Early Initiation of Highly Active Antiretroviral Therapies for Aids: Dynamic choice with Endogenous and Exogenous Learning
Texte intégral
(2) CIRANO Le CIRANO est un organisme sans but lucratif constitué en vertu de la Loi des compagnies du Québec. Le financement de son infrastructure et de ses activités de recherche provient des cotisations de ses organisations-membres, d’une subvention d’infrastructure du Ministère du Développement économique et régional et de la Recherche, de même que des subventions et mandats obtenus par ses équipes de recherche. CIRANO is a private non-profit organization incorporated under the Québec Companies Act. Its infrastructure and research activities are funded through fees paid by member organizations, an infrastructure grant from the Ministère du Développement économique et régional et de la Recherche, and grants and research mandates obtained by its research teams. Les organisations-partenaires / The Partner Organizations PARTENAIRE MAJEUR . Ministère du Développement économique, de l’Innovation et de l’Exportation PARTENAIRES . Alcan inc. . Banque du Canada . Banque Laurentienne du Canada . Banque Nationale du Canada . Banque Royale du Canada . Bell Canada . BMO Groupe financier . Bombardier . Bourse de Montréal . Caisse de dépôt et placement du Québec . Fédération des caisses Desjardins du Québec . GazMétro . Hydro-Québec . Industrie Canada . Ministère des Finances du Québec . Pratt & Whitney Canada . Raymond Chabot Grant Thornton . Ville de Montréal . École Polytechnique de Montréal . HEC Montréal . Université Concordia . Université de Montréal . Université du Québec . Université du Québec à Montréal . Université Laval . Université McGill . Université de Sherbrooke ASSOCIÉ À : . Institut de Finance Mathématique de Montréal (IFM2) . Laboratoires universitaires Bell Canada . Réseau de calcul et de modélisation mathématique [RCM2] . Réseau de centres d’excellence MITACS (Les mathématiques des technologies de l’information et des systèmes complexes) Les cahiers de la série scientifique (CS) visent à rendre accessibles des résultats de recherche effectuée au CIRANO afin de susciter échanges et commentaires. Ces cahiers sont écrits dans le style des publications scientifiques. Les idées et les opinions émises sont sous l’unique responsabilité des auteurs et ne représentent pas nécessairement les positions du CIRANO ou de ses partenaires. This paper presents research carried out at CIRANO and aims at encouraging discussion and comment. The observations and viewpoints expressed are the sole responsibility of the authors. They do not necessarily represent positions of CIRANO or its partners.. ISSN 1198-8177.
(3) Early Initiation of Highly Active Antiretroviral Therapies for Aids: Dynamic Choice with Endogenous and * Exogenous Learning Pierre Lasserre†, Jean-Paul Moatti‡, Antoine Soubeyran§ Résumé / Abstract Le bien-fondé d’administrer précocement des traitements antirétroviraux à haute activité (HAART) aux personnes infectées par le VIH reste objet de débats dans le monde, car leurs bienfaits à court terme peuvent compromettre les traitements futurs si se développent des souches résistantes du virus. Par ailleurs retarder le recours aux HAART comporte un coût d’opportunité thérapeutique si la santé du patient se dégrade au point qu’il ne peut plus bénéficier par la suite des traitements encore en cours de développement. Nous formulons un modèle à deux périodes où l’adoption du traitement de première période est irréversible et engage le futur, alors que des informations et connaissances nouvelles, exogènes et endogènes, déterminent les conditions entourant la décision thérapeutique de deuxième période. Paradoxalement, sous des conditions reflétant bien les enjeux du recours aux HAART, il s’avère que l’effet résistance éventuel a d’autant moins de chance d’importer pour la décision optimale, que sa gravité est élevée. Mots clés : décisions thérapeutiques, incertitude, information, irréversibilité, traitement, apprentissage endogène, apprentissage exogène Criteria for initiation of highly active antiretroviral treatments (HAART) in HIV-infected patients remain a matter of debate world-wide because short-term benefits have to be balanced with costs of these therapies, and restrictions placed on future treatment options if resistant viral strains develop. On the other hand, postponing the introduction of HAART may involve a therapeutic opportunity cost if a patient’s health is allowed to deteriorate to such an extent of becoming unable to benefit from new treatments currently under development when they become available. We introduce a two period model where period one treatment adoption is an irreversible act with future, but uncertain, consequences. New information, both endogenous and exogenous, arises over time and shapes the conditions surrounding the second period therapeutic decision. A surprising result is that, under conditions that appear close to those surrounding the HAART debate, the magnitude of the feared resistance effect has no effect on leaves the optimal treatment decision as far as it is high enough. Keywords: therapeutic decisions, uncertainty, information, irreversibility, treatment, endogenous learning, exogenous learning Codes JEL : I18, C61 *. Financial support from the FQRSC funds, CHRS, IFM2 and the CNRS is gratefully acknowledged. We thank Stéphane Méchoulan and the participants to the 3rd Canadian Health Study Group Conference. We also thank two anonymous referees; one of them gave us comments too helpful and insightful to be given credit properly within the paper. Forthcoming, Journal of Health Economics. † Département des sciences économiques, Université du Québec à Montréal, CIRANO, and GREQAM. ‡. Faculté d’économie et gestion, Université de la Méditerranée, GREQAM, and INSERM Research Unit 379. Département des sciences économiques, Université de la Méditerranée, and GREQAM, Route des Milles, 13290 Les Milles, France, tel. : 33 (0) 4 42 93 59 80, e-mail: soubey@univ-aix.fr §.
(4) YA|iNaW|NA #h?} |i *@t| tii? )i@htc |i U*?U@* U@hi Lu OWV?uiU|i_ TiLT*i @t Mii? tM t|@?|@**) ?i?Ui_ M) |i ?|hL_U|L? Lu |i O}*) U|i ?|hi|hLh@* Ahi@|4i?| EO+A At |hi@|4i?| UL4M?it tiih@* |ih@Tit @ttLU@|?} ?i OWVtTiUU ThL |i@ti ?M|Lht EWtc @?_c 4Lhi hiUi?|*)c ?L? ?U*iLt_i hiihti |h@?tUhT|@ti ?M|Lht E+AWtc | ThiLt*) i t|?} @?|hi|hLh@* _h}tc |i U*iLt_i +iihti Ah@? tUhT|@ti W?M|Lht E+AW 5Lh||ih4 t|_it EOL}} i| @*c bbH@( hT) i| @*c 2ff @i U*i@h*) ThLi_ O+A |ih@Tit |L Mi igiU|i ? _iUhi@t?} h@* hiT*U@|L? @?_ hi_U?} 4LhM_|) @?_ 4Lh|@*|) @4L?} OWV?uiU|i_ T@|i?|t OLiihc 4@Lh ?Uih |@?|it hi4@? @ML| |i LT|4@* Uh|ih@ uLh |ih@T) ?|@|L?c @t i** @t |i _Lt@}it @?_ tTiUU O+A UL4M?@|L?t |@| ** i?thi *L?}|ih4 iU@U) EB@**@?|c 2fff hhi?| hiUL44i?_@|L?t uLh ?|@|L? Lu O+A ? T@|i?|t ?uiU|i_ | 4@? 44?L_iUi?U) ht |)Ti OWV @hi M@ti_ L? |i UL4M?@|L? Lu |L ML*L}U@* 4@h! ihtc #e A*)4TLU)|i Ui** UL?|t @?_ T*@t4@ OWV + *ii*t Ai hi*@|i ThL}?Lt|U @*i Lu i@U 4@h!ih uL**L?} ?|@|L? Lu |ih@T) @t ?L| Mii? u**) U@h@U|ih3i_ ,@h *ih }_i*?it ihi i@*) M@ti_ L? |i Th?UT*i Lu <| i@h*)c | @h_<c @*|L} |i *L?}|ih4 4T*U@|L?t Lu |t @TThL@U ihi ?!?L? Ek)h@!_it @?_ B@h?Lc 2ff 5?Ui |i?c |i L?*) U*i@h ?|ih?@|L?@* UL?ti?tt t |@| O+A tL*_ Mi ?|@|i_ MiuLhi #e Ui** UL?|t MiUL4i *Lih |@? 2ff%4UhLw MiU@ti ?uLh4*) }ih h@|it Lu _ti@ti ThL}hittL? |L _i@| @?_ W#5 Lh _i@| @4L?} T@|i?|t t|@h|?} +V |ih@T) @i Mii? LMtihi_ ? T@|i?|t @?} @UUitt |L O+A Mi*L |t |hitL*_ EOL}}c 2ff ? |i L|ih @?_c |ihi t ?L U*i@h i_i?Ui i|ih _i*@) ? ?|@|L? Lu +V |ih@T) E+A ?|* |t |hitL*_ Lu 2ff%4UhLw 4@) *i@_ |L @ TLLhih h@* *L@_ hi tTL?ti uLh T@|i?|t | 4@? 44?L_iUi?U) ht E**Tt i| @*c 2ff #i |L *@U! Lu i_i?Uic UL?|h) }_i*?it 4@) t}?U@?|*) _gih uLh hiUL44i?_@|L?t @ML| T@|i?|t | #e *)4TLU)|it Mi|ii? 2ff @?_
(5) Df Ui**t%4w #gihi?Uit @hi ii? 4Lhi ThL?L?Ui_ uLh T@|i?|t | #e *)4TLU)|it. :
(6) Df Ui**t%4w @?_ i? UL4. M??} #e |hitL*_t | |Lti ti_ uLh h@* *L@_ E+MLc 2ff2( +iUL44i?_@|L?t.
(7) Lu |i @?i* L? *?U@* h@U|Uit uLh Ahi@|4i?| Lu OWVc 2ff2( W_i4)Lhc 2ff2 iU@ti Lu ?Uhi@ti_ @@hi?itt Lu |i @U||) @?_ |L U|) Lu Uhhi?| _h}tc |i |hitL*_ uLh ?|@|L? Lu |ih@T) @t tu|i_ |L @ *@|ih |4i ? |i ULhti Lu OWV _ti@ti At tu| t ?L| tL 4U |i hit*| Lu @?) Mi||ih !?L*i_}i Lu |i ?i?Ui Lu T@|i?|t< U@h@U|iht|Ut L? u|hi L|UL4it uhL4 |hi@|4i?|c @t | hiiU|t }i?ih@* !?L*i_}i Lh Lhhit @ML| |i igiU| Lu |i _h}t hhitTiU|i Lu |i ?|@* UL?_|L? Lu |i T@|i?| Ai LT|4@* |4i |L ?|@|i |ih@T) hi4@?t 4ThiUti*) _i?i_ Evi? i| @*c 2ff2( #i*uh@tt)c 2ff2 4@Lh tti @t |L _L | |i _ii*LT4i?| Lu hitt|@?Uic @?_ |i tMti^i?| *Ltt Lu _h} @U||)c U 4@) Mi U@ti_ M) @ @hi|) Lu T@h4@UL*L}U@* @?_ ML*L}U@* E#itU@4Tt i| @*c 2fff @t i** @t Mi@Lh@* u@U|Lht E@|ihtL? i| @*c 2fff ?i TL|i?|@* *L?}|ih4 UL?ti^i?Ui t UhLtthitt|@?Ui |L @*|ih?@|i OWV |hi@|4i?|t ?L| )i| ThitUhMi_ E#ii!t i| @*c bb. Ai ThLtTiU| Lu hitt|@?Ui t @ !i) T@h@4i|ih uLh U*?U@* _iUtL?4@!?} @ML| ?|@|L? Lu O+A MiU@ti | |hi@|i?t |L 4@!i ?__@* T@|i?|t ?hitTL?ti |L |ih ht| *?i hi}4i? @?_ |L hi_Ui |i igiU|i?itt Lu t|U?} |L L|ih @@*@M*i Lh u|hi hi}4i?t ? U@ti Lu u@*hi Lu ThiLt O+A UL4M?@|L?t W?_ii_c hL*L}U@* |hi@|4i?| u@*hi @t Mii? hiTLh|i_ ? UhU@ DfI Lu ?ti*iU|i_ T@|i?|t |? L?i )i@h ?|@|L? Lu @ WUL?|@??} hi}4i? E@? Oiit!c 2ffc @?_ tU u@*hi t 4Lhi uhi^i?| i? T@|i?|t @_ hiUii_ ThiLt +V |hi@|4i?| Ewi L?} i| @*c 2ff2 Ai TL|i?|@* hitt|@?Ui ?_Ui_ M) |hi@|?} |LL i@h*) 4t| Mi M@*@?Ui_ @}@?t| |i TL|i?|@**) i^@**) @h4u* UL?ti^i?Ui Lu ?L| @TT*)?} @?) |hi@|4i?| W? |@| U@tic @ T@|i?| 4@) _i|ihLh@|i |L tU @? i |i?| |@| i ** ?L| Mi @M*i |L _ihi |i Mi?i|t 4 Dv. uhvlvwdqfh wr dqwlelrwlfv/ wudqvplvvlrq ri KLY uhvlvwdqw vwudlqv wr rwkhuv lv hvvhqwldoo| dq h{whu0 qdolw|1 Lq wklv sdshu/ zh gr qrw irfxv rq wkdw h{whuqdolw| idflqj wkh khdowk| srsxodwlrq dowkrxjk lw frxog hdvlo| eh dgdswhg wr vwxg| wkdw sduwlfxodu dvshfw ri uhvlvwdqfh1 Zh udwkhu irfxv rq krz wkh survshfw ri uhvlvwdqfh lqgxfhg e| phglfdwlrq lqwr wkh yluxvhv fduulhg e| d jlyhq sdwlhqw vkrxog eh wdnhq lqwr dffrxqw1 Zkhq ghdolqj zlwk wklv lvvxh/ d glhuhqw h{whuqdolw| dulvhv iurp wkh idfw wkdw gluhfw lqglylgxdo wuhdwphqw frvwv duh w|slfdoo| vhqvlwlyh wr wkh qxpehu ri lqglylgxdov xqghu wkhuds|/ dqg/ srvvleo|/ wr wkh h{shulhqfh dftxluhg e| wuhdwlqj rwkhu sdwlhqwv hduolhu1 Zh foduli| frqglwlrqv xqghu zklfk/ sdudgr{lfdoo|/ lghqwlfdo sdwlhqwv pd| eh jlyhq glhuhqw wuhdwphqwv1 Zh dovr hpskdvl}h wkdw hduo| wuhdwphqw pd| do0 orz folqlfldqv wr odwhu h{sorlw glhuhqfhv lq vxvfhswlelolw| wr wuhdwphqw dprqj lqlwldoo| xqglvwlqjxlvkdeoh sdwlhqwv1. 2.
