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rs rt rt rt - - PowerPoint PPT Presentation

Feb 01, 2023 134 likes •873 views

rs rt rt rt s rst r

slide-1
SLIDE 1

❚♦✇❛r❞s ❛♥ ■♠♣❛rt✐❛❧ ❙❤♦rt ❚❛✢ ❱❛r✐❛♥t

❈✳ ❚❡♥♥❡♥❤♦✉s❡

❯♥✐✈❡rs✐t② ♦❢ ◆❡✇ ❊♥❣❧❛♥❞ ❇✐❞❞❡❢♦r❞✱ ▼❛✐♥❡ ✶

slide-2
SLIDE 2

❼ ▼♦t✐✈❛t✐♦♥ ❼ ❇❛❝❦❣r♦✉♥❞ ♦♥ ❚❛✢ ❼ ❙♦♠❡ ♣♦ss✐❜❧❡ r✉❧❡s❡ts ❼ ❲❤❛t✬s ♥❡①t❄

✷

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SLIDE 3

❼ ▼♦t✐✈❛t✐♦♥ ❼ ❇❛❝❦❣r♦✉♥❞ ♦♥ ❚❛✢ ❼ ❙♦♠❡ ♣♦ss✐❜❧❡ r✉❧❡s❡ts ❼ ❲❤❛t✬s ♥❡①t❄

✷

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SLIDE 4

❼ ▼♦t✐✈❛t✐♦♥ ❼ ❇❛❝❦❣r♦✉♥❞ ♦♥ ❚❛✢ ❼ ❙♦♠❡ ♣♦ss✐❜❧❡ r✉❧❡s❡ts ❼ ❲❤❛t✬s ♥❡①t❄

✷

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SLIDE 5

❼ ▼♦t✐✈❛t✐♦♥ ❼ ❇❛❝❦❣r♦✉♥❞ ♦♥ ❚❛✢ ❼ ❙♦♠❡ ♣♦ss✐❜❧❡ r✉❧❡s❡ts ❼ ❲❤❛t✬s ♥❡①t❄

✷

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SLIDE 6

▼♦t✐✈❛t✐♦♥

slide-7
SLIDE 7

■t st❛rts ✇✐t❤ ❛ tr✐♣ t♦ t❤❡ ◆❛t✐♦♥❛❧ ▼✉s❡✉♠ ✐♥ ❊❞✐♥❜✉r❣❤ ❲❤❛t ❣❛♠❡ ✐s t❤✐s❄ Pr♦❜❛❜❧② ❍♥❡❢❛t❛✢

✸

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SLIDE 8

■t st❛rts ✇✐t❤ ❛ tr✐♣ t♦ t❤❡ ◆❛t✐♦♥❛❧ ▼✉s❡✉♠ ✐♥ ❊❞✐♥❜✉r❣❤ ❲❤❛t ❣❛♠❡ ✐s t❤✐s❄ Pr♦❜❛❜❧② ❍♥❡❢❛t❛✢

✸

slide-9
SLIDE 9

■t st❛rts ✇✐t❤ ❛ tr✐♣ t♦ t❤❡ ◆❛t✐♦♥❛❧ ▼✉s❡✉♠ ✐♥ ❊❞✐♥❜✉r❣❤ ❲❤❛t ❣❛♠❡ ✐s t❤✐s❄ Pr♦❜❛❜❧② ❍♥❡❢❛t❛✢

✸

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SLIDE 10

■t st❛rts ✇✐t❤ ❛ tr✐♣ t♦ t❤❡ ◆❛t✐♦♥❛❧ ▼✉s❡✉♠ ✐♥ ❊❞✐♥❜✉r❣❤ ❲❤❛t ❣❛♠❡ ✐s t❤✐s❄ Pr♦❜❛❜❧② ❍♥❡❢❛t❛✢

✸

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SLIDE 11

❚❛✢ ❣❛♠❡s

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SLIDE 12

❲❤❛t ❛r❡ ❚❛✢ ❣❛♠❡s❄

✹

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SLIDE 13

❲❤❛t ❛r❡ ❚❛✢ ❣❛♠❡s❄

Z0ZrsrsrZ0Z 0Z0Z0s0Z0Z0 Z0Z0Z0Z0Z0Z rZ0Z0S0Z0Zr s0Z0SRS0Z0s rs0SRJRS0sr s0Z0SRS0Z0s rZ0Z0S0Z0Zr Z0Z0Z0Z0Z0Z 0Z0Z0s0Z0Z0 Z0ZrsrsrZ0Z

✹

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SLIDE 14

❲❤❛t ❛r❡ ❚❛✢ ❣❛♠❡s❄

Z0ZrsrsrZ0Z 0Z0Z0s0Z0Z0 Z0Z0Z0Z0Z0Z rZ0Z0S0Z0Zr s0Z0SRS0Z0s rs0SRJRS0sr s0Z0ZRS0Z0s rZ0Z0S0Z0Zr Z0Z0Z0Z0Z0Z 0Z0ZRs0Z0Z0 Z0ZrsrsrZ0Z

