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UNCORRECTED PROOF
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Contents lists available at ScienceDirect
PH=JL.QKL=EK2AL@HHDA;9LAGFK
journal homepage: http://ees.elsevier.com
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1. Introduction
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UNCORRECTED PROOF
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2. Literature review
''
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D=9<=JK 9;@ K9DH AF<ANA<M9D AF L@= ?JGMH EGN=K >GJO9J< AF L@= >GJE
G> L@= ;@9AF '=9<=JK 9F< >GDDGO=JK LJQ LG MH<9L= L@=AJ HGKALAGF AF L@=
O@GD= K=9J;@ KH9;= $L @9K L@= 9<N9FL9?=K G> KAEHD= KLJM;LMJ= >=O H9J9
E=L=JK 9F< KLJGF? JG:MKLF=KK K 9 J=KMDL E9FQ J=K=9J;@=JK MLADAR= ..
LG J=KGDN= N9JAGMK GHLAEAR9LAGF HJG:D=EK 9F< L@= J=KMDLK 9J= K9LAK>QAF?
K E=FLAGF=< =9JDA=J AF L@= HJG;=KK G> K=9J;@ . E9Q EAKK KGE=
N9DM9:D= 9J=9K G> L@= K=9J;@ KH9;= /@AK H9H=J AFLJG<M;=K L@= MH<9LAF?
KLJ9L=?Q G> .. AFLG L@= . LG EALA?9L= ALK <=X;A=F;Q =>>=;LAN=DQ /@=
MH<9LAF? KLJ9L=?Q G> .. AK L@= ;GJ= H9JL G> L@= .. O@A;@ AK =PLJ9;L=<
9K L@= J=MH<9L= >GJEMD9 G> L@= F=O HGHMD9LAGF $L AK =PH=;L=< L@9L L@=
AL=J9LAN= MH<9LAF? E=L@G< G> .. HD9QK 9 ;JM;A9D JGD= AF . K ;9F :=
K==F .. @9K :==F =PL=FKAN=DQ 9HHDA=< LG HJ9;LA;9D HJG:D=EK 5@9F? =L
9D /@= AFLJG<M;LAGF G> L@AK MH<9LAF? KLJ9L=?Q AK LG KLJ=F?L@=F
L@= ;GFN=J?=F;= KH==< G> L@= :9KA; . =>>=;LAN=DQ HHDQAF? .. LG
KO9JE:9K=< GHLAEAR=JK AK 9 J=D9LAN=DQ HGL=FLA9D AEHJGN=E=FL K;@=E=
UNCORRECTED PROOF
+-5<A2@.9 D=2>@'E?@2:?+6@5==960.@6<;? DDD DDDD
9EGF? J=K=9J;@=JK -=K=9J;@=JK AF 5@9G #M9F? 49F MLA
DAR=< .. LG XF< LOG H9J9E=L=JK G> L@= KMHHGJL N=;LGJ E9;@AF= .1(
AF L@= *=EAKKAGF HJ=<A;LAGF HJG:D=E /@=Q J=;GEE=F<=< L@9L L@=AJ
KLM<Q ;9F 9DKG := =PL=F<=< LG 9<<J=KK EGJ= 9KH=;LK G> 9AJ HGDDMLAGF 9F<
=F=J?Q ;GF;=JFK "MG 5@9F? "M 5@9F? !9F 'A @=F?
"M 'N 'AM 29F? 'AM .@9F? 5@M .M 'A
5@M +9F? @=N9DDA=J 2=A 1G ::9KKA ::9KKA
#=A<9JA 9F< (AJB9DADA HJ=K=FL=< 9 DG?A;9D 9HHJG9;@ :9K=< GF
.. 9:GML L@= =PLJ9;LAGF G> H9J9E=L=JK >GJ H@GLGNGDL9A; ;=DDK AF 9 <M9D
<AG<= EG<=D -ARCDD9@ #9KK9FA=F D@GK=FQ 9F< "MF9K=C9J9F
HJ=K=FL=< 9F AEHJGN=< .. ;9DD=< .. :9K=< GF :AF9JQ A<=9K
9F< EG<AX=< 9J;L9F LJ9FK>GJE9LAGF $F L@9L ;9K= L@= H=J>GJE9F;= G>
.. O9K 9:D= LG := KA?FA>A;9FLDQ J9AK=< ;GEH9J=< LG L@= GJA?AF9D ..
#9K9FA=F 9F< D!=J?9FQ 9HHDA=< .. LG 9 EMDLAJ=?AGF @Q
:JA< J=F=O9:D= HGO=J >GJ 9<BMKLAF? L@J== H9J9E=L=JK G> HJGHGJLAGF9DAF
L=?J9D–<A>>=J=FLA9D +$ ;GFLJGDD=JK LQHA;9D HJG:D=E G> )+ ;GE:AF=<
GHLAEAR9LAGF GF L@= KLJ=F?L@ G> .. O9K HJGHGK=< >GJ L@= EAFAEME ;GE
HD=LAGF LAE= G> K@GH K;@=<MDAF? .MF #M ,A9F 'AM @=
4GMKK=> &9E=D :==< 9F< 4M ;9E= MH OAL@ 9 @Q:JA< GH
LAEAR9LAGF 9HHJG9;@ :9K=< GF .. LG GHLAEAR= L@= DGKK K=FKALANALQ AF<=P
AF H9J9DD=D ;9H9;ALGJK XJKLGJ<=J <A?AL9D <A>>=J=FLA9LGJ OAL@ @A?@ ;GE
HML9LAGF9D =>X;A=F;Q XF= HJ=;AKAGF OA<= :9F<OA<L@ KLJGF? KL9:ADALQ
9F< EAFAEME H@9K= AFXFAL= AEHMDK= J=KHGFK= O9K <=NAK=< MKAF? ..
>GJ L@= H9JL G> =D=;LJG;9J<AG?J9H@A; O9N= ;GEHD=P <=L=;LAGF 9HHDA;9LAGF
)9Q9C .9@9 &9J (9F<9D /@= H9LL=JF KQFL@=KAK G> L@=
;GF>GJE9D 9FL=FF9 9JJ9Q ;GE:AF=< OAL@ .. 9F< 2* ..2* O9K
HJ=K=FL=< :Q +J9:@9C9J 9F< .9LQ9F9J9Q9F9 $FKHAJ=< :Q L@=
9:GN= OGJCK L@= MH<9LAF? KLJ9L=?Q G> .. AK AFLJG<M;=< AFLG . LG AE
HJGN= ALK GHLAEAR9LAGF ;9H9:ADALQ AF 9<N9F;=
+#
"2* AEAL9L=K L@= KG;A9D D=N=D 9F< @MFLAF? :=@9NAGJ G> L@= ?J=Q OGD>
9F< 9;@A=N=K L@= HMJHGK= G> GHLAEARAF? :9K=< GF L@= HJG;=KK G> LJ9;C
AF? =F;AJ;DAF? @MFLAF? 9F< 9LL9;CAF? L@= HJ=Q $F L=JEK G> KGDNAF? L@=
GHLAEAR9LAGF HJG:D=EK L@= ;GFN=J?=F;= KH==< 9F< KGDMLAGF 9;;MJ9;Q G>
"2* H=J>GJE O=DD
$F 9<<ALAGF LG L@= .. MH<9LAF? KLJ9L=?Q "2* MH<9LAF? KLJ9L=?Q AK
9DKG AFLJG<M;=< AFLG . AF L@AK KLM<Q KLM<Q :Q .AF?@ =L 9D AFKHAJ=<
L@= A<=9 .AF?@ .AF?@ $F L@9L OGJC L@=Q HJGHGK=< 9 F=O
9HHJG9;@ ;9DD=< @Q:JA< "2*. AF O@A;@ "2* O9K MLADAR=< LG =PHDGAL
L@= >=9LMJ= KH9;= O@AD= . O9K =EHDGQ=< LG =PHDGJ= L@= K=9J;@ KH9;=
!MJL@=J L@= HMJHGK= G> AFLJG<M;AF? . 9AE=< LG EG<A>Q L@= <AJ=;LAGF
9F< KH==< G> L@= ?J9Q OGDN=K $FKL=9< L@= MH<9LAF? KLJ9L=?Q G> "2* AK
MK=< LG J=MH<9L= L@= HGHMD9LAGF ?=F=J9L=< :9K=< GF . AF GMJ OGJC
$F L@= DAL=J9LMJ= "2* O9K 9DKG MK=< LG := ;GE:AF=< OAL@ GL@=J
KGDN=JK >GJ J=9DARAF? HJ9;LA;9D HJG:D=EK AF 9 EGJ= =>X;A=FL O9Q 9A
=L 9D 'A =L 9D 9 29F? =L 9D 2=A =L 9D
5@9G =L 9D 5@M =L 9D M<9FA 9F< @M
<9K9E9 ;GE:AF=< 9 F=O J9F<GEAR9LAGF L=;@FGDG?Q OAL@ "2* LG KLM<Q
L@= MF;GFKLJ9AF=< L=KL :=F;@E9JC >MF;LAGF 9F< GHLAE9D KGDMLAGFK G> H9J
LA9D <AK;@9J?= AF L@= LJ9FK>GJE=J M<9FA @M<9K9E9 +J9<
@9F -GQ 9F< +9D MLADAR=< "2* LG KGDN= L@= =;GFGEA; DG9<
<AKLJA:MLAGF HJG:D=E :9K=< GF L@= ;GE:AF9LAGF G> GHLAE9D GH=J9LAGF
KLJ9L=?A=K FGN=D E=L@G< G> EMDLAD=N=D L@J=K@GD<AF? :9K=< GF "2*
O9K HJ=K=FL=< AF &@9AJMRR9E9F @9M<@MJQ O@A;@ KM?
?=KL=< L@= FGN=D E=L@G< @9< KLJGF? KL9:ADALQ 9F< @A?@ IM9DALQ G> KGDM
LAGF ;GEH9J=< OAL@ GL@=J (K $:J9@AE D9RAR 9F< 'M HJ=
K=FL=< 9F AEHJGN=< "2* MKAF? >GMJ KLJ9L=?A=K AF;DM<AF? L@= ;@9GLA;
DG?AKLA; E9H L@= GHHGKALAGF:9K=< D=9JFAF? L@= <A>>=J=FLA9D =NGDMLAGF
9D?GJAL@E 9F< L@= <AKJMHLAGF GH=J9LGJ $F L@= 9JLA;D= &9E:GB
&9E:GB HJ=K=FL=< 9F AEHJGN=< 9D?GJAL@E :9K=< GF 9 ;GE:AF9
LAGF G> +.* 9F< "2* >GJ J=KGDNAF? KAF?D=9J=9 MFAL ;GEEALE=FL HJG:
D=E AF L@= =D=;LJA; HGO=J KQKL=E /@= A<=9 G> L@= HJGHGK=< 9HHJG9;@ AK
L@9L L@= HGKALAGF G> L@= XJKL HGHMD9LAGF O9K MH<9L=< =EHDGQAF? L@= +.*
9F< L@=F AL >MJL@=J MH<9L=< MKAF? "2* 29F =L 9D J=9DAR=< 9
F=O >GJE G> E9PAEME HGO=J HGAFL LJ9;CAF? ;GFLJGDD=J OAL@ J9HA< ;GF
N=J?=F;= KH==< 9F< XF= H=J>GJE9F;= L@JGM?@ ;GE:AFAF? .. 9F< "2*
LG AEHJGN= L@= GHLAE9DALQ G> KGDMLAGFK AF L@= GJA?AF9D ..
2BE G45@ 0<;02=@
/@AK H9H=J AFLJG<M;=< L@= '! E=;@9FAKE AFLG . LG >MJL@=J :MAD<
MH ALK DG;9D K=9J;@ ;9H9;ALQ /@= AFLJG<M;=< '! E=;@9FAKE KA?FA>A;9FLDQ
AEHJGN=K :GL@ L@= DG;9D K=9J;@ ;9H9;ALQ G> . 9F< L@= IM9DALQ G> KGDM
LAGFK ?=F=J9L=< :9K=< GF L@= GJA?AF9D H9J9<A?E '! AK 9 J9F<GE O9DC 9H
HDA=< AF 9 N9JA=LQ G> (K LG :GGKL L@= H=J>GJE9F;= G> L@=AJ GHLAEAR9LAGF
;9H9:ADALQ @=F 3M 29F? 5@9G #=A<9JA =L 9D
#M9F? =L 9D 'MG =L 9D 4M 29F? 'A .M 9F< 2M
<=KA?F=< 9 FGN=D '!:9K=< 2* '2* LG GHLAEAR= ;=JL9AF
;GFLJGDD=J H9J9E=L=JK .AEMD9LAGF J=KMDLK K@GO=< L@9L '2* @9< ?GG<
LJ9;CAF? H=J>GJE9F;= 9F< JG:MKLF=KK F=O '! :9K=< GF :AG?=G?J9H@Q
GHLAEAR=J O9K HJGHGK=< 9F< 9HHDA=< LG L@= GHLAE9D <=KA?F G> J=AF>GJ;=<
;GF;J=L= ;9FLAD=N=J J=L9AFAF? O9DD MF<=J K=AKEA; DG9< Q<G?<M
GM 9F< M9F HJ=K=FL=< 9 F=O ;GFLJGD H9J9E=L=J G> L@= K@AH
:GJF= 9MLGE9LA; D9F<AF? KQKL=E MKAF? HA?=GF AFKHAJ=< GHLAEAR=J :9K=<
GF L@= '! E=;@9FAKE /G =F@9F;= L@= H=J>GJE9F;= G> L@= ;D9KKA;9D 9D
?GJAL@E GK .9FLGK G=D@G GJ9 9F< (9JA9FA HM:DAK@=< 9
N9JA9FL G> L@= 9D?GJAL@E L@9L ;GE:AF=< L@= LJMF;9L=< '! E=;@9FAKE
9F< HGHMD9LAGF <AN=JKALQ LG AEHJGN= ;JGKKGN=J 9F< EML9LAGF GH=J9LAGFK
9F< 9NGA< HJ=E9LMJ= ;GFN=J?=F;= .=N=J9D J9F<GE 9D?GJAL@EK :9K=<
GF '!K O=J= HJGHGK=< LG DG;9L= KH9JK= L9J?=LK AF 9 L@J==<AE=FKAGF9D
:GMF<=< =FNAJGFE=FL 9F< =PH=JAE=FL9D J=KMDLK <=EGFKLJ9L=< L@9L L@=
AEHJGN=< E=L@G< ;GMD< <G 9 :=LL=J BG: L@9F FGFJ9F<GE KQKL=E K=9J;@
AF L@= H9H=J &==L=J =L 9D
5@GM 'AF? 9F< 'MG HJGHGK=< 9F AEHJGN=< 2* :9K=<
GF L@= '! KLJ9L=?Q F9E=< '2* >GJ J=KGDNAF? L@= J=9DOGJD< =F?AF==J
AF? HJG:D=EK /@=Q G:K=JN=< L@9L AL G:L9AF=< @A?@=J ;GFN=J?=F;= KH==<
9F< =>X;A=F;Q L@9F L@= GJA?AF9D 2* /G 9<N9F;= L@= =>X;9;Q G> L@=
EGL@Y9E= GHLAEAR9LAGF (!* 'A 5@GM 5@9F? 9F< .GF?
<=N=DGH=< 9F AEHJGN=< '!:9K=< (!* F9E=DQ '(!* '(!* J=9;@=<
LG 9 :=LL=J =IMADA:JAME :=LO==F L@= =PHDGJ9LAGF 9F< =PHDGAL9LAGF ;9H9
:ADALA=K L@9L E9C=K AL >9KL=J 9F< EGJ= JG:MKL ;GEH9J=< LG L@= ;D9KKA;
(!* @=F =L 9D HJ=K=FL=< 9 N9JA9FL G> 2* GF L@= :9KAK G>
'! 9F< ;@9GLA; DG;9D K=9J;@ LG >MJL@=J KLJ=F?L@=F L@= ;9H9;ALQ G> =PHDG
J9LAGF 9F< =PHDGAL9LAGF 3M =L 9D HJ=K=FL=< 9 FGN=D @Q:JA< (!*
OAL@ "9MKKA9F EML9LAGF "( 9M;@Q EML9LAGF ( 9F< '=NQ EML9
LAGF '( >GJ L@= AEHJGN=E=FL G> L@= :9KA; (!* 'MG =L 9D
HJ=K=FL=< 9F AEHJGN=< ?J9KK@GHH=J GHLAEAR9LAGF 9D?GJAL@E "* ;GE
:AF=< OAL@ "( '( 9F< GHHGKALAGF:9K=< D=9JFAF? LG @GD< 9 HJGH=J :9D
9F;= AF ?DG:9D K=9J;@ 9F< DG;9D K=9J;@ #M9F? 9F< !=F? HJ=
K=FL=< 9F AEHJGN=< !* :9K=< GF L@= '! E=;@9FAKE O@A;@ 9AE=< LG
9;@A=N= L@= GHLAEAR9LAGF G> LOG ;JALA;9D H9J9E=L=JK AF L@= KMHHGJL N=;LGJ
E9;@AF= .1( AF <A9?FGKAF? :J=9KL ;9F;=J
3. Components of SGLSCA
'
. AK 9 E=L9@=MJAKLA; 9D?GJAL@E OAL@ 9 E=<AG;J= H=J>GJE9F;= ;J=
9L=< :Q (AJB9DADA $L XJKL ?=F=J9L=K EMDLAHD= AFALA9D J9F<GE ;9F
<A<9L= KGDMLAGFK 9F< J=DA=K GF LJA?GFGE=LJA; EG<=DK LG 9;@A=N= KGE= J9F
<GE BMEHK :=LO==F KAF= 9F< ;GKAF= >MF;LAGFK LG EGN= L@= KO9JE AF L@=
<AJ=;LAGF G> 9 ?DG:9D GHLAEME . 9DKG AFL=?J9L=K EMDLAHD= J9F<GE 9F<
LAE=N9JQAF? H9J9E=L=JK LG @GD< 9 :9D9F;= :=LO==F =PHDGJ9LGJQ 9F< =P
HDGALAN= AF;DAF9LAGFK
$F L@= =PHDGAL9LAGF H@9K= L@= J9F<GE KGDMLAGFK OADD := ;@9F?=< 9L 9
KDGO=J J9L= ;GEH9J=< OAL@ L@GK= AF L@= =PHDGJ9LAGF H@9K= /@= MH<9L=
UNCORRECTED PROOF
+-5<A2@.9 D=2>@'E?@2:?+6@5==960.@6<;? DDD DDDD
>GJEMD9 ;9F := <=K;JA:=< 9K :=DGO
O@=J= AK L@= HGKALAGF G> L@= ;MJJ=FL KGDMLAGF AF L@= <AE=F
KAGF 9L L@= =N9DM9LAGF AK 9 J9F<GE FME:=J AK L@= HG
KALAGF G> L@= L=JEAF9D HGAFL AF L@= <AE=FKAGF 9F< AK 9F 9:KGDML=
N9DM= /@= HMJHGK= G> N9JA9:D= AK LG LJ9FK>GJE LOG <A>>=J=FL K=9J;@
KH9;=K /@AK 9J=9 9HH=9JK AF L@= AFF=J KH9;= G> 9F< GJ AF ALK GML=J
KH9;= 9L J9F<GE MJAF? L@= =N9DM9LAGF AL DAF=9JDQ <=;J=9K=K >JGE LG
LG KLJ=F?L@=F L@= =PHDGJ9LGJQ 9F< =PHDGALAN= D=9FAF?K 9K >GDDGOK
O@=J= AF<A;9L=K L@= ;MJJ=FL =N9DM9LAGF AK L@= E9PAEME FME
:=J G> =N9DM9LAGFK 9F< AK ;GFKL9FL
!MJL@=JEGJ= L@= N9JA9:D= AK 9 J9F<GE FME:=J >GJ MH<9L
AF? L@= F=PL KGDMLAGF AF L@= JA?@L <AJ=;LAGF /@= N9JA9:D= AK 9 J9F<GE
FME:=J >JGE LG O@A;@ 9AEK 9L J9F<GEDQ =F@9F;AF? GJ O=9C
=FAF? L@= AFYM=F;= G> L@= L9J?=L KGDMLAGF GF L@= ;MJJ=FL KGDMLAGF
L D9KL L@= N9JA9:D= 9AEK 9L J9F<GEDQ K=D=;LAF? L@= MH<9L= >GJEMD9 AF
KAF= >MF;LAGF GJ ;GKAF= >MF;LAGF AF I
. AFLJG<M;=K KAF= 9F< ;GKAF= >MF;LAGFK AFLG L@= MH<9L= >GJEMD9
/@9L AK O@Q AL AK ;9DD=< . !A? AF<A;9L=K L@= AFYM=F;=K GF KAF= 9F<
;GKAF= GF L@= F=PL KGDMLAGF O@A;@ AF<A;9L=K L@9L L@= HJGHGK=< =IM9LAGF
<=XF=K 9 KH9;= :=LO==F LOG KGDMLAGFK AF L@= K=9J;@ KH9;= /@= KOAL;@
AF? EG<= G> KAF= 9F< ;GKAF= E9C=K LOG KGDMLAGFK G> L@= =IM9LAGF J=NGDN=
9JGMF< =9;@ GL@=J 9F< MH<9L= AL=J9LAN=DQ $L =FKMJ=K L@= >MDD MK= G> KH9;=
:=LO==F LOG K;@=E=K /G XF< 9 ?DG:9DDQ GHLAE9D KGDMLAGF L@= K=9J;@
KH9;= K@GMD< := AF;DM<=< AF L@= ;MJJ=FL 9J=9 GJ GMLKA<= 9J=9
K K@GOF AF !A? AL <=HA;LK L@= >MF;LAGF9D EG<=D 9>>=;L=< :Q KAF=
9F< ;GKAF= >MF;LAGFK OAL@AF L@= J9F<GE FME:=J AF /@AK X?MJ=
AF<A;9L=K @GO ;@9F?AF? L@= N9DM= G> L@= KAF= 9F< ;GKAF= >MF;LAGF <=L=J
Fig. 1. $EH9;LK G> .AF= 9F< GKAF= AF L@= F=PL HGKALAGF
EAF=K L@= F=PL KL=H G> L@= ;MJJ=FL KGDMLAGF $F L@AK ;9K= L@=J= 9J= LOG
LJ=F<K GF= AK LGO9J< L@= AFF=J <AJ=;LAGF G> L@= ;MJJ=FL K=9J;@ KH9;= 9F<
L@= GL@=J AK AF L@= <AJ=;LAGF G> GMLKA<= KH9;= /@= AEHD=E=FL9LAGF AK MK
AF? <=XFAF? 9 J9F<GE N9JA9:D= >JGE LG π K 9 J=KMDL L@AK E=;@
9FAKE =FKMJ=K >MDD MLADAR9LAGF G> L@= =PHDGJ9LAGF 9F< =PHDGAL9LAGF H@9K=K
LG KGE= =PL=FL
!GJ L@= ?=F=J9D KL=HK G> . AL :=?AFK LG H=J>GJE GHLAEAR9LAGF :9K=<
GF AFALA9DARAF? L@= J9F<GE KGDMLAGFK )=PL L@= GHLAE9D J=KMDL AK J=L9AF=<
KG >9J 9F< J=?9J<=< 9K L@= L9J?=L KGDMLAGF LG MH<9L= GL@=J KGDMLAGFK J=D
9LAN=DQ (=9FO@AD= L@= K=9J;@ KH9;= AK =PHDGJ=< KL=H :Q KL=H MKAF? L@=
>GJEMD9 AF;DM<AF? L@= KAF= 9F< ;GKAF= >MF;LAGFK OAL@ 9 ?J9<M9D AF;J=9K=
G> LAE= 2@AD= L@= =N9DM9LAGF ;GMFL=J <=>9MDLK LG @A?@=J L@9F L@= E9P
AEME FME:=J G> =N9DM9LAGFK . L=JEAF9L=K L@= HJG;=KK G> GHLAEAR9
LAGF /@= HK=M<G;G<= G> . AK K@GOF AF D?GJAL@EK
Algorithm 1. +K=M<G;G<=G>.
