HAL Id: hal-00265868
https://hal.archives-ouvertes.fr/hal-00265868
Submitted on 20 Mar 2008HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished 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.
Microwave dielectric constant of liquid hydrocarbons:
Application to the depth estimation of Titan’s lakes
Philippe Paillou, K. L. Mitchell, Stephen D. Wall, Gilles Ruffié, C. Wood, R.
D. Lorenz, Ellen R. Stofan, J.I. Lunine, R. Lopes, P. Encrenaz
To cite this version:
!"#$%&'()*+"),)#-$"#*#%./-'.-*%0*,"12"+*34+$%#'$5%./6*788,"#'-"%.*-%*-3)*
+)8-3*)/-"9'-"%.*%0*:"-'.;/*,'<)/
!"#$#%%&'!(#$$)*+,'-(.$'/#01"&$$2,'30&%"&4'5($$2,'6#$$&7'8*99#:;,'<"(.$&7'5))=>,'8($%"'?).&4@A,'B$$&4'
30)9(4C,'D)4(0"(4'?*4#4&E,'8)7($F'?)%&72,'!#&..&'B41.&4(@G
!"#$%&'%()'*+,-&'./01234&'.23546&'789:&'93;3<653&'=#&'%$#&'>?($&'%()'*7!+&'96;;34&'.23546&'
-9/356@32A'$416546'?5;@1@B@6&'CB4;05&'#D&'%$#&'*80E5;'F0GH15;'%51I62;1@A'#9:&':3B26/&'(J&'%$#&'
K920L6MA')6;6324E&')64@02@0N5&'O#&'%$#&'P:B532'35<'9/356@32A':3Q023@02A&'CB4;05&'#D&'%$#&'
+"Q;62I3@0126'<6'9321;&':R)(#&'9321;&'.23546
=>*?.-$%+2#-"%.
K#0(4,'0"&'7&1)4='7(0&$$#0&'#4'7#@&'#4'0"&'7)$(.'7F70&Q,'#7'($7)'0"&')4$F'Q))4'W#0"'('0"#1R'(0Q)7%"&.&P' K#0(4'#7'('%.#41#%($'71#&40#9#1')L_&10#J&')9'0"&'<(77#4#U\*FT&47'Q#77#)4'W"#1"'"(7'L&&4'#4').L#0'(.)*4=' 3(0*.4'7#41&'D*$F'2OO>P'K"&'8HIH8'#470.*Q&40'aB$(1"#'&0'($P,'2OO>b'#7'('"#T"'9.&M*&41F'-*UL(4=' Z+;PEG'6\@'X'2P+G'1Q['.(=(.,'W"#1"'#7'(L$&'0)'#Q(T&'K#0(4V7'7*.9(1&'0".)*T"'#07'(0Q)7%"&.&P'K"&'3H8' Z3F40"&0#1'H%&.0*.&'8(=(.['Q)=&'($$)W7'0"&'#470.*Q&40'0)'Q(%'0"&'7*.9(1&')9'K#0(4'W#0"'('7%(0#($' .&7)$*0#)4'(7'"#T"'(7';AO'QP'3&J&.($'9$FLF7')J&.'K#0(4'"(J&'L&&4'%&.9).Q&='LF'0"&'<(77#4#'7%(1&1.(90]' 0"&F'.&J&($&='('J&.F'T&)$)T#1($$F'=#J&.7&'(4='F)*4T'7*.9(1&,'W#0"'=)Q&U$#R&'J)$1(4#1'1)470.*107,'9$)W7' (4='7#4*)*7'1"(44&$7,'=*4&7,'$(R&7'(4='7&(7'aB$(1"#'&0'($P,'2OOAc'B$(1"#'&0'($P,'2OOCc'?).&4@'&0'($P,' 2OOC(c'?).&4@'&0'($P,'2OOCLc'?)