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r t strs t r t r t ts r r ttr

  1. ❇r❡❛❦✐♥❣ ❧❡♣t♦♥✐❝ s②♠♠❡tr✐❡s ✇✐t❤ ❛ ▼❛❥♦r♦♥✿ ❲❤❡♥ ▲❡♣t♦♥ ❋❧❛✈♦✉r ❱✐♦❧❛t✐♦♥ ♠❡❡ts ✇❛r♠ ❉❛r❦ ▼❛tt❡r ▲✉❝✐❡♥ ❍❡✉rt✐❡r P❛r✐s✱ ◆♦✈ ✷✵✶✻ ▲✳ ❍❡✉rt✐❡r P❛r✐s✱ ◆♦✈ ✷✵✶✻

  2. ❇❛s❡❞ ♦♥ ✿ ▲✳❍✳✱ ❉✳ ❚❡r❡s✐✱ ❆r①✐✈ ✿ ✶✻✵✼✳✵✶✼✾✽ ❉❛r❦ ♠❛tt❡r ❛♥❞ ♦❜s❡r✈❛❜❧❡ ▲❡♣t♦♥ ❋❧❛✈♦✉r ❱✐♦❧❛t✐♦♥ ▲✳❍✳✱ ❨✳ ❩❤❛♥❣✱ ❆r❳✐✈ ✿ ✶✻✵✾✳✵✺✽✽✷ ❙✉♣❡r♥♦✈❛ ❈♦♥str❛✐♥ts ♦♥ ▼❛ss✐✈❡ ✭Ps❡✉❞♦✮❙❝❛❧❛r ❈♦✉♣❧✐♥❣ t♦ ◆❡✉tr✐♥♦s ▲✳ ❍❡✉rt✐❡r P❛r✐s✱ ◆♦✈ ✷✵✶✻

  3. ✧ ✧ ✧ ✪ ✪ ✪ ✐♥ ✜rst ❛♣♣r♦①✐♠❛t✐♦♥ ◆❡✉tr✐♥♦ ♠❛ss❡s❄ ❘✐❣❤t ❍❛♥❞❡❞ ❢r✐❡♥❞s❄ ❉❛r❦ ▼❛tt❡r❄ ■♥✢❛t♦♥❄ ❍✐❡r❛r❝❤② ♣r♦❜❧❡♠❄ ❆♥❞ s♦ ♠❛♥② ♠♦r❡✳✳✳ ■♥tr♦❞✉❝t✐♦♥ ❚❤❡ st❛♥❞❛r❞ ♠♦❞❡❧ ✐s ✈❡r② s✉❝❝❡ss❢✉❧ ✳✳✳ ▲✳ ❍❡✉rt✐❡r P❛r✐s✱ ◆♦✈ ✷✵✶✻

  4. ✧ ✧ ✧ ✪ ✪ ✪ ◆❡✉tr✐♥♦ ♠❛ss❡s❄ ❘✐❣❤t ❍❛♥❞❡❞ ❢r✐❡♥❞s❄ ❉❛r❦ ▼❛tt❡r❄ ■♥✢❛t♦♥❄ ❍✐❡r❛r❝❤② ♣r♦❜❧❡♠❄ ❆♥❞ s♦ ♠❛♥② ♠♦r❡✳✳✳ ■♥tr♦❞✉❝t✐♦♥ ❚❤❡ st❛♥❞❛r❞ ♠♦❞❡❧ ✐s ✈❡r② s✉❝❝❡ss❢✉❧ ✳✳✳ ✐♥ ✜rst ❛♣♣r♦①✐♠❛t✐♦♥ ▲✳ ❍❡✉rt✐❡r P❛r✐s✱ ◆♦✈ ✷✵✶✻

  5. ✧ ✧ ✪ ✪ ✪ ✧ ❘✐❣❤t ❍❛♥❞❡❞ ❢r✐❡♥❞s❄ ❉❛r❦ ▼❛tt❡r❄ ■♥✢❛t♦♥❄ ❍✐❡r❛r❝❤② ♣r♦❜❧❡♠❄ ❆♥❞ s♦ ♠❛♥② ♠♦r❡✳✳✳ ■♥tr♦❞✉❝t✐♦♥ ❚❤❡ st❛♥❞❛r❞ ♠♦❞❡❧ ✐s ✈❡r② s✉❝❝❡ss❢✉❧ ✳✳✳ ✐♥ ✜rst ❛♣♣r♦①✐♠❛t✐♦♥ ◆❡✉tr✐♥♦ ♠❛ss❡s❄ ▲✳ ❍❡✉rt✐❡r P❛r✐s✱ ◆♦✈ ✷✵✶✻

