umd | atmospheric and oceanic scienceekalnay/dissertations/... · k0?1 +2)+j!1 +)c,jd@!)c+!4 . 8 u...
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Acknowledgements
; K1 ?AK)+-0* ), K 201M+A ,- E+,E*+ -,A D0EE,A)(2? 1+ (2 K** W(2JD ,- NKFD. F(AD)
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NC+2 DC+ *,D) C+A C0DMK2J *KD) 1,2)C. ; )A0*F KEEA+/(K)+ 1F /,11())++ 1+1M+AD3 BA,-.
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1+ ), K/C(+L+ 1F ?,K* +L+2 (2 *(L(2? K*,2+ (2 A1+A(/K -,A -(L+ F+KAD. %C(D
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; KEEA+/(K)+ .AD. %KW+1KDK 8(F,DC( K2J 'CA(D .K2-,A)C -,A EA,L(J(2? D,0A/+
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Table of Contents
A/W2,N*+J?+1+2)D....................................................................................................... (( %KM*+ ,- ',2)+2)D......................................................................................................... ((( 4(D) ,- %KM*+D ................................................................................................................ L 4(D) ,- F(?0A+D ............................................................................................................. L(( 'CKE)+A b ;2)A,J0/)(,2................................................................................................. b
b.b 62:F (2 )C+ EA+D+2/+ ,- 1,J+* +AA,AD ........................................................ 2 b.2 AJKE)(L+ +D)(1K)(,2 ,- (2-*K)(,2 -K/),A ....................................................... c b.d .(K?2,D(D ,- ,MD+ALK)(,2 +AA,A D)K)(D)(/D ..................................................... V b.4 SE+/(-(/ ?,K*D ,- )C(D J(DD+A)K)(,2 ............................................................... I b.c O0)*(2+ ,- )C+ )C+D(D .................................................................................... f
'CKE)+A 2 %C+,A+)(/K* KDE+/)D.................................................................................... bH 2.b ;2)A,J0/)(,2............................................................................................... bH 2.2 %C+,AF ,- )C+ 4,/K* 62D+1M*+ %AK2D-,A1 :K*1K2 F(*)+A P46%:FQ......... bH
2.2.b ;2)A,J0/)(,2 ), JK)K KDD(1(*K)(,2......................................................... bH 2.2.2 F,A+/KD) +AA,A /,LKA(K2/+ K2J )C+ +2D+1M*+ :K*1K2 -(*)+A................. b2 2.2.d 4,/K* +2D+1M*+ )AK2D-,A1 :K*1K2 -(*)+A ............................................ bc
2.d 8+)C,JD ), J+K* N()C 1,J+* +AA,AD (2 )C+ 62:F....................................... bf 2.d.b 80*)(E*(/K)(L+ (2-*K)(,2 ....................................................................... bf 2.d.2 AJJ()(L+ (2-*K)(,2 ................................................................................ bY 2.d.d .++ K2J JK S(*LK M(KD +D)(1K)(,2 8+)C,J P.JS8Q ............................ 2H 2.d.4 #K+W +) K* P2HHVQ M(KD +D)(1K)(,2 D/C+1+........................................... 2d 2.d.c 4,NT.(1+2D(,2K* 8+)C,J P4.8Q ..................................................... 24
2.4 AJKE)(L+ +D)(1K)(,2 ,- (2-*K)(,2 -K/),A K2J ,MD+ALK)(,2 +AA,AD ................ 2V 2.4.b AJKE)(L+ +D)(1K)(,2 ,- (2-*K)(,2 EKAK1+)+A ........................................ 2V 2.4.2 AJKE)(L+ +D)(1K)(,2 ,- ,MD+ALK)(,2 +AA,AD.......................................... 2Y 2.4.d S(10*)K2+,0D +D)(1K)(,2 ,- (2-*K)(,2 K2J ,MD+ALK)(,2 +AA,AD ............. dH 2.4.4 S1,,)C(2? ........................................................................................... dH
'CKE)+A d %C+ 46%:F E+A-,A1K2/+ (2 E+A-+/) 1,J+* +ZE+A(1+2)D.......................... d2 d.b ;2)A,J0/)(,2............................................................................................... d2 d.2 %C+ SB66.S 1,J+* ................................................................................. d2 d.d 6ZE+A(1+2)K* D+)0E.................................................................................... dd d.4 SK1E*(2? +AA,AD......................................................................................... d4 d.c 46%:F E+A-,A1K2/+ (2 K E+A-+/) 1,J+* +ZE+A(1+2)................................ dI
'CKE)+A 4 A//,02)(2? -,A K2J /,AA+/)(2? 1,J+* +AA,AD (2 )C+ 46%:F ..................... 42 4.b ;2)A,J0/)(,2............................................................................................... 42 4.2 N'6BRN'A& A+K2K*FD(D PNN&Q ............................................................... 42
4.2.b NN& ,MD+ALK)(,2D............................................................................... 42 4.2.2 'CKAK/)+A(D)(/D ,- 1,J+* +AA,AD ........................................................... 4d
4.d 6--+/)D ,- 1,J+* +AA,AD ,2 )C+ 46%:F ..................................................... 4I 4.d.b 6ZE+A(1+2)K* D+)0E.............................................................................. 4I 4.d.2 g',2)A,* A02` A+D0*)D............................................................................ 4I
4.4 A//,02)(2? -,A K2J /,AA+/)(2? 1,J+* +AA,AD............................................. 4Y 4.4.b 6ZE+A(1+2)K* J+D(?2............................................................................ 4Y
(((
4.4.2 80*)(E*(/K)(L+ (2-*K)(,2 ....................................................................... 4Y 4.4.d AJJ()(L+ (2-*K)(,2 ................................................................................ cd 4.4.4 .++ K2J JK S(*LK 1+)C,J N()C (2-*K)(,2 P.JS8UQ ............................. cV 4.4.c 4,NTJ(1+2D(,2K* 1,J+* +AA,A /,AA+/)(,2 ........................................... Vc 4.4.V OL+AK** /,1EKA(D,2............................................................................. IV
4.c S011KAF K2J J(D/0DD(,2........................................................................... fd 'CKE)+A c S(10*)K2+,0D +D)(1K)(,2 ,- (2-*K)(,2 -K/),A K2J ,MD+ALK)(,2 +AA,AD N()C(2
)C+ 46%:F ................................................................................................ fI c.b ;2)A,J0/)(,2............................................................................................... fI c.2 4,NT,AJ+A 1,J+* A+D0*)D ........................................................................... fI
c.2.b %C+ 4,A+2XTYV 1,J+*.......................................................................... fI c.2.2 B+A-+/) 1,J+* +ZE+A(1+2)D.................................................................. ff c.2.d ;1E+A-+/) 1,J+* +ZE+A(1+2)D ............................................................. Yd
c.d SB66.S 1,J+* A+D0*)D ........................................................................... bHH c.4 S011KAF ................................................................................................. bHc
'CKE)+A V ',2/*0D(,2D K2J -0)0A+ J(A+/)(,2D........................................................... bHI #(M*(,?AKECF ............................................................................................................. bbb
(L
List of Tables
%KM*+ d.b3 A2K*FD(D &8S6 ,- cHH CBK C+(?C) -(+*J 0D(2? 46%:F N()C dH +2D+1M*+
1+1M+AD (2 )C+ /KD+D ,- KEE*F(2? /0)T,-- *,/K*(XK)(,2 ,A ,MD+ALK)(,2 +AA,A /,LKA(K2/+
*,/K*(XK)(,2. %C+ &8S6 (D )+1E,AK**F KL+AK?+J -,A K 1,2)C K-)+A )C+ (2()(K* bcTJKFD
DE(2T0E E+A(,J K2J DEK)(K**F KL+AK?+J ,L+A )C+ ?*,M+. A 10*)(E*(/K)(L+ (2-*K)(,2 -K/),A
,- ! hH.H4 (D KEE*(+J. %N, EKAK1+)+AD@ )C+ *,/K* EK)/C D(X+ ! K2J )C+ ,MD+ALK)(,2K*
+AA,A /,LKA(K2/+ D/K*+" @ KA+ )02+J............................................................................. dV
%KM*+ 4.b3 A2K*FD(D &8S6 ,- 2HH CBK u @ cHHCBK # @ fcH CBK $ K2J Y2c CBK
% -(+*JD@ )+1E,AK**F KL+AK?+J -,A K 1,2)C K-)+A )C+ (2()(K* DE(2T0E E+A(,J MF KEE*F(2?
J(--+A+2) K1E*()0J+D ,- 10*)(E*(/K)(L+ (2-*K)(,2. ......................................................... cd
%KM*+ 4.23 A2K*FD(D &8S6 ,- cHH CBK C+(?C) 0D(2? )C+ .JS8U N()C J(--+A+2) /C,(/+D
,- P # @ r Q. <C+2 r hH P (.+. E0A+ .JS8Q@ K D1K** -K/),A P ! hH.HcQ ,- )C+
10*)(E*(/K)(L+ (2-*K)(,2 (D KEE*(+J ), EA+L+2) )C+ -(*)+A J(L+A?+2/+. F,A )C+ ,)C+A
/C,(/+D ,- r @ 2, 10*)(E*(/K)(L+ (2-*K)(,2 (D 0D+J. F,A /,1EKA(D,2@ )C+ E0A+ KJJ()(,2
(2-*K)(,2 KEE*(/K)(,2 (D K*D, DC,N2 P# hH K2J r hb.cQ................................................ cf
%KM*+ 4.d3 ',1EKA(D,2 ,- K2K*FD(D &8S6 M+)N++2 )C+ KEE*(/K)(,2D ,- KJJ()(L+
(2-*K)(,2@ )C+ .JS8U K2J )C+ D(1E*(-(+J .JS8U. &+D0*)D KA+ DC,N2 -,A 2HH CBK
X,2K* N(2J Pu Q@ cHH CBK C+(?C) P # Q@ fcH CBK DE+/(-(/ C01(J()F P $ Q K2J Y2c CBK
)+1E+AK)0A+ P % Q -(+*JD@ )+1E,AK**F KL+AK?+J -,A K 1,2)C K-)+A )C+ (2()(K* DE(2T0E
E+A(,J. ......................................................................................................................... Vc
%KM*+ c.b3 %(1+ 1+K2 ,- KJKE)(L+ (2-*K)(,2 ! K2J )C+ /,AA+DE,2J(2? K2K*FD(D +AA,A@
KL+AK?+J ,L+A )C+ *KD) bHHH D)+ED ,- K 2HHHTD)+E KDD(1(*K)(,2 NC+2 )C+ ,MD+ALK)(,2K*
L
+AA,A LKA(K2/+ PDE+/(-(+JQ (D E+A-+/)*F W2,N2. F,A /,1EKA(D,2@ )C+ LK*0+ ,- M+D) )02+J
/,2D)K2) (2-*K)(,2 K2J ()D A+D0*)(2? K2K*FD(D +AA,A KA+ K*D, DC,N2............................... YH
%KM*+ c.23 %(1+ 1+K2 ,- KJKE)(L+ (2-*K)(,2 EKAK1+)+A ! K2J )C+ A+D0*)(2? K2K*FD(D
+AA,A@ KL+AK?+J ,L+A )C+ *KD) bHHH D)+ED ,- K 2HHH D)+E KDD(1(*K)(,2 (2 )C+ /KD+ )CK) )C+
DE+/(-(+J ,MD+ALK)(,2 LKA(K2/+ (D +()C+A bR4 ,A 4 )(1+D )C+ )A0+ QP2
'o" QP2
to" ................ Yb
%KM*+ c.d3 AD (2 %KM*+ c.2@ M0) KJKE)(L+*F +D)(1K)(2? M,)C )C+ (2-*K)(,2 -K/),A K2J
,MD+ALK)(,2 +AA,A LKA(K2/+........................................................................................... Yd
%KM*+ c.43 'KD+ A3 )C+ M+D) )02+J /,2D)K2) (2-*K)(,2 K2J )C+ A+D0*)(2? K2K*FD(D &8S6i
'KD+ #3 )(1+ 1+K2 ,- KJKE)(L+ (2-*K)(,2 PN()C E+A-+/) " o2 hbQ K2J )C+ A+D0*)(2?
K2K*FD(D &8S6i 'KD+ '3 )(1+ 1+K2 ,- KJKE)(L+ (2-*K)(,2 K2J ,MD+ALK)(,2 +AA,A@
+D)(1K)+J D(10*)K2+,0D*F ,2T*(2+@ K2J )C+ A+D0*)(2? K2K*FD(D &8S6. 6K/C /KD+ (D
)+D)+J -,A J(--+A+2)# @ K1E*()0J+ ,- AK2J,1 1,J+* +AA,AD. &+D0*)D KA+ KL+AK?+J ,L+A
)C+ *KD) bHHH K2K*FD(D D)+ED. ........................................................................................ YV
%KM*+ c.c3 AD (2 %KM*+ c.4@ M0) (2 )C+ EA+D+2/+ ,- K /,2D)K2) 1,J+* M(KD N()C J(--+A+2)
K1E*()0J+D P# Q. .......................................................................................................... Yf
%KM*+ c.V3 %(1+ 1+K2 ,- ,MD+ALK)(,2 +AA,A LKA(K2/+ P" o2 Q@ KJKE)(L+ (2-*K)(,2 P! Q@ )C+
+2D+1M*+ -,A+/KD) 1+K2 A1D +AA,A K2J )C+ +2D+1M*+ -,A+/KD) DEA+KJ (2 )C+ /KD+D ,- A3
M+D) )02+J /,2D)K2) (2-*K)(,2i #3 KJKE)(L+ (2-*K)(,2 +D)(1K)+J N()C )A0+ ,MD+ALK)(,2
+AA,A LKA(K2/+i '3 D(10*)K2+,0D +D)(1K)(,2 ,- M,)C " o2 K2J ! . &+D0*)D KA+ A+E,A)+J KD
K2 KL+AK?+ ,L+A )C+ *KD) bHHH D)+ED ,- K 2HHHTD)+E KDD(1(*K)(,2............................... bHH
L(
4(D) ,- F(?0A+D
F(?0A+ d.b3 %C+ *,/K*(XK)(,2 -K/),A Q2
+ZEP 2
2
"$ d%& KD )C+ -02/)(,2 ,- AK)(,2 JR" ...... dI
F(?0A+ d.23 A2K*FD(D &8S6 PD,*(J /0AL+Q K) cHH CBK -,A )C+ E+A(,J M+)N++2 HHHH
\%' b ^K20KAF bYfI K2J bfHH \%' bc F+MA0KAF bYfI. %C+ ,MD+ALK)(,2K* +AA,A
D)K2JKAJ J+L(K)(,2D KA+ DC,N2 KD JKDC *(2+D NC+A+L+A KEE*(/KM*+. %C+ -,0A EK2+*D
-A,1 )C+ ),E ), )C+ M,)),1 /,AA+DE,2J ), X,2K* N(2J@ ?+,E,)+2)(K* C+(?C)@ )+1E+AK)0A+
K2J DE+/(-(/ C01(J()F@ A+DE+/)(L+*F............................................................................. df
F(?0A+ d.d3 %C+ MK/W?A,02J PVTC,0A -,A+/KD)Q +AA,A -(+*J PDCKJ+JQ K2J )C+ +2D+1M*+
DEA+KJ ,- cHH CBK C+(?C) -(+*J P/,2),0AQ K) K2 KAM()AKAF )(1+. .................................... 4H
F(?0A+ d.43 #K/W?A,02J &8S6 K) K** EA+DD0A+ *+L+*D PD,*(J *(2+Q K2J MK/W?A,02J
+2D+1M*+ DEA+KJ PJKDC+J *(2+Q ,- C+(?C) -(+*J@ )+1E,AK**F KL+AK?+J -,A ,2+T1,2)C
K-)+A )C+ DE(2T0E E+A(,J. .............................................................................................. 4b
F(?0A+ 4.b3 8+K2 ,- VTC,0A SB66.S -,A+/KD) +AA,AD (2()(K*(X+J -A,1 )C+ NN& -(+*JD
P1,J+* M(KDQ@ )+1E,AK**F KL+AK?+J ,L+A )C+ +ZE+A(1+2)K* E+A(,J M+)N++2 HHHH \%' b
^K20KAF@ bYfI K2J bfHH \%' bc F+MA0KAF@ bYfI 0D(2? bf4 DK1E*+D. ....................... 44
F(?0A+ 4.23 %,E K2J 1(JJ*+ EK2+*D3 )C+ -(AD) )N, *+KJ(2? 6OF EK))+A2D ,- )C+ Y2c CBK
)+1E+AK)0A+ 1,J+* +AA,A K2,1K*,0D -(+*JD 0D(2? DK1E*+D (2 )C+ +ZE+A(1+2)K* E+A(,J
M+)N++2 HHHH \%' b ^K20KAF@ bYfI K2J bfHH \%' bc F+MA0KAF bYfI. %C+(A
/,AA+DE,2J(2? BA(2/(EK* ',1E,2+2)D PA+J *(2+ -,A B'b K2J ?A++2 *(2+ -,A B'2Q KA+
DC,N2 -,A K2 KAM()AKAF E+A(,J (2 ^K20KAF ,- bYfI. %C+ +ZE*K(2+J LKA(K2/+D -,A )C+D+
)N, 6OF 1,J+D KA+ dc.Ij K2J d2.cj A+DE+/)(L+*F................................................... 4V
L((
F(?0A+ 4.d3 A2K*FD(D &8S6 PD,*(J /0AL+Q K2J MK/W?A,02J &8S6 PJ,))+J /0AL+Q K) K**
EA+DD0A+ *+L+*D ,- C+(?C) -(+*J NC+2 KDD(1(*K)(2? )C+ gA+K*(D)(/` ,MD+ALK)(,2D -A,1
NN&@ )+1E,AK**F KL+AK?+J -,A K 1,2)C K-)+A )C+ (2()(K* DE(2T0E E+A(,J. F,A
/,1EKA(D,2@ )C+ K2K*FD(D &8S6 (2 )C+ E+A-+/) 1,J+* +ZE+A(1+2) NC+A+ KDD(1(*K)(2?
)C+ gD(10*K)+J` ,MD+ALK)(,2D -A,1 SB66.S g2K)0A+ A02` (D K*D, DC,N2 PJKDC+J
/0AL+Q. P<+ 2,)+ )CK) (2 K 1,A+ A+K*(D)(/ 1,J+*@ N()C K *KA?+A (2-*K)(,2@ )C+ (1E+A-+/)
1,J+* K2K*FD(D J,+D 2,) J+)+A(,AK)+ KD 10/C KD (2 )C(D +ZK1E*+@ +.?.@ F(?0A+ 2 (2
SX02F,?C +) K*. 2HHIQ ................................................................................................. 4f
F(?0A+ 4.43 #K/W?A,02J +2D+1M*+ DEA+KJ (2 C+(?C) -(+*J K) K** EA+DD0A+ *+L+*D
)+1E,AK**F KL+AK?+J ,L+A K 1,2)C K-)+A )C+ (2()(K* DE(2T0E E+A(,J (2 )C+ /KD+D ,-
E+A-+/) 1,J+* KDD(1(*K)(2? ,MD+ALK)(,2D ?+2+AK)+J -A,1 )C+ SB66.S g2K)0A+` A02
PJKDC+J /0AL+Q K2J (1E+A-+/) 1,J+* KDD(1(*K)(2? ,MD+ALK)(,2D ?+2+AK)+J -A,1 )C+
NN& -(+*J.................................................................................................................... cH
F(?0A+ 4.c3 S/C+1K)(/ ,- MK/W?A,02J +2D+1M*+D K2J )C+ g)A0)C` (2 )C+ EA+D+2/+ ,-
1,J+* +AA,AD. %C+ D,*(J /0AL+D A+EA+D+2) )C+ )AKa+/),A(+D ,- )N, +2D+1M*+D NC(*+ )C+
g)A0)C` PJKDC+J /0AL+Q CKD ()D ,N2 JF2K1(/D. ............................................................. cb
F(?0A+ 4.V3 %(1+ D+A(+D ,- )C+ ?*,MK*TKL+AK?+J K2K*FD(D &8S6 (2 )C+ /KD+D ,- )C+
g/,2)A,*` A02 PJKDC+J /0AL+Q@ ! hb.c 10*)(E*(/K)(L+ (2-*K)(,2 PJ,))+J /0AL+Q K2J r hb.c
KJJ()(L+ (2-*K)(,2 PD,*(J /0AL+Q. %C+ -,0A EK2+*D -A,1 )C+ ),E ), )C+ M,)),1 /,AA+DE,2J
), 2HH CBK u @ cHH CBK # @ fcH CBK $ K2J Y2c CBK % -(+*JD@ A+DE+/)(L+*F. ............... cc
F(?0A+ 4.I3 A2K*FD(D &8S6 K) K** EA+DD0A+ *+L+*D )+1E,AK**F KL+AK?+J -,A ,2+ 1,2)C
K-)+A )C+ (2()(K* CK*- 1,2)C DE(2T0E E+A(,J -,A X,2K* N(2J P*+-)Q K2J )+1E+AK)0A+ PA(?C)Q
(2 )C+ /KD+D ,- KJJ()(L+ 2,(D+ N()C K1E*()0J+ Ahb.c PD,*(J *(2+Q@ )C+ .JS8 ),?+)C+A
L(((
N()C KJJ()(L+ 2,(D+ N()C K1E*()0J+ AhH.2c PJKDC+J *(2+Q K2J )C+ .JS8 ),?+)C+A N()C
KJJ()(L+ 2,(D+ N()C K1E*()0J+ AhH.VH PJ,))+J *(2+Q..................................................... cY
F(?0A+ 4.f3 %,E EK2+*3 %(1+T1+K2 ,- SB66.S VTC,0A -,A+/KD) PM(KDQi 8(JJ*+ EK2+*3
%(1+T1+K2 ,- )C+ +D)(1K)+J M(KD -(+*Ji #,)),1 EK2+*3 %(1+T1+K2 ,- J+M(KD+J
-,A+/KD) K-)+A D0M)AK/)(2? )C+ +D)(1K)+J M(KD -A,1 )C+ SB66.S -,A+/KD) PM(KD ,- )C+
J+M(KD+J -,A+/KD)Q (2 )C+ /KD+ ,- KEE*F(2? )C+ .JS8U. %C+ A+D0*)D KA+ DC,N2 -,A 2HH
CBK X,2K* N(2J K2J )+1E,AK**F KL+AK?+J -,A K 1,2)C K-)+A )C+ (2()(K* DE(2T0E E+A(,J.
..................................................................................................................................... Vb
F(?0A+ 4.Y3 SK1+ KD F(?0A+ 4.f@ +Z/+E) -,A fcH CBK ................................................... V2
F(?0A+ 4.bH3 %(1+ D+A(+D ,- )C+ M(KD+J SB66.S -,A+/KD) +AA,A PA+J *(2+Q@ )C+
+D)(1K)+J M(KD MF )C+ .JS8U PM*K/W *(2+Q@ K2J )C+ +AA,A ,- )C+ J+M(KD+J -,A+/KD) MF
D0M)AK/)(2? )C+ M(KD -A,1 )C+ M(KD+J SB66.S -,A+/KD) P?A++2 J,))+J *(2+Q ,- )C+ Y2c
CBK )+1E+AK)0A+ -(+*J K) Pb2Hk6@ dHkSQ NC+A+ K *KA?+ J(0A2K* M(KD (D EA+D+2)+J. ....... V4
F(?0A+ 4.bb3 ',1EKA(D,2 ,- K2K*FD(D &8S6 N()C )(1+TKL+AK?+J M(KD +D)(1K)+J -A,1
,2+T1,2)C EA(,A DK1E*+D PD,*(J /0AL+Q K2J +D)(1K)+J -A,1 cTF+KA /*(1K),*,?F PJ,))+J
/0AL+Q. %(1+ D+A(+D KA+ DC,N2 -,A 2HH CBK X,2K* N(2J@ cHH CBK )+1E+AK)0A+ K2J fcH
CBK DE+/(-(/ C01(J()F.................................................................................................. Vf
F(?0A+ 4.b23 %(1+ D+A(+D ,- ?*,MK*TKL+AK?+J K2K*FD(D &8S6 /,AA+/)+J -,A )C+ /,2D)K2)
M(KD N()C PJ,))+J *(2+Q K2J N()C,0) PD,*(J *(2+Q J(0A2K* M(KD /,AA+/)(,2 -,A )+1E+AK)0A+
K) Y2c CBK P*+-)Q K2J fcH CBK PA(?C)Q........................................................................... VY
F(?0A+ 4.bd3 A2K*FD(D &8S6 J(--+A+2/+ M+)N++2 )C+ A02D N()C K2J N()C,0) J(0A2K*
M(KD /,AA+/)(,2@ KL+AK?+J -,A K 1,2)C K-)+A )C+ (2()(K* DE(2T0E E+A(,J@ -,A )+1E+AK)0A+
(Z
K) Y2c CBK P*+-)Q K2J fcH CBK PA(?C)Q. %C+ ?A++2 /,*,A (2J(/K)+D )C+ &8S6 A+J0/)(,2
MF (2/*0J(2? )C+ J(0A2K* M(KD /,AA+/)(,2...................................................................... VY
F(?0A+ 4.b43 %(1+ D+A(+D ,- ?*,MK**F KL+AK?+J K2K*FD(D &8S6 /,AA+/)+J -,A )C+
/,2D)K2) K2J J(0A2K* M(KD N()C PJ,))+J *(2+Q K2J N()C,0) PD,*(J *(2+Q )C+ D)K)+T
J+E+2J+2) +AA,A /,AA+/)(,2 -,A )+1E+AK)0A+ K) cHH CBK P*+-)Q K2J 1+A(J(,2K* N(2J K)
Y2c CBK PA(?C)Q. ........................................................................................................... Ib
F(?0A+ 4.bc3 %C+ -(AD) )CA++ *+KJ(2? S>. D)A0/)0A+D M+)N++2 )C+ 1,J+* D)K)+
K2,1K*(+D P/,2),0ADQ K2J )C+ 1,J+* +AA,A K2,1K*(+D PDCKJ+DQ (2 1+A(J(,2K* N(2J K)
Y2c CBK (2 ^K20KAF -,A bYf2TbYfV@ K2J )C+ K2K*FD(D &8S6 J(--+A+2/+ M+)N++2 )C+
A02D N()C K2J N()C,0) )C+ D)K)+TJ+E+2J+2) +AA,A /,AA+/)(,2@ KL+AK?+J ,L+A )C+ E+A(,J
-A,1 bb ^K20KAF bYfI ), db ^K20KAF bYfI PM,)),1 A(?C) EK2+*Q. %C+ ?A++2 /,*,A
(2J(/K)+D )C+ &8S6 A+J0/)(,2 MF (2/*0J(2? )C+ D)K)+TJ+E+2J+2) +AA,A /,AA+/)(,2. 8,D)
,- )C+ A+J0/)(,2 (D -,02J (2 )C+ /(A/*+J A+?(,2D NC+A+ )C+ *+KJ(2? /,0E*+J D(?2K*D KA+
)C+ D)A,2?+D). ............................................................................................................... I2
F(?0A+ 4.bV3 %(1+ D+A(+D ,- )C+ ?*,MK*TKL+AK?+J K2K*FD(D &8S6 ,- )C+ cHH CBK # K2J
Y2c CBK % -(+*JD@ (2 )C+ /KD+D ,- )C+ 4.8 K*,2+ PJKDC+J /0AL+Q@ r hb.c KJJ()(L+
(2-*K)(,2 PJ,))+J /0AL+Q K2J )C+ 4.8 ),?+)C+A N()C KJJ()(L+ (2-*K)(,2 N()C K2
K1E*()0J+ r hH.4 PD,*(J /0AL+Q. ................................................................................... I4
F(?0A+ 4.bI3 SK1+ KD F(?0A+ 4.Y@ +Z/+E) (2 )C+ /KD+ ,- KEE*F(2? )C+ 4.8U.............. Ic
F(?0A+ 4.bf3 A2K*FD(D &8S6 K) K** EA+DD0A+ *+L+*D (2 )C+ /KD+D ,- )C+ 4.8U PM*K/W
J,))+J *(2+Q@ )C+ .JS8U PM*K/W JKDC+J *(2+Q@ KJJ()(L+ (2-*K)(,2 PM*K/W D,*(J *(2+Q@
D(1E*(-(+J .JS8U P?A++2 *(2+Q K2J 10*)(E*(/K)(L+ (2-*K)(,2 PM*0+ *(2+Q. %C+ -,0A
EK2+*D /,AA+DE,2J ), 0TN(2J -(+*J@ )+1E+AK)0A+ -(+*J@ C+(?C) -(+*J K2J DE+/(-(/
Z
C01(J()F -(+*J@ A+DE+/)(L+*F. %C+ KL+AK?+D KA+ )KW+2 -,A K 1,2)C K-)+A )C+ (2()(K* CK*-T
1,2)C DE(2T0E E+A(,J. ................................................................................................. If
F(?0A+ 4.bY3 SK1+ KD )C+ ),ET*+-) EK2+* (2 F(?0A+ 4.bf@ M0) K*D, DC,ND )C+ A+D0*) -,A
)C+ g/,2)A,* A02` PA+J *(2+Q. <+ 2,)+ K?K(2 )CK) (2 K 1,A+ A+K*(D)(/ ,E+AK)(,2K* 1,J+*@
)C+ 2+?K)(L+ +--+/) ,- 1,J+* +AA,AD (D 2,) KD *KA?+ KD (2 )C(D g/,2)A,* A02` K2J K
D(?2(-(/K2) K1,02) ,- (2-*K)(,2 *+KJD ), M+))+A A+D0*)D +L+2 (2 )C+ KMD+2/+ ,- M(KD
/,AA+/)(,2 P+.?.@ SX02F,?C +) K*. 2HHIQ. ...................................................................... IY
F(?0A+ 4.2H3 [*,MK*TKL+AK?+J KMD,*0)+ LK*0+ ,- )C+ J(--+A+2/+ M+)N++2 K2K*FD(D K2J
)C+ NN& g)A0)C` PK2K*FD(D M(KDQ K) K** EA+DD0A+ *+L+*D (2 )C+ /KD+D ,- )C+ 4.8U PM*K/W
J,))+J *(2+Q@ )C+ .JS8U PM*K/W JKDC+J *(2+Q K2J KJJ()(L+ (2-*K)(,2 PM*K/W D,*(J *(2+Q.
%C+ -,0A EK2+*D /,AA+DE,2J ), 0TN(2J -(+*J@ )+1E+AK)0A+ -(+*J@ C+(?C) -(+*J K2J
DE+/(-(/ C01(J()F -(+*J@ A+DE+/)(L+*F. %C+ ?*,MK*TKL+AK?+J KMD,*0)+ M(KD (D /K*/0*K)+J
MF KL+AK?(2? )C+ J(--+A+2/+ M+)N++2 K2K*FD(D K2J NN& ,L+A ,2+ 1,2)C PM(KDQ K) +K/C
1,J+* ?A(J E,(2)@ )C+2 -(2J(2? )C+ KMD,*0)+ LK*0+ -,A )C+ M(KD -(+*JD@ K2J -(2K**F )KW(2?
K DEK)(K* KL+AK?+ ,- )C+D+ KMD,*0)+ LK*0+D ,L+A )C+ NC,*+ ?*,M+. ............................... fH
F(?0A+ 4.2b3 4fTC,0A -,A+/KD) &8S6 K) K** EA+DD0A+ *+L+*D (2 )C+ /KD+D ,- )C+ 4.8U
PM*K/W J,))+J *(2+Q@ )C+ .JS8U PM*K/W JKDC+J *(2+Q@ K2J KJJ()(L+ (2-*K)(,2 PM*K/W D,*(J
*(2+Q. %C+ -,0A EK2+*D /,AA+DE,2J ), 0TN(2J -(+*J@ )+1E+AK)0A+ -(+*J@ C+(?C) -(+*J K2J
DE+/(-(/ C01(J()F -(+*J@ A+DE+/)(L+*F. %C+ KL+AK?+D KA+ )KW+2 ,L+A K** -,A+/KD)D D)K)+J
M+)N++2 HHHH \%' b F+MA0KAF bYfI K2J bfHH \%' bc F+MA0KAF bYfI.................... f2
F(?0A+ c.b3 %(1+ D+A(+D ,- ,2T*(2+ +D)(1K)+J ,MD+ALK)(,2 +AA,AD ,- u @ % @ $ @ K2J 'p
-,A )C+ -(AD) cH K2K*FD(D )(1+ D)+ED P/,AA+DE,2J(2? ), HHX ^K2 b )CA,0?C HVX ^K2 bd@
bYf2Q ......................................................................................................................... bH2
Z(
F(?0A+ c.23 %(1+ D+A(+D ,- +D)(1K)+J (2-*K)(,2 -K/),A@ (2 )C+ /KD+D ,- 0D(2? K E+A-+/)*F
DE+/(-(+J ,MD+ALK)(,2 +AA,A LKA(K2/+ PJKDC+JTJ,))+J *(2+Q K2J 0D(2? K2 (2()(K**F
+AA,2+,0D ,MD+ALK)(,2 +AA,A LKA(K2/+ M0) +D)(1K)(2? () KJKE)(L+*F PD,*(J *(2+Q......... bHd
F(?0A+ c.d3 %(1+ D+A(+D ,- ?*,MK* KL+AK?+J K2K*FD(D &8S +AA,A ,- cHH CBK
)+1E+AK)0A+ K2J ?+,E,)+2)(K* C+(?C) -,A ^K20KAF K2J F+MA0KAF bYf2 N()C )C+ KJKE)(L+
(2-*K)(,2@ (2 )C+ /KD+D ,- 0D(2? K E+A-+/)*F DE+/(-(+J ,MD+ALK)(,2 +AA,A LKA(K2/+ PA+J
*(2+Q K2J 0D(2? K2 (2()(K**F NA,2? ,MD+ALK)(,2 +AA,A LKA(K2/+ M0) +D)(1K)(2? ()
KJKE)(L+*F P?A++2 *(2+Q. ............................................................................................. bH4
Z((
Chapter 1
Introduction
.K)K KDD(1(*K)(,2 K*?,A()C1D D++W ), -(2J )C+ ,E)(1K* /,1M(2K)(,2 ,- 1,J+*
-,A+/KD) PlMK/W?A,02JmQ K2J )C+ KLK(*KM*+ ,MD+ALK)(,2D ), ?+2+AK)+ (1EA,L+J (2()(K*
/,2J()(,2D PlK2K*FD(DmQ -,A 201+A(/K* N+K)C+A EA+J(/)(,2D. 8,D) KDD(1(*K)(,2 D/C+1+D
KA+ MKD+J ,2 )C+ *(2+KA +D)(1K)(,2 )C+,AF (2 NC(/C )C+ MK/W?A,02J K2J )C+
,MD+ALK)(,2D KA+ ?(L+2 K N+(?C) EA,E,A)(,2K* ), )C+ (2L+AD+ ,- )C+(A /,AA+DE,2J(2?
