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Pr sttt Prs r trts ss rs rtr rsss r

  1. Pr♦❜❧❡♠ st❛t❡♠❡♥t Pr❡✈✐♦✉s ✇♦r❦ ❈♦♥tr✐❜✉t✐♦♥s ❈♦♥❝❧✉s✐♦♥s ❚♦✇❛r❞s ❯♥❞❡r✇❛t❡r ❱✐❞❡♦ ❚r❛♥s♠✐ss✐♦♥ ▲❛✉r❛ ❉✉❜r❡✉✐❧ ❱❛❧❧ ✶ , ✷ ❉❛♥✐❡❧ ❙✉r❛ ✶ ▼✐❧✐❝❛ ❙t♦❥❛♥♦✈✐❝ ✷ ✶ ▼❛ss❛❝❤✉s❡tts ■♥st✐t✉t❡ ♦❢ ❚❡❝❤♥♦❧♦❣② ✷ ◆♦rt❤❡❛st❡r♥ ❯♥✐✈❡rs✐t② ❆❈▼ ■♥t❡r♥❛t✐♦♥❛❧ ❲♦r❦s❤♦♣ ♦♥ ❯♥❞❡r✇❛t❡r ◆❡t♦✇r❦s ✭❲❯❲◆❡t✮ ❙❡❛tt❧❡✱ ❉❡❝❡♠❜❡r ✶✲✷✱ ✷✵✶✶ ▲❛✉r❛ ❉✉❜r❡✉✐❧ ❱❛❧❧✱ ❉❛♥✐❡❧ ❙✉r❛✱ ▼✐❧✐❝❛ ❙t♦❥❛♥♦✈✐❝ ❚♦✇❛r❞s ❯♥❞❡r✇❛t❡r ❱✐❞❡♦ ❚r❛♥s♠✐ss✐♦♥ ❙❧✐❞❡ ✶

  2. Pr♦❜❧❡♠ st❛t❡♠❡♥t Pr❡✈✐♦✉s ✇♦r❦ ❈♦♥tr✐❜✉t✐♦♥s ❈♦♥❝❧✉s✐♦♥s ❖✉t❧✐♥❡ ❖✈❡r✈✐❡✇ ✶ Pr❡✈✐♦✉s ✇♦r❦ ✷ ❈♦♥tr✐❜✉t✐♦♥s ✸ ❉♦♣♣❧❡r ❝♦♠♣❡♥s❛t✐♦♥ ❛❧❣♦r✐t❤♠ ▼P❊●✲✹ ❡rr♦r r❡s✐❧✐❡♥❝❡ t♦♦❧s ■♥✲❛✐r ❊①♣❡r✐♠❡♥t❛❧ ❚❡sts ❈♦♥❝❧✉s✐♦♥s ✹ ▲❛✉r❛ ❉✉❜r❡✉✐❧ ❱❛❧❧✱ ❉❛♥✐❡❧ ❙✉r❛✱ ▼✐❧✐❝❛ ❙t♦❥❛♥♦✈✐❝ ❚♦✇❛r❞s ❯♥❞❡r✇❛t❡r ❱✐❞❡♦ ❚r❛♥s♠✐ss✐♦♥ ❙❧✐❞❡ ✷

  3. Pr♦❜❧❡♠ st❛t❡♠❡♥t Pr❡✈✐♦✉s ✇♦r❦ ❈♦♥tr✐❜✉t✐♦♥s ❈♦♥❝❧✉s✐♦♥s ❖✉t❧✐♥❡ ❖✈❡r✈✐❡✇ ✶ Pr❡✈✐♦✉s ✇♦r❦ ✷ ❈♦♥tr✐❜✉t✐♦♥s ✸ ❉♦♣♣❧❡r ❝♦♠♣❡♥s❛t✐♦♥ ❛❧❣♦r✐t❤♠ ▼P❊●✲✹ ❡rr♦r r❡s✐❧✐❡♥❝❡ t♦♦❧s ■♥✲❛✐r ❊①♣❡r✐♠❡♥t❛❧ ❚❡sts ❈♦♥❝❧✉s✐♦♥s ✹ ▲❛✉r❛ ❉✉❜r❡✉✐❧ ❱❛❧❧✱ ❉❛♥✐❡❧ ❙✉r❛✱ ▼✐❧✐❝❛ ❙t♦❥❛♥♦✈✐❝ ❚♦✇❛r❞s ❯♥❞❡r✇❛t❡r ❱✐❞❡♦ ❚r❛♥s♠✐ss✐♦♥ ❙❧✐❞❡ ✸

