Zinc oxide growth and its interfaces with metals observed by photoemission

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Zinc oxide growth and its interfaces with metals

observed by photoemission

Ekaterina Chernysheva

To cite this version:

Ekaterina Chernysheva. Zinc oxide growth and its interfaces with metals observed by photoemission.

Physics [physics]. Université Pierre et Marie Curie - Paris VI, 2017. English. �NNT : 2017PA066192�.

�tel-01666148�

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Université Pierre et Marie Curie

Ecole Doctorale 397 « Physique et Chimie des Matériaux »

Institut des NanoScience de Paris, Equipe « Oxydes en Basses Dimensions »

Unité Mixte CNRS/Saint-Gobain Recherche « Surface du Verre et Interfaces »

Zinc oxide growth and its interfaces with metals

observed by photoemission

Par Ekaterina CHERNYSHEVA

Thèse de doctorat de Physique

Dirigée par Rémi LAZZARI et Sergey GRACHEV

Présentée et soutenue publiquement le 24 Mars 2017

Devant un jury composé de :

M. Bruno Domenichini

Professeur (ICB)

Rapporteur

M. Gunnar Niklasson

Professeur (Uppsala)

Rapporteur

M. Olof Karis

Professeur (Uppsala)

Examinateur

M. Fabrice Bournel

Maître de conférences (LCPMR)

Examinateur

M. Sergey Grachev

Ingénieur (Saint-Gobain Recherche)

Examinateur

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❢✉♥❝%✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼ ✷✳✶✳✹ ▼❡%❛❧$ ♦♥ ❩♥❖ ❛♥❞ %❤❡✐& ❡❧❡❝%&✐❝❛❧ ❝♦♥%❛❝% ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ✷✳✶✳✹✳✶ ❇❛$✐❝$ ♦❢ ❡❧❡❝%&✐❝❛❧ ❝♦♥%❛❝% ❛% ♠❡%❛❧✲$❡♠✐❝♦♥❞✉❝%♦& ✐♥%❡&❢❛❝❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ✷✳✶✳✹✳✷ ▼❡%❛❧ ♦♥ ♣♦❧❛& ❩♥❖ $✉&❢❛❝❡$✿ ❢&♦♠ ❣&♦✇%❤ ♠♦❞❡ %♦ ❡❧❡❝%&♦♥✐❝ ♣&♦♣❡&%✐❡$ ✳ ✳ ✹✸ ✷✳✶✳✹✳✸ ❊❧❡❝%&✐❝❛❧ ❝♦♥%❛❝% ❛♥❞ ❙❝❤♦%%❦② ❜❛&&✐❡& ❛% ♠❡%❛❧✴❩♥❖ ✐♥%❡&❢❛❝❡$✿ ❛ &❡✈✐❡✇ ✳ ✳ ✹✹ ✷✳✶✳✺ ❈♦♥❝❧✉$✐♦♥$ ❛♥❞ ❣♦❛❧$ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺

(4)

✷✳✷ ❆❣ $❤✐♥ ✜❧♠ ❣+♦✇$❤ ♦♥ ❩♥❖ ❜❛2❛❧ 2✉+❢❛❝❡2 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻ ✷✳✷✳✶ ❩♥❖ 2✉+❢❛❝❡ ♣+❡♣❛+❛$✐♦♥ ❛♥❞ ✐$2 $♦♣♦❣+❛♣❤② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻ ✷✳✷✳✷ ▼♦+♣❤♦❧♦❣②✱ ❡♣✐$❛①② ❛♥❞ ♣❧❛2♠♦♥✐❝2 ♦❢ ❆❣ ✜❧♠2 ♦♥ ❩♥❖ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ✷✳✷✳✸ ❆$♦♠✐❝ 2$+✉❝$✉+❡ ❛♥❞ ❡♣✐$❛①② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ✷✳✷✳✹ ❋✐❧♠ ♠♦+♣❤♦❧♦❣② ❛2 2❡❡♥ ❜② ❙❚▼ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹ ✷✳✷✳✺ ❋✐❧♠ ❣+♦✇$❤ ❛2 ❞❡$❡+♠✐♥❡❞ ❜② ❯❱✲✈✐2✐❜❧❡ 2♣❡❝$+♦2❝♦♣② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹ ✷✳✸ ❲♦+❦ ❢✉♥❝$✐♦♥✱ ❜❛♥❞ ❜❡♥❞✐♥❣ ❛♥❞ ❙❝❤♦$$❦② ❜❛++✐❡+ ❛$ ❆❣✴❩♥❖ ✐♥$❡+❢❛❝❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼ ✷✳✸✳✶ ❊①♣❡+✐♠❡♥$❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼ ✷✳✸✳✷ ❙♣❡❝$+♦2❝♦♣✐❝ ✜♥❣❡+♣+✐♥$2 ♦❢ ❤②❞+♦❣❡♥❛$✐♦♥ ❛♥❞ ❤②❞+♦①②❧❛$✐♦♥✿ ❤②❞+♦①②❧ ❣+♦✉♣2 ❛♥❞ ❡$❝❤✐♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼ ✷✳✸✳✸ ❱❛❧❡♥❝❡ ❜❛♥❞ ❡✈♦❧✉$✐♦♥ ❞✉+✐♥❣ 2✐❧✈❡+ ❞❡♣♦2✐$✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷ ✷✳✸✳✹ ❲♦+❦ ❢✉♥❝$✐♦♥ ❡✈♦❧✉$✐♦♥ ✉♣♦♥ 2✐❧✈❡+ ❞❡♣♦2✐$✐♦♥✿ ❜❛+❡ ✈❡+2✉2 ❤②❞+♦❣❡♥❛$❡❞ 2✉+❢❛❝❡2 ✳ ✳ ✻✹ ✷✳✸✳✺ ❈❤❛♥❣❡2 ♦❢ ✇♦+❦ ❢✉♥❝$✐♦♥✱ ❜❛♥❞ ❜❡♥❞✐♥❣ ❛♥❞ ✐♦♥✐③❛$✐♦♥ ❡♥❡+❣② ✉♣♦♥ 2✐❧✈❡+ ❞❡♣♦2✐$✐♦♥✿ $❤❡ ❝❤❛+❣❡ $+❛♥2❢❡+ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻ ✷✳✸✳✻ ❙❝❤♦$$❦② ❜❛++✐❡+ ❛♥❞ ❜❛♥❞ ❛❧✐❣♥♠❡♥$ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾ ✷✳✸✳✻✳✶ ❚❤❡ ✐❞❡❛❧ ❝♦♥$❛❝$ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾ ✷✳✸✳✻✳✷ ❆❝$✉❛❧ ❙❝❤♦$$❦② ❝♦♥$❛❝$ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾ ✷✳✹ ❇❛♥❞ ❜❡♥❞✐♥❣ ❛$ $❤❡ ❩♥❖✲❆❣ ✐♥$❡+❢❛❝❡ 2$✉❞✐❡❞ ❜② ❍❆❳V❊❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵ ✷✳✹✳✶ ❩♥ ✷♣ ❝♦+❡ ❧❡✈❡❧ ❡✈♦❧✉$✐♦♥ ✇✐$❤ ♣❤♦$♦♥ ❡♥❡+❣② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶ ✷✳✹✳✶✳✶ ❊①♣❡+✐♠❡♥$❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶ ✷✳✹✳✶✳✷ ❉❛$❛ ❛♥❛❧②2✐2✿ ❜❛♥❞ ❜❡♥❞✐♥❣✲❞❡♣❡♥❞❡♥$ ♣❡❛❦ ♣♦2✐$✐♦♥ ❛♥❞ ❜+♦❛❞❡♥✐♥❣ ✳ ✳ ✳ ✳ ✼✸ ✷✳✹✳✷ ▼♦❞❡❧❧✐♥❣ ♦❢ ❜❛♥❞ ❜❡♥❞✐♥❣ ❡✛❡❝$2 ♦♥ ♣❤♦$♦❡♠✐22✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹ ✷✳✹✳✸ ❋✐$ ♦❢ ❡①♣❡+✐♠❡♥$❛❧ ❞❛$❛ ❛♥❞ 2✐♠✉❧❛$✐♦♥ ♦❢ ❧✐♥❡ 2❤❛♣❡2 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻ ✷✳✹✳✹ V♦2✐$✐♦♥ ♦❢ $❤❡ ❋❡+♠✐ ❧❡✈❡❧ ❛♥❞ ❞✐2❝✉22✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✾ ✷✳✺ ❙✉♠♠❛+② ❛♥❞ ❝♦♥❝❧✉2✐♦♥2 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✵ ✸ ❩♥❖ $❤✐♥ ✜❧♠* ✇✐$❤ ❝♦♥$.♦❧❧❡❞ ♦.✐❡♥$❛$✐♦♥ ❣.♦✇♥ ❜② .❛❞✐♦ ❢.❡6✉❡♥❝② ♠❛❣♥❡$.♦♥ *♣✉$✲ $❡.✐♥❣ ✽✷ ✸✳✶ ■♥$+♦❞✉❝$✐♦♥✿ ❩♥❖ $❤✐♥ ✜❧♠2 ❛♥❞ ♣♦❧❛+✐$② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✷ ✸✳✶✳✶ ❈♦♥$❡①$ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✷ ✸✳✶✳✷ ❩♥❖ $❤✐♥ ✜❧♠ ♣♦❧❛+✐$② ❞❡$❡❝$✐♦♥ ❛♥❞ ❝♦♥$+♦❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✸ ✸✳✷ ❙❛♠♣❧❡2 ❛♥❞ ❡①♣❡+✐♠❡♥$❛❧ ♣+♦$♦❝♦❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✹ ✸✳✸ ❩♥❖ ❞❡♣♦2✐$✐♦♥ +❛$❡ ❛♥❞ ❣+♦✇$❤ ♠❡❝❤❛♥✐2♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✺ ✸✳✹ ❚❤✐♥ ✜❧♠ ♠✐❝+♦2$+✉❝$✉+❡ ❛♥❞ ❞❡❢❡❝$2 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✾ ✸✳✺ ❩♥❖ ♦+✐❡♥$❛$✐♦♥ ❛2 ❛ ❢✉♥❝$✐♦♥ ♦❢ ❜✐❛2 ❛♥❞ $❡♠♣❡+❛$✉+❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✶ ✸✳✻ ❈♦♥❝❧✉2✐♦♥2 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✸ ✹ ❘❡❛❝$✐♦♥ ❛$ $❤❡ ❚✐✲❩♥❖ $❤✐♥ ✜❧♠ ✐♥$❡.❢❛❝❡ ✾✹ ✹✳✶ ❈❤❡♠✐❝❛❧ +❡❛❝$✐♦♥ ❛$ $❤❡ ♠❡$❛❧✴♦①✐❞❡ ✐♥$❡+❢❛❝❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✹ ✹✳✷ ❘❡❛❝$✐♦♥ ❜❡$✇❡❡♥ ❩♥❖ ❛♥❞ ❚✐ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✻ ✹✳✷✳✶ ❇✉❧❦ ♣❤❛2❡ ❡\✉✐❧✐❜+✐❛ ✐♥ $❤❡ ❩♥✲❚✐✲❖ 2②2$❡♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✻ ✹✳✷✳✷ ❘❡❛❝$✐♦♥ ❛$ $❤❡ ✐♥$❡+❢❛❝❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✽ ✹✳✸ ▼♦❞❡❧ 2$❛❝❦ 2$+✉❝$✉+❡ ❛♥❞ ❡①♣❡+✐♠❡♥$❛❧ ♣+♦$♦❝♦❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✾ ✹✳✹ ❍❆❳V❊❙ ❞❛$❛ ✐♥$❡+♣+❡$❛$✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✶ ✹✳✹✳✶ ❙♣❡❝$+❛ ♦✈❡+✈✐❡✇ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✶ ✹✳✹✳✷ ❚✐ ✷p ❝♦+❡ ❧❡✈❡❧ ❛♥❛❧②2✐2 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✷ ✹✳✹✳✷✳✶ ❋✐$$✐♥❣ $❤❡ ❚✐ ✷p ❜❛❝❦❣+♦✉♥❞ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✷ ✹✳✹✳✷✳✷ ❚✐ ✷p ✜$$✐♥❣ ♣❛+❛♠❡$❡+2 ❢+♦♠ ❧✐$❡+❛$✉+❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✹ ✹✳✹✳✷✳✸ ❚✐ ✷p ❝♦+❡ ❧❡✈❡❧ ♣❛+❛♠❡$❡+2 ❞❡$❡+♠✐♥❡❞ ❢+♦♠ $❤❡ +❡❢❡+❡♥❝❡ 2❛♠♣❧❡2 ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✹ ✹✳✹✳✷✳✹ ❚✐ ✷p ✜$$✐♥❣ ❞❡$❛✐❧2 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✺ ✹✳✹✳✸ ❩♥ ✷p✸✴✷ ❝♦+❡ ❧❡✈❡❧ ❛♥❛❧②2✐2 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✻ ✹✳✹✳✸✳✶ ❩♥ ✷p✸✴✷ ✜$$✐♥❣ ♣❛+❛♠❡$❡+2 ❢+♦♠ ❧✐$❡+❛$✉+❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✻ ✹✳✹✳✸✳✷ ❩♥ ✷p✸✴✷ ❝♦+❡ ❧❡✈❡❧ ♣❛+❛♠❡$❡+2 ❞❡$❡+♠✐♥❡❞ ❢+♦♠ $❤❡ +❡❢❡+❡♥❝❡ 2❛♠♣❧❡2 ✳ ✳ ✳ ✳ ✶✵✻ ✹✳✹✳✸✳✸ ❩♥ ✷p ✜$$✐♥❣ ❞❡$❛✐❧2 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✼ ✹✳✺ ❚✐ ✷p ❛♥❞ ❩♥ ✷p 2♣❡❝$+❛ ❡✈♦❧✉$✐♦♥ ✐♥ $❤❡ ❩♥❖ ✭❘❚✱ ✷✾✳✼✮ ✴ ❚✐ ✴ ▼♦ 2❛♠♣❧❡ ❛❢$❡+ ❛♥♥❡❛❧✐♥❣ ✐♥ ✈❛❝✉✉♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✼ ✹✳✺✳✶ ❖❜2❡+✈❛$✐♦♥ ♦❢ ❝♦+❡ ❧❡✈❡❧ ❡✈♦❧✉$✐♦♥ ❛2 ❛ ❢✉♥❝$✐♦♥ ♦❢ ❛♥♥❡❛❧✐♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✼ ✹✳✺✳✷ ❚✐ ♦①✐❞❛$✐♦♥ 2$❛$❡ ❡✈❛❧✉❛$✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✾ ✷

