Marcos Mansano Furlan
Orientadora: Profa. Dra. Maristela Oliveira dos Santos
Dissertação apresentada ao Instituto de Ciências Matemáticas e de Computação - ICMC-USP, como parte dos requisitos para obtenção do título de Mestre em Ciências - Ciências de Computação e Matemática Computacional. VERSÃO REVISADA.
USP – São Carlos Maio/2011
SERVIÇO DE PÓS-GRADUAÇÃO DO ICMC-USP
Data de Depósito: 12/05/2011
❆●❘❆❉❊❈■▼❊◆❚❖❙
Pr✐♠❡✐r❛♠❡♥t❡ ❣♦st❛r✐❛ ❞❡ ❛❣r❛❞❡❝❡r ❛♦s ♠❡✉s ♣❛✐s ▼♦❛❝✐r ❡ ❙✉❡❧✐ ♣❡❧❛ ❞❡❞✐❝❛çã♦✱ ❛♠♦r✱ ❡ ♣♦r t♦❞♦s ♦s ❝♦♥s❡❧❤♦s ❡ ❡①❡♠♣❧♦s q✉❡ ✜③❡r❛♠ ❝♦♠ q✉❡ ❡✉ ♠❡ t♦r♥❛ss❡ ✉♠❛ ♣❡ss♦❛ ♠❡❧❤♦r✳
➚ ♠✐♥❤❛ ♦r✐❡♥t❛❞♦r❛ ▼❛r✐st❡❧❛ ❖❧✐✈❡✐r❛ ❞♦s ❙❛♥t♦s ♣❡❧❛ ♦r✐❡♥t❛çã♦✱ ❞❡❞✐❝❛çã♦✱ ♣❛❝✐✲ ê♥❝✐❛✱ ❛♠✐③❛❞❡ ❡ ♣❡❧❛ ❝♦♥✜❛♥ç❛ ❞❡♣♦s✐t❛❞❛ ❞✉r❛♥t❡ ♦ ❞❡❝♦rr❡r ❞❡st❡ tr❛❜❛❧❤♦✳
❆♦s ❛♠✐❣♦s ❞❡ ❧❛❜♦r❛tór✐♦ s❡♠♣r❡ ♣r❡s❡♥t❡s ❡ ❛ ❞✐s♣♦s✐çã♦ ♣❛r❛ ♦ q✉❡ ❢♦ss❡ ♥❡❝❡ssár✐♦✱ ♥♦s ♠♦♠❡♥t♦s ❞❡ tr❛❜❛❧❤♦ ❡ ❞❡ ❧❛③❡r✳
❆♦ ❱✐❝t♦r✱ ▼ár❝✐♦ ❡ ❚❛♠❛r❛✱ ♣♦r t❡r❡♠ ♠❡ r❡❝❡❜✐❞♦ tã♦ ❜❡♠ ❡♠ ❙ã♦ ❈❛r❧♦s ❡ ♣♦r t♦❞♦s ♦s ❝♦♥s❡❧❤♦s ❡ ♠♦♠❡♥t♦s ❢❡❧✐③❡s ❞❡ ❤❛♣♣② ❤♦✉rs ❡ ♣ós ❤❛♣♣② ❤♦✉rs ✭♣♦st♦✮✳
❆♦s ♠❡✉s ❛♠✐❣♦s ❞❡ P✐r❛t✐♥✐♥❣❛ ❡ ❛rr❡❞♦r❡s✱ ♣❡❧❛ ❛♠✐③❛❞❡ ❡ ♣♦r ❡st❛r❡♠ ♣r❡s❡♥t❡s ❡♠ ♠✐♥❤❛ ✈✐❞❛✳ ❯♠ ❛❣r❛❞❡❝✐♠❡♥t♦ ❡s♣❡❝✐❛❧ ❛♦s ♠❡✉s ❣r❛♥❞❡s ❛♠✐❣♦s ❞❡ ❣r❛❞✉❛çã♦ ●✉✐❧❤❡r♠❡✱ ❮❣♦r ❡ ❲❡s❧❡② ♣❡❧♦s ❝♦♥s❡❧❤♦s ❡ ❛♣♦✐♦ ♥♦s ♠♦♠❡♥t♦s ❞❡ ✐♥❝❡rt❡③❛s✳
❆♦s ♠❡♠❜r♦s ❞❛s ❜❛♥❝❛s ❞❡ q✉❛❧✐✜❝❛çã♦ ❡ ❞❡ ❞❡❢❡s❛ ♣♦r t♦❞❛s ❛s s✉❣❡stõ❡s ❡ ❝♦♥s❡❧❤♦s ❢❡✐t♦s ♣❛r❛ ♠❡❧❤♦r❛r ❡st❡ tr❛❜❛❧❤♦✳
❆ t♦❞♦s ♦s ❢✉♥❝✐♦♥ár✐♦s ❞♦ ■❈▼❈ q✉❡✱ ❞✐r❡t❛ ♦✉ ✐♥❞✐r❡t❛♠❡♥t❡✱ ❝♦♥tr✐❜✉ír❛♠ ❝♦♠ ❡st❡ tr❛❜❛❧❤♦✳ Pr✐♥❝✐♣❛❧♠❡♥t❡ às ❢✉♥❝✐♦♥ár✐❛s ❞❛ s❡❝r❡t❛r✐❛ ❞❛ Pós✲❣r❛❞✉❛çã♦ ♣♦r t♦❞❛ ♦ ❛✉①í❧✐♦ ♦❢❡r❡❝✐❞♦ ♣❛r❛ q✉❡ ❡st❡ tr❛❜❛❧❤♦ ♣✉❞❡ss❡ s❡r ❝♦♥❝❧✉í❞♦✳
❘❊❙❯▼❖
❖ ♣r♦❜❧❡♠❛ ❞❡ ❞✐♠❡♥s✐♦♥❛♠❡♥t♦ ❞❡ ❧♦t❡s ❞❡t❡r♠✐♥❛ ✉♠ ♣❧❛♥♦ ❞❡ ♣r♦❞✉çã♦ q✉❡ ❛♣♦✐❛ às t♦♠❛❞❛s ❞❡ ❞❡❝✐sõ❡s✱ ❛ ♠é❞✐♦ ♣r❛③♦✱ ❡♠ ♠❡✐♦s ✐♥❞✉str✐❛✐s✳ ❊st❡ ♣❧❛♥♦ ❞❡ ♣r♦❞✉çã♦ ✐♥❞✐❝❛ ❛s q✉❛♥t✐❞❛❞❡s ❞❡ ❝❛❞❛ ✐t❡♠ q✉❡ ❞❡✈❡♠ s❡r ♣r♦❞✉③✐❞❛s ❡♠ ❝❛❞❛ ♣❡rí♦❞♦ ❞♦ ❤♦r✐✲ ③♦♥t❡ ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦✱ ❞❡ ❛❝♦r❞♦ ❝♦♠ ✉♠ ♦❜❥❡t✐✈♦ ❞❛❞♦ ❡ s❛t✐s❢❛③❡♥❞♦ ❛ ❞❡♠❛♥❞❛ ❞♦s ❝❧✐❡♥t❡s✳ ❉✐✈❡rs♦s ♠ét♦❞♦s ❞❡ s♦❧✉çã♦ ❢♦r❛♠ ♣r♦♣♦st❛s ♥❛ ❧✐t❡r❛t✉r❛✱ ❝♦♥s✐❞❡r❛♥❞♦ ❛ ❞✐✲ ✜❝✉❧❞❛❞❡ ❞❡ s♦❧✉çã♦ ❞❡ ❛❧❣✉♠❛s ❝❧❛ss❡s ❞❡ ♣r♦❜❧❡♠❛s ❡ ❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ ♠ét♦❞♦s q✉❡ ❣❡r❡♠ s♦❧✉çõ❡s ❞❡ ❛❧t❛ q✉❛❧✐❞❛❞❡ ❡♠ ✉♠ t❡♠♣♦ ❝♦♠♣✉t❛❝✐♦♥❛❧ ❛❞❡q✉❛❞♦✳ ◆❡st❡ tr❛❜❛❧❤♦✱ ❛❜♦r❞❛♠♦s ❤❡✉ríst✐❝❛s ❜❛s❡❛❞❛s ♥❛ ❢♦r♠✉❧❛çã♦ ♠❛t❡♠át✐❝❛ ✭▲P✲❛♥❞✲✜①✱ r❡❧❛①✲❛♥❞✲✜① ❡ ✜①✲❛♥❞✲♦♣t✐♠✐③❡✮✱ ✉♠❛ ♠❡t❛❤❡✉ríst✐❝❛ ✭❛❧❣♦r✐t♠♦ ❞❡ ❛❜❡❧❤❛s✮ ❡ ❞♦✐s ♠ét♦❞♦s ❤í❜r✐❞♦s✱ ✉t✐❧✐③❛❞♦s ♥❛ s♦❧✉çã♦ ❞❡ ❞♦✐s ♣r♦❜❧❡♠❛s ❞✐st✐♥t♦s ❞❡ ❞✐♠❡♥s✐♦♥❛♠❡♥t♦ ❞❡ ❧♦t❡s ♠✉❧t✐❡stá✲ ❣✐♦ ❝♦♠ ❧✐♠✐t❛çã♦ ❞❡ ❝❛♣❛❝✐❞❛❞❡✳ ❈♦♥s✐❞❡r❛♠♦s t❛♠❜é♠✱ ❛ ✉t✐❧✐③❛çã♦ ❞❡ três ❢♦r♠✉❧❛çõ❡s ❞❛ ❧✐t❡r❛t✉r❛✱ ♣❛r❛ ✈❡r✐✜❝❛r ❛ ✐♥✢✉ê♥❝✐❛ ❞❡ ❝❛❞❛ ✉♠❛ s♦❜r❡ ❛s ❛❜♦r❞❛❣❡♥s ❞❡ s♦❧✉çã♦ ✈❡r✐✜❝❛❞❛s✳ ❖s r❡s✉❧t❛❞♦s ❝♦♠♣✉t❛❝✐♦♥❛✐s ❞❡♠♦♥str❛r❛♠ q✉❡ ♦s ♠ét♦❞♦s ❜❛s❡❛❞♦s ♥❛ ❢♦r♠✉❧❛çã♦ ♠❛t❡♠át✐❝❛ ❞♦ ♣r♦❜❧❡♠❛ s❡ ♠♦str❛r❛♠ ❡✜❝✐❡♥t❡s✱ ♠❛s ❧✐♠✐t❛❞♦s ♥♦r♠❛❧♠❡♥t❡ ❛ ót✐♠♦s ❧♦❝❛✐s✱ ❡♥q✉❛♥t♦ ♦s ♠ét♦❞♦s ❤í❜r✐❞♦s ♣✉❞❡r❛♠ s✉♣❡r❛r ❡st❡s ót✐♠♦s ❧♦❝❛✐s✱ ✉t✐❧✐✲ ③❛♥❞♦ ❝♦♥❝❡✐t♦s ❞❛ ♠❡t❛❤❡✉ríst✐❝❛ ❛❧❣♦r✐t♠♦ ❞❡ ❛❜❡❧❤❛s ♣❛r❛ ✐st♦✳ ❆❧é♠ ❞✐ss♦✱ ♣✉❞❡♠♦s ✈❡r✐✜❝❛r ❛ ✐♥✢✉ê♥❝✐❛ ❞❡ ✉♠❛ ❢♦r♠✉❧❛çã♦ ✏❢♦rt❡✑ s♦❜r❡ ❛s s♦❧✉çõ❡s ❣❡r❛❞❛s ♣❡❧❛s ❛❜♦r✲ ❞❛❣❡♥s ❞❡ s♦❧✉çã♦✱ ❞❡♠♦♥str❛♥❞♦ q✉❡ ♠ét♦❞♦s ❜❛s❡❛❞♦s ❡♠ r❡❧❛①❛çã♦ ❧✐♥❡❛r ❝♦♥s❡❣✉❡♠ ♦❜t❡r ♠❛✐♦r❡s ✈❛♥t❛❣❡♥s ❞❡st❡ t✐♣♦ ❞❡ ❢♦r♠✉❧❛çã♦✱ ♠❛s ♦✉tr❛s ❛❜♦r❞❛❣❡♥s ♣♦❞❡♠ ♦✉ ♥ã♦ ♦❜t❡r ❡st❛s ✈❛♥t❛❣❡♥s✱ ❞❡♣❡♥❞❡♥❞♦ ❞♦ ♣r♦❜❧❡♠❛ ❛❜♦r❞❛❞♦✳
❆❇❙❚❘❆❈❚
❚❤❡ ❧♦t✲s✐③✐♥❣ ♣r♦❜❧❡♠ ❞❡t❡r♠✐♥❡s ❛ ♣r♦❞✉❝t✐♦♥ ♣❧❛♥✱ ✇❤✐❝❤ s✉♣♣♦rts t❤❡ ❞❡❝✐s✐♦♥ ♠❛✲ ❦✐♥❣✱ ✐♥ t❤❡ ♠❡❞✐✉♠ t❡r♠✱ ❛t t❤❡ ✐♥❞✉str✐❛❧ ❡♥✈✐r♦♥♠❡♥t✳ ❚❤✐s ♣r♦❞✉❝t✐♦♥ ♣❧❛♥ ✐♥❞✐❝❛t❡s t❤❡ ❛♠♦✉♥ts ♦❢ ❡❛❝❤ ✐t❡♠ t♦ ❜❡ ♣r♦❞✉❝❡❞ ✐♥ ❡❛❝❤ ♣❡r✐♦❞ ♦❢ t❤❡ ♣❧❛♥♥✐♥❣ ❤♦r✐③♦♥✱ ❛❝❝♦r✲ ❞✐♥❣ t♦ ❛ ❣✐✈❡♥ ♦❜❥❡❝t✐✈❡ ❛♥❞ s❛t✐s❢②✐♥❣ ❝✉st♦♠❡r✬s ❞❡♠❛♥❞✳ ❉✐✈❡rs❡ s♦❧✉t✐♦♥ ♠❡t❤♦❞s ❤❛✈❡ ❜❡❡♥ ♣r♦♣♦s❡❞ ✐♥ t❤❡ ❧✐t❡r❛t✉r❡✱ ❝♦♥s✐❞❡r✐♥❣ t❤❡ ❞✐✣❝✉❧t② ♦❢ s♦❧✈✐♥❣ s♦♠❡ ♣r♦❜❧❡♠ ❝❧❛ss❡s ❛♥❞ t❤❡ ♥❡❡❞ ♦❢ ♠❡t❤♦❞s t♦ ❣❡♥❡r❛t❡ s♦❧✉t✐♦♥s q✉✐❝❦❧②✳ ■♥ t❤✐s ✇♦r❦✱ ✇❡ ❞❡✈❡❧♦♣ ♠❛t❤❡✉r✐st✐❝s ✭▲P✲❛♥❞✲✜①✱ r❡❧❛①✲❛♥❞✲✜① ❛♥❞ ✜①✲❛♥❞✲♦♣t✐♠✐③❡✮✱ ♦♥❡ ♠❡t❛❤❡✉r✐st✐❝ ✭❜❡❡s ❛❧❣♦r✐t❤♠✮ ❛♥❞ t✇♦ ❤②❜r✐❞ ♠❡t❤♦❞s✱ ✉s❡❞ t♦ s♦❧✈❡ t✇♦ ❞✐✛❡r❡♥t ♠✉❧t✐❧❡✈❡❧ ❝❛♣❛❝✐t❛t❡❞ ❧♦t✲s✐③✐♥❣ ♣r♦❜❧❡♠s✳ ❲❡ ❛❧s♦ ❝♦♥s✐❞❡r t❤❡ ✉s❡ ♦❢ t❤r❡❡ ❞✐✛❡r❡♥t ❢♦r♠✉❧❛t✐♦♥s ♦❢ t❤❡ ❧✐t❡r❛✲ t✉r❡ t♦ ✈❡r✐❢② t❤❡ ✐♥✢✉❡♥❝❡ ♦❢ ❡❛❝❤ ♦♥❡ ♦♥ t❤❡ s♦❧✉t✐♦♥s ❛♣♣r♦❛❝❤❡s✳ ❚❤❡ ❝♦♠♣✉t❛t✐♦♥❛❧ r❡s✉❧ts s❤♦✇ t❤❛t t❤❡ ♠❛t❤❡✉r✐st✐❝s ♣r♦✈❡❞ t♦ ❜❡ ❡✣❝✐❡♥t✱ ❜✉t ✉s✉❛❧❧② ❧✐♠✐t❡❞ t♦ ❧♦❝❛❧ ♦♣t✐♠❛✱ ✇❤✐❧❡ t❤❡ ❤②❜r✐❞ ♠❡t❤♦❞s ❝♦✉❧❞ ❡s❝❛♣❡ ❢r♦♠ t❤❡s❡ ❧♦❝❛❧ ♦♣t✐♠❛✱ ✉s✐♥❣ ❝♦♥❝❡♣ts ♦❢ ❜❡❡s ❛❧❣♦r✐t❤♠ t♦ ❞♦ t❤✐s✳ ❆❞❞✐t✐♦♥❛❧❧②✱ ✇❡ t❡st t❤❡ ❡✛❡❝t ♦❢ ❛ t✐❣❤t ❢♦r♠✉❧❛t✐♦♥ ♦♥ t❤❡ s♦❧✉t✐♦♥s ❛♣♣r♦❛❝❤❡s✱ ❞❡♠♦♥str❛t✐♥❣ t❤❛t ▲P✲❜❛s❡❞ ❤❡✉r✐st✐❝s ❝❛♥ ♦❜t❛✐♥ ❢✉rt❤❡r ❛❞✲ ✈❛♥t❛❣❡s ❢r♦♠ t❤✐s t②♣❡ ♦❢ ❢♦r♠✉❧❛t✐♦♥✱ ❜✉t ♦t❤❡r ❛♣♣r♦❛❝❤❡s ❝❛♥ t❛❦❡ t❤❡s❡ ❛❞✈❛♥t❛❣❡s✱ ❞❡♣❡♥❞✐♥❣ ♦♥ t❤❡ ♣r♦❜❧❡♠ ❛❞❞r❡ss❡❞✳
❙❯▼➪❘■❖
✶ ■♥tr♦❞✉çã♦ ♣✳ ✶
✷ ❘❡✈✐sã♦ ❞❛ ▲✐t❡r❛t✉r❛ ♣✳ ✼
✷✳✶ Pr♦❜❧❡♠❛ ❞❡ ❞✐♠❡♥s✐♦♥❛♠❡♥t♦ ❞❡ ❧♦t❡s ♠♦♥♦❡stá❣✐♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✼
✷✳✷ Pr♦❜❧❡♠❛ ❞❡ ❞✐♠❡♥s✐♦♥❛♠❡♥t♦ ❞❡ ❧♦t❡s ♠✉❧t✐❡stá❣✐♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✵
✸ Pr♦❜❧❡♠❛s ❆❜♦r❞❛❞♦s ♣✳ ✶✾
✸✳✶ Pr♦❜❧❡♠❛ ❞❡ ❞✐♠❡♥s✐♦♥❛♠❡♥t♦ ❞❡ ❧♦t❡s ♠✉❧t✐❡stá❣✐♦ ❝♦♠ ❧✐♠✐t❛çã♦ ❞❡
❝❛♣❛❝✐❞❛❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✵
✸✳✶✳✶ ❋♦r♠✉❧❛çã♦ ❆❣r❡❣❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✶
✸✳✶✳✷ ❋♦r♠✉❧❛çã♦ ♣♦r ▲♦❝❛❧✐③❛çã♦ ❞❡ ❋❛❝✐❧✐❞❛❞❡s s❡❣✉♥❞♦ ❙❛❤❧✐♥❣ ❡t ❛❧✳
✭✷✵✵✾✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✷
✸✳✶✳✸ ❋♦r♠✉❧❛çã♦ ♣♦r ▲♦❝❛❧✐③❛çã♦ ❞❡ ❋❛❝✐❧✐❞❛❞❡s s❡❣✉♥❞♦ ❙t❛❞t❧❡r ✭✷✵✵✸✮ ♣✳ ✷✸
✸✳✷ Pr♦❜❧❡♠❛ ❞❡ ❞✐♠❡♥s✐♦♥❛♠❡♥t♦ ❞❡ ❧♦t❡s ♠✉❧t✐❡stá❣✐♦ ❝♦♠ ❧✐♠✐t❛çã♦ ❞❡
❝❛♣❛❝✐❞❛❞❡ ❡ ♣r❡s❡r✈❛çã♦ ❞❛ ♣r❡♣❛r❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✹
✸✳✷✳✶ ❋♦r♠✉❧❛çã♦ ❆❣r❡❣❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✻
✸✳✷✳✷ ❋♦r♠✉❧❛çã♦ ♣♦r ▲♦❝❛❧✐③❛çã♦ ❞❡ ❋❛❝✐❧✐❞❛❞❡s s❡❣✉♥❞♦ ❙❛❤❧✐♥❣ ❡t ❛❧✳
✭✷✵✵✾✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✽
✹ ❆❜♦r❞❛❣❡♥s ❞❡ ❙♦❧✉çã♦ ♣✳ ✸✸
✹✳✶ ❍❡✉ríst✐❝❛s ❜❛s❡❛❞❛s ♥❛ ❢♦r♠✉❧❛çã♦ ♠❛t❡♠át✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✹
✹✳✶✳✶ ❍❡✉ríst✐❝❛ ▲P✲❛♥❞✲✜① ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✹
✹✳✶✳✷ ❍❡✉ríst✐❝❛s r❡❧❛①✲❛♥❞✲✜① ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✺
✹✳✶✳✸ ❍❡✉ríst✐❝❛s ❞♦ t✐♣♦ ✜①✲❛♥❞✲♦♣t✐♠✐③❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✵
✹✳✷ ▼❡t❛❤❡✉ríst✐❝❛ ❛❧❣♦r✐t♠♦ ❞❡ ❛❜❡❧❤❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✼
✹✳✸ ▼ét♦❞♦s ❤í❜r✐❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✸
✹✳✸✳✶ Pr✐♠❡✐r❛ ❤❡✉ríst✐❝❛ ❤í❜r✐❞❛✿ ✜①✲❛♥❞✲♦♣t✐♠✐③❡ ❝♦♠ ❛❧❣♦r✐t♠♦ ❞❡
❛❜❡❧❤❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✹
✹✳✸✳✷ ❙❡❣✉♥❞❛ ❤❡✉ríst✐❝❛ ❤í❜r✐❞❛✿ ❛❧❣♦r✐t♠♦ ❞❡ ❛❜❡❧❤❛s ❝♦♠ ✜①✲❛♥❞✲
♦♣t✐♠✐③❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✻
✺ ❚❡st❡s ❈♦♠♣✉t❛❝✐♦♥❛✐s ♣✳ ✻✶
✺✳✶ ■♥stâ♥❝✐❛s ❞❡ ❚❡st❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✶
✺✳✶✳✶ ■♥stâ♥❝✐❛s ❞❡ ❚❡♠♣❡❧♠❡✐❡r ❡ ❉❡rstr♦✛ ✭✶✾✾✻✮ ❡ ❙t❛❞t❧❡r ❡ ❙ür✐❡
✭✷✵✵✵✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✷
✺✳✶✳✷ ■♥stâ♥❝✐❛s ❞❡ t❡st❡ ❞❡ ❚❡♠♣❡❧♠❡✐❡r ❡ ❇✉s❝❤❦ü❤❧ ✭✷✵✵✾✮ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✺
✺✳✷ ❘❡s✉❧t❛❞♦s ❈♦♠♣✉t❛❝✐♦♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✽
✺✳✷✳✶ Pr♦❜❧❡♠❛ ❞❡ ❞✐♠❡♥s✐♦♥❛♠❡♥t♦ ❞❡ ❧♦t❡s ♠✉❧t✐❡stá❣✐♦ ❝♦♠ ❧✐♠✐t❛✲
çã♦ ❞❡ ❝❛♣❛❝✐❞❛❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✼✶
✺✳✷✳✶✳✶ ❆♥á❧✐s❡ ❞♦s r❡s✉❧t❛❞♦s ❝♦♠ ❢♦❝♦ ♥❛ ❢♦r♠✉❧❛çã♦ ✉t✐❧✐③❛❞❛ ♣✳ ✼✶
✺✳✷✳✶✳✷ ❆♥á❧✐s❡ ❞♦s r❡s✉❧t❛❞♦s ❝♦♠ ❢♦❝♦ ♥❛s ❛❜♦r❞❛❣❡♥s ❞❡ s♦❧✉çã♦ ♣✳ ✼✾
✺✳✷✳✷ Pr♦❜❧❡♠❛ ❞❡ ❞✐♠❡♥s✐♦♥❛♠❡♥t♦ ❞❡ ❧♦t❡s ♠✉❧t✐❡stá❣✐♦ ❝♦♠ ❧✐♠✐t❛✲
çã♦ ❞❡ ❝❛♣❛❝✐❞❛❞❡ ❡ ♣r❡s❡r✈❛çã♦ ❞❛ ♣r❡♣❛r❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✽✷
✺✳✷✳✷✳✶ ❆♥á❧✐s❡ ❞♦s r❡s✉❧t❛❞♦s ❝♦♠ ❢♦❝♦ ♥❛ ❢♦r♠✉❧❛çã♦ ✉t✐❧✐③❛❞❛ ♣✳ ✽✸
✺✳✷✳✷✳✷ ❆♥á❧✐s❡ ❞♦s r❡s✉❧t❛❞♦s ❝♦♠ ❢♦❝♦ ♥❛s ❛❜♦r❞❛❣❡♥s ❞❡ s♦❧✉çã♦ ♣✳ ✾✷
❘❡❢❡rê♥❝✐❛s ❇✐❜❧✐♦❣rá✜❝❛s ♣✳ ✾✾
❆ ❘❡❢♦r♠✉❧❛çã♦ ♣♦r ❧♦❝❛❧✐③❛çã♦ ❞❡ ❢❛❝✐❧✐❞❛❞❡s ♣✳ ✶✵✺
❆✳✶ ❖ ♣r♦❜❧❡♠❛ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❞❡ ❢❛❝✐❧✐❞❛❞❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✵✻
❆✳✷ ❘❡❢♦r♠✉❧❛çã♦ ♣♦r ❧♦❝❛❧✐③❛çã♦ ❞❡ ❢❛❝✐❧✐❞❛❞❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✵✼
▲■❙❚❆ ❉❊ ❚❆❇❊▲❆❙
✶ ❈❛r❛❝t❡ríst✐❝❛s ❞❛s ✐♥stâ♥❝✐❛s ❞❡ t❡st❡ ❞❡ ❙t❛❞t❧❡r ❡ ❙ür✐❡ ✭✷✵✵✵✮ ✳ ✳ ✳ ✳ ♣✳ ✻✷
✷ ❚❡♠♣♦s ❞❡ ♣r❡♣❛r❛çõ❡s ❞❛ ❝❧❛ss❡ ❇✰✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✹
