❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ ❘✐♦ ●r❛♥❞❡ ❞♦ ◆♦rt❡ ❈❡♥tr♦ ❞❡ ❈✐ê♥❝✐❛s ❊①❛t❛s ❡ ❞❛ ❚❡rr❛
❉❡♣❛rt♠❡♥t♦ ❞❡ ■♥❢♦r♠át✐❝❛ ❡ ▼❛t❡♠át✐❝❛ ❆♣❧✐❝❛❞❛ Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❙✐st❡♠❛s ❡ ❈♦♠♣✉t❛çã♦
▼❡str❛❞♦ ❆❝❛❞ê♠✐❝♦ ❡♠ ❙✐st❡♠❛s ❡ ❈♦♠♣✉t❛çã♦
❙❡❣♠❡♥t❛çã♦ ❋✉③③② ❞❡ ■♠❛❣❡♥s ❈♦❧♦r✐❞❛s ❝♦♠
❈❛r❛❝t❡ríst✐❝❛s ❚❡①t✉r❛✐s✿ ❯♠❛ ❆♣❧✐❝❛çã♦ ❛
❘♦❝❤❛s ❙❡❞✐♠❡♥t❛r❡s
❍é❧✐♦ ❞❡ ❆❧❜✉q✉❡rq✉❡ ❙✐❡❜r❛
❍é❧✐♦ ❞❡ ❆❧❜✉q✉❡rq✉❡ ❙✐❡❜r❛
❙❡❣♠❡♥t❛çã♦ ❋✉③③② ❞❡ ■♠❛❣❡♥s ❈♦❧♦r✐❞❛s ❝♦♠
❈❛r❛❝t❡ríst✐❝❛s ❚❡①t✉r❛✐s✿ ❯♠❛ ❆♣❧✐❝❛çã♦ ❛ ❘♦❝❤❛s
❙❡❞✐♠❡♥t❛r❡s
❉✐ss❡rt❛çã♦ ❞❡ ▼❡str❛❞♦ ❛♣r❡s❡♥t❛❞❛ ❛♦ Pr♦✲ ❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❙✐st❡♠❛s ❡ ❈♦♠♣✉t❛çã♦ ❞♦ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ■♥❢♦r♠á✲ t✐❝❛ ❡ ▼❛t❡♠át✐❝❛ ❆♣❧✐❝❛❞❛ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ ❘✐♦ ●r❛♥❞❡ ❞♦ ◆♦rt❡ ❝♦♠♦ r❡✲ q✉✐s✐t♦ ♣❛r❝✐❛❧ ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞♦ ❣r❛✉ ❞❡ ▼❡str❡ ❡♠ ❙✐st❡♠❛s ❡ ❈♦♠♣✉t❛çã♦✳
▲✐♥❤❛ ❞❡ ♣❡sq✉✐s❛✿
Pr♦❝❡ss❛♠❡♥t♦ ❞❡ ■♠❛❣❡♥s ❉✐❣✐t❛✐s
❖r✐❡♥t❛❞♦r
Pr♦❢✳ ❉r✳ ❇r✉♥♦ ▼♦tt❛ ❞❡ ❈❛r✈❛❧❤♦
PP❣❙❈ ✕ Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❙✐st❡♠❛s ❡ ❈♦♠♣✉t❛çã♦ ❉■▼❆♣ ✕ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ■♥❢♦r♠át✐❝❛ ❡ ▼❛t❡♠át✐❝❛ ❆♣❧✐❝❛❞❛
❈❈❊❚ ✕ ❈❡♥tr♦ ❞❡ ❈✐ê♥❝✐❛s ❊①❛t❛s ❡ ❞❛ ❚❡rr❛ ❯❋❘◆ ✕ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ ❘✐♦ ●r❛♥❞❡ ❞♦ ◆♦rt❡
❉✐ss❡rt❛çã♦ ❞❡ ▼❡str❛❞♦ s♦❜ ♦ tít✉❧♦ ❙❡❣♠❡♥t❛çã♦ ❋✉③③② ❞❡ ■♠❛❣❡♥s ❈♦❧♦r✐❞❛s ❝♦♠ ❈❛✲ r❛❝t❡ríst✐❝❛s ❚❡①t✉r❛✐s✿ ❯♠❛ ❆♣❧✐❝❛çã♦ ❛ ❘♦❝❤❛s ❙❡❞✐♠❡♥t❛r❡s ❛♣r❡s❡♥t❛❞❛ ♣♦r ❍é❧✐♦ ❞❡ ❆❧❜✉q✉❡rq✉❡ ❙✐❡❜r❛ ❡ ❛❝❡✐t❛ ♣❡❧♦ Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❙✐st❡♠❛s ❡ ❈♦♠♣✉t❛çã♦ ❞♦ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ■♥❢♦r♠át✐❝❛ ❡ ▼❛t❡♠át✐❝❛ ❆♣❧✐❝❛❞❛ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ ❘✐♦ ●r❛♥❞❡ ❞♦ ◆♦rt❡✱ s❡♥❞♦ ❛♣r♦✈❛❞❛ ♣♦r t♦❞♦s ♦s ♠❡♠❜r♦s ❞❛ ❜❛♥❝❛ ❡①❛♠✐♥❛❞♦r❛ ❛❜❛✐①♦ ❡s♣❡❝✐✜❝❛❞❛✿
Pr♦❢✳ ❉r✳ ❇r✉♥♦ ▼♦tt❛ ❞❡ ❈❛r✈❛❧❤♦ Pr❡s✐❞❡♥t❡
❉■▼❆♣ ✕ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ■♥❢♦r♠át✐❝❛ ❡ ▼❛t❡♠át✐❝❛ ❆♣❧✐❝❛❞❛ ❯❋❘◆ ✕ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ ❘✐♦ ●r❛♥❞❡ ❞♦ ◆♦rt❡
Pr♦❢✳ ❉r✳ ❙❡❧❛♥ ❘♦❞r✐❣✉❡s ❞♦s ❙❛♥t♦s ❊①❛♠✐♥❛❞♦r
❉■▼❆♣ ✕ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ■♥❢♦r♠át✐❝❛ ❡ ▼❛t❡♠át✐❝❛ ❆♣❧✐❝❛❞❛ ❯❋❘◆ ✕ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ ❘✐♦ ●r❛♥❞❡ ❞♦ ◆♦rt❡
Pr♦❢✳ ❉r✳ ❆♥tô♥✐♦ ❈❛r❧♦s ●❛② ❚❤♦♠é ❊①❛♠✐♥❛❞♦r
❉❈❈ ✕ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❈✐ê♥❝✐❛ ❞❛ ❈♦♠♣✉t❛çã♦ ❯❋❘❏ ✕ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ ❘✐♦ ❞❡ ❏❛♥❡✐r♦
❆❣r❛❞❡❝✐♠❡♥t♦s
❆❣r❛❞❡ç♦ ❛ ♠✐♥❤❛ ♠ã❡ ■✈❛♥✐t❛ ♣❡❧♦ ❛♠♦r✱ ❝❛r✐♥❤♦ ❡ ❞❡❞✐❝❛çã♦ ✐♥❝♦♥❞✐❝✐♦♥❛✐s✱ q✉❡ s❡r✈✐r❛♠ ❞❡ ❛❧✐❝❡r❝❡ ♥❡st❛ ❥♦r♥❛❞❛✳
❆♦ ♠❡✉ ♦r✐❡♥t❛❞♦r ❉r✳ ❇r✉♥♦ ▼♦tt❛ ❞❡ ❈❛r✈❛❧❤♦ ♣♦r t♦❞♦ ❡♠♣❡♥❤♦✱ s❛❜❡❞♦r✐❛ ❡ ❝♦♠♣r❡❡♥sã♦ ❝♦♥❝❡❞✐❞♦s ❡ ♣❡❧❛ ♦♣♦rt✉♥✐❞❛❞❡ ❞❡ ❝r❡s❝✐♠❡♥t♦ ❡ ❛♣r❡♥❞✐③❛❞♦✳
◗✉❡ ♦s ✈♦ss♦s ❡s❢♦rç♦s ❞❡s❛✜❡♠ ❛s ✐♠♣♦ss✐❜✐❧✐❞❛❞❡s✱ ❧❡♠❜r❛✐✲✈♦s ❞❡ q✉❡ ❛s ❣r❛♥❞❡s ❝♦✐s❛s ❞♦ ❤♦♠❡♠ ❢♦r❛♠ ❝♦♥q✉✐st❛❞❛s ❞♦ q✉❡ ♣❛r❡❝✐❛ ✐♠♣♦ssí✈❡❧✳
❙❡❣♠❡♥t❛çã♦ ❋✉③③② ❞❡ ■♠❛❣❡♥s ❈♦❧♦r✐❞❛s ❝♦♠
❈❛r❛❝t❡ríst✐❝❛s ❚❡①t✉r❛✐s✿ ❯♠❛ ❆♣❧✐❝❛çã♦ ❛ ❘♦❝❤❛s
❙❡❞✐♠❡♥t❛r❡s
❆✉t♦r✿ ❍é❧✐♦ ❞❡ ❆❧❜✉q✉❡rq✉❡ ❙✐❡❜r❛ ❖r✐❡♥t❛❞♦r✭❛✮✿ ❉r✳ ❇r✉♥♦ ▼♦tt❛ ❞❡ ❈❛r✈❛❧❤♦
❘❡s✉♠♦
❆ ❙❡❣♠❡♥t❛çã♦ ❞❡ ✐♠❛❣❡♥s é ♦ ♣r♦❝❡ss♦ ❞❡ r♦t✉❧❛❣❡♠ ❞❡ ♣✐①❡❧s ❡♠ ❞✐❢❡r❡♥t❡s ♦❜❥❡t♦s✱ ✉♠ ♣❛ss♦ ✐♠♣♦rt❛♥t❡ ❡♠ ❞✐✈❡rs♦s s✐st❡♠❛s ❞❡ ♣r♦❝❡ss❛♠❡♥t♦ ❞❡ ✐♠❛❣❡♥s✳ ❊st❡ tr❛❜❛❧❤♦ ♣r♦♣õ❡ ✉♠ ♠ét♦❞♦ ❞❡ ❛❣r✉♣❛♠❡♥t♦ ♣❛r❛ ❛ s❡❣♠❡♥t❛çã♦ ❞❡ ✐♠❛❣❡♥s ❞✐❣✐t❛✐s ❝♦❧♦r✐❞❛s ❝♦♠ ♣r♦♣r✐❡❞❛❞❡s t❡①t✉r❛✐s✳ ■st♦ é ❢❡✐t♦ ❛tr❛✈és ❞❛ r❡❞✉çã♦ ❞❡ ❞✐♠❡♥s✐♦♥❛❧✐❞❛❞❡ ❞♦s ❤✐s✲ t♦❣r❛♠❛s ❞❛s ✐♠❛❣❡♥s ❝♦❧♦r✐❞❛s ❡ ❞♦ ✉s♦ ❞❛ ❉✐✈❡r❣ê♥❝✐❛ ❙❦❡✇ ♥♦ ❝á❧❝✉❧♦ ❞❛s ❢✉♥çõ❡s ❞❡ ❛✜♥✐❞❛❞❡ ❢✉③③②✳ ❊ss❡ t✐♣♦ ❞❡ ❛❜♦r❞❛❣❡♠ é ❛❞❡q✉❛❞❛ à s❡❣♠❡♥t❛çã♦ ❞❡ ✐♠❛❣❡♥s ❝♦❧♦r✐✲ ❞❛s q✉❡ ♣♦ss✉❛♠ ❝❛r❛❝t❡ríst✐❝❛s t❡①t✉r❛✐s✱ ❝♦♠♦ ✐♠❛❣❡♥s ❣❡♦❧ó❣✐❝❛s✱ ❞❡r♠❛t♦s❝ó♣✐❝❛s ❡ ♦✉tr❛s ✐♠❛❣❡♥s ♥❛t✉r❛✐s✱ ❝♦♠♦ ✐♠❛❣❡♥s q✉❡ ❝♦♥t❡♥❤❛♠ ♠♦♥t❛♥❤❛s✱ ❣r❛♠❛ ♦✉ ✢♦r❡st❛s✳ ❆❧é♠ ❞✐ss♦✱ r❡s✉❧t❛❞♦s ❡①♣❡r✐♠❡♥t❛✐s ❞♦ ❛❣r✉♣❛♠❡♥t♦ ❞❡ t❡①t✉r❛s ❝♦❧♦r✐❞❛s ✉s❛♥❞♦ ✐♠❛✲ ❣❡♥s ❞❡ r♦❝❤❛s s❡❞✐♠❡♥t❛r❡s ♣♦r♦s❛s sã♦ ❛♣r❡s❡♥t❛❞♦s ❡ ❛♥❛❧✐s❛❞♦s ❡♠ t❡r♠♦s ❞❡ ♣r❡❝✐sã♦ ♣❛r❛ ❝♦♠♣r♦✈❛r s✉❛ ❡❢❡t✐✈✐❞❛❞❡✳
❋✉③③② ❙❡❣♠❡♥t❛t✐♦♥ ♦❢ ❈♦❧♦r❡❞ ■♠❛❣❡s ✇✐t❤ ❚❡①t✉r❛❧