%&7'&0'($P,'2OOEc'8(=&L(*T"'&0'($P,'2OOEbP K"&'K#0(4'9$FLF')4'22''D*$F'2OOC,'R4)W4'(7'K+C,'.&J&($&='0"&'9#.70'&d0.(U0&..&70.#($'$(R&7'a30)9(4'&0' ($P,'2OOEbP'H'C+;O'RQ'$)4T'3H8'7W(0",'9.)Q'Q#=U4).0"&.4'$(0#0*=&7'0)'4&(.'0"&'Y).0"'%)$&,'#Q(T&=' Q).&'0"(4'EA'.(=(.U=(.R'%(01"&7,'9.)Q';'RQ'0)'Q).&'0"(4'EO'RQ'#4'7#@&'Z7&&'e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d%&10&='0)'L&'(L*4=(40'(4='70(L$&')4'0"&'7*.9(1&')9'K#0(4'4&(.'0"&'%)$&7'a?*4#4&'&0'($P,'+fG;c' 8(44)*'&0'($P,'2OOCc'K)L#&'&0'($P,'2OOCc'/#0.#'&0'($P,'2OOEb,'30)9(4'&0'($P'Z2OOE['1)41$*=&'0"(0'0"&7&'=(.R' 70.*10*.&7 ' (.& ' $(R&7 ' 1)40(#4#4T ' $#M*#= ' "F=.)1(.L)47P ' K"& ' &d(10 ' 1)Q%)7#0#)4 ' )9 ' 0"#7 ' $#M*#= ' #7 ' 70#$$' *4R4)W4,'L*0 '#0 '#7 ' 1)47#=&.&= '0) 'L&' Q(#4$F 'methane and/or ethane probably containing dissolved nitrogen [Mitri et al., 2007]P'3&J&.($'=&%.&77#)47'")W&J&.'%.&7&40'('L.#T"0&.'.(=(.'.&0*.4'(4='Q#T"0'L&'L)00)Q'7#T4($'#7'4)0'1)Q%$&0&$F'(00&4*(0&=P'<"(4T&7'#4'σO'(.&'*4$#R&$F'0)'L&'1(*7&='LF'('W#4='&99&10'
.)*T"&4#4T'0"&'$(R&V7'7*.9(1&,'(7'0#=($'W#4=7'(0'"#T"'$(0#0*=&7'(.&'%.&=#10&='0)'L&'(4').=&.')9'Q(T4#0*=&' $)W&.'0"(4'0"(0'4&&=&='0)'9).Q'1(%#$$(.F'W(J&7'#4'$#M*#='"F=.)1(.L)47'a?).&4@'&0'($P,'2OOAbP
'S4').=&.'0)'M*(40#0(0#J&$F'Q)=&$'0"&'.(=(.'.&7%)47&')J&.'K#0(4V7'$(R&7,'('R&F'%(.(Q&0&.'#7'4&&=&=]' 0"&'=#&$&10.#1'1)470(40')9'$#M*#='"F=.)1(.L)47,'#4'%(.0#1*$(.'$#M*#='Q&0"(4&P'K"#7'%(.(Q&0&.'1)40.)$7'0"&' (00&4*(0#)4 'Z(4= '0"&4'%&4&0.(0#)4 '=&%0"[ ')9'0"&'.(=(. 'W(J&,'(4='($7)'0"& '.&9$&10#J#0F')9'0"& '$#M*#=' 7*.9(1&P ' e&W ' .&9&.&41&7 ' %.)J#=& ' =#&$&10.#1 ' 1)470(40 ' )9 ' $#M*#= ' "F=.)1(.L)47 ' (0 ' -*UL(4=, ' (4= ' 4)' Q&(7*.&Q&40'9).'$#M*#='Q&0"(4&'#7'(J(#$(L$&]'&70#Q(0&7'.(4T&'9.)Q'+PA'0)'2PO'9).'0"&'.&($'%(.0')9'0"&' =#&$&10.#1'1)470(40,'W"#$&'0"&'$)77'0(4T&40'#7'1)47#=&.&='0)'L&'#4'0"&'+OU;'X'+OUA'.(4T&'aK")Q%7)4'(4='
3M*F.&7,'+ffOc'3&4'&0'($P,'+ff2b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
