Marques
Licenciatura em Matemática
Relatório de Estágio
Dissertação para obtenção do Grau de Mestre em Ensino de Matemática no 3.º ciclo do Ensino Básico e no
Secundário
Orientadora: Professora Doutora Helena Rocha,
Professora Auxiliar, Faculdade de Ciências e Tecnologia
da Universidade Nova de Lisboa
Co-orientadora: Licenciada Rosário Lopes,
Professora, Escola Secundária com 3.º ciclo do Ensino
Básico António Gedeão
Júri: Junho 2014
Presidente: Professora Doutora Maria Helena Coutinho Gomes de Almeida Santos Arguente: Professor Doutor Filipe José Gonçalves Pereira Marques
❈♦♣②r✐❣❤t✿ ❏♦sé ❈❛r❧♦s ❞❛ ❙✐❧✈❛ ❘❛♥❣❡❧ ❞❡ ❆❧♠❡✐❞❛ ▼❛rq✉❡s✱ ❋❈❚✴❯◆▲✱ ❯◆▲
❆ ❋❛❝✉❧❞❛❞❡ ❞❡ ❈✐❡♥❝✐❛s ❡ ❚❡❝♥♦❧♦❣✐❛ ❡ ❛ ❯♥✐✈❡rs✐❞❛❞❡ ◆♦✈❛ ❞❡ ▲✐s❜♦❛ té♠ ♦ ❞✐r❡✐t♦✱ ♣❡r♣ét✉♦ ❡ s❡♠ ❧✐♠✐t❡s ❣❡♦❣rá✜❝♦s✱ ❞❡ ❛rq✉✐✈❛r ❡ ♣✉❜❧✐❝❛r ❡st❛ ❞✐ss❡rt❛çã♦ ❛tr❛✈és ❞❡ ❡①❡♠♣❧❛r❡s ✐♠♣r❡ss♦s r❡♣r♦❞✉③✐❞♦s ❡♠ ♣❛♣❡❧ ♦✉ ❞❡ ❢♦r♠❛ ❞✐❣✐t❛❧✱ ♦✉ ♣♦r q✉❛❧q✉❡r ♦✉tr♦ ♠❡✐♦ ❝♦♥❤❡❝✐❞♦ ♦✉ q✉❡ ✈❡♥❤❛ ❛ s❡r ✐♥✈❡♥t❛❞♦✱ ❡ ❞❡ ❛ ❞✐✈✉❧❣❛r ❛tr❛✈❡s ❞❡ r❡♣♦s✐tôr✐♦s ❝✐❡♥t✐✜❝♦s ❡ ❞❡ ❛❞♠✐t✐r ❛ s✉❛ ❝ô♣✐❛ ❡ ❞✐st♥✐❜✉✐ç❛♦ ❝♦♠ ♦❜❥❡❝t✐✈♦s ❡❞✉❝❛❝✐♦♥❛✐s ♦✉ ❞❡ ✐♥✈❡st✐❣❛❝❛♦✱ ♥ã♦ ❝♦♠❡r❝✐❛✐s✱ ❞❡s❞❡ q✉❡ s❡❥❛ ❞❛❞♦ ❝ré❞✐t♦ ❛♦ ❛✉t♦r ❡ ❡❞✐t♦r
r✐✈❛❞❛s❀ ●❡♦♠❡tr✐❛❀ Pr♦❜❧❡♠❛s❀ ❉✐✜❝✉❧❞❛❞❡s
❆ ♣r❡s❡♥t❡ ❞✐ss❡rt❛çã♦ ❡stá ❞✐✈✐❞✐❞❛ ❡♠ ❞✉❛s ♣❛rt❡s✿ ❛ ♣r✐♠❡✐r❛ r❡✲ ❢❡r❡♥t❡ ❛♦ r❡❧❛tór✐♦ ❞❡ ❡stá❣✐♦ ❛ s❡❣✉♥❞❛ ❛♦ tr❛❜❛❧❤♦ ❞❡ ✐♥✈❡st✐❣❛çã♦ ♥❛ ♣rát✐❝❛ ♣❡❞❛❣ó❣✐❝❛✳
❖ r❡❧❛tór✐♦ ❞❡ ❡stá❣✐♦ ❡♥❝♦♥tr❛✲s❡ ❞✐✈✐❞✐❞♦ ❡♠ ❝✐♥❝♦ s❡❝çõ❡s✿ ■♥tr♦✲ ❞✉çã♦✱ ❆❣r✉♣❛♠❡♥t♦ ❞❡ ❊s❝♦❧❛s ❆♥tó♥✐♦ ●❡❞❡ã♦✱ ❆ ❡s❝♦❧❛ ❞❡ ❡stá❣✐♦✱ Prát✐❝❛ P❡❞❛❣ó❣✐❝❛ ❡ ❘❡✢❡①ã♦ ❈rít✐❝❛✳ ◆❡st❛ ♣❛rt❡ ❝❛r❛❝t❡r✐③♦✉✲s❡ ✜s✐❝❛♠❡♥t❡ ♦ ❆❣r✉♣❛♠❡♥t♦ ❞❡ ❡s❝♦❧❛s ❆♥tó♥✐♦ ●❡❞❡ã♦ ❡ ♦s ❛❧✉♥♦s✱ ❝❛r❛❝t❡r✐③♦✉✲s❡ ♦ ❧♦❝❛❧ ❡ ❛ t✉r♠❛ ❞❡ ❡stá❣✐♦✱ r❡s✉♠✐✉✲s❡ ♦ tr❛❜❛❧❤♦ ❞❡✲ s❡♥✈♦❧✈✐❞♦ ♣❡❧♦ ❡st❛❣✐ár✐♦ ♥❛ ❡s❝♦❧❛ ❞❡ ❡stá❣✐♦ ❡✱ ♣♦r ✜♠✱ ❢♦✐ ❢❡✐t♦ ✉♠❛ r❡✢❡①ã♦ ❝rít✐❝❛ ❞♦ tr❛❜❛❧❤♦✳
❖ tr❛❜❛❧❤♦ ❞❡ ✐♥✈❡st✐❣❛çã♦ ♥❛ ♣rát✐❝❛ ♣❡❞❛❣ó❣✐❝❛✱ ❛ s❡❣✉♥❞❛ ♣❛rt❡ ❞❡st❡ tr❛❜❛❧❤♦✱ ❡♥❝♦♥tr❛✲s❡ ❞✐✈✐❞✐❞♦ ❡♠ ✺ s❡❝çõ❡s✿ ■♥tr♦❞✉çã♦✱ ❘❡✈✐✲ sã♦ ❞❡ ❧✐t❡r❛t✉r❛✱ ▼❡t♦❞♦❧♦❣✐❛✱ ❆♥á❧✐s❡ ❞❡ ❞❛❞♦s ❡ ❈♦♥❝❧✉sã♦✳
❈♦♠ ❡st❡ ♣r♦❥❡t♦ ♣r❡t❡♥❞❡✉✲s❡ ♣❡r❝❡❜❡r ❝♦♠♦ é q✉❡ ♦s ❛❧✉♥♦s ❢❛③❡♠ ❝♦♥❡①õ❡s ♠❛t❡♠át✐❝❛s✳ ❈♦♠ ❡ss❡ ✐♥t✉✐t♦ ❛♥❛❧✐s♦✉✲s❡ ❝♦♠♦ é q✉❡ q✉❛✲ tr♦ ❛❧✉♥♦s✱ ❞❡ ✉♠❛ t✉r♠❛ ❞♦ ✶✷✳➸ ❛♥♦✱ r❡s♦❧✈✐❛♠ ❞♦✐s ♣r♦❜❧❡♠❛s ❡♥✈♦❧✲ ✈❡♥❞♦ ❝♦♥❡①õ❡s ❡♥tr❡ ♦s t❡♠❛s ❞❛ ❣❡♦♠❡tr✐❛ ❡ ❞❛s ❞❡r✐✈❛❞❛s✳ ❆♥❛❧✐s♦✉✲ s❡ ♦ ♠ét♦❞♦ ❞❡ r❡s♦❧✉çã♦ ❞♦ ♣r♦❜❧❡♠❛✱ ❡♠ q✉❡ ❢❛s❡ é q✉❡ s✉r❣❡♠ ❛s ❝♦♥❡①õ❡s ♥❛ r❡s♦❧✉çã♦ ❞♦s ♣r♦❜❧❡♠❛s ❡ ❛s ♣r✐♥❝✐♣❛✐s ❞✐✜❝✉❧❞❛❞❡s s❡♥✲ t✐❞❛s ♣❡❧♦s ❛❧✉♥♦s✳
❈♦♠ ❡st❡ ❡st✉❞♦✱ ❝♦♥❝❧✉✐✉✲s❡ q✉❡ ♦s ❛❧✉♥♦s q✉❡ tê♠ ♦ ❝♦♥❝❡✐t♦ ❞❡ ❞❡r✐✈❛❞❛ ✐♥t❡r✐♦r✐③❛❞♦ ❝♦♥s❡❣✉❡♠ ❢❛③❡r✱ ❝♦♠ ❛❧❣✉♠ ❛✉①í❧✐♦✱ ❛ ❝♦♥❡①ã♦ ❞❡♥tr♦ ❞❡st❡ t❡♠❛✱ ♣♦ré♠ t♦❞♦s ♦s ❛❧✉♥♦s s❡♥t✐r❛♠ ❞✐✜❝✉❧❞❛❞❡s ❡♠ ❢❛③❡r ❛ ❝♦♥❡①ã♦ ❡♥tr❡ ❞✐✈❡rs♦s t❡♠❛s✳ ❚♦❞♦s ♦s ❛❧✉♥♦s r❡s♦❧✈❡♠ ♦s ♣r♦❜❧❡♠❛s ♣❛ss❛♥❞♦ ♣♦r ❞✉❛s ❢❛s❡s✱ ❛ ❝♦♠♣r❡❡♥sã♦ ❞♦ ♣r♦❜❧❡♠❛ ❡ ❛ ❡❧❛❜♦r❛çã♦ ❡ ❡①❡❝✉çã♦ ❞♦ ♣❧❛♥♦ ❞❡ r❡s♦❧✉çã♦ ❞♦ ♣r♦❜❧❡♠❛✱ s❡♥❞♦ q✉❡ ❛s ❝♦♥❡①õ❡s s✉r❣✐r❛♠ s❡♠♣r❡ ♥❡st❛ s❡❣✉♥❞❛ ❢❛s❡✳
●❡♦♠❡tr②❀ Pr♦❜❧❡♠s❀ ❉✐✣❝✉❧t✐❡s
❚❤❡ ♣r❡s❡♥t ❞✐ss❡rt✐♦♥ ✐s ❞✐✈✐❞❡❞ ✐♥ t✇♦ ♣❛rts✿ t❤❡ ✜rst ♦♥❡ r❡❢❡rs t♦ t❤❡ t❡❛❝❤❡r tr❛✐♥✐♥❣ r❡♣♦rt ❛♥❞ t❤❡ s❡❝♦♥❞ ♦♥❡ r❡❢❡rs t♦ t❤❡ ❡❞✉❝❛t✐♦♥❛❧ ♣r❛❝t✐❝❡ ✐♥✈❡st✐❣❛t✐♦♥ ✇♦r❦✳
❚❤❡ t❡❛❝❤❡r tr❛✐♥✐♥❣ r❡♣♦rt ✐s ❞✐✈✐❞❡❞ ✐♥ ✜✈❡ s❡❝t✐♦♥s✿ ■♥tr♦❞✉❝✲ t✐♦♥✱ ❆♥tó♥✐♦ ●❡❞❡ã♦ s❝❤♦♦❧ ❣r♦✉♣✐♥❣✱ ❚❤❡ t❡❛❝❤❡r tr❛✐♥✐♥❣ s❝❤♦♦❧✱ P❡❞❛❣♦❣✐❝❛❧ Pr❛❝t✐❝❡ ❛♥❞ ❈r✐t✐❝❛❧ ❘❡✢❡❝t✐♦♥✳ ■t ✇❛s ♠❛❞❡ ❛ ♣❤②s✐❝❛❧ ❝❤❛r❛❝t❡r✐③❛t✐♦♥ ♦❢ ❆♥tó♥✐♦ ●❡❞❡ã♦ s❝❤♦♦❧ ❣r♦✉♣✐♥❣ ❛♥❞ ♦❢ t❤❡ st✉✲ ❞❡♥ts✳ ❆❧s♦✱ ✐t ✇❛s ♠❛❞❡ ❛ ♣❤②s✐❝❛❧ ❝❤❛r❛❝t❡r✐③❛t✐♦♥ ♦❢ t❤❡ ❆♥tó♥✐♦ ●❡❞❡ã♦ s❝❤♦♦❧ ❛♥❞ ❛♥ ❛♣r❡s❡♥t❛t✐♦♥ ♦❢ t❤❡ ❝❧❛ss st✉❞❡♥t✬s t❤❛t ❤❛✈❡ ❜❡❡♥ ❛❝❝♦♠♣❛♥✐❡❞ ✐♥ t❤❡ t❡❛❝❤❡r tr❛✐♥✐♥❣✱ ❛♥❞ ❛ r❡♣♦rt ♦❢ ✇♦r❦ ❞♦♥❡✳ ❋✐♥❛❧❧②✱ ✇❛s ❞♦♥❡ ❛ ❝r✐t✐❝❛❧ r❡✢❡❝t✐♦♥ ♦❢ t❤❡ ✇♦r❦ ❞❡✈❡❧♦♣❡❞✳
❚❤❡ ✇♦r❦ ♦❢ ❡❞✉❝❛t✐♦♥❛❧ ♣r❛❝t✐❝❡ ✐♥✈❡st✐❣❛t✐♦♥ ✇♦r❦✱ t❤❡ s❡❝♦♥❞ ♣❛rt✱ ✐s ❞✐✈✐❞❡❞ ✐♥ ✜✈❡ s❡❝t✐♦♥s✿ ■♥tr♦❞✉❝t✐♦♥✱ ▲✐t❡r❛t✉r❡ r❡✈✐❡✇✱ ▼❡t❤♦❞✲ ♦❧♦❣②✱ ❆♥❛❧②s✐s ♦❢ ❞❛t❡s ❛♥❞ ❈♦♥❝❧✉s✐♦♥✳