❋❡❛t✉r❡s✿ ❆♥ ❆♣♣❧✐❝❛t✐♦♥ t♦ ❙❡❞✐♠❡♥t❛r② ❘♦❝❦s
❆✉t❤♦r✿ ❍é❧✐♦ ❞❡ ❆❧❜✉q✉❡rq✉❡ ❙✐❡❜r❛ ❙✉♣❡r✈✐s♦r✿ ❉r✳ ❇r✉♥♦ ▼♦tt❛ ❞❡ ❈❛r✈❛❧❤♦
❆❜str❛❝t
■♠❛❣❡ s❡❣♠❡♥t❛t✐♦♥ ✐s t❤❡ ♣r♦❝❡ss ♦❢ ❧❛❜❡❧✐♥❣ ♣✐①❡❧s ♦♥ ❞✐✛❡r❡♥t ♦❜❥❡❝ts✱ ❛♥ ✐♠♣♦rt❛♥t st❡♣ ✐♥ ♠❛♥② ✐♠❛❣❡ ♣r♦❝❡ss✐♥❣ s②st❡♠s✳ ❚❤✐s ✇♦r❦ ♣r♦♣♦s❡s ❛ ❝❧✉st❡r✐♥❣ ♠❡t❤♦❞ ❢♦r t❤❡ s❡❣♠❡♥t❛t✐♦♥ ♦❢ ❝♦❧♦r ❞✐❣✐t❛❧ ✐♠❛❣❡s ✇✐t❤ t❡①t✉r❛❧ ❢❡❛t✉r❡s✳ ❚❤✐s ✐s ❞♦♥❡ ❜② r❡❞✉❝✐♥❣ t❤❡ ❞✐♠❡♥s✐♦♥❛❧✐t② ♦❢ ❤✐st♦❣r❛♠s ♦❢ ❝♦❧♦r ✐♠❛❣❡s ❛♥❞ ✉s✐♥❣ t❤❡ ❙❦❡✇ ❉✐✈❡r❣❡♥❝❡ t♦ ❝❛❧❝✉❧❛t❡ t❤❡ ❢✉③③② ❛✣♥✐t② ❢✉♥❝t✐♦♥s✳ ❚❤✐s ❛♣♣r♦❛❝❤ ✐s ❛♣♣r♦♣r✐❛t❡ ❢♦r s❡❣♠❡♥t✐♥❣ ✐♠❛❣❡s t❤❛t ❤❛✈❡ ❝♦❧♦r❢✉❧ t❡①t✉r❛❧ ❢❡❛t✉r❡s s✉❝❤ ❛s ❣❡♦❧♦❣✐❝❛❧✱ ❞❡r♠♦s❝♦♣✐❝ ❛♥❞ ♦t❤❡r ♥❛t✉r❛❧ ✐♠❛❣❡s✱ ❛s ✐♠❛❣❡s ❝♦♥t❛✐♥✐♥❣ ♠♦✉♥t❛✐♥s✱ ❣r❛ss ♦r ❢♦r❡sts✳ ❋✉rt❤❡r♠♦r❡✱ ❡①♣❡r✐♠❡♥t❛❧ r❡s✉❧ts ♦❢ ❝♦❧♦r❡❞ t❡①t✉r❡ ❝❧✉st❡r✐♥❣ ✉s✐♥❣ ✐♠❛❣❡s ♦❢ ❛q✉✐❢❡rs✬ s❡❞✐♠❡♥t❛r② ♣♦r♦✉s r♦❝❦s ❛r❡ ♣r❡s❡♥t❡❞ ❛♥❞ ❛♥❛❧②③❡❞ ✐♥ t❡r♠s ♦❢ ♣r❡❝✐s✐♦♥ t♦ ✈❡r✐❢② ✐ts ❡✛❡❝t✐✈❡♥❡ss✳
▲✐st❛ ❞❡ ❋✐❣✉r❛s
✶✳✶ ❊t❛♣❛s ❞♦ Pr♦❥❡t♦ ❞❡ ▼♦❞❡❧❛❣❡♠ ❡ ❙✐♠✉❧❛çã♦ ❞❡ P♦r♦s✐❞❛❞❡ ❡ P❡r♠❡❛❜✐❧✐✲
❞❛❞❡ ❞❡ ❘♦❝❤❛s ❙❡❞✐♠❡♥t❛r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✻
✷✳✶ ❆ ♣r✐♠❡✐r❛ ✐♠❛❣❡♠ ❞✐❣✐t❛❧ ❬❊❤r❡♥❜❡r❣✱ ✷✵✶✵❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✽
✷✳✷ ❘❡♣r❡s❡♥t❛çã♦ ❞❡ ✉♠❛ ✐♠❛❣❡♠ ❞✐❣✐t❛❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✾
✷✳✸ ❘❡♣r❡s❡♥t❛çã♦ ❣rá✜❝❛ ❞♦s ♣r✐♥❝✐♣❛✐s ♠♦❞❡❧♦s ❞❡ ❝♦r❡s ❬❑✐♦s❦❡❛✱ ✷✵✶✷❪✳ ✳ ✳ ♣✳ ✶✾
✷✳✹ ▼♦❞❡❧♦ ❈✐❡ ▲✯❛❜ ❬❆♥❣❤✐♥♦♥✐✱ ✷✵✶✶❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✵
✷✳✺ ❆ ❛♣❛rê♥❝✐❛ ❞❡ ✉♠❛ ❝♦r ❝♦♠ ♦s ♠❡s♠♦s ✈❛❧♦r❡s ❞❡ ❝♦r❡s ♣♦❞❡ ✈❛r✐❛r ❡♠ ❞✐❢❡r❡♥t❡s ❞✐s♣♦s✐t✐✈♦s ✭❞✐❢❡r❡♥ç❛s ♠❛✐s ❛♣❛r❡♥t❡s ♥❛ ✈❡rsã♦ ❞✐❣✐t❛❧✮ ❬P❡tr♦✈✱
✷✵✶✵❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✶
✷✳✻ ❯♠❛ ✐♠❛❣❡♠ ❡ s❡✉ ❤✐st♦❣r❛♠❛ ❝♦❧♦r✐❞♦ ♦r❞❡♥❛❞♦ ♣❡❧♦ ♥ú♠❡r♦ ❞❡ ♦❝♦rrê♥❝✐❛
❞❛s ❝♦r❡s ❬❈❤❡♥❣ ❡t ❛❧✳✱ ✷✵✶✶❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✶
✷✳✼ ❆♠♦str❛ ❞❡ t❡①t✉r❛s ❝♦♠♣❧❡①❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✷
✸✳✶ ❋✉♥❝✐♦♥❛♠❡♥t♦ ❞♦ ▼❖❋❙ ❬❈❛r✈❛❧❤♦ ❡t ❛❧✳✱ ✷✵✵✺❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✵
✸✳✷ ▼♦❞❡❧♦ ❞❛ s♦❧✉çã♦ ♣r♦♣♦st❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✸
✸✳✸ ❊①❡♠♣❧♦ ❞❡ s❡❣♠❡♥t❛♥çã♦ ❝♦♠ ❡s❝♦❧❤❛s ✐♥❛❞❡q✉❛❞❛s ❞❡ s❡♠❡♥t❡s✳ ✳ ✳ ✳ ✳ ♣✳ ✸✹
✸✳✹ ❊①❡♠♣❧♦ ❞❡ ♣♦♥t♦ ❞❡ ❝♦rt❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✺
✸✳✺ ■♠❛❣❡♠ ♦r✐❣✐♥❛❧ ❝♦♠ t❡①t✉r❛s ✭♣❛rt❡ s✉♣❡r✐♦r ❞❛ ✐♠❛❣❡♠✮ ❡ ❛ ✐♠❛❣❡♠ r❡✲ s✉❧t❛♥t❡ ❛♣ós ❛ r❡q✉❛♥t✐③❛çã♦ ❞❡ s❡✉ ❤✐st♦❣r❛♠❛ ❛ ✼✵ ♥í✈❡✐s ❞❡ ✐♥t❡♥s✐❞❛❞❡
✭♣❛rt❡ ✐♥❢❡r✐♦r ❞❛ ✐♠❛❣❡♠✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✾
✹✳✶ ❆♠♦str❛ ❞❡ ✐♠❛❣❡♠ ❝♦♠ ✐♠♣❡r❢❡✐çõ❡s ♥❛ ❛q✉✐s✐çã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✶
✹✳✷ ❆♠♦str❛ ❛✸✶ ❡ s❡✉ ❣r♦✉♥❞ tr✉t❤✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✷
✹✳✸ ❆♠♦str❛ ❛✵✹✱ ❣r♦✉♥❞ tr✉t❤✱ s❡❣♠❡♥t❛çã♦ ❡ ♠❛tr✐③ ❞❡ ❝♦♥❢✉sã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✻
✹✳✺ ❆♠♦str❛ ❛✶✵✱ ❣r♦✉♥❞ tr✉t❤✱ s❡❣♠❡♥t❛çã♦ ❡ ♠❛tr✐③ ❞❡ ❝♦♥❢✉sã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✽
✹✳✻ ❆♠♦str❛ ❛✶✶✱ ❣r♦✉♥❞ tr✉t❤✱ s❡❣♠❡♥t❛çã♦ ❡ ♠❛tr✐③ ❞❡ ❝♦♥❢✉sã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✾
✹✳✼ ❆♠♦str❛ ❛✶✷✱ ❣r♦✉♥❞ tr✉t❤✱ s❡❣♠❡♥t❛çã♦ ❡ ♠❛tr✐③ ❞❡ ❝♦♥❢✉sã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✵
✹✳✽ ❆♠♦str❛ ❛✶✻✱ ❣r♦✉♥❞ tr✉t❤✱ s❡❣♠❡♥t❛çã♦ ❡ ♠❛tr✐③ ❞❡ ❝♦♥❢✉sã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✶
✹✳✾ ❆♠♦str❛ ❛✶✼✱ ❣r♦✉♥❞ tr✉t❤✱ s❡❣♠❡♥t❛çã♦ ❡ ♠❛tr✐③ ❞❡ ❝♦♥❢✉sã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✷
✹✳✶✵ ❆♠♦str❛ ❛✷✷✱ ❣r♦✉♥❞ tr✉t❤✱ s❡❣♠❡♥t❛çã♦ ❡ ♠❛tr✐③ ❞❡ ❝♦♥❢✉sã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✸
✹✳✶✶ ❆♠♦str❛ ❛✸✶✱ ❣r♦✉♥❞ tr✉t❤✱ s❡❣♠❡♥t❛çã♦ ❡ ♠❛tr✐③ ❞❡ ❝♦♥❢✉sã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✹
✹✳✶✷ ❆♠♦str❛ ❛✸✷✱ ❣r♦✉♥❞ tr✉t❤✱ s❡❣♠❡♥t❛çã♦ ❡ ♠❛tr✐③ ❞❡ ❝♦♥❢✉sã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✺
✹✳✶✸ ❆♠♦str❛ ❛✹✻✱ ❣r♦✉♥❞ tr✉t❤✱ s❡❣♠❡♥t❛çã♦ ❡ ♠❛tr✐③ ❞❡ ❝♦♥❢✉sã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✻
✹✳✶✹ ❆♠♦str❛ ❛✹✼✱ ❣r♦✉♥❞ tr✉t❤✱ s❡❣♠❡♥t❛çã♦ ❡ ♠❛tr✐③ ❞❡ ❝♦♥❢✉sã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✼
✹✳✶✺ ❆♠♦str❛ ❛✺✵✱ ❣r♦✉♥❞ tr✉t❤✱ s❡❣♠❡♥t❛çã♦ ❡ ♠❛tr✐③ ❞❡ ❝♦♥❢✉sã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✽
