▼■❘❊▲▲❆ ❆◆❚❯◆❊❙ ❉❊ ▼❆●❆▲❍➹❊❙
❆▲●❖❘■❚▼❖ ❊❋■❈■❊◆❚❊ P❆❘❆ ❈➪▲❈❯▲❖ ❉❊ ▼❆P❆❙ ❉❊
❱■❙■❇■▲■❉❆❉❊ ❊▼ ❚❊❘❘❊◆❖❙ ❆❘▼❆❩❊◆❆❉❖❙ ❊▼
▼❊▼Ó❘■❆ ❊❳❚❊❘◆❆
❉✐ss❡rt❛çã♦ ❛♣r❡s❡♥t❛❞❛ à ❯♥✐✈❡r✲ s✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❱✐ç♦s❛✱ ❝♦♠♦ ♣❛rt❡ ❞❛s ❡①✐❣ê♥❝✐❛s ❞♦ Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❈✐ê♥❝✐❛ ❞❛ ❈♦♠♣✉t❛çã♦✱ ♣❛r❛ ♦❜t❡♥çã♦ ❞♦ tí✲ t✉❧♦ ❞❡ ▼❛❣✐st❡r ❙❝✐❡♥t✐❛❡✳
❱■➬❖❙❆
▼■❘❊▲▲❆ ❆◆❚❯◆❊❙ ❉❊ ▼❆●❆▲❍➹❊❙
❆▲●❖❘■❚▼❖ ❊❋■❈■❊◆❚❊ P❆❘❆ ❈➪▲❈❯▲❖ ❉❊ ▼❆P❆❙ ❉❊
❱■❙■❇■▲■❉❆❉❊ ❊▼ ❚❊❘❘❊◆❖❙ ❆❘▼❆❩❊◆❆❉❖❙ ❊▼
▼❊▼Ó❘■❆ ❊❳❚❊❘◆❆
❉✐ss❡rt❛çã♦ ❛♣r❡s❡♥t❛❞❛ à ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❱✐ç♦s❛✱ ❝♦♠♦ ♣❛rt❡ ❞❛s ❡①✐❣ê♥✲ ❝✐❛s ❞♦ Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❈✐✲ ê♥❝✐❛ ❞❛ ❈♦♠♣✉t❛çã♦✱ ♣❛r❛ ♦❜t❡♥çã♦ ❞♦ tí✲ t✉❧♦ ❞❡ ▼❛❣✐st❡r ❙❝✐❡♥t✐❛❡✳
❆♣r♦✈❛❞❛ ❡♠ ✷✹ ❞❡ ❛❜r✐❧ ❞❡ ✷✵✵✾
❱❧❛❞✐♠✐r ❖❧✐✈❡✐r❛ ❉✐ ■♦r✐♦
✭❈♦✲❖r✐❡♥t❛❞♦r✮
❆♥❞ré ●✉st❛✈♦ ❞♦s ❙❛♥t♦s
❈❛r❧♦s ❆✳ ❆❧✈❛r❡s ❙♦❛r❡s ❘✐❜❡✐r♦
✭❈♦✲❖r✐❡♥t❛❞♦r✮
❈❧♦❞♦✈❡✉ ❆✉❣✉st♦ ❉❛✈✐s ❏✉♥✐♦r
❆❣r❛❞❡❝✐♠❡♥t♦s
✑◆♦t❤✐♥❣ ✇❡ ❛❝❤✐❡✈❡ ✐♥ t❤✐s ✇♦r❧❞ ✐s ❛❝❤✐❡✈❡❞ ❛❧♦♥❡✳ ■t ✐s ❛❧✇❛②s ❛❝❤✐❡✈❡❞ ✇✐t❤ ♦t❤❡rs t❡❛❝❤✐♥❣ ✉s ❛❧♦♥❣ t❤❡ ✇❛②✳✑ ▲❡❡ ❏✳ ❈♦❧❛♥ ❚❡♥❤♦ ♠✉✐t♦ ♦r❣✉❧❤♦ ❞❡ ❡s❝r❡✈❡r ❡ss❡s ❛❣r❛❞❡❝✐♠❡♥t♦s✳ ❖r❣✉❧❤♦ ❡ss❡ q✉❡ ❛❞✈é♠ ❞❛ ♠✐♥❤❛ ❝r❡♥ç❛ ❞❡ q✉❡ s♦③✐♥❤♦s ♥ã♦ ❝❤❡❣❛♠♦s ♠✉✐t♦ ❧♦♥❣❡✱ ❡ ♣♦❞❡r ❛❣r❛❞❡❝❡r ♠❡ ❢❛③ ❧❡♠❜r❛r q✉❡ ❡ss❛ é ♠❛✐s ✉♠❛ ✈✐tór✐❛ q✉❡ ❛❧❝❛♥ç♦ ❛♦ ❧❛❞♦ ❞❛q✉❡❧❡s q✉❡ ❛♠♦✳
❈♦♠❡ç♦ ❛❣r❛❞❡❝❡♥❞♦ ❛ ❉❡✉s ♣♦r ♠❡ ♣r♦✈❡r ❞✐r❡çã♦ t♦❞♦s ♦s ♠♦♠❡♥t♦s ❞❛ ♠✐♥❤❛ ✈✐❞❛✳ P♦ré♠ ♦ q✉❡ ♠❛✐s ❞❡✈♦ ❛ ❊❧❡ é t❡r ♠❡ ♣r♦♣♦r❝✐♦♥❛❞♦ ❝♦♥✈✐✈❡r ❝♦♠ ♣❡ss♦❛s ♠❛r❛✈✐❧❤♦s❛s ♣❛r❛ ❛s q✉❛✐s ❝♦♥t✐♥✉♦ ❡ss❡s ❛❣r❛❞❡❝✐♠❡♥t♦s✳
❆❣r❛❞❡ç♦ ❛♦s ♠❡✉s ♣❛✐s✱ ❏❡❞❡r ❡ ▼❛r✐❛♥❛✱ ♣♦r s❡r❡♠ ♠❡✉ ❛❧✐❝❡r❝❡ ❡ t❡r❡♠ ♠❡ ❞❛❞♦ ❛ ♦♣♦rt✉♥✐❞❛❞❡ ❞❡ss❛ ❝♦♥q✉✐st❛ ♠❡ ❡♥s✐♥❛♥❞♦ ♦ ✈❛❧♦r ❡ ❛ ❣r❛t✐✜❝❛çã♦ ❞♦ ❝♦♥❤❡❝✐♠❡♥t♦✳ ❆❣r❛❞❡ç♦ t❛♠❜é♠ à t♦❞❛ ❛ ♠✐♥❤❛ ❢❛♠í❧✐❛ ✲ ✐r♠ã♦s✱ ♠ã❡s ✭❙♦♥✐♥❤❛ ❡ ❊❞✐❧③❛✮✱ ❛✈ós✱ t✐♦s✱ ♣r✐♠♦s ❡ ❛♠✐❣♦s ✲ q✉❡ s❡♠♣r❡ ♠❡ ❛♣♦✐❛r❛♠✱ ♠❡ ❡♥✈✐❛r❛♠ ❜♦❛s ❡♥❡r❣✐❛s ❡ ❝♦♠❡♠♦r❛r❛♠✱ ❞❡ ♣❡rt♦ ♦✉ ❞❡ ❧♦♥❣❡✱ ♠✐♥❤❛s ✈✐tór✐❛s✳
❚❡♥❤♦ ♠✉✐t♦ ❛ ❛❣r❛❞❡❝❡r ❛♦ ♠❡✉ ♠❛r✐❞♦✱ ■s❛❛❝✳ ◆✉♥❝❛ ♣♦❞❡r❡✐ ❡sq✉❡❝❡r ❞❡ s❡✉ ✐♥❝❡♥t✐✈♦ ✐♥✐❝✐❛❧✱ q✉❛♥❞♦ ❛✐♥❞❛ ér❛♠♦s ❛♠✐❣♦s✱ s❡✉s ❝♦♥s❡❧❤♦s ♠❡ ❛❥✉❞❛r❛♠ ❛ ❡st❛r ♦♥❞❡ ❡st♦✉✳ ❚❛♠❜é♠ ♥ã♦ ♣♦ss♦ ❡sq✉❡❝❡r ❞❡ s❡✉ ❝❛r✐♥❤♦ ❡ ❝♦♠♣r❡❡♥sã♦ ❞✉r❛♥t❡ t♦❞♦ ♦ t❡♠♣♦ ❞❡❞✐❝❛❞♦ ❛♦ ♠❡str❛❞♦✱ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ❞✉r❛♥t❡ ❛s ♥♦✐t❡s✱ ♠❛❞r✉❣❛❞❛s ❡ ✜♥s ❞❡ s❡♠❛♥❛ ❞❡❞✐❝❛❞♦s ❛♦ ❡st✉❞♦✳
❆❣r❛❞❡ç♦ t❛♠❜é♠ ❛♦s ❛♠✐❣♦s ❡ ❝♦♠♣❛♥❤❡✐r♦s ❞❡ tr❛❜❛❧❤♦ ❞❛ ❆❚❆◆ ♣♦r t❡r❡♠ ❡♥t❡♥❞✐❞♦ ❛ ✐♠♣♦rtâ♥❝✐❛ ❡ ❣r❛♥❞✐♦s✐❞❛❞❡ ❞❡ss❡ ♠♦♠❡♥t♦✳
❋❛ç♦ ✉♠ ❛❣r❛❞❡❝✐♠❡♥t♦ ❡s♣❡❝✐❛❧ ❛♦ ♠❡✉ ❝♦♠♣❛♥❤❡✐r♦ ♥❡ss❡ ♣r♦❥❡t♦✱ ❙❛❧❧❡s✱ s❡♠ ❡❧❡ ❝❡rt❛♠❡♥t❡ ❡st❡ tr❛❜❛❧❤♦ ♥ã♦ t❡r✐❛ t✐❞♦ t❛♠❛♥❤❛ ♣r♦♣♦rçã♦✳
❆❣r❛❞❡ç♦ t❛♠❜é♠ ❡s♣❡❝✐❛❧♠❡♥t❡ ❛♦ ♠❡✉ ♦r✐❡♥t❛❞♦r Pr♦❢✳ ▼❛r❝✉s✳ ◆ã♦ ♣♦❞❡r✐❛ ❞❡✐①❛r ❞❡ ❞❡♠♦♥str❛r ♠✐♥❤❛ ❣r❛t✐❞ã♦ ❛ ❡ss❡ ♠❡str❡ q✉❡ ♠❡ ❛❝♦♠♣❛♥❤♦✉ ❞✉r❛♥t❡ ❛ ❣r❛❞✉❛çã♦ ❡ ❛❝r❡❞✐t♦✉ ♠✐♠ ♣❛r❛ ❛ r❡❛❧✐③❛çã♦ ❞♦ ♠❡str❛❞♦✱ ♠❡s♠♦ ❡✉ ♥ã♦ ❞❡❞✐❝❛♥❞♦ t❡♠♣♦ ✐♥t❡❣r❛❧ à ❧❡✐t✉r❛ ❞❡ ❧✐✈r♦s ❡ ❛rt✐❣♦s✱ ❛♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞♦ tr❛❜❛❧❤♦ ❡ à ❡s❝r✐t❛ ❞❡ss❛ ❞✐ss❡rt❛çã♦✳ ❈♦♠ s❡✉ ❡st✐❧♦ ❞❡ ❡♥s✐♥❛r ❡ ♣❡sq✉✐s❛r✱ ❡❧❡ ♠❡ ❛♣♦♥t♦✉ ❛ ❞✐r❡çã♦ ❝❡rt❛✳ ❆ ❡❧❡ ♠❡✉ ♠✉✐t♦ ♦❜r✐❣❛❞❛✦
❊♥✜♠✱ ❛❣r❛❞❡ç♦ à ✉♠❛ r❡❝❡♥t❡ ❡ ♠❛r❛✈✐❧❤♦s❛ r❡❛❧✐③❛çã♦✿ ♠❡✉ ❜❡❜ê✳ ❆ ♣r❡s❡♥ç❛ ❞❡ss❛ ♣❡❞❛❝✐♥❤♦ ❞❡ ✈✐❞❛ ❡♠ ♠❡✉ ✈❡♥tr❡ ♠❡ ❞❡✉ ❡♥❡r❣✐❛ ❡ ❢♦rç❛ ♣❛r❛ ❛ ❝♦♥❝❧✉sã♦ ❞❡st❡ tr❛❜❛❧❤♦✳ ◆❡ss❡ ♠♦♠❡♥t♦✱ ♠❛✐s ❞♦ q✉❡ ♥✉♥❝❛✱ ♣♦ss♦ ❞✐③❡r q✉❡ ♥ã♦ ♦❜t✐✈❡ ❡ss❛ ❝♦♥q✉✐st❛ s♦③✐♥❤❛✦
❮♥❞✐❝❡
❮♥❞✐❝❡ ❞❡ ❚❛❜❡❧❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✈ ❮♥❞✐❝❡ ❞❡ ❋✐❣✉r❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✈✐ ❮♥❞✐❝❡ ❞❡ ❈ó❞✐❣♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✈✐✐✐ ❘❡s✉♠♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✐① ❆❜str❛❝t ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ① ■♥tr♦❞✉çã♦ ●❡r❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶ ❈❛♣ít✉❧♦ ✶ ❘❡❢❡r❡♥❝✐❛❧ ❚❡ór✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼ ✶✳✶ ❘❡♣r❡s❡♥t❛çã♦ ❞❡ s✉♣❡r❢í❝✐❡s ❞❡ t❡rr❡♥♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼ ✶✳✷ ❱✐s✐❜✐❧✐❞❛❞❡ ❡♠ ❚❡rr❡♥♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶ ✶✳✷✳✶ ❊str✉t✉r❛s ❞❡ ❱✐s✐❜✐❧✐❞❛❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷ ✶✳✷✳✷ ❉❡t❡r♠✐♥❛çã♦ ❞❡ ❱✐s✐❜✐❧✐❞❛❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹ ✶✳✸ ❆❧❣♦r✐t♠♦s ❡✜❝✐❡♥t❡s ❡♠ ♠❡♠ór✐❛ ❡①t❡r♥❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼ ✶✳✸✳✶ ▼♦❞❡❧♦ ❡ ❛✈❛❧✐❛çã♦ ❞❡ ❛❧❣♦r✐t♠♦s ❡♠ ♠❡♠ór✐❛ ❡①t❡r♥❛ ✳ ✳ ✳ ✳ ✳ ✶✼ ✶✳✸✳✷ ❆♠❜✐❡♥t❡s ♣❛r❛ ♣r♦❥❡t♦ ❞❡ ❛❧❣♦r✐t♠♦s ❡♠ ♠❡♠ór✐❛ ❡①t❡r♥❛ ✳ ✳ ✳ ✶✾ ❈❛♣ít✉❧♦ ✷ ❚r❛❜❛❧❤♦s ❘❡❧❛❝✐♦♥❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸ ✷✳✶ ❱✐s✐❜✐❧✐❞❛❞❡ ❡♠ ❚❡rr❡♥♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸ ✷✳✷ ❆❧❣♦r✐t♠♦s ❡♠ ♠❡♠ór✐❛ ❡①t❡r♥❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾ ❈❛♣ít✉❧♦ ✸ ❆❧❣♦r✐t♠♦ ♣❛r❛ ❈á❧❝✉❧♦ ❞♦ ❱✐❡✇s❤❡❞ ❡♠ t❡rr❡♥♦s ❛r✲