$FALA9DAR=9K=LG>K=9J;@9?=FLK,
2@AD=
N9DM9L==9;@K=9J;@9?=FL:9K=<GFL@=G:B=;LAN=>MF;LAGF
0H<9L=L@=:=KLKGDMLAGFG:L9AF=<KG>9J
0H<9L= 9F<
*:L9AFL@=F=PLHGHMD9LAGFNA9 I
-=LMJFL@=:=KLKGDMLAGF9F<HGKALAGF
'' A=1.@6;4 ?@>.@24E
.. MH<9LAF? KLJ9L=?Q AK L@= ;GJ= ;GEHGF=FL G> .. O@A;@ HJ=K=JN=K
L@= 9<N9FL9?=K G> .. $L =PL=F<K L@= K=9J;@ J9F?= F=9J L@= GHLAE9D KG
DMLAGF AEHJGN=K L@= ;9H9:ADALQ G> K=9J;@AF? 9F< KH==<K MH L@= ;GFN=J
?=F;= KH==< /@= >MF<9E=FL9D A<=9 AK L@9L L@= F=PL HGKALAGF AK MH<9L=<
:9K=< GF . 9F< L@=F >MJL@=J MH<9L=< MKAF? .. MH<9LAF? KLJ9L=?Q
!AJKL L@= HGHMD9LAGF MH<9L=< :9K=< GF . AK 9KKA?F=< LG LOG
?JGMHK GF= AK L@= D=9<=J 9F< L@= GL@=J E=E:=JK 9J= >GDDGO=JK /@=
D=9<=J AK J=?9J<=< 9K 9 F=O D=9<=J AF L@= .. MH<9L= KLJ9L=?Q LG ?MA<=
L@= HGHMD9LAGF $F L@= K=9J;@ KH9;= L@= D=9<=J KL9F<K 9L L@= LGH G> L@=
;@9AF 9F< 9<BMKLK L@= HGKALAGF :9K=< GF L@= DG;9LAGF G> L@= >GG< O@AD=
>GDDGO=JK >GDDGO L@= D=9<=J 9F< EGN= LGO9J< L@= >GG< /@= DG;9LAGF G>
L@= MH<9L= >GJEMD9 AK <=K;JA:=< 9K :=DGO
O@=J= AK L@= XJKL HGKALAGF AF L@= =N9DM9LAGF <=FGL=K L@=
:=KL KGDMLAGF AF L@= =N9DM9LAGF :Q >9J E=9FK L@= MHH=J :GMF<
Fig. 2. /@= >MF<9E=FL9D HJAF;AHD= G> .
UNCORRECTED PROOF
+-5<A2@.9 D=2>@'E?@2:?+6@5==960.@6<;? DDD DDDD
G> <AE=FKAGF J=HJ=K=FLK L@= DGO=J :GMF< G> <AE=FKAGF
9F< 9J= J9F<GE FME:=JK
/@= N9JA9:D= AK L@= EGKL NAL9D H9J9E=L=J AF .. MH<9LAF? KLJ9L=?Q
:=;9MK= AL 9;@A=N=K 9 :9D9F;= AF =PHDGJ9LGJQ 9F< =PHDGAL9LAN= L=F<=F;A=K
9K <=XF=< 9K >GDDGOK
O@=J= AK L@= ;MJJ=FL =N9DM9LAGF 9F< AK L@= E9PAEME FME:=J G>
=N9DM9LAGFK
/@= H9J9E=L=J :GL@ 9F< 9J= J9F<GE FME:=JK >JGE LG +9
J9E=L=J <=L=JEAF=K L@= KL=H D=F?L@ LGO9J< L@= L9J?=L KGDMLAGF =9;@
LAE= 9F< <=L=JEAF=K L@= <AJ=;LAGF G> L@= F=PL KGDMLAGF AF;DM<AF? L@=
<AJ=;LAGF G> HGKALAN= AFXFALQ GJ F=?9LAN= AFXFALQ
!GJ MH<9L=K G> >GDDGO=J HGKALAGFK L@= >GDDGOAF? =IM9LAGFK 9J= =E
HDGQ=<
O@=J= K@GOK L@= HGKALAGF G> >GDDGO=J K9DH AF <AE=F
KAGF AK LAE= AK L@= AFALA9D KH==< 9F< O@=J=
.AF;= L@= GHLAEAR9LAGF LAE= AK <=H=F<=FL GF =N9DM9LAGF L@= FME:=J
G> =N9DM9LAGFK AK AF;J=9K=< :Q GF= O@=F 9KK=KKAF? L@= KGDMLAGF 9F< ;GF
KA<=JAF? L@AK >GJEMD9 AK <=XF=< 9K :=DGO
O@=J= 9F< 9J= J=KH=;LAN=DQ L@= HGKALAGF G> L@= MH<9L=< >GD
DGO=JK 9F< L@= HGKALAGF G> L@= >GDDGO=JK :=>GJ= L@=Q :JAF? MHLG<9L= AF
<AE=FKAGF $F K@GJL L@= HK=M<G;G<= G> .. MH<9LAF? KLJ9L=?Q AK
K@GOF :=DGO O@=J= E=9FK L@= FME:=J G> K=9J;@ 9?=FLK
Algorithm 2. +K=M<G;G<=G>..MH<9LAF?KLJ9L=?Q
Input: ,2?@6;.@6<;$<?6@6<;?!.D?A/9/
If
.=L 9F< LG:=J9F<GEFME:=JK:=LO==F9F<
0H<9L=L@=HGKALAGFG>L@=D=9<=J:Q I
Else
0H<9L=L@=HGKALAGFG>L@=>GDDGO=JK:Q I
End If
End For
Output: ,
+# A=1.@6;4 ?@>.@24E
/@= "2* MH<9LAF? KLJ9L=?Q AK L@= ;=FLJ9D H9JL G> "2* O@A;@ HJ=
K=JN=K L@= E=JAL G> "2* /@= HGHMD9LAGF MH<9L=< :9K=< GF . AK 9K
KA?F=< LG LOG ?JGMHK /@= LGH L@J== AF<ANA<M9DK 9J= J=?9J<=< 9K D=9<=JK
9F< L@= J=KL 9K >GDDGO=JK =KA<=K L@=Q 9J= J=?9J<=< 9K L@= L@J== CAF<K
G> OGDN=K AF L@= "2* MH<9L= KLJ9L=?Q
/@= "2* MH<9LAF? KLJ9L=?Q KMHHGJLK L@= =PHDGJ9LGJQ 9F< =PHDGAL9
LAN= H9LL=JFK G> L@AK E=L@G< /@= HJAF;AHD= G> L@AK DG?A; AK LG EAEA; L@=
D=9<=JK@AH @A=J9J;@Q 9F< @MFLAF? E=;@9FAKEK G> L@= >9F;Q ?J=Q OGDN=K
$L <ANA<=K L@= =FLAJ= ?J=Q OGD> HGHMD9LAGF AFLG >GMJ LQH=K F9E=DQ 9DH@9
:=L9 <=DL9 9F< GE=?9 /@= XJKL L@J== D=9<=JK F9E=< 9F< DG;9L=
L@= LGH G> ;@9AFK ;GDD=;LAGF G> E=KK9?=K >JGE =9;@ G> L@= L@J== D=9<
=JK AK MK=< LG ?MA<= L@= GL@=J OGDN=K 9;@ OGD>K HGKALAGF AK MH<9L=<
OAL@ L@= >GDDGOAF? E9L@=E9LA;9D >GJEMD9
$F ?=F=J9D ?J=Q OGDN=K KMJJGMF< L@=AJ >GG< O@=F @MFLAF? /@= >GD
DGOAF? >GJEMD9LAGFK =KL9:DAK@ L@= E9L@=E9LA;9D EG<=D G> L@AK :=@9NAGJ
O@=J= 9J= L@= HGKALAGF N=;LGJK G>
9J= ;G=>X;A=FL N=;LGJK 9F< E=9F L@= <AKL9F;= N=;
LGJK :=LO==F /@= H9J9E=L=J 9 AK DAF=9JDQ D=KK=F=< FME:=J
>JGE LG <MJAF? L@= HJG;=KK G> =N9DM9LAGF 9F< H9J9E=L=JK 9F< 9J=
J9F<GE FME:=JK AF /@= HK=M<G;G<= G> L@= "2* MH<9LAF? KLJ9L
=?Q AK >GJEMD9L=< 9K :=DGO
Algorithm 3+K=M<G;G<=G>"2*MH<9LAF?KLJ9L=?Q
$FHML ,?!.D?
*:L9AFL@=N=;LGJ
*:L9AFL@=N=;LGJKG>
*:L9AFL@=N=;LGJK 9F<
*:L9AFL@=N=;LGJK 9F<
!AF<L@=F=PLHGHMD9LAGFG> ,
End For
Output: ,
2BE G45@ ?@>.@24E
/@= J9F<GEAR9LAGF H@9K= G> GHLAEAR=JK ;9F AEH9;L GF L@= =PHDG
J9LAGF 9F< =PHDGAL9LAGF AF;DAF9LAGFK /@= '! AK 9 J9F<GE E=L@G< OAL@
L@= >=9LMJ= G> J9F<GE O9DC O@A;@ AK MK=< >GJ L@= GHLAEAR9LAGF HJG;=KK
G> L@= (K )GL9:DQ AF 9F MF;=JL9AF =FNAJGFE=FL '! ;9F := :=F=X;A9D
>GJ AEHJGNAF? L@= K=9J;@AF? =>X;A=F;Q /@= KL=H D=F?L@ ?G> '! AK K@GOF
9K >GDDGOK
O@=J= A9F< B9J= <J9OF >JGE FGJE9D <AKLJA:MLAGFK AK 9 ;GFKL9FL
O@A;@ AK =IM9D LG /@9L AK
O@=J=
/@AK <AKLJA:MLAGF G:=QK L@= =PH=;L=< '=NQ <AKLJA:MLAGF >GJ
O@=J= AK L@= KE9DD=KL KL=H $F HJAF;AHD= 9;LM9DDQ ;9F :=
J=?9J<=< 9K 9 K=FKA:D= N9DM= DAC= – -=K=9J;@=K AF<A;9L= L@9L
'! ;9F E9PAEAR= L@= =>X;A=F;Q G> K=9J;@AF? AF 9F MF;=JL9AF =FNAJGF
E=FL K 9 J=KMDL L@= '! E=;@9FAKE AK ;GE:AF=< OAL@ . LG AF;J=9K=
L@= J9F<GEF=KK G> L@= .’K HGHMD9LAGF KG L@9L L@= XJKL LOG MH<9LAF?
UNCORRECTED PROOF
+-5<A2@.9 D=2>@'E?@2:?+6@5==960.@6<;? DDD DDDD
KLJ9L=?A=K 9NGA< >9DDAF? AFLG DG;9D GHLAEAR9LAGF AF <==H K=9J;@ !GJ =P
9EHD= L@= F=O HGHMD9LAGF AK MH<9L=< :9K=< GF . /@=F L@= .. 9F<
"2* MH<9LAF? KLJ9L=?A=K ;GMD< L@=GJ=LA;9DDQ D=9< LG L@= HGKKA:ADALQ G>
KGE= AF<ANA<M9DK KL9?F9LAF? GJ D=9NAF? L@= E9PAEME K=9J;@ J9F?= KM;@
9K KGE= K9DH AF<ANA<M9DK GJ ?J9Q OGD> AF<ANA<M9DK $L @=DHK C==H L@= HGH
MD9LAGF 9DAN= MKAF? L@= '! KLJ9L=?Q LG EGN= AF L9F<=E OAL@ L@=K= LOG J=
F=O9D KLJ9L=?A=K 9F< J=HD9;= AF<ANA<M9DK L@9L @9N= D=>L L@= K=9J;@ RGF= GJ
:=;GE= KL9?F9FL /@= HK=M<G;G<= G> L@= '! KLJ9L=?Q AK 9K :=DGO O@=J=
H9J9E=L=J AK .;GFKL9FL L@9L AK =IM9D LG $L E=9FK L@= AFYM=F;= G>
D=F?L@ ?GF L@= HGHMD9LAGF ,
Algorithm 4. +K=M<G;G<=G>'!KLJ9L=?Q
Input: ,8
.=LH9J9E=L=J /2@.?64:.AB
"=LKL=HD=F?L@ ?G>'!MH<9LAF?KLJ9L=?Q:9K=<GF I
End For
Output: ,
4. Structure of SGLSCA
/@= GJA?AF9D . @9K KGE= J=D9LAN= <AK9<N9FL9?=K DAC= >9DDAF? AFLG
9F GHLAE9D DG;9D KGDMLAGF KDGO ;GFN=J?=F;= =;9MK= KAF= 9F< ;GKAF=
>MF;LAGFK 9J= =EHDGQ=< LG K==C L@= O@GD= K=9J;@ KH9;= 9DL=JF9L=DQ AL
G>L=F J=KMDLK AF EAKKAF? KGE= >JMAL>MD KH9;=K GJ K=9J;@AF? AFKA<= KGE=
KH9;=K J=H=9L=<DQ =KA<=K >GJ KGE= ;GEHD=P GHLAEAR9LAGF HJG:D=EK
. E9Q >9AD LG @GD< <=DA;9L= KL9:ADALQ 9F< >9DD AFLG DG;9D GHLAEME K
H=;A9DDQ O@=F >9;AF? @A?@<AE=FKAGF9D 9F< EMDLAEG<9D >MF;LAGFK L@=
K@GJL;GEAF?K G> . OADD := =PH=JA=F;=< /@=J=>GJ= L@J== KLJ9L=?A=K 9J=
AFLJG<M;=< F9E=DQ .. MH<9LAF? KLJ9L=?Q "2* MH<9LAF? KLJ9L=?Q 9F<
'! KLJ9L=?Q LG 9M?E=FL L@= GN=J9DD ;9H9:ADALQ G> L@= :9KA; . /@= F=O
HGHMD9LAGF G:L9AF=< :9K=< GF . >MJL@=J MH<9L=K :Q O9Q G> .. "2*
9F< '! MH<9LAF? KLJ9L=?Q /@= ?G9D AK LG >MJL@=J =F@9F;= L@= DG;9D 9F<
?DG:9D K=9J;@ ;9H9:ADALQ G> L@= GJA?AF9D .
D20A@6<; <3 ' '
!AJKL L@= GJA?AF9D AFALA9D HGHMD9LAGF AK MH<9L=< :9K=< GF L@= :9KA;
. $F L@9L ;9K= OAL@ ;GFKMEAF? 9 ;=JL9AF FME:=J G> =N9DM9LAGF LAE=K
L@= F=O HGHMD9LAGF AK G:L9AF=< O@A;@ O= ;9DD L@= HGHMD9LAGF G:L9AF=<
:9K=< GF . )=PL L@= F=O HGHMD9LAGF AK <ANA<=< AFLG D=9<=JK 9F<
>GDDGO=JK 2@=F 9<GHLAF? L@= .. MH<9LAF? KLJ9L=?Q L@= D=9<=J AK L@=
:=KL AF<ANA<M9D AF L@= HGHMD9LAGF G:L9AF=< :9K=< GF . /@= D=9<=J
?MA<=K >GDDGO=JK LGO9J< >GG< :9K=< GF L@= MH<9L=< >GJEMD9 G> ..
2@=F 9<GHLAF? L@= "2* MH<9LAF? KLJ9L=?Q L@= D=9<=JK 9J= ;MJJ=FLDQ L@=
LGH L@J== AF<ANA<M9DK AF L@= HGHMD9LAGF G:L9AF=< :9K=< GF . O@A;@
AK 9F< OGDN=K /@J== D=9<=JK ?MA<= >GDDGO=JK LGO9J< >GG< :9K=<
GF L@= MH<9L=< >GJEMD9 G> "2* /@=K= LOG KLJ9L=?A=K 9AE LG >MJL@=J =F
@9F;= L@= =PHDGJ9LAGF ;9H9:ADALQ G> L@= GJA?AF9D . AF L@= K=9J;@ KH9;=
/G >MJL@=J =F@9F;= L@= 9:ADALQ G> . L@= '! KLJ9L=?Q AK AFLJG<M;=< LG
9NGA< >9DDAF? AFLG L@= DG;9D GHLAE9D KGDMLAGF >GJ J9F<GE AF<ANA<M9D O9DC
AF?
2@=F 9<GHLAF? L@= '! KLJ9L=?Q =9;@ AF<ANA<M9D G> L@= HGHMD9LAGF G:
L9AF=< :9K=< GF . LJA=K LG O9DC J9F<GEDQ -=E9JC9:DQ L@J== KLJ9L=
?A=K 9J= H9J9DD=D 9F< AF<=H=F<=FL $F L@9L ;9K= L@J== F=O HGHMD9LAGFK
9J= G:L9AF=< O@A;@ 9J= F9E=< HGHMD9LAGF . " 9F< ' /@= XF9D GH
LAE9D HGHMD9LAGF AK K=D=;L=< :9K=< GF ?J==<Q K=D=;LAGF >GJ L@=K= L@J==
HGHMD9LAGFK L D9KL AL AK J=?9J<=< 9K L@= XJKL ?=F=J9LAGF HGHMD9LAGF G:
L9AF=< :9K=< GF ."'. ."'. G:L9AFK L@= K=;GF< ?=F=J9LAGF G> L@=
HGHMD9LAGF AF L@= K9E= O9Q MJAF? L@= HJG;=KK L@= :=KL KGDMLAGF AK
;GFLAFMGMKDQ MH<9L=< /@= KH=;AX; HJG;=KK G> ?J==<Q K=D=;LAGF AK LG K=
D=;L L@= AF<ANA<M9D OAL@ L@= KE9DD=KL XLF=KK N9DM=K 9K L@= :=KL AF<ANA<
M9D 9L L@= ;MJJ=FL HGKALAGF G> L@= XF9D HGHMD9LAGF !AF9DDQ L@= F=O
HGHMD9LAGF AK J=?9J<=< 9K L@= ;MJJ=FL ?=F=J9LAGF HGHMD9LAGF LG MH<9L=
L@= F=PL?=F=J9LAGF HGHMD9LAGF MFLAD L@= FME:=J G> =N9DM9LAGFK AK =P
@9MKL=<
$F L@AK H9H=J =9;@ L=KL >MF;LAGF AK AF<=H=F<=FLDQ L=KL=< LAE=K
2@=F ."'. H=J>GJEK 9 L=KL GF 9 KH=;AX; L=KL >MF;LAGF L@=J= 9J= 9
LGL9D G> =N9DM9LAGFK L@9L F==< LG := ;GFKME=< $L ;9F :=
CFGOF L@9L L@= FME:=J G> =N9DM9LAGFK AK 9DO9QK ;GFKME=< O@=F =N9DM
9LAF? L@= XLF=KK G> AF<ANA<M9DK AF GF= HGHMD9LAGF K >GJ ."'. L@=J=
9J= LOG HD9;=K O@=J= L@= FME:=J G> =N9DM9LAGFK AK ;GFKME=< *F= AK LG
=N9DM9L= L@= AFALA9D HGHMD9LAGF GJ L@= HJ=NAGMK ?=F=J9LAGF AF L@= AFALA9D
KL9?= G> ."'. 9F< L@= GL@=J AK LG =N9DM9L= L@= . " 9F< ' HGHMD9
LAGFK AF L@= KL9?= G> ?J==<Q K=D=;LAGF /@=J= 9J= AF<ANA<M9DK AF =9;@
HGHMD9LAGF O@A;@ E=9FK L@9L =N9DM9LAGFK 9J= J=IMAJ=< LG ;GFKME= AF
GJ<=J LG =N9DM9L= GF= HGHMD9LAGF $F L@= KL9?= G> =P=;MLAGF G> ."'.
