❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ▼❛t♦ ●r♦ss♦
❈❛♠♣✉s ❯♥✐✈❡rs✐tár✐♦ ❞♦ ❆r❛❣✉❛✐❛ ■♥st✐t✉t♦ ❞❡ ❈✐ê♥❝✐❛s ❊①❛t❛s ❡ ❞❛ ❚❡rr❛
▼❊❙❚❘❆❉❖ P❘❖❋■❙❙■❖◆❆▲ ❊▼ ▼❆❚❊▼➪❚■❈❆ ❊▼ ❘❊❉❊ ◆❆❈■❖◆❆▲
❆ ❘❊❙❖▲❯➬➹❖ ❉❊ P❘❖❇▲❊▼❆❙ ❆P▲■❈❆❉❆ ➚
▼❖❉❊▲❆●❊▼ ❉❊ ➪❘❊❆❙ ❊ ❱❖▲❯▼❊❙ ❉❖❙
P❖▲■❊❉❘❖❙ ❉❊ P▲❆❚➹❖
❘■❈❆❘❉❖ ❊▲■❆❙ ❏❘❊■●❊
▼❡str❛❞♦ Pr♦✜ss✐♦♥❛❧ ❡♠ ▼❛t❡♠át✐❝❛✿ P❘❖❋▼❆❚✴❙❇▼❖r✐❡♥t❛❞♦r✿ Pr♦❢✳ ❉r✳ ❈❛r❧♦s ❘♦❞r✐❣✉❡s ❞❛ ❙✐❧✈❛
❚r❛❜❛❧❤♦ ✜♥❛♥❝✐❛❞♦ ♣❡❧❛ ❈❛♣❡s
❆ ❘❊❙❖▲❯➬➹❖ ❉❊ P❘❖❇▲❊▼❆❙ ❆P▲■❈❆❉❆ ➚
▼❖❉❊▲❆●❊▼ ❉❊ ➪❘❊❆❙ ❊ ❱❖▲❯▼❊❙ ❉❖❙
P❖▲■❊❉❘❖❙ ❉❊ P▲❆❚➹❖
❇❛rr❛ ❞♦ ●❛rç❛s✱ ✶✹ ❞❡ s❡t❡♠❜r♦ ❞❡ ✷✵✶✺✳
Pr♦❢✳ ❉r✳ ❈❛r❧♦s ❘♦❞r✐❣✉❡s ❞❛ ❙✐❧✈❛ ❖r✐❡♥t❛❞♦r
❇❛♥❝❛ ❡①❛♠✐♥❛❞♦r❛✿
Pr♦❢✳ ❉r✳ ❈❛r❧♦s ❘♦❞r✐❣✉❡s ❞❛ ❙✐❧✈❛ ✭❖r✐❡♥t❛❞♦r✮ Pr♦❢✳ ❉r✳ ❉❛♥✐❡❧ ❞❛ ❙✐❧✈❡✐r❛ ●✉✐♠❛rã❡s ✭❈❯❆✲❯❋▼❚✮ Pr♦❢✳ ❉r✳ ▼❛r❝❡❧♦ ❆❧♠❡✐❞❛ ❞❡ ❙♦✉③❛ ✭❯❋●✮
Dados Internacionais de Catalogação na Fonte.
Ficha catalográfica elaborada automaticamente de acordo com os dados fornecidos pelo(a) autor(a).
Permitida a reprodução parcial ou total, desde que citada a fonte.
J89r Jreige, Ricardo Elias.
A Resolução de Problemas Aplicada à Modelagem de Áreas e Volumes dos Poliedros de Platão / Ricardo Elias Jreige. -- 2015
117 f. : il. color. ; 30 cm.
Orientador: Dr. Carlos Rodrigues da Silva.
Dissertação (mestrado profissional) - Universidade Federal de Mato Grosso, Instituto de Ciências Exatas e da Terra, Programa de Pós-Graduação em Matemática, Cuiabá, 2015.
Inclui bibliografia.
❉❡❞✐❝♦ ❡st❛ ❞✐ss❡rt❛çã♦ ❛♦s ♠❡✉s ♠❛r❛✈✐❧❤♦s♦s ✜❧❤♦s✱ ❊❧✐❛s ❘✐❝❛r❞♦ ▼♦t❛ ❏r❡✐❣❡ ❡ ❘❛❢❛❡❧ ❘✐❝❛r❞♦ ▼♦t❛ ❏r❡✐❣❡✱ ♣♦r s❡r❡♠ ♠❡✉ ❛❧✐❝❡r❝❡ ❡ ❝♦♥❢♦rt♦ ❡s✲ ♣✐r✐t✉❛❧ ❡✱ t❛♠❜é♠✱ à ♠✐♥❤❛ ❢❛♠í❧✐❛ ♣♦r t❡r❡♠ ♠❡ ♠♦t✐✈❛❞♦ ❡ ❛✉①✐❧✐❛❞♦ ♥❡st❛ ❜✉s❝❛ ♣❡❧♦ ❝♦♥❤❡❝✐♠❡♥t♦✳
❆●❘❆❉❊❈■▼❊◆❚❖❙
❆❣r❛❞❡ç♦✱ ♣r✐♠❡✐r❛♠❡♥t❡ ❛ ❉❡✉s✱ ♣♦✐s s❡♠ s✉❛ ♣❡r♠✐ssã♦ ♥❛❞❛ s❡r✐❛ ♣♦ssí✈❡❧✳ ❆❣r❛❞❡ç♦ ❛♦s ♣r♦❢❡ss♦r❡s ❞❛ ❯❋▼❚✿ ❉r✳ ❆❞✐❧s♦♥✱ ❉r✳ ❏✉❛♥✱ ▼s✳ ❆♥❞r❡②✱ ▼s✳ ❘❡♥❛t♦ ❡ ▼s✳ ▲í✈✐♦✳ ❱♦❝ês ❢♦r❛♠ ❢✉♥❞❛♠❡♥t❛✐s ♣❛r❛ ♠❡✉ ❝r❡s❝✐♠❡♥t♦ ♣r♦✜ss✐♦♥❛❧ ❡ ♣❡ss♦❛❧✳ ❊s♣❡r♦✱ ❛❧❣✉♠ ❞✐❛✱ ❛❧❝❛♥ç❛r ♦ ❝♦♥❤❡❝✐♠❡♥t♦ ❡ ❛ s❛❜❡❞♦r✐❛ q✉❡ ✈♦❝ês ♣♦ss✉❡♠✳
❆❣r❛❞❡ç♦ ❛♦s ♠❡✉s ❛♠✐❣♦s✴✐r♠ã♦s✱ ❉❡✉s❛❣✉✐♠❛r✱ ❘♦❞r✐❣♦✱ ❋❡r♥❛❞♦ ❡ ❙✐♥és✐♦ ♣♦r t❡r❡♠ ❧✉t❛❞♦ ❧❛❞♦ ❛ ❧❛❞♦ ❝♦♠✐❣♦✱ ❛✉①✐❧✐❛♥❞♦✲♠❡ ♥♦s ♠♦♠❡♥t♦s ❞❡ ❢r❛q✉❡③❛ ❡ ❞✐✜❝✉❧❞❛❞❡s✳ ❊ss❛ ✈✐tór✐❛ t❛♠❜é♠ é ❞❡ ✈♦❝ês✳
❆❣r❛❞❡ç♦ ❛♦ ♣r♦❢❡ss♦r ▼✐❣✉❡❧ ❈❛♠❛r❣♦ ♣❡❧♦ ✐♥❝❡♥t✐✈♦ ❡ ❛♣♦✐♦ ❞✉r❛♥t❡ ♦ ♠❡str❛❞♦✳ ❆❣r❛❞❡ç♦ ❛♦s ❞♦✉t♦r❡s ♠❡♠❜r♦s ❞❛ ❜❛♥❝❛✱ Pr♦❢✳ ❉❛♥✐❡❧ ❞❛ ❙✐❧✈❡✐r❛ ●✉✐♠❛rã❡s ✭❈❯❆✲❯❋▼❚✮ ❡ Pr♦❢✳ ▼❛r❝❡❧♦ ❆❧♠❡✐❞❛ ❞❡ ❙♦✉③❛ ✭❯❋●✮ ♣❡❧❛s ❝♦♥tr✐❜✉✐çõ❡s s✐❣♥✐✜❝❛t✐✈❛s q✉❡ ❡♥❣r❛♥❞❡❝❡r❛♠ ❡st❡ tr❛❜❛❧❤♦✳
❆❣r❛❞❡ç♦ ❛♦s ♠❡✉s ♣❛✐s✱ ❊❧✐❛s ❡ ▼♦✉♥❛✱ ❡ ❡♠ ♥♦♠❡ ❞❡❧❡s ❡st❡♥❞♦ à ♠✐♥❤❛ ❢❛♠í❧✐❛✱ ♣♦✐s s❡♠ ❡❧❡s ♥ã♦ t❡r✐❛ ❛❧❝❛♥ç❛❞♦ ❡st❛ ✈✐tór✐❛✳ ❊❧❡s ❢♦r❛♠ ❞❡❝✐s✐✈♦s ♣❛r❛ ♦ ❝✉♠♣r✐♠❡♥t♦ ❞❡st❛ ❡t❛♣❛ ❞❡ ♠✐♥❤❛ ✈✐❞❛✱ ❞❛♥❞♦✲♠❡ s✉♣♦rt❡ ❡ â♥✐♠♦ ❛ t♦❞♦ ✐♥st❛♥t❡✱ ♥ã♦ ♠❡ ❞❡✐①❛♥❞♦ ❞❡s✐st✐r✳
❆❣r❛❞❡ç♦ ❛ ♠✐♥❤❛ ❡s♣♦s❛ ❡ ✜❧❤♦s✱ ♣♦✐s ❡❧❡s ❛❣✉❡♥t❛r❛♠ ♠❡✉s ♠♦♠❡♥t♦s ❞❡ ♥❡r✲ ✈♦s✐s♠♦✱ ❛♣r❡❡♥sã♦ ❡ ❛♥❣úst✐❛✳ ❋♦r❛♠ ♠❡✉ s✉♣♦rt❡ ❡ ✈❡♥❝❡r❛♠ ❝♦♠✐❣♦✳
❆❣r❛❞❡ç♦ ❛♦ Pr♦❢♠❛t ♣❡❧❛ ♦♣♦rt✉♥✐❞❛❞❡✱ ❛ ❯❋▼❚ ♣♦r t❡r ♠❡ ❛❝♦❧❤✐❞♦ ❡ ❛ ❈❛♣❡s ♣♦r t❡r ✜♥❛♥❝✐❛❞♦ ♠❡✉ ♠❡str❛❞♦✳
❊✱ ✜♥❛❧✐③❛♥❞♦✱ ❛❣r❛❞❡ç♦✱ ❡♠ ❡s♣❡❝✐❛❧✱ ❛♦ ♣r♦❢❡ss♦r ❉r✳ ❈❛r❧♦s ❘♦❞r✐❣✉❡s ♣♦r t❡r s✐❞♦ ♠❛✐s q✉❡ ✉♠ ❡①❝❡❧❡♥t❡ ♣r♦❢❡ss♦r ❡ ♦r✐❡♥t❛❞♦r✱ ♣♦r t❡r s✐❞♦ ❛♠✐❣♦✱ ❝♦♠♣❛♥❤❡✐r♦✱ ❝♦♥s❡❧❤❡✐r♦✱ ✉♠ ❡①❡♠♣❧♦ ❛ s❡r s❡❣✉✐❞♦✳ ▲❡♠❜r♦✲♠❡ ❞❡ ❝❛❞❛ ❧✐çã♦ ❞❛❞❛✱ q✉❡ ❧❡✈❛r❡✐ ♣♦r t♦❞❛ ✈✐❞❛ ❡ ❛s ♣❛ss❛r❡✐ ♣❛r❛ ♠✐♥❤❛s ❣❡r❛çõ❡s✳ ❱♦❝ê é ❤✉♠✐❧❞❡ ❡ ❡①tr❛♦r❞✐♥ár✐♦✳ ❈♦♠ ✈♦❝ê ❛♣r❡♥❞✐ ♠❛✐s q✉❡ ❞✐s❝✐♣❧✐♥❛s ♠❛t❡♠át✐❝❛s✳ ❏❛♠❛✐s ❡sq✉❡❝❡r❡✐ t✉❞♦ q✉❡ ❢❡③ ♣♦r ♠✐♠✳
➚ t♦❞♦s ♠❡✉ ♠✉✐t♦ ♦❜r✐❣❛❞♦✦
❉á ✐♥str✉çã♦ ❛♦ sá❜✐♦✱ ❡ ❡❧❡ s❡ ❢❛rá ♠❛✐s sá❜✐♦❀ ❡♥s✐♥❛ ♦ ❥✉st♦ ❡ ❡❧❡ ❛✉♠❡♥t❛rá ❡♠ ❡♥t❡♥❞✐♠❡♥t♦✳
Pr♦✈ér❜✐♦s ✾✿ ✾
❘❊❙❯▼❖
❊st❡ tr❛❜❛❧❤♦ ♣r❡t❡♥❞❡ ♠♦str❛r ❛ ✐♠♣♦rtâ♥❝✐❛ ❞❡ s❡ ✉t✐❧✐③❛r ♦ ♠ét♦❞♦ ❤❡✉ríst✐❝♦ ♦✉ ♠é✲ t♦❞♦ ❞❡ P♦❧②❛ ❝♦♠♦ ♠❡t♦❞♦❧♦❣✐❛ ❡✜❝✐❡♥t❡ ♥♦ ❡♥s✐♥♦ ❞❛ ♠❛t❡♠át✐❝❛✳ ❊st❛ s❡rá ❛♣❧✐❝❛❞❛ ♥❛ ❝♦♥str✉çã♦ ❞❡ ♠♦❞❡❧♦s ♠❛t❡♠át✐❝♦s ❝❛♣❛③❡s ❞❡ ❝❛❧❝✉❧❛r ❛ ár❡❛ ❡ ♦ ✈♦❧✉♠❡ ❞♦s ❝✐♥❝♦ ♣♦❧✐❡❞r♦s ❝♦♥✈❡①♦s r❡❣✉❧❛r❡s✳ ❖ ❝♦♥t❡①t♦ ❤✐stór✐❝♦ ❞♦ ❝♦♥t❡ú❞♦ ❛ s❡r ❛♣❧✐❝❛❞♦ ♥❛ s❛❧❛ ❞❡ ❛✉❧❛ é ❢✉♥❞❛♠❡♥t❛❧ ♣❛r❛ q✉❡ ♦ ❛❧✉♥♦ ❡♥t❡♥❞❛ ❛s r❡❧❛çõ❡s ♠❛t❡♠át✐❝❛s q✉❡ s❡rã♦ ❝♦♥s✲ tr✉í❞❛s✳ ❆ss✐♠✱ ♣r♦❝✉r♦✉✲s❡ ❢❛③❡r ✉♠ ❜r❡✈❡ ❝♦♠❡♥tár✐♦ ❛❝❡r❝❛ ❞❛ ❤✐stór✐❛ ❞♦s ♣♦❧✐❡❞r♦s✱ r❡ss❛❧t❛♥❞♦ ❛❧❣✉♠❛s ❞❡✜♥✐çõ❡s ❡ t❡♦r❡♠❛s r❡❧❡✈❛♥t❡s ♥♦ ❡st✉❞♦ ❞❡st❡s só❧✐❞♦s✳ ◆♦ ❡♥✲ t❛♥t♦✱ ♦ ❢♦❝♦ ♣r✐♥❝✐♣❛❧ ❞❡st❡ tr❛❜❛❧❤♦ é ♦ ♠ét♦❞♦ ❞❡ r❡s♦❧✉çã♦ ❞❡ ♣r♦❜❧❡♠❛s ♦✉ ♠ét♦❞♦ ❤❡✉ríst✐❝♦ ❡ s✉❛ ❝♦♥tr✐❜✉✐çã♦ ♣❛r❛ ♦ ❡♥s✐♥♦ ❞❛ ♠❛t❡♠át✐❝❛✱ ❞❡st❛❝❛♥❞♦ ❛ ♣❛rt✐❝✉❧❛r✐❞❛❞❡ ❞❡ s✉❛s ❡t❛♣❛s✳ ❊st❛ ♠❡t♦❞♦❧♦❣✐❛ s❡rá ❛♥❛❧✐s❛❞❛ ❡♠ ❞✐✈❡rs❛s ❛t✐✈✐❞❛❞❡s✱ ❛ ✜♠ ❞❡ ♠♦str❛r ❝♦♠♦ ♦ ♣r♦❢❡ss♦r ❞❡✈❡ ❞❡s❡♥✈♦❧✈ê✲❧❛s s❡❣✉♥❞♦ ❡st❡ ❛❧❣♦r✐t♠♦✳ Pr❡t❡♥❞❡✲s❡ ❛✐♥❞❛ ❢❛③❡r ✉♠❛ ❛❜♦r❞❛❣❡♠ s✉❝✐♥t❛ ❛❝❡r❝❛ ❞❛ ♠♦❞❡❧❛❣❡♠ ♥❛ ♠❛t❡♠át✐❝❛ ❡ s✉❛ ✐♠♣♦rtâ♥❝✐❛ ♥❛ ❝♦♥str✉✲ çã♦ ❞❡ ❝♦♥❝❡✐t♦s ♠❛t❡♠át✐❝♦s✳ ❆❧é♠ ❞❡ ♠♦str❛r ♦s r❡s✉❧t❛❞♦s ❡ ❛♥á❧✐s❡s ❞❛ ✉t✐❧✐③❛çã♦ ❞♦ ♠ét♦❞♦ ❤❡✉ríst✐❝♦ ❡♠ ❛❧❣✉♥s ♣r♦❜❧❡♠❛s ♣r♦♣♦st♦s ♣❛r❛ ♦s ❛❧✉♥♦s ❞♦ ✸♦ ❛♥♦ ❞♦ ❊♥s✐♥♦
▼é❞✐♦✱ q✉❡ ♠♦str❛rã♦ ❛ r❡❧❡✈â♥❝✐❛ ❞❡st❡ ♠ét♦❞♦ ❝♦♠♦ ♠❡t♦❞♦❧♦❣✐❛ ❢❛✈♦rá✈❡❧ à r❡s♦❧✉çã♦ ❞❡ ♣r♦❜❧❡♠❛s ♠❛t❡♠át✐❝♦s✳
P❛❧❛✈r❛s ❝❤❛✈❡✿ ❘❡s♦❧✉çã♦ ❞❡ Pr♦❜❧❡♠❛s✱ ▼❡t♦❞♦❧♦❣✐❛✱ ❊♥s✐♥♦✱ ▼♦❞❡❧❛❣❡♠✱ P♦❧✐❡❞r♦s ❞❡ P❧❛tã♦✳
❆❇❙❚❘❆❈❚
❚❤✐s ✇♦r❦ ❛✐♠s t♦ s❤♦✇ t❤❡ ✐♠♣♦rt❛♥❝❡ ♦❢ ✉s✐♥❣ t❤❡ ❤❡✉r✐st✐❝ ♠❡t❤♦❞ ♦r P♦❧②❛ ♠❡t❤♦❞ ❛s ❛♥ ❡✛❡❝t✐✈❡ ♠❡t❤♦❞♦❧♦❣② ✐♥ ♠❛t❤❡♠❛t✐❝s ❡❞✉❝❛t✐♦♥✳ ❚❤✐s ✇✐❧❧ ❜❡ ❛♣♣❧✐❡❞ ✐♥ t❤❡ ❝♦♥s✲ tr✉❝t✐♦♥ ♦❢ ♠❛t❤❡♠❛t✐❝❛❧ ♠♦❞❡❧s ❛❜❧❡ t♦ ❝❛❧❝✉❧❛t❡ t❤❡ ❛r❡❛ ❛♥❞ ✈♦❧✉♠❡ ♦❢ t❤❡ ✜✈❡ r❡❣✉❧❛r ❝♦♥✈❡① ♣♦❧②❤❡❞r❛✳ ❚❤❡ ❤✐st♦r✐❝❛❧ ❝♦♥t❡①t ♦❢ t❤❡ ❝♦♥t❡♥t t♦ ❜❡ ❛♣♣❧✐❡❞ ✐♥ t❤❡ ❝❧❛ssr♦♦♠ ✐s ❝r✉❝✐❛❧ ❢♦r t❤❡ st✉❞❡♥t t♦ ✉♥❞❡rst❛♥❞ ♠❛t❤❡♠❛t✐❝❛❧ r❡❧❛t✐♦♥s❤✐♣s t♦ ❜❡ ❜✉✐❧t✳ ❙♦✱ ✇❡ tr✐❡❞ t♦ ♠❛❦❡ ❛ ❜r✐❡❢ ❝♦♠♠❡♥t ❛❜♦✉t t❤❡ ❤✐st♦r② ♦❢ ♣♦❧②❤❡❞r❛✱ ❤✐❣❤❧✐❣❤t✐♥❣ s♦♠❡ r❡❧❡✈❛♥t ❞❡✜♥✐t✐♦♥s ❛♥❞ t❤❡♦r❡♠s ✐♥ t❤❡ st✉❞② ♦❢ t❤❡s❡ s♦❧✐❞s✳ ❍♦✇❡✈❡r✱ t❤❡ ♠❛✐♥ ❢♦❝✉s ♦❢ t❤✐s ✇♦r❦ ✐s t❤❡ ♠❡t❤♦❞ ♦❢ ♣r♦❜❧❡♠ s♦❧✈✐♥❣ ♦r ❤❡✉r✐st✐❝ ♠❡t❤♦❞ ❛♥❞ ✐ts ❝♦♥tr✐❜✉t✐♦♥ t♦ t❤❡ t❡❛❝❤✐♥❣ ♦❢ ♠❛t❤❡♠❛t✐❝s✱ ❤✐❣❤❧✐❣❤t✐♥❣ t❤❡ ♣❡❝✉❧✐❛r✐t② ♦❢ ✐ts st❛❣❡s✳ ❚❤✐s ♠❡t❤♦❞♦❧♦❣② ✇✐❧❧ ❜❡ ❛♥❛❧②③❡❞ ✐♥ ✈❛r✐♦✉s ❛❝t✐✈✐t✐❡s ✐♥ ♦r❞❡r t♦ s❤♦✇ ❤♦✇ t❤❡ t❡❛❝❤❡r s❤♦✉❧❞ ❞❡✈❡❧♦♣ t❤❡♠ ✉♥❞❡r t❤✐s ❛❧❣♦r✐t❤♠✳ ❚❤❡ ❛✐♠ ✐s ❛❧s♦ t♦ ♠❛❦❡ ❛ ❜r✐❡❢ ❛♣♣r♦❛❝❤ ❛❜♦✉t ♠♦❞❡❧✐♥❣ ✐♥ ♠❛t❤❡✲ ♠❛t✐❝s ❛♥❞ ✐ts ✐♠♣♦rt❛♥❝❡ ✐♥ t❤❡ ❝♦♥str✉❝t✐♦♥ ♦❢ ♠❛t❤❡♠❛t✐❝❛❧ ❝♦♥❝❡♣ts✳ ■♥ ❛❞❞✐t✐♦♥ t♦ s❤♦✇✐♥❣ t❤❡ r❡s✉❧ts ❛♥❞ ❛♥❛❧②s✐s ✉s✐♥❣ t❤❡ ❤❡✉r✐st✐❝ ♠❡t❤♦❞ ✐♥ ❝❡rt❛✐♥ ♣r♦❜❧❡♠s ♣♦s❡❞ t♦ st✉❞❡♥ts ♦❢ t❤❡ ✸r❞ ②❡❛r ♦❢ ❤✐❣❤ s❝❤♦♦❧✱ ✇❤✐❝❤ s❤♦✇ t❤❡ r❡❧❡✈❛♥❝❡ ♦❢ t❤✐s ♠❡t❤♦❞ ❛s ❢❛✈♦r❛❜❧❡ ❛♣♣r♦❛❝❤ t♦ s♦❧✈✐♥❣ ♠❛t❤❡♠❛t✐❝❛❧ ♣r♦❜❧❡♠s✳
❑❡②✇♦r❞s✿ ❚r♦✉❜❧❡s❤♦♦t✐♥❣✱ ▼❡t❤♦❞♦❧♦❣②✱ ❊❞✉❝❛t✐♦♥✱ ▼♦❞❡❧✐♥❣✱ P♦❧②❤❡❞r❛ ♦❢ P❧❛t♦✳
❙✉♠ár✐♦
❆●❘❆❉❊❈■▼❊◆❚❖❙ ✻
❘❊❙❯▼❖ ✽
❆❇❙❚❘❆❈❚ ✾
▲■❙❚❆ ❉❊ ❋■●❯❘❆❙ ✶✹
▲■❙❚❆ ❉❊ ❚❆❇❊▲❆❙ ✶✺
■◆❚❘❖❉❯➬➹❖ ✶✻
✶ ❖❙ P❖▲■❊❉❘❖❙ ❉❊ P▲❆❚➹❖ ✶✾
✶✳✶ ❍✐stór✐❛ ❞♦s P♦❧✐❡❞r♦s ❞❡ P❧❛tã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✶✳✷ P♦❧✐❡❞r♦s ❡ ♦ ❚❡♦r❡♠❛ ❞❡ ❊✉❧❡r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✶✳✸ P♦❧✐❡❞r♦s ❞❡ P❧❛tã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽
✷ ❆ ❍❊❯❘❮❙❚■❈❆ ❉❆ ❘❊❙❖▲❯➬➹❖ ❉❊ P❘❖❇▲❊▼❆❙ ✸✸
✷✳✶ ❚✐♣♦s ❞❡ Pr♦❜❧❡♠❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✷✳✶✳✶ Pr♦❜❧❡♠❛s ❘♦t✐♥❡✐r♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✷✳✶✳✷ Pr♦❜❧❡♠❛s ❘❡❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼ ✷✳✶✳✸ Pr♦❜❧❡♠❛s ❘❡❝r❡❛t✐✈♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✷✳✶✳✹ Pr♦❜❧❡♠❛s ◆ã♦✲r♦t✐♥❡✐r♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾ ✷✳✷ ❆s ❊t❛♣❛s ❞♦ ▼ét♦❞♦ ❍❡✉ríst✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ✷✳✷✳✶ ❈♦♠♣r❡❡♥sã♦ ❞♦ Pr♦❜❧❡♠❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷ ✷✳✷✳✷ ❊st❛❜❡❧❡❝✐♠❡♥t♦ ❞❡ ✉♠ P❧❛♥♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✷✳✷✳✸ ❊①❡❝✉çã♦ ❞♦ P❧❛♥♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺ ✷✳✷✳✹ ❘❡tr♦s♣❡❝t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺
✷✳✷✳✺ ❈♦♠♣r❡❡♥❞❡♥❞♦ ♦ ▼ét♦❞♦ ❆tr❛✈és ❞❡ ❊①❡♠♣❧♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻ ✷✳✸ ▼♦❞❡❧❛❣❡♠ ▼❛t❡♠át✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻
✸ ❖ ▼➱❚❖❉❖ ❍❊❯❘❮❙❚■❈❖ ❆P▲■❈❆❉❖ ◆❆ ❈❖◆❙❚❘❯➬➹❖ ❉❊ ▼❖✲
❉❊▲❖❙ ▼❆❚❊▼➪❚■❈❖❙ ✺✽
✸✳✶ ➪r❡❛ ❚♦t❛❧ ❞♦s P♦❧✐❡❞r♦s ❘❡❣✉❧❛r❡s ❞❡ P❧❛tã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ✸✳✶✳✶ ❆t✐✈✐❞❛❞❡ ✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵ ✸✳✶✳✷ ❆t✐✈✐❞❛❞❡ ✷ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✸✳✶✳✸ ❆t✐✈✐❞❛❞❡ ✸ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹ ✸✳✷ ❱♦❧✉♠❡ ❞♦s P♦❧✐❡❞r♦s ❘❡❣✉❧❛r❡s ❞❡ P❧❛tã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸ ✸✳✷✳✶ ❆t✐✈✐❞❛❞❡ ✹ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸ ✸✳✷✳✷ ❆t✐✈✐❞❛❞❡ ✺ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺ ✸✳✷✳✸ ❆t✐✈✐❞❛❞❡ ✻ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✾ ✸✳✷✳✹ ❆t✐✈✐❞❛❞❡ ✼ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✸ ✸✳✷✳✺ ❆t✐✈✐❞❛❞❡ ✽ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✵ ✸✳✷✳✻ ❱❡r✐✜❝❛çã♦ ❈♦♥❝r❡t❛ ❞♦s ▼♦❞❡❧♦s ❊♥❝♦♥tr❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✸ ✸✳✷✳✼ ❆♥á❧✐s❡ ❞♦ ◗✉❡st✐♦♥ár✐♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✺
❈❖◆❙■❉❊❘❆➬Õ❊❙ ❋■◆❆■❙ ✾✾
❘❊❋❊❘✃◆❈■❆❙ ❇■❇▲■❖●❘➪❋■❈❆❙ ✶✵✶
❆P✃◆❉■❈❊ ✶✿ ❆t✐✈✐❞❛❞❡s ❡❧❛❜♦r❛❞❛s ♣❛r❛ ❛♣❧✐❝❛çã♦ ❞♦ ▼ét♦❞♦ ❍❡✉rís✲
t✐❝♦ ✶✵✹
❆P✃◆❉■❈❊ ✷✿ P❧❛♥✐✜❝❛çã♦ ❞♦s P♦❧✐❡❞r♦s ❘❡❣✉❧❛r❡s ❞❡ P❧❛tã♦ ✶✶✸
▲✐st❛ ❞❡ ❋✐❣✉r❛s
✶✳✶ P♦❧✐❡❞r♦s ❘❡❣✉❧❛r❡s ❞❡ P❧❛tã♦✿ ❊❧❡♠❡♥t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✶✳✷ P♦❧✐❡❞r♦s ❘❡❣✉❧❛r❡s ❞❡ P❧❛tã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ✶✳✸ ▼♦❞❡❧♦ ❞❡ ❑❡♣❧❡r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ✶✳✹ P♦❧✐❡❞r♦ ❝♦♥✈❡①♦ ❡ ♥ã♦ ❝♦♥✈❡①♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✶✳✺ P♦❧✐❣♦♥♦s ✕ r❡❧❛çã♦ ❡♥tr❡ ✈ért✐❝❡s ❡ ❛r❡st❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✶✳✻ P♦❧✐❡❞r♦ r❡t✐r❛♥❞♦✲s❡ ✉♠❛ ❞❡ s✉❛s ❢❛❝❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✶✳✼ P♦❧✐❡❞r♦s✿ r❡❧❛çã♦ ❞❡ ❊✉❧❡r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✶✳✽ P♦❧✐❡❞r♦✿ ◆ã♦ ❡✉❧❡r✐r❛♥♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✶✳✾ P♦❧✐❡❞r♦s ❞❡ P❧❛tã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷
✷✳✶ P❧❛♥t❛ ❜❛✐①❛ ❞♦ t❡rr❡♥♦ ❡ ❝❛s❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ✷✳✷ P❧❛♥t❛ ❜❛✐①❛ ❞♦ t❡rr❡♥♦ ❡ ❝❛s❛ ✲ ✐♥s❡rçã♦ ❞❡ ✈❛❧♦r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹ ✷✳✸ P❧❛♥t❛ ❜❛✐①❛ ❞♦ t❡rr❡♥♦ ❡ ❝❛s❛ ✲ ✐♥s❡rçã♦ ❞❡ ✈❛❧♦r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹
✸✳✶ P♦❧✐❡❞r♦s✿ ❤❡①❛❡❞r♦ r❡❣✉❧❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵ ✸✳✷ ❆t✐✈✐❞❛❞❡ ✶ ✲ ❊✳❘✳▼✳❏✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵ ✸✳✸ ❆t✐✈✐❞❛❞❡ ✶ ✲ ■✳▼✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✸✳✹ P♦❧✐❡❞r♦s✿ t❡tr❛❡❞r♦✱ ♦❝t❛❡❞r♦ ❡ ✐❝♦s❛❡❞r♦ r❡❣✉❧❛r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷ ✸✳✺ ❆t✐✈✐❞❛❞❡ ✷ ✲ ❆✳❍✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸ ✸✳✻ ❆t✐✈✐❞❛❞❡ ✷ ✲ ❨✳❈✳●✳❘✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹ ✸✳✼ P♦❧✐❡❞r♦s✿ ❞♦❞❡❝❛❡❞r♦ r❡❣✉❧❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹ ✸✳✽ ❚r✐â♥❣✉❧♦ ■sós❝❡❧❡s ■ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺ ✸✳✾ ❚r✐â♥❣✉❧♦ ■sós❝❡❧❡s ■■ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻ ✸✳✶✵ ❚r✐â♥❣✉❧♦ ❆❇❍ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼ ✸✳✶✶ ❆t✐✈✐❞❛❞❡ ✸ ✲ ❨✳❈✳●✳❘✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾ ✸✳✶✷ ❆t✐✈✐❞❛❞❡ ✸ ✲ ▼✳●✳▼✳▲✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵
✸✳✶✸ P❡♥tá❣♦♥♦ ❘❡❣✉❧❛r ❆❇❈❉❊ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶ ✸✳✶✹ ❚r✐â♥❣✉❧♦ ❇❖❍ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷ ✸✳✶✺ P♦❧✐❡❞r♦s✿ ❤❡①❛❡❞r♦ r❡❣✉❧❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸ ✸✳✶✻ ❆t✐✈✐❞❛❞❡ ✹ ✲ ❆✳❍✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹ ✸✳✶✼ ❆t✐✈✐❞❛❞❡ ✹ ✲ ❊✳❱✳❇✳❊✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹ ✸✳✶✽ P♦❧✐❡❞r♦s✿ t❡tr❛❡❞r♦ r❡❣✉❧❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺ ✸✳✶✾ ❆t✐✈✐❞❛❞❡ ✺ ✲ ❊✳❘✳▼✳❏✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻ ✸✳✷✵ ❆t✐✈✐❞❛❞❡ ✺ ✲ ❊✳❱✳❇✳❊✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✼ ✸✳✷✶ ❚❡tr❛❡❞r♦ ❘❡❣✉❧❛r✿ ❚r✐â♥❣✉❧♦ ❆❍❇ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✽ ✸✳✷✷ P♦❧✐❡❞r♦s✿ ♦❝t❛❡❞r♦ r❡❣✉❧❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✾ ✸✳✷✸ ❆t✐✈✐❞❛❞❡ ✻ ✲ ❆✳❍✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✵ ✸✳✷✹ ❆t✐✈✐❞❛❞❡ ✻ ✲ ❊✳❘✳▼✳❏✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✶ ✸✳✷✺ P✐râ♠✐❞❡ ❞❡ ❜❛s❡ q✉❛❞r❛❞❛✿ ❚r✐â♥❣✉❧♦ ❆❍❇ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✷ ✸✳✷✻ P♦❧✐❡❞r♦s✿ ❞♦❞❡❝❛❡❞r♦ r❡❣✉❧❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✸ ✸✳✷✼ ❆t✐✈✐❞❛❞❡ ✼ ✲ ❊✳❘✳▼✳❏✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✹ ✸✳✷✽ ❆t✐✈✐❞❛❞❡ ✼ ✲ ❨✳❈✳●✳❘✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✺ ✸✳✷✾ P✐râ♠✐❞❡ ✐♥s❡r✐❞❛ ♥♦ ❞♦❞❡❝❛❡❞r♦ r❡❣✉❧❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✻ ✸✳✸✵ P❡♥tá❣♦♥♦✿ ❚r✐â♥❣✉❧♦ ❆❖❇ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✼ ✸✳✸✶ P✐râ♠✐❞❡✿ ❚r✐â♥❣✉❧♦ ❆❖❱ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✽ ✸✳✸✷ P♦❧✐❡❞r♦s✿ ✐❝♦s❛❡❞r♦ r❡❣✉❧❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✵ ✸✳✸✸ ❆t✐✈✐❞❛❞❡ ✽ ✲ ■✳▼✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✶ ✸✳✸✹ ❆t✐✈✐❞❛❞❡ ✽ ✲ ❨✳❈✳●✳❘✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✶ ✸✳✸✺ ■❝♦s❛❡❞r♦ r❡❣✉❧❛r✿ P✐râ♠✐❞❡ ❆❇❈❱ ✐♥s❝r✐t❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✷ ✸✳✸✻ P✐râ♠✐❞❡ ❆❇❈❱ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✷ ✸✳✸✼ ❱❡r✐✜❝❛çã♦ ❞♦ ✈♦❧✉♠❡ ❞♦ ❤❡①❛❡❞r♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✹ ✸✳✸✽ ❱❡r✐✜❝❛çã♦ ❞♦ ✈♦❧✉♠❡ ❞♦ t❡tr❛❡❞r♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✹ ✸✳✸✾ ❱❡r✐✜❝❛çã♦ ❞♦ ✈♦❧✉♠❡ ❞♦ ♦❝t❛❡❞r♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✹ ✸✳✹✵ ❱❡r✐✜❝❛çã♦ ❞♦ ✈♦❧✉♠❡ ❞♦ ♦❝t❛❡❞r♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✹ ✸✳✹✶ ❱❡r✐✜❝❛çã♦ ❞♦ ✈♦❧✉♠❡ ❞♦ ❞♦❞❡❝❛❡❞r♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✹ ✸✳✹✷ ❱❡r✐✜❝❛çã♦ ❞♦ ✈♦❧✉♠❡ ❞♦ ✐❝♦s❛❡❞r♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✹ ✸✳✹✸ ◗✉❡st✐♦♥ár✐♦ ✵✶ ✕ ♣✳ ✶✶✷ ✕ ❛❧✉♥❛ ❨✳❈✳●✳❘✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✺ ✸✳✹✹ ◗✉❡st✐♦♥ár✐♦ ✵✶ ✕ ♣✳ ✶✶✷ ✕ ❛❧✉♥♦ ❊✳❱✳❇✳❊✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✻
✸✳✹✺ ◗✉❡st✐♦♥ár✐♦ ✵✷ ✕ ♣✳ ✶✶✷ ✕ ❛❧✉♥❛ ■✳▼✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✻ ✸✳✹✻ ◗✉❡st✐♦♥ár✐♦ ✵✸ ✕ ♣✳ ✶✶✷ ✕ ❛❧✉♥♦ ❆✳❍✳P✳❖✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✼ ✸✳✹✼ ◗✉❡st✐♦♥ár✐♦ ✵✸ ✕ ♣✳ ✶✶✷ ✕ ❛❧✉♥❛ ■✳▼✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✼ ✸✳✹✽ ◗✉❡st✐♦♥ár✐♦ ✵✹ ✕ ♣✳ ✶✶✷ ✕ ❛❧✉♥♦ ❆✳❍✳P✳❖✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✼ ✸✳✹✾ ◗✉❡st✐♦♥ár✐♦ ✵✹ ✕ ♣✳ ✶✶✷ ✕ ❛❧✉♥❛ ■✳▼✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✼ ✸✳✺✵ P♦❧✐❡❞r♦s✿ ❤❡①❛❡❞r♦ r❡❣✉❧❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✹ ✸✳✺✶ P♦❧✐❡❞r♦s✿ t❡tr❛❡❞r♦✱ ♦❝t❛❡❞r♦ ❡ ✐❝♦s❛❡❞r♦ r❡❣✉❧❛r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✺ ✸✳✺✷ P♦❧✐❡❞r♦s✿ ❞♦❞❡❝❛❡❞r♦ r❡❣✉❧❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✻ ✸✳✺✸ P♦❧✐❡❞r♦s✿ ❤❡①❛❡❞r♦ r❡❣✉❧❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✼ ✸✳✺✹ P♦❧✐❡❞r♦s✿ t❡tr❛❡❞r♦ r❡❣✉❧❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✽ ✸✳✺✺ P♦❧✐❡❞r♦s✿ ♦❝t❛❡❞r♦ r❡❣✉❧❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✾ ✸✳✺✻ P♦❧✐❡❞r♦s✿ ❞♦❞❡❝❛❡❞r♦ r❡❣✉❧❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✵ ✸✳✺✼ P♦❧✐❡❞r♦s✿ ✐❝♦s❛❡❞r♦ r❡❣✉❧❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✶ ✺✽ P❧❛♥✐✜❝❛çã♦ ❞♦ ❚❡tr❛❡❞r♦ ❘❡❣✉❧❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✸ ✺✾ P❧❛♥✐✜❝❛çã♦ ❞♦ ❍❡①❛❡❞r♦ ❘❡❣✉❧❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✹ ✻✵ P❧❛♥✐✜❝❛çã♦ ❞♦ ❖❝t❛❡❞r♦ ❘❡❣✉❧❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✺ ✻✶ P❧❛♥✐✜❝❛çã♦ ❞♦ ❉♦❞❡❝❛❡❞r♦ ❘❡❣✉❧❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✻ ✻✷ P❧❛♥✐✜❝❛çã♦ ❞♦ ■❝♦s❛❡❞r♦ ❘❡❣✉❧❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✼
▲✐st❛ ❞❡ ❚❛❜❡❧❛s
✷✳✶ ❘❡❣✐str♦ ❞❛ ✶❛ ❧❡✐t✉r❛ ❞♦ ♣❛❞rã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾
✷✳✷ ❘❡❣✐str♦ ❞❛ ✷❛ ❧❡✐t✉r❛ ❞♦ ♣❛❞rã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾
✷✳✸ ❘❡❣✐str♦ ❞❛ ✸❛ ❧❡✐t✉r❛ ❞♦ ♣❛❞rã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾
✷✳✹ ❘❡❣✐str♦ ❞❛s ✐♥❢♦r♠❛çõ❡s ❝♦♥t✐❞❛s ♥♦ ❡♥✉♥❝✐❛❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶ ✷✳✺ ❘❡❣✐str♦ ❞❛s ✐♥❢♦r♠❛çõ❡s ❛♣ós ❛ ✶❛ ♦❜s❡r✈❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶
■◆❚❘❖❉❯➬➹❖
✏❖ ❛❧✉♥♦ ♠✉✐t❛s ✈❡③❡s ♥ã♦ r❡s♦❧✈❡ ♣r♦❜❧❡♠❛s ❞❡ ♠❛t❡♠át✐❝❛✱ ♥ã♦ ♣♦rq✉❡ ♥ã♦ s❛❜❡ ♠❛t❡♠át✐❝❛✱ ♠❛s ♣♦rq✉❡ ♥ã♦ s❛❜❡ ❧❡r ♦ ❡♥✉♥❝✐❛❞♦ ❞♦ ♣r♦❜❧❡♠❛✑ ❬✳✳✳❪ ✏◆ã♦ ❜❛st❛ ❡♥s✐♥❛r só ❛s r❡❧❛çõ❡s ♠❛t❡♠át✐❝❛s✿ é ♣r❡❝✐s♦ t❛♠❜é♠ ♦ ♣♦rt✉❣✉ês q✉❡ ❛ ♠❛t❡♠át✐❝❛ ✉s❛✑✳
✭❈❆●▲■❆❘■ ✭✷✵✵✸✮ ❛♣✉❞ ■❚❆❈❆❘❆▼❇■✱ ✷✵✶✵✱ ♣✳✶✸✲✶✹✮
◆ã♦ é ♠✉✐t♦ r❛r♦ ♦❜s❡r✈❛r ♥❛s ❡s❝♦❧❛s ❞✐s❝✉rs♦s ❞❡ ❛❧✉♥♦s ❛✜r♠❛♥❞♦ q✉❡ ❛ ▼❛✲ t❡♠át✐❝❛ é ❛ ❞✐s❝✐♣❧✐♥❛ ♠❛✐s ❞✐❢í❝✐❧ ❞❡ s❡r ❝♦♠♣r❡❡♥❞✐❞❛✱ ♣♦ré♠ q✉❛♥❞♦ ♣❡r❣✉♥t❛♠♦s ♦ ♣♦rq✉ê ❞❡ t❛❧ ♣❡♥s❛♠❡♥t♦✱ s✐♠♣❧❡s♠❡♥t❡ ✜❝❛♠♦s s❡♠ ✉♠❛ r❡s♣♦st❛ s❛t✐s❢❛tór✐❛ q✉❡ ❡①♣❧✐✲ q✉❡ ❡st❛ s✐t✉❛çã♦✳ ❆ss✐♠✱ ✉♠ ❞♦s ❞❡s❛✜♦s ❞♦ ♣r♦❢❡ss♦r ❞❡ ▼❛t❡♠át✐❝❛ é ♣r♦♠♦✈❡r ✉♠❛ r✉♣t✉r❛ ♥♦ ♣❛r❛❞✐❣♠❛ ❞❡ q✉❡ ❡❧❛ s♦♠❡♥t❡ ♣♦❞❡ s❡r ❛♣r❡♥❞✐❞❛ ♣♦r ✉♠❛ ♠✐♥♦r✐❛ ❞❡ ❛❧✉♥♦s✱ t✐❞♦s ❝♦♠♦ ✐♥t❡❧✐❣❡♥t❡s ♣❡❧♦s ❝♦❧❡❣❛s ❞❡ s❛❧❛ ❞❡ ❛✉❧❛✳
❆ss✐♠✱ ❛ ❞✐✜❝✉❧❞❛❞❡ ❡♥❝♦♥tr❛❞❛ ♣❡❧♦s ❛❧✉♥♦s ❡♠ ❝♦♠♣r❡❡♥❞❡r ❝♦♥t❡ú❞♦s ♠❛t❡♠á✲ t✐❝♦s ♠♦t✐✈♦✉ ❛ ❡❧❛❜♦r❛çã♦ ❞❡st❡ t❡①t♦✱ s❡♥❞♦ q✉❡ ♦ ♠ét♦❞♦ ❤❡✉ríst✐❝♦ ❛♣❧✐❝❛❞♦ ❛ r❡s♦❧✉çã♦ ❞❡ ♣r♦❜❧❡♠❛s s❡rá ✉t✐❧✐③❛❞♦ ♣❛r❛ ♣r♦♠♦✈❡r ❛ ❛♣r❡♥❞✐③❛❣❡♠ ❞❛ ▼❛t❡♠át✐❝❛ ❞❡ ❢♦r♠❛ s✐❣♥✐✲ ✜❝❛t✐✈❛ ❡ ❡✜❝✐❡♥t❡✳ P♦✐s✱ ❡st❛ ♠❡t♦❞♦❧♦❣✐❛ ♣r♦♠♦✈❡ ❛ ❜✉s❝❛ ❞♦ ❝♦♥❤❡❝✐♠❡♥t♦ ♠❛t❡♠át✐❝♦ ❛tr❛✈és ❞❡ ✐♥❞❛❣❛çõ❡s ❡ ♣❡sq✉✐s❛✱ ❧❡✈❛♥❞♦ ♦ ❛❧✉♥♦ ❛ ❡❧❛❜♦r❛r ❡ q✉❡st✐♦♥❛r ❡str❛té❣✐❛s ❞❡ r❡s♦❧✉çã♦ ❞♦s ♣r♦❜❧❡♠❛s q✉❡ s❡rã♦ ❛♣r❡s❡♥t❛❞❛s ❡✱ ❛ss✐♠✱ ❝r✐❛♥❞♦ ♥♦✈♦s q✉❡st✐♦♥❛♠❡♥t♦s ❡✱ ❝♦♥s❡q✉❡♥t❡♠❡♥t❡✱ ♦✉tr❛s s✐t✉❛çõ❡s✲♣r♦❜❧❡♠❛s✳ ❙❡❣✉♥❞♦ ❈❛r✈❛❧❤♦ ✭✶✾✾✹✱ ♣✳ ✽✷✮✱
❬✳✳✳❪ ◆ã♦ s❡ ❛♣r❡♥❞❡ ▼❛t❡♠át✐❝❛ ♣❛r❛ r❡s♦❧✈❡r ♣r♦❜❧❡♠❛s ❡✱ s✐♠✱ s❡ ❛♣r❡♥❞❡ ▼❛t❡♠át✐❝❛ r❡s♦❧✈❡♥❞♦ ♣r♦❜❧❡♠❛s✳ ❉✐❛♥t❡ ❞❡ss❛ ♣❡rs♣❡❝t✐✈❛✱ q✉❛❧q✉❡r s✐t✉❛çã♦ q✉❡ ✈✐s❡ ❢❛✈♦r❡❝❡r ♦ ❛♣r❡♥❞✐③❛❞♦ ❞❡✈❡ ❝♦♥st✐t✉✐r✲s❡ ❡♠ s✐t✉❛çã♦ ♣r♦❜❧❡♠❛ ♣❛r❛ ♦ ❛❧✉♥♦ ❛ q✉❡ s❡ ❞❡st✐♥❛✱ ♦✉ s❡❥❛✱ ❛ ♣r♦♣♦st❛ ❞❡ t❛r❡❢❛ ❢❡✐t❛ ♣❡❧♦ ♣r♦❢❡ss♦r ❞❡✈❡ s❡r tã♦ ✐♥t❡r❡ss❛♥t❡ q✉❡ ❝r✐❡✱ ♥❛ ❝❧❛ss❡✱ ✉♠ ❝❧✐♠❛ ❞❡ ♣❡sq✉✐s❛✱ ❞❡ ❜✉s❝❛ ❞❡ s♦❧✉çã♦ ♣❛r❛ ♦s ♣r♦❜❧❡♠❛s q✉❡ ❡♠❡r✲ ❣✐r❡♠ ❞❛ ♣r♦♣♦st❛✳ ◆❡ss❛ ♣❡rs♣❡❝t✐✈❛ ♥ã♦ ❡①✐st❡ ✧❛✉❧❛✧❞❡ r❡s♦❧✉çã♦ ❞❡ ♣r♦❜❧❡♠❛s ❡ s✐♠ s✐t✉❛çõ❡s ❞❡ ❡♥s✐♥♦ ♦♥❞❡✱ ❛ ♣❛rt✐r ❞❡ ♣❡sq✉✐s❛s s♦❜r❡ ♣r♦❜❧❡♠❛s ❡♠❡r❣❡♥t❡s ♦✉ ❞❡ ♣r♦♣♦st❛s ♣r♦❜❧❡♠❛t✐③❛❞♦r❛s✱ é ❡❧❛❜♦r❛❞♦ ♦ ❝♦♥❤❡❝✐♠❡♥t♦ ♠❛t❡♠át✐❝♦✱ ❡ ❡ss❛ ❡❧❛❜♦r❛çã♦ s✉s❝✐t❛ ♥♦✈♦s ♣r♦❜❧❡♠❛s✳
Pr❡t❡♥❞❡✲s❡ ❛❜♦r❞❛r ❛s ❡t❛♣❛s ❞♦ ♠ét♦❞♦ ❞❡ r❡s♦❧✉çã♦ ❞❡ ♣r♦❜❧❡♠❛s ❞❡s❡♥✈♦❧✲ ✈✐❞♦ ♣♦r P♦❧②❛✶ ✭✷✵✵✻✮✱ ❛♣❧✐❝❛♥❞♦✲♦ ♥❛ ❡❧❛❜♦r❛çã♦ ❞❡ ♠♦❞❡❧♦s ♠❛t❡♠át✐❝♦s q✉❡ r❡s♦❧✈❛♠
♣r♦❜❧❡♠❛s r❡❧❛❝✐♦♥❛❞♦s ❛♦ ❝á❧❝✉❧♦ ❞❡ ár❡❛s ❡ ✈♦❧✉♠❡s ❞♦s ♣♦❧✐❡❞r♦s r❡❣✉❧❛r❡s ❞❡ P❧❛tã♦✳ ❆tr❛✈és ❞❡st❡s✱ s❡rá ♠♦str❛❞❛ ❛ r❡❧❡✈â♥❝✐❛ ❡ ✐♠♣♦rtâ♥❝✐❛ ❞♦ ♠ét♦❞♦ ❤❡✉ríst✐❝♦ ❝♦♠♦ ♠❡t♦✲ ❞♦❧♦❣✐❛ ♥♦ ❡♥s✐♥♦ ❞❛ ♠❛t❡♠át✐❝❛✱ s❡♥❞♦ ❡st❡ ♦ ♣r✐♥❝✐♣❛❧ ♦❜❥❡t✐✈♦ ❞❡st❡ t❡①t♦ ❞✐ss❡rt❛t✐✈♦✳ ❊st❡ tr❛❜❛❧❤♦ ❢♦✐ r❡❛❧✐③❛❞♦ ❛tr❛✈és ❞❡ ♣❡sq✉✐s❛ ❜✐❜❧✐♦❣rá✜❝❛ ❡ ❞❡ ❡st✉❞♦ ❞❡ ❝❛s♦ q✉❡ ♠♦str❛rá ❛ ❡✜❝✐ê♥❝✐❛ ❞♦ ♠ét♦❞♦ ❤❡✉ríst✐❝♦ ♥♦ ❡♥s✐♥♦ ❡ ♥❛ ❛♣r❡♥❞✐③❛❣❡♠ ❞❛ ♠❛t❡✲ ♠át✐❝❛✳ ◆❡❧❡ s❡rá ❛♣r❡s❡♥t❛❞♦ ✉♠ ❜r❡✈❡ ❤✐stór✐❝♦ ❞❛ ♦r✐❣❡♠ ❞♦s ♣♦❧✐❡❞r♦s ❞❡ P❧❛tã♦✱ ❞❡st❛❝❛♥❞♦ ❛❧❣✉♠❛s ❞❡✜♥✐çõ❡s ✐♠♣♦rt❛♥t❡s ❡ ♦s t❡♦r❡♠❛s ♠❛✐s r❡❧❡✈❛♥t❡s ❛❝❡r❝❛ ❞❡st❡ t❡♠❛✱ t❛✐s ❝♦♠♦✿ ❖ ❝♦♥❝❡✐t♦ ❞❡ ♣♦❧✐❡❞r♦✱ ♦ ❚❡♦r❡♠❛ ❞❡ ❊✉❧❡r✱ ❛ ❞❡✜♥✐çã♦ ❞❡ ♣♦❧✐❡❞r♦s r❡❣✉❧❛r❡s ❞❡ P❧❛tã♦✱ ❜❡♠ ❝♦♠♦ ❞❡♠♦♥str❛çã♦ ❞❡ q✉❡ ❤á ❛♣❡♥❛s ❝✐♥❝♦ ❞❡❧❡s✳
❋♦r❛♠ ❛✐♥❞❛ ❛❜♦r❞❛❞♦s ♦s ❛s♣❡❝t♦s ❝♦♥❝❡✐t✉❛✐s ❞♦ ♠ét♦❞♦ ❤❡✉ríst✐❝♦ ✭❝♦♥❥✉♥t♦ ❞❡ r❡❣r❛s ❡ ♠ét♦❞♦s q✉❡ ❝♦♥❞✉③❡♠ à ❞❡s❝♦❜❡rt❛✱ à ✐♥✈❡♥çã♦ ❡ à r❡s♦❧✉çã♦ ❞❡ ♣r♦❜❧❡♠❛s✮✱ ❛tr❛✈és ❞❡ ✉♠❛ ❢✉♥❞❛♠❡♥t❛çã♦ t❡ór✐❝❛ ❛❝❡r❝❛ ❞❛ r❡s♦❧✉çã♦ ❞❡ ♣r♦❜❧❡♠❛s ♠❛t❡♠át✐❝♦s✱ ❜❛s❡❛❞♦s ♥❛s ❞❡✜♥✐çõ❡s ❡①♣♦st❛s ♥♦ ❧✐✈r♦ ❆ ❛rt❡ ❞❡ r❡s♦❧✈❡r ♣r♦❜❧❡♠❛s ❞❡ P♦❧②❛ ✭✷✵✵✻✮✳ ❆❧é♠ ❞❡ ❝♦♥❝❡✐t✉❛r ♣r♦❜❧❡♠❛s ♠❛t❡♠át✐❝♦s ❡ ❝❧❛ss✐✜❝❛r ♦s t✐♣♦s ♠❛✐s ❝♦♠✉♥s ✉t✐❧✐③❛❞♦s ❡♠ s❛❧❛ ❞❡ ❛✉❧❛✱ ❝♦♠ s❡✉s ❞❡✈✐❞♦s ❡①❡♠♣❧♦s✳ ❋♦r❛♠ ❛♣r❡s❡♥t❛❞❛s ❛s ❡t❛♣❛s ❞♦ ♠ét♦❞♦ ❤❡✉ríst✐❝♦ r❡ss❛❧t❛♥❞♦ ♦s ❛s♣❡❝t♦s ♠❛✐s s✐❣♥✐✜❝❛t✐✈♦s ❞❡ ❝❛❞❛ ✉♠❛ ❞❡❧❛s✳ ❋♦r❛♠ r❡❛❧✐③❛❞❛s ❛❧❣✉♠❛s ❛♣❧✐❝❛çõ❡s ❞♦ ♠ét♦❞♦ ❤❡✉ríst✐❝♦ ❡♠ ❞✐✈❡rs❛s ❛t✐✈✐❞❛❞❡s ♠❛t❡♠át✐❝❛s✱ ❛ ✜♠ ❞❡ ♠♦str❛r ❝♦♠♦ ♦ ♣r♦❢❡ss♦r ❞❡✈❡ ♣r♦❝❡❞❡r ❞✉r❛♥t❡ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ s✐t✉❛çõ❡s✲♣r♦❜❧❡♠❛s ✉t✐❧✐③❛♥❞♦ ❡st❡ ♠ét♦❞♦✳ ❋♦✐ ❛❜♦r❞❛❞♦✱ s✉❝✐♥t❛♠❡♥t❡✱ ❛❧❣✉♥s ❝♦♥❝❡✐t♦s ❞❡ ♠♦❞❡❧❛❣❡♠ ♥❛ ♠❛t❡♠át✐❝❛ ❡ s✉❛ s✐❣♥✐✜❝❛çã♦ ♥❛ ♠❛t❡♠át✐❝❛✳
❈♦♥st❛ t❛♠❜é♠ ❛ ❛♣❧✐❝❛çã♦ ❞♦ ♠ét♦❞♦ ❤❡✉ríst✐❝♦ ♥❛ ❝♦♥str✉çã♦ ❞❡ ❛❧❣✉♥s ♠♦✲ ❞❡❧♦s ♠❛t❡♠át✐❝♦s ♦♥❞❡ s❡ ♣r❡t❡♥❞❡ ♠♦str❛r q✉❡ é ♣♦ssí✈❡❧ ♣❛r❛ ♦s ❛❧✉♥♦s ❝♦♥str✉ír❡♠
✶●❡♦r❣❡ P♦❧②❛ ♥❛s❝❡✉ ❛ ✶✸ ❞❡ ❉❡③❡♠❜r♦ ❞❡ ✶✽✽✼ ❡♠ ❇✉❞❛♣❡st❡ ✭❍✉♥❣r✐❛✮✱ ❞❡ ❢❛♠í❧✐❛ ❥✉❞❛✐❝❛ ❞❡ ♦r✐❣❡♠
♣♦❧❛❝❛✳ ❋❛❧❡❝❡✉ ❛ ✼ ❞❡ ❙❡t❡♠❜r♦ ❞❡ ✶✾✽✺ ❡♠ P❛❧♦ ❆❧t♦✱ ♥❛ ❈❛❧✐❢ór♥✐❛ ✭❊st❛❞♦s ❯♥✐❞♦s✮✳ ❋♦✐ ✉♠ ❡①❝❡❧❡♥t❡ ❡st✉❞❛♥t❡ ♥♦ ❡♥s✐♥♦ s❡❝✉♥❞ár✐♦✱ ❛♣❡s❛r ❞❛ ❡s❝♦❧❛ q✉❡ ❢r❡q✉❡♥t❛✈❛ ✈❛❧♦r✐③❛r ♠✉✐t♦ ❛ ❛♣r❡♥❞✐③❛❣❡♠ ❝♦♠ ❜❛s❡ ♥❛ ♠❡♠ór✐❛✱ ♣rát✐❝❛ q✉❡ ❝♦♥s✐❞❡r❛✈❛ ♠♦♥ót♦♥❛ ❡ s❡♠ ✉t✐❧✐❞❛❞❡✳
❋♦✐ ♣r♦❢❡ss♦r ❞❡ ♠❛t❡♠át✐❝❛ ❞❡ ✶✾✶✹ ❛ ✶✾✹✵ ♥♦ ❊❚❍ ❩ür✐❝❤ ♥❛ ❙✉íç❛✱ ❡ ❞❡ ✶✾✹✵ ❛ ✶✾✺✸ ♥❛ ❙t❛♥❢♦r❞ ❯♥✐✲ ✈❡rs✐t②✳ P♦❧②❛ ♣❡r♠❛♥❡❝❡✉ ❝♦♠♦ ♣r♦❢❡ss♦r ❡♠ér✐t♦ ❞❡ ❙t❛♥❢♦r❞ ♦ r❡st♦ ❞❡ s✉❛ ✈✐❞❛ ❡ ❝❛rr❡✐r❛✳ ❚r❛❜❛❧❤♦✉ ❝♦♠ ✉♠❛ ✈❛r✐❡❞❛❞❡ ❞❡ tó♣✐❝♦s ♠❛t❡♠át✐❝♦s✱ ✐♥❝❧✉✐♥❞♦ sér✐❡s✱ t❡♦r✐❛ ❞♦s ♥ú♠❡r♦s✱ ❛♥á❧✐s❡ ♠❛t❡♠át✐❝❛✱ ❣❡♦♠❡tr✐❛✱ á❧❣❡❜r❛✱ ❝♦♠❜✐♥❛tór✐❛ ❡ ♣r♦❜❛❜✐❧✐❞❛❞❡✳ ❚❛♠❜é♠ é ♥♦tá✈❡❧ s✉❛ ❝♦♥tr✐❜✉✐çã♦ ♣❛r❛ ❛ ❤❡✉ríst✐❝❛ ❡♠ ❡❞✉❝❛çã♦ ♠❛t❡♠át✐❝❛✳
◆♦ ✐♥í❝✐♦ ❞❡ s✉❛ ❝❛rr❡✐r❛✱ P♦❧②❛ ❡s❝r❡✈❡✉✱ ❥✉♥t❛♠❡♥t❡ ❝♦♠ ●á❜♦r ❙③❡❣ö✱ ❞♦✐s ❧✐✈r♦s q✉❡ tr❛❜❛❧❤❛✈❛♠ ❛ r❡s♦❧✉çã♦ ❞❡ ♣r♦❜❧❡♠❛s✿ Pr♦❜❧❡♠❛s ❡ ❚❡♦r❡♠❛s ❞❡ ❆♥á❧✐s❡✳ P♦st❡r✐♦r♠❡♥t❡✱ ❝♦♠❡ç♦✉ ❛ ♣❡sq✉✐s❛r s♦❜r❡ ♠ét♦❞♦s ❞❡ r❡s♦❧✉çã♦ ❞❡ ♣r♦❜❧❡♠❛s✳ ❊♠ ■♥ ❍♦✇ t♦ ❙♦❧✈❡ ■t✱ P♦❧②❛ ❞á ✉♠❛ ✐❞❡✐❛ ❣❡r❛❧ ❞❛ ❤❡✉ríst✐❝❛ ❞❡ ♣r♦❜❧❡♠❛s ♠❛t❡♠át✐❝♦s ❡ ♥ã♦✲♠❛t❡♠át✐❝♦s✳
♠♦❞❡❧♦s ♠❛t❡♠át✐❝♦s q✉❡ ♥ã♦ ❧❤❡s ❢♦r❛♠ ❛♣r❡s❡♥t❛❞♦s ❡♠ s✉❛ ❡s❝♦❧❛r✐③❛çã♦✱ ❛tr❛✈és ❞♦ ♠ét♦❞♦ ❞❡ r❡s♦❧✉çã♦ ❞❡ ♣r♦❜❧❡♠❛s ❞❡s❡♥✈♦❧✈✐❞♦ ♣♦r P♦❧②❛ ✭✷✵✵✻✮✳ ❆ss✐♠✱ ❢♦r❛♠ ❝♦♥✈✐✲ ❞❛❞♦s ♣❛r❛ ❛♣❧✐❝❛çã♦ ❞❡st❡ ♠ét♦❞♦ ♦s ❛❧✉♥♦s ❞❛ ✸❛ sér✐❡ ❞♦ ❊♥s✐♥♦ ▼é❞✐♦ ❞♦ ❈♦❧é❣✐♦
❖❜❥❡t✐✈♦ ❞❡ ❏✉ss❛r❛✲●❖ q✉❡ ❛❝❡✐t❛r❛♠ ♣❛rt✐❝✐♣❛r ❞❡st❛ ♣r♦♣♦st❛ ❞❡ ❡♥s✐♥♦✳
❈♦♠ ❡st❡s ❛❧✉♥♦s ❢♦✐ ❢❡✐t♦ ✉♠ ❡st✉❞♦ ✐♥✐❝✐❛❧ ♣❛r❛ r❡❧❡♠❜r❛r ❛❧❣✉♥s ❝♦♥❝❡✐t♦s ❣❡✲ ♦♠étr✐❝♦s ❡ ❛❧❣é❜r✐❝♦s q✉❡ s❡r✐❛♠ ♥❡❝❡ssár✐♦s ♣❛r❛ ❡①❡❝✉çã♦ ❞♦ ♠ét♦❞♦✱ ♣♦✐s ♦ ❝♦♥❤❡✲ ❝✐♠❡♥t♦ ♣ré✈✐♦ é ❢✉♥❞❛♠❡♥t❛❧ ♣❛r❛ ❝♦♥str✉çã♦ ❞❡ ♥♦✈♦s ❝♦♥❝❡✐t♦s✳ ❆❧❣✉♠❛s r❡s♦❧✉çõ❡s ♦❜t✐❞❛s ♣❡❧♦s ❛❧✉♥♦s✱ ♥❛ ❝♦♥str✉çã♦ ❞♦s ♠♦❞❡❧♦s✱ ❝♦♥st❛♠ ♥❡st❡ t❡①t♦ ❞✐ss❡rt❛t✐✈♦✳ P❛r❛ ❝❛❞❛ ❛t✐✈✐❞❛❞❡ ♣r♦♣♦st❛ à ❡❧❡s ❢♦✐ ❛♣r❡s❡♥t❛❞❛ ✉♠❛ ♣♦ssí✈❡❧ s♦❧✉çã♦✳ ❖s ♠♦❞❡❧♦s ❡♥❝♦♥✲ tr❛❞♦s ♣❡❧♦s ❛❧✉♥♦s ❢♦r❛♠ t❡st❛❞♦s ❡①♣❡r✐♠❡♥t❛❧♠❡♥t❡ ✉t✐❧✐③❛♥❞♦ ♣♦❧✐❡❞r♦s r❡❣✉❧❛r❡s ❞❡ P❧❛tã♦ ❡♠ ❛❝rí❧✐❝♦✱ ✈❡r✐✜❝❛♥❞♦ ❛ ✈❛❧✐❞❛❞❡ ❞♦s ♠♦❞❡❧♦s ❡♥❝♦♥tr❛❞♦s✱ ♦✉ s❡❥❛✱ ♦❜s❡r✈❛♥❞♦ q✉❡ s❛t✐s❢❛③❡♠ ❛s ❝♦♥❞✐çõ❡s ✐♥✐❝✐❛✐s ❞♦s ♣r♦❜❧❡♠❛s ❛♣r❡s❡♥t❛❞♦s✳
❋♦✐ ❛♣r❡s❡♥t❛❞♦ ❛ ❛♥á❧✐s❡ ❞❡ ✉♠ q✉❡st✐♦♥ár✐♦ r❡s♣♦♥❞✐❞♦ ♣❡❧♦s ❛❧✉♥♦s q✉❡ ♣❛rt✐❝✐✲ ♣❛r❛♠ ❞❛ ❛♣❧✐❝❛çã♦ ❞♦ ♠ét♦❞♦ ❞❡ P♦❧②❛ q✉❡ ♠♦str❛ ❛ s❛t✐s❢❛çã♦ ❡♠ s❡ ❛♣r❡♥❞❡r ✉♠❛ ♥♦✈❛ té❝♥✐❝❛ ❞❡ ❡st✉❞♦✳ ◆♦ ❞❡❝♦rr❡r ❞❡st❛ ❞✐ss❡rt❛çã♦ s❡rá ♠♦str❛❞♦ q✉❡ ♦ ♠ét♦❞♦ ❤❡✉ríst✐❝♦ ❢♦✐ ❝♦♠♣r❡❡♥❞✐❞♦ ❡ ❡①❡❝✉t❛❞♦ ❝♦♠ ê①✐t♦✱ ❡♠ t♦❞❛s ❛s ❡t❛♣❛s✱ ♣❡❧♦s ❛❧✉♥♦s q✉❡ ♣❛rt✐❝✐♣❛r❛♠ ❞❛ ❛♣❧✐❝❛çã♦ ♣rát✐❝❛ ❞❡st❡✱ r❡❢♦rç❛♥❞♦ s✉❛ ✐♠♣♦rtâ♥❝✐❛ ❝♦♠♦ ♠❡t♦❞♦❧♦❣✐❛ ♥♦ ❡♥s✐♥♦ ❡ ♥❛ ❛♣r❡♥❞✐③❛❣❡♠ ❞❛ ♠❛t❡♠át✐❝❛✳
❊s♣❡r❛✲s❡ q✉❡ ❡st❡ tr❛❜❛❧❤♦ ❝♦♥tr✐❜✉❛ ♣❛r❛ ♦ ❡♥s✐♥♦ ❞❡ ▼❛t❡♠át✐❝❛✱ ❞❡s♣❡r✲ t❛♥❞♦ ♥♦s ❛❧✉♥♦s ♦ ✐♥t❡r❡ss❡ ❡♠ r❡s♦❧✈❡r ♣r♦❜❧❡♠❛s ❞❡s❛✜❛❞♦r❡s q✉❡ ♣r♦❞✉③❛ ✉♠ ❝♦✲ ♥❤❡❝✐♠❡♥t♦ s✐❣♥✐✜❝❛t✐✈♦✱ ❡ q✉❡ ❡st❡ ❛♣r❡♥❞✐③❛❞♦ ♣♦ss❛ s❡r✈✐r ❞❡ ♣❛râ♠❡tr♦ ♣❛r❛ r❡s♦❧✈❡r ♦✉tr❛s s✐t✉❛çõ❡s✲♣r♦❜❧❡♠❛s s❡♠❡❧❤❛♥t❡s✳
❈❛♣ít✉❧♦ ✶
❖❙ P❖▲■❊❉❘❖❙ ❉❊ P▲❆❚➹❖
✏❬✳✳✳❪ ◗✉❡ ♥✐♥❣✉é♠ q✉❡ ✐❣♥♦r❡ ❛ ❣❡♦♠❡tr✐❛ ❡♥tr❡ ❛q✉✐ ❬✳✳✳❪✑✳
✭P❧❛tã♦ ❛♣✉❞ ❇♦②❡r✱ ✷✵✶✵✱ ♣✳ ✺✽✮
❆♥t❡s ❞❡ s❡❣✉✐r♠♦s ❝♦♠ ♦ ❡st✉❞♦ ❛❝❡r❝❛ ❞♦ ♠ét♦❞♦ ❞❡ r❡s♦❧✉çã♦ ❞❡ ♣r♦❜❧❡♠❛s ♥♦ ❡♥s✐♥♦ ❡ ❛♣r❡♥❞✐③❛❣❡♠ ❞❛ ♠❛t❡♠át✐❝❛✱ ✈❛♠♦s ❝♦♥❤❡❝❡r ✉♠ ♣♦✉❝♦ ❞❛ ♦r✐❣❡♠ ❞❛ s✐t✉❛çã♦ ♣r♦❜❧❡♠❛ ♥❛ q✉❛❧ ❡st❛ ♣❡sq✉✐s❛ ❢❛③ ♣❛rt❡✱ ♦✉ s❡❥❛✱ ❛ ❤✐stór✐❛ ❞♦s P♦❧✐❡❞r♦s ❞❡ P❧❛tã♦✳
✶✳✶ ❍✐stór✐❛ ❞♦s P♦❧✐❡❞r♦s ❞❡ P❧❛tã♦
❙❡❣✉♥❞♦ ▼❛rq✉❡s ✭✷✵✶✺✮✱ P❧❛tã♦ ♥❛s❝❡✉ ❡♠ ❆t❡♥❛s ♥♦ ❛♥♦ ✹✷✼ ❛✳❈✳ ❡ ♠♦rr❡✉ ♣♦r ✈♦❧t❛ ❞❡ ✸✹✼ ❛✳❈✳❀ s❡✉ ♥♦♠❡ ✈❡r❞❛❞❡✐r♦ ❡r❛ ❆r✐stót❡❧❡s✱ s❡♥❞♦ q✉❡ r❡❝❡❜❡✉ ♦ ♥♦♠❡ ❞❡ P❧❛tã♦ ❞❡✈✐❞♦ ❛ s❡✉ ✈✐❣♦r ❢ís✐❝♦ ❡ ❞❛ ❧❛r❣✉r❛ ❞♦s s❡✉s ♦♠❜r♦s ✭♣❧❛t♦s s✐❣♥✐✜❝❛ ❧❛r❣✉❡③❛✮✳
P♦r s❡r ❛♣❛r❡♥t❛❞♦ ❞❡ ♣♦❧ít✐❝♦s ❝♦♥❤❡❝✐❞♦s ♥❛ é♣♦❝❛✱ P❧❛tã♦ s❡ ✐♥t❡r❡ss❛✈❛ ♣♦r ♣♦❧ít✐❝❛✳ ❆♦s ✈✐♥t❡ ❛♥♦s ❞❡ ✐❞❛❞❡✱ t♦r♥❛✲s❡ ❞✐s❝✐♣❧✐♥♦ ❞❡ ❙ó❝r❛t❡s✱ ❝♦♠ ♦ ♦❜❥❡t✐✈♦ ❞❡ s❡ ❛♣r♦❢✉♥❞❛r ♥❛ ✈✐❞❛ ♣♦❧ít✐❝❛✳ P♦ré♠✱ é ❛ ❋✐❧♦s♦✜❛ q✉❡ r❡♣r❡s❡♥t❛ ❡ ❞á s✐❣♥✐✜❝❛❞♦ ❛ s✉❛ ❡①✐stê♥❝✐❛✳ P❧❛tã♦ ❡s❝r❡✈❡✉ ❝❡r❝❛ ❞❡ tr✐♥t❛ ❞✐á❧♦❣♦s ❡♠ q✉❡ r❡ss❛❧t❛ ❛s ✐❞❡♦❧♦❣✐❛s ❞❡ ❙ó❝r❛t❡s✱ ❡①♣r❡ss❛♥❞♦ ❛ ❜❡❧❡③❛ ❞♦ ♣❡♥s❛♠❡♥t♦ s♦❝rát✐❝♦✳❚✐♠❡✉ é ✉♠ ❞❡ s❡✉s ❞✐á❧♦❣♦s✱ ❝♦♥st✐t✉í❞♦ ❞❡ ✉♠ ❧♦♥❣♦ ♠♦♥ó❧♦❣♦ ❞♦ ♣❡rs♦♥❛❣❡♠ tít✉❧♦✱ ❡s❝r✐t♦ ♣♦r ✈♦❧t❛ ❞❡ ✸✻✵ ❛✳❈✱ ❛♣r❡s❡♥t❛ ❛ ❡s♣❡❝✉❧❛çã♦ s♦❜r❡ ❛ ♥❛t✉r❡③❛ ❞♦ ♠✉♥❞♦ ❢ís✐❝♦ ❡ ♦s s❡r❡s ❤✉♠❛♥♦s✳
❙ó❧✐❞♦s ❝♦♥✈❡①♦s ❝✉❥❛s ❢❛❝❡s sã♦ ♣♦❧í❣♦♥♦s ♣❧❛♥♦s r❡❣✉❧❛r❡s ❝♦♥❣r✉❡♥t❡s sã♦ ❞❡✲ ♥♦♠✐♥❛❞♦s só❧✐❞♦s ♣❧❛tô♥✐❝♦s✳ ❊st❛ ❞❡s✐❣♥❛çã♦ s❡ ❞❡✈❡ ❛ P❧❛tã♦✱ q✉❡ ♦s r❡✈❡❧♦✉ ❝❡r❝❛ ❞❡ ✹✵✵ ❛✳❈✳✳ ◆♦ ❡♥t❛♥t♦✱ ❛ ❡①✐stê♥❝✐❛ ❞❡st❡s só❧✐❞♦s ❥á ❤❛✈✐❛ s✐❞♦ r❡❝♦♥❤❡❝✐❞❛ ♣❡❧♦s ♣✐t❛❣ór✐✲ ❝♦s❀ ❡♥q✉❛♥t♦ ♦s ❡❣í♣❝✐♦s ✉t✐❧✐③❛r❛♠ ❛❧❣✉♥s ❞❡❧❡s ❡♠ s✉❛ ❛rq✉✐t❡t✉r❛ ❡ ❡♠ ♦✉tr♦s ♦❜❥❡t♦s
❝♦♥str✉í❞♦s ♣♦r ❡❧❡s✳
❙❡❣✉♥❞♦ ▼❛rq✉❡s ✭✷✵✶✺✮✱ é ♣r♦✈á✈❡❧ q✉❡ ❛ ❞❡s❝♦❜❡rt❛ ❞♦s só❧✐❞♦s ♣❧❛tô♥✐❝♦s ♦❝♦r✲ r❡✉ ♥✉♠ ❡♥❝♦♥tr♦ ❡♥tr❡ ❆rq✉✐t❛s ✭✹✷✽❛✳❈✳ ✲ ✸✺✵❛✳❈✳✮ ❡ P❧❛tã♦✱ ❡♠ ❈❡❝í❧✐❛✱ ♥♦ s✉❧ ❞❡ ■tá❧✐❛✳ P❛r❛ P❧❛tã♦ ♦ ❯♥✐✈❡rs♦ ❡r❛ ❝♦♥st✐t✉í❞♦ ♣♦r ✉♠ ❝♦r♣♦ ❡ ✉♠❛ ❛❧♠❛✱ ♦✉ ✐♥t❡❧✐❣ê♥❝✐❛✳ ❆ ♠❛✲ tér✐❛ é ❝♦♠♣♦st❛ ❞❡ ♣♦rçõ❡s ❧✐♠✐t❛❞❛s ♣♦r tr✐â♥❣✉❧♦s ♦✉ q✉❛❞r❛❞♦s✱ ❡st❡s ❢♦r♠❛♠ ✈ár✐♦s ❡❧❡♠❡♥t♦s q✉❡ ❞✐❢❡r❡♥❝✐❛♠ ♣❡❧❛ ♥❛t✉r❡③❛ ❞❛ ❢♦r♠❛ ❞❛s s✉❛s s✉♣❡r❢í❝✐❡s ♣❡r✐❢ér✐❝❛s✳
❙❡ ❛s s✉♣❡r❢í❝✐❡s ❢♦ss❡♠ q✉❛❞r❛❞❛s ❢♦r♠❛r✐❛ ♦ ❝✉❜♦ ✭❡❧❡♠❡♥t♦ ❚❡rr❛✮❀ P❧❛tã♦ ❛❝r❡❞✐t❛✈❛ q✉❡ át♦♠♦s ❞❛ t❡rr❛ s❡r✐❛♠ ❝✉❜♦s✱ ♣♦✐s ❡st❡s ♣♦❞❡r✐❛♠ s❡r ❝♦❧♦❝❛❞♦s ❧❛❞♦ ❛ ❧❛❞♦✱ ❞❡ ❢♦r♠❛ q✉❡ s❡ ❝r✐❛ss❡ ✉♠❛ ❡str✉t✉r❛ ❡stá✈❡❧✳ ❙❡ ❢♦ss❡♠ tr✐â♥❣✉❧♦s✱ ❢♦r♠❛r✐❛♠ ✉♠ t❡tr❛❡❞r♦ ✭❡❧❡♠❡♥t♦ ❢♦❣♦✮✱ ❝✉❥❛ ♥❛t✉r❡③❛ ♣❡♥❡tr❛♥t❡✱ ❡st❛✈❛ s✐♠❜♦❧✐③❛❞❛ ❢♦r♠❛ ♣♦♥t✐❛❣✉❞❛ ❞❡ s❡✉s ✈ért✐❝❡s✳ ❖ ❛r ❡r❛ r❡♣r❡s❡♥t❛❞♦ ♣❡❧♦ ♦❝t❛❡❞r♦✱ ♣♦✐s ❡❧❡ ❛❝r❡❞✐t❛✈❛ q✉❡ ♦ át♦♠♦ ❞❡ ❛r ❡r❛ ✉♠ ♣♦❧✐❡❞r♦ ❝♦♠ ♦✐t♦ ❢❛❝❡s ❡✱ ❛ á❣✉❛✱ ❡r❛ r❡♣r❡s❡♥t❛❞❛ ♣❡❧♦ ✐❝♦s❛❡❞r♦✱ ♣♦r ❛❝r❡❞✐t❛r q✉❡ ❡st❡ ❡r❛ ❛ ❢♦r♠❛ ❞♦ át♦♠♦ ❞❡ á❣✉❛✳ ❊❧❡ ❛✐♥❞❛ ❛❝r❡❞✐t❛✈❛ q✉❡✱ ❛tr❛✈és ❞❡ ✉♠❛ ✐♥t❡r✈❡♥çã♦ ✐♥t❡❧✐❣❡♥t❡✱ ✉♠ só❧✐❞♦ ♣❧❛tô♥✐❝♦ ♣♦❞❡r✐❛ s❡ tr❛♥s❢♦r♠❛r ❡♠ ♦✉tr♦✱ ❡①❝❡t♦ ♦ ❝✉❜♦✱ q✉❡ s❡ tr❛♥s❢♦r♠❛✈❛ ♥❡❧❡ ♣ró♣r✐♦✳ ❖ ❞♦❞❡❝❛❡❞r♦✱ ❝❤❡✐♦ ❞❡ ❤❛r♠♦♥✐❛✱ s✐♠❜♦❧✐③❛✈❛ ♦ ♣ró♣r✐♦ ❯♥✐✈❡rs♦✳ ❙❡❣✉♥❞♦ ❊✈❡s ✭✷✵✵✹✱ ♣✳ ✶✶✹✮✿
❏♦❤❛♥♥ ❑❡♣❧❡r ✭✶✺✼✶✲✶✻✸✵✮✱ ♠❡str❡ ❞❛ ❛str♦♥♦♠✐❛✱ ♠❛t❡♠át✐❝♦ ❡ ♥✉♠❡✲ r♦❧♦❣✐st❛✱ ❞❡✉ ✉♠❛ ❡①♣❧✐❝❛çã♦ ❡♥❣❡♥❤♦s❛ ♣❛r❛ ❛s ❛ss♦❝✐❛çõ❡s ❞♦ ❚✐♠❡✉✳ ■♥t✉✐t✐✈❛♠❡♥t❡ ❡❧❡ ❛ss✉♠✐✉ q✉❡✱ ❞❡ss❡s só❧✐❞♦s✱ ♦ t❡tr❛❡❞r♦ ❛❜❛r❝❛ ♦ ♠❡✲ ♥♦r ✈♦❧✉♠❡ ♣❛r❛ ❛ s✉❛ s✉♣❡r❢í❝✐❡✱ ❛♦ ♣❛ss♦ q✉❡ ♦ ✐❝♦s❛❡❞r♦ ♦ ♠❛✐♦r✳ ❆❣♦r❛✱ ❡ss❛s r❡❧❛çõ❡s ✈♦❧✉♠❡✲s✉♣❡r❢í❝✐❡ sã♦ q✉❛❧✐❞❛❞❡s ❞❡ s❡❝✉r❛ ❡ ✉♠✐✲ ❞❛❞❡✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ ❡ ❝♦♠♦ ❢♦❣♦ é ♦ ♠❛✐s s❡❝♦ ❞♦s q✉❛tr♦ ✏❡❧❡♠❡♥t♦s✑ ❡ ❛ á❣✉❛ ♦ ♠❛✐s ú♠✐❞♦✱ ♦ t❡tr❛❡❞r♦ ❞❡✈❡ r❡♣r❡s❡♥t❛r ♦ ❢♦❣♦ ❡ ♦ ✐❝♦s❛❡✲ ❞r♦ ❛ á❣✉❛✳ ❆ss♦❝✐❛✲s❡ ♦ ❝✉❜♦ ❝♦♠ ❛ t❡rr❛ ♣♦rq✉❡ ♦ ❝✉❜♦✱ ❛ss❡♥t❛♥❞♦ q✉❛❞r❛❞❛♠❡♥t❡ s♦❜r❡ ✉♠❛ ❞❡ s✉❛s ❢❛❝❡s✱ t❡♥❤❛ ♠❛✐♦r ❡st❛❜✐❧✐❞❛❞❡✳ ❖ ♦❝t❛❡❞r♦✱ s❡❣✉r♦ ❢r♦✉①❛♠❡♥t❡ ♣♦r ❞♦✐s ❞❡ s❡✉s ✈ért✐❝❡s ♦♣♦st♦s✱ ❡♥tr❡ ♦ ✐♥❞✐❝❛❞♦r ❡ ♦ ♣♦❧❡❣❛r✱ ❢❛❝✐❧♠❡♥t❡ r♦❞♦♣✐❛✱ t❡♥❞♦ ❛ ❡st❛❜✐❧✐❞❛❞❡ ❞♦ ❛r✳ ❋✐✲ ♥❛❧♠❡♥t❡✱ ❛ss♦❝✐❛✲s❡ ♦ ❞♦❞❡❝❛❡❞r♦ ❝♦♠ ♦ ❯♥✐✈❡rs♦ ♣♦rq✉❡ ♦ ❞♦❞❡❝❛❡❞r♦ t❡♠ ✶✷ ❢❛❝❡s ❡ ♦ ③♦❞í❛❝♦ t❡♠ ✶✷ s❡çõ❡s✳
❋✐❣✉r❛ ✶✳✶✿ P♦❧✐❡❞r♦s ❘❡❣✉❧❛r❡s ❞❡ P❧❛tã♦✿ ❊❧❡♠❡♥t♦s
P❧❛tã♦ ❢♦✐ ♦ ♣r✐♠❡✐r♦ ♠❛t❡♠át✐❝♦ ❛ ❞❡♠♦♥str❛r q✉❡ ❡①✐st❡♠ ❛♣❡♥❛s ❝✐♥❝♦ ♣♦❧✐❡❞r♦s r❡❣✉❧❛r❡s✳ ◆♦ s❡✉ ❞✐á❧♦❣♦ ❚✐♠❡✉ ❡❧❡ ❢❛③ r❡❢❡rê♥❝✐❛s ❛ t♦❞♦s ❡❧❡s❀ ❞❡st❛ ❢♦r♠❛✱ ❡❧❡s ♣❛ss❛r❛♠ ❛ s❡r ❞❡♥♦♠✐♥❛❞♦s ❞❡ só❧✐❞♦s ♣❧❛tô♥✐❝♦s✳
❋✐❣✉r❛ ✶✳✷✿ P♦❧✐❡❞r♦s ❘❡❣✉❧❛r❡s ❞❡ P❧❛tã♦
▼❡s♠♦ s❡♥❞♦ ❞❡♥♦♠✐♥❛❞♦s ❝♦♠♦ só❧✐❞♦s ♣❧❛tô♥✐❝♦s✱ Pró❝❧✉s ✭✹✶✶✲✹✽✺ ❞✳❈✳✮ ❛tr✐✲ ❜✉✐ ❛ ❝♦♥str✉çã♦ ❞❡st❡s ♣♦❧✐❡❞r♦s ❛ P✐tá❣♦r❛s ✭✺✻✾❛✳❈✳✲ ✹✼✺❛✳❈✳✮✱ s✉♣♦♥❞♦ ❛✐♥❞❛ q✉❡ é ❞❡st❡ ♦ t❡♦r❡♠❛✿ ❍á s♦♠❡♥t❡ ❝✐♥❝♦ ♣♦❧✐❡❞r♦s r❡❣✉❧❛r❡s✳ ❙é❝✉❧♦s ♠❛✐s t❛r❞❡✱ ♦s ♣♦❧✐❡❞r♦s r❡❣✉❧❛r❡s ✐♥s♣✐r❛r❛♠ ❏♦❤❛♥♥❡s ❑❡♣❧❡r ✭✶✺✼✶✲✶✻✸✵ ❞✳❈✳✮✱ ❛strô♥♦♠♦ ❛❧❡♠ã♦✱ ♥♦ ❡st✉❞♦ ❞♦ ♠♦✈✐♠❡♥t♦ ❞♦s s❡✐s ♣❧❛♥❡t❛s q✉❡ ❡r❛♠ ❝♦♥❤❡❝✐❞♦s ✭❙❛t✉r♥♦✱ ❏ú♣✐t❡r✱ ▼❛rt❡✱ ❚❡rr❛✱ ❱é♥✉s ❡ ▼❡r❝úr✐♦✮✳ ❑❡♣❧❡r ✐♠❛❣✐♥♦✉ ✉♠ ♠♦❞❡❧♦ ❞♦ s✐st❡♠❛ s♦❧❛r ❝♦♠♣♦st♦ ♣♦r ❡s❢❡r❛s ❝♦♥❝ê♥tr✐❝❛s ✐♥s❝r✐t❛s ❡ ❝✐r❝✉♥s❝r✐t❛s ❛ ✉♠ ❝✉❜♦✱ ❛ ✉♠ t❡tr❛❡❞r♦✱ ❛ ✉♠ ♦❝t❛❡❞r♦✱ ❛ ✉♠ ❞♦❞❡❝❛❡❞r♦ ❡ ❛ ✉♠ ✐❝♦s❛❡❞r♦✳
❋✐❣✉r❛ ✶✳✸✿ ▼♦❞❡❧♦ ❞❡ ❑❡♣❧❡r
❖ ♠♦❞❡❧♦ ❞❡ ❑❡♣❧❡r s❡ ✐♥✐❝✐❛ ❝♦♠ ✉♠❛ ❡s❢❡r❛ ❡①t❡r♥❛✱ q✉❡ r❡♣r❡s❡♥t❛ ❛ ór❜✐t❛ ❞❡ ❙❛t✉r♥♦✱ ❞❡♥tr♦ ❞❡st❛ s❡ ✐♥s❝r❡✈❡✱ s✉❝❡ss✐✈❛♠❡♥t❡✿ ✉♠ ❝✉❜♦✱ ❛ ❡s❢❡r❛ ❞❡ ❏ú♣✐t❡r✱ ✉♠ t❡tr❛❡❞r♦✱ ❛ ❡s❢❡r❛ ❞❡ ▼❛rt❡✱ ✉♠ ❞♦❞❡❝❛❡❞r♦✱ ❛ ❡s❢❡r❛ ❞❛ ❚❡rr❛✱ ✉♠ ♦❝t❛❡❞r♦ ❡ ✜♥❛❧♠❡♥t❡ ❛ ❡s❢❡r❛ ❞❡ ▼❡r❝úr✐♦✱ ❝♦♠♦ ♠♦str❛ ❛ ✜❣✉r❛ ✶✳✸✳
❍♦❥❡ ♦ ❡st✉❞♦ ❞♦s só❧✐❞♦s ♣❧❛tô♥✐❝♦s é ♠❛✐s t♦♣♦❧ó❣✐❝♦ ❝♦♠♦ ✈❡r❡♠♦s ♥♦s tó♣✐❝♦s ❛ s❡❣✉✐r✳
✶✳✷ P♦❧✐❡❞r♦s ❡ ♦ ❚❡♦r❡♠❛ ❞❡ ❊✉❧❡r
◆❡st❛ s❡çã♦ ❛❜♦r❞❛r❡♠♦s ❛❧❣✉♠❛s ❞❡✜♥✐çõ❡s ❡ t❡♦r❡♠❛s ✐♠♣♦rt❛♥t❡s ♥♦ ❡st✉❞♦ ❞♦s ♣♦❧✐❡❞r♦s✱ ❡st❡s s❡rã♦ ❛♣r❡s❡♥t❛❞♦s ❞❡ ❢♦r♠❛ ♠❛✐s ❝♦♠♣❧❡t❛ ♣❛r❛ q✉❡ ♥ã♦ ❤❛❥❛ ✉♠❛ ❞✉❛❧✐❞❛❞❡ ❞❡ ✐♥t❡r♣r❡t❛çõ❡s✳ ❆ss✐♠✱ s❡❣✉♥❞♦ ▲✐♠❛ ❡t✳ ❛❧✳ ✭✷✵✵✻✱ ♣✳ ✷✽✸✮✱ ♣♦❞❡✲s❡ ❞❡✜♥✐r ♣♦❧✐❡❞r♦ ❝♦♠♦ s❡♥❞♦
❬✳✳✳❪ ✉♠❛ r❡✉♥✐ã♦ ❞❡ ✉♠ ♥ú♠❡r♦ ✜♥✐t♦ ❞❡ ♣♦❧í❣♦♥♦s ♣❧❛♥♦s ❝❤❛♠❛❞♦s ❢❛❝❡s ♦♥❞❡✿
❛✮ ❈❛❞❛ ❧❛❞♦ ❞❡ ✉♠ ❞❡ss❡s ♣♦❧í❣♦♥♦s é t❛♠❜é♠ ❧❛❞♦ ❞❡ ✉♠✱ ❡ ❛♣❡♥❛s ✉♠✱ ♦✉tr♦ ♣♦❧í❣♦♥♦✳
❜✮ ❆ ✐♥t❡rs❡çã♦ ❞❡ ❞✉❛s ❢❛❝❡s q✉❛✐sq✉❡r ♦✉ é ✉♠ ❧❛❞♦ ❝♦♠✉♠✱ ♦✉ é ✉♠ ✈ért✐❝❡ ♦✉ é ✈❛③✐❛✳
❈❛❞❛ ❧❛❞♦ ❞❡ ✉♠ ♣♦❧í❣♦♥♦✱ ❝♦♠✉♠ ❛ ❡①❛t❛♠❡♥t❡ ❞✉❛s ❢❛❝❡s✱ é ❝❤❛♠❛❞♦ ✉♠❛ ❛r❡st❛ ❞♦ ♣♦❧✐❡❞r♦ ❡ ❝❛❞❛ ✈ért✐❝❡ ❞❡ ✉♠❛ ❢❛❝❡ é ✉♠ ✈ért✐❝❡ ❞♦ ♣♦❧✐✲ ❡❞r♦✳
❝✮ ➱ s❡♠♣r❡ ♣♦ssí✈❡❧ ✐r ❞❡ ✉♠ ♣♦♥t♦ ❞❡ ✉♠❛ ❢❛❝❡ ❛ ✉♠ ♣♦♥t♦ ❞❡ q✉❛❧✲ q✉❡r ♦✉tr❛✱ s❡♠ ♣❛ss❛r ♣♦r ♥❡♥❤✉♠ ✈ért✐❝❡ ✭♦✉ s❡❥❛✱ ❝r✉③❛♥❞♦ ❛♣❡♥❛s ❛r❡st❛s✮✳
❚♦❞♦ ♣♦❧✐❡❞r♦ ✭♥♦ s❡♥t✐❞♦ ❞❛ ❞❡✜♥✐çã♦ ❛❝✐♠❛✮✱ ❧✐♠✐t❛ ✉♠❛ r❡❣✐ã♦ ❞♦ ❡s♣❛ç♦ ❝❤❛♠❛❞❛ ❞❡ ✐♥t❡r✐♦r ❞❡ss❡ ♣♦❧✐❡❞r♦✳
▲♦❣♦✱ s❡❣✉♥❞♦ ❡st❛ ❞❡✜♥✐çã♦✱ ♦s só❧✐❞♦s r❡♣r❡s❡♥t❛❞♦s ❞❛ ✜❣✉r❛ ✶✳✹✷sã♦ ♣♦❧✐❡❞r♦s✳
❋✐❣✉r❛ ✶✳✹✿ P♦❧✐❡❞r♦ ❝♦♥✈❡①♦ ❡ ♥ã♦ ❝♦♥✈❡①♦
✷❋✐❣✉r❛ ❛♣r❡s❡♥t❛❞❛ ♥❛ t❡❧❛ ❞♦ ●❡♦❣❡❜r❛✳ ▼✉✐t❛s ✜❣✉r❛s ❛♣r❡s❡♥t❛❞❛s ♥❡st❛ ♣❡sq✉✐s❛ s❡rã♦ ❝r✐❛❞❛s
❝♦♠ ❡st❡ s♦❢t✇❛r❡✳
❆✐♥❞❛✱ s❡❣✉♥❞♦ ▲✐♠❛ ❡t✳ ❛❧✳ ✭✷✵✵✻✮✱ ♣♦❞❡✲s❡ ❛✜r♠❛r q✉❡ ✉♠ ♣♦❧✐❡❞r♦ é ❝♦♥✈❡①♦ s❡ ♦ s❡✉ ✐♥t❡r✐♦r t❛♠❜é♠ ❢♦r ❝♦♥✈❡①♦✳ P❛r❛ ♠❡❧❤♦r ❝♦♠♣r❡❡♥sã♦ ❞❡st❛ ❞❡✜♥✐çã♦✱ ♣♦❞❡✲s❡ ❞❡❞✉③✐r q✉❡ ✉♠ ♣♦❧✐❡❞r♦ é ❝♦♥✈❡①♦ s❡ ❢♦r ♣♦ssí✈❡❧ tr❛ç❛r ✉♠❛ r❡t❛ q✉❛❧q✉❡r ✭♥ã♦ ♣❛r❛❧❡❧❛ ❛ ♥❡♥❤✉♠❛ ❞❡ s✉❛s ❢❛❝❡s✮✱ ❡st❛ ♦ ✐♥t❡r❝❡♣t❛r✱ ♥♦ ♠á①✐♠♦✱ ❡♠ ❞♦✐s ♣♦♥t♦s❀ ❝❛s♦ ❝♦♥trár✐♦ ❞✐③❡♠♦s q✉❡ ♦ ♣♦❧✐❡❞r♦ é ♥ã♦ ❝♦♥✈❡①♦✱ ❝♦♠♦ é ♣♦ssí✈❡❧ ♦❜s❡r✈❛r ♥❛ ✜❣✉r❛ ✶✳✹✳
❖✉tr❛ ❞❡✜♥✐çã♦ ❞❡ ♣♦❧✐❡❞r♦s ❝♦♥✈❡①♦s é ❛♣r❡s❡♥t❛❞❛ ♣♦r ❉♦❧❝❡ ❡ P♦♠♣❡♦ ✭✶✾✾✸✱ ♣✳✶✷✹✮✱ ❝✉❥♦ ❡♥✉♥❝✐❛❞♦ é✿
❈♦♥s✐❞❡r❡♠♦s ✉♠ ♥ú♠❡r♦ ✜♥✐t♦ ♥ ✭n≥4✮ ❞❡ ♣♦❧í❣♦♥♦s ♣❧❛♥♦s ❝♦♥✈❡①♦s
✭♦✉ r❡❣✐õ❡s ♣♦❧✐❣♦♥❛✐s ❝♦♥✈❡①❛s✮ t❛✐s q✉❡✿ ❛✮ ❞♦✐s ♣♦❧í❣♦♥♦s ♥ã♦ ❡stã♦ ♥✉♠ ♠❡s♠♦ ♣❧❛♥♦❀
❜✮ ❝❛❞❛ ❧❛❞♦ ❞❡ ♣♦❧í❣♦♥♦ é ❝♦♠✉♠ ❛ ❞♦✐s ❡ s♦♠❡♥t❡ ❞♦✐s ♣♦❧í❣♦♥♦s❀ ❝✮ ♦ ♣❧❛♥♦ ❞❡ ❝❛❞❛ ♣♦❧í❣♦♥♦ ❞❡✐①❛ ♦s ❞❡♠❛✐s ♣♦❧í❣♦♥♦s ♥✉♠ ♠❡s♠♦ s❡♠✐✲ ❡s♣❛ç♦✳
◆❡ss❛s ❝♦♥❞✐çõ❡s✱ ✜❝❛♠ ❞❡t❡r♠✐♥❛❞♦s ♥ s❡♠✐✲❡s♣❛ç♦s✱ ❝❛❞❛ ✉♠ ❞♦s q✉❛✐s t❡♠ ♦r✐❣❡♠ ♥♦ ♣❧❛♥♦ ❞❡ ✉♠ ♣♦❧í❣♦♥♦ ❡ ❝♦♥té♠ ♦s r❡st❛♥t❡s✳ ❆ ✐♥t❡rs❡❝çã♦ ❞❡ss❡s s❡♠✐✲❡s♣❛ç♦s é ❝❤❛♠❛❞♦ ♣♦❧✐❡❞r♦ ❝♦♥✈❡①♦✳
❊♠ q✉❛❧q✉❡r ♣♦❧✐❡❞r♦✱ ❞❡♥♦♠✐♥❛✲s❡ ❢❛❝❡s ❞♦ ♣♦❧✐❡❞r♦ ❛ ❝❛❞❛ ✉♠❛ ❞❡ s✉❛s r❡❣✐õ❡s ♣♦❧✐❣♦♥❛✐s✱ ❡♥q✉❛♥t♦ q✉❡ ❛ ✐♥t❡rs❡❝çã♦ ❞❡ ❞✉❛s ❞❡ s✉❛s ❢❛❝❡s r❡❝❡❜❡ ♦ ♥♦♠❡ ❞❡ ❛r❡st❛s ❞♦ ♣♦❧✐❡❞r♦✳ ❏á ♦ ❡♥❝♦♥tr♦ ❞❡ três ♦✉ ♠❛✐s ❛r❡st❛s ❝❤❛♠❛✲s❡ ✈ért✐❝❡s ❞♦ ♣♦❧✐❡❞r♦✳ ❘❡♣r❡s❡♥✲ t❛r❡♠♦s ♦ ♥ú♠❡r♦ ❞❡ ❢❛❝❡s✱ ❞❡ ❛r❡st❛s ❡ ❞❡ ✈ért✐❝❡s ♣♦r F✱ A ❡ V✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳
❙❡❣✉♥❞♦ ▲✐♠❛ ❡t✳ ❛❧✳ ✭✷✵✵✻✱ ♣✳✷✽✹✮✱
❬✳✳✳❪ ❝♦♠♦ ❛s ❢❛❝❡s ♣♦❞❡♠ s❡r ❞❡ ❣ê♥❡r♦s ❞✐❢❡r❡♥t❡s✱ r❡♣r❡s❡♥t❛r❡♠♦s ♣♦r
Fn(n≥3) ♦ ♥ú♠❡r♦ ❞❡ ❢❛❝❡s q✉❡ ♣♦ss✉❡♠ ♥ ❧❛❞♦s✳ ❉❛ ♠❡s♠❛ ❢♦r♠❛✱
❝♦♠♦ ♦s ✈ért✐❝❡s t❛♠❜é♠ ♣♦❞❡♠ s❡r ❞❡ ❣ê♥❡r♦s ❞✐❢❡r❡♥t❡s✱ r❡♣r❡s❡♥t❛✲ r❡♠♦s ♣♦r Vn ♦ ♥ú♠❡r♦ ❞❡ ✈ért✐❝❡s ♥♦s q✉❛✐s ❝♦♥❝♦rr❡♠ ♥ ❛r❡st❛s✱ ❡
♦❜s❡r✈❡ q✉❡✱ ♣❡❧♦ ✐t❡♠ ✭❜✮ ❞❛ ❞❡✜♥✐çã♦ ❞♦ ♣♦❧✐❡❞r♦✱ ❝❛❞❛ ✈ért✐❝❡ é ✉♠ ♣♦♥t♦ ❝♦♠✉♠ ❛ três ♦✉ ♠❛✐s ❛r❡st❛s✳
❆ss✐♠✱ é ♣♦ssí✈❡❧ ❞❡❞✉③✐r ❛s r❡❧❛çõ❡s ❛❜❛✐①♦✿
F =F3+F4+F5+...+Fn
V =V3+V4+V5+...+Vn
❈♦♠♦ ❛s ❢❛❝❡s q✉❡ ❢♦r♠❛♠ ♦s ♣♦❧✐❡❞r♦s ♣♦❞❡♠ s❡r ❞❡ t✐♣♦s ❞✐❢❡r❡♥t❡s✱ ❝❛❞❛ ✉♠ ❞❡❧❡s ♣♦❞❡♠ ♣♦ss✉✐r ✉♠❛ q✉❛♥t✐❞❛❞❡ ❞❡ ❛r❡st❛s ❞✐❢❡r❡♥t❡s✳ ❆ss✐♠✱ s❡ q✉✐s❡r♠♦s ❝♦♥tá✲❧❛s ❞❡✈❡♠♦s ♠✉❧t✐♣❧✐❝❛r ♦ ♥ú♠❡r♦ ❞❡ ❢❛❝❡s tr✐❛♥❣✉❧❛r❡s ♣♦r ✸✱ ♦ ♥ú♠❡r♦ ❞❡ ❢❛❝❡s q✉❛❞r❛♥✲ ❣✉❧❛r❡s ♣♦r ✹✱ ♦ ♥ú♠❡r♦ ❞❡ ❢❛❝❡s ♣❡♥t❛❣♦♥❛✐s ♣♦r ✺ ❡ ❛ss✐♠ s✉❝❡ss✐✈❛♠❡♥t❡❀ ❡♠ s❡❣✉✐❞❛✱
s♦♠❛♠♦s ♦s r❡s✉❧t❛❞♦s✳ P♦ré♠✱ ❛♦ ❢❛③❡r ✐ss♦ ❡st❛r❡♠♦s ❝♦♥t❛♥❞♦ ❝❛❞❛ ❛r❡st❛ ❞✉❛s ✈❡③❡s✱ ❥á q✉❡ ❡st❛ é ♦r✐❣✐♥❛❞❛ ❞❛ ✐♥t❡rs❡❝çã♦ ❞❡ ❞✉❛s ❢❛❝❡s ❞✐st✐♥t❛s✳ ❆ss✐♠✱ ♦ ♥ú♠❡r♦ ❞❡ ❛r❡st❛s ❞❡ q✉❛❧q✉❡r ♣♦❧✐❡❞r♦ ♣♦❞❡ s❡r r❡♣r❡s❡♥t❛❞♦ ♣♦r
A = 1
2 ·(3F3 + 4F4+ 5F5+ 6F6+...+nFn).
▼✉❧t✐♣❧✐❝❛♥❞♦✲s❡ ❛♠❜♦s ♦s ♠❡♠❜r♦s ❞❛ ✐❣✉❛❧❞❛❞❡ ♣♦r2✱ ♦❜t❡r❡♠♦s ❛ r❡❧❛çã♦
2A= 3F3+ 4F4+ 5F5+ 6F6+...+nFn.
❆ ❝♦♥t❛❣❡♠ ❞♦ ♥ú♠❡r♦ ❞❡ ❛r❡st❛s t❛♠❜é♠ ♣♦❞❡ s❡r r❡❛❧✐③❛❞❛ ✉t✐❧✐③❛♥❞♦ ♦s ✈ért✐✲ ❝❡s ❞♦ ♣♦❧✐❡❞r♦✳ ❈❛❞❛ ✉♠ ❞❡st❡s é ♦ ❡♥❝♦♥tr♦ ❞❡ três ♦✉ ♠❛✐s ❛r❡st❛s❀ ❧♦❣♦✱ s❡ ❝♦♥t❛r♠♦s q✉❛♥t❛s ❛r❡st❛s ❝♦♥❝♦rr❡♠ ❡♠ ❝❛❞❛ ✈ért✐❝❡ ❡ s♦♠❛r♠♦s ♦s r❡s✉❧t❛❞♦s✱ ♦❜t❡r❡♠♦s ♦ ❞♦❜r♦ ❞♦ ♥ú♠❡r♦ ❞❡ ❛r❡st❛s ✭♣♦rq✉❡ ❝❛❞❛ ❛r❡st❛ t❡rá s✐❞♦ ❝♦♥t❛❞❛ ❞✉❛s ✈❡③❡s✿ ❡♠ ✉♠ ❡①tr❡♠♦ ❡ ♥♦ ♦✉tr♦✮✳ ▲♦❣♦✱ s❡❣✉❡ q✉❡
A= 1
2·(3V3+ 4V4+ 5V5+ 6V6+...+nVn).
▼✉❧t✐♣❧✐❝❛♥❞♦✲s❡ ❛♠❜♦s ♦s ❧❛❞♦s ❞❛ ✐❣✉❛❧❞❛❞❡ ♣♦r2✱ t❡r❡♠♦s ❛ r❡❧❛çã♦
2A= 3V3+ 4V4 + 5V5+...+nVn.
❱❡❥❛ ❛✐♥❞❛ q✉❡ ♣♦❞❡♠♦s ❞❡❞✉③✐r ❞✉❛s ❞❡s✐❣✉❛❧❞❛❞❡s ❛ ♣❛rt✐r ❞❡ss❛s ❡q✉❛çõ❡s✳ ❆ ♣r✐♠❡✐r❛ ❡q✉❛çã♦ ❣❡r❛ ❛ ❞❡s✐❣✉❛❧❞❛❞❡
2A= 3F3+ 4F4 + 5F5+ 6F6+...+nFn
= 3(F3+F4 +F5+F6+...+Fn) +F4+ 2F5+ 3F6+...+ (n−1)Fn
= 3F +F4+ 2F5+ 3F6+...+ (n−1)Fn
≥3F
❉❛ s❡❣✉♥❞❛ ❡q✉❛çã♦ ❞❡❞✉③✲s❡ q✉❡✿
2A = 3V3+ 4V4+ 5V5+...+nVn
= 3(V3+V4+V5+V6+...+Vn) +V4+ 2V5+ 3V6+...+ (n−1)Vn
= 3V +V4 + 2V5+ 3V6+...+ (n−1)Vn
≥3V
❆ ✐❣✉❛❧❞❛❞❡2A= 3F s♦♠❡♥t❡ é ✈á❧✐❞❛ s❡ ♦ ♣♦❧✐❡❞r♦ ♣♦ss✉✐r ❛♣❡♥❛s ❢❛❝❡s tr✐❛♥❣✉✲
❧❛r❡s✱ s❡♥❞♦ q✉❡ ♥❡st❡ ❝❛s♦ t❡r❡♠♦sF4 =F5 =F6 =...=Fn+1 = 0, n >3✳ ❆♥❛❧♦❣❛♠❡♥t❡✱ ❛ ✐❣✉❛❧❞❛❞❡2A = 3V só é ✈❡r❞❛❞❡✐r❛ s❡ ❡♠ t♦❞♦s ♦s ✈ért✐❝❡ ❝♦♥❝♦rr❡r❡♠ ❛♣❡♥❛s três ❛r❡s✲
t❛s✱ s❡♥❞♦ q✉❡ ♥❡st❡ ❝❛s♦ t❡r❡♠♦sV4 =V5 =V6 =...=Vn+1 = 0, n >3✳
❆❣♦r❛✱ ❡♥✉♥❝✐❛r❡♠♦s ♦ ❢♦❝♦ ❝❡♥tr❛❧ ❞❡st❛ s❡çã♦ ❛♦ t❡♦r❡♠❛ ♦✉ r❡❧❛çã♦ ❞❡ ❊✉✲ ❧❡r✳ ❙❡❣✉♥❞♦ ❉♦❧❝❡ ❡ P♦♠♣❡♦ ✭✶✾✾✸✱ ♣✳✶✷✹✮✱ ✏P❛r❛ t♦❞♦ ♣♦❧✐❡❞r♦ ❝♦♥✈❡①♦✱ ♦✉ ♣❛r❛ s✉❛ s✉♣❡r❢í❝✐❡✱ ✈❛❧❡ ❛ r❡❧❛çã♦
V −A+F = 2,
❡♠ q✉❡ ❱ é ♦ ♥ú♠❡r♦ ❞❡ ✈ért✐❝❡✱ ❆ é ♦ ♥ú♠❡r♦ ❞❡ ❛r❡st❛s ❡ ❋ é ♦ ♥ú♠❡r♦ ❞❡ ❢❛❝❡s ❞♦ ♣♦❧✐❡❞r♦✑✳
❉❡♠♦♥str❛çã♦✿ ❙❡rá ❛♣r❡s❡♥t❛❞♦ ❛ ❞❡♠♦♥str❛çã♦ ❞♦ ❚❡♦r❡♠❛ ❞❡ ❊✉❧❡r s❡❣✉♥❞♦ ❉♦❧❝❡ ❡ P♦♠♣❡♦ ✭✶✾✾✸✮✳ ❊st❛ s❡rá ❞✐✈✐❞✐❞❛ ❡♠ ❞✉❛s ❡t❛♣❛s✳
✶❛ ❡t❛♣❛✿ ❊♠ ❝❛rát❡r ♣r❡❧✐♠✐♥❛r✱ ♠♦str❛r❡♠♦s ♣❡❧♦ Pr✐♥❝í♣✐♦ ❞❡ ■♥❞✉çã♦ ▼❛✲
t❡♠át✐❝❛ ✭P■▼✮ s♦❜r❡ ♦ ♥ú♠❡r♦ ❞❡ ❢❛❝❡s q✉❡✱ ♣❛r❛ ✉♠❛ s✉♣❡r❢í❝✐❡ ♣♦❧✐é❞r✐❝❛ ❧✐♠✐t❛❞❛ ❝♦♥✈❡①❛ ❛❜❡rt❛✱ ✈❛❧❡ ❛ r❡❧❛çã♦
Va−Aa+Fa= 1,
♦♥❞❡ Va✱ Aa ❡ Fa r❡♣r❡s❡♥t❛ ♦ ♥ú♠❡r♦ ❞❡ ✈ért✐❝❡s✱ ❛r❡st❛ ❡ ❢❛❝❡s ❞❛ s✉♣❡r❢í❝✐❡ ♣♦❧✐é❞r✐❝❛
❧✐♠✐t❛❞❛ ❛❜❡rt❛✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ✐✮ P❛r❛ Fa = 1✳
◆❡st❡ ❝❛s♦✱ tr❛t❛✲s❡ ❞❡ ✉♠❛ ú♥✐❝❛ s✉♣❡r❢í❝✐❡✱ ♦✉ s❡❥❛✱ ✉♠ ♣♦❧í❣♦♥♦ ♣❧❛♥♦ ❝♦♥✈❡①♦ ❞❡ ♥ ❧❛❞♦s✳ ▲♦❣♦✱ ❡st❡ ❛✐♥❞❛ ♣♦ss✉✐ ♥ ✈ért✐❝❡s✳ ❖✉ s❡❥❛✱ Aa = n ❡ Va = n✳ ❖❜s❡r✈❡
❛❧❣✉♠❛s s✉♣❡r❢í❝✐❡s✿
❋✐❣✉r❛ ✶✳✺✿ P♦❧✐❣♦♥♦s ✕ r❡❧❛çã♦ ❡♥tr❡ ✈ért✐❝❡s ❡ ❛r❡st❛s
