t r t
play

t rt r r - PowerPoint PPT Presentation

tr t ts s t rt r r sr


  1. ■♥tr♦ ●❙ ❇❛t❝❤ ❆♣♣❧✐❝❛t✐♦♥s ❈♦♥❝❧✉s✐♦♥ ❇❛t❝❤ ●r♦t❤✲❙❛❤❛✐ ❖❧✐✈✐❡r ❇❧❛③② ●❡♦r❣ ❋✉❝❤s❜❛✉❡r ▼❛❧✐❦❛ ■③❛❜❛❝❤è♥❡ ❆♠❛♥❞✐♥❡ ❏❛♠❜❡rt ❍❡r✈é ❙✐❜❡rt ❉❛♠✐❡♥ ❱❡r❣♥❛✉❞ ❊◆❙ ✲ P❛r✐s ✲ ❋r❛♥❝❡ ❆❈◆❙ ✷✵✶✵ ✶ ✴ ✷✷

  2. ●r♦t❤ ❙❛❤❛✐ Pr♦♦❢ ❙②st❡♠ ✷ ❇❛t❝❤✐♥❣ ❚❡❝❤♥✐q✉❡ ✸ ❆♣♣❧✐❝❛t✐♦♥s ✹ ■♥tr♦ ●❙ ❇❛t❝❤ ❆♣♣❧✐❝❛t✐♦♥s ❈♦♥❝❧✉s✐♦♥ ■♥tr♦❞✉❝t✐♦♥ ✶ ✷ ✴ ✷✷

  3. ❇❛t❝❤✐♥❣ ❚❡❝❤♥✐q✉❡ ✸ ❆♣♣❧✐❝❛t✐♦♥s ✹ ■♥tr♦ ●❙ ❇❛t❝❤ ❆♣♣❧✐❝❛t✐♦♥s ❈♦♥❝❧✉s✐♦♥ ■♥tr♦❞✉❝t✐♦♥ ✶ ●r♦t❤ ❙❛❤❛✐ Pr♦♦❢ ❙②st❡♠ ✷ ✷ ✴ ✷✷

  4. ❆♣♣❧✐❝❛t✐♦♥s ✹ ■♥tr♦ ●❙ ❇❛t❝❤ ❆♣♣❧✐❝❛t✐♦♥s ❈♦♥❝❧✉s✐♦♥ ■♥tr♦❞✉❝t✐♦♥ ✶ ●r♦t❤ ❙❛❤❛✐ Pr♦♦❢ ❙②st❡♠ ✷ ❇❛t❝❤✐♥❣ ❚❡❝❤♥✐q✉❡ ✸ ✷ ✴ ✷✷

  5. ■♥tr♦ ●❙ ❇❛t❝❤ ❆♣♣❧✐❝❛t✐♦♥s ❈♦♥❝❧✉s✐♦♥ ■♥tr♦❞✉❝t✐♦♥ ✶ ●r♦t❤ ❙❛❤❛✐ Pr♦♦❢ ❙②st❡♠ ✷ ❇❛t❝❤✐♥❣ ❚❡❝❤♥✐q✉❡ ✸ ❆♣♣❧✐❝❛t✐♦♥s ✹ ✷ ✴ ✷✷

  6. ■♥tr♦ ●❙ ❇❛t❝❤ ❆♣♣❧✐❝❛t✐♦♥s ❈♦♥❝❧✉s✐♦♥ ◆■❩❑ ◆■❲■ ❇✐❧✐♥❡❛r ❙❳❉❍ ✴ ❉▲■◆ ■♥tr♦❞✉❝t✐♦♥ ✶ ◆♦♥ ■♥t❡r❛❝t✐✈❡ ❩❡r♦ ❑♥♦✇❧❡❞❣❡ Pr♦♦❢ ◆♦♥ ■♥t❡r❛❝t✐✈❡ ❲✐t♥❡ss ■♥❞✐st✐♥❣✉✐s❤❛❜❧❡ Pr♦♦❢ ❇✐❧✐♥❡❛r ●r♦✉♣s ❙t❛♥❞❛r❞ ❆ss✉♠♣t✐♦♥s ●r♦t❤ ❙❛❤❛✐ Pr♦♦❢ ❙②st❡♠ ✷ ❇❛t❝❤✐♥❣ ❚❡❝❤♥✐q✉❡ ✸ ❆♣♣❧✐❝❛t✐♦♥s ✹ ✸ ✴ ✷✷

