i)L?_ hM|h@}iG BLL_#i@* tti| hUi L?_t ?
W?UL4T*i|i @h!i|t
aL? O LUh@?i @?_ ait
t 5@@+i^iL|}{
a@?@h) 2Sc bbb
Devwudfw
Rqh riwhq zdqwv wr ydoxh d ulvn| sd|r e| uhihuhqfh wr sulfhv ri rwkhu dvvhwv udwkhu
wkdq e| h{sorlwlqj ixoo0hgjhg hfrqrplf prghov1 Krzhyhu/ wklv dssurdfk euhdnv grzq
li rqh fdqqrw qg d shuihfw uhsolfdwlqj sruwirolr1 Zh lpsrvh zhdn hfrqrplf uhvwulfwlrqv
wr ghulyh xvhixoo| wljkw erxqgv rq dvvhw sulfhv lq wklv vlwxdwlrq1 Wkh erxqgv dvvxph
wkdw lqyhvwruv zrxog zdqw wr ex| dvvhwv zlwk kljk Vkdush udwlrv ~ _jrrg ghdov% ~ dv
zhoo dv sxuh duelwudjh rssruwxqlwlhv1 Zh vkrz krz wr fdofxodwh wkh sulfh erxqgv lq
rqh0shulrg/ pxowlshulrg dqg frqwlqxrxv wlph frqwh{wv1 Zh vkrz wkdw wkh pxowlshulrg
sureohp fdq eh vroyhg uhfxuvlyho| dv d vhtxhqfh ri rqh0shulrg sureohpv1 Zh fdofxodwh
erxqgv lq rswlrq sulflqj h{dpsohv lqofxglqj lqiuhtxhqw wudglqj dqg dq rswlrq zulwwhq
rq d qrqwudghg hyhqw/ dqg zh xvh wkh erxqgv wr h{soruh wkh hfrqrplf vljqlfdqfh ri
rswlrq sulflqj suhglfwlrqv1 Zh qg wkdw pxfk yduldwlrq lq V)S833 lqgh{ rswlrq sulfhv
ryhu wlph dqg dfurvv vwulnh sulfhv wv zlwklq wkh erxqgv1
Xqlyhuvlw| ri Fklfdjr/ Ihghudo Uhvhuyh Edqn ri Fklfdjr dqg QEHU1
|Xqlyhuvlw| ri Fklfdjr
}Dgguhvv fruuhvsrqghqfh wr Mrkq Frfkudqh/ Judgxdwh Vfkrro ri Exvlqhvv/ Xqlyhuvlw| ri Fklfdjr/ 4434
H1 8;wk Vw1/ Fklfdjr LO 9396:1 +::6, :35 638</ mrkq1frfkudqhCjve1xfklfdjr1hgx1
{Zh wkdqn Gdylg Edfnxv/ Jhrujh Frqvwdqwlqlghv/ Nhqw Gdqlho/ Grxjodv Gldprqg/ Dqguhd Hlvihogw/ Oduv
Kdqvhq/ Nhq Vlqjhowrq/ Vwhyh Urvv/ pdq| vhplqdu sduwlflsdqwv dqg hvshfldoo| \dflqh Dlw0Vdkdold iru xvhixo
frpphqwv1 Wklv uhvhdufk zdv sduwldoo| vxssruwhg e| wkh Xqlyhuvlw| ri Fklfdjr Judgxdwh Vfkrro ri Exvlqhvv
dqg e| d judqw iurp wkh QVI dgplqlvwhuhg e| wkh QEHU1
W?|hL_U|L?
Ai u?_@4i?|@* ^it|L? Lu ?@?U@* iUL?L4Ut t L |L @*i ?Uih|@? T@)Lgt 6Lh 4@?)
@TT*U@|L?t ? iUL?L4Ut @?_ ?@?Ui @ hi*@|i ThU?} @TThL@U t @TThLTh@|i W? |iti
@TT*U@|L?t i @hi L?*) ?|ihit|i_ ? |i @*i Lu @ tTiUU T@)Lgc i |@!i @t }i? |i
ThUit Lu L|ih @tti|t |L| ^it|L??} |ih u?_@4i?|@* iUL?L4U _i|ih4?@?|tc @?_ i
@?| |L 4@!i @t ui iUL?L4U @tt4T|L?t @t TLttM*i
T|L? ThU?} t |i U*@ttU U@tiG i @?| |L !?L |i @*i Lu @? LT|L? }i? |i ThUi
Lu |i ?_ih*)?} t|LU! Ai |iLh) Lu *@U! @?_ 5UL*it Eb. @?_ ih|L? Eb.M t @
}hi@| tUUitt Lu |t @TThL@U ,i? |L} @? LT|L? T@)Lg t ^|i _gihi?| uhL4 |@|
Lu @ t|LU! Lh ML?_c |i) tLi_ L UL?|?Lt _)?@4U |h@_?} U@? UL4T*i|i @ 4@h!i|
AihiuLhic |i LT|L? T@)Lg U@? Mi TihuiU|*) hiT*U@|i_ M) UL?|?Lt |h@_?} ? |i t|LU!
@?_ ML?_c @?_ |i LT|L?<t @*i U@? Mi _i|ih4?i_ }i? |@| Lu |i t|LU! @?_ ML?_ V@
|t hL*i ? LT|L? ThU?} |iLh)c |i hi*@|i 4i|L_ t ti_ ? 4@?) iUL?L4U @TT*U@|L?t
Lu ?@?Ui |iLh)c tU @t |i hi@*LT|L? @*i Lu hhiihtM*i ?it|4i?| EuLh i @4T*ic Mi*
@?_ ,Mih*) bbSc # | @?_ ?_)U! bbe +Ltt< Eb.SM hM|h@}i hU?} AiLh) |hit |L
_i|ih4?i |i i TiU|i_ h@|i Lu hi|h? Lu @ TLh|uL*L }i? |i i TiU|i_ hi|h?t Lu Ru@U|Lh
TLh|uL*Ltc @?_ |L| Thiuihi?Ui @tt4T|L?t ,i? @TT@hi?|*) iUL?L4UtM@ti_ |iLhit
tU @t |i @T|@* tti| hU?} L_i* @hi |)TU@**) @TT*i_ ? @ hi*@|i @)c t?Ui L?i
_i|ih4?it i TiU|i_ hi|h?t L? @tti|tc TLh|uL*Lt Lh ?it|4i?| ThLiU|tc |@!?} |i 4@h!i|
i TiU|i_ hi|h? @t }i? hi*@|i @TThL@U tc @TThLTh@|i*)c ti_ uLh 4@?) @TT*U@|L?t
Lu @tti|ThU?} |iLh) |L ULhTLh@|i ?@?Ui 6Lh i @4T*ic L?i i @4?it |i hi|h?t L? R*!i
tiUh|it |L _i|ih4?i |i ULt| Lu U@T|@* uLh @ tTiUU ThLiU|
*@tc @ Thi*) Thiuihi?Uiuhii @TThL@U Lu|i? Mhi@!t _L? ?i 4@) ?L| Mi @M*i |L |h@_i
UL?|?Lt*)( |ihi 4@) Mi t|@|i @h@M*it Ei} t|LU@t|U t|LU! L*@|*|) @?_ ?|ihit| h@|i
|@| _L ?L| ULhhitTL?_ |L |h@_i_ @tti|t( |i ii?| L? U @? LT|L? Lh hi@* T@)Lg _iTi?_t
4@) ?L| Mi @ |h@_i_ @tti| Lh | 4@) Mi tL |?*) |h@_i_ |@| | t ?L| tiu* uLh i_}?} W?
u@U|c u LT|L?t hi@**) UL*_ Mi TihuiU|*) @?_ ULt|*itt*) hiT*U@|i_ M) L|ih *^_ @tti|tc | t
?*!i*) |@| LT|L?t L*_ Mi |h@_i_ ? |i ht| T*@Ui
`i ti @ *||*i iUL?L4Utc @ t*}| t|hi?}|i??} Lu ?L@hM|h@}i @?_ *@ Lu L?i ThUi
@h}4i?|tc |L }hi@|*) hit|hU| |i h@?}i Lu @*it Lu @ ht!) T@)Lg ? |iti t|@|L?tc |L|
@?} |L u@** M@U! L? UL4T*i|i*) tTiUi_ iUL?L4U 4L_i*t tU @t |i UL?t4T|L?M@ti_
@tti| ThU?} 4L_i*
Ai M@tU _i@ t 4Lt| t4T*) i T*@?i_ ? @ L?iTihL_ i?hL?4i?| `i @?| |L *i@h?
@ML| |i @*i Lu @ uLUt T@)Lg %S|nc |@!?} @t }i? |i ThUit T| Lu @ ti| Lu M@tt T@)Lgt
Lh i_}?} @tti|t |n
_tUL?| u@U|Lh Lh 4@h}?@* |*|) }hL| h@|i 6|n }i?ih@|it |i @*i R| Lu @?) T@)Lg
%|n M)
R ' . E6% E
Oihi @?_ Mi*L i tTThitt |4i tMtUhT|t ?*itt |i) @hi ?iUitt@h) uLh U*@h|) Ai T@)Lgc
@*ic @?_ _tUL?| u@U|Lh U@? Mi hi@* Lh ?L4?@* Ai i t|i?Ui Lu tU @ _tUL?| u@U|Lh Lh
4@h}?@* |*|) @t @ TLh|uL*L ?|ihThi|@|L?G | t i^@*i?| |L |i *@ Lu L?i ThUi |@|
@?) |L @)t Lu UL?t|hU|?} |i t@4i T@)Lg @i |i t@4i @*i Atc u |i uLUt T@)Lg
%S U@? Mi TihuiU|*) hiT*U@|i_ uhL4 |i M@tt @tti| T@)Lgt c i @i i?L} ?uLh4@|L? |L
_i|ih4?i |t @*i i @U|*) `i? hiT*U@|L? t *itt |@? TihuiU|c Liihc |i i t|i?Ui Lu
@ _tUL?| u@U|Lh Lh *@ Lu L?i ThUi t@)t ?L|?} @ML| |i @*i Lu |i uLUt @tti|c @?_ i
?ii_ 4Lhi _tUL?| u@U|Lh hit|hU|L?t
Ai 4Lhi i U@? hit|hU| |i _tUL?| u@U|Lhc |i 4Lhi i U@? *i@h? @ML| @tti| @*it
`i hi^hi |@| |i _tUL?| u@U|Lh ThUi @ ti| Lu M@tt @tti|tc |@| | t ?L??i}@|ic @?_ i
4TLti @? TTih ML?_ L? |t L*@|*|) Atc |i *Lih }LL__i@* ML?_ tL*it
' 4? .E6%S r| T ' .E6 ( 6 f( jE6 *-s c
t6
ihi
' *Lih }LL__i@* ML?_c
6 ' _tUL?| u@U|Lhc
%S ' uLUt T@)Lg |L Mi @*i_c i} %S ' 4@ E7A gc f uLh @ U@** LT|L?c
Tc
' ThUi @?_ T@)Lgt Lu M@tt @tti|t EiU|Lhtc i} t|LU! @?_ ML?_c
' ThitTiUi_ L*@|*|) ML?_c
-s ' ht! uhii ?|ihit| h@|ic
.c j '
UL?_|L?@* 4i@? @?_ @h@?Uic
2
E2
@?_ |i TTih }LL__i@* ML?_ 7 tL*it |i ULhhitTL?_?} 4@ 44
RV@*i 4i@?t L 4U @ T@h|U*@h ?it|Lh | 4@h}?@* |*|) }hL| 6 L*_ Mi
**?} |L T@) uLh @ 4@h}?@* ^@?||) Lu |i T@)Lg At ti?ti Lu @*i 4@!it ?L @tt4T|L?t
@ML| i|ih |i uLUt T@)Lg t |h@_i_ Lh ?L|c Lh i|ih |i ?it|Lh @*hi@_) L*_t tL4i
Lu | Lh ?L| OLiihc |t ti?ti Lu @*i t ?L| |i i^*Mh4 ThUi Lu @ ihi|LuLhi ?|h@_i_
tiUh|) @u|ih @}i?|t M) @** |i) @?| Lu |
Ai ht| UL?t|h@?|c T ' .E6 i?uLhUit |i hi*@|iThU?} _i@ |@| i |@!i @t }i?
|i ThUit Lu @ ti| Lu M@tt @tti|t `i ti |i ThUit Lu |iti @tti|t |L *i@h? @ML| |i _tUL?|
u@U|Lhc ?L| Ui iht@
Ai tiUL?_ UL?t|h@?| 6 f t @ U*@ttU @?_ i@! U@h@U|ih3@|L? Lu 4@h}?@* |*|)
EAi _t|?U|L? Mi|ii? 6 : f @?_ 6 f t ?4TLh|@?| uLh Lh hit*|t At @tt4T|L?
@*tL @t @ TLh|uL*L ?|ihThi|@|L? E+Ltt b.SUc O@?ti? @?_ +U@h_ bH.G | t i^@*i?| |L
|i @Mti?Ui Lu @hM|h@}i LTTLh|?|itc U 4i@?t |@| u @ T@)Lg t ?L??i}@|i ? iih)
t|@|i Lu ?@|hic |t @*i 4t| @*tL Mi ?L??i}@|i Wu i !?Lc Tih@Tt M) @ ht!@|||_i
thi)c |@| @? ?it|Lh ** |@!i T@h| ? @?) @hM|h@}i LTTLh|?|)c |i? i !?L |@| t
4@h}?@* |*|) t ?L??i}@|i Ai @MLi ThLM*i4 | |i ht| |L UL?t|h@?|t *i@_t |L
i**!?L? @hM|h@}i ML?_t L? |i @*i
Ai L*@|*|) UL?t|h@?| jE6 *-s t Lh ??L@|L? `i ?|i?_ | @t @ t4*@h i@!
hit|hU|L? L? 4@h}?@* |*|)c @ ?@|h@* ?i | t|iT i? @Mti?Ui Lu @hM|h@}i @*L?i _Lit ?L|
}i ThiUti i?L} @?tiht W| @*tL @t @ TLh|uL*L ?|ihThi|@|L? O@?ti? @?_ a@}@??@|@?
Ebb tL |@| @ _tUL?| u@U|Lh L*@|*|) hit|hU|L? t i^@*i?| |L @? TTih *4| L?
|i 5@hTi h@|L Lu 4i@? i Uitt hi|h? |L t|@?_@h_ _i@|L? hiUti*)c |i) tL |@|
.E6-e m. E-e m
j E6
' f u @?_ L?*) u
c
e
j E- . E6
@?_ i @i .E6 ' *-s u |ihi t @ ht!uhii h@|i
AihiuLhic u i !?Lc Tih@Tt
M) @ ht!@|||_i thi)c |@| @? ?it|Lh ** |@!i T@h| @| |i 4@h}? ? @?) TLh|uL*L
|@| _i*iht 5@hTi h@|L }hi@|ih |@? c |i? i !?L |@| t 4@h}?@* |*|) t@|tit
jE6 *-s `i U@** |i ML?_t L? @*i U@*U*@|i_ | |t @__|L?@* UL?t|h@?| }LL_
_i@* ML?_t MiU@ti |i) @tt4i |@| ?it|Lht L*_ @?| |L |h@_i @?) }LL_ _i@*t *@h}i
5@hTi h@|Lt @t i** @t Thi @hM|h@}i LTTLh|?|it
Aihi t @ *L?} |h@_|L? ? ?@?Ui |@| hi}@h_t } 5@hTi h@|Lt @t R}LL_ _i@*t |@|
@hi ?*!i*) |L thic t?Ui ?it|Lht L*_ ^U!*) }h@M |i4 T +Ltt Eb.S ML?_t A
hit_@*t M) @tt4?} |@| ?L TLh|uL*L U@? @i 4Lhi |@? |Ui |i 4@h!i| 5@hTi h@|Lc
U 5@?!i? Ebb2 U@**t R@TThL 4@|i @hM|h@}i @Uk?*@) EbbD Uh|U3it 6@4@ @?_
6hi?U Ebb M) ?L|?} @| tii4 *!i i Uitti*) } 5@hTi h@|Lt wi_L| EbbD U@**t
@ } 5@hTi h@|L @ RB @hM|h@}i @?_ h*it | L|
Ai _tUL?| u@U|Lh L*@|*|) UL?t|h@?| t @*tL @ @) Lu 4TLt?} i@! Lh hLMt| Thi_U
|L?t Lu iUL?L4U 4L_i*t ?i 4@) ?L| t |L 4TLti |i u** t|hU|hi Lu @? iUL?L4U @tti|
ThU?} 4L_i*c uLh i @4T*i @ |*|) u?U|L? @?_ @ tTiUU@|L? Lu |i L?| _t|hM|L? Lu
UL?t4T|L? @?_ @tti| T@)Lgt 5|**c @ _i h@?}i Lu tU 4L_i*t 4T*) |@| 4@h}?@* h@|it
Lu tMt|||L? @hi ?L| L|h@}iLt*) L*@|*ic @t i** @t TLt|i 6h|ih4Lhic |i t|@?_@h_
_i@|L? Lu |i _tUL?| u@U|Lhc *i @ i@! Thi_U|L? Lu @ tU @ 4L_i*c 4@) Mi 4Lhi
hLMt| |L 4L_i* @?_ _@|@ tTiUU@|L? ihhLht |@? @hi |i UL@h@?Uit Lu T@)Lgt | |i
_tUL?| u@U|Lh M) U tU 4L_i*t }i?ih@|i @*it
54*@h*)c |i tTiUit |@| |i 4@h!i| TLh|uL*L t 4i@?@h@?Ui iUi?| Wu
i i |i |iLh) @?_ 4@h!i| ThL ) uLh |i i@*| TLh|uL*L @t @TThL 4@|L?tc
|i? i Mi*ii |@| |i 4@h!i| TLh|uL*L tL*_?<| Mi |LL ?iUi?|G 5@hTi h@|Lt Lu L|ih
TLh|uL*Lt tL*_ ?L| Mi _h@4@|U@**) }ih |@? |@| Lu |i 4@h!i| TLh|uL*L ? |i L|ih
@?_c u |i 4@h!i| hi|h? t ii? t*}|*) ?iUi?|c UL@h@?Uit | |i 4@h!i| hi|h? U@?