@>*!)'/2$)9).-/*%0*-3)*A"),)#-$"#*B%./-'.-*%0*CDE
5&'*7&='('9.&&U7%(1&'Q&0")='a6")=T()4R(.'&0'($P,'+fGfb'0)'Q&(7*.&'0"&'=#&$&10.#1'1)470(40')9' ?Y6P'N*.'7F70&Q'1)47#70&=')9'('7&0')9'0W)'9)1*7&='&$$#%0#1($'(40&44(7'Z+O'X'+;'6\@'9.&M*&41F'.(4T&[,' )4&'LT'*7&='(7'(4'&Q#00&.'(4='0"&')0"&.'(7'('.&1&%0).P'H'%)$F70F.&4&'L)d'Z)9'=#&$&10.#1'1)470(40'1$)7&' 0)'0"&')4&')9'(#.[')9'R4)W4'=#Q&47#)47'W(7'%$(1&='(0'0"&'9)1($'%)#40'L&0W&&4'0"&'0W)'(40&44(7,'(4=' 9#$$&='W#0"'0"&'$#M*#='0)'L&'Q&(7*.&=P' 'i&10).'4&0W).R'(4($F@&.7'HY8SK3`';E;2AH'(4='H6S?BYK' BG;C>h'W&.&'*7&='(7'7)*.1&'T&4&.(0).'(4='.&1&%0).P'H'9#.70'Q&(7*.&Q&40'W(7'%&.9).Q&=')4'0"&'&Q%0F' %)$F70F.&4&'L)d'#4').=&.'0)'Q&(7*.&'7F70&Q'$)77&7'(4='%&.9).Q'1($#L.(0#)4P'5&'0"&4'9#$$&='0"&'L)d'W#0"' ?Y6'(4='%&.9).Q&= '('7&1)4='Q&(7*.&Q&40 'Z7&&'e#T*.&'2'0)%[P'5&'Q&(7*.&= 'L)0"'.&9$&10#)4 '(4=' 0.(47Q#77#)4 ' 1)&99#1#&407, ' W"#1" ' ($$)W&= ' *7 ' 0) ' 1)Q%*0& ' 0"& ' .&($ ' %(.0 ' (4= ' #Q(T#4(.F ' %(.07 ' )9 ' 0"&' =#&$&10.#1'1)470(40')9'0"&'Q(0&.#($P'5&'#4#0#($$F'%&.9).Q&='7&J&.($')*0=)).'&d%&.#Q&407'*7#4T'$#M*#=' 4#0.)T&4'#4').=&.'0)'0&70')*.'7&0U*%]'W&')L0(#4&='('%&.Q#00#J#0F')9'+P>A'(4='('$)77'0(4T&40')9'+OU>'(0'+O'
6\@,'1)47#70&40'W#0"'%.&J#)*7'Q&(7*.&Q&407'a3Q#0"'&0'($P,'+ff+bP'5&'&70#Q(0&'0"&'Q&(7*.&Q&40'&..).' 0)'(L)*0'+Og')4'L)0"'0"&'.&($'(4='#Q(T#4(.F'%(.07')9'0"&'=#&$&10.#1'1)470(40P 5&'%&.9).Q&='9)*.'Q&(7*.&Q&407')4'0"&'7(Q&'?Y6'7(Q%$&'Z0"&'%)$F70F.&4&'L)d'W(7'&Q%0#&='(4=' .&U9#$$&='&(1"'0#Q&[,'W"#1"'1)Q%)7#0#)4'W(7'fOg'Q&0"(4&,'Ag'4#0.)T&4'(4='Ag')0"&.'"F=.)1(.L)47' ZQ(#4$F'&0"(4&'(4='%.)%(4&[P'5&')L0(#4&='(4'(J&.(T&'=#&$&10.#1'1)470(40''ε'^'+PEA'X'OPOO2_,'0"(0'#7'(' $)77'0(4T&40')9'+P+>'+OU;'(0'('9.&M*&41F')9'+;'6\@,'1$)7&'0)'0"&'*%%&.'$#Q#0'%.)%)7&='LF'a3&4'&0'($P,'
+ff2b,'L*0'"#T"&.'0"(4'0"&'A'+OU>' J($*&'Q&(7*.&='LF'a5"#99&4,'+fAOb'9).')0"&.'$#M*#='"F=.)1(.L)47P'
F>*!%+),".G*-3)*H'+'$*I'#</#'--)$".G*%0*:"-'.*C'<)/
