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r ts r Ptrs rrs r s rst t tts t s


  1. ❖✈❡r✈✐❡✇ ❈ t②♣❡s r❡✈✐❡✇✳ P♦✐♥t❡rs ❛♥❞ ❛rr❛②s r❡✈✐❡✇✳ ❯s✐♥❣ ❛♥❞ ✉♥❞❡rst❛♥❞✐♥❣ t❤❡ ❧✐♠✐t❛t✐♦♥s ♦❢ t②♣❡❞❡❢ ✬s✳ ❈♦♠♣❧❡① ❞❡❝❧❛r❛t✐♦♥s✳ ❆❉❚s r❡✈✐❡✇✳ ❈ ✐❞✐♦♠s✳ ❯s✐♥❣ ❛s②♠♠❡tr✐❝ ❜♦✉♥❞s✳ ❊①t❡r♥❛❧ ✈❛r✐❛❜❧❡ ❞❡❝❧❛r❛t✐♦♥s✳ ❉②♥❛♠✐❝ ♠❡♠♦r② ❛❧❧♦❝❛t✐♦♥✳ ❖❖P ✐♥ ❈✳ ❚❤❡ ❈ ♣r❡♣r♦❝❡ss♦r✳ ❆❞✈❛♥❝❡❞ ❈ ❚♦♣✐❝s

  2. Pr✐♠✐t✐✈❡ ❈ ❚②♣❡s Pr✐♠✐t✐✈❡ t②♣❡s ✐♥❝❧✉❞❡✿ ■♥t❡❣r❛❧ t②♣❡s✿ ✐♥ ♦r❞❡r ♦❢ ♥♦♥✲❞❡❝r❡❛s✐♥❣ s✐③❡ ❝❤❛r ✱ s❤♦rt ✱ ✐♥t ✱ ❧♦♥❣ ✱ ❧♦♥❣ ❧♦♥❣ ✳ ❙✐❣♥❡❞ ❜② ❞❡❢❛✉❧t✱ ❝❛♥ ❜❡ ♠❛❞❡ ✉♥s✐❣♥❡❞ ❜② ✉s✐♥❣ ♠♦❞✐✜❡r ✉♥s✐❣♥❡❞ ✭❜✉t t❤❡ s✐❣♥❡❞✲♥❡ss ♦❢ ♣❧❛✐♥ ✉♥♠♦❞✐✜❡❞ ❝❤❛r ✐s ✉♥❞❡✜♥❡❞✮✳ ❊①❛♠♣❧❡s ✭✐♥✐t✐❛❧✐③❡rs ❝❛♥ ❜❡ ♦♠✐tt❡❞✱ ❜✉t ❛r❡ ✉s✉❛❧❧② ❛ ❣♦♦❞ ✐❞❡❛ ✇❤❡♥❡✈❡r ♣♦ss✐❜❧❡ t♦ ❛✈♦✐❞ ✉♥✐♥✐t✐❛❧✐③❡❞ ✈❛r✐❛❜❧❡ ❡rr♦rs✮✿ ✉♥s✐❣♥❡❞ ❝❤❛r ❝✶ ❂ ✬❛✬✱ ❝✷ ❂ ✬❜✬❀ ❝❤❛r ❝ ❂ ❝✶ ✰ ✶❀ ✴✴s✐❣♥❡❞✲♥❡ss ♥♦t ❦♥♦✇♥✳ ❧♦♥❣ ❧♦♥❣ ❧❡♥❣t❤ ❂ ✶✵✷✹▲▲❀ ✉♥s✐❣♥❡❞ ✐♥t ✐♥❞❡① ❂ ✵❀ ❋❧♦❛t✐♥❣ ♣♦✐♥t t②♣❡s✿ ✐♥ ♦r❞❡r ♦❢ ♥♦♥✲❞❡❝r❡❛s✐♥❣ s✐③❡ ❢❧♦❛t ✱ ❞♦✉❜❧❡ ✱ ❧♦♥❣ ❞♦✉❜❧❡ ✳ ✢♦❛t r❡s✉❧t ❂ ✵✳✵❀ ❝♦♥st ❧♦♥❣ ❞♦✉❜❧❡ ♣✐✷ ❂ ✷ ✯ P■❀ ❆❞✈❛♥❝❡❞ ❈ ❚♦♣✐❝s