✺

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SLIDE 15

❲❤❛t ❛r❡ ❚❛✢ ❣❛♠❡s❄

Z0ZrsrsrZ0Z 0Z0Z0s0Z0Z0 Z0Z0Z0Z0Z0Z rZ0Z0S0Z0Zr s0Z0SRS0Z0s rs0SRJRS0sr s0Z0ZRS0Z0s rZ0Z0S0Z0Zr Z0Z0Z0ZrZ0Z 0Z0ZRs0Z0Z0 Z0Zrsrs0Z0Z

✻

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SLIDE 16

❲❤❛t ❛r❡ ❚❛✢ ❣❛♠❡s❄

Z0ZrsrsrZ0Z 0Z0Z0s0Z0Z0 Z0Z0Z0Z0Z0Z rZ0Z0S0Z0Zr s0Z0SRS0Z0s rs0SRJRS0sr s0Z0ZRZ0Z0s rZ0Z0S0Z0Zr Z0Z0Z0ZrZ0Z 0Z0ZRsRZ0Z0 Z0Zrsrs0Z0Z

✼

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SLIDE 17

❲❤❛t ❛r❡ ❚❛✢ ❣❛♠❡s❄

Z0ZrsrsrZ0Z 0Z0Z0s0Z0Z0 Z0Z0Z0Z0Z0Z rZ0Z0S0Z0Zr s0Z0SRS0Z0s rs0SRJRS0sr s0Z0ZRZ0Z0s rZ0Z0S0Z0Zr Z0Z0Z0ZrZ0Z 0Z0ZRZRZ0Z0 Z0Zrsrs0Z0Z

✽

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SLIDE 18

❲❤❛t ❛r❡ ❚❛✢ ❣❛♠❡s❄

Z0Z0J0Z0Z0Z 0S0ZrZ0Z0Z0 Z0Z0Z0Z0Z0Z 0Z0Z0ZRZ0Z0 Z0s0Z0Z0Z0Z 0Z0Z0Z0Z0Z0 Z0Z0Z0Z0Z0Z 0Z0Z0Z0Z0Z0 Z0Z0Z0Z0Z0Z 0Z0Z0Z0Z0s0 Z0Z0Z0Z0Z0Z

✾

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SLIDE 19

❲❤❛t ❛r❡ ❚❛✢ ❣❛♠❡s❄

J0Z0Z0Z0Z0Z 0S0ZrZ0Z0Z0 Z0Z0Z0Z0Z0Z 0Z0Z0ZRZ0Z0 Z0s0Z0Z0Z0Z 0Z0Z0Z0Z0Z0 Z0Z0Z0Z0Z0Z 0Z0Z0Z0Z0Z0 Z0Z0Z0Z0Z0Z 0Z0Z0Z0Z0s0 Z0Z0Z0Z0Z0Z

✶✵

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SLIDE 20

❲❤❛t ❛r❡ ❚❛✢ ❣❛♠❡s❄

Z0Z0Z0Z0Z0Z 0S0ZrZ0Z0Z0 Z0Z0JrZ0Z0Z 0Z0ZrZRZ0Z0 Z0Z0Z0Z0Z0Z 0Z0Z0Z0Z0Z0 Z0ZrZ0Z0Z0Z 0Z0Z0Z0Z0Z0 Z0Z0Z0Z0Z0Z 0Z0Z0Z0Z0Z0 Z0Z0Z0Z0Z0Z

✶✶

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SLIDE 21

❲❤❛t ❛r❡ ❚❛✢ ❣❛♠❡s❄

Z0Z0Z0Z0Z0Z 0S0ZrZ0Z0Z0 Z0ZrJrZ0Z0Z 0Z0ZrZRZ0Z0 Z0Z0Z0Z0Z0Z 0Z0Z0Z0Z0Z0 Z0Z0Z0Z0Z0Z 0Z0Z0Z0Z0Z0 Z0Z0Z0Z0Z0Z 0Z0Z0Z0Z0Z0 Z0Z0Z0Z0Z0Z

✶✷

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SLIDE 22

▼❛♥② ✈❛r✐❛♥ts ❆❧✇❛②s ❧♦♦♣② ❆❧✇❛②s ♣❛rt✐s❛♥

✶✸

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SLIDE 23

▼❛♥② ✈❛r✐❛♥ts ❆❧✇❛②s ❧♦♦♣② ❆❧✇❛②s ♣❛rt✐s❛♥

✶✸

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SLIDE 24

▼❛♥② ✈❛r✐❛♥ts ❆❧✇❛②s ❧♦♦♣② ❆❧✇❛②s ♣❛rt✐s❛♥

✶✸

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SLIDE 25

▼❛♥② ✈❛r✐❛♥ts ❆❧✇❛②s ❧♦♦♣② ❆❧✇❛②s ♣❛rt✐s❛♥

✶✸

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SLIDE 26

❚❤✐s ❧♦♦❦s ✐♠♣❛rt✐❛❧✦ ❈❛♥ ✇❡ ❛♥❛❧②③❡ ✐t❄

✶✹

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SLIDE 27

❚❤✐s ❧♦♦❦s ✐♠♣❛rt✐❛❧✦ ❈❛♥ ✇❡ ❛♥❛❧②③❡ ✐t❄

✶✹

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SLIDE 28

❚❤✐s ❧♦♦❦s ✐♠♣❛rt✐❛❧✦ ❈❛♥ ✇❡ ❛♥❛❧②③❡ ✐t❄

✶✹

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SLIDE 29

❘✉❧❡s❡ts

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SLIDE 30
  • ❛♠❡ ❡♥❞s ✇❤❡♥ ❦✐♥❣ ❝❛♥✬t ♠♦✈❡ ✭❡①✐t ♦r ❝❛♣t✉r❡❞✮