♠❛③❡♥❛❞♦s ❡♠ ♠❡♠ór✐❛ ❡①t❡r♥❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ✸✳✶ ❖ ♠ét♦❞♦ ❞❡ ❋r❛♥❦❧✐♥ ❡ ❘❛② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ✸✳✷ ❆❧❣♦r✐t♠♦ ❡♠ ▼❡♠ór✐❛ ❊①t❡r♥❛ ✲ ❊▼❱❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✸✳✷✳✶ ■♠♣❧❡♠❡♥t❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ✸✳✷✳✷ ❈♦♠♣❧❡①✐❞❛❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ❈❛♣ít✉❧♦ ✹ ❆✈❛❧✐❛çã♦ ❞❡ ❊✜❝✐ê♥❝✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺ ✹✳✶ ❖ ❛❧❣♦r✐t♠♦ ❞❡ ❍❛✈❡r❦♦rt ❡t ❛❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺ ✹✳✷ ❊①♣❡r✐♠❡♥t♦s ❡ ❛✈❛❧✐❛çã♦ ❞❡ ❡✜❝✐ê♥❝✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼ ✹✳✷✳✶ ❘❡s✉❧t❛❞♦s ❡①♣❡r✐♠❡♥t❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼
✹✳✷✳✷ ❈♦♠♣❛r❛çã♦ ❝♦♠ ❋r❛♥❦❧✐♥ ❡ ❘❛② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵ ✹✳✷✳✸ ❈♦♠♣❛r❛çã♦ ❝♦♠ ❍❛✈❡r❦♦rt ❡t ❛❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹ ❈♦♥❝❧✉sõ❡s ●❡r❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽ ❆♣ê♥❞✐❝❡ ❆ ❖ ❆❧❣♦r✐t♠♦ ❞❡ ❍❛✈❡r❦♦rt ❡t ❛❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶ ❘❡❢❡rê♥❝✐❛s ❇✐❜❧✐♦❣rá✜❝❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺
❮♥❞✐❝❡ ❞❡ ❚❛❜❡❧❛s
✶ ❚❡♠♣♦ ❞❡ ❡①❡❝✉çã♦ ❞♦ ❛❧❣♦r✐t♠♦ ❞❡ ❱❛♥ ❑r❡✈❡❧❞ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸ ✸✳✶ P❛râ♠❡tr♦s ❞❡ ❝♦♥✜❣✉r❛çã♦ ❞♦ st①①❧ ✿✿ ✈❡❝t♦r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷
✸✳✷ ❊str❛té❣✐❛s ❞❡ s✐♥❛❧✐③❛çã♦ ❡♠ ❞✐s❝♦s ♣❛r❛❧❡❧♦s s✉♣♦rt❛❞❛s ♣❡❧❛ ❙❚❳❳▲ ✳ ✹✹ ✸✳✸ ❊str❛té❣✐❛s ❞❡ ♣❛❣✐♥❛çã♦ s✉♣♦rt❛❞❛s ♣❡❧❛ ❙❚❳❳▲ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹ ✸✳✹ ▼❡♠❜r♦s ❞♦ t✐♣♦ st①①❧ ✿✈❡❝t♦r ✉s❛❞♦s ♣❡❧♦ ❊▼❱❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹
✹✳✶ ❚❡♠♣♦ ♠é❞✐♦ ❞❡ ❡①❡❝✉çã♦ ❞♦ ❊▼❱❙ ✭❡♠ s❡❣✉♥❞♦s✮ ✉t✐❧✐③❛♥❞♦ ✶ ●❇ ❡ ✷✺✻ ▼❇ ❡♠ ♣♦rçõ❡s ❞♦ t❡rr❡♥♦ ❞♦ ❇r❛s✐❧ ❝♦♠ ❞✐❢❡r❡♥t❡s t❛♠❛♥❤♦s ❡ ❞✐❢❡r❡♥t❡s ♣♦s✐❝✐♦♥❛♠❡♥t♦s ❞♦ ♦❜s❡r✈❛❞♦r ❡ ✈❛r✐❛♥❞♦ ❛ ❛❧t✉r❛ ❞♦ ♦❜✲ s❡r✈❛❞♦r ❛❝✐♠❛ ❞♦ t❡rr❡♥♦ ✭❣❡r❛♥❞♦ ✈✐❡✇s❤❡❞ ❝♦♠ ♥ú♠❡r♦ ❞✐❢❡r❡♥t❡ ❞❡ ♣♦♥t♦s ✈✐sí✈❡✐s ✲ ♠♦str❛❞♦ ♥❛ ❝♦❧✉♥❛ ★ Pts ❱✐s✳✮✳ ❊♠ t♦❞♦s ♦s ❝❛s♦s✱ ♦ r❛✐♦ ❞❡ ✐♥t❡r❡ss❡ ❝♦❜r❡ t♦❞♦ ♦ t❡rr❡♥♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ✹✳✷ ❈♦♠♣❛r❛çã♦ ❞♦ t❡♠♣♦ ❞❡ ❡①❡❝✉çã♦ ❞♦ ❊▼❱❙ ❡ ❞♦ ❲❘❋❴❱❙ ✉s❛♥❞♦
✶●❇ ❞❡ ❘❆▼✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺
❮♥❞✐❝❡ ❞❡ ❋✐❣✉r❛s
✶ ■♠❛❣❡♠ ❞♦ ❘✐♦ ❆♠❛③♦♥❛s t✐r❛❞❛ ♣♦r ❛str♦♥❛✉t❛ ❡♠ ❛❣♦st♦ ❞❡ ✷✵✵✽✳ ✳ ✳ ✷ ✷ ■♠❛❣❡♠ ❞❛ ❈r❛t❡r❛ ❞❛ ❙❡rr❛ ❞❛ ❈❛♥❣❛❧❤❛ ❧♦❝❛❧✐③❛❞❛ ♥♦ ❚♦❝❛♥t✐♥s✳ ✳ ✳ ✳ ✷ ✶✳✶ ❊t❛♣❛s ❞♦ ♣r♦❝❡ss♦ ❞❡ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ✉♠ ▼❉❚ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽ ✶✳✷ ❈❧❛ss❡s ❞❡ ♠♦❞❡❧♦s ❞✐❣✐t❛✐s ❞❡ t❡rr❡♥♦✿ ✭❛✮ ❚■◆❀ ✭❜✮ ▼❉❊❀ ✭❝✮ ▼❛♣❛
❞❡ ❈✉r✈❛s ❞❡ ◆í✈❡❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾ ✶✳✸ ■♥t❡r♣♦❧❛çã♦ ❜✐❧✐♥❡❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵ ✶✳✹ ❱✐❡✇s❤❡❞ ✲ ❚❡rr❡♥♦ ❞♦ ❧❛❣♦ ❈❤❛♠♣❧❛✐♥ ❲❡st ✲ ❉✐✈✐s❛ ❊❯❆✲❈❛♥❛❞á ✳ ✳ ✶✷ ✶✳✺ q1 ❡q2 sã♦ ❤♦r✐③♦♥t❡s ❧♦❝❛✐s✱q2 é ✉♠ ❤♦r✐③♦♥t❡ ❣❧♦❜❛❧❀k1 é ♦ ♦✛s❡t ❧♦❝❛❧
❞❡ s1 ❡ h1 é s❡✉ ♦✛s❡t ❣❧♦❜❛❧✱ ♦ ♠❡s♠♦ ♦❝♦rr❡ ♣❛r❛ s2❀ s1 ♥ã♦ é ✈✐sí✈❡❧
♣♦r p ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹ ✶✳✻ ❱✐s✐❜✐❧✐❞❛❞❡ ❞❡ ♣♦♥t♦s✿ p1 ❡ p4 sã♦ ✈✐sí✈❡✐s ❛ ♣❛rt✐r ❞❡ p0❀ p2 ❡ p3 ♥ã♦
sã♦ ✈✐sí✈❡✐s ❛ ♣❛rt✐r ❞❡ p0✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺
✶✳✼ ❘❛st❡r✐③❛çã♦ ❞❡ ❧✐♥❤❛✿ ❝é❧✉❧❛s ♠❛✐s ❡s❝✉r❛s sã♦ ❛ r❡♣r❡s❡♥t❛çã♦ r❛st❡r ❞❛ ❧✐♥❤❛ q✉❡ ♣❛ss❛ ♣♦r ❡❧❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻ ✶✳✽ ❙✐st❡♠❛ ❞❡ ❝♦♦r❞❡♥❛❞❛s ❡s❢ér✐❝❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼ ✶✳✾ ❱✐s✐❜✐❧✐❞❛❞❡ ❡♠ ❚■◆✿ ♣♦♥t♦q1 ♥ã♦ é ✈✐sí✈❡❧ ♣♦rp❞❡✈✐❞♦ ❛f1 ❡ ♦ ♣♦♥t♦
q2 é ✈✐sí✈❡❧ ♣♦r p✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼
✶✳✶✵ ▼♦❞❡❧♦ ❞❡ ♠❡♠ór✐❛ ❤✐❡rárq✉✐❝♦ tí♣✐❝♦ ❞❡ s✐st❡♠❛s ✉♥✐♣r♦❝❡ss❛❞♦s✱ ✐♥✲ ❝❧✉✐♥❞♦ r❡❣✐str❛❞♦r❡s✱ ❝❛❝❤❡ ❞❡ ✐♥str✉çõ❡s✱ ❝❛❝❤❡ ❞❡ ❞❛❞♦s✱ ❝❛❝❤❡ ♥í✈❡❧ ✷ ✭▲✷✮✱ ♠❡♠ór✐❛ ✐♥t❡r♥❛ ❡ ❞✐s❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽ ✶✳✶✶ ❊str✉t✉r❛ ❞❛ ❙❚❳❳▲ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ✷✳✶ ❱✐❡✇s❤❡❞ ❞❡ p ❡♠ ✉♠❛ ❚■◆ ♥♦ ♣❧❛♥♦ xy ❡ ♣r♦❥❡t❛❞♦ ❡♠ xz ❝♦♠♦ ♦
♣❧❛♥♦ ❞❡ ✈✐sã♦ ❞❡ p✳ ➪r❡❛s ❡s❝✉r❛s ♥ã♦ sã♦ ✈✐sí✈❡✐s ♣♦r p✳ ❆r❡st❛s ♠❛✐s ❣r♦ss❛s ♠❛r❝❛♠ ♦ ❤♦r✐③♦♥t❡ ♥♦ ♣❧❛♥♦ xy ❡ ❛s ❛r❡st❛s s✉♣❡r✐♦r❡s ♥♦ ♣❧❛♥♦ xz✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✷✳✷ ▲❛❞♦s ♠❛✐s ❞✐st❛♥t❡s ✭❧✐♥❤❛s ❡s♣❡ss❛s✮ ❞❡ ✉♠❛ r❡❣✐ã♦ ❛❧✈♦✱ ❡ ❛s ❧✐♥❤❛s
❞❡ ✈✐s❛❞❛ ❞♦ ♦❜s❡r✈❛❞♦r p♣❛r❛ ✉♠❛ ❞❛s r❡❣✐õ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✸✳✶ ❈á❧❝✉❧♦ ❞♦viewshed✿ ❧✐♥❤❛s ❞❡ ✈✐s❛❞❛ ❝♦♠ s✉❛s r❡s♣❡❝t✐✈❛s r❛st❡r✐③❛çõ❡s ✸✸ ✸✳✷ P♦♥t♦s ❡s❝✉r♦s ♠♦str❛♠ ❛ r❛st❡r✐③❛çã♦ ❞❛s ❧✐♥❤❛s ❛♣r❡s❡♥t❛❞❛s ♥❛ ❋✐✲
❣✉r❛ ✿ ✭❛✮ ✐♥❝r❡♠❡♥t❛♥❞♦ x ❡ ❝❛❧❝✉❧❛♥❞♦ y ❡ ✭❜✮ ✐♥❝r❡♠❡♥t❛♥❞♦ y ❡ ❝❛❧❝✉❧❛♥❞♦ x ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ✸✳✸ ❈é❧✉❧❛ ✐♥t❡r❝❡♣t❛❞❛ ♣♦r ♠❛✐s ❞❡ ✉♠❛ ▲❖❙✳ ❈é❧✉❧❛ c é ✐♥t❡r❡❝❡♣t❛❞❛
♣❡❧❛s ❧✐♥❤❛s ✸ ❡ ✹✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺
✸✳✹ ◆✉♠❡r❛çã♦ ❞❛s ❧✐♥❤❛s ❞❡ ✈✐s❛❞❛ ❝♦♠ ✐♥í❝✐♦ ♥♦ ♦❜s❡r✈❛❞♦rp❡♠ s❡♥t✐♥❞♦ ❛♥t✐✲❤♦rár✐♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✸✳✺ ▲✐♥❤❛s ❞❡ ✈✐sã♦ ✐♥t❡r❝❡♣t❛♥❞♦ ✉♠❛ ❝é❧✉❧❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼ ✸✳✻ Pr♦❥❡çã♦ ❞❡ ▲❖❙ ❡ ❝á❧❝✉❧♦ ❞♦s í♥❞✐❝❡s ❞❡ ✉♠❛ ❝é❧✉❧❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✸✳✼ ❊sq✉❡♠❛ ❞♦ st①①❧✿✿✈❡❝t♦r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷ ✹✳✶ ❆❧❣♦r✐t♠♦ ❞❡ ✈❛rr❡❞✉r❛ ♥♦ ♣❧❛♥❞♦ ❞❡ ❱❛♥ ❑r❡✈❡❧❞✿ ✭❛✮ ❈❛❞❛ ❝é❧✉❧❛ é
♠❛r❝❛❞❛ ❝♦♠ s❡✉s três ❡✈❡♥t♦s❀ ✭❜✮ ❈é❧✉❧❛s ❛t✐✈❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻ ✹✳✷ ■♠❛❣❡♠ ❞❡ s❛té❧✐t❡ ❞♦ t❡rr❡♥♦ ✉s❛❞♦ ♣❛r❛ ♦s t❡st❡s✿ ✭❛✮ ✈✐sã♦ ❣❡r❛❧ ❞♦
t❡rr❡♥♦ ❡ ✭❜✮ s❡♣❛r❛çã♦ ❞❛s r❡❣✐õ❡s ❞❡ ❞✐❢❡r❡♥t❡s t❛♠❛♥❤♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵ ✹✳✸ ❖ t❡♠♣♦ ❞❡ ♣r♦❝❡ss❛♠❡♥t♦ ✐♥t❡r♥♦ ❡ ❡①t❡r♥♦ ✉s❛♥❞♦ ✷✺✻ ▼❇ ❡ ✶ ●❇
❞❡ ❘❆▼ ❡♠ t❡rr❡♥♦s ❞❡ ✸✶✶ ▼❇✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✹✳✹ ❖ t❡♠♣♦ ❞❡ ♣r♦❝❡ss❛♠❡♥t♦ ✐♥t❡r♥♦ ❡ ❡①t❡r♥♦ ✉s❛♥❞♦ ✷✺✻ ▼❇ ❡ ✶ ●❇
❞❡ ❘❆▼ ❡♠ t❡rr❡♥♦s ❞❡ ✶✶✷✷ ▼❇✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✹✳✺ ❖ t❡♠♣♦ ❞❡ ♣r♦❝❡ss❛♠❡♥t♦ ✐♥t❡r♥♦ ❡ ❡①t❡r♥♦ ✉s❛♥❞♦ ✷✺✻ ▼❇ ❡ ✶ ●❇
❞❡ ❘❆▼ ❡♠ t❡rr❡♥♦s ❞❡ ✹✷✻✹ ▼❇✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷ ✹✳✻ ❖ t❡♠♣♦ ❞❡ ♣r♦❝❡ss❛♠❡♥t♦ ✐♥t❡r♥♦ ❡ ❡①t❡r♥♦ ✉s❛♥❞♦ ✷✺✻ ▼❇ ❡ ✶ ●❇
❞❡ ❘❆▼ ❡♠ t❡rr❡♥♦s ❞❡ ✻✶✵✸ ▼❇✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷ ✹✳✼ ❚❡rr❡♥♦ ❞♦ ❍❛✈❛í ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹ ✹✳✽ ❚❡rr❡♥♦ ❞♦ ❧❛❣♦ ❈❤❛♠♣❧❛✐♥ ❲❡st ✲ ❉✐✈✐s❛ ❊❯❆✲❈❛♥❛❞á ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹ ✹✳✾ ❈♦♠♣❛r❛çã♦ ❞♦ t❡♠♣♦ ❞❡ ❡①❡❝✉çã♦ ❞♦ ❊▼❱❙ ❡ ❞♦ ❲❘❋❴❱❙ ✉s❛♥❞♦
✶●❇ ❞❡ ❘❆▼ ❡♠ t❡rr❡♥♦s ❞❡ ✶✳✹✺ ●❇ ❡ ✷ ●❇✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻ ✹✳✶✵ ❈♦♠♣❛r❛çã♦ ❞♦ t❡♠♣♦ ❞❡ ❡①❡❝✉çã♦ ❞♦ ❊▼❱❙ ❡ ❞♦ ■❖❴❱❙ ✉s❛♥❞♦ ✶
●❇ ❡ ✷✺✻ ▼❇ ❞❡ ❘❆▼✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼ ❆✳✶ ❱❛rr❡❞✉r❛ ♣♦r ❞✐str✐❜✉✐çã♦✳ ❆ ♠❛tr✐③ é ❞✐✈✐❞✐❞❛ ❡♠M/B s❡t♦r❡s r❛❞✐✲
❛✐s❀ ❝é❧✉❧❛s ♣♦❞❡♠ ❝r✉③❛r ③❡r♦✱ ✉♠ ♦✉ ♠❛✐s ❧✐♠✐t❡s ❞♦s s❡t♦r❡s ✳ ✳ ✳ ✳ ✳ ✼✷ ❆✳✷ ❙❡❣♠❡♥t♦s ❝♦rr❡s♣♦♥❞❡♠ ❛ ❝é❧✉❧❛s ✭❛✮ ♥❛rr♦✇ ❡ ✭❜✮ ✇✐❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸
❮♥❞✐❝❡ ❞❡ ❈ó❞✐❣♦s
✸✳✶ ❊str✉t✉r❛s ✉t✐❧✐③❛❞❛s ♥❛ ✐♠♣❧❡♠❡♥t❛çã♦ ❞♦ ❊▼❱❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✸✳✷ Pr♦tót✐♣♦ ❞♦ ♠ét♦❞♦ st①①❧ ✿ s♦rt ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹
✸✳✸ ❊str✉t✉r❛s ✉t✐❧✐③❛❞❛s ♣❛r❛ ❝♦♠♣❛r❛r ❡❧❡♠❡♥t♦s ❞♦ t✐♣♦ ❈❡❧✉❧❛■♥❞✐❝❡ ❡ P❛r❖r❞❡♥❛❞♦ ♣❡❧♦ ♠ét♦❞♦ st①①❧ ✿ s♦rt ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺
✸✳✹ ●❡r❛çã♦ ❞❛ ❧✐st❛ ❞❡ ✈❛rr❡❞✉r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻ ✸✳✺ ❉❡t❡r♠✐♥❛çã♦ ❞♦s í♥❞✐❝❡s ❞❡ ✉♠❛ ❝é❧✉❧❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼ ✸✳✻ ❉❡t❡r♠✐♥❛çã♦ ❞❛ ❝é❧✉❧❛ ❞❛ ❜♦r❞❛ ❞♦ q✉❛❞r❛❞♦ ❞❡ ✈❛rr❡❞✉r❛ q✉❡ ♣❛ss❛
♣♦r ✉♠❛ ❞❡t❡r♠✐♥❛❞❛ ▲❖❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ✸✳✼ ❉❡t❡r♠✐♥❛çã♦ ❞❛ ✈✐s✐❜✐❧✐❞❛❞❡ ❞❛ ❝é❧✉❧❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ✸✳✽ ●❡r❛çã♦ ❞❛ ♠❛tr✐③ ❞❡ ✈✐❡✇s❤❡❞ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶
❘❡s✉♠♦
▼❆●❆▲❍➹❊❙✱ ▼✐r❡❧❧❛ ❆♥t✉♥❡s ❞❡✱ ▼✳❙❝✳✱ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❱✐ç♦s❛✱ ❆❜r✐❧ ❞❡ ✷✵✵✾✳ ❆❧❣♦r✐t♠♦ ❡✜❝✐❡♥t❡ ♣❛r❛ ❝á❧❝✉❧♦ ❞❡ ♠❛♣❛s ❞❡ ✈✐s✐❜✐❧✐❞❛❞❡ ❡♠ t❡rr❡♥♦s ❛r♠❛③❡♥❛❞♦s ❡♠ ♠❡♠ór✐❛ ❡①t❡r♥❛✳ ❖r✐❡♥t❛❞♦r✿ ▼❛r❝✉s ❱✐♥í❝✐✉s ❆❧✈✐♠ ❆♥❞r❛❞❡✳ ❈♦✲❖r✐❡♥t❛❞♦r❡s✿ ❱❧❛❞✐♠✐r ❖❧✐✈❡✐r❛ ❉✐ ■♦r✐♦ ❡ ❈❛r❧♦s ❆✳ ❆❧✈❛r❡s ❙♦❛r❡s ❘✐❜❡✐r♦✳
❈♦♠ ❛ ♠❛✐♦r ❞✐s♣♦♥✐❜✐❧✐❞❛❞❡ ❞❡ ❞❛❞♦s ❞❡t❛❧❤❛❞♦s ❞❡ t❡rr❡♥♦s✱ ♠✉✐t❛s ❛♣❧✐❝❛✲ çõ❡s ♣r❡❝✐s❛♠ ♣r♦❝❡ss❛r ❣r❛♥❞❡s ár❡❛s ❣❡♦❣rá✜❝❛s ❡♠ ❛❧t❛ r❡s♦❧✉çã♦✳ ❖ ♣r♦❝❡ss❛♠❡♥t♦ ♠❛ss✐✈♦ ❞❡ ❞❛❞♦s ❡♥✈♦❧✈✐❞♦ ❡♠ t❛✐s ❛♣❧✐❝❛çõ❡s ❝r✐♦✉ ❣r❛♥❞❡s ❞❡s❛✜♦s ♣❛r❛ ♦s ❙■●s ❡ ♥❡❝❡ss✐t❛ ❞❡ ❛❧❣♦r✐t♠♦s ♦t✐♠✐③❛❞♦s t❛♥t♦ ♣❛r❛ ♣r♦❝❡ss❛♠❡♥t♦ ✐♥t❡r♥♦ q✉❛♥t♦ ♣❛r❛ tr❛♥s❢❡rê♥❝✐❛ ❞❡ ❞❛❞♦s✳ ❯♠❛ ❞❡ss❛s ❛♣❧✐❝❛çõ❡s é ♦ ❝á❧❝✉❧♦ ❞❡ ♠❛♣❛s ❞❡ ✈✐s✐❜✐❧✐❞❛❞❡ ♦✉ ✈✐❡✇s❤❡❞✱ q✉❡ ❝♦♥s✐st❡ ❡♠ ♦❜t❡r ♦ ❝♦♥❥✉♥t♦ ❞❡ ♣♦♥t♦s ✈✐sí✈❡✐s ❛ ♣❛rt✐r ❞❡ ✉♠ ♣♦♥t♦p✳ ◆❡ss❡ tr❛❜❛❧❤♦✱ ♥ós ❛♣r❡s❡♥t❛♠♦s ✉♠ ❡st✉❞♦ ❡ ❝♦♠♦ r❡s✉❧t❛❞♦ ✉♠ ❛❧❣♦r✐t♠♦ ❡✜❝✐❡♥t❡ ♣❛r❛ ❝❛❧❝✉❧❛r ♦ ✈✐❡✇s❤❡❞ ❡♠ t❡rr❡♥♦s ❛r♠❛③❡♥❛❞♦s ❡♠ ♠❡♠ór✐❛ ❡①t❡r♥❛✳ ❆ ❝♦♠♣❧❡✲ ①✐❞❛❞❡ ❞♦ ❛❧❣♦r✐t♠♦ é ✉♠❛ ❢✉♥çã♦ ❞♦ ♥ú♠❡r♦ ❞❡ ♦♣❡r❛çõ❡s ❞❡ ❡♥tr❛❞❛ ❡ s❛í❞❛ ❣❛st❛s ♣❛r❛ ❝❛❧❝✉❧❛r ❛ ✈✐s✐❜✐❧✐❞❛❞❡ ❡✱ ❝♦♠♦ ♠♦str❛♠ ♦s r❡s✉❧t❛❞♦s✱ ♦ ❛❧❣♦r✐t♠♦ ♣r♦♣♦st♦ ♣♦ss✉✐ ❞❡s❡♠♣❡♥❤♦ ♠❡❧❤♦r q✉❡ ♦s ❛❧❣♦r✐t♠♦s ❝♦♥❤❡❝✐❞♦s ❞❡s❝r✐t♦s ❡♠ ❧✐t❡r❛t✉r❛✳
❆❜str❛❝t
▼❆●❆▲❍➹❊❙✱ ▼✐r❡❧❧❛ ❆♥t✉♥❡s ❞❡✱ ▼✳❙❝✳✱ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❱✐ç♦s❛✱ ❆♣r✐❧ ♦❢ ✷✵✵✾✳ ❊✣❝✐❡♥t ❛❧❣♦r✐t❤♠ t♦ ❞❡t❡r♠✐♥❡ t❤❡ ✈✐❡✇s❤❡❞ ✐♥ t❡rr❛✐♥s st♦r❡❞ ✐♥ ❡①t❡r♥❛❧ ♠❡♠♦r②✳ ❆❞✈✐s❡r✿ ▼❛r❝✉s ❱✐♥í❝✐✉s ❆❧✈✐♠ ❆♥❞r❛❞❡✳ ❈♦✲❆❞✈✐s❡rs✿ ❱❧❛❞✐♠✐r ❖❧✐✈❡✐r❛ ❉✐ ■♦r✐♦ ❛♥❞ ❈❛r❧♦s ❆✳ ❆❧✈❛r❡s ❙♦❛r❡s ❘✐❜❡✐r♦✳
❆s ♠♦r❡ ❞❡t❛✐❧❡❞ t❡rr❛✐♥ ❞❛t❛ ❜❡❝♦♠❡ ❛✈❛✐❧❛❜❧❡✱ ♠❛♥② t❡rr❛✐♥ ❛♣♣❧✐❝❛t✐♦♥s ♠✉st ♣r♦❝❡ss ❧❛r❣❡ ❣❡♦❣r❛♣❤✐❝ ❛r❡❛s ❛t ❤✐❣❤❡r r❡s♦❧✉t✐♦♥s✳ ❚❤❡ ♠❛ss✐✈❡ ❞❛t❛ ♣r♦❝❡ss✐♥❣ ✐♥✈♦❧✈❡❞ ✐♥ s✉❝❤ ❛♣♣❧✐❝❛t✐♦♥s ♣r❡s❡♥ts s✐❣♥✐✜❝❛♥t ❝❤❛❧❧❡♥❣❡s t♦ ●■❙ ❛♥❞ r❡q✉✐r❡s ❛❧❣♦✲ r✐t❤♠s t❤❛t ❛r❡ ♦♣t✐♠✐③❡❞ ❢♦r ❜♦t❤ ❞❛t❛ tr❛♥s❢❡r ❛♥❞ ❢♦r ❝♦♠♣✉t❛t✐♦♥✳ ❖♥❡ ♦❢ t❤❡s❡ ❛♣♣❧✐❝❛t✐♦♥s ✐s t❤❡ ✈✐❡✇s❤❡❞ ❝♦♠♣✉t❛t✐♦♥✱ t❤❛t ✐s✱ t♦ ❞❡t❡r♠✐♥❡ ❛❧❧ ✈✐s✐❜❧❡ ♣♦✐♥ts ❢r♦♠ ❛ ❣✐✈❡♥ ♣♦✐♥tp✳ ■♥ t❤✐s ✇♦r❦✱ ✇❡ ♣r❡s❡♥t ❛♥ st✉❞② ❛♥❞✱ ❛s ❛ r❡s✉❧t✱ ❛♥ ❡✣❝✐❡♥t ❛❧❣♦✲ r✐t❤♠ t♦ ❝♦♠♣✉t❡ t❤❡ ✈✐❡✇s❤❡❞ ♦♥ t❡rr❛✐♥s st♦r❡❞ ✐♥ ❡①t❡r♥❛❧ ♠❡♠♦r②✳ ❚❤❡ ❛❧❣♦r✐t❤♠ ❝♦♠♣❧❡①✐t② ✐s ❛ ❢✉♥❝t✐♦♥ ♦❢ t❤❡ ♥✉♠❜❡r ♦❢ ■✴❖ ♦♣❡r❛t✐♦♥s r❡q✉✐r❡❞ t♦ ❝❛❧❝✉❧❛t❡ t❤❡ ✈✐❡✇s❤❡❞ ❛♥❞✱ ❛s s❤♦✇♥ ❜② t❤❡ r❡s✉❧ts✱ ♦✉r ❛❧❣♦r✐t❤♠ ✐s ♠♦r❡ ❡✣❝✐❡♥t t❤❛♥ ♦t❤❡r ❛❧❣♦r✐t❤♠s ❞❡s❝r✐❜❡❞ ✐♥ t❤❡ ❧✐t❡r❛t✉r❡✳
■♥tr♦❞✉çã♦ ●❡r❛❧
◆♦s ú❧t✐♠♦s ❛♥♦s✱ ❞❛❞♦s s♦❜r❡ ❛ s✉♣❡r❢í❝✐❡ ❞❛ ❚❡rr❛ tê♠ s✐❞♦ ♣r♦❞✉③✐❞♦s ❡♠ ❧❛r❣❛ ❡s✲ ❝❛❧❛✱ ❞❡✈✐❞♦ ❛♦s ❛✈❛♥ç♦s t❡❝♥♦❧ó❣✐❝♦s ♥❛ ❝♦❧❡t❛ ❞❡ ❞❛❞♦s ❞❡ t❡rr❡♥♦s✱ ❝♦♠♦ ♦s s✐st❡♠❛s ❞❡ ✈❛rr❡❞✉r❛ ❛ r❛❞❛r ✭▲■❉❆❘ ❡ ■❋❙❆❘✮ ✭❏❡♥s❡✱ ✷✵✵✼✮✳ ❊ss❡s s✐st❡♠❛s sã♦ ❝❛♣❛③❡s ❞❡ ❣❡r❛r r❛♣✐❞❛♠❡♥t❡ ♠♦❞❡❧♦s ❞✐❣✐t❛✐s ❞❡♥s♦s ❡ ❛❝✉r❛❞♦s ❞❛ t♦♣♦❣r❛✜❛✱ ♣♦r ✐ss♦ tê♠ s✐❞♦ ❡①tr❡♠❛♠❡♥t❡ ✉t✐❧✐③❛❞♦s ♣❛r❛ ❛♣❧✐❝❛çõ❡s q✉❡ ♥❡❝❡ss✐t❛♠ ❞❡ ♠❛✐♦r ✐♥❢♦r♠❛çã♦ ♥♦s ♠♦❞❡❧♦s ❞✐❣✐t❛✐s ❞❡ t❡rr❡♥♦✱ t❛✐s ❝♦♠♦ ♦s ❙✐st❡♠❛s ❞❡ ■♥❢♦r♠❛çã♦ ●❡♦❣rá✜❝❛ ✭❙■●s✮✳ ●r❛♥❞❡ q✉❛♥t✐❞❛❞❡ ❞❡ ✐♥❢♦r♠❛çõ❡s t❛♠❜é♠ t❡♠ s✐❞♦ ❝r✐❛❞❛ ❛ ♣❛rt✐r ❞❡ ✈ár✐❛s ❛♣❧✐❝❛çõ❡s ❝♦♠♦ ❜❛♥❝♦s ❞❡ ❞❛❞♦s✱ ❝♦♠♣✉t❛çã♦ ❝✐❡♥tí✜❝❛✱ ❣rá✜❝♦s✱ ❡♥tr❡t❡♥✐♠❡♥t♦✱ ♠✉❧t✐♠í❞✐❛✱ s❡♥s♦r❡s✱ ❛♣❧✐❝❛çõ❡s ❞❛ ✐♥t❡r♥❡t ❡ ❡✲♠❛✐❧✳ ❖ ♣r♦❥❡t♦ ❞❛ ◆❆❙❆ ❊❛rt❤ ❖❜s❡r✈✐♥❣ ❙②st❡♠ ✭◆❆❙❆✬s ❊❛rt❤ ❖❜s❡r✈✐♥❣ ❙②st❡♠ ✭❊❖❙✮✱ ✷✵✵✾✮✱ ♣❛rt❡ ♣r✐♥❝✐♣❛❧ ❞♦ ♣r♦❥❡t♦ ❊❛rt❤ ❙❝✐❡♥❝❡ ❊♥t❡r♣r✐s❡✱ ♣r♦❞✉③ ♣❡t❛❜②t❡s ✭1015 ❜②t❡s✮ ❞❡ ❞❛❞♦s r❛st❡r
♣♦r ❛♥♦✳ P❛r❛ s❡ t❡r ✐❞é✐❛ ❞❛ q✉❛♥t✐❞❛❞❡ ❞❡ ❞❛❞♦s ❛ q✉❡ ✐ss♦ s❡ r❡❢❡r❡✱ ✉♠ ♣❡t❛❜②t❡ ❡q✉✐✈❛❧❡ ❛♣r♦①✐♠❛❞❛♠❡♥t❡ ❛♦ ♠❡s♠♦ ✈♦❧✉♠❡ ❞❡ ✐♥❢♦r♠❛çã♦ ❡♠ ✉♠ ❜✐❧❤ã♦ ❞❡ ❧✐✈r♦s ❢♦r♠❛t❛❞♦s ❣r❛✜❝❛♠❡♥t❡✳ ❆s ✜❣✉r❛s ✶ ❡ ✷ r❡♣r❡s❡♥t❛♠ ❛♣❡♥❛s 6M B ❞❡♥tr❡ ♦s ♣❡t❛❜②t❡s ❡♠ ✐♠❛❣❡♥s ❛r♠❛③❡♥❛❞♦s ♣❡❧♦ ❊❖❙ ♥♦ ❛♥♦ ❞❡ ✷✵✵✽✳
❖s ❜❛♥❝♦s ❞❡ ❞❛❞♦s ❞❡ ✐♠❛❣❡♥s ❞❡ s❛té❧✐t❡s ♦♥❧✐♥❡ ✉s❛✲ ❞♦s ♣❡❧♦ ▼✐❝r♦s♦❢t ❚❡rr❛❙❡r✈❡r ✭♣❛rt❡ ❞♦ ▼❙◆ ❱✐rt✉❛❧ ❊❛rt❤✮ ✭❚❡rr❛❙❡r✈❡r✲❯❙❆✿ ▼✐❝r♦s♦❢t✬s ♦♥❧✐♥❡ ❞❛t❛❜❛s❡ ♦❢ s❛t❡❧❧✐t❡ ✐♠❛❣❡s✱ ✷✵✵✾✮ ❡ ●♦✲ ♦❣❧❡ ❊❛rt❤ ✭●♦♦❣❧❡ ❊❛rt❤ ♦♥❧✐♥❡ ❞❛t❛❜❛s❡ ♦❢ s❛t❡❧❧✐t❡ ✐♠❛❣❡s✱ ✷✵✵✾✮ ♣♦ss✉❡♠ ♦ t❛♠❛♥❤♦ ❞❡ ✈ár✐♦s t❡r❛❜②t❡s ✭1012 ❜②t❡s✮✳ ❖ ❞❛t❛ ✇❛r❡❤♦✉s❡ ❞♦ ❲❛❧✲▼❛rt ❝♦♥té♠
♠❡t❛❞❡ ❞❡ ✉♠ ♣❡t❛❜②t❡ ✭✺✵✵ t❡r❛❜②t❡s✮ ❞❡ ❞❛❞♦s✳ ❈♦♠ t❛❧ ✈♦❧✉♠❡ ❞❡ ✐♥❢♦r♠❛çõ❡s✱ ♦ ♠❛✐♦r ❞❡s❛✜♦ é ❡♥❝♦♥tr❛r ❢♦r♠❛s ❡✜❝✐❡♥t❡s ❞❡ ♠❛♥✐♣✉❧❛çã♦ ❡ ♣r♦❝❡ss❛♠❡♥t♦✱ ♦✉ ❣r❛♥❞❡ ♣❛rt❡ ❞❡ss❛ ✐♥❢♦r♠❛çã♦ s❡ t♦r♥❛rá ✐♥út✐❧✳
