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This is an author’s version published in: http://oatao.univ-toulouse.fr/23564
To cite this version:
Berkoune, Karima. Approche mathématique pour la Modulation de
Largeur d'Impulsion (MLI) pour la conversion statique de l'énergie électrique : application aux onduleurs multiniveaux. PhD,
l’Universit´e Toulouse 3 Paul Sabatier (UT3 Paul Sabatier), 2016
TH `
ESE
En vue de l’obtention du
DOCTORAT DE L’UNIVERSIT´
E DE TOULOUSE
D´elivr´e par :l’Universit´e Toulouse 3 Paul Sabatier (UT3 Paul Sabatier)
Pr´esent´ee et soutenue le01/07/2016 par :
Karima BERKOUNE
Approche Math´ematique pour la Modulation de Largeur d’Impulsion pour la conversion statique de l’´energie ´electrique : Application aux
onduleurs multiniveaux.
JURY
M. Seddik BACHA Professeur des universit´es, G2ELab
Rapporteur M. Nicolas PATIN Maˆıtre de conf´erence HDR,
UTC
Rapporteur Mme. Ilhem SLAMA
BELKHODJA
Professeur des universit´es, TUNIS
Membre du Jury M. Philippe LEMOIGNE Professeur des universit´es, L2EP Membre du Jury M. Patrick AUSTIN Professeur des universit´es,
LAAS
Membre du Jury M. Paul-Etienne VIDAL Maˆıtre de conf´erence,
LGP-ENIT
Directeur de th´ese M. Fr´ed´eric ROTELLA Professeur des universit´es,
LGP-ENIT
Co-encadrant de th´ese
´
Ecole doctorale et sp´ecialit´e :
GEET : G´enie Electrique
Unit´e de Recherche :
Laboratoire G´enie de Production LGP
Directeur de Th`ese :
M. Paul-Etienne VIDAL
Rapporteurs :
❚❛❜❧❡ ❞❡& ♠❛(✐*+❡&
❘❡♠❡#❝✐♠❡♥'( ✾ ◆♦'❛'✐♦♥( ✶✶ ❘.(✉♠. ✶✸ ❆❜('#❛❝' ✶✺ ■♥'#♦❞✉❝'✐♦♥ ❣.♥.#❛❧❡ ✷✺ ✶ ▲❛ ❝♦♥✈❡#(✐♦♥ ('❛'✐;✉❡ ❞❡ ❧✬.♥❡#❣✐❡ ✷✾✶✳✶ ❈♦♥&(✐(✉(✐♦♥ ❞✬✉♥ ❝♦♥✈❡+(✐&&❡✉+ &(❛(✐5✉❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✶✳✷ ▲❡& ♦♥❞✉❧❡✉+& ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✶✳✷✳✶ ❉♦♠❛✐♥❡ ❞✬❛♣♣❧✐❝❛(✐♦♥ ❞✬♦♥❞✉❧❡✉+& ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✶✳✷✳✷ ❉✐✛<+❡♥(& (②♣❡& ❞✬♦♥❞✉❧❡✉+& ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ✶✳✷✳✷✳✶ ❖♥❞✉❧❡✉+ ❞❡ ❝♦✉+❛♥( ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ✶✳✷✳✷✳✷ ❖♥❞✉❧❡✉+ ❞❡ (❡♥&✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✶✳✷✳✸ ❆+❝❤✐(❡❝(✉+❡& ✐❞<❛❧❡& ❞❡& ♦♥❞✉❧❡✉+& ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✶✳✷✳✸✳✶ ▲❛ ❝❡❧❧✉❧❡ <❧<♠❡♥(❛✐+❡ ❞❡ ❝♦♠♠✉(❛(✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✶✳✷✳✸✳✷ ❖♥❞✉❧❡✉+ ❡♥ ♣♦♥( ♠♦♥♦♣❤❛&< ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼ ✶✳✷✳✸✳✸ ❖♥❞✉❧❡✉+ (+✐♣❤❛&< ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✶✳✷✳✸✳✹ ▲❡& ♦♥❞✉❧❡✉+& ♠✉❧(✐♥✐✈❡❛✉① ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ✶✳✸ H✐❧♦(❛❣❡ ❞❡& ♦♥❞✉❧❡✉+& ❞❡ (❡♥&✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺ ✶✳✸✳✶ ▲❡& &(+❛(<❣✐❡& ❞❡ ♠♦❞✉❧❛(✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺ ✶✳✸✳✶✳✶ ▲❡& &(+❛(<❣✐❡& ❞❡ ▼♦❞✉❧❛(✐♦♥ ❞❡ ▲❛+❣❡✉+ ❞✬■♠♣❧✉&✐♦♥ &✐♥✉&♦L❞❛❧❡ ✺✻ ✶✳✸✳✶✳✷ ▲❡& &(+❛(<❣✐❡& ❞❡ ♠♦❞✉❧❛(✐♦♥ ✈❡❝(♦+✐❡❧❧❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵ ✶✳✸✳✶✳✸ ▲❡& &(+❛(<❣✐❡& ❞❡ ♠♦❞✉❧❛(✐♦♥ ❞<✈❡❧♦♣♣<❡& ♣♦✉+ ❧❡& ❛+❝❤✐(❡❝(✉+❡&
❞✬♦♥❞✉❧❡✉+& ♠✉❧(✐♥✐✈❡❛✉① ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹ ✶✳✸✳✷ ▲✐❡♥& ❡♥(+❡ ♠♦❞✉❧❛(✐♦♥ ❡( ❛+❝❤✐(❡❝(✉+❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽ ✶✳✹ ❈♦♥❝❧✉&✐♦♥ ❡( ♦+✐❡♥(❛(✐♦♥ ❞❡ ❧✬<(✉❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾
✷ ▼♦❞$❧❡' ❣)♥)+✐-✉❡' ♣♦✉+ ❧❛ ♠✐'❡ ❡♥ 2✉✈+❡ ❞❡' '4+❛4)❣✐❡' ❞❡ ♠♦❞✉❧❛4✐♦♥' ✼✸ ✷✳✶ ■♥(+♦❞✉❝(✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸ ✷✳✷ ▼✐&❡ ❡♥ 7✉✈+❡ ❞✉ ♠♦❞*❧❡ ♠♦②❡♥ ♣♦✉+ ✉♥❡ &(+❛(;❣✐❡ ▼▲■ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹ ✷✳✷✳✶ ❆♣♣❧✐❝❛(✐♦♥ @ ✉♥❡ ❝❡❧❧✉❧❡ ❞❡ ❝♦♠♠✉(❛(✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹ ✷✳✷✳✷ ❆♣♣❧✐❝❛(✐♦♥ @ ✉♥ &②&(*♠❡ (+✐♣❤❛&; @ ❞❡✉① ♥✐✈❡❛✉① ❞❡ (❡♥&✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻ ✷✳✷✳✷✳✶ ▼♦❞*❧❡ ✐♥✐(✐❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻ ✷✳✷✳✷✳✷ ❙✐♠♣❧✐✜❝❛(✐♦♥ ❞✉ ♠♦❞*❧❡ ✐♥✐(✐❛❧ ❡♥ ✈✉❡ ❞❡ ❧✬♦❜(❡♥(✐♦♥ ❞✬✉♥ ❡♥✲