  6. ✧ ✪ ✪ ✪ ✧ ✧ ❉❛r❦ ▼❛tt❡r❄ ■♥✢❛t♦♥❄ ❍✐❡r❛r❝❤② ♣r♦❜❧❡♠❄ ❆♥❞ s♦ ♠❛♥② ♠♦r❡✳✳✳ ■♥tr♦❞✉❝t✐♦♥ ❚❤❡ st❛♥❞❛r❞ ♠♦❞❡❧ ✐s ✈❡r② s✉❝❝❡ss❢✉❧ ✳✳✳ ✐♥ ✜rst ❛♣♣r♦①✐♠❛t✐♦♥ ◆❡✉tr✐♥♦ ♠❛ss❡s❄ ❘✐❣❤t ❍❛♥❞❡❞ ❢r✐❡♥❞s❄ ▲✳ ❍❡✉rt✐❡r P❛r✐s✱ ◆♦✈ ✷✵✶✻

  7. ✪ ✪ ✪ ✧ ✧ ✧ ■♥✢❛t♦♥❄ ❍✐❡r❛r❝❤② ♣r♦❜❧❡♠❄ ❆♥❞ s♦ ♠❛♥② ♠♦r❡✳✳✳ ■♥tr♦❞✉❝t✐♦♥ ❚❤❡ st❛♥❞❛r❞ ♠♦❞❡❧ ✐s ✈❡r② s✉❝❝❡ss❢✉❧ ✳✳✳ ✐♥ ✜rst ❛♣♣r♦①✐♠❛t✐♦♥ ◆❡✉tr✐♥♦ ♠❛ss❡s❄ ❘✐❣❤t ❍❛♥❞❡❞ ❢r✐❡♥❞s❄ ❉❛r❦ ▼❛tt❡r❄ ▲✳ ❍❡✉rt✐❡r P❛r✐s✱ ◆♦✈ ✷✵✶✻

  8. ✪ ✪ ✧ ✧ ✧ ✪ ❍✐❡r❛r❝❤② ♣r♦❜❧❡♠❄ ❆♥❞ s♦ ♠❛♥② ♠♦r❡✳✳✳ ■♥tr♦❞✉❝t✐♦♥ ❚❤❡ st❛♥❞❛r❞ ♠♦❞❡❧ ✐s ✈❡r② s✉❝❝❡ss❢✉❧ ✳✳✳ ✐♥ ✜rst ❛♣♣r♦①✐♠❛t✐♦♥ ◆❡✉tr✐♥♦ ♠❛ss❡s❄ ❘✐❣❤t ❍❛♥❞❡❞ ❢r✐❡♥❞s❄ ❉❛r❦ ▼❛tt❡r❄ ■♥✢❛t♦♥❄ ▲✳ ❍❡✉rt✐❡r P❛r✐s✱ ◆♦✈ ✷✵✶✻

  9. ✪ ✧ ✧ ✧ ✪ ✪ ❆♥❞ s♦ ♠❛♥② ♠♦r❡✳✳✳ ■♥tr♦❞✉❝t✐♦♥ ❚❤❡ st❛♥❞❛r❞ ♠♦❞❡❧ ✐s ✈❡r② s✉❝❝❡ss❢✉❧ ✳✳✳ ✐♥ ✜rst ❛♣♣r♦①✐♠❛t✐♦♥ ◆❡✉tr✐♥♦ ♠❛ss❡s❄ ❘✐❣❤t ❍❛♥❞❡❞ ❢r✐❡♥❞s❄ ❉❛r❦ ▼❛tt❡r❄ ■♥✢❛t♦♥❄ ❍✐❡r❛r❝❤② ♣r♦❜❧❡♠❄ ▲✳ ❍❡✉rt✐❡r P❛r✐s✱ ◆♦✈ ✷✵✶✻

  10. ✧ ✧ ✧ ✪ ✪ ✪ ■♥tr♦❞✉❝t✐♦♥ ❚❤❡ st❛♥❞❛r❞ ♠♦❞❡❧ ✐s ✈❡r② s✉❝❝❡ss❢✉❧ ✳✳✳ ✐♥ ✜rst ❛♣♣r♦①✐♠❛t✐♦♥ ◆❡✉tr✐♥♦ ♠❛ss❡s❄ ❘✐❣❤t ❍❛♥❞❡❞ ❢r✐❡♥❞s❄ ❉❛r❦ ▼❛tt❡r❄ ■♥✢❛t♦♥❄ ❍✐❡r❛r❝❤② ♣r♦❜❧❡♠❄ ❆♥❞ s♦ ♠❛♥② ♠♦r❡✳✳✳ ▲✳ ❍❡✉rt✐❡r P❛r✐s✱ ◆♦✈ ✷✵✶✻