5&'*7&='0"&'K+C'$(R&'$#70'#4'K(L$&'+'(4='('7#Q%$&'0W)U$(F&.'71(00&.#4T'Q)=&$'0)'.&%.)=*1&')L7&.J&=' σO''J($*&7P'B(1"'$(R&'W(7'Q)=&$&='(7'('7*%&.9#1#($'7Q))0"'0)%'$(F&.')9'$#M*#='Q&0"(4&')9'0"#1R4&77'<,'
W"#1"'1)J&.7'('.)*T"&.'L)00)Q'$(F&.'Q(=&')9'0")$#4U$#R&'Q(0&.#($7P'K"&'0)%'$(F&.'#7'1"(.(10&.#@&='LF'#07' =#&$&10.#1'1)470(40'Zε1'^'+PEA'X'OPOO2_['(4='7*.9(1&'.)*T"4&77'Z"&#T"0'70(4=(.='=&J#(0#)4'σ+,'1)..&$(0#)4'
$&4T0" '?+[P'K"&'L)00)Q'$(F&.'#7'($7)'1"(.(10&.#@&='LF'#07'=#&$&10.#1'1)470(40'Zε2' ^'2P2O'X'OPO+_,'7&&'
a8)=.#T*&@'&0'($P,'2OO;b['(4='.)*T"4&77'Zσ2,'?2[P'K"#7'0W)U$(F&.'Q)=&$'#7'#$$*Q#4(0&='LF'('.(=(.'W(J&'
)9'W(J&$&4T0" 'λ0' (..#J#4T'W#0"'(4'#41#=&41&'(4T$& 'θP'S4').=&.'0)'0(R&'#40)'(11)*40'J(.#)*7'7*.9(1&'
.)*T"4&77'1)4=#0#)47'Z9.)Q'J&.F'7Q))0"'0)'J&.F'.)*T"'7*.9(1&7'1)Q%(.&='0)'0"&'.(=(.'W(J&$&4T0"[,'W&' *7&='=#99&.&40'L(1R71(00&.#4T'Q)=&$7]'SB/'ZS40&T.($'BM*(0#)4'/)=&$['ae*4T'&0'($P'+ff2b,'!N'Z!"F7#1($' N%0#17['Q)=&$'a`$(LF'&0'($P,'+fG2b'(4='6N'Z6&)Q&0.#1'N%0#17['Q)=&$'ae*4T'(4='B)Q,'+fG+bP'K"&' 1)Q%$&0&'=&71.#%0#)4')9'0"&'0W)U$(F&.'71(00&.#4T'Q)=&$'1(4'L&'9)*4='#4'a!(#$$)*'&0'($P,'2OOCbP'K"&'0)0($' L(1R71(00&.&='%)W&.'σO'9).'('T#J&4'$(R&'#7'0"&4'0"&'7*Q')9'('7*.9(1&'71(00&.#4T'0&.Q'Z71(00&.#4T'9.)Q'0"&'
$#M*#= ' Q&0"(4& ' 7*.9(1&, ' W& ' =#= ' 4)0 ' 0(R& ' #40) ' (11)*40 ' J)$*Q& ' 71(00&.#4T ' LF ' "&0&.)T&4�#&7 ' ).' 7*7%&47#)47 ' #4 ' 0"& ' $#M*#=[ ' (4= ' ( ' 7*LU7*.9(1& ' 71(00&.#4T ' 0&.Q ' Z71(00&.#4T ' 9.)Q ' 0"& ' $(R&V7 ' L)00)Q,' (00&4*(0&='LF'('0W)UW(F'%(0"'0".)*T"'0"&'$#M*#=[P'5&'1)47#=&.&='"&.&'('j4)'W#4=k'"F%)0"&7#7,'#P&P' 1"(4T&7'#4'σO'(.&')4$F'=*&'0)'1"(4T&7'#4'$(R&'=&%0"]'=(.R&70'$(R&7'(.&'0"&'=&&%&70'Z)4$F'('W&(R'.&0*.4' 9.)Q'0"&'7Q))0"'$#M*#='Q&0"(4&'7*.9(1&,'0"&'L)00)Q'1)40.#L*0#)4'LT'1)Q%$&0&$F'(00&4*(0&='LF'0"&' 0"#1R'$#M*#='$(F&.[,'(4='L.#T"0&70'$(R&7'(.&'=.F'Z70.)4T'.&0*.4'9.)Q'0"&'.)*T"')%&4U(#.'L)00)Q[P S4').=&.'0)'1($#L.(0&')*.'Q)=&$,'W&'=&.#J&='.)*T"4&77'%(.(Q&0&.7'Zσ,'?