✸ ❚❡♠♣♦s ❡♥tr❡ ♣❡❞✐❞♦s ❞❛s ❝❧❛ss❡s ❆✰ ❡ ❇✰✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✹
✹ P♦r❝❡♥t❛❣❡♠ ❞❡ ✉t✐❧✐③❛çã♦ ❞♦s r❡❝✉rs♦s ❞❛s ❝❧❛ss❡s ❆✰ ❡ ❇✰✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✺
✺ ❈❛r❛❝t❡ríst✐❝❛s ❞❛s ✐♥stâ♥❝✐❛s ❞❡ t❡st❡ ❞❡ ❚❡♠♣❡❧♠❡✐❡r ❡ ❇✉s❝❤❦ü❤❧ ✭✷✵✵✾✮ ♣✳ ✻✺
✻ ❚❡♠♣♦s ❞❡ ♣r❡♣❛r❛çõ❡s ♣♦r ♥ú♠❡r♦ ❞❡ ✐t❡♥s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✼
✼ ❚❡♠♣♦s ❡♥tr❡ ♣❡❞✐❞♦s ♣♦r ♥ú♠❡r♦ ❞❡ ✐t❡♥s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✼
✽ P♦r❝❡♥t❛❣❡♠ ❞❡ ✉t✐❧✐③❛çã♦ ♣♦r ♥ú♠❡r♦ ❞❡ r❡❝✉rs♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✼
✾ ❉❡s✈✐♦ ♣❡r❝❡♥t✉❛❧ ♠é❞✐♦ ✲ ❍❡✉ríst✐❝❛s ❜❛s❡❛❞❛s ❡♠ r❡❧❛①❛çã♦ ❧✐♥❡❛r ✳ ✳ ♣✳ ✼✷
✶✵ ❉❡s✈✐♦ ♣❛❞rã♦ ♣❡r❝❡♥t✉❛❧ ✲ ❍❡✉ríst✐❝❛s ❜❛s❡❛❞❛s ❡♠ r❡❧❛①❛çã♦ ❧✐♥❡❛r ✳ ✳ ♣✳ ✼✷
✶✶ ❚❡♠♣♦ ❝♦♠♣✉t❛❝✐♦♥❛❧ ♠é❞✐♦ ✲ ❍❡✉ríst✐❝❛s ❜❛s❡❛❞❛s ❡♠ r❡❧❛①❛çã♦ ❧✐♥❡❛r ♣✳ ✼✸
✶✷ P❡r❝❡♥t✉❛❧ ❞❡ ♠❡❧❤♦r✐❛ ✲ ❍❡✉ríst✐❝❛s ❜❛s❡❛❞❛s ❡♠ r❡❧❛①❛çã♦ ❧✐♥❡❛r ✳ ✳ ✳ ♣✳ ✼✸
✶✸ P❡r❝❡♥t✉❛❧ ❞❡ ❢❛❝t✐❜✐❧✐❞❛❞❡ ✲ ❍❡✉ríst✐❝❛s ❜❛s❡❛❞❛s ❡♠ r❡❧❛①❛çã♦ ❧✐♥❡❛r ✳ ♣✳ ✼✹
✶✹ ❉❡s✈✐♦ ♣❡r❝❡♥t✉❛❧ ♠é❞✐♦ ✲ ❍❡✉ríst✐❝❛s ❞♦ t✐♣♦ ✜①✲❛♥❞✲♦♣t✐♠✐③❡ ✳ ✳ ✳ ✳ ✳ ♣✳ ✼✹
✶✺ ❉❡s✈✐♦ ♣❛❞rã♦ ♣❡r❝❡♥t✉❛❧ ✲ ❍❡✉ríst✐❝❛s ❞♦ t✐♣♦ ✜①✲❛♥❞✲♦♣t✐♠✐③❡ ✳ ✳ ✳ ✳ ♣✳ ✼✹
✶✻ ❚❡♠♣♦ ❝♦♠♣✉t❛❝✐♦♥❛❧ ♠é❞✐♦ ✲ ❍❡✉ríst✐❝❛s ❞♦ t✐♣♦ ✜①✲❛♥❞✲♦♣t✐♠✐③❡ ✳ ✳ ✳ ♣✳ ✼✺
✶✽ P❡r❝❡♥t✉❛❧ ❞❡ ❢❛❝t✐❜✐❧✐❞❛❞❡ ✲ ❍❡✉ríst✐❝❛s ❞♦ t✐♣♦ ✜①✲❛♥❞✲♦♣t✐♠✐③❡ ✳ ✳ ✳ ✳ ♣✳ ✼✻
✶✾ ❉❡s✈✐♦ ♣❡r❝❡♥t✉❛❧ ♠é❞✐♦ ❡ ❞❡s✈✐♦ ♣❛❞rã♦ ♣❡r❝❡♥t✉❛❧ ✲ ▼❡t❛❤❡✉ríst✐❝❛
❛❧❣♦r✐t♠♦ ❞❡ ❛❜❡❧❤❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✼✻
✷✵ ❚❡♠♣♦ ❝♦♠♣✉t❛❝✐♦♥❛❧ ♠é❞✐♦ ✲ ▼❡t❛❤❡✉ríst✐❝❛ ❛❧❣♦r✐t♠♦ ❞❡ ❛❜❡❧❤❛s ✳ ✳ ♣✳ ✼✻
✷✶ P❡r❝❡♥t✉❛❧ ❞❡ ♠❡❧❤♦r✐❛ ❡ ♣❡r❝❡♥t✉❛❧ ❞❡ ❢❛❝t✐❜✐❧✐❞❛❞❡ ✲ ▼❡t❛❤❡✉ríst✐❝❛
❛❧❣♦r✐t♠♦ ❞❡ ❛❜❡❧❤❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✼✼
✷✷ ❉❡s✈✐♦ ♣❡r❝❡♥t✉❛❧ ♠é❞✐♦ ✲ ❍❡✉ríst✐❝❛s ❤í❜r✐❞❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✼✽
✷✸ ❉❡s✈✐♦ ♣❛❞rã♦ ♣❡r❝❡♥t✉❛❧ ✲ ❍❡✉ríst✐❝❛s ❤í❜r✐❞❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✼✽
✷✹ ❚❡♠♣♦ ❝♦♠♣✉t❛❝✐♦♥❛❧ ♠é❞✐♦ ✲ ❍❡✉ríst✐❝❛s ❤í❜r✐❞❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✼✽
✷✺ P❡r❝❡♥t✉❛❧ ❞❡ ♠❡❧❤♦r✐❛ ✲ ❍❡✉ríst✐❝❛s ❤í❜r✐❞❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✼✽
✷✻ P❡r❝❡♥t✉❛❧ ❞❡ ❢❛❝t✐❜✐❧✐❞❛❞❡ ✲ ❍❡✉ríst✐❝❛s ❤í❜r✐❞❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✼✾
✷✼ ❉❡s✈✐♦ ♣❡r❝❡♥t✉❛❧ ♠é❞✐♦ ✲ ❍❡✉ríst✐❝❛s ❜❛s❡❛❞❛s ❡♠ r❡❧❛①❛çã♦ ❧✐♥❡❛r ✳ ✳ ♣✳ ✽✸
✷✽ ❉❡s✈✐♦ ♣❛❞rã♦ ♣❡r❝❡♥t✉❛❧ ✲ ❍❡✉ríst✐❝❛s ❜❛s❡❛❞❛s ❡♠ r❡❧❛①❛çã♦ ❧✐♥❡❛r ✳ ✳ ♣✳ ✽✹
✷✾ ❚❡♠♣♦ ❝♦♠♣✉t❛❝✐♦♥❛❧ ♠é❞✐♦ ✲ ❍❡✉ríst✐❝❛s ❜❛s❡❛❞❛s ❡♠ r❡❧❛①❛çã♦ ❧✐♥❡❛r ♣✳ ✽✹
✸✵ P❡r❝❡♥t✉❛❧ ❞❡ ♠❡❧❤♦r✐❛ ✲ ❍❡✉ríst✐❝❛s ❜❛s❡❛❞❛s ❡♠ r❡❧❛①❛çã♦ ❧✐♥❡❛r ✳ ✳ ✳ ♣✳ ✽✺
✸✶ P❡r❝❡♥t✉❛❧ ❞❡ ❢❛❝t✐❜✐❧✐❞❛❞❡ ✲ ❍❡✉ríst✐❝❛s ❜❛s❡❛❞❛s ❡♠ r❡❧❛①❛çã♦ ❧✐♥❡❛r ✳ ♣✳ ✽✺
✸✷ ❉❡s✈✐♦ ♣❡r❝❡♥t✉❛❧ ♠é❞✐♦ ✲ ❍❡✉ríst✐❝❛s ❞♦ t✐♣♦ ✜①✲❛♥❞✲♦♣t✐♠✐③❡ ✳ ✳ ✳ ✳ ✳ ♣✳ ✽✻
✸✸ ❉❡s✈✐♦ ♣❛❞rã♦ ♣❡r❝❡♥t✉❛❧ ✲ ❍❡✉ríst✐❝❛s ❞♦ t✐♣♦ ✜①✲❛♥❞✲♦♣t✐♠✐③❡ ✳ ✳ ✳ ✳ ♣✳ ✽✼
✸✹ ❚❡♠♣♦ ❝♦♠♣✉t❛❝✐♦♥❛❧ ♠é❞✐♦ ✲ ❍❡✉ríst✐❝❛s ❞♦ t✐♣♦ ✜①✲❛♥❞✲♦♣t✐♠✐③❡ ✳ ✳ ✳ ♣✳ ✽✼
✸✺ P❡r❝❡♥t✉❛❧ ❞❡ ♠❡❧❤♦r✐❛ ✲ ❍❡✉ríst✐❝❛s ❞♦ t✐♣♦ ✜①✲❛♥❞✲♦♣t✐♠✐③❡ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✽✽
✸✻ P❡r❝❡♥t✉❛❧ ❞❡ ❢❛❝t✐❜✐❧✐❞❛❞❡ ✲ ❍❡✉ríst✐❝❛s ❞♦ t✐♣♦ ✜①✲❛♥❞✲♦♣t✐♠✐③❡ ✳ ✳ ✳ ✳ ♣✳ ✽✽
✸✼ ❉❡s✈✐♦ ♣❡r❝❡♥t✉❛❧ ♠é❞✐♦ ❡ ❞❡s✈✐♦ ♣❛❞rã♦ ♣❡r❝❡♥t✉❛❧ ✲ ▼❡t❛❤❡✉ríst✐❝❛
❛❧❣♦r✐t♠♦ ❞❡ ❛❜❡❧❤❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✽✾
✸✽ ❚❡♠♣♦ ❝♦♠♣✉t❛❝✐♦♥❛❧ ♠é❞✐♦ ✲ ▼❡t❛❤❡✉ríst✐❝❛ ❛❧❣♦r✐t♠♦ ❞❡ ❛❜❡❧❤❛s ✳ ✳ ♣✳ ✽✾
✸✾ P❡r❝❡♥t✉❛❧ ❞❡ ♠❡❧❤♦r✐❛ ❡ ♣❡r❝❡♥t✉❛❧ ❞❡ ❢❛❝t✐❜✐❧✐❞❛❞❡ ✲ ▼❡t❛❤❡✉ríst✐❝❛
❛❧❣♦r✐t♠♦ ❞❡ ❛❜❡❧❤❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✾✵
✹✶ ❉❡s✈✐♦ ♣❛❞rã♦ ♣❡r❝❡♥t✉❛❧ ✲ ❍❡✉ríst✐❝❛s ❤í❜r✐❞❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✾✶
✹✷ ❚❡♠♣♦ ❝♦♠♣✉t❛❝✐♦♥❛❧ ♠é❞✐♦ ✲ ❍❡✉ríst✐❝❛s ❤í❜r✐❞❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✾✶
✹✸ P❡r❝❡♥t✉❛❧ ❞❡ ♠❡❧❤♦r✐❛ ✲ ❍❡✉ríst✐❝❛s ❤í❜r✐❞❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✾✷
✹✹ P❡r❝❡♥t✉❛❧ ❞❡ ❢❛❝t✐❜✐❧✐❞❛❞❡ ✲ ❍❡✉ríst✐❝❛s ❤í❜r✐❞❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✾✷
▲■❙❚❆ ❉❊ ❋■●❯❘❆❙
✶ ❊str✉t✉r❛s ❞❡ ♣r♦❞✉t♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸
✷ P❛rt✐çã♦ ❞♦ ❤♦r✐③♦♥t❡ ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✾
