Multi-view dimensionality reduction for multi-modal biometrics
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(2) 2013-ENST-0061. EDITE - ED 130. Doctorat ParisTech THÈSE pour obtenir le grade de docteur délivré par. TELECOM ParisTech Spécialité « Signal and Image » présentée et soutenue publiquement par. Xuran ZHAO 24.10.2013. Réduction de la Dimensionalité Multivue pour la Biométrie Multimodal. Directeur de thèse : Nicholas Evans & Jean-Luc Dugelay. Jury M. Fabio Roli, Professeur, University of Cagliari M. Christophe Rosenburger, Professeur, ENSICAEN M. John Mason, Professeur, Swansea University M. Vincent Despiegel, Chercheur, MORPHO M. Nicholas Evans, Maitre de conférences, EURECOM M. Jean-Luc Dugelay, Professeur, EURECOM TELECOM ParisTech école de l’Institut Télécom - membre de ParisTech. Président Rapporteur Rapporteur Examinateur Directeur de thèse Directeur de thèse.
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(4) ❆❝❦♥♦✇❧❡❞❣❡♠❡♥+, ❚❤"❡❡ ②❡❛"& ❛❣♦ ✇❤❡♥ ■ ❣♦, ♠② ♠❛&,❡" ❞❡❣"❡❡✱ ■ &❛✐❞ ,♦ ♠②&❡❧❢✿ ✏■ ❞♦♥✬, ✇❛♥, ,♦ ❜❡ ❛ &♦❢,✇❛"❡ ❡♥❣✐♥❡❡"✱ &♦ ■ ✇✐❧❧ ❞♦ &♦♠❡ "❡&❡❛"❝❤ ✐♥&,❡❛❞✑✱ ❛♥❞ ,❤❛, ✇❛& ❤♦✇ ■ &,❛",❡❞ ♠② 9❤✳❉✳ ■ ,❤❡♥ ❢♦✉♥❞ ,❤❛, "❡&❡❛"❝❤ ✐& ♣"❡,,② ❧✐❦❡ ❛ ❣❛♠❡✳ ■ ✇❛& ❛&&✐❣♥❡❞ ✇✐,❤ ❛ ,♦♣✐❝✱ ♥❛♠❡❧② ♠✉❧,✐✲ ♠♦❞❛❧ ❜✐♦♠❡,"✐❝&✱ ♠✉❝❤ ❧✐❦❡ ❜❡✐♥❣ ,♦❧❞✿ ✏❚❤✐& ✐& ②♦✉" ❣❛♠❡ ❢♦" ,❤❡ ♥❡①, ,❤"❡❡ ②❡❛"&✑✳ ❙♦ ■ ✜❣✉"❡ ♦✉, ,❤❡ "✉❧❡&✱ ❧♦♦❦ ❛, ❤♦✇ ♦,❤❡"& ♣❧❛②✱ ❛♥❞ ,"② ,♦ ♣❧❛② ❜❡,,❡"✳ ❆❢,❡" ,❤"❡❡ ②❡❛"&✱ ■ ❛♠ &,✐❧❧ ♥♦, &✉"❡ ✐❢ ■ ❝❛♥ "❡❛❧❧② ♣❧❛② ❜❡,,❡" ,❤❛♥ ,❤❡ ♦,❤❡"&✱ ❜✉, ❛♠ ♣❛",✐❝✉❧❛"❧② ❤❛♣♣② ✇✐,❤ ,✇♦ ,❤✐♥❣&✿ ✜"&,✱ ■ ❡♥❥♦②❡❞ ,❤❡ ❣❛♠❡❀ ❛♥❞ &❡❝♦♥❞✱ ■ ❛♠ ✇✐❧❧✐♥❣ ,♦ ❝♦♥,✐♥✉❡ ♣❧❛②✐♥❣ ❛& ❛ ♣♦&,✲❞♦❝ "❛,❤❡" ,❤❛♥ ,♦ &❛② ✏■ F✉✐,✑✳ ■ ❤❛❞ ❛ ✈❡"② ❣♦♦❞ ,✐♠❡ &,✉❞②✐♥❣ ❛♥❞ ✇♦"❦✐♥❣ ❛, ❊❯❘❊❈❖▼✱ ❛♥❞ ❧✐✈✐♥❣ ✉♥❞❡" ,❤❡ &✉♥&❤✐♥❡ ♦❢ ❈♦,❡✲❞✬❆③✉"✳ ■ ✇♦✉❧❞ ❧✐❦❡ ,♦ ,❤❛♥❦ ❛ ❧♦, ♦❢ ♣❡♦♣❧❡✳ ❖❢ ❝♦✉"&❡✱ ■ ✇❛♥, ,♦ ✜"&, ❡①♣"❡&& ♠② ❣"❡❛,❡&, ❣"❛,✐,✉❞❡ ,♦ ♠② ,❤❡&✐& &✉♣❡"✈✐&♦"& ❉"✳ ◆✐❝❤♦❧❛& ❊✈❛♥& ❛♥❞ ❉"✳ ❏❡❛♥✲ ▲✉❝ ❉✉❣❡❧❛②✱ ✇❤♦ ❣❛✈❡ ♠❡ ,❤✐& ♦♣♣♦",✉♥✐,② ❛♥❞ ❤❡❧♣❡❞ ♠❡ ✐♥ ❛❧❧ ❛&♣❡❝,&✳ ■ "❡♠❡♠❜❡" ❛ ❋"✐❞❛② ❧❛,❡ ♥✐❣❤, ,❤"❡❡ ②❡❛"& ❛❣♦✱ ✇❤❡♥ ◆✐❝❦ ✇❛& ❛, ❤♦♠❡ ❜✉, &,✐❧❧ ✇♦"❦✐♥❣ ✇✐,❤ ♠❡ ♦♥ ♠② ✜"&, ♣❛♣❡" ❜② &❡♥❞✐♥❣ ❤✐& "❡✈✐&✐♦♥& ❜② ❊✲♠❛✐❧&✳ ❆, ✶✵✿✸✵ 9▼✱ ❤❡ ❊✲♠❛✐❧❡❞ ♠❡✿ ✏■ ❤❛✈❡ ,♦ ❧❡❛✈❡ ❢♦" ❛ ✇❤✐❧❡ ,♦ ❣✐✈❡ ♠② ❜❛❜② ❣✐"❧ ❛ &❤♦✇❡"✱ ❛♥❞ ✇✐❧❧ ❝♦♠❡ ❜❛❝❦ ✐♥ ❤❛❧❢ ❛♥ ❤♦✉"✳✑ ■, ✐& ❤❛"❞ ,♦ ❡①♣"❡&& ♠② ❣"❛,✐,✉❞❡ ,♦ ❤✐♠✱ ❜✉, ■ ❦♥♦✇ ,❤❛, ■ ♦✇❡ ❤✐♠ &♦ ♠✉❝❤✳ ■, ✐& ❛❧&♦ ♠② ❣"❡❛,❡&, ♣❧❡❛&✉"❡ ,♦ ✇♦"❦ ✉♥❞❡" ,❤❡ &✉♣❡"✈✐&✐♦♥ ♦❢ 9"♦❢✳ ❉✉❣❡❧❛② ✇❤♦ &❤❛"❡❞ ✇✐,❤ ♠❡ ❤✐& "✐❝❤ ❡①♣❡"✐❡♥❝❡ ✐♥ ❜♦,❤ "❡&❡❛"❝❤ ❛♥❞ ,❡❛❝❤✐♥❣✱ ❛♥❞ ❣❛✈❡ ♠❡ ❛ ❧♦, ♦❢ ✇♦♥❞❡"❢✉❧ ✐❞❡❛& ♦♥ ♠② "❡&❡❛"❝❤✳ ▼② &✐♥❝❡"❡ ❛♣♣"❡❝✐❛,✐♦♥ ❛❧&♦ ❣♦❡& ,♦ ♠② ,❤❡&✐& ❝♦♠♠✐,,❡❡ ♠❡♠❜❡"& ❢♦" ,❤❡✐" &✉♣♣♦",&✳ ■ ✇♦✉❧❞ ❧✐❦❡ ,♦ ,❤❛♥❦ ❛❧❧ ,❤❡ ❥✉"② ♠❡♠❜❡"& ❢♦" ,❤❡✐" ♣"❡❝✐♦✉& ,✐♠❡ ,♦ "❡❛❞ ♠② ♠❛♥✉&❝"✐♣,✳ ■ ❛❧&♦ ✇❛♥, ,♦ ,❤❛♥❦ ♠② ❝✉""❡♥, ❛♥❞ ♣"❡✈✐♦✉& ❝♦❧❧❡❣❡&✱ ✐♥❝❧✉❞✐♥❣ ❆♥,✐,③❛ ❉❛♥,❝❤❡✈❛✱ ◆❡&❧✐ ❊"❞♦❣♠✉&✱ ❈❛"♠❡❧♦ ❱❡❧❛"❞♦✱ ❘✉✐ ▼✐♥✱ ❍❛❥❡" ❋"❛❞✐✱ ◆❡&❧✐❤❛♥ ❑♦&❡✱ ❆♥❞"❡❛ ▼❊▲▲❊✱ ❆&♠❛❛ ❋✐❧❧❛,"❡✱ ❈❤"✐&,❡❧❧❡ ❨❡♠❞❥✐ ❚❝❤❛&&✐✱ ❋❡❞❡"✐❝♦ ❆❧❡❣"❡✱ ●✐♦✈❛♥♥✐ ❙♦❧❞✐ ❛♥❞ ▲❡❡❧❛ ●✉❞✉♣✉❞✐ ✇❤♦ &❤❛"❡❞ ❦♥♦✇❧❡❞❣❡ ❛♥❞ ❡①♣❡"✐❡♥❝❡ ✇✐,❤ ♠❡ ❤❛❞ ❤❛✈❡ ♣❧❡❛&❛♥, ❞✐&❝✉&&✐♦♥&✳ ■ ♠✉&, ❛❧&♦ ,❤❛♥❦ ,❤❡ ♠❡♠❜❡"& ♦❢ ✏❊❯❘❊❈❖▼ ❈❤✐♥❡&❡ ,❡❛♠✑✱ ✐♥❝❧✉❞✐♥❣ ❳✐❛♦❧❛♥ ❙❤❛✱ ❍❡♥❣ ❈✉✐✱.
