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  1. ❙❡❛r❝❤✐♥❣ ❢♦r ❧❡♣t♦♥✐❝ ♥✉♠❜❡r ♥♦♥✲❝♦♥s❡r✈❛t✐♦♥ ✇✐t❤ ◆❊▼❖✲✸ ❛♥❞ ❙✉♣❡r◆❊▼❖ ❋r❛♥ç♦✐s ▼❛✉❣❡r ♦♥ ❜❡❤❛❧❢ ♦❢ t❤❡ ◆❊▼❖✲✸✴❙✉♣❡r◆❊▼❖ ❝♦❧❧❛❜♦r❛t✐♦♥ ▲P❈ ❈❛❡♥✱ ❊◆❙■❈❆❊◆✱ ❯♥✐✈❡rs✐té ❞❡ ❈❛❡♥✱ ❈◆❘❙✴■◆✷P✸✱ ❈❛❡♥✱ ❋r❛♥❝❡ ❚❆❯P✬✵✾✱ ❘♦♠❛✱ ❏✉❧② ✶✲✺✱ ✷✵✵✾ ❋✳ ▼❛✉❣❡r ▲P❈ ❈❛❡♥✱ ❊◆❙■❈❆❊◆✱ ❯♥✐✈❡rs✐té ❞❡ ❈❛❡♥✱ ❈◆❘❙✴■◆✷P✸✱ ❈❛❡♥✱ ❋r❛♥❝❡ ✶ ✴ ✸✷

  2. ◆❡✉tr✐♥♦ ❊tt♦r❡ ▼❛❥♦r❛♥❛ ❖❜s❡r✈❛t♦r② ❖✉t❧✐♥❡ ◆❊▼❖✲✸✿ ◮ t❡❝❤♥✐q✉❡ ◮ r❡s✉❧ts ◮ ♣❧❛♥s ❙✉♣❡r◆❊▼❖✿ ◮ ♥❡✇ ❣❡♥❡r❛t✐♦♥ ❡①♣❡r✐♠❡♥t ◮ ❘✫❉ st❛t✉s ◮ ♣❧❛♥s ❋✳ ▼❛✉❣❡r ▲P❈ ❈❛❡♥✱ ❊◆❙■❈❆❊◆✱ ❯♥✐✈❡rs✐té ❞❡ ❈❛❡♥✱ ❈◆❘❙✴■◆✷P✸✱ ❈❛❡♥✱ ❋r❛♥❝❡ ✷ ✴ ✸✷

  3. P❤②s✐❝s ✇✐t❤ t❤❡ ◆❊▼❖✲✸ ❞❡t❡❝t♦r ✉ ✉ ❞ ❞ ❞ ✉ ❱✲❆ ❲ P❤②s✐❝s ❣♦❛❧s ❡ − ▲ ❙❡❛r❝❤ ❢♦r ✵ νββ ❞❡❝❛② ✭ ∆ ▲ ❂ ✷✮✿ ν ▼ ( ❆ , ❩ ) → ( ❆ , ❩ + ✷ ) ✰ ✷ ❡ − ❡ − ▲ s❡♥s✐t✐✈✐t②✿ ❚ ✶ / ✷ ≃ ✶✵ ✷✹ ② ❲ ❱✲❆ < ♠ ν > ∼ ✵✳✸✲✵✳✺ ❡❱ ❞ ❞ ❞ ✉ ✉ ✉ ❙❡❛r❝❤ ❢♦r ✵ νββχ ✵ ✭▼❛❥♦r♦♥✮ ( ❆ , ❩ ) → ( ❆ , ❩ + ✷ ) ✰ ✷ ❡ − ✰ χ ✵ ✭ χ ✵ ✮ ✉ ✉ s❡♥s✐t✐✈✐t②✿ ❚ ✶ / ✷ ≃ ✶✵ ✷✸ ② ❞ ❞ ❞ ✉ ❲ ■♥✈❡st✐❣❛t❡ ✷ νββ ❞❡❝❛② ✭ ∆ ▲ ❂ ✵✮✿ ( ❆ , ❩ ) → ( ❆ , ❩ + ✷ ) ✰ ✷ ❡ − ✰ ✷ ¯ ❡ − ν ❡ ▲ ν ▲ χ ✵ � = ♥✉❝❧❡✐✱ ❞❡❝❛②s t♦ ❡①❝✐t❡❞ st❛t❡s✱ ν ▲ ❙❙❉ ✈s✳ ❍❙❉ ♠❡❝❤❛♥✐s♠s✱ ♥✳♠✳❡✳ ❡ − ▲ ❲ ❞ ❞ ❞ ✉ ✉ ✉ ❋✳ ▼❛✉❣❡r ▲P❈ ❈❛❡♥✱ ❊◆❙■❈❆❊◆✱ ❯♥✐✈❡rs✐té ❞❡ ❈❛❡♥✱ ❈◆❘❙✴■◆✷P✸✱ ❈❛❡♥✱ ❋r❛♥❝❡ ✸ ✴ ✸✷

