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❘❡❝♦❣♥✐t✐♦♥ ♦❢ ❖♥❧✐♥❡ ❍❛♥❞✇r✐tt❡♥

▼❛t❤❡♠❛t✐❝❛❧ ❊①♣r❡ss✐♦♥s ✉s✐♥❣

❈♦♥t❡①t✉❛❧ ■♥❢♦r♠❛t✐♦♥

❋r❛♥❦ ❉❡♥♥✐s ❏✉❧❝❛ ❆❣✉✐❧❛r

❆ t❤❡s✐s

s✉❜♠✐tt❡❞ t♦ t❤❡ ■♥st✐t✉t❡ ♦❢ ▼❛t❤❡♠❛t✐❝s ❛♥❞ ❙t❛t✐st✐❝s

♦❢ ❯♥✐✈❡rs✐t② ♦❢ ❙ã♦ P❛✉❧♦

❛♥❞ P♦❧②t❡❝❤ ◆❛♥t❡s s❝❤♦♦❧ ♦❢ ❯♥✐✈❡rs✐t② ♦❢ ◆❛♥t❡s

✐♥ ♣❛rt✐❛❧ ❢✉❧❢✐❧❧♠❡♥t ♦❢ t❤❡ r❡q✉✐r❡♠❡♥ts

❢♦r t❤❡ ❞❡❣r❡❡ ♦❢

❞♦❝t♦r ♦❢ ♣❤✐❧♦s♦♣❤②

❉♦❝t♦r❛❧ Pr♦❣r❛♠✿ ❈♦♠♣✉t❡r ❙❝✐❡♥❝❡

❆❞✈✐s♦r✿ ◆✐♥❛ ❙✳ ❚✳ ❍✐r❛t❛

❈♦✲❆❞✈✐s♦r✿ ❈❤r✐st✐❛♥ ❱✐❛r❞✲●❛✉❞✐♥

❈♦✲❆❞✈✐s♦r✿ ❍❛r♦❧❞ ▼♦✉❝❤èr❡

❚❤❡ ❛✉t❤♦r r❡❝❡✐✈❡❞ ✜♥❛♥❝✐❛❧ s✉♣♣♦rt ❢r♦♠ ❋❆P❊❙P

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❘❡❝♦❣♥✐t✐♦♥ ♦❢ ❖♥❧✐♥❡ ❍❛♥❞✇r✐tt❡♥

▼❛t❤❡♠❛t✐❝❛❧ ❊①♣r❡ss✐♦♥s ✉s✐♥❣

❈♦♥t❡①t✉❛❧ ■♥❢♦r♠❛t✐♦♥

❊st❛ ✈❡rsã♦ ❞❛ t❡s❡ ❝♦♥té♠ ❛s ❝♦rr❡çõ❡s ❡ ❛❧t❡r❛çõ❡s s✉❣❡r✐❞❛s ♣❡❧❛ ❈♦♠✐ssã♦ ❏✉❧❣❛❞♦r❛ ❞✉r❛♥t❡ ❛ ❞❡❢❡s❛ ❞❛ ✈❡rsã♦ ♦r✐❣✐♥❛❧ ❞♦ tr❛❜❛❧❤♦✱ r❡❛❧✐③❛❞❛ ❡♠ ✷✾✴✵✹✴✷✵✶✻✳ ❯♠❛ ❝ó♣✐❛ ❞❛ ✈❡rsã♦ ♦r✐❣✐♥❛❧ ❡stá ❞✐s♣♦♥í✈❡❧ ♥♦ ■♥st✐t✉t♦ ❞❡ ▼❛t❡♠át✐❝❛ ❡ ❊st❛tíst✐❝❛ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❙ã♦ P❛✉❧♦✳

❈♦♠✐ssã♦ ❏✉❧❣❛❞♦r❛✿

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❆❦♥♦✇❧❡❞❣♠❡♥ts

❚❤✐s t❤❡s✐s ✇♦✉❧❞ ♥♦t ❤❛✈❡ ❜❡❡♥ ♣♦ss✐❜❧❡ ✇✐t❤♦✉t t❤❡ s✉♣♣♦rt ♦❢ ♠❛♥② ♣❡♦♣❧❡✳ ❋✐rst✱ ■ ✇♦✉❧❞ ❧✐❦❡ t♦ t❤❛♥❦ ♠② ❛❞✈✐s♦rs ◆✐♥❛ ❙✳ ❚✳ ❍✐r❛t❛✱ ❈❤r✐st✐❛♥ ❱✐❛r❞✲●❛✉❞✐♥ ❛♥❞ ❍❛r♦❧❞ ▼♦✉❝❤èr❡✳ ◆✐♥❛✱ t❤❛♥❦ ②♦✉ ❢♦r s❤❛r✐♥❣ ❝♦✉♥t❧❡ss ❤♦✉rs ♦❢ ❞✐s❝✉ss✐♦♥s✱ ❢♦r ②♦✉r ❛❞✈✐❝❡ ❛♥❞ s✉♣♣♦rt✱ ❛♥❞ ❢♦r ❜❡✐♥❣ ❛❧s♦ ❛ ❣♦♦❞ ❢r✐❡♥❞ ❛❧♦♥❣ t❤❡s❡ ❧❛st ②❡❛rs✳ ❈❤r✐st✐❛♥ ❛♥❞ ❍❛r♦❧❞✱ t❤❛♥❦ ②♦✉ ❢♦r s❤❛r✐♥❣ ②♦✉r ❦♥♦✇❧❡❞❣❡ ❛♥❞ ❡①♣❡r✐❡♥❝❡ ✇✐t❤ ♠❡✳ ❚❤❛♥❦ ②♦✉ ❛❧❧ ❢♦r r❡❛❞✐♥❣ ♠② ❞r❛❢ts ♦❢ r❡♣♦rts ❛♥❞ ♣❛♣❡rs✱ ❛♥❞ ❣✐✈✐♥❣ ♠❡ ♠❛♥② ❤❡❧♣❢✉❧ ❝♦♠♠❡♥ts✳ ❨♦✉ ♣r♦✈✐❞❡❞ ♠❡ ✇✐t❤ ❛♥ ✐❞❡❛❧ ❜❛❧❛♥❝❡ ♦❢ ❣✉✐❞❛♥❝❡ ❛♥❞ ❢r❡❡❞♦♠✳

■ ❛♠ ❛❧s♦ t❤❛♥❦❢✉❧ t♦ ♠② ❝♦✲❛✉t❤♦rs ❲✐❧❧✐❛♥ ❨✳ ❍♦♥❞❛ ❛♥❞ ❆❧❡①❛♥❞r❡ ◆♦♠❛✱ ❢♦r ②♦✉r ❝♦❧❧❛❜♦✲ r❛t✐♦♥ ❞✉r✐♥❣ t❤❡ ❞❡✈❡❧♦♣♠❡♥t ♦❢ t❤✐s ✇♦r❦✳ ■ ❛♠ ❣r❛t❡❢✉❧ t♦ t❤❡ ♠❡♠❜❡rs ♦❢ t❤❡ ❈♦♠♣✉t❡r ❱✐s✐♦♥ ●r♦✉♣ ♦❢ t❤❡ ■♥st✐t✉t❡ ♦❢ ▼❛t❤❡♠❛t✐❝s ❛♥❞ ❙t❛t✐st✐❝s ♦❢ ❯♥✐✈❡rs✐t② ♦❢ ❙ã♦ P❛✉❧♦✱ ❛♥❞ ♠❡♠❜❡rs ♦❢ t❤❡ ■♥st✐t✉t ❞❡ ❘❡❝❤❡r❝❤❡ ❡♥ ❈♦♠♠✉♥✐❝❛t✐♦♥s ❡t ❈②❜❡r♥ét✐q✉❡ ❞❡ ◆❛♥t❡s ♦❢ ❯♥✐✈❡rs✐t② ♦❢ ◆❛♥t❡s✳ ❚❤❛♥❦s ❢♦r ♣r♦✈✐❞✐♥❣ ♠❡ ❛ ❢r✐❡♥❞❧② ✇♦r❦✐♥❣ ❡♥✈✐r♦♥♠❡♥t✳

■ ❛❧s♦ ✇❛♥t t♦ t❤❛♥❦ ♠② ❛♠❛③✐♥❣ ❢r✐❡♥❞s ❆♥t❤♦♥② ▼❡♥❞❡③✱ ❑❛r✐♥❛ ❊s♣✐♥♦③❛✱ ❘♦s❛r✐♦ ▼❡❞✐♥❛✱ ❏♦r❣❡ ●✉❡✈❛r❛✱ ▲❡✐ss✐ ❈❛st❛ñ❡❞❛✱ ▲❡❛♥❞r♦ ❚✐❝❧✐❛✱ ❆❧❢♦♥s♦ P❤♦❝❝♦✱ ❏✉❛♥ ●✉t✐❡rr❡③✱ ❘❡♥③♦ ●♦♠❡③✱ ❊❞✇✐♥ ❉❡❧❣❛❞♦✱ ❙♦✜❛♥❡ ▼❡❞❥❦♦✉♥❡✱ ❆❧❡❥❛♥❞r❛ ❘✐♦s✱ ▲✉✐s ❈és♣❡❞❡s✳ ❚❤❛♥❦ ②♦✉ ❱❛♥❡ss❛ ❱❛❧❞✐✈✐❡③♦ ❢♦r t❤❡ ✇♦♥❞❡r❢✉❧ ②❡❛rs ♦♥ ♠② s✐❞❡✳ ❚❤❛♥❦ ②♦✉ ❘♦s❛♥❣❡❧❛ ❈❛♠❛r❣♦ ❢♦r s✉❝❤ ❧♦✈❡❧② ♠♦♠❡♥ts ②♦✉ ❣❛✈❡ ♠❡✳ ■ ❛♠ r❡❛❧❧② ❧✉❝❦② ❢♦r ✜♥❞✐♥❣ s♦ ❣r❡❛t ♣❡♦♣❧❡ ❛s ❛❧❧ ♦❢ ②♦✉✳

■ ❛❧s♦ ❛❝❦♥♦✇❧❡❞❣❡ t❤❡ ✜♥❛♥❝✐❛❧ s✉♣♣♦rt ♦❢ ♠② st✉❞✐❡s ❜② ❋❆P❊❙P✱ t❤r♦✉❣❤ ❛ ▼❛st❡rs s❝❤♦❧✲ ❛rs❤✐♣✱ ●r❛♥t ♥✉♠❜❡r ✷✵✶✵✴✵✹✹✾✶✲✵❀ ❛ ❉✐r❡❝t ❉♦❝t♦r❛t❡ s❝❤♦❧❛rs❤✐♣✱ ●r❛♥t ♥✉♠❜❡r ✷✵✶✷✴✵✽✸✽✾✲✶❀ ❛♥❞ ❛ ❘❡s❡❛r❝❤ ■♥t❡r♥s❤✐♣s ❆❜r♦❛❞ ✭❇❊P❊✮ s❝❤♦❧❛rs❤✐♣✱ ●r❛♥t ♥✉♠❜❡r ✷✵✶✸✴✶✸✺✸✺✲✵✳

❋✐♥❛❧❧②✱ ■ ✇♦✉❧❞ ❧✐❦❡ t♦ t❤❛♥❦ ♠② ♣❛r❡♥ts✱ ■s❛❜❡❧ ❆❣✉✐❧❛r ❛♥❞ P❛✉❧✐♥♦ ❏✉❧❝❛❀ ♠② s✐st❡rs✱ ❈❛r✲ ♠❡♥✱ ❙♦♥✐❛✱ ▼❛♥✉❡❧❛❀ ❛♥❞ ♠② ❜r♦t❤❡rs✱ ❙❛♠✐r✱ ■✈❛♥✱ ❛♥❞ ❏✉❧✐♦✳ ❚❤❛♥❦s ❢♦r t❤❡ ❛♠❛③✐♥❣ s✉♣♣♦rt✱ ❡♥❝♦✉r❛❣❡♠❡♥t✱ ❛♥❞ ❧♦✈❡ ②♦✉ ♣r♦✈✐❞❡ ♠❡✳ ❚❤❡ ♣❛ss✐♦♥ ❢♦r ❡①♣❧♦r✐♥❣✱ ❧❡❛r♥✐♥❣✱ ❛♥❞ ❤❛r❞ ✇♦r❦ t❤❛t ②♦✉ t❛✉❣❤t ♠❡ ❧❡❞ ♠❡ t❤r♦✉❣❤ ♠② st✉❞✐❡s✳

