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R*A;1, 6" >,1A,8 /& :&.8*-. &. +, :;<&1=, /& :1,<,5("
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
5 B > 5 :0 [( A : A 9 ) − 7]
(:)
4,:*80,'*&./( +, &';,'*-. `D 8& A,1,.:*?, E;& +, :&.8*-. /& :1,<,5( ,0&':,/, )(1 +,8
]
(C )
@. +, )1C':*',D +(8 B,+(1&8 :=)*'(8 /&+ 2,1A&. /& 5,+-. B,1=,. /& 3Y , _\ :(.&+,/,8 !" "#$#%#$ :-,-6(+.'6 4' ,-./+0. 8- ,6'3'9; : : H:(.&+,/,8J /& ',/, ;., /& +,8 8&''*(.&8 /& :;<&1=, /& :1,<,5(" N, :&.8*-. /& :1,<,5( , +, ';,+ &8:,1C &M);&8:, +, :;<&1=, &. '(./*'*(.&8 .(12,+&8 &8 *A;,+ , +, 2CM*2, :&.8*-. )&12*8*<+& 2&.(8 &+ 2,1A&. /& 5,+-.D I 8& ',+';+, /& +, 8*A;*&.:& 2,.&1,P
: : = 5 :0 − 5 ?
(7B)
!"="3 >,+'8+,1 +, 2
-$./$* &' 0'.1,.$2)34
&8:, )1*2&1, 8&''*-. /& :;<&1=, /& :1,<,5( &8:C +*2*:,/, )(1 +, :&.8*-. /& :1,<,5( : : ( -A9 7) /&:&12*.,/, )1&B*,2&.:&D I 8& ',+';+, '(. +, 8*A;*&.:& &';,'*-.P
: : ( -A9 7) −7=@C×7B ? ( 0 6:0 ) 67 6 67 + 0 :0 < < (77) = ? −
6:: ( -A9 7)
7=@C×7B 0 :: ( -A9 7) −
4* +, +(.A*:;/ /& +, )1*2&1, 8&''*-. .( &8 8;0*'*&.:& ),1, +, )1(0;./*/,/ :(:,+ /&+ )(?(D +, +(.A*:;/ 2CM*2, /& +, 8&A;./, 8&''*-. 8& ',+';+, '(. +, 8*A;*&.:& &';,'*-.P
6:: ( -A9 9 )
=
: : ( -A9 9 ) − : : ( -A9 7)
7=@C × 7B ? 0 :: ( -A9 9 ) < < −
(79)
4*D ,/*'*(.,+2&.:&D &8 .&'&8,1*, ;., :&1'&1, 8&''*-. /& :;<&1=, /& :1,<,5(D +, +(.A*:;/ /& L8:, 8& ',+';+, '(. +, 8*A;*&.:& &';,'*-.P
6:: (-A9 ?)
=
(: : (-A9 ?)
−
: : ( -A9 9 ) )
7=@C ×7B ? 0 :: (-A9 ?) < < −
(7?)
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
"#$#$#% <6-/+0. +.,-6.'# N, 8,1:, /& )&10(1,'*-. &8:C 8;5&:, , ;., )1&8*-. *.:&1., /& '&/&.'*, ';,./( +, )1&8*-. *.:&1., &5&1'*/, &8 2,I(1 E;& +, )1&8*-. &M:&1.," @8:, /*0&1&.'*,+ /& )1&8*-. 8& );&/& )1&8&.:,1D )(1 &5&2)+(D ';,./( 8& *./;'&. )1&8*(.&8 &. +, 8;)&10*'*& ),1, ,+AU. '(.:1(+ /& <1(:& &. &+ )(?( ( ,+A;., ()&1,'*-. /& '&2&.:,'*-. 0(1?,/," N, '(./*'*-. E;& /&<& ';2)+*18& ),1, &+ /*8&9( &8P
; >C
>
> C < &>C
(7@)
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
; >9 > >9 < &>9
(7;)
7(./& ; >9 &8 +, 1&8*8:&.'*, , +, )1&8*-. /& '(+,)8( /& +, :;<&1=, E;& 8& B, , ;:*+*?,1D >9 &8 +, 2CM*2, )1&8*-. /& '(+,)8( /& :1,<,5( &8)&1,/,D I < &>9 &8 &+ 0,':(1 /& /*8&9( , +, )1&8*-. /& '(+,)8( H,/*2&.8*(.,+J" N(8 B,+(1&8 /& 1&8*8:&.'*, ,+ '(+,)8( I , +, )1&8*-. *.:&1., /& +,8 :;<&1=,8 /& )&10(1,'*-. 8& &.';&.:1,. &. >'34'/ 8-4 ?<@ !D ,8= '(2( &. ',:C+(A(8 /& 0,<1*',.:&8 # N(8 0,':(1&8 /& /*8&9( , +, )1&8*-. *.:&1., < &>C I '(+,)8( < &>9 (8'*+,. &.:1& #"# I #"Y" _
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
"13 :-;1 ;1+4- +=44-3=
Q;.:( /& :,.A&.'*,
Q;.:( /& :,.A&.'*,
& R;&1?, /& ),./&( c \
7*1&''*-. /& +, a.,"
D%E & A
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&