(8) uhL4 @ ?ic 4Lhi @_@?Ui_c |ih@T) i? | MiUL4it @@*@M*i At ** Mi U@**i_ |i |ih@Ti|U LTTLh|?|) ULt| igiU| Ai |ih@Ti|U _iUtL? 4t| Mi 4@_i L? |i M@tt Lu _@|@ |@| @hi ?L| u**) 4@ |hi_c ?_ih 4@Lh ?Uih|@?|it @ML| |ih UL?ti^i?Uit L? OWV?uiU|i_ TihtL?t wi@h??} |@!it T*@Ui Lih |4ic @?_ 4@) |@!i |L uLh4tG | 4@) Mi i?_L}i?Ltc @?_ | 4@) Mi i L}i?Lt ,?_L}i?Lt *i@h??} 4@) |@!i 4@?) uLh4t uLh |i _iUtL? 4@!iht hitTL?tM*i uLh @_4?t|ih?} O+A |ih@Tit( Liih @? itti?|@* T@h| Lu | t *i@h? ?} M) |hi@|?}c |i T@h|U*@h uLh4 Lu *i@h??} M) _L?} @TT*)?} ? |t UL?|i | `i? |i) |hi@| @ T@|i?|c U*?U@?t hi*@|i T@h|U*@h T@|i?| U@h@U|iht|Ut | T@h|U*@h L|UL4itc @?_ |i 4Lhi T@|i?|t |i) |hi@|c |i Mi||ih |i) *i@h? i|ih @ T@h|U*@h hitTL?ti ? @ T@|i?| t h@?_L4 Lh t |i t}? Lu @ t)t|i4@|U L|UL4i ) |hi@|?} T@|i?|tc |i U*?U@?t |t *i@h? @ML| i@U ?__@* hitTL?ti?itt |L |hi@|4i?| @?_ |i ThLM@M*i hitTL?ti?itt Lu |i t@4i ?__@* T@|i?|t |L uh|ihc u|hic |hi@|4i?| , L}i?Lt *i@h??} t ?uLh4@|L? }i?ih@|i_ ?_iTi?_i?|*) uhL4 |i U*?U@? _i UtL? 4@!ih 6Lh i @4T*i u?_@4i?|@* @?_ _ii*LT4i?| hiti@hU @ML| O+A t U@hhi_ L| M) @hLt |i@4t @?_ }i?ih@|it ?uLh4@|L? TM*ti_ ? tUi?|U Lh?@*tc Mi*@)i_ M) |i T@h4@Ui|U@* ?_t|h)c i|U A@| ?uLh4@|L? t LMtihi_ M) |i U*? U@?t L 4@!i _iUtL?t L? O+A |hi@|4i?|c L T_@|i |ih !?L*i_}i Lih |4i | |i) _L ?L| ?i?Ui |i tTii_ @| U |i ?uLh4@|L? t }i?ih@|i_ ?Lh |t UL?|i?| At ?uLh4@|L? }i?ih@|L? ThLUitt t i L}i?Lt |L |i _iUtL? 4@!ih Ai 4L_i* Thiti?|i_ ? |t T@Tih uLh4@*3it @?_ tL*it |i |ih@Ti|U _*i44@ i|ih Lh ?L|c @?_ i?c |L ?|@|i @ |ih@T)( | @*tL _i@*t | |i iUL?L4U _*i44@ Lu i}|?} ?@?U@* ULt| UL?t_ih@|L?t @}@?t| i@*| Mi?i|t W| ?ULhTLh@|it i?_L}i ?Lt @?_ i L}i?Lt @hh@* Lu ?uLh4@|L? Ai 4L_i* @?@*)tit @?_ i*Tt ?_iht|@?_ |i LT|4@* _iUtL? ThLUitt W| it|@M*tit @?_ h@|L?@*3it tL4i thTht?} hit*|t *|L} i TiU|i_ |L|@* ULt|t @?_ Mi?i|t @hi *?i@h ? |i tiUL?_ TihL_c *i@h??} M) |hi@|?}c M) @**L?} |i ti*iU|L? Lu T@|i?|t @UULh_?} |L i TiU|i_ hitTL?ti?ittc 4@!it |i LMiU|i u?U|L? UL?U@i At U@**t uLh ?|ihLh |hi@|4i?| t@hit ? |i
(9).
(10) tiUL?_ TihL_ uLh ThiLt*) |hi@|i_ T@|i?|tc *i |i LT|4@* _iUtL? uLh ?@>i T@ |i?|t t @ ULh?ih tL*|L?. 2. 6h|ih4Lhic |i ht| TihL_ _iUtL? @ML| |i ThLTLh|L?. Lu T@|i?|t hiUi?} |hi@|4i?| @giU|t |i tiUL?_ TihL_ ULUi At @TTi?t @ |L U@??i*t 6ht| *i@h??} M) |hi@|?} 4T*it |@| TihL_ 2 |hi@|4i?| ULt|t @?_ Mi?i|t _iTi?_t L? |i ?4Mih Lu T@|i?|t |hi@|i_ ? TihL_ ( tiUL?_c hhitTiU|i Lu @U^hi_ !?L*i_}i M) |i U*?U@? _iUtL? 4@!ihc |i |ih@Ti|U Mi?i|t Lu |hi@|4i?| ? Ti hL_ 2 _iTi?_ L? i|ih Lh ?L| @ T@|i?| @t Mii? |hi@|i_ MiuLhi Ai UL4M?@|L? Lu ?|ihLh @?_ ULh?ih tL*|L?t |L |i tiUL?_ TihL_ |hi@|4i?| _iUtL?t t 4TLh|@?| ? @?@*)t?} ti^i?|@* i@*| _iUtL?t ?L*?} ?Uih|@?|) @?_ *i@h??} uLh |i uL**L?} hi@tL? ULh?ih tL*|L? t ?L| @giU|i_ M) @ t4@** T@h@4i|ih U@?}i( @? ?|ihLh tL*|L? ?Lh4@**) t t @ hit*|c tL4i T@h@4i|iht @giU| |i LT|4@* _iUtL? ? TihL_ 2 *i tL4i _L ?L|c _iTi?_?} L? i|ih |i) Mi@h L? |i ULh?ih tL*|L? Lh |i ?|ihLh L?i 6h|ih4Lhi |t T@h@4i|ih ti?t||) _iTi?_t L? |i ht| TihL_ _iUtL?c MiU@ti |i TihL_ 2 _iUtL? t UL?_|L?@* L? | W? @ ti?tM*i UL?}h@|L? Lu |i hi*i@?| tUi?|U T@h@4i|ihtc h@* hitt|@?Ui |h?t L| |L Mi hhi*i@?| |L |i TihL_ |hi@|4i?| _iUtL?c _itT|i |i u@U| |@| ML| |i ht| TihL_ t@hi @?_ L?i Lu |i tiUL?_ TihL_ t@hit @hi t|hU|*) ?|ihLh ih@Tt 4Lhi thTht?} t |@| hitt|@?Ui |L u|hi |ih@T) t 4Lhi *!i*) |L Mi hhi* i@?|c |i }ih |i 4@}?|_i Lu |i ui@hi_ igiU| At @TTi?t MiU@ti |i LT|44 _iUtL? h*i 4T*it UL4T*i|i ThL|iU|L? @}@?t| @? L|UL4i ?L*?} hitt|@?Ui i? |i 4@}?|_i Lu |@| igiU| t }c *i | 4@) ?L*i L?*) T@h|@* ThL|iU|L? i? |i ThLtTiU| Lu hitt|@?Ui t *itt _hi@_u* Ai hit| Lu |i T@Tih t Lh}@?3i_ @t uL**Lt W? |i ?i | tiU|L? i ?|hL_Ui @ 5 Lq. d prgho wkdw ohiw wkh ghflvlrq pdnhu xqdeoh wr vhohfw sdwlhqwv dffruglqj wr h{shfwhg uhvsrqvlyh0 qhvv/ exw kdg ulvlqj shu sdwlhqw frvwv ri wuhdwphqw lq hdfk shulrg gxh wr ghfuhdvlqj uhwxuqv/ d vlplodu rxwfrph zrxog rewdlq1 Dowkrxjk suhylrxvo| wuhdwhg dqg qdyh sdwlhqwv zrxog eh exqgohg zlwklq wkh vdph/ frqyh{/ frvw ixqfwlrq/ vlqfh wkh| uhfhlyhg wkh vdph wuhdwphqw lq wkh vdph shulrg/ h{shfwhg ehqh0 wv zrxog vwloo glhu iru wkh wzr jurxsv vr wkdw d vlpsoh uxoh zrxog dulvh iru shulrg 5= li yludo uhvlvwdqfh kdv ehhq lqgxfhg e| Wkhuds| 4 lq wkh jurxs wkdw uhfhlyhg lw/ wuhdw qdyh sdwlhqwv lq sulrulw|/ wkhq +srv0 vleo|, dovr wuhdw vrph suhylrxvo| wuhdwhg sdwlhqwv> li Wkhuds| 4 wxuqv rxw qrw wr fuhdwh yludo uhvlvwdqfh/ wuhdw suhylrxvo| wuhdwhg sdwlhqwv lq sulrulw|/ wkhq +srvvleo|, dovr wuhdw vrph qdyh sdwlhqwv1. e.
(11) 4L_i* |@| i M|t |i 4@? ui@|hit t| _tUtti_G hhiihtM*i |ih@Ti|U _iUtL?t @hi 4@_i ?_ih ?Uih|@?|) ? @ _)?@4U ti|T( }i?ih@* ?uLh4@|L? @ML| |ih@Tit ?uL*_t i L}i?Lt*) _h?} |i TihL_ ?_ih tUh|?) tL |@| _iUtL?t 4@) Mi hi}hi||i_ i TLt|. ii? u |i) ihi ?L| 4t|@!it i @?|i( t4*|@?Lt*) ?uLh4@|L? L? ?__@*. hitTL?ti?itt |L |hi@|4i?| t }i?ih@|i_ i?_L}i?Lt*) M) |hi@|?} T@|i?|t Ai ThLM*i4 t tL*i_ M) t|LU@t|U _)?@4U ThL}h@44?}c t|@h|?}c ? 5iU|L?
(12) c | |i *@t| TihL_c @?_ UL?|??}c ? 5iU|L? ec | |i ht| TihL_ @?_ |i Lih@** tL*|L? 5iU|L? D }it |i ?||L? ?_ih*)?} |i _iUtL? h*ic i T*@?t @?_ h@|L?@*3it ) @?_ i? |i hitt|@?Ui igiU| 4@)c Lh 4@) ?L|c @giU| |i LT|4@* TihL_ _iUtL?c @?_ uh|ih _tUttit |i *?! Lu |i 4L_i* | hi@* LT|L?t @?_ |i hL*i Lu ?uLh4@|L? W? |i L?U*tL?c i }L M@U! |L |i }i?ih@* 4i_U@* *|ih@|hi @?_ h@ti ttit |@| UL*_ ?L| Mi |@U!*i_ |L| uh|ih Lh! 2 7j`jA|B, |jiBVj|W WNWj | A|ji6jaBi+ ijj,B|NA Nu. AuNi6B|NA 2. Bi?ih@* uh@4iLh!. `i ti @ t4T*i |LTihL_ 4L_i* |L 44U |i ULUit u@Ui_ M) i@*| _iUtL? 4@!ih UL?uhL?|i_ | @ tUUitti L Lu ?i |ih@Tit | 4@Lh i @?|i ?Uih|@?|it @ML| |ih igiU|i?itt At _iUtL? 4@!ih t @ U*?U@? UL?Uih?i_ ML| | T@|i?|t i** Mi?} @?_ | |ih@Ti|U ULt|t @| |i @}}hi}@|i *ii* ** ULt|t @?_ |*|) *ii*t @hi i Thitti_ ? UL4T@h@M*i Thiti?| @*i ?|t | |i Mi}???} Lu |i ht| TihL_c @ ?i |ih@T)c Aih@T) c MiUL4it @@*@M*i *|L} |t igiU|t @hi ?L| )i| u**) it|@M*ti_c |i U*?U@? _iU_it i|ih Lh ?L| |L ThitUhMi | |L tL4i Lh @** T@|i?|t Ai |ih@T) @t |L igiU|tG @ !?L? i TiU|i_ Uhhi?| |*|) 4ThLi4i?| 0 uLh |i T@|i?|( @?_ @? ?!?L? u|hi igiU| L? |i iU@U) Lu u|hi |hi@|4i?|t 6|hi |hi@|4i?|t 4@) UL?tt| ? @_4?t|ih?} @ tiUL?_ |ih@T)c Aih@T) 2c U ** MiUL4i @@*@M*i ? |i tiUL?_ TihL_c ? @_4?t|ih?} Aih@T) c Lh ? D.
(13) t?} ?L |ih@T) @| @** `i @tt4i |@| ?L hi*i@?| tTiUU ?uLh4@|L? L? ?__@* T@|i?|t t !?L? |L |i _iUtL? 4@!ih @| |i Mi}???} Lu TihL_ L?ti^i?|*)c *i ?__@* hitTL?tit |L Aih@T) 4@) _gih @UhLtt T@|i?|t i TLt|c |i i TiU|i_ TihL_ |*|) 4ThLi4i?| t |i t@4i uLh @** |hi@|i_ T@|i?|t i @?|i N?*!i |i Uhhi?| TihL_ igiU|c Lti i TiU|i_ @*i t !?L?c |i i TiU|i_ igiU| Lu t?} Aih@T) c L? u|hi |hi@|4i?|t ** Mi !?L? L?*) @| |i Mi}???} Lu TihL_ 2 | |@| |4ic |i |hi@|4i?| LT|L?t @hiG ?L |hi@|4i?|( @_4?t|ih?} L*_ Aih@T) ( @_4?t|ih?} ?i Aih@T) 2 iuLhi @ _iUtL? t 4@_ic |i hit*|t Lu uh|ih hiti@hU @?_ i Tih4i?| hii@* i|ih Aih@T) ?_Uit h@* hitt|@?Ui |t hi_U?} |i Mi?i|t uhL4 ML| Aih@T) @?_ Aih@T) 2c Lhc L? |i UL?|h@h)c *i@it |i T@|i?| ||ih @?_ ? @ Mi||ih TLt|L? |L Mi?i| uhL4 i|ih |ih@T) Wu Aih@T) |h?t L| |L Uhi@|i hitt|@?| h@* t|h@?tc | ** Mi *@Mi**i_ <M@_< EK ( ? |i LTTLt|i U@tic | ** Mi *@Mi**i_ <}LL_< E} AL hiTi@|c |i _gihi?Ui Mi|ii? @ }LL_c @?_ @ M@_c hi@*3@|L?c uLh Aih@T) _Lit ?L| *i ? |t Uhhi?| |*|) igiU| M| ? |t u|hi 4T@U| |hL} |i 4iU@?t4 Lu h@* hitt|@?Ui @?_ |ih@Ti|U LTTLh|?|) ULt| Wu Aih@T) ThLit igiU|i E} c |@| Mi?iU@* igiU| ** Mi ui*| _h?} |i ?i | TihL_ ? |i uLh4 Lu @ Mi||ih hitTL?ti |L 4i_U@|L? @_4?t|ihi_ ? TihL_ 2 `i|ih Aih@T) |h?t L| } Lh K t @ U@h@U|iht|U Lu |i |ih@T)c ?L| @ 4@||ih Lu ?__@* T@|i?| hitTL?ti?it | |i Mi}???} Lu TihL_ | t @tt4i_ |@| Aih@T) ** |h? L| } | ThLM@M*|) c @?_ K L|ihti uh@U|L? @ Lu |i |L|@* ?4Mih Lu OWV?uiU|i_ T@|i?|t @hi ThitUhMi_ Aih@T) ( |i hi4@??} uh@U|L? E @ @hi ?L| |hi@|i_ Ai _h@|L? Lu |i ht| TihL_ ULhhitTL?_t |L |i |4i ?iUitt@h) uLh ThLTih|) K Lh } Lu Aih@T) |L hii@* |ti*uc @?_ uLh Aih@T) 2 |L hi@U |i ThitUhT|L? t|@}i( |iti. |L ThLUittit @hi |i hit*| Lu i L}i?Lt tUi?|U hiti@hU @?_ i Tih4i?|@|L? Ai? TihL_ 2 Mi}?t( |i |ih@Ti|U _iUtL? 4@_i @| |i Mi}???} Lu TihL_ 2 t |i *@t| hi*i@?| _iUtL? @?_ |t igiU|t ULih |i hit| Lu |i _iUtL? 4@!?} Lh3L?. S.
