❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❇r❛sí❧✐❛
■♥st✐t✉t♦ ❞❡ ❈✐ê♥❝✐❛s ❊①❛t❛s
❉❡♣❛rt❛♠❡♥t♦ ❞❡ ▼❛t❡♠át✐❝❛
Pr♦❣r❛♠❛ ❞❡ ▼❡str❛❞♦ Pr♦✜ss✐♦♥❛❧ ❡♠
▼❛t❡♠át✐❝❛ ❡♠ ❘❡❞❡ ◆❛❝✐♦♥❛❧
❆s ❞✐❢❡r❡♥t❡s ✐♥t❡r♣r❡t❛çõ❡s ❞♦ ❛❧❣♦r✐t♠♦
s✐♠♣❧❡① ♥❛ r❡s♦❧✉çã♦ ❞❡ ♣r♦❜❧❡♠❛s ❞❡
♣r♦❣r❛♠❛çã♦ ❧✐♥❡❛r
▼❛r❝❡❧♦ ❊✉stáq✉✐♦ ❙♦❛r❡s ❞❡ ▲✐♠❛ ❏ú♥✐♦r
❇r❛sí❧✐❛
❆s ❞✐❢❡r❡♥t❡s ✐♥t❡r♣r❡t❛çõ❡s ❞♦ ❛❧❣♦r✐t♠♦
s✐♠♣❧❡① ♥❛ r❡s♦❧✉çã♦ ❞❡ ♣r♦❜❧❡♠❛s ❞❡
♣r♦❣r❛♠❛çã♦ ❧✐♥❡❛r
❚r❛❜❛❧❤♦ ❞❡ ❈♦♥❝❧✉sã♦ ❞❡ ❈✉rs♦ ❛♣r❡s❡♥t❛❞♦ ❛♦ ❉❡✲ ♣❛rt❛♠❡♥t♦ ❞❡ ▼❛t❡♠át✐❝❛ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❇r❛sí✲ ❧✐❛✱ ❝♦♠♦ ♣❛rt❡ ❞♦s r❡q✉✐s✐t♦s ♣❛r❛ ♦❜t❡♥çã♦ ❞♦ ❣r❛✉ ❞❡ ▼❡str❡✳
❖r✐❡♥t❛❞♦r✿ Pr♦❢✳ ❉r✳ ❍❡❧❞❡r ❞❡ ❈❛r✈❛❧❤♦ ▼❛t♦s
❇r❛sí❧✐❛
Ficha catalográfica elaborada automaticamente, com os dados fornecidos pelo(a) autor(a)
Ed
Eustáquio Soares de Lima Júnior, Marcelo
As diferentes interpretações do algoritmo simplex na resolução de problemas de programação linear / Marcelo Eustáquio Soares de Lima Júnior; orientador Helder Carvalho. -- Brasília, 2015.
149 p.
Dissertação (Mestrado - Mestrado Profissional em Matemática) -- Universidade de Brasília, 2015.
❚♦❞♦s ♦s ❞✐r❡✐t♦s r❡s❡r✈❛❞♦s✳ ➱ ♣r♦✐❜✐❞❛ ❛ r❡♣r♦❞✉çã♦ t♦t❛❧ ♦✉ ♣❛r❝✐❛❧ ❞❡st❡ tr❛❜❛❧❤♦ s❡♠ ❛ ❛✉t♦r✐③❛çã♦ ❞❛ ✉♥✐✈❡rs✐❞❛❞❡✱ ❞♦ ❛✉t♦r ❡ ❞♦ ♦r✐❡♥t❛❞♦r✳
❉❡❞✐❝❛tór✐❛
❆❣r❛❞❡❝✐♠❡♥t♦s
❘❡s✉♠♦
❆ ♣r✐♥❝✐♣❛❧ ✐❞❡✐❛ ❞❡st❡ tr❛❜❛❧❤♦ ❢♦✐ ❞❡ ❛♣❧✐❝❛r ♦ ❝♦♥t❡ú❞♦ Pr♦❣r❛♠❛çã♦ ▲✐♥❡❛r ♥♦ ❊♥s✐♥♦ ▼é❞✐♦ ❞❡ ❢♦r♠❛ ❝♦♥t❡①t✉❛❧✐③❛❞❛ ❡ ❝♦♠ ❛ ✉t✐❧✐③❛çã♦ ❞♦s s♦t✇❛r❡s ●❡♦❣❡❜r❛ ❡ ♦ ❊①❝❡❧✳ ◆❡st❡ tr❛❜❛❧❤♦ ❛❜♦r❞❛♠♦s ❛ ♠❡t♦❞♦❧♦❣✐❛ ❞❛ r❡s♦❧✉çã♦ ❞❡ ♣r♦❜❧❡♠❛s✱ ♣❛rt✐♥❞♦ ❞❡ ❡①❡♠♣❧♦s q✉❡ ❜✉sq✉❡♠ ❛ ♦t✐♠✐③❛çã♦ ❛tr❛✈és ❞❛ ♣r♦❣r❛♠❛çã♦ ❧✐♥❡❛r✳ ❖ ❡①♣❡r✐♠❡♥t♦ t❡♠ ♣♦r ♦❜❥❡t✐✈♦ ♣r✐♥❝✐♣❛❧ ❞❡s❝r❡✈❡r ❛ ❛❜♦r❞❛❣❡♠ ✉t✐❧✐③❛❞❛ ♥❛ ✐♠♣❧❡♠❡♥t❛çã♦ r❡❛❧✐③❛❞❛ ❛ ♣❛rt✐r ❞❡ss❡s ♣r♦❜❧❡♠❛s✳
P❛❧❛✈r❛s✲❝❤❛✈❡
❆❜str❛❝t
❚❤❡ ♠❛✐♥ ✐❞❡❛ ♦❢ t❤✐s ✇♦r❦ ✇❛s t♦ ❛♣♣❧② t❤❡ ▲✐♥❡❛r Pr♦❣r❛♠♠✐♥❣ ✐♥ s❡❝♦♥❞❛r② ❡❞✉❝❛t✐♦♥ ❝♦♥t❡♥t ✐♥ ❝♦♥t❡①t ❛♥❞ ✇✐t❤ t❤❡ ✉s❡ ♦❢ ●❡♦❣❡❜r❛ s♦t✇❛r❡s ❛♥❞ ❊①❝❡❧✳ ❚❤✐s ♣❛♣❡r ❞❡❛❧s ✇✐t❤ t❤❡ ♠❡t❤♦❞♦❧♦❣② ♦❢ s♦❧✈✐♥❣ ♣r♦❜❧❡♠s✱ st❛rt✐♥❣ ✇✐t❤ ❡①❡♠♣❧s ✐♥✈♦❧✲ ✈✐♥❣ ♦♣t✐♠✐③❛t✐♦♥ t❤r♦✉❣❤ ❧✐♥❡❛r ♣r♦❣r❛♠♠✐♥❣✳ ❚❤❡ ❡①♣❡r✐♠❡♥t✬s ♠❛✐♥ ♦❜❥❡❝t✐✈❡ ✐s t♦ ❞❡s❝r✐❜❡ t❤❡ ❛♣♣r♦❛❝❤ ✉s❡❞ ✐♥ t❤❡ ✐♠♣❧❡♠❡♥t❛t✐♦♥ ❝❛rr✐❡❞ ♦✉t ❢r♦♠ t❤❡s❡ ♣r♦❜❧❡♠s✳
❑❡②✇♦r❞s
▲✐st❛ ❞❡ ❋✐❣✉r❛s
✶ ❈✐❝❧♦ P❉❈❆✿ P❧❛✐♥✱ ❉♦✱ ❈❤❡❝❦ ❡ ❆❝t ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✷ ▼♦❞❡❧❛❣❡♠ ❝♦♠♦ tr❛❞✉çã♦ ❞❡ ❡♥t❡ ❞♦ ♠✉♥❞♦ r❡❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✸ ❋❛s❡s ❞♦ ♣r♦❝❡ss♦ ❞❡ ♠♦❞❡❧❛❣❡♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✹ ❊✈♦❧✉çã♦ ❞❛ t❡♠♣❡r❛t✉r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✺ ❙♦❧✉çã♦ ❣❡♦♠étr✐❝❛ ❞❛ s✐t✉❛çã♦ ♣r♦❜❧❡♠❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾ ✻ ❙♦❧✉çã♦ ❞❡ ✉♠ ❛❧✉♥♦ ❞♦ 7o ❛♥♦ ❡♥s✐♥♦ ❢✉♥❞❛♠❡♥t❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶
✼ ❙♦❧✉çã♦ ❞❡ ✉♠ ❛❧✉♥♦ ❞♦ 8o ❛♥♦ ❞♦ ❡♥s✐♥♦ ❢✉♥❞❛♠❡♥t❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶
✽ ❙♦❧✉çã♦ ♣❛❞rã♦ ❞❡ ✉♠ ❛❧✉♥♦ ❞❛ 2a sér✐❡ ❞♦ ❡♥s✐♥♦ ♠é❞✐♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷
✷✺ ➪r❡❛ ❞♦ q✉❛❞r✐❧át❡r♦ ❆❇❈❉ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷ ✷✻ ❘❡t❛ q✉❡ ❝♦♥té♠ ♦s ♣♦♥t♦s ❆ ❡ ❇ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ✷✼ ❈♦♥str✉çã♦ ❞❡ r❡t❛s ♣❛r❛❧❡❧❛s ❡ ♣❡♥♣❡♥❞✐❝✉❧❛r❡s ❛ ✉♠❛ r❡t❛ ❞❛❞❛ ✳ ✳ ✳ ✺✹ ✷✽ ●rá✜❝♦ ❞❡ ✉♠❛ ❢✉♥çã♦f(x) =ax+b ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻
✷✾ ❘❡t❛ q✉❡ ❝♦♥té♠ ♦s ♣♦♥t♦sP(2,3) ❡ Q= (4,−1) ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ✸✵ ❈♦❡✜❝✐❡♥t❡s ❞❡f(x) =ax+b ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾
✸✶ ●rá✜♦ ❞♦ ♠♦♥t❛♥t❡ ❞❡ ✉♠❛ ❛♣❧✐❝❛çã♦ ✜♥❛♥❝❡✐r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵ ✸✷ ❖♣çõ❡s ❛ss♦❝✐❛❞❛s ❛♦ ♦❜❥❡t♦ ❘❡t❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✸✸ ar =as ⇒r//s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷
✸✹ ∄ar ❡ ∄as ⇒r//s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷
✸✺ ar 6=as ⇒r ❡ s sã♦ ❝♦♥❝♦rr❡♥t❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸
✸✻ ■♥t❡r❝❡♣t♦s ❞❛ r❡t❛ ❝♦♠ ♦s ❡✐①♦s ❝♦♦r❞❡♥❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹ ✸✼ P♦❧í❣♦♥♦ABCD ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺
✸✽ ❘❡s♦❧✉çã♦ ❣rá✜❝❛ ❞❡ ✐♥❡q✉❛çõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻ ✸✾ ❊st✉❞♦ ❞❡ s✐♥❛❧ ❞❡ f(x) = x2−6x+ 8 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼
✹✵ ●rá✜❝♦ ❞❡f(x) =x3−6x2+ 11x−60 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽
✹✶ ❙♦❧✉çã♦ ❞❡ x3−6x2+ 11x−6<0✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾
✹✷ ❙❡♠✐♣❧❛♥♦s ❞❡ ♦r✐❣❡♠ ✈❡rt✐❝❛❧ ♦✉ ❤♦r✐③♦♥t❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵ ✹✸ ❘❡tâ♥❣✉❧♦ ❆❇❈❉ ❞♦ ❡①❡♠♣❧♦ ✶✵ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷ ✹✹ ❆ r❡t❛y =ax+b ❡ ♦s s❡♠✐♣❧❛♥♦s ♣♦r ❡❧❛ ❞❡t❡r♠✐♥❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸
✹✺ ❙❡♠✐♣❧❛♥♦ 2x+ 3y≥12 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹ ✹✻ ❙♦❧✉çã♦ ❞❡ 2x−4y <6 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺ ✹✼ ❙♦❧✉çã♦ ❞♦ s✐st❡♠❛ ❞❡ ✐♥❡q✉❛çõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻ ✹✽ ❙♦❧✉çõ❡s ♣❛rt✐❝✉❧❛r❡s ❞❡ x+ 2y = 6 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✼ ✹✾ ❙✐st❡♠❛ ❧✐♥❡❛r ✐♠♣♦ssí✈❡❧ ❞❡ ❞✉❛s ❡q✉❛çõ❡s ❡ ❞✉❛s ✐♥❝ó❣♥✐t❛s ✳ ✳ ✳ ✳ ✳ ✳ ✼✽
✺✵ ■♥t❡r♣r❡t❛çã♦ ❣❡♦♠étr✐❝❛ ❞❛ s♦❧✉çã♦ ❞♦ s✐st❡♠❛ ♣♦ssí✈❡❧ ❡ ❞❡t❡r♠✐♥❛❞♦ ✼✾ ✺✶ ❙♦❧✉çã♦ ❞♦ s✐st❡♠❛ ❧✐♥❡❛r ❞❡ ❡q✉❛çõ❡s 2x−3y = 19 ❡x+y= 2 ✳ ✳ ✳ ✳ ✽✵ ✺✷ ❈❧❛ss✐✜❝❛çã♦ ❞❡ ✉♠ s✐st❡♠❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✵ ✺✸ ❙✐st❡♠❛s ❡q✉✐✈❛❧❡♥t❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✷ ✺✹ ■♥t❡r♣r❡t❛çã♦ ❣❡♦♠étr✐❝❛ ❞❡ ✉♠ s✐st❡♠❛3×3 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✺ ✺✺ ■❞é✐❛s ❝❡♥tr❛✐s ❞♦ ❝á❧❝✉❧♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✽ ✺✻ ❘❡t❛ s❡❝❛♥t❡ ❛ ❢✉♥çã♦f(x) ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✾ ✺✼ ❘❡t❛ t❛♥❣❡♥t❡ ❛ ❢✉♥çã♦ f(x) ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✵ ✺✽ ❘❡❧❛çã♦ ❡♥tr❡ ♣♦s✐çã♦ ❡ ❞❡s❧♦❝❛♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✶ ✺✾ ❚❛①❛ ❞❡ ✈❛r✐❛çã♦ ❞❡ f(x) = x2 ♥♦ ●❡♦❣❡❜r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✺
✻✵ ❋✉♥çã♦ r❡❛❧ ❞❡ ❞✉❛s ✈❛r✐á✈❡✐s r❡❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✺ ✻✶ ●rá✜❝♦ ❞❡f(x, y) =x2+y2 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✻
✻✷ ❈✉r✈❛s ❞❡ ♥í✈❡❧ ❞❡ f(x, y) =x2+y2 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✼
✻✸ ➶♥❣✉❧♦ ❡♥tr❡ ♦s ✈❡t♦r❡s~u ❡~v ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✵
✻✹ ❆❧❣♦r✐t♠♦ s✐♠♣❧❡① ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✸ ✻✺ ❘❡❣✐ã♦ ❝♦♥✈❡①❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✽ ✻✻ ❆❧❣♦r✐t♠♦ s✐♠♣❧❡① ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✸ ✻✼ ❘❡str✐çõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✸ ✻✽ ■♥t❡rs❡çã♦ ❞♦s s❡♠✐♣❧❛♥♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✼ ✻✾ ❙♦❧✉çã♦ ❞♦ s✐st❡♠❛ ❞❡ ✐♥❡q✉❛çõ❡s ❞❡t❡r♠✐♥❛❞❛s ♣❡❧❛s r❡str✐çõ❡s ❞♦ PP▲ ✶✶✽ ✼✵ P♦❧í❣♦♥♦DABC ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✾
✼✶ A ❣❡r❛ ♦ ✈❛❧♦r ♠á①✐♠♦ ❞❡ f(x, y) = 6x+ 7y ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✵
✼✷ ❊♠♣❛t❡ ♥❛ ❡♥tr❛❞❛ ❞❡ ✈❛r✐á✈❡✐s ♥❛ ❜❛s❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✶ ✼✸ ❉❡❣❡♥❡r❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✷ ✼✹ ▼ú❧t✐♣❧❛s s♦❧✉çõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✸
▲✐st❛ ❞❡ ❚❛❜❡❧❛s
✶ ❘❡str✐çõ❡s ❞❡ ❛❧✐♠❡♥t♦s ♥❛ ❞✐❡t❛ ❛❧✐♠❡♥t❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ✷ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ ❝✉st♦s ❞❡ ❡①❡❝✉çã♦ ❞♦s ❛❧❣♦r✐t♠♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✸ ❚❛❜❡❧❛ Pr♦❣r❡ss✐✈❛ ♣❛r❛ ❝á❧❝✉❧♦ ❞♦ ■❘P❋ ❞❡ ✷✵✶✺ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷ ✹ ❙✐♠✉❧❛çõ❡s ❞❡ ❝á❧❝✉❧♦ ❞♦ ■❘❘❋ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✺ ■♥❝❧✐♥❛çã♦ ❞❡ I ♣❛r❛ ❛❧❣✉♥s ✈❛❧♦r❡s ❞❡ h ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✸
✻ ❚❛❜❧❡❛✉ ✐♥✐❝✐❛❧ ❞♦ ❡①❡♠♣❧♦ ✻✼ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✹ ✼ ❚❛❜❧❡❛✉ ❛♣ós 1a ✐t❡r❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✹
✽ ❚❛❜❧❡❛✉ ❛♣ós 2a ✐t❡r❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✺
❙✉♠ár✐♦
✶ ■♥tr♦❞✉çã♦ ✶✾
✶✳✶ ❘❡s♦❧✉çã♦ ❞❡ s✐t✉❛çõ❡s✲♣r♦❜❧❡♠❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✶✳✷ ❖ ❡♥s✐♥♦ ♠é❞✐♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✶✳✸ ❙❡çõ❡s ❞❡ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞♦ tr❛❜❛❧❤♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸
✷ ▼♦❞❡❧❛❣❡♠ ✷✺
✷✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✷✳✷ ❇✉s❝❛♥❞♦ ♦✉tr❛ s♦❧✉çã♦ ♣❛r❛ ✉♠ ♣r♦❜❧❡♠❛ ♣r♦♣♦st♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✷✳✸ ❋❛t♦r❡s q✉❡ ❝♦♥tr✐❜✉❡♠ ♣❛r❛ ❛ ♠♦❞❡❧❛❣❡♠ ♠❛t❡♠át✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾ ✷✳✹ P❡sq✉✐s❛ ❖♣❡r❛❝✐♦♥❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ✷✳✹✳✶ ❖ q✉❡ é Pr♦❣r❛♠❛çã♦ ▲✐♥❡❛r❄ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✷✳✹✳✷ ❯♠ ❡①❡♠♣❧♦ ✐♥tr♦❞✉tór✐♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹
✸ ❆❧❣♦r✐t♠♦s ✸✻
✸✳✶ ❋❧✉①♦❣r❛♠❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✸✳✷ ❈♦♠♣❛r❛♥❞♦ ❛❧❣♦r✐t♠♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾ ✸✳✸ ❯♠ ❡①❡♠♣❧♦ ❞❡ ❛t✐✈✐❞❛❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷ ✸✳✸✳✶ ❈♦♠♣r❡❡♥sã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷ ✸✳✸✳✷ ▼❛t❡♠❛t✐③❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✸✳✸✳✸ ❆✈❛❧✐❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺ ✸✳✹ ❖ s✐♠♣❧❡① ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼
✹ ❖ ●❡♦❣❡❜r❛ ✹✽
✹✳✸ Pr✐♥❝✐♣❛✐s ♦❜❥❡t♦s ❞♦ ●❡♦❣❡❜r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵ ✹✳✸✳✶ P♦♥t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵ ✹✳✸✳✷ ❘❡t❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵ ✹✳✸✳✸ ❙❡❧❡t♦r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵ ✹✳✸✳✹ ❋✉♥çõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶ ✹✳✸✳✺ ❈♦♠❛♥❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶
✺ ❋✉♥❞❛♠❡♥t♦s t❡ór✐❝♦s ✺✺
✺✳✶ ❆ ❡q✉❛çã♦ ❞❛ r❡t❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺ ✺✳✶✳✶ P♦s✐çõ❡s r❡❧❛t✐✈❛s ❡♥tr❡ r❡t❛s ❝♦♣❧❛♥❛r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷ ✺✳✶✳✷ ❊q✉❛çã♦ s❡❣♠❡♥tár✐❛ ❞❛ r❡t❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸ ✺✳✷ ■♥❡q✉❛çõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺ ✺✳✷✳✶ ■♥❡q✉❛çõ❡s ❞❡✜♥✐❞❛s ❡♠ R ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼ ✺✳✷✳✷ ■♥❡q✉❛çõ❡s ❞❡✜♥✐❞❛s ❡♠ R2 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵
✺✳✷✳✸ ❙❡♠✐♣❧❛♥♦s ❞❡ ♦r✐❣❡♠ ♦❜❧íq✉❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷ ✺✳✸ ❙✐st❡♠❛s ▲✐♥❡❛r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻ ✺✳✸✳✶ ❊q✉❛çõ❡s ❧✐♥❡❛r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✼ ✺✳✸✳✷ ❙✐st❡♠❛ ❧✐♥❡❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✽ ✺✳✸✳✸ ❘❡♣r❡s❡♥t❛çã♦ ♠❛tr✐❝✐❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✶ ✺✳✸✳✹ ❊s❝❛❧♦♥❛♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✶ ✺✳✸✳✺ ❆♥á❧✐s❡ ❞❡ ❞❡s❡♠♣❡♥❤♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✺
✻ ◆♦çõ❡s ❞❡ ❈á❧❝✉❧♦ ✽✽
✻✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✽ ✻✳✷ ❚❛①❛ ❞❡ ✈❛r✐❛çã♦ ❡ ❞❡r✐✈❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✾ ✻✳✷✳✶ ■♥t❡r♣r❡t❛çã♦ ❝✐♥❡♠át✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✶
✻✳✷✳✷ ❆ ❞❡r✐✈❛❞❛ ❡♥q✉❛♥t♦ r❡s✉❧t❛❞♦ ❞❡ ❛♣r♦①✐♠❛çõ❡s s✉❝❡ss✐✈❛s ✳ ✳ ✳ ✾✷ ✻✳✸ ❋✉♥çõ❡s r❡❛✐s ❞❡ ❞✉❛s ✈❛r✐á✈❡✐s r❡❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✺ ✻✳✹ ❉❡r✐✈❛❞❛s ♣❛r❝✐❛✐s ❡ ❣r❛❞✐❡♥t❡ ❞❡ ✉♠❛ ❢✉♥çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✽
✼ ❖ ▼ét♦❞♦ ❙✐♠♣❧❡① ✶✵✸
✼✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✸ ✼✳✷ ❈♦♥❝❡✐t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✹ ✼✳✸ ❚❡♦r❡♠❛s ❢✉♥❞❛♠❡♥t❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✼ ✼✳✹ ❖ ❛❧❣♦r✐t♠♦ s✐♠♣❧❡① ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✾ ✼✳✹✳✶ ❈♦❡✜❝✐❡♥t❡ ❞❡ ❝✉st♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✵ ✼✳✹✳✷ ❖ t❛❜❧❡❛✉ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✶ ✼✳✺ ▼ét♦❞♦ ❣rá✜❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✻ ✼✳✻ ❈❛s♦s ❡①❝❡♣❝✐♦♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✵ ✼✳✻✳✶ ❊♠♣❛t❡ ♥❛ ❡♥tr❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✵ ✼✳✻✳✷ ❉❡❣❡♥❡r❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✶ ✼✳✻✳✸ ▼ú❧t✐♣❧❛s s♦❧✉çõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✷ ✼✳✼ ❈♦♠♣❧❡①✐❞❛❞❡ ❝♦♠♣✉t❛❝✐♦♥❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✹ ✼✳✼✳✶ ❈✉st♦ ❞❡ ❡①❡❝✉çã♦ ❞♦ s✐♠♣❧❡① ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✹ ✼✳✽ ❊①❝❡❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✺ ✼✳✽✳✶ ❘❡q✉✐s✐t♦s ❞❡ ❤❛r❞✇❛r❡ ❡ s♦❢t✇❛r❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✺ ✼✳✽✳✷ ❙♦❧✈❡r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✺ ✼✳✽✳✸ ■♥st❛❧❛çã♦ ❞♦ ❙♦❧✈❡r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✻ ✼✳✽✳✹ ❉❡✜♥✐♥❞♦ ❡ r❡s♦❧✈❡♥❞♦ ✉♠ ♣r♦❜❧❡♠❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✼ ✼✳✾ ❖ ♣r♦❜❧❡♠❛ ❞❛ ❞✐❡t❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✶