✹✳✶✻ ❘❡s✉❧t❛❞♦s ❞❛s s❡❣♠❡♥t❛çõ❡s ❞♦ ♠ét♦❞♦ ♣r♦♣♦st♦ ✭❛❝✐♠❛ ❡ ❛ ❞✐r❡✐t❛✮✱ ❋❈▼
✭❛❜❛✐①♦ ❡ ❛ ❡sq✉❡r❞❛✮ ❡ ♦ ♠ét♦❞♦ ♣r♦♣♦st♦ ♣♦r ❙❛♠❡t ✭❛❜❛✐①♦ ❡ ❛ ❞✐r❡✐t❛✮✳ ♣✳ ✻✵
✹✳✶✼ ❘❡s✉❧t❛❞♦s ❞❛s s❡❣♠❡♥t❛çõ❡s ❞♦ ♠ét♦❞♦ ♣r♦♣♦st♦ ✭❛❝✐♠❛ ❡ ❛ ❞✐r❡✐t❛✮✱ ❋❈▼
▲✐st❛ ❞❡ ❚❛❜❡❧❛s
✸✳✶ ❋✉♥çõ❡s ❞❡ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ ❞✐str✐❜✉✐çõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✶
✹✳✶ ❚❡st❡ ❞♦s ♣❛râ♠❡tr♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✷
✹✳✷ ❚❡st❡ ❞❡ ❞❡s❡♠♣❡♥❤♦ ❞❛s ❢♦r♠❛s ❞❡ ♣r♦❝❡ss❛♠❡♥t♦ ✭r❡s✉❧t❛❞♦ ❡♠ s❡❣✉♥❞♦s✮✳ ♣✳ ✹✸
✹✳✸ ❘❡s✉❧t❛❞♦s ❞❛ s❡❣♠❡♥t❛çã♦ ♥❛s ✶✸ ❛♠♦str❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✹
✹✳✹ ❘❡s✉❧t❛❞♦s ❞❛ s❡❣✉♥❞❛ s❡❣♠❡♥t❛çã♦ ❞❛s ❛♠♦str❛s ❛✸✶✱ ❛✸✷✱ ❛✹✻ ❡ ❛✺✵✳ ✳ ✳ ♣✳ ✹✺
▲✐st❛ ❞❡ ❆❜r❡✈✐❛t✉r❛s ❡ ❙✐❣❧❛s
▼❖❋❙ ✕ ▼✉❧t✐✲❖❜❥❡❝t ❋✉③③② ❙❡❣♠❡♥t❛t✐♦♥
❋▼▼ ✕ ❋✐♥✐t❡ ▼✐①t✉r❡ ▼♦❞❡❧
●▼▼ ✕ ●❛✉ss✐❛♥ ▼✐①t✉r❡ ▼♦❞❡❧
❊▼ ✕ ❊①♣❡❝t❛t✐♦♥ ▼❛①✐♠✐③❛t✐♦♥
❙✉♠ár✐♦
✶ ■♥tr♦❞✉çã♦ ♣✳ ✶✹
✶✳✶ ❉❡s❝r✐çã♦ ❞♦ Pr♦❜❧❡♠❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✹
✶✳✷ ▼♦t✐✈❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✺
✶✳✸ ❖❜❥❡t✐✈♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✼
✶✳✹ ❖r❣❛♥✐③❛çã♦ ❞♦ tr❛❜❛❧❤♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✼
✷ ❊♠❜❛s❛♠❡♥t♦ ❚❡ór✐❝♦ ❡ ❚r❛❜❛❧❤♦s ❘❡❧❛❝✐♦♥❛❞♦s ♣✳ ✶✽
✷✳✶ ■♠❛❣❡♥s ❉✐❣✐t❛✐s ❡ s✉❛s ❈❛r❛❝t❡ríst✐❝❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✽
✷✳✷ ❙❡❣♠❡♥t❛çã♦ ❞❡ ■♠❛❣❡♥s ❉✐❣✐t❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✶
✷✳✷✳✶ ❙❡❣♠❡♥t❛çã♦ ♣♦r ▲✐♠✐❛r✐③❛çã♦ ✭❚❤r❡s❤♦❧❞✐♥❣✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✸
✷✳✷✳✷ ❙❡❣♠❡♥t❛çã♦ ♣♦r ❈r❡s❝✐♠❡♥t♦ ❞❡ ❘❡❣✐õ❡s ✭❘❡❣✐♦♥ ●r♦✇✐♥❣✮ ✳ ✳ ♣✳ ✷✸
✷✳✷✳✸ ❙❡❣♠❡♥t❛çã♦ ♣♦r ❉✐✈✐sã♦ ❡ ❋✉sã♦ ✭❙♣❧✐tt✐♥❣ ❛♥❞ ▼❡r❣✐♥❣✮ ✳ ✳ ✳ ✳ ♣✳ ✷✹
✷✳✷✳✹ ❙❡❣♠❡♥t❛çã♦ ♣♦r ❆❣r✉♣❛♠❡♥t♦ ✭❈❧✉st❡r✐♥❣✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✹
✷✳✸ ❚r❛❜❛❧❤♦s ❘❡❧❛❝✐♦♥❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✺
✸ ❙❡❣♠❡♥t❛çã♦ ❋✉③③② ❞❡ ■♠❛❣❡♥s ❈♦❧♦r✐❞❛s ❝♦♠ ❈❛r❛❝t❡ríst✐❝❛s ❚❡①✲
t✉r❛✐s ♣✳ ✷✽
✸✳✶ ❚é❝♥✐❝❛s ❯t✐❧✐③❛❞❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✽
✸✳✶✳✶ ❙❡❣♠❡♥t❛çã♦ ❋✉③③② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✽
✸✳✶✳✷ ❉✐✈❡r❣ê♥❝✐❛ ❙❦❡✇ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✵
✸✳✶✳✸ Pr♦❝❡ss❛♠❡♥t♦ ❞❡ ❍✐st♦❣r❛♠❛s ❈♦❧♦r✐❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✶
✸✳✷ ❖ ▼ét♦❞♦ Pr♦♣♦st♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✷
✸✳✷✳✷ ❙❡❧❡çã♦ ❞❛s ❙❡♠❡♥t❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✸
✸✳✷✳✸ ❈♦♥✜❣✉r❛çã♦ ❞♦s P❛râ♠❡tr♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✹
✸✳✷✳✹ ❋❛s❡ ❞❡ Pré✲♣r♦❝❡ss❛♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✺
✸✳✷✳✺ ❋❛s❡ ❞❡ Pr♦❝❡ss❛♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✻
✸✳✸ ❖ ❆♣❧✐❝❛t✐✈♦ ❉❡s❡♥✈♦❧✈✐❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✼
✸✳✸✳✶ ❚❡st❡s ■♥✐❝✐❛✐s ❞♦ ❆♣❧✐❝❛t✐✈♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✽
✹ ❆♣❧✐❝❛çã♦ ❛ ❘♦❝❤❛s ❙❡❞✐♠❡♥t❛r❡s ♣✳ ✹✵
✹✳✶ ❉❡✜♥✐çã♦ ❞❛s ❆♠♦str❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✵
✹✳✷ ▼ét♦❞♦ ♣❛r❛ ❆✈❛❧✐❛çã♦ ❞♦s ❘❡s✉❧t❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✶
✹✳✸ ❆♥á❧✐s❡ ❡ ❉✐s❝✉ssã♦ ❞♦s ❘❡s✉❧t❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✸
✹✳✹ ❈♦♠♣❛r❛çã♦ ❝♦♠ ❖✉tr♦s ▼ét♦❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✾
✺ ❈♦♥s✐❞❡r❛çõ❡s ❋✐♥❛✐s ♣✳ ✻✶
❘❡❢❡rê♥❝✐❛s ♣✳ ✻✸
❆♥❡①♦ ❆ ✲✲ ❘❡s✉♠♦ ❞♦ Pr♦❥❡t♦ ▼♦❞❡❧❛❣❡♠ ❡ ❙✐♠✉❧❛çã♦ ❈♦♠♣✉t❛❝✐♦♥❛❧ ❞❡ P♦r♦s✐❞❛❞❡ ❡ P❡r♠❡❛❜✐❧✐❞❛❞❡ ❞❡ ❘♦❝❤❛s ❙❡❞✐♠❡♥t❛r❡s ❆q✉í❢❡r❛s
✶✹
✶ ■♥tr♦❞✉çã♦
◆❡st❡ ❝❛♣ít✉❧♦ s❡rá ❛♣r❡s❡♥t❛❞❛ ❛ ❝♦♥t❡①t✉❛❧✐③❛çã♦ ❞♦ t❡♠❛✱ q✉❡ ❞❡♠♦♥str❛ ❛ ♥❡❝❡s✲ s✐❞❛❞❡ ❞♦ ♣r♦❝❡ss♦ ❞❡ s❡❣♠❡♥t❛çã♦ ❞❡ ✐♠❛❣❡♥s ❞✐❣✐t❛✐s ❡♠ ❞✐✈❡rs❛s ár❡❛s ❞❡ ❛t✉❛çã♦✳ ➱ ❛♣r❡s❡♥t❛❞♦ ✉♠ ♣❛♥♦r❛♠❛ ❛t✉❛❧ ❞❛ ár❡❛ ❞❡ s❡❣♠❡♥t❛çã♦ ❞❡ ✐♠❛❣❡♥s ❝♦♠ ❢♦❝♦ ♥❛ té❝♥✐❝❛ ❞❡ ❛❣r✉♣❛♠❡♥t♦ ❞❡ ✐♠❛❣❡♥s ❡ ✐♥tr♦❞✉③✐❞♦ ❛❧❣✉♥s ❝♦♥❝❡✐t♦s r❡❢❡r❡♥t❡s ❛♦ ♣r♦❝❡ss❛♠❡♥t♦ ❞❡ ✐♠❛❣❡♥s ❞✐❣✐t❛✐s✳ ❖ ❝❛♣ít✉❧♦ t❛♠❜é♠ ❝♦♥té♠ ❛ ♠♦t✐✈❛çã♦ ❞❡st❡ tr❛❜❛❧❤♦✱ s❡✉s ♦❜❥❡t✐✈♦s ❡ ✉♠ r❡s✉♠♦ ❞❡ s✉❛ ❡str✉t✉r❛✳
✶✳✶ ❉❡s❝r✐çã♦ ❞♦ Pr♦❜❧❡♠❛
