Pxowlsoh Htxloleuld dqg Plqlpxp
Zdjhv lq Oderu Pdunhwv zlwk
Lqirupdwlrqdo Iulfwlrqv dqg
Khwhurjhqhrxv Surgxfwlrq
Whfkqrorjlhv
Jhudug M1 ydq ghq Ehuj
Qryhpehu 6/ 4<<<
Devwudfw
Lw lv riwhq dujxhg wkdw d pdqgdwru| plqlpxp zdjh lv elqglqj rqo| li wkh
zdjh ghqvlw| glvsod|v d vslnh dw lw1 Lq wklv sdshu zh dqdo|}h d prgho zlwk
zdjh vhwwlqj/ vhdufk iulfwlrqv/ dqg khwhurjhqhrxv surgxfwlrq whfkqrorjlhv/
lq zklfk lpsrvlwlrq ri d plqlpxp zdjh dhfwv zdjhv hyhq wkrxjk/ diwhu
lpsrvlwlrq/ wkh orzhvw zdjh lq wkh pdunhw h{fhhgv wkh plqlpxp zdjh/ dqg
vxevhtxhqw derolwlrq ri wkh plqlpxp zdjh grhv qrw dhfw zdjhv1 Wkh
prgho kdv pxowlsoh htxloleuld dv d uhvxow ri wkh idfw wkdw wkh uhvhuydwlrq
zdjh ri wkh xqhpsor|hg dqg wkh orzhvw surgxfwlrq whfkqrorj| lq xvh di0
ihfw hdfk rwkhu1 Xqghu fhuwdlq frqglwlrqv/ lpsrvlwlrq ri d plqlpxp zdjh
lpsuryhv vrfldo zhoiduh1
Ghsduwphqw
ri Hfrqrplfv/ Iuhh Xqlyhuvlw| Dpvwhugdp/ Gh Erhohoddq 4438/
43;4 KY Dpvwhugdp/ Wkh Qhwkhuodqgv/ FHSU/ dqg Wlqehujhq Lqvwlwxwh1
H0pdlo= jehujChfrq1yx1qo1
Nh|zrugv= zdjhv/ surgxfwlylw|/ mre vhdufk/ xqhpsor|phqw/ lpshuihfw lqirupdwlrq1
Wkdqnv wr Ndwkdulqd Ulfkdugvrq/ Mlp Doeuhfkw/ dqg sduwlflsdqwv dw wkh Zrunvkrs lq Hpslulfdo
Hfrqrplfv ri wkh Xqlyhuvlw| ri Fklfdjr/ iru xvhixo frpphqwv1
4
Lqwurgxfwlrq
Ai igiU| Lu @ 4?44 @}i L? ?i4T*L)4i?| @t Mii? tMiU| Lu @ *@h}i ?4
Mih Lu i4ThU@* t|_it +iUi?|*)c @h_ @?_ khi}ih EbbD @i U@t| _LM| L?
|i TihUii_ t_L4 |@| |t igiU| t TLt|i *|L} |ih hit*|t @hi tL4i
@| UL?|hLiht@*c |i) @i Mii? ?i?|@* @t i** Etii uLh i @4T*i ki??@?c
bbD AL ThL_i @ |iLhi|U@* i T*@?@|L? Lu @ 3ihL ELh ?i}@|i igiU|c @h_
@?_ khi}ih EbbD ?| @| 4L?LTtL?) 4L_i*t Lu |i *@MLh 4@h!i| Ah@_|L?@**)c
|i Thiti?Ui Lu 4L?LTtL?) TLih @t Mii? @ttLU@|i_ | }iL}h@TU@**) tL*
@|i_ 4@h!i|tc @?_ @t tU |i hi*i@?Ui Lu 4L?LTtL?) 4L_i*t @t Mii? T| ?|L
^it|L? OLiihc | t M) ?L i**!?L? |@| |i Thiti?Ui Lu ?uLh4@|L?@*
uhU|L?t ELh ti@hU uhU|L?t L? |i *@MLh 4@h!i| }it i4T*L)iht 4L?LTtL?)
TLih @t i**2 @tU@**)c u h4t T@) @}it |@| @hi t|hU|*) t4@**ih |@? |i
ThL_U||) *ii* Lu |i Lh!iht |i? |i) U@? t|** 4@?|@? @ TLt|i Lh!uLhUi
@?_ i@h? @ ThL|c MiU@ti | |@!it |4i uLh |i Lh!iht |L ?_ @ Mi||ih T@)?}
LM
Ai 4TLt|L? Lu @ 4@?_@|Lh) 4?44 @}i hi_Uit |i _i}hii |L U
i4T*L)iht U@? i T*L| |ih 4L?LTtL?) TLih t *L?} @t |i 4?44 @}i _Lit
?L| i Uii_ |i ThL_U||) *ii*c | 4ihi*) hi_t|hM|it T@h| Lu |i hi?|t Lu |i
4@|U uhL4 |i h4 |L |i Lh!ihc @?_ @t tU | _iUhi@tit |i _gihi?Ui Mi|ii?
4@h}?@* *@MLh ThL_U||) @?_ |i @}i W? @ M@tU i^*Mh4 ti@hU 4L_i*
uh@4iLh!c |t tu|t |i L*i @}i _t|hM|L? T@h_c M| ?i4T*L)4i?| t
?L| @giU|i_ Etii V@? _i? ih} @?_ +__ihc bbH W? 4Lhi }i?ih@* uh@4iLh!tc
?i4T*L)4i?| _iUhi@tit u |i T@h_ tu| Lu |i @}i _t|hM|L? ?_Uit
?i4T*L)i_ Lh!iht |L @UUiT| LMt 4Lhi uhi^i?|*) Etii h_i|| @?_ Lh|i?ti?c
bbHc @?_ L?|i4Ttc +LM? @?_ V@? _i? ih}c bbb Lh ?Uhi@ti |ih ti@hU
?|i?t|) W? |i ht| U@tic |i 4TLt|L? Lu @ 4?44 @}i t ?@4M}Lt*)
i*u@hi?Uhi@t?}
W? |t UL?|i |c @ 4?44 @}i U@? @i |i @__|L?@* Mi?iU@* igiU| Lu
_h?} L| *itt ThL_U|i h4t L?t_ih @ uhU|L?@* *@MLh 4@h!i| ? U
_gihi?| h4t @i _gihi?| ThL_U|L? |iU?L*L}it W? i^*Mh4c |i h4t
| @ t4@**ih 4@h}?@* hii?i ThL_U| ** Lgih *Lih @}it |@? |i h4t
| @ }ih 4@h}?@* hii?i ThL_U| iih|i*ittc |i uLh4ih |)Ti Lu h4t
@i @ TLt|i t|i@_)t|@|i *@MLh uLhUi @?_ ThL|t *ii* ? |i L?i @?_c |ih
i4T*L)iit ** @UUiT| @?) LM Lgih uhL4 @ }ThL_U||) h4 OLiihc L? |i
4 Vhh
Eurzq/ Jlour| dqg Nrkhq +4<;5, iru d vxuyh| ri uhvhdufk xs wr wkh hduo| hljkwlhv dqg
Fdug dqg Nuxhjhu +4<<8, iru d uhfhqw vxuyh|1
5 Vhh Erdo dqg Udqvrp +4<<:, iru d uhfhqw vxuyh| rq prqrsvrq|1
L|ih @?_c |ihi ** @*@)t Mi ?i4T*L)i_ Lh!iht L Thiuih @ |i4TLh@h) LM
@| @ *LThL_U||) h4 Lih @ ThL*L?}i_ tTi** Lu ?i4T*L)4i?| Etii L?|i4Ttc
+LM? @?_ V@? _i? ih}c 2fff Atc |iti *LThL_U||) h4t U@? ULi t|
| L|ih h4t OLiihc 4TLt|L? Lu @ tUi?|*) } 4?44 @}i **
4@!i |iti *LThL_U||) h4t }L M@?!hT| t @ hit*|c @u|ih 4TLt|L?c
Lh!iht ** L?*) Mi i4T*L)i_ @| }ThL_U||) h4tc @?_ |L|@* tLU@* i*u@hi
4@) ?Uhi@ti Etii ,U!t|i? @?_ `L*T?c bbf
** Lu |i 4?44 @}i igiU|t 4i?|L?i_ @MLi @hi UL4T@h@|it|@|Ut
hit*|t _ihi_ uLh i^*Mh4 ti@hU 4L_i*t Lu |i *@MLh 4@h!i| Etii Mi*L uLh
@ 4Lhi _i|@*i_ _tUttL? Lu |i *|ih@|hi W? |t T@Tih i i @4?i @ 4?
44 @}i igiU| |@| @t ?L| Mii? _i|iU|i_ MiuLhi At igiU| uL**Lt uhL4 |i
i t|i?Ui Lu 4*|T*i i^*Mh@ L? |i *@MLh 4@h!i|c ? |i UL?|i | Lu ?uLh4@
|L?@* uhU|L?t @?_ _tTihtL? Lu h4t< ThL_U|L? |iU?L*L}it AL ?_iht|@?_
|i i t|i?Ui Lu 4*|T*i i^*Mh@ ?||i*)c ?L|i ht| Lu @** |@| |i @}i Lgih
M) @ h4 4t| Mi ? Mi|ii? |i hitih@|L? @}i Lu |i ?i4T*L)i_ @?_ |i
ThL_U||) *ii* Lu |i h4 EWu |i Lgih u@**t tLh| Lu |i hitih@|L? @}i |i?
?L Lh!iht U@? Mi @||h@U|i_ Ai _i@ Mi?_ |i 4*|T*U|) Lu i^*Mh4
t |i? @t uL**Lt @tU@**)c @ *@MLh 4@h!i| @t i|ih E }ThL_U||) @t
i** @t *LThL_U||) h4tc | ?i4T*L)i_ Lh!iht t?} @ *L hitih@|L?
@}ic Lh E2 }ThL_U||) h4t L?*)c | ?i4T*L)i_ Lh!iht t?} @ }
hitih@|L? @}i W? |i tiUL?_ i^*Mh4c |i } hitih@|L? @}i @U|t @t @
M?_?} *Lih ML?_ L? |i ti| Lu ThL_U|L? |iU?L*L}it |@| i?@M*i @ TLt|i
ThL| Tih Lh!ih W| h*it L| ThL_U|L? @| @ *L ThL_U||) *ii* Lc ?
}i?ih@* Eic ? ML| i^*Mh@c T@h| Lu |i hi?| Lu ThL_U|L? t _t|hM|i_ |L
|i Lh!iht ? |i uLh4 Lu |i @}i Ai hit*|?} @}i _t|hM|L? uLh |i
tiUL?_ i^*Mh4 _L4?@|it |i @}i _t|hM|L? ? |i ht| i^*Mh4 At
? |h? t|it |i }ih hitih@|L? @}i ? |i tiUL?_ i^*Mh4 Atc
|i hitih@|L? @}i Lu |i ?i4T*L)i_ @giU|t |i ti| Lu ThL|@M*i ThL_U|L?
|iU?L*L}itc *i |i ti| Lu ThL_U|L? |iU?L*L}it ? ti ? |h? @giU|t |i hi
tih@|L? @}i @*ic @?_ |t t)t|i4 Lu }*) ?L?*?i@h i^@|L?t @t 4*|T*i
tL*|L?t
6 Dfhprjox
+4<<:, ghulyhv d uhvxow rq pxowlsolflw| ri vwhdg|0vwdwh htxloleuld lq d pdwfklqj
prgho1 Lq wkdw prgho +frqwudu| wr wkh htxloleulxp vhdufk prgho lq wkh suhvhqw vwxg|,/ d up
lv hhfwlyho| htxlydohqw wr d vlqjoh mre/ upv hqgrjhqrxvo| fkrrvh wkhlu surgxfwlrq whfkqrorj|
sulru wr surgxfwlrq/ zdjhv iroorz iurp ghfhqwudol}hg edujdlqlqj/ zrunhuv fdqqrw vhdufk rq wkh
mre/ dqg oderu pdunhw wljkwqhvv ghshqgv rq wkh xqhpsor|phqw udwh1 Pxowlsoh htxloleuld fdq
rffxu ehfdxvh wkh rxwvlgh rswlrq ri zrunhuv zkr qg d edg mre ghshqgv rq wkh udwh dw zklfk
wkh| fdq qg d jrrg mre> li wkh odwwhu lv kljk wkhq wklv pd| gulyh wkh zdjh ri wkh edg mre xs wr
dq xqsurwdeoh ohyho1 Wkh suhflvh frqglwlrqv iru pxowlsolflw| duh yhu| glhuhqw iurp rxuv1 Iru
2
5TTLti |@| |i *@MLh 4@h!i| t ? |i ht| i^*Mh4c | L? @ih@}i
*Lih @}it @?_ *itt iUi?| ThL_U|L? |@? ? |i tiUL?_ i^*Mh4 L
UL?t_ih |i 4TLt|L? Lu @ 4?44 @}i i Uii_?} |i ThL_U||) *ii* Lu
|i *LThL_U||) h4t Ai *@||ih h4t ** }L M@?!hT|c @?_ |i hit*|?}
i^*Mh4 t |i tiUL?_ i^*Mh4c | L? @ih@}i }ih @}it @?_ 4Lhi
iUi?| ThL_U|L? EW? @ M@tU 4L_i*c |ihi t ?L igiU| L? ?i4T*L)4i?| @|
@** Wu |i 4?44 @}i t tMti^i?|*) @ML*ti_c |i *@MLh 4@h!i| 4@) ?L|
_i@|i uhL4 |i EtiUL?_ i^*Mh4 W? |@| U@tic @ |i4TLh@h) 4TLt|L? Lu
ELh ?Uhi@ti ? |i 4?44 @}i t tUi?| |L uLhUi |i *@MLh 4@h!i| uhL4
|i ?u@Lh@M*i |L |i u@Lh@M*i i^*Mh4
Ai i4ThU@* hiti@hU L? 4?44 @}i igiU|t }i?ih@**) @tt4it |@| uLh @
4?44 @}i |L Mi M?_?}c | t ?iUitt@h) |@| |i @}i _i?t|) _tT*@)t @ tT!i
@| |i 4?44 @}i At tT!i t |L}| |L U@T|hi LMt | ThL_U||)
@| Lh @MLi |i 4?44 @}i @t i** @t Mi*L |i 4?44 @}i Ai *@||ih
LMt 4@) i t| |i4TLh@h*) MiU@ti Lu LM ThL|iU|L? *i}t*@|L? Lh MiU@ti Lu |i
u@U| |@| u@U|Lh tMt|||L? @?_ ?it|4i?| |@!i |4i Wu @ tT!i t @Mti?| |i?c
M) @?@*L}) |L |i UL4Ti||i 4L_i*c | t @h}i_ |@| Lh!iht @?_ @}it @hi
L?*) 4@h}?@**) @giU|i_ M) @ U@?}i ? |i 4?44 @}i Ai @?@*)tt ? |i
Thiti?| T@Tih @t h@_U@**) _gihi?| 4T*U@|L?t 6ht|c u |i 4TLt|L? Lu @
4?44 @}i U@?}it |i i^*Mh4 L|UL4ic |i? |i @}i _i?t|) ? |i
?i i^*Mh4 _Lit ?L| ?iUitt@h*) @i @ tT!i @| |i *Lit| @}i W?_ii_c
|i *Lit| @}i U@? Mi t|hU|*) *@h}ih |@? |i 4@?_@|Lh) 4?44 @}i h
hit*|t @hi |t UL?tt|i?| | _@|@ L? hiTi@|i_ UhLtttiU|L?t tL?} |@|
|i 4?44 @}i *ii* @giU|t |i t@Ti Lu |i @}i _i?t|) ii? |L} |i
*@||ih _Lit ?L| @i @ tT!i @| |i 4?44 @}i *ii* Etii i} t|hLtc
bbec
L i @4?it 5i_t _@|@ 5iUL?_*)c u |ihi @hi 4*|T*i i^*Mh@ |i? |i
@ML*t4i?| Lu |i 4?44 @}i 4@) ?L| @giU| |i i^*Mh4 At UL*_
*i@_ |L |i ihhL?iLt UL?U*tL? |@| |i 4?44 @}i @t |ihiuLhi hhi*i@?|
L|i |@| | 4*|T*i i^*Mh@c |i ?L|L? Lu RM?_?} MiUL4it tL4i@|
?U*i@h
#h?} |i T@t| _iU@_ic |i |iLhi|U@* @?_ i4ThU@* @?@*)tt Lu i^*Mh4
ti@hU 4L_i*t @t MiUL4i _itThi@_ Etii thi)t M) V@? _i? ih}c bbbc @?_
Lh|i?ti? @?_ tt@h_itc bbb Lt| Lu |t *|ih@|hi M*_t L? h_i|| @?_
Lh|i?ti? EbbHc L _ii*LT @ 4L_i* | L4L}i?iLt Lh!iht @?_ h4t ?
U Lh!iht @hi @**Li_ |L ti@hU L? |i LMc @?_ L? Lh|i?ti? Ebbfc L
i |i?_t |t 4L_i* M) ?|hL_U?} i|ihL}i?i|) W? |i L4L}i?iLt 4L_i*c
|i TLttM*|) Lu L?|iLM ti@hU t @ tUi?| UL?_|L? uLh @}i _tTihtL?
h{dpsoh/ lq rxu pdlq prgho/ htxloleulxp lv dozd|v xqltxh li rq0wkh0mre vhdufk lv lpsrvvleoh1
? i^*Mh4 W? |@| U@tic LM|LLM |h@?t|L?t @hi 4TLh|@?| uLh 4@?|@??}
|i Lh!uLhUi Lu @ h4 OLiihc | t }i?ih@**) @U!?L*i_}i_ |@|c |L i T*@?
|i t@Ti Lu |i @}i _t|hM|L?c | t ?iUitt@h) |L @**L uLh i|ihL}i?i|) ?
ThL_U|L? *ii*t @t i** Etii V@? _i? ih} @?_ +__ihc bbHc @?_ L?|i4Ttc
+LM? @?_ V@? _i? ih}c 2fff Ai hit*|?} 4L_i*t t@|tu) @ *@h}i ?4Mih Lu
t|)*3i_ u@U|t Lu |i *@MLh 4@h!i|c T@h|U*@h*) UL?Uih??} |i hi*@|L?t Mi|ii?
LM _h@|L?tc @}itc @?_ |i t3it Lu h4t Etii i} +__ih @?_ V@? _i? ih}c
bb.
W? |t T@Tihc i @_LT| |i Mi?U4@h! 4L_i* _ii*LTi_ M) Lh|i?ti? Ebbfc
? U Lh!iht ti@hU L? |i LM @?_ ThL_U|L? |iU?L*L}it @hi _tTihti_
@UhLtt h4te W?_ii_c uLh i TLt|L?@* hi@tL?tc i ** 4Lt|*) @tt4i |@| |ihi
@hi |L TLttM*i ThL_U||) *ii*t At 4L_i* t tUi?|*) hU uLh Lh Th
TLtit Wu ML| |)Tit Lu h4t @hi @U|i |i? ?i4T*L)i_ @?_ i4T*L)i_ Lh!iht
hiUii LM Lgiht uhL4 ML| |)Titc @?_ Lh!iht @| *LThL_U||) h4t 4Li
|L }ThL_U||) h4t i?iih |i) }i| |i LTTLh|?|)
Ai 4L_i* M) Lh|i?ti? Ebbf | i|ihL}i?iLt h4t @?_ L4L}i?iLt
Lh!iht @t Mii? TLT*@h ? |i i4ThU@* @?@*)tt Lu i^*Mh4 ti@hU 6Lh
i @4T*ic L*tc kiuih @?_ i4@?? EbbDc 2fffc L*t Ebb.c @?_ ?3i*
i| @* Ebbb it|4@|i |t 4L_i* @**L?} uLh @ ?|i ?4Mih Lu _gihi?| h4
|)Tit Ai) @h}i |@| ? }i?ih@* @ h@|ih t4@** ?4Mih Lu h4 |)Tit }it @
hi@tL?@M*i | |L |i 4@? ^@?|*it Lu |i @}i _t|hM|L? W| tL*_ Mi t|hitti_
|@| ?L?i Lu |t *|ih@|hi @t @__hitti_ |i tti Lu 4*|T*U|) Lu i^*Mh4c
Lh uLh |@| t@!i |i TLttM*|) |@| i^*Mh4 4@) t|U ? hitTL?ti |L TL*U)
U@?}it Lh|i?ti? Ebbf _ihit 4@?) ThLTih|it Lu |i i^*Mh4 tL*|L?t
L?|i4Ttc +LM? @?_ V@? _i? ih} E2fff @?@*)3i @ 4L_i* | @ UL?|?Lt
_t|hM|L? Lu _gihi?| ThL_U|L? |iU?L*L}it At 4L_i* t @M*i |L }i @
TihuiU| | |L @}i _@|@c M| _i |L |t UL4T*i |) | t *itt @4i?@M*i |L @ uLh4@*
@?@*)tt Lu UL?_|L?t uLh 4*|T*U|) Lu i^*Mh4
Ai L|*?i Lu |i T@Tih t @t uL**Lt W? 5iU|L? 2 i Thiti?| |i 4L_i* W?