DE+/(-(+J +AA,A /,LKA(K2/+D. AD D0/C@ )C+ K//0AK/F ,- K JK)K KDD(1(*K)(,2 D/C+1+ A+*(+D
C(?C*F ,2 )C+ W2,N*+J?+ ,- )C+ +AA,A D)K)(D)(/D ,- M,)C )C+ 1,J+* MK/W?A,02J K2J )C+
,MD+ALK)(,2D. %C+ ,MD+ALK)(,2 +AA,A /,LKA(K2/+ (D 0D0K**F KDD01+J ), M+ J(K?,2K* K2J
)(1+ (2LKA(K2). ;) (D 2,) K ?,,J KEEA,Z(1K)(,2 ), KDD01+ )C+ MK/W?A,02J +AA,A
/,LKA(K2/+ (D K*D, D)K)(,2KAF D(2/+ () (D K/)0K**F -*,NTJ+E+2J+2). ;2 EAK/)(/+@ C,N+L+A@
+D)(1K)(2? )C+ )(1+TJ+E+2J+2) MK/W?A,02J +AA,A /,LKA(K2/+ (D J(--(/0*). ;2 d.>A&
P+.?. BKAA(DC K2J .+AM+A@ bYY2Q@ K JK)K KDD(1(*K)(,2 D/C+1+ 0D+J (2 1K2F ,E+AK)(,2K*
/+2)+AD@ )C+ MK/W?A,02J +AA,A /,LKA(K2/+ (D KDD01+J ), M+ (D,)A,E(/ K2J D)K)(,2KAF. ;2
)C+ :K*1K2 -(*)+A P:F@ :K*1K2 bYVHQ@ )C+ MK/W?A,02J +AA,A /,LKA(K2/+ (D EA,EK?K)+J
+ZE*(/()*F N()C K *(2+KA 1,J+*. 62D+1M*+TMKD+J :K*1K2 -(*)+A P62:FQ )+/C2(]0+D
(2D)+KJ +D)(1K)+ )C+ MK/W?A,02J +AA,A /,LKA(K2/+D -A,1 K2 +2D+1M*+ ,- -,A+/KD)D
NC(/C K**,ND )C+1 (2 )C+,AF ), (2/*0J+ (2-,A1K)(,2 ,2 )C+ -*,NTJ+E+2J+2) +AA,A ,-
JKF PM,)C )+1E,AK**F K2J DEK)(K**F LKA(K2)Q. F,A 1,A+ MK/W?A,02J ,- )C+ 62:F@ )C+
A+KJ+AD KA+ A+/,11+2J+J ), A+-+A@ -,A +ZK1E*+@ 6L+2D+2 PbYY4Q@ =,0)+WK1+A K2J
b
8()/C+** PbYYfQ@ A2J+AD,2 P2HHbQ@ <C()KW+A K2J =K1(** P2HH2Q@ %(EE+)) +) K*. P2HHdQ@
O)) +) K*. P2HH4Q@ 6L+2D+2 P2HHdQ.
8,D) D)0J(+D ), JK)+ CKL+ )+D)+J 62:F DFD)+1D 02J+A E+A-+/) 1,J+*
KDD01E)(,2D K2J N()C D(10*K)+J ,MD+ALK)(,2D P)C+(A +AA,A D)K)(D)(/D KA+ E+A-+/)*F
W2,N2Q. O2*F N()C(2 )C+ *KD) -+N F+KAD CKL+ 62:F 1+)C,JD M++2 )+D)+J (2
KDD(1(*K)(2? A+K* ,MD+ALK)(,2D. ;2 )C+ A+K*TN,A*J KEE*(/K)(,2D@ D+L+AK* (DD0+D CKL+ ),
M+ J+K*) N()C@ D0/C KD3 bQ 1,J+* +AA,AD@ 2Q (2/,2L+2(+2/+ ,A (2-+KD(M(*()F ,- 1K20K**F
)02(2? )C+ (2-*K)(,2 -K/),A NC+2 () (D A+?(,2K* K2JR,A LKA(KM*+ J+E+2J+2)@ dQ
+AA,2+,0D*F DE+/(-(+J ,MD+ALK)(,2 +AA,A D)K)(D)(/D@ 4Q (1E+A-+/) -,ANKAJ ,MD+ALK)(,2
,E+AK),A@ cQ 2,2T[K0DD(K2()F ,- -,A+/KD) K2J ,MD+ALK)(,2 +AA,AD@ +)/. ;2 )C(D
J(DD+A)K)(,2@ N+ -,/0D ,2 )C+ -(AD) )CA++ (DD0+D. 8+)C,JD ), J+K* N()C )C+1 KA+
(2L+D)(?K)+J K2J )+D)+J.
b.b 62:F (2 )C+ EA+D+2/+ ,- 1,J+* +AA,AD
62:F 1+)C,JD CKL+ M++2 DC,N2 ), M+ 1,A+ K//0AK)+ )CK2 d.T>KA 02J+A )C+
KDD01E)(,2 ,- K E+A-+/) 1,J+* P8(F,DC( 2HHc@ 4(0 +) K* 2HHVQ. =,N+L+A@ (2 )C+ A+K*
N,A*J@ -,A+/KD) +AA,AD J+A(L+ 2,) ,2*F -A,1 +AA,AD (2 )C+ (2()(K* /,2J()(,2D M0) K*D,
-A,1 +AA,AD J0+ ), )C+ 1,J+* J+-(/(+2/(+D. %C+ *K))+A )FE+ ,- +AA,A (D 0D0K**F /K**+J
,ode! error/ %C+ D,0A/+D ,- 1,J+* +AA,A /K2 M+ J0+ ), *K/W ,- A+D,*0)(,2@ KEEA,Z(1K)+
EKAK1+)+A(XK)(,2D ,- ECFD(/K* EA,/+DD+D@ 201+A(/K* J(DE+AD(,2@ +)/. F,A KDD(1(*K)(,2
,- A+K* ,MD+ALK)(,2D@ )C+ KDD01E)(,2 ,- K E+A-+/) 1,J+* 10D) M+ JA,EE+J. AD K A+D0*)@
)C+A+ (D 2, ?0KAK2)++ )CK) )C+ 62:F N(** M+ D)(** M+))+A )CK2 d.T>KA JK)K KDD(1(*K)(,2
DFD)+1D NC+2 KDD(1(*K)(2? A+K* ,MD+ALK)(,2D. ;2 -K/)@ 8(F,DC( P2HHcQ CKD DC,N2 )CK)
1,J+* +AA,A CKD K D)A,2?+A 2+?K)(L+ (2-*0+2/+ ,2 )C+ E+A-,A1K2/+ ,- )C+ 62:F )CK2
2
,2 )C+ d.T>KA. A//,02)(2? -,A 1,J+* +AA,AD (D (1E,A)K2) M0) (D K*D, )C+ 1,D) J(--(/0*)
(DD0+ -,A 62:F DFD)+1D.
8+)C,JD ), J+K* N()C 1,J+* +AA,AD N+A+ (2)A,J0/+J J+/KJ+D K?, (2 )C+
+2?(2++A(2? /,1102()F. ;2 )C+ 1+)+,A,*,?(/K* /,1102()F@ 02)(* A+/+2)*F@ D,*L(2? )C(D
EA,M*+1 CKD M++2 A+/+(L(2? N(J+DEA+KJ K))+2)(,2. .++ K2J JK S(*LK PbYYf@ C+A+K-)+A
A+-+AA+J KD .JSQ EA,E,D+J K 1+)C,J -,A )C+ ,2T*(2+ +D)(1K)(,2 K2J /,AA+/)(,2 ,-
1,J+* M(KD NC+A+ )C+ EA(,A +D)(1K)+ ,- )C+ M(KD (D 0EJK)+J MF 0D(2? )C+ :K*1K2 -(*)+A.
%C(D M(KD /,AA+/)(,2 1+)C,J P.JS8@ C+A+K-)+AQ CKD M++2 D0//+DD-0**F )+D)+J@ -,A
+ZK1E*+@ MF .++ K2J %,J*(2? P2HHHQ@ 'KA),2 +) K*. P2HHHQ@ 8KA)(2 +) K*. P2HH2Q@
'C+E0A(2 +) K*. P2HHcQ. &+/+2)*F@ #K+W +) K* P2HHVQ J+L+*,E+J K2,)C+A M(KD /,AA+/)(,2
1+)C,J NC(/C (D D(1(*KA ), )C+ .JS8 +Z/+E) -,A K//,02)(2? -,A )C+ /A,DDT/,AA+*K)(,2
,- 02/+A)K(2)(+D (2 1,J+* D)K)+ K2J M(KD )CK) CKJ M++2 (?2,A+J (2 )C+ .JS8. %C+F
D0//+DD-0**F )+D)+J )C(D KEEA,K/C N()C )C+ 4,A+2XTYV 1,J+*. =,N+L+A@ M,)C ,- )C+D+
)N, 1+)C,JD KDD01+ K D)+KJF -,A+/KD) 1,J+* -,A )C+ M(KD. %C(D A+D0*)D (2 M+(2? *(1()+J
), +D)(1K)+ ,2*F )C+ D*,N*F LKAF(2? /,1E,2+2) ,- -,A+/KD) +AA,AD. ;2 A+K*()F@ 1,J+*
+AA,A 1KF M+ )(1+TLKA(K2). %, /,AA+/) )C+ +L,*L(2? 1,J+* +AA,A@ K2 +1E(A(/K*
/,AA+/)(,2 )CK) J+E+2JD ,2 )C+ (2D)K2)K2+,0D D)K)+ ,- )C+ 1,J+* CKD M++2 EA,E,D+J ),
/,AA+/) )C+ gD)K)+TJ+E+2J+2) +AA,A` P4+()C bYIfi .+*S,*+ K2J =,0 bYYYQ. %C(D 1+)C,J
A+*(+D ,2 )C+ /A,DD /,LKA(K2/+ M+)N++2 )C+ 1,J+* +AA,A K2J )C+ 1,J+* D)K)+. .(A+/)
/,1E0)K)(,2 ,- )C+ M(KD /,AA+/)(,2 )+A1 ,2 +K/C 1,J+* ?A(J E,(2) (D (2 EAK/)(/+
EA,C(M()(L+ -,A )C+ ,E+AK)(,2K* -,A+/KD) 1,J+*. #0(*J(2? ,2 N,AWD ,- 4+()C PbYIfQ@
.K2-,A)C +) K* P2HHIQ EA,E,D+J K2 K*)+A2K)(L+ KEEA,K/C MKD+J ,2 S>. ), +D)(1K)+ )C+
D)K)+TJ+E+2J+2) +AA,A N()C 10/C *,N+A /,1E0)K)(,2K* /,D). .K2-,A)C +) K*. K*D,
d
/,AA+/)+J )C+ D)K)+T(2J+E+2J+2) 1,J+* +AA,A MF +ZEK2J(2? 1,J+* +AA,AD (2), K M(KD K2J
*,N ,AJ+A 6OFD )CK) /,0*J /,AA+/) ,)C+A +AA,AD D0/C KD )C,D+ KDD,/(K)+J N()C )C+
J(0A2K* /F/*+. %C+F -,02J )C(D *,NTJ(1+2D(,2K* 1+)C,J P4.8@ C+A+K-)+AQ ), M+ L+AF
D0//+DD-0* K2J +--(/(+2) /,1E0)K)(,2K**F. =,N+L+A@ (2 )C+(A +ZE+A(1+2)D )C+A+ (D 2,
JK)K KDD(1(*K)(,2 (2L,*L+J@ D(2/+ )C+ (2()(K* /,2J()(,2D KA+ KDD01+J ), M+ E+A-+/). ;) (D
N,A)CNC(*+ ), (2L+D)(?K)+ NC+)C+A )C+ KEE*(/K)(,2 ,- )C+ 4.8 /K2 M+ +ZEK2J+J ),
1,A+ A+K*(D)(/ D()0K)(,2D NC+A+ )C+ -,A+/KD)TK2K*FD(D (D /F/*+J K2J@ KD K A+D0*)@ -,A+/KD)
+AA,A (2/*0J+D M,)C 1,J+* +AA,A K2J JF2K1(/K* ?A,N(2? +AA,A J0+ ), )C+ (1E+A-+/)
(2()(K* /,2J()(,2.
A** ,- )C+ 1+)C,JD 1+2)(,2+J KM,L+ KA+ 1+K2) ), +D)(1K)+ K2J A+1,L+ 1,J+*
M(KD -A,1 )C+ -,A+/KD)D@ NC(/C /K2 M+ KEE*(+J ), K2F JK)K KDD(1(*K)(,2 DFD)+1. F,A
62:F DFD)+1D@ +2*KA?(2? MK/W?A,02J +AA,A LKA(K2/+ (D K2,)C+A NKF ), CK2J*+ 1,J+*
+AA,AD. A2J+AD,2 K2J A2J+AD,2 PbYYYQ (2)A,J0/+J )C+ (J+K ,- 10*)(E*(/K)(L+ (2-*K)(,2.
',AKXXK +) K*. P2HH2Q KJJ+J AK2J,1 E+A)0AMK)(,2D ), MA+J L+/),AD K2J -,02J ()
(1EA,L+J )C+(A KM(*()F ), A+EA+D+2) MK/W?A,02J +AA,AD. ',AKXXK +) K* P2HHIQ -,02J )C+
KJJ()(L+ (2-*K)(,2 N,AW+J 10/C M+))+A )CK2 )C+ 10*)(E*(/K)(L+ (2-*K)(,2 (2 )C+ 46:F
PO)) +) K*. 2HH4Q N()C(2 K E+A-+/) 1,J+* +ZE+A(1+2). A*)C,0?C )C+ 10*)(E*(/K)(L+ K2J
KJJ()(L+ (2-*K)(,2 N+A+ (2()(K**F (2)A,J0/+J ), K1+*(,AK)+ DK1E*(2? +AA,AD J0+ ), D1K**
+2D+1M*+ D(X+ (2 )C+ E+A-+/) 1,J+* D/+2KA(,@ )C+F CKL+ M++2 A+/+2)*F 0D+J ), K//,02)
-,A 1,J+* +AA,AD (2 KDD(1(*K)(2? A+K* ,MD+ALK)(,2D. <C()KW+A +) K*. P2HH4Q 0D+J
10*)(E*(/K)(L+ (2-*K)(,2 K2J ,M)K(2+J K M+))+A A+K2K*FD(D )CK2 )C+ N'6B d.T>KA (2 )C+
1(JJ*+ K2J *,N )A,E,DEC+A+ -A,1 A+K* D0A-K/+ EA+DD0A+ ,MD+ALK)(,2D. =,0)+WK1+A +)
K*. P2HHcQ EKAK1+)+A(X+J 1,J+* +AA,AD N()C gKJJ()(L+ +AA,A` MF KJJ(2? AK2J,1 2,(D+ ),
4
+K/C -,A+/KD) +2D+1M*+ 1+1M+A. %C+ /,LKA(K2/+ ,- )C+ AK2J,1 2,(D+ CKD )C+ DK1+
D)A0/)0A+ K2J D/K*+JTJ,N2 K1E*()0J+ KD )C+ d.T>KA MK/W?A,02J +AA,A /,LKA(K2/+. %C+
A+D0*)D DC,N+J )CK) )C+ ]0K*()F ,- )C+(A +2D+1M*+ :K*1K2 -(*)+A NKD /,1EKAKM*+ ),
d.T>KA 0D(2? A+K* ,MD+ALK)(,2D. =K1(** +) K*. P2HHcQ /,1EKA+J J(--+A+2) NKFD ),
EKAK1+)+A(X+ KJJ()(L+ +AA,A. <C()KW+A +) K* P2HHIQ ?+2+AK)+J KJJ()(L+ 2,(D+ MF
AK2J,1*F D+*+/)(2? DK1E*+D -A,1 )C+ VTC,0A )+2J+2/(+D -(+*J ,- )C+ N'6BRN'A&
A+K2K*FD(D PNN&@ :K*2KF +) K*. bYYVQ D)K)+D K2J -,02J () ?KL+ 1,A+ K//0AK)+ K2K*FD(D
)CK2 )C+ 10*)(E*(/K)(L+ (2-*K)(,2 NC+2 KDD(1(*K)(2? A+K* ,MD+ALK)(,2D 0D(2? )C+ N'6B
[FS 1,J+*. A** ,- )C+D+ 1+)C,JD KA+ DE+/(-(/ ), 62:F DFD)+1D. %C+F +2*KA?+ )C+
MK/W?A,02J +2D+1M*+ DEA+KJ N()C,0) /CK2?(2? )C+ +2D+1M*+ 1+K2. %, ,0A M+D)
W2,N*+J?+@ )C+A+ CKL+ M++2 2, /,1EKA(D,2D D, -KA M+)N++2 )C+D+ LKA(K2/+T+2*KA?(2?
1+)C,JD K2J )C,D+ +D)(1K)(2? K2J A+1,L(2? 1,J+* +AA,A -A,1 )C+ +2D+1M*+ 1+K2
P+.?. .JS8 K2J 4.8Q.
b.2 AJKE)(L+ +D)(1K)(,2 ,- (2-*K)(,2 -K/),A
%C,0?C 10*)(E*(/K)(L+ K2J KJJ()(L+ (2-*K)(,2 D/C+1+D KA+ N(J+*F 0D+J (2 62:F
DFD)+1D (2 M,)C )C+ E+A-+/) K2J (1E+A-+/) 1,J+* +ZE+A(1+2)D@ )C+D+ KJa02/)
K*?,A()C1D A+]0(A+ /,2D(J+AKM*+ )02(2? -,A ?,,J E+A-,A1K2/+. 8K20K**F )02(2? )C+
(2-*K)(,2 EKAK1+)+A (D /,11,2 (2 )C+ 62:F +ZE+A(1+2)D M0) (D +ZE+2D(L+@ D(2/+@ ,2
()D ,N2@ )C+ -,A+/KD)TK2K*FD(D /F/*+ J,+D A+]0(A+ 1K2F +2D+1M*+ 1+1M+AD. 6L+2
N,AD+@ () M+/,1+D (2-+KD(M*+ (- )C+ (2-*K)(,2 -K/),A (D A+?(,2K* K2JR,A LKA(KM*+
J+E+2J+2). <K2? K2J #(DC,E P2HHdQ KJ,E) )C+ 1KZ(101 *(W+*(C,,J EKAK1+)+A
+D)(1K)(,2 )C+,AF ,- .++ PbYYcQ ), +D)(1K)+ )C+ (2-*K)(,2 -K/),A -A,1 )C+ (22,LK)(,2
c
o0'er1ation5,inu'50a67ground D)K)(D)(/D (2 )C+(A
+2D+1M*+ -,A+/KD) D/C+1+. 8(F,DC( P2HHcQ A+E,A)+J )C+ 0D+ ,- K D(1(*KA 1+)C,J ),
+D)(1K)+ )C+ MK/W?A,02J +AA,A (2-*K)(,2 -K/),A N()C(2 62:F. A*)C,0?C )C+ A+D0*)D N+A+
DK)(D-K/),AF () (D ,ML(,0D )CK) )C(D (2-*K)(,2 +D)(1K)(,2 1+)C,J A+*(+D ,2 )C+ KDD01E)(,2
,- K E+A-+/) W2,N*+J?+ ,- )C+ ,MD+ALK)(,2K* +AA,A /,LKA(K2/+
nQboP RHHPdd '!'& %9% tra6e
R . %C(D KDD01E)(,2 (D
LK*(J -,A )C+ D(10*K)+J ,MD+ALK)(,2D M0) 1KF 2,) -,A A+K* ,MD+ALK)(,2D. <C+2
KDD(1(*K)(2? A+K* JK)K@ N+ 2++J K 1+)C,J ), ,M)K(2 )C+ /,AA+/) D)K)(D)(/D ,- ,MD+ALK)(,2
+AA,AD (- N+ NK2) ), KEE*F )C+ D/C+1+ -,A ,2T*(2+ +D)(1K)(2? (2-*K)(,2 -K/),A.
b.d .(K?2,D(D ,- ,MD+ALK)(,2 +AA,A D)K)(D)(/D
#+D(J+D )C+ (DD0+ ,- )C+ A+]0(A+1+2) ,- /,AA+/) ,MD+ALK)(,2 +AA,A D)K)(D)(/D (2 )C+
,2T*(2+ +D)(1K)(,2 ,- )C+ (2-*K)(,2 -K/),A J(D/0DD+J KM,L+@ )C+ ,MD+ALK)(,2 +AA,A
D)K)(D)(/D )C+1D+*L+D KA+ L+AF (1E,A)K2) ), )C+ JK)K KDD(1(*K)(,2@ D(2/+ )C+F J(A+/)*F
J+)+A1(2+ )C+ A+*K)(L+ N+(?C) ?(L+2 ), )C+ ,MD+ALK)(,2D. =,N+L+A@ (2 )C+ A+K* N,A*J@
)C(D (2-,A1K)(,2 (D 2,) E+A-+/)*F W2,N2. &+/+2) J(K?2,D)(/ N,AW P.+DA,X(+AD K2J
;LK2,L 2HHb@ %K*K?AK2J bYYY@ 'KAJ(2K*( +) K*. 2HH4@ 'CKE2(W +) K*. 2HHV@ K2J ,)C+ADQ
D0??+D) )CK) (22,LK)(,2 K2J ,)C+A D)K)(D)(/D /K2 M+ 0D+J ), J(K?2,D+ M,)C ,MD+ALK)(,2
K2J MK/W?A,02J +AA,AD. A -,A10*K)(,2 ,2 )C+ /,D) -02/)(,2 ,- D0/C J(K?2,D)(/D CKD
M++2 EA,E,D+J K2J )+D)+J (2 K LKA(K)(,2K* -AK1+N,AW. #0(*J(2? ,2 )C+D+ N,AWD@
.+DA,X(+AD +) K*. P2HHcQ P.6AHc C+A+K-)+AQ J+L+*,E+J K D+) ,- J(K?2,D)(/D MKD+J ,2
)C+ /,1M(2K)(,2D ,- o0'er1ation5,inu'5ana!:'i'@ o0'er1ation5,inu'50a67ground K2J
0a67ground5,inu'5ana!:'i' t, KJKE)(L+*F )02+ ,MD+ALK)(,2 K2J MK/W?A,02J +AA,AD.
=+A+ N+ KJKE) ,2+ ,- )C+D+ J(K?2,D)(/D -,A +D)(1K)(2? ,MD+ALK)(,2 +AA,A LKA(K2/+ (2),
)C+ 62:F. F,A 1,A+ J+)K(*D@ )C+ A+KJ+A (D A+-+AA+J ), D+/)(,2 2.4.2 (2 'CKE)+A 2.
V
b.4 SE+/(-(/ ?,K*D ,- )C(D J(DD+A)K)(,2
%C+ 1K(2 ?,K* ,- )C(D )C+D(D (D ), (1EA,L+ )C+ E+A-,A1K2/+ ,- )C+ 62:F (2
KDD(1(*K)(2? A+K* ,MD+ALK)(,2D K2J@ KD K A+D0*)@ ), K//+*+AK)+ )C+ J+L+*,E1+2) ,- 62:F
DFD)+1D ),NKAJD ,E+AK)(,2K* KEE*(/K)(,2D. %, KDD(1(*K)+ )C+ A+K* ,MD+ALK)(,2D@ 1,J+*
+AA,A (D )C+ 1,D) (1E,A)K2) K2J J(--(/0*) (DD0+ ), J+K* N()C. 8+)C,JD CKL+ M++2
EA,E,D+J ), +()C+A K//,02) -,A 1,J+* +AA,A (2 )C+ D+/,2J 1,1+2) ,- )C+ +2D+1M*+ MF
+2*KA?(2? MK/W?A,02J +AA,A LKA(K2/+ ,A ), +D)(1K)+ K2J /,AA+/) 1,J+* M(KD -,A )C+
+2D+1M*+ 1+K2. =,N+L+A@ )C+A+ (D *())*+ A+D+KA/C ,2 /,1EKA(2? 1+)C,JD M+)N++2
)C+D+ )N, KEEA,K/C+D. ;2 KJJ()(,2@ )C+ (1E+A-+/) W2,N*+J?+ ,- ,MD+ALK)(,2 +AA,A
D)K)(D)(/D K2J )C+ (2/,2L+2(+2/+ ,- 1K20K**F )02(2? (2-*K)(,2 -K/),A KA+ )C+ ,)C+A )N,
(DD0+D N+ NK2) ), KJJA+DD (2 )C(D )C+D(D. F,A )C+D+ E0AE,D+D@ )C+ EA+D+2) A+D+KA/C K(1D
), (2L+D)(?K)+ )C+ -,**,N(2? ]0+D)(,2D3
b. AA+ M(KD A+1,LK* 1+)C,JD ?+2+AK**F M+))+A )CK2 )C,D+ ,2*F +2*KA?(2?
MK/W?A,02J +AA,A LKA(K2/+p <CK) KA+ )C+ A+*K)(L+ KJLK2)K?+ K2J J(DKJLK2)K?+
M+)N++2 )N, 1Ka,A M(KD A+1,LK* 1+)C,JD3 .JS8 K2J 4.8p
2. .,+D ,2T*(2+ (2-*K)(,2 +D)(1K)(,2 N,AW N()C,0) )C+ /,AA+/) ,MD+ALK)(,2 +AA,A
(2-,A1K)(,2p ;- 2,)@ /,0*J N+ J+L+*,E K NKF ), D(10*)K2+,0D*F +D)(1K)+ M,)C
)C+ (2-*K)(,2 K2J ,MD+ALK)(,2 +AA,ADp
%, K/C(+L+ )C+ ?,K*@ 4,/K* 62D+1M*+ %AK2D-,A1 :K*1K2 F(*)+A P46%:F@ =02)
+) K*. 2HHIQ@ (D /C,D+2 KD K EA,ZF ,- )C+ 62:F (2 )C(D D)0JF J0+ ), ()D +--(/(+2/F K2J
+KDF K//+DD -,A 0D@ KD () (D J+L+*,E+J K) )C+ \2(L+AD()F ,- 8KAF*K2J. 46%:F (D
J+L+*,E+J -A,1 4,/K* 62D+1M*+ :K*1K2 F(*)+A PO)) +) K* 2HH4@ SX02F,?C +) K*. 2HHcQ
M0) (D /,1E0)K)(,2K**F 10/C -KD)+A. ;) CKD M++2 0D+J ), KDD(1(*K)+ D(10*K)+J
I
,MD+ALK)(,2D (2 )C+ NASA -L['8 1,J+* P4(0 +) K*. 2HHVQ K2J )C+ A+D0*)D CKL+ DC,N2
() ,0)E+A-,A1D d.>KA +L+AFNC+A+. ;2 D(1E*+ 1,J+*@ () CKD M++2 DC,N2 ), E+A-,A1
D(1(*KA*F ), 4.T>KA P:K*2KF +) K*. 2HHIQ. <()C A+K* JK)K@ SX02F,?C +) K*. P2HHIQ
A+E,A)+J )CK) )C+ 46%:F (D 1,A+ K//0AK)+ )CK2 )C+ SS; P,E+AK)(,2K* d.>A&Q (2 )C+
S= +Z)AK)A,E(/D@ K2J /,1EKAKM*+ (2 N= +Z)AK)A,E(/D K2J %A,E(/D MF D(1E*F 0D(2?
10*)(E*(/K)(L+ (2-*K)(,2 ), K//,02) -,A 1,J+* +AA,AD. =+A+ N+ (2L+D)(?K)+ 1,A+
D,EC(D)(/K)+J )+/C2(]0+D -,A )A+K)(2? 1,J+* +AA,AD K2J 1+)C,JD -,A ,2T*(2+ +D)(1K)(2?
(2-*K)(,2 -K/),A N()C(2 )C+ 46%:F@ K2J ), J+L+*,E K JK)K KDD(1(*K)(,2 DFD)+1 /KEKM*+
,- KDD(1(*K)(2? A+K* N+K)C+A ,MD+ALK)(,2D. %C,0?C N+ -,/0D ,2 )C+ 46%:F@ )C+ A+D0*)D
KA+ KEE*(/KM*+ ), ,)C+A 62:F DFD)+1D.
b.c O0)*(2+ ,- )C+ )C+D(D
'CKE)+A 2 J+D/A(M+D )C+ )C+,AF ,- K** )C+ 1+)C,JD 0D+J (2 )C(D +2)(A+ J(DD+A)K)(,2@
(2/*0J(2? )C+ 46%:F PD+/)(,2 2.2Q@ )+/C2(]0+D -,A )A+K)(2? 1,J+* +AA,AD PD+/)(,2 2.dQ@
K2J 1+)C,JD -,A ,2T*(2+ +D)(1K)(2? (2-*K)(,2 K2J ,MD+ALK)(,2 +AA,AD PD+/)(,2 2.4Q. ;2
'CKE)+A d@ )C+ 46%:F (D (1E*+1+2)+J (2 K2 A['8 1,J+*@ )C+ SB66.S 1,J+*@
02J+A )C+ E+A-+/) 1,J+* KDD01E)(,2@ K2J ()D E+A-,A1K2/+ (D +ZK1(2+J. ;2 'CKE)+A 4@
N+ JA,E )C+ E+A-+/) 1,J+* KDD01E)(,2 MF KDD(1(*K)(2? ,MD+ALK)(,2D ?+2+AK)+J -A,1
)C+ N'6BRN'A& A+K2K*FD(D -(+*JD. %C+ E+A-,A1K2/+ ,- )C+ 46%:F N()C,0)
K//,02)(2? -,A 1,J+* +AA,AD (D +ZK1(2+J K2J /,1EKA+J N()C )CK) (2 )C+ E+A-+/) 1,J+*
D/+2KA(,. %N, (2-*K)(,2 D/C+1+D P10*)(E*(/K)(L+ K2J KJJ()(L+ (2-*K)(,2Q K2J )N, M(KD
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K2K*FD+D /K2 M+ EA,/+DD+J (2 EKAK**+*.
2.d 8+)C,JD ), J+K* N()C 1,J+* +AA,AD (2 )C+ 62:F
;2 )C+ EA+L(,0D D+/)(,2 1,J+* +AA,AD KA+ KDD01+J ), M+ [K0DD(K2 2,(D+.
=,N+L+A@ (2 A+K*()F@ )C+F KA+ 0D0K**F M(KD+J. %C+ ,L+AK** 1,J+* +AA,AD KA+ )C+
/,1M(2K)(,2 ,- 1,J+* M(KD K2J AK2J,1 2,(D+. ;2 'CKE)+A b@ N+ CKL+ (2)A,J0/+J
D+L+AK* 1+)C,JD -,A CK2J*(2? 1,J+* +AA,AD. =+A+ N+ -,/0D ,2 (DD0+D A+*K)+J ),
(1E*+1+2)K)(,2 ,- )C+D+ 1+)C,JD.
2.d.b 80*)(E*(/K)(L+ (2-*K)(,2
80*)(E*(/K)(L+ (2-*K)(,2 D(1E*F (2-*K)+D )C+ +2D+1M*+ +AA,A /,LKA(K2/+ @ MF K
-K/),A bU! ), KEEA,Z(1K)+ )C+ g)A0+` +AA,A /,LKA(K2/+
9eP
9P
9e
9 PP QbP !'3 P2.2dQ
NC+A+ ! (D K )02KM*+ EKAK1+)+A. P2.2dQ EA,L(J+D K2 (2/A+KD+ (2 )C+ +2D+1M*+
/,LKA(K2/+ ), K//,02) -,A )C+ 1,J+* +AA,AD NC(/C KA+ 2,) (2/*0J+J (2 )C+
,A(?(2K* . ;1E*(/()*F )C(D 1+)C,J KDD01+D )CK) 1,J+* +AA,AD CKL+ )C+ DK1+ +AA,A
9eP
9eP
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D)A0/)0A+ KD )C+ (2)+A2K* +AA,AD D, )CK) )C+(A +AA,A /,LKA(K2/+ Q /K2 M+ A+EA+D+2)+J MF
JF2K1(/K**F +L,*L+J +AA,A /,LKA(K2/+ . 9eP
2.d.2 AJJ()(L+ (2-*K)(,2
AJJ()(L+ (2-*K)(,2 EKAK1+)+A(X+D 1,J+* +AA,AD MF KJJ(2? AK2J,1 E+A)0AMK)(,2D
N()C K /+A)K(2 /,LKA(K2/+ D)A0/)0A+@ ), +K/C +2D+1M*+ -,A+/KD) 1+1M+A K-)+A () CKD
M++2 EA,EK?K)+J -A,1 )C+ EA+L(,0D K2K*FD(D +2D+1M*+ 0D(2? K JF2K1(/K* 1,J+*. ;2
)C+,AF@ KJJ()(L+ (2-*K)(,2 DC,0*J K))+1E) ), D+*+/) E+A)0AMK)(,2D /,2D(D)+2) (2 D)A0/)0A+
N()C )C+ 1,J+* +AA,AD. =,N+L+A *())*+ (D W2,N2 KM,0) )C+ A+K* 1,J+* +AA,A /,LKA(K2/+
D)A0/)0A+@ )C+ KJJ()(,2K* E+A)0AMK)(,2D CKL+ M++2 ?+2+AK)+J (2 D+L+AK* J(--+A+2) NKFD.
=,0)+WK1+A +) K* P2HHcQ /C,D+ AK2J,1 E+A)0AMK)(,2D /,2D(D)+2) (2 D)A0/)0A+ N()C K
d.T>KA MK/W?A,02JT+AA,A /,LKA(K2/+i =K1(** +) K* P2HHcQ EKAK1+)+A(X+J KJJ()(L+
+AA,A KD )C+ J(--+A+2/+D M+)N++2 )N, -,A+/KD)D N()C J(--+A+2) A+D,*0)(,2i <C()KW+A +) K*
P2HHIQ ?+2+AK)+J KJJ()(L+ 2,(D+ MF AK2J,1*F D+*+/)(2? DK1E*+D -A,1 )C+ VTC
)+2J+2/(+D -(+*J ,- N'6BRN'A& A+K2K*FD(D PNN&Q D)K)+D. %C,D+ KJJ()(L+
E+A)0AMK)(,2D J(--+A (2 )C+ DEK/+ D)A0/)0A+ K2J )C+A+ (D 2, /,2/*0D(,2 D, -KA ,2 NC(/C
,- )C+1 (D ,E)(1K*. ;2 )C(D D)0JF@ N+ /C,D+ )C+ NN& VTC,0A )+2J+2/(+D -,A )C+
KJJ()(L+ (2-*K)(,2 D/C+1+ K2J )02+J )C+(A K1E*()0J+.