❖ ♣r♦❝❡ss❛♠❡♥t♦ ❞❡ ✐♠❛❣❡♥s ❞✐❣✐t❛✐s é ✉♠ ❝❛♠♣♦ ❛❜r❛♥❣❡♥t❡ ❡ q✉❡ ❛❧❣✉♠❛s ✈❡③❡s é ❞❡✜♥✐❞♦ ❝♦♠♦ q✉❛❧q✉❡r ❢♦r♠❛ ❞❡ ♣r♦❝❡ss❛♠❡♥t♦ ❞❡ ❞❛❞♦s ♥♦ q✉❛❧ ❛ ❡♥tr❛❞❛ ❡ ❛ s❛í❞❛ sã♦ ✐♠❛❣❡♥s✳ ❆ ❞❡✜♥✐çã♦ ❞❡ ●♦♥③❛❧❡③✱ ❲♦♦❞s ❡ ❊❞❞✐♥s ❬●♦♥③❛❧❡③ ❡t ❛❧✳✱ ✷✵✵✾❪ ❛ ❡st❡♥❞❡✉ ❞❡ ♠❛♥❡✐r❛ ❛ ❡♥❣❧♦❜❛r ♦s ♣r♦❝❡ss♦s q✉❡ ❡①tr❛❡♠ ❛tr✐❜✉t♦s ❛ ♣❛rt✐r ❞❡ ✐♠❛❣❡♥s✱ ✐♥❝❧✉✐♥❞♦ ♦ r❡❝♦♥❤❡❝✐♠❡♥t♦ ❞❡ ♦❜❥❡t♦s ✐♥❞✐✈✐❞✉❛✐s✳
❖ ❝♦♠♣❧❡①♦ s✐st❡♠❛ ✈✐s✉❛❧ ❤✉♠❛♥♦ ❝♦♥s❡❣✉❡ ❞✐s❝❡r♥✐r t❡①t✉r❛s ❡ ❞❡t❛❧❤❡s ❝♦♠ r❛♣✐❞❡③ ❡ ❡✜❝✐ê♥❝✐❛ ❡♠ ✐♠❛❣❡♥s✳ P♦ré♠✱ s❡ ❢♦r ♥❡❝❡ssár✐♦ ❛ ✉♠❛ ♣❡ss♦❛ ❝♦♥t♦r♥❛r t♦❞❛s ❛s ❢♦❧❤❛s ❞❡ ✉♠ ❡♥♦r♠❡ ❝❛r✈❛❧❤♦ ❡♠ ✉♠❛ ✐♠❛❣❡♠ ❞✐❣✐t❛❧✱ ❡st❡ ♣r♦❝❡ss♦ s❡r✐❛ ❧♦♥❣♦ ❡ ár❞✉♦✱ ❝♦♠♦ ❡♠ ❞✐✈❡rs❛s ♦✉tr❛s t❛r❡❢❛s r❡❧❛❝✐♦♥❛❞❛s✳ ❊ss❛ t❛r❡❢❛✱ ♥♦ ❡♥t❛♥t♦✱ ♣♦❞❡ s❡r ❡①❡❝✉t❛❞❛ ❞❡ ❢♦r♠❛ rá♣✐❞❛ ❡ ❝♦♠ ✉♠ ❛❧t♦ ❣r❛✉ ❞❡ ❡✜❝✐ê♥❝✐❛ ♣♦r ♠❡✐♦ ❞❛ s❡❣♠❡♥t❛çã♦ ❞❡ ✐♠❛❣❡♥s ❞✐❣✐t❛✐s✱ ♣r♦❝❡ss♦ ❞❡ r♦t✉❧❛❣❡♠ ❞♦s ♣✐①❡❧s ❞❡ ✉♠❛ ✐♠❛❣❡♠ ❡♠ ❞✐❢❡r❡♥t❡s ♦❜❥❡t♦s ❬❈❛r✈❛❧❤♦ ❡t ❛❧✳✱ ✷✵✵✺❪✳
✶✺ ❣❡♦❧ó❣✐❝♦s✱ ❛♣❧✐❝❛çõ❡s ♠✐❧✐t❛r❡s❀ ❛té ♠❛♣❡❛♠❡♥t♦ ♣♦r s❛té❧✐t❡ ❬❋✐❧❤♦ ❛♥❞ ◆❡t♦✱ ✶✾✾✾❪✳
❖ ❝r❡s❝❡♥t❡ ❛✉♠❡♥t♦ ❞❡ ❛♣❧✐❝❛t✐✈♦s q✉❡ tr❛❜❛❧❤❛♠ ❝♦♠ ✐♠❛❣❡♥s ❞✐❣✐t❛✐s ❝❤❛♠❛ ❛ ❛t❡♥çã♦ ♣❛r❛ ❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ tr❛t❛r ❡ ✐♥t❡r♣r❡t❛r s❡✉s ❞❛❞♦s ❞❡ ❢♦r♠❛ ♦t✐♠✐③❛❞❛✱ ♣r✐♥❝✐✲ ♣❛❧♠❡♥t❡ q✉❛♥❞♦ ❛♣r❡s❡♥t❛❞♦s ❡♠ ❣r❛♥❞❡ q✉❛♥t✐❞❛❞❡✱ ❝♦♠♣❧❡①✐❞❛❞❡ ❞❡ t❡①t✉r❛s ♦✉ ❛❧t❛ q✉❛❧✐❞❛❞❡ ❞❡ r❡s♦❧✉çã♦✳ ❆❧é♠ ❞✐ss♦✱ ❡st❛ ♥♦✈❛ s✐t✉❛çã♦ ❞♦s ❞❛❞♦s ❢❛③ ❛s té❝♥✐❝❛s ❞❡ ♣r♦✲ ❝❡ss❛♠❡♥t♦ ❞❡ ✐♠❛❣❡♥s ♠❛✐s ❛♥t✐❣❛s s❡ t♦r♥❛r❡♠ ✐♥❡✜❝❛③❡s ♦✉ t❡r❡♠ ✉♠ ❡❧❡✈❛❞♦ t❡♠♣♦ ❞❡ ♣r♦❝❡ss❛♠❡♥t♦ ❬●♦r❞❛♥ ❡t ❛❧✳✱ ✷✵✵✷❪✳ ❖✉tr♦ ♣r♦❜❧❡♠❛ é ❛ ❞✐✜❝✉❧❞❛❞❡ ♥♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ❛❧❣♦r✐t♠♦s ❝♦♠ ❛ ✜♥❛❧✐❞❛❞❡ ❞❡ ❛✉t♦♠❛t✐③❛r ♦ ♣r♦❝❡ss♦ ❞❡ s❡❣♠❡♥t❛çã♦ ❞❡ ✐♠❛❣❡♥s✱ ❡st❛ é ✉♠❛ ❞❛s t❛r❡❢❛s ♠❛✐s ❝♦♠♣❧❡①❛s ❞❛ ár❡❛ ❞❡ ♣r♦❝❡ss❛♠❡♥t♦ ❞❡ ✐♠❛❣❡♥s ❬●♦♥③❛❧❡③ ❛♥❞ ❲♦♦❞s✱ ✷✵✵✼❪✱ ♣♦✐s r❡q✉❡r ♦ ❝♦♥❤❡❝✐♠❡♥t♦ ♣ré✈✐♦ s♦❜r❡ ❛s ❝❛r❛❝t❡ríst✐❝❛s ❞❛ ✐♠❛❣❡♠ ❡ ❛ ✉t✐❧✐③❛çã♦ ❞❡ ❤❡✉ríst✐❝❛s ♣❛r❛ s✉❛ ✐♠♣❧❡♠❡♥t❛çã♦✱ ❡ ❛✐♥❞❛✱ ♥ã♦ s❡ ❛❞❛♣t❛♠ ❜❡♠ às ❛♣❧✐❝❛çõ❡s ❣❡♥ér✐❝❛s✳
❊♥tr❡ ❛s ❞✐✈❡rs❛s té❝♥✐❝❛s ♣❛r❛ ❛ s❡❣♠❡♥t❛çã♦ ❞❡ ✐♠❛❣❡♥s✱ ♦ ❛❧❣♦r✐t♠♦ ▼❖❋❙ ✭▼✉❧t✐✲ ❖❜❥❡❝t ❋✉③③② ❙❡❣♠❡♥t❛t✐♦♥✮ ✉t✐❧✐③❛ ❞✉❛s té❝♥✐❝❛s ♣r✐♥❝✐♣❛✐s✿ ❛ s❡❣♠❡♥t❛çã♦ ♣♦r ❝r❡s❝✐✲ ♠❡♥t♦ ❞❡ r❡❣✐õ❡s✱ q✉❡ ❝♦♥s✐st❡ ❜❛s✐❝❛♠❡♥t❡ ❡♠ ✉♥✐r ♣✐①❡❧s ❛❞❥❛❝❡♥t❡s ♣❛r❛ ❢♦r♠❛r r❡❣✐õ❡s ❛tr❛✈és ❞❡ ✉♠ ❝r✐tér✐♦ ❞❡ ❤♦♠♦❣❡♥❡✐❞❛❞❡ q✉❡ ❞❡✈❡ s❡r s❛t✐s❢❡✐t♦ ♣❛r❛ q✉❡ ❤❛❥❛ ❛ ❝♦♠❜✐♥❛✲ çã♦ ❡♥tr❡ ♦s ♣✐①❡❧s ❡ ❛s r❡❣✐õ❡s❀ ❡ ❛ s❡❣♠❡♥t❛çã♦ ❢✉③③②✱ q✉❡ ❞❡t❡r♠✐♥❛ ♣❛r❛ ❝❛❞❛ ❡❧❡♠❡♥t♦ ❞❛ ✐♠❛❣❡♠ ✉♠ ❣r❛✉ ❞❡ ♣❡rt✐♥ê♥❝✐❛ ✐♥❞✐❝❛♥❞♦ ❛ ❝❡rt❡③❛ ❞❡ss❡ ❡❧❡♠❡♥t♦ ♣❡rt❡♥❝❡r ♦✉ ♥ã♦ ❛ ❞❡t❡r♠✐♥❛❞♦ ♦❜❥❡t♦ ❡①✐st❡♥t❡ ♥❛ ✐♠❛❣❡♠ ❬❈❛r✈❛❧❤♦ ❡t ❛❧✳✱ ✷✵✵✺❪✳ ❊♥tr❡t❛♥t♦✱ ♦ ❛❧❣♦✲ r✐t♠♦ ▼❖❋❙ ❡♥❝♦♥tr❛ ♣r♦❜❧❡♠❛s ❡♠ s✉❛ ❡✜❝✐ê♥❝✐❛ q✉❛♥❞♦ ❛ ✐♠❛❣❡♠ ❝♦♥té♠ t❡①t✉r❛s ❝♦♠♣❧❡①❛s✳
❖ ♣r❡s❡♥t❡ tr❛❜❛❧❤♦ ♣r♦♣õ❡ ✉♠ ♥♦✈♦ ♠ét♦❞♦ ❞❡ s❡❣♠❡♥t❛çã♦✱ ✉♠❛ ❛❞❛♣t❛çã♦ ❛♦ ❛❧❣♦r✐t♠♦ ▼❖❋❙ ❛✉♠❡♥t❛♥❞♦ s✉❛ ❡✜❝✐ê♥❝✐❛✱ q✉❛♥❞♦ tr❛❜❛❧❤❛♥❞♦ ❝♦♠ ❛ ♥♦✈❛ s✐t✉❛çã♦ ❞❡s❝r✐t❛ ❞♦s ❞❛❞♦s ❞❛s ✐♠❛❣❡♥s ❞✐❣✐t❛✐s✳ P❛r❛ ✐ss♦✱ ❛ ❛❞❛♣t❛çã♦ ♣r♦♣õ❡ ✉♠❛ ♥♦✈❛ ❢❛s❡ ❞❡ ♣ré✲♣r♦❝❡ss❛♠❡♥t♦ ❡ ❛ ❛❧t❡r❛çã♦ ❞❛ s❡❣♠❡♥t❛çã♦ ♣♦r ❝r❡s❝✐♠❡♥t♦ ❞❡ r❡❣✐õ❡s ♣❛r❛ s❡❣✲ ♠❡♥t❛çã♦ ♣♦r ❛❣r✉♣❛♠❡♥t♦ ✉t✐❧✐③❛♥❞♦✲s❡ ❞❛ ❉✐✈❡r❣ê♥❝✐❛ ❙❦❡✇ ❝♦♠♦ ❢✉♥çã♦ ❞❡ ❛✜♥✐❞❛❞❡✳ ❆ ✈❛❧✐❞❛çã♦ ❞❡st❛ ♥♦✈❛ té❝♥✐❝❛ s❡rá ❢❡✐t❛ ♣♦r ❛❣r✉♣❛r ✶✸ ✐♠❛❣❡♥s ❣❡♦❧ó❣✐❝❛s ❞❡ r♦❝❤❛s s❡❞✐♠❡♥t❛r❡s ❛q✉í❢❡r❛s ❡ ♣♦rt❛❞♦r❛s ❞❡ ❤✐❞r♦❝❛r❜♦♥❡t♦s ❡♠ três ♦❜❥❡t♦s ❞✐st✐♥t♦s s❡❣✉♥❞♦ s✉❛ ♣❡r♠❡❛❜✐❧✐❞❛❞❡✳
✶✳✷ ▼♦t✐✈❛çã♦
✶✻ ❘♦❝❤❛s ❙❡❞✐♠❡♥t❛r❡s ❆q✉í❢❡r❛s ❡ P♦rt❛❞♦r❛s ❞❡ ❍✐❞r♦❝❛r❜♦♥❡t♦s✱ q✉❡ ♣r♦♣õ❡ ♦ ❞❡s❡♥✈♦❧✲ ✈✐♠❡♥t♦ ❞❡ ✉♠ s♦❢t✇❛r❡ ♣❛r❛ ❛ ♠♦❞❡❧❛❣❡♠ ❡ s✐♠✉❧❛çã♦ ❞❡ ♣♦r♦s✐❞❛❞❡ ❡ ♣❡r♠❡❛❜✐❧✐❞❛❞❡ ❞❡ r♦❝❤❛s s❡❞✐♠❡♥t❛r❡s✱ ❝♦♠ ❛♣❧✐❝❛çõ❡s ❡♠ ❛q✉í❢❡r♦s ❡ ❡♠ r❡s❡r✈❛tór✐♦s ❞❡ ❤✐❞r♦❝❛r❜♦♥❡t♦s✳ ❖ r❡s✉♠♦ ❞♦ ♣r♦❥❡t♦ s❡ ❡♥❝♦♥tr❛ ♥♦ ❆◆❊❳❖ ❆✳
❖ ♣r♦❥❡t♦ s❡ ❞✐✈✐❞❡ ❡♠ q✉❛tr♦ ❣r❛♥❞❡s ❡t❛♣❛s✿ ❛ ❛q✉✐s✐çã♦ ❢ís✐❝❛ ❞❛s ❛♠♦str❛s ❡ s✉❛ tr❛♥s❢♦r♠❛çã♦ ❡♠ ✐♠❛❣❡♥s ❞✐❣✐t❛✐s❀ ❛ s❡❣♠❡♥t❛çã♦ ❞❛s ❛♠♦str❛s✱ ✉t✐❧✐③❛♥❞♦ ♦ ♠ét♦❞♦ ♣r♦♣♦st♦ ♥❡st❡ tr❛❜❛❧❤♦❀ ❛ ♣r♦❞✉çã♦ ❞❡ ✉♠ ♠♦❞❡❧♦ ❞❡ ❛rq✉✐t❡t✉r❛ ❞❡ ♣♦r♦s ✭P❆▼✮ ❡ ❞❛ ♠❛❧❤❛ ❡♠ três ❞✐♠❡♥sõ❡s ✭✸❉✮❀ ❡ ❛ s✐♠✉❧❛çã♦ ❞♦ ♣r♦❝❡ss♦ ❢ís✐❝♦ ❞❡ ✢✉①♦ ❞♦s ✢✉✐❞♦s✱ ❝♦♠♦ ♣♦❞❡ s❡r ✈✐st♦ ♥❛ ❋✐❣✉r❛ ✶✳✶✳ ❆ ✐♠♣♦rtâ♥❝✐❛ ❞❡ss❡ ♣r♦❥❡t♦ ✈❡♠ ❞♦ ❢❛t♦ ❞❡ q✉❡ ♦ ❡♥t❡♥❞✐♠❡♥t♦ ❞♦s ✢✉①♦s ❞❡ ✢✉✐❞♦s ❛tr❛✈és ❞❡ ♠❡✐♦s ♣♦r♦s♦s ♣❡r♠✐t❡♠ ✉♠❛ ♠❡❧❤♦r ❡①♣❧♦r❛çã♦ ❡ ♣r❡s❡r✈❛çã♦ ❞♦s r❡s❡r✈❛tór✐♦s ❞❡ á❣✉❛s s✉❜t❡rrâ♥❡❛s ✭❛q✉í❢❡r♦s✮ ❡ ♣❡tró❧❡♦✳