  4. ❚❤❡ ◆❊▼❖✲✸ ❡①♣❡r✐♠❡♥t❛❧ t❡❝❤♥✐q✉❡ ❈❛❧♦r✐♠❡tr② ✰ ❚r❛❝❦✐♥❣ ❈❤❛r❣❡❞ ♣❛rt✐❝❧❡ P❛rt✐❝❧❡ ✐♥❞✐✈✐❞✉❛❧ ❘❡❝♦♥str✉❝t✐♦♥ ♦❢ ✜♥❛❧ st❛t❡ tr❛❥❡❝t♦r② ❡♥❡r❣② ❛♥❞ ❚❖❋ ❉❡❝❛② ✈❡rt❡① t♦♣♦❧♦❣②✿ ◮ ❡ ± ✐♥❞✐✈✐❞✉❛❧ ❡♥❡r❣② ◮ ❝❤❛r❣❡❞ ♣❛rt✐❝❧❡ tr❛❥❡❝t♦r② ◮ ♠❛❣♥❡t✐❝ ✜❡❧❞ ❝✉r✈❛t✉r❡ β − ◮ ✈❡rt❡① ◮ ❛♥❣✉❧❛r ❞✐str✐❜✉t✐♦♥ r ❡ β − t � ♥ ❡ ❇ ◮ t✐♠❡ ♦❢ ✢✐❣❤t ♠ ✐ ❤ ② t ✐ t r ✐ ❧ r ♦ r ✐ ♦ ❛ ❧ ❛ ❧ ❛ ❢ ❧ ✉ ❝ ✉ ❡ ♥ ❇❛❝❦❣r♦✉♥❞ r❡❥❡❝t✐♦♥ t❤r♦✉❣❤ ❡ ❞ ❝ ❞ ❛ ♠ ♦ r ❡ r ✉ t ▼ ❣ ✉ ♦ ♥ ❧ ♣❛rt✐❝❧❡ ✐❞❡♥t✐✜❝❛t✐♦♥✿ ❡ − ✱ ❡ + ✱ γ ✱ α s ❤ ♦ ❡ ✈ ♠ β ❣ ✐ β ❍ ❣ ❣ ❡ ♥ ❙ ✐ ❦ ❝ ❙♦✉r❝❡ ✐s s❡♣❛r❛t❡❞ ❢r♦♠ t❤❡ ❛ r t ❞❡t❡❝t♦r✿ ❝❛♥ ♠❡❛s✉r❡ s❡✈❡r❛❧ ββ ✐s♦t♦♣❡s ❋✳ ▼❛✉❣❡r ▲P❈ ❈❛❡♥✱ ❊◆❙■❈❆❊◆✱ ❯♥✐✈❡rs✐té ❞❡ ❈❛❡♥✱ ❈◆❘❙✴■◆✷P✸✱ ❈❛❡♥✱ ❋r❛♥❝❡ ✹ ✴ ✸✷