❚❤❡ ❛✐♠ ♦❢ t❤✐s ✇♦r❦ ✐s t♦ ✉♥❞❡rst❛♥❞ ❤♦✇ st✉❞❡♥ts ❞♦ ♠❛t❤❡♠❛t✐❝ ❝♦♥♥❡❝t✐♦♥s✱ ❛♥❞ ❢♦r t❤❛t ■ ❛♥❛❧②s❡❞ ❤♦✇ ❢♦✉r st✉❞❡♥ts✱ ♦❢ ❛ ❝❧❛ss ♦❢ 12th❣r❛❞❡✱ s♦❧✈❡ t✇♦ ♣r♦❜❧❡♠s ✐♥✈♦❧✈✐♥❣ ❝♦♥♥❡❝t✐♦♥s ❜❡t✇❡❡♥ ❣❡♦♠❡✲ tr② ❛♥❞ ❞❡r✐✈❛t✐✈❡s✳ ■t ✇❛s ❛♥❛❧②③❡❞ t❤❡ ♠❡t❤♦❞ ♦❢ ♣r♦❜❧❡♠ s♦❧✈✐♥❣✱ ✇❤✐❝❤ ❛r❡ t❤❡ ♣❤❛s❡ ✇❤❡r❡ ❝♦♥♥❡❝t✐♦♥s ❛♣♣❡❛rs ❛♥❞ ❝♦rr❡s♣♦♥❞s t♦ t❤❡ ♠❛❥♦r st✉❞❡♥t✬s ❞✐✣❝✉❧t✐❡s✳
■♥ t❤✐s ✇♦r❦✱ ■ ❤❛✈❡ ❝♦♥❝❧✉❞❡❞ t❤❛t st✉❞❡♥ts ✇✐t❤ t❤❡ ❝♦♥❝❡♣t ♦❢ ❞❡r✐✈❛✲ t✐✈❡s ✐♥t❡r✐♦r✐③❡❞ ❝❛♥ ❞♦ ❝♦♥♥❡❝t✐♦♥s ✇✐t❤✐♥ ❛ t❤❡♠❡✱ ✇✐t❤ s♦♠❡ ❤❡❧♣✱ ❜✉t ❛❧❧ st✉❞❡♥ts ❤❛✈❡ ❞✐✣❝✉❧t✐❡s ❞♦✐♥❣ ❝♦♥♥❡❝t✐♦♥s ❜❡t✇❡❡♥ ✈❛r✐♦✉s t❤❡♠❡s✳ ❆❧❧ st✉❞❡♥ts s♦❧✈❡ ♣r♦❜❧❡♠s t❤r♦✉❣❤ t✇♦ ♣❤❛s❡s✱ t❤❡ ✜rst ❝♦♠♣r✐s✐♥❣ t❤❡ ♣r♦❜❧❡♠ ❝♦♠♣r❡❤❡♥s✐♦♥ ❛♥❞ t❤❡ s❡❝♦♥❞ ❡♥✈♦❧✈✐♥❣ t❤❡ ❡st❛❜❧✐s❤✐♥❣ ❛♥❞ ❡①❡❝✉t✐♦♥ ♦❢ t❤❡ ♣❧❛♥✳ ■t ✇❛s ♦❜s❡r✈❡❞ t❤❛t ❝♦♥♥❡❝✲ t✐♦♥s ❛♣♣❡❛rs ❛❧✇❛②s ✐♥ t❤❡ s❡❝♦♥❞ ♣❤❛s❡✳
❞✐s♣♦♥✐❜✐❧✐❞❛❞❡ q✉❡ ❝♦♥st❛♥t❡♠❡♥t❡ ❞❡♠♦♥str♦✉✱ ❡ ♣❡❧♦ r✐❣♦r ❡ ❝❛♣❛❝✐❞❛❞❡ ♦r✐❡♥t❛❞♦r❛ ✉♠ ♠✉✐t♦ ♦❜r✐❣❛❞♦✳ ❆♦s ♣r♦❢❡ss♦r❡s ❞♦✉t♦r❡s ❆♥tó♥✐♦ ❉♦♠✐♥❣♦s ❡ ❍❡❧❡♥❛ ❘♦❝❤❛✱ ❖r✐❡♥t❛❞♦r❡s ❈✐❡♥tí✜❝♦s✱ ♣❡❧❛ ❝rít✐❝❛ ❡ ♦r✐❡♥t❛çã♦ ❞❛❞❛ ❛♦ ❧♦♥❣♦ ❞♦ tr❛❜❛❧❤♦ ❞❡ ✐♥✈❡st✐❣❛çã♦✳
❆♦s ♣r♦❢❡ss♦r❡s ❞♦✉t♦r❡s ❋✐❧✐♣❡ ▼❛rq✉❡s ❡ ▼❛r✐❛ ❍❡❧❡♥❛ ❙❛♥t♦s ♣❡❧♦s ❝♦♥s❡✲ ❧❤♦s ❡ ❝♦♠❡♥tár✐♦s q✉❡ ♠❡ ❛❥✉❞❛r❛♠ ❛ ♠❡❧❤♦r❛r ♦ ♠❡✉ ❞❡s❡♠♣❡♥❤♦✳ ❆♦s ❛❧✉♥♦s ❛♥ó♥✐♠♦s q✉❡ ♣❛rt✐❝✐♣❛r❛♠ ❡♠ t♦❞♦ ❡st❡ tr❛❜❛❧❤♦✳
➚s ♣❡ss♦❛s q✉❡ ❞✐s♣❡♥s❛r❛♠ ♦ s❡✉ t❡♠♣♦ ❛ ❧❡r ❡ ❛ ❞❛r s✉❣❡stõ❡s ♣❛r❛ ❛ ♠❡❧❤♦r✐❛ ❞♦ ♣r❡s❡♥t❡ tr❛❜❛❧❤♦✱ ✉♠ ♠✉✐t♦ ♦❜r✐❣❛❞♦✳
■ ❘❡❧❛tór✐♦ ❞❡ ❊stá❣✐♦ ✶
✶ ■♥tr♦❞✉çã♦ ✹
✷ ❆❣r✉♣❛♠❡♥t♦ ❞❡ ❊s❝♦❧❛s ❆♥tó♥✐♦ ●❡❞❡ã♦ ✺
✸ ❆ ❡s❝♦❧❛ ❞❡ ❡stá❣✐♦ ✶✸
✹ Prát✐❝❛ P❡❞❛❣ó❣✐❝❛ ✶✽
✺ ❘❡✢❡①ã♦ ❈rít✐❝❛ ✸✼
■■ ❈♦♥❡①õ❡s ▼❛t❡♠át✐❝❛s ❡♥tr❡ ●❡♦♠❡tr✐❛ ❡ ❉❡r✐✈❛❞❛s ✲
❊st✉❞♦ ❞❡ ❈❛s♦ ✹✵
✶ ■♥tr♦❞✉çã♦ ✹✻
✷ ❘❡✈✐sã♦ ❞❡ ▲✐t❡r❛t✉r❛ ✺✵
✸ ▼❡t♦❞♦❧♦❣✐❛ ✻✻
✹ ❆♥á❧✐s❡ ❞❡ ❞❛❞♦s ✼✹
✺ ❈♦♥❝❧✉sã♦ ✶✷✵
❘❡❢❡rê♥❝✐❛s ✶✷✸
✻ ❆♥❡①♦ ✶ ✶✷✼
✼ ❆♥❡①♦ ✷ ✶✷✽
■ ❘❡❧❛tór✐♦ ❞❡ ❊stá❣✐♦ ✶
✶ ■♥tr♦❞✉çã♦ ✹
✷ ❆❣r✉♣❛♠❡♥t♦ ❞❡ ❊s❝♦❧❛s ❆♥tó♥✐♦ ●❡❞❡ã♦ ✺
✷✳✶ ❈❛r❛❝t❡r✐③❛çã♦ ❋ís✐❝❛ ❞♦ ❆❣r✉♣❛♠❡♥t♦ ❞❡ ❡s❝♦❧❛s ❆♥tó♥✐♦ ●❡✲ ❞❡ã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺ ✷✳✶✳✶ ❊s❝♦❧❛ ❇ás✐❝❛ ✶✳➸ ❝✐❝❧♦ ❡ ❏❛r❞✐♠ ❞❡ ■♥❢â♥❝✐❛ ❞♦ ▲❛r❛♥✲
❥❡✐r♦ ♥✳➸ ✸ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻ ✷✳✶✳✷ ❊s❝♦❧❛ ❇ás✐❝❛ ✶✳➸ ❝✐❝❧♦ ❞♦ ❆❧❢❡✐t❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼ ✷✳✶✳✸ ❊s❝♦❧❛ ❇ás✐❝❛ ✶✳➸ ❝✐❝❧♦ ❈♦✈❛ ❞❛ P✐❡❞❛❞❡ ♥✳➸ ✶ ✳ ✳ ✳ ✳ ✳ ✽ ✷✳✶✳✹ ❊s❝♦❧❛ ❇ás✐❝❛ ✶✳➸ ❝✐❝❧♦ ❈♦✈❛ ❞❛ P✐❡❞❛❞❡ ♥✳➸ ✷ ✳ ✳ ✳ ✳ ✳ ✾ ✷✳✶✳✺ ❊s❝♦❧❛ ❇ás✐❝❛ ✷✳➸ ❡ ✸✳➸ ❝✐❝❧♦ ❈♦♠❛♥❞❛♥t❡ ❈♦♥❝❡✐çã♦ ❡
❙✐❧✈❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵ ✷✳✶✳✻ ❊s❝♦❧❛ ❙❡❝✉♥❞ár✐❛ ❝♦♠ ✸✳➸ ❝✐❝❧♦ ❞♦ ❊♥s✐♥♦ ❇ás✐❝♦ ❞❡
❆♥tó♥✐♦ ●❡❞❡ã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶ ✷✳✷ ❈❛r❛❝t❡r✐③❛çã♦ ❞♦s ❛❧✉♥♦s ❞♦ ❆❣r✉♣❛♠❡♥t♦ ❞❡ ❊s❝♦❧❛s ❆♥tó✲
♥✐♦ ●❡❞❡ã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶
✸ ❆ ❡s❝♦❧❛ ❞❡ ❡stá❣✐♦ ✶✸
✸✳✶ ❈❛r❛❝t❡r✐③❛çã♦ ❋ís✐❝❛ ❞❛ ❊s❝♦❧❛ ❙❡❝✉♥❞ár✐❛ ❝✴ ✸✳➸ ❝✐❝❧♦ ❞♦ ❊♥s✐♥♦ ❇ás✐❝♦ ❞❡ ❆♥tó♥✐♦ ●❡❞❡ã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸ ✸✳✷ ❆ t✉r♠❛ ❞♦ ✶✷✳➸ ❳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹ ✸✳✷✳✶ ❈❛r❛❝t❡r✐③❛çã♦ ❞❛ t✉r♠❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹
✹ Prát✐❝❛ P❡❞❛❣ó❣✐❝❛ ✶✾
✹✳✻ ❆✉❧❛s ❞❡ ❛♣♦✐♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✹✳✼ ❆t✐✈✐❞❛❞❡ ❡①tr❛❝✉rr✐❝✉❧❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼
✶ ■♥tr♦❞✉çã♦
❖ ♣r❡s❡♥t❡ r❡❧❛tór✐♦ ❞❡ ❡stá❣✐♦ ❢♦✐ ❡❧❛❜♦r❛❞♦ ❝♦♠♦ tr❛❜❛❧❤♦ ✜♥❛❧ ❞❛ ❝❛❞❡✐r❛ ❊stá❣✐♦ ❖r✐❡♥t❛❞♦✱ ✐♥t❡❣r❛❞❛ ♥♦ ♣❧❛♥♦ ❞❡ ❡st✉❞♦s ❞♦ ▼❡str❛❞♦ ❡♠ ❊♥s✐♥♦ ❞❛ ▼❛t❡♠át✐❝❛ ❞♦s ❡♥s✐♥♦s ❜ás✐❝♦ ❡ s❡❝✉♥❞ár✐♦✳
❖ ❡stá❣✐♦ ♦r✐❡♥t❛❞♦ ❞❡❝♦rr❡✉ ♥❛ ❡s❝♦❧❛ ❙❡❝✉♥❞ár✐❛ ❝♦♠ ✸➸ ❝✐❝❧♦ ❞♦ ❊♥s✐♥♦ ❇ás✐❝♦ ❞❡ ❆♥tó♥✐♦ ●❡❞❡ã♦✱ ❡s❝♦❧❛ s❡❞❡ ❞♦ ❆❣r✉♣❛♠❡♥t♦ ❞❡ ❊s❝♦❧❛s ❆♥tó♥✐♦ ●❡❞❡ã♦✱ s✐t✉❛❞❛ ♥♦ ❝♦♥❝❡❧❤♦ ❞❡ ❆❧♠❛❞❛✳ ❖ ❡stá❣✐♦ ❞❡❝♦rr❡✉ ❞✉r❛♥t❡ ♦ ❛♥♦ ❧❡t✐✈♦ ✷✵✶✸✴✷✵✶✹✱ s♦❜ ❛ ♦r✐❡♥t❛çã♦ ❞❛ Pr♦❢❡ss♦r❛ ❘♦sár✐♦ ▲♦♣❡s ❡ ❛ s✉♣❡r✈✐✲ sã♦ ❞♦s r❡s♣♦♥sá✈❡✐s ❝✐❡♥tí✜❝♦s ❞❛ ❋❈❚✲❯◆▲✱ ❛ Pr♦❢❡ss♦r❛ ❉♦✉t♦r❛ ▼❛r✐❛ ❍❡❧❡♥❛ ❙❛♥t♦s ❡ ♦ Pr♦❢❡ss♦r ❉♦✉t♦r ❋✐❧✐♣❡ ▼❛rq✉❡s✳ ❖ tr❛❜❛❧❤♦ ❞❡ ❡stá❣✐♦ ❞❡s❡♥✈♦❧✈❡✉✲s❡ ♥✉♠❛ t✉r♠❛ ❞♦ ✶✷✳➸ ❛♥♦ ❞♦ ❝✉rs♦ ❈✐❡♥t✐✜❝♦✲❍✉♠❛♥íst✐❝♦ ❞❡ ❈✐ê♥❝✐❛s ❡ ❚❡❝♥♦❧♦❣✐❛s✱ ♥❛ ❞✐s❝✐♣❧✐♥❛ ❞❡ ▼❛t❡♠át✐❝❛ ❆✳
◆♦ ♣r❡s❡♥t❡ r❡❧❛tór✐♦ é ❢❡✐t❛ ✉♠❛ ❝❛r❛❝t❡r✐③❛çã♦ ❞❛ ❡s❝♦❧❛✱ ❞❛ t✉r♠❛ ❡ ❞♦ tr❛❜❛❧❤♦ ❞❡s❡♥✈♦❧✈✐❞♦ ♣❡❧♦ ❡st❛❣✐ár✐♦ ❛♦ ❧♦♥❣♦ ❞♦s três ♣❡rí♦❞♦s ❞♦ ❛♥♦ ❧❡t✐✈♦ ✷✵✶✸✴✷✵✶✹✳