  7. � ■♥tr♦ ●❙ ❇❛t❝❤ ❆♣♣❧✐❝❛t✐♦♥s ❈♦♥❝❧✉s✐♦♥ ◆■❩❑ ◆■❲■ ❇✐❧✐♥❡❛r ❙❳❉❍ ✴ ❉▲■◆ ❉❡✜♥✐t✐♦♥ ❆ ◆■❩❑ ♣r♦♦❢ ✐s ❛ ♥♦♥✲✐♥t❡r❛❝t✐✈❡ ♣r♦t♦❝♦❧ ❧❡tt✐♥❣ ♦♥❡ ♣❛rt② ♣r♦✈✐♥❣ t♦ ❛♥♦t❤❡r t❤❛t ❛ st❛t❡♠❡♥t ✐s tr✉❡✱ ✇✐t❤♦✉t r❡✈❡❛❧✐♥❣ ❛♥②t❤✐♥❣ ♦t❤❡r t❤❛♥ t❤❡ ✈❡r❛❝✐t② ♦❢ t❤❡ st❛t❡♠❡♥t✳ ❆❧✐❝❡ ♣♦ss❡ss❡s ❛ s❡❝r❡t s ∈ L ✇✐t❤ ❛ ✇✐t♥❡ss θ s ✳ ■ ❦♥♦✇ ❛ s❡❝r❡t ① ∈ L ❍❡r❡ ✐s t❤❡ ♣r♦♦❢ Π( θ s ) ❇♦❜ ✐s ♥♦✇ ❝♦♥✈✐♥❝❡❞ ❆❧✐❝❡ ♣♦ss❡ss❡s ❛ s❡❝r❡t ① ∈ L ✳ ✹ ✴ ✷✷

  8. � ■♥tr♦ ●❙ ❇❛t❝❤ ❆♣♣❧✐❝❛t✐♦♥s ❈♦♥❝❧✉s✐♦♥ ◆■❩❑ ◆■❲■ ❇✐❧✐♥❡❛r ❙❳❉❍ ✴ ❉▲■◆ ❉❡✜♥✐t✐♦♥ ❆ ◆■❲■ ♣r♦♦❢ ✐s ❛ ♥♦♥✲✐♥t❡r❛❝t✐✈❡ ♣r♦t♦❝♦❧ ✇❤❡r❡ t❤❡ ✈❡r✐✜❡r ❝❛♥✬t ❞✐st✐♥❣✉✐s❤ t✇♦ ✐♥st❛♥❝❡s ♦❢ ❞✐✛❡r❡♥t s❡❝r❡ts✳ ❆❧✐❝❡ ♣♦ss❡ss❡s s❡❝r❡t ❛ s❡❝r❡t s ∈ L ✇✐t❤ ❛ ✇✐t♥❡ss θ s ∈ ❚ = { θ ✶ , ..., θ ♥ } ✳ ❇♦❜ ❦♥♦✇s ❚ ✳ ■ ❦♥♦✇ ❛ s❡❝r❡t ① ∈ L ❍❡r❡ ✐s t❤❡ ♣r♦♦❢ Π ❇♦❜ ❝❛♥✬t ❞❡❝✐❞❡ ✇❤✐❝❤ s❡❝r❡t ✐s ❦♥♦✇♥ ❜② ❆❧✐❝❡✱ ❞❡s♣✐t❡ ❤✐s ❦♥♦✇❧❡❞❣❡ ♦❢ ❚ ✳ ✺ ✴ ✷✷

  9. ■♥tr♦ ●❙ ❇❛t❝❤ ❆♣♣❧✐❝❛t✐♦♥s ❈♦♥❝❧✉s✐♦♥ ◆■❩❑ ◆■❲■ ❇✐❧✐♥❡❛r ❙❳❉❍ ✴ ❉▲■◆ ❇✐❧✐♥❡❛r ●r♦✉♣s G ✶ , G ✷ , G ❚ ✜♥✐t❡ ❝②❝❧✐❝ ❣r♦✉♣s ♦❢ ♦r❞❡r ♣ ❣ ✶ ❣❡♥❡r❛t❡s G ✶ ✱ ❣ ✷ ❣❡♥❡r❛t❡s G ✷ ❡ : G ✶ × G ✷ → G ❚ ❡ ( ❣ ✶ , ❣ ✷ ) ❣❡♥❡r❛t❡s G ❚ ❡ ( ❣ ❛ ✶ , ❣ ❜ ✷ ) = ❡ ( ❣ ✶ , ❣ ✷ ) ❛❜ ✻ ✴ ✷✷

