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trt t P t t - - PowerPoint PPT Presentation

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P r trt t trt t P t t trt

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SLIDE 1
  • P❯ ◗❘

❍❛❧❧❣❡✐r ▲✐❡♥ ■♥tr♦❞✉❝t✐♦♥ t♦ ◗❘ ❈♦♠♣✉t✐♥❣ t❤❡ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥ ♦♥ t❤❡ ●P❯ ❘❡s✉❧ts

◗❘ ❢❛❝t♦r✐③❛t✐♦♥ ♦♥ t❤❡ ●P❯

❍❛❧❧❣❡✐r ▲✐❡♥ ✷✹t❤ ♦❢ ▼❛②

✶

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SLIDE 2
  • P❯ ◗❘

❍❛❧❧❣❡✐r ▲✐❡♥ ■♥tr♦❞✉❝t✐♦♥ t♦ ◗❘ ❈♦♠♣✉t✐♥❣ t❤❡ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥ ♦♥ t❤❡ ●P❯ ❘❡s✉❧ts

❖✉t❧✐♥❡

✶

■♥tr♦❞✉❝t✐♦♥ t♦ ◗❘

✷

❈♦♠♣✉t✐♥❣ t❤❡ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥

✸

◗❘ ❢❛❝t♦r✐③❛t✐♦♥ ♦♥ t❤❡ ●P❯

✹

❘❡s✉❧ts

✷

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SLIDE 3
  • P❯ ◗❘

❍❛❧❧❣❡✐r ▲✐❡♥ ■♥tr♦❞✉❝t✐♦♥ t♦ ◗❘ ❈♦♠♣✉t✐♥❣ t❤❡ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥ ♦♥ t❤❡ ●P❯ ❘❡s✉❧ts

❖✉t❧✐♥❡

✶

■♥tr♦❞✉❝t✐♦♥ t♦ ◗❘

✷

❈♦♠♣✉t✐♥❣ t❤❡ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥

✸

◗❘ ❢❛❝t♦r✐③❛t✐♦♥ ♦♥ t❤❡ ●P❯

✹

❘❡s✉❧ts

✸

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SLIDE 4
  • P❯ ◗❘

❍❛❧❧❣❡✐r ▲✐❡♥ ■♥tr♦❞✉❝t✐♦♥ t♦ ◗❘ ❈♦♠♣✉t✐♥❣ t❤❡ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥ ♦♥ t❤❡ ●P❯ ❘❡s✉❧ts

❲❤❛t ✐s ◗❘❄

❚❤❡ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥ ♦❢ ❛ ♠❛tr✐① ❆ ❣✐✈❡s t✇♦ ♥❡✇ ♠❛tr✐❝❡s ◗ ❛♥❞ ❘ s✉❝❤ t❤❛t ❆ = ◗❘ ◗ ✐s ♦rt❤♦❣♦♥❛❧ ⇒ ◗◗❚ = ■ ❘ ✐s ✉♣♣❡r tr✐❛♥❣✉❧❛r ❊①❛♠♣❧❡ ❆ ◗ ❘   ✵ ✵ ✻ ✶ ✷ ✸ ✵ ✹ ✺   =   ✵ ✵ ✶ −✶ ✵ ✵ −✵ −✶ ✵     −✶ −✷ −✸ ✵ −✹ −✺ ✵ ✵ ✻  

✹

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SLIDE 5
  • P❯ ◗❘

❍❛❧❧❣❡✐r ▲✐❡♥ ■♥tr♦❞✉❝t✐♦♥ t♦ ◗❘ ❈♦♠♣✉t✐♥❣ t❤❡ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥ ♦♥ t❤❡ ●P❯ ❘❡s✉❧ts

❆♣♣❧✐❝❛t✐♦♥s ♦❢ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥s

◗❘ ❢❛❝t♦r✐③❛t✐♦♥ ❤❛s ❛ ❧❛r❣❡ ♥✉♠❜❡r ♦❢ ❛♣♣❧✐❝❛t✐♦♥s ❋✐♥❞✐♥❣ ❡✐❣❡♥✈❛❧✉❡s ♦❢ ♠❛tr✐❝❡s ❈❛❧❝✉❧❛t✐♥❣ t❤❡ s✐♥❣✉❧❛r ✈❛❧✉❡ ❞❡❝♦♠♣♦s✐t✐♦♥ ✭❙❱❉✮ ❚❤❡ ❧✐♥❡❛r ❧❡❛st sq✉❛r❡s ♣r♦❜❧❡♠ ❈♦✉❧❞ ❛❧s♦ ❜❡ ✉s❡❞ ❢♦r s♦❧✈✐♥❣ ❧✐♥❡❛r ❡q✉❛t✐♦♥s✿ ❆① = ❜ ⇒ ◗❘① = ❜ ⇒ ❘① = ◗❚❜

