❯◆■❱❊❘❙■❉❆❉❊ ❋❊❉❊❘❆▲ ❉❊ ❯❇❊❘▲➶◆❉■❆ ❋❆❈❯▲❉❆❉❊ ❉❊ ❈■✃◆❈■❆ ❉❆ ❈❖▼P❯❚❆➬➹❖
P❘❖●❘❆▼❆ ❉❊ PÓ❙✲●❘❆❉❯❆➬➹❖ ❊▼ ❈■✃◆❈■❆ ❉❆ ❈❖▼P❯❚❆➬➹❖
▼■◆❊❘❆➬➹❖ ❉❊ P❘❊❋❊❘✃◆❈■❆❙ ❈❖◆❚❊❳❚❯❆■❙ ❋❯❩❩❨
❏❯▲■❊❚❊ ❆P❆❘❊❈■❉❆ ❘❆▼❖❙ ❈❖❙❚❆
❯◆■❱❊❘❙■❉❆❉❊ ❋❊❉❊❘❆▲ ❉❊ ❯❇❊❘▲➶◆❉■❆ ❋❆❈❯▲❉❆❉❊ ❉❊ ❈■✃◆❈■❆ ❉❆ ❈❖▼P❯❚❆➬➹❖
P❘❖●❘❆▼❆ ❉❊ PÓ❙✲●❘❆❉❯❆➬➹❖ ❊▼ ❈■✃◆❈■❆ ❉❆ ❈❖▼P❯❚❆➬➹❖
❏❯▲■❊❚❊ ❆P❆❘❊❈■❉❆ ❘❆▼❖❙ ❈❖❙❚❆
▼■◆❊❘❆➬➹❖ ❉❊ P❘❊❋❊❘✃◆❈■❆❙ ❈❖◆❚❊❳❚❯❆■❙ ❋❯❩❩❨
❉✐ss❡rt❛çã♦ ❞❡ ▼❡str❛❞♦ ❛♣r❡s❡♥t❛❞❛ à ❋❛❝✉❧❞❛❞❡ ❞❡ ❈✐ê♥✲ ❝✐❛ ❞❛ ❈♦♠♣✉t❛çã♦ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❯❜❡r❧â♥❞✐❛✱ ▼✐♥❛s ●❡r❛✐s✱ ❝♦♠♦ ♣❛rt❡ ❞♦s r❡q✉✐s✐t♦s ❡①✐❣✐❞♦s ♣❛r❛ ♦❜✲ t❡♥çã♦ ❞♦ tít✉❧♦ ❞❡ ▼❡str❡ ❡♠ ❈✐ê♥❝✐❛ ❞❛ ❈♦♠♣✉t❛çã♦✳ ➪r❡❛ ❞❡ ❝♦♥❝❡♥tr❛çã♦✿ ❇❛♥❝♦ ❞❡ ❉❛❞♦s✳
❖r✐❡♥t❛❞♦r❛✿
Pr♦❢❛✳ ❉r❛✳ ❙❛♥❞r❛ ❆♣❛r❡❝✐❞❛ ❞❡ ❆♠♦
❯◆■❱❊❘❙■❉❆❉❊ ❋❊❉❊❘❆▲ ❉❊ ❯❇❊❘▲➶◆❉■❆ ❋❆❈❯▲❉❆❉❊ ❉❊ ❈■✃◆❈■❆ ❉❆ ❈❖▼P❯❚❆➬➹❖
P❘❖●❘❆▼❆ ❉❊ PÓ❙✲●❘❆❉❯❆➬➹❖ ❊▼ ❈■✃◆❈■❆ ❉❆ ❈❖▼P❯❚❆➬➹❖
❖s ❛❜❛✐①♦ ❛ss✐♥❛❞♦s✱ ♣♦r ♠❡✐♦ ❞❡st❡✱ ❝❡rt✐✜❝❛♠ q✉❡ ❧❡r❛♠ ❡ r❡❝♦♠❡♥❞❛♠ ♣❛r❛ ❛ ❋❛✲ ❝✉❧❞❛❞❡ ❞❡ ❈✐ê♥❝✐❛ ❞❛ ❈♦♠♣✉t❛çã♦ ❛ ❛❝❡✐t❛çã♦ ❞❛ ❞✐ss❡rt❛çã♦ ✐♥t✐t✉❧❛❞❛ ✏▼✐♥❡r❛çã♦ ❞❡ Pr❡❢❡rê♥❝✐❛s ❈♦♥t❡①t✉❛✐s ❋✉③③②✑ ♣♦r ❏✉❧✐❡t❡ ❆♣❛r❡❝✐❞❛ ❘❛♠♦s ❈♦st❛ ❝♦♠♦ ♣❛rt❡ ❞♦s r❡q✉✐s✐t♦s ❡①✐❣✐❞♦s ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞♦ tít✉❧♦ ❞❡ ▼❡str❡ ❡♠ ❈✐ê♥❝✐❛ ❞❛ ❈♦♠✲ ♣✉t❛çã♦✳
❯❜❡r❧â♥❞✐❛✱ ✷✸ ❞❡ ✵✺ ❞❡ ✷✵✶✹
❖r✐❡♥t❛❞♦r❛✿
Pr♦❢❛✳ ❉r❛✳ ❙❛♥❞r❛ ❆♣❛r❡❝✐❞❛ ❞❡ ❆♠♦ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❯❜❡r❧â♥❞✐❛
❇❛♥❝❛ ❊①❛♠✐♥❛❞♦r❛✿
Pr♦❢❛✳ ❉r❛✳ ▼❛r✐❧❞❡ ❚❡r❡③✐♥❤❛ Pr❛❞♦ ❙❛♥t♦s ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❙ã♦ ❈❛r❧♦s
❯◆■❱❊❘❙■❉❆❉❊ ❋❊❉❊❘❆▲ ❉❊ ❯❇❊❘▲➶◆❉■❆ ❋❆❈❯▲❉❆❉❊ ❉❊ ❈■✃◆❈■❆ ❉❆ ❈❖▼P❯❚❆➬➹❖
P❘❖●❘❆▼❆ ❉❊ PÓ❙✲●❘❆❉❯❆➬➹❖ ❊▼ ❈■✃◆❈■❆ ❉❆ ❈❖▼P❯❚❆➬➹❖
❉❛t❛✿ ✷✸ ❞❡ ✵✺ ❞❡ ✷✵✶✹
❆✉t♦r✿ ❏✉❧✐❡t❡ ❆♣❛r❡❝✐❞❛ ❘❛♠♦s ❈♦st❛
❚ít✉❧♦✿ ▼✐♥❡r❛çã♦ ❞❡ Pr❡❢❡rê♥❝✐❛s ❈♦♥t❡①t✉❛✐s ❋✉③③② ❋❛❝✉❧❞❛❞❡✿ ❋❛❝✉❧❞❛❞❡ ❞❡ ❈✐ê♥❝✐❛ ❞❛ ❈♦♠♣✉t❛çã♦
●r❛✉✿ ▼❡str❛❞♦
❋✐❝❛ ❣❛r❛♥t✐❞♦ à ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❯❜❡r❧â♥❞✐❛ ♦ ❞✐r❡✐t♦ ❞❡ ❝✐r❝✉❧❛çã♦ ❡ ✐♠♣r❡ssã♦ ❞❡ ❝ó♣✐❛s ❞❡st❡ ❞♦❝✉♠❡♥t♦ ♣❛r❛ ♣r♦♣ós✐t♦s ❡①❝❧✉s✐✈❛♠❡♥t❡ ❛❝❛❞ê♠✐❝♦s✱ ❞❡s❞❡ q✉❡ ♦ ❛✉t♦r s❡❥❛ ❞❡✈✐❞❛♠❡♥t❡ ✐♥❢♦r♠❛❞♦✳
❆✉t♦r
❖ ❆❯❚❖❘ ❘❊❙❊❘❱❆ P❆❘❆ ❙■ ◗❯❆▲◗❯❊❘ ❖❯❚❘❖ ❉■❘❊■❚❖ ❉❊ P❯❇▲■❈❆➬➹❖ ❉❊❙❚❊ ❉❖❈❯▼❊◆❚❖✱ ◆➹❖ P❖❉❊◆❉❖ ❖ ▼❊❙▼❖ ❙❊❘ ■▼P❘❊❙❙❖ ❖❯ ❘❊P❘❖✲ ❉❯❩■❉❖✱ ❙❊❏❆ ◆❆ ❚❖❚❆▲■❉❆❉❊ ❖❯ ❊▼ P❆❘❚❊❙✱ ❙❊▼ ❆ P❊❘▼■❙❙➹❖ ❊❙❈❘■❚❆ ❉❖ ❆❯❚❖❘✳
❝
❉❡❞✐❝❛tór✐❛
❆❣r❛❞❡❝✐♠❡♥t♦s
❆ ❉❡✉s✱ ♣♦r ♠❡ ❢♦rt❛❧❡❝❡r ♥♦s ♠♦♠❡♥t♦s ♠❛✐s ❞✐❢í❝❡✐s ♣❡r❝♦rr✐❞♦s ♥❡ss❛ ❝❛♠✐♥❤❛❞❛✳ ❆♦s ♠❡✉s ♣❛✐s ❏♦✈❡♥✐❧t♦♥ ❡ ❘❛✐♠✉♥❞❛✱ ♠❡✉s ✐r♠ã♦s ➱❞❡r✱ ❍❡❧❞❡r ❡ ❍❡❧✐t♦♥✱ ♠❡✉s s♦❜r✐♥❤♦s ❘✉❛♥ ❡ ■s❛❜❡❧❧❛ ❡ ❛s ♠✐♥❤❛s ❝✉♥❤❛❞❛s ❙✐♠♦♥❡ ❡ ❑ê♥✐❛ ♣♦r t❡r❡♠ ♠❡ ❛♣♦✐❛❞♦ ❞✉r❛♥t❡ ❡st❛ ❝❛♠✐♥❤❛❞❛ ❡ ♣♦r ❝♦♠♣r❡❡♥❞❡r❡♠ ❛ ♠✐♥❤❛ ❛✉sê♥❝✐❛ ❡♠ t❛♥t♦s ♠♦♠❡♥t♦s✳
❆ ♠✐♥❤❛ ♦r✐❡♥t❛❞♦r❛ Pr♦❢❛ ❙❛♥❞r❛✱ ♣❡❧❛ ♦♣♦rt✉♥✐❞❛❞❡✱ ♦r✐❡♥t❛çã♦✱ ♣❛❝✐ê♥❝✐❛✱ ❡♥s✐♥❛✲ ♠❡♥t♦s ❡ ♣r♦✜ss✐♦♥❛❧✐s♠♦ ❞✉r❛♥t❡ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡st❡ tr❛❜❛❧❤♦✳ ❊s♣❡❝✐❛❧♠❡♥t❡ ♣♦r t❡r ❛❝r❡❞✐t❛❞♦ ❡♠ ♠✐♠ ❡ ♣❡❧♦ ❝r❡s❝✐♠❡♥t♦ ♣r♦✜ss✐♦♥❛❧ q✉❡ ♠❡ ♣r♦♣♦r❝✐♦♥♦✉ ❞✉r❛♥t❡ ❡st❡ ♣❡rí♦❞♦✳
❆♦s ♠❡✉s t✐♦s ❲❛❣♥❡r ❡ ▲✉❝✐♥é✐❛✱ ♣❡❧♦ ❛♣♦✐♦ ♥♦ ♠♦♠❡♥t♦ q✉❡ ♣r❡❝✐s❡✐ ♥♦ ✐♥í❝✐♦ ❞❡st❛ ❡t❛♣❛✳ ❆❣r❛❞❡❝❡♥❞♦ ❡❧❡s✱ ❛❣r❛❞❡ç♦ ❛ t♦❞❛ ♠✐♥❤❛ ❢❛♠í❧✐❛ ♣❡❧♦ ❛♣♦✐♦✱ ♦r❛çõ❡s ❡ ✐♥❝❡♥t✐✈♦ ❞✉r❛♥t❡ ❡st❛ ❝❛♠✐♥❤❛❞❛✳
❆ t♦❞♦s ♦s ♠❡✉s ✈❡r❞❛❞❡✐r♦s ❛♠✐❣♦s q✉❡ ♠❡s♠♦ ❧♦♥❣❡ s❡♠♣r❡ ❡st✐✈❡r❛♠ ❝♦♠✐❣♦✳ ❊♠ ❡s♣❡❝✐❛❧ ❛ ■s❛❜❡❧ ❡ ▲❛❡rt❡ ❆❧❧❛♥✱ s❡♠ ✈♦❝ês ♦ ✐♥í❝✐♦ ❞❡st❡ tr❛❜❛❧❤♦ ♥ã♦ s❡r✐❛ ♣♦ssí✈❡❧✳ ❆♦s ♠❡✉s ♠❡str❡s ●✐✉❧✐❛♥♦ ❱✐❛♥❛ ❡ ❋❡❧✐♣❡ ❈és❛r ♣♦r t❡r❡♠ ❛❝r❡❞✐t❛❞♦ ❡♠ ♠✐♠✳ ❊ ✉♠ ❛❣r❛❞❡❝✐♠❡♥t♦ ❡s♣❡❝✐❛❧ ❛ ♠✐♥❤❛ ❛♠✐❣❛ ❙❛♥t❛♥❛ ❈♦✉t✐♥❤♦ q✉❡ ♠❡s♠♦ s❡♠ ♠❡ ❝♦♥❤❡❝❡r ♠❡ ❛❝♦❧❤❡✉ ♥♦ ✐♥í❝✐♦ ❞❡st❛ ❝❛♠✐♥❤❛❞❛✳
❆♦s ♠❡✉s ❝♦❧❡❣❛s ❞❡ ❧❛❜♦r❛tór✐♦✱ ♠❡✉s ❝♦♠♣❛♥❤❡✐r♦s ❞❡ ❧✉t❛ ❞✐ár✐❛ q✉❡ s❡ t♦r♥❛r❛♠ ✈❡r❞❛❞❡✐r♦s ❛♠✐❣♦s✳ ❖❜r✐❣❛❞❛ ♣❡❧♦ ✐♥❝❡♥t✐✈♦ ❡ ❝♦♦♣❡r❛çã♦ ❞✉r❛♥t❡ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡st❡ tr❛❜❛❧❤♦✳ ❊♠ ❡s♣❡❝✐❛❧ ❛♦ ❘♦♠❡rs♦♥✱ ❚❛✛❛r❡❧✱ ❘❛❢❛❡❧✱ ❏❛q✉❡❧✐♥❡✱ ❏♦✐❝②✱ ▲✉❝✐❛♥❡✱ ❉❛♥✐✱ ❈rí❝✐❛✱ ▼❛r❝♦s✱ ●✉✐❧❤❡r♠❡✱ ▼②❧❧❡♥❡ ❡ ❈r✐s✳
❆s ♠✐♥❤❛s ❛♠✐❣❛s ●❡②❝②✱ ❈❧❡✐❛♥❡ ❡ ❊♠❛♥✉❡❧❧❡ q✉❡ ❝♦♠♣❛rt✐❧❤❛r❛♠ ❝♦♠✐❣♦ ✈ár✐♦s ♠♦♠❡♥t♦s í♠♣❛r❡s ❞✉r❛♥t❡ ❡st❡ ♣❡rí♦❞♦✳ ❆❣r❛❞❡ç♦ t❛♠❜é♠ às ♠✐♥❤❛s ❛♠✐❣❛s ▼❛r✐❛♥♥❛✱ ❇r✉♥❛✱ ◆❛tá❧✐❛ ❡ ❈í♥t✐❛ ♣❡❧♦ ❝♦♠♣❛♥❤❡✐r✐s♠♦ ❡ ❛♠✐③❛❞❡ s✐♥❝❡r❛ ❞✉r❛♥t❡ ❡st❛ ❥♦r♥❛❞❛✳