&❡♠❜❧❡ ❞❡ &♦❧✉(✐♦♥& ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✾ ✷✳✷✳✸ ❊①♣+❡&&✐♦♥ ❞❡& +❡❧❛(✐♦♥& ❡♥(+❡ ❧❛ ♣♦+(❡✉&❡ ❡( ❧❛ ♠♦❞✉❧❛♥(❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✵ ✷✳✷✳✹ ❇✐❧❛♥ ❞✉ ♠♦❞*❧❡ ✐♥✐(✐❛❧ ♣+;&❡♥(; ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✸ ✷✳✸ ❉;✈❡❧♦♣♣❡♠❡♥( ❞✬✉♥ ♠♦❞*❧❡ ❣;♥;+✐N✉❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✸ ✷✳✸✳✶ ❊①(❡♥&✐♦♥ ❞✉ ♠♦❞*❧❡ ✐♥✐(✐❛❧ ❛✉① &(+❛(;❣✐❡& ❞❡ ♠♦❞✉❧❛(✐♦♥ ✈❡❝(♦+✐❡❧❧❡ ✳ ✳ ✳ ✽✸ ✷✳✸✳✶✳✶ ❆♣♣❧✐❝❛(✐♦♥ @ ✉♥❡ ❝❡❧❧✉❧❡ ❞❡ ❝♦♠♠✉(❛(✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✹ ✷✳✸✳✶✳✷ ❆♣♣❧✐❝❛(✐♦♥ @ ✉♥ ♦♥❞✉❧❡✉+ ❝❧❛&&✐N✉❡ @ ❞❡✉① ♥✐✈❡❛✉① ❞❡ (❡♥&✐♦♥ ✳ ✽✺ ✷✳✸✳✷ ❆♣♣❧✐❝❛(✐♦♥ ❞✉ ♠♦❞*❧❡ ✐♥✐(✐❛❧ ❛✉① ❛+❝❤✐(❡❝(✉+❡& ♠✉❧(✐♥✐✈❡❛✉① ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✻ ✷✳✸✳✷✳✶ ▼♦❞*❧❡ ❞✬✉♥❡ ♣❤❛&❡ @ ❝❡❧❧✉❧❡& ;❧;♠❡♥(❛✐+❡& ✐♠❜+✐N✉;❡& ✳ ✳ ✳ ✳ ✳ ✽✻ ✷✳✸✳✷✳✷ ❊①(❡♥&✐♦♥ @ ✉♥ ♦♥❞✉❧❡✉+ (+✐♣❤❛&; ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✵ ✷✳✸✳✸ ❆♣♣❧✐❝❛(✐♦♥ ❞✉ ♠♦❞*❧❡ ❣;♥;+✐N✉❡ ♠✉❧(✐♥✐✈❡❛✉① ❛✉① ❛+❝❤✐(❡❝(✉+❡& +;❡❧❧❡&
♠✉❧(✐♥✐✈❡❛✉① @ ❝❡❧❧✉❧❡& ✐♠❜+✐N✉;❡& ❡( @ ❝❡❧❧✉❧❡& ❡♥ &;+✐❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✸ ✷✳✸✳✸✳✶ ❖♥❞✉❧❡✉+ @ ❝❛♣❛❝✐(;& ✢♦((❛♥(❡& @ N ♥✐✈❡❛✉① ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✸ ✷✳✸✳✸✳✷ ❖♥❞✉❧❡✉+ ❡♥ ♣♦♥( ❡♥ ❍ ✭❍ ❇+✐❞❣❡✮ @ N ♥✐✈❡❛✉① ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✻ ✷✳✸✳✹ ●;♥;+❛❧✐&❛(✐♦♥ ❞❡ ❧❛ ♠;(❤♦❞❡ ❞❡ ♠♦❞;❧✐&❛(✐♦♥ @ ❞✬❛✉(+❡& ❛+❝❤✐(❡❝(✉+❡&
♣✐❧♦(;❡& ♣❛+ ❧❡& ✐♥&(❛♥(& ❞❡ ❝♦♠♠✉(❛(✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✾ ✷✳✸✳✹✳✶ ❈❛& ❞❡ ❧✬♦♥❞✉❧❡✉+ @ ❞✐♦❞❡& ❝❧❛♠♣;❡& @ (+♦✐& ♥✐✈❡❛✉① ❞❡ (❡♥&✐♦♥ ✳ ✾✾ ✷✳✸✳✹✳✷ ❈❛& ❞✉ ❝♦♥✈❡+(✐&&❡✉+ ♠♦❞✉❧❛✐+❡ ♠✉❧(✐♥✐✈❡❛✉① @ (+♦✐& ♥✐✈❡❛✉① ❞❡
(❡♥&✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✸ ✷✳✹ ❈♦♥❝❧✉&✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✼
✸ ❊①♣+❡''✐♦♥ ❞❡' ❡♥'❡♠❜❧❡' ❞❡ '♦❧✉4✐♦♥' ✶✵✾
✸✳✶ ■♥(+♦❞✉❝(✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✾ ✸✳✷ ●;♥;+❛❧✐(;& &✉+ ❧❡& ✐♥✈❡+&❡& ❣;♥;+❛❧✐&;❡& ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✾ ✸✳✷✳✶ ◆♦(✐♦♥ ❞✬✐♥✈❡+&❡& ❣;♥;+❛❧✐&;❡& ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✵ ✸✳✷✳✷ ❘;&♦❧✉(✐♦♥ ❞✬✉♥ &②&(*♠❡ ❧✐♥;❛✐+❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✶ ✸✳✷✳✸ ❋❛❝(♦+✐&❛(✐♦♥ ❞❡ +❛♥❣ ♠❛①✐♠❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✷ ✸✳✸ ❆♣♣❧✐❝❛(✐♦♥ @ ✉♥ ♦♥❞✉❧❡✉+ (+✐♣❤❛&; ❝❧❛&&✐N✉❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✷ ✸✳✹ ▼✐&❡ ❡♥ 7✉✈+❡ ❞❡ ❧✬♦✉(✐❧ ♠❛(❤;♠❛(✐N✉❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✹
✸✳✹✳✶ ❊①♣+❡&&✐♦♥& ❞❡& ❡♥&❡♠❜❧❡& ❞❡ &♦❧✉(✐♦♥& @ ♣❛+(✐+ ❞❡& ♠♦❞*❧❡& ♠♦②❡♥& ❞✬♦♥✲ ❞✉❧❡✉+& (+✐♣❤❛&;& @ N ♥✐✈❡❛✉① ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✹ ✸✳✹✳✶✳✶ ❖♥❞✉❧❡✉+ @ ❝❛♣❛❝✐(;& ✢♦((❛♥(❡& ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✺ ✸✳✹✳✶✳✷ ❖♥❞✉❧❡✉+ ❍✲❇+✐❞❣❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✼
✸✳✹✳✷ ❊①♣+❡&&✐♦♥& ❞❡& ❡♥&❡♠❜❧❡& ❞❡ &♦❧✉(✐♦♥& 6 ♣❛+(✐+ ❞❡& ♠♦❞*❧❡& ♠♦②❡♥& ❞✬♦♥✲ ❞✉❧❡✉+& (+✐♣❤❛&;& 6 3 ♥✐✈❡❛✉① ❞❡ (❡♥&✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✾ ✸✳✹✳✷✳✶ ❈❛& ❞✬✉♥ ♦♥❞✉❧❡✉+ 6 ❞✐♦❞❡& ❝❧❛♠♣;❡& ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✾ ✸✳✹✳✷✳✷ ❈❛& ❞✬✉♥ ♦♥❞✉❧❡✉+ ♠♦❞✉❧❛✐+❡ ♠✉❧(✐♥✐✈❡❛✉① ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✷ ✸✳✺ ❈♦♥❝❧✉&✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✺ ✹ ❊①❡♠♣❧❡' ❞✬❛♣♣❧✐❝❛-✐♦♥' ✶✷✼ ✹✳✶ ■♥(+♦❞✉❝(✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✼ ✹✳✷ ❆♣♣❧✐❝❛(✐♦♥ 6 ✉♥ ♦♥❞✉❧❡✉+ (+✐♣❤❛&; ❝❧❛&&✐E✉❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✼ ✹✳✷✳✶ ▼♦❞*❧❡ ❞❡ ❧✬♦♥❞✉❧❡✉+ (+✐♣❤❛&; ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✽ ✹✳✷✳✶✳✶ ❊①♣+❡&&✐♦♥ ❞❡& &♦❧✉(✐♦♥& ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✽ ✹✳✷✳✶✳✷ ❚+❛♥&❧❛(✐♦♥ ❞❡ ❧❛ &♦❧✉(✐♦♥ ❞❡ ❜❛&❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✵ ✹✳✷✳✷ ❘;&✉❧(❛(& ❞❡ &✐♠✉❧❛(✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✵ ✹✳✷✳✷✳✶ ▼▲■ &✐♥✉&♦✐❞❛❧❡ ❙L❲▼ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✶ ✹✳✷✳✷✳✷ ▼▲■ 6 &;E✉❡♥❝❡ ③;+♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✸ ✹✳✷✳✷✳✸ ❖♣(✐♠✐&❛(✐♦♥ ❡( ❝❤♦✐① ♣♦✉+ ❧❡ ❞❡❣+; ❞❡ ❧✐❜❡+(; ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✺ ✹✳✷✳✸ ❘;❛❧✐&❛(✐♦♥ ❡①♣;+✐♠❡♥(❛❧❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✺ ✹✳✷✳✸✳✶ ■♥(+♦❞✉❝(✐♦♥ 6 ❧❛ ❝❛+(❡ ❞❙L❆❈❊ ❉❙✶✶✵✹ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✺ ✹✳✷✳✸✳✷ ❘;❛❧✐&❛(✐♦♥ ❡( ❞❡&❝+✐♣(✐♦♥ ❞✉ ❜❛♥❝ ❞✬❡&&❛✐& ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✵ ✹✳✷✳✸✳✸ ❘;&✉❧(❛(& ❡①♣;+✐♠❡♥(❛✉① ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✶ ✹✳✸ ▼♦❞*❧❡ ❞✬♦♥❞✉❧❡✉+ 6 ❝❛♣❛❝✐(;& ✢♦((❛♥(❡& 6 (+♦✐& ♥✐✈❡❛✉① ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✾ ✹✳✸✳✶ ▼♦❞*❧❡ ❞❡ ❧✬♦♥❞✉❧❡✉+ 6 ❝❛♣❛❝✐(;& ✢♦((❛♥(❡& 6 (+♦✐& ♥✐✈❡❛✉① ❞❡ (❡♥&✐♦♥ ✳ ✳ ✶✺✾ ✹✳✸✳✷ ❘;&✉❧(❛(& ❞❡ &✐♠✉❧❛(✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻✷ ✹✳✹ ❈♦♥❝❧✉&✐♦♥ ❞✉ ❝❤❛♣✐(+❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻✼ ❈♦♥❝❧✉'✐♦♥ ❣6♥67❛❧❡ ✶✻✾ ✺ ❆♥♥❡①❡' ✶✽✸ ❆♥♥❡①❡ ❆ ▲❡' '❡♠✐✲❝♦♥❞✉❝-❡✉7' ✶✽✺ ❆♥♥❡①❡ ❇ ❊①♣7❡''✐♦♥ ❞❡' 7❡❧❛-✐♦♥' ❡♥-7❡ ❧❛ ♣♦7-❡✉'❡ ❡- ❧❛ ♠♦❞✉❧❛♥-❡ ✶✽✼ ❇✳✶ L+❡♠✐*+❡ ❝♦♥❞✐(✐♦♥ ❞❡ (+❛✈❛✐❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽✼ ❇✳✶✳✶ ❚+✐❛♥❣❧❡ ❜♦+♥; ❡♥(+❡ [0, 1] ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽✼ ❇✳✶✳✶✳✶ ❚+✐❛♥❣❧❡ ❞✐+❡❝( ❡♥(+❡ [0, 1] ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽✽ ❇✳✶✳✶✳✷ ❚+✐❛♥❣❧❡ ✐♥✈❡+&; ❡♥(+❡ [0, 1] ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽✾ ❇✳✶✳✷ ❉❡♥( ❞❡ &❝✐❡ ❜♦+♥;❡ ❡♥(+❡ [0, 1] ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾✶ ❇✳✶✳✷✳✶ ❉❡♥( ❞❡ &❝✐❡ ❞✐+❡❝(❡ ❡♥(+❡ [0, 1] ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾✶ ❇✳✶✳✷✳✷ ❉❡♥( ❞❡ &❝✐❡ ✐♥✈❡+&;❡ ❡♥(+❡ [0, 1] ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾✸ ❇✳✶✳✸ ❚+✐❛♥❣❧❡ ❜♦+♥; ❡♥(+❡ [−1 2, 1 2] ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾✹ ❇✳✶✳✸✳✶ ❚+✐❛♥❣❧❡ ❞✐+❡❝( ❡♥(+❡ [−1 2, 1 2] ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾✹ ❊◆■❚✲▲●L ✷✵✶✻ ✺
❇✳✶✳✸✳✷ ❚+✐❛♥❣❧❡ ✐♥✈❡+&4 ❡♥(+❡ [−1 2, 1 2] ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾✻ ❇✳✶✳✹ ❉❡♥( ❞❡ &❝✐❡ ❜♦+♥4❡ ❡♥(+❡ [−1 2, 1 2] ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾✽ ❇✳✶✳✹✳✶ ❉❡♥( ❞❡ &❝✐❡ ❞✐+❡❝(❡ ❡♥(+❡ [−1 2, 1 2] ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾✽ ❇✳✶✳✹✳✷ ❉❡♥( ❞❡ &❝✐❡ ✐♥✈❡+&4❡ ❡♥(+❡ [−1 2, 1 2]✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾✾ ❆♥♥❡①❡ ❈ ❘❛♣♣❡❧) ♠❛+❤-♠❛+✐/✉❡) ✷✵✶ ❈✳✶ =+♦❞✉✐( ❞❡ ❑+♦♥❡❝❦❡+ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵✶ ❈✳✶✳✶ =+♦♣+✐4(4& ❞✉ ♣+♦❞✉✐( ❞❡ ❦+♦♥❡❝❦❡+ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵✶ ❈✳✷ ❋❛❝(♦+✐&❛(✐♦♥ ❞✉ +❛♥❣ ♠❛①✐♠❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵✷ ❈✳✸ ❉✐✛4+❡♥(❡& ♠❛(+✐❝❡& ✉(✐❧✐&4❡& ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵✷
❆♥♥❡①❡ ❉ ❋✐❝❤❡ +❡❝❤♥✐/✉❡ ❞❡ ❙❊▼■❑❘❖◆ ✷✵✺
❆♥♥❡①❡ ❊ ❈❛❧❝✉❧ ❞❡) ♣❡@+❡) ♣❛@ ❝♦♠♠✉+❛+✐♦♥ ✷✶✶
❊✳✶ ❊①♣+❡&&✐♦♥ ❞❡& ❝♦✉+❛♥(& ♠♦②❡♥& ❡( ❡✣❝❛❝❡& ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶✸ ❊✳✶✳✶ ❈♦✉+❛♥( ♠♦②❡♥ ❞❛♥& ❧✬✐♥(❡++✉♣(❡✉+ T1 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶✸ ❊✳✶✳✷ ❈♦✉+❛♥( ♠♦②❡♥ ❞❛♥& ❧❛ ❞✐♦❞❡ D2 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶✸ ❊✳✶✳✸ ❈♦✉+❛♥( ♠♦②❡♥ ❞❛♥& T2 ❡( D1 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶✸ ❊✳✶✳✹ ❈♦✉+❛♥( ❡✣❝❛❝❡ ❞❛♥& ❧✬✐♥(❡++✉♣(❡✉+ T1 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶✹ ❊✳✶✳✺ ❈♦✉+❛♥( ❡✣❝❛❝❡ ❞❛♥& ❧❛ ❞✐♦❞❡ D2 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶✹ ❊✳✶✳✻ ❈♦✉+❛♥( ❡✣❝❛❝❡ ❞❛♥& T2 ❡( D1 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶✹ ❆♥♥❡①❡ ❋ ❙❝❤-♠❛) ▼▲■ ✉+✐❧✐)-) )♦✉) ▼❆❚▲❆❇ ✷✶✺ ✻ ❊◆■❚✲▲●= ✷✵✶✻
❆ ♠❡& (+-& ❝❤❡+& ♣❛+❡♥(& ❆ ♠❡& ❢+*+❡& ❡( &3✉+ ❆ (♦✐ ❈♦+❡♥(✐♥
✓ ▲❛ ❝♦♥♥❛✐&&❛♥❝❡ &✬❛❝:✉✐❡+( ♣❛+ ❧✬❡①♣-+✐❡♥❝❡✱ (♦✉( ❧❡ +❡&(❡ ♥✬❡&( :✉❡ ❞❡ ❧✬✐♥❢♦+♠❛(✐♦♥✳ ✔ ❆❧❜❡+( ❊✐♥&(❡✐♥
❘❡♠❡#❝✐♠❡♥'(
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▼▲■ ▼♦❞✉❧❛"✐♦♥ ❞❡ ▲❛.❣❡✉. ❞✬■♠♣✉❧&✐♦♥ 3❲▼ 3✉❧&❡ ❲✐❞"❤ ▼♦❞✉❧❛"✐♦♥ ❙3❲▼ ❙✐♥✉&♦✐❞❛❧ 3✉❧&❡ ❲✐❞"❤ ▼♦❞✉❧❛"✐♦♥ ❚❍■3❲▼ ❚❤✐.❞ ❍❛.♠♦♥✐❝ ■♥❥❡❝"✐♦♥ 3✉❧&❡ ❲✐❞"❤ ▼♦❞✉❧❛"✐♦♥ ❉3❲▼ ❉✐&❝♦♥"✐♥✉♦✉& 3✉❧&❡ ❲✐❞"❤ ▼♦❞✉❧❛"✐♦♥ ■●❇❚ ■♥&✉❧❛"❡❞✲●❛"❡ ❇✐♣♦❧❛. ❚.❛♥&✐&"♦. ▼❖❙❋❊❚ ▼❡"❛❧ ❖①✐❞❡ ❙❡♠✐❝♦♥❞✉❝"♦. ❋✐❡❧❞ ❊✛❡❝" ❚.❛♥&✐&"♦. ❇❏❚ ❇✐♣♦❧❛. ❏✉♥❝"✐♦♥ ❚.❛♥&✐&"♦. ●❚❖ ●❛"❡ ❚✉.♥ ❖✛ ◆3❈ ◆❡✉".❛❧ 3♦✐♥" ❈❧❛♠♣❡❞ ❋❈ ❋❧②✐♥❣ ❈❛♣❛❝✐"♦. ▼▼❈ ▼♦❞✉❧❛. ▼✉❧"✐❧❡✈❡❧ ❈♦♥✈❡."❡. ❍❱❉❈ ❍✐❣❤✲❱♦❧"❛❣❡ ❉✐.❡❝" ❈✉..❡♥" ❙❱▼ ❙♣❛❝❡ ❱❡❝"♦. ▼♦❞✉❧❛"✐♦♥ ❇❋ ❇❛&&❡ ❋.IJ✉❡♥❝❡ ❍❋ ❍❛✉"❡ ❋.IJ✉❡♥❝❡ 3❙ 3❤❛&❡ ❙❤✐❢"❡❞ ❈❉ ❈❛..✐❡. ❉✐&♣♦&✐"✐♦♥3❖❉ 3❤❛&❡ ❖♣♣♦&✐"✐♦♥ ❉✐&♣♦&✐"✐♦♥ 3❉ 3❤❛&❡ ❉✐&♣♦&✐"✐♦♥
❆3❖❉ ❆❧"❡.♥❛"✐✈❡ 3❤❛&❡ ❖♣♣♦&✐"✐♦♥ ❉✐&♣♦&✐"✐♦♥
❍ ❍②❜.✐❞ 3❙❈3❲▼ 3❤❛&❡ ❙❤✐❢"❡❞ ❈❛..✐❡. 3✉❧&❡ ❲✐❞"❤ ▼♦❞✉❧❛"✐♦♥ ❉❉▲ ❉❡❣.I& ❉❡ ▲✐❜❡."I ❙❱❉ ❙✐♥❣✉❧❛. ❱❛❧✉❡ ❉❡❝♦♠♣♦&✐"✐♦♥ ❉❙3 ❉✐❣✐"❛❧ ❙✐❣♥❛❧ 3.♦❝❡&&♦. ❚❍❉ ❚♦"❛❧ ❍❛.♠♦♥✐❝ ❉✐&"♦."✐♦♥ ❋❋❚ ❋❛&" ❋♦✉.✐❡. ❚.❛♥&❢♦.♠❛"✐♦♥ ❊◆■❚✲▲●3 ✷✵✶✻ ✶✶
❘!"✉♠!