✸ ❊str✉t✉r❛ ❞❡ ♣r♦❞✉t♦ ❝♦♠ ❞✐✈✐sã♦ ♣♦r r❡❝✉rs♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✻
✹ ❙❡q✉❡♥❝✐❛♠❡♥t♦ ❞❛ ♣r♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✻
✺ ▲P✲❛♥❞✲✜① ❝♦♠ α = 0,2 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✺
✻ ❊str✉t✉r❛ ❞❡ ♣r♦❞✉t♦ ❝♦♠ ❞✐✈✐sã♦ ♣♦r r❡❝✉rs♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✽
✼ ❊①❡♠♣❧♦ ❞❡ ♣r♦❞✉çã♦✱ ❝♦♥s✐❞❡r❛♥❞♦ ❧❡❛❞✲t✐♠❡ ❞❡ ✉♠ ♣❡rí♦❞♦✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✽
✽ P❛rt✐❝✐♦♥❛♠❡♥t♦ ❞❛ ♣r✐♠❡✐r❛ ❤❡✉ríst✐❝❛ r❡❧❛①✲❛♥❞✲✜①✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✾
✾ P❛rt✐❝✐♦♥❛♠❡♥t♦ ❞❛ s❡❣✉♥❞❛ ❤❡✉ríst✐❝❛ r❡❧❛①✲❛♥❞✲✜①✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✾
✶✵ P❛rt✐❝✐♦♥❛♠❡♥t♦ ❞❛ t❡r❝❡✐r❛ ❤❡✉ríst✐❝❛ r❡❧❛①✲❛♥❞✲✜①✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✵
✶✶ ■t❡r❛çõ❡s ❞❛ ❤❡✉ríst✐❝❛ ✜①✲❛♥❞✲♦♣t✐♠✐③❡ ❝♦♠ ♣❛rt✐❝✐♦♥❛♠❡♥t♦ ♣♦r ✐t❡♥s✳ ♣✳ ✹✷
✶✷ P❛rt✐❝✐♦♥❛♠❡♥t♦ ♣♦r ✐t❡♥s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✸
✶✸ P❛rt✐❝✐♦♥❛♠❡♥t♦ ♣♦r ♣❡rí♦❞♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✹
✶✹ ❈❧❛ss✐✜❝❛çã♦ ❞❡ ♠ét♦❞♦s ❤í❜r✐❞♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✹
✶✺ P❛rt✐çã♦ ❞♦ ✐t❡♠ ✷ ❡ ♣❛rt✐çã♦ ❛❧❡❛tór✐❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✺
✶✻ ❈r✐❛çã♦ ❞❡ ✉♠❛ ❛❜❡❧❤❛ s❡❣✉✐❞♦r❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✻
✶✽ ❊str✉t✉r❛s ❞❡ ♣r♦❞✉t♦s ❞❛ ❝❧❛ss❡ ❆✰✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✸
✶✾ ❊str✉t✉r❛s ❞❡ ♣r♦❞✉t♦s ❞❛ ❝❧❛ss❡ ✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✻
✷✵ ●rá✜❝♦ ❞❡ q✉❛❧✐❞❛❞❡ ❞❡ s♦❧✉çã♦ ❝♦♠ ❜❛rr❛ ❞❡ ❡rr♦s ✐❣✉❛❧ ❛♦ ❞❡s✈✐♦ ♣❛❞rã♦✳ ♣✳ ✽✵
✷✶ ●rá✜❝♦ ❞❡ q✉❛❧✐❞❛❞❡ ❞❡ s♦❧✉çã♦ ❝♦♠ ❜❛rr❛ ❞❡ ❡rr♦s ✐❣✉❛❧ ❛♦ ❞♦❜r♦ ❞♦
❞❡s✈✐♦ ♣❛❞rã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✽✵
✷✷ ●rá✜❝♦ ❞❡ q✉❛❧✐❞❛❞❡ ❞❡ s♦❧✉çã♦ ❝♦♠ ❜❛rr❛ ❞❡ ❡rr♦s ✐❣✉❛❧ ❛♦ ❞❡s✈✐♦ ♣❛❞rã♦✳ ♣✳ ✽✶
✷✸ ●rá✜❝♦ ❞❡ q✉❛❧✐❞❛❞❡ ❞❡ s♦❧✉çã♦ ❝♦♠ ❜❛rr❛ ❞❡ ❡rr♦s ✐❣✉❛❧ ❛♦ ❞♦❜r♦ ❞♦
❞❡s✈✐♦ ♣❛❞rã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✽✶
✷✹ ●rá✜❝♦ ❞❡ ♦t✐♠❛❧✐❞❛❞❡ ♠é❞✐❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✽✷
✷✺ ●rá✜❝♦ ❞❡ q✉❛❧✐❞❛❞❡ ❞❡ s♦❧✉çã♦ ❝♦♠ ❜❛rr❛ ❞❡ ❡rr♦s ✐❣✉❛❧ ❛♦ ❞❡s✈✐♦ ♣❛❞rã♦✳ ♣✳ ✾✸
✷✻ ●rá✜❝♦ ❞❡ q✉❛❧✐❞❛❞❡ ❞❡ s♦❧✉çã♦ ❝♦♠ ❜❛rr❛ ❞❡ ❡rr♦s ✐❣✉❛❧ ❛♦ ❞♦❜r♦ ❞♦
❞❡s✈✐♦ ♣❛❞rã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✾✸
✷✼ ●rá✜❝♦ ❞❡ ♦t✐♠❛❧✐❞❛❞❡ ♠é❞✐❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✾✹
✷✽ ●r❛❢♦ ❞❡ r❡❞❡ r❡♣r❡s❡♥t❛♥❞♦ ♦ ♣r♦❜❧❡♠❛ ❞❡ ❞✐♠❡♥s✐♦♥❛♠❡♥t♦ ❞❡ ❧♦t❡s
▲■❙❚❆ ❉❊ ❆❇❘❊❱■❆❚❯❘❆❙ ❊ ❙■●▲❆❙
❇❋❖✶ Pr✐♠❡✐r❛ ❤❡✉ríst✐❝❛ ❤í❜r✐❞❛
❇❋❖✷✲P✶ ❙❡❣✉♥❞❛ ❤❡✉ríst✐❝❛ ❤í❜r✐❞❛ ❝♦♠ ♣❛rt✐❝✐♦♥❛♠❡♥t♦ ♣♦r ✐t❡♥s ❇❋❖✷✲P✷ ❙❡❣✉♥❞❛ ❤❡✉ríst✐❝❛ ❤í❜r✐❞❛ ❝♦♠ ♣❛rt✐❝✐♦♥❛♠❡♥t♦ ♣♦r ♣❡rí♦❞♦s ❇❋❖✷✲P✸ ❙❡❣✉♥❞❛ ❤❡✉ríst✐❝❛ ❤í❜r✐❞❛ ❝♦♠ ♣❛rt✐❝✐♦♥❛♠❡♥t♦ ♣♦r ✐t❡♥s ❡
♣♦r ♣❡rí♦❞♦s
❋❖✲P✶ ❍❡✉ríst✐❝❛ ❞♦ t✐♣♦ ✜①✲❛♥❞✲♦♣t✐♠✐③❡ ❝♦♠ ♣❛rt✐❝♦♥❛♠❡♥t♦ ♣♦r ✐t❡♥s
❋❖✲P✷ ❍❡✉ríst✐❝❛ ❞♦ t✐♣♦ ✜①✲❛♥❞✲♦♣t✐♠✐③❡ ❝♦♠ ♣❛rt✐❝♦♥❛♠❡♥t♦ ♣♦r ♣❡rí♦❞♦s
❋❖✲P✸ ❍❡✉ríst✐❝❛ ❞♦ t✐♣♦ ✜①✲❛♥❞✲♦♣t✐♠✐③❡ ❝♦♠ ♣❛rt✐❝♦♥❛♠❡♥t♦ ♣♦r ✐t❡♥s ❡ ❞❡♣♦✐s ♣♦r ♣❡rí♦❞♦s
❋❖✲P✹ ❍❡✉ríst✐❝❛ ❞♦ t✐♣♦ ✜①✲❛♥❞✲♦♣t✐♠✐③❡ ❝♦♠ ♣❛rt✐❝♦♥❛♠❡♥t♦ ♣♦r ♣❡rí♦❞♦s ❡ ❞❡♣♦✐s ♣♦r ✐t❡♥s
▲P❋ ❍❡✉ríst✐❝❛ ❞♦ t✐♣♦ ▲P✲❛♥❞✲✜①
❘❋✶ ❍❡✉ríst✐❝❛ r❡❧❛①✲❛♥❞✲✜① ❝♦♠ ♣❛rt✐❝✐♦♥❛♠❡♥t♦ ♣♦r ♣❡rí♦❞♦s ❘❋✷ ❍❡✉ríst✐❝❛ r❡❧❛①✲❛♥❞✲✜① ❝♦♠ ♣❛rt✐❝✐♦♥❛♠❡♥t♦ ♣♦r ♥í✈❡❧ ❞❛ ❡s✲
tr✉t✉r❛ ❞❡ ♣r♦❞✉t♦
✶
❈❆P❮❚❯▲❖ ✶
■◆❚❘❖❉❯➬➹❖
❆ ❣❧♦❜❛❧✐③❛çã♦ ♦❝♦rr✐❞❛ ♥❛ ❡❝♦♥♦♠✐❛ ❞✉r❛♥t❡ ❛s ú❧t✐♠❛s ❞é❝❛❞❛s t❡♠ ❣❡r❛❞♦ ✉♠ ❛✉✲ ♠❡♥t♦ ♥❛ ❝♦♠♣❡t✐t✐✈✐❞❛❞❡ ❡♥tr❡ ❡♠♣r❡s❛s ♣❡❧♦s ♠❡r❝❛❞♦s ❝♦♥s✉♠✐❞♦r❡s✳ ❆❧é♠ ❞✐ss♦✱ ♦ ❛✉♠❡♥t♦ ♥❛ ❞❡♠❛♥❞❛ ❞❡ ♣r♦❞✉t♦s ✐♥❞✉str✐❛❧✐③❛❞♦s ♦❝❛s✐♦♥♦✉ ❛ ♥❡❝❡ss✐❞❛❞❡ ❞♦ ❣❡r❡♥❝✐❛✲ ♠❡♥t♦ ❞♦ ♣r♦❝❡ss♦ ♣r♦❞✉t✐✈♦ ❞❡ ❢♦r♠❛ ♠❛✐s ❡✜❝✐❡♥t❡✳ ❊st❡s ❢❛t♦r❡s ❣❡r❛r❛♠ ❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ ✉♠ ❡st✉❞♦ ❛❞❡q✉❛❞♦ ❞❛s ❝♦♥❞✐çõ❡s ❞❡ ♣r♦❞✉çã♦ ❞❛s ❡♠♣r❡s❛s ♣❛r❛ ❛✉①✐❧✐❛r ❛ t♦♠❛❞❛ ❞❡ ❞❡❝✐sã♦ ❛ ✜♠ ❞❡ ❝✉♠♣r✐r s❡✉s ♦❜❥❡t✐✈♦s✳ ◆❡st❡ ❝♦♥t❡①t♦✱ ♦ ♣❧❛♥❡❥❛♠❡♥t♦ ❞❛ ♣r♦❞✉çã♦ s✉r❣❡ ❝♦♠♦ ✉♠❛ ❢❡rr❛♠❡♥t❛ ❞❡ ❛✉①í❧✐♦ ♥❛ t♦♠❛❞❛ ❞❡ ❞❡❝✐sõ❡s✳
❊♠ P♦❝❤❡t ❡ ❲♦❧s❡② ✭✷✵✵✻✮ ♦ ♣❧❛♥❡❥❛♠❡♥t♦ ❞❛ ♣r♦❞✉çã♦ é ✈✐st♦ ❝♦♠♦ ♦ ♣❧❛♥❡❥❛♠❡♥t♦ ❞❡ ❛q✉✐s✐çõ❡s ❞❡ r❡❝✉rs♦s ❡ ♠❛tér✐❛s ♣r✐♠❛s✱ ❜❡♠ ❝♦♠♦ ❛s ❛t✐✈✐❞❛❞❡s ❞♦ ♣❧❛♥❡❥❛♠❡♥t♦ ❞❛ ♣r♦❞✉çã♦ q✉❡ sã♦ r❡q✉❡r✐❞❛s ♣❛r❛ tr❛♥s❢♦r♠❛r ❛s ♠❛tér✐❛s ♣r✐♠❛s ❡♠ ♣r♦❞✉t♦s✶ ✜♥❛✐s✱ ❞❡ ❢♦r♠❛ ❛ s✉♣r✐r ❛ ❞❡♠❛♥❞❛ ❞♦s ❝❧✐❡♥t❡s ❞❡ ♠❛♥❡✐r❛ ❡✜❝✐❡♥t❡✳