5iU|L? i _ihi |i i^*Mh@ ?_ih |i @tt4T|L? |@| |i LM Lgih @hh@*
h@|it uLh |i Lh!iht _L ?L| _iTi?_ L? |i 4i@thi Lu @U|i h4t ? |i iUL?L4)
At t @ t|hL?} @tt4T|L? hh@* h@|it _iTi?_ L? |i 4@|U?} |iU?L*L}) ?
|i *@MLh 4@h!i|c @?_ u |i 4i@thi Lu h4t _iUhi@tit |i? |i 4@|U?} h@|i
4@) _iUhi@ti @t i** W? 5iU|L? e i |ihiuLhi i |i?_ |i 4L_i* |L _i@* |
|t At i |i?tL? @t ?L| Mii? i @4?i_ ? |i @MLi4i?|L?i_ *|ih@|hi L?
i^*Mh4 ti@hU W| |h?t L| |@| |i hit*|t @hi hLMt| | hitTiU| |L |t
7 Pruwhqvhq +4<<3,
+vhh ehorz,1
dovr doorzv iru khwhurjhqhlw| ri zrunhuv* rssruwxqlw| frvwv ri hpsor|phqw
e
W? 5iU|L?t @?_ e i @*tL _tUtt |i i4ThU@* hi*i@?Ui Lu 4*|T*i i^
*Mh@c M) i @4??} tL4i U@tit uhL4 |i i4ThU@* *|ih@|hi W? T@h|U*@hc i
tL |@| |i it|4@|it ? ?3i* i| @* Ebbb uLh tTiUU *@MLh 4@h!i|t @hi tU
|@| |iti 4@h!i|t _tT*@) 4*|T*i i^*Mh@ W? 5MtiU|L? e i tL |@|
|i hit*|t _ihi_ uLh |i 4L_i* | |L ThL_U||) *ii*t U@? Mi i |i?_i_
|L 4L_i*t | 4Lhi }i?ih@* ThL_U||) _t|hM|L?t 5iU|L? D _i@*t | |i
igiU|t Lu U@?}it ? |i 4?44 @}i W? 5iU|L? S i i @4?i @? @*|ih?@|i
4L_i* ? U ?i4T*L)i_ Lh!iht @hi i|ihL}i?iLt | hitTiU| |L |i *ii*
Lu |ih ?i4T*L)4i?| Mi?i|t At 4L_i* }i?ih@|it 4*|T*i i^*Mh@ @t i**c
uLh itti?|@**) |i t@4i hi@tL? @t ? |i M@tU 4L_i* 5iU|L? . UL?U*_it
5
Wkh prgho iudphzrun
iU@ti |i 4L_i* uh@4iLh! t _tUtti_ ? Lh|i?ti? Ebbf @t i** @t ?
tMti^i?| i4ThU@* t|_itc |i Thiti?| i TLt|L? U@? Mi Mhiu Ai 4L_i*
UL?t_iht @ *@MLh 4@h!i| UL?tt|?} Lu @ UL?|?4 Lu Lh!iht @?_ h4t Ai
4i@thi Lu Lh!iht t _i?L|i_ M) 6c @?_ |i 4i@thi Lu ?i4T*L)i_ Lh!iht M)
W? Lh|i?ti? Ebbfc |i 4i@thi Lu h4t t ?Lh4@*3i_ |L L?i Oihic i 4t|
Mi 4Lhi i T*U| L? |t W? @ }i? t|i@_)t|@|i i^*Mh4c |ihi U@? Mi @U|i
EThL|@M*i h4t @t i** @t ?L?@U|i *@|i?| h4t |@| 4@) Mi @U|i ? @?L|ih
i^*Mh4 `i @tt4i |@| |i |L|@* 4i@thi Lu h4t E@U|i Lh TL|i?|@**)
@U|i t i_c uLh i @4T*i MiU@ti | t _i|ih4?i_ M) U@T|@* i?_L4i?|tc @?_
i _i?L|i |t 4i@thi M) ? w@|ih L? i ** tii |@| u @** ?i4T*L)i_ Lh!iht
@UUiT| @?) ?L??i}@|i @}i Lgih |i? |i 4i@thi Lu @U|i h4t t @*tL i^@*
|L ?
Ai tTT*) t_i Lu |i 4L_i* t i^@*i?| |L @ t|@?_@h_ T@h|@* LM ti@hU
4L_i* | L?|iLM ti@hU Etii Lh|i?ti?c bHS `Lh!iht LM|@? @}i Lu
uihtc U @hi h@?_L4 _h@?}t uhL4 |i @}i Lgih _t|hM|L? 8 Ec @| @?
i L}i?Lt h@|i bf i? ?i4T*L)i_ @?_ b i? i4T*L)i_ `i?iih @? Lu
uih @hhitc |i _iUtL? @t |L Mi 4@_i i|ih |L @UUiT| | Lh |L hiiU| | @?_
ti@hU uh|ih uLh @ Mi||ih Lgih 6h4t TLt| @}i Lgiht @?_ |i) _L ?L| M@h}@?
Lih |i @}i w@)Lgt @UUhi @| |i UL?t|@?| i L}i?Lt h@|i B Ai LTTLh|?
|) ULt| Lu i4T*L)4i?| t _i?L|i_ M) K @?_ t @tt4i_ |L Mi UL?t|@?| @UhLtt
?__@*t @?_ |L Mi ?U*ti Lu ?i4T*L)4i?| Mi?i|t @?_ ti@hU ULt|t `i
|@!i f bf c b c B 4 @?_ K fD Ai LT|4@* @UUiT|@?Ui t|h@|i}) uLh |i
8 Iru
h{srvlwlrqdo uhdvrqv zh uhvwulfw dwwhqwlrq wr wkh olplwlqj fdvh lq zklfk wkh zrunhuv*
glvfrxqw udwh lv lqqlwhvlpdoo| vpdoo1 Wkh uhvxowv duh urexvw zlwk uhvshfw wr wklv1
D
?i4T*L)i_ t |i? U@h@U|ih3i_ M) @ hitih@|L? @}i t@|tu)?}
' K n Ebf b ]"
8 E
_
B n b E 8 E
E
W| t ?L| _U*| |L tL |@| |t i^@|L? _Lit }i @ ?^i tL*|L? uLh }i? |i L|ih @h@M*it @?_ u?U|L?tS
,4T*L)i_ Lh!iht @UUiT| @?) @}i Lgih |@| i Uii_t |ih Uhhi?| @}i W?
t4c Lh!iht U*4M |i LM *@__ih |L LM|@? }ih @}itc M| |t igLh| 4@) Mi
uht|h@|i_ M) @ |i4TLh@h) tTi** Lu uhU|L?@* ?i4T*L)4i?|
L UL?t_ih |i Lt Lu Lh!iht 6ht|c ?L|i |@| @U|i h4t _L ?L| Lgih
@ @}i Mi*L c tL |@| @** @}i Lgiht ** Mi @UUiT|@M*i uLh |i ?i4T*L)i_
L?ti^i?|*)c |i L uhL4 ?i4T*L)4i?| |L i4T*L)4i?| t bf Ai L uhL4
i4T*L)4i?| |L ?i4T*L)4i?| t BE6 W? @ t|i@_) t|@|i |iti Lt @hi i^@*
@?_ |i hit*|?} h@|i *6 Lu ?i4T*L)i_ Lh!iht i^@*t B*EB n bf wi| |i _t|hM|L? Lu @}it T@_ |L @ UhLtttiU|L? Lu i4T*L)iit @i _t|h
M|L? u?U|L? C Aiti @}it @hi L? @ih@}i }ih |@? |i @}it Lgihi_c
MiU@ti Lu |i L Lu i4T*L)iit |L Mi||ih T@)?} LMt Ai t|LU! Lu i4T*L)iit
| @ @}i *itt Lh i^@* |L @t 4i@thi CEE6 Ai L ?|L |t
t|LU! UL?tt|t Lu ?i4T*L)i_ L @UUiT| @ @}i *itt |@? Lh i^@* |L c @?_ |t
L t i^@* |L bf 8 E Ai L L| Lu |t t|LU! UL?tt|t Lu |Lti L MiUL4i
?i4T*L)i_c BCEE6 @?_ |Lti L hiUii @ LM Lgih |@| i Uii_t c
b E 8 ECEE6 W? |i t|i@_) t|@|ic |i Lt ?|L @?_ L| Lu |i
t|LU! @hi i^@*c tL
CE '
B8 E
B n b E 8 E
E2
ihi i @i tMt|||i_ uLh 6hL4 |i |L @}i _t|hM|L?t i _ihi |i t|i@_)t|@|i tTT*) Lu *@MLh
,Em8 |L @? i4T*L)ih ti||?} @ @}i c ihi i i T*U|*) ?_U@|i |t _iTi?_
i?Ui L? |i @}it Lgihi_ M) L|ih h4t 5L4i@| *LLti*)c L?i 4@) t@) |@|
|t 4t| i^@* |i ?4Mih Lu Lh!iht i@h??} ? @ t|i@_) t|@|ic __i_ M) |i
?4Mih Lu h4t T@)?} ? |i t|i@_) t|@|i L|i |@| | t @tt4i_ |@| @ h4
T@)t |i t@4i @}i |L @** Lu |t i4T*L)iit wi| ?@ _i?L|i |i 4i@thi Lu @U|i
h4t E|t t ?L| @ u?_@4i?|@* 4L_i* _i|ih4?@?| M| h@|ih @? i^*Mh4
L|UL4i. t @ hit*|c
Wkh ghulydwlyh ri wkh ohiw0kdqg vlgh zlwk uhvshfw wr ! htxdov rqh1 Li 3 4 wkhq wkh
ghulydwlyh ri wkh u1k1v1 z1u1w1 ! lv qhjdwlyh ru }hur1 Li 3 ? 4 wkhq wkh ghulydwlyh ri wkh u1k1v1
z1u1w1 ! lv srvlwlyh dqg xqlirupo| vpdoohu wkdq rqh1
: Dv phqwlrqhg lq wkh lqwurgxfwlrq/ dqg pd| ghshqg rq q 1 Zh ghdo zlwk wklv lq
3
4
d
Vhfwlrq 71
9
S
,Em8 '
'
6
BEB n b ?@ EB n b E 8 E2
6Bbf EB n b ?@ EB n bf EB n b E 8 E2
E
5ii L?|i4Ttc +LM? @?_ V@? _i? ih} E2fff uLh @ uLh4@* @?@*)tt Ai i^@
|L? @MLi L?*) L*_t u 8 _Lit ?L| @i 4@tt TL?|tc U t tL? Mi*L
6h|ihc ? |t i^@|L?c @t Lu ULhti |L i Uii_ Ei _L ?L| UL?t_ih @
4@?_@|Lh) 4?44 @}i ?|* 5iU|L? D W| t i@t*) tii? |@| , ?Uhi@tit ? L? |i tTTLh| Lu 8 L UL?t_ih @ h4 | @ L R Lu 4@h}?@* hii?i ThL_U| }i?ih@|i_
M) i4T*L)?} L?i Lh!ih 6Lh UL?i?i?Uic i @tt4i |@| R _Lit ?L| _iTi?_
L? |i ?4Mih Lu i4T*L)iitc i i @tt4i |@| |i ThL_U|L? u?U|L? t
*?i@h ? i4T*L)4i?| `i hiuih |L |t h4 @t @ h4 Lu |)Ti R @?_ |L R @t |i
E*@MLh ThL_U||) Lu |t h4 ,@U h4 ti|t @ @}i tL @t |L 4@ 43i |t
t|i@_)t|@|i ThL| L ER ,Em8 }i? 8 @?_ }i? |i Mi@Lh Lu Lh!iht
`i _t|?}t Mi|ii? |L |)Tit Lu h4t ? |t *@MLh 4@h!i| 6h4t Lu
|)Ti R2 ER @i @ ThL_U|L? |iU?L*L}) |@| }it |i4 @ *L E} *@MLh
ThL_U||) R2 ER c | R : R2 W| tL*_ Mi t|hitti_ |@| |t ThL_U||)
*ii* t @ h4 U@h@U|iht|U @?_ ?L| @ Lh!ih U@h@U|iht|U ?i 4@) |?! Lu @
4@h!i| ? U ?__@*t | @ Uih|@? *ii* Lu i_U@|L? @hi i4T*L)@M*i ?
|L _gihi?| LUUT@|L?t uh@U|L? ^ Lu |i |L|@* 4i@thi Lu h4t E@U|i Lh
TL|i?|@**) @U|i UL?tt|t Lu |)TiR h4tc @?_ |i hi4@??} uh@U|L? ^ UL?
tt|t Lu |)TiR2 h4t `i |@!i ^ E@?_ |ihiuLhi |i 4i@thit ML| |)Tit Lu h4t
^? @?_ E ^? |L Mi i_ 6Lh i @4T*ic |iti 4@) @i Mii? _i|ih4?i_ M)
U@T|@* i?_L4i?|t W?_ii_c Ui4L}* @?_ 54ih Ebb. tL |@| ThL_U|
|) _tTihtL? U@? Mi i T*@?i_ @t @? i^*Mh4 L|UL4i M) *i||?} i @?|i
L4L}i?iLt h4t ULLti |ih U@T|@* MiuLhi ThL_U|L? t|@h|t *|ih?@|i*)c
ThL_U||) _tTihtL? 4@) Mi |i hit*| Lu _gihi?Uit ? ThL_U| 4@h!i| TLih
`i |@!i R : K @?_ f ^ Wu R K |i? |ihi L*_ Mi ?L ThL_U|L?c @t
@** Lh!iht L*_ Mi Mi||ih Lg M) Mi?} ?i4T*L)i_
Lh|i?ti? Ebbf _ihit @ ?4Mih Lu ThLTih|it Lu @?) i^*Mh4 6ht| Lu
@**c @ @}i Lgih |@| @||h@U|t Lh!iht t ThL| 4@ 43?} L?*) u ?L 4@tt Lu
L|ih i4T*L)iht Lgih L?ti^i?|*)c |i i^*Mh4 @}i Lgih _t|hM|L? 8
@t ?L 4@tt TL?| At t @ u?_@4i?|@* ThLTih|) Lu i^*Mh4 ti@hU 4L_i*t
| L?|iLM ti@hU W| uL**Lt uhL4 |i u@U| |@| @ 4@tt TL?| @| t@) W
?_Uit @?) h4 T@)?} W |L Lgih @ @}i t*}|*) }ih |@? W c MiU@ti |i?
.
|t t|i@_)t|@|i *@MLh uLhUi ** Mi tMt|@?|@**) *@h}ih @| |i ULt| Lu L?*) @ tiUL?_
Lh_ih _iUhi@ti ? |i ThL| Tih Lh!ih At ThLTih|) 4T*it |@| @** Lh!iht
u@Ui @ ?L?_i}i?ih@|i @}i Lgih _t|hM|L?c @?_ LM|LLM |h@?t|L?t _L LUUh
LhiLihc @?) i^*Mh4 t @t)44i|hU ? Thi Eh4t< t|h@|i}it ELh t)44i|hU
? 4 i_ Eh4t< t|h@|i}it A@| tc i^@*i?| h4t Lgih _gihi?| @}itc )i|
|i) hiUii |i t@4i ThL| L L|i |@| |i u?U|L? ,Em8 ?Uhi@tit ?
c tL |ihi t @ TLt|i hi*@|L? Mi|ii? |i t3i Lu |i h4 @?_ |i @}i |
Lgiht *@h}i Et4@** @}i 4T*it |@| |i i | h@|i Lu Lh!iht @| |i h4 t
hi*@|i*) t4@** E*@h}ic @?_ |@| @ hi*@|i*) *@h}i Et4@** uh@U|L? Lu @** Lh!iht
Uhhi?|*) i4T*L)i_ ? |i iUL?L4) t **?} |L Lh! @| |i h4 Oi?Uic ? |ih4t
Lu |L|@* ThL|t Lu @ h4c |ihi t @ |h@_iLg Mi|ii? |i ThL| Tih Lh!ih @?_
|i t|i@_)t|@|i ?4Mih Lu Lh!iht @| |i h4H
tiUL?_ ThLTih|) t |@| ThL|4@ 43?} @}it uLh |)TiR i4T*L)iht @hi
*@h}ih |@? ThL|4@ 43?} @}it uLh |)TiR2 i4T*L)ihtc u ML| |)Tit @hi @U|
ic @?_ |@| |ihi t ?L }@T Mi|ii? |i ULhhitTL?_?} T@h|t Lu |i tTTLh| Lu 8 W?_ii_c h4t | @ }ih *@MLh ThL_U||) Lgih }ih @}itc @i @ *@h}ih
*@MLh uLhUi @?_ @i *@h}ih ThL| Lt |@? h4t | *Lih *@MLh ThL_U||)
|h_ ThLTih|) t |@| |i *Lit| @}i ? |i 4@h!i| i^@*t |i hitih@|L?
@}i Lu |i ?i4T*L)i_ Wu |i *Lit| @}i L*_ i Uii_ |i hitih@|L? @}i
|i? |i h4 Lgih?} |@| *Lit| @}i L*_ ?Uhi@ti |t ThL| Tih Lh!ih M)
*Lih?} |i Lgihc |L| @?) *Ltt ? |t t|i@_) t|@|i *@MLh uLhUi L|i |@| @
h4 @*@)t Lgih @ @}i |@| t t4@**ih |@? |t ThL_U||) *ii*c t?Ui |i) U@?
