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Análise da abundância e detecção direta num modelo de matéria escura

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❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ P❛r❛✐❜❛

❈❡♥tr♦ ❞❡ ❈✐❫❡♥❝✐❛s ❊①❛t❛s ❞❡ ❞❛ ◆❛t✉r❡③❛ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❋✓✏s✐❝❛

❆♥✓❛❧✐s❡ ❞❛ ❆❜✉♥❞❫❛♥❝✐❛ ❡ ❉❡t❡❝✘❝⑦❛♦ ❉✐r❡t❛ ♥✉♠ ▼♦❞❡❧♦

❞❡ ▼❛t✓❡r✐❛ ❊s❝✉r❛✳

❆♥t♦♥✐♦ ❈❛r❧♦s ❖❧✐✈❡✐r❛ ❙❛♥t♦s

❏♦⑦❛♦ P❡ss♦❛

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❆♥t♦♥✐♦ ❈❛r❧♦s ❖❧✐✈❡✐r❛ ❙❛♥t♦s

❆♥✓❛❧✐s❡ ❞❛ ❆❜✉♥❞❫❛♥❝✐❛ ❡ ❉❡t❡❝✘❝⑦❛♦

❉✐r❡t❛ ♥✉♠ ▼♦❞❡❧♦ ❞❡ ▼❛t✓❡r✐❛

❊s❝✉r❛

❖r✐❡♥t❛❞♦r✿ P❛✉❧♦ ❙✓❡r❣✐♦ ❘✳ ❙✐❧✈❛

❉✐ss❡rt❛✘❝⑦❛♦ ❛♣r❡s❡♥t❛❞❛ ❛♦ ❈✉rs♦ ❞❡ P✓♦s✲ ●r❛❞✉❛✘❝⑦❛♦ ❡♠ ❋✓✏s✐❝❛ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❛ P❛r❛✓✏❜❛✱ ❝♦♠♦ r❡q✉✐s✐t♦ ♣❛r❝✐❛❧ ♣❛r❛ ♦❜✲ t❡♥✘❝⑦❛♦ ❞♦ ❣r❛✉ ❞❡ ▼❡str❡ ❡♠ ❋✓✏s✐❝❛✳

❏♦⑦❛♦ P❡ss♦❛

❆❜r✐❧ ❞❡ ✷✵✶✹

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S237a Santos, Antonio Carlos Oliveira.

Análise da abundância e detecção direta num modelo de matéria escura / Antonio Carlos Oliveira Santos.- João Pessoa, 2014.

90f. : il.

Orientador: Paulo Sérgio R. Silva Dissertação (Mestrado) - UFPB/CCEN

1. Física. 2. Matéria escura. 3. Física de partículas. 4.Detecção direta. 5. Extensão de Gauge.

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✒❆

♠✐♥❤❛ q✉❡r✐❞❛ ❢❛♠✓✏❧✐❛✱

♠❡✉ ♣❛✐✱ ♠✐♥❤❛ ♠⑦❛❡✱ ❡ ❛ ♠✐♥❤❛ ✐r♠⑦❛③✐♥❤❛✭❇❯■❆❚❈❍❆❑❆✦✮✳

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❆❣r❛❞❡❝✐♠❡♥t♦s

✎ ❈♦♠♦ ❜❡♠ ❞✐ss❡ ❱♦❧t❛✐r❡✿ ❙❡ ❉❡✉s ♥⑦❛♦ ❡①✐st✐ss❡✱ t❡r✐❛ s✐❞♦ ♣r❡❝✐s♦ ✐♥✈❡♥t✓❛✲❧♦✳ ▼✉✐t♦ ❞❡✈♦ ❛ ❉❡✉s ♣❡❧❛ ✐♥s♣✐r❛✘❝⑦❛♦✱ ♣❛❝✐❫❡♥❝✐❛✱ s❛✓✉❞❡ ❡ ❜♦❛s ♦♣♦rt✉♥✐❞❛❞❡s✳ ❆❣r❛❞❡✘❝♦ ❛♦s ♠❡✉s ♣❛✐s✱ ❆♥t♦♥✐♦ ❡ ▼❛❣❣②✱ ❡ ❛ ♠✐♥❤❛ ✐r♠⑦❛③✐♥❤❛ ♣❡❧♦ ❛♣♦✐♦✱ ❡①❡♠♣❧♦ ❞❡ ✈✐❞❛✳

✎ ❆♦ ♣r♦❢❡ss♦r Pr♦❢✳ P❛✉❧♦ ❙✓❡r❣✐♦ ❘✳ ❙✐❧✈❛ ♣❡❧❛ ♦r✐❡♥t❛✘❝⑦❛♦✳

✎ ■❣✉❛❧♠❡♥t❡ ❛♦ ❋❛r✐♥❛❧❞♦ ◗✉❡✐r♦③ ♣❡❧❛ ♦r✐❡♥t❛✘❝⑦❛♦ ❡ ♣❛❝✐❫❡♥❝✐❛✳

✎ ❚❛♠❜✓❡♠ ❛♦ ♣r♦❢❡ss♦r ❈❛r❧♦s P✐r❡s ♣❡❧♦ s✉♣♦rt❡ ♥❡st❡ tr❛❜❛❧❤♦✳

✎ ❆♦s ♠❡✉s ♣r♦❢❡ss♦r❡s q✉❡ s❡r✈✐r❛♠ ❞❡ ❡①❡♠♣❧♦ ♥❛ ❢♦r♠❛✘❝⑦❛♦ ❛❝❛❞❫❡♠✐❝❛✳

✎ ◆♦✈❛♠❡♥t❡ ❛♦s ❣r❛♥❞❡s ❛♥t✐❣♦s ❛♠✐❣♦s q✉❡ ❝♦♥q✉✐st❡✐ ♥❛ ❣r❛❞✉❛✘❝⑦❛♦✿ ■t❛❧❧♦ ✭❧♦❧♦✮✱ ❘❡♥❛t❛ ✭✈✐❞❛ ❜♦❛✮✱ ❚✐❛❣♦✭❜❡✐✘❝♦❧❛✮ ❡ ❏♦⑦❛♦✭❇♦sq✉✐♥❤♦✮ ❡ ❛♦s ♥♦✈♦s ❞❛ P✓♦s✲●r❛❞✉❛✘❝⑦❛♦✳

✎ ❆♦ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❋✓✏s✐❝❛ ♣♦r ♣r♦♣♦r❝✐♦♥❛r ✉♠ ❡♥s✐♥♦ ❞❡ q✉❛❧✐❞❛❞❡ ❡ ✐♥❢r❛❡str✉t✉r❛✳

✎ ❆♦ ❈◆P◗ ♣❡❧♦ s✉♣♦rt❡ ☞♥❛♥❝❡✐r♦✳

✎ ❊ ☞♥❛❧♠❡♥t❡✱ ❛♦s ❛♠✐❣♦s q✉❡ ♥⑦❛♦ ❡st⑦❛♦ ❛q✉✐✳

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❘❡s✉♠♦

◆❡st❛ ❞✐ss❡rt❛✘❝⑦❛♦ ❝♦♥s✐❞❡r❛♠♦s ✉♠❛ ❡①t❡♥s⑦❛♦ ❛❜❡❧✐❛♥❛ ♠✓✏♥✐♠❛ ❧♦❝❛❧✱ ❞❡ ❝❛r❣❛ ❇ ✸▲❡✱

❧✐✈r❡ ❞❡ ❛♥♦♠❛❧✐❛s✱ ♦♥❞❡ ❢♦✐ ✐♥tr♦❞✉③✐❞♦ ✉♠ ❢✓❡r♠✐♦♥ ❞❡ ▼❛❥♦r❛♥❛ ❞❡ ♠⑦❛♦ ❞✐r❡✐t❛ ❥✉♥t❛♠❡♥t❡ ❝♦♠ ✉♠ ♥♦✈♦ ❜✓♦s♦♥ ❡s❝❛❧❛r✱ r❡s♣♦♥s✓❛✈❡❧ ♣❡❧❛ q✉❡❜r❛ ❡s♣♦♥t❫❛♥❡❛ ❞❛ s✐♠❡tr✐❛ ❧♦❝❛❧✱ ❡ ✉♠ ❡s❝❛❧❛r ❝❛rr❡❣❛❞♦ ❝♦♥❡❝t❛♥❞♦ ❛ ❢❛♠✓✏❧✐❛ ❞❡ ❧✓❡♣t♦♥s ❛♦ ❢✓❡r♠✐♦♥ ❞❡ ▼❛❥♦r❛♥❛✳ ❊st❡ ♠♦❞❡❧♦ t❡♠ ♣♦r ♦❜❥❡t✐✈♦ ❢♦r♥❡❝❡r ✉♠❛ t❡♦r✐❛ ❞❡ ❜❛✐①❛s ❡♥❡r❣✐❛s ♣❛r❛ ❛ ♠❛t✓❡r✐❛ ❡s❝✉r❛ ❛tr✐❜✉✓✏❞❛ ❛ ✉♠ ❢✓❡r♠✐♦♥ ❞❡ ▼❛❥♦r❛♥❛✳ ▲♦❣♦✱ ❜❛s❡❛❞♦ ❡♠ ❛❧❣✉♥s ❡①♣❡r✐♠❡♥t♦s ✭❡♠ ♣❛rt✐❝✉❧❛r ❛q✉❡❧❡s ❝✉❥♦ ♣r✐♥❝✐♣❛❧ ♦❜❥❡t✐✈♦ ✓❡ ❛ ❞❡t❡❝✘❝⑦❛♦ ❞✐r❡t❛ ❞❡ ✉♠❛ ♣♦ss✓✏✈❡❧ ♥♦✈❛ ♣❛rt✓✏❝✉❧❛ ❛tr✐❜✉✓✏❞❛ ✒❛ ❡st❛ ♠❛t✓❡r✐❛✮✱ ✐r❡♠♦s ✈✐♥❝✉❧❛r ♦s ♣❛r❫❛♠❡tr♦s ❞❡ ♥♦ss♦ ♠♦❞❡❧♦ ❛ ☞♠ ❞❡ ✈❡r✐☞❝❛r s✉❛ ❛♣❧✐❝❛❜✐❧✐❞❛❞❡ ♥❡st❡ ❝❡♥✓❛r✐♦✳ P❛r❛ ✐st♦✱ ✉t✐❧✐③❛r❡♠♦s ♦ ♣r♦❣r❛♠❛ ❝♦♠♣✉t❛❝✐♦♥❛❧ ♠✐❝r❖▼❊●❆s ✭q✉❡ ✉t✐❧✐③❛ ♦ ❈❛❧❝❍❊P✮ ❛ ☞♠ ❞❡ ❝❛❧❝✉❧❛r ❛❧❣✉♥s ♦❜s❡r✈✓❛✈❡✐s ❞♦ ♠♦❞❡❧♦✱ t❛✐s ❝♦♠♦ ❛ ❛❜✉♥❞❫❛♥❝✐❛ ❡ s❡❝✘❝⑦❛♦ tr❛♥s✈❡rs❛❧ ❞❡ ❝❤♦q✉❡ ❞♦ ❡s♣❛❧❤❛♠❡♥t♦ ❡❧✓❛st✐❝♦ ❡♥tr❡ ❛ ♠❛t✓❡r✐❛ ❡s❝✉r❛ ❡ ♦ ♥✉❝❧❡♦♥ ❡✱ ❡♠ s❡❣✉✐❞❛✱ ❝♦♠♣❛r❛♠♦s ❛♦s ❞❛❞♦s ❡①♣❡r✐♠❡♥t❛✐s ❞♦ P❧❛♥❝❦ ✭❛❜✉♥❞❫❛♥❝✐❛✮ ❡ ▲❯❳ ✭s❡✘❝⑦❛♦ ❞❡ ❝❤♦q✉❡✮✳ ❘❡s✉❧t❛❞♦s ♣r❡❧✐♠✐♥❛r❡s ❛♣♦♥t❛♠ ♣❛r❛ ❛ ✈❛❧✐❞❛❞❡ ❞♦ ♠♦❞❡❧♦ ❞✐❛♥t❡ ❞❛s r❡str✐✘❝⑦♦❡s ✐♠♣♦st❛s ♣❡❧❛s ♦❜s❡r✈❛✘❝⑦♦❡s✱ ♣♦ss✐❜✐❧✐t❛♥❞♦ ❛ ♣❡rs♣❡❝t✐✈❛ ❞❡ ❛♣❧✐❝❛✘❝⑦❛♦ ❞❡st❛ ❡①t❡♥s⑦❛♦ ❡♠ ♦✉tr♦s ❝♦♥t❡①t♦s✱ ❝♦♠♦ ♦s ❞❛ ❞❡t❡❝✘❝⑦❛♦ ✐♥❞✐r❡t❛ ❞❛ ♠❛t✓❡r✐❛ ❡s❝✉r❛✳

P❛❧❛✈r❛s✲❝❤❛✈❡s✿ ▼❛t✓❡r✐❛ ❊s❝✉r❛✱ ❋✓✏s✐❝❛ ❞❡ P❛rt✓✏❝✉❧❛s✱ ❉❡t❡❝✘❝⑦❛♦ ❉✐r❡t❛✱ ❊①t❡♥s⑦❛♦ ❞❡ ●❛✉❣❡ ❇ ✸▲❡✳

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❆❜str❛❝t

■♥ t❤✐s ✇♦r❦ ✇❡ ❝♦♥s✐❞❡r ❛ ♠✐♥✐♠❛❧ ❧♦❝❛❧ ❛❜❡❧✐❛♥ ❣❛✉❣❡ ❣r♦✉♣ ❡①t❡♥s✐♦♥ ✇✐t❤ ❝❤❛r❣❡ ❇ ✸▲❡ ❛♥♦♠❛❧②✲❢r❡❡✳ ❲❡ ❛❞❞ ❛ r✐❣❤t✲❤❛♥❞❡❞ s✐♥❣❧❡t ▼❛❥♦r❛♥❛ ❢❡r♠✐♦♥ ♣❧✉s ❛ ♥❡✉tr❛❧ ❛♥❞

❝❤❛r❣❡❞ s❝❛❧❛rs✱ r❡s♣♦♥s✐❜❧❡ ❢♦r s♣♦♥t❛♥❡♦✉s s②♠♠❡tr② ❜r❡❛❦✐♥❣ ❛♥❞ ❛ ❝❤❛r❣❡❞ s✐♥❣❧❡t s❝❛❧❛r t♦ ♣r♦✈✐❞❡ ❛ ❝♦♥♥❡❝t✐♦♥ ❜❡t✇❡❡♥ t❤❡ ❡❧❡❝tr♦♥ ❛♥❞ t❤❡ ▼❛❥♦r❛♥❛ ❢❡r♠✐♦♥✳ ❚❤❡ ❛✐♠ ♦❢ t❤✐s ♠♦❞❡❧ ✐s ♣r♦✈✐❞❡ ❛ ❧♦✇ ❡♥❡r❣② t❤❡♦r② t♦ ❉❛r❦ ♠❛tt❡r ❛s ❛ ▼❛❥♦r❛♥❛ ❢❡r♠✐♦♥✳ ❚❤❡r❡ ❛r❡ s❡✈❡r❛❧ ❡✈✐❞❡♥❝❡s ♦❢ ❛ ♥❡✇ ❦✐♥❞ ♦❢ ❛ ♥♦♥✲❜❛r②♦♥✐❝ ♠❛tt❡r ❜✉t ✐ts ♥❛t✉r❡ ❛♥❞ ♣r♦♣❡rt✐❡s ❛r❡ ♥♦t ✇❡❧❧ ❡st❛❜❧✐s❤❡❞✳ ❙♦✱ ❜❛s❡❞ ✐♥ s♦♠❡ ❡①♣❡r✐♠❡♥ts ✭✐♥ ♣❛rt✐❝✉❧❛r t❤♦s❡ t❤❛t ♠❛✐♥ ❢♦❝✉s ✐s t❤❡ ❞✐r❡❝t ❞❡t❡❝t✐♦♥✮✱ ✇❡ ❛r❡ ❣♦✐♥❣ t♦ ❝♦♥str❛✐♥t s♦♠❡ ♣❛r❛♠❡t❡rs ♦❢ t❤❡ ♠♦❞❡❧ t♦ t❡st ✐ts ❢❡❛s✐❜✐❧✐t② ✐♥ t❤✐s ❝♦♥t❡①t✳ ❲❡ ❤❛✈❡ ✉s❡❞ ❛ ❝♦♠♣✉t❛t✐♦♥❛❧ ♣r♦❣r❛♠ ❝❛❧❧❡❞ ♠✐❝r❖▼❊●❆s ✭❜❛s❡❞ ♦♥ ❈❛❧❈❍❊P✮ t♦ ❝♦♠♣✉t❡ t❤❡ ❛❜✉♥❞❛♥❝❡ ❛♥❞ s❝❛tt❡r✐♥❣ ❝r♦ss s❡❝t✐♦♥ ❜❡t✇❡❡♥ ❞❛r❦ ♠❛tt❡r ❛♥❞ ♥✉❝❧❡♦♥ ❛♥❞ ❝♦♠♣❛r❡ ✇✐t❤ t❤❡ ❡①♣❡r✐♠❡♥t❛❧ ❝♦♥str❛✐♥ts ❛r✐s✐♥❣ ❢r♦♠ P❧❛♥❝❦ ✭❛❜✉♥❞❛♥❝❡✮ ❛♥❞ ▲❯❳ ✭s❝❛tt❡r✐♥❣ ❝r♦ss s❡❝t✐♦♥✮✳ ❲❡ s❤♦✇ t❤❛t t❤❡ r❡s✉❧ts s✉♣♣♦rt t❤❡ r❡str✐❝t✐♦♥s ✐♠♣♦s❡❞ ❜② t❤❡ ♦❜s❡r✈❛t✐♦♥s ♣r♦✈✐❞✐♥❣ ❢✉t✉r❡ ♣❡rs♣❡❝t✐✈❡s ❢♦r t❤✐s ❡①t❡♥s✐♦♥✱ ❧✐❦❡ ✐♥❞✐r❡❝t ❞❡t❡❝t✐♦♥ ♦❢ ❞❛r❦ ♠❛tt❡r✳