❋✐❣✉r❛ ✶✳✶✿ ❊t❛♣❛s ❞♦ Pr♦❥❡t♦ ❞❡ ▼♦❞❡❧❛❣❡♠ ❡ ❙✐♠✉❧❛çã♦ ❞❡ P♦r♦s✐❞❛❞❡ ❡ P❡r♠❡❛❜✐❧✐❞❛❞❡ ❞❡ ❘♦❝❤❛s ❙❡❞✐♠❡♥t❛r❡s
✶✼
✶✳✸ ❖❜❥❡t✐✈♦s
❉❡♥tr♦ ❞♦ ❝♦♥t❡①t♦ ❛♣r❡s❡♥t❛❞♦✱ ❡st❡ tr❛❜❛❧❤♦ t❡♠ ❝♦♠♦ ♦❜❥❡t✐✈♦ ❣❡r❛❧ ♣r♦♣♦r ✉♠❛ ❛❞❛♣t❛çã♦ ❛♦ ❛❧❣♦r✐t♠♦ ▼❖❋❙ ♣❛r❛ ❛ s❡❣♠❡♥t❛çã♦ ❞❡ ✐♠❛❣❡♥s ❝♦❧♦r✐❞❛s ❝♦♠ ❝❛r❛❝t❡rís✲ t✐❝❛s t❡①t✉r❛✐s✳
❖ ♣r✐♠❡✐r♦ ♦❜❥❡t✐✈♦ ❡s♣❡❝í✜❝♦ é ✐♠♣❧❡♠❡♥t❛r ✉♠❛ ✐♥t❡r❢❛❝❡ ❛♠✐❣á✈❡❧✱ q✉❡ ❢❛❝✐❧✐t❡ ❛ ✉t✐❧✐③❛çã♦ ❞♦ ♠ét♦❞♦ ♣r♦♣♦st♦ ♥♦ ❛❣r✉♣❛♠❡♥t♦ ❞❛s ✐♠❛❣❡♥s ❞✐❣✐t❛✐s✱ ❝♦♠♦ t❛♠❜é♠✱ s❡❥❛ ❝❛♣❛③ ❞❡ ❛✈❛❧✐❛r s❡✉ ♣ró♣r✐♦ ❞❡s❡♠♣❡♥❤♦ ♥❛ s❡❣♠❡♥t❛çã♦ ❞❛s ✐♠❛❣❡♥s ❛tr❛✈és ❞♦ ❢♦r♥❡❝✐♠❡♥t♦ ❞♦ ❣r♦✉♥❞ tr✉t❤ ❞♦ ♣r♦❜❧❡♠❛✳
❖ s❡❣✉♥❞♦ ♦❜❥❡t✐✈♦ ❡s♣❡❝í✜❝♦ é s❡❣♠❡♥t❛r ❛s ✐♠❛❣❡♥s r♦❝❤♦s❛s ❞♦ ♣r♦❥❡t♦ ▼♦❞❡❧❛✲ ❣❡♠ ❡ ❙✐♠✉❧❛çã♦ ❈♦♠♣✉t❛❝✐♦♥❛❧ ❞❡ P♦r♦s✐❞❛❞❡ ❡ P❡r♠❡❛❜✐❧✐❞❛❞❡ ❞❡ ❘♦❝❤❛s ❙❡❞✐♠❡♥t❛r❡s ❆q✉í❢❡r❛s ❡ P♦rt❛❞♦r❛s ❞❡ ❍✐❞r♦❝❛r❜♦♥❡t♦s ❡♠ três ❣r✉♣♦s ❞✐st✐♥t♦s✱ s❡❣✉♥❞♦ ❛ s✉❛ ♣❡r✲ ♠❡❛❜✐❧✐❞❛❞❡✳
❖ ú❧t✐♠♦ ♦❜❥❡t✐✈♦ ❡s♣❡❝í✜❝♦ é ❛✈❛❧✐❛r ♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ❞❛ ❛♣❧✐❝❛çã♦ ❞♦ ♠ét♦❞♦ ♣r♦♣♦st♦ ♥❛ s❡❣♠❡♥t❛çã♦ ❞❛s ✐♠❛❣❡♥s r♦❝❤♦s❛s ❞♦ ♣r♦❥❡t♦ ❝✐t❛❞♦✱ ❞❡ ❛❝♦r❞♦ ❝♦♠ s✉❛ ❡✜❝✐ê♥❝✐❛ ❡♠ ❝♦♠♣❛r❛çã♦ ❛ ✉♠ ❣r♦✉♥❞ tr✉t❤ ❞❛❞♦✱ ♦♥❞❡ ❛ s❡❣♠❡♥t❛çã♦ é ❢❡✐t❛ ❛ ♠ã♦ ♣♦r ✉♠ ❡s♣❡❝✐❛❧✐st❛✳
✶✳✹ ❖r❣❛♥✐③❛çã♦ ❞♦ tr❛❜❛❧❤♦
✶✽
✷ ❊♠❜❛s❛♠❡♥t♦ ❚❡ór✐❝♦ ❡ ❚r❛❜❛❧❤♦s
❘❡❧❛❝✐♦♥❛❞♦s
◆❡st❡ ❝❛♣ít✉❧♦ é ❛♣r❡s❡♥t❛❞♦ ♦ ❝♦♥t❡①t♦ t❡ór✐❝♦ ❞❛s ♣r✐♥❝✐♣❛✐s ár❡❛s t❡♠át✐❝❛s q✉❡ ❡♥✈♦❧✈❡♠ ❡st❡ tr❛❜❛❧❤♦ ❡ ✉♠ ❧❡✈❛♥t❛♠❡♥t♦ ❞♦s tr❛❜❛❧❤♦s r❡❧❛❝✐♦♥❛❞♦s✿ ✐♠❛❣❡♥s ❞✐❣✐t❛✐s ❡ s✉❛s ❝❛r❛❝t❡ríst✐❝❛s✱ s❡❣♠❡♥t❛çã♦ ❞❡ ✐♠❛❣❡♥s ❞✐❣✐t❛✐s✱ ✜♥❛❧✐③❛♥❞♦ ❝♦♠ ✉♠ ❧❡✈❛♥t❛♠❡♥t♦ ❞♦s tr❛❜❛❧❤♦s r❡❧❛❝✐♦♥❛❞♦s✳
✷✳✶ ■♠❛❣❡♥s ❉✐❣✐t❛✐s ❡ s✉❛s ❈❛r❛❝t❡ríst✐❝❛s
❆ ♣r✐♠❡✐r❛ ✐♠❛❣❡♠ ❞✐❣✐t❛❧ ❞❛t❛ ❞❡ ✶✾✺✼ ✭❋✐❣✉r❛ ✷✳✶✮ ❡ ❢♦✐ ❡s❝❛♥❡❛❞❛ ♣♦r ✉♠ ❛♣❛r❛t♦ ✐♥✈❡♥t❛❞♦ ♣♦r ❘✉ss❡❧ ❑✐rs❝❤ q✉❡ tr❛♥s❢♦r♠♦✉ ❛ ❢♦t♦ r❡❛❧ ❞❡ s❡✉ ✜❧❤♦ ❲❛❧❞❡♥ ❡♠ ✉♠❛ ✐♠❛❣❡♠ ❞✐❣✐t❛❧ ❢♦r♠❛❞❛ ♣♦r ✉♠❛ ♠❛tr✐③ q✉❛❞r❛❞❛ ❞❡ ✶✼✻ ♣✐①❡❧s ❬❊❤r❡♥❜❡r❣✱ ✷✵✶✵❪✳
❋✐❣✉r❛ ✷✳✶✿ ❆ ♣r✐♠❡✐r❛ ✐♠❛❣❡♠ ❞✐❣✐t❛❧ ❬❊❤r❡♥❜❡r❣✱ ✷✵✶✵❪✳
❆ ❝♦♥✈❡♥çã♦ ✐♥✈❡♥t❛❞❛ ♣♦r ❘✉ss❡❧ ❑✐rs❝❤ é ❛ ❜❛s❡ ✉t✐❧✐③❛❞❛ ❛té ♦s ❞✐❛s ❛t✉❛✐s✱ ❝♦♠♦ ♣♦❞❡✲s❡ ♦❜s❡r✈❛r ❡♠ ❬●♦♥③❛❧❡③ ❛♥❞ ❲♦♦❞s✱ ✷✵✵✼❪✱ q✉❡ ❞❡✜♥❡ ✐♠❛❣❡♠ ❞✐❣✐t❛❧ ❝♦♠♦ ♦ t❡r♠♦ q✉❡ s❡ r❡❢❡r❡ à ❢✉♥çã♦ ❜✐❞✐♠❡♥s✐♦♥❛❧ ❞❡ ✐♥t❡♥s✐❞❛❞❡ ❞❡ ❧✉③ f(x, y)✱ ♦♥❞❡ x ❡ y ❞❡♥♦t❛♠
✶✾ ✭♦✉ ♥í✈❡❧ ❞❡ ❝✐♥③❛✮ ❞❛ ✐♠❛❣❡♠ ♥❛q✉❡❧❡ ♣♦♥t♦✱ ❡♥q✉❛♥t♦ q✉❡ ♥❛s ✐♠❛❣❡♥s ❞✐❣✐t❛✐s ❝♦❧♦r✐❞❛s ♦✉ ♠✉❧t✐❜❛♥❞❛✱ ♦ ✈❛❧♦r ❞❡f ❡♠ q✉❛❧q✉❡r ♣♦♥t♦ (x, y) é ✉♠ ✈❛❧♦r ✈❡t♦r✐❛❧ ✭❋✐❣✉r❛ ✷✳✷✮✳
❋✐❣✉r❛ ✷✳✷✿ ❘❡♣r❡s❡♥t❛çã♦ ❞❡ ✉♠❛ ✐♠❛❣❡♠ ❞✐❣✐t❛❧✳
❆s ❞✐✈❡rs❛s ♣♦ss✐❜✐❧✐❞❛❞❡s ❞❡ r❡♣r❡s❡♥t❛çã♦ ❞❛s ✐♠❛❣❡♥s ❝♦❧♦r✐❞❛s ✜③❡r❛♠ ♦s ♣❡sq✉✐✲ s❛❞♦r❡s ❞❛ ár❡❛ ❝r✐❛r❡♠ ♣❛❞rõ❡s ♣❛r❛ ❛ ❢♦r♠❛çã♦ ❞❛s ❝♦r❡s ♦✉ ♠♦❞❡❧♦s ❞❡ ❝♦r❡s✳ ❊①✐st❡♠ ❞✐✈❡rs♦s ♠♦❞❡❧♦s ❞❡ ❝♦r❡s ♣❛r❛ r❡♣r❡s❡♥t❛r ❛s ✐♠❛❣❡♥s ♠✉❧t✐❜❛♥❞❛s✱ s❡♥❞♦ ♦s ♠❛✐s ✉t✐❧✐✲ ③❛❞♦s ♦ ♠♦❞❡❧♦ ❘●❇✱ ❈▼❨❑ ❡ ❍❙▲ ✭❋✐❣✉r❛ ✷✳✸✮✳
❋✐❣✉r❛ ✷✳✸✿ ❘❡♣r❡s❡♥t❛çã♦ ❣rá✜❝❛ ❞♦s ♣r✐♥❝✐♣❛✐s ♠♦❞❡❧♦s ❞❡ ❝♦r❡s ❬❑✐♦s❦❡❛✱ ✷✵✶✷❪✳
✷✵ ❛t✐♥❣✐❞❛ ♣♦r ❞✐✈❡rs♦s ❞✐s♣♦s✐t✐✈♦s✳ ❖ ♠♦❞❡❧♦ ❍❙▲ ✭❚♦♥❛❧✐❞❛❞❡✱ ❙❛t✉r❛çã♦ ❡ ▲✉♠✐♥â♥❝✐❛✮ é ✉♠ ♠♦❞❡❧♦ ❜❛s❡❛❞♦ ♥♦s tr❛❜❛❧❤♦s ❞♦ ♣✐♥t♦r ❆❧❜❡rt ❍✳ ▼✉♥s❡❧❧ ✭q✉❡ ❝r✐♦✉ ♦ ❆t❧❛s ❞❡ ▼✉♥s❡❧❧✮✱ ❡ é ✉♠ ♠♦❞❡❧♦ ❞❡ r❡♣r❡s❡♥t❛çã♦ ❞✐t♦ ✏♥❛t✉r❛❧✑✱ ♦✉ s❡❥❛✱ ♣ró①✐♠♦ ❞❛ ♣❡r❝❡♣çã♦ ✜s✐♦❧ó❣✐❝❛ ❞❛ ❝♦r ♣❡❧♦ ♦❧❤♦ ❤✉♠❛♥♦ ❬❑✐♦s❦❡❛✱ ✷✵✶✷❪✳
❆ ❈♦♠✐ssã♦ ■♥t❡r♥❛❝✐♦♥❛❧ ❞❡ ■❧✉♠✐♥❛çã♦ ✭❈■❊✮ ❞❡✜♥❡ ♣❛❞rõ❡s q✉❡ ♣❡r♠✐t❡♠ ✐❞❡♥t✐✲ ✜❝❛r ✉♠❛ ❝♦r ✐♥❞❡♣❡♥❞❡♥t❡ ❞♦s ♣❡r✐❢ér✐❝♦s ✉s❛❞♦s✱ ✉t✐❧✐③❛♥❞♦ ❛ ❝❛♣❛❝✐❞❛❞❡ ❞❡ ♣❡r❝❡♣çã♦ ❞❡ ❝♦r ♣❡❧♦ ♦❧❤♦ ❤✉♠❛♥♦✱ ❡st❛ ✐♥❞❡♣❡♥❞ê♥❝✐❛ ❞❡ s❡✉ ♠❛✐s ♥♦✈♦ ♣❛❞rã♦ ❈■❊✲▲✯❛❜ ✭▲✉♠✐✲ ♥â♥❝✐❛✱ ❱❡r❞❡ ❛♦ ▼❛❣❡♥t❛ ❡ ❆③✉❧ ❛♦ ❆♠❛r❡❧♦✮ ❢❛③ ❝♦♠ q✉❡ ❛♣❧✐❝❛t✐✈♦s r❡❝♦♥❤❡❝✐❞♦s ❝♦♠♦ ♦ P❤♦t♦❙❤♦♣ ✉t✐❧✐③❡♠ ♦ ♠♦❞❡❧♦ ❈■❊✲▲✯❛❜ ❝♦♠♦ ✐♥t❡r♠❡❞✐ár✐♦ ♥❛ tr❛♥s❢♦r♠❛çã♦ ❡♥tr❡ ♠♦❞❡❧♦s ✭❋✐❣✉r❛ ✷✳✹✮✳
❋✐❣✉r❛ ✷✳✹✿ ▼♦❞❡❧♦ ❈✐❡ ▲✯❛❜ ❬❆♥❣❤✐♥♦♥✐✱ ✷✵✶✶❪✳
❆ ❋✐❣✉r❛ ✷✳✺ ❛♣r❡s❡♥t❛ ✉♠❛ ❞✐❢❡r❡♥ç❛ ✈✐s✉❛❧ ♥❛s ❝♦r❡s ❘●❇✭✷✺✺✱ ✵✱ ✵✮ ❡ ❘●❇✭✵✱ ✵✱ ✷✺✺✮✱ q✉❛♥❞♦ ✈✐s✉❛❧✐③❛❞❛s ❡♠ ❞✐❢❡r❡♥t❡s ❞✐s♣♦s✐t✐✈♦s ❬P❡tr♦✈✱ ✷✵✶✵❪✳ ❊st❛ ❞✐❢❡r❡♥ç❛ ♣♦❞❡ s❡r ❛♠❡♥✐③❛❞❛ ♣❡❧❛ ✉t✐❧✐③❛çã♦ ❞♦ ♠♦❞❡❧♦ ❈■❊✲▲✯❛❜✳
❖ ❤✐st♦❣r❛♠❛ ❞❡ ✉♠❛ ✐♠❛❣❡♠ é ❛ ❞✐str✐❜✉✐çã♦ ❞❡ s✉❛s ✐♥t❡♥s✐❞❛❞❡s✱ ♦♥❞❡ ♦ ❡✐①♦ x
sã♦ ❛s ❝♦r❡s ❡ ♦ ❡✐①♦ f(x) s✉❛s ♦❝♦rrê♥❝✐❛s ✭❋✐❣✉r❛ ✷✳✻✮✳ ❊st❡ ♠✉❞❛rá ❞❡ ❛❝♦r❞♦ ❝♦♠ ♦ ♠♦❞❡❧♦ ❞❡ ❝♦r❡s ✉t✐❧✐③❛❞♦✳ ❖ t❛♠❛♥❤♦ ❞❡ ✉♠ ❤✐st♦❣r❛♠❛ ♥♦ ♠♦❞❡❧♦ ❘●❇✱ q✉❡ ✉s❛ ✶ ❇②t❡ ♣♦r ❝❛♥❛❧✱ é ❞❡ ✶✻✳✼✼✼✳✷✶✻ ♣♦s✐çõ❡s ❡♠ x✱ s❡♥❞♦ ❡①tr❡♠❛♠❡♥t❡ ❝♦♠✉♠ ❛ ♠❛✐♦r✐❛ ❞❡ss❛s
