/rg+i+qLr+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++FBH !( #$%!"!#$!%&'(')$!*+,,$!-)./,$!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!012',+!"!3$44'/!5677 8'.,'$*/!3/2+99' -*)3",(%$),*+"6+5%$,*+,"+$2$)<$'()&*+,(66$+%($<"*)(+#(%+8)"&4+,"+2*68'(0+ξ20+#*33"$'*+3/%"2(%(+6(+3(58()&"+([8$<"*)"+ 2$6",(+B-*1.#)'""J.,,*2&(.#)*#*)-%;;*)%#)*#;%)*% O?/rqP+d+C@DCC+o+ξ2L+++WO?/rgP+d+C@DCC+i+ξ2L+ OqiP+d+ξ2L+i+ξ2Z+W+OrqgP+d+ξ2Z -*)3",(%$),*+t$L+d+D@E+a+DCgBW+tuZ+d+Da+DCgD\+W+ξ2Z+mm+ξ2L+mm+C@DCC+'*6;gD+*&&()"$'* t$L+d+D@E+a+DCgB+d+C@DCC+a+ξ2L+j+C@DCC OqiP+d+D@E+a+DCgB+'*6;gDW+#q+d+\@^\@ 9%B%#"J.,,*2&(.#)*#*)-%;;*)%#)*#;%)*% O?/rqP+d+C@DCC+g+ξ2B O?/rgP+d+C@DCC+i+ξ2B+ OqiP+d+ξ2L+i+ξ2Z OrqgP+d+ξ2Z+F+(+)*)+OrqgP+d+C@CDC+i+ξ2Z+/*'(+%"#*%&$&*+)(6+9"J@BH ξ2Z+mm+ξ2L ξ2\+d+ξ2B+d+C@CDC+'*6;gD !$+/8"+3"+/$6/*6$+J$/"6'()&( t$L+d+D@E+a+DCgB+d+C@DDC+a+ξ2L+j+C@CKC OqiP+d+D@B+a+DCgB+'*6;gDW+#q+d+\@EL@ 7"+,"'*3&%$+J$/"6'()&(+/.(+&$6(+$##%*//"*+R+([8"2$6()&(+$66Q$##%*//"*+V$3$&*+386+V"6$)/"*+,(66(+'*6"+(,+"6+V"6$)/"*+,(66(+ /$%"/.(+)(66$+3*68<"*)(@ F>(%+"+/$6/*6"+3&(/."*'(&%"/"+R+3('#%(+/*%%(&&*+83$%(+6$+[8$)&"&4+,"+3*3&$)<$+(3#%(33$+")+'*6"0+")+$//*%,*+/*)+"6+3"3&('$+ 7I@+k(6+#$33$&*+2()"2$+,"+#%(J(%()<$+8&"6"<<$&*+"6+/*)/(&&*+,"+([8"2$6()&(@+;$+'$33$+([8"2$6()&(+,"+8)$+3*3&$)<$0+$)/.(+ )*&$+/*'(+'$33$+,"+/*'V")$<"*)(0+(%$+o+(+J*%3(+")+#$%&(+$)/*%$+6*+R+g+,"+83*+/*'8)(+#(%+8)+/."'"/*+$)$6"&"/*@+7(/*),*+ [8(3&*+$##%*//"*+6(+3*3&$)<(+%($5"3/*)*+3(/*),*+8)*+3&(33*+)8'(%*+,"+([8"2$6()&"+(+)*)+%"386&$+)(/(33$%"*+3/%"2(%(+(+ V"6$)/"$%(+6$+%($<"*)(+/."'"/$@ v(,"$'*+/*'(+#*33"$'*+%$<"*)$6"<<$%(+&$6(+$##%*//"*+$66$+68/(+,(6+/*)/(&&*+,"+5%$,*+,"+$2$)<$'()&*+,(66$+%($<"*)(@+ >$%&"$'*+,$66Q([8$<"*)(+ Δ)"+d+Fν"jνbH+Δ)b+ /.(+(3#6"/"&$),*+"6+)8'(%*+,(66(+'*6"+,(66$+3#(/"(+/."'"