✷ ❆❣r✉♣❛♠❡♥t♦ ❞❡ ❊s❝♦❧❛s ❆♥tó♥✐♦ ●❡❞❡ã♦
✷✳✶ ❈❛r❛❝t❡r✐③❛çã♦ ❋ís✐❝❛ ❞♦ ❆❣r✉♣❛♠❡♥t♦ ❞❡ ❡s❝♦❧❛s ❆♥tó✲ ♥✐♦ ●❡❞❡ã♦
❖ ❆❣r✉♣❛♠❡♥t♦ ❞❡ ❊s❝♦❧❛s ❆♥tó♥✐♦ ●❡❞❡ã♦ ✭❆❊❆●✮ ❝♦♥st✐t✉✐✉✲s❡ ❛ ✷✷ ❞❡ ❆❜r✐❧ ❞❡ ✷✵✶✸✱ r❡✉♥✐♥❞♦ s❡✐s ❡s❝♦❧❛s✱ ❝♦♠ ♥í✈❡✐s ❞❡ ❡♥s✐♥♦ r❡♣❛rt✐❞♦s ❡♥tr❡ ♦ ♣ré✲❡s❝♦❧❛r ❡ ♦ ❙❡❝✉♥❞ár✐♦✿
✕ ❊s❝♦❧❛ ❇ás✐❝❛ ✶✳➸ ❝✐❝❧♦ ❡ ❏❛r❞✐♠ ❞❡ ■♥❢â♥❝✐❛ ❞♦ ▲❛r❛♥❥❡✐r♦ ♥✳➸ ✸ ❀
✕ ❊s❝♦❧❛ ❇ás✐❝❛ ✶✳➸ ❝✐❝❧♦ ❞♦ ❆❧❢❡✐t❡❀
✕ ❊s❝♦❧❛ ❇ás✐❝❛ ✶✳➸ ❝✐❝❧♦ ❞❛ ❈♦✈❛ ❞❛ P✐❡❞❛❞❡ ♥✳➸ ✶❀
✕ ❊s❝♦❧❛ ❇ás✐❝❛ ✶✳➸ ❝✐❝❧♦ ❞❛ ❈♦✈❛ ❞❛ P✐❡❞❛❞❡ ♥✳➸ ✷❀
✕ ❊s❝♦❧❛ ❇ás✐❝❛ ✷✳➸ ❡ ✸✳➸ ❝✐❝❧♦ ❈♦♠❛♥❞❛♥t❡ ❈♦♥❝❡✐çã♦ ❡ ❙✐❧✈❛❀
✕ ❊s❝♦❧❛ ❙❡❝✉♥❞ár✐❛ ❝♦♠ ✸✳➸ ❝✐❝❧♦ ❞♦ ❊♥s✐♥♦ ❇ás✐❝♦ ❞❡ ❆♥tó♥✐♦ ●❡❞❡ã♦ ✭s❡❞❡ ❞♦ ❛❣r✉♣❛♠❡♥t♦✮✳
P❛r❛ ❛❧é♠ ❞♦ ❡♥s✐♥♦ r❡❣✉❧❛r✱ ♦ ❛❣r✉♣❛♠❡♥t♦ ❛♣r❡s❡♥t❛ t❛♠❜é♠ ❛s s❡❣✉✐♥t❡s ♦❢❡rt❛s ❢♦r♠❛t✐✈❛s✿
✕ ❈✉rs♦s ❞❡ ❊❞✉❝❛çã♦ ❡ ❋♦r♠❛çã♦✿
✕ ❏❛r❞✐♥❛❣❡♠ ❡ ❊s♣❛ç♦s ❱❡r❞❡s❀ ✕ ❆ss✐st❡♥t❡ ❆❞♠✐♥✐str❛t✐✈♦❀
✕ ❙❡r✈✐ç♦s ❞♦♠ést✐❝♦s✴❆♣♦✐♦ ❢❛♠✐❧✐❛r ❡ à ❝♦♠✉♥✐❞❛❞❡✳
✕ ❈✉rs♦s Pr♦✜ss✐♦♥❛✐s✿
✕ ❚é❝♥✐❝♦ ❞❛ ❆♣♦✐♦ à ■♥❢â♥❝✐❛❀ ✕ ❚é❝♥✐❝♦ ❞❡ ❘❡❝❡çã♦❀
✕ ❆♥✐♠❛❞♦r ❙ó❝✐♦✲❝✉❧t✉r❛❧✳
❚♦❞❛s ❛s ❡s❝♦❧❛s s❡ s✐t✉❛♠ ♥♦ ❝♦♥❝❡❧❤♦ ❞❡ ❆❧♠❛❞❛✱ r❡♣❛rt✐♥❞♦✲s❡ ❡♥tr❡ ❛s ❢r❡❣✉❡s✐❛s ❯♥✐ã♦ ❞❛s ❋r❡❣✉❡s✐❛s ❞❡ ▲❛r❛♥❥❡✐r♦ ❡ ❋❡✐❥ó ✭❯❋▲❋✮ ❡ ❯♥✐ã♦ ❞❛s ❋r❡❣✉❡s✐❛s ❞❡ ❆❧♠❛❞❛✱ ❈♦✈❛ ❞❛ P✐❡❞❛❞❡✱ Pr❛❣❛❧ ❡ ❈❛❝✐❧❤❛s ✭❯❋❆❈PP❈✮✱ ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛ t❛❜❡❧❛ s❡❣✉✐♥t❡✿
❊s❝♦❧❛s ❯❋▲❋ ❯❋❆❈PP❈
❊✳❇✳✶✴❏✳■✳ ▲❛r❛♥❥❡✐r♦ ♥✳➸ ✸ ①
❊✳❇✳ ✶ ❞♦ ❆❧❢❡✐t❡ ①
❊✳❇✳ ✶ ❈♦✈❛ ❞❛ P✐❡❞❛❞❡ ♥✳➸ ✶ ①
❊✳❇✳ ✶ ❈♦✈❛ ❞❛ P✐❡❞❛❞❡ ♥✳➸ ✷ ①
❊✳❇✳ ✷✱✸ ❈♦♠❛♥❞❛♥t❡ ❈♦♥❝❡✐çã♦ ❡ ❙✐❧✈❛ ①
❊✳❙✳ ❝✴✸✳➸ ❝✐❝❧♦ ❆♥tó♥✐♦ ●❡❞❡ã♦ ①
❚❛❜❡❧❛ ✷✳✶✿ ❉✐str✐❜✉✐çã♦ ❞❛s ❡s❝♦❧❛s ❞♦ ❆❊❆● ♣❡❧❛s ❞✉❛s ❢r❡❣✉❡s✐❛s ❞♦ ❝♦♥✲ ❝❡❧❤♦ ❞❡ ❆❧♠❛❞❛
❆s ❡s❝♦❧❛s ❞♦ ✶✳➸ ❝✐❝❧♦✱ ✐♥✐❝✐❛❧♠❡♥t❡✱ ♣❡rt❡♥❝✐❛♠ ❛♦ ❆❣r✉♣❛♠❡♥t♦ ❱❡rt✐❝❛❧ ❞❡ ❊s❝♦❧❛s ❈♦♠❛♥❞❛♥t❡ ❈♦♥❝❡✐çã♦ ❡ ❙✐❧✈❛✱ t❡♥❞♦ ✐♥t❡❣r❛❞♦ ♦ ❆❣r✉♣❛♠❡♥t♦ ❞❡ ❊s❝♦❧❛s ❆♥tó♥✐♦ ●❡❞❡ã♦ ❡♠ ❆❜r✐❧ ❞❡ ✷✵✶✸✳
❆♣r❡s❡♥t❛✲s❡✱ ❞❡ s❡❣✉✐❞❛✱ ✉♠❛ ❜r❡✈❡ ❝❛r❛❝t❡r✐③❛çã♦ ❢ís✐❝❛ ❡ ❤✐stór✐❝❛ ❞❛s ❡s❝♦❧❛s ❞♦ ❆❣r✉♣❛♠❡♥t♦✳ ◆♦ ❡♥t❛♥t♦✱ s❡rá ❡❢❡t✉❛❞❛ ❛♣❡♥❛s ✉♠❛ ❜r❡✈❡ r❡✲ ❢❡rê♥❝✐❛ ❤✐stór✐❝❛ à ❊✳❙✳ ❝✴✸✳➸ ❝✐❝❧♦ ❞❡ ❆♥tó♥✐♦ ●❡❞❡ã♦✱ ✉♠❛ ✈❡③ q✉❡ ❡st❛ ❡s❝♦❧❛✱ ♦♥❞❡ ❞❡❝♦rr❡✉ ♦ ❡stá❣✐♦✱ s❡rá ❝❛r❛❝t❡r✐③❛❞❛ ♠❛✐s ❛♣r♦❢✉♥❞❛❞❛♠❡♥t❡ ♥✉♠❛ s❡❝çã♦ ♣♦st❡r✐♦r✳
✷✳✶✳✶ ❊s❝♦❧❛ ❇ás✐❝❛ ✶✳➸ ❝✐❝❧♦ ❡ ❏❛r❞✐♠ ❞❡ ■♥❢â♥❝✐❛ ❞♦ ▲❛r❛♥❥❡✐r♦ ♥✳➸ ✸
❋✐❣✉r❛ ✷✳✶✿ ❊✳❇✳ ✶✴❏✳■✳ ❞♦ ▲❛r❛♥❥❡✐r♦ ♥✳➸ ✸
❆ ❊✳❇✳ ✶✴❏✳■✳ ▲❛r❛♥❥❡✐r♦ ♥✳➸ ✸ s✐t✉❛✲s❡ ♥❛ ❯♥✐ã♦ ❞❛s ❋r❡❣✉❡s✐❛s ❞❡ ▲❛r❛♥❥❡✐r♦ ❡ ❋❡✐❥ó✱ ♥❛ ❘✉❛ ❏♦sé ❆❢♦♥s♦✳ ❊st❛ ❡s❝♦❧❛ ❢♦✐ ✐♥❛✉❣✉r❛❞❛ ❛ ✶ ❞❡ ❖✉t✉❜r♦ ❞❡ ✶✾✽✾ ❝♦♠ ❛ ❢✉♥çã♦ ❞❡ ❡s❝♦❧❛ ❜ás✐❝❛ ❞♦ ✶✳➸ ❝✐❝❧♦ ❡✱ ♠❛✐s t❛r❞❡✱ ❛ ❏❛♥❡✐r♦ ❞❡ ✶✾✾✽✱ ♣❛ss♦✉ ❛ ✐♥❝❧✉✐r ❛s ❢✉♥çõ❡s ❞❡ ❏❛r❞✐♠ ❞❡ ■♥❢â♥❝✐❛✱ ❢✉♥❝✐♦♥❛❞♦✱ ♥♦
❡♥t❛♥t♦✱ ❝♦♠♦ ❞✉❛s ❡s❝♦❧❛s ✐♥❞❡♣❡♥❞❡♥t❡s✳ ❙ó ❡♠ ✷✵✵✸✱ q✉❛♥❞♦ ✐♥t❡❣r♦✉ ♦ ❆❣r✉♣❛♠❡♥t♦ ❱❡rt✐❝❛❧ ❞❡ ❊s❝♦❧❛s ❈♦♠❛♥❞❛♥t❡ ❈♦♥❝❡✐çã♦ ❡ ❙✐❧✈❛ é q✉❡ ❡st❛s ❞✉❛s ❡s❝♦❧❛s ♣❛ss❛r❛♠ ❛ ❝♦♥st✐t✉✐r ✉♠❛ só ❡s❝♦❧❛ ❞❡s✐❣♥❛❞❛ ♣❡❧♦ ♣r❡s❡♥t❡ ♥♦♠❡✳
❆ ✈✐st❛ ❛ér❡❛ ❞❛ ❡s❝♦❧❛ é ❛♣r❡s❡♥t❛❞❛ ♥❛ ✜❣✉r❛ ✷✳✷✱ ♦♥❞❡ s❡ ♦❜s❡r✈❛ ❛ ❞✐str✐❜✉✐çã♦ ❞♦ ❡❞✐❢í❝✐♦s✱ ❞♦s r❡❝✐♥t♦s ❞❡s♣♦rt✐✈♦s ❡ ❞❛s ár❡❛s ♥ã♦ ❡❞✐✜❝❛❞❛s✳ ❈♦♠♦ s❡ ♣♦❞❡ ♦❜s❡r✈❛r ♥❡st❛ ✜❣✉r❛✱ ❛ ❡s❝♦❧❛ é ❝♦♥st✐t✉í❞❛ ♣♦r ❞♦✐s ❡❞✐❢í❝✐♦s✱ ♦♥❞❡ ❢✉♥❝✐♦♥❛♠ ♦ ❡♥s✐♥♦ ♣ré✲❡s❝♦❧❛r ❡ ♦ ❡♥s✐♥♦ ❜ás✐❝♦✳
❋✐❣✉r❛ ✷✳✷✿ ❱✐st❛ ❛ér❡❛ ❞❛ ❊✳❇✳ ✶✴❏✳■✳ ❞♦ ▲❛r❛♥❥❡✐r♦ ♥✳➸ ✸✳ ❘❡t✐r❛❞♦ ❞❡✿ ❤tt♣s✿✴✴♠❛♣s✳❣♦♦❣❧❡✳♣t✴
✷✳✶✳✷ ❊s❝♦❧❛ ❇ás✐❝❛ ✶✳➸ ❝✐❝❧♦ ❞♦ ❆❧❢❡✐t❡
❋✐❣✉r❛ ✷✳✸✿ ❱✐st❛ ❛ér❡❛ ❞❛ ❊✳❇✳ ✶ ❞♦ ❆❧❢❡✐t❡✳ ❘❡t✐r❛❞♦ ❞❡✿ ❤tt♣s✿✴✴♠❛♣s✳❣♦♦❣❧❡✳♣t✴
❆ ❊✳❇✳ ✶ ❞♦ ❆❧❢❡✐t❡ s✐t✉❛✲s❡ ♥❛ ❯♥✐ã♦ ❞❛s ❋r❡❣✉❡s✐❛s ❞❡ ▲❛r❛♥❥❡✐r♦ ❡ ❋❡✐❥ó✱ ♥❛ ❘✉❛ ❏♦sé ❈❛r❧♦s ❞❡ ▼❡❧♦✱ ♥✉♠ t❡rr❡♥♦ ♠✐❧✐t❛r ❞❛ ❇❛s❡ ◆❛✈❛❧ ❞♦ ❆❧❢❡✐t❡ ❡ ❢♦✐ ✐♥❛✉❣✉r❛❞❛ ❡♠ ✶✾✺✼✳
◆❛ ✜❣✉r❛ ✷✳✸ ❡stá r❡♣r❡s❡♥t❛❞♦ ♦ ❡s♣❛ç♦ ❡s❝♦❧❛r ✭❧✐♠✐t❛❞♦ ❛ ✈❡r♠❡❧❤♦✮✱ ❝♦♥st✐t✉í❞♦ ♣♦r ❡❞✐❢í❝✐♦s✱ r❡❝✐♥t♦s ❞❡s♣♦rt✐✈♦s ❡ ár❡❛s ♥ã♦ ❡❞✐✜❝❛❞❛s✳ ❆ ❡s❝♦❧❛ é ❝♦♥st✐t✉í❞❛ ♣♦r q✉❛tr♦ ❡❞✐❢í❝✐♦s✱ ❞♦✐s ❞❡❧❡s ♦♥❞❡ ❢✉♥❝✐♦♥❛♠ ❛s ❛✉❧❛s ❞♦ ❡♥s✐♥♦ ❜ás✐❝♦ ❡ ♥♦s ♦✉tr♦s ❞♦✐s ❞❡❝♦rr❡♠ ❛s ❛t✐✈✐❞❛❞❡s ❢ís✐❝♦✲♠♦t♦r❛s ❡ ❞❡ ❡♥r✐q✉❡❝✐♠❡♥t♦ ❝✉rr✐❝✉❧❛r✱ s❡♥❞♦ t❛♠❜é♠ ✉t✐❧✐③❛❞♦s ♣❡❧♦ ❈❡♥tr♦ ❞❡ ❆♣♦✐♦ ❙♦❝✐❛❧ ❞♦ ❆❧❢❡✐t❡✳
✷✳✶✳✸ ❊s❝♦❧❛ ❇ás✐❝❛ ✶✳➸ ❝✐❝❧♦ ❈♦✈❛ ❞❛ P✐❡❞❛❞❡ ♥✳➸ ✶
❆ ❊✳❇✳ ✶ ❈♦✈❛ ❞❛ P✐❡❞❛❞❡ ♥✳➸ ✶ s✐t✉❛✲s❡ ♥❛ ❯♥✐ã♦ ❞❛s ❋r❡❣✉❡s✐❛s ❞❡ ❆❧♠❛❞❛✱ ❈♦✈❛ ❞❛ P✐❡❞❛❞❡✱ Pr❛❣❛❧ ❡ ❈❛❝✐❧❤❛s✱ ♥❛ ❆✈❡♥✐❞❛ ❞❛ ❋✉♥❞❛çã♦✳ ■♥❛✉❣✉r❛❞❛ ❡♠ ✶✾✹✽✱ ❡st❛ ❡s❝♦❧❛ ❡r❛✱ ✐♥✐❝✐❛❧♠❡♥t❡✱ ❛♣❡♥❛s ❢r❡q✉❡♥t❛❞❛ ♣♦r r❛♣❛r✐❣❛s✳