%C+ 10*)(E*(/K)(L+ (2-*K)(,2 K2J KJJ()(L+ (2-*K)(,2 KA+ )N, D(1E*+ 1+)C,JD -,A
K//,02)(2? -,A )C+ +--+/) ,- 1,J+* +AA,AD ,2 )C+ -,A+/KD) +AA,A D)K)(D)(/D@ M0) N()C,0)
/,AA+/)(2? )C+ 1,J+* +AA,AD -A,1 )C+ +2D+1M*+ 1+K2. <()C K M(KD+J -,A+/KD) .++ K2J
JK S(*LK PbYYfQ CKL+ DC,N2 )C+ A+D0*)(2? K2K*FD(D (D K*D, M(KD+J +L+2 (- )C+ -,A+/KD)
+AA,A D)K)(D)(/D KA+ E+A-+/)*F DE+/(-(+J. ;2 )C+,AF@ (- )C+ DFD)+1K)(/ 1,J+* +AA,AD /K2 M+
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+ZK/)*F +D)(1K)+J@ J(A+/)*F A+1,L(2? )C+1 -A,1 )C+ +2D+1M*+ 1+K2 DC,0*J A+D0*) (2 K
M+))+A K2K*FD(D. S+L+AK* D/C+1+D CKL+ M++2 (2)A,J0/+J ), +D)(1K)+ K2J /,AA+/) 1,J+*
+AA,AD.
2.d.d .++ K2J JK S(*LK M(KD +D)(1K)(,2 8+)C,J P.JS8Q
4+) 0D J+-(2+ )C+ g)A0+` M(KD KD
(%&) t9t xxb P2.24Q
K2J 0D+ @ ), J+2,)+ )C+ g,MD+AL+J M(KD` K2J g-,A+/KD)+J M(KD`@ A+DE+/)(L+*F@
KDD01(2? N+ CKL+ K DFD)+1 ), ,MD+AL+ )C+ M(KD K2J K 1,J+* ), -,A+/KD) )C+ M(KD.
ob 9b
.++ K2J JK S(*LK PbYYfQ J+L+*,E+J K )N,TD)K?+ M(KD +D)(1K)(,2 K*?,A()C1@ (2
NC(/C )C+ +D)(1K)(,2 EA,/+J0A+D -,A )C+ M(KD K2J )C+ D)K)+ KA+ /KAA(+J ,0) D0//+DD(L+*F.
A) )C+ -(AD) D)+E ,- )C+ K2K*FD(D EA,/+DD@ M(KD (D +D)(1K)+J ,2 +L+AF 1,J+* ?A(J E,(2) MF
KDD(1(*K)(2? )C+ 9ore6a't5,inu'5o0'er1ation A+D(J0K*D NC(/C (2/*0J+D )C+
1,J+* M(KD K2J +AA,AD J0+ ), (1E+A-+/) (2()(K* /,2J()(,2D KD N+**@ KD )C+ ,MD+AL+J M(KD
0D(2? :K*1K2 -(*)+A +]0K)(,2
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KD (2 P2.bQ K2J )C+ -,A+/KD) +AA,A /,LKA(K2/+ -,A M(KD@ J+-(2+J KD3
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bnQboP %''& RHHPHPK %9AA
%9AA0 ## P2.2YQ
%C+ D/K*KA # (D K )02KM*+ EKAK1+)+A NC(/C /,2)A,*D )C+ KJKE)KM(*()F ,- )C+
+D)(1K)+J M(KD. ;- # (D ),, D1K** )C+ +D)(1K)+J M(KD +L,*L+D D*,N*F K2J 1KF )KW+ ),,
*,2? ), DE(2T0E ,A 1KF 2,) /KE)0A+ )C+ )(1+TJ+E+2J+2) LKA(KM(*()F ,- )C+ )A0+ M(KD.
;-# (D ),, *KA?+ )C+2 ),, 10/C ,- )C+ A+D(J0K*D K) K EKA)(/0*KA K2K*FD(D
)(1+ N(** M+ K))A(M0)+J ), )C+ M(KD K2J 2,) +2,0?C ), )C+ (2)+A2K* +AA,AD.
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A) )C+ D+/,2J D)+E@ )C+ K2K*FD(D -,A )C+ D)K)+ LKA(KM*+D (D ,M)K(2+J 0D(2? )C+
D)K2JKAJ K2K*FD(D EA,/+J0A+ N()C )C+ 02M(KD+J -,A+/KD) D)K)+ a9 bx %
QnPoQP a9oA
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AD -,A )C+ M(KD -,A+/KD) 1,J+*@ -,**,N(2? 'KA),2 +) K* P2HHHQ N+ N(** 0D+ K
JK1E+J E+AD(D)+2/+@
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9i b%& bb 4 P2.d2Q
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M(KD ()D+*- K2J )CK) () (D g-,A?,))+2` N()C )(1+.
%C+ /,D) ,- )C+ .JS8 (D KM,0) )N(/+ )CK) ,- 2, M(KD +D)(1K)(,2@ D(2/+ )C+
0EJK)+J +]0K)(,2D KA+ D,*L+J )N(/+@ -(AD) -,A )C+ M(KD +D)(1K)(,2 K2J )C+2 -,A )C+ D)K)+
2b
LKA(KM*+D. =,N+L+A@ )C(D J,0M*+ /,D) EA,M*+1 /K2 M+ KL,(J+J (- # ttb (2 NC(/C /KD+
P2.2YQ M+/,1+D
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AK#&
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N+ ,M)K(2 K D(1E*(-(+J L+AD(,2 ,- .++ K2J JK S(*LK D/C+1+ P&KJKW,L(/C +) K*.@ 2HHbQ.
QnPoQP 99oA
99a ; bxyKbxx %%'%& P2.d4Q
QnPo 99oA
9a ; bxyKbb %%%& # P2.dcQ
;2 )C(D KEEA,K/C )C+ /,1E0)K)(,2K* ,- P2.dcQ (D K*1,D) /,D) -A++ K-)+A )C+ D)K)+
K2K*FD(D CKD M++2 0EJK)+J MF P2.d4Q@ D(2/+ (D D(1E*F )C+
K2K*FD(D (2/A+1+2) -,A )C+ D)K)+ LKA(KM*+D.
ax QnPo 99oA 0; %% xyK
;2 )C+ KEE*(/K)(,2 ,- )C+ .JS8 ), )C+ 46%:F@ 2, KJJ()(,2K* +2D+1M*+ 1+1M+AD
KA+ A+]0(A+J -,A )C+ M(KD D(2/+ )C+ M(KD -,A+/KD) +AA,A /,LKA(K2/+ (D ,M)K(2+J
J(A+/)*F -A,1 )C+ D)K)+ -,A+/KD) +AA,A /,LKA(K2/+ . F,A )C+ D+/,2J K2K*FD(D D)+E (2
NC(/C )C+ D)K)+ LKA(KM*+D KA+ 0EJK)+J@ M+/K0D+ )C+ K2K*FD(D +]0K)(,2D P2.dHQTP2.dbQ -,A
)C+ D)K)+ LKA(KM*+D KA+ +ZK/)*F )C+ DK1+ KD )C,D+ (2 )C+ )AKJ()(,2K* :K*1K2 -(*)+A +Z/+E)
)CK) )C+ ,A(?(2K* -,A+/KD) CKD M++2 A+E*K/+J MF )C+ M(KDT/,AA+/)+J -,A+/KD)@ N+ /K2
J(A+/)*F 0)(*(X+ )C+ K*?,A()C1 P2.22Q. F,A )C+ -(AD) D)+E@ (2 NC(/C )C+ M(KD K2K*FD(D (D
E+A-,A1+J@ )C+ (1E*+1+2)K)(,2 (D J(--+A+2). F(AD) N+ J, 2,) 2++J /K*/0*K)+ )C+ K2K*FD(D
+2D+1M*+ E+A)0AMK)(,2D D(2/+ )C+A+ (D 2, +2D+1M*+ -,A )C+ M(KD. S+/,2J@ )C+ -,A10*K ,-
:K*1K2 ?K(2 -,A M(KD (D D*(?C)*F J(--+A+2) -A,1 )CK) -,A D)K)+ LKA(KM*+D. ;2 ,AJ+A ),
900P
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bbb snQbPssQboP %%% %''& RHIHRHXK %%90 >## P2.dVQ
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2.2.d.
2.d.4 #K+W +) K* P2HHVQ M(KD +D)(1K)(,2 D/C+1+
#KD+J ,2 )C+ 'tate 'pa6e aug,entation 1+)C,J P+.?. ^KXN(2DW( bYIHQ@ #K+W +)
K*. P2HHVQ EA,E,D+ K D/C+1+ -,A )C+ 62:F ), ,M)K(2 )C+ ,E)(1K* +D)(1K)+D ,- )C+ D)K)+
K2J M(KD LKA(KM*+D D(10*)K2+,0D*F. ;2 )C(D 1+)C,J M,)C )C+ D)K)+ K2J M(KD CKL+
+2D+1M*+ 1+1M+AD K2J -,A +K/C 1+1M+A )C+ D)K)+ L+/),A (D K0?1+2)+J N()C )C+
02/+A)K(2 1,J+* M(KD L+/),A. %C+ K2K*FD(D 0EJK)+D )C+ K0?1+2)+J L+/),A
667
899:
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bx
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MF KDD(1(*K)(2? ,MD+ALK)(,2D ,- )C+ D)K)+ LKA(KM*+D@ NC+A+ x (D )C+ 1,J+* D)K)+ K2J
1,J+* M(KD. \2*(W+ (2 .JS8@ )C+A+ (D 2, KDD01+J (2 )C(D D/C+1+. %C+ M(KD (D
0EJK)+J MF D)K)+ ,MD+ALK)(,2D )CA,0?C )C+ /A,DDT/,AA+*K)(,2 M+)N++2 )C+ -,A+/KD) D)K)+
K2J M(KD@ NC(*+ )C(D /A,DDT/,AA+*K)(,2 (D KDD01+J ), M+ X+A, (2 .JS8. %C+A+-,A+@ )C+
1Ka,A J(--+A+2/+ M+)N++2 .JS K2J #K+W +) K*. (D )CK) )C+ -,A1+A 0D+D )C+ M(KD +AA,A
/,LKA(K2/+ NC(/C (D KDD01+J ), M+ EA,E,A)(,2K* ), D)K)+ +AA,A /,LKA(K2/+@ NC(*+
)C+ *K))+A A+*(+D ,2 )C+ /A,DD /,LKA(K2/+ M+)N++2 )C+ M(KD K2J D)K)+ LKA(KM*+D. ;2
KJJ()(,2@ #K+W +) K*. P2HHVQ /,2D(J+A l/,AA+/)(2?m )C+ ,MD+ALK)(,2 M(KD N()C A+DE+/) ),
)C+ 1,J+*@ AK)C+A )CK2 )C+ 1,J+* N()C A+DE+/) ), )C+ ,MD+ALK)(,2 (2 ,AJ+A ), 1K(2)K(2
)C+ K2K*FD(D N()C(2 )C+ 1,J+* K))AK/)(,2.
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1,J+* +AA,AD. ;- K A+-+A+2/+ D)K)+ (D KLK(*KM*+ ), KEEA,Z(1K)+ )C+ K)1,DEC+A(/ )A0)C
P(2 ,0A /KD+ N+ 0D+ )C+ N'6BRN'A& A+K2K*FD(DQ@ )C+ VTC,0A -,A+/KD) +AA,A /K2 M+
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+AA,AD ,L+A K /+A)K(2 )(1+ E+A(,J K2J )C+ *+KJ(2? 6OFD -A,1 )C+
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/,1E,2+2) (D ?(L+2 MF )C+ *+KJ(2? S(2?0*KA >+/),A .+/,1E,D()(,2 PS>.Q 1,J+D
PS>.DQ ,- )C+ /,LKA(K2/+ ,- )C+ /,0E*+J 1,J+* D)K)+ K2,1K*(+D
K2J /,AA+DE,2J(2? +AA,A K2,1K*(+D u . 4 K2J 8 KA+ )C+ 201M+A ,-
*+KJ(2? 1,J+D ,- 6OFD K2J S>.D@ A+DE+/)(L+*F. %C+ DEK)(K* -(+*JD b @ K2J KA+
)(1+T(2J+E+2J+2) K2J EA+T/,1E0)+J 0D(2? )C+ DK1E*+D (2 )C+ )AK(2(2? E+A(,J. <+ /K**
)C(D KEEA,K/C *,NTJ(1+2D(,2K* M+/K0D+ )C+ DCKE+ ,- )C+ 1,J+* +AA,AD (D EA+T+D)(1K)+J
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24
D+EKAK)+*F NC+A+KD ,2*F )C+ K1E*()0J+D PBA(2/(EK* ',1E,2+2)D@ B'DQ QPt!= K2J
QPt,< NC(/C CKL+ K 10/C *,N+A J(1+2D(,2 P4 K2J 8Q )CK2 )C+ -0** 1,J+* J(1+2D(,2@
KA+ +D)(1K)+J ,2*(2+.
.0A(2? )C+ )AK(2(2? E+A(,J@ )C+ )(1+TD+A(+D ,- != (D /K*/0*K)+J MF EA,a+/)(2? )C+
6OFD ,2), . S(2/+ !e uex != (D J,1(2K)+J MF M(KD (2 )C+ J(0A2K* /F/*+@ )C+ )(1+T
J+E+2J+2) QPt!= /K2 M+ +D)(1K)+J MF KL+AK?(2? )C+ != ,L+A )C+ J(0A2K* /F/*+ (2 )C+
)AK(2(2? E+A(,J. F,A +ZK1E*+@ N+ /K2 0D+ )C+ DK1E*+D (2 )C+ )AK(2(2? E+A(,J ),
/K*/0*K)+ )C+ KL+AK?+ != -,A HHX@ HVX@ b2X K2J bfX D+EKAK)+*F K2J KEE*F )C+1 (2 )C+
/0AA+2) )(1+TD)+E.
&K)C+A )CK2 /K*/0*K)(2? .K2-,A)C +) K*. ,M)K(2+J )C+ +AA,A
K2,1K*(+D K) )C+ /0AA+2) )(1+ D)+E t MKD+J ,2 )C+ D)K)(D)(/K* /,AA+*K)(,2 ,- )C+
S>. 1,J+ , K2J /0AA+2) D)K)+ K2,1K*(+D . .+2,)+ @ K2J
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K2,1K*(+D K) )(1+ D)+E 2 (2 )C+ )AK(2(2? E+A(,J@ )C+ B'D K2J
,f QPu n9x
QPuex n QPn', QPn,< KA+
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)C+ /0AA+2) )(1+ D)+E t /K2 M+ /,1E0)+J MF
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NC+A+ N+ CKL+ 0)(*(X+J )C+ /0AA+2) D)K)+ K2,1K*(+D K2J )C+ /,AA+*K)(,2
M+)N++2 )C+ D)K)+ K2,1K*(+D K2J )C+ +AA,A K2,1K*(+D ), ,M)K(2 )C+ D)K)+TJ+E+2J+2)
+AA,AD. #F E*0??(2? P2.4HQ (2), P2.4bQ@ P2.4bQ /K2 M+ D(1E*(-(+J ),
QPu t9x
,9
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QPQPu 2
> P2.42Q
N,N NCK) A+1K(2D ), M+ J+)+A1(2+J (D C,N ), ?+) )C+ DK1E*+D ,- VTC,0A
-,A+/KD) +AA,A . ;2 )C(D D)0JF@ -,**,N(2? .K2-,A)C +) K*.P2HHIQ@ (2 )C+ )AK(2(2? E+A(,J
N+ A02 )C+ SB66.S (2()(K*(X+J N()C )C+ N'6BRN'A& A+K2K*FD(D PNN&Q -(+*JD K2J
)KW+ )C+ J(--+A+2/+D M+)N++2 )C+ SB66.S VTC,0A -,A+/KD)D K2J NN& -(+*JD LK*(J K)
)C+ DK1+ )(1+ ), ,M)K(2 )C+ DK1E*+D ,- .
ex
ex
2.4 AJKE)(L+ +D)(1K)(,2 ,- (2-*K)(,2 -K/),A K2J ,MD+ALK)(,2 +AA,AD
2.4.b AJKE)(L+ +D)(1K)(,2 ,- (2-*K)(,2 EKAK1+)+A
.+2,)(2? KD )C+ (22,LK)(,2D@ (.+. )C+ J(--+A+2/+ M+)N++2 )C+
,MD+ALK)(,2D K2J )C+(A MK/W?A,02J /,02)+AEKA)D . %C0D
QP 0o0o ; xyd %&%
QP 0; x
2V
QPQPQPQP 0o0tto0o ;;; !H!xxxyd %5%'%&%
=+A+ K2J KA+ )C+ ,MD+ALK)(,2 K2J MK/W?A,02J +AA,A.
%C+2 )C+ /,LKA(K2/+ ,- )C+ (22,LK)(,2 (D
QP too ; xy! %& t00 xx! %&
%%00%oo%0o0o H!!H!!dd ()'((&)) %% QP
NC+A+ )C+ ,MD+ALK)(,2K* +AA,AD KA+ KDD01+J ), M+ 02/,AA+*K)+J N()C )C+
MK/W?A,02J +AA,AD . \D(2? )C+ J+-(2()(,2D ,- MK/W?A,02J +AA,A /,LKA(K2/+ P2.bQ K2J
,MD+ALK)(,2 +AA,A /,LKA(K2/+ P2.2Q@ N+ CKL+
o!
0!
RHHPdd '(&) %%%9%
0o0o QP P2.4dQ
%C(D (D K /*KDD(/K* K2J N(J+*FT0D+J A+*K)(,2DC(E )CK) EA,L(J+D K ?*,MK* /C+/W ,2 )C+
DE+/(-(/K)(,2 ,- )C+ D01 ,- MK/W?A,02J +AA,A K2J ,MD+ALK)(,2 +AA,A /,LKA(K2/+D (2
,MD+ALK)(,2K* DEK/+. ;- & (D E+A-+/)*F W2,N2@ P2.4dQ /K2 M+ 0D+J ), J(K?2,D+ )C+
K//0AK/F ,- )C+ DE+/(-(+J MK/W?A,02J +AA,A /,LKA(K2/+.
A2,)C+A J(K?2,D)(/ ,2 MK/W?A,02J +AA,AD /K2 M+ ,M)K(2+J MF )C+ /,1M(2K)(,2 ,-
(22,LK)(,2 K2J ana!:'i'5,inu'50a67ground P.+DA,X(+AD +) K*. 2HHcQ. S(2/+
/K2 M+ NA())+2
0o%d 0a%d
0a%d
0o0a0a
0a ;; %% &%5%& HKdxxHxxd QPQPQP
%C+A+-,A+ N+ CKL+
()(&) %%%%%
0o0o%
0o0a QPQP ddHKdd
8K)A(Z HK (D ?(L+2 MF @ )C0D bQP %' RHHPHHP %9%9
()'(&) %%%
%%%
0o0o%9%9%
0o0a QPQPQP b ddRHHPHHPdd
',1M(2(2? N()C P2.4dQ@ )C(D NC,*+ +ZEA+DD(,2 D(1E*(-(+D ),
2I
%9%0o0a HHPdd (&) %% QP P2.44Q
(- )C+ 1K)A(/+D DE+/(-(+J (2 K?A++ N()C )C+ )A0+
/,LKA(K2/+D -,A MK/W?A,02J K2J ,MD+ALK)(,2 +AA,A@
bQP %'& RHHPHHPHK %9%9
P2.4dQ K2J P2.44Q EA,L(J+ )N, /,2D(D)+2/F /C+/WD ,2 MK/W?A,02J +AA,A
/,LKA(K2/+ (2 ,MD+ALK)(,2 DEK/+. ;2 )C+ +2D+1M*+ -(*)+A@ M+/K0D+ ,- K LKA(+)F ,- +AA,AD@
)C+ +2D+1M*+ +AA,A /,LKA(K2/+ +D)(1K)+J -A,1 )C+ +2D+1M*+ ,- -,A+/KD) -(+*JD
)+2JD ), 02J+A+D)(1K)+ )C+ )A0+ MK/W?A,02J +AA,A /,LKA(K2/+ K2J 10*)(E*(/K)(L+
(2-*K)(,2 (D K2 K))+1E) ), A+/)(-F )C(D@ N()C
9eP
9e
9 PP QbP !'& P2.4cQ
B*0??(2? P2.4cQ (2), P2.4dQ ,A P2.44Q K2J /,2D(J+A(2? ,2*F )C+ J(K?,2K* )+A1@ N+ /K2
+D)(1K)+ ,2T*(2+ )C+ (2-*K)(,2 -K/),A ! MF
bQP
QPs %%
&! %%
HHPRdd
9e
0o%
0o
%r%r
P2.4VQ
bQP
s %&! %%
HHPdd
9e
0o%
0a
%r P2.4IQ
NC+A+ %r J+2,)+D )C+ )AK/+ ,- K 1K)A(Z.
<+ J+2,)+ P2.4VQ K2J P2.4IQ KD D=EF 1+)C,J K2J G=EHD=E 1+)C,J@
A+DE+/)(L+*F. A2 K//0AK)+ +D)(1K)+ ,- ! -A,1 )C+D+ )N, 1+)C,JD A+]0(A+D K /,AA+/)
,MD+ALK)(,2 +AA,A /,LKA(K2/+. %C(D (D ,ML(,0D -,A P2.4VQ M0) K*D, (1E*(/()*F )A0+ -,A
P2.4IQ NC+A+ ()D+*- (D MKD+J ,2 )C+ 0D+ ,- P?+2+AK**F (2/,AA+/)Q DE+/(-(+J
,MD+ALK)(,2 +AA,A LKA(K2/+D.
0a%d
2f
2.4.2 AJKE)(L+ +D)(1K)(,2 ,- ,MD+ALK)(,2 +AA,AD
%C+ o0'er1ation5,inu'5ana!:'i' J(--+A+2/+D KA+ ?(L+2 MF ao%d
QP aoao ; xyd %&%
0o%9
0o
0o0o
0o0o
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;;
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%'%5
%'%&
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dHKI
xyHKxy
xyKxy
bQP
QP
QPQP
QnPo
%C+2 )C+ D)K)(D)(/K* +ZE+/)K)(,2 ,- )C+ /A,DDTEA,J0/) M+)N++2 K2J (D ao%d 0o%d
()'(&) %%%
%%%
0o0o%9%
0oao QPQPQP b ddRHHPRdd P2.4fQ
B*0??(2? P2.4dQ (2), P2.4fQ@ N+ CKL+
Rdd (&) %%%
0oao QP P2.4YQ
(- )C+ 1K)A(/+D DE+/(-(+J (2 K?A++ N()C )C+ )A0+
/,LKA(K2/+D -,A MK/W?A,02J K2J ,MD+ALK)(,2 +AA,A. %C(D (D )C+ J(K?2,D)(/ EA,L(J(2? K
/,2D(D)+2/F /C+/W ,2 ,MD+ALK)(,2 +AA,A /,LKA(K2/+. O2+ KEE*(/K)(,2 ,- )C(D J(K?2,D)(/
(D ), J(K?2,D+ ,MD+ALK)(,2 +AA,A LKA(K2/+ ,--*(2+ ,A ,2T*(2+ +D)(1K)+ (). F,A K2F D0MD+)
,- ,MD+ALK)(,2D N()C ,MD+ALK)(,2D@ () (D E,DD(M*+ ), /,1E0)+ )C+ LKA(K2/+
bQP %'& RHHPHHPHK %9%9
i ip
i0I
oI
aI
p
I
oIii0oi
%aoio p::::p
i
RQQPPRQPQPQsPb
2 %%&& 1&
%% dd" P2.cHQ
NC+A+ (D )C+ LK*0+ ,- ,MD+ALK)(,2 oI: I K2J @ KA+ )C+(A K2K*FD(D K2J MK/W?A,02J
/,02)+AEKA)D.
aI: 0
I:
2Y
<+ J+2,)+ P2.cHQ KD D=GHD=E 1+)C,J. %C+ K//0AK/F ,- )C(D 1+)C,J A+*(+D ,2
K2J NC(/C J+E+2J )C+1D+*L+D ,2 )C+ ,MD+ALK)(,2 K2J MK/W?A,02J
P)C+A+-,A+ ,2 (2-*K)(,2 -K/),A (2 62:FQ +AA,AD LKA(K2/+D.
ao%d 0o%d
2.4.d S(10*)K2+,0D +D)(1K)(,2 ,- (2-*K)(,2 K2J ,MD+ALK)(,2 +AA,AD
AD J(D/0DD+J (2 )C+ EA+L(,0D )N, D+/)(,2D@ KJKE)(L+ +D)(1K)(,2 ,- (2-*K)(,2
A+]0(A+D )C+ E+A-+/) ,MD+ALK)(,2 +AA,A LKA(K2/+ NC(*+ K2 K//0AK)+ +D)(1K)+ ,-
A+*(+D ,2 )C+ ,E)(1K* (2-*K)(,2 -K/),A. %C(D M+/,1+D K 2,2*(2+KA EA,M*+1 NC+2
2+()C+A )C+ ,E)(1K* (2-*K)(,2 -K/),A 2,A )A0+ (D W2,N2 M+-,A+CK2J K2J M,)C ,-
)C+1 2++J ), M+ +D)(1K)+J ,2T*(2+. ;2 )C(D /KD+@ N+ EA,E,D+ ), +D)(1K)+ )C+ (2-*K)(,2
K2J ,MD+ALK)(,2 +AA,AD D(10*)K2+,0D*F N()C(2 K2K*FD(D /F/*+ K2J K**,N )C+ DFD)+1
()D+*- ), )KW+ D,1+ )(1+ ), /,2L+A?+ ), )C+ ,E)(1K* LK*0+ PAK2?+Q -,A ,MD+ALK)(,2 +AA,A
LKA(K2/+ P(2-*K)(,2 -K/),AQ.
2QP o"
2QP o"
2QP o"
2.4.4 S1,,)C(2?
<+ +D)(1K)+ )C+ ,MD+ALK)(,2 +AA,A LKA(K2/+D K2J (2-*K)(,2 EKAK1+)+A KJKE)(L+*F
K) +K/C K2K*FD(D )(1+ D)+E. =,N+L+A@ )C+ 201M+A ,- DK1E*+D KLK(*KM*+ K) +K/C D)+E
1KF 2,) M+ +2,0?C ), KL,(J *KA?+ DK1E*(2? +AA,A. %, (2/A+KD+ )C+ DK1E*(2?@ N+ 0D+
KJKE)(L+ A+?A+DD(,2 MKD+J ,2 K D(1E*+ D/K*KA :F KEEA,K/C 0D0K**F 0D+J ), E,D)T
EA,/+DD 1,J+* ,0)E0) P+.?. :K*2KF 2HHd@ AEE+2J(Z 'Q ), K//010*K)+ EKD) (2-,A1K)(,2
K2J 1KW+ )C+ ,MD+ALK)(,2 +AA,A LKA(K2/+ K2J (2-*K)(,2 ?AKJ0K**F /,2L+A?+ ), )C+
,E)(1K* LK*0+ NC(*+ D)(** K**,N(2? -,A )(1+ LKA(K)(,2D. %C(D KEEA,K/C /K2 M+ )C,0?C) KD
K )(1+ D1,,)C+A K2J CKD M++2 0D+J MF 8(F,DC( 2HHc. <+ A+?KAJ )C+ +D)(1K)(,2
,M)K(2+J J(A+/)*F -A,1 D=EF ,A G=EHD=E ,A D=GHD=E KD K2 ,MD+AL+J +D)(1K)+
dH
o# P+()C+A ,A o!s 2QsP oo" (2 )C(D D)0JFQ -,A )C+ /0AA+2) )(1+ D)+E. ;2D)+KJ ,- J(A+/)*F
0D(2? () KD )C+ -(2K* +D)(1K)(,2 -,A )CK) )(1+ D)+E@ N+ 0D+ D(1E*+ D/K*KA :F KEEA,K/C ),
M+D) /,1M(2+ K2J @ )C+ LK*0+ J+A(L+J MF E+AD(D)+2/+ -A,1 )C+ EA+L(,0D )(1+
D)+E@ ), ?+) K 2+N +D)(1K)+ J+2,)+J KD )C+ K2K*FD(D 3
o# 9#
a#
9o
o99oa
1111
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&### P2.cbQ
NC+A+ P Q J+2,)+D )C+ -,A+/KD) P,MD+ALK)(,2K*Q +AA,A LKA(K2/+ -,A )C+ KJKE)(L+
A+?A+DD(,2. %C+ A+*K)(L+ AK)(, ,- R J+)+A1(2+D )C+ J+?A++ ,- D1,,)C(2?. %C+
M(??+A )C(D AK)(,@ )C+ 1,A+ ,M)K(2+J -A,1 /0AA+2) D)+E N(** M+ D1,,)C+J. %C+ +AA,A
LKA(K2/+ ,- " (D ?(L+2 MF
? 9 ? o
? o ? 9
o#
a#
9o9
9a 1
1111 QbP'
%& P2.c2Q
ADD01(2? E+AD(D)+2/+ KD )C+ -,A+/KD) 1,J+* -,A )C+ +D)(1K)+J LKA(KM*+@ K2J
K**,N(2? -,A D,1+ +AA,A (2 )C+ lE+AD(D)+2/+ -,A+/KD)m P:K*2KF@ 2HHd@ AEE+2J(Z 'Q@ N+
CKL+3
ta
t9 ## &'b P2.cdQ
ta
t9 !11 &'b P2.c4Q
C+A+ @ (D K EKAK1+)+A NC(/C K**,ND )C+ D*,N (2/A+KD+ ,- )C+ -,A+/KD) +AA,A. A*)C,0?C
)N, KJJ()(,2K* /,2)A,* EKAK1+)+AD3 )C+ ,MD+ALK)(,2 +AA,A LKA(K2/+ K2J +AA,A ?A,N)C
EKAK1+)+A
? o
@ CKL+ M++2 (2)A,J0/+J C+A+@ 8(F,DC( 2HHc CKD DC,N2 )C+ -(2K* +D)(1K)+ (D
2,) D+2D()(L+ ), +()C+A ,- )C+1. F,**,N(2? 8(F,DC( 2HHc@ N+ 0D+ hb.H K2J ? o @ hb.Hd
(2 )C(D D)0JF.
db
Chapter 3
The LETKF performance in perfect model experiments
d.b ;2)A,J0/)(,2
;2 )C(D 'CKE)+A@ N+ (1E*+1+2) )C+ 46%:F (2), K2 A['8 1,J+*@ )C+ SB66.S
1,J+*@ 02J+A )C+ KDD01E)(,2 ,- K E+A-+/) 1,J+*. ;DD0+D A+*K)+J ), DK1E*(2? +AA,AD KA+
KJJA+DD+J. %C+ E+A-,A1K2/+ ,- )C+ 46%:F (D +ZK1(2+J MF /C+/W(2? )C+
/CKAK/)+A(D)(/D ,- )C+ K2K*FD(D@ MK/W?A,02J +AA,AD K2J )C+(A +2D+1M*+ DEA+KJ. %C,D+
/CKAK/)+A(D)(/D N(** M+ D+AL+J KD K A+-+A+2/+ ), )C+ +ZE+A(1+2)D (2 2+Z) /CKE)+A NC+A+
1,J+* (D 2, *,2?+A E+A-+/).
d.2 %C+ SB66.S 1,J+*
%C+ SB66.S PS(1E*(-(+J BKAK1+)+A(XK)(,2D@ EA(1()(L6T6]0K)(,2 .S2K1(/DQ
1,J+* P8,*)+2( 2HHdQ (D K A+/+2)*F J+L+*,E+J K)1,DEC+A(/ ?+2+AK* /(A/0*K)(,2 1,J+*
PA['8Q N()C D(1E*(-(+J ECFD(/K* EKAK1+)+A(XK)(,2D )CK) KA+ /,1E0)K)(,2K**F
+--(/(+2)@ M0) )CK) 1K(2)K(2 )C+ MKD(/ /CKAK/)+A(D)(/D ,- K D)K)+T,-T)C+TKA) A['8 N()C
/,1E*+Z ECFD(/D.
%C+ SB66.S 1,J+* D,*L+D )C+ EA(1()(L+ +]0K)(,2 -,A EA,?2,D)(/ LKA(KM*+D ,-
X,2K* N(2J P Q@ 1+A(J(,2K* N(2J P 1 Q@ )+1E+AK)0A+ P% Q@ DE+/(-(/ C01(J()F P Q@ K2J
D0A-K/+ EA+DD0A+ P Q K) )C+ )A02/K)(,2 ,- NKL+201M+A dH@ /,AA+DE,2J(2? ), YVr4f
?A(J E,(2)D K2J I D(?1K *+L+*D PH.YcH@ H.fdc@ H.Vfc@ H.cbH@ H.d4H@ H.2HH@ H.HfHQ. %C+
(2E0)D KA+ ,2*F )KW+2 (2 D(?1K *+L+*D@ M0) )C+ A+D0*)(2? -,A+/KD)D KA+ (2 M,)C D(?1K
*+L+*D K2J EA+DD0A+ *+L+*D PY2c@ fcH@ IHH@ cHH@ dHH@ 2HH@ bHH CBKQ.
u $
'p
d2
d.d 6ZE+A(1+2)K* D+)0E
<+ KEE*(+J )C+ 46%:F ), )C+ SB66.S 1,J+* (2 )C+ E+A-+/) 1,J+* D/+2KA(,
NC+A+ K )A0+ l2K)0A+ A02m (D ?+2+AK)+J MF (2)+?AK)(2? )C+ SB66.S 1,J+* -A,1 HHHH
\%' b ^K20KAF@ bYfI@ 0D(2? )C+ N'6BTN'A& &+K2K*FD(D PNN&Q KD )C+ (2()(K*
/,2J()(,2@ 02)(* bfHH \%' bc F+MA0KAF@ bYfI. %C+ ,MD+ALK)(,2D KA+ D(10*K)+J MF
KJJ(2? 2,A1K**FTJ(D)A(M0)+J AK2J,1 2,(D+ ), )C+ 2K)0A+ A02@ K2J KA+ KLK(*KM*+ K) +K/C
1,J+* ?A(J E,(2)D -,A K2J +L+AF ,)C+A 1,J+* ?A(J -,A @ (2 M,)C X,2K* K2J
1+A(J(,2K* J(A+/)(,2D@ (.+. 2cj ,- )C+ 201M+A ,- 1,J+* ?A(J E,(2)D. %C+ K1E*()0J+D ,-
)C+ ,MD+ALK)(,2 +AA,AD KA+ b 1RD -,A N(2J@ b : -,A % @ bH
'p $%1u @@@
1u@ T4 W?RW? -,A K2J bCBK
-,A . F,A +K/C -,A+/KD)TK2K*FD(D /F/*+@ )C+ SB66.S 1,J+* (D 0D+J ), ?+2+AK)+ )C+ VT
C,0A -,A+/KD) K2J )C+ ,MD+ALK)(,2D KA+ KDD(1(*K)+J MF )C+ 46%:F.