  4. Pr♦❜❧❡♠ st❛t❡♠❡♥t Pr❡✈✐♦✉s ✇♦r❦ ❈♦♥tr✐❜✉t✐♦♥s ❈♦♥❝❧✉s✐♦♥s Pr♦❜❧❡♠ st❛t❡♠❡♥t ▲❛✉r❛ ❉✉❜r❡✉✐❧ ❱❛❧❧✱ ❉❛♥✐❡❧ ❙✉r❛✱ ▼✐❧✐❝❛ ❙t♦❥❛♥♦✈✐❝ ❚♦✇❛r❞s ❯♥❞❡r✇❛t❡r ❱✐❞❡♦ ❚r❛♥s♠✐ss✐♦♥ ❙❧✐❞❡ ✹

  5. Pr♦❜❧❡♠ st❛t❡♠❡♥t Pr❡✈✐♦✉s ✇♦r❦ ❈♦♥tr✐❜✉t✐♦♥s ❈♦♥❝❧✉s✐♦♥s ❖✉t❧✐♥❡ ❖✈❡r✈✐❡✇ ✶ Pr❡✈✐♦✉s ✇♦r❦ ✷ ❈♦♥tr✐❜✉t✐♦♥s ✸ ❉♦♣♣❧❡r ❝♦♠♣❡♥s❛t✐♦♥ ❛❧❣♦r✐t❤♠ ▼P❊●✲✹ ❡rr♦r r❡s✐❧✐❡♥❝❡ t♦♦❧s ■♥✲❛✐r ❊①♣❡r✐♠❡♥t❛❧ ❚❡sts ❈♦♥❝❧✉s✐♦♥s ✹ ▲❛✉r❛ ❉✉❜r❡✉✐❧ ❱❛❧❧✱ ❉❛♥✐❡❧ ❙✉r❛✱ ▼✐❧✐❝❛ ❙t♦❥❛♥♦✈✐❝ ❚♦✇❛r❞s ❯♥❞❡r✇❛t❡r ❱✐❞❡♦ ❚r❛♥s♠✐ss✐♦♥ ❙❧✐❞❡ ✺

  6. Pr♦❜❧❡♠ st❛t❡♠❡♥t Pr❡✈✐♦✉s ✇♦r❦ ❈♦♥tr✐❜✉t✐♦♥s ❈♦♥❝❧✉s✐♦♥s ❖❋❉▼ ✰ ▼P❊●✹ ❛♣♣r♦❛❝❤ ❱✐❞❡♦ ❝♦♠♣r❡ss✐♦♥ t❡❝❤♥✐q✉❡✿ ▼P❊●✲✹ st❛♥❞❛r❞ − → ✶✵ ❦❜♣s ❇❛♥❞✇✐❞t❤ ❡✣❝✐❡♥t ♠♦❞✉❧❛t✐♦♥✿ ❖rt❤♦❣♦♥❛❧ ❋r❡q✉❡♥❝②✲❉✐✈✐s✐♦♥ ▼✉❧t✐♣❧❡①✐♥❣ ✭❖❋❉▼✮ − →∼ ✾✵ ❦❜♣s ▲❛✉r❛ ❉✉❜r❡✉✐❧ ❱❛❧❧✱ ❉❛♥✐❡❧ ❙✉r❛✱ ▼✐❧✐❝❛ ❙t♦❥❛♥♦✈✐❝ ❚♦✇❛r❞s ❯♥❞❡r✇❛t❡r ❱✐❞❡♦ ❚r❛♥s♠✐ss✐♦♥ ❙❧✐❞❡ ✻

  7. Pr♦❜❧❡♠ st❛t❡♠❡♥t Pr❡✈✐♦✉s ✇♦r❦ ❈♦♥tr✐❜✉t✐♦♥s ❈♦♥❝❧✉s✐♦♥s ❙②st❡♠ ❞❡s✐❣♥ ▲❛✉r❛ ❉✉❜r❡✉✐❧ ❱❛❧❧✱ ❉❛♥✐❡❧ ❙✉r❛✱ ▼✐❧✐❝❛ ❙t♦❥❛♥♦✈✐❝ ❚♦✇❛r❞s ❯♥❞❡r✇❛t❡r ❱✐❞❡♦ ❚r❛♥s♠✐ss✐♦♥ ❙❧✐❞❡ ✼

