Testing Metric Properties Michal Parnas The

 !! "#
!!$ %&'()*
+,-./012+3/ 4/- 4,0
5 6
5788 99 : ;<8
!! =!8<
68 !!$ %&'()*
> /?/@2A?B 43/C 4/- 4,0
DEFGHIJG
KLMLNO PONQLR STUROSV UMW LM TUQNLRXYUQ NQOO PONQLRS TYUZ UM LPT[QNUMN Q[YO LM \UQL[XS WLS]
RLTYLMOS SXR^ US O\[YXNL[MUQZ _L[Y[`Z UMW SNUNLSNLRSa b MUNXQUY cUPLYZ [c TQ[_YOPS R[MROQMLM`
PONQLRS LS WORLWLM`V `L\OM U PUNQLd e V f^ON^OQ [Q M[N LN LS U WLSNUMRO PONQLR [c U ROQNULM TQO]
WONOQPLMOW NZTOa gOQO fO R[MSLWOQ N^O c[YY[fLM` QOYUdOW \OQSL[M [c SXR^ WORLSL[M TQ[_YOPSh K[Q
UMZ `L\OM PUNQLd e UMW TUQUPONOQ iV fO UQO LMNOQOSNOW LM WONOQPLMLM` j_Z TQ[_LM` e k f^ON^OQ
e ^US U TUQNLRXYUQ PONQLR TQ[TOQNZ l V [Q f^ON^OQ LN LS i]mno cQ[P ^U\LM` N^O TQ[TOQNZa pM i]mno
fO POUM N^UN UN YOUSN UM i]cQURNL[M [c N^O OMNQLOS [c e PXSN _O P[WLqOW S[ N^UN LN [_NULMS N^O
TQ[TOQNZa r^O UY`[QLN^P PUZ sXOQZ N^O PUNQLd [M OMNQLOS e tuvwx [c LNS R^[LROV UMW LS UYY[fOW U
R[MSNUMN TQ[_U_LYLNZ [c OQQ[Qa
yO WOSRQL_O UY`[QLN^PS c[Q NOSNLM` zXRYLWOUM PONQLRSV NQOO PONQLRS UMW XYNQUPONQLRSa KXQ]
N^OQP[QOV fO TQOSOMN UM UY`[QLN^P N^UN NOSNS f^ON^OQ U PUNQLd e LS UM n{{ o|}~n€ ‚ƒ€on€o~„a
pM UYY RUSOS N^O sXOQZ R[PTYOdLNZ UMW QXMMLM` NLPO UQO T[YZM[PLUY LM …†i UMW LMWOTOMWOMN [c
N^O SL‡O [c N^O PUNQLda KLMUYYZV [XQ UY`[QLN^PS RUM _O XSOW N[ S[Y\O QOYUdOW \OQSL[MS [c N^O
R[QQOST[MWLM` SOUQR^ TQ[_YOPS LM NLPO N^UN LS SX_]YLMOUQ LM N^O SL‡O [c N^O PUNQLda
! "#$ %$ %& '()* + ,
- - - - . - - * / - * 0 / * 1 2- 34456578 9 86:5;< * ! ! , - - *
+ ! = - *> ? , - 2- - ! @ A * * - ! AB @ - - ! )*
0 - ! - -2
C :DC 8:6E 68<65FG * H - = I
D: FD6 - - 2 - I <JDKL4 M8 9 D45N 84 <5GF5N ;3F6LE
I * O . P Q P ! = R - - = I - RB , *
0 - = RST 3: * U ! - 2
V . ! * 0
- ! B W ! W %XR*
YZ[ \ ]^Z_`^ a + -2 2 b "P( c
d %e f f f e P g - W %XR 5F48C 8F48F6 P )* 1 . =
= "hei ( hei j b * 0 - - - W b *
1 . ! . W *
k l - - ! W
m %XR)XRn )*
k 1 W V - ! m %XR)XRn ) -*
k 1 W V - ! A S459 8F<5DF3L o K;L5483F p 86:5; m A A)XR)*
k l - ! 3CC :Dq59 368 KL6:39 86:5;* ! r - ! = r S3CC :Dq59 368 rB ) ! ! = s hei j "P(
t= "hei ( u = s "hei ( t v r * ! r R) - . = rB w xy z{| } ~z€|{ }‚~ƒ „… {ƒ†‡zˆ„„€‰Š ‹ƒ ‚~ƒ {|ƒ {ƒ†‡ ŒŽ‘’“ ‹|zƒ }”{‚}‰ ‹ƒ ‡ƒ}ˆ • Ž“–Œ—˜ŒŽ‘’“™ š}‡ƒ‰Š
{|ƒ ›†„›ƒ†{zƒ~ „… ~‰‡‡ƒ{†‰Š {†z}ˆ€ƒœzˆƒ‚}z{‰Š }ˆž ˆ„ˆœˆƒ€}{zŸz{‰ }†ƒ „ƒ‰ƒžŠ ‚{ ‹ƒ ž„ ˆ„{ ˆƒ”ƒ~~}†‰ †ƒ‚z†ƒ {|}{
¡¢£¤ ¥ ¦ § …„† ƒŸƒ†‰ ¢ ©¨ ¤ ™ ª~ ‹ƒ }{ƒ† ~|„‹ Š {|z~ †ƒ}«}{z„ˆ z~ zˆƒŸz{}ƒ …„† {|ƒ ›†„ƒ‡~ ‹ƒ ~„Ÿƒ™
%
= - RB )* 1 W m %XR)XRn )*
rB - ,!
! P %XR* ! - - = RB * H
B W ! ! *
]
Z]^a + * + 2
"P(* ? , - B - * 1 , B ! * 1 3L
3E< , ! *
1 - ! ! ,
B * 1 B 56F8<<8< *
0 , B - - C J3<8< * @ - ! *
0 !
* * "% ( "#() *
`] ` \ ]_ `] [ a - , , ! "% ( ! B
* * "% %' &() * * " () "#( w "%% (*
"% (*
1 - * - *
! ) ! K9 8:5;3L 3q DFD9 E :DML89 * 1 - , ! " (* l * * "##( - ! = . - = m P )* 2 " ( m P P ) - * 1 ! !) V ) * * "% ()* ! - = * 1 2- 2- * AB @ W ! 2 !
, ! 2 A *
l ! = ) - , ) = s "= u = s "# W $ # *
0 - - ! " ( H B $ > $ * l $ % m P ) "%# % (* - #
H B $ % "%(* 1 H B - - ! = - ! = s "= u = s "% v r - .
, = ss "= u = ss "% v r "%(* , m P ) = ss "= u = ss "% v &r "%(*
! ) ! - ! - $ % ) - ! P %XR)* l ! - ! -*
Y[ ` a 0 ? # - -2 * 0 ? & - ? ! ? ' * 1
@ ? * ? - - - *
0 - - - *
! 86 I M8 3 "#$ " % #&' DT 9 36:5;8< ( L86 = M8
3F P Q P 9 36:5q ( 3F4 L86 $ v R v % ) J8 9 36:5q = 5< RS* + # T :D9 J375FG C :DC 8:6E I ( 5T 6J8 9 5F59 K9
T :3;65DF DT = ,< 8F6:58< -39 DFG 3LL P 8F6:58<. 6J36 <JDKL4 M8 9 D45N 84 <D 6J36 = DM635F< C :DC 8:6E
I 5< G:8368: 6J3F R ) / 6J8: 5<8 ( = 5< RS0 1$ 2 % 6D J375FG C :DC 8:6E I )
6 & %2& 789 + 19 $ #7& : ; T D: 3 9 36:5q C :DC 8:6E I
5< G578F 3 45<63F;8 C3:39 868: R 3F4 9 3E < K8:E = DF 8F6:58< = "hei ( DT 56< ;JD5;8 ) =T = J3< C :DC 8:6E
I 6J8F 6J8 3LG D:56J9 <JDKL4 + 0 0 % "& ( 3F4 5T = 5< RST 3: T :D9 J375FG C :DC 8:6E I ( 6J8F 6J 8 3LG D:56J9
<JDKL4 #%> % 0 & 56J C :DM3M5L56E 36 L83<6 #X& )
3 4 5 1 , . B * 0 - -B * - - , *
1 ! - B
*
? 5 @
8 <3E 6J36 3F P QP 9 36:5q = 5< 3 "2 % AB $C B 72& + 80 % 9 36:5q
5T 6J8 T DLLD 5FG ;DF4565DF< JDL4 D
E ) F D: 878:E hei j "P( ( = "hei ( G $ ( J8:8 = "he h( c $ T D: 878:E h H8$ 8C 8%9 +& 7I 7&' J )
K ) F D: 878:E hei j "P( ( = "hei ( c = "i e h( H2' ; ; %& #' J )
L ) F D: 878:E hei e j "P( ( = "hei ( v = "he ( M = " ei ( H& #7+ 89 1% 78% N A+ 17&' J )
T = 689
=
E
5< <6:8FG6J8F84 6D :8< K5:8 6J36 = "hei (
O
$ T D: 878:E h cP i ( 6J8F = 5< 3
B 72& + 80 %
9 36:5q )
l - = B
* + - . = "hei ( Q R„†‡ }‰Š } S›~ƒ‚ž„ T ‡ƒ{†z” z~ } ›}z† SU £ V T ‹|ƒ†ƒ U z~ } ~ƒ{ }ˆž V W U X U Y Z [\ z~ } S›~ƒ‚ž„ T žz~{}ˆ”ƒ
…‚ˆ”{z„ˆ ™ ] ƒˆ”ƒŠ z… z~ } S›~ƒ‚ž„ T žz~{}ˆ”ƒ ‡ }{†z« Š {|ƒˆ S ¡^ ¥£ V _ T Š ‹|ƒ†ƒ V _ S¢£¤ T © ¡¢£¤ ¥ Š z~ } S›~ƒ‚ž„ T ‡ƒ{†z”™
&
h cP i 2 2 , * 0 - . ! ! %XR) P ) - . - P) R)*
0 - - - = , - , B * l ! - *
86 M8 3 68<65FG 3LG D:56J9 T D: 3 C :DC 8:6E I DT C <8K4DS45<63F;8 9 36:5;8< ( JD<8
;D::8;6F8<< :8L58< DF = DM8E5FG ;DF4565DF< -E. 3F4 -K. 5F 8N F565DF K )L ) J8F 6J 8:8 8q5<6< 3 68<65FG
3LG D:56J9 s T D: 6J8 C :DC 8:6E I JD<8 ;D::8;6F8<< 4D8< FD6 :8LE DF 6J8<8 3<<K9C 65DF< ) F K:6J8:9 D:8 (
5T R) 3F4 R) 3:8 6J8 < K8:E ;D9C L8q56E 3F4 :KFF5FG 659 8 DT ( :8<C 8;6578LE ( 6J 8F 6J8 < K8:E
;D9C L8q56E 3F4 :KFF5FG 659 8 DT s 3:8 m RX#) M %XR)) 3F4 m RX#) M %XR)) ( :8<C 8;6578LE )
!