(14) 22 Aih@T) @giU|t |i 4T@U| Lu Aih@T) 2 Atc @| |i Mi}???} Lu |i tiUL?_ TihL_c |i ?uLh4@|L? @ML| |i *L?}h? igiU|t Lu Aih@T) t hii@*i_ @?_ Aih@T) 2 MiUL4it @@*@M*i
(15) Ai i TiU|i_ igiU| Lu Aih@T) 2 L? @ T@|i?|<t i**Mi?} _iTi?_t L? i|ih |i T@|i?| @t hiUii_ Aih@T) Lh ?L| @?_c u |i T@|i?| @t hiUii_ Aih@T) c | _iTi?_t L? i|ih Aih@T) @t hii@*i_ |ti*u K Lh } `i ?L|i .K @?_ .} |i ULhhitTL?_?} i TiU|i_ |*|) }@? L? |i @ih@}i T@|i?| |@| @t ?_ih}L?i Aih@T) ( i ?L|i .? |i i TiU|i_ |*|) }@? L? @? ?|hi@|i_c Lh ?@>ic T@|i?| Ai uLhi}L?} _tUttL? 4T*itG. .K .? .} Wu Aih@T) hii@*t |ti*u. }. E. @ T@|i?| *iu| ?|hi@|i_ ? TihL_ 4@) i TiU| *itt. Mi?i| uhL4 Aih@T) 2 |@? @ ThiLt*) |hi@|i_ T@|i?|c MiU@ti |i uLh4ih @t Mii? @**Li_ |L _i|ihLh@|i *i |i *@||ih @t Mii? ThL|iU|i_ uhL4 @hLt t)4T|L4t Lu |i _iti@ti M) Aih@T) |L| i Tihi?U?} |i _ii*LT4i?| Lu @?) h@* hitt|@?Ui At t |i |ih@Ti|U LTTLh|?|) ULt|c 4i@thi_ M) |i _gihi?Ui. .} .? . E2. W? UL?|h@t|c u Aih@T) |h?t L| Kc ?@>i T@|i?|t Mi?i| 4Lhi uhL4 |i ?i |hi@|4i?| |@? ThiLt*) |hi@|4i?| T@|i?|t MiU@ti |i uLh4ih _L ?L| @hMLh hitt|@?| t|h@?t Lu |i ht ti*iU|i_ Lh ThL4L|i_ M) Ahi@|4i?| At t |i hitt|@?Ui igiU|c 4i@thi_ M) |i _gihi?Ui. .? .K . E
(16) . Dv srlqwhg rxw e| d uhihuhh/ sdwlhqwv pd| qrw lq uhdolw| uhfhlyh ru shufhlyh wkh vdph lqirupdwlrq dv wkh ghflvlrq pdnhu1 Wklv/ dqg wkh idfw wkdw frvwv pd| qrw eh shuihfwo| lqwhuqdol}hg/ pd| pdnh lw glfxow iru wkh ghflvlrq pdnhu wr rewdlq sdwlhqw djuhhphqw iru wkh ghvluhg wuhdwphqw1 6. ..
(17) Ai |ih@Ti|U LTTLh|?|) ULt| i Thittit hi}hi|t i Tihi?Ui_ i TLt| uLh ?L| @?} ThitUhMi_ Aih@T) i? |i *@||ih |h?t L| } ( |i hitt|@?Ui igiU| i Thittit hi}hi|t i Tihi?Ui_ i TLt| uLh @?} ThitUhMi_ Aih@T) i? |i *@||ih |h?t L| K. Aih@T) 4@) @*tL Mi @TT*i_ Lh hi@TT*i_ ? TihL_ 2c | i TiU|i_ |*|) }@?t. eK e? e} e W? u@U| O+A |ih@Tit EAih@T) 2 UL4M?i ?i OWV tTiUU W<t @?_ +AW<t | ThiLt*) i t|?} @?|hi|hLh@* _h}t EAih@T) `i @tt4i |@| Aih@T) 2 ?ULhTLh@|it |i ?i tUi?|U !?L*i_}i @U^hi_ _h?} TihL_ c tL |@| | _Lit @| *i@t| @t i** @t Aih@T) ? i@U TLttM*i U@tiG. eK .K( e? .?( e} .} `i. uh|ih @tt4i |@| ULt| UL?t_ih@|L?t _L ?L| ?|ihuihi | |i _L4?@?Ui Lu Aih@T) 2c tL |@| Aih@T) ** t4T*) ?L| Mi ti_ ? TihL_ 2D. 2
(18). Lt|t @?_ T@|i?| tTiUU hitTL?ti?itt. AL|@* ULt|t _iTi?_ L? |i |L|@* ?4Mih Lu T@|i?|t ?_ih}L?} Aih@T) c ? TihL_ c Lh Aih@T) 2c ? TihL_ 2 #tUL?|i_ ?| ULt|t _gih Mi|ii? TihL_t MiU@ti |i |hi@|4i?|t _gihc |i *i?}| Lu |i TihL_t _gihS c @?_ _tUL?| u@U|Lht _gih Wu ULt|t Tih T@|i?| ihi UL?t|@?|c _i?|U@* T@|i?|t L*_ hiUii _i?|U@* |hi@|4i?|c *i@_?} |L ULh?ih tL*|L?t E3ihL Lh L?i uLh |i ThLTLh|L?t Lu T@|i?|t @_4?t|ihi_ @ |hi@|4i?| #iUhi@t?} hi|h?t 4@) i T*@? |i u@U| |@| ThLTLh|L?t t|hU|*) Mi|ii? 3ihL @?_ L?i @hi |)TU@**) LMtihi_ OLiih @?L|ihc 4Lhi ThLuL?_c t|U@|L? uLh ?|ih4i_@|i ThLTLh|L?t Lu T@ |i?|t |hi@|i_ Et|hU|*) Mi|ii? 3ihL @?_ L?ic L*_ Mi u T@|i?|t _gihi_ ? |hi@|4i?| 7 Dowkrxjk. lw dssolhv wr sdwlhqwv wkdw duh qdyh dw wkh ehjlqqlqj ri shulrg 5/ hq lv glhuhqw iurp %/ zklfk dssolhv wr qdlyh sdwlhqwv dw wkh ehjlqqlqj ri shulrg 4/ ehfdxvh zh duh qrw dvvxplqj wkdw shulrgv kdyh wkh vdph gxudwlrq/ dqg ehfdxvh doo xwlolw| dqg frvw pdjqlwxghv duh h{suhvvhg lq suhvhqw ydoxh whupv1 8 Lq idfw wkh whfkqrorjlfdo surjuhvv rffxulqj ehwzhhq wkh wzr shulrgv pd| qrw frqfhuq rqo| wkhudshx0 wlf hflhqf| exw dovr surgxfwlrq whfkqrorj| dqg frvwv/ doorzlqj dffhvv wr pruh vrsklvwlfdwhg phglfd0 wlrqv1 Lq dq| fdvh/ wklv k|srwkhvlv lv qrw fuxfldo1 Uhod{lqj lw frpsolfdwhv wkh prgho dqg lwv uhvroxwlrq zlwkrxw eulqjlqj dq| ixuwkhu lqvljkwv1 9 Zh wklqn ri shulrg 5 dv uhsuhvhqwlqj wkh zkroh uhpdlqlqj wlph rqfh Wkhuds| 5 lv dydlodeoh/ zkloh shulrg 4 uhsuhvhqwv d vkruwhu shulrg ryhu zklfk lqirupdwlrq derxw wkh uhvlvwdqfh0lqgxflqj fkdudfwhulvwlf ri Wkhuds| 4 ehfrphv dydlodeoh dqg Wkhuds| 5 ehfrphv rshudwlrqqdo1. H.
(19) hitTL?ti?ittc @?_ UL*_ Mi _t|?}ti_ @UULh_?}*). W? u@U|c *i |i _iUtL? 4@!ih _Lit ?L| L*_ @?) ?uLh4@|L? |@| L*_ @**L ih |L _tUh4?@|i Mi|ii? T@|i?|t @| |i Mi}???} Lu TihL_ c @_4?t|ih?} Aih@T) ? TihL_ 4@) hii@* tTiUU ?uLh 4@|L? @ML| ?__@* T@|i?|t | |i Mi}???} Lu TihL_ 2c |i U*?U@? 4@) |i? Mi ? @ TLt|L? |L _tUh4?@|i Mi|ii? T@|i?|t @UULh_?} |L i TiU|i_ hitTL?ti?itt h@|ih |@? 4@!i _iUtL?t M@ti_ L?*) L? |i @ih@}i i TiU|i_ igiU|t _i?|i_ ? |i ThiLt tMtiU|L? #gihi?Uit ? T@|i?| hitTL?ti?ittc u |i) @htic 4@) Mi _itUhMi_ ? |ih4t Lu _gihi?Uit ? |ih@Ti|U igiU| @?_%Lh ? ULt|t Lu |hi@|4i?| *|L} |t 4@!it @ _gihi?Ui |L |i T@|i?|c | _Lit ?L| |L |i _iUtL? 4@!ihc L U@hit @ML| |i ?i| igiU|G |*|) 4?t ULt| `i 4ih}i |iti |L TLttM*i U@??i*t Lu _gihi?|@|L? ?_ih @ t?}*i 4Mhi**@c U@**i_ ULt| uLh t4T*U|) At @| i ** U@** ULt| ?U*_it ML| |i UL?i?|L?@* tTT*) t_i ULt| Lu @_4?t|ih?} |i |hi@|4i?|c @?_c L? |i _i4@?_ t_ic @?) TLttM*i |*|) *Ltt Lh }@? |L @ T@h|U*@h T@|i?| _i |L T@|i?| tTiUU hitTL?ti?itt |L |hi@|4i?| ihL_ G 5?Ui TihL_ t hi*@|i*) tLh|c i @tt4i _iUhi@t?} hi|h?t _i |L tL4i i_ u@U|Lht At t |i tLh|h? t|@|L? Lu tU@hi hitLhUit U U*?U@?t t@**) u@UiG ?Uhi@t?} |i ?4Mih Lu T@|i?|t ?_ih}L?} |ih@T) t@**) 4TLtit @ t|h@? L? i_ u@U|Lht @?_ 4@) hi^hi |i @U^t|L? Lu ?i i_ i^T4i?|t |@| L*_ L|ihti ?L| Mi hi^hi_ At i )TL|it3i @? ?Uhi@t?} UL?i ULt| u?U|L? Lu |i ?4Mih Lu T@|i?|t ?_ih}L?} |ih@T) ? TihL_ *|L} |ihi 4@) Mi _gihi?Uit ? T@|i?| hitTL?ti?itt |@| ** |h@?t*@|i ?|L _gihi?| i TLt| hi@*3@|L?tc |i U*?U@? @t ?L ?uLh4@|L? |@| ti UL*_ ti |L ti*iU| T@|i?|t @UULh_?}*) L?ti^i?|*)c |i |L|@* i TiU|i_ ULt| Lu |hi@|4i?| i @?|i _iTi?_t L?*) L? |i |L|@* ?4Mih Lu T@|i?|tG S E5 ' 2 S5 2 ihi S t @ TLt|i T@h@4i|iht |@| hiiU|t |iU?L*L}) @?_ |i UL?t|h@?|t : Zh. duh judwhixo wr dq dq|prxv uhihuhh iru vxjjhvwlqj wklv srvvlelolw|/ dv zhoo dv pdq| rwkhu lp0. suryhphqwv wr wkh sdshu1. b.
(20) Lu i@*| tihUitc *i 5 t |i ?4Mih Lu T@|i?|t ?_ih}L?} Aih@T) wi| ? @?_ @ Mi hitTiU|i*) |i |L|@* TLT*@|L? Lu OWV ?uiU|i_ T@|i?|t @?_ |i ThLTLh|L? Lu |@| TLT*@|L? |@| hiUiit Aih@T) ( |i?. 5. ' ?@( u TLT*@|L? t ?Lh4@*3i_ |L c @?_. ?|t @hi ULti? tL |@| S ' c |i? 5 ' @ @?_ |i |L|@* i TiU|i_ ULt| Lu Aih@T) t E '. |S @. 2 @ 2. Ee. ihL_ 2G. | |i Mi}???} Lu TihL_ 2c |i U*?U@? @t @ _ih ti| Lu _iUtL? TLttM*|it |L ULLti uhL4 6Lh i@U TLttM*i |)Ti Lu T@|i?|c ti U@? @Mt|@? uhL4 @?) |hi@|4i?|( ti U@? ThitUhMi Aih@T) ( Lh ti U@? ThitUhMi Aih@T) 2 `i @i @*hi@_) 4@_i @tt4T|L?t 4T*)?} |@| t?} Aih@T) ? TihL_ 2 t ?iih LT|4@* tL i ** ?L| _tUtt |i ULt| Lu @_4?t|ih?} Aih@T) ? TihL_ 2 `i|ih | t @_4?t|ihi_ |L ThiLt*) |hi@|i_ T@|i?|t Lh |L ?@>i T@|i?|tc Aih @T) 2 ?L*it @ UL44L? ThL|LUL*i uLh i@U T@|i?| }@?c ? |i @Mti?Ui Lu @?) Thi_U|@M*i _gihi?Uit ? hitTL?ti?itt Mi|ii? T@|i?|tc |i i TiU|i_ |L|@* ULt| _i Ti?_t L? |i |L|@* ?4Mih EThiLt*) |hi@|i_ T*t ?@>i T@|i?|t Lu T@|i?|t |hi@|i_ OLiihc u TihL_ 2 @t @ *L?}ih _h@|L?c |i @tt4T|L? Lu _iUhi@t?} hi|h?t 4@) ?L| Mi @TThLTh@|iH L?ti^i?|*)c i? TLttM*i _gihi?Uit ? hitTL?ti?itt @hi ?L| |@!i? ?|L @UUL?|c i TiU|i_ |L|@* ULt|t Lu Aih@T) 2 @hi @tt4i_ |L Mi *?i@h*) ?Uhi@t?} ? |i |L|@* ?4Mih Lu T@|i?|t |hi@|i_G |@!i @?) T@|i?|( t i TiU|i_ ULt| Lu Ahi@|4i?| t 7 wi| t ?|hL_Ui _gihi?Uit ? ?__@* hitTL?ti?itt Wu |hi@|?} tL4i T@|i?|t ? TihL_ @**Lt |i U*?U@? |L h@?! |i4 @UULh_?} |L i TiU|i_ hitTL?ti?ittc |i? 4Lhi hitTL?ti T@|i?|t tL*_ Mi }i? ThLh|) Lih *itt hitTL?ti L?it uLh |hi@|4i?| ? TihL_ 2 Wu @** ThiLt*) |hi@|i_ T@|i?|t @hi }i? Aih@T) 2c |i @ih@}i ; Frqyh{. frvwv lq wkh wrwdo qxpehu ri sdwlhqwv duh frpsdwleoh zlwk wkh uhvxowv wkdw zh duh jrlqj wr. suhvhqw/ exw qrw qhfhvvdu|1. f.