❖♥❧② ❛♥❛❧②③❡❞ ✇✐t❤ ❦✐♥❣ ❛♥❞ ♦♥❡ s♦❧❞✐❡r ❑✐♥❣ ♠♦✈❡s ◆✴❲ P♦ss✐❜❧❡ s♦❧❞✐❡r ♠♦✈❡♠❡♥t ♠❡❝❤❛♥✐❝s ❼ ❆♥② ❞✐r❡❝t✐♦♥✱ ❡♥❞✐♥❣ ❝❧♦s❡r t♦ ❑ ❼ ❖♥❧② ◆✴❲ ❼ ❖♥❧② ❙✴❊ ❼ ❙t❛② st❛t✐♦♥❛r②

✶✺

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SLIDE 31
  • ❛♠❡ ❡♥❞s ✇❤❡♥ ❦✐♥❣ ❝❛♥✬t ♠♦✈❡ ✭❡①✐t ♦r ❝❛♣t✉r❡❞✮

❖♥❧② ❛♥❛❧②③❡❞ ✇✐t❤ ❦✐♥❣ ❛♥❞ ♦♥❡ s♦❧❞✐❡r ❑✐♥❣ ♠♦✈❡s ◆✴❲ P♦ss✐❜❧❡ s♦❧❞✐❡r ♠♦✈❡♠❡♥t ♠❡❝❤❛♥✐❝s ❼ ❆♥② ❞✐r❡❝t✐♦♥✱ ❡♥❞✐♥❣ ❝❧♦s❡r t♦ ❑ ❼ ❖♥❧② ◆✴❲ ❼ ❖♥❧② ❙✴❊ ❼ ❙t❛② st❛t✐♦♥❛r②

✶✺

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SLIDE 32
  • ❛♠❡ ❡♥❞s ✇❤❡♥ ❦✐♥❣ ❝❛♥✬t ♠♦✈❡ ✭❡①✐t ♦r ❝❛♣t✉r❡❞✮

❖♥❧② ❛♥❛❧②③❡❞ ✇✐t❤ ❦✐♥❣ ❛♥❞ ♦♥❡ s♦❧❞✐❡r ❑✐♥❣ ♠♦✈❡s ◆✴❲ P♦ss✐❜❧❡ s♦❧❞✐❡r ♠♦✈❡♠❡♥t ♠❡❝❤❛♥✐❝s ❼ ❆♥② ❞✐r❡❝t✐♦♥✱ ❡♥❞✐♥❣ ❝❧♦s❡r t♦ ❑ ❼ ❖♥❧② ◆✴❲ ❼ ❖♥❧② ❙✴❊ ❼ ❙t❛② st❛t✐♦♥❛r②

✶✺

slide-33
SLIDE 33
  • ❛♠❡ ❡♥❞s ✇❤❡♥ ❦✐♥❣ ❝❛♥✬t ♠♦✈❡ ✭❡①✐t ♦r ❝❛♣t✉r❡❞✮

❖♥❧② ❛♥❛❧②③❡❞ ✇✐t❤ ❦✐♥❣ ❛♥❞ ♦♥❡ s♦❧❞✐❡r ❑✐♥❣ ♠♦✈❡s ◆✴❲ P♦ss✐❜❧❡ s♦❧❞✐❡r ♠♦✈❡♠❡♥t ♠❡❝❤❛♥✐❝s ❼ ❆♥② ❞✐r❡❝t✐♦♥✱ ❡♥❞✐♥❣ ❝❧♦s❡r t♦ ❑ ❼ ❖♥❧② ◆✴❲ ❼ ❖♥❧② ❙✴❊ ❼ ❙t❛② st❛t✐♦♥❛r②

✶✺

slide-34
SLIDE 34
  • ❛♠❡ ❡♥❞s ✇❤❡♥ ❦✐♥❣ ❝❛♥✬t ♠♦✈❡ ✭❡①✐t ♦r ❝❛♣t✉r❡❞✮

❖♥❧② ❛♥❛❧②③❡❞ ✇✐t❤ ❦✐♥❣ ❛♥❞ ♦♥❡ s♦❧❞✐❡r ❑✐♥❣ ♠♦✈❡s ◆✴❲ P♦ss✐❜❧❡ s♦❧❞✐❡r ♠♦✈❡♠❡♥t ♠❡❝❤❛♥✐❝s ❼ ❆♥② ❞✐r❡❝t✐♦♥✱ ❡♥❞✐♥❣ ❝❧♦s❡r t♦ ❑ ❼ ❖♥❧② ◆✴❲ ❼ ❖♥❧② ❙✴❊ ❼ ❙t❛② st❛t✐♦♥❛r②