  8. Pr♦❜❧❡♠ st❛t❡♠❡♥t ❉♦♣♣❧❡r ❝♦♠♣❡♥s❛t✐♦♥ ❛❧❣♦r✐t❤♠ Pr❡✈✐♦✉s ✇♦r❦ ▼P❊●✲✹ ❡rr♦r r❡s✐❧✐❡♥❝❡ t♦♦❧s ❈♦♥tr✐❜✉t✐♦♥s ■♥✲❛✐r ❊①♣❡r✐♠❡♥t❛❧ ❚❡sts ❈♦♥❝❧✉s✐♦♥s ❖✉t❧✐♥❡ ❖✈❡r✈✐❡✇ ✶ Pr❡✈✐♦✉s ✇♦r❦ ✷ ❈♦♥tr✐❜✉t✐♦♥s ✸ ❉♦♣♣❧❡r ❝♦♠♣❡♥s❛t✐♦♥ ❛❧❣♦r✐t❤♠ ▼P❊●✲✹ ❡rr♦r r❡s✐❧✐❡♥❝❡ t♦♦❧s ■♥✲❛✐r ❊①♣❡r✐♠❡♥t❛❧ ❚❡sts ❈♦♥❝❧✉s✐♦♥s ✹ ▲❛✉r❛ ❉✉❜r❡✉✐❧ ❱❛❧❧✱ ❉❛♥✐❡❧ ❙✉r❛✱ ▼✐❧✐❝❛ ❙t♦❥❛♥♦✈✐❝ ❚♦✇❛r❞s ❯♥❞❡r✇❛t❡r ❱✐❞❡♦ ❚r❛♥s♠✐ss✐♦♥ ❙❧✐❞❡ ✽

  9. Pr♦❜❧❡♠ st❛t❡♠❡♥t ❉♦♣♣❧❡r ❝♦♠♣❡♥s❛t✐♦♥ ❛❧❣♦r✐t❤♠ Pr❡✈✐♦✉s ✇♦r❦ ▼P❊●✲✹ ❡rr♦r r❡s✐❧✐❡♥❝❡ t♦♦❧s ❈♦♥tr✐❜✉t✐♦♥s ■♥✲❛✐r ❊①♣❡r✐♠❡♥t❛❧ ❚❡sts ❈♦♥❝❧✉s✐♦♥s ❚✇♦ ❝♦♥tr✐❜✉t✐♦♥s ✶ ❉♦♣♣❧❡r ❝♦♠♣❡♥s❛t✐♦♥ ❛❧❣♦r✐t❤♠ ✰ ❉✐✛❡r❡♥t✐❛❧❧② ❝♦❤❡r❡♥t ❞❡t❡❝t✐♦♥ ✷ ▼P❊●✲✹ ❡rr♦r r❡s✐❧✐❡♥❝❡ t♦♦❧s ▲❛✉r❛ ❉✉❜r❡✉✐❧ ❱❛❧❧✱ ❉❛♥✐❡❧ ❙✉r❛✱ ▼✐❧✐❝❛ ❙t♦❥❛♥♦✈✐❝ ❚♦✇❛r❞s ❯♥❞❡r✇❛t❡r ❱✐❞❡♦ ❚r❛♥s♠✐ss✐♦♥ ❙❧✐❞❡ ✾

  10. Pr♦❜❧❡♠ st❛t❡♠❡♥t ❉♦♣♣❧❡r ❝♦♠♣❡♥s❛t✐♦♥ ❛❧❣♦r✐t❤♠ Pr❡✈✐♦✉s ✇♦r❦ ▼P❊●✲✹ ❡rr♦r r❡s✐❧✐❡♥❝❡ t♦♦❧s ❈♦♥tr✐❜✉t✐♦♥s ■♥✲❛✐r ❊①♣❡r✐♠❡♥t❛❧ ❚❡sts ❈♦♥❝❧✉s✐♦♥s ❖✉t❧✐♥❡ ❖✈❡r✈✐❡✇ ✶ Pr❡✈✐♦✉s ✇♦r❦ ✷ ❈♦♥tr✐❜✉t✐♦♥s ✸ ❉♦♣♣❧❡r ❝♦♠♣❡♥s❛t✐♦♥ ❛❧❣♦r✐t❤♠ ▼P❊●✲✹ ❡rr♦r r❡s✐❧✐❡♥❝❡ t♦♦❧s ■♥✲❛✐r ❊①♣❡r✐♠❡♥t❛❧ ❚❡sts ❈♦♥❝❧✉s✐♦♥s ✹ ▲❛✉r❛ ❉✉❜r❡✉✐❧ ❱❛❧❧✱ ❉❛♥✐❡❧ ❙✉r❛✱ ▼✐❧✐❝❛ ❙t♦❥❛♥♦✈✐❝ ❚♦✇❛r❞s ❯♥❞❡r✇❛t❡r ❱✐❞❡♦ ❚r❛♥s♠✐ss✐♦♥ ❙❧✐❞❡ ✶✵

