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  1. ❆ ❙✐♠♣❧❡ ❙❡♠❛♥t✐❝s ❢♦r ❆r✐st♦t❡❧✐❛♥ ❆♣♦❞❡✐❝t✐❝ ❙②❧❧♦❣✐st✐❝s ❙❛r❛ ▲✳ ❯❝❦❡❧♠❛♥ ✶ ✫ ❙♣❡♥❝❡r ❏♦❤♥st♦♥ ■♥st✐t✉t❡ ❢♦r ▲♦❣✐❝✱ ▲❛♥❣✉❛❣❡✱ ❛♥❞ ❈♦♠♣✉t❛t✐♦♥ ❙✳▲✳❯❝❦❡❧♠❛♥❅✉✈❛✳♥❧ ❀ s♣❡♥❝❡r❴❥♦❤♥st♦♥❴✽✻✵✸❅②❛❤♦♦✳❝♦♠ ❆✐▼▲ ✷✵✶✵ ✷✼ ❆✉❣✉st ✷✵✶✵✱ ▼♦s❝♦✇ ✶ ❋✉♥❞❡❞ ❜② t❤❡ ◆❲❖ ♣r♦❥❡❝t ✏❉✐❛❧♦❣✐❝❛❧ ❋♦✉♥❞❛t✐♦♥s ♦❢ ❙❡♠❛♥t✐❝s✑ ✭❉✐❋♦❙✮ ✐♥ t❤❡ ❊❙❋ ❊✉r♦❈♦❘❡s ♣r♦❣r❛♠♠❡ ▲♦❣■❈❈❈ ✭▲♦❣■❈❈❈✲❋P✵✵✹❀ ❉◆ ✷✸✶✲✽✵✲✵✵✷❀ ❈◆ ✷✵✵✽✴✵✽✸✶✹✴●❲✮✳ ❯❝❦❡❧♠❛♥ ✫ ❏♦❤♥st♦♥ ✭■▲▲❈✮ ❆ s✐♠♣❧❡ s❡♠❛♥t✐❝s✳ ✳ ✳ ✷✼ ❆✉❣ ✶✵ ✶ ✴ ✷✷

  2. ▲❡t ❆ ❇ ❈ r❛♥❣❡ ♦✈❡r ❛ s❡t ❚❊❘▼ ♦❢ t❡r♠s✳ ❲❡ ❤❛✈❡ ❢♦✉r t②♣❡s ♦❢ ❛ss❡rt♦r✐❝ ❝❛t❡❣♦r✐❝❛❧ ♣r♦♣♦s✐t✐♦♥s✿ ❆❛❇ ❵ ❆ ❜❡❧♦♥❣s t♦ ❛❧❧ ❇ ✬ ❵❆❧❧ ❇ ❛r❡ ❆ ✬ ✭✉♥✐✈❡rs❛❧ ❛✣r♠❛t✐✈❡✮ ❆❡❇ ❵ ❆ ❜❡❧♦♥❣s t♦ ♥♦ ❇ ✬ ❵◆♦ ❇ ✐s ❆ ✬ ✭✉♥✐✈❡rs❛❧ ♥❡❣❛t✐✈❡✮ ❆✐❇ ❵ ❆ ❜❡❧♦♥❣s t♦ s♦♠❡ ❇ ✬ ❵❙♦♠❡ ❇ ✐s ❆ ✬ ✭♣❛rt✐❝✉❧❛r ❛✣r♠❛t✐✈❡✮ ❆♦❇ ❵ ❆ ❞♦❡s ♥♦t ❜❡❧♦♥❣ t♦ s♦♠❡ ❇ ✬ ❵❙♦♠❡ ❇ ✐s ♥♦t ❆ ✬ ✭♣❛rt✐❝✉❧❛r ♥❡❣❛t✐✈❡✮ ❚❤❡ t❡r♠ ♣r❡❝❡❞✐♥❣ t❤❡ ❝♦♣✉❧❛ ✐s t❤❡ ♣r❡❞✐❝❛t❡ t❡r♠ ❛♥❞ t❤❡ t❡r♠ s✉❝❝❡❡❞✐♥❣ ✐t ✐s t❤❡ s✉❜❥❡❝t t❡r♠✳ ❆r✐st♦t❡❧✐❛♥ ✭❛ss❡rt♦r✐❝✮ s②❧❧♦❣✐st✐❝s ✭✶✮ ❯❝❦❡❧♠❛♥ ✫ ❏♦❤♥st♦♥ ✭■▲▲❈✮ ❆ s✐♠♣❧❡ s❡♠❛♥t✐❝s✳ ✳ ✳ ✷✼ ❆✉❣ ✶✵ ✷ ✴ ✷✷