}i?ih@|i @hM|h@h*) *@h}i ThU?} ihhLht Ek@?_i* @?_ 5|@4M@} bbD
6?@**)c |i L*@|*|) UL?t|h@?| t @? i@t) @) |L Th?i ?hi@tL?@M*i _tUL?| u@U|Lht
|? |i @hM|h@}i ML?_t 6Lh i @4T*ic |i *Lih @hM|h@}i ML?_ ' f uLh @ U@** LT|L?
hi^hit 4@h}?@* |*|) |@| t 3ihL uLh @** t|@|it Lu ?@|hi ? U |i LT|L? ?tit ? |i
4L?i) Ai TTih @hM|h@}i ML?_ ' 7 hi^hit @ _tUL?| u@U|Lh |@| t L?*) ?L?3ihL
? |i |L t|@|it Lu ?@|hi | |i 4Lt| i |hi4i t|LU! ThUit AL} ?L??i}@|ic |iti
_tUL?| u@U|Lht @hi ?*!i*) U@h@U|ih3@|L?t Lu @?)L?i<t 4@h}?@* |*|) Aiti _tUL?|
u@U|Lht @h) @ }hi@| _i@* @UhLtt t|@|it Lu ?@|hic @?_ @i @ } @h@?Ui Ai L*@|*|)
UL?t|h@?| ii_t L| tL4i Lu |iti @hM|h@}iuhii M| t|** R?hi@tL?@M*i _tUL?| u@U|Lht
@?_ |ih ULhhitTL?_?} LT|L? ThUit
t @ t4T*i i @4T*ic UL?t_ih @ U@** LT|L? L? |i 5:Dff ?_i | t|h!i ThUi g '
e
mffc |hii 4L?|t |L i Th@|L?c @?_ ?L ?|ih4i_@|i |h@_?} 6}hi Thiti?|t |i TTih
@?_ *Lih }LL__i@* ML?_t uLh |t U@ti
dW?tih| 6}hi ihio
`i ti T@h@4i|ih @*it .E- ' Ic jE- ' SI uLh |i t|LU! ?_i hi|h? @?_ @?
ht!uhii h@|i -s ' DI E`i hiTLh| @** T@h@4i|iht @| @??@* uhi^i?U) @?_ @_t| |L |i
@TThLTh@|i |4i Lh3L? ? |i U@*U*@|L?t AL U@*Mh@|i |i _tUL?| u@U|Lh L*@|*|) UL?
t|h@?|c i @tt4i |@| |i ?it|Lh L*_ |@!i @?) LTTLh|?|) | 5@hTi h@|L |Ui |@|
Lu |i 5:Dffc ' 2 .E- -s *jE- ' f 5?Ui 4Lt| u?_ 4@?@}iht tii4 _itTih@|i
uLh @ih@}i hi|h?t @ ui TihUi?| @MLi |i 5:Dff ?_i c |t @*i tii4t UL?tih@|i
At @*i _LM*it |i @*hi@_) |hLM*?} i^|) Thi44 T33*i( | 4T*it |@| |i t|@?_@h_
_i@|L? Lu 4@h}?@* |*|) }hL| jE6 ' *-s t i^@* |L |t 4i@?c .E6 ' *-s c @?_
?i@h*) ffI Tih )i@h OLiihc |t t |i Ui?|h@* T@h@4i|ih |@| @ tih 4t| ?T| |L |i
U@*U*@|L?( | t i@t) |L U@?}i |c @?_ Lh UL?|hM|L? t |L tL L |L U@*U*@|i }LL__i@*
ML?_t uLh @|iih @*i Lu |t *4| |@| |i tih |?!t t @TThLTh@|ic ?L| |L @_LU@|i
@ tTiUU @*i
Ai }hi ?U*_it |i *Lih @hM|h@}i ML?_t fc g*-s Ai TTih @hM|h@}i
ML?_ t|@|it |@| 7c M| |t eD *?i t |LL u@h T |L | L? |i ih|U@* tU@*i @?_ t|**
tii @?)|?} i*ti t ? 4@?) Th@U|U@* t|@|L?tc |i @hM|h@}i ML?_t @hi tL _i |@|
|i) @hi Lu *||*i ti
Ai TTih }LL__i@* ML?_ t 4U |}|ih |@? |i TTih @hM|h@}i ML?_ 6Lh i @4T*ic
u |i t|LU! ThUi t mbDc |i i?|hi h@?}i Lu LT|L? ThUit Mi|ii? |i TTih ML?_ Lu m2 @?_
|i TTih @hM|h@}i ML?_ Lu mbD t h*i_ L| Ai *Lih }LL__i@* ML?_ t |i t@4i @t
|i *Lih @hM|h@}i ML?_ uLh t|LU! ThUit *itt |@? @ML| mbf @?_ }hi@|ih |@? @ML| mf
W? Mi|ii? mbf @?_ mfc |i }LL__i@* ML?_ 4ThLit L? |i *Lih @hM|h@}i ML?_
Ai _| Lu |i ML?_t t *@h}ihc @ML| mc @| |i 4L?i) |@? | t u@h ? |i 4L?i) Lh
L| Lu |i 4L?i) T|L?t @hi @h_it| |L i_}i @| |i 4L?i)c MiU@ti |i ?L?*?i@h|) Lu |i
LT|L? T@)Lg @t @ u?U|L? Lu t|LU! ThUi t }hi@|it| ihi AihiuLhic |i hit_@* LT|L?
T@)Lg *itt Mit| @TThL 4@|i i_}i t *@h}it| ? |t hi}L? OLiihc |i _| Lu |i
ML?_t t @ 4U *@h}ih uh@U|L? Lu |i U@** LT|L? @*i uLh L| Lu |i 4L?i) LT|L?t L? |i
D
*iu| @?_ t_i Lu |i }h@T W? |t ti?tic @t i** @t i? |h@?t*@|i_ |L 4T*i_ L*@|*|itc
|i ML?_t @hi _ih uLh L|Lu|i 4L?i) LT|L?t
AL} L?i t ?@|h@**) ?U*?i_ |L *LL! uLh t4@** ML?_tc *@h}i ML?_t U@? Mi @t ?|ihit|
?} @t t4@** ML?_tc @?_ 4@)Mi 4Lhi tL 54@** ML?_t UL?h4 |@| hiT*U@|L? @h}4i?|t
@hi }LL_ @TThL 4@|L?t w@h}i ML?_t @h? t |@| hiT*U@|L? @h}4i?|t @hi TLLh @T
ThL 4@|L?tc |@| @tt4T|L?t @ML| ?4i@thi_ 4@h!i| ThUit Lu ht! @hi 4TLh|@?| |L
|i @?tihc @?_ |@| uh|ih _tUL?| u@U|Lh hit|hU|L?t L*_ Mi tiu* |L hit|hU| |i h@?}i
Lu @*it
6}hi ?U*_it |i *@U!5UL*it LT|L? @*i uLh hiuihi?Uic @*|L} | _Lit ?L| @TT*)
|L |t i @4T*i t?Ui |i ?it|Lh U@??L| |h@_i UL?|?Lt*) Ai }LL__i@* ML?_t UL?ih}i
|L *@U!5UL*it @t |i hiM@*@?U?} ?|ih@* t 4@_i 4Lhi uhi^i?|c M| |i) UL?ih}i |L @ *?i
|@| _giht uhL4 |i *@U!5UL*it @*i @t |i L*@|*|) ML?_ t *Lihi_ *i 4@?|@??}
@ i_ |h@_?} ?|ih@* 5|**c | t ?Ui |L tii |@| |i }LL__i@* ML?_t ?U*_i |i *@U!
5UL*it @*i @?_ @i |i t@4i }i?ih@* t@Tic t?Ui |i *@U!5UL*it @*i t Lu|i? @?
i Ui**i?| @TThL 4@|L? |L LMtihi_ LT|L? ThUit
L| @** @*it L|t_i |i }LL__i@* ML?_t 4T*) } 5@hTi h@|Lt Lh @hM|h@}i LTTLh
|?|it 5U @*it 4}| Mi }i?ih@|i_ M) @ TLt|i M| }*) L*@|*i _tUL?| u@U|Lhc @?_
}i?ih@|i_ M) @?L|ih *itt L*@|*i M| tL4i|4it ?i}@|i _tUL?| u@U|Lhc M| ?L _tUL?|
u@U|Lh }i?ih@|it |iti @*it |@| t t4*|@?iLt*) ?L??i}@|i @?_ hitTiU|t |i L*@|*|)
UL?t|h@?|
W| 4@!it ti?ti |L _i?i ML?_t @t i _Lc @?_ |L h*i L| |iti @*it|L ?|ihtiU| _tUL?|
u@U|Lh hit|hU|L?t E6 : fc jE6 *-s h@|ih |@? |L ?|ihtiU| |i @*i hi}L?t E?L
@hM|h@}ic *4|i_ 5@hTi h@|L uLh4i_ uhL4 i@U _tUL?| u@U|Lh hit|hU|L? t4*|@?iLt*)
Wu i !?L |@| @? ?it|Lh ** ?it| ? @?) @hM|h@}i LTTLh|?|) Lh |@!i @?) 5@hTi h@|L
}hi@|ih |@? c |i? i !?L |@| t 4@h}?@* |*|) t@|tit ML| hit|hU|L?t Oi L*_
?_ @ |*|)4ThL?} |h@_i uLh @*it L|t_i |i }LL__i@* ML?_tc ii? |L} |Lti
@*it 4@) ?L| 4T*) @ } 5@hTi h@|Lc @? @hM|h@}i LTTLh|?|)c Lh @?) L|ih t4T*i
TLh|uL*L ?|ihThi|@|L? 54T*i TLh|uL*L ?|ihThi|@|L?tc *i t|LhU@**) 4TLh|@?|c @hi
*!i*) |L u@** M) |i @)t_i @t i @__ 4Lhi _tUL?| u@U|Lh hit|hU|L?t Lh ?|ihtiU| t4T*i
L?it 6h|ih4Lhic Lh 4i|L_ uLh i |i?_?} |i ThLM*i4 |L @?_*i 4*|T*i TihL_t hi^hit
S
@ ?L??i}@|i _tUL?| u@U|Lhc tL @}@? i 4t| 4TLti ML| UL?t|h@?|t
? |i L|ih @?_c ? 4@?) @TT*U@|L?t |i }LL_ _i@* hi}L? t L?*) ih) t*}|*) t4@**ih
|@? |i ?|ihtiU|L? Lu @ *4|i_ 5@hTi h@|L hi}L? @?_ |i @hM|h@}iuhii hi}L?c @?_ i
@i @?@*)|U uLh4*@t uLh |iti |L hi}L?t Ai _gihi?Ui }i|t t4@**ih @t |i |4i ?|ih@*
}i|t tLh|ihc @?_ _t@TTi@ht i?|hi*) ? |i UL?|?Lt |4i *4| AihiuLhic ?|ihtiU|?}
|i *4|i_ 5@hTi h@|L @?_ @hM|h@}i uhii hi}L?t 4@) Mi @ UL?i?i?| @TThL 4@|L? uLh
4@?) @TT*U@|L?t
BLL__i@* ML?_t tL*_ Mi tiu* ? 4@?) t|@|L?t ? U @ hi*@|i ThU?} @TThL@U
t @TThLTh@|i M| TihuiU| hiT*U@|L? t ?L| TLttM*i ui i @4T*itG |h@_ih U@? ti
|i ML?_t @t M) @?_ ti** TL?|t ? |i ti@hU uLh R}LL_ _i@*t ? @tti| 4@h!i|t E|
|i t@* @h??} ^it|L? Lu ) |i 4@h!i| *i@it }LL_ _i@*t ?_tULihi_ 2 M@?!
Lh L|ih ?t|||L? |@| 4@h!i|t Lh t)?|it3it ?L?|h@_i_ tiUh|it U@? ti }LL__i@*
ML?_t @t M_ @?_ @t! ThUit BLL__i@* ML?_t U@? Mi ti_ @t iUL?L4U 4i@thit Lu
|i @UUh@U) Lu LT|L? ThU?} uLh4*@t hM|h@}iM@ti_ uLh4*@t Thi_U| ?L ihhLhc tL |@|
R4i@thi4i?| ihhLht ? ThUit 4t| Mi |@U!i_ L? |L |i 4L_i*t Ai ML?_t U@? |i** t
U LT|L? ThUit tL*_ *i U*Lti |L @hM|h@}iM@ti_ uLh4*@tc @?_ U U@? *i u@h uhL4
|i Thi_U|L?t Lu |Lti uLh4*@tc t?} @? iUL?L4U 4i@thi Lu _t|@?Ui e T|L? ThU?}
|iU?^it @hi ?Uhi@t?}*) @TT*i_ |L Rhi@* LT|L?t ? U@T|@* M_}i|?}c ?it|4i?| |
hhiihtM*|it @?_ TL*U) ^it|L?t hi*@|i ThU?} @TThL@U t @TThLTh@|ic M| |i
uLUt T@)Lgt |)TU@**) U@??L| Mi TihuiU|*) hiT*U@|i_ D T|L? ThU?} uLh4*@t @hi Lu|i?
ti_ ? ht! @ttitt4i?|c |L ^@?|u) |i i TLthi Lu @ TLt|L? Lh ?t|||L? |L @hLt ht!
u@U|Lht W| t tiu* |L @ttitt tU ht!t i? TihuiU| hiT*U@|L? t 4TLttM*ic @?_ |L ^@?|u)
|i 4TLh|@?Ui Lu 4@h!i| ThUi Lu ht! @tt4T|L?t
5iU|L? 2 tLt L |L U@*U*@|i }LL__i@* ML?_t ? t?}*i TihL_c 4*|T*i TihL_ @?_
UL?|?Lt |4i UL?|i |t `i ?_ @ hiUhti tL*|L? |L |i 4*|TihL_ ThLM*i4c i i
tL |@| |i *Lih ML?_ |L_@) tL*it |i L?iTihL_ ThLM*i4 | |i *Lih ML?_ |L4Lh
hL @t T@)Lg At uLh4*@|L? 4@!it |i 4*|TihL_ ThLM*i4 UL4T|@|L?@**) ui@tM*i W?
UL?|?Lt |4ic | *i@_t |L @ T@h|@* _gihi?|@* i^@|L? uLh |i ML?_t At t Lh Ui?
|h@* |iLhi|U@* UL?|hM|L?c @?_ | 4@!it |i |iU?^i hi*i@?| uLh tihLt LT|L?ThU?}
@TT*U@|L?tc U @hi @** ?ihi?|*) _)?@4U W? T@h|U*@hc i U@? @?_*i UL?|?Lt |h@_
?} i?hL?4i?|t ? U 4@h!i| ?UL4T*i|i?itt UL4it uhL4 ?L?|h@_i_ t|@|i @h@M*it Lh
.
LT|L?t h||i? L? ?L?|h@_i@M*i ii?|t
W? tiU|L? c i i T*Lhi tiih@* @TT*U@|L?tc ? T@h| |L i4T@t3i |@| |i ML?_t @hi
Th@U|U@* @?_ i@t*) UL4T|@M*i @?_ ? T@h| uLh |i iUL?L4U ?|ihit| Lu |i @?tiht `i
tL |i U@*U*@|L?t Mi?_ |i t4T*i *@U!5UL*it i @4T*i Lu 6}hi ( i tL L
|L ML?_ LT|L? _i*|@t E_ih@|i Lu LT|L? ThUi | hitTiU| |L t|LU! ThUi( i U@*U*@|i
LT|L? ThUi ML?_t i? L|ih LT|L?t @hi ti_ @t i_}i @tti|t( i U@*U*@|i 4*|TihL_
ML?_t t?} @ _tUhi|i 4*|?L4@* 4L_i*c @?_ i UL4T@hi |i hit*|t |L ?_i LT|L?
ThUit( i U@*U*@|i ML?_t L? @? LT|L? tMiU| |L RM@tt ht! @? LT|L? L? @ ?L?|h@_i_
?_ih*)?} tiUh|) Lh ii?| |@| t 4TihuiU|*) ULhhi*@|i_ | M@tt @tti| T@)Lgt LUh@?i
@?_ 5@@+i^iL Ebbb Thiti?| @ 4Lhi i |i?_i_ @TT*U@|L? |L LT|L? ThU?} ? UL?|?Lt
|4i | t|LU@t|U ?|ihit| h@|i @?_ t|LU! L*@|*|)
2
@*U*@|?} }LL__i@* ML?_t
2
?i TihL_
`i t|@h| | |i t4T*it| t|@|L? Aihi t L?i TihL_ @?_ ?L ?|ih4i_@|i |h@_?} ?|*
|i T@)Lg %S t hi@*3i_ AhL}L|c i @tt4i |@| L?i Lu |i M@tt T@)Lgt t ht!*ittc tL
i U@? h|i .E6 ' *-s W| t UL?i?i?| |L i Thitt |i L*@|*|) UL?t|h@?| @t @ tiUL?_
4L4i?| Atc Lh ThLM*i4 E2 MiUL4it
' 4? . E6 %S r| T ' . E6 c . 62 2c 6 fc
t6
E
ihi 2 E n 2 *-s 2 `i Thit4i @ t|@|t|U@* 4L_i* uLh |i _t|hM|L? Lu |i T@)Lgt
c tL |@| i U@? U@*U*@|i 4L4i?|t ** i TiU|@|L?t @?_ ThLM@M*|it hiuih |L |i |hi
4i@thi 6Lh @?) tL*|L? |L i t|c Lu ULhtic L?i 4t| TU! @ tUi?|*) *@h}i ML?_ |L
ThUi |i M@tt @tti|tc
. 62
2 4?
6
r| . E6 ' Tc 6 f
Ai ThLM*i4 @t |L ?i^@*|) UL?t|h@?|t Oi?Ui i ?_ @ tL*|L? M) |h)?} @** |i
UL4M?@|L?t Lu M?_?} @?_ ?L?M?_?} UL?t|h@?|tc ? Lh_ih Lu |ih i@ti Lu U@*U*@|L?c
@t uL**LtG `i @tt4i |i L*@|*|) UL?t|h@?| M?_t @?_ |i TLt||) UL?t|h@?| t
t*@U! At t |i i@tit| U@tic t?Ui i @i @?@*)|U uLh4*@t uLh |i ML?_t @?_ _tUL?|
H
u@U|Lh ? |t U@ti Wu |i hit*|?} _tUL?| u@U|Lh 6 t ?L??i}@|ic |t t |i tL*|L?
Wu ?L|c 2 i @tt4i |@| |i L*@|*|) UL?t|h@?| t t*@U! @?_ |i TLt||) UL?t|h@?|
M?_t At UL?}h@|L? _i*iht |i @hM|h@}i ML?_ L? @*i `i ?_ |i 4?44
@h@?Ui _tUL?| u@U|Lh |@| }i?ih@|it |i @hM|h@}i ML?_ Wu |t _tUL?| u@U|Lh t@|tit
|i L*@|*|) UL?t|h@?|c |t t |i tL*|L? Wu ?L|c i tL*i |i ThLM*i4 | ML|
UL?t|h@?|t M?_?} i | i tL L |L @?_*i i@U U@ti
2
VL*@|*|) UL?t|h@?| M?_tc TLt||) UL?t|h@?| t t*@U!
Wu |i TLt||) UL?t|h@?| t t*@U!c |i ThLM*i4 hi_Uit |L
' 4? .E6 %S r| T ' . E6 c . 62 2 t6
Ee
+@|ih |@? tL*i |t ThLM*i4 _hiU|*) | w@}h@?}i 4*|T*iht L? |i UL?t|h@?|tc i ti|
T Lh|L}L?@* _iUL4TLt|L?t Lu |i uLUt T@)Lg %S @?_ _tUL?| u@U|Lh 6 Ai tL*|L?
|i? TLTt L| EAi tL*|L? t|h@|i}) t _i |L O@?ti? @?_ a@}@??@|@? bb At ThLM*i4
t _@* |L |iht
q
6}hi 2 _itUhMit |i _i@ f U c U 5 -
r
_i?L|it |i tT@Ui Lu
T@)Lgt Lu TLh|uL*Lt Lu |i M@tt @tti|t AL} }h@Ti_ @t @ *?ic f t |)TU@**) @? ??|i
_4i?tL?@* tT@Ui `i !?L @** ThUit ? fc M| |i T@)Lg %S |@| i t |L @*i _Lit
?L| *i ? f
dW?tih| 6}hi 2 ihio
`i Lh|L}L?@**) _iUL4TLti |i uLUt T@)Lg %S ?|L @? @TThL 4@|i i_}i %S @?_ @
hit_@* c M) ThLiU|L? Ew5 hi}hittL?