  10. ■♥tr♦ ●❙ ❇❛t❝❤ ❆♣♣❧✐❝❛t✐♦♥s ❈♦♥❝❧✉s✐♦♥ ◆■❩❑ ◆■❲■ ❇✐❧✐♥❡❛r ❙❳❉❍ ✴ ❉▲■◆ ❙❳❉❍✴ ❉▲■◆ ❛ss✉♠♣t✐♦♥s ❙❳❉❍ ●✐✈❡♥ ( ♣ , G ✶ , G ✷ , G ❚ , ❡ , ❣ ✶ , ❣ ✷ ) ✱ ( ✉ , ✉ ① , ✉ ② , ✉ ③ ) ❛♥❞ ( ✉ , ✉ ① , ✉ ② , ✉ ① · ② ) ❛r❡ ❝♦♠♣✉t❛t✐♦♥❛❧❧② ✐♥❞✐st✐♥❣✉✐s❤❛❜❧❡✳✭❉❉❍ ✐s ❤❛r❞ ✐♥ ❜♦t❤ ❣r♦✉♣✮ ❉▲■◆ ●✐✈❡♥ ( ♣ , G , G ❚ , ❡ , ❣ ) ✱ ( ✉ , ✈ , ✇ , ✉ ❛ , ✈ ❜ , ✇ ❝ ) ❛♥❞ ( ✉ , ✈ , ✇ , ✉ ❛ , ✈ ❜ , ✇ ❛ + ❜ ) ❛r❡ ❝♦♠♣✉t❛t✐♦♥❛❧❧② ✐♥❞✐st✐♥❣✉✐s❤❛❜❧❡✳ ✼ ✴ ✷✷

  11. ■♥tr♦ ●❙ ❇❛t❝❤ ❆♣♣❧✐❝❛t✐♦♥s ❈♦♥❝❧✉s✐♦♥ ◆♦t❛t✐♦♥ ❚②♣❡s ♦❢ ❊q✉❛t✐♦♥s Pr♦♦❢ ❡❧❡♠❡♥ts ■♥tr♦❞✉❝t✐♦♥ ✶ ●r♦t❤ ❙❛❤❛✐ Pr♦♦❢ ❙②st❡♠ ✷ ◆♦t❛t✐♦♥ ❚②♣❡s ♦❢ ❊q✉❛t✐♦♥s Pr♦♦❢ ❡❧❡♠❡♥ts ❇❛t❝❤✐♥❣ ❚❡❝❤♥✐q✉❡ ✸ ❆♣♣❧✐❝❛t✐♦♥s ✹ ✽ ✴ ✷✷

  12. ■♥tr♦ ●❙ ❇❛t❝❤ ❆♣♣❧✐❝❛t✐♦♥s ❈♦♥❝❧✉s✐♦♥ ◆♦t❛t✐♦♥ ❚②♣❡s ♦❢ ❊q✉❛t✐♦♥s Pr♦♦❢ ❡❧❡♠❡♥ts ❛ ,� ◆ ❛♥❞ � A , � ❜ ∈ Z ♥ B ∈ G ♥ ✳ � ❛ ,� ❜ � := � ♥ ❛ , � B� := � ♥ ✐ = ✶ B ❛ ✐ � � A , � B� := � ♥ � � ✐ = ✶ ❛ ✐ · ❜ ✐ � � ✐ = ✶ ❡ ( A ✐ , B ✐ ) ✐ ✭❙❳❉❍✮ • : G ♥ × ❦ × G ♥ × ❦ → G ❦ × ❦ ✶ ✷ ❚ ❝ • � ❞ := ( � ♥ � ℓ = ✶ ❡ ( ❝ ℓ, ✐ , ❞ ℓ, ❥ )) ✶ ≤ ✐ , ❥ ≤ ❦ s • : G ♥ × ✸ × G ♥ × ✸ → G ✸ × ✸ ✭❉▲■◆✮ ❚ s • � �� ♥ ℓ = ✶ ❡ ( ❝ ℓ, ✐ , ❞ ℓ, ❥ ) ✶ / ✷ ❡ ( ❝ ℓ, ❥ , ❞ ℓ, ✐ ) ✶ / ✷ � � ❞ := ❝ ✶ ≤ ✐ , ❥ ≤ ✸ ✾ ✴ ✷✷