✺

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SLIDE 6
  • P❯ ◗❘

❍❛❧❧❣❡✐r ▲✐❡♥ ■♥tr♦❞✉❝t✐♦♥ t♦ ◗❘ ❈♦♠♣✉t✐♥❣ t❤❡ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥ ♦♥ t❤❡ ●P❯ ❘❡s✉❧ts

❆♣♣❧✐❝❛t✐♦♥✿ ❊✐❣❡♥✈❛❧✉❡ ✜♥❞✐♥❣ ✉s✐♥❣ ◗❘

❲❡ ✇❛♥t t♦ ✜♥❞ t❤❡ ❡✐❣❡♥✈❛❧✉❡s λ ♦❢ t❤❡ ♠❛tr✐① ❆❀ ✐✳❡✳ t❤❡ ✈❛❧✉❡s λ s✉❝❤ t❤❛t ❆λ✐ = λ✐✈✱ ❢♦r s♦♠❡ ✈❡❝t♦r ✈✳

✶ ❈♦♠♣✉t❡ t❤❡ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥ ◗❘ = ◗✵❘✵ = ❆ = ❆✵✳ ✷ ❈♦♠♣✉t❡ ❆✶ = ❘✵◗✵ ✸ ❈♦♠♣✉t❡ t❤❡ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥ ◗✶❘✶ = ❆✶ ✹ ■t❡r❛t❡ ✉♥t✐❧ ❝♦♥✈❡r❣❡♥❝❡✳

❚❤❡ r❡❛❧ ❡✐❣❡♥✈❛❧✉❡s t❤❡♥ ❧✐❡ ❛❧♦♥❣ t❤❡ ❞✐❛❣♦♥❛❧ ♦❢ t❤❡ ❧❛st ❆❦✳

✻

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SLIDE 7
  • P❯ ◗❘

❍❛❧❧❣❡✐r ▲✐❡♥ ■♥tr♦❞✉❝t✐♦♥ t♦ ◗❘ ❈♦♠♣✉t✐♥❣ t❤❡ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥ ♦♥ t❤❡ ●P❯ ❘❡s✉❧ts

❖✉t❧✐♥❡

✶

■♥tr♦❞✉❝t✐♦♥ t♦ ◗❘

✷

❈♦♠♣✉t✐♥❣ t❤❡ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥

✸

◗❘ ❢❛❝t♦r✐③❛t✐♦♥ ♦♥ t❤❡ ●P❯

✹

❘❡s✉❧ts

✼

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SLIDE 8
  • P❯ ◗❘

❍❛❧❧❣❡✐r ▲✐❡♥ ■♥tr♦❞✉❝t✐♦♥ t♦ ◗❘ ❈♦♠♣✉t✐♥❣ t❤❡ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥ ♦♥ t❤❡ ●P❯ ❘❡s✉❧ts

❈♦♠♣✉t✐♥❣ t❤❡ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥

▼❛♥② ❞✐✛❡r❡♥t ✇❛②s ♦❢ ❝♦♠♣✉t✐♥❣ ❆ = ◗❘

  • r❛♠✲❙❝❤♠✐❞t ♦rt❤♦❣♦♥❛❧✐③❛t✐♦♥

❍♦✉s❡❤♦❧❞❡r r❡✢❡❝t✐♦♥ tr❛♥s❢♦r♠❛t✐♦♥s

  • ✐✈❡♥s r♦t❛t✐♦♥s

■ ✇✐❧❧ ❢♦❝✉s ♦♥ ❝♦♠♣✉t✐♥❣ ◗❘ ❜② ❍♦✉s❡❤♦❧❞❡r r❡✢❡❝t♦r tr❛♥s❢♦r♠❛t✐♦♥s✳

✽

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SLIDE 9
  • P❯ ◗❘

❍❛❧❧❣❡✐r ▲✐❡♥ ■♥tr♦❞✉❝t✐♦♥ t♦ ◗❘ ❈♦♠♣✉t✐♥❣ t❤❡ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥ ♦♥ t❤❡ ●P❯ ❘❡s✉❧ts

