• Ingen resultater fundet

The balance of power in closely held corporations

N/A
N/A
Info
Hent
Protected

Academic year: 2022

Del "The balance of power in closely held corporations"

Copied!
43
0
0

Indlæser.... (se fuldtekst nu)

Hele teksten

(1)

The balance of power in closely held corporations

Bennedsen, Morten; Wolfenzon, Daniel

Document Version Final published version

Publication date:

1999

License CC BY-NC-ND

Citation for published version (APA):

Bennedsen, M., & Wolfenzon, D. (1999). The balance of power in closely held corporations.

Link to publication in CBS Research Portal

General rights

Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.

Take down policy

If you believe that this document breaches copyright please contact us (research.lib@cbs.dk) providing details, and we will remove access to the work immediately and investigate your claim.

Download date: 07. Nov. 2022

(2)

Institut for Nationaløkonomi

Handelshøjskolen i København

Working paper 10-99

THE BALANCE OF POWER IN CLOSELY HELD CORPORATIONS

Morten Bennedsen Daniel Wolfenzon

Department of Economics

- Copenhagen Business School Solbjerg Plads 3, DK-2000 Frederiksberg

(3)

Ai @*@?Ui Lu Lih ? *Lti*) Oi*_

LhTLh@|L?t |

Lh|i? i??i_ti?

: #@?i* `L*ui?3L?

Mt|h@U|

`i @?@*)3i @ U*Lti*) i*_ ULhTLh@|L? U@h@U|ih3i_ M) |i @Mti?Ui Lu @ hit@*i 4@h!i| uLh t@hit @?_ M) TL|i?|@**) @?} tiih@* t}?€U@?| t@hiL*_iht Ai uL?_ih Lu |i €h4 4@) LT|4@**) ULLti |L _t|hM|i L|?} TLih |L tiih@* *@h}i t@hiL*_iht t?Ui |t uLhUit |i4 |L uLh4 UL@*|L?t |L LM|@?

UL?|hL* UL@*|L?c M) }hLT?} |i U@t Lt Lu |t 4i4Mihtc ?|ih?@*3it |L

@ *@h}ih i |i?| |i UL?ti^i?Uit Lu |t @U|L?t @?_ i?Ui |@!it 4Lhi iUi?|

@U|L?t |@? |t ?__@* 4i4Miht Ai 4L_i* @t L|ih 4T*U@|L?t uLh |i L?ihtT t|hU|hi Lu @ U*Lti*) i*_ ULhTLh@|L?G L?it@hiL?iL|i h*i 4ThLit iUi?U)( |i LT|4@* L?ihtT t|hU|hi @t i|ih L?i _L4?@?|

t@hiL*_ih Lh tiih@* i^@*t3i_ t@hiL*_iht( @?_c €?@**)c iUi?U) _iUhi@tit

| |i ?4Mih Lu t}?€U@?| t@hiL*_iht c.w ,BttuWB|NAH B2c Be

lj+NiatH *Lti*) i*_ ULhTLh@|L?tc L?ihtT t|hU|hic UL?|hL* _*

|L?c UL?|hL**?} UL@*|L?c L?i t@hi L?i L|i

|Zh duh judwhixo wr Rolyhu Kduw/ Idxvwr Sdqxq}l/ Dqguhl Vkohlihu/ wkh sduwlflsdqwv ri wkh Rujdql}dwlrq Oxqfk dw Kduydug Xqlyhuvlw| dqg dq dqrq|prxv uhihuhh iru xvhixo vxjjhvwlrqv dqg frpphqwv1

Frshqkdjhq Exvlqhvv Vfkrro/ Fhqwuh iru Lqgxvwuldo Hfrqrplfv dqg Fhq0 wuh iru Oderxu Pdunhw dqg Vrfldo Uhvhdufk1 Lqvwlwxwh ri Hfrqrplfv/ Vroe0 mhuj Sodgv 6/ 5333 Frshqkdjhq I/ Ghqpdun1 Hpdlo= 6O;WOta"/ ZHE=

kwws=22zzz1fev1gn2ghsduwphqwv2hfrq2vwd2pehqqhgvhq2pruwhq1kwp1

Kduydug Xqlyhuvlw|1 Ghsduwphqw ri Hfrqrplfv/ Olwwdxhu Fhqwuh/ Kduydug Xqlyhuvlw|/

Fdpeulgjh/ PD 3546;1 Hpdlo= aN,ujA5;"5Aj|tuBtBiBiaja1

(4)

 W?|hL_U|L?

`i @?@*)3i U*Lti*) i*_ ULhTLh@|L?t U@h@U|ih3i_ M) |i @Mti?Ui Lu @ hit@*i 4@h!i| uLh t@hit @?_ M) TL|i?|@**) @?} tiih@* t}?€U@?| t@hiL*_iht

*Lti*) i*_ ULhTLh@|L?t @hi |i _L4?@?| uLh4 Lu L?ihtT ? _ii*LT?}

@?_ |h@?t|L?@* iUL?L4itc @t i** @t ? 4Lt| `it| ,hLTi@? iUL?L4it ,i?

? |i N5c L| Lu S 4**L? ULhTLh@|L?tc HcDff L?*) ihi TM*U*) i*_ ? bHb EN5 hi@ Lu |i i?tt Ebb U|i_ ? LTihc Lgii @?_ B*tL? EbbD Ai ULhTLh@|i }Lih?@?Ui *|ih@|hi @t }i?ih@**) uLUti_ L? €h4t | i|ih _tTihti_ L?ihtT t|hU|hi Eih*i @?_ i@?t Eb2 @?_ BhLtt4@?

@?_ O@h| EbHf Lh @ t?}*i UL?|hL**?} t@hiL*_ih Eai?ti? @?_ iU!*?}

Eb.Sc 5*iuih @?_ Vt?) EbHS @?_ h!@h|c BhL4M @?_ @??3 Ebb.

W? |i uLh4ih U@tic t@hiL*_iht @hi |LL t4@** @?_ _tLh}@?3i_ |L 4TLti |ih

** @?_c @t @ hit*|c UL?|hL* hit_it ? |i @?_t Lu |i 4@?@}ih W? |i *@||ihc

|i _L4?@?| t@hiL*_ih _U|@|it ULhTLh@|i TL*U) i|ih M) 4@?@}?} |i

€h4 _hiU|*)c Lh M) U*Lti*) 4L?|Lh?} |i 4@?@}?} |i@4 Ai hi4@??}

t@hiL*_iht *@U! i|ih |i TLih Lh |i ?Ui?|it |L LTTLti |i UL?|hL**?}

t@hiL*_ih<t _iUtL?t

W? |i Thiti?| T@Tih i uLUt L? €h4t ihi t@hiL*_iht @hi tUi?|*)

*@h}i ?L| |L thhi?_ih UL?|hL* |L |i 4@?@}ih ii? |L} ?L?i Lu |i t@hi L*_iht @hi @M*i |L UL?|hL* |i €h4 @*L?i W? |iti €h4t ULhTLh@|i TL*U) t

|i hit*| Lu |i ?|ih@U|L? @4L?} |i tiih@* *@h}i t@hiL*_iht

`i @h}i |@| |i ThTLti Lu @?} 4*|T*i *@h}i t@hiL*_iht t |L Thi i?| @ t?}*i t@hiL*_ih uhL4 |@!?} ?*@|ih@* @U|L?t |@| 4}| h| L|ih t@hiL*_ihtc tU @t _ih|?} u?_t uhL4 |i €h4 Wu @ _ihtL? _iUtL? t

|L Mi |@!i?c | ** hi^hi |i UL?ti?| Lu @ UL@*|L? Lu t@hiL*_iht 5?Ui @ UL@*|L? Lu t@hiL*_iht _ih|t *itt |@? @?) Lu |t ?__@* 4i4Mihtc |i

?|@* L?ih tii!t |i T@h|UT@|L? Lu L|ih *@h}i t@hiL*_iht ? Lh_ih |L

4Jrphv dqg Qrydhv +4<<<, qg wkdw ;91<( ri wkh forvho| khog frusrudwlrqv lq wkh Qdwlrqdo Vxuyh| ri Vpdoo Exvlqhvv Ilqdqfhv +QVVEI, zlwk dqqxdo vdohv deryh 43 ploo1 XVG kdyh dw ohdvw rqh odujh vkduhkroghu dqg 8:15( kdyh pruh wkdq rqh odujh vkduhkroghu1



(5)

_*|i ih TLih @?_ UL?ti^i?|*) UL44| |L uLh4?} @ UL?|hL**?} UL@*|L?

W? Lh 4L_i*c @ €h4<t ?|@* L?ihc ? ?ii_ Lu i |ih?@* U@T|@*c ti**t L|it

@?_ U@t Lt |L i@*| UL?t|h@?i_ L|t_i ?it|Lht ?Ui |i L?ihtT t|hU|hi t _i|ih4?i_c |ihi t @ UL?|hL* UL?|it| @4L?} UL4Ti|?} UL@*|L?t

|L ti3i UL?|hL* Lu |i €h4 L?|hL* t @*i_ M) t@hiL*_iht MiU@ti |

@**Lt |i4 |L i?L) Th@|i Mi?i€|t `i @tt4i |@| |iti Mi?i€|t UL4i

@| |i i Ti?ti Lu ?L?UL?|hL**?} t@hiL*_iht @?_c 4LhiLihc |@| |i) @hi

?iUi?| |L i |h@U| Ai L|UL4i Lu |i UL?|hL* UL?|it| t ?i?Ui_ M)

|i L?ihtT t|hU|hic ic M) ?4Mih Lu L|it @?_ U@t Lt |@| i@U t@hiL*_ih @t AihiuLhic i? _iU_?} |i L?ihtT t|hU|hic |i ?|@*

L?ih |@!it ?|L @UUL?| ?L| L?*) |i ?ii_ |L h@ti u?_tc M| @*tL |i @) ? U |i L?ihtT t|hU|hi ** ?i?Ui |i UL?|hL* UL?|it|

h hit*|t @ML| L?ihtT @hi _hi? M) |L LTTLt?} igiU|t U i U@** |i @*}?4i?| @?_ |i UL@*|L? uLh4@|L? igiU| Ai @*}?4i?| igiU| t

|i TLt|i hi*@|L? |@| i t|t Mi|ii? |i U@t L t|@!i Lu |i UL?|hL**?}

UL@*|L? @?_ |L|@* €h4 @*i Ai 4Lhi U@t Lt |i UL?|hL**?} UL@*|L?

TLttittitc |i 4Lhi | ?|ih?@*3it |i ULt|t Lu |t @U|L?tc @?_ i?Uic |i uiih ULt|*) Th@|i Mi?i€|t | i |h@U|t At igiU| t t4*@h |L |@| ? ai?ti? @?_

iU!*?} Eb.S

Ai tiUL?_ @?_ ?Li* igiU| @htit uhL4 t@hiL*_ih i^*Mh4 Mi@Lh

@| |i |4i Lu UL@*|L? uLh4@|L? ?Ui L|it @?_ U@t Lt @hi _t|hM|i_c 4@?) _gihi?| UL@*|L?t @i tUi?| L|?} TLih |L UL?|hL* |i €h4 OL iihc L| Lu |iti UL@*|L?tc |i L?i | |i t4@**it| U@t L t|@!i ?t

|i UL?|hL* UL?|it| At t MiU@ti | @t |i *@h}it| }hLT Lu t@hiL*_iht E? |ih4 Lu U@t Lt |L i ThLTh@|i uhL4 At 4T*it |@|c UL?_|L?@*

L? @?} tUi?| L|?} TLih |L UL?|hL* |i €h4c |t UL@*|L? uLh4@|L?

igiU| |i?_t |L 4?43i |i U@t L t|@!i Lu |i ???} UL@*|L?