❋✐❣✉r❛ ✷✳✹✿ ❱✐st❛ ❛ér❡❛ ❞❛ ❊✳❇✳ ✶ ❈♦✈❛ ❞❛ P✐❡❞❛❞❡ ♥✳➸✶✳ ❘❡t✐r❛❞♦ ❞❡✿ ❤tt♣s✿✴✴♠❛♣s✳❣♦♦❣❧❡✳♣t✴
◆❛ ✜❣✉r❛ ✷✳✹ ♦ ❡s♣❛ç♦ ❡s❝♦❧❛r ❡stá ❧✐♠✐t❛❞♦ ❛ ✈❡r♠❡❧❤♦ ❡ é ♣♦ssí✈❡❧ ♦❜✲ s❡r✈❛r três ❡❞✐❢í❝✐♦s✿ ♦ ❡❞✐❢í❝✐♦ ♣r✐♥❝✐♣❛❧✱ ♦♥❞❡ ❡stã♦ ❧♦❝❛❧✐③❛❞❛s ❛ ♠❛✐♦r✐❛ ❞❛s s❛❧❛s ❞❡ ❛✉❧❛✱ ❡ ♦s ♦✉tr♦s ❞♦✐s ❡❞✐❢í❝✐♦s✱ ♦♥❞❡ ❢✉♥❝✐♦♥❛ ✉♠❛ s❛❧❛ ❞❡ ❛✉❧❛✱ ♠❛s t❛♠❜é♠ ♦✉tr♦s r❡❝✉rs♦s✱ ♥♦♠❡❛❞❛♠❡♥t❡ ♦ r❡❢❡✐tór✐♦ ❡ ♦ ❆✳❚✳▲✳
❋✐❣✉r❛ ✷✳✺✿ ❊✳❇✳ ✶ ❈♦✈❛ ❞❛ P✐❡❞❛❞❡ ♥✳➸ ✶
✷✳✶✳✹ ❊s❝♦❧❛ ❇ás✐❝❛ ✶✳➸ ❝✐❝❧♦ ❈♦✈❛ ❞❛ P✐❡❞❛❞❡ ♥✳➸ ✷
❆ ❊✳❇✳ ✶ ❈♦✈❛ ❞❛ P✐❡❞❛❞❡ ♥✳➸ ✷ s✐t✉❛✲s❡ ♥❛ ❯♥✐ã♦ ❞❛s ❋r❡❣✉❡s✐❛s ❞❡ ❆❧♠❛❞❛✱ ❈♦✈❛ ❞❛ P✐❡❞❛❞❡✱ Pr❛❣❛❧ ❡ ❈❛❝✐❧❤❛s✱ ♥❛ ❘✉❛ ▼❛③❛❣ã♦✳ ■♥❛✉❣✉r❛❞❛ ❡♠ ✶✾✺✶✱ ❡st❛ ❡s❝♦❧❛ ❢♦✐✱ ❡♠ ✷✵✵✻✱ s✉❜♠❡t✐❞❛ ❛ ♦❜r❛s ❞❡ r❡♠♦❞❡❧❛çã♦ ❡ ❛♠♣❧✐❛çã♦✳
❋✐❣✉r❛ ✷✳✻✿ ❱✐st❛ ❛ér❡❛ ❞❛ ❊✳❇✳ ✶ ❈♦✈❛ ❞❛ P✐❡❞❛❞❡ ♥✳➸ ✷✳ ❘❡t✐r❛❞♦ ❞❡✿ ❤tt♣s✿✴✴♠❛♣s✳❣♦♦❣❧❡✳♣t✴
❆ ✜❣✉r❛ ✷✳✻ é ✉♠❛ ✐♠❛❣❡♠ ❛ér❡❛ ❞♦ ❡s♣❛ç♦ ❡s❝♦❧❛r ✭❧✐♠✐t❛❞♦ ❛ ✈❡r♠❡❧❤♦✮✱ é ❝♦♥st✐t✉í❞♦ ♣♦r ❞♦✐s ❡❞✐❢í❝✐♦s✱ ♦♥❞❡ ❞❡❝♦rr❡♠ ❛s ❛✉❧❛s ❞♦ ❡♥s✐♥♦ ❜ás✐❝♦✳ ❖❜s❡r✈❛♠✲s❡✱ t❛♠❜é♠ ♦✉tr♦s ❝♦♥st✐t✉✐♥t❡s ❞♦ ❡s♣❛ç♦ ❡s❝♦❧❛r✱ t❛✐s ❝♦♠♦ ♦s r❡❝✐♥t♦s ❞❡s♣♦rt✐✈♦s ❡ ❛s ár❡❛s ♥ã♦ ❡❞✐✜❝❛❞❛s✳
❋✐❣✉r❛ ✷✳✼✿ ❊✳❇✳ ✶ ❈♦✈❛ ❞❛ P✐❡❞❛❞❡ ♥✳➸ ✷
✷✳✶✳✺ ❊s❝♦❧❛ ❇ás✐❝❛ ✷✳➸ ❡ ✸✳➸ ❝✐❝❧♦ ❈♦♠❛♥❞❛♥t❡ ❈♦♥❝❡✐çã♦ ❡ ❙✐❧✈❛
❆ ❊✳❇✳ ✷✱ ✸ ❈♦♠❛♥❞❛♥t❡ ❈♦♥❝❡✐çã♦ ❡ ❙✐❧✈❛ ❡stá s✐t✉❛❞❛ ♥❛ ❯♥✐ã♦ ❞❛s ❋r❡❣✉❡✲ s✐❛s ❞❡ ❆❧♠❛❞❛✱ ❈♦✈❛ ❞❛ P✐❡❞❛❞❡✱ Pr❛❣❛❧ ❡ ❈❛❝✐❧❤❛s✱ ♥❛ ❘✉❛ ❈♦♠❛♥❞❛♥t❡ ❊✉❣é♥✐♦ ❈♦♥❝❡✐çã♦ ❙✐❧✈❛✳ ❆ ❡s❝♦❧❛ ❢♦✐ ❝r✐❛❞❛ ❡♠ ✶✾✼✸✱ ❝♦♥t✉❞♦ ❛♣❡♥❛s ❡♠ ❖✉t✉❜r♦ ❞❡ ✶✾✼✺ ❝♦♠❡ç♦✉ ❛ ❢✉♥❝✐♦♥❛r ♥♦ ♣r❡s❡♥t❡ ❧♦❝❛❧✳ ❊st❛ ❡s❝♦❧❛ ❢♦✐ ❡s❝♦❧❛✲s❡❞❡ ❞♦ ❆❣r✉♣❛♠❡♥t♦ ❱❡rt✐❝❛❧ ❞❡ ❡s❝♦❧❛s ❈♦♠❛♥❞❛♥t❡ ❈♦♥❝❡✐çã♦ ❡ ❙✐❧✈❛ ❛té ✷✵✶✸✱ ❛❧t✉r❛ ❡♠ q✉❡ ✐♥t❡❣r♦✉ ♦ ❆❣r✉♣❛♠❡♥t♦ ❞❡ ❊s❝♦❧❛s ❆♥tó♥✐♦ ●❡❞❡ã♦✳
❋✐❣✉r❛ ✷✳✽✿ ❱✐st❛ ❛ér❡❛ ❞❛ ❊✳❇✳ ✷✱✸ ❈♦♠❛♥❞❛♥t❡ ❈♦♥❝❡✐çã♦ ❡ ❙✐❧✈❛✳ ❘❡t✐r❛❞♦ ❞❡✿ ❤tt♣s✿✴✴♠❛♣s✳❣♦♦❣❧❡✳♣t✴
◆❛ ✜❣✉r❛ ✷✳✽ ♦❜s❡r✈❛✲s❡ ♦ ❡s♣❛ç♦ ❡s❝♦❧❛r✱ ❧✐♠✐t❛❞♦ ❛ ✈❡r♠❡❧❤♦✱ q✉❡ é ❝♦♥st✐t✉í❞♦ ♣♦r ❞♦✐s ♣❛✈✐❧❤õ❡s✱ ♦♥❞❡ ❢✉♥❝✐♦♥❛♠ ❛s s❛❧❛s ❞❡ ❛✉❧❛s ❡ ♦✉tr❛s ❡str✉t✉r❛s ✐♥❡r❡♥t❡s à ❣❡stã♦ ❡ à ✈✐❞❛ ❡s❝♦❧❛r✱ ❡ ♣♦r ❞♦✐s ❝❛♠♣♦s ❞❡ ❥♦❣♦s ❡
♦s ❜❛❧♥❡ár✐♦s✳
❋✐❣✉r❛ ✷✳✾✿ ❊✳❇✳ ✷✱✸ ❈♦♠❛♥❞❛♥t❡ ❈♦♥❝❡✐çã♦ ❡ ❙✐❧✈❛
✷✳✶✳✻ ❊s❝♦❧❛ ❙❡❝✉♥❞ár✐❛ ❝♦♠ ✸✳➸ ❝✐❝❧♦ ❞♦ ❊♥s✐♥♦ ❇ás✐❝♦ ❞❡ ❆♥tó✲ ♥✐♦ ●❡❞❡ã♦
❆ ❊✳❙✳ ❝✴ ✸✳➸ ❝✐❝❧♦ ❞❡ ❆♥tó♥✐♦ ●❡❞❡ã♦ ❧♦❝❛❧✐③❛✲s❡ ♥❛ ❯♥✐ã♦ ❞❛s ❋r❡❣✉❡s✐❛s ❞❡ ▲❛r❛♥❥❡✐r♦ ❡ ❋❡✐❥ó✱ ♥❛ ❆❧❛♠❡❞❛ ●✉❡rr❛ ❏✉♥q✉❡✐r♦✳ ❆ ❡s❝♦❧❛ ❢♦✐ ✐♥❛✉❣✉r❛❞❛ ❡♠ ✶✾✽✸✱ ❝♦♥t✉❞♦ ❛♣❡♥❛s ❡♠ ✶✾✽✹✱ ❝♦♠❡ç♦✉ ❛ ❢✉♥❝✐♦♥❛r ❡♠ ♣❧❡♥♦✱ ❝♦♠ t✉r♠❛s ❞♦ ✼✳➸ ❛♦ ✾✳➸ ❛♥♦✳ ◆♦ ❛♥♦ ❧❡t✐✈♦ ✶✾✽✽✴✶✾✽✾✱ ❝♦♠❡ç♦✉ ❛ ❢✉♥❝✐♦♥❛r ♦ ❡♥s✐♥♦ s❡❝✉♥❞ár✐♦✱ ❝♦♠ t✉r♠❛s ❞♦ ✶✵✳➸ ❛♦ ✶✷✳➸ ❛♥♦✳
❋✐❣✉r❛ ✷✳✶✵✿ ❊✳❙✳ ❝✴✸ ❆♥tó♥✐♦ ●❡❞❡ã♦
✷✳✷ ❈❛r❛❝t❡r✐③❛çã♦ ❞♦s ❛❧✉♥♦s ❞♦ ❆❣r✉♣❛♠❡♥t♦ ❞❡ ❊s❝♦❧❛s ❆♥tó♥✐♦ ●❡❞❡ã♦
◆♦ ✐♥í❝✐♦ ❞♦ ❛♥♦ ❧❡t✐✈♦ ✷✵✶✸✴✷✵✶✹✱ ♦ ❛❣r✉♣❛♠❡♥t♦ t✐♥❤❛ ✷✸✵✷ ❛❧✉♥♦s ✐♥s❝r✐t♦s✱ ❞✐✈✐❞✐❞♦s ♣♦r ✾✾ t✉r♠❛s✳ ◆❛ t❛❜❡❧❛ s❡❣✉✐♥t❡ ❛♣r❡s❡♥t❛✲s❡ ❛ ❞✐str✐❜✉✐çã♦ ❞♦ ♥ú♠❡r♦ ❞❡ ❛❧✉♥♦s ❡ ❞❡ t✉r♠❛s ♣♦r ❝✐❝❧♦s ❞❡ ❡♥s✐♥♦✳
◆í✈❡✐s ❞❡ ❡♥s✐♥♦ ◆ú♠❡r♦ ❞❡ ❛❧✉♥♦s ◆ú♠❡r♦ ❞❡ t✉r♠❛s
Pré✲❡s❝♦❧❛r ✶✻✺ ✼
✶✳➸ ❈✐❝❧♦ ✽✸✷ ✸✻
✷✳➸ ❈✐❝❧♦ ✸✼✽ ✶✻
✸✳➸ ❈✐❝❧♦ ✺✹✻ ✷✸
❙❡❝✉♥❞ár✐♦ ✸✽✶ ✶✼
❚♦t❛❧ ❆❣r✉♣❛♠❡♥t♦ ✷✸✵✷ ✾✾
❚❛❜❡❧❛ ✷✳✷✿ ❉✐✈✐sã♦ ❞❡ ♥ú♠❡r♦ ❞❡ ❛❧✉♥♦s ❡ ❞❡ t✉r♠❛s ♣♦r ❝✐❝❧♦ ❞❡ ❡♥s✐♥♦
❖❜s❡r✈❛♥❞♦ ❛ t❛❜❡❧❛ ✷✳✷✱ ❝♦♥❝❧✉✐✲s❡ q✉❡ ♦ ❝✐❝❧♦ ❞❡ ❡♥s✐♥♦ ❝♦♠ ♠❛✐♦r ♥ú♠❡r♦ ❞❡ ❛❧✉♥♦s ❡✱ ❝♦♥s❡q✉❡♥t❡♠❡♥t❡✱ ❞❡ t✉r♠❛s é ♦ ✶✳➸ ❈✐❝❧♦✳
❆ ú♥✐❝❛ ❡s❝♦❧❛ ❞♦ ❛❣r✉♣❛♠❡♥t♦ ❝♦♠ ❡♥s✐♥♦ s❡❝✉♥❞ár✐♦ é ❛ ❊s❝♦❧❛ ❙❡✲ ❝✉♥❞ár✐♦ ❝✴ ✸✳➸ ❝✐❝❧♦ ❞♦ ❊♥s✐♥♦ ❇ás✐❝♦ ❞❡ ❆♥tó♥✐♦ ●❡❞❡ã♦ ✭s❡❞❡ ❞♦ ❛❣r✉♣❛✲ ♠❡♥t♦✮✱ q✉❡ s❡ ✐rá ❞❡s✐❣♥❛r ♣♦r ❊❙❆●✱ ♦♥❞❡ ❡①✐st❡♠ ❞❡③❛ss❡t❡ t✉r♠❛s ❞♦ ❊♥s✐♥♦ ❙❡❝✉♥❞ár✐♦✱ ❞✐✈✐❞✐❞❛s ♣❡❧♦s ❈✉rs♦s ❈✐❡♥tí✜❝♦ ❍✉♠❛♥íst✐❝♦ ❈✐ê♥❝✐❛s ❡ ❚❡❝♥♦❧♦❣✐❛s✱ ❈✐ê♥❝✐❛s ❙ó❝✐♦❡❝♦♥ó♠✐❝❛s ❡ ▲í♥❣✉❛s ❡ ❍✉♠❛♥✐❞❛❞❡s ❡ ♣❡❧♦s ❈✉rs♦s Pr♦✜ss✐♦♥❛✐s ❞❡ ❚é❝♥✐❝♦ ❞❡ ❆♣♦✐♦ à ■♥❢â♥❝✐❛✱ ❚é❝♥✐❝♦ ❞❡ ❘❡❝❡çã♦ ❡ ❞❡ ❆♥✐♠❛❞♦r ❙ó❝✐♦❝✉❧t✉r❛❧✳ ❆ ♣❛rt✐r ❞❛ ❝♦♥st✐t✉✐çã♦ ❞♦ ❆❣r✉♣❛♠❡♥t♦ ❞❡ ❊s✲ ❝♦❧❛s ❆♥tó♥✐♦ ●❡❞❡ã♦ ❛s t✉r♠❛s ❞♦ ✸✳➸ ❝✐❝❧♦ ❞❛ ❊s❝♦❧❛ ❇ás✐❝❛ ❈♦♠❛♥❞❛♥t❡ ❈♦♥❝❡✐çã♦ ❡ ❙✐❧✈❛ ♣❛ss❛r❛♠ ❛ ❢✉♥❝✐♦♥❛r ♥❛ ❡s❝♦❧❛ s❡❞❡ ✭❊❙❆●✮✳ ❉❡st❛ ❢♦r♠❛ ❛ ❊s❝♦❧❛ ❇ás✐❝❛ ❈♦♠❛♥❞❛♥t❡ ❈♦♥❝❡✐çã♦ ❡ ❙✐❧✈❛ ✜❝♦✉ ❞❡❞✐❝❛❞❛ ❡♠ ❡①❝❧✉s✐✈♦ ❛♦ ✷✳➸ ❝✐❝❧♦✳