▲❡" ❝♦♥✈❡+,✐""❡✉+" ❞✬!❧❡❝,+♦♥✐1✉❡ ❞❡ ♣✉✐""❛♥❝❡ "♦♥, ❞❡ ♣❧✉" ❡♥ ♣❧✉" ❡①♣❧♦✐,!" ♥♦,❛♠♠❡♥, ❞❛♥" ❧❡" ❛♣♣❧✐❝❛,✐♦♥" ♥!❝❡""✐,❛♥, ❧❛ ✈❛+✐❛,✐♦♥ ❞❡ ✈✐,❡""❡ ❞❡ ♠❛❝❤✐♥❡"✳ ▲✬✉,✐❧✐"❛,✐♦♥ ❞❡ ❝♦♠♣♦"❛♥," ♣❧✉" ♣❡+❢♦+♠❛♥," ❡, ♣❧✉" ♣✉✐""❛♥," ❝♦✉♣❧!" 8 ❞❡ ♥♦✉✈❡❧❧❡" ",+✉❝,✉+❡" ♠✉❧,✐♥✐✈❡❛✉① ❛✉,♦+✐"❡ ❧✬❛❝❝9" 8 ❞❡ ♥♦✉✈❡❛✉① ❝❤❛♠♣" ❛♣♣❧✐❝❛,✐❢"✱ ♦✉ ❞❡" ❢♦♥❝,✐♦♥♥❡♠❡♥," 8 ♣❧✉" ❤❛✉, +❡♥❞❡♠❡♥,✳ ❈❡" ❝♦♥✈❡+,✐""❡✉+" ",❛,✐1✉❡" "♦♥, ❝❛♣❛❜❧❡" ❞❡ ❣!+❡+✱ ♣❛+ ✉♥ ♣✐❧♦,❛❣❡ ❛❞❛♣,!✱ ❧❡" ,+❛♥"❢❡+," ❞✬!♥❡+❣✐❡ ❡♥,+❡ ❞✐✛!+❡♥,❡" "♦✉+❝❡" ❡, ❞✐✛!+❡♥," +!❝❡♣,❡✉+" "❡❧♦♥ ❧❛ ❢❛♠✐❧❧❡ ❞❡ ❝♦♥✈❡+,✐""❡✉+ ✉,✐❧✐"!❡✳ ❆✉ "❡✐♥ ❞❡ ❧✬✐♥,❡+❢❛❝❡ ❞❡ ♣✐❧♦,❛❣❡✱ ✉♥ "❝❤!♠❛ ♣❛+,✐❝✉❧✐❡+ ♣❡+♠❡, ❞❡ ❣!♥!+❡+ ❞❡" "✐❣♥❛✉① ❞❡ ❝♦♠♠❛♥❞❡ ♣♦✉+ ❧❡" ✐♥,❡++✉♣,❡✉+"✱ ✐❧ "✬❛❣✐, ❞❡ ❧❛ ♠♦❞✉❧❛,✐♦♥ ❡, ♣❡✉, @,+❡ ✈✉❡ ♣❛+ ❞❡✉① ❛♣♣+♦❝❤❡" ❞✐✛!+❡♥,❡" ✿ ▲✬❛♣♣+♦❝❤❡ ✐♥,❡+"❡❝,✐✈❡ ✐""✉❡ ❞✬✉♥❡ ❝♦♠♣❛+❛✐"♦♥ ♠♦❞✉❧❛♥,❡✲♣♦+,❡✉"❡ ✭❛♣♣❡❧!❡ ❡♥ ❛♥❣❧❛✐" ❝❛++✐❡+ ❜❛"❡❞ D❲▼✮ ❡, ❧✬❛♣♣+♦❝❤❡ ✈❡❝,♦+✐❡❧❧❡ ♦H ❧❡" "✐❣♥❛✉① ❞❡ ♣✐❧♦,❛❣❡ ❞❡" ,+♦✐" ❜+❛" ❞❡ ♣♦♥," "♦♥, ❝♦♥"✐❞!+!" ❝♦♠♠❡ ✉♥ ✈❡❝,❡✉+ ❣❧♦❜❛❧ ✉♥✐1✉❡ ✭❛♣♣❡❧!❡ ▼♦❞✉❧❛,✐♦♥ ❱❡❝,♦+✐❡❧❧❡ ❙❱▼✮✳ ▲❡ ❜✉, ❞❡ ❧❛ ▼▲■ ❡", ❞❡ ❣!♥!+❡+ ✉♥❡ ✈❛❧❡✉+ ♠♦②❡♥♥❡ ❞❡ ❧❛ ,❡♥"✐♦♥ ❧❛ ♣❧✉" ♣+♦❝❤❡ ♣♦""✐❜❧❡ ❞✉ "✐❣♥❛❧ ♠♦❞✉❧!✳ ▲❛ ❝♦♠♠❛♥❞❡ ✉"✉❡❧❧❡ ♣❛+ ❝♦♠♣❛+❛✐"♦♥ ♠♦❞✉❧❛♥,❡✲♣♦+,❡✉"❡ ❞❛♥" ❧❡ ❝❛" ❞❡" ❛+❝❤✐,❡❝,✉+❡" ♠✉❧,✐♥✐✈❡❛✉① ♥!❝❡""✐,❡ ❛✉,❛♥, ❞❡ ♣♦+,❡✉"❡" ,+✐❛♥❣✉❧❛✐+❡" 1✉✬✐❧ ② ❛ ❞❡ ❝❡❧❧✉❧❡" 8 ❝♦♠♠❛♥❞❡+ ❛✉ "❡✐♥ ❞✬✉♥ ❜+❛"✳ D❧✉" ❣!♥!+❛❧❡♠❡♥,✱ ❧❛ ",+❛,!❣✐❡ ❞❡ ♠♦❞✉❧❛,✐♦♥ ❞❡ ❝❤❛❝✉♥❡ ❞❡" ,♦♣♦❧♦❣✐❡" ♠✉❧,✐♥✐✈❡❛✉① ❡", ❝❤♦✐"✐❡ ❡♥ "❡ ❜❛"❛♥, "✉+ ❞❡" ❝+✐,9+❡" 8 ♦♣,✐♠✐"❡+ ❧✐!" 8 ❧❛ 1✉❛❧✐,! ❞❡" ❢♦+♠❡" ❞✬♦♥❞❡" ♣+♦❞✉✐,❡" ♦✉ ♦❜,❡♥✉❡"✱ "✉✐,❡ 8 ❧❛ ❝♦♥✈❡+"✐♦♥✳ ▲❡ ❝❤♦✐① ❞❡ ❧❛ ✈❛+✐❛❜❧❡ ❞❡ ❝♦♠♠❛♥❞❡ 8 ✐♠♣❧!♠❡♥,❡+ ❞❛♥" ❧❡ "❝❤!♠❛ ▼▲■ ❢❛✐, ❛♣♣❡❧ 8 ❧✬❡①♣❡+,✐"❡ ❞❡ ❧✬❡①♣!+✐♠❡♥,❛,❡✉+ ❡, "❡ +!❢9+❡ ♣❡✉ ❛✉ ♠♦❞9❧❡ ♠❛,❤!♠❛,✐1✉❡ ✐♥✐,✐❛❧ 1✉✐ ♣❡✉,✲@,+❡ !,❛❜❧✐, ♣♦✉+ ❝❛+❛❝,!+✐"❡+ ❧❡ ❢♦♥❝,✐♦♥♥❡♠❡♥, ❞❡ ❧✬❛+❝❤✐,❡❝,✉+❡ ❞✬!❧❡❝,+♦♥✐1✉❡ ❞❡ ♣✉✐""❛♥❝❡✳ ❊♥ ❝❡ 1✉✐ ❝♦♥❝❡+♥❡ ❧❡" ",+❛,!❣✐❡" ✈❡❝,♦+✐❡❧❧❡" ❙❱▼✱ ✉♥❡ ❛❜"❡♥❝❡ ❞❡ ♠♦❞9❧❡ ❝♦♠♣❛,✐❜❧❡ ❛✈❡❝ ❧❡" ♠♦❞9❧❡"✱ ❜❛"!" "✉+ ✉♥❡ ❝♦♠♣❛+❛✐"♦♥ ♠♦❞✉❧❛♥,❡✲ ♣♦+,❡✉"❡✱ ❞✬♦♥❞✉❧❡✉+" ❡", ❝♦♥",❛,!❡✳ ▲❡" ,②♣❡" ❞✬♦♥❞✉❧❡✉+" ,+✐♣❤❛"!" 8 ❞❡✉① ♦✉ 8 N ♥✐✈❡❛✉① ❞❡ ,❡♥"✐♦♥ ❛❞♠❡,,❡♥, ✉♥ ♠♦❞9❧❡ "♦✉" ❢♦+♠❡ ❞✬!1✉❛,✐♦♥" ❞✬✉♥ "②",9♠❡ ❧✐♥!❛✐+❡ ❝♦♠♣❛,✐❜❧❡ 1✉✐ "✬!❝+✐, "♦✉" ❧❛ ❢♦+♠❡ V = f(α) ❞❛♥" ❧❡ ❝❛" ❞✬✉♥❡ ▼▲■ "✐♥✉"♦N❞❛❧❡ ❡, V = f(τ) ❞❛♥" ❧❡ ❝❛" ❞✬✉♥❡ ❙❱▼✱ ❛✈❡❝ V ❧❡" ,❡♥"✐♦♥" ❞❡ ♣❤❛"❡✱ α ❧❡" +❛♣♣♦+," ❝②❝❧✐1✉❡" ❡, τ ❧❡" ✐♥",❛♥," ❞❡ ❝♦♠♠✉,❛,✐♦♥✳ ❉❛♥" ❝❡,,❡ ❝♦♥✜❣✉+❛,✐♦♥ ❜❛"✐1✉❡ ✐❧ ❡", ❝♦♥",❛,! 1✉❡ ❧❛ ♠❛,+✐❝❡ ❧✐❛♥, ❝❡" ,❡♥"✐♦♥" ❛✉① +❛♣♣♦+," ❝②❝❧✐1✉❡" ✭♦✉ ❛✉① ✐♥",❛♥," ❞❡ ❝♦♠♠✉,❛,✐♦♥✮ ♥✬❛❞♠❡, ♣❛" ❞✬✐♥✈❡+"❡✱ ❝❡ 1✉✐ +❡✈✐❡♥, 8 ❞✐+❡ 1✉✬✐❧ ♥✬❡", ♣❛" ♣♦""✐❜❧❡✱ ❛✈❡❝ ❧❡" ,❤!♦+✐❡" ✉"✉❡❧❧❡" ❞❡" ❢♦♥❝,✐♦♥" ❧✐♥!❛✐+❡"✱ ❞❡ +!"♦✉❞+❡ ❝❡ "②",9♠❡ ❛✜♥ ❞✬❡①♣+✐♠❡+ ❧❡" +❛♣♣♦+," ❝②❝❧✐1✉❡" ✭♦✉ ❧❡" ✐♥",❛♥," ❞❡ ❝♦♠♠✉,❛,✐♦♥✮ ❡♥ ❢♦♥❝,✐♦♥ ❞❡" ,❡♥"✐♦♥" ❞❡ +!❢!+❡♥❝❡"✳ ❈✬❡", ❝❡ 1✉✐ ❊◆■❚✲▲●D ✷✵✶✻ ✶✸❡①♣❧✐*✉❡ *✉✬❛✉❥♦✉/❞✬❤✉✐ ✉♥ ❜♦♥ ♥♦♠❜/❡ ❞✬✐♠♣❧!♠❡♥4❛4✐♦♥" ♣/❛4✐*✉❡" ❞❡ ♠♦❞✉❧❛4✐♦♥ "❡ ❢❛✐4✱ "✉✐4❡ 7 ✉♥❡ ❛♥❛❧②"❡ ❡①♣!/✐♠❡♥4❛❧❡ ❞❡" ❝♦♥"!*✉❡♥❝❡" ❞✬✉♥ ❝❤♦✐① ❞❡ "4/❛4!❣✐❡ "✉/ ❧❡" ✈❛/✐❛❜❧❡" ❞✬✐♥4!/<4✳ ❈❡44❡ !4✉❞❡ ♣/♦♣♦"❡ ❧❡ ❞!