%S ' %S n c
%S RoJE%S mf ' .E%S .E
3
c
%S %
S ED
) UL?t|hU|L? .E
%S ' fc .E ' f t t t|@?_@h_ ? |?!?} @ML| w5 hi}hittL?tc
6}hi 2 hiThiti?|t .E ' f M) T*L||?} @| h}| @?}*it |L |i f T*@?i
Zlwk | ^{3 {f `3 / zh dvvxph H||3 ? 4/ l1h1
prphqwv1 Zh dvvxph wkdw uhgxqgdqw dvvhwv
|
kdyh ehhq suxqhg iurp wkh vshflfdwlrq vr H||3 lv qrqvlqjxodu1 Zh dovr olplw frqvlghudwlrq wr glvfrxqw
idfwruv p 5 O5 1 Kdqvhq dqg Mdjdqqdwkdq +4<<4, glvfxvv wkhvh whfkqlfdo dvvxpswlrqv1
4 Vlqfh zh qhhg vhfrqg prphqwv/ wkh| kdg ehwwhu eh ghqhg1
lv lq O5 / wkh vsdfh ri doo udqgrp yduldeohv zlwk qlwh vhfrqg
b
#tUL?| u@U|Lht 6 }i?ih@|i |i ThUit Lu T@)Lgt % ? f M) @? ??ih ThL_U| R ' .E6%
** TL?|t L? |i _@ti_ *?i 4@h!i_ 6 ? 6}hi 2 @i |i t@4i ??ih ThL_U| .E6%
| iU|Lht % 5 f @?_ i?Ui }i?ih@|i |i t@4i ThUit L? f 5U _tUL?| u@U|Lht U@? Mi
hiThiti?|i_ @t %W ' RoJE6mf T*t Lh|L}L?@* UL4TL?i?|t At u@U| @**Lt t |L 4TLti
|i ThU?} UL?t|h@?| 6Lh4@**)c
wi44@ _tUL?| u@U|Lh 6 ThUit |i M@tt @tti|tc R ' . E6 c u @?_ L?*) u | t Lu
|i uLh4
6 ' %W n n "c
ES
%W ' T .E
E.
ihi
3
t@|tit R ' .E%W% M) UL?t|hU|L?c t @? @hM|h@h) ?4Mihc " t @?) h@?_L4 @h@M*i
| .E"% ' fc .E" ' fc @?_ t |i hit_@* _i?i_ ? i^@|L? ED
hLLut @hi ? |i @TTi?_ `i ** ^U!*) tii |@| i @?| |L ULLti " ' fc tL i @hi
hi_Ui_ |L ULLt?} @ t?}*i ?4Mih h@|ih |@? ULLt?} @ h@?_L4 @h@M*i 6
5?Ui tiUL?_ 4L4i?| _i?it _t|@?Ui ? 6}hi 2c |i ti| Lu _tUL?| u@U|Lht |@| t@|tit
|i L*@|*|) UL?t|h@?| .E62 2 *it ?t_i |i UhU*i tL? @hL?_ |i Lh}? At
hit|hU|i_ h@?}i Lu _tUL?| u@U|Lht ** ThL_Ui @ hit|hU|i_ h@?}i Lu @*it uLh |i hit_@*
@?_ i?Ui uLh |i uLUt T@)Lg %S Ai 4@ 44 @?_ 4?44 @*it ** Mi }i?ih@|i_
i? i TU! |L i @U|*) t@|tu) |i L*@|*|) UL?t|h@?| *||*i 4Lhi uLh4@**)c
hLTLt|L? Ai _tUL?| u@U|Lh |@| }i?ih@|it |i *Lih ML?_ t
6 ' %W EH
' .E%W%S .E2 Eb
y
x 2
x .E%W2 'w
2
Ef
@?_ |i ML?_ t
ihi
.E Ai TTih ML?_ t }i? M) ' f
Ai ht| |ih4 ? i^@|L? Eb t |i @*i Lu |i @TThL 4@|i i_}i TLh|uL*Lc
.E%W%S ' .E%W%S ' .E6
%S E
uLh @?) _tUL?| u@U|Lh 6 |@| ThUit M@tt @tti|t EOihi @?_ Mi*L i ti |i u@U| |@|
.E%+ ' .d% RoJE+mfo Ai tiUL?_ |ih4 t |i *Lit| TLttM*i @*i Lu |i hit_@* UL?tt|i?| | |i _tUL?| u@U|Lh L*@|*|) ML?_G
.E2 ' .E ' .dE%W n o ' .E6
Ai ML?_t @hi |}|ih u |i L*@|*|) UL?t|h@?| t t4@**ihc u |i hit_@* t t4@**ihc
Lh u |i @TThL 4@|i i_}i t Mi||ih AL tii |t ThiUti*)c i U@? h|i |i t3i Lu |i
ML?_t @t
t
t
t
t
s
' 2 2 .E%W2 .E2 ' 2 .E%S2 2 .E%W2 -2
ihi
-2 E2
.E
%S2
.E2 '
.E%S2
.E%S2
W? |i ht| i ThittL?c i hi*@|i |i t3i Lu |i ML?_t |L |i t3i Lu |i hit_@*
t
.E2
_hiU|*) W? |i tiUL?_ i ThittL?c i tL |@| @ }ih -2 Lu @ hi}hittL? Lu |i uLUt @tti|
L? |i M@tt @tti|t *i@_t |L |}|ih ML?_t 5L4i Lu |i _tUL?| u@U|Lh L*@|*|) t Rti_
T ? ThU?} |i M@tt @tti|t ?*) |@| TLh|L? Lu |i L*@|*|) ML?_ ? i Uitt Lu |i
_tUL?| u@U|Lh L*@|*|) .E%W2 hi^hi_ |L ThUi |i M@tt @tti|t U@? Mi @TT*i_ |L |i ThUi
Lu |i hit_@*
6Lh U@*U*@|L?t | t tiu* |L tMt|||i |i _i?|L?t Lu %W @?_ ? i^@|L? Eb |L
LM|@?
' T .E
.E %S 3
t
2 T .E
3 T
t
.E%S2 .E%S .E
3 .E
%S
E
Ai TTih ML?_ t |i t@4i uLh4*@ | @ n t}? ? uhL?| Lu |i t^@hi hLL| At
uLh4*@ t 4U *itt Thi||)c M| | tLt i T*U|*) L |L U@*U*@|i |i ThUi ML?_ uhL4 @
t|@|t|U@* 4L_i* uLh |i tiUL?_ 4L4i?|t Lu c %S Nt?} EHc i UiU! |i @tt4T|L? |@| |i _tUL?| u@U|Lh t ? u@U| TLt|i ? iih)
t|@|i Lu ?@|hi Wu tLc |t t |i }LL__i@* ML?_ Wu ?L|c i ThLUii_ |L |i ?i | t|iT
22
L| UL?t|h@?|t M?_
i | i tL L |L ?_ |i ML?_t ? @ L?i TihL_ 4L_i* i? ML| UL?t|h@?|t M?_
AL} |t t |i |h_ t|iT ? |i ThLUi_hic | t i@tit| |L _itUhMi |t U@ti ht| W? |i
}iL4i|h) Lu 6}hi 2c | t ?L| ?iUitt@h*) |hi |@| |i .E62 2 ti| *it ?t_i |i 6 f
ti| Wu | _Lit uLh tL4i t|@|it Lu ?@|hi @?_ ?L| uLh L|ihtc |i? ML| UL?t|h@?|t M?_
W?|hL_U?} w@}h@?}i 4*|T*ihtc |i ThLM*i4 t
' 4? 4@
t6:f tbcB:f
. E6 %S n b d. E6 To n
l
B k 2
. 6 2
2
Ai ht| Lh_ih UL?_|L?t |L |t ThLM*i4 )i*_ @ _tUL?| u@U|Lh |@| t @ |h?U@|i_ *?i@h
UL4M?@|L? Lu |i T@)Lgtc
#
6 ' 4@
$
%
%S n b
%S n b
cf ' B
B
&n
Ee
Ai *@t| i^@*|) _i?it |i don ?L|@|L? uLh |h?U@|L? AL _ihi |t i ThittL?c |@!i
T@h|@* _ih@|it | hitTiU| |L 6 ? i@U t|@|i `i UL*_ T*} i ThittL? Ee ?|L
|i UL?t|h@?|tc @?_ tL*i ?4ihU@**) uLh w@}h@?}i 4*|T*iht b @?_ B |@| i?uLhUi |i
UL?t|h@?|t *@tc |t ThLUi_hi hi^hit |i tL*|L? Lu @ t)t|i4 Lu ?L?*?i@h i^@|L?t ?
Ebc Bc U t Lu|i? @ ?4ihU@**) _U*| Lh ?t|@M*i ThLM*i4
O@?ti?c Oi@|L? @?_ w||4ih EbbD tL L |L hiU@t| |i ThLM*i4 @t @ 4@ 43@|L?c
U t ?4ihU@**) 4U i@tih W?|ihU@?}?} 4? @?_ 4@ c
' 4@
4? .E6 %S n b d. E6 To n
tbcB:f t6:f
l
B k 2
. 6 2 2
ED
Ai ??ih 4?43@|L? )i*_t |i t@4i ht| Lh_ih UL?_|L?t Ee *}}?} |Lti ht|Lh_ih
UL?_|L?t ?|L |i L|ih 4@ 43@|L? Lu ED @?_ t4T*u)?}c i LM|@?
' 4@
tbcB:f
;
?
%
B
%S n b
. = 2
B
&n2 <
@
B
b T 2 >
2
ES
`i ti@hU ?4ihU@**) Lih Ebc B |L ?_ |i tL*|L? |L |t ThLM*i4 Ai TTih ML?_ t
uL?_ M) hiT*@U?} 4@ | 4? @?_ hiT*@U?} B : f | B f
2
2
Lt||) M?_tc L*@|*|) t t*@U!
Wu |i L*@|*|) UL?t|h@?| t t*@U! @?_ |i TLt||) UL?t|h@?| M?_tc |i ThLM*i4 hi_Uit
|L
' 4? . E6 %S r| T ' . E6 c 6 : f
t6
Aiti @hi |i @hM|h@}i ML?_t ?i U@? Lu|i? _i_Ui |i @hM|h@}i ML?_t uLh tTiUU
ThLM*i4t |L| i T*U|*) tL*?} @ 4?43@|L? W| t @ *?i@h ThL}h@4 L|ihti W|
hi4@?t Liih |L UiU! i|ih |i _tUL?| u@U|Lh L*@|*|) UL?t|h@?| U@? Mi t@|ti_
@| |i @hM|h@}i ML?_
#i?L|i |i *Lih @hM|h@}i ML?_ M) , Ai 4?44 @h@?Ui EtiUL?_ 4L4i?| _t
UL?| u@U|Lh |@| }i?ih@|it |i @hM|h@}i ML?_ , tL*it
%
2
2
.E6 4? ' 4? .E6 r|
t6
T
,
&
#
%
'. 6
&$
%S
c 6 : f
Nt?} |i t@4i UL?}@|i 4i|L_c |t ThLM*i4 t i^@*i?| |L
q
.E624? ' 4@ . d E>%S n o
n2
r
tc>
2 T2>, }@?c i ti@hU ?4ihU@**) uLh Ec> |L tL*i |t ThLM*i4 Wu .E624? c , t |i
tL*|L? |L |i }LL__i@* ML?_( u ?L| i ThLUii_ | |i U@ti |@| ML| UL?t|h@?|t @hi
M?_?} _itUhMi_ @MLi
22
*|T*i TihL_t @ hiUhti tL*|L?
L?t_ih |i t@4i ThLM*i4c M| @**L L?i ?|ih4i_@|i TihL_ @| U |i ?it|Lh U@?
U@?}i t TLh|uL*L Lu |i M@tt @tti|t AL !iiT |i ?L|@|L? t4T*ic i _L ?L| ?U*_i
?|ih4i_@|i T@)Lgtc M| |t t @ t4T*i i |i?tL? Nt?} |4i TihL_t @?_ 2 uLh |i
hiM@*@?U?} _@|i @?_ ?@* _@|i hitTiU|i*)c |i LMiU|i u?U|L? uLh |i *Lih ML?_ t
f ' 4? .f E6 62 %S2 t6 c 62 ihi .| E ' .EmU| _i?L|it UL?_|L?@* i TiU|@|L?
i |c |i UL?t|h@?|t Ai _tUL?| u@U|Lht 6 @?_ 62 4t| ThUi |i M@tt @tti|tc tL i
hi^hi
Tf ' .f E6 T
T ' . E62
2
uLh @** ?uLh4@|L? ti|t Uc
`i }i?ih@*3i |i _tUL?| u@U|Lh L*@|*|) UL?t|h@?| |L |i hi^hi4i?| |@| |i L*@|*|)
? i@U TihL_ hitTiU| @ ML?_2c
.f E62 2f ( . E622 2 EH
Ai L*@|*|) UL?t|h@?|t 4@) Mi u?U|L?t Lu ?uLh4@|L? Et|@|ic @?_ |t @**L |4i
@h)?} ht! Thi4@ 6?@**)c i hi^hi _tUL?| u@U|Lht |L Mi ?L??i}@|i
6 fc 62 f
L i U@? t|@|i |i |L TihL_ ThLM*i4 @?_ |t hiUhti tL*|L?
hLTLt|L? 2 Ai |LTihL_ ThLM*i4
f ' 4? .f E662 %S2 t|
t6 c62 Tf ' .fE6 Tc .fE62 2fc 6 fc
T ' .E62
2 c
.E622 2 ;U c 62 f
Eb
E2f
@t |i t@4i tL*|L? @t |i ti^i?Ui Lu L?iTihL_ ThLM*i4t
' 4? .E62 %S2 r| T ' .E62
t62 2 c
. E622 2 c 62 f
E2
f ' 4? .fE6 r| Tf ' .fE6 Tc .fE62 2fc 6 f
t6 Ai ThLLu t ? |i @TTi?_ @tU@**)c t?Ui 6 f @?_ |i UL?t|h@?| ti|t L? 6 @?_
62 _L ?L| @giU| i@U L|ihc |i tL*|L? |L |i |LTihL_ ThLM*i4 4? .f E6 .E62%S 4t| 4?43i . E62%S ? i@U t|@|i Lu ?@|hi @| |4i Wu 6 f ihi TLttM*i i L*_
5 Dq
dowhuqdwlyh frqvwudlqw pljkw eh wkdw wkh wzr0shulrg Vkdush udwlr lv ehorz d jlyhq ydoxh/
k
l
H3 +p4 p5 ,5 D5 =
+4:,
Wklv frqvwudlqw grhv qrw ohdg wr d uhfxuvlyh vroxwlrq1 Wkh frqvwudlqw +4;, lpsolhv d frqvwudlqw ri wkh irup
+4:,/
k
l
H3 +p4 p5 ,5 @ H3 p54 H4 p55 H3 p54 D54 D53 D54 >
exw wkh frqyhuvh lv qrw wuxh1 Wkhuhiruh/ lqglylgxdo frqvwudlqwv jlyh vkdushu erxqgv wkdq d wzr0shulrg
frqvwudlqw1
Wkh Vkdush udwlr vfdohv zlwk wkh vtxduh urrw ri wkh wlph shulrg1 Dq dssursuldwh qxphulfdo ydoxh iru wkh
erxqg xvlqj d vl{0prqwk wudglqj lqwhuydo lv wkh vtxduh urrw ri wkh dssursuldwh ydoxh iru d rqh0|hdu wudglqj
lqwhuydo1
e
@?| |L 4@ 43i . E62 %S ? tL4i t|@|it Lu ?@|hi( |i 6 f @tt4T|L? h*it |t L|
5?Ui |i ML?_t @hi ?L| ThUit Lh T@)Lgt Lu |h@_i_ tiUh|itc | t ?L| ?|@**) LMLt |@|
L?i U@? UL4T|i |i _@|i f ML?_ t?} |i _@|i ML?_ @t @ RT@)Lgc M| |i ThLTLt|L?
ihit |@| | t ULhhiU| |L _L tL
Ai hiUhti t|@|i4i?| i |i?_t ? @? LMLt @) |L 4*|T*i TihL_t AL UL4T|i
4*|TihL_ ML?_tc i U@? ?L Lh! M@U!@h_G uLh @ T@)Lg @| A c UL4T|i L?i TihL_
ML?_t @t MiuLhi @| A Ai?c UL4T|i ML?_t @| A 2 t?} |i A ML?_t @t
T@)Lgtc @?_ tL uLh|
2
L?|?Lt |4i
L|@|L?
@tt?} |L UL?|?Lt |4i t UL?UiT|@**) t|h@}|uLh@h_c M| |i ?L|@|L? t ?@L_
@M*) @ M| _gihi?|
L?t_ih @? @tti| | ThUi 7| |@| }it @ t|hi@4 Lu T@)Lgt Lh __i?_t (|_| _tUL?| u@U|Lh t @ ThLUitt \| |@| }i?ih@|it |i ThUi M)
7| \| ' .|
] "
r'f
\|nr (|nr _r
E22
Ai UL?|?Lt |4i @?_ _tUhi|i |4i _tUL?| u@U|Lh UL?UiT|t @hi hi*@|i_ M) 6|n '
\|n *\| }@?c i tTThitt |4i tMtUhT|t ihi |i) @hi ?L| ?iUitt@h)c i} i h|i
\ ' \|
Nt?} E22 @| | @?_ | n {|c i U@? ?_ |i UL?|?Lt |4i i^@*i?| |L R ' . E6%c
f'
.| d_ E\7o (
n _|
\7
7
E2
Wu |ihi t @? ?t|@?|@?iLt*) ht!uhii h@|i o| c E@ tiUh|) | ThUi L?i |@| T@)t (| '
o| c Lh @ 4L?i) 4@h!i| @UUL?| Lti @*i }hLt @| _* ' o| _| |i? i^@|L? E2 4T*it
#
_\
.|
\
$
' o| _|
At i^@|L? t |i UL?|?Lt|4i UL?|ihT@h| |L -s ' *.E6
,^@|L? E2 4T*it
#
$
_7
(
_\ _7
.|
n
o _| ' .|
7
7
\ 7
D
E2e
At i^@|L? t |i UL?|?Lt|4i UL?|ihT@h| |L .E-e ' SJE6c -e *.E6 uLh i Uitt
hi|h?t -e Atc @ tiUh|) | _gtL? _5 tL*_ @i @? i TiU|i_ i Uitt hi|h? i^@*
|L
#
$
_\
.|
_5 _|
\
At ^@?||) t |i R4@h!i| ThUi Lu |i ht! _5c @?_ |t i^@|L? @**Lt t |L |h@?t*@|i
Mi|ii? 4@h!i| ThUi Lu ht! hit|hU|L?t @?_ _tUL?| u@U|Lh hit|hU|L?t
Ai UL?|?Lt |4i i^@*i?| |L |i *?! Mi|ii? 5@hTi h@|Lt @?_ _tUL?| u@U|Lh
L*@|*|) m. E-e m *j E-e j E6 *. E6c U@? Mi uL?_ uhL4 E2 @t
E
>7 o2
_\2
_| .| 2
j72
\
ihi >
7 .|E_7*7 n (*7 _| t |i UL?_|L?@* i TiU|i_ hi|h? @?_ j72 .| E_7 2 *7 2 t
|i UL?_|L?@* @h@?Ui Lu hi|h?