  3. P♦✐♥t❡r ❚②♣❡s ■❢ ❚ ✐s ❛ t②♣❡✱ t❤❡♥ ❚ ✯ ✐s ♦❢ t②♣❡ ♣♦✐♥t❡r t♦ ❚ ✳ ❊①❛♠♣❧❡s✿ ✐♥t ✐❀ ✐♥t ✯✐P ❂ ✫✐❀ ❝♦♥st ✐♥t ✯✐❝P ❂ ✫✐❀ ✴✴✈❛❧✉❡ ♣♦✐♥t❡❞ t♦ ❝❛♥♥♦t ❜❡ ✴✴❝❤❛♥❣❡❞ ✈✐❛ ♣♦✐♥t❡r ✐♥t ✯ ❝♦♥st ❝✐P ❂ ✫✐❀ ✴✴♣♦✐♥t❡r ❝❛♥♥♦t ❜❡ ❝❤❛♥❣❡❞✳ ❡♥✉♠ ④ ◆ ❂ ✶✵ ⑥❀ ❞♦✉❜❧❡ ✯❞P ❂ ♠❛❧❧♦❝ ✭◆ ✯ s✐③❡♦❢ ✭ ❞♦✉❜❧❡ ✮✮❀ ✈♦✐❞ ✯❣❡♥❡r✐❝P ❂ ❞P❀ ✴✴♠✉st ❜❡ ❝❛st t♦ ♣♦✐♥t❡r t♦ ✴✴s♣❡❝✐✜❝ t②♣❡ ❜❡❢♦r❡ ❜❡✐♥❣ ✉s❡❞✳ ✳✳✳ qs♦rt ✭❣❡♥❡r✐❝P✱ ◆✱ s✐③❡♦❢ ✭ ❞♦✉❜❧❡ ✮✱ ❞♦✉❜❧❡s❈♦♠♣❛r❡✮❀ ❆❞✈❛♥❝❡❞ ❈ ❚♦♣✐❝s

  4. ❆rr❛② ❚②♣❡s ■❢ ❚ ✐s ❛ t②♣❡✱ t❤❡♥ ❚ ❬❪ ✐s ♦❢ t②♣❡ ❛rr❛② ♦❢ ❚ ✭❝♦rr❡s♣♦♥❞s t♦ ❛ s❡q✉❡♥❝❡ ♦❢ t②♣❡s ❚ ✮✳ ◆♦t❡ t❤❛t t❤❡ ♥✉♠❜❡r ♦❢ ❡❧❡♠❡♥ts ✐♥ t❤❡ ❛rr❛② ✐s ♥♦t ♣❛rt ♦❢ t❤❡ t②♣❡✳ ◆♦ ♠✉❧t✐✲❞✐♠❡♥s✐♦♥❛❧ ❛rr❛②s ❜✉t ❝❛♥ ❤❛✈❡ ❛rr❛② ♦❢ ❛rr❛②s✳ ❊①❛♠♣❧❡s✿ ✐♥t ❛❬✶✵❪❀ ✴✴✉♥✐♥✐t✐❛❧✐③❡❞ ✴✴✭✉♥❧❡ss st❛t✐❝ ✭t♦♣✲❧❡✈❡❧✮ t❤❡♥ ✵✮✳ ❞♦✉❜❧❡ ♣✐▼✉❧ts❬❪ ❂ ④ P■✱ ✷ ✯ P■✱ ✸ ✯ P■ ⑥❀ ✢♦❛t ♠✉❧t✐❬✺❪❬✶✵❪❀ ✴✴❛rr❛② ♦❢ ✺ ❛rr❛②✬s ♦❢ ✶✵ ✢♦❛ts✳ ✴✴♣♦ss✐❜❧❡ ❡rr♦r✱ ♥♦ t❡r♠✐♥❛t✐♥❣ ✬ \ ✵✬ ❝❤❛r ♠❡ss❛❣❡❬❪ ❂ ④ ✬❤✬✱ ✬❡✬✱ ✬❧✬✱ ✬❧✬✱ ✬♦✬ ⑥❀ ❆❞✈❛♥❝❡❞ ❈ ❚♦♣✐❝s