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❘❡s✉♠♦

❏✉❧❝❛✲❆❣✉✐❧❛r✱ ❋✳ ❉✳ ❘❡❝♦♥❤❡❝✐♠❡♥t♦ ♦♥❧✐♥❡ ❞❡ ❡①♣r❡ssõ❡s ♠❛t❡♠át✐❝❛s ♠❛♥✉s❝r✐t❛s ✉s✲ ❛♥❞♦ ✐♥❢♦r♠❛çã♦ ❝♦♥t❡①t✉❛❧✳ ✷✵✶✻✳ ❚❡s❡ ✭❉♦✉t♦r❛❞♦✮ ✲ ■♥st✐t✉t♦ ❞❡ ▼❛t❡♠át✐❝❛ ❡ ❊st❛tíst✐❝❛✱ ❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❙ã♦ P❛✉❧♦✱ ❙ã♦ P❛✉❧♦✱ ✷✵✶✻✳

❊①♣r❡ssõ❡s ♠❛t❡♠át✐❝❛s ♠❛♥✉s❝r✐t❛s ♦♥❧✐♥❡ ❡stã♦ ❝♦♥st✐t✉í❞❛s ♣♦r s❡q✉ê♥❝✐❛s ❞❡ tr❛ç♦s✳ ❖ r❡✲ ❝♦♥❤❡❝✐♠❡♥t♦ ❛✉t♦♠át✐❝♦ ❞❡ t❛✐s ❡①♣r❡ssõ❡s r❡q✉❡r ❛ s♦❧✉çã♦ ❞❡ três s✉❜♣r♦❜❧❡♠❛s✿ s❡❣♠❡♥t❛çã♦ ❞❡ sí♠❜♦❧♦s✱ ❝❧❛ss✐✜❝❛çã♦ ❞❡ sí♠❜♦❧♦s ❡ ❛♥á❧✐s❡ ❡str✉t✉r❛❧ ✭✐st♦ é✱ ❛ ✐❞❡♥t✐✜❝❛çã♦ ❞❡ r❡❧❛çõ❡s ❡s♣❛❝✐❛✐s✱ t❛✐s ❝♦♠♦ s♦❜r❡s❝r✐t♦ ❡ s✉❜s❝r✐t♦✱ ❡♥tr❡ sí♠❜♦❧♦s✮✳ ❯♠❛ ❞❛s ❞✐✜❝✉❧❞❛❞❡s ♣r✐♥❝✐♣❛✐s ❞♦ ♣r♦❜❧❡♠❛ é ❛ ❛♠❜✐❣✉✐❞❛❞❡ ♥♦ ♥í✈❡❧ ❞❡ sí♠❜♦❧♦s ♦✉ r❡❧❛çõ❡s✱ q✉❡ ❢r❡q✉❡♥t❡♠❡♥t❡ s✉❣❡r❡ ✈ár✐❛s ♣♦ssí✈❡✐s ✐♥t❡r♣r❡✲ t❛çõ❡s ❞❡ ✉♠❛ ♠❡s♠❛ ❡①♣r❡ssã♦✳

❆❧❣✉♥s ♠ét♦❞♦s ❞❡ r❡❝♦♥❤❡❝✐♠❡♥t♦ tr❛t❛♠ ♦ ♣r♦❜❧❡♠❛ ❞❡ ♠❛♥❡✐r❛ s❡q✉❡♥❝✐❛❧✱ ♦♥❞❡ ✉♠ ♣r♦❝❡ss♦ ❞❡ s❡❣♠❡♥t❛çã♦ ❡ ❝❧❛ss✐✜❝❛çã♦ ❞❡ sí♠❜♦❧♦s é s❡❣✉✐❞♦ ❞❡ ❛♥á❧✐s❡ ❡str✉t✉r❛❧✳ ❯♠ ♣r♦❜❧❡♠❛ ♣r✐♥❝✐♣❛❧ ❞❡ t❛✐s ♠ét♦❞♦s é q✉❡ ❡❧❡s ❞❡t❡r♠✐♥❛♠ ✐♥t❡r♣r❡t❛çõ❡s ♥♦ ♥í✈❡❧ ❞❡ sí♠❜♦❧♦s s❡♠ ❝♦♥s✐❞❡r❛r ✐♥❢♦r♠❛çã♦ ❡str✉t✉r❛❧✱ ❛ q✉❛❧ é ✐♠♣♦rt❛♥t❡ ♣❛r❛ s♦❧✉❝✐♦♥❛r ❛♠❜✐❣✉✐❞❛❞❡s✳ P❛r❛ s♦❧✉❝✐♦♥❛r ❡ss❡ ♣r♦❜❧❡♠❛✱ ♠ét♦✲ ❞♦s ♠❛✐s r❡❝❡♥t❡s ❛❞❛♣t❛r❛♠ té❝♥✐❝❛s ❞❡ ♣❛rs✐♥❣ ❞❡ str✐♥❣s✳ ❉❛❞♦ q✉❡ ❣r❛♠át✐❝❛s ❞❡ str✐♥❣s ❢♦r❛♠ ♦r✐❣✐♥❛❧♠❡♥t❡ ♣r♦❥❡t❛❞❛s ♣❛r❛ ♠♦❞❡❧❛r ❛rr❛♥❥♦s ❧✐♥❡❛r❡s ❞❡ t♦❦❡♥s ✭❝♦♠♦ t❡①t♦✱ ♦♥❞❡ sí♠❜♦❧♦s sã♦ ❛rr❛♥❥❛❞♦s ❞❡ ❡sq✉❡r❞❛ ❛ ❞✐r❡✐t❛✮✱ ❛ ❡str✉t✉r❛ ♥ã♦ ❧✐♥❡❛r ❞♦s sí♠❜♦❧♦s ♠❛t❡♠át✐❝♦s ✭❞❛❞❛ ♣❡❧♦s ♠✉❧t✐♣❧❡s t✐♣♦s ❞❡ r❡❧❛çõ❡s ❡s♣❛❝✐❛✐s✮ é ♠♦❞❡❧❛❞❛ ❝♦♠♦ ✉♠❛ ❝♦♠♣♦s✐çã♦ ❞❡ r❡❣r❛s ❞❡ ♣r♦❞✉çã♦ ❞❡ ❡str✉t✉r❛s ❧✐♥❡❛r❡s✳ ❉❡ss❛ ♠❛♥❡✐r❛✱ ♦ ♣❛rs✐♥❣ ❞❡ ✉♠❛ ❡①♣r❡ssã♦ ❝♦♥s✐st❡ ❡♠ ❞❡t❡r♠✐♥❛r ❡str✉t✉r❛s ❧✐♥❡❛r❡s ♥❛ ❡①♣r❡ssã♦ q✉❡ sã♦ ❝♦♥s✐st❡♥t❡s ❝♦♠ ❛s ❡str✉t✉r❛s ❞❛s r❡❣r❛s ❞❡ ♣r♦❞✉çã♦✳ ❊ss❡ ú❧t✐♠♦ ♣❛ss♦ r❡q✉❡r ❛ ✐♥tr♦❞✉çã♦ ❞❡ r❡str✐çõ❡s✱ ❜❛s❡❛❞❛s ♥❛ ❞❡✜♥✐çã♦ ❞❡ ✉♠❛ ♦r❞❡♠ ❡♠ r❡❧❛çã♦ ❛♦ t❡♠♣♦ ♦✉ ❡s♣❛ç♦✱ ♣❛r❛ ❧✐♥❡❛r✐③❛r ♦s ❝♦♠♣♦♥❡♥t❡s ❞❛ ❡①♣r❡sã♦✳ ❖s r❡q✉❡r✐♠❡♥t♦s ❞❛s ❣r❛♠át✐❝❛s ❞❡ str✐♥❣s ♥ã♦ ❛♣❡♥❛s ❧✐♠✐t❛♠ ❛ ❡❢❡❝t✐✈✐❞❛❞❡ ❞♦s ♠ét♦❞♦s✱ ♠❛s t❛♠❜é♠ ❞✐✜❝✉❧t❛♠ ❛ ❡①t❡♥sã♦ ❞♦s ♠ét♦❞♦s ♥❛ ✐♥❝❧✉sã♦ ❞❡ ♥♦✈❛s ❡str✉t✉r❛s✳

◆❡st❡ tr❛❜❛❧❤♦✱ ♦ ♣r♦❜❧❡♠❛ ❞❡ r❡❝♦♥❤❡❝✐♠❡♥t♦ ❞❡ ❡①♣r❡ssõ❡s ♠❛t❡♠át✐❝❛s é ♠♦❞❡❧❛❞♦ ❝♦♠♦ ✉♠ ♣r♦❜❧❡♠❛ ❞❡ ♣❛rs✐♥❣ ❞❡ ❣r❛❢♦s✳ ❆ r❡♣r❡s❡♥t❛çã♦ ♣♦r ♠❡✐♦ ❞❡ ❣r❛❢♦s ♥❛s r❡❣r❛s ❞❡ ♣r♦❞✉çã♦ ♣❡r♠✐t❡ ✉♠❛ r❡♣r❡s❡♥t❛çã♦ ❞✐r❡t❛ ❞❛s ❡str✉t✉r❛s ♥ã♦ ❧✐♥❡❛r❡s ❞❛s ❡①♣r❡ssõ❡s ♠❛t❡♠át✐❝❛s✳ ❖ ❛❧❣♦r✐t♠♦ ❞❡ ♣❛rs✐♥❣ ❞❡t❡r♠✐♥❛ ♣❛rt✐çõ❡s ❞♦s tr❛ç♦s ❞❡ ❡♥tr❛❞❛ q✉❡ ✐♥❞✉③❡♠ ❣r❛❢♦s ✐s♦♠♦r❢♦s ❛♦s ❣r❛❢♦s ❞❛s r❡❣r❛s ❞❡ ♣r♦❞✉çã♦✳ P❛r❛ ♠✐t✐❣❛r ♦ ❝✉st♦ ❝♦♠♣✉t❛❝✐♦♥❛❧✱ r❡str✐♥❣✐♠♦s ❛s ♣♦ssí✈❡✐s ♣❛rt✐çõ❡s ❛ ❛q✉❡❧❛s ❞❡r✐✈❛❞❛s ❞❡ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ♣♦ssí✈❡✐s sí♠❜♦❧♦s ❡ r❡❧❛çõ❡s ✐❞❡♥t✐✜❝❛❞♦s ♣♦r ❝❧❛ss✐✜❝❛❞♦r❡s ♣r❡✈✐❛♠❡♥t❡ tr❡✐♥❛❞♦s✳ ❯♠ ❝♦♥❥✉♥t♦ ❞❡ rót✉❧♦s q✉❡ ✐♥❞✐❝❛ ✐♥t❡r♣r❡t❛çõ❡s ❛❧t❡r♥❛t✐✈❛s é ❛ss♦❝✐❛❞♦ ❛ ❝❛❞❛ sí♠❜♦❧♦ ❡ r❡❧❛çã♦❀ ❛ ❞❡❝✐sã♦ ❞❛ ♠❡❧❤♦r ✐♥t❡r♣r❡t❛çã♦ é r❡❛❧✐③❛❞❛ ♣❡❧♦ ♣❛rs❡r✳ ❖ ♣❛rs❡r ❝♦♥str✉✐ ✉♠❛ ✢♦r❡st❛ ♥❛ q✉❛❧ ✉♠❛ ár✈♦r❡ r❡♣r❡s❡♥t❛ ✉♠❛ ♣♦ssí✈❡❧ ✐♥t❡r♣r❡t❛çã♦ ❞❛ ❡♥tr❛❞❛✱ ❡ ❛tr✐❜✉✐ ✉♠ ❝✉st♦ ❞❡ ✐♥t❡r♣r❡t❛çã♦ ♣❛r❛ ❝❛❞❛ ár✈♦r❡✱ ❜❛s❡❛❞♦ ♥❛s r❡❧❛çõ❡s ❡ sí♠❜♦❧♦s ❞❡✜♥✐❞❛s ♥❛ ár✈♦r❡✳ ❖ r❡s✉❧t❛❞♦ ❞♦ r❡❝♦♥❤❡❝✐♠❡♥t♦ é ❞❛❞♦ ♣❡❧❛ ❡①tr❛çã♦ ❞❡ ✉♠❛ ár✈♦r❡ ❝♦♠ ❝✉st♦ ♠í♥✐♠♦✳