`| |iti |L igiU|tc i U@? i T*@? |i ULUi Mi|ii? hi|@??} @MtL*|i UL?|hL* @?_ _*|?} UL?|hL* L|i |@| |i ?|@* L?ih Mi@htc |hL} |i ThUi Lu |i tiUh|it ti ti**tc @?) ?iUi?U) U@ti_ M) _ihtL? Wu |i

2

(6)

?|@* L?ih @t i?L} i@*| |L €?@?Ui |i €h4 @?_ hi|@? @ ih) *@h}i TLh|L? Lu |i U@t Ltc t@) HfIc |i? | t LT|4@* uLh ih |L hi|@? UL?|hL*

) _L?} tLc |i ???} UL@*|L?c U ** UL?|@? L?*) |i ?|@* L?ihc

** @i @ UL?t_ih@M*i uh@U|L? Lu |i U@t Lt OLiihc u |i ?|@*

L?ih<t i@*| L?*) @**Lt ih |L hi|@? @ t4@**ih uh@U|L?c t@) DDIc |i?

hi|@??} UL?|hL* t ?L| LT|4@* L?t_ih @? @*|ih?@|i L?ihtT t|hU|hi

? U |i ?|@* L?ih ti**t I Lu U@t Lt @?_ L|it |L i@U Lu |L

?it|Lht `| |t L?ihtT t|hU|hic @ UL@*|L? Lu |L t@hiL*_iht **

uLh4 |L UL?|hL* |i €h4 Ai UL?|hL**?} ML_) ** @i SS2I Lu |i U@t Ltc

@?_ ** |@!i 4Lhi iUi?| @U|L? |@? @ UL?|hL**?} ML_) | L?*) DDI

*i@h*)c |i ?|@* L?ih L*_ *!i |@| |i UL@*|L? |@| UL?|hL* |i €h4

?U*_i @** |hii t@hiL*_iht E|i @*}?4i?| igiU| M|c L?Ui L|it @?_ U@t Lt @hi _t|hM|i_c t@hiL*_iht ?Ui?|it @hi |L uLh4 @ UL?|hL**?} UL@*|L?

|@| i ThLTh@|it |i *@h}it| ti| Lu t@hiL*_iht E|i UL@*|L? uLh4@|L? igiU|

@?_c UL?ti^i?|*)c L?i t@hiL*_ih t *iu| L|

L| @** @)t |L _*|i TLih }i?ih@|i |i t@4i @*i uLh |i €h4 W?_ii_c 4Lt| Lu |i @?@*)tt ** Mi _iL|i_ |L ?_iht|@?_?} |i LT|4@* L?ihtT t|hU|hi i? 4Lhi |@? L?i t}?€U@?| t@hiL*_ih t Thiti?| 6ht|c i _i€?i |i UL?UiT| Lu UL?|hL* t|hU|hi @t |i UL**iU|L? Lu UL@*|L?t | t Ui?| TLih |L UL?|hL* |i €h4 @?_ €?_ |@|c uLh@?) TLttM*i UL?|hL* t|hU|hic

|ihi t @ L?it@hiL?iL|i L?ihtT t|hU|hi |@| 4@ 43it iUi?U) Ai ?||L? t |@| _i@|L?t uhL4 L?it@hiL?iL|i Uhi@|i t@hiL*_iht

| @ } L|i |L U@t L h@|Lc @?_ |i UL@*|L? uLh4@|L? igiU| |i?_t |L

?U*_i |iti t@hiL*_iht ? |i UL?|hL**?} UL@*|L? t @ hit*|c |t UL@*

|L? i?_t T | @ t4@** U@t L t|@!ic U t _i|h4i?|@* |L iUi?U) 6L**L?} |i ?|@* UL?|hM|L?t uhL4 BhLtt4@? @?_ O@h| EbHH @?_

O@hht @?_ +@ EbHHc @? i |i?ti *|ih@|hi L? |i LT|4@*|) Lu L?i t@hiL?iL|i @t _ii*LTi_ Ai ?Li* ui@|hi Lu Lh hit*| t |@| | t

?L| _ihi_ ? |i UL?|i | Lu |@!iLiht Atc Lh 4L_i* t Mi||ih t|i_ |L i T*@? |i u@U| |@| _i@|L?t uhL4 |i L?it@hiL?iL|i h*i @hi t4@** ?

(7)

4Lt| UL?|hitc @?_ ?L| L?*) ? |Lti | @U|i 4@h!i|t uLh ULhTLh@|i UL?|hL*

Ew@ Lh|@ i| @* Ebbb

5iUL?_c i it|@M*t |i hi*@|L?tT Mi|ii? iUi?U) @?_ |i ?4Mih Lu t@hiL*_iht W? T@h|U*@hc i tL |@| @t |i ?4Mih Lu t@hiL*_iht t ?Uhi@ti_c iUi?U) 4t| _iU*?i Ah_c i tL |@| |i Mit| L?ihtT t|hU|hi t i|ih L?i ihi |ihi t @ t?}*i *@h}i t@hiL*_ihc Lh L?i ihi t@hiL*_iht @hi hL}*) Lu |i t@4i t3i Ai ?||L? uLh |iti |L hit*|t t t4*@hG t U@t Lt @hi _t|hM|i_ @4L?} 4Lhi t@hiL*_iht Lh @t |i) @hi _t|hM|i_ 4Lhi ?ii?*)c | ** Mi i@tih |L €?_ @ UL@*|L? | tUi?|

L|?} TLih @?_ @ hi*@|i*) t4@** U@t L t|@!i *|L} uLh _gihi?|

hi@tL?tc |t *@t| hit*| t t4*@h |L @ hit*| uL?_ ? ~iMi* EbbDc ihi |i L?ihtT t|hU|hi t _i|ih4?i_ M) |i ?it|Lht L @**LU@|i |ih i@*|

@UhLtt €h4t ? Lh_ih |L hiUii @ *@h}ih t@hi Lu |i Th@|i Mi?i€|t

W? Lh @?@*)tt i?uLhUi@M*i UL?|h@U|t @4L?} |i L?iht U@? 4ThLi i Ui?U) W? 4@?) U*Lti*) i*_ ULhTLh@|L?t UL?|h@U|t Lih UL4TLt|L?t Lu |i ML@h_c L|?} h*itc @?_ i|L h}|tc @hi ti_ LhiLihc *i}@* tUL*@ht t|hL?}*)

@_ti Th@U||L?iht |L h|i tU UL?|h@U|t E<i@* Ebbf N?uLh|?@|i*)c

|iti UL?|h@U|t @hi ?L| @*@)t i?uLhUi_ W? |i N5c ?|* hiUi?|*) UL?|h@U|t

|@| @*|ihi_ |i t|@||Lh) t)t|i4 Lu }Lih?@?Ui ? @ ULhTLh@|L? ihi ?L| }i?

ih@**) @UUiT|i_ M) ULh|t h hit*|t @ML| |i LT|4@* L?ihtT t|hU|hi L*_ t|** Mi @*_c ii? ? |i Thiti?Ui Lu tU UL?|h@U|tc @t *L?} @t |ihi t tL4i TLt|i ThLM@M*|) |@| @ UL@*|L? Lu t@hiL*_iht ** €?_ @ @) |L

*i}@**) Mhi@U< |i @}hii4i?| `i _tUtt |iti ttit uh|ih ? 5iU|L? S 5*iuih @?_ Vt?) Ebb. @h}i |@|c ? 4Lt| UL?|hitc |i hi*i@?|

@}i?U) ThLM*i4 |@| ULhTLh@|i }Lih?@?Ui tL*_ @__hitt t |@| Lu |i UL?

|hL**?} t@hiL*_ih i ThLTh@|?} |i 4?Lh|) t@hiL*_iht h@|ih |@? |@|

Lu |i 4@?@}ih i ThLTh@|?} @** t@hiL*_iht L?ti^i?|*)c @ ?4Mih Lu T@Tiht E?U*_?} |i Uhhi?| L?i t}}it| |@| |i Thiti?Ui Lu *@h}i t@hi L*_iht t @ 4iU@?t4 ti_ |L 4|}@|i tU i ThLTh@|L? w@ Lh|@ i| @*

Ebbb @?_ @}@?L @?_ +Li* EbbH @h}i |@| L|ih *@h}i t@hiL*_iht hi e

(8)

_Ui _ihtL? M) 4L?|Lh?} |i UL?|hL**?} t@hiL*_ih BL4it @?_ L@it Ebbb uLUt L? L i TLt| M@h}@??} ThLM*i4t @4L?} *@h}i t@hiL*_iht 4@) ThL|iU| 4?Lh|) t@hiL*_iht ? @ 4L_i* |@| }?Lhit |i t|h@|i}U @t TiU|t Lu UL@*|L? uLh4@|L? Aih @?@*)tt UL4T*i4i?| Lhtc t?Ui i uLUt L? |i uLh4@|L? ThLUitt Lu |i UL?|hL**?} UL@*|L? @?_ @tt4i @@) i TLt|

M@h}@??} ThLM*i4t @4L?} |t 4i4Miht

6?@**)c Lh hit*| |@| UL?|hL* _*|L? t @? igiU|i 4iU@?t4 |L hi_Ui _ihtL? i? |ihi t |i TLttM*|) Lu _ihtL? t _@4i|hU@**) LTTLti_

|L |@| Lu w@ Lh|@ i| @* Ebbb @?_ iMUU! Ebbb Aiti T@Tiht @h}i

|@| ? UL?|hit | TLLh ?it|Lh ThL|iU|L? UL?|hL* tL*_ Mi UL?Ui?|h@|i_

MiU@ti L|ihti tL4iL?i UL*_ ti3i | |L| u**) T@)?} uLh | W? Lh 4L_i* Lu @ U*Lti*) i*_ ULhTLh@|L?c |t U@??L| @TTi? t?Ui L?Ui |i ?|@*

L?ih ti**t |i tiUh|it |ihi t ?L 4@h!i| uLh |i4 W? @__|L?c |i ?|@*

L?ih hiUiit u** T@)4i?| uLh |i Mi?i€|t Lu UL?|hL* |@| M)iht i TiU| |L }i| @?_ |ihiuLhi t ?L| Lhhi_ @ML| *LLt?} UL?|hL* M| h@|ih @ML| |i

|L|@* @*i Lu |i €h4

Ai hit| Lu |i T@Tih t Lh}@?3i_ @t uL**Lt 5iU|L? 2 *@)t L| |i 4L_i*

W? 5iU|L? i @?@*)3i |i UL@*|L? uLh4@|L? ThLUitt W? 5iU|L? e i €

|i UL?|hL* t|hU|hi Eic |i L|?} _t|hM|L? @?_ tL |i LT|4@*|) Lu L?it@hiL?iL|i W? 5iU|L? D i UL4T*i|i*) tL*i uLh |i LT|4@* L?ih tT t|hU|hi Eic ML| |i UL?|hL* t|hU|hi @?_ |i U@t L _t|hM|L?

5iU|L? S ThL_it tTTLh| uLh Lh @?@*)tt ? |i *i}@* *|ih@|hi L? U*Lti*) i*_ ULhTLh@|L?t @?_ ? |i **t|h@|iwi) ihtt @h!@* 5@*it LhTLh@|L?

U@ti 6?@**)c 5iU|L? . UL?U*_it

2 Ai L_i*

Ai |4?} Lu |i 4L_i* t tL? ? 6}hi  | _@|i fc @? i?|hiThi?ih @t

|i LTTLh|?|) Lu ti||?} T @ €h4 @| @ ULt| g  `i @tt4i |@| |i i?|hiThi?ih<t i@*| t ?L| tUi?| |L ULih |i i?|hi ti| T ULt|c tL ti t

D

(9)

!

6h4 it|@M*ti_

@| ULt| g

,?|hiThi?ih ti**t L|it @?_ U@t Lt

5@hiL*_ih 4ii|?} | ML@h_ ti*iU|L?G

iih) t@hiL*_ih

@??L?Uit @ UL@*|L?

U

`???} ML@h_ _ih|t _ @?_ T@)t _

? __i?_t

| ' f |'  | ' 2

6}hi G |4i *?i ML?_ |L LM|@? L|t_i €?@?Ui

Aihi t @ *@h}i TLL* Lu TL|i?|@* ?it|Lh U @Mt?} ?L|@|L? i _i?L|i M) ' ic2c c j ,@U ?it|Lh @t @ € *ii* Lu i@*|c `c 5

`i hiuih |L i@U ?it|Lh M) t ?4Mih Lh ?_i c @?_ Lh_ih |i4 tU |@|

` `2 ` `i @tt}? |i ?4Mih f |L |i i?|hiThi?ih @?_

_i?L|i M) `f ih ?|@* i@*| Ai i?|hiThi?ih ULLtit @ tMti| Lu |iti

?it|Lht |L MiUL4i t@hiL*_iht Lu |i €h4 @?_ ti**t |L i@U L?i Lu |i4 @ ETL|i?|@**) _gihi?| ?4Mih Lu L|it @?_ U@t L h}|t Ai i?|hiThi?ih 4}| _iU_i |L ti** L| Lh t|@) @t @ t@hiL*_ih

Ai €?@* L?ihtT t|hU|hi t |i? _itUhMi_ M) @ ti| Lu t@hiL*_iht U E|Uifj @?_ @ ?4Mih Lu L|itcc @?_ @ uh@U|L? Lu |i €h4<t U@t Lc Sc uLh i@U t@hiL*_ih 5 U `i _i€?i 'ijMU @?_ U 'iSjMU @t

|i ThL€*i Lu L|it @?_ U@t L h}|t

| _@|i  |ihi t @ t@hiL*_ih 4ii|?} |@| i*iU|t |i ML@h_ Lu |i €h4 ,@U t@hiL*_ih L|it uLh L?i Lu |i TL|i?|@* ML@h_t L| |L h*i L| @?) TL|i?|@* ML@h_c i @tt4i |@| @** UL@*|L?t U @hi U@?__@|it Ai

???} UL@*|L? t |i L?i |@| hiUiit |i 4Lt| L|itc ihi |i ?4Mih Lu L|it |@| @ UL@*|L? U hiUiit t UL4T|i_ M) |i t44?} |i L|it Lu |i t@hiL*_iht |@| L|i_ uLh W? |i U@ti Lu @ |i_ L|ic |i UL@*|L? tTTLh|i_ M) |i t@hiL*_ih | |i *Lit| ?4Mih ?t 6Lh

?t|@?Uic u |i i?|hiThi?ih hi4@?t @t @ t@hiL*_ih @?_ |ihi t @ DfDf

S

(10)

|ic |i UL@*|L? tTTLh|i_ M) |i i?|hiThi?ih ?t At 4}| hiiU| |i TLih |i i?|hiThi?ih @t @t |i uL?_ih Lu |i €h4 W? @?) ii?|c | _Lit ?L|

4@||ih L |i |iMhi@!ih t @?_ i t4T*) @TT*) |t |iMhi@!?} @tt4T|L?

|L t4T*u) |i L|?} }@4i2

| _@|i 2 |i ML@h_ ? T*@Ui _ih|t _ Lu |i hii?i @?_ T@)t L| |i hi4@??} TLh|L? ? __i?_t `i @tt4i |@| u?_t @hi *Lt| i? _ihtL?

t U@hhi_ L| Ai ULt| Lu _ihtL? t i4ML_i_ ? |i _ihtL? |iU?L*L}) E 6Lh @ *ii* Lu _ihtL? _c |i _ih|i_ @4L?| hiUii_ M) |i ML@h_ t L?*) E_c U t@|t€itG

Ef ' fc Ef ' c E ' fc @?_ E f

Ai _ihtL? |iU?L*L}) ULhhitTL?_t ? itti?Ui |L ai?ti? @?_ iU!*?}<t Eb.S _i@ Lu i |h@U|L? Lu ?L?TiU?@h) Mi?i€|t Ai t@4i ti| Lu @tt4T

|L?t uLh |i _ihtL? |iU?L*L}) U@? Mi uL?_ ? h!@h| i| @* EbbH

`i @tt4i |@| |i _ih|i_ @4L?| t _t|hM|i_ @4L?} ML@h_ 4i4 Miht ? ThLTLh|L? |L |i @4L?| Lu U@t L h}|t |i) L? Ai hi@tL?

uLh |t @_LU @tt4T|L? t |@| i @?| |L uLUt L? |i UL?U| Mi|ii?