$
'p
<+ D)KA) )C+ +ZE+A(1+2) MF A022(2? dH (2()(K* +2D+1M*+D K) HHHH \%' b
^K20KAF@ bYfI. %C+ dH (2()(K* +2D+1M*+D KA+ /A+K)+J MF KJJ(2? )C+ AK2J,1 2,(D+ ), )C+
l2K)0A+ A02m -,A+/KD)D K) HVHH \%' b ^K20KAF@ bYfI. ;2 )C(D NKF@ )C+ (2()(K* +2D+1M*+
1+K2 (D V C,0AD KEKA) -A,1 )C+ )A0)C. %C,0?C )C+ -(2K* A+D0*)D K-)+A )C+ DE(2T0E E+A(,J
KA+ 2,) D+2D()(L+ ), )C+ (2()(K* +2D+1M*+D@ K ?,,J (2()(K* /,2J()(,2 P2,) ),, -KA -A,1 )C+
)A0)CQ C+*ED ), DC,A)+2 )C+ DE(2T0E )(1+. <()C ,0A D+))(2? ,- )C+ (2()(K* /,2J()(,2D@ )C+
DE(2T0E )(1+ (D KM,0) bc JKFD NC(*+ () (D 1,A+ )CK2 ,2+ 1,2)C (2 )C+ +ZE+A(1+2)D (2
8(F,DC( 2HHc. %C+ +ZE+A(1+2) A02D -,A ,2+ K2J K CK*- 1,2)C )(** bfHH \%' bc
F+MA0KAF@ 2HHI K2J ,2*F )C+ *KD) 1,2)C K-)+A )C+ DE(2T0E E+A(,J (D A+E,A)+J ), L+A(-F
)C+ DFD)+1.
dd
d.4 SK1E*(2? +AA,AD
;2 K2F +2D+1M*+ JK)K KDD(1(*K)(,2 DFD)+1@ K *(1()+J : +2D+1M*+ 1+1M+AD KA+
0D+J ), A+EA,J0/+ )C+ NrN -,A+/KD) +AA,A /,LKA(K2/+ 1K)A(Z @ NC+A+ N (D )C+
201M+A ,- J+?A++D ,- -A++J,1 ,- )C+ 1,J+*. %, KL,(J )C+ -(*)+A J(L+A?+2/+ J0+ ),
D1K** DK1E*+D@ D,1+ KJJ()(,2K* EA,/+DD(2? ,- DK1E*+ /,LKA(K2/+ (D 0D0K**F
2+/+DDKAF. %C+ )N, /,11,2 1+)C,JD KA+ 10*)(E*(/K)(L+ (2-*K)(,2 PA2J+AD,2 K2J
A2J+AD,2 bYYYQ K2J *,/K*(XK)(,2 P=K1(** +) K*.@ 2HHbi =,0)+WK1+A K2J 8()/C+**@
2HHbQ )+/C2(]0+D. 80*)(E*(/K)(L+ (2-*K)(,2 D(1E*F (2-*K)+D )C+ -,A+/KD) +AA,A /,LKA(K2/+
MF K -K/),A ! D*(?C)*F *KA?+A )CK2 b@ NC(/C (D +]0(LK*+2) ), (2-*K)(2? )C+ +2D+1M*+
DEA+KJ MF K -K/),A
9P
9P
9P
bb %!'&A .
4,/K*(XK)(,2 K*?,A()C1D KA+ 1+K2) ), /,AA+/) -,A +AA,AD (2 )C+ DK1E*+ /,LKA(K2/+
M+)N++2 ,MD+ALK)(,2D K2J 1,J+* D)K)+ LKA(KM*+D. ;2 )C+ 46%:F@ )C+ K2K*FD(D (D
E+A-,A1+J (2 K *,/K* EK)/C /+2)+A+J MF K 1,J+* ?A(J E,(2) -,A NC(/C N+ )AF ), -(2J )C+
,E)(1K* K2K*FD(D. O2*F )C+ ,MD+ALK)(,2D N()C(2 )C+ *,/K* M,Z KA+ 0D+J ), 0EJK)+ )C+
/+2)AK* E,(2). %C(D /K2 M+ A+?KAJ+J KD K /0),--TMKD+J *,/K*(XK)(,2 K*?,A()C1. ;2 ,0A
+ZE+A(1+2)D@ )C+ *,/K* EK)/C (D D(1E*F K )N,TJ(1+2D(,2K* D]0KA+ M,Z N()C *+2?)C
2 ! Ub (2 M,)C Z K2J F 1,J+* ?A(J DEK/+. %C+ ECFD(/K* DCKE+ ,- )C+ *,/K* EK)/C (D 2,) K
D]0KA+ J0+ ), )C+ /,2L+A?+2/+ ,- )C+ 1+A(J(K2D (2 C(?C+A *K)()0J+D. %C+ /0),--
*,/K*(XK)(,2 D/C+1+ -,A/+D )C+ /,AA+*K)(,2D M+)N++2 )C+ K2K*FD(D E,(2) K2J
,MD+ALK)(,2D ,0)D(J+ )C+ *,/K* EK)/C ), M+ X+A, M0) N()C,0) J(D)(2?0(DC(2? )C+
,MD+ALK)(,2D (2D(J+ )C+ *,/K* EK)/C. %C(D D/C+1+ 1KF 2,) M+ K//0AK)+ +2,0?C D(2/+ (2
,0A +ZE+A(1+2)D N+ CKL+ ,2*F dH +2D+1M*+ 1+1M+AD@ D, )CK) )C+ /,AA+*K)(,2D (2D(J+
)C+ *,/K* EK)/C /,0*J CKL+ DK1E*(2? +AA,AD@ +DE+/(K**F -,A )C,D+ ,MD+ALK)(,2D )CK) KA+
d4
,2 )C+ M,AJ+A ,- )C+ *,/K* EK)/C. ;2 )C(D D)0JF@ M+D(J+D )C+ /0)T,-- *,/K)(,2@ N+ KEE*F
)C+ ,MD+ALK)(,2 +AA,A /,LKA(K2/+ *,/K*(XK)(,2 P8(F,DC( 2HHcQ ), A+J0/+ ,A A+1,L+
)C+D+ DE0A(,0D /,AA+*K)(,2D.
RR !b%3 $ Pd.bQ
Q2
+ZEP 2
2
"$ d%& Pd.2Q
NC+A+ J+2,)+D )C+ J(D)K2/+ -A,1 )C+ K2K*FD(D E,(2) K2J ,MD+ALK)(,2 *,/K)(,2 K2J d
" )C+ *,/K*(XK)(,2 D/K*+. %C+A+-,A+ N+ CKL+@
bb QP %%'& RHHPHPK !$%9%9
bQP %'B RHPHHP %9%9 !! $$ Pd.dQ
6]0K)(,2 Pd.dQ (2J(/K)+D )CK) )C+ ,MD+ALK)(,2 +AA,A /,LKA(K2/+ *,/K*(XK)(,2 (D K2
KEEA,Z(1K)(,2 ,- )C+ *,/K*(XK)(,2 ,- P=,0)+WK1+A K2J 8()/C+**@ 2HHbQ. F(?0A+ d.b
DC,ND )C+ *,/K*(XK)(,2 -K/),A
9P
$ KD )C+ -02/)(,2 ,- )C+ AK)(, JR" @ (2J(/K)(2? )C+
/,AA+*K)(,2 (D A+J0/+J ), VHj ,- ()D ,A(?(2K* D(X+ -,A ,MD+ALK)(,2 K) )C+ J(D)K2/+ Jh" @
NC(*+ )C+ ,MD+ALK)(,2 +--+/) (D -,A/+J ), M+ 2+KA X+A, K) )C+ J(D)K2/+ *KA?+A )CK2 d.c" .
#,)C )C+ (2-*K)(,2 -K/),A K2J *,/K*(XK)(,2 D/K*+ 2++J ), M+ )02+J. %, D(1E*(-F )C+
)KDW ,- )02(2? N+ -(AD) -(Z+J )C+ (2-*K)(,2 -K/),A ), M+ H.H4. %KM*+ d.b /,1EKA+D )C+
K2K*FD(D &8S6 ,- cHHCBK C+(?C) 0D(2? /0)T,-- *,/K)(,2 K2J ,MD+ALK)(,2 +AA,A
/,LKA(K2/+ *,/K)(,2 N()C dH +2D+1M*+ 1+1M+AD. <()C /0)T,-- *,/K*(XK)(,2@ )C+ M+D)
A+D0*) (D ,M)K(2+J N()C )C+ D1K**+D) *,/K* EK)/C. %C+ 0D+ ,- ,MD+ALK)(,2 +AA,A
*,/K*(XK)(,2 K**,ND )C+ 46%:F ), 0D+ *KA?+A EK)/C+D N()C 1,A+ ,MD+ALK)(,2D.
A/)0K**F@ NC+2 )C+ *,/K*(XK)(,2 D/K*+" (D -(Z+J@ )C+ A+D0*)D KA+ 2,) D+2D()(L+ ), )C+
*,/K* EK)/C D(X+ ! . %C+ D1K**+D) K2K*FD(D +AA,A 2.dd (2 %KM*+ d.b (D ,MD+AL+J N()C K
dc
*,/K* EK)/C D(X+ ! hd K2J K2 ,MD+ALK)(,2K* +AA,A /,LKA(K2/+ *,/K*(XK)(,2 D/K*+" hb.c.
\D(2? )C(D D+))(2? ,- *,/K*(XK)(,2 D/K*+D@ N+ )C+2 )02+J )C+ (2-*K)(,2 -K/),A K2J -,02J
)CK) ! hH.Hc (D D*(?C)*F M+))+A )CK2 ! hH.H4.
%KM*+ d.b3 A2K*FD(D &8S6 ,- cHH CBK C+(?C) -(+*J 0D(2? 46%:F N()C dH +2D+1M*+
1+1M+AD (2 )C+ /KD+D ,- KEE*F(2? /0)T,-- *,/K*(XK)(,2 ,A ,MD+ALK)(,2 +AA,A /,LKA(K2/+
*,/K*(XK)(,2. %C+ &8S6 (D )+1E,AK**F KL+AK?+J -,A K 1,2)C K-)+A )C+ (2()(K* bcTJKFD
DE(2T0E E+A(,J K2J DEK)(K**F KL+AK?+J ,L+A )C+ ?*,M+. A 10*)(E*(/K)(L+ (2-*K)(,2 -K/),A
,- hH.H4 (D KEE*(+J. %N, EKAK1+)+AD@ )C+ *,/K* EK)/C D(X+ ! ! K2J )C+ ,MD+ALK)(,2K*
+AA,A /,LKA(K2/+ D/K*+" @ KA+ )02+J.
%C+ *,/K* EK)/C D(X+ ! b 2 d
cHHv &8S6 P1Q P" h#Q 2.d4 2.VV d.bY
cHHv &8S6 P1Q P" h2.HQ 2.4b
cHHv &8S6 P1Q P" hb.cQ 2.dc 2.dd
dV
−6 −4 −2 0 2 4 60
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
d / σ
ρ
F(?0A+ d.b3 %C+ *,/K*(XK)(,2 -K/),A Q2
+ZEP 2
2
"$ d%& KD )C+ -02/)(,2 ,- AK)(,2 JR"
d.c 46%:F E+A-,A1K2/+ (2 K E+A-+/) 1,J+* +ZE+A(1+2)
F(?0A+ d.2 D011KA(X+D )C+ KDD(1(*K)(,2 A+D0*)D N()C ,0A -(2K* D+))(2? ,- )C+
/,2-(?0AK)(,2D P !hd@ " hb.c@ ! hH.Hc K2J dH +2D+1M*+ 1+1M+ADQ -,A )C+ 46%:F
02J+A )C+ E+A-+/) 1,J+* KDD01E)(,2. SC,N2 KA+ )(1+TD+A(+D ,- A,,)T1+K2TD]0KA+
PA1DQ K2K*FD(D +AA,A PJ+-(2+J KD K2K*FD(D 1(20D )A0+ D)K)+Q@ KL+AK?+J ,L+A )C+ NC,*+
?*,M+@ -,A X,2K* N(2J P u Q@ ?+,E,)+2)(K* C+(?C) PvQ@ )+1E+AK)0A+ P Q K2J DE+/(-(/
C01(J()F P Q. #F KDD(1(*K)(2? )C+ ,MD+ALK)(,2D +L+AF VTC,0A@ )C+ K2K*FD(D +AA,A
A+J0/+D AKE(J*F -A,1 K *KA?+ (2()(K* LK*0+ K2J KEEA,K/C+D K D)KM*+ *+L+*. ;) (D /*+KA )CK)
K-)+A )C+ (2()(K* DE(2T0E E+A(,J@ )C+ K2K*FD(D &8S6 -,A K** )C+ LKA(KM*+D KA+ 10/C
D1K**+A )CK2 )C+ ,MD+ALK)(,2K* +AA,A D)K2JKAJ J+L(K)(,2D.
%
$
dI
F(?0A+ d.23 A2K*FD(D &8S6 PD,*(J /0AL+Q K) cHH CBK -,A )C+ E+A(,J M+)N++2 HHHH
\%' b ^K20KAF bYfI K2J bfHH \%' bc F+MA0KAF bYfI. %C+ ,MD+ALK)(,2K* +AA,A
D)K2JKAJ J+L(K)(,2D KA+ DC,N2 KD JKDC *(2+D NC+A+L+A KEE*(/KM*+. %C+ -,0A EK2+*D
-A,1 )C+ ),E ), )C+ M,)),1 /,AA+DE,2J ), X,2K* N(2J@ ?+,E,)+2)(K* C+(?C)@ )+1E+AK)0A+
K2J DE+/(-(/ C01(J()F@ A+DE+/)(L+*F.
df
%, -(2J NCF )C+ 46%:F E+A-,A1D N+**@ N+ /,1EKA+ )C+ +2D+1M*+ DEA+KJ N()C
)C+ +2D+1M*+ 1+K2 +AA,A. 'KAAF(2? ,0) E+A-+/) 1,J+* +ZE+A(1+2)D@ NC+A+ N+ W2,N
)C+ )A0)C@ K**,ND 0D ), /K*/0*K)+ )C+ +2D+1M*+ 1+K2 +AA,A@ NC(/C (D )C+ +2D+1M*+ 1+K2
1(20D )C+ )A0)C. %C+ +2D+1M*+ DEA+KJ (D J+-(2+J KD )C+ VTC,0A -,A+/KD) +AA,A J+L(K)(,2
N()C A+DE+/) ), )C+ +2D+1M*+ 1+K2. ;2 )C+ +2D+1M*+ -(*)+A@ )C+ MK/W?A,02J +AA,A
/,LKA(K2/+ (D KEEA,Z(1K)+J 0D(2? )C+ DK1E*+ /,LKA(K2/+ -A,1 K2 +2D+1M*+ ,- 1,J+*
-,A+/KD)D. %, ,M)K(2 K ?,,J E+A-,A1K2/+@ N+ A+]0(A+ )CK) )C+ +2D+1M*+ DEA+KJ M+
A+EA+D+2)K)(L+ ,- )C+ )A0+ MK/W?A,02J +AA,A (2 M,)C D)A0/)0A+ K2J 1K?2()0J+. F(?0A+
d.d DC,ND )C+ MK/W?A,02J +AA,A -(+*J PDCKJ+JQ K2J )C+ +2D+1M*+ DEA+KJ P/,2),0AQ K)
K2 KAM()AKAF )(1+. ;2 ?+2+AK* )C+D+ )N, -(+*JD K?A++ N()C +K/C ,)C+A L+AF N+**@
(2J(/K)(2? )C+ +2D+1M*+ DEA+KJ CKD /KE)0A+J )C+ -,A+/KD) +AA,A D)A0/)0A+.
AD -,A )C+ K1E*()0J+@ N+ /,1EKA+ )C+ MK/W?A,02J &8S6 K2J )C+ DEA+KJ
KL+AK?+J ,L+A )C+ NC,*+ ?*,M+ PF(?0A+ d.4Q. %C+ LK*0+ ,- DEA+KJ (D K *())*+ D1K**+A (2
)C+ *,N+A *+L+* K2J C(?C+A (2 )C+ 0EE+A *+L+*D (2 )+A1D ,- )C+ MK/W?A,02J &8S6. #0)
(2 ?+2+AK*@ )C+F KA+ /*,D+ +2,0?C ), +K/C ,)C+A K) K** *+L+*D. %C+A+-,A+ N+ /K2
/,2/*0J+ )CK) N()C ,0A D+))(2? ,- /,2-(?0AK)(,2D P !hd@ " hb.c@ hH.Hc K2J dH
+2D+1M*+ 1+1M+ADQ@ )C+ DEA+KJ K1,2? dH +2D+1M*+ 1+1M+AD CKD /KE)0A+J N+** M,)C
)C+ )A0+ +AA,A D)A0/)0A+ K2J )C+ )A0+ +AA,A 1K?2()0J+.
!
dY
F(?0A+ d.d3 %C+ MK/W?A,02J PVTC,0A -,A+/KD)Q +AA,A -(+*J PDCKJ+JQ K2J )C+ +2D+1M*+
DEA+KJ ,- cHH CBK C+(?C) -(+*J P/,2),0AQ K) K2 KAM()AKAF )(1+.
4H
F(?0A+ d.43 #K/W?A,02J &8S6 K) K** EA+DD0A+ *+L+*D PD,*(J *(2+Q K2J MK/W?A,02J
+2D+1M*+ DEA+KJ PJKDC+J *(2+Q ,- C+(?C) -(+*J@ )+1E,AK**F KL+AK?+J -,A ,2+T1,2)C
K-)+A )C+ DE(2T0E E+A(,J.
4b
Chapter 4
Accounting for and correcting model errors in the LETKF
4.b ;2)A,J0/)(,2
;2 'CKE)+A d@ N+ CKL+ DC,N2 )C+ 46%:F N,AWD L+AF N+** (2 )C+ E+A-+/) 1,J+*
D/+2KA(,. ;2 A+K*()F@ C,N+L+A@ )C+ 201+A(/K* 1,J+* (D 2+L+A E+A-+/). ;2 )C(D /CKE)+A N+
JA,E )C+ KDD01E)(,2 ,- K E+A-+/) 1,J+* MF KDD(1(*K)(2? ,MD+ALK)(,2D D(10*K)+J -A,1
)C+ N'6BRN'A& &+K2K*FD(D PNN&Q KD (2 8(F,DC( P2HHcQ. S+L+AK* 1+)C,JD ),
K//,02) -,A K2JR,A /,AA+/) 1,J+* +AA,AD KA+ )+D)+J.
4.2 N'6BRN'A& A+K2K*FD(D PNN&Q
4.2.b NN& ,MD+ALK)(,2D
%, KDD+DD )C+ E+A-,A1K2/+ ,- )C+ 46%:F (2 )C+ EA+D+2/+ ,- 1,J+* +AA,AD@ N+
A+E*K/+ )C+ g2K)0A+` A02 (2 )C+ E+A-+/) 1,J+* +ZE+A(1+2)D MF )C+ NN& -(+*JD. S(2/+
)C+ NN& KDD(1(*K)+J A+K* ,MD+ALK)(,2D@ N+ KDD01+ )C+ NN& -(+*JD KA+ K2 KEEA,Z(1K)+
+D)(1K)+ ,- )C+ 02W2,N2 g)A0+ K)1,DEC+A+`. A ]0K2)()K)(L+ LK*(JK)(,2 ,- )C(D
KDD01E)(,2 (D M+F,2J )C+ D/,E+ ,- )C(D A+D+KA/C. <+ KJJ )C+ AK2J,1 2,(D+ N()C )C+
DK1+ D)K2JKAJ J+L(K)(,2 0D+J (2 )C+ E+A-+/) 1,J+* +ZE+A(1+2)D ), D(10*K)+ )C+ NN&
,MD+ALK)(,2D. %C+ J+2D()F ,- ,MD+ALK)(,2D A+1K(2D )C+ DK1+ KD )CK) (2 'CKE)+A d.
S(2/+ )C+ NN& JK)K KA+ ,2 EA+DD0A+ *+L+*D K2J N+ E+A-,A1 )C+ 46%:F (2 SB66.S
D(?1K /,,AJ(2K)+D@ -,A D(1E*(/()F@ )C+ NN& ,MD+ALK)(,2D KA+ /,2L+A)+J ), )C+
SB66.S D(?1K /,,AJ(2K)+D J+)+A1(2+J MF )C+ SB66.S -,A+/KD)+J . =,A(X,2)K*
K2J L+A)(/K* *(2+KA (2)+AE,*K)(,2D KA+ A+]0(A+J ), ,M)K(2 )C+ (2)+AE,*K)+J ,MD+ALK)(,2D
'p
42
(2 SB66.S D(?1K /,,AJ(2K)+D. (D 0D+J ), J+)+A1(2+ )C+ N+(?C)(2? -,A )C+
L+A)(/K* (2)+AE,*K)(,2.
p*,?
4.2.2 'CKAK/)+A(D)(/D ,- 1,J+* +AA,AD
S(2/+ )C+ ,MD+ALK)(,2D KA+ ?+2+AK)+J -A,1 )C+ NN& NC(*+ )C+ SB66.S CKD ()D
,N2 /*(1K),*,?F@ )C+ 1,J+* (D 2, *,2?+A E+A-+/). %, (2L+D)(?K)+ )C+ SB66.S 1,J+*
+AA,AD K?K(2D) )C+ NN& -(+*J@ )C+ SB66.S 1,J+* (D A02 +L+AF V C,0AD 0D(2? NN& KD
)C+ (2()(K* /,2J()(,2D K2J )C+ VTC,0A -,A+/KD) +AA,AD KA+ /K*/0*K)+J MF )C+ J(--+A+2/+D
M+)N++2 )C+ SB66.S VTC,0A -,A+/KD)D K2J )C+ NN& L+A(-(+J K) )C+ DK1+ )(1+.
ADD01(2? )C+ NN& (D K2 +D)(1K)(,2 ,- )C+ 02W2,N2 g)A0)C`@ )C+D+ VTC,0A -,A+/KD)
+AA,AD KA+ K2 KEEA,Z(1K)(,2 ,- )C+ g)A0+` 1,J+* +AA,AD.
F(?0A+ 4.b DC,ND )C+ SB66.S VTC,0A -,A+/KD) +AA,AD K?K(2D) )C+ NN& -(+*J ,-
)C+ )CA++ EA,?2,D)(/ LKA(KM*+D PX,2K* N(2J@ )+1E+AK)0A+ K2J DE+/(-(/ C01(J()FQ K2J
,2+ J(K?2,D)(/ LKA(KM*+ P?+,E,)+2)(K* C+(?C)Q@ )+1E,AK**F KL+AK?+J ,L+A ,0A
+ZE+A(1+2)K* E+A(,J M+)N++2 HHHH \%' b ^K20KAF@ bYfI K2J bfHH \%' bc F+MA0KAF@
bYfI 0D(2? bf4 DK1E*+D. %C+ )(1+T1+K2 ,- -,A+/KD) +AA,AD (D A+?KAJ+J KD )C+ 1,J+*
M(KD. F,A X,2K* N(2J@ )C+ *KA?+D) M(KD (D -,02J (2 )C+ E,*KA A+?(,2D ,A KDD,/(K)+J N()C
)C+ E,D()(,2 ,- )C+ a+). F,A )+1E+AK)0A+@ )C+ M(KD (D D(?2(-(/K2) K) *,N+A ,A 0EE+A *+L+*D
P1,D)*F ,L+A *K2JQ M0) D1K** K) )C+ cHH CBK *+L+*. %C+ M(KD ,- DE+/(-(/ C01(J()F (D
*KA?+ (2 )C+ A+?(,2 NC+A+ )C+ LK*0+ ,- )C+ C01(J()F ()D+*- (D *KA?+@ (.+.@ (2 )C+ )A,E(/D
K2J K) *,N *+L+*D. AD -,A )C+ ?+,E,)+2)(K* C+(?C)@ )C+ *KA?+D) M(KD /K2 M+ D++2 ,L+A
+*+LK)+J D0A-K/+ )+AAK(2@ NC(/C (D J0+ ), )C+ ),E,?AKEC(/ J(--+A+2/+D (2 )C+ SB66.S
1,J+ K2J )C+ NN& -(+*J.
4d
F(?0A+ 4.b3 8+K2 ,- VTC,0A SB66.S -,A+/KD) +AA,AD (2()(K*(X+J -A,1 )C+ NN& -(+*JD
P1,J+* M(KDQ@ )+1E,AK**F KL+AK?+J ,L+A )C+ +ZE+A(1+2)K* E+A(,J M+)N++2 HHHH \%' b
^K20KAF@ bYfI K2J bfHH \%' bc F+MA0KAF@ bYfI 0D(2? bf4 DK1E*+D.
44
#+D(J+D )C+ )(1+TKL+AK?+J M(KD@ N+ K*D, (2L+D)(?K)+ )C+ )(1+TLKAF(2? /,1E,2+2)
,- 1,J+* +AA,A ), D++ (- )C+A+ (D K2,)C+A D(?2(-(/K2) D(?2K* NC(/C (D 2,) (2/*0J+J (2 )C+
)(1+TKL+AK?+J M(KD P.K2-,A)C +) K*. 2HHIQ. %, J, D,@ N+ D0M)AK/) )C+ )(1+TKL+AK?+J
M(KD -A,1 )C+ )(1+ D+A(+D ,- 1,J+* +AA,AD@ K2J /,1E0)+ )C+ +1E(A(/K* ,A)C,?,2K*
-02/)(,2 P6OFDQ -,A )C+ 1,J+* +AA,A K2,1K*,0D -(+*JD. F(?0A+ 4.2 DC,ND )C+ -(AD) )N,
6OF EK))+A2D K2J )C+(A /,AA+DE,2J(2? )(1+ K1E*()0J+D@ BA(2/(EK* ',1E,2+2)D PB'DQ
-,A )+1E+AK)0A+ K) )C+ M,)),1 *+L+* PY2c CBKQ. ;) (D /*+KA )CK) M,)C ,- )C+1 /,AA+DE,2J
), K J(0A2K* LKA(K)(,2 ,- SB66.S 1,J+* M(KD. ',1M(2(2? )C+ 6OFD K2J B'D@ N+
-,02J )C+ SB66.S 1,J+* 02J+A+D)(1K)+D P,L+A+D)(1K)+DQ )C+ 2+KATD0A-K/+ *,/K*
JKF)(1+ P2(?C))(1+Q )+1E+AK)0A+D. %C(D (D J0+ ), )C+ *K/W ,- J(0A2K* /CK2?+D (2 D,*KA
-,A/(2? (2 )C+ SB66.S 1,J+*. %C(D J+)+/)+J )+1E+AK)0A+ J(0A2K* M(KD (D 1K(2*F ,L+A
*K2J K2J *KA?+D) 2+KA )C+ D0A-K/+ PY2c CBKQ M0) K*D, D(?2(-(/K2) K) fcH CBK. <+ J(J 2,)
,MD+AL+ K D(?2(-(/K2) J(0A2K* M(KD D(?2K* (2 ,)C+A *+L+*D K2J ,)C+A LKA(KM*+D.
4c
F(?0A+ 4.23 %,E K2J 1(JJ*+ EK2+*D3 )C+ -(AD) )N, *+KJ(2? 6OF EK))+A2D ,- )C+ Y2c CBK
)+1E+AK)0A+ 1,J+* +AA,A K2,1K*,0D -(+*JD 0D(2? DK1E*+D (2 )C+ +ZE+A(1+2)K* E+A(,J
M+)N++2 HHHH \%' b ^K20KAF@ bYfI K2J bfHH \%' bc F+MA0KAF bYfI. %C+(A
/,AA+DE,2J(2? BA(2/(EK* ',1E,2+2)D PA+J *(2+ -,A B'b K2J ?A++2 *(2+ -,A B'2Q KA+
DC,N2 -,A K2 KAM()AKAF E+A(,J (2 ^K20KAF ,- bYfI. %C+ +ZE*K(2+J LKA(K2/+D -,A )C+D+
)N, 6OF 1,J+D KA+ dc.Ij K2J d2.cj A+DE+/)(L+*F.
4V
4.d 6--+/)D ,- 1,J+* +AA,AD ,2 )C+ 46%:F
4.d.b 6ZE+A(1+2)K* D+)0E
%, KDD+DD )C+ +--+/) ,- 1,J+* +AA,AD ,2 )C+ E+A-,A1K2/+ ,- )C+ 46%:F@ N+
KDD(1(*K)+ )C+ NN& ,MD+ALK)(,2D +L+AF VTC,0A N()C )C+ 46%:F 0D(2? )C+ DK1+
/,2-(?0AK)(,2D KD )C,D+ (2 )C+ E+A-+/) 1,J+* +ZE+A(1+2)D P!hd@ " hb.c@ hH.Hc K2J
dH +2D+1M*+ 1+1M+ADQ. ADD(1(*K)(,2D N+A+ E+A-,A1+J -,A )C+ E+A(,J M+)N++2 HHHH
\%' b ^K20KAF bYfI K2J bfHH \%' bc F+MA0KAF@ bYfI. %C+ (2()(K* +2D+1M*+D K) HHHH
\%' b ^K20KAF N+A+ ?+2+AK)+J MF KJJ(2? AK2J,1 2,(D+ ), )C+ NN& -(+*J K) HHHH
\%' 2 ^K20KAF. N, +Z)AK 1+)C,J (D KEE*(+J ), J+K* N()C 1,J+* +AA,AD. %C(D
+ZE+A(1+2) (D A+?KAJ+J KD )C+ gcontrol run` -,A )C+ *K)+A +ZE+A(1+2)D (2 D+/)(,2 4.4.
A-)+A K2 (2()(K* DE(2T0E E+A(,J ,- CK*-T1,2)C@ )C+ K2K*FD+D K2J -,A+/KD)D KA+ L+A(-(+J
K?K(2D) )C+ NN& -(+*J NC(/C (D KDD01+J ), M+ K2 +D)(1K)(,2 ,- )C+ 02W2,N2 )A0)C.
!
4.d.2 g',2)A,* A02` A+D0*)D
F(?0A+ 4.d DC,ND )C+ K2K*FD(D K2J MK/W?A,02J &8S6 K) K** EA+DD0A+ *+L+*D ,-
)C+ ?+,E,)+2)(K* C+(?C) -(+*J. F,A /,1EKA(D,2@ )C+ K2K*FD(D &8S6 ,- C+(?C) (2 )C+
/KD+ ,- E+A-+/) 1,J+* (D K*D, DC,N2. <+ /K2 D++ )C+ D)A,2? 2+?K)(L+ (2-*0+2/+ ,- )C+
1,J+* +AA,AD ,2 )C+ E+A-,A1K2/+ ,- )C+ 46%:F. ;2 )C+ EA+D+2/+ ,- 1,J+*D +AA,AD@ )C+
cHH CBK C+(?C) K2K*FD(D &8S6 CKD (2/A+KD+J -A,1 2.4 1 ), cH 1 J0+ ), )C+ 1,J+*
+AA,AD K2J )C+(A K//010*K)+J +--+/)D. <()C K 1,A+ D,EC(D)(/K)+J K2J C(?CTA+D,*0)(,2
201+A(/K* 1,J+*@ D0/C KD )C,D+ /0AA+2)*F 0D+J (2 ,E+AK)(,2@ )C+ 2+?K)(L+ (2-*0+2/+
DC,0*J M+ 10/C D1K**+A M0) N(** D)(** +Z(D) KD *,2? KD )C+ 1,J+* (D 2,) E+A-+/).
4I
RMSE (perfect vs. imperfect model)
F(?0A+ 4.d3 A2K*FD(D &8S6 PD,*(J /0AL+Q K2J MK/W?A,02J &8S6 PJ,))+J /0AL+Q K) K**
EA+DD0A+ *+L+*D ,- C+(?C) -(+*J NC+2 KDD(1(*K)(2? )C+ gA+K*(D)(/` ,MD+ALK)(,2D -A,1
NN&@ )+1E,AK**F KL+AK?+J -,A K 1,2)C K-)+A )C+ (2()(K* DE(2T0E E+A(,J. F,A
/,1EKA(D,2@ )C+ K2K*FD(D &8S6 (2 )C+ E+A-+/) 1,J+* +ZE+A(1+2) NC+A+ KDD(1(*K)(2?
)C+ gD(10*K)+J` ,MD+ALK)(,2D -A,1 SB66.S g2K)0A+ A02` (D K*D, DC,N2 PJKDC+J
/0AL+Q. P<+ 2,)+ )CK) (2 K 1,A+ A+K*(D)(/ 1,J+*@ N()C K *KA?+A (2-*K)(,2@ )C+ (1E+A-+/)
1,J+* K2K*FD(D J,+D 2,) J+)+A(,AK)+ KD 10/C KD (2 )C(D +ZK1E*+@ +.?.@ F(?0A+ 2 (2
SX02F,?C +) K*. 2HHIQ
4f
%, (2L+D)(?K)+ NCF )C+ 46%:F E+A-,A1D E,,A*F (2 )C+ EA+D+2/+ ,- *KA?+ 1,J+*
+AA,AD N()C,0) KJJ()(,2K* (2-*K)(,2@ N+ E*,) )C+ MK/W?A,02J +2D+1M*+ DEA+KJ ,- )C+
C+(?C) -(+*J PF(?0A+ 4.4Q. ;) (D (2)+A+D)(2? ), -(2J )CK) )C+ DEA+KJ (D D(1(*KA ), )CK) (2 )C+
E+A-+/) 1,J+* +ZE+A(1+2)@ K2J 10/C D1K**+A )CK2 )C+ K/)0K* -,A+/KD) +AA,A DC,N2 MF
)C+ J,))+J *(2+ (2 F(?0A+ 4.d@ (2J(/K)(2? )CK) )C+ -,A+/KD) +2D+1M*+D KA+ gM*(2J` ),
1,J+* +AA,AD. %C(D /K2 M+ /*+KA*F +ZE*K(2+J MF )C+ D/C+1K)(/ (2 F(?0A+ 4.c NC+A+ )C+
J(--+A+2/+ M+)N++2 +2D+1M*+D (D D1K** M0) )C+ NC,*+ D+) ,- +2D+1M*+D (D -KA -A,1 )C+
g)A0)C`. ;2 )C(D /KD+@ )C+ +2D+1M*+ DEA+KJ 02J+A+D)(1K)+D )C+ K/)0K* -,A+/KD) +AA,A@
*+KJD ), )C+ NA,2? /,2-(J+2/+ ), )C+ -,A+/KD)D K2J *+DD N+(?C) ), )C+ ,MD+ALK)(,2D K2J@
KD K A+D0*)@ ), *KA?+ K2K*FD(D +AA,AD KD (2 )C+ g/,2)A,* A02` PF(?0A+ 4.dQ.