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✐✈

❝♦♠ ✈ár✐♦s ♠ét♦❞♦s ❞❡s❝r✐t♦s ♥❛ ❧✐t❡r❛t✉r❛✳ ❆ ♣❡s❛r ❞♦ ♣❛rs✐♥❣ ❞❡ ❣r❛❢♦s s❡r ✉♠ ♣r♦❝❡ss♦ ❝♦♠♣✉t❛✲ ❝✐♦♥❛❧♠❡♥t❡ ❝❛r♦✱ ❛ r❡str✐çã♦ ❞♦ ❡s♣❛ç♦ ❞❡ ❜✉s❝❛ ♣r♦♣♦st♦ r❡❞✉③ ❛ ❝♦♠♣❧❡①✐❞❛❞❡ ♦ s✉✜❝✐❡♥t❡ ♣❛r❛ ♣❡r♠✐t✐r ✉♠❛ ❛♣❧✐❝❛çã♦ ♣rát✐❝❛ ❞❛ ❛❜♦r❞❛❣❡♠✳ ❆❞✐❝✐♦♥❛❧♠❡♥t❡✱ ❞❛❞♦ q✉❡ ❛ ❛❜♦r❞❛❣❡♠ ♥ã♦ ♣r❡s✲ s✉♣õ❡ ❡str✉t✉r❛s ♣❛rt✐❝✉❧❛r❡s ❞❛s ❡①♣r❡ssõ❡s ♠❛t❡♠át✐❝❛✱ ♦ ♠ét♦❞♦ t❡♠ ♣♦t❡♥❝✐❛❧ ♣❛r❛ s❡r ❛❞❛♣t❛❞♦ ♣❛r❛ ♦ r❡❝♦♥❤❡❝✐♠❡♥t♦ ❞❡ ♦✉tr❛s ❡str✉t✉r❛s ❜✐❞✐♠❡♥s✐♦♥❛✐s✳

❯♠❛ ❝♦♥tr✐❜✉✐çã♦ s❡❝✉♥❞❛r✐❛ ❞❡st❡ tr❛❜❛❧❤♦ é ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ✉♠❛ ❢r❛♠❡✇♦r❦ ♣❛r❛ ❝♦♥✲ str✉çã♦ ❛✉t♦♠át✐❝❛ ❞❡ ❜❛♥❝♦s ❞❡ ❞❛❞♦s ❞❡ ❡①♣r❡ssõ❡s ♠❛t❡♠át✐❝❛s ♠❛♥✉s❝r✐t❛s✳ ❆ ❢r❛♠❡✇♦r❦ t❡♠ s✐❞♦ ✐♠♣❧❡♠❡♥t❛❞❛ ♥✉♠ s✐st❡♠❛ ✉s❛❞♦ ♣❛r❛ ❝r✐❛r ♣❛rt❡ ❞❛s ❛♠♦str❛s ❞❡ ❡①♣r❡ssõ❡s ✉s❛❞❛s ♣❛r❛ ❛✈❛❧✐❛çã♦ ❞♦ ♠ét♦❞♦ ❞❡ r❡❝♦♥❤❡❝✐♠❡♥t♦✳

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❆❜str❛❝t

❏✉❧❝❛✲❆❣✉✐❧❛r✱ ❋✳ ❉✳ ❘❡❝♦❣♥✐t✐♦♥ ♦❢ ❖♥❧✐♥❡ ❍❛♥❞✇r✐tt❡♥ ▼❛t❤❡♠❛t✐❝❛❧ ❊①♣r❡ss✐♦♥s ✉s✐♥❣ ❈♦♥t❡①t✉❛❧ ■♥❢♦r♠❛t✐♦♥✳ ✷✵✶✻✳ P❤❉ t❤❡s✐s ✲ ■♥st✐t✉t❡ ♦❢ ▼❛t❤❡♠❛t✐❝s ❛♥❞ ❙t❛t✐st✐❝s✱ ❯♥✐✈❡rs✐t② P❛✉❧♦✱ ❙ã♦ P❛✉❧♦✱ ✷✵✶✻✳

❖♥❧✐♥❡ ❤❛♥❞✇r✐tt❡♥ ♠❛t❤❡♠❛t✐❝❛❧ ❡①♣r❡ss✐♦♥s ❝♦♥s✐st ♦❢ s❡q✉❡♥❝❡s ♦❢ str♦❦❡s✱ ✉s✉❛❧❧② ❝♦❧❧❡❝t❡❞ t❤r♦✉❣❤ ❛ t♦✉❝❤ s❝r❡❡♥ ❞❡✈✐❝❡✳ ❆✉t♦♠❛t✐❝ r❡❝♦❣♥✐t✐♦♥ ♦❢ ♦♥❧✐♥❡ ❤❛♥❞✇r✐tt❡♥ ♠❛t❤❡♠❛t✐❝❛❧ ❡①♣r❡s✲ s✐♦♥s r❡q✉✐r❡s s♦❧✈✐♥❣ t❤r❡❡ s✉❜♣r♦❜❧❡♠s✿ s②♠❜♦❧ s❡❣♠❡♥t❛t✐♦♥✱ s②♠❜♦❧ ❝❧❛ss✐✜❝❛t✐♦♥✱ ❛♥❞ str✉❝t✉r❛❧ ❛♥❛❧②s✐s ✭t❤❛t ✐s✱ t❤❡ ✐❞❡♥t✐✜❝❛t✐♦♥ ♦❢ s♣❛t✐❛❧ r❡❧❛t✐♦♥s✱ ❛s s✉❜s❝r✐♣t ♦r s✉♣❡rs❝r✐♣t✱ ❜❡t✇❡❡♥ s②♠✲ ❜♦❧s✮✳ ❆ ♠❛✐♥ ✐ss✉❡ ✐♥ t❤❡ r❡❝♦❣♥✐t✐♦♥ ♣r♦❝❡ss ✐s ❛♠❜✐❣✉✐t② ❛t s②♠❜♦❧ ♦r r❡❧❛t✐♦♥ ❧❡✈❡❧s t❤❛t ♦❢t❡♥ ❧❡❛❞s t♦ s❡✈❡r❛❧ ❧✐❦❡❧② ✐♥t❡r♣r❡t❛t✐♦♥s ♦❢ ❛♥ ❡①♣r❡ss✐♦♥✳

❙♦♠❡ ♠❡t❤♦❞s tr❡❛t t❤❡ r❡❝♦❣♥✐t✐♦♥ ♣r♦❜❧❡♠ ❛s ❛ ♣✐♣❡❧✐♥❡ ♣r♦❝❡ss✱ ✐♥ ✇❤✐❝❤ s②♠❜♦❧ s❡❣♠❡♥t❛t✐♦♥ ❛♥❞ ❝❧❛ss✐✜❝❛t✐♦♥ ✐s ❢♦❧❧♦✇❡❞ ❜② str✉❝t✉r❛❧ ❛♥❛❧②s✐s✳ ❆ ♠❛✐♥ ❞r❛✇❜❛❝❦ ♦❢ s✉❝❤ ♠❡t❤♦❞s ✐s t❤❛t t❤❡② ❝♦♠♣✉t❡ s②♠❜♦❧ ❧❡✈❡❧ ✐♥t❡r♣r❡t❛t✐♦♥s ✇✐t❤♦✉t ❝♦♥s✐❞❡r✐♥❣ str✉❝t✉r❛❧ ✐♥❢♦r♠❛t✐♦♥✱ ✇❤✐❝❤ ✐s ❡ss❡♥t✐❛❧ t♦ s♦❧✈❡ ❛♠❜✐❣✉✐t✐❡s✳ ❚♦ ❝♦♣❡ ✇✐t❤ t❤✐s ❞r❛✇❜❛❝❦✱ ♠♦r❡ r❡❝❡♥t ♠❡t❤♦❞s ❛❞❛♣t str✐♥❣ ♣❛rs✐♥❣ t❡❝❤♥✐q✉❡s t♦ ❞r✐✈❡ t❤❡ r❡❝♦❣♥✐t✐♦♥ ♣r♦❝❡ss✳ ❆s str✐♥❣ ❣r❛♠♠❛rs ✇❡r❡ ♦r✐❣✐♥❛❧❧② ❞❡s✐❣♥❡❞ t♦ ♠♦❞❡❧ ❧✐♥❡❛r ❛rr❛♥❣❡♠❡♥ts ♦❢ ♦❜❥❡❝ts ✭❧✐❦❡ ✐♥ t❡①t✱ ✇❤❡r❡ s②♠❜♦❧s ❛r❡ ❛rr❛♥❣❡❞ ♦♥❧② t❤r♦✉❣❤ ❧❡❢t✲t♦✲ r✐❣❤t r❡❧❛t✐♦♥s✮✱ ♥♦♥✲❧✐♥❡❛r ❛rr❛♥❣❡♠❡♥ts ♦❢ ♠❛t❤❡♠❛t✐❝❛❧ s②♠❜♦❧s ✭❣✐✈❡♥ ❜② t❤❡ ♠✉❧t✐♣❧❡ r❡❧❛t✐♦♥ t②♣❡s ♦❢ ♠❛t❤❡♠❛t✐❝s✮ ❛r❡ ♠♦❞❡❧❡❞ ❛s ❝♦♠♣♦s✐t✐♦♥s ♦❢ ♣r♦❞✉❝t✐♦♥ r✉❧❡s ❢♦r ❧✐♥❡❛r str✉❝t✉r❡s✳ ❚❤❡♥✱ ♣❛rs✐♥❣ ❛♥ ❡①♣r❡ss✐♦♥ ✐♥✈♦❧✈❡s s❡❛r❝❤✐♥❣ ❢♦r ❧✐♥❡❛r str✉❝t✉r❡s ✐♥ t❤❡ ❡①♣r❡ss✐♦♥ t❤❛t ❛r❡ ❝♦♥s✐st❡♥t ✇✐t❤ t❤❡ str✉❝t✉r❡ ♦❢ t❤❡ ♣r♦❞✉❝t✐♦♥ r✉❧❡s✳ ❚❤✐s ❧❛st st❡♣ r❡q✉✐r❡s t❤❡ ✐♥tr♦❞✉❝t✐♦♥ ♦❢ ❝♦♥str❛✐♥ts ♦r ❛ss✉♠♣t✐♦♥s✱ s✉❝❤ ❛s str♦❦❡ ✐♥♣✉t ♦r❞❡r ♦r ✈❡rt✐❝❛❧ ❛♥❞ ❤♦r✐③♦♥t❛❧ ❛❧✐❣♥♠❡♥ts✱ t♦ ❧✐♥❡❛r✐③❡ t❤❡ ❡①♣r❡ss✐♦♥ ❝♦♠♣♦♥❡♥ts✳ ❚❤❡s❡ r❡q✉✐r❡♠❡♥ts ♥♦t ♦♥❧② ❧✐♠✐t t❤❡ ❡✛❡❝t✐✈❡♥❡ss ♦❢ t❤❡ ♠❡t❤♦❞s✱ ❜✉t ❛❧s♦ ♠❛❦❡ ❞✐✣❝✉❧t t❤❡✐r ❡①t❡♥s✐♦♥ t♦ ✐♥❝❧✉❞❡ ♥❡✇ ❡①♣r❡ss✐♦♥ str✉❝t✉r❡s✳

■♥ t❤✐s t❤❡s✐s✱ ✇❡ ♠♦❞❡❧ t❤❡ r❡❝♦❣♥✐t✐♦♥ ♣r♦❜❧❡♠ ❛s ❛ ❣r❛♣❤ ♣❛rs✐♥❣ ♣r♦❜❧❡♠✳ ❚❤❡ ❣r❛♣❤✲❜❛s❡❞ ❞❡s❝r✐♣t✐♦♥ ♦❢ r❡❧❛t✐♦♥s ✐♥ t❤❡ ♣r♦❞✉❝t✐♦♥ r✉❧❡s ❛❧❧♦✇s ❞✐r❡❝t ♠♦❞❡❧✐♥❣ ♦❢ ♥♦♥✲❧✐♥❡❛r ♠❛t❤❡♠❛t✐❝❛❧ str✉❝t✉r❡s✳ ❖✉r ♣❛rs✐♥❣ ❛❧❣♦r✐t❤♠ ❞❡t❡r♠✐♥❡s r❡❝✉rs✐✈❡ ♣❛rt✐t✐♦♥s ♦❢ t❤❡ ✐♥♣✉t str♦❦❡s t❤❛t ✐♥❞✉❝❡ ❣r❛♣❤s ♠❛t❝❤✐♥❣ t❤❡ ♣r♦❞✉❝t✐♦♥ r✉❧❡ ❣r❛♣❤s✳ ❚♦ ♠✐t✐❣❛t❡ t❤❡ ❝♦♠♣✉t❛t✐♦♥❛❧ ❝♦st✱ ✇❡ ❝♦♥str❛✐♥ t❤❡ ♣♦ss✐❜❧❡ ♣❛rt✐t✐♦♥s t♦ ❣r❛♣❤s ❞❡r✐✈❡❞ ❢r♦♠ s❡ts ♦❢ s②♠❜♦❧ ❛♥❞ r❡❧❛t✐♦♥ ❤②♣♦t❤❡s❡s✱ ❝❛❧❝✉❧❛t❡❞ ✉s✐♥❣ ♣r❡✈✐♦✉s❧② tr❛✐♥❡❞ ❝❧❛ss✐✜❡rs✳ ❆ s❡t ♦❢ ❧❛❜❡❧s t❤❛t ✐♥❞✐❝❛t❡ ❧✐❦❡❧② ✐♥t❡r♣r❡t❛t✐♦♥s ✐s ❛ss♦❝✐❛t❡❞ t♦ ❡❛❝❤ s②♠❜♦❧ ❛♥❞ r❡❧❛t✐♦♥ ❤②♣♦t❤❡s✐s✱ ❛♥❞ tr❡❛t♠❡♥t ♦❢ ❛♠❜✐❣✉✐t② ❛t s②♠❜♦❧ ❛♥❞ r❡❧❛t✐♦♥ ❧❡✈❡❧s ✐s ❧❡❢t t♦ t❤❡ ♣❛rs✐♥❣ ♣r♦❝❡ss✳ ❚❤❡ ♣❛rs✐♥❣ ❛❧❣♦r✐t❤♠ ❜✉✐❧❞s ❛ ❢♦r❡st ✐♥ ✇❤✐❝❤ ❡❛❝❤ tr❡❡ ❝♦rr❡s♣♦♥❞s t♦ ❛♥ ✐♥t❡r♣r❡t❛t✐♦♥ ❝♦❤❡r❡♥t ✇✐t❤ t❤❡ ❣r❛♠♠❛r✳ ❲❡ ❞❡✜♥❡ ❛ s❝♦r❡ ❢✉♥❝t✐♦♥✱ ♦♣t✐♠✐③❡❞ t❤r♦✉❣❤ tr❛✐♥✐♥❣ ❞❛t❛✱ t❤❛t ❛ss♦❝✐❛t❡s ❛ ❝♦st t♦ ❡❛❝❤ tr❡❡✳ ❲❡ t❤❡♥ s❡❧❡❝t ❛ tr❡❡ ✇✐t❤ ♠✐♥✐♠✉♠ ❝♦st ❛s r❡s✉❧t✳