❍♦✉s❡❤♦❧❞❡r r❡✢❡❝t✐♦♥ tr❛♥s❢♦r♠❛t✐♦♥s

❍♦✉s❡❤♦❧❞❡r r❡✢❡❝t✐♦♥ tr❛♥s❢♦r♠❛t✐♦♥ ♠❛tr✐❝❡s ❍ r❡✢❡❝ts ❛ ✈❡❝t♦r ❛❝r♦ss ❛ ❤②♣❡r♣❧❛♥❡✳ ❉❡✜♥✐t✐♦♥ ❚❤❡ ❤♦✉s❡❤♦❧❞❡r tr❛♥s❢♦r♠❛t✐♦♥ ♠❛tr✐① ❢♦r r❡❛❧ ♠❛tr✐❝❡s ✐s ❞❡✜♥❡❞ ❛s ❍ = ■ − ✷✈✈❚ ✇❤❡r❡ ✈ ✐s t❤❡ ♥♦r♠❛❧ ♦❢ t❤❡ ❤②♣❡r♣❧❛♥❡ t♦ r❡✢❡❝t ❛❝r♦ss✳ ❍♦✉s❡❤♦❧❞❡r r❡✢❡❝t♦rs ❛r❡ ♦rt❤♦❣♦♥❛❧

✾

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SLIDE 10
  • P❯ ◗❘

❍❛❧❧❣❡✐r ▲✐❡♥ ■♥tr♦❞✉❝t✐♦♥ t♦ ◗❘ ❈♦♠♣✉t✐♥❣ t❤❡ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥ ♦♥ t❤❡ ●P❯ ❘❡s✉❧ts

❈♦♠♣✉t✐♥❣ t❤❡ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥

❚❤❡ ❣♦❛❧ ✐s t♦ t✉r♥ t❤❡ ♣r♦❞✉❝t ❍∗❆ ✐♥t♦ ❛♥ ✉♣♣❡r tr✐❛♥❣✉❧❛r ♠❛tr✐①✱ ✇❤❡r❡ ❍∗ ✐s ♥ − ✶ ❤♦✉s❡❤♦❧❞❡r r❡✢❡❝t♦rs✳ ❲❡ ❝❤♦♦s❡ ✈ = ✉ ||✉||✷ ❛♥❞ ✉ = ① + s❣♥(①❥)||①||✷❡✶ ✇❤❡r❡ ① ✐s t❤❡ ❥✬t❤ ❝♦❧✉♠♥ ✈❡❝t♦r ♦❢ ❆ t♦ ❜❡ r❡✢❡❝t❡❞✱ ❛♥❞ ❡✶ ✐s t❤❡ ✉♥✐t ✈❡❝t♦r ❍ = ■ − ✷✈✈❚

✶✵

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SLIDE 11
  • P❯ ◗❘

❍❛❧❧❣❡✐r ▲✐❡♥ ■♥tr♦❞✉❝t✐♦♥ t♦ ◗❘ ❈♦♠♣✉t✐♥❣ t❤❡ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥ ♦♥ t❤❡ ●P❯ ❘❡s✉❧ts

❈♦♠♣✉t✐♥❣ t❤❡ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥

❆ = [❛✶❛✷❛✸] =   ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗   ❋✐rst st❡♣✱ s❡t ❥ = ✶ ❛♥❞ ❝♦♠♣✉t❡ t❤❡ ❤♦✉s❡❤♦❧❞❡r r❡✢❡❝t♦r ◗✶ = ❍✶✳ ❚❤✐s r❡✢❡❝ts ❛✶ t♦ ❡✶✿ ◗✶❆ =   ∗ ∗ ∗ ✵ ∗ ∗ ✵ ∗ ∗  

✶✶

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SLIDE 12
  • P❯ ◗❘

❍❛❧❧❣❡✐r ▲✐❡♥ ■♥tr♦❞✉❝t✐♦♥ t♦ ◗❘ ❈♦♠♣✉t✐♥❣ t❤❡ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥ ♦♥ t❤❡ ●P❯ ❘❡s✉❧ts

❈♦♠♣✉t✐♥❣ t❤❡ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥

❆ = [❛✶❛✷❛✸] =   ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗   ◆❡①t✱ s❡t ◗✷ = ■✶×✶ ✵ ✵ ❍✷