4 %X %X& 2 w )*
+ s - 2 XR hei j "P( 2
- ) = "hei ( G $ - = "hei ( c $ h c i )* ) = "hei ( c = "i e h(* 0 ) ) s w * 0 hei j "P( ) ) P - - % u % u ) O % u n O 'X w* = I B ! !*
1 "P( Q "P( ) ) P * ! = s = ,
) ) hei * O h j "P( = s "he h( c $ h cP i = "hei ( $ - = s "hei ( B * hei = "hei ( cP = "i e h( - = s "hei ( c = s "i e h( c = "hei (* ? = = s P = RB I = s B I *
H- s - * = "hei ( s 2 ) ) , * 0 ) ) , s w* - + 0 0 % "& #%> % 0& *
? = I - s *
= RB I = s , w = s - 'X * s w = - 'X -*
0 - - ! = * ? ! - * - = - ! * 1 - %* l - ,*
- - * l - - * 1 - - h i , -
h i * 1 - hei )* h he h) ,
$ *
? 3F
A 1& #+ ; % & #70 & #% %
E)
K)
3 5T 6J8 T DLLD 5FG JDL4< D
@
8 <3E 6J36 3 6:88 56J C D<56578 85GJ6< DF 6J8 84G 8< 5<
5< :DD684 3F4 6J8 45<63F;8 M86 88F L83T 3F4 6J8 :DD6 5< 6J8 <39 8 N q 84 73LK8 )
6 LL 5F68:F3L FD48< 5F J378 36 L83<6 K ;J5L4:8F )
@ 8 <3E 6J36 3F P Q P 9 36:5q = 5< 3F
3F KL6:39 86:5; 6:88 T D: J5;J 6J8 T DLLD 5FG JDL4< D
? E) K) F
A 1& #+ ; %& #70
5T 6J8:8 8q5<6<
J 8:8 8q5<6< 3 E S6DS E 9 3CC 5FG T :D9 "P( DF6D 6J 8 L8378< DT )
D: 3FE 6 D L8378< hei 5F 6J8 6:88( h)e i )) c = "hei ( )
l - - hei ) h)e i ))*
1 - , - *
3
3 6
9 86:5; 5< 3F KL6:39 86:5; 5T 3F4 DFLE 5T T D: 878:E hei e (
= "hei ( v ! d = "he (e = "i e (g f
=
F C3:65;KL3: 6J5< 59C L58< 6J36 T D: 878:E h ( i 3F4
(
5T = "he (
O
= "i e ( 6J8F = "hei ( c = "he ( )
? - "P( - , - *
3 F D: 3 G578F 9 36:5q = 3F4 3 <KM<86 "P( ( 8 <3E 6J36
3F KL6:39 86:5; 6:88 5< 0 $ 82 72& % 8& 56J = DF 5T T D: 878:E hei j ( hei ) c = "hei ( ) @J8F
c "P( 8 <59C LE <3E 6J36 5< ;DF<5<68F6 56J = )
? ? 0 - 2- = ! . - = * V ! "% ()*
- - = "P( !)* 1 B
- W * 2 - d %e f f f e g*
0 P Q P ! = d %e f f f e g *
3 '
1
2
3
4
5
1 2 3 4
8 10 10
10 10
2
5
10
10
6
6
1
4
1
2
4
4
4
4
2
1
1
2
2
4
5
4
1
1
4
3
1
2
4
4
1
3
3
1
1
2
5 4
1
3
[MSNQXRNL[M [c UM XYNQUPONQLR NQOO N^UN LS R[MSLSNOMN fLN^ N^O URR[PTUMZLM` PUNQLd jf^LR^ LS
SZPPONQLR UMW [M N^O WLU`[MUYka pM N^O qQSN SNU`O UMW UQO TXN UN OsXUY WLSNUMRO j^UYc N^O WLSNUMRO
_ONfOOM N^OPk cQ[P N^O Q[[Na y^OM LS UWWOWV LN LS UN WLSNUMRO `QOUNOQ N^UM cQ[P V UMW S[ U MOf Q[[N LS
RQOUNOWa y^OM LS UWWOWV N^O RY[SOSN T[LMN LS V UMW N^O T[LMN [c WOTUQNXQO [c LS UN WLSNUMRO … cQ[P [M
N^O TUN^ _ONfOOM UMW N^O Q[[Na KLMUYYZV LS RY[SOSN N[ US fOYYV UMW LNS T[LMN [c WOTUQNXQO LS UN WLSNUMRO
cQ[P M[WO a
% %* 0W c d %e #g - % # .
> *
#* i c &e f f f e ) i e e = )*
) di g*
0 P Q P ! = ! i - = c d %e f f f ei u %g*
%* % v i - = "i e ( W *
#* 0 = "i e ( O # e ) - ) - - - - i - * - - *
&*
- ) ! e ) c ) ! e ) e ) e )* 0 ) e ) - - e ) e ) . * 0 - i *
l , ? & + B 48C3:6K:8 CD5F6 i * 0 i - ? #) , * %*
? =T = 5< 3F KL6:39 86:5; ( 6J 8F 3< ;DF<6:K;684 5F 6J8
L6:39 86:5; :88 ! DF<6:K;65DF
:D;84K:8( 5< ;DF<5<68F6 56J = DF )
4
l i * 1 i c # - * c d %e fffei u %g - = i u % G #* l - i - = di g*
H - i !