ML@h_ 4i4Miht @?_ 4?Lh|) t@hiL*_iht @?_ ?L| L? UL?U|t @4L?} ML@h_

4i4Miht `| |i tTiU€U t@h?} h*i |@| i ti 4i4Miht Lu @?) TL|i?

|@* ML@h_ ?@?4Lt*) @}hii L? |i *ii* Lu _ihtL? Etii UL44i?|t @u|ih wi44@  Mi*L W? @__|L?c L|ih hi@tL?@M*i t@h?} h*it tU @t RTih i@_ Lh RThLTLh|L?@* |L L|it _L ?L| }@h@?|ii i t|i?Ui Lu i^*Mh4 ?

|i L|?} }@4i uLh @** TLttM*i L?ihtT t|hU|hit

wi||?}_EcUc Mi |i *ii* Lu _ihtL? |@| UL@*|L??_ih|@!it i?

|i ThL€*i Lu U@t L h}|t @?_ L|it t }i? M) U@?_ c |i T@)Lg |L i@U

5Wlhv duh kdqgohg glhuhqwo| lq sudfwlfh1 Iru lqvwdqfh/ lq X1V1 zkhq wkhuh lv d wlh ru d cghdgorfn*/ d vkduhkroghu fdq dvn d frxuw iru clqyroxqwdu| glvvroxwlrq* ri wkh frusrudwlrq ru d mxgjh fdq lpsrvh d ex|0rxw dw d mxglfldoo| ghwhuplqhg sulfh +Kdplowrq/ 4<<9,1

6Dovr/ wkhuh duh rwkhu sodxvleoh jdphv zlwk zhdnhu dvvxpswlrqv wkdw vhohfw wkh vdph zlqqlqj frdolwlrq1 Lq Ehqqhgvhq dqg Zroihq}rq +4<<<, zh prgho d vlwxdwlrq lq zklfk d pdqdjhu kdv wr ceuleh* vkduhkroghuv lq rughu wr eh doorzhg wr glyhuw1 Wkh frdolwlrq wkh pdqdjhu fkrrvhv wr euleh lv wkh vdph dv wkh zlqqlqj frdolwlrq lq wklv prgho1

.

(11)

t@hiL*_ih tG ZEcUc '

+SE_EcUc n SS

MSE_EcUc u 5c

SE_EcUc L|ihti E

wi||?} Mi |i ThUi |@| ?it|Lh T@)tc |i i?|hiThi?ih tL*it |i uL*

*L?} ThLM*i4 @| _@|i fG

UatfctSc4@ MUctMU3tfZfEcUc n [

MU3tf

g tMiU| |L t |i ???} UL@*|L? Lu |i L|?} }@4ic

`fnS

MU3tf gc

4?i`c ZEcUcj ;5U ifj

E2

Ai i?|hiThi?ih ULLtit |i ti| Lu t@hiL*_iht Lu |i €h4 uhL4 |i ti| Lu L|t_i ?it|Lht T*t ihti*u At ti|c Uc 4@) Lh 4@) ?L| ?U*_i |i i?|hiThi?ih 5i @*tL ULLtit |i ?4Mih Lu U@t L h}|t @?_ L|it uLh i@U t@hiL*_ih @?_ |i @4L?| i@U L|t_i ?it|Lh T@)t *i@h*)c i?

ULLt?} |i L?ihtT t|hU|hic |i i?|hiThi?ih UL?t_iht |i igiU| |t t|hU|hi ** @i L? |i UL?|hL* UL?|it| E€ht| UL?t|h@?| Ai i?|hiThi?ih

@*tL ?ii_t |L h@ti i?L} u?_t |L T@) |i ti| T ULt| EtiUL?_ UL?t|h@?| Ai

€?@* UL?t|h@?|c U@T|hit |L hit|hU|L?t L? G ? L|t_i ?it|Lh U@??L|

T@) 4Lhi |@? t i@*| @?_c ?_ih |i @tt4T|L? Lu @ 3ihL ?|ihit| h@|ic i@U L|t_i ?it|Lh T@h|UT@|it L?*) uc @| *i@t|c i Mhi@!t ii?

*i@h*)c |i *@t| UL?t|h@?| 4t| Mi M?_?} uLh @** L|t_i ?it|Lht t?Ui

|i i?|hiThi?ih U@h}it |i 4@ 44 TLttM*i A@| tc i|ih ' Z

i? Z ` Lh ' ` i? Z : ` W? |i *@||ih U@tic Liihc

|i i?|hiThi?ih L*_ Mi *LLt?} tL4i hi?|t |L L?i Lu |i ?it|Lht Et?Ui Z *i@h*)c ti |hit |L @L_ |t U@ti u TLttM*i W?_ii_c | t i@t)

|L tL |@|c u |ihi t @| *i@t| L?i L?ihtT _t|hM|L? | U |i i?|hiThi?ih U@? €?@?Ui |i €h4 |L| }?} L| hi?|t |i? @| |i tL*|L?

i ** @i 'Z Wu |i i?|hiThi?ih t i@*|) i?L}c Lh |ihi @hi @ ui hi*@|i*) i@*|) L|t_i ?it|Lhtc |t ** ?_ii_ Mi |i U@ti

W? }i?ih@* |i? i ** @i |@| ' Z U 4T*it |@| |i i?

|hiThi?ih hiUiit |i i?|hi @*i |@| |i €h4 }i?ih@|it W? tU @ U@tic H

(12)

ih LMiU|i L*_ Mi |L 4@ 43i |i @*i Lu |i €h4 tMiU| |L Z

` uLh @** 5U ifj At t |i LMiU|i u?U|L? i @i ? 4?_ ? 5iU

|L?t e @?_ D

@h@U|ih3@|L? Lu |i i^*Mh4

W? |t tiU|L? i @?@*)3i |i tM}@4i |@| t|@h|t @| _@|i  `i |@!i @t }i?

|i L?ihtT _t|hM|L?c |@| tc |i ti| Lu t@hiL*_ihtU @?_ |i U@t L

@?_ L|i ThL€*itcU@?_ `i @hi ?|ihit|i_ ? |L @tTiU|t Lu |i i^*Mh4G

|i _i?||) Lu |i ???} UL@*|L? @?_ |i @4L?| Lu _ihtL? |@| | U@hhit L| Ai @?tih |L |t *@t| ^it|L? t }i? ? |i uL**L?} *i44@

wi44@  5TTLti |@| UL@*|L? t |i ML@h_ @?_ |@| U @?_ @hi |i U@t L @?_ L|i ThL€*i Ai *ii* Lu _ihtL? _EcUc t@|t€itG

E_EcUc '[

M

S E

W? @__|L? |i *ii* Lu _ihtL? t _iUhi@t?} ? |i U@t L t|@!i Lu |i

???} UL@*|L?

Ai ThLLuc U MiU@ti Lu |t t4T*U|) i L4|c ThLUii_t M) tL?}

|@| i^@|L? E t |i €ht| Lh_ih UL?_|L? Lu |i 4@ 43@|L? ThLM*i4 Lu i ih) 4i4Mih Lu |i ML@h_ Oi?Uic |i) ?@?4Lt*) @}hii |L _ih|_EcUc 6h|ih4Lhic t?Ui E fc i^@|L? E 4T*it |@| _ihtL? _iUhi@tit

| |i U@t L t|@!i Lu |i ???} UL@*|L? At t |i @*}?4i?| igiU|

i _tUtti_ ? |i W?|hL_U|L?G Ai ???} UL@*|L? ?|ih?@*3it |L @ *@h}ih i |i?| |i UL?ti^i?Uit Lu |t @U|L?t @?_ i?Ui i?}@}it ? *itt _ihtL?c |i 4Lhi U@t Lt | TLttittit

Nt?} Thit|h@|i}) tM}@4iTihuiU| i^*Mh4 @t Lh tL*|L? UL?UiT|

uLh |i L|?} }@4ic *i@it t | @ *@h}i ?4Mih Lu i^*Mh@ W? u@U|c i? ?L t@hiL*_ih @t 4Lhi |@? DfI Lu |i L|itc | U@? Mi tL? |@|

b

(13)

@?) UL@*|L? U@? Mi tTTLh|i_ @t @ ???} ML@h_e AihiuLhic i ti @ ULLTih@|i hi€?i4i?|G W? |i L|?} }@4i @| _@|i c i hi^hi |@| ?L UL@*|L? Lu t@hiL*_iht U@? L?|*) _i@|ic @?_ M) _L?} tL ?Uhi@ti |i T@)Lg |L i@U L?i Lu |i4 Atc i hi^hi |i i^*Mh4 |L Mi @ t|hL?}

i^*Mh4 ? |i ti?ti Lu 4@?? EbDb

W?||i*)c |i UL@*|L? Lu ML@h_ 4i4Miht 4t| @i tUi?| L|?}

TLih |L Mi i*iU|i_ W? T@h|U*@hc t?Ui |t UL@*|L? i ThLTh@|it |i UL@*

|L? Lu ?L?ML@h_ 4i4Mihtc | 4t| Mi @M*i |L Mi@| |t *@||ih UL@*|L? @|

|i t@hiL*_iht< 4ii|?} At }it hti |L |i UL?UiT| Lu @ t|hL?} UL@*|L?c U ThLit tiu* ? U@h@U|ih3?} |i i^*Mh@

#i€?|L?  vwurqj frdolwlrq hi*@|i |L |i L|?} _t|hM|L? t @ UL@*|L? ? U i|ihG

 Ai t4 Lu |i L|it Lu |t 4i4Miht t t|hU|*) *@h}ih |@? DfIc Lh 2 Ai t4 Lu |i L|it t i @U|*) DfI @?_ |i t@hiL*_ih | |i 4?

44 ?_i t @ 4i4Mih

*tLc @ zhdn frdolwlrq hi*@|i |L t L?i |@| t ?L| t|hL?} hi*@|i |L iuLhi t|@|?} hLTLt|L? c i _i€?i 7E @t |i UL**iU|L? Lu @** t|hL?}

UL@*|L?t hi*@|i |L @ L|?} _t|hM|L? A@| tc

7E 'if U Gf t t|hL?} hi*@|i |L j

hLTLt|L?  6Lh |i tM}@4i |@| t|@h|t @| _@|i c @? i^*Mh4 @*@)t i t|t uLh @?) |L _t|hM|L?tU@?_ LhiLihc ? @** i^*Mh@ |i ???}

UL@*|L?c Wc t @ t|hL?} UL@*|L? | |i 4?44 U@t L Lu @** t|hL?}

UL@*|L?t A@| tc

W 5@h}4?

M7E

[

M

S Ee

7Vxssrvh hyhu| vkduhkroghu yrwhv iru frdolwlrq G/ zkhuh G lv dq| frdolwlrq1 Qr vkduh0 kroghu fdq/ e| xqlodwhudoo| ghyldwlqj/ fkdqjh wkh uhvxowv ri wkh hohfwlrq1 Khqfh/ wklv lv dq htxloleulxp1

f

(14)

Aihi 4}| Mi 4@?) UL@*|L?t |@| 4?43i |i t4 Lu U@t Lt W?

@| uL**Ltc i @tt4i |@| @?) Lu |iti UL@*|L?t t |i ???} UL@*|L?

| i^@* ThLM@M*|)D

Ai hit*| t ?||i*) @TTi@*?} Ai UL@*|L? Lu ML@h_ 4i4Miht i ThLTh@|it |i UL@*|L? Lu ?L?ML@h_ 4i4Miht Oi?Uic ML@h_ 4i4Miht 4t|

@i tUi?| L|?} TLih |L Mi@| |i UL@*|L? Lu ?L?ML@h_ 4i4Mihtc ic

|i ???} ML@h_ 4t| Mi t|hL?} 6h|ih4Lhic |i UL@*|L? | |i t4@**

it| U@t L t|@!i Lu @** |i t|hL?} UL@*|L?t ?t MiU@tic Lu @** |i t|hL?}

UL@*|L?tc | t |i L?i Lti 4i4Miht Mi?i€| |i 4Lt| uhL4 _ihtL? t?Ui

|i) @i @ RM}}ih ti| E? |ih4t Lu U@t Lt Lu ?L?ML@h_ 4i4Miht |L i ThLTh@|i uhL4 At t @| i |ih4i_ |i UL@*|L? uLh4@|L? igiU| ?

|i W?|hL_U|L? ) ti*iU|?} |i t|hL?} UL@*|L? | |i t4@**it| U@t L t|@!ic |i UL@*|L? uLh4@|L? igiU| ThL_it @ UL?|ihi}| |L |i i?

|hiThi?ih<t LMiU|i Lu 4@ 43?} |i U@t L Lu |i ???} UL@*|L?