♣♦s✐çõ❡s ❝♦♠ ❛ ♦❝♦rrê♥❝✐❛ ③❡r♦✳ ❯♠❛ ❢♦r♠❛ ❝♦♠✉♠ ❞❡ ✈✐s✉❛❧✐③❛çã♦ ❞♦ ❤✐st♦❣r❛♠❛ ❞❡ ✉♠❛ ✐♠❛❣❡♠ ❝♦❧♦r✐❞❛ é ❛ s✉❛ ❞✐✈✐sã♦ ♣♦r ❝❛♥❛❧ ❞❡ ❝♦r✱ ♦✉ s❡❥❛✱ ♥♦ ♠♦❞❡❧♦ ❘●❇ t❡rí❛♠♦s ✸ ❤✐st♦❣r❛♠❛s ✭✈❡r♠❡❧❤♦✱ ✈❡r❞❡ ❡ ❛③✉❧✮ r❡♣r❡s❡♥t❛♥❞♦ ♦ ❤✐st♦❣r❛♠❛ ❣❡r❛❧ ❞❛ ✐♠❛❣❡♠✳
✷✶
❋✐❣✉r❛ ✷✳✺✿ ❆ ❛♣❛rê♥❝✐❛ ❞❡ ✉♠❛ ❝♦r ❝♦♠ ♦s ♠❡s♠♦s ✈❛❧♦r❡s ❞❡ ❝♦r❡s ♣♦❞❡ ✈❛r✐❛r ❡♠ ❞✐❢❡r❡♥t❡s ❞✐s♣♦s✐t✐✈♦s ✭❞✐❢❡r❡♥ç❛s ♠❛✐s ❛♣❛r❡♥t❡s ♥❛ ✈❡rsã♦ ❞✐❣✐t❛❧✮ ❬P❡tr♦✈✱ ✷✵✶✵❪✳
❋✐❣✉r❛ ✷✳✻✿ ❯♠❛ ✐♠❛❣❡♠ ❡ s❡✉ ❤✐st♦❣r❛♠❛ ❝♦❧♦r✐❞♦ ♦r❞❡♥❛❞♦ ♣❡❧♦ ♥ú♠❡r♦ ❞❡ ♦❝♦rrê♥❝✐❛ ❞❛s ❝♦r❡s ❬❈❤❡♥❣ ❡t ❛❧✳✱ ✷✵✶✶❪✳
❞❡ ❡❧❡♠❡♥t♦s r❡❧❛t✐✈❛♠❡♥t❡ ♦r❞❡♥❛❞♦s ♦✉ ♣❛❞rõ❡s✱ q✉❡ ✐♥❞✐✈✐❞✉❛❧♠❡♥t❡ ♥ã♦ r❡♣r❡s❡♥t❛♠ ♠✉✐t♦✱ ♠❛s✱ s❡ ♦❜s❡r✈❛❞♦s ❣❧♦❜❛❧♠❡♥t❡✱ t❛✐s ❡❧❡♠❡♥t♦s ♣♦❞❡♠ s❡r ✉s❛❞♦s ♣❛r❛ ✐❞❡♥t✐✜❝❛r ✉♠❛ ❞❡t❡r♠✐♥❛❞❛ ár❡❛ ♥❛ ✐♠❛❣❡♠ ❬●♦♦❧ ❡t ❛❧✳✱ ✶✾✽✺❪✳ ❆ ❋✐❣✉r❛ ✷✳✼ ❛♣r❡s❡♥t❛ q✉❛tr♦ t❡①t✉r❛s ❝♦❧♦r✐❞❛s ❝♦♠♣❧❡①❛s✱ ❡①tr❛í❞❛s ❞❡ ❢♦t♦s r❡❛✐s ❞❡ ❞✐❢❡r❡♥t❡s ♣❛✐s❛❣❡♥s ♥❛t✉r❛✐s✳
✷✳✷ ❙❡❣♠❡♥t❛çã♦ ❞❡ ■♠❛❣❡♥s ❉✐❣✐t❛✐s
✷✷
❋✐❣✉r❛ ✷✳✼✿ ❆♠♦str❛ ❞❡ t❡①t✉r❛s ❝♦♠♣❧❡①❛s✳
❆ s❡❣♠❡♥t❛çã♦ ❞❡ ✐♠❛❣❡♥s ♣♦❞❡ s❡r ❞✐✈✐❞✐❞❛ ❡♠ s✉♣❡r✈✐s✐♦♥❛❞❛ ♦✉ ♥ã♦✲s✉♣❡r✈✐s✐♦♥❛❞❛✳ ◆♦ ♣r✐♠❡✐r♦ ❝❛s♦✱ ❝❧❛ss❡s sã♦ ♣ré✲❞❡✜♥✐❞❛s r❡s✉❧t❛♥❞♦ ❡♠ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ✐♠❛❣❡♥s ♠❛r❝❛✲ ❞❛s✱ ❝♦♠ ❜❛s❡ ♥❡ss❡ ❝♦♥❥✉♥t♦ ✉♠ ❝❧❛ss✐✜❝❛❞♦r é tr❡✐♥❛❞♦ ♣❛r❛ ❝❛♣t✉r❛r ❛s ❝❛r❛❝t❡ríst✐❝❛s ❞♦s ♣✐①❡❧s ❡♠ ❝❛❞❛ ❝❧❛ss❡✳ ❖ ❝❧❛ss✐✜❝❛❞♦r é ❡♥tã♦ ❛♣❧✐❝❛❞♦ ❛ ♥♦✈❛s ✐♠❛❣❡♥s ❞❡ t❡st❡ s❡♥❞♦ ❛tr✐❜✉í❞♦ ✉♠ ♥í✈❡❧ ❞❡ ❝❧❛ss❡ ♣❛r❛ ❝❛❞❛ ♣✐①❡❧✳ ◆❛ s❡❣♠❡♥t❛çã♦ ♥ã♦✲s✉♣❡r✈✐s✐♦♥❛❞❛ ♥ã♦ ♦❝♦rr❡ ❛tr✐❜✉✐çã♦ ❞❡ ❝❧❛ss❡s✱ q✉❡ sã♦ ❡①tr❛í❞❛s ❞✐r❡t❛♠❡♥t❡ ❞♦s ♣❛❞rõ❡s ❬▲✐ ❡t ❛❧✳✱ ✷✵✶✷❜❪✳
✷✸ ✉s❛❞♦ ♥❡st❡ tr❛❜❛❧❤♦ ♣❡rt❡♥❝❡ ❛♦ ú❧t✐♠♦ t✐♣♦✳
✷✳✷✳✶ ❙❡❣♠❡♥t❛çã♦ ♣♦r ▲✐♠✐❛r✐③❛çã♦ ✭❚❤r❡s❤♦❧❞✐♥❣✮
❆ ❧✐♠✐❛r✐③❛çã♦ é ✉♠ ♠ét♦❞♦ ❞❡ s❡❣♠❡♥t❛çã♦ ❞❡ ✐♠❛❣❡♥s ❝♦♥❤❡❝✐❞♦ ♣♦r ❝♦♥✈❡rt❡r ✉♠❛ ✐♠❛❣❡♠ ❡♠ ♥í✈❡❧ ❞❡ ❝✐♥③❛ ❡♠ ✉♠❛ ✐♠❛❣❡♠ ❜✐♥ár✐❛✳ ❊ss❡ ♣r♦❝❡ss♦ é r❡❛❧✐③❛❞♦ ♣♦r ♠❡✐♦ ❞❛ ❞❡✜♥✐çã♦ ❞❡ ✉♠ ❧✐♠✐t❡ ❞❡♥tr♦ ❞♦ ❡s♣❛ç♦ ❞❡ t♦♥s ❞❡ ❝✐♥③❛ ♥❛ ✐♠❛❣❡♠ ♦r✐❣✐♥❛❧✱ ❡♠ s❡❣✉✐❞❛ ♦s ♣✐①❡❧s ❛❜❛✐①♦ ❞♦ ❧✐♠✐t❡ sã♦ s❡❧❡❝✐♦♥❛❞♦s ❝♦♠♦ ♣❡rt❡♥❝❡♥t❡s ❛♦ ♣r✐♠❡✐r♦ ❣r✉♣♦ ❡ ♦s ❞❡♠❛✐s ♣✐①❡❧s sã♦ s❡❧❡❝✐♦♥❛❞♦s ♣❛r❛ ♦ s❡❣✉♥❞♦ ❣r✉♣♦✳ ❊st❛ ✐♠❛❣❡♠ é ❝♦♠✉♠❡♥t❡ ❛♣r❡s❡♥t❛❞❛ ❝♦♠♦ ❜✐♥ár✐❛ ♦✉ ❞❡ ❞♦✐s ♥í✈❡✐s ❬❑✉❧❦❛r♥✐✱ ✷✵✶✷❪✳ ❊ss❡ ♣r♦❝❡ss♦ ❡stá r❡♣r❡s❡♥t❛❞♦ ❛❜❛✐①♦ ♣❛r❛ ❧✐♠✐❛r✐③❛çã♦ ❡♠ ❡s❝❛❧❛ ❞❡ ❝✐♥③❛✿
g(x, y) =
(
0, f(x, y)< T,
1, f(x, y)≥T, ✭✷✳✶✮
♦♥❞❡T é ♦ ✈❛❧♦r ❞♦ ❧✐♠✐❛r q✉❡ s❡♣❛r❛ ♦s ♣✐①❡❧s ❡♠ ❞✉❛s ❝❧❛ss❡s❀ f(x, y) é ♦ ✈❛❧♦r ♦r✐❣✐♥❛❧ ❞❛ ✐♥t❡♥s✐❞❛❞❡ ❞♦ ♣✐①❡❧ ❡g(x, y)é ♦ ✈❛❧♦r r❡s✉❧t❛♥t❡ ❞♦ ♣✐①❡❧ ❛♣ós ❛ ❧✐♠✐❛r✐③❛çã♦ t❡r s✐❞♦ r❡❛❧✐③❛❞❛✱ ♣r♦❞✉③✐♥❞♦ ❛ss✐♠✱ ✉♠❛ ✐♠❛❣❡♠ ❜✐♥ár✐❛✳ P❛r❛ ✐♠❛❣❡♥s ❝♦❧♦r✐❞❛s✱ ♣♦r ❡①❡♠♣❧♦✱ ✐♠❛❣❡♥s ❝♦♠ r❡♣r❡s❡♥t❛çã♦ ❘●❇✱ ❛ ❝♦r ❞❡ ✉♠ ♣✐①❡❧ é ✉♠❛ ♠✐st✉r❛ ❞❡ três ❝♦r❡s ♣r✐♠✐t✐✈❛s✿ ✈❡r♠❡❧❤♦✱ ✈❡r❞❡ ❡ ❛③✉❧✳ ❈❛❞❛ ♣✐①❡❧ ❞❛ ✐♠❛❣❡♠ ♣♦❞❡ s❡r ✈✐st♦ ❝♦♠♦ ✉♠ ✈❡t♦r ❝♦♥t❡♥❞♦ três ❝♦♠♣♦♥❡♥t❡s q✉❡ r❡♣r❡s❡♥t❛♠ ❛s q✉❛♥t✐❞❛❞❡s ❞❛s três ❝♦r❡s ♣r✐♠✐t✐✈❛s ❡♠ ✉♠ ♣✐①❡❧✳ ❆ ❧✐♠✐❛r✐③❛çã♦ ❞❡ ❤✐st♦❣r❛♠❛s é ✉♠❛ té❝♥✐❝❛ ❞❡ s❡❣♠❡♥t❛çã♦ ❜❛st❛♥t❡ ♣♦♣✉❧❛r q✉❡ ♣r♦❝✉r❛ ♣♦r ♣✐❝♦s ❡ ✈❛❧❡s ♥♦ ❤✐st♦❣r❛♠❛✱ ♠❛s só ♦❜té♠ ❜♦♥s r❡s✉❧t❛❞♦s s❡ ♦s ♣✐❝♦s ❞♦♠✐♥❛♥t❡s ♥♦ ❤✐st♦❣r❛♠❛ ♣✉❞❡r❡♠ s❡r ❝♦rr❡t❛♠❡♥t❡ r❡❝♦♥❤❡❝✐❞♦s✱ ♦✉ s❡❥❛✱ ♥❛ ❛✉sê♥❝✐❛ ❞❡ r✉í❞♦s ♦✉ ✈❛r✐❛çã♦ ❜r✉s❝❛ ❬❙❛❤♦♦ ❡t ❛❧✳✱ ✶✾✽✽❪✱ ❬❙✐❛♥❣ ❚❛♥ ❛♥❞ ▼❛t ■s❛✱ ✷✵✶✶❪✳
✷✳✷✳✷ ❙❡❣♠❡♥t❛çã♦ ♣♦r ❈r❡s❝✐♠❡♥t♦ ❞❡ ❘❡❣✐õ❡s ✭❘❡❣✐♦♥ ●r♦✇✐♥❣✮
❖ ♣r♦❝❡❞✐♠❡♥t♦ ❞❡ ❝r❡s❝✐♠❡♥t♦ ❞❡ r❡❣✐õ❡s ❝♦♥s✐st❡ ❜❛s✐❝❛♠❡♥t❡ ❡♠ ✉♥✐r ♣✐①❡❧s ❛❞❥❛✲ ❝❡♥t❡s ♣❛r❛ ❢♦r♠❛r r❡❣✐õ❡s✳ ❆ ❛ss♦❝✐❛çã♦ ❡♥tr❡ ♦s ♣✐①❡❧s ✈✐③✐♥❤♦s ♦✉ r❡❣✐õ❡s ♥♦ ♣r♦❝❡ss♦ ❞❡ ❝r❡s❝✐♠❡♥t♦ é ❞❡t❡r♠✐♥❛❞❛ ♣♦r ✉♠ ❝r✐tér✐♦ ❞❡ ❤♦♠♦❣❡♥❡✐❞❛❞❡ q✉❡ ❞❡✈❡ s❡r s❛t✐s❢❡✐t♦ ♣❛r❛ q✉❡ ❤❛❥❛ ❝♦♠❜✐♥❛çã♦ ❡♥tr❡ ♦s ♣✐①❡❧s ❡ r❡❣✐õ❡s ❬❑❛♠❞✐ ❛♥❞ ❑r✐s❤♥❛✱ ✷✵✶✷❪✳
❈❤❡♥✱ ▲✐♥ ❡ ❈❤❡♥ ❬❈❤❡♥ ❡t ❛❧✳✱ ✶✾✾✶❪ ❞❡s❝r❡✈❡♠ ♦ ♣r♦❝❡ss♦ ❞❡ ❞❡✜♥✐çã♦ ❞❛s ♠❡❞✐❞❛s ❞❡ ❤♦♠♦❣❡♥❡✐❞❛❞❡ ♣❛r❛ ❛ s❡❣♠❡♥t❛çã♦ ❜❛s❡❛❞❛ ♥❛ r❡❣✐ã♦ t♦♠❛♥❞♦(x, y)∈N✱ ❝♦♠♦ s❡♥❞♦ ❛s
✷✹ ♦ ❞♦♠í♥✐♦ ❞❡ ✉♠❛ ✐♠❛❣❡♠ ❝♦♠m ❧✐♥❤❛s ❡n ❝♦❧✉♥❛s ❞❡♥♦t❛❞♦ ♣♦rI✱ ♦✉ s❡❥❛✱I =m×n✳
❆ss✐♠✱ ✉♠❛ ❢✉♥çã♦ ❞❛ ✐♠❛❣❡♠ ♣♦❞❡ s❡r ❞❡✜♥✐❞❛ ❝♦♠♦ ♦ ♠❛♣❡❛♠❡♥t♦ f : m×n → G✳
❯♠❛ r❡❣✐ã♦ R ❞❡ ✉♠❛ ✐♠❛❣❡♠ é ❞❡✜♥✐❞❛ ❝♦♠♦ ✉♠ s✉❜❝♦♥❥✉♥t♦ ❤♦♠♦❣ê♥❡♦ ❝♦♥❡❝t❛❞♦
❞❡I ❝♦♠ r❡❧❛çã♦ ❛ ❛❧❣✉♥s ❝r✐tér✐♦s ❝♦♠♦ t♦♥❛❧✐❞❛❞❡ ♦✉ t❡①t✉r❛✳P ❞❡♥♦t❛ ✉♠ ♣r❡❞✐❝❛❞♦
❧ó❣✐❝♦ ♣❛r❛ ❛ ♠❡❞✐❞❛ ❞❡ ❤♦♠♦❣❡♥❡✐❞❛❞❡ ❞❡✜♥✐❞❛ s♦❜r❡R t❛❧ q✉❡✿