5|@|t|U@* 4L_i*
`i ?ii_ @ t|@|t|U@* 4L_i*c |i i^@*i?| Lu |i 4L4i?|t Lu |i M@tt @?_ uLUt @tti|t
.E c .E
c .E%S c
i|U ? |i _tUhi|i |4i uLh4*@t Ai t|@|t|U@* 4L_i* 4t| _itUhMi
|i UL?_|L?@* 4L4i?|t @| iih) TL?| ? |4i `i 4L_i* |i ThUi ThLUittit Lu @? ?7 _4i?tL?@* iU|Lh Lu M@tt @tti|t M) @ _gtL?c
_7
' >7 E7c Tc |_| n j7 E7c Tc |_5
7
E2D
ihi 5 t @ ?7 _4i?tL?@* iU|Lh Lu ?_iTi?_i?| hL?@? 4L|L?tc @?_ .E_5 _5 ' U
Ai M@tt @tti|t 4@) T@) __i?_t @| h@|i (E7c Tc |_| T hiThiti?|t @? ?T _4i?tL?@*
iU|Lh Lu @__|L?@* t|@|i @h@M*it |@| uL**L
_T ' >T E7c Tc |_| n jT 5 E7c Tc |_5 n jT E7c Tc |_
E2S
ihi _ t @? ?T _4i?tL?@* iU|Lh Lu hL?@? ?Uhi4i?|t Lh|L}L?@* |L _5 G .E_ _ '
U( .E_ _5 ' f `i @}@? @tt4i |@| |ihi t @? ?t|@?|@?iLt*) ht! uhii h@|i oE7c Tc |_| At
6 Udwkhu
xqghuvwdqg glylvlrq wr rshudwh hohphqw e| hohphqw rq yhfwruv/ h1j1/
wkdq frpsolfdwh wkh qrwdwlrq/
gV@V @ gV4 @V4 gV5 @V5 = Zkhq h{solflw hqxphudwlrq ri dujxphqwv lv qrw qhfhvvdu|/ zh zulwh V
iru V+w, dqg V dqg V iru V +V> Y> w, dqg V +V> Y> w,1 Zh dvvxph wkdw doo glxvlrq sdudpdwhuv/ V +V> Y> w,>
V +V> Y> w,> Y +V> Y> w,> Y +V> Y> w,> hwf1 duh frqwlqxrxv lq doo wkhlu dujxphqwv1 Zh dvvxph wkdw doo yduldqfh0
fryduldqfh pdwulfhv vxfk dv V +V> Y> w,V +V> Y> w,3 > Y +V> Y> w,Y +V> Y> w,3 duh qrq0vlqjxodu iru doo V 5 UqV /
Y 5 UqY / w 5 ^3> W `=
S
@tt4T|L? t ?L| itti?|@*c M| | t4T*it |i @*}iMh@ @?_ Thiti?|@|L? `i? o @hit
t|LU@t|U@**)c | t L?i Lu |i t|@|i @h@M*it ? T
Ai ThLM*i4
`i @?| |L @*i @? @tti| |@| T@)t UL?|?Lt __i?_t @| h@|i %S E7c Tc |_| @?_ |
@ |ih4?@* T@)4i?| %SA E7c Tc A `i 4}| ?L| Mi @M*i |L TihuiU|*) i_}i Lh hiT*U@|i |t
@tti| uLh |L hi@tL?tG Ai ht!t @ttLU@|i_ | ?T ?L?|h@_i_ tLU!t U@??L| Mi i_}i_c
@?_ |i T@)Lg %S 4@) _iTi?_ L? |i ?L?|h@_i_ @h@M*it T Ai ThLM*i4 t ?L |L ULLti @ _tUL?| u@U|Lh ThLUitt |L 4?43i |i @tti| @*i
| '
4?
t\r c |r$A .|
] A
\r S
\A S
%r _r n .|
%A
\|
r'| \|
E2.
tMiU| |L |i UL?t|h@?|t |@| |i _tUL?| u@U|Lh ThUit |i M@tt @tti|t 7c o @| i@U
4L4i?| ? |4ic 2 |i ?t|@?|@?iLt L*@|*|) Lu |i _tUL?| u@U|Lh ThLUitt t *itt |@? @
ThitTiUi_ @*i 2 ELhc 4Lhi }i?ih@**)c *itt |@? @ ThLUitt E7c Tc |2 @| i@U 4L4i?| ?
|4i @?_ |i _tUL?| u@U|Lh t TLt|i \r : fc | r A Ai TTih ML?_ uL**Lt M)
hiT*@U?} 4? | 4@ 5?Ui |ihi @hi ?L 4Tt ? ?it @h@M*itc i @__ |L Lh *t| Lu
iUL?L4U @tt4T|L?t L? |i _tUL?| u@U|Lh |@| | @*tL uL**Lt @ _gtL? ThLUitt |L|
4Tt
#gihi?|@* t|@|i4i?|t
Ai ThLM*i4 U@? Mi tL*i_ hiUhti*)c M) ThLTLt|L? 2 Atc i U@? t|_) L |L
4Li L?i t|iT M@U! ? |4ic
] |n{|
| \| ' 4? .|
t\r r'|
\r %Sr _r n .| E\|n{| |n{| Lhc uLh t4@** |4i ?|ih@*tc
|\| ' 4? .| i%S{| n E | n { E\| n {\j t{\
wi||?} {| $ fc i U@? h|i |i LMiU|i ? _gihi?|@* uLh4c
%S
.| d_ E\o
f ' | _| n 4?
c
t_\
\
tMiU| |L |i UL?t|h@?|t `i U@? @*tL h|i E2H @t
#
_ %S|
_\ _
.|
n _| os _| ' 4? .|
t_\
\ .
E2H
$
5?Ui |i tiUL?_ @?_ |h_ |ih4t L? |i *iu| @?_ t_i @hi i_c |i UL?_|L? ti?tM*) |i**t
t |L ?_ |i *Lit| @*i M) 4@ 43?} |i _hu| .| _ @| i@U _@|i
L?t|h@?|t
L i i Thitt |i UL?t|h@?|t t ? |i _tUhi|i |4i U@tic i Lh|L}L?@*3i |i
_tUL?| u@U|Lh @?_ |i? |i tL*|L? TLTt L|
wi44@ 2 \| t @ _tUL?| u@U|Lh _hi? M) _5c _ |@| ThUit |i M@tt @tti|t 7c o u @?_
L?*) u | U@? Mi hiThiti?|i_ @t
ihi
_\
_\W
' W _
\
\
E2b
_\W
o_| >
7 P3
7 j7 _5(
\W
(
>
7 >7 n o( P7 ' j7 j7 7
@?_ t @? @hM|h@h)e ?T 4@|h At ThLTLt|L? t |i LMLt UL?|?Lt|4i UL?|ihT@h| |L *i44@ c @?_ @t |i
t@4i }iL4i|hU ?|ihThi|@|L? @t ? 6}hi 2 `i U@? *i| _\*\ *L@_ L? @__|L?@* tLU!tc
Lh|L}L?@* |L ML| T @?_ 7c | ?L igiU| L? |t @M*|) |L ThUi uLUt Lh M@tt @tti|t
6Lh |t hi@tL? |i ThLTLt|L? ^@*it R_hi? M) _5c _ OLiihc Lh 4?43@|L? Lh
4@ 43@|L? Lu @tti| @*it ** @}@? T| tU *L@_?} |L 3ihL EAt ThLTLt|L? @?_ ThLLu
@hi t4*@h |L hLTLt|L? ? Oi @?_ i@htL? bb2
Ai L*@|*|) UL?t|h@?| t
_\2
.|
2
_| \2
@?_ i?Uic t?} E2bc
2 _\W2
.|
' 2 >
7 P3
7 7 >
_| \W2
Ef
) i Thitt?} |i UL?t|h@?|t @ E2b @?_ Efc i @i @}@? hi_Ui_ |i ThLM*i4
Lu ULLt?} |i t|LU@t|U ThLUitt uLh \ |L |i ULUi Lu *L@_?}t L? |i ?Ltit _ |
?!?L? @*itc tMiU| |L @ ^@_h@|U UL?t|h@?| L? 5?Ui i @hi TU!?} _gihi?|@*t
k
U W 3 4 5 gwl ? 4 dqg H kh{s 4 U W mym5 gwl ? 4> wr hqvxuh wkdw wkh
uhtxluh H h{s 45 3 V V V
5 3
vwrfkdvwlf lqwhjudov wkdw ghvfuleh wkh g|qdplfv ri duh zhoo0ghqhg1
7 Zh
H
@?_ @i h*i_ L| 4Ttc |i TLt||) UL?t|h@?| L? |i ULUi Lu _\ t t*@U! tL *L?} @t
\ : f
Nt?} i^@|L? E2bc t |i iU|Lh Lu 4@h!i| ThUit Lu ht!t Lu |i _ tLU!tG
#
$
_\
.
_ ' _|
\
Atc |i ThLM*i4 t i^@*i?| |LG ?_ @| i@U _@|i |i @tt}?4i?| Lu 4@h!i| ThUit Lu ht!
|L |i _ tLU!t |@| 4?43it E4@ 43it |i uLUt T@)Lg @*ic tMiU| |L |i UL?t|h@?|
|@| |i |L|@* Et4 Lu t^@hi_ 4@h!i| ThUi Lu ht! t ML?_i_ M) 2 5L*|L?tG @ _gihi?|@* U@h@U|ih3@|L?
| i@U 4L4i?|c |i ML?_ U@*U*@|L? t ?L i @U|*) |i t@4i @t ? |i L?i TihL_
_tUhi|i |4i U@ti | @ t*@U! TLt||) UL?t|h@?| OLiihc i UiT| uLh |i 4L4i?| t|
MiuLhi |i |ih4?@* _@|ic |i uLUt T@)Lg t |i ?i | TihL_<t *Lih ML?_ Atc i LM|@?
@ *Lih ML?_ @| i@U 4L4i?| |@| _iTi?_t L? |i _t|hM|L? Lu |i *Lih ML?_ @| |i
?i | 4L4i?| Aiti hit*|t 4t| Mi t|h?} |L}i|ih ? Lh_ih |L LM|@? |i *Lih ML?_ @|
i@U 4L4i?| ? |ih4t Lu |i ?_ih*)?} @tt4i_ t|LU@t|U ThLTih|it Lu |i uLUt @?_ M@tt
@tti|t
AL Mi tTiUUc i @tt4i |@| |i *Lih ML?_ uL**Lt @ _gtL? ThLUittc tL i h|i
_
' > E7c Tc |_| n j5 E7c Tc |_5 n j E7c Tc |_
E
j5 @?_ j U@T|hi |i t|LU@t|U iL*|L? Lu |i ML?_ Lih |i ?i | ?t|@?| AihiuLhic
@ _gihi?|@* Lh 4L4i?||L4L4i?| U@h@U|ih3@|L? Lu |i ML?_ ** |i** t > ? |ih4t Lu
j5 @?_ j hLTLt|L? Ai *Lih ML?_ _tUL?| u@U|Lh \| uL**Lt
_\
_\W
' W _
\
\
@?_ > c j5 @?_ j t@|tu) |i hit|hU|L?
#
E2
$
%S
_\W
> n
o ' .|
j5 _5 n j
_|
\W
ihi
v
'
2 _\W2 j
t
.|
_| \W2 j j
E
Ee
Ai TTih ML?_ ThLUitt | @?_ _tUL?| u@U|Lh \| @i |i t@4i hiThiti?|@|L? | ' b
Ai t|@|i4i?| @?_ ThLLu Lu |t ThLTLt|L? @hi t|h@}|uLh@h_ @?@*L}it |L ThLTLt|L?
@?_ @i |i t@4i }iL4i|hU ?|ihThi|@|L? @t tL? ? 6}hi 2 _\W*\W t |i UL4M?@
|L? Lu M@tt @tti| tLU!t |@| ThUit |i M@tt @tti|t M) UL?t|hU|L?c ? @?@*L}) |L %W Ai
|ih4 j _ ULhhitTL?_t |L |i ihhLh c @?_ j j
ULhhitTL?_t |L .E 2 Ai ThLTLt|L?
*LL!t @ *||*i _gihi?| MiU@ti ?L i ULLti @ iU|Lh h@|ih |@? @ ?4Mih `i UL*_
_i?i @ hit_@* j _ @?_ |i? |i ThLM*i4 L*_ hi_Ui |L ULLt?} @ ?4Mihc |i *L@_
?} Lu _\ L? |t hit_@* W| t ?L| UL?i?i?| |L _L tL ? |t U@ti t?Ui j TL|i?|@**)
U@?}it Lih |4i
t ? |i _tUhi|i|4i U@tic i U@? T*} ? |i _i?|L? Lu \W |L LM|@? i T*U|c u *itt
?||ic i ThittL?t uLh |i LT|4@* _tUL?| u@U|Lh @?_ |i hit*|?} *Lih ML?_c
t
j
_\
' o_| n >
7 P3
j
_5
2 >
7 P3
7 t
_
7 7
7 >
\
j j
ED
t
t
%S
P3 >
2>
o '>
7 P3
j
j
n
7 7 7 j j 7 7 5
ES
> n
T@h|@* _gihi?|@* i^@|L? uLh |i ML?_t
`i @i ?L @ _gihi?|@* U@h@U|ih3@|L? Lu |i *Lih ML?_ @?_ |i _tUL?| u@U|Lh
|@| }i?ih@|it |i *Lih ML?_ `i @i |L U@? |L}i|ih |Lti _gihi?|@* U@h@U|ih3@
|L?t
6ht|c i ?_ @ T@h|@* _gihi?|@* i^@|L? uLh |i ML?_t `i )TL|it3i @ tL*|L?
E7c Tc | `i ti W|L<t *i44@ |L _ihi i ThittL?t uLh > @?_ j5 c j ? |ih4t Lu |i
T@h|@* _ih@|it Lu E7c Tc | `i tMt|||i |iti i ThittL?t ?|L hit|hU|L? ES Ai
4iU@?Ut @hi hi*i}@|i_ |L |i @*}iMh@U TTi?_ c LUh@?i @?_ 5@@+i^iL EbbH Ai
hit*| t }*)c M| t|h@}|uLh@h_ |L i@*@|i ?4ihU@**)c @?_ @?@*)|U@**) ? tTiU@* U@tit
W| i Thittit |i |4i _ih@|i Y*Y| ? |ih4t Lu _ih@|it | hitTiU| |L t|@|i @h@M*itc
@?_ |t U@? Mi ti_ |L Lh! M@U! uhL4 @ |ih4?@* TihL_
hLTLt|L? e Ai *Lih ML?_ E7c Tc | t |i tL*|L? |L |i T@h|@* _gihi?|@* i^@|L?
%S o n
n
Y
n
Y|
[ Y2
[ Y2
[ Y2
7 7 j7 j7 n
EjT 5 jT 5 n jT jT n
7 j7 jT 5 '
2 c Y7 Y7
2 c YT YT
Y7
YT
c
2f
(
'
o
7
E7 7 n >
7 P3
7 j7 jT 5 >T T n
t
t
2 >
7 P3
7 T jT jT T
7 >
tMiU| |L |i ML?_@h) UL?_|L?t ThL_i_ M) |i uLUt @tti| T@)Lg %SA T _i?L|it |i iU
|Lh | |)TU@* i*i4i?| Y*YT @?_ E7 7 _i?L|it |i iU|Lh | |)TU@* i*i4i?| 7 Y*Y7 +iT*@U?} n | MiuLhi |i t^@hi hLL| }it |i T@h|@* _gihi?|@* i^@|L? t@|ti_ M)
|i TTih ML?_
L|i |@| |i _hu| Lu |i M@tt @tti|t >7 i?|iht ?|L |i T@h|@* _gihi?|@* i^@|L?t uLh
|i ML?_t }@?c @U|@* @?_ ?L| t| ht!?i|h@* ThLM@M*|it 4@||ih
tTiU@* U@ti ? U i !?L |i _tUL?| u@U|Lh
W? }i?ih@*c |i \ ThLUitt _iTi?_t L? |i T@h@4i|iht j Oi?Uic |L| tL*?} |i
@MLi T@h|@* _gihi?|@* i^@|L? i _L ?L| !?L L |L tThi@_ |i *L@_?} Lu _\ @UhLtt
|i 4*|T*i tLhUit Lu ht! _ Lti ht! ThUit i _L ?L| LMtihi ,^@*i?|*)c i _L
?L| !?L L |L LT|4@**) tThi@_ |i |L|@* 4@h!i| ThUi Lu ht! @UhLtt |i i*i4i?|t Lu _
Atc ? }i?ih@* i U@??L| ti @? ?|i}h@|L? @TThL@U |L ?_ |i ML?_( ic i U@??L|
U@h@U|ih3i \ i?L} |L t4T*) U@*U*@|i
#
$
] A
\r S
\A S
| ' .|
%r _r n .|
% \| A
r'| \|
OLiihc u |ihi t L?*) L?i tLU! _c |i? i _L?<| @i |L Lhh) @ML| L |i *L@_?}
Lu _\ tThi@_t @UhLtt 4*|T*i tLhUit Lu ht! U@? Mi _i|ih4?i_ t4T*) M) |i L*@|*|)
UL?t|h@?| W? |t tTiU@* U@tic _ @?_ j @hi tU@*@ht Oi?Ui i^@|L? E2 t4T*it @t
uL**Lt
hLTLt|L? D W? |i tTiU@* U@ti |@| |ihi t L?*) L?i i |h@ ?Lti _ _h?} |i T ThLUittc
i U@? ?_ |i LT|44 _tUL?| u@U|Lh \ _hiU|*) @t
t
_\
' o_| >
7 P3
j
_5
2 >
7 P3
7 _
7 >
7 7
\
W? tL4i @TT*U@|L?tc |i *L@_?} Lu _\ L? 4*|T*i tLU!t _ 4@) Mi UL?t|@?| Lih |4i
W? tU U@titc L?i U@? @}@? UL?t|hU| |i _tUL?| u@U|Lh @?_ tL*i uLh ML?_t M) ETLttM*)
?4ihU@* ?|i}h@|L?c @L_?} |i tL*|L? Lu @ T@h|@* _gihi?|@* i^@|L?
2
TT*U@|L?t
*@U!5UL*it | ?L ?|ih4i_@|i |h@_?}
`i t|@h| M) U@*U*@|?} ML?_t L? U@** LT|L? @*it ? |i *@U!5UL*it ti|T | ?L
|h@_?} ?|* i Th@|L? Ai hit*|t ihi Thiti?|i_ ? 6}hi Ai U@** LT|L? T@)Lg t
%S ' 4@ E7A gc f
ihi 7A ' t|LU! ThUi @| i Th@|L?c g ' t|h!i ThUi Ai i_}i @tti|t @hi |i ?_ih*)?}
t|LU! | Uhhi?| ThUi 7 @?_ @ ht!uhii ML?_ | hi|h? -s Ai t|LU! hi|h? - ' 7A *7
t *L}?Lh4@**) _t|hM|i_ `i ti |i *L}?Lh4@* _i?t|) |L U@*U*@|i @** |i ht| @?_ tiUL?_
4L4i?|t Lu |i t|LU! @?_ LT|L? T@)Lgt 6Lh i @4T*ic
. E%S ] " g
'7
-
s E- _7
g*7
Ai _ih@|L? @?_ i ThittL? Lu |iti 4L4i?|t @hi *L?} @?_ ?i?*}|i??}c tL i hi*i}@|i
|i4 |L |i @*}iMh@U TTi?_ c LUh@?i @?_ 5@@+i^iL EbbH `| |iti 4L4i?|t
? @?_c i uL**L |i ThLUi_hi _itUhMi_ ? tiU|L? 2
2
T|L?t @t i_}i @tti|t
Ai *@U!5UL*it ti|T t u@4Lt uLh t|LhU@* hi@tL?tc @?_ MiU@ti | _i*iht @ U*Lti_uLh4
tL*|L? | UL?|?Lt |h@_?} OLiihc L|ih @tti|t 4@) ThL_i Mi||ih @TThL 4@|i
i_}it ? @? ?UL4T*i|i 4@h!i| W? T@h|U*@hc LT|L?t | _gihi?| t|h!i ThUit @i
T@)Lgt 4Lhi t4*@h |L |@| Lu |i LT|L? @| @?_c tL |i) 4@) ThL_i t@hTih ?uLh4@|L?
@ML| @? LT|L?<t @*i |@? _Lit |i ?_ih*)?} t|LU! AihiuLhic i i @4?i L L?i U@?
** ? LT|L? ThUit @UhLtt t|h!it | ?L _)?@4U i_}?}
iU@?U@**)c i t| ?U*_i L|ih LT|L?t | LMtihi_ ThUit ? |i T@)Lg tT@Ui f
@*L?} | |i ?_ih*)?} t|LU! @?_ @ ht!uhii ML?_c @?_ i ti ?|i}h@*t @}@?t| |i *L}
?Lh4@* _i?t|) |L U@*U*@|i |i hi^hi_ 4L4i?|t `i @}@? hi*i}@|i |i *i?}|) i@*@|L?
Lu |i ?|i}h@*t |L |i @*}iMh@U TTi?_ c LUh@?i @?_ 5@
@+i^iL EbbH
6}hi tLt }LL__i@* ML?_t @t @ u?U|L? Lu t|h!i ThUic t?} |i t@4i |hii
4L?| Lh3L? @?_ T@h@4i|iht @t MiuLhi Ai M*@U! t^@hit T*L| |i ThUit Lu |hii LT|L?t
22
Lti ThUit @hi LMtihi_ Ai Uhit }i ML?_t L? |i @*i Lu @? @__|L?@* LT|L?