❙❡❣✉♥❞♦ ❑❛r✐♠✐ ❡t ❛❧✳ ✭✷✵✵✸✮ ♦ ♣❧❛♥❡❥❛♠❡♥t♦ ❞❛ ♣r♦❞✉çã♦ ❡♥❣❧♦❜❛ ❞❡❝✐sõ❡s ❞❡ ❝✉rt♦✱ ♠é❞✐♦ ❡ ❧♦♥❣♦ ♣r❛③♦✳ ◆♦ ♣❧❛♥❡❥❛♠❡♥t♦ ❞❡ ❧♦♥❣♦ ♣r❛③♦✱ ♦✉ ♣❧❛♥❡❥❛♠❡♥t♦ ❞❡ ♥í✈❡❧ ❡str❛té✲ ❣✐❝♦✱ ♦ ❢♦❝♦ ❡stá ❡♠ ❛♥t❡❝✐♣❛r ❛s ♥❡❝❡ss✐❞❛❞❡s ❡♥✈♦❧✈✐❞❛s t❛✐s ❝♦♠♦ ❞❡❝✐sõ❡s ❡str❛té❣✐❝❛s ❞❡ ❡s❝♦❧❤❛ ❞❡ ♣r♦❞✉t♦s✱ ❡q✉✐♣❛♠❡♥t♦s ❡ ♣r♦❝❡ss♦s✱ ❧♦❝❛❧✐③❛çã♦ ❞❡ ❢❛❝✐❧✐❞❛❞❡s ❡ ♣❧❛♥❡❥❛♠❡♥t♦ ❞❡ r❡❝✉rs♦s✳ ❖ ♣❧❛♥❡❥❛♠❡♥t♦ ❞❡ ♠é❞✐♦ ♣r❛③♦✱ ♦✉ ♣❧❛♥❡❥❛♠❡♥t♦ ❞❡ ♥í✈❡❧ tát✐❝♦✱ ❡♥✈♦❧✈❡ ❞❡❝✐sõ❡s s♦❜r❡ ❛s ♥❡❝❡ss✐❞❛❞❡s ❞❡ ♠❛t❡r✐❛✐s✱ ❡ ❡st❛❜❡❧❡❝❡ ❛s q✉❛♥t✐❞❛❞❡s ❛ s❡r❡♠ ♣r♦❞✉③✐✲ ❞❛s ♦✉ ♦ t❛♠❛♥❤♦ ❞♦s ❧♦t❡s ❡♠ ❝❛❞❛ ♣❡rí♦❞♦ ❞❡ ✉♠ ❤♦r✐③♦♥t❡ ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦✱ ❞❡ ♠♦❞♦
✷ ❉✐ss❡rt❛çã♦ ❞❡ ▼❡str❛❞♦
❛ ♦t✐♠✐③❛r ❛❧❣✉♥s ❝r✐tér✐♦s ❞❡ ❞❡s❡♠♣❡♥❤♦✱ ❡♥q✉❛♥t♦ ❛t❡♥❞❡ ❛ ❞❡♠❛♥❞❛ s❛t✐s❢❛③❡♥❞♦ ❛s r❡str✐çõ❡s ❡①✐st❡♥t❡s✳ ❖ ♣❧❛♥❡❥❛♠❡♥t♦ ❞❡ ❝✉rt♦ ♣r❛③♦✱ ♦✉ ♣❧❛♥❡❥❛♠❡♥t♦ ❞❡ ♥í✈❡❧ ♦♣❡r❛❝✐♦✲ ♥❛❧✱ ✉s✉❛❧♠❡♥t❡ ❡♥✈♦❧✈❡ ❞❡❝✐sõ❡s ❞♦ ❞✐❛✲❛✲❞✐❛ ♦✉ s❡♠❛♥❛✲❛✲s❡♠❛♥❛✱ ❝♦♠♦ ♣♦r ❡①❡♠♣❧♦✱ ♦ s❡q✉❡♥❝✐❛♠❡♥t♦ ❞❛ ♣r♦❞✉çã♦✳
❊st❡ tr❛❜❛❧❤♦ ❢♦❝❛ ♦ ♣r♦❜❧❡♠❛ ❞❡ ❞✐♠❡♥s✐♦♥❛♠❡♥t♦ ❞❡ ❧♦t❡s q✉❡ s❡ ❡♥q✉❛❞r❛ ♥♦ ♥í✈❡❧ tát✐❝♦ ❞♦ ♣❧❛♥❡❥❛♠❡♥t♦ ❞❛ ♣r♦❞✉çã♦✳ ❖ ♣r♦❜❧❡♠❛ ❞❡ ❞✐♠❡♥s✐♦♥❛♠❡♥t♦ ❞❡ ❧♦t❡s ❝♦♥s✐st❡ ❡♠ ❞❡t❡r♠✐♥❛r ♦ t❛♠❛♥❤♦ ❞♦s ❧♦t❡s ❞❡ ❝❛❞❛ ♣r♦❞✉t♦ q✉❡ s❡rá ♣r♦❞✉③✐❞♦ ❛♦ ❧♦♥❣♦ ❞❡ ✉♠ ❤♦r✐③♦♥t❡ ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦ ❝♦♠ ❚ ♣❡rí♦❞♦s✱ ❝♦♠ ♦ ✐♥t✉✐t♦ ❞❡ s✉♣r✐r ❛s ❞❡♠❛♥❞❛s✱ s❡♠ ❛tr❛s♦s✳ ❖ ♦❜❥❡t✐✈♦ ❞♦ ♣r♦❜❧❡♠❛ é ♠✐♥✐♠✐③❛r ♦s ❝✉st♦s ♣r♦❞✉t✐✈♦s✱ t❛✐s ❝♦♠♦✱ ❝✉st♦s ❞❡ ♣r❡♣❛r❛çõ❡s ❞❡ ♠áq✉✐♥❛s✱ ❝✉st♦s ❞❡ ❡st♦q✉❡ ❡✱ ❡♠ ❛❧❣✉♥s ❝❛s♦s✱ ❝✉st♦s ❞❡ ♣r♦❞✉çã♦ ❡ ❝✉st♦s ❞❡ ❤♦r❛s ❡①tr❛s✳
❖s ♣r♦❜❧❡♠❛s ❞❡ ❞✐♠❡♥s✐♦♥❛♠❡♥t♦ ❞❡ ❧♦t❡s ♣♦❞❡♠ s❡r ❞✐✈✐❞✐❞♦s ❡♠ ♠♦♥♦❡stá❣✐♦ ❡ ♠✉❧t✐❡stá❣✐♦✳ ❖ ♣r♦❜❧❡♠❛ ♠♦♥♦❡stá❣✐♦ s❡ ❝❛r❛❝t❡r✐③❛ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ♣♦r t❡r ♣r♦❞✉t♦s s❡♥❞♦ ♣r♦❞✉③✐❞♦s ❡♠ ✉♠ ♠❡s♠♦ ♠❡✐♦ ❞❡ ♣r♦❞✉çã♦ ♠❛s s❡♠ r❡❧❛çã♦ ❞❡ ♣r♦❞✉çã♦ ❡♥tr❡ ❡❧❡s✱ ♦✉ s❡❥❛✱ ❛ ♣r♦❞✉çã♦ ❞❡ ✉♠ ♣r♦❞✉t♦ ♥ã♦ ❞❡♣❡♥❞❡ ❞❛ ♣r♦❞✉çã♦ ❞❡ ♦✉tr♦ ♣r♦❞✉t♦✳ ❖ ♣r♦❜❧❡♠❛ ♠✉❧t✐❡stá❣✐♦ s❡ ❝❛r❛❝t❡r✐③❛ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ♣♦r t❡r ♠ú❧t✐♣❧♦s ♣r♦❞✉t♦s s❡♥❞♦ ♣r♦❞✉③✐❞♦s ❡♠ ✉♠ ♠❡s♠♦ ♠❡✐♦ ❞❡ ♣r♦❞✉çã♦✱ s❡❣✉♥❞♦ ✉♠❛ ❡str✉t✉r❛ ❞❡ ♣r♦❞✉t♦ ❜❡♠ ❞❡✜♥✐❞❛✳ ❉❡st❛ ❢♦r♠❛✱ ❛❧❣✉♥s ♣r♦❞✉t♦s tê♠ s✉❛ ♣r♦❞✉çã♦ ❞❡♣❡♥❞❡♥❞♦ ❞❛ ♣r♦❞✉çã♦ ❞♦s ♣r♦❞✉t♦s s✉❝❡ss♦r❡s✳
❈❛♣ít✉❧♦ ✶✳ ■♥tr♦❞✉çã♦ ✸
♠❡s♠❛ ♠❛♥❡✐r❛✱ t❛♠❜é♠ ♣♦❞❡♠♦s ✈❡r✐✜❝❛r q✉❡ ❛ ❡str✉t✉r❛ ❞❡ ♣r♦❞✉t♦ s❡q✉❡♥❝✐❛❧ é ✉♠ ❝❛s♦ ❡s♣❡❝í✜❝♦ ❞❛ ❡str✉t✉r❛ ❞❡ ♣r♦❞✉t♦ ❞❡ ♠♦♥t❛❣❡♠✱ ♦♥❞❡ ❝❛❞❛ ♣r♦❞✉t♦ t❡♠ ♥♦ ♠á①✐♠♦ ✉♠ ❝♦♠♣♦♥❡♥t❡✳
❛✮ ❊str✉t✉r❛ ❣❡r❛❧ ❜✮ ❊str✉t✉r❛ ❞❡ ♠♦♥t❛❣❡♠ ❝✮ ❊str✉t✉r❛ s❡q✉❡♥❝✐❛❧ ❋✐❣✉r❛ ✶✿ ❊str✉t✉r❛s ❞❡ ♣r♦❞✉t♦✳
❙❡❣✉♥❞♦ ▼❛❡s ❡t ❛❧✳ ✭✶✾✾✶✮ ♦s ♣r♦❜❧❡♠❛s ❞❡ ❞✐♠❡♥s✐♦♥❛♠❡♥t♦ ❞❡ ❧♦t❡ ♠✉❧t✐❡stá❣✐♦ ❛❜♦r❞❛❞♦s ♥❛ ❧✐t❡r❛t✉r❛ sã♦ ❝♦♠✉♠❡♥t❡ s✐♠♣❧✐✜❝❛çõ❡s ❞❛ r❡❛❧✐❞❛❞❡✳ ■ss♦ ♦❝♦rr❡ ♣♦✐s ✉♠ ♣r♦❜❧❡♠❛ r❡❛❧ t❡♠ ♠✉✐t❛s ❝❛r❛❝t❡ríst✐❝❛s ♣❛rt✐❝✉❧❛r❡s✱ ❝♦♠♦ ❧✐♠✐t❛çã♦ ❞❡ ❝❛♣❛❝✐❞❛❞❡✱ ♣♦s✲ s✐❜✐❧✐❞❛❞❡ ❞❡ ✉t✐❧✐③❛çã♦ ❞❡ ❤♦r❛s ❡①tr❛s ❡ ♣♦ss✐❜✐❧✐❞❛❞❡ ❞❡ ❛tr❛s♦s ♥♦ ❛t❡♥❞✐♠❡♥t♦ ❞❛ ❞❡✲ ♠❛♥❞❛✱ ❡♥tr❡ ♦✉tr♦s✳ ❉❡✈✐❞♦ ❛♦ ♥ú♠❡r♦ ❞❡ ❝❛r❛❝t❡ríst✐❝❛s q✉❡ ♣♦❞❡♠ s❡r ❝♦♥s✐❞❡r❛❞❛s✱ ♣♦❞❡ ❤❛✈❡r ✉♠❛ ❞✐✜❝✉❧❞❛❞❡ ♥❛ ♠♦❞❡❧❛❣❡♠ ❡ ❡st❡s ♠♦❞❡❧♦s ♣♦❞❡r✐❛♠ s❡r tr❛tá✈❡✐s ❛♣❡♥❛s ♣❛r❛ ❡①❡♠♣❧♦s ♠✉✐t♦ ♣❡q✉❡♥♦s✳ ❆✐♥❞❛ s❡❣✉♥❞♦ ▼❛❡s ❡t ❛❧✳ ✭✶✾✾✶✮✱ ❛ ❞✐✜❝✉❧❞❛❞❡ ❞❡ s♦❧✉çã♦ ❞❡ ✉♠ ♣r♦❜❧❡♠❛ ❞❡ ❞✐♠❡♥s✐♦♥❛♠❡♥t♦ ❞❡ ❧♦t❡s é ❞❡♣❡♥❞❡♥t❡ ❞♦ ♥ú♠❡r♦ ❞❡ ✐t❡♥s✱ ❞❛ ❡str✉✲ t✉r❛ ❞❡ ♣r♦❞✉t♦✱ ❞♦ ♥ú♠❡r♦ ❞❡ r❡❝✉rs♦s ✭♥♦s ❝❛s♦s ♦♥❞❡ ❡①✐st❡ ♠❛✐s ❞❡ ✉♠ r❡❝✉rs♦✮✱ ❞❛ ❝❛♣❛❝✐❞❛❞❡ ❧✐♠✐t❛❞❛ ❞♦s r❡❝✉rs♦s ❡ ❞♦ ♥ú♠❡r♦ ❞❡ ♣❡rí♦❞♦s ❞♦ ❤♦r✐③♦♥t❡ ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦✳ ❆❧é♠ ❞✐ss♦✱ ❡①✐st❡♠ ❛❧❣✉♠❛s ❝❛r❛❝t❡ríst✐❝❛s ❛❞✐❝✐♦♥❛✐s q✉❡ ♣♦❞❡♠ s❡r ✐♥❝♦r♣♦r❛❞❛s ❛ ✉♠ ♣r♦❜❧❡♠❛ ❡s♣❡❝í✜❝♦✱ ❝♦♠♦ t❡♠♣♦ ❡ ❝✉st♦ ❞❡ ♣r❡♣❛r❛çã♦ ♣❛r❛ ❛ ♣r♦❞✉çã♦✱ ♣r❡s❡r✈❛çã♦ ❞❡ ♣r❡♣❛r❛çã♦ ❡♥tr❡ ♣❡rí♦❞♦s ✭s❡t✉♣ ❝❛rr②✲♦✈❡r✮✱ ♣r❡♣❛r❛çã♦ ❞❡♣❡♥❞❡♥t❡ ❞❛ s❡q✉ê♥❝✐❛ ❞❡ ♣r♦❞✉çã♦✱ ❛tr❛s♦ ♥❛ ❡♥tr❡❣❛ ❞❡ ♣r♦❞✉t♦s ✭❜❛❝❦❧♦❣❣✐♥❣✮✱ ♣❡r❞❛ ❞❡ ✈❡♥❞❛s ✭❜❛❝❦♦r❞❡r✮ ❡ ❧❡❛❞✲t✐♠❡ ♣♦s✐t✐✈♦✳ ▲❡❛❞✲t✐♠❡ é ♦ t❡♠♣♦ ♥❡❝❡ssár✐♦ ♣❛r❛ q✉❡ ✉♠ ✐t❡♠ ❡st❡❥❛ ♣r♦♥t♦ ♣❛r❛ ♦ ✉s♦ ❛♣ós ♦ ✐♥í❝✐♦ ❞❡ s✉❛ ♣r♦❞✉çã♦✱ ❡ss❡ t❡♠♣♦ é ✉t✐❧✐③❛❞♦ ♣❛r❛ ❡✈✐t❛r q✉❡ ❡st❡ ✐t❡♠ t❡♥❤❛ s✉❛ ♣r♦❞✉çã♦ ✐♥✐❝✐❛❞❛ ❛♥t❡s q✉❡ s❡✉s ❝♦♠♣♦♥❡♥t❡s t❡♥❤❛♠ s✉❛s ♣r♦❞✉çõ❡s ❝♦♥❝❧✉í❞❛s✱ ♣♦r ❡①❡♠♣❧♦✱ ♥ã♦ ♣♦❞❡♠♦s ✉t✐❧✐③❛r ✉♠ ♣❛r❛❢✉s♦ q✉❡ ♥ã♦ ❡stá t♦t❛❧♠❡♥t❡ ♣r♦❞✉③✐❞♦ ♣❛r❛ ♣r❡♥❞❡r ♦ t❛♠♣♦ ❞❡ ✉♠❛ ♠❡s❛✳