/$+#*33"$'*+3/%"2(%( ΔO'"+j+FA"+jνb+HP+d+ΔO'b+jFAbjν"HP I)&(%#%(&$),* + 6Q858$56"$)<$ + /*'( + 858$56"$)<$ + &%$ + 56" + ([8"2$6()&" + /."'"/" + /.( + .$))* + %($5"&* + 2(,"$'* + /.( + A "+ jνb+ %$##%(3()&$ + 6$ + '$33$ + ([8"2$6()&( + ,(66$ + 3*3&$)<$ + "g(3"'$ + ( + A bjν" +6$ + '$33$ + ([8"2$6()&( + ,(66$ + 3*3&$)<$ + bg(3"'$@ + I6+ /*(JJ"/"()&(+3&(/."*'(&%"/*+νb+Fν"H+%$##%(3()&$0+")+[8(3&*+/$3*0+"6+)8'(%*+,"+([8"2$6()&"+,(66$+3#(/"(+"g(3"'$+Fbg(3"'$H+#(%+ '*6(+,"+3#(/"(+"g(3"'$+Fbg(3"'$H@ >(%+6$+%($<"*)(+$/",*gV$3( qL7r\+i+L+k$rq+"+k$L7r\+i+L+qLr+ $VV"$'*+/.(+L+([8"2$6()&"+,"+$/",*+3*6J*%"/*+%($5"3/*)*+/*)+L+([8"2$6()&"+,"+",%*33",*+,"+3*,"*@+ >(%+6$+%($<"*)(+,"+/*'#6(33$<"*)( ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++?5krZ+i+L+t-k+"+t?5F-kHL+i+tkrZ ΔO'?5kr j+FA+?5kr +jL+HP+d+ΔO't-k+jAt-kP Z Z 6$+'$33$+([8"2$6()&(+,"+?5krZ+2$6(+A+?5kr +jL@ Z !) 012',+!"!3$44'/!5677!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!''#$%'"!#$!%&'(')$!*+,,$!-)./,$ 82$:/!:'!$;$*<$(+*9/ >(%+/*'#6(&(<<$+%"#*%&"$'*+$)/.(+"6+5%$,*+,"+$2$)<$'()&*+,"+8)$+%($<"*)(+(3#%(33*+")+([8"2$6()&"@+`33*+3"+*&&"()(+ ,$66Q([8$<"*)(+/.(+,(J")"3/(+"6+5%$,*+,"+$2$)<$'()&*+'*6&"#6"/$),*+()&%$'V"+"+'('V%"+#(%+νb+f νb+)"+d+νb+)"C+i+νb+ν"+ξ >(%+[8$)&*+%"#*%&$&*+3*#%$+#*33"$'*+3/%"2(%( (["+d+(["C+i+ξQ ,*2(+ξQ+d+νb+ν"+ξ+%$##%(3()&$+"6+5%$,*+,"+$2$)<$'()&*+,(66$+%($<"*)(+")+([8"2$6()&"+,"+%($<"*)(@+:!"'()3"*)$6'()&(=+"6+ #%*,*&&*+2$6(+([8"2$6()&"+,"+%($<"*)(0+")J$&&"+F([ "j'*6"HF'*6"j'*6%a)H'*6%a)+≡+(["+≡+([%a)@+IS.2(%-'#;$%&;*,"*.#/*/.1'&(' # "S2;%#)',"*#'K2*/."'&(*T#*&#.$$%-)%#$%&#*"#;*;('1.#<!#)'""'#2&*(U#)*#1*;2-.#',"*#-*(*'&'#$C'#*"#$%&$'((%#)*#'K2*/."'&('#A # %,,*#;2B'-4"2%#'#)*).((*$.1'&('#).&&%;%?H 8./)$53''"/'3+7(1""," I)+&(%'*,")$'"/$+/."'"/$+/*)3",(%"$'*+6$+2$%"$<"*)(+,"+()&$6#"$+3&$),$%,+,"+8)$+%($<"*)(+/."'"