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s Pt ts tt ts ts r r t

  1. ❲❡ ❤❛✈❡ ✉s❡❞ ♠❛♥② P②t❤♦♥ ❢✉♥❝t✐♦♥s ▼❛t❤❡♠❛t✐❝❛❧ ❢✉♥❝t✐♦♥s✿ ❈❤✳✸✿ ❋✉♥❝t✐♦♥s ❛♥❞ ❜r❛♥❝❤✐♥❣ ❢r♦♠ ♠❛t❤ ✐♠♣♦rt ✯ ② ❂ s✐♥✭①✮✯❧♦❣✭①✮ ❖t❤❡r ❢✉♥❝t✐♦♥s✿ ❍❛♥s P❡tt❡r ▲❛♥❣t❛♥❣❡♥ ✶ , ✷ ♥ ❂ ❧❡♥✭s♦♠❡❧✐st✮ ✐♥t❡❣❡rs ❂ r❛♥❣❡✭✺✱ ♥✱ ✷✮ ❋✉♥❝t✐♦♥s ✉s❡❞ ✇✐t❤ t❤❡ ❞♦t s②♥t❛① ✭❝❛❧❧❡❞ ♠❡t❤♦❞s ✮✿ ❙✐♠✉❧❛ ❘❡s❡❛r❝❤ ▲❛❜♦r❛t♦r② ✶ ❈ ❂ ❬✺✱ ✶✵✱ ✹✵✱ ✹✺❪ ✐ ❂ ❈✳✐♥❞❡①✭✶✵✮ ★ r❡s✉❧t✿ ✐❂✶ ❯♥✐✈❡rs✐t② ♦❢ ❖s❧♦✱ ❉❡♣t✳ ♦❢ ■♥❢♦r♠❛t✐❝s ✷ ❈✳❛♣♣❡♥❞✭✺✵✮ ❈✳✐♥s❡rt✭✷✱ ✷✵✮ ❆✉❣ ✶✺✱ ✷✵✶✺ ❲❤❛t ✐s ❛ ❢✉♥❝t✐♦♥❄ ❙♦ ❢❛r ✇❡ ❤❛✈❡ s❡❡♥ t❤❛t ✇❡ ♣✉t s♦♠❡ ♦❜❥❡❝ts ✐♥ ❛♥❞ s♦♠❡t✐♠❡s ❣❡t ❛♥ ♦❜❥❡❝t ✭r❡s✉❧t✮ ♦✉t ♦❢ ❢✉♥❝t✐♦♥s✳ ◆♦✇ ✐t ✐s t✐♠❡ t♦ ✇r✐t❡ ♦✉r ♦✇♥ ❢✉♥❝t✐♦♥s✦ ❋✉♥❝t✐♦♥s ❛r❡ ♦♥❡ ♦❢ t❤❡ ♠♦st ✐♠♣♦rt t♦♦❧s ✐♥ ♣r♦❣r❛♠♠✐♥❣ P②t❤♦♥ ❢✉♥❝t✐♦♥ ❢♦r ✐♠♣❧❡♠❡♥t✐♥❣ ❛ ♠❛t❤❡♠❛t✐❝❛❧ ❢✉♥❝t✐♦♥ ❚❤❡ ♠❛t❤❡♠❛t✐❝❛❧ ❢✉♥❝t✐♦♥ ❋ ( ❈ ) = ✾ ✺ ❈ + ✸✷ ❋✉♥❝t✐♦♥ ❂ ❛ ❝♦❧❧❡❝t✐♦♥ ♦❢ st❛t❡♠❡♥ts ✇❡ ❝❛♥ ❡①❡❝✉t❡ ❝❛♥ ❜❡ ✐♠♣❧❡♠❡♥t❡❞ ✐♥ P②t❤♦♥ ❛s ❢♦❧❧♦✇s✿ ✇❤❡r❡✈❡r ❛♥❞ ✇❤❡♥❡✈❡r ✇❡ ✇❛♥t ❞❡❢ ❋✭❈✮✿ ❋✉♥❝t✐♦♥ ❝❛♥ t❛❦❡ ✐♥♣✉t ♦❜❥❡❝ts ✭❛r❣✉♠❡♥ts✮ ❛♥❞ ♣r♦❞✉❝❡ r❡t✉r♥ ✭✾✳✵✴✺✮✯❈ ✰ ✸✷ ♦✉t♣✉t ♦❜❥❡❝ts ✭r❡t✉r♥❡❞ r❡s✉❧ts✮ ◆♦t❡✿ ❋✉♥❝t✐♦♥s ❤❡❧♣ t♦ ♦r❣❛♥✐③❡ ♣r♦❣r❛♠s✱ ♠❛❦❡ t❤❡♠ ♠♦r❡ ✉♥❞❡rst❛♥❞❛❜❧❡✱ s❤♦rt❡r✱ r❡✉s❛❜❧❡✱ ❛♥❞ ❡❛s✐❡r t♦ ❡①t❡♥❞ ❋✉♥❝t✐♦♥s st❛rt ✇✐t❤ ❞❡❢ ✱ t❤❡♥ t❤❡ ♥❛♠❡ ♦❢ t❤❡ ❢✉♥❝t✐♦♥✱ t❤❡♥ ❛ ❧✐st ♦❢ ❛r❣✉♠❡♥ts ✭❤❡r❡ ❈ ✮ ✲ t❤❡ ❢✉♥❝t✐♦♥ ❤❡❛❞❡r ■♥s✐❞❡ t❤❡ ❢✉♥❝t✐♦♥✿ st❛t❡♠❡♥ts ✲ t❤❡ ❢✉♥❝t✐♦♥ ❜♦❞② ❲❤❡r❡✈❡r ✇❡ ✇❛♥t✱ ✐♥s✐❞❡ t❤❡ ❢✉♥❝t✐♦♥✱ ✇❡ ❝❛♥ ✧st♦♣ t❤❡ ❢✉♥❝t✐♦♥✧ ❛♥❞ r❡t✉r♥ ❛s ♠❛♥② ✈❛❧✉❡s✴✈❛r✐❛❜❧❡s ✇❡ ✇❛♥t ❋✉♥❝t✐♦♥s ♠✉st ❜❡ ❝❛❧❧❡❞ ❋✉♥❝t✐♦♥s ❝❛♥ ❤❛✈❡ ❛s ♠❛♥② ❛r❣✉♠❡♥ts ❛s ②♦✉ ❧✐❦❡ ❆ ❢✉♥❝t✐♦♥ ❞♦❡s ♥♦t ❞♦ ❛♥②t❤✐♥❣ ❜❡❢♦r❡ ✐t ✐s ❝❛❧❧❡❞ ▼❛❦❡ ❛ P②t❤♦♥ ❢✉♥❝t✐♦♥ ♦❢ t❤❡ ♠❛t❤❡♠❛t✐❝❛❧ ❢✉♥❝t✐♦♥ ❞❡❢ ❋✭❈✮✿ r❡t✉r♥ ✭✾✳✵✴✺✮✯❈ ✰ ✸✷ ② ( t ) = ✈ ✵ t − ✶ ✷ ❣t ✷ ❛ ❂ ✶✵ ❋✶ ❂ ❋✭❛✮ ★ ❝❛❧❧ t❡♠♣ ❂ ❋✭✶✺✳✺✮ ★ ❝❛❧❧ ♣r✐♥t ❋✭❛✰✶✮ ★ ❝❛❧❧ s✉♠❴t❡♠♣ ❂ ❋✭✶✵✮ ✰ ❋✭✷✵✮ ★ t✇♦ ❝❛❧❧s ❞❡❢ ②❢✉♥❝✭t✱ ✈✵✮✿ ❋❞❡❣r❡❡s ❂ ❬❋✭❈✮ ❢♦r ❈ ✐♥ ❬✵✱ ✷✵✱ ✹✵❪❪ ★ ♠✉❧t✐♣❧❡ ❝❛❧❧s ❣ ❂ ✾✳✽✶ r❡t✉r♥ ✈✵✯t ✲ ✵✳✺✯❣✯t✯✯✷ ✭❱✐s✉❛❧✐③❡ ❡①❡❝✉t✐♦♥✮ ★ s❛♠♣❧❡ ❝❛❧❧s✿ ② ❂ ②❢✉♥❝✭✵✳✶✱ ✻✮ ② ❂ ②❢✉♥❝✭✵✳✶✱ ✈✵❂✻✮ ◆♦t❡✿ ② ❂ ②❢✉♥❝✭t❂✵✳✶✱ ✈✵❂✻✮ ❚❤❡ ❝❛❧❧ ❋✭❈✮ ♣r♦❞✉❝❡s ✭r❡t✉r♥s✮ ❛ ❢❧♦❛t ♦❜❥❡❝t✱ ✇❤✐❝❤ ♠❡❛♥s t❤❛t ② ❂ ②❢✉♥❝✭✈✵❂✻✱ t❂✵✳✶✮ ❋✭❈✮ ✐s r❡♣❧❛❝❡❞ ❜② t❤✐s ❢❧♦❛t ♦❜❥❡❝t✳ ❲❡ ❝❛♥ t❤❡r❡❢♦r❡ ♠❛❦❡ t❤❡ ✭❱✐s✉❛❧✐③❡ ❡①❡❝✉t✐♦♥✮ ❝❛❧❧ ❋✭❈✮ ❡✈❡r②✇❤❡r❡ ❛ ❢❧♦❛t ❝❛♥ ❜❡ ✉s❡❞✳

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