❊①♣❡r✐♠❡♥t❛❧ ❡✈❛❧✉❛t✐♦♥ s❤♦✇s t❤❛t t❤❡ ♣r♦♣♦s❡❞ ♠❡t❤♦❞ ✐s ♠♦r❡ ❛❝❝✉r❛t❡ t❤❛♥ s❡✈❡r❛❧ st❛t❡ ♦❢ t❤❡ ❛rt ♠❡t❤♦❞s✳ ❊✈❡♥ t❤♦✉❣❤ ❣r❛♣❤ ♣❛rs✐♥❣ ✐s ❛ ❝♦♠♣✉t❛t✐♦♥❛❧❧② ❡①♣❡♥s✐✈❡ ♣r♦❝❡ss✱ t❤❡ ✉s❡ ♦❢ s②♠❜♦❧ ❛♥❞ r❡❧❛t✐♦♥ ❤②♣♦t❤❡s❡s t♦ ❝♦♥str❛✐♥ t❤❡ s❡❛r❝❤ s♣❛❝❡ ✐s ❛❜❧❡ t♦ ❡✛❡❝t✐✈❡❧② r❡❞✉❝❡ ❝♦♠♣❧❡①✐t②✱

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✈✐

❛❧❧♦✇✐♥❣ ♣r❛❝t✐❝❛❧ ❛♣♣❧✐❝❛t✐♦♥ ♦❢ t❤❡ ♣r♦❝❡ss✳ ❋✉rt❤❡r♠♦r❡✱ s✐♥❝❡ t❤❡ ♣r♦♣♦s❡❞ ♣❛rs✐♥❣ ❛❧❣♦r✐t❤♠ ❞♦❡s ♥♦t ♠❛❦❡ ❞✐r❡❝t ✉s❡ ♦❢ str✉❝t✉r❛❧ ♣❛rt✐❝✉❧❛r✐t✐❡s ♦❢ ♠❛t❤❡♠❛t✐❝❛❧ ❡①♣r❡ss✐♦♥s✱ ✐t ❤❛s ♣♦t❡♥t✐❛❧ t♦ ❜❡ ❛❞❛♣t❡❞ ❢♦r ♦t❤❡r t✇♦✲❞✐♠❡♥s✐♦♥❛❧ ♦❜❥❡❝t r❡❝♦❣♥✐t✐♦♥ ♣r♦❜❧❡♠s✳

❆s ❛ s❡❝♦♥❞❛r② ❝♦♥tr✐❜✉t✐♦♥ ♦❢ t❤✐s t❤❡s✐s✱ ✇❡ ❤❛✈❡ ♣r♦♣♦s❡❞ ❛ ❢r❛♠❡✇♦r❦ t♦ ❛✉t♦♠❛t✐③❡ t❤❡ ♣r♦❝❡ss ♦❢ ❜✉✐❧❞✐♥❣ ❤❛♥❞✇r✐tt❡♥ ♠❛t❤❡♠❛t✐❝❛❧ ❡①♣r❡ss✐♦♥ ❞❛t❛s❡ts✳ ❚❤❡ ❢r❛♠❡✇♦r❦ ❤❛s ❜❡❡♥ ✐♠♣❧❡✲ ♠❡♥t❡❞ ✐♥ ❛ ❝♦♠♣✉t❡r s②st❡♠ ❛♥❞ ✉s❡❞ t♦ ❣❡♥❡r❛t❡ ♣❛rt ♦❢ t❤❡ s❛♠♣❧❡s ✉s❡❞ ✐♥ t❤❡ ❡①♣❡r✐♠❡♥t❛❧ ♣❛rt ♦❢ t❤✐s t❤❡s✐s✳

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❈♦♥t❡♥ts

▲✐st ♦❢ ❋✐❣✉r❡s ①✐

▲✐st ♦❢ ❚❛❜❧❡s ①✈✐✐

✶ ■♥tr♦❞✉❝t✐♦♥ ✶

✶✳✶ ▼♦t✐✈❛t✐♦♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶

✶✳✷ ❚❤❡ r❡❝♦❣♥✐t✐♦♥ ♣r♦❜❧❡♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷

✶✳✸ ❚❤✐s t❤❡s✐s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺

✶✳✸✳✶ ❖❜❥❡❝t✐✈❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺

✶✳✸✳✷ ❑❡② ✐❞❡❛s ❡①♣❧♦r❡❞ ✐♥ t❤✐s t❤❡s✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻

✶✳✸✳✸ ▼❛❥♦r ❝♦♥tr✐❜✉t✐♦♥s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾

✶✳✹ ❚❤❡s✐s ♦r❣❛♥✐③❛t✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾

✷ Pr❡✈✐♦✉s ✇♦r❦ ✶✶

✷✳✶ ❇❛❝❦❣r♦✉♥❞ ♦♥ ♣❛rs✐♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶

✷✳✶✳✶ ❈❨❑ ❛❧❣♦r✐t❤♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸

✷✳✷ ❙❡q✉❡♥t✐❛❧ ❆♣♣r♦❛❝❤❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺

✷✳✸ ■♥t❡❣r❛t❡❞ ❛♣♣r♦❛❝❤❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽

✷✳✹ ❉✐s❝✉ss✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷

✸ ❚❤❡ ♣r♦♣♦s❡❞ r❡❝♦❣♥✐t✐♦♥ ❢r❛♠❡✇♦r❦ ✷✺

✸✳✶ ●r❛♣❤ ●r❛♠♠❛r t♦ ♠♦❞❡❧ ▼❛t❤❡♠❛t✐❝❛❧ ❊①♣r❡ss✐♦♥s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺

✸✳✶✳✶ ❆ ❝♦♥t❡①t✲❢r❡❡ ❣r❛♣❤ ❣r❛♠♠❛r ❢♦r ♠❛t❤❡♠❛t✐❝❛❧ ❡①♣r❡ss✐♦♥s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺

✸✳✶✳✷ ❈♦♠♣❛r✐s♦♥ ✇✐t❤ ♦t❤❡r ♠❛t❤❡♠❛t✐❝❛❧ ❡①♣r❡ss✐♦♥ ❣r❛♠♠❛rs ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼

✸✳✷ P❛rs❡ tr❡❡ ❛♥❞ ❢♦r❡st ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵

✸✳✸ ❚❤❡ ♣r♦♣♦s❡❞ ❛♣♣r♦❛❝❤ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶

✸✳✸✳✶ ❍②♣♦t❤❡s❡s ❣r❛♣❤ ❣❡♥❡r❛t♦r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶

✸✳✸✳✷ ●r❛♣❤ P❛rs❡r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺

✸✳✹ ❉✐s❝✉ss✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻

✹ ❙②♠❜♦❧ ❤②♣♦t❤❡s✐s ❝❧❛ss✐✜❝❛t✐♦♥ ✸✾

✹✳✶ ●❡♥❡r❛t✐♦♥ ♦❢ str♦❦❡ ❣r♦✉♣s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾

✹✳✷ ❙②♠❜♦❧ ❤②♣♦t❤❡s✐s ❝❧❛ss✐✜❝❛t✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵

✹✳✷✳✶ Pr❡♣r♦❝❡ss✐♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵

✹✳✷✳✷ ❖♥❧✐♥❡ s②♠❜♦❧ ❢❡❛t✉r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵

✹✳✷✳✸ ❖✤✐♥❡ s②♠❜♦❧ ❢❡❛t✉r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹

(10)

✈✐✐✐ ❈❖◆❚❊◆❚❙

✹✳✸ ❊①♣❡r✐♠❡♥t❛t✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼

✹✳✸✳✶ ❊①♣❡r✐♠❡♥t❛❧ s❡t✉♣✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼

✹✳✸✳✷ ❘❡s✉❧ts ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽

✹✳✹ ❉✐s❝✉ss✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵

✺ ❘❡❧❛t✐♦♥ ❝❧❛ss✐✜❝❛t✐♦♥ ✺✶

✺✳✶ Pr♦❜❧❡♠ ♦✈❡r✈✐❡✇ ❛♥❞ st❛t❡✲♦❢✲t❤❡✲❛rt ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶

✺✳✷ ❋❡❛t✉r❡ s❡t ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸

✺✳✷✳✶ ❘❡❧❛t✐♦♥ ✐♠❛❣❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸

✺✳✷✳✷ ●❡♦♠❡tr✐❝ ❢❡❛t✉r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹

✺✳✷✳✸ ❈❛t❡❣♦r② ✈❡❝t♦rs ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺

✺✳✸ ❊①♣❡r✐♠❡♥t❛t✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺

✺✳✸✳✶ ❊①♣❡r✐♠❡♥t❛❧ s❡t✉♣✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺

✺✳✸✳✷ ❘❡s✉❧ts ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻

✺✳✹ ❉✐s❝✉ss✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼

✻ ▼❛t❤❡♠❛t✐❝❛❧ ❡①♣r❡ss✐♦♥s ♣❛rs✐♥❣ t❡❝❤♥✐q✉❡ ✻✶

✻✳✶ P❛rs❡ ❋♦r❡st ❈♦♥str✉❝t✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶

✻✳✶✳✶ ❚♦♣✲❞♦✇♥ ♣❛rs✐♥❣ ❛❧❣♦r✐t❤♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸

✻✳✶✳✷ ❱❛❧✐❞ str♦❦❡ ♣❛rt✐t✐♦♥s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺

✻✳✷ ❖♣t✐♠❛❧ ♣❛rs❡ tr❡❡ ❡①tr❛❝t✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻

✻✳✷✳✶ ❘❛♥❦✐♥❣ ❢✉♥❝t✐♦♥s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼

✼ ❊①♣❡r✐♠❡♥t❛t✐♦♥ ✼✶

✼✳✶ ❊①♣❡r✐♠❡♥t❛❧ s❡t✉♣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶

✼✳✷ P❛r❛♠❡t❡r s❡tt✐♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸

✼✳✷✳✶ ❍②♣♦t❤❡s❡s ❣r❛♣❤ ❣❡♥❡r❛t✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸

✼✳✷✳✷ ●r❛♣❤ ♣❛rs✐♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺

✼✳✸ ❘❡s✉❧ts✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻

✼✳✹ ❉✐s❝✉ss✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✵

✽ ❆ ❢r❛♠❡✇♦r❦ t♦ ❜✉✐❧❞ ♦♥❧✐♥❡ ❤❛♥❞✇r✐tt❡♥ ♠❛t❤❡♠❛t✐❝❛❧ ❡①♣r❡ss✐♦♥ ❞❛t❛s❡ts ✽✸

✽✳✶ ■♥tr♦❞✉❝t✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✸

✽✳✷ ❉❡s✐r❡❞ q✉❛❧✐t✐❡s ♦❢ ♠❛t❤❡♠❛t✐❝❛❧ ❡①♣r❡ss✐♦♥ ❞❛t❛s❡ts ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✹

✽✳✸ ❚❤❡ ❞❛t❛s❡t ❝r❡❛t✐♦♥ ♣r♦❝❡❞✉r❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✹

✽✳✹ ❚❤❡ ❊①♣r❡ss▼❛t❝❤ s②st❡♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✺

✽✳✹✳✶ ❊①♣r❡ss▼❛t❝❤ ❛r❝❤✐t❡❝t✉r❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✻