  3. ❆r✐st♦t❡❧✐❛♥ ✭❛ss❡rt♦r✐❝✮ s②❧❧♦❣✐st✐❝s ✭✶✮ ▲❡t ❆ , ❇ , ❈ . . . r❛♥❣❡ ♦✈❡r ❛ s❡t ❚❊❘▼ ♦❢ t❡r♠s✳ ❲❡ ❤❛✈❡ ❢♦✉r t②♣❡s ♦❢ ❛ss❡rt♦r✐❝ ❝❛t❡❣♦r✐❝❛❧ ♣r♦♣♦s✐t✐♦♥s✿ ❆❛❇ ❵ ❆ ❜❡❧♦♥❣s t♦ ❛❧❧ ❇ ✬ ↔ ❵❆❧❧ ❇ ❛r❡ ❆ ✬ ✭✉♥✐✈❡rs❛❧ ❛✣r♠❛t✐✈❡✮ ❆❡❇ ❵ ❆ ❜❡❧♦♥❣s t♦ ♥♦ ❇ ✬ ↔ ❵◆♦ ❇ ✐s ❆ ✬ ✭✉♥✐✈❡rs❛❧ ♥❡❣❛t✐✈❡✮ ❆✐❇ ❵ ❆ ❜❡❧♦♥❣s t♦ s♦♠❡ ❇ ✬ ↔ ❵❙♦♠❡ ❇ ✐s ❆ ✬ ✭♣❛rt✐❝✉❧❛r ❛✣r♠❛t✐✈❡✮ ❵ ❆ ❞♦❡s ♥♦t ❜❡❧♦♥❣ t♦ s♦♠❡ ❇ ✬ ↔ ❵❙♦♠❡ ❇ ✐s ♥♦t ❆ ✬ ❆♦❇ ✭♣❛rt✐❝✉❧❛r ♥❡❣❛t✐✈❡✮ ❚❤❡ t❡r♠ ♣r❡❝❡❞✐♥❣ t❤❡ ❝♦♣✉❧❛ ✐s t❤❡ ♣r❡❞✐❝❛t❡ t❡r♠ ❛♥❞ t❤❡ t❡r♠ s✉❝❝❡❡❞✐♥❣ ✐t ✐s t❤❡ s✉❜❥❡❝t t❡r♠✳ ❯❝❦❡❧♠❛♥ ✫ ❏♦❤♥st♦♥ ✭■▲▲❈✮ ❆ s✐♠♣❧❡ s❡♠❛♥t✐❝s✳ ✳ ✳ ✷✼ ❆✉❣ ✶✵ ✷ ✴ ✷✷

  4. ❆r✐st♦t❡❧✐❛♥ ✭❛ss❡rt♦r✐❝✮ s②❧❧♦❣✐st✐❝s ✭✷✮ ❉❡✜♥✐t✐♦♥ ❆ tr✐♣❧❡ S = � ▼ , ♠ , ❝ � ✱ ✇❤❡r❡ ▼ ✱ ♠ ✱ ❛♥❞ ❝ ❛r❡ ❝❛t❡❣♦r✐❝❛❧ ♣r♦♣♦s✐t✐♦♥s✱ ✐s ❛ s②❧❧♦❣✐s♠ ✐❢ ▼ ✱ ♠ ✱ ❛♥❞ ❝ ❝♦♥t❛✐♥ ❡①❛❝t❧② t❤r❡❡ ❞✐st✐♥❝t t❡r♠s✱ ♦❢ ✇❤✐❝❤ t❤❡ ♣r❡❞✐❝❛t❡ ♦❢ ❝ ✭❝❛❧❧❡❞ t❤❡ ♠❛❥♦r t❡r♠✮ ❛♣♣❡❛rs ✐♥ ▼ ❛♥❞ t❤❡ s✉❜❥❡❝t ♦❢ ❝ ✭❝❛❧❧❡❞ t❤❡ ♠✐♥♦r t❡r♠✮ ❛♣♣❡❛rs ✐♥ ♠ ✱ ❛♥❞ ▼ ❛♥❞ ♠ s❤❛r❡ ❛ t❡r♠ ✭❝❛❧❧❡❞ t❤❡ ♠✐❞❞❧❡ t❡r♠✮ ✇❤✐❝❤ ✐s ♥♦t ♣r❡s❡♥t ✐♥ ❝ ✳ ❲❡ ❝❛❧❧ ▼ t❤❡ ♠❛❥♦r ♣r❡♠✐s❡✱ ♠ t❤❡ ♠✐♥♦r✱ ❛♥❞ ❝ t❤❡ ❝♦♥❝❧✉s✐♦♥✳ ❯❝❦❡❧♠❛♥ ✫ ❏♦❤♥st♦♥ ✭■▲▲❈✮ ❆ s✐♠♣❧❡ s❡♠❛♥t✐❝s✳ ✳ ✳ ✷✼ ❆✉❣ ✶✵ ✸ ✴ ✷✷