  11. ■♥tr♦❞✉❝t✐♦♥ ❚❤❡ st❛♥❞❛r❞ ♠♦❞❡❧ ✐s ✈❡r② s✉❝❝❡ss❢✉❧ ✳✳✳ ✐♥ ✜rst ❛♣♣r♦①✐♠❛t✐♦♥ ✧ ◆❡✉tr✐♥♦ ♠❛ss❡s❄ ✧ ❘✐❣❤t ❍❛♥❞❡❞ ❢r✐❡♥❞s❄ ✧ ❉❛r❦ ▼❛tt❡r❄ ✪ ■♥✢❛t♦♥❄ ✪ ❍✐❡r❛r❝❤② ♣r♦❜❧❡♠❄ ✪ ❆♥❞ s♦ ♠❛♥② ♠♦r❡✳✳✳ ▲✳ ❍❡✉rt✐❡r P❛r✐s✱ ◆♦✈ ✷✵✶✻

  12. ▼♦t✐✈❛t✐♦♥s ◆❡✉tr✐♥♦ ♠❛ss❡s ✿ ❙❡❡s❛✇ ▼❡❝❤❛♥✐s♠❄ − g R Σ ν R − h L ν = √ √ ν L H ν R + h . c .. ν c ¯ ¯ ✷ ✷ θ ≈ m D hv M R = . ✷ gv Σ ( m ✶ M R ) ✶ / ✷ ≈ h , v ✶ , ✸ × ✶✵ − ✾ ( m ✶ ✶ / ✷ ✶ / ✷ ( M R ( ✷✹✻ ●❡❱ ∼ ✵ , ✶ ❡❱ ) ▼❡❱ ) ) . v ❙❡❡s❛✇ ♣r♦❝❡ss ⇒ ❚✐♥② ❨✉❦❛✇❛ ❝♦✉♣❧✐♥❣s ▲✳ ❍❡✉rt✐❡r P❛r✐s✱ ◆♦✈ ✷✵✶✻

  13. ❈❤❛r❣❡ ❆ss✐❣♥♠❡♥t ❨✉❦❛✇❛ str✉❝t✉r❡ ◆❡✉tr✐♥♦ ▼❛ss❡s ♣r♦t❡❝t❡❞ ❛t ❛❧❧ ♦r❞❡r ✭❜❡❢♦r❡ ❙❙❇ ♦❢ ✶ ✮ ▲❛r❣❡ ❨✉❦❛✇❛s ❛❧❧♦✇❡❞ P❤❡♥♦♠❡♥♦❧♦❣✐❝❛❧ ♦❜s❡r✈❛❜❧❡s✳✳✳ ▼♦t✐✈❛t✐♦♥s ■❞❡❛ ✿ ❆ss✐❣♥ ❣❧♦❜❛❧ U ( ✶ ) l ❝❤❛r❣❡s t♦ ❧❡♣t♦♥s✱ ❘❍ ❛♥❞ ▲❍ ♥❡✉tr✐♥♦s ❬❇r❛♥❝♦ ❡t✳ ❛❧✳ ✬✽✾✱ ❇❛❜✉✱ ▼❛✱ ✬✽✾✱ P✐❧❛❢ts✐s ✬✵✺❪ ▲✳ ❍❡✉rt✐❡r P❛r✐s✱ ◆♦✈ ✷✵✶✻

  14. ◆❡✉tr✐♥♦ ▼❛ss❡s ♣r♦t❡❝t❡❞ ❛t ❛❧❧ ♦r❞❡r ✭❜❡❢♦r❡ ❙❙❇ ♦❢ ✶ ✮ ▲❛r❣❡ ❨✉❦❛✇❛s ❛❧❧♦✇❡❞ P❤❡♥♦♠❡♥♦❧♦❣✐❝❛❧ ♦❜s❡r✈❛❜❧❡s✳✳✳ ▼♦t✐✈❛t✐♦♥s ■❞❡❛ ✿ ❆ss✐❣♥ ❣❧♦❜❛❧ U ( ✶ ) l ❝❤❛r❣❡s t♦ ❧❡♣t♦♥s✱ ❘❍ ❛♥❞ ▲❍ ♥❡✉tr✐♥♦s ❬❇r❛♥❝♦ ❡t✳ ❛❧✳ ✬✽✾✱ ❇❛❜✉✱ ▼❛✱ ✬✽✾✱ P✐❧❛❢ts✐s ✬✵✺❪ ❈❤❛r❣❡ ❆ss✐❣♥♠❡♥t ⇒ ❨✉❦❛✇❛ str✉❝t✉r❡ ▲✳ ❍❡✉rt✐❡r P❛r✐s✱ ◆♦✈ ✷✵✶✻