❑❡②✇♦r❞s✿ ❉❛r❦ ▼❛tt❡r✱ P❛rt✐❝❧❡ ♣❤②s✐❝s✱ ❉✐r❡❝t ❞❡t❡❝t✐♦♥ ♦❢ ❉❛r❦ ▼❛tt❡r✱ ❇ ✸▲❡ ●❛✉❣❡

❡①t❡♥s✐♦♥✳

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❙✉♠✓❛r✐♦

✶ ■♥tr♦❞✉✘❝⑦❛♦ ✶

✶✳✶ ▼❛t✓❡r✐❛ ❊s❝✉r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶

✶✳✶✳✶ ❊✈✐❞❫❡♥❝✐❛s ●r❛✈✐t❛❝✐♦♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶

✶✳✶✳✷ ◆❛t✉r❡③❛ ❞❛ ▼❛t✓❡r✐❛ ❊s❝✉r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽

✶✳✶✳✸ Pr♦❞✉✘❝⑦❛♦ ❚✓❡r♠✐❝❛ ❞❛ ❲■▼P ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺

✷ ❉❡t❡❝✘❝⑦❛♦ ❉✐r❡t❛ ❞❡ ▼❛t✓❡r✐❛ ❊s❝✉r❛ ✷✷

✷✳✶ ❇✉s❝❛ ♣❡❧❛ ▼❛t✓❡r✐❛ ❊s❝✉r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷

✷✳✷ ❉❡t❡❝✘❝⑦❛♦ ■♥❞✐r❡t❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷

✷✳✸ ❉❡t❡❝✘❝⑦❛♦ ❡♠ ❈♦❧✐s♦r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸

✷✳✹ ❉❡t❡❝✘❝⑦❛♦ ❉✐r❡t❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹

✷✳✹✳✶ ❉❆▼❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺

✷✳✹✳✷ ❈♦●❡◆❚ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼

✷✳✹✳✸ ❈❉▼❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽

✷✳✹✳✹ ❳❡♥♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷

✷✳✹✳✺ ▲❯❳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻

✷✳✹✳✻ ❆♥❛❧✐s❡ ❞❡ ❞❛❞♦s✿ ❛❧❣✉♥s ❢❛t♦r❡s ❢✉♥❞❛♠❡♥t❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽

✸ ▼♦❞❡❧♦ ❯✭✶✮❳ ❞❡ ❝❛r❣❛ ❳ ❂ ❇ ✸▲❡ ✹✷

(10)

✸✳✶ ▼♦❞❡❧♦ ♠✓✏♥✐♠♦ ❞♦ ❢✓❡r♠✐♦♥ ❞❡ ▼❛❥♦r❛♥❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷

✸✳✷ ❈❛r❣❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸

✸✳✸ ❙❡t♦r ❡s❝❛❧❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹

✸✳✸✳✶ ❈✓❛❧❝✉❧♦s ♣❛r❛ ♦ ❡s❝❛❧❛r ❝❛rr❡❣❛❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼

✸✳✸✳✷ ❉❡r✐✈❛❞❛ ❞♦ ❝❛♠♣♦ ✣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼

✸✳✸✳✸ ❉❡r✐✈❛❞❛ ❞♦ ♥♦✈♦ ❡s❝❛❧❛r ♥❡✉tr♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾

✸✳✸✳✹ ■♥t❡r❛✘❝⑦♦❡s ❡♥tr❡ ♦ ❢✓❡r♠✐♦♥ ❞❡ ▼❛❥♦r❛♥❛ ❡ ♦s ❡s❝❛❧❛r❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵

✸✳✹ ❙❡t♦r ❋❡r♠✐❫♦♥✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶

✹ ❘❡s✉❧t❛❞♦s ✺✺

✹✳✶ ❆❜✉♥❞❫❛♥❝✐❛ r❡❧✓✏q✉✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺

✹✳✷ ❉❡t❡❝✘❝⑦❛♦ ❞✐r❡t❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻

✺ ❈♦♥❝❧✉s⑦♦❡s ✻✷

❆ ▼❡❞✐✘❝⑦❛♦ ❞❛ ✈❡❧♦❝✐❞❛❞❡ ❞❡ ●❛❧✓❛①✐❛s ♣♦r ♠❡✐♦ ❞♦ ❞❡s✈✐♦ ❞❛ ❧✉③ ♣❛r❛ ♦ ✈❡r✲

♠❡❧❤♦✳ ✼✵

❇ ❆♣r♦①✐♠❛✘❝⑦❛♦ ♣❛r❛ ♦s ❛✉t♦✲❡st❛❞♦s ❞❡ ♠❛ss❛✳ ✼✸

❈ ❱✓❡rt✐❝❡s ❞♦s ❡s❝❛❧❛r❡s ✼✹

❈✳✵✳✶ ❱✓❡rt✐❝❡s ❞♦s ❡s❝❛❧❛r❡s ♥❡✉tr♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺

❈✳✵✳✷ ❱✓❡rt✐❝❡s ❞♦ ❡s❝❛❧❛r ❝❛rr❡❣❛❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✼

❉ ❈❛♥❛✐s ❞❡ ❛♥✐q✉✐❧❛✘❝⑦❛♦ ❞❛ ♠❛t❡r✐❛ ❡s❝✉r❛✳ ✼✽

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●❧♦ss✓❛r✐♦

◆●❈ ◆♦✈♦ ❈❛t✓❛❧♦❣♦ ●❡r❛❧ ♦✉✱ ❡♠ ✐♥❣❧❫❡s✱ ◆❡✇ ●❡♥❡r❛❧ ❈❛t❛❧♦❣✳ ❈❛t✓❛❧♦❣♦ ❝♦♠ ♠❛✐s ❞❡ ✽✵✵✵ ❛str♦s✱ ❞❡♥tr❡ ❡❧❡s ❣❛❧✓❛①✐❛s ❡ ♥❡❜✉❧♦s❛s✳ ■♥✐❝✐❛❞♦ ❡♠ ✶✽✽✵✳ ✹

❤❛❧♦ ❖ ❍❛❧♦✱ ✓❡ ❛ r❡❣✐⑦❛♦ ❡s❢✓❡r✐❝❛ ❝♦♠ ❝❡♥tr♦ ❝♦♠✉♠ ❛♦ ❞❛ ❣❛❧✓❛①✐❛✱ q✉❡ s❡ ❡①t❡♥❞❡♥❞❡ ♠✉✐t♦ ❛❧✓❡♠ ❞♦ ❝♦♥t❡✓✉❞♦ ✈✓✏s✐✈❡❧✳ ❊st❛ ❛✉r❡✓♦❧❛✱ ❝♦♠♦ t❛♠❜✓❡♠ ✓❡ ❝♦♥❤❡❝✐❞❛✱ ❝♦♥t✓❡♠ ❛ ♠❛✐♦r ♣❛rt❡ ❞❛ ♠❛ss❛ ♣❡rt❡♥❝❡♥t❡ ❛♦ ❝♦♥❥✉♥t♦ ❤❛❧♦ ♠❛✐s ❣❛❧✓❛①✐❛✳ ❆❝r❡❞✐t❛✲s❡ q✉❡ ❡st❛ ❝♦♥✲ t❡♥❤❛ ❣r❛♥❞❡ q✉❛♥t✐❞❛❞❡ ❞❡ ♠❛t✓❡r✐❛ ❡s❝✉r❛✶

❧✉♠✐♥♦s✐❞❛❞❡ ❊♠ ❛str♦♥♦♠✐❛✱ ❧✉♠✐♥♦s✐❞❛❞❡ ✓❡ ❛ q✉❛♥t✐❞❛❞❡ ❞❡ ❡♥❡r❣✐❛ q✉❡ ✉♠ ❝♦r♣♦ ✐rr❛❞✐❛ ❡♠ ✉♠❛ ✉♥✐❞❛❞❡ ❞❡ t❡♠♣♦ ❬✶❪✳ ✶✱ ✹

♠❛t✓❡r✐❛ ❜❛r✐❫♦♥✐❝❛ ❆ ♠❛t✓❡r✐❛ ❜❛r✐❫♦♥✐❝❛ ♥❛ ❛str♦♥♦♠✐❛ r❡❢❡r❡✲s❡ ✒❛ t♦❞❛ ♠❛t✓❡r✐❛ ❧✉♠✐♥♦s❛✱ ♣❧❛♥❡t❛s✱ ❡str❡❧❛s ✐♥❝❧✉✐♥❞♦ s✉❛s s✉❜❡str✉t✉r❛s✱ ✓❛t♦♠♦s✱ q✉❛r❦s✱ ❧✓❡♣t♦♥s✱ ❞❡ ✉♠❛ ❢♦r♠❛ ♠❡♥♦s ❡s♣❡❝✐☞❝❛ q✉❡ ♥❛ ❢✓✏s✐❝❛ ❞❡ ♣❛rt✓✏❝✉❧❛s ♦♥❞❡ ❧✓❡♣t♦♥s s⑦❛♦ ❞✐❢❡r❡♥t❡s ❞❡ ❜✓❛r✐♦♥s ❬✶❪✳

♣❝ P❛rs❡❝ ✓❡ ✉♠❛ ✉♥✐❞❛❞❡ ❞❡ ❝♦♠♣r✐♠❡♥t♦ ❞❡☞♥✐❞❛ ❝♦♠♦ ❛ ❞✐st❫❛♥❝✐❛ ❡♥tr❡ ❛ ❚❡rr❛ ❡ ❛ ▲✉❛ ✭✶♣❝ ❂ ✸❀ ✵✽✻ ✂ ✶✵✶✻♠✮✳

r❡❞s❤✐❢t ❊st❡ ✓❡ ♦ ❡❢❡✐t♦ ❉♦♣♣❧❡r ❛♣❧✐❝❛❞♦ ✒❛ ❧✉③✳ ✓❆t♦♠♦s ❡♠✐t❡♠ ❢✓♦t♦♥s ❡♠ ❢r❡q✉❫❡♥❝✐❛s ❜❡♠ ❡s♣❡❝✐☞❝❛s✳ ❆♦ ❞❡t❡❝t❛r ✉♠ ❢✓♦t♦♥ ❡♠✐t✐❞♦ ♣♦r ✉♠ ❞❡st❡s ✓❛t♦♠♦s s❡ ❞✐st❛♥❝✐❛♥❞♦ ❞♦ ❞❡t❡❝t♦r ❛ ❢r❡q✉❫❡♥❝✐❛ ♠❡❞✐❞❛ ❞✐♠✐♥✉✐✳ ❈♦♠♦ ❛ ❧✉③ ✈❡r♠❡❧❤❛ ✓❡ ✉♠❛ ❞❛s ♠❛✐s ❢r❛❝❛s ❞♦ ❡s♣❡❝tr♦ ✈✐s✓✏✈❡❧ ❞✐③✲s❡ ❡♥t⑦❛♦ q✉❡ ❛ r❛❞✐❛✘❝⑦❛♦ ❡♠✐t✐❞❛ ♣❡❧❛ ❢♦♥t❡ ❢♦✐ ❞❡s✈✐❛❞❛ ♣❛r❛ ♦ ✈❡r♠❡❧❤♦✳ ✷

❖s t❡r♠♦s ❝♦♥t✐❞♦s ♥❡st❡ ❣❧♦ss✓❛r✐♦ ❡st⑦❛♦ ♣r❡s❡♥t❡s ❛♦ ❧♦♥❣♦ ❞❡st❡ tr❛❜❛❧❤♦ ✭♣✓❛❣✐♥❛s ✐♥❞✐❝❛❞❛s ♣❡❧♦s

♥✓✉♠❡r♦s ❡♠ ✈❡r♠❡❧❤♦✮ ❣r✐❢❛❞♦s ❡♠ ✈❡r♠❡❧❤♦✳

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❈❛♣✓✏t✉❧♦ ✶

■♥tr♦❞✉✘❝⑦❛♦

◆❡st❡ ❝❛♣✓✏t✉❧♦✱ s❡r⑦❛♦ ❛♣♦♥t❛❞❛s ❛❧❣✉♠❛s ❞❛s ♣r✐♥❝✐♣❛✐s ❡✈✐❞❫❡♥❝✐❛s s♦❜r❡ ▼❛t✓❡r✐❛ ❊s❝✉r❛ ✭▼❊✮✳ ❱❡r❡♠♦s q✉❡ ❡❧❛s s✉r❣❡♠ ♣r❡❞♦♠✐♥❛♥t❡♠❡♥t❡ ❞❡ ♦❜s❡r✈❛✘❝⑦♦❡s ❣r❛✈✐t❛❝✐♦♥❛✐s✱ ♦✉ s❡❥❛✱ ❞❡ ❣r❛♥❞❡s ❡str✉t✉r❛s✱ q✉❡ ✐♥❞✐❝❛♠ ❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ ✉♠❛ r❡❢♦r♠✉❧❛✘❝⑦❛♦ ❞❛ t❡♦r✐❛ ❣r❛✈✐t❛✲ ❝✐♦♥❛❧ ♣❛❞r⑦❛♦ ♦✉ ❞❡ ✉♠❛ ♥♦✈❛ ❢♦r♠❛ ❞❡ ♠❛t✓❡r✐❛✱ s❡♥❞♦ ❡st❛ ✓✉❧t✐♠❛✱ ❛ ✐❞❡✐❛ ❝❤❛✈❡ ❞❡st❛ ❞✐ss❡rt❛✘❝⑦❛♦✳