❖ ❊♥s✐♥♦ Pré✲❡s❝♦❧❛r ❡stá ♣r❡s❡♥t❡ ❡♠ ❞✉❛s ❡s❝♦❧❛s✱ ♥❛ ❊s❝♦❧❛ ❇ás✐❝❛ ✶✳➸ ❝✐❝❧♦ ❞♦ ❆❧❢❡✐t❡ ❡ ❊s❝♦❧❛ ❇ás✐❝❛ ✶✳➸ ❝✐❝❧♦ ❡ ❏❛r❞✐♠ ❞❡ ■♥❢â♥❝✐❛ ❞♦ ▲❛r❛♥❥❡✐r♦ ♥✳➸ ✸✱ ❝♦♠ ✶✻✺ ❛❧✉♥♦s ❞✐str✐❜✉í❞♦s ♣♦r s❡t❡ t✉r♠❛s✳
❆ ♠é❞✐❛ ❞♦ ♥ú♠❡r♦ ❞❡ ❛❧✉♥♦s ♣♦r t✉r♠❛ s✐t✉❛✲s❡ ♥♦s ✈✐♥t❡ ❡ q✉❛tr♦ ❛❧✉♥♦s✱ ❡♠ ❝❛❞❛ ♥í✈❡❧ ❞❡ ❡♥s✐♥♦✳ ❆s t✉r♠❛s ❝♦♠ ♠❡♥♦r ♥ú♠❡r♦ ❞❡ ❛❧✉♥♦s ❡♥❝♦♥tr❛♠✲s❡ ♥♦ ❡♥s✐♥♦ ❙❡❝✉♥❞ár✐♦✳
✸ ❆ ❡s❝♦❧❛ ❞❡ ❡stá❣✐♦
✸✳✶ ❈❛r❛❝t❡r✐③❛çã♦ ❋ís✐❝❛ ❞❛ ❊s❝♦❧❛ ❙❡❝✉♥❞ár✐❛ ❝✴ ✸✳➸ ❝✐❝❧♦ ❞♦ ❊♥s✐♥♦ ❇ás✐❝♦ ❞❡ ❆♥tó♥✐♦ ●❡❞❡ã♦
❆ ❊✳❙✳ ❝✴✸ ❝✐❝❧♦ ❞❡ ❆♥tó♥✐♦ ●❡❞❡ã♦ s✐t✉❛✲s❡ ♥❛ ❯♥✐ã♦ ❞❛s ❋r❡❣✉❡s✐❛s ❞❡ ▲❛r❛♥❥❡✐r♦ ❡ ❋❡✐❥ó ❡ é ❝♦♥st✐t✉í❞❛ ♣♦r ❝✐♥❝♦ ♣❛✈✐❧❤õ❡s✱ ✉♠ ❜❧♦❝♦ ♣ré✲❢❛❜r✐❝❛❞♦ ❡ ✉♠ ♣❛✈✐❧❤ã♦ ❞❡s♣♦rt✐✈♦ ✭✜❣✉r❛ ✸✳✶✮✳
❋✐❣✉r❛ ✸✳✶✿ ❱✐st❛ ❛ér❡❛ ❞❛ ❊✳❙✳ ❝✴✸✳➸ ❝✐❝❧♦ ❆♥tó♥✐♦ ●❡❞❡ã♦✳ ❖ ❡s♣❛ç♦ ❡s❝♦❧❛r ❡stá ❧✐♠✐t❛❞♦ ❝♦♠ ✉♠❛ ❧✐♥❤❛ ❛ ✈❡r♠❡❧❤♦✳
❘❡t✐r❛❞♦ ❞❡✿ ❤tt♣s✿✴✴♠❛♣s✳❣♦♦❣❧❡✳♣t✴
◆❛ ✈✐st❛ ❛ér❡❛ ❞❛ ✜❣✉r❛ ✸✳✶ ♥ã♦ é ♦❜s❡r✈á✈❡❧ ✉♠ ❝❛♠♣♦ ❞❡ ❢✉t❡❜♦❧ s✐♥✲ tét✐❝♦ q✉❡ s✉❜st✐t✉✐✉ ♦ ❛♥t✐❣♦ ❝❛♠♣♦ ❞❡ ❥♦❣♦s✳ ❊st❡ ❡s♣❛ç♦ ❡♠❜♦r❛ ❣❡r✐❞♦ ♣♦r ❡♥t✐❞❛❞❡ ❡①t❡r♥❛ é ✉t✐❧✐③❛❞♦ ♣❡❧♦s ❛❧✉♥♦s ♣❛r❛ ❛ ♣rát✐❝❛ ❞❡s♣♦rt✐✈❛✳ ❆s r❡st❛♥t❡s ❛t✐✈✐❞❛❞❡s ❧❡t✐✈❛s ❞❡❝♦rr❡♠ ❡♠ ❞✐❢❡r❡♥t❡s ❡s♣❛ç♦s ❞✐str✐❜✉í❞♦s ♣♦r s❡✐s ♣❛✈✐❧❤õ❡s✿
✕ P❛✈✐❧❤ã♦ ❍ ✲ s❡♠ s❛❧❛s ❞❡ ❛✉❧❛✱ é ♦ ❧♦❝❛❧ ♦♥❞❡ ❢✉♥❝✐♦♥❛♠ ♦s s❡r✈✐ç♦s ❛❞♠✐♥✐str❛t✐✈♦s✱ ❛ ❜✐❜❧✐♦t❡❝❛✴❝❡♥tr♦ ❞❡ r❡❝✉rs♦s✱ ❛ r❡♣r♦❣r❛✜❛✱ s❛❧❛ ❞❡ ♣r♦❢❡ss♦r❡s✱ ❣❛❜✐♥❡t❡ ❞❡ ♣r✐♠❡✐r♦s s♦❝♦rr♦s✱ ❣❛❜✐♥❡t❡ ❞♦s ❞✐r❡t♦r❡s ❞❡ t✉r♠❛✱ ❣❛❜✐♥❡t❡ ❞❛ ❝❤❡❢❡ ❞❡ ❛ss✐st❡♥t❡s ♦♣❡r❛❝✐♦♥❛✐s✴ ❆❙❊✴ tr❛❜❛❧❤♦ ❞❡ ♣r♦❢❡ss♦r❡s✱ ❣❛❜✐♥❡t❡ ❞❡ ❢♦t♦❣r❛✜❛✴ ♣r♦❥❡t♦ ❊♥❡❛s✱ s❛❧❛ ❞❛ ❞✐r❡çã♦✱ s❛❧❛ ❞❡ ❡st✉❞♦✱ ❣❛❜✐♥❡t❡ ❞♦ ❈❆❉❊✴ tr❛❜❛❧❤♦ ♣❛r❛ ♣r♦❢❡ss♦r❡s ❡ ❣❛❜✐♥❡t❡ ❞❡ ♣r❡✈❡♥çã♦ ❞❛ ✐♥❞✐s❝✐♣❧✐♥❛❀
✕ P❛✈✐❧❤ã♦ ❊ ✲ é ❝♦♥st✐t✉í❞♦ ♣♦r s❛❧❛s ❞❡ ❛✉❧❛s✱ ✉♠❛ s❛❧❛ ❞❡ ■♥❢♦r♠át✐❝❛✱ ✉♠❛ s❛❧❛ ❞❡ ❈✐ê♥❝✐❛s ◆❛t✉r❛✐s ❡ ●❡♦❧♦❣✐❛ ❡ ✉♠❛ s❛❧❛ ❞❡ ❊❞✉❝❛çã♦ ❱✐✲ s✉❛❧✱ s❛❧❛ ❞❡ ❊▼❘❈✱ ❣❛❜✐♥❡t❡ ❞❡ ❛♣♦✐♦ à ♠❛t❡♠át✐❝❛✴❡❞✉❝❛çã♦ ♣❛r❛ ❛
s❛ú❞❡✱ ❧❛❜♦r❛tór✐♦ ❞❡ ♠❛t❡♠át✐❝❛ ❡ ✉♠❛ s❛❧❛ ❡q✉✐♣❛❞❛ ❝♦♠ ❝♦♠♣✉t❛✲ ❞♦r❡s❀
✕ P❛✈✐❧❤ã♦ ❘ ✲ ♥ã♦ t❡♠ s❛❧❛s ❞❡ ❛✉❧❛✱ ♥❡st❡ ♣❛✈✐❧❤ã♦ ❢✉♥❝✐♦♥❛♠ ♦ r❡❢❡✐✲ tór✐♦✱ ♦ ❜❛r ❡ ❛ s❛❧❛ ❞❡ ❝♦♥✈í✈✐♦ ❞♦s ❛❧✉♥♦s ❡ ❞♦ ♣❡ss♦❛❧ ♥ã♦ ❞♦❝❡♥t❡❀
✕ P❛✈✐❧❤ã♦ ❉ ✲ ❡st❡ ❡❞✐❢í❝✐♦ é ❝♦♥st✐t✉í❞♦ ♣♦r s❛❧❛s ❞❡ ❛✉❧❛✱ ♦s ❧❛❜♦r❛tó✲ r✐♦s ❞❡ ❋ís✐❝❛✱ ❞❡ ❇✐♦❧♦❣✐❛ ❡ ❞❡ ◗✉í♠✐❝❛✱ ♦s ❣❛❜✐♥❡t❡s ❞❡ Ps✐❝♦❧♦❣✐❛ ❡ ❖r✐❡♥t❛çã♦ ❡s❝♦❧❛r ❡ ❞♦ ❈♦♥s❡❧❤♦ ●❡r❛❧❀
✕ P❛✈✐❧❤ã♦ ▲ ✲ ♣❛✈✐❧❤ã♦ ♦♥❞❡ ❢✉♥❝✐♦♥❛♠ ❛s s❛❧❛s ❞❡ ❚❡❛tr♦✱ ❊❞✉❝❛çã♦ ❚❡❝♥♦❧ó❣✐❝❛✱ ❈❡râ♠✐❝❛✱ ❛ss♦❝✐❛çã♦ ❞❡ ❡st✉❞❛♥t❡s✱ s❛❧❛ ❞❡ ❝♦♥✈í✈✐♦ ❡ ❥♦❣♦s ❡ ✉♠❛ ♣❛♣❡❧❛r✐❛❀
✕ P❛✈✐❧❤ã♦ ❆ ✲ ❜❧♦❝♦ ♣ré✲❢❛❜r✐❝❛❞♦✱ ♦♥❞❡ ❢✉♥❝✐♦♥❛♠ s❛❧❛s ❞❡ ❛✉❧❛s ❡ ✉♠ ❣❛❜✐♥❡t❡ ❞❡ ❛ss✐st❡♥t❡s ♦♣❡r❛❝✐♦♥❛✐s✳
❚♦❞❛s ❛s s❛❧❛s ❞❡ ❛✉❧❛s tê♠ ♣r♦❥❡t♦r ❡ ❝♦♠♣✉t❛❞♦r ❡ ❛❧❣✉♠❛s s❛❧❛s tê♠✱ t❛♠❜é♠✱ q✉❛❞r♦ ✐♥t❡r❛t✐✈♦✳ ❊①✐st❡♠ ❞✉❛s s❛❧❛s ❞❡ ✐♥❢♦r♠át✐❝❛✱ ❝♦♠ ✈ár✐♦s ❝♦♠♣✉t❛❞♦r❡s ♣❛r❛ ✉s♦ ❞♦s ❛❧✉♥♦s ❡✱ ♣❛r❛ ❛❧é♠ ❞❡ss❡s ❞♦✐s ❡s♣❛ç♦s✱ ♦s ❛❧✉♥♦s ♣♦❞❡♠ ✉t✐❧✐③❛r ❝♦♠♣✉t❛❞♦r❡s ❡♠ ❞✉❛s s❛❧❛s ❞❡ ❛✉❧❛✱ ♥❛ ❜✐❜❧✐♦t❡❝❛ ❡ ♥❛ s❛❧❛ ❞❡ ❡st✉❞♦✳
❖ ❡❞✐❢í❝✐♦ ❝♦♠ ♣✐♦r❡s ❝♦♥❞✐çõ❡s é ♦ ♣❛✈✐❧❤ã♦ ❆✱ ♣♦✐s é ✉♠ ♣ré✲❢❛❜r✐❝❛❞♦✱ q✉❡ s❡ ❡♥❝♦♥tr❛ ❜❛st❛♥t❡ ❞❡❣r❛❞❛❞♦✱ ✉♠❛ ✈❡③ q✉❡ s❡ tr❛t❛ ❞❡ ✉♠ ♣❛✈✐❧❤ã♦ q✉❡ s❡ ♣r❡✈✐❛ s❡r t❡♠♣♦rár✐♦ ❡✱ ♥♦ ❡♥t❛♥t♦✱ ❢✉♥❝✐♦♥❛ ❤á ♠❛✐s ❞❡ ✷✵ ❛♥♦s✳ ❆s s❛❧❛s tê♠ ✉♠ ✐s♦❧❛♠❡♥t♦ tér♠✐❝♦ ♠✉✐t♦ ❢r❛❝♦✱ s❡♥❞♦✱ ♣♦r ✐ss♦✱ ♠✉✐t♦ q✉❡♥t❡s ♥♦ ❱❡rã♦ ❡ ♠✉✐t♦ ❢r✐❛s ♥♦ ■♥✈❡r♥♦✳ ❊①✐st❡✱ ♥♦ ❡♥t❛♥t♦✱ ✉♠❛ ♣r❡♦❝✉♣❛çã♦ ❝♦♥st❛♥t❡ ❞❛ ❣❡stã♦ ♥❛ ♠❛♥✉t❡♥çã♦ ❞❛s ❝♦♥❞✐çõ❡s ♠í♥✐♠❛s ❞❡ ❢✉♥❝✐♦♥❛♠❡♥t♦ ❞❡st❡ ♣❛✈✐❧❤ã♦✱ ❡ss❡♥❝✐❛❧ ❛♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❛ ❛t✐✈✐❞❛❞❡ ❧❡t✐✈❛ ❞✐ár✐❛✳
❆ ♠♦✈✐♠❡♥t❛çã♦ ❡♥tr❡ ❛ ♠❛✐♦r✐❛ ❞♦s ♣❛✈✐❧❤õ❡s ♣♦❞❡ s❡r ❡❢❡t✉❛❞❛ ♣♦r ✉♠ ❝❛♠✐♥❤♦ ❝♦♠ ✉♠❛ ❝♦❜❡rt✉r❛ ❞❡ ♣r♦t❡çã♦ ♣❛r❛ ❛ ❝❤✉✈❛✳
✸✳✷ ❆ t✉r♠❛ ❞♦ ✶✷✳➸ ❳ ✸✳✷✳✶ ❈❛r❛❝t❡r✐③❛çã♦ ❞❛ t✉r♠❛
◆♦ ❛♥♦ ❧❡t✐✈♦ ✷✵✶✸✴✷✵✶✹✱ ❛ ♦r✐❡♥t❛❞♦r❛ ♣❡❞❛❣ó❣✐❝❛✱ ♣r♦❢❡ss♦r❛ ❘♦sár✐♦ ▲♦✲ ♣❡s✱ ❧❡❝✐♦♥♦✉ três t✉r♠❛s✱ ❞✉❛s ❞♦ ✶✷✳➸ ❛♥♦ ❞❡ ▼❛t❡♠át✐❝❛ ❆ ❡ ♦✉tr❛ ❞♦ ❝✉rs♦ ❈❊❋✳ ❖ ❡st❛❣✐ár✐♦ ❡st❛✈❛ r❡s♣♦♥sá✈❡❧ ♣♦r ❛❝♦♠♣❛♥❤❛r ✉♠❛ ❞❛s t✉r♠❛s ❞♦
✶✷✳➸ ❛♥♦✱ ❛ t✉r♠❛ ❞♦ ✶✷✳➸ ❳ ♦✉ ✶✷✳➸ ❨✳ ❉✉r❛♥t❡ ❛ ♣r✐♠❡✐r❛ s❡♠❛♥❛ ♦ ♣r♦❢❡s✲ s♦r ❡st❛❣✐ár✐♦ ❛❝♦♠♣❛♥❤♦✉ ♦ tr❛❜❛❧❤♦ ❞❡s❡♥✈♦❧✈✐❞♦ ♥❛s ❞✉❛s t✉r♠❛s ❞♦ ✶✷➸ ❛♥♦✱ t❡♥❞♦ ♣♦st❡r✐♦r♠❡♥t❡ ♦♣t❛❞♦ ♣♦r ❞❡s❡♥✈♦❧✈❡r ♦ tr❛❜❛❧❤♦ ❞❡ ❡stá❣✐♦ ❝♦♠ ❛ t✉r♠❛ ❳✳ ❊st❛ ❡s❝♦❧❤❛ ❞❡✈❡✉✲s❡✱ ❡ss❡♥❝✐❛❧♠❡♥t❡✱ ❛♦ ❢❛❝t♦ ❞♦s ❛❧✉♥♦s s❡r❡♠ ♠❛✐s ♣❛rt✐❝✐♣❛t✐✈♦s ❡♠ ❛✉❧❛ ❡✱ ♣❡❧❛s s✉❛s ❝❛r❛❝t❡ríst✐❝❛s✱ ♣r❡✈✐❛✲s❡ ♠❛✐s ❢á❝✐❧ ❛ s✉❛ ❝♦❧❛❜♦r❛çã♦ ♥♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞♦ tr❛❜❛❧❤♦ ❞❡ ✐♥✈❡st✐❣❛çã♦✳