Ai @hM|h@}i ML?_t E6 : f UL?t|h@?| ? |t U@ti t|@|i |@| |i LT|L? ThUi 4t| Mi @
UL?U@i u?U|L? Lu t|h!i ThUic @?_ 4t| LMi) |i t|@?_@h_ U@** @hM|h@}i ML?_t
dW?tih| 6}hi ihio
Ai }LL__i@* ML?_t 4ThLi L? |i @hM|h@}i ML?_t |hL}L| Aih t4@** t3i
}it tL4i t|U@|L? |L |i UL44L? Th@U|Ui Lu _h@?} @ t4LL| *?i |hL} LMtihi_
LT|L? ThUitc M| | @*tL @h?t |@| t4@** _gihi?Uit ? L L?i _h@t tU @ *?i U@? @i
@ _h@4@|U igiU| L? |i 5@hTi h@|Lt Lu LT|L?M@ti_ TLh|uL*Lt Ai }LL__i@* ML?_t @hi
4U |}|ih |@? @hM|h@}i ML?_t Mi)L?_ |i *@t| |h@_i LT|L?tc ihi UL?U@|) T*@Uit
uiih hit|hU|L?t L? @*i ih@**c |i ML?_t @hi 4U |}|ih |@? |Lti Lu 6}hi c
ihu)?} |i ?||L? |@| L|ih LT|L?t @hi @ Mi||ih @TThL 4@|i i_}i uLh @ }i? LT|L?
|@? t |i ?_ih*)?} tiUh|)
#i*|@t
T|L? ThU?} |iLh) t ti_ i |i?ti*) |L ^@?|u) ht! i TLthic M) 4i@th?} L 4U
@? LT|L? @*i L*_ U@?}i u @? ?_ih*)?} t|@|i @h@M*i tU @t |i t|LU! ThUi U@?}i_
At ti?t||) t !?L? @t |i LT|L?<t R_i*|@ Oihi i i TiU| E@| Mit| @ h@?}i uLh _i*|@t
h@|ih |@? @ ?4Mih E#i*|@t @hi @*tL ti_ |L UL?t|hU| i_}itc M| @hi *itt ?|ihit|?}
uLh |@| ThTLti ? @? ?UL4T*i|i 4@h!i|t UL?|i | 6Lh i @4T*ic i @*hi@_) !?L L |L
UL?t|hU| @ i_}i |@| 4?43it |i @h@?Ui Lu hit_@* ht!c %
S ' RoJE%S mf
5TTLti i LMtihi @? LT|L? ThUic U i h|i @t E7c Tc gc A | 7 ' t|LU!
ThUic T ' @__|L?@* t|@|i @h@M*it Eu @?)c g ' t|h!i ThUi @?_ A ' |4i |L i Th@|L?
`i @?| |L !?Lc L L*_ |i LT|L? ThUi U@?}i u |i t|LU! ThUi U@?}i_ @ M|c
E7 n {7c Tc gc A q *@tc Lh 4i|L_t }i ML?_t L? |i ThUit Lu L|ih tiUh|itc tU
@t E7c Tc g n {gc A c ?L| |i t@4i tiUh|) ? @ _gihi?| t|@|i Lu |i Lh*_
AL ?uih ThUit ? @ _gihi?| t|@|i uhL4 |i ThUit Lu L|ih tiUh|itc i @tt4i |@| |i
LT|L? @*i t L4L}i?Lt Lu _i}hii L?i ? |i t|LU! ThUi @?_ t|h!i ThUic 7 @?_ gG
Ek7c Tc kgc A ' kE7c Tc gc A 2
At @tt4T|L? M@tU@**) t@)t |@| |i ?|t E_L**@ht Lh Ui?|t Lu |i ?_ih*)?} ThUi @hi
hhi*i@?| ih|L? Eb.M tLt |@| |t @tt4T|L? L*_t i? |i _t|hM|L? Lu hi|h?t
t ?_iTi?_i?| Lu |i *ii* Lu |i @tti| ThUi OL4L}i?i|) 4T*it
Y
Y
7n
g ' Y7
Yg
Oi?Ui i U@? i@*@|i _i*|@t |
Y g
Y
' Y7
7
Yg 7
E.
AL U@*U*@|i @ _ih@|ic i @i |L t|@h| @| @ TL?| | @ !?L? Lh )TL|it3i_
LT|L? @*i E|ihti @** i !?L t |@| |i @*i t ? @ ML?_ ?L @?_ ? @?L|ih
ML?_ @| | n {|( |i |4i @?_ i?Ui t|@|i _ih@|i U@? Mi ??|i `i U@*U*@|i ML?_t
@| |i M*@U! t^@hit @| U LT|L? ThUit @hi LMtihi_ | tU @ TL?|c |i 4@ 44
@?_ 4?44 t*LTit Lu |i ML?_t Y*Yg @?_ Y*Yg _i|ih4?i 4@ 44 @?_ 4?44
_i*|@t @ i^@|L? E.
dW?tih| 6}hi e ihio
6}hi e Thiti?|t @ }h@T Lu TTih @?_ *Lih _i*|@ ML?_t UL4T|i_ ? |t @)c t?}
|i t@4i ti|T @t 6}hi 5?Ui |i t*LTit Lu |i }LL__i@* ML?_t @hi t4@**ih |@? |Lti
Lu |i @hM|h@}i ML?_t @| @** Lu |i LMtihi_ LT|L? ThUitc |i }LL__i@* _i*|@ ML?_t @hi
|}|ih |@? _i*|@ ML?_t M@ti_ L? @hM|h@}i ML?_t @*L?i W? |t ?4ihU@* i @4T*ic |i
}@? t ?L| |@| *@h}i uLh |i Ui?|h@* LT|L? @*ic t?Ui |i t*LTit Lu |i }LL__i@* ML?_t
? 6}hi ihi ?L| |@| 4U *itt |@? |i t*LTit Lu |i @hM|h@}i ML?_t Ai }@? t
^|i *@h}i uLh |i ht| @?_ *@t| LT|L?c ihi @hM|h@}i ML?_t _i?
W? t4c |i }LL__i@* ML?_t U@? Mi ti_ ? |t @) |L ^@?|u) ht!i TLthic @?_ |L
@ttitt |i ?Uih|@?|) ? ht!i TLthi U@*U*@|L?t |@| @tt4i 4@h!i| ThUit uLh ?|h@_i_
ht!t
e
4*|TihL_ 4*|?L4@* @TThL@U |L ?_i LT|L?t
5L u@h i @i ti_ |i *@U!5UL*it *L}?Lh4@* i?hL?4i?| |L ?_iht|@?_ L Lh ML?_t
Lh! ? @ i**?_iht|LL_ ti|T Oihi i Thti @ 4Lhi tihLt @TT*U@|L? |L 5:Dff ?_i
2e
LT|L? ThU?} `i U@*U*@|i ML?_t L? @ |hii4L?| ?_i U@** LT|L? `i ti @ ii!*)
|h@_?} ?|ih@*c tL i |ih@|i |i ML?_ U@*U*@|L? M@U! 2 |4it uhL4 i Th@|L? Ai *@U!
Lu UL?|?Lt i_}?} t t|** |i tLhUi Lu 4@h!i| ?UL4T*i|i?itt `i 4L_i* |i t|LU! hi|h?
@t @ uhii*) tTiUi_ 4*|?L4@* h@|ih |@? @ *L}?Lh4@* #tUhi|i M| uhi^i?| |h@_?}
@?_ 4*|?L4@* t|@|t|U@* 4L_i*t }i @ UL?i?i?| @?_ UL44L?*) ti_ i?hL?4i?| uLh
|i ?4ihU@* @TT*U@|L? Lu LT|L?ThU?} |iU?^it `i @}@? ULLti @ _tUL?| u@U|Lh
L*@|*|) |@h}i| i^@* |L |Ui |i 4@h!i| 5@hTi h@|L
L_i*?} |i hi|h? _t|hM|L?
Ai @U|@* t|LU! ?_i hi|h? _t|hM|L? ui@|hit u@||ih |@*t |@? |i *L}?Lh4@* _t|h
M|L? AihiuLhic i ti @ !ih?i* it|4@|i Lu |i i4ThU@* hi|h? _t|hM|L? `i ti| T @
}h_ Lu hi|h? @*it - @| |i ii!*) i_}?} ?|ih@* | @ttLU@|i_ ThLM@M*|) @*it Z 5?Ui i @hi ?L| ThU?} M) @hM|h@}ic |t _t|hM|L? ?ii_ ?L| Mi M?L4@* Lh }i?ih@|i_
M) @ M?L4@* |hii W?t|i@_c i ti @ *@h}i ?4Mih Lu }h_ TL?|t |L @UUh@|i*) U@T|hi |i
i4ThU@* hi|h? _t|hM|L? `i ti hi|h? _@|@ -| |L @tt}? ThLM@M*|it Z @ @ B@tt@?
!ih?i*c
Z ' & A
[
- 3- 2
3E | e
|'
uLh i@U c ihi t @ i}| ULti? t@**) @| ff @?_ & t @ UL?t|@?| ULti? tL |@|
|i ThLM@M*|it t4 |L L?i At ThLUi_hi @tt4it |@| |i hi|h? _@|@ -| @| i@U _@|i
| @hi _h@? uhL4 |i t@4i ?UL?_|L?@* _t|hM|L? At @tt4T|L? t 4Lhi hi@tL?@M*i
uLh i Uitt Lh hi@* hi|h?t |@? uLh ?L4?@* hi|h?tc tL i ti uLh -| |i 5:Dff hi|h? *itt
|i Ahi@th) M** h@|i T*t |i UL?t|@?| DI ?|ihit| h@|i |@| i ti ? |i LT|L? ThU?}
U@*U*@|L?t `i ti |i u** +5 _@*) 5:Dff _@|@ t@4T*ic a*) bS2#iUi4Mih bbS
6}hi D Thiti?|t |i hit*|?} _t|hM|L? Lu ii!*) hi|h?t ,@U |h@?}*i hiThiti?|t
L?i }h_ TL?| Lu |i 4*|?L4@* _t|hM|L? Ai T*t t}?t T*L| |@* @*it Lu |i @U|@*
hi|h? _@|@( |ih i}| L? |i }h@T t @hM|h@h) vL U@? tii |i u@| |@*t Lu |i _t|hM|L?c
_hi? M) |i LUU@tL?@* tTiU|@U*@h L|*ih hi|h?tc itTiU@**) Uh@tit
dW?tih| 6}hi D ihio
`i @tt4i |@| |t 4*|?L4@* t |i UL?_|L?@* hi|h? _t|hM|L? @?_ |@| | t
?_iTi?_i?| Lih |4i `i UiU!i_ |@| |i *L?} Lh3L? _t|hM|L?t 4T*i_ M) U@??}
2D
|L}i|ih i4ThU@* _t|hM|L?t @t ? 6}hi D @hi ?L| M@_ @TThL 4@|L?t |L |i @U|@*
*L?}Lh3L? _t|hM|L?t __?} UL?_|L??} ?uLh4@|L? Et|LU@t|U L*@|*|)c tih@* ULh
hi*@|L? ? hi|h?tc i|U t @? 4TLh|@?| i |i?tL?c U ** @**L uLh @h@|L? ? |i
ML?_t Lih |4ic M| ** @__ t|@|i @h@M*it
@*U*@|?} ML?_t
`i ti| T @ }h_ Lu t|LU! ThUit i7 j At }h_ 4@) Mi ?ih Lh UL@htih |@? |i hi|h?
_t|hM|L? }h_ | i@U _@|ic i hiThiti?| |i *Lih ETTih ML?_ u?U|L? E7c | M)
|t @*i L? |i }h_ Lu t|LU! ThUit AL i@*@|i 4L4i?|tc i ?|ihTL*@|i E7c | L? |i
t|LU! ThUi }h_ 6Lh i @4T*ic tTTLti i !?L E7c | n {| @?_ i t |L ?_ E7c |
5|@h| @| t|LU! ThUi }h_ ?_i c |4i | 6Lh i@U i*i4i?| Lu |i hi|h? }h_ - c i ?_
|i ULhhitTL?_?} @*i Lu |i t|LU! ThUi @| |4i | n {|c 7 - ) *?i@h ?|ihTL*@|L?c
i ?_ |i ML?_ @| |t TL?|c E7 - c | n {| Lc M) t44?} Lih t|@|it i}|i_
M) |i @ttLU@|i_ ThLM@M*|itc i U@? ?_ @** |i hi^hi_ 4L4i?|t uLh |i |4i| ML?_
U@*U*@|L?
Ai _tUL?| u@U|Lh t |i ULUi @h@M*ic @?_ | t ?L @ iU|Lh | L?i i*i4i?| uLh
iih) TL?| L? |i hi|h? }h_ | i@U t|LU! ThUi }h_TL?|c i ht| UL4T|i |i ThUi
ML?_t @tt4?} |@| L?*) |i L*@|*|) UL?t|h@?| M?_t Wu |i hit*|?} _tUL?| u@U|Lh t
TLt|i E@| iih) TL?| L? |i hi|h? }h_c |t t |i tL*|L? @?_ |i TLt||) UL?t|h@?| t
t*@U! Wu ?L|c i UL4T|i @hM|h@}i ML?_tDc @?_ i UL4T|i |i 4?44 tiUL?_ 4L4i?|
8 Ulwfknhq +4<;8, jlyhv d vroxwlrq iru wkh duelwudjh erxqgv lq d pxowlqrpldo hqylurqphqw/ wkh vroxwlrq wr
wkh olqhdu surjudpplqj sureohp
plq H+p{f , v=w= s @H+p{,> p 3=
ipj
Wkh xsshu erxqg kdv qrq}hur glvfrxqw idfwru lq wkh vpdoohvw +4, dqg odujhvw +Q, uhwxuq vwdwhv/
p4 @
4 UQ Ui
4 Ui UQ
> pQ @
=
i
4 U UQ U4
Q Ui UQ U4
Wkh orzhu erxqg glvfrxqw idfwru lv rqo| qrq}hur lq wkh wzr vwdwhv +l> m, zlwk uhwxuq mxvw deryh dqg ehorz
wkh ulvniuhh udwh/
4 Um Ui
4 Ui Ul
> pm @
=
pl @
i
l U Um Ul
m Ui Um Ul
Wkhvh glvfrxqw idfwruv duh qrw xqltxh> rwkhu glvfrxqw idfwruv fdq dovr jhqhudwh wkh duelwudjh erxqgv1 Wkhuh0
iruh/ wr whvw zkhwkhu wklv duelwudjh erxqg vroxwlrq lv wkh vroxwlrq wr wkh jrrg0ghdo erxqg/ zh xvh wkhvh
glvfrxqw idfwruv wr frpsxwh wkh duelwudjh erxqg/ dqg wkhq zh vhdufk iru wkh plqlpxp yduldqfh glvfrxqw
idfwru wkdw jhqhudwhv wkh duelwudjh erxqg1
2S
_tUL?| u@U|Lh ?ii_i_ |L @||@? |i @hM|h@}i ML?_t Wu |@| tiUL?_ 4L4i?| t *itt |@? |t
ML?_ 2 c |i @hM|h@}i ML?_t @hi |i tL*|L? @?_ |i _tUL?| u@U|Lh L*@|*|) UL?t|h@?|
t t*@U! Wu ?L|c i UL4T|i |i ML?_t | ML| L*@|*|) @?_ TLt||) UL?t|h@?|t M?_?}
@t _itUhMi_ @MLi
+it*|t
6}hi S Thiti?|t ML?_tc |h@?t*@|i_ |L 4T*i_ L*@|*|it Ai 4__*i *?i 4TLtit
3ihL 4@h!i| ThUic Lh ht!?i|h@* @*@|L?c Lu |i hit_@* ht! M) t4T*) ti||?} ' f ?
|i ML?_ uLh4*@ Eb Ai TTih ML?_ @?_ 3ihLhit_@*ht!ThUi U@*U*@|L?t tL @
ThL?L?Ui_ L*@|*|) t4*i At t4*i t _hi? M) |i u@| |@*t ? |i hi|h? _t|hM|L?
OLiihc |i *Lih ML?_ _Lit ?L| tL 4U u @?) t4*ic @?_ | hi_Uit |L |i *Lih
@hM|h@}i ML?_ T@t| @ Uih|@? TL?| AihiuLhic @ hLMt| L*@|*|) t4*i _iTi?_t L? |}|ih
ML?_t L? 4@h!i| ThUit Lu hit_@* ht! |@? i @i 4TLti_c Lh 4Lhi uhi^i?| |@? ii!*)
hiM@*@?U?}
dW?tih| 6}hi S @?_ 6}hi . ihi Ai) tL*_ Mi U*Lti i?L} |L}i|ih |@| hi@_iht U@?
UL4T@hi |i4o
`*i ?|ihThi|?} |iti hit*|tc !iiT ? 4?_ |@| 4T*i_ L*@|*|) t @ }*) ?L?*?i@h
u?U|L?c @?_ ih) t4@** ThUi U@?}it uLh u@h uhL4 |i 4L?i) LT|L?t |h@?t*@|i |L ih) *@h}i
U@?}it ? 4T*i_ L*@|*|) 6Lh i @4T*ic @| @ t|LU! ThUi Lu e2c ihi |i *Lih }LL__i@*
ML?_ 4ii|t |i *Lih @hM|h@}i ML?_c LT|L? ThUit @hi _hi? M) |i ThLM@M*|) Lu @
e2%e2 ' fI _iU*?i ? t|LU! ThUit | |t t|LU! ThUic |i *@U!5UL*it ThUi | DI
L*@|*|) t L?*) .bf3S _L**@ht @MLi |i @hM|h@}i ML?_- ,i? |i TTih }LL__i@*
ML?_ t L?*) D%U @MLi |i @hM|h@}i ML?_ 6h|ih4Lhic |i hit*|t ? |t h@?}i @hi
_hi? M) |i i |hi4i |@* it|4@|it ? |i ThLM@M*|) _t|hM|L?c @?_ tL @hi tMiU| |L
tMt|@?|@* t@4T*?} ?Uih|@?|) ?i 4Lhi Uh@t ? |i t@4T*i UL*_ _LM*i |iti LT|L?
@*it
AL UL4T@hi |iti ML?_t | @U|@* LT|L?t ThUitc 6}hi . Thiti?|t _@|@ L? _@*)
U*Lt?} , 5:Dff ?_i LT|L? ThUit uLh |hii 4L?|t ? bbSS
9 Zh
suhvhqw yrodwlolw| fxuyhv iru wkh hqg ri Pdufk/ Mxqh/ Vhswhpehu dqg Ghfhpehu/ zkhq wkh ixoohvw vhw
ri rswlrqv dfurvv vwulnh sulfhv lv dydlodeoh1 Zh frqyhuw sxw sulfhv wr fdoo htxlydohqw xvlqj sxw0fdoo sdulw|/
2.
Ai _@|@ tL |i i**!?L? L*@|*|) t4*iG 4T*i_ L*@|*|it EThUit @hi }ih uLh
u@h|ih ?|i4L?i) U@**t @?_ i^@*i?| L|Lu|i 4L?i) T|t L? |i h}| @?_ t_i Lu |i
}h@T At hti ? L*@|*|) t @ *||*i t|iiTih |@? |@| Thi_U|i_ M) Lh U@*U*@|L? Lu |i
ML?_tc M| ?L| M) 4U EL|i |@| |i Lh3L?|@* tU@*i L? 6}hi S i |i?_t u@h|ih |L |i
*iu| |@? |@| Lu 6}hi .c tL )L L?*) tii L?i t_i Lu |i Thi_U|i_ t4*i Ai U@*U*@|L?
hiT*U@|it |i 4T*i_ L*@|*|it Lu |i u@h uhL4 |i 4L?i) LT|L?t 5?Ui |i *Lih ML?_
t ?iih Mi*L DI @?_ |i LT|L? _@|@ }Lit @t *L @t fI |i T33*i ? |i _@|@ t |i *L
4T*i_ L*@|*|) Lu |i ?i@h4L?i) LT|L?t
Aihi t tL4i @h@M*|) @UhLtt t|h!i ThUit E}h@Ti_ @t @h@M*|) @UhLtt t|LU! ThUit
uLh @?) }i? _@|ic @?_ |i @h@|L? Mi|ii? T|t @?_ U@**t E?L| tL? t @ML| |i t@4i
At @h@M*|) t 4U t4@**ih |@? |i t3i Lu |i ML?_t ?i t |i4T|i_ |L UL?U*_i
|@| @h@M*|) @UhLtt t|h!it t iUL?L4U@**) ?4TLh|@?| AL |@!i |t UL?U*tL? tihLt*)
Liihc i tL*_ UL?t_ih i_}?} i@U LT|L? | @** |i L|ih LT|L?tc M| @*tL |@!i
tihLt*) |i **^_|) @?_ M_%@t! tThi@_ Lu @** |i L|ih LT|L?tc itTiU@**) |Lti u@h uhL4
|i 4L?i)
Aihi t @*tL @ Uih|@? @4L?| Lu @h@M*|) @UhLtt |4iG |i Uhit tu| T Lh _L? M)
@ML| e TL?|t Lu 4T*i_ L*@|*|) At t @*tL *itt |@? |i t3i Lu |i ML?_t At LM
tih@|L? t}}it|t |@| @? 4TLh|@?| uh@U|L? Lu LMtihi_ @h@|L? ? 4T*i_ L*@|*|) Lih
|4i 4@) t4T*) Mi _i |L @h@|L? |? }LL__i@* ML?_t |@| t _U*| |L ThL|@M*)
i_}i @@)c ?L| _i |L @h@|L? ? |i UL?_|L?@* @h@?Ui Lu t|LU! hi|h?t W? |t U@tic
|i @M*|) |L i_}i L?i LT|L? | @?L|ih ** ?L| U@?}i |i TU|hic t?Ui |i L*i
Uhi @?_iht T Lh _L?