✶✳✶ ▼❛t✓❡r✐❛ ❊s❝✉r❛

✶✳✶✳✶ ❊✈✐❞❫❡♥❝✐❛s ●r❛✈✐t❛❝✐♦♥❛✐s

■♥✐❝✐❛❧♠❡♥t❡✱ ❛ ♠❛✐♦r ♣❛rt❡ ❞❛s ✐♥❢♦r♠❛✘❝⑦♦❡s q✉❡ t✓✏♥❤❛♠♦s s♦❜r❡ ❝♦r♣♦s ❝❡❧❡st❡s ❡r❛ ❜❛s❡✲ ❛❞❛ ❡♠ ❢✓♦t♦♥s ❡ ❛✐♥❞❛✱ ❞❡ ❢♦r♠❛ ♠❛✐s ✐♥❣❫❡♥✉❛✱ ❛tr❛✈✓❡s ❞❛ ❧✉③ ✈✐s✓✏✈❡❧✳ ▼❡s♠♦ ❛ss✐♠ ❛♣✓♦s ✉♠❛ r❡❛♥✓❛❧✐s❡ ❞♦ ♠♦✈✐♠❡♥t♦ ❞❛s ♦s❝✐❧❛✘❝⑦♦❡s ❞❡ ❡str❡❧❛s ♣r✓♦①✐♠❛s ❛♦ ♣❧❛♥♦ ❣❛❧✓❛t✐❝♦✱ ✐♥✐❝✐❛❧♠❡♥t❡ ❢❡✐t❛ ♣❡❧♦ ❛str❫♦♥♦♠♦ ❛❧❡♠⑦❛♦ ❑❛♣t❡②♥ ✭✶✾✷✷✮ ❬✷❪✱ ❏❡❛♥s ❡♠ ✶✾✷✷ ❬✸❪ r❡♣♦rt♦✉ ✉♠ ❞♦s ♣r✐♠❡✐✲ r♦s ✐♥❞✓✏❝✐♦s ❞❡ ✉♠❛ ♣♦ss✓✏✈❡❧ ▼❊✳ ❈♦♥❢r♦♥t❛♥❞♦ ♦s r❡s✉❧t❛❞♦s ❞❡ ♦❜t❡♥✘❝⑦❛♦ ❞❛ ♠❛ss❛ ❡st❡❧❛r ♣♦r ♠❡✐♦ ❞❛ ❞✐♥❫❛♠✐❝❛ ❡ ♣❡❧❛❧✉♠✐♥♦s✐❞❛❞❡ ♦❜s❡r✈❛❞❛ ❡❧❡ ✈❡r✐☞❝♦✉ ❛ ❡①✐st❫❡♥❝✐❛ ❞❡ ✉♠❛ ♠❛ss❛ ❞✉❛s ✈❡③❡s ♠❛✐♦r q✉❡ ❛ ❞❛ ❡str❡❧❛ ✈✐s✓✏✈❡❧✱ ❝❤❛♠❛♥❞♦✲❛s ❞❡ ❡str❡❧❛s ❡s❝✉r❛s ✭❭❉❛r❦ st❛rs✧✱ ♣✓❛❣✳ ✸✷✮✳ ❯♠❛ ❛♥✓❛❧✐s❡ ♠❛✐s ❞❡t❛❧❤❛❞❛ r❡❛❧✐③❛❞❛ ♣♦r ❊❞✇✐♥ P✳ ❍✉❜❜❧❡ ❡♠ ✶✾✷✻ ❬✹❪✱ ❝♦♥t❛♥❞♦ ❝♦♠ ❛ ♦❜s❡r✈❛✘❝⑦❛♦ ❞❡ q✉❛tr♦❝❡♥t❛s ❣❛❧✓❛①✐❛s ✭❡ ♥❡❜✉❧♦s❛s✮✱ s❡♥❞♦ ❡st✉❞❛❞❛s ❝❛r❛❝t❡r✓✏st✐❝❛s ❝♦♠♦✱❧✉♠✐♥♦s✐❞❛❞❡✱ ❞✐❫❛♠❡tr♦✱ ❞✐str✐❜✉✐✘❝⑦❛♦✱ ❞❡♥s✐❞❛❞❡ ❡ ♠❛ss❛✱ t❛♠❜✓❡♠ ❛ss✐♥❛❧❛r❛♠ ♣❛r❛ ❛ ❡①✐st❫❡♥❝✐❛ ❞❡ ✉♠❛ ♠❛ss❛ ❛❧✓❡♠ ❞♦ ❝♦♥t❡✉❞♦ ❞♦s ❛str♦s ✈✐s✓✏✈❡✐s✳

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✶✳ ■♥tr♦❞✉✘❝⑦❛♦ ✷

♥⑦❛♦ ❝♦♥t❛✈❛♠ ❝♦♠ ♠✉✐t♦s ❞❛❞♦s ❡st❛t✓✏st✐❝♦s ❡ ❡①✐st✐❛♠ ✐♥❝❡rt❡③❛s ♥♦ r❛✐♦ ❞♦ ❆❣❧♦♠❡r❛❞♦✳ ◆♦t❡ q✉❡ ✐ss♦ ✓❡ ✐♠♣♦rt❛♥t❡ ♣♦✐s ♦s ❝✓❛❧❝✉❧♦s ♣r❡❝✐s❛♠ ❝♦♥s✐❞❡r❛r q✉❛✐s ❣❛❧✓❛①✐❛s ♣❡rt❡♥❝❡♠ ♦✉ ♥⑦❛♦ ❛♦ ❆❣❧♦♠❡r❛❞♦✳ ◆⑦❛♦ s❛❜❡r ❝♦♠ ♣r❡❝✐s⑦❛♦ ♦ r❛✐♦ ❧❡✈❛ ❛ ✐♥❝❧✉s⑦❛♦✱ ♦✉ ♥⑦❛♦✱ ❞❡ ❣❛❧✓❛①✐❛s ♥♦ ❣r✉♣♦✱ ♦ q✉❡ ✐♥✌✉❡♥❝✐❛r✓❛ ❞✐r❡t❛♠❡♥t❡ ♥❛ ♠❛ss❛ ❛❢❡r✐❞❛✳ ▼❡s♠♦ ❛ss✐♠✱ ♦ ❡①❝❡ss♦ ❞❡ ♠❛ss❛ ❡♥❝♦♥tr❛❞♦ ❡st✓❛ ❞❡ ❛❝♦r❞♦ ❝♦♠ ♦✉tr♦s r❡s✉❧t❛❞♦s ❡♥❝♦♥tr❛❞♦s ♣❛r❛ ♦✉tr♦s ❆❣❧♦♠❡r❛✲ ❞♦s ❝♦♠♦ ♥❛s ♠❡❞✐❞❛s ❞❡ ❙♠✐t❤ ✶✾✸✻ ❬✻❪✱ ❛♦ ❡st✉❞❛r ❣❛❧✓❛①✐❛s ❞♦ ❆❣❧♦♠❡r❛❞♦ ❞❡ ❱✐r❣♦✱ ♦ q✉❡ ❢♦✐ ❝♦♥☞r♠❛❞❛ ♣♦r ❩✇✐❝❦② ❡♠ ✶✾✸✼ ❬✼❪✳

❯t✐❧✐③❛♥❞♦ t✓❡❝♥✐❝❛s ❜❛s❡❛❞❛s ♥♦ ❞❡s✈✐♦ ❞❛ ❧✉③ ♣❛r❛ ♦ ✈❡r♠❡❧❤♦ ✭r❡❞s❤✐❢t✱ ❆♥❡①♦ ❆✮ ❑❛❤♥ ❡ ❲♦❧t❥❡r ✭✶✾✺✾✮ ❬✽❪ ❝♦♥s❡❣✉✐r❛♠ ♠❡❞✐r ❛ ♠❛ss❛ ❞♦ s✐st❡♠❛ ❞❡ ❣❛❧✓❛①✐❛s✱ ❱✐❛ ▲✓❛❝t❡❛ ❡ ❆♥❞r❫♦♠❡❞❛✱ ❝♦♥st❛t❛♥❞♦ ✉♠ ✈❛❧♦r ❞❡ ▼ ✕ ✶❀ ✽ ✂ ✶✵✶✷

☞✶✳ P♦r✓❡♠✱ ♦s ✈❛❧♦r❡s ♠❡❞✐❞♦s

❝♦♠ ♦s ♠✓❡t♦❞♦s ✉s✉❛✐s✷ ❡r❛♠ ❞❛ ♦r❞❡♠ ❞❡ ✷❀ ✵ ✂ ✶✵✶✶

☞✳ ❊st❡ ❢♦✐ ♦ ♣r✐♠❡✐r♦ r❡s✉❧t❛❞♦ q✉❡

❛♣♦♥t❛✈❛ ✉♠❛ ♠❛ss❛ ❛❞✐❝✐♦♥❛❧ ♥♦ ●r✉♣♦ ❧♦❝❛❧ ❞❡ ❣❛❧✓❛①✐❛s ✭❝♦♥❥✉♥t♦ ❞❡ ✸✺ ❣❛❧✓❛①✐❛s✱ ✐♥❝❧✉✐♥❞♦ ❛ ❞❡ ❆♥❞r❫♦♠❡❞❛ ❡ ❛ ♥♦ss❛✱ ❝♦♠ ✉♠ ❞✐❫❛♠❡tr♦ ❛♣r♦①✐♠❛❞♦ ❞❡ ✶✵ ♠✐❧❤⑦♦❡s ❞❡ ❛♥♦s ❧✉③✮✳ ❊✐♥❛st♦ ❡ ▲②♥❞❡♥♥✲❇❡❧❧ ✭✶✾✽✷✮✱ t❛♠❜✓❡♠ ☞③❡r❛♠ ❝✓❛❧❝✉❧♦s s♦❜r❡ ❛ ♠❛ss❛ ❞♦ ●r✉♣♦ ▲♦❝❛❧✱ ✉t✐❧✐③❛♥❞♦ ♦s ❞❛❞♦s ♠❛✐s r❡❝❡♥t❡s ❞❛ ✓❡♣♦❝❛✱ ❡♥❝♦♥tr❛♥❞♦ ♦ ✈❛❧♦r t♦t❛❧ ❞❡ ✭✹❀ ✺ ✝ ✵❀ ✺✮ ✂ ✶✵✶✷

☞✳

❆✐♥❞❛ s♦❜r❡ ❛ ✈❡❧♦❝✐❞❛❞❡ ❞❡ r♦t❛✘❝⑦❛♦ ❞❛s ❣❛❧✓❛①✐❛s ♣♦❞❡♠♦s ✉t✐❧✐③❛r ❛s ▲❡✐s ❞❡ ◆❡✇t♦♥ ♣❛r❛ ✉♠❛ ♣❛rt✓✏❝✉❧❛ ❞❡ ♣r♦✈❛ ❞❡s❝r❡✈❡♥❞♦ ✉♠❛ ✓♦r❜✐t❛ ❝✐r❝✉❧❛r ✐♠❡rs❛ ❡♠ ✉♠❛ ❞✐str✐❜✉✐✘❝⑦❛♦ ❞❡ ♠❛ss❛ ❝♦♠ r❛✐♦ t♦t❛❧ ❘✳ ❉❡♥tr♦ ❞❛ r❡❣✐⑦❛♦ ❞❡ ♠❛t✓❡r✐❛✱ ❛♣❧✐❝❛♥❞♦ ❛s ❧❡✐s ❞❡ ◆❡✇t♦♥✱

❣ ❂ ●▼✭r✮ r✷ ❂

✈✷ ❝

r ✮ ✈❝❂ r ●▼✭r✮ r ❂ ✽ ❁ ✿ q ●▼

r ❀ r ❃ ❘

q

✹●✙✚

✸ r❀ r ❁ ❘ ✮ ▼✭r✮ ❂ ✹✙✚ r

✸ ❀

✭✶✳✶✮

❡s♣❡r❛♠♦s q✉❡ ❛ ✈❡❧♦❝✐❞❛❞❡ ❝r❡s✘❝❛ ❧✐♥❡❛r♠❡♥t❡ ❝♦♠ ❛ ❞✐st❫❛♥❝✐❛ ♠❡❞✐❞❛✱ r✱ ❛ ♣❛rt✐r ❞♦ ❝❡♥tr♦ ❞❛ ❣❛❧✓❛①✐❛ ❡ ❛♦ s❛✐r ❞❛ r❡❣✐⑦❛♦ ❞❡ ♠❛ss❛ s✉❛ ✈❡❧♦❝✐❞❛❞❡ ❝❛✐❛ ♣r♦♣♦r❝✐♦♥❛❧♠❡♥t❡ ❛ r❛✐③ ❞♦ ✐♥✈❡rs♦ ❞❛ ❞✐st❫❛♥❝✐❛✱ ♦ q✉❡ ♦❜s❡r✈❛♠♦s ♥❛ ❝✉r✈❛ ❆ ❞❛ ☞❣✉r❛ ✶✳✶✱ s❡♥❞♦ ❣ ❛ ❛❝❡❧❡r❛✘❝⑦❛♦ ❞❛ ❣r❛✈✐❞❛❞❡ ❞❡✈✐❞♦ ❛ ❞❡♥s✐❞❛❞❡ ❞❡ ♠❛ss❛ ✚✳

☞ s❡ tr❛t❛ ❞❛ ♠❛ss❛ ❞♦ ❙♦❧ ✭✶✵✸✵❦❣✮

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✶✳ ■♥tr♦❞✉✘❝⑦❛♦ ✸

❋✐❣✉r❛ ✶✳✶✿ ❈✉r✈❛ ❞❛ ✈❡❧♦❝✐❞❛❞❡ ❞❡ r♦t❛✘❝⑦❛♦ ❞❡ ❣❛❧✓❛①✐❛s ✭♦r❞❡♥❛❞❛✮✱ ✈✱ ❡♠ ❢✉♥✘❝⑦❛♦ ❞❛ ❞✐st❫❛♥❝✐❛ ❞♦ ❡✐①♦ ❞❡ r♦t❛✘❝⑦❛♦ ✭❛❜❝✐ss❛✮✱ r✱ ❞♦ ❛❣❧♦♠❡r❛❞♦✱ s❡♠ ▼❛t✓❡r✐❛ ❊s❝✉r❛✱ ❝✉r✈❛ ❆✱ q✉❡ ♦❜❡❞❡❝❡ ❡q✳ ✭✶✳✶✮ ❞❡❝❛✐♥❞♦ ❝♦♠♣✶❂r✳ ■♥❝❧✉✐♥❞♦ ▼❊ ✭❝✉r✈❛ ❇✮✱ ❛ ✈❡❧♦❝✐❞❛❞❡ ❞♦s ❝♦r♣♦s✱ ❛❧✓❡♠ ❞♦ ❝❡♥tr♦ ❧✉♠✐♥♦s♦ ♦♥❞❡ s❡ ❝♦♥❝❡♥tr❛ ❛ ♠❛t✓❡r✐❛ ✈✐s✓✏✈❡❧✱ ♥⑦❛♦ ❞✐♠✐♥✉✐✱ s❡❣✉❡ ❞❡ ❢♦r♠❛ ❛♣r♦①✐♠❛❞❛♠❡♥t❡ ❝♦♥st❛♥t❡✳

P♦r✓❡♠✱ ❇❛❜❝♦❝❦ ✭✶✾✸✾✮ ❬✾❪ r❡♣♦rt♦✉ q✉❡ ❛❧❣✉♠❛s r❡❣✐⑦♦❡s ❞❛ ❣❛❧✓❛①✐❛✱ ❞❡ ❆♥❞r❫♦♠❡❞❛ ✭▼✸✶✮ ♣♦ss✉✓✏❛♠ ✈❡❧♦❝✐❞❛❞❡s ❞❡ r♦t❛✘❝⑦❛♦ ♠✉✐t♦ ❛❝✐♠❛ ❞♦ ♣r❡❞✐t♦✳ ❏✓❛ ♥❛ ❞✓❡❝❛❞❛ ❞❡ ✼✵✱ ❘✉❜✐♥ ❡ ❋♦r❞ ❬✶✵❪ t❛♠❜✓❡♠ ♦❜t✐✈❡r❛♠ ❝✉r✈❛s ❞❡ ✈❡❧♦❝✐❞❛❞❡ ❜❛st❛♥t❡ ❞✐❢❡r❡♥t❡s ❞♦ ❡s♣❡r❛❞♦ ♣❡❧❛s ❧❡✐s ❞❡ ◆❡✇t♦♥✱ ❛♣❧✐❝❛❞❛ ❛♣❡♥❛s ❛♦s ❝♦r♣♦s ✈✐s✓✏✈❡✐s ✭☞❣✉r❛ ✶✳✷✮✳

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✶✳ ■♥tr♦❞✉✘❝⑦❛♦ ✹

❊♠ s❡❣✉✐❞❛✱ ❘♦❜❡rts ❡ ❘♦ts ✭✶✾✼✸✮ ❬✶✶❪ ♦❜t✐✈❡r❛♠ ❛s ❝✉r✈❛s ❞❡ r♦t❛✘❝⑦❛♦ ❞❛ ▼✸✶ ❡♠ ❞✐st❫❛♥❝✐❛s ❛❝✐♠❛ ❞❡ ✸✵❦♣❝ ♣♦r ♠❡✐♦ ❞❡ ♦♥❞❛s ❞❡ r✓❛❞✐♦✱ ☞❣✉r❛ ✶✳✸✳ ◆♦t❡ q✉❡ ❡❧❛ ✓❡ ♠✉✐t♦ s❡♠❡❧❤❛♥t❡ ✒❛ ❝✉r✈❛ ❇ ❞❛ ☞❣✉r❛✶✳✶✱