L@= AFALA9D ?=F=J9LAGF HGHMD9LAGF AK MH<9L=< :9K=< GF L@=K= L@J== KLJ9L=
?A=K LG G:L9AF L@= F=PL ?=F=J9LAGF HGHMD9LAGF 9 LGL9D G> =N9DM9LAGFK
9J= ;GFKME=< O@A;@ AK AF;DM<AF? =N9DM9LAGFK G> L@= AFALA9D HGHMD9
LAGF 9F< =N9DM9LAGFK G> . " 9F< ' HGHMD9LAGFK
$F ;GF;DMKAGF >JGE L@= AFALA9D HGHMD9LAGF LG L@= XJKL ?=F=J9LAGF HGH
MD9LAGF ."'. ;GFKME=< 9 LGL9D G> =N9DM9LAGFK !JGE L@= XJKL
?=F=J9LAGF HGHMD9LAGF LG L@= K=;GF< ?=F=J9LAGF HGHMD9LAGF AL 9DKG ;GF
KME=K =N9DM9LAGFK 9F< KG GF +JAE9JADQ .. 9F< "2* MH<9L
AF? KLJ9L=?Q <G=K FGL AFNGDN= L@= =N9DM9LAGF G> KH=;AX; AF<ANA<M9DK KG
L@= FME:=J G> =N9DM9LAGFK AK FGL ;GFKME=< AF LOG KLJ9L=?A=K .H=;A>A
;9DDQ L@= ;MJJ=FL ;GFKMEHLAGF =N9DM9LAGFK 9J= J=KH=;LAN=DQ AFLJG<M;=<
AF L@GK= LOG KLJ9L=?A=K LG G:L9AF L@= H9J9E=L=J AF L@= .. MH<9LAF?
KLJ9L=?Q 9F< L@= H9J9E=L=J AF "2* MH<9LAF? KLJ9L=?Q ."'. KLGHK
ALK OGJC >GJ GF= J9F<GE L=KL G> 9 H9JLA;MD9J >MF;LAGF MFLAD
=N9DM9LAGFK 9J= =P@9MKL=<
>.:2C<>8 <3 ' '
/@= GN=J9DD >J9E=OGJC G> ."'. AK K@GOF AF !A? K K@GOF L@=
;=FLJ9D H9JL G> ."'. DA=K AF L@= AFLJG<M;=< L@J== KLJ9L=?A=K .. 9F<
"2* MH<9LAF? KLJ9L=?A=K 9J= MK=< LG ;GF<M;L 9F AF<=HL@ K=9J;@ AF L@=
KH9;= G> L@= KGDMLAGF 9F< >MJL@=J :GGKL L@= K=9J;@ ;9H9:ADALQ G> L@= 9D
?GJAL@E '! MH<9LAF? KLJ9L=?Q H=J>GJEK 9 J9F<GE K=9J;@ AF L@= K=9J;@
AF? KH9;= LG KLGH L@= 9D?GJAL@E JMFFAF? AFLG L@= DG;9D GHLAEME /@=
HK=M<G;G<= >GJ L@= =FLAJ= >J9E=OGJC AK K@GOF AF D?GJAL@E
K O= CFGO >JGE D?GJAL@E L@= AFALA9DAR=< HGHMD9LAGF AK MH<9L=<
MKAF? L@= GJA?AF9D . 9F< L@=F L@AK HGHMD9LAGF AK >MJL@=J MH<9L=<
:9K=< GF L@= .. "2* 9F< '! MH<9L= KLJ9L=?A=K 9L L@= K9E= LAE= !A
F9DDQ L@J== HGHMD9LAGFK 9J= G:L9AF=< O@A;@ AK F9E=< . " 9F< ' HGH
MD9LAGFK J=KH=;LAN=DQ !AF9DDQ L@= :=KL HGHMD9LAGF AK K=D=;L=< :9K=< GF
?J==<Q K=D=;LAGF 9EGF? L@J== HGHMD9LAGFK /@= :=KL HGHMD9LAGF AK J=
?9J<=< 9K L@= F=PL ?=F=J9LAGF LG KL9JL 9 F=O HJG;=KK G> MH<9LAF? MFLAD
L@= FME:=J G> =N9DM9LAGFK AK =P@9MKL=<
Algorithm 5. +K=M<G;G<=G>."'.
$FALA9DAR9LAGF "!.D?? @ 9/A/
,SDD…D"T 2?@6;.@6<;$<?6@6<;S T 2?@6;.@6<;6@;2??S T
$FALA9DAR=GJA?AF9DHGHMD9LAGF9LXJKL?=F=J9LAGF
N9DM9L=L@=AFALA9DHGHMD9LAGF
.GJLHGHMD9LAGF ,:9K=<GFXLF=KK9F<K9N=AL9K
While ? !.D?
If @
N9DM9L=L@=F=O ,
GE:AF= ,OAL@ ,? 9F<G:L9AFL@=HGHMD9LAGF
.GJL 9F<MH<9L=L@=:=KLKGDMLAGFG:L9AF=<KG>9J
0H<9L= ,?
UNCORRECTED PROOF
+-5<A2@.9 D=2>@'E?@2:?+6@5==960.@6<;? DDD DDDD
Fig. 3. !J9E=OGJC G> ."'.
End If
0H<9L= 9KL@==KLAF9LAGF+GKALAGF9F<0H<9L=L@==KLAF9LAGF!ALF=KK
0H<9L=L@==KLAF9LAGF+GKALAGF9KL@=D=9<=JG>K9DHK
0H<9L=L@= 9KL@=D=9<=JKG>OGDN=K
=XF=L@=N9DM=G>H9J9E=L=J .9F<
For 6 LG)
For 7 LG
=XF=L@=N9DM=G>H9J9E=L=J 9F<
IF
0H<9L=L@=KGDMLAGFMKAF?L@=XJKL=PHJ=KKAGFG> I
Else
0H<9L=L@=KGDMLAGFMKAF?L@=K=;GF<=PHJ=KKAGFG> I
End If
End For
End For
"9AFL@=HGHMD9LAGF.:9K=<GF..MH<9LAF?KLJ9L=?Q
"9AFL@=HGHMD9LAGF":9K=<GF"2*MH<9LAF?KLJ9L=?Q
"9AFL@=HGHMD9LAGF':9K=<GF'!KLJ9L=?Q
JAF?:9;CL@=KGDMLAGFKG>L@=HGHMD9LAGF."9F<'?GAF?GMLKA<=
*:L9AFL@=:=KLHGHMD9LAGF:9K=<GF?J==<QK=D=;LAGF9EGF?L@=HGHMD9LAGF."9F<
'
/9C=L@=:=KLHGHMD9LAGF9KL@=F=PL?=F=J9LAGF
-=?9J<L@=HGHMD9LAGFG>F=PL?=F=J9LAGF9KF=O ,
@@
End While
-=LMJFL@= 2?@6;.@6<;$<?6@6<; 9F< 2?@6;.@6<;6@;2??
<:=A@.@6<;.9 0<:=92D6@E
/@= ;GEHML9LAGF9D ;GEHD=PALQ G> =9;@ @=MJAKLA; 9D?GJAL@E <=L=J
EAF=K @GO DGF? L@= E=L@G< F==<K LG X?MJ= GML L@= XF9D J=KMDL /@=
;GEHML9LAGF9D ;GEHD=PALQ G> L@= HJGHGK=< ."'. AK ;GEHGK=< G> K=N=F
9KH=;LK /@=Q 9J= AFALA9DAR9LAGF XLF=KK =N9DM9LAGF MH<9LAF? G> AF<ANA<
M9DK MH<9LAF? KLJ9L=?Q G> .. MH<9LAF? KLJ9L=?Q G> "2* '! KLJ9L
=?Q 9F< GHLAEME HGHMD9LAGF K=D=;LAGF .AF;= L@= LAE= ;GFKMEHLAGF G>
XLF=KK =N9DM9LAGF <=H=F<K GF L@= KH=;AX; GHLAEAR9LAGF HJG:D=E L@9L
O= 9HHDA=< L@= ;GEHML9LAGF9D ;GEHD=PALQ 9F9DQKAK >G;MK=K GF L@= GL@=J
>GMJ 9KH=;LK /@= ;GEHML9LAGF9D ;GEHD=PALQ G> L@= 9D?GJAL@E LG AFA
LA9DAR= L@= "AF<ANA<M9D AK #" (GJ=GN=J L@= ;GEHML9LAGF9D ;GE
HD=PALQ G> L@= AF<ANA<M9D MH<9LAF? KLJ9L=?Q AF L@= HGHMD9LAGF AK
#( H " #( H " H AF;DM<AF? K==CAF? L@= GHLAE9D KGDMLAGF 9F<
MH<9LAF? L@= HGKALAGF G> AF<ANA<M9DK O@=J= (J=HJ=K=FLK L@= E9PAEME
FME:=J G> =N9DM9LAGFK 9F< J=HJ=K=FLK L@= <AE=FKAGF G> KH=;AX; HJG:
D=EK /@= ;GEHML9LAGF9D ;GEHD=PALQ G> L@= .. MH<9LAF? KLJ9L=?Q 9F<
"2* MH<9LAF? KLJ9L=?Q 9J= :GL@ #( H " H /@= ;GEHML9LAGF9D
;GEHD=PALQ G> L@= '! KLJ9L=?Q AK #( H " L D9KL L@= ;GEHML9LAGF9D
;GEHD=PALQ G> L@= GHLAEME HGHMD9LAGF K=D=;LAGF AK #( H " $F K@GJL
L@= ;GEHML9LAGF9D ;GEHD=PALQ G> L@= GJA?AF9D . AK #) \
( ( H 9F< L@= XF9D ;GEHML9LAGF9D ;GEHD=PALQ G> ."'.
AK #" H (H HH "
5. Experimental results
/@= L=KLK @9N= :==F GJ?9FAR=< AF 9 N=JQ ;GEHJ=@=FKAN= E9FF=J
/@= O@GD= =PH=JAE=FL AK ;9JJA=< GML AF >GMJ 9KH=;LK !AJKL 9 K=JA=K G>
. N9JA9FLK OAL@ <A>>=J=FL MH<9LAF? KLJ9L=?A=K 9J= HJGHGK=< F9E=DQ
."'. .". .'. "'. .. ". 9F< '. /@JGM?@ ;GF
<M;LAF? ;GEH9JAKGFK GF :=F;@E9JC >MF;LAGFK K=D=;L=< >JGE
:=F;@E9JC >MF;LAGFK 9F< $ :=F;@E9JC HJG:D=EK L@=
:=KL . N9JA9FL AK G:L9AF=< /@=F ."'. AK ;GEH9J=< OAL@ GL@=J
;GEH=LALAN= (K AF L@= K9E= =FNAJGFE=FL )=PL L@= HJGHGK=< ."'.
AK 9DKG ;GEH9J=< 9?9AFKL GL@=J KL9L=G>L@=9JL AEHJGN=< . N9JA9FLK
L D9KL L@= ;GEH9JAKGF :=LO==F ."'. OAL@ GL@=J 9<N9F;=< 9D?G
JAL@E AK 9DKG ;GF<M;L=< AF L@AK K=;LAGF DD L@= >GDDGOAF? =PH=JAE=FLK 9J=
;9JJA=< GML MF<=J L@= K9E= =FNAJGFE=FL MKAF? K=9J;@ 9?=FLK LG ;GF
<M;L =N9DM9LAGFK DKG AL AK =KK=FLA9D LG FGL= L@9L =9;@ AF
NGDN=< >MF;LAGF AK AF<=H=F<=FLDQ L=KL=< LAE=K LG EALA?9L= L@= =>>=;LK
G> J9F<GEF=KK
2;05:.>8 3A;0@6<; B.961.@6<;
$F L@AK H9H=J :=F;@E9JC >MF;LAGFK 9J= HA;C=< GML >JGE :=F;@
E9JC >MF;LAGFK 9F< $ :=F;@E9JC >MF;LAGFK O@A;@
UNCORRECTED PROOF
+-5<A2@.9 D=2>@'E?@2:?+6@5==960.@6<;? DDD DDDD
9J= MLADAR=< >GJ :=F;@E9JCAF? L@= =>X;9;Q G> ."'. 9F< GL@=J ;GMFL=J
H9JLK 2= ;@GGK= >MF;LAGFK G> N9JAGMK LQH=K >JGE :=F;@E9JC >MF;
LAGFK (=9FO@AD= >MF;LAGFK G> <A>>=J=FL LQH=K 9J= ;@GK=F >JGE $
:=F;@E9JC >MF;LAGFK /@= KGMJ;= G> >MF;LAGFK K=D=;L=< AK
<=K;JA:=< AF /9:D= !GJ =P9EHD= L@= L=KL >MF;LAGFK ! ! ! !
! 9F< ! 9J= XDL=J=< GML >JGE MFAEG<9D >MF;LAGFK G> :=F;@E9JC
>MF;LAGFK 9F< L=KL >MF;LAGFK ! ! 9F< ! 9J= K=D=;L=< >JGE KAE
HD= EMDLAEG<9D >MF;LAGFK G> $ :=F;@E9JC >MF;LAGFK $L AK
OGJL@ FGLAF? L@9L L@= >GDDGOAF? =PH=JAE=FL AK ;GF<M;L=< :9K=< GF L@=K=
:=F;@E9JC >MF;LAGFK
!GJ L=KL >MF;LAGFK AL ;9F := <ANA<=< AFLG L@J== ;9L=?GJA=K AF;DM<AF?
MFAEG<9D EMDLAEG<9D 9F< XP=<<AE=FKAGF >MF;LAGFK /@= MFAEG<9D
>MF;LAGFK 9K 9F GHLAGF >GJ L@= L=KL=< 9D?GJAL@E @9N= MFAIM= >=9LMJ=K
O@A;@ AK L@9L L@=J= AK GFDQ GF= GHLAE9D N9DM= AF L@= O@GD= KH9;= 9F< FG
DG;9D GHLAE9DALQ '* 0FDAC= L@= MFAEG<9D >MF;LAGFK L@= EMDLAEG<9D
;9K= @9K 9 D9J?= FME:=J G> '* L@9L ;9F AF;J=9K= OAL@ <AE=FKAGF O@A;@
=F9:D=K L@= EMDLAEG<9D ;9K= LG L=KL L@= =PHDGJ9LAGF ;9H9;ALQ G> L@=
E=L@G< 9F< L@= ;9H9:ADALQ G> BMEHAF? GML G> '* =KA<=K L@=J= AK GFDQ
GF= ?DG:9D GHLAE9D KGDMLAGF >GJ L@= XP=<<AE=FKAGF9D 9F< EMDLAEG<9D
>MF;LAGFK .AF;= L@= HJ=NAGMK KGDMLAGF AK J=D9LAN=DQ KE9DD L@= K=9J;@
9?=FL F==<K LG 9<BMKL L@= KL=H KAR= 9<9HLAN=DQ K 9 J=KMDL L@=K= :=F;@
E9JC >MF;LAGFK 9J= ;J=<AL9:D= LG L=KL 9F< E9C= 9 ;GEHJ=@=FKAN= =N9DM9
LAGF G> L@= H=J>GJE9F;= HJG:D=EK :9K=< GF ;=JL9AF 9<<ALAGF9D ;GF<ALAGFK
L@9L ;9F := KGDN=<
/@= FME=JA;9D N9DM=K G> L@= =PH=JAE=FL9D J=KMDLK 9J= 9F9DQR=< AF
LOG 9KH=;LK /@= 9N=J9?= J=KMDLK N? G> L@= GHLAEAR9LAGF >MF;LAGF N9D
M=K 9F< L@= KL9F<9J< <=NA9LAGF .L< 9J= ;@GK=F LG 9KK=KK L@= HGL=F
LA9D G> L@= J=D=N9FL GHLAEAR=JK /@= GHLAE9D KGDMLAGF >GJ =9;@ >MF;LAGF AK
Table 1
=K;JAHLAGF G> L@= :=F;@E9JC >MF;LAGFK
$ !MF;LAGF=IM9LAGF .=9J;@J9F?= *HLAEMEN9DM=
0FAEG<9D>MF;LAGFK
! 6−7
! 6−7
! 6−7
! 6−7
! 6−7
! 6−7
(MDLAEG<9D!MF;LAGFK
! 6−7
! 6−7
! 6−7
! 6−7
!AP=<<AE=FKAGF(MDLAEG<9D
! 6−7
! 6−7
! 67
! 67
0FAEG<9D9F<.AEHD=(MDLAEG<9D!MF;LAGFK
! -GL9L=<#A?@GF<ALAGF=< DDAHLA;!MF;LAGF 6−7
! .@A>L=<9F<-GL9L=<-GK=F:JG;C’K!MF;LAGF 6−7
! .@A>L=<9F<-GL9L=<;CD=Q’K!MF;LAGF 6−7
! .@A>L=<9F<-GL9L=<2=A=JKLJ9KK!MF;LAGF!MF;LAGF 6−7
#Q:JA<!MF;LAGFK
! .@A>L=<9F<-GL9L=<.;@O=>=D’K!MF;LAGF 6−7
! .@A>L=<9F<-GL9L=<&9LKMMJ9!MF;LAGF 6−7
! .@A>L=<9F<-GL9L=<#?:9L!MF;LAGF 6−7
! .@A>L=<9F<-GL9L=< PH9F<=<"JA=O9FC’K+DMK-GK=F:JG;C’K!MF;LAGF 6−7
! .@A>L=<9F<-GL9L=< PH9F<=<.;9[=J’K!MF;LAGF 6−7
! #Q:JA<!MF;LAGF) 6−7
! #Q:JA<!MF;LAGF) 6−7
! #Q:JA<!MF;LAGF) 6−7
! #Q:JA<!MF;LAGF) 6−7
GEHGKALAGF!MF;LAGFK
! GEHGKALAGF!MF;LAGF) 6−7
! GEHGKALAGF!MF;LAGF) 6−7
! GEHGKALAGF!MF;LAGF) 6−7
! GEHGKALAGF!MF;LAGF) 6−7
! GEHGKALAGF!MF;LAGF) 6−7
! GEHGKALAGF!MF;LAGF) 6−7
! GEHGKALAGF!MF;LAGF) 6−7
UNCORRECTED PROOF
+-5<A2@.9 D=2>@'E?@2:?+6@5==960.@6<;? DDD DDDD
E9JC=< AF :GD< AF L@= L9:D= =KA<=K 9 FGFH9J9E=LJA; KL9LAKLA;9D L=KL G>
L@= KA?FA>A;9F;= D=N=D G> L@= 2AD;GPGF KA?F J9FC L=KL AK =EHDGQ=< LG
L=KL O@=L@=J L@= HJGHGK=< 9D?GJAL@E H=J>GJE=< KA?FA>A;9FLDQ :=LL=J L@9F
GL@=JK GJ FGL !MJL@=JEGJ= AL AK OGJL@Q G> FGL= L@9L L@= KQE:GD “
”E=9FK O@=L@=J ."'. AK KMH=JAGJ =IM9D GJ AF>=JAGJ LG GL@=J ;GE
H9JAKGF 9D?GJAL@EK J=KH=;LAN=DQ !AF9DDQ L@= H=J>GJE9F;= G> 9DD L=KL 9D
?GJAL@EK AK E=9KMJ=< :9K=< GF L@= !JA=<E9F L=KL 9K 9 >MJL@=J KL9LAKLA;9D
;GEH9JAKGF L L@= =F< G> L@= L9:D= O= HJGNA<= 9F 9N=J9?= J9FCAF? G>
L@=K= L=KL 9D?GJAL@EK 9K O=DD
Table 2
N=J9?= J9FCAF? G> . N9JA9FLK ;GE:AF=< OAL@ GL@=J (K
-9FC -1
...
."2*
.
..
.+.*
.2*
.(!*
.
.!
(52 0<:=<;2;@ 3<A;1.@6<;
$L AK 9 ?9E=;@9F?AF? H@9K= LG 9F9DQR= L@= AFYM=F;= G> =9;@ =D=
E=FL 9F< MF<=JKL9F<K @GO =9;@ G> L@=E ;GFLJA:ML=K LG L@= ;GF;DM<AF?
H=J>GJE9F;= KL9:ADALQ 9F< ;GKL G> ;GEHML9LAGF 5=F? 'AM 29F?
