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s tr r rr sts r sr rst r Pt

  1. ❚❤❡ ❙✐♠♣s♦♥ ❝♦♥❥❡❝t✉r❡ ✭❢♦r r❡❣✉❧❛r ❝♦♠♣♦s✐t✐♦♥s✮ ❙✐♠♦♥ ❍❡♥r② ✭▼❛s❛r②❦ ❯♥✐✈❡rs✐t②✱ ❇r♥♦✮ ❈❚✷✵✶✽✱ P♦♥t❛ ❉❡❧❣❛❞❛✱ ❏✉❧② ✶✶t❤✱ ✷✵✶✽ ❙✳❍❡♥r② ▼❛s❛r②❦ ❚❤❡ ❙✐♠♣s♦♥ ❝♦♥❥❡❝t✉r❡ ✭❢♦r r❡❣✉❧❛r ❝♦♠♣♦s✐t✐♦♥s✮ ✶✶✴✵✼ ✶ ✴ ✶✸

  2. ■t ✐♥✈♦❧✈❡ t❤❡ ❢♦❧❧♦✇✐♥❣ t❤r❡❡ ♣❛♣❡rs✿ ✏◆♦♥✲✉♥✐t❛❧ ♣♦❧②❣r❛♣❤s ❛r❡ ❛ ♣r❡s❤❡❛✈❡s ❝❛t❡❣♦r②✑ ✭❍✳ ❆r❳✐✈ ✶✼✶✶✳✵✵✼✹✹✮ ❋r♦♠ ❧❛st ❖❝t♦❜r❡✳ ✏❲❡❛❦ ♠♦❞❡❧ ❝❛t❡❣♦r✐❡s ✐♥ ❝❧❛ss✐❝❛❧ ❛♥❞ ❝♦♥str✉❝t✐✈❡ ♠❛t❤❡♠❛t✐❝s✑ ✭❍✳ ❆r❳✐✈ ✶✽✵✼✳✵✷✻✺✵✮ ❋r♦♠ ❨❡st❡r❞❛②✳ ✏❘❡❣✉❧❛r ♣♦❧②❣r❛♣❤s ❛♥❞ t❤❡ ❙✐♠♣s♦♥ ❝♦♥❥❡❝t✉r❡✑ ✭❍✳ ❆r❳✐✈ ✶✽✵✼✳✵✷✻✷✼✮ ❋r♦♠ ❨❡st❡r❞❛②✳ ✳✳✳ ❛♣♣r♦①✐♠❛t❡❧② ✷✷✵ ♣❛❣❡s ✐♥ t♦t❛❧✳ ■✬♠ ♣r❡s❡♥t✐♥❣ ❛ ✈❡r② r❡❝❡♥t ♣r♦♦❢ ♦❢ ❛ ❢♦r♠ ♦❢ t❤❡ ❙✐♠♣s♦♥ ❝♦♥❥❡❝t✉r❡✳ ❙✳❍❡♥r② ▼❛s❛r②❦ ❚❤❡ ❙✐♠♣s♦♥ ❝♦♥❥❡❝t✉r❡ ✭❢♦r r❡❣✉❧❛r ❝♦♠♣♦s✐t✐♦♥s✮ ✶✶✴✵✼ ✷ ✴ ✶✸

  3. ✏❲❡❛❦ ♠♦❞❡❧ ❝❛t❡❣♦r✐❡s ✐♥ ❝❧❛ss✐❝❛❧ ❛♥❞ ❝♦♥str✉❝t✐✈❡ ♠❛t❤❡♠❛t✐❝s✑ ✭❍✳ ❆r❳✐✈ ✶✽✵✼✳✵✷✻✺✵✮ ❋r♦♠ ❨❡st❡r❞❛②✳ ✏❘❡❣✉❧❛r ♣♦❧②❣r❛♣❤s ❛♥❞ t❤❡ ❙✐♠♣s♦♥ ❝♦♥❥❡❝t✉r❡✑ ✭❍✳ ❆r❳✐✈ ✶✽✵✼✳✵✷✻✷✼✮ ❋r♦♠ ❨❡st❡r❞❛②✳ ✳✳✳ ❛♣♣r♦①✐♠❛t❡❧② ✷✷✵ ♣❛❣❡s ✐♥ t♦t❛❧✳ ■✬♠ ♣r❡s❡♥t✐♥❣ ❛ ✈❡r② r❡❝❡♥t ♣r♦♦❢ ♦❢ ❛ ❢♦r♠ ♦❢ t❤❡ ❙✐♠♣s♦♥ ❝♦♥❥❡❝t✉r❡✳ ■t ✐♥✈♦❧✈❡ t❤❡ ❢♦❧❧♦✇✐♥❣ t❤r❡❡ ♣❛♣❡rs✿ ✏◆♦♥✲✉♥✐t❛❧ ♣♦❧②❣r❛♣❤s ❛r❡ ❛ ♣r❡s❤❡❛✈❡s ❝❛t❡❣♦r②✑ ✭❍✳ ❆r❳✐✈ ✶✼✶✶✳✵✵✼✹✹✮ ❋r♦♠ ❧❛st ❖❝t♦❜r❡✳ ❙✳❍❡♥r② ▼❛s❛r②❦ ❚❤❡ ❙✐♠♣s♦♥ ❝♦♥❥❡❝t✉r❡ ✭❢♦r r❡❣✉❧❛r ❝♦♠♣♦s✐t✐♦♥s✮ ✶✶✴✵✼ ✷ ✴ ✶✸