➚ ❋❛♠í❧✐❛ ●PP✲❯❜❡r❧â♥❞✐❛✱ ♣❡❧❛s ♦r❛çõ❡s✱ ✐♥t❡r❝❡ssõ❡s ❡ ❛♠✐③❛❞❡ ❞✉r❛♥t❡ ♦ ❞❡s❡♥✈♦❧✲ ✈✐♠❡♥t♦ ❞❡st❡ tr❛❜❛❧❤♦✳ ❊ ✉♠ ❛❣r❛❞❡❝✐♠❡♥t♦ ❡s♣❡❝✐❛❧ ❛♦ s❡❝r❡tár✐♦ ❞❛ Pós✲●r❛❞✉❛çã♦ ❊r✐s✈❛❧❞♦✱ ♣❡❧♦ ❝❛r✐♥❤♦✱ ❛♠✐③❛❞❡ ❡ ❣❡♥t✐❧❡③❛ q✉❡ s❡♠♣r❡ ♠❡ ❛t❡♥❞❡✉✳
❘❡s✉♠♦
◆♦s ú❧t✐♠♦s ❛♥♦s✱ ♠✉✐t❛s ♣❡sq✉✐s❛s ♥❛ ár❡❛ ❞❡ ♠✐♥❡r❛çã♦ ❞❡ ♣r❡❢❡rê♥❝✐❛s sã♦ ❢♦❝❛❞❛s ♥♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ♠ét♦❞♦s ♣❛r❛ ♠✐♥❡r❛r ✉♠ ♠♦❞❡❧♦ ❞❡ ♣r❡❢❡rê♥❝✐❛ ❛ ♣❛rt✐r ❞❡ r❡♣r❡✲ s❡♥t❛çõ❡s ❞❡ ♣r❡❢❡rê♥❝✐❛s ❝r✐s♣✱ t❛✐s ❝♦♠♦✱ ❝♦♥❥✉♥t♦ ❞❡ ♣❛r❡s ❞❡ t✉♣❧❛s✱ r❛♥❦✐♥❣ ❞❡ t✉♣❧❛s ❡ ❢✉♥çõ❡s s❝♦r❡✳ ◆❡st❛ ♣❡sq✉✐s❛✱ é ❛♣r❡s❡♥t❛❞♦ ♦ ❛❧❣♦r✐t♠♦ ❋✉③③②Pr❡❢▼✐♥❡r✱ ❞❡s❡♥✈♦❧✈✐❞♦ ♣❛r❛ ♠✐♥❡r❛r ✉♠ ♠♦❞❡❧♦ ❞❡ ♣r❡❢❡rê♥❝✐❛ ❝♦♥t❡①t✉❛❧ ❢✉③③② ❛ ♣❛rt✐r ❞❡ ✉♠❛ r❡♣r❡s❡♥t❛çã♦ ❞❡ ♣r❡❢❡rê♥❝✐❛ ❞❡♥♦♠✐♥❛❞❛ r❡❧❛çã♦ ❞❡ ♣r❡❢❡rê♥❝✐❛ ❢✉③③②✳ ❊st❡ t✐♣♦ ❞❡ r❡♣r❡s❡♥t❛çã♦ é ❝♦♠♣♦st❛ ♣♦r ✉♠ ❝♦♥❥✉♥t♦ ❞❡ tr✐♣❧❛s ❞♦ t✐♣♦ ✭✉,✈,♥✮✱ ♦♥❞❡ ✉ ❡ ✈ sã♦ t✉♣❧❛s ❛✈❛❧✐❛❞❛s
♣❡❧♦ ✉s✉ár✐♦ ❡ ♥ é ♦ ❣r❛✉ ❞❡ ♣r❡❢❡rê♥❝✐❛ ❞❛ t✉♣❧❛ ✉ s♦❜r❡ ❛ t✉♣❧❛ ✈✳
❆s r❡❧❛çõ❡s ❞❡ ♣r❡❢❡rê♥❝✐❛s ❢✉③③② ♣♦ss✐❜✐❧✐t❛♠ ❛✐♥❞❛✱ ♦ ❡st✉❞♦ ❞❛ ❝♦♥s✐stê♥❝✐❛ ❞❛s ♣r❡❢❡rê♥❝✐❛s ❞♦s ✉s✉ár✐♦s ❡ ♥❡st❡ ❝♦♥t❡①t♦✱ sã♦ ❛♣r❡s❡♥t❛❞♦s ❞♦✐s ♠ét♦❞♦s ❞❡ r❡♣❛r❛çã♦ ❞❡ ✐♥❝♦♥s✐stê♥❝✐❛ ❞❡ss❛s r❡❧❛çõ❡s✱ ♥♦♠❡❛❞♦s✿ ❘❛♥❣❡ ❱♦t✐♥❣ ◆ã♦ ■♥❝r❡♠❡♥t❛❧ ❡ ❘❛♥❣❡ ❱♦t✐♥❣ ■♥❝r❡♠❡♥t❛❧✳ ❆♠❜♦s ♦s ♠ét♦❞♦s sã♦ ❜❛s❡❛❞♦s ❡♠ ✉♠❛ té❝♥✐❝❛ ❞❡ s✐st❡♠❛ ❞❡ ✈♦t❛çã♦ ❡ sã♦ ✉t✐❧✐③❛❞♦s ♣❛r❛ r❡♣❛r❛r ❛ ✐♥❝♦♥s✐stê♥❝✐❛ ❞❛s r❡❧❛çõ❡s ❞❡ ♣r❡❢❡rê♥❝✐❛s ❢✉③③② ✐♥❢❡r✐❞❛s ♣❡❧♦ ❋✉③③②Pr❡❢▼✐♥❡r✳ ❯♠❛ sér✐❡ ❞❡ ❡①♣❡r✐♠❡♥t♦s ❡♠ ❞❛❞♦s r❡❛✐s ❢♦r❛♠ r❡❛❧✐③❛❞♦s✱ ♣❛r❛ ✈❛❧✐❞❛r ❛ ♣r♦♣♦st❛ ❞♦ ❛❧❣♦r✐t♠♦ ❋✉③③②Pr❡❢▼✐♥❡r ❡ ❞♦s ♠ét♦❞♦s ❞❡ r❡♣❛r❛çã♦ ❞❡ ✐♥❝♦♥s✐stê♥❝✐❛✳ ❖s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s s❡ ♠♦str❛♠ ❜❛st❛♥t❡ s❛t✐s❢❛tór✐♦s✱ q✉❛♥❞♦ ❝♦♠♣❛r❛❞♦s ❝♦♠ ♦ ❡st❛❞♦ ❞❛ ❛rt❡ ❡♠ r❡❧❛çã♦ ❛ ❛❧❣♦r✐t♠♦s ❞❡ ♠✐♥❡r❛çã♦ ❞❡ ♣r❡❢❡rê♥❝✐❛s ❡ ♠ét♦❞♦s ❞❡ r❡♣❛r❛çã♦ ❞❡ ✐♥❝♦♥s✐stê♥❝✐❛✳
❆❜str❛❝t
■♥ r❡❝❡♥t ②❡❛rs✱ ♠✉❝❤ r❡s❡❛r❝❤❡s ✐♥ Pr❡❢❡r❡♥❝❡ ▼✐♥✐♥❣ ❤❛s ❢♦❝✉s❡❞ ♦♥ ❞❡✈❡❧♦♣♠❡♥t ♦❢ ♠❡t❤♦❞s ❢♦r ♠✐♥✐♥❣ ❛ ♣r❡❢❡r❡♥❝❡ ♠♦❞❡❧ ❢r♦♠ ❝r✐s♣ ♣❛✐r✇✐s❡ r❡♣r❡s❡♥t❛t✐♦♥✳ ■♥ t❤✐s r❡s❡✲ ❛r❝❤✱ ✐s ♣r❡s❡♥t❡❞ t❤❡ ❋✉③③②Pr❡❢▼✐♥❡r ❛❧❣♦r✐t❤♠✱ ❞❡✈❡❧♦♣❡❞ ❢♦r ♠✐♥✐♥❣ ❢✉③③② ❝♦♥t❡①t✉❛❧ ♣r❡❢❡r❡♥❝❡ ♠♦❞❡❧ ❢r♦♠ ❢✉③③② ♣r❡❢❡r❡♥❝❡ r❡❧❛t✐♦♥✳ ❚❤✐s t②♣❡ ♦❢ ♣r❡❢❡r❡♥❝❡ r❡♣r❡s❡♥t❛t✐♦♥ ✐s ❝♦♠♣♦s❡❞ ❜② ❛ s❡t ♦❢ tr✐♣❧❡s ✭✉,✈,♥✮✱ ✇❤❡r❡✱ ✉ ❛♥❞ ✈ ❛r❡ t✉♣❧❡s ❡✈❛❧✉❛t❡❞ ❜② ✉s❡r ❛♥❞ ♥
✐s t❤❡ ❞❡❣r❡❡ ♦❢ ♣r❡❢❡r❡♥❝❡ ♦❢ t✉♣❧❡ ✉ ✇✐t❤ r❡s♣❡❝t t♦ ✈✳
❚❤❡ ❢✉③③② ♣r❡❢❡r❡♥❝❡ r❡❧❛t✐♦♥s ❡♥❛❜❧❡ t❤❡ st✉❞② ♦❢ t❤❡ ❝♦♥s✐st❡♥❝② ♦❢ ✉s❡rs ❛♥❞ ✐♥ t❤✐s ❝♦♥t❡①t✱ ❛r❡ ♣r❡s❡♥t❡❞ t✇♦ ♠❡t❤♦❞s ❢♦r r❡♣❛✐r ✐♥❝♦♥s✐st❡♥❝② ♦❢ t❤❡s❡ r❡❧❛t✐♦♥s✿ ◆♦ ■♥❝r❡♠❡♥t❛❧ ❘❛♥❣❡ ❱♦t✐♥❣ ❛♥❞ ■♥❝r❡♠❡♥t❛❧ ❘❛♥❣❡ ❱♦t✐♥❣✳ ❇♦t❤ ♠❡t❤♦❞s ❛r❡ ❜❛s❡❞ ♦♥ t❡❝❤♥✐❝❛❧ ❱♦t✐♥❣ ❙②st❡♠ ❛♥❞ ❛r❡ ✉s❡❞ ❢♦r r❡♣❛✐r t❤❡ ✐♥❝♦♥s✐st❡♥❝② ♦❢ ❢✉③③② ♣r❡❢❡r❡♥❝❡ r❡❧❛t✐♦♥s ✐♥❢❡rr❡❞ ❜② ❋✉③③②Pr❡❢▼✐♥❡r✳ ❆ s❡t ♦❢ ❡①♣❡r✐♠❡♥ts ✐♥ r❡❛❧ ❞❛t❛ ✇❡r❡ ♣❡r❢♦r♠❡❞ t♦ ✈❛❧✐❞❛t❡ t❤❡ ❋✉③③②Pr❡❢▼✐♥❡r ❛❧❣♦r✐t❤♠ ❛♥❞ t❤❡ ♠❡t❤♦❞s ❢♦r r❡♣❛✐r ✐♥❝♦♥s✐st❡♥❝②✳ ❚❤❡ r❡s✉❧ts q✉✐t❡ s❛t✐s❢❛❝t♦r② ✇❤❡♥ ❝♦♠♣❛r❡❞ ✇✐t❤ t❤❡ st❛t❡ ♦❢ t❤❡ ❛rt r❡❣❛r❞✐♥❣ Pr❡❢❡r❡♥❝❡ ▼✐♥✐♥❣ ❆❧❣♦r✐t❤♠s ❛♥❞ ▼❡t❤♦❞s ❢♦r ❘❡♣❛✐r ■♥❝♦♥s✐st❡♥❝②✳
❙✉♠ár✐♦
▲✐st❛ ❞❡ ❋✐❣✉r❛s ①①✐
▲✐st❛ ❞❡ ❚❛❜❡❧❛s ①①✐✐✐
▲✐st❛ ❞❡ ❆❜r❡✈✐❛t✉r❛s ❡ ❙✐❣❧❛s ①①✈
✶ ■♥tr♦❞✉çã♦ ✷✼
✷ ❈♦♥❝❡✐t♦s Pr❡❧✐♠✐♥❛r❡s ✸✶
✷✳✶ ▼✐♥❡r❛çã♦ ❞❡ Pr❡❢❡rê♥❝✐❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✷✳✷ ❘❡♣r❡s❡♥t❛çõ❡s ❞❡ Pr❡❢❡rê♥❝✐❛s ❈r✐s♣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✷✳✷✳✶ P❛r❡s ❞❡ t✉♣❧❛s ❈r✐s♣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✷✳✷✳✷ ❘❛♥❦✐♥❣ ❞❡ ❚✉♣❧❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ✷✳✷✳✸ ❋✉♥çã♦ ❙❝♦r❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ✷✳✸ ❘❡♣r❡s❡♥t❛çõ❡s ❞❡ Pr❡❢❡rê♥❝✐❛s ❋✉③③② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✷✳✸✳✶ P❛r❡s ❞❡ t✉♣❧❛s ❋✉③③② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✷✳✸✳✷ ❘❡❧❛çã♦ ❞❡ Pr❡❢❡rê♥❝✐❛ ❋✉③③② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✷✳✹ ❚r❛♥s❢♦r♠❛çõ❡s ❞❡ ❘❡♣r❡s❡♥t❛çõ❡s ❞❡ Pr❡❢❡rê♥❝✐❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼ ✷✳✹✳✶ ❖❜t❡♥çã♦ ❞♦s ❱❛❧♦r❡s ❞❛ ▼❛tr✐③ ❞❡ Pr❡❢❡rê♥❝✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✷✳✹✳✷ ❘❡✜♥❛♠❡♥t♦ ❞❛ ❖❜t❡♥çã♦ ❞♦s ❱❛❧♦r❡s ❞❛ ▼❛tr✐③ ❞❡ Pr❡❢❡rê♥❝✐❛ ✳ ✳ ✸✾ ✷✳✺ ▼♦❞❡❧♦s ❞❡ Pr❡❢❡rê♥❝✐❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷ ✷✳✺✳✶ ▼♦❞❡❧♦s ❞❡ Pr❡❢❡rê♥❝✐❛s ◆ã♦ ❈♦♥❞✐❝✐♦♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷ ✷✳✺✳✷ ▼♦❞❡❧♦s ❞❡ Pr❡❢❡rê♥❝✐❛s ❈♦♥❞✐❝✐♦♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹ ✷✳✻ ◆♦çõ❡s ❞❡ ❈♦♥s✐stê♥❝✐❛ ❡♠ ❘❡❧❛çõ❡s ❞❡ Pr❡❢❡rê♥❝✐❛s ❋✉③③② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺ ✷✳✻✳✶ ❚r❛♥s✐t✐✈✐❞❛❞❡ ❋r❛❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻ ✷✳✻✳✷ ❚r❛♥s✐t✐✈✐❞❛❞❡ ❆❞✐t✐✈❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼ ✷✳✻✳✸ ❉✐s❝✉ssã♦ s♦❜r❡ ❛s Pr♦♣r✐❡❞❛❞❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ✷✳✼ ❈♦♥s✐❞❡r❛çõ❡s ❞♦ ❈❛♣ít✉❧♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽
①✈✐✐✐ ❙✉♠ár✐♦
✸ ❚r❛❜❛❧❤♦s ❘❡❧❛❝✐♦♥❛❞♦s ✹✾
✸✳✶ ▼✐♥❡r❛çã♦ ❞❡ Pr❡❢❡rê♥❝✐❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ✸✳✷ ▼ét♦❞♦s ❞❡ ❘❡♣❛r❛çã♦ ❞❡ ■♥❝♦♥s✐stê♥❝✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ✸✳✸ ❈♦♥s✐❞❡r❛çõ❡s ❞♦ ❈❛♣ít✉❧♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹ ✹ ❇❛❝❦❣r♦✉♥❞✿ ▼✐♥❡r❛çã♦ ❞❡ Pr❡❢❡rê♥❝✐❛s ❈♦♥t❡①t✉❛✐s ❈r✐s♣ ✺✺ ✹✳✶ ❋♦r♠❛❧✐③❛çã♦ ❞♦ Pr♦❜❧❡♠❛ ❞❡ ▼✐♥❡r❛çã♦ ♥♦ ❈❡♥ár✐♦ ❈r✐s♣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺ ✹✳✷ ❖ ❆❧❣♦r✐t♠♦ ❈Pr❡❢▼✐♥❡r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽ ✹✳✷✳✶ ❊t❛♣❛ ✶ ✲ ❉❡s❝♦❜❡rt❛ ❞♦ ❣r❛❢♦ ● ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽ ✹✳✷✳✷ ❊t❛♣❛ ✷ ✲ ❈á❧❝✉❧♦ ❞❛s ❚❛❜❡❧❛s ❞❡ Pr♦❜❛❜✐❧✐❞❛❞❡s ❈♦♥❞✐❝✐♦♥❛✐s ✳ ✳ ✳ ✻✷ ✹✳✸ ❈♦♥s✐❞❡r❛çõ❡s ❞♦ ❈❛♣ít✉❧♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷
✺ ▼✐♥❡r❛çã♦ ❞❡ Pr❡❢❡rê♥❝✐❛s ❈♦♥t❡①t✉❛✐s ❋✉③③② ✻✸
✺✳✶ ❋♦r♠❛❧✐③❛çã♦ ❞♦ Pr♦❜❧❡♠❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸ ✺✳✷ ❖ ❆❧❣♦r✐t♠♦ ❋✉③③②Pr❡❢▼✐♥❡r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼ ✺✳✷✳✶ ❆♣r❡♥❞✐③❛❣❡♠ ❞❛ ❚♦♣♦❧♦❣✐❛ ❞❛ ❘❡❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽ ✺✳✷✳✷ ❈á❧❝✉❧♦ ❞❛s ❚❛❜❡❧❛s ❞❡ Pr♦❜❛❜✐❧✐❞❛❞❡s ❈♦♥❞✐❝✐♦♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶ ✺✳✸ ❈♦♥s✐❞❡r❛çõ❡s ❞♦ ❈❛♣ít✉❧♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷
✻ ▼ét♦❞♦s ❞❡ ❘❡♣❛r❛çã♦ ❞❡ ■♥❝♦♥s✐stê♥❝✐❛ ✼✸
✻✳✶ ▼ét♦❞♦ ❇❚❋ ✭❳✉ ❡t ❛❧✳✱ ✷✵✶✸✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸ ✻✳✶✳✶ ❊♥❝♦♥tr❛♥❞♦ ❛s ✐♥❝♦♥s✐stê♥❝✐❛s ❞❡ ✉♠❛ ❘❡❧❛çã♦ ❞❡ Pr❡❢❡rê♥❝✐❛ ❋✉③③② ✼✹ ✻✳✶✳✷ ❘❡♣❛r❛♥❞♦ ❛s ✐♥❝♦♥s✐stê♥❝✐❛s ❞❡ ✉♠❛ ❘❡❧❛çã♦ ❞❡ Pr❡❢❡rê♥❝✐❛ ❋✉③③② ✼✼ ✻✳✷ ❘❛♥❣✐♥❣ ❱♦t✐♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✾ ✻✳✷✳✶ ❱❡rsã♦ ✶ ✲ ❘❛♥❣❡ ❱♦t✐♥❣ ◆ã♦✲■♥❝r❡♠❡♥t❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✵ ✻✳✷✳✷ ❱❡rsã♦ ✷ ✲ ❘❛♥❣✐♥❣ ❱♦t✐♥❣ ■♥❝r❡♠❡♥t❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✸ ✻✳✸ ❈♦♥s✐❞❡r❛çõ❡s ❞♦ ❈❛♣ít✉❧♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✺
✼ ❘❡s✉❧t❛❞♦s ❊①♣❡r✐♠❡♥t❛✐s ✽✼
✼✳✶ ❉❛❞♦s ❞❡ ❚❡st❡ ❡ ❚é❝♥✐❝❛ ❞❡ ❆♠♦str❛❣❡♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✼ ✼✳✷ ❱❛❧✐❞❛çã♦ ❞❛ ❤✐♣ót❡s❡ ❞❛ r❡❧❡✈â♥❝✐❛ ❞♦ ❣r❛✉ ❞❡ ♣r❡❢❡rê♥❝✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✽ ✼✳✷✳✶ ●r✉♣♦ ❞❡ ❚❡st❡ ✶✿ ❊s❝♦❧❤❛ ❞♦ ❈❧❛ss✐✜❝❛❞♦r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✾ ✼✳✷✳✷ ●r✉♣♦ ❞❡ ❚❡st❡ ✷✿ ■♥✢✉ê♥❝✐❛ ❞❛s ❋❛✐①❛s ❞❡ Pr❡❢❡rê♥❝✐❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✵ ✼✳✷✳✸ ●r✉♣♦ ❞❡ ❚❡st❡ ✸✿ ❈♦♠♣❛r❛çã♦ ❞♦ ❋✉③③②Pr❡❢▼✐♥❡r ♥♦ ❝❡♥ár✐♦ ❈r✐s♣
❙✉♠ár✐♦ ①✐①
✼✳✹ ❈♦♥s✐❞❡r❛çõ❡s ❞♦ ❈❛♣ít✉❧♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✷
✽ ❈♦♥❝❧✉sã♦ ❡ ❚r❛❜❛❧❤♦s ❋✉t✉r♦s ✶✵✸
✽✳✶ P✉❜❧✐❝❛çõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✹ ✽✳✷ ❚r❛❜❛❧❤♦s ❋✉t✉r♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✺
▲✐st❛ ❞❡ ❋✐❣✉r❛s
✶✳✶ ❉✐❛❣r❛♠❛ ❞❡ ▲❡✐t✉r❛ ❞❛ ❉✐ss❡rt❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✷✳✶ ❉✐❛❣r❛♠❛ ●❡r❛❧✿ ❆❧❣♦r✐t♠♦ ❞❡ ▼✐♥❡r❛çã♦ ❞❡ Pr❡❢❡rê♥❝✐❛s ✲ ❘❡♣r❡s❡♥t❛♥❞♦