* ei ) c = " ei (* h j h cP - - %*
#*
&*
0 = - = "i e h( c = " e h(*
s h he s) c * i e h) c i e ) M e s ) M s e h)
= " ei (
= " e h( = " ei (
= " e h(
c
M u
M
#
#
# #
c = " e h(
c = "i e h(
%)
0 = "i e h( c = " ei ( - i e h) c = " ei ( i e h) c = "i e h(
. *
- 2- = "i e h( v = " ei ( - i = "i e h( c = " ei (* i e h) c i e ) i e h) c = "i e h(*
+ = "P( . - = * l - - "P( . "P( * 0
= - * l = RB - ) * 1
- , - ,*
"P( - - * l <;3 DL4 * l - - = i jP *
! 86 M8 3F KL6:39 86:5; 6:88 6J36 5< ;DF<5<68F6 56J = DF
) @ 8 <3E 6J36 3 CD5F6 i jX 5< 0 $ 82 72& % 8& 56J ( 5T 3T 68: 3445FG i 6D ME 3CC LE5FG 6J8 C :D;84K:8
6 44S D5F6 -i e e = . ( 6J8 :8<KL65FG 6:88 5F 3F KL6:39 86:5; 6:88 ) / 6J 8: 5<8 ( i 5< 780 $ 82 72 & % 8&
56J ) J8 <86 DT CD5F6< 5F "P( 6J36 3:8 ;DF<5<68F6 56J 5< 48FD684 ME )
0 = c "P( * i jX - = * ? . , -
- )*
? l - - - * l , *
3 ! 86 "P( M8 <K;J 6J36 6J8:8 8q5<6< 3F KL6:39 86:5;
6:88 6J36 5< ;DF<5<68F6 56J = DF ) F D: 83;J CD5F6 i j ( ;DF<548: 3LL 56< 45<63F;8< 6D CD5F6<
5F -3;;D:45FG 6D = . ) J8F 6 D CD5F6< M8LDFG 6D 6J8 <39 8 0 1+22 5F 6J8 "+ #& 7& 7$ 8 DT ( 5T 3LL
6J85: C 35:S 5<8 45<63F;8< 6D CD5F6< 5F 3:8 6J8 <39 8 )
? #*
1
1
1
1
2
2
3
3
2
C1
1
1
1
C3
C2
C4
2
3
4
C5
C6
5
bM LYYXSNQUNL[M [c N^O TUQNLNL[M LMWXROW _Z U SRU [YWa K[Q OdUPTYOV N^O T[LMNS LM UQO UYY UN
WLSNUMRO cQ[P V UN WLSNUMRO cQ[P V UMW UN WLSNUMRO … cQ[P T[LMNS V UMW a r^O SRU [YW WLSNUMRO
_ONfOOM O\OQZ u UMW w LS a
# * - ! - h i * + = - = *
! 86 M8 3F KL6:39 86:5; 6:88 6J36 5< ;DF<5<68F6 56J
= DF ) ! DF<548: -3< 3 9 8F63L 8qC 8:59 8F6. 3445FG 3LL CD5F6< 5F "P( 6D ME 3CC LE5FG 6J 8
C :D;84K:8 6 44S D5F6 -i e e = ) 6D 3LL CD5F6< i jX 78 "+ #+ 11% 1( 3F4 L86 6J8 :8<KL65FG 6:88 M8 )n
-
J5;J 5< ( ME 48N F565DF ( 3F 8q68F<5DF DT 6J 8 45<63F;8
J8F ( L86 e ) M8 6J8 45<63F;8 5F4K;84 ME 5F4K;84 ME DF 6J8 C 35:< DT CD5F6< 5F . )
? 3
0 = hei hei ) c = "hei ( h i . )* ? hei = "hei ( v hei )*
1 hei j - = * 1 - , *
„ ƒ } z{{ƒ ‡„†ƒ ›†ƒ”z~ƒŠ ƒ{ ƒ {|ƒ ‡ }«z‡‚‡ Ÿ}‚ƒ zˆ Š }ˆž ”„ˆ~zžƒ† †~{ }žžzˆ€ {„ } ”{z{z„‚~ ›„zˆ{
‹|„~ƒ
žz~{}ˆ”ƒ …†„‡ } ›„zˆ{~ z~ €†ƒ}{ƒ† {|}ˆ ™ … ‹ƒ ˆ„‹ ”„ˆ~zžƒ† }žžzˆ€ } ›„zˆ{~ zˆ ¡^ ¥ {„ {|ƒˆ
{|ƒ†ƒ z~ ˆƒŸƒ† } ˆƒƒž {„ ”†ƒ}{ƒ } ˆƒ‹ †„„{Š }ˆž {|ƒ }žžz{z„ˆ ›†„”ƒ~~ z~ ‹ƒ žƒ ˆƒž™ yƒ ”}ˆ ˆ„‹ †ƒ‡„Ÿƒ {|ƒ
›„zˆ{ …†„‡ {|ƒ {†ƒƒŠ }ˆž ƒ{ {|ƒ †ƒ~‚{zˆ€ {†ƒƒ ƒ ™ ª~„ ˆ„{ƒ {|}{ ‰ „‚† }~~‚‡›{z„ˆ {|}{ ¡¢£¤ ¥ ¦ § …„† ƒŸƒ†‰ ¢ ©¨ ¤ Š }
›„zˆ{ ¤ ”}ˆˆ„{ ƒ }žžƒž zˆ {|ƒ ~}‡ƒ ›}”ƒ zˆ {|ƒ {†ƒƒ }~ }ˆ ƒ«z~{zˆ€ ›„zˆ{ zˆ ™
! 86 M8 3F KL6:39 86:5; 6:88 6J36 5< ;DF<5<68F6 56J = DF )
C35: DT CD5F6< hei j 3:8 <354 6D M8 3 I 7$ 1+ & 789 "+ 7# 56J :8<C 8;6 6D ( 5T 856J8: -E. h 3F4 i 3:8
5F 45 8:8F6 ;L3<<8< 5F 3F4 = "hei ( cP hei ) ( D: -K. h 3F4 i M8LDFG 6D 6J8 <39 8 ;L3<< 5F 3F4
= "hei ( O hei ) )
? 6
+ = - * l - = RB - V - *
l - *
E)
K)
L)
F5T D:9 LE 3F4 5F48C 8F48F6LE <8L8;6 c m %XR)XRn ) CD5F6< T :D9 "P( ) 8FD68 6J 8 <86 DT
C D5F6< <8L8;684 ME )
! DF<6:K;6 3 <;3 DL4 6:88 3< 48<;:5M84 5F 6J8 L6:39 86:5; :88 ! DF<6:K;65DF :D;84K:8 )
=T T D: 3FE 6 D C D5F6< hei j ( hei ) c
P = "hei ( 6J8F #%> % 0& )
4 F5T D:9 LE 3F4 5F48C 8F48F6LE <8L8;6 c m %XR) C 35:< DT CD5F6< 5F "P( )
)
3
3 T 3FE DT 6J8 CD5F6< <8L8;684 5F 68C
)
=
)
)
=
5< 5F;DF<5<68F6 56J 6J8F
#%> % 0& )
3:6565DF 6J8 # CD5F6< <8L8;684 5F 68C 5F6D ;L3<<8< 3;;D:45FG 6D 6J 8 C3:6565DF 5F4K;8<
ME 6J8 <;3 DL4 ) =T 3FE DT 6J8 C 35:< 5< 3 75DL365FG C 35: 6J8F #%> % 0& )
T FD <68C ;3K<84 :8 8;65DF 6J 8F
6
LG D:56J9
E
+ 0 0 % "& )
5< 3 68<65FG 3LG D:56J9 T D: KL6:39 86:5;< )
H - w 87548F;8 = *
+ 1 # - ? ! 86 6J8 F36K:3L 68<65FG 3LG D:56J9 M8 6J 8 3LG D:56J9 6J36 <59C LE <8L8;6< 3 KF5T D:9
<39C L8 DT M # c m %XR)XRn ) C D5F6< T :D9 "P( -
J8:8 3F4 3:8 48N F 84 3< 5F 6 LG D:56J9 E. (
3F4 3;;8C 6< 5T 3F4 DFLE 5T 6J8:8 5< 3F KL6:39 86:5; 6:88 ;DF<5<68F6 56J = DF 6J8 <39C L8 )
F36K:3L 3LG D:56J9 5< 3 68<65FG 3LG D:56J9 T D: KL6:39 86:5;< )
J8F 6J 8
+ = - * l - = RB - w - #X&* 2 1 # - - * 0 - - , *
! 86 "P( M8 <K;J 6J36 6J8:8 8q5<6< 3F KL6:39 86:5; 6:88 6J36 5< ;DF<5<68F6 56J = DF ) 6 C35: DT CD5F6< hei j 3:8 <354 6D M8 2 % "+ #+ &% B 56J :8<C 8;6 6D
5T 6J8E M8LDFG 6D 45 8:8F6 ;L3<<8< DT 6J 8 C3:6565DF ) / 6J8: 5<8( 6J 8E 3:8 8$ 8C2 % "+ #+&% B )
? ? "P( B P * l = RB n P P - n w - n ? ' ? * 1 - * 1 - , ! = s = s "hei ( c hei )
hei j "P(* 1 = s , , )* - = s = RP P B P P n
n - n - )* = *
2 - <8C3:365FG * 1 - , *
? = "he ( cP = "i e ( )
@
8 <3E 6J36 3 CD5F6
5< 3
2 % "+ #+& $ #
T D: 3 C35: DT CD5F6< hei ( 5T
1 - , ! , &* ) * H = hei *
8 <3E 6J36 CD5F6 5< 3F C % % 0& 7I % 2 % "+ #+& $ # 56J
:8<C 8;6 6D ( 5T 6J8 FK9 M8: DT C35:< DT CD5F6< 5F 6J36 3:8 FD6 <8C3:3684 56J :8<C 8;6 6D MK6 3:8
<8C3:3684 56J :8<C 8;6 6D d g ( 5< 36 L83<6 P ) )
? @
, j B - - * P ) - d g - )* 0 B
P ) *
l - C J3<8< * + - .