(5)

✹✳✺✳✸ ❩♥ ♦①✐❞❛+✐♦♥ ,+❛+❡ ❛♥❞ ❝❤❡♠✐❝❛❧ ❡♥✈✐3♦♥♠❡♥+ ❡✈❛❧✉❛+✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✷ ✹✳✺✳✹ ❉✐,❝✉,,✐♦♥ ♦♥ +❤❡ ♦❜,❡3✈❡❞ ❡✈♦❧✉+✐♦♥, ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✹ ✹✳✻ ❊✛❡❝+ ♦❢ ❩♥❖ +❤✐❝❦♥❡,, ♦♥ ❚✐✲❩♥❖ 3❡❛❝+✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✻ ✹✳✻✳✶ ❚✐ ✷p ,♣❡❝+3❛ ❡✈♦❧✉+✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✻ ✹✳✻✳✷ ❩♥ ✷p✸✴✷ ,♣❡❝+3❛ ❡✈♦❧✉+✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✼ ✹✳✻✳✸ ❉✐,❝✉,,✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✼ ✹✳✼ ❊✛❡❝+ ♦❢ +❤❡ ❩♥❖ ❝3②,+❛❧❧✐♥❡ D✉❛❧✐+② ♦♥ +❤❡ ❚✐✲❩♥❖ 3❡❛❝+✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✽ ✹✳✼✳✶ ❚✐ ✷p ,♣❡❝+3❛ ❡✈♦❧✉+✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✽ ✹✳✼✳✷ ❩♥ ✷p ,♣❡❝+3❛ ❡✈♦❧✉+✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✾ ✹✳✼✳✸ ❉✐,❝✉,,✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✾ ✹✳✽ ❊✛❡❝+ ♦❢ ❛ ❚✐❖① ♣❛,,✐✈❛+✐♦♥ ❧❛②❡3 ♦♥ +❤❡ ❚✐✲❩♥❖ 3❡❛❝+✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✵ ✹✳✽✳✶ ❚✐ ✷p ,♣❡❝+3❛ ❡✈♦❧✉+✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✵ ✹✳✽✳✷ ❩♥ ✷p ,♣❡❝+3❛ ❡✈♦❧✉+✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✵ ✹✳✽✳✸ ❉✐,❝✉,,✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✶ ✹✳✾ ❚❉❙ ,+✉❞② ♦❢ +❤❡ ❚✐✲❩♥❖ 3❡❛❝+✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✶ ✹✳✾✳✶ ❉✐,❝✉,,✐♦♥ ♦❢ +❤❡ ❚❉❙ 3❡,✉❧+, ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✺ ✹✳✶✵ ❙❝❡♥❛3✐♦ ♦❢ +❤❡ 3❡❛❝+✐♦♥ ❛+ ❚✐✴❩♥❖ ✐♥+❡3❢❛❝❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✻ ✹✳✶✵✳✶ ❆ ,✉♠♠❛3② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✻ ✹✳✶✵✳✷ ❘❡❛❝+✐♦♥ ,❝❡♥❛3✐♦ ❜❛,❡❞ ♦♥ ❍❆❳N❊❙✱ ❚❉❙✱ ❊N▼❆✱ ❛♥❞ +❤❡3♠♦❞②♥❛♠✐❝ ,✐♠✉❧❛+✐♦♥, ✳ ✶✷✽ ❈♦♥❝❧✉&✐♦♥& ✶✸✶ ❇✐❜❧✐♦❣-❛♣❤② ✶✸✸ ▲✐&3 ♦❢ ❋✐❣✉-❡& ✶✹✹ ▲✐&3 ♦❢ ❚❛❜❧❡& ✶✺✶ ✸

(6)