(21) ULt| Tih T@|i?| ** Mi ?U@?}i_ @| 7 ( M| u L?*) |i 4Lhi hitTL?ti L?it @hi 7 L?ti^i?|*)c @4L?} |hi@|i_c |i @ih@}i i TiU|i_ ULt| Tih T@|i?| ** Mi *Lih |@? |i }hLT Lu ThiLt*) |hi@|i_ T@|i?|tc |i i TiU|i_ 4@h}?@* ULt| Lu |hi@|?} @ ?i T@|i?| ?Uhi@tit |. c |i ThLTLh|L? Lu T@|i?|t |hi@|i_ ? TihL_ 2. Ai @M*|). |L ti*iU| T@|i?|t @UULh_?} |L |hi@|4i?| hitTL?ti?itt t 4i@thi_ @t |i @M*|) |L h@?! |i4 ? Lh_ih Lu _iUhi@t?} i TiU|i_ hitTL?ti?itt E?Uhi@t?} i TiU|i_ ULt| L? @ UL?|?Ltc ?|ic ULt| ?|ih@* `i? |t @M*|) _Lit ?L| i t|c @** T@|i?|t @i |i t@4i i TiU|i_ ULt| Lu |hi@|4i?| ? 4ThLi4i?| ? |i @M*|) |L ti*iU| 4i@?t |@| uiih @?_%Lh t4@**ih 4t|@!it LUUh ? |i h@?!?} ThLUitt tL |@| |i _gihi?Ui ? i TiU|i_ ULt| Mi|ii? |i 4Lt| hitTL?ti E*i@t| i TiU|i_ ULt| T@|i?| @?_ |i *i@t| hitTL?ti E}it| i TiU|i_ ULt| T@|i?| htitc *i |i @ih@}i Lih @** T@|i?|t 7 `i @tt4i |@| |i @M*|) |L h@?! T@|i?|t 4ThLit | |i ?4Mih Lu hi4@?t T@|i?|t |hi@|i_ ? TihL_ hiUti*)c @t tL? ? TTi?_ G. wi44@ u |i @M*|) |L ti*iU| T@|i?|t @UULh_?} |L i TiU|i_ ?__@* hitTL?ti?itt t ?L?i t|i?| i?. @ ' f @?_ ?Uhi@tit @t @ htitc @?_(. u |i i TiU|i_ ULt| Tih ThiLt*) |hi@|i_ T@|i?| t _t|hM|i_ ?uLh4*) @UULh_?} |L |i ?4Mih Lu ThiLt*) |hi@|i_ T@|i?|t }i? Aih@T) 2c @?_ |i _t|hM|L? @ih@}i. 7 b t c |i? |i |L|@* i TiU|i_ ULt| Lu |hi@|?} @ ThLTLh|L? Lu ?@ ThiLt*) |hi@|i_ T@|i?|t t E|@!?}. ? ' . A Ec @ ' @f E@ n 2 @2 E E@ f E@ ihi. f E@ @?_ E@c hitTiU|i*) |i i. TiU|i_ ?__@* ULt| Lu |hi@|?} |i T@|i?|. UL?t_ihi_ |i 4Lt| hitTL?tic @?_ |i i TiU|i_ ?__@* ULt| Lu |hi@|?} |i T@|i?|. Wklv glvwulexwlrq lv frqglwlrqdo rq Lw zrxog eh lqwhuhvwlqj wr vshfli| xqghu zklfk frqglwlrqv rq wkh xqfrqglwlrqdo glvwulexwlrq ri frvwv shu sdwlhqw dqg rq wkh ohduqlqj surfhvv/ vxfk d xqlirup frqglwlrqdo glvwulexwlrq ri h{shfwhg frvw shu sdwlhqw zrxog dulvh1 Lq Dsshqgl{ 5 zh surylgh dq h{dpsoh ri d vxflhqw frqglwlrq dv dq looxvwudwlrq1 <. d=. .
(22) 7 UL?t_ihi_ |i *i@t| hitTL?tic @hi tU |@| f E@n2 E@ ' At *i44@ **t|h@|it |@| |i @M*|) |L _tUh4?@|i Mi|ii? T@|i?|t @UULh_?} |L |hi@|4i?| hitTL?ti?itt UL?uiht UL?i |) ?. |L |i |L|@* ULt| Lu Ahi@|4i?| 2. hiUti*)c ? |i U@ti Lu @? L|ihti *?i@h |L|@* ULt| u?U|L? @?_ @ ?uLh4 UL?_ |L?@* _t|hM|L? Lu i TiU|i_ ?__@*T@|i?| hitTL?ti?ittc | 4@!it |i |L|@* ULt| u?U|L? ^@_h@|U ? . @ @?_ |i _gihi?Ui E@ E@ ?Uhi@tit uhL4 3ihL |L tL4i TLt|i ?4Mih @t @ ?Uhi@tit 6Lh i @4T*ic |@!?} E@ ' 7 @ @?_ E@ ' 7 n @c }it A Ec @ ' 7 2 @ @ n 2 E@ ED Ai @ih@}i Lu. E@ @?_ E@ t 7 f. . uLh @?). . f. f. 2. . 2. 2. At t |i |L|@* i TiU|i_ ULt| u?U|L? @tt4i_ |L L*_ uLh ThiLt*) |hi@|i_ T@|i?|t ? |i hit| Lu |i T@Tih 4@Lh tti ? _iUtL?t L? O+A |ih@Tit @t |L _L | M@*@?U?} ULt|t @?_ Mi?i|tG u Aih@T) |h?t L|. Kc. |i _iUtL? 4@!ih i TLt| tit ti @_. ?L| @_4?t|ihi_ |@| |ih@T)( |i @ih@}i ThiL*) |hi@|i_ T@|i?| t ?L *L?}ih ? @ TLt|L? |L Mi?i| uhL4 Aih@T) 2c *ic L? |i UL?|h@h)c @ ?@>i T@|i?| ** Mi?i|( |t 4T*it |@| @ ?@|h@* @tt4T|L? U@h@U|ih3?} |i ThLM*i4 @| @?_ tG. .K 7 .?. ES. Ai ThLM*i4 u@Ui_ M) |i U*?U@? t @ UL**iU|i LT|43@|L? ThLM*i4c ?@4i*) |i 4@ 43@|L? Lu i TiU|i_ ?Uhi4i?|@* |*|) |L |i L*i TLT*@|L? Lu OWV?uiU|i_ T@|i?|tc 4?t |L|@* i TiU|i_ ULt| Lu |hi@|4i?|tf iU@ti |i tiUL?_TihL_ _iUtL? t UL?_|L?@* L? |i ULUi 4@_i ? TihL_ c |i tL*|L? t Mit| LM|@?i_ M) M@U!@h_ 43 Zh. devwudfw iurp frqvlghulqj wkh frqvhtxhqfhv ri wkh KLY wuhdwphqw ghflvlrqv rq rwkhu fdwhjrulhv. ri sdwlhqwv1. 2.
(23) ?_U|L? At 4i@?t 4@ 43?} |i ?i| i TiU|i_ ?Uhi4i?|@* |*|) @| |i Mi}???} Lu |i tiUL?_ TihL_ uLh i@U TLttM*i t|@|i Lu |i Lh*_c UL?t_ih?}c ? i@U t|@|ic |i _iUtL? 4@_i ? TihL_ ?Ui |iti @hLt tiUL?_TihL_ ThL}h@4t @i Mii? tL*i_c | MiUL4it TLttM*i |L LT|43i |i ht|TihL_ LT|4@* i
(24) . @?|i. ULUi. 7jWNAaVjiNa NV|65B|NA. | |i Mi}???} Lu TihL_ 2c |ihi @hi |L TLttM*i t|@|it Lu ?@|hiG Aih@T) @t |h?i_ L| Kc Lh | @t |h?i_ L| } ( @?_ |i _iUtL? 4@!ih u@Uit |L }hLTt Lu T@|i?|tG ThiLt*) |hi@|i_ T@|i?|tc @?_ ?@>i T@|i?|t 6h|ih4Lhic |i _iUtL? 4@!ih @t @U^hi_ tL4i U@T@M*|) |L ti*iU| T@|i?|t @UULh_?} |L ?__@* i TiU|i_ hitTL?ti ?itt( |t @M*|) i t|t L?*) | hitTiU| |L |i }hLT Lu ThiLt*) |hi@|i_ T@|i?|t. Kc |i @h@M*it |L ULLti @hi |i ThLTLh|L?t K @?_ \K Lu hitTiU|i*) ?@ ThiLt*) |hi@|i_ @?_ ? E @ ?|hi@|i_ T@|i?|t( ? t|@|i }c |i ULhhitTL?_?} ULUi @h@M*it @hi } @?_ \} L?_|L?@* L? Aih@T) @?} |h?i_ L| Kc @?_ }i? TihL_ |hi@|4i?| _iUtL? @c |i LT|44 ?i| i TiU|i_ @*i Lu @_4?t|ih?} Aih@T) 2 |L ThLTLh|L?t K @?_ \K Lu hitTiU|i*) ?@ ThiLt*) |hi@|i_ @?_ @?_ ? E @ ?|hi@|i_ T@|i?|t t E|@!?} ? ' |L| *Ltt Lu }i?ih@*|) @?_ t?} EDG 2 7 T E@mK ' 4@c\ .K@K 2 @ @K n 2 E@K n .? E @ \K 7 E @ \K W? t|@|i. K. K. ihi |i ht| |L |ih4t }i |L|@* i TiU|i_ |*|) }@?t UL44L? |L @** @K ThiLt*) |hi@|i_ T@|i?|t |@| hiUii Aih@T) 2c ?i| Lu i TiU|i_ |hi@|4i?| ULt|t ?U*_?} T@|i?| tTiUU ULt|t Lh |*|) U@?}it( @?_ |i *@t| |L |ih4t }i |L|@* i TiU|i_ |*|) }@?t |L ?@>i T@|i?|tc ?i| Lu i TiU|i_ |hi@|4i?| ULt|t( @t _tUtti_ i@h*ihc ?@>i T@|i?|t U@??L| Mi _t|?}ti_ @UULh_?} |L hitTL?ti?itt tL |@| |i i TiU|i_ ULt| Tih T@|i?| t 7 uLh @?) Lu |i E @ \K T@|i?|t uhL4 |@| }hLT }i? Aih@T) 2.
(25).
(26) #i??} 4@. fK ctK. fK. fK ' @K @?_ tK ' E @ \K @t _iUtL? @h@M*itc |i ThLM*i4 MiUL4it . . .K 7 n 2 @. 2 fK2 n tK .? 7 c f fK @( f tK @ . . E.. Ai ThLM*i4 t *?i@h ? tK @?_ UL?U@i ? fK Ai tL*|L? uLh fK tG ; A ? fc. @ @K = .K f E@ c @ : @K. fKW ' A. EH. ihic u | i t|tc |i Uh|U@* @*i @K t }i? M) |i UL?_|L?G . . @K ' 2 .K 7 . Eb. 5?Ui f E@ ' 7 2 @ t |i *Lit| TLttM*i i TiU|i_ ULt| Tih ThiLt*) |hi@|i_ T@|i?|c |i h*i U@**t uLh @Mt|@??} uhL4 @_4?t|ih?} Aih@T) 2 |L ThiLt*) |hi@|i_ T@|i?|t. @ t }ih |@? @Kc uLh T@|i?|t i TiU|i_ |L hitTL?_ Mit| Ai UL?_|L? @ @K 4i@?t |@| .K f E@ fc i ii? |i Mit| hitTL?_?} T@|i?| t ?L| i TiU|i_. i UiT|c i?. |L Mi?i| uhL4 Aih@T) 2 Ai tL*|L? uLh tK tG. tKW ' @ . Ef. W| U@**t uLh @_4?t|ih?} Aih@T) 2 |L @** ?@>i T@|i?|t. } _@T|?} |i ?L|@|L? ? @*i Lu @_4?t|ih?} Aih@T) 2 |L f}. Ai @?@*)tt t @*4Lt| _i?|U@* u Aih@T) |h?t L| LMLt u@tL?c |i LT|44 ?i| i TiU|i_. e.
(27) ThiLt*) |hi@|i_ @?_ t} ?@>i T@|i?|t tG T. E@m} ' 4@. f} ct}. . f}. 2. 7 n @ .} 2. 2. n t}. f}. . .?. 7 . . c. f f}. . ( f t}. @. . @. E. Ai tL*|L? uLh f} tG. W. f}. ihi. @}. '. t |i Uh|U@* @*i Lu. ; A ? A =. @. @. c @ @}. .}. . f. E2. E@ c @ : @}. @| U |i tL*|L? uLh. f}. tu|t uhL4 @ ULh?ih. tL*|L? ihi @** ThiLt*) |hi@|i_ T@|i?|t @hi @_4?t|ihi_ Aih@T) 2c |L @? ?|ihLh tL*|L? ihi tL4i T@|i?|t |@| @hi i TiU|i_ |L hitTL?_ TLLh*) @hi ?L| @_4?t|ihi_ |i |ih@T) Wu | i t|tc @} t _i?i_ M) |i UL?_|L?G @}. '2. . .}. . 7 . E
(28) . . Ai tL*|L? uLh t} tG W. t}. ' @ . Ee. W| U@**t uLh @_4?t|ih?} Aih@T) 2 |L @** ?@>i T@|i?|t @t i? Aih@T) |h?t L| K `*i ?@>i T@|i?|t hiUii Aih@T) 2 i|ih Aih@T) |h?t L| } Lh Kc |i !i) _gihi?Ui Mi|ii? @| @TTi?t ? t|@|i. }. @?_ @| @TTi?t ? t|@|i. K. *ii* Lu ThiLt*) |hi@|i_ T@|i?|t Wu @ ULh?ih tL*|L? LUUht ? t|@|i. LUUht @| |i }c. | ?L*it. |hi@|?} @** ThiLt*) |hi@|i_ T@|i?|t( *i u @ ULh?ih tL*|L? LUUht ? t|@|i. Kc. |. ?L*it |hi@|?} ?L?i Lu |i ThiLt*) |hi@|i_ T@|i?|t W? U@ti Lu ?|ihLh tL*|L?tc ? t|@|i. Kc. Mi?} @M*i |L _tUh4?@|i @UULh_?} |L T@|i?| hitTL?ti?itt i?@M*it |i. _iUtL? 4@!ih |L ti*iU| |i T@|i?|t i TiU|i_ |L hitTL?_ Mit| @?_ @_4?t|ih |i4 Aih@T) 2 W? UL?|h@t|c ? t|@|i }c |i ?@|h@* _iUtL? L*_ Mi |L |hi@| @** ThiLt*) D.