@*@)t @||@? @ TLt|i ThL| M) Lgih?} |i hitih@|L? @}i Lu |i ?i4T*L)i_
6
Htxloleuld
W? |t tiU|L? i tL |@| |i 4L_i* Lu 5iU|L? 2 U@? @i 4*|T*i i^*Mh@
W? L?i i^*Mh4c @** @U|i h4t @hi |)TiR h4tc ihi@t ? |i L|ihc ML|
|)Tit @hi @U|i `i @hi UL?Uih?i_ | ?L?ULLTih@|i t|i@_)t|@|i i^*Mh@
5L4i@| *LLti*)c tU i^*Mh@ U@? Mi |L}| |L UL?tt| Lu @ hitih@|L? @}i
@?_ @ @}i Lgih _t|hM|L? 8 tU |@| E t@|tit E }i? 8 c @?_ E
8 uL**Lt uhL4 |i h4t< 4@ 43@|L?t Lu |ih L? t|i@_)t|@|i ThL| Lt
Lq wklv uhvshfw/ wkhuh lv d vwurqj vlplodulw| wr _wxuqryhu frvwv% hflhqf| zdjh prghov> vhh
h1j1 Vwljolw} +4<;8, dqg Zhlvv +4<<4,1 Wkh prgho vhwxs dovr vkduhv ihdwxuhv zlwk Uhlqjdqxp
+4<:<,/ zkr vwxglhv htxloleulxp vhdufk lq frqvxphu surgxfw pdunhwv/ dqg zlwk Prqwjrphu|
+4<<4,/ zkr vwxglhv d rqh0vkrw prgho ri htxloleulxp vhdufk zlwk surgxfwlylw| glvshuvlrq rq
wkh oderu pdunhw1 Vhh Ulgghu dqg Ydq ghq Ehuj +4<<:,/ Dfhprjox dqg Vklphu +4<<:, dqg
Prqwjrphu| +4<<4, iru ryhuylhzv ri wkh hpslulfdo hylghqfh vxssruwlqj wkhvh w|shv ri prghov1
;
H
614
Rqo| kljk0surgxfwlylw| upv
`i t|@h| M) @tt4?} |@| L?*) |)TiR h4 |)Tit @hi @U|i ? i^*Mh4 At
4t| Mi ihi_c M) UiU!?} i|ih ? i^*Mh4 R2 Wu |i *@||ih _Lit ?L|
L*_ |i? |ihi t @? ?Ui?|i uLh |)TiR2 h4t |L i?|ih |i 4@h!i| `i _ihi
|i i^*Mh4 tL*|L? @t uL**LtG ht| _ihi |i @}i Lgih _t|hM|L? uLh @
}i? ?!?L? R ( |i? U@*U*@|i |i @U|@* hitih@|L? @}i M) tMt|||?}
|i @}i Lgih _t|hM|L? ?|L i^@|L? E 6?@**)c UiU! i|ih |i hit*|?}
i Uii_t R2 Wu L?*) |)TiR h4t @hi @U|i |i? i @i @ 4L_i* | L4L}i?iLt h4t
Ai i^*Mh4 ? tU @ 4L_i* @t Mii? tL*i_ 4@?) |4it ? |i *|ih@|hi
Etii i} h_i|| @?_ Lh|i?ti?c bbH L|i |@| ihi |i 4i@thi ?@ Lu @U|i
h4t i^@*t ^? 6Lh @ }i? R c |i t|i@_)t|@|i ThL| L Lu @ h4 Lgih?}
i^@*t ER ,Em8 Nt?} i^@|L? Ec |t ? |h? i^@*t
ER 6Bbf
^ ? EB n bf EB n b W? i^*Mh4c @** L|ih h4t @i |i t@4i ThL| L Atc @** ThL|4@ 43?}
@}it t@|tu) |i i^@*|) Lu ER ,Em8 |L |i i ThittL? @MLic | ,Em8 @t ? E At U@? Mi tL*i_ uLh 8 c
#
B n b
8 E '
b
v
R R $
8 @t tTTLh| Ec c |
#
'
B
B n b
$2
3 #
n C B
B n b
Ee
$24
D R
ED
MLt*)c |t *it Mi|ii? @?_ R 6h|ih4Lhic
#
B
CE '
b
v
R R $
ES
@?_
,Em8 '
6Bbf
R ^ ? EB n bf EB n b R b
E.
) tMt|||?} Ee ?|L Ec | uL**Lt |@|
'
EB n b 2 K n Ebf b b R
EB n b 2 n Ebf b b
EH
At t@|tit R2 u @?_ L?*) u
Ebf b b ER R2 EB n b 2 ER2 K
Eb
W? t4c
hLTLt|L? Aihi t @? i^*Mh4 ? U L?*) |)TiR h4t @hi @U|i u
@?_ L?*) u Ebf b b ER R2 EB n b 2 ER2 K
?4Mih Lu UL44i?|t @hi ? Lh_ih 6ht| Lu @**c ?L|i |@| |i UL?_|L?
Eb _Lit ?L| _iTi?_ L? ^ Lh L? ?@ Lh ? Lh 6 5iUL?_*)c |i UL?_|L? U@? Mi
4@_i 4Lhi |h@?tT@hi?| M) i @4??} tTiU@* U@tit 6Lh i @4T*ic |i i^*Mh4
@MLi _Lit ?L| i t| u ML| R2 K @?_ b : bf At 4@!it ti?tiG u ti@hU ?
i4T*L)4i?| t 4Lhi iUi?| |@? ti@hU ? ?i4T*L)4i?| |i? @? ?i4T*L)i_
Lh!ih @UUiT|t @ LM | @ @}i i^@* |L Kc tL |i? |)TiR2 h4t U@? 4@!i @
TLt|i ThL| |ih tTiU@* U@tit @hi _tUtti_ ? 5MtiU|L? Aihi i @*tL
_tUtt |i i4ThU@* T*@tM*|) Lu |i UL?_|L?
615
Kljk0surgxfwlylw| upv dv zhoo dv orz0surgxfwlylw|
upv
L tTTLti |@| h4t Lu ML| |)Tit @hi @U|i ? i^*Mh4 At 4t| @}@?
Mi ihi_c M) UiU!?} i|ih ? i^*Mh4 R2 Wu |i *@||ih _Lit ?L|
L*_ |i? |)TiR2 h4t ** _t@TTi@h uhL4 |i 4@h!i|
Ai i ThittL?t uLh |i i^*Mh4 ? tU @ 4L_i* uL**L uhL4 |i i^*M
h4 ThLTih|it *t|i_ ? 5iU|L? 2 L|i |@| ihi |i 4i@thi ?@ Lu @U|i h4t
e @?_ Ec
e i^@*t ? Ai tTTLh| Lu 8 UL?tt|t Lu |L @_@Ui?| T@h|tc t@) Ec 6Lh @ }i? R2 c |i t|i@_)t|@|i ThL| L Lu @ |)TiR2 h4 Lgih?} i^@*t
ER2 ,Em8 Nt?} i^@|L? Ec |t ? |h? i^@*t
ER2 6Bbf
? EB n bf EB n b W? i^*Mh4c @** L|ih |)TiR2 h4t @i |i t@4i ThL| L Atc @** ThL|
4@ 43?} @}it Lu |)TiR2 h4t t@|tu) |i i^@*|) Lu ER2 ,Em8 |L
f
|i i ThittL? @MLic | ,Em8 @t ? E At U@? Mi tL*i_ uLh 8 E L?
e
5 Ec c
#
B n b
8 E '
b
v
R2 R2 $
Ef
e ' ^ t @ hit*|c
ihi e uL**Lt uhL4 |i hit|hU|L? |@| 8 E
e '
#
B n b ^
B n b
$2
3 #
$2 4
B
n
b
^
D R2
n C E
B n b
At *it Mi|ii? @?_ R2 L|i |@| u ^ ' f @?_ R2 ' R |i? |i i ThittL?
@MLi i^@*t ? EDc @t | tL*_
L *i| t |h? |L |)TiR h4t 6Lh @ }i? c @?_ uLh }i? Mi@Lh Lu
|)TiR2 h4tc |i t|i@_)t|@|i ThL| L Lu @ |)TiR h4 Lgih?} e i^@*t
e m8
e Nt?} i^@|L? Ec |t i^@*t
ER ,E
e
ER 6Bbf EB n b ? EB n bf EB n b ^2
W? i^*Mh4c @** L|ih |)TiR h4t @i |i t@4i ThL| L Atc @** ThL|
4@ 43?} @}it Lu |)TiR h4t t@|tu) |i i^@*|) Lu ER ,Em8 |L
|i i ThittL? @MLic | ,Em8 @t ? E At U@? Mi tL*i_ uLh 8 E L?
e c
5 Ec
#
B n b ^
B n b
8 E '
b
B n b
v
R R $
E2
ihi uL**Lt uhL4 8 E ' c | 8 @t @MLic
#
'
B
B n b ^
$2
3 #
e n C B
B n b ^
$24
D R
e
U U@? Mi hih||i? t?} |i i^@|L? uLh c
#
B
' R ER R2 B n b ^
$2
#
B
ER2 B n b
$2
E
,^@|L?t EfE UL?t|||i 8 }i? W| t 4TLh|@?| |L hi@*3i |@|c ihi
@t i** @t ? |i ThiLt tMtiU|L?c |i t@Ti Lu 8 hiiU|t |i M@h}@??} TLih
Lu Lh!iht t
@t i4T*L)iht *Lih _i}hii Lu ti@hU uhU|L?t uLh i4T*L)i_
LM tii!iht Ei @ } b *B ThL_it @? ?Ui?|i uLh h4t |L T@) }ih @}it
Wu ti@hU uhU|L?t @hi *Lihc |i? @ h4 T@)?} @ }ih @}i L*_ Mi @M*i |L
?Uhi@ti |t *@MLh uLhUi tMt|@?|@**) Etii +__ih @?_ V@? _i? ih}c bb.
) tMt|||?} EfE ?|L Ec @?_ @u|ih |i_Lt U@*U*@|L?tc | uL**Lt
|@|
'
EB n b 2 K n Ebf b b ESR n E SR2 EB n b 2 n Ebf b b
| S _i?i_ @t
#
S'
EB n b ^
B n b ^
Ee
$2
L|i |@| f S @?_ |@| |i _i?L4?@|Lh Lu t TLt|i Ai i ThittL? uLh
t t4*@h |L |i i ThittL? EH uLh |i L4L}i?iLt 4L_i* Ai L?*) _gihi?Ui
t |@| |i ThL_U||) *ii* ? |i L4L}i?iLt 4L_i* t hiT*@Ui_ M) @ i}|i_
@ih@}i Lu |i ThL_U||it ? |i Thiti?| 4L_i* Ai i}|t S @?_ S hiiU|
|i hi*@|i 4TLh|@?Ui Lu R @?_ R2 uLh |i ?i4T*L)i_ ?__@*b W? }i?ih@*c
S _Lit ?L| i^@* ^ At t MiU@ti h4t |@!i h4 i|ihL}i?i|) ?|L @UUL?|
i? |i) ti| @}itc @?_ MiU@ti Lh!iht U@? 4Li uhL4 *LThL_U||) h4t
|L }ThL_U||) h4t Wu ^ ' f E^ ' |i? S ' f ES ' @?_ i^@*t |i
hitih@|L? @}i ? |i L4L}i?iLt 4L_i* | R ' R2 ER ' R Ai i}|
S ?Uhi@tit ? ^ @?_ b *B At 4@!it ti?tic @t @ } @*i Lu ^ 4i@?t |@|
}ThL_U||) LMt @hi @M?_@?|c *i @ } @*i Lu b *B 4i@?t |@| | t
hi*@|i*) i@t) |L 4Li ^U!*) |L @ LM | @ } ThL_U||)
W| ?L hi4@?t |L UiU! i|ih R2 At U@? Mi tL? |L L*_ u @?_
L?*) u
Ebf b b SER R2 EB n b 2 ER2 K
ED
W? t4c
hLTLt|L? 2 Aihi t @? i^*Mh4 ? U ML| |)Tit Lu h4t @hi @U|i u
@?_ L?*) u Ebf b b SER R2 EB n b 2 ER2 K
< Wklv
fdq eh vhhq iurp wkh h{suhvvlrq iru wkh phdq zdjh HJ +z, hduqhg e| hpsor|hg zrunhuv
iru d jlyhq orzhvw zdjh z ? s5 /
HJ +z, @
. 4
z.
4
. 4
+fs4 . +4 f,s5 ,
Vlqfh zrunhuv gr qrw glvfrxqw wkh ixwxuh/ HJ +z, lv wkh h{shfwhg vwhdg|0vwdwh lqfrph rz lq
hpsor|phqw iru d fxuuhqwo| xqhpsor|hg zrunhu1
2
) UL4M??} hLTLt|L?t @?_ 2 i LM|@?
hLTLt|L? Aihi i t| i @U|*) |L i^*Mh@ u @?_ L?*) u
Ebf b b
R2 K
Ebf b b
:
S
EB n b 2
R R2
EB n b 2
ES
L|i |@| bf c b @?_ B L?*) @giU| |iti ?i^@*|it M) @) Lu |i h@|Lt bf *B @?_
b *B *tL ?L|i |@| |i 4__*i |ih4 L?*) _iTi?_t L? 4L?i|@h) L @h@M*it
ihi@t |i *iu|@?_ @?_ h}|@?_ t_it L?*) _iTi?_ L? |4i h@|it E|L}
|i h}|@?_ t_i @*tL _iTi?_t L? |i uh@U|L? ^ Lu }ThL_U||) h4t
At 4T*it uLh i @4T*i |@| u bf : b |i? |ihi @hi @*@)t @*it Lu Kc R c R2
tU |@| |ihi @hi 4*|T*i i^*Mh@
6}hi _tT*@)t |i @_4ttM*i i^*Mh4 UL4M?@|L?t Lu @?_ |i *Lit|
ThL_U||) @4L?} @U|i h4t ? |i 4@h!i| Wu R t |i *Lit| R @4L?} @U|i
h4t |i? @** @*it Lu ? Mi|ii? R2 @?_ R @hi ui@tM*ic ihi@t u R2 t |i
*Lit| R @4L?} ThL|@M*i h4t |i? @** @*it Lu Mi*L R2 @hi ui@tM*i W?
}i?ih@*c | U@??L| Mi h*i_ L| |@| ML| *?i ti}4i?|t UL?|@? @? i^*Mh4
TL?|c Lh |@| ?i|ih UL?|@?t tU @ TL?|
Wu ES t t@|ti_ |i? |i ?^i @*it Lu |i t|hU|h@* _i|ih4?@?|t tT
TLh| |L _gihi?| i^*Mh@c @?_ |i 4L_i* _Lit ?L| Thi_U| U L?i ** Mi
hi@*3i_ @?_ U L?i ** ?L| t i T*@?i_ ? |i ?|hL_U|L?c |t t @? 4
T*U@|L? Lu |i ?|ih@U|L? Mi|ii? |i hitih@|L? @}i Lu |i ?i4T*L)i_ @?_
|i _t|hM|L? Lu |iU?L*L}it |@| @_4| ThL|@M*i ThL_U|L? Ai hitih@|L?
@}i @giU|t |i _t|hM|L? Lu R @4L?} @U|i h4t M) @) Lu |i hit|hU|L?
|@| |iti R tL*_ i Uii_ Atc @giU|t |i *Lih ML?_ Lu |i tTTLh| Lu
|i _t|hM|L? Lu R @4L?} @U|i h4t L?ihti*)c |i _t|hM|L? Lu R @4L?}
@U|i h4t @giU|t |i hitih@|L? @}ic MiU@ti T@h| Lu |i hi?| Lu ThL_U|L?
t _t|hM|i_ |L |i Lh!iht ? |i uLh4 Lu |i @}i At igiU| Lh!t M) @) Lu
|i i TiU|i_ @}i ? i4T*L)4i?| #i |L |i ?L?*?i@h|) Lu |i hi*@|L? Mi|ii?
@?_ Rc |i hitih@|L? @}i _Lit ?L| _iTi?_ L? |i i TiU|@|L? Lu Rc M|
h@|ih L? |i i TiU|@|L? Lu @ 4L?L|L?i |h@?tuLh4@|L? Lu R @4L?} @U|i h4t
Wu |i _t|hM|L? Lu R tu|t |L |i h}| |i? |i @}i ELgih _t|hM|L? tu|t
|L |i h}|c @?_ u Lh!iht ti@hU 4Lhi i@t*) *i ?i4T*L)i_ |@? *i i4
T*L)i_ Eic bf : b |i? |t 4T*it @ }ih hitih@|L? @}iG | 4@!it ti?ti
|L Mi 4Lhi ti*iU|i *i ?i4T*L)i_
W? |i ?i | tMtiU|L? i }L ?|L 4Lhi _i|@* UL?Uih??} |i U@tit ? U
4*|T*i i^*Mh@ 4@) LUUhc @?_ |ih hitTiU|i i4ThU@* hi*i@?Ui
616
Glvfxvvlrq
6ht| Lu @**c | t tiu* |L _t|?}t Mi|ii? i|ih bf t t4@**ih |@?c i^@*
|Lc Lh *@h}ih |@? b Wu |i) @hi i^@*c |i? ti@hU *i ?i4T*L)i_ t @t iu
uiU|i @t ti@hU *i i4T*L)i_c @?_ UL?ti^i?|*) |i hitih@|L? @}i Lu |i
?i4T*L)i_ t i^@* |L |i ?t|@?|@?iLt |*|) L *i Mi?} ?i4T*L)i_c
U t |i @*i Lu *ithi K At 4i@?t |@| |ihi t ?L uii_M@U! uhL4 |i
ThL_U||) ELh @}i _t|hM|L? |L |i hitih@|L? @}ic @?_ |i i^*Mh4
t ?^i 6hL4 |i ThLTLt|L?t @MLic L?*) |)TiR h4t @hi @U|i g R2 Kc
*i ML| |)Tit @hi @U|i g R2 : Kc U t ?||i*) LMLt Atc
Wu bf ' b |i? |ihi i t|t @ ?^i i^*Mh4
Wu K R2 |i? L?*) |)TiR h4t @hi @U|i Wu K R2 |i? ML| |)Tit @hi @U|i
L UL?t_ih |i U@ti bf : b Ai? Lh!iht ti@hU 4Lhi i@t*) *i ?i4
T*L)i_ |@? *i i4T*L)i_c tL | 4@!it ti?ti |L Mi 4Lhi ti*iU|i *i ?i4
T*L)i_ |@? u bf ihi i^@* |L b L?ti^i?|*)c |i hitih@|L? @}i i Uii_t
K LhiLihc @t @h}i_ ? |i ThiLt tMtiU|L?c }ih @}it @hi @ttLU@|i_
| @ }ih hitih@|L? @}i ) i*@MLh@|?} L? ES i LM|@?
Wu bf : b |i? |ihi @*@)t i t|t @? i^*Mh4
Wu K R2 |i? |i i^*Mh4 t ?^i EL?*) |)TiR h4t @hi @U|i Wu K R2
|i? i @i i|ih L?i Lu |i uL**L?} |hii t|@|L?tG i^*Mh4 t ?^i
@?_ L?*) |)TiR h4t @hi @U|ic i^*Mh4 t ?^i @?_ ML| |)Tit @hi @U|ic
Lh ML| i^*Mh@ @hi TLttM*i ** |hii U@tit @hi @||@?@M*i uLh t|@M*i T@h@4i|ih
@*it
Ai i4ThU@* i_i?Ui ? |i *|ih@|hi t}}it|t |@| ? }i?ih@* bf : b 6Lh i @4T*ic +__ih @?_ V@? _i? ih} EbbH it|4@|i |iti T@h@4i|iht uLh @
?4Mih Lu ,# UL?|hitc @?_ |i) ?_ |@|c |)TU@**)c bf t @ML| |L |L i
|4it @t *@h}i @t b Etii @*tL L?|i4Ttc +LM? @?_ V@? _i? ih}c 2fffc uLh @
_tUttL? Lu i4ThU@* hit*|t ? |i *|ih@|hi W?_ii_c uLh T*@tM*i T@h@4i|ih
@*itc |ihi @hi }i?ih@**) 4*|T*i i^*Mh@ 6Lh i @4T*ic @ uhU|L?@* ?i4
T*L)4i?| h@|i Lu S2DI ULhhitTL?_t |L bf *B ' D Wu ? @__|L? bf ' b |i?
|i *iu|@?_ t_i Lu ES i^@*t @ML| e W| t ?L| ?hi@tL?@M*i |L i TiU| |i
4__*i |ih4 Lu ES |L Mi t4@**ih |@? |@| 6Lh i @4T*ic u K Mi U*Lti |L |i ?
i4T*L)4i?| Mi?i|t *ii*c @?_ |i Lh!ih U@? ULLti Mi|ii? |L LUUT@|L?tc
L?i U @t @ ThL_U||) *ii* U t ff 4L?i|@h) ?|t Tih 4L?| *@h}ih
|@? K @?_ |i L|ih 2ffc |i? |i 4__*i |ih4 i^@*t L?i t @ hit*|c i @i
e
4*|T*i i^*Mh@c i UiT| uLh @*it Lu S U*Lti |L L?i W? |ih4t Lu ^c i @i
4*|T*i i^*Mh@ uLh @** @*it Lu ^ t4@**ih |@? @ML| fD 5Lc ? |t i @4T*ic
u |i ThL_U||) _t|hM|L? t t!ii_ |L |i h}| E|ihi @hi 4Lhi h4t |
*LThL_U||) LMt |@? | }ThL_U||) LMt |i? |ihi @hi 4*|T*i
i^*Mh@
, @4T*i AL Mi 4Lhi tTiUUc |@!i bf ' fDc b ' ffDc B '
fffc R2 ' ffc R ' 2ffc ^ ' f2D E|L |L}|tc |iti 4@) Mi
}*_iht @?_ 4L?|t Ai? ? L?i i^*Mh4 ' fHec ' Hfc
|)Tit Lu h4t @hi @U|ic ihi@t ? |i L|ih ' Sc ' bHc
|)TiR h4t @hi @U|i W? ML| U@tit *6 ' ffS2D
ffc K '
? #|U
@?_ ML|
@?_ L?*)
, @4T*i 2 ?3i* i| @* Ebbb it|4@|i i^*Mh4 ti@hU 4L_i*t uLh @ ?4Mih
Lu _gihi?| #@?t *@MLh 4@h!i|tc @tt4?} |@| R @t @ _tUhi|i _t|hM|L?