✶✺

slide-35
SLIDE 35
  • ❛♠❡ ❡♥❞s ✇❤❡♥ ❦✐♥❣ ❝❛♥✬t ♠♦✈❡ ✭❡①✐t ♦r ❝❛♣t✉r❡❞✮

❖♥❧② ❛♥❛❧②③❡❞ ✇✐t❤ ❦✐♥❣ ❛♥❞ ♦♥❡ s♦❧❞✐❡r ❑✐♥❣ ♠♦✈❡s ◆✴❲ P♦ss✐❜❧❡ s♦❧❞✐❡r ♠♦✈❡♠❡♥t ♠❡❝❤❛♥✐❝s ❼ ❆♥② ❞✐r❡❝t✐♦♥✱ ❡♥❞✐♥❣ ❝❧♦s❡r t♦ ❑ ❼ ❖♥❧② ◆✴❲ ❼ ❖♥❧② ❙✴❊ ❼ ❙t❛② st❛t✐♦♥❛r②

✶✺

slide-36
SLIDE 36
  • ❛♠❡ ❡♥❞s ✇❤❡♥ ❦✐♥❣ ❝❛♥✬t ♠♦✈❡ ✭❡①✐t ♦r ❝❛♣t✉r❡❞✮

❖♥❧② ❛♥❛❧②③❡❞ ✇✐t❤ ❦✐♥❣ ❛♥❞ ♦♥❡ s♦❧❞✐❡r ❑✐♥❣ ♠♦✈❡s ◆✴❲ P♦ss✐❜❧❡ s♦❧❞✐❡r ♠♦✈❡♠❡♥t ♠❡❝❤❛♥✐❝s ❼ ❆♥② ❞✐r❡❝t✐♦♥✱ ❡♥❞✐♥❣ ❝❧♦s❡r t♦ ❑ ❼ ❖♥❧② ◆✴❲ ❼ ❖♥❧② ❙✴❊ ❼ ❙t❛② st❛t✐♦♥❛r②

✶✺

slide-37
SLIDE 37
  • ❛♠❡ ❡♥❞s ✇❤❡♥ ❦✐♥❣ ❝❛♥✬t ♠♦✈❡ ✭❡①✐t ♦r ❝❛♣t✉r❡❞✮

❖♥❧② ❛♥❛❧②③❡❞ ✇✐t❤ ❦✐♥❣ ❛♥❞ ♦♥❡ s♦❧❞✐❡r ❑✐♥❣ ♠♦✈❡s ◆✴❲ P♦ss✐❜❧❡ s♦❧❞✐❡r ♠♦✈❡♠❡♥t ♠❡❝❤❛♥✐❝s ❼ ❆♥② ❞✐r❡❝t✐♦♥✱ ❡♥❞✐♥❣ ❝❧♦s❡r t♦ ❑ ❼ ❖♥❧② ◆✴❲ ❼ ❖♥❧② ❙✴❊ ❼ ❙t❛② st❛t✐♦♥❛r②

✶✺

slide-38
SLIDE 38

❊♥❞ ❝❧♦s❡r t♦ ❑

s0Z0s0Z 0ZrZ0Z0 ZrJrZ0Z 0ZrZ0Z0 s0Z0s0Z 0Z0Z0s0 Z0Z0Z0s

▲♦♦❦s s✐♠♣❧❡✱ ❜✉t

✶✻

slide-39
SLIDE 39

❊♥❞ ❝❧♦s❡r t♦ ❑

s0Z0s0Z 0ZrZ0Z0 ZrJrZ0Z 0ZrZ0Z0 s0Z0s0Z 0Z0Z0s0 Z0Z0Z0s

▲♦♦❦s s✐♠♣❧❡✱ ❜✉t

✶✻

slide-40
SLIDE 40

❊♥❞ ❝❧♦s❡r t♦ ❑

s0Z0s0Z 0ZrZ0Z0 ZrJrZ0Z 0ZrZ0Z0 s0Z0s0Z 0Z0Z0s0 Z0Z0Z0s

▲♦♦❦s s✐♠♣❧❡✱ ❜✉t

0Z0Z0Z0Z0Z0Z0Z0s0Z0Z Z0Z0Z0Z0Z0Z0Z0Z0ZrZ0 0Z0Z0Z0Z0Z0Z0Z0Z0Z0Z Z0Z0Z0Z0Z0Z0Z0Z0Z0Z0 0Z0Z0Z0Z0Z0Z0Z0Z0Z0Z s0Z0Z0Z0Z0Z0Z0Z0Z0Z0 0s0Z0Z0Z0Z0Z0Z0Z0Z0Z Z0Z0Z0Z0Z0Z0Z0Z0Z0Z0 0ZrZ0Z0Z0Z0Z0Z0Z0Z0Z Z0ZrZ0Z0Z0Z0Z0Z0Z0Z0 0Z0Z0Z0Z0Z0Z0s0Z0Z0Z Z0Z0Z0Z0ZrZ0Z0Z0Z0Z0 0Z0Z0Z0ZrJrZ0Z0Z0Z0Z Z0Z0Z0Z0ZrZ0Z0Z0Z0Z0 0Z0Z0Z0Z0Z0s0Z0Z0Z0Z Z0Z0Z0Z0Z0Z0s0Z0Z0Z0 0Z0Z0Z0Z0Z0Z0ZrZ0Z0Z Z0Z0ZrZ0Z0Z0Z0Z0Z0Z0 0Z0Z0Z0s0Z0Z0Z0Z0Z0Z Z0Z0Z0s0Z0Z0Z0Z0Z0Z0 ✶✻