(29) |hi@|i_ T@|i?|t( Mi?} @M*i |L _tUh4?@|i @UULh_?} |L T@|i?| hitTL?ti?itt i?@M*it |i _iUtL? 4@!ih |L 4ThLi |@| h*i M) i*4?@|?} |i Lht| hitTL?_?} T@|i?|t uhL4 |@| }hLT W| hi4@?t |hic @?_ U@? Mi tL? |@|c @|iih |i *ii* Lu T@|i?| _tUh4?@|L? 4@_i TLttM*i M) ThLh *i@h??} |hL} Aih@T) c 4Lhi ThiLt*) |hi@|i_ T@|i?|t ** Mi }i? Aih@T) 2 u Aih@T) |h?t L| } |@? u | |h?t L| K. T W E@mK |i @*i u?U|L? ? t|@|i K( tM t|||?} E2 @?_ Ee ?|L E )i*_t T W E@m} |i @*i u?U|L? ? t|@|i } `i}|?} |iti |L u?U|L?t M) |ih hitTiU|i ThLM@M*|it Lu @?_ @?_ @__?} |i4 T 5Mt|||?} EH @?_ Ef ?|L E. )i*_t. )i*_t |i tiUL?_ TihL_ @*i u?U|L?c }?} |i ?i| i TiU|i_ TihL_ 2 |L|@* i*u@hi }@? @t @ u?U|L? Lu |i ThLTLh|L? Lu T@|i?|t @?} hiUii_ Aih@T) ? TihL_ G. L E@. '. '. W T E@m} n E T W E@mK ; A 7 n @ E.} .? n E E @ .? 7 c f @ @} A . A ? A A A A A 2 7 7 A . n @ n E @ . } ? A 2 2 A ? 7 c @} @ @K ED n E E @ . ? A A A A A 7 n @ 2 n E @ .? 7 A . } A 2 2 A A A A 2 = 7 7 n E 2 .K n 2 @ n E @ .? c @K @ . e. 8it| VjiNa NV|65B|NA. ihL_ |hi@|4i?| _iUtL? t M@ti_ L? |i t44@|L? Lu TihL_ T@)Lgt @?_ TihL_ 2 T@)Lgt. ` E@ ' E@ n L E@ 44 Ixqfwlrq. X. +d, lv vwdwhg khuh iru wkh fdvh. wkh irupxodwlrq lq wkh dowhuqdwlyh fdvh. dj. . dj ? d e. de =. S. / l1h1 ^Hj . He ` @5. ES. . F1. Wkh uhdghu fdq dgmxvw.
(30) ihi L E@ t }i? M) ED @?_ E@ ' 0@ |S E@ }it |i |*|) }@?t i TiU|i_ ? TihL_ uLh |i ThLTLh|L? @ Lu T@|i?|t @_4?t|ihi_ Aih@T) c ?i| Lu |i |L|@* i TiU|i_ ULt| Lu |hi@|4i?| ? TihL_ c }i? M) Ee2 Ai |L|@* T@)Lg u?U|L?c @? i @4T*i Lu U t Thiti?|i_ }h@TU@**) ? 6}hi c ?ih|t uhL4 ED |t |hiiti}4i?| t|hU|hi ,@U ti}4i?| t _i?i_ Lih L?i Lu |i ?|ih@*t _i*4|i_ M) fc @} c @K c @?_ c U ULhhitTL?_ |L |i @hLt TLttM*i UL4M?@|L?t Lu TihL_ 2 |hi@|4i?|t Ai t*LTi Lu ` t @ UL?|?Lt u?U|L? Lu @c @ t4LL|?itt _i |L |i u@U| |@| tL4i LT|44 TihL_ 2 t@hit @hi ?|ihLh Lih tL4i h@?}it 6Lh |i T@h@4i|iht ti_ |L _h@ 6}hi c |i u?U|L? t UL?U@ic @ ThLTih|) UL?uihhi_ |L | M) |i @tt4i_ UL?i |) Lu |S E@ (
(31) | @*tL hi@Uit |t 4@ 44 @| @? ?|ihLh @*i Lu @ `*i L|ih T@h@4i|iht 4@) ThL_Ui @*i u?U|L?t |@| hi@U |ih 4@ 44 @| @ ' f Lh @ ' c |i UL?}h@|L? Lu 6}hi ULhhitTL?_t |L |i LMtihi_ t|)*3i_ u@U|t @?_ Mit| ?_ih*?it |i |h@_i Lgt Mi|ii? hitt|@?Ui @?_ |ih@Ti|U LTTLh|?|) ULt|c @?_ Mi|ii? @U|?} ?Lc *i@h??} @U|i*)c Lh *i@h??} T@tti*)c ?L*i_ ? _iUtL?t @ML| O+A |ih@Tit 6hL4 ML| |i 4i_U@* @?_ |i iUL?L4U TL?| Lu itc |i ht|TihL_ |hi@|4i?| _iUtL? t |i? 4Lt| _U*| @?_ ?|ihit|?} MiU@ti |iti |h@_i Lgt @hi Lu UL44i?th@|i 4@}?|_itc hit*|?} ? @? ?|ihLh ULUi uLh @ `i ** uLUt |i @?@*)tt L? |t UL?}h@|L?c *i@?} |L |i hi@_ih |i L?t Lu 4@!?} |i 4?Lh @_t|4i?|t hi^hi_ uLh @*|ih?@|i UL?}h@|L?t |@| 4@) Mi||ih hiiU| L|ih _iUtL? 4@!?} t|@|L?te 45 Wklv. dvvxphv wkdw sdwlhqwv ohiw xqwuhdwhg gr qrw h{shulhqfh dq| xwlolw| fkdqjh qru fkdqjh lq phglfdo frvwv gxulqj shulrg 4 dv d uhvxow ri wkh wuhdwphqw ri rwkhu sdwlhqwv1 46 Frqfdylw| dovr uhvxowv li rqh dvvxphv ghfuhdvlqj uhwxuqv wr ohduqlqj e| wuhdwlqj1 47 Wkh iroorzlqj sdudphwhuv zhuh xvhg= F @ 4> He @ 3=:> Hq @ 4=4> Hj @ 4=5> wkh| lpso| dj @ 3=7 iurp +46, > dqg de @ =9 iurp +<,1 Rwkhu sdudphwhuv zhuh= % @ =8/ dqg @ =81. ..
(32) W(a). high resistance effect. .. low resistance effect. 0. ab. ag. ab 1. a. 6}hi G i| i TiU|i_ |L TihL_ @*i u?U|L? `i? |i tL*|L? t ?|ihLh @t ? 6}hi c |t ThLTih|it U@? Mi @?@*)3i_ uhL4 ' f At UL?_|L? 4@) Mi t@|ti_ L? @?) Lu |i |hii. Y` Y@. |i ht|Lh_ih UL?_|L?. @ ?|ih@*t L? U ` E@ t _i?i_. Aiti ?|ih@*t i@U ULhhitTL?_t |L @ T@h|U*@h. |ih@Ti|U h*i |L Mi ti_ ? TihL_ 2GD |i ThLTih|it Lu |i TihL_ tL*|L? 4@) Y` Y@. _gih @UULh_?}*) 5i||?} )i*_t L?i TLttM*i @*i Lu. @W. ' fc |i ht|Lh_ih UL?_|L? uLh @? ?|ihLh tL*|L? uLh i@U Lu |i ?|ih@*t 5?Ui |i ?|ih@*t @hi ?L|. Lih*@TT?} @?_ ULih @** TLttM*i ThLTLh|L?tc @?_ t?Ui |i. `. u?U|L? t UL?U@i tL. |@| |t 4@ 44 t ?^ic |ihi t @| 4Lt| L?i Lu |i |hii TLttM*i U@?__@|i @*it Lu ; A A A A ?. @W ' A A A A =. @W |@| @*tL *it ? |i ULhhitTL?_?} ?|ih@* Lu _i?|L? Lu ` E@ Etii ED @?_ ES G S . . . . E.} .? E .? 7 n 0 u f @W 2 .} 7 2 7 e .? 7 0 u 2 .} 7 @W 2 7 .K . } e3 e3 e 2 . . @W . 0 . } K ? K
(33)
(34) 7. 48 Dv. E. . 7. 7. u 2. 7. . E.. ghvfulehg lq wkh suhylrxv vhfwlrq/ iru d jlyhq sdudphwhu frpelqdwlrq/ wkh uxoh ghshqgv rq d. dqg frqvlvwv lq= hlwkhu +olqh 4 ri +4:,, wuhdwlqj doo suhylrxvo| wuhdwhg dqg doo qd yh sdwlhqwv lq vwdwh j zkloh wuhdwlqj doo qd yh sdwlhqwv dqg qr suhylrxvo| wuhdwhg rqhv lq vwdwh e> ru +olqh 5 ri +4:,, wuhdwlqj doo qdlyh sdwlhqwv/ dqg vrph suhylrxvo| wuhdwhg rqhv lq vwdwh j zkloh wuhdwlqj doo qd yh sdwlhqwv dqg qr suhylrxvo| wuhdwhg rqhv lq vwdwh e> ru hovh +olqh 6 ri +4:,, wuhdw doo qd yh sdwlhqwv dqg doo exw vrph suhylrxvo| wuhdwhg rqhv lq vwdwh j> zkloh wuhdwlqj doo qd yh rqhv dqg qrqh exw vrph ri wkh suhylrxvo| wuhdwhg rqhv lq vwdwh e1. 49 Zh. frqwlqxh zlwk wkh fdvh fdvh dj ? de > dv ehiruh lw lv lpphgldwh wr dgmxvw wkh irupxod iru wkh. dowhuqdwlyh fdvh fdvh dj. . de 1. H.
(35) 6Lh |i T@h@4i|ih UL4M?@|L? ti_ ? 6}hi c. |i tL*|L? t @W ' fD.G |t @*i . . . Lu @W c LM|@?i_ uhL4 |i |h_ *?i Lu E. c @*tL *it ? |i ?|ih@* 2 7 .K c c i dec o @t hi^hi_ 6Lh4*@ E. ?_U@|it |@| |i LT|44 ThLTLh|L? Lu T@|i?|t tM4||i_ |L Aih @T) ? }i?ih@* _iTi?_t L? 0 |i _hiU| i TiU|i_ T@|i?| |*|) }@? uhL4 |@| |ih@T) ? TihL_ c L? |i i TiU|i_ TihL_ 2 |*|) }@?t .} Lh .K |@| @hi 4@_i TLttM*i M) |i ti Lu Aih@T) ? TihL_ c L? |i |*|) }@? .? 4@_i TLttM*i ? TihL_ 2 M) @Mt|@??} uhL4 Aih@T) ? TihL_ c @?_ L? |i T@h@4i|iht S E?Lh4@*3i_ |L L?i @?_ 7 |@| U@h@U|ih3i |i i TiU|i_ ULt| Lu @TT*)?} Aih@T) ? TihL_ @?_ Aih@T). 2 ? TihL_ 2 5?Ui |i) @hi ?L| LMtihi_ i @?|ic TihL_ 2 ULt|t @?_ |*|) }@?t @hi i}|i_ @UULh_?} |L |i ThLM@M*|) |@| Aih@T) |h?t L| } D $tWttNA. D Ai LT|4@* _iUtL? Ai LT|4@* _iUtL? t|h@|i}) U@? Mi ?|ihThi|i_ @t @TT*)?} |i uL**L?} Th?UT*i W? TihL_ ULLti |i ThLTLh|L?. @. Lu T@|i?|t |hi@|i_ ? |i Uhhi?| TihL_c M| _L ?L|. UL44| |L @?) _iUtL? uLh TihL_ 2 W?t|i@_c TLt|TL?i |i TihL_ 2 _iUtL?c t4T*) ULLt?} |i h*i |@| ** Mi ti_ ? TihL_ 2c M@ti_ L? |i ?i ?uLh4@|L? |@| ** Mi @U^hi_ ? |i 4i@?|4ic @?_ L? |i ?|@* ULUi Lu @ Ai TihL_ 2 h*i _i?it |i ThLTLh|L?t Lu T@|i?|t uhL4 |i }hLT Lu ThiLt*) |hi@|i_ T@|i?|tc @?_ |i }hLT Lu ?@>i T@|i?|tc |@| ** hiUii Aih@T) 2 Ai ThL TLh|L?t _gih @UULh_?} |L |i }hLT UL?t_ihi_c @UULh_?} |L |i i L}i?Lt*) }@|ihi_ ?uLh4@|L? E|i t|@|i Lu ?@|hic @?_ @UULh_?} |L |i i?_L}i?Lt*) }@|ihi_ ?uLh4@ |L? E*i@h??} M) |hi@|?} L?ti^i?|*)c |i TihL_ _iUtL? L? 4: Vhh. irrwqrwh 471. @. @giU|t |i TihL_. Lw lv vlpsoh/ dowkrxjk whglrxv/ wr vshoo rxw wkh frqglwlrqv rq wkh prgho sd0. d wr olh lq hdfk ri wkh wkuhh srvvleoh lqwhuydov1 Iru wr olh lq ^de > 4` > wkh sdudphwhuv pxvw vdwlvi| de d 4 ru 5 F He h{dpsoh/ lq rughu 5 H F +4 , F He 7 Hq F % 41 Vhh wkh glvfxvvlrq ehorz iru dq lqwhusuhwdwlrq1 j 6 6 udphwhuv wkdw hqvxuh wkh pd{lpl}lqj ydoxh. d. b.
(36) 2 _iUtL? |hL} |L U@??i*t 6ht| | _i|ih4?it |i t3i Lu |i |L }hLTt Lu T@ |i?|t i t|?} @| |i Mi}???} Lu TihL_ 2 5iUL?_ | _i|ih4?it @| t !?L? @ML| ?__@* T@|i?|t hitTL?ti?itt |L |ih@T) @4L?} |i }hLT Lu ThiLt*) |hi@|i_ T@|i?|t( |t ? |h? @**Lt |i U*?U@? |L _tUh4?@|i Mi|ii? ThiLt*) |hi@|i_ T@|i?|t @UULh_?} |L |ih ttUiT|M*|) |L |hi@|4i?| N?_ih tU UhU4t|@?Uitc |i TihL_ ULUi Lu. @. t ?L| M@ti_ L?*) L? TihL_. ULt|t @?_ Mi?i|t( | @*tL tii!t |L ThL4L|i u|hi i TLthi |L }LL_ L|UL4it @?_ hi_Ui i TLthi |L M@_ L|UL4it AL **t|h@|i M) @) Lu |i tL*|L? ULhhitTL?_?} |L 6}hi @}@?c ihi @W t }i? M) |i |h_ *?i ? E. c UL?t_ih |i LT|4@* tiUL?_ TihL_ UL?|?}i?| t@hit ? |@| ?t|@?Ui W? U@ti Aih@T) |h?t L| |L ?_Ui h@* hitt|@?Ui EL|UL4i Kc |i i TiU|i_ ?i|LuULt| |*|) }@? uhL4 Aih@T) 2 L*_ Mi ?i}@|i L? @ih@}i uLh ThiLt*) |hi@|i_ T@|i?|tG 3ihL i TLthi |L |@| M@_ L|UL4i UL*_ Mi @Uii_ M) ?L| @_4?t|ih?} @?) |ih@T)( Liihc @4L?} |iti T@|i?|tc |i Mit| hitTL?_?} L?it L*_ Mi?i| uhL4 Aih@T) 2c ThL_i_ |i U*?U@? @_ i?L} ?uLh4@|L? |L ti*iU| |i4 | tUi?| ThiUtL? At U@? Mi _L?i L?*) u i?L} *i@h??} M) |hi@|?} @t LUUhi_ ? TihL_ Ai ht| TihL_ t@hi Lu T@|i?|t ?_ih}L?} Aih@T) t |ihiuLhi ti| }ih |@? | L*_ Mi L|ihti t u@h @t ?@>i T@|i?|t @hi UL?Uih?i_c |i ?i| i TiU|i_ }@? Lu @_4?t|ih?} Aih@T) 2 t TLt|i L? @ih@}i uLh @?) @( *ic i TLt|c tL4i Lu |i4 4@) |h? L| ?L| |L hitTL?_ i**c |ihi t ?L @) |L ti*iU| |i4 @?_ *i@i |i4 ?|hi@|i_ MiU@ti ?L ?uLh4@|L? @t Mii? }@|ihi_ @ML| |i4G 4@ 44 i TLthi t @Uii_ M) @_4?t|ih?} |i |ih@T) |L @** ?@i T@|i?|t W? U@ti Lu @ }LL_ L|UL4i. }. uLh Aih@T) c |i ?i| i TiU|i_ }@? Lu @_4?t|ih?}. Aih@T) 2 |L ThiLt*) |hi@|i_ T@|i?|t t TLt|i L? @ih@}iG @ } i TLthi U@? Mi @Uii_ M) @_4?t|ih?} |i |ih@T) |L @** tU T@|i?|t( Liihc i TLt|c tL4i Lu |i4 4@) t|** |h? L| |L hitTL?_ TLLh*) uh|ih }@? U@? Mi @Uii_ u |i *i@t| ttUiT|M*i T@|i?|t U@? Mi ti*iU|i_ | i?L} @UUh@U) @?_ *iu| ?|hi@|i_ }@?c |i _iUtL? 4@!ih @U^hit |@| @M*|) M) |hi@|?} 4Lhi T@|i?|t ? TihL_ |@? ti 2f.
