❉❊❚❊❈➬➹❖ ❉❊ ▼❯❉❆◆➬❆❙ ❊ ❘❊❈❯P❊❘❆➬➹❖
❉❊ ❋❖❘▼❆ ❊▼ ▼❆P❆❙ ✸❉ ❇❆❙❊❆❉❖❙ ❊▼
P❆❯▲❖ ▲■▲▲❊❙ ❏❖❘●❊ ❉❘❊❲❙ ❏❘
❉❊❚❊❈➬➹❖ ❉❊ ▼❯❉❆◆➬❆❙ ❊ ❘❊❈❯P❊❘❆➬➹❖
❉❊ ❋❖❘▼❆ ❊▼ ▼❆P❆❙ ✸❉ ❇❆❙❊❆❉❖❙ ❊▼
◆❯❱❊◆❙ ❉❊ P❖◆❚❖❙
❉✐ss❡rt❛çã♦ ❛♣r❡s❡♥t❛❞❛ ❛♦ Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❈✐ê♥❝✐❛ ❞❛ ❈♦♠♣✉t❛çã♦ ❞♦ ■♥st✐t✉t♦ ❞❡ ❈✐ê♥❝✐❛s ❊①❛t❛s ❞❛ ❯♥✐✈❡r✲ s✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ▼✐♥❛s ●❡r❛✐s ❝♦♠♦ r❡✲ q✉✐s✐t♦ ♣❛r❝✐❛❧ ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞♦ ❣r❛✉ ❞❡ ▼❡str❡ ❡♠ ❈✐ê♥❝✐❛ ❞❛ ❈♦♠♣✉t❛çã♦✳
❖r✐❡♥t❛❞♦r✿ Pr♦❢✳ ▼❛r✐♦ ❋❡r♥❛♥❞♦ ▼♦♥t❡♥❡❣r♦ ❈❛♠♣♦s
❝
✷✵✵✾✱ P❛✉❧♦ ▲✐❧❧❡s ❏♦r❣❡ ❉r❡✇s ❏r✳
❚♦❞♦s ♦s ❞✐r❡✐t♦s r❡s❡r✈❛❞♦s✳
❉r❡✇s ❏r✱ P❛✉❧♦ ▲✐❧❧❡s ❏♦r❣❡
❉✼✼✻❞ ❉❡t❡❝çã♦ ❞❡ ▼✉❞❛♥ç❛s ❡ ❘❡❝✉♣❡r❛çã♦ ❞❡ ❋♦r♠❛ ❡♠ ▼❛♣❛s ✸❉ ❇❛s❡❛❞♦s ❡♠ ◆✉✈❡♥s ❞❡ P♦♥t♦s ✴ P❛✉❧♦ ▲✐❧❧❡s ❏♦r❣❡ ❉r❡✇s ❏r✳ ✖ ❇❡❧♦ ❍♦r✐③♦♥t❡✱ ✷✵✵✾
①①①✱ ✶✸✵ ❢✳ ✿ ✐❧✳ ❀ ✷✾❝♠
❉✐ss❡rt❛çã♦ ✭♠❡str❛❞♦✮ ✖ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ▼✐♥❛s ●❡r❛✐s
❖r✐❡♥t❛❞♦r✿ Pr♦❢✳ ▼❛r✐♦ ❋❡r♥❛♥❞♦ ▼♦♥t❡♥❡❣r♦ ❈❛♠♣♦s
✶✳ ❘♦❜ót✐❝❛ ✲ ❚❡s❡s✳ ✷✳ ■♠❛❣❡♠ tr✐❞✐♠❡♥s✐♦♥❛❧ ✲ ❚❡s❡s✳ ■✳ ❚ít✉❧♦✳
❬❋♦❧❤❛ ❞❡ ❆♣r♦✈❛çã♦❪
◗✉❛♥❞♦ ❛ s❡❝r❡t❛r✐❛ ❞♦ ❈✉rs♦ ❢♦r♥❡❝❡r ❡st❛ ❢♦❧❤❛✱❡❧❛ ❞❡✈❡ s❡r ❞✐❣✐t❛❧✐③❛❞❛ ❡ ❛r♠❛③❡♥❛❞❛ ♥♦ ❞✐s❝♦ ❡♠ ❢♦r♠❛t♦ ❣rá✜❝♦✳ ❙❡ ✈♦❝ê ❡st✐✈❡r ✉s❛♥❞♦ ♦ ♣❞❢❧❛t❡①✱
❛r♠❛③❡♥❡ ♦ ❛rq✉✐✈♦ ♣r❡❢❡r❡♥❝✐❛❧♠❡♥t❡ ❡♠ ❢♦r♠❛t♦ P◆● ✭♦ ❢♦r♠❛t♦ ❏P❊● é ♣✐♦r ♥❡st❡ ❝❛s♦✮✳
❙❡ ✈♦❝ê ❡st✐✈❡r ✉s❛♥❞♦ ♦ ❧❛t❡① ✭♥ã♦ ♦ ♣❞❢❧❛t❡①✮✱ t❡rá q✉❡ ❝♦♥✈❡rt❡r ♦ ❛rq✉✐✈♦ ❣rá✜❝♦ ♣❛r❛ ♦ ❢♦r♠❛t♦ ❊P❙✳ ❊♠ s❡❣✉✐❞❛✱ ❛❝r❡s❝❡♥t❡ ❛ ♦♣çã♦ ❛♣♣r♦✈❛❧❂④♥♦♠❡ ❞♦ ❛rq✉✐✈♦⑥
❆❣r❛❞❡❝✐♠❡♥t♦s
▼✐♥❤❛ tr❛❥❡tór✐❛ ❛té ❝❤❡❣❛r ❛ ❡st❡ ♣♦♥t♦✱ ✜♥❛❧✐③❛♥❞♦ ♦ ♠❡str❛❞♦ ♥❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡✲ ❞❡r❛❧ ❞❡ ▼✐♥❛s ●❡r❛✐s✱ ♣❛ss♦✉ ♣♦r ❞✐✈❡rs♦s ♣❛ss♦s✳ ❙❡✐ q✉❡ ♥ã♦ ❝♦♥s✐❣♦ ❛❣r❛❞❡❝❡r ❛ t♦❞♦s✱ ♠❛s ❡s♣❡r♦ ♥ã♦ ❡sq✉❡❝❡r ❞❡ ♥✐♥❣✉é♠✳
●♦st❛r✐❛ ❞❡ ❛❣r❛❞❡❝❡r✱ ♣r✐♠❡✐r❛♠❡♥t❡✱ à ♠✐♥❤❛ ♠ã❡✱ ▼❛r✐❛ ❞❛ ●r❛ç❛✱ ♣❡❧♦ ❛♣♦✐♦ ✐♥❝♦♥❞✐❝✐♦♥❛❧ ❞❛❞♦ ❛ t♦❞❛s ❛s ❧♦✉❝✉r❛s q✉❡ ❥á ✜③✱ ❡ ❛✐♥❞❛ ✈♦✉ ❢❛③❡r✱ ♣r✐♥❝✐♣❛❧♠❡♥t❡ q✉❛♥❞♦ ❞❡❝✐❞✐ ❧❛r❣❛r ♦ s✉❧ ❞♦ ❇r❛s✐❧ ❡ ❝♦rr❡r ❛trás ❞❡ ✉♠ s♦♥❤♦ ❡♠ ▼✐♥❛s ●❡r❛✐s✳ ❆♦ ♠❡✉ ♣❛✐✱ P❛✉❧♦✱ ❡ ♠❡✉ ✐r♠ã♦✱ ▼❛✉r♦✱ ♣❡❧❛s ♣❛❧❛✈r❛s ❞❡ ✐♥❝❡♥t✐✈♦✳ ➚ Pr♦❢❛✳ ❙✐❧✈✐❛ ❇♦t❡❧❤♦✱ ♣♦r t❡r s❡♠♣r❡ ♠❡ ❛♣♦✐❛❞♦ ♠✉✐t♦ ❡ ♠❡ ♠♦str❛❞♦ ❛s ♠✐♥❤❛s ❝❛♣❛❝✐❞❛❞❡s✱ ❞❛s q✉❛✐s s❡♠♣r❡ ❞✉✈✐❞❡✐✳ ❆♦ ♠❡✉ ✏s❡❣✉♥❞♦✑ ✐r♠ã♦ ❊♥❣✳ ❋á❜✐♦ P❡❞r♦tt✐✱ ♣♦r t❡r s❡♠♣r❡ ❛❝r❡❞✐t❛❞♦ ❡♠ ♠✐♠✱ ❛❧é♠ ❞❡ t❡r ♠❡ ❞❛❞♦ ❛ ✐♥❢r❛✲❡str✉t✉r❛ q✉❛♥❞♦ ❝❤❡❣✉❡✐ ❛ ❇❡❧♦ ❍♦r✐③♦♥t❡✳ ❚❛♠❜é♠ ❛♦s ✏✐r♠ã♦s ❞❡ ❇❍✑✱ ❊♥❣✳ ❘♦❞r✐❣♦ ▼♦r❛s❝♦ ❡ ❊♥❣✳ ▼❛r❝❡❧♦ ▼♦tt❛✱ ♣❡❧❛s ✈ár✐❛s ❤♦r❛s ❞❡ ❛❧❡❣r✐❛ q✉❡ ♠❡ ♣r♦♣♦r❝✐♦♥❛r❛♠ ♥❡ss❡ ❧✉❣❛r tã♦ ❞✐st❛♥t❡✳ ❚❛♠❜é♠✱ ❛♦s ❛♠✐❣♦s ❏♦ã♦ ❡ ❆❧❡①❛♥❞r❡✱ ♣♦r t❡r❡♠ ❞✐✈✐❞✐❞♦ ♠❛✐s q✉❡ ✉♠❛ ❝❛s❛ ❝♦♠✐❣♦✳ P❡❧❛s ❝♦♥✈❡rs❛s✱ ♣❡❧❛s ❛✉❧❛s ❞❡ ✈✐♦❧ã♦✱ ❝❛♥t♦✱ ✐t❛❧✐❛♥♦ ❡✱ ❡♠ ❡s♣❡❝✐❛❧✱ ❞❡ ✈✐❞❛ ❡ ✈✐✈ê♥❝✐❛✳ ➚ Pr♦❢❛✳ Pr✐s❝✐❧❛ ▼❛rt✐♥s ♣♦r t❡r ♠❡ ❛❥✉❞❛❞♦ ♠✉✐t♦ ♥❛ ♣r♦♣♦st❛ ❞❡ ❞✐ss❡rt❛çã♦✳ ◆ã♦ ♣♦ss♦ ❡sq✉❡❝❡r✱ t❛♠❜é♠✱ ❞❡ ♠❡✉s ❡①✲❝♦❧❡❣❛s ❞❡ ❊♥❣✳ ❞❡ ❈♦♠♣✉t❛çã♦ ❞❛ ❋❯❘●✱ ♣♦r t❡r❡♠ s❡♠♣r❡ ♠❡ ❞❛❞♦ ❛q✉❡❧❛ r❡❝❡♣çã♦ ❡♠ P♦rt♦ ❆❧❡❣r❡ ♥❛s ♠✐♥❤❛s ♣♦✉❝❛s ✐❞❛s ❛♦ ❙✉❧ ❡ ❝♦♠♣❛rt✐❧❤❛❞♦ ❝♦♠✐❣♦ ♠✐♥❤❛s ❞ú✈✐❞❛s ❡ ❢r✉str❛çõ❡s ❡♠ r❡❧❛çã♦ ❛♦ ❢✉t✉r♦ s❡♠♣r❡ ✐♥❝❡rt♦✿ ❚♦♠ás✱ ❉❛♥✐❡❧✱ ❯❧✐ss❡s✱ ❏✉❧✐❛♥♦ ❡ ■❣♦r✳
◗✉❡r✐❛ ❛❣r❛❞❡❝❡r✱ ❡s♣❡❝✐❛❧♠❡♥t❡✱ ❛♦ Pr♦❢✳ ▼ár✐♦ ❈❛♠♣♦s✱ ♣♦✐s s❡ ♥ã♦ ❢♦ss❡ ❛q✉❡❧❡ ❝♦♥✈✐t❡ ♥♦ ❙❇❆■ ❞❡ ✷✵✵✼✱ ❝♦♠ ❝❡rt❡③❛ ♥ã♦ t❡r✐❛ ✈✐♥❞♦ ♣❛r❛ ❇❡❧♦ ❍♦r✐③♦♥t❡✳ P♦r t♦❞♦ ✐♥❝❛♥sá✈❡❧ ❛♣♦✐♦ ❡ ❡♥s✐♥❛♠❡♥t♦s ♣❛ss❛❞♦s ❞✉r❛♥t❡ ❡ss❛ ❧♦♥❣❛ ❥♦r♥❛❞❛ ❡✱ ❝❧❛r♦✱ ♣❡❧♦ ❛♣♦✐♦ ♥❛ ♠✐♥❤❛ ✐❞é✐❛ ♠❛❧✉❝❛ ❞❡ s❛✐r ❞♦ ♣❛ís ❞✉r❛♥t❡ ♦ ♠❡str❛❞♦✳ ➚s s✉❛s s❡♠♣r❡ sá❜✐❛s ♣❛❧❛✈r❛s✱ ♠✉✐t♦ ♦❜r✐❣❛❞♦✦
❆❣r❛❞❡ç♦ ❛ t♦❞♦s ♦s ♣r♦❢❡ss♦r❡s q✉❡ t✐✈❡ ❞✉r❛♥t❡ ❛ ✈✐❞❛✱ ♣♦✐s ❝❛❞❛ ✉♠ t❡✈❡ ✉♠❛ ♣❛r❝❡❧❛ ✐♠♣♦rt❛♥t❡ ♥❛ ♠✐♥❤❛ ❢♦r♠❛çã♦✱ ❝♦♠♦ ❡♥❣❡♥❤❡✐r♦✱ ♣❡sq✉✐s❛❞♦r ❡ ❝♦♠♦ ❝✐❞❛❞ã♦✳ ❘❡❝❡♥t❡♠❡♥t❡✱ ❛♦s ♣r♦❢❡ss♦r❡s ❞♦s q✉❛✐s ❢✉✐ ❛❧✉♥♦ ♥❛ ❯❋▼●✱ Pr♦❢✳ ▲✉✐③ ❈❤❛✐♠♦✇✐❝③✱ Pr♦❢✳ ❆♥tô♥✐♦ ▲♦✉r❡✐r♦ ❡ Pr♦❢✳ ●❡r❛❧❞♦ ❘♦❜s♦♥✱ ♣❡❧♦s ❝♦♥❤❡❝✐♠❡♥t♦s ✐♠♣♦rt❛♥t❡s q✉❡
♠❡ ♣❛ss❛r❛♠✳ ❆♦s ♣r♦❢❡ss♦r❡s q✉❡ ♣❛rt✐❝✐♣❛r❛♠ ❞❛ ❜❛♥❝❛ ❞❡ ❞❡❢❡s❛ ❞❡st❛ ❞✐ss❡rt❛çã♦✱ ♦s q✉❛✐s ❛❣r❡❣❛r❛♠ ✈❛❧✐♦s❛s s✉❣❡stõ❡s ❛ ❡st❡ tr❛❜❛❧❤♦✳ ❆♦ Pr♦❢✳ ❍✉❣♦ ❱✐❡✐r❛ ◆❡t♦✱ ❡s♣❡❝✐❛❧♠❡♥t❡✱ ♣❡❧❛ r❡✈✐sã♦ ❝r✐t❡r✐♦s❛ ❞♦ t❡①t♦✳
❆❣r❛❞❡ç♦✱ t❛♠❜é♠✱ ❛ t♦❞♦s ♦s ❝♦❧❡❣❛s ❞♦ ❱❡❘▲❛❜ q✉❡ ❞✐✈✐❞✐r❛♠ ❝♦♠✐❣♦ ❛❧❣✉✲ ♠❛s ❤♦r❛s ❞❡ ❧❛③❡r ❡ tr❛❜❛❧❤♦✱ ❝♦♠ ❞✐s❝✉ssõ❡s té❝♥✐❝❛s ♦✉ ♥ã♦✱ ♠❛s q✉❡ ❢♦r❛♠ ♠✉✐t♦ ✐♠♣♦rt❛♥t❡ ♣❛r❛ q✉❡ ❡✉ ❝❤❡❣❛ss❡ ❛♦ ✜♠ ❞❡ss❛ ❡t❛♣❛✳ ❉❛ ■♥✐❝✐❛çã♦ ❈✐❡♥tí✜❝❛✿ ❙♦r✐❛♥♦✱ ❈♦st❛✱ ❇❛❧❜✐♥♦✱ ❘❡♥❛t♦✱ ❉✐♠❛s✱ ❇r✉♥♦ ❡ ❆❧❧②s♦♥✳ ❉♦ ♠❡str❛❞♦ ✭♠✉✐t♦s ❤♦❥❡ ❡♠ ❞✐❛ ❥á ♥♦ ❞♦✉t♦r❛❞♦✮✿ ❆r♠❛♥❞♦✱ ❉♦✉❣❧❛s✱ ❊r✐❝❦s♦♥✱ ❘❡♥❛t♦✱ ❘❛❢❛❡❧✱ ❚❤✐❛❣♦ ❡ ❈❛♥t♦♥✐✳ ❚❛♠❜é♠ ❛♦s ❞♦✉t♦r❛♥❞♦s✿ ❱✐❧❛r✱ P❡❞r♦✱ ▼❛r❝❡❧♦✱ ❙❛♥❞r♦✱ ❲❛❣♥❡r ❡ ❈❡❧s♦✳ ❊✱ ❝❧❛r♦✱ ❛♦ ♥♦ss♦ ❝♦❧❛❜♦r❛❞♦r ❲♦❧♠❛r✳