(5) ✹ ❳✉❡❧✐❛♥❣ ▲✐✉✱ ❘✉✐ ▼✐♥✱ ❑❛✐❥✐❡ ❩❤♦✉✱ ❙❤❡♥❣②✉♥ ▲✐✉✱ ❳✐❛♦❤✉ ❲✉✱ ❍❛✐❢❛♥ ❨✐♥✱ ❳✐♥♣✐♥❣ ❨✐✱ ◗✐❛♥:✉✐ ▲✐✱ ❏✐♥②✉❛♥ ❈❤❡♥ ❢:♦♠ ✇❤♦♠ ■ ❤❛✈❡ ❧❡❛:♥A ❡♥♦:♠♦✉B ❦♥♦✇❧❡❞❣❡ ✐♥ ❜♦A❤ :❡B❡❛:❝❤ ❛♥❞ ❧✐❢❡✳ ■ ✇♦✉❧❞ ❧✐❦❡ A♦ A❤❛♥❦ ❛❧❧ ♠② ❢:✐❡♥❞B ❛A ❊❯❘❊❈❖▼ ❢♦: A❤❡ ❝♦❧♦✉:❢✉❧ ❧✐❢❡ ■ ❡♥❥♦②❡❞ ❞✉:✐♥❣ A❤❡ ♣❛BA A❤:❡❡ ②❡❛:B✳ ❆A ❧❛BA✱ ■ ✇♦✉❧❞ ❣✐✈❡ ♠② ❤❡❛:A❢❡❧A A❤❛♥❦B A♦ ♠② ❢❛♠✐❧②✳ ▼② ♣❛:❡♥AB ❛❧✇❛②B ❡♥❝♦✉:❛❣❡ ♠❡ ✇❤❡♥ ■ ❡①♣❡:✐❡♥❝❡❞ ❛ ❞✐✣❝✉❧A A✐♠❡✳ ❋✐♥❛❧❧②✱ ♠② ❧♦✈❡ ❣♦❡B A♦ ♠② ✇✐❢❡ ❏✐♦♥❣❥✐♦♥❣ ▼♦✱ ✇❤♦ ❤❛B B❤❛:❡❞ ✶✵✲②❡❛:B A✐♠❡ ✇✐A❤ ♠❡ ❛♥❞ ❛❧✇❛②B B✉♣♣♦:A❡❞ ♠❡✳.
(6) ❆❜"#$❛❝# ❇✐♦♠❡%&✐❝ ❞❛%❛ ✐* ♦❢%❡♥ &❡♣&❡*❡♥%❡❞ ❜② ❤✐❣❤✲❞✐♠❡♥*✐♦♥❛❧ ❢❡❛%✉&❡ ✈❡❝%♦&* ✇❤✐❝❤ ❝♦♥%❛✐♥ *✐❣♥✐❢✲ ✐❝❛♥% ✐♥%❡&✲*❡**✐♦♥ ✈❛&✐❛%✐♦♥✳ ❊✣❝✐❡♥% ❞✐♠❡♥*✐♦♥❛❧✐%② &❡❞✉❝%✐♦♥ %❡❝❤♥✐:✉❡* ❛&❡ %❤✉* ♥❡❡❞❡❞ ✐♥ ♦&❞❡& %♦ ❡①%&❛❝% ❝❧❛**✲❞✐*❝&✐♠✐♥❛%✐✈❡✱ ❧♦✇✲❞✐♠❡♥*✐♦♥❛❧ ❢❡❛%✉&❡* ❛♥❞ %♦ ❛%%❡♥✉❛%❡ ✉♥✇❛♥%❡❞ ✈❛&✐❛%✐♦♥* ✇❤✐❝❤ ✐* &❡❞✉♥❞❛♥% %♦ &❡❝♦❣♥✐%✐♦♥✳ ❙✉❝❤ ❞✐*❝&✐♠✐♥❛%✐✈❡ ❞✐♠❡♥*✐♦♥❛❧✐%② &❡❞✉❝%✐♦♥ %❡❝❤♥✐:✉❡* ❣❡♥❡&❛❧❧② ❢♦❧❧♦✇ ❛ *✉♣❡&✈✐*❡❞ ❧❡❛&♥✐♥❣ *❝❤❡♠❡✱ ✐♥ ✇❤✐❝❤ ❛ *✉❜*♣❛❝❡ ♣&♦❥❡❝%✐♦♥ ✐* ❧❡❛&♥❡❞ ✇✐%❤ ❢❡❛%✉&❡✲❧❛❜❡❧ ♣❛✐&*✳ ❍♦✇❡✈❡&✱ ❧❛❜❡❧❧❡❞ %&❛✐♥✐♥❣ ❞❛%❛ ✐* ❣❡♥❡&❛❧❧② ❧✐♠✐%❡❞ ✐♥ :✉❛♥%✐%② ❛♥❞ ♦❢%❡♥ ❞♦❡* ♥♦% &❡❧✐❛❜❧② &❡♣&❡*❡♥% %❤❡ ✐♥%❡&✲*❡**✐♦♥ ✈❛&✐❛%✐♦♥ ❡♥❝♦✉♥%❡&❡❞ ✐♥ %❡*% ❞❛%❛✳ ❚❤❡ ❧✐♠✐%❡❞ *✐③❡ ♦❢ ❧❛❜❡❧❧❡❞ %&❛✐♥✐♥❣ *❡% ♦❢%❡♥ ❧❡❛❞* %♦ ❜✐❛*❡❞ ♣&♦❥❡❝%✐♦♥ ♠❛%&✐❝❡* ❛♥❞ ❞❡❣&❛❞❡❞ &❡❝♦❣♥✐%✐♦♥ ♣❡&❢♦&♠❛♥❝❡✳ ❚❤✐* %❤❡*✐* ♣&♦♣♦*❡* %♦ ✉*❡ ♠✉❧%✐✲✈✐❡✇ ❞✐♠❡♥*✐♦♥❛❧✐%② &❡❞✉❝%✐♦♥ ✭▼❱❉❘✮ ✇❤✐❝❤ ❛✐♠* %♦ ❡①%&❛❝% ❞✐*❝&✐♠✐♥❛%✐✈❡ ❢❡❛%✉&❡* ✐♥ ♠✉❧%✐✲♠♦❞❛❧ ❜✐♦♠❡%&✐❝ *②*%❡♠*✱ ✇❤❡&❡ ❞✐✛❡&❡♥% ♠♦❞❛❧✲ ✐%✐❡* ❛&❡ &❡❣❛&❞❡❞ ❛* ❞✐✛❡&❡♥% ✈✐❡✇* ♦❢ %❤❡ *❛♠❡ ❞❛%❛✳ ■♥*%❡❛❞ ♦❢ %&❛✐♥✐♥❣ ♦♥ ❢❡❛%✉&❡✲❧❛❜❡❧ ♣❛✐&*✱ ▼❱❉❘ ♣&♦❥❡❝%✐♦♥* ❛&❡ %&❛✐♥❡❞ ♦♥ ❢❡❛%✉&❡✲❢❡❛%✉&❡ ♣❛✐&* ✇❤❡&❡ ❧❛❜❡❧ ✐♥❢♦&♠❛%✐♦♥ ✐* ♥♦% &❡:✉✐&❡❞✳ ❙✐♥❝❡ ✉♥❧❛❜❡❧❧❡❞ ❞❛%❛ ✐* ❡❛*✐❡& %♦ ❛❝:✉✐&❡ ✐♥ ❧❛&❣❡ :✉❛♥%✐%✐❡*✱ ❛♥❞ ❜❡❝❛✉*❡ ♦❢ %❤❡ ♥❛%✉&❛❧ ❝♦✲❡①✐*%❡♥❝❡ ♦❢ ♠✉❧%✐♣❧❡ ✈✐❡✇* ✐♥ ♠✉❧%✐✲♠♦❞❛❧ ❜✐♦♠❡%&✐❝ ♣&♦❜❧❡♠*✱ ❞✐*❝&✐♠✐♥❛♥%✱ ❧♦✇✲❞✐♠❡♥*✐♦♥❛❧ *✉❜*♣❛❝❡* ❝❛♥ ❜❡ ❧❡❛&♥% ✉*✐♥❣ %❤❡ ♣&♦♣♦*❡❞ ▼❱❉❘ ❛♣♣&♦❛❝❤❡* ✐♥ ❛ ❧❛&❣❡❧② ✉♥*✉♣❡&✈✐*❡❞ ♠❛♥♥❡&✳ ❆❝❝♦&❞✐♥❣ %♦ ❞✐✛❡&❡♥% ❢✉♥❝%✐♦♥❛❧✐%✐❡* ♦❢ ❜✐♦♠❡%&✐❝ *②*%❡♠*✱ ♥❛♠❡❧② &❡❝♦❣♥✐%✐♦♥ ✭✐♥❝❧✉❞✲ ✐♥❣ ✐❞❡♥%✐✜❝❛%✐♦♥ ❛♥❞ ✈❡&✐✜❝❛%✐♦♥✮✱ ❝❧✉*%❡&✐♥❣✱ ❛♥❞ &❡%&✐❡✈❛❧✱ ✇❡ ♣&♦♣♦*❡ %❤&❡❡ ▼❱❉❘ ❢&❛♠❡✲ ✇♦&❦* ✇❤✐❝❤ ♠❡❡% %❤❡ &❡:✉✐&❡♠❡♥%* ❢♦& ❡❛❝❤ ❢✉♥❝%✐♦♥❛❧✐%②✳ ❚❤❡ ♣&♦♣♦*❡❞ ❛♣♣&♦❛❝❤❡*✱ ❤♦✇✲ ❡✈❡&✱ *❤❛&❡ %❤❡ *❛♠❡ *♣✐&✐%✿ ❛❧❧ ♠❡%❤♦❞* ❛✐♠ %♦ ❧❡❛&♥ ❛ ♣&♦❥❡❝%✐♦♥ ❢♦& ❡❛❝❤ ✈✐❡✇ *✉❝❤ %❤❛% ❛ ❝❡&%❛✐♥ ❢♦&♠ ♦❢ ❛❣&❡❡♠❡♥% ✐* ❛%%❛✐♥❡❞ ✐♥ %❤❡ *✉❜*♣❛❝❡* ❛❝&♦** ❞✐✛❡&❡♥% ✈✐❡✇*✳ ❚❤❡ ♣&♦♣♦*❡❞ ▼❱❉❘ ❢&❛♠❡✇♦&❦* ❝❛♥ %❤✉* ❜❡ ✉♥✐✜❡❞ ✐♥%♦ ♦♥❡ ❣❡♥❡&❛❧ ❢&❛♠❡✇♦&❦ ❢♦& ♠✉❧%✐✲✈✐❡✇ ❞✐♠❡♥✲ *✐♦♥❛❧✐%② &❡❞✉❝%✐♦♥ %❤&♦✉❣❤ *✉❜*♣❛❝❡ ❛❣&❡❡♠❡♥%✳ ❲❡ &❡❣❛&❞ %❤✐* ♥♦✈❡❧ ❝♦♥❝❡♣% ♦❢ *✉❜*♣❛❝❡ ❛❣&❡❡♠❡♥% %♦ ❜❡ %❤❡ ♣&✐♠❛&② ❝♦♥%&✐❜✉%✐♦♥ ♦❢ %❤✐* %❤❡*✐*✳.
(7)
(8) ❈♦♥#❡♥#% ✶ ■♥#$♦❞✉❝#✐♦♥. ✶✶. ✶✳✶. ❈♦♥%&✐❜✉%✐♦♥* ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✶✷. ✶✳✷. ❖✉%❧✐♥❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✶✼. ✷ ❇✐♦♠❡#$✐❝ ❙②0#❡♠0 ❛♥❞ ❉✐♠❡♥0✐♦♥❛❧✐#② ❘❡❞✉❝#✐♦♥. ✶✾. ✷✳✶. ❇✐♦♠❡%&✐❝* ❙②*%❡♠* ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✶✾. ✷✳✷. ❋✉♥❝%✐♦♥❛❧✐%✐❡* ♦❢ ❇✐♦♠❡%&✐❝* ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✷✶. ✷✳✷✳✶. ❱❡&✐✜❝❛%✐♦♥ ❛♥❞ ✐❞❡♥%✐✜❝❛%✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✷✶. ✷✳✷✳✷. ❈❧✉*%❡&✐♥❣ ❛♥❞ &❡%&✐❡✈❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✷✸. ❇✐♦♠❡%&✐❝ ❋❡❛%✉&❡ ❘❡♣&❡*❡♥%❛%✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✷✺. ✷✳✸✳✶. ▲♦❝❛❧ ❜✐♥❛&② ♣❛%%❡&♥* ✭▲❇D✮ ❢♦& ❢❛❝❡ &❡♣&❡*❡♥%❛%✐♦♥. ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✷✻. ✷✳✸✳✷. ●❛✉**✐❛♥ ♠✐①%✉&❡ ♠♦❞❡❧* ✭●▼▼✮ ❢♦& ✈♦✐❝❡ &❡♣&❡*❡♥%❛%✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳. ✷✽. ❈✉&*❡ ♦❢ ❉✐♠❡♥*✐♦♥❛❧✐%② ❛♥❞ ❉✐♠❡♥*✐♦♥❛❧✐%② ❘❡❞✉❝%✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✸✵. ✷✳✹✳✶. ❈✉&*❡ ♦❢ ❞✐♠❡♥*✐♦♥❛❧✐%② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✸✶. ✷✳✹✳✷. ❉✐♠❡♥*✐♦♥❛❧✐%② ❘❡❞✉❝%✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✸✷. ▼✉❧%✐♣❧❡ ❘❡♣&❡*❡♥%❛%✐♦♥ ♦❢ ❇✐♦♠❡%&✐❝ ❉❛%❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✸✻. ✷✳✺✳✶. ▼✉❧%✐✲♠♦❞❛❧ ❜✐♦♠❡%&✐❝* ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✸✻. ✷✳✺✳✷. ❋✉*✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✸✼. ✷✳✸. ✷✳✹. ✷✳✺. ✷✳✻ ✷✳✼. D&♦❜❧❡♠ ❙%❛%❡♠❡♥%✿ ❉✐*❝&✐♠✐♥❛%✐✈❡ ❋❡❛%✉&❡ ❊①%&❛❝%✐♦♥ ❢&♦♠ ❯♥❧❛❜❡❧❧❡❞✱ ▼✉❧%✐✲✈✐❡✇ ❉❛%❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✸✽. ❙✉♠♠❛&② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✸✽. ✸ ❙#❛#❡✲♦❢✲#❤❡✲❛$# ✐♥ ▼❱❉❘. ✹✶. ✸✳✶. ▼✉❧%✐✲❱✐❡✇ ❉✐♠❡♥*✐♦♥❛❧✐%② ❘❡❞✉❝%✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✹✶. ✸✳✷. ▼❱❉❘ ❇❛*❡❞ ♦♥ ❈❛♥♦♥✐❝❛❧ ❈♦&&❡❧❛%✐♦♥ ❆♥❛❧②*✐* ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✹✷.