`i @i Lu ULhti UL?_U|i_ 4@?) 4Lhi i Tih4i?|t |@? i @i tT@Ui |L tL t
|i |4i |L i Th@|L? ?Uhi@titc |i Thi_U|i_ 4T*i_ L*@|*|) Uhit @||i? L|c @?_ |i
hi}L? ? U |i *Lih ML?_ *it @MLi |i @hM|h@}i ML?_ ?Uhi@tit 6Lh tLh|ih |4it
|L i Th@|L?c |i Thi_U|i_ L*@|*|) t4*it t|iiTi?c M| |i ML?_t MiUL4i _ih `| @
4L?|*) i_}?} ?|ih@*c |i TTih ML?_ t @ML| |i t@4i M| |i *Lih ML?_ t *LLtih
Ai 4L?|*) ?|ih@* @*tL ThL_Uit @ t|iiTih L*@|*|) t4*i |L |i h}| @?_ @ t@**Lih L?i
F @ S . V N@Ui = Zh fkrrvh wkh lqwhuhvw udwh hdfk prqwk ehwzhhq 4 dqg 8(/ wr ehvw pdwfk sxw dqg
fdoo lpsolhg yrodwlolw| fxuyhv1 Wr frqirup zlwk wkh rwkhu jxuhv/ zh wudqvirup +lpsolhg, fdoo sulfhv zlwk
d frpprq vwrfn sulfh V dqg ydu|lqj vwulnhv N wr fdoo sulfhv zlwk d frpprq vwulnh sulfh N @ 433 dqg
ydu|lqj vwrfn sulfh V @ V N @N e| dvvxplqj olqhdu krprjhqhlw|/ F+V N @N> N , @ N @N F+V > N,=
2H
|L |i *iu| Ai 4L?|*) hi|h? _t|hM|L? @t *@h}ih Uh@tit @?_ t4@**ih TLt|i L|*iht
At u@U| t}}it|t |@| L?i 4@) Mi||ih 4@|U i4ThU@* L*@|*|) t4*it u L?i U@*Mh@|it |i
ii!*) hi|h? _t|hM|L? |L 4Lhi @UUh@|i*) hiiU| |i 4T*i_ |hii4L?| _t|hM|L?
D
@tt ht! @?_ hi@* LT|L?t
5TTLti i @?| |L @*i @ ,hLTi@? U@** LT|L? L? @? ii?| T |@| t ?L| @ |h@_i_ @tti|c
M| t ULhhi*@|i_ | @ |h@_i_ @tti| |@| U@? Mi ti_ @t @? @TThL 4@|i i_}i Aihi t
@? ?@L_@M*i RM@tt ht! Mi|ii? |i LT|L? @?_ |i tiUh|it |@| U@? Mi ti_ |L i_}i
|i LT|L?c ii? u i U@? |h@_i UL?|?Lt*) At t|@|L? t UL44L? | hi@* LT|L?tc
?L??@?U@* LT|L?t ELT|L?t L? @hT*@?i ThU@titc @?_ ? |i @TT*U@|L? Lu LT|L? ThU?}
|iU?^it |L hi@* ?it|4i?|t 6Lh i @4T*i T UL*_ hiThiti?| |i ThUi Lu @ ?L?_h@M*i
}LL_c @?_ L?i @?|t |L @*i |i h}| |L M*_ @? ?it|4i?| ThLiU| |@| U@? ThL_Ui L?i
?| Lu |i }LL_ @| ULt| g ,i? Thi*) ?@?U@* LT|L?t @hi ?Uhi@t?}*) h||i? L? ii?|t
|@| @hi ?L| |h@_i_ @tti|tc tU @t U@|@t|hLTi ?th@?Ui LT|L?t 6Lh LT|L?t L? |h@_i_ M|
**^_ ?_ih*)?} @tti|tc | t Lu|i? Mi||ih |L i_}i @? LT|L? | @? 4TihuiU|*) ULhhi*@|i_
M| 4Lhi *^_ @tti|
Ai |ih4?@* T@)Lg t
%SA ' 4@ ETA gc f
`i 4L_i* |i L?| iL*|L? Lu |i |h@_i_ @tti| 7 @?_ |i ii?| T L? U |i LT|L? t
h||i? @t
_7
' >7 _| n j7 _5c
7
_T
' >T _| n jT 5 _5 n jT _c
T
.E_5 2 ' .E_2 ' c .E_5_ ' f
Aihi t @*tL @ UL?t|@?| ht!uhii h@|i o
5?Ui |i ti|T t tL U*Lti |L |i *@U!5UL*it ti|Tc i U@? }i U*Lti_ uLh4 tL*|L?t
|L |i }LL__i@* ML?_t ? |t U@ti
Lh ' Tf
e#A s
s
_ n jT A ge3oA _ jT A
2
2
2b
EH
ihi E _i?L|it |i *iu| |@* Lu |i ?Lh4@* _t|hM|L? @?_
jT2
_T 2
' jT2 5 n jT2 T2
*?ETf*g n E# n o A
s
jT A
v
%
#
$&
t
2
2
T 7 4 @
4
jT
27
>7 o
>T o
( T j7
j
#
$ T
_T _7
jT 5
SJoo
c
'
T 7
jT
.|
_ # 7 4 +
@ '
n TTih ML?_
*Lih ML?_
At i ThittL? t i @U|*) |i *@U!5UL*it uLh4*@ | |i @__|L? Lu |i # |ih4 Ai
*@U!5UL*it uLh4*@ @TTi@ht @t @ tTiU@* U@tic # ' f i? T ' 7 >T i?|iht |i uLh4*@
MiU@ti |i ii?| T 4@) ?L| }hL @| |i t@4i h@|i @t |i @tti| 7 MLt*)c |i ULhhi*@|L?
4 Mi|ii? T tLU!t @?_ @tti| tLU!t i?|iht |i uLh4*@c @?_ @t |t ULhhi*@|L? _iU*?itc |i
ML?_t _i? Ai ML?_t @*tL _i? @t |i L*@|*|) UL?t|h@?| MiUL4it *@h}ih hi*@|i
|L |i @tti| 5@hTi h@|Lt 7 `i _ihi i^@|L? EH M) @TT*)?} |i _tUL?| u@U|Lh ?|i}h@|L? |iU?^i _itUhMi_
? ThLTLt|L? D TT*)?} |@| ThLTLt|L?c |i *Lih ML?_ t }i?ih@|i_ M) |i _tUL?|
u@U|Lh
t
_\
' o_| 7 _5 2 27 _
\
@?_ |i ML?_ t |i? }i? M)
%
&
\
| ' .| A 4@ ETA g
\|
Ai TTih ML?_ t }i?ih@|i_ | @ n ? uhL?| Lu |i t^@hi hLL| 7A c TA @?_ \A @hi L?|*)
*L}?Lh4@**) _t|hM|i_c tL |i _LM*i ?|i}h@* _i??} |i i TiU|@|L? t t|h@}|uLh@h_
|L TihuLh4 ?Ui @}@?c i hi*i}@|i |i @*}iMh@ |L |i @*}iMh@ TTi?_ c LUh@?i @?_
5@@+i^iL EbbH
t @ ?4ihU@* i @4T*ic i L?Ui @}@? UL?t_ih @ U@** LT|L? | |hii 4L?|t |L
i Th@|L? @?_ t|h!i @*i ff AL !iiT |i i @4T*i @t t4T*i @t TLttM*ic i tTiUu) |@|
T @t |i t@4i _hu| @?_ L*@|*|) @t |i t|LU! ?_i E>T ' >7 c jT ' j7 `i tTiUu) |i
f
ULhhi*@|L? Mi|ii? _T @?_ |i t|LU! ?_i 4 ' fbc @?_ i @}@? ti @ _tUL?| u@U|Lh
L*@|*|) ML?_ i^@*i?| |L |Ui |i 4@h!i| 5@hTi h@|L 6}hi H Thiti?|t |i TTih
@?_ *Lih ThUi ML?_t
dW?tih| 6}hi H ihio
t MiuLhic |i _L**@h t3i Lu |i ML?_t t t4@**ih uLh L| Lu |i 4L?i) LT|L?t M| |i
ThLTLh|L?@* t3i Lu |i ML?_t tL? ? |i }hi t t4@**ih uLh ? |i 4L?i) LT|L?t
Ai ML?_t @hi tMt|@?|@*c @?_ _ih @MLi |i *@U!5UL*it @*i |@? Mi*L |. |
ffI ihhLht Ai ihhLht ?Uhi@ti @t |4i |L i Th@|L? ?Uhi@tit Ai }hi i*Tt t |L
i@*@|i |i UL44L? TihUiT|L? |@| *@U!5UL*it t @ }LL_ @TThL 4@|L? ii? i? |t
@tt4T|L?t @hi L*@|i_c @t ? |t U@ti
e
, |i?tL?t
U!?} |i M@tt @tti|t @?_ L*@|*|) UL?t|h@?|
Ai t3i Lu |i ML?_t t _hiU|*) hi*@|i_ |L |i t3i Lu |i hit_@*c Lh |i -2 ? @
hi}hittL? Lu LT|L? T@)Lgt L? M@tt @tti| T@)Lgt W| t |ihiuLhi |i4T|?} |L ti *L|t Lu
M@tt @tti|tc M| t?} uLh -2 t _@?}ihLtc t?Ui | t @h_ |L M*_ @ Mi*i@M*i @?_ t|@M*i
4L_i* Lu |i L?| _t|hM|L? Lu @ *@h}i ?4Mih Lu @tti|t At t ?L| t| @? tti uLh
iUL?L4i|hU@?tG w@h}i i_}iu?_ *Lttit ? |i t44ih Lu bbH ihi T@h|*) @||hM|i_ |L |LL
*L it|4@|it Lu |i ULhhi*@|L? Mi|ii? )i*_ tThi@_t L? _gihi?| ML?_ U*@ttit EOi?h^it
@?_ k@? bbH @?) M@tt @tti|t U@? Mi 4Lhi i@t*) @UUL44L_@|i_ i? @ |iLhi|U@*
t|hU|hi }Lih?t |ih L?| _t|hM|L?c @t @t |i U@ti i? i ti_ L|ih LT|L?t @t
M@tt @tti|t
Ai t3i Lu Lh ML?_t t @*tL _hiU|*) hi*@|i_ |L |i _gihi?Ui Mi|ii? |i 4@ 44
_tUL?| u@U|Lh L*@|*|) @?_ |i L*@|*|) ti_ T ? ThU?} |i M@tt @tti|tc 2 .E%W2
At u@U| t}}it|t |@| L?i ?U*_i } 5@hTi h@|L M@tt @tti|t |L LM|@? |}|ih ML?_tc
ii? u |Lti @tti|t @hi ?L| i** ULhhi*@|i_ | |i uLUt T@)Lg OLiihc | 4@) Mi Mi||ih
: Zh
gr qrw uhsruw lpsolhg yrodwlolwlhv/ ehfdxvh wkh kljko| qrqolqhdu lpsolhg yrodwlolw| phwulf lv qrw ds0
sursuldwh lq wklv fdvh1 Iru h{dpsoh/ wkh orzhu sulfh erxqg fdq idoo ehorz wkh orzhu duelwudjh erxqg/ zlwk
qr ylrodwlrq ri duelwudjh vlqfh wkh fruuhodwlrq lv qrw shuihfw1 Zh fdqqrw hyhq fdofxodwh lpsolhg yrodwlolwlhv ri
vxfk sulfhv1
|L *Lih |i L*@|*|) UL?t|h@?| 2 ?t|i@_ At ThLUi_hi }it T @|iih ti |i i |h@
@tti|t @_ @t i_}itc M| | @L_t |i UL?t|hU|L? Lu @ *@h}i L?| _t|hM|L? 4L_i*
6Lh i @4T*ic i? ThU?} ML?_ LT|L?t L?i UL*_ ti @ L*@|*|) UL?t|h@?| i^@* |L
|i 4@h!i| 5@hTi h@|L @?_ i U*_i |i 4@h!i| uhL4 |i ti| Lu M@tt @tti|tc h@|ih |@?
ti @ UL?t|h@?| i^@* |L |Ui |i 4@h!i| 5@hTi h@|L @?_ M*_ @ 4L_i* Lu |i L?|
_t|hM|L? Lu t|LU!t @?_ ML?_t 54*@h*)c i ti_ @ UL?t|h@?| Lu |Ui |i 4@h!i| 5@hTi
h@|L @?_ }?Lhi_ |i TLttM*|) Lu } 5@hTi h@|Lc *L q t|h@|i}it tU @t 6@4@ @?_
6hi?U<t Ebb @*i TLh|uL*Lc h@|ih |@? ?U*_i |i4c 4L_i* |i4c @?_ ti @ Tih@Tt
4Lhi hi@*t|U UL?t|h@?| E}i? |ih Thiti?Ui Lu uLh |4it |i 4@h!i| 5@hTi h@|L
Ah@?t@U|L?t ULt|t
5TiUu)?} uhU|L?*itt |h@_?} @| _tUhi|i ?|ih@*t t @ Uh_i @) |L @?_*i |h@?t@U|L?t
ULt|t h L?iTihL_ U@*U*@|L?t UL*_ ?U*_i i T*U| |h@?t@U|L?t ULt|tc t?} w||4ih<t
EbbS tL*|L? uLh O@?ti?a@}@??@|@? ML?_t | |h@?t@U|L?t ULt|t | |t _Lit
?L| tL*i |i Ui?|h@* ThLM*i4c ?@4i*) |L ?_ |i LT|4@* |4it @| U |L |h@_i ? @
UL?|?Lt|4i uh@4iLh! | |h@?t@U|L?t ULt|t 6Lh |t hi@tL?c 4Lt| Lu |i *|ih@|hi
L? LT|L? ThU?} ML?_t | i T*U| |h@?t@U|L?t ULt|t @*tL UL?t_iht |LTihL_ @?@*)tt
Lh @_LU |h@_?} h*itc uLh i @4T*i wi*@?_ EbHDc L?t|@?|?_it EbbHc L?t|@?|?_it
@?_ ~@hTLTL*L Ebb.
Lhi _tUL?| u@U|Lh hit|hU|L?t
__?} uh|ih _tUL?| u@U|Lh hit|hU|L?t t @ ?@|h@* @) |L |}|i? |i ML?_t
wi) EbHD @?_ L?t|@?|?_it EbbH U@*U*@|i LT|L? ThUi ML?_t M) @tt4?} |@|
|i _tUL?| u@U|Lh _iU*?it 4L?L|L?U@**) | @ t|@|i @h@M*i `i @i @ hi*@|i_ UL?_|L?G
|i UL@h@?Ui Mi|ii? t|LU! hi|h?t @?_ |i _tUL?| u@U|Lh 4t| Mi ?i}@|i |L }i?ih@|i
TLt|i i TiU|i_ hi|h?t E|i ThU?} UL?t|h@?| | }*LM@* 4L?L|L?U|) t 4Lhi t|h?}i?|
|@? UL@h@?Uic @?_ |t UL?t|h@?| 4@) |}|i? |i ML?_t
h ML?_t @**L |i Lht| U@ti |@| 4@h}?@* |*|) }hL| t TihuiU|*) ULhhi*@|i_ |
@ TLh|uL*L Lu M@tt @?_ uLUt @tti|t
W? 4@?) U@tit L?i UL*_ Uhi_M*) 4TLti @ t@hTih
*4| |@? 4 L? |t ULhhi*@|L? |L LM|@? |}|ih ML?_t
ih?@h_L @?_ wi_L| Ebbb ti |i hit|hU|L? @ 6 K |L t@hTi? |i ?L@hM|h@}i
2
hit|hU|L? 4 6 : fc @?_ U*iih*) hi*@|i |t ML?_ |@!i? @*L?i |L TLh|uL*L R}@?%*Ltt
h@|Lt At hit|hU|L? t hi*@|i_ |L |i L*@|*|) hit|hU|L?G TTih @?_ *Lih ML?_t L?
6 4T*) @ ML?_ L? |t @h@?Uic @?_ M) iM)ti<t ?i^@*|) @ @h@?Ui ML?_ 4T*it
|@| |i ThLM@M*|) Lu 6 i Uii_?} TTih @?_ *Lih ML?_t U@? Mi 4@_i @?t?}*) t4@**
h Ui?|h@* ThLTLt|L? 2 |@| L?i U@? tL*i 4*|TihL_ ThLM*i4t hiUhti*) }Lit |hL}
? |t U@ti
ih?@h_L @?_ wi_L| @*tL t}}it| |@| L?i 4TLti @ 6*+ K ihi + t @? i T*U|
_tUL?| u@U|Lh 4L_i* tU @t |i UL?t4T|L?M@ti_ 4L_i* Lh c @t @ @) Lu 4TLt?}
@ Ri@! 4T*U@|L? Lu |@| T@h|U*@h 4L_i* w4|t L? jE6*+ Lh jE6 + 4}| Mi
|iU?U@**) i@tih |L 4TLtic itTiU@**) ? UL?|?Lt |4ic M| |t _i@ U@? @*tL Mi @__i_
N?|* L?i @t hiULihi_ @ |hi _tUL?| u@U|Lh 6|n ' q ES|n* ES| c uh|ih hit|hU|L?t
** @*@)t |}|i? ML?_t *tLc @?_ _itT|i Lh i |i?_i_ 4L|@|L?c L?i tL*_?<| Mi
|LL _L}4@|U @ML| U i@! hit|hU|L? t Mit| ) |ih ?@|hic i@! hit|hU|L?t **
@_4| @*it |@| @hi t|h@?}i @UULh_?} |L t|hL?}ih Lh _gihi?| hit|hU|L?t AihiuLhic
|i @hLt hit|hU|L?t @hi ?L| UL4Ti||Lht ?i tL*_ 4TLti @t 4@?) _tUL?| u@U|Lh
hit|hU|L?t @t @TT*) |L @ }i? t|@|L?c @?_c Tih@Tt 4Lt| 4TLh|@?|*)c | U L?i
U@? t|** UL?i?i?|*) U@*U*@|i ML?_t uLh @ }i? @TT*U@|L?
*|T*i uLUt @tti|t
`i @i i4T@t3i_ @ t?}*i uLUt @tti| 6Lh tL4i @TT*U@|L?tc tU @t i @4??} |i
ti| Lu ?_i LT|L?t @UhLtt t|h!i ThUic | 4@) 4@!i 4Lhi ti?ti |L ?_ @ ML?_ L? |i @*it
ERc R2c R c Lu tiih@* uLUt T@)Lgt t4*|@?iLt*) h@|ih |@? UL?t_ih i@U uLUt T@)Lg
? tL*@|L?