  • ❚❤❡♥✱

◗✷◗✶❆ =   ∗ ∗ ∗ ✵ ∗ ∗ ✵ ✵ ∗   = ❘

✶✷

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SLIDE 13
  • P❯ ◗❘

❍❛❧❧❣❡✐r ▲✐❡♥ ■♥tr♦❞✉❝t✐♦♥ t♦ ◗❘ ❈♦♠♣✉t✐♥❣ t❤❡ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥ ♦♥ t❤❡ ●P❯ ❘❡s✉❧ts

❈♦♠♣✉t✐♥❣ t❤❡ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥

❲❡ ♥♦✇ ❤❛✈❡ ❆ = [❛✶❛✷❛✸] =   ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗   ◗✷◗✶❆ =   ∗ ∗ ∗ ✵ ∗ ∗ ✵ ✵ ∗   = ❘ ❙❡tt✐♥❣ ◗ = ◗❚

✶ ◗❚ ✷ ❛♥❞ ♠✉❧t✐♣❧②✐♥❣ ❜② ◗ ♦♥ ❜♦t❤ s✐❞❡s ❣✐✈❡s

◗❚❆ = ❘ ⇒ ◗◗❚❆ = ❆ = ◗❘

✶✸

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SLIDE 14
  • P❯ ◗❘

❍❛❧❧❣❡✐r ▲✐❡♥ ■♥tr♦❞✉❝t✐♦♥ t♦ ◗❘ ❈♦♠♣✉t✐♥❣ t❤❡ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥ ♦♥ t❤❡ ●P❯ ❘❡s✉❧ts

❖✉t❧✐♥❡

✶

■♥tr♦❞✉❝t✐♦♥ t♦ ◗❘

✷

❈♦♠♣✉t✐♥❣ t❤❡ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥

✸

◗❘ ❢❛❝t♦r✐③❛t✐♦♥ ♦♥ t❤❡ ●P❯

✹

❘❡s✉❧ts

✶✹

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SLIDE 15
  • P❯ ◗❘

❍❛❧❧❣❡✐r ▲✐❡♥ ■♥tr♦❞✉❝t✐♦♥ t♦ ◗❘ ❈♦♠♣✉t✐♥❣ t❤❡ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥ ♦♥ t❤❡ ●P❯ ❘❡s✉❧ts

❇❧♦❝❦❡❞ ❍♦✉s❡❤♦❧❞❡r ◗❘

❈❛❧❝✉❧❛t✐♥❣ ◗❘ ✉s✐♥❣ t❤❡ ♠❡t❤♦❞ ❛❜♦✈❡ ✐s ✐♥❡✣❝✐❡♥t✿ ▲♦ts ♦❢ r❛♥❦ ✶ ✉♣❞❛t❡s t♦ t❤❡ ✐❞❡♥t✐t② ♠❛tr✐① ✭❢r♦♠ ❞❡✜♥✐t✐♦♥ ♦❢ ❍♦✉s❡❤♦❧❞❡r✿ ❍ = ■ − ✷✈✈❚✮ ■♥❡✣❝✐❡♥t ♠❡♠♦r② ❜❛♥❞✇✐❞t❤ ✉t✐❧✐③❛t✐♦♥ ✭❋♦r ●P❯s✿ ▲♦ts ♦❢ ❣❧♦❜❛❧ ♠❡♠♦r② ❛❝❝❡ss❡s✮✳ ❲❡ ♥❡❡❞ ❛♥♦t❤❡r r❡♣r❡s❡♥t❛t✐♦♥✳ ❲❡ ❝❛♥ r❡♣r❡s❡♥t t❤❡ ❍♦✉s❡❤♦❧❞❡r ♠❛tr✐❝❡s ❛s ◗❚

♠×r = ◗✶◗✷...◗r... = ■ + ❲❨ ❚

✇❤❡r❡ ❲❦ = [❲❦−✶, ◗❦−✶(✷✈❦)] ❛♥❞ ❨❦ = [❨❦−✶, ✈❦] ✶

✶❈✳ ❍✳ ❇✐s❝❤♦❢✱ ❈✳❱✳ ▲♦❛♥✿ ❚❤❡ ❲❨ ❘❡♣r❡s❡♥t❛t✐♦♥ ❢♦r Pr♦❞✉❝ts ♦❢

❍♦✉s❡❤♦❧❞❡r ▼❛tr✐❝❡s

✶✺

slide-16
SLIDE 16
  • P❯ ◗❘

❍❛❧❧❣❡✐r ▲✐❡♥ ■♥tr♦❞✉❝t✐♦♥ t♦ ◗❘ ❈♦♠♣✉t✐♥❣ t❤❡ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥ ♦♥ t❤❡ ●P❯ ❘❡s✉❧ts