  4. ✏❘❡❣✉❧❛r ♣♦❧②❣r❛♣❤s ❛♥❞ t❤❡ ❙✐♠♣s♦♥ ❝♦♥❥❡❝t✉r❡✑ ✭❍✳ ❆r❳✐✈ ✶✽✵✼✳✵✷✻✷✼✮ ❋r♦♠ ❨❡st❡r❞❛②✳ ✳✳✳ ❛♣♣r♦①✐♠❛t❡❧② ✷✷✵ ♣❛❣❡s ✐♥ t♦t❛❧✳ ■✬♠ ♣r❡s❡♥t✐♥❣ ❛ ✈❡r② r❡❝❡♥t ♣r♦♦❢ ♦❢ ❛ ❢♦r♠ ♦❢ t❤❡ ❙✐♠♣s♦♥ ❝♦♥❥❡❝t✉r❡✳ ■t ✐♥✈♦❧✈❡ t❤❡ ❢♦❧❧♦✇✐♥❣ t❤r❡❡ ♣❛♣❡rs✿ ✏◆♦♥✲✉♥✐t❛❧ ♣♦❧②❣r❛♣❤s ❛r❡ ❛ ♣r❡s❤❡❛✈❡s ❝❛t❡❣♦r②✑ ✭❍✳ ❆r❳✐✈ ✶✼✶✶✳✵✵✼✹✹✮ ❋r♦♠ ❧❛st ❖❝t♦❜r❡✳ ✏❲❡❛❦ ♠♦❞❡❧ ❝❛t❡❣♦r✐❡s ✐♥ ❝❧❛ss✐❝❛❧ ❛♥❞ ❝♦♥str✉❝t✐✈❡ ♠❛t❤❡♠❛t✐❝s✑ ✭❍✳ ❆r❳✐✈ ✶✽✵✼✳✵✷✻✺✵✮ ❋r♦♠ ❨❡st❡r❞❛②✳ ❙✳❍❡♥r② ▼❛s❛r②❦ ❚❤❡ ❙✐♠♣s♦♥ ❝♦♥❥❡❝t✉r❡ ✭❢♦r r❡❣✉❧❛r ❝♦♠♣♦s✐t✐♦♥s✮ ✶✶✴✵✼ ✷ ✴ ✶✸

  5. ✳✳✳ ❛♣♣r♦①✐♠❛t❡❧② ✷✷✵ ♣❛❣❡s ✐♥ t♦t❛❧✳ ■✬♠ ♣r❡s❡♥t✐♥❣ ❛ ✈❡r② r❡❝❡♥t ♣r♦♦❢ ♦❢ ❛ ❢♦r♠ ♦❢ t❤❡ ❙✐♠♣s♦♥ ❝♦♥❥❡❝t✉r❡✳ ■t ✐♥✈♦❧✈❡ t❤❡ ❢♦❧❧♦✇✐♥❣ t❤r❡❡ ♣❛♣❡rs✿ ✏◆♦♥✲✉♥✐t❛❧ ♣♦❧②❣r❛♣❤s ❛r❡ ❛ ♣r❡s❤❡❛✈❡s ❝❛t❡❣♦r②✑ ✭❍✳ ❆r❳✐✈ ✶✼✶✶✳✵✵✼✹✹✮ ❋r♦♠ ❧❛st ❖❝t♦❜r❡✳ ✏❲❡❛❦ ♠♦❞❡❧ ❝❛t❡❣♦r✐❡s ✐♥ ❝❧❛ss✐❝❛❧ ❛♥❞ ❝♦♥str✉❝t✐✈❡ ♠❛t❤❡♠❛t✐❝s✑ ✭❍✳ ❆r❳✐✈ ✶✽✵✼✳✵✷✻✺✵✮ ❋r♦♠ ❨❡st❡r❞❛②✳ ✏❘❡❣✉❧❛r ♣♦❧②❣r❛♣❤s ❛♥❞ t❤❡ ❙✐♠♣s♦♥ ❝♦♥❥❡❝t✉r❡✑ ✭❍✳ ❆r❳✐✈ ✶✽✵✼✳✵✷✻✷✼✮ ❋r♦♠ ❨❡st❡r❞❛②✳ ❙✳❍❡♥r② ▼❛s❛r②❦ ❚❤❡ ❙✐♠♣s♦♥ ❝♦♥❥❡❝t✉r❡ ✭❢♦r r❡❣✉❧❛r ❝♦♠♣♦s✐t✐♦♥s✮ ✶✶✴✵✼ ✷ ✴ ✶✸

