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  1. ■♥tr♦❞✉❝t✐♦♥ t♦ q✉❛♥❞❧❡s ❈❡♥tr❛❧ ❡①t❡♥s✐♦♥ ✐♥ t❤❡ ❡①❛❝t ❝♦♥t❡①t ❈♦✈❡r✐♥❣ t❤❡♦r② ♦❢ q✉❛♥❞❧❡s ❆ ●❛❧♦✐s✲t❤❡♦r❡t✐❝ ❛♣♣r♦❛❝❤ t♦ t❤❡ ❝♦✈❡r✐♥❣ t❤❡♦r② ♦❢ q✉❛♥❞❧❡s ❱❛❧ér✐❛♥ ❊✈❡♥ ❯❈▲ ✷✺t❤ ❏❛♥✉❛r② ✷✵✶✹✱ ❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❈♦✐♠❜r❛ ✶✴✶✾

  2. ■♥tr♦❞✉❝t✐♦♥ t♦ q✉❛♥❞❧❡s ❈❡♥tr❛❧ ❡①t❡♥s✐♦♥ ✐♥ t❤❡ ❡①❛❝t ❝♦♥t❡①t ❈♦✈❡r✐♥❣ t❤❡♦r② ♦❢ q✉❛♥❞❧❡s ■♥tr♦❞✉❝t✐♦♥ t♦ q✉❛♥❞❧❡s ✶ ❈❡♥tr❛❧ ❡①t❡♥s✐♦♥ ✐♥ t❤❡ ❡①❛❝t ❝♦♥t❡①t ✷ ❈♦✈❡r✐♥❣ t❤❡♦r② ♦❢ q✉❛♥❞❧❡s ✸ ✷✴✶✾

  3. ■♥tr♦❞✉❝t✐♦♥ t♦ q✉❛♥❞❧❡s ❈❡♥tr❛❧ ❡①t❡♥s✐♦♥ ✐♥ t❤❡ ❡①❛❝t ❝♦♥t❡①t ❈♦✈❡r✐♥❣ t❤❡♦r② ♦❢ q✉❛♥❞❧❡s ■♥tr♦❞✉❝t✐♦♥ t♦ q✉❛♥❞❧❡s ✶ ❈❡♥tr❛❧ ❡①t❡♥s✐♦♥ ✐♥ t❤❡ ❡①❛❝t ❝♦♥t❡①t ✷ ❈♦✈❡r✐♥❣ t❤❡♦r② ♦❢ q✉❛♥❞❧❡s ✸ ✸✴✶✾

  4. ✶ ❛ ❛ ❛ ❛ ❛♥❞ ❛ ❛ ❢♦r ❛❧❧ ❛ ❆ ❀ ✶ ❜ ✶ ❜ ❛ ❜ ❛ ❛♥❞ ❛ ❜ ❛ ❢♦r ❛❧❧ ❛ ✱ ❜ ❆ ❀ ❛ ❜ ❝ ❛ ❝ ❜ ❝ ❛♥❞ ✶ ❜ ✶ ❝ ✶ ❝ ✶ ❜ ✶ ❝ ❢♦r ❛❧❧ ❛ ✱ ❜ ✱ ❝ ❛ ❛ ❆ ✳ ❉❡♥♦t❡ ◗♥❞ t❤❡ ❝♦rr❡s♣♦♥❞✐♥❣ ❝❛t❡❣♦r②✳ ■t ✐s ❛ ✈❛r✐❡t② ♦❢ ✉♥✐✈❡rs❛❧ ❛❧❣❡❜r❛s✳ ■♥tr♦❞✉❝t✐♦♥ t♦ q✉❛♥❞❧❡s ❈❡♥tr❛❧ ❡①t❡♥s✐♦♥ ✐♥ t❤❡ ❡①❛❝t ❝♦♥t❡①t ❈♦✈❡r✐♥❣ t❤❡♦r② ♦❢ q✉❛♥❞❧❡s ❉❡✜♥✐t✐♦♥ ✭❉✳ ❏♦②❝❡✱ ❙✳ ▼❛t✈❡❡✈✮ ❆ q✉❛♥❞❧❡ ✐s ❛ s❡t ❆ ✇✐t❤ t✇♦ ❜✐♥❛r② ♦♣❡r❛t✐♦♥s ⊳ ❛♥❞ ⊳ − ✶ s❛t✐s❢②✐♥❣ t❤❡ ❢♦❧❧♦✇✐♥❣ ✐❞❡♥t✐t✐❡s ✿ ✹✴✶✾