D
+iuihi?Uit
Mi*c ?_hi @?_ a@?Ui ,Mih*)c bbSc RT|4@* W?it|4i?| | Lt|*) +iihtM*
|)c +ii Lu ,UL?L4U 5|_it Sc DHDb
ih?@h_Lc ?|L?L @?_ *ih wi_L|c bbbc RB@? wLtt @?_ tti| hU?}c aLh?@* Lu
L*|U@* ,UL?L4)c |t tti
*@U!c 6tUih @?_ )hL? 5UL*itc b.c RAi V@*@|L? Lu T|L?t @?_ LhTLh@|i w@M*
|itc aLh?@* Lu L*|U@* ,UL?L4)c Hc S.SDe
LUh@?ic aL? O @?_ ait
t 5@@+i^iLc bbHc R*}iMh@U TTi?_ |L i)L?_ hM
|h@}i< c @?tUhT|c N?iht|) Lu U@}Lc @@*@M*i uhL4 |i @|Lht Lh @|
||TG%%}tMUU@}Li_%u@U%L?ULUh@?i%
LUh@?ic aL? O @?_ ait
t 5@@+i^iLc bbbc BLL__i@* LT|L? ThUi ML?_t |
t|LU@t|U L*@|*|) @?_ t|LU@t|U ?|ihit| h@|ic 4@?tUhT|c N?iht|) Lu U@}L
L?t|@?|?_itc BiLh}i c bbHc RAh@?t@U|L?t Lt|t @?_ |i VL*@|*|) W4T*i_ M) T|L?
hUitc @?tUhT|c Bh@_@|i 5ULL* Lu t?ittc N?iht|) Lu U@}L
L?t|@?|?_itc BiLh}i @?_ A@*i@ ~@hTLTL*Lc bb.c RL?_t L? T|L? hUit
? @? W?|ih|i4TLh@* 5i||?} | hLTLh|L?@* Ah@?t@U|L? Lt|t @?_ *|T*i 5iUh
|itc @?tUhT|c Bh@_@|i 5ULL* Lu t?ittc N?iht|) Lu U@}L
# |c ?@t @?_ + ?_)U!c bbec W?it|4i?| N?_ih N?Uih|@?|)c h?Ui|L? aG h?Ui
|L? N?iht|) hitt
6@4@c ,}i?i 6 @?_ ki??i| + 6hi?Uc bbc RL44L? 6@U|Lht ? |i +i|h?t L? 5|LU!t
@?_ L?_tc aLh?@* Lu 6?@?U@* ,UL?L4Utc DS
O@?ti?c w@ht i|ih @?_ 5UL|| +U@h_c bH.c RAi +L*i Lu L?_|L??} W?uLh4@|L? ?
#i_U?} Ait|@M*i +it|hU|L?t W4T*i_ M) #)?@4U tti| hU?} L_i*tc ,UL?L
4i|hU@c DDc DH.Se
O@?ti?c w@ht i|ih @?_ +@ a@}@??@|@?c bbc RW4T*U@|L?t Lu 5iUh|) @h!i| #@|@
uLh L_i*t Lu #)?@4U ,UL?L4itc aLh?@* Lu L*|U@* ,UL?L4)c bbc 22D2S2
e
O@?ti?c w@ht i|ihc aL? Oi@|L? @?_ ,h3L w||4ihc bbDc R,UL?L4i|hU ,@*@|L? Lu
tti| hU?} L_i*tc Ai +ii Lu 6?@?U@* 5|_itc Hc 2.2.e
Oic O@ @?_ i* i@htL?c bb2c RL?t4T|L? @?_ Lh|uL*L L*Uit | W?UL4T*i|i
@h!i|tG Ai W??|i #4i?tL?@* @tic aLh?@* Lu ,UL?L4U AiLh)c Dec 2DbfD
Oi?h^itc #@?@ @?_ aLtiT k@?c bbHc RwittL?t Lu @ wL?}c OL| 544ihc i vLh!
A4itc #iU S
k@?_i*c 54i* @?_ +LMih| 6 5|@4M@} EbbDc RLh|uL*L W?iUi?U) @?_ |i hLtt
5iU|L? Lu , TiU|i_ +i|h?tc aLh?@* Lu 6?@?Uic Dfc D.He
wi_L|c *ihc bbDc R,tt@)t L? +t! @?_ +i|h? ? |i 5|LU! @h!i|c # _ttih|@|L?c
@tt@Uti||t W?t|||i Lu AiU?L*L})
wi*@?_c O@)?i ,c bHDc RT|L? hU?} @?_ +iT*U@|L? | Ah@?t@U|L?t Lt|tc aLh?@*
Lu 6?@?Uic jwc 2Hf
wi)c O@4c bHDc RNTTih @?_ wLih L?_t Lu | @?_ @** T|L? V@*iG 5|LU@t|U
#L4?@?Ui TThL@Uc aLh?@* Lu 6?@?Uic efc b.2.
w||4ihc ,h3L B ac bbSc Rtti| hU?} ? ,UL?L4it | 6hU|L?tc ,UL?L4i|hU@c Sec
ebS.
@Uk?*@)c h@}c bbDc R*|u@U|Lh L_i*t #L L| , T*@? #i@|L?t uhL4 |i
c aLh?@* Lu 6?@?U@* ,UL?L4Utc Hc 2H
ih|L?c +LMih| c b.Mc RAiLh) Lu +@|L?@* T|L? hU?}c i** aLh?@* Lu ,UL?L4Ut
@?_ @?@}i4i?| 5Ui?Uic ec eH
+|U!i?c i|ih Oc bHDc R? T|L? hU?} L?_tc aLh?@* Lu 6?@?Uic efc 2b2
+Lttc 5|ii?c b.S@c RT|L?t @?_ ,Ui?U)c "@h|ih*) aLh?@* Lu ,UL?L4Utc bfc .DHb
+Lttc 5|ii?c b.SMc RAi hM|h@}i hU?} AiLh) Lu @T|@* tti| hU?}c aLh?@* Lu
,UL?L4U AiLh)c c eSf
+Lttc 5|ii? b.SUc R+t!c +i|h? @?_ hM|h@}ic ? +t! @?_ +i|h? ? 6?@?Uic VL*4i
c W 6hi?_ @?_ a U!t*ih ,_tc Hb2Hc @4Mh_}iG @**?}ih
D
5@?!i?c a@)c bb2c RAi hhi?| 5|@|i Lu |i hM|h@}i hU?} AiLh)c aLh?@* Lu
6?@?Ui e.c DSb.e
S
S
hLLut Lu *i44@t @?_ ThLTLt|L?t
hLLu Lu *i44@
WuG .E ' .E" ' f tL .dE%W n n " o ' .E%W ' T
?*) uG 6Lh @?) 6 |@| t@|tit T '.E6 c i @i RoJE6m ' .E6 .E
|i w5 ThLiU|L? uLh4*@c @?_ |i? RoJE6m ' T .E
3
3
M)
' %W M) |i @tt4T|L?
|@| T ' .E6 #i?i @ hit_@* B ' 6 %W ) UL?t|hU|L?c .EB ' f Atc @?)
_tUL?| u@U|Lh 6 U@? Mi hiThiti?|i_ @t 6 ' %W n B hLiU|?} B L? @?_ _i??} " @t |i
hit_@* @}@?c i LM|@? 6 ' %W n n "
hLLu Lu ThLTLt|L?
`i tMt|||i uLh 6 uhL4 i^@|L? ES |L i Thitt |i L*@|*|) UL?t|h@?| @t
.E62 ' .E%W2 n 2.E 2 n .E"2 2
@?_ |L i Thitt |i LMiU|i @t
.d6%So ' .E%W%S n .E%S n .E"%S ' .E%W %S n .E2
Eb
Ai ThLM*i4 ?L hi_Uit |L |i ULUi Lu @?_ " 5?Ui " L?*) @TTi@ht ? |i ?i^@*|)
UL?t|h@?|c i ULLti " ' f |L i@!i? |@| UL?t|h@?| @t 4U @t TLttM*i L i @i @
*?i@h LMiU|i tMiU| |L @ ^@_h@|U UL?t|h@?|c @?_ L?i T@h@4i|ih |L ULLti 5L *L?}
@t 9' f tL .E2 9' fc |i L*@|*|) UL?t|h@?| M?_t @?_ i t4T*) TU! |L t@|tu) |i
UL?t|h@?|c *i@_?} |L i^@|L? Ef ,^@|L?t EH @?_ Eb uL**L M) tMt|||?} ?|L
i^@|L? ES @?_ ?|L |i LMiU|ic i^@|L? Eb
Ai 5@hTi h@|L ML?_ 4t| Mi }hi@|ih |@? Lh i^@* |L |@| }i?ih@|i_ M) |i M@tt
@tti|tc 2 .E%W2 ' T .E
3 Tc
Lu ULhtic Lh |ihi t ?L _tUL?| u@U|Lh |@| ii?
t@|tit |i UL?t|h@?|t Wu ' f |i? |i L*@|*|) UL?t|h@?| _Lit ?L| M?_ ?) _tUL?|
u@U|Lh 6 |@| t@|tit |i ThU?} UL?t|h@?| ThL_Uit |i t@4i ThUi uLh %S c tL ' '
.E%W %S hLLu Lu ThLTLt|L? 2
#i?L|i M) l @?_ l2EU |i UL?t|h@?| ti|t L? 6 c 62 _i?i_ M) Eb @?_ E2f hitTiU
.
|i*) Nt?} |i *@ Lu |ih@|i_ i TiU|@|L?tc i U@? h|i
f ' 4?
4?
t6 Ml t62 Ml2 EU .f d6 .E62%S2 o 5TTLti |i tL*|L? |L |t ThLM*i4 }it . E62%S2 : ? tL4i t|@|i Lu ?@|hi @| |4i
Wu |t ihi |hic L?i UL*_ *Lih . E62 %S2 ? |@| t|@|i |L| L*@|?} @?) Lu |i
UL?t|h@?|tc M) _i?|L? Lu 5?Ui 6 : fc |t @U|L? L*_ *Lih .f d6 .E62%S2 oc
UL?|h@h) |L |i @tt4T|L? |@| i t|@h|i_ @| @ tL*|L? |L |i |LTihL_ ThLM*i4
hLLu Lu *i44@ 2
`i ihu) |@| \ t@|tit |i M@tU ThU?} i^@|L? E2c uLh |i ht! uhii h@|i @?_ M@tt
@tti|t wMih@**) t?} .E_7_ ' f @?_ .E_5_ ' fc
#
_\
.|
\
#
_\7
.|
\7
$
#
(
_7
n _| ' .|
7
7
$
$
' o_|
#
_\W
n .|
\W
$
#
_\W _7
n .|
\W 7
$
n
(
_| '
7
(
' >7 o >
7 P7 j7 j7 n
_| ' f
7
3
?*) u L*_t M) ThLiU|L?c @t ? *i44@
hLLu Lu ThLTLt|L? 5Mt|||?} i^@|L? E2b ?|L |i ThLM*i4 E2H ? Lh_ih |L 4TLti |i ThU?} UL?t|h@?|c
|i ThLM*i4 t
%
&
#
$
#
$
%S
_E\W
_
_\W2
2
f ' _| n .|
4?
.
_
t|
.
|
|
t
\W _|
\W2
Nt?} i^@|L? E uLh _* ? |i *@t| |ih4c |i ThLM*i4 t
%
&
#
$
%S
_E\W
_\W2
2
f'
n .|
4?
j
t|
.
|
t
_|
\W
_|
\W2
Eef
At t @ *?i@h LMiU|i ? | @ ^@_h@|U UL?t|h@?| AihiuLhic @t *L?} @t j 9' fc
|i UL?t|h@?| M?_t @?_ |i LT|4@* t }i? M) Ee ' }it |i 4@ 44 t?Ui
: f *}}?} |i LT|4@* @*i uLh ? Eef }it
j j
%
&
%S
_ E\W f'
n .|
j
_|
\W
H
6Lh U*@h|)c @?_ i T*L|?} |i u@U| |@| _\W _Lit ?L| *L@_ L? _c i h|i |i 4__*i |ih4
@t
%
&
#
_ E\W
_\W
'
>
o
n
j5 _5
.|
.
|
_|
\W
_|
\W
$
Wu j ' fc @?) *i@_t |L |i t@4i ThUi ML?_ W? |t U@ti i U@? 4Lt| t4T*) |@!i
' f
b
.
6}hi U@T|L?t
6}hi T|L? ThUi ML?_t @t @ u?U|L? Lu t|LU! ThUi T|L?t @i |hii 4L?|t |L
i Th@|L? @?_ t|h!i ThUi g ' mff Ai ML?_t @tt4i ?L |h@_?} ?|* i Th@|L?c @?_
@ _tUL?| u@U|Lh L*@|*|) ML?_ ' f ULhhitTL?_?} |L |Ui |i 4@h!i| 5@hTi h@|L
Ai t|LU! t *L}?Lh4@**) _t|hM|i_ | T@h@4i|iht U@*Mh@|i_ |L @? ?_i LT|L?
6}hi 2 L|@|L? @?_ }iL4i|h) f ' tT@Ui Lu TLh|uL*Lt Lu M@tt@tti| T@)Lgt
'
M@tt @tti| T@)Lgt %S ' uLUt @tti| T@)Lg %S ' Mit| @TThL 4@|i i_}i ' hit_@*
Ai t|h@}| _@ti_ *?i 6 G T ' .E6 t |i tT@Ui Lu @** _tUL?| u@U|Lht |@| ThUi |i
M@tt T@)Lgt Ai tL*_ t|h@}| *?i 4@h!i_ 6 : f t |i tT@Ui Lu @** TLt|i _tUL?|
u@U|Lht |@| ThUi |i M@tt @tti|t Ai _@ti_ UhU*i t |i ti| Lu @** h@?_L4 @h@M*it |
tiUL?_ 4L4i?| *itt |@? 2 6}hi L?_t L? LT|L? @*it | |hii 4L?|t |L i Th@|L?c ?L ?|ih4i_@|i
|h@_?} T|L?t @hi i_}i_ | t|LU!c ?|ihit| h@|ic @?_ LT|L?t Lti ThUit @?_ t|h!it
@hi 4@h!i_ | t^@hit
6}hi e L?_t L? LT|L? ThUit _i*|@t Y*Y7 | |hii 4L?|t |L i Th@|L?c ?L
?|ih4i_@|i |h@_?}
6}hi D *|?L4@* hi|h? _t|hM|L? ||i_ uhL4 +5 5:Dff ii!*) hi|h? _@|@
Ai T*t t}?t 4@h! hi|h? LMtih@|L?t *@h}ih |@? n% DIc @t 4i@thi_ L? |i @ t
Aih i}| t @hM|h@h)
6}hi S NTTih @?_ *Lih }LL__i@* ML?_t uLh 5:Dff ?_i LT|L?t | 4L?|t
|L i Th@|L? @?_ t|h!i ThUi g ' ff Ai t|LU! hi|h? uL**Lt @ 4*|?L4@* _t|hM|L?
||i_ |L 5:Dff hi|h? _@|@ ,@U LT|L? t i_}i_ | |i ?_i @?_ @ DI ht!uhii h@|i
Oi_}i TLh|uL*Lt 4@) Mi U@?}i_ ii!*)
6}hi . W4T*i_ L*@|*|it uLh , 5:Dff ?_i T| LT|L?t | 4L?|t |L
i Th@|L?c bbS
6}hi H BLL__i@* ML?_t uLh @ ,hLTi@? U@** LT|L? h||i? L? @? ii?| T Lti
tLU!t @hi ULhhi*@|i_ fb | |i t|LU! ?_i tLU!t L?|?Lt |h@_?} t @**Li_ Ahii
4L?|t |L i Th@|L?c @?_ L|ih T@h@4i|iht 4@|U |i ?_i ef
H
H
*}iMh@ TTi?_
@h|@* _gihi?|@* i^@|L?
hLLu Lu ThLTLt|L? Ee `i }itt |@| |i ML?_ t @ |Ui_gihi?|@M*i u?U|L? Lu |i
t|@|i @h@M*itc
' E7c Tc |
Ai?c i U@? ti W|L<t *i44@ |L hi*@|i |i |ih4t > c j5 c j ? |i *@ Lu 4L|L? uLh c
_
' > _| n j5 _5 n j _
|L T@h|@* _ih@|it Lu |i u?U|L? E7c Tc |G
_ ' | _| n 7 _7 n T _T
[
[
[
n
7 7 _7 _7 n
T T _T _T n
7 T _7 _T
2 c
2 c
c
ihi % _i?L|it YE7c Tc |*Y% 5Mt|||?} uLh |i 7 @?_ T ThLUittit uhL4 i^@|L?t
E2D @?_ E2Sc
_ ' | _| n E7 7 E>7 _| n j7 _5 n T E>T _| n jT 5 _5 n jT _ n
5
?7
?T
[
[
7
n
7 7 7 7 j7 j7 n
T T EjT 5 jT 5 n jT jT 2
2
n
c '
?
?T
7 [
[
' '
c '
6
7 T 7 j7 jT 5 8 _|c
ihi E7 7 ?_U@|it i*i4i?| M) i*i4i?| 4*|T*U@|L?c @?_ jT 5 _i?L|it |i | hL
Lu jT 5 c i|U AihiuLhic i U@? h|i > @?_ j5 c j ? |ih4t Lu _ih@|it Lu |i E
u?U|L?c
> ' | n E7 7 >7 n T >T n
n
[
7 7 7 7 j7 j7 2
[
[
T T EjT 5 jT 5 n jT jT n
7 T 7 j7 jT 5
2
@?_
j5 ' E77 j7 n T jT 5
j ' T jT e
`i hiULih |i |ih4t ?ii_i_ ? i^@|L? ES
2 j j
' T jT jT T
@?_
j5 j7 P3
7 ' dE7 7 j7 n T jT 5 o j7 P3
7
7 >
7 >
' E7 7 >
7 n T jT 5 j7 P3
7 7 >
*}}?} |iti i ThittL?t ? hit|hU|L? ES @?_ t4T*u)?}c i LM|@? |i T@h|@* _gih
i?|@* i^@|L? }i? ? ThLTLt|L? Ee
H2
H2
@*U*@|?} ML?_t ? |i *L}?Lh4@* i?hL?4i?|
VL*@|*|) UL?t|h@?|
Ai t|LU! hi|h? - ' 7A *7 t *L}?Lh4@**) _t|hM|i_c | 4L4i?|t
s
. E*? - ' > j2 A ( j E*? - ' j A
2
Ai hi^hi_ 4L4i?|t @hi 4Lt| i@t*) t44@h3i_ ? @ tiUL?_ 4L4i?| 4@|h |
%
.
ihi
%S2
%S
%S &
] "
5
k
' - -s
6
7 2 k2 2g7k n g 2 kf
2 A
9
:
E2
>
n
j
'7
e
8
7k2 gk
eoA E7k gkf eEon>A e2oA
#
$
*? Eg*7 >A
s
s
kf '
s E- _- ' n j A
2
g*7
j A
#
$
] "
s
*? Eg*7 >A
>A
s
j A
k '
-s E- _- ' e 2
g*7
j A
#
$
] "
s
2 A
*?
Eg*7
>A
2
>
n
j
2
s
k2 '
- s E- _- ' eE
j A
2
g*7
j A
@?_ E ' x E t |i h}| |@* Lu |i ?Lh4@* _i?t|) Ai h}| @?_ t_i Lu |iti
i ThittL?t uL**L uhL4 t|@?_@h_ ThLTih|it Lu *L}?Lh4@* _t|hM|L?t | tL4i |i_Lt
@*}iMh@ *}}?} |iti uLh4*@t ?|L E }it |i ML?_ | t*@U! TLt||) UL?t|h@?|
e2
l
c
H22
iU!?} 6 f
AL UiU! |@| |i _tUL?| u@U|Lh ThL_Ui_ M) |i @?@*)|U tL*|L? t TLt|ic i i Thitt
| @t @ TLh|uL*L Lu |i t|LU! ML?_ @?_ LT|L? Ai?c t?Ui |i ?|ihit| h@|i @?_ t|LU! hi|h?
@hi ?L??i}@|ic |i i}|t Lu |i _tUL?| u@U|Lh L? i@U Lu |i t|LU!c ML?_c @?_ LT|L?
4t| Mi TLt|i Wic ? Lh_ih uLh
K
7A
n S-s n _E4@ E7A gc f f
7
|L L*_ @t 7A h@?}it Lih Efc 4c i 4t| @i
S f
K
Ee
g
n S-s f
7
K
n _ f
7
AL ?_ |i i}|t Lu 6 L? |i t|LU! ML?_ @?_ LT|L?c i tMt|||i uhL4 |i _i?|L?c
| @ ' n uLh TTih ML?_ @?_ @ ' uLh *Lih ML?_ 5|@h| |
6 ' %W n @
6hL4 |i _i?|L?tc
%W ' T .E
3
' %S %S
%S ' .E%S .E
3
i U@? h|i
6 ' T .E
3
n @E%S .E%S .E
3
@?_ i?Uic
6 ' ET @.E%S .E
At i ThittL? }it 6 ? |ih4t Lu |t i}|t L?