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SLIDE 41

❙♦❧❞✐❡r ♠♦✈❡s ◆✴❲

0ZrZ0Z0Z0Z0Z0Z s0Z0Z0Z0Z0Z0Z0 0s0Z0Z0Z0Z0Z0Z Z0Z0Z0Z0ZrZ0Z0 0Z0Z0Z0Z0ZrZ0Z Z0Z0s0Z0Z0Z0Z0 0Z0Z0s0Z0Z0Z0Z Z0Z0Z0ZrZ0Z0Z0 0Z0Z0ZrJ0Z0s0Z Z0ZrZ0Z0Z0Z0Z0 0Z0Z0Z0Z0Z0Z0Z Z0Z0Z0ZrZ0Z0Z0 0Z0Z0Z0ZrZ0Z0Z Z0Z0Z0Z0Z0Z0Z0

❚❤✐s ✐s r❡❛❧❧② ❥✉st ❜❧♦❝❦✐♥❣ ♥✐♠ ✇✐t❤ ❛ str❛♥❣❡ ❜❧♦❝❦✐♥❣ ♠❡❝❤❛♥✐❝ ◆♦t ❛♥❛❧②③❡❞

✶✼

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SLIDE 42

❙♦❧❞✐❡r ♠♦✈❡s ◆✴❲

0ZrZ0Z0Z0Z0Z0Z s0Z0Z0Z0Z0Z0Z0 0s0Z0Z0Z0Z0Z0Z Z0Z0Z0Z0ZrZ0Z0 0Z0Z0Z0Z0ZrZ0Z Z0Z0s0Z0Z0Z0Z0 0Z0Z0s0Z0Z0Z0Z Z0Z0Z0ZrZ0Z0Z0 0Z0Z0ZrJ0Z0s0Z Z0ZrZ0Z0Z0Z0Z0 0Z0Z0Z0Z0Z0Z0Z Z0Z0Z0ZrZ0Z0Z0 0Z0Z0Z0ZrZ0Z0Z Z0Z0Z0Z0Z0Z0Z0

❚❤✐s ✐s r❡❛❧❧② ❥✉st ❜❧♦❝❦✐♥❣ ♥✐♠ ✇✐t❤ ❛ str❛♥❣❡ ❜❧♦❝❦✐♥❣ ♠❡❝❤❛♥✐❝ ◆♦t ❛♥❛❧②③❡❞

✶✼

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SLIDE 43

❙♦❧❞✐❡r ♠♦✈❡s ◆✴❲

0ZrZ0Z0Z0Z0Z0Z s0Z0Z0Z0Z0Z0Z0 0s0Z0Z0Z0Z0Z0Z Z0Z0Z0Z0ZrZ0Z0 0Z0Z0Z0Z0ZrZ0Z Z0Z0s0Z0Z0Z0Z0 0Z0Z0s0Z0Z0Z0Z Z0Z0Z0ZrZ0Z0Z0 0Z0Z0ZrJ0Z0s0Z Z0ZrZ0Z0Z0Z0Z0 0Z0Z0Z0Z0Z0Z0Z Z0Z0Z0ZrZ0Z0Z0 0Z0Z0Z0ZrZ0Z0Z Z0Z0Z0Z0Z0Z0Z0

❚❤✐s ✐s r❡❛❧❧② ❥✉st ❜❧♦❝❦✐♥❣ ♥✐♠ ✇✐t❤ ❛ str❛♥❣❡ ❜❧♦❝❦✐♥❣ ♠❡❝❤❛♥✐❝ ◆♦t ❛♥❛❧②③❡❞

✶✼

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SLIDE 44

▲❡t ❙ ♠♦✈❡ ❙✴❊✱ ❜✉t ❞♦♥✬t ♣❛ss ❑ ❲❤② ✇♦✉❧❞ ❛ s♦❧❞✐❡r r❡♠♦✈❡ t❤❡♠s❡❧❢ ❢r♦♠ t❤❡ ❝♦✉♣❄ ❑ ❝❛♥ ♣❛ss s♦❧❞✐❡r

✶✽

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SLIDE 45

▲❡t ❙ ♠♦✈❡ ❙✴❊✱ ❜✉t ❞♦♥✬t ♣❛ss ❑ ❲❤② ✇♦✉❧❞ ❛ s♦❧❞✐❡r r❡♠♦✈❡ t❤❡♠s❡❧❢ ❢r♦♠ t❤❡ ❝♦✉♣❄ ❑ ❝❛♥ ♣❛ss s♦❧❞✐❡r

✶✽

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SLIDE 46

▲❡t ❙ ♠♦✈❡ ❙✴❊✱ ❜✉t ❞♦♥✬t ♣❛ss ❑ ❲❤② ✇♦✉❧❞ ❛ s♦❧❞✐❡r r❡♠♦✈❡ t❤❡♠s❡❧❢ ❢r♦♠ t❤❡ ❝♦✉♣❄