  5. ✶ ❜ ✶ ❜ ❛ ❜ ❛ ❛♥❞ ❛ ❜ ❛ ❢♦r ❛❧❧ ❛ ✱ ❜ ❆ ❀ ❛ ❜ ❝ ❛ ❝ ❜ ❝ ❛♥❞ ✶ ❜ ✶ ❝ ✶ ❝ ✶ ❜ ✶ ❝ ❢♦r ❛❧❧ ❛ ✱ ❜ ✱ ❝ ❛ ❛ ❆ ✳ ❉❡♥♦t❡ ◗♥❞ t❤❡ ❝♦rr❡s♣♦♥❞✐♥❣ ❝❛t❡❣♦r②✳ ■t ✐s ❛ ✈❛r✐❡t② ♦❢ ✉♥✐✈❡rs❛❧ ❛❧❣❡❜r❛s✳ ■♥tr♦❞✉❝t✐♦♥ t♦ q✉❛♥❞❧❡s ❈❡♥tr❛❧ ❡①t❡♥s✐♦♥ ✐♥ t❤❡ ❡①❛❝t ❝♦♥t❡①t ❈♦✈❡r✐♥❣ t❤❡♦r② ♦❢ q✉❛♥❞❧❡s ❉❡✜♥✐t✐♦♥ ✭❉✳ ❏♦②❝❡✱ ❙✳ ▼❛t✈❡❡✈✮ ❆ q✉❛♥❞❧❡ ✐s ❛ s❡t ❆ ✇✐t❤ t✇♦ ❜✐♥❛r② ♦♣❡r❛t✐♦♥s ⊳ ❛♥❞ ⊳ − ✶ s❛t✐s❢②✐♥❣ t❤❡ ❢♦❧❧♦✇✐♥❣ ✐❞❡♥t✐t✐❡s ✿ ❛ ⊳ ❛ = ❛ ❛♥❞ ❛ ⊳ − ✶ ❛ = ❛ ❢♦r ❛❧❧ ❛ ∈ ❆ ❀ ✹✴✶✾

  6. ❛ ❜ ❝ ❛ ❝ ❜ ❝ ❛♥❞ ✶ ❜ ✶ ❝ ✶ ❝ ✶ ❜ ✶ ❝ ❢♦r ❛❧❧ ❛ ✱ ❜ ✱ ❝ ❛ ❛ ❆ ✳ ❉❡♥♦t❡ ◗♥❞ t❤❡ ❝♦rr❡s♣♦♥❞✐♥❣ ❝❛t❡❣♦r②✳ ■t ✐s ❛ ✈❛r✐❡t② ♦❢ ✉♥✐✈❡rs❛❧ ❛❧❣❡❜r❛s✳ ■♥tr♦❞✉❝t✐♦♥ t♦ q✉❛♥❞❧❡s ❈❡♥tr❛❧ ❡①t❡♥s✐♦♥ ✐♥ t❤❡ ❡①❛❝t ❝♦♥t❡①t ❈♦✈❡r✐♥❣ t❤❡♦r② ♦❢ q✉❛♥❞❧❡s ❉❡✜♥✐t✐♦♥ ✭❉✳ ❏♦②❝❡✱ ❙✳ ▼❛t✈❡❡✈✮ ❆ q✉❛♥❞❧❡ ✐s ❛ s❡t ❆ ✇✐t❤ t✇♦ ❜✐♥❛r② ♦♣❡r❛t✐♦♥s ⊳ ❛♥❞ ⊳ − ✶ s❛t✐s❢②✐♥❣ t❤❡ ❢♦❧❧♦✇✐♥❣ ✐❞❡♥t✐t✐❡s ✿ ❛ ⊳ ❛ = ❛ ❛♥❞ ❛ ⊳ − ✶ ❛ = ❛ ❢♦r ❛❧❧ ❛ ∈ ❆ ❀ ( ❛ ⊳ ❜ ) ⊳ − ✶ ❜ = ❛ ❛♥❞ ( ❛ ⊳ − ✶ ❜ ) ⊳ ❜ = ❛ ❢♦r ❛❧❧ ❛ ✱ ❜ ∈ ❆ ❀ ✹✴✶✾