[')9'0"&'0W)'$(F&.7'9.)Q'0W)' &d0.&Q&'71(00&.#4T'1(7&7')L7&.J&='#4'K(L$&'+P''I(.R&70'$(R&7'ZσO'$)W&.'0"(4'X2A'=h['W&.&'1)47#=&.&='0)' L&'J&.F'=&&%'$(R&7,'9).'W"#1"'0"&'L(1R71(00&.#4T')9'0"&'*%%&.'$#M*#='$(F&.'#7'%.&J(#$#4T')4'0"&'L)00)QP' K"&F'W&.&'0"&4'*7&='0)'=&.#J&'0F%#1($'.)*T"4&77'%(.(Q&0&.7')9'0"&'7Q))0"'$#M*#='7*.9(1&'ZSB/'*7&=[]' σ+'^'OP+A'1Q'(4='?+'^'+P>O'1Q'9).'('Q&(4'#41#=&41&'(4T$&')9';;) 'F#&$=7'('σO'J($*&')9'X2CPG'=hP'K"&'
#7'9.)Q'0"&'.)*T"'0")$#4UQ(0&.#($'L)00)QP'K"&F'W&.&'*7&='0)'&70#Q(0&'0"&'.)*T"4&77'%(.(Q&0&.7')9'0"&' .)*T"&.'$(R&'L)00)Q'Z6N'Q)=&$'*7&=[]'σ2'^'2PO'1Q'(4='?2'^'CPO'1Q'9).'('Q&(4'#41#=&41&'(4T$&')9';;)'
F#&$=7'('σO'J($*&')9'X++PG'=hP'BJ&40*($$F,'('.(4T&')9'.)*T"4&77'%(.(Q&0&.'(4='#41#=&41&'(4T$&'J($*&7' 7")*$='L&'1)47#=&.&='#4').=&.'0)'%.)=*1&'Q).&'1)Q%$&0&'7#Q*$(0#)4'.&7*$07,'L*0'W&'(.&'"&.&'Q(#4$F' #40&.&70&='#40)'9#.70').=&.'.&7*$07'0)'1)470.(#4'0"&'=&%0"')9'K#0(4V7'$(R&7P
J>*C'<)/*A)8-3*K/-"9'-"%.
`7#4T'%.&J#)*7$F'9#d&='%(.(Q&0&.7'#4')*.'0W)U$(F&.'71(00&.#4T'Q)=&$,'W&'1)Q%*0&='0"&).&0#1($'σO' J($*&7'9).'('J(.F#4T'0"#1R4&77')9'0"&'$#M*#='9#$$#4T'0"&'$(R&7P'K"&')L0(#4&= 'σO' X'=&%0"'.&$(0#)47"#%'#7' %.&7&40&='#4'e#T*.&'2'L)00)Q'9).'(4'#41#=&41&'(4T$& 'θ' ^'2G, ';;,';G)P'K"&'#41#=&41&'(4T$&'Q(#4$F'1)40.)$7'0"& 'j7(0*.(0#)4'$&J&$k')9 'σO]'$)W&.'#41#=&41&'(4T$&'$&(=7'0)'('"#T"&.'L(1R71(00&.#4T'$&J&$')9'
=(.R'$(R&7P'5&'($7)'7")W'#4'e#T*.&'2'L)00)Q'0"&'σO'X'=&%0"'.&$(0#)47"#%'9).'('$#M*#='W#0"'('$)W&.'$)77'
0(4T&40'ZA'+OU>['#4').=&.'0)'#$$*70.(0&'0"&'#Q%).0(41&')9'0"#7'%(.(Q&0&.'Z0"&'$)W&.'0"&'$)77'0(4T&40,'0"&'
9#$$&=k'(77*Q%0#)47]'#4'('W#4=F'1)40&d0,')4&'W)*$='&d%&10'0"&'$(.T&.'$(R&7'0)'L&'0"&'Q).&'$#R&$F'0)'"(J&' .#%%$&7'(4='W(J&7,'1(*7#4T'.)*T"&4#4T'(4='0"*7'.(=(.'L.#T"0&4#4TP
K"&'%.)%)7&='σO'X'=&%0"'.&$(0#)47"#%,'($0")*T"'L(7&=')4'('7#Q%$&'71(00&.#4T'Q)=&$'(4=')4'('j4)'