  15. ▲❛r❣❡ ❨✉❦❛✇❛s ❛❧❧♦✇❡❞ P❤❡♥♦♠❡♥♦❧♦❣✐❝❛❧ ♦❜s❡r✈❛❜❧❡s✳✳✳ ▼♦t✐✈❛t✐♦♥s ■❞❡❛ ✿ ❆ss✐❣♥ ❣❧♦❜❛❧ U ( ✶ ) l ❝❤❛r❣❡s t♦ ❧❡♣t♦♥s✱ ❘❍ ❛♥❞ ▲❍ ♥❡✉tr✐♥♦s ❬❇r❛♥❝♦ ❡t✳ ❛❧✳ ✬✽✾✱ ❇❛❜✉✱ ▼❛✱ ✬✽✾✱ P✐❧❛❢ts✐s ✬✵✺❪ ❈❤❛r❣❡ ❆ss✐❣♥♠❡♥t ⇒ ❨✉❦❛✇❛ str✉❝t✉r❡ ◆❡✉tr✐♥♦ ▼❛ss❡s ♣r♦t❡❝t❡❞ ❛t ❛❧❧ ♦r❞❡r ✭❜❡❢♦r❡ ❙❙❇ ♦❢ U ( ✶ ) l ✮ ▲✳ ❍❡✉rt✐❡r P❛r✐s✱ ◆♦✈ ✷✵✶✻

  16. P❤❡♥♦♠❡♥♦❧♦❣✐❝❛❧ ♦❜s❡r✈❛❜❧❡s✳✳✳ ▼♦t✐✈❛t✐♦♥s ■❞❡❛ ✿ ❆ss✐❣♥ ❣❧♦❜❛❧ U ( ✶ ) l ❝❤❛r❣❡s t♦ ❧❡♣t♦♥s✱ ❘❍ ❛♥❞ ▲❍ ♥❡✉tr✐♥♦s ❬❇r❛♥❝♦ ❡t✳ ❛❧✳ ✬✽✾✱ ❇❛❜✉✱ ▼❛✱ ✬✽✾✱ P✐❧❛❢ts✐s ✬✵✺❪ ❈❤❛r❣❡ ❆ss✐❣♥♠❡♥t ⇒ ❨✉❦❛✇❛ str✉❝t✉r❡ ◆❡✉tr✐♥♦ ▼❛ss❡s ♣r♦t❡❝t❡❞ ❛t ❛❧❧ ♦r❞❡r ✭❜❡❢♦r❡ ❙❙❇ ♦❢ U ( ✶ ) l ✮ ▲❛r❣❡ ❨✉❦❛✇❛s ❛❧❧♦✇❡❞ ▲✳ ❍❡✉rt✐❡r P❛r✐s✱ ◆♦✈ ✷✵✶✻

  17. ▼♦t✐✈❛t✐♦♥s ■❞❡❛ ✿ ❆ss✐❣♥ ❣❧♦❜❛❧ U ( ✶ ) l ❝❤❛r❣❡s t♦ ❧❡♣t♦♥s✱ ❘❍ ❛♥❞ ▲❍ ♥❡✉tr✐♥♦s ❬❇r❛♥❝♦ ❡t✳ ❛❧✳ ✬✽✾✱ ❇❛❜✉✱ ▼❛✱ ✬✽✾✱ P✐❧❛❢ts✐s ✬✵✺❪ ❈❤❛r❣❡ ❆ss✐❣♥♠❡♥t ⇒ ❨✉❦❛✇❛ str✉❝t✉r❡ ◆❡✉tr✐♥♦ ▼❛ss❡s ♣r♦t❡❝t❡❞ ❛t ❛❧❧ ♦r❞❡r ✭❜❡❢♦r❡ ❙❙❇ ♦❢ U ( ✶ ) l ✮ ▲❛r❣❡ ❨✉❦❛✇❛s ❛❧❧♦✇❡❞ ↪ P❤❡♥♦♠❡♥♦❧♦❣✐❝❛❧ ♦❜s❡r✈❛❜❧❡s✳✳✳ ▲✳ ❍❡✉rt✐❡r P❛r✐s✱ ◆♦✈ ✷✵✶✻

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