(37) L*_ L|ihtic |ihiM) ?Uhi@t?} i TLthi |L |i }LL_ L|UL4i L tU TLttM*|) i t|t | hitTiU| |L ?@>i T@|i?|tG |i) @** hiUii Aih@T) 2. D2 Vh@* hitt|@?Ui @?_ |ih@Ti|U LTTLh|?|) ULt| t 4i?|L?i_ @| |i Mi}???} Lu |t T@Tihc @ 4@Lh tti ? O+A |ih@T) t |i _ii*LT4i?| Lu hitt|@?Ui |L |hi@|4i?|t Ai 4@}?|_i Lu |i i TiU|i_ h@* hitt|@?Ui igiU| t .? .K : f ? |i L|ih @?_ |ihi t @? LTTLh|?|) ULt| Lu ?L| @_4?t|ih?} @ O+A |ih@T) MiuLhi |i TLttM*i @_ihti hitt|@?Ui igiU| t !?L?G |i T@|i?| 4@) _i|ihLh@|i |L |i TL?| Lu ?L| Mi?} @M*i |L Mi?i| uhL4 ?i |ih@Ti|U _ii*LT4i?|t Ai 4@}?|_i Lu |i i TiU|i_ |ih@Ti|U LTTLh|?|) ULt| t. .}. . .? . Ai _*i44@. u@Ui_ M) |i U*?U@? _iUtL? 4@!ih ? TihL_ hit*|t uhL4 |i |i?tL? Mi|ii? |iti |L 4@}?|_itc @?_ |@!it @** |t _h@4@|U ti?ti i? |i LT|4@* @*i Lu @ t ?|ihLhG ? tU U@tic L?i L*_ i TiU| |i LT|4@* @*i Lu @ |L Mi ti?t|i |L ML| |i hitt|@?Ui igiU| @?_ |i |ih@Ti|U LTTLh|?|) ULt|c 4@!?} |iti tUi?|U _@|@ UhU@* |L |i |ih@Ti|U _iUtL? At ?||L? |h?t L| ?L| |L Mi ?iUitt@h*) |hi Lhi ThiUti*)c ?_ih T@h@4i|ih hit|hU|L?t ULhhitTL?_?} Mit| |L |i i @4T*i Lu O+A |ih@Titc |i 4@}?|_i Lu |i hitt|@?Ui igiU| t hhi*i@?| ThL_i_ | t M} i?L} 6}hi @t Mii? _it}?i_ |L **t|h@|i |t T@h@_L U@* hit*| Ai UL?|?Lt Uhi **t|h@|i @ T@h@4i|ih UL4 M?@|L? ihi. .K. c *i | t@|tit hit|hU|L?t E @?_ ES c t hi*@|i*) } At. 4i@?tc L|ih |?}t i^@*c |@| |i i TiU|i_ h@* hitt|@?Ui igiU| .? .K t hi*@|i*) t4@** W? |@| U@tic |i LT|4@* @*i @W LUUht |L |i h}| Lu @K At ULhhitTL?_t |L @ @*i Lu @ |? |i |h_ TLttM*i ?|ih@*c d@K c o c tL |@| |i tL*|L? t }i? M) |i |h_ *?i Lu E. G |i uLh4*@ ?_U@|it |@| @t ?||L? t}}it|tc. W. @. W. @. ? |@| U@ti _iTi?_t L?. .K. ( ThiUti*)c. t @ _iUhi@t?} u?U|L? Lu |i i TiU|i_ h@* hitt|@?Ui igiU|. OLiihc @| }ih *ii*t Lu |i hitt|@?Ui igiU|c |i t|@|L? t _gihi?| @t **t|h@|i_ M) |i _@ti_ Uhi Ai? |i LT|44 LUUht ? |i tiUL?_ ?|ih@* d@} c. o ML|. @K c. MiU@ti |i ` E@ Uhi @t @ _gihi?| t@Ti @?_ MiU@ti |i @*i Lu @K t ?L }ih. 2.
(38) ? |@| ?|ih@*c @t U@? Mi ihi_ M) ?tTiU|?} |i tiUL?_ *?i Lu E. c. W. @. _Lit ?L|. _iTi?_ L? .K LhiLihc |i hitt|@?Ui igiU| 4@) ?Uhi@ti M) @?) @4L?| Ei. .K. 4@). _4?t M) @?) @4L?|c |ihi ** Mi ?L igiU| L? |i LT|44 W? u@U| |i }ih |i i TiU|i_ h@* hitt|@?Ui igiU|c |i tLh|ih |i ?|ih@* d@K c o Lih U | t hi*i@?|( |@| ?|ih@* 4@) ii? _t@TTi@h `@| t |i iUL?L4U @?_ |ih@Ti|U ?||L? i T*@??} |t ?i TiU|i_ hit*|q W| hit_it | |i _iUtL? h*i |L 4?43i i TLthi |L M@_ L|UL4it @?_ 4@ 43i i TLthi |L }LL_ L|UL4itG i? |i hitt|@?Ui igiU| t }c |i LT|4@* h*i t |L ULLti 3ihL i TLthi |L |i M@_ L|UL4i OLiih 3ihL i TLthi t UL4T@|M*i | tL4i T@|i?|t hiUi?} Aih@T) ? TihL_ G | t @Uii_ M) ?L| @_4?t|ih?} Aih@T) 2 |L |iti T@|i?|t ? U@ti Aih@T) |h?t L| K OLiihc u Aih@T) |h?t L| } c @?} @ TLL* Lu ThiLt*) |hi@|i_ T@|i?|t @**Lt @ Mi||ih i TLthi |L |i }LL_ L|UL4i At hit*| LUUht ? @ uh@4iLh! |@| 4@) Mi 4Lhi Lu @? i @4T*i |@? @ }i?ih@* U@ti OLiih |t i @4T*i t M@ti_ L? !i) ui@|hit Lu O+A |ih@Tit @?_ L? 4TLh|@?| t|)*3i_ u@U|t W? T@h|U*@h |i ThLTLh|L?t Lu T@|i?|t hiUi?} |ih@T) ? ML| TihL_t @hi t|hU|*) ?|ihLhH wi@h??} Uhi@|it i|ihL}i?i|) @4L?} T@|i?|t Ai 4L_i* tLt |@| |i TLttM*i hhi*i@?Ui Lu |i hitt|@?Ui igiU| t UL4T@|M*i | _gihi?Uit ? T@|i?| hitTL?ti?ittc @*|L} |iti _gihi?Uit U@? Mi tL? ?L| |L Mi ?iUitt@h) uLh |i hit*| |L LUUh Ai) @hi t4T*) L?i Lu |i 4@? t|U@|L?t uLh LMtihi_ _gihi?Uit ? ?__@* |hi@|4i?|t AL ui@|hit @hi 4TLh|@?| |L |i hit*| Ai ht| L?i t |i Thiti?Ui Lu @| *i@t| |L _t|?U| }hLTt Lu T@|i?|t ? TihL_ 2c hit*|?} ? @ 4 |hi Lu ULh?ih tL*|L?t @?_ ?|ihLh tL*|L?t W? @ 4L_i* ihi @** tL*|L?t ihi ?|ihLhc |i hit*| L*_ ?L| L*_c MiU@ti |ihi L*_ ?L| i t| @?) t|@|L? ihi |i _iUtL? 4@!ih UL*_ @L_ i TLthi |L |i M@_ L|UL4i UL4T*i|i*) ,i? |L}c |i ?||L? MhL}| T M) Lh 4; Wkhuh. duh vhyhudo uhdvrqv zk| sursruwlrqv ri sdwlhqwv wuhdwhg pljkw eh lqwhulru/ vrph ri zklfk suredeo| frpsdwleoh zlwk vrph uhohydqfh iru wkh uhvlvwdqfh hhfw1 Krzhyhu/ wkh vlpsohvw zd| wr jhqhudwh lqwhulru sursruwlrqv ri sdwlhqwv lv wr dvvxph lqfuhdvlqj h{shfwhg shu sdwlhqw frvwv/ dqg wkh prvw qdwxudo zd| wr gr vr lq wkh devhqfh ri sdwlhqw vshflf lqirupdwlrq lv wr dvvxph wkdw h{shfwhg shu sdwlhqw frvwv ghshqg rqo| rq wkh qxpehu ri sdwlhqwv uhfhlylqj wkh wkhuds|1 Vxfk d prgho/ dowkrxjk ohvv vrsklvwlfdwhg/ jhqhudwhv vlplodu uhvxowv1. 22.
(39) hit*| L*_ i*T i@*@|i |i t|@|L?G u |i _iUtL? 4@!ih U@? hi_Ui i TLt|L? |L |i M@_ L|UL4i M) ULUi Lu TihL_ 2 _iUtL? h*ic |i? |i 4@}?|_i Lu |i M@_ L|UL4i _Lit ?L| 4@||ih @t 4U W? |i Thiti?| 4L_i*c U@?}it ? i TiU|i_ h@* hitt |@?Uic i? } i?L}c _L ?L| @giU| TihL_ 2 _iUtL? UL?Uih??} ThiLt*) |hi@|i_ T@|i?|tG ?L?i t }i? Aih@T) 2 ? t|@|i. K. Ai tiUL?_ ui@|hi t |i hhiihtM*|). Lu |i @U|L?t |@!i? M) |i _iUtL? 4@!ihc UL4M?i_ | ?Uih|@?|) |@!?} |i uLh4 Lu ?i ?uLh4@|L? @hh?} Lih |4i `|L| |t tiUL?_ ui@|hic |ihi L*_ Mi ?L i TLthi |L |i M@_ L|UL4i t?Ui |i _iUtL? UL*_ Mi ?_L?i. D
(40) @|i?| L4L}i?i|)c *i@h??}c @?_ hi@* LT|L?t AL @ }LL_ U*?U@?c i@U T@|i?| t ?^i vi|c ?*itt tTiUU ?uLh4@|L? t !?L? @ML| ?__@* T@|i?|tc |i) 4t| Mi UL?t_ihi_ L4L}i?Lt wi@h??} @ML| ?_ _@* i@*| U@h@U|iht|Ut t @ |ih@Ti|U @U| h 4L_i* t|hittit |t ui@|hi M) @tt4?} |@| ?L tTiUU ?uLh4@|L? t !?L? @| ht| @ML| ?__@*t ? |i _i }hLT Lu OWV ?uiU|i_ T@|i?|tc M| |@| *i@h??} @ML| ?__@*t LUUht M) |hi@|?} L?ti^i?|*)c @| |i Mi}???} Lu TihL_ 2c |ihi t @ }hLT Lu i|ihL}i?Lt ?__@*tc UL?tt|?} Lu T@|i?|t L @i hiUii_ Aih@T) ( @?_ @ }hLT Lu L4L}i?Lt ?__ @*tc UL?tt|?} Lu ?@>i T@|i?|t W? |i ht| }hLTc |i U*?U@? t @M*i |L ti*iU| T@|i?|t @UULh_?} |L i TiU|i_ hitTL?ti?itt |L Aih@T) 2( ? |i tiUL?_ }hLTc |i U*?U@? t ?@M*i |L 4@!i tU @ _t|?U|L? At *i@h??} M) |hi@|?} ThL_Uit T@|i?| _u uihi?|@|L?c @?_ T@|i?| _gihi?|@|L? U@? Mi ti_ uLh @ Mi||ih @**LU@|L? Lu hitLhUit _iL|i_ |L Aih@T) 2 Etii LtU@?h @?_ 54|c 2ffc uLh @ i L? i Tih4i?|@|L? wi@h??} M) |hi@|?} t i?_L}i?Lt ? |@| | _iTi?_t L? @ Aihi t @*tL i L}i?Lt *i@h??} ? |i _iUtL? ThLM*i4 @__hitti_ ? |t T@Tih( | |@!it |i uLh4 Lu ?uLh4@|L? MiUL4?} @@*@M*i @| |i Mi}???} Lu TihL_ 2 ?L 4@||ih |i _iUtL? L? @ At ?uLh 4@|L? L? ?_Ui_ h@* hitt|@?Ui hit*|t uhL4 |i }i?ih@* +:# @?_ i Tih4i?|@|L? U@hhi_ L| ?_iTi?_i?|*) Luc M| LMtihi_ M)c |i _iUtL? 4@!ih , L}i?Lt *i@h??} Lih |4i t |)TU@* Lu hi@* LT|L?t W| t ?Uih|@?|) L? u|hi h@* hitt|@?Ui TLttM*) ?_Ui_ M) Aih@T) c UL4M?i_ | |i hhiihtM*|) Lu @?) 2
(41).