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V&.(1 0;&1?, /& )L./;+(
DFE
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>=@; × 7B
= −
N(.A*:;/ /& +, <,11&., ,+ )1*2&1 );.:( /& :,.A&.'*,
R*A;1, !" R;&1?,8 +,:&1,+&8 &. +, <,11&., I '(2)(.&.:&8 /&+ &.8,2<+& /& 0(./("
`
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+
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=
B=;(& 8 − & '67 )
P6:13-4 S13
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6: S13
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B=9;
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=
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0 < 6 *'4θ 67 < :
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0 -7 H:(.&+,/,8J 1&E;&1*/(" 7& ,';&1/( '(. +, &M)&1*&.'*,D 8& 8;A*&1& ;. B,+(1 *.*'*,+ /& #\ 2" 8(<1&
S%
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3" 7&:&12*.,1D &. :,<+,8D &+ )&8( &. &+ ,*1& /& +(8 +,8:1,<,11&.,8 0 H+<8X)*&J" 67 6" >,+';+,1 &+ 0,':(1 /& 0+(:,'*-. < D ;8,./( < +, &';,'*-. 3" !" >,+';+,1 +, ',1A, '(2)1&8*B, /& +(8 +,8:1, <,11&.,8 9 967 H:(.&+,/,8J '(. +, 8*A;*&.:&
RGb
R*A;1, ] 7*,A1,2, ),1, /&:&12*.,1 &+ Q;.:( /& W,.A&.'*,"
9 967 = 0 -7
−
>=@; ×7B @ 0 67 < < 6: ,+6θ −
Y" 7&:&12*.,1 +, +,8:1,<,11&.,8 ; 67 8*A;*&.:& &';,'*-.P
; 67
=
1*A*/&? H+<8e)A3J
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(7:)
/& +(8 '(. +,
(7C )
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9 " = C9@ 6: 967 ; 67
B=;
(9B)
_" >,+';+,1 +, 0;.'*-. :1,8'&./&.:,+ C H,/*2&.8*(.,+J '(. +, 8*A;*&.:& &M)1&8*-.P
D =
?(1%6 " − " ) "?
(97)
&';,'*-.P F&1&.'*, /& G.A&.*&1=,
d
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`" >,+';+,1 &+ '+,1( &.:1& &+ ,A;5&1( I &+ /*C2&:1( &M:&1*(1 /& +(8 +,8:1,<,11&.,8 H);+A,/,8J '(. +, &';,'*-. #_"
*.'1&2&.:,1D 1&/;'*1 ( 2,.:&.&1 &+ C.A;+( /&+ )(?(" $6-01 :63.1 5- .=3<-37/=
d" >,+';+,1 +, +(.A*:;/ /& +, <,11&., ,+ )1*2&1 );.:( /& :,.A&.'*, 6: H2J '(. +, 8*A;*&.:& &';,'*-.P
7=9 ×7B @ ; 67 6: = 0 67 < < (,+6 θ ) D −
B=9;
(99) &>E%F
#\" 4* &+ B,+(1 /& 6: D ',+';+,/( &. &+ ),8( dD &8 /*0&1&.:& /&+ 8;);&8:( &. &+ ),8( #D ',+';+,1 ;. )1(2&/*( /& ,2<(8 B,+(1&8 '(. +, 8*A;*&.:& &';,'*-.P
6: =
6: ( 0@-F 7 ) + 6: ( 0@-F 9 )
9
(9?)
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#\
&>E1F
$6-0= H6-4[= 5- :=35-1
$6-0= H6-4[= 5- :\356>1 (/4-77/83 5- >= +=44-3 =
R*A;1, _" >,2<*( /& );.:( /& :,.A&.'*, I 0;&1?,8 +,:&1,+&8 E;& ,':U,. &. +, <,11&.,"
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F&1&.'*, /& G.A&.*&1=,
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' '
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% + ! '
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