✽ ❚❡♦r✐❛ ❞♦ ❈♦♥s✉♠✐❞♦r ✶✸✹
✽✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✹ ✽✳✷ ❘❡str✐çã♦ ❖rç❛♠❡♥tár✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✺ ✽✳✸ ▼✉❞❛♥ç❛s ♥❛ r❡t❛ ♦rç❛♠❡♥tár✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✻ ✽✳✸✳✶ ▼✉❞❛♥ç❛s ♥❛ r❡♥❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✻ ✽✳✸✳✷ ▼✉❞❛♥ç❛s ♥♦s ♣r❡ç♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✼ ✽✳✹ ❯♠❛ s✐t✉❛çã♦ ♣r♦❜❧❡♠❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✼ ✽✳✹✳✶ ❙♦❧✉çã♦ ♣❡❧♦ ♠ét♦❞♦ ❣❡♦♠étr✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✾ ✽✳✹✳✷ ❙♦❧✉çã♦ ❞♦ ♣r♦❜❧❡♠❛ ♣r♦♣♦st♦ ♥♦ ❡①❡♠♣❧♦ ✸✵ ✉t✐❧✐③❛♥❞♦ ♦ ❙♦❧✈❡r ✶✹✶ ✽✳✹✳✸ ❙♦❧✉çã♦ ❡♥✈♦❧✈❡♥❞♦ ♠ét♦❞♦ ❛❧❣é❜r✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✷
✾ ❈♦♥s✐❞❡r❛çõ❡s ✜♥❛✐s ✶✹✺
✶ ■♥tr♦❞✉çã♦
●❡♦r❣❡ Pó❧②❛✱ ♠❛t❡♠át✐❝♦ ❤ú♥❣❛r♦ q✉❡ ✈✐✈❡✉ ❡♥tr❡ ✶✽✽✼ ❡ ✶✾✽✺✱ ❡♠ s✉❛ ♦❜r❛ ✧❆ ❛rt❡ ❞❡ r❡s♦❧✈❡r ♣r♦❜❧❡♠❛s✧ ❬✷✶❪✱ ❛✜r♠❛ q✉❡
✧✉♠❛ ❣r❛♥❞❡ ❞❡s❝♦❜❡rt❛ r❡s♦❧✈❡ ✉♠ ❣r❛♥❞❡ ♣r♦❜❧❡♠❛✱ ♠❛s ❤á s❡♠♣r❡ ✉♠❛ ♣✐t❛❞❛ ❞❡ ❞❡s❝♦❜❡rt❛ ♥❛ r❡s♦❧✉çã♦ ❞❡ q✉❛❧q✉❡r ♣r♦❜❧❡♠❛✳ ❖ Pr♦❜❧❡♠❛ ♣♦❞❡ s❡r ♠♦❞❡st♦✱ ♠❛s s❡ ❡❧❡ ❞❡s❛✜❛r ❛ ❝✉r✐♦s✐❞❛❞❡ ❡ ♣✉s❡r ❡♠ ❥♦❣♦ ❛s ❢❛❝✉❧❞❛❞❡s ✐♥✈❡♥t✐✈❛s✱ q✉❡♠ ♦ r❡s♦❧✈❡r ♣♦r s❡✉s ♠❡✐♦s✱ ❡①♣❡r✐♠❡♥t❛ ♦ s❡♥t✐♠❡♥t♦ ❞❛ ❛✉t♦❝♦♥✜❛♥ç❛ ❡ ❣♦③❛rá ♦ tr✐✉♥❢♦ ❞❛ ❞❡s❝♦❜❡rt❛✧✳
❆♣♦♥t❛❞❛ ♣♦r ❡st✉❞♦s ❡ ♣❡sq✉✐s❛s ❡♠ ❡❞✉❝❛çã♦ ♠❛t❡♠át✐❝❛✱ ❛ r❡s♦❧✉çã♦ ❞❡ ♣r♦❜❧❡✲ ♠❛s ❡✱ ❞❡ ♠♦❞♦ ♠❛✐s ❣❡r❛❧✱ ❛ r❡s♦❧✉çã♦ ❞❡ s✐t✉❛çõ❡s✲♣r♦❜❧❡♠❛✱ ✈❡♠ s❡ ❝♦♥s♦❧✐❞❛♥❞♦ ❝♦♠♦ ❡str❛té❣✐❛ ❞❡ ❛♣r❡♥❞✐③❛❣❡♠ só❧✐❞❛ ♥♦ ❡♥s✐♥♦ ❞❡ ♠❛t❡♠át✐❝❛ ❝♦♠ ❛❜♦r❞❛❣❡♠ q✉❡ ♣♦ss✐❜✐❧✐t❛ ❛❝❡ss♦ ❛♦ ❝♦♥❤❡❝✐♠❡♥t♦ ❝♦♥str✉í❞♦ ♣❡❧❛ s♦❝✐❡❞❛❞❡✱ ♣❛rt✐♥❞♦ ❞♦ ❤❛❜✐t❛t ❞♦ ❛❧✉♥♦ ❡ s❡ ❞❡s❡♥✈♦❧✈❡♥❞♦ ❛ ♣❛rt✐r ❞♦ ❝♦♥t✐♥✉✉♠ ❞❡ ✐t❡r❛çõ❡s ❞❡s❡♥✈♦❧✈✐❞❛s ♣♦r ❡❧❡ ❝♦♠ ♦ ♠❡✐♦ q✉❡ ♦ ❝❡r❝❛✳
❊♥q✉❛♥t♦ ♠❡t♦❞♦❧♦❣✐❛ ❞❡ ❡♥s✐♥♦✱ ❛ r❡s♦❧✉çã♦ ❞❡ s✐t✉❛çõ❡s✲♣r♦❜❧❡♠❛s ❝♦♥s✐st❡ ❡♠ ❛♣r❡s❡♥t❛r ❛♦ ❛❧✉♥♦ s✐t✉❛çõ❡s q✉❡ ❡st✐♠✉❧❡♠ ❛ s✉❛ ❝✉r✐♦s✐❞❛❞❡ ❡ ❛✉①✐❧✐❡♠ ♥❛ ❝♦♥s✲ tr✉çã♦ ❞❡ ❝♦♥❝❡✐t♦s ♠❛t❡♠át✐❝♦s✳ P♦ré♠✱ s❡✉ ✉s♦ ♥❛s ❛✉❧❛s ❞❡ ♠❛t❡♠át✐❝❛ é ❛✐♥❞❛ ♠✉✐t♦ s✉♣❡r✜❝✐❛❧ ❡ ❡♥❝♦♥tr❛ ♠✉✐t❛ r❡s✐stê♥❝✐❛ ♣♦r ♣❛rt❡ ❞♦s ♣r♦❢❡ss♦r❡s✱ q✉❡ ❝♦♥s✐❞❡✲ r❛♠ s✐t✉❛çã♦✲♣r♦❜❧❡♠❛ ❝♦♠♦ ✉♠ s✐♠♣❧❡s ♣r♦❜❧❡♠❛✱ ❣❡r❛❧♠❡♥t❡ ✉s❛❞♦ ❝♦♠♦ ❡①❡r❝í❝✐♦ ❞❡ ✜①❛çã♦ ❞❡ ❝♦♥t❡ú❞♦s✳
❖ ❝♦♥❝❡✐t♦ ❞❡ s✐t✉❛çã♦✲♣r♦❜❧❡♠❛ é ♠❛✐s ❛♠♣❧♦ ❞♦ q✉❡ s✐♠♣❧❡s♠❡♥t❡ ♣r♦❜❧❡♠❛ ♣♦r ❡♥✈♦❧✈❡r ❛♣❧✐❝❛çõ❡s ❝♦♥❝r❡t❛s ❡ ❞✐✈❡rs♦s ❝♦♠♣♦♥❡♥t❡s ❞❛ ♠❛t❡♠át✐❝❛ ❡ ❞❡ ♦✉tr❛s ár❡❛s ❞❡ ❝♦♥❤❡❝✐♠❡♥t♦ ❡♠ s✉❛ r❡s♦❧✉çã♦✳ P♦r ♠❡✐♦ ❞❡ ❝♦♥❝❡✐t♦s✱ té❝♥✐❝❛s ❡ ❛❧❣♦r✐t♠♦s ♠❛t❡✲ ♠át✐❝♦s ♣r♦❝✉r❛✲s❡ ♠♦❞❡❧❛r ✉♠❛ s✐t✉❛çã♦ r❡❛❧✱ ♦r❣❛♥✐③❛♥❞♦ ♦s ❞❛❞♦s ❡♠ t❛❜❡❧❛s✱ tr❛✲ ç❛♥❞♦ ❣rá✜❝♦s✱ ❡❧❛❜♦r❛♥❞♦ ❡q✉❛çõ❡s ♦✉ ❢✉♥çõ❡s✱ ❞❡s❡♥✈♦❧✈❡♥❞♦ ❝á❧❝✉❧♦s ❡ r❡❛❧✐③❛♥❞♦ ❛♥á❧✐s❡s ❞♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s✳ ❊♠ ❣❡r❛❧✱ s✐t✉❛çõ❡s✲♣r♦❜❧❡♠❛ sã♦ ♣r♦❜❧❡♠❛s q✉❡ ❡①✐✲ ❣❡♠ ♣❡sq✉✐s❛✱ ❧❡✈❛♥t❛♠❡♥t♦ ❞❡ ❞❛❞♦s ❡ ♣♦❞❡♠ s❡r ❛♣r❡s❡♥t❛❞♦s ♥❛ ❢♦r♠❛ ❞❡ ♣r♦❥❡t♦s ❛ s❡r❡♠ ❞❡s❡♥✈♦❧✈✐❞♦s ♦✉ ✐♠♣❧❡♠❡♥t❛❞♦s ✉s❛♥❞♦ ❝♦♥❤❡❝✐♠❡♥t♦s ❡ ♣r✐♥❝í♣✐♦s ❞❡ ♦✉tr❛s ár❡❛s ❞❡ ❝♦♥❤❡❝✐♠❡♥t♦✳
P❛r❛ ♦ ❧❡✐t♦r ✐♥t❡r❡ss❛❞♦ ❡♠ ♠❛✐s ❝♦♥❤❡❝✐♠❡♥t♦s ❛❝❡r❝❛ ❞❡ s✐t✉❛çã♦✲♣r♦❜❧❡♠❛✱ r❡✲ ❝♦♠❡♥❞❛♠♦s ❛ r❡❢❡rê♥❝✐❛ ❬✶✵❪✳
✶✳✶ ❘❡s♦❧✉çã♦ ❞❡ s✐t✉❛çõ❡s✲♣r♦❜❧❡♠❛
P❛r❛ P♦❧②❛ ❬✷✶❪✱ ❛ r❡s♦❧✉çã♦ ❞❡ ✉♠ ♣r♦❜❧❡♠❛ ❡♥✈♦❧✈❡ ❞❡s❛✜♦ ❡ ❞❡s❝♦❜❡rt❛✱ ✉♠❛ ✈❡③ q✉❡ ♥ã♦ ❡①✐st❡ ✉♠ ♠ét♦❞♦ rí❣✐❞♦ ♦✉ ❛❧❣♦r✐t♠♦ q✉❡ ♣♦ss❛ s❡r ❛♣❧✐❝❛❞♦ ♣❛r❛ s❡♠♣r❡ ♦❜t❡r ❛ s♦❧✉çã♦✳ ❙❡❣✉♥❞♦ P♦❧②❛✱ ❡①✐st❡♠ ❡stá❣✐♦s ❞❡ ♣❡♥s❛♠❡♥t♦ q✉❡ ❛✉①✐❧✐❛♠ ♦ ❛❧✉♥♦ ♥❡st❡ ♣r♦❝❡ss♦ ❡ ✐♥❝❧✉❡♠ ❛ ❝♦♠♣r❡❡♥sã♦ ❞♦ ♣r♦❜❧❡♠❛✱ ❡st❛❜❡❧❡❝✐♠❡♥t♦ ❞❡ ✉♠ ♣❧❛♥♦ ❞❡ ❛çã♦✱ ❡①❡❝✉çã♦ ❞♦ ♣❧❛♥♦ ❡ ♦ r❡tr♦s♣❡❝t♦✳ ❊ss❛s ❡t❛♣❛s ❛ss❡♠❡❧❤❛♠✲s❡ à ♠❡t♦❞♦❧♦❣✐❛ ♣❛r❛ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ♣r♦❝❡ss♦s✱ ❝♦♥❤❡❝✐❞❛ ♥❛s ❣r❛♥❞❡s ♦r❣❛♥✐③❛çõ❡s ❝♦♠♦ ❈✐❝❧♦ P❉❈❆ ♦✉ ❈✐❝❧♦ ❞❡ ❉❡♠✐♥❣✱ ♠♦str❛❞♦ ♥❛ ❋✐❣✉r❛ ✶✳
❋✐❣✉r❛ ✶✿ ❈✐❝❧♦ P❉❈❆✿ P❧❛✐♥✱ ❉♦✱ ❈❤❡❝❦ ❡ ❆❝t
❚❛❧ ♠❡t♦❞♦❧♦❣✐❛ ❛✉①✐❧✐❛ ♥♦ ❞✐❛❣♥óst✐❝♦✱ ❛♥á❧✐s❡ ❡ ♣r♦❣♥óst✐❝♦ ❞❡ ♣r♦❜❧❡♠❛s ♦r❣❛♥✐✲ ③❛❝✐♦♥❛✐s✱ s❡♥❞♦ ❡①tr❡♠❛♠❡♥t❡ út✐❧ ♣❛r❛ ❛ s♦❧✉çã♦ ❞❡ ♣r♦❜❧❡♠❛s✳ P♦✉❝♦s ✐♥str✉♠❡♥t♦s s❡ ♠♦str❛♠ tã♦ ❡❢❡t✐✈♦s ♣❛r❛ ❛ ❜✉s❝❛ ❞♦ ❛♣❡r❢❡✐ç♦❛♠❡♥t♦ q✉❛♥t♦ ❡st❡ ♠ét♦❞♦ ❞❡ ♠❡✲ ❧❤♦r✐❛ ❝♦♥tí♥✉❛✱ t❡♥❞♦ ❡♠ ✈✐st❛ q✉❡ ❡❧❡ ❝♦♥❞✉③ ❛ ❛çõ❡s s✐st❡♠át✐❝❛s q✉❡ ♣r♦♣♦r❝✐♦♥❛♠ ❜♦♥s r❡s✉❧t❛❞♦s ♥❛ s♦❜r❡✈✐✈ê♥❝✐❛ ❡ ❝♦❧❛❜♦r❛♠ ♣❛r❛ ♦ ❝r❡s❝✐♠❡♥t♦ ❞❛s ♦r❣❛♥✐③❛çõ❡s✳
❆ ♠❡t♦❞♦❧♦❣✐❛ ❢♦✐ ❞❡s❡♥✈♦❧✈✐❞❛ ♣♦r ❲❛❧t❡r ❆✳ ❙❤❡✇❤❛rt ❬✺❪ ♥❛ ❞é❝❛❞❛ ❞❡ ✸✵ ❡ ❝♦♥✲ s❛❣r❛❞❛ ♣♦r ❲✐❧❧✐❛♥ ❊❞✇❛r❞s ❉❡♠✐♥❣ ❬✺❪ ❬✶✽❪ ❛ ♣❛rt✐r ❞❛ ❞é❝❛❞❛ ❞❡ ✺✵✱ q✉❛♥❞♦ ❢♦✐ ❡♠♣r❡❣❛❞❛ ❝♦♠ s✉❝❡ss♦ ♥❛s ❡♠♣r❡s❛s ❥❛♣♦♥❡s❛s ♣❛r❛ ✐♥❝r❡♠❡♥t♦ ♥❛ q✉❛❧✐❞❛❞❡ ❞❡ s❡✉s ♣r♦❝❡ss♦s✳ ❖ ❈✐❝❧♦ P❉❈❆ t❡♠ ❝♦♠♦ ♦❜❥❡t✐✈♦ ❡①❡r❝❡r ♦ ❝♦♥tr♦❧❡ ❞♦s ♣r♦❝❡ss♦s✱ ♣♦❞❡♥❞♦
s❡r ✉s❛❞♦ ❞❡ ❢♦r♠❛ ❝♦♥tí♥✉❛ ♣❛r❛ s❡✉ ❣❡r❡♥❝✐❛♠❡♥t♦ ❡♠ ✉♠❛ ♦r❣❛♥✐③❛çã♦✱ ♣♦r ♠❡✐♦ ❞♦ ❡st❛❜❡❧❡❝✐♠❡♥t♦ ❞❡ ✉♠❛ ❞✐r❡tr✐③ ❞❡ ❝♦♥tr♦❧❡ ✭♣❧❛♥❡❥❛♠❡♥t♦ ❞❛ q✉❛❧✐❞❛❞❡✮✱ ❞♦ ♠♦♥✐t♦✲ r❛♠❡♥t♦ ❞♦ ♥í✈❡❧ ❞❡ ❝♦♥tr♦❧❡ ❛ ♣❛rt✐r ❞❡ ♣❛❞rõ❡s ♣ré✲❡st❛❜❡❧❡❝✐❞♦s ❡ ❞❛ ♠❛♥✉t❡♥çã♦ ❞❛ ❞✐r❡tr✐③ ❛t✉❛❧✐③❛❞❛✱ r❡s❣✉❛r❞❛♥❞♦ ❛s ♥❡❝❡ss✐❞❛❞❡s ❞♦ ♣ú❜❧✐❝♦ ❛❧✈♦✳
❙✉❛ ✉t✐❧✐③❛çã♦ ❡stá ✐♥t✐♠❛♠❡♥t❡ ❧✐❣❛❞❛ ❛♦ ❡♥t❡♥❞✐♠❡♥t♦ ❞♦ ❝♦♥❝❡✐t♦ ❞❡ ♣r♦❝❡ss♦✱ ♦✉ s❡❥❛✱ ❞❡ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❛çõ❡s ❡ ❛t✐✈✐❞❛❞❡s ✐♥t❡r✲r❡❧❛❝✐♦♥❛❞❛s✱ q✉❡ sã♦ ❡①❡❝✉t❛❞❛s ♣❛r❛ ❛❧❝❛♥ç❛r ✉♠ ♣r♦❞✉t♦✱ r❡s✉❧t❛❞♦ ♦✉ s❡r✈✐ç♦ ♣r❡❞❡✜♥✐❞♦✳ ❈❛❞❛ ♣r♦❝❡ss♦ é ❝❛r❛❝t❡✲ r✐③❛❞♦ ♣♦r s✉❛s ❡♥tr❛❞❛s✱ ❛s ❢❡rr❛♠❡♥t❛s ❡ té❝♥✐❝❛s q✉❡ ♣♦❞❡♠ s❡r ❛♣❧✐❝❛❞❛s ❡ ❛s s❛í❞❛s r❡s✉❧t❛♥t❡s✳ P❉❈❆ é ✉♠ ❛❝rô♥✐♠♦ ❞❡ P✭♣❧❛✐♥✮✱ ❉✭❞♦✮✱ ❈✭❝❤❡❝❦✮ ❡ ❆✭❛❝t✮✿
• P❧❛✐♥✿
➱ ❛ ❢❛s❡ ♦♥❞❡ ♦❜❥❡t✐✈♦s sã♦ ❡st❛❜❡❧❡❝✐❞♦s✱ ♣r♦❝❡❞✐♠❡♥t♦s ♥❡❝❡ssár✐♦s ♥❛ r❡s♦❧✉çã♦ sã♦ ♣❧❛♥❡❥❛❞♦s✱ ❞❛❞♦s ♣❛r❛ ♠❡❧❤♦r ❝♦♠♣r❡❡♥❞❡r ❞♦ q✉❡ s❡rá ❞❡s❡♥✈♦❧✈✐❞♦ sã♦ ❝♦❧❡t❛❞♦s ❡ ❡str❛té❣✐❛s ♣❛r❛ ♠❡❧❤♦r ❛❧❝❛♥ç❛r ♦ r❡s✉❧t❛❞♦ ♣r♦❝✉r❛❞♦ sã♦ tr❛ç❛❞❛s✳ ❙❡ ♥❡❝❡ssár✐♦✱ sã♦ ❡st✉❞❛❞♦s ❝❛s♦s ♣❛rt✐❝✉❧❛r❡s ♦✉ ❡♠ ♣❡q✉❡♥❛ ❡s❝❛❧❛ ❞♦ ♣r♦❜❧❡♠❛ ❛ s❡r r❡s♦❧✈✐❞♦✳
• ❉♦✿
◆❡ss❛ ❢❛s❡ ♦❝♦rr❡ ❛ ❡①❡❝✉çã♦ ❞♦ ♣❧❛♥♦ ❞❡s❡♥✈♦❧✈✐❞♦ ♥❛ ❢❛s❡ ❛♥t❡r✐♦r✳ P♦r ❡♥✈♦❧✈❡r ❛s♣❡❝t♦s ♦♣❡r❛❝✐♦♥❛✐s ❞❛ r❡s♦❧✉çã♦ ❞♦ ♣r♦❜❧❡♠❛✱ ❝♦♠♣r❡❡♥❞❡ ♣❡sq✉✐s❛s ❡ s✐♠✉❧❛✲ çõ❡s ❡✱ ♥♦ ❡s❝♦♣♦ ❞❛ ♠❛t❡♠át✐❝❛✱ ✐♥❝❧✉✐ ♣r♦❝❡❞✐♠❡♥t♦s ❛❧❣é❜r✐❝♦s ❡ ❛r✐t♠ét✐❝♦s ❞♦s ♣r♦❜❧❡♠❛s✳
• ❈❤❡❝❦✿
▼♦♠❡♥t♦ q✉❡ ❝♦♥s✐st❡ ❡♠ ✈❡r✐✜❝❛r s❡ ♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s sã♦ ❝♦♠♣❛tí✈❡✐s ❝♦♠♦ ❢♦r❛ ♣r♦♣♦st♦ ♥♦ ♣r♦❜❧❡♠❛✱ s❡ ♣❡rt❡♥❝❡♠ ❛♦ s❡✉ ❞♦♠í♥✐♦✱ ❛t❡♥❞❡♥❞♦ s✉❛s r❡s✲ tr✐çõ❡s✳ ■st♦ ♣♦ss✐❜✐❧✐t❛ ♠❡❧❤♦r ❝♦♠♣r❡❡♥sã♦ ❞♦ ♣r♦❜❧❡♠❛✱ r❡❞✉③✐♥❞♦ ❛ ❞✐stâ♥❝✐❛ ❡♥tr❡ ♦ q✉❡ ❢♦✐ ❡①✐❣✐❞♦ ❡ ♦ q✉❡ ❢♦✐ ❞❡s❡♥✈♦❧✈✐❞♦✳
• ❆❝t✿
P♦r s❡r ❛ ú❧t✐♠❛ ❢❛s❡ ❞♦ ❝✐❝❧♦✱ é r❡s♣♦♥á✈❡❧ ♣♦r ♣r❡♣❛r❛r ❛ ❝♦♥t✐♥✉✐❞❛❞❡ ❞♦ ♣r♦✲ ❝❡ss♦✱ ❛❣✐♥❞♦ s♦❜r❡ ♦ q✉❡ ❢♦✐ ❞❡s❡♥✈♦❧✈✐❞♦✱ ❜✉s❝❛♥❞♦ ♥♦✈♦s ♣r♦❜❧❡♠❛s ♦✉ ♠♦❞✐✜✲ ❝❛♥❞♦ ♦ ♣r♦❜❧❡♠❛ r❡s♦❧✈✐❞♦ ♣❛r❛ r❡t♦r♥❛r ❛ ❢❛s❡ ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦✱ ❡♠ ♥♦✈♦ ❝✐❝❧♦ q✉❡ ❝♦♥t❛ ❝♦♠ ❛♣r❡♥❞✐③❛❞♦ ❣❡r❛❞♦ ♣❡❧♦ ❝✐❝❧♦ ❛♥t❡r✐♦r✳
❯♠❛ ❞❛s ❛♣❧✐❝❛çõ❡s ♠❛✐s ✐♠♣♦rt❛♥t❡s ❞♦ ❝✐❝❧♦ P❉❈❆ ❡stá ❡♠ ❛♥❛❧✐s❛r ❡ s♦❧✉❝✐♦♥❛r ♣r♦❜❧❡♠❛s✱ ♣❡r♠✐t✐♥❞♦ ♦ ❝♦♥tr♦❧❡ ❞❡ q✉❛❧✐❞❛❞❡ ❞✉r❛♥t❡ t♦❞❛s ❛s ❢❛s❡s ❞✬♦ ♣r♦❝❡ss♦✳ ❊♥q✉❛♥t♦ ♠❡t♦❞♦❧♦❣✐❛✱ ♦ P❉❈❆ ♣♦❞❡ s❡r ❛❞♦t❛❞♦ ❝♦♠♦ ❡str❛té❣✐❛ ♣❛r❛ ❛✉①✐❧✐❛r ♥♦ ♣r♦❝❡ss♦ ❞❡ ❡♥s✐♥♦✱ ♠❛s ♥ã♦ ❞❡✈❡ s❡r ✈✐st♦ ❝♦♠♦ ♣r♦❝❡❞✐♠❡♥t♦ ❞❡ ❡s❝♦♣♦ ❧✐♠✐t❛❞♦ ❛ s❡r ❡♥❝❡rr❛❞♦ q✉❛♥❞♦ ❢♦r❡♠ ❝✉♠♣r✐❞♦s ❝❡rt♦s ❝r✐tér✐♦s✱ ♠❛s s✐♠ ❝♦♠♦ ❝✐❝❧♦ ❡♠ ❝♦♥st❛♥t❡ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦✱ ♦♥❞❡ ♥♦✈❛s ✐t❡r❛çõ❡s s❡rã♦ ♣❧❛♥❡❥❛❞❛s ❡♠ ❢✉♥çã♦ ❞❡ s✉❝❡ss♦ ♦❜t✐❞♦ ❡♠ ✐t❡r❛çõ❡s ❛♥t❡r✐♦r❡s✳
◆♦ ❝❛♣ít✉❧♦ ✼ ❞❛ r❡❢❡rê♥❝✐❛ ❬✶✽❪✱ t❡♠✲s❡ ♠❛✐s ❡❧❡♠❡♥t♦s ❛❝❡r❝❛ ❞♦ ❈✐❝❧♦ P❉❈❆ ❡ ♠ét♦❞♦s ❞❡ ❝♦♥tr♦❧❡ ❞❡ q✉❛❧✐❞❛❞❡✳
✶✳✷ ❖ ❡♥s✐♥♦ ♠é❞✐♦
❆ ▲❡✐no ✾✳✸✾✹ ❞❡ ✷✵ ❞❡ ❞❡③❡♠❜r♦ ❞❡ ✶✾✾✻ ❡st❛❜❡❧❡❝❡ ❛s ❞✐r❡tr✐③❡s ❡ ❜❛s❡s ❞❛ ❡❞✉❝❛çã♦
♥❛❝✐♦♥❛❧ ❡ ♣r♦♣õ❡s ♣r✐♥❝í♣✐♦s ❡ ♦❜❥❡t✐✈♦s q✉❡ ♥♦rt❡❛rã♦ ♣♦❧ít✐❝❛s ❞♦ s✐st❡♠❛ ❡❞✉❝❛❝✐♦♥❛❧ ❜r❛s✐❧❡✐r♦✳ ❆♦ ❧♦♥❣♦ ❞❡ ✾✷ ❛rt✐❣♦s✱ sã♦ ❛♣r❡s❡♥t❛❞❛s ❞❡✜♥✐çõ❡s ❡ ♣r♦♣♦st❛s ❝❛r❛❝t❡rís✲ t✐❝❛s ♣❛r❛ ❝❛❞❛ ✉♠ ❞♦s s❡❣♠❡♥t♦s ❞❛ ❡❞✉❝❛çã♦ ❜ás✐❝❛ ❜r❛s✐❧❡✐r❛✳ ❖ ❛rt✐❣♦ ✸✺ ❛tr✐❜✉✐ ❛♦ ❡♥s✐♥♦ ♠é❞✐♦ ❛ ❝❛r❛❝t❡ríst✐❝❛ ❞❡ t❡r♠✐♥❛❧✐❞❛❞❡ ♣♦r s❡r ❛ ❡t❛♣❛ ✜♥❛❧ ❞❛ ❡❞✉❝❛çã♦ ❜áss✐❝❛ ❡ ❛♣r❡s❡♥t❛ s✉❛s ✜♥❛❧✐❞❛❞❡s✿
❆rt✳ ✸✺✳ ❖ ❡♥s✐♥♦ ♠é❞✐♦✱ ❡t❛♣❛ ✜♥❛❧ ❞❛ ❡❞✉❝❛çã♦ ❜ás✐❝❛✱ ❝♦♠ ❞✉r❛çã♦ ♠í♥✐♠❛ ❞❡ três ❛♥♦s✱ t❡rá ❝♦♠♦ ✜♥❛❧✐❞❛❞❡s✿
■✳ ❛ ❝♦♥s♦❧✐❞❛çã♦ ❡ ♦ ❛♣r♦❢✉♥❞❛♠❡♥t♦ ❞♦s ❝♦♥❤❡❝✐♠❡♥t♦s ❛❞q✉✐r✐❞♦s ♥♦ ❡♥s✐♥♦ ❢✉♥❞❛♠❡♥t❛❧✱ ♣♦ss✐❜✐❧✐t❛♥❞♦ ♦ ♣r♦ss❡❣✉✐♠❡♥t♦ ❞❡ ❡st✉❞♦s❀ ■■✳ ❛ ♣r❡♣❛r❛çã♦ ❜ás✐❝❛ ♣❛r❛ ♦ tr❛❜❛❧❤♦ ❡ ❛ ❝✐❞❛❞❛♥✐❛ ❞♦ ❡❞✉❝❛♥❞♦✱ ♣❛r❛
❝♦♥t✐♥✉❛r ❛♣r❡♥❞❡♥❞♦✱ ❞❡ ♠♦❞♦ ❛ s❡r ❝❛♣❛③ ❞❡ s❡ ❛❞❛♣t❛r ❝♦♠ ✢❡①✐❜✐✲ ❧✐❞❛❞❡ ❛ ♥♦✈❛s ❝♦♥❞✐çõ❡s ❞❡ ♦❝✉♣❛çã♦ ♦✉ ❛♣❡r❢❡✐ç♦❛♠❡♥t♦ ♣♦st❡r✐♦r❡s❀ ■■■✳ ♦ ❛♣r✐♠♦r❛♠❡♥t♦ ❞♦ ❡❞✉❝❛♥❞♦ ❝♦♠♦ ♣❡ss♦❛ ❤✉♠❛♥❛✱ ✐♥❝❧✉✐♥❞♦ ❛ ❢♦r✲ ♠❛çã♦ ét✐❝❛ ❡ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❛ ❛✉t♦♥♦♠✐❛ ✐♥t❡❧❡❝t✉❛❧ ❡ ❞♦ ♣❡♥✲ s❛♠❡♥t♦ ❝rít✐❝♦❀ ❡
■❱✳ ❛ ❝♦♠♣r❡❡♥sã♦ ❞♦s ❢✉♥❞❛♠❡♥t♦s ❝✐❡♥tí✜❝♦✲t❡❝♥♦❧ó❣✐❝♦s ❞♦s ♣r♦❝❡ss♦s ♣r♦❞✉t✐✈♦s✱ r❡❧❛❝✐♦♥❛♥❞♦ ❛ t❡♦r✐❛ ❝♦♠ ❛ ♣rát✐❝❛✱ ♥♦ ❡♥s✐♥♦ ❞❡ ❝❛❞❛ ❞✐s❝✐♣❧✐♥❛✳
❚❛✐s ✜♥❛❧✐❞❛❞❡s ❞❡✈❡♠ s❡r ♠❛t❡r✐❛❧✐③❛❞❛s ♥❛ ❝♦♥str✉çã♦ ❞❡ ❝✉rrí❝✉❧♦ q✉❡ ❝♦♥t❡♠✲ ♣❧❡ ❛ ❡❞✉❝❛çã♦ t❡❝♥♦❧ó❣✐❝❛ ❜ás✐❝❛✱ ❛ ❝♦♠♣r❡❡♥sã♦ ❞♦ s✐❣♥✐✜❝❛❞♦ ❞❛ ❝✐ê♥❝✐❛✱ ♦ ♣r♦❝❡ss♦ ❤✐stór✐❝♦ ❞❡ tr❛♥s❢♦r♠❛çã♦ ❞❛ s♦❝✐❡❞❛❞❡ ❡ ❞❛ ❝✉❧t✉r❛ t❡♥❞♦ ❛ ❧í♥❣✉❛ ♣♦rt✉❣✉❡s❛ ❝♦♠♦ ✐♥str✉♠❡♥t♦ ❞❡ ❝♦♠✉♥✐❝❛çã♦✱ ❛❝❡ss♦ ❛♦ ❝♦♥❤❡❝✐♠❡♥t♦ ❡ ❡①❡r❝í❝✐♦ ❞❛ ❝✐❞❛❞❛♥✐❛ ❡ ♠❡t♦✲ ❞♦❧♦❣✐❛ ❞❡ ❡♥s✐♥♦ ❡ ❞❡ ❛✈❛❧✐❛çã♦ q✉❡ ❡st✐♠✉❧❡♠ ❛ ✐♥✐❝✐❛t✐✈❛ ❞♦s ❡st✉❞❛♥t❡s✱ ❡❧❡♠❡♥t♦s ❡ss❡s ✈♦❧t❛❞♦ ♣❛r❛ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ❝♦♠♣❡tê♥❝✐❛s ❜ás✐❝❛s✱ ❝♦♠ ♣r❡s❡♥ç❛ ❞❡ ❡❧❡✲ ♠❡♥t♦s q✉❡ r❡♠❡t❡♠ à ✐♥t❡r❞✐s❝✐♣❧✐♥❛r✐❞❛❞❡ ❡ ❝♦♥t❡①t✉❛❧✐③❛çã♦✱ ♣❡rt❡❝❡♥t❡s ❛ ✉♠❛ ❜❛s❡ ♥❛❝✐♦♥❛❧ ❝♦♠✉♠ q✉❡ ♣r♦♣✐❝✐❡♠ ❢♦r♠❛çã♦ ❣❡r❛❧ ❡ ♣r❡♣❛r❛çã♦ ❜ás✐❝❛ ♣❛r❛ ♦ ♠❡r❝❛❞♦ ❞❡ tr❛❜❛❧❤♦✳
◆❛ s♦❝✐❡❞❛❞❡ ❛t✉❛❧✱ ❝❛r❛❝t❡r✐③❛❞❛ ♣❡❧❛ ❡s❝❛ss❡③ ❞❡ r❡❝✉rs♦s ❡ ❝♦♥st❛♥t❡ ❜✉s❝❛ ♣❡❧❛ ♦t✐♠✐③❛çã♦ ❞❡ ♣r♦❝❡ss♦s✱ ❛ Pr♦❣r❛♠❛çã♦ ▲✐♥❡❛r t❡♠ s❡ t♦r♥❛❞♦ ✉♠ ❢❛t♦r ❡str❛té❣✐❝♦ ♥❛ ❜✉s❝❛ ❞♦s ♠❡❧❤♦r❡s r❡s✉❧t❛❞♦s ♣♦r ♦r❣❛♥✐③❛çõ❡s ❞❡ ❞✐❢❡r❡♥t❡s ♣♦rt❡s ❝✉❥♦s ♦❜❥❡t✐✈♦s✱ ♠✉✐t❛s ✈❡③❡s✱ r❡s✉♠❡♠✲s❡ ❛ ♠✐♥✐♠✐③❛r t❡♠♣♦ ❡ ❣❛st♦s ♦✉ ♠❛①✐♠✐③❛r ❧✉❝r♦ ❡ ♣r♦❞✉✲ çã♦✳ ❊ss❛s ❝❛r❛❝t❡ríst✐❝❛s ❡✈✐❞❡♥❝✐❛♠ ✐♠♣♦rt❛♥t❡s ❛♣❧✐❝❛çõ❡s ❞❡ t❡♠❛s ♠❛t❡♠át✐❝♦s ❝♦♠♦ ♦ ❡st✉❞♦ ❛♥❛❧ít✐❝♦ ❞❛ r❡t❛ ❡ s✐st❡♠❛s ❧✐♥❡❛r❡s✱ ❝r✐❛♥❞♦ ❛ss♦❝✐❛çã♦ t❡♦r✐❛✲♣rát✐❝❛ ❡ ❝♦❧❛❜♦r❛♥❞♦ ♣❛r❛ ❛ ❢♦r♠❛çã♦ ❞❡ ♥♦✈♦ ♣❡r✜❧ ♣❛r❛ ♦ ❡♥s✐♥♦ ♠é❞✐♦✱ ❡s♣❡❝✐❛❧♠❡♥t❡ ♥❛ ✈✐♥✲ ❝✉❧❛çã♦ ❛♦ ♠❡r❝❛❞♦ ❞❡ tr❛❜❛❧❤♦ ❡ ❝♦♥❤❡❝✐♠❡♥t♦ ❞❡ ❛s♣❡❝t♦s t❡❝♥♦❧ó❣✐❝♦s ❞♦s ♣r♦❝❡ss♦s ♣r♦❞✉t✐✈♦s✳
✶✳✸ ❙❡çõ❡s ❞❡ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞♦ tr❛❜❛❧❤♦
❖ ♣r✐♥❝✐♣❛❧ ♦❜❥❡t✐✈♦ ❞❡st❡ tr❛❜❛❧❤♦ é ❛♣r❡s❡♥t❛r ✉♠❛ ♣r♦♣♦st❛ ❞❡ ❡♥s✐♥♦ ❡ ❛♣r❡♥✲ ❞✐③❛❣❡♠ ❞❡ ✉♠❛ ♣❛rt❡ ❞❛ ♠❛t❡♠át✐❝❛ ♣❛r❛ ♦ ❡♥s✐♥♦ ♠é❞✐♦✱ t❡♥❞♦ ❝♦♠♦ ❝❡♥ár✐♦ ❛ ♠♦❞❡❧❛❣❡♠ ♠❛t❡♠át✐❝❛ ❡ ❛ ♣r♦❣r❛♠❛çã♦ ❧✐♥❡❛r✱ ✉t✐❧✐③❛♥❞♦ ♣r♦❜❧❡♠❛s r❡❛✐s ♦❜s❡r✈❛❞♦s ♥♦ ❝♦♥t❡①t♦ ❡❝♦♥ô♠✐❝♦ ❡ ♣r♦❞✉t✐✈♦ ❞♦ sé❝✉❧♦ ❳❳■✳ P❛r❛❧❡❧❛♠❡♥t❡✱ s❡rã♦ ❞❡s❡♥✈♦❧✈✐❞♦s r❡❝✉rs♦s ❞✐❞át✐❝♦s q✉❡ ❛✉①✐❧✐❡♠ ♥❛ ❢✉♥❞❛♠❡♥t❛çã♦ t❡ór✐❝❛ ❡ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❛❧❣é❜r✐❝♦ ❞♦ s✐♠♣❧❡①✱ ♣r✐♥❝✐♣❛❧ ❛❧❣♦r✐t♠♦ ♣❛r❛ r❡s♦❧✈❡r ♣r♦❜❧❡♠❛s ❞❡ss❛ ♥❛t✉r❡③❛✳
◆♦ ❝❛♣ít✉❧♦ ✷ ✲ ▼♦❞❡❧❛❣❡♠ ✲ s❡rã♦ ❞❡❧✐♥❡❛❞♦s ♦s ❝♦♥❝❡✐t♦s ❞❡ ♠♦❞❡❧❛❣❡♠ ♠❛t❡♠á✲ t✐❝❛ ❡ ♣r♦❣r❛♠❛çã♦ ❧✐♥❡❛r✱ q✉❡ ♥♦rt❡✐❛♠ ❡st❡ tr❛❜❛❧❤♦✳ ❉✐s❝✉t✐r✲s❡✲ã♦ ❡str❛té❣✐❛s ♥❛ ❛❜♦r❞❛❣❡♠ ❡ ♠♦❞❡❧❛❣❡♠ ❞❡ss❡s ♣r♦❜❧❡♠❛s✱ ❜❡♠ ❝♦♠♦ ❡❧❡♥❝❛r ❢❛t♦r❡s q✉❡ ✐♥t❡r❢❡r❡♠ ♥❛ ❝❛♣❛❝✐❞❛❞❡ ❞❡ ♠♦❞❡❧❛r ♦✉ ♥❛ s✐❣♥✐✜❝â♥❝✐❛ ❞♦ ♠♦❞❡❧♦ ❞❡s❡♥✈♦❧✈✐❞♦✳
❖ ❝❛♣ít✉❧♦ ✸ ✲ ❆❧❣♦r✐t♠♦s ✲ ❛♣r❡s❡♥t❛ ❛ ♥♦çã♦ ❞❡ ❛❧❣♦r✐t♠♦ ❡ ❝♦♠♦ ♣♦❞❡ s❡r ❡♠✲ ♣r❡❣❛❞♦✱ ♥❛ ❡❞✉❝❛çã♦ ❜ás✐❝❛✱ ♥❛ ❝♦♠♣r❡❡♥sã♦ ❡ r❡s♦❧✉çã♦ ❞❡ ♣r♦❜❧❡♠❛s✳ ❈♦❝♦♠✐t❛♥t❡✲ ♠❡♥t❡ s❡rã♦ ♣r♦♣♦st♦s ♣r♦❜❧❡♠❛s s✐♠♣❧❡s ❝♦♠ ♦❜❥❡t✐✈♦ ❞❡ ❞❡s❡♥✈♦❧✈❡r ♦ ❡♥❝❛❞❡❛♠❡♥t♦
❧ó❣✐❝♦ ❞❡ ❛çõ❡s ♥❛ ❝♦♥str✉çã♦ ❞❡ ❛❧❣♦r✐t♠♦s ❜❡♠ ❝♦♠♦ s✉❛ ❛♥á❧✐s❡ ❞❡ ❝♦♠♣❧❡①✐❞❛❞❡✳ ❖ ❝❛♣ít✉❧♦ ✹ ✲ ❖ ●❡♦❣❡❜r❛ ✲ ❞❡st✐♥❛✲s❡ ❛ ❛♣r❡s❡♥t❛r ❛s ❢✉♥❝✐♦♥❛❧✐❞❛❞❡s ❞♦ s♦❢t✇❛r❡ ♥❡❝❡ssár✐♦s ♣❛r❛ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❛s ❛t✐✈✐❞❛❞❡s ♣r♦♣♦st❛s ♥♦s ❝❛♣ít✉❧♦s ✺✱ ✻✱ ✼ ❡ ✽✳
◆♦s ❝❛♣ít✉❧♦s ✺ ✲ ❋✉♥❞❛♠❡♥t♦s ❚❡ór✐❝♦s ✲ ❡ ✻ ✲ ❋✉♥❞❛♠❡♥t♦s ❞❡ ❈á❧❝✉❧♦ ✲ s❡rã♦ ❞❡s❡♥✈♦❧✈✐❞♦s ♦s ❛s♣❡❝t♦s t❡ór✐❝♦s q✉❡ ❢✉♥❞❛♠❡♥t❛♠ ❛ ❝♦rr❡çã♦ ❡ ❡✜❝✐ê♥❝✐❛ ❞♦ s✐♠✲ ♣❧❡①✱ ♣r✐♥❝✐♣❛❧ ❛❧❣♦r✐t♠♦ ❛❞♦t❛❞♦ ♥❛ r❡s♦❧✉çã♦ ❞❡ ♣r♦❜❧❡♠❛s ❞❡ ♣r♦❣r❛♠❛çã♦ ❧✐♥❡❛r✳ ❆♣r❡s❡♥t❛r✲s❡✲ã♦ ❡❧❡♠❡♥t♦s q✉❡ ♠♦str❛♠ ❛ ✐♠♣♦rtâ♥❝✐❛ ❞❛ ❛ss♦❝✐❛çã♦ ❞❡ ❝♦♥❝❡✐t♦s ❛❧✲ ❣é❜r✐❝♦s às s✉❛s r❡s♣❡❝t✐✈❛s ✈❡rsõ❡s ❣❡♦♠étr✐❝❛s✱ ❡♠ ❡s♣❡❝✐❛❧ ♥❛s s❡çõ❡s q✉❡ tr❛t❛♠ ❞❡ ❡q✉❛çã♦ ❞❛ r❡t❛✱ ✐♥❡q✉❛çõ❡s ❞❡ ♣r✐♠❡✐r♦ ❣r❛✉ ❝♦♠ ❞✉❛s ✐♥❝ó❣♥✐t❛s✱ r❡s♦❧✉çã♦ ❞❡ s✐st❡♠❛s ❧✐♥❡❛r❡s✱ ♥♦çõ❡s ❞❡ ❢✉♥çã♦ ❡ ❞❡r✐✈❛❞❛s✳
❖ ❝❛♣ít✉❧♦ ✼ ✲ ▼ét♦❞♦ ❙✐♠♣❧❡① ✲ ❞❡st✐♥❛✲s❡ ❛♦ ❆❧❣♦r✐t♠♦ ❙✐♠♣❧❡① ❡♠ s✉❛s ✈❡rsõ❡s ♠❛✐s ❝♦♥❤❡❝✐❞❛s✱ ❝✉❥♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ é ❢❡✐t♦ ❛ ♣❛rt✐r ❞❡ ♣r♦❜❧❡♠❛s ❞❡✜♥✐❞♦s ♥♦ R2✱
❡♠ ✈✐rt✉❞❡ ❞♦ ❛s♣❡❝t♦ ❣❡♦♠ét✐❝♦ ❛❞♦t❛❞♦ ♥❛ s✉❛ r❡s♦❧✉çã♦✳ P❛r❛ ♣r♦❜❧❡♠❛s ❞❡✜♥✐❞♦s ❡♠ ❞✐♠❡♥sõ❡s s✉♣❡r✐♦r❡s✱ ♦ ❢♦❝♦ s❡rá ♥❛ ♠♦❞❡❧❛❣❡♠ ❡ r❡s♦❧✉çã♦ ♣❡❧♦ ♠ét♦❞♦ ❛❧❣é❜r✐❝♦✱ ❝♦♠ ♣♦st❡r✐♦r ✈❡r✐✜❝❛çã♦ ♥♦ ▼✐❝r♦s♦❢t ❊①❝❡❧✳
P♦r ✜♠✱ ♦ ❝❛♣ít✉❧♦ ✽ ✲ ❚❡♦r✐❛ ❞♦ ❈♦♥s✉♠✐❞♦r ✲ ❛♣r❡s❡♥t❛ ❛ ♠♦❞❡❧❛❣❡♠ ❞❡ ✉♠❛ ✐♠♣♦rt❛♥t❡ t❡♦r✐❛ ❞❛ ♠✐❝r♦❡❝♦♥♦♠✐❛ q✉❡ ❡st❛❜❡❧❡❝❡ ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞♦ ❝♦♥s✉♠✐❞♦r ✐♥❞✐✈✐❞✉❛❧ ❢r❡♥t❡ às ❞❡❝✐sõ❡s ❞❡ ❝♦♥s✉♠♦✱ ♥❛ ❡s❝♦❧❤❛ ❞♦s ♠❡❧❤♦r❡s ♣r♦❞✉t♦s ❞❡♥tr♦ ❞❛q✉✐❧♦ q✉❡ ❡❧❡s ♣♦❞❡♠ ❛❞q✉✐r✐r✳
✷ ▼♦❞❡❧❛❣❡♠
✷✳✶ ■♥tr♦❞✉çã♦
❙❡❣✉♥❞♦ ♦ ◆♦✈♦ ❉✐❝✐♦♥ár✐♦ ❆✉ré❧✐♦ ❞❛ ▲í♥❣✉❛ P♦rt✉❣✉❡s❛✱ 4a ❡❞✐çã♦✱ ✷✵✵✾✱ ❞❡✜♥❡✲s❡
♣♦r ♠♦❞❡❧♦ ♦ ♦❜❥❡t♦ ❞❡s✐❣♥❛❞♦ ❛ s❡r r❡♣r♦❞✉③✐❞♦ ♣♦r ✐♠✐t❛çã♦✱ ✉♠❛ r❡♣r❡s❡♥t❛çã♦ ❡♠ ♣❡q✉❡♥❛ ❡s❝❛❧❛ ❞❡ ❛❧❣♦ q✉❡ s❡ ❞❡s❡❥❛ ❡①❡❝✉t❛r ❡♠ ❞✐♠❡♥sõ❡s r❡❛✐s✱ ✉♠ ♠♦❧❞❡✳ ❉❡ss❛ ❞❡✜♥✐çã♦✱ ✐♥❢❡r❡✲s❡✱ ❡♠ ❧✐♥❤❛s ❣❡r❛✐s✱ q✉❡ ♠♦❞❡❧❛❣❡♠ ❡stá r❡❧❛❝✐♦♥❛❞❛ á ♦♣❡r❛çã♦ ❞❡ r❡♣r❡s❡♥t❛r ✉♠ ❡♥t❡ ❞♦ ♠✉♥❞♦ r❡❛❧ ♣♦r ♠❡✐♦ ❞❡ ✉♠ ♠♦❞❡❧♦✱ ❡♠ ♣r♦❝❡ss♦ ❞❡ tr❛❞✉çã♦ ❞♦ ♠✉♥❞♦ r❡❛❧✱ ♠❡❞✐❛♥t❡ s✐♠♣❧✐✜❝❛çõ❡s ❛ ♣❛rt✐r ❞❡ ♦❜❥❡t♦s ♣r❡✈✐❛♠❡♥t❡ ❝♦♥str✉í❞♦s✱ ❝♦♥❢♦r♠❡ r❡♣r❡s❡♥t❛♠♦s ♥❛ ✜❣✉r❛ ✷✳
❋✐❣✉r❛ ✷✿ ▼♦❞❡❧❛❣❡♠ ❝♦♠♦ tr❛❞✉çã♦ ❞❡ ❡♥t❡ ❞♦ ♠✉♥❞♦ r❡❛❧
◆❛s ❝✐ê♥❝✐❛s ♠❛t❡♠át✐❝❛s✱ ♦ ♣r♦❝❡ss♦ ❞❡ ♠♦❞❡❧❛❣❡♠ ❡stá ❛ss♦❝✐❛❞♦ à ❝❛♣❛❝✐❞❛❞❡ ❞❡ tr❛♥s❢♦r♠❛r ♣r♦❜❧❡♠❛s r❡❛✐s ❡♠ ❝♦♥t❡①t♦s ❝✉❥❛ r❡s♦❧✉çã♦ s❡❥❛ ❞❡ ♣♦ssí✈❡❧ ❡①❡❝✉çã♦✱ ❛ ♣❛rt✐r ❞❡ ❤❛❜✐❧✐❞❛❞❡s ❡ ❝♦♠♣❡tê♥❝✐❛s ❞❡s❡♥✈♦❧✈✐❞❛s✱ ♣❛r❛ ♣♦st❡r✐♦r ✐♥t❡r♣r❡t❛çã♦ ❡ ♠❛♣❡❛♠❡♥t♦ ♥♦ ♠✉♥❞♦ r❡❛❧✳
◆♦ ❡♥t❛♥t♦✱ ♦ ♣r♦❝❡ss♦ ♣♦❞❡ s♦❢r❡r ❛❥✉st❡s ❡♠ ❢✉♥çã♦ ❞❛ ❝♦♠♣❧❡①✐❞❛❞❡ ❞❡ ♣r♦❜❧❡✲ ♠❛s r❡❛✐s ❡ ❞❛ s✐♠♣❧✐❝✐❞❛❞❡ ❞❡ ❡❧❡♠❡♥t♦s ♠❛t❡♠át✐❝♦s ♥♦r♠❛❧♠❡♥t❡ ❡♠♣r❡❣❛❞♦s ♥❛ ❝♦♥str✉çã♦ ❞♦s ♠♦❞❡❧♦s✳ ◆❛ ✐♥s✉✜❝✐ê♥❝✐❛ ❞❡ ❡❧❡♠❡♥t♦s ♥❡❝❡ssár✐♦s ♣❛r❛ ❛ ❝♦♥str✉çã♦ ❞❡ ✉♠ ♠♦❞❡❧♦✱ ❢❛③✲s❡ ♥❡❝❡ssár✐❛ ❛ ❝r✐❛çã♦ ❞❡ ♥♦✈♦s ❡❧❡♠❡♥t♦s ♦✉ ♦ ❡st❛❜❡❧❡❝✐♠❡♥t♦ ❞❡ ♥♦✈❛s r❡❧❛çõ❡s✳ P♦rt❛♥t♦✱ ❛♦ ❝r✐❛r ♥♦✈♦s ♠♦❞❡❧♦s✱ ❛ s♦❝✐❡❞❛❞❡ ❝♦❧❛❜♦r❛ ♣❛r❛ ♦ ❞❡s❡♥✲ ✈♦❧✈✐♠❡♥t♦ ❞❛ ♣ró♣r✐❛ ♠❛t❡♠át✐❝❛ ✉♠❛ ✈❡③ q✉❡✱ s❡❣✉♥❞♦ ❯❜✐r❛t❛♥ ❉❛♠❜rós✐♦ ❬✷❪✱ ✧❆ ♠♦❞❡❧❛❣❡♠ ♠❛t❡♠át✐❝❛ é ♠❛t❡♠át✐❝❛ ♣♦r ❡①❝❡❧ê♥❝✐❛✧ ♣♦r r❡♣r❡s❡♥t❛r ❢❛t♦s ❡ ❢❡♥ô♠❡✲ ♥♦s ♦❜s❡r✈❛❞♦s ♥♦ q✉♦t✐❞✐❛♥♦✱ ♣♦r ♠❡✐♦ ❞❡ ❡♥t✐❞❛❞❡s ❡ r❡❧❛❝✐♦♥❛♠❡♥t♦s q✉❡ ♣♦❞❡♠ s❡r s♦❝✐❛❧✐③❛❞♦s✳
❉❡ ❢♦r♠❛ ❣❡r❛❧✱ ❛ ❝♦♥str✉çã♦ ❞❡ ✉♠ ♠♦❞❡❧♦ ♣❛r❛ ❛ r❡s♦❧✉çã♦ ❞❡ ✉♠ ♣r♦❜❧❡♠❛
r❡s✉♠❡✲s❡ ❛♦ ❝✉♠♣r✐♠❡♥t♦ ❞❡ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❡stá❣✐♦s ❞❡ ❝✉♥❤♦ ♦♣❡r❛❝✐♦♥❛❧ ♦♥❞❡ sã♦ ❞❡✜♥✐❞♦s ♦❜❥❡t✐✈♦s✱ ✈❛r✐á✈❡✐s ❞❡ ❞❡❝✐sã♦ ❡ ❝♦♥tr♦❧❡ ❡ ♥í✈❡✐s ❞❡ ❞❡t❛❧❤❛♠❡♥t♦✱ ❝♦♥st✐✲ t✉✐♥❞♦ ♠❡t♦❞♦❧♦❣✐❛ q✉❡ ♠✉✐t♦ s❡ ❛ss❡♠❡❧❤❛ ❛♦s ♠ét♦❞♦s ❣❡r❡♥❝✐❛✐s ❞❡ ♠❡❧❤♦r✐❛ ❝♦♥tí✲ ♥✉❛ ❝♦♠♦ ♦ ❝✐❝❧♦ P❉❈❆✳ ❊♠❜♦r❛ ♥ã♦ ❛♣r❡s❡♥t❡♠ ❧✐♠✐t❡s ❜❡♠ ❞❡✜♥✐❞♦s✱ ❡✈✐❞❡♥❝✐❛♠✲s❡ três ❢❛s❡s ♥♦ ♣r♦❝❡ss♦ ❞❡ ♠♦❞❡❧❛❣❡♠✿ ❝♦♠♣r❡❡♥sã♦✱ ♠❛t❡♠❛t✐③❛çã♦ ❡ ❛✈❛❧✐❛çã♦✱ ❝✉❥♦s ♠❛r❝♦s ♣r✐♥❝✐♣❛✐s sã♦ ❛♣r❡s❡♥t❛❞♦s ♥❛ ✜✐❣✉r❛ ✸✳
❋✐❣✉r❛ ✸✿ ❋❛s❡s ❞♦ ♣r♦❝❡ss♦ ❞❡ ♠♦❞❡❧❛❣❡♠
✶✳ ❈♦♠♣r❡❡♥sã♦✿
❆ ❝♦♥str✉çã♦ ❞❡ ✉♠ ♠♦❞❡❧♦ é ❞❡s❡♥❝❛❞❡❛❞❛ ♣❡❧❛ ♣❧❡♥❛ ❛♣r♦♣r✐❛çã♦ ❡ ❝♦♥❤❡❝✐✲ ♠❡♥t♦ ❞♦ ♣r♦❜❧❡♠❛ ❛ s❡r ♠♦❞❡❧❛❞♦✱ ❛❝r❡s❝✐❞❛ ❞❛ ❢❛♠✐❧✐❛r✐③❛çã♦ ❝♦♠ ❢❡rr❛♠❡♥t❛s ❛ s❡r❡♠ ✉t✐❧✐③❛❞❛s ♥♦ ♣r♦❝❡ss♦✱ ❡♠ ❛çõ❡s q✉❡ ❡♥✈♦❧✈❡♠ ❡st✉❞♦✱ ♣❡sq✉✐s❛ ❡ s✐♠✉✲ ❧❛çã♦✳ ❆ ❞✐♥â♠✐❝❛✱ ♥❡ss❡ ♠♦♠❡♥t♦✱ ❝♦♥s✐st❡ ❡♠ ❛❣❧✉t✐♥❛r ❡❧❡♠❡♥t♦s q✉❡ ❝♦♥tr✐✲ ❜✉❛♠ ♣❛r❛ ❛ ❢♦r♠❛❧✐③❛çã♦ ♠❛t❡♠át✐❝❛ ♥❡❝❡ssár✐❛ ♥❛ ❢❛s❡ ❞❡ ♠❛t❡♠❛t✐③❛çã♦✳
✷✳ ▼❛t❡♠❛t✐③❛çã♦✿
➱ ♦ ♠♦♠❡♥t♦ ♥♦ q✉❛❧ ♦❝♦rr❡✱ ❞❡ ❢❛t♦✱ ❛ tr❛❞✉çã♦ ❞❛ s✐t✉❛çã♦✲♣r♦❜❧❡♠❛ ♣❛r❛ ❛ ❧✐♥❣✉❛❣❡♠ ♠❛t❡♠át✐❝❛ ❡ ❝♦♥s❡q✉❡♥t❡ r❡s♦❧✉çã♦✳ ❍❛❜✐❧✐❞❛❞❡s ❝♦♠♦ ✐♥t✉✐çã♦ ❡ ❝r✐❛t✐✈✐❞❛❞❡ sã♦ ❡ss❡♥❝✐❛✐s ♣❛r❛ ❝❧❛ss✐✜❝❛r ✐♥❢♦r♠❛çõ❡s✱ ❞❡s❝♦♥s✐❞❡r❛♥❞♦ ❛q✉❡❧❛s q✉❡ ❢♦r❡♠ ✐rr❡❧❡✈❛♥t❡s✱ ❞❡❝✐❞✐r q✉❡ ♠❡t❛s ❞❡✈❡♠ s❡r ♣r♦❝✉r❛❞❛s✱ s❡❧❡❝✐♦♥❛r ✈❛r✐á✲ ✈❡✐s r❡❧❡✈❛♥t❡s ❡ ❝♦♥st❛♥t❡s r❡❧❛❝✐♦♥❛❞❛s✱ ✉s❛r ♥♦t❛çã♦ ♠❛t❡♠át✐❝❛ ❛❞❡q✉❛❞❛ ❛♦ ❝❡♥ár✐♦ ❡ ❞❡s❝r❡✈❡r ♠❛t❡♠❛t✐❝❛♠❡♥t❡ ❛ r❡❧❛çã♦ ❡♥tr❡ t♦❞♦s ❡ss❡s t❡r♠♦s✳
❆♦ ✜♥❛❧ ❞❡ss❛ ❡t❛♣❛✱ ✉♠❛ r❡s♣♦st❛ q✉❡ ❛t❡♥❞❛ t♦❞❛s ❛s r❡str✐çõ❡s ❧❡✈❛♥t❛❞❛s ❞❡✈❡ s❡r ❡①♣❧✐❝✐t❛❞❛ ♦✉ ♦s ❡❧❡♠❡♥t♦s ❡❧❡♥❝❛❞♦s ❞❡✈❡♠ s❡r s✉✜❝✐❡♥t❡s ♣❛r❛ ❝♦♠♣r♦✈❛r ❛ s✉❛ ✐♥❡①✐stê♥❝✐❛✳
✸✳ ❆✈❛❧✐❛çã♦✿
❯♠❛ ✈❡③ ❞❡t❡r♠✐♥❛❞❛ ❛ s♦❧✉çã♦ ❞♦ ♣r♦❜❧❡♠❛✱ ❢❛③✲s❡ ♥❡❝❡ssár✐❛ ❛ ✈❛❧✐❞❛çã♦ ❞❡ss❡s r❡s✉❧t❛❞♦s ❡ ❞♦ ♣❧❛♥❡❥❛♠❡♥t♦ ❞♦s ♣ró①✐♠♦s ♣❛ss♦s ❛ s❡r❡♠ ❡①❡❝✉t❛❞♦s✳ ❊str❛té✲ ❣✐❛s ❝♦♠♦ r❡❢♦r♠✉❧❛çã♦ ❞♦ ♣r♦❜❧❡♠❛ s♦❧✉❝✐♦♥❛❞♦✱ ❡❧❛❜♦r❛çã♦ ❞❡ ♦✉tr♦ ♠ét♦❞♦ ❞❡ r❡s♦❧✉çã♦ ♣❛r❛ ♦ ♠❡s♠♦ ♣r♦❜❧❡♠❛ ♦✉ ❛✐♥❞❛ ❛ ❜✉s❝❛ ❞❡ ♣r♦❜❧❡♠❛s ❝♦♠ ♠❛✐♦r ❣r❛✉ ❞❡ ❝♦♠♣❧❡①✐❞❛❞❡ ♣♦❞❡♠ s❡r ✉t✐❧✐③❛❞❛s ♣❛r❛ ♣r❡♣❛r❛r ✉♠❛ ♥♦✈❛ ✐t❡r❛çã♦ ❞♦ ❈✐❝❧♦ ❞❡ ❉❡♠✐♥❣✳ ❍❛✈❡♥❞♦ ♥❡❝❡ss✐❞❛❞❡✱ ❝❛s♦ ❛ s♦❧✉çã♦ ❝♦♥str✉í❞❛ ♥ã♦ s❡❥❛ ❛❞❡q✉❛❞❛✱ ❛s ❡t❛♣❛s ❛♥t❡r✐♦r❡s ❞❡✈❡♠ s❡r r❡✈✐s✐t❛❞❛s ♥❛ ❜✉s❝❛ ❞❛ s♦❧✉çã♦ ❞❡ ❡✈❡♥t✉❛✐s ✐♥✲ ❝♦♥s✐stê♥❝✐❛s✳
✷✳✷ ❇✉s❝❛♥❞♦ ♦✉tr❛ s♦❧✉çã♦ ♣❛r❛ ✉♠ ♣r♦❜❧❡♠❛ ♣r♦♣♦st♦
❯♠❛ ♣♦ssí✈❡❧ ✐♠♣❧❡♠❡♥t❛çã♦ ❞♦ ❡stá❣✐♦ ✜♥❛❧ ❞❛ ♠❡t♦❞♦❧♦❣✐❛ ♣r♦♣♦st❛ ❝♦♥s✐st❡ ❡♠✱ ❛ ♣❛rt✐r ❞♦ ♠♦❞❡❧♦ ❡❧❛❜♦r❛❞♦ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ♣r♦♣♦st♦✱ ❡❧❛❜♦r❛r ♦✉tr♦ ♠♦❞❡❧♦ ♠❛t❡♠á✲ t✐❝♦✱ q✉❡ ♥ã♦ ✉t✐❧✐③❡ ❞❛s ♠❡s♠❛s ❤❛❜✐❧✐❞❛❞❡s ❛♥t❡r✐♦r♠❡♥t❡ ❡♠♣r❡❣❛❞❛s✱ ♣❛r❛ r❡s♦❧✈❡r ♦ ♠❡s♠♦ ♣r♦❜❧❡♠❛✳ ◆♦ ♥♦✈♦ ❝❡♥ár✐♦✱ r❡str✐♥❣❡♠✲s❡ ❛s ❢❡rr❛♠❡♥t❛s ❞✐s♣♦♥í✈❡✐s ❡ ✐♥s✲ t✐❣❛ ♦ ❛❧✉♥♦ ❛ ❛♥❛❧✐s❛r ♦ ❝♦♥t❡①t♦ ♣♦r ót✐❝❛ ❞✐❢❡r❡♥t❡ ❞❛ q✉❡ ✐♥✐❝✐❛❧♠❡♥t❡ ❝♦st✉♠❛ ✈❡r✱ ❝♦♠♦ ♣♦❞❡ s❡r ♦❜s❡r✈❛❞♦ ♥♦ ✐t❡♠ s❡❣✉✐♥t❡✱ ♣r♦♣♦st♦ ♣❛r❛ ❛❧✉♥♦s ❞♦9o ❛♥♦ ❞♦ ❡♥s✐♥♦
❢✉♥❞❛♠❡♥t❛❧✱ ❛♦ ❡st✉❞❛r ♦ t❡♠❛ ❋✉♥çã♦ ❆✜♠✳
❖ s❡❣♠❡♥t♦ ❞❡ r❡t❛ ❛♣r❡s❡♥t❛❞♦ ♥❛ ✜❣✉r❛ ✹ ♠♦str❛ ❛ ❡✈♦❧✉çã♦ ❞❛ t❡♠♣❡r❛✲ t✉r❛ ❡♠ r❡❣✐ã♦ ♣ró①✐♠❛ ❛ P♦rt♦ ❆❧❡❣r❡✱ ❝❛♣✐t❛❧ ❞♦ ❘✐♦ ●r❛♥❞❡ ❞♦ ❙✉❧✱ ❡♥tr❡ ✺ ❡ ✶✶ ❤♦r❛s✳
❋✐❣✉r❛ ✹✿ ❊✈♦❧✉çã♦ ❞❛ t❡♠♣❡r❛t✉r❛
❈❛❧❝✉❧❛r ♦ ✐♥st❛♥t❡ ❡♠ q✉❡ ❛ t❡♠♣❡r❛t✉r❛ é ♥✉❧❛✳
❉❡ ❢♦r♠❛ ❣❡r❛❧✱ ♦ ♠♦❞❡❧♦ ♣r♦♣♦st♦ ❝♦♥s✐st❡ ❡♠ ❞❡t❡r♠✐♥❛r ❛ ❢✉♥çã♦ ❛✜♠✱ f(t) = at+b✱ ❝✉❥♦ ❣rá✜❝♦ ❝♦♥té♠ ♦ s❡❣♠❡♥t♦ ❞❡ r❡t❛ ❞❡ ❡①tr❡♠♦s
✭✺✱ ✲✷✮ ❡ ✭✶✶✱ ✶✵✮ ♣❛r❛✱ ❛ s❡❣✉✐r✱ ❞❡t❡r♠✐♥❛r ♦ ♠♦♠❡♥t♦ ❡♠ q✉❡ ♦ ❣rá✜❝♦ ❞❡ f ✐♥t❡r❝❡♣t❛ ♦ ❡✐①♦ ❤♦r✐③♦♥t❛❧✳ ❆ss✐♠✱ r❡♣r❡s❡♥t❛♥❞♦ ♣♦r f(t) = at+b
❛ t❡♠♣❡r❛t✉r❛ r❡❣✐str❛❞❛ ♥❛s ♣r♦①✐♠✐❞❛❞❡s ❞❛ ❝❛♣✐t❛❧ ❣❛ú❝❤❛ ♥♦ ✐♥st❛♥t❡
t ∈[5,11]✱ ❡s❝r❡✈❡✲s❡f(5) = 5a+b=−2❡f(11) = 11a+b = 10✳ ❙✉❜tr❛✐♥❞♦ ❡ss❛s ❡q✉❛çõ❡s✱ ♦❜t❡♠✲s❡
f(11)−f(5) = (11a+b)−(5a+b) = (10)−(−2)
⇒ 6a = 12
⇒ a= 2
❡✱ ♣❛r❛ ♦ ✈❛❧♦r ♦❜t✐❞♦ ❞❡a✱ ❝♦♥❝❧✉✐✲s❡ q✉❡b =−12✳ P♦rt❛♥t♦✱f(t) = 2t−12 ❡ ♦ ✐♥st❛♥t❡ ♥♦ q✉❛❧ ❛ t❡♠♣❡r❛t✉r❛ s❡ ❛♥✉❧❛ é ❛ r❛✐③ ❞❛ ❡q✉❛çã♦ f(t) = 0✱ ♦✉ s❡❥❛✱ t = 6 ❤♦r❛s✳
❘❡s♦❧✈✐❞♦ ♦ ♣r♦❜❧❡♠❛ ❡ ❡♥❝♦♥tr❛❞❛ ❛ s♦❧✉çã♦✱ ❛ ♥♦✈❛ ✐t❡r❛çã♦ ❞♦ ❝✐❝❧♦ ♣♦❞❡r✐❛ s❡r ❞❡s❡♥❝❛❞❡❛❞❛ ❝♦♠ ❛ ♣r♦♣♦st❛ ❞❡ ❝r✐❛çã♦ ❞❡ ♥♦✈♦ ♠♦❞❡❧♦ q✉❡ ♥ã♦ ✉t✐❧✐③❡ ❤❛❜✐❧✐❞❛❞❡s ❝♦♥t❡♠♣❧❛❞❛s ♥♦ ♠♦❞❡❧♦ ❛♣r❡s❡♥t❛❞♦✳ ❖✉ s❡❥❛✱ ❞❡t❡r♠✐♥❛r ♦ ♠♦♠❡♥t♦ ❡♠ q✉❡ ❛ t❡♠✲
♣❡r❛t✉r❛ s❡ t♦r♥♦✉ ✐❣✉❛❧ ❛ ③❡r♦ s❡♠ ✉s❛r ❝♦♥❝❡✐t♦s r❡❧❛❝✐♦♥❛❞♦s ❛ ❋✉♥çã♦ ❆✜♠ ♦✉ ❊q✉❛çã♦ ❞❛ ❘❡t❛ ❡✱ ✉♠ ♠♦❞❡❧♦ q✉❡ ❛t❡♥❞❡ ♦ ♥♦✈♦ q✉❡st✐♦♥❛♠❡♥t♦ ♣r♦♣♦st♦ r❡s✉♠❡✲ s❡ ❡♠ ♦❜s❡r✈❛r ❛ ♣r♦♣♦r❝✐♦♥❛❧✐❞❛❞❡ ❡♠ ✜❣✉r❛s s❡♠❡❧❤❛♥t❡s✱ ❝♦♠♦ s❡ ✈ê ♥❛ ✜❣✉r❛ ✺✳
❋✐❣✉r❛ ✺✿ ❙♦❧✉çã♦ ❣❡♦♠étr✐❝❛ ❞❛ s✐t✉❛çã♦ ♣r♦❜❧❡♠❛
P❛r❛ t❛❧✱ s❡rã♦ ❝♦♥s✐❞❡r❛❞♦s ♦s ♣♦♥t♦s A = (5,−2)✱ P = (x,0)✱ B = (11,10)✱
C= (5,0)❡ D= (11,0)✱ ❡♠ q✉❡ x r❡♣r❡s❡♥t❛rá ♦ ✐♥st❛♥t❡ ❡♠ q✉❡ ❛ t❡♠♣❡r❛t✉r❛ s❡rá
♥✉❧❛✳ P♦r s❡r❡♠ ♣❛r❛❧❡❧♦s ♦s s❡❣♠❡♥t♦s AC ❡ BD✱ ♦s tr✐â♥❣✉❧♦s AP C ❡ P BD sã♦
s❡♠❡❧❤❛♥t❡s✳ ▲♦❣♦
AC BD =
P C P D ⇒
2 10 =
x−5
11−x ⇒5x−25 = 11−x⇒x= 6
◆♦✈❛♠❡♥t❡✱ ♥♦ ✐♥st❛♥t❡t = 6h✱ ❛ t❡♠♣❡r❛t✉r❛ r❡❣✐str❛❞❛ ❢♦✐ ♥✉❧❛✳
✷✳✸ ❋❛t♦r❡s q✉❡ ❝♦♥tr✐❜✉❡♠ ♣❛r❛ ❛ ♠♦❞❡❧❛❣❡♠ ♠❛t❡♠át✐❝❛
❆ ♠♦❞❡❧❛❣❡♠ ♠❛t❡♠át✐❝❛ ♦r✐❣✐♥❛✲s❡ ❡♠ ♣r♦❜❧❡♠❛s ❞♦ q✉♦t✐❞✐❛♥♦ ❝✉❥❛s r❡s♦❧✉çõ❡s ❡♥✲ ✈♦❧✈❡♠ tr❛❞✉çã♦ ❞♦ ❝♦♥t❡①t♦ ❛♣r❡s❡♥t❛❞♦ ♣❛r❛ ❛ ❧✐♥❣✉❛❣❡♠ ♠❛t❡♠át✐❝❛✱ ♣❛r❛ ♣♦st❡r✐♦r ✈❡r✐✜❝❛çã♦ ❡ ✈❛❧✐❞❛çã♦ ❛ ♣❛rt✐r ❞❡ ❞❛❞♦s r❡❛✐s✳ ❈♦♥s❡q✉❡♥t❡♠❡♥t❡✱ ✉♠ ♠♦❞❡❧♦ ❝♦♥s✲ tr✉í❞♦ r❡✢❡t❡ ❝❛r❛❝t❡ríst✐❝❛s ❞❡ q✉❡♠ ♦ ❡❧❛❜♦r♦✉✱ ❝♦♠♦ ✐♥t❡r♣r❡t❛çã♦ ❞❛ r❡❛❧✐❞❛❞❡ ♥❛
q✉❛❧ ❡stá ✐♠❡rs♦✱ ❤❛❜✐❧✐❞❛❞❡s ❝♦❣♥✐t✐✈❛s q✉❡ ❞❡s❡♥✈♦❧✈❡✉✱ ♠❛t✉r✐❞❛❞❡ ♠❛t❡♠át✐❝❛ ❛❞✲ q✉✐r✐❞❛ ❡ ❢❡rr❛♠❡♥t❛s ♠❛t❡♠át✐❝❛s ❞✐s♣♦♥í✈❡✐s ♥♦ ♣r♦❝❡ss♦✳ P♦rt❛♥t♦✱ ❛ ❝❛♣❛❝✐❞❛❞❡ ❞❡ ❡①♣r❡ssã♦ ❞♦ ♠♦❞❡❧♦ é ❞✐r❡t❛♠❡♥t❡ ❛❢❡t❛❞❛ ♣❡❧❛ ✈✐sã♦ ❞❡ ♠✉♥❞♦ ❞❡ q✉❡♠ ♦ ❞❡s❡♥✲ ✈♦❧✈❡ ❡ ❝♦♠♦ ✐♥t❡r♣r❡t❛ ❛s r❡❧❛çõ❡s ❡♥tr❡ ♦s ♦❜❥❡t♦s ♥❡❧❡ ❝♦♥t✐❞♦✱ ❢❛t♦s ❝♦♥✜r♠❛❞♦s ❝♦♠ ❛ ❛♣❧✐❝❛çã♦ ❞❡ ✉♠ t❡st❡ ❞✐❛❣♥óst✐❝♦ ❛♣❧✐❝❛❞♦ ♣❛r❛ ❛❧✉♥♦s ❞❛s q✉❛tr♦ sér✐❡s ✜♥❛✐s ❞♦ ❡♥s✐♥♦ ❢✉♥❞❛♠❡♥t❛❧ ❡ três sér✐❡s ❞♦ ❡♥s✐♥♦ ♠é❞✐♦✳
❈♦♠♦ ♣❛rt❡ ❞♦ ♣r♦❥❡t♦ ♣❡❞❛❣ó❣✐❝♦ ❞♦ ❈♦❧é❣✐♦ ❙❛♥t♦ ❆❣♦st✐♥❤♦✱ ❡s❝♦❧❛ ♣❛rt✐❝✉❧❛r ❞❡ ❇❡❧♦ ❍♦r✐③♦♥t❡✱ ♦ t❡st❡ ❞✐❛❣♥óst✐❝♦ ❞❡ ♠❛t❡♠át✐❝❛ é ❢♦r♠❛❞♦ ♣♦r ✶✵ ✐t❡♥s ❢❡❝❤❛❞♦s ❡ ✷ ❛❜❡rt♦s✱ ❡❧❛❜♦r❛❞♦s ♣❡❧❛ ❡q✉✐♣❡ ❞❡ ♣r♦❢❡ss♦r❡s ❞❡♠❛t❡♠át✐❝❛ ❞❛ ❡s❝♦❧❛ ❝♦♠ ♦ ♦❜❥❡t✐✈♦ ❞❡ ❡①♣❧✐❝✐t❛r ❝♦♥❝❡✐t♦s ❛✐♥❞❛ ♥ã♦ ❛ss✐♠✐❧❛❞♦s ♣r♦♣♦st♦s ♣❛r❛ sér✐❡s ❛♥t❡r✐♦r❡s✳ ❯♠ ❞♦s ✐t❡♥s ❛❜❡rt♦s✱ ♣r♦♣♦st♦ ♣❛r❛ t♦❞❛s ❛s sér✐❡s q✉❡ ♣❛rt✐❝✐♣❛r❛♠ ❞♦ t❡st❡ ❡ r❡s♣♦♥❞✐❞♦ ♣♦r ❛♣r♦①✐♠❛❞❛♠❡♥t❡ ✶✵✵✵ ❛❧✉♥♦s✱ ❢♦✐ ❡❧❛❜♦r❛❞♦ ♣❛r❛ ❡✈✐❞❡♥❝✐❛r ❞✐❢❡r❡♥t❡s s♦❧✉çõ❡s ♣❛r❛ ♦ ♠❡s♠♦ ♣r♦❜❧❡♠❛ ❡ ❡stá tr❛♥s❝r✐t♦ ❛ s❡❣✉✐r✿
❊♠ ✉♠ r❡st❛✉r❛♥t❡ ❤á ✷✵ ♠❡s❛s✱ t♦❞❛s ♦❝✉♣❛❞❛s✱ ❛❧❣✉♠❛s ❝♦♠ ✹ ♣❡ss♦❛s✱ ❡ ♦✉tr❛s ❝♦♠ ❛♣❡♥❛s ✷ ♣❡ss♦❛s✱ ♥✉♠ t♦t❛❧ ❞❡ ✻✽ ❢r❡❣✉❡s❡s✳ ◗✉❛♥t❛s ♠❡s❛s sã♦ ♦❝✉♣❛❞❛s ♣♦r ✷ ♣❡ss♦❛s❄
❊♠ ❢✉♥çã♦ ❞❛ ❤❡t❡r♦❣❡♥❡✐❞❛❞❡ ❞❛ ♣♦♣✉❧❛çã♦ s✉❜♠❡t✐❞❛ ❛♦ t❡st❡✱ ❢♦r♠❛❞❛ ♣♦r ❛❧✉✲ ♥♦s ❝♦♠ ✐❞❛❞❡ ❡♥tr❡ ✶✶ ❡ ✶✼ ❛♥♦s✱ ❞❡st❛❝❛r❛♠✲s❡ três ♠♦❞❡❧♦s q✉❡ ♣❡r♠✐t✐r❛♠ ✐♥❝❧✉✐r ❝❛❞❛ ✐♥❞✐✈í❞✉♦ ❡♠ ✉♠❛ ❞❡ três ❝❛t❡❣♦r✐❛s ❡♠ ❢✉♥çã♦ ❞❛ ♣r♦✜❝✐ê♥❝✐❛ ❛♣r❡s❡♥t❛❞❛ ♣♦r ❡❧❡✿ ❝♦♥t❛t♦✱ s✐st❡♠❛t✐③❛çã♦ ♦✉ ❛♣r♦❢✉♥❞❛♠❡♥t♦✳
P❛r❛ ♦ ✐t❡♠ ❡♠ ❡st✉❞♦✱ ❛s s♦❧✉çõ❡s ❛♣r❡s❡♥t❛❞❛s ❡✈✐❞❡♥❝✐❛r❛♠ ❛❧❣❡❜r✐③❛çã♦ ❞♦ ♣❡♥s❛r ♠❛t❡♠át✐❝♦ à ♠❡❞✐❞❛ q✉❡ ♦ ✐♥❞✐✈í❞✉♦ s❡ ❛♣r♦①✐♠❛ ❞❛s sér✐❡s ✜♥❛✐s ❞❛ ❡❞✉❝❛çã♦ ❜ás✐❝❛✱ q✉❛♥❞♦ ❛ á❧❣❡❜r❛ ❛♣r❡s❡♥t❛✱ ❢❛❝❡ à ❡str✉t✉r❛ ❝✉rr✐❝✉❧❛r✱ ❣r❛♥❞❡ ♣r♦❝❡ss♦ ❞❡ s✐st❡♠❛t✐③❛çã♦ ❡ ❛♣r♦❢✉♥❞❛♠❡♥t♦✳
❆ ❛✉sê♥❝✐❛ ❞♦ ✉s♦ ❞❛ á❧❣❡❜r❛ ❢♦✐ ♦❜s❡r✈❛❞♦ ♥♦ ❣r✉♣♦ ❢♦r♠❛❞♦ ♣♦r ❛❧✉♥♦s ❞♦ 6o ❡
7o ❛♥♦s ❞♦ ❡♥s✐♥♦ ❢✉♥❞❛♠❡♥t❛❧✱ ❝♦♠ ✐❞❛❞❡ ♠é❞✐❛ ❡♥tr❡ ✶✶ ❡ ✶✷ ❛♥♦s✱ ♦♥❞❡ ❡❧❡♠❡♥t♦s
❛❧❣é❜r✐❝♦s ♥ã♦ ❢♦r❛♠✱ ❡♠ s✉❛ t♦t❛❧✐❞❛❞❡✱ ❛♣r❡s❡♥t❛❞♦s ❡ s✐st❡♠❛t✐③❛❞♦s✳ ◆❡ss❡ ❣r✉♣♦✱ ♦s ✐♥❞✐✈í❞✉♦s r❡❝♦rr❡r❛♠ ♠❛✐s s✐st❡♠❛t✐❝❛♠❡♥t❡ às q✉❛tr♦ ♦♣❡r❛çõ❡s ❛r✐t♠ét✐❝❛s ❜ás✐✲ ❝❛s✱ ❛❞✐çã♦✱ s✉❜tr❛çã♦✱ ♠✉❧t✐♣❧✐❝❛çã♦ ❡ ❞✐✈✐sã♦✱ ♣❛r❛ r❡s♦❧✈❡r ♦ ♣r♦❜❧❡♠❛✳ ◆♦ ❡♥t❛♥t♦✱ ❢♦r❛♠ r❛r❛s ❛s ♦❝♦rrê♥❝✐❛s ❞❡ ❥✉st✐✜❝❛t✐✈❛s ♥❛s tr❛♥s✐çõ❡s ♦✉ ♣❛ss❛❣❡♥s ❡s❝♦❧❤✐❞❛s✳ ◆❛ ✜❣✉r❛ ✻ t❡♠✲s❡ s♦❧✉çã♦ ❞❡ ✉♠ ❛❧✉♥♦ ❞♦7o ❛♥♦ ❞♦ ❡♥s✐♥♦ ❢✉♥❞❛♠❡♥t❛❧✿