Ai _gihi?| 4@h!i|t @hi _i?i_ M) |i ThLTih|it Lu |i Lh!iht ? | ,@U
4@h!i| t @tt4i_ |L @i |t L? h4t ?i Lu |i *@MLh 4@h!i|t UL?|@?t |i
Lh!iht | @ M@Ui*Lh _i}hii L @hi @}i_ Mi|ii? 22 @?_ f At ?U*_it
@ML| 2DI Lu |i #@?t TLT*@|L? @}i_ Mi|ii? S @?_ .D 6Lh |t 4@h!i|c
|i it|4@|L? ThLUi_hi ThL_Uit |L _gihi?| 4@tt TL?|t uLh R E|ihi t ?L
i_i?Ui uLh @ |h_ 4@tt TL?| Ai t|hU|h@* T@h@4i|iht @hi it|4@|i_ |L
Mi bf ' ffec b ' fffbc B ' ffc K ' e2Hc R2 ' 2.c R ' 2bc ^ ' f2b
E4L?i|@h) Lt @hi ? bH #@?t khL?ih Tih Lht( |4i h@|it @hi ? ii!t
?3i* i| @* Ebbb hiTLh| |i ULhhitTL?_?} it|4@|it Lu @?_ |L Mi De @?_
2Dc hitTiU|i*) Ai t|hU|h@* T@h@4i|iht @*tL tTTLh| @?L|ih i^*Mh4c
| ' Se @?_ ' b W? ML| U@titc *6 ' f2H L|i |@| |i _@|@
_i?|u) |i ht|4i?|L?i_ i^*Mh4
W? |ih i4ThU@* @?@*)ttc ?3i* i| @* Ebbb }?Lhi 4@?_@|Lh) 4?44
@}it Aihi @hi @U|@**) |L |)Tit Lu 4?44 @}it ? #i?4@h! Etii ai?ti?c
+LtL*4 @?_ 54|c bbef Ai @*it Lu |i }it| Lu |iti uLh t@*@hi_
Lh!iht @hi }i?ih@**) U*Lti |L |i LMtihi_ *Lit| @}it ? |i *@MLh 4@h!i|t ?
?3i* i| @* Ebbb Wu |i *Lit| @}i t i^@* |L @ 4?44 @}i |i? |i
hitih@|L? @}i t ?_i?|i_( i L?*) !?L |@| | t t4@**ih |@? Lh i^@*
|L |i LMtihi_ *Lit| @}i W? |@| U@tic |i hiTLh|i_ it|4@|it Lu @?_ K UL*_
Mi T@h_ M@ti_c @?_ |ihi 4}| @U|@**) Mi *itt tULTi uLh 4*|T*i i^*Mh@
43 Hdfk
eurdgo|0ghqhg vhfwru +olnh wkh phwdo vhfwru, kdv d plqlpxp zdjh wkdw lv ghwhuplqhg
lq fhqwudo zdjh qhjrwldwlrqv ehwzhhq wudgh xqlrqv dqg hpsor|hu rujdql}dwlrqv1 Lq dgglwlrq/
hdfk up kdv plqlpxp zdjhv wkdw duh ghwhuplqhg lq qhjrwldwlrqv ehwzhhq wkh upv dqg orfdo
eudqfkhv ri wkh uhohydqw xqlrqv1
D
+iU@** Liih |@| |i hiTLh|i_ it|4@|i Lu K t @*hi@_) ih) *L Ee2Hc ihi@t
LMtihi_ @}it @hi _tTihti_ ? |i ?|ih@* dDec 2Do @?_ |i LMtihi_ 4i@? @}i
Lgih i^@*t e 6hL4 i_ihti? @?_ 54| EbbH | uL**Lt |@| |i 4?44
?UL4i tTTLh| *ii* EtLU@* @ttt|@?Ui%i*u@hic ?U*_?} _tUhi|L?@h) Mi?i|t
@?_ Lt?} Mi?i|t ? #i?4@h! ? |i i@h*) bHft }i?ih@**) i Uii_t D W|
|ihiuLhi tii4t ?*!i*) |@| @?_ K @hi tMt|@?|@**) t4@**ih |@? it|4@|i_
W? u@U|c |i) UL*_ Mi ?_ihit|4@|i_ ? U@ti Lu tThLt _tTihtL? Lu LMtihi_
@}it _i |L 4i@thi4i?| ihhLht
6Lh 4Lt| L|ih 4@h!i|tc ?3i* i| @* Ebbb ?_ i_i?Ui Lu 4Lhi |@? |L
4@tt TL?|t `i |h? |L |t ? 5MtiU|L? e
W| t ?t|hU|i |L UL?t_ih |i U@ti bf b @t i**c ii? |L} |t tii4t |L
Mi i4ThU@**) *itt hi*i@?|c @?_ ii? |L}c @t i ** tii tLh|*)c |ihi @hi
?L 4*|T*i i^*Mh@ W? |t U@tic Lh!iht ti@hU *itt i@t*) *i ?i4T*L)i_
|@? *i i4T*L)i_ L?ti^i?|*)c |i hitih@|L? @}i t t4@**ih |@? K Ai
}ih |i @}itc |i 4Lhi 4TLh|@?| | t |L *i@i ?i4T*L)4i?| @t ^U!*) @t
TLttM*ic tL |i *Lih |i hitih@|L? @}i ) i*@MLh@|?} L? ES i LM|@?
Wu bf b |i? i^*Mh4 t ?^i Lh ?L?i t|i?|
Wu K R2 |i? |i i^*Mh4 t ?^i EML| |)Tit Lu h4t @hi @U|i Wu K R2
|i? i @i i|ih L?i Lu |i uL**L?} |hii t|@|L?tG i^*Mh4 t ?^i
@?_ L?*) |)TiR h4t @hi @U|ic i^*Mh4 t ?^i @?_ ML| |)Tit @hi @U|ic
Lh i^*Mh4 t ?L?i t|i?| ** |hii U@tit @hi @||@?@M*i uLh t|@M*i T@h@4i|ih
@*it
6hL4 |i ?||L? Mi?_ |i 4*|T*U|) Lu i^*Mh@ ? |i U@ti bf : b c |
t LMLt |@| 4*|T*U|) t ?L| |L Mi i TiU|i_ ? |t hiihti U@ti iUitt@h)
UL?_|L?t uLh ?L?i t|i?Ui @hi |@| bf b @?_ K R2 t ** Mi _tUtti_
Mi*Lc |i *@||ih t ?*!i*) |L LUUh ? @? iUL?L4) ? U @ 4?44 @}i t
4TLti_ |@| i Uii_t |i ?i4T*L)4i?| Mi?i|t *ii*
W| 4@) Mi ?|ihit|?} |L i @4?i @ ui *4|?} U@tit 6Lh R2 tUi?|*)
U*Lti |L R c |i i^*Mh4 t ?^i E| ML| |)Tit Lu h4t @U|i W? |i
*4|c Lu ULhtic |i i^*Mh4 tL*|L? t i^@* |L |i ?^i tL*|L? uLh |i
L4L}i?iLt 4L_i* EU t |i i^*Mh4 u L?*) |)TiR h4t @hi @U|i
L UL?t_ih |i *4|?} U@ti b ' fc i |i i4T*L)i_ _L ?L| hiUii
@*|ih?@|i LM Lgiht W| t |i? LT|4@* uLh @}iti||?} h4t |L Lgih @ @}i
i^@* |L |i hitih@|L? @}i Lu |i ?i4T*L)i_ gih?} @ }ih @}i L*_
?L| ?Uhi@ti |ih Lh!uLhUi Ai hit*|?} i^*Mh4 t |i? |i t@4i @t ? |i
S
4L_i* ? U L?i h4 t 4L?LTL*t| ? |i *@MLh 4@h!i|G @** h4t Lgih @ @}i
i^@* |L |i @*i Lu *ithi K E|i R4L?LTL*t|U tL*|L?( tii #@4L?_c b.
Atc i @i |i i^*Mh4 ? U L?*) |)TiR h4t @hi @U|i u K R2 c
@?_ |i L|ih i^*Mh4 u K R2 W? @?) U@tic i^*Mh4 i t|t @?_ t ?^i
6?@**)c UL?t_ih @| @TTi?t u ti@hU uhU|L?t @?t Wu bf @TThL@Uit
4c i u |i ?i4T*L)i_ ?_ LMt ?t|@?|@?iLt*)c |i? |i) U@? @gLh_ |L
Mi i |hi4i*) ti*iU|i | hitTiU| |L @}i Lgiht t @ hit*|c @TThL@Uit
R c tL L?*) |)TiR h4t @hi @U|i @?_ |i i^*Mh4 t ?^i W? |i *4|c
|i i^*Mh4 @}i Lgih @?_ @}i _t|hM|L?t @hi _i}i?ih@|i ? R Wu b
@TThL@Uit ??|)c i u |i i4T*L)i_ ?_ LMt ?t|@?|@?iLt*)c |i? Lh!iht
?t|@?|@?iLt*) 4Li |L |i |LT Lu |i @}i *@__ihc @?_ |i @}i _t|hM|L? C
@TThL@Uit |i _i}i?ih@|i _t|hM|L? @| R W? |t U@ti _Lit ?L| @TThL@U R c
@?_ ?i|ih _Lit 8 OLiihc |t t hhi*i@?|c MiU@ti @? ?i4T*L)i_ Lh!ihc
TL? *i@?} ?i4T*L)4i?|c 44i_@|i*) 4Lit |L @ @}i R t @ hit*|c h4
ThL|t |i?_ |L 3ihL W| uL**Lt uhL4 ES |@| |t i^*Mh4c U U@? Mi
*@Mi*i_ |i RUL4Ti||i tL*|L?c t ?^ic @?_ t tU |@| ML| |)Tit Lu
h4t @hi @U|ic @*|L} |i |)TiR2 h4t *Lti |ih i4T*L)iit ?t|@?|@?iLt*)
wi| t hi|h? |L |i t|@|L? ? U |L i^*Mh@ @hi TLttM*i Ai i^
*Mh4 | L?*) |)TiR h4t t |L Mi Thiuihhi_c t?Ui i4T*L)i_ Lh!iht @hi
L? @ih@}i 4Lhi ThL_U|i ? |t i^*Mh4c ihi@t ?i4T*L)4i?| t |i
t@4i ? ML| i^*Mh@ ? ?i4T*L)i_ Lh!ih UL?|hM|it K |L tLU@* i*u@hic
ihi@t @? i4T*L)i_ Lh!ih |L}i|ih | t i4T*L)ih UL?|hM|it |i hi?| Lu
|i 4@|Uc U i^@*t |i ThL_U||) *ii* *|ih?@|i*)c |i) UL?|hM|i
|i ThL_U||) *ii* 4?t K E|i ht| U@ti U@? LUUh u |i ?L?4L?i|@h) @*i
Lu *ithi t 3ihL @?_ ?i4T*L)4i?| Mi?i|t @hi ?@?Ui_ i |ih?@**) 6Lh i TLt
|L?@* UL?i?i?Ui i @_LT| |i ht| U@ti( Liihc |i hit*|t @hi hLMt| |
hitTiU| |L |t W? |i i^*Mh4 | L?*) |)TiR h4tc |i tLU@* i*u@hi L
V W |i? i^@*t
VW '
B6
b6
Kn f
R
B n bf
B n bf
W? |i L|ih i^*Mh4c |i tLU@* i*u@hi L V WW i^@*t
V WW '
B6
b6
e 2 n E CER
e o
Kn f
dCER
B n bf
B n bf
ihi C _i?L|it |i UhLtttiU|L?@* @}i _t|hM|L? @4L?} Lh!iht *i@h*)c
V WW V W 44 Wkh
dvvxpswlrq wkdw surgxfwlrq lv olqhdu lq wkh qxpehu ri hpsor|hhv lv lpsruwdqw khuh>
ghfuhdvlqj uhwxuqv wr vfdoh zrxog plwljdwh wkh hhfw1
.
e U@? Mi i Thitti_ ? |ih4t Lu 8 Ec
e U i^@*t
Nt?} i^@|L? E2c CE
WW
^ t @ hit*|c V i^@*t
%
&
B6
bf 6
BE ^
WW
Kn
R V '
ER R2 B n bf
B n bf
B n b ^
tL V WW ?Uhi@tit ? b @?_ ? ^ At 4@!it ti?ti Wu b t *@h}i |i? Lh!iht
4Li ^U!*) uhL4 |)TiR2 LMt |L |)TiR LMt W? |i Lh_t Lu Ui4L}* @?_
54ih Ebb.c i^*Mh4 t 4Lhi iUi?| MiU@ti Lh!iht U@? @Uii @ 4Lhi
iUi?| @**LU@|L? M) t@4T*?} 4Lhi h4t Wu ^ t *@h}i |i? |ihi @hi ?L| 4@?)
|)TiR2 LMt ? |i ht| T*@Ui
617
Pruh wkdq wzr up w|shv
L?UiT|@**)c | t t|h@}|uLh@h_ |L }i?ih@*3i |i @MLi @?@*)tt |L @ ?|i
?4Mih Lu h4 |)Tit |@| t *@h}ih |@? |L 6Lh @?) TLttM*i *Lit| ThL_U|
|) *ii* @4L?} @U|i h4tc | @t |L Mi UiU!i_ i|ih |i ULhhitTL?_?}
hitih@|L? @}i t ML| Mi*L |@| *ii* @?_ @MLi |i }it| ThL_U||) *ii*
@4L?} |i ?L?@U|i h4t OLiihc u i ?Uhi@ti |i ?4Miht Lu h4 |)Titc
|i T@h@4i|ih ?i^@*|) |@| U@h@U|ih3it i|ih @? i^*Mh4 i t|t | @**
TLttM*i h4 |)Tit MiUL4it i |hi4i*) U4MihtL4i W? TTi?_ i Thiti?|c
|L| ThLLuc |i u** U@h@U|ih3@|L? Lu |i i^*Mh@ ? |i 4L_i* | |hii
TLttM*i h4 |)Tit W? |@| 4L_i*c |i |hii ThL_U||) @*it @hi |@!i? |L
t@|tu) f R R2 R 4 @?_ R : K `i _i?L|i |i uh@U|L? Lu |)TiR h4t
@4L?} |i |L|@* 4i@thi Lu h4t E@U|i Lh ?L?@U|i M) ^ c | f ^
@?_ ^ n ^2 n ^ ' W? |t 4L_i*c |ihi @hi |hii TLttM*i i^*Mh@c ULhhit
TL?_?} |L i|ih R c Lh R R2 c Lh R2 W? |i tiUL?_ U@tic @
uh@U|L? ^ *E^ n ^2 E@ uh@U|L? ^2 *E^ n ^2 Lu @U|i h4t @t ThL_U||) R
E@t ThL_U||) R2 , @4T*i 6Lh @ ?4Mih Lu _gihi?| *@MLh 4@h!i|t ? #i?4@h!c ?3i* i| @*
Ebbb Etii , @4T*i 2 it|4@|i |i _t|hM|L? Lu R |L @i |hii 4@tt TL?|t
At ?U*_it |i 4@h!i| uLh L4i? @}i_ Mi*L 22 | *itt |@? } tULL*c
|i 4@h!i| uLh L4i? @}i_ @MLi Df | } tULL*c |i 4@h!i| uLh ?__@*t
@}i_ Mi|ii? @?_ Df | @ M@Ui*Lh _i}hiic @?_ |i 4@h!i| uLh ?__@*t
@}i_ Mi|ii? 22 @?_ Df | @ 4@t|ih _i}hii @?_ }ih Nt?} |i hit*|t ?
TTi?_ | U@? Mi tL? |@| ? @** |iti *@MLh 4@h!i|tc |ihi i t| i @U|*)
|L TLttM*i i^*Mh@ Aihi t @? i^*Mh4 ? U @** |hii h4 |)Tit @hi
@U|i EU t |i i^*Mh4 |@| t _i?|i_ M) |i _@|@c @?_ |ihi t @?
H
i^*Mh4 ? U L?*) |)TiR h4t @hi @U|i Ai hitih@|L? @}i ? U@ti
Lu L?*) |)TiR h4t @?_ |)TiR2 h4t t Mi*L R c tL |ihi t ?L i^*Mh4
| L?*) |)TiR h4t @?_ |)TiR2 h4t
, @4T*i e L*t Ebb. it|4@|it i^*Mh4 ti@hU 4L_i*t uLh @ ?4Mih Lu
_gihi?| N5 *@MLh 4@h!i|tc @tt4?} |@| R @t @ _tUhi|i _t|hM|L? Ai
ti|T t t4*@h |L ?3i* i| @* Ebbb ?i Lu |i *@MLh 4@h!i|t UL?Uih?t
u**|4i LMt uLh 4@*i UL**i}i }h@_@|it L ihi @}i_ Mi|ii? e @?_ 22 ?
b.b @?_ L @hi uL**Li_ ?|* bb Ai ?4Mih Lu h4 |)Tit t it|4
@|i_ |L i^@* Ai L|ih hiTLh|i_ t|hU|h@* T@h@4i|ih it|4@|it @hi bf '
ffc b ' fffSec B ' fff2c R ' Sf.c R2 ' Hfec R ' fDc ^2 ' f2Hc ^ ' ffH
E? N5 #L**@ht @?_ ii!t2 W? @__|L?c c ,C Ec @?_ @hi it|4@|i_ |L
Mi D2c DSec @?_ Hf.c hitTiU|i*) 6hL4 i^@|L?t E @?_ E2 | uL**Lt |@|
EB n bf ' EB n b K n Ebf b ,C Ec @?_ |t U@? Mi ti_ |L LM|@? |i
it|4@|i |@| K ' bbH Ai i^*Mh4 | h4 |)Tit t ?^i OLiihc
| t U*i@h |@| |i it|4@|i_ @*i Lu K t 4T*@tM*) *L At t 4@) Mi @
UL?ti^i?Ui Lu 4i@thi4i?| ihhLht ? |i @}i _@|@ Wu |i |hi *Lit| @}i ?
|i 4@h!i| t }ih |@? |i LMtihi_ *Lit| @}ic @?_ u |t t }?Lhi_c |i?
@?_ K @hi ?_ihit|4@|i_ 5TTLti |@| |i |hi @*i Lu K t Sf #L**@ht
Tih ii! E?t|i@_ Lu bbH( | |i? uL**Lt |@| ? |i i^*Mh4 | @** |hii
h4 |)Tit |i hitih@|L? @}i Lu |i ?i4T*L)i_ )L?} 4@*i UL**i}i }h@_@|it
t e #L**@ht Tih ii! ?t|i@_ Lu D2 Ai? |ihi @hi |L TLttM*i i^*Mh@G
L?i ? U @** |hii h4 |)Tit @hi @U|ic @?_ L?i ? U L?*) |)TiR @?_
|)TiR2 h4t @hi @U|i
Ai *@MLh 4@h!i|t ? , @4T*it 2e 4@) _tT*@) @__|L?@* i^*Mh@c ? U
Uhhi?|*) *@|i?| h4t @hi @U|i ALti h4t @i ThL_U||) *ii*t |@| @hi
Mi*L |i Uhhi?| hitih@|L? @}i Lh 4@?_@|Lh) 4?44 @}i W| U@??L|
Mi ?uihhi_ i4ThU@**) i|ih @__|L?@* i^*Mh@ i t| Lh @| ThL_U||)
*ii*t |Lti h4t @ic t4T*) MiU@ti i _L ?L| LMtihi @?) @U||) @| Uhhi?|*)
*@|i?| h4t
L tTTLti |@| |i _t|hM|L? Lu R t UL?|?Lt*) _t|hM|i_ @UhLtt h4t
45 Wkh
prgho hvwlpdwhg e| Erzoxv +4<<:, dovr doorzv iru wudqvlwlrq udwhv lqwr dqg iurp qrq0
sduwlflsdwlrq1 Iru rxu sxusrvhv/ zh pd| surfhhg e| vlpso| dgglqj wkh ydoxh ri wkh wudqvlwlrq
udwh wr qrq0sduwlflsdwlrq 4 wr wkh ydoxh ri 1 Wkh iruphu lv vr vpdoo iru wklv pdunhw wkdw wklv
grhv qrw dhfw wkh uvw irxu gljlwv ri wkh ydoxh ri 1
46 Ri frxuvh/ lq wkdw fdvh/ wkh rwkhu hvwlpdwhv pd| eh eldvhg dv zhoo1 Qrwdeo|/ li wkh prgho
wulhv wr w dq hpslulfdo zdjh gdwd glvwulexwlrq wkdw kdv d idwwhu ohiw0kdqg wdlo wkdq lw vkrxog
kdyh/ wkhq 4 pd| eh xqghu0hvwlpdwhg1
b
`i _i?L|i |i _t|hM|L? u?U|L? Lu R @UhLtt @** @U|i @?_ ?L?@U|i h4t M)
Kf ER At t @ t|hU|h@* _i|ih4?@?| 6Lh UL?i?i?Ui i @tt4i |@| Kf @t
@ TLt|i @?_ UL?|?Lt*) _gihi?|@M*i _i?t|) f L? |i tTTLh| ERf c Rc |
f Rf R 4 `i @tt4i |@| Kf EK c U t @ ?iUitt@h) UL?_|L? |L
@i ThL_U|L?
wi| R _i?L|i |i ?44 ThL_U||) Lu h4t U 4@!i @ ThL| @?_ |t
@hi @U|i L? |i 4@h!i| At t Lu ULhti ?L| @ t|hU|h@* _i|ih4?@?| Ai
4i@thi Lu @U|i h4t ?@ i^@*t E Kf ER? wi| KER _i?L|i |i _t|hM|L?