❋✐❣✉r❛ ✶✳✸✿ ❱❡❧♦❝✐❞❛❞❡ ❞❡ r♦t❛✘❝⑦❛♦ ❞❛ ❣❛❧✓❛①✐❛ ✭❘♦❜❡rts ❡ ❘♦ts ✭✶✾✼✸✮ ❬✶✶❪ ❡♠ ❢✉♥✘❝⑦❛♦ ❞❛ ❞✐st❫❛♥❝✐❛s ❡♠ r❡❧❛✘❝⑦❛♦ ❛♦ s❡✉ ❝❡♥tr♦ ❞❡ r♦t❛✘❝⑦❛♦✳

❋❛③❡♥❞♦ ✉s♦ ❞❡st❛s t✓❡❝♥✐❝❛s ❞❡ ♦❜t❡♥✘❝⑦❛♦ ❞❛ ♠❛ss❛ t♦t❛❧ ❞❡ ❣❛❧✓❛①✐❛s✱ s❡ ♣♦❞❡ ♠❡❞✐r ❛ r❛③⑦❛♦ ❡♥tr❡ ♠❛ss❛ ❡ ❧✉♠✐♥♦s✐❞❛❞❡✳ ❙❡ ❛ ♠❛ss❛ ❞♦s ❝♦r♣♦s ❢♦r ❛tr✐❜✉✓✏❞❛ s♦♠❡♥t❡ ❛♦s ♦❜❥❡t♦s ✈✐s✓✏✈❡✐s✱ ❡s♣❡r❛✲s❡ q✉❡ ❛ ♠❛ss❛ ❞✐♠✐♥✉❛ ❛♦ ♣❛ss♦ ❡♠ q✉❡ ❛ ❧✉♠✐♥♦s✐❞❛❞❡ t❛♠❜✓❡♠ ❞❡❝r❡s✘❝❛✱ ♦✉ s❡❥❛✱ q✉❡ ❛ ♠❛t✓❡r✐❛ s✐❣❛ ❛ ♠❡s♠❛ ❞✐str✐❜✉✐✘❝⑦❛♦ ❞❛ ❧✉③✳ ❊♥tr❡t❛♥t♦✱ ♣❛r❛ ❛ ❣❛❧✓❛①✐❛ ▼✸✶✱ ♣♦r ❡①❡♠♣❧♦✱ ✐st♦ ♥⑦❛♦ ♦❝♦rr❡✱ ❝❤❡❣❛♥❞♦ ❛ ✈❛❧♦r❡s ❞❡ ▼❂▲ ❂ ✷✵✵✱ s❡♥❞♦ ▼ ❛ ♠❛ss❛ ❞♦ ❛str♦ ❡ ▲ s✉❛ ❧✉♠✐♥♦s✐❞❛❞❡✳ ❊st❡ r❡s✉❧t❛❞♦ ☞❝❛ ❜❛st❛♥t❡ ❡✈✐❞❡♥t❡ ♥♦s ❣r✓❛☞❝♦s ❞❡ ✈❛♥ ❆❧❜❛❞❛ ❡ ❙❛♥❝✐s✐ ✭✶✾✽✻✮ ❬✶✷❪✱ ♥❛ ☞❣✉r❛ ✶✳✹✱ ♦♥❞❡ t❡♠♦s ❛s ✈❡❧♦❝✐❞❛❞❡s ❞❡ r♦t❛✘❝⑦❛♦ ❞❛s ❣❛❧✓❛①✐❛s ◆●❈ ✷✹✵✸ ❡

◆●❈ ✸✶✾✽ ♠✉✐t♦ ❛❝✐♠❛ ❞❛ ❡st✓❛✈❡❧ s✉♣♦rt❛❞❛ ♣❡❧❛ ♠❛t✓❡r✐❛ ✈✐s✓✏✈❡❧ ❝♦♥t✐❞❛✱ ❡q✉✐✈❛❧❡♥❞♦ ❛ ✈❡❧♦❝✐❞❛❞❡ ❞❡ ❡s❝❛♣❡✳ P♦❞❡♠♦s ✈❡r q✉❡✱ s❡ ❛ ✓✉♥✐❝❛ ❝♦♥tr✐❜✉✐✘❝⑦❛♦ ❞❡ ♠❛t✓❡r✐❛ ❢♦ss❡ ❛ ✈✐s✓✏✈❡❧✱ ❛ ✈❡❧♦❝✐❞❛❞❡ ❞❡ r♦t❛✘❝⑦❛♦ ❞❡✈❡r✐❛ s❡❣✉✐r ♦ ♣❡r☞❧ ❞❛ ❝✉r✈❛ ❝♦♥t✓✏♥✉❛✱ ❞❡❝❛✐♥❞♦ ❝♦♠♦ ♥❛ ❡q✳ ✭✶✳✶✮✱ ♣❛r❛ r ❃ ❘✱ ♠❛s ♦ ♦❜s❡r✈❛❞♦ s✉❣❡r❡✱ ♥♦✈❛♠❡♥t❡✱ q✉❡ ❛❧✓❡♠ ❞♦ ❝♦♥t❡✓✉❞♦ ✈✐s✓✏✈❡❧ t❡♠♦s ✉♠ ❝♦♥t❡✓✉❞♦ ❡①tr❛ ❞❡ ♠❛t✓❡r✐❛ ♥⑦❛♦ ❧✉♠✐♥♦s❛✳

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✶✳ ■♥tr♦❞✉✘❝⑦❛♦ ✺

❋✐❣✉r❛ ✶✳✹✿ ❱❡❧♦❝✐❞❛❞❡ ❞❡ r♦t❛✘❝⑦❛♦ ❞❡ ❣❛❧✓❛①✐❛s ❬✶✷❪✳ ◆♦s ❣r✓❛☞❝♦s ❛ ❡ ❜ t❡♠♦s ♦s ✈❛❧♦r❡s ❞❛ ❧✉♠✐♥♦s✐❞❛❞❡ ❡♠ ❢✉♥✘❝⑦❛♦ ❞❛ ❞✐st❫❛♥❝✐❛ ❞♦ ❝❡♥tr♦ ❞❡ s✉❛s ❣❛❧✓❛①✐❛s✱ ◆●❈ ✷✹✵✸ ✭❧❛❞♦ ❡sq✉❡r❞♦✮ ❡ ◆●❈ ✸✶✾✽ ✭❧❛❞♦ ❞✐r❡✐t♦✮✳ ❆ ❧✉♠✐♥♦s✐❞❛❞❡ ✐♥❞✐❝❛ ❛ r❡❣✐⑦❛♦ ♦♥❞❡ t❡♠♦s ❛ ♠❛t✓❡r✐❛ ✈✐s✓✏✈❡❧✳ ❊♠ ❝ ❡ ❞✱ ♦❜s❡r✈❛✲s❡ ❛s ❝✉r✈❛s ❞❛ ✈❡❧♦❝✐❞❛❞❡ ❞❡ ✓♦r❜✐t❛ ❡♠ t♦r♥♦ ❞♦ ❝❡♥tr♦ ❞♦ ❛❣❧♦♠❡r❛❞♦ ❡♠ ❢✉♥✘❝⑦❛♦ ❞❛ ❞✐st❛♥❝✐❛ ❞♦ ❡✐①♦ ❞❡ r♦t❛✘❝⑦❛♦✳

❞❡ ❡str❡❧❛s ♣r✓♦①✐♠❛s ❛♦ ♣❧❛♥♦ ❣❛❧✓❛t✐❝♦ ♦s ♣❡sq✉✐s❛❞♦r❡s ❑✉✐❥❦❡♥ ❡ ●✐❧♠♦r❡ ✭✶✾✽✾✮ ❬✶✸❪ ❡ ●✐❧♠♦r❡ ❡t ❛❧✳ ✭✶✾✽✾✮ ❬✶✹❪ ♣r♦❝✉r❛r❛♠ ♣♦r q✉❛♥t✐❞❛❞❡s ❞❡ ▼❛t✓❡r✐❛ ❊s❝✉r❛ ♥♦ ❞✐s❝♦ ❣❛❧✓❛t✐❝♦ ❡ ❝♦♥❝❧✉✓✏r❛♠ q✉❡ ♠❡♥♦s ❞❡ ✶✺✪ ❞❡ s❡✉ ❝♦♥t❡✓✉❞♦ ❡r❛ ❝♦♠♣♦st♦ ♣♦r ❡st❛✳

(17)

✶✳ ■♥tr♦❞✉✘❝⑦❛♦ ✻

❞❡ ♠❛t✓❡r✐❛✳ ❆ ❞❡t❡r♠✐♥❛✘❝⑦❛♦ ❞♦ ❣✓❛s ❞♦ ❛❣❧♦♠❡r❛❞♦ ♣♦❞❡ s❡r ❢❡✐t❛ ❛tr❛✈✓❡s ❞♦ ❡s♣❡❝tr♦ ❞❡ r❛✐♦✲ ❳ ❡♠✐t✐❞♦ ♣❡❧♦ ❣✓❛s ❡ ♣❡❧♦ ❡❢❡✐t♦ ❙✉♥②❛❡✈✲❩❡❧❞♦✈✐❝❤ q✉❡ s❡ tr❛t❛ ❞❛ ✐♥t❡r❛✘❝⑦❛♦ ❞❡ ❢✓♦t♦♥s ❞❛ ❘❛❞✐❛✘❝⑦❛♦ ❈✓♦s♠✐❝❛ ❞❡ ❋✉♥❞♦ ✭❈♦s♠✐❝ ▼✐❝r♦✇❛✈❡ ❇❛❝❦❣r♦✉♥❞ ❘❛❞✐❛t✐♦♥✱ ❈▼❇❘✮✱ ❢❛❧❛r❡♠♦s ❞❡st❛ ♠❛✐s ❛❞✐❛♥t❡✱ ❝♦♠ ♦s ❡❧✓❡tr♦♥s ❡♥❡r❣✓❡t✐❝♦s ❞♦ ❣✓❛s ❛❞q✉✐r✐♥❞♦ ❡♥❡r❣✐❛ ♣❡❧♦ ❡❢❡✐t♦ ✐♥✈❡rs♦ ❈♦♠♣t♦♥✱ ❡❧✓❡tr♦♥s ❞❡ ❛❧t❛ ❡♥❡r❣✐❛ ❢♦r♥❡❝❡♥❞♦ ❡♥❡r❣✐❛ ♣❛r❛ ❢✓♦t♦♥s✳ ❉❡st❡ ♠♦❞♦✱ ❝♦♠♣❛r❛♥❞♦ ♦ ❡s♣❡❝tr♦ ❞♦ ❈▼❇❘ ❝♦♠ ❡ s❡♠ ♦ ❡❢❡✐t♦✱ ❝❛❧❝✉❧❛✲s❡ ❛ ♠❛ss❛ t♦t❛❧ ❞❡ ❣✓❛s✳

❖✉tr♦ ❡❢❡✐t♦ ✉t✐❧✐③❛❞♦ ♣❛r❛ ❛❢❡r✐✘❝⑦❛♦ ❞❡ ♠❛ss❛ s❡ tr❛t❛ ❞♦ ❢❛s❝✐♥❛♥t❡ ❢❡♥❫♦♠❡♥♦ ❞❛s ❧❡♥t❡s ❣r❛✈✐t❛❝✐♦♥❛✐s✱ ❝✉❥❛ t❡♦r✐❛ ❢♦✐ ❝r✐❛❞❛ ♣♦r ❊✐♥st❡✐♥ ❡ ♣❡❧❛ ♣r✐♠❡✐r❛ ✈❡③ ♦❜s❡r✈❛❞❛ ❡♠ ✶✾✶✾✱ ❡♠ ✉♠ ❡❝❧✐♣s❡ s♦❧❛r✳ ◆❡st❡ ❢❡♥❫♦♠❡♥♦✱ ❛ tr❛❥❡t✓♦r✐❛ ❞♦ ❢✓♦t♦♥ ✓❡ ❛❢❡t❛❞❛ ❞❡✈✐❞♦ ❛ ❝✉r✈❛t✉r❛ ❞♦ ❡s♣❛✘❝♦ t❡♠♣♦ ❣❡r❛❞❛ ♣♦r ✉♠ ❝❛♠♣♦ ❣r❛✈✐t❛❝✐♦♥❛❧✱ ☞❣✳ ✭✶✳✺✮✳ ❊st❡ ❡❢❡✐t♦ ✓❡ ❣❡r❛❧♠❡♥t❡ ❝❧❛ss✐☞❝❛❞♦ ❡♠✿ ❧❡♥t❡s ❣r❛✈✐t❛❝✐♦♥❛✐s ❢♦rt❡s ✭q✉❛♥❞♦ ♦ ❛str♦ q✉❡ ❝✉r✈❛ ♦s r❛✐♦s ❞❡ ❧✉③ s❡ tr❛t❛ ❞❡ ✉♠ ♦❜❥❡t♦✱ ♦✉ ♦❜❥❡t♦s✱ ❡①tr❡♠❛♠❡♥t❡ ♠❛ss✐✈♦✱ ❝♦♠♦ ❛❣❧♦♠❡r❛❞♦s ❞❡ ❣❛❧✓❛①✐❛s✱ ♣♦r ❡①❡♠♣❧♦✱ q✉❡ ♣♦ss✉✐ ❛ ❝❛r❛❝t❡r✓✏st✐❝❛ ❞❡ ❣❡r❛r ✐♠❛❣❡♥s ♠✓✉❧t✐♣❧❛s ❡ ❞✐st♦r❝✐❞❛s✱ ❡♠ ❢♦r♠❛ ❞❡ ❛r❝♦s✮✱ ❧❡♥t❡s ❣r❛✈✐t❛❝✐♦♥❛✐s ❢r❛❝❛s ✭❝❛s♦ ♦ ♦❜❥❡t♦ r❡s♣♦♥s✓❛✈❡❧ ♣❡❧❛ ❧❡♥t❡ s❡❥❛ ♠❡♥♦s ♠❛ss✐✈♦✱ ❣❡r❛♥❞♦ ✐♠❛❣❡♥s ❞❛ ❢♦♥t❡ ❧✉♠✐♥♦s❛ ♠❡♥♦s ❞✐st♦r❝✐❞❛s✮ ❡ ♠✐❝r♦❧❡♥t❡s ✭q✉❡ ♣♦❞❡ s❡r ❝❛✉s❛❞❛ ♣♦r ♣❡q✉❡♥❛s ❡str❡❧❛s✱ ♥⑦❛♦ ❣❡r❛♥❞♦ ✐♠❛❣❡♥s ♠✓✉❧t✐♣❧❛s✳ ❆ ❢♦♥t❡ ❞❡ ❧✉③ t❡♠ s❡✉ ❜r✐❧❤♦ ❛♠✲ ♣❧✐☞❝❛❞♦✱ ♣♦rt❛♥t♦✱ ❡st❡ t✐♣♦ ❞❡ ❧❡♥t❡ ✓❡ ❜❛st❛♥t❡ ✉t✐❧✐③❛❞❛ ♥❛ ♣r♦❝✉r❛ ❞❡ ♣❧❛♥❡t❛s✱ ❡str❡❧❛s ❛♥⑦❛s✱ ❡ ♦✉tr♦s ❛str♦s q✉❡ ❛♣r❡s❡♥t❛♠ ❜❛✐①❛ ❧✉♠✐♥♦s✐❞❛❞❡✮✳

❋✐❣✉r❛ ✶✳✺✿ ■❧✉str❛✘❝⑦❛♦ ❞♦ ❡❢❡✐t♦ ❣r❛✈✐t❛❝✐♦♥❛❧ s♦❜r❡ ❛ ❧✉③✱ ❧❡♥t❡ ❣r❛✈✐t❛❝✐♦♥❛❧✳