  6. ■✬♠ ♣r❡s❡♥t✐♥❣ ❛ ✈❡r② r❡❝❡♥t ♣r♦♦❢ ♦❢ ❛ ❢♦r♠ ♦❢ t❤❡ ❙✐♠♣s♦♥ ❝♦♥❥❡❝t✉r❡✳ ■t ✐♥✈♦❧✈❡ t❤❡ ❢♦❧❧♦✇✐♥❣ t❤r❡❡ ♣❛♣❡rs✿ ✏◆♦♥✲✉♥✐t❛❧ ♣♦❧②❣r❛♣❤s ❛r❡ ❛ ♣r❡s❤❡❛✈❡s ❝❛t❡❣♦r②✑ ✭❍✳ ❆r❳✐✈ ✶✼✶✶✳✵✵✼✹✹✮ ❋r♦♠ ❧❛st ❖❝t♦❜r❡✳ ✏❲❡❛❦ ♠♦❞❡❧ ❝❛t❡❣♦r✐❡s ✐♥ ❝❧❛ss✐❝❛❧ ❛♥❞ ❝♦♥str✉❝t✐✈❡ ♠❛t❤❡♠❛t✐❝s✑ ✭❍✳ ❆r❳✐✈ ✶✽✵✼✳✵✷✻✺✵✮ ❋r♦♠ ❨❡st❡r❞❛②✳ ✏❘❡❣✉❧❛r ♣♦❧②❣r❛♣❤s ❛♥❞ t❤❡ ❙✐♠♣s♦♥ ❝♦♥❥❡❝t✉r❡✑ ✭❍✳ ❆r❳✐✈ ✶✽✵✼✳✵✷✻✷✼✮ ❋r♦♠ ❨❡st❡r❞❛②✳ ✳✳✳ ❛♣♣r♦①✐♠❛t❡❧② ✷✷✵ ♣❛❣❡s ✐♥ t♦t❛❧✳ ❙✳❍❡♥r② ▼❛s❛r②❦ ❚❤❡ ❙✐♠♣s♦♥ ❝♦♥❥❡❝t✉r❡ ✭❢♦r r❡❣✉❧❛r ❝♦♠♣♦s✐t✐♦♥s✮ ✶✶✴✵✼ ✷ ✴ ✶✸