Lu R @4L?} @U|i h4tc
KER '
Kf ER Kf ER
Kf ER
E.
| R R
L?|i4Ttc +LM?c @?_ V@? _i? ih} E2fff ThL_i @ UL4Thii?ti |iLh
i|U@* @?_ i4ThU@* @?@*)tt Lu |i 4L_i* | @ }i?ih@* UL?|?Lt _t|hM|L?
uLh R Ai) tL |@| R ' 4@ iRf c jc |@| ' c @?_ |@| Rc ?_ih
|i @tt4T|L? |@| R @t @ ?|i 4i@?c i ,Kf ER 4 5L4i@| *LLti*)c
L?i 4@) t|@|i |@|c ? U@ti Lu @ UL?|?Lt ThL_U||) _t|hM|L?c L?*) L?i
@}i t ThL| 4@ 43?} uLh @ h4 Lu @ }i? |)Ti R At _i?it |i 4@TT?}
' gER W? i^*Mh4c g t ?Uhi@t?} @?_ ?L?*?i@h ? R @?_ _iTi?_i?| @**
t|hU|h@* _i|ih4?@?|te Ai _t|hM|L? Lu @}i Lgiht t 8 E ' KEg 3 E
W? }i?ih@*c ?L i T*U| i ThittL?t i t| uLh i^*Mh4 tL*|L?t
6}hi 2 _tT*@)t |i @_4ttM*i i^*Mh4 UL4M?@|L?t Lu @?_ |i *Lit|
ThL_U||) R @4L?} @U|i h4t ? |i 4@h!i| @*i R : Rf U@? L?*) Mi |i
*Lit| R @4L?} @U|i h4t u | i^@*t Wu Rf t |i *Lit| R @4L?} ThL|@M*i
h4t |i? @** @*it Lu Mi*L Rf @hi ui@tM*iD
Nt?} ?4ihU@* i @4T*itc L?|i4Ttc +LM?c @?_ V@? _i? ih} E2fff tL
|@| uLh Uih|@? t|hU|h@* T@h@4i|ih @*it |ihi t @ ?^i i^*Mh4c *i
uLh L|iht |ihi t ?L i^*Mh4c @?_ uLh )i| L|iht |ihi @hi 4*|T*i i^*Mh@
d jlyhq ydoxh ri !/ dqgk zlwk =@ 4 / wkh htxloleulxp N vdwlvhv
Us
5
5 l
5
z @ N +s, @ s + . 4 +s,, +s !,@+ . 4 , . s + . 4 +{,, g{ iru doo s 5 +s> s,1
48 Vxssrvh zh zrxog dvvxph wkdw wkh uhvhuydwlrq zdjh ri wkh xqhpsor|hg kdv d {hg jlyhq
ydoxh/ dqg vxssrvh zh zrxog vroyh wkh htxloleulxp jlyhq wklv ydoxh ri !1 Wklv jlyhv rxwfrphv
iru N> I> J hwf1 jlyhq !1 E| vxevwlwxwlqj wklv J lqwr htxdwlrq +4, zh rewdlq dqrwkhu ydoxh ri
!/ qdpho| wkh ydoxh wkdw lv rswlpdo jlyhq wklv J1 Zh pd| gr wklv iru glhuhqw vwduwlqj ydoxhv
ri !/ dqg wkh lqwhuvhfwlrqv ri wkh uhvxowlqj frqwlqxrxv fxuyh zlwk wkh gldjrqdo +78r , olqh jlyh
wkh htxloleulxp ydoxhv ri !1 Iru d jlyhq htxloleulxp ydoxh ri !/ wkh fruuhvsrqglqj ydoxh ri s
fdq eh ghulyhg lq Iljxuh 5 e| jrlqj iurp wkh yhuwlfdo d{lv wr wkh krul}rqwdo d{lv xvlqj wkh vrolg
fxuyh1 Qrwh wkdw wkh vdph surfhgxuh fdq eh shuiruphg zlwk Iljxuh 41
47 Iru
2f
Bi? |i hit*|t ? |i ThiLt tMtiU|L?tc | t ?||i*) T*@tM*i |@| i
4@) }i| 4*|T*i i^*Mh@ Ai igiU| Lu |i ThL_U||) _t|hM|L? L? |i
hitih@|L? @}i Lh!t M) @) Lu |i i TiU|@|L? Lu @ 4L?L|L?i |h@?tuLh4@|L?
Lu Rc @?_ @ _tUhi|i _t|hM|L? | @ ?|i ?4Mih Lu TL?|t Lu tTTLh| U@? Mi
@TThL 4@|i_ i** M) @ UL?|?Lt _t|hM|L?c ? |ih4t Lu i TiU|@|L?t
MLt*)c u bf ' b |i? |ihi t @ ?^i i^*Mh4 L?|i4Ttc +LM?c
@?_ V@? _i? ih} E2fff @*tL ThLi |@| |ihi @*@)t i t|t @? i^*Mh4 u
R 4c ThL_i_ |@| |ihi t @ 4@?_@|Lh) 4?44 @}iS Ai |)Ti Lu
?L?i t|i?Ui Lu i^*Mh4 |@| LUUht u R t _tUhi|i | @ ?|i ?4Mih Lu
TL?|t @?_ bf b _Lit ?L| U@hh) Lih |L |i 4L_i* | UL?|?Lt Rc MiU@tic
M@tU@**)c |i _t|hM|L? KER t ?L UL?|?Lt ? R OLiihc u R ' 4 |i?
|ihi t @ _gihi?| |)Ti Lu ?L?i t|i?Ui Lu i^*Mh4 5L4i@| *LLti*)c u ?Uhi@tit |i? |i _t|hM|L? Lu R @4L?} @U|i h4t 4@) MiUL4i 4U 4Lhi
@||h@U|ic Tt?} T ii? 4Lhic i|U
W? TTi?_ 2 i ThLi |i uL**L?} @__|L?@* hit*|G
Wu bf : b c @?_ u |i UL?|?Lt _t|hM|L? Kf @t @? ?Uhi@t?} u@*hi h@|ic
@?_ Rf Kc |i? |ihi t @ ?^i i^*Mh4
Ai u@*hi h@|i ELh @3@h_ h@|i Lu |i _t|hM|L? Kf t _i?i_ @t f ER*Kf ERc
| Kf ' Kf Ai _t|hM|L? @t @? ?Uhi@t?} u@*hi h@|i EW6+ u |i
_ih@|i Lu |i u@*hi h@|i t ?L??i}@|i uLh @** R 5 ERf c R W6+ t i^@*i?|
|L *L} UL?U@|) Lu Kf @?_ t 4T*i_ M) *L} UL?U@|) Lu f 5L4i@| *LLti*)c L?i 4@) t@) |@| W6+ 4T*it |@| |i h}|@?_ |@* Lu Kf
tL*_ Mi @| *i@t| @t |? @t |i |@* Lu @? i TL?i?|@* _t|hM|L? , @4T*it Lu
W6+ _t|hM|L?t Lu ?L??i}@|i h@?_L4 @h@M*it @hi i TL?i?|@* _t|hM|L?t
@?_ ?Lh4@* _t|hM|L?t |h?U@|i_ uhL4 Mi*L 6Lh L|ih i @4T*it @?_ @ thi)
Lu |iti UL?UiT|tc tii V@? _i? ih} Ebbe N?uLh|?@|i*)c W6+ t @? ?|i?@M*)
t|hL?} @tt4T|L? uLh ThL_U||) _t|hM|L?t L?|i4Ttc +LM? @?_ V@? _i?
ih} E2fff tL |@| |i i^*Mh4 Kf tL*_ @U|@**) @i @ ih) u@| h}|
@?_ |@* u |i 4L_i* t |L }i @? @UUh@|i | |L @}i _@|@ W?||i*)c |t 4@)
Mi T*@tM*ic @t |i ThL_U||) _t|hM|L? _L4?@|it |i @}i _t|hM|L?c
@?_ |ihi t @M?_@?| i4ThU@* i_i?Ui |@| @}i ELgih _t|hM|L?t @i
u@||ih h}|@?_ |@*t |@? @t hi^hi_ M) W6+ Etii V@? _i? ih}c bbe W? u@U|c
L?|i4Ttc +LM? @?_ V@? _i? ih} E2fff ThL_i _hiU| h4_@|@ i_i?Ui
|@| |i _t|hM|L? Lu R @t @ u@| |@* @?_ t ?L| W6+ Etii 6Lht*?_ @?_ w?_c
bb.c uLh t4*@h i_i?Ui AihiuLhic |i @MLi ?^i?itt hit*| t Lu *4|i_
49 Wkh
frqglwlrq wkdw wkhuh lv d pdqgdwru| plqlpxp zdjh lv qrw qhfhvvdu|1
2
tiu*?itt
7
Hqgrjhqrxv mre rhu duulydo udwhv
t 4i?|L?i_ ? |i ?|hL_U|L?c | UL*_ Mi @h}i_ |@| bf @?_ b 4@) _iTi?_
L? ?@ At L*_ @i 4T*U@|L?t uLh |i @?@*)tt @MLic t?Ui ?@ t t4@**ih ?
|i i^*Mh4 | L?*) |)TiR h4t |@? ? |i L|ih i^*Mh4 Ai @) ?
U bf @?_ b _iTi?_ L? ?@ uL**Lt uhL4 |i 4@|U?} |iU?L*L}) L? |i *@MLh
4@h!i| @?_ |i ti@hU Mi@Lh Lu Lh!iht @?_ h4t Wu ?@ _iUhi@tit |i?c L?
|i L?i @?_c |ihi @hi *itt h4t |L Mi t@4T*i_ M) Lh!iht ? |i L|ih @?_c
|i hi4@??} h4t ** Mi *@h}ih E|i) ** @i *@h}ih *@MLh uLhUit tL |i) 4@)
i** Mi i@tih |L *LU@|i M) ti@hU?} Lh!iht Wu |iti igiU|t UL?|ihM@*@?Ui |i?
bf @?_ b @hi ?_iTi?_i?| Lu ?@ c @?_ |i hit*|t Lu |i ThiLt tiU|L? uL**L
W? |t tiU|L? i @_LT| @ 4Lhi }i?ih@* @TThL@U 5TTLti |@| bf @?_
b @hi ML| u?U|L?t Lu ?@ c M| |@| |ihi t @ UL?t|@?| k tU |@| @*@)t
b E?@ *bf E?@ ' k EMi*L i ThL_i @ t|U@|L? uLh tU @ tTiUU@|L? ?
|ih4t Lu @ 4@|U?} u?U|L? 5?Ui i @hi ?|ihit|i_ ? |i i |i?| |L U
|i ThiLt hit*|t L? 4*|T*U|) Lu i^*Mh@ U@hh) |hL}c i @tt4i ? |t
tiU|L? |@| f k EtL bf : b 6hL4 hLTLt|L? c |i i^*Mh4 ?
U L?*) |)TiR h4t @hi @U|i i t|t u @?_ L?*) u kE kEbf E^?2 ER R2 EB n kbf E^?2 ER2 K 6hL4 hLTLt|L? 2c |i i^*Mh4 ? U
ML| |)Tit Lu h4t @hi @U|i i t|t u @?_ L?*) u kE kEbf E?2 ^ 2 ER R2 EB n kbf E?^2 ER2 K Atc |iti |L i^*Mh@ ML| i t| u @?_ L?*) u
kE kEbf E^?2
R2 K
kE kEbf E?2 ^ 2
:
EB n kbf E^?2
R R2
EB n kbf E?^2
EH
EL|i |@| @| |t t|@}i i U@??L| ThiU*_i i t|i?Ui Lu 4Lhi i^*Mh@ Ai
?i^@*|it @MLi 4T*) |i uL**L?}c
hLTLt|L? e 6Lh @?) B @?_ k |ihi @hi @*it Lu R c R2 @?_ K uLh U ML|
i^*Mh@ i t|c u @?_ L?*) u |i uL**L?} ?i^@*|) L*_tc
bf E^? : ^bf E?
Eb
W?||i*)c | 4@) tii4 |@| |t UL?_|L? t @*@)t t@|ti_ u |i 4@|U
?} |iU?L*L}) _tT*@)t _iUhi@t?} hi|h?t |L tU@*i ? |i ?4Mih Lu ti@hU?}
?__@*tc U t @ u@h*) ??LULt @tt4T|L? EuLh i @4T*ic |t uL**Lt u
|i 4@|U?} h@|i _tT*@)t UL?t|@?| hi|h?t |L tU@*i ? |i ?4Mih Lu ti@hU?}
22
?__@*t @?_ |i ?4Mih Lu @U@?Uit |@!i? |L}i|ih OLiihc |i t|@|L?
t tL4i@| 4Lhi UL4T*U@|i_ |@? |tc MiU@ti ?L |i ?i4T*L)4i?| h@|i
@*tL _iTi?_t L? ?@ c @?_ ?i4T*L)i_ @?_ i4T*L)i_ ti@hUiht @i _gihi?| ti@hU
?|i?t|it
AL ThLUii_c i @tt4i |@| |i L Lu UL?|@U|t Mi|ii? Lh!iht @?_ i4
T*L)iht t @ u?U|L? Ec Lu |i RigiU|i 4i@thi Lu ti@hU?} Lh!iht @?_
|i 4i@thi Lu @U@?Uit W? *?i | |i *|ih@|hic |t u?U|L? t U@**i_ |i
4@|U?} u?U|L? E?L|i |@| ihi RUL?|@U| u?U|L? L*_ Mi @ 4Lhi @TThLTh
@|i ?@4i 6ht| UL?t_ih |i tiUL?_ @h}4i?| Lu Ec L|i |@| @** @U|i
h4t @*@)t @?| |L i T@?_c @t |i ThL| Tih @__|L?@* Lh!ih t @*@)t t|hU|*)
TLt|i Aiti h4t @*@)t @i @ @U@?U)c @?_ |i) @| T@tti*) uLh ti@hU?}
Lh!iht Atc |i 4i@thi Lu @U@?Uit i^@*t |i 4i@thi ?@ Lu @U|i h4t
L *i| t |h? |L |i ht| @h}4i?| Lu Ec ** Lh!iht @*@)t ti@hU uLh
EMi||ih LMt Ai RigiU|i 4i@thi Lu ti@hU?} Lh!iht 4@) _gih uhL4 |i
4i@thi Lu ti@hU?} Lh!iht 6 MiU@ti | |@!it ?|L @UUL?| |@| tL4i Lh!
iht 4@) @i _gihi?| ti@hU ?|i?t|it |@? L|iht `i @tt4i |@| Lh!iht<
ti@hU ?|i?t|it @hi @*@)t @| |ih T)tU@* 4@ 44c U _iTi?_t L? |i
Lh!ih<t *@MLh 4@h!i| t|@|i M| _Lit ?L| @h) @UhLtt Lh!iht wi| k 5 Efc
_i?L|i |i hi*@|i ti@hU iUi?U) Lu ti@hU M) i4T*L)i_ Lh!iht ? UL4T@htL?
|L ?i4T*L)i_ Lh!iht Ai? |i igiU|i 4i@thi Lu ti@hU?} Lh!iht U@? Mi
h||i? @t n kE6 W| uL**Lt |@|
bf E?@ '
E n kE6 c ?@ c
n kE6 b E?@ '
E n kE6 c ?@ k E2f
n kE6 tL |@| ?_ii_ k b *bf `i @i |L UiU! i|ih |i ?i^@*|) Eb L*_t AL ThLUii_c i @tt4i
|@| Ec _tT*@)t UL?t|@?| hi|h?t |L tU@*i E+5c U t ? *?i | |i i4
ThU@* *|ih@|hi L? 4@|U?} u?U|L?t uLh |i *@MLh 4@h!i| Etii i} Lh|i?ti?
@?_ tt@h_itc bbb W? T@h|U*@hc i @_LT| @ +5 LMM#L}*@t tTiUU@|L?c
E n kE6 c ?@ ' > E n kE6 3q ?q@
E2
6Lh i@ti Lu i TLt|L? i h*i L| |@| q ' c tL |@| f q L|i |@|
q ' f ThL_Uit |i 4L_i* Lu |i ThiLt tiU|L?
W| t tiu* |L t|@h| @tt4?} E?ULhhiU|*) |@| E2f @?_ E2 _i|ih4?i L
bf U@?}it ? hitTL?ti |L ?@ EtL |@| t @ i_ UL?t|@?| W| t t|h@}|uLh@h_
|L tii |@| bf |i? ?Uhi@tit | ?@ c M| |@| |i ?Uhi@ti t tUi?|*) 4L_it|
uLh ?i^@*|) Eb |L L*_ uLh @?) f ^ E|t _Lit ?L| _iTi?_ L? |i
LMM#L}*@t tTiUU@|L?
2
W? hi@*|)c @*tL U@?}it | ?@ 6hL4 5iU|L? 2c
E?@ B
'
6
B n bf E?@ E22
) tMt|||?} E22 ?|L E2fc t?} E2c i LM|@? @ hi*@|L? |@| U@? Mi h||i?
@t |i ?ihti Lu |i u?U|L? bf E?@ u q : fc
?@ '
bfq > q 6
%
B
k n E k
B n bf
&
E2
W| U@? Mi tL? |@| |t u?U|L? t ?Uhi@t?}c. tL bf ?Uhi@tit ? ?@ 6hL4
E22c |t 4T*it |@| _iUhi@tit | ?@ At ? |h? 4T*it |@| bf ?Uhi@tit
t|hL?}ih | ?@ |@? u ihi @ i_ UL?t|@?| W? Lh_tc @? ?Uhi@ti ? |i
?4Mih Lu @U|i h4t ?Uhi@tit |i LM Lgih @hh@* h@|i Lu |i ?i4T*L)i_c
U ? |h? _iUhi@tit ?i4T*L)4i?|c @?_ |t }it @ uh|ih MLLt| |L |i
@hh@* h@|i Lu |i hi4@??} ?i4T*L)i_
W| hi4@?t |L i @4?i ?_ih U UL?_|L?t bf _Lit ?L| ?Uhi@ti tL t|hL?}*)
| ?@ |@| Eb _Lit ?L| L*_ @?)4Lhi 6Lh hi@tL?t Lu UL?|?|) | t U*i@h
|@| u E?@ t h@|ih ?ti?t|i |L ?@ Ei} MiU@ti q t t4@** Lh u Ec t
h@|ih ?ti?t|i |L |t tiUL?_ @h}4i?| Ei} MiU@ti q t t4@** |i? Eb t|**
L*_t Lhi }i?ih@**)c i @i
hLTLt|L? D Wu |i T@h@4i|ih q Lu |i 4@|U?} u?U|L? t@|tit
fq
s
n
k
2 2
|i? uLh @?) B @?_ uLh @?) ^ 5 Efc L?i U@? @*@)t ?_ @*it Lu R c R2 @?_ K
tU |@| ML| i^*Mh@ i t|
Ai ThLLu t ? TTi?_ Ai UL?_|L? L? q t ^|i i@! 6Lh 4L_ih@|i
@*it Lu kc |i TTih ML?_ i Uii_t f.Dc U t *@h}ih |@? |)TU@* it|4@|it
Lu q W? , @4T*i ? |i ThiLt tiU|L?c k ' fc U ULhhitTL?_t |L
q f.b W? u@U|c |i @MLi tUi?| UL?_|L? L? q t M) ?L 4i@?t ?iUitt@h)
W? , @4T*i c |i ?i^@*|) bf E^? : ^bf E? L*_t uLh @** ^ uLh @*it Lu q @t
s
} @t fH2 W? }i?ih@*c |L}c u q t 4U }ih |@? E n k*2c @?_ t ih)
U*Lti |L c |i? |t ?i^@*|) _Lit ?L| L*_ uLh @?) ^ W| tL*_ @*tL Mi ?L|i_
4: Wkh ghulydwlyh ri q zlwk uhvshfw wr lv sursruwlrqdo wr
d
3
{ 4+4 . {,5 {5 . +4 ,+4 ,{ . 4 / zlwk { @ 3 @1
4
srvlwlyh iru doo { 31
2e
Wkh whup lq vtxduh eudfnhwv lv
|@| u k t U*Lti |L |i? |i h@?}i Lu @*it Lu R c R2 @?_ K uLh U 4*|T*i
i^*Mh@ i t| t ih) ?@hhL
L *i| t |h? |L |i tLU@* i*u@hi Lt Ai i?||it V W @?_ V WW @hi _i?i_
@t ? |i ThiLt tiU|L?c |i L?*) _gihi?Ui Mi?} |@| V W ?L t @ u?U|L?