  5. ❆r✐st♦t❡❧✐❛♥ ✭❛ss❡rt♦r✐❝✮ s②❧❧♦❣✐st✐❝s ✭✸✮ ❚❤❡ t❤r❡❡ ✇❛②s t❤❛t ♠❛❥♦r✱ ♠✐♥♦r✱ ❛♥❞ ♠✐❞❞❧❡ t❡r♠s ✐♥ t❤❡ ♣r❡♠✐s❡s ❝❛♥ ❜❡ ❛rr❛♥❣❡❞ ❛r❡ ❝❛❧❧❡❞ ✜❣✉r❡s✿ ✶st ✷♥❞ ✸r❞ ❆ ✖ ❇ ❇ ✖ ❆ ❆ ✖ ❇ ❇ ✖ ❈ ❇ ✖ ❈ ❈ ✖ ❇ ❆ ✖ ❈ ❆ ✖ ❈ ❆ ✖ ❈ ❋✐❣✉r❡✿ ❚❤❡ ❚❤r❡❡ ❋✐❣✉r❡s ❆ ✜❣✉r❡ ✇✐t❤ t❤r❡❡ ❝♦♣✉❧❛❡ ❛❞❞❡❞ ✐s ❝❛❧❧❡❞ ❛ ❵♠♦♦❞✬✳ ❯❝❦❡❧♠❛♥ ✫ ❏♦❤♥st♦♥ ✭■▲▲❈✮ ❆ s✐♠♣❧❡ s❡♠❛♥t✐❝s✳ ✳ ✳ ✷✼ ❆✉❣ ✶✵ ✹ ✴ ✷✷

  6. ❖♥❡ ♦❢ t❤❡ ♠♦st ❞✐✣❝✉❧t t♦ ✉♥❞❡rst❛♥❞ ❧♦❣✐❝❛❧ s②st❡♠s ✐♥ ❤✐st♦r②✳ ❙t❛rt✐♥❣ ✇✐t❤ s♦♠❡ ♦❢ ❤✐s ♦✇♥ st✉❞❡♥ts✱ ♠❛♥② ❤❛✈❡ ❝♦♥s✐❞❡r❡❞ ❆r✐st♦t❧❡✬s ♠♦❞❛❧ s②❧❧♦❣✐st✐❝ t♦ ❜❡ ❛♥②✇❤❡r❡ ❢r♦♠ ❝♦♥❢✉s❡❞ t♦ s✐♠♣❧② ✇r♦♥❣✳ ❆r✐st♦t❡❧✐❛♥ ♠♦❞❛❧ s②❧❧♦❣✐st✐❝s ❉❡✈❡❧♦♣❡❞ ✐♥ ❝❤❛♣t❡rs ✸ ❛♥❞ ✽✕✷✷ ♦❢ t❤❡ Pr✐♦r ❆♥❛❧②t✐❝s ✳ ❋♦✉r ♠♦❞❛❧✐t✐❡s✿ ▲ ✱ ❳ ✱ ▼ ✱ ◗ ✭♥❡❝❡ss❛r②✱ ❛ss❡rt♦r✐❝✱ ♣♦ss✐❜❧❡✱ ❛♥❞ ❝♦♥t✐♥❣❡♥t✮✳ ❯❝❦❡❧♠❛♥ ✫ ❏♦❤♥st♦♥ ✭■▲▲❈✮ ❆ s✐♠♣❧❡ s❡♠❛♥t✐❝s✳ ✳ ✳ ✷✼ ❆✉❣ ✶✵ ✺ ✴ ✷✷