/$+#%*,*&&"+(+%($5()&"+ )(6+6*%*+3&$&*+3&$),$%,0+$66$+&('#(%$&8%$+M+(,+$66$+#%(33"*)(+,"+D+V$%+FDa+DC B+ >$HH0+8&"6"<<$),*+"6+3"'V*6* +Δ%qC0+$,+ (3('#"*+$+LKZ+t+OZP kL+F5H+i+Z+qLF5H++!++L+kqZF5H+Δ%qC+d+g+KD@BCL+c_++F*++$+2*6&(+o+KD@BCL+c_j'*6H@ I) + (JJ(&&" + "6 + 3"'V*6* +Δ% +)*) + %$##%(3()&$ + 8)$ + ,"JJ(%()<$ + J")"&$ + '$ + 8)$ + %$#","&4 + ," + 2$%"$<"*)( + ,(66$ + 5%$),(<<$+ &(%'*,")$'"/$+/*)3",(%$&$+%"3#(&&*+$6+5%$,*+,"+$2$)<$'()&*+,(66$+%($<"*)(0+/"*R +Δ% +≡+ ∂j∂ξ+ OLP@+;Q8)"&4+,"+'"38%$+R+ c"6*b*86(+#(%+'*6(+,"+5%$,*+,"+$2$)<$'()&*+,(66$+%($<"*)(W+#(%+6$+%($<"*)(+/*)3",(%$&$+o+KD@BCL+c_j+'*6 %a) +0+/"*R+#(%+ '*6(+,"+$<*&*+*##8%(+#(%+Z+'*6"+,"+",%*5()*+/.(+%($5"3/*)*0+(+#(%+,8(+'*6"+,"+$''*)"$/$+/.(+3"+J*%'$)*+w >(%+6$+3&(33$+%($<"*)(0+$+#%(33"*)(+3&$),$%,+(,+$66$+&('#(%$&8%$+M0+6$+2$%"$<"*)(+,"+()(%5"$+6"V(%$+3"+3/%"2(+")+J8)<"*)(+,("+ #*&()<"$6"+/."'"/"+3&$),$%,+,"+%($5()&"+Fν"+m+CH+(+#%*,*&&"+Fν"+l+CH Δ%]C+d+Σ"+ν"+µ"C µ"C+d+∂]"Cj∂)" ;$+2$%"$<"*)(+Δ%]C+)*)+%$##%(3()&$+8)$+,"JJ(%()<$+J")"&$+'$+6$+%$#","&4+,"+2$%"$<"*)(+,(66Q()(%5"$+6"V(%$+3&$),$%,+,(66$+ %($<"*)(+%"3#(&&*+$6+5%$,*+,"+$2$)<$'()&* Δ%]C+d+∂]Cj∂ξ+d+Σ"+F∂)"j∂ξH+F∂]"Cj∂)"H@ -*)3",(%"$'*+6$+%($<"*)(+/."'"/$+/.(+5()(%$+"6+#*&()<"$6(+,(66$+#"6$+;(/6$)/.x+$6/$6")$ y)F3H+i+L+A)rLF3H+"+y)rF3H+i+L+A)LrZF3H+ Δ%]+d+g+)+Y+`+z+g+LK^+c_j+'*6%a) M$6(+2$6*%(+3"+*&&"()(+/*)3",(%$),*+)+d+L+'*6+( gj+'*6%a)+0+Y+d+Kp\EB+-j+'*6+(g0+(+,$6+2$6*%(+,(6+#*&()<"$6(+#(%+6$+#"6$+ '"38%$&*+$+/"%/8"&*+$#(%&*0+#$%"+$+`+z+D@B+v@ I6+%($5()&(+6"'"&$)&(+,"+8)$+#"6$+;(/6$)/.x+R+"6+,"*33",*+,"+'$)5$)(3(@+r5)"+#"6$+)(+/*)&"()(+/"%/$+p+5+0+[8"),"+"6+5%$,*+,"+ $2$)<$'()&*+&*&$6(+,(66$+%($<"*)(+2$6( ξ+z+FpjEp@K\HjL+d+C@CZ\B+'*6%a) ;Q()(%5"$+&*&$6(+J*%)"&$+,$66$+#"6$+2$6( Δ]+d+Δ%]+a+ξ+d+F∂]j∂ξH+a+ξ+d+gLK^+a+C@CZ\B+d+g+DC@L+c_ 1)$ + ,(66( + /$%$&&(%"3&"/.