(9) ❈♦♥#❡♥#%. ✽ ✸✳✷✳✶. %&✐♥❝✐♣❧❡- ♦❢ ❈❈❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✹✷. ✸✳✷✳✷. ❆♣♣❧✐❝❛4✐♦♥ ♦❢ ❈❈❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✹✸. ▼❱❉❘ ❇❛-❡❞ ♦♥ ❙✐♠✐❧❛&✐4② ●&❛♣❤- ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✹✹. ✸✳✸✳✶. ▼✉❧4✐✲✈✐❡✇ -♣❡❝4&❛❧ ❡♠❜❡❞❞✐♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✹✹. ✸✳✸✳✷. ▼✉❧4✐✲✈✐❡✇ ❙♣❡❝4&❛❧ ❝❧✉-4❡&✐♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✹✻. ✸✳✹. %&♦♣♦-❡❞ ▼❱❉❘ ❆♣♣&♦❛❝❤ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✹✽. ✸✳✺. ❙✉♠♠❛&② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✺✵. ✸✳✸. ✹ ▼❱❉❘ ❜② ■♥❝*❡♠❡♥-❛❧ ❈♦✲-*❛✐♥✐♥❣. ✺✶. ✹✳✶. ▼♦4✐✈❛4✐♦♥- ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✺✶. ✹✳✷. ▲❉❆ ✱❈♦✲4&❛✐♥✐♥❣ ❛♥❞ ❈♦✲▲❉❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✺✹. ✹✳✷✳✶. ▲❉❆ ❛♥❞ -♠❛❧❧ -❛♠♣❧❡ -✐③❡ ♣&♦❜❧❡♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✺✹. ✹✳✷✳✷. ❈♦✲4&❛✐♥✐♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✺✺. ✹✳✷✳✸. ❈♦✲▲❉❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✺✻. ❆♣♣❧✐❝❛4✐♦♥ 4♦ ❙❡♠✐✲-✉♣❡&✈✐-❡❞ ❆✉❞✐♦✲✈✐-✉❛❧ ❙♣❡❛❦❡& ❘❡❝♦❣♥✐4✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳. ✺✼. ✹✳✸✳✶. ❋❡❛4✉&❡ ❡①4&❛❝4✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✺✽. ✹✳✸✳✷. ❙✉❜-♣❛❝❡ ❧❡❛&♥✐♥❣. ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✺✾. ✹✳✸✳✸. ■❞❡♥4✐✜❝❛4✐♦♥ ❛♥❞ ✈❡&✐✜❝❛4✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✻✵. ❊①♣❡&✐♠❡♥4❛❧ ✇♦&❦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✻✶. ✹✳✹✳✶. ▼♦❜✐♦ ❛✉❞✐♦✲✈✐-✉❛❧ ❞❛4❛❜❛-❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✻✶. ✹✳✹✳✷. ❊①♣❡&✐♠❡♥4❛❧ &❡-✉❧4- ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✻✷. ❈♦♣✐♥❣ ✇✐4❤ ❖✉4✲♦❢✲❝❧❛-- ❉❛4❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✻✹. ✹✳✺✳✶. ❙♣❛&-❡ &❡♣&❡-❡♥4❛4✐♦♥ ❝❧❛--✐✜❡& ❛♥❞ ♦✉4✲♦❢✲❝❧❛-- -❛♠♣❧❡ ❞❡4❡❝4✐♦♥ ✳ ✳. ✻✺. ✹✳✺✳✷. ❈♦✲▲❉❆✲❙❘❈ ❛❧❣♦&✐4❤♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✻✼. ❊①♣❡&✐♠❡♥4❛❧ ❘❡-✉❧4- ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✻✾. ✹✳✻✳✶. ❉❛4❛❜❛-❡ ❛♥❞ ♣&♦4♦❝♦❧- ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✻✾. ✹✳✻✳✷. ❘❡-✉❧4- ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✼✵. ❙✉♠♠❛&② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✼✷. ✹✳✸. ✹✳✹. ✹✳✺. ✹✳✻. ✹✳✼. ✺ ▼❱❉❘ ❜② ❙✉❜9♣❛❝❡ ❈❧✉9-❡*✐♥❣ ❆❣*❡❡♠❡♥-. ✼✸. ✺✳✶. ▼♦4✐✈❛4✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✼✹. ✺✳✷. ▲❉❆✱ ❦✲♠❡❛♥-✱ ❛♥❞ ❝♦✲4&❛✐♥✐♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✼✺. ✺✳✷✳✶. ▲❉❆ ❛♥❞ ❦✲♠❡❛♥- ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✼✺. ✺✳✷✳✷. ❈♦✲4&❛✐♥✐♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✼✻. ▼✉❧4✐✲✈✐❡✇ -✉❜-♣❛❝❡ ❝❧✉-4❡&✐♥❣✿ ❛ ❝♦✲4&❛✐♥✐♥❣ ❛❧❣♦&✐4❤♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✼✼. ✺✳✸.
(10) ❈♦♥#❡♥#%. ✾. ✺✳✸✳✶. ❆♥ ❛❧❣♦+✐-❤♠✿ ❈♦❑♠▲❉❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✼✼. ✺✳✸✳✷. ❆♥ ✐❧❧✉8-+❛-✐✈❡ ❡①❛♠♣❧❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✼✾. ✺✳✸✳✸. ▼❛-❤♠❛-✐❝❛❧ ❛♥❛❧②8✐8 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✽✶. ✺✳✸✳✹. ❊①-❡♥8✐♦♥8 ♦❢ ❈♦❑♠▲❉❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✽✸. ✺✳✹. ❘❡❧❛-❡❞ ✇♦+❦8 ❛♥❞ ❛♥❛❧②8✐8 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✽✺. ✺✳✺. ❊①♣❡+✐♠❡♥-8 ❛♥❞ ❞✐8❝✉88✐♦♥8 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✽✼. ✺✳✺✳✶. ❊✈❛❧✉❛-✐♦♥ ♠❡-+✐❝8 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✽✽. ✺✳✺✳✷. ❆✉❞✐♦✲✈✐8✉❛❧ 8♣❡❛❦❡+ ❝❧✉8-❡+✐♥❣ ✭❝♦♥❞✐-✐♦♥❛❧ ✐♥❞❡♣❡♥❞❡♥❝❡ ❛88✉♠♣-✐♦♥ 8❛-✐8✜❡❞✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✺✳✺✳✸ ✺✳✻. ✽✾. ❍❛♥❞✇+✐--❡♥ ❞✐❣✐- ❝❧✉8-❡+✐♥❣ ❛♥❞ -❡①- ❞♦❝✉♠❡♥- ❝❧✉8-❡+✐♥❣ ✭❈♦♥❞✐-✐♦♥❛❧ ✐♥❞❡♣❡♥❞❡♥❝❡ ❛88✉♠♣-✐♦♥ ♥♦- ❢✉❧❧② 8❛-✐8✜❡❞✮ ✳ ✳ ✳ ✳ ✳ ✳. ✾✸. ❙✉♠♠❛+② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✾✼. ✻ ▼❱❉❘ ❜② ❙✉❜)♣❛❝❡ ●/❛♣❤ ❆❣/❡❡♠❡♥5. ✾✾. ✻✳✶. ▼♦-✐✈❛-✐♦♥8 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳. ✻✳✷. ▲♦❝❛❧✐-② O+❡8❡+✈✐♥❣ O+♦❥❡❝-✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✷. ✻✳✸. ❈♦✲▲OO ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✸. ✻✳✹. ✻✳✺. ✾✾. ✻✳✸✳✶. ❖❜❥❡❝-✐✈❡ ❢✉♥❝-✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✸. ✻✳✸✳✷. ❆❧❣♦+✐-❤♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✹. ✻✳✸✳✸. ❆♣♣❧✐❝❛-✐♦♥ -♦ ♠✉❧-✐❜✐♦♠❡-+✐❝ +❡-+✐❡✈❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✺. ❊①♣❡+✐♠❡♥-❛❧ +❡8✉❧-8 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✻ ✻✳✹✳✶. ❉❛-❛❜❛8❡8 ❛♥❞ O+♦-♦❝♦❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✼. ✻✳✹✳✷. ❘❡8✉❧-8 ❛♥❞ ❛♥❛❧②8✐8 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✾. ❙✉♠♠❛+② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✹. ✼ ❈♦♥❝❧✉)✐♦♥. ✶✶✺. ✼✳✶. ❈♦♥-+✐❜✉-✐♦♥8 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✺. ✼✳✷. ❋✉-✉+❡ ❲♦+❦. ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✼. ❆ ❙❡♠✐✲)✉♣❡/✈✐)❡❞ ❋❛❝❡ ❘❡❝♦❣♥✐5✐♦♥ ✇✐5❤ ▲❉❆ ❙❡❧❢✲5/❛✐♥✐♥❣. ✶✶✾. ❆✳✶ ■♥-+♦❞✉❝-✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✾ ❆✳✷ ▲❉❆ ❙❡❧❢✲-+❛✐♥✐♥❣ ❆❧❣♦+✐-❤♠. ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✶. ❆✳✷✳✶ ❇❛8❡❧✐♥❡ 8②8-❡♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✶ ❆✳✸ ▲❉❆ 8❡❧❢✲-+❛✐♥✐♥❣ ❛❧❣♦+✐-❤♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✷ ❆✳✹ ❊①♣❡+✐♠❡♥-❛❧ ❘❡8✉❧-8 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✸ ❆✳✹✳✶ ❚+❛♥❞✉❝-✐✈❡ ❝♦♥✜❣✉+❛-✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✹.
(11) ❈♦♥#❡♥#%. ✶✵. ❆✳✹✳✷ ❙❡♠✐✲+✉♣❡.✈✐+❡❞ ❝♦♥✜❣✉.❛7✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✺ ❆✳✹✳✸ ❙✐♥❣❧❡ 7.❛✐♥✐♥❣ ✐♠❛❣❡ 7❡+7 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✻ ❆✳✺ ❈♦♥❝❧✉+✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✼. ❇✐❜❧✐♦❣&❛♣❤✐❡. ✶✸✽.