5=F? 'AM 29F? 3A9G 5@M (9 3A= @=N9DDA=J
2=A $F L@AK K=;LAGF O= 9F9DQR= O@Q .. 9F< "2* 9J= AF
LJG<M;=< AF ."'. "AN=F L@= OA<= N9JA=LQ G> O=DDCFGOF (K O=
XJKL <=XF= L@= :9KA; 9D?GJAL@EK ;GN=J=< AF L@AK H9H=J AFLG 9 J=K=9J;@
K;GH= AF;DM<AF? . "2* .. +.* 2* (!* 9F< ! 2=
AFLJG<M;= =9;@ G> L@=K= 9D?GJAL@EK AFLG . 9F< G:K=JN= L@= XF9D =P
H=JAE=FL9D J=KMDLK /@= KH=;AX; =PH=JAE=FL9D J=KMDLK 9J= K@GOF AF /9:D=
O@=J= ... E=9FK L@= AFLJG<M;LAGF G> .. AF . PH=JAE=FLK
9J= ;9JJA=< GML MF<=J L@= K9E= =FNAJGFE=FL MKAF? K=9J;@ 9?=FLK
LG ;GF<M;L =N9DM9LAGFK K ;9F := K==F AF /9:D= L@= X
F9D J=KMDLK G> . ;GE:AF=< OAL@ .. 9F< "2* 9J= J9FC=< XJKL 9F<
K=;GF< 9F< L@= XF9D 9N=J9?= N9DM=K 9J= 9F< J=
KH=;LAN=DQ DKG !A? K@GOK L@= ;GFN=J?=F;= HDGLK G> L@=K= . N9JA
9FLK GF >MF;LAGFK 9F< /@= GN=J9DD
H=J>GJE9F;= G> . AK J9FC=< L@AJ< :ML L@= ;GFN=J?=F;= KH==< 9F<
L@= XF9D GHLAEAR9LAGF J=KMDL 9J= KLADD AFKM>X;A=FL >GJ L@= MFAEG<9D >MF;
LAGFK ! 9F< L@= EMDLAEG<9D >MF;LAGF ! .. .+.* .2
.(!* . .! 9J= EGJ= DAC=DQ LG >9DD AFLG DG;9D GHLAEAR9LAGF
L@9F ... 9F< ."2* O@A;@ ;9F := K==F >JGE L@= >MF;LAGFK !
! 9F< ! AF !A?
Fig. 4. GFN=J?=F;= ;MJN=K G> . N9JA9FLK ;GE:AF=< OAL@ GL@=J (K GF K=D=;L=< :=F;@E9JC >MF;LAGFK
UNCORRECTED PROOF
+-5<A2@.9 D=2>@'E?@2:?+6@5==960.@6<;? DDD DDDD
$F ;GF;DMKAGF AF DA?@L G> L@= 9:GN= 9F9DQKAK O= >MJL@=J =F@9F;= L@=
=PHDGJ9LAGF ;9H9:ADALA=K G> L@= GJA?AF9D . :9K=< GF AFLJG<M;AF? ..
9F< "2* AFLG . $L AK OGJL@ KL9LAF? L@9L L@=K= LOG KLJ9L=?A=K 9J= AF
<=H=F<=FL 9F< AFLJG<M;=< OAL@GML AFL=J>=JAF? OAL@ =9;@ GL@=J /@AK AK
=NA<=FL AF L@= >9;L L@9L HGHMD9LAGFK G:L9AF=< :9K=< GF . 9J= :=AF? >MJ
L@=J =PHDGJ=< AF <=HL@ L@JGM?@ L@= 9:GN= KLJ9L=?A=K J=KH=;LAN=DQ DKG
LG 9NGA< MFJ=9KGF9:D= K=9J;@ L@= '! KLJ9L=?Q AK AFLJG<M;=< LG 9NGA<
>9DDAF? AFLG 9 DG;9D GHLAEME /@= 9:GN= L@J== KLJ9L=?A=K 9J= AF<=H=F<=FL
G> =9;@ GL@=J =9;@ KLJ9L=?Q ?=F=J9L=K 9 F=O HGHMD9LAGF :9K=< GF L@=
GJA?AF9D . 9F< L@= XF9D HGHMD9LAGF AK G:L9AF=< :9K=< GF L@= ?J==<Q
K=D=;LAGF G> L@= XJKL L@J== HGHMD9LAGFK 2@=F AF<=H=F<=FL AF<ANA<M9DK G>
L@= L@J== KLJ9L=?A=K 9J= ?=F=J9L=< L@= ;MJJ=FL GHLAE9D AF<ANA<M9D AK G:
L9AF=< :9K=< GF L@= O9Q G> ;GEH9JAKGF $F L@AK O9Q =9;@ AF<ANA<M9D AF
L@= XF9D HGHMD9LAGF AK 9F GHLAE9D AF<ANA<M9D =KL9:DAK@=< GF L@J== KLJ9L=
?A=K
(52 0<:=<;2;@ .;.9E?6?
$F .=;LAGF L@J== KLJ9L=?A=K 9J= AFLJG<M;=< AF L@= :9KA; . F9E=<
L@= .. MH<9LAF? KLJ9L=?Q L@= "2* MH<9LAF? KLJ9L=?Q 9F< L@= '! KLJ9L
=?Q /G =N9DM9L= L@= =>>=;LK G> =9;@ KLJ9L=?Q 9F< L@=AJ ;GE:AF9LAGF O=
<=N=DGH=< <A>>=J=FL . N9JA9FLK O@A;@ 9J= K@GOF AF /9:D= 2@=J=
“.”“"”9F< “'”J=KH=;LAN=DQ J=HJ=K=FL “.. MH<9LAF? KLJ9L=?Q”“"2*
MH<9LAF? KLJ9L=?Q”9F< “'! KLJ9L=?Q” $F /9:D= “″K@GOK L@9L .
;GE:AF=K L@AK KLJ9L=?Q 9F< ”″K@GOK L@9L L@= HJGHGK=< KLJ9L=?Q AK FGL
9<GHL=< !GJ AFKL9F;= "'. K@GOK . ;GE:AF=K L@= “"2* MH<9LAF?
KLJ9L=?Q”OAL@ L@= “'! KLJ9L=?Q”OAL@GML “.. MH<9LAF? KLJ9L=?Q”
/@= H=J>GJE9F;= G> . N9JA9FLK AK L=KL=< MKAF? :=F;@E9JC
>MF;LAGFK !GJ 9 >9AJ ;GEH9JAKGF L@= H9J9E=L=JK ;GEEGFDQ MK=< AF L@=
=PH=JAE=FL 9J= K=L 9K <=K;JA:=< 9:GN= 9F< L@= <AE=FKAGF O= K=D=;L AK
=KA<=K O= MLADAR=< L@= !JA=<E9F L=KL LG =P9EAF= L@= 9N=J9?= J9FC
AF? N9DM=K G> L@= AFNGDN=< 9D?GJAL@EK LG >MJL@=J AFN=KLA?9L= L@= <A>>=J
=F;=K :=LO==F L@= N9JAGMK 9HHJG9;@=K ;;GJ<AF? LG L@= J=KMDL AF /9:D=
AL AK J9L@=J ;D=9J L@9L L@= :9KA; . OAL@ L@J== KLJ9L=?A=K 9L L@= K9E=
LAE= @9K L@= KE9DD=KL 9N=J9?= N9DM= 9F< J9FCK XJKL 9EGF? L@=E /@MK
Table 3
19JAGMK . N9JA9FLK OAL@ L@J== KLJ9L=?A=K
. " '
..
..
".
'.
.".
.'.
"'.
."'.
Table 4
N=J9?= J9FCAF? N9DM=K G> N9JAGMK . N9JA9FLK
-9FC -1
."'. 1 2.058823
.'.
.".
"'.
..
".
'.
.
AL 9DKG AF<A;9L=K L@9L ."'. H=J>GJEK L@= :=KL AF J=KGDNAF? L@=K= :=F;@
E9JC >MF;LAGFK ;GEH9J=< OAL@ GL@=J N9JA9FLK
/G K@GO L@= KMH=JAGJALQ G> ."'. AFLMALAN=DQ ;GFN=J?=F;= ;MJN=K G>
."'. .'. .". "'. .. ". '. 9F< . >GJ KGE=
:=F;@E9JCK 9J= G>>=J=< AF !A? K K@GOF AL =FKMJ=K L@9L ."'.
@9K L@= :=KL ;GFN=J?=F;= H=J>GJE9F;= AF J=9DARAF? L@= ! ! ! !
! ! ! ! 9F< ! !GJ ! 9F< ! AL @9K 9 <GEAF9FL L=F
<=F;Q LG ;GFN=J?= IMA;CDQ DL@GM?@ AL AK KDA?@LDQ OGJK= L@9F "'. AL
=F<K MH OAL@ 9 KE9DD EAFAEME L@9F "'. /=KL >MF;LAGF ! AFALA9DDQ
;GFN=J?=K LG L@= EAFAEME G> KG L@9L O= ;9FFGL K== L@= ;GFN=J?=F;=
;MJN= AF L@= X?MJ= /@AK L=F<=F;Q ;9F := <=L=;L=< J=>=J LG ! ! !
! ! 9F< ! OAL@ ."'. ;GFN=J?AF? IMAL= IMA;CDQ AF =N9DM9
LAGFK – K 9 J=KMDL AL ;9F AF>=J L@9L L@= .. MH<9LAF? KLJ9L=?Q
"2* MH<9LAF? KLJ9L=?Q 9F< '! KLJ9L=?Q @9N= 9 ;=JL9AF HJGEGLAGF =>>=;L
GF L@= GJA?AF9D . 9F< 9DD L@= . N9JA9FLK @9N= KAEAD9J ;GFN=J?=FL
LJ=F<K G> O@A;@ ."'. H=J>GJEK :=KL !AF9DDQ :9K=< GF L@= 9F9DQKAK G>
L@= 9:GN= ."'. AK ;@GK=F 9K L@= :=KL N9JA9FL >GJ . AF L@= J=E9AF
AF? L=KLK
<:=.>6?<; C6@5 C2998;<C; !?
$F L@AK K=;LAGF L@= H=J>GJE9F;= G> ."'. AK =P9EAF=< :9K=< GF
>MF;LAGFK K=D=;L=< >JGE :=F;@E9JC K=L 9F< $ :=F;@
E9JC HJG:D=EK K L@= =PH=JAE=FLK <=K;JA:=< :=DGO L@= H9J9E=L=J K=L
LAF?K >GJ AFNGDN=< E=L@G<K 9J= K@GOF AF /9:D= =KA<=K 9DD 9D?GJAL@EK
JMF AF L@= K9E= L=KL =FNAJGFE=FL 9F< GL@=J L=KL H9J9E=L=JK 9J= DAKL=<
AF .=;LAGF /G =N9DM9L= L@= GHLAEAR9LAGF H=J>GJE9F;= G> ."'. L@=
AEHJGN=< . AK ;GEH9J=< OAL@ L@= L=F KM;;=KK>MD (K .LGJF
+JA;= . "9F<GEA =L 9D 9 +.* &=FF=<Q :=J
@9JL "2* (AJB9DADA =L 9D . (AJB9DADA
2* (AJB9DADA '=OAK (!* (AJB9DADA 9L D?G
JAL@E 49F? : !AJ=YQ D?GJAL@E ! 49F? 9 9F<
.. (AJB9DADA =L 9D DD L=KLK 9J= AEHD=E=FL=< 9;;GJ<AF? LG
L@= KM??=KLAGFK G> :=F;@E9JC >MF;LAGFK /@= =PH=JAE=FL9D J=KMDLK 9J=
AF<A;9L=< AF /9:D= O@A;@ DAKLK L@= N? AF<=P 9F< .L< AF<=P G:L9AF=<
:9K=< GF 9DD AFNGDN=< 9D?GJAL@EK /@= EAFAEME N9DM=K G> =9;@ L=KL >MF;
LAGF 9J= K@GOF AF :GD< 9F< L@= KE9DD=J L@= N9DM= L@= :=LL=J L@= 9D?G
JAL@E H=J>GJEK AF L@= ;MJJ=FL L=KL >MF;LAGF $L AK =9KQ LG K== L@9L L@=
."'. ?=F=J9L=K :=LL=J H=J>GJE9F;= ;GEH9J=< LG GL@=J E=L@G<K AF AF
NGDN=< HJG:D=EK K L@= =PH=JAE=FL9D J=KMDLK G> :=F;@E9JC >MF;LAGFK
AF<A;9L=< 9L L@= =F< G> /9:D= ."'. J9FC=< XJKL 9EGF? <A>>=J=FL
:=F;@E9JC >MF;LAGFK /@=J=>GJ= ."'. AK ;9H9:D= G> ?9AFAF? 9 :=LL=J
KGDMLAGF AF 9 KE9DD J9F?= ;GEH9J=< LG GL@=J O=DDCFGOF (K
!GJ ! ! ! 9F< ! ."'. ?=LK L@= GHLAE9D KGDMLAGF IMA;CDQ
O@AD= 9DD GL@=J E=L@G<K >9DD AFLG KGE= FGFGHLAE9D KGDMLAGFK O@A;@
K@GOK L@9L ."'. @9K <J9E9LA;9DDQ AEHJGN=< L@= KGDMLAGFK G> MFA
EG<9D >MF;LAGFK !GJ ! ."'. H=J>GJEK O=DD :ML . G>>=JK L@= :=KL
KGDMLAGFK .AF;= L@= EMDLAEG<9D >MF;LAGFK @9N= E9FQ '* L@=Q 9J= N=JQ
KMAL9:D= LG ;GFXJE L@= =PHDGAL9LAGF 9:ADALQ K ;9F := K==F >JGE /9:D=
L@= G:L9AF=< J=KMDLK G> ."'. GF !! HJG:D=EK 9J= KE9DD=J L@9F
GL@=J AFNGDN=< 9D?GJAL@EK KG AL AK HJGH=J >GJ L@= HJGHGK=< E=L@G<K LG
L9;CD= EMDLAEG<9D >MF;LAGFK
K >GJ !! ."'. 9<N9F;=K J=KMDLK :Q 9 ?=F=J9D NA=O PHDA;
ALDQ KH=9CAF? ."'. ?=LK L@= :=KL J=KMDLK GF ! O@AD= . G:L9AFK L@=
:=KL J=KMDLK GF !! $L KM??=KLK L@9L ."'. @9K L@= KMH=JAGJ 9:AD
ALQ AF L@= =PHDGJ9LAGF H@9K= /@9L AK :=;9MK= L@9L ."'. AK ;GEHGK=<
G> L@= .. MH<9LAF? KLJ9L=?Q "2* MH<9LAF? KLJ9L=?Q 9F< '! KLJ9L=?Q
O@A;@ AK ;GF<M;AN= LG KLJ=F?L@=F L@= 9:ADALQ G> =PHDGJ9LAGF 9F< =PHDGAL9
LAGF LG 9 KA?FA>A;9FL =PL=FL !GJ L@= GL@=J :=F;@E9JC >MF;LAGFK AF
$ ."'. KLADD @9K 9F =P;=DD=FL H=J>GJE9F;= !GJ =P9E
HD= 9K >GJ !! =N=F L@GM?@ 9 KDA?@LDQ KE9DD ?9H AK =KL9:DAK@=< AL
AK ?=F=J9DDQ :=LL=J L@9F EGKL G> L@= GL@=J 9D?GJAL@EK $L ?=LK L@= EAFA
EME GHLAE9D KGDMLAGF GF ! !MJL@=JEGJ= AL ?=LK :=LL=J H=J>GJE9F;=
UNCORRECTED PROOF
+-5<A2@.9 D=2>@'E?@2:?+6@5==960.@6<;? DDD DDDD
Fig. 5. GFN=J?=F;= ;MJN=K G> N9JAGMK . N9JA9FLK GF K=D=;L=< :=F;@E9JC >MF;LAGFK
L@9F GL@=J EGKL 9D?GJAL@EK AF L=JEK G> ! ! ! ! ! 9F< !
!GJ ! ! 9F< ! AL AK ;D=9J L@9L ."'. G:L9AFK KGE=O@9L ;GE
H=LALAN= KGDMLAGFK ;GEH9J=< OAL@ . O@AD= ."'. AK KMH=JAGJ LG GL@=J
AFNGDN=< E=L@G<K KM;@ 9K L@= . AF L=JEK G> ;GEHGKALAGF >MF;LAGFK DAC=
!!
/@= .L< AF<=P ;9F J=Y=;L L@= <=?J== G> L@= ;MJJ=FL HGHMD9LAGF <AKLJA
:MLAGF $F L@=GJQ L@= KE9DD=J L@= .L< L@= :=LL=J L@= 9;;MJ9;Q 9F< KL9
:ADALQ G> L@= E=L@G< K K@GOF AF /9:D= O= ;9F ;GF;DM<= L@9L L@=
."'. H=J>GJEK :=LL=J GF !–! ! 9F< !–! L@9F GL@=J AF
NGDN=< E=L@G<K /@GM?@ L@= KL9F<9J< <=NA9LAGF G> ."'. GF ! !
9F< !–! <G=K FGL K@GO L@= EGKL J=DA9:D= KL9:ADALQ 9EGF? L@GK= 9D
?GJAL@EK L@= KL9:ADALQ AK KLADD 9;;=HL9:D= K ;9F := K==F >JGE L@= 9N=J
9?= XLF=KK N9DM= L@= J=KMDLK K@GO L@9L ."'. @9K :=LL=J H=J>GJE9F;=
L@9F GL@=J E=L@G<K =KA<=K 9K L@= “ ”KQE:GD AF<A;9L=K 9EGF?
:=F;@E9JC >MF;LAGFK ."'. AK KA?FA>A;9FLDQ KMH=JAGJ LG :9KA;
. 9F< . GF 9F< >MF;LAGFK 9F< =IM9D LG L@=E GF 9F<
>MF;LAGFK J=KH=;LAN=DQ ."'. K@GOK MK L@= HGO=J>MD ;GFN=J?=F;=
9:ADALQ 9F< AL G:L9AFK KMH=JAGJ KGDMLAGFK GF ! ! ! ! ! !
! ! 9F< ! 9K K@GOF AF !A?
;;GJ<AF?DQ L@JGM?@ L@= 9F9DQKAK G> L@= 9:GN= K=JA=K G> =PH=JAE=F
L9D J=KMDLK O= ;9F AF<A;9L= L@9L L@= AFLJG<M;LAGF G> L@J== ;GEHGF=FLK
FGL GFDQ <J9E9LA;9DDQ =F@9F;=K L@= ;GFN=J?=F;= KH==< G> L@= GJA?AF9D
. >GJ L@= MFAEG<9D >MF;LAGFK :ML 9DKG =F9:D=K . LG J=<M;= L@= HGK
KA:ADALQ G> >9DDAF? AFLG '* 9F< :9D9F;= L@= ;9H9:ADALQ G> ?DG:9D K=9J;@
9F< DG;9D K=9J;@ N=F L@GM?@ L@= XF9D GHLAEAR9LAGF J=KMDLK G> ."'.
GF KGE= >MF;LAGFK 9J= FGL K9LAK>9;LGJQ 9K =PH=;L=< AL AK 9<EAJ9:D= AF
L=JEK G> L@= ;GFN=J?=F;= J9L= GEH9J=< OAL@ O=DDCFGOF (K
."'. @9K G:L9AF=< :=LL=J J=KMDLK 9F< IMA;C=J ;GFN=J?=F;= J9L=K AF
EGKL ;9K=K 2= ;9F ;GF;DM<= L@9L L@= ;GE:AF9LAGF G> L@J== KLJ9L=?A=K AF
. @9K MH?J9<=< L@= KL9:ADALQ 9F< =>X;9;Q G> L@= :9KA; . LG 9 ;GFKA<
=J9:D= =PL=FL
' ' B2>?A? <@52> 6:=><B21 ' B.>6.;@?
$F L@AK K=;LAGF ."'. E9C=K 9 ;GEH=LALAGF OAL@ KL9L=G>L@=9JL
. N9JA9FLK LG N9DA<9L= ALK =>>=;LAN=F=KK /@=K= . N9JA9FLK 9J= *.
:< D9RAR =L 9D .+.* $KK9 =L 9D .
)=F9N9L@ %9LGL@ ". &ME9J =L 9D (.
,M =L 9D E. . "MHL9 ==H
/@= ;GEH9JAKGF G> ."'. OAL@ GL@=J AEHJGN=< . N9JA9FLK AF
>MF;LAGFK AK K@GOF AF /9:D= /@= J=KMDLK 9J= L=KL=< MF<=J L@= K9E=
=FNAJGFE=FL AF;DM<AF? L@= N9DM=K G> N? 9F< .L< K >GJ L@= MFAEG<9D
>MF;LAGFK DAC= !! ."'. GMLH=J>GJEK GL@=J AEHJGN=< . 9D?G
JAL@EK K ;9F := K==F ."'. XF9DDQ G:L9AFK L@= KE9DD=KL GHLAE9D N9D
M=K GF MFAEG<9D >MF;LAGFK <M= LG L@= AFYM=F;= G> L@= ;GE:AF9LAGF G>
.. 9F< "2* MH<9LAF? KLJ9L=?Q !GJ ! ."'. @9K ;=JL9AF ;GEH=L
ALAN=F=KK OAL@ (. ."'. G:L9AFK L@= :=KL J=KMDLK GF EMDLAEG<9D
>MF;LAGFK DAC= !! O@A;@ :=F=XLK >JGE L@= J9F<GE O9DC HJAF;AHD=
G> '! KLJ9L=?Q !GJ XP=<<AE=FKAGF EMDLAEG<9D >MF;LAGFK DAC= !!