At |i?tL?c @t i _itUhMi Mi*Lc t @| _hit 4Lt| Lu |i hit*|t ? Lh

@?@*)tt

Aihi @hi |L ?|ih4i_@|i hit*|t ?ii_i_ uLh |i ThLLu Lu |t ThLTLt

|L? `i t|@|i |i4 @t *i44@t @?_ |i? t!i|U |i ThLLu Lu hLTLt|L?  Ai UL4T*i|i ThLLu Lu |t ThLTLt|L?c @*L?} | @** L|ih ThLLutc t ? |i

@TTi?_

wi44@ 2 6 @ U@t L _t|hM|L? U Ai uL**L?} L*_tG

t@hiL*_ih Thiuiht Mi?} L? |i ML@h_ |L ?L| Mi?} L? |i ML@h_

6Lh @?) |L ML@h_t ? U @ t@hiL*_ih T@h|UT@|itc ti Thiuiht |i L?i | |i t4@**ih U@t L t|@!i

@h| E t t|h@}|uLh@h_G @ t@hiL*_ih Thiuiht |L i ThLTh@|i |L Mi?}

i ThLTh@|i_ *tLc t?Ui @ UL?|hL**?} UL@*|L? | @ t4@**ih U@t L t|@!i _ih|t 4Lhi |@? L?i | @ *@h}ih U@t L t|@!i Ewi44@  @ t@hiL*_ih

8Qrwh wkdw xqolnh zlwk wkh Qdvk htxloleulxp frqfhsw/ h{lvwhqfh ri htxloleulxp lv qrw jxdudqwhhg zkhq wkh frqfhsw ri vwurqj htxloleulxp lv xvhg1 Krzhyhu/ gxh wr rxu vkdulqj uxoh/ zh kdyh h{lvwhqfh iru hyhu| srvvleoh rzqhuvkls vwuxfwxuh1



(15)

}i|t @ *@h}ih uh@U|L? Lu |i €h4<t hii?i i? ti T@h|UT@|it ? |i UL@*|L?

| |i t4@**ih U@t L t|@!i At t |i ?||L? uLh @h| E Ai ?i |

*i44@ it|@M*tit tL4i Lu |i ThLTih|it Lu t|hL?} UL@*|L?t wi44@ 6 @ L|?} _t|hM|L? Ai uL**L?} L*_tG

UL@*|L? t t|hL?} u @?_ L?*) u |t UL4T*i4i?| E|i UL@*|L? uLh4i_

M) |i 4i4Miht |@| _L ?L| Mi*L?} |L | t i@!

?) |L t|hL?} UL@*|L?t @i @| *i@t| L?i t@hiL*_ih ? UL44L?

`| |iti |L *i44@tc i U@? i T*@? |i hit*| Lu hLTLt|L?  6ht|c @ i@! UL@*|L? U@??L| Mi tTTLh|i_ ? i^*Mh4 @t |i ???} ML@h_ Ai hi@tL? t |@| u tU @ UL@*|L? ihi |i ???} ML@h_c |i t@hiL*_iht |@|

_L ?L| Mi*L?} |L | L*_ @i @ ThL€|@M*i _i@|L?G L|?} uLh |i UL@*|L?

uLh4i_ M) |i4ti*it ) wi44@ Ec |i _i@|?} UL@*|L? t t|hL?}c @?_

i?Ui | L*_ Mi i*iU|i_ @t |i ???} ML@h_ W? @__|L?c M) wi44@ 2Ec i@U Lu |i 4i4Miht Lu |i _i@|?} UL@*|L? L*_ Mi Mi||ih Lg MiU@tic

@t @ hit*| Lu |i _i@|L?c |i) }L uhL4 Mi?} i ThLTh@|i_ |L i ThLTh@|?}

L|iht

5iUL?_c @ t|hL?} UL@*|L? |@| _Lit ?L| 4?43i |i t4 Lu U@t Lt

@4L?} |i t|hL?} UL@*|L?t U@??L| Mi tTTLh|i_ @t |i ???} ML@h_ Ai hi@tL? t |@|c u tU @ UL@*|L? ihi |i ???} ML@h_c |ihi L*_ Mi @ ThL€|@M*i _i@|L? uLh |i 4i4Miht Lu @?) t|hL?} UL@*|L?t | @ t4@**ih U@t L t|@!iG L|?} uLh |i UL@*|L? uLh4i_ M) |i4ti*it 5?Ui |i _i@|?} UL@*|L? t t|hL?} | L*_ ? LhiLihc @** |i 4i4Miht Lu |i _i@|?} UL@*|L? L*_ Mi Mi||ih Lg 6ht|c |Lti L __ ?L| Mi*L?} |L |i

???} ML@h_ @| |i ThLTLti_ i^*Mh4 L*_ MiUL4i ML@h_ 4i4Miht Oi?Uic M) wi44@ 2Ec |i) L*_ Mi Mi||ih Lg 5iUL?_c |Lti L __

Mi*L?} |L |i ???} ML@h_ @| |i ThLTLti_ i^*Mh4 L*_ MiUL4i ML@h_

4i4Miht Lu @ ML@h_ | @ t4@**ih U@t L t|@!i Atc M) wi44@ 2Ec

|i) L*_ @*tL Mi Mi||ih Lg

6?@**)c |ihi t @*@)t @| *i@t| L?i i^*Mh4 ihi |i UL@*|L? |@|

2

(16)

4?43it |i t4 Lu U@t Lt @4L?} |i t|hL?} UL@*|L?tcWc ?t W?_ii_c i tL |@| u iih)L?i L|it uLhWc ?L UL@*|L? Lu t@hiL*_iht _i@|it UL@*|L? Lu t@hiL*_iht |@| t i@! U@??L| U@?}i |i hit*|t Lu |i i*iU|L?

M) _i@|?} @?_ i?Ui i L?*) UL?t_ih _i@|L?t Lu t|hL?} UL@*|L?t | iih) |L t|hL?} UL@*|L?t @i @ t@hiL*_ih ? UL44L? Ewi44@ E @?_

|ihiuLhi L?i Lu |i 4i4Miht Lu W 4t| Mi*L?} |L |i _i@|?} UL@*|L?

5?Ui |t t@hiL*_ih t 4@_i Mi||ih Lg M) _i@|?} |i?c M) wi44@ 2Ec ti 4t| Mi @ 4i4Mih Lu |i ?i ML@h_ E|i L?i hit*|?} uhL4 |i _i@|L?

@?_c M) wi44@ 2Ec |t ?i ML@h_ 4t| @i *itt U@t L |@?W Oi?Uic

|i ?i ML@h_ t i@! EM) _i€?|L?c ?L t|hL?} UL@*|L? U@? @i *itt U@t L |@?W @?_ _ih|t 4Lhi |@?W | t?Ui |i ?i ML@h_ t i@! M|

|i _i@|?} UL@*|L? t t|hL?}c |ihi 4t| Mi @ _i@|?} t@hiL*_ih |@|

t ?L| ? |i ?i ML@h_ 5?Ui |i ?i ML@h_ _ih|t 4Lhi |@? Wc |ihi t

?L @) ? U |t t@hiL*_ih U@? Mi Mi||ih Lg AihiuLhic ?L UL@*|L?

_i@|it uhL4 |i ThLTLti_ i^*Mh4

? @__|L?@* t4T*€U@|L? U@? Mi 4@_i |L hLTLt|L?  Ai _i@ t

|@| @ t|hL?} UL@*|L? |@| @t @| *i@t| L?i t|hL?} ThLTih tMti| t ?iih |i

???} UL@*|L? Ai hi@tL? t |@| tU @ UL@*|L? @t 4Lhi U@t L |@?

|t t|hL?} ThLTih tMti| Atc | ?iih @t |i 4?44 t4 Lu U@t Lt

@4L?} |i t|hL?} UL@*|L?t W? Lh_ih |L €?_ @ ???} UL@*|L?c @||i?|L?

U@? |ihiuLhi Mi hit|hU|i_ |L t|hL?} UL@*|L?t @?} |i ThLTih|) |@| ?L?i Lu |ih ThLTih tMti|t @hi t|hL?} `i U@** |iti UL@*|L?t hi*i@?| t|hL?}

UL@*|L?t

#i€?|L? 2 uhohydqw vwurqj frdolwlrq hi*@|i |L @ L|?} _t|hM|L?

t @ t|hL?} UL@*|L? Ehi*@|i |L Lti ThLTih tMti|t @hi @** i@! Ehi*@|i

|L W? @__|L?c @ uhohydqw vkduhkroghu t L?i |@| Mi*L?}t |L @| *i@t|

L?i hi*i@?| t|hL?} UL@*|L?



(17)

UULh_?} |L |t _tUttL?c i^@|L? Ee U@? Mi hih||i? @tG W 5@h}4?

M-E

[

M

Sc ED

ihi-E t |i UL**iU|L? Lu @** hi*i@?| t|hL?} UL@*|L?t hi*@|i |Lc |@|

tc

-E 'if U Gf t @ hi*i@?| t|hL?} UL@*|L? hi*@|i |L j

+i*i@?| t|hL?} UL@*|L?t U@? Mi tii? @t |i UL@*|L?t UL4Ti|?} uLh UL?|hL*

Aiti UL@*|L?t @i |i 4?44 ?4Mih Lu t@hiL*_iht ?iUitt@h) |L @4@tt tUi?| L|it |L ti3i UL?|hL* i4Miht Lu @ hi*i@?| t|hL?} UL@*|L? U@?

LM|@? UL?|hL* @?_ t@hi |i Th@|i Mi?i€|t @4L?} |i4ti*it @?_c |ihiuLhic

@i ?L ?Ui?|it |L @__ @__|L?@* t@hiL*_iht

? i*i4i?| Lu |i h@?}i Lu -E t @ UL**iU|L? Lu UL@*|L?t @?} |i ThLTih|) |@| |iti UL@*|L?t @hi |i L?*) U@?__@|it |L ti3i UL?|hL* Lu |i

€h4 Aihi @hic ? }i?ih@*c 4@?) L|?} _t|hM|L?t |@| }i?ih@|i |i t@4i UL**iU|L? Lu hi*i@?| t|hL?} UL@*|L?t W?|ihU@?}?} @?) |L tU L|?}

_t|hM|L?t EM| !iiT?} |i _t|hM|L? Lu U@t Lt € i_ _Lit ?L| @giU|

|i _i?||) Lu |i ???} UL@*|L?c |i @4L?| Lu _ihtL?c Lh |i €?@* T@)Lg

|L i@U t@hiL*_ih A@| tc @** |i ?uLh4@|L? @ML| |i L|?} _t|hM|L?

t t44@h3i_ M) |i UL**iU|L? Lu hi*i@?| t|hL?} UL@*|L?t |i) }i?ih@|i `i hiuih |L i@U Lu |iti UL**iU|L?t @t @ UL?|hL* t|hU|hi

#i€?|L? frqwuro vwuxfwxuh t @ UL**iU|L? Lu @** |i hi*i@?| t|hL?}

UL@*|L?t hi*@|i |L tL4i L|?} _t|hM|L?

`i U@? |i? |?! Lu |i i?|hiThi?ih @t ULLt?}c @| _@|i fc |i ?4Mih Lu t@hiL*_ihtc |i UL?|hL* t|hU|hi EU t i^@*i?| |L ULLt?} @?) Lu

|i L|?} _t|hM|L?t |@| }i?ih@|i |t UL?|hL* t|hU|hi @?_ |i U@t L _t|hM|L?

AL U*@hu) |i UL?UiT|tc i ThL_i @? i @4T*i L?t_ih |i L|?} _t

|hM|L? E2fIcDIceDI Ai UL**iU|L? Lu t|hL?} UL@*|L?t hi*@|i |L |t

e

(18)

L|?} _t|hM|L? t 7EE2fIcDIceDI 'i ic2jc icjc i2cjc ic2cj j OLiihc UL@*|L? ic2cj t ?L| hi*i@?| t|hL?} MiU@ti tL4i Lu |t ThLTih tMti|t @hi t|hL?} UL@*|L?t Oi?Uic |i UL**iU|L? Lu hi*i@?| t|hL?} UL@*|L?t uLh |t L|?} _t|hM|L? t -EE2fIcDIceDI ' i ic2jc icjc i2cj j 54*@h*)c t|@h|?} uhL4 |i L|?} _t|hM|L? Eccc L?i LM|@?t |@|

-EEcc ' i ic2jc icjc i2cj j AihiuLhic i t@) |@| |i L|?} _t

|hM|L?t Ecc @?_ E2fIcDIceDI }i?ih@|i |i t@4i UL?|hL* t|hU|hi i ic2jc icjc i2cj j

e ?it@hiL?iL|i

W? |t tiU|L? i @TT*) hLTLt|L?  |L }@? ?t}| ?|L |i LT|4@* @) Lu M?_*?} U@t Lt @?_ L|it `i _L ?L| UL?t_ih )i| |i UL4T*i|i ThLM*i4 Lu

|i i?|hiThi?ih Ei^@|L? E2 Lu _it}??} @| _@|i f |i L?ihtT t|hU|hi +@|ihc i t|@h| | @ }i? UL?|hL* t|hU|hi @?_ @t! @| t |i U@t L ThL€*i |@| 4@ 43it |i @*i Lu |i €h4

) wi44@ c 4@ 43?} |i @*i Lu |i €h4 hi^hit 4@ 43?} |i U@t L t|@!i Lu |i ML@h_ Atc }i? @ UL?|hL* t|hU|hic |i }L@* t |L _t|hM|i U@t Lt tL |@| |i ???} UL@*|L? @t @t 4U U@t Lt @t TLttM*i

AL € _i@t i Thiti?| @? i @4T*i MiuLhi i t|@|i |i 4@? hit*| Lu |t tiU|L? L?t_ih |i UL?|hL* t|hU|hi U ' i ic2jc icjc i2cj j Aihi

@hi 4@?) L|?} _t|hM|L?t |@| }i?ih@|iUE|@| tc 4@?) _gihi?|<t tU

|@| -E 'Uc M| i !?L uhL4 Lh _tUttL? @MLi |@| |i i^*Mh4 t ?L| @giU|i_ M) U Lu |i4 i ti

L?t_ih |i U@t L _t|hM|L? E2fIc2fIcSfI Ai U@t Lt Lu

|i hi*i@?| t|hL?} UL@*|L?tic2jcicjc @?_i2cj@hi efIc HfIc @?_ HfI hitTiU|i*) AihiuLhic M) hLTLt|L? c UL@*|L? ic2jc U @t efI Lu

|i U@t Lc L*_ Mi |i ???} UL@*|L?