❇❧♦❝❦❡❞ ❍♦✉s❡❤♦❧❞❡r ◗❘

❲❡ ♣❛rt✐t✐♦♥ t❤❡ ❝♦❧✉♠♥s ♦❢ ❆ ✐♥t♦ ♠ × r ❜❧♦❝❦s✳ ■♥✐t✐❛❧✐③❡ ◗ ← ■

✶ ❋♦r ❡❛❝❤ ❜❧♦❝❦✿ ❈♦♠♣✉t❡ ◗♠×r = ■ + ❲❨ ❚ ✶

❈♦♠♣✉t❡ r ❍♦✉s❡❤♦❧❞❡r ✈❡❝t♦rs ✭t❤❡ ✈ ✈❡❝t♦rs✮✱ ❛♥❞ ✉♣❞❛t❡ t❤❡ ❝✉rr❡♥t ❜❧♦❝❦ ♦❢ ❆

✷

❈♦♠♣✉t❡ t❤❡ ❲ ❛♥❞ ❨ ♠❛tr✐❝❡s ✉s✐♥❣ t❤❡s❡ ✈❡❝t♦rs✳

✷ ❆♣♣❧② ❆r❡st ← ❆r❡st + ❨❲ ❚❆r❡st ✸ ❆♣♣❧② ◗r❡st ← ◗r❡st + ❨❲ ❚◗r❡st ✶✻

slide-17
SLIDE 17
  • P❯ ◗❘

❍❛❧❧❣❡✐r ▲✐❡♥ ■♥tr♦❞✉❝t✐♦♥ t♦ ◗❘ ❈♦♠♣✉t✐♥❣ t❤❡ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥ ♦♥ t❤❡ ●P❯ ❘❡s✉❧ts

❇❧♦❝❦❡❞ ❍♦✉s❡❤♦❧❞❡r ◗❘

❈❯❇▲❆❙ ❦❡r♥❡❧s ❛r❡ ✉s❡❞ ❛s ❛ ❜❛s✐s ❢♦r t❤❡ ●P❯ ✐♠♣❧❡♠❡♥t❛t✐♦♥✳

✶ ❇❛s❡❧✐♥❡✿ ❋♦r✲❧♦♦♣ ✐s ❡①❡❝✉t❡❞ ❛s✲✐s ♦♥ t❤❡ ❈P❯✱ ❝❛❧❧✐♥❣

❦❡r♥❡❧s ❢♦r ❡❛❝❤ ♠❛tr✐①✴✈❡❝t♦r ♦♣❡r❛t✐♦♥✳

✷ ❲❤❡♥❡✈❡r ♣♦ss✐❜❧❡✱ ❝♦♠❜✐♥❡ ♠✉❧t✐♣❧❡ ❈❯❇▲❆❙ ❝❛❧❧s ✐♥t♦ ❛

❝✉st♦♠ ❦❡r♥❡❧

✸ ❚❤❡② ✉t✐❧✐③❡ s❤❛r❡❞ ♠❡♠♦r②✱ ❜✉t t❤❡② ❞♦♥✬t s❛② ❤♦✇

✭❡①❝❡♣t ❢♦r ♠❛tr✐①✲✈❡❝t♦r ♠✉❧t✐♣❧②✱ ♦♥ ♥❡①t s❧✐❞❡✮✳

✶✼

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SLIDE 18
  • P❯ ◗❘

❍❛❧❧❣❡✐r ▲✐❡♥ ■♥tr♦❞✉❝t✐♦♥ t♦ ◗❘ ❈♦♠♣✉t✐♥❣ t❤❡ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥ ♦♥ t❤❡ ●P❯ ❘❡s✉❧ts