❆t✉❛❧♠❡♥t❡✱ ❛❧❣✉♠❛s ❞❛s ♠❛✐s ✐♠♣♦rt❛♥t❡s ❛♣❧✐❝❛çõ❡s ❡♠ ❧❛r❣❛ ❡s❝❛❧❛ ❡♥✈♦❧✲ ✈❡♠ ♦ ♣r♦❝❡ss❛♠❡♥t♦ ❞❡ ❞❛❞♦s ❞❡ t❡rr❡♥♦s✳ ❆♣❧✐❝❛çõ❡s t❛✐s ❝♦♠♦ ❛ ❝♦♠♣✉t❛çã♦ ❞❛ ♣❡rs✐stê♥❝✐❛ t♦♣♦❧ó❣✐❝❛ ❡ ❛ ❝♦♥str✉çã♦ ❞❛ ár✈♦r❡ ❞❡ ❝♦♥t♦r♥♦ ❞❡ t❡rr❡♥♦s ✭❆❣❣❛r✇❛❧ ❡t ❛❧✳✱ ✷✵✵✻✮✱ ♦ ❝á❧❝✉❧♦ ❞♦ ✢✉①♦ ❤✐❞r♦❧ó❣✐❝♦ ❡ ❛ ❞❡t❡r♠✐♥❛çã♦ ❞❡ ❜❛❝✐❛s ❤✐❞r♦❣rá✜❝❛s ✭❆r❣❡ ❡t ❛❧✳✱ ✷✵✵✸✮ sã♦ ❛❧❣✉♥s ❡①❡♠♣❧♦s✳ ❖ ❝á❧❝✉❧♦ ❞♦s ♣♦♥t♦s ✈✐sí✈❡✐s ❞❡ ✉♠ t❡rr❡♥♦
■♥tr♦❞✉çã♦ ●❡r❛❧ ✷
❋✐❣✉r❛ ✶✿ ■♠❛❣❡♠ ❞♦ ❘✐♦ ❆♠❛③♦♥❛s t✐r❛❞❛ ♣♦r ❛str♦♥❛✉t❛ ❡♠ ❛❣♦st♦ ❞❡ ✷✵✵✽✳
❋✐❣✉r❛ ✷✿ ■♠❛❣❡♠ ❞❛ ❈r❛t❡r❛ ❞❛ ❙❡rr❛ ❞❛ ❈❛♥❣❛❧❤❛ ❧♦❝❛❧✐③❛❞❛ ♥♦ ❚♦❝❛♥t✐♥s✳
■♥tr♦❞✉çã♦ ●❡r❛❧ ✸
✐♠♣♦rt❛♥t❡s ✉t✐❧✐③❛çõ❡s ♣rát✐❝❛s✱ t❛✐s ❝♦♠♦ ❞❡t❡r♠✐♥❛r ♦ ♥ú♠❡r♦ ♠í♥✐♠♦ ❞❡ t♦rr❡s ❞❡ ❝❡❧✉❧❛r ♥❡❝❡ssár✐❛s ♣❛r❛ ❝♦❜r✐r ✉♠❛ r❡❣✐ã♦ ✭❇❡♥✲▼♦s❤❡ ❡t ❛❧✳✱ ✷✵✵✼❀ ❇❡s♣❛♠②❛t♥✐❦❤ ❡t ❛❧✳✱ ✷✵✵✶❀ ▼✉rr❛② ❡t ❛❧✳✱ ✷✵✵✼❀ ❘❛♥❛✱ ✷✵✵✺✮✱ ♦t✐♠✐③❛r ♦ ♥ú♠❡r♦ ❡ ❛ ♣♦s✐çã♦ ❞❡ ❣✉❛r✲ ❞❛s ♣❛r❛ ❝♦❜r✐r ✉♠❛ r❡❣✐ã♦ ✭❋r❛♥❦❧✐♥ ❡ ❱♦❣t✱ ✷✵✵✻❀ ❊✐❞❡♥❜❡♥③✱ ✷✵✵✷❀ ❈❛❧❞✇❡❧❧ ❡t ❛❧✳✱ ✷✵✵✸✮✱ ♦t✐♠✐③❛r ♦ ♣❧❛♥❡❥❛♠❡♥t♦ ❞❡ r♦t❛s ❡♠ t❡rr❡♥♦s ✭▲❡❡ ❡ ❙t✉❝❦②✱ ✶✾✾✽✮✱ ❡t❝✳
❆❧é♠ ❞❛ ✐♠♣♦rtâ♥❝✐❛ ❞❛s ❛♣❧✐❝❛çõ❡s ❡♥✈♦❧✈❡♥❞♦ ♦ ❝á❧❝✉❧♦ ❞♦ ✈✐❡✇s❤❡❞✱ ❛ ♠❛✐♦r ♠♦t✐✈❛çã♦ ❞❡ss❡ tr❛❜❛❧❤♦ é ♦ ❛✉♠❡♥t♦ s✐❣♥✐✜❝❛t✐✈♦ ❞❛ q✉❛♥t✐❞❛❞❡ ❞❡ ❝♦♠♣✉t❛çã♦ ♥❡❝❡ssár✐❛ ♣❛r❛ ❛ ❡①❡❝✉çã♦ ❞❡ss❛ ❛♣❧✐❝❛çã♦ ❡♠ t❡rr❡♥♦s ♠❛✐♦r❡s q✉❡ ❛ ♠❡♠ór✐❛ ✐♥t❡r♥❛✳ ❆ ❚❛❜❡❧❛ ✶ ❛♣r❡s❡♥t❛ ♦ t❡♠♣♦ ❞❡ ❡①❡❝✉çã♦ ♣❛r❛ ❞❡t❡r♠✐♥❛r ♦ ✈✐❡✇s❤❡❞ ❡♠ t❡rr❡♥♦s ❞❡ ❞✐❢❡r❡♥t❡s t❛♠❛♥❤♦s ♣❡❧♦ ❛❧❣♦r✐t♠♦ ❞❡ ❱❛♥ ❑r❡✈❡❧❞ ✭❱❛♥ ❑r❡✈❡❧❞✱ ✶✾✾✻✮✱ q✉❡ é ✉♠ ❞♦s ❛❧❣♦r✐t♠♦s ♠❛✐s ❡✜❝✐❡♥t❡s ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❞♦ ✈✐❡✇s❤❡❞ ❡♠ ♠❡♠ór✐❛ ✐♥t❡r♥❛✳ ❱❛❧❡ r❡ss❛❧t❛r q✉❡ ❡ss❡s ❞❛❞♦s ❢♦r❛♠ ♦❜t✐❞♦s ♥♦ tr❛❜❛❧❤♦ ✭❍❛✈❡r❦♦rt ❡t ❛❧✳✱ ✷✵✵✼✮ ❡ ❢♦r❛♠ ❝♦❧❡t❛❞♦s ✉t✐❧✐③❛♥❞♦ ✉♠❛ ♠áq✉✐♥❛ P♦✇❡r ▼❛❝✐♥t♦s❤ ●✺ ❝♦♠ ♣r♦❝❡ss❛❞♦r ❞✉❛❧ ❞❡ ✷✳✺●❍③✱ ✺✶✷ ❑❇ ❞❡ ❝❛❝❤❡ ♣♦r ♣r♦❝❡ss❛❞♦r✱ ✶●❇ ❞❡ ❘❆▼ ❡ ❍❉ s❡r✐❛❧✲❆❚❆ ❞❡ ✼✷✵✵ ❘P▼✳ ❉❡ ❛❝♦r❞♦ ❝♦♠ ❛ ❚❛❜❡❧❛ ✶✱ ✉♠ ❛✉♠❡♥t♦ ♠♦❞❡st♦ ♥♦ t❛♠❛♥❤♦ ❞♦s ♠♦❞❡❧♦s ❞❡ t❡rr❡♥♦ ❝❛✉s❛ ✉♠❛ ❡①♣❧♦sã♦ ❞❡ ❝✉st♦ ✐♥❛❝❡✐tá✈❡❧✱ ❣❡r❛♥❞♦ ❛té ♠❡s♠♦ ❛ ✐♠♣♦ss✐❜✐❧✐❞❛❞❡ ❞❡ ♣r♦❝❡ss❛♠❡♥t♦ ❞♦s t❡rr❡♥♦s✳
❚❛♠❛♥❤♦ ❞♦ ❚❡rr❡♥♦ ❚❡♠♣♦ ❞❡ ❡①❡❝✉çã♦ ✭s✮
✼ ▼❇ ✽
✷✺ ▼❇ ✸✽
✹✵ ▼❇ ✽✵
✶✶✾ ▼❇ ✼✸✻
✷✻✼ ▼❇ ❢❛❧❤❛ ❞❡ ❛❧♦❝❛çã♦ ❞❡ ♠❡♠ór✐❛ ❚❛❜❡❧❛ ✶✿ ❚❡♠♣♦ ❞❡ ❡①❡❝✉çã♦ ❞♦ ❛❧❣♦r✐t♠♦ ❞❡ ❱❛♥ ❑r❡✈❡❧❞
❊♠❜♦r❛ ✉♠❛ ❣r❛♥❞❡ q✉❛♥t✐❞❛❞❡ ❞❡ ❞❛❞♦s s✐❣♥✐✜q✉❡ ✉♠❛ ♠❛✐♦r r✐q✉❡③❛ ❞❡ ❞❡✲ t❛❧❤❡s ❡ ❛✉♠❡♥t❡ ♦ ♣♦t❡♥❝✐❛❧ ❞❛s ❛♣❧✐❝❛çõ❡s✱ ✐st♦ ❝❛✉s❛ ♣r♦❜❧❡♠❛s ❞❡ ❡s❝❛❧❛❜✐❧✐❞❛❞❡ ♣❛r❛ ♦s ❛❧❣♦r✐t♠♦s ❡①✐st❡♥t❡s✱ ♣♦✐s ♦ ❛✉♠❡♥t♦ ❞♦s r❡q✉✐s✐t♦s ❝♦♠♣✉t❛❝✐♦♥❛✐s ♥❡❝❡s✲ sár✐♦s ♣❛r❛ ♦ ❜♦♠ ❞❡s❡♠♣❡♥❤♦ ❞♦ ❛❧❣♦r✐t♠♦ s✉♣❡r❛ ❡♠ ♠✉✐t♦ ♦ ❛✉♠❡♥t♦ ❞♦s ❞❛❞♦s ❛ s❡r❡♠ ♣r♦❝❡ss❛❞♦s✳ P♦r ❡①❡♠♣❧♦✱ ♦ t❛♠❛♥❤♦ ❞❛ ♠❡♠ór✐❛ ✐♥t❡r♥❛ t❡♠ s♦❢r✐❞♦ ❛✉✲ ♠❡♥t♦ ❞❡✈✐❞♦ às ♥♦✈❛s t❡❝♥♦❧♦❣✐❛s✱ ♠❛s ♥ã♦ ❝♦♠ ❛ r❛♣✐❞❡③ ♥❡❝❡ssár✐❛ ♣❛r❛ s❛t✐s❢❛③❡r ❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ ❛♣❧✐❝❛çõ❡s ❡♠ ❧❛r❣❛ ❡s❝❛❧❛ q✉❡✱ ♣❛r❛ ❛❧❝❛♥ç❛r ❛ ❡✜❝✐ê♥❝✐❛✱ ♣r❡❝✐s❛♠ ❞❡ t♦❞♦s ♦s ❞❛❞♦s ❛❝❡ssí✈❡✐s ❛ ♣❛rt✐r ❞❛ ♠❡♠ór✐❛ ✐♥t❡r♥❛✳
■♥tr♦❞✉çã♦ ●❡r❛❧ ✹
s♦❧✉çã♦ ✉t✐❧✐③❛❞❛ é ❛ ❞✐♠✐♥✉✐çã♦ ❞❛ r❡s♦❧✉çã♦ ❞❛ r❡♣r❡s❡♥t❛çã♦ ❞♦ t❡rr❡♥♦✳ P♦ré♠✱ ❡ss❛s ❡str❛té❣✐❛s ♣♦❞❡♠ s✉♣r✐♠✐r ♦s ❡❢❡✐t♦s ❞❡ ✈❛r✐❛çõ❡s r❡❧❛t✐✈❛♠❡♥t❡ ♣❡q✉❡♥❛s ♥♦s ❞❛❞♦s ❞❡ ❡❧❡✈❛çã♦ ❡ ♣♦❞❡♠ ❣❡r❛r ✉♠ ❣r❛♥❞❡ ✐♠♣❛❝t♦ ♥❛ ✈✐s✐❜✐❧✐❞❛❞❡✱ ♣♦✐s ❡ss❛ é ✉♠❛ ❛♣❧✐❝❛çã♦ ♦♥❞❡ q✉❛❧q✉❡r ❞✐❢❡r❡♥ç❛ ❞♦ ♠♦❞❡❧♦ ❞✐❣✐t❛❧ ♣❛r❛ ♦ t❡rr❡♥♦ ♦r✐❣✐♥❛❧ ♣♦❞❡ ❝❛✉s❛r ❞✐st♦rçõ❡s ✐♥❛❝❡✐tá✈❡✐s ♥♦ r❡s✉❧t❛❞♦✳ ❆❧é♠ ❞✐ss♦✱ ❣❡r❛❧♠❡♥t❡✱ q✉❛❧q✉❡r t❡♥t❛t✐✈❛ ❞❡ ❞✐♠✐♥✉✐çã♦ ❞❡ t❛♠❛♥❤♦ ❞♦s ♠♦❞❡❧♦s ❞✐❣✐t❛✐s é ✐♥s✉✜❝✐❡♥t❡ ♣❛r❛ ❡✈✐t❛r q✉❡ ✉♠❛ ♣❛rt❡ ❞♦s ❞❛❞♦s s❡❥❛ ❛r♠❛③❡♥❛❞❛ ❡♠ ♠❡♠ór✐❛ ❡①t❡r♥❛✱ ❞❛❞♦ ♦ ❣r❛♥❞❡ t❛♠❛♥❤♦ ❞♦s ♠♦❞❡❧♦s ❣❡r❛❞♦s ❛t✉❛❧♠❡♥t❡✳
P♦rt❛♥t♦✱ ❛ ♠❛✐♦r✐❛ ❞♦s ❛❧❣♦r✐t♠♦s ❛t✉❛✐s ♣❛r❛ ❝á❧❝✉❧♦ ❞❡ ✈✐❡✇s❤❡❞ ♥ã♦ sã♦ ❝❛♣❛③❡s ❞❡ ❛r♠❛③❡♥❛r ❡ ♣r♦❝❡ss❛r ♦s ♠♦❞❡❧♦s ❞✐❣✐t❛✐s ✐♥t❡r♥❛♠❡♥t❡✱ ❡①✐❣✐♥❞♦ q✉❡ ❡st❡s ❞❛❞♦s s❡❥❛♠ ♣r♦❝❡ss❛❞♦s ❡♠ ♠❡♠ór✐❛ ❡①t❡r♥❛✳ ■ss♦ t♦r♥❛ ❡ss❡s ❛❧❣♦r✐t♠♦s ♣♦✉❝♦ ❡✜❝✐❡♥t❡s ♣♦✐s✱ ❛♦ ❧✐❞❛r ❝♦♠ ❞❛❞♦s q✉❡ ♥ã♦ ❝❛❜❡♠ ♥❛ ♠❡♠ór✐❛ ✐♥t❡r♥❛✱ ♦ t❡♠♣♦ ❣❛st♦ ♥❛s ♦♣❡r❛çõ❡s ❞❡ ❡♥tr❛❞❛ ❡ s❛í❞❛ r❡s✉❧t❛♥t❡s ❞♦ ❛❝❡ss♦ ❡ tr❛♥s❢❡rê♥❝✐❛ ❞❡ ❞❛❞♦s ❞❡✴♣❛r❛ ❛ ♠❡♠ór✐❛ ❡①t❡r♥❛ é ♠✉✐t♦ ♠❛✐♦r q✉❡ ♦ t❡♠♣♦ ♣❛r❛ ♣r♦❝❡ss❛♠❡♥t♦ ✐♥t❡r♥♦✳ P♦r ✐ss♦✱ ♦s ❛❧❣♦r✐t♠♦s q✉❡ r❡❛❧✐③❛♠ ❡st❡ t✐♣♦ ❞❡ ♣r♦❝❡ss❛♠❡♥t♦ ♣r❡❝✐s❛♠ ♠✐♥✐♠✐③❛r ♦ ❛❝❡ss♦ ❛♦s ❞❛❞♦s✳