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✶✳ ■♥tr♦❞✉✘❝⑦❛♦ ✼

♠❛t✓❡r✐❛ ❜❛r✐❫♦♥✐❝❛✱ ♥⑦❛♦ ✓❡ ♦ ❧♦❝❛❧ ❡♠ q✉❡ s❡ ❝♦♥❝❡♥tr❛ ❛ ♠❛✐♦r q✉❛♥t✐❞❛❞❡ ❞❡ ♠❛ss❛ s❡❣✉♥❞♦ ❛ ♠❡❞✐❞❛ ♣♦r ❧❡♥t❡ ❣r❛✈✐t❛❝✐♦♥❛❧✱ ❝♦♥❢♦r♠❡ ♣♦❞❡♠♦s ✈❡r ♥❛ ☞❣✳ ✭✶✳✻✮✳ ◆♦✈❛♠❡♥t❡ t❡♠♦s ❡✈✐❞❫❡♥❝✐❛s q✉❡ ✐♥❞✐❝❛♠ ▼❊✳

❋✐❣✉r❛ ✶✳✻✿ ❆❝✐♠❛ t❡♠♦s ❛ ❝♦❧✐s⑦❛♦ ❡♥tr❡ ❣❛❧✓❛①✐❛s ♥♦ ❛❣❧♦♠❡r❛❞♦ ❞❛ ❜❛❧❛ ❬✶✻❪✳ ❆s ❝✉r✈❛s ❞❡ ♥✓✏✈❡❧✱ ❡♠ ✈❡r❞❡✱ ✐❧✉str❛♠ ❛ ❧♦❝❛❧✐③❛✘❝⑦❛♦ ❞❛ r❡❣✐⑦❛♦ q✉❡ ❝♦♥❝❡♥tr❛ ♠❛✐s ♠❛ss❛✳ ❖s t♦♥s ❡♠ ✈❡r♠❡❧❤♦✱ ❝✉❧♠✐♥❛♥❞♦ ❡♠ ❛♠❛r❡❧♦ ✭✐❧✉str❛✘❝⑦❛♦ ❞❛ ✐♥t❡♥s✐❞❛❞❡ ❞♦ ❡s♣❡❝tr♦ ❞❡ r❛✐♦s✲❳✮✱ r❡♣r❡s❡♥t❛♠ ❛ r❡❣✐⑦❛♦ ❝♦♠ ♠❛✐♦r ❝♦♥❝❡♥tr❛✘❝⑦❛♦ ❞❡ ❣✓❛s✱ ♠❛t✓❡r✐❛ ❜❛r✐❫♦♥✐❝❛✳

❆❧✓❡♠ ❞❛ ♠❡❞✐❞❛ ❞❛ q✉❛♥t✐❞❛❞❡ ❞❡ ▼❊✱ ❝✐❡♥t✐st❛s t❛♠❜✓❡♠ ❡st⑦❛♦ ♣❡sq✉✐s❛♥❞♦ ❢✉♥✘❝⑦♦❡s q✉❡ ♠❡❧❤♦r ❞❡s❝r❡✈❛♠ s✉❛ ❞✐str✐❜✉✐✘❝⑦❛♦ ❞❡ ❞❡♥s✐❞❛❞❡✳ ❯t✐❧✐③❛♥❞♦ s✐♠✉❧❛✘❝⑦♦❡s ❞❡ ◆✲❝♦r♣♦s ❜❛s❡❛❞♦s ❡♠ ♠♦❞❡❧♦s ❞❡ ▼❊ ♣❡s❛❞❛ ✸ ✭♦♥❞❡ ❛ ▼❛t✓❡r✐❛ ❊s❝✉r❛ ♥⑦❛♦ ❝♦❧✐❞❡✱ s❡♥❞♦ tr❛t❛❞❛ ❝♦♠♦ tr❛♥s♣❛r❡♥t❡ ♣♦r ♦✉tr❛s ❢♦r✘❝❛s✱ ❝♦♥tr✐❜✉✐♥❞♦ ❛♣❡♥❛s ❣r❛✈✐t❛❝✐♦♥❛❧♠❡♥t❡✮ ◆❛✈❛rr♦ ❡t ❛❧✳ ✭✶✾✾✼✮ ❝❤❡❣♦✉ ❛ s❡❣✉✐♥t❡ ❞✐str✐❜✉✐✘❝⑦❛♦ ♣❛r❛ ❛ ▼❊ ❡♠ ♥♦ss❛ ❣❛❧✓❛①✐❛

✚✭r✮ ❂ ✚✐

✭r❂rs✮ ✭✶ ✰ r❂rs✮✷❀ ✭✶✳✷✮

s❡♥❞♦ r ❛ ❞✐st❫❛♥❝✐❛ ❡♠ r❡❧❛✘❝⑦❛♦ ❛♦ ❝❡♥tr♦ ❞♦ ❤❛❧♦✱ rs ♦ s❡♠✐✲❡✐①♦ ♠❛✐♦r ❞❛ ❛✉r✓❡♦❧❛ ❣❛❧✓❛t✐❝❛

❡❧✐♣s♦✐❞❡ ❡ ✚✐ ❛ ❞❡♥s✐❞❛❞❡ ❞♦ ❍❛❧♦ ♥♦ ♠♦♠❡♥t♦ ❞❡ s❡✉ ❝♦❧❛♣s♦✳ P♦r✓❡♠✱ ❡st❛ ❞✐str✐❜✉✐✘❝⑦❛♦

❞✐✈❡r❣❡ ♥♦ ❝❡♥tr♦ ❞♦ ❤❛❧♦✳ ❊st✉❞♦s ♣♦st❡r✐♦r❡s r❡❛❧✐③❛❞♦s ♣♦r ◆❛✈❛rr♦ ❡t ❛❧✳ ✭✷✵✶✵✮ ❬✶✼❪ ❝❤❡❣❛r❛♠ ❛ ❝♦♥❝❧✉s⑦❛♦ q✉❡ ♦ ♣❡r☞❧ ❞❡ ❞❡♥s✐❞❛❞❡ q✉❡ r❡♣r❡s❡♥t❛ ♠❡❧❤♦r ❛ ❞✐str✐❜✉✐✘❝⑦❛♦ ❞♦s ❤❛❧♦s ✓❡ ❞❛❞♦ ♣♦r ❬✶✼❪

✚✭r✮ ❂ ✚✭✵✮ ❡①♣❤ ✭r❂r✵✮✶❂◆

❀ ✭✶✳✸✮

s❡♥❞♦ q✉❡ r ❡①♣r❡ss❛ ❛ ❞✐st❫❛♥❝✐❛ ❡♠ r❡❧❛✘❝⑦❛♦ ❛♦ ❝❡♥tr♦ ❞♦ ❤❛❧♦✱ r✵ ♦ r❛✐♦ ❡❢❡t✐✈♦ ❞♦ ❝♦♥❥✉♥t♦

❞❡ ❛str♦s✱ ✚✭✵✮ ✓❡ ❛ ❞❡♥s✐❞❛❞❡ ♥❛ ♣♦s✐✘❝⑦❛♦ r✵✱ r❛✐♦ ♠❡❞✐❞♦ ❛ ♣❛rt✐r ❞♦ ❝❡♥tr♦ ❞♦ ❤❛❧♦ q✉❡

❝♦♥t✓❡♠ ♠❡t❛❞❡ ❞❡ s✉❛ ♠❛ss❛ ❡ ◆ s❡ tr❛t❛ ❞❡ ✉♠ ♣❛r❫❛♠❡tr♦ ❞❡ ❛❥✉st❡ ✭❛❧t❡r❛ ❛ ❝✉r✈❛t✉r❛ ❞♦

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✶✳ ■♥tr♦❞✉✘❝⑦❛♦ ✽

♣❡r☞❧✮✱ ❡st❛ ❡q✳ t❛♠❜✓❡♠ ✓❡ ❝♦♥❤❡❝✐❞❛ ❝♦♠♦ ♣❡r☞❧ ❞❡ ❊✐♥❛st♦✳ P♦r✓❡♠✱ ♦✉tr❛s ❛♥✓❛❧✐s❡s ❢❡✐t❛s ♣♦r ❍✉♠♣❤r❡② ❡ ❇♦✉t❡ ✭✷✵✶✵✮ ❬✶✽❪✱ ✉t✐❧✐③❛♥❞♦ ❞❛❞♦s ❞♦ ❖❜s❡r✈❛t✓♦r✐♦ ❞❡ ❘❛✐♦s✲❳ ❈❤❛♥❞r❛ ❞❡ ✼ ❣r✉♣♦s ❞❡ ❣❛❧✓❛①✐❛s ❡ ✶✵ ❛❣❧♦♠❡r❛❞♦s✱ ❝❤❡❣❛♥❞♦ ❛♦ r❡s✉❧t❛❞♦ ❞❡ q✉❡ ❛♠❜♦s ♦s ♣❡r☞s✱ ❡q✉❛✘❝⑦♦❡s ✭✶✳✷✮ ❡ ✭✶✳✸✮✱ r❡♣r❡s❡♥t❛♠ ❜❡♠ ❛ ❞✐str✐❜✉✐✘❝⑦❛♦ ❞❡ ❞❡♥s✐❞❛❞❡ ❞❛ ▼❊✳

✶✳✶✳✷ ◆❛t✉r❡③❛ ❞❛ ▼❛t✓❡r✐❛ ❊s❝✉r❛

❈♦♠♦ ✈✐♠♦s ❛♥t❡r✐♦r♠❡♥t❡✱ ❡①✐st❡♠ ❞✐✈❡rs❛s ❡✈✐❞❫❡♥❝✐❛s ❞❡ ▼❊ ♣r♦✈❡♥✐❡♥t❡s ❞❡ ♦❜✲ s❡r✈❛✘❝⑦♦❡s ❣r❛✈✐t❛❝✐♦♥❛✐s✳ ◆❡st❛ s❡✘❝⑦❛♦✱ ✐r❡♠♦s ❛❜♦r❞❛r ✉♠ ♣♦✉❝♦ ♠❛✐s s♦❜r❡ ❛ s✉❛ ♥❛t✉r❡③❛✱ ❜❛s❡❛♥❞♦✲♥♦s ❡♠ ❞❛❞♦s ♣r✐♥❝✐♣❛❧♠❡♥t❡ ❝♦s♠♦❧✓♦❣✐❝♦s✳

❆ ♣r✐♠❡✐r❛ ✐❞❡✐❛✱ ❛ ♠❛✐s ♥❛t✉r❛❧✱ ❛♣♦♥t❛ ♣❛r❛ ✉♠❛ ▼❊ ❝♦♠♣♦st❛ ♣♦r♠❛t✓❡r✐❛ ❜❛r✐❫♦♥✐❝❛

❞❡ ❜❛✐①❛ ❧✉♠✐♥♦s✐❞❛❞❡✱ ❞❡♥tr❡ ❡❧❛s✱ ❡str❡❧❛s ❞❡ ❜❛✐①❛ ♠❛ss❛ ❝♦♠♦ ❛♥⑦❛s ❜r❛♥❝❛s ❡ ♠❛rr♦♥s q✉❡ s⑦❛♦ ♣r❛t✐❝❛♠❡♥t❡ ✐♥✈✐s✓✏✈❡✐s ❛♦s ❞❡t❡❝t♦r❡s t❡rr❡str❡s ♥❛ ♠❛✐♦r ♣❛rt❡ ❞♦ t❡♠♣♦✳ ❊st❡s ❛str♦s ❢❛③❡♠ ♣❛rt❡ ❞♦ ❣r✉♣♦ ❞❡ ❝♦r♣♦s ❞❡♥♦♠✐♥❛❞♦s ▼❆❈❍❖❙ ✭▼❛ss✐✈❡ ❈♦♠♣❛❝t ❍❛❧♦ ❖❜❥❡❝ts✱ ❖❜❥❡t♦s ▼❛ss✐✈♦s ♥♦ ❍❛❧♦ ❞❛ ●❛❧✓❛①✐❛✮ ❬✶✾❪✱ q✉❡ ❛♣❛r❡♥t❡♠❡♥t❡ ❝♦♠♣⑦♦❡♠ ♦ ❝♦♥t❡✓✉❞♦ ❭❡s❝✉r♦✧ ❞♦ ♣❧❛♥♦ ❣❛❧✓❛t✐❝♦ ✉♠❛ ✈❡③ q✉❡ s⑦❛♦ ♣r❡✈✐st♦s ♣❡❧❛ t❡♦r✐❛ ❞❛ ❢♦r♠❛✘❝⑦❛♦ ❞❡ ❣❛❧✓❛①✐❛s✳ P♦r ♦✉tr♦ ❧❛❞♦ ♠❡❞✐❞❛s ❞❛ ❡✈♦❧✉✘❝⑦❛♦ ❞❡ ❣❛❧✓❛①✐❛s ❡ ❣r❛♥❞❡s ❡str✉t✉r❛s ♥⑦❛♦ ❢❛✈♦r❡❝❡♠ ❛ ▼❛t✓❡r✐❛ ❊s❝✉r❛ ❜❛r✐❫♦♥✐❝❛✳

P♦r ✈♦❧t❛ ❞❛ ❞✓❡❝❛❞❛ ❞❡ ✼✵✱ ♥♦✈♦s ❛♣❛r❛t♦s t❡❝♥♦❧✓♦❣✐❝♦s ♣❡r♠✐t✐r❛♠ ♠❡❞✐✘❝⑦♦❡s ♠✉✐t♦ ♠❛✐s ❛♣✉r❛❞❛s ❜❛s❡❛❞❛s ❡♠ ❛♥✓❛❧✐s❡s ❞♦ ❞❡s✈✐♦ ❞❛ ❧✉③ ♣❛r❛ ♦ ✈❡r♠❡❧❤♦ ❞❡ ❣❛❧✓❛①✐❛s q✉❡ ❡r❛♠ ♣r❛t✐❝❛♠❡♥t❡ ✐♥✈✐s✓✏✈❡✐s ♣❛r❛ ♦s ❛str❫♦♥♦♠♦s✳ ❊st❡ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ♣♦ss✐❜✐❧✐t♦✉ ✉♠ s♦☞st✐❝❛❞♦ ♠❛♣❡❛♠❡♥t♦ ❞♦ ❝✓❡✉✱ ❬✷✵✱✷✶❪ ❝♦♠♦ ♣♦❞❡♠♦s ✈❡r ♥❛ ☞❣✉r❛ ✶✳✼✳ ◆❡st❡ r❡s✉❧t❛❞♦ ♣♦❞❡♠♦s ♦❜s❡r✈❛r q✉❡ ❣r✉♣♦s ❡ ❛❣❧♦♠❡r❛❞♦s ❞❡ ❣❛❧✓❛①✐❛s s❡ ♦r❣❛♥✐③❛♠ ❡♠ ❡str✉t✉r❛s ❛♣r♦①✐♠❛❞❛♠❡♥t❡ ✉♥✐❞✐♠❡♥s✐♦♥❛✐s✱ ☞❧❛♠❡♥t♦s❛s✱ ❝♦♠ ❧❛❝✉♥❛s ❡♥tr❡ ❡❧❛s✳ ❈♦♠ ❡st❛ ✐♥❢♦r♠❛✘❝⑦❛♦✱ ♠♦❞❡❧♦s ❞❛ ❢♦r♠❛✘❝⑦❛♦ ❞❡ ❡str✉t✉r❛s ♣✉❞❡r❛♠ s❡r ❛✈❛❧✐❛❞♦s ❧❡✈❛♥❞♦ ❛ ✐❞❡✐❛ ❞❡ q✉❡ ❛ ❢♦r♠❛✘❝⑦❛♦ ❞❡ ❡str✉t✉r❛s ❝♦♠❡✘❝♦✉ ❜❡♠ ♠❛✐s ❝❡❞♦ ❞♦ q✉❡ s❡ ❡s♣❡r❛✈❛✳

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✶✳ ■♥tr♦❞✉✘❝⑦❛♦ ✾

❋✐❣✉r❛ ✶✳✼✿ ❱❛✉❝♦✉❧❡✉rs ❡t ❛❧✳ ✶✾✼✻ ❬✷✵❪✳ ❉✐str✐❜✉✐✘❝⑦❛♦ ❞❡ ❣❛❧✓❛①✐❛s ❡♠ ❢✉♥✘❝⑦❛♦ ❞♦ ❞❡s✈✐♦ ❞❛ ❧✉③ ♣❛r❛ ♦ ✈❡r♠❡❧❤♦✱ ❛♥❡①♦ ❆✱ ❡ ♦ ❫❛♥❣✉❧♦✳ ◆♦t❡ q✉❡✱ ❛♣❡s❛r ❞❡ ✐❞❡✐❛ ❞❡ ✐s♦tr♦♣✐❛✱ ❡①✐st❡♠ r❡❣✐⑦♦❡s ❞❡ ♠❛✐♦r ❛❣❧✉t✐♥❛♠❡♥t♦ ❞❡ ❣❛❧✓❛①✐❛s ❡ ♦✉tr❛s q✉❛s❡ ✈❛③✐❛s✳ ❆ ☞❣✳ ✭❜✮ ✓❡ s❡♠❡❧❤❛♥t❡ ❛ ☞❣✳ ✭❛✮✱ ♣♦r✓❡♠ ❝♦♥s✐❞❡r❛♥❞♦ ♠❡♥♦r ❞✐st❫❛♥❝✐❛ ❡ ❜r✐❧❤♦✳ ◆❛ ☞❣✳ ✭❝✮ t❡♠♦s ✉♠❛ ♣r♦❥❡✘❝⑦❛♦ ❞♦s ♦❜❥❡t♦s ♥♦ ❝✓❡✉✳