✹ ❉✐ss❡rt❛çã♦ ❞❡ ▼❡str❛❞♦
❞❡ ❝❛♣❛❝✐❞❛❞❡ t♦r♥❛✲s❡ ◆P✲❈♦♠♣❧❡t♦✱ ❝❛s♦ ♦s t❡♠♣♦s ❞❡ ♣r❡♣❛r❛çõ❡s s❡❥❛♠ ♥ã♦ ♥✉❧♦s✱ ❝♦♠♦ ❢♦✐ ❞❡♠♦♥str❛❞♦ ❡♠ ▼❛❡s ❡t ❛❧✳ ✭✶✾✾✶✮✳ P♦rt❛♥t♦✱ ♦ s✐♠♣❧❡s ❢❛t♦ ❞❡ ❡♥❝♦♥tr❛r ✉♠❛ s♦❧✉çã♦ ❢❛❝tí✈❡❧ ♣❛r❛ ✉♠❛ ✐♥stâ♥❝✐❛ ❞❡st❡ ♣r♦❜❧❡♠❛✱ ❡♠ ❛❧❣✉♥s ❝❛s♦s✱ s❡ t♦r♥❛ ✉♠❛ t❛r❡❢❛ ❞✐❢í❝✐❧✳ ❉❡st❛ ❢♦r♠❛✱ ♦❜t❡r ✉♠❛ s♦❧✉çã♦ ♣❛r❛ ❞❡t❡r♠✐♥❛❞♦s ♣r♦❜❧❡♠❛s ❝♦♥s✐❞❡r❛♥❞♦ ✐♥stâ♥❝✐❛s ❞❡ ♠é❞✐♦ ❡ ❣r❛♥❞❡ ♣♦rt❡ ♣♦❞❡♠ t♦r♥❛r✲s❡ ✐♥✈✐á✈❡✐s ♣❛r❛ ♠ét♦❞♦s ❡①❛t♦s✳ P♦r ❡st❡ ♠♦t✐✈♦✱ ♣♦❞❡✲s❡ ❢❛③❡r ♥❡❝❡ssár✐♦ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ❤❡✉ríst✐❝❛s q✉❡✱ ♠❡s♠♦ s❡♠ ♦❢❡r❡❝❡r ❣❛r❛♥t✐❛s ❞❡ ♦t✐♠❛❧✐❞❛❞❡✱ ♣♦ss❛♠ ❣❡r❛r s♦❧✉çõ❡s ❞❡ ❜♦❛ q✉❛❧✐❞❛❞❡ ❞❡♥tr♦ ❞❡ ✉♠ t❡♠♣♦ ❛❝❡✐tá✈❡❧ ♣❛r❛ ✐♥stâ♥❝✐❛s ❞❡ ♣♦rt❡ r❛③♦á✈❡❧✳ ❯♠❛ ♦✉tr❛ ❡str❛té❣✐❛ s❡r✐❛ ❞❡s❡♥✈♦❧✈❡r ❛❜♦r❞❛❣❡♥s q✉❡ ❡♥❝♦♥tr❡♠ s♦❧✉çõ❡s q✉❛s❡ ót✐♠❛s ✭✈❡r P♦❝❤❡t ❡ ❲♦❧s❡② ✭✷✵✵✻✮✮✳
◆❡st❛ ❞✐ss❡rt❛çã♦ ❞❡ ♠❡str❛❞♦ sã♦ ❛❜♦r❞❛❞♦s ♣r♦❜❧❡♠❛s ❞❡ ❞✐♠❡♥s✐♦♥❛♠❡♥t♦ ❞❡ ❧♦t❡s ♠✉❧t✐❡stá❣✐♦✱ ♠❛✐s ❡s♣❡❝✐✜❝❛♠❡♥t❡ ♦s ♣r♦❜❧❡♠❛s ❛♣r❡s❡♥t❛❞♦s ❡♠ ❚❡♠♣❡❧♠❡✐❡r ❡ ❉❡rstr♦✛ ✭✶✾✾✻✮ ❡ ❙❛❤❧✐♥❣ ❡t ❛❧✳ ✭✷✵✵✾✮✳ ❖ ♣r♦❜❧❡♠❛ ❛♣r❡s❡♥t❛❞♦ ❡♠ ❚❡♠♣❡❧♠❡✐❡r ❡ ❉❡rstr♦✛ ✭✶✾✾✻✮ ❢♦✐ ❝♦♥s✐❞❡r❛❞♦ ❡♠ ✈ár✐♦s tr❛❜❛❧❤♦s ♥❛ ❧✐t❡r❛t✉r❛✱ ❝♦♠♦ ❡♠ ❙t❛❞t❧❡r ✭✷✵✵✸✮ ❡ ❆❦❛rt✉♥❛❧✐ ❡ ▼✐❧❧❡r ✭✷✵✵✾✮✱ ❡ ❝♦♥s✐st❡ ❡♠ ✉♠ ♣r♦❜❧❡♠❛ ❞❡ ❞✐♠❡♥s✐♦♥❛♠❡♥t♦ ❞❡ ❧♦t❡s ♠✉❧t✐❡stá❣✐♦ ❝♦♠ ❧✐♠✐t❛çã♦ ❞❛ ❝❛♣❛❝✐❞❛❞❡✱ ❡ t❡♠♣♦s ❡ ❝✉st♦s ❞❡ ♣r❡♣❛r❛çõ❡s ♥ã♦ ♥✉❧♦s✳ ❖ ♣r♦❜❧❡♠❛ ❛♣r❡✲ s❡♥t❛❞♦ ❡♠ ❙❛❤❧✐♥❣ ❡t ❛❧✳ ✭✷✵✵✾✮ ❝♦♥s✐st❡ ❡♠ ✉♠ ♣r♦❜❧❡♠❛ ❞❡ ❞✐♠❡♥s✐♦♥❛♠❡♥t♦ ❞❡ ❧♦t❡s ♠✉❧t✐❡stá❣✐♦ ❝♦♠ ❧✐♠✐t❛çã♦ ❞❡ ❝❛♣❛❝✐❞❛❞❡ ❡ ♣r❡s❡r✈❛çã♦ ❞❛ ♣r❡♣❛r❛çã♦✳ ◆❡st❡ s❡❣✉♥❞♦ ♣r♦❜❧❡♠❛✱ ❝♦♥s✐❞❡r❛♠ t❛♠❜é♠ ♦s t❡♠♣♦s ❡ ❝✉st♦s ❞❡ ♣r❡♣❛r❛çõ❡s ♥ã♦ ♥✉❧♦s✱ ❧❡❛❞✲t✐♠❡ ♣♦s✐t✐✈♦ ❞❡ ✉♠ ♣❡rí♦❞♦ ✭✐♥❞❡♣❡♥❞❡♥t❡ ❞♦ ✐t❡♠✮ ❡ ❡st♦q✉❡s ✐♥✐❝✐❛✐s ♣♦s✐t✐✈♦s✳
P❛r❛ ♦❜t❡♥çã♦ ❞❡ s♦❧✉çõ❡s ♣❛r❛ t❛✐s ♣r♦❜❧❡♠❛s✱ ❞❡s❡♥✈♦❧✈❡♠♦s ♠ét♦❞♦s ❤❡✉ríst✐❝♦s ❜❛s❡❛❞♦s ♥❛ ❢♦r♠✉❧❛çã♦ ♠❛t❡♠át✐❝❛ ❞♦ ♣r♦❜❧❡♠❛✱ ♠❡t❛❤❡✉ríst✐❝❛s ♣✉r❛s ❡ ❛❧❣♦r✐t♠♦s ❤í❜r✐❞♦s✱ ❜❡♠ ❝♦♠♦ ❞✐s❝✉t✐♠♦s ❡ ❛♥❛❧✐s❛♠♦s ❛❧❣✉♠❛s ❛❜♦r❞❛❣❡♥s ❞❡ s♦❧✉çã♦ ❞❛ ❧✐t❡r❛t✉r❛✱ ♣r♦♣♦st❛s ♣❛r❛ t❛✐s ♣r♦❜❧❡♠❛s✳ ❖s ♠ét♦❞♦s ❤❡✉ríst✐❝♦s sã♦ ❛❜♦r❞❛❣❡♥s ❞♦s t✐♣♦s r❡❧❛①✲ ❛♥❞✲✜① ✭r❡❧❛①❛ ❡ ✜①❛✮✱ ✜①✲❛♥❞✲♦♣t✐♠✐③❡ ✭✜①❛ ❡ ♦t✐♠✐③❛✮ ❡ ▲P✲❛♥❞✲✜① ✭▲P ❡ ✜①❛✮✳
❈❛♣ít✉❧♦ ✶✳ ■♥tr♦❞✉çã♦ ✺
❆ ♠❡t❛❤❡✉ríst✐❝❛ ❞❡s❡♥✈♦❧✈✐❞❛ ♣❛r❛ ♦s ♣r♦❜❧❡♠❛s ❛❜♦r❞❛❞♦s s❡ ❜❛s❡✐❛ ♥♦ ❛❧❣♦r✐t♠♦ ❞❡ ❛❜❡❧❤❛s ✭P❍❆▼ ❡t ❛❧✳✱ ✷✵✵✺✮ ❡ ♦s ♠ét♦❞♦s ❤í❜r✐❞♦s ❝♦♥s✐❞❡r❛♠ ❛s ✐❞é✐❛s ❞❡ ❛❧❣♦r✐t♠♦s ❝♦❧❛✲
❜♦r❛t✐✈♦s ♣r♦♣♦st❛s ♣♦r P✉❝❤✐♥❣❡r ❡ ❘❛✐❞❧ ✭✷✵✵✺✮ ❡ ❏♦✉r❞❛♥ ❡t ❛❧✳ ✭✷✵✵✾✮✱ ❡ sã♦ ❝♦♠♣♦st❛s ♣❡❧❛ ♠❡t❛❤❡✉ríst✐❝❛ ❛❧❣♦r✐t♠♦ ❞❡ ❛❜❡❧❤❛s ❡ ♣❡❧❛ ❤❡✉ríst✐❝❛ ✜①✲❛♥❞✲♦♣t✐♠✐③❡✳
❖s ♠ét♦❞♦s ❞❡ s♦❧✉çã♦ ❢♦r❛♠ t❡st❛❞♦s ❝♦♥s✐❞❡r❛♥❞♦ ♦s ❞♦✐s ♣r♦❜❧❡♠❛s ❛❜♦r❞❛❞♦s✳ ❆❧é♠ ❞✐ss♦✱ r❡❢♦r♠✉❧❛♠♦s ♦s ♣r♦❜❧❡♠❛s ❞❡ ❛❝♦r❞♦ ❝♦♠ r❡❢♦♠✉❧❛çõ❡s ❝❧áss✐❝❛s ❞❛ ❧✐t❡r❛t✉r❛✳ P❛r❛ ❝❛❞❛ ✉♠❛ ❞❛s ❢♦r♠✉❧❛çõ❡s✱ ❛♥❛❧✐s❛♠♦s ❛s s♦❧✉çõ❡s ♦❜t✐❞❛s ♣❡❧♦s ♠ét♦❞♦s ❞❡ s♦❧✉çã♦✱ ❞✐s❝✉t✐♥❞♦ ❛s ✈❛♥t❛❣❡♥s ❞❡ ❝❛❞❛ ❛❜♦r❞❛❣❡♠ ❡♠ r❡❧❛çã♦ às ❢♦r♠✉❧❛çõ❡s ❞♦s ♣r♦❜❧❡♠❛s✳
✼
❈❆P❮❚❯▲❖ ✷
❘❊❱■❙➹❖ ❉❆ ▲■❚❊❘❆❚❯❘❆
❆ ❛♣r❡s❡♥t❛çã♦ ❞❡st❡ ❝❛♣ít✉❧♦ ❢♦✐ ❞✐✈✐❞✐❞❛ ❡♠ ❞✉❛s ♣❛rt❡s✳ ◆❛ ♣r✐♠❡✐r❛✱ sã♦ ❛♣r❡s❡♥✲ t❛❞♦s ❛❧❣✉♥s tr❛❜❛❧❤♦s s♦❜r❡ ♦ ♣r♦❜❧❡♠❛ ❞❡ ❞✐♠❡♥s✐♦♥❛♠❡♥t♦ ❞❡ ❧♦t❡s ♠♦♥♦❡stá❣✐♦✳ ◆❛ s❡❣✉♥❞❛✱ sã♦ ❞✐s❝✉t✐❞♦s ❛❧❣✉♥s tr❛❜❛❧❤♦s s♦❜r❡ ♦ ♣r♦❜❧❡♠❛ ❞❡ ❞✐♠❡♥s✐♦♥❛♠❡♥t♦ ❞❡ ❧♦t❡s ♠✉❧t✐❡stá❣✐♦✱ ❡ tr❛❜❛❧❤♦s ❝♦rr❡❧❛❝✐♦♥❛❞♦s ❛♦s ♣r♦❜❧❡♠❛s ❛❜♦r❞❛❞♦s ♥❡st❛ ❞✐ss❡rt❛çã♦✳
✷✳✶ Pr♦❜❧❡♠❛ ❞❡ ❞✐♠❡♥s✐♦♥❛♠❡♥t♦ ❞❡ ❧♦t❡s ♠♦♥♦❡stá✲
❣✐♦
❖ ♣r♦❜❧❡♠❛ ❞❡ ❞✐♠❡♥s✐♦♥❛♠❡♥t♦ ❞❡ ❧♦t❡s ♠♦♥♦❡stá❣✐♦ ❝❛r❛❝t❡r✐③❛✲s❡ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ♣♦r ✉♠ ♠❡✐♦ ❞❡ ♣r♦❞✉çã♦ ♦♥❞❡ sã♦ ♣r♦❞✉③✐❞♦s ✉♠ ♦✉ ♠❛✐s ♣r♦❞✉t♦s s❡♠ r❡❧❛çã♦ ❞✐r❡t❛ ❡♥tr❡ s✐✳ ■st♦ s✐❣♥✐✜❝❛ q✉❡ ❝❛❞❛ ♣r♦❞✉t♦ ♥ã♦ t❡♠ ♦✉tr♦s ♣r♦❞✉t♦s ❞❡st❡ ♠❡✐♦ ❞❡ ♣r♦❞✉çã♦ ❝♦♠♦ s❡✉s ❝♦♠♣♦♥❡♥t❡s ❡✱ ❛♦ ♠❡s♠♦ t❡♠♣♦✱ ♥ã♦ é ❝♦♠♣♦♥❡♥t❡ ❞❡ ♥❡♥❤✉♠ ♦✉tr♦ ♣r♦❞✉t♦✳
❖ ♣r♦❜❧❡♠❛ ❞❡ ❞✐♠❡♥s✐♦♥❛♠❡♥t♦ ❞❡ ❧♦t❡s ♠♦♥♦❡stá❣✐♦ t❡♠ s✐❞♦ ♠✉✐t♦ ❡st✉❞❛❞♦ ♥❛ ❧✐t❡r❛t✉r❛✳ ❯♠ ❞♦s ♣r✐♠❡✐r♦s tr❛❜❛❧❤♦s ♥❡st❛ ár❡❛ ❢♦✐ ♦ ❞❡ ❲❛❣♥❡r ❡ ❲❤✐t✐♥ ✭✶✾✺✽✮ q✉❡ tr❛t❛ ❞♦ ❝♦♠♣r♦♠✐ss♦ ❡♥tr❡ ❝✉st♦s ❞❡ ♣r❡♣❛r❛çã♦ ❡ ❞❡ ❡st♦q✉❡✳ ❖ ♣r♦❜❧❡♠❛ ❝♦♥s✐❞❡r❛ ❞❡♠❛♥❞❛ ❞✐♥â♠✐❝❛ ❡ ❞❡t❡r♠✐♥íst✐❝❛ ❞❡ ✉♠ ú♥✐❝♦ ✐t❡♠✱ s❡♠ r❡str✐çã♦ ❞❡ ❝❛♣❛❝✐❞❛❞❡✳ ◆❡st❡ tr❛❜❛❧❤♦✱ ♦s ❛✉t♦r❡s ❛♣r❡s❡♥t❛r❛♠ ✉♠ ♠ét♦❞♦ ót✐♠♦ ❜❛s❡❛❞♦ ❡♠ ♣r♦❣r❛♠❛çã♦ ❞✐♥â♠✐❝❛✱ ♦ q✉❛❧ é ❛♠♣❧❛♠❡♥t❡ ✉t✐❧✐③❛❞♦ ♥♦s ❞✐❛s ❛t✉❛✐s✳