▼❛✐s ❡s♣❡❝✐✜❝❛♠❡♥t❡✱ ❛♣❧✐❝❛çõ❡s ❡♠ ❧❛r❣❛ ❡s❝❛❧❛ q✉❡ ♠❛♥✐♣✉❧❛♠ ❞❛❞♦s ❡♠ ♠❡♠ór✐❛ ❡①t❡r♥❛ ❞❡✈❡♠ t❡r s❡✉s ❛❧❣♦r✐t♠♦s ♣r♦❥❡t❛❞♦s ❡ ❛♥❛❧✐s❛❞♦s s♦❜ ✉♠ ♠♦❞❡❧♦ ❝♦♠♣✉t❛❝✐♦♥❛❧ q✉❡ ❛✈❛❧✐❛ ❛ ❝♦♠♣❧❡①✐❞❛❞❡ ❝♦♥s✐❞❡r❛♥❞♦ ❛s ♦♣❡r❛çõ❡s ❞❡ tr❛♥s❢❡rê♥❝✐❛ ❞❡ ❞❛❞♦s ❛♦ ✐♥✈és ❞❛s ♦♣❡r❛çõ❡s ❞❡ ♣r♦❝❡ss❛♠❡♥t♦ ♥❛ ❈P❯✳ ❉✐✈❡rs♦s ♠♦❞❡❧♦s tê♠ s✐❞♦ ❝r✐❛❞♦s ♣r♦♣♦♥❞♦ ❞❡t❡r♠✐♥❛r ❛ ❝♦♠♣❧❡①✐❞❛❞❡ ❞♦s ❛❧❣♦r✐t♠♦s ❝♦♥s✐❞❡r❛♥❞♦ ♦ ♥ú♠❡r♦ ❞❡ ♦♣❡r❛çõ❡s ❞❡ ❡♥tr❛❞❛ ❡ s❛í❞❛ ❡①❡❝✉t❛❞❛s❀ ✉♠ ❞❡❧❡s é ♦ ♠♦❞❡❧♦ ❞❡ ❆❣❣❛r✇❛❧ ❡ ❱✐tt❡r ✭❆❣❣❛r✇❛❧ ❡ ❱✐tt❡r✱ ✶✾✽✽✮✳ ❆❧❣♦r✐t♠♦s q✉❡ ✉t✐❧✐③❛♠ ❡ss❡ t✐♣♦ ❞❡ ♠♦❞❡❧♦ sã♦ ❣❡r❛❧♠❡♥t❡ ❝❤❛♠❛❞♦s ❞❡ ❛❧❣♦r✐t♠♦s ❡♠ ♠❡♠ór✐❛ ❡①t❡r♥❛ ♦✉ ■✴❖ ❡✣❝✐❡♥t ❛❧❣♦r✐t❤♠s✳ ❆❧❣♦r✐t♠♦s ❡♠ ♠❡♠ór✐❛ ❡①t❡r♥❛ tê♠ ♦ ♦❜❥❡t✐✈♦ ❞❡ ❞✐♠✐♥✉✐r ♦ ♥ú♠❡r♦ ❞❡ ❛❝❡ss♦s ❛♦s ❞❛❞♦s ❛r♠❛③❡♥❛❞♦s ❡①t❡r♥❛♠❡♥t❡✳ P❛r❛ ✐ss♦✱ ❡ss❡s ❛❧❣♦r✐t♠♦s ✉t✐❧✐③❛♠ ❡str✉t✉r❛s ❞❡ ❞❛❞♦s ❡♠ ❞✐s❝♦ q✉❡ ♦r❣❛♥✐③❛♠ ❡ ♣❡r♠✐t❡♠ ♦ ❛❝❡ss♦ ❛♦s ❞❛❞♦s ❞❡ ❢♦r♠❛ ❡✜❝✐❡♥t❡✱ ❛❧é♠ ❞❡ ❛❧❣♦r✐t♠♦s q✉❡ ♠❛♥✐♣✉❧❛♠ ❡ss❡s ❞❛❞♦s ♥❛ ♣ró♣r✐❛ ♠❡♠ór✐❛ ❡①t❡r♥❛✱ ✉t✐❧✐③❛♥❞♦ ♦ ♠í♥✐♠♦ ♣♦ssí✈❡❧ ❞❡ ♦♣❡r❛çõ❡s ❞❡ ❡♥tr❛❞❛ ❡ s❛í❞❛✳ ❉❡✈✐❞♦ ❛ ♣❡sq✉✐s❛s ❡①t❡♥s✐✈❛♠❡♥t❡ r❡❛❧✐③❛❞❛s s♦❜r❡ ❛ ♠❛♥✐♣✉❧❛çã♦ ❞❡ ❣r❛♥❞❡ ✈♦❧✉♠❡ ❞❡ ❞❛❞♦s✱ ❡ss❡s ❛❧❣♦r✐t♠♦s ♣♦❞❡♠ s❡ ❝♦♥❝❡♥tr❛r ♥❛ r❡s♦❧✉çã♦ ❞♦ ♣r♦❜❧❡♠❛ ❛ q✉❡ s❡ ♣r♦♣õ❡♠ ❝♦♠ ♦ ❛✉①í❧✐♦ ❞❡ ❜✐❜❧✐♦t❡❝❛s q✉❡ ❞✐s♣♦♥✐❜✐❧✐③❛♠ ❞✐✈❡rs❛s ❡str✉t✉r❛s ❡ ❛❧❣♦r✐t♠♦s q✉❡ ♣r♦❝❡ss❛♠ ❞❛❞♦s ❡♠ ♠❡♠ór✐❛ ❡①t❡r♥❛✱ ❡♥❝❛♣s✉❧❛♥❞♦ ❛ ❢♦r♠❛ ❝♦♠♦ ❡ss❡ ♣r♦❝❡ss❛♠❡♥t♦ é r❡❛❧✐③❛❞♦ ✭❆r❣❡ ❡t ❛❧✳✱ ✷✵✵✷❛❀ ❉❡♠❡♥t✐❡✈ ❡t ❛❧✳✱ ✷✵✵✺✮✳
■♥tr♦❞✉çã♦ ●❡r❛❧ ✺
❱✐❡✇s❤❡❞✮✳ ❆ ❡str❛té❣✐❛ ❞❡ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞♦ ❊▼❱❙ ❝♦♥s✐st✐✉ ❞❡ ❞✐✈❡rs❛s ❡t❛♣❛s ✐♥❝❧✉✐♥❞♦ ❛ ❡s❝♦❧❤❛ ❞❡ ✉♠ ♠♦❞❡❧♦ ❞❡ r❡♣r❡s❡♥t❛çã♦ ♣❛r❛ ♦ t❡rr❡♥♦ ✉t✐❧✐③❛❞♦ ♣❡❧♦ ❛❧✲ ❣♦r✐t♠♦❀ ♦ ❡st✉❞♦ ❡ ❛ ❞❡✜♥✐çã♦ ❞❡ ✉♠ ❛❧❣♦r✐t♠♦ ❡♠ ♠❡♠ór✐❛ ✐♥t❡r♥❛ ♣❛r❛ s❡r ✉s❛❞♦ ❝♦♠♦ ❜❛s❡ ♣❛r❛ ♦ ❛❧❣♦r✐t♠♦ ❡♠ ♠❡♠ór✐❛ ❡①t❡r♥❛ ✶❀ ♦ ❡st✉❞♦ ❞♦s ♠❡❧❤♦r❡s ♠♦❞❡❧♦s
❡ té❝♥✐❝❛s ❞❡ tr❛t❛♠❡♥t♦ ❞❡ ❞❛❞♦s ❡♠ ♠❡♠ór✐❛ ❡①t❡r♥❛❀ ♦ ♣r♦❥❡t♦ ❡ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞♦ ❛❧❣♦r✐t♠♦ ❡♠ s✐❀ ❡ ❡st✉❞♦s ❝♦♠♣❛r❛t✐✈♦s ❝♦♠ ♦✉tr♦s ❛❧❣♦r✐t♠♦s ❝♦♥❤❡❝✐❞♦s q✉❡ r❡s♦❧✈❛♠ ♦ ♠❡s♠♦ ♣r♦❜❧❡♠❛ ♣❛r❛ ❛t❡st❛r ❛ ❡✜❝✐ê♥❝✐❛ ❞♦ ❊▼❱❙✳
❚♦❞❛s ❛s ❡t❛♣❛s ❞❡ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞♦ ❊▼❱❙ ❢♦r❛♠ ❞✐✈✐❞✐❞❛s ❡♠ ❝❛♣ít✉❧♦s ❡ s❡rã♦ ❛♣r❡s❡♥t❛❞❛s ❛♦ ❧♦♥❣♦ ❞❛ ❞✐ss❡rt❛çã♦✳ ▼❛s✱ r❡s✉♠✐❞❛♠❡♥t❡✱ ♦ ❊▼❱❙ é ✉♠ ❛❧❣♦r✐t♠♦ ❡✜❝✐❡♥t❡ ♣❛r❛ ❝á❧❝✉❧♦ ❞♦ ✈✐❡✇s❤❡❞ ❞❡ ♣♦♥t♦s ❡♠ t❡rr❡♥♦s r❡♣r❡s❡♥t❛❞♦s ♣♦r ▼❉❊s ✷ ❛r♠❛③❡♥❛❞♦s ❡♠ ♠❡♠ór✐❛ ❡①t❡r♥❛✳ ❖ ❛❧❣♦r✐t♠♦ é ✉♠❛ ❛❞❛♣t❛çã♦ ❞♦
♠ét♦❞♦ ❞❡s❡♥✈♦❧✈✐❞♦ ♣♦r ❋r❛♥❦❧✐♥ ❡ ❘❛② ✭❋r❛♥❦❧✐♥✱ ✷✵✵✷✮ ♣❛r❛ ❝á❧❝✉❧♦ ❞❡ ✈✐❡✇s❤❡❞ ❡♠ ♠❡♠ór✐❛ ✐♥t❡r♥❛ ♣❡r♠✐t✐♥❞♦ ❛ ♠❛♥✐♣✉❧❛çã♦ ❡✜❝✐❡♥t❡ ❞❡ ❣r❛♥❞❡s t❡rr❡♥♦s ✭✻●❇ ♦✉ ♠❛✐s✮✳ ❖ ❣r❛♥❞❡ ♥ú♠❡r♦ ❞❡ ❛❝❡ss♦s ❛♦ ❞✐s❝♦ é ♦t✐♠✐③❛❞♦ ♣❡❧♦ ✉s♦ ❞❛ ❜✐❜❧✐♦t❡❝❛ ❙❚❳❳▲ ✭❉❡♠❡♥t✐❡✈ ❡t ❛❧✳✱ ✷✵✵✺✮✳ ❆ ❝♦♠♣❧❡①✐❞❛❞❡ ❞♦ ❊▼❱❙ é ❛♥❛❧✐s❛❞❛ s♦❜ ♦ ♠♦❞❡❧♦ ♣r♦♣♦st♦ ♣♦r ❆❣❣❛r✇❛❧ ❡ ❱✐tt❡r ✭❆❣❣❛r✇❛❧ ❡ ❱✐tt❡r✱ ✶✾✽✽✮✳ ❈♦♠♣❛r❛♥❞♦ ♥♦ss♦ ❛❧❣♦r✐t♠♦ ❝♦♠ ♦ ❛❧❣♦r✐t♠♦ ❞❡ ❋r❛♥❦❧✐♥ ❡ ❘❛②✱ ♦ ♥♦ss♦ s❡ ♠♦str♦✉ ✸✳✺ ✈❡③❡s ♠❛✐s rá♣✐❞♦ ❡ ❝♦♥s❡❣✉✐✉ ♣r♦❝❡ss❛r t❡rr❡♥♦s ♠❛✐♦r❡s q✉❡ ✺ ●❇ ❡♥q✉❛♥t♦ q✉❡ ♦ ❛❧❣♦r✐t♠♦ ❞❡ ❋r❛♥❦❧✐♥ ❡ ❘❛② só ❢♦✐ ❝❛♣❛③ ❞❡ ♣r♦❝❡ss❛r t❡rr❡♥♦s ❞❡✱ ♥♦ ♠á①✐♠♦✱ ✷ ●❇✳ ❆❧é♠ ❞✐ss♦✱ ❝♦♠♣❛r❛♥❞♦ ♦ ❊▼❱❙ ❝♦♠ ♦ ❛❧❣♦r✐t♠♦ ♣r♦♣♦st♦ ♣♦r ❍❛✈❡r❦♦rt ❡t ❛❧✳ ✭❚♦♠❛ ❡t ❛❧✳✱ ✷✵✵✼✮✱ t❛♠❜é♠ ♣r♦♣♦st♦ ♣❛r❛ ❝❛❧❝✉❧❛r ♦ ✈✐❡✇s❤❡❞ ❡♠ ♠❡♠ór✐❛ ❡①t❡r♥❛✱ ♣♦❞❡♠♦s ❞✐③❡r q✉❡ ♦ ❊▼❱❙ s❡ ♠♦str♦✉ ♠❛✐s ❞❡ ✼ ✈❡③❡s ♠❛✐s rá♣✐❞♦✱ ❛❧é♠ ❞❡ s❡r ♠❛✐s s✐♠♣❧❡s ❡ ❢á❝✐❧ ❞❡ ✐♠♣❧❡♠❡♥t❛r✳
❖r❣❛♥✐③❛çã♦ ❞❛ ❉✐ss❡rt❛çã♦
❖ ❈❛♣ít✉❧♦ ✷ ❞❡s❝r❡✈❡ ❢✉♥❞❛♠❡♥t♦s t❡ór✐❝♦s q✉❡ s❡r✈✐r❛♠ ❞❡ ❜❛s❡ ♣❛r❛ ♦ ♣r♦❥❡t♦ ❞♦ ❛❧❣♦r✐t♠♦ ❡♠ ♠❡♠ór✐❛ ❡①t❡r♥❛✳ ◆❛ ❙❡çã♦ ✷✳✶✱ ❛♣r❡s❡♥t❛♠♦s ♦s ♠♦❞❡❧♦s ❞❡ r❡✲ ♣r❡s❡♥t❛çã♦ ❞❡ t❡rr❡♥♦s ♠❛✐s ❝♦♥❤❡❝✐❞♦s ❡ ♦s ❝r✐tér✐♦s ✉t✐❧✐③❛❞♦s ♣❛r❛ ❛ ❞❡✜♥✐çã♦ ❞♦ ♠♦❞❡❧♦ ❛ s❡r ✉t✐❧✐③❛❞♦ ♥♦ ♣r♦❥❡t♦ ❞♦ ❛❧❣♦r✐t♠♦ ❊▼❱❙✳ ❆ ❙❡çã♦ ✷✳✷ ❛♣r❡s❡♥t❛ ❞❡t❛❧❤❡s ❞♦s ❞✐✈❡rs♦s ♣r♦❜❧❡♠❛s ❞❡ ✈✐s✐❜✐❧✐❞❛❞❡ ❡♠ t❡rr❡♥♦s✱ ✐♥❝❧✉✐♥❞♦ ❛ ❞❡t❡r♠✐♥❛çã♦ ❞♦ ✈✐✲ ❡✇s❤❡❞✳ ❆ ❙❡çã♦ ✷✳✸ ❛♣r❡s❡♥t❛ ♦ r❡s✉❧t❛❞♦ ❞❡ ♣❡sq✉✐s❛s r❡❝❡♥t❡s s♦❜r❡ ❛ ♠❛♥✐♣✉❧❛çã♦ ❞❡ ❣r❛♥❞❡s ✈♦❧✉♠❡s ❞❡ ✐♥❢♦r♠❛çõ❡s ✐♥❝❧✉✐♥❞♦ ❛ ❞❡✜♥✐çã♦ ❞❡ ♠♦❞❡❧♦s ❝♦♠♣✉t❛❝✐♦♥❛✐s ❡ ❡str✉t✉r❛s ❞❡ ❞❛❞♦s ♣❛r❛ ♣r♦❥❡t♦ ❡ ❛♥á❧✐s❡ ❞❡ ❛❧❣♦r✐t♠♦s ♣❛r❛ ♠❛♥✐♣✉❧❛çã♦ ❞❡ ❞❛❞♦s ❡♠ ♠❡♠ór✐❛ ❡①t❡r♥❛✳
✶❆ ✐❞é✐❛ ❢♦✐ ❛❞❛♣t❛r ✉♠ ❛❧❣♦r✐t♠♦ ❥á ❡①✐st❡♥t❡ ♣❛r❛ ❛❝❡ss❛r ❡ ♣r♦❝❡ss❛r ❞❡ ❢♦r♠❛ ❡✜❝✐❡♥t❡ ♦s ❞❛❞♦s
❡♠ ♠❡♠ór✐❛ ❡①t❡r♥❛
■♥tr♦❞✉çã♦ ●❡r❛❧ ✻