L?t_ih ?L |i U@t L _t|hM|L? Ecc ** |i hi*i@?| t|hL?}

D

(19)

UL@*|L?t @i U@t Lt Lu 2c @?_ |ihiuLhi i@U @t @? i^@* ThLM@M*|) Lu

???} *i@h*)c |t U@t L _t|hM|L? t Mi||ih |@? |i ThiLt L?ic U )i*_i_ @ ???} UL@*|L? | U@t L Lu L?*) efI LhiLihc | U@?

Mi i@t*) tL? |@| |i U@t L _t|hM|L? UW ' Ecc t |i LT|4@*

_t|hM|L? uLh |t UL?|hL* t|hU|hiS

`i @hi ?|ihit|i_ ? |i hi*@|L? Mi|ii? |i LT|4@* U@t L _t|hM|L?

UW @?_ |i L|?} _t|hM|L?t |@| }i?ih@|i |i UL?|hL* t|hU|hi U W?

|t T@h|U*@h U@tic |i L|?} _t|hM|L? W ' Ecc }i?ih@|it |i }i?

UL?|hL* t|hU|hi U'i ic2jcicjc i2cj j Etii |i i @4T*i @| |i i?_ Lu

|i ThiLt tiU|L? Oi?Uic i t@) |@| |ihi i t|t @ L?it@hiL?iL|i L?ihtT t|hU|hiW 'UW ' Ecc |@| 4@ 43it iUi?U) uLh |i }i?

UL?|hL* t|hU|hi U.

Ai ThiLt i @4T*ic |L} t4T*ic 4}| @TTi@h UL?U_i?|@* MiU@tic

| |hii t@hiL*_ihtc |ihi @hi ?L| |@| 4@?) UL?|hL* t|hU|hit `i ThL _i Mhi) |L @__|L?@* i @4T*it | D t@hiL*_iht MiuLhi t|@|?} |i 4@? hit*| 6ht|c t|@h|?} | |i UL?|hL* t|hU|hi U ' i i2ccecDjc icDjc icejcicjc ic2j jc i LM|@? EM) tL*?} @ t4*@h ThLM*i4 |L |@|

? uLL|?L|i S E*.c*.c*.c*.c*. @t |i LT|4@* U@t L _t|hM|L?

W| U@? i@t*) Mi UiU!i_ |@| |i L|?} _t|hM|L? E*.c*.c*.c*.c*.

? |h? }i?ih@|it |i UL?|hL* t|hU|hi U ?L|ih i @4T*i t |i UL?|hL*

U*@tt U ' i ic2cjcic2cejciccejc icDjci2ccDjc i2cecDjc icecDj j

| |t ULhhitTL?_?} LT|4@* U@t L _t|hM|L? E2*.c*.c*.c*.c2*.

U @}@? }i?ih@|it U

9Wkh sureohp wr vroyh iru wklv frqwuro vwuxfwxuh lv=

pd{f plqif4. f5> f4. f6> f5. f6j vxfk wkdw f4. f5. f6@ 4=

:Wklv lv qrw wr vd| wkdw wklv lv wkh rqo| rzqhuvkls vwuxfwxuh wkdw pd{lpl}hv hflhqf|

lq wklv frqwuro vwuxfwxuh1 Qru lv lw wkh fdvh wkdw dq| rqh0vkduh0rqh0yrwh glvwulexwlrq lv rswlpdo iru wkh frqwuro vwuxfwxuh lw jhqhudwhv1 Wkh uhvxow lv zhdnhu1 Lw vd|v wkdw wkhuh lv rqh rqh0vkduh0rqh0yrwh rzqhuvkls vwuxfwxuh wkdw pd{lpl}hv hflhqf|1

S

(20)

hLTLt|L? 2 }i?ih@*3it |iti i @4T*it |L@?) UL?|hL* t|hU|hi t ?L|i_

@MLic 4@ 43?} iUi?U) t i^@*i?| |L 4@ 43?} |i U@t L Lu |i

???} UL@*|L? OLiihc M) hLTLt|L? c |i ???} UL@*|L? t |i L?i

| |i 4?44 U@t L Lu @** hi*i@?| t|hL?} UL@*|L?t AihiuLhic |i LT|4@* U@t L _t|hM|L?UWuLh @ }i? UL?|hL* t|hU|hiUt |i tL*|L?

|L |i uL**L?} ThLM*i4G

4@ U 4?

MU

[

M

S ES

hLTLt|L? 2 6 @ UL?|hL* t|hU|hi Uc @?_ *i| UW Mi |i LT|4@* U@t L _t|hM|L? uLh |t UL?|hL* t|hU|hi Ai L|?} _t|hM|L? W ' UW }i?ih@|it Uc ic -EW 'U

Ai ThLTLt|L? t|@|it |@|c uLh @?) UL?|hL* t|hU|hic |ihi t @ L?it@hi L?iL|i L?ihtT t|hU|hi W ' UW tU |@| UW t |i LT|4@* U@t L _t|hM|L? uLh |i }i? UL?|hL* t|hU|hic @?_W }i?ih@|it |i }i? UL?|hL*

t|hU|hi Ai hit*| uL**Lt uhL4 |i |i?tL? Mi|ii? |i @*}?4i?| igiU|c U hi^hit |@| |i ???} UL@*|L? @i |i *@h}it| TLttM*i U@t L t|@!ic @?_ |i UL@*|L? uLh4@|L? igiU|c U ti*iU|t |i hi*i@?| t|hL?}

UL@*|L? | |i t4@**it| U@t L t|@!i `i ti |t |i?tL? |L tL |@|

|i }i? UL?|hL* t|hU|hiU@?_ |i UL?|hL* t|hU|hi-EW @hic ? u@U|c |i t@4i AL ThLi |t u@U|c i tL |@| |i UL@*|L?t ? U@hi hi*i@?| t|hL?}

UL@*|L?t hi*@|i |L WH

6ht|c uhL4 ih LMiU|i Lu ?Uhi@t?} |i U@t Lt Lu @** |i UL@*|L?t ? Uc | U@? Mi tL? |@|c @| |i tL*|L?UWc |i i?|hiThi?ih LM|@?t |@| |i U@t Lt Lu @** UL@*|L?t ? U i Uii_ DfI 5?Ui W 'UWc | |i L|?}

_t|hM|L? Wc @** UL@*|L?t ? U @i 4Lhi |@? DfI Lu |i L|itc ic @**

UL@*|L?t ? U@hi t|hL?} hi*@|i |L W

5iUL?_c |L i T*@? L |i i^*Mh4 Mi@Lh Lh!tc i €ht| t|@|i |i uL**L?} *i44@G

;Wkdw lv/ zh h{sodlq zk| U U+y,1 Wkh surri ri U+y, U lv ohvv lqwhuhvwlqj dqg fdq eh irxqg lq wkh dsshqgl{1

.

(21)

wi44@ e wi| t@hiL*_ih f Mi @ 4i4Mih Lu UL@*|L? 5U Aihi i t|t

@ _gihi?| UL@*|L? (5U Lu U t@hiL*_ih f t @ 4i4Mih tU |@|c ifj _

( ifj'>

At hit*| t@)t |@| uLh iih) UL@*|L? ? Uc |ihi t @?L|ih UL@*|L? ? U tU |@| |iti |L @hi R@*4Lt| _tL?| W?||i*)c |t hit*| t hi*@|i_

|L |i u@U| |@| |i hi*i@?| t|hL?} UL@*|L?t @i |i 4?44 ?4Mih Lu t@hiL*_iht |@| i?thit tUi?| L|?} TLih

wi44@ e t tiu* uLh ti||?} @? TTih ML?_ L? |i U@t L |@| @?) Lu |i UL@*|L?t ? U@i @| |i tL*|L? Ai _i@ t t4T*i W4@}?ic t|

uLh |i t@!i Lu i T*@?@|L?c |@| |i LMiU|i t |L 4@ 43i |i 4?44

@4L?| Lu U@t L TLttitti_ M) i@U Lu |L _tL?| UL@*|L?t MLt*)c

|t U@??L| Mi *@h}ih |@? DfI t4*@h *L}U @TT*it |L |i U@ti ihi

|i |L UL@*|L?t @hi R@*4Lt| _tL?| ? |i ti?ti Lu wi44@ e W? |t U@tic Liihc |i TTih ML?_ t tU |@| |i UL@*|L?t ?U@i U@t Lt |@|

_L ?L| i Uii_ DfI M) R|LL 4U At 4T*it |@| i? L?i t@hiL*_ih ?

@?) Lu |iti UL@*|L?t t hi4Li_c |i t4 _hLTt |L @ €}hi Mi*L DfI W?

|ih4t Lu WE' UW |t 4T*it |@| |i UL@*|L?t ? U @hi t|hL?}c M| |@|

i? L?i t@hiL*_ih t hi4Li_c |i hi4@??} t@hiL*_iht uLh4 @ i@!

UL@*|L? | |t t i @U|*) @| i @?|i_c MiU@ti | 4T*it |@| |i UL@*|L?t ? U@hi hi*i@?| t|hL?} hi*@|i |L Wc ic U-EW

Ai *|ih@|hi L? |i LT|4@* M?_*?} Lu U@t Lt @?_ L|it t i |i?tic Lh}?@|?} uhL4 |i Lh! Lu BhLtt4@? @?_ O@h| EbHH @?_ O@hht @?_ +@

EbHH Lt| Lu |iti 4L_i*t _ihi |i LT|4@* M?_*?} ? |i UL?|i | Lu |@!iLiht W?t|i@_c i _ihi |i LT|4@*|) Lu L?it@hiL?iL|i ? |i

@Mti?Ui Lu @ TL|i?|@* |@!iLih Oi?Uic Lh 4L_i* t Mi||ih t|i_ |L t|_)

€h4t ? UL?|hit ? U |@!iLiht @hi h@hi W?_ii_c Lh @?@*)tt t UL?tt|i?|

| |i i4ThU@* i_i?Ui Lu w@ Lh|@i| @*Ebbb |@| €?_t t4@** _i@|L?t uhL4 L?it@hiL?iL|i ? @** |i UL?|hit Lu |ih t@4T*i U ?U*_it 4@?) UL?|hit | ?L @U|i 4@h!i|t uLh ULhTLh@|i UL?|hL*

H

(22)

D ?ihtT t|hU|hiG |i ?4Mih @?_ t3i Lu |i t@hiL*_iht

W? |i *@t| tiU|L?c i _tUtti_ |i ThLTih|it Lu |i Mit| U@t L _t|h M|L? uLh @ }i? UL?|hL* t|hU|hi W? |t tiU|L?c i @hi ?|ihit|i_ ? |i i?|hiThi?ih<t UL4T*i|i ThLM*i4 Lu ULLt?} @| _@|i fc |i ti| Lu t@hiL*_ihtc

|i UL?|hL* t|hU|hi @?_ |i U@t L _t|hM|L? Ei^@|L? E2

W? Th?UT*ic ? Lh_ih |L tL*i |i i?|hiThi?ih<t UL4T*i|i ThLM*i4c i ?ii_

|L UL?t_ih iih) TLttM*i ?4Mih Lu t@hiL*_iht @?_c uLh @ }i? ?4Mihc @**

TLttM*i UL?|hL* t|hU|hit 6Lh i@U Lu |iti U@titc i ?ii_ |L tL*i @ ThLM*i4 t4*@h |L |@| ? i^@|L? ESc @__?} |i ?it|Lh<t i@*| UL?t|h@?|t AL t4T*u) |t |i_Lt ThLUi_hic i t|@|i hLTLt|L? W? @__|L? |L t4 T*u)?} |i ti@hU uLh @ tL*|L?c |t ThLTLt|L? ThL_it tL4i ?|ihit|?}

?t}|t

W? hLTLt|L? i t|@h| | @ }i? ?4Mih Lu t@hiL*_ihtG U hi*i

@?| t@hiL*_iht @?_ @?) ?4Mih Lu ?L?hi*i@?| t@hiL*_iht @?_ UL4T|i

|i Mit| UL?|hL* t|hU|hi @?_ U@t L _t|hM|L? hLTLt|L? |@!it

|i ?4Mih Lu hi*i@?| t@hiL*_iht @t }i? @?_ @tt4it |@| t@hiL*_iht

@i i?L} i@*| |L M) |i uh@U|L? Lu U@t L @tt}?i_ |L |i4 @| |i tL*|L? At t tiu* MiU@ti | ti|t @? TTih ML?_ |L |i T@)Lgt |i i?

|hiThi?ih U@? LM|@? | @ }i? ?4Mih Lu hi*i@?| t@hiL*_iht ELMLt*)c

?|hL_U?} i@*| UL?t|h@?|t U@??L| 4ThLi |i @*i Lu |i 4@ 43@|L?