✽ ❉✐ss❡rt❛çã♦ ❞❡ ▼❡str❛❞♦
❡stá❣✐♦ ❝♦♠ ♠ú❧t✐♣❧♦s ✐t❡♥s✱ ❧✐♠✐t❛çã♦ ❞❡ ❝❛♣❛❝✐❞❛❞❡✱ t❡♠♣♦s ❡ ❝✉st♦s ❞❡ ♣r❡♣❛r❛çõ❡s ♥ã♦ ♥✉❧♦s✳ ❖s ❛✉t♦r❡s ♣r♦♣✉s❡r❛♠ ✉♠ ♠ét♦❞♦ ❤❡✉ríst✐❝♦ ♠✉✐t♦ ✉t✐❧✐③❛❞♦ ❞❡✈✐❞♦ ❛ s✉❛ s✐♠✲ ♣❧✐❝✐❞❛❞❡ ❡ ❡✜❝✐ê♥❝✐❛✳ ❆ ❤❡✉ríst✐❝❛ s❡ ❜❛s❡✐❛ ❡♠ r❡❧❛①❛çã♦ ❧❛❣r❛♥❣✐❛♥❛ ✭❲❖▲❙❊❨✱ ✶✾✾✽✮✱
s❡♥❞♦ ❝♦♠♣♦st❛ ❞❡ três ♣❛ss♦s✳ ◆♦ ♣r✐♠❡✐r♦ ♣❛ss♦ é ❢❡✐t❛ ✉♠❛ r❡❧❛①❛çã♦ s♦❜r❡ ❛s r❡s✲ tr✐çõ❡s ❞❡ ❝❛♣❛❝✐❞❛❞❡ ✉t✐❧✐③❛♥❞♦ ♦s ♠✉❧t✐♣❧✐❝❛❞♦r❡s ❧❛❣r❛♥❣✐❛♥♦s✱ ❞❡st❛ ❢♦r♠❛✱ ♦❜té♠✲s❡ ✉♠ s✉❜♣r♦❜❧❡♠❛ ♣❛r❛ ❝❛❞❛ ✐t❡♠✳ ❈❛❞❛ s✉❜♣r♦❜❧❡♠❛ é r❡s♦❧✈✐❞♦ ♣❡❧♦ ❛❧❣♦r✐t♠♦ ót✐♠♦ ❞❡ ❲❛❣♥❡r ❡ ❲❤✐t✐♥ ✭✶✾✺✽✮✳ ❊♠ ❣❡r❛❧✱ ♦s r❡s✉❧t❛❞♦s ❞♦s s✉❜♣r♦❜❧❡♠❛s q✉❛♥❞♦ ✐♥t❡❣r❛❞♦s ♥ã♦ ❛t❡♥❞❡♠ ❛s r❡str✐çõ❡s ❞❡ ❝❛♣❛❝✐❞❛❞❡✱ ❡♥tã♦ ✉♠❛ ❤❡✉ríst✐❝❛ ❞❡ tr❛♥s❢❡rê♥❝✐❛ ❞❡ ♣r♦✲ ❞✉çã♦ é ✉t✐❧✐③❛❞❛ ♣❛r❛ t❡♥t❛r ❢❛❝t✐❜✐❧✐③❛r ❛ s♦❧✉çã♦✳ ◆♦ ú❧t✐♠♦ ♣❛ss♦✱ ♦s ♠✉❧t✐♣❧✐❝❛❞♦r❡s ❧❛❣r❛♥❣✐❛♥♦s sã♦ ❛t✉❛❧✐③❛❞♦s ♣❡❧♦ ♠ét♦❞♦ ❞❡ ♦t✐♠✐③❛çã♦ ❞♦ s✉❜❣r❛❞✐❡♥t❡ ✭❲❖▲❙❊❨✱ ✶✾✾✽✮✳
❆r❛✉❥♦ ❡ ❆r❡♥❛❧❡s ✭✷✵✵✵✮ ❝♦♥s✐❞❡r❛♠ ♦ ♠❡s♠♦ ♣r♦❜❧❡♠❛ ❞❡ ❚r✐❣❡✐r♦ ❡t ❛❧✳ ✭✶✾✽✾✮ ❡ ♠♦❞✐✜❝❛♠ ♦ ♠ét♦❞♦ ♣r♦♣♦st♦ ♣❛r❛ ❝♦♥s✐❞❡r❛r ❝✉st♦s ✈❛r✐á✈❡✐s ♥♦ t❡♠♣♦✳ ❇❛s❡❛❞♦s ♥❛s ❝♦♥❞✐çõ❡s ❞❡ ♦t✐♠❛❧✐❞❛❞❡ ✭●❊❖❋❋❘■❖◆✱ ✶✾✼✹✮✱ ♦s ❛✉t♦r❡s ♣r♦♣✉s❡r❛♠ ♠❡❧❤♦r✐❛s ♣❛r❛ ♦
♠ét♦❞♦ ❞❡ ❚r✐❣❡✐r♦ ❡t ❛❧✳ ✭✶✾✽✾✮✳ ◆❛s ❝♦♥❝❧✉sõ❡s ❞♦ tr❛❜❛❧❤♦✱ ♦s ❛✉t♦r❡s ❝♦♥s✐❞❡r❛♠ q✉❡ ❛s ♠❡❧❤♦r✐❛s ❢♦r❛♠ ♣❡r❝❡♥t✉❛❧♠❡♥t❡ ♣❡q✉❡♥❛s✱ ❡ ✐st♦ ♣♦❞❡ t❡r ♦❝♦rr✐❞♦ ❞❡✈✐❞♦ ❛ ❡✜❝✐ê♥❝✐❛ ❞♦ ♠ét♦❞♦ ❞❡ ❢❛❝t✐❜✐❧✐③❛çã♦ ❞❡ ❚r✐❣❡✐r♦ ❡t ❛❧✳ ✭✶✾✽✾✮✳
❈❛♣ít✉❧♦ ✷✳ ❘❡✈✐sã♦ ❞❛ ▲✐t❡r❛t✉r❛ ✾
❋✐❣✉r❛ ✷✿ P❛rt✐çã♦ ❞♦ ❤♦r✐③♦♥t❡ ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦✳ ■♠❛❣❡♠ ❛❞❛♣t❛❞❛ ❞❡ ▼❡r❝é ❡ ❋♦♥t❛♥ ✭✷✵✵✸✮✳
❏❛♥s ❡ ❉❡❣r❛❡✈❡ ✭✷✵✵✹✮ ❛❜♦r❞❛♠ ♦ ♣r♦❜❧❡♠❛ ❞❡ ❞✐♠❡♥s✐♦♥❛♠❡♥t♦ ❞❡ ❧♦t❡ ♠♦♥♦❡stá❣✐♦ ❝♦♠ ♠ú❧t✐♣❧♦s ✐t❡♥s✱ r❡str✐çõ❡s ❞❡ ❝❛♣❛❝✐❞❛❞❡✱ t❡♠♣♦s ❡ ❝✉st♦s ❞❡ ♣r❡♣❛r❛çõ❡s ♥ã♦ ♥✉❧♦s ❡ ❡st♦q✉❡ ✐♥✐❝✐❛❧ ♥ã♦ ♥✉❧♦✳ ❖s ❛✉t♦r❡s ❢❛③❡♠ ✉♠❛ r❡❢♦r♠✉❧❛çã♦ ❞♦ ♣r♦❜❧❡♠❛ ♣❡❧❛ ❛❜♦r❞❛❣❡♠ ❞♦ ♠❡♥♦r ❝❛♠✐♥❤♦ ✭❊PP❊◆❀ ▼❆❘❚■◆✱ ✶✾✽✼✮✳ ❖s ❛✉t♦r❡s ❛♣❧✐❝❛♠ ❞❡❝♦♠♣♦s✐çã♦ ❉❛♥t③✐❣✲
❲♦❧❢❡ ❛♦ ♠♦❞❡❧♦ r❡❢♦r♠✉❧❛❞♦✱ ❞❡❝♦♠♣♦♥❞♦ ♦ ♣r♦❜❧❡♠❛ ♣♦r ♣❡rí♦❞♦s✳ ◆❡st❡ tr❛❜❛❧❤♦ t❛♠❜é♠ é ❢❡✐t❛ ✉♠❛ ❞✐s❝✉ssã♦ s♦❜r❡ ♦s ❧✐♠✐t❛♥t❡s ❞❛ ❧✐t❡r❛t✉r❛ ❝♦♠ ♦ ♠♦❞❡❧♦ ♦r✐❣✐♥❛❧ ❡ sã♦ ❛♣r❡s❡♥t❛❞♦s ♥♦✈♦s ❧✐♠✐t❛♥t❡s ♣❛r❛ ♦ ♣r♦❜❧❡♠❛✳
❖ ♣r♦❜❧❡♠❛ ❞❡ ❞✐♠❡♥s✐♦♥❛♠❡♥t♦ ❞❡ ❧♦t❡s ♠♦♥♦❡stá❣✐♦ ♣♦❞❡ s❡r ✈✐st♦ ❝♦♠♦ ✉♠❛ r❡✲ ❧❛①❛çã♦ ❞♦ ♣r♦❜❧❡♠❛ ♠✉❧t✐❡stá❣✐♦✱ ♣♦✐s ♥❡st❡ ❝❛s♦ ♣♦❞❡rí❛♠♦s ✐❣♥♦r❛r ❛ ❡str✉t✉r❛ ❞❡ ♣r♦❞✉t♦ ❡①✐st❡♥t❡ ❡ r❡s♦❧✈❡r ♦ ♣r♦❜❧❡♠❛ ❝♦♠♦ s❡ ❛ ❞❡♠❛♥❞❛ ❞❡ ❝❛❞❛ ♣r♦❞✉t♦ ❢♦ss❡ ✐♥✲ ❞❡♣❡♥❞❡♥t❡✳ ❊st❡ t✐♣♦ ❞❡ r❡❧❛①❛çã♦ ♣♦ss✐❜✐❧✐t❛ ❛ ✉t✐❧✐③❛çã♦ ❞♦s ♠ét♦❞♦s ❞❡ s♦❧✉çã♦ ❞❡ ♣r♦❜❧❡♠❛s ♠♦♥♦❡stá❣✐♦ ❡♠ ❤❡✉ríst✐❝❛s ❞❡ ❞❡❝♦♠♣♦s✐çã♦ ♣❛r❛ ❛ s♦❧✉çã♦ ❞❡ ♣r♦❜❧❡♠❛s ♠✉❧✲ t✐❡stá❣✐♦✳ ❖ ♠ét♦❞♦ ♣r♦♣♦st♦ ❡♠ ❚❡♠♣❡❧♠❡✐❡r ❡ ❉❡rstr♦✛ ✭✶✾✾✻✮ ✉t✐❧✐③❛ ✉♠❛ ❛❜♦r❞❛❣❡♠ ❞❡st❡ t✐♣♦ ♣❛r❛ ❛ r❡s♦❧✉çã♦ ❞♦ ♣r♦❜❧❡♠❛ ❝♦♥s✐❞❡r❛❞♦✳
✶✵ ❉✐ss❡rt❛çã♦ ❞❡ ▼❡str❛❞♦
✷✳✷ Pr♦❜❧❡♠❛ ❞❡ ❞✐♠❡♥s✐♦♥❛♠❡♥t♦ ❞❡ ❧♦t❡s ♠✉❧t✐❡stá✲
❣✐♦
❖ ♣r♦❜❧❡♠❛ ❞❡ ❞✐♠❡♥s✐♦♥❛♠❡♥t♦ ❞❡ ❧♦t❡s ♠✉❧t✐❡stá❣✐♦ ❝❛r❛❝t❡r✐③❛✲s❡ ♣♦r ✉♠ ♠❡✐♦ ❞❡ ♣r♦❞✉çã♦ ♦♥❞❡ sã♦ ♣r♦❞✉③✐❞♦s ✐t❡♥s ❝♦♠ r❡❧❛çã♦ ❞✐r❡t❛ ❞❡ ♣r♦❞✉çã♦ ❡♥tr❡ s✐✳ ■st♦ s✐❣♥✐✜❝❛ q✉❡ ❝❛❞❛ ♣r♦❞✉t♦ ♣♦❞❡ t❡r ♦✉tr♦s ♣r♦❞✉t♦s ❞❡st❡ ♠❡✐♦ ❞❡ ♣r♦❞✉çã♦ ❝♦♠♦ s❡✉s ❝♦♠♣♦♥❡♥t❡s ❡ ♣♦❞❡ s❡r ❝♦♠♣♦♥❡♥t❡ ❞❡ ♦✉tr♦s ♣r♦❞✉t♦s ❞❡st❡ ♠❡s♠♦ ♠❡✐♦✱ ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛ ❡str✉t✉r❛ ❞❡ ♣r♦❞✉t♦ ✭✈❡r ❋✐❣✉r❛ ✶✮✳
❯♠ ♠♦❞❡❧♦ ♠❛t❡♠át✐❝♦ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❡ ❞✐♠❡♥s✐♦♥❛♠❡♥t♦ ❞❡ ❧♦t❡s ♠✉❧t✐❡stá❣✐♦ ❝♦♠ r❡str✐çã♦ ❞❡ ❝❛♣❛❝✐❞❛❞❡ ❢♦✐ ♣r♦♣♦st♦ ❡♠ ❇✐❧❧✐♥❣t♦♥ ❡t ❛❧✳ ✭✶✾✽✸✮✱ ✉♠ ❞♦s tr❛❜❛❧❤♦s ♣✐♦♥❡✐r♦s ♥❡st❡ tó♣✐❝♦✳ ◆❡st❡ ❛rt✐❣♦✱ ♦s ❛✉t♦r❡s ❛♣r❡s❡♥t❛♠ ✉♠❛ ❢♦r♠✉❧❛çã♦ ♠❛t❡♠át✐❝❛ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❡st❡♥❞❡♥❞♦ ❛ ❢♦r♠✉❧❛çã♦ ❞♦ ♣r♦❜❧❡♠❛ ❞❡ ❞✐♠❡♥s✐♦♥❛♠❡♥t♦ ❞❡ ❧♦t❡s ♠♦♥♦❡stá❣✐♦ ❝♦♠ r❡str✐çã♦ ❞❡ ❝❛♣❛❝✐❞❛❞❡✳ ❉❡st❡ ❡♥tã♦✱ ♦ ♣r♦❜❧❡♠❛ t❡♠ s✐❞♦ ❛❜♦r❞❛❞♦ ♥❛ ❧✐t❡r❛t✉r❛✱ ❞❡ ✐♥ú♠❡r❛s ♠❛♥❡✐r❛s ❡ ❝♦♠ ✈❛r✐❛❞❛s ❝❛r❛❝t❡ríst✐❝❛s✳ ◆❛ ❢♦r♠✉❧❛çã♦ ❛ s❡❣✉✐r✱ ❝♦♥s✐❞❡r❡♠ q✉❡✿
• ❆tr❛s♦s ❞❡ ✐t❡♥s ✜♥❛✐s ♥ã♦ sã♦ ♣❡r♠✐t✐❞♦s❀
• ❯♠ ✐t❡♠ só ♣♦❞❡ s❡r ♣r♦❞✉③✐❞♦ q✉❛♥❞♦ ♦s s❡✉s ❝♦♠♣♦♥❡♥t❡s ❡st✐✈❡r❡♠ ❞✐s♣♦♥í✈❡✐s❀
• ❊①✐st❡♠ ❧✐♠✐t❡s ❞❛ ❝❛♣❛❝✐❞❛❞❡ ❞❡ r❡❝✉rs♦s ✭♣♦❞❡♠ s❡r ♠áq✉✐♥❛s✱ ♦♣❡rár✐♦s✱ ❡♥tr❡ ♦✉tr♦s✮ q✉❡ ❞❡✈❡♠ s❡r r❡s♣❡✐t❛❞♦s❀