  7. ❈✳❙✐♠♣s♦♥ ✭✶✾✾✽✮✿ ✐t ❝❛♥♥♦t ❜❡ tr✉❡✳ ❊❝❦♠❛♥♥✲❍✐❧t♦♥ ❛r❣✉♠❡♥t✿ ✏ ✷ ✑ ✐s ❛❜❡❧✐❛♥✳ ✲ ■♥ ✏✇❡❛❦✑ ✲❣r♦✉♣♦✐❞s t❤✐s ❝♦♠♠✉t❛t✐✈✐t② ✐s ❣✐✈❡♥ ❜② ❛ ❜r❛✐❞✐♥❣✳ ✲ ■♥ str✐❝t ✲❝❛t❡❣♦r② ✐t ✐s ❛ str✐❝t ❝♦♠♠✉t❛t✐✈✐t②✳ ✭✐✳❡✳ tr✐✈✐❛❧ ❜r❛✐❞✐♥❣✱ ✇❤✐❝❤ ❝♦rr❡s♣♦♥❞s t♦ ❛ ✈❛♥✐s❤✐♥❣ ♦❢ t❤❡ ❲❤✐t❡❤❡❛❞ ♣r♦❞✉❝t ✸ ✮✳ ✷ ✷ ❙✐♠♣s♦♥ ❝♦♥❥❡❝t✉r❡✿ ❙tr✐❝t ✲❝❛t❡❣♦r✐❡s ✇✐t❤ ✇❡❛❦ ❍♦ ❙♣❛❝❡s ♥ ❍♦ ✉♥✐ts ❛♥❞ ✇❡❛❦ ✐♥✈❡rs❡s ❙✐♠♣s♦♥✬s s✉❣❣❡st✐♦♥✿ ❥✉st ❢♦❧❧♦✇ ❑❛♣r❛♥♦✈ ❛♥❞ ❱♦❡✈♦❞s❦②✬s str❛t❡❣②✳ ▼✳❑❛♣r❛♥♦✈ ❛♥❞ ❱✳❱♦❡✈♦❞s❦② ✭✶✾✾✶✮✿ � � ❙tr✐❝t ∞ ✲❝❛t❡❣♦r✐❡s ✇❤♦s❡ ❍♦ ( ❙♣❛❝❡s ) ≃ π ♥ ❍♦ ❛rr♦✇s ❛r❡ ✇❡❛❦❧② ✐♥✈❡rt✐❜❧❡ ❙✳❍❡♥r② ▼❛s❛r②❦ ❚❤❡ ❙✐♠♣s♦♥ ❝♦♥❥❡❝t✉r❡ ✭❢♦r r❡❣✉❧❛r ❝♦♠♣♦s✐t✐♦♥s✮ ✶✶✴✵✼ ✸ ✴ ✶✸

  8. ❊❝❦♠❛♥♥✲❍✐❧t♦♥ ❛r❣✉♠❡♥t✿ ✏ ✷ ✑ ✐s ❛❜❡❧✐❛♥✳ ✲ ■♥ ✏✇❡❛❦✑ ✲❣r♦✉♣♦✐❞s t❤✐s ❝♦♠♠✉t❛t✐✈✐t② ✐s ❣✐✈❡♥ ❜② ❛ ❜r❛✐❞✐♥❣✳ ✲ ■♥ str✐❝t ✲❝❛t❡❣♦r② ✐t ✐s ❛ str✐❝t ❝♦♠♠✉t❛t✐✈✐t②✳ ✭✐✳❡✳ tr✐✈✐❛❧ ❜r❛✐❞✐♥❣✱ ✇❤✐❝❤ ❝♦rr❡s♣♦♥❞s t♦ ❛ ✈❛♥✐s❤✐♥❣ ♦❢ t❤❡ ❲❤✐t❡❤❡❛❞ ♣r♦❞✉❝t ✸ ✮✳ ✷ ✷ ❙✐♠♣s♦♥ ❝♦♥❥❡❝t✉r❡✿ ❙tr✐❝t ✲❝❛t❡❣♦r✐❡s ✇✐t❤ ✇❡❛❦ ❍♦ ❙♣❛❝❡s ♥ ❍♦ ✉♥✐ts ❛♥❞ ✇❡❛❦ ✐♥✈❡rs❡s ❙✐♠♣s♦♥✬s s✉❣❣❡st✐♦♥✿ ❥✉st ❢♦❧❧♦✇ ❑❛♣r❛♥♦✈ ❛♥❞ ❱♦❡✈♦❞s❦②✬s str❛t❡❣②✳ ▼✳❑❛♣r❛♥♦✈ ❛♥❞ ❱✳❱♦❡✈♦❞s❦② ✭✶✾✾✶✮✿ � � ❙tr✐❝t ∞ ✲❝❛t❡❣♦r✐❡s ✇❤♦s❡ ❍♦ ( ❙♣❛❝❡s ) ≃ π ♥ ❍♦ ❛rr♦✇s ❛r❡ ✇❡❛❦❧② ✐♥✈❡rt✐❜❧❡ ❈✳❙✐♠♣s♦♥ ✭✶✾✾✽✮✿ ✐t ❝❛♥♥♦t ❜❡ tr✉❡✳ ❙✳❍❡♥r② ▼❛s❛r②❦ ❚❤❡ ❙✐♠♣s♦♥ ❝♦♥❥❡❝t✉r❡ ✭❢♦r r❡❣✉❧❛r ❝♦♠♣♦s✐t✐♦♥s✮ ✶✶✴✵✼ ✸ ✴ ✶✸

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