ThL}h@4

t @? **t|h@|L?c tTTLti |@| | |hii t@hiL*_ihtc @?_ UL?t_ih?}

i@*| UL?t|h@?|tc |i i?|hiThi?ih 4@?@}it |L @i @ ???} UL@*|L? | SSI Lu |i U@t Lt 5L*_ ti UL?t_ih tL*?} |i ThLM*i4 @}@? uLh uLh t@hiL*_ihtq Ai @?tih t ?L MiU@tic M) hLTLt|L? c | uLh t@hiL*_ihtc |i ???} UL@*|L? @t @ 4@ 44 U@t L t|@!i Lu SfI ,i? 4Lhi ?|ihit|?}*)c |ihi t ?L ?ii_ |L UL?t_ih L?ihtT t|hU|hit | 4Lhi |@? t@hiL*_iht MiU@tic @t i tL ? hLTLt|L? c @t |i ?4Mih

b

(23)

Lu hi*i@?| t@hiL*_iht t ?Uhi@ti_c iUi?U) t hi_Ui_

`i ?L t|@|i hLTLt|L? L|i |@| h@|ih |@? ThL_?} |i LT|4@*

UL?|hL* t|hU|hic i ThL_i L?i Lu |i L|?} _t|hM|L?t }i?ih@|?} tU

@ UL?|hL* t|hU|hi L| thTht?}*)c |i L?ihtT t|hU|hit |h? L| |L Mi L?it@hiL?iL|i L?ihtT t|hU|hit

hLTLt|L? 5TTLti |i ?4Mih Lu hi*i@?| t@hiL*_iht tUb @?_ |ihi t

@?) ?4Mih Lu ?L?hi*i@?| t@hiL*_iht W? |i LT|4@* L?ihtT t|hU|hi

|i ?L?hi*i@?| t@hiL*_iht hiUii ?i|ih L|it ?Lh U@t Ltc |i U hi*i

@?| t@hiL*_iht hiUii EUc @?_ |i U@t L t|@!i |i ???} UL@*|L?

t bc ihic

Wu U ' c U''  @?_ b' 

Wu U t L__c U'' EUcUc cU @?_ b ' 2 n 2U

Wu U t ii?c U'' EUn cUn c cUn2 c c Un c iih) t@hiL*_ih

@t Un L|it @?_ U@t L i UiT| L?i QL U@? Mi @?)L?iQ L @t 2Un @?_ b ' 2 n 2EUn

W?||i*)c t4@** t@hiL*_iht _iUhi@ti iUi?U) MiU@ti |i) |i?_ |L Mi

?U*_i_ ? |i ???} UL@*|L? M| UL?|hM|i *||*i U@t L |L | Ai Mit|

@) |L _t|hM|i U@t Lt t |i? |L tThi@_ |i4 ii?*) @UhLtt t@hiL*_

ihtc t?Ui |t 4@ 43it |i t3i Lu |i t4@**it| t@hiL*_ih Ai _gihi?Ui Mi|ii? |i L__ @?_ ii? U@tit t _i |L |i |iMhi@!?} h*i OLiihc |i hit*| @?_ |i ?||L? uLh ML| U@tit @hi t4*@h

5L4i UL44i?|t hi*@|?} |L hLTLt|L? @hi ? Lh_ih 6ht|c | t U*i@h

|@| @t |i ?4Mih Lu hi*i@?| t@hiL*_iht ?Uhi@titc iUi?U) t hi_Ui_

At t MiU@ti @t U@t Lt @?_ L|it @hi _t|hM|i_ @4L?} 4Lhi TiLT*ic | t i@tih uLh @ UL@*|L? | t| i?L} L|it @?_ U@t Lt |L uLh4 @?_ Mi i*iU|i_ |L |i ML@h_ At 4@) Mi L?i i T*@?@|L? uLh |i u@U| |@| U*Lti*) i*_ ULhTLh@|L?t |i?_ |L @i t| @ ui t@hiL*_iht

<Wkhuh gr qrw h{lvw frqwuro vwuxfwxuhv zlwk wzr uhohydqw vkduhkroghuv1

2f

(24)

5iUL?_c |i L?ihtT t|hU|hi Lu @ €h4 ** Mi i|ih L?i ? U |ihi t L?i *@h}i t@hiL*_ih Lh L?i ? U |ihi @hi 4@?) i^@* t3i_ t@hi L*_ihtf 54*@h hit*|t U@? Mi uL?_ ? ~iMi* EbbD @?_ h!@h| i| @*

Ebb.

Ai |h_ UL44i?| hi*@|it |L |i L?it@hiL?iL|i _tUttL? Lu |i Thi Lt tiU|L? ) hLTLt|L? 2c i !?L |@|c uLh @ }i? UL?|hL* U*@ttc |ihi t

@ L?it@hiL?iL|i L?ihtT t|hU|hi |@| 4@ 43it iUi?U) OLiihc

|t t ?L| |hi uLh @?) L?it@hiL?iL|i L?ihtT _t|hM|L? iih|i

*ittc |i iUi?U) *Ltt Lu t?} @?) L?it@hiL?iL|i _t|hM|L? ?t|i@_

Lu |i LT|4@* _t|hM|L? }Lit |L 3ihL @t |i ?4Mih Lu hi*i@?| t@hiL*_

iht ?Uhi@tit At t MiU@tic @t i t@ ? |i ThLLu Lu hLTLt|L? 2c @?) L?it@hiL?iL|i L?ihtT _t|hM|L? ThL_Uit @ ???} UL@*|L? | 4Lhi |@? DfI Lu |i U@t L @?_c M) hLTLt|L? c |i U@t L Lu |i

???} UL@*|L? @| |i tL*|L? }i|t U*Ltih |L DfI @t |i ?4Mih Lu hi*i@?|

t@hiL*_iht ?Uhi@tit At hit*| T@h@**i*t |Lti uL?_ uLh |i LT|4@*|) Lu L?it@hiL?iL|i i? |ihi t _tTihti_ L?ihtT OLiihc i @hi ?|ih it|i_ ? U@tit ? U |ihi t @ t4@** ?4Mih Lu t@hiL*_iht W? |iti U@tit

|i iUi?U) *Ltt Lu t?} @?) L?it@hiL?iL|i L?ihtT t|hU|hi UL*_

Mi t}?€U@?|

6?@**)c @t 4i?|L?i_ @MLic hLTLt|L? t tiu* uLh tL*?} |i i?

|hiThi?ih<t UL4T*i|i ThLM*i4 Ei^@|L? E2 `i tL*i |t ThLM*i4 uLh @ T@h|U*@h _ihtL? |iU?L*L}) ? |i uL**L?} i @4T*i

, @4T*i

5TTLti |@| |i _ihtL? |iU?L*L}) t ^@_h@|U E_ '_ 2_2 6h|ih 4Lhic tTTLti uLh t4T*U|) |@| |i i?|hiThi?ih _Lit ?L| hi|@? @?) U@t L Lh L|it +iU@** |@| |i ti| Lu L|t_i ?it|Lht t @?_ i@U L?i @t

@ *ii* Lu i@*| ` 6?@**)c tTTLti |@| |i ?it|4i?| hi^hi_ g .H

43Zkhq zhdowk frqvwudlqwv duh lqfoxghg/ wkh| pljkw suhyhqw wkh hqwuhsuhqhxu iurp hv0 wdeolvklqj dq rzqhuvkls vwuxfwxuh zlwk htxdo vl}hg vkduhkroghuv1 Krzhyhu/ wkh rzqhuvkls vwuxfwxuh vkh fkrrvhv zrxog eh dv forvh dv srvvleoh1

(25)

At *@t| ?i^@*|) }@h@?|iit |@| |i i?|hiThi?ih t @M*i |L h@ti tUi?|

u?_t |L ti| T |i €h4 ii? i? _ihtL? t @t } @t 

`i tL*i |i @MLi i @4T*i uLh tL4i TLttM*i @*it Lu E`c c ` +it*|G W? |t i @4T*ic |i i?|hiThi?ih<t ULUi t }i? M)G

 Wu ` Hc |i Mit| L?ihtT t|hU|hi t L?i ihi t@hiL*_ih  @t UL4T*i|i UL?|hL* Eic 4Lhi |@? DfI Lu |i L|it @?_ @t *@h}i @ U@t L t|@!i @t ti U@? @gLh_ Ai hit| Lu |i U@t L @?_ L|it @hi tL*_

|L L|ih ?it|Lht( Liihc |i ?4Mih Lu ?it|Lht Lh |ih t3i _Lit

?L| 4@||ih

2 Wu `c `2c @?_ ` Mi*L?} |L |i ?|ih@* d.DecHc |i LT|4@* L?ihtT t|hU|hi t L?i ihi i@U L?i Lu |i4 hiUiit  Lu ML| L|it @?_ U@t L

`i UL*_ UL?|?i _L?} |t 4@TT?} uhL4 E`c c ` |L |i LT|4@*

L?ihtT t|hU|hi( Liihc |i |L U@tit @MLi @hi tUi?| |L **t|h@|i

|i 4@? TL?|t

Wu |i i@*|it| ?it|Lh @t i@*|` c |i? €ht| Mit| U@? Mi @Uii_

M) ti**?} |i i?|hi €h4 |L |t t@hiL*_ih OLiihc u €ht| Mit| U@??L| Mi

@Uii_c | _Lit ?L| ?iUitt@h*) 4T*) |@| |i i?|hiThi?ih tL*_ ti** |i

€h4 |L 4Lhi |@? L?i hi*i@?| t@hiL*_ih U|@**)c M) hLTLt|L? c i

!?L |@| |i Mit| |i i?|hiThi?ih U@? _L | |hii ELh 4Lhi hi*i@?|

t@hiL*_iht t |@| |i ???} UL@*|L? @i 2 Lu |i U@t L Oi?Uic @t

*L?} @t |ihi t L?i ?it|Lh | i?L} i@*| |L M) 4Lhi |@? 2 Lu |i U@t Lc |i L?ihtT t|hU|hi ihi |t ?it|Lh @t t|hU|*) 4Lhi |@?

DfI Lu |i L|it t Mi||ih |@? @?) L|ih L?ihtT t|hU|hi

AL U@*U*@|i |i ?iUitt@h) i@*| *ii*c ?L|Ui |@| |i }i? _ihtL?

|iU?L*L}) 4T*it @? i^*Mh4 _ihtL? *ii* Lu _W ' %c ihi %t |i U@t L Lu |i ???} UL@*|L? Ai _L4?@?| t@hiL*_ih i*iU|t ihti*u |L

22

(26)

|i ML@h_ @?_ hiUiit |i i?|hi Th@|i Mi?i€| Oi?Uic |i @*i Lu M)?}

4Lhi |@? DfI Lu |i L|it @?_ S U@t L uLh |t t@hiL*_ih tc qE_W n_W _W2

2 ' 

2ES2n 

At i^@|L? 4T*it |@| |i i@*| ?ii_i_ |L M) @| *i@t| |L |h_t Lu |i U@t L t H

`i? ?L?i Lu |i TL|i?|@* t@hiL*_iht @t tUi?| i@*| |L M) @|

*i@t| 2 Lu |i U@t Lc |i? @? L?ihtT t|hU|hi | L?i hi*i@?| t@hi L*_ih t ?L| LT|4@* ) hLTLt|L? c i !?L |@| |i 4Lhi hi*i@?|

t@hiL*_iht |ihi @hic |i *@h}ih |i iUi?U) *Ltt Oi?Uic |i ?@|h@* t|iT t |L UL?t_ih L?ihtT t|hU|hit | |hii hi*i@?| t@hiL*_iht *tLc M) hLTLt|L? c i !?L |@| |i Mit| L?ihtT t|hU|hi | |hii hi*i@?|

t@hiL*_iht t L?i ihi ML| L|it @?_ U@t Lt @hi _t|hM|i_ i^@**)

@4L?} t@hiL*_ihtc |@| t 'U' Ecc `| |t L?ihtT t|hU|hic

@?) UL@*|L? Lu 2 t@hiL*_iht U@? MiUL4i |i ???} ML@h_ Oi?Ui @ t@hi L*_ih t ? |i ML@h_ | ThLM@M*|) 2 @?_ i? ti t ? |i ML@h_ ti hiUiit @*u |i Th@|i Mi?i€|t ** TL|i?|@* ???} ML@h_t @i U@t L Lu 2 4T*)?} |@| _W '  2 '  | _@|i f i@U Lu |i u|hi t@hiL*_iht T@)t uLh |i U@t L @?_ Th@|i Mi?i€|t ti i TiU|t |L hiUiiG



E_W n2



2E_W _W2

2 ' .