  5. ❙tr✉❝t✉r❡ ❚②♣❡s ■❢ ❚✶ ✱ ❚✷ ✱ ✳✳✳ ❚♥ ❛r❡ t②♣❡s✱ t❤❡♥ str✉❝t ④ ❚✶ t✶❀ ✳✳✳ ❚♥ t♥ ⑥ ✐s ❛ str✉❝t✉r❡ t②♣❡ ✭❝♦rr❡s♣♦♥❞s t♦ ❝❛rt❡s✐❛♥ ♣r♦❞✉❝t ♦❢ t②♣❡s ❚✶ ① ❚✷ ① ✳✳✳ ① ❚♥ ✮✳ ❋✐❡❧❞s t✶ ✱ ✳✳✱ t♥ ❧❛✐❞ ♦✉t s❡q✉❡♥t✐❛❧❧② ✐♥ ♠❡♠♦r② ✭✇✐t❤ ♣♦ss✐❜❧❡ ❤♦❧❡s ✐♥ ❜❡t✇❡❡♥ t♦ r❡s♣❡❝t ❛❧✐❣♥♠❡♥t r❡str✐❝t✐♦♥s✮✳ ❊①❛♠♣❧❡s✿ t②♣❡❞❡❢ str✉❝t ④ ✴✴t②♣❡❞❡❢ ❛❧✐❛s ❢♦r t②♣❡ ❞♦✉❜❧❡ ①❀ ❞♦✉❜❧❡ ② ⑥ P♦✐♥t✷❀ ✴✴❆ t②♣❡ ✇❤✐❝❤ ❝❛♥ ❜❡ ✉s❡❞ ❢♦r s✐♥❣❧②✲❧✐♥❦❡❞ ❧✐st ♥♦❞❡ t②♣❡❞❡❢ str✉❝t ◆♦❞❡❙tr✉❝t ④ ✴✴◆♦❞❡❙tr✉❝t ✐s str✉❝t t❛❣ ✈♦✐❞ ✯✈❛❧✉❡❀ str✉❝t ◆♦❞❡❙tr✉❝t ✯s✉❝❝❀ ⑥ ◆♦❞❡❀ ❆❞✈❛♥❝❡❞ ❈ ❚♦♣✐❝s

  6. ❙tr✉❝t✉r❡ ❚②♣❡s ■♥✐t✐❛❧✐③❛t✐♦♥ ✴✴P♦s✐t✐♦♥❛❧ ✐♥✐t✐❛❧✐③❛t✐♦♥ P♦✐♥t✷ ❧✐♥❡❬❪ ❂ ④ ④ ✵✱ ✵ ⑥✱ ④ ✶✱ ✶ ⑥✱ ⑥❀ ✴✴♣r❡❢❡r❛❜❧② ✉s❡ ❝✾✾ ❞❡s✐❣♥❛t❡❞ ✐♥✐t✐❛❧✐③❡r P♦✐♥t✷ tr✐❛♥❣❧❡❬❪ ❂ ④ ④ ✳① ❂ ✵✱ ✳② ❂ ✵ ⑥✱ ④ ✳② ❂ ✶✱ ✳① ❂ ✵ ⑥✱ ④ ✳① ❂ ✶✱ ✳② ❂ ✵ ⑥ ⑥❀ ❆❞✈❛♥❝❡❞ ❈ ❚♦♣✐❝s