4.4 A//,02)(2? -,A K2J /,AA+/)(2? 1,J+* +AA,AD
4.4.b 6ZE+A(1+2)K* J+D(?2
<+ CKL+ D++2 )C+ MKJ E+A-,A1K2/+ ,- )C+ 46%:F (2 )C+ EA+D+2/+ ,- 1,J+*
+AA,AD N()C,0) /,AA+/)(2? ,A K//,02)(2? -,A )C+(A +--+/)D. ;2 )C(D D+/)(,2 N+ )+D) D+L+AK*
1+)C,JD J+D/A(M+J (2 'CKE)+A 2 ), J+K* N()C 1,J+* +AA,AD. AD (2 )C+ g/,2)A,* A02`@ N+
A02 )C+ SB66.ST46%:F -,A )C+ E+A(,J HHHH \%' b ^K20KAF@ bYfI ), bfHH \%' bc
F+MA0KAF@ bYfI K2J )C+ L+A(-(/K)(,2 D)K)(D)(/D KA+ /,1E0)+J -,A K2K*FD+D K2J -,A+/KD)D
K?K(2D) )C+ NN& -(+*JD K-)+A )C+ (2()(K* DE(2T0E E+A(,J ,- CK*-T1,2)C.
4.4.2 80*)(E*(/K)(L+ (2-*K)(,2
80*)(E*(/K)(L+ (2-*K)(,2 (D K 1+)C,J ), J+K* N()C 1,J+* +AA,AD )CK) (D
D)AK(?C)-,ANKAJ ), (1E*+1+2) D(2/+ () CKD K*A+KJF M++2 0D+J (2 )C+ E+A-+/) 1,J+*
+ZE+A(1+2)D. &K)C+A )CK2 M+(2? 0D+J ), EA+L+2) )C+ +2D+1M*+ -A,1 /,**KED(2? J0+ ),
4Y
F(?0A+ 4.43 #K/W?A,02J +2D+1M*+ DEA+KJ (2 C+(?C) -(+*J K) K** EA+DD0A+ *+L+*D
)+1E,AK**F KL+AK?+J ,L+A K 1,2)C K-)+A )C+ (2()(K* DE(2T0E E+A(,J (2 )C+ /KD+D ,-
E+A-+/) 1,J+* KDD(1(*K)(2? ,MD+ALK)(,2D ?+2+AK)+J -A,1 )C+ SB66.S g2K)0A+` A02
PJKDC+J /0AL+Q K2J (1E+A-+/) 1,J+* KDD(1(*K)(2? ,MD+ALK)(,2D ?+2+AK)+J -A,1 )C+
NN& -(+*J.
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+2Db
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1,J+* +AA,AD. %C+ D,*(J /0AL+D A+EA+D+2) )C+ )AKa+/),A(+D ,- )N, +2D+1M*+D NC(*+ )C+
g)A0)C` PJKDC+J /0AL+Q CKD ()D ,N2 JF2K1(/D.
cb
)C+ *(1()+J +2D+1M*+ 1+1M+AD (2 )C+ /KD+ ,- E+A-+/) 1,J+*@ C+A+ () (D (2)+2J+J ),
+2*KA?+ )C+ +2D+1M*+ -,A+/KD) +AA,A /,LKA(K2/+ ), K//,02) -,A 1,J+* +AA,AD. %C(D
1+)C,J KDD01+D )CK) 1,J+* +AA,A CKD )C+ DK1+ +AA,A D)A0/)0A+ KD )C+ JF2K1(/K**F
+L,*L+J +AA,A D(2/+ )C+ +2*KA?+1+2) (D J,2+ (2 )C+ DEK/+ DEK22+J MF )C+ +2D+1M*+D.
<+ )02+ )C+ (2-*K)(,2 -K/),A (2 )+A1D ,- )C+ K2K*FD(D +AA,A. %KM*+ 4.b EA,L(J+D )C+
K2K*FD(D &8S6 ,- )+D)(2? J(--+A+2) (2-*K)(,2 -K/),AD. #+D(J+D )C+ cHH CBK C+(?C) -(+*J
NC(/C (D ,-)+2 0D+J KD K EA,ZF ,- )C+ E+A-,A1K2/+ ,- K -,A+/KD) ,A K JK)K KDD(1(*K)(,2
DFD)+1@ )C+ &8S6 KA+ K*D, DC,N2 -,A 2HH CBK u @ fcH CBK $ K2J Y2c CBK % NC+A+
*KA?+ /,2D)K2) M(KD+D ,A *KA?+ J(0A2K* M(KD+D KA+ -,02J. #F (2/A+KD(2? )C+ (2-*K)(,2 ),
M+ b.H ,A *KA?+A@ K** )C+ A+D0*)D KA+ D(?2(-(/K2)*F M+))+A )CK2 )C+ g/,2)A,* A02` NC+A+ K
L+AF D1K** (2-*K)(,2 -K/),A Hc.H&! (D 0D+J. ;) D++1D )CK) -,A J(--+A+2) -(+*JD@ )C+
,E)(1K* (2-*K)(,2 (D J(--+A+2). F,A )C+ ?+,E,)+2)(K* C+(?C) -(+*J@ K *KA?+ (2-*K)(,2
P Q (D A+]0(A+J@ NC(*+ K 10/C D1K**+A (2-*K)(,2 PH.2&! H.b&! Q (D ,E)(1K* -,A )C+ Y2c
CBK C01(J()F -(+*J. %C+ &8S6 -,A )C+ 2HH CBK u -(+*J D++1D *+DD D+2D()(L+ ), )C+
LK*0+ ,- )C+ (2-*K)(,2. %C+D+ A+D0*)D (2J(/K)+ )CK) N+ 1KF 2++J J(--+A+2) (2-*K)(,2
-K/),AD -,A J(--+A+2) -(+*JD. <+ D++ )CK) )C+ SB66.S 1,J+* M(KD+D KA+ /,1E*(/K)+J@
J+E+2J(2? ,2 LKA(KM*+D@ *+L+*D K2J A+?(,2D. ;J+K**F@ )C+ ,E)(1K* (2-*K)(,2 -K/),A DC,0*J
M+ K -02/)(,2 ,- LKA(KM*+D@ A+?(,2D@ K2J *+L+*D. =,N+L+A@ (2 EAK/)(/+@ )02(2? )CK) W(2J
,- (2-*K)(,2 (D EA,C(M()(L+. ;2 )C(D D)0JF N+ D)(** /,2D(J+A )C+ (2-*K)(,2 -K/),A KD K D(2?*+
201M+A K2J /C,,D+ )C+ LK*0+ ,- c.b&! KD ()D ,E)(1K* /C,(/+@ K*)C,0?C () (D 2,)
,E)(1K* -,A K** )C+ -(+*JD.
c2
%KM*+ 4.b3 A2K*FD(D &8S6 ,- 2HH CBK u @ cHHCBK # @ fcH CBK $ K2J Y2c CBK
% -(+*JD@ )+1E,AK**F KL+AK?+J -,A K 1,2)C K-)+A )C+ (2()(K* DE(2T0E E+A(,J MF KEE*F(2?
J(--+A+2) K1E*()0J+D ,- 10*)(E*(/K)(L+ (2-*K)(,2.
F(+*JD
P02()Q
2HH CBK
u P1RDQ
cHH CBK
# P1Q
fcH CBK
$ P?RW?Q
Y2c CBK
% P :Q
&! H.Hc Pg/,2)A,* A02`Q c.4c 4f.cH H.Yd d.bY
&! b.HH 2.2H 2V.YV H.cV 2.H4
&! b.cH 2.bY 2c.f4 H.cY 2.H2
&! b.Ic 2.2b 2c.I4 H.Vb 2.Hc
&! 2.HH 2.2I 2c.cI H.Vd 2.Hc
&! 2.2c 2.d2 2c.Vc H.VV 2.HY
4.4.d AJJ()(L+ (2-*K)(,2
%, (1E*+1+2) )C+ KJJ()(L+ (2-*K)(,2 D/C+1+@ N+ AK2J,1*F D+*+/)+J DK1E*+D
-A,1 K D0MD+) ,- NN& VTC,0A )+2J+2/F -(+*JD P<C()KW+A +) K*. 2HHIQ (2 ^K20KAF K2J
F+MA0KAF -,A )C+ F+KAD bYf2TbYfV. \2*(W+ AK2J,1 201M+AD@ )C+D+ AK2J,1*F D+*+/)+J
VTC,0A )+2J+2/F -(+*JD KA+ ?+,D)A,EC(/K**F MK*K2/+J. ;2 +K/C K2K*FD(D /F/*+@ N+
AK2J,1*F D+*+/) dH )+2J+2/F -(+*JD@ D/K*+ )C+1@ K2J KJJ )C+ J(--+A+2/+D M+)N++2 )C+D+
D/K*+J -(+*JD ), +K/C MK/W?A,02J +2D+1M*+ 1+1M+A@ (.+.
779e
97 rqxx '& QP P4.bQ
NC+A+ N+ A+]0(A+ )CK)
H&7q P4.2Q
K2J J+2,)+
cd
Qqq &%
77 P4.dQ
C+A+ (D )C+ (2J+Z -,A +K/C +2D+1M*+ 1+1M+A@ K2J D, J+2,)+D )C+
+2D+1M*+ -,A+/KD). (D )C+ KJJ()(L+ 2,(D+ KJJ+J ), +2D+1M*+ 1+1M+A W@ K2J
7 QP79ex 7tJ
7q r (D ()D
K1E*()0J+. ;2 )C(D NKF@ N+ (2/A+KD+ )C+ MK/W?A,02J +2D+1M*+ DEA+KJ N()C,0)
/CK2?(2? )C+ +2D+1M*+ 1+K2. %C+ 1,J(-(+J -,A+/KD) +AA,A /,LKA(K2/+ (D K/)0K**F ?(L+2
MF
%99999 QQPP xxxxP %%&
%%9e
9e
9e
9e r qqxxxx 2QQPP '%%&
P4.4Q QP 2r9e '&
9eP (D )C+ +2D+1M*+ +AA,A /,LKA(K2/+ M+-,A+ KJJ(2? )C+ AK2J,1 2,(D+. <+ )02+ )C+
D/K*+ r -,A )C+ AK2J,1 DK1E*+D K2J -,02J r hb.c (D ,E)(1K* -,A ,0A KEE*(/K)(,2. %C(D
LK*0+ (D 10/C *KA?+A )CK2 )C+ ,E)(1K* LK*0+ H.dd -,02J MF <C()KW+A +) K*. P2HHIQ (2
)C+(A KEE*(/K)(,2. O2+ A+KD,2 (D )CK) )C+F KJJ+J )C+ AK2J,1 )+2J+2/F -(+*JD ), K2K*FD(D
+2D+1M*+D AK)C+A )CK2 MK/W?A,02J +2D+1M*+Di K2,)C+A (1E,A)K2) A+KD,2 (D )CK) )C+(A
KDD(1(*K)(,2 1,J+* P)C+ *,N+A A+D,*0)(,2 L+AD(,2 ,- )C+ ,E+AK)(,2K* N'6B ?*,MK*
-,A+/KD) DFD)+1Q (D 10/C 1,A+ A+K*(D)(/ )CK2 )C+ SB66.S 1,J+* 0D+J C+A+@ D, )CK)
)C+ 1,J+* +AA,AD (2L,*L+J KA+ 10/C D1K**+A (2 )C+(A /KD+.
F(?0A+ 4.V DC,ND )C+ K2K*FD(D &8S6 ,- 2HH CBK u @ cHH CBK # @ fcH CBK $ K2J
Y2c CBK % -(+*JD@ MF KEE*F(2? )C+ NN& VTC,0A )+2J+2/(+D D/K*+J MF b.c KD )C+
KJJ()(L+ 2,(D+. F,A /,1EKA(D,2@ )C+ A+D0*)D -A,1 c.b&! 10*)(E*(/K)(L+ (2-*K)(,2 K2J
)C+ g/,2)A,* A02` KA+ K*D, DC,N2. #,)C (2-*K)(,2 D/C+1+D A+D0*) (2 10/C M+))+A
c4
F(?0A+ 4.V3 %(1+ D+A(+D ,- )C+ ?*,MK*TKL+AK?+J K2K*FD(D &8S6 (2 )C+ /KD+D ,- )C+
g/,2)A,*` A02 PJKDC+J /0AL+Q@ ! hb.c 10*)(E*(/K)(L+ (2-*K)(,2 PJ,))+J /0AL+Q K2J r hb.c
KJJ()(L+ (2-*K)(,2 PD,*(J /0AL+Q. %C+ -,0A EK2+*D -A,1 )C+ ),E ), )C+ M,)),1 /,AA+DE,2J
), 2HH CBK u @ cHH CBK # @ fcH CBK $ K2J Y2c CBK % -(+*JD@ A+DE+/)(L+*F.
cc
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cHH CBK C+(?C) CKD M++2 A+J0/+J MF KM,0) cHj. AJJ()(L+ (2-*K)(,2 ,0)E+A-,A1D
10*)(E*(/K)(L+ (2-*K)(,2 (2 K** -(+*JD +DE+/(K**F (2 )C+ fcH CBK $ K2J Y2c CBK % -(+*JD.
%C+ J(0A2K* +AA,A D(?2K* (D D)(** /*+KA (2 )C+ Y2c CBK % -(+*J N()C 10*)(E*(/K)(L+
(2-*K)(,2 NC(*+ () J(DKEE+KA+J N()C KJJ()(L+ (2-*K)(,2.
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(2-*K)(,2 ), K//,02) -,A DFD)+1T2,(D+. %C+ KJJ()(L+ 2,(D+ (D ,M)K(2+J (2 )C+ DK1+ NKF
KD )CK) (2 D+/)(,2 4.4.d. <+ /K** )C+ .JS8 K0?1+2)+J N()C KJJ()(L+ 2,(D+ .JS8U.
&+/K** )CK) (2 )C+ E0A+ .JS8 PD+/)(,2 2.d.dQ@ )C+ -,A+/KD) 1,J+* -,A M(KD (D
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LKA(KM*+D P
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900 PP #&
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)C+ K1E*()0J+ P r Q ,- KJJ()(L+ 2,(D+ (D K2,)C+A EKAK1+)+A ), M+ )02+J.
%, D(1E*(-F )C+ )KDW ,- )02(2? )C+ )CA++ EKAK1+)+AD@ -(AD) N+ -(Z # hH.c
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cV
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(D (2/,AA+/) -,A )C+ /0AA+2) )(1+ D)+E. ;J+K**F N+ 1KF 2++J K M+))+A M(KD EA+J(/)(,2 ),
/KE)0A+ )C(D M(KD (2 K DF2,E)(/ )(1+D/K*+. =+A+@ ), D(1E*(-F@ N+ A+J0/+ 4 ), M+ *+DD
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(1EK/) ,- M(KD -A,1 )C+ EA+L(,0D )(1+ D)+E.
N,N N+ -(Z 4 hH.Y K2J )02+ )C+ EK(AD ,- P# @ r Q. %C+ A+D0*)D KA+ D011KA(X+J (2
%KM*+ 4.2. ;) (D /*+KA )CK) K//,02)(2? -,A AK2J,1 DFD)+1T2,(D+ (D +DD+2)(K* (2 ,AJ+A ),
CKL+ K ?,,J E+A-,A1K2/+ ,- )C+ 46%:F. <()C,0) )C+ KJJ()(L+ 2,(D+@ )C+ E0A+ .JS8
P r hHQ (D 2,) KM*+ ), M+K) )C+ E0A+ KJJ()(L+ (2-*K)(,2 P# hHQ N()C K2 ,E)(1K* K1E*()0J+
,- r hb.c. #F KJJ(2? K D1K** KJJ()(L+ 2,(D+ P r hH.2cQ@ )C+ .JS8U ,0)E+A-,A1D )C+
E0A+ KJJ()(L+ (2-*K)(,2 D/C+1+ M0) )C+ ,E)(1K* /C,(/+ ,- # (D *KA?+ P# hH.IcQ. <C+2
(2/A+KD(2? r ), M+ H.c@ )C+ LK*0+ ,- )C+ ,E)(1K*# A+J0/+D ), H.c. %C+D+ A+D0*)D /K2 M+
M+))+A 02J+AD),,J MF )C+ +ZEA+DD(,2 ,- P NC+A+9AA
900 P#& # (D K2 +ZE*(/() EKAK1+)+A
K2J r (D K2 (1E*(/() -K/),A PD(2/+ (D K--+/)+J MF 9AAP r )CA,0?C +]0K)(,2 4.4Q ),
J+)+A1(2+ )C+ M(KD -,A+/KD) +AA,A /,LKA(K2/+ . <C+2 900P r (D D1K**@ )C+ DFD)+1 A+]0(A+D
K M(? LK*0+ ,- # ), ,M)K(2 K2 ,E)(1K* @ NC(*+ KD 900P r (2/A+KD+D@ )C+ ,E)(1K* LK*0+ ,-
# J+/A+KD+D M+/K0D+ )C+ -,A+/KD) +AA,A /,LKA(K2/+ -,A )C+ D)K)+ LKA(KM*+D CKD
K*A+KJF M++2 (2/A+KD+J. #F (2/A+KD(2?
9AAP
r -A,1 X+A, ), H.c@ K M(? (1EA,L+1+2) (D -,02J.
#+F,2J r hH.c@ () D++1D )CK) )C+A+ (D K*1,D) 2, A,,1 ), (1EA,L+.
cI
%KM*+ 4.23 A2K*FD(D &8S6 ,- cHH CBK C+(?C) 0D(2? )C+ .JS8U N()C J(--+A+2) /C,(/+D
,- P # @ r Q. <C+2 r hH P (.+. E0A+ .JS8Q@ K D1K** -K/),A P hH.HcQ ,- )C+
10*)(E*(/K)(L+ (2-*K)(,2 (D KEE*(+J ), EA+L+2) )C+ -(*)+A J(L+A?+2/+. F,A )C+ ,)C+A
/C,(/+D ,-
!
r @ 2, 10*)(E*(/K)(L+ (2-*K)(,2 (D 0D+J. F,A /,1EKA(D,2@ )C+ E0A+ KJJ()(,2
(2-*K)(,2 KEE*(/K)(,2 (D K*D, DC,N2 P# hH K2J r hb.cQ.
# H.H H.2c H.cH H.Ic b.HH
r hH dI.b dc.H dd.Y
r hH.2c 22.c 22.H bf.Y bY.2
r hH.c bY.f bI.V 2H.4 2H.b
r hH.V bI.d
r hb.c 2d.f
%, /,1EKA+ )C+ E+A-,A1K2/+D ,- )C+ .JS8U K2J )C+ KJJ()(L+ (2-*K)(,2 D/C+1+
-,A )C+ ,)C+A LKA(KM*+D K2J K) )C+ ,)C+A *+L+*D@ )C+ K2K*FD(D &8S6 ,- X,2K* N(2J K2J
)+1E+AK)0A+ K) K** L+A)(/K* *+L+*D KA+ DC,N2 (2 F(?0A+ 4.I. <()C M(KD /,AA+/)(,2@ K
D1K** KJJ()(L+ 2,(D+ PAhH.2cQ /K2 M+K) )C+ A+D0*) -A,1 )C+ 2, M(KD /,AA+/)(,2 A02@
NC+A+KD K *KA?+ K1,02) ,- KJJ()(L+ 2,(D+ PAhb.cQ (D A+]0(A+J ), K//,02) -,A M,)C )C+
M(KD K2J )C+ DFD)+1T2,(D+. %C+ ,E)(1K* A+D0*)D N()C M(KD /,AA+/)(,2 PAhH.VQ KA+
D(?2(-(/K2)*F M+))+A )CK2 )C+ E0A+ KJJ()(L+ (2-*K)(,2 KEE*(/K)(,2. %C+D+ A+D0*)D D0??+D)
)CK) A+1,L(2? )C+ M(KD -A,1 )C+ +2D+1M*+ 1+K2 (D 1,A+ K//0AK)+ )CK2 K//,02)(2? -,A
)C+1 (2 )C+ D+/,2J 1,1+2) ,- )C+ +2D+1M*+@ ,2 /,2J()(,2 )CK) )C+ +D)(1K)+J M(KD+D
KA+ ?,,J +2,0?C ), A+EA+D+2) )C+ )A0+ -,A+/KD) M(KD+D. <+ 2,)+ )CK) )C+ /,2)A,*
K2K*FD(D +AA,A /K22,) M+ E*,))+J (2 F(?0A+ 4.I M+/K0D+ () (D 2Td )(1+D *KA?+A )CK2 )C+
+AA,A ,M)K(2+J N()C K** )C+ KEEA,K/C+D ), J+K* N()C 1,J+* +AA,AD.
cf
F(?0A+ 4.I3 A2K*FD(D &8S6 K) K** EA+DD0A+ *+L+*D )+1E,AK**F KL+AK?+J -,A ,2+ 1,2)C
K-)+A )C+ (2()(K* CK*- 1,2)C DE(2T0E E+A(,J -,A X,2K* N(2J P*+-)Q K2J )+1E+AK)0A+ PA(?C)Q
(2 )C+ /KD+D ,- KJJ()(L+ 2,(D+ N()C K1E*()0J+ Ahb.c PD,*(J *(2+Q@ )C+ .JS8 ),?+)C+A
N()C KJJ()(L+ 2,(D+ N()C K1E*()0J+ AhH.2c PJKDC+J *(2+Q K2J )C+ .JS8 ),?+)C+A N()C
KJJ()(L+ 2,(D+ N()C K1E*()0J+ AhH.VH PJ,))+J *(2+Q.
%, KDD+DD )C+ +D)(1K)+J M(KD -(+*JD -A,1 )C+ .JS8U@ N+ E*,) )C+ )(1+ 1+K2 ,-
)C+ +D)(1K)+J M(KD -(+*J@ )(1+ 1+K2 ,- )C+ M(KD+J SB66.S VCA -,A+/KD)@ K2J ,- )C+
J+M(KD+J -,A+/KD) P1KJ+ MF D0M)AK/)(2? )C+ +D)(1K)+J M(KD -A,1 )C+ M(KD+J -,A+/KD)Q
-,A 2HH CBK X,2K* N(2J PF(?0A+ 4.fQ. #+-,A+ )C+ M(KD /,AA+/)(,2@ )C+ VTC,0A SB66.S
-,A+/KD) -(+*J (D D(?2(-(/K2)*F M(KD+J. 4KA?+ -,A+/KD) M(KD+D /K2 M+ -,02J (2 E,*KA
A+?(,2D ,A KDD,/(K)+J N()C )C+ a+). ;) (D A+1KAWKM*+ )CK) )C+ +D)(1K)+J M(KD -(+*J
/KE)0A+D )C+ D)A0/)0A+ ,- )C+ -,A+/KD) M(KD N+**@ )C,0?C )C+ K1E*()0J+ (D (2 ?+2+AK*
D,1+NCK) D1K**+A. %C+ K/)0K* -,A+/KD) M(KD+D DC,0*J M+ +ZE+/)+J ), M+ *KA?+A )CK2 )C+
+D)(1K)+J LK*0+D D(2/+ )C+ D/C+1+ (D 2,) E+A-+/). ;2 KJJ()(,2@ )C+ .JS8 (D J+D(?2+J ),
/KE)0A+ )C+ D*,N*F LKAF(2? /,1E,2+2) ,- -,A+/KD) +AA,AD NC(*+ )C+ A+1K(2(2?
/,1E,2+2)D /K2 M+ K//010*K)+J KD )C+ JK)K KDD(1(*K)(,2 DFD)+1 (D /F/*+J. A-)+A
cY
D0M)AK/)(2? )C+ +D)(1K)+J M(KD -A,1 )C+ ,A(?(2K* M(KD+J -,A+/KD)@ )C+ J+M(KD+J -,A+/KD)
+ZC(M()D D(?2(-(/K2)*F *+DD M(KD. <()C )C+ J+M(KD+J -,A+/KD)D@ () (D 2,) D0AEA(D(2? )CK) N+
,M)K(2 K M+))+A K2K*FD(D )CK2 N()C )C+ E0A+ KJJ()(L+ (2-*K)(,2 KEE*(/K)(,2 K2J )CK) )C+
A+]0(A+J KJJ()(L+ 2,(D+ (D 10/C D1K**+A D(2/+ 1,D) ,- )C+ 1,J+* M(KD CKD K*A+KJF M++2
A+1,L+J. <+ 0D+ )C+ )+A1 gJ+M(KD+J` -,A+/KD) AK)C+A )CK2 g02M(KD+J` -,A+/KD) M+/K0D+
)C+ M(KD+D KA+ 2,) /,1E*+)+*F A+1,L+J. %C+ A+1K(2(2? M(KD+D KA+ 1,D)*F (2 )C+ D/K*+D
/*,D+ ), )C+ 1,J+* A+D,*0)(,2@ NC(/C D0??+D)D )CK) )C+ .JS8 (D *+DD +--(/(+2) NC+2 )C+
M(KD+D KA+ (2 )C+ D1K**+D) D/K*+D. %C(D (D /,2-(A1+J (2 F(?0A+ 4.Y DC,N(2? )C+ .JS8U
J,+D 2,) /KE)0A+ )C+ M(KD N+** (2 fcH CBK X,2K* N(2J NC+A+ N+ D++ )C+ D1K**TD/K*+
/CKAK/)+A(D)(/ ,- )C+ 1,J+* M(KD PD++ F(?0A+ 4.bQ. ;2 ,0A +ZE+A(1+2)D@ N+ CKL+
,MD+ALK)(,2D K) +L+AF ,)C+A ?A(J E,(2) )C+A+-,A+ )C+ .JS8U A+*(+D ,2 )C+ D0AA,02J(2?
,MD+ALK)(,2D ), +D)(1K)+ M(KD K) )C,D+ 02T,MD+AL+J 1,J+* ?A(JD. ;- )C+ M(KD+D KA+ (2 )C+
D/K*+D /*,D+ ), )C+ 1,J+* A+D,*0)(,2 P+.?.@ )C+ ,EE,D()+ D(?2 ,- M(KD M+)N++2 )N,
KJaK/+2) E,(2)DQ@ )C+ +D)(1K)(,2 -,A )C+ 02T,MD+AL+J ?A(JD /K2 M+ gM*(2J` ,A K) *+KD)
02J+A+D)(1K)+ )C+ g)A0+` M(KD. AD K A+D0*)@ )C+ gJ+M(KD+J` -,A+/KD) K) fcH CBK (D D)(**
M(KD+J K2J N,AD+ )CK2 )CK) K) 2HH CBK.
VH
F(?0A+ 4.f3 %,E EK2+*3 %(1+T1+K2 ,- SB66.S VTC,0A -,A+/KD) PM(KDQi 8(JJ*+ EK2+*3
%(1+T1+K2 ,- )C+ +D)(1K)+J M(KD -(+*Ji #,)),1 EK2+*3 %(1+T1+K2 ,- J+M(KD+J
-,A+/KD) K-)+A D0M)AK/)(2? )C+ +D)(1K)+J M(KD -A,1 )C+ SB66.S -,A+/KD) PM(KD ,- )C+
J+M(KD+J -,A+/KD)Q (2 )C+ /KD+ ,- KEE*F(2? )C+ .JS8U. %C+ A+D0*)D KA+ DC,N2 -,A 2HH
CBK X,2K* N(2J K2J )+1E,AK**F KL+AK?+J -,A K 1,2)C K-)+A )C+ (2()(K* DE(2T0E E+A(,J.
Vb
F(?0A+ 4.Y3 SK1+ KD F(?0A+ 4.f@ +Z/+E) -,A fcH CBK
V2
<+ CKL+ D++2 )C+ *KA?+ )+1E+AK)0A+ J(0A2K* M(KD+D 2+KA )C+ D0A-K/+ ,L+A *K2J
PF(?0A+ 4.2Q@ NC(*+ )C+ .JS8 (2 ()D ,A(?(2K* J+D(?2 K(1D ), /,AA+/) )C+ D*,N*F LKAF(2?
M(KD. %, D++ (- () (D KM*+ ), CK2J*+ )C+ -KD)TLKAF(2? M(KD@ N+ E*,) )C+ +D)(1K)+J M(KD ,-
)C+ Y2c CBK )+1E+AK)0A+ -(+*J K) K DE+/(-(+J *,/K)(,2 Pb2Hk6@ dHkSQ (2 A0D)AK*(K NC+A+
K *KA?+ J(0A2K* M(KD (D EA+D+2)+J (2 F(?0A+ 4.2. AD D++2 (2 F(?0A+ 4.bH@ )C+ +D)(1K)+J
M(KD -,**,ND )C+ -,A+/KD) +AA,A M0) )C+ K1E*()0J+ (D 10/C D1K**+A. %C(D (D M+/K0D+ )C+
K2K*FX+J M(KD+D CKL+ M++2 /,2)K1(2K)+J MF )C+ M(KD+D K) )C+ EA+L(,0D )(1+@ NC(/C KA+
J(--+A+2) -A,1 )C+ M(KD K) )C+ /0AA+2) )(1+. N+L+A)C+*+DD@ )C+ )(1+ D+A(+D ,- +D)(1K)+J
M(KD (D (2 ECKD+ N()C )CK) ,- )C+ -,A+/KD) +AA,A@ D, )CK) K) *+KD) )C+ J(A+/)(,2 ,- M(KD
/,AA+/)(,2 (D /,AA+/). <()C D0/C D1K** K1E*()0J+@ )C+ +D)(1K)+J M(KD (D KM*+ ), /,AA+/)
,2*F K D1K** E,A)(,2 ,- )C+ J(0A2K* M(KD P)C+ J+M(KD+J -,A+/KD) +ZC(M()D K *())*+ D1K**+A
+AA,A )CK2 )C+ M(KD+J -,A+/KD)Q.
%C+ .JS8U N,AWD ?+2+AK**F N+**@ K2J (D M+))+A )CK2 )C+ KJJ()(L+ (2-*K)(,2
1+)C,J. =,N+L+A@ )C(D M(KD /,AA+/)(,2 D/C+1+ (D A+*K)(L+*F +ZE+2D(L+ D(2/+ () J,0M*+D
)C+ K2K*FD(D )(1+. %, KJJA+DD )C(D EA,M*+1@ N+ (1E*+1+2) K D(1E*(-(+J L+AD(,2 ,- )C+
.JS8 P&KJKW,L(/C +) K*. 2HHbQ. %C+ D(1E*(-(+J K*?,A()C1 1,J(-(+J )C+ :K*1K2 ?K(2
-,A M(KD @ ), M+ bnQboP %''& RHHPHPK %9AA
%9AA0 ##
AA%9
AA%9
AA0 KRHHPHPK ## &'5 %bno P4.cQ
,2 /,2J()(,2 )CK) # (D D1K** +2,0?C. %C+ +ZEA+DD(,2 ,- P4.cQ (1E*(+D )CK) )C+ K2K*FD(D
(2/A+1+2) -,A )C+ M(KD (D EA,E,A)(,2K* ), )C+ K2K*FD(D (2/A+1+2) -,A )C+ D)K)+ LKA(KM*+.
%C0D@ )C+ M(KD K2K*FD(D EA,/+DD (D /,1E0)K)(,2K**F -A++ (- () (D J,2+ K-)+A )C+ D)K)+
K2K*FD(D CKD M++2 0EJK)+J PD++ D+/)(,2 2.d.d (2 'CKE)+A 2 -,A J+)K(*DQ.
Vd
F(?0A+ 4.bH3 %(1+ D+A(+D ,- )C+ M(KD+J SB66.S -,A+/KD) +AA,A PA+J *(2+Q@ )C+
+D)(1K)+J M(KD MF )C+ .JS8U PM*K/W *(2+Q@ K2J )C+ +AA,A ,- )C+ J+M(KD+J -,A+/KD) MF
D0M)AK/)(2? )C+ M(KD -A,1 )C+ M(KD+J SB66.S -,A+/KD) P?A++2 J,))+J *(2+Q ,- )C+ Y2c
CBK )+1E+AK)0A+ -(+*J K) Pb2Hk6@ dHkSQ NC+A+ K *KA?+ J(0A2K* M(KD (D EA+D+2)+J.
<+ )KW+ )C+ DK1+ D+))(2? ,- )C+ EKAK1+)+AD KD )C+ ,E)(1K* /C,(/+ 0D+J (2 )C+
.JS8U P Y.H&4 @# hH.c@ r hH.VQ K2J A02 )C+ SB66.ST46%:F DFD)+1 N()C )C+
D(1E*(-(+J .JS8U. %C+ A+D0*)(2? K2K*FD(D (D N,AD+ )CK2 )CK) -A,1 )C+ .JS8U -,A K**
)C+ LKA(KM*+D M0) M+))+A )CK2 )CK) -A,1 )C+ E0A+ KJJ()(L+ (2-*K)(,2 (2 )C+ cHH CBK C+(?C)
-(+*J K2J /,1EKAKM*+ A+D0*)D KA+ -,02J (2 )C+ ,)C+A -(+*JD@ +Z/+E) -,A DE+/(-(/ C01(J()F
-(+*JD P%KM*+ 4.dQ.
%C(D A+D0*) (D 2,) 02+ZE+/)+J. F(AD)@ (2 )C+ D(1E*(-(+J KEEA,K/C@ N+ 0D+ # hH.c
D, )CK) )C+ KDD01E)(,2 ,- K D1K**# (D 2,) 1+). S+/,2J@ )C+ .JS8U 0EJK)+D )C+ M(KD
V4
-(+*J -(AD) )C+2 0D+D )C+ /0AA+2) gK2K*FD(D` M(KD ), ,M)K(2 )C+ J+M(KD+J -,A+/KD) NC(*+
N()C )C+ D(1E*(-(+J L+AD(,2 N+ CKL+ ), 0D+ )C+ g-,A+/KD)` M(KD P0D0K**F )KW+2 -A,1 )C+
EA+L(,0D )(1+ K2J@ KD K A+D0*)@ *+DD K//0AK)+ )CK2 )C+ gK2K*FD(D` M(KDQ D(2/+ )C+ M(KD
K2K*FD(D (D J,2+ K-)+A )C+ D)K)+ LKA(KM*+D CKL+ M++2 0EJK)+J.
%KM*+ 4.d3 ',1EKA(D,2 ,- K2K*FD(D &8S6 M+)N++2 )C+ KEE*(/K)(,2D ,- KJJ()(L+
(2-*K)(,2@ )C+ .JS8U K2J )C+ D(1E*(-(+J .JS8U. &+D0*)D KA+ DC,N2 -,A 2HH CBK
X,2K* N(2J Pu Q@ cHH CBK C+(?C) P # Q@ fcH CBK DE+/(-(/ C01(J()F P Q K2J Y2c CBK
)+1E+AK)0A+ P
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P02()Q
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u P1RDQ
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.JS8U b.IV bI.d2 H.4I b.dH
4.4.c 4,NTJ(1+2D(,2K* 1,J+* +AA,A /,AA+/)(,2
%C+ *,NTJ(1+2D(,2K* 1+)C,J P4.8Q K))+1E)D ), /,AA+/) )CA++ )FE+D ,- 1,J+*
+AA,AD3 bQ %(1+TKL+AK?+J M(KD /,AA+/)(,2i 2Q .(0A2K* M(KD /,AA+/)(,2i K2J dQ S)K)+T
J+E+2J+2) +AA,A /,AA+/)(,2. .K2-,A)C +) K*. P2HHIQ D0//++J+J (2 /,AA+/)(2? 1,J+*
+AA,AD J0A(2? )C+ -,A+/KD) E+A(,J NC(*+ 2+?*+/)(2? +AA,AD (2 )C+ (2()(K* /,2J()(,2 ), M+
E+A-+/). =+A+ N+ )+D) )C(D 1+)C,J (2 K 1,A+ A+K*(D)(/ D()0K)(,2. %C+ -,A+/KD)TK2K*FD(D (D
/F/*+J D, )CK) N+ CKL+ M,)C )C+ +AA,AD (2 )C+ (2()(K* /,2J()(,2D K2J )C+ 1,J+* +AA,AD.