V B - - - ! * - - - - B 0 - - - <39 8 ;L3<<
B )*
? ! 86 "P( M8 3 ;L3<< 5F <K;J 6J36 6J8:8 3:8 36 9 D<6 P CD5F6< 5F 6J36
3:8 S8 8;6578 <8C3:36D:< 56J :8<C 8;6 6D ) J8F 6J8:8 8q5<6< 3F KL6:39 86:5; -<63: <J3C 84. 6:88 <K;J 6J36 T D: 36 9 D<6 # M & )P t t DT 6J 8 C35:< hei j ( 8 J378 hei ) cP = "hei ( )
0 &*# - - *
86 v P M8 3F 5F68G 8: ( 3 Q :83L 73LK84 9 36:5q 3F4 $ v e v % ) KCCD<8 6J36
T D: 36 L83<6 u P DT 6J 8 :D < h 5F ( 6J8:8 8q5<6< 3 73LK8 <K;J 6J36 T D: 36 L83<6 u P DT 6J 8
? ? !
%$
8F6:58< "hei ( 8 J378 "hei ( c ( 3F4 6J36 3F 3F3LDG DK< ;L359 JDL4< T D: 6J 8 ;DLK9 F< DT ) J8F
6J8:8 8q5<6< 3 <5FGL8 73LK8( 48FD684 ( <K;J 6J36 T D: 3LL MK6 36 9 D<6 # M & )P DT 6J 8 8F6:58<
"hei ( ( 8 J378 "hei ( c )
h j d %e f f f e g ) h - )
* l - ) BC K:8 P - )
)* P - ) B *
l "hei ( :D S:8C :8<8F636578 - h B "hei ( c * ! , ;DLK9 FS
:8C :8<8F636578 * 1 FD6 -B P M P c M ) P * ? B
M ) P * -B B
u # M ) P *
H- - h u # M ) P -B
B * ? - ! - * 1
# M ) P M P c
# M & )P - , i "hei ( -B B B i "hei ( -B B
)*
4
? B ! = = h j B - * , h - = P ) * l ! u P
= "hei ( h - - = "hei ( c = )* 1 v P O P * + h - u P - * 1 % v i v u u P ) c P = "he ( = "hei ( cP = "he (* - h P - P ) h - *
? P B - &*&
- c = c c * 1 ! # M & )P t t = - = "hei ( c * H - = "hei ( O $ h cP i O $ * ! , B B - X#* 1 - *
4 4
+ = - * l = RB *
c c * l - c %X C J3<8< - >
s c # * 0 - - w ? & - - = )* - N q 84 - B - P * 1 4 4 3
%%
%
% u ) v
f
1 <D9 8 - B - ) P %X *
+ , - ) B
P P u %)* 0 - B B P ) * 0
- %X * - 'X c %X - = P B - *
86 "P( M8 <K;J 6J36 6J 8:8 8q5<6< 3F KL6:39 86:5; 6:88 6J36 5< ;DF<5<68F6 56J = DF
( 3F4 6J8 FK9 M8: DT S8 8;6578 <8C3:36D:< 56J :8<C 8;6 6D 5< MDKF484 ME P ) =T = 5< RST 3: T :D9
M85FG 3F KL6:39 86:5; ( 6J8F 6J8:8 3:8 856J8: 9 D:8 6J3F P 5F;DF<5<68F6 CD5F6< 56J :8<C 8;6 6D ( D:
9 D:8 6J3F P 75DL365FG C 35:< 56J :8<C 8;6 6D )
1+ 7; !
1 - 'X c ? w ? ' ? * 12
%X B P - *
1 - * + 36 9 D<6 P 36 9 D<6 P * l ! - , = s - = RP = *
%* hei j = s "hei ( c hei ) c = "hei ()* ? h j i j = s "hei ( c hei ) c = "hei ()*
#* hei j ) 0 h i = s "hei ( c hei )* = s =
)*
) 0 h i B = s "hei ( c d hei )e hei )g - &*#* 12 - = s *) = s = - = "hei ( c "hei ( O hei )) # M & )P t t v P t t hei j = "hei ( cP hei )*
&* 0 h jP i jP = s "hei ( c hei ) - = "hei (* ?
P P - = s = *
1 - = s = R R
R
P M P t t M P v RP #
%#
- , hei - = "hei ( cP hei ) *
? = * 1 - - P %XR) s - = RB * ! - *
, = "P( "P( - B * H - "P( m P t t)* + 1 # - - t t c %XRn )) P B - - )* &*# ! B)
# M & )P t t hei j - hei ) cP = "hei (* - , - B * - 1 # - - = RP *
? - *
0 - ! ? & 3CC :Dq59 368 * H - ! = ! ;LD<8 5F 6J8 $ % FD:9 *
r <K;J 6J36 "= u = s "% v r )
6
9 36:5q = 5< 3 r C A 1& #+ ; %& #70 5T 6J8:8 8q5<6< 3F KL6:39 86:5; = s
- - ! = r R
= rB w = - #X& RB rB ,! )* 1 ! r c $)* 1 , = rB * + ! - rB - -)* ?- ! = RB rB w - - - ! - - *
l , ! *
r 6 F KL6:39 86:5; 6:88 5< r C 0 $ 82 72&% 8& 56J 3 9 36:5q = DF ( 5T
T D: 878:E hei j ( t hei ) u = "hei ( t v r ) = F ;3<8 c "P( ( 8 <59C LE <3E 6J36 5< r S;DF<5<68F6
56J = )
%&
l - "%#( B rB - rB = *
? ! 86 M8 3F KL6:39 86:5; 6:88 6J36 5< r S;DF<5<68F6 56J 3F
P Q P 9 36:5q = DF "P( ) @ 8 <3E 6J36 CD5F6 i jX 5< B 56J 5T 6J 8 T DLLD 5FG JDL4< )
! 86 M8 6J8 6:88 :8<KL65FG T :D9 3445FG i 6D ME 3CC LE5FG 6J 8 C :D;84K:8 6 44S D5F6i e e = )
-48<;:5M84 5F KM<8;65DF L )E. ) J8F 8 3< 6J36 T D: 878:E j ( t i e ) u = "i e ( t v ) ! 86 48FD68 6J8 <86 DT 3LL S;DF<5<68F6 CD5F6< 5F "P( )
! 86 = M8 3F P Q P 9 36:5q 3F4 hei j "P( ) 6 CD5F6 j "P( 5< ;3LL84
3 C 2 % "+ #+ & $ # T D: h 3F4 i 5T t= "he ( u = "i e ( t O )
=T h 3F4 i J378 3 S<8C3:36D: 5F 6J8 <86 ( 6J8F 6J8E 3:8 C2 % "+ #+ &% B ME )
8 <3E 6J36 3 CD5F6 j "P( 5< 3F e )C % % 0 & 7I %
2 % "+ #+& $ # 56J :8<C 8;6 6D "P( ( 5T 6J 8 FK9 M8: DT C35:< DT CD5F6< 5F "P( 6J36 3:8 S<8C3:3684 ME
d g ( 3F4 3:8 S<8C3:3684 ME ( 5< 36 L83<6 P ) )
@
! 86 = M8 3F P Q P 9 36:5q 3F4 hei j "P( )
56J :8<C 8;6 6D "P( ( 5T 856J8: D
3F4 i 3:8 3 I 7$ 1+& 789
"+ 7# @
8 <3E 6J36 h
J 8:8 8q5<6< 3 #r S<8C 3:36D: j <K;J 6J36 t= "hei ( u ! d = "he (e = "i e (g t O #r F D: <D9 8 j -6J36 5< FD6 F8;8<<3:5LE 3 #r S<8C3:36D:. ( = "hei ( O ! d = "he (e = "i e (g t M #r )
E) K)
E)
K)
3 4 F5T D:9 LE 3F4 5F48C 8F48F6LE <8L8;6 c
<8L8;684 ME )
%XR)XRn ) CD5F6< 5F "P( ) 8FD68 6J8 <86 DT CD5F6<
! DF<6:K;6 3 <;3 DL4 6:88 6J36 5< r S;DF<5<68F6 56J = DF
6J5< 5< FD6 CD<<5ML8 #%> % 0& )
F5T D:9 LE 3F4 5F48C 8F48F6LE <8L8;6 c
L)
K<5FG 6J8 3LG D:56J9 5F E K ) =T
"P( )
;J8; J86J8: 56 5< &r S;DF<5<68F6 56J ) =T FD6 )
F
D: 83;J CD5F6 <8L8;684 5F 68C
)
F
D: 83;J C35: DT CD5F6< <8L8;684 5F 68C
L(
%XR ) C35:< DT CD5F6< 5F
L(
#%> % 0 & )
;J8; J86J8: 6J 8E 3:8 3 75DL365FG C35: ( 3F4 5T <D #%> % 0 & )
)
T FD <68C ;3K<84 :8 8;65DF 6J 8F
=
+ 0 0 % "& )
LG D:56J9 K 3;;8C 6< 878:E 9 36:5q = 6J36 5< 3 r SKL6:39 86:5; ( 3F4 :8 8;6< 56J C :DM3M5L56E
36 L83<6 #X& 3FE = 6J36 5< RST 3: T :D9 M85FG 3 r SKL6:39 86:5; T D: <D9 8 N q 84 ;DF<63F6 )
3
1 *
6
*
%
- - ! 86 6J8 F36K:3L 68<65FG 3LG D:56J9 M8 6J 8 3LG D:56J9 6J36 <59C LE <8L8;6< 3 KF5T D:9
<39C L8 DT m %XRn ) CD5F6< T :D9 "P( 3F4 3;;8C 6< 5T 3F4 DFLE 5T 56 5< CD<<5ML8 6D ;DF<6:K;6 3 6:88 6J36
5< r S;DF<5<68F6 56J = DF 6J8 <39C L8 ) J8F 6J5< 3LG D:56J9 3;;8C 6< 878:E 9 36:5q = 6J36 5< 3 r S
KL6:39 86:5; ( 3F4 :8 8;6< 56J C :DM3M5L56E 36 L83<6 #X& 3FE = 6J36 5< RST 3: T :D9 M85FG 3 r SKL6:39 86:5;
T D: <D9 8 N q 84 ;DF<63F6 )
l 1 . * 1 , - , *
86 = M8 3 r SKL6:39 86:5; ( 3F4 L86 M8 3F KL6:39 86:5; 6:88 6J36 5< r S;DF<5<68F6 56J
= DF "P( ) J8F 878:E CD5F6 i jX 5< &r S;DF<5<68F6 56J )
!