W#4=k ' "F%)0"&7#7, ' 1(4 ' ")W&J&. ' L& ' *7&= ' 0) ' )L0(#4 ' 9#.70 ' ).=&. ' &70#Q(0&7 ' 9). ' 0"& ' $)W&. ' $#Q#07 ' )9' "F=.)1(.L)4'J)$*Q&'1)40(#4&='#4'$(R&7'a?).&4@'&0'($P,'2OOEb]'9).'#470(41&,'$(R&'mCC'#7'(0'$&(70'>'Q'=&&%' (4='"(7'(4'(.&(')9'2AO'RQ2,'7)'#0'7")*$='1)40(#4'('Q#4#Q*Q'J)$*Q&')9'+'RQ;')9'$#M*#='"F=.)1(.L)47P'
e#4($$F,')4&'1(4')L7&.J&'#4'e#T*.&'2'L)00)Q'0"(0'σO'%.&7&407'('70.)4T'J(.#(0#)4'ZQ).&'0"(4'+A'=h['9).'('
.(0"&.'7Q($$'1"(4T&'#4'$(R&'=&%0"'9).'7"($$)W'$(R&7'Z$&77'0"(4'A'Q[P'K"#7'"#T"'7&47#0#J#0F')9'0"&'.(=(.' 7#T4($ ' 1(4 'L& ' *7&= ' 0)' =&0&10 'Q&0&.U71($& '$&J&$ '1"(4T&7 ' )9' K#0(4V7 '$(R&7] 'Q)4#0).#4T ')9 '0#=& '&99&10' a?).&4@'&0'($P,'2OO;b'(4='7&(7)4($'1"(4T&7'LF'&J(%).(0#)4 'a/#0.#'&0'($P,'2OOEb'9).'#470(41&,'W"&4' .&%&(0&='3H8'1)J&.(T&')9'0"&'Y).0"'%)$(.'.&T#)47'W#$$'L&'(J(#$(L$&P
7#<.%&,)+G9).-/
K"&'(*0").7'(.&'T.(0&9*$'0)'6(@'=&'e.(41&'Z?P'I*M*&74&,'HP'?&'<$)(.&1,'HP'!&#T4:,'!"P'?)#7&$['9).' T#J#4T'(11&77'0)'#07'?Y6'9(1#$#0#&7'#4'/)40)#.'=&'h.&0(T4&,'(4='0)'HT#$&40'K&1"4)$)T#&7'ZBP'<")$$#&.,'IP' e&..&0['9).'%.)J#=#4T'BG;C>h'iYHPH)0)$).#)/
B$(1"#,'<"P,'&0'($P,'j8HIH8]'K"&'<(77#4#'K#0(4'8(=(.'/(%%&.k,'$G346'$416546')6I16N;,'J)$P'++A,'%%P' E+U++O,'2OO>P B$(1"#,'<"P,'&0'($P,'j<(77#4#'8(=(.'J#&W7'0"&'7*.9(1&')9'K#0(4k,'$416546,'J)$P';OG,'%%P'fEOUfE>,'2OOAP B$(1"#,'<"P,'&0'($P,'jK#0(4'8(=(.'Q(%%&.')L7&.J(0#)47'9).'<(77#4#'K;'9$FLFk, 'T3@B26,'J)$P'>>+,'%%P' EOfUE+;,'2OOCPe*4T,'HP-P,'nP'?#,'-P3P'<"&4,'jh(1R71(00&.#4T'9.)Q'('.(4=)Q$F'.)*T"'=#&$&10.#1'7*.9(1&k,'?RRR'C235;V' W60;41V')6M0@6'$65;15U,'J)$P';O,'4)P'2,'%%P';ACU;Cf,'+ff2P 6")=T()4R(.,'IP-P,'iPiP'i(.(=(4,'iP-P'i(.(=(4,'jH'9.&&U7%(1&'Q&0")='9).'Q&(7*.&Q&40')9'=#&$&10.#1' 1)470(407'(4='$)77'0(4T&407'(0'Q#1.)W(J&'9.&M*&41#&7k,'?RRR'C235;V'?5;@2V'(63;V,'J)$P';G,'4)P';,'%%P' EGfUEfC,'+fGfP ?)%&7,'8P/P<P,'&0'($P,'j<.F)J)$1(4#1'e&(0*.&7')4'K#0(4o7'3*.9(1&'(7'8&J&($&='LF'0"&'<(77#4#'K#0(4' 8(=(.'/(%%&.k,'?432B;&'J)$P'+GC,'%%P';fAU>+2,'2OOEP ?).&4@,'8PIP,'&0'($P,'jK"&'7&(7')9'K#0(4k,'R"$,'J)$P'G>,'4)'+>,'%%P'+2A,'+;+U+;2,'2OO;P ?).