❆❝❦♥♦✇❧❡❞❣❡♠❡♥+,

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❤"♦✉❣❤ ❤❡✐" ✐♥ ❡"♥)❤✐♣) ❛ ❙●❘ ❛♥❞ ■◆❙2✳ ■ ❛♠ ❤❛♣♣② ♦ ❦♥♦✇ ②♦✉ ✕ ②♦✉ ❛"❡ )✐♠♣❧② ❤❡ ❜❡) ✳ ❚❤✐) 2❤❉ ✇♦✉❧❞ ♥♦ ❜❡ ♣♦))✐❜❧❡ ✇✐ ❤♦✉ ♦✉" ❝♦❧❧❛❜♦"❛ ♦") ♦♥ )②♥❝❤"♦ "♦♥ ❡①♣❡"✐♠❡♥ ) ❢"♦♠ ❯♣♣)❛❧❛ ❯♥✐✈❡")✐ ② ❛♥❞ ❍❡❧♠❤♦❧ ③ ❩❡♥ "✉♠ ❇❡"❧✐♥✿ ❘❡❜❡❝❦❛ ▲✐♥❞❜❧❛❞✱ ❇❡" "❛♥❞ 2❤✐❧✐♣♣❡✱ ❛♥❞ ▼✐❤❛❡❧❛ ●♦"❣♦✐✳ ❚❤❛♥❦ ②♦✉ ❢♦" ♠❛❦✐♥❣ ✐ ❤❛♣♣❡♥ ❜❡✐♥❣ ❤❡"❡ ❞❛② ❛♥❞ ♥✐❣❤ ✳ ❆♥❞ ■ )✐♥❝❡"❡❧② ❤❛♥❦ ❖❧♦❢ ❑❛"✐) ❛♥❞ ❍M❦❛♥ ❘❡♥)♠♦ ❢♦" ②♦✉" ❣✉✐❞❛♥❝❡ ❛♥❞ ❡①♣❡" ✐)❡ ✐♥ ❡"♠) ♦❢ ♦✉" ❝♦❧❧❛❜♦"❛ ✐♦♥✳ ❲❡ ❛❧)♦ ❤❛❞ ❛ ❝❤❛♥❝❡ ♦ ❡①❝❤❛♥❣❡ ❛♥❞ ❝♦❧❧❛❜♦"❛ ❡ ♦♥ ❩♥❖ ❤✐♥ ✜❧♠) ✇✐ ❤ ♦✉" ❝♦❧❧❡❛❣✉❡) ❢"♦♠ ◆■▼❙✱ ❏❛♣❛♥✿ ◆❛♦❦✐ ❖❤❛)❤✐ ❛♥❞ ❇❡♥❥❛♠✐♥ ❉✐❡""❡✳ ❚❤❛♥❦ ②♦✉ ❖❤❛)❤✐✲)❛♥ ❛♥❞ ❇❡♥❥❛♠✐♥ ❢♦" ❤❡ ❞✐)❝✉))✐♦♥) ❣♦✐♥❣ ❜❡②♦♥❞ ❤❡ ❝♦❧❧❛❜♦"❛ ✐♦♥✱ ❛♥❞ ❢♦" ②♦✉" ❤❡❧♣ ✇✐ ❤ 2▲ ♠❡❛)✉"❡♠❡♥ )✳ ■ ✇♦✉❧❞ ❛❧)♦ ❧✐❦❡ ♦ ❡①♣"❡)) ♠② ❣"❛ ✐ ✉❞❡ ♦ ❤❡ "❡✈✐❡✇❡") ❛♥❞ ❥✉"② ♠❡♠❜❡") ✇❤♦ ❦✐♥❞❧② ❛❝❝❡♣ ❡❞ ♦ ❡✈❛❧✲ ✉❛ ❡ ♠② ❤❡)✐)✿ 2"♦❢✳ ❇"✉♥♦ ❉♦♠❡♥✐❝❤✐♥✐✱ 2"♦❢✳ ●✉♥♥❛" ◆✐❦❧❛))♦♥✱ 2"♦❢✳ ❖❧♦❢ ❑❛"✐)✱ ❛♥❞ ❉"✳ ❋❛❜"✐❝❡ ❇♦✉"♥❡❧✳ ▲❛) ❜✉ ♥♦ ❧❡❛) ✱ ■ ✇♦✉❧❞ ❧✐❦❡ ♦ ❤❛♥❦ ♠② ❋❛♠✐❧② ❛♥❞ ❋"✐❡♥❞) ❢♦" ❤❡✐" ❧♦✈❡✱ ♣❛ ✐❡♥❝❡✱ ❝♦♥ ✐♥✉♦✉) )✉♣♣♦" ❛♥❞ "✉) ✐♥ ♠❡✳ ❚❤❛♥❦ ②♦✉ ❉✐♠❛✲♠②✲❧♦✈❡✱ ▼♦♠✱ ●"❛♥♥②✱ ❆)✐②❛✱ ❋"❛♥❝✐❛✱ ❋❡"❞✐♥❛♥❞✱ ❉✐♠❛ ■✳✱ ❆" ✉"✱ ❲✐❧❧✐❛♠✱ ❆✈✐)❤❡❦✱ ❚❛♥②❛✱ ▲❡"❛✱ ❉❛♦✉❞❛✱ ❉✐♠❛ ❊✳✱ ▲❡♦♥✐❞✱ ❉❛"✐❛✱ ❙❡"❣❡②✱ ❇❡♥❥❛♠✐♥✱ ◆✐❝♦❧❛✱ ❏✲2❛✉❧✱ ❏❡❛♥✲❈❧❛✉❞❡✱ ❏❇✱ ❏❡❛♥✲❨✈♦♥✱ ❆②♠❡"✐❝✱ ❉❛♠✐❡♥✱ ▼❛①✐♠❡✱ ❈♦"✐♥♥❡✱ ◆❛ ❛)❤❛✱ ❚✐♠❛✱ ■♥❞✐"❛✱ ❱❛♥②❛✱✳✳ ❛♥❞ ❛❧❧ ❤❡ ❞❡❛"❡) ♣❡♦♣❧❡ ❛"♦✉♥❞ ♠❡✳ ❚❤❛♥❦ ②♦✉✳ ✺

(8)

❘!"✉♠! ❡♥ ❢(❛♥*❛✐"