✽✳✺ ❘❡s✉❧ts✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✵

✾ ❈♦♥❝❧✉s✐♦♥s ❛♥❞ ❢✉t✉r❡ ✇♦r❦ ✾✸

✾✳✶ ❙②♠❜♦❧ s❡❣♠❡♥t❛t✐♦♥ ❛♥❞ ❝❧❛ss✐✜❝❛t✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✸

✾✳✷ ❘❡❧❛t✐♦♥ ❝❧❛ss✐✜❝❛t✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✹

✾✳✸ ●r❛♣❤ ♣❛rs✐♥❣✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✺

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❈❖◆❚❊◆❚❙ ✐①

✶✵ ❘és✉♠é ét❡♥❞✉ ❡♥ ❢r❛♥ç❛✐s ✾✼

❆ ❈❘❖❍▼❊✲✷✵✶✹ ❙②♠❜♦❧ ❤②♣♦t❤❡s✐s ❝❧❛ss✐✜❝❛t✐♦♥ ✶✵✺

❇ ❍②♣♦t❤❡s✐s ❣r❛♣❤ ❧❛❜❡❧s ♣❡r s②♠❜♦❧ ❛♥❞ r❡❧❛t✐♦♥ ✶✵✼

❇✐❜❧✐♦❣r❛♣❤② ✶✶✶

(12)
(13)

▲✐st ♦❢ ❋✐❣✉r❡s

✶✳✶ ❖♥❧✐♥❡ ❤❛♥❞✇r✐tt❡♥ ♠❛t❤❡♠❛t✐❝❛❧ ❡①♣r❡ss✐♦♥ s❛♠♣❧❡ ♦❢ t❤❡ ❈❘❖❍▼❊✲✷✵✶✹

❞❛t❛s❡t ✭▼♦✉❝❤èr❡ ❡t ❛❧✳✱ ✷✵✶✹✮✳ ❚❤❡ s❛♠♣❧❡ r❡♣r❡s❡♥ts t❤❡ ❡①♣r❡ss✐♦♥ Pk

n=1

xnzn✳ ■t

✐s ❝♦♠♣♦s❡❞ ♦❢ ❛ s❡q✉❡♥❝❡ ♦❢ str♦❦❡s str = {str1, . . . , str13}✱ ✇❤❡r❡ stri ✐s t❤❡ ith

str♦❦❡✱ ❝♦♥s✐❞❡r✐♥❣ t❤❡ ✐♥♣✉t ♦r❞❡r✳ ❊❛❝❤ str♦❦❡ ✐s ❝♦♠♣♦s❡❞ ♦❢ ❛ s❡q✉❡♥❝❡ ♦❢ t✇♦✲ ❞✐♠❡♥s✐♦♥❛❧ ❝♦♦r❞✐♥❛t❡s✱ r❡♣r❡s❡♥t❡❞ ❛s ❛ s❡q✉❡♥❝❡ ♦❢ ♣♦✐♥ts✱ ✇❤❡r❡ ❣r❡❡♥ ❛♥❞ r❡❞

♣♦✐♥ts ✐♥❞✐❝❛t❡ t❤❡ ✜rst ❛♥❞ ❧❛st ♣♦✐♥t ♦❢ ❡❛❝❤ str♦❦❡✱ r❡s♣❡❝t✐✈❡❧②✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸

✶✳✷ ❆♠❜✐❣✉♦✉s ❤❛♥❞✇r✐tt❡♥ s②♠❜♦❧s✳ ❚❤❡② ❝♦✉❧❞ ❜❡ ✐♥t❡r♣r❡t❡❞ ❛s ✭❛✮ ✏+✑ ♦r ✏t✑✱ ✭❜✮

✏6✑ ♦r ✏G✑✱ ✭❝✮ ✏9✑ ♦r ✏q✑ ❛♥❞ ✭❞✮ ✏P✑ ♦r ✏p✑✳ ❊①tr❛❝t❡❞ ❢r♦♠ ❈❘❖❍▼❊✲✷✵✶✹

❞❛t❛s❡t ✭▼♦✉❝❤èr❡ ❡t ❛❧✳✱✷✵✶✹✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸

✶✳✸ ❆♠❜✐❣✉♦✉s ♠❛t❤❡♠❛t✐❝❛❧ ❡①♣r❡ss✐♦♥✳ ❚❤❡ ❡①♣r❡ss✐♦♥ ✐s ❝♦♠♣♦s❡❞ ♦❢ ✜✈❡ str♦❦❡s✱ t❤❛t ✐s(str1, . . . , str5)✳ ❙tr♦❦❡s{str4, str5}❝♦✉❧❞ ❜❡ ✐♥t❡r♣r❡t❡❞ ❛s t❤❡ s②♠❜♦❧ ✏4✑ ♦r ❛s ❛

s✉❜❡①♣r❡ss✐♦♥ ✏<1✑✱{str1, str2} ❝♦✉❧❞ ❜❡ ✐♥t❡r♣r❡t❡❞ ❛s s②♠❜♦❧ ✏p✑ ♦r ✏P✑ ❛♥❞ t❤❡

r❡❧❛t✐♦♥ ❜❡t✇❡❡♥{str1, str2} ❛♥❞{str3} ❝♦✉❧❞ ❜❡ ❤♦r✐③♦♥t❛❧ ♦r s✉♣❡rs❝r✐♣t✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹

✶✳✹ ❚❤❡ r❡❝♦❣♥✐t✐♦♥ s❝❤❡♠❡ ♦❢ t❤❡ t❡❝❤♥✐q✉❡ ♣r♦♣♦s❡❞ ✐♥ t❤✐s t❤❡s✐s✳ ●r❛② r❡❝t❛♥❣❧❡s

r❡♣r❡s❡♥t t❤❡ ♠❛✐♥ ♠♦❞✉❧❡s t❤❛t ❝♦♠♣♦s❡ t❤❡ ❛♣♣r♦❛❝❤✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼

✷✳✶ ✭❛✮ ❆ ●r❛♠♠❛r ❛♥❞ ✭❜✮ ❛ ♣❛rs❡ tr❡❡ ❜✉✐❧t ✇✐t❤ t❤❡ ❣r❛♠♠❛r✳ ❚❤❡ ❡❧❡♠❡♥ts ♦❢ t❤❡

❣r❛♠♠❛r ❛r❡ N = {N ame, Sentences, List}✱ T = {tom, dick, harry, and, ,}✱ R ✐s

❝♦♠♣♦s❡❞ ♦❢ t❤❡ s❡✈❡♥ r✉❧❡s ✭✏⑤✑ s❡♣❛r❛t❡s r✉❧❡s ✇✐t❤ t❤❡ s❛♠❡ ♥♦♥✲t❡r♠✐♥❛❧ ✐♥ t❤❡

❧❡❢t ❤❛♥❞ s✐❞❡✮✱ ❛♥❞I =Sentences✳ ❊①tr❛❝t❡❞ ❢r♦♠●r✉♥❡ ❛♥❞ ❏✳❍✭✷✵✵✽✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷

✷✳✷ ❈❨❑ ♣❛rs✐♥❣ ❡①❛♠♣❧❡✳ ❊①tr❛❝t❡❞ ❢r♦♠ ❨❛♠❛♠♦t♦ ❡t ❛❧✳ ✭✷✵✵✻✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹

✷✳✸ ❊①❛♠♣❧❡ ♦❢ ❣r❛♠♠❛r ✉s❡❞ ✐♥ ❨❛♠❛♠♦t♦ ❡t ❛❧✳ ✭✷✵✵✻✮✳ ❘✉❧❡s ♠❛r❦❡❞ ✇✐t❤ ✯ ❝❛♥♥♦t

❜❡ ❛♣♣❧✐❡❞ ✐t❡r❛t✐✈❡❧②✳ ✯✯ ♠❡❛♥s t❤❛t t❤❡ ✇r✐t✐♥❣ ♦r❞❡r ♦❢ t❤❡ ✷ s②♠❜♦❧s ❝❛♥ ❝❤❛♥❣❡ ❛♥❞ t❤❛t t❤❡ r✉❧❡s ✇✐t❤ ♣❡r♠✉t❛t✐♦♥ ♦❢ t❤❡ ♦r❞❡r ❛r❡ ✐♥❝❧✉❞❡❞✳ ❆❜❜r❡✈✐❛t❡❞ ♥❛♠❡s ♦❢ ❡①♣r❡ss✐♦♥ ❡❧❡♠❡♥ts ❛r❡ ❛s ❢♦❧❧♦✇s✿ ❊❳P✿ ❡①♣r❡ss✐♦♥✱ ❙❨▼✿ s②♠❜♦❧✱ ❋❯◆❈✿ ❢✉♥❝t✐♦♥✱ ▲■◆❊✿ ❢r❛❝t✐♦♥ ❧✐♥❡✱ ❉▲■◆❊✿ ❢r❛❝t✐♦♥ ❧✐♥❡ ✇✐t❤ ❞❡♥♦♠✐♥❛t♦r✱ ◆▲■◆❊✿ ❢r❛❝t✐♦♥ ❧✐♥❡ ✇✐t❤ ♥✉♠❡r❛t♦r✱ ❘❖❖❚✿ r♦♦t s✐❣♥✱ ❆❈❈✿ ❛❝❝❡♥t✱ ❘P❆❘✿ r✐❣❤t ♣❛r❡♥t❤❡s✐s✱ ▲P❆❘✿ ❧❡❢t ♣❛r❡♥t❤❡s✐s✱ ❳❘P❆❘✿ ❡①♣r❡ss✐♦♥ ✇✐t❤ r✐❣❤t ♣❛r❡♥t❤❡s✐s✱ ❳▲P❆❘✿ ❡①♣r❡ss✐♦♥ ✇✐t❤

❧❡❢t ♣❛r❡♥t❤❡s✐s✱ ❍❙✿ ❤❛♥❞✇r✐tt❡♥ str♦❦❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺

✷✳✹ ✭❛✮ ■♥♣✉t ❡①♣r❡ss✐♦♥ ❛♥❞ ✭❜✮ s②♠❜♦❧ ❤②♣♦t❤❡s❡s ♥❡t✳ ❊①tr❛❝t❡❞ ❢r♦♠❑♦s❝❤✐♥s❦✐ ❡t ❛❧✳

✭✶✾✾✺✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻

✷✳✺ ❙♣❛t✐❛❧ r❡❣✐♦♥s r❡❧❛t✐✈❡ t♦ s②♠❜♦❧s✳ ❊①tr❛❝t❡❞ ❢r♦♠ ❩❛♥✐❜❜✐ ❡t ❛❧✳✭✷✵✵✷✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽

✷✳✻ ❋✉③③② r❡❣✐♦♥s ❛ss♦❝✐❛t❡❞ ✇✐t❤ ❛ s②♠❜♦❧✳ ■♥t❡rs❡❝t✐♦♥ ♦❢ t❤❡ ❢✉③③② r❡❣✐♦♥s ❞❡✜♥❡ ❛s

❛♠❜✐❣✉✐t② ③♦♥❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾

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①✐✐ ▲■❙❚ ❖❋ ❋■●❯❘❊❙

✷✳✼ ❋✉③③② r✲❈❋● ❡①❛♠♣❧❡✳ ❊①tr❛❝t❡❞ ❢r♦♠ ▼❛❝▲❡❛♥ ❛♥❞ ▲❛❜❛❤♥ ✭✷✵✶✸✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵

✷✳✽ ❆♥ ❡①♣r❡ss✐♦♥ ✈✐♦❧❛t✐♥❣ t❤❡ ❤♦r✐③♦♥t❛❧ ♦r❞❡r✐♥❣ ❛ss✉♠♣t✐♦♥✳ ❚❤❡ s✉♠♠❛t✐♦♥ ❛♥❞ ✐ts

❛r❣✉♠❡♥ts ♠✉st st❛rt ❜❡❢♦r❡Y✱ ❜✉t t❤❡ ❧❡tt❡r C✕ ✐♥ t❤❡ ❛r❣✉♠❡♥t ♦❢ t❤❡ s✉♠♠❛t✐♦♥

✕ ❜❡❣✐♥s ❛❢t❡rY✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵

✷✳✾ ❙❛♠♣❧❡ r✉❧❡s ♦❢❈❡❧✐❦ ❛♥❞ ❨❛♥✐❦♦❣❧✉✭✷✵✶✶✮✱ ❚❤❡ s②♠❜♦❧ ✏⑤✑ ✐♥❞✐❝❛t❡s t❤❛t ❛♥② ♦❢ t❤❡

s②♠❜♦❧s ❛t t❤❡✐r s✐❞❡s ♠❛② ❜❡ ❛ ❧❛❜❡❧ ♦❢ t❤❡ ✈❡rt❡①✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷

✷✳✶✵ P❛rs❡ ❛❧❣♦r✐t❤♠ ♦❢ ❈❡❧✐❦ ❛♥❞ ❨❛♥✐❦♦❣❧✉✭✷✵✶✶✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷

✸✳✶ ●r❛♣❤ ●r❛♠♠❛r ❡①❛♠♣❧❡✳ ❇❧❛❝❦ ❛rr♦✇s s❡♣❛r❛t❡ t❤❡ r❡♣❧❛❝❡❞ ❛♥❞ r❡♣❧❛❝✐♥❣ ❣r❛♣❤s ♦❢ t❤❡ r✉❧❡s ❛♥❞ ❣r❛② ❛rr♦✇s r❡♣r❡s❡♥t t❤❡ ❡❞❣❡s ♦❢ ❡❛❝❤ ❣r❛♣❤✳ ❚❤❡ ❡❧❡♠❡♥ts ♦❢ t❤❡

❣r❛♠♠❛r ❛r❡✿ ♥♦♥✲t❡r♠✐♥❛❧s ◆❂④▼❊✱ ❚❘▼✱ ❖P✱ ❈❍❆❘⑥✱ t❡r♠✐♥❛❧s ❚ ❂ ④✰✱✲✱<✱>✱

❛✱ ✳ ✳ ✳ ✱③✱ ❆✱ ✳ ✳ ✳ ✱ ❩✱ ✵✱ ✳ ✳ ✳ ✱ ✾⑥✱ ✐♥✐t✐❛❧ ❣r❛♣❤ ■ ❝♦rr❡s♣♦♥❞s t♦ t❤❡ ❧❡❢t ❤❛♥❞ s✐❞❡ ❣r❛♣❤

♦❢ r✉❧❡ r✲✶✱ ❛♥❞ r✉❧❡s ❘ ❂ ④r✲✶✱. . .✱ r✲✼✸⑥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻

✸✳✷ ●r❛♣❤ ❣❡♥❡r❛t✐♦♥ t❤r♦✉❣❤ r✉❧❡ ❛♣♣❧✐❝❛t✐♦♥s✳ ❆t ❡❛❝❤ r✉❧❡ ❛♣♣❧✐❝❛t✐♦♥✱ t❤❡ r❡♣❧❛❝❡❞ ❣r❛♣❤ ♥♦❞❡s ❛r❡ ❞❡♣✐❝t❡❞ ✐♥ ❞❛r❦ ❣r❛② ♥♦❞❡s ❛♥❞ t❤❡ ❡♠❜❡❞❞✐♥❣ ❡❞❣❡s ✇✐t❤ ❞❛s❤❡❞

❛rr♦✇s✳ ❘✉❧❡ ❛♣♣❧✐❝❛t✐♦♥s ❛❢t❡r r✲✼ ❛r❡ ♦♠✐tt❡❞ ✭❞♦tt❡❞ ❛rr♦✇✮✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽

✸✳✸ ●r❛♣❤s ❣❡♥❡r❛t❡❞ ✇✐t❤ t❤❡ ❣r❛♠♠❛r ✐♠♣❧❡♠❡♥t❡❞ ❢♦r ❡①♣❡r✐♠❡♥t❛t✐♦♥✳ ❚❤❡ ❣r❛♣❤s

❝♦rr❡s♣♦♥❞ t♦ ❡①♣❡ss✐♦♥s ✭❛✮Pbc<1✱ ✭❜✮ a+bc d❛♥❞ ✭❝✮a√3x+y✳ ❱❡rt✐❝❡s ❛♥❞ ❡❞❣❡s

❛r❡ ❧❛❜❡❧❡❞ ✇✐t❤ t❤❡✐r s②♠❜♦❧ ❛♥❞ r❡❧❛t✐♦♥ ❝❧❛ss❡s ✱ r❡s♣❡❝t✐✈❡❧②✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽

✸✳✹ ■♥t❡❣r❛t✐♦♥ r✉❧❡ ❡①❛♠♣❧❡ ✉s❡❞ ✐♥▼❛❝▲❡❛♥ ❛♥❞ ▲❛❜❛❤♥✭✷✵✶✸✮ ✭❛✮ ❛♥❞ ✐ts ❝♦rr❡s♣♦♥❞✲

✐♥❣ r❡♣r❡s❡♥t❛t✐♦♥ ✉s✐♥❣ ❣r❛♣❤ ❣r❛♠♠❛r ✭❜✮✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾

✸✳✺ ●r❛♣❤ ❣r❛♠♠❛r r✉❧❡ ❡①❛♠♣❧❡s ♣r♦♣♦s❡❞ ✐♥ ❈❡❧✐❦ ❛♥❞ ❨❛♥✐❦♦❣❧✉ ✭✷✵✶✶✮✳ ❊❛❝❤ r✉❧❡

❞❡✜♥❡s t❤❡ r❡♣❧❛❝❡♠❡♥t ♦❢ ❛ s✐♥❣❧❡ ✈❡rt❡① ❣r❛♣❤ ✐♥ t❤❡ ❘❍❙ ✇✐t❤ ❛ ❣r❛♣❤ t❤❛t ❤❛s ❛ ❝❡♥tr❛❧ ♥♦❞❡✱ ❛♥❞ s✉rr♦✉♥❞✐♥❣ ♥♦❞❡s ❝♦♥♥❡❝t❡❞ ♦♥❧② t♦ t❤❡ ❝❡♥tr❛❧ ♥♦❞❡ ✭st❛r ❣r❛♣❤✮✳ ❚❤❡ s②♠❜♦❧ ✏⑤✑ ✐♥❞✐❝❛t❡s t❤❛t t❤❡ s②♠❜♦❧ ❛t ✐ts ❧❡❢t ♦r r✐❣❤t ♠❛② ❜❡ ❛ ❧❛❜❡❧ ♦❢ t❤❡

✈❡rt❡①✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵

✸✳✻ P❛rs❡ tr❡❡ ❡①❛♠♣❧❡ ❢♦r t❤❡ ❡①♣r❡ss✐♦♥Pb <1✱ ❝♦♥s✐❞❡r✐♥❣ t❤❡ ❣r❛♠♠❛r ♦❢ ❋✐❣✉r❡ ✸✳✶✳

❚❤❡ r♦♦t ♦❢ t❤❡ tr❡❡ ✭✐♥s✐❞❡ t❤❡ t♦♣✲♠♦st r❡❝t❛♥❣❧❡✮ ❝♦rr❡s♣♦♥❞s t♦ t❤❡ ✐♥✐t✐❛❧ ❣r❛♣❤ ♦❢ t❤❡ ❣r❛♠♠❛r✳ ❚❤❡ ❛♣♣❧✐❡❞ r✉❧❡s ❛r❡ ❞❡♣✐❝t❡❞ ❛s ❛rr♦✇s ❢r♦♠ ❛ ✈❡rt❡① ✭♦r s✐♥❣❧❡ ✈❡rt❡① ❣r❛♣❤✮ t♦ ❛ r❡❝t❛♥❣❧❡ t❤❛t ❝♦♥t❛✐♥s t❤❡ tr❛♥s❢♦r♠❡❞ ❣r❛♣❤✳ ❊❛❝❤ r✉❧❡ ✐s ✐❞❡♥t✐✜❡❞

✉s✐♥❣ t❤❡ ❝♦❞❡s ❞❡✜♥❡❞ ✐♥ t❤❡ ❣r❛♠♠❛r✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶

✸✳✼ ❆ ♣❛rs❡ ♣❛rs❡ ❢♦r❡st ✭❜✮ r❡♣r❡s❡♥t✐♥❣ ♠✉❧t✐♣❧❡ ✐♥t❡r♣r❡t❛t✐♦♥s ♦❢ ❛ ♠❛t❤❡♠❛t✐❝❛❧ ❡①✲ ♣r❡ss✐♦♥ ✭❛✮✳ ▲❛❜❡❧s ♦♥ ❛rr♦✇s ✐♥❞✐❝❛t❡ t❤❡ ❣r❛♠♠❛r r✉❧❡s✳ ❘❡❞ ❛rr♦✇s r❡♣r❡s❡♥t ❛

♣❛rs❡ tr❡❡ t❤❛t ❝♦rr❡s♣♦♥❞s t♦ t❤❡ ✐♥t❡r♣r❡t❛t✐♦♥ ✏Pb4✑✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷

✸✳✽ ❚❤❡ r❡❝♦❣♥✐t✐♦♥ s❝❤❡♠❡ ♦❢ t❤❡ t❡❝❤♥✐q✉❡ ♣r♦♣♦s❡❞ ✐♥ t❤✐s t❤❡s✐s✳ ●r❛② r❡❝t❛♥❣❧❡s

r❡♣r❡s❡♥t t❤❡ ♠❛✐♥ ♠♦❞✉❧❡s t❤❛t ❝♦♠♣♦s❡ t❤❡ ❛♣♣r♦❛❝❤✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸

✸✳✾ ❍②♣♦t❤❡s❡s ❣r❛♣❤ ❡①❛♠♣❧❡✳ ❱❡rt✐❝❡s r❡♣r❡s❡♥t s②♠❜♦❧ ❤②♣♦t❤❡s❡s ❛♥❞ ❡❞❣❡s r❡♣r❡s❡♥t r❡❧❛t✐♦♥s ❜❡t✇❡❡♥ s②♠❜♦❧s✳ ❚❤❡ ❧❛❜❡❧s ❛ss♦❝✐❛t❡❞ t♦ s②♠❜♦❧s ❛♥❞ r❡❧❛t✐♦♥s ✐♥❞✐❝❛t❡

t❤❡✐r ♠♦st ❧✐❦❡❧② ✐♥t❡r♣r❡t❛t✐♦♥s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹

✹✳✶ ✭❛✮✱ ✭❜✮✱ ❛♥❞ ✭❝✮ s❤♦✇ r❛✇ s②♠❜♦❧ s❛♠♣❧❡s ❛♥❞ ✭❞✮✱ ✭❡✮ ❛♥❞ ✭❢✮ t❤❡✐r ❝♦rr❡s♣♦♥❞✐♥❣

(15)

▲■❙❚ ❖❋ ❋■●❯❘❊❙ ①✐✐✐

✹✳✷ ❙❤❛♣❡ ❝♦♥t❡①t ♦❢ t✇♦ ♣♦✐♥ts ♦❢ ❛ s②♠❜♦❧ ✏✷✑✿ ✭❛✮ ❛♥❞ ✭❝✮ s❤♦✇ t❤❡ s❛♠♣❧❡❞ ♣♦✐♥ts ❛♥❞ t❤❡ ❧♦❣ ♣♦❧❛r ❤✐st♦❣r❛♠ ❜✐♥s ✉s❡❞ t♦ ❝❛❧❝✉❧❛t❡ s❤❛♣❡ ❝♦♥t❡①t✳ ✭❜✮ ❛♥❞ ✭❞✮ s❤♦✇ t❤❡ s❤❛♣❡ ❝♦♥t❡①t ❤✐st♦❣r❛♠ r❡❧❛t✐✈❡ t♦ ✭❛✮ ❛♥❞ ✭❝✮ r❡s♣❡❝t✐✈❡❧②❀ ❞❛r❦ ❝❡❧❧s ♠❡❛♥ ❤✐❣❤❡r

✈❛❧✉❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷

✹✳✸ ❋✉③③② ❜✐♥s ✐♥ t❤❡ ✭❛✮ r❛❞✐❛❧ ❛♥❞ ✭❜✮ ❛♥❣✉❧❛r ❝♦♦r❞✐♥❛t❡s✳ ❚❤❡ ❛rr♦✇s ✐♥ t❤❡ ❛♥❣✉❧❛r

❝♦♦r❞✐♥❛t❡ r❡♣r❡s❡♥t ✐ts ❝✐r❝✉❧❛r ♥❛t✉r❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷

✹✳✹ ❋♦✉r ❞✐✛❡r❡♥t ♣♦s✐t✐♦♥s ✐♥ ❛ ❜✐♥Binij✳ ❘❡❣✐♦♥s ❜❡t✇❡❡♥ ❞♦tt❡❞ ❧✐♥❡s ✐♥❞✐❝❛t❡ tr❛♥s✐✲

t✐♦♥ ❛r❡❛s ❜❡t✇❡❡♥ ❜✐♥s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸

✹✳✺ ❙❤❛♣❡ ❝♦♥t❡①t ❡①tr❛❝t✐♦♥ ❢♦r ❛rt✐✜❝✐❛❧ ♥❡✉r❛❧ ♥❡t✇♦r❦s✳ ✭❛✮ ❙❤❛♣❡ ❝♦♥t❡①t ✐s ❡①tr❛❝t❡❞ ♦♥❧② ❛t s♦♠❡ s❛♠♣❧❡❞ ♣♦✐♥ts✳ ✭❜✮ ❚❤❡ ❡①tr❛❝t❡❞ s❤❛♣❡ ❝♦♥t❡①t ✈❡❝t♦rs ❛r❡ ❝♦♥❝❛t❡✲

♥❛t❡❞ t♦ ❢♦r♠ ❛ ❢❡❛t✉r❡ ✈❡❝t♦r t❤❛t ✐s ✉s❡❞ ❛s ✐♥♣✉t t♦ ❛ ♥❡✉r❛❧ ♥❡t✇♦r❦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺

✹✳✻ ❇✐❞✐♠❡♥s✐♦♥❛❧ ✭20×20 ❝❡❧❧s✮ ❤✐st♦❣r❛♠s ❝❛❧❝✉❧❛t❡❞ ❢r♦♠ s❛♠♣❧❡s ♦❢ s②♠❜♦❧s ✏✸✑✱ ✏✳✑✱

✏✶✑ ❛♥❞ ✏s✑✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻

✹✳✼ ❙②♠❜♦❧ ❤②♣♦t❤❡s❡s ❡①❛♠♣❧❡s ❛♥❞ t❤❡✐r ❝♦rr❡s♣♦♥❞✐♥❣ ❝♦♥t❡①t✉❛❧ ❤✐st♦❣r❛♠s✳✳ ✳ ✳ ✳ ✳ ✹✼

✹✳✽ ❙②♠❜♦❧ ❝❧❛ss❡s ✇✐t❤ ❧♦✇❡st r❡❝♦❣♥✐t✐♦♥ r❛t❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾

✺✳✶ ▼❛t❤❡♠❛t✐❝❛❧ ❡①♣r❡ss✐♦♥s ✇✐t❤ ❛♠❜✐❣✉♦✉s r❡❧❛t✐♦♥s ❜❡t✇❡❡♥ s✉❜❡①♣r❡ss✐♦♥s ✐♥ ❜❧✉❡ ❛♥❞ r❡❞✳ ❚❤❡ r❡❧❛t✐♦♥ ✐♥ ✭❛✮ ♠❛② ❜❡ ❝♦♥s✐❞❡r❡❞ ❛s ❤♦r✐③♦♥t❛❧ ♦r s✉❜s❝r✐♣t ❛♥❞ ✐♥ ✭✷✮

✐t ❝❛♥ ❜❡ ✐♥t❡r♣r❡t❡❞ ❛s ❤♦r✐③♦♥t❛❧ ♦r s✉♣❡rs❝r✐♣t✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶

✺✳✷ ❈r✐s♣ r❡❣✐♦♥s t❤❛t ❞❡✜♥❡ r❡❧❛t✐♦♥s r❡❧❛t✐✈❡ t♦ ❛ s②♠❜♦❧✳ ❘❡❣✐♦♥s ❛r❡ ❞❡✜♥❡❞ ❛❝✲ ❝♦r❞✐♥❣ t♦ t❤❡ s②♠❜♦❧ ❝❛t❡❣♦r②✱ t❤❛t ✐s ✐♥❞✐❝❛t❡❞ ❜❡❧♦✇ ❡❛❝❤ s②♠❜♦❧✳ ❊①tr❛❝t❡❞ ❢r♦♠❩❛♥✐❜❜✐ ❡t ❛❧✳ ✭✷✵✵✷✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷

✺✳✸ ❋✉③③② r❡❣✐♦♥s t❤❛t ❞❡✜♥❡ r❡❧❛t✐♦♥s r❡❧❛t✐✈❡ t♦ ❛ s②♠❜♦❧✳ ❊①tr❛❝t❡❞ ❢r♦♠ ❩❤❛♥❣ ❡t ❛❧✳

✭✷✵✵✺✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷

✺✳✹ ●❡♦♠❡tr✐❝ ❢❡❛t✉r❡s✳F ✐s ❞❡✜♥❡❞ ❛s t❤❡ ❞✐st❛♥❝❡ ❜❡t✇❡❡♥ t❤❡ ❝❡♥t❡rs ♦❢ t❤❡ ❜♦✉♥❞✐♥❣

❜♦①❡s ♦❢ t❤❡ s✉❜❡①♣r❡ss✐♦♥s✳cenh❛♥❞cenv r❡♣r❡s❡♥t t❤❡ ❝♦♦r❞✐♥❛t❡s✱ ✐♥ ① ❛♥❞ ② ❛①✐s

r❡s♣❡❝t✐✈❡❧②✱ ♦❢ t❤❡ ❝❡♥tr♦✐❞ ♦❢ ✐ts ♣❛r❛♠❡t❡r✳ ❊①tr❛❝t❡❞ ❢r♦♠ ➪❧✈❛r♦ ❛♥❞ ❩❛♥✐❜❜✐

✭✷✵✶✸✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸

✺✳✺ ❘❡❧❛t✐♦♥ ✐♠❛❣❡ ❡①❛♠♣❧❡s ❝❛❧❝✉❧❛t❡❞ ❢r♦♠ r❡❧❛t✐♦♥s ♦❢ t❤❡ ❡①♣r❡ss✐♦♥ ♦❢ ❋✐❣✉r❡ ✭❛✮✳

❘❡❧❛t✐♦♥ ✐♠❛❣❡s ❝♦rr❡s♣♦♥❞ t♦ r❡❧❛t✐♦♥s✿ ✭❜✮ ❛❜♦✈❡✭−✱ax0+by0+c✮✱ ✭❝✮ ❜❡❧♦✇✭−✱

a2+b2✮ ✱ ✭❞✮ ✐♥s✐❞❡✭ a2 +b2✮✱ ✭❡✮ ❤♦r✐③♦♥t❛❧✭+ c✮✱ ✭❢✮ s✉❜s❝r✐♣t✭x 0✮ ✭❣✮

s✉♣❡rs❝r✐♣t✭a✱2✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹

✺✳✻ ◆♦r♠❛❧✐③❡❞ ✭✈❛❧✉❡s ❜❡t✇❡❡♥ ✵ ❛♥❞ ✶✮ ❜❛s❡ ♣♦s✐t✐♦♥ ❛♥❞ ❤❡✐❣❤t✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺

✺✳✼ ◆✉♠❜❡r ♦❢ r❡❧❛t✐♦♥ s❛♠♣❧❡s ♣❡r ❝❧❛ss ✐♥ t❤❡ ✭❛✮ tr❛✐♥✐♥❣ ❛♥❞ ✭❜✮ t❡st s❡ts✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻

✺✳✽ ▼✐s❝❧❛ss✐✜❝❛t✐♦♥ ❡①❛♠♣❧❡s✳ ❊❛❝❤ ✐♠❛❣❡ ❧❛❜❡❧ ✐♥❞✐❝❛t❡s t❤❡ tr✉❡ r❡❧❛t✐♦♥ ❝❧❛ss ❢♦❧❧♦✇❡❞

❜② t❤❡ ❝❧❛ss✐✜❡r✬s ♦✉t♣✉t✱ t❤❛t ✐s✿ tr✉❡ r❡❧❛t✐♦♥→♦✉t♣✉t✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽

✻✳✶ ❚❤❡ ♣❛rs❡ ❢♦r❡st ❝♦♥str✉❝t✐♦♥ st❡♣ r❡❝❡✐✈❡s ❛ s❡t ♦❢ str♦❦❡s ❛s ✐♥♣✉t ✭❛✮ ❛♥❞ ✉s❡s ❛ ❣r❛♣❤ ❣r❛♠♠❛r ✭❜✮ t♦ ❜✉✐❧❞ ❛ ♣❛rs❡ ❢♦r❡st str✉❝t✉r❡ ✭❝✮✳ ❆ ♣❛rs❡ ❢♦r❡st st♦r❡s ♠✉❧t✐♣❧❡ ✐♥t❡r♣r❡t❛t✐♦♥s ♦❢ t❤❡ ✐♥♣✉t ❛s ♣❛rs❡ tr❡❡s✳ ❘❡❞ ❛rr♦✇s ♦❢ t❤❡ ♣❛rs❡ ❢♦r❡st r❡♣r❡s❡♥t

❛ ❛ ♣❛rs❡ tr❡❡ t❤❛t ❝♦rr❡s♣♦♥❞s t♦ t❤❡ ✐♥t❡r♣r❡t❛t✐♦♥ ✏Pb4✧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷

✻✳✷ ❚✇♦ ♣❛rt✐t✐♦♥s ♦❢ ❛ str♦❦❡ s❡t ❛❝❝♦r❞✐♥❣ t♦ ❛ ♣r♦❞✉❝t✐♦♥ r✉❧❡s✬s ❣r❛♣❤✳ ❇❧✉❡ ❧✐♥❡s

(16)

①✐✈ ▲■❙❚ ❖❋ ❋■●❯❘❊❙

✻✳✸ ❆ ❤②♣♦t❤❡s❡s ❣r❛♣❤ ❛♥❞ ✈❡rt✐❝❡s ❢♦r♠❡❞ ❜② ❝♦♥tr❛❝t✐♥❣ ❡❞❣❡s✳ ❚❤❡ ❞❛s❤❡❞ ❛rr♦✇s ♦❢

t❤❡ ✈❡rt❡① ❝♦♠♣♦s❡❞ ♦❢ str♦❦❡sPb r❡♣r❡s❡♥t ✐♥❤❡r✐t❡❞ ❡❞❣❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻

✻✳✹ P❛rs❡ tr❡❡ ♦❢ ❡①♣r❡ss✐♦♥ Pb < 1✱ ❡①tr❛❝t❡❞ ❢r♦♠ t❤❡ ♣❛rs❡ ❢♦r❡st ♦❢ ❋✐❣✉r❡ ✻✳✶✭❝✮✳

◆♦❞❡s ❛r❡ ✐♥❞❡①❡❞ ❛sxi✱ ❢♦ri= 1, . . . ,9✳ ❙✐♠✐❧❛r❧②✱ ✈❡rt✐❝❡s ❛♥❞ ❡❞❣❡s ♦❢ t❤❡ ✐♥st❛♥t✐✲

❛t❡❞ ❣r❛♣❤s ❛r❡ r❡s♣❡❝t✐✈❡❧② ✐♥❞❡①❡❞ ❛svj✱ ❢♦rj= 1, . . . ,12✱ ❛♥❞ek✱ ❢♦rk= 1, . . . ,3✳

◆♦❞❡s ✇✐t❤ t❡r♠✐♥❛❧ s②♠❜♦❧s ❛r❡ ❞❡♣✐❝t❡❞ ✇✐t❤ ❞♦✉❜❧❡ ❧✐♥❡ ❜♦r❞❡rs✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾

✼✳✶ ❙②♠❜♦❧✱ r❡❧❛t✐♦♥✱ ❛♥❞ ❡①♣r❡ss✐♦♥ ❧❡✈❡❧ r❡❝❛❧❧ ♦❢ t❤❡ ❤②♣♦t❤❡s❡s ❣r❛♣❤ ❣❡♥❡r❛t✐♦♥ st❡♣✱

❢♦r t❤r❡s❤♦❧❞s ✐♥ t❤❡ r❛♥❣❡ [0.1−1.0]✳ ❋♦r ❡❛❝❤ s②♠❜♦❧ t❤r❡s❤♦❧❞ ✈❛❧✉❡✱ ✈❛❧✉❡s ❢♦r

t❤❡ r❡❧❛t✐♦♥ t❤r❡s❤♦❧❞ ❛r❡ ✈❛r✐❡❞ ❢r♦♠0.1t♦ 1.0✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸

✼✳✷ ▼❡❛♥ ♦❢ s②♠❜♦❧ ❛♥❞ r❡❧❛t✐♦♥ ❤②♣♦t❤❡s✐s ❧❛❜❡❧s ♣❡r s②♠❜♦❧ ❛♥❞ r❡❧❛t✐♦♥✱ r❡s♣❡❝t✐✈❡❧②✳ ❚❤❡ ❧❡❢t ❤❛♥❞ ❛①✐s ✐♥❞✐❝❛t❡s t❤❡ ♥✉♠❜❡r ♦❢ ❧❛❜❡❧s ♣❡r s②♠❜♦❧ ❛♥❞ r❡❧❛t✐♦♥✳ ❚❤❡ r✐❣❤t

❤❛♥❞ ❛①✐s ✐♥❞✐❝❛t❡s t❤❡ ♣❡r❝❡♥t❛❣❡ ♦❢ r❡❝♦❣♥✐③❡❞ ❡①♣r❡ss✐♦♥s✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹

✼✳✸ ❊①♣r❡ss✐♦♥ r❡❝❛❧❧ ♦❜t❛✐♥❡❞ ❛t ❣r❛♣❤ ♣❛rs✐♥❣ ❛♥❞ ❤②♣♦t❤❡s❡s ❣r❛♣❤ ❣❡♥❡r❛t✐♦♥ st❛❣❡s✱

❢♦r ❞✐✛❡r❡♥t s②♠❜♦❧ ❛♥❞ r❡❧❛t✐♦♥s t❤r❡s❤♦❧❞s ✈❛❧✉❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺

✼✳✹ ❙②♠❜♦❧✱ r❡❧❛t✐♦♥✱ ❛♥❞ ❡①♣r❡ss✐♦♥ ❧❡✈❡❧ r❡❝❛❧❧ ♦❢ t❤❡ ❤②♣♦t❤❡s❡s ❣r❛♣❤ ❣❡♥❡r❛t✐♦♥ st❡♣✱