Vc
<+ 0D+ )C+ 46%:F KD )C+ JK)K KDD(1(*K)(,2 D/C+1+ K2J -,/0D ,2 )C+ (1EK/) ,- *,NT
J(1+2D(,2K* +AA,A /,AA+/)(,2 ,2 )C+ E+A-,A1K2/+ ,- )C+ 46%:F.
A. B0A+ 4.8
F(AD) N+ )+D) )C+ E0A+ 4.8@ (.+. N+ J, 2,) 0D+ K2F KJJ()(,2K* 1+)C,J P+.?.
KJJ()(L+ (2-*K)(,2Q ), K//,02) -,A DFD)+1T2,(D+. A D1K** LK*0+ P hH.HcQ ,-
10*)(E*(/K)(L+ (2-*K)(,2 (D KEE*(+J ), EA+L+2) )C+ +2D+1M*+ DEA+KJ -A,1 /,**KED(2?.
!
a/ %i,e5a1eraged 0ia' 6orre6tion
;2 )C(D D+/)(,2 N+ /,1EKA+ )C+ (1EK/) ,- )N, J(--+A+2) )AK(2(2? E+A(,JD ),
?+2+AK)+ )C+ )(1+TKL+AK?+J M(KD. 8,J+* +AA,AD KA+ DK1E*+J MF )C+ J(--+A+2/+ M+)N++2
)C+ NN& -(+*JD K2J )C+ VTC,0A SB66.S -,A+/KD)D D)KA)+J -A,1 )C+ NN& -(+*J. %,
,M)K(2 K )(1+TKL+AK?+J M(KD@ N+ 2++J K D0MD+) ,- 1,J+* +AA,A DK1E*+D ), J, )C+
KL+AK?+. %C+ M(KD -(+*JD DC,N2 (2 F(?0A+ 4.b KA+ ,M)K(2+J MF KL+AK?(2? )C+ bf4
DK1E*+D ,L+A ,0A +ZE+A(1+2)K* E+A(,J M+)N++2 HHHH \%' b ^K20KAF bYfI ), bfHH
\%' bc F+MA0KAF bYfI. =,N+L+A )C+D+ DK1E*+D N,0*J 2,) M+ KLK(*KM*+ M+-,A+CK2J
(2 K A+K* /KD+. =+A+ N+ )+D) )N, -+KD(M*+ )AK(2(2? E+A(,JD ,L+A NC(/C N+ KL+AK?+ )C+
1,J+* +AA,A DK1E*+D. O2+ (D ,2+ 1,2)C EA(,A ), )C+ +ZE+A(1+2)@ +.?.@ (- )C+
+ZE+A(1+2)K* )(1+ (D (2 ^K20KAF bYfI N+ 0D+ .+/+1M+A bYfV KD )C+ )AK(2(2? E+A(,Ji
)C+ ,)C+A (D MKD+J ,2 )C+ cTF+KA /*(1K),*,?F -,A )C+ F+KAD bYf2TbYfV@ -,**,N(2?
.K2-,A)C +) K*. P2HHIQ. %C+ )(1+TKL+AK?+J M(KD (D D+EKAK)+J -,A ^K20KAF K2J F+MA0KAF.
F(?0A+ 4.bb /,1EKA+D )C+ K2K*FD(D &8S6 ,- 2HH CBK X,2K* N(2J@ cHH CBK
)+1E+AK)0A+ K2J fcH CBK DE+/(-(/ C01(J()F 0D(2? )(1+TKL+AK?+J M(KD+D ,M)K(2+J -A,1
VV
)N, J(--+A+2) )AK(2(2? E+A(,JD. ;) /*+KA*F DC,ND )CK) )C+ /*(1K),*,?(/K* M(KD ?(L+D
M+))+A A+D0*)D )CK2 )C+ EA(,A ,2+T1,2)C M(KD +D)(1K)+. %C+ A+D0*)D -,A )C+ ,)C+A
LKA(KM*+D K2J K) )C+ ,)C+A *+L+*D KA+ D(1(*KA. %C0D@ (2 )C+ A+D) ,- ,0A +ZE+A(1+2)D -,A
)C+ *,NTJ(1+2D(,2K* M(KD /,AA+/)(,2@ )C+ DK1E*+D ,- 1,J+* +AA,A KA+ -A,1 )C+ cTF+KA
/*(1K),*,?(/K* JK)KD+).
0/ Kiurna! 0ia' 6orre6tion
<+ DKN )C+ D)A,2? D(?2K* ,- J(0A2K* M(KD 2+KA )C+ D0A-K/+ (2 )+1E+AK)0A+ -(+*JD
)CK) (D EA,a+/)+J ,2), )C+ -(AD) )N, *+KJ(2? 6OFD PF(?0A+ 4.2Q. ;2 ,AJ+A ), /,AA+/) )C+D+
J(0A2K* M(KD+D@ N+ /,1E0)+ )C+ -(AD) )N, *+KJ(2? 6OFD ,- )C+ +AA,A K2,1K*,0D -(+*JD
-,A )+1E+AK)0A+ K) )C+ M,)),1 )N, D(?1K *+L+*D P " hH.Yc K2J " hH.fdcQ 0D(2?
DK1E*+D -A,1 )C+ cTF+KA /*(1K),*,?(/K* JK)KD+). %C+ BA(2/(EK* ',1E,2+2)D PB'DQ ,-
)C+D+ )N, 1,J+D KA+ +D)(1K)+J MF EA,a+/)(2? )C+ *+KJ(2? +(?+2L+/),AD ,2), )C+ +AA,A
K2,1K*,0D -(+*JD. %C+ J(0A2K* 1K?2()0J+ ,- )C+ )N, 1,J+D (D +D)(1K)+J MF KL+AK?(2?
)C+ )(1+TD+A(+D ,- )C+ B'D ,L+A )C+ JK(*F /F/*+ -,A )C+ F+KAD bYf2TbYfV. A J(0A2K* M(KD
/,AA+/)(,2 (D /,1E0)+J KD K -02/)(,2 ,- )C+ )(1+ ,- JKF. F(?0A+ 4.b2 /,1EKA+D )C+
)+1E+AK)0A+ K2K*FD(D &8S6 K) Y2c CBK K2J fcH CBK N()C K2J N()C,0) )C+ J(0A2K* M(KD
/,AA+/)(,2. <()C ,2*F )C+ )(1+TKL+AK?+J M(KD /,AA+/)(,2@ )C+ K2K*FD(D &8S6 (D C(?C+A
K2J K D)A,2? J(0A2K* LKA(KM(*()F /K2 M+ -,02J. ',AA+/)(,2 (2/*0J(2? )C+ J(0A2K* M(KD
A+J0/+D )C+ ?*,MK*TKL+AK?+J K2K*FD(D &8S6 MF KM,0) bHj K) Y2c CBK K2J cj K) fcH
CBK K2J )C(D (1EA,L+1+2) /K2 M+ 1,D)*F K))A(M0)+J ), )C+ +AA,A A+J0/)(,2 ,L+A *K2J
PF(?0A+ 4.bdQ.
VI
F(?0A+ 4.bb3 ',1EKA(D,2 ,- K2K*FD(D &8S6 N()C )(1+TKL+AK?+J M(KD +D)(1K)+J -A,1
,2+T1,2)C EA(,A DK1E*+D PD,*(J /0AL+Q K2J +D)(1K)+J -A,1 cTF+KA /*(1K),*,?F PJ,))+J
/0AL+Q. %(1+ D+A(+D KA+ DC,N2 -,A 2HH CBK X,2K* N(2J@ cHH CBK )+1E+AK)0A+ K2J fcH
CBK DE+/(-(/ C01(J()F.
Vf
F(?0A+ 4.b23 %(1+ D+A(+D ,- ?*,MK*TKL+AK?+J K2K*FD(D &8S6 /,AA+/)+J -,A )C+ /,2D)K2)
M(KD N()C PJ,))+J *(2+Q K2J N()C,0) PD,*(J *(2+Q J(0A2K* M(KD /,AA+/)(,2 -,A )+1E+AK)0A+
K) Y2c CBK P*+-)Q K2J fcH CBK PA(?C)Q.
F(?0A+ 4.bd3 A2K*FD(D &8S6 J(--+A+2/+ M+)N++2 )C+ A02D N()C K2J N()C,0) J(0A2K*
M(KD /,AA+/)(,2@ KL+AK?+J -,A K 1,2)C K-)+A )C+ (2()(K* DE(2T0E E+A(,J@ -,A )+1E+AK)0A+
K) Y2c CBK P*+-)Q K2J fcH CBK PA(?C)Q. %C+ ?A++2 /,*,A (2J(/K)+D )C+ &8S6 A+J0/)(,2
MF (2/*0J(2? )C+ J(0A2K* M(KD /,AA+/)(,2.
VY
6/ State5dependent 6orre6tion
;2 KJJ()(,2 ), )C+ )(1+TKL+AK?+J K2J J(0A2K* M(KD@ N+ K*D, /,1E0)+ )C+ *+KJ(2?
1,J+ ,- )C+ S(2?0*KA >K*0+ .+/,1E,D()(,2 PS>.Q ,- )C+ /,LKA(K2/+ 1K)A(/+D
M+)N++2 )C+ D)K)+ K2,1K*(+D K2J )C+ 1,J+* +AA,A K2,1K*(+D ), K**,N K A+D(J0K*
/,AA+/)(,2 ,- )C+ D)K)+TJ+E+2J+2) +AA,AD PD++ D+/)(,2 2.d.c (2 'CKE)+A 2 -,A J+)K(*DQ.
%C+ S>. 1,J+D KA+ ?+2+AK)+J D+EKAK)+*F -,A J(--+A+2) LKA(KM*+D K2J *+L+*D 0D(2?
1,J+* +AA,A DK1E*+D -A,1 )C+ F+KAD bYf2TbYfV. %+2 S>. 1,J+D KA+ 0D+J ), /K*/0*K)+
)C+ D)K)+TJ+E+2J+2) 1,J+* +AA,A K2,1K*(+D. %, KL,(J DE0A(,0D *,2?TJ(D)K2/+
/,AA+*K)(,2D@ -,**,N(2? .K2-,A)C +) K*. P2HHIQ@ )C+ /,AA+*K)(,2D M+)N++2 )N, ?A(J
E,(2)D )CK) KA+ 1,A+ )CK2 c ?A(J E,(2)D KNKF -A,1 +K/C ,)C+A KA+ -,A/+J ), M+ X+A,.
%C+ (1EK/) ,- )C+ D)K)+TJ+E+2J+2) +AA,A /,AA+/)(,2 ,2 )C+ ?*,MK* KL+AK?+J
K2K*FD(D &8S6 (D ?+2+AK**F D1K** M0) E,D()(L+. F,A D,1+ ,- )C+ LKA(KM*+D K) /+A)K(2
*+L+*D P-,A +ZK1E*+@ cHHCBK )+1E+AK)0A+ -(+*J (2 F(?0A+ 4.b4Q@ )C+ E,D()(L+ K2J
2+?K)(L+ (1EK/) (D 1(Z+J N()C )(1+ NC(*+ -,A )C+ ,)C+AD N+ ,MD+AL+J )C+ /,2D(D)+2)
E,D()(L+ (1EK/) P-,A +ZK1E*+@ Y2cCBK 1+A(J(,2K* N(2J -(+*JQ )C,0?C )C+ (1EK/) (D
A+*K)(L+*F D1K**.
%, M+))+A 02J+AD)K2J )C+ A+D0*)D -,A )C+ Y2c CBK 1+A(J(,2K* N(2J -(+*J@ N+ E*,)
)C+ )CA++ *+KJ(2? /,0E*+J S>. 1,J+D M+)N++2 )C+ D)K)+ K2,1K*(+D K2J )C+ 1,J+*
+AA,A K2,1K*(+D 0D(2? )C+ /*(1K),*,?(/K* DK1E*+D (2 ^K20KAF -A,1 )C+ F+KAD bYf2TfV@
K2J )C+ )(1+TKL+AK?+J K2K*FD(D &8S6 A+J0/)(,2 MF (2/*0J(2? )C+ D)K)+TJ+E+2J+2)
+AA,A /,AA+/)(,2 PF(?0A+ 4.bcQ. F(AD) N+ D++ )C+ D)A,2?*F /,0E*+J 1,J+D (2J(/K)(2? K
D(?2(-(/K2) A+*K)(,2DC(E M+)N++2 )C+ 1,J+* +AA,A K2,1K*(+D K2J D)K)+ K2,1K*(+D. %C+2
N+ -(2J 1,D) ,- )C+ K2K*FD(D &8S6 A+J0/)(,2 K/)0K**F ,//0AD (2 )C+ A+?(,2D NC+A+ )C+
IH
/,0E*+J D(?2K* (D )C+ D)A,2?+D). S(2/+ N+ KDD01+ K *,/K* D)A0/)0A+ (2 )C+ /,LKA(K2/+
1K)A(/+D@ )C+ E,D()(L+ (1EK/) (D K*D, A+D)A(/)+J ), D,1+ /+A)K(2 *,/K* A+?(,2D. F,A )C,D+
KA+KD NC+A+ )C+A+ (D 2, /,0E*+J D(?2K*@ -,A +ZK1E*+ (2 )C+ D,0)C+A2 =+1(DEC+A+ K2J
)A,E(/D@ )C+ (1EK/) ,- )C+ D)K)+TJ+E+2J+2) +AA,A /,AA+/)(,2 (D 2+?*(?(M*+. %C(D +ZE*K(2D
NCF )C+ (1EA,L+1+2) -,A )C+ ?*,MK**F KL+AK?+J K2K*FD(D &8S6 (D D1K**@ )C,0?C
*,/K**F )C+ (1EA,L+1+2) /K2 M+ KD *KA?+ KD dHj.
F(?0A+ 4.b43 %(1+ D+A(+D ,- ?*,MK**F KL+AK?+J K2K*FD(D &8S6 /,AA+/)+J -,A )C+
/,2D)K2) K2J J(0A2K* M(KD N()C PJ,))+J *(2+Q K2J N()C,0) PD,*(J *(2+Q )C+ D)K)+T
J+E+2J+2) +AA,A /,AA+/)(,2 -,A )+1E+AK)0A+ K) cHH CBK P*+-)Q K2J 1+A(J(,2K* N(2J K)
Y2c CBK PA(?C)Q.
Ib
F(?0A+ 4.bc3 %C+ -(AD) )CA++ *+KJ(2? S>. D)A0/)0A+D M+)N++2 )C+ 1,J+* D)K)+
K2,1K*(+D P/,2),0ADQ K2J )C+ 1,J+* +AA,A K2,1K*(+D PDCKJ+DQ (2 1+A(J(,2K* N(2J K)
Y2c CBK (2 ^K20KAF -,A bYf2TbYfV@ K2J )C+ K2K*FD(D &8S6 J(--+A+2/+ M+)N++2 )C+
A02D N()C K2J N()C,0) )C+ D)K)+TJ+E+2J+2) +AA,A /,AA+/)(,2@ KL+AK?+J ,L+A )C+ E+A(,J
-A,1 bb ^K20KAF bYfI ), db ^K20KAF bYfI PM,)),1 A(?C) EK2+*Q. %C+ ?A++2 /,*,A
(2J(/K)+D )C+ &8S6 A+J0/)(,2 MF (2/*0J(2? )C+ D)K)+TJ+E+2J+2) +AA,A /,AA+/)(,2. 8,D)
,- )C+ A+J0/)(,2 (D -,02J (2 )C+ /(A/*+J A+?(,2D NC+A+ )C+ *+KJ(2? /,0E*+J D(?2K*D KA+
)C+ D)A,2?+D).
I2
#. 4.8 N()C (2-*K)(,2 P4.8UQ
S, -KA N+ CKL+ 2,) J+K*) N()C DFD)+1T2,(D+. AD (2 )C+ /KD+ ,- )C+ .JS8 1+)C,J@
N()C,0) CK2J*(2? )C(D AK2J,1 2,(D+@ )C+ 4.8 (D 2,) KM*+ ), M+K) KJJ()(L+ (2-*K)(,2
N()C K2 ,E)(1K* K1E*()0J+ r hb.c PF(?0A+ 4.bVQ. %, EKAK1+)+A(X+ DFD)+1T2,(D+@ N+
KJJ AK2J,1*F D+*+/)+J NN& VTC,0A )+2J+2/F -(+*J ), +K/C -,A+/KD) +2D+1M*+ 1+1M+A
K2J )02+ )C+(A K1E*()0J+ PKJJ()(L+ (2-*K)(,2Q. %C+ ,E)(1K* LK*0+ ,- r hH.4 (2 )C(D /KD+
(D 10/C D1K**+A )CK2 b.c NC(/C (D ,E)(1K* (2 )C+ E0A+ KJJ()(L+ (2-*K)(,2 KEE*(/K)(,2.
%C+ 4.8@ E*0D K D1K** K1,02) ,- KJJ()(L+ 2,(D+ P4.8U C+A+K-)+AQ@ ,0)E+A-,A1D )C+
E0A+ KJJ()(L+ (2-*K)(,2 D/C+1+ +L+AFNC+A+. %C+D+ A+D0*)D (2J(/K)+ )CK) (2 )C+ EA+D+2/+
,- /,1E*(/K)+J 1,J+* +AA,AD N+ CKL+ ), J+K* N()C M,)C 1,J+* M(KD K2J DFD)+1T2,(D+.
F,A )C+ M(KD+D@ +D)(1K)(2? K2J /,AA+/)(2? )C+1 -,A )C+ +2D+1M*+ 1+K2 ?(L+ M+))+A
A+D0*)D )CK2 K//,02)(2? -,A )C+(A +--+/)D (2 )C+ D+/,2J 1,1+2) ,- )C+ +2D+1M*+.
<+ CKL+ DC,N2 )CK) )C+ .JS8U (D *+DD K//0AK)+ NC+2 )C+ M(KD+D KA+ D1K**TD/K*+
PF(?0A+ 4.YQ. %, D++ (- )C+ 4.8U (D KM*+ ), CK2J*+ )C(D EA,M*+1@ N+ E*,) )C+ DK1+
-(?0A+ KD F(?0A+ 4.Y@ M0) 0D(2? )C+ 4.8U PF(?0A+ 4.bIQ. %C+ +D)(1K)+J M(KD -(+*J
/KE)0A+D )C+ D)A0/)0A+ ,- )C+ -,A+/KD) M(KD ]0()+ N+** +L+2 (2 D1K** D/K*+D. %C+
A+D0*)(2? gJ+M(KD+J` -,A+/KD) (D 10/C *+DD M(KD+J /,1EKA+J ), )CK) -A,1 )C+ .JS8U.
\2*(W+ )C+ .JS8U +D)(1K)(2? M(KD (2 ,MD+ALK)(,2 DEK/+@ )C+ M(KD +D)(1K)(,2 (2 )C+
4.8U (D J,2+ (2 1,J+* DEK/+. AD K A+D0*)@ )C+ 4.8U (D *+DD K--+/)+J MF )C+
,MD+ALK)(,2 J+2D()F K2J /K2 /KE)0A+ )C+ M(KD D)A0/)0A+ N+** K) K** 1,J+* ?A(J E,(2)D KD
*,2? KD )C+ M(KD D)A0/)0A+ (2 )C+ )AK(2(2? E+A(,J (D D(1(*KA ), )CK) (2 )C+ +ZE+A(1+2)K*
E+A(,J.
Id
F(?0A+ 4.bV3 %(1+ D+A(+D ,- )C+ ?*,MK*TKL+AK?+J K2K*FD(D &8S6 ,- )C+ cHH CBK # K2J
Y2c CBK % -(+*JD@ (2 )C+ /KD+D ,- )C+ 4.8 K*,2+ PJKDC+J /0AL+Q@ r hb.c KJJ()(L+
(2-*K)(,2 PJ,))+J /0AL+Q K2J )C+ 4.8 ),?+)C+A N()C KJJ()(L+ (2-*K)(,2 N()C K2
K1E*()0J+ r hH.4 PD,*(J /0AL+Q.
I4
F(?0A+ 4.bI3 SK1+ KD F(?0A+ 4.Y@ +Z/+E) (2 )C+ /KD+ ,- KEE*F(2? )C+ 4.8U.
Ic
4.4.V OL+AK** /,1EKA(D,2
<+ CKL+ KDD+DD+J )C+ E+A-,A1K2/+ ,- +K/C 1+)C,J D+EKAK)+*F. F(2K**F N+
/,1EKA+ )C+1 N()C +K/C ,)C+A. AD M+-,A+@ N+ L+A(-F )C+ A+D0*)D K?K(2D) )C+ NN&
-(+*JD@ K2J N+ /C,,D+ ,E)(1K* EKAK1+)+AD -,A +K/C 1+)C,J. F,A )C+ 4.8@ )C+ .JS8
K2J ()D D(1E*(-(+J L+AD(,2@ N+ KJJ KJJ()(L+ 2,(D+ K2J )C+(A ,E)(1K* K1E*()0J+ (D
/C,D+2 K//,AJ(2?*F.
a/ Gna!:'i' 1eri9i6ation
AD D++2 (2 F(?0A+ 4.bf@ )C+ 4.8U EA,L(J+D 10/C M+))+A K2K*FD+D )CK2 )C+ ,)C+A
1+)C,JD -,A K** )C+ LKA(KM*+D K2J K) K** *+L+*D. %C+ .JS8U ?+2+AK**F ,0)E+A-,A1D
M,)C (2-*K)(,2 D/C+1+D. ;)D D(1E*(-(+J L+AD(,2 (D N,AD+ )CK2 )C+ ,A(?(2K* L+AD(,2 M0) (D
/,1EKAKM*+ ), )C+ KJJ()(L+ (2-*K)(,2 P+Z/+E) -,A DE+/(-(/ C01(J()FQ K2J M+))+A )CK2 )C+
10*)(E*(/K)(L+ (2-*K)(,2 D/C+1+ )CK) CKD )C+ N,AD) A+D0*)D (2 K** -(L+ 1+)C,JD.
=,N+L+A@ () DC,0*J M+ 2,)+J )CK) K** )C+ 1+)C,JD CKL+ 1KJ+ K C0?+ K2K*FD(D
(1EA,L+1+2)D /,1EKA+J ), )C+ g/,2)A,* A02` PA+J *(2+ (2 F(?0A+ 4.bYQ. %C0D@ N+ /K2
/,2/*0J+ )CK) )C+ 46%:F N,0*J 2,) N,AW N+** N()C,0) K) *+KD) K//,02)(2? -,A )C+
+--+/)D ,- 1,J+* +AA,AD@ K2J )CK) /,AA+/)(2? 1,J+* M(KD+D (D@ (2 ?+2+AK*@ M+))+A )CK2
,2*F K//,02)(2? -,A )C+(A +--+/)D (2 )C+ D+/,2J 1,1+2) ,- )C+ +2D+1M*+ on tJe
6ondition tJat N+ CKL+ K ?,,J 1+)C,J ), +D)(1K)+ 1,J+* M(KD+D. %C+ +D)(1K)+J M(KD+D
KA+ 2,) ?,,J +2,0?C -,A )C+ D(1E*(-(+J .JS8U ), ,0)E+A-,A1 )C+ KJJ()(L+ (2-*K)(,2
D/C+1+ -,A 1,D) ,- )C+ LKA(KM*+D. =,N+L+A@ )C+ .JS8U ?+2+AK**F M+K)D )C+ KJJ()(L+
(2-*K)(,2. %C+ E+A-,A1K2/+ ,- )C+ 4.8U (D A+1KAWKM*+. ;) ,0)E+A-,A1D )C+ .JS8U (2
IV
K** )C+ -(+*JD )CA,0?C,0) K** EA+DD0A+ *+L+*D +DE+/(K**F K) *,N+A *+L+*D. F,A )C+ X,2K*
N(2J -(+*J@ N+ CKL+ DC,N2 )C(D (D J0+ ), M(KD (2 )C+ D1K** D/K*+@ NC(/C )C+ .JS8U
CK2J*+D *+DD +--(/(+2)*F. F,A )+1E+AK)0A+@ )C+ .JS8U /K2 ,2*F /,AA+/) K D1K** EKA) ,-
)C+ J(0A2K* M(KD.
%, -0A)C+A 02J+AD)K2J NCK) /K0D+D )C+ K2K*FD(D &8S6 J(--+A+2/+ M+)N++2
J(--+A+2) 1+)C,JD@ N+ +ZK1(2+ )C+ K2K*FD(D M(KD -,A +K/C 1+)C,J. S(2/+ M(KD (D K
)CA++TJ(1+2D(,2K* -(+*J@ (2 K DEK)(K* KL+AK?+@ K *KA?+ E,D()(L+ M(KD (2 ,2+ A+?(,2 /,0*J
/K2/+* ,0) K *KA?+ 2+?K)(L+ M(KD (2 K2,)C+A A+?(,2. %, KL,(J )C(D EA,M*+1@ N+ )KW+ )C+
KMD,*0)+ LK*0+ ,- M(KD M+-,A+ )C+ DEK)(K* KL+AK?+ PF(?0A+ 4.2HQ. AD )C+ .JS8U (D
M+))+A )CK2 ()D D(1E*(-(+J L+AD(,2 K2J KJJ()(L+ (2-*K)(,2 (D M+))+A )CK2 )C+ 10*)(E*(/K)(L+
(2-*K)(,2@ N+ /,2/+2)AK)+ ,2 /,1EKA(2? ,2*F )CA++ D/C+1+D3 )C+ 4.8U@ )C+ .JS8U
K2J KJJ()(L+ (2-*K)(,2 K*,2+. F(?0A+ 4.2H DC,ND )CK) )C+ K2K*FD(D M(KD ,- )C+ .JS8U
(D ?+2+AK**F D1K**+A )CK2 )CK) ,- KJJ()(L+ (2-*K)(,2@ NC(*+ )C+ 4.8U K2K*FD+D CKL+
10/C D1K**+A M(KD )CK2 )C+ ,)C+A )N, 1+)C,JD. %C+ M(KD J(--+A+2/+ M+)N++2 1+)C,JD
(D 2+KA*F KD *KA?+ KD )C+ &8S6 J(--+A+2/+ DC,N2 (2 F(?0A+ 4.bf P2,)+ )CK) )C+ E*,))(2?
D/K*+D (2 F(?0A+ 4.bf K2J F(?0A+ 4.2H KA+ )C+ DK1+Q. %C(D (2J(/K)+D )CK) )C+ K2K*FD(D
&8S6 J(--+A+2/+ M+)N++2 J(--+A+2) 1+)C,JD (D ), K *KA?+ +Z)+2) K))A(M0)KM*+ ), )C+(A
KM(*()F ), CK2J*+ 1,J+* M(KD.
II
F(?0A+ 4.bf3 A2K*FD(D &8S6 K) K** EA+DD0A+ *+L+*D (2 )C+ /KD+D ,- )C+ 4.8U PM*K/W
J,))+J *(2+Q@ )C+ .JS8U PM*K/W JKDC+J *(2+Q@ KJJ()(L+ (2-*K)(,2 PM*K/W D,*(J *(2+Q@
D(1E*(-(+J .JS8U P?A++2 *(2+Q K2J 10*)(E*(/K)(L+ (2-*K)(,2 PM*0+ *(2+Q. %C+ -,0A
EK2+*D /,AA+DE,2J ), 0TN(2J -(+*J@ )+1E+AK)0A+ -(+*J@ C+(?C) -(+*J K2J DE+/(-(/
C01(J()F -(+*J@ A+DE+/)(L+*F. %C+ KL+AK?+D KA+ )KW+2 -,A K 1,2)C K-)+A )C+ (2()(K* CK*-T
1,2)C DE(2T0E E+A(,J.
If
F(?0A+ 4.bY3 SK1+ KD )C+ ),ET*+-) EK2+* (2 F(?0A+ 4.bf@ M0) K*D, DC,ND )C+ A+D0*) -,A
)C+ g/,2)A,* A02` PA+J *(2+Q. <+ 2,)+ K?K(2 )CK) (2 K 1,A+ A+K*(D)(/ ,E+AK)(,2K* 1,J+*@
)C+ 2+?K)(L+ +--+/) ,- 1,J+* +AA,AD (D 2,) KD *KA?+ KD (2 )C(D g/,2)A,* A02` K2J K
D(?2(-(/K2) K1,02) ,- (2-*K)(,2 *+KJD ), M+))+A A+D0*)D +L+2 (2 )C+ KMD+2/+ ,- M(KD
/,AA+/)(,2 P+.?.@ SX02F,?C +) K*. 2HHIQ.
IY
F(?0A+ 4.2H3 [*,MK*TKL+AK?+J KMD,*0)+ LK*0+ ,- )C+ J(--+A+2/+ M+)N++2 K2K*FD(D K2J
)C+ NN& g)A0)C` PK2K*FD(D M(KDQ K) K** EA+DD0A+ *+L+*D (2 )C+ /KD+D ,- )C+ 4.8U PM*K/W
J,))+J *(2+Q@ )C+ .JS8U PM*K/W JKDC+J *(2+Q K2J KJJ()(L+ (2-*K)(,2 PM*K/W D,*(J *(2+Q.
%C+ -,0A EK2+*D /,AA+DE,2J ), 0TN(2J -(+*J@ )+1E+AK)0A+ -(+*J@ C+(?C) -(+*J K2J
DE+/(-(/ C01(J()F -(+*J@ A+DE+/)(L+*F. %C+ ?*,MK*TKL+AK?+J KMD,*0)+ M(KD (D /K*/0*K)+J
MF KL+AK?(2? )C+ J(--+A+2/+ M+)N++2 K2K*FD(D K2J NN& ,L+A ,2+ 1,2)C PM(KDQ K) +K/C
1,J+* ?A(J E,(2)@ )C+2 -(2J(2? )C+ KMD,*0)+ LK*0+ -,A )C+ M(KD -(+*JD@ K2J -(2K**F )KW(2?
K DEK)(K* KL+AK?+ ,- )C+D+ KMD,*0)+ LK*0+D ,L+A )C+ NC,*+ ?*,M+.
fH
0/ MN5Jour 9ore6a't 1eri9i6ation
S, -KA N+ CKL+ -,/0D+J ,2 )C+ /,1EKA(D,2D (2 )+A1D ,- )C+ K2K*FD(D K//0AK/F.
=,N+L+A@ )C+ ?,K* ,- J+L+*,E(2? 1,A+ K//0AK)+ K2K*FD+D (D ), (1EA,L+ )C+ DC,A)T)+A1
-,A+/KD)D. <()C(2 K2 (1E+A-+/) 1,J+*@ )C+ DC,A)T)+A1 -,A+/KD) +AA,AD /,1+ -A,1 M,)C
?A,N(2? +AA,AD (2 )C+ (2()(K* /,2J()(,2 K2J 1,J+* J+-(/(+2/(+D. <()C,0) /,AA+/)(2? )C+
1,J+* +AA,AD J0A(2? )C+ -,A+/KD) EA,/+DD@ N+ N,0*J *(W+ ), D++ (- )C+ KJLK2)K?+ ,- ,2+
1+)C,J /K2 M+ A+)K(2+J ,L+A )C+ -,A+/KD) E+A(,J. O)C+AN(D+@ )C+A+ N,0*J M+ 2, M+2+-()
(2 (1EA,L(2? )C+ (2()(K* K2K*FD(D ,2 )C+ DC,A)T)+A1 -,A+/KD)D. F(?0A+ 4.2b DC,ND )C+
?*,MK*TKL+AK?+J 4fTC,0A -,A+/KD) &8S6 K) K** EA+DD0A+ *+L+*D. %C+ KJLK2)K?+ ,-
.JS8U ,L+A KJJ()(L+ (2-*K)(,2 M+/,1+D *+DD ,ML(,0D -,A 1,D) ,- -(+*JD@ M0) A+1K(2D
D(?2(-(/K2) -,A ?+,E,)+2)(K* C+(?C) -(+*JD K) K** *+L+*D. %C+ M(? KJLK2)K?+ ,- )C+ 4.8U
,L+A )C+ ,)C+A )N, 1+)C,JD K*D, J+/A+KD+D J0+ ), )C+ /,2)K1(2K)(,2 ,- )C+ 1,J+*
+AA,AD. =,N+L+A@ () (D D)(** ]0()+ ,ML(,0D K2J D(?2(-(/K2)@ +Z/+E) -,A )C+ X,2K* N(2J
KM,L+ 2HH CBK K2J )C+ C01(J()F KM,L+ IHHCBK.
=+A+ N+ -,/0D+J ,2 )C+ (1EK/) ,- (2()(K* K2K*FD(D ,2 )C+ DC,A)T)+A1 -,A+/KD) K2J
J(J 2,) K))+1E) ), /,AA+/) )C+ 1,J+* +AA,AD J0A(2? )C+ -,A+/KD) EA,/+DD. ;2 A+K*()F@ )C+
*,NTJ(1+2D(,2K* 1+)C,J /K2 M+ 0D+J ), +D)(1K)+ K2J /,AA+/) )C+ DC,A)T)+A1 1,J+*
+AA,AD (2 )C+ -,A+/KD) ECKD+@ KD .K2-,A)C +) K*. P2HHIQ CKL+ J,2+ N()C )C+ SB66.S
1,J+*. %C(D /,AA+/)(,2@ NC(/C (D +KDF ), (1E*+1+2)@ N,0*J *+KJ ), 10/C M+))+A DC,A)T
)+A1 -,A+/KD).
fb
F(?0A+ 4.2b3 4fTC,0A -,A+/KD) &8S6 K) K** EA+DD0A+ *+L+*D (2 )C+ /KD+D ,- )C+ 4.8U
PM*K/W J,))+J *(2+Q@ )C+ .JS8U PM*K/W JKDC+J *(2+Q@ K2J KJJ()(L+ (2-*K)(,2 PM*K/W D,*(J
*(2+Q. %C+ -,0A EK2+*D /,AA+DE,2J ), 0TN(2J -(+*J@ )+1E+AK)0A+ -(+*J@ C+(?C) -(+*J K2J
DE+/(-(/ C01(J()F -(+*J@ A+DE+/)(L+*F. %C+ KL+AK?+D KA+ )KW+2 ,L+A K** -,A+/KD)D D)K)+J
M+)N++2 HHHH \%' b F+MA0KAF bYfI K2J bfHH \%' bc F+MA0KAF bYfI.
f2
4.c S011KAF K2J J(D/0DD(,2
;2 )C(D /CKE)+A N+ JA,EE+J )C+ KDD01E)(,2 ,- K E+A-+/) 1,J+* MF KDD(1(*K)(2?