❖ ❈❛♣ít✉❧♦ ✸ é ❞❡❞✐❝❛❞♦ ❛♦s tr❛❜❛❧❤♦s r❡❧❛❝✐♦♥❛❞♦s ❛♦ ❛ss✉♥t♦ ❞❛ ❞✐ss❡rt❛çã♦✿ ✈✐s✐❜✐❧✐❞❛❞❡ ❡♠ t❡rr❡♥♦s ❡ ❛❧❣♦r✐t♠♦s ❡♠ ♠❡♠ór✐❛ ❡①t❡r♥❛✳ ◆❛ ❙❡çã♦ ✸✳✶✱ ❛♣r❡s❡♥t❛✲ ♠♦s ♦s ❞✐✈❡rs♦s ❛❧❣♦r✐t♠♦s ♣❛r❛ ❝á❧❝✉❧♦ ❞❡ ✈✐❡✇s❤❡❞ ❡♠ ▼❉❊✬s ❡♥q✉❛♥t♦ ♥❛ ❙❡çã♦ ✸✳✷ ❞❡s❝r❡✈❡♠♦s ❛❧❣♦r✐t♠♦s r❡❝❡♥t❡s q✉❡ ✉t✐❧✐③❛♠ té❝♥✐❝❛s ❞❡ ♣r♦❝❡ss❛♠❡♥t♦ ❞❡ ❞❛❞♦s ❡♠ ♠❡♠ór✐❛ ❡①t❡r♥❛✳
❆ ♣r✐♥❝✐♣❛❧ ❢✉♥çã♦ ❞♦ ❈❛♣ít✉❧♦ ✹ é ❞❡s❝r❡✈❡r ♦ ❛❧❣♦r✐t♠♦ ❊▼❱❙✳ P❛r❛ t❛♥t♦✱ ❛ ❙❡çã♦ ✹✳✶ ❛♣r❡s❡♥t❛ ♦ ❛❧❣♦r✐t♠♦ ❞❡ ❋r❛♥❦❧✐♥ ❡ ❘❛② ✭❋r❛♥❦❧✐♥✱ ✷✵✵✷✮✱ ✉s❛❞♦ ❝♦♠♦ ❜❛s❡ ♣❛r❛ ♦ ❊▼❱❙ ❡ ❛ ❙❡çã♦ ✹✳✷ ❞❡s❝r❡✈❡ ♦ ❊▼❱❙ ❛♣r❡s❡♥t❛♥❞♦ ❞❡t❛❧❤❡s ❞❡ s✉❛ ✐♠♣❧❡♠❡♥t❛çã♦✳ ❆ ❙❡çã♦ ✹✳✸ ❛♣r❡s❡♥t❛ ❛ ❛♥á❧✐s❡ ❞❡ ❝♦♠♣❧❡①✐❞❛❞❡ ❞♦ ❛❧❣♦r✐t♠♦✳
❖ ❈❛♣ít✉❧♦ ✺ ♠♦str❛ ❛ ❛♥á❧✐s❡ ❞❡ ❡✜❝✐ê♥❝✐❛ ❞♦ ❊▼❱❙ ❛♣r❡s❡♥t❛♥❞♦ ♦s r❡s✉❧✲ t❛❞♦s ❞❛s ❝♦♠♣❛r❛çõ❡s r❡❛❧✐③❛❞❛s ♣❛r❛ ❛t❡st❛r s❡✉ ❞❡s❡♠♣❡♥❤♦✳ ◆❡ss❛ ❛♥á❧✐s❡✱ ✉t✐❧✐✲ ③❛♠♦s ❞✉❛s ❡str❛té❣✐❛s✿ ❝♦♠♣❛r❛r ♦ ❛❧❣♦r✐t♠♦ ❡♠ ♠❡♠ór✐❛ ❡①t❡r♥❛ ❝♦♠ ♦ ❛❧❣♦r✐t♠♦ ❞❡ ❋r❛♥❦❧✐♥ ❡ ❘❛② ✭❋r❛♥❦❧✐♥✱ ✷✵✵✷✮ ♣❛r❛ ♠♦str❛r s✉❛ ❡s❝❛❧❛❜✐❧✐❞❛❞❡ ❡ ❝♦♠♣❛rá✲❧♦ ❝♦♠ ✉♠ ♦✉tr♦ ❛❧❣♦r✐t♠♦ ❡♠ ♠❡♠ór✐❛ ❡①t❡r♥❛ ♣❛r❛ ❝á❧❝✉❧♦ ❞♦ ✈✐❡✇s❤❡❞✱ ♦ ❛❧❣♦r✐t♠♦ ❞❡ ❍❛✈❡r❦♦rt ❡t ❛❧✳ ✭❚♦♠❛ ❡t ❛❧✳✱ ✷✵✵✼✮✱ ♣❛r❛ ♠♦str❛r s❡✉ ❣❛♥❤♦ ❞❡ ❡✜❝✐ê♥❝✐❛✳ ❆ ❙❡çã♦ ✺✳✶ ♠♦str❛ ❛ ❞❡s❝r✐çã♦ ❞♦ ❛❧❣♦r✐t♠♦ ❞❡ ❍❛✈❡r❦♦rt ❡t ❛❧✳ ❆ ❙❡çã♦ ✺✳✷ ♠♦str❛ ❛ ❛♥á✲ ❧✐s❡ r❡❛❧✐③❛❞❛ ♣❛r❛ ❝♦♠♣r♦✈❛r ❛ ❡✜❝✐ê♥❝✐❛ ❞♦ ❛❧❣♦r✐t♠♦ ❊▼❱❙✳ ❏á ❛s s❡çõ❡s ✺✳✸ ❡ ✺✳✹ ❛♣r❡s❡♥t❛♠ ❛ ❝♦♠♣❛r❛çã♦ ❝♦♠ ♦ ❛❧❣♦r✐t♠♦ ❞❡ ❍❛✈❡r❦♦rt ❡t ❛❧✳ ❡ ❝♦♠ ♦ ❛❧❣♦r✐t♠♦ ❞❡ ❋r❛♥❦❧✐♥ ❡ ❘❛②✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳
❈❛♣ít✉❧♦ ✶
❘❡❢❡r❡♥❝✐❛❧ ❚❡ór✐❝♦
P❛r❛ ♦ ♣r♦❥❡t♦ ❞♦ ❛❧❣♦r✐t♠♦ ❛♣r❡s❡♥t❛❞♦ ♥❡st❛ ❞✐ss❡rt❛çã♦✱ ♣r❡❝✐s❛♠♦s ❞❡✜♥✐r ✉♠ ♠♦❞❡❧♦ ❞❡ r❡♣r❡s❡♥t❛çã♦ ❞❡ t❡rr❡♥♦s✱ ❡♥t❡♥❞❡r ❝♦♠♦ ♦❝♦rr❡ ♦ ❝á❧❝✉❧♦ ❞❛ ✈✐s✐❜✐❧✐❞❛❞❡ ❡♠ t❡rr❡♥♦s ❡ ❡s❝♦❧❤❡r ❛s ♠❡❧❤♦r❡s té❝♥✐❝❛s ❞❡ ♠❛♥✐♣✉❧❛çã♦ ❞❡ ❞❛❞♦s ❡♠ ♠❡♠ór✐❛ ❡①t❡r♥❛✳ ❚♦❞♦s ♦s ❝♦♥❝❡✐t♦s s♦❜r❡ ❡ss❛s q✉❡stõ❡s s❡rã♦ ❛♣r❡s❡♥t❛❞♦s ♥❛s ♣ró①✐♠❛s s❡çõ❡s✳
✶✳✶ ❘❡♣r❡s❡♥t❛çã♦ ❞❡ s✉♣❡r❢í❝✐❡s ❞❡ t❡rr❡♥♦
❉♦ ♣♦♥t♦ ❞❡ ✈✐st❛ ♠❛t❡♠át✐❝♦✱ ✉♠ t❡rr❡♥♦ ✭s✉♣❡r❢í❝✐❡ t♦♣♦❣rá✜❝❛✮ T ♣♦❞❡ s❡r ✈✐st♦ ❝♦♠♦ ❛ ✐♠❛❣❡♠ ❞❡ ✉♠❛ ❢✉♥çã♦ ❜✐❞✐♠❡♥s✐♦♥❛❧f ❞❡✜♥✐❞❛ s♦❜r❡ ✉♠ ❞♦♠í♥✐♦D❝♦♠♣❛❝t♦ ❡ ❝♦♥❡❝t❛❞♦ ♥♦ ♣❧❛♥♦ ❊✉❝❧✐❞✐❛♥♦ ✭❉❡ ❋❧♦r✐❛♥✐ ❡ ▼❛❣✐❧❧♦✱ ✷✵✵✸❀ ❉❡ ❋❧♦r✐❛♥✐ ❡t ❛❧✳✱ ✶✾✾✾✮✱ ✐st♦ é✱T = (x, y, f(x, y)), x, y ∈D✳ ❯♠ ♠♦❞❡❧♦ ❞✐❣✐t❛❧ ❞❡ t❡rr❡♥♦ ✭▼❉❚✮ é ✉♠ ♠♦❞❡❧♦ ❡♠ q✉❡ ❛ s✉♣❡r❢í❝✐❡ ❞♦ t❡rr❡♥♦ é ❝♦♥str✉í❞❛ ❛ ♣❛rt✐r ❞❡ ✉♠ ❝♦♥❥✉♥t♦ ✜♥✐t♦ ❞❡ ❞❛❞♦s ❞✐❣✐t❛✐s ✭♠❡❞✐❞❛s ❞❡ ❡❧❡✈❛çã♦✮ V = v0, ..., vn ∈ D ❡✱ ♣♦ss✐✈❡❧♠❡♥t❡✱ ✉♠ ❝♦♥❥✉♥t♦ ❞❡
s❡❣♠❡♥t♦s ❞❡ ❧✐♥❤❛ ♥ã♦✲s♦❜r❡♣♦st♦sE =e0, ..., em ❝✉❥❛s ❡①tr❡♠✐❞❛❞❡s ♣❡rt❡♥❝❡♠ ❛V✳
❯♠ ▼❉❚ ❝♦♥str✉í❞♦ ❡♠V r❡♣r❡s❡♥t❛ ✉♠❛ s✉♣❡r❢í❝✐❡ q✉❡ ✐♥t❡r♣♦❧❛✱ ♦✉ ❛♣r♦①✐♠❛✱ ❛s ♠❡❞✐❞❛s ❞❡ ❡❧❡✈❛çã♦ ❞♦s ♣♦♥t♦s ❞❡V✳
❖s ❞❛❞♦s ❡♠ V r❡♣r❡s❡♥t❛♠ ❛ ✈❛r✐❛çã♦ ❞❛ ❛❧t✐t✉❞❡ ❛♦ ❧♦♥❣♦ ❞♦ t❡rr❡♥♦✳ P❛r❛ q✉❡ ❡ss❡s ❞❛❞♦s✱ t❛♠❜é♠ ❝❤❛♠❛❞♦s ❞❡ ❛♠♦str❛s✱ s❡❥❛♠ r❡♣r❡s❡♥t❛t✐✈♦s✱ ❞❡✈❡✲s❡ ❝♦♥✲ s✐❞❡r❛r s✉❛ q✉❛♥t✐❞❛❞❡ ❡ t❛♠❜é♠ ♦ s❡✉ ♣♦s✐❝✐♦♥❛♠❡♥t♦ ❝♦♠ r❡❧❛çã♦ à ❞✐str✐❜✉✐çã♦ ❞❡ ❛❧t✐♠❡tr✐❛ ♥❛ s✉♣❡r❢í❝✐❡ ✭❋❡❧❣✉❡✐r❛s✱ ✷✵✵✶✮✳ P♦r ❡①❡♠♣❧♦✱ ✉♠❛ s✉♣❡r✲❛♠♦str❛❣❡♠ ♥✉♠❛ r❡❣✐ã♦ ♣❧❛♥❛ s✐❣♥✐✜❝❛ r❡❞✉♥❞â♥❝✐❛ ❞❡ ✐♥❢♦r♠❛çã♦✱ ❡♥q✉❛♥t♦ q✉❡ ♣♦✉❝♦s ♣♦♥t♦s ❡♠ ✉♠❛ r❡❣✐ã♦ ❞❡ r❡❧❡✈♦ ♠♦✈✐♠❡♥t❛❞♦ ✐♥❞✐❝❛♠ ❡s❝❛ss❡③ ❞❡ ✐♥❢♦r♠❛çã♦✳
❆s ❝❛r❛❝t❡r✐③❛çõ❡s ❞❡s❝r✐t❛s ❛❝✐♠❛ ❛♣r❡s❡♥t❛♠ ❞✉❛s ❡t❛♣❛s ❞♦ ♣r♦❝❡ss♦ ❞❡ ♠♦✲ ❞❡❧❛❣❡♠ ❞❡ ✉♠ ▼❉❚✿ ❛q✉✐s✐çã♦ ❞❛s ❛♠♦str❛s ♦✉ ❛♠♦str❛❣❡♠ ❡ ❣❡r❛çã♦ ❞♦ ♠♦❞❡❧♦
❘❡❢❡r❡♥❝✐❛❧ ❚❡ór✐❝♦ ✽
♣r♦♣r✐❛♠❡♥t❡ ❞✐t♦ ♦✉ ♠♦❞❡❧❛❣❡♠✳ ❊①✐st❡ ❛✐♥❞❛ ✉♠❛ t❡r❝❡✐r❛ ❡t❛♣❛ ❞❡✜♥✐❞❛ ❝♦♠♦ ❛ ✉t✐❧✐③❛çã♦ ❞♦ ♠♦❞❡❧♦ ♦✉ ❛♣❧✐❝❛çõ❡s✱ ✈❡❥❛ ❛ ❋✐❣✉r❛ ✶✳✶✳ ❈❛❞❛ ❡t❛♣❛ é ❞❡❝✐s✐✈❛ ♣❛r❛ ❛ q✉❛❧✐❞❛❞❡ ❞♦ ▼❉❚ ❣❡r❛❞♦✱ s❡♥❞♦ t❛♠❜é♠ ✐♥t❡r❞❡♣❡♥❞❡♥t❡s✱ ♦✉ s❡❥❛✱ ✉♠❛ ♣♦❞❡ ✐♥✲ ✢✉❡♥❝✐❛r ❞✐r❡t❛♠❡♥t❡ ♥❛ ♦✉tr❛✳ ❊♥tr❡t❛♥t♦✱ ❡①✐st❡ ✉♠❛ ♦r❞❡♠ ❧ó❣✐❝❛ ❞❡ ❡str✉t✉r❛çã♦ ♣❛r❛ ❝♦♥str✉çã♦ ❞❡ ✉♠ ▼❉❚✱ ❞❡✈❡♥❞♦✲s❡ ✐♥✐❝✐❛❧♠❡♥t❡ s❛❜❡r ❛ r❛③ã♦ ❞❛ ❣❡r❛çã♦ ❞♦ ♠♦❞❡❧♦✱ ♦✉ s❡❥❛✱ ♦ s❡✉ ♦❜❥❡t✐✈♦ ❡ ❛ s✉❛ ❛♣❧✐❝❛çã♦✳ ❆ ♣❛rt✐r ❞❡ss❛ ❞❡✜♥✐çã♦✱ ❥á s❡ ♣♦❞❡ t❡r ♥♦çã♦ ❞❛ ár❡❛ ❞❡ tr❛❜❛❧❤♦✱ ❞♦ t✐♣♦ ❞❡ t❡rr❡♥♦ q✉❡ s❡ q✉❡r ♠♦❞❡❧❛r✱ ❞❛ ❞✐s♣♦♥✐❜✐✲ ❧✐❞❛❞❡ ❞❡ ❞❛❞♦s ❞❡ ❡♥tr❛❞❛ ✭❛♠♦str❛❣❡♠✮ ❡ ❞♦ t✐♣♦ ❞❡ ♠♦❞❡❧♦ q✉❡ ✈❡♥❤❛ ❛ t❡r ♠❛✐♦r ❡✜❝✐ê♥❝✐❛ ♣❛r❛ ♦ t❡rr❡♥♦ r❡♣r❡s❡♥t❛❞♦✱ t❡♥❞♦ ❡♠ ✈✐st❛ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❛♣❧✐❝❛çõ❡s✳
❋✐❣✉r❛ ✶✳✶✿ ❊t❛♣❛s ❞♦ ♣r♦❝❡ss♦ ❞❡ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ✉♠ ▼❉❚