Z0Z0Z0Z0Z0Z 0Z0Z0Z0Z0Z0 Z0Z0Z0Z0Z0Z 0Z0Z0Z0Z0Z0 Z0Z0Z0Z0Z0Z 0ZRZ0Z0Z0Z0 Z0Z0Z0Z0J0Z 0Z0Z0Z0Z0Z0 Z0Z0Z0Z0Z0Z 0Z0Z0Z0Z0Z0 Z0Z0Z0Z0Z0Z

❑ ❝❛♥ ♣❛ss s♦❧❞✐❡r

✶✽

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SLIDE 47

▲❡t ❙ ♠♦✈❡ ❙✴❊✱ ❜✉t ❞♦♥✬t ♣❛ss ❑ ❲❤② ✇♦✉❧❞ ❛ s♦❧❞✐❡r r❡♠♦✈❡ t❤❡♠s❡❧❢ ❢r♦♠ t❤❡ ❝♦✉♣❄

Z0Z0Z0Z0Z0Z 0Z0Z0Z0Z0Z0 Z0Z0Z0Z0Z0Z 0Z0Z0Z0Z0Z0 Z0Z0Z0Z0Z0Z 0Z0Z0Z0ZRZ0 Z0Z0Z0Z0J0Z 0Z0Z0Z0Z0Z0 Z0Z0Z0Z0Z0Z 0Z0Z0Z0Z0Z0 Z0Z0Z0Z0Z0Z

❑ ❝❛♥ ♣❛ss s♦❧❞✐❡r

✶✾

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SLIDE 48

▲❡t ❙ ♠♦✈❡ ❙✴❊✱ ❜✉t ❞♦♥✬t ♣❛ss ❑ ❲❤② ✇♦✉❧❞ ❛ s♦❧❞✐❡r r❡♠♦✈❡ t❤❡♠s❡❧❢ ❢r♦♠ t❤❡ ❝♦✉♣❄

Z0Z0Z0Z0Z0Z 0Z0Z0Z0Z0Z0 Z0Z0Z0Z0Z0Z 0Z0Z0Z0Z0Z0 Z0Z0Z0Z0Z0Z 0Z0Z0Z0ZRZ0 Z0Z0Z0Z0J0Z 0Z0Z0Z0Z0Z0 Z0Z0Z0Z0Z0Z 0Z0Z0Z0Z0Z0 Z0Z0Z0Z0Z0Z

❑ ❝❛♥ ♣❛ss s♦❧❞✐❡r

✶✾

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SLIDE 49

▲❡t ❙ ♠♦✈❡ ❙✴❊✱ ❜✉t ❞♦♥✬t ♣❛ss ❑ ❲❤② ✇♦✉❧❞ ❛ s♦❧❞✐❡r r❡♠♦✈❡ t❤❡♠s❡❧❢ ❢r♦♠ t❤❡ ❝♦✉♣❄

Z0Z0Z0Z0Z0Z 0Z0Z0Z0Z0Z0 Z0Z0Z0Z0Z0Z 0Z0Z0Z0Z0Z0 Z0Z0Z0Z0Z0Z 0Z0Z0Z0ZRZ0 Z0Z0Z0J0Z0Z 0Z0Z0Z0Z0Z0 Z0Z0Z0Z0Z0Z 0Z0Z0Z0Z0Z0 Z0Z0Z0Z0Z0Z

❑ ❝❛♥ ♣❛ss s♦❧❞✐❡r

✷✵

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SLIDE 50

✲♣♦s✐t✐♦♥s

Z0Z0Z0Z0Z0Z 0Z0Z0Z0Z0Z0 Z0Z0ZrZ0Z0Z rZ0Z0Z0Z0Z0 ZrZ0Z0Z0Z0Z 0ZrZ0Z0Z0Z0 Z0ZrZ0Z0Z0Z 0Z0ZrZ0Z0Z0 Z0Z0Z0Z0Z0Z 0Z0Z0Z0s0Z0 Z0Z0Z0ZKZ0Z

✷✶

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SLIDE 51

✲♣♦s✐t✐♦♥s

Z0Z0s0Z0Z0Z 0Z0Z0Z0Z0Z0 Z0Z0Z0Z0Z0Z 0Z0Z0Z0Z0Z0 s0Z0Z0Z0Z0Z 0s0Z0Z0Z0Z0 Z0s0Z0Z0Z0Z 0Z0Z0Z0Z0Z0 Z0Z0Z0Z0Z0Z 0Z0Z0ZrZ0Z0 Z0Z0Z0J0Z0Z

