❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❙ã♦ P❛✉❧♦
■♥st✐t✉t♦ ❞❡ ❋ís✐❝❛ ❞❡ ❙ã♦ ❈❛r❧♦s
▲✉❝✐❛♥♦ ❇♦r❣❡s ❈❡♥s♦♥✐
❉✐♥â♠✐❝❛ ♠♦❧❡❝✉❧❛r ❡ r❡❞❡s ❝♦♠♣❧❡①❛s ♥♦
❡st✉❞♦ ❞❛ ❞✐❢✉sã♦ tér♠✐❝❛ ❡♠ ①✐❧❛♥❛s❡s ❞❛
❢❛♠í❧✐❛ ✶✶
▲✉❝✐❛♥♦ ❇♦r❣❡s ❈❡♥s♦♥✐
❉✐♥â♠✐❝❛ ♠♦❧❡❝✉❧❛r ❡ r❡❞❡s ❝♦♠♣❧❡①❛s ♥♦
❡st✉❞♦ ❞❛ ❞✐❢✉sã♦ tér♠✐❝❛ ❡♠ ①✐❧❛♥❛s❡s ❞❛
❢❛♠í❧✐❛ ✶✶
❉✐ss❡rt❛çã♦ ❛♣r❡s❡♥t❛❞❛ ❛♦ Pr♦❣r❛♠❛ ❞❡ Pós✲ ●r❛❞✉❛çã♦ ❡♠ ❋ís✐❝❛ ❞♦ ■♥st✐t✉t♦ ❞❡ ❋ís✐❝❛ ❞❡ ❙ã♦ ❈❛r❧♦s ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❙ã♦ P❛✉❧♦✱ ♣❛r❛ ♦❜t❡♥çã♦ ❞♦ tít✉❧♦ ❞❡ ♠❡str❡ ❡♠ ❈✐ê♥❝✐❛s✳
➪r❡❛ ❞❡ ❈♦♥❝❡♥tr❛çã♦✿ ❋ís✐❝❛ ❆♣❧✐❝❛❞❛ ✲ ❖♣çã♦ ❇✐♦♠♦❧❡❝✉❧❛r
❖r✐❡♥t❛❞♦r✿ Pr♦❢✳ ❉r✳ ▲❡❛♥❞r♦ ▼❛rtí♥❡③
❱❡rsã♦ ❈♦rr✐❣✐❞❛
✭✈❡rsã♦ ♦r✐❣✐♥❛❧ ❞✐s♣♦♥í✈❡❧ ♥❛ ❯♥✐❞❛❞❡ q✉❡ ❛❧♦❥❛ ♦ Pr♦❣r❛♠❛✮
❆❯❚❖❘■❩❖ ❆ ❘❊P❘❖❉❯➬➹❖ ❊ ❉■❱❯▲●❆➬➹❖ ❚❖❚❆▲ ❖❯ P❆❘❈■❆▲ ❉❊❙❚❊ ❚❘❆❇❆▲❍❖✱ P❖❘ ◗❯❆▲◗❯❊❘ ▼❊■❖ ❈❖◆❱❊◆❈■❖◆❆▲ ❖❯ ❊▲❊❚❘Ô◆■❈❖✱ P❆❘❆ ❋■◆❙ ❉❊ ❊❙❚❯❉❖ ❊ P❊❙◗❯■❙❆✱
❉❊❙❉❊ ◗❯❊ ❈■❚❆❉❆ ❆ ❋❖◆❚❊✳
Ficha catalográfica elaborada pelo Serviço de Biblioteca e Informação do IFSC, com os dados fornecidos pelo(a) autor(a)
Censoni, Luciano Borges
Dinâmica molecular e redes complexas no estudo da difusão térmica em xilanases da família 11 / Luciano Borges Censoni; orientador Leandro Martínez - versão corrigida -- São Carlos, 2013.
100 p.
Dissertação (Mestrado - Programa de Pós-Graduação em Física Aplicada Biomolecular) -- Instituto de Física de São Carlos, Universidade de São Paulo, 2013.
1. Proteínas. 2. Xilanases. 3. Redes complexas. 4. Difusão térmica. 5. Centralidade. I. Martínez,
❆●❘❆❉❊❈■▼❊◆❚❖❙
Pr❡t❡♥❞♦ s❡r s✉❝✐♥t♦✳ ❊st❡ tr❛❜❛❧❤♦ ❞✐✜❝✐❧♠❡♥t❡ t❡r✐❛ s✐❞♦ ♣♦ssí✈❡❧✱ ❡ ❝❡rt❛♠❡♥t❡ ♥ã♦ t❡r✐❛ s✐❣♥✐✜❝❛❞♦✱ s❡♠ ♦ ❛♣♦✐♦ ❡ ❛ ❝♦❧❛❜♦r❛çã♦ ❞❡ ✉♠ ❣r❛♥❞❡ ❝♦♥❥✉♥t♦ ❞❡ ♣❡ss♦❛s✳ ❈✐t♦✲❛s ❛q✉✐ ♣❛r❛ q✉❡ s❡ r❡❣✐str❡ ♦ ♠❡✉ ❛❣r❛❞❡❝✐♠❡♥t♦✳
❆❣r❛❞❡ç♦ ❛♦s ♠❡✉s ♣❛✐s✱ ▼❛r❝✐❛ ❡ ❖❧②♥t❤♦✱ ♣❡❧♦ ❛♣♦✐♦ ✐♥❝♦♥❞✐❝✐♦♥❛❧ ❡ s❛❝r✐❢í❝✐♦ ✐♥✈❡st✐❞♦s ♥❛ ♠✐♥❤❛ ❢♦r♠❛çã♦✳ ❖ tít✉❧♦ ❞❡ ♠❡str❡✱ ❛✐♥❞❛ q✉❡ ❛ss♦❝✐❛❞♦ ❛♦ ♠❡✉ ♥♦♠❡✱ s❡rá ♣r♦♣r✐❡❞❛❞❡ ❞❡❧❡s✳
❆❣r❛❞❡ç♦ ❛♦ ♠❡✉ ♦r✐❡♥t❛❞♦r✱ ▲❡❛♥❞r♦✱ ♣❡❧❛ ♦r✐❡♥t❛çã♦ ❡①tr❡♠❛♠❡♥t❡ ❝♦♠♣❡t❡♥t❡✱ ❛ss♦✲ ❝✐❛❞❛ à ❛♠✐③❛❞❡ ❡ ♣❛❝✐ê♥❝✐❛✱ ❡ ♣❡❧♦ s❡✉ ❡♥s✐♥❛♠❡♥t♦ ♠❛✐s ✐♠♣♦rt❛♥t❡✿ ♣❛r❛ q✉❡ s❡r✈❡ ✉♠ ♦r✐❡♥t❛❞♦r✳
❆❣r❛❞❡ç♦ ❛♦s ❝♦♠♣❛♥❤❡✐r♦s ❞❡ s❛❧❛✱ ▼❛r✐❛♥❛✱ ❍❡❧♦✐s❛✱ Pr♦❢✳ ❈❛♠✐❧❛ ❡ Pr♦❢✳ ❆❧❡ss❛♥❞r♦✱ ♣❡❧❛ ❛♠✐③❛❞❡✱ s✐♠♣át✐❛ ❡ ❡①t❡♥s❛ r❡s❡r✈❛ ❞❡ ❜♦♠ ❤✉♠♦r✳
❆❣r❛❞❡ç♦ ❛♦s ❛♠✐❣♦s✱ ♣❡❧❛ ♣r❡s❡♥ç❛ ❛♦ ❧♦♥❣♦ ❞♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞♦ tr❛❜❛❧❤♦ ❡ ❞❛ ♣❡ss♦❛✿ ❘♦❞r✐❣♦✱ P❡❞r♦ ◆❛♣♦❧❡ã♦✱ ❘♦❞♦❧❢♦ ❡ ▼✐❧❡♥❛✱ ❇r✉♥♦✱ ❙❛t♦✱ ❈❛✐♦✱ ❆♥♥❛✱ ▲✉✐s❛✱ P❛✉❧❛✱ ●❛❜r✐❡❧✱ P❡❞r♦ ❘❛♠ó♥ ❡ t♦❞♦s ♦s ♦✉tr♦s q✉❡ ♣♦r✈❡♥t✉r❛ ♠❡ ❢♦❣❡♠ ♠♦♠❡♥t❛♥❡❛♠❡♥t❡ à ❧❡♠❜r❛♥ç❛✳
❈❡rt❛✐♥ s❤❛♣❡s ❛♥❞ ♣❛tt❡r♥s ❤♦✈❡r ♦✈❡r ❞✐✛❡r❡♥t ♠♦♠❡♥ts ✐♥ t✐♠❡✱ ❤❛✉♥t✐♥❣ ❛♥❞ ✐♥s♣✐r✐♥❣ t❤❡ ✐♥❞✐✈✐❞✉❛❧s ❧✐✈✐♥❣ t❤r♦✉❣❤ t❤♦s❡ ♣❡r✐♦❞s✳ ❚❤❡ ❡♣✐❝ ❝❧❛s❤ ❛♥❞ s✉❜s❡q✉❡♥t r❡s♦❧✉t✐♦♥ ♦❢ t❤❡ ❞✐❛❧❡❝t✐❝ ❛♥✐♠❛t❡❞ t❤❡ ✜rst ❤❛❧❢ ♦❢ t❤❡ ♥✐♥❡t❡❡♥t❤ ❝❡♥t✉r②❀ t❤❡ ❉❛r✇✐♥✐❛♥ ❛♥❞ s♦❝✐❛❧ r❡❢♦r♠ ♠♦✈❡♠❡♥ts s❝❛tt❡r❡❞ ✇❡❜ ✐♠❛❣❡r② t❤r♦✉❣❤♦✉t t❤❡ s❡❝♦♥❞ ❤❛❧❢ ♦❢ t❤❡ ❝❡♥t✉r②✳ ❚❤❡ ✜rst ❢❡✇ ❞❡❝❛❞❡s ♦❢ t❤❡ t✇❡♥t✐❡t❤ ❝❡♥t✉r② ❢♦✉♥❞ t❤❡✐r ✉❧t✐♠❛t❡ ❡①♣r❡ss✐♦♥ ✐♥ t❤❡ ❡①✉❜❡r❛♥t ❛♥❛r❝❤② ♦❢ t❤❡ ❡①♣❧♦s✐♦♥✱ ✇❤✐❧❡ ❧❛t❡r ❞❡❝❛❞❡s ❧♦st t❤❡♠s❡❧✈❡s ✐♥ t❤❡ ❢❛❝❡❧❡ss r❡❣✐♠❡♥ ♦❢ t❤❡ ❣r✐❞✳ ❨♦✉ ❝❛♥ s❡❡ t❤❡ ❧❛st t❡♥ ②❡❛rs ♦r s♦ ❛s ❛ r❡t✉r♥ t♦ t❤♦s❡ ❱✐❝t♦r✐❛♥ ✇❡❜s ❬✳✳✳❪✳
❙t❡✈❡♥ ❏♦❤♥s♦♥✱ ❊♠❡r❣❡♥❝❡
❲♦r❦✐♥❣ ✇✐t❤ ❝♦♠♣✉t❡rs ❤❛s ♣r♦✈✐❞❡❞ ✉s ✇✐t❤ ❛ ♥❡✇ ♠❡t❛♣❤♦r ❢♦r t❤❡ ❧❛✇s ♦❢ ♥❛t✉r❡✿
t❤❡② ❝❛rr② ❛s ♠✉❝❤ ✭❛♥❞ ❛s ❧✐tt❧❡✮ ✐♥❢♦r♠❛t✐♦♥ ❛s ❛❧❣♦r✐t❤♠s✳
❘❊❙❯▼❖
❈❊◆❙❖◆■✱ ▲✳ ❇✳ ❉✐♥â♠✐❝❛ ♠♦❧❡❝✉❧❛r ❡ r❡❞❡s ❝♦♠♣❧❡①❛s ♥♦ ❡st✉❞♦ ❞❛ ❞✐❢✉sã♦ tér♠✐❝❛ ❡♠ ①✐❧❛♥❛s❡s ❞❛ ❢❛♠í❧✐❛ ✶✶✳ ✷✵✶✸✳ ✶✵✵ ♣✳ ❉✐ss❡rt❛çã♦ ✭▼❡str❛❞♦ ❡♠ ❈✐ê♥❝✐❛s✮ ✕ ■♥st✐t✉t♦ ❞❡ ❋ís✐❝❛ ❞❡ ❙ã♦ ❈❛r❧♦s✱ ❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❙ã♦ P❛✉❧♦✱ ❙ã♦ ❈❛r❧♦s✱ ✷✵✶✸✳
❆❇❙❚❘❆❈❚
❈❊◆❙❖◆■✱ ▲✳ ❇✳ ▼♦❧❡❝✉❧❛r ❞②♥❛♠✐❝s ❛♥❞ ❝♦♠♣❧❡① ♥❡t✇♦r❦s ✐♥ t❤❡ st✉❞② ♦❢ t❤❡r♠❛❧ ❞✐✛✉s✐♦♥ ✐♥ ❢❛♠✐❧② ✶✶ ①②❧❛♥❛s❡s✳ ✷✵✶✸✳ ✶✵✵ ♣✳ ❉✐ss❡rt❛çã♦ ✭▼❡str❛❞♦ ❡♠ ❈✐ê♥❝✐❛s✮ ✕ ■♥st✐t✉t♦ ❞❡ ❋ís✐❝❛ ❞❡ ❙ã♦ ❈❛r❧♦s✱ ❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❙ã♦ P❛✉❧♦✱ ❙ã♦ ❈❛r❧♦s✱ ✷✵✶✸✳