• P❛r❛ q✉❡ ✉♠ ✐t❡♠ ♣♦ss❛ s❡r ♣r♦❞✉③✐❞♦✱ ♦ r❡❝✉rs♦ ✉t✐❧✐③❛❞♦ ♣❛r❛ s✉❛ ♣r♦❞✉çã♦ ❞❡✈❡ ❡st❛r ♣r❡♣❛r❛❞♦ ♣❛r❛ ❛ ♠❡s♠❛✱ ❡ ❡st❛ ♣r❡♣❛r❛çã♦ ❞❡♠❛♥❞❛ ✉♠ ❝✉st♦ ❡ ✉♠ t❡♠♣♦ ♣❛r❛ s❡r ❢❡✐t❛✳
• ❚♦❞♦ ♠♦♠❡♥t♦ q✉❡ ✉♠ ✐t❡♠ ❢♦r ♣r♦❞✉③✐❞♦✱ ♦ r❡❝✉rs♦ ✉t✐❧✐③❛❞♦ ♥❛ ♣r♦❞✉çã♦ ❞❡✈❡ ❡s✲ t❛r ♣r❡♣❛r❛❞♦ ♣❛r❛ ♣r♦❞✉③í✲❧♦✱ ❡ ✐st♦ ✐♠♣❧✐❝❛ ❡♠ ✉♠ ❝✉st♦ q✉❡ ❞❡✈❡ s❡r ❝♦♥t❛❜✐❧✐③❛❞♦ ❡ ✉♠ t❡♠♣♦ ❞❡ ♣r♦❞✉çã♦ q✉❡ s❡rá ✉t✐❧✐③❛❞♦ ♣❛r❛ ❡st❡ ♣r❡♣❛r♦❀
• ❖ ❝✉st♦ ❞❡ ❡st♦q✉❡ é ❝❛❧❝✉❧❛❞♦ ❜❛s❡❛❞♦ ♥♦ ❡st♦q✉❡ ♥♦ ✜♥❛❧ ❞❡ ❝❛❞❛ ♣❡rí♦❞♦✳
P❛r❛ ❛ ❢♦r♠✉❧❛çã♦ ♠❛t❡♠át✐❝❛ ❞❡ ▼❛❡s ❡t ❛❧✳ ✭✶✾✾✶✮✱ ❝♦♥s✐❞❡r❡♠ ♦s ❝♦♥❥✉♥t♦s✱ ❛s ✈❛r✐á✈❡✐s ❡ ♦s ♣❛râ♠❡tr♦s ❞❡❝❧❛r❛❞♦s ❛❜❛✐①♦✳
❈♦♥❥✉♥t♦s ❡ í♥❞✐❝❡s
❈❛♣ít✉❧♦ ✷✳ ❘❡✈✐sã♦ ❞❛ ▲✐t❡r❛t✉r❛ ✶✶
S(i) ❈♦♥❥✉♥t♦ ❞❡ s✉❝❡ss♦r❡s ❞❡ i❀
Km ❈♦♥❥✉♥t♦ ❞❡ ✐t❡♥s ♣r♦❞✉③✐❞♦ ♣❡❧♦ r❡❝✉rs♦ m❀
B ❱❛❧♦r ♠✉✐t♦ ❣r❛♥❞❡✳
P❛râ♠❡tr♦s
Si ❈✉st♦ ❞❡ ♣r❡♣❛r❛çã♦ r❡❧❛❝✐♦♥❛❞♦ ❛♦ ✐t❡♠ i❀
hi ❈✉st♦ ❞❡ ❡st♦q✉❡ r❡❧❛❝✐♦♥❛❞♦ ❛♦ ✐t❡♠i❀
rij ❯♥✐❞❛❞❡s ❞♦ ✐t❡♠ i ♥❡❝❡ssár✐♦s ♣❛r❛ ♣r♦❞✉③✐r ✉♠❛ ✉♥✐❞❛❞❡ ❞♦ ✐t❡♠j❀
dit ❉❡♠❛♥❞❛ ❡①t❡r♥❛ ❞♦ ✐t❡♠ i ♥♦ ♣❡rí♦❞♦t❀
ˆ
Ii ❊st♦q✉❡ ✐♥✐❝✐❛❧ ❢ís✐❝♦ ❞♦ ✐t❡♠ i❀
ai ❚❡♠♣♦ ❞❡ ♣r♦❞✉çã♦ ❞❡ ❝❛❞❛ ✉♥✐❞❛❞❡ ❞♦ ✐t❡♠i❀
tsi ❚❡♠♣♦ ❞❡ ♣r❡♣❛r❛çã♦ ♣❛r❛ ❛ ♣r♦❞✉çã♦ ❞♦ ✐t❡♠ i❀
Cmt ❈❛♣❛❝✐❞❛❞❡ ❞♦ r❡❝✉rs♦m ♥♦ ♣❡rí♦❞♦ t✳
❱❛r✐á✈❡✐s ❞❡ ❉❡❝✐sã♦
Xit ◗✉❛♥t✐❞❛❞❡ ♣r♦❞✉③✐❞❛ ❞♦ ✐t❡♠ i♥♦ ♣❡rí♦❞♦ t❀
Iit ❊st♦q✉❡ ❞♦ ✐t❡♠ i ♥♦ ✜♥❛❧ ♣❡rí♦❞♦t❀
Yit ❱❛r✐á✈❡❧ ❞❡ ♣r❡♣❛r❛çã♦✴♣r♦❞✉çã♦ ❞♦ ✐t❡♠i ♥♦ ♣❡rí♦❞♦ t✳
✭Yit= 1 ✱ s❡ Xit>0
Yit = 0✱ ❝❛s♦ ❝♦♥trár✐♦✳✮
♠✐♥✐♠✐③❡ Z =
N X
i=1
T X
t=1
(si∗Yit+hi∗Iit) ✭✷✳✶✮
s✉❥❡✐t♦ ❛✿ Ii,t−1+Xit−Iit =dit+ X
j∈S(i)
rij ∗Xjt ∀i, t ✭✷✳✷✮ X
i∈Km
(ai∗Xit+tsi∗Yit)≤Cmt ∀m, t ✭✷✳✸✮
Xit≤B∗Yit ∀i, t ✭✷✳✹✮
Xit, Iit ≥0 ∀i, t ✭✷✳✺✮
Yit ∈ {0,1} ∀i, t ✭✷✳✻✮
✶✷ ❉✐ss❡rt❛çã♦ ❞❡ ▼❡str❛❞♦
♣❡rí♦❞♦ ❛t✉❛❧ ✭Iit✮✱ ❛ ♣r♦❞✉çã♦ ♥♦ ♣❡rí♦❞♦ ✭Xit✮✱ ❛ ❞❡♠❛♥❞❛ ❡①t❡r♥❛ ✭dit✮ ❡ ❛ ❞❡♠❛♥❞❛
✐♥t❡r♥❛ ✭ X
j∈S(i)
rij ∗Xjt✮✳ ❖❜s❡r✈❡ ❛q✉✐✱ q✉❡ ♦ ♠♦❞❡❧♦ ❛❝✐♠❛ ❞✐❢❡r❡ ❞❡ ✉♠ ♠♦❞❡❧♦ ♣❛r❛ ♦
♣r♦❜❧❡♠❛ ♠♦♥♦❡stá❣✐♦ ❞❡✈✐❞♦ ❛♦ t❡r♠♦ X
j∈S(i)
rij∗Xjt✳ ❊st❡ t❡r♠♦✱ r❡♣r❡s❡♥t❛ ❛ ❞❡♠❛♥❞❛
❞❡ ♣r♦❞✉çã♦ ❡♥tr❡ ♦s ✐t❡♥s✱ ♦✉ s❡❥❛✱ ✉♠ ✐t❡♠ i ❞❡✈❡ s❡r ♣r♦❞✉③✐❞♦ ❛♥t❡s ❞❛ ♣r♦❞✉çã♦ ❞❡
s❡✉s s✉❝❡ss♦r❡s ✭S(i)✮✱ ❞❡ ❢♦r♠❛ ❛ ❛t❡♥❞❡r s✉❛s ❞❡♠❛♥❞❛s ♣♦r ❝♦♠♣♦♥❡♥t❡s✳ ❆s r❡str✐çõ❡s
✭✷✳✸✮ sã♦ r❡s♣♦♥sá✈❡✐s ♣❡❧❛ ❧✐♠✐t❛çã♦ ❞❛ ❝❛♣❛❝✐❞❛❞❡ ❞❡ ❝❛❞❛ r❡❝✉rs♦ ❞✐s♣♦♥í✈❡❧ ❡♠ ❝❛❞❛ ♣❡rí♦❞♦✳ ❆s r❡str✐çõ❡s ✭✷✳✹✮ ❛ss❡❣✉r❛♠ ❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ ♣r❡♣❛r❛çã♦ ❝❛s♦ ❤❛❥❛ ♣r♦❞✉çã♦ ❞♦ ✐t❡♠ i ♥♦ ♣❡rí♦❞♦ t✳ ❆s ✈❛r✐á✈❡✐s ❞❡ ♣r❡♣❛r❛çã♦ sã♦ ❞♦ t✐♣♦ ❜✐♥ár✐♦ ✭✷✳✻✮ ❡ ❛s ❞❡♠❛✐s
sã♦ r❡❛✐s ❡ ♣♦s✐t✐✈❛s ✭✷✳✺✮✳
❊♠ ▼❛❡s ❡t ❛❧✳ ✭✶✾✾✶✮ ❢♦r❛♠ ♣r♦♣♦st❛s ❛❧❣✉♠❛s ❤❡✉ríst✐❝❛s ❜❛s❡❛❞❛s ❡♠ r❡❧❛①❛çã♦ ❧✐♥❡❛r✱ ♣❛r❛ ❛ s♦❧✉çã♦ ❞♦ ♣r♦❜❧❡♠❛ ✭✷✳✶✮✲✭✷✳✻✮✱ ❛❧é♠ ❞❡ ✉♠ ❡st✉❞♦ ❞❛ ❝♦♠♣❧❡①✐❞❛❞❡ ❞♦ ♣r♦❜❧❡♠❛✳ ❖ ♠♦❞❡❧♦ ♠❛t❡♠át✐❝♦ ✉t✐❧✐③❛❞♦ ♥❛s ❤❡✉ríst✐❝❛s ❢♦✐ ✉♠❛ r❡❢♦r♠✉❧❛çã♦ ❞♦ ♠♦❞❡❧♦ ✭✷✳✶✮✲✭✷✳✻✮ ♣♦r ❧♦❝❛❧✐③❛çã♦ ❞❡ ❢❛❝✐❧✐❞❛❞❡s ✭❱❡r ❆♣ê♥❞✐❝❡ ❆✮✳ ❆ ♣r✐♠❡✐r❛ ❤❡✉ríst✐❝❛ ❝♦♥s✐st❡ ❡♠ ✜①❛r ✉♠❛ ✈❛r✐á✈❡❧ ❞❡ ♣r❡♣❛r❛çã♦ ❛ ❝❛❞❛ ✐t❡r❛çã♦✱ s❡♥❞♦ q✉❡ s❡ ♦ ✈❛❧♦r ❞❛ ✈❛r✐á✈❡❧ ❢♦r ✐♥t❡✐r♦ ♥❛ s♦❧✉çã♦ r❡❧❛①❛❞❛✱ ❡st❛ ✈❛r✐á✈❡❧ é ✜①❛❞❛ ❡ ♣❛ss❛ ♣❛r❛ ❛ ♣ró①✐♠❛ ✐t❡r❛çã♦✳ ❈❛❞❛ ✐t❡r❛çã♦ ❞❛ ❤❡✉ríst✐❝❛ ❝♦rr❡s♣♦♥❞❡ ❛ r❡s♦❧✉çã♦ ❞♦ ♣r♦❜❧❡♠❛ r❡❧❛①❛❞♦✳
❆ s❡❣✉♥❞❛ ❤❡✉ríst✐❝❛ ❞❡ ▼❛❡s ❡t ❛❧✳ ✭✶✾✾✶✮ é s❡♠❡❧❤❛♥t❡ ❛ ♣r✐♠❡✐r❛✱ ♣♦ré♠ s❡ ❜❛s❡✐❛ ♥♦ ❢❛t♦ q✉❡ ♦s ✈❛❧♦r❡s ❢r❛❝✐♦♥ár✐♦s ❞❛s ✈❛r✐á✈❡✐s ❞❡ ♣r❡♣❛r❛çã♦ ♥♦r♠❛❧♠❡♥t❡ ♥ã♦ ❛♣❛r❡❝❡♠ s♦③✐♥❤♦s✱ ❡❧❡s s❡ ❡♥❝♦♥tr❛♠ ❡♠ ✉♠❛ s❡q✉ê♥❝✐❛ ❞❡ ❢r❛çõ❡s ❡ ❛ ❤❡✉ríst✐❝❛ tr❛❜❛❧❤❛ ✉t✐❧✐③❛♥❞♦ ❡st❡ ❢❛t♦✳ ❊❧❛ t❡♥t❛ ❞❡s❝♦❜r✐r ✉♠❛ s❡q✉ê♥❝✐❛ ❞❡ ✈❛❧♦r❡s ❢r❛❝✐♦♥ár✐♦s ♥❛s ✈❛r✐á✈❡✐s ❞❡ ♣r❡✲ ♣❛r❛çã♦ ❡ ❛s ❝♦♥❞❡♥s❛ ❡♠ ✉♠❛ ú♥✐❝❛ ♣r❡♣❛r❛çã♦✱ ✜①❛♥❞♦ ❛ ♣r✐♠❡✐r❛ ✈❛r✐á✈❡❧ ❞❛ s❡q✉ê♥❝✐❛ ❡♠ ✉♠ ❡ ❛s ❞❡♠❛✐s ❡♠ ③❡r♦✳ ❆ t❡r❝❡✐r❛ ❤❡✉ríst✐❝❛ ❝♦♥s✐st❡ ❡♠ ✉♠❛ ❛❜♦r❞❛❣❡♠ ❞♦ t✐♣♦ ▲P✲❛♥❞✲✜①✱ ❞❡♥♦♠✐♥❛❞❛ ♣❡❧♦s ❛✉t♦r❡s ❞❡ ✉♠ ❜r❛♥❝❤✲❛♥❞✲❜♦✉♥❞ ♣❛r❝✐❛❧✳ ❆ ❤❡✉ríst✐❝❛ é ❝♦♠♣♦st❛ ❞❡ três ♣❛ss♦s✱ ♥♦ ♣r✐♠❡✐r♦ ♣❛ss♦ r❡s♦❧✈❡✲s❡ ❛ r❡❧❛①❛çã♦ ❧✐♥❡❛r ❞♦ ♣r♦❜❧❡♠❛✳ ◆♦ s❡❣✉♥❞♦ ♣❛ss♦ ✜①❛♠✲s❡ ❛s ✈❛r✐á✈❡✐s ❞❡ ♣r❡♣❛r❛çã♦ q✉❡ r❡s✉❧t❛r❛♠ ❡♠ ✈❛❧♦r❡s ✐♥t❡✐r♦s ♥❛ s♦❧✉çã♦ ❞♦ ♣r♦❜❧❡♠❛ r❡❧❛①❛❞♦✱ ❡ ♥♦ ú❧t✐♠♦ ♣❛ss♦ r❡s♦❧✈❡✲s❡ ✉♠ ❜r❛♥❝❤✲❛♥❞✲❜♦✉♥❞ ❝♦♥s✐✲ ❞❡r❛♥❞♦ ♦ s✉❜♣r♦❜❧❡♠❛ ✜①❛❞♦ ♥♦ s❡❣✉♥❞♦ ♣❛ss♦✳ ❆❧é♠ ❞❡st❛s ❤❡✉ríst✐❝❛s✱ q✉❡ s❡❣✉♥❞♦ ♦s ❛✉t♦r❡s ❢♦r❛♠ ❛s ♣r✐♠❡✐r❛s ❞❡st❡ t✐♣♦ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛✱ ♥♦ ❛rt✐❣♦ ❢♦✐ ❞❡♠♦♥str❛❞♦ q✉❡ ✉♠ ♣r♦❜❧❡♠❛ ❞❡ ❞✐♠❡♥s✐♦♥❛♠❡♥t♦ ❞❡ ❧♦t❡s ❝♦♠ t❡♠♣♦s ❞❡ ♣r❡♣❛r❛çã♦ ♣♦s✐t✐✈♦s ♣❡rt❡♥❝❡ ❛ ❝❧❛ss❡ ◆P✲❈♦♠♣❧❡t♦✳