&4@,'8PIP,'&0'($P,'j3&(U7*.9(1&'W(J&'T.)W0"'*4=&.'&d0.(0&..&70.#($'(0Q)7%"&.&7]'!.&$#Q#4(.F'W#4=' 0*44&$'&d%&.#Q&407'W#0"'(%%$#1(0#)4'0)'/(.7'(4='K#0(4k,'?432B;,'J)$P'+EA,'%%P'AACUACO,'2OOAP ?).&4@,'8PIP,'&0'($P,'jK#0(4V7'F)*4T'7*.9(1&]'S4#0#($'#Q%(10'1.(0&.'7*.J&F'LF'<(77#4#'8HIH8'(4='Q)=&$' 1)Q%(.#7)4k,'W60GEA;V')6;V':6@@V,'J)$P';>,'?OE2O>,'=)#]+OP+O2fl2OOC6?O2GfE+,'2OOC(P ?).&4@,'8PIP,'&0'($P,'jK"&'7(4='7&(7')9'K#0(4]'<(77#4#'8HIH8')L7&.J(0#)47')9'$)4T#0*=#4($'=*4&7k,' $416546,'J)$P';+2,'%%P'E2>UE2E,'2OOCLP ?).&4@,'8PIP,'&0'($P,'jK#0(4V7'#4J&40).F')9').T(4#1'7*.9(1&'Q(0&.#($k,'W60GEA;V')6;V':6@@V,'2OOE,'#4'%.&77P ?*4#4&,'DPSP,'IPDP'30&J&47)4,'pP?P'p*4T,'jB0"(4&')1&(47')4'K#0(4k,'$416546,'J)$P'222,'%%P'+22fU+2;O,' +fG;P /#0.#,'6P,'HP!P'3")WQ(4,'DPSP'?*4#4&,'8PIP'?).&4@,'j\F=.)1(.L)4'$(R&7')4'K#0(4k,'?432B;,'J)$P'+GC,'4)P' +,'%%P';GAU;f>,'2OOEP !(#$$)*,'!"P,'/P'<.(%&(*,'<"P'B$(1"#,'3P'5($$,'!P'B41.&4(@,'j/)=&$7')9'3H8'L(1R71(00&.#4T'9).'L.#T"0' 9$)W7 ' (4= ' =(.R ' 7%)07 ' )4 ' K#0(4k, '80B253/ ' 0X ' W60GEA;143/ ' )6;6324E, ' J)$P ' +++, 'B++O++, ' =)#] +OP+O2fl2OOCDBOO2E2>,'2OOCP
8(=&L(*T",'DP,'&0'($P,'j/)*40(#47')4'K#0(4'NL7&.J&='LF'<(77#4#'8HIH8k,'?432B;,'J)$P'+f2,'%%P'EEUf+,' 2OOEP
O"G2$)*=>*Bd0.(10')9'K+C'3H8'7W(0"'7")W#4T'=(.R'%(01"&7'#40&.%.&0&='(7'$(R&7'1)40(#4#4T'$#M*#='
O"G2$)*@>'C0GY'!).#4T'?Y6'#4'0"&'%)$F70F.&4&'L)dP'BQ#00#4T'(4='.&1&#J#4T'(40&44(7'($$)W'0)'Q&(7*.&'
0"&'=#&$&10.#1'1)470(40'#4'0"&'+O'X'+;'6\@'9.&M*&41F'.(4T&P'\0@@0MY'K)0($'3H8'L(1R71(00&.&='%)W&.' J&.7*7'$(R&'=&%0"'(0'(4'#41#=&41&'(4T$&')9'2G),';;)'(4=';G)P'!$(#4'$#4&7'1)..&7%)4='0)'('$)77'0(4T&40')9'
O"G2$)*F>'C0GY'\#70)T.(Q')9'σO'=#70.#L*0#)4'9).'0"&'EE'$(R&7,'7")W#4T'0W)'Q(#4'T.)*%7]'jL.#T"0'$(R&7k'
W#0"'σO'"#T"&.'0"(4'X+f'=h'(4='j=(.R'$(R&7k'W#0"'σO'$)W&.'0"(4'X22'=hP'\0@@0MY'!$)0')9'K+C'$(R&'(.&('
Z#4'RQ2['J&.7*7'Q&(4'σ
O'Z#4'=h[]'7Q($$&.'$(R&7'(.&'($7)'0"&'L.#T"0&70,'W"#$&'$(.T&.')4&7'(.&'0"&'=(.R&70,'