❛ ❡t❛♣❛ ❞❡ ❡①tr❛çã♦ ❞♦ ♠♦❞❡❧♦ ❞❡ ♣r❡❢❡rê♥❝✐❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ✷✳✷ ❉✐❛❣r❛♠❛ ●❡r❛❧✿ ▼♦❞❡❧♦ ❞❡ Pr❡❢❡rê♥❝✐❛s ✲ ❘❡♣r❡s❡♥t❛♥❞♦ ❛ ❡t❛♣❛ ❞❡ ✉s♦
❞♦ ♠♦❞❡❧♦ ❞❡ ♣r❡❢❡rê♥❝✐❛s ❡①tr❛í❞♦ ♣❡❧♦ ❛❧❣♦r✐t♠♦ ❞❡ ♠✐♥❡r❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ✷✳✸ ❇❛♥❝♦ ❞❡ ❉❛❞♦s ❞❡ Pr❡❢❡rê♥❝✐❛s ❈r✐s♣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✷✳✹ ❘❛♥❦✐♥❣ ❞❡ ❚✉♣❧❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ✷✳✺ ❋✉♥çã♦ ❙❝♦r❡ s♦❜r❡ ❚✉♣(❘) ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺
✷✳✻ ❇❛♥❝♦ ❞❡ ❉❛❞♦s ❞❡ Pr❡❢❡rê♥❝✐❛s ❋✉③③② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✷✳✼ ❊sq✉❡♠❛ ●❡r❛❧ ✲ ❚r❛♥s❢♦r♠❛çã♦ ❞❡ ◆♦t❛s ❞❡ t✉♣❧❛s ❡♠ ▼❛tr✐③ ❞❡ Pr❡❢❡rê♥❝✐❛ ✸✼ ✷✳✽ ❊sq✉❡♠❛ ●❡r❛❧ ✲ ❖❜t❡♥❞♦ ♦ ❣r❛✉ ❞❡ ♣r❡❢❡rê♥❝✐❛ ✉s❛♥❞♦ ❛ ❢✉♥çã♦ ❢1 = ✉✐
✉❥ ✳ ✸✾
✹✳✶ Pr♦❝❡ss♦ ❞❛ ▼✐♥❡r❛çã♦ ❞❡ Pr❡❢❡rê♥❝✐❛s ❈♦♥t❡①t✉❛✐s ♥♦ ❝❡♥ár✐♦ ❈r✐s♣ ✳ ✳ ✳ ✺✺ ✹✳✷ ❊①❡♠♣❧♦ ❞❡ ❘❡❞❡ ❞❡ Pr❡❢❡rê♥❝✐❛s ❇❛②❡s✐❛♥❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻ ✹✳✸ ❇❛♥❝♦ ❞❡ ❉❛❞♦s ❞❡ Pr❡❢❡rê♥❝✐❛ P ❡ ❞✉❛s ❡str✉t✉r❛s ●1 ❡ ●2 ❝❛♥❞✐❞❛t❛s à
❘P❇ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ✺✳✶ ❖ Pr♦❜❧❡♠❛ ●❡r❛❧ ❞❡ ▼✐♥❡r❛çã♦ ❞❡ Pr❡❢❡rê♥❝✐❛s ❈♦♥t❡①t✉❛✐s ❋✉③③② ✳ ✳ ✳ ✳ ✻✹ ✺✳✷ Pr♦❝❡ss♦ ❞❛ ▼✐♥❡r❛çã♦ ❞❡ Pr❡❢❡rê♥❝✐❛s ❈♦♥t❡①t✉❛✐s ♥♦ ❝❡♥ár✐♦ ❋✉③③② ✳ ✳ ✳ ✻✺ ✺✳✸ ✭❛✮ ❉✐❛❣r❛♠❛ ●❡r❛❧ ❞❛ ❚r❛♥s❢♦r♠❛çã♦ ♣♦r ❋❛✐①❛s ❞❡ Pr❡❢❡rê♥❝✐❛s ❡ ✭❜✮
❊①❡♠♣❧♦ ❞❛ ❚r❛♥s❢♦r♠❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺ ✺✳✹ ❇❛♥❝♦ ❞❡ ❉❛❞♦s ❞❡ Pr❡❢❡rê♥❝✐❛ ❋✉③③② P ❡ ❞✉❛s ❡str✉t✉r❛s ❝❛♥❞✐❞❛t❛s ●1
❡ ●2 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵ ✻✳✶ ✭❛✮ ❘❡❧❛çã♦ ❞❡ Pr❡❢❡rê♥❝✐❛ ❋✉③③② ▼ ✭❜✮ ▼❛tr✐③ ❞❡ ❆❞❥❛❝ê♥❝✐❛ ❊ ❡ ✭❝✮ ●r❛❢♦
❉✐r❡❝✐♦♥❛❞♦ r❡♣r❡s❡♥t❛♥❞♦ ❊ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺ ✻✳✷ ▼❛tr✐③ ❊ ❡ ▼❛tr✐③ ❊3 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺ ✻✳✸ ❖❜t❡♥çã♦ ❞❛ ♠❛tr✐③ ❇ ♣❡❧♦ ♣r♦❞✉t♦ ❍❛❞❛♠❛r❞ ❞❡ ❊2 ❡ ❊❚ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻
①①✐✐ ▲✐st❛ ❞❡ ❋✐❣✉r❛s
▲✐st❛ ❞❡ ❚❛❜❡❧❛s
✷✳✶ ❘❡❣r❛s ❞❡ Pr❡❢❡rê♥❝✐❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✷✳✷ ▲✐st❛ ❞❡ ❈❛rr♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✷✳✸ ❋✐❧♠❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹ ✸✳✶ ❈♦♠♣❛r❛çã♦ ❞♦s ❚r❛❜❛❧❤♦s ❈♦rr❡❧❛t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷ ✻✳✶ ❋❛✐①❛s ❞❡ Pr❡❢❡rê♥❝✐❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✶ ✻✳✷ ■❧✉str❛çã♦ ❞❡ ❘❡s✉❧t❛❞♦s ❞♦ ❋✉③③②Pr❡❢▼✐♥❡r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✷ ✻✳✸ ■❧✉str❛çã♦ ❞♦s ❘❡s✉❧t❛❞♦s ❞❛ té❝♥✐❝❛ ❘❛♥❣❡ ❱♦t✐♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✷ ✼✳✶ ❇❛♥❝♦s ❞❡ ❉❛❞♦s ❊s❝♦❧❤✐❞♦s ♣❛r❛ ❊①♣❡r✐♠❡♥t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✽ ✼✳✷ ❆❝✉rá❝✐❛ ❞♦s ❈❧❛ss✐✜❝❛❞♦r ❝♦♠ ❋❡rr❛♠❡♥t❛ ❲❡❦❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✾ ✼✳✸ ■♥✢✉ê♥❝✐❛ ❞♦s ❈❧❛ss✐✜❝❛❞♦r❡s✿ ❛❝❝✱ r❡✈♦❝ ❡ ♣r❡❝ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✵ ✼✳✹ ■♥✢✉ê♥❝✐❛ ❞♦s ❈❧❛ss✐✜❝❛❞♦r❡s✿ t❝ ❡ t❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✵ ✼✳✺ ❋❛✐①❛s ❞❡ Pr❡❢❡rê♥❝✐❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✶ ✼✳✻ ■♥✢✉ê♥❝✐❛ ❞❛s ❋❛✐①❛s ❞❡ Pr❡❢❡rê♥❝✐❛s ✭❛❝❝✱ r❡✈♦❝ ❡ ♣r❡❝✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✶ ✼✳✼ ■♥✢✉ê♥❝✐❛ ❞❛s ❋❛✐①❛s ❞❡ Pr❡❢❡rê♥❝✐❛s ✭t❝ ❡ t❛✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✶ ✼✳✽ ❋✉③③②Pr❡❢▼✐♥❡r✿ ❈r✐s♣ × ❋✉③③② ✭❛❝❝✱ r❡✈♦❝ ❡ ♣r❡❝✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✸
✼✳✾ ❋✉③③②Pr❡❢▼✐♥❡r✿ ❈r✐s♣ × ❋✉③③② ✭t❝ ❡ t❛✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✸
✼✳✶✵ ❋✉③③②Pr❡❢▼✐♥❡r ✲❈r✐s♣ × ❈Pr❡❢▼✐♥❡r ✭❛❝❝✱ r❡✈♦❝ ❡ ♣r❡❝✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✺
✼✳✶✶ ❋✉③③②Pr❡❢▼✐♥❡r✿ ❈r✐s♣ × ❈Pr❡❢▼✐♥❡r ✭t❝ ❡ t❛✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✺
✼✳✶✷ ❈Pr❡❢▼✐♥❡r × ❋✉③③②Pr❡❢▼✐♥❡r ✭❈r✐s♣ ❡ ❋✉③③②✮ ❛❝❝✱ r❡✈♦❝ ❡ ♣r❡❝ ✳ ✳ ✳ ✳ ✳ ✳ ✾✺
✼✳✶✸ ❈Pr❡❢▼✐♥❡r × ❋✉③③②Pr❡❢▼✐♥❡r✿ ✭❈r✐s♣ ❡ ❋✉③③②✮ t❝ ❡ t❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✻