✈❡❧♦♣♣❡♠❡♥4 ❞✬✉♥❡ ❢♦/♠✉❧❛4✐♦♥ ❣!♥!/✐*✉❡ ♣♦✉/ ❧❛ ♠♦❞!❧✐"❛4✐♦♥ ❞❡" ♦♥❞✉❧❡✉/" ❞❡ 4❡♥"✐♦♥ ❡4 ❡♥ ♣❛/4✐❝✉❧✐❡/ ❞❡" ♦♥❞✉❧❡✉/" ♠✉❧4✐♥✐✈❡❛✉①✳ ❈❡44❡ ♠!4❤♦❞❡✱ ♣♦✉/ ❧❛ ❢♦/♠✉❧❛4✐♦♥ ❞❡ ♠♦❞?❧❡" ❣!♥!/✐*✉❡"✱ ❡"4 ♣❡♥"!❡ ♣♦✉/ ❢❛❝✐❧✐4❡/ ❧❛ ♠✐"❡ ❡♥ @✉✈/❡ ❞❡" "4/❛4!❣✐❡" ❞❡ ♠♦❞✉❧❛4✐♦♥✳ ▲✬❡①4❡♥"✐♦♥ ❞✉ ♠♦❞?❧❡ ♠♦②❡♥ ♦❜4❡♥✉ ♣♦✉/ ❧❡" "②"4?♠❡" 4/✐♣❤❛"!" ❡"4 /!❛❧✐"!❡ ♣♦✉/ ❧❡" "4/✉❝4✉/❡" ✉"✉❡❧❧❡" 7 N ♥✐✈❡❛✉① ❞❡ 4❡♥"✐♦♥ 4❡❧❧❡" *✉❡ ❧❛ "4/✉❝4✉/❡ ❞✬♦♥❞✉❧❡✉/ ❞❡ 4②♣❡ 7 ❝❛♣❛❝✐4!" ✢♦44❛♥4❡" ❡4 ❞❡ 4②♣❡ ♣♦♥4 ❡♥ ❍✳ ▲✬✐❞!❡ ❡"4 ❞❡ ❣!♥!/❛❧✐"❡/ ❧❡ ♠♦❞?❧❡ ❡4 ❧❛ ♠!4❤♦❞❡ "✉/ ❞❡" ❛/❝❤✐4❡❝4✉/❡" /!❡❧❧❡" ♠✉❧4✐♥✐✈❡❛✉①✱ *✉❡ ❝❡ "♦✐4 ♣❛/ ❧❛ ♠♦❞✉❧❛4✐♦♥ ▼▲■ "✐♥✉"♦F❞❛❧❡ ❡♥ ❡①♣/✐♠❛♥4 ❧❡" /❛♣♣♦/4" ❝②❝❧✐*✉❡" ❝♦♠♠❡ ✈❛/✐❛❜❧❡ ❞❡ "♦/4✐❡✱ ♦✉ ❧❛ ❙❱▼ ❡①♣/✐♠❛♥4 ❧❡" ✐♥"4❛♥4" ❞❡ ❝♦♠♠✉4❛4✐♦♥✳ ❈❡44❡ ❛♣♣/♦❝❤❡ ❞❡ ♠♦❞!❧✐"❛4✐♦♥ ❝♦♥"✐"4❡ 7 ❡①♣/✐♠❡/ ♠❛4❤!♠❛4✐*✉❡♠❡♥4 ❧❡" ❡♥"❡♠❜❧❡" ❞❡ "♦❧✉4✐♦♥" ♣♦✉/ ❧❛ ❣!♥!/❛4✐♦♥ ❞❡" "4/❛4!❣✐❡" ❞❡ ♠♦❞✉❧❛4✐♦♥ ♣♦✉/ ♣❧✉"✐❡✉/" ❛/❝❤✐✲ 4❡❝4✉/❡" ❞✬♦♥❞✉❧❡✉/" !4✉❞✐!"✳ ❈❡❧❛ ❡♥ ✉4✐❧✐"❛♥4 ✉♥ ♦✉4✐❧ ♠❛4❤!♠❛4✐*✉❡ ♣❡/♠❡44❛♥4 ❧❛ /!"♦❧✉4✐♦♥ ❞❡" "②"4?♠❡" ❧✐♥!❛✐/❡"✳ ▲❛ /!"♦❧✉4✐♦♥ ❞❡ ❝❡" "②"4?♠❡" ❞✬!*✉❛4✐♦♥" ❧✐♥!❛✐/❡" ❝♦♠♣❛4✐❜❧❡" ♣❡/♠❡4 ❞❡ 4/♦✉✈❡/ ❞❡" ❞❡❣/!" ❞❡ ❧✐❜❡/4!✱ 7 ✐❞❡♥4✐✜❡/ ❞❛♥" ✉♥ ♣/❡♠✐❡/ 4❡♠♣"✱ ♣✉✐" 7 ❡①♣/✐♠❡/ ❞❛♥" ✉♥ ❞❡✉①✐?♠❡ 4❡♠♣" ❡♥ !4❛❜❧✐""❛♥4 ❧❡ ❧✐❡♥ ❛✈❡❝ ❧❡" ❝/✐4?/❡" 7 ♦♣4✐♠✐"❡/ ♣♦✉/ ❞❡" ❛/❝❤✐4❡❝4✉/❡" ❞♦♥♥!❡"✳ ❉❡✉① ❡①❡♠♣❧❡" ❞✬❛♣♣❧✐❝❛4✐♦♥ ♦♥4 !4! ♠✐" ❡♥ @✉✈/❡✱ ✉♥ ♣/❡♠✐❡/ ❝♦♥❝❡/♥❡ ❧❡" ♦♥❞✉❧❡✉/" ❝❧❛"✲ "✐*✉❡" 7 ❞❡✉① ♥✐✈❡❛✉① ❞❡ 4❡♥"✐♦♥ ❡4 ❧❡ ❞❡✉①✐?♠❡ ✉♥ ♦♥❞✉❧❡✉/ 7 ❝❛♣❛❝✐4!" ✢♦44❛♥4❡" 7 4/♦✐" ♥✐✈❡❛✉① ❞❡ 4❡♥"✐♦♥✳ ▲❡" /!"✉❧4❛4" ❞❡ "✐♠✉❧❛4✐♦♥ ❡4 ❞✬❡①♣!/✐♠❡♥4❛4✐♦♥ "❡/♦♥4 ✐❧❧✉"4/!"✳ ✶✹ ❊◆■❚✲▲●R ✷✵✶✻
❆❜"#$❛❝#
❚❤❡ ♣♦✇❡$ ❡❧❡❝#$♦♥✐❝ ❝♦♥✈❡$#❡$" ❛$❡ ✐♥❝$❡❛"✐♥❣❧② ❡①♣❧♦✐#❡❞ ✐♥ ♣❛$#✐❝✉❧❛$ ✐♥ ❛♣♣❧✐❝❛#✐♦♥" $❡6✉✐✲ $✐♥❣ ✈❛$✐❛❜❧❡ "♣❡❡❞ ♠❛❝❤✐♥❡"✳ ❚❤❡ ✉"❡ ♦❢ ♠♦$❡ ❡✣❝✐❡♥# ❛♥❞ ♠♦$❡ ♣♦✇❡$❢✉❧ ❝♦♠♣♦♥❡♥#" ❝♦✉♣❧❡❞ ✇✐#❤ ♥❡✇ ♠✉❧#✐❧❡✈❡❧ "#$✉❝#✉$❡" ✇✐❞❡♥" #❤❡ ✜❡❧❞" ♦❢ ❛♣♣❧✐❝❛#✐♦♥ ❛♥❞ ❛❧❧♦✇" ❤✐❣❤ ❡✣❝✐❡♥❝② ❢✉♥❝#✐♦✲ ♥✐♥❣✳ ❚❤❡"❡ ❝♦♥✈❡$#❡$" ❛$❡ ❛❜❧❡ #♦ ♠❛♥❛❣❡✱ ✇✐#❤ ❛ "✉✐#❛❜❧❡ ❝♦♥#$♦❧✱ #❤❡ ❡♥❡$❣② #$❛♥"❢❡$ ❜❡#✇❡❡♥ ❞✐✛❡$❡♥# "♦✉$❝❡" ❛♥❞ ❞✐✛❡$❡♥# $❡❝❡✐✈❡$" ❞❡♣❡♥❞✐♥❣ ♦♥ #❤❡ ✉"❡❞ ❝♦♥✈❡$#❡$ ❢❛♠✐❧②✳ ■♥ #❤❡ ❝♦♥#$♦❧ ✐♥#❡$❢❛❝❡✱ ❛ ♣❛$#✐❝✉❧❛$ ♣❛##❡$♥ ✐" ✉"❡❞ #♦ ❣❡♥❡$❛#❡ ❝♦♥#$♦❧ "✐❣♥❛❧" ❢♦$ #❤❡ "✇✐#❝❤❡"✱ ✐# ✐" #❤❡ ♠♦❞✉❧❛#✐♦♥✳ ●❡♥❡$❛❧❧②✱ #❤❡ ♠♦❞✉❧❛#✐♦♥ "#$❛#❡❣② #❛❦❡" #✇♦ ❢♦$♠" ✿ ❛ ▼♦❞✉❧❛#✐♦♥ ❜❛"❡❞ ♦♥ ❝♦♠✲ ♣❛$❛✐"♦♥ ♠♦❞✉❧❛#✐♥❣ ✲ ❝❛$$✐❡$ ✭❈❛$$✐❡$ ❜❛"❡❞ F✉❧"❡ ❲✐❞#❤ ▼♦❞✉❧❛#✐♦♥✱ ✭❈F❲▼✮✮ ♦$ ❛ ❱❡❝#♦$ ▼♦❞✉❧❛#✐♦♥ ✭❙❱▼✮✳ ❚❤❡ ♣✉$♣♦"❡ ♦❢ #❤❡ F❲▼ ✐" #♦ ❣❡♥❡$❛#❡ ❛ "✐❣♥❛❧ ✇❤✐❝❤ ❤❛" ❛ ♠❡❛♥ ✈❛❧✉❡ ❛" ♥❡❛$❡"# ❛" ♣♦""✐❜❧❡ #♦ #❤❡ ❞❡"✐$❡❞ "✐♥✉"♦✐❞❛❧ "✐❣♥❛❧✳ ❚❤❡ ✉"✉❛❧ ❝♦♥#$♦❧ ❜② F❲▼✱ ✐♥ #❤❡ ❝❛"❡ ♦❢ ♠✉❧#✐✲❧❡✈❡❧ ❛$❝❤✐#❡❝#✉$❡"✱ $❡6✉✐$❡" ❛" ♠❛♥② #$✐❛♥❣✉❧❛$ ❝❛$$✐❡$" ❛" #❤❡$❡ ❛$❡ ❝❡❧❧" #♦ ❜❡ ❝♦♥#$♦❧✲ ❧❡❞ ✇✐#❤✐♥ ❛♥ ❛$♠✳ ❚❤❡ ♠♦❞✉❧❛#✐♦♥ "#$❛#❡❣② "❡❧❡❝#✐♦♥ ❢♦$ ❡❛❝❤ ♠✉❧#✐❧❡✈❡❧ #♦♣♦❧♦❣② ✐" ❜❛"❡❞ ♦♥ ♦♣#✐♠✐③✐♥❣ ❝$✐#❡$✐❛" $❡❧❛#❡❞ #♦ #❤❡ 6✉❛❧✐#② ♦❢ #❤❡ ♣$♦❞✉❝❡❞ ✇❛✈❡❢♦$♠" ❛❢#❡$ #❤❡ ❝♦♥✈❡$"✐♦♥✳ ❚❤❡ ❝❤♦✐❝❡ ♦❢ #❤❡ ✈❛$✐❛❜❧❡ #♦ ✐♠♣❧❡♠❡♥# ✐♥ #❤❡ F❲▼ "❝❤❡♠❡ $❡6✉✐$❡" ❡①♣❡$#✐"❡ ♦❢ #❤❡ ❡①♣❡$✐♠❡♥#❡$ ❛♥❞ $❡❢❡$" ❧✐##❧❡ #♦ #❤❡ ✐♥✐#✐❛❧ ♠❛#❤❡♠❛#✐❝❛❧ ♠♦❞❡❧ #❤❛# ❝❛♥ ❜❡ ❡"#❛❜❧✐"❤❡❞ #♦ ❝❤❛$❛❝#❡$✐③❡ #❤❡ ♦♣❡$❛#✐♦♥ ♦❢ #❤❡ ♣♦✇❡$ ❡❧❡❝#$♦♥✐❝" ❛$❝❤✐#❡❝#✉$❡✳ ❈♦♥❝❡$♥✐♥❣ #❤❡ ✈❡❝#♦$ "#$❛#❡❣✐❡" ❙❱▼✱ #❤❡ ❧❛❝❦ ♦❢ ❛ ❝♦♠♣❛#✐❜❧❡ ♠♦❞❡❧ ✇✐#❤ F❲▼ ✐♥✈❡$#❡$" ✐" ♦❜"❡$✈❡❞✳ ❚❤❡ #❤$❡❡✲♣❤❛"❡ ✐♥✈❡$#❡$" ✇✐#❤ #✇♦ ♦$ N ✈♦❧#❛❣❡ ❧❡✈❡❧" ❝❛♥ ❜❡ ♠♦❞❡❧❡❞ ✐♥ #❤❡ ❢♦$♠ ♦❢ ❡6✉❛#✐♦♥" ♦❢ ❛ ❝♦♠♣❛#✐❜❧❡ ❧✐♥❡❛$ "②"#❡♠ #❤❛# ✐" ✇$✐##❡♥ ❛" V = f(α) ✐♥ #❤❡ ❝❛"❡ ♦❢ ❛ "✐♥✉"♦✐❞❛❧ F❲▼ ❛♥❞ V = f(τ) ✐♥ #❤❡ ❝❛"❡ ♦❢ ❙❱▼✱ ✇✐#❤ V $❡♣$❡"❡♥#" ♣❤❛"❡ ✈♦❧#❛❣❡"✱ α ✐" ❛ ❞✉#② ❝②❝❧❡ ❛♥❞ τ #❤❡ "✇✐#❝❤✐♥❣ ✐♥"#❛♥#"✳ ■♥ #❤✐" ❜❛"✐❝ ❝♦♥✜❣✉$❛#✐♦♥✱ ✐# ✐" ❢♦✉♥❞ #❤❛# #❤❡ ♠❛#$✐① ❧✐♥❦✐♥❣ #❤❡"❡ ✈♦❧#❛❣❡" ❞✉#② ❝②❝❧❡" ✭♦$ "✇✐#❝❤✐♥❣ #✐♠❡"✮ ❛❞♠✐#" ♥♦ ✐♥✈❡$"❡✱ ✇❤✐❝❤ ♠❡❛♥" #❤❛# ✐# ✐" ♥♦# ♣♦""✐❜❧❡ ✇✐#❤ #❤❡ ✉"✉❛❧ ❧✐♥❡❛$ ❢✉♥❝#✐♦♥" #❤❡♦$✐❡" #♦ "♦❧✈❡ #❤✐" "②"#❡♠ ✐♥ ♦$❞❡$ #♦ ❡①♣$❡"" #❤❡ ❞✉#② $❛#✐♦" ✭♦$ #❤❡ ✐♥"#❛♥#" ♦❢ "✇✐#❝❤✐♥❣✮ ❛" ❛ ❢✉♥❝#✐♦♥ ♦❢ #❤❡ $❡❢❡$❡♥❝❡ ✈♦❧#❛❣❡"✳ ❚❤✐" ✐" #❤❡ $❡❛"♦♥ #❤❛# #♦❞❛② ❛ ♥✉♠❜❡$ ♦❢ ♣$❛❝#✐❝❛❧ ✐♠♣❧❡♠❡♥#❛#✐♦♥" ♦❢ ♠♦❞✉❧❛#✐♦♥ ✐" ❞♦♥❡ ❛❢#❡$ ❡①♣❡$✐♠❡♥#❛❧ ❛♥❛❧②"✐" ♦❢ #❤❡ ❝♦♥"❡6✉❡♥❝❡" ♦❢ "#$❛#❡❣② ❝❤♦✐❝❡" ♦♥ #❤❡ ✈❛$✐❛❜❧❡" ♦❢ ✐♥#❡$❡"#✳ ❚❤✐" "#✉❞② ♣$♦♣♦"❡" #❤❡ ❞❡✈❡❧♦♣♠❡♥# ♦❢ ❛ ❣❡♥❡$✐❝ ❢♦$♠✉❧❛#✐♦♥ ❢♦$ #❤❡ ♠♦❞❡❧✐♥❣ ♦❢ ✈♦❧#❛❣❡ ✐♥✈❡$#❡$" ❛♥❞ ❡"♣❡❝✐❛❧❧② ♠✉❧#✐❧❡✈❡❧ ✐♥✈❡$#❡$"✳ ❚❤❡ ❞❡✈❡❧♦♣♠❡♥# ♦❢ ❣❡♥❡$✐❝ ♠♦❞❡❧" ❢♦$ #❤❡ ✐♠♣❧❡♠❡♥#❛#✐♦♥ ♦❢ ♠♦❞✉❧❛#✐♦♥ "#$❛#❡❣✐❡" ✐" ✐❧❧✉"#$❛#❡❞✳ ❚❤❡ ❡①#❡♥"✐♦♥ ♦❢ #❤❡ ❛✈❡$❛❣❡ ♠♦❞❡❧ #♦ #❤❡ #❤$❡❡✲♣❤❛"❡ "②"#❡♠" ✐" ♣❡$❢♦$♠❡❞ #♦ #❤❡ ✉"✉❛❧ "#$✉❝#✉$❡" ♦❢ N ❧❡✈❡❧" "✉❝❤ ❛" #❤❡ ✢♦❛#✐♥❣ ❝❛♣❛❝✐#② ❛♥❞ ❍ ❜$✐❞❣❡ ✐♥✈❡$#❡$"✳ ❚❤❡ ✐❞❡❛ ✐" #♦ ❣❡♥❡$❛❧✐③❡ #❤❡ ♠♦❞❡❧ #♦ #❤❡ ♠✉❧#✐✲❧❡✈❡❧ ❛$❝❤✐#❡❝#✉$❡"✱ ✇❤❡#❤❡$ ❜② #❤❡ "✐♥✉"♦✐❞❛❧ F❲▼ ♠♦❞✉❧❛#✐♦♥ ❡①♣$❡""✐♥❣ #❤❡ ❛❧♣❤❛ ❊◆■❚✲▲●F ✷✵✶✻ ✶✺❛" ❛♥ ♦✉#♣✉# ✈❛$✐❛❜❧❡✱ ♦$ ❜② #❤❡ ❙❱▼ ❡①♣$❡""✐♥❣ #❛✉✳ ❚❤✐" #❤❡"✐" ❛✐♠" #♦ ❞❡✜♥❡ ❛ ♠♦❞❡❧✐♥❣ ❛♣♣$♦❛❝❤ ❛♥❞ ♠❛#❤❡♠❛#✐❝❛❧❧② ❡①♣$❡"" #❤❡ "❡# ♦❢ "♦❧✉#✐♦♥" ✐♥ ♦$❞❡$ #♦ ❣❡♥❡$❛#❡ ♠♦❞✉❧❛#✐♦♥ "#$❛✲ #❡❣✐❡" ❢♦$ ✈❛$✐♦✉" ❛$❝❤✐#❡❝#✉$❡" ♦❢ ✐♥✈❡$#❡$" "#✉❞✐❡❞✳ ❚❤✐" ✇✐❧❧ ❜❡ ❞♦♥❡ ✉"✐♥❣ ❛ #♦♦❧ ❢♦$ "♦❧✈✐♥❣ ❧✐♥❡❛$ "②"#❡♠"✳ ❚❤✐" $❡"♦❧✉#✐♦♥ ✐" ❜❛"❡❞ ♦♥ ✜♥❞✐♥❣ ❞❡❣$❡❡" ♦❢ ❢$❡❡❞♦♠✱ #♦ ❜❡ ✐❞❡♥#✐✜❡❞ ❛# ✜$"#✱ #❤❡♥ ❡①♣$❡"" #❤❡♠ ✐♥ ❛ "❡❝♦♥❞ "#❡♣ ❜② ❡"#❛❜❧✐"❤✐♥❣ #❤❡ ❧✐♥❦ ✇✐#❤ #❤❡ ❝$✐#❡$✐❛ #♦ ♦♣#✐♠✐③❡ ❢♦$ ❣✐✈❡♥ ❛$❝❤✐#❡❝#✉$❡"✳ ❚✇♦ ❡①❛♠♣❧❡" ♦❢ ❛♣♣❧✐❝❛#✐♦♥ ❤❛✈❡ ❜❡❡♥ ✐♠♣❧❡♠❡♥#❡❞ ♦♥ ❝♦♥✈❡♥#✐♦♥❛❧ #✇♦ ❧❡✈❡❧" ♦❢ ✈♦❧#❛❣❡ ✐♥✈❡$#❡$" ❛♥❞ #❤❡ #❤#$❡❡ ❧❡✈❡❧" ✢②✐♥❣ ❝❛♣❛❝✐#♦$ ✈♦❧#❛❣❡ ✐♥✈❡$#❡$✳ ✶✻ ❊◆■❚✲▲●I ✷✵✶✻
❚❛❜❧❡ ❞❡& ✜❣✉*❡&
✶✳✶ ▲❡& .✉❛/*❡ ❢❛♠✐❧❧❡& ❞❡& ❝♦♥✈❡*/✐&&❡✉*&✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✶✳✷ ❙❝❤<♠❛ ❞❡ ♣*✐♥❝✐♣❡ ❞✬✉♥ ❝♦♥✈❡*/✐&&❡✉* ❞❡ ❢*<.✉❡♥❝❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✶✳✸ ❉♦♠❛✐♥❡ ❞✬❛♣♣❧✐❝❛/✐♦♥ ❞❡ ❧✬■●❇❚ ❡/ ❞❡& ❛✉/*❡& ❞✐&♣♦&✐/✐❢& ❞❡ ❝♦♠♠✉/❛/✐♦♥
❝♦♥❝✉**❡♥/& ❬✻❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ✶✳✹ ❊①❡♠♣❧❡ ❞❡ ❝❛*❛❝/<*✐&/✐.✉❡& &/❛/✐.✉❡& ❞❡& ✐♥/❡**✉♣/❡✉*& ✐❞<❛✉① ✭■●❇❚✰❉✐♦❞❡