  7. ❆r✐st♦t❡❧✐❛♥ ♠♦❞❛❧ s②❧❧♦❣✐st✐❝s ❉❡✈❡❧♦♣❡❞ ✐♥ ❝❤❛♣t❡rs ✸ ❛♥❞ ✽✕✷✷ ♦❢ t❤❡ Pr✐♦r ❆♥❛❧②t✐❝s ✳ ❋♦✉r ♠♦❞❛❧✐t✐❡s✿ ▲ ✱ ❳ ✱ ▼ ✱ ◗ ✭♥❡❝❡ss❛r②✱ ❛ss❡rt♦r✐❝✱ ♣♦ss✐❜❧❡✱ ❛♥❞ ❝♦♥t✐♥❣❡♥t✮✳ ❖♥❡ ♦❢ t❤❡ ♠♦st ❞✐✣❝✉❧t t♦ ✉♥❞❡rst❛♥❞ ❧♦❣✐❝❛❧ s②st❡♠s ✐♥ ❤✐st♦r②✳ ❙t❛rt✐♥❣ ✇✐t❤ s♦♠❡ ♦❢ ❤✐s ♦✇♥ st✉❞❡♥ts✱ ♠❛♥② ❤❛✈❡ ❝♦♥s✐❞❡r❡❞ ❆r✐st♦t❧❡✬s ♠♦❞❛❧ s②❧❧♦❣✐st✐❝ t♦ ❜❡ ❛♥②✇❤❡r❡ ❢r♦♠ ❝♦♥❢✉s❡❞ t♦ s✐♠♣❧② ✇r♦♥❣✳ ❯❝❦❡❧♠❛♥ ✫ ❏♦❤♥st♦♥ ✭■▲▲❈✮ ❆ s✐♠♣❧❡ s❡♠❛♥t✐❝s✳ ✳ ✳ ✷✼ ❆✉❣ ✶✵ ✺ ✴ ✷✷

  8. ✇❤✐❧❡ ❛r❣✉♠❡♥ts ♦❢ t❤❡ ❢♦r♠ ❆ ❜❡❧♦♥❣s t♦ ❛❧❧ ❇✳ ◆❡❝❡ss❛r✐❧② ❇ ❜❡❧♦♥❣s t♦ ❛❧❧ ❈✳ ❚❤❡r❡❢♦r❡✱ ♥❡❝❡ss❛r✐❧② ❆ ❜❡❧♦♥❣s t♦ ❛❧❧ ❈✳ ❛r❡ ✐♥✈❛❧✐❞✳ ❬ Pr✐♦r ❆♥❛❧②t✐❝s ✸✵❛✶✺✕✸✵❛✸✸❪✳ ❚❤❡♦♣❤r❛st✉s✿ ❜♦t❤ s②❧❧♦❣✐s♠s ❛r❡ ✐♥✈❛❧✐❞✖♥♦t❤✐♥❣ ❢♦❧❧♦✇s ✇❤❡♥ ♦♥❡ ♣r❡♠✐s❡ ✐s ♥❡❝❡ss❛r② ❛♥❞ t❤❡ ♦t❤❡r ❛ss❡rt♦r✐❝✳ ❾✉❦❛s✐❡✇✐❝③✿ ❜♦t❤ s②❧❧♦❣✐s♠s ❛r❡ ✈❛❧✐❞✳ ❚❤❡ ❚✇♦ ❇❛r❜❛r❛s ❆❝❝♦r❞✐♥❣ t♦ ❆r✐st♦t❧❡✱ ❛r❣✉♠❡♥ts ♦❢ t❤❡ ❢♦r♠ ◆❡❝❡ss❛r✐❧② ❆ ❜❡❧♦♥❣s t♦ ❛❧❧ ❇✳ ❇ ❜❡❧♦♥❣s t♦ ❛❧❧ ❈✳ ❚❤❡r❡❢♦r❡✱ ♥❡❝❡ss❛r✐❧② ❆ ❜❡❧♦♥❣s t♦ ❛❧❧ ❈✳ ❛r❡ ✈❛❧✐❞✱ ❯❝❦❡❧♠❛♥ ✫ ❏♦❤♥st♦♥ ✭■▲▲❈✮ ❆ s✐♠♣❧❡ s❡♠❛♥t✐❝s✳ ✳ ✳ ✷✼ ❆✉❣ ✶✵ ✻ ✴ ✷✷

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