  11. Pr♦❜❧❡♠ st❛t❡♠❡♥t ❉♦♣♣❧❡r ❝♦♠♣❡♥s❛t✐♦♥ ❛❧❣♦r✐t❤♠ Pr❡✈✐♦✉s ✇♦r❦ ▼P❊●✲✹ ❡rr♦r r❡s✐❧✐❡♥❝❡ t♦♦❧s ❈♦♥tr✐❜✉t✐♦♥s ■♥✲❛✐r ❊①♣❡r✐♠❡♥t❛❧ ❚❡sts ❈♦♥❝❧✉s✐♦♥s ❉♦♣♣❧❡r ❊✛❡❝t ❚❤❡ s✐❣♥❛❧ ✐s s❝❛❧❡❞ ✐♥ t✐♠❡ ❜② t❤❡ ❢❛❝t♦r ( ✶ + ❛ ) ❊❛❝❤ s✉❜❝❛rr✐❡r ❡①♣❡r✐❡♥❝❡s ❛ ❢r❡q✉❡♥❝② s❤✐❢t ❡ ❥❛ ω ❦ t ▲❛✉r❛ ❉✉❜r❡✉✐❧ ❱❛❧❧✱ ❉❛♥✐❡❧ ❙✉r❛✱ ▼✐❧✐❝❛ ❙t♦❥❛♥♦✈✐❝ ❚♦✇❛r❞s ❯♥❞❡r✇❛t❡r ❱✐❞❡♦ ❚r❛♥s♠✐ss✐♦♥ ❙❧✐❞❡ ✶✶

  12. Pr♦❜❧❡♠ st❛t❡♠❡♥t ❉♦♣♣❧❡r ❝♦♠♣❡♥s❛t✐♦♥ ❛❧❣♦r✐t❤♠ Pr❡✈✐♦✉s ✇♦r❦ ▼P❊●✲✹ ❡rr♦r r❡s✐❧✐❡♥❝❡ t♦♦❧s ❈♦♥tr✐❜✉t✐♦♥s ■♥✲❛✐r ❊①♣❡r✐♠❡♥t❛❧ ❚❡sts ❈♦♥❝❧✉s✐♦♥s ❆❧❣♦r✐t❤♠ ❊st✐♠❛t✐♦♥ ♦❢ t❤❡ ❉♦♣♣❧❡r ❢❛❝t♦r ✉s✐♥❣ t❤❡ ♠❡❛s✉r❡❞ t✐♠❡ ❜❡t✇❡❡♥ ✶ ❛❞❥❛❝❡♥t ♣r❡❛♠❜❧❡s✿ ❛ = ❚ r① ❚ r① = ❚ t① ( ✶ + ❛ ) − ✶ ✭✶✮ ⇒ ❚ t① ❘❡s❛♠♣❧❡ t❤❡ r❡❝❡✐✈❡❞ s✐❣♥❛❧ ✇✐t❤ t❤❡ ❡st✐♠❛t❡❞ r❡s❛♠♣❧✐♥❣ r❛t❡✿ ✷ � � t ˜ ③ ( t ) = � ② ✶ + ❛ ▲❛✉r❛ ❉✉❜r❡✉✐❧ ❱❛❧❧✱ ❉❛♥✐❡❧ ❙✉r❛✱ ▼✐❧✐❝❛ ❙t♦❥❛♥♦✈✐❝ ❚♦✇❛r❞s ❯♥❞❡r✇❛t❡r ❱✐❞❡♦ ❚r❛♥s♠✐ss✐♦♥ ❙❧✐❞❡ ✶✷

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