91
98C$=-,&'O +*;*:*-=S*++% ;*:*9,S*++% /98:'=D/'8:,- :8$,A88;8:= D/)/+8>8 D+/@*++%
œ. +/$8>89 :8$, A88;8:= N 8)+89/&8-/ &=&'*9/. :=;(&'=98, S8 :8D9,: ;:=; (&'=98>8
;*:*9,S*++% :8D:/08-/+* +/ 8&+8-, :,<*++% )=.*:*+G,/$O+8>8 :,-+%++% D ;:/-8H
@/&'=+8H ( -=), -=;/)A8-8U .(+AG,U:
)(2
2
00
tFx =++
&&&
, (17.19)
)*
/
2
0
= ;
- *A-,-/$*+'+/ C8:&'A,&'O /98:'=D/'8:,-;
- 9/&/ :8$,A88;8:=;
-
A8*.,G,N+' D/>/&/++%, )(tx - (D/>/$O+*+/ A88:)=+/'/;
0
- -$/&+/ @/&'8'/ A8$=-/+O
)(
.
tF
!
=++
&&&
, (17.20)
)*
- 0/:/A'*:=&'=A/ D/>/&/++%, %A/ -=D+/@/N'O&% D :,-+%+O: /
0
= ;
!
/
.
2
0
= .
8D9,: œ -=D+/@/N98, -=08)%@= D -*:8>,)+8&+=0 0/:/A'*:=&'=A :*/AG,U &=&'*9= '/A=9
@=+89, S8? 98C$=-,&'O ;*:*-=S*++%
?($/ )(C* 9/$8U, +/;:=A$/) 001,0)(
x .
:8'* 98C$=-,&'O -=+=A+*++% ;8),U
(&* '/A= ,&+(N, , ;:= '/A89( ;*:*-=S*++,
)=+/9,@+, +/-/+'/C*++% - *$*9*+'/0 :8$,A88;8:= :,DA8 D:8&'/H'O. , +/-/+'/C*++%
98C('O -=A$=A/'= :(7+/G,H *$*9*+',-, '8?'8 %-='=&% ;:=@=+8H -,)98-. )/+,7
;8&'/+8-G, D/)/@/ )8G,$O+8 -=A8:=&'8-(-/'= 9*'8), D/&+8-/+=7 +/ -=D+/@*++,
&*:*)+O8>8 @/&( )8&%>+*++% -=;/)A8-8H :*/AG,NH )(tx ;:=;(&'=98>8 :,-+% ;*:*9,S*++%
œ.
=:/C*++% )$% @=&$/ ;*:*'=+/+O D+=D( +/>8:( -=;/)A8-=9 ; :8G*&89 )(tx :,-+% œ D/
@/&
9/N -=):
=
0
),( xdn
&&&
, (17.21)
)*
- <-=)A,&'O D9,+= 8:)=+/' :*/AG,U
;
),(
- )-89,:+/ S,$O+,&'O :8D;8),$( 8:)=+/' :*/AG,U , UU <-=)A8&',.
,-*+O œ ('-8:HN'O&% )(C* -=&8A=9, '=9 ?,$O<* -=&8A=9 ?()* :,-*+O :(7+(H@8>8
D(&=$$%, '89( S8 D-=@/7+8 ;:= :8D:/0(+A/0 ?*:('O D+/@+, A8*.,G,N+'= D/;/&( ':=-A8&',.
:= -=&8A89( :,-+, ;*:*'=+/++% ;8&$,)8-+,&'O ;*:*'=+/+O N +*D/$*C+8H :,)A,&+8H
;8),NH , U0+N @=&$8 ;:8'%>89 @/&(
('-8:HN'O&% D/ D/A8+89 (/&&8+/. 8), )$%
98C$=-8&',
0
('8?'8 .(+AG,U +/),7+8&',) '8>8, S8 D/ @/&
t +* -,)?()*'O&% C8)+8>8
;*:*'=+/++% 8)*:C=98:
!
"
#
$
%
&
= =
0
0
),(exp)exp( d
&&&
, (17.22)
)*
=
0
),( d
&&&
- +*?*D;*A/ -,)98-=.
-=;/)A( + 8:9/$O+8>8 0/:/A'*:( -;$=-(, S8 -=D+/@/N .8:9($/ (17.22) 98C+/ D/;=&/'=
( -=),:
'
(
'
)
*
'
+
'
,
-
!
!
"
#
$
$
%
&
.
/
=
=
2
0
0
2
exp
)(
)(
2
exp
|
R
R
&&
, (17.23)