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✶✳ ■♥tr♦❞✉✘❝⑦❛♦ ✶✵

❞❡s❝r❡✈❡r ✉♠❛ ✓♦r❜✐t❛ ❡st✓❛✈❡❧✱ q✉❡ ♥♦ ❝❛s♦ ❞♦s ♥❡✉tr✐♥♦s ❝❤❡❣❛ ❛ ✈❛❧♦r❡s ❞❡ ✹✵✵❡❱ ✭ ❬✷✷❪✱ ❝❛♣✳✶✽✮✱ ♦ q✉❡ ❡st✓❛ ❜❛st❛♥t❡ ❞✐st❛♥t❡ ❞❡ q✉❛❧q✉❡r ✐♥❝❡rt❡③❛ s♦❜r❡ ❛ ♠❛ss❛ ❞♦s ♥❡✉tr✐♥♦s✳

P♦rt❛♥t♦✱ ❞❡✈✐❞♦ ✒❛s ❝♦♥tr♦✈✓❡rs✐❛s ❛ r❡s♣❡✐t♦ ❞♦s ♥❡✉tr✐♥♦s ❝♦♠♦ ❝❛♥❞✐❞❛t♦ ✒❛ ▼❊✱ ♥♦✈❛s ✐❞❡✐❛s ❢♦r❛♠ ♣r♦♣♦st❛s✱ ♣♦r✓❡♠✱ ♦ q✉❡ ❛ ♠❛✐♦r✐❛ ❞❛s s✉❣❡st⑦♦❡s t✐♥❤❛♠ ❡♠ ❝♦♠✉♠ s❡r✐❛ ❛ ❝❛r❛❝t❡r✓✏st✐❝❛ ❞❡ s❡r ✉♠❛ ▼❛t✓❡r✐❛ ❊s❝✉r❛ ❢r✐❛ ✭❈❉▼ ✲ ❈♦❧❞ ❉❛r❦ ▼❛tt❡r✮✹✳ ❆♦ ❝♦♥tr✓❛r✐♦ ❞♦s ♥❡✉tr✐♥♦s✱ ❛s ♣❛rt✓✏❝✉❧❛s ❞♦ ♠♦❞❡❧♦ ❈❉▼ ❞❡✐①❛♠ ❞❡ s❡r r❡❧❛t✐✈✓✏st✐❝❛s ❛♥t❡s ❞♦ ♣❡r✓✏♦❞♦ ❞❡ ❢♦r♠❛✘❝⑦❛♦ ❞❡ ❡str✉t✉r❛s✳ ❈♦♠ s✉❛ ❜❛✐①❛ ✈❡❧♦❝✐❞❛❞❡ ❡st❛s s❡r⑦❛♦ ♠❛✐s s❡♥s✓✏✈❡✐s ✒❛s ♣❡rt✉r❜❛✘❝⑦♦❡s ♥♦ ✉♥✐✈❡rs♦ ♣r✐♠♦r❞✐❛❧ ✐♥✐❝✐❛♥❞♦ ♦ ♣r♦❝❡ss♦ ❞❡ ❢♦r♠❛✘❝⑦❛♦ ❞❡ ❡str✉t✉r❛s ♥♦ t❡♠♣♦ ♣r❡❞✐t♦ ♣❡❧❛ t❡♦r✐❛✳

❘❡t♦r♥❛♥❞♦ ❛♦ t✓♦♣✐❝♦ s♦❜r❡ ❛ q✉❛♥t✐❞❛❞❡ ❞❡ ♠❛t✓❡r✐❛✱ ✐♥✐❝✐❛❧♠❡♥t❡✱ ✉t✐❧✐③❛♥❞♦ ❞❛❞♦s ❞❛ ❞✐♥❫❛♠✐❝❛ ❞❡ ❣❛❧✓❛①✐❛s ❬✷✹④✷✽❪✱ ♦ ❝♦♥t❡✓✉❞♦ ❞❡ ♠❛t✓❡r✐❛ ❡r❛ ❡st✐♠❛❞♦ ❡♥tr❡ ✵❀ ✷ ❡ ✵❀ ✼ ❞♦ ✈❛❧♦r ❝r✓✏t✐❝♦ ❞❛ q✉❛♥t✐❞❛❞❡ t♦t❛❧ ❞❡ ❡♥❡r❣✐❛ ❞♦ ✉♥✐✈❡rs♦✱ ♦ q✉❡ ❧❡✈❛ ❛ ✐❞❡✐❛ ❞❡ ✉♠❛ ✉♥✐✈❡rs♦ ❛❜❡rt♦ ♦✉ ❞❡ r❡❛❧♠❡♥t❡ ❡①✐st✐r ❛❧❣✉♠❛ q✉❛♥t✐❞❛❞❡ ❞❡ ❡♥❡r❣✐❛ ❛❧✓❡♠ ❞♦ ♦❜s❡r✈❛❞♦ ❬✶❪✳ ❊st❡ t❡r♠♦ ❡①tr❛ ❢♦✐ ♣♦st♦ ♥❛ ❡q✉❛✘❝⑦❛♦ ❞❡ ❡st❛❞♦ ❞♦ ✉♥✐✈❡rs♦✱ ♣♦r ♠❡✐♦ ❞❛ ❈♦♥st❛♥t❡ ❞❡ ❊✐♥st❡✐♥ ✭♦✉✱ ❝♦♥st❛♥t❡ ❝♦s♠♦❧✓♦❣✐❝❛✱ ✄ ❬✷✷❪✮✱ q✉❡ ❢♦✐ ✐♥tr♦❞✉③✐❞❛ ♣♦r ❊✐♥st❡✐♥ ♣❛r❛ ❝♦♥tr❛♣♦r ♦ t❡r♠♦ ❞❡ ❛tr❛✘❝⑦❛♦✱ ❧❡✈❛♥❞♦ ❛ ✉♠❛ ❛ ❡q✉❛✘❝⑦❛♦ q✉❡ ❞❡s❝r❡✈❡ ✉♠ ✉♥✐✈❡rs♦ ❡st✓❛t✐❝♦✳ ❉❡✈✐❞♦ ✒❛ ❝❛r❫❡♥❝✐❛ ❞❡ ❞❛❞♦s ♦❜s❡r✈❛❝✐♦♥❛✐s✱ ♦ ✈❛❧♦r ♣❛r❛ ✄ s❡ tr❛t❛✈❛ ❞❡ ✉♠ ❛❥✉st❡ t❡✓♦r✐❝♦✳ ❊♥tr❡t❛♥t♦ ❝♦♠ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❛ t❡❝♥♦❧♦❣✐❛ ❡ ❞♦s ♠✓❡t♦❞♦s ♣❛r❛ ♦❜t❡♥✘❝⑦❛♦ ❞♦s ♣❛r❫❛♠❡tr♦s ❝♦s♠♦❧✓♦❣✐❝♦s ❡st❡ ♣r♦❜❧❡♠❛ ❢♦✐ ❝♦♥t♦r♥❛❞♦✳ ❉❡♥tr❡ ❡❧❡s✱ ❞♦✐s ❡①♣❡r✐♠❡♥t♦s tr♦✉①❡r❛♠ ❣r❛♥❞❡ r❡✈♦❧✉✘❝⑦❛♦✿ ✉♠ s❡ ❜❛s❡✐❛ ♥❛s ♠❡❞✐❞❛s ❞❛s ✌✉t✉❛✘❝⑦♦❡s ❞❛ ❈▼❇❘ ❬✷✷✱✷✾④✸✶❪ ❡ ♦ ♦✉tr♦ ♥❛s ♦❜s❡r✈❛✘❝⑦♦❡s ❞❡ s✉♣❡r♥♦✈❛s ❞✐st❛♥t❡s ❬✷✷✱✷✾✱✸✷✱✸✸❪✳ ❊st✉❞♦s ❞❛ ❈▼❇❘ ♣r✐✈✐❧❡❣✐❛♠ ♠♦❞❡❧♦s q✉❡ ♣r♦♣⑦♦❡♠ ♦ ✉♥✐✈❡rs♦ ♣r✐♠♦r❞✐❛❧ q✉❡♥t❡ ❡ ❝♦♠ ❛❧t♦ ❣r❛✉ ❞❡ ✐s♦tr♦♣✐❛ t✓❡r♠✐❝❛✳ ❊st❛ ❛♥✓❛❧✐s❡ ✐♥❞✐❝❛ q✉❡ ♦ ✉♥✐✈❡rs♦ ✐♥✐❝✐❛❧♠❡♥t❡ ❡r❛ t⑦❛♦ q✉❡♥t❡ q✉❡ ❡①✐st✐❛♠ ❛♣❡♥❛s ♥✓✉❝❧❡♦s ✐♦♥✐③❛❞♦s ✉♠❛ ✈❡③ q✉❡ ♦s ❢✓♦t♦♥s ♣♦ss✉✓✏❛♠ ❡♥❡r❣✐❛s ❛❧t✓✏ss✐♠❛s q✉❡ ✐♠♣♦ss✐❜✐❧✐t❛✈❛♠ ❛ ❢♦r♠❛✘❝⑦❛♦ ❞❡ ✓❛t♦♠♦s ✭❧♦❣♦ ❡r❛♠ ✐♦♥✐③❛❞♦s✮✳ ▼❡❞✐❞❛s s♦❜r❡ ❛ ❞✐str✐❜✉✐✘❝⑦❛♦ ❛♥❣✉❧❛r ❞♦ ❡s♣❡❝tr♦ ❞❡ ♣♦t❫❡♥❝✐❛ ❞❛ ❈▼❇❘ ♣❡r♠✐t❡ ♦❜t❡r ❞❛❞♦s s♦❜r❡ ❛ ❢♦r♠❛✘❝⑦❛♦ ❞♦s ✓❛t♦♠♦s ❧❡✈❡s ❡ ❡str✉t✉r❛s ♠❡❞✐♥❞♦ s❡✉s ♥✓✏✈❡✐s ❞❡ ❛♥✐s♦tr♦♣✐❛✳ ❆ ♣r✐♠❡✐r❛ t❡♥t❛t✐✈❛ ❞❡ ♠❡❞✐r t❛✐s ❛♥✐s♦tr♦♣✐❛s ❢♦✐ ♣♦r ♠❡✐♦ ❞♦ s❛t✓❡❧✐t❡ ❈❖❇❊ ✭❈♦s♠✐❝ ❇❛❝❦❣r♦✉♥❞ ❊①♣❧♦r❡r✮✱ ❡st❛✱ ♣♦r✓❡♠ ♥⑦❛♦ ❢♦✐ ♦❜s❡r✈❛❞❛✳ ❖ ❡①♣❡r✐♠❡♥t♦ s❡❣✉✐♥t❡✱ ❲✐❧❦✐♥s♦♥ ▼✐❝r♦✇❛✈❡ ❆♥✐s♦tr♦♣② Pr♦❜❡ ✭❲▼❆P✱ ❬✸✶❪✮ q✉❡✱ ❞❡ ❢❛t♦✱ ❢♦r♥❡❝❡✉ ♦s ♣r✐♠❡✐r♦s ❞❛❞♦s ❞❛s ♦s❝✐❧❛✘❝⑦♦❡s t✓❡r♠✐❝❛s ❞❛ ❈▼❇❘ ❡ ♣♦ss✐❜✐❧✐t♦✉ ❛ ♦❜t❡♥✘❝⑦❛♦ ❞❛ r❛③⑦❛♦ ❡♥tr❡ ❛ ❞❡♥s✐❞❛❞❡

▲❡♠❜r❛♠♦s q✉❡ ❛ ▼❊✱ ❡♠ ❛❧❣✉♥s ♠♦❞❡❧♦s ✐♥t❡r❛❣❡♠ ❝♦♠ ❛ ❧✉③✱ ♣♦r✓❡♠ ♦s ✈✓✏♥❝✉❧♦s ❛ss♦❝✐❛❞♦s ❛ ❡st❡

(22)

✶✳ ■♥tr♦❞✉✘❝⑦❛♦ ✶✶

❞❡ ♠❛t✓❡r✐❛ ❡ ❛ ❞❡♥s✐❞❛❞❡ ❝r✓✏t✐❝❛✺✱ t❛♠❜✓❡♠ ❝♦♥❤❡❝✐❞❛ ❝♦♠♦ ❛❜✉♥❞❫❛♥❝✐❛ ✭✡✮✱ q✉❡ ✓❡ ❝❛❧❝✉❧❛❞❛ ✉t✐❧✐③❛♥❞♦ ♦ ♠♦❞❡❧♦ ✄❈❉▼ ✳

❆ ✐❞❡✐❛ r❛③♦❛✈❡❧♠❡♥t❡ s✐♠♣❧❡s s♦❜r❡ ♦ ❈▼❇❘ s❡ tr❛t❛ ❞❡ s✉♣♦r ♦ ❝♦♥t❡✓✉❞♦ ❞❡ ❡♥❡r❣✐❛ ❞♦ ✉♥✐✈❡rs♦ ❝♦♠♦ ✉♠ ✌✉✐❞♦ ❝♦♠♣♦st♦ ❞❡ ❜✓❛r✐♦♥s✱ ❡❧✓❡tr♦♥s ❡ ❢✓♦t♦♥s✳ ❖s ❢✓♦t♦♥s ✒❛ t❡♠♣❡r❛t✉r❛ ❭❛♠❜✐❡♥t❡✧ ❞♦ ✉♥✐✈❡rs♦ ♣♦ss✉✓✏❛♠ ❡♥❡r❣✐❛ s✉☞❝✐❡♥t❡ ♣❛r❛ ✐♦♥✐③❛r ✓❛t♦♠♦s ❞❡ ❤✐❞r♦❣❫❡♥✐♦✱ ✐♠♣❡❞✐♥❞♦ ❛ ❢♦r♠❛✘❝⑦❛♦ ❞❡ ❤✐❞r♦❣❫❡♥✐♦ ♥❡✉tr♦✳ P♦r ♦✉tr♦ ❧❛❞♦✱ ❛ ❢♦r✘❝❛ ❣r❛✈✐t❛❝✐♦♥❛❧ ❛❣✐❛ ❛tr❛✐♥❞♦ ❛ ♠❛t✓❡r✐❛✱ ❝♦♠♣r✐♠✐♥❞♦ ♦ ✌✉✐❞♦✳ ❖❝♦rr✐❛ ❡♥t⑦❛♦ ✉♠❛ ♦s❝✐❧❛✘❝⑦❛♦✿ ❛ ❣r❛✈✐❞❛❞❡ ❛❣✐❛ ♥❛ t❡♥t❛t✐✈❛ ❞❡ ❛❣❧✉t✐♥❛r ❡ ♦s ❢✓♦t♦♥s ❞❡ ❞✐ss♦❝✐❛r ❛ ♠❛t✓❡r✐❛✱ ❡st❡ ♣r♦❝❡ss♦ ♣♦❞❡ s❡r ✈✐st♦ ❝♦♠♦ ✈✓❛r✐♦s ♦s❝✐❧❛❞♦r❡s ❤❛r♠❫♦♥✐❝♦s✳ ❈♦♥❢♦r♠❡ ♦ ✉♥✐✈❡rs♦ s❡ ❡①♣❛♥❞✐✉✱ ♦s ❢✓♦t♦♥s s♦❢r❡r❛♠ ♣❡r❞❛s ❞❡ ❡♥❡r❣✐❛ ❞❡✈✐❞♦ ❛♦ r❡❞s❤✐❢t ❛t✓❡ ♦ ♣♦♥t♦ ❞❡ ♥⑦❛♦ ♣♦ss✉✓✏r❡♠ ❡♥❡r❣✐❛ s✉☞❝✐❡♥t❡ ♣❛r❛ ✐♦♥✐③❛r ♦ ❤✐❞r♦❣❫❡♥✐♦✱ ❡st❡ ✓❡ ♦ ♠♦♠❡♥t♦ ❞❡♥♦♠✐♥❛❞♦ ❞❡s❛❝♦♣❧❛♠❡♥t♦ ✭❡♥tr❡ ❢✓♦t♦♥s ❡ ❡❧✓❡tr♦♥s✮ ❡ ❛❝♦♥t❡❝❡✉ q✉❛♥❞♦ ♦ ✉♥✐✈❡rs♦ t✐♥❤❛ ♣♦r ✈♦❧t❛ ❞❡ ✸✽✵✳✵✵✵ ❛♥♦s✳ ❯♠❛ ✈❡③ ❞❡s❛❝♦♣❧❛❞♦s ♦s ❢✓♦t♦♥s ❣✉❛r❞❛r❛♠ ❛s ✐♥❢♦r♠❛✘❝⑦♦❡s ❞❛s ✉❧t✐♠❛s ♦s❝✐❧❛✘❝⑦♦❡s ♥♦ ✌✉✐❞♦ ❜✓❛r✐♦♥s✲❡❧✓❡tr♦♥s✲ ❢✓♦t♦♥s q✉❡ s⑦❛♦ tr❛♥s❢❡r✐❞❛s ♣❛r❛ ❛s ❛♥✐s♦tr♦♣✐❛s ♠❡❞✐❞❛s ♥♦ ❈▼❇❘✱ ❛ss♦❝✐❛❞♦✱ ♣♦r ❡①❡♠♣❧♦✱ ❛♦ ❫❛♥❣✉❧♦ ❞❡ ♦❜s❡r✈❛✘❝⑦❛♦ ✭✒✮ ❡ ♦ ♥✓✉♠❡r♦ ❞❡ ♠✉❧t✐♣♦❧♦ ✭❧✮✳ ❈♦♥❢♦r♠❡ ❬✸✵❪✱ ❛ t❡♦r✐❛ ♣r❡❞✐③ q✉❡ ❛ ♣♦s✐✘❝⑦❛♦ ❞♦ ♣r✐♠❡✐r♦ ♣✐❝♦ ♥❛s ❛♥✐s♦tr♦♣✐❛s ❞♦ ❈▼❇❘ ❢♦r♥❡❝❡ ❛ q✉❛♥t✐❞❛❞❡ t♦t❛❧ ❞❡ ❡♥❡r❣✐❛ ❞♦ ✉♥✐✈❡rs♦ ✭❧✶ ✬ ✷✵✵❂♣✡❦✮✱ ❛♦ ❝♦♠♣❛r❛r ❝♦♠ ♦s ❞❛❞♦s ♦❜t❫❡♠✲s❡ ✡❦ ❂ ✶❀ ✵✷✳ ❖✉ s❡❥❛✿