? = rB ! = s "= u = s "% v r * i + B i e e = )* - = " ei ( W ei ) c = " ei (* H h j i e h) G e h)* l -
- h i = s - - *
4
%* = s "i e h( c = s " e h( G = s " ei ( ? "= u = s "% v r = "i e h( v = s "i e h( M r c = s " e h( M r v = " e h( M #r
0 - - = "i e h(
G
= " e h( u #r *
) i e h) c e h) G ei ) rB - = * 1
i e h) c e h) v = " e h( M r v = "i e h( M &r
0 - - i e h) G = "i e h( u &r *
) i e h) c ei ) G e h) ? i - = " ei ( v = "i e h( * 1 i e h) c ei ) c = " ei ( v = "i e h(f
i e h)
G
e h)
G
= " e h( u r
G
= "i e h( u &rf
#* = s "i e h( c = s " ei ( G = s " e h( 0 = "i e h( - = " ei ( u #r v = "i e h( v = " ei ( M #r
) i e h) c e h)
G
ei ) i e h) c e h) v = " e h( M r v = s " e h( M #r v = s "i e h( M #r v = "i e h( M &r
i e h)
G
ei ) c = " ei (
%'
G
= "i e h( u #r
) i e h) c ei ) G e h) l i e h) c ei ) c = " ei (* 1
= "i e h( u #r v = " ei ( c i e h) c = " ei ( v = "i e h(
&* = s " e h( c = s " ei ( G = s "i e h( - = "i e h( - = " ei ( v = "i e h( v = s "i e h( M r v = s " ei ( M r v = " ei ( M #r
l - .
= " e h( v = s " e h( M r c = s " ei ( M r v = " ei ( M #r
) i e h) c e h)
G
ei ) i e h) c e h) v = " e h( M r v O " ei ( M &r v = "i e h( M &r
i e h) G ei ) c = " ei (
) i e h) c ei ) G e h) 0 # *
G
= "i e h( u &r
! 86 = M8 3 r SKL6:39 86:5; ) J 8F T D: 878:E C35: DT C D5F6< hei j "P( ( 3F4 T D: 878:E CD5F6
j "P( ( 5T 5< 3 #r S<8C3:36D: T D: h 3F4 i 6J8F t= "hei ( u ! d = "he (e = "i e (g t v #r ( 3F4 D6J8: 5<8(
= "hei ( v ! d = "he (e = "i e (g M #r )
? = rB ! = s "= u = s "% v r *
1 j "P( t= s "he ( u = "he ( t v r t= s "i e ( u = "i e ( t v r *
0 #rB h i )* - = s "he ( cP = s "i e ( = s = s "hei ( c ! d = s "he (e = s "i e (g
! d = "he (e = "i e (g u #r v = "hei ( v ! d = "he (e = "i e (g M #r
4
0 #rB 1B %)
= s "hei ( v ! d = s "he (e = s "i e (g
= "hei ( v = s "hei ( M r v ! d = "he (e = "i e (g M #r
0 - *% *# = rB -
*
l - - 1 = RB m r)B w - #X&* O -
. - - - *
1 , - - - * ? B ! * , !
! , &* )*
%
? ! 86 = M8 3F P Q P 9 36:5q ( L86 M8 3F KL6:39 86:5; 6:88 6J36 5< r S;DF<5<68F6 56J =
DF "P( ( 3F4 L86 hei j n
) =T 6J8:8 8q5<6< 3 C D5F6 j 6J36 5< 3 r S<8C 3:36D: T D: h 3F4 i ( 3F4
h 3F4 i 3:8 FD6 75DL365FG 56J :8<C 8;6 6D ( 6J8F t hei ) u = "hei ( t v 'r )
? h i &rB - ! , ) - t= "he ( u he ) t v &r t= "i e ( u i e ) t v &r *
? rB h i t= "he ( u = "i e ( t O r t he ) u i e ) t O $ * % - hei ) c ! d he )e i e )g* h i #rB ) t= "hei ( u ! d = "he (e = "i e (g t v #r * 1 4
hei )
c ! d he )e i e )g v ! d = "he ( M &re = "i e ( M &r g v = "hei ( M 'r
! d he )e i e )g G = "hei ( u 'r *
1 ! &*# - - - *
86 b "P( M8 <K;J 6J36 6J8:8 3:8 36 9 D<6 P CD5F6< 5F b 6J36 3:8 e )S8 8;6578
<8C3:36D:< ) J8F 6J8:8 8q5<6< 3F KL6:39 86:5; -<63: <J3C 84. 6:88 <K;J 6J36 T D: 36 9 D<6 # M )P tb t DT 6J8 C 35:< hei j b ( 8 J378 t hei ) u = "hei ( t O n )
!
0 - , - *
86 v P M8 3F 5F68G 8: ( 3 Q :83L 73LK84 9 36:5q ( $ v e %X# ( 3F4 G $ )
KCCD<8 6J36 T D: 36 L83<6 u P DT 6J 8 :D < h 5F ( 6J8:8 8q5<6< 3 73LK8 <K;J 6J36 T D: 36 L83<6
u P DT 6J8 8F6:58< "hei ( 8 J378 t "hei ( u t v ( 3F4 6J36 3F 3F3LDG DK< ;L359 JDL4< T D: 6J 8
;DLK9 F< DT ) J8F 6J8:8 8q5<6< 3 <5FGL8 73LK8 ( <K;J 6J36 T D: 3LL MK6 36 9 D<6 # M & )P DT 6J 8
8F6:58< "hei ( ( 8 J378 t "hei ( u t v & )
!