Pr♦t❡✐♥s ❛r❡ t②♣✐❝❛❧❧② ❛❜❧❡ t♦ ♠❛♥t❛✐♥ ❛ ❢✉♥❝t✐♦♥❛❧ ❝♦♥❢♦r♠❛t✐♦♥ ♦♥❧② ✇✐t❤✐♥ ❛ ♥❛rr♦✇ r❛♥❣❡ ♦❢ t❡♠♣❡r❛t✉r❡s✳ ■♥ s♣✐t❡ ♦❢ t❤❡ ❝♦♠♣❧❡① ❝❡❧❧✉❧❛r ❤♦♠❡♦st❛t✐❝ ♠❛❝❤✐♥❡r②✱ ✐t ✐s ❦♥♦✇♥ t❤❛t ❛ ✈❛r✐❡t② ♦❢ ♠♦❧❡❝✉❧❛r ♣❤❡♥♦♠❡♥❛ ❝❛♥ ✐♥❞✉❝❡ ❧♦❝❛❧✐③❡❞ ✈✐❜r❛t✐♦♥❛❧ ✐♠❜❛❧❛♥❝❡s✱ ❛♥❞ t❤❛t t❤❡ ❡✣❝✐❡♥❝② ✇✐t❤ ✇❤✐❝❤ ❡❛❝❤ ♣r♦t❡✐♥ ❞✐ss✐♣❛t❡s t❤❡s❡ ♣❡rt✉r❜❛t✐♦♥s ♠❛② ❜❡ r❡❧❛t❡❞ t♦ ✐ts t♦✲ ❧❡r❛♥❝❡ ♦❢ ❤✐❣❤❡r t❡♠♣❡r❛t✉r❡s✳ ❚❤❡ tr❛♥s❢❡r❡♥❝❡ ♦❢ t❤❡r♠❛❧ ❡♥❡r❣② ❛♠♦♥❣ ❞✐✛❡r❡♥t s❡❝t✐♦♥s ♦❢ ❛ ♣r♦t❡✐♥ ❝❤❛✐♥ ✐s✱ ❤♦✇❡✈❡r✱ ❤❛r❞ t♦ ❝❤❛r❛❝t❡r✐③❡ ❡①♣❡r✐♠❡♥t❛❧❧②✳ ❆ t❤❡♦r❡t✐❝❛❧ ❛❧t❡r♥❛t✐✈❡ ❢♦r t❤❡ ✐♥✈❡st✐❣❛t✐♦♥ ♦❢ t❤❡s❡ ♠❡❝❤❛♥✐s♠s ✐s t❤❡ ✉s❡ ♦❢ ▼♦❧❡❝✉❧❛r ❉②♥❛♠✐❝s s✐♠✉❧❛t✐♦♥s✱ ♣❛r✲ t✐❝✉❧❛r❧② ✇❤❡♥ ❛ss♦❝✐❛t❡❞ ✇✐t❤ t❤❡ ❆♥✐s♦tr♦♣✐❝ ❚❤❡r♠❛❧ ❉✐✛✉s✐♦♥ ✭❆❚❉✮ t❡❝❤♥✐q✉❡✳ ■♥ t❤✐s ✇♦r❦✱ ✇❡ ✈❡r✐❢② t❤❡ ♣♦ss✐❜✐❧✐t② ♦❢ ✉s✐♥❣ ❝♦♥❝❡♣ts ❢r♦♠ ◆❡t✇♦r❦ ❚❤❡♦r② t♦ ❝♦♥str✉❝t ♠♦❞❡❧s ❢♦r ♣r♦t❡✐♥ str✉❝t✉r❡s✱ ❛♥❞ ✉s✐♥❣ t❤♦s❡ t♦ r❡✈❡❛❧ r❡s✐❞✉❡s ✇✐t❤ s✐❣♥✐✜❝❛♥t ❛❜✐❧✐t② t♦ ❞✐ss✐♣❛t❡ t❤❡r♠❛❧ ♣❡rt✉r❜❛t✐♦♥s✳ ❲❡ ✐♥✈❡st✐❣❛t❡ s❡✈❡r❛❧ ♣r♦t♦❝♦❧s ♦❢ ♥❡t✇♦r❦ ♠♦❞❡❧ ❝♦♥str✉❝t✐♦♥ ❢♦r ♣r♦✲ t❡✐♥s ♣r❡s❡♥t ✐♥ t❤❡ ❧✐t❡r❛t✉r❡✱ ❛♥❞ ✇❡ st✉❞② r❡♣r❡s❡♥t❛t✐✈❡ ❡①♣❡r✐♠❡♥t❛❧ ❞❛t❛ ❢r♦♠ t❤❡ ❙❈❖P ❞❛t❛❜❛s❡ t♦ r✐❣♦r♦✉s❧② ❝❛❧❝✉❧❛t❡ t❤❡ ♥❡❝❡ss❛r② ♣❛r❛♠❡t❡rs✳ ❲❡ ♣r♦❞✉❝❡ ❛ ♣r❡❝✐s❡ ❞❡✜♥✐t✐♦♥ ❢♦r t❤❡ ❝♦♥❝❡♣t ♦❢ ❝♦♥t❛❝t ❜❡t✇❡❡♥ ❛♠✐♥♦ ❛❝✐❞ r❡s✐❞✉❡s✱ ❛♥❞ ❢r♦♠ t❤✐s ✇❡ ❝❛❧❝✉❧❛t❡ t❤❡ ❝❡♥tr❛❧✐t② ♦❢ ❡❛❝❤ r❡s✐❞✉❡✳ ❲❡ t❤❡♥ s❤♦✇ t❤❛t✱ ✐♥ ❛ s❡t ♦❢ ❳②❧❛♥❛s❡s ❢♦r ✇❤✐❝❤ ✇❡ ❤❛✈❡ ❞❛t❛ ❢r♦♠ ❆❚❉ ❡①♣❡r✐♠❡♥ts✱ t❤❡ ❛❜✐❧✐t② t♦ ❞✐ss✐♣❛t❡ t❤❡r♠❛❧ ♣❡rt✉r❜❛t✐♦♥s ✐s ❤✐❣❤❧② ❝♦rr❡❧❛t❡❞ t♦ t❤❡ ❝❧♦s❡♥❡ss ❝❡♥tr❛❧✐t② ♦❢ ❡❛❝❤ r❡s✐❞✉❡✱ ♣r♦✈✐❞✐♥❣ ❛r❣✉♠❡♥ts ❢♦r t❤❡ ✉s❡ ♦❢ ♥❡t✇♦r❦ ♠♦❞❡❧s t♦ st✉❞② ♣r♦t❡✐♥ t❤❡r♠❛❧ st❛❜✐❧✐t②✳
▲■❙❚❆ ❉❊ ❋■●❯❘❆❙
❋✐❣✉r❛ ✶✳✶ ✲ ✭■✮ ❊①❡♠♣❧♦ ❞❡ ❧✐❣❛çõ❡s ♣❡♣tí❞✐❝❛s ✭❡♠ ❞❡st❛q✉❡✮ ♥❛ ❝❛❞❡✐❛ ♣r✐♥❝✐♣❛❧ ❡♠ ✉♠❛ ♣r♦t❡í♥❛✳ ➪t♦♠♦s ❞❡ ❖①✐❣ê♥✐♦ sã♦ r❡♣r❡s❡♥t❛❞♦s ❡♠ ✈❡r♠❡❧❤♦✱ ◆✐tr♦❣ê♥✐♦ ❡♠ ❛③✉❧ ❡ ❈❛r❜♦♥♦ ❡♠ ❝✐❛♥♦✳ ➪t♦♠♦s ❞❡ ❍✐❞r♦❣ê♥✐♦ ♥ã♦ sã♦ r❡♣r❡s❡♥t❛❞♦s✳ ❋✐❣✉r❛ ❣❡r❛❞❛ ❝♦♠ ♦ ♣r♦❣r❛♠❛ ❱▼❉ ✭✶✱ ✷✮✳ ✭■■✮ ❋♦r♠❛çã♦ ❞❡ ❧✐❣❛çã♦ ♣❡♣tí❞✐❝❛ ❛ ♣❛rt✐r ❞❡ ❞♦✐s ❛♠✐♥♦á❝✐❞♦s ✭❆❧❛♥✐♥❛s✱ ♥❛s q✉❛✐s ❈❍3 é ❛ ❝❛❞❡✐❛ ❧❛t❡r❛❧✮✱ ❝♦♠ ♣❡r❞❛ ❞❡ ✉♠❛ ♠♦❧é❝✉❧❛ ❞❡ á❣✉❛✳ ✷✷
❋✐❣✉r❛ ✶✳✷ ✲ ■❧✉str❛çã♦ ❞♦ ❝♦❧❛♣s♦ ❞♦ ♥ú❝❧❡♦ ❤✐❞r♦❢ó❜✐❝♦ ❞✉r❛♥t❡ ♦ ❡♥♦✈❡❧❛♠❡♥t♦ ❞❡ ✉♠❛ ♣r♦t❡í♥❛✳ ❈ír❝✉❧♦s ❝❤❡✐♦s r❡♣r❡s❡♥t❛♠ ❛♠✐♥♦á❝✐❞♦s ❤✐❞r♦❢ó❜✐❝♦s✱ ❡ ❝ír❝✉❧♦s ✈❛③✐♦s r❡♣r❡s❡♥t❛♠ ❛♠✐♥♦á❝✐❞♦s ❤✐❞r♦❢í❧✐❝♦s✳ ✭✸✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹
❋✐❣✉r❛ ✶✳✸ ✲ ■❧✉str❛çã♦ ❞♦ ♣r♦❝❡ss♦ ❞❡ ❞❡t❡r♠✐♥❛çã♦ ❞❛ ❡str✉t✉r❛ ❞❡ ♣r♦t❡í♥❛s ♣♦r ❉✐❢r❛çã♦ ❞❡ ❘❛✐♦s✲❳✳ ✭■✮ ❊①❡♠♣❧♦ ❞❡ ❝r✐st❛❧ ❞❡ ♣r♦t❡í♥❛✳ ✭✹✮✳ ✭■■✮ ❊①❡♠♣❧♦ ❞❡ ♣❛❞rã♦ ❞❡ ✐♥t❡♥s✐❞❛❞❡s ❞❡ ❘❛✐♦s✲❳ ❞✐❢r❛t❛❞♦s ♣♦r ✉♠ ❝r✐st❛❧ ❞❡ ♣r♦t❡í♥❛✳ ✭✺✮✳ ✭■■■✮ ❊①❡♠♣❧♦ ❞❡ ❞❡♥s✐❞❛❞❡ ❡❧❡trô♥✐❝❛ ❝❛❧❝✉❧❛❞❛ ❛ ♣❛rt✐r ❞❡ ✉♠ ♣❛❞rã♦ ❞❡ ❞✐❢r❛çã♦ ❞❡ ✉♠ ❝r✐st❛❧ ♣r♦t❡✐❝♦✱ ❝♦♠ ♠♦❞❡❧♦ ❞❡ ❝❛❞❡✐❛ ♣r✐♥❝✐♣❛❧ ❛❥✉st❛❞❛ à ❞❡♥s✐❞❛❞❡ ❡❧❡trô♥✐❝❛✳ ✭✻✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻
❋✐❣✉r❛ ✶✳✹ ✲ ✭■✮ ❳✐❧♦s❡✱ ✉♠❛ ♣❡♥t♦s❡✱ ❡♠ ❝♦♥✜❣✉r❛çã♦ ❧✐♥❡❛r ✭■■✮ ❳✐❧♦s❡ ❡♠ ❝♦♥✜❣✉✲ r❛çã♦ ❞❡ ❛♥❡❧ ✭■■■✮ ❘❡♣r❡s❡♥t❛çã♦ ❡str✉t✉r❛❧ ♣♦ssí✈❡❧ ❞♦ ①✐❧❛♥♦✱ ♣♦❧í♠❡r♦ ❤❡t❡r♦❣ê♥❡♦ ❡ r❛♠✐✜❝❛❞♦ ❞❡ ①✐❧♦s❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾
❋✐❣✉r❛ ✶✳✻ ✲ ❱✐sã♦ ❞❡ ✉♠❛ ①✐❧❛♥❛s❡ r❡♣r❡s❡♥t❛❞❛ ❝♦♠♦ s✉❛ s✉♣❡r❢í❝✐❡ ❛❝❡ssí✈❡❧ ❛♦ s♦❧✈❡♥t❡✱ ❝♦♠ ê♥❢❛s❡ ♥❛ ❢❡♥❞❛ ❝❛t❛❧ít✐❝❛✱ ♣❛r❛❧❡❧❛ à ♣❛❧♠❛ ❡ ❡♥✈♦❧✈✐❞❛ ♣❡❧♦s ❞❡❞♦s ❡ ♣❡❧♦ ❞❡❞ã♦✱ q✉❡ s❡ ❛♣r♦①✐♠❛♠ ❝♦❧♦❝❛♥❞♦ ♦s r❡sí❞✉♦s ❝❛t❛❧ít✐❝♦s ♥❛ ♣♦s✐çã♦ ❛♣r♦♣r✐❛❞❛✳ ❊❧❡♠❡♥t♦s ❞❡ ❡str✉t✉r❛ s❡❝✉♥❞ár✐❛ ❡stã♦ ❝♦❧♦r✐③❛❞♦s s❡❣✉♥❞♦ ♦ ♠❡s♠♦ ♣❛❞rã♦ ❞❛ ✜❣✉r❛ ✶✳✺✱ ❝♦♠ ❢♦❧❤❛s ❜❡t❛ ❡♠ ❛♠❛r❡❧♦✱ ❤é❧✐❝❡s ❛❧❢❛ ❡♠ r♦①♦ ❡ ❧♦♦♣s ❡♠ ❛③✉❧✳ ❋✐❣✉r❛ ❣❡r❛❞❛ ❝♦♠ ♦ ♣r♦❣r❛♠❛ ❱▼❉ ✭✶✱ ✼✱ ✽✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶
❋✐❣✉r❛ ✷✳✶ ✲ ■❧✉str❛çã♦ ❞❡ ♠♦✈✐♠❡♥t♦s ♠♦❧❡❝✉❧❛r❡s ❞❡ ❧❛r❣❛ ❡s❝❛❧❛ ❡♠ ✉♠❛ ❧✐♣❛s❡✱ ❝❛❧❝✉❧❛❞♦s ♣♦r ❛♥á❧✐s❡ ❞❡ ♠♦❞♦s ♥♦r♠❛✐s✳ ✭✾✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾
❋✐❣✉r❛ ✷✳✷ ✲ ❊①❡♠♣❧♦ ❞❡ ▼❛♣❛ ❞❡ ❉✐❢✉sã♦ ❚ér♠✐❝❛ ❡ ❞❡ ♠❛♣❛ ❞❡ ❝♦♥t❛t♦s ♣❛r❛ ✉♠ ❡①♣❡r✐♠❡♥t♦ ❞❡ ❆❚❉✳ ❖ ▼❛♣❛ ❞❡ ❉✐❢✉sã♦ ❚ér♠✐❝❛ t❛❜✉❧❛ ❛ r❡s♣♦st❛ tér♠✐❝❛ ❞❡ ❝❛❞❛ r❡sí❞✉♦ ❡♠ r❡❧❛çã♦ à ✐❞❡♥t✐❞❛❞❡ ❞♦ r❡sí❞✉♦ ❛q✉❡❝✐❞♦✳ ❘❡♣r♦❞✉③✐❞♦ ❝♦♠ ❛✉t♦r✐③❛çã♦ ❞❡ ✭✶✵✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵
❋✐❣✉r❛ ✷✳✸ ✲ ❊①❡♠♣❧♦ ❞❡ ♣r♦t❡í♥❛ ❝♦♠ r❡sí❞✉♦s ❝♦❧♦r✐③❛❞♦s ♣❛r❛ ❞❡♥♦t❛r ❝❛♣❛❝✐❞❛❞❡ ❞❡ tr❛♥s❢❡r✐r ❝❛❧♦r ♣❛r❛ ❛ ❡str✉t✉r❛ ✭✏❜♦♥s ❞✐❢✉s♦r❡s✑✮✱ ❛✉♠❡♥t❛♥❞♦ ❛ t❡♠♣❡r❛t✉r❛ ✜♥❛❧ ❞❛ ♣r♦t❡í♥❛ ♥✉♠ ❡①♣❡r✐♠❡♥t♦ ❞❡ ❆❚❉✳ ❘❡sí❞✉♦s ♠❡✲ ❧❤♦r❡s ❞✐❢✉s♦r❡s ❡stã♦ r❡♣r❡s❡♥t❛❞♦s ❡♠ ❝♦r❡s ♠❛✐s q✉❡♥t❡s✳ ❘❡♣r♦❞✉✲ ③✐❞♦ ❝♦♠ ❛✉t♦r✐③❛çã♦ ❞❡ ✭✶✵✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶
❋✐❣✉r❛ ✸✳✶ ✲ ❊①❡♠♣❧♦ ❞❡ ❣r❛❢♦✱ ❝♦♠ s❡✐s ♥ós ✭❝ír❝✉❧♦s ❡♠ ✈❡r❞❡✮ ❡ s❡✐s ❛r❡st❛s✳ ✭✶✶✮✳ ✹✺
❋✐❣✉r❛ ✸✳✷ ✲ ■❧✉str❛çã♦ ❞❡ ❞♦✐s ❣r❛❢♦s✳ ✭■✮ ❖ ♥ó r❡♣r❡s❡♥t❛❞♦ ❡♠ ✈❡r❞❡ r❡s✐❞❡ ♥✉♠❛ ♣♦s✐çã♦ ♣r✐✈✐❧❡❣✐❛❞❛✱ ❡①✐❜✐♥❞♦ ❣r❛✉ ♠✉✐t♦ ♠❛✐♦r q✉❡ t♦❞♦s ♦s ♦✉tr♦s✳ ❖ ♥ó ❡♠ ❛③✉❧ ❡①♣❡r✐♠❡♥t❛ s✐t✉❛çã♦ ♦♣♦st❛✳ ✭■■✮ ❖ ♥ó ❛q✉✐ r❡♣r❡s❡♥t❛❞♦ ❡♠ ✈❡r❞❡ ♣♦ss✉✐ ♦ ♠❡♥♦r ❣r❛✉ ❞❛ r❡❞❡✳ ❈♦♥t✉❞♦✱ s✉❛ ♣♦s✐çã♦ é ❝rít✐❝❛✿ s✉❛ r❡♠♦çã♦ r❡s✉❧t❛r✐❛ ♥❛ ♦❜t❡♥çã♦ ❞❡ ❞♦✐s ❝♦♠♣♦♥❡♥t❡s ❞❡s❝♦♥❡❝t❛❞♦s✳ ✹✻
❋✐❣✉r❛ ✸✳✸ ✲ ❊①❡♠♣❧♦ ❞❡ ❣r❛❢♦ ❡ ♠❛tr✐③ ❞❡ ❛❞❥❛❝ê♥❝✐❛ ❛ss♦❝✐❛❞❛✳ ✭✶✷✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽
❋✐❣✉r❛ ✸✳✹ ✲ ❊①❡♠♣❧♦s ❞❡ ❣r❛❢♦s ❝♦♠ ❡str✉t✉r❛s ❞✐st✐♥t❛s✳ ✭■✮ ▼❛❧❤❛ ❝♦♥str✉í❞❛ ❛ ♣❛rt✐r ❞❡ ❡str✉t✉r❛ ❧♦❝❛❧ r❡♣❡t✐t✐✈❛✳ ✭■■✮ ●r❛❢♦ ❛❧❡❛tór✐♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷
❋✐❣✉r❛ ✸✳✻ ✲ ■❧✉str❛çã♦ ❞❛s ❞❡s❝r✐çõ❡s ❛❜s♦❧✉t❛ ❡ r❡❧❛t✐✈❛✱ ♣❛r❛ ✉♠ s✐st❡♠❛ ❞❡ três ❡♥t✐❞❛❞❡s✳ ✭■✮ ❉❡s❝r✐çã♦ ❛❜s♦❧✉t❛✱ ❡♠ q✉❡ ❛s ♣♦s✐çõ❡s sã♦ ❞❡s❝r✐t❛s ❝♦♠ r❡❧❛çã♦ ❛ três ❡✐①♦s ♦rt♦❣♦♥❛✐s✳ ✭■■✮ ❉❡s❝r✐çã♦ r❡❧❛t✐✈❛✱ ❡♠ q✉❡ ❛s ❞✐stâ♥❝✐❛s ❡♥tr❡ ❝❛❞❛ ♣❛r ❞❡ ❡♥t✐❞❛❞❡s sã♦ ❡♥✉♠❡r❛❞❛s✱ ❡♠ ✈❡③ ❞❡ s✉❛s ♣♦s✐çõ❡s✳ ❆ ❛♣❧✐❝❛çã♦ ❞❡ ✉♠ ❝✉t♦✛ tr❛♥s❢♦r♠❛ ❛ ♠❛tr✐③ ❞❡ ❞✐stâ♥❝✐❛s ❡♠ ✉♠❛ ♠❛tr✐③ ❞❡ ❛❞❥❛❝ê♥❝✐❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺
❋✐❣✉r❛ ✹✳✶ ✲ ❉✐str✐❜✉✐çã♦ ❞❡ N ♣❛rtí❝✉❧❛s ♦❝✉♣❛♥❞♦ ✉♠ ✈♦❧✉♠❡ ❡s❢ér✐❝♦ ❞❡ r❛✐♦ R✳
❆ ♣❛rtí❝✉❧❛ ❞❡st❛❝❛❞❛✱ ❧♦❝❛❧✐③❛❞❛ ❛ ✉♠❛ ❞✐stâ♥❝✐❛d❞♦ ❝❡♥tr♦ ❞❛ ❡s❢❡r❛✱
❡♥①❡r❣❛m✈✐③✐♥❤♦s✱ ❝♦♥t✐❞♦s ♥❛ ❡s❢❡r❛ ❞❡✜♥✐❞❛ ♣❡❧❛ ❞✐stâ♥❝✐❛ ❞❡ ❝✉t♦✛ r✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶
❋✐❣✉r❛ ✹✳✷ ✲ ●rá✜❝♦ ❞❡ g(r) ♠é❞✐♦ ❝❛❧❝✉❧❛❞♦ s♦❜r❡ t♦❞❛s ❛s ❡str✉t✉r❛s ❞❛ ❜❛s❡
❙❈❖P✹✵✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹
❋✐❣✉r❛ ✹✳✸ ✲ ●rá✜❝♦ ❞❡ g(r) ♠é❞✐♦ ❝❛❧❝✉❧❛❞♦ s♦❜r❡ t♦❞❛s ❛s ❡str✉t✉r❛s ❞❛ ❜❛s❡
❙❈❖P✹✵✱ s✉❛✈✐③❛❞♦ ♣❡❧❛ ❛♣❧✐❝❛çã♦ ❞❡ ♠é❞✐❛ ♠ó✈❡❧ ❝♦♠ ❥❛♥❡❧❛ ❞❡ ✸ ♣♦♥t♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺
❋✐❣✉r❛ ✹✳✹ ✲ ●rá✜❝♦ ❞❡ gα(r) ♠é❞✐♦ ❝❛❧❝✉❧❛❞♦ s♦❜r❡ t♦❞❛s ❛s ❡str✉t✉r❛s ❞❛ ❜❛s❡
❙❈❖P✹✵✱ s✉❛✈✐③❛❞♦ ♣❡❧❛ ❛♣❧✐❝❛çã♦ ❞❡ ♠é❞✐❛ ♠ó✈❡❧ ❝♦♠ ❥❛♥❡❧❛ ❞❡ ✸ ♣♦♥t♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼
❋✐❣✉r❛ ✹✳✺ ✲ ■❧✉str❛çã♦ ❞♦ ♠ét♦❞♦ ❞❡ ❝♦♥t❛❣❡♠ ❞❡ ✈✐③✐♥❤♦s ❜❛s❡❛❞♦ ♥❛s ❞✐stâ♥❝✐❛s ❡♥tr❡ ♦s ❝❛r❜♦♥♦s Cα✳ ❖ át♦♠♦ ✐❧✉str❛❞♦ ❡♠ ❛③✉❧ é ♦ ❝❛r❜♦♥♦ ❛❧❢❛ ❞♦
r❡sí❞✉♦ ❞❡ ✐♥t❡r❡ss❡✳ ❖s ❝❛r❜♦♥♦s ❛❧❢❛ q✉❡ ❡stã♦ ❛ ♠❡♥♦s ❞❡ 8➴ ❞❡
❞✐stâ♥❝✐❛ ❞♦ ♠❡s♠♦ ❡stã♦ ✐❧✉str❛❞♦s ❡♠ ✈❡r♠❡❧❤♦✱ ❡ ♦s r❡sí❞✉♦s ❛♦s q✉❛✐s ❡❧❡s ♣❡rt❡♥❝❡♠✱ ❝♦♥s✐❞❡r❛❞♦s ✈✐③✐♥❤♦s ❞♦ r❡sí❞✉♦ ❞❡ ✐♥t❡r❡ss❡✱ ✐❧✉str❛❞♦s ❡♠ ❧❛r❛♥❥❛✳ ❋✐❣✉r❛ ❣❡r❛❞❛ ❝♦♠ ♦ ♣r♦❣r❛♠❛ ❱▼❉ ✭✶✱ ✷✮✳ ❖s ✈✐③✐♥❤♦s ❞♦ r❡sí❞✉♦ N ♣♦❞❡♠ s❡r s❡❧❡❝✐♦♥❛❞♦s✱ s❡❣✉♥❞♦ ❛ s✐♥t❛①❡ ❞♦
❱▼❉✱ ♣♦r ♠❡✐♦ ❞♦ ❝♦♠❛♥❞♦ ✭s❛♠❡ r❡s✐❞ ❛s ✭♥❛♠❡ ❈❆ ❛♥❞ ✇✐t❤✐♥ 8♦❢
✭♥❛♠❡ ❈❆ ❛♥❞ r❡s✐❞ N✮✮✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾
❋✐❣✉r❛ ✹✳✻ ✲ ■❧✉str❛çã♦ ❞♦ ♠ét♦❞♦ ❞❡ ❝♦♥t❛❣❡♠ ❞❡ ✈✐③✐♥❤♦s ❜❛s❡❛❞♦ ♥❛s ❞✐stâ♥❝✐❛s ❡♥tr❡ t♦❞♦s ♦s ♣❛r❡s ❞❡ át♦♠♦s✳ ❖s át♦♠♦s ❞♦ r❡sí❞✉♦ ❞❡ ✐♥t❡r❡ss❡ ❡stã♦ ✐❧✉str❛❞♦s ❡♠ ❛③✉❧✱ ❡ t♦❞♦s ♦s r❡sí❞✉♦s q✉❡ ❝♦♥té♠ ♣❡❧♦ ♠❡♥♦s ✉♠ át♦♠♦ ❛ ♠❡♥♦s ❞❡5➴ ❞❡ ❛❧❣✉♠ át♦♠♦ ❞♦ r❡sí❞✉♦ ❞❡ ✐♥t❡r❡ss❡ ❡stã♦
✐❧✉str❛❞♦s ❡♠ ❧❛r❛♥❥❛✳ ❋✐❣✉r❛ ❣❡r❛❞❛ ❝♦♠ ♦ ♣r♦❣r❛♠❛ ❱▼❉ ✭✶✱ ✷✮✳ ❖s ✈✐③✐♥❤♦s ❞♦ r❡sí❞✉♦ N ♣♦❞❡♠ s❡r s❡❧❡❝✐♦♥❛❞♦s✱ s❡❣✉♥❞♦ ❛ s✐♥t❛①❡ ❞♦
❋✐❣✉r❛ ✹✳✼ ✲ ●rá✜❝♦ ❞❡ gR(r) ♠é❞✐♦ ❝♦♥tr❛ r ♣❛r❛ t♦❞❛s ❛s ♣r♦t❡í♥❛s ❞❛ ❜❛s❡
❙❈❖P✹✵✳ ❖ ♣✐❝♦ ❡♠ t♦r♥♦ ❞❡ r = 1,5➴✱ ❝♦rr❡s♣♦♥❞❡♥t❡ ❛♦s ✈✐③✐♥❤♦s
❝♦✈❛❧❡♥t❡s✱ ❛t✐♥❣❡ ✉♠ ✈❛❧♦r ♠á①✐♠♦ ❡♠ t♦r♥♦ ❞❡ 100✱ ❡ ❢♦✐ s✉♣r✐♠✐❞♦
♣❛r❛ ♣r❡s❡r✈❛r ❛ ❝❧❛r❡③❛ ❞❛ ✜❣✉r❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶
❋✐❣✉r❛ ✹✳✽ ✲ ❊①❡♠♣❧♦ ❞❡ ❝✉r✈❛ ❞❡ t❡♠♣❡r❛t✉r❛ ✜♥❛❧ ✈❡rs✉s ♣♦s✐çã♦ ❞♦ r❡sí❞✉♦ ❛q✉❡✲ ❝✐❞♦ ♥❛ ❡str✉t✉r❛ ♣r✐♠ár✐❛✱ ❝♦♠ ❛❧❣✉♥s r❡sí❞✉♦s ❞❡st❛❝❛❞♦s ❡ s✉❛s r❡s✲ ♣❡❝t✐✈❛s ✐❞❡♥t✐❞❛❞❡s✳ ❆ ✐❞❡♥t✐❞❛❞❡ ❞♦ r❡sí❞✉♦ ❝♦rr❡❧❛❝✐♦♥❛✲s❡ ♠♦❞❡r❛✲ ❞❛♠❡♥t❡ ❝♦♠ ❛ s✉❛ ❝❛♣❛❝✐❞❛❞❡ ❞❡ ❛q✉❡❝❡r ❛ ♣r♦t❡í♥❛ ❝♦♠♦ ✉♠ t♦❞♦✱ ♠❛s ♥ã♦ ❡①♣❧✐❝❛ ♣♦r s✐ só ❛ ❢♦r♠❛ ❞❛ ❝✉r✈❛✳ ❘❡♣r♦❞✉③✐❞♦ ❝♦♠ ❛✉t♦r✐✲ ③❛çã♦ ❞❡ ✭✶✵✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸
❋✐❣✉r❛ ✹✳✾ ✲ ❙♦❜r❡♣♦s✐çã♦ ❡♥tr❡ ❛s ❝✉r✈❛s ♥♦r♠❛❧✐③❛❞❛s ❞❡ t❡♠♣❡r❛t✉r❛ ✜♥❛❧ ♣♦r r❡sí❞✉♦ ❡ ❝❡♥tr❛❧✐❞❛❞❡ ❞❡ ♣r♦①✐♠✐❞❛❞❡ ♣♦r r❡sí❞✉♦ ♣❛r❛ ❛ ①✐❧❛♥❛s❡ ❞❡ ✐❞❡♥t✐✜❝❛❞♦r ✶❋✺❏✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺
❋✐❣✉r❛ ✹✳✶✵ ✲❙♦❜r❡♣♦s✐çã♦ ❡♥tr❡ ❛s ❝✉r✈❛s ♥♦r♠❛❧✐③❛❞❛s ❞❡ t❡♠♣❡r❛t✉r❛ ✜♥❛❧ ♣♦r r❡sí❞✉♦ ❡ ❝❡♥tr❛❧✐❞❛❞❡ ❞❡ ♣r♦①✐♠✐❞❛❞❡ ♣♦r r❡sí❞✉♦ ♣❛r❛ ❛ ①✐❧❛♥❛s❡ ❞❡ ✐❞❡♥t✐✜❝❛❞♦r ✶▼✹❲✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻
❋✐❣✉r❛ ✹✳✶✶ ✲❙♦❜r❡♣♦s✐çã♦ ❡♥tr❡ ❛s ❝✉r✈❛s ♥♦r♠❛❧✐③❛❞❛s ❞❡ t❡♠♣❡r❛t✉r❛ ✜♥❛❧ ♣♦r r❡sí❞✉♦ ❡ ❝❡♥tr❛❧✐❞❛❞❡ ❞❡ ♣r♦①✐♠✐❞❛❞❡ ♣♦r r❡sí❞✉♦ ♣❛r❛ ❛ ①✐❧❛♥❛s❡ ❞❡ ✐❞❡♥t✐✜❝❛❞♦r ✶❳◆❇✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻
❋✐❣✉r❛ ✹✳✶✷ ✲❙♦❜r❡♣♦s✐çã♦ ❡♥tr❡ ❛s ❝✉r✈❛s ♥♦r♠❛❧✐③❛❞❛s ❞❡ t❡♠♣❡r❛t✉r❛ ✜♥❛❧ ♣♦r r❡sí❞✉♦ ❡ ❝❡♥tr❛❧✐❞❛❞❡ ❞❡ ♣r♦①✐♠✐❞❛❞❡ ♣♦r r❡sí❞✉♦ ♣❛r❛ ❛ ①✐❧❛♥❛s❡ ❞❡ ✐❞❡♥t✐✜❝❛❞♦r ✷❱❯❏✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✼
❋✐❣✉r❛ ✹✳✶✸ ✲❙♦❜r❡♣♦s✐çã♦ ❡♥tr❡ ❛s ❝✉r✈❛s ♥♦r♠❛❧✐③❛❞❛s ❞❡ t❡♠♣❡r❛t✉r❛ ✜♥❛❧ ♣♦r r❡sí❞✉♦ ❡ ❝❡♥tr❛❧✐❞❛❞❡ ❞❡ ♣r♦①✐♠✐❞❛❞❡ ♣♦r r❡sí❞✉♦ ♣❛r❛ ❛ ①✐❧❛♥❛s❡ ❞❡ ✐❞❡♥t✐✜❝❛❞♦r ✷❱❯▲✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✼
❋✐❣✉r❛ ✹✳✶✺ ✲●rá✜❝♦ ❞❡ ❞✐s♣❡rsã♦ ♣❛r❛ ❛ t❡♠♣❡r❛t✉r❛ ✜♥❛❧ ✈❡rs✉s ❝❡♥tr❛❧✐❞❛❞❡ ♣❛r❛ ❛ ♣r♦t❡í♥❛ ✶❋✺❏✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✶
❋✐❣✉r❛ ✹✳✶✻ ✲●rá✜❝♦ ❞❡ ❞✐s♣❡rsã♦ ♣❛r❛ ❛ t❡♠♣❡r❛t✉r❛ ✜♥❛❧ ✈❡rs✉s ❝❡♥tr❛❧✐❞❛❞❡ ♣❛r❛ ❛ ♣r♦t❡í♥❛ ✶▼✹❲✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✶
❋✐❣✉r❛ ✹✳✶✼ ✲●rá✜❝♦ ❞❡ ❞✐s♣❡rsã♦ ♣❛r❛ ❛ t❡♠♣❡r❛t✉r❛ ✜♥❛❧ ✈❡rs✉s ❝❡♥tr❛❧✐❞❛❞❡ ♣❛r❛ ❛ ♣r♦t❡í♥❛ ✶❳◆❇✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✷
❋✐❣✉r❛ ✹✳✶✽ ✲●rá✜❝♦ ❞❡ ❞✐s♣❡rsã♦ ♣❛r❛ ❛ t❡♠♣❡r❛t✉r❛ ✜♥❛❧ ✈❡rs✉s ❝❡♥tr❛❧✐❞❛❞❡ ♣❛r❛ ❛ ♣r♦t❡í♥❛ ✷❱❯❏✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✷
❋✐❣✉r❛ ✹✳✶✾ ✲●rá✜❝♦ ❞❡ ❞✐s♣❡rsã♦ ♣❛r❛ ❛ t❡♠♣❡r❛t✉r❛ ✜♥❛❧ ✈❡rs✉s ❝❡♥tr❛❧✐❞❛❞❡ ♣❛r❛ ❛ ♣r♦t❡í♥❛ ✷❱❯▲✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✸
▲■❙❚❆ ❉❊ ❚❆❇❊▲❆❙
❚❛❜❡❧❛ ✹✳✶ ✲▼❛❣♥✐t✉❞❡ ❞❛s ❝♦rr❡❧❛çõ❡s ❡♥tr❡ ❛s ♠❡❞✐❞❛s ❞❡ ❝❡♥tr❛❧✐❞❛❞❡ ❡ ❛ t❡♠✲ ♣❡r❛t✉r❛ ✜♥❛❧ ❞❡ ❝❛❞❛ r❡sí❞✉♦✱ ♣❛r❛ ♦ ❝♦♥❥✉♥t♦ ❞❡ ①✐❧❛♥❛s❡s ❡st✉❞❛❞❛s✳
❙❯▼➪❘■❖
✶ ■♥tr♦❞✉çã♦ ✷✶
✶✳✶ ▼♦❞❡❧❛❣❡♠ ❈♦♠♣✉t❛❝✐♦♥❛❧ ❞❡ Pr♦t❡í♥❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶
✶✳✷ ❳✐❧❛♥❛s❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽
✷ ❉✐♥â♠✐❝❛ ▼♦❧❡❝✉❧❛r ❡♠ Pr♦t❡í♥❛s ✸✸
✷✳✶ ❖ ❈♦♠♣✉t❛❞♦r ❝♦♠♦ ❋❡rr❛♠❡♥t❛ ❊①♣❡r✐♠❡♥t❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸
✷✳✷ ❉✐♥â♠✐❝❛ ▼♦❧❡❝✉❧❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹
✷✳✸ ❉✐❢✉sã♦ ❚ér♠✐❝❛ ❆♥✐s♦tró♣✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽
✸ ▼♦❞❡❧❛❣❡♠ ❞❡ Pr♦t❡í♥❛s ❝♦♠♦ ❘❡❞❡s ❈♦♠♣❧❡①❛s ✹✸
✸✳✶ ■♥tr♦❞✉çã♦ à ❚❡♦r✐❛ ❞❡ ❘❡❞❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸
✸✳✷ Pr♦t❡í♥❛s ❝♦♠♦ ❘❡❞❡s ❈♦♠♣❧❡①❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸
✹ ❘❡s✉❧t❛❞♦s ✺✾
✹✳✶ ❈♦♥str✉çã♦ ❞❡ ❘❡❞❡s q✉❡ ❘❡♣r❡s❡♥t❛♠ ❊str✉t✉r❛s ❞❡ Pr♦t❡í♥❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾
✹✳✷ Pr❡✈✐sã♦ ❞♦ ❋❧✉①♦ ❞❡ ❈❛❧♦r ♣♦r ♠❡✐♦ ❞❡ ❉❡s❝r✐t♦r❡s ❞❡ ❘❡❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷
✺ ❈♦♥❝❧✉sõ❡s ✽✺
❘❊❋❊❘✃◆❈■❆❙ ✽✾
❆P✃◆❉■❈❊ ❆ ✲✲ ❉❡♠♦♥str❛çõ❡s ✾✼
✷✶
❈❆P❮❚❯▲❖ ✶
■♥tr♦❞✉çã♦
✶✳✶ ▼♦❞❡❧❛❣❡♠ ❈♦♠♣✉t❛❝✐♦♥❛❧ ❞❡ Pr♦t❡í♥❛s
Pr♦t❡í♥❛s∗ sã♦ ♠❛❝r♦♠♦❧é❝✉❧❛s ❜✐♦❧ó❣✐❝❛s ❡♥❝♦♥tr❛❞❛s ❡♠ t♦❞❛s ❛s ❝é❧✉❧❛s ✈✐✈❛s✱ ❝♦rr❡s✲
♣♦♥❞❡♥❞♦ t✐♣✐❝❛♠❡♥t❡ à ♠❡t❛❞❡ ❞♦ ♣❡s♦ s❡❝♦ ❞❛ ♠❛✐♦r ♣❛rt❡ ❞♦s ♦r❣❛♥✐s♠♦s✳
❆ ❛❜✉♥❞â♥❝✐❛ ❡ ✈❛r✐❡❞❛❞❡ ❞❡ ❡①❡♠♣❧❛r❡s ❡♥❝♦♥tr❛❞♦s é ❝♦♥s❡q✉ê♥❝✐❛ ❞❡ s✉❛ ✐♠♣♦rtâ♥❝✐❛ ♥♦ ♠❡t❛❜♦❧✐s♠♦ ❝❡❧✉❧❛r✿ ❛ ♠❛✐♦r✐❛ ❞❛s ❢✉♥çõ❡s ❝❡❧✉❧❛r❡s sã♦ r❡❛❧✐③❛❞❛s ♣♦r ♣r♦t❡í♥❛s✱ q✉❡ ❛t✉❛♠ s♦❜r❡ ♦s ♦✉tr♦s t✐♣♦s✱ ♣❛ss✐✈♦s✱ ❞❡ ❜✐♦♠♦❧é❝✉❧❛s✱ s❡❣✉♥❞♦ ❛s ✐♥str✉çõ❡s ❛r♠❛③❡♥❛❞❛s ♥❛ ✐♥❢♦r♠❛çã♦ ❣❡♥ét✐❝❛✳
❉♦ ♣♦♥t♦ ❞❡ ✈✐st❛ ❜✐♦q✉í♠✐❝♦✱ ♣r♦t❡í♥❛s sã♦ ♣♦❧í♠❡r♦s ❧✐♥❡❛r❡s ❤❡t❡r♦❣ê♥❡♦s ❝♦♥st✐t✉í❞♦s ❞❡ ▲✲α✲❛♠✐♥♦á❝✐❞♦s ❧✐❣❛❞♦s ❡♥tr❡ s✐ ♣♦r ❧✐❣❛çõ❡s ♣❡♣tí❞✐❝❛s✱ t❛❧ ❝♦♠♦ ✐❧✉str❛❞♦ ♣❡❧❛ ✜❣✉r❛
✶✳✶✳ ❈♦♠ ❡s♣❛rs❛s ❡①❝❡çõ❡s†✱ t♦❞❛s ❛s ❝é❧✉❧❛s s✐♥t❡t✐③❛♠ ♣r♦t❡í♥❛s✱ ❡♠♣r❡❣❛♥❞♦ ✉♠ ❝♦♥❥✉♥t♦
❞❡ ❞✐❢❡r❡♥t❡s t✐♣♦s ❞❡ ❛♠✐♥♦á❝✐❞♦s ✭❡♠ ❣❡r❛❧ ✈✐♥t❡✱ ❝♦♠ ♣❡q✉❡♥❛s ✈❛r✐❛çõ❡s ❡♠ ❛❧❣✉♥s ♦r✲ ❣❛♥✐s♠♦s✮ q✉❡ ❞✐❢❡r❡♠ ❡♥tr❡ s✐ ♣❡❧♦ ❣r✉♣♦ s✉❜st✐t✉✐♥t❡ ❞♦ ❝❛r❜♦♥♦ ❝❡♥tr❛❧ ♦✉ ❝❛r❜♦♥♦ ❛❧❢❛ ✭Cα✮✱ ❞❡♥♦♠✐♥❛❞♦ ❞❡ ❝❛❞❡✐❛ ❧❛t❡r❛❧✳ ❆♦ s❡r ✐♥❝♦r♣♦r❛❞♦ ❛♦ ♣♦❧í♠❡r♦ ❞✉r❛♥t❡ ❛ sí♥t❡s❡✱ ❝❛❞❛