✼✳✶✹ ❚❡♠♣♦ ❞❡ ❊①❡❝✉çã♦ ✲ ❈r✐❛çã♦ ❡ ❯s♦ ❞♦ ▼♦❞❡❧♦ ❞❡ Pr❡❢❡rê♥❝✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✻ ✼✳✶✺ ▼é❞✐❛ ❞❡ ❈✐❝❧♦s ♣♦r ❇❉P✲❋ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✼ ✼✳✶✻ ❘❡s✉❧t❛❞♦s ❘❛♥❣❡ ❱♦t✐♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✽ ✼✳✶✼ ❚❛①❛s ❞❡ ❈♦♠♣❛r❛❜✐❧✐❞❛❞❡ ❡ ❆❧❡❛t♦r✐❡❞❛❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✽ ✼✳✶✽ ❘❡s✉♠♦✿ ▼é❞✐❛ ❞❡ ❈✐❝❧♦s ❞❛s ▼❛tr✐③❡s ❞❡ Pr❡❢❡rê♥❝✐❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✽
①①✐✈ ▲✐st❛ ❞❡ ❚❛❜❡❧❛s
✼✳✶✾ ❚❡♠♣♦ ❞❡ ❊①❡❝✉çã♦ ❞❛ ❚é❝♥✐❝❛ ❘❛♥❣❡ ❱♦t✐♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✾ ✼✳✷✵ P♦r❝❡♥t❛❣❡♠ ❞❡ Pr❡❡♥❝❤✐♠❡♥t♦ ❞❛s ♠❛tr✐③❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✵ ✼✳✷✶ ▼é❞✐❛ ❞❡ ❈✐❝❧♦s ♣♦r ❇❉P✲❋ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✵ ✼✳✷✷ ❈♦♠♣❛r❛çã♦✿ ❘❱ ■♥❝r❡♠❡♥t❛❧ ×▼ét♦❞♦ ❇❚❋ ✭❛❝❝✱ r❡✈♦❝ ❡ ♣r❡❝✮ ✳ ✳ ✳ ✳ ✳ ✶✵✶
✼✳✷✸ ❈♦♠♣❛r❛çã♦✿ ❘❱ ■♥❝r❡♠❡♥t❛❧ ×▼ét♦❞♦ ❇❚❋ ✭t❝ ❡ t❛✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✶
▲✐st❛ ❞❡ ❆❜r❡✈✐❛t✉r❛s ❡ ❙✐❣❧❛s
❛❝❝ ❆❝✉rá❝✐❛
❆● ❆❧❣♦r✐t♠♦ ●❡♥ét✐❝♦
❇❉P✲❈ ❇❛♥❝♦ ❞❡ ❉❛❞♦s ❞❡ Pr❡❢❡rê♥❝✐❛s ❈r✐s♣ ❇❉P✲❋ ❇❛♥❝♦ ❞❡ ❉❛❞♦s ❞❡ Pr❡❢❡rê♥❝✐❛s ❋✉③③② ❇❚❋ ❇❛s❡❛❞♦ ❡♠ ❚r❛♥s✐t✐✈✐❞❛❞❡ ❋r❛❝❛
❈ ❈✐❝❧♦s
❈P✲◆❡t ❈♦♥t❡①t✉❛❧ Pr❡❢❡r❡♥❝❡ ◆❡t✇♦r❦ ❈Pr❡❢▼✐♥❡r ❈♦♥t❡①t✉❛❧ Pr❡❢❡r❡♥❝❡ ▼✐♥✐♥❣
❞ ❉✐❛
❞′ ❉✐❢❡r❡♥ç❛
¯
❞′ ❉✐❢❡r❡♥ç❛ ▼é❞✐❛
❋✉③③②Pr❡❢▼✐♥❡r ❋✉③③② Pr❡❢❡r❡♥❝❡ ▼✐♥✐♥❣
❣♣ ●r❛✉ ❞❡ Pr❡❢❡rê♥❝✐❛
❣♣♠❛① ●r❛✉ ❞❡ Pr❡❢❡rê♥❝✐❛ ▼á①✐♠♦ ❣♣♠✐♥ ●r❛✉ ❞❡ Pr❡❢❡rê♥❝✐❛ ▼í♥✐♠♦ ❣♣♣ ●r❛✉ ❞❡ Pr❡❢❡rê♥❝✐❛ Pr❡❞✐t♦ ❣♣r ●r❛✉ ❞❡ Pr❡❢❡rê♥❝✐❛ ❘❡❛❧
❍❆ ❍✐♣ót❡s❡ ❆❧t❡r♥❛t✐✈❛
❍❖ ❍✐♣ót❡s❡ ◆✉❧❛
❤rs ❍♦r❛s
♠❝ ▼é❞✐❛ ❞❡ ❈✐❝❧♦s
♠❝❡ ▼é❞✐❛ ❞❡ ❈✐❝❧♦s ❞❡ ✉♠❛ ▼❛tr✐③ ❊s♣❛rs❛ ♠❝❝ ▼é❞✐❛ ❞❡ ❈✐❝❧♦s ❞❡ ✉♠❛ ▼❛tr✐③ ❈❤❡✐❛
♠s❡❣ ▼✐❧✐ss❡❣✉♥❞♦s
P◆❡t Pr❡❢❡r❡♥❝❡ ◆❡t✇♦r❦
P❘❊❋ Pr❡❢❡rê♥❝✐❛
P❘❊❋r✈ Pr❡❢❡rê♥❝✐❛ ❞♦ ❘❛♥❣❡ ❱♦t✐♥❣
①①✈✐ ▲✐st❛ ❞❡ ❚❛❜❡❧❛s
♣r❡❝ Pr❡❝✐sã♦
❘P❇ ❘❡❞❡ ❞❡ Pr❡❢❡rê♥❝✐❛ ❇❛②❡s✐❛♥❛
❘P❇✲❝ ❘❡❞❡ ❞❡ Pr❡❢❡rê♥❝✐❛ ❇❛②❡s✐❛♥❛ ❞♦ ❝❡♥ár✐♦ ❈r✐s♣ ❘P❇✲❢ ❘❡❞❡ ❞❡ Pr❡❢❡rê♥❝✐❛ ❇❛②❡s✐❛♥❛ ❞♦ ❝❡♥ár✐♦ ❋✉③③②
❘❱ ❘❛♥❣❡ ❱♦t✐♥❣
r❡✈♦❝ ❘❡✈♦❝❛çã♦
s❡❣ ❙❡❣✉♥❞♦s
t❛ ❚❛①❛ ❞❡ ❆❧❡❛t♦r✐❡❞❛❞❡
t❝ ❚❛①❛ ❞❡ ❈♦♠♣❛r❛❜✐❧✐❞❛❞❡
❈❛♣ít✉❧♦
1
■♥tr♦❞✉çã♦
❖ ❣r❛♥❞❡ ❛✉♠❡♥t♦ ❞❡ ❞❛❞♦s ❡ ❛ ✈❡❧♦❝✐❞❛❞❡ ❝♦♠ q✉❡ ❡ss❡ ✈♦❧✉♠❡ ❝r❡s❝❡ ♣♦❞❡ ❝❛✉s❛r ❢r✉str❛çõ❡s ❛♦s ✉s✉ár✐♦s✱ q✉❛♥❞♦ ♦ ♠❡s♠♦ ♥❡❝❡ss✐t❛ ♦❜t❡r ❛❧❣✉♠❛ ✐♥❢♦r♠❛çã♦ ❞❡ ♠❛♥❡✐r❛ rá♣✐❞❛ ❡ s❡❧❡t✐✈❛✳ ◆❡st❡ ❝♦♥t❡①t♦✱ ♥♦s ú❧t✐♠♦s ✶✵ ❛♥♦s ♦ tó♣✐❝♦ ❞❡ ▼✐♥❡r❛çã♦ ❞❡ Pr❡❢❡rê♥✲ ❝✐❛s t❡♠ ❛tr❛í❞♦ ❜❛st❛♥t❡ ❛t❡♥çã♦ ♥❛ ❝♦♠✉♥✐❞❛❞❡ ❞❡ P❡sq✉✐s❛ ❡♠ ▼✐♥❡r❛çã♦ ❞❡ ❉❛❞♦s✱ ❞❡✈✐❞♦ ❛ s❡✉ ✐♠♣♦rt❛♥t❡ ♣❛♣❡❧ ♥♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ❙✐st❡♠❛s ❞❡ ❘❡❝♦♠❡♥❞❛çã♦ ✭❇✉r❣❡s ❡t ❛❧✳✱ ✷✵✵✺✮✱ ✭▲♦♣s ❡t ❛❧✳✱ ✷✵✶✶✮✳
❯♠ ❛❧❣♦r✐t♠♦ ❞❡ ♠✐♥❡r❛çã♦ ❞❡ ♣r❡❢❡rê♥❝✐❛s tr❛❜❛❧❤❛ ♥❛ ❡①tr❛çã♦ ❞❡ ✉♠ ♠♦❞❡❧♦ ❞❡ ♣r❡❢❡rê♥❝✐❛s ❛❝✉r❛❞♦ ❛ ♣❛rt✐r ❞❡ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❛♠♦str❛s ❞❡ ♣r❡❢❡rê♥❝✐❛s ❞♦ ✉s✉ár✐♦✳ ❖s ❢♦r♠❛❧✐s♠♦s ♠❛✐s ❝♦♠✉♥s ✉s❛❞♦s ♣❛r❛ r❡♣r❡s❡♥t❛r ❡ss❛s ❛♠♦str❛s ❞❡ ♣r❡❢❡rê♥❝✐❛s sã♦ ❢✉♥çõ❡s s❝♦r❡s ✭❇✉r❣❡s ❡t ❛❧✳✱ ✷✵✵✺✮✱ ✭▲♦♣s ❡t ❛❧✳✱ ✷✵✶✶✮✱ ✭❈r❛♠♠❡r ❡ ❙✐♥❣❡r✱ ✷✵✵✶✮✱ ♣❛r❡s ❞❡ t✉♣❧❛s ✭❞❡ ❆♠♦ ❡t ❛❧✳✱ ✷✵✶✷❜✮✱ ✭❞❡ ❆♠♦ ❡t ❛❧✳✱ ✷✵✶✷❛✮✱ ✭❑♦r✐❝❤❡ ❡ ❩❛♥✉tt✐♥✐✱ ✷✵✶✵✮ ❡ r❛♥❦✐♥❣ ❞❡ t✉♣❧❛s ✭❋r❡✉♥❞ ❡t ❛❧✳✱ ✷✵✵✸✮✱ ✭❏♦❛❝❤✐♠s✱ ✷✵✵✷✮✳
❆ ♠❛✐♦r✐❛ ❞❛s té❝♥✐❝❛s ❞❡ ♠✐♥❡r❛çã♦ ❞❡ ❞❛❞♦s ✉t✐❧✐③❛❞❛s ❡♠ s✐st❡♠❛s ❞❡ r❡❝♦♠❡♥❞❛çã♦ sã♦ ❛s té❝♥✐❝❛s ❞❡ ❝❧❛ss✐✜❝❛çã♦ tr❛❞✐❝✐♦♥❛✐s✳ ◆❡st❡ ❝❡♥ár✐♦✱ ♦ ❝♦♥❥✉♥t♦ ❞❡ tr❡✐♥❛♠❡♥t♦ é ❝♦♥st✐t✉í❞♦ ♣♦r t✉♣❧❛s ❛✈❛❧✐❛❞❛s ♣❡❧♦ ✉s✉ár✐♦✱ ♦♥❞❡ ❛s ♥♦t❛s sã♦ ❝♦♥s✐❞❡r❛❞❛s ❝❧❛ss❡s ❡ ♦ ❝❧❛ss✐✜❝❛❞♦r é ✉s❛❞♦ ♣❛r❛ ✐♥❢❡r✐r ❛ ♥♦t❛ q✉❡ ✉♠ ✉s✉ár✐♦ ❞❛r✐❛ ❛ ✉♠❛ ♥♦✈❛ t✉♣❧❛✳ ◆♦ ❡♥t❛♥t♦✱ ❞❡♣❡♥❞❡♥❞♦ ❞❛ ❛♣❧✐❝❛çã♦ ♦ ✉s♦ ❞♦ ❝❧❛ss✐✜❝❛❞♦r ♣❛r❛ ♣r❡❞✐③❡r ♥♦t❛s ❞♦ ✉s✉ár✐♦ ♥ã♦ é ✈✐á✈❡❧✳ P♦r ❡①❡♠♣❧♦✱ q✉❛♥❞♦ ✉♠ ✉s✉ár✐♦ ❛✈❛❧✐❛ ✉♠ ✜❧♠❡✱ ❛ ❝❧❛ss✐✜❝❛çã♦ ❞❛❞❛ ♥♦r♠❛❧♠❡♥t❡ ♥ã♦ ❡stá r❡❧❛❝✐♦♥❛❞❛ ❛♣❡♥❛s às ❝❛r❛❝t❡ríst✐❝❛s ❞♦ ✜❧♠❡✱ ♠❛s t❛♠❜é♠ às ❛✈❛❧✐❛çõ❡s ❢❡✐t❛s ♣❡❧♦ ✉s✉ár✐♦ ❡♠ ♦✉tr♦s ✜❧♠❡s✳
P♦rt❛♥t♦✱ ❛ ✐♥❢♦r♠❛çã♦ ✐♠♣♦rt❛♥t❡ ♥❡st❡ ❝♦♥t❡①t♦ ♥ã♦ é ❛ ❝❧❛ss✐✜❝❛çã♦ ❡①❛t❛ ❞♦s ✜❧♠❡s✱ ♠❛s ❝♦♠♦ ♦ ✉s✉ár✐♦ ❝♦♠♣❛r❛ ❞♦✐s ✜❧♠❡s✳ ❆ss✐♠✱ ♣❛r❛ ❛❧❣✉♠❛s ❛♣❧✐❝❛çõ❡s✱ ❛s té❝♥✐❝❛s ❞❡ ♠✐♥❡r❛çã♦ ❞❡ ♣r❡❢❡rê♥❝✐❛s ✉s❛❞❛s ♣❛r❛ ❡①tr❛✐r ✉♠ ♠♦❞❡❧♦ ❞❡ ♣r❡❢❡rê♥❝✐❛s ❛ ♣❛rt✐r ❞❡ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ♣❛r❡s ❞❡ t✉♣❧❛s sã♦ ♠❛✐s ❛❞❡q✉❛❞❛s✳