▲❡" ✜❧♠" ♠✐♥❝❡" "♦♥* ❝♦✉,❛♠♠❡♥* ❡♠♣❧♦②0" ♣♦✉, ❛♣♣♦,*❡, ❞❡ ♥♦✉✈❡❧❧❡" ❢♦♥❝*✐♦♥♥❛❧✐*0" ❛✉ ✈❡,,❡ ♣❧❛*✳ ❉❛♥" ✉♥❡ ❣,❛♥❞❡ ❣❛♠♠❡ ❞❡ ♣,♦❞✉✐*" ✐♥❞✉"*,✐❡❧" ♣♦✉, ❧❡ ❜8*✐♠❡♥* ❡* ❧✬❛✉*♦♠♦❜✐❧❡✱ ❧✬✐"♦❧❛*✐♦♥ *❤❡,♠✐<✉❡ ❡"* ❛♠0❧✐✲ ♦,0❡ ♣❛, ❧❡ ❞0♣>* ❞❡ ✜❧♠" ♥❛♥♦♠0*,✐<✉❡" ❞✬❛,❣❡♥* <✉✐ "♦♥* "✉✣"❛♠♠❡♥* ♠✐♥❝❡" ♣♦✉, ❧❛ *,❛♥"♣❛,❡♥❝❡ ♦♣*✐<✉❡ ♠❛✐" "✉✣"❛♠♠❡♥* 0♣❛✐" ♣♦✉, ,❡✢0*❡, ❧✬✐♥❢,❛,♦✉❣❡✳ ❈❡" ,❡✈B*❡♠❡♥*" ❜❛"✲❡♠✐""✐❢" "♦♥* ❞❡" ❡♠♣✐❧❡♠❡♥*" ❝♦♠✲ ♣❧❡①❡" ❞❡ ✜❧♠" ♠✐♥❝❡" <✉✐ "♦♥* ❞0♣♦"0" D ❧✬0❝❤❡❧❧❡ ✐♥❞✉"*,✐❡❧❧❡ ♣❛, ♣✉❧✈0,✐"❛*✐♦♥ ❝❛*❤♦❞✐<✉❡ "✉, ❧❡" ♣❛♥♥❡❛✉① ❞❡ ✈❡,,❡✳ ▲❡ ❞0♠♦✉✐❧❧❛❣❡ ♦✉ ❧❛ ❞0❧❛♠✐♥❛*✐♦♥ ♣❡✉✈❡♥* ,0❞✉✐,❡ ❧❛ ♣❡,❢♦,♠❛♥❝❡ ♦♣*✐<✉❡ ❡* ❧❛ ❞✉,❛❜✐❧✐*0 ❞✉ ♣,♦❞✉✐* ❡♥ ,❛✐"♦♥ ❞❡ ❧✬❛❞❤0"✐♦♥ ♠0❞✐♦❝,❡ ❡♥*,❡ ❧✬❆❣ ❡* ❧❡" ❝♦✉❝❤❡" ❛❞❥❛❝❡♥*❡"✳ ▲❡ ✜❧♠ ❞✬❆❣ ❡"* ♣❛, ❝♦♥✲ "0<✉❡♥* ♣,✐" ❡♥ "❛♥❞✇✐❝❤ ❡♥*,❡ ❞❡" ❝♦✉❝❤❡" *❡①*✉,0❡" ④✵✵✵✶⑥ ❞❡ ❩♥❖ <✉✐ "❡ *,♦✉✈❡ B*,❡ ❧❡ ♠❡✐❧❧❡✉, ❝❛♥❞✐❞❛* ♣♦✉, ❛♠0❧✐♦,❡, ❧❛ ❝,✐"*❛❧❧✐"❛*✐♦♥ ❡* ❧✬❛❞❤0"✐♦♥✳ ❉❡" ❝♦✉❝❤❡" ❞✐*❡" ❜❧♦<✉❡✉," ❞❡ ♠0*❛✉① ❞❡ *,❛♥"✐*✐♦♥ *❡❧" <✉❡ ❧❡ ❚✐ "♦♥* 0❣❛❧❡♠❡♥* ❛❥♦✉*0❡" D ❧✬✐♥*❡,❢❛❝❡✳ ❉❛♥" ❝❡ ❝❛❞,❡ ✐♥❞✉"*,✐❡❧✱ ❝❡**❡ *❤O"❡ "✬❡"* ♣❡♥❝❤0❡ "✉, ❞✐✈❡," ❛"✲ ♣❡❝*" ❢♦♥❞❛♠❡♥*❛✉① ❞❡" ✐♥*❡,❢❛❝❡" ♠0*❛✉①✴❩♥❖ ❡♥ ❝♦♠❜✐♥❛♥* ❞❡" ❛♣♣,♦❝❤❡" ❞❡ "❝✐❡♥❝❡ ❞❡" "✉,❢❛❝❡" "✉, ❞❡" ♠♦♥♦❝,✐"*❛✉① ❡* ❞❡" ✜❧♠" ♣✉❧✈0,✐"0"✳ Q❧✉"✐❡✉," "*,❛*0❣✐❡" ❞❡ ♠❡"✉,❡ ❡* "②"*O♠❡" ♠♦❞O❧❡" ♦♥* 0*0 ❡♠♣❧♦②0" ♣♦✉, ❛❜♦,❞❡, ❧❡" <✉❡"*✐♦♥ ❞✉ ❝♦♥*❛❝* 0❧❡❝*,✐<✉❡ D ❧✬✐♥*❡,❢❛❝❡ ❆❣✴❩♥❖✱ ❞✉ ❝♦♥*,>❧❡ ❞❡ ❧❛ ♣♦❧❛,✐*0 ❞❛♥" ❧❡" ✜❧♠" ♣✉❧✈0,✐"0" ❞❡ ❩♥❖ ❡* ❞❡ ❧✬0✈♦❧✉*✐♦♥ ❞❡ ❧❛ ❝❤✐♠✐❡ D ✉♥❡ ✐♥*❡,❢❛❝❡ ❡♥*❡,,0❡ ❚✐✴❩♥❖ ❧♦," ❞✬✉♥ *,❛✐*❡♠❡♥* *❤❡,♠✐<✉❡✳ ❉❡" ✜❧♠" ❞✬❆❣✱ ❞❡ ❧❛ "♦✉"✲♠♦♥♦❝♦✉❝❤❡ ❥✉"<✉✬D ❧❛ ♣❡,❝♦❧❛*✐♦♥✱ ♦♥* 0*0 0❧❛❜♦,0" ♣❛, 0✈❛♣♦,❛*✐♦♥ *❤❡,♠✐<✉❡ "✉, ❞❡" "✉,❢❛❝❡" (1×1) ❞❡ ❩♥❖✭✵✵✵✶✮ *❡,♠✐♥0❡" ❖ ♦✉ ❩♥ ❡* ♣,0♣❛,0❡" ♣❛, ❜♦♠❜❛,❞❡♠❡♥*✴,❡❝✉✐* "♦✉" ✈✐❞❡✳ ▲❛ ❞✐✛,❛❝*✐♦♥✱ ❧❛ ♠✐❝,♦"❝♦♣✐❡ ❡* ❧❛ ♣❧❛"♠♦♥<✐✉❡ ♦♥* ❞0♠♦♥*,0 ✉♥❡ ❝,♦✐""❛♥❝❡ 0♣✐*❛①✐❛❧❡ ✭✶✶✶✮ ❤❡①❛❣♦♥❡✴❤❡①❛❣♦♥❡ "♦✉" ❧❛ ❢♦,♠❡ ❞❡ ♣❛,*✐❝✉❧❡" D *♦✐*" ♣❧❛*"✳ ▲✬0♣✐*❛①✐❡ ❡"* ❡①♣❧✐<✉0❡ ♣❛, ✉♥❡ ♥✉❝❧0❛*✐♦♥✴❝,♦✐""❛♥❝❡ ♣,0❢0,❡♥*✐❡❧❧❡ "✉✐✈❛♥* ❧❡" ❜♦,❞" ❞❡ ♠❛,❝❤❡" ♣♦❧❛✐,❡"✳ ▲❡ ❧✐❡♥ ❡♥*,❡ ♠♦,♣❤♦❧♦❣✐❡✱ ♣♦❧❛,✐*0 ❡* ❛❞"♦,♣*✐♦♥ ❞✬❤②❞,♦❣O♥❡ "✉, ❧✬❛❧✐❣♥❡♠❡♥* ❞❡ ❜❛♥❞❡" D ❧✬✐♥*❡,❢❛❝❡ ❆❣✴❩♥❖ ❛ 0*0 ❡①♣❧♦,0 ❡♥ ❝♦♠❜✐♥❛♥* ❧❛ ♣❤♦*♦0♠✐""✐♦♥ ❯❱ ♦✉ "♦✉" ,❛②♦♥" ❳ ❞✉,"✳ ▲❡" "✉,❢❛❝❡" ♥❛*✐✈❡" ♣,0"❡♥*❡♥* ✉♥❡ ❢♦,*❡ ❝♦✉,❜✉,❡ ❞❡ ❜❛♥❞❡ ✈❡," ❧❡ ❤❛✉* ❡* ❧❛ ♣,0♣❛,❛*✐♦♥ ❞❡ "✉,❢❛❝❡ ❝♦♥❞✉✐* D ✉♥ "❡♠✐✲❝♦♥❞✉❝*❡✉, ❞0❣0♥0,0 ❛②❛♥* ✉♥ ♥✐✈❡❛✉ ❞❡ ❋❡,♠✐ ❛✉✲❞❡""✉" ❞❡ ❧❛ ❜❛♥❞❡ ❞❡ ✈❛❧❡♥❝❡✳ ▲✬❡①♣♦"✐*✐♦♥ D ❧✬❤②❞,♦❣O♥❡ ❛*♦♠✐<✉❡ ❝♦✉,❜❡ ❧❡" ❜❛♥❞❡" ✈❡," ❧❡ ❜❛"✱ ❡* ❍ ,0❛❣✐* ❝❤✐♠✐<✉❡♠❡♥* ❛✈❡❝ ❧❡" ❞❡✉① ❢❛❝❡"✳ ❆✉① ♣,❡♠✐❡," "*❛❞❡" ❞❡ ❧❛ ❝,♦✐""❛♥❝❡ <✉✐ ❝♦,,❡"♣♦♥❞❡♥* D ❧❛ ❢♦,♠❛*✐♦♥ ❞❡ ♣❛,*✐❝✉❧❡" ✷❉✱ ✉♥ *,❛♥"❢❡,* ❞❡ ❝❤❛,❣❡ ❛ ❧✐❡✉ D ❧✬✐♥*❡,❢❛❝❡ ❝♦♥❞✉✐"❛♥* D ✉♥ ❞✐♣>❧❡✳ ❊♥"✉✐*❡✱ ❧✬❛❞"♦,♣*✐♦♥ ❞✬❆❣ ❞❡✈✐❡♥* ,❛♣✐❞❡♠❡♥* ♠0*❛❧❧✐<✉❡✳ Q♦✉, ❞❡" ✜❧♠" 0♣❛✐"✱ ❧❡ ❝♦♥*❛❝* 0❧❡❝*,✐<✉❡ ❆❣✴❩♥❖ ❡"* ❞❡ *②♣❡ ❙❝❤♦**❦② ❛✈❡❝ ✉♥❡ ❤❛✉*❡✉, ❞❡ ❜❛,,✐O,❡ ❞❡ ✵✳✺✲✵✳✼ ❡❱✱ ✐♥❞0♣❡♥❞❛♠♠❡♥* ❞❡ ❧❛ *❡,♠✐♥❛✐"♦♥ ♦✉ ❞❡ ❧✬❤②❞,♦❣0♥❛*✐♦♥✳ ▲❡ ❝♦♥*,>❧❡ ❞❡ ❧❛ *❡,♠✐♥❛✐"♦♥ ❡* ❞❡ ❧❛ ❝,✐"*❛❧❧✐♥✐*0 ❞❡ ✜❧♠" ❞❡ ❩♥❖ ❞0♣♦"0" ♣❛, ♣✉❧✈0,✐"❛*✐♦♥ ❝❛*❤♦❞✐<✉❡ "✉, ❞❡ ❙✐ ❛ 0*0 "②"*0♠❛*✐<✉❡♠❡♥* ❡①♣❧♦,0 ❡♥ ❢♦♥❝*✐♦♥ ❞❡ ❧❛ *❡♠♣0,❛*✉,❡ ❞✉ "✉❜"*,❛* ❡* ❞❡ "❛ ♣♦❧❛,✐"❛*✐♦♥ 0❧❡❝*,✐<✉❡✳ ▲❛ ✈✐*❡""❡ ❞❡ ❝,♦✐""❛♥❝❡ ♣❡✉* B*,❡ ❢♦,*❡♠❡♥* ✐♥✢✉❡♥❝0❡ ♣❛, ✉♥ ❡✛❡* ❝♦♠❜✐♥0 ❞❡ ,❡✲♣✉❧✈0,✐"❛*✐♦♥ ❡* ❞❡ *❡♠♣0,❛*✉,❡✳ ❙✉, ✉♥ "✉❜"*,❛* ❝❤❛✉❞✱ ❧❛ ❢♦,♠❛*✐♦♥ ❞❡ ❙✐❖①❡*✴♦✉ ❧✬✐♥*❡,❞✐✛✉"✐♦♥ "♦♥* ❢❛✈♦,✐"0❡" ,❛❧❡♥*✐""❛♥* ❣,❛♥❞❡♠❡♥* ❧❛ ✈✐*❡""❡ ❞❡ ❝,♦✐""❛♥❝❡✳ ❚♦✉" ❧❡" 0❝❤❛♥*✐❧❧♦♥" "♦♥* ♣♦❧②❝,✐"*❛❧❧✐♥"✱ *❡①*✉,0" ④✵✵✵✷⑥✳ ❊♥ ✉*✐❧✐"❛♥* ✉♥❡ ❡♠♣,❡✐♥*❡ "♣0❝✐✜<✉❡ D ❧❛ ♣♦❧❛,✐*0 ❞❛♥" ❧❡ "♣❡❝*,❡ ❳ ❞❡ ❧❛ ❜❛♥❞❡ ❞❡ ✈❛❧❡♥❝❡ ❞❡ ❩♥❖✱ ✉♥ ❞✐❛❣,❛♠♠❡ ❡①♣0,✐♠❡♥*❛❧ *❡♠♣0,❛*✉,❡✴♣♦❧❛,✐"❛*✐♦♥ ❛ 0*0 ♦❜*❡♥✉ ❞0♠♦♥*,❛♥* ❧❡" ❝♦♥❞✐*✐♦♥" ♣♦✉, ❧❡"<✉❡❧❧❡" ❧❛ ♣♦❧❛,✐*0 ♣❡✉* B*,❡ ❝♦♥*,>❧0❡✳ ▲❛ ,0❛❝*✐♦♥ ✐♥*❡,❢❛❝✐❛❧❡ ❡♥*,❡ ❝❡" ✜❧♠" ❞❡ ❩♥❖ ❡* ❧❡ ❚✐ ❛ 0*0 0*✉❞✐0❡ ❞❛♥" ❞❡" ❡♠♣✐❧❡♠❡♥*" ♠♦❞O❧❡ ❙✐ ✴ ❩♥❖ ✴ ❚✐ ✴ ▼♦ ❧♦," ❞❡ *,❛✐*❡♠❡♥*" *❤❡,♠✐<✉❡"✳ ❊♥ ❝,♦✐"❛♥* ♣❤♦*♦0♠✐""✐♦♥ ❤❛✉*❡ 0♥❡,❣✐❡ ❡* ❧❛ ❞0"♦,♣*✐♦♥ *❤❡,♠✐<✉❡✱ ✐❧ ❛ 0*0 ❞0♠♦♥*,0 <✉❡ ❧❛ ,0❛❝*✐♦♥ ,0❞♦① ❚✐✲❩♥❖ ❞♦♥♥❡ ❧✐❡✉ D ❧❛ ❢♦,♠❛*✐♦♥ ❞✬✉♥ ❡♥"❡♠❜❧❡ ❞❡ "♦✉"✲ ♦①②❞❡" ❞❡ ❚✐ ❡* ❞❡ ❩♥ ♠0*❛❧❧✐<✉❡ <✉✐ ❞0"♦,❜❡ ❞❡ ❧✬0❝❤❛♥*✐❧❧♦♥✳ ❆♣,O" ✉♥ ,❡❝✉✐* D ✺✺✵➦ ❈✱ ❚✐✹✰_{❞❡✈✐❡♥* ❞♦♠✐♥❛♥*} ❡* ✉♥ ❝♦♠♣♦"0 ♠✐①*❡ ❩♥❚✐❖① "❡ ❢♦,♠❡ D ❧✬✐♥*❡,❢❛❝❡✳ ▲✬✐♥✢✉❡♥❝❡ ❞❡ ❧❛ <✉❛♥*✐*0 ❞❡ ❩♥❖ ❡* ❞❡ "❛ ❝,✐"*❛❧❧✐♥✐*0 ❛ 0❣❛❧❡♠❡♥* 0*0 ❛❜♦,❞0❡✳ ❈❡" ❝♦♥"*❛*❛*✐♦♥" ♦♥* 0*0 ❝♦,,0❧0❡" ❛✈❡❝ ❞❡" "✐♠✉❧❛*✐♦♥" *❤❡,♠♦❞②♥❛♠✐<✉❡" ❞✉ ❞✐❛❣,❛♠♠❡ ❞❡ ♣❤❛"❡ ❚✐✲❩♥❖✳ ✻