  5. ❚❤❡ ◆❊▼❖✲✸ ❞❡t❡❝t♦r ▼❛✐♥ ❝❤❛r❛❝t❡r✐s✐t✐❝s ❙♦✉r❝❡✿ ✶✵ ❦❣ ♦❢ ββ ✐s♦t♦♣❡s✱ ❙ ❂✷✵ ♠ ✷ ✱ ❡ ≃ ✻✵ ♠❣✴❝♠ ✷ ❚r❛❝❦✐♥❣ ❞❡t❡❝t♦r✿ ❞r✐❢t ✇✐r❡ ❝❤❛♠❜❡r ♦♣❡r❛t✐♥❣ ✐♥ ●❡✐❣❡r ♠♦❞❡ ✭✻✶✽✵ ❝❡❧❧s✮ ❣❛s✿ ❍❡✰✹✪ ❡t❤②❧ ❛❧❝♦❤♦❧✰✶✪❆r ✰✵✳✶✪❍ ✷ ❖✱ r❛❞♦♥ ❢r❡❡ ❈❛❧♦r✐♠❡t❡r✿ ✶✾✹✵ ♣❧❛st✐❝ s❝✐♥t✐❧❧❛t♦rs ❝♦✉♣❧❡❞ t♦ ❧♦✇ r❛❞✐♦❛❝t✐✈✐t② P▼❚s ▼❛❣♥❡t✐❝ ✜❡❧❞✿ ✷✺ ❣❛✉ss ●❛♠♠❛ s❤✐❡❧❞✿ ♣✉r❡ ■r♦♥ ✭✶✽ ❝♠✮ ◆❡✉tr♦♥ s❤✐❡❧❞✿ ❜♦r❛t❡❞ ✇❛t❡r ✭✸✵ ❝♠✱ ❡①t✳ ✇❛❧❧✮✱ ✇♦♦❞ ✭✹✵ ❝♠✱ t♦♣✰❜♦tt♦♠✮ ❘♥ tr❛♣♣✐♥❣ ❢❛❝✐❧✐t② ✰ t❡♥t ▲♦✇ r❛❞✐♦❛❝t✐✈✐t② ♠❛t❡r✐❛❧s ❋ré❥✉s ❯♥❞❡r❣r♦✉♥❞ ▲❛❜♦r❛t♦r② ✭✹✽✵✵ ♠✳✇✳❡✳✮ ❋✳ ▼❛✉❣❡r ▲P❈ ❈❛❡♥✱ ❊◆❙■❈❆❊◆✱ ❯♥✐✈❡rs✐té ❞❡ ❈❛❡♥✱ ❈◆❘❙✴■◆✷P✸✱ ❈❛❡♥✱ ❋r❛♥❝❡ ✺ ✴ ✸✷

  6. ❚❤❡ ◆❊▼❖✲✸ ❞❡t❡❝t♦r ββ ❞❡❝❛② ✐s♦t♦♣❡s ■s♦t♦♣❡ ▼❛ss ✭❣✮ ◗ ββ ✭❦❡❱✮ 5 4 ✹✽ ❈❛ 6 3 ✶✺✵ ◆❞ ✵ νββ s❡❛r❝❤ ✰ ✷ νββ ♠❡❛s✳ ✾✻ ❩r ✶✵✵ ▼♦ 2 ✶✵✵ ▼♦ 7 ✽✷ ❙❡ ✻✾✶✹ ✸✵✸✹ ✶✵✵ ▼♦ ✽✷ ❙❡ ✽✷ ❙❡ ✶✵✵ ▼♦ ✾✸✷ ✷✾✾✺ 1 8 ✷ νββ ♠❡❛s✉r❡♠❡♥t ✶✵✵ ▼♦ ♥❛t ❚❡ ✶✶✻ ❈❞ ✹✵✺ ✷✽✵✺ 0 9 ✶✸✵ ❚❡ ❈✉ ✾✻ ❩r ✾✳✹ ✸✸✺✵ ✶✺✵ ◆❞ ✸✼✳✵ ✸✸✻✼ ✶✵✵ ▼♦ ♥❛t ❚❡ 10 19 ✹✽ ❈❛ ✼✳✵ ✹✷✼✷ ✶✶✻ ❈❞ ✶✵✵ ▼♦ ✶✸✵ ❚❡ ✹✺✹ ✷✺✷✾ 11 18 ❊①t❡r♥❛❧ ❜❛❝❦❣r♦✉♥❞ ♠❡❛s✉r❡♠❡♥t ✶✸✵ ❚❡ ✶✵✵ ▼♦ s❡❡ ✶✸✵ ❚❡ ♥❛t ❚❡ ✹✾✶ ✶✵✵ ▼♦ 12 17 ✶✵✵ ▼♦ ✶✵✵ ▼♦ ✶✵✵ ▼♦ ❈✉ ✻✷✶ ✲ 13 16 14 15 ❊♥r✐❝❤❡❞ ✐s♦t♦♣❡s ♣r♦❞✉❝❡❞ ❜② ❝❡♥tr✐❢✉❣❛t✐♦♥ ✐♥ ❘✉ss✐❛ ❋✳ ▼❛✉❣❡r ▲P❈ ❈❛❡♥✱ ❊◆❙■❈❆❊◆✱ ❯♥✐✈❡rs✐té ❞❡ ❈❛❡♥✱ ❈◆❘❙✴■◆✷P✸✱ ❈❛❡♥✱ ❋r❛♥❝❡ ✻ ✴ ✸✷