❛ q✉❛♥t✐❞❛❞❡ ❞❡ ❡♥❡r❣✐❛ ❡ ❝♦♠♣♦♥❡♥t❡s ❞❡ ♠❛t✓❡r✐❛ s⑦❛♦ ♦❜t✐❞♦s ♣❡❧♦ ❛❥✉st❡ ❞♦ ♠♦❞❡❧♦ ❞❡ ✌✉✐❞♦✱ s❡❣✉♥❞♦ ❛ ☞❣✳ ✭✶✳✽✮✱ ❛♦s ❞❛❞♦s✱ ♣♦r ❡①❡♠♣❧♦ ♦s ❞♦ ❡①♣❡r✐♠❡♥t♦ P❧❛♥❝❦✱ ☞❣✳ ✭✶✳✾✮✳ ❈♦♠♦ ❢❛❧❛r❡♠♦s ♠❛✐s ❛❞✐❛♥t❡✱ ❛tr❡❧❛❞♦ ❛ ❡st❛ t❡♦r✐❛ t❡♠♦s ❛ ❞❛ ❇✐❣ ❇❛♥❣ ◆✉❝❧❡♦ss✓✏♥t❡s❡ q✉❡ ❞❡s❝r❡✈❡✱ ❝♦♠ ❜♦♠ ❛❝♦r❞♦✱ ❛ q✉❛♥t✐❞❛❞❡ ❞❡ ❡❧❡♠❡♥t♦s ❧❡✈❡s✱ ❝♦♠♦ ✷❍❀❍❡❀ ❉❀❍❡ ❡▲✐✳ ❉❡st❛ ❢♦r♠✉❧❛✘❝⑦❛♦✱ ♣♦❞❡♠♦s ♦❜t❡r ❛ q✉❛♥t✐❞❛❞❡ ❞❡ ❜✓❛r✐♦♥s ♥❡❝❡ss✓❛r✐❛ ♣❛r❛ ❢♦r♠❛✘❝⑦❛♦

❞❡st❡s ✓❛t♦♠♦s✳ ❆♦ ❝♦♠♣❛r❛r ❛s t❡♦r✐❛s ❝♦♠ ♦s ❡①♣❡r✐♠❡♥t♦s ♣❡r❝❡❜❡✲s❡ q✉❡ ❡①✐st❡ ♠✉✐t♦ ♠❛✐s ❡♥❡r❣✐❛ ❡ ♠❛t✓❡r✐❛ q✉❡ ❛♣❡♥❛s ❛ q✉❛♥t✐❞❛❞❡ ❞❡ ❜✓❛r✐♦♥s✱ ❡❧✓❡tr♦♥s ❡ ❢✓♦t♦♥s✳ P♦r✓❡♠✱ ✉♠❛ ✈❡③ q✉❡ ❛ t❡♦r✐❛ ❞❛ ◆✉❝❧❡♦ss✓✏♥t❡s❡ ❡st✓❛ ❜❡♠ ❡st❛❜❡❧❡❝✐❞❛ ❡st❡ ♥♦✈♦ ❝♦♥t❡✓✉❞♦ ❞❡ ❡♥❡r❣✐❛ ♥⑦❛♦ ♣♦❞❡ ✐♥✌✉❡♥❝✐❛r ♥♦s r❡s✉❧t❛❞♦s ❞♦ ❞❡s❛❝♦♣❧❛♠❡♥t♦✱ ✐ss♦ ✐♠♣❧✐❝❛ q✉❡ ♦ ♥♦✈♦ ❝♦♥t❡✓✉❞♦ ♣r❡❝✐s❛ ✐♥t❡r❛❣✐r ♠✉✐t♦ ❢r❛❝❛♠❡♥t❡ ♥❡st❡ ♣❡r✓✏♦❞♦✳ ❖ ♠♦❞❡❧♦ q✉❡ ♠❛✐s s❡ ❛❥✉st❛ ❛s ❝♦♥❞✐✘❝⑦♦❡s r❡q✉❡r✐❞❛s ✓❡ ♦ ✄❈❉▼✳ ❈♦♥❢♦r♠❡ ♣♦❞❡♠♦s ✈❡r ♥❛ ☞❣✳ ✭✶✳✾✮✱ ❛ ❝✉r✈❛ ❡♠ ✈❡r❞❡✳

P♦❞❡♠♦s ✈❡r ❞❛ ☞❣✉r❛ ✶✳✽ ♦ q✉❛♥t♦ ♦ ♠♦❞❡❧♦ ✄❈❉▼ ✈❛r✐❛ ❝♦♥❢♦r♠❡ ❛ ♠✉❞❛♥✘❝❛ ❞❡ s❡✉s ♣❛r❫❛♠❡tr♦s✳ P❛r❛ ✉♠❛ r❡✈✐s⑦❛♦ r❡❝♦♠❡♥❞❛♠♦s ❛ ❧❡✐t✉r❛ ❞♦s ❝❛♣✓✏t✉❧♦s ✺✱ ✻✱ ✼ ❡ ✽ ❞❛ r❡❢❡r❫❡♥❝✐❛ ❬✷✾❪✳ ❆❜❛✐①♦✱ ☞❣✉r❛ ✶✳✾✱ t❡♠♦s ❛s ❛♥✐s♦tr♦♣✐❛s ❞♦ ♠❡s♠♦ ❡s♣❡❝tr♦ ♠❡❞✐❞♦ ❞❛

(23)

✶✳ ■♥tr♦❞✉✘❝⑦❛♦ ✶✷

❋✐❣✉r❛ ✶✳✽✿ ❖ ❣r✓❛☞❝♦ ♠♦str❛ ❛ s❡♥s✐❜✐❧✐❞❛❞❡ ❞♦ ♠♦❞❡❧♦ ✄❈❉▼ ❡♠ ❢✉♥✘❝⑦❛♦ ❞♦s s❡✉s ♣❛r❫❛♠❡tr♦s✱ s⑦❛♦ ❡❧❡s ❝✉r✈❛t✉r❛ ✭❛✮✱ q✉❛♥t✐❞❛❞❡ ❞❡ ❡♥❡r❣✐❛ ❡s❝✉r❛ ✭❜✮✱ ❛❜✉♥❞❫❛♥❝✐❛ ❞❡ ❜✓❛r✐♦♥s ✭❝✮✱ ❛❜✉♥❞❫❛♥❝✐❛ ❞❡ ♠❛t✓❡r✐❛ ✭❞✮ ❬✸✹❪✳

❈▼❇❘ ♦❜t✐❞♦ ♣❡❧♦ ❊①♣❡r✐♠❡♥t♦ P❧❛♥❝❦ ❬✸✺❪✳ ❆ ❝✉r✈❛ ❡♠ ✈❡r❞❡ q✉❡ ♠❡❧❤♦r s❡ ❛❥✉st❛ ❛♦s ❞❛❞♦s ♠❡❞✐❞♦s ❢♦r♥❡❝❡ ♦s ✈❛❧♦r❡s ❝♦♠♦ ❝✉r✈❛t✉r❛✱ q✉❛♥t✐❞❛❞❡ ❞❡ ❡♥❡r❣✐❛ ❡s❝✉r❛✱ ❛❜✉♥❞❫❛♥❝✐❛ ❞❡ ❜✓❛r✐♦♥s ❡ ❛ ❛❜✉♥❞❫❛♥❝✐❛ t♦t❛❧ ❞❡ ♠❛t✓❡r✐❛ ❝♦♥❢♦r♠❡ ♦ ♠♦❞❡❧♦ ✄❈❉▼✱ ✈✐st♦ ♥❛ ☞❣✉r❛✶✳✽✳

❖✉tr❛ ❢♦♥t❡ ❞✐st✐♥t❛ ❞❡ ✐♥❢♦r♠❛✘❝⑦❛♦ s♦❜r❡ ♦s ♣❛r❫❛♠❡tr♦s ❝♦s♠♦❧✓♦❣✐❝♦s ♣r♦✈✓❡♠ ❞❛ ♦❜✲ s❡r✈❛✘❝⑦❛♦ ❞❡ s✉♣❡r♥♦✈❛s✳ ❈♦♠♣❛r❛♥❞♦ s✉❛s ❧✉♠✐♥♦s✐❞❛❞❡s ✭✉♠❛ ✈❡③ q✉❡ ❡st❛ ✓❡ ❝❛r❛❝t❡r✓✏st✐❝❛ ❞♦ s❡✉ ❡st❛❞♦ ❞❡ ❡✈♦❧✉✘❝⑦❛♦✮ ❡ ❞❡s✈✐♦s ❞❛s r❛✐❛s ❡s♣❡❝tr❛✐s ✭r❡❞s❤✐❢t✮ ♣♦❞❡♠♦s ♦❜t❡r ✐♥❢♦r♠❛✘❝⑦♦❡s s♦❜r❡ ❛ t❛①❛ ❞❡ ❡①♣❛♥s⑦❛♦ ❞♦ ✉♥✐✈❡rs♦ ❡♠ ❞✐❢❡r❡♥t❡s ♣❡r✓✏♦❞♦s✳ ❖ r❡s✉❧t❛❞♦ ♦❜t✐❞♦ ❛♣♦♥t❛ ♣❛r❛ ✉♠ ✉♥✐✈❡rs♦ ❡♠ ❡①♣❛♥s⑦❛♦ ❛❝❡❧❡r❛❞❛ ❝♦♥☞r♠❛♥❞♦ ♦ ♠♦❞❡❧♦ ❝♦s♠♦❧✓♦❣✐❝♦ q✉❡ ❝♦♥s✐❞❡r❛ ❛ ❝♦♥st❛♥t❡ ❝♦s♠♦❧✓♦❣✐❝❛ ✭✄✮ ❝♦♠♦ ❢♦♥t❡ ❞❡st❛ ❛❝❡❧❡r❛✘❝⑦❛♦✳ ❉❡ ♣♦ss❡ ❞❡st❛s ✐♥❢♦r♠❛✘❝⑦♦❡s ✭✷❞❋●❘❙ ❬✸✻❪✱ ❙❉❙❙ ❬✸✼❪ ❡ ♦ ❲▼❆P ❬✸✶❪ ✮✱ ✉♠❛ ❛♥✓❛❧✐s❡ ✐♥❞❡♣❡♥❞❡♥t❡ ❞❡ ♠♦❞❡❧♦ ♣♦❞❡ s❡r r❡❛❧✐③❛❞❛ ❝✉❧♠✐♥❛♥❞♦ ♥♦ ❣r✓❛☞❝♦ ❞❛ ☞❣✉r❛ ✶✳✶✵✳

❆ r❡❣✐⑦❛♦ ❝♦♠✉♠ ❡♥tr❡ ♦s ❞❛❞♦s ❛♣♦♥t❛ ♣❛r❛ ♦ ✈❛❧♦r ❞❡ ❛❜✉♥❞❫❛♥❝✐❛ ❞❛ ♠❛t✓❡r✐❛ ✡♠ ❂ ✵❀ ✷✼ ✝

✵❀ ✵✷✱ q✉❡ ♥⑦❛♦ ❡st✓❛ ❞✐st❛♥t❡ ❞♦s r❡s✉❧t❛❞♦s ♣r❡❞✐t♦s ♣♦r ❖str✐❦❡s ❡ ❙t❡❡✐♥❤❛r❞t ✭✶✾✾✺✮✱ ✡♠ ❂

✵❀ ✸✳ ◆♦ ❝❛s♦ ❞❛ ❝♦♥st❛♥t❡ ❞❡ ❍✉❜❜❧❡ t❡♠♦s ❤ ❂ ✵❀ ✼✶ ✝ ✵❀ ✵✷✱ ✡❜ ❂ ✵❀ ✵✹✶ ✝ ✵❀ ✵✵✷ ❝♦♠ ✐ss♦

(24)

✶✳ ■♥tr♦❞✉✘❝⑦❛♦ ✶✸

❋✐❣✉r❛ ✶✳✾✿ ❆♥✐s♦tr♦♣✐❛s ❞❛ t❡♠♣❡r❛t✉r❛ ❛❢❡r✐❞❛s ❞♦ ❡s♣❡❝tr♦ ❞❡ ♣♦t❫❡♥❝✐❛ ❞❛ ❈▼❇❘ ♦❜t✐❞♦ ♣❡❧♦ ❊①♣❡r✐♠❡♥t♦ P❧❛♥❝❦ ❬✸✺❪✳ ❆ ❝✉r✈❛✱ ❝♦♥❢♦r♠❡ ❛ ☞❣✳ ✭✶✳✽✮✱ q✉❡ ♠❡❧❤♦r s❡ ❛❥✉st❛ ❛♦s ❞❛❞♦s ❞♦ P❧❛♥❝❦ ❢♦r♥❡❝❡ ♦s ✈❛❧♦r❡s ❞❡ ✡▼❛t❡r✐❛❀ ✡❜✱ ❝✉r✈❛t✉r❛ ❡ ♦ ❞❛ ❝♦♥st❛♥t❡ ❝♦s♠♦❧✓♦❣✐❝❛✳