❛♥/✐ ♣❛*❛❧❧K❧❡✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✶✳✺ ✭❛✮ ❖♥❞✉❧❡✉* ❞❡ ❝♦✉*❛♥/ ❡/ ✭❜✮ ❋♦*♠❡& ❞✬♦♥❞❡&✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ✶✳✻ ✭❛✮ ❖♥❞✉❧❡✉* ❞❡ /❡♥&✐♦♥ ❡/ ✭❜✮ ❋♦*♠❡& ❞✬♦♥❞❡&✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✶✳✼ ❖♥❞✉❧❡✉* ❡♥ ♣♦♥/ ❡♥ ❍✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✶✳✽ ✭❛✮ ❈❡❧❧✉❧❡ ❞❡ ❝♦♠♠✉/❛/✐♦♥ ❡/ ✭❜✮ ❋♦*♠❡ ❞✬♦♥❞❡ ❞❡ ❧❛ /❡♥&✐♦♥ Vao✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✶✳✾ ❖♥❞✉❧❡✉* ♠♦♥♦♣❤❛&<✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼ ✶✳✶✵ ✭❛✮ ❚❡♥&✐♦♥ Vao ❡/ ✭❜✮ ❚❡♥&✐♦♥ Vbo✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼ ✶✳✶✶ ❆❧❧✉*❡ ❞❡ ❧❛ /❡♥&✐♦♥ ❞❡ ❝❤❛*❣❡ Vab✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✶✳✶✷ ❖♥❞✉❧❡✉* /*✐♣❤❛&<✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✶✳✶✸ ❈♦♠♠❛♥❞❡ ❞❡& ✐♥/❡**✉♣/❡✉*&✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾ ✶✳✶✹ ✭❛✮ ❚❡♥&✐♦♥ ❝♦♠♣♦&<❡ Vab ❡/ ✭❜✮ ❚❡♥&✐♦♥ ❝♦♠♣♦&<❡ Vca✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾
✶✳✶✺ ❆❧❧✉*❡ ❞❡ ❧❛ /❡♥&✐♦♥ &✐♠♣❧❡ Van✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵
✶✳✶✻ ❍✐&/♦❣*❛♠♠❡ ❞❡ ❧✬<✈♦❧✉/✐♦♥ ❞❡& ❝♦♠♣♦&❛♥/& ❞❡ ♣✉✐&&❛♥❝❡ ❬✶✷❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✶✳✶✼ ❇*❛& ❞✬♦♥❞✉❧❡✉* ◆W❈ X /*♦✐& ♥✐✈❡❛✉①✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹ ✶✳✶✽ ❚❡❝❤♥✐.✉❡ ❞❡ ♠♦❞✉❧❛/✐♦♥ ❡/ &✐❣♥❛✉① ❞❡ ❝♦♠♠❛♥❞❡ ❞❡ K1 ❡/ K2 ❞✬✉♥ ♦♥❞✉❧❡✉*
◆W❈ X /*♦✐& ♥✐✈❡❛✉① ❞❡ /❡♥&✐♦♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺ ✶✳✶✾ ❚❡♥&✐♦♥ ❞❡ &♦*/✐❡ ❡/ ❝♦✉*❛♥/ ❞❡ ❝❤❛*❣❡ ♣♦✉* ✉♥ ♦♥❞✉❧❡✉* ◆W❈ X /*♦✐& ♥✐✈❡❛✉① ✳ ✳ ✹✻ ✶✳✷✵ ❖♥❞✉❧❡✉* /*✐♣❤❛&< ❡♥ ❝❛&❝❛❞❡ X N ♥✐✈❡❛✉① ❞❡ /❡♥&✐♦♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼ ✶✳✷✶ ❇*❛& ❞✬♦♥❞✉❧❡✉* ❡♥ ❝❛&❝❛❞❡ X /*♦✐& ♥✐✈❡❛✉①✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ✶✳✷✷ ❚❡❝❤♥✐.✉❡ ❞❡ ♠♦❞✉❧❛/✐♦♥ ❞✬✉♥ ♦♥❞✉❧❡✉* ❡♥ ❝❛&❝❛❞❡ X /*♦✐& ♥✐✈❡❛✉①✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ✶✳✷✸ ❋♦*♠❡& ❞✬♦♥❞❡ ❞❡ ❧❛ /❡♥&✐♦♥ ❡/ ❞✉ ❝♦✉*❛♥/ ❞✬✉♥ ♦♥❞✉❧❡✉* ❡♥ ❝❛&❝❛❞❡ X /*♦✐& ♥✐✈❡❛✉① ✹✾ ✶✳✷✹ ❇*❛& ❞✬♦♥❞✉❧❡✉* ❋❈ X /*♦✐& ♥✐✈❡❛✉①✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ✶✳✷✺ ❚❡❝❤♥✐.✉❡ ❞❡ ♠♦❞✉❧❛/✐♦♥ ❡/ &✐❣♥❛✉① ❞❡ ❝♦♠♠❛♥❞❡ ❞❡ K1 ❡/ K2 ❞✬✉♥ ♦♥❞✉❧❡✉*
❋❈ X /*♦✐& ♥✐✈❡❛✉①✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶ ✶✳✷✻ ❚❡♥&✐♦♥ ❞❡ &♦*/✐❡ ❡/ ❝♦✉*❛♥/ ❞❡ ❝❤❛*❣❡ ♣♦✉* ✉♥ ♦♥❞✉❧❡✉* ❋❈ X /*♦✐& ♥✐✈❡❛✉①✳ ✳ ✳ ✺✶ ✶✳✷✼ ❇*❛& ❞✬♦♥❞✉❧❡✉* ▼▼❈ X /*♦✐& ♥✐✈❡❛✉①✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷
✶✳✷✽ ❙❝❤2♠❛ ❞❡ ♠♦❞✉❧❛5✐♦♥ ❞✬♦♥❞✉❧❡✉* ❞❡ 5❡♥&✐♦♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺ ✶✳✷✾ ❙❝❤2♠❛ ❞❡ ♣*✐♥❝✐♣❡ ❞❡ ❧✬❡♥&❡♠❜❧❡ ❞✉ &②&5=♠❡ ❝♦♠♠❛♥❞❡✲♦♥❞✉❧❡✉*✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻ ✶✳✸✵ B*✐♥❝✐♣❡ ❞❡ ❧❛ ❣2♥2*❛5✐♦♥ ❞❡ ❧❛ ▼▲■ &✐♥✉&✲5*✐❛♥❣❧❡ ❬✹✼❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽ ✶✳✸✶ ■♥❥❡❝5✐♦♥ ❞✬❤❛*♠♦♥✐K✉❡ ✸ ❬✹✾❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ✶✳✸✷ ❖♥❞✉❧❡✉* 5*✐♣❤❛&2 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵ ✶✳✸✸ ❘❡♣*2&❡♥5❛5✐♦♥ ❞❛♥& ❧❡ ♣❧❛♥ αβ ❞❡& ✈❡❝5❡✉*& ❞❡ 5❡♥&✐♦♥ ❞❡ ❧✬♦♥❞✉❧❡✉*✱ ❞2✜♥✐5✐♦♥
❞❡& &❡❝5❡✉*& ❬✺✾❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✶✳✸✹ ❘❡♣*2&❡♥5❛5✐♦♥ ❞❛♥& ❧❡ ♣❧❛♥ αβ ❞❡ ❧❛ 5❡♥&✐♦♥ ❞❡ *2❢2*❡♥❝❡ &✉* ❧❡ &❡❝5❡✉* ✶✳ ✳ ✳ ✳ ✳ ✻✷ ✶✳✸✺ ❘❡♣*2&❡♥5❛5✐♦♥ ❞❡& 5❡♥&✐♦♥& V1, V2 ❡5 V0 &✉* ❧❡ &❡❝5❡✉* ✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷
✶✳✸✻ ❙5*❛52❣✐❡ ❞❡ ♠♦❞✉❧❛5✐♦♥ B❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺ ✶✳✸✼ ❙5*❛52❣✐❡ ❞❡ ♠♦❞✉❧❛5✐♦♥ B❉✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻ ✶✳✸✽ ❙5*❛52❣✐❡ ❞❡ ♠♦❞✉❧❛5✐♦♥ B❖❉✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻ ✶✳✸✾ ❙5*❛52❣✐❡ ❞❡ ♠♦❞✉❧❛5✐♦♥ ❆B❖❉✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼ ✶✳✹✵ ❙5*❛52❣✐❡ ❞❡ ♠♦❞✉❧❛5✐♦♥ ❍✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽ ✶✳✹✶ ❈❤❛U♥❡ ❞✬❛❝5✐♦♥ ❞✉ ♠♦❞=❧❡ ❞✉ ❝♦♥✈❡*5✐&&❡✉* ❡5 ❞❡ &❛ ❝❤❛*❣❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵ ✷✳✶ ❙❝❤2♠❛ 5②♣❡ ❞✉♥❡ ▼▲■ &✐♥✉&♦✐❞❛❧❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹ ✷✳✷ ❙❝❤2♠❛ ❞✬✉♥❡ ❝❡❧❧✉❧❡ ❞❡ ❝♦♠♠✉5❛5✐♦♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺ ✷✳✸ ❆❧❧✉*❡ ❞❡ ❧❛ 5❡♥&✐♦♥ ❞✉ ❜*❛& Vao✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺
✷✳✹ ❙❝❤2♠❛ ❞❡ ❢♦♥❝5✐♦♥♥❡♠❡♥5 ❞❡ ❧✬♦♥❞✉❧❡✉* 5*✐♣❤❛&2✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻ ✷✳✺ ▼♦❞=❧❡ ❞❡ ❧✬❡♥&❡♠❜❧❡ ❖♥❞✉❧❡✉* ✲ ❈❤❛*❣❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✽ ✷✳✻ ■❧❧✉&5*❛5✐♦♥ ❞❡ ❞✐✛2*❡♥5& &❝❤2♠❛& ❞❡ ❝♦♠♣❛*❛✐&♦♥ ♠♦❞✉❧❛♥5❡✲♣♦*5❡✉&❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✵ ✷✳✼ ■❧❧✉&5*❛5✐♦♥ ❞❡ ❧❛ ❝♦♠♣❛*❛✐&♦♥ ❞❛♥& ❧❡ ❝❛& ✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✶ ✷✳✽ ❆❧❧✉*❡ ❞❡ ❧❛ 5❡♥&✐♦♥ ♣❡♥❞❛♥5 ✉♥❡ ♣2*✐♦❞❡ ❞❡ ❝♦♠♠✉5❛5✐♦♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✹ ✷✳✾ ❈❡❧❧✉❧❡& ❞❡ ❝♦♠♠✉5❛5✐♦♥ ✐♠❜*✐K✉2❡& ❬✼✽❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✼ ✷✳✶✵ ❇*❛& ❞✬♦♥❞✉❧❡✉* X ❝❡❧❧✉❧❡& ✐♠❜*✐K✉2❡& X N ♥✐✈❡❛✉①✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✼ ✷✳✶✶ ❙❝❤2♠❛ ❞❡ ❝❛❧❝✉❧ ❞❡ ❧❛ 5❡♥&✐♦♥ ❛✉ &❡✐♥ ❞✬✉♥❡ ❝❡❧❧✉❧❡ ❞❡ ❝♦♠♠✉5❛5✐♦♥ X N ♥✐✈❡❛✉①✳ ✽✽ ✷✳✶✷ ❆❧❧✉*❡ ❞❡ ❧❛ 5❡♥&✐♦♥ ♣❡♥❞❛♥5 ✉♥❡ ♣2*✐♦❞❡ ❞❡ ❝♦♠♠✉5❛5✐♦♥ Tc✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✾ ✷✳✶✸ ❇*❛& ❞✬♦♥❞✉❧❡✉* ❋❈ X N ♥✐✈❡❛✉①✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✸ ✷✳✶✹ ❆❧❧✉*❡ ❞❡ ❧❛ 5❡♥&✐♦♥ Vao ♣❡♥❞❛♥5 ✉♥❡ ♣2*✐♦❞❡ ❞❡ ❝♦♠♠✉5❛5✐♦♥ Tc✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✺ ✷✳✶✺ ❇*❛& ❞✬♦♥❞✉❧❡✉* ❍ X N ♥✐✈❡❛✉① ❞❡ 5❡♥&✐♦♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✼ ✷✳✶✻ ❇*❛& ❞✬♦♥❞✉❧❡✉* ❍ X N ♥✐✈❡❛✉① ❞❡ 5❡♥&✐♦♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✽ ✷✳✶✼ ❇*❛& ❞✬♦♥❞✉❧❡✉* ◆B❈ X 5*♦✐& ♥✐✈❡❛✉①✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✵ ✷✳✶✽ ❆❧❧✉*❡ ❞❡ ❧❛ 5❡♥&✐♦♥ ❞✬✉♥ ❜*❛& ❞✬♦♥❞✉❧❡✉* X ◆B❈ ❛✉ ❝♦✉*& ❞✬✉♥❡ ♣2*✐♦❞❡ ❞❡
❝♦♠♠✉5❛5✐♦♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✵ ✷✳✶✾ ❇*❛& ❞✬♦♥❞✉❧❡✉* ▼▼❈ X 5*♦✐& ♥✐✈❡❛✉① ❞❡ 5❡♥&✐♦♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✹ ✷✳✷✵ ❆❧❧✉*❡ ❞❡ ❧❛ 5❡♥&✐♦♥ ❞✬✉♥ ❜*❛& ❞✬♦♥❞✉❧❡✉* ▼▼❈ ❡♥ ❢♦♥❝5✐♦♥ ❞❡ ❧✬25❛5 ❞❡& ✐♥5❡*✲
*✉♣5❡✉*&✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✹ ✷✳✷✶ ❙❝❤2♠❛ ❢♦♥❝5✐♦♥♥❡❧ ❞✉ ♠♦❞=❧❡ ❞❡ ❧✬♦♥❞✉❧❡✉* ❡5 ❞❡ &❛ ❝❤❛*❣❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✽ ✸✳✶ ❙❝❤2♠❛ &②♥♦♣5✐K✉❡ ❞❡ ❧❛ ❣2♥2*❛5✐♦♥ ❞❡& ❡♥&❡♠❜❧❡& ❞❡ &♦❧✉5✐♦♥&✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✷