  13. ■♥tr♦ ●❙ ❇❛t❝❤ ❆♣♣❧✐❝❛t✐♦♥s ❈♦♥❝❧✉s✐♦♥ ◆♦t❛t✐♦♥ ❚②♣❡s ♦❢ ❊q✉❛t✐♦♥s Pr♦♦❢ ❡❧❡♠❡♥ts P❛✐r✐♥❣✲♣r♦❞✉❝t ❡q✉❛t✐♦♥✿ � � A , � Y� · � � X , � B� · � � X , Γ � Y� = t ❚ ▼✉❧t✐✲s❝❛❧❛r ♠✉❧t✐♣❧✐❝❛t✐♦♥ ❡q✉❛t✐♦♥ ✭✐♥ G ✶ ✮✿ ① , � ❛ , � ① , Γ � � � B� · � � Y� · � � Y� = ❚ ◗✉❛❞r❛t✐❝ ❡q✉❛t✐♦♥ ✐♥ Z ◆ ① ,� � � ❛ ,� ② � + � � ❜ � + � � ① , Γ � ② � = t ✶✵ ✴ ✷✷

  14. ■♥tr♦ ●❙ ❇❛t❝❤ ❆♣♣❧✐❝❛t✐♦♥s ❈♦♥❝❧✉s✐♦♥ ◆♦t❛t✐♦♥ ❚②♣❡s ♦❢ ❊q✉❛t✐♦♥s Pr♦♦❢ ❡❧❡♠❡♥ts ✭❉▲■◆✮ P❛✐r✐♥❣ Pr♦❞✉❝t ❊q✉❛t✐♦♥✿ � � A , � Y� · � � Y , Γ � Y� = t ❚ ❞ , φ ) ∈ G ♥ × ✸ × G ✸ × ✸ ✐s t❤❡ ❚❤❡ ✈❡r✐✜❝❛t✐♦♥ r❡❧❛t✐♦♥ ♦❢ ❛ ♣r♦♦❢ ( � ❢♦❧❧♦✇✐♥❣✿ � s � � s � � s � ι ( � • � � • Γ � • � A ) ❞ ⊙ ❞ ❞ = ι ❚ ( t ❚ ) ⊙ � ✉ φ ✶✶ ✴ ✷✷

  15. ■♥tr♦ ●❙ ❇❛t❝❤ ❆♣♣❧✐❝❛t✐♦♥s ❈♦♥❝❧✉s✐♦♥ ❙♠❛❧❧ ❊①♣ ❋♦r ❛ ❢❡✇ ♣❛✐r✐♥❣s ❧❡ss ❖✉r ❘❡s✉❧t ■♥tr♦❞✉❝t✐♦♥ ✶ ●r♦t❤ ❙❛❤❛✐ Pr♦♦❢ ❙②st❡♠ ✷ ❇❛t❝❤✐♥❣ ❚❡❝❤♥✐q✉❡ ✸ ❙♠❛❧❧ ❊①♣♦♥❡♥ts ❚❡st ❋♦r ❛ ❢❡✇ ♣❛✐r✐♥❣s ❧❡ss ❈♦♠♣❧✐❝❛t✐♦♥ ❖✉r ❘❡s✉❧t ❆♣♣❧✐❝❛t✐♦♥s ✹ ✶✷ ✴ ✷✷

  16. ■♥tr♦ ●❙ ❇❛t❝❤ ❆♣♣❧✐❝❛t✐♦♥s ❈♦♥❝❧✉s✐♦♥ ❙♠❛❧❧ ❊①♣ ❋♦r ❛ ❢❡✇ ♣❛✐r✐♥❣s ❧❡ss ❖✉r ❘❡s✉❧t ❙♠❛❧❧ ❊①♣♦♥❡♥ts ❚❡st✱ ❇●❘ ❊❈✬✾✽ � ❦ ✶ ✐ = ✶ ❡ ( ❢ ✐ , ✶ , ❤ ✐ , ✶ ) ❝ ✐ , ✶ = ❆ ✶   . . . � ❦ ♥ ✐ = ✶ ❡ ( ❢ ✐ , ♥ , ❤ ✐ , ♥ ) ❝ ✐ , ♥ = ❆ ♥  ✶✸ ✴ ✷✷

Download Presentation
Download Policy: The content available on the website is offered to you 'AS IS' for your personal information and use only. It cannot be commercialized, licensed, or distributed on other websites without prior consent from the author. To download a presentation, simply click this link. If you encounter any difficulties during the download process, it's possible that the publisher has removed the file from their server.

Recommend


More recommend