."'. KLADD @9K KA?FA>A;9FL 9<N9FL9?=K O@A;@ AK J=Y=;L=< AF L@= IM9D
ALQ 9F< KL9:ADALQ G> L@= KGDMLAGF $F L=JEK G> !! L@= GHLAE9D J=KMDL
G:L9AF=< :9K=< GF ."'. AK L@= KE9DD=KL ;GEH9J=< LG GL@=J . N9JA
UNCORRECTED PROOF
+-5<A2@.9 D=2>@'E?@2:?+6@5==960.@6<;? DDD DDDD
Table 5
+9J9E=L=JK K=LLAF? >GJ AFNGDN=< 9D?GJAL@EK
(=L@G< +9J9E=L=J
."'. . 8
.
+.*
"2* .
. .
2*
(!* / @ .
>
!
..
(−. C:6; C:.D .
.+.* ! " B:.D C:.D C:6;
E. . &
. 0:6; 0:.D =&
". 129@.
*. .
'.# ;F H.AF $/ $?
'.# $/ >
. "A:?@ 9
$2* . 6 7 . 6−–7 / >
'2* . 6 7 . 6−–7 / 5
%:6; %:.D
'* %:6; %:.D
'+.* C 67 0
'+.* C 0 0 (
9FLK N=F L@GM?@ XF9D GHLAE9D KGDMLAGFK GF ! ! 9F< ! @9N= 9
DALLD= :AL G> ;GEH=LALAN= HJ=KKMJ= OAL@ (. L@= GN=J9DD H=J>GJE9F;=
AK KLADD =PH=;L=< >GJ MK =KA<=K L@GM?@ L@= KL9:ADALQ G> ."'. AK FGL
J9FC=< XJKL GF L@= >MF;LAGFK ! ! !! !! 9F< ! ALK
GHLAE9D KGDMLAGF AK 9K O= =PH=;L=< 9F< L@= KL9:ADALQ AK K9LAK>9;LGJQ 9K
O=DD K DAKL=< 9L L@= =F< G> /9:D= ."'. AK KA?FA>A;9FLDQ KMH=JAGJ LG
(. .+.* E. . ". 9F< *. GF
9F< >MF;LAGFK J=KH=;LAN=DQ
DKG L@= ;GFN=J?=F;= ;MJN=K G> KGE= ;D9KKA; >MF;LAGFK 9J= ;@G
K=F >JGE >MF;LAGFK O@A;@ 9J= K@GOF AF !A? >GJ ;GEH9J9LAN=
9F9DQKAK $L =P@A:ALK L@= ;GFN=J?=F;= KH==< 9F< XF9D GHLAE9D J=KMDLK G>
."'. 9F< GL@=J AEHJGN=< . N9JA9FLK K >GJ L@= MFAEG<9D HJG:
D=EK DAC= ! ! 9F< ! AL ;9F := 9F9DQR=< L@9L ."'. GMLH=J>GJEK
GL@=J AEHJGN=< . N9JA9FLK K 9 J=KMDL ."'. =P@A:ALK KLJGF? ;GF
N=J?=F;= 9:ADALQ >GJ L@= MFAEG<9D >MF;LAGFK 9F< AL @9K KMH=JAGJ KGDM
LAGFK K K@GOF AF !A? AL ;9F := ;GF;DM<=< L@9L ."'. K@GOK
L@= =P;=DD=FL ;GFN=J?=F;= H=J>GJE9F;= O@=F <=9DAF? OAL@ L@= ! HJG:
D=EK O@AD= GL@=J AEHJGN=< . N9JA9FLK 9J= IMA;CDQ <JGHHAF? AFLG '*
!GJ EMDLAEG<9D >MF;LAGFK DAC= ! ! 9F< ! ."'. ;GFN=J?=K
KDA?@LDQ KDGO=J L@9F (. 9F< .+.* 9L L@= =N9DM9LAGF LAE=K G>
– :ML MDLAE9L=DQ @9K 9 KE9DD=J ;GFN=J?=F;= N9DM= #=F;=
L@= H=J>GJE9F;= G> ."'. AK EM;@ :=LL=J L@9F :GL@ G> L@=E K >GJ
! 9F< ! ."'. =P@A:ALK KLJGF? ;GFN=J?=F;= ;GEH9J=< OAL@ GL@=J
AEHJGN=< . N9JA9FLK
/G KME MH ."'. L=F<K LG H=J>GJE >9KL=J ;GFN=J?=F;= J9L=K GF
! ! ! ! 9F< ! /@GM?@ L@= ;GFN=J?=F;= KH==< G> ."'.
AK H9JLA9DDQ DAEAL=< LG KH=;AX; D=N=DK AL G:L9AFK :=LL=J GHLAE9D N9DM= X
F9DDQ ;GEH9J=< OAL@ GL@=J AEHJGN=< . N9JA9FLK DAC= ! ! !
9F< ! /@= J=KMDLK KM??=KL L@9L AFL=?J9LAF? .. MH<9LAF? KLJ9L=?Q 9F<
"2* MH<9LAF? KLJ9L=?Q AFLG L@= . ;9F 9;LAN=DQ KLJ=F?L@=F <AN=JKA
X;9LAGF 9F< L@= ;GFN=J?=F;= KOA>LF=KK G> L@= :9KA; . L L@= K9E=
LAE= L@= '! KLJ9L=?Q AK ;GE:AF=< LG E9C= L@= J9F<GE AF<ANA<M9D O9DC
AF L@= =PHDGJ9LAGF AFL=JN9D 9F< :MAD< L@= ;9H9;ALQ G> L@= 9D?GJAL@E LG
9NGA< L@= '* )GL GFDQ L@= AFLJG<M;LAGF G> L@J== KLJ9L=?A=K @=A?@L=FK
L@= H=J>GJE9F;= G> GJA?AF9D . AF L=JEK G> XF9D GHLAE9D KGDMLAGF 9F<
;GFN=J?=F;= J9L= :ML AL 9DKG C==HK L@= JA?@L :9D9F;= AF ALK K=FKALAN=
;GJ=K
<:=.>6?<; C6@5 <@52> .1B.;021 ?@.@2<3@52.>@ !?
$F L@AK K=;LAGF LG >MJL@=J @A?@DA?@L L@= 9<N9FL9?=K G> L@= ."'.
K=N=J9D GL@=J 9<N9F;=< (K AF;DM<AF? .M;;=KK#AKLGJQ :9K=< <9HLAN=
OAL@ 'AF=9J +GHMD9LAGF .AR= -=<M;LAGF 9F< M;DA<=9F F=A?@:GJ@GG<
'.# ;F H.AF O9< DA .M?9FL@9F '.# /9F
9:= !MCMF9?9 K=D>9<9HLAN= . ,AF #M9F?
.M?9FL@9F AEHJGN=< 2* $2* /M:AK@9L :MK@9JA9@
$<JAK DB9J9@ '2* 'AF? 5@GM 'MG ;DGM<
EG<=D 5@GM 3A= 'A (9 GDD9:GJ9LAN= 9F< Q
F9EA; '=9JFAF? G> *HHGKAL= +GHMD9LAGF '* 4GF? #= 'A
5@GM GEHJ=@=FKAN= '=9JFAF? +.* '+.* 9G =L 9D
9F< ?AF? '=9<=J 9F< @9DD=F?=JK '+.* 2 ) @=F =L
9D 9J= AFNGDN=< >GJ ;GEH9JAKGF /@= <=L9AD=< ;GEH9JAKGF J=
KMDLK GF L@= 9J= K@GOF AF /9:D= $L AK H9JLA;MD9JDQ =NA<=FL L@9L
L@= ."'. AK KMH=JAGJ LG GL@=J ;MLLAF?=<?= (K >GJ EGKL KALM9LAGFK
/@= XF9D L=KL J=KMDLK 9J= DAKL=< AF /9:D= AF O@A;@ O= ;9F G:K=JN=
L@9L L@= ."'. J9FCK XJKL 9EGF? :=F;@E9JC HJG:D=EK /@=J=>GJ=
."'. ;9F K==C :=LL=J KGDMLAGFK AF EGKL K=D=;L=< :=F;@E9JC HJG:D=EK
;GEH9J=< LG GL@=J KL9L=G>L@=9JL (K
."'. HJGNA<=K L@= :=KL J=KMDLK GF !–! ! 9F< !–! :=F;@
E9JC >MF;LAGFK K=D=;L=< >JGE ;D9KKA; >MF;LAGFK (GJ=GN=J L@= HJ=;A
KAGF N9DM=K G> L@=K= >MF;LAGFK 9J= KE9DD=J L@9F GL@=JK 9F< L@= ;GFN=J
?=F;= KH==< AK >9KL=J L@9F GL@=J ;GMFL=JH9JLK AF L@= AFALA9D KL9?= K >GJ
! ! !–! 9 KDA?@LDQ KE9DD ?9H AK =KL9:DAK@=< :ML AL AK ?=F=J9DDQ
:=LL=J L@9F EGKL GL@=J AFNGDN=< (K -=?9J<AF? L@= J=KL G> :=F;@
E9JC >MF;LAGFK >JGE $ 9K ;9F := K==F AF /9:D= ."'.
;GEH=L=K OAL@ '.# GF !! N=F L@GM?@ L@= H=J>GJE9F;= G>
."'. GF !! AK FGL L@= :=KL AL AK K9LAK>9;LGJQ 9K O= =PH=;L=<
!GJ L@= >MF;LAGFK !! ."'. K@GOK L@= J9HA< ;GFN=J?=F;= 9L L@=
:=?AFFAF? 9F< ?=L L@= :=KL N9DM= XF9DDQ O@AD= GL@=J AFNGDN=< E=L@G<K
=N=FLM9DDQ L=F< LG ;GFN=J?= 9F< G:L9AF ?=F=J9D N9DM= !JGE L@= 9F9DQKAK
G> KL9F<9J< <=NA9LAGF AL ;9F := K==F L@9L L@= GN=J9DD H=J>GJE9F;= G> L@=
."'. AK KL9:D= ;GEH9J=< OAL@ GL@=J (K $F H9JLA;MD9J ."'. @9K
KE9DD=J KL9F<9J< <=NA9LAGF N9DM=K GF !! 9F< !! O@A;@ AF<A
;9L=K L@9L ."'. H=J>GJEK EGJ= KL9:DQ /@GM?@ ."'. <G=K FGL K@GO
L@= EGKL 9;LAN= KL9:ADALQ GF !! ."'. H=J>GJEK K9LAK>9;LGJADQ GF
L@= XF9D ;GFN=J?=F;= N9DM= $F 9<<ALAGF AL AK <=L=JEAF=< L@9L ."'.
AK KMH=JAGJ LG '.# ;F H.AF '.# . $2* '2*
'* '+.* 9F< '+.* $F L@= =PH=JAE=FL L@= H=J>GJE9F;= G>
'.# AK K=;GF< GFDQ LG ."'. #GO=N=J ."'. AK KA?FA>A;9FLDQ
KMH=JAGJ LG '.# GF >MF;LAGFK 9F< =IM9D LG L@=E GF >MF;
LAGFK J=KH=;LAN=DQ =KA<=K ."'. G:L9AFK L@= DGO=KL -1 AF /9:D=
O@A;@ AK =IM9D LG $F ;GF;DMKAGF . @9K KLJGF? ;GEH=LALAN=
F=KK OAL@ L@=K= 9<N9F;=< KL9L=G>L@=9JL (K <M= LG L@= ;GE:AF9LAGF G>
L@J== KLJ9L=?A=K
=KA<=K 9K K@GOF AF !A? FAF= ;GFN=J?=F;= ;MJN=K >JGE L@=K=
:=F;@E9JC >MF;LAGFK 9J= K=D=;L=< >GJ >MJL@=J 9F9DQKAK *F L@= O@GD=
."'. H=J>GJEK L@= EGKL J9HA< ;GFN=J?=F;= KH==< 9F< G:L9AFK L@=
KE9DD=KL GHLAE9D N9DM=K 9EGF? L@=K= 9<N9F;=< E=L@G<K $F H9JLA;MD9J
L@= XF9D ;GFN=J?=FL N9DM=K G> ! ! ! 9F< ! 9J= L@= KE9DD
=KL L@9F GL@=J 9<N9F;=< KL9L=G>L@=9JL (K $L ;9F := K==F L@9L !
9F< ! L=F< LG XF< L@= :=KL J=KMDL IMAL= J9HA<DQ -=?9J<AF? L@= !
! 9F< ! >MF;LAGFK AL AK =NA<=FL L@9L ."'. GMLH=J>GJEK GL@=J
AFNGDN=< E=L@G<K AF N9JAGMK ;GF<ALAGFK O@AD= GL@=JK ?=L KLM;C AF DG
;9D GHLAEME =9JDQ $F ;GF;DMKAGF L@= GN=J9DD H=J>GJE9F;= G> ."'.
AK 9DKG GMLKL9F<AF? 9DGF? OAL@ >9KL=J ;GFN=J?=F;= KH==< 9F< :=LL=J GH
LAE9D N9DM= $L H=J>GJEK :=LL=J L@9F GL@=JK 9F< J9FCK XJKL 9EGF? 9DD
L@= E=L@G<K AF L=JEK G> L@= GHLAE9D N9DM=K 9F< KL9:ADALQ O@=L@=J L@=Q
9J= L=KL=< GF L@= MFAEG<9D EMDLAEG<9D GJ XP=<<AE=FKAGF EMDLAEG<9D
UNCORRECTED PROOF
+-5<A2@.9 D=2>@'E?@2:?+6@5==960.@6<;? DDD DDDD
Table 6
-=KMDLK G> ."'. 9F< O=DDCFGOF (K GF :=F;@E9JC >MF;LAGFK
F1 F2 F3
N? .L< N? .L< N? .L<
SGLSCA 0.0000E + 00 0.0000E + 00 0.0000E + 00 0.0000E + 00 0.0000E + 00 0.0000E + 00
− − − −
. − − − − − −
. − − − − −
"2* 0.0000E + 00 0.0000E + 00 0.0000E + 00 0.0000E + 00 − 0.0000E + 00
2* 0.0000E + 00 0.0000E + 00 0.0000E + 00 0.0000E + 00
(!*
+.*
− − − −
!
.. − − − − − −
F4 F5 F6
N? .L< N? .L< N? .L<
SGLSCA 0.0000E + 00 0.0000E + 00 1.4243 −01 3.5425 −05 3.4116 −05
− − − −
. − −
. − − − − −
"2* − − − − −
2* 2.4159E + 01 − − −
(!*
+.* −
! −
.. − − − −
F7 F8 F9
N? .L< N? .L< N? .L<
SGLSCA −1.2569E + 04 1.0138 −02 0.0000E + 00 0.0000E + 00 8.8818 −16 0.0000E + 00
− − − − −
. − − −
. − 0.0000E + 00 0.0000E + 00
"2* − 0.0000E + 00 0.0000E + 00 − −
2* − 0.0000E + 00 0.0000E + 00 − −
(!* −
+.* − −
− −
! − −
.. − −
F10 F11 F12
N? .L< N? .L< N? .L<
SGLSCA 0.0000E + 00 0.0000E + 00 9.9800 −01 − 3.0749 −04 −
0.0000E + 00 0.0000E + 00 9.9800 −01 0.0000E + 00 − −
. 0.0000E + 00 0.0000E + 00 9.9800 −01 0.0000E + 00 3.0749 −04 8.2807 −20
. − − 9.9800 −01 − − −
"2* 0.0000E + 00 0.0000E + 00 − −
2* − − 9.9800 −01 − − −
(!* 9.9800 −01 0.0000E + 00 − −
+.* − − −
− − − −
! − − − −
.. − − 9.9800 −01 − − −
F13 F14 F15
N? .L< N? .L< N? .L<
SGLSCA −1.0153E + 01 − −1.0403E + 01 −
− −1.0403E + 01 1.8724 −15
. −1.0153E + 01 0.0000E + 00 −1.0403E + 01 1.8724 −15 1.0259E + 06 2.5075E + 05
. − −
"2* −1.0153E + 01 − −1.0403E + 01 −
2* −1.0153E + 01 − −1.0403E + 01 −
(!* − −
+.* − −
UNCORRECTED PROOF
+-5<A2@.9 D=2>@'E?@2:?+6@5==960.@6<;? DDD DDDD
− −
! − − − −
.. − −
F16 F17 F18
N? .L< N? .L< N? .L<
SGLSCA − 6.1471E + 02
2.0644E + 01 − 1.4669E + 00
. 4.1436E + 02 − −
. −
"2* −
2* −
(!* −
+.* 3.1852 −02
−
! − −
.. 5.2002E + 02 −
F19 F20 F21
N? .L< N? .L< N? .L<
SGLSCA 1.2003E + 03 − −
8.0386 −02 −
. − 3.4250 −02
. −
"2* 3.9487E + 03
2* − −
(!* −
+.* − −
− −
! 2.2125E + 02 − 1.4401E + 03
.. − −
F22 F23 F24
N? .L< N? .L< N? .L<
SGLSCA − −
− −
. 2.1777E + 00 − 3.9091E + 03 2.2843E + 02
. 1.4340 −01
"2* 1.6106E + 03 −
2* −
(!* −
+.* − −
−
! −
.. 1.5078E + 03 −
F25 F26 F27
N? .L< N? .L< N? .L<
SGLSCA
. 1.8701E + 03 2.4283E + 01 2.0528E + 03 1.4211E + 01 3.1549E + 03 1.9868E + 02
.
"2*
2*
(!*
+.*
!
..
F28 F29 F30
N? .L< N? .L< N? .L<
SGLSCA 2.5000E + 03 0.0000E + 00 2.6000E + 03 0.0000E + 00 2.7000E + 03 0.0000E + 00
− −
. − −
. −
"2* 2.6000E + 03 −
2*
(!*
UNCORRECTED PROOF
+-5<A2@.9 D=2>@'E?@2:?+6@5==960.@6<;? DDD DDDD
+.* −
−
!
.. −
F31 F32 F33
N? .L< N? .L< N? .L<
SGLSCA 2.9000E + 03 0.0000E + 00 3.0000E + 03 0.0000E + 00 3.1000E + 03 0.0000E + 00
.
.
"2*
2*
(!*
+.*
!
..
F34 Overall Rank
N? .L< -9FC -1
SGLSCA 3.2000E + 03 0.0000E + 00 1 ~ 2.000000
.
.
"2*
2*
(!*
+.*
!
..