❛♠✐♥♦á❝✐❞♦ ❢♦r♠❛ ✉♠❛ ❧✐❣❛çã♦ ❝♦✈❛❧❡♥t❡ ❝♦♠ ❛ ❡①tr❡♠✐❞❛❞❡ ❝❛r❜♦①✐❧❛t♦ ❡①♣♦st❛ ❞♦ ❛♥t❡r✐♦r✱ q✉❡ ♣❡r❞❡ ✉♠ ❣r✉♣♦ ❤✐❞r♦①✐❧❛ ♥❛ ❢♦r♠❛ ❞❡ á❣✉❛✳ ❉❡♥♦♠✐♥❛♠♦s ❡♥tã♦ ♦ ❣r✉♣♦ q✉❡ s♦❜r❛✱ q✉❡ é ✐♥❝♦r♣♦r❛❞♦ à s❡q✉ê♥❝✐❛✱ ❞❡ r❡sí❞✉♦ ❞❡ ❛♠✐♥♦á❝✐❞♦ ♦✉ s✐♠♣❧❡s♠❡♥t❡ r❡sí❞✉♦✱ ♥♦♠❡♥❝❧❛t✉r❛ q✉❡ s❡rá ❛❞♦t❛❞❛ ♥❡st❡ tr❛❜❛❧❤♦ ❞❛q✉✐ ❡♠ ❞✐❛♥t❡✳
❆ ❝❛❞❛ ♣r♦t❡í♥❛ ❝♦rr❡s♣♦♥❞❡ ✉♠❛ s❡q✉ê♥❝✐❛ ❜❡♠ ❞❡✜♥✐❞❛ ❞❡ ❛♠✐♥♦á❝✐❞♦s✱ ❞❡♥♦♠✐♥❛❞❛ ❡str✉t✉r❛ ♣r✐♠ár✐❛❀ ❡①♣❡r✐♠❡♥t❛❧♠❡♥t❡✱ ✈❡r✐✜❝❛✲s❡ q✉❡✱ ❛♣ós ❤✐❞ró❧✐s❡ ❝♦♠♣❧❡t❛ ❞❡ t♦❞❛s ❛s ❧✐❣❛çõ❡s ♣❡♣tí❞✐❝❛s✱ ❝❛❞❛ ♣r♦t❡í♥❛ ❣❡r❛ ✉♠❛ ♠✐st✉r❛ ❞❡ ❛♠✐♥♦á❝✐❞♦s ❝♦♠ ✉♠❛ ❞❛❞❛ ❝♦♠♣♦✲
∗❊st❡ ❝❛♣✐t✉❧♦ é ❜❛s❡❛❞♦ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ♥♦ ❝♦♥t❡ú❞♦ ❞❡ ✭✶✸✮✱ ❝✉❥❛ ❧❡✐t✉r❛ é r❡❝♦♠❡♥❞❛❞❛ ❛♦s ❧❡✐t♦r❡s ✐♥t❡✲ r❡ss❛❞♦s ❡♠ ❛♣r♦❢✉♥❞❛r s❡✉ ❝♦♥❤❡❝✐♠❡♥t♦ ❞♦s tó♣✐❝♦s ❛♣r❡s❡♥t❛❞♦s✳ ❖✉tr❛s r❡❢❡rê♥❝✐❛s ❝♦♥s✉❧t❛❞❛s s❡rã♦ ❝✐t❛❞❛s ❛♦ ❧♦♥❣♦ ❞♦ t❡①t♦✱ q✉❛♥❞♦ ❛♣r♦♣r✐❛❞♦✳
✷✷ ✶ ■♥tr♦❞✉çã♦
I)
II)
❋✐❣✉r❛ ✶✳✶ ✕ ✭■✮ ❊①❡♠♣❧♦ ❞❡ ❧✐❣❛çõ❡s ♣❡♣tí❞✐❝❛s ✭❡♠ ❞❡st❛q✉❡✮ ♥❛ ❝❛❞❡✐❛ ♣r✐♥❝✐♣❛❧ ❡♠ ✉♠❛ ♣r♦t❡í♥❛✳ ➪t♦♠♦s ❞❡ ❖①✐❣ê♥✐♦ sã♦ r❡♣r❡s❡♥t❛❞♦s ❡♠ ✈❡r♠❡❧❤♦✱ ◆✐tr♦❣ê♥✐♦ ❡♠ ❛③✉❧ ❡ ❈❛r❜♦♥♦ ❡♠ ❝✐❛♥♦✳ ➪t♦♠♦s ❞❡ ❍✐❞r♦❣ê♥✐♦ ♥ã♦ sã♦ r❡♣r❡s❡♥t❛❞♦s✳ ❋✐❣✉r❛ ❣❡r❛❞❛ ❝♦♠ ♦ ♣r♦❣r❛♠❛ ❱▼❉ ✭✶✱ ✷✮✳ ✭■■✮ ❋♦r♠❛çã♦ ❞❡ ❧✐❣❛çã♦ ♣❡♣tí❞✐❝❛ ❛ ♣❛rt✐r ❞❡ ❞♦✐s ❛♠✐♥♦á❝✐❞♦s ✭❆❧❛♥✐♥❛s✱ ♥❛s q✉❛✐s ❈❍3 é ❛ ❝❛❞❡✐❛ ❧❛t❡r❛❧✮✱ ❝♦♠ ♣❡r❞❛ ❞❡ ✉♠❛ ♠♦❧é❝✉❧❛ ❞❡ á❣✉❛✳
s✐çã♦✱ ❝❛r❛❝t❡ríst✐❝❛ ❡ ✐♥✈❛r✐❛♥t❡✳ ❖ t✐♣♦ ❡ ❛ ♦r❞❡♠ ❞♦s r❡sí❞✉♦s ♥❛ ❝❛❞❡✐❛✱ ❝❛❞❛ q✉❛❧ ❝♦♠ ♣r♦♣r✐❡❞❛❞❡s ❢ís✐❝♦✲q✉í♠✐❝❛s ❞✐st✐♥t❛s✱ ❞❡t❡r♠✐♥❛ ✉♥✐✈♦❝❛♠❡♥t❡ ❛ ❝♦♥❢♦r♠❛çã♦ ❛ss✉♠✐❞❛ ✭♦✉ ♣❡q✉❡♥♦ ♥ú♠❡r♦ ❞❡ ❝♦♥❢♦r♠❛çõ❡s ❛ss✉♠✐❞❛s✮ ♣❡❧❛ ♠❡s♠❛ ❡♠ s♦❧✉çã♦✱ ♥✉♠ ♣r♦❝❡ss♦ ❞❡♥♦♠✐✲ ♥❛❞♦ ❡♥♦✈❡❧❛♠❡♥t♦✳ ❊st❛ ❝♦♥❢♦r♠❛çã♦✱ q✉❡ ❞❡♥♦♠✐♥❛♠♦s ❡str✉t✉r❛ ❞❛ ♣r♦t❡í♥❛✱ é ❡stá✈❡❧✱ ❡ ❞❛ s✉❛ r❡♣r♦❞✉t✐❜✐❧✐❞❛❞❡ ❞❡♣❡♥❞❡ ❛ ♠❛♥✉t❡♥çã♦ ❞❛ ❤♦♠❡♦st❛s❡✱ ❡✱ ♣♦r ❝♦♥s❡q✉ê♥❝✐❛✱ ❞❛ ✈✐❞❛ ❞❛ ❝é❧✉❧❛✳
✶✳✶ ▼♦❞❡❧❛❣❡♠ ❈♦♠♣✉t❛❝✐♦♥❛❧ ❞❡ Pr♦t❡í♥❛s ✷✸
✐♥❢♦r♠❛çã♦ ♥❡❝❡ssár✐❛ ❡ s✉✜❝✐❡♥t❡ ♣❛r❛ ♦ ❡♥♦✈❡❧❛♠❡♥t♦ ❡♠ s♦❧✉çã♦ é ❝♦♥t✐❞❛ ❝♦♠♣❧❡t❛♠❡♥t❡ ♥❛ s❡q✉ê♥❝✐❛ ❞❡ ❛♠✐♥♦á❝✐❞♦s✳
❆ r❡♣r♦❞✉t✐❜✐❧✐❞❛❞❡ ❞♦ ❡♥♦✈❡❧❛♠❡♥t♦ ❞❡ ❡str✉t✉r❛s ❞❡ ♣r♦t❡í♥❛ s❡ ❞❡✈❡✱ ❡♠ ❣r❛♥❞❡ ♠❡❞✐❞❛✱ à ♠❛♥✉t❡♥çã♦ ❞❡ ❝♦♥❞✐çõ❡s ♣r❡❝✐s❛s ❞❡♥tr♦ ❞♦ ❛♠❜✐❡♥t❡ ❝❡❧✉❧❛r✳ P♦r ♦✉tr♦ ❧❛❞♦✱ ♠❡s♠♦ s♦❜ ❝♦♥❞✐çõ❡s ❝♦♥tr♦❧❛❞❛s✱ ❛ ♠❛✐♦r ♣❛rt❡ ❞❛s s❡q✉ê♥❝✐❛s ❞❡ ❛♠✐♥♦á❝✐❞♦s ♥ã♦ ❛t✐♥❣❡ ♥❡♥❤✉♠❛ ❝♦♥✲ ✜❣✉r❛çã♦ ♣❛rt✐❝✉❧❛r♠❡♥t❡ ❜❡♠ ❞❡t❡r♠✐♥❛❞❛✳ P❛r❛ ❡①♣❧✐❝❛r ❡st❡ ❝♦♠♣♦rt❛♠❡♥t♦✱ é ♥❡❝❡ssár✐♦ ❞❡t❛❧❤❛r ♦s ♠❡❝❛♥✐s♠♦s q✉❡ ❧❡✈❛♠ ❛♦ ❡♥♦✈❡❧❛♠❡♥t♦✳
❚♦❞❛ ♣r♦t❡í♥❛✱ q✉❛♥❞♦ s✐♥t❡t✐③❛❞❛✱ ❝♦♥s✐st❡ ❡♠ ✉♠❛ ❝❛❞❡✐❛ ❧✐♥❡❛r ❞❡ r❡sí❞✉♦s ❞❡ ❛♠✐♥♦á❝✐✲ ❞♦s ❡①♣♦st♦s ❛♦ s♦❧✈❡♥t❡✳ ❈❛❞❛ ✉♠ ❞♦s ✈✐♥t❡ ❛♠✐♥♦á❝✐❞♦s ♣r❡✈✐st♦s ♥♦ ❝ó❞✐❣♦ ❣❡♥ét✐❝♦ ❞❡ ✉♠ ♦r❣❛♥✐s♠♦ ❡①✐❜❡ ♣r♦♣r✐❡❞❛❞❡s ❢ís✐❝♦✲q✉í♠✐❝❛s ♣ró♣r✐❛s✱ t❛✐s ❝♦♠♦ ✈♦❧✉♠❡✴ár❡❛ ❞❡ s✉♣❡r❢í❝✐❡✱ ❝❛r❣❛ ❡❧étr✐❝❛ ❡♠ ♣❍ ✜s✐♦❧ó❣✐❝♦ ❡ ♥ú♠❡r♦ ❞❡ ❛❝❡♣t♦r❡s✴❞♦❛❞♦r❡s ❞❡ ❧✐❣❛çã♦ ❞❡ ❍✐❞r♦❣ê♥✐♦❀ ♣♦❞❡♠♦s ❞✐✈✐❞✐✲❧♦s✱ ❞❡ ♠♦❞♦ ❣❡r❛❧✱ ❡♥tr❡ ❛♠✐♥♦á❝✐❞♦s ❛♣♦❧❛r❡s✱ ♣♦❧❛r❡s ❡ ❝❛rr❡❣❛❞♦s✳ ❆ ♣r✐♥✲ ❝í♣✐♦✱ ♣♦❞❡rí❛♠♦s ❝♦♥s✐❞❡r❛r q✉❡ ❛ ❢♦r♠❛çã♦ ❞❡ ✐♥t❡r❛çõ❡s ❡❧❡tr♦stát✐❝❛s ❡♥tr❡ ❛♠✐♥♦á❝✐❞♦s ❝❛rr❡❣❛❞♦s ❡ ❞❡ ❧✐❣❛çõ❡s ❞❡ ❍✐❞r♦❣ê♥✐♦ ❡♥tr❡ ❣r✉♣♦s ❞♦❛❞♦r❡s ❡ ❛❝❡♣t♦r❡s ❞❡ ❛♠✐♥♦á❝✐❞♦s ♣♦❧❛r❡s é ❛ ❢♦rç❛ ♠♦tr✐③ ❞♦ ♣r♦❝❡ss♦ ❞❡ ❡♥♦✈❡❧❛♠❡♥t♦✳ ❈♦♥t✉❞♦✱ ❝♦♠ ❛ ❝❛❞❡✐❛ ❡st❡♥❞✐❞❛✱ ❝❛❞❛ ✉♠ ❞❡st❡s r❡sí❞✉♦s ❢❛③ ✐♥t❡r❛çõ❡s ❞♦ ♠❡s♠♦ t✐♣♦ ❝♦♠ ❛s ♠♦❧é❝✉❧❛s ❞❡ á❣✉❛ ❞♦ s♦❧✈❡♥t❡✱ ❞❡ ♠♦❞♦ q✉❡ ❛ ❢♦r♠❛çã♦ ❞❡ ✐♥t❡r❛çõ❡s ♥ã♦✲❝♦✈❛❧❡♥t❡s ❡♥tr❡ r❡sí❞✉♦s ♥ã♦ é✱ ❡♥❡r❣❡t✐❝❛♠❡♥t❡✱ ✉♠ ❢❛t♦r ❞❡t❡r♠✐♥❛♥t❡ ♣♦r s✐ só✳
❈♦♥s✐❞❡r❛çõ❡s ❡st❛tíst✐❝❛s✱ ♣♦r ♦✉tr♦ ❧❛❞♦✱ ❛ ♣r✐♥❝í♣✐♦✱ ♥ã♦ ❧❛♥ç❛♠ ❧✉③ s♦❜r❡ ♦ ❡♥✐❣♠❛✳ ❖ ❡st❛❞♦ ❡♥♦✈❡❧❛❞♦ ✈✐❛ ❞❡ r❡❣r❛ ❡①✐❜❡ ❛❧t♦ ❣r❛✉ ❞❡ ♦r❣❛♥✐③❛çã♦✱ s❡♥❞♦ ❛ ♣♦s✐çã♦ r❡❧❛t✐✈❛ ❞❡ ❝❛❞❛ át♦♠♦ ♠✉✐t❛s ✈❡③❡s ❜❡♠ ❞❡✜♥✐❞❛ ❝♦♠ ♣r❡❝✐sã♦ q✉❡ ❝❤❡❣❛ ❛ ♥ã♦ ♠❛✐s ❞♦ q✉❡ ♦ ❞♦❜r♦ ❞♦ s❡✉ ❞✐â♠❡tr♦ ✭✶✹✮✳ ❆ tr❛♥s✐çã♦ ❞❡ ✉♠ ❡st❛❞♦ ❞❡s♥❛t✉r❛❞♦ ❡ss❡♥❝✐❛❧♠❡♥t❡ ❛❧❡❛tór✐♦✱ ♣❛r❛ ♦ q✉❛❧ ✐♥ú♠❡r❛s ❝♦♥✜❣✉r❛çõ❡s sã♦ ❛❝❡ssí✈❡✐s✱ ♣❛r❛ ✉♠ ❡st❛❞♦ ❡♥♦✈❡❧❛❞♦ ❛❧t❛♠❡♥t❡ ❡str✉t✉r❛❞♦ ❡♥✈♦❧✈❡✱ ❡♥tã♦✱ ❛ ♦❜t❡♥çã♦ ❞❡ ✉♠ ❛❧t♦ ❣r❛✉ ❞❡ ♦r❣❛♥✐③❛çã♦✱ ❝♦♠ ❝♦♥❝♦♠✐t❛♥t❡ ❞✐♠✐♥✉✐çã♦ s✐❣♥✐✜❝❛t✐✈❛ ❞❡ ❡♥tr♦♣✐❛✱ ❡♥❡r❣❡t✐❝❛♠❡♥t❡ ❞❡s❢❛✈♦rá✈❡❧✳ ❙♦❜ ❡st❡ ❡♥❢♦q✉❡✱ ❛ t❡♥❞ê♥❝✐❛ ❞❛s ❝❛❞❡✐❛s ❞❡ s❡ ❡♥♦✈❡❧❛r t♦r♥❛✲s❡ ✈❡r❞❛❞❡✐r❛♠❡♥t❡ ❞❡s❝♦♥❝❡rt❛♥t❡✳
✷✹ ✶ ■♥tr♦❞✉çã♦