(42) @U|L? ULti? ? TihL_ c |@| }it hti |L |i T@h|U*@h _iUtL? h*i _itUhMi_ @MLiG ThL4L|i u|hi i TLthi |L }LL_ L|UL4it( @L_ u|hi i TLthi |L M@_ L?it vi| |i ThLM*i4 _giht uhL4 4Lt| |)TU@* hi@* LT|L? ThLM*i4t bEi} # | @?_ ?_)U!c bbe ? @| *i@t| |hii hitTiU|t 6ht| |i uLUt L? |4?} t *4|i_ ihi @t |ihi @hi L?*) |L TihL_t W? @ |)TU@* hi@*LT|L? ThLM*i4c ULLt?} @? i ihU3i _@|i LT|4@**) t Ui?|h@* |L @Ui?} |i }it| TLttM*i @*i uLh |i LT|L? Ai @*i Lu i M*|) *it ? |i @M*|) |L 4@!i |@| ULUi Oihi |i |4?} i M*|) UL?tt|t ? _iU_?} @| |L _L @| |L TL?|t ? |4i( @*|L} *4|i_c |t i M*|) }i?ih@|it @? LT|43?} Mi@Lh U t |)TU@* Lu hi@* LT|L?t Ai tiUL?_ _gihi?Ui t |@| ML| |i t|@|i @?_ |i ?@|hi Lu |i _iUtL? U@?}i Lih |4i ? Lh O+A 4L_i*c *ic ? @ |)TU@* hi@* LT|L? 4L_i*c |i t|@|i U@?}it M| |i _iUtL? hi4@?t |i t@4i Ei} ?it| Lh ?L| W?_ii_c ? TihL_ 2 Lu Lh 4L_i*c |i U*?U@? _iUtL? 4@!ih u@Uit ML| @ _gihi?| t|@|i Lu ?@|hi E|i igiU| Lu Aih@T) L? Aih@T) 2 @t Mii? hii@*i_ @?_ @ ?i ti| Lu _iUtL?t E@_4?t|ih Aih@T) 2 Lh ?L|c h@|ih |@? Aih@T) `i |?! |@| |t t @? 4TLh|@?| ui@|hi Lu 4@?) _iUtL? ThLM*i4tc ?U*_?} i@*| U@hi _iUtL?tc |@| ?ii_t uh|ih @?@*)tt }L?} Mi)L?_ |i Uhhi?| T@Tih Ai |h_ _gihi?Ui t i?_L}i?Lt *i@h??}( i?_L}i?Lt *i@h??} t ?L| ?UL4T@|M*i | hi@* LT|L?t( | t t4T*) ?L| Lu|i? ?|hL_Ui_ ? |@| *|ih@|hi S NAW,tNA BAa ,6|B|NAt Ai @__|L?@* }@?t ? *ui i TiU|@?U) @ttLU@|i_ | O+A UL4M?@|L?t @hi ?L| )i| ThiUti*) !?L? 5|_it |@| @||i4T|i_ |L 4L_i* |i 4T@U| Lu @?|hi|hLh@* |hi@| 4i?|t @i ThL_i_ it|4@|L?t ? |i h@?}i Lu S |L 2e )i@ht uLh |i ?Uhi@ti ? @? ?__@*<t *ui i TiU|@?U) uhL4 OWV ?uiU|L? |L _i@| uLh T@|i?|t |hi@|i_ ? Lh| 4ihU@ E*Lihc Bihti?}Lh? : Bh@?|c 2fff (`LL_ i| @*c 2fff@ OLiihc ?Uih|@?|it hi4@? @ML| |i *L?}|ih4 iU@U) Lu O+A |ih@Tit 4< Wkhuh. duh ihz lqvwdqfhv ri uhdo rswlrqv ehlqj xvhg lq irupxodwlqj khdowk ghflvlrqv1 Wkh rqhv wkdw zh duh dzduh ri kdyh wr gr zlwk lqyhvwphqwv lq htxlsphqwv ru whfkqrorj| +Pruhwwr ) Ohydjjl/ 5337> Sdophu dqg Vplwk 5333,1 D uhodwhg olwhudwxuh dgguhvvhv irrg vdihw|/ elrglyhuvlw|/ jhqhwlfdoo| prglhg fursv/ dqg uhvlvwdqfh wr dqwlelrwlfv ru shvwlflghv +Pruho hw do1/ 5336> Od{plqdud|dq/ 5336> Ndvvdu dqg Odvvhuuh/ 5337> Vdolq/ 5333,1. 2e.
(43) 6Lh i @4T*ic hiUi?| i_i?Ui @t tL? |i Tihtt|i?Ui Lu h@* hiT*U@|L? ii? ? tU Uittu**) |hi@|i_ T@|i?|t E~@?} i| @*c bbb( 6?3 i| @*c bbb W? tU UL?|i | | t ?L| thTht?} |@| UL4T*i|i UL?ti?tt @t ?L| Mii? hi@Ui_ Lh*__ic @4L?} U*?U@?t @?_ i@*| @|Lh|itc @ML| |i Mit| t|@?_@h_t Lu Th@U|Ui uLh O+A _i*ih) W? T@h|U*@hc U*?U@* }_i*?it t|** _gih Mi|ii? UL?|hitc @?_ tL4i|4it ?t_i i@U UL?|h)c @ML| |i i*}M*|) Uh|ih@ uLh O+A ?|@|L? ,4ThU@* t|_it _h@ UL? U|?} UL?U*tL?t L? |i 4@||ihG tL4i Lu |i4 t|hL?}*) ^it|L? @}}hitti i@h*) ti Lu O+A EAiM@t i| @*c 2ffc ihi@t L|iht @_LU@|i ih) i@h*) ?|@|L? E@t tLL? @t OWV?uiU|i_ T@|i?|t @i *itt Dff #e Ui**t%4UhLw L? ULt|igiU|i?itt }hL?_t E5U@U!4@?c 2ff W?|ihit|?}*)c |i uLh4ih |h) |L @UUL?| uLh |i hitt|@?Ui igiU| *i |i *@||ih }?Lhi | LhiLihc @|iih |i }_i*?itc thi)t @4L?} ThitUhM?} T)tU@?t tL @ }hi@| @h@M*|) Lu @|||_it |L@h_ ?|@|L? Lu O+A |hi@|4i?| EM@_@ i| @*c bbb ( +ii_! i| @*c bbb ( k|@@|@c V@? +L4T@i) : 5i*_tc 2fff ( w@?_4@? i| @*c 2fff W? _ii*LT?} UL?|hitc ihi |i @t| 4@Lh|) Lu OWV ?uiU|i_ TiLT*i Uhhi?|*) *ic @UUitt |L @?|hi|hLh@* |hi@|4i?| @t ?L| UL?t_ihi_ @ ui@tM*i |iU?U@* @?_ iUL?L4U LT|L? ?|* hiUi?|*) EV@? h@@} i| @*c bb.( ?tLh| @?_ AiL!*c 2fff 6L**L?} |i N?|i_ @|L?t Bi?ih@* tti4M*) 5TiU@* 5ittL? L? W#5 ? 2ffc @ 4*|*@|ih@* B*LM@* 6?_ |L 6}| W#5c AMihU*Ltt @?_ @*@h@ @t Mii? it|@M*ti_ @| |i Mi }???} Lu 2ff2c @?_ |i }L@* Lu tU@*?} T @UUitt |L O+A ? _ii*LT?} UL?|hit t ?Uhi@t?}*) t@hi_ M) }Lih?4i?|t @?_ ?|ih?@|L?@* _L?Lh Lh}@?t@|L?t i|ii? bbS @?_ 2fffc i Ti?ti _h} ULt|t ihi |i 4@Lh M@hhih uLh _gtL? Lu O+A ? |iti UL?|hit W? |i *@t| |hii )i@htc t}?U@?| hi_U|L?t ? |i ThUit Lu @?|hi|hL h@* @?_ L|ih OWVhi*@|i_ _h}t @i Mii? MhL}| @ML| ? _ii*LT?} UL?|hit | |i }hi@|it| ?ii_ uLh @UUitt |L O+A h t4T*i t|LU@t|U _)?@4U 4L_i* Lu @ ti^i?|@* |ih@Ti|U ULUi | ?|ih4i _@h) hii*@|L? @?_ @U^t|L? Lu ?uLh4@|L? ?_ih*?it |i 4TLh|@?Ui Lu i TiU|@|L?t @ML| igiU|i?itt @?_ ULt|t ? Uhhi?| @?_ u|hi |ih@Titc @t i** @t |i 4TLh|@?Ui Lu ?_Ui_ h@* hitt|@?Ui @?_ |ih@Ti|U LTTLh|?|) ULt| Ai ui@h |@| _gtL? 2D.
(44) Lu O+A 4@) tThi@_ h@* hitt|@?Ui |i?_t |L MiUL4i |i 4Lt| TLihu* @h}4i?| ? u@Lh Lu *4|?} Lh _i*@)?} @UUitt |L @?|hi|hLh@* |hi@|4i?| | |i i4ThU@* *ii*c |ihi t i_i?Ui uhL4 |i h@3*@? ThL}h@44i Lu ?iht@* ULih@}i uLh O+A @?_ uhL4 T*L| i Tih4i?|t ? uhU@? UL?|hit tU @t 5i?i}@* @?_ N}@?_@ |@| h@* hitt|@?Ui @?_ ?L?@_ihi?Ui @hi ?L| @ }hi@|ih ThLM*i4 ? ULLh|t Lu T@|i?|t |hi@|i_ ? _ii*LT?} UL?|hit i? UL4T@hi_ |L _@|@ uhL4 _ii*LTi_ UL?|hit EA@?h i| @*c 2ff2( 5*ih@ i| @*c 2ff2( `i_*i i| @*c 2ff2( w@hi?| i| @*c 2ff2 N?*@|ih@* @|||_it @?_ @h}4i?|tc tU @t |i L?it hiUL44i?_?} |L |L*_ Lh _i*@) @UUitt |L O+A ? Uih|@? }hLTt Lu T@|i?|t Lh UL?|hit E5i?@!c bb. ( 5|i@h|c bb. ( #c bbH uLh ui@h Lu TLttM*i _gtL? Lu _h}hitt|@?| OWV t|h@?tc i Thitt ih) ^it|L?@M*i 4T*U| |h@_iLgt LhiLihc @ 4@? UL?U*tL? Lu Lh 4L_i* t |@|c i? |ihi t @ t}?U@?| ht! Lu hitt|@?Ui _i |L |ih@Ti|U u@*hi Lu ?|@* i t|?} |hi@|4i?|tc _gihi?Uit ? |i it|4@|L? Lu |t ht! tL*_ ?L| ?i?Ui |i LT|4@* _iUtL? @ML| |i t3i Lu |i OWV?uiU|i_ TLT*@|L? i*}M*i uLh ?|@|L? Lu O+A @h@_L U@**)c | t ? |i U@ti ihi i TiU|@|L?t @ML| hitt|@?Ui @hi h@|ih LT|4t|U E|i Ti?L4i?L? ** Mi *4|i_ |@| _gihi?Uit ? it|4@|L?t Lu |t Ti?L4i?L? 4@) Mi @ u@U|Lh Lu @h@M*|) ? LT|4@* |hi@|4i?| ?|@|L? iU@ti |iti UL?U*tL?t @hi ^|i UL?|ih?||ic |i) 4@) i*T U*@hu) Uhhi?| ?UL?tt|i?Uit Mi|ii? hiUL44i?_@|L?t @?_ Th@U|U@* Mi@Lht Lu OWV%W#5 U*?U@?t @?_ TM*U i@*| i Tih|t L? |i L?i @?_c @?_ |i i Thitti_ ti| Lu Thiuihi?Uit @?_ i TiU|@|L?t Lu |iti t@4i _iUtL?4@!ihtc L? |i L|ih @?_ EBihMih| i| @*c 2fff 4@Lh *4|@|L? Lu Lh 4L_i* t |@| i uLUt L? |i 4T@U| Lu |i _iUtL? |L ?|@|i |hi@|4i?| L? @ TLT*@|L? U t @*hi@_) OWV?uiU|i_ 6hL4 @ TM*U i@*| TihtTiU|ic ?i}@|i i |ih?@*|it @ttLU@|i_ | |i _gtL? Lu hitt|@?| OWVt|h@?t ?|L |i hit| Lu |i TLT*@|L?c @hi 4TLh|@?| u@U|Lht EBiLg@h_c *TtL?c bbS h 4L_i* U@? Mi @_@T|i_ |L |@!i |iti i |ih?@*|it ?|L @UUL?|. 2S.
(45) +,6,+,,5 W5`+AOc @?_ A,kNwc ` E2fff hi@!?} |i t*i?UiG ti||?} hi@*t|U ThLh|it uLh W#5 UL?|hL* ? *itt _ii*LTi_ UL?|hit w@?Ui|
(46) DSc DDSf h|t OWV @ttLU@|L? EOWV B_i*?it LLh_?@|?} L44||ii Ebb. B_i *?it uLh @?|hi|hLh@* |hi@|4i?| Lu OWV tihLTLt|i ?__@*t w@?Ui|c
(47) ebc feSfb2 w`,+c 5c B,+5O,B+c Oc B+Ac + E2fff |@*i Lu |L u|hit G OWV @?_ @?|hi|hLh@* |ih@T) ? 5@? 6h@?UtUL 5Ui?Uic 2H.c SDfSDe +,A,+c ac ,+c #c 6W5Owc i| @* Ebb. ?|hi|hLh@* |ih@T) uLh OWV ?uiU|L? ? bb. NT_@|i_ hiUL44i?_@|L?t Lu |i W?|ih?@|L?@* W#5 5LUi|)N5 T@?i* ac 2..c bS2bSb i?|ih uLh #ti@tit L?|hL* E# EbbH +iTLh| Lu |i WO @?i* |L _i?i Th?UT*it Lu |ih@T) Lu OWV ?uiU|L? B_i*?it uLh |i ti Lu @?|hi|hLh@* @}i?|t ? OWV?uiU|i_ @_*|t @?_ @_L*itUi?|t `+ c e. E++Dc e
(48) H2 #,w6+W55vc a6 E,_ Ebbb B_i*?it uLh |i ti Lu @?|hi|hLh@* |ih@Tit ? OWV ?uiU|L? +iTLh| |L |i ?t|h) Lu Oi@*| : 5LU@* g@ht 6*@44@hL? ,_tc @ht #,55c #c 6w#+,c c wV,~c V E2fff iU@?t4t Lu hL*L}U u@* hi ? ThiLt*) ?|hi@|i_ OWV?uiU|i_ T@|i?|t uhL4 @ |h@* Lu ?_U|L?4@?|i?@?Ui |ih@T) Ah* i}i E}i?Ui @|L?@*i _i +iUihUit th *i 5W# f.2 5|_) Ai@4 ac 2H
(49) c 2fD #,,k5c 5Bc 5WAOc c Ow#Wvc : kOc a Ebb. OWV ThL|i@ti ?M|Lht hii uLh U*?U@?t ac 2..c eDD
(50) #,w6+W55v a 6 Ei_ E2ff2 hti i? U@h}i _it TihtL??it ?uiU|iit T@h *i VWO +@TTLh| 2ff2 +iUL44@?_@|L? _ }hLTi _<i Tih|t @ ?t|hi _i *@ 5@?|ic _i *@ 6@4**i i| _it TihtL??it @?_U@Tiit i_iU?i 5Ui?Uitc 6*@44@hL?G @ht #WjWAc @?_ W#vkc + 5 Ebbe W?it|4i?| ?_ih N?Uih|@?|) h?Ui|L? N?iht|) hittG h?Ui|L? 6W~W #c wk5 ac 5WwwW a# i| @* Ebbb w@|i?| ?uiU|L? Lu #enA Ui**t ThL_it @ 4iU@?t4 uLh *ui*L?} Tihtt|i?Ui Lu OWV ii? ? T@|i?|t L? igiU|i UL4M?@|L? |ih@T) @| i_c Dc D2D. BwwAc a, E2fff 5|h@|i}it uLh *L?}|ih4 tUUitt ? |i |hi@|4i?| Lu OWV ?uiU|L? ac 2H
(51) c
(52) 2b
(53)
(54) e B,66+#c vc OWwW5c A EbbS +@|L?@* iT_i4Ut @?_ |ih TM*U UL?|hL* W?|* ,UL +ic
(55) .c Sf
(56) S2
(57) B,+,+Ac c +5A,c c wc kc ,++W,c c B5 ,+Bc # E2fff L4M?@|L? @?|hi|hLh@* |ih@T) G i@*| U@hi ThL_iht UL?uhL?| i4ih}?} _*i44@t W#5 +,c 2c efbe2 O,+c 5 i| @* E2ff2 5U@*?} T @?|hi|hLh@* |ih@T) ? hitLhUi*4|i_ ti||?}tG }_i*?it uLh @ TM*U i@*| @TThL@U `Lh*_ Oi@*| h}@?3@|L?c Bi?i@ O,OAc 6 c B+Ac + c ,A+Nw5c ac i| @* EbbH 5i @* |h@?t4ttL? Lu @? OWV @h@?| hitt|@?| |L 4*|T*i hiihti|h@?tUhT|@ti @?_ ThL|i@ti ?M|Lht i ,?}*@?_ aLh?@* Lu i_U?ic
(58)
(59) bc
(60) f. 2..