>MF;LAGFK /@= HJAE9JQ ;9MK= AK L@9L L@= HJGHGK=< 9D?GJAL@E =EHDGQK
.. MH<9LAF? KLJ9L=?Q "2* MH<9LAF? KLJ9L=?Q 9F< '! KLJ9L=?Q O@A;@
;9F :GGKL L@= ;9H9;ALQ G> =PHDGJAF? 9F< =PHDGALAF? AF L@= O@GD= K=9J;@
KH9;= 9F< =>>=;LAN=DQ <=;J=9K= L@= L=F<=F;Q G> LJ9HHAF? AFLG L@= DG;9D
GHLAEME 9K O=DD
;;GJ<AF? LG L@= 9F9DQKAK G> L@= 9:GN= K=JA=K G> =PH=JAE=FL9D J=
KMDLK ."'. ;9F E9C= 9 J=DA9:D= ;GEH9JAKGF OAL@ GL@=J 9<N9F;=<
KL9L=G>L@=9JL (K !AJKL L@= AFLJG<M;LAGF G> L@= '! KLJ9L=?Q E9C=K L@=
HJGHGK=< E=L@G< K@GO 9 >9KL=J J9L= G> ;GFN=J?=F;= >GJ L@= MFAEG<9D
>MF;LAGFK /@=F L@= ;GE:AF9LAGF G> .. 9F< "2* MH<9LAF? KLJ9L=?A=K
>MJL@=J :GGKLK L@= =PHDGJ9LAGF 9:ADALQ G> L@= GJA?AF9D . GF EMDLAEG<9D
>MF;LAGFK $F ;GF;DMKAGF ;GEH9J=< OAL@ GL@=J 9<N9F;=< KL9L=G>L@=9JL
(K FGL GFDQ L@= AFLJG<M;LAGF G> L@J== KLJ9L=?A=K @=A?@L=F L@= H=J>GJ
E9F;= G> GJA?AF9D . AF L=JEK G> XF9D GHLAE9D KGDMLAGF 9F< ;GFN=J
?=F;= J9L= :ML 9DKG C==HK L@= JA?@L :9D9F;= AF <AN=JKAX;9LAGF 9F< AFL=FKA
X;9LAGF LJ=F<K K 9 J=KMDL O= K== L@9L L@= HJGHGK=< ."'. AK ;9H9:D=
G> L9;CDAF? FME=JGMK :=F;@E9JC HJG:D=EK =>X;A=FLDQ
+.9909<08 @6:2 0<?@
/@= O9DD;DG;C LAE= G> ."'. 9F< GL@=J AFNGDN=< 9D?GJAL@EK AF
L@AK H9H=J AK K@GOF AF /9:D=K – $L AK OGJL@ FGLAF? L@9L L@= =P
H=JAE=FLK 9<GHL K=9J;@ 9?=FLK LG ;GF<M;L =N9DM9LAGFK
!GJ MFAX=< ;GEH9J9LAN= 9F9DQKAK L@= J=KMDLK AF L@= L9:D= 9J= 9DD AF K=;
GF<K !AJKL /9:D= =P@A:ALK L@= O9DD;DG;C LAE= ;GFKME=< :9K=< GF
."'. .'. .". "'. .. ". '. 9F< . /G EGJ=
NANA<DQ <=K;JA:= L@= O9DD;DG;C LAE= G> L@GK= . N9JA9FLK L@= O9DD;DG;C
LAE= HJGHGJLAGF ;@9JL AK K@GOF AF !A? $L ;9F := K==F L@9L HJGHGK=<
."'. ;GFKME=K EGJ= O9DD;DG;C LAE= L@9F L@= :9KA; . 9K =PH=;L=<
9K 9 KA<= =>>=;L G> F=O ;GEHGF=FLK /@= E9AF J=9KGF O@Q ."'. ;GKLK
9 ;GFKA<=J9:D= HJGHGJLAGF G> LAE= AK L@9L L@= AFLJG<M;LAGF G> L@J== KLJ9L=
?A=K =KA<=K AL ;9F := K==F L@9L . ;GE:AFAF? L@J== KLJ9L=?A=K ;GF
KME= EGJ= O9DD;DG;C LAE= L@9F ;GE:AFAF? GF= GJ LOG KLJ9L=?A=K $L
AK =9KQ LG MF<=JKL9F< L@9L AF L@= K9E= L=KL =FNAJGFE=FL 9K EGJ= KLJ9L=
?A=K 9J= 9<<=< L@= ;GEHD=PALQ G> L@= GJA?AF9D . OADD := @A?@=J 9F<
L@= LAE= LG G:L9AF L@= XF9D GHLAE9D KGDMLAGF OADD := DGF?=J 9K 9 DG?A;9D
KA<= =>>=;L
K K@GOF AF /9:D=K – L@= O9DD;DG;C LAE= ;GFKME=< :9K=< GF
."'. AK ;GEH9J=< OAL@ GL@=J O=DDCFGOF E=L@G<K /@= =PH=JAE=FL9D
J=KMDLK K@GO L@9L L@= O9DD;DG;C LAE= ;GKL :9K=< GF ."'. AK J=D9LAN=DQ
EM;@ O@A;@ AK KDA?@LDQ D=KK=J L@9F L@9L G> L@= :9KA; 9F< ! !GJ EGJ=
NANA<DQ <=K;JA:AF? L@= O9DD;DG;C LAE= G> L@GK= :9KA; 9F< 9<N9F;=< E=L@
G<K L@= O9DD;DG;C LAE= HJGHGJLAGF ;@9JL AK K@GOF AF !A? *F L@=
GF= @9F< ;GEH9J=< OAL@ L@= K9E= LQH= G> AEHJGN=< . N9JA9FLK AL AK
;D=9J L@9L L@= ;GEHML9LAGF9D ;GKL G> (. AK L@= @A?@=KL AF L=JEK G> LAE=
GN=J9DD *F L@= GL@=J @9F< ;GEH9J=< OAL@ GL@=J KL9L=G>L@=9JL (K
."'. AK KMH=JAGJ GN=J '.# ;F H.AF '.# 9F< . AF L=JEK
G> LAE= ;GKL
N=F L@GM?@ L@= LAE= ;GFKMEHLAGF G> ."'. AK @A?@=J L@9F L@9L G>
KGE= GJA?AF9D 9D?GJAL@EK 9F< AEHJGN=< . N9JA9FLK ."'. H=J>GJEK
:=LL=J AF ;GFN=J?=F;= KH==< 9F< KGDMLAGF IM9DALQ /@=J=>GJ= O@=F L@=
LAE= 9F< J=KGMJ;=K 9J= MFDAEAL=< 9F< L@= <=;AKAGFE9C=JK H9Q EGJ= 9L
L=FLAGF LG L@= IM9DALQ G> L@= XF9D KGDMLAGF ."'. AK G:NAGMKDQ 9 :=LL=J
;@GA;= LG J=KGDN= L@= GHLAEAR9LAGF HJG:D=E /@GM?@ ."'. ;GFKME=K
EGJ= LAE= H9J9DD=D ;GEHMLAF? ;9F := MK=< LG <=;J=9K= L@= LAE= ;GF
KME=< /@=J=>GJ= O@=F <=;AKAGFE9C=JK GJ MK=JK H9Q EGJ= 9LL=FLAGF LG
L@= IM9DALQ G> L@= KGDMLAGF 9F< 9NGA< <JGHHAF? AFLG DG;9D GHLAEME L@=
HJGHGK=< E=L@G< AK EGJ= 9HHDA;9:D= N=F L@GM?@ L@= KGDMLAGF ;9F :=
>GMF< IMA;CDQ L@JGM?@ 9 J9F<GE K=9J;@ L@= MDLAE9L= ?G9D AK LG XF< 9
EGJ= KL9:D= GHLAEAR=J AF KM>X;A=FL LAE= /@AK KM>X;A=FL LAE= AK 9 KM:B=;
LAN= E=LJA; O@A;@ <=H=F<K GF <=;AKAGFE9C=JK MK=JK ;9D;MD9LAGF :M<
?=LK GJ J=KGMJ;=K $F ;GF;DMKAGF L@=J= EMKL := 9 ;=JL9AF LJ9<=G[ :=
LO==F =>X;A=F;Q 9F< 9;;MJ9;Q O@=F KGDNAF? HJ9;LA;9D GHLAEAR9LAGF HJG:
D=EK
UNCORRECTED PROOF
+-5<A2@.9 D=2>@'E?@2:?+6@5==960.@6<;? DDD DDDD
Fig. 6. GFN=J?=F;= ;MJN=K G> ."'. 9F< O=DDCFGO (K GF K=D=;L=< :=F;@E9JC >MF;LAGFK
6B2>?6@E .;1 96:6@.@6<;?
/G >MJL@=J K@GO L@= =PHDGJ9LAGF 9F< =PHDGAL9LAGF ;9H9;ALQ G> HJG
HGK=< ."'. L@= 9N=J9?= <AKL9F;= :=LO==F K=9J;@ @AKLGJQ LJ9B=;LGJQ
9F< KGDMLAGF 9L =9;@ AL=J9LAGF 9J= IM9DAL9LAN=DQ EGFALGJ=< DKG L@= DAE
AL9LAGFK G> L@= HJGHGK=< ."'. 9J= 9F9DQR=< AF L@AK K=;LAGF
/@= <AN=JKALQ ;GEH9JAKGF =PH=JAE=FL G> ."'. 9F< . 9J= ;GF
<M;L=< /@= =PH=JAE=FLK 9J= ;9JJA=< GML MF<=J L@= K9E= =FNAJGFE=FL
9K E=FLAGF=< =9JDA=J MKAF? K=9J;@ 9?=FLK LG ;GF<M;L AL=J9LAGFK
9;@ AFNGDN=< >MF;LAGF AK L=KL=< LAE=K AF<=H=F<=FLDQ LG EALA?9L= L@=
=>>=;LK G> J9F<GEF=KK =KA<=K FAF= J=HJ=K=FL9LAN= L=KL >MF;LAGFK >JGE
:=F;@E9JC >MF;LAGFK AF;DM<AF? MFAEG<9D >MF;LAGF EMDLAEG<9D >MF;
LAGF @Q:JA< >MF;LAGF 9F< ;GEHGKAL= >MF;LAGF 9J= K=D=;L=< LG K@GO L@=
<AN=JKALQ G> L@= HJGHGK=< ."'. /@= <AN=JKALQ ?J9H@ G> L@= 9N=J9?=
M;DA<=9F <AKL9F;= :=LO==F K=9J;@ 9?=FLK AK K@GOF AF !A? $L ;9F
:= K==F L@9L L@= 9N=J9?= M;DA<=9F <AKL9F;= G> ."'. AK EGJ= H=J=?JA
F9L=< L@9F L@= GJA?AF9D . O@A;@ E=9FK L@9L L@= F=O AEHJGN=E=FL
=>>=;LAN=DQ AF;J=9K=K L@= ;GFN=J?=F;= HGL=FLA9D G> . $L ;9F := AF>=JJ=<
L@9L 9 ?JGMH E=E:=J G> L@= HGHMD9LAGF ;9F L9C= 9<N9FL9?= G> L@= :=KL
AF>GJE9LAGF 9N9AD9:D= AF L@= O@GD= =NGDMLAGF9JQ ?JGMH $L K@GOK L@= HJG
HGK=< ."'. ?MA<=K L@= HGHMD9LAGF LG 9 <=KAJ9:D= 9J=9 G> L@= K=9J;@
KH9;= =>X;A=FLDQ 9K=< GF L@= 9:GN= 9F9DQKAK O= ;9F <=L=JEAF= L@9L L@=
HJGHGK=< KLJ9L=?A=K ;9F KEGGL@DQ KLJ=F?L@=F L@= H=J>GJE9F;= G> .
;;GJ<AF? LG L@= 9:GN= =PH=JAE=FL9D 9F9DQKAK O= ;9F AF>=J L@9L
."'. AK KMH=JAGJ LG GL@=J AFNGDN=< 9D?GJAL@EK $L AK =E:J9;=< AF :=L
L=J KGDMLAGFK 9F< >9KL=J ;GFN=J?=F;= KH==< #GO=N=J ;GFKA<=JAF? 9DD
L@= G:K=JN=< 9<N9FL9?=K AL 9DKG @9K KGE= DAEAL9LAGFK KAEAD9J LG GL@=J
KO9JE:9K=< E=L@G<K /@= ;GE:AF9LAGF G> L@J== KLJ9L=?A=K =>>=;LAN=DQ
AEHJGN=K L@= IM9DALQ G> L@= GHLAE9D KGDMLAGF 9F< KLJ=F?L@=FK L@= H=J>GJ
E9F;= G> L@= :9KA; . O@AD= AL ;GKLK EGJ= LAE= LG G:L9AF L@= GHLAE9D
KGDMLAGF /@=J=>GJ= L@=J= EMKL := 9 H9JLA;MD9J LJ9<=G[ :=LO==F =>X
;A=F;Q 9F< 9;;MJ9;Q O@=F KGDNAF? HJ9;LA;9D =F?AF==JAF? HJG:D=EK !MJ
L@=JEGJ= H9J9E=L=J K=LLAF?K 9>>=;L L@= H=J>GJE9F;= G> ."'. AF;DM<
AF? H9J9E=L=J 9F< G> L@= GJA?AF9D . H9J9E=L=J G> L@=
.. MH<9LAF? KLJ9L=?Q H9J9E=L=J 9F< G> "2* MH<9LAF? KLJ9L
=?Q 9F< H9J9E=L=J G> '! KLJ9L=?Q #=F;= L@= <=;AKAGFE9C=J F==<K LG
:= ;9J=>MD 9F< XJKL O=DD LMF= L@= E=L@G< ;GFKA<=JAF? L@= F9LMJ= G> L@=
KLM<A=< HJG:D=E LG J=9;@ <=KAJ9:D= KGDMLAGFK =KA<=K L@= AFLJG<M;LAGF
G> L@J== KLJ9L=?A=K J=DA=K GF L@= IM9DALQ G> L@= AFALA9D KGDMLAGF G> L@= :9KA;
.
6. Discussion and summary
/@AK H9H=J HJGHGK=K 9F AEHJGN=< . O@A;@ ;GE:AF=K L@J== KLJ9L=
?A=K AF;DM<AF? “.. MH<9LAF? KLJ9L=?Q”“"2* MH<9LAF? KLJ9L=?Q”9F<
“'! KLJ9L=?Q” LG AEHJGN= L@= H=J>GJE9F;= G> L@= . *F L@= GF= @9F<
L@= XJKL LOG MH<9LAF? KLJ9L=?A=K 9J= MK=< >MJL@=J LG AEHJGN= L@= DG;9D
=PHDGAL9LAGF ;9H9:ADALQ G> . *F L@= GL@=J @9F< “'! KLJ9L=?Q”AK =E
HDGQ=< LG >MJL@=J KLJ=F?L@=F L@= <AN=JKAX;9LAGF G> . 9F< 9NGA< <=
L=JAGJ9LAF? AFLG 9 DG;9D GHLAEME /@= ;GE:AF9LAGF G> L@= L@J== KLJ9L=
?A=K =>>=;LAN=DQ :9D9F;=K L@= ;9H9;ALQ G> <AN=JKAX;9LAGF 9F< AFL=FKAX;9
LAGF /@= KH=;AX; HJG;=KK AK LG MH<9L= L@= AFALA9DAR=< HGHMD9LAGF OAL@
. 9F< L@=F 9<GHL “.. MH<9LAF? KLJ9L=?Q”“"2* MH<9LAF? KLJ9L
UNCORRECTED PROOF
+-5<A2@.9 D=2>@'E?@2:?+6@5==960.@6<;? DDD DDDD
Table 7
-=KMDLK G> ."'. 9F< O=DDCFGOF (K GF :=F;@E9JC >MF;LAGFK
F1 F2 F3
N? .L< N? .L< N? .L<
SGLSCA 0.0000E + 00 0.0000E + 00 0.0000E + 00 0.0000E + 00 0.0000E + 00 0.0000E + 00
(. − − − −
.+.*
E. 0.0000E + 00 0.0000E + 00 0.0000E + 00 0.0000E + 00 − 0.0000E + 00
. 0.0000E + 00 0.0000E + 00 0.0000E + 00 0.0000E + 00 0.0000E + 00 0.0000E + 00
". 0.0000E + 00 0.0000E + 00 0.0000E + 00 0.0000E + 00 0.0000E + 00 0.0000E + 00
*. − − − − − −
F4 F5 F6
N? .L< N? .L< N? .L<
SGLSCA 0.0000E + 00 0.0000E + 00 2.5255E + 01 2.6600 −01 3.9839 −05 4.1474 −05
(. − − −
.+.* −
E. − − − −
. − 0.0000E + 00 − −
". − 0.0000E + 00 − − −
*. − − − − −
F7 F8 F9
N? .L< N? .L< N? .L<
SGLSCA − 6.6805 −09 0.0000E + 00 0.0000E + 00 8.8818 −16 0.0000E + 00
(. −8.9718E + 222 − − −
.+.* − −
E. − 0.0000E + 00 0.0000E + 00
. − 0.0000E + 00 0.0000E + 00 8.8818 −16 0.0000E + 00
". − 0.0000E + 00 0.0000E + 00 8.8818 −16 0.0000E + 00
*. − 0.0000E + 00 0.0000E + 00 − 0.0000E + 00
F10 F11 F12
N? .L< N? .L< N? .L<
SGLSCA 0.0000E + 00 0.0000E + 00 9.9800 −01 1.8130 −16 3.0749 −04 1.4590 −12
(. − − 9.9800 −01 1.8130 −16 − −
.+.* − − 9.9800 −01 − − −
E. 0.0000E + 00 0.0000E + 00 − − −
. 0.0000E + 00 0.0000E + 00 9.9800 −01 − − −
". 0.0000E + 00 0.0000E + 00 − − − −
*. 0.0000E + 00 0.0000E + 00 − − −
F13 F14 F15
N? .L< N? .L< N? .L<
SGLSCA −1.0153E + 01 3.0741 −11 −1.0403E + 01 1.6981 −11 2.3353E + 06 1.1802E + 06
(. − −
.+.* − −
E. − −
. −1.0153E + 01 − −1.0403E + 01 −
". − −
*. − − − −
F16 F17 F18
N? .L< N? .L< N? .L<
SGLSCA − 6.1186E + 02
(. 5.2000E + 02 9.9282 −03
.+.* 5.3163E + 02 2.8431E + 01 −
E. −
. − 1.8131E + 00
". −
*. −
F19 F20 F21
N? .L< N? .L< N? .L<
SGLSCA 3.9959E + 03 − 1.4003E + 03 5.3801 −02
(. 1.2002E + 03 − −
.+.* −
E. −
. 2.6750E + 02 −
". 1.6127 −01
*. −
UNCORRECTED PROOF
+-5<A2@.9 D=2>@'E?@2:?+6@5==960.@6<;? DDD DDDD
F22 F23 F24
N? .L< N? .L< N? .L<
SGLSCA 1.5071E + 03 1.7115E + 00 1.6108E + 03 7.0818 −01 4.7087E + 05 2.1888E
(. −
.+.* −
E. −
. −
". −
*. −
PH9F<
F25 F26 F27
N? .L< N? .L< N? .L<
SGLSCA 4.1239E 03 3.0413E 03 3.7226E 03 1.8438E 03 1.7620E 05
(.
.+.* 1.2704E 05
E.
.
".
*.
F28 F30F29 F30
N? .L< N? .L< N? .L<
SGLSCA 2.5000E 03 0.0000E 00 2.6000E 03 0.0000E 00 2.7000E 03 0.0000E 00
(.
.+.*
E. −
. 2.5000E 03 0.0000E 00 2.6000E 03 − 2.7000E 03 0.0000E 00
". 2.5000E 03 0.0000E 00 2.6000E 03 − 2.7000E 03 0.0000E 00
*. 2.6000E 03 − 2.7000E 03 −
F31 F32 F33
N? .L< N? .L< N? .L<
SGLSCA 2.9000E 03 0.0000E 00 3.0000E 03 0.0000E 00 3.1000E 03 0.0000E 00
(.
.+.*
E.
.
". 2.9000E 03 0.0000E 00 3.0000E 03 0.0000E 00 3.1000E 03 0.0000E 00
*.
F34 *N=J9DD-9FC
N? .L< -9FC −-1
SGLSCA 3.2000E 03 0.0000E 00 1 U1.176471
(.
.+.*
E.
.
".
*.
=?Q”9F< “'! KLJ9L=?Q”LG MH<9L= L@= HGHMD9LAGF J=9DAR=< :9K=< GF .
9L L@= K9E= LAE= $F L@AK ;9K= L@J== F=O HGHMD9LAGFK 9J= G:L9AF=< 9F<
O= F9E= L@=E . " 9F< ' HGHMD9LAGFK !AF9DDQ O= K=D=;L L@= XF9D :=KL
HGHMD9LAGF :9K=< GF ?J==<Q K=D=;LAGF
!JGE L@= HJGHGK=< AEHJGN=< KLJ9L=?Q LG L@= XF9DDQ AEHD=E=FL=<
E=L@G< 9F< L@=F LG L@= N=JAX;9LAGF G> L@= H=J>GJE9F;= G> L@= HJG
HGK=< E=L@G< O= E9<= 9 K=JA=K G> =PH=JAE=FL9D L=KLK $L AK OGJL@ FGL
AF? L@9L L@= L=KL =FNAJGFE=FL @=J= AK L@= K9E= 9F< L@= >MF;LAGF L=KL K=L
MK=< AK L@= K9E= 9K O=DD !AJKL L@J== AEHJGN=< KLJ9L=?A=K 9J= HJGHGK=<
9F< AFLJG<M;=< LG . A?@L ;GEH9J9LAN= =PH=JAE=FLK 9J= =KL9:DAK@=<
/@JGM?@ L@= 9F9DQKAK G> L@= J=KMDLK O= ;9F G:L9AF 9F AEHJGN=< .
;GE:AFAF? L@J== KLJ9L=?A=K F9E=DQ ."'. O@A;@ H=J>GJEK :=KL ;GE
H9J=< OAL@ GL@=J ;GE:AF9LAGFK /@= EGKL KMH=JAGJ AK E9AFDQ J=Y=;L=<
AF L@= 9<N9FL9?= G> L@= KGDMLAGF 9F< L@= ;GFN=J?=F;= KH==< G> L@= KGDM
LAGF )=PL ."'. AK ;GEH9J=< OAL@ L=F GL@=J O=DDCFGOF (K AF GJ
<=J LG L=KL L@= KMH=JAGJALQ G> L@= ;MJJ=FL AEHJGN=< E=L@G< /@JGM?@ L@=
9F9DQKAK G> L@= J=KMDLK L@= GN=J9DD H=J>GJE9F;= G> ."'. J9FCK XJKL
K ;9F := K==F GF MFAEG<9D >MF;LAGFK EMDLAEG<9D >MF;LAGFK @Q:JA<
!MF;LAGFK 9F< ;GEHGKALAGF >MF;LAGFK L@= ;GFN=J?=F;= KH==< 9F< KM
H=JAGJALQ G> L@= KGDMLAGF 9J= KMH=JAGJ $F GJ<=J LG >MJL@=J @A?@DA?@L L@=
9<N9F;=< F9LMJ= G> L@= AEHJGN=< E=L@G< L@= F=O .:9K=< E=L@G<
AK ;GEH9J=< OAL@ AEHJGN=< . AF DAL=J9LMJ= /@= ;GEH9JAKGF J=KMDLK
K@GO L@9L ."'. @9K :=LL=J GN=J9DD H=J>GJE9F;= L@9F GL@=J 9D?GJAL@EK
9F< ALK GN=J9DD H=J>GJE9F;= J9FCK XJKL DKG ."'. AK ;GEH9J=< OAL@
GL@=J KL9L=G>L@=9JL (K LG >MJL@=J L=KL L@= HGL=FLA9D G> L@= HJGHGK=<
E=L@G< 2= ;9F ;GF;DM<= L@9L L@= ;GEHJ=@=FKAN= H=J>GJE9F;= G> L@=
HJGHGK=< E=L@G< KMJH9KK=K GL@=J 9<N9F;=< E=L@G<K /@=J=>GJ= O= ;9F
AF>=J L@9L L@= HJGHGK=< ."'. @9K KA?FA>A;9FLDQ AEHJGN=< L@= ?DG:9D
K=9J;@ 9F< DG;9D K=9J;@ ;9H9:ADALA=K ;GEH9J=< OAL@ L@= GJA?AF9D . 9F<
L@9L ."'. ;9F G:L9AF KMH=JAGJ H=J>GJE9F;= ;GEH9J=< LG GL@=J LQH=K
G> 9D?GJAL@EK DL@GM?@ E9FQ J=K=9J;@=JK FGO AF;GJHGJ9L= GL@=J 9D?G
JAL@EK AFLG . L@= AEHJGN=E=FL KLJ9L=?A=K HJGHGK=< AF L@AK H9H=J 9J=
AFFGN9LAN=
UNCORRECTED PROOF
+-5<A2@.9 D=2>@'E?@2:?+6@5==960.@6<;? DDD DDDD
Fig. 7. GFN=J?=F;= ;MJN=K G> K=D=;L=< :=F;@E9JC >MF;LAGFK
7. SGLSCA for the engineering benchmarks
$F J=9DOGJD< HJG:D=EK 9F< KAEMD9LAGF KLM<A=K O= E9Q F==< LG <=9D
OAL@ <A>>=J=FL DAEAL9LAGFK 9F< 9<<ALAGF9D G:B=;LAN=K >GJ KGE= G> L@= N9JA
9:D=K !M !GJLAFG 'A +9;= 49F? 'N 'A 3M 49F?