✷✷

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SLIDE 52

✲♣♦s✐t✐♦♥s ▲♦♦❦s ♠♦❞✉❧❛r r❡❧❛t✐✈❡ t♦ ❞✐st❛♥❝❡ ❢r♦♠ ♠❛✐♥ ❞✐❛❣♦♥❛❧

✷✸

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SLIDE 53

✲♣♦s✐t✐♦♥s ▲♦♦❦s ♠♦❞✉❧❛r r❡❧❛t✐✈❡ t♦ ❞✐st❛♥❝❡ ❢r♦♠ ♠❛✐♥ ❞✐❛❣♦♥❛❧

✷✸

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SLIDE 54

✲♣♦s✐t✐♦♥s

✷✹

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SLIDE 55

❆ss✉♠❡ 푎 ≤ 푏 ❛♥❞ |푎 − 푏| = 푟 ❚❤❡♦r❡♠ (퐾 = (푎, 푏), 푆 = (푐, 푑)) ∈  ✐✛ ❖t❤❡r✇✐s❡

✷✺

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SLIDE 56

❆ss✉♠❡ 푎 ≤ 푏 ❛♥❞ |푎 − 푏| = 푟 ❚❤❡♦r❡♠ (퐾 = (푎, 푏), 푆 = (푐, 푑)) ∈  ✐✛ 퐾 = (0, 푏) ⇒ 푆 = (0, 푏 − 1) 퐾 = (푎, 푎) ⇒ 푆 ∈ {(푎 − 1, 푎), (푎, 푎 − 1), (푘, 푘) ∶ 푘 < (푎 − 1)} 퐾 = (푎 − 1, 푎) ⇒ 푆 ∈ {(푎 − 1, 푎 − 1), (푘 − 1, 푘) ∶ 1 ≤ 푘 ≤ (푎 − 2)} 퐾 = (푎 − 2, 푎) ⇒ 푆 ∈ {(푎 − 2, 푎 − 1), (푘 − 2, 푘) ∶ 2 ≤ 푘 ≤ (푎 − 2)} ❖t❤❡r✇✐s❡ 푆 ∈ {(푎, 푏 − 1)}∪ {(푎 − 1 − 2푘푟 − 푖, 푏 − 1, 2푘푟 − 푖) ∶ (푟 − 1) ≤ 푖 ≤ 2푟, 푘 ≥ 0}∪ {(푎 − 1 − 2푘푟 − 푖, 푏 − 1 − 2(푘 + 1)푟 − 푖) ∶ 1 ≤ 푖 ≤ (푟 − 2), 푘 ≥ 0}

✷✺

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SLIDE 57

퐻 = {(푎 − 1, 푖) ∶ 푖 ≤ 푏 − 푟} 푉1 = {(푖, 푏) ∶ 푖 ≤ 푎} 푉2 = {(푖, 푗) ∶ 푖 ∈ [0, 푎 − 1], 푗 ∈ [푏 − 1 − 푟, 푏 − 2]} 푅 = {(푎 − 1 − 2푘푟 − 푖, 푏 − 1 − 2푘푟 − 푗) ∶ 1 ≤ 푖 ≤ (푟 − 2), (푟 − 1) ≤ 푗 ≤ 2푟, 푘 ≥ 0}

✷✻

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SLIDE 58

퐾 ♠♦✈❡s t♦ (푎, 푎)✱ r❡♠♦✈✐♥❣ s♦❧❞✐❡r ❢r♦♠ ♣❧❛②

✷✼

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SLIDE 59

퐾 ♠♦✈❡s ❲❡st ♥❡①t t♦ 푆

✷✽

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SLIDE 60

퐾 ♠♦✈❡s ❲❡st t♦ ❞✐❛❣♦♥❛❧ ❢r♦♠ 푆✱ ♦r ♦✛✲❞✐❛❣♦♥❛❧ ❛s ♥❡❡❞❡❞✳

✷✾

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SLIDE 61

■❢ ❑✐♥❣ ♠♦✈❡s ❛❧❧ r❡s♣♦♥s❡s t♦  ❛r❡ ❛♥❛❧♦❣♦✉s □ ❲❤❛t ✐❢ t❤❡ s♦❧❞✐❡rs ❛r❡ st❛t✐♦♥❛r②❄ ❱❛r✐❛♥t ♦❢ ❇❧♦❝❦✐♥❣ ◆✐♠

✸✵

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SLIDE 62

■❢ ❑✐♥❣ ♠♦✈❡s ❛❧❧ r❡s♣♦♥s❡s t♦  ❛r❡ ❛♥❛❧♦❣♦✉s □ ❲❤❛t ✐❢ t❤❡ s♦❧❞✐❡rs ❛r❡ st❛t✐♦♥❛r②❄ ❱❛r✐❛♥t ♦❢ ❇❧♦❝❦✐♥❣ ◆✐♠

✸✵

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SLIDE 63

■❢ ❑✐♥❣ ♠♦✈❡s ❛❧❧ r❡s♣♦♥s❡s t♦  ❛r❡ ❛♥❛❧♦❣♦✉s □ ❲❤❛t ✐❢ t❤❡ s♦❧❞✐❡rs ❛r❡ st❛t✐♦♥❛r②❄ ❱❛r✐❛♥t ♦❢ ❇❧♦❝❦✐♥❣ ◆✐♠

✸✵

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SLIDE 64

■❢ ❑✐♥❣ ♠♦✈❡s ❛❧❧ r❡s♣♦♥s❡s t♦  ❛r❡ ❛♥❛❧♦❣♦✉s □ ❲❤❛t ✐❢ t❤❡ s♦❧❞✐❡rs ❛r❡ st❛t✐♦♥❛r②❄ ❱❛r✐❛♥t ♦❢ ❇❧♦❝❦✐♥❣ ◆✐♠