❞♦ ❯♥✐✈❡rs♦ ❡♠ ✭✶✸❀ ✼ ✝ ✵❀ ✷✮ ✂ ✶✵✾❛♥♦s✳

❆❣♦r❛ ✐r❡♠♦s ❡♥✉♥❝✐❛r ❛❧❣✉♠ ♣♦ss✓✏✈❡✐s ❝❛♥❞✐❞❛t♦s ✒❛ ▼❊✳ ❈♦♠♦ ✈✐♠♦s ❛♥t❡r✐♦r♠❡♥t❡ ♦s ♥❡✉tr✐♥♦s ❡st⑦❛♦ ❞❡s❝❛rt❛❞♦s ♣❡❧♦ ♠♦❞❡❧♦ ✄❈❉▼✳ ❊st❛s ♣❛rt✓✏❝✉❧❛s ♥⑦❛♦ ❝♦♥s❡❣✉❡♠ s❡ ❛❞❡q✉❛r ❛♦ ✈❛❧♦r ❞❛ ❛❜✉♥❞❫❛♥❝✐❛ ♠❡❞✐❞❛ ♣❛r❛ ❛ ▼❊✳ ❯♠❛ ✈❡③ ❝♦♥☞r♠❛❞♦ q✉❡✱ ❛♦ ♠❡♥♦s✱ ❞♦✐s ♥❡✉tr✐✲ ♥♦s ♣♦ss✉❡♠ ✉♠❛ ♣❡q✉❡♥❛ ♠❛ss❛ ✭♠✗ ❁ ✷❡❱ ✮✱ s✉❛ ❛❜✉♥❞❫❛♥❝✐❛ ❛t✉❛❧ ✓❡ ❞❛❞❛ ♣❡❧❛ s❡❣✉✐♥t❡

❡q✉❛✘❝⑦❛♦

✡✗❤✷ ❂

✐❂❡❀✖❀✜

♠✗✐

✾✸❡❱ ✭✶✳✹✮

s❡♥❞♦ ❤ ❂ ✵✿✼✵✹ ✝ ✵✿✵✷✺✱ ♦ ♣❛r❫❛♠❡tr♦ ❞❡ ❍✉❜❜❧❡ ❬✸✽❪✱ q✉❡ r❡s✉❧t❛ ❡♠ ✡✗❤✷ ❁ ✵❀ ✵✻❡❱✱ q✉❡

❡st❛ ❜❡♠ ❛❜❛✐①♦ ❞♦ ✈❛❧♦r ❡s♣❡r❛❞♦ ♣❛r❛ ❛ ▼❊✳

(25)

✶✳ ■♥tr♦❞✉✘❝⑦❛♦ ✶✹

❋✐❣✉r❛ ✶✳✶✵✿ ❆♥✓❛❧✐s❡ ♠♦❞❡❧♦ ✐♥❞❡♣❡♥❞❡♥t❡ ❞❛ ❛❜✉♥❞❫❛♥❝✐❛✳ ❊♠ ❛③✉❧ ❞❛❞♦s ❡①♣❡r✐♠❡♥t❛✐s ♣r♦✈❡♥✐❡♥t❡s ❞♦s ❡st✉❞♦s s♦❜r❡ ❙✉♣❡r♥♦✈❛s✱ ❡♠ ❧❛r❛♥❥❛ ❞❛❞♦s ♦❜s❡r✈❛❝✐♦♥❛✐s ❞❛ r❛❞✐❛✘❝⑦❛♦ ❝✓♦s♠✐❝❛ ❞❡ ❢✉♥❞♦ ❡ ❡♠ ✈❡r❞❡ ❞❛❞♦s ❞♦s ❡st✉❞♦s s♦❜r❡ ❛s ♦s❝✐❧❛✘❝⑦♦❡s ♣r✐♠♦r❞✐❛✐s ❞❛ ❣r❛✈✐❞❛❞❡✳ ❉✐❢❡r❡♥t❡s ❛❜♦r❞❛❣❡♥s ♣♦ss✉❡♠ ✈❛❧♦r❡s ❡♠ ❝♦♠✉♠✳

♦ ❤✐❣❣s✐♥♦ ✭s✉♣❡r♣❛r❝❡✐r♦s ❞♦s ❜✓♦s♦♥s ❞♦ ♠♦❞❡❧♦ ♣❛❞r⑦❛♦ ❞❛ ❢✓✏s✐❝❛ ❞❡ ♣❛rt✓✏❝✉❧❛s ✭▼P✮✱ ❞❛ ❝♦rr❡♥t❡ ♥❡✉tr❛✱ ❩✱ ❞♦ ❢✓♦t♦♥ ❡ ❞♦ ❤✐❣❣s✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✮✳ ❙❡✉ ❛✉t♦✲❡st❛❞♦ ♠❛✐s ❧❡✈❡✱ ♣♦ss✉✐ ✉♠❛ s✐♠❡tr✐❛ q✉❡ ♦ ✐♠♣❡❞❡ ❞❡ ❞❡❝❛✐r ❡♠ ♣❛rt✓✏❝✉❧❛s ♠❛✐s ❧❡✈❡s ❞♦ ▼P✱ t♦r♥❛♥❞♦✲♦ ❛ ♣❛rt✓✏❝✉❧❛ ♠❛✐s ❧❡✈❡ ❡st✓❛✈❡❧ s❡❣✉♥❞♦ ❡st❛ s✐♠❡tr✐❛ ✭♦✉ s❡✉ t❡♠♣♦ ❞❡ ✈✐❞❛ ♣r❡❝✐s❛ s❡r ♥♦ ♠✓✏♥✐♠♦ ♦ ❞❛ ✐❞❛❞❡ ❞♦ ✉♥✐✈❡rs♦✮✳

❯♠❛ ✐❞❡✐❛ ✐❣✉❛❧♠❡♥t❡ ✐♥t❡r❡ss❛♥t❡ ❝♦rr❡s♣♦♥❞❡ ❛♦ ❛①✐♦♥ ❬✹✵❪✱ ✉♠❛ ♣❛rt✓✏❝✉❧❛ s✉❣❡r✐❞❛ ♣❛r❛ r❡s♦❧✈❡r ♦ ♣r♦❜❧❡♠❛ ❞❡ ✈✐♦❧❛✘❝⑦❛♦ ❞❡ ❈P ✭❝❛r❣❛ ❡ ♣❛r✐❞❛❞❡✮ ❞♦ s❡t♦r ❞❛ ❢♦r✘❝❛ ❢♦rt❡ ❞♦ ▼P✱ q✉❡ ♥⑦❛♦ ✓❡ ♦❜s❡r✈❛❞♦ ❡①♣❡r✐♠❡♥t❛❧♠❡♥t❡✳

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✶✳ ■♥tr♦❞✉✘❝⑦❛♦ ✶✺

❡ ❡st❛✱ ✉♠❛ ✈❡③ q✉❡ ❛✐♥❞❛ ♥⑦❛♦ ❢♦✐ ❞❡t❡❝t❛❞❛✱ ♣r❡❝✐s❛ s❡r ♣❡q✉❡♥❛✳ ❊♠ ♣r✐♥❝✓✏♣✐♦✱ q✉❛❧q✉❡r ♣❛rt✓✏❝✉❧❛ ♣♦❞❡r✐❛ s❡ ♣r♦♣❛❣❛r ❡♠ ✉♠❛ ♦✉ ♠❛✐s ❞✐♠❡♥s⑦♦❡s ❡①tr❛s ❝♦♠♣❛❝t❛s✱ ♦♥❞❡✱ ♠♦❞♦s ❞❡ ✈✐❜r❛✘❝⑦❛♦ ❞♦s ❝❛♠♣♦s ♥❡st❛ ❞✐♠❡♥s⑦♦❡s ❝♦♠♣❛❝t❛s ♦r✐❣✐♥❛♠ ♣❛rt✓✏❝✉❧❛s q✉❡ ♣♦❞❡♠ s❡r ❝❤❛♠❛✲ ❞❛s ❞❡ ♣❛rt✓✏❝✉❧❛s ♣❛r❝❡✐r❛ ❞❡ ❑❛❧✉③❛✲❑❧❡✐♥✳ ❆❧❣✉♥s ❞❡st❡s ♣❛r❝❡✐r♦s s❛t✐s❢❛③❡♠ ♦s ✈✓✏♥❝✉❧♦s ♥❡❝❡ss✓❛r✐♦s ♣❛r❛ ✉♠ ❜♦♠ ❝❛♥❞✐❞❛t♦ ✒❛ ▼❊ ✭s⑦❛♦ ❡st✓❛✈❡✐s✱ ❢r✐♦s✱ ♥❡✉tr♦s ❡ ❢♦r♥❡❝❡♠ ♦ ✈❛❧♦r ❝♦rr❡t♦ ♣❛r❛ ✒❛ ❛❜✉♥❞❛♥❝✐❛✮✳ ❈❛♠♣♦s q✉❡ s❡ ♣r♦♣❛❣❛♠ ♥❛ ❞✐♠❡♥s⑦❛♦ ❡①tr❛ ♣♦ss✉❡♠ ♠♦♠❡♥t♦ q✉❛♥t✐③❛❞♦ ✭♣✷ ✘ ✶❂❘✮✱ ♦♥❞❡ ❘ ✓❡ ♦ ❝♦♠♣r✐♠❡♥t♦ ❞❛ ❞✐♠❡♥s⑦❛♦ ❡①tr❛ ❬✹✶❪✱ ❡ s✉❛ ♠❛ss❛ ✓❡ ❜❛s✐✲

❝❛♠❡♥t❡ ♦ ♠♦♠❡♥t♦ ❛♦ ❧♦♥❣♦ ❞❛ ❞✐♠❡♥s⑦❛♦ ❡①tr❛ q✉❛♥t✐③❛❞♦ ❡♠ ✉♥✐❞❛❞❡s ❞❡ ✶❂❘✷ ❛♦ ♣❛ss♦

q✉❡✱ ♣♦❞❡♠♦s t❡r ❘ ✘ ❚ ❡❱ ✶✱ ♦✉ s❡❥❛✱ t❡r❡♠♦s ✉♠❛ ♣❛rt✓✏❝✉❧❛✱ s✉♣♦♥❞♦ ❡st✓❛✈❡❧✱ ♥❛ ❢❛✐①❛ ❞❡

♠❛ss❛ ❞❡ ❛❧❣✉♥s ❘ ✘ ❚ ❡❱✱ q✉❡ ❝♦♥❝♦r❞❛ ❝♦♠ ❛❧❣✉♥s ♠♦❞❡❧♦s ❞❡ ▼❊ ❬✹✷✱✹✸❪ ✳

✶✳✶✳✸ Pr♦❞✉✘❝⑦❛♦ ❚✓❡r♠✐❝❛ ❞❛ ❲■▼P

◆❡st❛ s❡✘❝⑦❛♦ ❛❜♦r❞❛r❡♠♦s ✉♠❛ ❧✐♥❤❛ t❡✓♦r✐❝❛ q✉❡ ❞❡s❝r❡✈❡✱ ❞❡ ❢♦r♠❛ ♠✉✐t♦ s❛t✐s❢❛t✓♦r✐❛✱ ♦ ♣r♦❝❡ss♦ ❞❡ ♣r♦❞✉✘❝⑦❛♦ ❞❛ ▼❊ ♥♦s ♣r✐♠✓♦r❞✐♦s ❞♦ ✉♥✐✈❡rs♦✳ ❊st❛ ❝♦♥❥❡❝t✉r❛ ♣♦ss✉✐ ❢♦rt❡s ❧✐❣❛✘❝⑦♦❡s ❝♦♠ ❛ t❡♦r✐❛ ❞❛ ❇✐❣ ❇❛♥❣ ♥✉❝❧❡♦ss✓✏♥t❡s❡ q✉❡ ❡①♣❧✐❝❛✱ ❝♦♠ ❜♦♠ ♥✓✏✈❡❧ ❞❡ ♣r❡❝✐s⑦❛♦✱ ❛ q✉❛♥t✐❞❛❞❡ ❞❡ ❡❧❡♠❡♥t♦s ❧❡✈❡s ✭❉✱ ✹❍❡✱❍❡ ❡▲✐✮ ♥♦ ❯♥✐✈❡rs♦ ✳ P❛r❛ ✉♠❛ ❜♦❛ ✐♥tr♦❞✉✘❝⑦❛♦

r❡❝♦♠❡♥❞❛♠♦s ❛ ❧❡✐t✉r❛ ❞♦s ❝❛♣✓✏t✉❧♦s ✷✱✸ ❡ ✹ ❞❛ r❡❢❡r❫❡♥❝✐❛ ❬✷✾❪✳ ❊♠ r❡❧❛✘❝⑦❛♦ ❛ ▼❊✱ ❲■▼P ♥❡st❡ ❝♦♥t❡①t♦✱ t❡♠♦s q✉❡ ♥♦s ♣r✐♠✓♦r❞✐♦s ❞♦ ✉♥✐✈❡rs♦ ✻ ❡❧❛ ❡st❛✈❛ ❡♠ ❡q✉✐❧✓✏❜r✐♦ ❝♦♠ ❛s ♣❛rt✓✏❝✉❧❛s ❞♦ ▼P ✼ ❡ ❡st❛s ❡st❛✈❛♠ ❛❝♦♣❧❛❞❛s ❛♦ ♣❧❛s♠❛ ❞♦ ✉♥✐✈❡rs♦✱ ❝♦♠♦ ♥♦ ❞✐❛❣r❛♠❛ ❛❜❛✐①♦

▼❊ ✰ ▼❊ ✩ ▼P ✰ ▼P✿ ✭✶✳✺✮

P♦r✓❡♠✱ ❞❡✈✐❞♦ ✒❛ ❡①♣❛♥s⑦❛♦ ❞♦ ✉♥✐✈❡rs♦✱ q✉❡ ❧❡✈❛ ❛♦ ❡s❢r✐❛♠❡♥t♦ ❞♦ ♣❧❛s♠❛✱ ❡st❛ r❡❛✘❝⑦❛♦ s❛✐✉ ❞♦ ❡q✉✐❧✓✏❜r✐♦✱ ♦✉ s❡❥❛✱ ❛s ♣❛rt✓✏❝✉❧❛s ❞♦ ▼P ♥⑦❛♦ ♣♦ss✉✓✏❛♠ ♠❛✐s ❡♥❡r❣✐❛ s✉☞❝✐❡♥t❡ ♣❛r❛ s❡ ❛♥✐q✉✐❧❛r ❡♠ ✉♠ ♣❛r ❞❡ ❲■▼Ps ✭♦❝♦rr❡♥❞♦ ❛♣❡♥❛s ▼❊ ✰ ▼❊ ✦ ▼P ✰ ▼P✮✳ ■ss♦✱ ❡♠ ❣❡r❛❧✱ ♦❝♦rr❡ q✉❛♥❞♦ ✭♠❊❂❚ ✮ ✘ ✶✵✱ ♦✉ s❡❥❛✱ q✉❛♥❞♦ ❛ t❡♠♣❡r❛t✉r❛ ❞♦ ✉♥✐✈❡rs♦ ✓❡ ❛♣r♦①✐♠❛❞❛♠❡♥t❡

❞❡③ ✈❡③❡s ♠❡♥♦r q✉❡ ❛ ♠❛ss❛ ❞❛ ▼❊✱ t❛♠❜✓❡♠ ✈❡r❡♠♦s ✐ss♦ ♠❛✐s ❛❞✐❛♥t❡✳ ❆ss✐♠ ❛ ▼❊ ❝♦♥t✐♥✉❛ s❡ ❛♥✐q✉✐❧❛♥❞♦✱ ❢❛③❡♥❞♦ ❝♦♠ q✉❡ s✉❛ ❛❜✉♥❞❫❛♥❝✐❛ ❞❡❝❛✐❛ ❝♦♠ ❡ ♠▼❊❂❚✱ s❡♥❞♦ ❚ ❛

t❡♠♣❡r❛t✉r❛ ❞♦ ✉♥✐✈❡rs♦✳ ■ss♦ ♣♦❞❡r✐❛ ♦❝❛s✐♦♥❛r ♦ s❡✉ ❞❡s❛♣❛r❡❝✐♠❡♥t♦✱ ♣♦r✓❡♠✱ q✉❛♥❞♦ s✉❛

❖ ♣❡r✓✏♦❞♦ ♠❛✐s ❡s♣❡❝✐☞❝♦ ✐r✓❛ ❞❡♣❡♥❞❡r ❞❡ ❛❧❣✉♥s ♣❛r❫❛♠❡tr♦s ❝♦♠♦ ♠❛ss❛ ❞❛ ❲■▼P ❡ s✉❛ s❡✘❝⑦❛♦ ❞❡

❝❤♦q✉❡✱ ❝♦♠♦ ✈❡r❡♠♦s ♠❛✐s ❛❞✐❛♥t❡✳

Referências

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