.@A 29F? /9F? 5@GF? .@A 29F? 5@GF? /9F?
@=F? -9F 'AM 5@9F? #=F;= O= K=D=;L=< KGE=
=F?AF==JAF? HJG:D=EK LG >MJL@=J N=JA>Q L@= HGL=FLA9D G> L@= HJGHGK=<
.:9K=< N9JA9FL AF @9F<DAF? ;9K=K OAL@ ;GFKLJ9AF=< N9JA9:D=K $F L@AK
K=;LAGF ."'. @9K =PH=JAE=FL=< GF L@J== <A>>=J=FL =F?AF==JAF? <=KA?F
HJG:D=EK L=FKAGF;GEHJ=KKAGF KHJAF? <=KA?F HJG:D=E /. $:=9E <=
KA?F HJG:D=E $ 9F< HJ=KKMJ= N=KK=D <=KA?F HJG:D=E +1 O@A;@
9J= =PL=FKAN=DQ 9HHDA=< AF L@= J=K=9J;@ ;GEEMFALQ LG =N9DM9L= L@= ;GF
KLJ9AF=< GHLAEAR9LAGF ;9H9:ADALQ G> L@= (K
(' =></92:
/@= ?G9D G> L@AK HJG:D=E AK LG XF< L@= :=KL KGDMLAGF >GJ /. $F L@AK
EG<=DAF? ."'. AK MK=< LG GHLAEAR= L@J== <=KA?F N9JA9:D=K AL=J9LAN=DQ
/@= E9AF H9J9E=L=JK AFNGDN=< 9J= AF;DM<AF? OAJ= <A9E=L=J E=9F
;GAD <A9E=L=J 9F< L@= FME:=J G> 9;LAN= ;GADK /@= J=D9L=< EG<=D
G> L@= HJG:D=E AK K@GOF :=DGO
GFKA<=J
*:B=;LAN=
.M:B=;LLG
19JA9:D=J9F?=K
/@AK GHLAEAR9LAGF HJG:D=E @9K :==F J=KGDN=< :Q KGE= J=K=9J;@=JK MKAF?
N9JAGMK E=L@G<K !GJ =P9EHD= #= 9F< 29F? 9<GHL=< L@= +.*
LG J=KGDN= L@AK =F?AF==JAF? HJG:D=E =>>=;LAN=DQ 9F< L@= XF9D GHLAEAR9
LAGF J=KMDL O9K G=DDG G=DDG @9K MLADAR=< 9 "=F=LA;
D?GJAL@E " LG K=LLD= AL OAL@ L@= :=KL O=A?@L G> =KA<=K
AL @9K :==F J=KGDN=< :Q L@= AEHJGN=< #9JEGFQ .=9J;@ $#. 9D?GJAL@E
(9@<9NA =L 9D &9N=@ 9F< &@9Q9L9R9< MK=< -9Q
*HLAEAR9LAGF -* LG J=KGDN= AL 9F< L@= XF9D J=KMDLK K@GO=< L@= :=KL
O=A?@L G> DKG L@AK HJG:D=E O9K J=K=9J;@=< :Q LOG E=L@
G<K =D=?MF<M (9JD=J 9F< JGJ9
/@= <=L9AD=< ;GEH9JAKGF J=KMDLK 9J= <=EGFKLJ9L=< AF /9:D= $L
;9F := K==F L@9L ."'. ?=LK :=LL=J KMH=JAGJALQ LG GL@=J KGDMLAGFK AF
L@= DAL=J9LMJ= =KA<=K L@= GJA?AF9D . ;9FFGL KMJH9KK -* 9F< +.*
>GJ J=KGDNAF? L@AK HJG:D=E <=KHAL= L@= H=J>GJE9F;= G> ."'. /9CAF?
UNCORRECTED PROOF
+-5<A2@.9 D=2>@'E?@2:?+6@5==960.@6<;? DDD DDDD
Table 8
-=KMDLK G> ."'. 9F< 9<N9F;=< (K GF :=F;@E9JC >MF;LAGFK
PH9F<
F1 F2 F3
N? .L< N? .L< N? .L<
SGLSCA 0.0000E + 00 0.0000E + 00 0.0000E + 00 0.0000E + 00 0.0000E + 00 0.0000E + 00
'.# ;F H.AF − 0.0000E + 00 − − − −
'.# − 0.0000E + 00 − − − −
. − − − − − −
$2* 0.0000E + 00 0.0000E + 00 0.0000E + 00 0.0000E + 00
'2* − − − −
− −
'* − − − − −
'+.* − − − −
'+.* − − − −
F4 F5 F6
N? .L< N? .L< N? .L<
SGLSCA 0.0000E + 00 0.0000E + 00 1.7343 −01 4.8067 −05 5.1124 −05
'.# −;F H.AF − − − −
'.# − − − −
. − − − −
$2* − − − − −
'2* − − − −
− −
'* − −
'+.* − 7.9359 −01 − −
'+.* − − − −
F7 F8 F9
N? .L< N? .L< N? .L<
SGLSCA − 7.4952 −03 0.0000E + 00 0.0000E + 00 8.8818 −16 0.0000E + 00
'.# −;F H.AF −1.2828E + 04 −
'.# − − − −
. − − − −
$2* − 0.0000E + 00 0.0000E + 00 − −
'2* − − −
−
'* − −
'+.* − 0.0000E + 00 0.0000E + 00 − −
'+.* − −
F10 F11 F12
N? .L< N? .L< N? .L<
SGLSCA 0.0000E + 00 0.0000E + 00 9.9800 −01 2.3406 −16 3.0749 −04 −
'.# −;F H.AF − − 9.9800 −01 0.0000E + 00 − −
'.# − − 9.9800 −01 0.0000E + 00 − −
. − − 9.9800 −01 0.0000E + 00 3.0749 −04 6.9985 −20
$2* 0.0000E + 00 0.0000E + 00 9.9800 −01 − − −
'2* − − 9.9800 −01 − − −
− − − −
'* − −
'+.* 0.0000E + 00 0.0000E + 00 9.9800 −01 0.0000E + 00 − −
'+.* − − 9.9800 −01 − − −
F13 F14 F15
N? .L< N? .L< N? .L<
SGLSCA −1.0153E + 01 − −1.0403E + 01 −
'.# −;F H.AF − − 2.4645E + 03
'.# − −1.0403E + 01 − 2.0868E + 03
. −1.0153E + 01 0.0000E + 00 −1.0403E + 01 −
$2* −1.0153E + 01 − −1.0403E + 01 −
'2* − −
− −
'* − −
'+.* −1.0153E + 01 − −1.0403E + 01 −
'+.* −1.0153E + 01 − −1.0403E + 01 1.7764 −15
F16 F17 F18
UNCORRECTED PROOF
+-5<A2@.9 D=2>@'E?@2:?+6@5==960.@6<;? DDD DDDD
N? .L< N? .L< N? .L<
SGLSCA −
'.# −;F H.AF 5.2001E + 02 5.9529 −03
'.# 4.0008E + 02 2.0067 −01 5.2001E + 02 −
. − 6.0863E + 02 1.3922E + 00
$2* −
'2* −
−
'* −
'+.* −
'+.* −
F19 F20 F21
N? .L< N? .L< N? .L<
SGLSCA − −
'.# −;F H.AF 1.6722E + 02 1.2001E + 03 2.3581 −02 −
'.# 2.8180E + 03 1.2001E + 03 − −
. − 1.4002E + 03 −
$2* − −
'2* − −
− −
'* − −
'+.* − 2.4456 −02
'+.* − −
F22 F23 F24
N? .L< N? .L< N? .L<
SGLSCA −
'.# −;F H.AF −
'.# 1.5058E + 03 1.6093E + 03 − 3.0722E + 03 6.1179E + 02
. 2.8221 −01
$2* −
'2* −
−
'* −
'+.* 1.3167E + 00 −
'+.* −
F25 F26 F27
N? .L< N? .L< N? .L<
SGLSCA
'.# −;F H.AF
'.# 2.1838E + 03 5.6472E + 01 2.7805E + 03 1.7358E + 02
.
$2*
'2*
'*
'+.* 1.8878E + 03 2.8831E + 01
'+.*
F28 F29 F30
N? .L< N? .L< N? .L<
SGLSCA 2.5000E + 03 0.0000E + 00 2.6000E + 03 0.0000E + 00 2.7000E + 03 0.0000E + 00
'.# −;F H.AF −
'.# − −
. −
$2* −
'2* −
−
'* −
'+.* − − −
'+.* −
F31 F32 F33
N? .L< N? .L< N? .L<
SGLSCA 2.9000E + 03 0.0000E + 00 3.0000E + 03 0.0000E + 00 3.1000E + 03 0.0000E + 00
'.# −;F H.AF
'.#
UNCORRECTED PROOF
+-5<A2@.9 D=2>@'E?@2:?+6@5==960.@6<;? DDD DDDD
.
$2*
'2*
'*
'+.*
'+.*
F34 *N=J9DD-9FC
N? .L< -9FC −-1
SGLSCA 3.2000E + 03 0.0000E + 00 1 U2.911765
'.# ;F H.AF
'.#
.
$2*
'2*
'*
'+.*
'+.*
Fig. 8. GFN=J?=F;= ;MJN=K G> ."'. 9F< 9<N9F;=< (K GF K=D=;L=< :=F;@E9JC >MF;LAGFK
=N=JQL@AF? AFLG 9;;GMFL L@= ."'. <J9E9LA;9DDQ =F@9F;=K L@= H=J>GJ
E9F;= G> L@= GJA?AF9D . 9F< ;9F := J=?9J<=< 9K 9 >9NGJ9:D= KGDMLAGF
>GJ L@AK HJG:D=E
=></92:
FGL@=J =F?AF==JAF? HJG:D=E OGJL@ KLM<QAF? AK L@= $ HJG:D=E
O@A;@ 9AEK LG 9LL9AF L@= GHLAE9D ;GKL /@AK HJG:D=E AK ;GEHJAK=< G>
UNCORRECTED PROOF
+-5<A2@.9 D=2>@'E?@2:?+6@5==960.@6<;? DDD DDDD
Table 9
/@= O9DD;DG;C LAE= ;GKL G> N9JAGMK . N9JA9FLK GF :=F;@E9JC >MF;LAGFK
! ."'. .'. .". "'. .. ". '. .
!
!
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>GMJ H9J9E=L=JK AF;DM<AF? D=F?L@ @=A?@L 9F< LOG L@A;CF=KK=K /@= J=
D9L=< EG<=D G> L@= HJG:D=E AK K@GOF :=DGO
GFKA<=J
*:B=;LAN=
.M:B=;LLG
19JA9:D=J9F?=K
/@= ."'. O9K =EHDGQ=< LG <=9D OAL@ L@AK HJG:D=E AF;DM<AF? KAP
GL@=J AFNGDN=< GHLAEAR9LAGF 9D?GJAL@EK .QE:AGLA; *J?9FAKEK .=9J;@
.*. @=F? +J9QG?G <9HLAN= -=KHGFK= .MJ>9;= (=L@G<
GDG?Q -.( (9F=K@ =L 9D . "9F<GEA =L 9D :
9F< $EHJGN=< -.( $-.( (9F=K@ =L 9D AF L@AK K=;LAGF
=KA<=K L@= GJA?AF9D . @9K :==F 9<GHL=< 9F< /9:D= DAKL=< K=N=F
<A>>=J=FL L=KL J=KMDLK >GJ J=KGDNAF? L@= $ HJG:D=E
K ;9F := K==F >JGE /9:D= ."'. G:L9AFK 9F GHLAEME ;GKL G>
$L AF<A;9L=K L@= XF9D J=KMDL AK KMHHGK=< LG := 9 EAFAEME
O@=F L@= 9F< 9J= K=L 9K 9F< /@=J=>GJ=
AL AF<A;9L=K L@9L ."'. ;9F J=KGDN= L@AK HJG:D=E =>>=;LAN=DQ 9F< ;9F G>
>=J =>>=;LAN= KGDMLAGFK >GJ L@= $ HJG:D=E
$* =></92:
+1 AK 9 HJG:D=E L@9L ;9F := LJ=9L=< :9K=< GF ."'. O@A;@ 9AEK
LG E9C= L@= ;GKL G> L@= ;QDAF<JA;9D N=KK=D D=9KL /@= >GMJ H9J9E=L=JK L@9L
F==< LG := <=L=JEAF=< AF L@AK EG<=D 9J= L@= L@A;CF=KK G> L@= @=9<
L@= L@A;CF=KK G> L@= K@=DD L@= D=F?L@ G> L@= ;QDAF<JA;9D K=;LAGF OAL@
GML ;GFKA<=JAF? L@= @=9< 9F< L@= AFF=J J9<AMK /@= E9L@=E9LA;9D
EG<=D G> L@AK HJG:D=E AK K@GOF :=DGO
GFKA<=J
*:B=;LAN=
.M:B=;LLG
19JA9:D=J9F?=K
#= 9F< 29F? K=LLD=< L@AK HJG:D=E :9K=< GF +.* 9F< L@= J=
UNCORRECTED PROOF
+-5<A2@.9 D=2>@'E?@2:?+6@5==960.@6<;? DDD DDDD
Table 10
/@= O9DD;DG;C LAE= ;GKL G> O=DDCFGOF (K GF :=F;@E9JC >MF;LAGFK
! . +.* "2* 2* (!* ! ..
!
!
!
!
!
!
!
!
!
!
!
!
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KMDL 9LL9AF=< O9K 0HJ=LA 9F< =: 9HHDA=< " LG
L@AK HJG:D=E 9F< 9LL9AF=< L@= :=KL N9DM= G> =KA<=K NGDM
LAGF .LJ9L=?A=K . (=RMJ9(GFL=K G=DDG $#. (9@<9NA
=L 9D 9F< E9L@=E9LA;9D E=L@G< &9FF9F &J9E=J
.9F<?J=F O=J= 9DD MK=< LG KGDN= L@=K= HJG:D=EK
/@= GHLAEAR9LAGF J=KMDL G> L@= AFNGDN=< E=L@G<K AF L@AK K=;LAGF 9:GML
L@= +1 HJG:D=E AK K@GOF AF /9:D= K ;9F := K==F L@= ."'. G:
L9AFK 9 EAFAEME N9DM= G> AK O@A;@ AF<A;9L=K L@9L L@= EGKL
9HHJGHJA9L= ;GKL ;QDAF<JA;9D +1 AK L@= KE9DD=KL O@=F 9F< 9J=
=IM9D LG 9F< K AK K@GOF AF /9:D=
."'. G:L9AFK 9 EAFAEME ;GKL AF 9DD AFNGDN= 9D?GJAL@EK /@=J=
>GJ= ."'. HJGNA<=K ?J=9L @=DH :=QGF< L@= GL@=J 9D?GJAL@EK >GJ L@=
+1 HJG:D=E
$F L@AK K=;LAGF 9;;GJ<AF? LG L@= KLM<Q G> L@J== =F?AF==JAF? HJG:D=EK
L@= XF9D J=KMDLK @=DH MK LG CFGO L@9L ."'. AK ;9H9:D= G> <=;A<AF?
HJ9;LA;9D =F?AF==JAF? <=KA?F HJG:D=EK OAL@ :=LL=J KGDMLAGFK L@9F GL@=J
AFNGDN=< JAN9DK (=9FO@AD= AL AK N=JAX=< L@9L L@= HJGHGK=< EMDLA;GJ=
."'. ;9F KGDN= L@= ;GFKLJ9AFL GHLAEAR9LAGF HJG:D=E =>>=;LAN=DQ
8. Conclusions and future directions
$F L@AK H9H=J 9 FGN=D EMDLA;GJ= . E=L@G<GDG?Q ."'. AK HJG
HGK=< O@A;@ AFL=?J9L=K .. "2* 9F< '! E=;@9FAKE AFLG L@= :9KA;
. LG KLJ=F?L@=F ALK H=J>GJE9F;= .H=;A>A;9DDQ L@= MH<9LAF? KLJ9L=?A=K
G> .. 9F< "2* 9J= ;GGH=J9L=< LG >MJL@=J :GGKL L@= =PHDGJ9LAGF 9F<
=PHDGJ9LAGF <JA>LK 9F< '! MH<9LAF? KLJ9L=?Q AK ;GFKA<=J=< LG H=J>GJE
L@= J9F<GE AF<ANA<M9D O9DC AF L@= =PHDGJ9LAGF AFL=JN9D 9F< >MJL@=J =F
@9F;= L@= ;9H9;ALQ G> L@= 9D?GJAL@E LG =K;9H= >JGE DG;9D GHLAE9D !GJ
L@= K9C= G> JA?GJGMKDQ N9DA<9LAF? L@= H=J>GJE9F;= G> ."'. KGE=
O=DDCFGOF (K 9F< 9<N9F;=< KL9L=G>L@=9JL (K AF;DM<AF? .
+.* "2* . 2* ! .. (!* . N9JA9FLK
'.# ;F H.AF '.# . $2* '2* '*
'+.* 9F< '+.* 9J= AFNGDN=< >GJ ;GEH9JAKGF GF :=F;@E9JC
>MF;LAGFK K=D=;L=< >JGE :=F;@E9JC >MF;LAGFK 9F< $
HJG:D=EK /@= XF9D KAEMD9LAGF J=KMDLK @9N= K@GOF L@= =NA<=FL KMH=JA
GJALQ G> L@= HJGHGK=< ."'. 9F< 9DKG ;GFXJE=< L@9L ."'. KA?FA>A
;9FLDQ =F@9F;=K L@= MF<=JDQAF? =PHDGJ9LAGF 9F< =PHDGAL9LAGF ;9H9;ALA=K
G> . 9F< C==HK L@= E=L@G< 9O9Q >JGE L@= DG;9D GHLAEME 9K O=DD $F
9<<ALAGF ."'. HJ=K=FL=< AF L@AK H9H=J K@GOK @A?@ ;GFN=J?=F;= 9:AD
ALQ 9F< AL <=L=;LK KMH=JAGJ KGDMLAGFK LG HJ9;LA;9D =F?AF==JAF? HJG:D=EK
$F >MLMJ= OGJCK L@= >GDDGOAF? <AJ=;LAGFK 9J= N9DM9:D= !AJKL ."'.
;9F := 9HHDA=< LG <AK;J=L= 9F< EMDLAG:B=;LAN= N9JA=LA=K >GJ KGDNAF? <AK
;J=L= L9KCK .MF 4=F 4A =KA<=K ?AN=F L@= =PAKL=F;= G> FM
E=JGMK 9D?GJAL@EK ;GEH9JAF? L@= AEHJGN=E=FLK E9<= :9K=< GF =E
:=<<AF? ;GJ=K OADD := 9F =P;ALAF? <AJ=;LAGF $F 9<<ALAGF ."'. ;9F
9DKG := MK=< >GJ H9J9E=L=J LMFAF? >GJ L@= E9;@AF= D=9JFAF? E=L@G<K
KM;@ 9K KMHHGJL N=;LGJ E9;@AF=K @=F =L 9D #M9F? =L 9D
'A =L 9D .@=F =L 9D 29F? @=F
=PLJ=E= D=9JFAF? E9;@AF=K @=F =L 9D @=F 5@9F?
'MG 3M 5@9F? 'A =L 9D ; 'MG =L 9D
29F? =L 9D : 9F< ;GFNGDMLAGF9D F=MJ9D F=LOGJCK 'A =L 9D
'A 'AM /9F? '=A .MF 3M= 5@9F? 4=F
.MF 3M= 5@9F? 4=F 'N 5@9F? 29F? 29F? /9F?
UNCORRECTED PROOF
+-5<A2@.9 D=2>@'E?@2:?+6@5==960.@6<;? DDD DDDD
Table 11
/@= O9DD;DG;C LAE= ;GKL G> AEHJGN=< . N9JA9FLK GF :=F;@E9JC >MF;LAGFK
! (. .+.* E. . ". *.
!