Lu ^?c t?Ui | _iTi?_t L? bf E^? W? UL4T@htL? |L |i ThiLt tiU|L?c V W t
?L *Lih Wu |i @hh@* h@|it _iTi?_ L? |i 4i@thi Lu @U|i h4t |i? |i
@hh@* h@|it ? |i i^*Mh4 | L?*) |)TiR h4t @hi *Lih |@? MiuLhi
At ?Uhi@tit |i ?i4T*L)4i?| h@|ic U ? |h? _iUhi@tit tLU@* i*u@hi t
@ hit*|c |i _gihi?Ui Mi|ii? V W @?_ V WW t ?L t4@**ih |@? MiuLhic
B n bf E? W
b E?E ^
R K
EV E^? V WW ' f
ER R2 Eb E? bf E^?
B6
B n kbf E?^
B n bf E^? f
Ai ht| |ih4 L? |i h}|@?_ t_i hiThiti?|t |i u@4*@h ThL_U||) }@?
uLh |i |)TiR i^*Mh4 Ai tiUL?_ |ih4 hiThiti?|t |i *Ltt _i |L ?Uhi@ti_
?i4T*L)4i?| N?_ih h@|ih i |hi4i UL?_|L?tc |i t4 U@? Mi ?i}@|i Aihi
_L ?L| tii4 |L Mi |h@?tT@hi?| UL?_|L?t L? |i t|hU|h@* T@h@4i|iht ?_ih
U |i t4 t @*@)t TLt|iH
6?@**)c i hi|h? |L |i i @4T*it _tUtti_ ? |i ThiLt tiU|L? W? |iti
i @4T*itc R c R2 @?_ K @i i_ @*itc tL |@| |i @MLi ThLTLt|L? U@??L| Mi
@TT*i_ `i U@? Liih UiU! uLh U @*it Lu bf E^? ELh uLh U @*it Lu
q |ihi @hi 4*|T*i i^*Mh@c M) i @4??} |i ?i^@*|it EH Ai @*it
Lu |i LM Lgih @hh@* h@|it }i? ? |i ThiLt tiU|L? ULhhitTL?_ |L |i
i^*Mh4 ? U ML| |)Tit Lu h4t @hi @U|ic tL |i tiUL?_ ?i^@*|) ?
EH t t@|ti_ @?_ |t i^*Mh4 _i?|i*) i t|t 6Lh |i L|ih i^*Mh4
|L i t|c |i ht| ?i^@*|) ? EH @t |L L*_ At ?i^@*|) U@? Mi hih||i?
@t @? ?i^@*|) L? bf E^?c
bf E^? :
u
k n
B
3
3
kE kER R2 R2 K
3
, @4T*i EUL?|?i_ +iU@** |@| bf E? ' fD @?_ |@| 2DI Lu |i h4t @i
@ } ThL_U||) `| ML| |)Tit Lu h4t @U|ic |i 4i@? tLU@* i*u@hi
V WW *6 i^@*t DS UULh_?} |L |i @MLi ?i^@*|)c |i i^*Mh4 | L?*)
} ThL_U||) h4t i t|t u bf E^? ff.2 5Lc ? |Lti U@tit |ihi @hi
4; Vzlqqhuwrq
+4<<9, h{dplqhv dq htxloleulxp vhdufk prgho zlwk zdjh vhwwlqj/ ghfuhdvlqj
uhwxuqv wr vfdoh lq surgxfwlrq/ dqg devhqfh ri rq0wkh0mre vhdufk1 Wkh htxloleulxp lv xqltxh/
exw plqlpxp zdjh lqfuhdvhv pd| uhvxow lq pruh uhmhfwlrq ri dssolfdqwv e| upv dv zhoo dv kljkhu
surgxfwlrq hflhqf|1 Dv lq rxu prgho/ wkh qhw hhfwv rq zhoiduh dv zhoo dv xqhpsor|phqw pd|
eh srvlwlyh dw wkh vdph wlph1
2D
|L i^*Mh@ L?t_ih |i i^*Mh4 | L?*) |)TiR h4t `|? |i
h@?}i Lu @_4ttM*i @*it Lu bf E^?c |i *Lit| tLU@* i*u@hi @?_ |i }it|
?i4T*L)4i?| h@|i @hi @||@?i_ u bf E^? ' ff.2 At }it *6 ' f2 @?_
V W E^?*6 ' .S At tLU@* i*u@hi t t|** }ih |@? V WW _itT|i |i u@U|
|@| ?i4T*L)4i?| @t @*4Lt| _LM*i_ Wu bf E^? : ff.2 |i? V W E^? t ii?
}ih( u bf E^? ' bf E? ' fD |i? V W E^?*6 ' HH Ai @*it Lu q |@|
}i 4@|U?} u?U|L?t U }i?ih@|i bf E^? ff.2 U@? Mi _i|ih4?i_ M)
i@*@|?} E2f @?_ E2 @| ^? @?_ ? t @ hit*|c f q fDf
, @4T*i 2 EUL?|?i_ +iU@** |@| ihi bf E? ' ffe @?_ |@| @ML| I Lu
|i h4t @i @ } ThL_U||) V WW *6 i^@*t 2b Ai i^*Mh4 |
L?*) } ThL_U||) h4t i t|t u bf E^? ff2 Wu bf E^? ' ff2 |i? |i
i^*Mh4 | L?*) |)TiR h4t @t *6 ' fH @?_ V W E^?*6 ' .D Atc
tLU@* i*u@hi t @}@? t|** }ih |@? ? |i L|ih i^*Mh4 EWu bf E^? ' ffe
|i? V W E^?*6 ' HHe Ai @*it Lu q ? dfc f22o }i 4@|U?} u?U|L?t U
}i?ih@|i bf E^? ff2
8
D plqlpxp zdjh
W? |t tiU|L? i uLUt L? 4@h!i|t | 4*|T*i i^*Mh@c |@| tc i @tt4i
|@| ES L*_tc U 4T*it |@| bf : b @?_ K R2 wi| W @?_ WW _i?L|i
|i hitih@|L? @}it ? |i i^*Mh4 ? U L?*) |)TiR h4t @hi @U|i
@?_ ? |i L|ih i^*Mh4c hitTiU|i*) L tTTLti |@| |i *@MLh 4@h!i|
t ? |i i^*Mh4 ? U ML| |)Tit Lu h4t @hi @U|ic @?_ tTTLti |@|
@ 4@?_@|Lh) 4?44 @}i u t 4TLti_ `i @tt4i u** ULih@}i Lu |t
4?44 @}i `i U@? _t|?}t Mi|ii? i U@tit _iTi?_?} L? |i hi*@|i
@*i Lu u E Wu u WW |i? |t _Lit ?L| @i @?) igiU| L? |i i^*Mh4 L|UL4i
E Wu WW u R2 |i? |i i^*Mh4 t t|** tU |@| ML| |)Tit Lu
h4t @hi @U|i OLiihc u hiT*@Uit WW @t |i *Lit| @}i ? |i 4@h!i|
Ai 4@h!i| TLih Lu Lh!iht ?Uhi@tit @| |i i Ti?ti Lu |i h4t< 4L?LTtL?)
TLih t @ hit*|c |i L*i @}i ELgih _t|hM|L? tu|t T@h_t At @t
@ TLt|i igiU| Lu |i hitih@|L? @}i WW | ht| t}| L?i 4@) |?! |@|
|i ?i WW 4@) i Uii_ u OLiihc |t t ?L| TLttM*i @t | L*_ 4T*) |@|
2S
|ihi @hi |L _gihi?| i^*Mh@ ? U ML| |)Tit Lu h4t @hi @U|ib Ai
i^*Mh4 L|UL4it EfE @hi t|** @*_c ThL_i_ |@| t hiT*@Ui_ M) u E Wu R2 u W |i? |)TiR2 h4t U@??L| LTih@|i ThL|@M*) @?)
4Lhic @?_ |i ?u@Lh@M*i i^*Mh4 t hiT*@Ui_ M) |i u@Lh@M*i i^*Mh42f
OLiihc |i L|UL4i Lu |i *@||ih i^*Mh4 t ?L| @giU|i_ ? @?) @) M) u
t?Ui | t t4@**ih |@? W t @ hit*|c |i 4TLt|L? Lu u ?_Uit @ tu| ?
|i i^*Mh4c M| |i @*i Lu u |ti*u _Lit ?L| i?|ih |i ?i i^*Mh4
L|UL4it Ai 4?44 @}i t t|hU|*) t4@**ih |@? |i *Lit| @}i ? |i
4@h!i|c @?_ UL?ti^i?|*) |i @}i ELgih _i?t|) _Lit ?L| _tT*@) @ tT!i @| |
E# Wu W u R |i? @}@? |i ?u@Lh@M*i i^*Mh4 t hiT*@Ui_ M) |i
u@Lh@M*i i^*Mh4c M| ?L u @giU|t |i L|UL4i Lu |i *@||ih i^*Mh4
t?Ui | t |i *Lit| @}i ? |i 4@h!i| Ai L|UL4i ? U@ti Lu @ L4L}i?iLt
4L_i* | ' u @t Mii? @?@*)3i_ i |i?ti*) ? V@? _i? ih} @?_ +__ih
EbbH2
E, Wu u R |i? ML| |)TiR @?_ |)TiR2 h4t U@??L| LTih@|i ThL|@M*)c
@?_ |ihi ** ?L| Mi @?) ThL_U|L?
W| t @*tL ?|ihit|?} |L i @4?i |i igiU| Lu @ tMti^i?| @ML*|L? Lu |i
4?44 @}i 6Lh |t i ?ii_ |L Mi 4Lhi tTiUU @ML| |i _i|ih4?@?|t Lu
4@h!i| i?|h) M) Uhhi?|*) *@|i?| h4t `i t4T*) @tt4i |@|c u @U|i h4t
@hi @*hi@_) Thiti?|c |i? |i i?|h) ULt|t u@Ui_ M) |i *@|i?| h4t @hi tL *@h}i
|@| |ihi t ?L i?|h) ii? u |i i TiU|i_ ?t|@?|@?iLt ThL| L Lu |i *@|i?|
h4 MiUL4it TLt|i _i |L |i @ML*|L? Lu |i 4?44 @}i At t Lu
ULhti ?*!i*) @t @ *L?}h? L|UL4ic M| | UL*_ Mi hi}@h_i_ @t @ 4i_4h?
L|UL4i 4Lhi tLTt|U@|i_ @?@*)tt L*_ Mi i |hi4i*) _U*|c @t | L*_
@*tL @i |L _i@* | L|Lui^*Mh4 _)?@4Ut
4< Wkh
h{suhvvlrq iru ! lq fdvh ! ? zO ? s5 lv dv iroorzv/
!
@
+ . 4 ,5 e . +3 4 ,zO . +3 4 ,4 +fs4 . +4 f,s5 ,
+ . 4 ,+ . 3 ,
zlwk f dv lq +47,1 Wkh h{suhvvlrq rq wkh uljkw0kdqg vlgh lv vpdoohu wkdq zO l wkh h{suhvvlrq
rq wkh uljkw0kdqg vlgh ri +47, lv vpdoohu wkdq zO 1
53 Lq sudfwlfh/ wkh plqlpxp zdjh ohyho pd| qrw eh ghwhuplqhg e| pd{lpl}dwlrq ri vrfldo
zhoiduh1 Vreho +4<<<, frqylqflqjo| dujxhv wkdw wkh uhodwlyh vwuhqjwk ri lqwhuhvw jurxsv lq wkh
srolwlfdo surfhvv lv dq lpsruwdqw ghwhuplqdqw1
54 Wkh h{suhvvlrq iru ! lq fdvh ! zO ? s4 lv dv iroorzv/
!
@
+ . 4 ,5 e . +3 4 ,zO . +3 4 ,4 s4
+ . 4 ,+ . 3 ,
Wkh h{suhvvlrq rq wkh uljkw0kdqg vlgh lv vpdoohu wkdq zO l wkh h{suhvvlrq rq wkh uljkw0kdqg
vlgh ri +;, lv vpdoohu wkdq zO 1
2.
Wu u t @ML*ti_ ? Ec |i? ?L|?} U@?}it W? Ec E# @?_ E,c |i
i^*Mh4 L|UL4it _L U@?}i W? E @?_ E#c |i ti| Lu @U|i h4t _Lit ?L|
U@?}ic M| |i @}i _t|hM|L? tu|t |L@h_t *Lih @}it Ai i^*Mh4
? E hi|h?t |L |i i^*Mh4 | L|UL4it |@| @hi i^@* |L |Lti MiuLhi
4TLt|L? Lu u W? Ec |i i^*Mh4 L|UL4i _Lit ?L| U@?}ic 4i@??}
|@| |i |i4TLh@h) 4TLt|L? Lu u @t it|@M*ti_ @ Tih4@?i?| tu| uhL4 |i
?u@Lh@M*i |L |i u@Lh@M*i i^*Mh4
wi| t hi|h? |L |i igiU|t Lu |i 4TLt|L? Lu u MLt*)c |i 4Lt|
?|ihit|?} U@tit @MLi @hi E @?_ E#c MiU@ti |i? |i 4?44 @}i ?_Uit
@ tu| |L |i 4Lhi u@Lh@M*i i^*Mh4 @ti E t |i 4Lt| ?|h}?} 6hL4
|i u@U| |@| |i 4?44 @}i t t|hU|*) t4@**ih |@? |i *Lit| @}i ? |i
4@h!i|c @ U@t@* LMtihih 4@) ?_Ui |@| |i 4?44 @}i t ?L| RM?_?}
@?_ t |t hhi*i@?| W?_ii_c i 4@) Mi t|hi?}|i?i_ ? |t Mi*iu ? U@ti Lu
@? @ML*|L? Lu |i 4?44 @}ic t?Ui |i *@||ih _Lit ?L| @giU| i^*Mh4
W| t 4TLh|@?| |L t|hitt |@| |iti hit*|t @hi ?L| _i |L |i @tt4T|L? |@|
R U@? L?*) @||@? |L @*it +iU@** uhL4 5MtiU|L? e |@| 4*|T*i i^*Mh@
@hi TLttM*i u R @t @ UL?|?Lt _t|hM|L? Lh @ _tUhi|i _t|hM|L? |
4Lhi |@? |L TL?|t Lu tTTLh| W? |i 4L_i* | @ UL?|?Lt*) _t|hM|i_
Rc |i 4TLt|L? Lu @ 4?44 @}i ? Mi|ii? |i |L hitih@|L? @}it |@|
@hi @ttLU@|i_ | |i |L i^*Mh@ i?thit |@| L?i Lu |i i^*Mh@ U@??L|
i t| @?)4Lhic M| | _Lit ?L| @giU| |i L|UL4i Lu |i L|ih i^*Mh4 At
ULhhitTL?_t |L U@ti E @MLi
Ai 4?44 @}i igiU|t @hi UL?tt|i?| | @ ?4Mih Lu t|)*3i_ u@U|t
Etii @h_ @?_ khi}ihc bbD 6ht|c ? }i?ih@*c @? ?Uhi@ti ? |i 4?44
@}i _iUhi@tit @}i @h@|L? 5iUL?_*)c @? ?Uhi@ti ? |i 4?44 @}i _Lit
?L| @i @ *@h}i igiU| L? i4T*L)4i?| W? |i 4L_i* ihtL?t Lu 5iU|L? c
|i i4T*L)4i?| igiU| t 3ihL @t *L?} @t |i 4?44 @}i _Lit ?L| UhLtt |i
}it| R ? |i 4@h!i| W? |i 4L_i* Lu 5iU|L? e |i i4T*L)4i?| igiU| t 3ihL
@t *L?} @t |i 4?44 @}i _Lit ?L| UhLtt R2 Wu | _Litc |i? |i 4@}?|_i Lu
|i ?i}@|i i4T*L)4i?| igiU| _iTi?_t L? |i t@Ti Lu |i 4@|U?} u?U|L?
Ah_*)c @? ?Uhi@ti ? |i 4?44 @}i @t @ TLt|i igiU| L? @}it @MLi
|
W| t Lu|i? @h}i_ |@| @ tT!i ? |i @}i _i?t|) @| |i 4?44 @}i
?_U@|it |@| |i 4?44 @}i @t @? igiU| L? |i @}i _i?t|)c ihi@t |i
@Mti?Ui Lu tU @ tT!i ?_U@|it |@| |i 4?44 @}i t hhi*i@?| *i@h*)c
|i hit*|t @MLi ^it|L? |i ?iht@* @*_|) Lu tU @ i W| tL*_ Mi
t|hitti_ |@| Lh 4L_i* _Lit ?L| ThiU*_i |i Thiti?Ui Lu @ tT!i @| u W? U@ti
E @MLic |i @}i ELgih _i?t|) _tT*@)t @ tT!i @| u u |i *@||ih t L?*)
2H
4@h}?@**) *Lih |@? R2 W? |i *@||ih U@tic @** |)TiR2 h4t @hi @U|ic @?_ |i)
@hi @** uLhUi_ |L T@) @ @}i ? Mi|ii? u @?_ R2 *!iti t|@|L? LUUht
? U@ti E# @MLic u u t L?*) 4@h}?@**) *Lih |@? R L?|i4Ttc +LM? @?_
V@? _i? ih} E2fff tL |@| tU @ RUL?}it|L? tT!i ? |i @}i _i?t|) @|
u U@? @*tL Mi }i?ih@|i_ u R t UL?|?Lt*) _t|hM|i_ W?|ihit|?}*)c @}i _@|@
uhL4 ,hLTi@? UL?|hit Lu|i? _L ?L| _tT*@) @ tT!i @| |i 4?44 @}i ii?
|L} |ihi t |)TU@**) u** UL4T*@?Ui Etii i_i?Ui ? t|hLtc
bbec kL??}c
+__ih @?_ V@? _i? ih}c bbDc V@? _i? ih} @?_ +__ihc bbHc ?3i* i| @*c
bbbc @?_ L?|i4Ttc +LM? @?_ V@? _i? ih}c 2fff
L *i| t |h? |L tL4i Th@U|U@* ttit |@| UL4i T u L?i L*_ ti |i
@MLi ?t}|t uLh TL*U) 6ht| Lu @**c ? hi@*|)c _gihi?| ?__@*t @i _u
uihi?| ?__@*tTiUU ThL_U||) UL4TL?i?|t Ai 4L_i* uh@4iLh! _Lit
?L| @**L uLh _tTihtL? Lu tU UL4TL?i?|t |? @ *@MLh 4@h!i| AihiuLhic
|i hit*|t tii4 |L Mi 4Lhi hi*i@?| uLh *@MLh 4@h!i|t | @ L4L}i?iLt !?_
Lu Lh!c ihi ?__@*tTiUU ThL_U||) _gihi?Uit @hi hi*@|i*) t4@**
5iUL?_*)c hiU@** |@| h4t @hi @tt4i_ |L ti| @}it h@|ih |@? M@h}@? Lih
@}it | Lh!iht Ai |iLhi|U@* t|_it M) @???} Ebb @?_ ,**?}ti?