  7. ❉②❛♥❛♠✐❝❛❧❧② ❆❧❧♦❝❛t❡❞ ❉②♥❛♠✐❝❛❧❧② ❙✐③❡❞ ❆rr❛② ❆❧t❡r♥❛t✐✈❡ ✶ ❯s❡s ✷ ❜❧♦❝❦s ♦❢ ❞②♥❛♠✐❝❛❧❧② ❛❧❧♦❝❛t❡❞ ♠❡♠♦r②✿ t②♣❡❞❡❢ str✉❝t ④ ✐♥t ♥❊❧❡♠❡♥ts❀ ✴✴★ ♦❢ ❡❧❡♠❡♥ts ✈♦✐❞ ✯✯❡❧❡♠❡♥ts❀ ✴✴♣♦✐♥t❡r t♦ ❛rr❛② ♦❢ ❣❡♥❡r✐❝ ❡❧❡♠❡♥ts ⑥ ❉②♥❆rr❛②✶❀ ❡♥✉♠ ④ ◆✶ ❂ ✷✷ ⑥❀ ❉②♥❆rr❛②✶ ✯❛✶ ❂ ♠❛❧❧♦❝ ✭ s✐③❡♦❢ ✭❉②♥❆rr❛②✶✮✮❀ ❛✶✲ > ♥❊❧❡♠❡♥ts ❂ ◆✶❀ ❛✶✲ > ❡❧❡♠❡♥ts ❂ ♠❛❧❧♦❝ ✭◆✶ ✯ s✐③❡♦❢ ✭ ✈♦✐❞ ✯✮✮❀ ❢♦r ✭ ✐♥t ✐ ❂ ✵❀ ✐ < ◆✶❀ ✐✰✰✮ ❛✶✲ > ❡❧❡♠❡♥ts❬✐❪ ❂ ✐❀ ❛✶✲ > ❡❧❡♠❡♥ts❬✹❪ ❂ ✳✳✳❀ ✴✴♦❦ ❛✶✲ > ❡❧❡♠❡♥ts❬✷✷❪ ❂ ✳✳✳❀ ✴✴✉♥♣r❡❞✐❝t❛❜❧❡ r✉♥t✐♠❡ ❡rr♦r ❆❞✈❛♥❝❡❞ ❈ ❚♦♣✐❝s

  8. ❉②❛♥❛♠✐❝❛❧❧② ❆❧❧♦❝❛t❡❞ ❉②♥❛♠✐❝❛❧❧② ❙✐③❡❞ ❆rr❛② ❆❧t❡r♥❛t✐✈❡ ✶ ❈♦♥t✐♥✉❡❞ ❆❞✈❛♥❝❡❞ ❈ ❚♦♣✐❝s

  9. ❉②❛♥❛♠✐❝❛❧❧② ❆❧❧♦❝❛t❡❞ ❉②♥❛♠✐❝❛❧❧② ❙✐③❡❞ ❆rr❛②✿ ❍❛❝❦ ■♥ tr❛❞✐t✐♦♥❛❧ ❈✱ ✐t ✐s ♣♦ss✐❜❧❡ t♦ ✉s❡ s✐♥❣❧❡ ❜❧♦❝❦ ♦❢ ♠❡♠♦r②✱ ✉s✐♥❣ ❛ ❤❛❝❦✿ t②♣❡❞❡❢ str✉❝t ④ ✐♥t ♥❊❧❡♠❡♥ts❀ ✴✴★ ♦❢ ❡❧❡♠❡♥ts ✈♦✐❞ ✯❡❧❡♠❡♥ts❬✶❪❀ ✴✴❛rr❛② ♦❢ ❣❡♥❡r✐❝ ❡❧❡♠❡♥ts ✴✴✐s ♣❛rt ♦❢ str✉❝t ⑥ ❉②♥❆rr❛②✷❀ ❡♥✉♠ ④ ◆✷ ❂ ✷✷ ⑥❀ ❉②♥❆rr❛②✷ ✯❛✷ ❂ ♠❛❧❧♦❝ ✭ s✐③❡♦❢ ✭❉②♥❆rr❛②✷✮ ✰ ✭◆✷ ✲ ✶✮✯ s✐③❡♦❢ ✭ ✈♦✐❞ ✯✮✮❀ ❛✷✲ > ♥❊❧❡♠❡♥ts ❂ ◆✷❀ ❢♦r ✭ ✐♥t ✐ ❂ ✵❀ ✐ < ◆✷❀ ✐✰✰✮ ❛✷✲ > ❡❧❡♠❡♥ts❬✐❪ ❂ ✐❀ ❛✷✲ > ❡❧❡♠❡♥ts❬✹❪ ❂ ✳✳✳❀ ✴✴♦❦ ❛✷✲ > ❡❧❡♠❡♥ts❬✷✷❪ ❂ ✳✳✳❀ ✴✴✉♥♣r❡❞✐❝t❛❜❧❡ r✉♥t✐♠❡ ❡rr♦r ❆❞✈❛♥❝❡❞ ❈ ❚♦♣✐❝s

  10. ❉②❛♥❛♠✐❝❛❧❧② ❆❧❧♦❝❛t❡❞ ❉②♥❛♠✐❝❛❧❧② ❙✐③❡❞ ❆rr❛②✿ ❍❛❝❦ ❈♦♥t✐♥✉❡❞ ❆❞✈❛♥❝❡❞ ❈ ❚♦♣✐❝s

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