4 1 *' - &*&* - - h 48F<8 ! u P "hei (
- t "hei ( u t v * l , * l "hei ( :D S
:8C :8<8F636578 - t "hei ( u t v * l , ;DLK9 FS:8C :8<8F636578
* 1 &*& - # M )P -B B *
l 2 - h u # M )P -B
B * "hei ( - t "hei ( u t v *
l 2- P " ei ( i ) t "hei (u " ei ( t v
# * # M )P M P c # M & )P " ei ( - t " ei ( u t v & *
4 4 = ! = b * h j b
e )B * l ! - ) h # P = "hei ( t= "hei ( u t O X#* 1 - h - * + , -2 - )* , = "hei ( %
! P = "hei (* 1 P = "hei ( - - P ) i e t= "hei ( u = "he ( t O h - e )B )* c = "hei ( M X# # P = "he ( t= "he ( u t O X#*
1 - *' - c = c c # c X# *
+ - ! * l - , *
! 86 "P( M8 <K;J 6J36 6J8:8 8q5<6< 3F KL6:39 86:5; 6:88 6J36 5< r S;DF<5<68F6 56J = DF -3F4 <D ( 5F C3:65;KL3: ( 5< 8LL 48N F84. ) ! 86 h jP ( 3F4 48N F8 D
x
Q
c di jP 6J8:8 5< FD > S<8C3:36D: T D: i 3F4 h 5F ( 3F4 = "hei ( hei ) u gf #)
J8F C D5F6 h 5< e > e )S 780 $ ##% 0& 56J :8<C 8;6 6D
(
5T
x
Q O
P )
2 h - i - h ) = "hei ( , hei ) * l - = "hei ( , h i *)
l - - = RB ! *
! 86 M8 <K;J 6J36 6J8:8 8q5<6< 3F KL6:39 86:5; 6:88 6J36 5< r S;DF<5<68F6 56J = DF
( 3F4 T K:6J8:9 D:8( 6J8:8 3:8 36 9 D<6 P CD5F6< 6J36 3:8 FD6 &r S;DF<5<68F6 56J 3F4 36 9 D<6
P C35:< DT DT 75DL365FG CD5F6< 56J :8<C 8;6 6D ) =T 6J 8 FK9 M8: DT e > e )S5F;D::8;6 C D5F6< 5F
"P( 5< 36 9 D<6 P ( J8:8 > G r ( 6J8F = 5< RS;LD<8 6D M85FG 3 ! d > e gSKL6:39 86:5; )
l - RP hei - t= "hei ( u hei ) t v
! d > e g* ? - *
e > e )B "P( h j c x Q *
hei 4
%* hei j t= "hei ( u hei ) t c t= "hei ( u hei ) t v r *
? h j i j n
t= "hei ( u hei ) t c t= "hei ( u hei ) t v &r *
#* hei j n
i jP ) 0 h i > B *& t= "hei ( u hei ) t v 'r > G r)*
) - hei ) u v = "hei ( v hei ) M 'r * 1 , . - , * . ! hei ) c ! d he )e i e )g hei j
)* 1 h i P
hei j n
- = "hei ( v ! d = "he (e = "i e (g M #r v ! d "he ( M
&re "i e ( M &r g M #r c hei ) M 'r
&* - = - - *
%
)
)
)
)
1 1 1 1 hei h jP n
P *
- P *
h jX i j P h jP t t v P )*
hei h j P *
2 * 1 -
* 0
- K<8T KL C D5F6< * + - - - *
4
@
DF8 DT 6J8 T DLLD 5FG ;DF4565DF< JDL4< D
E) 8 <3E 6J36 3 CD5F6 h jX 5< e )S A2 %* A 1 56J :8<C 8;6 6D ( 5T
J 8:8 3:8 36 L83<6 P ) C35:< DT CD5F6< 6J36 3:8 75DL365FG 56J :8<C 8;6 6D dhg )
86 c di j e = "i e h( = "i e ( g M8 6J8 <86 DT CD5F6< 6J36 3:8 ;LD<8: 6D h 6J3F 6D
3FE CD5F6 5F ) J8F 6J8:8 3:8 36 L83<6 P ) C 35:< DT CD5F6< i e j ( <K;J 6J36 = "i e ( G
! d = "i e h(e = " e h(g u ( J5L8 T D: 878:E j ( = "i e ( ! d = "i e (e = " e (g u )
K) !
0 = 2 - )*
J8:8 8q5<6< ;DF<63F6< > e e 3F4 A > e e A <K;J 6J36 e v > 3F4 A n G r ( T D:
J5;J 6J8 T DLLD 5FG JDL4< ) ! 86 M8 <K;J 6J36 6J8:8 8q5<6< 3F KL6:39 86:5; 6:88 6J36 5< r S;DF<5<68F6
56J = 3F4 T K:6J8:9 D:8 D
J 8 FK9 M8: DT > Re A > r)S8 8;6578 <8C3:36D:< 56J :8<C 8;6 6D 5< 36 9 D<6 RP k J 8 FK9 M8: DT CD5F6< 6J36 3:8 FD6 &r S;DF<5<68F6 56J :8<C 8;6 6D 5< 36 9 D<6 n RP )
k
T 6J8 FK9 M8: DT Re A r)SK<8T KL CD5F6< 56J :8<C 8;6 6D 5< L8<< 6J3F RP (
6J8F 6J 8 FK9 M8: DT Re A n re A r)S5F;D::8;6 CD5F6< 56J :8<C 8;6 5< 36 9 D<6
=
RP )
4 + Re A n re A r)B - RP * l - Re A r)B - RP * - * + -
- - > e e A > e e A *
+ - , *
&rB - * 1 u n )RP G RP * h j - - h ! RP h)*
l 2 h j * c , @. #)* i j j i %
i e )
c = "i e (* ? h &rB - - t he ) u = "he ( t v &r * , hei ) c ! d he )e i e )g t hei ) u ! d = "i e (e = "he (g t v &r *
H- , - t= "he ( u= "i e ( t v A n r t hei ) u= "i e ( t v A n M &)r *
? , ) = "hei ( hei ) u A r - i j j = "hei ( = "i e ( u A u A n u &)r
&)
i j A n rB h i i e j #A n rB * * > Re A > r)B RP * 0 - A > c #A n - ! B > R M # R) P t t i e j t= "i e ( u # ) t v &A n re
- ) * l :8C :8<8F636578 - *
? t t G RP > M # ) X&# B > t t *
n c di j = "hei ( # ) u &A n r u #r g* 2 , h * l - *
%* t t G > t t 1 i e j = "i e (
G
O
# ) u &A n r
! d = "i e h(e = " e h(g M #r
1 i - dhg* 1 %
%
%
%
%
t t u t t G t t u t t O t t G RP ) G RP ) e
&#
&#
'
'
- . v X'* 1 h , )*
#* t t > t t* c t t O > t t* 0 i e j = "i e ( v # ) M &A n r
v d = "i e h(e = " e h(g M A n M #)r
@. &) j = "i e ( v d = "i e (e = " e (g M A n
M
' u A )r
)
c d j i gf
l i j G DD4 C3:6F8: - t t O n t t* B > t t ) - > t t G > t t G RP * l n - - i j )*
#$
j * @. ) j = "i e ( = " e ( M A n M ' uA )r *
A O A M ' j = "i e ( = " e (* 1 j n
i *
A O A n M ' M A ) j e s j = " e s( ! d = " e (e = " s e (g u A r * , ) = " e s( G ! d = " ei (e = " s ei (g u A n r A n v A X - = " e s( G ! d = " ei (e = " s ei (g u A r * 1 t t u % t t O & t t u % t t O % t t u % t t O % RP ) G RP ) e
&#
&#
% &#
%$
v X%$ f 1 i )*
0 , - 2 !
* l - k v u n # M > ) X&# v X v X%$ *
k A > c #A n A O A n M ' M A ) A G A n *
l k e c # e e n c # c # > c # > *
k A n c A > c %# A c & A c *
4 4 3
1 - - 1 #* 0 = rB *% *# - *
l *
+ 1 # - - * c %XR ) s c XR) * 0 - - * * ? - - 1 # > Re A > r)B RP Re A r)B RP - !
- * 0 RP ) , ) - - w - ? ' * - , c %X > R) M %X R) c %XR ) - ) RP ) RP *
0 rB - = - w ? #
* 0 ? # &rB
- n RP - - w ? * - - * Re A n re A r)B
- RP * = RB A rB P e v > A n G r) - * *
#%
0 - - ) * l - , *
; % & #70. (
3 5 5T 6J8:8 8q5<6< 3 6:88 @ 8 <3E 6J36 3F P Q P 9 36:5q = 5< 3 & #% % ; %& #70 -D: 3F + B B 7& 7I %
56J CD<56578 85GJ6< DF 6J8 84G 8< ( T D: J5;J 6J8 T DLLD 5FG JDL4< D
E) J 8:8 8q5<6< 3 9 3CC 5FG T :D9 "P( 5F6D 6J8 FD48< DT )
K) 6
LL 5F68:F3L FD48< 5F 6J8 6:88 6D J5;J FD h j "P( 5< 9 3CC 84 6D ( J378 48G:88 G:8368: 6J3F
L) F
K)
D: 878:E hei j "P( ( h)e i )) c = "hei ( )
0 , - - BB = B
* - - - = * 0
? - - - BB . P) . R)*
l - J 8:8 8q5<6< 3F 3LG D:56J9 T D: 68<65FG J86J 8: 3 9 36:5q = 5< 3 6:88 9 86:5; ) J 8
3LG D:56J9 63 8< 3 <39C L8 DT <5 8 m %XR)XRn ) ( 3F4 J3< < K8:E ;D9C L8q56E 3F4 :KFF5FG 659 8 6J36
3:8 36 9 D<6 < K34:365; 5F 6J 8 <39C L8 <58 )
3
^`[Z ` []] ]`[ a ? V B
- = * 2- "##( * - i . i i . *
^ ^`] ` []] ` a 1 , ! , &*&) ! , &* ) - - *
] _ [` ` a "P( ! - = * - * H - * H -
= * + = - *
] _ ^` ] a l , - - ,
! , &* )* 0 h j A h) - h * - ##
* h j h , A h) c $ * 1 hei j "P( , hei )
c A h) M A i ) M e )
- h i e ) * H - ! )*
= hei j = "hei ( c hei ) hei = "hei ( v hei )*
_ `
[^a , ! , &* )*
] ]^` _ [ ` a 1 B
* m %XRn ) - = * 0 m %XR) 2 * 1 . , - - - , *
] [ ` [^a ? B , ! ,B
&* )* 1 , , - *
! 86 M8 <K;J 6J36 6J8:8 8q5<6< 3 6:88 6J36 5< ;DF<5<68F6 56J =
DF ) @ 8 <3E 6J36 3 C D5F6 j 5< 3 2 % "+ #+& $ # 56J :8<C 8;6 6D T D: 3 FDFS<8C3:3684 C35: DT CD5F6<
hei j ( 5T 856J8: DF8 DT 6J8 T DLLD 5FG JDL4< D
E)
K)
D6J h 3F4 i 3:8 ;DF<5<68F6 56J 3F4 6J8E 3:8 <8C 3:3684 56J :8<C 8;6 6D d g )
o 56J 8: h D: i 5< 5F;DF<5<68F6 56J )
1 , ! , &*%$) ,
)*
1 &*#
- *
86 "P( M8 3 ;L3<< 5F ( 3F4 L86 M8 6J8 ;D9 9 DF CD5F6 DT 48C3:6K:8 DT
6J8 CD5F6< 5F T :D9 ) =T 6J8:8 3:8 36 9 D<6 P CD5F6< 5F 6J36 3:8 S8 8;6578 <8C3:36D:< 56J
:8<C 8;6 6D ( 6J8F 6J8:8 8q5<6< 3 <KM6:88 <K;J 6J36 D
!