De At UL?€h4t T@h| 2 Lu |i hit*| @MLi

iuLhi *i@?} |t tiU|L?c i 4@!i @ ui UL44i?|t 6ht|c i?` t ?

|i ?|ih@* dHc |i LT|4@* L?ihtT t|hU|hi @t L?i hi*i@?| @?_ u@h*)

*@h}i t@hiL*_ih @?_ ETL|i?|@**) 4@?) ?L?hi*i@?| 4?Lh|) t@hiL*_iht L|i |@| |t L?ihtT t|hU|hi t ?L| L?i Lu |Lti ThitUhMi_ ? hLTLt

|L? At t MiU@ti i@*| UL?t|h@?|t uLhUi |i i?|hiThi?ih |L _i@|i uhL4 @? L?ihtT t|hU|hi ihi |ihi t @ t@hiL*_ih | ffI Lu ML|

U@t L @?_ L|it A@| tc i? i@*| UL?t|h@?|t @hi ?|hL_Ui_c |i

2

(27)

hit*|?} L?ihtT t|hU|hit @hi ?L| ?iUitt@h*) |Lti ThitUhMi_ ? hLTL t|L? iih|i*ittc |t ThLTLt|L? }it tL4i TTih ML?_t U @hi i*Tu* ? hi@U?} @ tL*|L?

5iUL?_c |i i?|hiThi?ih ULLtit @? L?ihtT t|hU|hi | |hii hi*i

@?| t@hiL*_ihtc ii? i? @?} L?i hi*i@?| t@hiL*_ih @?_ 4@?) ?L?

hi*i@?| t@hiL*_iht t ui@tM*i A@| tc Lh @h}4i?| t ?L| E|i |h@*

L?i |@|c i? i@*| UL?t|h@?|t 4@!i @?} L?i hi*i@?| t@hiL*_ih ?

@Ui@M*ic |i i?|hiThi?ih tL*_ @__ 4Lhi hi*i@?| t@hiL*_iht W?t|i@_c

|i i?|hiThi?ih t|Uit |L |hii t@hiL*_iht uLh iUi?U) hi@tL?t ) _t

|hM|?} TLih @4L?} |hii t@hiL*_iht ? tU @ @) |@| ?L ?__@*

t@hiL*_ih @t @MtL*|i TLihc |i i?|hiThi?ih uLhUit t@hiL*_iht |L uLh4

@ UL@*|L? |L LM|@? UL?|hL*

6?@**)c @? L?ihtT t|hU|hi | i^@*t3i_ ?it|Lht t ?L| @ UL?ti

^i?Ui Lu i^@* i@*| E@U|@**)c ? Lh i @4T*i i t| hi^hi |@| i@U t@hiL*_ih<t i@*| Mi ? |i ?|ih@* d.DecH +@|ihc | t |i Mit| @) |L

@L_ @?} t4@** t@hiL*_iht L UL?|hM|i *||*i U@t L |L |i ???}

UL@*|L?

S #tUttL?

5@hiL*_iht @i @UUitt |L 4iU@?t4t |@| hi_Ui tL4i Lu |i UL?U|t i @i @?@*)3i_ ? |t T@Tih 6Lh ?t|@?Uic |i ULhTLh@|i U@h|ih ELh @ t@hiL*_ih @}hii4i?| 4@) ThL_i 4?Lh|) t@hiL*_iht | i|L h}|t L?

Uih|@? 4TLh|@?| TL*U) ttitc | 4@) t|@|i |@| |i ML@h_ 4t| Mi i*iU|i_

t?} @ U4*@|i L|?} h*i }@h@?|ii?} @ T*@Ui L? |i ML@h_ uLh 4?Lh|) L?ihtc Lh | 4@) i T*U|*) ?U*_i |i UL4TLt|L? Lu |i ML@h_

5U ?|@|it 4ThLi iUi?U) ? Lh 4L_i* W?_ii_ €ht| Mit| U@? Mi LM|@? M) UL?|h@U|@**) hi^h?} |@| @** t@hiL*_iht @i @ T*@Ui ? |i ML@h_ W? tU UhU4t|@?Uitc Lh @?@*)tt L*_ t|** Mi @*_ uLh @| *i@t|

44Lw fdq eh vkrzq wkdw wklv lv wkh fdvh zkhq Z4 lv lq wkh lqwhuydo ^5 l s

5 5l>464;, +wklv lqwhuydo lv qrw hpsw| ehfdxvh l ?4:4;,/ dqg Z4/ Z5/ dqg Z6 ehorqj wr ^4:87>464;,1

2e

(28)

|hii hi@tL?t

6ht|c uhL4 |i 4@?) U@tit MhL}| |L ULh| @?_ |i 4@?) _tUttL?t ? ULhTLh@|i *@ MLL!tc i UL?U*_i |@| ?L| @** UL?U|t Mi|ii? t@hiL*_iht

? U*Lti*) i*_ ULhTLh@|L?t @hi tL*i_ W? |i @Mti?Ui Lu ^@?||@|i _@|@ L?

*@ U@titc i Mhi) Thiti?| |i wi) ihtt @h!@* 5@*it LhTLh@|L? U@ti

@h!@* 5@*it LhTLh@|L? @t uL?_i_ ? bSf M) ki??i| ` wi) Ai ULhTLh@|L? @t ?L*i_ ? |i t@*i Lu i*iU|hL?U i^T4i?| 5L4i )i@ht

@u|ih |i uL?_@|L?c |i ULhTLh@|L? L?ihtT t|hU|hi UL?tt|i_ Lu |hii t@hiL*_ihtG wi) | efI Lu |i t|LU!c VU|Lh Bt| | @?L|ih efIc

@?_ +LMih| @!@* | |i hi4@??} 2fI E|ihi ihi ?L _i@|L?t uhL4 L?it@hiL?iL|i ** |i t@hiL*_iht Lh!i_ uLh |i ULhTLh@|L? @?_ ihi

?L*i_ ? |i 4@?@}i4i?| Lu |

W? bHfc Bt| @?_ @!@* L|i_ |L €hi wi) @t @? i4T*L)ih Lu |i ULhTLh@

|L? @?_ igiU|i*) i U*_i_ 4 uhL4 4@?@}i4i?| wi)c Liihc !iT| t t@hit 5LL? @u|ihc Bt| @t Lgihi_ |i LTTLh|?|) |L Mi @ t@*it hiThiti?

|@|i uLh TT*i L4T|iht L i T*U|*) @TThL@Ui_ @h!@* MiU@ti Lu |t Mt?itt hiT|@|L? OLiihc ?t|i@_ Lu Lgih?} |i LTTLh|?|) |L @h!@*c Bt| @?_ @!@* uLh4i_ |ih L? ULhTLh@|L?c B% @h!i|?}c |L hiThiti?|

TT*i *i@h*)c M) _L?} tLc Bt| @?_ @!@* _ih|i_ hitLhUit uhL4 @h!@*

M) t|i@*?} @ ThLiU| |@| Mi*L?}i_ |L |i ULhTLh@|L?

u|ih it|@M*t?} B% @h!i|?}c Bt| @?_ @!@* _ih|i_ @__|L?@* hi tLhUit uhL4 @h!@*G 5iih@* B% t@*itTiLT*i ihi L? @h!@* T@)hL**c i Ti?tit uLh Mt?itt |hTt hi*@|i_ |L B% ihi U@h}i_ |L @h!@*c @?_ B%

hi?|i_ LUi tT@Ui uhL4 @h!@* @| @ ThUi t}?€U@?|*) Mi*L 4@h!i| @*i Ai wi) ihtt @h!@* 5@*it LhTLh@|L?U@ti €|t ?Ui*) ?|L Lh 4L_i*c t?Ui | t @ ULhTLh@|L? | |hii t}?€U@?| L?iht t Lh 4L_i* Thi_U|tc @ UL@*|L? ti3it UL?|hL* @?_ @ UL?U| Mi|ii? |t UL@*|L? @?_ |i hi4@??}

4?Lh|) t@hiL*_ih @htit 6h|ih4Lhic |i UL@*|L? |@| U@T|hit UL?|hL*

@t |i 4?44 U@t L ThLTih|) @t Thi_U|i_ M) hLTLt|L?  6?@**)c

|i UL?|hL**?} UL@*|L? _ih|t t}?€U@?| @4L?| Lu hitLhUit uhL4 |i €h4 2D

(29)

? @ 4Lhi }i?ih@* *ii*c <i@* EbH.c ? t _tUttL? Lu t@hiL*_ih _tT|it ? U*Lti*) i*_ ULhTLh@|L?tc LMtihit RAi 4Lt| uhi^i?|*) LUUhh?}

UL?U| Lu ?|ihit| t Mi|ii? @U|i t@hiL*_ihtc i t@hiL*_ihLUiht Lh i4T*L)iitc @?_ t@hiL*_iht L @hi ?L| @U|i ? |i Mt?itt 6h|ih4Lhic i i T*U|*) @U!?L*i_}it |i hL*i Lu @ TLih UL?|it| |? |i U*Lti*) i*_

ULhTLh@|L? @?_ |i _U*|it ? i?uLhU?} UL?|h@U|t @4L?} t@hiL*_ihtG ROL*_iht Lu @ 4@Lh|) Lu |i L|?} t@hit ? @ ULhTLh@|L?c |hL}

|ih @M*|) |L i*iU| @?_ UL?|hL* @ 4@Lh|) Lu |i _hiU|Lht @?_ |L _i|ih4?i |i L|UL4i Lu t@hiL*_iht< L|it L? L|ih 4@||ihtc

@i |hi4i?_Lt TLih |L Mi?i€| |i4ti*it @| |i i Ti?ti Lu 4?Lh|) t@hiL*_ihtAh@_|L?@**)c 4ihU@? ULh|t @i Mii?

hi*U|@?| |L ?|ihuihi ? |i ?|ih?@* @g@ht Lu ULhTLh@|L?tc ii?

i? 4?Lh|) t@hiL*_iht U*@4 |i) @hi Mi?} t^ii3i_ L| Lh L|ihti LTThitti_ 6h|ih4Lhic 4@?) ULh|t @TT@hi?|*) uii*

|@| |ihi t @ *i}|4@|i tTihi ? U UL?|hL**?} t@hiL*_iht U@? @U| ? |ih L? ?|ihit| ii? u |i 4?Lh|) tgiht

5iUL?_c ii? u |ihi t @ UL?|h@U| |@| }it iih) t@hiL*_ih @ ti@| L? |i ML@h_ Lh i|L TLih Lih @** _iUtL?tc @ UL@*|L? Lu t@hiL*_iht L*_ @i

?Ui?|it |L ?@*_@|i tU @ UL?|h@U| ?i @) |L @UUL4T*t |t t |L @h}i

? ULh| |@| |i UL?|h@U| @*|iht |i t|@||Lh) tUi4i E|i t)t|i4 tTiU€i_

M) *@ @UULh_?} |L U ULhTLh@|L?t tL*_ Mi }Lih?i_ *|L} N5 ULh|t @hi ?L ih) i M*i ? |i |)Ti Lu UL?|h@U|t |@| |i) TL*_c |t @t

?L| @*@)t Mii? |i U@ti W? u@U| @t O@4*|L? EbbS T|t |G R@tit tU @t

|itic i|ih Lh ?L| ULhhiU|*) _iU_i_c **t|h@|i |i Tih@ti 4T@U| Lu |i t|@||Lh) tUi4i L? _U@* |L}| @?_ |i _@?}ih Lu @tt4?} |@| t4T*) MiU@ti @** T@h|it ? ?|ihit| @}hii |L @ @h@|L? ? |i t|@||Lh) tUi4ic

|i @h@|L? t @*_ ET@}i bDc i4T@tt @__i_ W? Lh 4L_i*c ii? @ t4@** ThLM@M*|) |@| |i @}hii4i?| @4L?} t@hiL*_iht ** Mi ?@*_@|i_

@?_ |@| |i ML@h_ ** Mi _i|ih4?i_ M) @? i*iU|L? t i?L} |L hi?_ih Lh

@?@*)tt @*_

6?@**)c ii? u | t ui@tM*i |L ThL|iU| 4?Lh|) t@hiL*_iht |hL} UL?

|h@U|t @?_ |iti UL?|h@U|t @hi i?uLhUi@M*i ? ULh|tc }?} UL?|hL* |L @** t@hi 2S

(30)

L*_iht U@? Mi ULt|*) uLh hi@tL?t i _L ?L| 4L_i* ? |t T@Tih W| tii4t |@|c

? }i?ih@*c |ihi t @ |h@_i Lg Mi|ii? 4@?@}ih@* i M*|) @?_ |i _i}hii Lu ThL|iU|L? @gLh_i_ |L 4?Lh|) t@hiL*_iht Wu |i ULhTLh@|i U@h|ih ELh t@hiL*_ih @}hii4i?| ThL_it 4?Lh|) t@hiL*_iht | ui ThL|iU|L?tc

|i) @hi *?ih@M*i |L |i !?_ Lu ?iUi?| i T*L|@|L? |@| i @i Th ti_ ? |i Thiti?| @?@*)tt ? |i L|ih @?_c u 4?Lh|) t@hiL*_iht @hi

@gLh_i_ |LL t|hL?} @ ThL|iU|L?c | 4@) t}?€U@?|*) hit|hU| |i UL?|hL**?}

UL@*|L?<t @M*|) |L }Lih? |i €h4c @?_ | 4@) @*tL h@ti |i ThLM@M*|) Lu ULt|*) _i@_*LU!t @4L?} |i L?iht W?_ii_c |t |h@_iLg t i |i?ti*) _tUtti_ ? |i *i}@* *|ih@|hi L? U*Lti*) i*_ ULhTLh@|L?t 6Lh ?t|@?Uic ,@t|ihMhLL! @?_ 6tUi* Ebb ?L|Ui |@|G R#h@u|iht Lu |i Lh}@?3?} _LU 4i?|t Lu @ U*Lti*) i*_ ULhTLh@|L? U@??L| @L_ @ |h@_iLg ? |i L?i @?_c

|i) 4t| ThL_i tL4i ThL|iU|L? |L 4?Lh|) ?it|Lht |L i?thi |@| |i) hiUii @? @_i^@|i hi|h? L? |i 4?Lh|) t@hiL*_ih<t ?it|4i?| u |i i?|hi tUUii_t ? |i L|ih @?_c |i) U@??L| }i |i 4?Lh|) |LL 4@?) h}|tc uLh |i 4?Lh|) 4}| i ihUti |ih h}|t ? LTTLh|?t|U u@tL? |L _ih| hi|h?t2

. L?U*tL?t

`i @i @?@*)3i_ @ 4L_i* Lu @ U*Lti*) i*_ ULhTLh@|L? | ?L?|h@?tuih@M*i t@hit @?_ TL|i?|@**) 4Lhi |@? L?i t}?€U@?| t@hiL*_ih W? |i 4L_i*

|i L?ihtT t|hU|hi _i|ih4?it U }hLT Lu L?iht ti3it UL?|hL* Lih

|i €h4 `i @i @h}i_ |@| | 4@) Mi ? |i ?|@* L?ih<t ?|ihit| |L _*|i ih L? TLih M) _t|hM|?} L|it @4L?} tiih@* *@h}i t@hiL*_iht At _*|L? Lu TLih UL44|t |i ?|@* L?ih |L uLh4 @ UL@*|L? |L LM|@?