@?_ +Lti? Ebb. i @4?i ?_ih U UL?_|L?t @ h4 t 4Lhi *!i*) |L ti|
@}it h@|ih |@? M@h}@? Lih |i4 L| UL?U*_i |@| @}i ti||?} t 4Lhi
hi*i@?| uLh LMt |@| hi^hi *itt t!**t Ah_*)c @ 4?44 @}i t LMLt*) @
4Lhi hi*i@?| TL*U) ?t|h4i?| uLh *@MLh 4@h!i|t | hi*@|i*) *L ThL_U|
|) *ii*t W? t4c |i hit*|t ? |i Thiti?| T@Tih tii4 |L Mi T@h|U*@h*) hi*i@?|
uLh *@MLh 4@h!i| ti}4i?|t @| |i ML||L4 Lu |i iUL?L4)c | LMt |@| _L ?L|
hi^hi } t!**t
5TTLti |@| |i *@MLh 4@h!i| UL?tt|t Lu @ ?4Mih Lu tiT@h@|i *@MLh 4@h!i|t
U@**i_ ti}4i?|t ,@U ti}4i?| t @ tiT@h@|i *@MLh 4@h!i| Lu |t L?c @?_ Lh!iht
? @ T@h|U*@h ti}4i?| @hi L4L}i?iLt `|? @ ti}4i?|c *@MLh ThL_U||)
4@) Mi _tTihti_ @4L?} |i h4t |@| @hi @U|i ? |i ti}4i?| W? i@U ti}
4i?|c |i i^*Mh4 |i? t @t ? Lh 4L_i* OLiihc ti}4i?|t 4@) _gih ?
|ih4t Lu |ih ?__@*tTiUU ThL_U||)c tL |i _t|hM|L? Lu R 4@) @h)
@UhLtt ti}4i?|t W? |@| U@tic |i 4TLt|L? Lu @ 4?44 @}i |@| i Uii_t |i
}it| TLttM*i ThL_U||) *ii* |? @ T@h|U*@h ti}4i?| U@tit @** h4t
? |@| ti}4i?| |L MiUL4i ?ThL|@M*i ** ?__@*t @ttLU@|i_ | |@|
ti}4i?| |i? MiUL4i Tih4@?i?|*) ELh t|hU|h@**) ?i4T*L)i_ wi| |i _t|h
M|L? Lu R @4L?} |i TLT*@|L? Lu ?__@*t Mi _i?L|i_ M) M E6Lh i @4T*ic
u |ihi @hi |L ti}4i?|tc L?i | .DI Lu @** ?__@*t @?_ | R ' 2ff
@?_ L?i | 2DI Lu @** ?__@*t @?_ | R ' Dff |i? ME% ' f.D uLh
2b
% 5 d2ffc Dff Ai? |i ?i4T*L)4i?| h@|i t i^@* |L
B
'
E MEu n MEu 6 B n bf
Ai ht| @?_ tiUL?_ |ih4 L? |i h}|@?_ t_i hiiU| uhU|L?@* ?i4T*L)4i?|
@?_ t|hU|h@* ?i4T*L)4i?|c hitTiU|i*) Oihic i @tt4i |@| @ t?}*i @*i
Lu u L*_t uLh @** ti}4i?|t22 W? |i Uhhi?| ti|T | t Liih LT|4@* |L @i
@ _gihi?| 4?44 @}i uLh i@U ti}4i?| At Lu ULhti hi^hit !?L*i_}i
Lu |i }it| ThL_U||) @*i ? i@U ti}4i?| W? 4@?) ,hLTi@? UL?|hitc
|h@_i ?L?t @?_ i4T*L)ih ui_ih@|L?t 4ii| iih) )i@h |L ?i}L|@|i |i 4?44
@}i uLh _gihi?| ti}4i?|t Ei _gihi?| LUUT@|L?t |? _gihi?| tiU|Lht Lu
|i *@MLh 4@h!i| 5U ?i}L|@|i_ ti}4i?|tTiUU 4?44 @}it @hi Lu|i?
tMti^i?|*) *i}@**) 4TLti_ M) |i }Lih?4i?| Ai @?@*)tt ? |t tiU|L?
ThL_it @ t|U@|L? Lu |t Th@U|Ui
9
Khwhurjhqhrxv xqhpsor|hg zrunhuv
5L u@h i @i @tt4i_ |@| Lh!iht @hi L4L}i?iLtc @?_c ? T@h|U*@hc |@|
|i LTTLh|?|) @*i Lu i4T*L)4i?| K t @ i_ UL?t|@?| At @tt4T|L?
t L*@|i_ u tL4i Lh!iht i?L) *ithi 4Lhi |@? L|ihtc Lu u ?i4T*L)4i?|
Mi?i|t @hi _tTihti_ W? |t tiU|L? i tL |@| |i 4@? hit*|t @MLi @hi
hLMt| | hitTiU| |L |t `i @?@*)3i @? i^*Mh4 ti@hU 4L_i* ? U
Lh!iht L? |i t@4i *@MLh 4@h!i| U@? @i _gihi?| ?__@*tTiUU K @?_
h4t U@? @i _gihi?| ThL_U|L? |iU?L*L}it 6Lh i TLt|L?@* hi@tL?t i
?L @Mt|h@U| uhL4 ti@hU L? |i LM 6h|ih4Lhic i t4T*) @tt4i |@| |i
K U@? @||@? |L TLttM*i @*it EK @?_ K2 c | ThLM@M*|it Z @?_ Zc
@?_ E@}@? |@| R U@? @||@? |L TLttM*i @*it ER @?_ R2 | ThLM@M*|it
^ @?_ ^ Ai hi*i@?| |iLhi|U@* *|ih@|hi ?U*_it @U?? EbHf @?_
*MhiU| @?_ i** EbHec L @U|@**) @tt4i @ UL?|?Lt _t|hM|L? Lu R
@UhLtt h4t Ai *MhiU| @?_ i** EbHe 4L_i* t it|4@|i_ M) ,U!t|i? @?_
`L*T? Ebbf Lh|i?ti? Ebbf _ihit @ ?4Mih Lu ThLTih|it Lu i^*Mh@ ?
@ 4L_i* | _tUhi|i K @?_ R
Wu ?i4T*L)i_ Lh!iht @i _gihi?| K |i? ? }i?ih@* |i) @*tL @i _gihi?|
hitih@|L? @}it Ai 4Lt| 4TLh|@?| i^*Mh4 ThLTih|) t |@| |i tTTLh|
Lu |i i^*Mh4 @}i Lgih _t|hM|L? t @ tMti| Lu ELh UL?U_it | |i
ti| Lu ?i4T*L)i_ Lh!iht< hitih@|L? @}it @tU@**)c @?) L|ih Lgih @*i
55 Li K lv frqwlqxrxv/ dqg zO lv lq lwv vxssruw/ wkhq w|slfdoo| wkh ydoxh ri wkh srsxodwlrq zdjh
ghqvlw| dw zO. lv srvlwlyh1
f
U@? Mi 4ThLi_ TL? M) Lgih?} |i hitih@|L? @}i Mi*L |i LgihG |t }it
@ }ih ThL| Tih Lh!ih |L| @?) *Ltt ? |i t3i Lu |i *@MLh uLhUi Lu |i
h4 ?L|ih i^*Mh4 ThLTih|) t |@| }ihThL_U||) h4t Lgih }ih
@}it @?_ @hi |ihiuLhi @M*i |L @||h@U| 4Lhi Lh!iht
`i @tt4i |@| K2 R2 K R L|i uhL4 i^@|L? E |@| @ Lh!ih<t
hitih@|L? @}i t ?L @*@)t *@h}ih |@? Lh i^@* |L t Mi?i|t *ii* K E|@!i
b ' f( |i) @hi i^@* g K ' ,^*Mh4 t i|ih tU |@| 2 R2 c Lh
tU |@| 2 R2 W? |i ht| U@tic @** h4t @hi @U|i A)TiR2 h4t Lgih 2 c
@?_ |)TiR h4t 4@) Lgih @?_%Lh 2 c _iTi?_?} L? |i T@h@4i|ih @*it W?
|i tiUL?_ U@tic L?*) |)TiR h4t @hi @U|ic @?_ |i) 4@) Lgih @?_%Lh 2 W? TTi?_ e i ThLi |i uL**L?} hit*|
hLTLt|L? S W? |i 4L_i* | i|ihL}i?i|) Lu Lh!iht< ?i4T*L)4i?| Mi?i
|tc @tt4i |@|
ZEB n bf ER K2 : EB n Zbf EK K2 E2e
Aihi i t| i @U|*) |L i^*Mh@ u @?_ L?*) u
B
B
K R2
:
bf ^
R2 K2
bf
E2D
W? L?i i^*Mh4c L?*) |)TiR h4t @hi @U|i W? |i L|ihc ML| |)Tit @hi
@U|i Wu E2D t ?L| t@|ti_ |i? |ihi i t|t i @U|*) L?i i^*Mh4
EL|i |@| R @?_ Z _L ?L| @giU| E2Dc ihi@t R2 _Lit ?L| @giU| E2ec tL |@|
E2e U@??L| Mi ? UL?U| | E2D
Ai 4iU@?t4 Mi?_ |i 4*|T*U|) Lu i^*Mh4 t itti?|@**) |i t@4i
@t ? 5iU|L? W? L?i Lu |i i^*Mh@c ML| }ThL_U||) @?_ *LThL_U||)
h4t @hi @U|i W? |@| i^*Mh4c |i uLh4ih h4t Lgih K @?_ |i *@||ih h4t
Lgih 2 c U ? |h? @t @ h@|ih *L @*i W? |i L|ih i^*Mh4c L?*) }
ThL_U||) h4t @hi @U|ic @?_ |i) Lgih K Ai ?i4T*L)i_ Lh!iht |
@ *L Mi?i|t *ii* |i? @i @ h@|ih } hitih@|L? @}i 2 W?_ii_c ?
|t tiUL?_ i^*Mh4c 2 : R2 c tL 2 @U|t @t @ M?_?} *Lih ML?_ L? |i
ti| Lu ThL_U|L? |iU?L*L}it |@| i?@M*i @ TLt|i ThL| Tih Lh!ih W| h*it
L| ThL_U|L? @| |i *L ThL_U||) *ii* Ai hit*|?} @}it @hi }ih
|@? ? |i ht| i^*Mh4 At ? |h? t|it |i }ih hitih@|L? @}i
? |i tiUL?_ i^*Mh4 Atc *!i ? 5iU|L? c |i hitih@|L? @}i Lu |i
?i4T*L)i_ @giU|t |i ti| Lu ThL|@M*i ThL_U|L? |iU?L*L}itc *i |i ti|
Lu ThL_U|L? |iU?L*L}it ? ti ? |h? @giU|t |i hitih@|L? @}ic @?_ |t
t)t|i4 @t 4*|T*i tL*|L?t
?@*L}Lt |L 5iU|L? ec L?i 4@) @h}i |@| bf 4@) _iTi?_ L? |i 4i@thi
Lu @U|i h4t ?@ OLiihc | t i@t) |L tii uhL4 E2D |@|c *!i ? 5iU|L? ec
|i UL?_|L? Eb L? bf E^? t ?iUitt@h) @?_ tUi?| uLh ML| i^*Mh@ |L Mi
TLttM*i 5TiUU@**)c u E2e t t@|ti_ |i? |ihi @hi @*it Lu R2 c K @?_ K2 uLh
U ML| i^*Mh@ i t|c u @?_ L?*) u bf E^? : ^bf E?
Ai @?@*)tt Lu 4?44 @}i igiU|t t @*tL itti?|@**) |i t@4i @t MiuLhi
A@| tc L?i 4@) t?}*i L| |i i^*Mh4 | L?*) |)TiR h4t M) 4TLt?}
@ 4?44 @}i u t@|tu)?} R2 u R Wu |t u t t4@**ih |@? K |i? |
t t|hU|*) t4@**ih |@? |i ?i *Lit| @}i ? |i 4@h!i| W? UL4T@htL? |L |i
ThiLt tiU|L?tc |i 4L_i* | i|ihL}i?iLt K ThL_it @? @__|L?@* hi@tL?
uLh tLU@* i*u@hi |L Mi }ih ? U@ti Lu |i i^*Mh4 | L?*) |)TiR h4t
Ei ? U@ti Lu @ 4?44 @}i i Uii_?} R2 At hi@tL? t ?L|?} M| |i
|h@_|L?@* @h}4i?| uLh @ 4?44 @}i ? 4L?LTtL?t|U *@MLh 4@h!i|tG |
?Uhi@tit i4T*L)4i?| Etii *MhiU| @?_ i**c bHec @?_ ,U!t|i? @?_ `L*T?c
bbf W? |i i^*Mh4 ? U ML| |)Tit Lu h4t @hi @U|ic |)TiK ?_
_@*t hiiU| LM Lgiht uhL4 |)TiR2 h4t OLiihc ? |i L|ih i^*Mh4c
@** LM Lgiht @hi @*@)t @UUiT|i_c tL ?i4T*L)4i?| t *Lih
L|i |@| 4TLt|L? Lu @ hi*@|i*) } 4?44 @}ic @t @ 4i@?t |L t?}*i
L| |i _ith@M*i i^*Mh4c tL*_ Mi Thiuihhi_ Lih @? Lih@** ?Uhi@ti Lu
?i4T*L)4i?| Mi?i|t | @? @4L?| { R2 K2 Ai *@||ih TL*U) @*tL
i?thit |@| |)TiR2 h4t @hi ?L| @U|i( Liihc |i ?i Mi?i|t *ii* K n {
Lu |i |)TiK ?__@*t 4@) Mi *@h}ih |@? R c ? U U@ti |iti ?__@*t
** MiUL4i Tih4@?i?|*) ?i4T*L)i_
W? Ai i|ih*@?_tc @t ? 4@?) L|ih UL?|hitc |i *ii* Lu tLU@* @ttt|@?Ui
Mi?i|t uLh ?i4T*L)i_ Lh!iht t 4Lt|*) _i|ih4?i_ M) LtiL*_ UL4TLt|L?
Etii V@? _i? ih}c V@? _ih k*@@ @?_ V@? htc bbHc uLh _i|@*t( ?i4T*L)i_
Lh!iht 4@) Mi i?||*i_ |L tU Mi?i|t u |ih ?i4T*L)4i?| ?th@?Ui i?|
|*i4i?| @t i Thi_ Ai 4L_i* ? |t tiU|L? @t tL4i hi*i@?Ui uLh |i *@MLh
4@h!i| Lu tU Lh!iht W4TLt|L? Lu @ 4?44 @}i t| Mi*L |i }it|
TLttM*i tLU@* @ttt|@?Ui *ii* @t |i @_@?|@}it |@| E |i i^*Mh4 t tU
|@| Lh!iht L?*) Lh! @| }ihThL_U||) h4t @?_ E2 uhU|L?@* ?i4T*L)
4i?| t hi_Ui_
:
Frqfoxvlrq
W? |t T@Tih i @i i @4?i_ |i 4|@* _iTi?_i?Ui Lu |i hitih@|L? @}i
Lu |i ?i4T*L)i_ @?_ |i 4?44 ThL_U||) *ii* @| U ThL_U|L? t
ThL|@M*i 5TiUU@**)c i tLi_ |@| |t _iTi?_i?Ui U@? }i?ih@|i 4*|T*
2
U|) Lu i^*Mh4 Nt?} hit*|t uhL4 |i *|ih@|hi L? t|hU|h@* it|4@|L? Lu
i^*Mh4 ti@hU 4L_i*tc i tLi_ |@| 4*|T*U|) t @? i4ThU@**) hi*i@?|
Ti?L4i?L? Aiti hit*|t hi4@? @*_ ?_ih @ ?4Mih Lu 4L_i* i |i?tL?t
W? T@h|U*@hc i @UUL?|i_ uLh |i u@U| |@| |i Lh!iht< LM Lgih @hh@* h@|it
_iTi?_ L? |i ?4Mih Lu ThL_U|i h4t W? @__|L?c i i @4?i_ @ 4L_i*
? U ?i4T*L)i_ Lh!iht _gih ? |ih4t Lu |ih ?i4T*L)4i?| Mi?i|t Lh
@*i Lu *ithi W? |@| U@tic |i *Lit| hitih@|L? @}i @4L?} |i ?i4T*L)i_
?|ih@U|t | |i *Lit| ThL|@M*i ThL_U||) *ii*
Aiti hit*|t 4T*) |@| @ 4?44 @}i TL*U) U@? Mi uh|u**) @TT*i_ |L
t?}*i L| |i _ith@M*i i^*Mh4 W? tU @ U@tic |i hit*|?} 4?44 @}i
4@) hL?}u**) @TTi@h |L Mi hhi*i@?|c @t |t @*i U@? Mi t|hU|*) t4@**ih |@?
|i *Lit| @}i ? |i 4@h!i| Ai hit*|t ThL_i @ t|U@|L? Lu @ TL*U) ?
U 4?44 @}it @hi tiU|LhtTiUU @?_ LUUT@|L?tTiUU
Uhihuhqfhv
Ui4L}*c # Ebb.c RBLL_ LMt ihtt M@_ LMtG |iLh) @?_ tL4i i_i?Uic
`Lh!?} T@Tihc WAc @4Mh_}i
Ui4L}*c # @?_ + 54ih Ebb.c R,Ui?| @}i _tTihtL?c `Lh!?} T@Tihc
h?Ui|L? N?iht|)c h?Ui|L?
*MhiU|c a` @?_ i** EbHec R? i^*Mh4 4L_i* Lu ti@hU ?i4T*L)
4i?|c aLh?@* Lu L*|U@* ,UL?L4)c b2c H2eHef
L@*c ` @?_ + +@?tL4 Ebb.c RL?LTtL?) ? |i *@MLh 4@h!i|c aLh?@*
Lu ,UL?L4U w|ih@|hic Dc HS2
L?|i4Ttc c a +LM?c @?_ Ba @? _i? ih} Ebbbc R? i4ThU@* i^*M
h4 LM ti@hU 4L_i* | ti@hU L? |i LM @?_ i|ihL}i?iLt Lh!iht @?_
h4tc W?|ih?@|L?@* ,UL?L4U +iic uLh|UL4?}
L?|i4Ttc c a +LM?c @?_ Ba @? _i? ih} E2fffc R,^*Mh4 ti@hU
| UL?|?Lt ThL_U||) _tTihtL?G |iLh) @?_ ?L?T@h@4i|hU it|4@
|L?c W?|ih?@|L?@* ,UL?L4U +iic uLh|UL4?}
L*tc a Ebb.c R ti@hU ?|ihThi|@|L? Lu 4@*iui4@*i @}i _gihi?|@*tc
aLh?@* Lu w@MLh ,UL?L4Utc Dc S2DSD.
L*tc ac kiuihc @?_ B+ i4@?? EbbDc R,t|4@|L? Lu i^*Mh4
@}i _t|hM|L?t | i|ihL}i?i|)c aLh?@* Lu TT*i_ ,UL?L4i|hUtc fc
5b5
L*tc ac kiuihc @?_ B+ i4@?? E2fffc R,^*Mh4 ti@hU 4L_
i*t @?_ |i |h@?t|L? uhL4 tULL* |L Lh!c W?|ih?@|L?@* ,UL?L4U +iic
uLh|UL4?}
hL?c c B*hL)c @?_ kLi? EbH2c RAi igiU| Lu |i 4?44 @}i L?
i4T*L)4i?| @?_ ?i4T*L)4i?|c aLh?@* Lu ,UL?L4U w|ih@|hic 2fc eH.
D2H
?3i*c Oc a ht|i?ti?c ai?ti?c kiuihc w kLhtL*4c w tc B+
i4@??c @?_ +LtL*4 Ebbbc R5TiUU@|L? @?_ it|4@|L? Lu i^*M
h4 ti@hU 4L_i*tc +ii Lu ,UL?L4U #)?@4Utc uLh|UL4?}
h_i||c k @?_ #A Lh|i?ti? EbbHc R`@}i _gihi?|@*tc i4T*L)ih t3ic @?_
?i4T*L)4i?|c W?|ih?@|L?@* ,UL?L4U +iic bc 2D.2.