,MD+ALK)(,2D D(10*K)+J -A,1 N'6BRN'A& &+K2K*FD(D. <()C,0) /,AA+/)(2? 1,J+*
+AA,AD ,A K) *+KD) K//,02)(2? -,A )C+(A +--+/)D@ )C+ E+A-,A1K2/+ ,- )C+ 46%:F ,2 )C+
SB66.S 1,J+* (D E,,A. %C+ +2D+1M*+ DEA+KJ (D gM*(2J` ), 1,J+* +AA,AD KD DC,N2 MF
)C+ -K/) )CK) N+ -,02J +2D+1M*+ DEA+KJ ,- K2 (1E+A-+/) 1,J+* (D D(1(*KA (2 K1E*()0J+
), )CK) ,- K E+A-+/) 1,J+*. AD K A+D0*)@ (2 )C+ EA+D+2/+ ,- 1,J+* +AA,AD@ )C+ MK/W?A,02J
+AA,A +D)(1K)+J -A,1 )C+ +2D+1M*+ DEA+KJ 02J+A+D)(1K)+D )C+ K/)0K* -,A+/KD) +AA,AD
/K0D+J MF M,)C )C+ JF2K1(/K**F +L,*L+J +AA,AD K2J )C+ 1,J+* J+-(/(+2/(+D.
8+)C,JD (1E*+1+2)+J (2 )C(D /CKE)+A ), CK2J*+ 1,J+* +AA,AD (2/*0J+ M,)C
10*)(E*(/K)(L+ (2-*K)(,2 K2J KJJ()(L+ (2-*K)(,2 NC(/C K//,02) -,A 1,J+* +AA,AD MF
+2*KA?(2? )C+ MK/W?A,02J +AA,A LKA(K2/+@ K2J )N, M(KD /,AA+/)(,2 1+)C,JD P.++ K2J
JK S(*LK 1+)C,J K2J *,NTJ(1+2D(,2K* 1+)C,JQ NC(/C +D)(1K)+ )C+ 1,J+* M(KD+D K2J
A+1,L+ )C+1 -A,1 )C+ -,A+/KD) EA(,A ), )C+ K2K*FD(D. %C+ A+D0*)D KA+ D011KA(X+J KD
-,**,ND3
(Q 80*)(E*(/K)(L+ (2-*K)(,2 N()C K D(2?*+ (2-*K)(,2 -K/),A (D N,AD+ )CK2 KJJ()(L+
(2-*K)(,2. <+ 1KF +ZE+/) K M+))+A A+D0*) -,A 10*)(E*(/K)(L+ (2-*K)(,2 (-
KEE*F(2? J(--+A+2) (2-*K)(,2 -K/),AD -,A J(--+A+2) LKA(KM*+D K2J J(--+A+2) KA+KD.
((Q 8,J+* +AA,AD (2/*0J+ 1,J+* M(KD+D K2J DFD)+1T2,(D+. ;2-*K)(,2 1+)C,JD
K//,02) -,A )C+ ),)K* 1,J+* +AA,AD NC(*+ M(KD /,AA+/)(,2 1+)C,JD ,2*F /,AA+/)
1,J+* M(KD+D. %C+ E0A+ M(KD /,AA+/)(,2 D/C+1+D P4.8 K2J .JS8Q ?(L+
N,AD+ A+D0*)D )CK2 )C+ (2-*K)(,2 D/C+1+D.
fd
(((Q A-)+A K//,02)(2? -,A DFD)+1T2,(D+@ )C+ M(KD /,AA+/)(,2 1+)C,JD N()C
(2-*K)(,2 P4.8U K2J .JS8UQ KA+ ?+2+AK**F D0E+A(,A ), K2F ,- )C+ (2-*K)(,2
1+)C,JD. %C+ K2K*FD+D KA+ 1,A+ K//0AK)+ K2J *+DD M(KD+J.
(LQ %C+ .JS8U J,0M*+D )C+ /,D) ,- )C+ K2K*FD(D@ M0) ()D D(1E*(-(+J L+AD(,2 (D
K*1,D) /,D) -A++ -,A 0EJK)(2? )C+ M(KD +D)(1K)+. A*)C,0?C )C+ A+D0*)D -A,1 )C+
D(1E*(-(+J L+AD(,2 KA+ N,AD+ )CK2 )C+ ,A(?(2K* L+AD(,2@ )C+F KA+ /,1EKAKM*+
), )C+ KJJ()(L+ (2-*K)(,2.
LQ %C+ .JS8U A+*(+D ,2 ,MD+ALK)(,2D. AD K A+D0*)@ () (D *+DD +--(/(+2) -,A )C,D+
02,MD+AL+J E,(2)D@ +DE+/(K**F NC+2 M(KD+D KA+ L+AF D1K**TD/K*+. %C+ 4.8U
0D+D NN& P,A ,)C+A A+K2K*FD(DQ K2J SB66.S -,A+/KD)@ M,)C (2 1,J+* DEK/+@
), +D)(1K)+ 1,J+* +AA,AD. %C+A+-,A+@ () (D *+DD K--+/)+J MF )C+ ,MD+ALK)(,2
J+2D()F.
L(Q ;2 )C+ KMD+2/+ ,- K ?,,J M(KD -,A+/KD) 1,J+*@ )C+ .JS8U K(1D ), /,AA+/)
)C+ D*,N*F LKAF(2? M(KD. F,A )C+ -KD)TLKAF(2? M(KD P-,A +ZK1E*+ )C+ J(0A2K*
M(KD (2 )+1E+AK)0A+ -(+*JD K) )C+ *,N+A *+L+*DQ@ () (D KM*+ ), /KE)0A+ )C+ )(1+T
LKAF(2? D(?2K* M0) )C+ /,AA+/)(,2 (D ),, D1K**. #F /,1E0)(2? )C+ 6OFD ,- )C+
M(KD K2,1K*(+D@ )C+ 4.8U (D +--+/)(L+ (2 A+1,L(2? )C+ J(0A2K* M(KD.
L((Q %C+ 4.8U A+D0*)D (2 K JAK1K)(/K**F M+))+A K2K*FD(D )CK2 )C+ .JS8U
+DE+/(K**F K) )C+ *,N+A *+L+*D. %C(D 1KF M+ +ZE*K(2+J MF )C+ A+KD,2D (2 LQ
K2J L(Q. %C+ KJLK2)K?+ (D D)(** D(?2(-(/K2) (2 )C+ 4fTC,0A -,A+/KD).
%C+ SB66.S 1,J+* CKD 10/C *KA?+A +AA,AD )CK2 1,A+ KJLK2/+J ,E+AK)(,2K*
1,J+*D. <()C ,E+AK)(,2K* ['8D@ )C+ K2K*FD(D J(--+A+2/+D M+)N++2 J(--+A+2) 1+)C,JD
f4
N,0*J M+ 10/C D1K**+A. O0A A+D0*)D ,- *,NTJ(1+2D(,2K* +AA,AD +D)(1K)(,2 1KF M+ ),,
,E)(1(D)(/@ D(2/+ (2 ,0A KEE*(/K)(,2D N+ KDD01+ )C+ NN& -(+*J (D K2 KEEA,Z(1K)(,2 ,-
)C+ 02W2,N2 )A0)C K2J 0D+ () ), ?+2+AK)+ )C+ DK1E*+D ,- 1,J+* +AA,AD. ;2 EAK/)(/+@ )C+
NN& -(+*J /,0*J M+ M(KD+J K2J ?+2+AK)(2? ?,,J DK1E*+D ,- 1,J+* +AA,AD (D K
/CK**+2?+ ), )C+ 4.8U. %C+ 1+)C,J N+ CKL+ 0D+J@ J+A(L(2? )C+ M(KD -A,1 VTC,0A
-,A+/KD) +AA,AD (2()(K*(X+J -A,1 K A+K2K*FD(D@ /K2 M+ 0D+J@ K2J K 1,A+ KJLK2/+J
A+K2K*FD(D P+.?.@ 6&AT4H ,A ^&AT2cQ DC,0*J F(+*J K M+))+A DK1E*+ )CK2 )C+ NN&.
A2,)C+A E,DD(M*+ NKF (D ), 0D+ )C+ K2K*FD(D (2/A+1+2)D ,M)K(2+J -A,1 )C+ -,A+/KD)T
K2K*FD(D /F/*+D 0D(2? )C+ DK1+ 1,J+*. ;2 )C(D /KD+@ ()+AK)(,2D (2 )C+ )AK(2(2? E+A(,J KA+
A+]0(A+J (2 ,AJ+A ), ,M)K(2 A+KD,2KM*+ 1,J+* +AA,A DK1E*+D D(2/+ )C+ K//0AK/F ,- )C+
K2K*FD(D K2J )C+ ?,,J2+DD ,- 1,J+* +AA,A DK1E*+D KA+ J+E+2J+2) ,2 +K/C ,)C+A. <+
(2)+2J ), (2L+D)(?K)+ )C(D (J+K K2J ), D++ NC+)C+A )C+ -(2K* 1,J+* +AA,A DK1E*+D K-)+A
/,2L+A?+2/+ KA+ ?,,J +2,0?C ), A+EA+D+2) )C+ )A0+ 1,J+* +AA,AD.
AD -,A )C+ .JS8U N+ CKL+ D++2 () D)A,2?*F A+*(+D ,2 )C+ ,MD+ALK)(,2D. ;2 ,0A
+ZE+A(1+2)D@ ,MD+ALK)(,2D KA+ EA+))F J+2D+@ NC(*+ (2 EAK/)(/+ )C+ M(KD /,AA+/)(,2 (D
+ZE+/)+J ), M+ *+DD +--(/(+2) (2 )C+ ?*,MK* K2K*FD(D DFD)+1 (- AKN(2D,2J+ D,02J(2?D
,2*F KA+ 0D+J. O2+ 1KF KA?0+ )CK) DK)+**()+ ,MD+ALK)(,2D /K2 M+ 0D+J ), KL,(J )C(D
EA,M*+1 D(2/+ )C+(A J+2D()F (D L+AF C(?C. =,N+L+A@ DK)+**()+ AKJ(K2/+ ,MD+ALK)(,2D
)C+1D+*L+D KA+ D0Ma+/) ), M(KD+D J0+ ), +AA,AD (2 )C+ (2D)A01+2) /K*(MAK)(,2 K2J (2 )C+
,MD+ALK)(,2 ,E+AK),A P+.?. =KAA(D K2J :+**F 2HHbQ. ',AA+/)(2? )C+ DK)+**()+ ,MD+ALK)(,2
M(KD+D (D K2,)C+A /CK**+2?(2? KA+K -,A JK)K KDD(1(*K)(,2.
;2 D011KAF@ )C+ E+A-,A1K2/+ ,- )C+ 46%:F /K2 M+ D+A(,0D*F J+?AKJ+J NC+2
0D(2? A+K* ,MD+ALK)(,2D M0) N()C,0) K//,02)(2? -,A 1,J+* +AA,AD. =,N+L+A@ )C+A+ KA+
fc
D+L+AK* 1+)C,JD )CK) /K2 M+ (1E*+1+2)+J ), K//,02) -,A )C+D+ 1,J+* +AA,AD. O- K**
)C+D+ 1+)C,JD@ )C+ *,NTJ(1+2D(,2K* 1+)C,J N()C (2-*K)(,2 P4.8UQ NC+A+ )C+ )(1+T
KL+AK?+J 1,J+* M(KD@ J(0A2K* M(KD K2J D)K)+TJ+E+2J+2) +AA,AD KA+ +D)(1K)+J -A,1 K
*KA?+ 201M+A ,- VTC,0A -,A+/KD) +AA,AD@ ?(L+D )C+ M+D) A+D0*)D.
fV
Chapter 5
Simultaneous estimation of inflation factor and observation
errors within the LETKF
c.b ;2)A,J0/)(,2
;2 /CKE)+A 4@ N+ CKL+ D++2 )C+ (1E,A)K2) A,*+ ,- 10*)(E*(/K)(L+ ,A KJJ()(L+
(2-*K)(,2 (2 )C+ 46%:F@ M0) K*D, +ZE+A(+2/+J )C+ (2/,2L+2(+2/+ ,- 1K20K**F )02(2?
)C+D+ EKAK1+)+AD. =+A+ N+ )+D) )C+ 1+)C,JD ), +D)(1K)+ ,2T*(2+ )C+ (2-*K)(,2 -K/),A.
=,N+L+A@ )C+ +D)(1K)(,2 ,- (2-*K)(,2 A+*(+D ,2 )C+ (2-,A1K)(,2 ,- ,MD+ALK)(,2 +AA,AD
NC(/C ()D+*- (D K W+F /,1E,2+2) (2 )C+ K//0AK/F ,- )C+ A+D0*)(2? K2K*FD(D. ;2 )C(D
/CKE)+A N+ KJKE)(L+*F +D)(1K)+ ,MD+ALK)(,2K* +AA,AD P-,A +K/C )FE+ ,- (2D)A01+2)Q K2J
)C+ (2-*K)(,2 -K/),A -,A )C+ MK/W?A,02J +AA,A D(10*)K2+,0D*F N()C(2 )C+ 46%:F 0D(2?
)C+ 1+)C,J N+ EA,E,D+J (2 D+/)(,2 2.4@ /,2D(J+A(2? )CK) )C+D+ )N, +D)(1K)+D KA+
J+E+2J+2) ,2 +K/C ,)C+A. <+ -(AD) )+D) ,0A 1+)C,J (2 K *,NT,AJ+A 1,J+* )C+2
(1E*+1+2) () (2), K 1,A+ A+K*(D)(/ 1,J+*.
c.2 4,NT,AJ+A 1,J+* A+D0*)D
c.2.b %C+ 4,A+2XTYV 1,J+*
%C+ 4,A+2XTYV 1,J+* P4,A+2X bYYVi 4,A+2X K2J 61K20+*@ bYYfQ (D ?(L+2 MF
OA<A@AAdtdA
iiiii '%%& %'% 2bb Pc.bQ
NC+A+@ K2J )C+ M,02JKAF (D /F/*(/. AD (2 4,A+2X PbYYVQ@ N+ /C,,D+ Nh4H
K2J Fhf.H (2 NC(/C /KD+ )C(D 1,J+* M+CKL+D /CK,)(/K**F. 6]0K)(,2 Pc.bQ (D D,*L+J
@@b Pi "&
fI
N()C K 4)CT,AJ+A &02?+T:0))K D/C+1+ 0D(2? K )(1+ D)+E ,- H.Hb 2,2TJ(1+2D(,2K* 02()D
-,A NC(/C )C+ 4,A+2X DFD)+1 (D /,1E0)K)(,2K**F D)KM*+. 4,A+2X K2J 61K20+* PbYYfQ
CKL+ DC,N2 )CK) K )(1+ (2/A+1+2) ,- H.Hc A,0?C*F /,AA+DE,2JD ), V C,0AD ,- )C+ A+K*
K)1,DEC+A(/ +L,*0)(,2 D, )CK) N+ /C,D+ KD ,0A K2K*FD(D )(1+ D)+E Hc.H&!t .
c.2.2 B+A-+/) 1,J+* +ZE+A(1+2)D
F(AD) N+ )+D) ,0A 1+)C,J (2 )C+ E+A-+/) 1,J+* D/+2KA(, (2 NC(/C )C+
10*)(E*(/K)(L+ (2-*K)(,2 (D 0D+J ), EA+L+2) -(*)+A J(L+A?+2/+ J0+ ), D1K** +2D+1M*+
D(X+. <+ ?+2+AK)+ )C+ g)A0+` D)K)+ MF (2)+?AK)(2? )C+ 4,A+2XTYV 1,J+* -,A 2HHH
K2K*FD(D D)+ED. N,A1K**F J(D)A(M0)+J AK2J,1 2,(D+ N()C D)K2JKAJ J+L(K)(,2 hb (D
)C+2 KJJ+J ), )C+ g)A0)C` ), ?+2+AK)+ )C+ ,MD+ALK)(,2D. <+ KDD(1(*K)+ )C+D+
,MD+ALK)(,2D +L+AF K2K*FD(D /F/*+ 0D(2? )C+ 46%:F N()C bH +2D+1M*+ 1+1M+AD.
F,**,N(2? )C+ A+/,11+2JK)(,2 ,- O)) +) K* 2HH4@ N+ 0D+ K /0),-- MKD+J *,/K*(XK)(,2
N()C K *,/K* EK)/C ! hV NC(/C /,L+AD bd 1,J+* ?A(JD. 4H ,MD+ALK)(,2D KA+ KDD01+J
KLK(*KM*+ K2J *,/K)+J K) 1,J+* ?A(J E,(2)D D, )CK) 2, (2)+AE,*K)(,2 (D A+]0(A+J. S(2/+
)C+ 2,A1K**F J(D)A(M0)+J 2,(D+ (D 02/,AA+*K)+J K2J )C+ +AA,A LKA(K2/+ (D b@ )C+ )A0+
,MD+ALK)(,2 +AA,A 1K)A(Z (D J(K?,2K*@ (.+. .
2o"
IIR && QP2
tot "
%C+ 4,A+2XTYV 1,J+* K2J )C+ 46%:F KA+ )C+2 0D+J ), KDD(1(*K)+ -,A 2HHH
K2K*FD(D )(1+ D)+ED@ M0) A+D0*)D KA+ ,2*F A+E,A)+J -,A )C+ *KD) bHHH D)+ED.
a/ Corre6t!: 'pe6i9ied o0'er1ation 1arian6e
<+ -(AD) KDD01+ )CK) )C+ ,MD+ALK)(,2 +AA,A LKA(K2/+ (D E+A-+/)*F W2,N2@ (.+.@ )C+
DE+/(-(+J LK*0+ (D h hb. ;2 )C(D /KD+ N+ J, 2,) +D)(1K)+ )C+ ,MD+ALK)(,2 QP2
'o" QP2
to"
ff
+AA,AD@ M0) K))+1E) ), +D)(1K)+ ,2T*(2+ )C+ (2-*K)(,2 EKAK1+)+A 0D(2? )C(D /,AA+/)*F
DE+/(-(+J ,MD+ALK)(,2 +AA,A LKA(K2/+. <+ -,02J )CK) )C+ l,MD+AL+Jm (2-*K)(,2 #!o
J(A+/)*F ,M)K(2+J -A,1 D=EF ,A G=EHD=E PD++ D+/)(,2 2.4.b -,A J+)K(*DQ CKD *KA?+
,D/(**K)(,2D K) +K/C K2K*FD(D )(1+ J0+ ), DK1E*(2? ,- ),, -+N ,MD+ALK)(,2D (2 )C(D *,NT
,AJ+A 1,J+*. ;2 ,AJ+A ), KL,(J K2 02A+K*(D)(/K**F *KA?+ DK1E*(2? +AA,A )CK) 1KF ,//0A
K2J KMA0E)*F A0(2 )C+ +D)(1K)(,2@ N+ (1E,D+ A+KD,2KM*+ 0EE+A K2J *,N+A *(1()D (2 )C+
l,MD+AL+Jm (2-*K)(,2 $ @ +.?.@ #!o 2.Hsb.H C!C% o M+-,A+ KEE*F(2? )C+ D(1E*+ D/K*KA :F
D1,,)C(2? EA,/+J0A+ J+D/A(M+J (2 D+/)(,2 2.4.4. %C+ -(2K* +D)(1K)+ ,- ! K-)+A
D1,,)C(2? (D )C+2 0D+J ), (2-*K)+ )C+ MK/W?A,02J +2D+1M*+ DEA+KJ. ;2 K 1,A+ A+K*(D)(/
JK)K KDD(1(*K)(,2 DFD)+1 N()C K *KA?+ 201M+A ,- KLK(*KM*+ ,MD+ALK)(,2D@ <K2? K2J
#(DC,E P2HHdQ CKL+ DC,N2 )C+ l,MD+AL+Jm (2-*K)(,2 #!o /K*/0*K)+J J(A+/)*F -A,1 D=EF
A+1K(2+J N()C(2 K A+KD,2KM*+ AK2?+. ;2 )CK) D()0K)(,2@ )C+A+ (D 2, 2++J ), EA+D/A(M+ K
AK2?+ -,A $ M0) D1,,)C(2? ,- )C+ +D)(1K)+D 1(?C) D)(** M+ J+D(AKM*+. #!o
%KM*+ c.b DC,ND )CK) D=EF K2J G=EHD=E 1+)C,JD EA,J0/+ D(1(*KA A+D0*)D
N()C +D)(1K)+J ! KA,02J H.H4 K2J K2 K2K*FD(D +AA,A ,- KM,0) H.2H. %C+D+ A+D0*)D KA+
]0()+ D(1(*KA ), )C+ M+D) )02+J /,2D)K2) (2-*K)(,2 ,M)K(2+J -A,1 1K2F )02(2? )A(K*D.
%C+ +ZE+A(1+2)D (2 %KM*+ c.b N(** D+AL+ KD K M+2/C1KAW -,A )C+ *K))+A +ZE+A(1+2)D
NC+A+ (D 2,) E+A-+/)*F DE+/(-(+J. 2o"
fY
%KM*+ c.b3 %(1+ 1+K2 ,- KJKE)(L+ (2-*K)(,2 ! K2J )C+ /,AA+DE,2J(2? K2K*FD(D +AA,A@
KL+AK?+J ,L+A )C+ *KD) bHHH D)+ED ,- K 2HHHTD)+E KDD(1(*K)(,2 NC+2 )C+ ,MD+ALK)(,2K*
+AA,A LKA(K2/+ PDE+/(-(+JQ (D E+A-+/)*F W2,N2. F,A /,1EKA(D,2@ )C+ LK*0+ ,- M+D) )02+J
/,2D)K2) (2-*K)(,2 K2J ()D A+D0*)(2? K2K*FD(D +AA,A KA+ K*D, DC,N2.
! 1+)C,J QP
2'o" ! &8S6
D=EF b H.H44 H.2H2
G=EHD=E b H.H42 H.2H2
@tuned< 6on'tant b H.H4V H.2Hb
0/ Rn6orre6t!: 'pe6i9ied o0'er1ation error 1arian6e
;2 A+K*()F N+ J, 2,) +ZK/)*F W2,N )C+ )A0+ LK*0+ ,- )C+ ,MD+ALK)(,2 +AA,A
LKA(K2/+@ K2J )C+ DE+/(-(+J LK*0+ 0D+J (2 )C+ K2K*FD(D (D ,2*F K2 +D)(1K)+. O0A D+/,2J
+ZE+A(1+2) N()C )C+ 4,A+2XTYV 1,J+* (D ), 0D+ K2 +AA,2+,0D*F DE+/(-(+J NC(/C
(D +()C+A ,2+ ]0KA)+A ,A 4 )(1+D )C+ D(X+ ,- )C+ )A0+ @ +]0(LK*+2) ), ,2+TCK*- ,A
)N(/+ )C+ )A0+ ,MD+ALK)(,2K* +AA,A D)K2JKAJ J+L(K)(,2. <()C *KA?+ h4.H@ +L+2 (-
+D)(1K)+J ! (D D(1(*KA ), ()D ,E)(1K* LK*0+ )C+ K2K*FD(D &8S +AA,A (D *KA?+ P%KM*+ c.2Q@
M+/K0D+ )C+ 46%:F ?(L+D 10/C N+(?C) ), )C+ MK/W?A,02J K2J *+DD N+(?C) ), )C+
,MD+ALK)(,2D@ 1KW(2? )C+ ]0K*()F ,- )C+ A+D0*)(2? K2K*FD(D +Z)A+1+*F J+?AKJ+J.
QP2
'o"
QP2
to"
QP2
'o"
AD -,A )C+ /KD+ ,- hH.2c N+ CKL+ 2,)(/+J )C+ +D)(1K)+J CKD M01E+J
(2), )C+ 0EE+AT*(1() H.2 ,- )C+ EA+D/A(M+J AK2?+@
QP2
'o" QP2
to" !
2.Hsb.H C!C% o . <+ /C+/W+J (2
J+)K(* K2J -,02J )C+ l,MD+AL+Jm (2-*K)(,2 #!o K) +K/C D(2?*+ K2K*FD(D )(1+ D)+E (D
K*NKFD *KA?+A )CK2 H.2@ M0) N+ -,A/+J () ), M+ H.2. %C+A+-,A+ (2J++J J(J 2,) #!o
YH
A+EA+D+2) )C+ LK*0+ +D)(1K)+J -A,1 +]0K)(,2 D=EF ,A G=EHD=E. O0A +ZE+A(+2/+
(2J(/K)+D )CK) 2.Hsb.H C!C% o (D K A+KD,2KM*+ AK2?+ ,- ! NC+2 (D /,AA+/)*F
DE+/(-(+J. %C+A+ (D 2, A+KD,2 ), KDD01+ () N(** D)(** M+ N()C(2 )C(D 2,A1K* AK2?+ (2 )C(D
KM2,A1K* +ZE+A(1+2). <()C,0) )C(D /,2D)AK(2)@ N+ ,M)K(2
2o"
! ), M+ I.VI PV.fdQ N()C )C+
+D)(1K)(,2 1+)C,J D=EF PG=EHD=EQ K2J )C+ A+D0*)(2? K2K*FD(D A1D +AA,A ,- H.fH
PH.IYQ 10/C *KA?+ )CK2 )C+ ,E)(1K* LK*0+ ,- H.2.
%KM*+ c.23 %(1+ 1+K2 ,- KJKE)(L+ (2-*K)(,2 EKAK1+)+A ! K2J )C+ A+D0*)(2? K2K*FD(D
+AA,A@ KL+AK?+J ,L+A )C+ *KD) bHHH D)+ED ,- K 2HHH D)+E KDD(1(*K)(,2 (2 )C+ /KD+ )CK) )C+
DE+/(-(+J ,MD+ALK)(,2 LKA(K2/+ (D +()C+A bR4 ,A 4 )(1+D )C+ )A0+ QP2
'o" QP2
to"
! 1+)C,J QP2
'o" ! &8S6
D=EF H.2 H.2V4
G=EHD=E
H.2c H.2 H.2Vd
D=EF H.H4H b.IYH
G=EHD=E
4.H H.HbV b.4dY
6/ Gdapti1e e'ti,ation o9 0otJ tJe in9!ation and tJe o0'er1ation error 1arian6e
<+ CKL+ D++2 )CK) 2+()C+A D=EF 2,A G=EHD=E N,AW NC+2 +D)(1K)(2? )C+
(2-*K)(,2 EKAK1+)+A (- )C+ DE+/(-(+J ,MD+ALK)(,2 +AA,A (2-,A1K)(,2 (D NA,2?. ;2 )C+
)C(AJ +ZE+A(1+2)@ N+ +D)(1K)+ )C+ ,MD+ALK)(,2 LKA(K2/+ K2J (2-*K)(,2 D(10*)K2+,0D*F
MF 0D(2? D=GHD=E K2J D=EF P,A G=EHD=EQ -,**,N+J MF )C+ D(1E*+ :F 1+)C,J.
Yb
<+ D)KA) ,0A +ZE+A(1+2) N()C K2 (2()(K* 1(DDTDE+/(-(/K)(,2 ,- )C+ ,MD+ALK)(,2
+AA,A LKA(K2/+. %KM*+ c.d DC,ND )CK) 2, 1K))+A C,N E,,A*F )C+ (2()(K* DE+/(-(+J
(D P,2+T]0KA)+A ,A -,0A )(1+D )C+ )A0+ Q@ )C+ D=GHD=E 1+)C,J CKD )C+ KM(*()F ),
/,AA+/) (). ;) (D A+1KAWKM*+ )CK) )C+ )(1+ 1+K2 ,- +D)(1K)+J ,L+A )C+ *KD) bHHH
K2K*FD(D D)+E (D +DD+2)(K**F )C+ DK1+ KD )C+ )A0+ . <()C )C+ /,AA+/)+J & 1K)A(Z@ N+
,M)K(2 K A+KD,2KM*+ KJKE)(L+ (2-*K)(,2
QP2
inio"
2o"
" o2
2o"
! NC(/C (D KM,0) H.H4 -,A K** )C+ /KD+D (2 %KM*+
c.d. %C+ A+D0*)(2? K2K*FD(D A1D +AA,AD KA+ K*D, D(1(*KA ), )CK) ,- )C+ M+2/C1KAW. %C+
A+D0*)D KA+ 2,) D+2D()(L+ ), )C+ (2()(K* (2/,AA+/) LK*0+ ,- @ D(2/+ (D ?AKJ0K**F
/,AA+/)+J K2J A+K/C+D ()D g)A0+` LK*0+ K-)+A K )AK2D()(,2 E+A(,J 2, 1K))+A NCK) (2()(K*
LK*0+ (D DE+/(-(+J.
QP2
inio"2o"
<+ CKL+ DC,N2 )CK) )C+ +D)(1K)(,2 ,- )C+ KJKE)(L+ (2-*K)(,2 K*,2+ J,+D 2,) N,AW
N()C (2/,AA+/)*F DE+/(-(+J ,MD+ALK)(,2 +AA,AD. #F +D)(1K)(2? )C+ (2-*K)(,2 K2J
,MD+ALK)(,2 +AA,AD D(10*)K2+,0D*F@ ,0A 1+)C,J CKD )C+ KM(*()F ), A+)A(+L+ M,)C )C+(A
g)A0+` LK*0+D. <+ 2,N /C+/W NC+)C+A D=GHD=E /K2 A+)A(+L+ K /,AA+/) ,MD+ALK)(,2
+AA,A LKA(K2/+ (- )C+ (2-*K)(,2 (D NA,2?*F DE+/(-(+J. FA,1 )C+ EA+L(,0D +ZE+A(1+2)D N+
W2,N )C+ ,E)(1K* (2-*K)(,2 -K/),A (D KM,0) H.H4. ;- N+ -(Z () K2J 02J+ATDE+/(-F () ), M+
H.Hb@ N+ ?+) )C+ +D)(1K)+J hbH.dd@ D0??+D)(2? )C+ +D)(1K)(,2D ,- (2-*K)(,2 -K/),A
K2J ,MD+ALK)(,2 +AA,AD J+E+2J ,2 +K/C ,)C+A. \2*+DD ,2+ ,- )C+1 (D E+A-+/)*F W2,N2
,A K) *+KD) KEEA,Z(1K)+D )C+ g)A0)C`@ N+ CKL+ ), +D)(1K)+ M,)C ,- )C+1 D(10*)K2+,0D*F.
2o"
Y2
%KM*+ c.d3 AD (2 %KM*+ c.2@ M0) KJKE)(L+*F +D)(1K)(2? M,)C )C+ (2-*K)(,2 -K/),A K2J
,MD+ALK)(,2 +AA,A LKA(K2/+
& 1+)C,J ! 1+)C,J QP
2inio" " o
2 ! &8S6
D=EF H.YYY H.H44 H.2H4
G=EHD=E
H.2c b.HHH H.H42 H.2H2
D=EF H.YYf H.H42 H.2H2
D=GHD=E
G=EHD=E
4.H H.YYY H.H4d H.2Hd
c.2.d ;1E+A-+/) 1,J+* +ZE+A(1+2)D
<+ CKL+ )+D)+J ,0A 1+)C,J (2 )C+ 46%:F N()C )C+ D(10*K)+J ,MD+ALK)(,2D K2J
DC,N2 ()D KM(*()F ), A+)A(+L+ )C+ )A0+ ,MD+ALK)(,2 +AA,A LKA(K2/+ K2J )C+ ,E)(1K*
(2-*K)(,2 EKAK1+)+A (2 D0/C K2 (J+K*(X+J DFD)+1. ;2 )C(D D+/)(,2 N+ -,/0D ,2 K 1,A+
A+K*(D)(/ D()0K)(,2 MF (2)A,J0/(2? 1,J+* +AA,AD. &+/K** K** /A()+A(K 0E,2 NC(/C ,0A
1+)C,J (D MKD+J ,2 )C+ KDD01E)(,2 )CK) 1K)A(Z (D
,E)(1K*@ NC(/C (D )C+ /KD+ (- K2J ,2*F (- )C+ DE+/(-(+J 1K)A(Z
bQP %'& RHHPHHPHK %9%9
9P - K2J R (2 ,0A
DFD)+1 K?A++ N()C )C+ )A0+ /,LKA(K2/+D -,A MK/W?A,02J K2J ,MD+ALK)(,2. ;2 )C+ E+A-+/)
1,J+* D/+2KA(,@ )C+ A+]0(A+J (2-*K)(,2 (D K D1K** 201M+A K2J )C+ (2-*K)+J -,A+/KD) +AA,A
/,LKA(K2/+ N()C K A+KD,2KM*+ 201M+A ,- +2D+1M*+ 1+1M+AD 0D0K**F /K2
KEEA,Z(1K)+ N+** )C+ )A0+ MK/W?A,02J +AA,A /,LKA(K2/+@ M0) )C(D (D 2,) )C+ /KD+ -,A K2
(1E+A-+/) 1,J+*. <()C,0) K2 KJJ()(,2K* 1+)C,J -,A 1,J+* +AA,A /,AA+/)(,2@
9e)P(1 !'
Yd
/,LKA(K2/+ (2-*K)(,2 CKD M++2 0D+J ), EA,L(J+ K2 (2/A+KD+ (2 )C+ +2D+1M*+ LKA(K2/+ ),
K//,02) -,A )C+ +--+/) ,- 1,J+* +AA,AD. ;2 )C(D /KD+ )C+ -,A+/KD) +AA,A
/,LKA(K2/+ 1KF 2,) M+ ?,,J +2,0?C ), A+EA+D+2) )C+ )A0+ MK/W?A,02J
+AA,A /,LKA(K2/+. O0A ?,K* C+A+ (D ), )+D) NC+)C+A ,0A ,2T*(2+ +D)(1K)(,2 K*?,A()C1
N(** D)(** N,AW N+** (2 K 1,A+ A+K*(D)(/ D()0K)(,2.
9e
9 )P(1P !'&
a/ Sando, ,ode! error'
F(AD)@ N+ (2L+D)(?K)+ ,0A D/C+1+ (2 )C+ EA+D+2/+ ,- AK2J,1 1,J+* +AA,AD (2
NC(/C )C+ K/)0K* K)1,DEC+A+ (D KDD01+J ), M+CKL+ *(W+ K 2,(DF L+AD(,2 ,- )C+
201+A(/K* -,A+/KD) 1,J+*. %C+ +L,*0)(,2 ,- )C+ g)A0+` K)1,DEC+A+ (D D(10*K)+J MF
KJJ(2? )C+ X+A,T1+K2 AK2J,1 2,(D+ ), )C+ 4,A+2XTYV 1,J+* K) +K/C 1,J+* )(1+ D)+E3
iiiiii OAAAA
dtdA
D# 2''%%& %'% QP 2bb Pc.2Q
NC+A+ Qb@HPs PiD K2J # (D K /,2D)K2) -K/),A. O0A -,A+/KD) 1,J+* (D )C+ D)K2JKAJ
4,A+2XTYV 1,J+* DC,N2 (2 Pc.bQ. ;2 )C(D NKF@ N+ CKL+ (2)A,J0/+J )C+ AK2J,1 1,J+*
+AA,AD.