P(R) =
(
❱❡r❞❛❞❡✐r♦, H(R)∈D∗,
❋❛❧s♦, H(R)∈/D∗, ✭✷✳✷✮
♦♥❞❡ H : R → D é ✉♠❛ ❢✉♥çã♦ ♣❛r❛ ❛✈❛❧✐❛r ❛ ❤♦♠♦❣❡♥❡✐❞❛❞❡ ❞❡ ✉♠❛ r❡❣✐ã♦ R ❡ D∗ é
✉♠ s✉❜❝♦♥❥✉♥t♦ ♣r❡❞❡✜♥✐❞♦ ❞❡ ❛❧❝❛♥❝❡ D✳ ❉❡ss❡ ♠♦❞♦ ❛ s❡❣♠❡♥t❛çã♦ ❞❡ ✉♠❛ ✐♠❛❣❡♠ é
✉♠❛ ♣❛rt✐çã♦ ❞❡ I ❡♠ ✈ár✐❛s r❡❣✐õ❡s ❤♦♠♦❣ê♥❡❛s ❡ ❝♦♥❡①❛s Ri, i = 1, ..., m✳ ❆s r❡❧❛çõ❡s ❡♥tr❡ ❛s r❡❣✐õ❡s sã♦ ❞❡✜♥✐❞❛s ❝♦♠♦ s❡❣✉❡ ❛❜❛✐①♦✿
✶✳ I =Um i=1Ri;
✷✳ Ri∩Rj =∅✱ ♣❛r❛ t♦❞♦ 1≤i, j ≤m, i6=j; ✸✳ P(Ri) = ✈❡r❞❛❞❡✐r♦✱ ♣❛r❛ t♦❞♦ i
✹✳ P(Ri∩Rj) = ❢❛❧s♦✱ ♣❛r❛ t♦❞♦ 1≤i, j ≤m, i 6=j;
✷✳✷✳✸ ❙❡❣♠❡♥t❛çã♦ ♣♦r ❉✐✈✐sã♦ ❡ ❋✉sã♦ ✭❙♣❧✐tt✐♥❣ ❛♥❞ ▼❡r❣✐♥❣✮
❆ ❛❜♦r❞❛❣❡♠ ♣r♦♣♦st❛ ♣♦r ❬❍♦r♦✇✐t③ ❛♥❞ P❛✈❧✐❞✐s✱ ✶✾✼✹❪ é ✉♠❛ té❝♥✐❝❛ ❞❡ s❡❣♠❡♥t❛✲ çã♦ ❜❛s❡❛❞❛ ❡♠ r❡❣✐õ❡s q✉❡ ❞✐✈✐❞❡ ♦ ♣r♦❜❧❡♠❛ ❞❡ ❝r❡s❝✐♠❡♥t♦ ❞❡ r❡❣✐õ❡s ❡♠ ❞✉❛s ❡t❛♣❛s✿ ❛ ❞✐✈✐sã♦ ✭s♣❧✐t✮ ❡ ❛ ❢✉sã♦ ✭♠❡r❣❡✮✳ ❆ ❞✐✈✐sã♦ é ✉♠❛ ❢❛s❡ ❞❡ ♣ré✲♣r♦❝❡ss❛♠❡♥t♦ q✉❡ ✈✐s❛ r❡❞✉③✐r ♦ ♥ú♠❡r♦ ❞❡ ❢✉sõ❡s q✉❡ s❡rã♦ ♥❡❝❡ssár✐♦s ♣❛r❛ r❡s♦❧✈❡r ♦ ♣r♦❜❧❡♠❛✳ ◆❛ ❡t❛♣❛ ❞❡ ❞✐✈✐sã♦ ✉♠❛ ✐♠❛❣❡♠ é ♣❛rt✐❝✐♦♥❛❞❛ ❡♠ r❡❣✐õ❡s q✉❛❞r❛❞❛s ♦❜❡❞❡❝❡♥❞♦ ❛ ✉♠ ♣r✐♠❡✐r♦ ❝r✐✲ tér✐♦ ❞❡ ❤♦♠♦❣❡♥❡✐❞❛❞❡✱ ❡♠ s❡❣✉✐❞❛✱ ✉♠❛ té❝♥✐❝❛ ❞❡ ❝r❡s❝✐♠❡♥t♦ ❞❡ r❡❣✐õ❡s é ❡s❝♦❧❤✐❞❛ ♣❛r❛ ❢✉♥❞✐r ❡ss❛s r❡❣✐õ❡s q✉❛❞r❛❞❛s ❡♠ r❡❣✐õ❡s ♠❛✐♦r❡s✱ q✉❡ ❡st❡❥❛♠ ❡♠ ❝♦♥❢♦r♠✐❞❛❞❡ ❝♦♠ ✉♠ s❡❣✉♥❞♦ ❝r✐tér✐♦ ❞❡ ❤♦♠♦❣❡♥❡✐❞❛❞❡✳
✷✳✷✳✹ ❙❡❣♠❡♥t❛çã♦ ♣♦r ❆❣r✉♣❛♠❡♥t♦ ✭❈❧✉st❡r✐♥❣✮
✷✺ ♦♥❞❡ ✉♠ ❣r❛♥❞❡ ♥ú♠❡r♦ ❞❡ ❛♠♦str❛s ✭♣✐①❡❧s ❝♦♠ ❞✐❢❡r❡♥t❡s ✐♥t❡♥s✐❞❛❞❡s✮ é ❝♦♥✈❡rt✐❞♦ ❡♠ ✉♠ ♣❡q✉❡♥♦ ♥ú♠❡r♦ ❞❡ ♣r♦tót✐♣♦s r❡♣r❡s❡♥t❛t✐✈♦s ♦✉ ❝❧✉st❡rs✳ ❉✐✈❡rs❛s ♠❡❞✐❞❛s ❞❡ s✐♠✐❧❛r✐❞❛❞❡ ♣♦❞❡♠ s❡r ❡s❝♦❧❤✐❞❛s ♣❛r❛ ✐❞❡♥t✐✜❝❛r ❝❧❛s❡s✱ t❛✐s ❝♦♠♦✿ ❛ ❞✐stâ♥❝✐❛✱ ❝♦♥❡❝✲ t✐✈✐❞❛❞❡✱ ✐♥t❡♥s✐❞❛❞❡✱ ❡♥tr❡ ♦✉tr❛s ❬❙♦✇♠②❛ ❛♥❞ ❙❤❡❡❧❛ ❘❛♥✐✱ ✷✵✶✶❪✳ ❆ s❡❣♠❡♥t❛çã♦ ♣♦r ❛❣r✉♣❛♠❡♥t♦ é ✉♠ ❝❛♠♣♦ ❛♠♣❧♦ ❡ ❝♦♠ ❞✐✈❡rs❛s s♦❧✉çõ❡s ♣r♦♣♦st❛s✳ ❊♥tr❡ s✉❛s ♣r✐♥❝✐♣❛✐s s♦❧✉çõ❡s s❡ ❡♥❝♦♥tr❛♠ ♦s q✉❛tr♦ ❛❧❣♦r✐t♠♦s ❡♥✉♠❡r❛❞♦s ❛❜❛✐①♦✳
✶✳ ❑✲♠❡❛♥s
✷✳ ❋✉③③② ❈✲♠❡❛♥s
✸✳ ❍✐❡r❛r❝❤✐❝❛❧ ❈❧✉st❡r✐♥❣
✹✳ ▼✐①t✉r❡ ♦❢ ●❛✉ss✐❛♥s
❆❧❣♦r✐t♠♦s ❞❡ ❛❣r✉♣❛♠❡♥t♦ ❢✉③③② ✐♥tr♦❞✉③❡♠ ❛ ✐♥❝❡rt❡③❛ ♣❛r❛ ❛ ♣❡rt✐♥ê♥❝✐❛ ❞❡ ❝❛❞❛ ♣✐①❡❧ ❞❛ ✐♠❛❣❡♠ ❡ tê♠ s✐❞♦ ❛♣❧✐❝❛❞♦s ❝♦♠ s✉❝❡ss♦ ❛♦ ♣r♦❝❡ss♦ ❞❡ s❡❣♠❡♥t❛çã♦ ❞❡ ✐♠❛❣❡♥s✳ ❖ ❝♦♥❝❡✐t♦ ❞❡ ❝♦♥❥✉♥t♦s ❢✉③③② t❡♠ ❛ ✜♥❛❧✐❞❛❞❡ ❞❡ ❞❛r ✉♠ tr❛t❛♠❡♥t♦ ♠❛t❡♠át✐❝♦ ❛ t❡r♠♦s ❧✐♥❣✉íst✐❝♦s s✉❜❥❡t✐✈♦s✱ t❛✐s ❝♦♠♦✿ ❛♣r♦①✐♠❛❞❛♠❡♥t❡✱ ❡♠ t♦r♥♦ ❞❡✱ ❡ ❛❜❛✐①♦ ❞❡✳ P♦r ♠❡✐♦ ❞❡ss❛ té❝♥✐❝❛ ♦ ❝♦♥❤❡❝✐♠❡♥t♦ ✐♠♣r❡❝✐s♦ ♣♦❞❡ s❡r ✉t✐❧✐③❛❞♦ ♣❛r❛ ❞❡✜♥✐r ✉♠ ❡✈❡♥t♦ ❬❩❛❞❡❤ ❡t ❛❧✳✱ ✶✾✼✺❪✳ ❯♠ ❝♦♥❥✉♥t♦ ❢✉③③② A é r❡♣r❡s❡♥t❛❞♦ ❝♦♠♦✿
A={µA(xi)xi, i={1,2, ..., n}, ✭✷✳✸✮
♦♥❞❡✱µA(xi)r❡♣r❡s❡♥t❛ ♦ ♥í✈❡❧ ❞❡ ♣❡rt✐♥ê♥❝✐❛ ❞♦ ❡❧❡♠❡♥t♦xi ❛♦ ❝♦♥❥✉♥t♦ ❆✳ ❖s ❝♦♥❥✉♥t♦s ❢✉③③② sã♦ ❞❡s❝r✐t♦s ❝♦♠♦ ✉♠❛ ❝♦❧❡çã♦ ❞❡ ♦❜❥❡t♦s ❝✉❥♦s ✈❛❧♦r❡s ❞❡ ♣❡rt✐♥ê♥❝✐❛ ❡stã♦ ♥♦ ✐♥t❡r✈❛❧♦ [0,1]✳ ❖s ✈❛❧♦r❡s ❞❡ ♣❡rt✐♥ê♥❝✐❛ ✐♥❞✐❝❛♠ q✉❛❧ ♦ ♥í✈❡❧ ❞❡ ❝♦♠♣❛t✐❜✐❧✐❞❛❞❡ q✉❡ ♦
❡❧❡♠❡♥t♦ t❡♠ ❝♦♠ ❛s ♣r♦♣r✐❡❞❛❞❡s ♦✉ ❝❛r❛❝t❡ríst✐❝❛s ❞♦ ❝♦♥❥✉♥t♦ ❬P❡❞r②❝③ ❛♥❞ ●♦♠✐❞❡✱ ✶✾✾✽❪✳
✷✳✸ ❚r❛❜❛❧❤♦s ❘❡❧❛❝✐♦♥❛❞♦s
✷✻ ❖ ❝❛♠♣♦ ❞❡ ❛♣❧✐❝❛çã♦ ❞❛ s❡❣♠❡♥t❛çã♦ ❞❡ ✐♠❛❣❡♥s t❡♠ ❡✈♦❧✉í❞♦ ❜❛st❛♥t❡ ❛♦ ❧♦♥❣♦ ❞♦ t❡♠♣♦✱ ❞❡s❡♠♣❡♥❤❛♥❞♦ ✉♠ ♣❛♣❡❧ ✐♠♣♦rt❛♥t❡ ❡♠ ❞✐✈❡rs❛s ár❡❛s✱ t❛✐s ❝♦♠♦✿ ❞✐❛❣♥óst✐❝♦ ❞❡ ❞♦❡♥ç❛s ❬❑r✉❣❡r ❡t ❛❧✳✱ ✶✾✼✹❪❀ ❬❈❤✐♥✲❍s✐♥❣ ❡t ❛❧✳✱ ✶✾✾✽❪❀ ❬❱❛❞❛♣❛rt❤✐ ❛♥❞ ❱❛r♠❛✱ ✷✵✶✷❪❀ ❧♦❝❛❧✐③❛çã♦ ❞❡ ♦❜❥❡t♦s ❡♠ ✐♠❛❣❡♥s ❞❡ s❛té❧✐t❡ ❬▼❛r❝❛❧ ❡t ❛❧✳✱ ✷✵✶✵❪❀ ❬▲✉❝✐❡❡r ❛♥❞ ❙t❡✐♥✱ ✷✵✵✷❪❀ ❬❖s♠❛♥ ❡t ❛❧✳✱ ✷✵✵✾❪❀ s✐st❡♠❛s ❞❡ r❡❝♦♥❤❡❝✐♠❡♥t♦ ❢❛❝✐❛❧ ❬❆❦❜❛r✐ ❛♥❞ ▼♦③❛✛❛r✐✱ ✷✵✶✵❪❀ ❬❨❛♥ ❡t ❛❧✳✱ ✷✵✵✽❪❀ ❬▲✐②✐♥❣ ❛♥❞ ❨✉❡✱ ✷✵✵✽❪❀ s✐st❡♠❛s ❞❡ ❝♦♥tr♦❧❡ ❛✉t♦♠át✐❝♦ ❞❡ trá❢❡❣♦ ❬P❤❛❧❣✉♥✐ ❡t ❛❧✳✱ ✷✵✶✸❪❀ ❬❈✉❝❝❤✐❛r❛ ❡t ❛❧✳✱ ✷✵✵✵❪ ❡ ❣❡♦❝✐ê♥❝✐❛s ❬▲❡✲▼♦✐❣♥❡ ❛♥❞ ❚✐❧t♦♥✱ ✶✾✾✺❪❀ ❬▲♦t❢② ❡t ❛❧✳✱ ✷✵✵✹❪❀ ❬❩❤♦✉ ❛♥❞ ❘❡♥✱ ✷✵✶✷❪✳
❆ ❞✐✈❡rs✐❞❛❞❡ ❞❡ ✉s♦s ❡ s❡✉s ❞✐❢❡r❡♥t❡s t✐♣♦s ❞❡ ❞❛❞♦s ❢❛③❡♠ ❝♦♠ q✉❡ ♥ã♦ ❡①✐st❛ ✉♠❛ s♦❧✉çã♦ ú♥✐❝❛ ♣❛r❛ t♦❞❛s ❛s ❛♣❧✐❝❛çõ❡s ❞❛ s❡❣♠❡♥t❛çã♦ ❞❡ ✐♠❛❣❡♥s✳ ❉❡ss❡ ♠♦❞♦✱ ❞✐❢❡r❡♥t❡s ♠❡t♦❞♦❧♦❣✐❛s tê♠ s✐❞♦ ♣r♦♣♦st❛s ♥❛ t❡♥t❛t✐✈❛ ❞❡ ❢♦r♥❡❝❡r ✉♠❛ s❡❣♠❡♥t❛çã♦ ♠❛✐s ♣r❡❝✐s❛ ❡ r❡❞✉③✐❞♦ ❡s❢♦rç♦ ❝♦♠♣✉t❛❝✐♦♥❛❧✳ ❉✐❢❡r❡♥t❡s t✐♣♦s ❞❡ ❛❧❣♦r✐t♠♦s ❞❡ s❡❣♠❡♥t❛çã♦ ♣♦r ❛❣r✉✲ ♣❛♠❡♥t♦ tê♠ s✐❞♦ ❞❡s❡♥✈♦❧✈✐❞♦s ❞❡s❞❡ ❡♥tã♦✱ ✐♥❝❧✉✐♥❞♦ ♠ét♦❞♦s ❜❛s❡❛❞♦s ❡♠ ár✈♦r❡ ❬❨❛♥❣ ❡t ❛❧✳✱ ✷✵✵✽❪✱ ♠✉t✉❛❧✐❞❛❞❡ ❡♥tr❡ ♦ ✈✐③✐♥❤♦ ♠❛✐s ♣ró①✐♠♦ ✭♠✉t✉❛❧ ♥❡❛r❡st ♥❡✐❣❤❜♦r✮ ❬❍✉ ❛♥❞ ❇❤❛t♥❛❣❛r✱ ✷✵✶✷❪✱ ❛❣r✉♣❛♠❡♥t♦ ❤✐❡rárq✉✐❝♦ ❬❈❛r❡❧ ❡t ❛❧✳✱ ✷✵✶✸❪ ❡ ❛❣r✉♣❛♠❡♥t♦ ❝♦♠ ❜❛s❡ ❡♠ ♠í♥✐♠♦s q✉❛❞r❛❞♦s ❬❯❝❤✐②❛♠❛ ❛♥❞ ❆r❜✐❜✱ ✶✾✾✹❪✳ ❆ ❧ó❣✐❝❛ ❢✉③③② t❛♠❜é♠ é ✉♠❛ té❝✲ ♥✐❝❛ ❜❛st❛♥t❡ ❡♠♣r❡❣❛❞❛ q✉❛♥❞♦ s❡ tr❛t❛ ❞❡ ♣r♦❝❡ss❛♠❡♥t♦ ❡ r❡❝♦♥❤❡❝✐♠❡♥t♦ ❞❡ ✐♠❛❣❡♥s ❡ t❡♠ s✐❞♦ ❝♦♥st❛♥t❡♠❡♥t❡ ❡♠♣r❡❣❛❞❛ ♥♦s ♠ét♦❞♦s ❞❡ ❛❣r✉♣❛♠❡♥t♦✱ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ❡♠ ❝♦♥❥✉♥t♦ ❝♦♠ ♦✉tr❛s té❝♥✐❝❛s✳ ❊①❡♠♣❧♦s ❞❡ss❛ ❛♣❧✐❝❛çã♦ ♣♦❞❡♠ s❡r ✈✐st♦s ♥♦s tr❛❜❛❧❤♦s ❞❡ ❬▲✐ ❡t ❛❧✳✱ ✷✵✶✷❛❪❀ ❬❇❡❡✈✐ ❡t ❛❧✳✱ ✷✵✶✵❪❀ ❬❨✉❣❛♥❞❡r ❡t ❛❧✳✱ ✷✵✶✷❪✳