@h_c # @?_ khi}ih EbbDc )| @?_ 4i@thi4i?|c h?Ui|L? N?iht|)
hittc h?Ui|L?
e
#@4L?_c Eb.c R 4L_i* Lu ThUi @_t|4i?|c aLh?@* Lu ,UL?L4U
AiLh)c c DSSH
,U!t|i?c ~ @?_ kW `L*T? Ebbfc R,t|4@|?} @ 4@h!i| i^*Mh4 ti@hU
4L_i* uhL4 T@?i* _@|@ L? ?__@*tc ,UL?L4i|hU@c DHc .HHfH
,**?}ti?c A @?_ J
+Lti? Ebb.c R6 i_ Lh i M*iq `@}i ti||?} ? ti@hU
i^*Mh4c `Lh!?} T@Tihc 5|LU!L*4 5ULL* Lu ,UL?L4Utc 5|LU!L*4
6Lht*?_c @?_ A w?_ Ebb.c R@h}@??}c U@T|@* uLh4@|L? @?_ ?i4T*L)
4i?|G @ T||)U*@) @TThL@Uc `Lh!?} T@Tihc NTTt@*@ N?iht|)c NTTt@*@
ai?ti?c c +LtL*4c @?_ 54| Ebbec RN?i4T*L)4i?| @?_ 4?44
@}it @ 4UhLiUL?L4i|hU @?@*)ttc `Lh!?} T@Tihc N?iht|) Lu @htc
@ht
ki??@?c a EbbDc RAi i*ti igiU|t Lu 4?44 @}itc aLh?@* Lu ,UL?L4U
w|ih@|hic c bDfbSD
kL??}c c B +__ihc @?_ Ba @? _i? ih} EbbDc R5|hU|h@* @?_ uhU|L?@*
?i4T*L)4i?| ? @? i^*Mh4 ti@hU 4L_i* | i|ihL}i?iLt @}i?|tc
aLh?@* Lu TT*i_ ,UL?L4i|hUtc fc 55D
@U??c +# EbHfc RaLM ti@hU @?_ |i *@MLh _hLTL| ThLM*i4 hiUL?t_ihi_c
"@h|ih*) aLh?@* Lu ,UL?L4Utc bDc SbH.
@???}c Ebbc R,?_L}i?Lt *@MLh 4@h!i| ti}4i?|@|L? ? @ 4@|U?}
4L_i*c `Lh!?} T@Tihc i?|hi uLh ,UL?L4U ihuLh4@?Uic wL?_L?
L?|}L4ih)c a# Ebbc R,^*Mh4 @}i _tTihtL? @?_ ?|ih?_t|h) @}i
_gihi?|@*tc "@h|ih*) aLh?@* Lu ,UL?L4Utc fSc S.b
Lh|i?ti?c #A EbHSc RaLM ti@hU @?_ *@MLh 4@h!i| @?@*)ttc ? ti?
ui*|ih @?_ + w@)@h_c i_|Lhtc O@?_MLL! Lu w@MLh ,UL?L4Utc Lh|OL**@?_c
4t|ih_@4
Lh|i?ti?c #A Ebbfc R,^*Mh4 @}i _t|hM|L?tG @ t)?|ittc ? a O@h
|L} i| @*c i_|Lhc @?i* _@|@ @?_ *@MLh 4@h!i| t|_itc Lh|OL**@?_c 4t
|ih_@4
Lh|i?ti?c #A @?_ tt@h_it Ebbbc Ri _ii*LT4i?|t ? 4L_i*t Lu
ti@hU ? |i *@MLh 4@h!i|c ? O@?_MLL! Lu w@MLh ,UL?L4Utc Lh|OL**@?_c
4t|ih_@4c uLh|UL4?}
t|hLtc
A Ebbec R#L 4?44 @}it 4@||ihq Ai U@ti Lu 5i_t 4??} @?_
4@?u@U|h?}c ? OL*4*?_c i_|Lhc @)c hL_U||)c @?_ L*U)c 6W,6c
5|LU!L*4
D
i_ihti?c a @?_ 54| EbbHc RwL ?UL4it ? #i?4@h!c bHfbbDc
`Lh!?} T@Tihc N?iht|) Lu @htc @ht
+i?}@?4c a Eb.bc R t4T*i 4L_i* Lu i^*Mh4 ThUi _tTihtL?c aLh?@*
Lu L*|U@* ,UL?L4)c H.c HDHDH
+__ihc B @?_ Ba @? _i? ih} Ebb.c R,4ThU@* i^*Mh4 ti@hU 4L_i*tc
? # khiTt @?_ k6 `@**tc i_|Lhtc _@?Uit ? ,UL?L4Ut @?_ ,UL?L
4i|hUtG AiLh) @?_ TT*U@|L?tc @4Mh_}i N?iht|) hittc @4Mh_}i
+__ihc B @?_ Ba @? _i? ih} EbbHc R,t|4@|?} 4i@thit Lu *@MLh 4@h!i|
4TihuiU|L? uLh i ,# UL?|hitc t?} @}}hi}@|i _@|@ ? @? i^*Mh4
ti@hU uh@4iLh!c `Lh!?} T@Tihc 6hii N?iht|) 4t|ih_@4c 4t|ih_@4
5LMi*c +5 Ebbbc RAiLh) @?_ i_i?Ui L? |i TL*|U@* iUL?L4) Lu |i 4?
44 @}ic aLh?@* Lu L*|U@* ,UL?L4)c f.c .S.HD
5|}*|3c a, EbHDc R,^*Mh4 @}i _t|hM|L?tc ,UL?L4U aLh?@*c bDc
DbDSH
5??ih|L?c k EbbSc R?44 @}it ? @? i^*Mh4 ti@hU 4L_i* |
_4?t?} hi|h?t |L *@MLh ? ThL_U|L?c aLh?@* Lu w@MLh ,UL?L4Utc ec
efDD
V@? _i? ih}c Ba Ebbec RAi igiU|t Lu U@?}it Lu |i LM Lgih @hh@* h@|i
L? |i _h@|L? Lu ?i4T*L)4i?|c aLh?@* Lu w@MLh ,UL?L4Utc 2c e.HebH
V@? _i? ih}c Ba Ebbbc R,4ThU@* ?uihi?Ui | i^*Mh4 ti@hU 4L_i*t
Lu |i *@MLh 4@h!i|c ,UL?L4U aLh?@*c fbc 62H6fS
V@? _i? ih}c Ba @?_ B +__ih EbbHc R? i4ThU@* i^*Mh4 ti@hU
4L_i* Lu |i *@MLh 4@h!i|c ,UL?L4i|hU@c SSc H22
V@? _i? ih}c Bac @? _ih k*@@c @?_ a @? ht EbbHc R?|i
t@?U|L?t @?_ |i |h@?t|L? h@|i uhL4 i*u@hi |L Lh!c `Lh!?} T@Tihc A?
Mih}i? W?t|||ic 4t|ih_@4
`ittc Ebbc ,Ui?U) @}itc *@hi?_L? hittc uLh_
S
Dsshqgl{
Dsshqgl{ 41 Wkuhh up w|shv1
Aihi t @? i^*Mh4 ? U L?*) |)TiR h4t @hi @U|i u @?_ L?*) u
Ebf b b
R K
2
2
EB n b R R2
At t Lu ULhti i^@*i?| |L hLTLt|L?
Aihi t @? i^*Mh4 ? U |)TiR @?_ |)TiR2 h4t @hi @U|i M|
|)TiR h4t @hi ?L| @U|i u @?_ L?*) u
R2 K
R R2
|
#
S'
:
EB n b ^
B n b ^
Ebf b b
S
EB n b 2
SER K
SER R2 n ER2 R $2
c
|
^'
E2S
^
^ n ^2
L|i |@| f S Ai ht| ?i^@*|) ? E2S t Lu ULhti i^@*i?| |L
hLTLt|L? 2
6?@**)c |ihi t @? i^*Mh4 ? U @** |hii h4 |)Tit @hi @U|i u @?_
L?*) u
Ebf b b
EB n b 2
|
#
S '
R K
S ER R2 n S2 ER2 R EB n b ^
B n b ^
$2
#
@?_
S2 '
EB n b E^ n ^2 B n b E^ n ^2 $2
tL |@| f S S2
W| U@??L| Mi h*i_ L| @ ThLh |@| |ihi @hi 4*|T*i i^*Mh@ wi|c uLh @
}i? i^*Mh4c |i ?4Miht ? @ ti| ij ?_U@|i U h4 |)Tit @hi @U|i
W| t TLttM*i |@| uLh }i? T@h@4i|ih @*it |ihi i t| ic 2c jc ic 2jc @?_ ij
i^*Mh@ W| t @*tL TLttM*i |@| uLh }i? T@h@4i|ih @*it |ihi i t| ic 2c j
@?_ ij i^*Mh@ M| ?L ic 2j i^*Mh4 W| t @*tL TLttM*i |@| uLh }i?
T@h@4i|ih @*it |ihi i t| ic 2j @?_ ij i^*Mh@ M| ?L ic 2c j i^*M
h4
.
Dsshqgl{ 51 Xqltxhqhvv lq fdvh ri LIU glvwulexwlrqv1
Wu bf : b @?_ Rf K |i?c M) i^@|L? Ec @?) i^*Mh4 tL*|L? uLh t@|tit Rf c U 4T*it |@| @?) i^*Mh4 tL*|L? uLh R t@|tit R ' ) tMt|||?} 8 E ' gER ?|L i^@|L? Ec t?} |i i ThittL? uLh gER ?
uLL|?L|i ec @?_ t?} |i hi*@|L? Mi|ii? K @?_ Kf c @?_ 4TLt?} |@| R ' c
i LM|@?c
' K n Ebf b ]R%
Kf ER
BKf E n b Kf ER
&2
_R
E2.
?) i^*Mh4 t U@h@U|ih3i_ M) @ tL*|L? Lu |t i^@|L? uLh L?t_ih
|i *iu|@?_ @?_ h}|@?_ t_it @t u?U|L?t Lu L? EKc R | Kc |i *iu|@?_
t_i t t4@**ih |@? |i h}|@?_ t_i Ai *iu|@?_ t_i t t|hU|*) ?Uhi@t?}
iih)ihi Ai h}|@?_ t_i t ?L| _iUhi@t?} iih)ihi uLh iih) TLttM*i
Kf AL ThLUii_c UL?t_ih |i _ih@|i Lu |i h}|@?_ t_i | hitTiU| |L At i^@*t
bf b
B
%
b B
EB n b 2
n
f E ] R
r
Kf E
#
Kf ER
Kf E
$
&
K ER
f
_R
Kf E
E2H
|
r E% '
2b B 2 %
EB n b %
`i @TT*) T@h|@* ?|i}h@|L? |L E2Hc }L?} uhL4 r EKf ER*Kf Ef ER*Kf E |L
|t ?|i}h@* rEKf ER*Kf E Ai u?U|L? rE% i^@*t
rE% '
b B%2
c
EB n b %2
W? |i ThLUittc i i T*L| |i u@U| |@| |i W6+ ThLTih|) 4T*it |@| f ER*Kf ER
t t|hU|*) *@h}ih |@? f uLh @** R U*Lti |L R u|ih 4U hih|?}c | uL**Lt |@|
E2H i^@*t
#
bf b f E ] R
Kf ER
r
B
Kf E Kf E
$
_
_R
#
Kf ER
f ER
$
_R
Wu Kf t W6+ |i? |i _ih@|i Lu Kf ER*f ER t ?i}@|i uLh @** R R AihiuLhic
E2H t ?i}@|i uLh @** 5 EKc R At 4T*it |@| |i h}|@?_ t_i Lu E2.
H
t _iUhi@t?} iih)ihi t @ hit*|c |ihi t @| 4Lt| L?i tL*|L? |L E2. Wu
R 4 |i? i @*hi@_) !?L uhL4 L?|i4Ttc +LM? @?_ V@? _i? ih} E2fff
|@| |ihi i t|t @? i^*Mh4c tL |i? |i i^*Mh4 t ?^i Wu R ' 4 |i?
| uL**Lt _hiU|*) uhL4 E2. |@| |ihi t @*@)t @ @*i Lu @| U ML| t_it
?|ihtiU|c tL |i? |i i^*Mh4 t ?^i @t i** Dsshqgl{ 61 Surri ri Sursrvlwlrq 81
Ai UL?_|L? Eb L*_t uLh @** f ^ g |i ?ihti u?U|L? ?@ Ebf t@|tit
bf
?@ Ebf ?
bf E?
uLh @** f bf bf E?c ihi bf t |i @h}4i?| Lu |i u?U|L? ?@ Ec @?_ ? @?_
bf E? @hi i_ UL?t|@?|t `i ht| UL?t_ih |i U@ti q : f ,^@|L? E2 U@?
Mi hih||i? @t
?@
'
?
#
bf
bf E?
$ q
k n E k BnBbf
k n E k BnbBf E?
AihiuLhic ?@ *? bf *bf E? g
3
3
bf E? q
bf q
EB n kbf EB n kbf E?
B n bf
B n bf E?
E2b
3
`i @*hi@_) !?L |@| bf E?@ bf E?c tL u |i u?U|L? % q EB n k%*EB n %
t|hU|*) ?Uhi@tit ? % uLh % 5 Efc bf E?oc |i? |i ?i^@*|) E2b t |hi uLh @**
bf 5 Efc bf E? Ei uLh @** ^ 5 Efc Ai _ih@|i Lu |t u?U|L? | hitTiU|
|L % t ThLTLh|L?@* |L
kE q%2 n BE n k 2q% n B 2 E q
Ef
*i@h*)c |i @*it Lu |t i ThittL? @hi TLt|i uLh iih) % f u |i tiUL?_
ULiUi?| BE n k 2q t ?L??i}@|i At }it |i tUi?| UL?_|L?
f q E n k*2 , ThittL? Ef t @ tiUL?__i}hii TL*)?L4@* ? % u|ih
s
tL4i i*@MLh@|L? | uL**Lt |@| |t @*it @hi TLt|i L? W+ g E k*2 s
q E n k*2c @?_ |t @*it @hi TLt|i L? W+ i UiT| @| L?i TL?| g
s
s
q ' E k*2 Lh q ' E n k*2 At }it |i tiUL?_ tUi?| UL?_
s
s
|L?G E k*2 q E n k*2 AL}i|ihc |i |L UL?_|L?t hit*| ?
s
f q E n k*2 W? u@U|c |i *@||ih }it @ UL4T*i|i U@h@U|ih3@|L? Lu |i
b
T@h@4i|ih @*it uLh U Ef t TLt|i uLh @** % f i UiT| TLttM*) uLh L?i
% @*ic }i? |@| f kc q 6?@**)c u q ' f |i bf _Lit ?L| _iTi?_ L? ?@ c
tL Eb t |h@**) t@|ti_ uLh iih) f ^ Dsshqgl{ 71 Surri ri Sursrvlwlrq 91
uh@U|L? Z E@ uh@U|L? Z Lu |i Lh!iht @t K ' K EK ' K2 @?_ @ uh@U|L?
^ E@ uh@U|L? ^ Lu |i TLttM*i h4t @t R ' R ER ' R2 Ai L?*) TLttM*i
@}i Lgiht @hi @?_ 2 Ai ti| Lu TLttM*i @}i Lgih _t|hM|L?t 8 E U@?
Mi t44@h3i_ M) h8 E ' ' ' h8 E ' 2 | f Ai
T@h@4i|iht c 2 @?_ hi4@? |L Mi _i|ih4?i_ 6hL4 i^@|L? E | uL**Lt
|@| ' K @?_ |@|
2 '
BK2 n bf K
B n bf L *i| t i @4?i |i t|i@_)t|@|i *@MLh uLhUit Lu h4t T@)?} @?_ Lu
h4t T@)?} 2 ?@*L}Lt |L |i _ih@|L? Lu i^@|L? E2c i ?_ |@| |i
uh@U|L? C Lu i4T*L)i_ Lh!iht i@h??} i^@*t
C ' B n bf n Zbf E B n bf ZBE U t L?i 4?t |i uh@U|L? i@h??} 2 Oihi i ti |i u@U| |@| @ Lh!ih t
?_gihi?| Mi|ii? i@h??} 2 @| @ |)TiR2 h4 @?_ i@h??} 2 @| @ |)TiR h4
L|i |@| C : c ?_U@|?} |@| |)TiR h4t ** Mi *@h}ih |@? |)TiR2 h4t
|)TiR2 h4c u @U|ic @*@)t Lgiht 2 EhiU@** |@| R2 K At 4i@?t
|@| |i i^*Mh4 @*i Lu 4t| t@|tu) ^ L UL?t_ih @ |)TiR
h4 Wu | Lgiht K |i? |i ThL| L i^@*t ER K C E6 *c ihi@t u
| Lgiht 2 |i? |t L i^@*t ER 2 E C E6 *E tL*|L?
uLh 5 Efc ^ 4i@?t |@| |)TiR @hi ?_gihi?| Mi|ii? Lgih?} i|ih Lu |iti
@}it Ai ThL| Lt |i? 4t| Mi i^@* u|ih tL4i |i_Lt U@*U*@|L?t |t
U@? Mi tL? |L 4T*) |@|
ZEB n bf ER K2 ' EB n Zbf EK K2 E
ih@Tt thTht?}*)c |t _Lit ?L| _iTi?_ L? @| @** Atc ? |i T@|L*L}U@*
U@ti ? U |t i^@*|) t t@|ti_c iih) @*i Lu ? dfc ^o @_4|t @? i^*M
h4 L?ti^i?|*)c i |i? @i @? ??|i ?4Mih Lu i^*Mh@ E|t TiU*@h
hit*| t Liih ?L| hLMt| | hitTiU| |L |i ?U*tL? Lu @ _tUL?| h@|i ?
ef
|i ?__@*t< LT|43@|L? ThLM*i4( tii Lh|i?ti? @?_ tt@h_itc bbH Wu
|i *iu|@?_ t_i Lu E t t4@**ih |@? |i h}|@?_ t_ic |i? Lgih?} 2
t @*@)t 4Lhi ThL|@M*i |@? Lgih?} K L?ti^i?|*)c |i i^*Mh4 @*i
Lu t 3ihLc @?_ 2 t _hi? _L? |L K2 L|i |@| |t t |hi hi}@h_*itt Lu
|i @*i Lu ^c |@| tc hi}@h_*itt Lu i|ih |ihi @hi @?) @U|i |)TiR2 h4t
L?ti^i?|*)c u |i *iu|@?_ t_i Lu E t t4@**ih |@? |i h}|@?_ t_ic
|i? |i ?^i i^*Mh4 t |@| @** @}it i^@* K2 ** h4t @hi |i? @U|ic
M| @** ?__@*t | K ' K @hi Tih4@?i?|*) ?i4T*L)i_
L tTTLti |@| |i *iu|@?_ t_i Lu E i Uii_t |i h}|@?_ t_i `i
t|@h| @tt4?} |@| h4t Lu ML| |)Tit @hi @U|i ? i^*Mh4 At 4t| Mi
ihi_c M) UiU!?} i|ih ? i^*Mh4 2 R2 Lc K t @*@)t |i 4Lt|
ThL|@M*i @}i Lgih uLh |)TiR h4t L?ti^i?|*)c |i i^*Mh4 i^@*t
^c @?_ 2 i^@*t EBK2 n bf ^K *EB n bf ^ W? t4c @** |)TiR h4t Lgih K @?_
@** |)TiR2 h4t Lgih |t @*i Lu 2 Aihi L*_t |@| 2 R2 g |i ht|
?i^@*|) Lu E2D L*_t
L @}@? tTTLti |@| |i *iu|@?_ t_i Lu E i Uii_t |i h}|@?_ t_ic
M| ?L @tt4i |@| L?*) |)TiR h4t @hi @U|i ? i^*Mh4 At 4t| Mi
ihi_c M) UiU!?} i|ih ? i^*Mh4 2 R2 }@?c K t @*@)t |i 4Lt|
ThL|@M*i @}i Lgih uLh |)TiR h4t L?ti^i?|*)c |i i^*Mh4 i^@*t
c @?_ 2 i^@*t EBK2 n bf K *EB n bf Aihi L*_t |@| 2 R2 g |i tiUL?_
?i^@*|) Lu E2D L*_t At ThLit |i ThLTLt|L? e
© Copyright 2026 Paperzz