  7. ❉❡♥♦t❡ ◗♥❞ t❤❡ ❝♦rr❡s♣♦♥❞✐♥❣ ❝❛t❡❣♦r②✳ ■t ✐s ❛ ✈❛r✐❡t② ♦❢ ✉♥✐✈❡rs❛❧ ❛❧❣❡❜r❛s✳ ■♥tr♦❞✉❝t✐♦♥ t♦ q✉❛♥❞❧❡s ❈❡♥tr❛❧ ❡①t❡♥s✐♦♥ ✐♥ t❤❡ ❡①❛❝t ❝♦♥t❡①t ❈♦✈❡r✐♥❣ t❤❡♦r② ♦❢ q✉❛♥❞❧❡s ❉❡✜♥✐t✐♦♥ ✭❉✳ ❏♦②❝❡✱ ❙✳ ▼❛t✈❡❡✈✮ ❆ q✉❛♥❞❧❡ ✐s ❛ s❡t ❆ ✇✐t❤ t✇♦ ❜✐♥❛r② ♦♣❡r❛t✐♦♥s ⊳ ❛♥❞ ⊳ − ✶ s❛t✐s❢②✐♥❣ t❤❡ ❢♦❧❧♦✇✐♥❣ ✐❞❡♥t✐t✐❡s ✿ ❛ ⊳ ❛ = ❛ ❛♥❞ ❛ ⊳ − ✶ ❛ = ❛ ❢♦r ❛❧❧ ❛ ∈ ❆ ❀ ( ❛ ⊳ ❜ ) ⊳ − ✶ ❜ = ❛ ❛♥❞ ( ❛ ⊳ − ✶ ❜ ) ⊳ ❜ = ❛ ❢♦r ❛❧❧ ❛ ✱ ❜ ∈ ❆ ❀ ( ❛ ⊳ ❜ ) ⊳ ❝ = ( ❛ ⊳ ❝ ) ⊳ ( ❜ ⊳ ❝ ) ❛♥❞ ( ❛ ⊳ − ✶ ❜ ) ⊳ − ✶ ❝ = ( ❛ ⊳ − ✶ ❝ ) ⊳ − ✶ ( ❜ ⊳ − ✶ ❝ ) ❢♦r ❛❧❧ ❛ ✱ ❜ ✱ ❝ ∈ ❆ ✳ ✹✴✶✾

  8. ■♥tr♦❞✉❝t✐♦♥ t♦ q✉❛♥❞❧❡s ❈❡♥tr❛❧ ❡①t❡♥s✐♦♥ ✐♥ t❤❡ ❡①❛❝t ❝♦♥t❡①t ❈♦✈❡r✐♥❣ t❤❡♦r② ♦❢ q✉❛♥❞❧❡s ❉❡✜♥✐t✐♦♥ ✭❉✳ ❏♦②❝❡✱ ❙✳ ▼❛t✈❡❡✈✮ ❆ q✉❛♥❞❧❡ ✐s ❛ s❡t ❆ ✇✐t❤ t✇♦ ❜✐♥❛r② ♦♣❡r❛t✐♦♥s ⊳ ❛♥❞ ⊳ − ✶ s❛t✐s❢②✐♥❣ t❤❡ ❢♦❧❧♦✇✐♥❣ ✐❞❡♥t✐t✐❡s ✿ ❛ ⊳ ❛ = ❛ ❛♥❞ ❛ ⊳ − ✶ ❛ = ❛ ❢♦r ❛❧❧ ❛ ∈ ❆ ❀ ( ❛ ⊳ ❜ ) ⊳ − ✶ ❜ = ❛ ❛♥❞ ( ❛ ⊳ − ✶ ❜ ) ⊳ ❜ = ❛ ❢♦r ❛❧❧ ❛ ✱ ❜ ∈ ❆ ❀ ( ❛ ⊳ ❜ ) ⊳ ❝ = ( ❛ ⊳ ❝ ) ⊳ ( ❜ ⊳ ❝ ) ❛♥❞ ( ❛ ⊳ − ✶ ❜ ) ⊳ − ✶ ❝ = ( ❛ ⊳ − ✶ ❝ ) ⊳ − ✶ ( ❜ ⊳ − ✶ ❝ ) ❢♦r ❛❧❧ ❛ ✱ ❜ ✱ ❝ ∈ ❆ ✳ ❉❡♥♦t❡ ◗♥❞ t❤❡ ❝♦rr❡s♣♦♥❞✐♥❣ ❝❛t❡❣♦r②✳ ■t ✐s ❛ ✈❛r✐❡t② ♦❢ ✉♥✐✈❡rs❛❧ ❛❧❣❡❜r❛s✳ ✹✴✶✾

