P strt Prr r Pr - PDF document

❈▼P❯❚ ✸✷✺✿ ❆❜str❛❝t Pr♦❣r❛♠♠✐♥❣ ❉r✳ ❇✳ Pr✐❝❡ ❛♥❞ ❉r✳ ●✳ ●r❡✐♥❡r ✶✾t❤ ❖❝t♦❜❡r ✷✵✵✹ ❉r✳ ❇✳ Pr✐❝❡ ❛♥❞ ❉r✳ ●✳ ●r❡✐♥❡r ❈▼P❯❚ ✸✷✺✿ ❆❜str❛❝t Pr♦❣r❛♠♠✐♥❣ ✶ ❆❜str❛❝t Pr♦❣r❛♠♠✐♥❣ ◮ λ ❈❛❧❝✉❧✉s ❤❛s ♣r❡❝✐s❡ s❡♠❛♥t✐❝s✱ s✐♠♣❧❡ s②♥t❛①✱ s✐♠♣❧❡ ❡✈❛❧✉❛t✐♦♥ ◮ ■ts ❛❧s♦ ❡①tr❡♠❡❧② t❡❞✐♦✉s ◮ ❙t❛♥❞❛r❞ ✐❞✐♦♠s ❢♦r ♠❛♥② ❤✐❣❤✲❧❡✈❡❧ ❝♦♥tr♦❧ ❝♦♥str✉❝ts ◮ ❯s❡ ❛❜str❛❝t ✐❞✐♦♠s ✐♥ ♣❧❛❝❡ ♦❢ λ ✲❝❛❧❝✉❧✉s ◮ ❊❛s② t♦ r❡❛❞ ◮ ●✉❛r❛♥t❡❡❞ s❡♠❛♥t✐❝s ❛♥❞ s✐♠♣❧❡ ❡✈❛❧✉❛t✐♦♥ ◮ ❙✐♠♣❧❡ ♣❛rs❡r ❝♦♥✈❡rts ❛❜str❛❝t✐♦♥s t♦ ✐❞✐♦♠s ◮ λ ❝❛❧❝✉❧✉s s♦❧✈❡s ♣r♦❜❧❡♠ ❉r✳ ❇✳ Pr✐❝❡ ❛♥❞ ❉r✳ ●✳ ●r❡✐♥❡r ❈▼P❯❚ ✸✷✺✿ ❆❜str❛❝t Pr♦❣r❛♠♠✐♥❣ ✷

❆❜str❛❝t Pr♦❣r❛♠♠✐♥❣✿ ❉❛t❛t②♣❡s ◮ ◆✉♠❜❡rs✿ ✉s❡ ❈❤✉r❝❤✬s ✷ ❛r❣ ❢✉♥❝t✐♦♥ r❡♣r❡s❡♥t❛t✐♦♥ ◮ ■♥t❡❣❡rs✿ ♥ ≡ ✭ λ s ③ ⑤ s ❦ ③✮ ✇❤❡r❡ s ❦ ✐s ❛ str✐♥❣ ♦❢ ❦ s ✬s ◮ ❇♦♦❧❡❛♥ ✈❛❧✉❡s✿ ❚ ≡ ✭ λ ❝ ❞⑤ ❝✮ ❛♥❞ ❋ ≡ ✭ λ ❝ ❞ ⑤ ❞✮ ◮ ▲✐st ◮ ❈♦♥s ❝❡❧❧ ✭▼ ✳ ◆✮ ≡ ✭ λ ③ ⑤ ③ ♠ ♥✮ ◮ ▲✐st ✭❛ ❜ ❝ ✵✮✿ ✭ λ ③ ⑤ ③ ❛ ✭ λ ③ ⑤ ③ ❜ ✭ λ ③ ⑤ ③ ❝ ✵✮✮✮ ◮ ❙tr✐♥❣✿ tr❡❛t ❝❤❛rs ❛s ❛♥ ✐♥t❡❣❡r ✐♥ ❜❛s❡ ✷✺✻ ◮ ❊❛❝❤ ❝❤❛r r❡♣❧❛❝❡❞ ❜② ❆❙❈■■ ✈❛❧✉❡ ◮ ❍❊▲▲❖ ≡ ❍✯✷✺✻ ✹ ✰❊✯✷✺✻ ✸ ✰▲✯✷✺✻ ✷ ✰▲✯✷✺✻ ✶ ✰❖✯✷✺✻ ✵ ❉r✳ ❇✳ Pr✐❝❡ ❛♥❞ ❉r✳ ●✳ ●r❡✐♥❡r ❈▼P❯❚ ✸✷✺✿ ❆❜str❛❝t Pr♦❣r❛♠♠✐♥❣ ✸ ❆❜str❛❝t Pr♦❣r❛♠♠✐♥❣✿ ❋✉♥❝t✐♦♥s ◮ ❆ss✉♠❡ ♣r✐♠✐t✐✈❡ ♦♣❡r❛t♦rs ♦♥ ❞❛t❛t②♣❡s ❞❡✜♥❡❞ ◮ ▼❛t❤❡♠❛t✐❝❛❧ ♦♣s✿ ❛❞❞✱ s✉❜✱ ♠✉❧✱ ❞✐✈✱ ③❡r♦♣ ◮ ▲✐st ♦♣s✿ ❝♦♥s✱ ❝❛r✱ ❝❞r ◮ ❇♦♦❧❡❛♥ ♦♣❡r❛t♦rs✿ ❛♥❞✱ ♦r✱ ♥♦t ◮ ❆❧❧♦✇ st❛♥❞❛r❞ ♠❛t❤❡♠❛t✐❝❛❧ ♥♦t❛t✐♦♥s ◮ ■♥✜① ♥♦t❛t✐♦♥✿ ✶✰✷ ≡ ✭✰ ✶ ✷✮ ≡ ✭ λ ① ② ⑤ ✭ λ s ③ ⑤ ① s ✭② s ③✮ ✮ ✮ ✶ ✷ ◮ ❋✉♥❝t✐♦♥❛❧ ♥♦t❛t✐♦♥✿ ❢✭①✮ ≡ ✭ λ ② ⑤ . . . ✮ ① sq✉❛r❡✭✷✮ ≡ ✭ λ ② ⑤ ✭✯ ② ②✮✮ ✷ ≡ ✭ λ ② ⑤ � ♠✉❧t✐♣❧✐❝❛t✐♦♥✲✐❞✐♦♠ � ✮ ✷ ❉r✳ ❇✳ Pr✐❝❡ ❛♥❞ ❉r✳ ●✳ ●r❡✐♥❡r ❈▼P❯❚ ✸✷✺✿ ❆❜str❛❝t Pr♦❣r❛♠♠✐♥❣ ✹

❈♦♥❞✐t✐♦♥❛❧s ■❋ ①❁✵ ❚❍❊◆ ✲① ❊▲❙❊ ① ◮ λ ✲❝❛❧❝✉❧✉s tr❛♥s❧❛t✐♦♥❄ ✭ λ ①②③⑤①②③✮ ①❁✵ ✲① ① ◮ ◆❖❚❊✿ ♠✉st ❤❛✈❡ ❜♦t❤ ❚❍❊◆ ❛♥❞ ❊▲❙❊ ❝❧❛✉s❡s✳ ❲❤②❄ ◮ λ ✲❝❛❧❝✉❧✉s ♣r❡❞✐❝❛t❡s r❡s♦❧✈❡ t♦ ❚ ♦r ❋ ◮ ❚ ❝❤♦♦s❡s ✜rst ❛r❣✉♠❡♥t ◮ ❋ ❝❤♦♦s❡s s❡❝♦♥❞ ❛r❣✉♠❡♥t ◮ ▼✉st ❤❛✈❡ ❛♥ ❛r❣✉♠❡♥t ❢♦r ❡❛❝❤ ❝❛s❡ ♦r ♣r♦❣r❛♠ ✇✐❧❧ ❜❡❤❛✈❡ str❛♥❣❡❧② ❉r✳ ❇✳ Pr✐❝❡ ❛♥❞ ❉r✳ ●✳ ●r❡✐♥❡r ❈▼P❯❚ ✸✷✺✿ ❆❜str❛❝t Pr♦❣r❛♠♠✐♥❣ ✺ ❙♣❡❝✐❛❧ ❋♦r♠s✿ ▲❊❚ ❜② ❊①❛♠♣❧❡s ◮ ■♥ ❛❜str❛❝t ♣r♦❣r❛♠♠✐♥❣ ✇❡ ❞❡✜♥❡ ✏ ▲❊❚ ❆◆❉ ■◆ ✑ s♣❡❝✐❛❧ ❢♦r♠ ▲❊❚ ①❂✺ ■◆ ①✰✶ → ✻ ▲❊❚ ①❂✷ ■◆ ▲❊❚ ②❂✷ ■◆ ①✰② → ✹ ▲❊❚ ①❂✷ ❆◆❉ ②❂✷ ■◆ ①✰② ✹ → ▲❊❚ ❢✭①✮❂①✯① ❆◆❉ ②❂✸ ■◆ ▲❊❚ ①❂❢✭②✮ ■◆ ① → ✾ ❉r✳ ❇✳ Pr✐❝❡ ❛♥❞ ❉r✳ ●✳ ●r❡✐♥❡r ❈▼P❯❚ ✸✷✺✿ ❆❜str❛❝t Pr♦❣r❛♠♠✐♥❣ ✻

❙♣❡❝✐❛❧ ❋♦r♠s✿ ▲❊❚ ❙❡♠❛♥t✐❝s ■ ▲❊❚ ① ❂ � ❊ � ■◆ � ❇❖❉❨ � ◮ λ ❝❛❧❝✉❧✉s tr❛♥s❧❛t✐♦♥❄ ✭ λ ① ⑤ � ❇❖❉❨ � ✮ � ❊ � ▲❊❚ ① ❂ � ❊ � ■◆ ▲❊❚ ② ❂ � ❋ � ■◆ � ❇❖❉❨ � ◮ λ ❝❛❧❝✉❧✉s tr❛♥s❧❛t✐♦♥❄ ✭ λ ①⑤ ✭ λ ②⑤ � ❇❖❉❨ � ✮ � ❊ � ✮ � ❋ � ▲❊❚ ① ❂ � ❊ � ❆◆❉ ② ❂ � ❋ � ■◆ � ❇❖❉❨ � ◮ λ ❝❛❧❝✉❧✉s tr❛♥s❧❛t✐♦♥❄ P❛r❛❧❧❡❧ s✉❜st✐t✉t✐♦♥ ✭ λ ①②⑤ � ❇❖❉❨ � ✮ � ❊ �� ❋ � ❉r✳ ❇✳ Pr✐❝❡ ❛♥❞ ❉r✳ ●✳ ●r❡✐♥❡r ❈▼P❯❚ ✸✷✺✿ ❆❜str❛❝t Pr♦❣r❛♠♠✐♥❣ ✼ ❙♣❡❝✐❛❧ ❋♦r♠s✿ ▲❊❚ ❙❡♠❛♥t✐❝s ■■ ▲❊❚ ① ❂ � ❊ � ■◆ ▲❊❚ ① ❂ � ❋ � ■◆ � ❇❖❉❨ � ◮ λ ❝❛❧❝✉❧✉s tr❛♥s❧❛t✐♦♥❄ ✭ λ ①⑤ ✭ λ ①⑤ � ❇❖❉❨ � ✮ � ❊ � ✮ � ❋ � ▲❊❚ ① ❂ � ❊ � ▲❊❚ ① ❂ � ❋ � ❆◆❉ ② ❂ ① ■◆ � ❇❖❉❨ � ◮ λ ❝❛❧❝✉❧✉s tr❛♥s❧❛t✐♦♥❄ ✭ λ ①⑤ ✭ λ ①②⑤ � ❇❖❉❨ � ✮ � ❋ � ①✮ � ❊ � ▲❊❚ ❢✭①✮ ❂ � ❊ � ■◆ � ❇❖❉❨ � ◮ λ ❝❛❧❝✉❧✉s tr❛♥s❧❛t✐♦♥❄ ◮ ❈❧♦s❡r✿ ▲❊❚ ❢ ❂ ✭ λ ①⑤ � ❊ � ✮ ■◆ � ❇❖❉❨ � ✭ λ ❢⑤ � ❇❖❉❨ � ✮ ✭ λ ① ⑤ � ❊ � ✮ ◮ λ ✲❝❛❧❝✉❧✉s ❣✐✈❡s ♣r❡❝✐s❡ ♠❡❛♥✐♥❣ t♦ ❡❛❝❤ ❝❛s❡ ♦❢ ▲❊❚ ❉r✳ ❇✳ Pr✐❝❡ ❛♥❞ ❉r✳ ●✳ ●r❡✐♥❡r ❈▼P❯❚ ✸✷✺✿ ❆❜str❛❝t Pr♦❣r❛♠♠✐♥❣ ✽