✷✽ ❈❛♣ít✉❧♦ ✶✳ ■♥tr♦❞✉çã♦
❖ tr❛❜❛❧❤♦ ♣r♦♣♦st♦ ❡♠ ❞❡ ❆♠♦ ❡t ❛❧✳ ✭✷✵✶✷❛✮ ✐♠♣❧❡♠❡♥t❛ ✉♠ ❛❧❣♦r✐t♠♦ ♥♦♠❡❛❞♦ ❈Pr❡❢▼✐♥❡r ♣❛r❛ ♠✐♥❡r❛r ✉♠ ♠♦❞❡❧♦ ❞❡ ♣r❡❢❡rê♥❝✐❛s ❝♦♥t❡①t✉❛❧ ❝r✐s♣✱ ❛ ♣❛rt✐r ❞❡ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❛♠♦str❛s ❞❡ ♣r❡❢❡rê♥❝✐❛s ❞♦ ✉s✉ár✐♦ r❡♣r❡s❡♥t❛❞♦ ♣♦r ♣❛r❡s ❞❡ t✉♣❧❛s✳ ❖ ♠♦❞❡❧♦ ❞❡ ♣r❡❢❡rê♥❝✐❛s ♠✐♥❡r❛❞♦ ♣❡❧♦ ❛❧❣♦r✐t♠♦ é ❝♦♥s✐❞❡r❛❞♦ ❝r✐s♣✱ ♣♦✐s ❡❧❡ é ❡①tr❛í❞♦ ❞❡ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s ♦♥❞❡ ♦ ✉s✉ár✐♦ ❢♦r♥❡❝❡ s✉❛ ♣r❡❢❡rê♥❝✐❛ ❛tr❛✈és ❞❡ ✉♠❛ r❡s♣♦st❛ ✏s✐♠✑ ♦✉ ✏♥ã♦✑✳ ■st♦ é✱ ♦✉ ♦ ✉s✉ár✐♦ ♣r❡❢❡r❡ ❛ t✉♣❧❛ ✉ ❛ t✉♣❧❛ ✈ ✭❞❡♥♦t❛❞♦ ♣♦r ✉ ≻ ✈✮✱
♦✉ ❡❧❡ ♣r❡❢❡r❡ ❛ t✉♣❧❛ ✈ ❛ t✉♣❧❛ ✉ ✭❞❡♥♦t❛❞♦ ♣♦r ✈ ≻✉✮✳ ▲♦❣♦✱ ♦ ♠♦❞❡❧♦ ❞❡ ♣r❡❢❡rê♥❝✐❛s
❡①tr❛í❞♦ ♣❡❧♦ ❈Pr❡❢▼✐♥❡r ♣r❡❞✐③ s❡ ✉♠❛ ♥♦✈❛ t✉♣❧❛ ✇1 é ♣r❡❢❡rí✈❡❧ ❛ ✉♠❛ ♥♦✈❛ t✉♣❧❛ ✇2 ♦✉ s❡ ✇2 é ♣r❡❢❡rí✈❡❧ ❛ t✉♣❧❛ ✇1✳
❖ ♠♦❞❡❧♦ ❞❡ ♣r❡❢❡rê♥❝✐❛s ❡①tr❛í❞♦ ♣❡❧♦ ❈♣r❡❢▼✐♥❡r é ❝♦♥t❡①t✉❛❧✱ ♦✉ s❡❥❛✱ ❡❧❡ é ❝♦♥st✐✲ t✉í❞♦ ♣♦r ✉♠ ❝♦♥❥✉♥t♦ ❞❡ r❡❣r❛s ❞❡ ♣r❡❢❡rê♥❝✐❛s ❝♦♥t❡①t✉❛✐s ✭❲✐❧s♦♥✱ ✷✵✵✹✮ ❞❛ ❢♦r♠❛✿ ✏❙❊ ❁❝♦♥t❡①t♦❃ ❊◆❚➹❖ ❊❯ ♣r❡✜r♦ ✏✈❛❧♦r ✶✑ ❛ ✏✈❛❧♦r ✷✑✳ P♦r ❡①❡♠♣❧♦✱ ✉♠❛ r❡❣r❛ ❞❡ ♣r❡❢❡✲ rê♥❝✐❛ ❝♦♥t❡①t✉❛❧ ♥♦ ❝❡♥ár✐♦ ❞❡ ✜❧♠❡s ♣♦❞❡r✐❛ s❡r ❝♦♠♣♦st❛ ❞❛ s❡❣✉✐♥t❡ ❢♦r♠❛✿ P❛r❛ ♦s ✜❧♠❡s ❝✉❥♦ ❛t♦r é ❚♦♠ ❍❛♥❦s ✭❝♦♥t❡①t♦✮✱ ❡✉ ♣r❡✜r♦ ✏❈♦♠é❞✐❛✑ ❛ ✏❆çã♦✑✳ ❉❡ss❛ ❢♦r♠❛✱ ♦ ♠♦❞❡❧♦ ❞❡ ♣r❡❢❡rê♥❝✐❛s ❡①tr❛í❞♦ ♣❡❧♦ ❈♣r❡❢▼✐♥❡r é ❝❛♣❛③ ❞❡ ✐♥❢❡r✐r ✉♠❛ r❡❧❛çã♦ ❞❡ ♦r❞❡♠ s♦❜r❡ ❛s t✉♣❧❛s ✭♦ q✉❡ ❛ t❛r❡❢❛ ❞❡ ❝❧❛ss✐✜❝❛çã♦ ♥ã♦ é ❝❛♣❛③ ❞❡ ❛❧❝❛♥ç❛r✮✱ ✐st♦ é✱ ♦ ♠♦❞❡❧♦ é ❝❛♣❛③ ❞❡ ✐♥❢❡r✐r r❡❧❛❝✐♦♥❛♠❡♥t♦s ❞❡ tr❛♥s✐t✐✈✐❞❛❞❡ ✭s❡ ✉ ≻ ✈ ❡ ✈ ≻ ✇ ❡♥tã♦ ✉ ≻ ✇✮
s❛t✐s❢❛③❡♥❞♦ ❛ ♣r♦♣r✐❡❞❛❞❡ ❞❡ ✐rr❡✢❡①✐❜✐❧✐❞❛❞❡ ✭✐❢ ✉ ≻✈ ❡♥tã♦ ✈ 6≻✉✮✳
❚é❝♥✐❝❛s ❞❡ ♠✐♥❡r❛çã♦ ❞❡ ♣r❡❢❡rê♥❝✐❛s q✉❡ ✉s❛♠ ❝♦♠♦ ❞❛❞♦s ❞❡ ❡♥tr❛❞❛ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ♣❛r❡s ❞❡ t✉♣❧❛s✱ ♥♦r♠❛❧♠❡♥t❡ ❡①❡❝✉t❛♠ ✉♠❛ ❡t❛♣❛ ❞❡ ♣ré✲♣r♦❝❡ss❛♠❡♥t♦ ♣❛r❛ tr❛♥s✲ ❢♦r♠❛r ❛✈❛❧✐❛çõ❡s ❢❡✐t❛s ♣❡❧♦ ✉s✉ár✐♦ ❡♠ ♣❛r❡s ❞❡ t✉♣❧❛s✳ P♦r ❡①❡♠♣❧♦✱ s❡ ♦ ✉s✉ár✐♦ ❛✈❛❧✐❛ ✉♠❛ t✉♣❧❛ ✉ ❝♦♠ ♥♦t❛ ✺ ❡ ❛ t✉♣❧❛ ✈ ❝♦♠ ♥♦t❛ ✶✱ ❡st❛ ✐♥❢♦r♠❛çã♦ é tr❛♥s❢♦r♠❛❞❛ ♥♦ ♣❛r ✭✉,✈✮✳ ◆❡st❡ t✐♣♦ ❞❡ tr❛♥s❢♦r♠❛çã♦✱ ✉♠❛ ❣r❛♥❞❡ q✉❛♥t✐❞❛❞❡ ❞❡ ✐♥❢♦r♠❛çã♦ é ♣❡r❞✐❞❛✱
♣♦✐s✱ s❡ ♦ ✉s✉ár✐♦ ❛✈❛❧✐❛ss❡ ❛s t✉♣❧❛s ✉ ❡ ✈ ❝♦♠ ♥♦t❛s ✺ ❡ ✹ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ ♦ ♠❡s♠♦ ♣❛r ✭✉,✈✮ s❡r✐❛ ❢♦r♠❛❞♦✳ ◆♦ ❡♥t❛♥t♦✱ ♥❛ ♣r✐♠❡✐r❛ s✐t✉❛çã♦ ♦ ✉s✉ár✐♦ ♣r❡❢❡r❡ ❛ t✉♣❧❛ ✉ ❛
t✉♣❧❛ ✈ ❝♦♠ ✉♠❛ ✐♥t❡♥s✐❞❛❞❡ ♠❛✐♦r ❞♦ q✉❡ ♥❛ s❡❣✉♥❞❛ ♦♣çã♦✳
❈♦♠ ❜❛s❡ ♥❡ss❛s ✐♥❢♦r♠❛çõ❡s✱ ❡st❛ ❞✐ss❡rt❛çã♦ ❛♣r❡s❡♥t❛ ❛ ♣r♦♣♦st❛ ❞♦ ❛❧❣♦r✐t♠♦ ❋✉③③②Pr❡❢▼✐♥❡r✱ ♣❛r❛ ♠✐♥❡r❛r ✉♠ ♠♦❞❡❧♦ ❞❡ ♣r❡❢❡rê♥❝✐❛s ❝♦♥t❡①t✉❛❧ ❢✉③③② ❛ ♣❛rt✐r ❞❡ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❛♠♦str❛s ❞❡ ♣r❡❢❡rê♥❝✐❛s r❡♣r❡s❡♥t❛❞❛s ♣♦r tr✐♣❧❛s ✭✉,✈,♥✮✱ ♦♥❞❡ ✉ ❡ ✈ sã♦
t✉♣❧❛s ❛✈❛❧✐❛❞❛s ♣❡❧♦ ✉s✉ár✐♦ ❡ ♥ é ♦ ❣r❛✉ ❞❡ ♣r❡❢❡rê♥❝✐❛ ✭0 ≤ ♥ ≤ 1✮ ❞❛ t✉♣❧❛ ✉ s♦❜r❡
❛ t✉♣❧❛ ✈✳ ▲♦❣♦✱ ♦ ♠♦❞❡❧♦ ❞❡ ♣r❡❢❡rê♥❝✐❛s ❡①tr❛í❞♦ é ❝♦♥s✐❞❡r❛❞♦ ❢✉③③②✱ ♣♦✐s ❝♦♥s❡❣✉❡ ✐♥❢❡r✐r ♦ ❣r❛✉ ❞❡ ♣r❡❢❡rê♥❝✐❛ s♦❜r❡ ❞✉❛s ♥♦✈❛s t✉♣❧❛s ✇1 ❡ ✇2✳
P❛r❛ r❡❛❧✐③❛r ♦ ♣ré✲♣r♦❝❡ss❛♠❡♥t♦ ❞♦s ❞❛❞♦s ❡ ♦❜t❡r ✉♠ ❝♦♥❥✉♥t♦ ❞❡ tr✐♣❧❛s ❞♦ t✐♣♦ ✭✉,✈,♥✮ é ♥❡❝❡ssár✐♦ tr❛♥s❢♦r♠❛r ❛s ❛✈❛❧✐❛çõ❡s ❞❛s t✉♣❧❛s ❡♠ ✉♠❛ r❡❧❛çã♦ ❞❡ ♣r❡❢❡rê♥❝✐❛
✷✾
❢r❛❝❛ ❡ tr❛♥s✐t✐✈✐❞❛❞❡ ❛❞✐t✐✈❛ ✭❍❡rr❡r❛✲❱✐❡❞♠❛ ❡t ❛❧✳✱ ✷✵✵✹✮✱ ✭❍❡rr❡r❛✲❱✐❡❞♠❛ ❡t ❛❧✳✱ ✷✵✵✼✮✳ ❆s ❢✉♥çõ❡s ♠❛t❡♠át✐❝❛s ✉t✐❧✐③❛❞❛s ♥❡st❛ ❞✐ss❡rt❛çã♦ ❣❛r❛♥t❡♠ ❛ ❝♦♥s✐stê♥❝✐❛ ❞❛s r❡✲ ❧❛çõ❡s ❞❡ ♣r❡❢❡rê♥❝✐❛s ❢✉③③② ♣ré✲♣r♦❝❡ss❛❞❛s ♣❛r❛ ❝r✐❛r ♦ ❝♦♥❥✉♥t♦ ❞❡ tr✐♣❧❛s ✭✉,✈,♥✮✳
◆♦ ❡♥t❛♥t♦✱ ❛ r❡❧❛çã♦ ❞❡ ♣r❡❢❡rê♥❝✐❛ ❢✉③③② ❝♦♥st✐t✉í❞❛ ❞♦s ❣r❛✉s ❞❡ ♣r❡❢❡rê♥❝✐❛ ✐♥❢❡r✐❞♦s ♣❡❧♦ ❛❧❣♦r✐t♠♦ ❋✉③③②Pr❡❢▼✐♥❡r ♥ã♦ ❛t❡♥❞❡♠ ❡ss❛s ♣r♦♣r✐❡❞❛❞❡s✳ ◆❡st❡ ❝♦♥t❡①t♦✱ ❡st❡ tr❛❜❛❧❤♦ ❞❡ ❞✐ss❡rt❛çã♦ ❛♣r❡s❡♥t❛ t❛♠❜é♠✱ ❛ ♣r♦♣♦st❛ ❞❡ ✉♠ ♠ét♦❞♦ ❞❡ r❡♣❛r❛çã♦ ❞❡ ✐♥❝♦♥s✐stê♥❝✐❛ ❞❛s r❡❧❛çõ❡s ❞❡ ♣r❡❢❡rê♥❝✐❛s ❢✉③③② ✐♥❢❡r✐❞❛s ♣❡❧♦ ❋✉③③②Pr❡❢▼✐♥❡r✳ ❚❛❧ ♠é✲ t♦❞♦ é ❜❛s❡❛❞♦ ♥❛ té❝♥✐❝❛ ❞❡ s✐st❡♠❛ ❞❡ ✈♦t❛çã♦ ❘❛♥❣❡ ❱♦t✐♥❣ ✭❞❡ ❆♠♦ ❡t ❛❧✳✱ ✷✵✶✹✮ ❡ ❝♦♥s✐st❡ ❡♠ ✉t✐❧✐③❛r ❛s ♣r❡❞✐çõ❡s ❢❡✐t❛s ♣❡❧♦ ❋✉③③②Pr❡❢▼✐♥❡r✱ ♣❛r❛ t❡♥t❛r ❡❧✐♠✐♥❛r t♦❞❛s ❛s ✐♥❝♦♥s✐stê♥❝✐❛s ❞❡ ✉♠❛ r❡❧❛çã♦ ❞❡ ♣r❡❢❡rê♥❝✐❛ ❢✉③③②✳ ❉✐❛♥t❡ ❞✐ss♦✱ ♦ ♦❜❥❡t✐✈♦ ❣❡r❛❧ ❡ ♦❜❥❡t✐✈♦s ❡s♣❡❝í✜❝♦s ❞❡st❡ tr❛❜❛❧❤♦ ❞❡ ❞✐ss❡rt❛çã♦ sã♦✿