❧❛♠❡♥t♦✿ ❛♦ ❛♣r♦①✐♠❛r ♦s r❡sí❞✉♦s ❤✐❞r♦❢ó❜✐❝♦s ❡♥tr❡ s✐✱ ❡♠♣❛❝♦t❛♥❞♦✲♦s✱ é ♣♦ssí✈❡❧ ❞✐♠✐♥✉✐r ❛ ár❡❛ t♦t❛❧ ❞❛s ❝❛❞❡✐❛s ❧❛t❡r❛✐s ❤✐❞r♦❢ó❜✐❝❛s q✉❡ ✜❝❛ ❞❡ ❢❛t♦ ❡①♣♦st❛ ❛♦ s♦❧✈❡♥t❡✳ ❆♦ ❡♠♣❛❝♦t❛r t♦❞♦s ♦s r❡sí❞✉♦s ❤✐❞r♦❢ó❜✐❝♦s✱ ❢♦r♠❛♥❞♦ ♦ ❝❤❛♠❛❞♦ ❝♦r❡ ♦✉ ♥ú❝❧❡♦ ❤✐❞r♦❢ó❜✐❝♦✱ ❛ ❝❛❞❡✐❛ ❞❡ ❛♠✐♥♦á❝✐❞♦s ♠✐♥✐♠✐③❛ ❛ ár❡❛ ❤✐❞r♦❢ó❜✐❝❛ ❡♠ t♦r♥♦ ❞❛ q✉❛❧ ❛s ♠♦❧é❝✉❧❛s ❞❡ á❣✉❛ ❞❡✈❡♠ s❡ ♦r❣❛♥✐③❛r✱ s❡♥❞♦ ♣♦rt❛♥t♦ ✉♠ ♣r♦❝❡ss♦ ❡♥tr♦♣✐❝❛♠❡♥t❡ ❛❧t❛♠❡♥t❡ ❢❛✈♦rá✈❡❧✳ ❆ ✜❣✉r❛ ✶✳✷ é ✉♠ r❡♣r❡s❡♥t❛çã♦ s✐♠♣❧✐✜❝❛❞❛ ❞❡st❡ ♣r♦❝❡ss♦✳
❋✐❣✉r❛ ✶✳✷ ✕ ■❧✉str❛çã♦ ❞♦ ❝♦❧❛♣s♦ ❞♦ ♥ú❝❧❡♦ ❤✐❞r♦❢ó❜✐❝♦ ❞✉r❛♥t❡ ♦ ❡♥♦✈❡❧❛♠❡♥t♦ ❞❡ ✉♠❛ ♣r♦t❡í♥❛✳ ❈ír❝✉❧♦s ❝❤❡✐♦s r❡♣r❡s❡♥t❛♠ ❛♠✐♥♦á❝✐❞♦s ❤✐❞r♦❢ó❜✐❝♦s✱ ❡ ❝ír❝✉❧♦s ✈❛③✐♦s r❡♣r❡s❡♥t❛♠ ❛♠✐♥♦á❝✐❞♦s ❤✐❞r♦❢í❧✐❝♦s✳ ✭✸✮✳
✶✳✶ ▼♦❞❡❧❛❣❡♠ ❈♦♠♣✉t❛❝✐♦♥❛❧ ❞❡ Pr♦t❡í♥❛s ✷✺
♥ã♦ ❢❛③❡r ✐♥t❡r❛çõ❡s q✉❡ ❡①✐st❛♠ ❡♠ ❝♦♥❢♦r♠❛çõ❡s ❛❧t❡r♥❛t✐✈❛s ❡✴♦✉ ❡♠ ❛r♠❛❞✐❧❤❛s ❧♦❝❛✐s ❞♦ ♣r♦❝❡ss♦ ❞❡ ❡♥♦✈❡❧❛♠❡♥t♦ ✭❢❛✈♦rá✈❡✐s✱ ♣♦rt❛♥t♦✱ ♥♦ s❡♥t✐❞♦ ❝✐♥ét✐❝♦✮✳ ❆♦ ❡s❝♦❧❤❡r ❝✉✐❞❛❞♦s❛✲ ♠❡♥t❡ ♦ r❡sí❞✉♦ q✉❡ ♦❝✉♣❛ ❝❛❞❛ ♣♦s✐çã♦✱ ❛ s❡❧❡çã♦ ♥❛t✉r❛❧ ❡✈✐t❛ ❛ ❡①✐stê♥❝✐❛ ❞❡ ✐♥t❡r❛çõ❡s q✉❡ ✏❝♦♠♣❡t❡♠✑ ❡♥tr❡ s✐✱ ✏❢r✉str❛♥❞♦✑ ❛ ❡st❛❜✐❧✐❞❛❞❡ ❞♦ ❡st❛❞♦ ♥❛t✐✈♦✱ ❡ ♣r♦♠♦✈❡ ♦ s✉r❣✐♠❡♥t♦ ❞❡ ✐♥t❡r❛çõ❡s ✏❝♦❡r❡♥t❡s✑ ♦✉ ✏❝♦♥s✐st❡♥t❡s✑✳ ❊st❛ ♠á①✐♠❛✱ ❞❡♥♦♠✐♥❛❞❛ Pr✐♥❝í♣✐♦ ❞❛ ❋r✉str❛çã♦ ▼í♥✐♠❛✱ é ❛ ♣❡ç❛ q✉❡ ❝♦♠♣❧❡t❛ ❛ ❡①♣❧✐❝❛çã♦ t❡ór✐❝❛ ❞♦ ❡♥♦✈❡❧❛♠❡♥t♦ ❞❡ ♣r♦t❡í♥❛s ✭✶✹✮✳
❆ ❞❡s♣❡✐t♦ ❞❛ ❝♦♥✜❛❜✐❧✐❞❛❞❡ ❞♦ ♣r♦❝❡ss♦ ❞❡ ❡♥♦✈❡❧❛♠❡♥t♦ ❞❡ ♣r♦t❡í♥❛s ❞❡♥tr♦ ❞❛ ❝é❧✉❧❛ ❡ ❞♦ s❡✉ ❜♦♠ ❡♥t❡♥❞✐♠❡♥t♦ ❡♠ â♠❜✐t♦ ❣❡r❛❧✱ ❛ ♣r❡✈✐sã♦ ❞♦ ❡st❛❞♦ ♥❛t✐✈♦ ❞❡ ♣r♦t❡í♥❛s ❛ ♣❛rt✐r ❞❡ s✉❛s ❡str✉t✉r❛s ♣r✐♠ár✐❛s ❝♦♥t✐♥✉❛ ♥ã♦ s❡♥❞♦✱ ❞❡ ❢♦r♠❛ ❛❧❣✉♠❛✱ ❝♦rr✐q✉❡✐r❛ ✭✶✺✮✳ ▼❡❧❤♦r❡s r❡s✉❧t❛❞♦s✱ ♣♦r ♦✉tr♦ ❧❛❞♦✱ tê♠ s✐❞♦ ♦❜t✐❞♦s ♥❛ ❞❡t❡r♠✐♥❛çã♦ ❡①♣❡r✐♠❡♥t❛❧ ❞❡ s✉❛s ❡str✉t✉r❛s✱ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ❝♦♠ ♦ ❡♠♣r❡❣♦ ❞❡ té❝♥✐❝❛s q✉❡ ❡①♣❧♦r❛♠ ❛ ✐♥t❡r❛çã♦ ❞❛ ♠❛tér✐❛ ❝♦♠ ❛ r❛❞✐❛çã♦ ❡❧❡tr♦♠❛❣♥ét✐❝❛✳ ❚❛❧ ✐♥t❡r❛çã♦ t♦r♥❛✲s❡ r❛♣✐❞❛♠❡♥t❡ ♠❛✐s ❝♦♠♣❧✐❝❛❞❛ ♥❛ ♠❡❞✐❞❛ ❡♠ q✉❡ ❝r❡s❝❡♠ ♦ t❛♠❛♥❤♦ ❡ ❛ ❝♦♠♣❧❡①✐❞❛❞❡ ❞♦ s✐st❡♠❛ ❡st✉❞❛❞♦❀ ♥♦ ❝❛s♦ ❞❡ ♠❛❝r♦♠♦❧é❝✉❧❛s ❜✐♦❧ó❣✐❝❛s✱ ♦s ♣r✐♠❡✐r♦s ❛✈❛♥ç♦s s✐❣♥✐✜❝❛t✐✈♦s ❛❞✈✐❡r❛♠ ❞♦ ❡st✉❞♦ ❞❡ ❝r✐st❛✐s✳
❆ ❝r✐st❛❧✐③❛çã♦ é ✉♠❛ t❡♥❞ê♥❝✐❛ ❡s♣♦♥tâ♥❡❛ ❞❡ s♦❧✉çõ❡s s✉♣❡rs❛t✉r❛❞❛s❀ ♥♦ ❝❛s♦ ❞❡ ♣r♦✲ t❡í♥❛s✱ ❛s ❞✐✜❝✉❧❞❛❞❡s ✐♥❡r❡♥t❡s à ♣✉r✐✜❝❛çã♦✱ ❛ ❝♦❡①✐stê♥❝✐❛ ❞❡ ♠ú❧t✐♣❧❛s ❝♦♥❢♦r♠❛çõ❡s ❡♠ s♦❧✉çã♦ ❡ ♦ ♣❡q✉❡♥♦ ♥ú♠❡r♦ ❞❡ ❝♦♥t❛t♦s ✐♥t❡r♠♦❧❡❝✉❧❛r❡s ♣♦ssí✈❡✐s ❡♠ r❡❧❛çã♦ à ♠❛ss❛ ♠♦✲ ❧❡❝✉❧❛r ❢❛③❡♠ ❝♦♠ q✉❡ ♦ ♥í✈❡❧ ❞❡ s✉♣❡rs❛t✉r❛çã♦ ♥❡❝❡ssár✐♦ ♣❛r❛ ❛ ❢♦r♠❛çã♦ ❞❡ ❝r✐st❛✐s ❜❡♠✲ ♦r❞❡♥❛❞♦s s❡❥❛ ❛❧t♦ ❡♠ r❡❧❛çã♦ ❛ ♣❡q✉❡♥❛s ♠♦❧é❝✉❧❛s ♦✉ s❛✐s✱ ❡ q✉❡ ♦s ♠❡s♠♦s s❡❥❛♠ ♠❛✐s ❢rá❣❡✐s ✭✶✻✮✳ ❈♦♥t✉❞♦✱ ❝r✐st❛✐s ❞❡ ♣r♦t❡í♥❛s ✭t❛❧ ❝♦♠♦ ❝r✐st❛✐s ❡♠ ❣❡r❛❧✮ ❡①✐❜❡♠ ✉♠❛ ♣r♦♣r✐✲ ❡❞❛❞❡ q✉❡ ♦s t♦r♥❛ ✈❛❧✐♦s♦s ♣❛r❛ ❡st✉❞♦s ❡str✉t✉r❛✐s✿ s✉❛ ❝♦♠♣♦s✐çã♦ ✉♥✐❢♦r♠❡ ❡ r❡♣❡t✐t✐✈❛✱ ❝♦♥s✐st✐♥❞♦ ❡♠ ✐♥ú♠❡r❛s ✉♥✐❞❛❞❡s ✐❞ê♥t✐❝❛s ✭♦✉ q✉❛s❡ ✐❞ê♥t✐❝❛s✮ ✏❡♥❝❛✐①❛❞❛s✑ ✉♠❛s ♥❛s ♦✉tr❛s ❞❡ ♠❛♥❡✐r❛ ❜❡♠ ❞❡t❡r♠✐♥❛❞❛✱ ♣❡r♠✐t❡ q✉❡ ❡st❡s ✐♥t❡r❛❥❛♠ ❝♦♠ ❛ r❛❞✐❛çã♦ ❡❧❡tr♦♠❛❣♥ét✐❝❛ ❞❡ ♠❛♥❡✐r❛ ♣r❡✈✐sí✈❡❧✳ ◗✉❛♥❞♦ ✉♠ ❝r✐st❛❧ ❞❡ ♣r♦t❡í♥❛ é ❡①♣♦st♦ ❛ ✉♠ ❢❡✐①❡ ❞❡ r❛✐♦s✲❳✱ ❛ ❞✐r❡çã♦ ❡ ✐♥t❡♥s✐❞❛❞❡ ❞♦s r❛✐♦s✲❳ r❡✢❡t✐❞♦s ❞❡♣❡♥❞❡ ❞❛ s✉❛ ❡str✉t✉r❛✱ t♦r♥❛♥❞♦ ♣♦ssí✈❡❧ ❛ ❞❡t❡r♠✐♥❛çã♦ ❞❛ ♠❡s♠❛ ❛tr❛✈és ❞❡ ♠❛♥✐♣✉❧❛çã♦ ♠❛t❡♠át✐❝❛ ❞♦ ♣❛❞rã♦ ❞❡ ✐♥t❡♥s✐❞❛❞❡s ✭❛ ✜❣✉r❛ ✶✳✸ ✐❧✉str❛ ❛❧❣✉♥s ❞❡st❡s ♣❛ss♦s✮✳ ❊st❛ té❝♥✐❝❛✱ ❡①tr❡♠❛♠❡♥t❡ ✐♠♣♦rt❛♥t❡✱ é ❞❡♥♦♠✐♥❛❞❛ ❝r✐st❛❧♦❣r❛✜❛ ❞❡ ♣r♦t❡í♥❛s ❛ss♦❝✐❛❞❛ à ❞✐❢r❛çã♦ ❞❡ r❛✐♦s✲❳✱ ❡✱ ✐♥tr♦❞✉③✐❞❛ ♥❛ ❞é❝❛❞❛ ❞❡ ✶✾✺✵ ✭❞❡st❛❝❛♠♦s✱ ♣♦r ❡①❡♠♣❧♦✱ ✭✶✼✮✮✱ ✐♠♣✉❧s✐♦♥♦✉ ❛ ❇✐♦❧♦❣✐❛ ▼♦❧❡❝✉❧❛r ♥✉♠❛ t❡♥❞ê♥❝✐❛ r❡❢❡r✐❞❛ ♣♦r ❖♥✉❝❤✐❝ ❡t ❛❧✳ ❝♦♠♦ ❛ ✏♦❜s❡ssã♦ ♣♦r ❡str✉t✉r❛ ❞♦ sé❝✉❧♦ ❳❳✑ ✭✶✹✮✱ ❡♠ tr❛❞✉çã♦ ❧✐✈r❡✳
✷✻ ✶ ■♥tr♦❞✉çã♦
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❋✐❣✉r❛ ✶✳✸ ✕ ■❧✉str❛çã♦ ❞♦ ♣r♦❝❡ss♦ ❞❡ ❞❡t❡r♠✐♥❛çã♦ ❞❛ ❡str✉t✉r❛ ❞❡ ♣r♦t❡í♥❛s ♣♦r ❉✐❢r❛çã♦ ❞❡ ❘❛✐♦s✲ ❳✳ ✭■✮ ❊①❡♠♣❧♦ ❞❡ ❝r✐st❛❧ ❞❡ ♣r♦t❡í♥❛✳ ✭✹✮✳ ✭■■✮ ❊①❡♠♣❧♦ ❞❡ ♣❛❞rã♦ ❞❡ ✐♥t❡♥s✐❞❛❞❡s ❞❡ ❘❛✐♦s✲❳ ❞✐❢r❛t❛❞♦s ♣♦r ✉♠ ❝r✐st❛❧ ❞❡ ♣r♦t❡í♥❛✳ ✭✺✮✳ ✭■■■✮ ❊①❡♠♣❧♦ ❞❡ ❞❡♥s✐❞❛❞❡ ❡❧❡trô♥✐❝❛ ❝❛❧❝✉❧❛❞❛ ❛ ♣❛rt✐r ❞❡ ✉♠ ♣❛❞rã♦ ❞❡ ❞✐❢r❛çã♦ ❞❡ ✉♠ ❝r✐st❛❧ ♣r♦t❡✐❝♦✱ ❝♦♠ ♠♦❞❡❧♦ ❞❡ ❝❛❞❡✐❛ ♣r✐♥❝✐♣❛❧ ❛❥✉st❛❞❛ à ❞❡♥s✐❞❛❞❡ ❡❧❡trô♥✐❝❛✳ ✭✻✮✳