J 8 :DD6 DT 5< 6J 8 CD5F6 )
F D: 36 9 D<6 & M )P t t DT 6J8 C 35:< hei j ( 8 J378 hei ) c
P = "hei ( )
F D: 83;J h j ( 8 J378 he ) c A h) )
E) K)
L)
hei j - h i ;D9C365ML8 - ) i - - . h - )* - 4
#&
5F;D9C365ML8 * t t Q t t ! , - * hei j hei ) u = "hei (
A h) M A i ) u = "hei (
"hei ( c
c
')
#
#
"hei ( c $ * l "hei ( 0 hei j "hei ( - i *
[ ][` ]^ a h i $ v "hei ( v A h)e A i ))*
0 - , h j - ) i e j i - h "hei ( c "he (*
h B - "hei ( cP "he ( P ) * ? - - - &*# - P h - ) *
l - &*& # M & ) P t t * h j A c A h) u * @. ') hei j = "hei ( c A h) M A i ) u # "hei (
1 hei "hei ( c = "hei ( c A M A * 1 # M & ) P t t hei j - = "hei ( c A M A *
] a 0 - - - 2 hei ) c A M A * 0 - * @ h j A *
- V - , A * 1 - - *
%* hei j A G $ A G $ hei ) c A M A *
#* 0 A $ A $ hei ) c A h) M A i )*
1 - - * @ h - A G $ , - A * 0 A c $ h *)
@ h - A $ A h)* 1 * ? &*
Z ` ]
*
][] ]^ ]` ]] =
a l - - = %* hei - A G $ A G $ 0 hei - "hei ( c - hei ) c A M A c = "hei (* + hei "hei ( cP # M & ) P t t* 1 # M & ) P t t hei j hei ) c = "hei (*
#* hei - A $ hei j "hei ( v
A h)e A i ))* 1 A c A h) u $ A h) "hei ( * 0 "hei ( cP - 0 %*
#
TU
pC
dU(j)
t
di
TC
& 1 *
&* 0 hei l - M ) P t t* , hei e j i - h h i e * h B i j - h P * 1 - , t t v P * 0 t t O P P i j - h h - P t u % t G P ) h B )*
+ B P - P t t M P t t *
1 - = & M ) P t t*
[[] ` ]^^ ` ] _ [ ` a 1 1 # - - c c )* >
- 'X > - = ! B - P * l - = RB P - P w - )* + P - P - - ! = s - = RP * 1 ! = s , 1 # - , , * B hei - 2 - hei ) hei ) - , hei ) v hei ) hei j *
H 2 m %XRn ) 2
- - *
#'
- e j - e ) @ - *
1 c > e f f f e ) c > e f f f e ) e ) c u ) *
>
+ 89 M8445FG "P( AB @ * 1
459 8F<5DF ) - d h)g *
86 = M8 3F P Q P 9 36:5q ) =T 6J8:8 5< 3F 89 M8445FG "P( <K;J 6J36 h)e i )) c = "hei ( T D: 878:E hei j "P( ( 6J8F 8 <3E 6J36 = 5< 3 A C
B 7; % 82 7$ 8+ 1 A0 17B % + 8 ; %& #70 )
5 !
0 , - - BB = B
* - - - B@ ) - = @ * 0 - - ! = AB @ , A * 0 ? - - - BB . P ) . R)*
1 -* 1 "P( ,
! *
F D: 3 G578F 9 36:5q = 3F4 3 <KM<86 "P( ( 8 <3E
6J36 3F 89 M8445FG 5< 0 $ 82 72& % 8& 56J = DF ( 5T h)e i )) c = "hei ( T D: 878:E
hei j ) @ J8F c "P( 8 <59C LE <3E 6J36 6J 8 89 M8445FG 5< ;DF<5<68F6 56J = )
=T "P( 5< <K;J 6J36 6J8:8 8q5<6< 3F 89 M8445FG 6J36 5< 0 $ 82 72&% 8& 56J = DF ( 6J8F
8 <3E 6J36 5< A C % ; % B + 1% 56J :8<C 8;6 6D = )
- *
! 86 = M8 3F P QP 9 36:5q 3F4 L86 "P( M8 3 A S89 M843ML8 <KM<86
56J :8<C 8;6 6D = ) F D: 3FE <86 b "P( ( 5T 6J 8:8 8q5<6< 3F 89 M8445FG s b <K;J 6J36 D
s 5< 3F 8q 68F<5DF DT -6J36 5< ( s h) c h) T D: 878:E h j . K ) s 5< ;DF<5<68F6 56J = DF b )
L ) s) c ) 6J8F 6J8 89 M8445FG s 5< A 8 7N A% ) F K:6J8:9 D:8 ( T D: 878:E i j b ( s i ) ;3F M8 ;D9C K684 K<5FG DFLE 3F4 6J 8 73LK8< = "hei ( T D: 878:E h j )
1 = AB @ A d h)g ) ! .
s "P( ! - = *
U ! = AB - = B
- - = *
E)
#
1 , h > j $ e f f f e $) h = "h > e h (e $ e f f f e $)
- - * 1 B
! = - AB - = *
0 - * + - ) - V w * * !
) - * - - 2
,B) 2 *
l ! - ,* 0 , = P Q P ! *
? ! 86 "P( 3F4 L86 M8 3F 89 M8445FG DT 6J36 5< ;DF<5<68F6 56J = ( 3F4 5< 48:5784 ME 6J8 568:36578 C :D;84K:8
9 8F65DF84 3MD78 ) @ 8 <3E 6J36 3 CD5F6 i jX 5< 0 $ 82 72& % 8& 56J 5T 6J8:8 8q5<6< 3F 8q 68F<5DF
s di g DT 6J36 5< ;DF<5<68F6 56J = ) @ 8 <3E 6J36 i 5< 2& #$ 89 1' 0 $ 82 72&% 8& 56J 5T
s) c ) )
@ 8 48FD68 6J8 <86 DT CD5F6< 5F "P( 6J36 3:8 ;DF<5<68F6 56J ME ( 3F4 6JD<8 6J36 3:8 <6:DFGLE
;DF<5<68F6 ME )
0 = AB @ - * 1 ! i - = AB @ * H i - - * 1 - A c *
86 "P( M8 A S89 M843ML8 56J :8<C 8;6 6D = ( 3F4 L86 M8 6J8 89 M8445FG DM635F84 ME 3CC LE5FG 6J8 568:36578 C :D;84K:8 9 8F65DF84 83:L58: ) F D: 83;J CD5F6
i j ( L86 s i ) M8 3< 4868:9 5F84 ME 6J8 KF5 < K8 8q 68F<5DF DT 6D b c di g ) @ 8 <3E 6J36 3 C35:
DT C D5F6< hei j 3:8 3 I 7$ 1+ & 789 "+ 7# 56J :8<C 8;6 6D 5T s h)e s i )) cP = "hei ( )
!
# = AB @ - * , - * 0 i - ! s . * ) c A s . , , *
! 86 "P( M8 3 <KM<86 T D: J5;J 6J8:8 8q5<6 3F 89 M8445FG 6J36 5<
;DF<5<68F6 56J = DF ) =T = 5< RST 3: T :D9 M85FG 3 A S459 8F<5DF3L o K;L5483F 9 86:5; ( 6J8F 6J8:8
3:8 856J8: 9 D:8 6J3F P CD5F6< 6J36 3:8 FD6 <6:DFGLE ;DF<5<68F6 56J :8<C 8;6 6D D: 9 D:8 6J3F P 75DL365FG C35:< -DT <6:DFGLE
;DF<5<68F6 CD5F6<. )
) c A - ! FD6 <6:DFGLE ;DF<5<68F6 - FD6 ;DF<5<68F6 *
4 + P - P * l ! - ! AB @ = s = RP * = *
#
hei j "P( - = s "hei ( c s h)e s i )) - s "P( , - * h j s h) c h) h j s h) . ! b c di g* h j "P( ) - s h) * 1
= s = P ) P hei h i - *
? - - - - = A * *% w - ) - = AB @ RB ) - 1 - XR 2 - B * =
AB @ - * *% = RB AB @ % u ) %X&*
? - A M % *
1 - c d %g %) c $ e f f f e $) - * 0 - ! , )* + A - A * 0 w )* - 1 2 B - *
3 A)
%* c d %g %) c $ e f f f e $) j * 1 $)*
#* l ) v A w ) ) / c m A)XR) *
) 0 - #%> % 0& *
) - ) ! i - i ! , di g*
1 ) A)*
) - ) - #%> % 0& * - + 0 0 % "& *
3
J 8 3MD78 3LG D:56J9 5< 3 68<65FG 3LG D:56J9 T D: o K;L5483F 9 86:5;< )
H - w 87548F;8 = AB @
- AB - = )*
4 0 = AB @ *
1 = RB AB @ * N q 84 * *% P "P( - P * 0 , G > # #
- % u ) c > * ?