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(13) ❈❤❛♣$❡& ✶ ✕ ■♥$&♦❞✉❝$✐♦♥. ✶✷. ♦# ✇❤✐❝❤ ❡♥#♦❧❧❡❞ ✐❞❡♥,✐,② ,❤❡ ,❡., .❛♠♣❧❡ ❜❡❧♦♥❣. ,♦✳ ■♥ ♠♦., .,❛,❡✲♦❢✲,❤❡✲❛#, ❜✐♦♠❡,#✐❝ .②.,❡♠.✱ ❞❛,❛ .❛♠♣❧❡. ❛#❡ ♦❢,❡♥ #❡♣#❡.❡♥,❡❞ ❜② ❤✐❣❤✲❞✐♠❡♥.✐♦♥❛❧ ❢❡❛,✉#❡ ✈❡❝,♦#. ✭❡✳❣✳✱ ❧♦✲ ❝❛❧ ❜✐♥❛#② ♣❛,,❡#♥. ✭▲❇>✮ ❢♦# ❢❛❝❡ #❡❝♦❣♥✐,✐♦♥ ❬❆❤♦♥❡♥ ❡, ❛❧✳✱ ✷✵✵✻❪ ❛♥❞ ●❛✉..✐❛♥ ♠✐①,✉#❡ ♠♦❞❡❧ ✭●▼▼✮ .✉♣❡#✈❡❝,♦#. ❢♦# .♣❡❛❦❡# #❡❝♦❣♥✐,✐♦♥ ❬❈❛♠♣❜❡❧❧ ❡, ❛❧✳✱ ✷✵✵✻❪✮✳ ❚❤❡ ❤✐❣❤ ❞✐♠❡♥.✐♦♥❛❧✐,② ♦❢ ❜✐♦♠❡,#✐❝ ❢❡❛,✉#❡. ✐♥❝✉# ❤❡❛✈② .,♦#❛❣❡ ❛♥❞ ❝♦♠♣✉,❛,✐♦♥❛❧ ❜✉#❞❡♥.✱ ❛♥❞ ♠♦#❡ ✐♠♣♦#,❛♥,❧②✱ ,❤❡ .♦✲❝❛❧❧❡❞ ❝✉"#❡✲♦❢✲❞✐♠❡♥#✐♦♥❛❧✐.② ❬❇❡❧❧♠❛♥✱ ✶✾✻✶❪ ❝❛♥ ✐♠♣❛❝, ♦♥ ,❤❡ #❡❝♦❣♥✐,✐♦♥ ♣❡#❢♦#♠❛♥❝❡ ✐♥ ,❤❡ ❢♦❧❧♦✇✐♥❣ ❝♦♠♣❛#✐.♦♥ ♦# ❝❧❛..✐✜❝❛,✐♦♥ ♠♦❞✉❧❡✳ ❉✐✣❝✉❧,✐❡. ❛..♦❝✐❛,❡❞ ✇✐,❤ ,❤❡ ❤✐❣❤ ❞✐♠❡♥.✐♦♥❛❧✐,② ❛#❡ ❣❡♥❡#❛❧❧② ♦✈❡#❝♦♠❡ ,❤#♦✉❣❤ ,❤❡ ❛♣♣❧✐❝❛,✐♦♥ ♦❢ ❞✐♠❡♥.✐♦♥❛❧✐,② #❡❞✉❝,✐♦♥ ✭❉❘✮ ,❡❝❤♥✐P✉❡. ❬❏♦❧❧✐✛❡✱ ✷✵✵✺✱ ❇❛#,❧❡,, ❡, ❛❧✳✱ ✷✵✵✷✱ ◆✐②♦❣✐✱ ✷✵✵✹✱ ❇❡❧❤✉♠❡✉# ❡, ❛❧✳✱ ✶✾✾✼❪✱ ✇❤✐❝❤ ❧♦♦❦ ❢♦# ❛ ❧♦✇❡# ❞✐♠❡♥.✐♦♥❛❧ #❡♣#❡.❡♥,❛,✐♦♥ ♦❢ ,❤❡ ❤✐❣❤✲❞✐♠❡♥.✐♦♥❛❧ ❞❛,❛✳ ❉❡♣❡♥❞✐♥❣ ♦♥ ✇❤❡,❤❡# ❧❛❜❡❧ ✐♥❢♦#♠❛,✐♦♥ ✐. ♥❡❡❞❡❞✱ ❉❘ ,❡❝❤✲ ♥✐P✉❡. ❝❛♥ ❜❡ ❜#♦❛❞❧② ❝❛,❡❣♦#✐③❡❞ ✐♥,♦ .✉♣❡#✈✐.❡❞ ♦# ✉♥.✉♣❡#✈✐.❡❞ ♠❡,❤♦❞.✳ ❆ ❞✐❧❡♠♠❛ ❛#✐.❡. ❢#♦♠ ,❤❡ ,#❛❞❡✲♦✛ ❜❡,✇❡❡♥ ,❤❡ ❛✈❛✐❧❛❜✐❧✐,② ♦❢ ❧❛❜❡❧ ✐♥❢♦#♠❛,✐♦♥ ❛♥❞ ,❤❡ ❞✐.❝#✐♠✐♥❛✲ ,✐✈❡ ♣♦✇❡# ♦❢ ,❤❡ ❡①,#❛❝,❡❞ ❧♦✇✲❞✐♠❡♥.✐♦♥❛❧ ❢❡❛,✉#❡.✳ ❙✉♣❡#✈✐.❡❞ ♠❡,❤♦❞. .✉❝❤ ❛. ▲✐♥❡❛# ❉✐.❝#✐♠✐♥❛♥, ❆♥❛❧②.✐. ✭▲❉❆✮ ❬❇❡❧❤✉♠❡✉# ❡, ❛❧✳✱ ✶✾✾✼❪ ❤❛✈❡ ❤✐❣❤ ❞✐.❝#✐♠✐♥❛,✐✈❡ ♣♦✇❡#✱ ❜✉, #❡P✉✐#❡ ❧❛#❣❡ P✉❛♥,✐,② ♦❢ ♠❛♥✉❛❧❧② ❧❛❜❡❧❧❡❞ ,#❛✐♥✐♥❣ ❞❛,❛✳ ❯♥.✉♣❡#✈✐.❡❞ ♠❡,❤♦❞. .✉❝❤ ❛. >#✐♥❝✐♣❧❡ ❈♦♠♣♦♥❡♥, ❆♥❛❧②.✐. ✭>❈❆✮ ❬❏♦❧❧✐✛❡✱ ✷✵✵✺❪ ❞♦ ♥♦, #❡P✉✐#❡ ❝❧❛.. ❧❛❜❡❧.✱ ❜✉, ❣❡♥❡#❛❧❧② ❧❛❝❦ ❞✐.❝#✐♠✐♥❛,✐✈❡ ♣♦✇❡#✳ ■♥ ❜✐♦♠❡,#✐❝ ✐❞❡♥,✐✜❝❛,✐♦♥ ❛♥❞ ✈❡#✐✜❝❛,✐♦♥ .❡,,✐♥❣.✱ ♠❛♥✉❛❧❧② ❧❛❜❡❧❧❡❞ ❞❛,❛ ✐. ♥♦#♠❛❧❧② ❧✐♠✐,❡❞ ✐♥ ♥✉♠❜❡# ✇❤✐❧❡ ❧❛#❣❡ ❛♠♦✉♥, ♦❢ ✉♥❧❛❜❡❧❧❡❞ ❞❛,❛ ❝❛♥ ❜❡ ❡❛.✐❧② ❛❝P✉✐#❡❞ ❞✉#✐♥❣ ,❤❡ ♥♦#♠❛❧ .②.,❡♠ ✉.❡✳ ■♥ ♠✉❧,✐✲♠♦❞❛❧ ❜✐♦♠❡,#✐❝.✱ ❞✐✛❡#❡♥, ❜✐♦♠❡,#✐❝ ♠♦❞❛❧✐,✐❡. ❝❛♥ ❢♦#♠ ❞✐✛❡#❡♥, ✐♥♣✉,. ,♦ ❝❧❛..✐✜❝❛,✐♦♥ ❛❧❣♦#✐,❤♠.✳ ▼✉❧,✐♠♦❞❛❧ ❜✐♦♠❡,#✐❝ .②.,❡♠. ❝❛♥ ♦❜,❛✐♥ ♠✉❧,✐♣❧❡ .❡,. ♦❢ ✐♥❢♦#✲ ♠❛,✐♦♥ ❢#♦♠ ,❤❡ .❛♠❡ ♠♦❞❛❧✐,② ✭✐✳❡✳✱ ✷❉✰✸❉ ❢❛❝❡ #❡❝♦❣♥✐,✐♦♥✮ ❬❇♦✇②❡# ❡, ❛❧✳✱ ✷✵✵✻❪ ♦# ✐♥❢♦#♠❛,✐♦♥ ❢#♦♠ ❞✐✛❡#❡♥, ❜✐♦♠❡,#✐❝ ♠♦❞❛❧✐,✐❡. ✭✐✳❡✳ ❜✐♦♠❡,#✐❝ .②.,❡♠ ✇✐,❤ ❢❛❝❡ ❛♥❞ ✈♦✐❝❡✮✳ ❚❤❡ ❢✉.✐♦♥ ♦❢ ♠♦❞❛❧✐,✐❡. #❡♠❛✐♥. ❛ ❝❤❛❧❧❡♥❣✐♥❣ ♣#♦❜❧❡♠ ❛♥❞ ✐. ❣❡♥❡#❛❧❧② ,#❡❛,❡❞ ✐♥ ✐.♦❧❛,✐♦♥ ,♦ ,❤❛, ♦❢ ❤✐❣❤ ❞✐♠❡♥.✐♦♥❛❧✐,② ❬❘♦.. ❡, ❛❧✳✱ ✷✵✵✽❪✳ ❚❤✐. ,❤❡.✐. ,❛❝❦❧❡. ,❤❡ ❤✐❣❤ ❞✐♠❡♥.✐♦♥❛❧✐,② ♣#♦❜❧❡♠ ❛♥❞ ,❤❡ ♠✉❧,✐✲♠♦❞❛❧ ❢✉.✐♦♥ ♣#♦❜✲ ❧❡♠ ✐♥ ❛ ✉♥✐✜❡❞ ❢#❛♠❡✇♦#❦✳ ❯♥❞❡# ❛ ♠✉❧,✐✲♠♦❞❛❧ ❜✐♦♠❡,#✐❝ .❡,,✐♥❣ ❛♥❞ ❣✐✈❡♥ ❛❜✉♥❞❛♥, ✉♥❧❛❜❡❧❧❡❞ ❞❛,❛✱ ✇❡ ❛✐♠ ,♦ ❡①,#❛❝, ❤✐❣❤❧②✲❞✐.❝#✐♠✐♥❛,✐✈❡ ❢❡❛,✉#❡. ❢#♦♠ ♠✉❧,✐♣❧❡ ♠♦❞❛❧✐,✐❡. ✐♥ ❛♥ ✉♥.✉♣❡#✈✐.❡❞ ♠❛♥♥❡#✳. ✶✳✶ ❈♦♥%&✐❜✉%✐♦♥* ■♥ ,❤✐. .❡❝,✐♦♥✱ ✇❡ ❜#✐❡✢② .✉♠♠❛#✐③❡ ,❤❡ ❝♦♥,❡♥, ♦❢ ,❤❡ ,❤❡.✐. ❛♥❞ ,❤❡ ❝♦♥,#✐❜✉,✐♦♥.✳ ▼✉❧,✐✲♠♦❞❛❧ ❜✐♦♠❡,#✐❝ .②.,❡♠. ✉,✐❧✐③❡ ,✇♦ ♦# ♠♦#❡ ✐♥❞✐✈✐❞✉❛❧ ♠♦❞❛❧✐,✐❡. ,♦ ✐♠♣#♦✈❡ ,❤❡.