❞❛ ❡str✉t✉r❛ ❞❡ ♣r♦t❡í♥❛s ❣r❛♥❞❡s ✭✶✾✮✱ ♦s ♠❡s♠♦s t♦r♥❛♠ ❛❝❡ssí✈❡❧ ❛ ❞❡s❝r✐çã♦ ❞♦ ❝♦♥❥✉♥t♦ ✭♦✉ ❡♥s❡♠❜❧❡✮ ❞❡ ❝♦♥❢♦r♠❛çõ❡s ❛ss✉♠✐❞❛s ♣♦r ❝❛❞❛ ♣r♦t❡í♥❛ ❡♠ s♦❧✉çã♦✱ ❛❞✐❝✐♦♥❛♥❞♦ ✉♠❛ ❞✐♠❡♥sã♦ ❞✐♥â♠✐❝❛ às ✐♠❛❣❡♥s ❡stát✐❝❛s ❢♦r♥❡❝✐❞❛s ♣❡❧❛ ❞✐❢r❛çã♦ ❞❡ r❛✐♦s✲❳✳
❖ ♥ú♠❡r♦ ❞❡ ❡str✉t✉r❛s ❝♦♥❤❡❝✐❞❛s✱ ♣♦r s✉❛ ✈❡③✱ ❢♦r♥❡❝❡ s✉❜sí❞✐♦s ♣❛r❛ ❛ ♣r❡❞✐çã♦ ❝♦♠✲ ♣✉t❛❝✐♦♥❛❧ ❞❡ ❡str✉t✉r❛s ❛✐♥❞❛ ♥ã♦ ❞❡t❡r♠✐♥❛❞❛s✳ ◆♦s ♠❡❧❤♦r❡s ❝❛s♦s✱ ✉♠❛ ❞❛❞❛ ♣r♦t❡í♥❛ ❝✉❥❛ s❡qüê♥❝✐❛ ❞❡ ❛♠✐♥♦á❝✐❞♦s s❡ ❝♦♥❤❡❝❡ ❡ ❝✉❥❛ ❡str✉t✉r❛ s❡ q✉❡r ❞❡t❡r♠✐♥❛r ♣♦ss✉✐ ✉♠❛ ♦✉ ♠❛✐s ❤♦♠ó❧♦❣❛s✱ ❝✉❥❛s ❡str✉t✉r❛s ❥á sã♦ r❡s♦❧✈✐❞❛s ❡ ❞❛s q✉❛✐s s❡ ♣♦❞❡ ❡s♣❡r❛r ❛❧t♦ ❣r❛✉ ❞❡ s✐♠✐❧❛r✐❞❛❞❡✳ ❚✐♣✐❝❛♠❡♥t❡✱ ✉♠❛ s✐♠✐❧❛r✐❞❛❞❡ ❡♥tr❡ ❛s s❡q✉ê♥❝✐❛s ♠❛✐♦r q✉❡ ✸✵✪ ✐♥❞✐❝❛ ✉♠ ❣r❛✉ ❞❡ s❡♠❡❧❤❛♥ç❛ ❡str✉t✉r❛❧ ❛❧t♦ ♦ s✉✜❝✐❡♥t❡ ♣❛r❛ ❣✉✐❛r ❛ ❣❡r❛çã♦ ❞❡ ✉♠ ♠♦❞❡❧♦ ❜❛s❡❛❞♦ ♥♦ ❛❧✐♥❤❛♠❡♥t♦ ❞❛s ❡str✉t✉r❛s✳ ❊st❛ té❝♥✐❝❛ ❡ s✉❛s ✈❛r✐❛çõ❡s sã♦ ❡♥❣❧♦❜❛❞❛s ♣❡❧♦ t❡r♠♦ ✏♠♦❞❡❧❛✲ ❣❡♠ ♣♦r ❤♦♠♦❧♦❣✐❛✑✱ ❡ ❡①✐❜❡♠ ❛ ❝❛♣❛❝✐❞❛❞❡ ❞❡ r❡s♦❧✈❡r✱ ❡♠ t❡♠♣♦s ❝♦♠♣✉t❛❝✐♦♥❛✐s r❛③♦á✈❡✐s✱ ❡str✉t✉r❛s ❛♣r♦①✐♠❛❞❛s ✭❞❡ ❜❛✐①❛ r❡s♦❧✉çã♦✮ ♣❛r❛ ❣❡♥♦♠❛s ✐♥t❡✐r♦s ✭✶✺✮✳
✶✳✶ ▼♦❞❡❧❛❣❡♠ ❈♦♠♣✉t❛❝✐♦♥❛❧ ❞❡ Pr♦t❡í♥❛s ✷✼
q✉í♠✐❝♦s ❢✉♥❞❛♠❡♥t❛✐s✳ ❆♠❜❛s ❛s ❡str❛té❣✐❛s sã♦ ❢r❡q✉❡♥t❡♠❡♥t❡ ✉t✐❧✐③❛❞❛s ❡♠ ♣❛r❛❧❡❧♦✱ ❡ ❡♥❣❧♦❜❛❞❛s s♦❜ ♦ t❡r♠♦ ✏♠♦❞❡❧❛❣❡♠ ❛❜ ✐♥✐t✐♦✑✳ ❚é❝♥✐❝❛s ❞❡ ♠♦❞❡❧❛❣❡♠ ❛❜ ✐♥✐t✐♦ sã♦ ❝❛♣❛③❡s ❞❡ ❝♦♠♣✉t❛r✱ ❡♠ t❡♠♣♦ ❝♦♠♣✉t❛❝✐♦♥❛❧ r❛③♦á✈❡❧✱ ❡str✉t✉r❛s ♥❛t✐✈❛s ❛♣r♦①✐♠❛❞❛s ♣❛r❛ ♣r♦t❡í♥❛s ♣❡q✉❡♥❛s ✭✶✺✱ ✷✵✱ ✷✶✮✳
❯♠❛ ✈❛♥t❛❣❡♠ ❞♦s ♠ét♦❞♦s ❛❜ ✐♥✐t✐♦✱ ❛✐♥❞❛ q✉❡ ✐♠♣♦st❛ ♣❡❧❛s ❝❛r❛❝t❡ríst✐❝❛s ❞♦ ♣r♦❜❧❡♠❛✱ é q✉❡ ❡❧❡s ♠✉✐t❛s ✈❡③❡s sã♦✱ ❛♦ ❝♦♥trár✐♦ ❞♦s ♠ét♦❞♦s ❞❡ ♠♦❞❡❧❛❣❡♠ ♣♦r ❤♦♠♦❧♦❣✐❛✱ ♦❜r✐❣❛✲ ❞♦s ❛ ❝♦♥t❡r ❤✐♣ót❡s❡s s♦❜r❡ ❛ ♠❛♥❡✐r❛ ❛tr❛✈és ❞❛ q✉❛❧ ♣r♦t❡í♥❛s ❡①♣❧♦r❛♠ ❛s ❝♦♥✜❣✉r❛çõ❡s ♣♦ssí✈❡✐s ❛té ❡♥❝♦♥tr❛r ♦ ❡st❛❞♦ ♥❛t✐✈♦❀ ❞❡ ❢❛t♦✱ ✉♠❛ ❜✉s❝❛ ♣✉r❛♠❡♥t❡ ❛❧❡❛tór✐❛ ♥♦ ❡s♣❛ç♦ ❝♦♥❢♦r♠❛❝✐♦♥❛❧ r❡q✉❡r❡r✐❛ ❡s❝❛❧❛s ❞❡ t❡♠♣♦ ♠✉✐t♦ ♠❛✐♦r❡s ❞♦ q✉❡ ❝♦s♠♦❧ó❣✐❝❛s❀ ♦ ❢❛t♦ ❞❡ q✉❡ ♣r♦t❡í♥❛s ❡♥❝♦♥tr❛♠ s❡✉ ❡st❛❞♦ ♥❛t✐✈♦ ✐♥ ✈✐✈♦ ❡ ✐♥ ✈✐tr♦ é ❞❡♠♦♥str❛çã♦ s✉✜❝✐❡♥t❡ ❞❡ q✉❡ ❛ ❜✉s❝❛ ♥ã♦ é ❛❧❡❛tór✐❛✱ ❡ ❡✈✐❞ê♥❝✐❛s s✉❣❡r❡♠ q✉❡ ❛ ❜✉s❝❛ ❛❝♦♥t❡❝❡ ❤✐❡r❛rq✉✐❝❛♠❡♥t❡ ♥❛s ❡s❝❛❧❛s ❞❡ t❛♠❛♥❤♦✱ ❝♦♠ ❡str✉t✉r❛s ❧♦❝❛✐s s❡ ❢♦r♠❛♥❞♦ ♣r✐♠❡✐r♦✱ ❡ ✈❡❧♦❝✐❞❛❞❡s ❞❡ ❡♥♦✈❡❧❛♠❡♥t♦ s❡♥❞♦ ❝♦rr❡❧❛❝✐♦♥❛❞❛s ❝♦♠ ♦ ❣r❛✉ ❞❡ ❧♦❝❛❧✐❞❛❞❡ ❞❛ t♦♣♦❧♦❣✐❛ ❞❛ ❡str✉t✉r❛ ✭✶✺✮✳
❆ ♠❛♥❡✐r❛ ♠❛✐s ❞✐r❡t❛ ❞❡ ♠♦❞❡❧❛r ❛ ❡①♣❧♦r❛çã♦ ❝♦♥❢♦r♠❛❝✐♦♥❛❧ ❞❡ ✉♠❛ ♣r♦t❡í♥❛ é t❛♠❜é♠ ❛ ♠❛✐s ❝✉st♦s❛✿ r❡s♦❧✈❡r✱ ♥♦ t❡♠♣♦✱ ❛s ❡q✉❛çõ❡s ❞❡ ♠♦✈✐♠❡♥t♦ ❞❡ ❝❛❞❛ át♦♠♦ q✉❡ ❛ ❝♦♠♣õ❡✱ r❡❣✐❞❛s ♣❡❧❛s ❧❡✐s ❞❛ ▼❡❝â♥✐❝❛ ◗✉â♥t✐❝❛✳ ◆❛t✉r❛❧♠❡♥t❡✱ ❞✐✈❡rs❛s ❛♣r♦①✐♠❛çõ❡s ❞❡✈❡♠ s❡r ❡♠♣r❡❣❛❞❛s ♣❛r❛ q✉❡ ❡st❛ ❡str❛té❣✐❛ s❡ t♦r♥❡ ♠✐♥✐♠❛♠❡♥t❡ ✈✐á✈❡❧✿ ❞✐s❝r❡t✐③❛çã♦ ❞♦ t❡♠♣♦✱ ❞♦ ❡s♣❛ç♦✱ ❡ ❛ s✉❜st✐t✉✐çã♦ ❞❛s ✐♥t❡r❛çõ❡s ♣✉r❛♠❡♥t❡ q✉â♥t✐❝❛s ♣♦r ♣♦t❡♥❝✐❛✐s ❞❡ ✐♥t❡r❛çã♦ ❝♦♥t❡♥❞♦ ❣r❛♥❞❡ ♥ú♠❡r♦ ❞❡ ♣❛râ♠❡tr♦s✱ ♦s q✉❛✐s sã♦ ❛✜♥❛❞♦s ❡♥tr❡ s✐ ♣❛r❛ q✉❡ ♦ ♣♦t❡♥❝✐❛❧ ♦✉ ✏❝❛♠♣♦ ❞❡ ❢♦rç❛✑ r❡♣r♦❞✉③❛✱ s♦❜ ❞❡t❡r♠✐♥❛❞❛s ❝♦♥❞✐çõ❡s✱ r❡s✉❧t❛❞♦s ❡①♣❡r✐♠❡♥t❛✐s✳ ❊st❡ ❝♦♥❥✉♥t♦ ❞❡ ❝♦♥❞✐çõ❡s ❞❡✜♥❡ ❛ té❝♥✐❝❛ ❞❡ ❉✐♥â♠✐❝❛ ▼♦❧❡❝✉❧❛r✱ q✉❡ r❡❝❡❜❡rá ❛t❡♥çã♦ ❞❡t❛❧❤❛❞❛ ♥♦ ♣ró①✐♠♦ ❝❛♣ít✉❧♦ ♣♦r s❡r ❡①t❡♥s✐✈❛♠❡♥t❡ ❡♠♣r❡❣❛❞❛ ❛♦ ❧♦♥❣♦ ❞❡st❡ tr❛❜❛❧❤♦✳ ❖s ❝❛♠♣♦s ❞❡ ❢♦rç❛ ❝♦♠✉♠❡♥t❡ ❡♠♣r❡❣❛❞♦s ❡♠ s✐♠✉❧❛çõ❡s ❞❡ ❞✐♥â♠✐❝❛ ♠♦❧❡❝✉❧❛r ♣♦❞❡♠ s❡r ✉t✐❧✐③❛❞♦s ❞✐r❡t❛♠❡♥t❡ ❝♦♠♦ ❢✉♥çõ❡s ❞❡ ❡♥❡r❣✐❛ ♣❛r❛ ❛✈❛❧✐❛r ❛ q✉❛❧✐❞❛❞❡ ❞❡ ♠♦❞❡❧♦s ❣❡r❛❞♦s ♣❛r❛ ✉♠❛ ♣r♦t❡í♥❛ ❞❡ ❡str✉t✉r❛ ❞❡s❝♦♥❤❡❝✐❞❛✱ ❡ s✐♠✉❧❛çõ❡s ❝✉rt❛s sã♦ ❡✈❡♥t✉❛❧♠❡♥t❡ ✉t✐❧✐③❛❞❛s ♣❛r❛ r❡✜♥❛r ♠♦❞❡❧♦s ❞❡ ❜❛✐①❛ r❡s♦❧✉çã♦✳ ❈♦♥t✉❞♦✱ ❛ té❝♥✐❝❛ ❛✐♥❞❛ é ♣r♦✐❜✐t✐✈❛♠❡♥t❡ ❝✉st♦s❛ ♣❛r❛ ❣❡r❛r ♠♦❞❡❧♦s ❛ ♣❛rt✐r ❞❡ ❝♦♥❢♦r♠❛çõ❡s ❛❧❡❛tór✐❛s ♦✉ ❝♦♠♣❧❡t❛♠❡♥t❡ ❡st❡♥❞✐❞❛s ✭✷✶✮✳
✷✽ ✶ ■♥tr♦❞✉çã♦
♣r❡✈✐sã♦ ❞❡ ✐♥t❡r❛çõ❡s ♣r♦t❡í♥❛✲♣r♦t❡í♥❛ ♦✉ ❛ ❛tr✐❜✉✐çã♦ ❞❡ ❛t✐✈✐❞❛❞❡ ❝❛t❛❧ít✐❝❛ ❛ ♣r♦t❡í♥❛s ❞❡ ❢✉♥çã♦ ❞❡s❝♦♥❤❡❝✐❞❛✳
❖ ♣r❡s❡♥t❡ tr❛❜❛❧❤♦ s❡❣✉❡ ❡st❡ t❡♠❛✱ ❡♠♣r❡❣❛♥❞♦ ♠♦❞❡❧♦s s✐♠♣❧✐✜❝❛❞♦s ❜❛s❡❛❞♦s ♥❛ ❚❡♦r✐❛ ❞❡ ❘❡❞❡s ❈♦♠♣❧❡①❛s ♣❛r❛ ❛✈❛❧✐❛r ♣r♦♣r✐❡❞❛❞❡s ❞❡ ♣r♦t❡í♥❛s q✉❡ ♥ã♦ sã♦ ✐♠❡❞✐❛t❛♠❡♥t❡ ❡✈✐❞❡♥t❡s ♣❡❧❛ ✐♥s♣❡çã♦ ❞❛ ❡str✉t✉r❛✳ ❖ r❡s✉❧t❛❞♦ ♠❛✐s ❡❧❡❣❛♥t❡ ♦❜t✐❞♦ ❝♦♥s✐st❡ ♥❛ ✉t✐❧✐③❛çã♦ ✐♥♦✈❛❞♦r❛ ❞❡st❛ té❝♥✐❝❛ ❞❡ ♠♦❞❡❧❛❣❡♠ ♣❛r❛ ❛ ♣r❡✈✐sã♦ ❞♦ ✢✉①♦ ❞❡ ❡♥❡r❣✐❛ ✈✐❜r❛❝✐♦♥❛❧ ❡♠ ♣r♦t❡í♥❛s✱ ❝♦♠ ♦ ♦❜❥❡t✐✈♦ ✐♥✐❝✐❛❧ ❞❡ ❛✈❛❧✐❛r ❛ s✉❛ r❡s♣♦st❛ ❛ ❛❧t❛s t❡♠♣❡r❛t✉r❛s✳ ❈♦♠ ♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s✱ ❡st❛❜❡❧❡❝❡r❡♠♦s ❡♥tã♦ ✉♠❛ ♣♦♥t❡ ❡♥tr❡ ✉♠❛ té❝♥✐❝❛ ❜❛s❡❛❞❛ ❡♠ ❢ís✐❝❛ ✭♥♦ ❝❛s♦✱ ❛ ❉✐♥â♠✐❝❛ ▼♦❧❡❝✉❧❛r✮ ❡ ❛ té❝♥✐❝❛ ❞❡ ♠♦❞❡❧❛❣❡♠ ❡♠♣r❡❣❛❞❛✱ ❜❛s❡❛❞❛ ❡♠ r❡❞✉çã♦ ❞❡ ❡s❝❛❧❛ ❡ ❛❜str❛çã♦✳ ❆ té❝♥✐❝❛ ❞❡ ♠♦❞❡❧❛❣❡♠ s❡rá ❞❡t❛❧❤❛❞❛ ♥♦ ❝❛♣ít✉❧♦ ✸✱ ♣r❡❝❡❞✐❞❛ ♣♦r ✉♠❛ ✐♥tr♦❞✉çã♦ à t❡♦r✐❛ ❞❡ r❡❞❡s ❝♦♠♣❧❡①❛s✱ ❡ ♦s r❡s✉❧t❛❞♦s ❛♣r❡s❡♥t❛❞♦s ♥♦s ❝❛♣ít✉❧♦s s✉❜s❡q✉❡♥t❡s✳