✸✵

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SLIDE 65

■❢ ❑✐♥❣ ♠♦✈❡s ❛❧❧ r❡s♣♦♥s❡s t♦  ❛r❡ ❛♥❛❧♦❣♦✉s □ ❲❤❛t ✐❢ t❤❡ s♦❧❞✐❡rs ❛r❡ st❛t✐♦♥❛r②❄ ❱❛r✐❛♥t ♦❢ ❇❧♦❝❦✐♥❣ ◆✐♠

✸✶

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SLIDE 66

◆❡①t st❡♣s

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SLIDE 67

❋✉♥ ❣❛♠❡✦ ❲❤❛t✬s ♥❡①t❄ ▼✉❧t✐♣❧❡ s♦❧❞✐❡rs❄ ❱❛❧✉❡s ❢♦r ♠❛✐♥ r✉❧❡s❡t❄ ❍♦✇ t♦ ❣❡♥❡r❛❧✐③❡ t❤❡ ❜♦❛r❞ t♦ ❛ ❣r❛♣❤❄ ❲❤♦ ❝❛r❡s❄ ❙❡r✐♦✉s❧②✱ t❡❧❧ ♠❡ ✇❤♦ ❝❛r❡s✳

✸✷

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SLIDE 68

❋✉♥ ❣❛♠❡✦ ❲❤❛t✬s ♥❡①t❄ ▼✉❧t✐♣❧❡ s♦❧❞✐❡rs❄ ❱❛❧✉❡s ❢♦r ♠❛✐♥ r✉❧❡s❡t❄ ❍♦✇ t♦ ❣❡♥❡r❛❧✐③❡ t❤❡ ❜♦❛r❞ t♦ ❛ ❣r❛♣❤❄ ❲❤♦ ❝❛r❡s❄ ❙❡r✐♦✉s❧②✱ t❡❧❧ ♠❡ ✇❤♦ ❝❛r❡s✳

✸✷

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SLIDE 69

❋✉♥ ❣❛♠❡✦ ❲❤❛t✬s ♥❡①t❄ ▼✉❧t✐♣❧❡ s♦❧❞✐❡rs❄ ❱❛❧✉❡s ❢♦r ♠❛✐♥ r✉❧❡s❡t❄ ❍♦✇ t♦ ❣❡♥❡r❛❧✐③❡ t❤❡ ❜♦❛r❞ t♦ ❛ ❣r❛♣❤❄ ❲❤♦ ❝❛r❡s❄ ❙❡r✐♦✉s❧②✱ t❡❧❧ ♠❡ ✇❤♦ ❝❛r❡s✳

✸✷

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SLIDE 70

❋✉♥ ❣❛♠❡✦ ❲❤❛t✬s ♥❡①t❄ ▼✉❧t✐♣❧❡ s♦❧❞✐❡rs❄ ❱❛❧✉❡s ❢♦r ♠❛✐♥ r✉❧❡s❡t❄ ❍♦✇ t♦ ❣❡♥❡r❛❧✐③❡ t❤❡ ❜♦❛r❞ t♦ ❛ ❣r❛♣❤❄ ❲❤♦ ❝❛r❡s❄ ❙❡r✐♦✉s❧②✱ t❡❧❧ ♠❡ ✇❤♦ ❝❛r❡s✳

✸✷

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SLIDE 71

❋✉♥ ❣❛♠❡✦ ❲❤❛t✬s ♥❡①t❄ ▼✉❧t✐♣❧❡ s♦❧❞✐❡rs❄ ❱❛❧✉❡s ❢♦r ♠❛✐♥ r✉❧❡s❡t❄ ❍♦✇ t♦ ❣❡♥❡r❛❧✐③❡ t❤❡ ❜♦❛r❞ t♦ ❛ ❣r❛♣❤❄ ❲❤♦ ❝❛r❡s❄ ❙❡r✐♦✉s❧②✱ t❡❧❧ ♠❡ ✇❤♦ ❝❛r❡s✳

✸✷

slide-72
SLIDE 72

❋✉♥ ❣❛♠❡✦ ❲❤❛t✬s ♥❡①t❄ ▼✉❧t✐♣❧❡ s♦❧❞✐❡rs❄ ❱❛❧✉❡s ❢♦r ♠❛✐♥ r✉❧❡s❡t❄ ❍♦✇ t♦ ❣❡♥❡r❛❧✐③❡ t❤❡ ❜♦❛r❞ t♦ ❛ ❣r❛♣❤❄ ❲❤♦ ❝❛r❡s❄ ❙❡r✐♦✉s❧②✱ t❡❧❧ ♠❡ ✇❤♦ ❝❛r❡s✳

✸✷

slide-73
SLIDE 73

❋✉♥ ❣❛♠❡✦ ❲❤❛t✬s ♥❡①t❄ ▼✉❧t✐♣❧❡ s♦❧❞✐❡rs❄ ❱❛❧✉❡s ❢♦r ♠❛✐♥ r✉❧❡s❡t❄ ❍♦✇ t♦ ❣❡♥❡r❛❧✐③❡ t❤❡ ❜♦❛r❞ t♦ ❛ ❣r❛♣❤❄ ❲❤♦ ❝❛r❡s❄ ❙❡r✐♦✉s❧②✱ t❡❧❧ ♠❡ ✇❤♦ ❝❛r❡s✳

✸✷