(61) OBBc +5c O,AOc kVc vWc i| @* EbbH@ W4ThLi_ th@* @4L?} OWV ?uiU|i_ ?__@*t uL**L?} ?|@|L? Lu @?|hi|hLh@* |ih@T) ac 2.bc eDfeDe OBBc + 5( vWc ( Oc k a( `#c ,( +Wc k a( <5ONBO,55vc V( A,+c a 5 E2ff +@|it Lu _ti@ti ThL}hittL? M) M@ti*?i #e Ui** UL?| @?_ h@* *L@_ @u|ih ?|@|?} |hT*i_h} |ih@T)c aG Ai aLh?@* u Ai 4ihU@? i_U@* ttLU@|L?c 2HSE2fc 2DSH2D.. W#,v+c V E2ff2 L?|??} _iM@|i Lih OWV |ih@T) ?|@|L?c OWV *?U@* Ah@*tc
(62) E2c .
(63) .S k55+c W @?_ w55,++,c E2ffe 5TiUit hitih@|L? @?_ L_iht|) V@*iG +i@* T|L?t TThL@Uc aLh?@* Lu ,?hL?4i?|@* ,UL?L4Ut @?_ @?@}i 4i?|c eHE2c HD..b kWAOAc c V +,vc 5,c 5OW,w#5c ` E2fff )tU@? i Tihi?Ui ? |i U@hi Lu OWV?uiU|i_ TihtL?t t hi*@|i_ | i@h*ih @_LT|L? Lu ?i @?|hi|hLh@* |ih@T) a U^h W44?i #iU 5)?_h c 2ec fSe kv+WkW#,5c A ( BN+Wc E2ff A4?} Lu @?|hi|hLh@* |hi@|4i?| ?|@|L?c aG Ai aLh?@* u Ai 4ihU@? i_U@* ttLU@|L?c 2HDE
(64) c .f2 .f
(65) w#c +c AAWc ac ,++Wc Vc ON+#c : Ai 5|_) BhLT E2fff V@h@M*|) Lu @|||_it |L@h_ i@*) ?|@|L? Lu OA uLh OWV ?uiU|L?( @ t|_) Lu 6hi?U ThitUhM?} T)tU@?t W#5 +,c 2c ? Thitt wN+,Ac i| @* E2ff2 Ai 5i?i}@*iti }Lih?4i?|<t }*) @U|i @?|hi|hL h@* |ih@T) ?|@|iG @? H4L?| uL**LT t|_) W#5 Sc
(66) S
(67)
(68) .f wjW+vc + E2ff
(69) @||*?} +itt|@?Ui |L ?|ML|Ut @?_ it|U_it +itLhUit uLh |i 6|hic `@t?}|L?c #. w, WBc V( O,,c Bc ++W,+Wc ( wWNc ( +NV,~W,Ac 6( W+AOc w( 55NAc a ( AAWc a( +66Wc 6( w,+A i| @* E2ff2 hi_U|Lht Lu hL*L}U@* hiML?_ ? OWV?uiU|i_ T@|i?|t ?|@|?} @ ThL|i@ti ?M|Lh UL?|@??} hi}4i?c W#5 EwL?_L?c ,?}*@?_c SEc 22b wWAAw,c 5 a( OwA,c 5( +NAvc a( #+c , 5( +k`WA~c ( w wW,+c ( kNc +( ,ww+5c a `( Wkc ,( `v ,A w E2ff2 ?|hi|hLh@*_h} hitt|@?Ui @4L?} T@|i?|t hiUi?|*) ?uiU|i_ | OWVc Ai i ,?}*@?_ aLh?@* u i_U?ic
(70) e.ESc
(71) HD
(72) be +,wc c 6++f`c 5c `Nc 6c i| @* E2ff
(73) it|U_i hitt|@?Uic |i hiU@ |L?@h) h?UT*i @?_ |i hi}*@|L? Lu | ULh?G hi@* @?_ h@|L?@* LT|L? @TThL@Uit |L _iUtL? 4@!?} W?G wjW+vc + i_ @||*?} hitt|@?Ui |L @?|ML|Ut @?_ Tit|U_itG @? iUL?L4U @TThL@U +itLhUit uLh |i 6|hic `@t?}|L?c He2
(74) +,AAc : w,VBBWc + E2ffe W?it|4i?| ? OLtT|@* @hi AiU?L*L}) ?_ih #gihi?| hU@t?} +*itG +i@* T|L? TThL@Uc `Lh!?} @Tiht 2ffe.Dc 6L?_@3L?i ,? ,?hUL @||i 5+WWc B @?_ 5WAOc w E2ff Ai T|4@* wii* Lu , Tih4i?|@|L?c ,UL?L4i|hU@ Sbc S2bee N+Ovc , w( wwW,+c ( kwW5Oc w ( 55c 5 6( +c 6( 6wWBc A ( kN+c ( WA~c w( `wwOc 6 +( , ,A w E2ff 2H.
(75) O}*) @U|i @?|hi|hLh@* |ih@T) _iUhi@tit 4Lh|@*|) @?_ 4LhM_|) ? T@|i?|t | @_@?Ui_ OWV _ti@tic ??@*t u W?|ih?@* i_U?ic
(76) DEc .2S #Wcvc 5NVWww,cc +Wc c AAWc a Ebbb 6hi?U }i?ih@* Th@U|UL?iht<@|||_it |L@h_ |ih@Ti|U @_@?Uit ? OWV U@hi G hit*|t Lu @ ?@|L?@* thi) W?|* a 5A# : W#5c fc 2e
(77) 2eb w,+c 5 @?_ 5WAOc E2fff W?ULhTLh@|?} LT|L? @*it ?|L |i iUL?L4U i@*@|L? Lu i@*| U@hi |iU?L*L}itc aLh?@* Lu Oi@*| ,UL?L4Utc bEDc .DDSS A,+5c # wc 5`W#,ww5c 5c O+c a i| @* E2fff _ihi?Ui |L ThL |i@ti ?M|Lh |ih@T) @?_ L|UL4it ? T@|i?|t | OWV ?uiU|L? ?? W?|ih? i_c
(78)
(79) c 2
(80) f ,#+~c c #,w +,+c ac +w#c 6 Ebbb Oi|ihLti @* |h@?t 4ttL? Lu OWV t @ttLU@|i_ | } T*@t4@ h@* *L@_ *ii*t @?_ @ TLt|i h@* tL*@|L? ? |i ?uiU|i_ T@h|?ihc a U^h W44?i #iU 5)?_hc 2c 2f2D OWwwW5c ( 5A5~,`5kWc 5( `,,+c +( kW+kc ( 6+WwWc ( Www,+c V( V,+~~c ( wN#B+,c a #( w,#,+B,+,+c ( ,N+5W# 5AN#v B+N E2ff OWV h@* *L@_ hitTL?ti |L @?|hi|hLh@* |ih@T) @UULh_?} |L |i M@ti*?i #e Ui** UL?| @?_ h@* *L@_c aG Ai aLh?@* u Ai 4ihU@? i_U@* ttLU@|L?c 2HSE2fc 2DSf2DS. "NWc Ac ``,+c ac 5,`kc c i| @* E2fff Vh@* *L@_ @?_ i|ihLti @* |h@?t4ttL? Lu 4@? 44?L_iUi?U) ht |)Ti +@!@ hLiU| 5|_) BhLTc ,?}* a i_c
(81) e2c b2b2b +iUL44i?_@|L?t Lu |i @?i* L? *?U@* h@U|Uit uLh Ahi@|4i?| Lu OWV E2ff2 B_i*?it uLh t?} @?|hi|hLh@* @}i?|t @4L?} OWV?uiU|i_ @_*|t @?_ @_L*itUi?|t +iUL44i?_@|L?t ?_ +iTLh|tG LhM_|) ?_ Lh|@*|) `ii!*) +iTLh| i?|iht 6Lh #ti@ti L?|hL*c DE++.c DD +,,#aWkc c W#,w5c a,c O+5c ac `WB,+5c w Ebbb @?}?} @|||_it |L@h_t @?|hi|hLh@* |hi@|4i?| Lu OWV ?uiU|L? G @ ThLtTiU|i t|_) ? @ t@4T*i Lu #|U }i?ih@* Th@U|UL?iht W#5 +,c c eeD +W5AWBc ( +,5c "( k,,#vc ( `#,+wvc `( A,5c E2ff2 W?Uhi@t?} Thi@*i?Ui Lu hitt|@?Ui 4|@|L?t ? @?|hi|hLh@*?@>i ?__@*t | it|@M*ti_ OWV ?uiU|L? uhL4 bbS2ff ? 5| wLtc OWV *?U@* Ah@*tc
(82) E2c DD Sf +NWc +( ,+,BN,+c a( W+c a ( A,wc ( W+W++,c a ( B~w,~c a( BN,++c w( +,c 5( ++W~wBc a( wA,A ,A w E2ff2 +iUL44i?_@|L?t Lu |i 5T@?t W#5 5|_) BhLT EB,5W# @?_ |i @|L?@* _t *@? E5 uLh @?|hi|hLh@* |hi@|4i?| ? @_*| T@|i?|t | 4@? 4 4?L_iUi?U) ht ?uiU|L? ? 2ff2c ,?uih4i_@_it W?uiUULt@t ) UhLML*L}@ *? U@c 2fESc 2ee
(83) f
(84) 5wWc V E2fff +i@* T|L? TThL@U |L V@*?} 6LL_ 5@ui|) +t!tc U@T|ih ? ,UL?L4Ut Lu OG Lt|t @?_ i?i|tc w@h@? a N??iihc i_c ,@}@? hittG 5| @*c 22D2ef 5Okc +( Bw#W,c 5 a( `,W5A,Wc ( w5Wc ,( ~OBc O( 6+,,#,+Bc k E2ff Lt|igiU|i?itt Lu i@h*ih ?|@|L? Lu @?|hi|hLh@* 2b.
(85) |ih@T) uLh ??thi_ OWV?uiU|i_ @_*|tc 4ihU@? aLh?@* u M*U Oi@*|c bEbc eDSeS
(86) 5,kc Ebb. hi_U|?} @?|h@* UL4T*@?UiG T)tU@?<t hitTL?tM*|it t @|i?|t< h}|t a W?|* tt? )t ? W#5 @hic
(87) c eDH 5WwV,W+c A( #+5Ow,+c #, w( w,WA,c a #, ( WO,W+c A( # 5WwV,W+c V E2ff2 hi_U|Lht Lu ?_i|iU|@M*i T*@t4@ h@* *L@_ ? OWV TLt|i @_*|t hiUi?} @?|hi|hLh@* |ih@T) ? 5L|ih? h@3*c Ai h@3*@? aLh?@* u W?uiU|Lt #ti@titG ? U@* M*U@|L? u Ai h@3*@? 5LUi|) u W?uiU|Lt #ti@titc SEec Se. 5A,`+Ac B Ebb. _ihi?Ui |L @?|hi|hLh@* |ih@Tit W? V@? +Bc ,c 6,+vkc 5 : kA~c Ai 4T*U@|L?t Lu @?|hi|hLh@* |hi@|4i?|t W?uLh4@* UL?t*|@|L? Bi?i@c `O%NW#5c
(88) DDf AN+Wc ( +W#,c ,( #A5c ( +B#c B( ,wwc # w ( +B,5c 5( AV+,5c ( 6,++,W+c 5 ( 5A+w,5c B( + AW5 i| @* E2ff2 hi@*i?Ui Lu 4|@|L?t hi*@|i_ |L OWV @?|hi|hLh@* hitt|@?Ui ? h@3*@? T@|i?|t u@*?} O+Ac aLh?@* u *?U@* VhL*L})c 2DEc
(89) beS A,5c ( O,+vc k( ,5,c +( N+Ovc +( OW+c a( `#,+wvc ` B E2ff A4?} Lu @?|hi|hLh@* |ih@T)G Nti Lu @h!L 4L_i*?} @?_ _iUtL? @?@*)tt |L i@*@|i |i *L?}|ih4 4T*U@|L?t Lu |ih@T)c W#5 EwL?_L?c ,?}*@?_c DEDc DbDbb V O,,5`Wakc + ( V,w#kc ( Nw#,+c a `( ,,O+5Ac w( wB,c a ( ,Wa,c a O( O,A,w5c + E2ff L4M?@|L? Lu ThL|i@ti ?M|Lht uLh |i |hi@|4i?| Lu OWV?uiU|i_ T@|i?|tG @ hii Lu T@h4@ UL!?i|Ut @?_ U*?U@* i Tihi?Uic ?|h@* Aih@T)c SEec 2f22b V +Bc ,c 6,+vkc 5c kA~c Ebb. W4T@U| Lu @?|hi|hLh@* |hi@|4i?|t W?uLh4@* UL?t*|@|L? `O%5#%b.2c Bi?i@ V,wk,+c + Ebb. #iM@|?} _@* W#5 }_i*?it ac 2.Hc S
(90) `W,+Bc : 6+W,#w#c B EbbH M*U i@*| 4T*U@|L?t Lu @?| hi|hLh@* |ih@T) @?_ OWV _h} hitt|@?Ui ac 2.bc b..bH
(91) `,W#w,c a i| @* E2ff2 ttitt4i?| Lu @ T*L| @?|hi|hLh@* _h} |ih@T) ThL}h@44i ? N}@?_@G T@|i?|t< hitTL?tic th@*c @?_ _h} hitt|@?Ui w@?Ui|
(92) Sfc
Documents relatifs
Rqh ri wkh prvw dwwudfwlyh ihdwxuhv ri erxqghg0huuru hvwlpdwlrq lv wkh idfw wkdw lwv uhvxowv fdq eh jxdudqwhhg hyhq iru qrqolqhdu prghov dqg qlwh gdwd vhwv/ surylghg wkdw d ihz
• d’un appareil photo qui peut être utilisé pour mettre à jour le firmware de la télécommande radio sans fil (un D7100 est utilisé dans ce guide à
:H VKRZHG WKDW WKH (XURSHDQ VRLO IXQJDO GLYHUVLW\ YDULHV LQ WHUPV RI ULFKQHVV UHODWLYH DEXQGDQFH DQG GLVWULEXWLRQ DFFRUGLQJ WR ODQG XVHV IRUHVWV SDVWXUHV DUDEOH VRLOV VRLO
Imprimerie de ~ontligeon 61400 LA CHAPELLEMONTLIGEON Commission paritaire: n° 0708 T 83364 Dépot légal à parution. ISSN
In this subsection, we prove that computing the proper orientation number of a graph is still NP -hard for planar bipartite graphs of bounded degree.. The idea of our reduction
[r]
Li frvwv duh qlo/ wkh pdlq fkdqjhv duh lq vroxwlrq wr S 6= lq idfw htxdwlrq +54, ghvfulehv d vlwxdwlrq lq zklfk wkh sulqflsdo ghflghv wr lqyhvw lq LW iru doo w|shv ri djhqwv/ dqg wkh
WR HQVXUH WKDWDOO DVSHFWV RI UHSURGXFWLYH DQG VH[XDO KHDOWK LQFOXGLQJ LQWHU DOLD PDWHUQDODQG QHRQDWDO KHDOWK DUHLQFOXGHG ZLWKLQ QDWLRQDO PRQLWRULQJ DQG UHSRUWLQJ