P♦r ❤♦r❛✱ ❢❡❝❤❛r❡♠♦s ❡st❡ ❝❛♣ít✉❧♦ ❛♣r❡s❡♥t❛♥❞♦ ♦ ❝♦♥❥✉♥t♦ ❞❡ ❡str✉t✉r❛s ❡①♣❡r✐♠❡♥t❛✐s q✉❡ ❢♦r❛♠ ✉s❛❞❛s ♥❛s ❛♥á❧✐s❡s s✉❜s❡q✉❡♥t❡s✳ ❆s ♣r♦t❡í♥❛s ❡st✉❞❛❞❛s✱ ①✐❧❛♥❛s❡s✱ ❢♦r❛♠ ❡s❝♦❧❤✐✲ ❞❛s ❡♠ ♣❛rt❡ ♣♦r ❝❛r❛❝t❡ríst✐❝❛s ✐♥tr✐❣❛♥t❡s ❞❡ s✉❛s ❡str✉t✉r❛s✱ ♦♣❛❝❛s à ✐♥✈❡st✐❣❛çã♦ s✉♣❡r✜❝✐❛❧ ♣♦r s❡r❡♠ ❞❡♠❛s✐❛❞♦ s❡♠❡❧❤❛♥t❡s ❡♥tr❡ s✐ ❡ ❛♦ ♠❡s♠♦ t❡♠♣♦ ❛♣r❡s❡♥t❛r❡♠ ❝♦♠♣♦rt❛♠❡♥t♦s ❢♦rt❡♠❡♥t❡ ❞✐❢❡r❡♥t❡s✱ ♣♦ré♠ ❛♠✐❣á✈❡✐s ❛♦ ❡♠♣r❡❣♦ ❞❡ té❝♥✐❝❛s ♠❛t❡♠át✐❝❛s ❡ ❝♦♠♣✉t❛❝✐♦✲ ♥❛✐s ♣♦r s❡✉ t❛♠❛♥❤♦ r❡❞✉③✐❞♦ ❡ ❣❧♦❜✉❧❛r✐❞❛❞❡ ❡ ♣❡❧❛ ❞✐s♣♦♥✐❜✐❧✐❞❛❞❡ ❞❡ ❣r❛♥❞❡ q✉❛♥t✐❞❛❞❡ ❞❡ ❞❛❞♦s ❡①♣❡r✐♠❡♥t❛✐s✳
✶✳✷ ❳✐❧❛♥❛s❡s
✶✳✷ ❳✐❧❛♥❛s❡s ✷✾
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❋✐❣✉r❛ ✶✳✹ ✕ ✭■✮ ❳✐❧♦s❡✱ ✉♠❛ ♣❡♥t♦s❡✱ ❡♠ ❝♦♥✜❣✉r❛çã♦ ❧✐♥❡❛r ✭■■✮ ❳✐❧♦s❡ ❡♠ ❝♦♥✜❣✉r❛çã♦ ❞❡ ❛♥❡❧ ✭■■■✮ ❘❡♣r❡s❡♥t❛çã♦ ❡str✉t✉r❛❧ ♣♦ssí✈❡❧ ❞♦ ①✐❧❛♥♦✱ ♣♦❧í♠❡r♦ ❤❡t❡r♦❣ê♥❡♦ ❡ r❛♠✐✜❝❛❞♦ ❞❡ ①✐❧♦s❡✳
❳✐❧❛♥❛s❡s ❝❛t❛❧✐s❛♠ ❛ ❝❧✐✈❛❣❡♠ ❞♦ ❡sq✉❡❧❡t♦ β✲✶✱✹ ❡♠ ①✐❧❛♥♦s✱ ❧✐❜❡r❛♥❞♦ ♣❡q✉❡♥♦s ❢r❛❣✲
♠❡♥t♦s ❞❡ ❝♦♠♣♦s✐çã♦ ❤❡t❡r♦❣ê♥❡❛ ❞❡♥♦♠✐♥❛❞♦s ①✐❧♦✲♦❧✐❣ô♠❡r♦s✳ ❆ ❤✐❞ró❧✐s❡ ❝♦♠♣❧❡t❛ ❞❡ ①✐❧❛♥♦s ❞❡♣❡♥❞❡ ❞❡ ✉♠❛ ✈❛r✐❡❞❛❞❡ ❞❡ ❡♥③✐♠❛s✱ ❞❡✈✐❞♦ à s✉❛ ❝♦♠♣❧❡①✐❞❛❞❡✱ ❡ s✐st❡♠❛s ①✐❧❛♥♦❧í✲ t✐❝♦s ❝♦♠♣❧❡t♦s sã♦ t✐♣✐❝❛♠❡♥t❡ ❡♥❝♦♥tr❛❞♦s ❡♠ ♠✐❝r♦✲♦r❣❛♥✐s♠♦s q✉❡ ❞❡❝♦♠♣õ❡♠ ♠❛t❡r✐❛❧ ✈❡❣❡t❛❧ ✭✷✼✮✳
❖ t❡r♠♦ ①✐❧❛♥❛s❡✱ ♣♦r s✐✱ ✐♠♣❧✐❝❛ tã♦ s♦♠❡♥t❡ ❛t✐✈✐❞❛❞❡ ❝❛t❛❧ít✐❝❛ ❡♠ r❡❧❛çã♦ ❛♦ s✉❜str❛t♦ ①✐❧❛♥♦❀ ❝♦♥t✉❞♦✱ ❡st❛ ❝❛♣❛❝✐❞❛❞❡ é ❞❡♠♦♥str❛❞❛ ♣♦r ✉♠ ❣r❛♥❞❡ ♥ú♠❡r♦ ❞❡ ❡♥③✐♠❛s✱ às q✉❛✐s ❡stá ❛ss♦❝✐❛❞♦ ✉♠ ♥ú♠❡r♦ s✐❣♥✐✜❝❛t✐✈♦ ❞❡ t✐♣♦s ❞❡ ❡♥♦✈❡❧❛♠❡♥t♦ ❞✐❢❡r❡♥t❡s✱ ❜❡♠ ❝♦♠♦ ✉♠ ♥ú♠❡r♦ s✐❣♥✐✜❝❛t✐✈♦ ❞❡ ♠❡❝❛♥✐s♠♦s ❞❡ ❛t✉❛çã♦ ❞✐❢❡r❡♥t❡s✳ ❖ ❡st✉❞♦ ❞❛s ①✐❧❛♥❛s❡s✱ ❡♥tã♦✱ ♣❛ss❛ ♥❡❝❡ss❛r✐❛♠❡♥t❡ ♣♦r ✉♠❛ ❡t❛♣❛ ❞❡ ❝❧❛ss✐✜❝❛çã♦✳
❆ ❝❧✐✈❛❣❡♠ ❞♦ ①✐❧❛♥♦ é ❛ q✉❡❜r❛ ❞❡ ✉♠❛ ❧✐❣❛çã♦ ❣❧✐❝♦sí❞✐❝❛ ♣♦r ✐♥tr♦❞✉çã♦ ❞❡ ✉♠❛ ♠♦❧é❝✉❧❛ ❞❡ ❍2❖✳ ❳✐❧❛♥❛s❡s✱ sã♦✱ ♣♦rt❛♥t♦✱ ❣❧✐❝♦s✐❧✲❤✐❞r♦❧❛s❡s✳ ❙❡❣✉♥❞♦ ♦ s✐st❡♠❛ ♥✉♠ér✐❝♦ ❊❈ ❞❡
❝❧❛ss✐✜❝❛çã♦ ❞❡ ❡♥③✐♠❛s✱ ❜❛s❡❛❞♦ ♥♦ t✐♣♦ ❞❡ r❡❛çã♦ ❝❛t❛❧✐s❛❞❛✱ ♦ ❣r✉♣♦ ❞❛s ❣❧✐❝♦s✐❧ ❤✐❞r♦❧❛s❡s ✭❊❈ ✸✳✷✳✶✳①✮ q✉❡ ❛t✉❛ ♥❛ ❡♥❞♦❤✐❞ró❧✐s❡ ❞❡ ❧✐❣❛çõ❡s ✶✱✹✲β✲❉✲①✐❧♦sí❞✐❝❛s ❡♠ ①✐❧❛♥♦s é ♦ ❣r✉♣♦
✸✵ ✶ ■♥tr♦❞✉çã♦
❤✐❞r♦❧❛s❡s✱ ❞❛s q✉❛✐s s❡✐s ❝♦♥té♠ ❡♥③✐♠❛s ❝♦♠ ❛t✐✈✐❞❛❞❡ ①✐❧❛♥♦❧ít✐❝❛ ✭✷✼✮✳ ❉❡st❛s s❡✐s✱ ❞✉❛s sã♦ ♠❛❥♦r✐t❛r✐❛♠❡♥t❡ r❡❧❡✈❛♥t❡s✿ ❛ ❢❛♠í❧✐❛ ✶✵ ❡ ❛ ❢❛♠í❧✐❛ ✶✶✳
❙❡❣✉♥❞♦ ❈♦❧❧✐♥s ❡t ❛❧✳ ❡♠ ✭✷✼✮✱ ✏❬❆ ❢❛♠í❧✐❛ ✶✵❪ ❝♦♥s✐st❡ ❞❡ ❡♥❞♦✲✶✱✹✲β✲①✐❧❛♥❛s❡s ✭❊❈
✸✳✷✳✶✳✽✮✱ ❡♥❞♦✲✶✱✸✲β✲①✐❧❛♥❛s❡s ✭❊❈ ✸✳✷✳✶✳✸✷✮ ❡ ❝❡❧♦❜✐♦❤✐❞r♦❧❛s❡s ✭❊❈ ✸✳✷✳✶✳✾✶✮ ❬✳✳✳❪ ▼❡♠❜r♦s
❞❡st❛ ❢❛♠í❧✐❛ t✐♣✐❝❛♠❡♥t❡ t❡♠ ❣r❛♥❞❡ ♠❛ss❛ ♠♦❧❡❝✉❧❛r✱ ❜❛✐①♦ ♣♦♥t♦ ✐s♦❡❧étr✐❝♦ ❡ ❛♣r❡s❡♥t❛♠ ✉♠ ❡♥♦✈❡❧❛♠❡♥t♦ ❞♦ t✐♣♦ ❜❛rr✐❧ (α/β)8✑✳ ❊♠ ✭✷✾✮✱ r❡♣♦rt❛✲s❡ ♣❛r❛ ❛ ❢❛♠í❧✐❛ ✶✵ ✉♠ t❛♠❛♥❤♦
♠é❞✐♦ ❞❡ ✸✶✻ ❛♠✐♥♦á❝✐❞♦s✱ ❝♦♠ ✉♠ ♣❡r❝❡♥t✉❛❧ ❞❡ ✐❞❡♥t✐❞❛❞❡ ♠é❞✐♦ ❞❡ ✹✸✪✱ r❡s✉❧t❛♥❞♦ ❡♠ ✉♠❛ ♠❛ss❛ ♠♦❧❡❝✉❧❛r ♠é❞✐❛ ❡♠ t♦r♥♦ ❞❡ ✸✺ ❑❉❛✳
❍á ❡✈✐❞ê♥❝✐❛s ❞❡ q✉❡ ❛s ①✐❧❛♥❛s❡s ❞❡st❛ ❢❛♠í❧✐❛ ❛♣r❡s❡♥t❛♠ ❛t✐✈✐❞❛❞❡ ❝❛t❛❧ít✐❝❛ t❛♠❜é♠ ❡♠ s✉❜str❛t♦s ❝❡❧✉❧ós✐❝♦s ♣❡q✉❡♥♦s✳ ❊♠ ❝♦♥tr❛st❡✱ ❛ ❢❛♠í❧✐❛ ✶✶ é ❝❛r❛❝t❡r✐③❛❞❛ ♣❡❧❛ ❛❧t❛ ❡s♣❡❝✐✜❝✐❞❛❞❡ ❡ ♣❡❧♦ ❡♥♦✈❡❧❛♠❡♥t♦ ❞♦ t✐♣♦ β✲❥❡❧❧②✲r♦❧❧✱ ❝♦♠ ❜❛✐①♦ ♣❡s♦ ♠♦❧❡❝✉❧❛r❀ r❡♣♦rt❛✲s❡
♣❛r❛ ❛ ♠❡s♠❛ ❡♠ ✭✷✾✮ ✉♠ t❛♠❛♥❤♦ ♠é❞✐♦ ❞❡ ✶✽✺ ❛♠✐♥♦á❝✐❞♦s ❡ ✉♠ ♣❡r❝❡♥t✉❛❧ ❞❡ ✐❞❡♥t✐❞❛❞❡ ♠é❞✐♦ ❞❡ ✺✵✪✱ ❝♦♠ ♠❛ss❛ ♠♦❧❡❝✉❧❛r ♠é❞✐❛ ❞❡ ✷✶ ❑❉❛✳ ❯♠ ❡①❡♠♣❧❛r ❞❡st❛ ❢❛♠í❧✐❛ ♣♦❞❡ s❡r ❡♥❝♦♥tr❛❞♦ ♥❛ ✜❣✉r❛ ✶✳✺✳ ❉✐s❝♦rr❡r❡♠♦s ❜r❡✈❡♠❡♥t❡ s♦❜r❡ ❡ss❡ t✐♣♦ ❞❡ ❡♥♦✈❡❧❛♠❡♥t♦ ❡ s♦❜r❡ ❛s r❛③õ❡s ✐♥tr✐❣❛♥t❡s ♣❡❧❛s q✉❛✐s ❛s ①✐❧❛♥❛s❡s ❞❛ ❢❛♠í❧✐❛ ✶✶ sã♦ ♦s ❛❧✈♦s ❞❡st❡ tr❛❜❛❧❤♦ ❛ s❡❣✉✐r✳
Dedão
Palma
Hélice
Dedos
❋✐❣✉r❛ ✶✳✺ ✕ ❱✐sõ❡s ❞❡ ✉♠❛ ①✐❧❛♥❛s❡ ❞❛ ❢❛♠í❧✐❛ ✶✶✳ ➱ ♣♦ssí✈❡❧ ✈✐s✉❛❧✐③❛r ♦ ♣❛r ❞❡ ✜t❛s ❜❡t❛ ❛ss♦❝✐❛❞♦s ❛♦ ✏❞❡❞ã♦✑✱ ❝✉❥♦ ✈♦❧t❛ ❝♦♥té♠ ✉♠ r❡sí❞✉♦ ❣❧✉t❛♠❛t♦ q✉❡ ♣❛rt✐❝✐♣❛ ❞♦ sít✐♦ ❝❛t❛❧ít✐❝♦✱ ❡ ♦ ♣❛r ❞❡ ❢♦❧❤❛s ❜❡t❛ ❞♦❜r❛❞♦ s♦❜r❡ s✐ ♠❡s♠♦ ❛ss♦❝✐❛❞♦ ❛♦s ✏❞❡❞♦s✑ ❡ à ✏♣❛❧♠❛✑ ❞❛ ♠ã♦✱ q✉❡ ❝♦rr❡s♣♦♥❞❡ ❛♦ ♥ú❝❧❡♦ ❤✐❞r♦❢ó❜✐❝♦✳ ❋✐❣✉r❛s ❣❡r❛❞❛s ❝♦♠ ♦ ♣r♦❣r❛♠❛ ❱▼❉ ✭✶✱ ✼✮✳
❖ ❡♥♦✈❡❧❛♠❡♥t♦ ❞♦ t✐♣♦β✲❥❡❧❧②✲r♦❧❧ é ✉♠ ❡♥♦✈❡❧❛♠❡♥t♦ ♣r❡❞♦♠✐♥❛♥t❡♠❡♥t❡ ❝♦♠♣♦st♦ ♣♦r