●♦st❛r✐❛ ❞❡ ❛❣r❛❞❡❝❡r✱ t❛♠❜é♠✱ ❛ ♦♣♦rt✉♥✐❞❛❞❡ q✉❡ ♠❡ ❢♦✐ ❞❛❞❛ ♣❡❧♦ Pr♦❢✳ ❏♦r❣❡ ❉✐❛s ❞❡ ♣❡sq✉✐s❛r ❡♠ P♦rt✉❣❛❧✱ ♣♦r q✉❛s❡ ✽ ♠❡s❡s✱ ❡♠ ✉♠ ❧❛❜♦r❛tór✐♦ ❞❡ ♣❡sq✉✐s❛ ❡①❡♠♣❧❛r ❝♦♠ ♣❡ss♦❛s ❢❛♥tást✐❝❛s✳ ❊♥tr❡ ❡ss❛s ♣❡ss♦❛s ✐♥❝❧✉♦✱ ❡s♣❡❝✐❛❧♠❡♥t❡✱ ♦ Pr♦❢✳ ❘✉✐ ❘♦❝❤❛✱ ♣♦r t❡r ❛❝r❡❞✐t❛❞♦ ❡♠ ♠✐♠✱ ♠❡s♠♦ q✉❛♥❞♦ ♣❛r❡❝✐❛ q✉❡ ♥ã♦ ✐❛ ❞❛r ❝♦♥t❛✱ ♣❡❧♦s ❡♥s✐♥❛♠❡♥t♦s ❡ ❡♠♣❡♥❤♦ ❝♦♥st❛♥t❡ ♣❛r❛ ♠❡ ❛❥✉❞❛r✳ ❆♦s ❝♦❧❡❣❛s ❞❡ ▼❘▲ ❡ ■❙❘✱ ❞❡ t♦❞❛s ❛s ♣❛rt❡s ❞♦ ♠✉♥❞♦✱ sã♦ t❛♥t❛s ❝♦✐s❛s ❛ ❛❣r❛❞❡❝❡r✱ ♠❛s ❝❛❞❛ ✉♠ s❛❜❡ ❛ ✐♠♣♦rtâ♥❝✐❛ q✉❡ t❡✈❡ ♥❡ss❡ ♣❡rí♦❞♦ ✐♠♣♦rt❛♥t❡ ❞❛ ♠✐♥❤❛ ✈✐❞❛✳ ❆♦s ❝♦❧❡❣❛s ❜r❛s✐❧❡✐r♦s✿ ❉✐❡❣♦✱ ❏♦sé✱ ▲✉✐s ▼✐r✐s♦❧❛✱ ❖s✇❛❧❞♦✱ ❈r✐st✐❛♥♦✳ ❆♦s ❝♦❧❡❣❛s ❛❢r✐❝❛♥♦s✿ ❆❜❡❞ ❡ ❖♠❛r✳ ❆♦s ❝♦❧❡❣❛s ✐r❛♥✐❛♥♦s✿ ❍❛❞✐ ❡ ❑❛♠r❛❞✳ ❊ ❛♦s ❞✐✈❡rs♦s ❝♦❧❡❣❛s ♣♦rt✉❣✉❡s❡s✿ ◆✉♥♦✱ ❏♦ã♦ ▼❛❝❤❛❞♦✱ ❏♦ã♦ ▼♦♥t❡✐r♦✱ ▲✉ís ❙❛♥t♦s✱ ❈❛r❧♦s✱ ❆❧❡①❛♥❞r❡✱ ❘✐❝❛r❞♦✱ P❛✉❧❛ ❡ ❘✐t❛✳
▼❡ ❣✉st❛r✐❛ ❞❡ ❛❣r❛❞❡❝❡r ❡♥ ❡s♣❛ñ♦❧✱ ❛✉♥q✉❡ ♥♦s♦tr♦s s✐❡♠♣r❡ ❤❛❜❧❛♠♦s ❡♥ ✐♥❣❧és✱ ❛ ✉♥❛ ♣❡rs♦♥❛ ❢❡♥♦♠❡♥❛❧ q✉❡ ❝♦♥♦❝✐ ❡♥ P♦rt✉❣❛❧✱ ❡❧ Pr♦❢✳ P❡❞r♦ ◆✉ñ❡③✳ P♦r t♦❞♦ q✉❡ ♠❡ ❤❛② ❛②✉❞❛❞♦✱ tr❛❜❛❥❛♥❞♦ ❝♦♥❥✉♥t❛♠❡♥t❡✱ s✐❡♠♣r❡ ❝♦♥ ♥✉❡✈❛s ✐❞❡❛s ② ♣❛❧❛❜r❛s ❞❡ ❛♣♦②♦✳ P♦r ❝r❡❡r ❡♥ ♠✐ ② ♠❡ ❛②✉❞❛r ❛st❛ ♣♦r ❡❧ ❙❦②♣❡✳ ●r❛❝✐❛s ✏❝❛❜ró♥✑✳
❆❣r❛❞❡ç♦✱ t❛♠❜é♠✱ às ♣❡ss♦❛s q✉❡ ♠❡ ❛❥✉❞❛r❛♠ ❛ tr❛♥s❢♦r♠❛r ♠❡✉s ❞✐❛s ❡♠ P♦rt✉❣❛❧✱ ❡♠ ❞✐❛s ❜❡♠ ♠❡❧❤♦r❡s✱ ❞✐✈✐❞✐♥❞♦ ❝♦♠✐❣♦ ✉♠ ❧❛r✿ ❋❡r♥❛♥❞♦✱ ●❛❜r✐❡❧❛✱ ❏♦sé ❡✱ ❡s♣❡❝✐❛❧♠❡♥t❡✱ ■s❛❜❡❧❛✱ ♣♦r s❡r ✉♠❛ ♥❛♠♦r❛❞❛ ❢❛♥tást✐❝❛✱ ❛❧é♠ ✉♠❛ ❡①❝❡❧❡♥t❡ ❝♦rr❡t♦r❛ ♦rt♦❣rá✜❝❛✳ P♦r t❡r ♠❡ ❛❥✉❞❛❞♦ ❡ ❛♣♦✐❛❞♦ ✐♥❝❛♥s❛✈❡❧♠❡♥t❡✱ q✉❛♥❞♦ ❡✉ ♣❡♥s❛✈❛ ❡♠ ❞❡s✐st✐r ❞❡ t✉❞♦✱ ❛❧é♠ ❞❛ ♣❛❝✐ê♥❝✐❛ ✲ ❡ q✉❡ ♣❛❝✐ê♥❝✐❛✦ ✲ ❛❝❤♦ q✉❡ ♥❡♠ ❡❧❛ s❛❜✐❛ q✉❡ t✐♥❤❛ t❛♥t❛✳
❆❣r❛❞❡ç♦✱ ❛✐♥❞❛✱ ❛ ❈❆P❊❙ ♣❡❧♦ ❛♣♦✐♦ ✜♥❛♥❝❡✐r♦ ♥❡ss❡s q✉❛s❡ ✷ ❛♥♦s ❞❡ tr❛❜❛✲ ❧❤♦✳ ❚❛♠❜é♠ ❛♦ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❈✐ê♥❝✐❛ ❞❛ ❈♦♠♣✉t❛çã♦ ❞❛ ❯❋▼● ❡ t♦❞♦s ♦s s❡✉s ❢✉♥❝✐♦♥ár✐♦s ❡ ❝♦❧❛❜♦r❛❞♦r❡s✳
❆ t♦❞♦s ❛♠✐❣♦s ❡ ❝♦❧❡❣❛s✱ ❝✐t❛❞♦s ♦✉ ♥ã♦✱ ♠✉✐t♦ ♦❜r✐❣❛❞♦✦
✏P❛r❛ ♦❜t❡r ❛❧❣♦ q✉❡ ✈♦❝ê ♥✉♥❝❛ t❡✈❡✱ é ♣r❡❝✐s♦ ❢❛③❡r ❛❧❣♦ q✉❡ ♥✉♥❝❛ ❢❡③✑ ✭❆✉t♦r ❉❡s❝♦♥❤❡❝✐❞♦✮
❘❡s✉♠♦
❖ ♣r❡s❡♥t❡ tr❛❜❛❧❤♦ ♣r♦♣õ❡ ✉♠ ❛r❝❛❜♦✉ç♦ ♣❛r❛ ❞❡t❡r♠✐♥❛çã♦ ❡ s❡❣♠❡♥t❛çã♦ ❞❡ ♠✉✲ ❞❛♥ç❛s ❡♠ ♥✉✈❡♥s ❞❡ ♣♦♥t♦s ✸❉ ❞❡ ❢♦r♠❛ ❡✜❝✐❡♥t❡✳ ■♥✐❝✐❛❧♠❡♥t❡✱ é ❡❢❡t✉❛❞❛ ✉♠❛ s✐♠♣❧✐✜❝❛çã♦ ♥❡ss❡s ♣♦♥t♦s✱ ❣❡r❛♥❞♦ ✉♠❛ r❡♣r❡s❡♥t❛çã♦ ❡♠ ár✈♦r❡ q✉❡ ❜✉s❝❛ ♣r❡s❡r✈❛r ❛s ❝❛r❛❝t❡ríst✐❝❛s r❡❧❡✈❛♥t❡s ❞❛ ♥✉✈❡♠ ♣♦r ♠❡✐♦ ❞❛ ❡st✐♠❛çã♦ ❞❛ ✈❛r✐❛çã♦ ❞❛ s✉♣❡r❢í❝✐❡✳ ❆❧é♠ ❞✐ss♦✱ é ✉t✐❧✐③❛❞❛ ✉♠❛ ❝♦♠❜✐♥❛çã♦ ❞❡ ▼♦❞❡❧♦s ❞❡ ▼✐st✉r❛s ●❛✉ss✐❛♥❛s ✭●▼▼ ✮ ❡ ❞❛ ♠étr✐❝❛ ❞❡ ❞✐stâ♥❝✐❛ ❊❛rt❤ ▼♦✈❡r✬s ❉✐st❛♥❝❡ ✭❊▼❉✮✱ ♣♦r ♠❡✐♦ ❞❡ ✉♠❛ té❝♥✐❝❛ ❣✉❧♦s❛✳ ❊❧❛ ♣❡r♠✐t❡ ❞❡t❡❝t❛r ♦ q✉❡ é ♠✉❞❛♥ç❛ ❡♠ ✉♠ ❞❛❞♦ ❧♦❝❛❧✱ ❛ ♣❛rt✐r ❞❡ ❧❡✐t✉r❛s ♣ré✈✐❛s ❞♦ s❡♥s♦r✱ ❡ s❡❣♠❡♥t❛r ❛s ♠✉❞❛♥ç❛s ❞❡t❡❝t❛❞❛s✳
P❛r❛ r❡❝✉♣❡r❛çã♦ ❞❡ ❢♦r♠❛ ✸❉ sã♦ ♣r♦♣♦st♦s ❞♦✐s ♠ét♦❞♦s✳ Pr✐♠❡✐r❛♠❡♥t❡✱ ✉♠ ♥♦✈♦ ♠ét♦❞♦ ♣❛r❛ r❡❝✉♣❡r❛çã♦ ❞❡ ❢♦r♠❛s ❜ás✐❝❛s é ❞❡s❡♥✈♦❧✈✐❞♦✱ ♥♦ ❡s♣❛ç♦ ❞❛s ●❛✉s✲ s✐❛♥❛s✳ ❊ss❡ ♠ét♦❞♦ é ❧✐♠✐t❛❞♦ ❛ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ♣r✐♠✐t✐✈❛s ❣❡♦♠étr✐❝❛s q✉❡ ✐♥❝❧✉❡♠ ♣❧❛♥♦s✱ ❡s❢❡r❛s ❡ ❝✐❧✐♥❞r♦s✳ ❊ss❡ ♠ét♦❞♦ é ❝♦♠♣❛r❛❞♦✱ ❛♦ ❧♦♥❣♦ ❞♦ tr❛❜❛❧❤♦✱ ❝♦♠ ✉♠❛ ❛❜♦r❞❛❣❡♠ ♥♦ ❡s♣❛ç♦ ❊✉❝❧✐❞✐❛♥♦ ✉t✐❧✐③❛♥❞♦ ❘❛♥❞♦♠ ❙❛♠♣❧✐♥❣ ❈♦♥s❡♥s✉s ✭❘❆◆❙❆❈ ✮✳ ❯♠❛ s❡❣✉♥❞❛ ❛❜♦r❞❛❣❡♠ ✉t✐❧✐③❛ s✉♣❡rq✉á❞r✐❝❛s✱ ✈✐s❛♥❞♦ ❞❛r ✉♠❛ ♠❛✐♦r ❡①♣r❡ss✐✲ ✈✐❞❛❞❡ à r❡♣r❡s❡♥t❛çã♦ ❞❡ ❢♦r♠❛ ✸❉✳ ❊st❡ tr❛❜❛❧❤♦ ✉t✐❧✐③❛ ✉♠❛ ❛❜♦r❞❛❣❡♠ ♠✉❧t✐✲❡s❝❛❧❛ ❝♦♠ ♦ ♣❛r❛❞✐❣♠❛ s♣❧✐t✲❛♥❞✲♠❡r❣❡✱ q✉❡ ❜✉s❝❛ ✉❧tr❛♣❛ss❛r ♠í♥✐♠♦s ❧♦❝❛✐s ❞❛ s❡❣♠❡♥t❛✲ çã♦ ❢♦r♥❡❝✐❞❛ ♣❡❧❛ ●▼▼✱ ❜❡♠ ❝♦♠♦ ❞❛r ♠❛✐♦r ❡✜❝✐ê♥❝✐❛ ❛♦ ♠ét♦❞♦ ❝♦♠♦ ✉♠ t♦❞♦✳
❘❡s✉❧t❛❞♦s ❡①♣❡r✐♠❡♥t❛✐s ✉t✐❧✐③❛♥❞♦ ❞❛❞♦s s✐♠✉❧❛❞♦s ❡ r❡❛✐s ❢♦r❛♠ ♦❜t✐❞♦s ♣❛r❛ ❛✈❛❧✐❛r ❛ ❡✜❝á❝✐❛ ❞♦ ♠ét♦❞♦ ❞❡ s✐♠♣❧✐✜❝❛çã♦ ✉t✐❧✐③❛❞♦✱ ❛ss✐♠ ❝♦♠♦ ❞❛ ❛❜♦r❞❛❣❡♠ ❞❡ ❞❡t❡❝çã♦ ❞❡ ♠✉❞❛♥ç❛✳ ❖ ♠ét♦❞♦ ♣❛r❛ r❡❝✉♣❡r❛çã♦ ❞❡ ❢♦r♠❛s ❜ás✐❝❛s ♠♦str♦✉✲s❡ ♠❡✲ ❧❤♦r q✉❡ ♦ ♠ét♦❞♦ ✉t✐❧✐③❛♥❞♦ ♦ ❡s♣❛ç♦ ❊✉❝❧✐❞✐❛♥♦✱ ❡♠ t❡r♠♦s ❞❡ ❝✉st♦ ❝♦♠♣✉t❛❝✐♦♥❛❧ ❡ ❡①❛t✐❞ã♦✱ ♣♦ré♠✱ ❛♣r❡s❡♥t❛ ❛❧❣✉♠❛s r❡str✐çõ❡s q✉❡ sã♦ ❝♦♥t♦r♥❛❞❛s ♣❡❧♦ ✉s♦ ❞❡ s✉✲ ♣❡rq✉á❞r✐❝❛s✳
P❛❧❛✈r❛s✲❝❤❛✈❡✿ ❉❡t❡❝çã♦ ❞❡ ▼✉❞❛♥ç❛s✱ ▼❛♣❛s ✸❉✱ ❘❡❝✉♣❡r❛çã♦ ❞❡ ❋♦r♠❛✱ ❘♦❜ót✐❝❛ ▼ó✈❡❧✳
❆❜str❛❝t