( + #%")/"#$6" + ,(66$ + #"6$ + ;(/6$)/.x + $6/$6")$ + R + [8(66$ + ," + '$)&()(%( + "6 + #*&()<"$6( + (%*5$&* + /"%/$+ /*3&$)&(+#(%+6Q")&(%$+2"&$+,(66$+#"6$@+7(+$338'"$'*+8)+/$%"/*+,"+B+Ω+#*33"$'*+3&"'$%(+8)+&('#*+,"+2"&$+,(66$+#"6$+#(%+ '(<<*+,(66$+%(6$<"*)( &+d+T9+j+v ,$+/8"+&+z+Z^C+'")+F+d+L+'*6+(g+j'*6%a)+a+C@CZ\B+'*6%a)+a+Kp\EB+-j+'*6+(g+a+B+Ω+j+FD@B+v+a+pC+3+'")gDHH@ 9./)$53''"/,"&3'","+ ;$+3&(/."*'(&%"$+,(66$+%($<"*)(+/."'"/$+)*)+%$##%(3()&$+5()(%$6'()&(+6Q(2()&*+/."'"/*+(6('()&$%(+3(/*),*+/8"+(33$+3"+ 32*65(0+/"*R+"6+%($6(+'(//$)"3'*+,(66$+%($<"*)(+3(/*),*+/8"+3"+#$33$+,$"+%($5()&"+$"+#%*,*&&"@+;$+3&(/."*'(&%"$+,(66$+%($g !* #$%!"!#$!%&'(')$!*+,,$!-)./,$!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!012',+!"!3$44'/!5677 8'.,'$*/!3/2+99' <"*)(+/."'"/$+R+,(&(%'")$&$+(JJ(&&"2$'()&(+,$66$+3*''$+,"+&$)&" +'/'&(*#$C*1*$*#'"'1'&(.-*#%#B-%$';;*#'"'1'&(.-*+ /.(+ %$##%(3()&$)*+"6+'(//$)"3'*+,(66$+%($<"*)(@+I)+8)+#%*/(33*+(6('()&$%(+3"+%*'#(+*+3"+J*%'$+$6'()*+8)+6(5$'(+/."'"/*+ (+6$+3&(/."*'(&%"$+,(6+#%*/(33*+(6('()&$%(+R+6(5$&$+$66$+'*6(/*6$%"&4+,(6+#%*/(33*+%($&&"2*+(6('()&$%(f+3"+)*&"+/.(+3*)*+ 3&$&" + (JJ(&&"2$'()&( + *33(%2$&" + 3*6&$)&* + #%*/(33" + '*)*g0 + V"g + ( + &%"g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qLF5H+i+rL+F5H"+L+qLr+F6H F(+)*)+qL+i+DjL+rL+"+qLr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d+)"C+i+ν"+ξ+F&H #*33"$'*+,(J")"%(+)(6+'*,*+#"U+5()(%$6(+#*33"V"6(+6$+2(6*/"&4+,"+8)$+%($<"*)(+/."'"/$+/*)+6{([8$<"*)(+ 2+d+,ξ+j,&+d+FDjν"H+,+)"+j,& T8(3&$ + ,(J")"<"*)( + 3" + #8X + $##6"/$%( + 3"$ + $66$ + %($<"*)( + /."'"/$ + 5()(%$6( + 3"$ + $" + 3")5*6" + #$33" + (6('()&$%"0 + 8)$ + 2*6&$+ ",()&"J"/$&*+8)+#6$83"V"6(+'(//$)"3'*+,"+%($<"*)(@ k(6+/$3*+,"+%($<"*)"+/."'"/.