❢♦r t❤r❡s❤♦❧❞s ✐♥ t❤❡ r❛♥❣❡ [0.11.0]✳ ❚❤✐s r❡s✉❧ts ❛r❡ ❝❛❧❝✉❧❛t❡❞ ♦✈❡r t❤❡ t❡st s❡t

❡①♣r❡ss✐♦♥s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻

✼✳✺ ▼❡❛♥ ♦❢ s②♠❜♦❧ ❛♥❞ r❡❧❛t✐♦♥ ❤②♣♦t❤❡s✐s ❧❛❜❡❧s ♣❡r s②♠❜♦❧ ❛♥❞ r❡❧❛t✐♦♥✱ r❡s♣❡❝t✐✈❡❧②✱ ♦✈❡r t❤❡ t❡st s❡t ❡①♣r❡ss✐♦♥s✳ ❚❤❡ ❧❡❢t ❤❛♥❞ ❛①✐s ✐♥❞✐❝❛t❡s t❤❡ ♥✉♠❜❡r ♦❢ ❧❛❜❡❧s ♣❡r s②♠❜♦❧ ❛♥❞ r❡❧❛t✐♦♥✳ ❚❤❡ r✐❣❤t ❤❛♥❞ ❛①✐s ✐♥❞✐❝❛t❡s t❤❡ ♣❡r❝❡♥t❛❣❡ ♦❢ r❡❝♦❣♥✐③❡❞

❡①♣r❡ss✐♦♥s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✼

✼✳✻ ❊①❛♠♣❧❡s ♦❢ ❤❛♥❞✇r✐tt❡♥ ♠❛t❤❡♠❛t✐❝❛❧ ❡①♣r❡ss✐♦♥s t❤❛t ❤❛✈❡ ❜❡❡♥ ❝♦rr❡❝t❧② r❡❝♦❣✲

♥✐③❡❞ ❜② ♦✉r ♠❡t❤♦❞✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✽

✼✳✼ ❊①♣r❡ss✐♦♥s r❡❝♦❣♥✐③❡❞ ✇✐t❤ ❛ ❢❡✇ ❡rr♦rs✳ ❋♦r ❡❛❝❤ ❡①♣r❡ss✐♦♥✱ ✐ts ❣r♦✉♥❞ tr✉t❤ ❛♥❞

t❤❡ s②st❡♠✬s ♦✉t♣✉t ✐s s❤♦✇❡❞ ❛s✿ ❣r♦✉♥❞ tr✉t❤→ s②st❡♠✬s ♦✉t♣✉t✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✽

✽✳✶ ❊①♣r❡ss✐♦♥ ♠❛t❝❤✐♥❣ ❡①❛♠♣❧❡✳ ❱❡rt✐❝❛❧ ❧✐♥❡s ✐♥❞✐❝❛t❡ t❤❡ ♠❛t❝❤❡❞ s②♠❜♦❧s✳ ✳ ✳ ✳ ✳ ✳ ✽✺

✽✳✷ ❊①♣r❡ss▼❛t❝❤ ❛r❝❤✐t❡❝t✉r❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✼

✽✳✸ ▼♦❞❡❧ ❝♦❧❧❡❝t♦r✿ ❡①♣r❡ss✐♦♥ x= −b±√2ab2−4ac ✐s ❜❡✐♥❣ ❞❡✜♥❡❞ ❛s ❛ ♠♦❞❡❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✽

✽✳✹ ▼♦❞❡❧ ❡①♣r❡ss✐♦♥ ♦❢ ❋✐❣✉r❡ ✽✳✸ ✇✐t❤ ❛❧❧ ✐ts s②♠❜♦❧s ❧❛❜❡❧❡❞✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✽

✽✳✺ ■♥st❛♥❝❡ ❝❛♣t✉r❡r✿ ♠♦❞❡❧ ❡①♣r❡ss✐♦♥ ✐s s❤♦✇♥ ❛t t❤❡ t♦♣✱ t♦ ✐♥❞✐❝❛t❡ ✉s❡rs ✇❤❛t

✐♥st❛♥❝❡ t❤❡② ❤❛✈❡ t♦ ✇r✐t❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✾

✽✳✻ ▲❛❜❡❧✐♥❣ ❡❞✐t♦r✿ ❧❛❜❡❧✐♥❣ r❡s✉❧t ✐s s❤♦✇♥ ❛s ❛ ♠❛t❝❤✐♥❣ ❜❡t✇❡❡♥ ❧❛❜❡❧❡❞ s②♠❜♦❧s ♦❢ ♠♦❞❡❧ ❡①♣r❡ss✐♦♥ ✭❛t t❤❡ t♦♣✮ ❛♥❞ ✉♥❧❛❜❡❧❡❞ s②♠❜♦❧s ♦❢ t❤❡ ✐♥st❛♥❝❡ ❡①♣r❡ss✐♦♥ ✭❛t

t❤❡ ❜♦tt♦♠✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✵

✽✳✼ ❊①❛♠♣❧❡ ♦❢ ♠❛t❝❤✐♥❣ ✇✐t❤ ♠❛♥② ❧✐♥❡ s❡❣♠❡♥ts✿ ✭❛✮ ✇✐t❤ ❛❧❧ s❡❣♠❡♥ts✱ ✭❜✮ ❛♥❞ ✭❝✮

t✇♦ ❣r♦✉♣s ♦❢ ♥♦♥ ✐♥t❡rs❡❝t✐♥❣ s❡❣♠❡♥ts✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✶

❇✳✶ ▼❡❛♥ ♦❢ s②♠❜♦❧ ❛♥❞ r❡❧❛t✐♦♥ ❤②♣♦t❤❡s✐s ❧❛❜❡❧s ♣❡r s②♠❜♦❧ ❛♥❞ r❡❧❛t✐♦♥✱ r❡s♣❡❝t✐✈❡❧②❀ ❝❛❧❝✉❧❛t❡s ♦✈❡r t❤❡ t❡st s❡t✳ ❚❤❡ ❧❡❢t ❤❛♥❞ ❛①✐s ✐♥❞✐❝❛t❡s t❤❡ ♥✉♠❜❡r ♦❢ ❧❛❜❡❧s ♣❡r s②♠❜♦❧ ❛♥❞ r❡❧❛t✐♦♥✳ ❚❤❡ r✐❣❤t ❤❛♥❞ ❛①✐s ✐♥❞✐❝❛t❡s t❤❡ ♣❡r❝❡♥t❛❣❡ ♦❢ r❡❝♦❣♥✐③❡❞

(17)

▲■❙❚ ❖❋ ❋■●❯❘❊❙ ①✈

❇✳✷ ▼❡❛♥ ♦❢ s②♠❜♦❧ ❛♥❞ r❡❧❛t✐♦♥ ❤②♣♦t❤❡s✐s ❧❛❜❡❧s ♣❡r s②♠❜♦❧ ❛♥❞ r❡❧❛t✐♦♥✱ r❡s♣❡❝t✐✈❡❧②❀ ❝❛❧❝✉❧❛t❡s ♦✈❡r t❤❡ t❡st s❡t✳ ❚❤❡ ❧❡❢t ❤❛♥❞ ❛①✐s ✐♥❞✐❝❛t❡s t❤❡ ♥✉♠❜❡r ♦❢ ❧❛❜❡❧s ♣❡r s②♠❜♦❧ ❛♥❞ r❡❧❛t✐♦♥✳ ❚❤❡ r✐❣❤t ❤❛♥❞ ❛①✐s ✐♥❞✐❝❛t❡s t❤❡ ♣❡r❝❡♥t❛❣❡ ♦❢ r❡❝♦❣♥✐③❡❞

(18)
(19)

▲✐st ♦❢ ❚❛❜❧❡s

✷✳✶ ❍♦r✐③♦♥t❛❧ ♣❛rt✐t✐♦♥s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵

✹✳✶ ❙②♠❜♦❧ ❤②♣♦t❤❡s❡s ❝❧❛ss✐✜❡r ♦✉t❝♦♠❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽

✹✳✷ ❙②♠❜♦❧ ❈❧❛ss✐✜❝❛t✐♦♥ r❡s✉❧ts ✉s✐♥❣ t❤❡ tr❛✐♥✐♥❣✲✈❛❧✐❞❛t✐♦♥s s❡ts✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾

✹✳✸ ❙②♠❜♦❧ ❤②♣♦t❤❡s✐s ❝❧❛ss✐✜❝❛t✐♦♥ r❡s✉❧ts ✉s✐♥❣ t❤❡ ❈❘❖❍▼❊✲✷✵✶✹ t❡st s❡t ❛♥❞ ❝♦♠✲

♣❛r✐s♦♥ ♦❢ ♦✉r ♠❡t❤♦❞ ✇✐t❤ t❤❡ t♦♣ t❤r❡❡ r❡s✉❧ts ♦❢ t❤❡ ❈❘❖❍▼❊✲✷✵✶✹ ❝♦♠♣❡t✐t✐♦♥✳ ✹✾

✹✳✹ P❡r❝❡♥t❛❣❡ ♦❢ s②♠❜♦❧s ♠✐ss❝❧❛ss✐✜❡❞ ✇✐t❤ ♦t❤❡rs ✇✐t❤ s✐♠✐❧❛r s❤❛♣❡✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵

✺✳✶ ❘❡❧❛t✐♦♥ ❝❧❛ss✐✜❝❛t✐♦♥ r❛t❡s ✭✪✮ ✉s✐♥❣ t❤❡ ❈❘❖❍▼❊✲✷✵✶✹ tr❛✐♥✲✈❛❧✐❞❛t✐♦♥ s❡ts✳ ❈❱

❂ ❝❛t❡❣♦r② ✈❡❝t♦rs✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻

✺✳✷ ❈♦♥❢✉s✐♦♥ ♠❛tr✐① ❢♦r r❡❧❛t✐♦♥s ❝❧❛ss✐✜❝❛t✐♦♥ ♦❢ ❈❘❖❍▼❊✲✷✵✶✹ t❡st s❡t✳ ❚❤❡ ❛❝t✉❛❧

r❡❧❛t✐♦♥s ❛t r♦✇s ❛♥❞ t❤❡ ♣r❡❞✐❝t❡❞ ♦♥❡s ❛t ❝♦❧✉♠♥s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼

✼✳✶ ❈♦♠♣❛r✐s♦♥ ♦❢ s❝♦r✐♥❣ ❢✉♥❝t✐♦♥ ✉s✐♥❣ t❤❡ ✈❛❧✐❞❛t✐♦♥ s❡t ♦❢ ❈❘❖❍▼❊✲✷✵✶✹✳✳ ✳ ✳ ✳ ✳ ✳ ✼✻

✼✳✷ ❊①♣r❡ss✐♦♥ ❧❡✈❡❧ ❝♦♠♣❛r✐s♦♥ ♦❢ ♦✉r ♠❡t❤♦❞ ✇✐t❤ s②st❡♠s ♦❢ t❤❡ ❈❘❖❍▼❊✲✷✵✶✹ ❝♦♠✲

♣❡t✐t✐♦♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✼

✼✳✸ ❖❜❥❡❝t ❧❡✈❡❧ ❝♦♠♣❛r✐s♦♥ ♦❢ ♦✉r ♠❡t❤♦❞ ✇✐t❤ s②st❡♠s ♦❢ t❤❡ ❈❘❖❍▼❊✲✷✵✶✹ ❝♦♠♣❡✲

t✐t✐♦♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✾

✼✳✹ ❈♦♠♣❛r✐s♦♥ ♦❢ ♦✉r ♠❡t❤♦❞ ❛♥❞ ❙②st❡♠ ■■■ ❢♦r s②♠❜♦❧ ❤②♣♦t❤❡s✐s ❝❧❛ss✐✜❝❛t✐♦♥✱ ✉s✐♥❣

t❤❡ ❈❘❖❍▼❊✲✷✵✶✹ t❡st s❡t✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✾

✼✳✺ ❙♣❛t✐❛❧ r❡❧❛t✐♦♥s ❜❡t✇❡❡♥ s②♠❜♦❧s ✭♦❢ t❤❡ t❡st s❡t✮ t❤❛t ♣r❡s❡♥t❡❞ ♠♦r❡ ❡rr♦rs✳ ❊❛❝❤ r❡❧❛t✐♦♥ ✐s ✐❞❡♥t✐✜❡❞ ✇✐t❤ ❛ ♣r✐♥t❡❞ r❡♣r❡s❡♥t❛t✐♦♥✳ ❚❤❡ r❡❧❛t✐♦♥ ✐❞❡♥t✐t② ✐s ✐♠♣❧✐❝✐t

❜② t❤❡ r❡❧❛t✐✈❡ s②♠❜♦❧ ♣♦s✐t✐♦♥s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✵

(20)

Referências

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