❚❤✐s ✇♦r❦ ♣r♦♣♦s❡s ❛ ❢r❛♠❡✇♦r❦ t♦ ❡✣❝✐❡♥t❧② ❞❡t❡❝t ❛♥❞ s❡❣♠❡♥t ❝❤❛♥❣❡s ✐♥ ✸❉ ♣♦✐♥t ❝❧♦✉❞s✳ ■♥✐t✐❛❧❧②✱ ✇❡ s✐♠♣❧✐❢② t❤❡ ♣♦✐♥t ❝❧♦✉❞ ✇❤✐❝❤ ❣❡♥❡r❛t❡s ❛ tr❡❡ r❡♣r❡s❡♥t❛t✐♦♥ ✐♥ ♦r❞❡r t♦ ♣r❡s❡r✈❡ t❤❡ r❡❧❡✈❛♥t ❝❤❛r❛❝t❡r✐st✐❝s ✉s✐♥❣ s✉r❢❛❝❡ ✈❛r✐❛t✐♦♥ ❛s t❤❡ ❦❡② ❝♦♥s✲ tr❛✐♥t✳ ❚❤❡♥✱ ❛ ❝♦♠❜✐♥❡❞ ❛♣♣r♦❛❝❤ ✉s✐♥❣ ●❛✉ss✐❛♥ ▼✐①t✉r❡ ▼♦❞❡❧s ✭●▼▼✮ ❛♥❞ t❤❡ ❊❛rt❤ ▼♦✈❡r✬s ❉✐st❛♥❝❡ ✭❊▼❉✮ ✐s ♣r♦♣♦s❡❞✱ t♦❣❡t❤❡r ✇✐t❤ ❛ ❣r❡❡❞② t❡❝❤♥✐q✉❡✳ ■t ❞❡✲ t❡❝ts ✇❤❛t ❤❛s ❝❤❛♥❣❡❞ ✐♥ ❛ ❣✐✈❡♥ ❧♦❝❛❧❡ ❢r♦♠ ❛ ♣r❡✈✐♦✉s s❡♥s♦r r❡❛❞✐♥❣ ❛♥❞ s❡❣♠❡♥ts t❤❡ ❞❡t❡❝t❡❞ ♥♦✈❡❧t②✳
❚❤❡ ✸❉ s❤❛♣❡ r❡tr✐❡✈❛❧ ✐s ❛❝❤✐❡✈❡❞ ✉s✐♥❣ t✇♦ ❞✐✛❡r❡♥t ❛♣♣r♦❛❝❤❡s✳ ❚❤❡ ✜rst ❛♣♣r♦❛❝❤ ✐s ❛ ♥❡✇ ♠❡t❤♦❞ t❤❛t ✇❡ ❞❡✈❡❧♦♣❡❞ ✇❤✐❝❤ ❞✐r❡❝t❧② r❡tr✐❡✈❡s t❤❡ ❞❡t❡❝t❡❞ s❤❛♣❡ ✐♥ t❤❡ ●❛✉ss✐❛♥ s♣❛❝❡✳ ■t ✉s❡s ❛ ❧✐♠✐t❡❞ s❡t ♦r ❣❡♦♠❡tr✐❝ ♣r✐♠✐t✐✈❡s ✐♥❝❧✉❞✐♥❣ ♣❧❛♥❡s✱ s♣❤❡r❡s ❛♥❞ ❝②❧✐♥❞❡rs✳ ❚❤✐s ♠❡t❤♦❞ ✐s ❝♦♠♣❛r❡❞ ✇✐t❤ ❛♥♦t❤❡r ♦♥❡ t❤❛t ♦♣❡r❛t❡s ✐♥ t❤❡ ❊✉❝❧✐❞❡❛♥ s♣❛❝❡ ✉s✐♥❣ ❘❛♥❞♦♠ ❙❛♠♣❧✐♥❣ ❈♦♥s❡♥s✉s ✭❘❆◆❙❆❈✮✳
❚❤❡ s❡❝♦♥❞ ❛♣♣r♦❛❝❤ ✉s❡s s✉♣❡rq✉❛❞r✐❝ ♠♦❞❡❧s ❞✉❡ t♦ t❤❡✐r ❣♦♦❞ ❡①♣r❡ss✐✈❡♥❡ss ✐♥ r❡♣r❡s❡♥t✐♥❣ ♠♦r❡ ❣❡♥❡r❛❧✐③❡❞ t❤r❡❡ ❞✐♠❡♥s✐♦♥❛❧ s❤❛♣❡s✳ ■♥ ♦r❞❡r t♦ ❛❝❤✐❡✈❡ ❛ ❣♦♦❞ ❧❡✈❡❧ ♦❢ ❡✣❝✐❡♥❝② ❛♥❞ t♦ ♦✈❡r❝♦♠❡ t❤❡ ❧✐♠✐t❛t✐♦♥s ♦❢ ●▼▼ s❡❣♠❡♥t❛t✐♦♥✱ ❛ ♠✉❧t✐✲s❝❛❧❡ ❛♣♣r♦❛❝❤ ✉s✐♥❣ t❤❡ s♣❧✐t✲❛♥❞✲♠❡r❣❡ ♣❛r❛❞✐❣♠ ✇❛s ❞❡✈✐s❡❞ ❛♥❞ s✉❝❝❡ss❢✉❧❧② ✐♠♣❧❡♠❡♥✲ t❡❞✳
❊①♣❡r✐♠❡♥t❛❧ r❡s✉❧ts ✐♥ ❜♦t❤ r❡❛❧ ❛♥❞ s✐♠✉❧❛t❡❞ s❝❡♥❛r✐♦s ✇❡r❡ ♦❜t❛✐♥❡❞ t♦ ❡✈❛❧✉✲ ❛t❡ t❤❡ ❡✣❝❛❝② ♦❢ t❤❡ s✐♠♣❧✐✜❝❛t✐♦♥ ❛♥❞ ❝❤❛♥❣❡ ❞❡t❡❝t✐♦♥ ♠❡t❤♦❞s✳ ❚❤❡ s❤❛♣❡ r❡tr✐❡✈❛❧ ♠❡t❤♦❞ ✐♥ t❤❡ ●❛✉ss✐❛♥ s♣❛❝❡ s❤♦✇❡❞ ❜❡tt❡r r❡s✉❧ts t❤❛♥ t❤❡ ❊✉❝❧✐❞❡❛♥ s♣❛❝❡ ♠❡t❤♦❞✱ ❜♦t❤ ✐♥ ❛❝❝✉r❛❝② ❛♥❞ ❝♦♠♣✉t❛t✐♦♥❛❧ ❝♦st✳ ❚❤❡ ❧✐♠✐t❛t✐♦♥s ♦♥ s❤❛♣❡ r❡♣r❡s❡♥t❛t✐♦♥ ✇❡r❡ ❛❞❡q✉❛t❡❧② ♦✈❡r❝♦♠❡ ❜② t❤❡ ✉s❡ ♦❢ s✉♣❡rq✉❛❞r✐❝s✳
❑❡②✇♦r❞s✿ ❈❤❛♥❣❡ ❉❡t❡❝t✐♦♥✱ ✸❉ ▼❛♣s✱ ❙❤❛♣❡ ❘❡tr✐❡✈❛❧✱ ▼♦❜✐❧❡ ❘♦❜♦t✐❝s✳
▲✐st❛ ❞❡ ❋✐❣✉r❛s
✶✳✶ ❊①❡♠♣❧♦s ❞❡ r♦❜ôs ♠ó✈❡✐s ✉t✐❧✐③❛❞♦s ❡♠ ❜✉s❝❛ ❡ s❛❧✈❛♠❡♥t♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷ ✶✳✷ ▲❛s❡r s❝❛♥♥❡r ✸❉ ♠♦♥t❛❞♦ s♦❜r❡ ✈❡í❝✉❧♦ ♠ó✈❡❧✱ ❛❧é♠ ❞❡ ✉♠ ❡①❡♠♣❧♦ ❞❡
♥✉✈❡♠ ❞❡ ♣♦♥t♦s ✸❉ ❣❡r❛❞❛ ♣❡❧♦ s✐st❡♠❛ ❬✸❉ ▲❛s❡r ▼❛♣♣✐♥❣ ❈♦✳✱ ✷✵✵✾❪✳ ✳ ✸ ✶✳✸ ❊①❡♠♣❧♦ ❞❡ ❝❡♥ár✐♦ ♣❛r❛ ❞❡t❡❝çã♦ ❞❡ ♠✉❞❛♥ç❛ ❡ r❡❝♦♥❤❡❝✐♠❡♥t♦ ❞❡ ❢♦r♠❛✳ ✹
✷✳✶ ❙✐♠♣❧✐✜❝❛çã♦ ❞❡ ♥✉✈❡♠ ❞❡ ♣♦♥t♦s ♣r♦♣♦st♦ ♣♦r ❆❧❡①❛ ❡t ❛❧✳ ❬✷✵✵✶❪✳ ✳ ✳ ✳ ✳ ✾ ✷✳✷ ❙✐♠♣❧✐✜❝❛çã♦ ❞❡ ♥✉✈❡♠ ❞❡ ♣♦♥t♦s ✉t✐❧✐③❛♥❞♦ ❛❣r✉♣❛♠❡♥t♦ ❬P❛✉❧② ❡t ❛❧✳✱ ✷✵✵✷❪✳ ✶✶ ✷✳✸ ❙✐♠♣❧✐✜❝❛çã♦ ❡♠ ♥í✈❡✐s ♣r♦♣♦st❛ ♣♦r ●♦❜❜❡tt✐ ✫ ▼❛rt♦♥ ❬✷✵✵✹❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷ ✷✳✹ ❙✐♠♣❧✐✜❝❛çã♦ ❞❡ ✉♠❛ ♥✉✈❡♠ ❞❡ ♣♦♥t♦s ✉t✐❧✐③❛♥❞♦ ❛❧❣♦r✐t♠♦ ❖❇❇ ❬❩♦✉ ✫
❨❡✱ ✷✵✵✼❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸ ✷✳✺ ❉❡t❡❝çã♦ ❞❡ ♠✉❞❛♥ç❛ ❡♠ ✐♠❛❣❡♥s ✉t✐❧✐③❛♥❞♦ ♠ét♦❞♦ ♣r♦♣♦st♦ ♣♦r ❬❍✇❛♥❣
❡t ❛❧✳✱ ✷✵✵✽❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻ ✷✳✻ ❉❡t❡❝çã♦ ❞❡ ▼✉❞❛♥ç❛ ✉t✐❧✐③❛♥❞♦ ❞❛❞♦s ❛❞q✉✐r✐❞♦s ♣♦r ❧❛s❡r s❝❛♥♥❡r ❛❡r♦✲
tr❛♥s♣♦rt❛❞♦ ❝♦♠♣❛r❛❞♦s ❝♦♠ ❞❛❞♦s ❞❡ ❈❆❉ ❬❙t❡✐♥❧❡ ❡t ❛❧✳✱ ✶✾✾✾❪✳ ✳ ✳ ✳ ✳ ✶✼ ✷✳✼ ❉❡t❡❝çã♦ ❞❡ ♠✉❞❛♥ç❛ ✉t✐❧✐③❛♥❞♦ ❧❛s❡r s❝❛♥♥❡r ✸❉ ❬●✐r❛r❞❡❛✉✲▼♦♥t❛✉t
❡t ❛❧✳✱ ✷✵✵✺❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✷✳✽ ❉❡t❡❝çã♦ ❞❡ ♠✉❞❛♥ç❛ ✉s❛♥❞♦ ●❲❘ ❬▼❛rs❧❛♥❞ ❡t ❛❧✳✱ ✷✵✵✺❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸ ✷✳✾ ❉❡t❡❝çã♦ ❞❡ ♠✉❞❛♥ç❛ ✉t✐❧✐③❛♥❞♦ ✐♠❛❣❡♥s ❝♦❧♦r✐❞❛s ❬❱✐❡✐r❛ ◆❡t♦ ✫ ◆❡❤♠✲
③♦✇✱ ✷✵✵✽❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✷✳✶✵ ❉❡t❡❝çã♦ ❞❡ ♠✉❞❛♥ç❛ ✉t✐❧✐③❛♥❞♦ ✉♠❛ ❝â♠❡r❛ ❡ ✉♠❛ ❧❛s❡r s❝❛♥♥❡r ❬❆♥❞r❡✲
❛ss♦♥ ❡t ❛❧✳✱ ✷✵✵✼❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✷✳✶✶ ❘❡❝✉♣❡r❛çã♦ ❞❡ ❢♦r♠❛ ✉t✐❧✐③❛♥❞♦ ❢♦r♠❛s ❜ás✐❝❛s ❬❙❝❤♥❛❜❡❧ ❡t ❛❧✳✱ ✷✵✵✼❪✳ ✳ ✳ ✷✾ ✷✳✶✷ ❘❡❝✉♣❡r❛çã♦ ❞❡ ❢♦r♠❛ ✉t✐❧✐③❛♥❞♦ s✉♣❡rq✉á❞r✐❝❛s ❝♦♠ ♣❛r❛❞✐❣♠❛ r❡❝♦✈❡r✲
❛♥❞✲s❡❣♠❡♥t ❬▲❡♦♥❛r❞✐s ❡t ❛❧✳✱ ✶✾✾✼❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✷✳✶✸ ❘❡❝✉♣❡r❛çã♦ ❞❡ ❢♦r♠❛ ✉t✐❧✐③❛♥❞♦ s✉♣❡rq✉á❞r✐❝❛ ❝♦♠ ♠♦❞❡❧♦s ❝♦♥❤❡❝✐❞♦s
❬❇✐❡❣❡❧❜❛✉❡r ✫ ❱✐♥❝③❡✱ ✷✵✵✼❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ✷✳✶✹ ❘❡❝✉♣❡r❛çã♦ ❞❡ ❢♦r♠❛ ✉t✐❧✐③❛♥❞♦ s✉♣❡rq✉á❞r✐❝❛ ❡♠ ♥✉✈❡♠ ❞❡ ♣♦♥t♦s ♥ã♦
❡str✉t✉r❛❞❛s ❬❈❤❡✈❛❧✐❡r ❡t ❛❧✳✱ ✷✵✵✸❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸
✸✳✶ ❱✐sã♦ ❣❡r❛❧ ❞❛ ♠❡t♦❞♦❧♦❣✐❛ ♣r♦♣♦st❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✸✳✷ ❊①❡♠♣❧♦ ❞❡ ✈✐③✐♥❤❛♥ç❛ ❧♦❝❛❧ ✷❉ ✉t✐❧✐③❛♥❞♦ ❛❧❣♦r✐t♠♦ ❞♦s k✲✈✐③✐♥❤♦s ♠❛✐s
♣ró①✐♠♦s ❡♠ ✉♠ ♣♦♥t♦pj✱ ❝♦♠ k= 8 ❬P❛✉❧②✱ ✷✵✵✸❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾
✸✳✸ ❊①❡♠♣❧♦ ❞❡ ❡st✐♠❛çã♦ ✷❉ ❞❛ t❛♥❣❡♥t❡T(x)✭♥♦ ❝❛s♦✱ ✉♠❛ r❡t❛✮ ✉t✐❧✐③❛♥❞♦
❛ ❛♥á❧✐s❡ ❞❛ ❝♦✈❛r✐â♥❝✐❛ ❡♠ ✉♠❛ k✲✈✐③✐♥❤❛♥ç❛ ❡♠ t♦r♥♦ ❞❡ pj✱ ❝♦♠ k = 10✳ ✹✶
✸✳✹ ❊①❡♠♣❧♦ ❞❡ ❢r❛❣♠❡♥t❛çã♦ ❝❛✉s❛❞❛ ♣❡❧♦ ♠ét♦❞♦ ❞❡ ❛❣r✉♣❛♠❡♥t♦ ✐♥❝r❡♠❡♥✲ t❛❧ ❬P❛✉❧② ❡t ❛❧✳✱ ✷✵✵✷❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✸✳✺ ❊sq✉❡♠❛ ✷❉ ❞♦ ❛❧❣♦r✐t♠♦ ❞❡ ❛❣r✉♣❛♠❡♥t♦ ❤✐❡rárq✉✐❝♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹ ✸✳✻ ■❧✉str❛çã♦ ❞♦ ♣r♦❝❡ss♦ ❞❡ s✐♠♣❧✐✜❝❛çã♦ ❤✐❡rárq✉✐❝❛ ❬P❛✉❧②✱ ✷✵✵✸❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺ ✸✳✼ ❆❣r✉♣❛♠❡♥t♦s ❣❡r❛❞♦s ❛♣ós ♣r♦❝❡ss♦ ❞❡ s✐♠♣❧✐✜❝❛çã♦ ❡♠ ✉♠❛ ♥✉✈❡♠ ❞❡
♣♦♥t♦s ❞❡ ❛❧t❛ ❞❡♥s✐❞❛❞❡✱ ❝♦♠ r❡♣r❡s❡♥t❛çã♦ ✉t✐❧✐③❛♥❞♦ ❡❧✐♣só✐❞❡s ❬P❛✉❧②✱ ✷✵✵✸❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺ ✸✳✽ ❙❡❣♠❡♥t❛çã♦ ❞❡ s♦❧♦ ❡❢❡t✉❛❞❛ ♣❡❧♦ ❆❧❣♦r✐t♠♦ ❘❆◆❙❆❈ ❬▲❛✐ ✫ ❋♦①✱ ✷✵✵✾❪✳ ✹✻ ✸✳✾ ❉✐str✐❜✉✐çã♦ ●❛✉ss✐❛♥❛ ❜✐❞✐♠❡♥s✐♦♥❛❧ ❝♦♠✱ ♥♦ ♣❧❛♥♦ ✐♥❢❡r✐♦r✱ ❡❧✐♣s❡s ❝♦♥✲
❝ê♥tr✐❝❛s ❞❡ ✐❣✉❛✐s ♣r♦❜❛❜✐❧✐❞❛❞❡s ❬P❛❛❧❛♥❡♥ ❡t ❛❧✳✱ ✷✵✵✻❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ✸✳✶✵ ▼✐st✉r❛ ●❛✉ss✐❛♥❛ ❜✐❞✐♠❡♥s✐♦♥❛❧ ❢♦r♠❛❞❛ ♣♦r três ●❛✉ss✐❛♥❛s ❝♦♠✱ ♥♦
♣❧❛♥♦ ✐♥❢❡r✐♦r✱ ❡❧✐♣s❡s ❝♦♥❝ê♥tr✐❝❛s ❞❡ ✐❣✉❛✐s ♣r♦❜❛❜✐❧✐❞❛❞❡s ❬P❛❛❧❛♥❡♥ ❡t ❛❧✳✱ ✷✵✵✻❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ✸✳✶✶ ◆✉✈❡♠ ❞❡ ♣♦♥t♦s ✸❉ s✐♠✉❧❛❞♦s✱ à ❡sq✉❡r❞❛✱ ❝♦♠ s✉❛s r❡s♣❡❝t✐✈❛s r❡♣r❡s❡♥✲
t❛çõ❡s ♣♦r ●▼▼✱ à ❞✐r❡✐t❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻ ✸✳✶✷ ❊sq✉❡♠❛ q✉❡ ✐❧✉str❛ ❛ ❞❡t❡❝çã♦ ❡ s❡❣♠❡♥t❛çã♦ ❞❡ ♠✉❞❛♥ç❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽ ✸✳✶✸ ▼♦❞❡❧❛❣❡♠ ❞❛s ♠✉❞❛♥ç❛s ❞♦ ❡s♣❛ç♦ ❞❡ ●❛✉ss✐❛♥❛s ❝♦♠ ❢♦r♠❛s ❜ás✐❝❛s✳ ✳ ✳ ✻✶ ✸✳✶✹ ■❧✉str❛çã♦ ❞♦ r❡s✉❧t❛❞♦ ❞♦ ❛❧❣♦r✐t♠♦s ❞❡ r❡❝✉♣❡r❛çã♦ ❞❡ ❢♦r♠❛s ✉s❛♥❞♦ ❢♦r✲
♠❛s ❜ás✐❝❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸ ✸✳✶✺ ❉✐❛❣r❛♠❛ ❞❡ ✢✉①♦ ❞❡ ❞❛❞♦s ♣❛r❛ r❡❝✉♣❡r❛çã♦ ❞❡ ❢♦r♠❛s ✸❉ ✉s❛♥❞♦ s✉✲
♣❡rq✉á❞r✐❝❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼ ✸✳✶✻ ❙✉♣❡rq✉á❞r✐❝❛s ❣❡r❛❞❛s ❝♦♠ ❞✐❢❡r❡♥t❡s ✈❛❧♦r❡s ❞❡ǫ1 ❡ ǫ2✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽
✹✳✶ ❊①❡♠♣❧♦ ❞❡ ❞❛❞♦s s✐♠✉❧❛❞♦s ❝♦♠ ❞✐❢❡r❡♥t❡s ♥í✈❡✐s ❞❡ r✉í❞♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹ ✹✳✷ ▼♦♥t❛❣❡♠ ❞❡ ✉♠ ❧❛s❡r s❝❛♥♥❡r✱ ❥✉♥t♦ ❝♦♠ ✉♠❛ ✉♥✐❞❛❞❡ ❞❡ ♣❛♥✲t✐❧t ❡ ✉♠❛
❝❡♥tr❛❧ ✐♥❡r❝✐❛❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻ ✹✳✸ ▼♦♥t❛❣❡♠ ❞❡ ✉♠ ❧❛s❡r s❝❛♥♥❡r ✷❉ s♦❜r❡ ✉♠ r♦❜ô ♠ó✈❡❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✼
✺✳✶ ❊①❡♠♣❧♦ ❞❡ ❞❡t❡❝çã♦ ❞❡ ♠✉❞❛♥ç❛s ❡♠ ❞❛❞♦s s✐♠✉❧❛❞♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✶ ✺✳✷ ❉✐❢❡r❡♥ç❛ ♥❛ ❞❡t❡r♠✐♥❛çã♦ ❞♦ ♥ú♠❡r♦ ❞❡ ●❛✉ss✐❛♥❛s ♣❛r❛ ♦ ❛❣r✉♣❛♠❡♥t♦
♣♦r ●▼▼ ❡♠ ❞❛❞♦s ❝♦♠ ❡ s❡♠ s✐♠♣❧✐✜❝❛çã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✷ ✺✳✸ Pr♦❜❛❜✐❧✐❞❛❞❡ ❞❡ ❝❛❞❛ ♣♦♥t♦ ♣❡rt❡♥❝❡r à ●❛✉ss✐❛♥❛ ♠♦str❛❞❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✷
✺✳✹ ❉❡t❡❝çã♦ ❞❡ ♠✉❞❛♥ç❛s ❡♠ ❞❛❞♦s r❡❛✐s ✲ ❈♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s ✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✸ ✺✳✺ ❉❡t❡❝çã♦ ❞❡ ♠✉❞❛♥ç❛s ❡♠ ❞❛❞♦s r❡❛✐s ✲ ❈♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s ✷✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✹ ✺✳✻ ❉❡t❡❝çã♦ ❞❡ ♠✉❞❛♥ç❛s ❡♠ ❞❛❞♦s r❡❛✐s ✲ ❈♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s ✸✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✺ ✺✳✼ ❉❡t❡❝çã♦ ❞❡ ♠✉❞❛♥ç❛s ❡♠ ❞❛❞♦s r❡❛✐s ✲ ❈♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s ✹✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✼ ✺✳✽ ❉❡t❡❝çã♦ ❞❡ ♠✉❞❛♥ç❛s ❡♠ ❞❛❞♦s ❝♦♠♣❧❡t♦s ✲ ❈♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s ✹✳ ✳ ✳ ✳ ✳ ✽✽ ✺✳✾ ❉❡t❡❝çã♦ ❞❡ ♠✉❞❛♥ç❛s ❡♠ ❞❛❞♦s r❡❛✐s ✲ ❈♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s ✺✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✾ ✺✳✶✵ ❉❡t❡❝çã♦ ❞❡ ♠✉❞❛♥ç❛s ❡♠ ❞❛❞♦s ❝♦♠♣❧❡t♦s ✲ ❈♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s ✺✳ ✳ ✳ ✳ ✳ ✾✵ ✺✳✶✶ ❉❡t❡❝çã♦ ❞❡ ♠✉❞❛♥ç❛s ❡♠ ❞❛❞♦s r❡❛✐s ✲ ❈♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s ✻✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✶ ✺✳✶✷ ❉❡t❡❝çã♦ ❞❡ ♠✉❞❛♥ç❛s ❡♠ ❞❛❞♦s ❝♦♠♣❧❡t♦s ✲ ❈♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s ✻✳ ✳ ✳ ✳ ✳ ✾✷ ✺✳✶✸ ❆♥á❧✐s❡ ❝♦♠♣❛r❛t✐✈❛ ❞❡ r❡❝✉♣❡r❛çã♦ ❞❡ ❢♦r♠❛s ❜ás✐❝❛s ♣❛r❛ ❞❛❞♦s s✐♠✉❧❛❞♦s✳ ✾✻ ✺✳✶✹ ❘❡❝✉♣❡r❛çã♦ ❞❡ ❢♦r♠❛s ❜ás✐❝❛s ✉t✐❧✐③❛♥❞♦ ♦ ❡s♣❛ç♦ ❞❡ ●❛✉ss✐❛♥❛s ❡ ♦ ❡s♣❛ç♦
❊✉❝❧✐❞✐❛♥♦✱ ✐❧✉str❛♥❞♦ ❛ r❡❛♠♦str❛❣❡♠ ❡ ♠ét♦❞♦ ✐t❡r❛t✐✈♦ ❡♠ ❞❛❞♦s s✐♠✉❧❛❞♦s✳ ✾✼ ✺✳✶✺ ❆♥á❧✐s❡ ❝♦♠♣❛r❛t✐✈❛ ❞❡ r❡❝✉♣❡r❛çã♦ ❞❡ ✉♠❛ ♠✉❞❛♥ç❛ ❝♦♠♣♦st❛ ❞❡ ❞✉❛s
❢♦r♠❛s ❜ás✐❝❛s ✉s❛♥❞♦ ❞❛❞♦s s✐♠✉❧❛❞♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✽ ✺✳✶✻ ❆♥á❧✐s❡ ❝♦♠♣❛r❛t✐✈❛ ❞❡ r❡❝✉♣❡r❛çã♦ ❞❡ ❢♦r♠❛s ❜ás✐❝❛s ❡♠ ❞❛❞♦s r❡❛✐s ✳ ✳ ✳ ✾✾ ✺✳✶✼ ❘❡❝✉♣❡r❛çã♦ ❞❡ ❢♦r♠❛s ✉t✐❧✐③❛♥❞♦ s✉♣❡rq✉á❞r✐❝❛s ❡♠ ❞❛❞♦s s✐♠✉❧❛❞♦s✳ ✳ ✳ ✶✵✶ ✺✳✶✽ ❘❡❝✉♣❡r❛çã♦ ❞❡ ❢♦r♠❛s ✉t✐❧✐③❛♥❞♦ s✉♣❡rq✉á❞r✐❝❛s ❡♠ ❞❛❞♦s r❡❛✐s ✲ ❈♦♥❥✉♥t♦
❞❡ ❞❛❞♦s ✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✷ ✺✳✶✾ ❘❡❝✉♣❡r❛çã♦ ❞❡ ❢♦r♠❛s ✉t✐❧✐③❛♥❞♦ s✉♣❡rq✉á❞r✐❝❛s ❡♠ ❞❛❞♦s r❡❛✐s ✲ ❈♦♥❥✉♥t♦
❞❡ ❞❛❞♦s ✸ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✸ ✺✳✷✵ ❘❡❝✉♣❡r❛çã♦ ❞❡ ❢♦r♠❛s ✉t✐❧✐③❛♥❞♦ s✉♣❡rq✉á❞r✐❝❛s ❡♠ ❞❛❞♦s r❡❛✐s ✲ ❈♦♥❥✉♥t♦
❞❡ ❞❛❞♦s ✹ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✹ ✺✳✷✶ ❘❡❝✉♣❡r❛çã♦ ❞❡ ❢♦r♠❛s ✉t✐❧✐③❛♥❞♦ s✉♣❡rq✉á❞r✐❝❛s ❡♠ ❞❛❞♦s r❡❛✐s ✲ ❈♦♥❥✉♥t♦
❞❡ ❞❛❞♦s ✺✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✺ ✺✳✷✷ ❘❡❝✉♣❡r❛çã♦ ❞❡ ❢♦r♠❛s ✉t✐❧✐③❛♥❞♦ s✉♣❡rq✉á❞r✐❝❛s ❡♠ ❞❛❞♦s r❡❛✐s ✲ ❈♦♥❥✉♥t♦
❞❡ ❞❛❞♦s ✻✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✻
❆✳✶ ❉✐❛❣r❛♠❛ ❞❡ ♠ó❞✉❧♦s ❞♦ ♣r♦❥❡t♦ ■❘P❙✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✽ ❆✳✷ ❆❜♦r❞❛❣❡♠ ❞❡ ❙▲❆▼ ❤í❜r✐❞❛ ✉t✐❧✐③❛❞❛ ♥♦ ♣r♦❥❡t♦ ■❘P❙✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✽ ❆✳✸ ▼❛♣❛s ✸❉ ♦❜t✐❞♦s ❛ ♣❛rt✐r ❞❛ ❛❜♦r❞❛❣❡♠ ❞♦ ♣r♦❥❡t♦ ■❘P❙✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✾ ❆✳✹ ■♠❛❣❡♥s r❡❛✐s ❞♦s ❛♠❜✐❡♥t❡s ❞♦s ♠❛♣❛s ✸❉ ❞❛ ❋✐❣✉r❛ ❆✳✸✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✾ ❆✳✺ ❆r❝❛❜♦✉ç♦ ❡①♣❡r✐♠❡♥t❛❧ ❞♦ ♣r♦❥❡t♦ ■❘P❙✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✵ ❆✳✻ ❊str✉t✉r❛ ❜ás✐❝❛ ❞♦ ❈❛r♠❡♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✵
▲✐st❛ ❞❡ ❚❛❜❡❧❛s
✷✳✶ ❚r❛❜❛❧❤♦s ❡♠ s✐♠♣❧✐✜❝❛çã♦ ❞❡ ♥✉✈❡♠ ❞❡ ♣♦♥t♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹ ✷✳✷ ❚r❛❜❛❧❤♦s ❡♠ ❞❡t❡❝çã♦ ❞❡ ♠✉❞❛♥ç❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✷✳✸ ❚r❛❜❛❧❤♦s ❡♠ r❡❝✉♣❡r❛çã♦ ❞❡ ❢♦r♠❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹
✺✳✶ ❆♥á❧✐s❡ ❝♦♠♣❛r❛t✐✈❛ ❞❡ ❞❡t❡❝çã♦ ❞❡ ♠✉❞❛♥ç❛ ❝♦♠ s✐♠♣❧✐✜❝❛çã♦ ❞❛ ♥✉✈❡♠ ❞❡ ♣♦♥t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✻ ✺✳✷ ❆♥á❧✐s❡ ❝♦♠♣❛r❛t✐✈❛ ❡♥tr❡ ❛❧❣♦r✐t♠♦s ❞❡ r❡❝✉♣❡r❛çã♦ ❞❡ ❢♦r♠❛s ❜ás✐❝❛s ❡♠
❞❛❞♦s s✐♠✉❧❛❞♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✹ ✺✳✸ ❆♥á❧✐s❡ ❝♦♠♣❛r❛t✐✈❛ ❡♥tr❡ ❛❧❣♦r✐t♠♦s ❞❡ r❡❝✉♣❡r❛çã♦ ❞❡ ❢♦r♠❛s ❜ás✐❝❛s ❡♠
❞❛❞♦s r❡❛✐s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✵
❙✉♠ár✐♦
❆❣r❛❞❡❝✐♠❡♥t♦s ✈✐✐
❘❡s✉♠♦ ①✐
❆❜str❛❝t ①✐✐✐
▲✐st❛ ❞❡ ❋✐❣✉r❛s ①✈
▲✐st❛ ❞❡ ❚❛❜❡❧❛s ①✐①
▲✐st❛ ❞❡ ❆❧❣♦r✐t♠♦s ①①✈
▲✐st❛ ❞❡ ❆❜r❡✈✐❛çõ❡s ①①✈✐✐
▲✐st❛ ❞❡ ❙í♠❜♦❧♦s ①①✐①
✶ ■♥tr♦❞✉çã♦ ✶
✶✳✶ ❉❡✜♥✐çã♦ ❞♦ Pr♦❜❧❡♠❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶ ✶✳✷ ▼♦t✐✈❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷ ✶✳✸ ❈♦♥tr✐❜✉✐çõ❡s ❞♦ ❚r❛❜❛❧❤♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺ ✶✳✹ ❖r❣❛♥✐③❛çã♦ ❞♦ ❚❡①t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺
✷ ❚r❛❜❛❧❤♦s ❘❡❧❛❝✐♦♥❛❞♦s ✼
✷✳✶ ❙✐♠♣❧✐✜❝❛çã♦ ❞❡ ◆✉✈❡♠ ❞❡ P♦♥t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼ ✷✳✶✳✶ ❘❡s✉♠♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸ ✷✳✷ ❉❡t❡❝çã♦ ❞❡ ▼✉❞❛♥ç❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹ ✷✳✷✳✶ ❚é❝♥✐❝❛s ❞❡ ❉❡t❡❝çã♦ ❞❡ ▼✉❞❛♥ç❛s ❡♠ ❱✐sã♦ ❈♦♠♣✉t❛❝✐♦♥❛❧ ✳ ✳ ✶✺ ✷✳✷✳✷ ❚é❝♥✐❝❛s ❞❡ ❉❡t❡❝çã♦ ❞❡ ▼✉❞❛♥ç❛s ❡♠ ❋♦t♦❣r❛♠❡tr✐❛ ❡ ❙❡♥s♦r✐✲
❛♠❡♥t♦ ❘❡♠♦t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼ ✷✳✷✳✸ ❚é❝♥✐❝❛s ❞❡ ❉❡t❡❝çã♦ ❞❡ ▼✉❞❛♥ç❛s ❡♠ ❘♦❜ót✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵
✷✳✷✳✹ ❘❡s✉♠♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✷✳✸ ❘❡❝✉♣❡r❛çã♦ ❞❡ ❋♦r♠❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✷✳✸✳✶ ❋♦r♠❛s ❇ás✐❝❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✷✳✸✳✷ ❙✉♣❡rq✉á❞r✐❝❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾ ✷✳✸✳✸ ❘❡s✉♠♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹
✸ ▼❡t♦❞♦❧♦❣✐❛ ✸✺
✸✳✶ ❱✐sã♦ ●❡r❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✸✳✷ ❙✐♠♣❧✐✜❝❛çã♦ ❞❛ ◆✉✈❡♠ ❞❡ P♦♥t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✸✳✷✳✶ ❈♦♥❝❡✐t♦s ❇ás✐❝♦s ♣❛r❛ ❙✐♠♣❧✐✜❝❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✸✳✷✳✷ ❆❧❣♦r✐t♠♦ ❞❡ ❆❣r✉♣❛♠❡♥t♦ ❍✐❡rárq✉✐❝♦ ❝♦♠ ❘❡♣r❡s❡♥t❛çã♦
▼✉❧t✐✲❊s❝❛❧❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✸✳✷✳✸ ❘❡♠♦çã♦ ❞♦ ❙♦❧♦ ❡ ❞❡ ❖✉t❧✐❡rs ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹ ✸✳✸ ❉❡t❡❝çã♦ ❞❡ ▼✉❞❛♥ç❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻ ✸✳✸✳✶ ▼♦❞❡❧♦s ❞❡ ▼✐st✉r❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼ ✸✳✸✳✷ ❊❛rt❤ ▼♦✈❡r✬s ❉✐st❛♥❝❡ ✭❊▼❉✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺ ✸✳✸✳✸ ❆❧❣♦r✐t♠♦ ♣❛r❛ ❉❡t❡❝çã♦ ❡ ❙❡❣♠❡♥t❛çã♦ ❞❡ ▼✉❞❛♥ç❛s ✳ ✳ ✳ ✳ ✳ ✺✽ ✸✳✹ ❘❡❝✉♣❡r❛çã♦ ❞❡ ❋♦r♠❛s ✸❉ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ✸✳✹✳✶ ▼♦❞❡❧❛❣❡♠ ❯t✐❧✐③❛♥❞♦ ❋♦r♠❛s ❇ás✐❝❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵ ✸✳✹✳✷ ▼♦❞❡❧❛❣❡♠ ❯t✐❧✐③❛♥❞♦ ❙✉♣❡rq✉á❞r✐❝❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻
✹ ❆r❝❛❜♦✉ç♦ ❊①♣❡r✐♠❡♥t❛❧ ✼✸
✹✳✶ ❊①♣❡r✐♠❡♥t♦s ❯s❛♥❞♦ ❙✐♠✉❧❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸ ✹✳✷ ❊①♣❡r✐♠❡♥t♦s ❯s❛♥❞♦ ❉❛❞♦s ❘❡❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹ ✹✳✷✳✶ ▼♦♥t❛❣❡♠ ❊stát✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹ ✹✳✷✳✷ ▼♦♥t❛❣❡♠ ❉✐♥â♠✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻ ✹✳✸ ▼ó❞✉❧♦ ❞❡ ❙♦❢t✇❛r❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✼
✺ ❘❡s✉❧t❛❞♦s ✼✾
✺✳✶ ❉❡t❡❝çã♦ ❞❡ ▼✉❞❛♥ç❛s ❝♦♠ ❙✐♠♣❧✐✜❝❛çã♦ ❞❛ ◆✉✈❡♠ ❞❡ P♦♥t♦s ✳ ✳ ✳ ✳ ✳ ✼✾ ✺✳✷ ❘❡❝✉♣❡r❛çã♦ ❞❡ ❋♦r♠❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✸ ✺✳✷✳✶ ❋♦r♠❛s ❇ás✐❝❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✸ ✺✳✷✳✷ ❙✉♣❡rq✉á❞r✐❝❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✾
✻ ❈♦♥❝❧✉sõ❡s ✶✵✼
✻✳✶ ❉✐s❝✉ssã♦ ❞♦s ❘❡s✉❧t❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✼ ✻✳✷ ❉✐r❡çõ❡s ❋✉t✉r❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✾ ✻✳✸ P✉❜❧✐❝❛çõ❡s ❘❡❧❡✈❛♥t❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✶
❘❡❢❡rê♥❝✐❛s ❇✐❜❧✐♦❣rá✜❝❛s ✶✶✸
❆ Pr♦❥❡t♦ ■❘P❙ ✶✷✼
▲✐st❛ ❞❡ ❆❧❣♦r✐t♠♦s
✶ ❈❛❧❝✉❧❛ ❘❡❝✉rs✐✈❛♠❡♥t❡ ♦ ❆❧❣♦r✐t♠♦ ❞❡ ❆❣r✉♣❛♠❡♥t♦ ❍✐❡rárq✉✐❝♦ ✲
Calcula❴Arvore(Agrupamento A) ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸
✷ ❈❛❧❝✉❧❛ ▼✐st✉r❛ ●❛✉ss✐❛♥❛ ❞❛ ◆✉✈❡♠ ❞❡ P♦♥t♦s ❙✐♠♣❧✐✜❝❛❞❛ ✲
Calcula❴GM M(N uvem Simplif icada Y, Inteiro K0) ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺
✸ ❆❧❣♦r✐t♠♦ ♣❛r❛ ❙❡❧❡çã♦ ❞❡ ▼✉❞❛♥ç❛s ✲
Calcula❴M udanca(Conjuntos γ, θ)✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵
✹ ❆❧❣♦r✐t♠♦ ♣❛r❛ ❘❡❝✉♣❡r❛çã♦ ❞❡ ❋♦r♠❛s ❇ás✐❝❛s ♥♦ ❊s♣❛ç♦ ❊✉❝❧✐❞✐❛♥♦ ✳ ✻✹ ✺ ❆❧❣♦r✐t♠♦ ♣❛r❛ ❘❡❝✉♣❡r❛çã♦ ❞❡ ❋♦r♠❛s ❇ás✐❝❛s ♥♦ ❊s♣❛ç♦ ❞❡ ●❛✉ss✐❛♥❛s ✻✹
▲✐st❛ ❞❡ ❆❜r❡✈✐❛çõ❡s
✸❉✲◆❉❚ ✸❉ ◆♦r♠❛❧ ❉✐str✐❜✉t✐♦♥ ❚r❛♥s❢♦r♠ ❈❆❉ ❈♦♠♣✉t❡r✲❆✐❞❡❞ ❉❡s✐❣♥
❈❛r♠❡♥ ❈❛r♥❡❣✐❡ ▼❡❧❧♦♥ ❘♦❜♦t ◆❛✈✐❣❛t✐♦♥ ❚♦♦❧❦✐t ❉❋❚ ❉✐s❝r❡t❡ ❋♦✉r✐❡r ❚r❛♥s❢♦r♠
❉❙❖ ❉✐s❝r❡t❡ ❙❤❛♣❡ ❖♣❡r❛t♦r ❊❑❋ ❊①t❡♥❞❡❞ ❑❛❧♠❛♥ ❋✐❧t❡r ❊▼ ❊①♣❡❝t❛t✐♦♥✲▼❛①✐♠✐③❛t✐♦♥ ❊▼❉ ❊❛rt❤ ▼♦✈❡r✬s ❉✐st❛♥❝❡
❋❛st❋P❙ ❋❛st ▼❛r❝❤✐♥❣ ❋❛rt❤❡st P♦✐♥t ❙❛♠♣❧✐♥❣ ●▼▼ ●❛✉ss✐❛♥ ▼✐①t✉r❡ ▼♦❞❡❧
●P❙ ●❧♦❜❛❧ P♦s✐t✐♦♥✐♥❣ ❙②st❡♠ ●P❯ ●r❛♣❤✐❝s Pr♦❝❡ss✐♥❣ ❯♥✐t ●❲❘ ●r♦✇ ❲❤❡♥ ❘❡q✉✐r❡❞
❍❙❖▼ ❍❛❜✐t✉❛t✐♥❣ ❙❡❧❢✲❖r❣❛♥✐③✐♥❣ ▼❛♣s ■❈P ■t❡r❛t✐✈❡ ❈❧♦s❡st P♦✐♥t
■■❚❉ ■♥t❡❣r❛t✐♦♥ ♦❢ ■♥t❡♥s✐t② ❛♥❞ ❚❡①t✉r❡ ❉✐✛❡r❡♥❝❡s ■P❈ ■♥t❡r✲Pr♦❝❡ss✲❈♦♠♠✉♥✐❝❛t✐♦♥
■❘P❙ ■♥t❡❧❧✐❣❡♥t ❘♦❜♦t✐❝ P♦rt❡r ❙②st❡♠ ▲❆❉ ▲♦❝❛❧ ❆✈❡r❛❣❡ ♦❢ ❉✐✛❡r❡♥❝❡s ▲❘❋ ▲❛s❡r ❘❛♥❣❡r ❋✐♥❞❡r
▲❙❆❉ ▲♦❝❛❧ ❙✉♠ ♦❢ ❆❜s♦❧✉t❡ ❉✐✛❡r❡♥❝❡s ▲❙❙❉ ▲♦❝❛❧ ❙✉♠ ♦❢ ❙q✉❛r❡❞ ❉✐✛❡r❡♥❝❡s ▲❱◗ ▲❡❛r♥✐♥❣ ❱❡❝t♦r ◗✉❛♥t✐③❛t✐♦♥ ▼❊▼❙ ▼✐❝r♦✲❊❧❡❝tr♦✲▼❡❝❤❛♥✐❝❛❧ ❙②st❡♠s ▼▲ ▼❛①✐♠✉♠ ▲✐❦❡❧✐❤♦♦❞
▼❉▲ ▼✐♥✐♠✉♠ ❉❡s❝r✐♣t✐♦♥ ▲❡♥❣t❤ ▼▲❙ ▼♦✈✐♥❣ ▲❡❛st ❙q✉❛r❡s
▼❙❚ ▼✐♥✐♠✉♠ ❙♣❛♥♥✐♥❣ ❚r❡❡
❖❇❇ ❖r✐❡♥t❡❞ ❇♦✉♥❞❛r② ❇♦① P❈❆ Pr✐♥❝✐♣❛❧ ❈♦♠♣♦♥❡♥t ❆♥❛❧②s✐s P❉❋ Pr♦❜❛❜✐❧✐t② ❉❡♥s✐t② ❋✉♥❝t✐♦♥ ❘❆◆❙❆❈ ❘❛♥❞♦♠ ❙❛♠♣❧❡ ❈♦♥s❡♥s✉s ❘▼❙ ❘♦♦t ▼❡❛♥ ❙q✉❛r❡
❙■❋❚ ❙❝❛❧❡✲■♥✈❛r✐❛♥t ❋❡❛t✉r❡ ❚r❛♥s❢♦r♠ ❙▲❆▼ ❙✐♠✉❧t❛♥❡♦✉s ▲♦❝❛❧✐③❛t✐♦♥ ❛♥❞ ▼❛♣♣✐♥❣ ❙❖▼ ❙❡❧❢✲❖r❣❛♥✐③✐♥❣ ▼❛♣
❙◗ ❙✉♣❡rq✉á❞r✐❝❛s
❚❑▼ ❚❡♠♣♦r❛❧ ❑♦❤♦♥❡♥ ▼❛♣
❯❋▼● ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ▼✐♥❛s ●❡r❛✐s
❱❡❘▲❛❜ ▲❛❜♦r❛tór✐♦ ❞❡ ❱✐sã♦ ❈♦♠♣✉t❛❝✐♦♥❛❧ ❡ ❘♦❜ót✐❝❛
▲✐st❛ ❞❡ ❙í♠❜♦❧♦s
α ❈♦♥st❛♥t❡ ✉t✐❧✐③❛❞❛ ♥♦ ♣r♦❝❡ss♦ ❞❡ r❡♠♦çã♦ ❞❡ ♦✉t❧✐❡rs
γ ▼✐st✉r❛ ●❛✉ss✐❛♥❛✱ r❡♣r❡s❡♥t❛♥❞♦ ♦ ❝♦♥❥✉♥t♦ ❞❡ ♣❡s♦s ❡ ●❛✉ss✐❛♥❛s
∆ ❈♦♥❥✉♥t♦ ❞❡ ♠❛tr✐③❡s ❞❡ tr❛♥s❢♦r♠❛çã♦
ǫ ❋❛t♦r ❞❡ ❢♦r♠❛ ❞❛ s✉♣❡rq✉á❞r✐❝❛
λ ❈♦♥❥✉♥t♦ ❞❡ ❛✉t♦✈❛❧♦r❡s ❞❡ ✉♠❛ ♠❛tr✐③
Λ P❛râ♠❡tr♦s ❞❡ ✉♠❛ s✉♣❡rq✉á❞r✐❝❛
θ ❖✉tr❛ ❢♦r♠❛ ❞❡ r❡♣r❡s❡♥t❛r ♠✐st✉r❛s ●❛✉ss✐❛♥❛ ✭❝♦♠♦ γ✮ θk ●❛✉ss✐❛♥❛✱ r❡♣r❡s❡♥t❛❞❛ ♣❡❧❛ ♠é❞✐❛ ❡ ❞❡s✈✐♦ ♣❛❞rã♦
θi ▼✐st✉r❛ ●❛✉ss✐❛♥❛ ♥❛ ✐t❡r❛çã♦ i
θ∗ ▼✐st✉r❛ ●❛✉ss✐❛♥❛ ót✐♠❛
θ∗
(l,m) ▼✐st✉r❛ ●❛✉ss✐❛♥❛ ót✐♠❛ ❝♦♠ r❡str✐çã♦ ❞❡ ✉♠❛ ✉♥✐ã♦ ❡♥tr❡ ●❛✉ss✐❛♥❛s
ϑ ➶♥❣✉❧♦ ❞❡ ❣✉✐♥❛❞❛ ✭②❛✇✮
µ ▼é❞✐❛ ❞❡ ✉♠❛ ❞✐str✐❜✉✐çã♦ ●❛✉ss✐❛♥❛N
µk ▼é❞✐❛ ❡st✐♠❛❞♦ ♥♦ ▼✲❙t❡♣ ♣❛r❛ ❛ ●❛✉ss✐❛♥❛ k
π P❡s♦ ❞❡ ✉♠❛ ❞✐str✐❜✉✐çã♦ ●❛✉ss✐❛♥❛ ❛ss♦❝✐❛❞❛ ❛ ✉♠❛ ♠✐st✉r❛ ●❛✉ss✐❛♥❛ πk P❡s♦ ❡st✐♠❛❞♦ ♥♦ ▼✲❙t❡♣ ♣❛r❛ ❛ ●❛✉ss✐❛♥❛ k
Π P❡r♠✉t❛çã♦ ❞♦ ♣♦♥t♦ p ❝♦♠ t♦❞♦s ♦✉tr♦s ♣♦♥t♦s ❞❛ ♥✉✈❡♠ σ ❉❡s✈✐♦ ♣❛❞rã♦ r❡❧❛t✐✈♦ ❛ ✉♠ ❞❛❞♦ ❛❣r✉♣❛♠❡♥t♦ ❞❡ ❝♦✈❛r✐â♥❝✐❛C σk(pj) ❱❛r✐❛çã♦ ❞❛ s✉♣❡r❢í❝✐❡ ❞❛ ✈✐③✐♥❤❛♥ç❛ ❞♦ ♣♦♥t♦pj
σmax ▼á①✐♠❛ ✈❛r✐❛çã♦ ❞❛ s✉♣❡r❢í❝✐❡ t♦❧❡r❛❞❛
Σ ▼❛tr✐③ ❞❡ ❝♦✈❛r✐â♥❝✐❛ ❞❛ ✉♠❛ ❞✐str✐❜✉✐çã♦ ●❛✉ss✐❛♥❛N
Σk ❈♦✈❛r✐â♥❝✐❛ ❡st✐♠❛❞❛ ♥♦ ▼✲❙t❡♣ ♣❛r❛ ❛ ●❛✉ss✐❛♥❛ k
ϕ ➶♥❣✉❧♦ ❞❡ ❛r❢❛❣❡♠ ✭♣✐t❝❤✮ ψ ➶♥❣✉❧♦ ❞❡ r♦❧❛♠❡♥t♦ ✭r♦❧❧✮
Ψ ❈♦♥❥✉♥t♦ ❞❡ ♣r✐♠✐t✐✈❛s ❞❡ ❢♦r♠❛
a ❋❛t♦r ❞❡ ❡s❝❛❧❛ ❞❛ s✉♣❡rq✉á❞r✐❝❛ c ❋✉♥çã♦ ❝♦ss❡♥♦ s✐♠♣❧✐✜❝❛❞❛
C ❈♦♥❥✉♥t♦s ❞❡ ♣♦♥t♦s q✉❡ r❡♣r❡s❡♥t❛♠ ❛s ♠✉❞❛♥ç❛s s❡❣♠❡♥t❛❞❛s
C ▼❛tr✐③ ❞❡ ❝♦✈❛r✐â♥❝✐❛ ❞❛ ❦✲✈✐③✐♥❤❛♥ç❛ ❞❡ ♣
dij ▼étr✐❝❛ ❞❡ ❞✐stâ♥❝✐❛ ❡♥tr❡ ❞♦✐s ♣♦♥t♦s i ❡j
dGM M ❉✐stâ♥❝✐❛ ❡♥tr❡ ❞✉❛s ♠✐st✉r❛s ●❛✉ss✐❛♥❛s
E ▼❛tr✐③ ❞❡ ❢❛t♦r❡s ❞❡ ❡s❝❛❧❛
I ▼❛tr✐③ ❞❡ ♠♦♠❡♥t♦s ❝❡♥tr❛✐s ❞❡ ✉♠❛ s✉♣❡rq✉á❞r✐❝❛
K ❚❛♠❛♥❤♦ ❞❡ ✉♠❛ ▼✐st✉r❛ ●❛✉ss✐❛♥❛
L ❈♦♥st❛♥t❡ r❡❛❧ ✉t✐❧✐③❛❞❛ ♣❛r❛ ❡st✐♠❛çã♦ ❞♦s ♣❛râ♠❡tr♦s ❞♦ ♠♦❞❡❧♦ M ❉✐♠❡♥s✐♦♥❛❧✐❞❛❞❡ ❞♦s ❞❛❞♦s
npj ❱❡t♦r ♥♦r♠❛❧ ❛♦ ♣♦♥t♦pj ❡ à ✈✐③✐♥❤❛♥ç❛N
k pj
N ◆ú♠❡r♦ ❞❡ ♣♦♥t♦s ❞❡ ✉♠❛ ♥✉✈❡♠ ❞❡ ♣♦♥t♦s ♦✉ ❝❛r❞✐♥❛❧✐❞❛❞❡ ❞♦s ❞❛❞♦s ✐♥❞❡✲
♣❡♥❞❡♥t❡s
Nk
pj ❈♦♥❥✉♥t♦ ❞❡ í♥❞✐❝❡s ❞♦sk✲✈✐③✐♥❤♦s ❞♦ ♣♦♥t♦ pj ♥❛ ♥✉✈❡♠ ❞❡ ♣♦♥t♦s P
Nk P❛râ♠❡tr♦ ❞❡ ♥♦r♠❛❧✐③❛çã♦ ❡st✐♠❛❞♦ ♥♦ ▼✲❙t❡♣ ♣❛r❛ ❛ ●❛✉ss✐❛♥❛k N ❉✐str✐❜✉✐çã♦ ♥♦r♠❛❧ ♠✉❧t✐✈❛r✐á✈❡❧ ♦✉ ●❛✉ss✐❛♥❛
pi P♦♥t♦ ❝♦♠ í♥❞✐❝❡ i ❞❛ ♥✉✈❡♠ ❞❡ ♣♦♥t♦sP
pj P♦♥t♦ ❝♦♠ í♥❞✐❝❡ j ❞❛ ♥✉✈❡♠ ❞❡ ♣♦♥t♦sP
px P♦s✐çã♦ ❞♦ ❝❡♥tr♦ ❞❛ s✉♣❡rq✉á❞r✐❝❛ ♥♦ ❡✐①♦x
py P♦s✐çã♦ ❞♦ ❝❡♥tr♦ ❞❛ s✉♣❡rq✉á❞r✐❝❛ ♥♦ ❡✐①♦y
pz P♦s✐çã♦ ❞♦ ❝❡♥tr♦ ❞❛ s✉♣❡rq✉á❞r✐❝❛ ♥♦ ❡✐①♦z
pj ❈❡♥tró✐❞❡ ❞❛ ✈✐③✐♥❤❛♥ç❛ ❞❡ pj
P ◆✉✈❡♠ ❞❡ ♣♦♥t♦s ❝♦♠ t❛♠❛♥❤♦N ❡♠ R3
|P|max ❚❛♠❛♥❤♦ ♠á①✐♠♦ ❞❛ ♥✉✈❡♠ ❞❡ ♣♦♥t♦s P rk
pj ❘❛✐♦ ♠á①✐♠♦ ❢♦r♠❛❞♦ ♣❡❧♦s ❦✲✈✐③✐♥❤♦s ❞❡ pj
R ▼❛tr✐③ ❞❡ r♦t❛çã♦
s ❋✉♥çã♦ s❡♥♦ s✐♠♣❧✐✜❝❛❞❛
S ❖✉tr❛ ❢♦r♠❛ ❞❡ r❡♣r❡s❡♥t❛r ✉♠❛ ♥✉✈❡♠ ❞❡ ♣♦♥t♦s ❞❡ t❛♠❛♥❤♦N ✭❝♦♠♦ P✮ Sizep ◆ú♠❡r♦ ❞❡ ♣♦♥t♦s ❞❡s❡❥❛❞♦s ♥❛ ❛♠♦str❛
T ▼❛tr✐③ ❞❡ tr❛♥s❢♦r♠❛çã♦
T(x) P❧❛♥♦ ❚❛♥❣❡♥t❡ ❛ ❙✉♣❡r❢í❝✐❡ ❢♦r♠❛❞❛ ♣❡❧♦s ❛✉t♦✈❡t♦rv1 ❡v2
T r(Σ✮ ❚r❛ç♦ ❞❛ ♠❛tr✐③ ❞❡ ❝♦✈❛r✐â♥❝✐❛
Uth ▲✐♠✐❛r ♣❛r❛ ❞❡t❡r♠✐♥❛çã♦ ❞❡ ♠✉❞❛♥ç❛
v ❈♦♥❥✉♥t♦ ❞❡ ❛✉t♦✈❡t♦r❡s ❞❡ ✉♠❛ ♠❛tr✐③
X ❱❛r✐á✈❡❧ ❛❧❡❛tór✐❛
Y ❉❛❞♦s ✐♥❞❡♣❡♥❞❡♥t❡s✱ ♦✉ ❞❛❞♦s ❞❡ ❡♥tr❛❞❛
Zmax ❈♦♥st❛♥t❡ ✉t✐❧✐③❛❞❛ ♥♦ ♣r♦❝❡ss♦ ❞❡ ❡❧✐♠✐♥❛çã♦ ❞♦ ♣❧❛♥♦ ❞♦ ❝❤ã♦
❈❛♣ít✉❧♦ ✶
■♥tr♦❞✉çã♦
◆❡st❡ ♣r✐♠❡✐r♦ ❝❛♣ít✉❧♦ s❡rá ❛♣r❡s❡♥t❛❞❛ ✉♠❛ ❞❡✜♥✐çã♦ ❞♦ ♣r♦❜❧❡♠❛ tr❛t❛❞♦ ♥♦ tr❛❜❛✲ ❧❤♦✱ ❜❡♠ ❝♦♠♦ ❛s ♠♦t✐✈❛çõ❡s ❡ ❝♦♥tr✐❜✉✐çõ❡s✳ P♦r ✜♠✱ ❛ ♦r❣❛♥✐③❛çã♦ ❣❡r❛❧ ❞♦ tr❛❜❛❧❤♦ é ♠♦str❛❞❛ ✈✐s❛♥❞♦ ✐♥tr♦❞✉③✐r ❛s ♣❛rt❡s q✉❡ ♦ ❝♦♠♣õ❡♠✳
✶✳✶ ❉❡✜♥✐çã♦ ❞♦ Pr♦❜❧❡♠❛
❖ ♣r♦❜❧❡♠❛ ❞✐s❝✉t✐❞♦ ♥❡st❡ tr❛❜❛❧❤♦ r❡❢❡r❡✲s❡ à ❞❡t❡❝çã♦ ❞❡ ♠✉❞❛♥ç❛s ❡♠ ♠❛♣❛s ✸❉ ✭❡♠ ✐♥❣❧ês✱ ❝❤❛♥❣❡ ❞❡t❡❝t✐♦♥ ♦✉ ♥♦✈❡❧t② ❞❡t❡❝t✐♦♥✮✱ ❥✉♥t❛♠❡♥t❡ ❝♦♠ ♦ r❡❝♦♥❤❡❝✐♠❡♥t♦ ❞❛ ❢♦r♠❛ ❞❡ss❛s ♠✉❞❛♥ç❛s✳ ❊ss❡s ♠❛♣❛s ♣♦❞❡♠ s❡r ♦❜t✐❞♦s ♣♦r ♠❡✐♦ ❞❡ ❞✐✈❡rs❛s té❝♥✐✲ ❝❛s ❡ ❝♦♥t❡r ❞✐❢❡r❡♥t❡s t✐♣♦s ❞❡ ✐♥❢♦r♠❛çã♦✳ ◆❡st❡ tr❛❜❛❧❤♦✱ ❝♦♥s✐❞❡r❛✲s❡ q✉❡ ✉♠ ♠❛♣❛ ❞♦ ❛♠❜✐❡♥t❡ ❥á ❢♦✐ ♦❜t✐❞♦ ❛ ♣r✐♦r✐ ❡ q✉❡ é ♣♦ssí✈❡❧ ♦❜t❡r ✉♠ ♥♦✈♦ ♠❛♣❛ ✉t✐❧✐③❛♥❞♦✱ ♣♦r ❡①❡♠♣❧♦✱ ✉♠ r♦❜ô ❞♦t❛❞♦ ❞❡ s❡♥s♦r❡s✳ ❊ss❡ ♥♦✈♦ ♠❛♣❛ ❞❡✈❡ ❝♦♥t❡r ✐♥❢♦r♠❛çõ❡s tr✐❞✐✲ ♠❡♥s✐♦♥❛✐s ♥❛ ❢♦r♠❛ ❞❡ ✉♠❛ ♥✉✈❡♠ ❞❡ ♣♦♥t♦s ✸❉✱ ♠❛s s❡♠ r❡str✐çã♦ ♥❛ t♦♣♦❧♦❣✐❛ ❞❡st❛ ✐♥❢♦r♠❛çã♦✱ ♦✉ s❡❥❛✱ ♦s ♣♦♥t♦s ♣♦❞❡♠ s❡r ❡s♣❛rs♦s ❡ ♥ã♦✲✉♥✐❢♦r♠❡♠❡♥t❡ ❞✐str✐❜✉í❞♦s✳
❖❜s❡r✈❛✲s❡ q✉❡ ✉♠ ♠❡s♠♦ ❝♦♥❥✉♥t♦ ❞❡ ♣♦♥t♦s ✸❉ ♣♦❞❡ r❡♣r❡s❡♥t❛r ✉♠❛ ✐♥✜♥✐✲ ❞❛❞❡ ❞❡ ♦❜❥❡t♦s ❞♦ ♠✉♥❞♦ r❡❛❧✳ ❙❡♥❞♦ ❛ss✐♠✱ ❛♣❡♥❛s ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ♣♦♥t♦s é ♣♦✉❝♦ ❡①♣r❡ss✐✈♦ ♣❛r❛ t❛✐s r❡♣r❡s❡♥t❛çõ❡s✳ P♦❞❡♠ s❡r ✉t✐❧✐③❛❞♦s ♠♦❞❡❧♦s ♥ã♦✲♣❛r❛♠étr✐❝♦s ✭❝♦♠♦ tr✐❛♥❣✉❧❛çã♦ ❡♥tr❡ ♣♦♥t♦s✮ ❡ ♣❛r❛♠étr✐❝♦s ♣❛r❛ ❡ss❛s r❡♣r❡s❡♥t❛çõ❡s✳ ❊♥tr❡ ♦✉✲ tr❛s ✈❛♥t❛❣❡♥s✱ ❡st❡s ú❧t✐♠♦s sã♦ út❡✐s ♣❡❧❛ ❢❛❝✐❧✐❞❛❞❡ ❞❡ r❡♣r❡s❡♥t❛çã♦ ❡ ✐♥❞❡①❛çã♦ ❡✱ t❛♠❜é♠✱ ♣❡❧❛ ❝♦♠♣❛❝t❛çã♦ ❞♦s ❞❛❞♦s✳
❆ss✐♠✱ ♦ ♣r♦❜❧❡♠❛ ♣♦❞❡ s❡r ❞❡s❝r✐t♦ ❝♦♠♦✿ ❉❛❞♦ ✉♠ ♣❛r ❞❡ ♠❛♣❛s ✸❉ ❞❡ ✉♠ ♠❡s♠♦ ❛♠❜✐❡♥t❡ ✭✉♠ ❞❡❧❡s ❝♦♥❤❡❝✐❞♦ ❛ ♣r✐♦r✐ ❡ ♦✉tr♦ r❡❝é♠ ♦❜t✐❞♦✮ ❡♠ ✉♠ ♠❡s♠♦ s✐s✲ t❡♠❛ ❞❡ ❝♦♦r❞❡♥❛❞❛s✱ ❞❡t❡r♠✐♥❛r ♣♦♥t♦s ✐♥s❡r✐❞♦s ♦✉ ❡①❝❧✉í❞♦s ✭♠✉❞❛♥ç❛s✮ ♥♦ ♠❛♣❛ ♦r✐❣✐♥❛❧ ❝♦♠ r♦❜✉st❡③ ❛ r✉í❞♦✱ ❡ s❡❣♠❡♥t❛r ❡ r❡❝♦♥❤❡❝❡r ❛ ❢♦r♠❛ ❝♦rr❡s♣♦♥❞❡♥t❡ ❛♦ ❝♦♥❥✉♥t♦ ❞❡ ♣♦♥t♦s ❡①❝❧✉í❞♦s ♦✉ ✐♥s❡r✐❞♦s✱ ❝♦♠ ❜❛s❡ ❡♠ ✉♠ ♠♦❞❡❧♦✳ ■♠♣õ❡♠✲s❡ r❡str✐✲
✷ ❈❛♣ít✉❧♦ ✶✳ ■♥tr♦❞✉çã♦
çõ❡s t❡♠♣♦r❛✐s ❛♦ s✐st❡♠❛✱ r❡str✐çõ❡s ❡ss❛s r❡❧❛❝✐♦♥❛❞❛s ❛♦ t❡♠♣♦ ♣❛r❛ ❛q✉✐s✐çã♦ ❞♦s ♠❛♣❛s✳
✶✳✷ ▼♦t✐✈❛çã♦
❖ ♣r♦❜❧❡♠❛ ❞❡ ❞❡t❡❝çã♦ ❞❡ ♠✉❞❛♥ç❛ ❡ r❡❝✉♣❡r❛çã♦ ❞❡ ❢♦r♠❛ t❡♠ ❞✐✈❡rs❛s ❛♣❧✐❝❛çõ❡s ✐♠♣♦rt❛♥t❡s ❡♠ ❞✐✈❡rs❛s ár❡❛s ❞❛ ❝✐ê♥❝✐❛✳ ❯♠❛ ár❡❛ ♠✉✐t♦ ✐♠♣♦rt❛♥t❡ é ❛ s❡❣✉r❛♥ç❛ ❡ ✈✐❣✐❧â♥❝✐❛✱ ♥❛ q✉❛❧ ♦ ✉s♦ ❞❡ s✐st❡♠❛s r❡♠♦t♦s sã♦ ❝❛❞❛ ✈❡③ ♠❛✐s ✉t✐❧✐③❛❞♦s✱ ♣r✐♥❝✐♣❛❧✲ ♠❡♥t❡ ❝♦♠ ✉s♦ ❞❡ ❝â♠❡r❛s ❞❡ ✈í❞❡♦✳ P♦ré♠✱ ❛ ✐❞❡♥t✐✜❝❛çã♦ ❡ ❝❧❛ss✐✜❝❛çã♦ ❛✐♥❞❛ sã♦ r❡❛❧✐③❛❞❛s✱ ❡ss❡♥❝✐❛❧♠❡♥t❡✱ ❞❡ ❢♦r♠❛ ♠❛♥✉❛❧✳ ❉❡✈✐❞♦ à ❣r❛♥❞❡ q✉❛♥t✐❞❛❞❡ ❞❡ ✐♥❢♦r♠❛✲ çã♦ ❢♦r♥❡❝✐❞❛ ♣♦r ❡ss❡s s✐st❡♠❛s✱ ❛ ❡✜❝✐ê♥❝✐❛ ✜❝❛ ❝♦♠♣r♦♠❡t✐❞❛✳ ❆ss✐♠✱ ❛ ✐❞❡♥t✐✜❝❛çã♦ ❛✉t♦♠át✐❝❛ ❞❡ ♠✉❞❛♥ç❛s ♣♦❞❡ ❞❛r ✉♠❛ ❛✉t♦♥♦♠✐❛ ♠❛✐♦r ❛ t❛✐s s✐st❡♠❛s✳
❆❧é♠ ❞✐ss♦✱ ❛ ❞❡t❡❝çã♦ ❞❡ ♠✉❞❛♥ç❛ é ❡①tr❡♠❛♠❡♥t❡ ✐♠♣♦rt❛♥t❡ ♥♦ ❝♦♥t❡①t♦ ❞❡ ❜✉s❝❛ ❡ s❛❧✈❛♠❡♥t♦✱ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ❡♠ ❧♦❝❛✐s ❞❡ ❞✐❢í❝✐❧ ❛❝❡ss♦ ♦✉ ♣❡r✐❣♦s♦s ❛♦s s❡r❡s ❤✉♠❛♥♦s✳ ❘♦❜ôs ♠ó✈❡✐s ❡stã♦ s❡♥❞♦ ❝❛❞❛ ✈❡③ ♠❛✐s ✉t✐❧✐③❛❞♦s ♣❛r❛ t❛✐s t❛r❡❢❛s✱ ♣♦ré♠✱ ❞❛r ♠❛✐♦r ❛✉t♦♥♦♠✐❛ ❛ t❛✐s r♦❜ôs ❛✐♥❞❛ é ✉♠ ♦❜❥❡t✐✈♦ ❛ s❡r ❛❧❝❛♥ç❛❞♦✳ ❈♦♥s✐❞❡r❛♥❞♦ ✉♠ ❝♦♥❤❡❝✐♠❡♥t♦ ♣ré✈✐♦ ❞♦ ❛♠❜✐❡♥t❡✱ ♣♦❞❡✲s❡ ✉t✐❧✐③❛r ❛ ❞❡t❡❝çã♦ ❞❡ ♠✉❞❛♥ç❛ ♣❛r❛ ❜✉s❝❛r ♦❜❥❡t♦s ♦✉ ♣❡ss♦❛s ❞❡ ✐♥t❡r❡ss❡ ♥♦ ❧♦❝❛❧✱ ❝♦♠♦ ♣♦r ❡①❡♠♣❧♦ s♦❜r❡✈✐✈❡♥t❡s ♦✉ ♦❜❥❡t♦s ❡♠ ✐♥❝ê♥❞✐♦s✱ ❜❡♠ ❝♦♠♦ ❞❡t❡r♠✐♥❛r ❛ ❣r❛✈✐❞❛❞❡ ❞❡ ✉♠ ❞❡s❛str❡✳ ❆ ❋✐❣✉r❛ ✶✳✶ ✐❧✉str❛ ❞♦✐s ❡①❡♠♣❧♦s ❞❡ r♦❜ôs ♠ó✈❡✐s ✉t✐❧✐③❛❞♦s ❡♠ ❜✉s❝❛ ❡ s❛❧✈❛♠❡♥t♦✱ s❡♥❞♦ ♦ ♣r✐♠❡✐r♦ ❡①❡♠♣❧♦ ✉♠ r♦❜ô t❡rr❡str❡ ❞♦t❛❞♦ ❞❡ ❞✐✈❡rs♦s s❡♥s♦r❡s✱ ✐♥❝❧✉s✐✈❡ ❧❛s❡r s❝❛♥♥❡r ❬❆♥❞r✐❧✉❦❛ ❡t ❛❧✳✱ ✷✵✵✾❪✳ ❖ s❡❣✉♥❞♦ ❡①❡♠♣❧♦ tr❛t❛ ❞❡ ✉♠ r♦❜ô ❛ér❡♦ ✉t✐❧✐③❛❞♦ ♣❛r❛ ♠♦♥✐t♦r❛r ♦s ❞❡str♦ç♦s ❞❡ ✉♠ t❡rr❡♠♦t♦ ♥❛ ■tá❧✐❛ ❬◆❛r❞✐ ❡t ❛❧✳✱ ✷✵✵✼❪✳
❋✐❣✉r❛ ✶✳✶✳ ❊①❡♠♣❧♦s ❞❡ r♦❜ôs ♠ó✈❡✐s ✉t✐❧✐③❛❞♦s ❡♠ ❜✉s❝❛ ❡ s❛❧✈❛♠❡♥t♦✱ ✉♠ r♦❜ô ♠ó✈❡❧ t❡rr❡str❡✱ à ❡sq✉❡r❞❛✱ ❡ ✉♠ r♦❜ô ♠ó✈❡❧ ❛ér❡♦✱ ❡♠ ❞❡st❛q✉❡ à ❞✐r❡✐t❛✳
✶✳✷✳ ▼♦t✐✈❛çã♦ ✸
❧❛s❡r s❝❛♥♥❡rs✱ ❞❡✈✐❞♦ à ❜♦❛ r❡❧❛çã♦ ❝✉st♦ × ❜❡♥❡❢í❝✐♦✱ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ♣❡❧❛ ❛❧t❛ ❡①❛t✐✲
❞ã♦✳ ❆s ♠❡❧❤♦r❛s t❡❝♥♦❧ó❣✐❝❛s ♣❡r♠✐t✐r❛♠ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ❡q✉✐♣❛♠❡♥t♦s ❞❡ ❛❧t❛ q✉❛❧✐❞❛❞❡✱ ❝♦♠ ❝✉st♦s ❝❛❞❛ ✈❡③ ♠❡♥♦r❡s✱ ♠❛✐s rá♣✐❞♦s ❡ ❝♦♠ ❝❛♣❛❝✐❞❛❞❡ ❞❡ ♦❜t❡♥çã♦ ❞❡ ♥✉✈❡♠ ❞❡ ♣♦♥t♦s ❞❡ ❛❧t❛ ❞❡♥s✐❞❛❞❡✳ P♦ré♠✱ ♣❛r❛ ❧✐❞❛r ❝♦♠ ❣r❛♥❞❡s q✉❛♥t✐❞❛❞❡s ❞❡ ✐♥❢♦r♠❛çã♦✱ sã♦ ♥❡❝❡ssár✐♦s ♠ét♦❞♦s ❝❛❞❛ ✈❡③ ♠❛✐s ❡✜❝✐❡♥t❡ ❡ ❛✉t♦♠át✐❝♦s✱ ❛ ✜♠ ❞❡ q✉❡ ❡ss❛ ✐♥❢♦r♠❛çã♦ s❡❥❛ ❡❢❡t✐✈❛♠❡♥t❡ ✉t✐❧✐③❛❞❛✳
❆ ❋✐❣✉r❛ ✶✳✷ ✐❧✉str❛ ✉♠ ❧❛s❡r s❝❛♥♥❡r ✸❉ ♠♦♥t❛❞♦ s♦❜r❡ ✉♠ ✈❡í❝✉❧♦ ♠ó✈❡❧✱ ❥✉♥t❛♠❡♥t❡ ❝♦♠ ✉♠❛ ❝â♠❡r❛ ❞❡ ✈í❞❡♦✳ ❆❧é♠ ❞✐ss♦✱ ❛ ✜❣✉r❛ ♠♦str❛ ✉♠ ♠❛♣❛ ✸❉ ❞❡ ❛❧t❛ ❞❡♥s✐❞❛❞❡ ❡♠ ❝♦r❡s ❣❡r❛❞♦ ❛ ♣❛rt✐r ❢✉sã♦ ❞❡ ❛♠❜♦s ♦s s❡♥s♦r❡s✳
❋✐❣✉r❛ ✶✳✷✳ ▲❛s❡r s❝❛♥♥❡r ✸❉ ♠♦♥t❛❞♦ s♦❜r❡ ✈❡í❝✉❧♦ ♠ó✈❡❧✱ ❛❧é♠ ❞❡ ✉♠ ❡①❡♠♣❧♦ ❞❡ ♥✉✈❡♠ ❞❡ ♣♦♥t♦s ✸❉ ❣❡r❛❞❛ ♣❡❧♦ s✐st❡♠❛ ❬✸❉ ▲❛s❡r ▼❛♣♣✐♥❣ ❈♦✳✱ ✷✵✵✾❪✳
❈♦♥s✐❞❡r❛♥❞♦ ♦ ✉s♦ ❞❡ r♦❜ôs ♠ó✈❡✐s✱ ❛ ❞❡t❡❝çã♦ ❞❡ ♠✉❞❛♥ç❛ ❛✐♥❞❛ ♣♦❞❡ s❡r út✐❧ ♣❛r❛ ❛❧❝❛♥ç❛r ♦ ♦❜❥❡t✐✈♦ ❞❡ s❡ t❡r ✉♠ r♦❜ô ❝♦♠♣❧❡t❛♠❡♥t❡ ❛✉tô♥♦♠♦✱ ♣❛r❛ ❛❧❝❛♥ç❛r t❛❧ ♦❜❥❡t✐✈♦ é ♥❡❝❡ssár✐♦ r❡s♦❧✈❡r três ♣r♦❜❧❡♠❛s✿
• ❯s❛r ❛s ✐♥❢♦r♠❛çõ❡s ♣❡r❝❡❜✐❞❛s ♣❡❧♦s s❡♥s♦r❡s ❞❡ ❢♦r♠❛ ❛ ❝♦♥str✉✐r ✉♠❛ r❡♣r❡✲
s❡♥t❛çã♦ ❞♦ ❛♠❜✐❡♥t❡❀
• ▲♦❝❛❧✐③❛r✲s❡ ♥❡ss❛ r❡♣r❡s❡♥t❛çã♦❀
• ❉❡❝✐❞✐r q✉❛❧ s❡rá ♦ ♣ró①✐♠♦ ♠♦✈✐♠❡♥t♦❀
❊①✐st❡ ✉♠❛ ❣❛♠❛ ♠✉✐t♦ ❛♠♣❧❛ ❞❡ té❝♥✐❝❛s q✉❡ t❡♥t❛♠ r❡s♦❧✈❡r ♦s ❞♦✐s ♣r✐♠❡✐r♦s ♣r♦❜❧❡♠❛s✳ ❊❧❛s sã♦ ❝♦♥❤❡❝✐❞❛s ❝♦♠♦ té❝♥✐❝❛s ❞❡ ❙✐♠✉❧t❛♥❡♦✉s ▲♦❝❛❧✐③❛t✐♦♥ ❛♥❞ ▼❛♣✲ ♣✐♥❣ ✭❙▲❆▼ ✮✳ ❊ss❛s té❝♥✐❝❛s ❡st✐♠❛♠ ♦ ♠❛♣❛ ❞♦ ❛♠❜✐❡♥t❡ ❡ ❧♦❝❛❧✐③❛♠ ♦ r♦❜ô ♥❡ss❡ ♠❛♣❛✱ s❡♥❞♦ ❝♦♥❤❡❝✐❞❛s s✉❛s ♣❡r❝❡♣çõ❡s ❡ ♠♦✈✐♠❡♥t♦s✳
✹ ❈❛♣ít✉❧♦ ✶✳ ■♥tr♦❞✉çã♦
♣❡r♠✐t✐r q✉❡ ♦ r♦❜ô t♦♠❡ ❞❡❝✐sõ❡s s♦❜r❡ s❡✉s ♠♦✈✐♠❡♥t♦s✱ ♦✉ s❡❥❛✱ r❡s♦❧✈❛ ♦ t❡r❝❡✐r♦ ♣r♦❜❧❡♠❛ ❝✐t❛❞♦ ❛❝✐♠❛✱ é ♥❡❝❡ssár✐♦ ❞♦tá✲❧♦ ❞❛ ❝❛♣❛❝✐❞❛❞❡ ❞❡ ❞❡t❡❝t❛r ♠✉❞❛♥ç❛s ✐♠✲ ♣♦rt❛♥t❡s ♥♦ ❛♠❜✐❡♥t❡✳ ❆ss✐♠✱ q✉❛♥❞♦ ♦ r♦❜ô ❡stá s❡ ❧♦❝♦♠♦✈❡♥❞♦ ♣♦r ✉♠ ❧✉❣❛r ♣❡❧❛ s❡❣✉♥❞❛ ✈❡③✱ ❡❧❡ ♣♦❞❡ ❞❡t❡r♠✐♥❛r s❡ ❛❝♦♥t❡❝❡r❛♠ ♠✉❞❛♥ç❛s ❡ ❛t✉❛❧✐③❛r s✉❛ r❡♣r❡s❡♥✲ t❛çã♦ ✐♥t❡r♥❛✳
❯♠ ❡①❡♠♣❧♦ ✐♥t❡r❡ss❛♥t❡ ❞❡ ❛♣❧✐❝❛çã♦ ❞❡ss❡ s✐st❡♠❛ é ❡♠ ✉♠ ✈❡í❝✉❧♦ ❛✉tô♥♦♠♦ q✉❡ ❡stá tr❛❢❡❣❛♥❞♦ ♣♦r ✉♠❛ ✈✐❛ ♦❜str✉í❞❛ ♣♦r ❛❧❣✉♠ ♦❜❥❡t♦ ♥ã♦ ♣r❡✈✐st♦ ❛♥t❡r✐♦r✲ ♠❡♥t❡✳ ❆ ❋✐❣✉r❛ ✶✳✸ ✐❧✉str❛ ✉♠❛ ♣♦ssí✈❡❧ ❝❡♥ár✐♦✱ ♥♦ q✉❛❧ ❛♣ós ✉♠❛ t❡♠♣❡st❛❞❡ ✉♠❛ ár✈♦r❡ ♦❜str✉í ❛ ✈✐❛✱ ❢❛③❡♥❞♦ ❝♦♠ q✉❡ s❡❥❛ ♥❡❝❡ssár✐♦ ❞❡t❡❝t❛r ❛ ♠✉❞❛♥ç❛✱ ❜❡♠ ❝♦♠♦ r❡❝♦♥❤❡❝❡r ❛ ❢♦r♠❛ ♣❛r❛ ❝❛❧❝✉❧❛r s❡✉ ✈♦❧✉♠❡ ❡ ♣♦s✐çã♦✳ ❈♦♠ ✐ss♦ ♣❡r♠✐t✐♥❞♦ ✉♠ r❡✲ ♣❧❛♥❡❥❛♠❡♥t♦ ❞❛ tr❛❥❡tór✐❛✱ ❞❡s✈✐❛♥❞♦ ❞♦ ♦❜stá❝✉❧♦✳
❋✐❣✉r❛ ✶✳✸✳ ❊①❡♠♣❧♦ ❞❡ ❝❡♥ár✐♦ ♣❛r❛ ❞❡t❡❝çã♦ ❞❡ ♠✉❞❛♥ç❛ ❡ r❡❝♦♥❤❡❝✐♠❡♥t♦ ❞❡ ❢♦r♠❛✳