• ❖❜❥❡t✐✈♦ ●❡r❛❧
✕ ▼♦str❛r q✉❡ ♦ ❣r❛✉ ❞❡ ♣r❡❢❡rê♥❝✐❛ é ✉♠ ❢❛t♦r ✐♠♣♦rt❛♥t❡ ♣❛r❛ ♠✐♥❡r❛çã♦ ❞❡ ✉♠ ♠♦❞❡❧♦ ❞❡ ♣r❡❢❡rê♥❝✐❛s ♠❛✐s ❛❝✉r❛❞♦✳
• ❖❜❥❡t✐✈♦s ❊s♣❡❝í✜❝♦s
✕ ❋♦r♠❛❧✐③❛r ♦ ♣r♦❜❧❡♠❛ ❞❡ ♠✐♥❡r❛çã♦ ❞❡ ♣r❡❢❡rê♥❝✐❛s ❝r✐s♣ ♥♦ ❝❡♥ár✐♦ ❢✉③③②✳ ✕ ❉❡s❡♥✈♦❧✈❡r ♦ ❛❧❣♦r✐t♠♦ ❋✉③③②Pr❡❢▼✐♥❡r ♣r♦♣♦st♦ ♣❛r❛ s♦❧✉❝✐♦♥❛r ♦ ♣r♦❜❧❡♠❛
❞❡ ♠✐♥❡r❛çã♦ ❢✉③③②✳
✕ ❆♥❛❧✐s❛r ♦ ❞❡s❡♠♣❡♥❤♦ ❞♦ ❛❧❣♦r✐t♠♦ ❋✉③③②Pr❡❢▼✐♥❡r ❡♠ ❝♦♠♣❛r❛çã♦ ❝♦♠ ✉♠ tr❛❜❛❧❤♦ ❞♦ ❡st❛❞♦ ❞❛ ❛rt❡✱ ❡♠ r❡❧❛çã♦ à ♠✐♥❡r❛çã♦ ❞❡ ♠♦❞❡❧♦s ❞❡ ♣r❡❢❡rê♥✲ ❝✐❛s ❝♦♥t❡①t✉❛✐s✱ ❛tr❛✈és ❞❡ ♠❡❞✐❞❛s ❞❡ ❛✈❛❧✐❛çã♦ ❝♦♠♦✿ ❛❝✉rá❝✐❛✱ r❡✈♦❝❛çã♦✱ ♣r❡❝✐sã♦✱ t❛①❛ ❞❡ ❝♦♠♣❛r❛❜✐❧✐❞❛❞❡ ❡ t❛①❛ ❞❡ ❛❧❡❛t♦r✐❡❞❛❞❡✳
✕ ❉❡s❡♥✈♦❧✈❡r ♠ét♦❞♦s ❞❡ r❡♣❛r❛çã♦ ❞❡ ✐♥❝♦♥s✐stê♥❝✐❛ ❞❡ r❡❧❛çõ❡s ❞❡ ♣r❡❢❡rê♥❝✐❛s ❢✉③③②✳
✕ ❆♥❛❧✐s❛r ♦ ❞❡s❡♠♣❡♥❤♦ ❞♦ ♠ét♦❞♦ ❞❡ r❡♣❛r❛çã♦ ❞❡ ✐♥❝♦♥s✐stê♥❝✐❛ ♣r♦♣♦st♦✱ ❡♠ ❝♦♠♣❛r❛çã♦ ❝♦♠ ♦ ❡st❛❞♦ ❞❛ ❛rt❡✱ ❡♠ r❡❧❛çã♦ ❛ ♠ét♦❞♦s ❞❡ r❡♣❛r❛çã♦ ❞❡ ✐♥✲ ❝♦♥s✐stê♥❝✐❛ ❞❡ r❡❧❛çõ❡s ❞❡ ♣r❡❢❡rê♥❝✐❛s ❢✉③③② ❛tr❛✈és ❞❛s ♠❡❞✐❞❛s ❞❡ ❛✈❛❧✐❛çã♦✳ ❉✐❛♥t❡ ❞♦s ♦❜❥❡t✐✈♦s ❛q✉✐ ❝✐t❛❞♦s✱ ❛s ♣r✐♥❝✐♣❛✐s ❝♦♥tr✐❜✉✐çõ❡s ❞❡st❡ tr❛❜❛❧❤♦ sã♦✿
• ❋♦r♠❛❧✐③❛çã♦ ❞♦ Pr♦❜❧❡♠❛ ❞❡ ▼✐♥❡r❛çã♦ ❋✉③③② ✭❈❛♣ít✉❧♦ ✺✮✳
• ❉❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞♦ ❛❧❣♦r✐t♠♦ ❋✉③③②Pr❡❢▼✐♥❡r ♣❛r❛ ♠✐♥❡r❛çã♦ ❞❡ ♠♦❞❡❧♦s ❞❡ ♣r❡✲
❢❡rê♥❝✐❛s ❝♦♥t❡①t✉❛✐s ❢✉③③② ✭❈❛♣ít✉❧♦ ✺✮✳
• ❊st✉❞♦ ❞❛ ■♥✢✉ê♥❝✐❛ ❞♦ ●r❛✉ ❞❡ Pr❡❢❡rê♥❝✐❛ ❡♠ ❛❧❣♦r✐t♠♦s ❞❡ ♠✐♥❡r❛çã♦ ❞❡ ♣r❡❢❡✲
rê♥❝✐❛s ❝♦♥t❡①t✉❛✐s ✭❈❛♣ít✉❧♦ ✺ ❡ ❈❛♣ít✉❧♦ ✼✮✳
• ❉❡✜♥✐çã♦✱ ✐♠♣❧❡♠❡♥t❛çã♦ ❡ ✈❛❧✐❞❛çã♦ ❞❡ ♠ét♦❞♦s ❞❡ r❡♣❛r❛çã♦ ❞❡ ✐♥❝♦♥s✐stê♥❝✐❛ ❡♠
✸✵ ❈❛♣ít✉❧♦ ✶✳ ■♥tr♦❞✉çã♦
❊st❛ ❞✐ss❡rt❛çã♦ ❡♥❝♦♥tr❛✲s❡ ♦r❣❛♥✐③❛❞❛ ❝♦♠♦ ❞❡s❝r✐t♦ ❛❜❛✐①♦ ❡ ❛ ❋✐❣✉r❛ ✶✳✶ ❛♣r❡s❡♥t❛ ❛ s❡q✉ê♥❝✐❛ ❞❡ ❧❡✐t✉r❛ ❞❡st❡ tr❛❜❛❧❤♦ ❡ ❛s ❝♦♥tr✐❜✉✐çõ❡s ❞♦ tr❛❜❛❧❤♦ ❡stã♦ ❞❡st❛❝❛❞❛s ♥♦s r❡tâ♥❣✉❧♦s ❝♦♠ ❝♦r ❡s❝✉r❛✳
• ❖ ❈❛♣ít✉❧♦ ✷ ✐♥tr♦❞✉③ ♦s ❝♦♥❝❡✐t♦s ♣r❡❧✐♠✐♥❛r❡s ♥❡❝❡ssár✐♦s ♣❛r❛ ❝♦♠♣r❡❡♥❞❡r ❛ ♣r♦✲
♣♦st❛ ❞♦ ❛❧❣♦r✐t♠♦ ❋✉③③②Pr❡❢▼✐♥❡r✱ ♦ ❝♦♥t❡①t♦ q✉❡ ♦ ♠❡s♠♦ é ❛♣❧✐❝❛❞♦ ❡ ❛❧❣✉♠❛s ♥♦çõ❡s ❞❡ ❝♦♥s✐stê♥❝✐❛ ❡♠ ♣r❡❢❡rê♥❝✐❛s ❢✉③③②✳
• ◆♦ ❈❛♣ít✉❧♦ ✸ sã♦ ❛♣r❡s❡♥t❛❞♦s ♦s tr❛❜❛❧❤♦s r❡❧❛❝✐♦♥❛❞♦s ❛♦ tr❛❜❛❧❤♦ ♣r♦♣♦st♦ ♥❡st❛
❞✐ss❡rt❛çã♦✳
• ◆♦ ❈❛♣ít✉❧♦ ✹ sã♦ ❛♣r❡s❡♥t❛❞♦s✱ ❛ ❢♦r♠❛❧✐③❛çã♦ ❞♦ ♣r♦❜❧❡♠❛ ❞❡ ♠✐♥❡r❛çã♦ ❞❡ ♣r❡❢❡✲
rê♥❝✐❛s ♥♦ ❝❡♥ár✐♦ ❝r✐s♣✱ ❜❡♠ ❝♦♠♦✱ ♦ ❛❧❣♦r✐t♠♦ ❈Pr❡❢▼✐♥❡r ✭❞❡ ❆♠♦ ❡t ❛❧✳✱ ✷✵✶✷❛✮✱ ♣♦✐s✱ ♦ ♠❡s♠♦ é ❛ ❜❛s❡ ♣❛r❛ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞♦ ❋✉③③②Pr❡❢▼✐♥❡r ❡ ♦ ♣r✐♥❝✐♣❛❧ ❜❛✲ s❡❧✐♥❡ ❞❡ ❝♦♠♣❛r❛çã♦✳
• ❖ ❈❛♣ít✉❧♦ ✺ ❛♣r❡s❡♥t❛ ❛ ❢♦r♠❛❧✐③❛çã♦ ❞♦ ♣r♦❜❧❡♠❛ ❞❡ ♠✐♥❡r❛çã♦ ❞❡ ♣r❡❢❡rê♥❝✐❛s
❢✉③③② ❡ ❛♣r❡s❡♥t❛çã♦ ❞♦ ❛❧❣♦r✐t♠♦ ❋✉③③②Pr❡❢▼✐♥❡r✳
• ❖ ❈❛♣ít✉❧♦ ✻ ❛♣r❡s❡♥t❛ ♦s ♠ét♦❞♦s ❞❡ r❡♣❛r❛çã♦ ❞❡ ✐♥❝♦♥s✐stê♥❝✐❛ ❞❡ r❡❧❛çõ❡s ❞❡
♣r❡❢❡rê♥❝✐❛s ❢✉③③② ♣r♦♣♦st♦s ♥❡st❛ ❞✐ss❡rt❛çã♦ ❡ ♦ ♠ét♦❞♦ ❝♦♥s✐❞❡r❛❞♦ ❝♦♠♦ ❜❛s❡❧✐♥❡ ❞❡ ❝♦♠♣❛r❛çã♦✳
• ❖ ❈❛♣ít✉❧♦ ✼ ❛♣r❡s❡♥t❛ ♦s r❡s✉❧t❛❞♦s ❡①♣❡r✐♠❡♥t❛✐s ♦❜t✐❞♦s s♦❜r❡ ❞❛❞♦s r❡❛✐s✱ t❛♥t♦
♣❛r❛ ♦ ❛❧❣♦r✐t♠♦ ❋✉③③②Pr❡❢▼✐♥❡r✱ q✉❛♥t♦ ♣❛r❛ ♦s ♠ét♦❞♦s ❞❡ r❡♣❛r❛çã♦ ❞❡ ✐♥❝♦♥✲ s✐stê♥❝✐❛❀
• ❋✐♥❛❧♠❡♥t❡✱ ♦ ❈❛♣ít✉❧♦ ✽ ❛♣r❡s❡♥t❛ ❛s ❝♦♥❝❧✉sõ❡s ❡ tr❛❜❛❧❤♦s ❢✉t✉r♦s ♣❛r❛ ❡st❡
tr❛❜❛❧❤♦ ❞❡ ❞✐ss❡rt❛çã♦✳
❈❛♣ít✉❧♦
2
❈♦♥❝❡✐t♦s Pr❡❧✐♠✐♥❛r❡s
❊st❡ ❝❛♣ít✉❧♦ t❡♠ ❝♦♠♦ ♦❜❥❡t✐✈♦s✿ ✭✶✮ ❞❡s❝r❡✈❡r ♦ ♣r♦❜❧❡♠❛ ❣❡r❛❧ ❞❡ ✉♠ ❛❧❣♦r✐t♠♦ ❞❡ ▼✐♥❡r❛çã♦ ❞❡ Pr❡❢❡rê♥❝✐❛s✱ ✭✷✮ ❛♣r❡s❡♥t❛r ❞✐✈❡rs❛s ❢♦r♠❛s ❞❡ r❡♣r❡s❡♥t❛çã♦ ❞❡ ♣r❡❢❡rê♥❝✐❛s ❝r✐s♣ ❡ ❢✉③③②✱ ✭✸✮ ♠♦str❛r ❛❧❣✉♠❛s ❢♦r♠❛s ❞❡ tr❛♥s❢♦r♠❛r r❡♣r❡s❡♥t❛çõ❡s ❞❡ ♣r❡❢❡rê♥❝✐❛s✱ ✭✹✮ ❛♣r❡s❡♥t❛r ♦s ❛s♣❡❝t♦s ❞♦s ♠♦❞❡❧♦s ❡①tr❛í❞♦s ♣♦r ❛❧❣♦r✐t♠♦s ❞❡ ♠✐♥❡r❛çã♦ ❞❡ ♣r❡❢❡✲ rê♥❝✐❛s ❡ ✭✺✮ ✜♥❛❧♠❡♥t❡✱ ❛♣r❡s❡♥t❛r ❛❧❣✉♠❛s ♥♦çõ❡s ❞❡ ❝♦♥s✐stê♥❝✐❛ ❡♠ ♣r❡❢❡rê♥❝✐❛s ❢✉③③②✳ ❉❡st❛ ❢♦r♠❛✱ ❛ ❙❡çã♦ ✷✳✶ ❞❡s❝r❡✈❡ ♦s ♣r✐♥❝✐♣❛✐s ❛s♣❡❝t♦s ❡♥✈♦❧✈✐❞♦s ♥♦ ♣r♦❜❧❡♠❛ ❣❡r❛❧ ❞❡ ▼✐♥❡r❛çã♦ ❞❡ Pr❡❢❡rê♥❝✐❛s✳ ❊♠ s❡❣✉✐❞❛✱ ❛ ❙❡çã♦ ✷✳✷ ❛❜♦r❞❛ ❛❧❣✉♥s t✐♣♦s ❝♦♠✉♥s ❞❡ r❡♣r❡s❡♥t❛çõ❡s q✉❛♥t✐t❛t✐✈❛s ❞❡ ♣r❡❢❡rê♥❝✐❛s ❝r✐s♣ ❞♦ ✉s✉ár✐♦ ❡ s❡✉s ♣r✐♥❝✐♣❛✐s ❝♦♥❝❡✐t♦s✳ ❆ ❙❡çã♦ ✷✳✸ ♠♦str❛ r❡♣r❡s❡♥t❛çõ❡s ❞❡ ♣r❡❢❡rê♥❝✐❛s ❢✉③③② ✉t✐❧✐③❛❞❛s ♥❡st❡ tr❛❜❛❧❤♦ ❞❡ ❞✐s✲ s❡rt❛çã♦✳ ❆ ❙❡çã♦ ✷✳✹ ❛❜♦r❞❛ ❢✉♥çõ❡s ❞❡ tr❛♥s❢♦r♠❛çã♦ ❞❡ r❡♣r❡s❡♥t❛çõ❡s ❞❡ ♣r❡❢❡rê♥❝✐❛s✳ ❆ ❙❡çã♦ ✷✳✺ ❛❜♦r❞❛ ❛❧❣✉♥s ❛s♣❡❝t♦s s♦❜r❡ t✐♣♦s ❞❡ ♠♦❞❡❧♦s ❞❡ ♣r❡❢❡rê♥❝✐❛s ❡ ❛ ❙❡çã♦ ✷✳✻ ❞❡st❛❝❛ ❛❧❣✉♠❛s ♥♦çõ❡s ❞❡ ❝♦♥s✐stê♥❝✐❛ ❡♠ r❡❧❛çõ❡s ❞❡ ♣r❡❢❡rê♥❝✐❛s ❢✉③③②✳