>
A M % ! - P "P( - > * H - - - - - w)* 0 P ) G > % u ) c > * 1 w % u %X M %X ) c #X&*
+ 1 - *
86 6J8 F36K:3L 68<65FG 3LG D:56J9 M8 6J 8 3LG D:56J9 6J36 <59C LE <8L8;6< 3 KF5T D:9
<39C L8 DT m A AXR) CD5F6< T :D9 "P( 3F4 3;;8C 6< 5T 3F4 DFLE 5T 6J8 <39C L8 <8L8;684 5< A S89 M843ML8
56J :8<C 8;6 6D = ) J8F 6J8 F36K:3L 3LG D:56J9 5< 3 68<65FG 3LG D:56J9 T D: A S459 8F<5DF3L o K;L5483F
9 86:5;< )
!
- b AB - = - * - b b c d $ e f f f e u %g* l 2 - ! AB e f f f e > e ) c = "hei (
hei j b * ? - - B$ - ! u % - . "hei ( - "hei ( c > = "he $( M = "i e $( u = "hei ()* 1
- ! B, 2 A * 1 , 2 ! ! 2 - * 1 2 U *
4 0 = AB @ - *
l ! - = RB AB @ w - #X&* 1 - 1 @ w w AB - = )*
!
l P Q P ! = C :DC 8: AB @ ! "P( - = 3F4 5< DF8S6DSDF 8* l , C :DC 8: * 0 - - - - *
FE 3LG D:56J9 T D: 68<65FG C :DC 8: A S459 8F<5DF3L o K;L5483F 9 86:5;< :8< K5:8< P )
< K8:58< ) 59 5L3:LE ( 3FE 3LG D:56J9 T D: 68<65FG C :DC 8: 6:88 9 86:5;< :8< K5:8<
P ) < K8:58< ) J8<8
MDKF4< JDL4 T D: 68<65FG 3LG D:56J9 < 6J36 3:8 3LLD 84 6 DS<5484 8::D: C :DM3M5L56E )
3
6
] ][ Z ] a - - - - * ! = , - *
#
h c %e f f f e i c %e f f f e = "#h u %e #i u %( c = "#h u %e #i ( c = "#he #i u %( c = "#he #i ( c
ti u h t* 1 @ "P( d #h u %e #hg h j - = * * ? "P( - = - d %e f f f e g - h h M % - % #h u %e #h j "P( h)* 0 - = %B @ *
bM OP_OWWLM` R[MSLSNOMN fLN^ N^O PUNQLd e a b TULQ [c T[LMNS LS PUTTOW N[ OUR^ LMNO`OQ [M N^O
YLMO LM N^O QUM`O …v v a
= @ * l ! - = %)B AB @ A * 0 - = %)B * & w d #h u %e #hg
d #i u %e #i g d # u %e # g* + - h i * 1 j d #h u %e #hg j d #i u %e #i g j d # u %e # g
= " e ( c = " e ( M = " e (f
BB d #h u %e #he #i u %e #i e # u %e # g A)* 1 e j dhei e g cP j d # u %e # g j d # u %e # g
)e )) cP = " e (f
)
H- ! ! d %e f f f e g - 0. j d # u %e # g j d # u %e # g* 1 - 2- - * 1 W &* 1 1 1 "# %( P )* , - "P( - = P ) * ? BB - = %)B @ *
- - . . * l - V * 1 2 "P(
BB * 0 - w * H #h u % #h
% v h v * -B2- 5:6J43E
3:34Dq V P - #h u % #h * + *
` ] ][ Z ^a 0 W - - - * , @ * l - @ - %)B @ * - ] ][ _ &$
- V - ! , ! P . %* ? - 2- - ;T ) "%' #() - 2 *
1 - "P( * 1 ,
BB "P( - P X# .
* l 2 - - . * - - * '*
' + - @ *
, , #B @ * H
P X * 1
- - ! %)B @ * 1 - .
)*
H- - . - - - ! = * 1 , - . - B
! , ! * 1 - * 0 h - . . = "hei ()* U - . = "hei ( h ) h i )* 1 - . - * 1 - - - h*
%* 1 , - * 0 . - 1 , * H P > P - * 1 - x , - x
Q * + Q
x
Q
)* 0 - - . * 0 *
&%
#* 1 * 0
- - . * - - *
- - ) - . = "hei ( )* 0 V % P . - * 1 - - - "%'()*
1 - - * 0 , B )
- "P( * 0
! * 1 @ - )* - ! - *
+ - *
- R A @ ) *
? - w !
- ! - - - - * 1 V ! *
l O B O -2 * l - 2 2 O ? W O U *
&#
"%(
* +- * O * O * O * 1 * ! ! , )* =6 p DK:F3L DF ! D9C K65FG
# &) %$ & %$ ' % *
"#( H * + ?* ! O * ! * * 1 * 0 :D;8845FG< DT 6J8 F D:6ESF 5:<6
6 FFK3L E9CD<5K9 DF F DKF4365DF< DT ! D9C K68: ;58F;8 # $ #'$ #$$$ *
"&( H * + @ * O * O ?W* @V * 0
:D;8845FG< DT 6J8 F D:6586J 6 FFK3L E9CD<5K9 DF F DKF4365DF< DT ! D9C K68: ;58F;8 ' '' % *
" ( H * + O * 0* H- O ?W* - .* 0 :D;8845FG< DT 6J8 F D:6586J 6 FFK3L E9CD<5K9 DF F DKF4365DF<
DT ! D9C K68: ;58F;8 ' % *
"'( B + * U *
% %*
:88< 3F4 :Dq59 56E 8C :8<8F6365DF<* l H- 2 " ( * B? W + * @-* *
6 9 8:5;3F DK:F3L DT K9 3F 8F865;< % #&& #' % *
" ( * * 2* + *
= FT D:9 365DF :D;8<<5FG ! 8668:< # %' ##$ % *
" ( + * W w * ? O * * * 0 :DS
;8845FG< DT 6J8 6J 6 FFK3L o K:DC 83F E9CD<5K9 DF 6 LG D:56J9< -o 6 . %'' % #$$$ *
H ? O * ?B *
" ( l * * @ * ! * ! *
KLL865F DT p 36J89 365;3L 5DLDGE ) % % *
"%$( + * ! * @*)* :88< 3F4 58:3:;J5;3L 6:K;6K:8<* ? % *
H BO *
"%%( * @ ?* ?* * * O * - * ? B2* 0
:D;8845FG< DT 6J8 J5:6ES 8;DF4 6 FFK3L 6 !p E9CD<5K9 DF 6J 8 J8D:E DT ! D9C K65FG #' # % *
"%#( O * ?* 1 * l - * + , *
6 LG D:56J9 5;3 %& % #) %'' % % '*
"%&( * * H *
5DLDGE ' ) & $ % #*
K3:68:LE 8758
DF
"% (
* U ?* U- ! * * ! * DK:F3L DT 6J8 6 !p ' ) '& '$ % *
"%'(
* U ! * * * 0 :D;8845FG< DT 6J 8
J5:6ES F 5:<6 6 FFK3L 6 !p E9CD<5K9 DF 6J8 J8D:E DT ! D9C K65FG $ %' % * 1
6 LG D:56J9 5;3 *
&&
"% ( ? * @ * - 1 * l - *
:56J9 < # %%) # '$ % *
!
* DK:F3L DT
"% ( O * 2
* 1 ! * = FT D:9 365DF
! 8668:< # # ' # $ % *
"% (
"% (
* * 1 2 #$$$ *
!
6
LG DS
:D;8<<5FG
W * * O * ? * W - * =6 p DK:F3L DF ! D9C K65FG #' #) #'# # % % *
"#$( * * + * ? * * ?2*
K9 8:5;3L 3q DFD9 E* l * * % &*
"# %( * 1 * ! )* p 36 ) F 5 ) ! 3CD & '# % %*
"##( O * ?* l 1 * * ? O ? l * + * * + * DK:F3L
DT J8D:865;3L 5DLDGE % # %& % *
&