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❙✉♠♠❛$②

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●❧❛## ♣%♦❞✉❝*# ♦✛❡% ❛ ✉♥✐/✉❡ ♦♣♣♦%*✉♥✐*② *♦ %❡❞✉❝❡ ❣%❡❡♥❤♦✉#❡ ❣❛# ❡♠✐##✐♦♥# ❛♥❞ ♠✐*✐❣❛*❡ *❤❡ ❡✛❡❝*# ♦❢ ❝❧✐♠❛*❡ ❝❤❛♥❣❡✳ ❙✐♥❝❡ ♦✈❡% ✹✵✪ ♦❢ ❛❧❧ ❡♥❡%❣② ✐♥ *❤❡ ❊✉%♦♣❡❛♥ ❯♥✐♦♥ ✐# ✉#❡❞ ✐♥ ❜✉✐❧❞✐♥❣# ✭❋✐❣✳ ✶❛✮✱ ♠❛❦✐♥❣ ♥❡✇ ❛♥❞ ❡①✐#*✐♥❣ ♦♥❡# ❛# ❡♥❡%❣② ❡✣❝✐❡♥* ❛# ♣♦##✐❜❧❡ ✇✐❧❧ *❤✉# ❡♥❛❜❧❡ #✐❣♥✐✜❝❛♥* #*%✐❞❡# *♦✇❛%❞# *❤❡ ❛♠❜✐*✐♦✉# ❛♥❞ ♠❛♥❞❛*♦%② ❈❖2%❡❞✉❝*✐♦♥ ❣♦❛❧#✳ ▲♦✇✲❡♠✐##✐✈✐*② ✭▲♦✇✲❊✮ ✐♥#✉❧❛*✐♥❣ ❣❧❛③✐♥❣ ✇✐♥❞♦✇# ✭❋✐❣✳ ✶❜✱❝✮ ❛%❡ #♣❡❝✐❛❧❧② ❝♦❛*❡❞ ✇✐*❤ *%❛♥#♣❛%❡♥* #✐❧✈❡%✲❜❛#❡❞ *❤✐♥ ✜❧♠# ✭❛%♦✉♥❞ ✶✵ ♥♠✮ *❤❛* %❡✢❡❝* ❤❡❛*✱ ✐✳❡✳ ✐♥❢%❛%❡❞ %❛❞✐❛*✐♦♥ ✭■❘✮✱ ❜❛❝❦ ✐♥*♦ *❤❡ ❜✉✐❧❞✐♥❣✱ *❤❡%❡❜② %❡❞✉❝✐♥❣ *❤❡ ❤❡❛* ❧♦## *❤%♦✉❣❤ *❤❡ ✇✐♥❞♦✇ ❬✶✱ ✷❪✳ ❚❤❡ ■❘ %❡✢❡❝*✐✈✐*② ✐# ❞✐%❡❝*❧② ❝♦%%❡❧❛*❡❞ *♦ *❤❡ ♠❡*❛❧ ❡♠✐##✐✈✐*② ❛♥❞ *❤❡%❡❢♦%❡ *❤❡ ♠❡*❛❧ ❝♦♥❞✉❝*✐✈✐*②❀ *❤❡ ❤✐❣❤❡% *❤❡ ❝♦♥❞✉❝*✐✈✐*②✱ *❤❡ ❤✐❣❤❡% *❤❡ ■❘ %❡✢❡❝*✐✈✐*②✱ ❛♥❞ ✐♥ *✉%♥ *❤❡ ❜❡**❡% *❤❡ ✐♥#✉❧❛*✐♥❣ ♣%♦♣❡%*✐❡# ♦❢ *❤❡ ❣❧❛③✐♥❣✳ ■♥ ❛❞❞✐*✐♦♥✱ *❤❡ ❝♦❛*✐♥❣ #❤♦✉❧❞ ❛❧❧♦✇ ❢♦% ❧❛%❣❡ ❛♠♦✉♥*# ♦❢ ❢%❡❡ #♦❧❛% ❡♥❡%❣② *♦ ❡♥*❡% *❤❡ ❜✉✐❧❞✐♥❣✱ *❤❡%❡❜② ❤❡❛*✐♥❣ ✐* ♣❛##✐✈❡❧②✱ ❛# ✇❡❧❧ ❛# ♠❛①✐♠✉♠ ❧❡✈❡❧# ♦❢ ✈✐#✐❜❧❡ ❧✐❣❤* *%❛♥#♠✐##✐♦♥ ❢♦% ✐♥❝%❡❛#❡❞ ❝♦♠❢♦%* ✭❋✐❣✳ ✶❜✮✳ ❚❤❡ ❡♥❡%❣❡*✐❝ ♣❡%❢♦%♠❛♥❝❡ ♦❢ ❛ ✇✐♥❞♦✇ ✐# ❛##❡##❡❞ ❜② *❤❡ ❤❡❛* ❧♦## ❝♦❡✣❝✐❡♥* Ug ❛♥❞ #♦❧❛% ❢❛❝*♦% g✱ *❤❛* ♠❡❛#✉%❡# *❤❡ ♣❡%❝❡♥*❛❣❡ ♦❢ #♦❧❛% ❤❡❛* *❤❛* ♣❡♥❡*%❛*❡# *❤%♦✉❣❤ *❤❡ ❣❧❛##✳ ❚❤❡ ❧♦✇❡% Ug ❛♥❞✴♦% *❤❡ ❤✐❣❤❡% g✱ *❤❡ ♠♦%❡ ❡♥❡%❣② ❡✣❝✐❡♥* ✐# *❤❡ ✇✐♥❞♦✇✳ ❙✐❧✈❡% ✐# ❝♦♥✈❡♥*✐♦♥❛❧❧② ✉#❡❞ ❛# ✐* ✐# ❛♠♦♥❣ *❤❡ ♠❡*❛❧# ✇✐*❤ *❤❡ ❧♦✇❡#* ❜✉❧❦ %❡#✐#*✐✈✐*②✳ ❚❤✐# ❝❛❧❧# ❢♦% ♠❡*❛❧ ✜❧♠#✱ ✇❤✐❝❤ ❛%❡ ❛# *❤✐♥ ❛# ♣♦##✐❜❧❡ *♦ ♠❛①✐♠✐③❡ #♦❧❛% ❣❛✐♥ ❛♥❞ ✈✐#✐❜❧❡ ❧✐❣❤*✱ ②❡* ❛❧#♦ ❛# ❝♦♥❞✉❝*✐✈❡ ❛# ❝♦♥❝❡✐✈❛❜❧❡ ✭❧♦✇ ❤❡❛* ❧♦##✮✳ ■♥*%♦❞✉❝*✐♦♥ ♦❢ ❞♦✉❜❧❡ ❣❧❛③✐♥❣ ✭Ug∼ 2.5 ❲ · ♠−2· ❑−1✮ ✐♥ *❤❡ ✼✵✬# ❛❧❧♦✇❡❞ ❞✐✈✐❞✐♥❣ ❜② ❛ ❢❛❝*♦% ♦❢ *✇♦ *❤❡ ❤❡❛* ❧♦##❡# *❤%♦✉❣❤ ✇✐♥❞♦✇# ❝♦♠♣❛%❡❞ *♦ #✐♥❣❧❡ ❣❧❛③✐♥❣ ✭Ug∼ 6 ❲ · ♠−2· ❑−1✮✱ ❛♥❞ *❤❡ ✐♥*%♦❞✉❝*✐♦♥ ♦❢ ❧♦✇✲❊ ❣❧❛## ❢✉%*❤❡% ❞✐✈✐❞❡❞ ❤❡❛* ❧♦##❡# ❜② *❤❡ #❛♠❡ ❢❛❝*♦% ✭Ug∼ 1.2 ❲ · ♠−2· ❑−1✮ ✭❋✐❣✳ ✶❞✮✳ ❚♦❞❛②✱ ❧❡## *❤❛♥ ✶✺✪ ♦❢ ❊✉%♦♣❡ ❜✉✐❧❞✐♥❣# ❝♦♥*❛✐♥ ❡♥❡%❣②✲#❛✈✐♥❣ ❣❧❛##✳ ❚❤❡ ✉#❡ ♦❢ ❧♦✇✲❊ ❣❧❛## ✐♥ ❛❧❧ ♥❡✇ ❛♥❞ ❡①✐#*✐♥❣ ❜✉✐❧❞✐♥❣# ✐♥ ❊✉%♦♣❡ ✇♦✉❧❞ ❧❡❛❞ *♦ ❛ ♣♦*❡♥*✐❛❧ ❡♥❡%❣② #❛✈✐♥❣ ♣❡% ②❡❛% ♦❢ 900000 *❡%❛❥♦✉❧❡# ✭❚❏✮✱ ❧❡❛❞✐♥❣ *♦ ❛ %❡❞✉❝*✐♦♥ ✐♥ ❈❖2❡♠✐##✐♦♥# ♦❢ ✉♣ *♦ ✾✵ ♠✐❧❧✐♦♥ *♦♥# ❛♥♥✉❛❧❧②✱ ✐✳❡✳ ✸✵✪ ♦❢ *❤❡ ❛♥♥✉❛❧ *❛%❣❡* ♦❢ *❤❡ ❊✉%♦♣❡❛♥ ❯♥✐♦♥✳ ●✐✈❡♥ ✐♥❝%❡❛#✐♥❣❧② ❡♥❡%❣②✲#❛✈✐♥❣ %❡❣✉❧❛*✐♦♥ %✉❧❡#✱ *❤❡%❡ ✐# *❤✉# ❛ #*%♦♥❣ ✉%❣❡ *♦ ❢✉%*❤❡% ✐♠♣%♦✈❡ *❤❡ ❡♥❡%❣② #❛✈✐♥❣ ♣%♦♣❡%*✐❡# ♦❢ ❝♦❛*❡❞ ❣❧❛## ♣%♦❞✉❝*#✳ ❋♦% ✐♥#*❛♥❝❡✱ ❢♦% ❛ ❣✐✈❡♥ ❡♠✐##✐✈✐*② ✈❛❧✉❡✱ ❛ ✷✵✪ ❞❡❝%❡❛#❡ ✐♥ #✐❧✈❡% %❡#✐#*✐✈✐*② ✇♦✉❧❞ ②✐❡❧❞ ❛♥ ✐♥❝%❡❛#❡ ♦❢ ❣ ✈❛❧✉❡ ♦❢ ✺✪✱ ❝♦%%❡#♣♦♥❞✐♥❣ *♦ ❛ ♣♦*❡♥*✐❛❧ ❡♥❡%❣② #❛✈✐♥❣ ♣❡% ②❡❛% ♦❢ ❛%♦✉♥❞ 100000 ❚❏✱ ❛ #✐③❡❛❜❧❡ ✜❣✉%❡ ✐♥ *❤❡ ✇♦%❧❞✇✐❞❡ ♣%♦❜❧❡♠ ♦❢ ❣❧♦❜❛❧ ✇❛%♥✐♥❣✳ ❚❤❡%❡ ✐# *❤❡%❡❢♦%❡ ❛ ✜❡%❝❡ ✇♦%❧❞✲✇✐❞❡ ❝♦♠♣❡*✐*✐♦♥ ❛♠♦♥❣ ❣❧❛## ♠❛♥✉❢❛❝*✉%❡%# *♦ ✐♠♣%♦✈❡ *❤✐# ✜❣✉%❡✳ ◆♦* ♦♥❧② *❤❡ ❤♦✉#✐♥❣ ♠❛%❦❡* ✐# ❝♦♥❝❡%♥❡❞ ❜✉* ❛❧#♦ *❤❡ ❛✉*♦♠♦*✐✈❡ ♦♥❡ ✇✐*❤ *❤❡ #♣%❡❛❞ ♦❢ ❝❛% ❛✐%✲❝♦♥❞✐*✐♦♥✐♥❣ ✶_✳ ■♥ ✐♥❞✉#*%✐❛❧ ❣❧❛③✐♥❣#✱ ❆❣ ❧❛②❡%# ❛%❡ ❝♦♥✈❡♥*✐♦♥❛❧❧② ❞❡♣♦#✐*❡❞ ❜② ♠❛❣♥❡*%♦♥✲#♣✉**❡%✐♥❣ ✐♥ ❞❡❞✐❝❛*❡❞ ❢❛❝*♦%✲ ✐❡# ♦♥ ✇✐♥❞♦✇# ♣❛♥❡# ♦❢ 3 × 6 ♠2_{❀ ✐♥ *❤❡ ✈❛#* ♠❛❥♦%✐*② ♦❢ ♣%♦❞✉❝*#✱ ❛ *❤✐♥ ❩♥❖ ❧❛②❡% ✭❛%♦✉♥❞ ✶✵ ♥♠✮ ✐#} ✉#❡❞ ❛# ❛ ❝%②#*❛❧❧✐③❛*✐♦♥ ♦% #❡❡❞ ❧❛②❡% ✭❋✐❣✳ ✶❝✮✳ ❆#✐❞❡ ❢%♦♠ *❤❡ ❢❛❝* *❤❛* ✐* ✐# ❛ ❝❤❡❛♣ ❛♥❞ ✇❡❧❧✲♠❛#*❡%❡❞ ♠❛*❡%✐❛❧ ❛* *❤❡ ✐♥❞✉#*%✐❛❧ ❧❡✈❡❧✱ ❩♥❖ ❛❧❧♦✇# ❆❣ ❧❛②❡%# *♦ ❜❡ ♦✉*✲♦❢✲♣❧❛♥❡ ✭✶✶✶✮ *❡①*✉%❡❞ ✭❜✉* %❛♥❞♦♠ ✐♥ ♣❧❛♥❡✮❀ ✐* ✐# *♦❞❛② *❤❡ ♠❛*❡%✐❛❧ *❤❛* ②✐❡❧❞# *❤❡ ❧♦✇❡#* ❆❣ %❡#✐#*✐✈✐*②✳ ■*# ✐♥*%♦❞✉❝*✐♦♥ ✐♥ *❤❡ ♠✐❞❞❧❡ ✾✵✬# ❛❧❧♦✇❡❞ ❛ #✐❣♥✐✜❝❛♥* ❞❡❝%❡❛#❡ ♦❢ #✐❧✈❡% %❡#✐#*✐✈✐*② ✭❋✐❣✳ ✶❞✮✳ ❙✐♥❝❡ *❤❡♥✱ ♣❡%❢♦%♠❛♥❝❡ ✐♠♣%♦✈❡♠❡♥* ✈✐❛ ♦♣*✐♠✲ ✐③❛*✐♦♥ ♦❢ *❤❡ ❆❣✴❩♥❖ #②#*❡♠ ❛♥❞ #✉%%♦✉♥❞✐♥❣ ❞✐❡❧❡❝*%✐❝ ♠❛*❡%✐❛❧# ❤❛# ♦♥❧② ❜❡❡♥ ✐♥❝%❡♠❡♥*❛❧ *❤♦✉❣❤✱ ❛♥❞ ❤❛# %❡❛❝❤❡❞ ❛ ❧✐♠✐* *♦❞❛② ✭❋✐❣✳ ✶❞✮✳ ❆* ♣%❡#❡♥*✱ *❤❡ %❡#✐#*✐✈✐*② ♦❢ ♣♦❧②❝%②#*❛❧❧✐♥❡ ❆❣ *❤✐♥ ✜❧♠# ❡♠♣❧♦②❡❞ ✐# ♦❢ ❛%♦✉♥❞ ✸✳✺ µΩ·❝♠ ❢♦% ✶✵ ♥♠ *❤✐❝❦ ❆❣ ✜❧♠#✱ ✐✳❡✳ #✐❣♥✐✜❝❛♥*❧② ❤✐❣❤❡% *❤❛♥ *❤❡ ❜✉❧❦ ✈❛❧✉❡ ♦❢ ✶✳✻ µΩ·❝♠✳ ❆♥② ✐♠♣%♦✈❡♠❡♥* ♦❢ *❤✐# ✜❣✉%❡ ♦❢ ♠❡%✐* #❤♦✉❧❞ ❣♦ *❤%♦✉❣❤ ❛ ❞❡❡♣❡% ✉♥❞❡%#*❛♥❞✐♥❣ ♦❢ *❤❡ ❝♦%❡ ❆❣✴❩♥❖ ✐♥*❡%❢❛❝❡ *♦ ♣✐♥♣♦✐♥* *❤❡ ❦❡② ❧❡✈❡%#✳ ■♥ *❤✐# /✉❡#*✱ ❧♦✇✲❊ ❝♦❛*✐♥❣# ❜❡❝❛♠❡ ❛ #♦ ✜♥❡❧② *✉♥❡❞ #②#*❡♠# ✐♥ *❡%♠# ♦❢ ♠❛*❡%✐❛❧# ❛♥❞ ❞❡♣♦#✐*✐♦♥ ❝♦♥❞✐*✐♦♥# *❤❛* ❡❛❝❤ ❧❛②❡% ✭✉♣ *♦ ✷✵✮ ♣❧❛② ❛ ❦❡② %♦❧❡ ✇❤✐❝❤ #♦♠❡*✐♠❡# %❡♠❛✐♥# ❜❧✉%%❡❞✳ ❇❡✐♥❣ ❛ ♥♦❜❧❡ ♠❡*❛❧✱ #✐❧✈❡% ♣%❡#❡♥*# ❛ ✈❡%② ♣♦♦% ❝❤❡♠✐❝❛❧ ❛✣♥✐*② ✇✐*❤ *❤❡ ✉♥❞❡%❧②✐♥❣ ♦①✐❞❡❀ *❤❡ ✜❧♠ ♠♦%♣❤♦❧♦❣② ✉#❡❞ *♦ %❡✢❡❝* ■❘ ❧✐❣❤* ✐# *❤❡%❡❢♦%❡ *❤❡%♠♦❞②♥❛♠✐❝❛❧❧② ♦✉*✲♦❢✲❡/✉✐❧✐❜%✐✉♠ #✐♥❝❡ ✐♥*❡%❢❛❝❡ ✶_{■! ♠✉$! ❜❡ ♥♦!❡❞ !❤❛! !❤❡ ✇♦-❦✐♥❣ ♣-✐❝♥✐♣❧❡ ♦❢ ❧♦✇✲❊ ❝♦❛!✐♥❣$ ❝❛♥ ❜❡ ❛❧$♦ ✉$❡❞ ✐♥ ✇❛-♠ ❝❧✐♠❛!❡✱ !♦ ♣-❡✈❡♥! ❤❡❛!} !-❛♥$❢❡-❢-♦♠ !❤❡ ♦✉!$✐❞❡✳ ■♥ !❤✐$ ❝❛$❡✱ ♦♥❡ ♥❡❡❞$ $❡✈❡-❛❧ ❆❣ ❧❛②❡-$ !❤❛! $❤✐❢! !❤❡ ✇♦-❦✐♥❣ ✇❛✈❡❧❡♥!❤ ♦❢ !❤❡ ❝♦❛!✐♥❣ !♦ !❤❡ ♥❡❛- ✐♥❢-❛-❡❞ -❛♥❣❡✳ ✽