❆ t✉r♠❛ ❞♦ ✶✷✳➸ ❳✱ ❡r❛ ❝♦♥st✐t✉í❞❛ ♣♦r ✈✐♥t❡ ❡ s❡t❡ ❛❧✉♥♦s ❞♦s q✉❛✐s ✈✐♥t❡ ❡ ✉♠ ❡st❛✈❛♠ ✐♥s❝r✐t♦s ♥❛ ❞✐s❝✐♣❧✐♥❛ ❞❡ ▼❛t❡♠át✐❝❛ ❆ ❡ s❡✐s ❡r❛♠ ❛❧✉♥♦s ❛ss✐st❡♥t❡s q✉❡ ❛❝♦♠♣❛♥❤❛✈❛♠ ❛s ❛✉❧❛s r❡❣✉❧❛r♠❡♥t❡✳ ❉♦s ✈✐♥t❡ ❡ ✉♠ ❛❧✉♥♦s ✐♥s❝r✐t♦s✱ ✶✷ ❡r❛♠ ❞♦ s❡①♦ ♠❛s❝✉❧✐♥♦ ❡ ❛♣❡♥❛s ✾ ❞♦ s❡①♦ ❢❡♠✐♥✐♥♦✳ ❆s s✉❛s ✐❞❛❞❡s ✈❛r✐❛✈❛♠ ❡♥tr❡ ❡♥tr❡ ♦s ✶✻ ❡ ✶✽ ❛♥♦s✱ ❝♦♠♦ s❡ ♣♦❞❡ ♦❜s❡r✈❛r ♥♦ ❣rá✜❝♦ ❞❛ ✜❣✉r❛ ✸✳✷✳
❋✐❣✉r❛ ✸✳✷✿ ❉✐str✐❜✉✐çã♦ ❞❛s ■❞❛❞❡s ❞♦s ❛❧✉♥♦s ❞❛ t✉r♠❛ ✶✷✳➸ ❳
❆♥❛❧✐s❛♥❞♦ ❛ ✜❣✉r❛ ✸✳✷✱ ♦❜s❡r✈❛✲s❡ q✉❡ ❛ ♠❛✐♦r✐❛ ❞♦s ❛❧✉♥♦s t✐♥❤❛♠ ✶✻ ♦✉ ✶✼ ❛♥♦s ❡ ❛♣❡♥❛s ✻ ❛❧✉♥♦s ✭✷✵✪ ❞♦ t♦t❛❧ ❞❡ ❛❧✉♥♦s ❞❛ t✉r♠❛✮ t✐♥❤❛♠ ✶✽ ❛♥♦s✳ ❉❡st❡ ❢❛❝t♦ ♣♦❞❡✲s❡ ✐♥❢❡r✐r q✉❡ ♦s ❛❧✉♥♦s ❞❛ t✉r♠❛ ❡❢❡t✉❛r❛♠ ✉♠ ♣❡r❝✉rs♦ ❡s❝♦❧❛r s❡♠ r❡t❡♥çõ❡s✳
❈♦♠ ♦ ♦❜❥❡t✐✈♦ ❞❡ ❝♦♥❤❡❝❡r ♠❡❧❤♦r ♦ ♣❡r❝✉rs♦ ❞♦s ❛❧✉♥♦s✱ ♥❛ ❞✐s❝✐♣❧✐♥❛ ❞❡ ▼❛t❡♠át✐❝❛ ❆✱ ❛♦ ❧♦♥❣♦ ❞♦ ❡♥s✐♥♦ s❡❝✉♥❞ár✐♦✱ ❛♣r❡s❡♥t❛✲s❡ ♥♦ ❣rá✜❝♦ ❞❛ ✜❣✉r❛ ✸✳✸ ❛ ❞✐str✐❜✉✐çã♦ ❞❛s ❝❧❛ss✐✜❝❛çõ❡s ❞♦s ❛❧✉♥♦s ♥♦s ✶✵✳➸ ❡ ✶✶✳➸ ❛♥♦s✳ ❉❛ ❛♥á❧✐s❡ ❡ ✐♥t❡r♣r❡t❛çã♦ ❞❡st❡s ❞❛❞♦s é ♣♦ssí✈❡❧ ❝♦♥❝❧✉✐r q✉❡ ❛ ♠é❞✐❛ ❞♦s ❛❧✉♥♦s ❞❛ t✉r♠❛ à ❞✐s❝✐♣❧✐♥❛ ❢♦✐ ❞❡ ✶✷✱✽ ✈❛❧♦r❡s ♥♦ ✶✵✳➸ ❛♥♦ ❡ ❞❡ ✶✷ ✈❛❧♦r❡s ♥♦ ✶✶✳➸ ❛♥♦✳ ❆ ♦s❝✐❧❛çã♦ ♥❛ ♠é❞✐❛ ❞❡st❡s ❞♦✐s ❛♥♦s ❞❡ ❡s❝♦❧❛r✐❞❛❞❡ ❞❡✈❡✉✲s❡ ❛♦ ❢❛❝t♦ ❞❡ ♥♦ ✶✶✳➸ ❛♥♦✱ três ❛❧✉♥♦s t❡r❡♠ ❝❧❛ss✐✜❝❛çã♦ ♥❡❣❛t✐✈❛ ❡ ❛♦ ❢❛❝t♦ ❞❛s ❝❧❛ss✐✜❝❛çõ❡s ❞❛ t✉r♠❛ ♥ã♦ ✉❧tr❛♣❛ss❛r❡♠ ♦s ✶✺ ✈❛❧♦r❡s✱ ❡♥q✉❛♥t♦ ♥♦
✶✵✳➸ ❛♥♦ ❛s ❝❧❛ss✐✜❝❛çõ❡s s✐t✉❛r❛♠✲s❡ ❡♥tr❡ ♦s ✶✵ ❡ ♦s ✶✻ ✈❛❧♦r❡s✱ ❤❛✈❡♥❞♦✱ s♦♠❡♥t❡✱ ✉♠ ❛❧✉♥♦ ❝♦♠ ✶✵ ✈❛❧♦r❡s✱ ❡♥q✉❛♥t♦ ♥♦ ✶✶✳➸ ❛♥♦ q✉❛tr♦ ❞♦s ❛❧✉♥♦s ❛♣r❡s❡♥t❛✈❛♠ ❡st❛ ❝❧❛ss✐✜❝❛çã♦✳
❋✐❣✉r❛ ✸✳✸✿ ❈❧❛ss✐✜❝❛çõ❡s ❞♦s ❛❧✉♥♦s ❞❛ t✉r♠❛ ❞♦ ✶✷✳➸ ❳
❆ ♠❛✐♦r✐❛ ❞♦s ❛❧✉♥♦s ❞❛ t✉r♠❛ ✈✐✈✐❛ ♥❛ ❯♥✐ã♦ ❞❛ ❋r❡❣✉❡s✐❛s ❞❡ ▲❛r❛♥❥❡✐r♦ ❡ ❋❡✐❥ó ✭✶✵ ❛❧✉♥♦s✮✱ s❡✐s ❞♦s ❛❧✉♥♦s ✈✐✈✐❛♠ ♥❛ ❢r❡❣✉❡s✐❛ ❞❡ ❈♦rr♦✐♦s✱ ❡ ♦s r❡st❛♥t❡s ❛❧✉♥♦s ❞✐str✐❜✉✐❛♠✲s❡ ♣❡❧❛s ❢r❡❣✉❡s✐❛s ❞❛ ❯♥✐ã♦ ❞❛s ❋r❡❣✉❡s✐❛s ❞❡ ❈❤❛r♥❡❝❛ ❞❛ ❈❛♣❛r✐❝❛ ❡ ❙♦❜r❡❞❛ ❡ ❞❛ ❯♥✐ã♦ ❞❛s ❋r❡❣✉❡s✐❛s ❞❡ ❆❧♠❛❞❛✱ ❈♦✈❛ ❞❛ P✐❡❞❛❞❡✱ Pr❛❣❛❧ ❡ ❈❛❝✐❧❤❛s✳
❆ ♠❛✐♦r✐❛ ❞❡st❡s ❛❧✉♥♦s t✐♥❤❛ ❝♦♠♦ ❊♥❝❛rr❡❣❛❞♦ ❞❡ ❊❞✉❝❛çã♦ ❛ ♠ã❡ ✭✶✶ ❛❧✉♥♦s✮✱ ❛♣❡♥❛s ❞♦✐s ❛❧✉♥♦s ❡r❛♠ ♦s ♣ró♣r✐♦s ❊♥❝❛rr❡❣❛❞♦s ❞❡ ❊❞✉❝❛çã♦✱ ❡ ♦s r❡st❛♥t❡s t✐♥❤❛♠ ❝♦♠♦ ❊♥❝❛rr❡❣❛❞♦ ❞❡ ❊❞✉❝❛çã♦ ♦ ♣❛✐✳ ❖ s❡❣✉✐♥t❡ ❣rá✜❝♦ ❛♣r❡s❡♥t❛ ❛ ❞✐str✐❜✉✐çã♦ ❞♦s ❞✐❢❡r❡♥t❡s ♥í✈❡✐s ❞❡ ❡♥s✐♥♦ ❞♦s ❊♥❝❛rr❡❣❛❞♦s ❞❡ ❊❞✉❝❛çã♦✱ t❡♥❞♦ s✐❞♦ ❛♣❡♥❛s ❝♦♥s✐❞❡r❛❞♦s ♦s ❊♥❝❛rr❡❣❛❞♦s ❞❡ ❞❡③❛ss❡t❡ ❛❧✉♥♦s✱ ❥á q✉❡ ❞♦✐s ❛❧✉♥♦s ❡r❛♠ ❊♥❝❛rr❡❣❛❞♦s ❞❡ ❊❞✉❝❛çã♦ ❞❡ s✐ ♣ró♣r✐♦s ❡ s♦❜r❡ ♦s r❡st❛♥t❡s ❛❧✉♥♦s ♥ã♦ ❡①✐st✐❛ ✐♥❢♦r♠❛çã♦ ❞✐s♣♦♥í✈❡❧✳
❋✐❣✉r❛ ✸✳✹✿ ❉✐str✐❜✉✐çã♦ ❞♦s ♥í✈❡✐s ❞❡ ❡♥s✐♥♦ ❞♦s ❊♥❝❛rr❡❣❛❞♦s ❞❡ ❊❞✉❝❛çã♦
❆♥❛❧✐s❛♥❞♦ ❛ ✜❣✉r❛ ✸✳✹ ❝♦♥❝❧✉✐✲s❡ q✉❡ ♠❛✐s ❞❡ ♠❡t❛❞❡ ❞♦s ❊♥❝❛rr❡❣❛❞♦s ❞❡ ❊❞✉❝❛çã♦ ❝♦♠♣❧❡t❛r❛♠ ♣❡❧♦ ♠❡♥♦s ♦ ❡♥s✐♥♦ ❙❡❝✉♥❞ár✐♦✱ ✶✽✪ ❞♦s ❊♥❝❛r✲ r❡❣❛❞♦s ❞❡ ❊❞✉❝❛çã♦ t✐♥❤❛♠ ♦ ✸✳➸ ❝✐❝❧♦ ❝♦♠♣❧❡t♦✱ ❡ ❛♣❡♥❛s ✉♠ ❊♥❝❛rr❡❣❛❞♦ ❞❡ ❊❞✉❝❛çã♦ ❝♦♠♣❧❡t♦✉ ❛♣❡♥❛s ♦ ♥í✈❡❧ ❞❡ ❊♥s✐♥♦ ♠❛✐s ❜❛✐①♦ ✭✶➸ ❝✐❝❧♦✮✳
❆ ♠❛✐♦r✐❛ ❞♦s ❛❧✉♥♦s ❢r❡q✉❡♥t❛r❛♠ ❛ ♠❡s♠❛ t✉r♠❛ ❞❡s❞❡ ♦ ✼✳➸ ❛♥♦✱ s❡♥❞♦✱ ♣♦r ✐ss♦✱ ✉♠❛ t✉r♠❛ ❜❛st❛♥t❡ ✉♥✐❞❛✱ ❝♦♥st✐t✉✐♥❞♦ ✉♠ ❜♦♠ ❣r✉♣♦ ❞❡ tr❛❜❛❧❤♦✳ ◆♦ ❣❧♦❜❛❧✱ ♦s ❛❧✉♥♦s ❡r❛♠ tr❛❜❛❧❤❛❞♦r❡s ❡ r❡s♣♦♥sá✈❡✐s✱ ❝♦♥t✉❞♦ ❡①✐st✐❛♠ ❛❧❣✉♥s ❛❧✉♥♦s q✉❡ ♥ã♦ ❡r❛♠ ♣♦♥t✉❛✐s ❡ ❤❛✈✐❛ r❡❣✐st♦s ❞❡ ❛❧❣✉♠❛s ❝♦♥✈❡rs❛s ♣❛r❛❧❡❧❛s ❞✉r❛♥t❡ ❛s ❛✉❧❛s✳
❆ ♣r♦❢❡ss♦r❛ ♦r✐❡♥t❛❞♦r❛ ♥ã♦ ❝♦♥❤❡❝✐❛ ♦s ❛❧✉♥♦s✱ s❛❜❡♥❞♦ ❛♣❡♥❛s q✉❡ ❡st❡s t✐♥❤❛♠ t✐❞♦ ✉♠ ♣❡r❝✉rs♦ ❡s❝♦❧❛r ❞✐❢í❝✐❧ ♥❛ ❞✐s❝✐♣❧✐♥❛ ❞❡ ▼❛t❡♠át✐❝❛ ❆✱ ❝♦♠ ✈ár✐♦s ♣r♦❢❡ss♦r❡s ❛ ❧❡❝✐♦♥❛r ❛ ❞✐s❝✐♣❧✐♥❛ ❛♦ ❧♦♥❣♦ ❞♦ ✶✵➸ ❛♥♦✳ P♦r ♦✉tr♦ ❧❛❞♦ ❛ ✐rr❡❣✉❧❛r✐❞❛❞❡ ❞♦ ♣❡r❝✉rs♦ ❞♦s ❛❧✉♥♦s ♥♦ ✶✵➸ ❛♥♦ ✐♥✢✉❡♥❝✐♦✉ ♥❡❣❛t✐✈❛♠❡♥t❡ ❛ r❡❧❛çã♦ ❡♥tr❡ ♦s ❊♥❝❛rr❡❣❛❞♦s ❞❡ ❊❞✉❝❛çã♦ ❡ ♦ ❈♦♥s❡❧❤♦ ❞❡ ❚✉r♠❛✱ ♥♦ ❛♥♦ ❧❡t✐✈♦ ❛♥t❡r✐♦r✳ ◆ã♦ ♦❜st❛♥t❡ ❛ ✐♥❝❡rt❡③❛ s♦❜r❡ ❛ ❢♦r♠❛ ❝♦♠♦ ♦s ❛❧✉♥♦s ❡ ❊♥❝❛rr❡❣❛❞♦s ❞❡ ❊❞✉❝❛çã♦ ✐r✐❛♠ ❛❝♦♠♣❛♥❤❛r ♦ tr❛❜❛❧❤♦ ❛ ❞❡s❡♥✈♦❧✈❡r ♥❛ ❞✐s❝✐♣❧✐♥❛✱ é ❞❡ s❛❧✐❡♥t❛r ❛ ❜♦❛ r❡❝❡t✐✈✐❞❛❞❡ ❞♦s ❛❧✉♥♦s ❡ ❞♦s ❊♥❝❛rr❡❣❛❞♦s ❞❡ ❊❞✉❝❛çã♦ à ♣r❡s❡♥ç❛ ❞♦ ♣r♦❢❡ss♦r ❡st❛❣✐ár✐♦ ❡♠ s❛❧❛ ❞❡ ❛✉❧❛✳