  7. ββ ❡✈❡♥t s❡❧❡❝t✐♦♥✿ t❤❡ ( ✷ ❡ ) ✐♥t❡r♥❛❧ ❝❤❛♥♥❡❧ ❚r✐❣❣❡r ❚②♣✐❝❛❧ ≃ ✶ ▼❡❱ ✷ νββ ❝❛♥❞✐❞❛t❡ ❡✈❡♥t ✶ P▼❚ ❃ ✶✺✵ ❦❡❱ ✸ ●❡✐❣❡r ❝❡❧❧s ✭✷ ♥❡✐❣❤❜♦✉r ✰ ✶✮ ❚r✐❣❣❡r r❛t❡ ≃ ✼ ❍③ ❈r✐t❡r✐❛ ✷ tr❛❝❦s ✇✐t❤ ◗ < ✵ ✷ P▼❚s ❛ss♦❝✐❛t❡❞ ✇✐t❤ tr❛❝❦s ❝♦♠♠♦♥ ✈❡rt❡① ✐♥t❡r♥❛❧ ❡✈❡♥t ❢r♦♠ t❤❡ ❢♦✐❧ ✭❚❖❋ ❝✉t✮ ◆♦ ✉♥❛ss♦❝✐❛t❡❞ P▼❚ ✭ γ r❡❥❡❝t✐♦♥✮ ◆♦ ❞❡❧❛②❡❞ s❤♦rt tr❛❝❦s ✭ α r❡❥❡❝t✐♦♥ ❢r♦♠ ✷✶✹ ❇✐✲ ✷✶✹ P♦ ❝❛s❝❛❞❡✮ ββ r❛t❡✿ ✶ ❡✈❡♥t ✴ ✷✳✺ ♠✐♥✉t❡s ❋✳ ▼❛✉❣❡r ▲P❈ ❈❛❡♥✱ ❊◆❙■❈❆❊◆✱ ❯♥✐✈❡rs✐té ❞❡ ❈❛❡♥✱ ❈◆❘❙✴■◆✷P✸✱ ❈❛❡♥✱ ❋r❛♥❝❡ ✼ ✴ ✸✷

  8. ❊①♣❡❝t❡❞ ❜❛❝❦❣r♦✉♥❞s ✐♥ t❤❡ ( ✷ ❡ ) ❝❤❛♥♥❡❧ ❊①t❡r♥❛❧ ✭ γ ✢✉①✮✿ ▼❛♥② ✇❛②s t♦ γ ′′ γ ′ ♠✐♠✐❝ ❛ ββ ❡ + ❡ − γ ′ ❡ − s✐❣♥❛❧ γ γ γ ❡ − ❡ − ❡ − ◆❛t✉r❛❧ ❞♦✉❜❧❡ ❈♦♠♣t♦♥✰ ♣❛✐r r❛❞✐♦❛❝t✐✈✐t②✿ ❈♦♠♣t♦♥ ▼ö❧❧❡r ♣r♦❞✉❝t✐♦♥ ❯✴❚❤ ❝❤❛✐♥s ✭❘♥✮✱ ■♥t❡r♥❛❧ ✭s♦✉r❝❡ ❢♦✐❧ ❝♦♥t❛♠✐♥❛♥ts✮✿ ✹✵ ❑ γ ′ γ ′ ❈♦s♠✐❝ µ ❡ − ❡ − γ ◆❡✉tr♦♥s ❡ − β − β − β − ❆rt✐✜❝✐❛❧ r❛❞✐♦❛❝t✐✈✐t② β − ✰ β − ✰ β − ✰ ❈♦♠♣t♦♥ ▼ö❧❧❡r ■❈ ❋✳ ▼❛✉❣❡r ▲P❈ ❈❛❡♥✱ ❊◆❙■❈❆❊◆✱ ❯♥✐✈❡rs✐té ❞❡ ❈❛❡♥✱ ❈◆❘❙✴■◆✷P✸✱ ❈❛❡♥✱ ❋r❛♥❝❡ ✽ ✴ ✸✷

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