(11)

(12)

❤❡ ✉$❡ $✉❝❤ ♠❡ ❛❧❧✐❝ ✜❧♠ ❛$ +❛♥$♣❛+❡♥ ❡❧❡❝ +♦❞❡$✱ ✐♥ ♣❛+ ✐❝✉❧❛+ ✐♥ ❤❡ ❝♦♥ ❡① ♦❢ ❖+❣❛♥✐❝ ▲✐❣❤ ❊♠✐ ✐♥❣ ❉❡✈✐❝❡$✳ ❈❤❛♣ ❡+ ✷ ♣+❡$❡♥ $ ♦✉+ +❡$✉❧ $ ♦♥ ❤❡ ✐♥ ❡+♣❧❛② ❜❡ ✇❡❡♥ ✜❧♠ ♠♦+♣❤♦❧♦❣② ❛♥❞ ❙❝❤♦ ❦② ❜❛++✐❡+ ❛ ❤❡ ✐♥ ❡+❢❛❝❡ ❜❡ ✇❡❡♥ $✐❧✈❡+ ❛♥❞ ❤❡ ♣♦❧❛+ ❢❛❝❡$ ♦❢ ③✐♥❝ ♦①✐❞❡✳ ❚❤✐$ ♦+✐❡♥ ❛ ✐♦♥ ✇❛$ $❡❧❡❝ ❡❞ ❜❡❝❛✉$❡ ♦❢ ❤❡ ♣+❡❢❡+❡♥ ✐❛❧ ❝♦❧✉♠♥❛+ ❣+♦✇ ❤ ❛❧♦♥❣ ❤❡ ❝✲❛①✐$ ♦❢ $♣✉ ❡+❡❞ ❤✐♥ ✜❧♠$ ✭$❡❡ ❈❤❛♣ ❡+ ✸✮✳ ❚❤✐$ $✉+❢❛❝❡ $❝✐❡♥❝❡ $ ✉❞② ♦♥ $✐♥❣❧❡ ❝+②$ ❛❧ $✉+❢❛❝❡$ ❝♦♠❜✐♥❡❞ ❡❧❡❝ +♦♥ ❞✐✛+❛❝ ✐♦♥✱ ♥❡❛+✲✜❡❧❞ ♠✐❝+♦$❝♦♣②✱ ♦♣ ✐❝❛❧ $♣❡❝ +♦$❝♦♣② ❛♥❞ ♣❤♦ ♦❡♠✐$$✐♦♥✳ ❚❤❡ ❣♦❛❧ ✇❛$ ♦ ❛♥❛❧②$❡ ❤❡ +♦❧❡ ♦❢ ♣♦❧❛+✐ ② ❛♥❞ ❤❡ ✐♥ ❡+❛❝ ✐♦♥ ♦❢ ❤②❞+♦❣❡♥ ✇✐ ❤ ❩♥❖ ♦♥ ❜❛♥❞ ❜❡♥❞✐♥❣ ❛♥❞ ❙❝❤♦ ❦② ❜❛++✐❡+ ✇✐ ❤ ❆❣✳ ■♥ ❛♥ ♦+✐❣✐♥❛❧ ✇❛②✱ $✉+❢❛❝❡ $❡♥$✐ ✐✈✐ ② ♦❢ ✉❧ +❛✲✈✐♦❧❡ ❧❛❜♦+✲ ❛ ♦+② ♣❤♦ ♦❡♠✐$$✐♦♥ ❛♥❞ ❜✉❧❦ $❡♥$✐ ✐✈✐ ② ♦❢ ❍❆❳M❊❙ ✇❡+❡ ❛$$♦❝✐❛ ❡❞ ♦ ❞+❛✇ ❛ ❝♦♠♣❧❡ ❡ ❜❛♥❞ ❛❧✐❣♥♠❡♥ ❛ ❆❣✴❩♥❖ ✐♥ ❡+❢❛❝❡✳ ❚❤❡ ♣♦ ❡♥ ✐❛❧ +❛♥$❢❡+ ♦❢ ❤❡ ♦❜$❡+✈❛ ✐♦♥ ♠❛❞❡ ♦♥ $✐♥❣❧❡ ❝+②$ ❛❧$ ✐$ ❜❛$❡❞ ♦♥ ❤❡ ❛❜✐❧✐ ② ♦ ❝♦♥ +♦❧ ❤❡ ❝+②$ ❛❧❧♦❣+❛♣❤✐❝ ♦+✐❡♥ ❛ ✐♦♥ ✭✐✳❡✳ ❩♥❖✲❖ ♦+ ❩♥❖✲❩♥ ❡+♠✐♥❛ ✐♦♥✮ ♦❢ $♣✉ ❡+❡❞ ❩♥❖ ✜❧♠$✳ ❆$ ♣+❡✈✐♦✉$❧② $❤♦✇♥✱ ♦+✐❡♥ ❛ ✐♦♥ ✇❛$ ❝♦♥ +♦❧❧❡❞ ❜② ❛♣♣❧②✐♥❣ ❛ ♣♦❧❛+✐③❛ ✐♦♥ ♦ ❤❡ $❛♠♣❧❡ ❞✉+✐♥❣ ❣+♦✇ ❤ ❛♥❞ ❞❡ ❡❝ ❡❞ ❤+♦✉❣❤ ❛ $♣❡❝✐✜❝ ✜♥❣❡+♣+✐♥ ✐♥ ❤❡ ❳✲+❛② ♣❤♦ ♦❡♠✐$$✐♦♥ ✈❛❧❡♥❝❡ ❜❛♥❞ ❤❛ ✐$ +❡❧❛ ❡❞ ♦ ❤❡ ♦+✐❡♥ ❛ ✐♦♥ ♦❢ ❤❡ ❝✲❛①✐$ ♦❢ ❤❡ ✇✉+ ③✐ ❡ $ +✉❝ ✉+❡✳ ❆ ❝♦♠♣❧❡ ❡ ❡♠♣❡+❛ ✉+❡✲❜✐❛$ ♣❤❛$❡ ❞✐❛❣+❛♠ ✇❛$ ❡$ ❛❜❧✐$❤❡❞ $❤♦✇✐♥❣ ❤❡ $✉✐ ❛❜❧❡ ❝♦♥❞✐ ✐♦♥$ ♦ ❛✈♦✐❞ +❡✲$♣✉ ❡+✐♥❣ ♦❢ ❤❡ ❧❛②❡+ ❛♥❞ ♦ ❛❝❤✐❡✈❡ ❛ ❣✐✈❡♥ ♦+✐❡♥ ❛ ✐♦♥✳ ❙ ♦✐❝❤✐♦♠❡ +②✱ ❣+❛✐♥ $✐③❡ ❛♥❞ ❝+②$ ❛❧❧✐♥✐ ② ❛$ $❡❡♥ ❢+♦♠ ❞✐✛+❛❝ ✐♦♥✱ ❛ ♦♠✐❝ ❢♦+❝❡ ♠✐❝+♦$❝♦♣② ❛♥❞ ♣❤♦ ♦❧✉♠✐♥❡$❝❡♥❝❡ ✇❡+❡ ❝♦++❡❧❛ ❡❞ ✇✐ ❤ ❤❡ ❣+♦✇ ❤ ❝♦♥❞✐ ✐♦♥$✳ ❚❤♦$❡ ❧❛②❡+$ ✇❡+❡ ✉$❡❞ ❛$ $❤♦✇♥ ✐♥ ❤❡ ❧❛$ ❝❤❛♣ ❡+ ✭❈❤❛♣ ❡+ ✹✮ ♦ ❛❝❦❧❡ ❤❡ P✉❡$ ✐♦♥ ♦❢ ❤❡ ❝❤❡♠✐❝❛❧ +❡❛❝ ✐♦♥ ❛ ❚✐✴❩♥❖ ✐♥ ❡+❢❛❝❡✳ ❚❤❡ ✉$❡ ♦❢ ❤✐❣❤ ❦✐♥❡ ✐❝ ❡♥❡+❣② ♣❤♦ ♦❡❧❡❝ +♦♥$ ♦❢ ❍❆❳M❊❙ ❛♥❞ ❤❡ ❛$$♦❝✐❛ ❡❞ ✐♥❝+❡❛$❡ ♦❢ ✐♥❡❧❛$ ✐❝ ♠❡❛♥ ❢+❡❡ ♣❛ ❤$ ❛❧❧♦✇❡❞ ♦ ♣+♦❜❡ ✐♥ %✐&✉ ❤❡ ❡♠♣❡+❛ ✉+❡ ❞❡♣❡♥❞❡♥ ❝❤❡♠✐$ +② ❛ ❤❡ ❜✉+✐❡❞ ✐♥ ❡+❢❛❝❡✳ ▼♦✲❝❛♣♣❡❞ ❚✐✴❩♥❖ ✜❧♠$ ✇❡+❡ $♣❡❝✐❛❧❧② ❞❡$✐❣♥❡❞ ♦ ❢♦❧❧♦✇ ❤❡ +❡❛❝ ✐♦♥ ❛$ ❛ ❢✉♥❝ ✐♦♥ ♦❢ ❛♥♥❡❛❧✐♥❣ ❡♠♣❡+❛ ✉+❡✱ ✜❧♠ ❤✐❝❦♥❡$$ ❛♥❞ ❝+②$ ❛❧❧✐♥✐ ②✳ ❚❤❡ +❡❞✉❝ ✐♦♥ ♦❢ ❩♥❖ ❜② ❚✐ ✇❛$ P✉❛♥ ✐✜❡❞ ❜② ❛ ♣+❡✲ ❝✐$❡ ❞❡❝♦♠♣♦$✐ ✐♦♥ ✐♥ ❡+♠$ ♦❢ ♦①✐❞❛ ✐♦♥ ❞❡❣+❡❡ ♦❢ ❤❡ ❚✐ ❛♥❞ ❩♥ ❝♦+❡ ❧❡✈❡❧$✳ ❚❤❡ $♣❡❝ +♦$❝♦♣✐❝ ♦❜$❡+✈❛ ✐♦♥ ✇❡+❡ ❛❧$♦ ❝♦++❡❧❛ ❡❞ ✇✐ ❤ ❧❛❜♦+❛ ♦+② ❚❤❡+♠❛❧ ❉❡$♦+♣ ✐♦♥ ❙♣❡❝ +♦$❝♦♣② ❛♥❞ ❊❧❡❝ +♦♥ M+♦❜❡ ▼✐❝+♦$ ❆♥❛❧②$✐$ $❤♦✇✐♥❣ ❤❡ ♠♦+❡ ♦+ ❧❡$$ ✐♠♣❡❞❡❞ ❞✐✛✉$✐♦♥ ♦❢ ❢+❡❡ ❩♥ ❛❝+♦$$ ❤❡ $ ❛❝❦✳ ❋✐♥❛❧❧②✱ ❤❡$❡ ❡①♣❡+✐♠❡♥ ❛❧ ✜♥❞✐♥❣$ ✇❡+❡ +❛ ✐♦♥❛❧✐③❡❞ ❤+♦✉❣❤ ❤❡ $✐♠✉❧❛ ✐♦♥ ♦❢ ❤❡ ♣❤❛$❡ ❞✐❛❣+❛♠ ♦❢ ❤❡ ❩♥❖✲❚✐ $②$ ❡♠✳ ❚❤❡ ✜♥❛❧ ❝♦♥❝❧✉$✐♦♥ +❡✈✐❡✇$ ❤❡ ♠❛✐♥ +❡$✉❧ $ ♦❢ ❤✐$ ✇♦+❦ ❛♥❞ ♦♣❡♥$ $♦♠❡ ♣❡+$♣❡❝ ✐✈❡$ ♦♥ ✉♥+❡$♦❧✈❡❞ ✐$$✉❡$✳ ✶✵