❊st❡ ❛♠❜✐❡♥t❡ ❞❡ tr❛❜❛❧❤♦ ❢♦✐ ♣r♦♣í❝✐♦ às ❛♣r❡♥❞✐③❛❣❡♥s ❡✱ à ❞❛t❛ ❞❛ ❡♥tr❡❣❛ ❞❡st❡ r❡❧❛tór✐♦ é ♣♦ssí✈❡❧ ❛♣r❡s❡♥t❛r ♦s r❡s✉❧t❛❞♦s ❣❧♦❜❛✐s ❞❛ t✉r♠❛ à ❞✐s❝✐♣❧✐♥❛✳
❋✐❣✉r❛ ✸✳✺✿ ❈❧❛ss✐✜❝❛çã♦ ❞♦ ✸✳➸ ♣❡rí♦❞♦ ❞❛ t✉r♠❛ ✶✷✳➸ ❳
➱ ❞❡ r❡❛❧ç❛r✱ q✉❡ ❛♣❡s❛r ❞❡ ❛❧❣✉♠❛s ❝❧❛ss✐✜❝❛çõ❡s ✐♥❢❡r✐♦r❡s ❛ ✶✵ ✈❛❧♦r❡s✱ t♦❞♦s ♦s ❛❧✉♥♦s ❢♦r❛♠ ❛❞♠✐t✐❞♦s ❛ ❡①❛♠❡ ♥❛❝✐♦♥❛❧ ❝♦♠♦ ❛❧✉♥♦s ✐♥t❡r♥♦s✳
✹ Prát✐❝❛ P❡❞❛❣ó❣✐❝❛
❊st❛ t✉r♠❛✱ r❡❧❛t✐✈❛♠❡♥t❡ à ❞✐s❝✐♣❧✐♥❛ ❞❡ ▼❛t❡♠át✐❝❛ ❆✱ t✐♥❤❛ ♠❛tér✐❛ ♥ã♦ ❧❡❝✐♦♥❛❞❛ ❡♠ ❛♥♦s ❛♥t❡r✐♦r❡s ♥♦♠❡❛❞❛♠❡♥t❡ ♦ ❝❛♣ít✉❧♦ ❞❡ ❊st❛tíst✐❝❛ ❞♦ ✶✵✳➸ ❛♥♦ ❡ ❛ ✉♥✐❞❛❞❡ ❞❡ ❙✉❝❡ssõ❡s ❞♦ ✶✶✳➸ ❛♥♦ ❡ ♥ã♦ t❡♥❞♦ t❛♠❜é♠ s✐❞♦ ❝♦♥❝❧✉í❞♦ ♦ ❝❛♣ít✉❧♦ ❞❛s ❋✉♥çõ❡s ❞♦ ✶✶✳➸ ❛♥♦✳ ❉❡✈✐❞♦ ❛ ❡st❡s ❛tr❛s♦s ❡ ♣♦r s❡r ❛♥♦ ❞❡ ❊①❛♠❡ ◆❛❝✐♦♥❛❧ à ❞✐s❝✐♣❧✐♥❛✱ ❡r❛ ❢✉♥❞❛♠❡♥t❛❧ ❣❛r❛♥t✐r ♦ ❝✉♠♣r✐♠❡♥t♦ ✐♥t❡❣r❛❧ ❞♦ ♣r♦❣r❛♠❛ ❞♦ ❡♥s✐♥♦ s❡❝✉♥❞ár✐♦✱ ♣❡❧♦ q✉❡ ❛ ❡s❝♦❧❛ ♣r♦♣♦r❝✐♦♥♦✉ ❛ ❧❡❝✐♦♥❛çã♦ ❛❞✐❝✐♦♥❛❧ ❞❡ ✉♠ t❡♠♣♦ s❡♠❛♥❛❧ ❞❡ ✺✵ ♠✐♥✉t♦s ❛♦ ❧♦♥❣♦ ❞❡ t♦❞♦ ♦ ❛♥♦ ❧❡t✐✈♦✳ ❆ss✐♠✱ ♦ ❤♦rár✐♦ ❞❛ ❞✐s❝✐♣❧✐♥❛ ❢♦✐ ❝♦♥st✐t✉í❞♦ ♣♦r ♦✐t♦ ❜❧♦❝♦s ❞❡ ❝✐♥q✉❡♥t❛ ♠✐♥✉t♦s✱ ❞✐str✐❜✉í❞♦s s❡♠❛♥❛❧♠❡♥t❡ ❞❛ s❡❣✉✐♥t❡ ❢♦r♠❛✿
❍♦r❛s ✷✳➟ ❢❡✐r❛ ✸✳➟ ❢❡✐r❛ ✹✳➟ ❢❡✐r❛ ✺✳➟ ❢❡✐r❛ ✻✳➟ ❢❡✐r❛
✵✽✿✵✵✲✵✽✿✺✵ ▼❛t✳ ❆ ▼❛t✳ ❆ ▼❛t✳ ❆
✵✾✿✵✵✲✵✾✿✺✵ ▼❛t✳ ❆ ▼❛t✳ ❆ ▼❛t✳ ❆
✶✵✿✶✺✲✶✶✿✵✺ ✶✶✿✶✺✲✶✷✿✵✺ ✶✷✿✶✺✲✶✸✿✵✺
✶✸✿✸✵✲✶✹✿✷✵ ▼❛t✳❆ ✶✹✿✸✵✲✶✺✿✷✵ ▼❛t✳❆
❚❛❜❡❧❛ ✹✳✶✿ ❍♦rár✐♦ ❞❛ ❞✐s❝✐♣❧✐♥❛ ❞❡ ▼❛t❡♠át✐❝❛ ❆ ♣❛r❛ ♦ ✶✷✳➸ ❳
❖ ♣r♦❣r❛♠❛ ❞❡ ▼❛t❡♠át✐❝❛ ❆ ♣❛r❛ ♦ ✶✷✳➸ ❛♥♦ ❛t✉❛❧♠❡♥t❡ ❡♠ ✈✐❣♦r ❡stá ❞✐✈✐❞✐❞♦ ❡♠ três t❡♠❛s✿
✶✳ Pr♦❜❛❜✐❧✐❞❛❞❡s ❡ ❈♦♠❜✐♥❛tór✐❛❀
✷✳ ■♥tr♦❞✉çã♦ ❛♦ ❈á❧❝✉❧♦ ❉✐❢❡r❡♥❝✐❛❧ ■■❀
✸✳ ❚r✐❣♦♥♦♠❡tr✐❛ ❡ ◆ú♠❡r♦s ❈♦♠♣❧❡①♦s✳
❖ ♣r✐♠❡✐r♦ t❡♠❛ ❞✐✈✐❞❡✲s❡ ❡♠ três s✉❜t❡♠❛s✿
✶✳ ■♥tr♦❞✉çã♦ ❛♦ ❈á❧❝✉❧♦ ❞❛s Pr♦❜❛❜✐❧✐❞❛❞❡s✱ ♥♦ q✉❛❧ s❡ ✐♥tr♦❞✉③✱ ❡♥tr❡ ♦✉tr♦s✱ ♦ ❝♦♥❝❡✐t♦ ❞❡ ❡①♣❡r✐ê♥❝✐❛ ❛❧❡❛tór✐❛✱ ❞❡✜♥✐çã♦ ❢r❡q✉❡♥t✐st❛ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❡ ❞❡✜♥✐çã♦ ❝❧áss✐❝❛ ❞❡ ▲❛♣❧❛❝❡❀
✷✳ ❉✐str✐❜✉✐çã♦ ❞❡ ❋r❡q✉ê♥❝✐❛s ❘❡❧❛t✐✈❛s ❡ ❉✐str✐❜✉✐çã♦ ❞❡ Pr♦❜❛❜✐❧✐❞❛✲ ❞❡s✱ ♥♦ q✉❛❧ sã♦ ✐♥tr♦❞✉③✐❞♦s ❛❧❣✉♥s ❝♦♥❝❡✐t♦s r❡❧❛t✐✈♦s à ❞✐str✐❜✉✐çã♦ ❞❡ ❢r❡q✉ê♥❝✐❛s✱ t❛✐s ❝♦♠♦✿ ✈❛r✐á✈❡❧ ❛❧❡❛tór✐❛✱ ❢✉♥çã♦ ♠❛ss❛ ❞❡ ♣r♦❜❛✲ ❜✐❧✐❞❛❞❡✱ ♠♦❞❡❧♦ ❜✐♥♦♠✐❛❧ ❡ ♠♦❞❡❧♦ ♥♦r♠❛❧❀
✸✳ ❈á❧❝✉❧♦ ❈♦♠❜✐♥❛tór✐♦✱ ♥♦ q✉❛❧ ♦s ❝♦♥❝❡✐t♦s tr❛t❛❞♦s sã♦✿ ❛rr❛♥❥♦s s✐♠✲ ♣❧❡s ❡ ❝♦♠♣❧❡t♦s✱ ♣❡r♠✉t❛çõ❡s✱ ❝♦♠❜✐♥❛çõ❡s✱ tr✐â♥❣✉❧♦ ❞❡ P❛s❝❛❧ ❡ ❜✐✲ ♥ó♠✐♦ ❞❡ ◆❡✇t♦♥✳
❚❛❧ ❝♦♠♦ ♦ ♣r✐♠❡✐r♦ t❡♠❛ ❞♦ ✶✷✳➸ ❛♥♦✱ ♦ s❡❣✉♥❞♦ t❛♠❜é♠ s❡ ❞✐✈✐❞❡ ❡♠ três s✉❜t❡♠❛s✿
✶✳ ❋✉♥çõ❡s ❊①♣♦♥❡♥❝✐❛✐s ❡ ▲♦❣❛rít♠✐❝❛s✱ ♥♦ q✉❛❧ s❡ ❢❛③✱ ♣♦r ❡①❡♠♣❧♦✱ ✉♠ ❡st✉❞♦ ❞❛s ❢✉♥çõ❡s ❧♦❣❛rít♠✐❝❛s ❡ ❡①♣♦♥❡♥❝✐❛✐s✱ ❛♣r❡♥❞❡✲s❡ ❛ r❡s♦❧✈❡r ❡q✉❛çõ❡s ❡ ✐♥❡q✉❛çõ❡s ❡①♣♦♥❡♥❝✐❛✐s ❡ ❧♦❣❛rít♠✐❝❛s❀
✷✳ ❚❡♦r✐❛ ❞❡ ▲✐♠✐t❡s✱ ♥♦ q✉❛❧ sã♦ ✐♥tr♦❞✉③✐❞♦s ❝♦♥❝❡✐t♦s r❡❧❛t✐✈♦s ❛ ❧✐♠✐t❡s ❡ ❝♦♥t✐♥✉✐❞❛❞❡ ❞❛♥❞♦ ❛ ❞❡✜♥✐çã♦ ❞❡ ❧✐♠✐t❡ s❡❣✉♥❞♦ ❍❡✐♥❡✱ ✐♥tr♦❞✉③✐♥❞♦ ♦ ❝♦♥❝❡✐t♦ ❞❡ ❧✐♠✐t❡s ♥♦tá✈❡✐s ❡ ♦ ❝á❧❝✉❧♦ ❞❡ ❛❧❣✉♠ t✐♣♦ ❞❡ ✐♥❞❡t❡r♠✐✲ ♥❛çõ❡s❀
✸✳ ❈á❧❝✉❧♦ ❉✐❢❡r❡♥❝✐❛❧✱ q✉❡ é ❛ ❝♦♥t✐♥✉❛çã♦ ❞❡ ✉♠ t❡♠❛ ✐♥✐❝✐❛❞♦ ♥♦ ✶✶✳➸ ❛♥♦ ✭❈á❧❝✉❧♦ ❉✐❢❡r❡♥❝✐❛❧ ■✮✱ ♥♦ q✉❛❧ s❡ ❢❛③ ✉♠ ❡st✉❞♦ ♠❛✐s ♣♦r♠❡♥♦r✐✲ ③❛❞♦ ❞♦ ❈á❧❝✉❧♦ ❉✐❢❡r❡♥❝✐❛❧✱ ❞❡s❡♥✈♦❧✈❡♥❞♦ ❛❧❣✉♠❛s ♥♦çõ❡s ❞❛❞❛s ♥♦ ✶✶✳➸ ❛♥♦✳
❖ t❡r❝❡✐r♦ t❡♠❛ ❞✐✈✐❞❡✲s❡ ❡♠ ❞♦✐s s✉❜t❡♠❛s✱ ❋✉♥çõ❡s s❡♥♦✱ ❝♦ss❡♥♦ ❡ t❛♥❣❡♥t❡ ❡ ◆ú♠❡r♦s ❝♦♠♣❧❡①♦s✿
✶✳ ◆♦ t❡♠❛ ❋✉♥çõ❡s s❡♥♦✱ ❝♦ss❡♥♦ ❡ t❛♥❣❡♥t❡ é ❡❢❡t✉❛❞♦ ✉♠ ❡st✉❞♦ ❝♦♠✲ ♣❧❡t♦✱ ✉t✐❧✐③❛♥❞♦ ❞❡✜♥✐çõ❡s ❞❛❞❛s ♥♦ ♣r❡s❡♥t❡ ❛♥♦✱ ❞❛s ❢✉♥çõ❡s tr✐❣♦✲ ♥♦♠étr✐❝❛s ❛♥❛❧✐s❛❞❛s ♥♦ ✶✶✳➸ ❛♥♦ ❡ ❛♣r❡s❡♥t❛♠✲s❡ ❛♣❧✐❝❛çõ❡s ❞❡st❛s ❢✉♥çõ❡s ❡♠ s✐t✉❛çõ❡s r❡❛✐s❀
✷✳ ◆♦ s❡❣✉♥❞♦ s✉❜t❡♠❛✱ ◆ú♠❡r♦s ❝♦♠♣❧❡①♦s✱ ✐♥tr♦❞✉③✲s❡ ♦ ❝♦♥❝❡✐t♦ ❞❡ ♥ú♠❡r♦ ❝♦♠♣❧❡①♦✱ ❛s ❞✐❢❡r❡♥t❡s r❡♣r❡s❡♥t❛çõ❡s ❞❡st❡s ♥ú♠❡r♦s ❡ ❛❧❣✉✲ ♠❛s r❡♣r❡s❡♥t❛çõ❡s ❞❡ ❞♦♠í♥✐♦s ♣❧❛♥♦s ✉t✐❧✐③❛♥❞♦ ❝♦♥❞✐çõ❡s ❡♠ ✈❛r✐á✲ ✈❡❧ ❝♦♠♣❧❡①❛✳
❖s t❡♠❛s ❢♦r❛♠ ❧❡❝✐♦♥❛❞♦s ♣❡❧❛ ♦r❞❡♠ ❡♠ q✉❡ ❢♦r❛♠ ❛♣r❡s❡♥t❛❞♦s✳
❈♦♠♦ r❡❢❡r✐❞♦ ✐♥✐❝✐❛❧♠❡♥t❡✱ ❛ t✉r♠❛ ❳ ❞♦ ✶✷✳➸ ❛♥♦ ♥ã♦ ❝♦♠♣❧❡t♦✉ t♦❞❛s ❛s ✉♥✐❞❛❞❡s ❞♦s ❛♥♦s ❛♥t❡r✐♦r❡s✱ t❛✐s ❝♦♠♦✿
✶✳ ❙✉❝❡ssõ❡s ❘❡❛✐s ✲ ✶✶✳➸ ❛♥♦❀
✷✳ ❊st❛tíst✐❝❛ ✲ ✶✵✳➸ ❛♥♦✳
◆♦ t❡♠❛ ❞❛ ■♥tr♦❞✉çã♦ ❛♦ ❈á❧❝✉❧♦ ❞✐❢❡r❡♥❝✐❛❧ ■✱ ❋✉♥çõ❡s ❘❛❝✐♦♥❛✐s ❡ ❝♦♠ r❛❞✐❝❛✐s✱ t❛①❛ ❞❡ ✈❛r✐❛çã♦ ❡ ❞❡r✐✈❛❞❛ ❞♦ ✶✶✳➸ ❛♥♦ ♥ã♦ ❢♦✐ ❧❡❝✐♦♥❛❞❛ ❛ ♠❛tér✐❛ ❛té à ❞❡✜♥✐çã♦ ❞❡ ❞❡r✐✈❛❞❛ ❞❡ ✉♠❛ ❢✉♥çã♦✱ ❢❛❧t❛♥❞♦✱ ♣♦r ✐ss♦✱ ❧❡❝✐♦♥❛r ♦s s✉❜t❡♠❛s ❞❛ ❋✉♥çã♦ ❞❡r✐✈❛❞❛ ❡ ❉❡r✐✈❛❞❛ ❞❡ ❛❧❣✉♠❛s ❢✉♥çõ❡s ❡ ♦s t❡♠❛s ❋✉♥çõ❡s ❞❡✜♥✐❞❛s ♣♦r ❞♦✐s ♦✉ ♠❛✐s r❛♠♦s✱ ❖♣❡r❛çõ❡s ❝♦♠ ❢✉♥çõ❡s✱ ■♥✈❡rs❛ ❞❡ ✉♠❛ ❢✉♥çã♦ ❡ ❋✉♥çõ❡s ❝♦♠ r❛❞✐❝❛✐s q✉❛❞rát✐❝♦s ♦✉ ❝ú❜✐❝♦s✳