;2 )C+ E+A-+/) 1,J+* +ZE+A(1+2)D N+ CKL+ D++2 ,0A 1+)C,J (D 2,) D+2D()(L+ ),
)C+ (2()(K**F DE+/(-(+J ,MD+ALK)(,2K* +AA,A LKA(K2/+ K2J )C+ 1+)C,J ), /K*/0*K)+ )C+
l,MD+AL+Jm (2-*K)(,2 EKAK1+)+A. F,A MA+L()F@ N+ ,2*F )+D) ,0A 1+)C,J N()C
hH.2c K2J 0D+ D=EQP2
inio"F 1+)C,J ), +D)(1K)+ )C+ (2-*K)(,2 EKAK1+)+A. S(2/+ 1,A+
02/+A)K(2)(+D KA+ (2L,*L+J (2 )C+ (1E+A-+/) 1,J+* +ZE+A(1+2)D@ N+ (2/A+KD+ )C+
+2D+1M*+ D(X+ -A,1 bH ), 2H.
Y4
%KM*+ c.4 DC,ND )C+ +D)(1K)+J LK*0+D ,- ,MD+ALK)(,2 +AA,A@ KJKE)(L+ (2-*K)(,2
K2J )C+(A A+D0*)(2? K2K*FD(D +AA,AD MF 0D(2? D=GHD=E K2J D=EF D(10*)K2+,0D*F
P/KD+ 'Q (2 )C+ D()0K)(,2 ,- AK2J,1 1,J+* +AA,AD N()C J(--+A+2) K1E*()0J+D. F,A
/,1EKA(D,2@ N+ K*D, +D)(1K)+ ,2T*(2+ )C+ (2-*K)(,2 0D(2? )C+ g)A0+` ,MD+ALK)(,2 +AA,A
LKA(K2/+ P/KD+ #Q ,A 1K20K**F )02+ )C+ DFD)+1 ), -(2J )C+ ,E)(1K* )(1+T/,2D)K2)
(2-*K)(,2 P/KD+ AQ. ;) (D A+1KAWKM*+ )CK) K** )CA++ /KD+D ?(L+ D(1(*KA A+D0*)D. %C+ M(??+A
)C+ 1,J+* +AA,A@ )C+ M(??+A )C+ K2K*FD(D +AA,A K2J )C+ A+]0(A+J (2-*K)(,2 KA+. <C+2 )C+
,MD+ALK)(,2 +AA,A (D E+A-+/)*F W2,N2@ KJKE)(L+ (2-*K)(,2 P/KD+ #Q A+K/C+D K2 K2K*FD(D
+AA,A D(1(*KA ), )CK) -A,1 /,2D)K2) (2-*K)(,2. <()C,0) )C+ /,AA+/) ,MD+ALK)(,2 +AA,A
(2-,A1K)(,2 (2()(K**F@ N+ +D)(1K)+ () ,2T*(2+ ),?+)C+A N()C )C+ +D)(1K)(,2 ,- (2-*K)(,2@
K2J )C+ g)A0+` (D K*D, KEEA,Z(1K)+J P/KD+ 'Q. %C+ +D)(1K)+J (D +DD+2)(K**F )C+
DK1+ KD )C+ g)A0+` LK*0+ ,- b.H NC+2 )C+ K1E*()0J+ ,- )C+ AK2J,1 +AA,AD (D
" o2 " o
2
# h4 K2J
# h2H@ M0) D)(** /*,D+ +2,0?C ), ()D g)A0+` LK*0+ +L+2 N()C # hbHH. %C+ A+D0*)(2?
K2K*FD+D KA+ KD ?,,J KD )C,D+ -A,1 )C+ M+D) )02+J (2-*K)(,2. A** ,- )C+D+ (2J(/K)+ )CK)
)C+ D(10*)K2+,0D*F KJKE)(L+ K*?,A()C1 (D KM*+ ), EA,J0/+ D0//+DD-0* KDD(1(*K)(,2D ,L+A
K N(J+ AK2?+ ,- AK2J,1 1,J+* +AA,AD. 8K20K**F D+KA/C(2? -,A )C+ ,E)(1K* )(1+T
/,2D)K2) (2-*K)(,2 -K/),A P/KD+ AQ A+]0(A+D K /,2D(J+AKM*+ 201M+A ,- ()+AK)(,2D -,A +K/C
LK*0+ ,- # .
Yc
%KM*+ c.43 'KD+ A3 )C+ M+D) )02+J /,2D)K2) (2-*K)(,2 K2J )C+ A+D0*)(2? K2K*FD(D &8S6i
'KD+ #3 )(1+ 1+K2 ,- KJKE)(L+ (2-*K)(,2 PN()C E+A-+/) hbQ K2J )C+ A+D0*)(2?
K2K*FD(D &8S6i 'KD+ '3 )(1+ 1+K2 ,- KJKE)(L+ (2-*K)(,2 K2J ,MD+ALK)(,2 +AA,A@
+D)(1K)+J D(10*)K2+,0D*F ,2T*(2+@ K2J )C+ A+D0*)(2? K2K*FD(D &8S6. 6K/C /KD+ (D
)+D)+J -,A J(--+A+2)
" o2
# @ K1E*()0J+ ,- AK2J,1 1,J+* +AA,AD. &+D0*)D KA+ KL+AK?+J ,L+A
)C+ *KD) bHHH K2K*FD(D D)+ED.
'KD+
A3 -(Z+J hb.H " o2
P)02+JQ /,2D)K2) !
#3 -(Z+J hb.H " o2
KJKE)(L+ !
'3 KJKE)(L+ " o2
KJKE)(L+ !
# ! &8S6 ! &8S6 " o2 ! &8S6
4 H.bb H.2VH H.bHf H.2VH b.HHd H.bHd H.2Vb
2H H.2H H.d4f H.2Hc H.dcH H.YYf H.2H4 H.dcH
bHH H.4H H.4Ib H.dYf H.4I4 b.H2f H.dIH H.4Ic
0/ S:'te,ati6 ,ode! 0ia'
F,A ,0A -(2K* +ZE+A(1+2) N()C )C+ 4,A+2XTYV 1,J+*@ N+ (2)A,J0/+ K DFD)+1K)(/
1,J+* M(KD. ;2 )C+ *(2+KA +D)(1K)(,2 )C+,AF@ MKD(D ,- 1,D) JK)K KDD(1(*K)(,2 D/C+1+D@
M,)C MK/W?A,02J K2J ,MD+ALK)(,2 +AA,A L+/),AD KA+ KDD01+J ), M+ 02M(KD+J. S(2/+ )C(D
(D 2,) )C+ /KD+ (2 A+K*()F@ () N,0*J M+ (J+K* ), +D)(1K)+ K2J D0M)AK/) )C+ M(KD M+-,A+
0D(2? )C+ 1,J+* -,A+/KD) P.++ K2J JK S(*LK bYYf@ #K+W +) K* 2HHV@ .K2-,A)C +) K*.
2HHIQ. =+A+ N+ L(,*K)+ )C+ KDD01E)(,2 )CK) MK/W?A,02J (D 02M(KD+J (2 ,AJ+A ), /C+/W
)C+ M+CKL(,A ,- ,0A 1+)C,J (2 K 1,A+ A+K*(D)(/ D()0K)(,2 N()C 1,J+* M(KD.
YV
<+ ?+2+AK)+ )C+ 1,J+* M(KD KD (2 #K+W +) K* P2HHVQ MF KJJ(2? K /,2D)K2) D(2+
-02/)(,2 ), )C+ -,A/(2? )+A1 (2 )C+ 4,A+2XTYV 1,J+*.
iiiiii OAAAA
dtdA
=# 2''%%& %'% QP 2bb Pc.dQ
NC+A+ Qb2D(2PV.bP
ii
%& E= J+D/A(M+D )C+ DEK)(K* D)A0/)0A+ ,- )C+ 1,J+* M(KD K2J
# J+)+A1(2+D ()D D(X+. ;2 #K+W +) K*. P2HHVQ # hb@ /,AA+DE,2J(2? ), K gVTC,0A` -,A+/KD)
M(KD ,- Qb2D(2PHf.HHc.HQb2D(2PV.bQb2D(2PV.bP
iP
itP
i0i%
&2%
&!%
& EEE . %C(D M(KD
(D A+*K)(L+*F D1K** /,1EKA+J N()C )C+ ,MD+ALK)(,2 2,(D+ Pb.H (2 ,0A +ZE+A(1+2)DQ. =+A+
N+ +ZK1(2+ K N(J+A AK2?+ ,- 1,J+* M(KD MF KEE*F(2? J(--+A+2) /,+--(/(+2)D# . AD (2
+ZE+A(1+2)D -,A AK2J,1 1,J+* +AA,AD N+ K*D, )+D) ,0A 1+)C,J N()C 2H +2D+1M*+
1+1M+AD K2J N()C hH.2c K2J 0D+ D=EQP2
inio"F ), +D)(1K)+ )C+ (2-*K)(,2 EKAK1+)+A.
%KM*+ c.c DC,ND )C+ K2K*FD(D A+D0*)D ,M)K(2+J -A,1 )C+ M+D) )02+J (2-*K)(,2 P/KD+
AQ@ KJKE)(L+ (2-*K)(,2 N()C )C+ g)A0+` ,MD+ALK)(,2 +AA,A LKA(K2/+ P/KD+ #Q@ KJKE)(L+
(2-*K)(,2 K2J KJKE)(L+ ,MD+ALK)(,2 +AA,A LKA(K2/+ P/KD+ 'Q@ (2 )C+ EA+D+2/+ ,- 1,J+*
M(KD. ;) (D /*+KA )CK) 1,J+* M(KD CKD K 1,A+ 2+?K)(L+ +--+/) ,2 )C+ KDD(1(*K)(,2 DFD)+1
)CK2 AK2J,1 1,J+* +AA,A P%KM*+ c.4Q. <C+2 # hb@ /KD+D A@ # K2J ' ?(L+ K D(1(*KA
K2K*FD(D +AA,A. AD # (2/A+KD+D@ )C+ M+D) )02+J (2-*K)(,2 ?+)D )C+ M+D) A+D0*)D. %C+ 1+K2
LK*0+D ,- KJKE)(L+ (2-*K)(,2 (2 /KD+ # KA+ K*NKFD D1K**+A )CK2 )C+ M+D) )02+J (2-*K)(,2@
A+D0*)(2? (2 N,AD+ K2K*FD(D )CK2 )C+ /,2D)K2) (2-*K)(,2 /KD+. AD -,A /KD+ '@ )C+ 1+K2
,- KJKE)(L+ (D D1K**+A )CK2 ()D )A0+ LK*0+. =,N+L+A () (D (2)+A+D)(2? ), D++ )C+ " o2
YI
A+D0*)(2? K2K*FD(D (D K/)0K**F D*(?C)*F M+))+A )CK2 )CK) -A,1 KJKE)(L+ (2-*K)(,2 N()C )C+
)A0+ (2 /KD+ #. " o2
%KM*+ c.c3 AD (2 %KM*+ c.4@ M0) (2 )C+ EA+D+2/+ ,- K /,2D)K2) 1,J+* M(KD N()C J(--+A+2)
K1E*()0J+D P# Q.
'KD+
A3 -(Z+J hb.H " o2
P)02+JQ /,2D)K2) !
#3 -(Z+J hb.H " o2
KJKE)(L+ !
'3 KJKE)(L+ " o2
KJKE)(L+ !
# ! &8S6 ! &8S6 " o2 ! &8S6
b H.dc H.4Hc H.dd2 H.4Hf H.Yc2 H.dIY H.4Hf
d H.fH H.cc4 H.Vcf H.cIH H.Y4f H.Ibf H.cV4
c b.2H H.V2I H.Y4V H.Vdf H.YHH b.HIc H.Vdd
%, M+))+A 02J+AD)K2J )C+ A+D0*)D ,- %KM*+ c.c@ N+ /,1EKA+ )C+ -,A+/KD) +2D+1M*+
DEA+KJ N()C )C+ g)A0+` -,A+/KD) 1+K2 +AA,A P+2D+1M*+ 1+K2 1(20D )C+ )A0+ D)K)+Q
KL+AK?+J ,L+A K** 4H LKA(KM*+D -,A K** )CA++ /KD+D NC+2 1,J+* M(KD D(X+ # hd. %KM*+
c.V DC,ND )CK) )C+ DEK)(K**F KL+AK?+J DEA+KJ K?A++D N+** N()C )C+ -,A+/KD) +AA,A (2 /KD+
# M0) (D *KA?+A )CK2 )C+ -,A+/KD) +AA,A (2 /KD+ A K2J /KD+ '. &+/K** )CK) )C+ (2-*K)(,2
D/C+1+ (2-*K)+D )C+ +2D+1M*+ /,LKA(K2/+ ), KEEA,Z(1K)+ )C+ g)A0+` -,A+/KD) +AA,A
/,LKA(K2/+@ (.+.@ . ;2 )C+ EA+D+2/+ ,- 1,J+* M(KD@ )C(D (1E*(/()*F
KDD01+D )CK) )C+ D)A0/)0A+ ,- 1,J+* M(KD (D )C+ DK1+ KD )C+ JF2K1(/K* ?A,N(2? +AA,A
K2J )C+A+-,A+ /K2 K*D, M+ A+EA+D+2)+J MF )C+ +2D+1M*+ DEA+KJ. ;- )C(D KDD01E)(,2 (D
(2/,AA+/)@ (.+.@ )C+ (2-*K)+J +2D+1M*+ /,LKA(K2/+ (D 2,) ?,,J +2,0?C ), /KE)0A+ )C+ )A0+
9e
9 PP QbP !'&
Yf
-,A+/KD) +AA,A D)A0/)0A+@ )C+D+ +AA,AD *+KJ ), D0M,E)(1K* K2K*FD(D. ;2 ,0A +ZE+A(1+2)D@
)C+ 1,J+* M(KD (D K D(2+T-02/)(,2 (2 DEK/+ K2J /,2D)K2) N()C )(1+. %C(D DE+/(K*
D)A0/)0A+ (D CKAJ ), M+ A+EA+D+2)+J MF )C+ +2D+1M*+ /,LKA(K2/+ . =,N+L+A )C+
KJKE)(L+ (2-*K)(,2 +D)(1K)(,2 D/C+1+ D=E
9eP
F W2,ND 2,)C(2? KM,0) )C+D+ DEK)(K*
A+EA+D+2)K)(L+2+DD +AA,AD D(2/+ () (D ,2*F /,2/+A2+J N()C )C+ )AK/+ ,- /,LKA(K2/+. %C0D
bQP
QPs %%
&! %%
HHPRdd
9e
0o%
0o
%r%r
EA,J0/+D K D(2?*+ LK*0+ ,- (2-*K)(,2 NC(/C (D ,E)(1K* (2 )C+
D+2D+ ,- DEK)(K* KL+AK?+ M0) 2,) -,A )C+ (2J(L(J0K* ,MD+ALK)(,2. %C0D@ )C+ DEK)(K**FT
KL+AK?+J DEA+KJ (2 %KM*+ c.V -,A /KD+ # (D /,2D(D)+2) N()C )C+ -,A+/KD) 1+K2 +AA,A M0)
)C+ A+D0*)(2? K2K*FD(D (D 2,) ,E)(1K*. %C+ )02+J (2-*K)(,2 A+D0*) (D +ZE+/)+J ), M+ )C+
M+D) M+/K0D+ )C+ (2-*K)(,2 -K/),A (D A+E+K)+J*F )02+J (2 )+A1D ,- )C+ A+D0*)(2? K2K*FD(D
+AA,A. %C+ M+D) )02+J A+D0*) ,L+A/,1+D )C+ DEK)(K* A+EA+D+2)K)(L+2+DD +AA,AD MF ,L+AT
(2-*K)(2? )C+ +2D+1M*+ /,LKA(K2/+ ), ?(L+ 1,A+ N+(?C)D ), )C+ ,MD+ALK)(,2D. %C+D+
A+D0*)D KA+ /,2D(D)+2) N()C A2J+AD,2 2HHI NC+A+ K2 KJKE)(L+ (2-*K)(,2 -A,1 K
C(+AKA/C(/K* #KF+D(K2 NKD /,1EKA+J N()C )C+ M+D) )02+J )(1+T/,2D)K2) (2-*K)(,2. O0A
(2)+A+D) C+A+ (D (2 /KD+ ' NC+A+ N+ D(10*)K2+,0D*F +D)(1K)+ M,)C )C+ (2-*K)(,2 K2J )C+
,MD+ALK)(,2K* +AA,A LKA(K2/+. %C(D KEEA,K/C )+2JD ), ,L+A/,1+ )C+ DEK)(K*
A+EA+D+2)K)(L+2+DD +AA,AD (2 )C+ -,A+/KD) +AA,A /,LKA(K2/+ MF M,)C 02J+AT+D)(1K)(2? )C+
,MD+ALK)(,2 +AA,A LKA(K2/+ K2J ,L+AT(2-*K)(2? )C+ +2D+1M*+ /,LKA(K2/+. %C0D@ )C+
+D)(1K)+J ,MD+ALK)(,2 +AA,A LKA(K2/+ (D 2,) ,E)(1K* M0) )C+ K2K*FD(D (D (1EA,L+J
/,1EKA+J N()C /KD+ #. ;2 ,AJ+A ), ?+) )C+ M+D) +D)(1K)(,2 ,- M,)C K2J )C+ (2-*K)(,2
-K/),A@ K2 KJJ()(,2K* 1+)C,J (D A+]0(A+J ), A+1,L+ )C+ 1,J+* M(KD. %C+ A+KJ+A (D
A+-+AA+J ), 'CKE)+A 4.
" o2
YY
%KM*+ c.V3 %(1+ 1+K2 ,- ,MD+ALK)(,2 +AA,A LKA(K2/+ P Q@ KJKE)(L+ (2-*K)(,2 P Q@ )C+
+2D+1M*+ -,A+/KD) 1+K2 A1D +AA,A K2J )C+ +2D+1M*+ -,A+/KD) DEA+KJ (2 )C+ /KD+D ,- A3
M+D) )02+J /,2D)K2) (2-*K)(,2i #3 KJKE)(L+ (2-*K)(,2 +D)(1K)+J N()C )A0+ ,MD+ALK)(,2
+AA,A LKA(K2/+i '3 D(10*)K2+,0D +D)(1K)(,2 ,- M,)C K2J
" o2 !
" o2 ! . &+D0*)D KA+ A+E,A)+J KD
K2 KL+AK?+ ,L+A )C+ *KD) bHHH D)+ED ,- K 2HHHTD)+E KDD(1(*K)(,2.
'KD+ A3 -(Z+J hb.H " o
2
P)02+JQ /,2D)K2) !
#3 -(Z+J hb.H " o2
KJKE)(L+ !
'3 KJKE)(L+ " o2
KJKE)(L+ !
" o2 b.H b.H H.Y4f
! H.fH H.Vcf H.Ibf
6AA,A H.VVY H.VYd H.Vf2
SEA+KJ H.fbd H.I2I H.I44
c.d SB66.S 1,J+* A+D0*)D
;2 )C+ EA+L(,0D D+/)(,2 N+ CKL+ )+D)+J ,0A K*?,A()C1 (2 K *,NT,AJ+A 1,J+*
NC+A+ N+ CKL+ ,2*F ,2+ D+) ,- ,MD+ALK)(,2D N()C ,2+ g)A0+` ,MD+ALK)(,2 +AA,A
LKA(K2/+. ;2 )C(D D+/)(,2 N+ KEE*F ,0A KEEA,K/C ), K 1,A+ A+K*(D)(/ 1,J+*@ KDD(1(*K)(2?
K 201M+A ,- D+)D ,- ,MD+ALK)(,2D. %C+ D(X+ K2J 02() ,- J(--+A+2) D+)D ,- ,MD+ALK)(,2D
/K2 M+ J(--+A+2). %C+ SB66.S 1,J+*@ K2 K)1,DEC+A(/ ?+2+AK* /(A/0*K)(,2 1,J+*
PA['8Q N()C D(1E*(-(+J ECFD(/K* EKAK1+)+A(XK)(,2D (D 0D+J -,A )C(D E0AE,D+. F,A )C+
)(1+ M+(2?@ N+ KA+ /,2/+A2+J N()C K E+A-+/) 1,J+* /,2)+Z). 8,J+* +AA,AD KA+
J(D/0DD+J (2 'CKE)+A 4.
bHH
%C+ ,MD+ALK)(,2D KA+ ,M)K(2+J MF KJJ(2? X+A, 1+K2 2,A1K**F J(D)A(M0)+J 2,(D+
), )C+ g)A0+ D)K)+`@ )C+ )N,T1,2)C (2)+?AK)(,2 ,- )C+ SB66.S 1,J+* -A,1 ^K2 b ), F+M
2f (2 bYf2. %C+ ,MD+ALK)(,2D KA+ KLK(*KM*+ ,2 )C+ 1,J+* ?A(J K) +L+AF 4 ?A(J E,(2)D.
%C+ ,MD+AL+J LKA(KM*+D KA+ X,2K* N(2J Pu Q@ 1+A(J(,2K* N(2J P Q@ )+1E+AK)0A+ P% Q@
DE+/(-(/ C01(J()F P Q K2J D0A-K/+ EA+DD0A+ P Q N()C +AA,A D)K2JKAJ J+L(K)(,2D ,- b
1RD@ b 1RD@ b :@ bH
1
$ 'p
T4 W?RW? K2J bHH EK@ A+DE+/)(L+*F.
<+ J,0M*+ )C+ )A0+ ,MD+ALK)(,2K* +AA,AD ), ?+) ,0A -(AD) ?0+DD ,- )C+
,MD+ALK)(,2K* +AA,AD. <()C(2 )C+ 46%:F@ N+ +D)(1K)+ K2J /,AA+/) )C+D+ (2()(K**F
(2/,AA+/) ,MD+ALK)(,2 +AA,AD +L+AF K2K*FD(D )(1+ D)+E PVTC,0AQ. S(2/+ )C+ LK*0+ K2J
02() -,A J(--+A+2) ,MD+AL+J LKA(KM*+D KA+ K** J(--+A+2)@ N+ +D)(1K)+ )C+ ,MD+ALK)(,2K*
+AA,A LKA(K2/+ -,A +K/C ,MD+AL+J LKA(KM*+ D+EKAK)+*F.
FA,1 )C+ +ZE+A(1+2)D ,- 4,A+2XTYV 1,J+*@ N+ CKL+ D++2 )CK) KD *,2? KD )C+
,MD+ALK)(,2K* +AA,A (D A+/,L+A+J@ N+ /K2 ?+) D(1(*KA A+D0*)D NCK)+L+A N+ 0D+ +]0K)(,2
D=EF ,A G=EHD=E ), +D)(1K)+ )C+ (2-*K)(,2 EKAK1+)+A. %C+A+-,A+ C+A+ N+ N(** ,2*F
)+D) +]0K)(,2 D=EF NC(/C (D 1,A+ N(J+*F 0D+J.
F(?0A+ c.b DC,ND )C+ ,2T*(2+ +D)(1K)+J ,MD+ALK)(,2K* +AA,AD -,A +K/C ,MD+AL+J
LKA(KM*+. %C+ +ZE+A(1+2) D)KA)D -A,1 (2/,AA+/)*F DE+/(-(+J ,MD+ALK)(,2K* +AA,AD N()C 2
1RD -,A u K2J @ 2: -,A % @ 2rbH1 T4 W?RW? -,A $ K2J 2HH BK -,A . A-)+A dH K2K*FD(D
D)+ED@ (.+. KM,0) ,2+ N++W@ )C+ +D)(1K)+J ,MD+ALK)(,2K* +AA,AD KA+ K*A+KJF L+AF /*,D+ ),
)C+(A /,AA+DE,2J(2? )A0+ LK*0+D. O- K** D+)D ,- ,MD+ALK)(,2 +AA,AD@ )+1E+AK)0A+ +AA,A
/,2L+A?+D -KD)+D) P(2 KM,0) 2 JKFDQ. S(2/+ )C+ +D)(1K)(,2 ,- )C+ (2-*K)(,2 -K/),A MF
D=E
'p
F J+E+2JD ,2 )C+ K//0AK/F ,- )C+ DE+/(-(+J ,MD+ALK)(,2 +AA,A /,LKA(K2/+ R @ )C+A+
(D K J+*KF (2 )C+ )(1+ 2++J+J -,A )C+ (2-*K)(,2 -K/),A ), A+K/C K D)KM*F ,E)(1K* LK*0+
bHb
PD,*(J /0AL+ (2 F(?0A+ c.2Q /,1EKA+J ), )C+ /KD+ (2 NC(/C R (D DE+/(-(+J /,AA+/)*F
PJKDC+JTJ,))+J /0AL+ (2 F(?0A+ c.2Q. %C(D JKDC+JTJ,))+J /0AL+ /K2 M+ /,2D(J+A+J KD
)C+ ,E)(1K* /C,(/+ ,- )C+ KJKE)(L+ (2-*K)(,2 K) +K/C )(1+ D)+E@ K2J K-)+A )C+ DE(2T0E
E+A(,J@ )C+ D,*(J /0AL+ -,**,ND )C+ JKDC+JTJ,))+J /0AL+ L+AF N+**. %C(D (2J(/K)+D )CK)
2, 1K))+A C,N E,,A*F )C+ ,MD+ALK)(,2 +AA,A D)K)(D)(/D KA+ W2,N2 (2()(K**F@ KD *,2? KD
N+ +D)(1K)+ K2J /,AA+/) )C(D (2-,A1K)(,2 N+ /K2 ,M)K(2 K ]0()+ ?,,J KJKE)(L+ (2-*K)(,2
-K/),A K2J@ KD K A+D0*)@ ?,,J K2K*FD+D KD N+**. A /,1EKA(D,2 ,- )C+ K2K*FD(D +AA,AD
-A,1 )C+ +ZE+A(1+2) +D)(1K)(2? R N()C )C+ ,2+ (2 NC(/C R (D E+A-+/)*F W2,N2@
DC,ND )CK) ,0A KEEA,K/C -,A +D)(1K)(2? R N,AWD L+AF N+**. A*)C,0?C )C+ &8S +AA,AD
KA+ D*(?C)*F *KA?+A )CK2 )C,D+ -A,1 )C+ E+A-+/) R /KD+@ )C+F KA+ K*A+KJF ]0()+ ?,,J
PF(?0A+ c.dQ.
F(?0A+ c.b3 %(1+ D+A(+D ,- ,2T*(2+ +D)(1K)+J ,MD+ALK)(,2 +AA,AD ,- u @ % @ @ K2J
-,A )C+ -(AD) cH K2K*FD(D )(1+ D)+ED P/,AA+DE,2J(2? ), HHX ^K2 b )CA,0?C HVX ^K2 bd@
bYf2Q
$ 'p
bH2
0 50 100 150 200 250−0.05
0
0.05
0.1
0.15
0.2
0.25
0.3Estimated inflation
Analysis time steps
true Rest R
F(?0A+ c.23 %(1+ D+A(+D ,- +D)(1K)+J (2-*K)(,2 -K/),A@ (2 )C+ /KD+D ,- 0D(2? K E+A-+/)*F
DE+/(-(+J ,MD+ALK)(,2 +AA,A LKA(K2/+ PJKDC+JTJ,))+J *(2+Q K2J 0D(2? K2 (2()(K**F
+AA,2+,0D ,MD+ALK)(,2 +AA,A LKA(K2/+ M0) +D)(1K)(2? () KJKE)(L+*F PD,*(J *(2+Q.
bHd
cHH CBK %+1E+AK)0A+
cHH CBK [+,E,)+2)(K* C+(?C)
F(?0A+ c.d3 %(1+ D+A(+D ,- ?*,MK* KL+AK?+J K2K*FD(D &8S +AA,A ,- cHH CBK
)+1E+AK)0A+ K2J ?+,E,)+2)(K* C+(?C) -,A ^K20KAF K2J F+MA0KAF bYf2 N()C )C+ KJKE)(L+
(2-*K)(,2@ (2 )C+ /KD+D ,- 0D(2? K E+A-+/)*F DE+/(-(+J ,MD+ALK)(,2 +AA,A LKA(K2/+ PA+J
*(2+Q K2J 0D(2? K2 (2()(K**F NA,2? ,MD+ALK)(,2 +AA,A LKA(K2/+ M0) +D)(1K)(2? ()
KJKE)(L+*F P?A++2 *(2+Q.
bH4
c.4 S011KAF
%C+ K//0AK/F ,- K JK)K KDD(1(*K)(,2 DFD)+1 J+E+2JD ,2 KEEA,EA(K)+ D)K)(D)(/D -,A
,MD+ALK)(,2 K2J MK/W?A,02J +AA,AD. F,A )C+ +2D+1M*+ MKD+J :K*1K2 -(*)+A@ )02(2? )C+
(2-*K)(,2 EKAK1+)+A (D +ZE+2D(L+. %C+ ,2T*(2+ +D)(1K)(,2 1+)C,J /K2 ,Ma+/)(L+*F
+D)(1K)+ )C+ (2-*K)(,2 EKAK1+)+A M0) A+]0(A+D )C+ K//0AK)+ (2-,A1K)(,2 ,- ,MD+ALK)(,2K*
+AA,AD. ;2 )C(D D)0JF@ N+ +D)(1K)+ ,MD+ALK)(,2K* +AA,AD K2J )C+ (2-*K)(,2 /,+--(/(+2)
D(10*)K2+,0D*F N()C(2 )C+ 46%:F. %C+ A+D0*)D KA+ D011KA(X+J KD -,**,ND3
(Q %C+ KJKE)(L+ +D)(1K)(,2 ,- )C+ (2-*K)(,2 EKAK1+)+A N()C E+A-+/) ,MD+ALK)(,2
+AA,A LKA(K2/+ EA,J0/+D A+D0*)D )CK) KA+ KD ?,,J KD )C+ M+D) )02+J (2-*K)(,2
LK*0+D. %N, KJKE)(L+ 1+)C,JD@ D=EF K2J G=EHD=E@ ?(L+ D(1(*KA A+D0*)D.
#F /,2)AKD)@ )02(2? P(.+.@ D+KA/C(2? -,A )C+ M+D) )(1+T/,2D)K2) (2-*K)(,2Q
A+]0(A+D A+E+K)(2? 1K2F KDD(1(*K)(,2D.
((Q AJKE)(L+*F +D)(1K)(2? )C+ (2-*K)(,2 EKAK1+)+A K*,2+ J,+D 2,) N,AW N()C,0)
+D)(1K)(2? )C+ ,MD+ALK)(,2K* +AA,AD (- )C+ DE+/(-(+J ,MD+ALK)(,2K* +AA,A
LKA(K2/+ (D 2,) /,AA+/).
(((Q #F +D)(1K)(2? )C+ (2-*K)(,2 -K/),A K2J ,MD+ALK)(,2 +AA,A LKA(K2/+
D(10*)K2+,0D*F@ ,0A 1+)C,J N,AWD E+A-+/)*F (2 )C+ /KD+D ,- E+A-+/) 1,J+* K2J
AK2J,1 1,J+* +AA,AD. %C+ +D)(1K)+J ,MD+ALK)(,2 +AA,A LKA(K2/+D KA+ /*,D+
+2,0?C ), ()D )A0+ LK*0+@ K2J )C+ A+D0*)(2? K2K*FD+D KA+ KD ?,,J KD )C,D+ -A,1
)C+ M+D) )02+J (2-*K)(,2.
(LQ <C+2 )C+ -,A+/KD) 1,J+* CKD DFD)+1K)(/ M(KD@ )C+ M+D) )02+J (2-*K)(,2 ?(L+D )C+
M+D) K2K*FD(D MF ,L+AT(2-*K)(2? )C+ +2D+1M*+ /,LKA(K2/+. AJKE)(L+ (2-*K)(,2
N()C K E+A-+/) ,MD+ALK)(,2 +AA,A LKA(K2/+ A+E,A)D K N,AD+ K2K*FD(D A+D0*). ;- N+
bHc
K*D, +D)(1K)+ ,2T*(2+ )C+ ,MD+ALK)(,2 +AA,A LKA(K2/+@ )C+ +D)(1K)+J LK*0+
02J+AT+D)(1K)+D )C+ )A0+ ,MD+ALK)(,2 +AA,A LKA(K2/+ M0) C+*ED ), (1EA,L+ )C+
K2K*FD(D@ D(2/+ (2 )CK) /KD+ 1,A+ N+(?C) ?,+D ), )C+ ,MD+ALK)(,2D@ NC(/C K/)D ),
A+J0/+ )C+ (1EK/) ,- DFD)+1K)(/ 1,J+* M(KD.
LQ %C+ SB66.S 1,J+* +ZE+A(1+2)D DC,N )CK) )C+ +D)(1K)(,2 ,- ,MD+ALK)(,2
+AA,A LKA(K2/+ (D D0//+DD-0* (- KEE*(+J ), K 1,A+ A+K*(D)(/ C(?CTJ(1+2D(,2
1,J+* ), A+)A(+L+ )C+ )A0+ +AA,A LKA(K2/+ -,A J(--+A+2) )FE+D ,- (2D)A01+2)
D+EKAK)+*F.
bHV
Chapter 6
Conclusions and future directions
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KA+ KLK(*KM*+@ K 10*)(DFD)+1 +2D+1M*+ P:A(DC2K10)( +) K*. 2HHHQ NC+A+ N+ CKL+ K2
+2D+1M*+ -A,1 J(--+A+2) 1,J+*D@ 1KF M+ +ZE+/)+J ), K) *+KD) EKA)(K**F A+EA+D+2) 1,J+*
+AA,AD.
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KJJ()(L+ (2-*K)(,2. %C+ E0A+ M(KD A+1,LK* 1+)C,JD P.JS8 K2J 4.8Q A+1,L+ 1,J+*
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Bibliography
A2J+AD,2@ ^. 4.@ 2HHb3 A2 +2D+1M*+ KJa0D)1+2) :K*1K2 -(*)+A -,A JK)K KDD(1(*K)(,2.
=on/ Tea/ Se1/@ 129@ 2ff4T2YHd.
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-(*)+AD. %e!!u'@ 59A@ 2bHT224.
A2J+AD,2@ ^. 4. K2J S. 4. A2J+AD,2@ bYYY3 A 8,2)+ 'KA*, (1E*+1+2)K)(,2 ,- )C+ 2,2T
*(2+KA -(*)+A(2? EA,M*+1 ), EA,J0/+ +2D+1M*+ KDD(1(*K)(,2D K2J -,A+/KD)D. =on/
Tea/ Se1/U 127, 2I4bw2Icf.
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Se1/@ 131@ Vd4TV42.
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:K*1K2 -(*)+A(2? (2 )C+ EA+D+2/+ ,- 1,J+* M(KD@ %e!!u'@ 58A@ 2YdTdHV.
#(DC,E@ '. =.@ #. ^. 6)C+A),2@ K2J S. ^. 8Ka01JKA@ 2HHb3 AJKE)(L+ DK1E*(2? N()C )C+
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