!
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Fig. 9. GEH9JAKGF G> N9JAGMK . N9JA9FLK GF :=F;@E9JC >MF;LAGFK
5@9G /@= :AF9JQ N=JKAGF G> ."'. ;9F 9DKG := L9C=F AFLG ;GF
KA<=J9LAGF AF >=9LMJ= =PLJ9;LAGF 3AGF? 5@9F? 29F? "M
>=9LMJ= K=D=;LAGF HJG:D=EK #M9F? =L 9D 'A =L 9D :
5@9F? !9F 29F? 5@GM /9G 5@9F? =L 9D *L@=J
HJG:D=EK AF;DM<= HJG<M;LAGF 9F< <AKLJA:MLAGF HJG:D=E
'AM 'AM KG;A9D E9FM>9;LMJAF? GHLAEAR9LAGF 3M= 29F?
5@9F !=F? "MG ?=G?J9H@A; AF>GJE9LAGF KQKL=EK 5@M
29F? @=F 2M &AE 9F< NA<=G ;G<AF? GHLAEAR9LAGF
5@GM /A9F 5@M %AF .MF H9J9E=L=J =KLAE9LAGF G> KG
D9J ;=DD ::9KKA =L 9D %A9G =L 9D -A<@9 #=A<9JA
UNCORRECTED PROOF
+-5<A2@.9 D=2>@'E?@2:?+6@5==960.@6<;? DDD DDDD
Table 12
/@= O9DD;DG;C LAE= ;GKL G> 9<N9F;=< KL9L=G>L@=9JL (K GF :=F;@E9JC >MF;LAGFK
!'.# −;F H.AF '.# . $2* '2* '* '+.* '+.*
!
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29F? @=F 5@9F? =L 9D O@A;@ 9J= 9DKG AFL=J=KL
AF? LGHA;K L@9L OGJL@Q G> AFN=KLA?9LAGF AF L@= F=9J >MLMJ=
Declaration of Competing Interest
/@= 9ML@GJK <=;D9J= L@9L L@=Q @9N= FG CFGOF ;GEH=LAF? XF9F;A9D AF
L=J=KLK GJ H=JKGF9D J=D9LAGFK@AHK L@9L ;GMD< @9N= 9HH=9J=< LG AFYM=F;=
L@= OGJC J=HGJL=< AF L@AK H9H=J
Acknowledgments
/@AK J=K=9J;@ AK KMHHGJL=< :Q L@= 5@=BA9F? +JGNAF;A9D )9LMJ9D .;A
=F;= !GMF<9LAGF G> @AF9 '%! .;A=F;= 9F< /=;@FGDG?Q +D9F
+JGB=;L G> 2=FR@GM @AF9 5" 5" 9F< )9LAGF9D
)9LMJ9D .;A=F;= !GMF<9LAGF G> @AF9 0 (=<A;9D
9F< #=9DL@ /=;@FGDG?Q +JGB=;LK G> 5@=BA9F? HJGNAF;= - 9F<
"M9F?<GF? )9LMJ9D .;A=F;= !GMF<9LAGF (* (AF
AKLJQ G> <M;9LAGF AF @AF9 4GML@ !MF< +JGB=;L G> #ME9FALA=K 9F< .G
;A9D .;A=F;=K 4%5# .;A=FLAX; -=K=9J;@ /=9E +JGB=;L G> .@=F
R@=F $FKLALML= G> $F>GJE9LAGF /=;@FGDG?Q .5$$/&% )9LAGF9D
)9LMJ9D .;A=F;= !GMF<9LAGF G> @AF9
UNCORRECTED PROOF
+-5<A2@.9 D=2>@'E?@2:?+6@5==960.@6<;? DDD DDDD
Fig. 10. /AE= ;GFKMEHLAGF G> AFNGDN=< E=L@G<K GF :=F;@E9JC >MF;LAGFK
UNCORRECTED PROOF
+-5<A2@.9 D=2>@'E?@2:?+6@5==960.@6<;? DDD DDDD
Fig. 11. AN=JKALQ HDGL >GJ L=KL >MF;LAGFK
Table 13
-=KMDLK G> ."'. 9F< AFNGDN=< E=L@G<K >GJ /. HJG:D=E
(=L@G< *HLAE9DJ=KMDLK>GJH9J9E=L=JK
=KL
O=A?@L
SGLSCA 0.0126669
.
+.*#=29F?0.0157
"G=DDGG=DDG
-*&9N=@&@9Q9L9R9<
$#.(9@<9NA!=K9F?@9JQ
9E9F?AJ
GFKLJ9AFL;GJJ=;LAGFE=L@G<
=D=?MF<M
0.3159
(9L@=E9LA;9DGHLAEAR9LAGF
E=L@G<(9JD=JJGJ9
9.0185
UNCORRECTED PROOF
+-5<A2@.9 D=2>@'E?@2:?+6@5==960.@6<;? DDD DDDD
Table 14
-=KMDLK G> ."'. 9F< AFNGDN=< 9D?GJAL@EK >GJ $ HJG:D=E
D?GJAL@E *HLAE9DN9DM=K>GJH9J9E=L=JK *HLAEME;GKL
SGLSCA 50.006625958
.
(!*
(AJB9DADA
.*.@=F?
+J9QG?G
0.9
-.(
(9F=K@
(GL9N9DDA9F
!9LL9@A
37.05 2.31
."9F<GEA
49F?
D9NA:
0.9
$-.(
(9F=K@=L
9D
79.99 0.9
Table 15
-=KMDLK G> ."'. 9F< AFNGDN=< 9D?GJAL@EK >GJ L@= +1 HJG:D=E
D?GJAL@E *HLAEMEN9DM=K>GJH9J9E=L=JK
*HLAEME
;GKL
SGLSCA 5805.8660
. 15.2741
$#.
(9@<9NA
=L9D
+.*#=
29F?
0.8125 0.4375 42.091266
"0HJ=LA
=:
.(=RMJ9
(GFL=K
G=DDG
0.8125 0.4375
'9?J9F?A9F
EMDLAHDA=J
&9FF9F
&J9E=J
J9F;@9F<
:GMF<
.9F<?J=F
References
::9KKA ::9KKA - #=A<9JA *DAN9 @=F # #9:A: …29F? (
+9J9E=L=JK A<=FLAX;9LAGF G> H@GLGNGDL9A; ;=DD EG<=DK MKAF? =F@9F;=< =PHDGJ9LGJQ K9DH
;@9AFK:9K=< 9HHJG9;@ F=J?Q
::9KKA - ::9KKA #=A<9JA (AJB9DADA . F =Z;A=FL K9DH
KO9JEAFKHAJ=< 9D?GJAL@E >GJ H9J9E=L=JK A<=FLAX;9LAGF G> H@GLGNGDL9A; ;=DD EG<=DK
F=J?Q GFN=JKAGF 9F< (9F9?=E=FL –
:< D9RAR ( *DAN9 3AGF? . F AEHJGN=< *HHGKALAGF9K=< .AF= GKAF=
D?GJAL@E >GJ ?DG:9D GHLAEAR9LAGF PH=JL .QKL=EK OAL@ HHDA;9LAGFK –
O9< ) # DA ( 5 .M?9FL@9F + ) FK=E:D= KAFMKGA<9D <A>>=J=FLA9D ;G
N9JA9F;= E9LJAP 9<9HL9LAGF OAL@ M;DA<=9F F=A?@:GJ@GG< >GJ KGDNAF? :=F;@
E9JC HJG:D=EK $F $ GF?J=KK GF NGDMLAGF9JQ GEHML9LAGF +JG
;==<AF?K HH
Q<G?<M $ GKL GHLAEAR9LAGF G> J=AF>GJ;=< ;GF;J=L= ;9FLAD=N=J J=L9AFAF? O9DDK
MF<=J K=AKEA; DG9<AF? MKAF? 9 :AG?=G?J9H@Q:9K=< GHLAEAR9LAGF 9D?GJAL@E OAL@ '=NQ
YA?@LK F?AF==JAF? *HLAEAR9LAGF –
=D=?MF<M .LM<Q G> (9L@=E9LA;9D +JG?J9EEAF? (=L@G<K >GJ .LJM;LMJ9D
*HLAEAR9LAGF
9A 5 "M % 'MG % 5@9F? , @=F # +9F 5 …'A NGDNAF? 9F GHLAE9D
C=JF=D =PLJ=E= D=9JFAF? E9;@AF= :Q MKAF? 9F =F@9F;=< ?J=Q OGD> GHLAEAR9LAGF
KLJ9L=?Q PH=JL .QKL=EK OAL@ HHDA;9LAGFK
9G 4 5@9F? # 'A 2 5@GM ( 5@9F? 4 @9GN9DALOGF?K= 2
GEHJ=@=FKAN= D=9JFAF? H9JLA;D= KO9JE GHLAEAR9LAGF 9D?GJAL@E OAL@ DG;9D K=9J;@ >GJ
EMDLAEG<9D >MF;LAGFK $ /J9FK9;LAGFK GF NGDMLAGF9JQ GEHML9LAGF –
@=F #' 29F? " (9 9A 5) 'AM 2 29F? .% F =Z;A=FL
@Q:JA< C=JF=D =PLJ=E= D=9JFAF? E9;@AF= 9HHJG9;@ >GJ =9JDQ <A9?FGKAK G> +9JCAFKGF׳K
<AK=9K= )=MJG;GEHMLAF? –
@=F # #=A<9JA 5@9G 3 5@9F? ' @=F # <N9F;=< *JL@G?GF9D
'=9JFAF?JAN=F (MDLA.O9JE .AF= GKAF= *HLAEAR9LAGF !J9E=OGJC 9F< 9K= .LM<A=K
PH=JL .QKL=EK OAL@ HHDA;9LAGFK <GA@LLHK<GAGJ?
B=KO9
@=F # #M ' 'A # #GF? " 5@9F? / (9 % 'M 5 F =[=;LAN= E9;@AF=
D=9JFAF? 9HHJG9;@ >GJ HJG?FGKAK G> H9J9IM9L HGAKGFAF? H9LA=FLK MKAF? :DGG< JGMLAF=
AF<=P=K 9KA; DAFA;9D +@9JE9;GDG?Q /GPA;GDG?Q –
@=F # %A9G . #=A<9JA 29F? ( @=F 3 5@9G 3 F
GHHGKALAGF:9K=< KAF= ;GKAF= 9HHJG9;@ OAL@ DG;9D K=9J;@ >GJ H9J9E=L=J =KLAE9LAGF G>
H@GLGNGDL9A; EG<=DK F=J?Q GFN=JKAGF 9F< (9F9?=E=FL –
@=F # %A9G . 29F? ( #=A<9JA 5@9G 3 +9J9E=L=JK A<=FLAX;9LAGF
G> H@GLGNGDL9A; ;=DDK 9F< EG<MD=K MKAF? <AN=JKAX;9LAGF=FJA;@=< #9JJAK @9OCK
GHLAEAR9LAGF OAL@ ;@9GLA; <JA>LK %GMJF9D G> D=9F=J +JG<M;LAGF
<GA@LLHK<GAGJ?BB;D=HJG
@=F # 'A . #=A<9JA 29F? + 'A % 49F? 4 #M9F? Z;A=FL
EMDLAHGHMD9LAGF GMLHGKL >JMAL YQ<JAN=F GHLAEAR=JK !J9E=OGJC 9F< 9<N9F;=K AF
KMHHGJL N=;LGJ E9;@AF=K PH=JL .QKL=EK OAL@ HHDA;9LAGFK <GA@LLHK
<GAGJ?B=KO9
@=F # 29F? ( 5@9G 3 EMDLAKLJ9L=?Q =F@9F;=< KAF= ;GKAF= 9D?GJAL@E
>GJ ?DG:9D GHLAEAR9LAGF 9F< ;GFKLJ9AF=< HJ9;LA;9D =F?AF==JAF? HJG:D=EK HHDA=<
(9L@=E9LA;K 9F< GEHML9LAGF <GA@LLHK<GAGJ?
B9E;
@=F # 3M 4 29F? ( 5@9G 3 :9D9F;=< O@9D= GHLAEAR9LAGF 9D?GJAL@E
>GJ ;GFKLJ9AF=< =F?AF==JAF? <=KA?F HJG:D=EK HHDA=< (9L@=E9LA;9D (G<=DDAF?
–
@=F # 49F? #=A<9JA 5@9G 3 F >X;A=FL GM:D= <9HLAN= -9F
<GE .H9J= -=AF>GJ;=< 2@9D= *HLAEAR9LAGF D?GJAL@E PH=JL .QKL=EK OAL@ HHDA;9
LAGFK
@=F # 5@9F? , 'MG % 3M 4 5@9F? 3 F =F@9F;=< 9;L=JA9D !GJ9?AF?
*HLAEAR9LAGF 9F< ALK 9HHDA;9LAGF >GJ LJ9AFAF? C=JF=D =PLJ=E= D=9JFAF? E9;@AF=
HHDA=< .G>L GEHMLAF? <GA@LLHK<GAGJ?
B9KG;
@=F # 5@9F? , 'MG % 3M 4 5@9F? 3 F =F@9F;=< 9;L=JA9D !GJ9?AF?
*HLAEAR9LAGF 9F< ALK 9HHDA;9LAGF >GJ LJ9AFAF? C=JF=D =PLJ=E= D=9JFAF? E9;@AF=
HHDA=< .G>L GEHMLAF?
@=F 2) 5@9F? % 'AF 4 @=F ) 5@9F 5# @MF? #.# ….@A 4#
+9JLA;D= KO9JE GHLAEAR9LAGF OAL@ 9F 9?AF? D=9<=J 9F< ;@9DD=F?=JK $ /J9FK9;LAGFK
GF NGDMLAGF9JQ GEHML9LAGF –
@=F? (4 +J9QG?G .QE:AGLA; GJ?9FAKEK K=9J;@ F=O E=L9@=MJAKLA;
GHLAEAR9LAGF 9D?GJAL@E GEHML=JK 9F< .LJM;LMJ=K –
G=DDG G=DDG 0K= G> 9 K=D>9<9HLAN= H=F9DLQ 9HHJG9;@ >GJ =F?AF==JAF?
GHLAEAR9LAGF HJG:D=EK GEHML=JK AF $F<MKLJQ –
=F? 2 3M % 5@9G # F AEHJGN=< 9FL ;GDGFQ GHLAEAR9LAGF 9D?GJAL@E :9K=<
GF @Q:JA< KLJ9L=?A=K >GJ K;@=<MDAF? HJG:D=E $ ;;=KK –
=F? 2 5@9G # 5GM ' 'A " 49F? 3 2M FGN=D ;GDD9:GJ9LAN=
GHLAEAR9LAGF 9D?GJAL@E AF KGDNAF? ;GEHD=P GHLAEAR9LAGF HJG:D=EK .G>L GEHMLAF?
–
GK .9FLGK G=D@G ' GJ9 / (9JA9FA 1 A[=J=FLA9D =NGDMLAGF :9K=< GF
LJMF;9L=< 'VNQLQH= YA?@LK 9F< HGHMD9LAGF <AN=JKALQ E=9KMJ= LG KGDN= =;GFGEA; DG9<
<AKH9L;@ HJG:D=EK $FL=JF9LAGF9D %GMJF9D G> D=;LJA;9D +GO=J 9F< F=J?Q .QKL=EK
–
GM - M9F # 'VNQ YA?@L :9K=< HA?=GFAFKHAJ=< GHLAEAR9LAGF >GJ ;GFLJGD
H9J9E=L=JK GHLAEAR9LAGF AF 9MLGE9LA; ;9JJA=J D9F<AF? KQKL=E =JGKH9;= .;A=F;= 9F<
/=;@FGDG?Q –
D.@GJ:9?Q ( !9J9? ( (GMK9 D=KGCQ $ ( #Q:JA<AR9LAGF
G> .AF= GKAF= D?GJAL@E OAL@ .L=9<Q .L9L= "=F=LA; D?GJAL@E >GJ F?AF==JAF? =KA?F
+JG:D=EK $F <N9F;=K AF $FL=DDA?=FL .QKL=EK 9F< GEHMLAF? 1GD HH
M<9FA & @M<9K9E9 - +9JLA9D <AK;@9J?= <=L=;LAGF AF LJ9FK>GJE=J MKAF?
9<9HLAN= ?J=Q OGD> GHLAEAR=J :9K=< 9;GMKLA; =EAKKAGF L=;@FAIM= G?=FL F?AF==JAF?
<GA
!9F 4 29F? + #=A<9JA 29F? ( 5@9G 3 @=F # 'A
-9LAGF9DAR=< !JMAL YQ GHLAEAR9LAGF OAL@ KAF= ;GKAF= 9D?GJAL@E ;GEHJ=@=FKAN=
9F9DQKAK PH=JL .QKL=EK OAL@ HHDA;9LAGFK <GA@LLHK<GAGJ?
B=KO9
!M 3 !GJLAFG " 'A 2 +9;= + 49F? 4 2.)K9KKAKL=< GHHGJLMFAKLA;
F=LOGJC >GJ DGOD9L=F;Q E=KK9?= >GJO9J<AF? AF KH9JK= K=LLAF?K !MLMJ= ?=F=J9LAGF
;GEHML=J KQKL=EK – <GAB>MLMJ=
"9F<GEA # 49F? 3. D9NA # M;CGG K=9J;@ 9D?GJAL@E
E=L9@=MJAKLA; 9HHJG9;@ LG KGDN= KLJM;LMJ9D GHLAEAR9LAGF HJG:D=EK F?AF==JAF? OAL@
GEHML=JK –
"9F<GEA # 49F? 3. D9NA # JJ9LME M;CGG K=9J;@ 9D?GJAL@E
E=L9@=MJAKLA; 9HHJG9;@ LG KGDN= KLJM;LMJ9D GHLAEAR9LAGF HJG:D=EK F?AF==JAF? OAL@
GEHML=JK *$KQ F?AF==JAF? OAL@ GEHML=JK
UNCORRECTED PROOF
+-5<A2@.9 D=2>@'E?@2:?+6@5==960.@6<;? DDD DDDD
"MG % 5@9F? 3 "M ! 5@9F? # !9F 4 G=K 9AJ HGDDMLAGF KLAEMD9L=
=D=;LJA; N=@A;D= K9D=K EHAJA;9D =NA<=F;= >JGE LO=FLQ E9BGJ ;ALA=K AF @AF9 %GMJF9D
G> D=9F=J +JG<M;LAGF <GABB;D=HJG
"MHL9 . ==H & @Q:JA< K=D>9<9HLAN= KAF= ;GKAF= 9D?GJAL@E OAL@ GHHGKALAGF
:9K=< D=9JFAF? PH=JL .QKL=EK OAL@ HHDA;9LAGFK –
"MHL9 . ==H & #=A<9JA (G9Q=<A # @=F # #9JEGFAR=< K9DH
;@9AF:MADL GHLAEAR9LAGF F?AF==JAF? OAL@ GEHML=JK <GA
K
#9K9FA=F #( D!=J?9FQ .9DH KO9JE 9D?GJAL@E:9K=< GHLAE9D DG9<
>J=IM=F;Q ;GFLJGD G> @Q:JA< J=F=O9:D= HGO=J KQKL=EK OAL@ ;GEEMFA;9LAGF <=D9Q 9F<
=P;AL9LAGF ;JGKK;GMHDAF? =[=;L D=;LJA; +GO=J .QKL=EK -=K=9J;@
#= , 29F? ' F =[=;LAN= ;G=NGDMLAGF9JQ H9JLA;D= KO9JE GHLAEAR9LAGF
>GJ ;GFKLJ9AF=< =F?AF==JAF? <=KA?F HJG:D=EK F?AF==JAF? HHDA;9LAGFK G> JLAX;A9D
$FL=DDA?=F;= –
#=A<9JA (AJB9DADA . !9JAK # DB9J9@ $ (9>9JB9 ( @=F # #9JJAK
@9OCK GHLAEAR9LAGF D?GJAL@E 9F< 9HHDA;9LAGFK !MLMJ= "=F=J9LAGF GEHML=J
.QKL=EK –
#M9F? # !=F? 3 #=A<9JA 3M 4 29F? ( 'A9F? " …9A 3
-9LAGF9DAR=< KAF= ;GKAF= GHLAEAR9LAGF OAL@ =Z;A=FL K=9J;@AF? H9LL=JFK $ ;;=KK
–
#M9F? # !=F? 3 5@GM . %A9F? % @=F # 'A 4 'A F=O >JMAL YQ
GHLAEAR9LAGF 9D?GJAL@E =F@9F;=< KMHHGJL N=;LGJ E9;@AF= >GJ <A9?FGKAK G> :J=9KL ;9F
;=J :9K=< GF @A?@D=N=D >=9LMJ=K ( AGAF>GJE9LA;K
#M9F? # !=F?9 3 5@GM . %A9F? % @=F # 'A 4 'A F=O >JMAL
YQ GHLAEAR9LAGF 9D?GJAL@E =F@9F;=< KMHHGJL N=;LGJ E9;@AF= >GJ <A9?FGKAK G> :J=9KL
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H9J9<A?E &FGOD=<?=9K=< .QKL=EK –
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–
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UNCORRECTED PROOF
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BF=M;GE
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–
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>GJ ?DG:9D GHLAEAR9LAGF GN=J ;GFLAFMGMK KH9;=K %GMJF9D G> "DG:9D *HLAEAR9LAGF
–
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– <GAK
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–
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