❈♦♠♦ ♦ ❡①❛♠❡ ♥❛❝✐♦♥❛❧ ❞❡ ▼❛t❡♠át✐❝❛ ❆ ♥♦ ♣r❡s❡♥t❡ ❛♥♦ ❧❡t✐✈♦ ✭✷✵✶✸✴✷✵✶✹✮ r❡❢❡r❡✲s❡ à ♠❛tér✐❛ ❞♦ ✶✶✳➸ ❡ ✶✷✳➸ ❛♥♦✱ ❡r❛ ❞❡ t♦❞♦ ♦ ✐♥t❡r❡ss❡ ❧❡❝✐♦♥❛r ❛ ♠❛té✲ r✐❛ q✉❡ ♥ã♦ t✐♥❤❛ s✐❞♦ ❛❜♦r❞❛❞❛ ♥♦ ❛♥♦ ❛♥t❡r✐♦r✳ ❈♦♠ ❡st❡ ♦❜❥❡t✐✈♦✱ ♦♣t♦✉✲s❡ ♣♦r ❧❡❝✐♦♥❛r ❛s ❙✉❝❡ssõ❡s ❘❡❛✐s ❛♣ós ❛ ❝♦♥❝❧✉sã♦ ❞♦ t❡♠❛ ❞❛s Pr♦❜❛❜✐❧✐❞❛❞❡s ❡ ❛♥t❡s ❞❡ t❡r s✐❞♦ ✐♥✐❝✐❛❞♦ ♦ ❞❛ ■♥tr♦❞✉çã♦ ❛♦ ❈á❧❝✉❧♦ ❞✐❢❡r❡♥❝✐❛❧ ■■✳ ❘❡❧❛t✐✲ ✈❛♠❡♥t❡ à ■♥tr♦❞✉çã♦ ❛♦ ❈á❧❝✉❧♦ ❉✐❢❡r❡♥❝✐❛❧ ■✱ q✉❡ ♥ã♦ t✐♥❤❛ s✐❞♦ ❝♦♥❝❧✉í❞❛ ♥♦ ❛♥♦ ❛♥t❡r✐♦r✱ ❢♦✐ ❧❡❝✐♦♥❛❞❛ ❛♥t❡s ❞❡ ✐♥✐❝✐❛r ♦ ♠❡s♠♦ s✉❜t❡♠❛ ♥♦ ✶✷✳➸ ❛♥♦✳ ❉❡❝✐❞✐✉✲s❡✱ t❛♠❜é♠✱ ❧❡❝✐♦♥❛r ❛ ❡st❛tíst✐❝❛ ❞♦ ✶✵✳➸ ❛♥♦✱ ♣♦✐s✱ ❛♣❡s❛r ❞❡ ♥ã♦ s❡r❡♠ ❝♦♥t❡ú❞♦s ❡s♣❡❝í✜❝♦s ❞❡ ❡①❛♠❡ ♥❛❝✐♦♥❛❧✱ ❡st❡ t❡♠❛ é ❢✉♥❞❛♠❡♥t❛❧ ♣❛r❛ ❛ ❛♣r❡♥❞✐③❛❣❡♠ ❞❛s ♣r♦❜❛❜✐❧✐❞❛❞❡s✳ ❊st❛ ♠❛tér✐❛ ❢♦✐ ❧❡❝✐♦♥❛❞❛ ♥♦ ✐♥í❝✐♦ ❞♦ ❛♥♦ ❧❡t✐✈♦✱ ❛♥t❡s ❞❡ s❡r ✐♥✐❝✐❛❞♦ ♦ ♣r✐♠❡✐r♦ t❡♠❛ ❞♦ ✶✷✳➸ ❛♥♦✳ ❊sq✉❡♠❛t✐✲ ❝❛♠❡♥t❡✱ ♦ ♣❧❛♥♦ ❛♥✉❛❧ ❞❛ ❞✐s❝✐♣❧✐♥❛ ❢♦✐ ❞❡s❡♥✈♦❧✈✐❞♦ ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛ t❛❜❡❧❛ s❡❣✉✐♥t❡✿
P❡rí♦❞♦ ❚❡♠❛ ❆♥♦ ♥✳➸ ❞❡ ❜❧♦❝♦s
✶✳➸ ❊st❛tíst✐❝❛ ✶✵✳➸ ✶✵
✶✳➸ Pr♦❜❛❜✐❧✐❞❛❞❡s ✶✷✳➸ ✹✾
✶✳➸ ❙✉❝❡ssõ❡s ❘❡❛✐s ✶✶✳➸ ✷✹
✷✳➸ ■♥tr♦❞✉çã♦ ❛♦ ❈á❧❝✉❧♦ ❉✐❢❡r❡♥❝✐❛❧ ■■ ✶✷✳➸ ✽✽ ✷✳➸ ■♥tr♦❞✉çã♦ ❛♦ ❈á❧❝✉❧♦ ❉✐❢❡r❡♥❝✐❛❧ ■ ✶✶✳➸
✷✳➸ ❡ ✸✳➸ ❋✉♥çõ❡s ❚r✐❣♦♥♦♠étr✐❝❛s ✶✷✳➸ ✸✵
✸✳➸ ◆ú♠❡r♦s ❈♦♠♣❧❡①♦s ✶✷✳➸ ✷✵
❚❛❜❡❧❛ ✹✳✷✿ P❧❛♥♦ ❛♥✉❛❧ ❞❡ ▼❛t❡♠át✐❝❛ ❆ ♥♦ ✶✷✳➸ ❛♥♦ ❞❛ t✉r♠❛ ❳
◆❛ t❛❜❡❧❛ ✹✳✷ ♦ t❡♠❛ ■♥tr♦❞✉çã♦ ❛♦ ❈á❧❝✉❧♦ ❉✐❢❡r❡♥❝✐❛❧ ■ r❡❧❛t✐✈❛ ❛♦ ✶✶✳➸ ❛♥♦ ❢♦✐ s❡♣❛r❛❞♦ ❞❛ ■♥tr♦❞✉çã♦ ❛♦ ❈á❧❝✉❧♦ ❉✐❢❡r❡♥❝✐❛❧ ■■✱ ❝♦♥t✉❞♦ ♦s ❞♦✐s ❢♦r❛♠ ❧❡❝✐♦♥❛❞♦s ❡♠ s✐♠✉❧tâ♥❡♦✱ t❡♥❞♦ s✐❞♦ ✐♥t❡❣r❛❞♦s ♦s ❝♦♥❤❡❝✐♠❡♥t♦s ♥ã♦ ❛❜♦r❞❛❞♦s r❡❧❛t✐✈♦s ❛♦ ✶✶✳➸ ❛♥♦ ❞✉r❛♥t❡ ❛ ❛♣r❡♥❞✐③❛❣❡♠ ❞❛ ✉♥✐❞❛❞❡ ■♥tr♦❞✉çã♦ ❛♦ ❈á❧❝✉❧♦ ❉✐❢❡r❡♥❝✐❛❧ ■■✳
❈❛❞❛ ❜❧♦❝♦ r❡♣r❡s❡♥t❛ ✉♠❛ ❛✉❧❛ ❞❡ ✺✵ ♠✐♥✉t♦s ❡ ♦ ♥ú♠❡r♦ ❞❡ ❜❧♦❝♦s r❡❢❡✲ r✐❞♦ ♥❛ t❛❜❡❧❛ ✹✳✷ ❢♦✐ ❛ ♣r❡✈✐sã♦ ❛♣r❡s❡♥t❛❞❛ ♥♦ ♣❧❛♥♦ ❛♥✉❛❧ ❞❛ ❞✐s❝✐♣❧✐♥❛ ❞❡
▼❛t❡♠át✐❝❛ ❆ ❞♦ ✶✷✳➸ ❛♥♦ ✭✈❡r ❞♦ss✐❡r ❞❡ ❡stá❣✐♦✮✳ ❊st❡ ♣❧❛♥♦ ❢♦✐ ❡❧❛❜♦r❛❞♦ ♣❡❧❛s ♣r♦❢❡ss♦r❛s t✐t✉❧❛r❡s ❞♦ ✶✷✳➸ ❛♥♦✱ s❡♥❞♦ ❡❧❛s✱ ❛ ♣r♦❢❡ss♦r❛ ❘♦sár✐♦ ▲♦✲ ♣❡s✱ ❛ ♣r♦❢❡ss♦r❛ ●❡rtr✉❞❡s ❘✐❜❡✐r♦ ❡ ❛ ♣r♦❢❡ss♦r❛ ❆♥❛ P❛✉❧❛ ▼❛❝❤❛❞♦✳ ❆♦ ♥ú♠❡r♦ ❞❡ ❜❧♦❝♦s ❡♠ ❝❛❞❛ t❡♠❛✱ ❛❝r❡s❝❡♥t❛♠✲s❡✱ ❛✐♥❞❛✱ ♦ ♥ú♠❡r♦ ❞❡ ❜❧♦❝♦s ❞❡st✐♥❛❞♦s ❛♦s t❡st❡s✱ ✜❝❤❛s ❞❡ ❛✈❛❧✐❛çã♦✱ à ❛✉t♦❛✈❛❧✐❛çã♦ ❡ ❤❡t❡r♦❛✈❛❧✐❛çã♦✳ ❖s ♠❛♥✉❛✐s ❛❞♦t❛❞♦s ♥❛ ❊s❝♦❧❛ ❆♥tó♥✐♦ ●❡❞❡ã♦ ♥♦s três ❛♥♦s ❞♦ ❊♥s✐♥♦ s❡❝✉♥❞ár✐♦ ❢♦r❛♠✿
✕ ◆♦✈♦ ❊s♣❛ç♦ ✶✵ ✲ ▼❛t❡♠át✐❝❛ ❆ ✭❈♦st❛ ✫ ❘♦❞r✐❣✉❡s✱ ✷✵✶✸✮ ✙ ✶✵✳➸ ❛♥♦❀
✕ ◆♦✈♦ ❊s♣❛ç♦ ✶✶ ✲ ▼❛t❡♠át✐❝❛ ❆ ✭❈♦st❛ ✫ ❘♦❞r✐❣✉❡s✱ ✷✵✶✸✮ ✙ ✶✶✳➸ ❛♥♦❀
✕ ❨ ✶✷ ✲ ▼❛t❡♠át✐❝❛ ✶✷✳➸ ❛♥♦ ✭❆♥❞r❛❞❡✱ ❱✐❡❣❛s✱ P❡r❡✐r❛ ✫ P✐♠❡♥t❛✱ ✷✵✶✷✮ ✙ ✶✷✳➸ ❛♥♦✳
❖ ❡st❛❣✐ár✐♦ ❛ss✐st✐✉ às ❛✉❧❛s ❧❡❝✐♦♥❛❞❛s ♣❡❧❛ ♣r♦❢❡ss♦r❛ ♦r✐❡♥t❛❞♦r❛ ❞❛ t✉r♠❛ ❡s❝♦❧❤✐❞❛✱ ♦ q✉❡ ❧❤❡ ♣❡r♠✐t✐✉ ♥ã♦ só ♦❜s❡r✈❛r ❛s ♠❡t♦❞♦❧♦❣✐❛s ❞❡ ❡♥s✐♥♦ ❛♣❧✐✲ ❝❛❞❛s ❝♦♠♦ t❛♠❜é♠ ❛♣r❡♥❞❡r ❛ ❡✈✐❞❡♥❝✐❛r ❛❧❣✉♥s ♣♦r♠❡♥♦r❡s ❞♦ ♣r♦❣r❛♠❛ ❞❡ ♠❛t❡♠át✐❝❛ ♦ q✉❡ s❡rá✱ ❝❡rt❛♠❡♥t❡✱ ♠✉✐t♦ út✐❧ ♣❛r❛ ♦ s❡✉ ❢✉t✉r♦ ♣r♦✜ss✐♦✲ ♥❛❧ ♣♦❞❡♥❞♦✱ ❛ss✐♠✱ ❛✉①✐❧✐❛r ♠❡❧❤♦r ♦s ❛❧✉♥♦s ❛ ❝♦♠♣r❡❡♥❞❡r❡♠ ❞❡t❡r♠✐♥❛✲ ❞♦s ❝♦♥❝❡✐t♦s ❡✱ ❝♦♥s❡q✉❡♥t❡♠❡♥t❡✱ ❛ ❛❧❝❛♥ç❛r❡♠ ✉♠ ♠❡❧❤♦r ❛♣r♦✈❡✐t❛♠❡♥t♦ ❡ ✐♥t❡r❡ss❡ ♣❡❧❛ ❞✐s❝✐♣❧✐♥❛✳ ❉✉r❛♥t❡ ❛ r❡s♦❧✉çã♦ ❞❡ ❡①❡r❝í❝✐♦s ♣♦r ♣❛rt❡ ❞❛ t✉r♠❛ ❞❡ ❡stá❣✐♦✱ ❢♦✐ ❞❛❞❛ ❧✐❜❡r❞❛❞❡ ❛♦ ❡st❛❣✐ár✐♦ ♣❛r❛ ❡s❝❧❛r❡❝❡r ❞ú✈✐❞❛s✱ ♦ q✉❡ ❧❤❡ ♣❡r♠✐t✐✉ ❢❛♠✐❧✐❛r✐③❛r✲s❡ ❝♦♠ ❛s ❞✐✜❝✉❧❞❛❞❡s ❡ ♠♦t✐✈❛çõ❡s ❞♦s ❛❧✉♥♦s✳ ❉✉r❛♥t❡ ♦ ❛♥♦ ❧❡t✐✈♦ ❢♦r❛♠ ❞✐s❝✉t✐❞♦s✱ ❡♥tr❡ ♦ ❡st❛❣✐ár✐♦ ❡ ❛ ♣r♦❢❡ss♦r❛ ♦r✐✲ ❡♥t❛❞♦r❛✱ ♣♦r♠❡♥♦r❡s ❞❡ ❛❧❣✉♥s ❝♦♥❝❡✐t♦s✱ ❞❡✜♥✐çõ❡s ✉t✐❧✐③❛❞❛s✱ r❡s♦❧✉çõ❡s ❞❡ ❡①❡r❝í❝✐♦s ❡ ❛ s❡q✉ê♥❝✐❛ ❞♦ ♣r♦❣r❛♠❛ ❞❡ ♠❛t❡♠át✐❝❛ ♥♦s ♠❛♥✉❛✐s ❡s❝♦✲ ❧❛r❡s✱ ♦ q✉❡ ♣❡r♠✐t✐✉ ❛♦ ❡st❛❣✐ár✐♦ ✜❝❛r s❡♥s✐❜✐❧✐③❛❞♦ ♥ã♦ só ♣❛r❛ ❛❧❣✉♠❛s ❞✐✜❝✉❧❞❛❞❡s ❞♦s ❛❧✉♥♦s ♥❛ ❝♦♠♣r❡❡♥sã♦ ❞❡ ❞❡t❡r♠✐♥❛❞❛s ❞❡✜♥✐çõ❡s ❡ t❡♦r❡✲ ♠❛s✱ ❝♦♠♦ t❛♠❜é♠ ♣❛r❛ ❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ s❡r ❝rít✐❝♦ ❡♠ r❡❧❛çã♦ ❛♦ ✉s♦ ❞♦ ♠❛♥✉❛❧✳ P♦r ❡①❡♠♣❧♦✱ ♥✉♠ ❞♦s t❡♠❛s ❛s s♦❧✉çõ❡s ❞❡ ❛❧❣✉♥s ❡①❡r❝í❝✐♦s ❞♦ ♠❛♥✉❛❧ ❞♦ ✶✶➸ ❛♥♦ ♥ã♦ ❛♣r❡s❡♥t❛✈❛♠ ❛s ♥♦t❛çõ❡s ✉s❛❞❛s ♥♦s ❝♦♥❝❡✐t♦s ❡ ❡①❡♠♣❧♦s ❛♣r❡s❡♥t❛❞♦s ♥♦ ♣ró♣r✐♦ ♠❛♥✉❛❧✳