(+/*)&('#*%$)((+F%+d+D0L0+eH0+")+/8"+#*&%(VV(%*+(33(%(+/*")2*6&"+&8&&"+*+3*6*+8)$+#$%&(+,("+ %($&&"2"0+#*33"$'*+3/%"2(%(+ )"+d+)"C+i+Σ%+ν"%+ξ%+ 2%+d+,ξ%+j,& ,+)"+j,&+d+Σ%+ν"%+,ξ%+j,& :./;(&,<%$"(&" ?&&%$2(%3* + 6( + 3('#6"/" + (6$V*%$<"*)" + 3*#%$ + %"#*%&$&( + $VV"$'* + /(%/$&* + ," + J$% + 2(,(%( + /*'( + "6 + /*)/(&&* + ," + 5%$,* + ,"+ $2$)<$'()&*+,"+8)$+%($<"*)(+/."'"/$+R+,"+2$6","&4+5()(%$6(+(+'*6&*+8&"6(+)(6+,(3/%"2(%)(+56"+$3#(&&"+3&(/."*'(&%"/"0+ &(%'*,")$'"/"+(+/")(&"/"@ !"&=+#2"#73&'" `Q+ 8) + #"$/(%( + %")5%$<"$%( + Y%$)/* + -$6$3/"V(&&$ + #(% + " + 3855(%"'()&" + ( + /*)3"56" + ,$&" + #(% + '"56"*%$%( + 6$ + /."$%(<<$ + ,(6 + '$)*3/%"&&*@ !">3+"73&'"/*"*<"(=+#>"," D@+I@+>%"5*5")(0+!&(-%)2$(*%&#(%#=C'-1%)O&.1*$;#%4#!--'/'-;*E"'#P-%$';;';0+Z%,+`,@0+|"6(S0+I)&(%3/"()/(0+k(u+}*%c0+DKp^+F%"J(%"'()&*+)@D0+ M.@+!(+!*),(%0+;(/*)3+,(+M.(%'*,S)$'"[8(+(&+,(+-.b('"(g>.S3"[8(0+]$8&."(%gv"66$%30+>$%"30+DKLCH@+M%$,8<"*)(+"&$6"$)$+!&(-%)20*%&'#."". # ='-1%)*&.1*$.#)'*#P-%$';;*#!--'/'-;*E*"*0+$+/8%$+,"+?@+A@+;"[8*%"0+;(*)$%,*+`,"<"*)"+7/"()&"J"/.(0+9*'$0+DK^D@ L@+!VPWG#@2.&(*(*';:#V&*(;#.&)#<O1E%";#*&#PCO;*$."#GC'1*;(-O0+I@+A"663+`,@0+N6$/cu(66+7/"()&"J"/+>8V6"/$&"*)30+raJ*%,+DKEE0+#@ZE@ Z@+!@+]*<<"0+='-1%)*&.1*$.#GC*1*$.0+`,"<"*)"+k8*2$+-86&8%$0+9*'$0+II+`,"<"*)(+LCDD@ \@+M@+-2"&$30+W#X'N#I%%Q#.(#Y'.$(*%&#Y.(';0+_*8%)$6+*J+-.('"/$6+`,8/$&"*)0+:;0+DB^\+FDKKKH@+v(,"+$)/.(+9"J@L0+#@\K@ B@+_@+Y@+]$%3&0+=C'#ZM('&(#%4#Y'.$(*%&#.;#.#V&*4O*&,#>.;*;#4%-#<(%*$C*%1'(-O#*&#Z"'1'&(.-O#GC'1*;(-O+_*8%)$6+*J+-.('"/$6+`,8/$&"*)0+<=0+ DK\+FDK^\H@ p@+_@+-@+>."66"#30 +W#L-.BC*$."#Y'B-';'&(.(*%&#%4#I*1*(*&,#Y'.$(.&(0+_*8%)$6+*J+-.('"/$6+`,8/$&"*)0 +:=0+DC\E+FDKK\H+(+%"J(%"'()&"+"2"+ %"#*%&$&"@ !+ 012',+!"!3$44'/!!5677!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!''''#$%!"!#$!%&'(')$!*+,,$!-)./,$