❈✉st♦♠ ♠❛tr✐①✲✈❡❝t♦r ♠✉❧t✐♣❧②

❆ ❝✉st♦♠ ♠❛tr✐①✲✈❡❝t♦r ♠✉❧t✐♣❧② ❦❡r♥❡❧ ✇ = β❆✈ + α✇ ✇❛s ✐♠♣❧❡♠❡♥t❡❞ ❯s❡s ❛ ✈❡❝t♦r ❧❡♥❣t❤ ♦❢ ✻✹ ✭✷ ✇❛r♣s✮ ❑❡❡♣s ✈ ✐♥ s❤❛r❡❞ ♠❡♠♦r② ❖♥❡ t❤r❡❛❞ ❝♦♠♣✉t❡s ♦♥❡ ❡❧❡♠❡♥t ♦❢ ✇❀ ❦❡❡♣s ✐ts ❧♦❝❛❧ r❡s✉❧t ✐♥ ❛ r❡❣✐st❡r ❙♣❡❡❞✉♣ ♦✈❡r ❈❯❇▲❆❙ s❣❡♠✈✿ ❛❜♦✉t ✷.✺×

✶✽

slide-19
SLIDE 19
  • P❯ ◗❘

❍❛❧❧❣❡✐r ▲✐❡♥ ■♥tr♦❞✉❝t✐♦♥ t♦ ◗❘ ❈♦♠♣✉t✐♥❣ t❤❡ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥ ♦♥ t❤❡ ●P❯ ❘❡s✉❧ts

❖✉t❧✐♥❡

✶

■♥tr♦❞✉❝t✐♦♥ t♦ ◗❘

✷

❈♦♠♣✉t✐♥❣ t❤❡ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥

✸

◗❘ ❢❛❝t♦r✐③❛t✐♦♥ ♦♥ t❤❡ ●P❯

✹

❘❡s✉❧ts

✶✾

slide-20
SLIDE 20
  • P❯ ◗❘

❍❛❧❧❣❡✐r ▲✐❡♥ ■♥tr♦❞✉❝t✐♦♥ t♦ ◗❘ ❈♦♠♣✉t✐♥❣ t❤❡ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥ ♦♥ t❤❡ ●P❯ ❘❡s✉❧ts

❘❡s✉❧ts

❋✐❣✉r❡✿ ❙✉st❛✐♥❡❞ ●❋▲❖Ps r❛t❡

✷✵

slide-21
SLIDE 21
  • P❯ ◗❘

❍❛❧❧❣❡✐r ▲✐❡♥ ■♥tr♦❞✉❝t✐♦♥ t♦ ◗❘ ❈♦♠♣✉t✐♥❣ t❤❡ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥ ♦♥ t❤❡ ●P❯ ❘❡s✉❧ts

❘❡s✉❧ts

❋✐❣✉r❡✿ ❙♣❡❡❞✉♣ ♦✈❡r ■♥t❡❧ ▼❑▲ ✭●❚❳ ✷✽✵✮

✷✶

slide-22
SLIDE 22
  • P❯ ◗❘

❍❛❧❧❣❡✐r ▲✐❡♥ ■♥tr♦❞✉❝t✐♦♥ t♦ ◗❘ ❈♦♠♣✉t✐♥❣ t❤❡ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥ ◗❘ ❢❛❝t♦r✐③❛t✐♦♥ ♦♥ t❤❡ ●P❯ ❘❡s✉❧ts

❘❡s✉❧ts

❘❡s✉❧ts ❛r❡ ❢♦r s✐♥❣❧❡ ♣r❡❝✐s✐♦♥ ♦♥❧② ✭❘❡❛❧✐st✐❝❄✮✳ ❙✉st❛✐♥❡❞ r❛t❡ ✐s ✶✹✸ ●❋▲❖P❙✳ ❚❤❡ s♣❡❡❞✉♣ ❣r❛♣❤ ❞♦❡s♥✬t ♠❛❦❡ s❡♥s❡ ❈P❯ ✉s❡❞ ✐s ❛♥ ■♥t❡❧ ❳❡♦♥ ✷✳✽●❍③✳ ❙♣❡❡❞✉♣ ♦✈❡r ▼❑▲ ❢♦r ✹ t❤r❡❛❞s ✐s ❛❜♦✉t ✶ ❢♦r ✽✵✵✵ ×✽✵✵✵ ❲❤✐❝❤ ♠❡❛♥s t❤❛t ▼❑▲ r❛♥ ❛t ❛❜♦✉t ✶✹✸ ●❋▲❖P❙✭✦✦✮ ❢♦r ✹ t❤r❡❛❞s ❚❤✐s ✐s ♥♦t ❡①♣❧❛✐♥❡❞ ✐♥ t❤❡ ♣❛♣❡r✳

✷✷