  9. ■t ❞❡✜♥❡s ❛ q✉❛♥❞❧❡ ♥❛♠❡❞ tr✐✈✐❛❧ q✉❛♥❞❧❡ ✳ ❚❤❡ ❝♦rr❡s♣♦♥❞✐♥❣ ❝❛t❡❣♦r② ✐s ❞❡♥♦t❡❞ ◗♥❞ ✳ ✶ ❤ ✶ ❣❤ ❛♥❞ ❣ ✶ ▲❡t ● ❜❡ ❛ ❣r♦✉♣✱ ❞❡✜♥❡ ❣ ❤ ❤ ❤❣❤ ❢♦r ❛❧❧ ❣ ● ✳ ■t ❞❡✜♥❡s t❤❡ ❝♦♥❥✉❣❛t✐♦♥ q✉❛♥❞❧❡ ✳ ❤ ✶ ❤ ✳ ❚❤✐s ❞❡✜♥❡s t❤❡ ❝♦r❡ ▲❡t ● ❜❡ ❛ ❣r♦✉♣✱ ❞❡✜♥❡ ❣ ❤ ❤❣ q✉❛♥❞❧❡ ✳ ■♥tr♦❞✉❝t✐♦♥ t♦ q✉❛♥❞❧❡s ❈❡♥tr❛❧ ❡①t❡♥s✐♦♥ ✐♥ t❤❡ ❡①❛❝t ❝♦♥t❡①t ❈♦✈❡r✐♥❣ t❤❡♦r② ♦❢ q✉❛♥❞❧❡s ❊①❛♠♣❧❡s ▲❡t ❆ ❜❡ ❛ s❡t✱ ❞❡✜♥❡ ❛ ⊳ ❜ = ❛ ❛♥❞ ❛ ⊳ − ✶ ❜ = ❛ ❢♦r ❛❧❧ ❛ , ❜ ∈ ❆ ✳ ✺✴✶✾

  10. ✶ ❤ ✶ ❣❤ ❛♥❞ ❣ ✶ ▲❡t ● ❜❡ ❛ ❣r♦✉♣✱ ❞❡✜♥❡ ❣ ❤ ❤ ❤❣❤ ❢♦r ❛❧❧ ❣ ● ✳ ■t ❞❡✜♥❡s t❤❡ ❝♦♥❥✉❣❛t✐♦♥ q✉❛♥❞❧❡ ✳ ❤ ✶ ❤ ✳ ❚❤✐s ❞❡✜♥❡s t❤❡ ❝♦r❡ ▲❡t ● ❜❡ ❛ ❣r♦✉♣✱ ❞❡✜♥❡ ❣ ❤ ❤❣ q✉❛♥❞❧❡ ✳ ■♥tr♦❞✉❝t✐♦♥ t♦ q✉❛♥❞❧❡s ❈❡♥tr❛❧ ❡①t❡♥s✐♦♥ ✐♥ t❤❡ ❡①❛❝t ❝♦♥t❡①t ❈♦✈❡r✐♥❣ t❤❡♦r② ♦❢ q✉❛♥❞❧❡s ❊①❛♠♣❧❡s ▲❡t ❆ ❜❡ ❛ s❡t✱ ❞❡✜♥❡ ❛ ⊳ ❜ = ❛ ❛♥❞ ❛ ⊳ − ✶ ❜ = ❛ ❢♦r ❛❧❧ ❛ , ❜ ∈ ❆ ✳ ■t ❞❡✜♥❡s ❛ q✉❛♥❞❧❡ ♥❛♠❡❞ tr✐✈✐❛❧ q✉❛♥❞❧❡ ✳ ❚❤❡ ❝♦rr❡s♣♦♥❞✐♥❣ ❝❛t❡❣♦r② ✐s ❞❡♥♦t❡❞ ◗♥❞ ∗ ✳ ✺✴✶✾

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