UL?|hL*c @?_ |t Uhi@|it @ UL?|hL**?} ML_) | 4Lhi U@t Lc @?_ i?Ui L?i

|@| _ih|t *itt W? L|ih Lh_tc i ThLTLti _*|L? Lu TLih @t @ 4iU@?t4

|L UL44| |L *L *ii*t Lu _ihtL?

45Wklv wudgh0r lv dqdo|}hg lq rxu uhodwhg sdshu +Ehqqhgvhq dqg Zroihq}rq +4<<<,,1

2.

(31)

Aihi @hi t|** 4@?) ?|ihit|?} |LTUt @ML| U*Lti*) i*_ ULhTLh@|L?t |@|

i *i@i uLh u|hi hiti@hU t t}}it|i_ ? |i *@t| tiU|L?c @4L?} |i4 t

|i @?@*)tt Lu |i 4iU@?t4t Lu ULhTLh@|i }Lih?@?Ui |@| t@hiL*_iht U@?

_it}? |L 4|}@|i |i ?iUi?Uit hi*@|i_ |L |i i U*tL? Lu t@hiL*_iht uhL4 |i UL?|hL**?} UL@*|L? E@| i |ih4i_ |i UL@*|L? uLh4@|L? igiU|

2H

(32)

TTi?_

Surri ri Ohppd 5

Ohw F eh wkh zlqqlqj frdolwlrq1 Dw gdwh 5/ phpehuv ri F fkrrvh wkh ohyho ri glyhuvlrq1 Wkh sd|r wr hdfk vkduhkroghu l 5 F lv jlyhq e|=

f+4 g, . Sf

MfE+g,= +:,

Hdfk erdug phpehu uhfhlyhv d iudfwlrq f ri wkh yhuldeoh uhyhqxh +4 g,1 Lq dgglwlrq/ erdug phpehuv vsolw wkh sulydwh ehqhwv E+g, lq sursruwlrq wr wkhlu fdvk rzv1 Wkh uvw rughu frqglwlrq ri hdfk phpehu ri wkh zlqqlqj frdolwlrq lv wkh vdph/

dqg khqfh wkh| xqdqlprxvo| djuhh rq wkh glyhuvlrq ohyho g+F, ghqhg e|=

E+g+F,, @[

M

f= +;,

Wkh sd|r wr dq| vkduhkroghu l zkhq frdolwlrq F zlqv lv jlyhq e|=

X+F, @

+f+4 g+F,, .S S

MSE+g+F,, li l 5 F/

f+4 g+F,, rwkhuzlvh1 +<,

Sduw +l,= wr vkrz wkdw li vkduhkroghu l 5 F dqg l 95 G wkhq X+F, X+G,1 Qrwh wkdw

X+F, f+4 g+G,, .Sf

MfE+g+G,, f+4 g+G,, @ X+G,>

zkhuh wkh uvw lqhtxdolw| iroorzv ehfdxvh g+F, pd{lpl}hv wkh h{suhvvlrq lq htxd0 wlrq +:, iru dq| phpehu ri F1 Pruhryhu/ li fA 3/ wkh deryh lqhtxdolw| lv vwulfw1 Sduw +ll,= wr vkrz wkdw li vkduhkroghu l 5 F/ l 5 G/ dqg S

M(f A S

Mf wkhq X+F, X+G,1

Qrwh wkdw

X+F, f+4 g+G,, .Sf

MfE+g+G,,

f+4 g+G,, .Sf

M(fE+g+G,, @ X+G,>

zkhuh wkh uvw lqhtxdolw| iroorzv ehfdxvh g+F, pd{lpl}hv wkh h{suhvvlrq lq htxd0 wlrq +:, iru dq| phpehu ri F/ dqg wkh vhfrqg lqhtxdolw| iroorzv iurp S

M(f A SMf1 Pruhryhu/ li f A 3/ wkh lqhtxdolw| lv vwulfw1 Surri ri Ohppd 6

Sduw +l,= wr vkrz wkdw/ iru dq| yrwlqj glvwulexwlrq y/ F 5 V+y, li dqg rqo| li FS95 V+y,1

46fl A 3 lpsolhvS

l5Gfl ? 4 zklfk/ lq wxuq lpsolhv wkdw E+g+G,, A 31 Khqfh/ wkh vhfrqg lqhtxdolw| lv vwulfw1

2b

(33)

Wdnh dq| y/ dqg vxssrvh wkdw F 5 V+y,1 Wkhq hlwkhu d, S

My A 83( ru e, S

My @ 83( dqg wkh hqwuhsuhqhxu ehorqjv wr F1 Lq fdvh d,/ FS 95 V+y, eh0 fdxvh S

MSy ? 83(1 Lq fdvh e, FS 95 V+y, ehfdxvh S

MSy @ 83( dqg wkh hqwuhsuhqhxu lv qrw d phpehu ri FS +kh ehorqjv wr F,1 Wkh surri ri wkh rwkhu gluhfwlrq lv vlplodu1

Sduw +ll,= wr vkrz wkdw/ iru dq| yrwlqj glvwulexwlrq y/ li F 5 V+y, dqg G 5 V+y,/

wkhq F _ G 9@ >1

Wdnh dq| y/ dqg vxssrvh +wrzdugv d frqwudglfwlrq, wkdw F 5 V+y,/ G 5 V+y, dqg F _ G @ >1 E| ghqlwlrq ri V+y,/ S

My 83(/ S

M(y 83(/ dqg dw ohdvw rqh ri wkhvh lqhtxdolwlhv lv vwulfw ehfdxvh wkh hqwuhsuhqhxu lv dw prvw lq rqh ri wkh wzr frdolwlrqv1 Exw/S

MUy S

My.S

M(y A 433/ zkhuh wkh uvw lqhtxdolw|

iroorzv iurp wkh idfw wkdw F dqg G duh glvmrlqw1 Frqwudglfwlrq1 Surri ri Sursrvlwlrq 4

Wdnh dq| rzqhuvkls vwuxfwxuh f/ dqg y1 Zh glylgh wkh surri lq wkuhh vwhsv1e Vwhs 4= Zhdn erdugv duh qhyhu vxssruwhg lq htxloleulxp1

Vxssrvh +wrzdugv d frqwudglfwlrq, wkdw wkh zlqqlqj frdolwlrq F lv zhdn1D Frqvlghu wkh iroorzlqj ghyldwlrq= doo wkh phpehuv ri wkh frdolwlrq FS yrwh iru wkh frdolwlrq FS dw gdwh 41S Vlqfh F lv zhdn/ FS lv vwurqj +e| Ohppd 6+l,,/ dqg khqfh/ dv d uhvxow ri wkh ghyldwlrq/ FS lv hohfwhg1 Exw/ e| Ohppd 5+l,/ iru dq| l 5 FS/ X+FS, A X+F,1 Wkxv/ hyhu| phpehu ri FS lv ehwwhu r/ dqg dv d uhvxow frdolwlrq

FS ghyldwhv1 Frqwudglfwlrq1

Vwhs 5= Vwurqj erdugv zlwk pruh fdvk rz wkdw wkh plqlpxp dprqj doo vwurqj frdolwlrqv duh qhyhu vxssruwhg lq htxloleulxp1

Vxssrvh wrzdugv d frqwudglfwlrq wkdw wkh zlqqlqj erdug F lv vwurqj/ dqg wkdw wkhuh lv dqrwkhu vwurqj frdolwlrq G vxfk wkdw S

M(f ?S

Mf1 Frqvlghu wkh iroorzlqj ghyldwlrq= doo wkh phpehuv ri G yrwh iru frdolwlrq G dw gdwh 41. Vlqfh G lv vwurqj/

dv d uhvxow ri wkh ghyldwlrq/ frdolwlrq G lv hohfwhg1 Qrwh wkdw/ e| Ohppd 5+l,/ iru dq|

l 5 G dqg l 95 F/ X+G, A X+F,1 Dqg/ ehfdxvhS

M(f?S

Mf/ e| Ohppd 5+ll,/

iru dq| l 5 G dqg l 5 F/ X+G, A X+F,1 Wkxv/ hyhu| phpehu ri G lv ehwwhu r/

dqg dv d uhvxow frdolwlrq G ghyldwhv1 Frqwudglfwlrq1 Vwhs 6= Wkhuh lv dw ohdvw rqh htxloleulxp lq zklfk wkh vwurqj frdolwlrq zlwk wkh plqlpxp fdvk rz dprqj doo vwurqj frdolwlrqv lv vxssruwhg dv wkh zlqqlqj erdug1 Wkh surri lv e| frqvwuxfwlrq1 Ohw F eh wkh vwurqj frdolwlrq wkdw plqlpl}hv wkh vxp ri fdvk rzv dprqj doo vwurqj frdolwlrqv1 Frqvlghu wkh vlwxdwlrq lq zklfk doo

47Iru wklv surri dqg wkh iroorzlqj surriv zh gr qrw frqvlghu vkduhkroghuv zlwk 3 fdvk rz dqg srvlwlyh yrwhv1 Lw fdq eh vkrzq wkdw lw lv qhyhu rswlpdo wr kdyh vxfk d vkduhkroghu1

48Lq wklv surri zh uhihu wr frdolwlrqv dv ehlqj zhdn ru vwurqj1 Wkhvh frqfhswv duh uhodwlyh wr wkh yrwlqj glvwulexwlrq y1

49Lw lv srvvleoh wkdw/ dw wkh sursrvhg htxloleulxp/ vrph ri wkh phpehuv ri Ff duh douhdg|

yrwlqj iru frdolwlrq Ff vr/ lq idfw/ wkh| gr qrw ghyldwh1 Krzhyhu/ lw lv lpsrvvleoh wkdw doo wkh phpehuv ri Ff duh yrwlqj iru Ff dw wkh sursrvhg htxloleulxp/ ehfdxvh li wklv zdv wkh fdvh/ wkh zlqqlqj frdolwlrq zrxog eh Ffdqg qrw F1 Wr vlpsoli| h{srvlwlrq/ zh vd| wkdw wkh _phpehuv ri Ff ghyldwh/% exw lw vkrxog eh xqghuvwrrg wkdw rqo| wkrvh zkr duh qrw douhdg|

yrwlqj iru Ff ghyldwh1

4:D vlplodu frpphqw wr wkdw lq irrwqrwh +49, dssolhv khuh1

f

Referencer

RELATEREDE DOKUMENTER

iurp wkh kd}dug hvwlpdwlrq1 Dssduhqwo|/ wklv h{foxvlrq uhvwulfwlrq uhvxowv lq zhdnhu hvwlpdwlrq uhvxowv ri wkh prwlydwlrq hhfw1 Rqh uhdvrq iru wklv frxog eh wkdw 4, hqwlwohphqw

Wr frqfoxgh/ zh kdyh wzr glvwlqfw fdvhv1 Zkhq q q W / zkdw kdsshqv zkhq wkh uhodwlyh qxpehu ri vnloohg zrunhuv lqfuhdvhv lv wkdw/ dowkrxjk wkh fkdqfh ri jhwwlqj d mre lq wkh

R esultatet synes herefter at m åtte blive, at som m etider er meddelelse til den prim æ re transporthaver tilstrækkelig sikringsakt og som m etider ikke. Allerede

D et maa derfor gøres til G enstand for en særlig Undersøgelse, hvad der indbefattes under Begrebet fast Ejendom i T. frem, hvis en G enstand er stjaalet og

En saadan A d gan g til gennem Oplysninger at medvirke til Kendelsens Tilblivelse har rodfæstet Hjemmel i dansk Retsbevidsthed. G anske vist er

&#34;Laveste&#34; angiver den laveste tilladte energiklasse, som følge af udfasning via ecodesign mindstekrav til energieffektivitet.. &#34;År&#34; er det årstal, hvor reglerne

At jeg føler mig lykkelig, behøver jeg ikke at skrive Dig til, thi Du kjender mig for godt til, at Du ikke skulde vide, at jeg ikke vilde indgaae nogen saadan Forbindelse, uden naar

SDVWH[SHULHQFHV$GGLWLRQDOO\WKHFDVHVWXGLHVVKRZWKDWLQRUJDQL]DWLRQDOVHWWLQJV WKHUH DUH PXOWLSOH FRPPLWPHQWV WR PXOWLSOH LGHQWLWLHV DQG WKDW