3
@?_ %S `i t|** ?ii_ c
y
x 2
x .E%W2 'w
2
. E e
n @%S
Ee2
`U i i@*@|i t?} |i _i?|L?tc
.E%W2 ' T .E
3
T
.E2 ' .E%S2 . %S2 ' .E%S2 .E%S .E
. E %S 3
L i U@? UiU! i|ih Ee2 t@|tit |i hit|hU|L?t Lu Ee
H2
Lt||) UL?t|h@?|
W? |i TLt||) U@tic i ?ii_ |L i@*@|i |i tiUL?_ 4L4i?| Lu @ U@?__@|i _tUL?| u@U|Lhc
i^@|L? ES `i @}@? i@*@|i ?|i}h@*t @}@?t| |i *L}?Lh4@* _i?t|) uLh |i t|LU! hi|h?
.
;%
?
=
%S
n
B
b
&n2 <
@
>
'
] "
f
5
4@ 7
7 4@
s
- g
7 c f n bf - n b -
B
62
c f8 s E- _-
A@!?} L?*) |i T@h| Lu |i ?|i}h@* ihi |i L|ih 4@ LTih@|Lh t TLt|ic @?_ Mhi@!?}
T |i ?|i}h@* @UULh_?} |L |i @*i Lu |i ?|ihLh 4@ c i LM|@?
]
k
l
s g n Eb n 7 - 2 s E- _- n
b
s
f
B 2 Ebf - 3g B nEb n7- fc -: g7
k
l
]
s n b - 2 s E- _-
n 2 bf -s nb b
f
B
fc - g
B
7
L i i Thitt |i *4|t L? |i ?|i}h@*t @t h@?}it uLh |i h@?_L4 @h@M*i - 5?Ui
L?i ?ih|t @?_ : LTih@|Lht i? 4*|T*)?} M) @ ?i}@|i ?4Mihc |i hit*| _iTi?_t
L? |i t}?t Lu |i |ih4t 4*|T*)?} - ? |i ?|i}h@*t 6Lh |i ht| ?|i}h@* i @i
;
g - g 3bf -s
? b n7 : f G
B
7
b n7
g c g 3bf -s - 4 = b n7 f G 4@
B
7
b n7
54*@h*)c |i h@?}i uLh |i tiUL?_ ?|ih@* t
;
? b : f G f - 4? g c bf -s
B
7
b
bf -s - g
= b f G
B
b
7
Bi? |iti h@?}itc i ti |i u@U| |@| uLh - Q E>Ac j 2 A ci @i
] K
@
ES n _-2 s E- _- '
2
>n j2 k
s s l
' S dx EK x E@ o n 2S_e
x KW j A x @W j A n
k s s l
2
n_2 e2E>nj x KW 2j A x @W 2j A
2
W
W
ee
ihi
@W '
*? @ >A W *? K >A
s
s
c K '
j A
j A
L i U@? i@*@|i |i i TiU|@|L? ? i^@|L? ES uLh @?) @*i Lu Ebc Bc tL i U@?
ti@hU uLh EbcB |L 4?43i Lh 4@ 43i |i LT|L? @*i
H2e
*|T*i LT|L? ?|i}h@*t
Nt?} |i ?|i}h@* @}@?t| |i *L}?Lh4@* _i?t|)c i U@? ?_ |i UhLtt 4L4i?| Mi|ii? |L
U@** LT|L?t | t|h!it g @?_ g c
. %S%S ' 7 2k2 Eg4@ Eg n g 7kEg4@ n g g kf Eg4@ ihi g4@ ' 4@ Eg c g `i @*tL ti |i *L}?Lh4@* _i?t|) |L i@*@|i @?@*)|U@**) |i
LMiU|i uLh |i ML?_ | @ TLt|i _tUL?| u@U|Lhc i^@|L? ES
`i @hi @**Li_ |L |h@_i ? LT|L?t E LT|L?t i? i ?U*_i |i LT|L? i @hi
|h)?} |L ThUi At i h|i
.
;%
?
=
%S
n
B
b
&n2 <
@
>
'
] "
f
5
4@ 7
S
g c f n b
s
b
7
4@
n - n b n2 '
7
B
62
c f8 s E- _-
ihi b ' u |i ?_i hiuiht |L |i LT|L? i @hi |h)?} |L ThUi @?_ ihi |L| *Ltt
Lu }i?ih@*|) i @tt4i |@|
g g2 g A@!?} L?*) |i T@h| Lu |i ?|i}h@* ihi |i L|ih 4@ LTih@|Lh t TLt|ic
;%
?
%S n b
. =
B
&n2 <
@
>
'
ihi
('
] "
(f
5S
62
b 7 4@ - g c f n b
s nb
n
n2
7
7 '
8
B
s E- _-
S
g
s
' b 7 4@ - 7 c f n b n - n b n2 -
B
L i Mhi@! T |i ?|i}h@* tUUitti*) @UULh_?} |L |i @*i Lu |i ?|ihLh 4@ 43@
|L?tc t|@h|?} M) |@| ULhhitTL?_?} |L |i LT|L? | |i *@h}it| t|h!i
;%
?
%S n b
. =
B
&n2 <
@
%
&2
]" [
g
s
' 2
b 7 4@ - c f n b n- n b n2- s E- _>
B (f '
7
eD
53
4
3
4
62
[
[
]
7Cb n -s D
C
' 2
b
g
n
b
n
b 7 D -8 s E- _-n
n2
B u fc -: g7
'
'
53
4
3
4
62
[
[
]
s
7
C
D
C
n n 2
b n- b g n b n2 n
b 7 D -8 s E- _-n
B u fc -: g7 c- g7n
'
'
]
k
l
2
s nb
b
s E- _n n 2 b n -s nb n2 n
n2
g
B
fc - 7
B
ihi
b n -s u? '
u '
S
S
b
g
n
b
n
b
7
n2
' ' B
S
S
b n-s ' b g n b n2 n ' b 7 -
B
`i i Thitt |i *4|t L? |i ?|i}h@*t @t h@?}it uLh |i h@?_L4 @h@M*i - }@?c |i
hit*| _iTi?_t L? |i t}?t Lu |i |ih4t 4*|T*)?} - ? |i ?|i}h@*t 6Lh |i ht| ?|i}h@*
i @i
S
S
;
b n2 n b7
3b n -s n ' b g
A
g
' A
S
A
:fG
?
B
7 -
b n2 n '$b 7
#
S
S
s
b
n
b
7
3
b
n
b
g
A
n2
A
' f G 4@ g c n S ' - 4
A
=
B
7
b n2 n b 7
'
54*@h*)c uLh |i | ?|i}h@* i @i
;
#
$
S
s S b g
A
b n2 n ' b 7
A
gn 3b n - n
g
'
A
A
: f G 7 - 4?
?
B
7 c b n2 nS b 7
#
$ '
S
S
s
A
b
n
b
7
3
b
n
b
g
n2
A
' f G 4@ g c n S ' - gn
A
A
=
B
7
7
b n2 n b 7
'
@?_ ?@**) uLh |i *@t| ?|i}h@*
;
s
? b n2 : f G f - 4? g c b n B
7
b n2
b n -s
g
= b n2 f G
b n2 - 7
B
Bi? |iti h@?}itc i U@? i@*@|i |i i TiU|@|L? ? i^@|L? ES uLh @?) @*i Lu
Ebc Bc tL i U@? ti@hU uLh EbcB |L 4?43i Lh 4@ 43i |i LT|L? @*i
H
@tt ht!
+it|@|?} |i ThLM*i4c |ihi t @ tiUh|) |@| uL**Lt
_7
' >7 _| n j7 _5
7
eS
Aihi t @*tL @ ht!uhii h@|i o ? LT|L? t h||i? L? @? ?_ih*)?}c ?L?|h@_i_ ii?| T
Lti @*i t 4TihuiU|*) ULhhi*@|i_ | |i |h@_i_ tiUh|)
_T
' >T _| n jT 5 _5 n jT _
T
Ai tLU!t @hi Lh|L}L?@*3i_ |L
.E_5 2 ' .E_2 ' c .E_5_ ' f
`i @?| |L ThUi @ ,hLTi@? U@** LT|L? L? T c Lti |ih4?@* T@)Lg t
%SA ' 4@ ETA gc f
`i ThLUii_ M) U@h@U|ih3?} |i _tUL?| u@U|Lh ThLUitt h@|ih |@? tL*i @ T@h|@*
_gihi?|@* i^@|L?
s
_\
' o_| _5 n @ 2 2 _
\
ihi
>7 o
j7
@?_ @ ' n uLh |i TTih ML?_ @?_ @ ' uLh |i *Lih ML?_ Ai TTih @?_ *Lih
7 '
ThUi ML?_t @hi |ihiuLhi }i? M)
\A
f ' .
4@ ETA gc f \f
Ai t4T*i uLh4 Lu |i 7c T @?_ \ ThLUittit 4i@? |@| |i) @hi L?|*) *L}?Lh4@**) _t
|hM|i_c
s
>7 j72 A n j7 A 05
2
s
s
TA
2
' i T >T jT A n jT 5 A 05 n jT A 0
Tf
2
t
s
s
\A
2
2
2
' i T o A 7 A 05 n @ 7 A 0
\f
2
ihi 05 @?_ 0 @hi ?_iTi?_i?| ?Lh4@* Efc h@?_L4 @h@M*itc @?_
7A
'i T
7f
_T 2
jT ' .| 2 ' jT2 5 n jT2 T
2
`i U@? t4T*) TihuLh4 |i ?|i}h@* _i??} |i i TiU|@|L? Ai LT|L? t ? |i 4L?i)
i?
I
I
2
TA ' TfeE>T 3 2 jT A njT 5 A 05 njT A 0 : g
e.
*?Eg*Tf 2 s
s
jT 5 05 n jT 0 :
>T jT
A
2
A
`| @ _LM*i ?|i}h@* ? t}|c @ U@?}i Lu @h@M*it t tiu* #i?i ?i tLU!t
jT 0 n jT 5 05
jT
jT 5 0 jT 05
'
jT
B '
B2
Lhc ?ih|?}
jT B n jT 5 B2
jT
jT 5 B jT B2
05 '
jT
0 '
B @?_ B2 @hi @*tL ?_iTi?_i?| ?Lh4@* Efc @h@M*it Ai?c |i LT|L? t ? |i 4L?i) i?
*?Eg*Tf >T 2 jT2 A
s
B :
jT A
, Thitt?} |i i*i4i?|t Lu |i ?|i}h@?_ ? |ih4t Lu |i ?i tLU!tc
I
\A
'i T
\f
%
2
TA ' TfeE>T 3 2 jT A njT A B
t
s jT 5 B jT B2
s jT B n jT 5 B2
o 2 A 7 A
n @ 2 27 A
2
jT
jT
&
6
5
t
t
2 2 j
2 2 j
j
n
@
B
n
j
n
@
7 T5
7 T
s
7 T
7 T 5 B2 :
9
2
\A
9
:
' i T 7 o A n A
8
\f
2
jT
\A
\f
' i T
o 2 A 2
t
5
t
6
7 jT 5 n @ 2 27 jT s
7 jT n @ 2 27 jT 5 s
i T7
A B n
A B2 8
jT
jT
Lhc
\A
'i T
\f
k s
l
s
o 2 A i T K A B n K2 A B2
2
|
t
K
7 jT 5 n @ 2 27 jT '
jT
K2
7 jT n @ 2 27 jT 5
'
jT
t
eH
L|i ELh _hiU|*) M) *LL!?} @| @h@?Ui Lu \
K2
n
K22
'
'
'
'
%
t
t
2
2 2 j
j
n
@
n
j
n
@
2 27 jT 5
7 T5
7 T
7 T
jT2
l
k 2 2
2
2
2
2
2 2
2
2
2
2
j
n
@
E
j
n
j
n
@
E
j
7 T
7 T
7 T5 '
jT2 7 T 5
l
k 2 2
2
2
2
j
n
E
j
7 T '
jT2 7 T
2 2 &
'
Lc |i ?|i}h@*
'
I
E3o3 2 2 A ] ]
>T 3 2 jT2 A njT A B
E
e
T
e
g
f
*?Eg*Tf 3E>T 3 j2 A
2 T
2Z
I
B2 cB :
jT A
I
I
2 2
K
A
B
n
K
A
B
3
B
3
B
e 2 2 e 2 2 2
]
]
I
I
2
>T 3o3 2 EjT2 n2 oA
K
EjT nK A B 3 2 B2
d
2 A B2 3 2 B2
'
e
e
Tf e
2
*?Eg*Tf 3E>T 3 j A
2 T
2Z
B2
I
B :
jT A
]
]
I
I
2
2
K A B 3 2 B2 geE3o3 2 A
eK2 A B2 3 2 B2
e
2
*?Eg*Tf 3E>T 3 2 j A
T
2Z
B2
B :
jT IA
Ai ??ih ?|i}h@*t @hi |h?U@|i_ *L}?Lh4@*t Nti |i u@U| |@|
2
EB3K2
2
]
K2 ]
KB
3 B2
s
s
e2
e e _B '
e3 2 _B ' e 2 K E% Kc
B3K:%3K
2Z B:%
2Z
ihi E _i?L|it |i @hi@ ?_ih |i h}| |@* Lu |i ?Lh4@* _t|hM|L? TT*)?} |t
u@U|c
2
2
2
' s TfeE>T 3o3 2 EjT n A e 2 EjT nK A 2Z
3
4
]
I
s
*?Eg*Tf >T 2 jT2 A
2
s
C
EjT n K A D eK2 A B2 3 2 B2 B2
jT A
3
4
]
I
s
*?Eg*Tf >T 2 jT2 A
2
3o3 2 2 A 2 K2 A
E
C
D
s
s
ge
e
K A
eK2 A B2 3 2 B2 B2
2Z
jT A
L i U@? TihuLh4 |i tiUL?_ ?|i}h@|L? Aiti @hi i TiU|@|L?t Lu *L}?Lh4@*tc
2
] KB 3B2 *2
K2 ] 3 EB3K2
s
e e
_B ' s e 2 e 2 _B ' e 2 K
2Z
2Z
eb
tLc ?@**)
3
' TfeE>T 3o
3 2
geE3o
4
2
2 nE
2
3
3 2
s
*?Eg*Tf >T 2 jT2 A
jT nK oA C
s
EjT n K A D jT A
E jT A e dK
2
2n 2
4
s
*?Eg*Tf >T 2 jT2 A
A e EK K A C
s
K A D jT A
2
2
2n 2
2
54T*u)?}c
2 n jT2 n K22 n EjT n K 2
' 2 jT2 n K22 n jT2 n K2 n 2jT K
3
' 2jT K ' 2jT C
t
7 jT 5 n @ 2 27 jT jT
t
4
D'
' 27 jT 5 n 2@ 2 27 jT @?_
t
jT n K
7 jT 5 n @ 2 27 jT ' jT n
'
jT
t
jT2 7 jT 5 n @ 2 27 jT '
jT
tLc
3
E *?Eg*Tf >T n
s
2
2
' TfeE>T 3o37 jT 5 n@ 37 jT A E
C
3
2
2 jT
7 jT 5 n @
s
jT A
t
t
2
2 j
4
7 T A F
F
D
4
2
2
2
E *?Eg*Tf >T 2 jT 7 jT 5 n @ 7 jT A F
3oA
F
s
ge E
C
D
jT A
3
t
E *?Eg*Tf >T 7 jT 5 n @
2
2
s
' Tfe3oA eE>T 37 jT 5 n@ 37 jT A E
C
jT A
s
3
t
E *?Eg*Tf >T 7 jT 5 n @
s
ge3oA E
C
jT A
Df
2
2 j
7 T A
2
2 j
7 T A
4
s F
n jT A F
D
2
4
s F
jT A F
D
2
AL uh|ih t4T*u)c *i|
t
# ' >T o 7 jT 5 n @ 2 27 jT t
7 jT 5 n @ 2 27 jT ' >T o n jT
'
jT
t
7 jT 5 n @ 2 27 jT ' >T o n jT
'
jT
3
# ' >T o jT C
%
# '
v
2 t
7
4 @ 72 42 D
v
#
t
>T o >7 o
2
4@
42
jT
j7
27
%
#
v
t
2
# ' T 7 4 @
42
27
ihi
4
#
_T _7
jT 5
4'
' ULhh
c
jT
T 7
T '
$&
jT
$&
jT
$
>T o
jT
Ai?c i @i
#
*?Eg*Tf E# n o A
s
' Tf
jT A
#
*?Eg*Tf E# n o A
3oA
s
ge jT A
e#A $
s
jT A 2
$
s
n jT A 2
AL UL?ih| uhL4 |i h}| |@* Lu |i ?Lh4@* _i?t|) E |L |i *iu| |@* Ec ti
E% ' E%
#
*?ETf *g n E# n o A
s
' Tf
n
jT A
#
*?ETf*g n E# n o A
3oA
s
ge jT A
e#A D
$
s
jT A 2
$
s
jT A 2
6}hi G T|L? ThUi ML?_t @t @ u?U|L? Lu t|LU! ThUi T|L?t @i |hii 4L?|t |L
i Th@|L? @?_ t|h!i ThUi g ' mff Ai ML?_t @tt4i ?L |h@_?} ?|* i Th@|L?c @?_
@ _tUL?| u@U|Lh L*@|*|) ML?_ ' f ULhhitTL?_?} |L |Ui |i 4@h!i| 5@hTi h@|L
Ai t|LU! t *L}?Lh4@**) _t|hM|i_ | T@h@4i|iht U@*Mh@|i_ |L @? ?_i LT|L?
D2
X
x^ c
m>0
x
w
xc
x*
E(m2)<A2
m: p = E(mx)
6}hi 2G L|@|L? @?_ }iL4i|h) f ' tT@Ui Lu TLh|uL*Lt Lu M@tt@tti| T@)Lgt ' M@tt
@tti| T@)Lgt %S ' uLUt @tti| T@)Lg %
S ' Mit| @TThL 4@|i i_}i ' hit_@* Ai
t|h@}| _@ti_ *?i 6 G T ' .E6 t |i tT@Ui Lu @** _tUL?| u@U|Lht |@| ThUi |i M@tt
T@)Lgt Ai tL*_ t|h@}| *?i 4@h!i_ 6 : f t |i tT@Ui Lu @** TLt|i _tUL?| u@U|Lht
|@| ThUi |i M@tt @tti|t Ai _@ti_ UhU*i t |i ti| Lu @** h@?_L4 @h@M*it | tiUL?_
4L4i?| *itt |@? 2 D
6}hi G L?_t L? LT|L? @*it | |hii 4L?|t |L i Th@|L?c ?L ?|ih4i_@|i |h@_?}
T|L?t @hi i_}i_ | t|LU!c ?|ihit| h@|ic @?_ LT|L?t Lti ThUit @?_ t|h!it @hi
4@h!i_ | t^@hit
De
6}hi eG L?_t L? LT|L? ThUit _i*|@t Y*Y7 | |hii 4L?|t |L i Th@|L?c ?L ?|ih
4i_@|i |h@_?}
DD
6}hi DG *|?L4@* hi|h? _t|hM|L? ||i_ uhL4 +5 5:Dff ii!*) hi|h? _@|@
Ai T*t t}?t 4@h! hi|h? LMtih@|L?t *@h}ih |@? n% DIc @t 4i@thi_ L? |i @ t
Aih i}| t @hM|h@h)
DS
6}hi SG NTTih @?_ *Lih }LL__i@* ML?_t uLh 5:Dff ?_i LT|L?t | 4L?|t |L
i Th@|L? @?_ t|h!i ThUi g ' mff Ai t|LU! hi|h? uL**Lt @ 4*|?L4@* _t|hM|L?
||i_ |L 5:Dff hi|h? _@|@ ,@U LT|L? t i_}i_ | |i ?_i @?_ @ DI ht!uhii h@|i
Oi_}i TLh|uL*Lt 4@) Mi U@?}i_ ii!*)
D.
6}hi .G W4T*i_ L*@|*|it uLh , 5:Dff ?_i T| LT|L?t | 4L?|t |L i T
h@|L?c bbS
DH
6}hi HG BLL__i@* ML?_t uLh @ ,hLTi@? U@** LT|L? h||i? L? @? ii?| T Lti tLU!t
@hi ULhhi*@|i_ fb | |i t|LU! ?_i tLU!t UL?|?Lt |h@_?} t @**Li_ Ahii 4L?|t
|L i Th@|L?c @?_ L|ih T@h@4i|iht 4@|U |i ?_i Db
© Copyright 2026 Paperzz