❙♣❡❝✐❛❧ ❋♦r♠s✿ ▲❊❚ ❛♥❞ ❙❡❧❢✲r❡❢❡r❡♥❝❡ ▲❊❚ ❢✭♥✮ ❂ ■❋ ③❡r♦♣✭♥✮ ❚❍❊◆ ✶ ❊▲❙❊ ♥✯❢✭♥✲✶✮ ■◆ � ❇❖❉❨ � ◮ λ ❝❛❧❝✉❧✉s tr❛♥s❧❛t✐♦♥❄ ❆♣♣r♦①✐♠❛t❡❧②✿ ✭ λ ❢ ⑤ � ❇❖❉❨ � ✮ ✭ ✭ λ ①②③⑤①②③✮ ③❡r♦♣✭♥✮ ✶ ♥✯❢✭♥✲✶✮ ✮ ✭ λ ❢ ⑤ � ❇❖❉❨ � ✮ ✭ ✭ λ ①②③⑤①②③✮ ③❡r♦♣✭♥✮ ✶ ♥✯ ❢ ✭♥✲✶✮ ✮ ���� ↑ ◮ ❲❤❛t ❞♦❡s t❤❡ r❡❝✉rs✐✈❡ ❝❛❧❧ t♦ ❢ ♣♦✐♥t t♦❄ ■t ✐s ❛ ❢r❡❡ ✈❛r✐❛❜❧❡✦ ◮ ■s t❤✐s ❝♦rr❡❝t❄ ❨❡s✳ ❖t❤❡r✇✐s❡ ▲❊❚ ①❂✷ ■◆ ▲❊❚ ①❂✷✯① ■◆ � ❇❖❉❨ � ✇♦✉❧❞ ❢❛✐❧✿ ✭ λ ①⑤ ✭ λ ①⑤ � ❇❖❉❨ � ✮ ✷✯①✮ ✷ ❉r✳ ❇✳ Pr✐❝❡ ❛♥❞ ❉r✳ ●✳ ●r❡✐♥❡r ❈▼P❯❚ ✸✷✺✿ ❆❜str❛❝t Pr♦❣r❛♠♠✐♥❣ ✾ ❙♣❡❝✐❛❧ ❋♦r♠s✿ ▲❊❚❘❊❈ ▲❊❚❘❊❈ ❢✭♥✮ ❂ ■❋ ③❡r♦♣✭♥✮ ❚❍❊◆ ✶ ❊▲❙❊ ♥✯❢✭♥✲✶✮ ■◆ � ❇❖❉❨ � ◮ ❙♦♠❡t✐♠❡s ✇❡ ✇❛♥t ✈❛rs ✐♥ ❞❡✜♥✐t✐♦♥ t♦ r❡❢❡r t♦ t❤❡✐r ❧❛❜❡❧s ◮ ❉✐✛❡r❡♥t s❡♠❛♥t✐❝s t❤❛♥ ▲❊❚ ✖ ♥❡❡❞s ❞✐✛❡r❡♥t ♥❛♠❡ ◮ λ ✲❝❛❧❝✉❧✉s tr❛♥s❧❛t✐♦♥❄❯s❡ ❝♦♠❜✐♥❛t♦r ♦♣❡r❛t♦r ❨ ✭ λ ❢⑤ � ❇❖❉❨ � ✮ ✭❨ ✭ λ ❢⑤ ✭ λ ♥⑤ ③❡r♦♣✭♥✮ ✶ ♥✯❢✭♥✲✶✮✮ ✮✮ ✭ λ ❢ ⑤ � ❇❖❉❨ � ✮ ✭❨ ✭ λ ❢⑤ ✭ λ ♥⑤ ③❡r♦♣✭♥✮ ✶ ♥✯ ❢ ✭♥✲✶✮✮ ✮✮ ���� ���� ↑ ↑ ◮ ❆r❡ ✷ ❢✬s t❤❡ s❛♠❡❄ ◆♦✳ ❢ ✐♥ ❢✉♥❝t✐♦♥ ❞❡❢ ✐s ♥♦t ❢r❡❡✦ ❉r✳ ❇✳ Pr✐❝❡ ❛♥❞ ❉r✳ ●✳ ●r❡✐♥❡r ❈▼P❯❚ ✸✷✺✿ ❆❜str❛❝t Pr♦❣r❛♠♠✐♥❣ ✶✵