❆❧é♠ ❞❡st❛s✱ ✈ár✐❛s ♦✉tr❛s ❛♣❧✐❝❛çõ❡s ✉t✐❧✐③❛♠ ❛ ❛❜♦r❞❛❣❡♠ ❞❡ ❛❣r✉♣❛♠❡♥t♦✳ ❯♠ ❞♦s ♠♦❞❡❧♦s ❞❡ ❛❣r✉♣❛♠❡♥t♦ ♠❛✐s ✉s❛❞♦s ♣❛r❛ s❡❣♠❡♥t❛çã♦ ❞❡ ✐♠❛❣❡♥s é ♦ ✜♥✐t❡ ♠✐①t✉r❡ ♠♦❞❡❧ ✭❋▼▼✮ ❬❈❤❛t③✐s ❛♥❞ ❱❛r✈❛r✐❣♦✉✱ ✷✵✵✾❪✳ ❉❡♥tr❡ ♦s ✈ár✐♦s ♠ét♦❞♦s ❞❡ ❋▼▼✱ ♦ ●❛✉s✲ s✐❛♥ ♠✐①t✉r❡ ♠♦❞❡❧ ✭●▼▼✮ é ♦ ♠❛✐s ❝♦♠✉♠❡♥t❡ ❡s❝♦❧❤✐❞♦✱ ♣♦r s❡r ❞❡ ❢á❝✐❧ ✐♠♣❧❡♠❡♥t❛çã♦✱ ❛ss✉♠✐♥❞♦ ❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❝♦♥❞✐❝✐♦♥❛❧ ❝♦♠♦ ✉♠❛ ❞✐str✐❜✉✐çã♦ ❣❛✉ss✐❛♥❛✳
❱❛❞❛♣❛rt❤✐ ❡t ❛❧✳ ❬❱❛❞❛♣❛rt❤✐ ❛♥❞ ▼✉rt❤②✱ ✷✵✶✶❪ ✉t✐❧✐③❛r❛♠ ♦ ●▼▼ ❡ ♦ ❛❧❣♦r✐t♠♦ ❞❡ ❡①♣❡❝t❛t✐♦♥ ♠❛①✐♠✐③❛t✐♦♥ ✭❊▼✮ ♣❛r❛ s❡❣♠❡♥t❛r ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ✐♠❛❣❡♥s ♠é❞✐❝❛s✳ ❖s ❛✉✲ t♦r❡s ❝♦♥st❛t❛♠ q✉❡ ♦ ♠♦❞❡❧♦ ❣❛✉ss✐❛♥♦ ❛❞❛♣t❛✲s❡ ❜❡♠ q✉❛♥❞♦ ❛s ✐♠❛❣❡♥s sã♦ s✐♠étr✐❝❛s✱ ❝❛r❛❝t❡ríst✐❝❛ ♥ã♦ ❡♥❝♦♥tr❛❞❛ ♥❛s ✐♠❛❣❡♥s ♠é❞✐❝❛s✱ ♣♦r ✐ss♦ ✉t✐❧✐③❛r❛♠ t❛♠❜é♠ ♦ ♠♦❞❡❧♦ ❞❡ s❦❡✇ s②♠♠❡tr✐❝ ♠✐①t✉r❡ ❬❱❛❞❛♣❛rt❤✐ ❛♥❞ ❱❛r♠❛✱ ✷✵✶✷❪✳ ❆ s❡❣♠❡♥t❛çã♦ ❢♦✐ r❡❛❧✐③❛❞❛ ❛tr❛✈és ❞❛ té❝♥✐❝❛ ❞❡ ❛❣r✉♣❛♠❡♥t♦ ❋✉③③② ❈✲▼❡❛♥s ✭❋❈▼✮✱ ❡♥❝♦♥tr❛♥❞♦ r❡s✉❧t❛❞♦s ❜❛s✲ t❛♥t❡ s❛t✐s❢❛tór✐♦s q✉❡ ♣♦❞❡♠ s❡r ❛♣❧✐❝❛❞♦s ❡♠ ❞✐✈❡rs♦s ❝❛s♦s ❞❡ ♣❛t♦❧♦❣✐❛ ♠é❞✐❝❛✱ ♦♥❞❡ ❞♦❡♥ç❛s ❝♦♠♦ ♦ ♠❛❧ ❞❡ P❛r❦✐♥s♦♥ ♣♦❞❡♠ s❡r ✐❞❡♥t✐✜❝❛❞❛s ❝♦♠ ♣r❡❝✐sã♦✳
✷✼ ríst✐❝❛s t❡①t✉r❛✐s ❬❈❤❡♥ ❡t ❛❧✳✱ ✷✵✵✺❪❀ ❬❱❛s✉❦✐ ❛♥❞ ●❛♥❡s❛♥✱ ✷✵✵✺❪❀ ❬◆❛♥❞❛❣♦♣❛❧❛♥ ❡t ❛❧✳✱ ✷✵✶✵❪✱ três tr❛❜❛❧❤♦s ♠❡r❡❝❡♠ ❞❡st❛q✉❡✱ s❡❣✉♥❞♦ s✉❛ s✐♠✐❧❛r✐❡❞❛❞❡ ❝♦♠ ❛ ♣r♦♣♦st❛ ❛q✉✐ ❛♣r❡s❡♥t❛❞❛✿ ❙❛♥t♦s ❬❙❛♥t♦s✱ ✷✵✶✷❪ ❡st❡♥❞❡✉ ♦ ❛❧❣♦r✐t♠♦ ▼❖❋❙ ♣❛r❛ ❛ s❡❣♠❡♥t❛çã♦ ❞❡ ✐♠❛❣❡♥s t❡①t✉r❛✐s ❡♠ ❡s❝❛❧❛ ❞❡ ❝✐♥③❛✱ ✉t✐❧✐③❛♥❞♦ ❛ s❡❣♠❡♥t❛çã♦ ❢✉③③② ♣♦r ❝r❡s❝✐♠❡♥t♦ ❞❡ r❡❣✐õ❡s✱ ❝♦♥❝❧✉í♥❞♦ q✉❡ s❡✉s r❡s✉❧t❛❞♦s ❛❧❝❛♥ç❛♠ ✉♠❛ ♠❡❧❤♦r ❛❝✉rá❝✐❛ ❝♦♠ ❛ ✉t✐❧✐③❛çã♦ ❞❛ ❉✐✈❡r❣ê♥❝✐❛ ❙❦❡✇✱ ♣♦ré♠ ❝♦♠ ❡❧❡✈❛❞♦ ❝✉st♦ ❝♦♠♣✉t❛❝✐♦♥❛❧❀ ▼ú❥✐❝❛✲❱❛r❣❛s✱ ●❛❧❧❡❣♦s✲ ❋✉♥❡s ❡ ❘♦s❛❧❡s✲❙✐❧✈❛ ❬▼✉❥✐❝❛✲❱❛r❣❛s ❡t ❛❧✳✱ ✷✵✶✸❪ ♣r♦♣õ❡♠ ✉♠ r♦❜✉st♦ ❛❧❣♦r✐t♠♦ ♣❛r❛ ♦ ❛❣r✉♣❛♠❡♥t♦ ❢✉③③② ❞❡ ✐♠❛❣❡♥s ❝♦❧♦r✐❞❛s ❝♦♠ r✉í❞♦✱ ❡ ❛❝r❡s❝❡♥t❛♠ ❞♦✐s ♥♦✈♦s ❡st✐♠❛❞♦r❡s ❛♦ ❛❧❣♦r✐t♠♦ ❋❈▼ ❡ ❝♦♠♣❛r❛♠ s✉❛ s♦❧✉çã♦ ❝♦♠ s❡✐s ♦✉tr♦s ❛❧❣♦r✐t♠♦s ❜❡♠ ❝♦♥❝❡✐t✉❛✲ ❞♦s ♥♦ ❡st❛❞♦ ❞❛ ❛rt❡✳ ❖s ❡①♣❡r✐♠❡♥t♦s ♣r♦❞✉③✐r❛♠ ❛❝✉rá❝✐❛s q✉❡ ✈❛r✐❛♠ ♥♦ ✐♥t❡r✈❛❧♦ ❞❡[78.4%,84.8%] ❞❡ s❡✉ ♠ét♦❞♦ ♥❛ s❡❣♠❡♥t❛çã♦ ❞❡ ✐♠❛❣❡♥s ❝♦♠ r✉í❞♦s ❡ s❡♠♣r❡ s✉♣❡✲ r✐♦r ❛♦s ❞❡♠❛✐s ♠ét♦❞♦s ❝♦♠♣❛r❛❞♦s❀ ❡ ❙❛♠❡t✱ ❆♠r❛❤♦✈ ❡ ❩✐r♦❣❧✉ ❬❙❛♠❡t ❡t ❛❧✳✱ ✷✵✶✷❪ ♣r♦♣õ❡♠ ✉♠❛ té❝♥✐❝❛ ❜❛s❡❛❞❛ ♥❛s r❡❣r❛s ❢✉③③② ♣❛r❛ ❛ s❡❣♠❡♥t❛çã♦ ❞❡ ✐♠❛❣❡♥s ❞❡ ✜♥❛s s❡çõ❡s ❞❡ r♦❝❤❛s✳
✷✽
✸ ❙❡❣♠❡♥t❛çã♦ ❋✉③③② ❞❡ ■♠❛❣❡♥s
❈♦❧♦r✐❞❛s ❝♦♠ ❈❛r❛❝t❡ríst✐❝❛s
❚❡①t✉r❛✐s
❆ ♣r✐♠❡✐r❛ s❡çã♦ ❞❡st❡ ❝❛♣ít✉❧♦ ❝♦♥té♠ ❛s té❝♥✐❝❛s ✉t✐❧✐③❛❞❛s ♥♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞♦ ♠ét♦❞♦ ♣r♦♣♦st♦✳ ❆ s❡❣✉♥❞❛ s❡çã♦ ❛♣r❡s❡♥t❛ ❛ s♦❧✉çã♦ ♣r♦♣♦st❛ ♥❡st❡ tr❛❜❛❧❤♦ ♣❛r❛ ❛ s❡❣♠❡♥t❛çã♦ ❢✉③③② ❞❡ ✐♠❛❣❡♥s ❝♦❧♦r✐❞❛s ❝♦♠ ❝❛r❛❝t❡ríst✐❝❛s t❡①t✉r❛✐s✳ ❆♦ ✜♥❛❧ ❞❡st❡ ❝❛♣ít✉❧♦ ❡stá ❞❡s❝r✐t♦ ♦ ❛♣❧✐❝❛t✐✈♦ ❞❡s❡♥✈♦❧✈✐❞♦ ❡ ♦s ♣r✐♠❡✐r♦s t❡st❡s ❡①❡❝✉t❛❞♦s✳
✸✳✶ ❚é❝♥✐❝❛s ❯t✐❧✐③❛❞❛s
❆ s❡❣✉✐r✱ ❛s té❝♥✐❝❛s ✉t✐❧✐③❛❞❛s ♥♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞♦ ♠ét♦❞♦ ♣r♦♣♦st♦ sã♦ ❞❡s❝r✐t❛s✳ ■♥✐❝✐❛♥❞♦✲s❡ ♣❡❧❛ s❡❣♠❡♥t❛çã♦ ❢✉③③②✱ s❡❣✉✐❞❛ ❞❛ ❉✐✈❡r❣ê♥❝✐❛ ❙❦❡✇ ❡ ✜♥❛❧✐③❛♥❞♦ ❝♦♠ ♦ ♣r♦❝❡ss❛♠❡♥t♦ ❞❡ ❤✐st♦❣r❛♠❛s ❝♦❧♦r✐❞♦s✳
✸✳✶✳✶ ❙❡❣♠❡♥t❛çã♦ ❋✉③③②
❆ s❡❣♠❡♥t❛çã♦ ❢✉③③② t❡♠ ❛♣r❡s❡♥t❛❞♦ ❜❛st❛♥t❡ s✉❝❡ss♦✳ ❆ ♥♦çã♦ ❞❡ ❝♦♥❡❝t✐✈✐❞❛❞❡ ❢✉③③② ❝❛♣t✉r❛ ❛ ✐❞❡✐❛ ❞❡ ❝♦❡sã♦ ✭❤❛♥❣✐♥❣✲t♦❣❡t❤❡r♥❡ss✮ ❞♦s ❡❧❡♠❡♥t♦s ❞❛ ✐♠❛❣❡♠ ❡♠ ✉♠ ♦❜❥❡t♦ ♣♦r ♠❡✐♦ ❞❛ ❛tr✐❜✉✐çã♦ ❞❡ ✉♠❛ ❢♦rç❛ ❞❡ ❝♦♥❡①ã♦ ♣❛r❛ t♦❞♦s ♦s ❝❛♠✐♥❤♦s ✭❝♦rr❡♥t❡s✮ ♣♦ssí✈❡✐s ❡♥tr❡ t♦❞♦s ♦s ♣♦ssí✈❡✐s ♣❛r❡s ❞❡ ❡❧❡♠❡♥t♦s ❞❛ ✐♠❛❣❡♠✳ ❆ r❡❧❛çã♦ ❞❡ ❝♦♥❡❝t✐✈✐✲ ❞❛❞❡ é ❞❡✜♥✐❞❛ ♥♦ ❝♦♥❥✉♥t♦ ❞❡ s♣❡❧s ✭❞♦ ✐♥❣❧ês✱ s♣❛❝✐❛❧ ❡❧❡♠❡♥ts✮ ❜❛s❡❛❞♦ ♥❛ ❛✜♥✐❞❛❞❡✳ ❖ ✈❛❧♦r ❞❛ ❧✐❣❛çã♦ ❛tr✐❜✉í❞♦ ❛ ✉♠ ❡❧♦ (c, d) ❞❡ s♣❡❧s é ♦ ♠❛✐♦r ❞♦s ✏♣♦♥t♦s ❢♦rt❡s✑ ❞❡ t♦❞♦s ♦s ❝❛♠✐♥❤♦s ❞❡ c ♣❛r❛ d✳ ❆ ❢♦rç❛ ❞❡ ✉♠ ❝❛♠✐♥❤♦ é s✐♠♣❧❡s♠❡♥t❡ ❛ ♠❡♥♦r ❛✜♥✐❞❛❞❡ ❛♦
❧♦♥❣♦ ❞♦ ❝❛♠✐♥❤♦ ❬❙❛❤❛ ❛♥❞ ❯❞✉♣❛✱ ✷✵✵✶❪✳