✷✳✶ ▼✐♥❡r❛çã♦ ❞❡ Pr❡❢❡rê♥❝✐❛s
❆♥t❡s ❞❡ ♠♦str❛r ♦s ❞✐✈❡rs♦s t✐♣♦s ❞❡ r❡♣r❡s❡♥t❛çã♦ ❞❡ ♣r❡❢❡rê♥❝✐❛s✱ é ✐♠♣♦rt❛♥t❡ ♠♦str❛r ♦s ♣r✐♥❝✐♣❛✐s ❛s♣❡❝t♦s ❡♥✈♦❧✈✐❞♦s ♥♦ ♣r♦❜❧❡♠❛ ❣❡r❛❧ ❞❡ ▼✐♥❡r❛çã♦ ❞❡ Pr❡❢❡rê♥❝✐❛s ♥♦ q✉❛❧ ❡ss❛ ♣❡sq✉✐s❛ s❡ ❡♥❣❧♦❜❛✳
◆♦ ♣r♦❜❧❡♠❛ ❣❡r❛❧ ❞❡ ▼✐♥❡r❛çã♦ ❞❡ Pr❡❢❡rê♥❝✐❛s ✐❧✉str❛❞♦ ♣❡❧❛ ❋✐❣✉r❛ ✷✳✶✱ ✉♠ ❛❧✲ ❣♦r✐t♠♦ ❞❡ ▼✐♥❡r❛çã♦ r❡❝❡❜❡ ❝♦♠♦ ❡♥tr❛❞❛ ❛❧❣✉♠ t✐♣♦ ❞❡ r❡♣r❡s❡♥t❛çã♦ q✉❛♥t✐t❛t✐✈❛ ❞❡ ♣r❡❢❡rê♥❝✐❛s ❞❡ ✉♠ ✉s✉ár✐♦ ✧✉✧✱ t❛✐s ❝♦♠♦✿ r❛♥❦✐♥❣ ❞❡ t✉♣❧❛s✱ ♣❛r❡s ❞❡ t✉♣❧❛s✱ ❝♦♥❥✉♥t♦ ❞❡ tr✐♣❧❛s ❡ ❢✉♥çã♦ s❝♦r❡✳ ❊ss❛s r❡♣r❡s❡♥t❛çõ❡s sã♦ ❝♦♥s✐❞❡r❛❞❛s q✉❛♥t✐t❛t✐✈❛s✱ ♣♦✐s ❡♥✈♦❧✈❡ t✉❞♦ ❛q✉✐❧♦ q✉❡ ♦ ✉s✉ár✐♦ ❛✈❛❧✐♦✉✳
✸✷ ❈❛♣ít✉❧♦ ✷✳ ❈♦♥❝❡✐t♦s Pr❡❧✐♠✐♥❛r❡s
❋✐❣✉r❛ ✷✳✶✿ ❉✐❛❣r❛♠❛ ●❡r❛❧✿ ❆❧❣♦r✐t♠♦ ❞❡ ▼✐♥❡r❛çã♦ ❞❡ Pr❡❢❡rê♥❝✐❛s ✲ ❘❡♣r❡s❡♥t❛♥❞♦ ❛ ❡t❛♣❛ ❞❡ ❡①tr❛çã♦ ❞♦ ♠♦❞❡❧♦ ❞❡ ♣r❡❢❡rê♥❝✐❛s
❖ ❛❧❣♦r✐t♠♦ r❡t♦r♥❛ ❝♦♠♦ s❛í❞❛ ❛❧❣✉♠ t✐♣♦ ❞❡ r❡♣r❡s❡♥t❛çã♦ ❞❡ ♣r❡❢❡rê♥❝✐❛s q✉❛❧✐t❛✲ t✐✈❛✱ ❞❡✜♥✐❞❛ ♣❡❧♦ ▼♦❞❡❧♦ ❞❡ Pr❡❢❡rê♥❝✐❛s ✧▼✧❞♦ ✉s✉ár✐♦ ✧✉✧✳ ❊st❡ ♠♦❞❡❧♦ é ❝♦♥s✐❞❡r❛❞♦ q✉❛❧✐t❛t✐✈♦ ♣♦r s❡r ✉♠ ♠♦❞❡❧♦ ♠❛✐s ❝♦♠♣❛❝t♦ ❡ ♥ã♦ ♣♦ss✉✐r t♦❞❛s ❛s ❛✈❛❧✐❛çõ❡s ❞♦ ✉s✉ár✐♦✱ ♠❛s s✐♠✱ r❡❣r❛s ❝❛♣❛③❡s ❞❡ ♣r❡❞✐③❡r ❛ ♣r❡❢❡rê♥❝✐❛ s♦❜r❡ ♥♦✈❛s t✉♣❧❛s✳
❊①✐st❡♠ ❛❧❣♦r✐t♠♦s q✉❡ r❡t♦r♥❛♠ ❝♦♠♦ s❛í❞❛ r❡♣r❡s❡♥t❛çõ❡s q✉❛♥t✐t❛t✐✈❛s✱ ♥♦ ❡♥t❛♥t♦✱ ♦ ♣♦❞❡r ❞❡ ❡①♣r❡ss✐✈✐❞❛❞❡ ❞❛ ❡s♣❡❝✐✜❝❛çã♦ q✉❛❧✐t❛t✐✈❛ é ♠❛✐♦r q✉❡ ♥❛ ❡s♣❡❝✐✜❝❛çã♦ q✉❛♥✲ t✐t❛t✐✈❛✱ ✉♠❛ ✈❡③ q✉❡✱ ♥❡♠ t♦❞❛s ❛s r❡❧❛çõ❡s ❞❡ ♣r❡❢❡rê♥❝✐❛s ♣♦❞❡♠ s❡r ❡①♣r❡ss❛s ♣♦r ❢✉♥çõ❡s s❝♦r❡s ♦✉ r❛♥❦✐♥❣ ❞❡ t✉♣❧❛s✳ ❉❡ ✉♠ ♠♦❞♦ ❣❡r❛❧✱ ❛ ❛❜♦r❞❛❣❡♠ q✉❛❧✐t❛t✐✈❛ ♣r♦♣♦r✲ ❝✐♦♥❛ r❡❣r❛s ♠❛✐s ❝♦♠♣❛❝t❛s ❡ ❢á❝❡✐s ❞❡ ❛r♠❛③❡♥❛r✱ ♣♦❞❡♥❞♦ s❡r ✉t✐❧✐③❛❞❛s ♣❛r❛ ♣r❡❞✐③❡r ❛ ♣r❡❢❡rê♥❝✐❛ s♦❜r❡ t✉♣❧❛s ♥ã♦ ❛✈❛❧✐❛❞♦s ♣❡❧♦ ✉s✉ár✐♦✳
❋✐❣✉r❛ ✷✳✷✿ ❉✐❛❣r❛♠❛ ●❡r❛❧✿ ▼♦❞❡❧♦ ❞❡ Pr❡❢❡rê♥❝✐❛s ✲ ❘❡♣r❡s❡♥t❛♥❞♦ ❛ ❡t❛♣❛ ❞❡ ✉s♦ ❞♦ ♠♦❞❡❧♦ ❞❡ ♣r❡❢❡rê♥❝✐❛s ❡①tr❛í❞♦ ♣❡❧♦ ❛❧❣♦r✐t♠♦ ❞❡ ♠✐♥❡r❛çã♦
✷✳✷✳ ❘❡♣r❡s❡♥t❛çõ❡s ❞❡ Pr❡❢❡rê♥❝✐❛s ❈r✐s♣ ✸✸
✷✳✷ ❘❡♣r❡s❡♥t❛çõ❡s ❞❡ Pr❡❢❡rê♥❝✐❛s ❈r✐s♣
Pr❡❢❡rê♥❝✐❛s ♣♦❞❡♠ s❡r ❡①♣r❡ss❛s ❞❡ ❢♦r♠❛ q✉❛❧✐t❛t✐✈❛ ✭❞❡ ❆♠♦ ❡t ❛❧✳✱ ✷✵✶✷❛✮✱ ✭❍♦❧❧❛♥❞ ❡t ❛❧✳✱ ✷✵✵✸✮ ♦✉ q✉❛♥t✐t❛t✐✈❛ ✭❈♦❤❡♥ ❡t ❛❧✳✱ ✶✾✾✾✮✳ ❊♠ ❙t❡❢❛♥✐❞✐s ❡t ❛❧✳ ✭✷✵✶✶✮✱ ✈ár✐♦s tr❛❜❛❧❤♦s ❡♥✈♦❧✈❡♥❞♦ ❡ss❛s ❞✉❛s ❛❜♦r❞❛❣❡♥s sã♦ ❛♣r❡s❡♥t❛❞♦s✳ ◆❛ ❛❜♦r❞❛❣❡♠ q✉❛❧✐t❛t✐✈❛ ✉♠ ▼♦❞❡❧♦ ❞❡ Pr❡❢❡rê♥❝✐❛ é ❡①tr❛í❞♦ ♣♦r ✉♠ ❛❧❣♦r✐t♠♦ ❡ ❡st❡ ♠♦❞❡❧♦ é ✉t✐❧✐③❛❞♦ ♣❛r❛ ♣r❡❞✐③❡r ❛ ♣r❡❢❡rê♥❝✐❛ ❡♥tr❡ ♥♦✈❛s t✉♣❧❛s✳ ◆❛ ❛❜♦r❞❛❣❡♠ q✉❛♥t✐t❛t✐✈❛ ♦ ❛❧❣♦r✐t♠♦ r❡t♦r♥❛ ✉♠❛ r❡♣r❡s❡♥t❛çã♦ q✉❛♥t✐t❛t✐✈❛ ❞❡ ♣r❡❢❡rê♥❝✐❛ ♣❛r❛ t♦❞❛s ❛s t✉♣❧❛s✱ ♣♦r ❡①❡♠♣❧♦✱ ✉♠❛ ♥♦t❛ ♣❛r❛ ❝❛❞❛ t✉♣❧❛ ❞♦ ❜❛♥❝♦ ❞❡ ❞❛❞♦s✳ ❊ss❡ ♣r♦❝❡ss♦ s❡ t♦r♥❛ ✐♥✈✐á✈❡❧ q✉❛♥❞♦ s❡ t❡♠ ✉♠ ❣r❛♥❞❡ ❝♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s✳ ❊st❛ s❡çã♦ ❛❜♦r❞❛ ❛❧❣✉♠❛s ❢♦r♠❛s ❞❡ r❡♣r❡s❡♥t❛çã♦ ❞❡ ♣r❡❢❡rê♥❝✐❛s ❝r✐s♣ ❞♦ ✉s✉ár✐♦✳
✷✳✷✳✶ P❛r❡s ❞❡ t✉♣❧❛s ❈r✐s♣
❊ss❡ t✐♣♦ ❞❡ r❡♣r❡s❡♥t❛çã♦ ❞❡ ♣r❡❢❡rê♥❝✐❛s t❛♠❜é♠ ❝♦♥❤❡❝✐❞❛ ❝♦♠♦ ❜✐t✉♣❧❛s ♣♦❞❡ s❡r ✈✐st❛ ❡♠ ❞❡ ❆♠♦ ❡t ❛❧✳ ✭✷✵✶✷❛✮✳ ◆❡st❡ tr❛❜❛❧❤♦✱ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❜✐t✉♣❧❛s ❢♦r♠❛ ✉♠ ❜❛♥❝♦ ❞❡ ❞❛❞♦s ❞❡ ♣r❡❢❡rê♥❝✐❛s ❝r✐s♣✱ ❞❡✜♥✐❞♦ ❞❛ s❡❣✉✐♥t❡ ❢♦r♠❛✿
❉❡✜♥✐çã♦ ✷✳✶✳ ✭❇❛♥❝♦ ❞❡ ❉❛❞♦s ❞❡ Pr❡❢❡rê♥❝✐❛s ❈r✐s♣ ✭❇❉P✲❈✮✮ ❙❡❥❛ ❘ = (❆1,❆2, ...,❆♥)✉♠ ❡sq✉❡♠❛ r❡❧❛❝✐♦♥❛❧ ❡ ❚✉♣(❘)♦ ❝♦♥❥✉♥t♦ ❞❡ t✉♣❧❛s s♦❜r❡ ❘✳ ❯♠ ❜❛♥❝♦
❞❡ ❞❛❞♦s ❞❡ ♣r❡❢❡rê♥❝✐❛ ❝r✐s♣ s♦❜r❡ ❘ é ✉♠ ❝♦♥❥✉♥t♦ ✜♥✐t♦ P ⊆❚✉♣(❘)×❚✉♣(❘)q✉❡ é
❝♦♥s✐st❡♥t❡✱ ♦✉ s❡❥❛✱ s❡(✉,✈)∈ P ❡♥tã♦ (✈,✉) ∈/ P✳ ❖ ♣❛r(✉,✈)r❡♣r❡s❡♥t❛ ♦ ❢❛t♦ ❞❡ q✉❡
❡♥tr❡ ❛s t✉♣❧❛s ✉ ❡ ✈✱ ♦ ✉s✉ár✐♦ ♣r❡❢❡r❡ ✉✳
❋✐❣✉r❛ ✷✳✸✿ ❇❛♥❝♦ ❞❡ ❉❛❞♦s ❞❡ Pr❡❢❡rê♥❝✐❛s ❈r✐s♣
❆ ❋✐❣✉r❛ ✷✳✸❜ ✐❧✉str❛ ✉♠ ❡①❡♠♣❧♦ ❞❡ ❜❛♥❝♦ ❞❡ ❞❛❞♦s ❞❡ ♣r❡❢❡rê♥❝✐❛s s♦❜r❡ ✉♠ ❡s✲ q✉❡♠❛ r❡❧❛❝✐♦♥❛❧ ❘= (❆,❇,❈,❉)✱ ❝♦♠ ♦s ❞♦♠í♥✐♦s ❞❡✜♥✐❞♦s ♣♦r ❞♦♠(❆) ={❛1,❛2,❛3}✱
❞♦♠(❇) = {❜1,❜2}✱ ❞♦♠(❈) = {❝1,❝2} ❡ ❞♦♠(❉) = {❞1,❞2}✳ ❖ ❜❛♥❝♦ ❞❡ ❞❛❞♦s ❞❡
✸✹ ❈❛♣ít✉❧♦ ✷✳ ❈♦♥❝❡✐t♦s Pr❡❧✐♠✐♥❛r❡s
❞❛❞♦s ❞❡ ♣r❡❢❡rê♥❝✐❛s✱ é ♣♦ssí✈❡❧ ♦❜s❡r✈❛r q✉❡ ❛ t✉♣❧❛ t1(❛1,❛1,❝1,❞1)é ♣r❡❢❡rí✈❡❧ ❛ t✉♣❧❛
t2(❛1,❜1,❝1,❞2)✳
✷✳✷✳✷ ❘❛♥❦✐♥❣ ❞❡ ❚✉♣❧❛s
❊ss❛ ❢♦r♠❛ ❞❡ r❡♣r❡s❡♥t❛çã♦ ❞❡ ