r trs r tr ts t - - PowerPoint PPT Presentation

▲✐♥❡❛r ❋✐❧t❡rs ✎ ❆ ❧✐♥❡❛r ☞❧t❡r t❛❦❡s ✐♥♣✉t ①t ✐♥t♦ ♦✉t♣✉t ②t✿ ②t ❂

✶

❳

r❂✶

❛r①tr ❢♦r ❝♦❡✍❝✐❡♥ts ❛r❀ ✶ ❁ r ❁ ✶✳ ✎ ■❢ t❤❡ ✐♥♣✉t ✐s ❛ ✉♥✐t ✐♠♣✉❧s❡ ❛t t ❂ ✵✱ ①t ❂

✽ ❁ ✿

✶ t ❂ ✵ ✵ t ✻❂ ✵❀ t❤❡ ♦✉t♣✉t ✐s ②t ❂ ❛t✱ s♦ t❤❡ ❝♦❡✍❝✐❡♥ts ❛r❡ ❝❛❧❧❡❞ t❤❡ ✐♠♣✉❧s❡ r❡s♣♦♥s❡ ❢✉♥❝t✐♦♥ ♦❢ t❤❡ ☞❧t❡r✳

✶

✎ ❋♦r ❡①❛♠♣❧❡✱ ✇✐t❤ ❛✶ ❂ ✶❀ ❛✷ ❂ ✵✿✺❀ ❛✸ ❂ ✵✿✷ ❛♥❞ ❛r ❂ ✵ ♦t❤❡r✇✐s❡✿ ♣❛r✭♠❢r♦✇ ❂ ❝✭✷✱ ✶✮✮ ① ❂ ts✭r❡♣✭✵✱ ✷✵✮✱ st❛rt ❂ ✲✺✮ ①❬t✐♠❡✭①✮ ❂❂ ✵❪ ❂ ✶ ♣❧♦t✭①✱ t②♣❡ ❂ ✧❜✧✮ ❛❜❧✐♥❡✭❤ ❂ ✵✱ ❝♦❧ ❂ ✧r❡❞✧✱ ❧t② ❂ ✷✮ ② ❂ ❢✐❧t❡r✭①✱ ❝✭✵✱ ✶✱ ✵✳✺✱ ✲✵✳✷✮✱ s✐❞❡s ❂ ✶✮ ♣❧♦t✭②✱ t②♣❡ ❂ ✧❜✧✮ ❛❜❧✐♥❡✭❤ ❂ ✵✱ ❝♦❧ ❂ ✧r❡❞✧✱ ❧t② ❂ ✷✮ ✎ ■❢✱ ❛s ❤❡r❡✱ ❛r ❂ ✵ ❢♦r r ❁ ✵✱ t❤❡ ☞❧t❡r ✐s r❡❛❧✲t✐♠❡✱ ♦r ❝❛✉s❛❧✱ ♦r r❡❛❧✐③❛❜❧❡✳

✷

✎ ■❢ t❤❡ ✐♥♣✉t ✐s ❛ ✭❝♦♠♣❧❡①✮ ❝♦s✐♥❡ ✇❛✈❡✱ ①t ❂ ❘❡✐✭✷✙✦t✰✣✮❀ t❤❡ ♦✉t♣✉t ✐s ②t ❂

✶

❳

r❂✶

❛r❘❡✐❬✷✙✦✭tr✮✰✣❪ ❂ ①t

✶

❳

r❂✶

❛r❡✷✙✐✦r ❂ ①t❆✭✦✮❀ ✇❤❡r❡ ❆✭✦✮ ❂

✶

❳

r❂✶

❛r❡✷✙✐✦r ✐s ❝❛❧❧❡❞ t❤❡ ❢r❡q✉❡♥❝② r❡s♣♦♥s❡ ❢✉♥❝t✐♦♥ ♦❢ t❤❡ ☞❧t❡r✳

✸

✎ ❙❛♠❡ ❡①❛♠♣❧❡✿ ★ ❢✐❧t❡r✭✮ ❞♦❡s ♥♦t ✇♦r❦ ❢♦r ❝♦♠♣❧❡① ✐♥♣✉t✿ ❢✐❧t❡r✳❝♦♠♣❧❡① ❂ ❢✉♥❝t✐♦♥✭①✱ ✳✳✳✮ ④ ❝♦♠♣❧❡①✭r❡❛❧ ❂ ❢✐❧t❡r✭❘❡✭①✮✱ ✳✳✳✮✱ ✐♠❛❣ ❂ ❢✐❧t❡r✭■♠✭①✮✱ ✳✳✳✮✮ ⑥ ❘ ❂ ✷ ♦♠❡❣❛ ❂ ✵✳✷ ♣❤✐ ❂ ✶ ① ❂ ❘ ✯ ❡①♣✭✶✐ ✯ ✭✷ ✯ ♣✐ ✯ ♦♠❡❣❛ ✯ t✐♠❡✭①✮ ✰ ♣❤✐✮✮ ② ❂ ❢✐❧t❡r✳❝♦♠♣❧❡①✭①✱ ❝✭✵✱ ✶✱ ✵✳✺✱ ✲✵✳✷✮✱ s✐❞❡s ❂ ✶✮ ② ✴ ① ✎ ❙♦ ❆✭✵✿✷✮ ❂ ✵✿✵✻✻✸✶✷ ✶✿✸✻✷✺✵✻✐✳

✹

❇❛❝❦s❤✐❢t ❖♣❡r❛t♦r ✎ ❚❤❡ ☞❧t❡r ❝❛♥ ❜❡ ✇r✐tt❡♥ ②t ❂

✶

❳

r❂✶

❛r①tr ❂

✶

❳

r❂✶

❛r❇r①t ❂ ❛✭❇✮①t❀ ✇❤❡r❡ ❛✭❇✮ ❂

✶

❳

r❂✶

❛r❇r✿ ✎ ❚❤❡ ❢r❡q✉❡♥❝② r❡s♣♦♥s❡ ❢✉♥❝t✐♦♥ ✐s ❆✭✦✮ ❂ ❛

✏

❡✷✙✐✦✑ ✿

✺

• ❛✐♥ ❛♥❞ P❤❛s❡

✎ ❚❤❡ ❢r❡q✉❡♥❝② r❡s♣♦♥s❡ ❢✉♥❝t✐♦♥ ✐♥ ♣♦❧❛r ❝♦♦r❞✐♥❛t❡s✿ ❆✭✦✮ ❂ ❥❆✭✦✮❥ ❡①♣❢✐✣✭✦✮❣✿ ✎ ❥❆✭✦✮❥ ✐s t❤❡ ❣❛✐♥ ❢✉♥❝t✐♦♥ ✭♦r ❛♠♣❧✐t✉❞❡✮✳ ✎ ✣✭✦✮ ✐s t❤❡ ♣❤❛s❡ ❢✉♥❝t✐♦♥✳ ✎ ❊✳❣✳ ❞❡❧❛②✿ ②t ❂ ❆①t❉❀ ❆ ❃ ✵❀ ✮ ❆✭✦✮ ❂ ❆❡✷✙✐❉✦✱ s♦ ④ ❣❛✐♥ ❂ ❆✱ ❝♦♥st❛♥t✱ ④ ♣❤❛s❡ ❂ ✷✙❉✦✱ ❧✐♥❡❛r ✐♥ ✦ ✇✐t❤ s❧♦♣❡ ✷✙❉✳

✻

❚②♣❡s ♦❢ ❋✐❧t❡r ✎ ■❢ ②t ❂

♠

❳

r❂✵

❛r①tr t❤❡ ☞❧t❡r ✐s ❛ ❋✐♥✐t❡ ■♠♣✉❧s❡ ❘❡s♣♦♥s❡ ✭❋■❘✮ ☞❧t❡r✳ ✎ ■❢ ♠ ❂ ✶ ✐t ✐s ❛♥ ■♥☞♥✐t❡ ■♠♣✉❧s❡ ❘❡s♣♦♥s❡ ✭■■❘✮ ☞❧t❡r✳ ✎ ❙♦♠❡ ■■❘ ☞❧t❡rs ❛r❡ r❡❝✉rs✐✈❡✿ ②t ❂ ❛✵①t ✰

♠

❳

r❂✶

❜r②tr✿

✼

❆❘▼❆ ♠♦❞❡❧s ✎ ■❢ ①t ✐s ✇❤✐t❡ ♥♦✐s❡ ❛♥❞ t❤❡ ☞❧t❡r ✐s ❋■❘✱ ②t ✐s ▼❆✭♠✮✳ ✎ ■❢ ①t ✐s ✇❤✐t❡ ♥♦✐s❡ ❛♥❞ t❤❡ ☞❧t❡r ✐s r❡❝✉rs✐✈❡✱ ②t ✐s ❆❘✭♠✮✳ ✎ ●❡♥❡r❛❧ ❆❘▼❆ ✐s t❤❡ ♦✉t♣✉t ♦❢ ❛ ❝♦♠❜✐♥❡❞ ☞❧t❡r ❛♣♣❧✐❡❞ t♦ ✇❤✐t❡ ♥♦✐s❡✱ ✇✐t❤ ❛♥ ❋■❘ ☞❧t❡r ❢♦❧❧♦✇❡❞ ❜② ❛ r❡❝✉rs✐✈❡ ☞❧t❡r✳

✽

❖✉t♣✉t ❙♣❡❝tr✉♠ ✎ ■❢ t❤❡ ✐♥♣✉t ✐s ❛♥② st❛t✐♦♥❛r② ♣r♦❝❡ss ✇✐t❤ ❛✉t♦❝♦✈❛r✐❛♥❝❡s ✌①①✭❤✮✱ t❤❡ ❝♦✈❛r✐❛♥❝❡s ♦❢ t❤❡ ♦✉t♣✉t ❛r❡ ❝♦✈

✏

②t✰❤❀ ②t

✑

❂ ❝♦✈

✥❳

r

❛r①t✰❤r❀

❳

s

❛s①ts

✦

❂

❳

r

❳

s

❛r❛s❝♦✈

✏

①t✰❤r❀ ①ts

✑

❂

❳

r

❳

s

❛r❛s✌①①✭❤ r ✰ s✮✿ ✎ ❚❤✐s ❞♦❡s ♥♦t ❞❡♣❡♥❞ ♦♥ t✱ s♦ ❢②t❣ ✐s ✇❡❛❦❧② st❛t✐♦♥❛r② ✇✐t❤ ✌②②✭❤✮ ❂

❳

r

❳

s

❛r❛s✌①①✭❤ r ✰ s✮✿

✾

✎ ❙♦ t❤❡ ♣♦✇❡r s♣❡❝tr❛❧ ❞❡♥s✐t② ♦❢ ❢②t❣ ✐s ❢②②✭✦✮ ❂

❳

❤

✌②②✭❤✮❡✷✙✐✦❤ ❂

❳

❤

❳

r

❳

s

❛r❛s✌①①✭❤ r ✰ s✮❡✷✙✐✦❤ ❂

✥❳

r

❛r❡✷✙✐✦r

✦ ✥❳

s

❛s❡✰✷✙✐✦s

✦

✂

✷ ✹❳

❤

✌①①✭❤ r ✰ s✮❡✷✙✐✦✭❤r✰s✮

✸ ✺

❂ ❥❆✭✦✮❥✷❢①①✭✦✮✿ ✎ ■♥ ✇♦r❞s✱ ♦✉t♣✉t s♣❡❝tr✉♠ ❂ ✐♥♣✉t s♣❡❝tr✉♠ ✂ sq✉❛r❡❞ ❣❛✐♥✿

✶✵

✎ ❲❡ ❝❛♥ ❛❧s♦ ❝♦♠♣✉t❡ t❤❡ ❝r♦ss ❝♦✈❛r✐❛♥❝❡ ✌①②✭❤✮✿ ❝♦✈

✏

①t✰❤❀ ②t

✑

❂ ❝♦✈

✥

①t✰❤❀

❳

s

❛s①ts

✦

❂

❳

s

❛s❝♦✈

✏

①t✰❤❀ ①ts

✑

❂

❳

s

❛s✌①①✭❤ ✰ s✮✿ ✎ ❚❤✐s t♦♦ ❞♦❡s ♥♦t ❞❡♣❡♥❞ ♦♥ t✱ s♦ ❢①t❣ ❛♥❞ ❢②t❣ ❛r❡ ❥♦✐♥t❧② st❛t✐♦♥❛r② ✇✐t❤ ✌①②✭❤✮ ❂

❳

s

❛s✌①①✭❤ ✰ s✮✿

✶✶

✎ ❙♦ t❤❡ ❝r♦ss s♣❡❝tr❛❧ ❞❡♥s✐t② ✐s ❢①②✭✦✮ ❂

❳

❤

✌①②✭❤✮❡✷✙✐✦❤ ❂

❳

❤

❳

s

❛s✌①①✭❤ ✰ s✮❡✷✙✐✦❤ ❂

✧❳

s

❛s❡✷✙✐✦s

★

✂

✷ ✹❳

❤

✌①①✭❤ ✰ s✮❡✷✙✐✦✭❤✰s✮

✸ ✺

❂ ❆✭✦✮❢①①✭✦✮✿ ✎ ❙✐♠✐❧❛r❧②✱ ❢②①✭✦✮ ❂ ❆✭✦✮❢①①✭✦✮✱ ♦r ✐♥ ✇♦r❞s✱ ❝r♦ss s♣❡❝tr✉♠ ❂ ✐♥♣✉t s♣❡❝tr✉♠✂❢r❡q✉❡♥❝② r❡s♣♦♥s❡ ❢✉♥❝t✐♦♥✿

✶✷

✎ ◆♦t❡ t❤❛t t❤❡ sq✉❛r❡❞ ❝♦❤❡r❡♥❝② ✐s ✚✷

②✿①✭✦✮ ❂

❥❢②①✭✦✮❥✷ ❢①①✭✦✮❢②②✭✦✮ ❂ ❥❆✭✦✮❢①①✭✦✮❥✷ ❢①①✭✦✮❥❆✭✦✮❥✷❢①①✭✦✮ ❂ ✶ ❢♦r ❡✈❡r② ❢r❡q✉❡♥❝② ✦✳ ✎ ❚❤❛t ✐s✱ ✐❢ ♦♥❡ s❡r✐❡s ✐s ❛ ☞❧t❡r❡❞ ✈❡rs✐♦♥ ♦❢ ❛♥♦t❤❡r✱ t❤❡✐r sq✉❛r❡❞ ❝♦❤❡r❡♥❝② ✐s ✶ ❛t ❛❧❧ ❢r❡q✉❡♥❝✐❡s✳ ✎ ❚❤❡ ❝♦♥✈❡rs❡ ✐s ❛❧s♦ tr✉❡✳

✶✸

❊①❛♠♣❧❡s ✎ ❋✐rst ❞✐☛❡r❡♥❝❡✿ ②t ❂ ①t ①t✶✱ s♦ ❛✵ ❂ ✶❀ ❛✶ ❂ ✶✱ ❛♥❞ ❛r ❂ ✵ ♦t❤❡r✇✐s❡✳ ④ ❚❤❡ ❢r❡q✉❡♥❝② r❡s♣♦♥s❡ ❢✉♥❝t✐♦♥ ✐s ❆✭✦✮ ❂ ✶ ❡✷✙✐✦ ❂ ❡✙✐✦ ✏ ❡✙✐✦ ❡✙✐✦✑ ❂ ❡✙✐✦ ✂ ✷✐ s✐♥✭✙✦✮✿ ④ ❋♦r ✵ ✔ ✦ ✔ ✶❂✷✱ t❤❡ ❣❛✐♥ ❢✉♥❝t✐♦♥ ✐s ✷ s✐♥✭✙✦✮✿

♣❛r✭♠❢r♦✇ ❂ ❝✭✷✱ ✶✮✮❀ ♣❧♦t✭❢✉♥❝t✐♦♥✭①✮ s✐♥✭♣✐ ✯ ①✮✱ ❢r♦♠ ❂ ✵✱ t♦ ❂ ✵✳✺✮ ❛❜❧✐♥❡✭❤ ❂ ✵✱ ❧t② ❂ ✷✮ ♣❧♦t✭❢✉♥❝t✐♦♥✭①✮ s✐♥✭♣✐ ✯ ①✮❫✷✱ ❢r♦♠ ❂ ✵✱ t♦ ❂ ✵✳✺✮ ❛❜❧✐♥❡✭❤ ❂ ✵✱ ❧t② ❂ ✷✮

④ ❋♦r ✵ ✔ ✦ ✔ ✶❂✷✱ t❤❡ ♣❤❛s❡ ❢✉♥❝t✐♦♥ ✐s ✙✦ ✙❂✷✳

✶✹

✎ ❈❡♥t❡r❡❞ ♠♦✈✐♥❣ ❛✈❡r❛❣❡✿ ②t ❂ ✶ ✷♠ ✰ ✶

♠

❳

r❂♠

①tr✿ ④ ❚❤❡ ❢r❡q✉❡♥❝② r❡s♣♦♥s❡ ❢✉♥❝t✐♦♥ ✐s ✶ ✷♠ ✰ ✶

✵ ❅

♠

❳

r❂♠

❡✷✙✐✦r

✶ ❆ ❂ ❡✷✙✐✦♠ ❡✷✙✐✦✭♠✰✶✮

✭✷♠ ✰ ✶✮

✏

✶ ❡✷✙✐✦

✑

❂ s✐♥❬✭✷♠ ✰ ✶✮✙✦❪ ✭✷♠ ✰ ✶✮ s✐♥✭✙✦✮✿

✶✺

✎ ●❛✐♥ ❢✉♥❝t✐♦♥✿

♣❛r✭♠❢r♦✇ ❂ ❝✭✷✱ ✶✮✮❀ ♣❧♦t✭❢✉♥❝t✐♦♥✭①✮ s✐♥✭✶✸ ✯ ♣✐ ✯ ①✮ ✴ ✭✶✸ ✯ s✐♥✭♣✐ ✯ ①✮✮✱ ❢r♦♠ ❂ ✵✱ t♦ ❂ ✵✳✺✱ ❝♦❧ ❂ ✧❜❧✉❡✧✮❀ ❛❜❧✐♥❡✭❤ ❂ ✵✱ ❧t② ❂ ✷✮ ♣❧♦t✭❢✉♥❝t✐♦♥✭①✮ ❛❜s✭s✐♥✭✶✸ ✯ ♣✐ ✯ ①✮ ✴ ✭✶✸ ✯ s✐♥✭♣✐ ✯ ①✮✮✮✱ ❢r♦♠ ❂ ✵✱ t♦ ❂ ✵✳✺✱ ❛❞❞ ❂ ❚❘❯❊✮❀ ❛❜❧✐♥❡✭❤ ❂ ✵✱ ❧t② ❂ ✷✮ ♣❧♦t✭❢✉♥❝t✐♦♥✭①✮ ✭s✐♥✭✶✸ ✯ ♣✐ ✯ ①✮ ✴ ✭✶✸ ✯ s✐♥✭♣✐ ✯ ①✮✮✮❫✷✱ ❢r♦♠ ❂ ✵✱ t♦ ❂ ✵✳✺✮❀ ❛❜❧✐♥❡✭❤ ❂ ✵✱ ❧t② ❂ ✷✮

✎ P❤❛s❡ ❢✉♥❝t✐♦♥ ❛❧t❡r♥❛t❡s ❜❡t✇❡❡♥ ✵ ❛♥❞ ✙✳

✶✻

❆❘▼❆ ❙♣❡❝tr✉♠ ✎ ❆❘▼❆✭♣❀ q✮ ♠♦❞❡❧✿ ✣✭❇✮①t ❂ ✒✭❇✮✇t ❂ ②t❀ s❛②✳ ✎ ②t ✐s ☞❧t❡r❡❞ ✈❡rs✐♦♥s ♦❢ ❜♦t❤ ①t ❛♥❞ ✇t✱ s♦ ❢②②✭✦✮ ❂

☞ ☞ ☞✣ ✏

❡✷✙✐✦✑☞

☞ ☞

✷ ❢①①✭✦✮

❂

☞ ☞ ☞✒ ✏

❡✷✙✐✦✑☞

☞ ☞

✷ ❢✇✇✭✦✮✿

✎ ❙♦❧✈❡ ❢♦r ❢①①✭✦✮✿ ❢①①✭✦✮ ❂ ❢✇✇✭✦✮

☞ ☞ ☞✒ ✏

❡✷✙✐✦✑☞

☞ ☞

✷

☞ ☞ ☞✣ ✏

❡✷✙✐✦

✑☞ ☞ ☞

✷ ❂ ✛✷ ✇

☞ ☞ ☞✒ ✏

❡✷✙✐✦✑☞

☞ ☞

✷

☞ ☞ ☞✣ ✏

❡✷✙✐✦

✑☞ ☞ ☞

✷✿

✶✼

Pr❡✲✇❤✐t❡♥✐♥❣ ✎ ❘❡❝❛❧❧✿ t❤❡ s♣❡❝tr✉♠ ♦❢ t❤❡ ♦✉t♣✉t ♦❢ ❛ ☞❧t❡r ✐s ❢②②✭✦✮ ❂ ❥❆✭✦✮❥✷❢①①✭✦✮✿ ✎ ■❢ ✇❡ ❝❤♦♦s❡ t❤❡ ☞❧t❡r s♦ t❤❛t ❥❆✭✦✮❥✷ ❂ ❦ ❢①①✭✦✮❀ t❤❡♥ ❢②②✭✦✮ ✐s ❝♦♥st❛♥t✳ ✎ ❚❤❛t ✐s✱ t❤❡ ♦✉t♣✉t ♦❢ t❤❡ ☞❧t❡r ✐s ✇❤✐t❡ ♥♦✐s❡✳ ■t ✐s ❝❛❧❧❡❞ ❛ ♣r❡✲✇❤✐t❡♥✐♥❣ ☞❧t❡r ❢♦r t❤❡ ✐♥♣✉t ❢①t❣✳

✶✽

✎ ❖♥❡ ✇❛② t♦ ☞♥❞ ❛ ♣r❡✲✇❤✐t❡♥✐♥❣ ☞❧t❡r ✐s t♦ ☞t ❛♥ ❆❘ ♠♦❞❡❧ t♦ t❤❡ ✐♥♣✉t ❞❛t❛✱ ❜❡❝❛✉s❡ t❤❡ ♠♦❞❡❧ ❡q✉❛t✐♦♥ ✣✭❇✮①t ❂ ✇t ❞❡☞♥❡s s✉❝❤ ❛ ☞❧t❡r✳ ✎ ❊✈❡♥ ❛♣♣r♦①✐♠❛t❡ ♣r❡✲✇❤✐t❡♥✐♥❣ ❝❛♥ ❜❡ ❤❡❧♣❢✉❧✱ ❜❡❝❛✉s❡ ❛ ♥❡❛r❧② ❝♦♥st❛♥t ❢②②✭✦✮ ✐s ❡❛s✐❡r t♦ ❡st✐♠❛t❡ t❤❛♥ ❛ ❤✐❣❤❧② ✈❛r✐❛❜❧❡ ❢①①✭✦✮✳ ✎ ❚❤❡ r❡s✉❧t✐♥❣ ❡st✐♠❛t❡ ♦❢ ❢①①✭✦✮ ✐s t❤❡♥ ❫ ❢②②✭✦✮ ❥❆✭✦✮❥✷✿

✶✾