(14) ✶✳✶ ❈♦♥%&✐❜✉%✐♦♥*. ✶✸. "❡❝♦❣♥✐)✐♦♥ ❛❝❝✉"❛❝② ♦❢ ❝♦♥✈❡♥)✐♦♥❛❧ ✉♥✐✲♠♦❞❛❧ ♠❡)❤♦❞4✳ ■♥ ❛ ❜✐♠♦❞❛❧ ❜✐♦♠❡)"✐❝ 4②4)❡♠ ✇❤✐❝❤ ❡♠♣❧♦②4 )✇♦ ❞✐✛❡"❡♥) ♠♦❞❛❧✐)✐❡4✱ ❞❛)❛ 4❛♠♣❧❡4 ❝❛♥ ❜❡ "❡♣"❡4❡♥)❡❞ ❜② ♣❛✐"❡❞ ❢❡❛)✉"❡4. < X (1) , X (2) > ❛♥❞ ❛ 4✉❜❥❡❝) ✐❞❡♥)✐)② Y ❛4 ❛ )❛"❣❡) ✈❛"✐❛❜❧❡✳ ❙)❛)❡✲♦❢✲)❤❡✲❛") ❜✐♦♠❡)"✐❝ 4②4)❡♠4 ♦❢)❡♥ ♠❛❦❡ ✉4❡ ♦❢ ❤✐❣❤✲❞✐♠❡♥4✐♦♥❛❧ ❢❡❛)✉"❡4✱ )❤✉4 ❞✐♠❡♥4✐♦♥❛❧✐)② "❡❞✉❝)✐♦♥ ✭❉❘✮ )❡❝❤♥✐C✉❡4 ❛"❡ ♦❢)❡♥ ❛♣♣❧✐❡❞ )♦ ❛❧❧❡✈✐❛)❡ )❤❡ 4♦✲❝❛❧❧❡❞ ❝✉"4❡✲♦❢✲❞✐♠❡♥4✐♦♥❛❧✐)② ♣"♦❜❧❡♠ ✐♥ )❤❡ ❢♦❧❧♦✇✐♥❣ ❝❧❛44✐✜❝❛)✐♦♥ 4)❡♣✳ ❚❤✐4 )❤❡4✐4 "❡♣♦")4 ❛ 4)✉❞② ♦❢ ❉❘ ❛♣♣"♦❛❝❤❡4 ❢♦" ♠✉❧)✐✲♠♦❞❛❧ ❜✐♦♠❡)"✐❝4✳ ❈♦♠♠♦♥❧② "❡❢❡""❡❞ )♦ ❛4 ▼✉❧)✐✲✈✐❡✇ ❉✐♠❡♥4✐♦♥❛❧✐)② ❘❡❞✉❝)✐♦♥ ✭▼❱❉❘✮✱ )❤✐4 ✜❡❧❞ ❤❛4 ❛))"❛❝)❡❞ ❝♦♥4✐❞❡"❛❜❧❡ "❡4❡❛"❝❤ ✐♥)❡"❡4) ✐♥ "❡❝❡♥) ②❡❛"4✳ ▼♦4) ❡①✐4)✐♥❣ ▼❱❉❘ ❛❧❣♦"✐)❤♠4 ❛"❡ ❜❛4❡❞ ♦♥ ❈❛♥♦♥✐❝❛❧ ❈♦""❡❧❛)✐♦♥ ❆♥❛❧②4✐4 ✭❈❈❆✮ ❬❋♦4)❡" ❡) ❛❧✳✱ ✷✵✵✽❪ ❛♥❞ ✐)4 ✈❛"✐❛♥)4✳ ❚❤❡4❡ ❛❧❣♦"✐)❤♠4 ❣❡♥❡"❛❧❧② ❛✐♠ )♦ ❧❡❛"♥ ♣"♦❥❡❝)✐♦♥4 P (1) ❛♥❞ P (2) 4✉❝❤ )❤❛) )❤❡ ♣"♦❥❡❝)❡❞ 4❛♠♣❧❡4 P (1) X (1) ❛♥❞ P (2) X (2) ❛"❡ ♠❛①✐♠❛❧❧② ❝♦""❡❧❛)❡❞✳ ❲❤❡♥ ❛♣♣❧✐❡❞ )♦ ♣❛✐"❡❞ ❢❡❛)✉"❡4✱ )❤❡ ♠❛✐♥ ❛❞✈❛♥)❛❣❡ ♦❢ ▼❱❉❘ ♠❡)❤♦❞4 ♦✈❡" 4✐♥❣❧❡✲✈✐❡✇ ❉❘ ✐4 )❤❛) ♦♥❡ ✈✐❡✇ ❝❛♥ ❜❡ "❡❣❛"❞❡❞ ❛4 ✇❡❛❦ ❧❛❜❡❧4 ❢♦" )❤❡ ♦)❤❡"✳ ❆❝❝♦"❞✐♥❣❧②✱ ❝❧❛44✲4♣❡❝✐✜❝ ❞✐4❝"✐♠✐♥❛)✐✈❡ ❢❡❛)✉"❡4 ❝❛♥ )❤✉4 ❜❡ ❡①)"❛❝)❡❞ ❡✈❡♥ ✐❢ ❧❛❜❡❧❧❡❞ )"❛✐♥✐♥❣ 4❛♠♣❧❡4 ❛"❡ ❡✐)❤❡" ❧✐♠✐)❡❞ ✐♥ ♥✉♠❜❡" ♦" ❡♥)✐"❡❧② ❛❜4❡♥)✳ ■♥ ❝♦♥)"❛4) )♦ 4✉❝❤ ♣"❡✈✐♦✉4 ❛♣♣"♦❛❝❤❡4✱ )❤❡ ♥❡✇ ✇♦"❦ "❡♣♦")❡❞ ✐♥ )❤✐4 )❤❡4✐4 ❛❞❞"❡44❡4 )❤❡ ▼❱❉❘ ♣"♦❜❧❡♠ ❢"♦♠ ❛ ❞✐✛❡"❡♥) ❛♥❣❧❡✳ ■♥4♣✐"❡❞ ❜② )❤❡ ♣✐♦♥❡❡"✐♥❣ 4❡♠✐✲ 4✉♣❡"✈✐4❡❞ ❧❡❛"♥✐♥❣ ♠❡)❤♦❞ ❝♦✲#$❛✐♥✐♥❣ ❬❇❧✉♠ ❛♥❞ ▼✐)❝❤❡❧❧✱ ✶✾✾✽❜❪✱ )❤✐4 )❤❡4✐4 ✐♥)"♦❞✉❝❡4 ❛ ♥❡✇ ❝♦♥❝❡♣) ♦❢ )✉❜)♣❛❝❡ )#$✉❝#✉$❡ ❛❣$❡❡♠❡♥#✳ ❚❤❡ ♠❛✐♥ ✐❞❡❛ ✐♥✈♦❧✈❡4 ❧❡❛"♥✐♥❣ ♣"♦❥❡❝)✐♦♥4. P (1) ❛♥❞ P (2) ✱ 4✉❝❤ )❤❛) )❤❡ ❞❛)❛ 4)"✉❝)✉"❡ ♦❢ ♣"♦❥❡❝)❡❞ 4❛♠♣❧❡4 P (1) X (1) ❛♥❞ P (2) X (2) ✐4 ❛4 4✐♠✐❧❛" ❛4 ♣♦44✐❜❧❡✳ ❆❝❝♦"❞✐♥❣ )♦ ❞✐✛❡"❡♥) ❞❡✜♥✐)✐♦♥4 ♦❢ ❛❣$❡❡♠❡♥# ❛♥❞ ❞✐✛❡"❡♥) ❛♣✲ ♣❧✐❝❛)✐♦♥4✱ ♥❛♠❡❧② 4❡♠✐✲4✉♣❡"✈✐4❡❞ ❝❧❛44✐✜❝❛)✐♦♥✱ ✉♥4✉♣❡"✈✐4❡❞ ❝❧✉4)❡"✐♥❣ ❛♥❞ "❡)"✐❡✈❛❧✱ ✇❡ ♣"♦♣♦4❡ )❤"❡❡ ❞✐✛❡"❡♥) ▼❱❉❘ ❛♣♣"♦❛❝❤❡4✱ ✇❤✐❝❤ ❛"❡ ❞❡4❝"✐❜❡❞ ✐♥ )❤❡ ❢♦❧❧♦✇✐♥❣✳ ❚❤❡ ✜"4) ❛♣♣"♦❛❝❤ ✐4 ❛ ❞✐"❡❝) ❡①)❡♥4✐♦♥ ♦❢ ✐♥❝"❡♠❡♥)❛❧ ❝♦✲)"❛✐♥✐♥❣ )♦ 4❡♠✐✲4✉♣❡"✈✐4❡❞ ▼❱❉❘ ♣"♦❜❧❡♠4 ✈✐❛ )❤❡ ❝♦✲)"❛✐♥✐♥❣ ♦❢ ▲✐♥❡❛" ❉✐4❝"✐♠✐♥❛♥) ❆♥❛❧②4✐4 ✭▲❉❆✮ ❬❇❡❧❤✉♠❡✉" ❡) ❛❧✳✱ ✶✾✾✼❪ ♣"♦❥❡❝)✐♦♥4✳ ❚❤❡ ❛❧❣♦"✐)❤♠ ✐4 "❡❢❡""❡❞ )♦ ❛4 ❈♦✲▲❉❆ ❛♥❞ ✇❛4 ♣✉❜❧✐4❤❡❞ ✐♥ )❤❡ ♣"♦❝❡❡❞✐♥❣4 ♦❢ ■♥)❡"♥❛)✐♦♥❛❧ ❈♦♥❢❡"❡♥❝❡ ♦♥ ▼✉❧)✐♠❡❞✐❛ ❛♥❞ ❊①♣♦4✐)✐♦♥ ✭■❈▼❊✮ ✐♥ (1). (2). ✷✵✶✷✳ ❚❤❡ ✐♥♣✉) ✐♥✈♦❧✈❡4 ❛ 4♠❛❧❧ 4❡) ♦❢ )✇♦✲✈✐❡✇ ❧❛❜❡❧❧❡❞ )"❛✐♥✐♥❣ ❞❛)❛ {XL , XL ; Y } (1). (2). ❛♥❞ ❛ ❧❛"❣❡" ♣♦♦❧ ♦❢ ✉♥❧❛❜❡❧❧❡❞ ❞❛)❛ {XU , XU }✳ ❲❤✐❧❡ )❤❡ ❧❛"❣❡" ♣♦♦❧ ✐4 ✉♥❧❛❜❡❧❧❡❞✱ ✐)4. 4✐③❡ ✐4 ♠♦"❡ "❡♣"❡4❡♥)❛)✐✈❡ ♦❢ )❤❡ ✉♥❞❡"❧②✐♥❣ ❞❛)❛ ❞✐4)"✐❜✉)✐♦♥✳ ▲❉❆ ♣"♦❥❡❝)✐♦♥4 P (1) ❛♥❞. P (2) ❛"❡ ✐♥✐)✐❛❧❧② )"❛✐♥❡❞ ♦♥ ❡❛❝❤ ✈✐❡✇ ♦❢ )❤❡ ❧❛❜❡❧❧❡❞ )"❛✐♥✐♥❣ 4❡)✳ ❚❤❡ ✉♥❧❛❜❡❧❧❡❞ 4❡) ✐4 )❤❡♥ ♣"♦❥❡❝)❡❞ ✐♥)♦ )❤❡ 4❛♠❡ 4✉❜4♣❛❝❡4✱ ❛♥❞ 4❛♠♣❧❡4 ❛"❡ ❛44✐❣♥❡❞ ❧❛❜❡❧4 ❛❝❝♦"❞✐♥❣ )♦ ❛ ♥❡❛"❡4)✲❝❡♥)"♦✐❞ ❝❧❛44✐✜❡"✳ ❋♦" ❡❛❝❤ ✈✐❡✇✱ )❤❡ 4✉❜4❡) ♦❢ ✉♥❧❛❜❡❧❧❡❞ 4❛♠♣❧❡4 ✇❤✐❝❤ ❛"❡ ♠♦4) ❝♦♥✜❞❡♥)❧② ❧❛❜❡❧❧❡❞ ❛"❡ "❡♠♦✈❡❞ ❢"♦♠ )❤❡ ✉♥❧❛❜❡❧❧❡❞ 4❡) ❛♥❞ ❛❞❞❡❞ )♦ )❤❡ ❧❛❜❡❧❧❡❞ 4❡)✳ ❚❤❡ ▲❉❆ ♣"♦❥❡❝)✐♦♥4 ❛♥❞ ❝❧❛44✐✜❡"4 ❛"❡ )❤❡♥ "❡)"❛✐♥❡❞✳ ❚❤❡ ♣"♦❝❡44 ✐)❡"❛)❡4 ✉♥)✐❧ )❤❡ ✉♥❧❛✲ ❜❡❧❧❡❞ 4❡) ✐4 ❡♠♣)②✳ ❚❤❡ ♥❡✇ ❛❧❣♦"✐)❤♠ ✐4 4✉❝❝❡44❢✉❧ ✐♥ ✉)✐❧✐③✐♥❣ ✉♥❧❛❜❡❧❧❡❞ ❞❛)❛ )♦ ❛✈♦✐❞.
(15) ✶✹. ❈❤❛♣$❡& ✶ ✕ ■♥$&♦❞✉❝$✐♦♥. ♦✈❡%✲✜((✐♥❣ (♦ (❤❡ -♠❛❧❧❡% ❤❛♥❞✲❧❛❜❡❧❧❡❞ ❞❛(❛-❡(✳ ❲❤❡♥ (❡-(❡❞ ♦♥ (❤❡ ❜✐♠♦❞❛❧✱ ❢❛❝❡✲✈♦✐❝❡ ▼❖❇■❖ ❞❛(❛❜❛-❡ ❬▼❝❈♦♦❧ ❡( ❛❧✳✱ ✷✵✶✷❪✱ (❤❡ ♣%♦♣♦-❡❞ ❈♦✲▲❉❆ ❛❧❣♦%✐(❤♠ %❛✐-❡- ❛ ❜❛-❡❧✐♥❡ ✐❞❡♥(✐✜❝❛(✐♦♥ %❛(❡ ❢%♦♠ 71% (♦ 99% ✇❤✐❧❡ ✐♥ ❛ ✈❡%✐✜❝❛(✐♦♥ (❛-❦ (❤❡ ❊H✉❛❧ ❊%%♦% ❘❛(❡ ✭❊❊❘✮ ✐- %❡❞✉❝❡❞ ❢%♦♠ 16% (♦ ❧❡-- (❤❛♥ 1%✳ ■♥ ❛♥ ❡①(❡♥-✐♦♥ ♦❢ (❤✐- ✇♦%❦ ✇❤✐❝❤ ✇❛- ♣✉❜❧✐-❤❡❞ ✐♥ (❤❡ ♣%♦❝❡❡❞✐♥❣- ♦❢ ■♥(❡%♥❛(✐♦♥❛❧ ❈♦♥❢❡%❡♥❝❡ ♦♥ ❆❝♦✉-(✐❝-✱ ❙♣❡❡❝❤✱ ❛♥❞ ❙✐❣♥❛❧ O%♦❝❡--✐♥❣ ✭■❈❆❙❙O✮ ✷✵✶✸✱ ✇❡ -❤♦✇ (❤❛( ❙♣❛%-❡ ❘❡♣%❡-❡♥(❛(✐♦♥ ❈❧❛--✐✜❡% ✭❙❘❈✮ ❝♦✉❧❞ ❜❡ ❡♠♣❧♦②❡❞ (♦ %❡❥❡❝( ♦✉(✲♦❢✲❝❧❛-- -❛♠♣❧❡- ✇❤✐❝❤ ❜❡❧♦♥❣ (♦ ♥♦♥❡ ♦❢ (❤❡ %❡❣✐-(❡%❡❞ ❝❧❛--❡-✳ ■♥ %❡❧❛(❡❞ ✇♦%❦ ♣✉❜❧✐-❤❡❞ ✐♥ ♣%♦❝❡❡❞✐♥❣- ♦❢ ■♥(❡%♥❛(✐♦♥❛❧ ❈♦♥❢❡%❡♥❝❡ ♦♥ ■♠❛❣❡ O%♦❝❡--✐♥❣ ✭■❈■O✮ ✷✵✶✶ ❛♥❞ ❊✉%♦♣❡❛♥ ❙✐❣♥❛❧ O%♦❝❡--✐♥❣ ❈♦♥❢❡%❡♥❝❡ ✭❊❯❙■O❈❖✮ ✷✵✶✶✱ ✇❡ ❛❧-♦ ♣%♦♣♦-❡❞ ❛ -❡❧❢✲(%❛✐♥✐♥❣ ✈❡%-✐♦♥ ♦❢ (❤❡ ❛❧❣♦%✐(❤♠ ✇❤✐❝❤ ❝♦✉❧❞ ❜❡ ❛♣♣❧✐❡❞ (♦ -✐♥❣❧❡✲♠♦❞❛❧ -②-(❡♠-✳ ❚❤❡ -(❛♥❞❛%❞ ❝♦✲(%❛✐♥✐♥❣ ❛❧❣♦%✐(❤♠ ✐- -❡♠✐✲-✉♣❡%✈✐-❡❞ ❛♥❞ ♥❡❡❞- ❛( -♦♠❡ ❧❛❜❡❧❧❡❞ ❞❛(❛ ❢♦% ✐♥✐(✐❛❧✐③❛(✐♦♥✳ ❋♦% ♣✉%❡❧② ✉♥-✉♣❡%✈✐-❡❞ ❝❧✉-(❡%✐♥❣ ♣%♦❜❧❡♠-✱ ✇❡ ♣%♦♣♦-❡❞ ❛ ♠✉❧(✐✲✈✐❡✇ -✉❜-♣❛❝❡ ❝❧✉-(❡%✐♥❣ ❛❧❣♦%✐(❤♠ ✇❤✐❝❤ ✐- ❜❛-❡❞ ♦♥ ❛ ♠✉❧(✐✲✈✐❡✇ ❝❧✉-(❡% ❛❣%❡❡♠❡♥( ❛--✉♠♣(✐♦♥✳ ❲❡ ❝♦♥-✐❞❡% (❤❡ ♣%♦❜❧❡♠ ♦❢ ❝❧✉-(❡%✐♥❣ ❛ ❣%♦✉♣ ♦❢ ✉♥❧❛❜❡❧❧❡❞ (✇♦✲✈✐❡✇✱ ❤✐❣❤✲❞✐♠❡♥-✐♦♥❛❧ ❞❛(❛. X (1) , X (2) ✐♥(♦ k ❝❧✉-(❡%-✱ ❛♥❞ -❛♠♣❧❡- ✐♥ (❤❡ -❛♠❡ ❝❧❛-- ❛%❡ ❡①♣❡❝(❡❞ (♦ ❜❡ ❛--✐❣♥❡❞ (♦ (❤❡ -❛♠❡ ❝❧✉-(❡%✳ ❙✐♥❝❡ X (1) ❛♥❞ X (2) ❛%❡ ❞✐✛❡%❡♥( %❡♣%❡-❡♥(❛(✐♦♥- ♦❢ (❤❡ -❛♠❡ ✉♥❞❡%❧②✐♥❣ ❝❧❛--. Y ✱ ✐♥ ✐❞❡❛❧ ❝♦♥❞✐(✐♦♥-✱ ✐❞❡♥(✐❝❛❧ ❝❧✉-(❡%✐♥❣ %❡-✉❧(- ❛%❡ ❡①♣❡❝(❡❞ ✐%%❡-♣❡❝(✐✈❡ ♦❢ (❤❡ ✈✐❡✇ ✉-❡❞ ❢♦% ❝❧✉-(❡%✐♥❣✳ ❍♦✇❡✈❡%✱ (❤✐- ✐- ✉♥❧✐❦❡❧② ✐❢ ❝❧✉-(❡%✐♥❣ ✐- ♣❡%❢♦%♠❡❞ ✐♥ (❤❡ ♦%✐❣✐♥❛❧ ❢❡❛(✉%❡ -♣❛❝❡- X (1) ❛♥❞ X (2) -✐♥❝❡ (❤❡② ❛%❡ ❝♦%%✉♣(❡❞ ❜② ❞✐✛❡%❡♥( ✐♥(%❛✲❝❧❛-- ✈❛%✐❛(✐♦♥✳ ❚❤✐- (❤❡✲ -✐- ✐♥(%♦❞✉❝❡- ❛ ♥❡✇ ❛♣♣%♦❛❝❤ (♦ ♠✉❧(✐✲✈✐❡✇ -✉❜-♣❛❝❡ ❝❧✉-(❡%✐♥❣ ✇❤✐❝❤ -❡❡❦- ♣%♦❥❡❝(✐♦♥-. P (1) ❛♥❞ P (2) -✉❝❤ (❤❛( (❤❡ ❝❧✉-(❡%✐♥❣ %❡-✉❧(- ❛%❡ ✐♥ ♠❛①✐♠❛❧ ❛❣%❡❡♠❡♥( ✐♥ (❤❡ -✉❜-♣❛❝❡❛❝%♦-- ❡❛❝❤ ✈✐❡✇✳ ❲❡ -❤♦✇ (❤❛( (❤✐- ♦❜❥❡❝(✐✈❡ ❝❛♥ ❜❡ ♦❜(❛✐♥❡❞ ❜② ❝♦♠❜✐♥✐♥❣ (❤❡ -✐♠✲ ♣❧✐❝✐(② ♦❢ ❦✲♠❡❛♥- ❝❧✉-(❡%✐♥❣ ❛♥❞ ▲✐♥❡❛% ❉✐-❝%✐♠✐♥❛♥( ❆♥❛❧②-✐- ✭▲❉❆✮ ✇✐(❤✐♥ ❛ ❝♦✲(%❛✐♥✐♥❣ -❝❤❡♠❡✳ ❚❤❡ ♥❡✇ ❛❧❣♦%✐(❤♠ ❡①♣❧♦✐(- ❝❧✉-(❡% ✐♥❞✐❝❛(♦%- ♦❜(❛✐♥❡❞ ❢%♦♠ ❦✲♠❡❛♥- ❝❧✉-(❡%✐♥❣ ✐♥ ♦♥❡ ✈✐❡✇ (♦ ❧❡❛%♥ ❞✐-❝%✐♠✐♥❛(✐✈❡ -✉❜-♣❛❝❡- ✐♥ ❛♥♦(❤❡%✳ ❚❤❡ ❛❧❣♦%✐(❤♠ ✐- %❡❢❡%%❡❞ (♦ ❛❈♦❑♠▲❉❆✳ ❲❡ -❤♦✇ ♠❛(❤❡♠❛(✐❝❛❧❧② ❤♦✇ ▲❉❆ ♣%♦❥❡❝(✐♦♥- ❧❡❛%♥❡❞ ❢%♦♠ -❛♠♣❧❡- ✇✐(❤ %❛♥✲ ❞♦♠ ❧❛❜❡❧ ♥♦✐-❡ ❛%❡ ♣%♦❜❛❜✐❧✐-(✐❝❛❧❧② ❡H✉✐✈❛❧❡♥( (♦ (❤♦-❡ ❧❡❛%♥❡❞ ✇✐(❤ ❝❧❡❛♥ ❧❛❜❡❧- ❛♥❞ (❤❛( ❝%♦--✲✈✐❡✇ ❧❛❜❡❧❧✐♥❣✱ ♦% ❝♦✲(%❛✐♥✐♥❣✱ ✐- ❡✣❝✐❡♥( ✐♥ ❝♦%%❡❝(✐♥❣ ❡%%♦♥❡♦✉- -❛♠♣❧❡ ❧❛❜❡❧-✳ ❖❢ ♣❛%(✐❝✉❧❛% ♠❡%✐(✱ (❤❡ ❛❧❣♦%✐(❤♠ ❞♦❡- ♥♦( %❡H✉✐%❡ (❤❡ ♦♣(✐♠✐③❛(✐♦♥ ♦❢ ❛♥② ❤②♣❡%✲♣❛%❛♠❡(❡%-✳ ❚❤❡ ❡✛❡❝(✐✈❡♥❡-- ♦❢ (❤❡ ♣%♦♣♦-❡❞ ❛❧❣♦%✐(❤♠ ✐- ❞❡♠♦♥-(%❛(❡❞ ♥♦( ♦♥❧② ✐♥ -♣❡❛❦❡% ❝❧✉-(❡%✐♥❣ ❡①♣❡%✐♠❡♥(- ♦♥ (❤❡ -❛♠❡ ❜✐♠♦❞❛❧✱ ❢❛❝❡✲✈♦✐❝❡ ▼❖❇■❖ ❞❛(❛❜❛-❡✱ ❜✉( ❛❧-♦ ✐♥ ♠♦%❡ ❣❡♥❡%❛❧ ❝❧✉-(❡%✐♥❣ (❛-❦- -✉❝❤ ❛- ❤❛♥❞✇%✐((❡♥ ❞✐❣✐( ❝❧✉-(❡%✐♥❣ ❛♥❞ (❡①( ❞♦❝✉♠❡♥( ❝❧✉-(❡%✐♥❣✳ ❙✐❣✲ ♥✐✜❝❛♥( ✐♠♣%♦✈❡♠❡♥( ♦✈❡% ❛❧(❡%♥❛(✐✈❡ ♠✉❧(✐✲✈✐❡✇ ❝❧✉-(❡%✐♥❣ ❛♣♣%♦❛❝❤❡- -✉❝❤ ❛- ❈❈❆ ❛♥❞ ❝♦✲-♣❡❝(%❛❧ ❝❧✉-(❡%✐♥❣ ❛%❡ %❡♣♦%(❡❞✳ ❚❤✐- ✇♦%❦ ❤❛- ❜❡❡♥ -✉❜♠✐((❡❞ (♦ ❛ ❙♣❡❝✐❛❧ ■--✉❡ ♦♥ ❯♥-✉♣❡%✈✐-❡❞ ❛♥❞ ❙✉♣❡%✈✐-❡❞ ▲❡❛%♥✐♥❣ ✐♥ O❛((❡%♥ ❘❡❝♦❣♥✐(✐♦♥ ▲❡((❡%-✳.
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The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est
The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est
The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est
The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est
The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est
The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est
The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est
The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est