❖ t✐♣♦ ❞❡ ♠♦❞❡❧♦ ❞❡♣❡♥❞❡ ❞❛ ❢♦r♠❛ ❝♦♠♦ ♦s ♣♦♥t♦s ❞❡ V ✭❛♠♦str❛s✮ sã♦ ❡s❝♦✲ ❧❤✐❞♦s ♥♦ t❡rr❡♥♦✳ ❯♠❛ ❡s❝♦❧❤❛ ❛❧❡❛tór✐❛ ✭❡s♣❛❧❤❛❞❛✮ ❝❛r❛❝t❡r✐③❛ ❛ ❚■◆ ✭❚r✐❛♥❣✉❧❛t❡❞ ■rr❡❣✉❧❛r ◆❡t✇♦r❦✮✱ ❛ ❡s❝♦❧❤❛ ❞❡ ♣♦♥t♦s ❞✐str✐❜✉í❞♦s s♦❜r❡ ✉♠❛ ❣r❛❞❡ r❡❣✉❧❛r ❝❛r❛❝t❡✲ r✐③❛ ♦ ♠♦❞❡❧♦ ❞✐❣✐t❛❧ ❞❡ ❡❧❡✈❛çã♦ r❛st❡r✱ t❛♠❜é♠ ❝❤❛♠❛❞♦ ❞❡ ❉❊▼ ✭❉✐❣✐t❛❧ ❊❧❡✈❛t✐♦♥ ▼♦❞❡❧✮ ♦✉ ▼❉❊ ✭▼♦❞❡❧♦ ❉✐❣✐t❛❧ ❞❡ ❊❧❡✈❛çã♦✮✱ ❡ ❛ ❣❡r❛çã♦ ❞❡ ✐s♦❧✐♥❤❛s ❝❛r❛❝t❡r✐③❛ ♦s ▼❛♣❛s ❞❡ ❈✉r✈❛s ❞❡ ◆í✈❡❧✱ ✈❡❥❛ ❋✐❣✉r❛ ✶✳✷✳
❯♠❛ ❚■◆ ❛♣r♦①✐♠❛ s✉♣❡r❢í❝✐❡s ♣♦r ♣♦❧✐❡❞r♦s ❞❡ ❢❛❝❡s tr✐❛♥❣✉❧❛r❡s ♥ã♦ s♦❜r❡✲ ♣♦st❛s✱ ✉♠ ❡①❡♠♣❧♦ ❡stá ♥❛ ❋✐❣✉r❛ ✶✳✷✭❛✮✳ ●❡r❛❧♠❡♥t❡ ♦s ✈ért✐❝❡s ❞♦s ♣♦❧✐❡❞r♦s sã♦ ♦s ♣♦♥t♦s ❛♠♦str❛❞♦s ❞❛ s✉♣❡r❢í❝✐❡✳ ❊st❡ ♠♦❞❡❧♦ ♣♦❞❡ s❡r ✈✐st♦ ❝♦♠♦ ✉♠❛ ♣❛rt✐çã♦ ❞♦ ❞♦♠í♥✐♦ D ❡♠ r❡❣✐õ❡s tr✐❛♥❣✉❧❛r❡s ❝✉❥♦s ✈ért✐❝❡s sã♦ ♣♦♥t♦s ❞❡ V ❡ ❝✉❥❛s ❜♦r❞❛s sã♦ s❡❣♠❡♥t♦s ❞❡ E✳ ◆❡st❡ ❝❛s♦✱ ❛ ❢✉♥çã♦ f é ❞❡✜♥✐❞❛ ♣♦r ♣❛rt❡s✱ ❝♦♠♦ s❡♥❞♦ ✉♠❛ ❢✉♥çã♦ ❧✐♥❡❛r s♦❜r❡ ❝❛❞❛ ❢❛❝❡ tr✐❛♥❣✉❧❛r✳
❘❡❢❡r❡♥❝✐❛❧ ❚❡ór✐❝♦ ✾
❋✐❣✉r❛ ✶✳✷✿ ❈❧❛ss❡s ❞❡ ♠♦❞❡❧♦s ❞✐❣✐t❛✐s ❞❡ t❡rr❡♥♦✿ ✭❛✮ ❚■◆❀ ✭❜✮ ▼❉❊❀ ✭❝✮ ▼❛♣❛ ❞❡ ❈✉r✈❛s ❞❡ ◆í✈❡❧
❞♦s â♥❣✉❧♦s ♠í♥✐♠♦s ❞❡ ❝❛❞❛ tr✐â♥❣✉❧♦ ✭❙❝❤❡✇❝❤✉❦✱ ✶✾✾✻✮✳ ❊ss❡ ❝r✐tér✐♦ t❡♠ ❝♦♠♦ ♦❜❥❡t✐✈♦ ❡✈✐t❛r ❛ ❝r✐❛çã♦ ❞❡ tr✐â♥❣✉❧♦s ❛✜♥❛❞♦s ♦✉ ❝♦♠ â♥❣✉❧♦s ✐♥t❡r♥♦s ♠✉✐t♦ ❛❣✉❞♦s✱ ♦✉ s❡❥❛✱ ❛ s✉♣❡r❢í❝✐❡ ✜♥❛❧ ❞❡✈❡ ❝♦♥t❡r tr✐â♥❣✉❧♦s tã♦ ♣ró①✐♠♦s ❞❡ ❡q✉✐❧át❡r♦s q✉❛♥t♦ ♣♦ssí✈❡❧✳
▼❛t❡♠❛t✐❝❛♠❡♥t❡✱ ✉♠ ▼❉❊ ❝♦♥s✐st❡ ❞❡ ✉♠❛ ♣❛rt✐çã♦ ❞♦ ❞♦♠í♥✐♦D✉t✐❧✐③❛♥❞♦ ✉♠❛ ♠❛❧❤❛ r❡❣✉❧❛r ❞❡ r❡tâ♥❣✉❧♦s ♦✉ q✉❛❞r❛❞♦s ❞❡ ♠❡s♠♦ t❛♠❛♥❤♦ ✭❣❡r❛❧♠❡♥t❡✱ ❝❛❞❛ r❡tâ♥❣✉❧♦ é ❞❡♥♦♠✐♥❛❞♦ ♣✐①❡❧ ❡♠ ❛♥❛❧♦❣✐❛ às ✐♠❛❣❡♥s ❞✐❣✐t❛✐s✮✱ ✈❡❥❛ ❋✐❣✉r❛ ✶✳✷✭❜✮✳ ◆❡st❡ ❝❛s♦✱ ❛ ❢✉♥çã♦ f ✭t❛♠❜é♠ ❝❤❛♠❛❞❛ ❞❡ ❢✉♥çã♦ ❞❡ ✐♥t❡r♣♦❧❛çã♦✮ é ❞❡✜♥✐❞❛ ♣♦r ♣❛rt❡s s♦❜r❡ ❝❛❞❛ r❡tâ♥❣✉❧♦ ❡ ❞❡♣❡♥❞❡ ❞♦ ❣r❛✉ ❞❡ ❝♦♥t✐♥✉✐❞❛❞❡ ❞❡s❡❥❛❞♦✳ ❊ss❡ ❣r❛✉ ❞❡ ❝♦♥t✐♥✉✐❞❛❞❡ ❡stá r❡❧❛❝✐♦♥❛❞♦ ❝♦♠ ❛ ❢♦r♠❛ ❝♦♠♦ s❡rã♦ ❡st✐♠❛❞♦s ♦s ✈❛❧♦r❡s ❞❡ ❡❧❡✈❛çã♦ ❞❡ ♣♦♥t♦s q✉❡ ♥ã♦ ❢❛③❡♠ ♣❛rt❡ ❞❛ ♠❛tr✐③✱ q✉❡ é ❝♦♠♣♦st❛ ❛♣❡♥❛s ❞♦s ♣♦♥t♦s ❛♠♦str❛❞♦s ❞♦ ❝♦♥❥✉♥t♦V✳
❋✉♥çõ❡s ❞❡ ✐♥t❡r♣♦❧❛çã♦ sã♦ ✉s❛❞❛s ❡♠ ❛♠❜❛s ❛s r❡♣r❡s❡♥t❛çõ❡s✱ ▼❉❊ ❡ ❚■◆✱ q✉❛♥❞♦ é ♥❡❝❡ssár✐♦ s❛❜❡r ♦s ✈❛❧♦r❡s ❞❡ ❡❧❡✈❛çã♦ ❞❡ ♣♦♥t♦s q✉❡ ♥ã♦ ❢❛③❡♠ ♣❛rt❡ ❞❛ ♠❛tr✐③ ♦✉ ♥ã♦ sã♦ ♦s ✈ért✐❝❡s ❞♦s tr✐â♥❣✉❧♦s✳ ❆s ❢✉♥çõ❡s ❞❡ ✐♥t❡r♣♦❧❛çã♦ ♣♦❞❡♠ s❡r ❞❡✜♥✐❞❛s ❝♦♠♦ ❣❧♦❜❛✐s ♦✉ ❧♦❝❛✐s✳ ❆ ❢✉♥çã♦ ❣❧♦❜❛❧ é ❞❡♣❡♥❞❡♥t❡ ❞❡ t♦❞♦s ♦s ♣♦♥t♦s ❛♠♦str❛❞♦s✱ s❡♥❞♦ q✉❡ ❛ ❛❧t❡r❛çã♦ ❞❡ ✉♠ ✈❛❧♦r ❞❡ ❡♥tr❛❞❛ ❛❢❡t❛ t♦❞♦s ♦s ♣♦♥t♦s ❞♦ ♠♦❞❡❧♦✳ ❆s ❢✉♥çõ❡s ❧♦❝❛✐s sã♦ ❞❡✜♥✐❞❛s ♣❛r❛ ♣❡q✉❡♥❛s ♣♦rçõ❡s ❞♦s ♠♦❞❡❧♦s✱ s❡♥❞♦ ❛♣❧✐❝❛❞❛s s✉❝❡ss✐✈❛♠❡♥t❡ ❛té ❝♦❜r✐r t♦❞❛ ❛ ár❡❛ ❞♦s ♠❡s♠♦s✳ ❊ss❛s ♣♦rçõ❡s ♣♦❞❡♠ s❡r ❞❡✜♥✐❞❛s ♣♦r r❛✐♦s ❞❡ ✐♥✢✉ê♥❝✐❛✱ ♦✉ ♣♦r q✉❛♥t✐❞❛❞❡ ❞❡ ❛♠♦str❛s ✈✐③✐♥❤❛s✳ ◆❡ss❡ ❝❛s♦✱ ✉♠❛ ❛❧t❡r❛çã♦ ♥✉♠ ✈❛❧♦r ❞❡ ❡♥tr❛❞❛ ❛❢❡t❛ ❛♣❡♥❛s ♦ r❡s✉❧t❛❞♦ ❞❡ ✉♠ s✉❜❝♦♥❥✉♥t♦✳
❘❡❢❡r❡♥❝✐❛❧ ❚❡ór✐❝♦ ✶✵
t♦r♥❛♥❞♦ ❛ ✐♥t❡r♣♦❧❛çã♦ ❣❧♦❜❛❧ ♣♦✉❝♦ ❛♣r♦♣r✐❛❞❛ t❛♥t♦ ❡♠ r❡❧❛çã♦ ❛♦ t❡♠♣♦ ❞❡ ♣r♦✲ ❝❡ss❛♠❡♥t♦ q✉❛♥t♦ à ♣r❡❝✐sã♦ ❞♦ ♠♦❞❡❧♦✳ ❆ss✐♠✱ ♦s ✐♥t❡r♣♦❧❛❞♦r❡s ❧♦❝❛✐s sã♦ ♠❛✐s ✉t✐❧✐③❛❞♦s q✉❡ ♦s ❣❧♦❜❛✐s✳ ❖s ✐♥t❡r♣♦❧❛❞♦r❡s ❧♦❝❛✐s ♠❛✐s ❝♦♠✉♥s sã♦ ♦s ❧✐♥❡❛r❡s✱ ❜✐✲ ❧✐♥❡❛r❡s ❡ ♦s ✐♥t❡r♣♦❧❛❞♦r❡s ♣❡❧♦ ✐♥✈❡rs♦ ❞❛ ❞✐stâ♥❝✐❛ ❞♦s ✈✐③✐♥❤♦s ♠❛✐s ♣ró①✐♠♦s✳
❆ ✐♥t❡r♣♦❧❛çã♦ ❧✐♥❡❛r ❡♥✈♦❧✈❡ ❛ ♠❛♥✐♣✉❧❛çã♦ ❞❡ tr✐â♥❣✉❧♦s✱ ♣♦rt❛♥t♦✱ ♣❛r❛ ♦ ▼❉❊ é ♥❡❝❡ssár✐♦ ❞✐✈✐❞✐r ♦s r❡tâ♥❣✉❧♦s ❡♠ ❞♦✐s tr✐â♥❣✉❧♦s ❡ ♣❛r❛ ❛ ❚■◆ ♦s ♣ró♣r✐♦s tr✐â♥❣✉❧♦s ❞♦ ♠♦❞❡❧♦ sã♦ ✉t✐❧✐③❛❞♦s✳ ❆ ✐♥t❡r♣♦❧❛çã♦ ❧✐♥❡❛r ❞❡t❡r♠✐♥❛ ❛ ❡q✉❛çã♦ ❞♦s ♣❧❛♥♦s q✉❡ ♣❛ss❛♠ ♣❡❧♦s três ✈ért✐❝❡s ❞❡ ❝❛❞❛ ✉♠ ❞♦s tr✐â♥❣✉❧♦s ❞♦ ♠♦❞❡❧♦ ❡ ❛s ❡❧❡✈❛çõ❡s ♣❛r❛ ♦s ♣♦♥t♦s s✐t✉❛❞♦s ❡♥tr❡ ♦s ✈ért✐❝❡s ❞♦s tr✐â♥❣✉❧♦s sã♦ ❝❛❧❝✉❧❛❞❛s ❛tr❛✈és ❞❛ ❡q✉❛çã♦ ❞♦ ♣❧❛♥♦ q✉❡ ❝♦❜r❡ ❡ss❡ ♣♦♥t♦✳
❖ ✐♥t❡r♣♦❧❛❞♦r ❜✐❧✐♥❡❛r ♣♦ss✉✐ ❡ss❡ ♥♦♠❡ ♣♦r s❡ tr❛t❛r ❞❡ ✉♠❛ ✐♥t❡r♣♦❧❛çã♦ ❧✐♥❡❛r t❛♥t♦ ♥❛ ❤♦r✐③♦♥t❛❧ q✉❛♥t♦ ♥❛ ✈❡rt✐❝❛❧✳ P❛r❛ ✉♠ ▼❉❊✱ ❡ss❡ ✐♥t❡r♣♦❧❛❞♦r ❛♣r♦✲ ✈❡✐t❛ ❛s ❝❛r❛❝t❡ríst✐❝❛s ❞❡ ♦r❞❡♥❛çã♦ ❞❛s ♣♦s✐çõ❡s ❞❡ ❝❛❞❛ ✉♠ ❞♦s ✈ért✐❝❡s ❞♦s r❡tâ♥✲ ❣✉❧♦s✳ P♦r ❡①❡♠♣❧♦✱ ♥❛ ❋✐❣✉r❛ ✶✳✸✱ ❛ ✐♥t❡r♣♦❧❛çã♦ ❜✐❧✐♥❡❛r s♦❜r❡ ♦ r❡tâ♥❣✉❧♦ABCD✱ ❝♦♠ ♦ ♦❜❥❡t✐✈♦ ❞❡ ❞❡t❡r♠✐♥❛r ❛ ❡❧❡✈❛çã♦ ❞♦ ♣♦♥t♦ M✱ é r❡❛❧✐③❛❞❛ ❡♠ ❞♦✐s ♣❛ss♦s✿
• ■♥t❡r♣♦❧❛✲s❡ ❧✐♥❡❛r♠❡♥t❡ ♦s ♣♦♥t♦s E ❡ F ❛ ♣❛rt✐r ❞♦s ♣♦♥t♦s D ❡ C✱ ❡ A ❡ B✱ r❡s♣❡❝t✐✈❛♠❡♥t❡❀
• ■♥t❡r♣♦❧❛✲s❡ ♦ ♣♦♥t♦ M ❧✐♥❡❛r♠❡♥t❡ ❛ ♣❛rt✐r ❞♦s ♣♦♥t♦sE ❡ F✳
❋✐❣✉r❛ ✶✳✸✿ ■♥t❡r♣♦❧❛çã♦ ❜✐❧✐♥❡❛r
❏á ♦ ✐♥t❡r♣♦❧❛❞♦r ♣❡❧♦ ✐♥✈❡rs♦ ❞❛ ❞✐stâ♥❝✐❛ ❞♦s ✈✐③✐♥❤♦s ♠❛✐s ♣ró①✐♠♦s ❝❛❧❝✉❧❛ ♦ ✈❛❧♦r ❞❡ ❝❛❞❛ ♣♦♥t♦ ❛tr❛✈és ❞❡ ✉♠❛ ♠é❞✐❛ ❞♦s ✈❛❧♦r❡s ❞❡ s❡✉s ♣♦♥t♦s ✈✐③✐♥❤♦s ✉s❛♥❞♦ ♦ ✐♥✈❡rs♦ ❞❛ ❞✐stâ♥❝✐❛ ❡✉❝❧✐❞✐❛♥❛ ❡♥tr❡ ♦ ♣♦♥t♦ ❡ ❝❛❞❛ ✉♠ ❞♦s s❡✉s ✈✐③✐♥❤♦s ❝♦♠♦ ❢❛t♦r ❞❡ ♣♦♥❞❡r❛çã♦ ✭❇✉rr♦✉❣❤✱ ✶✾✽✻✮✳
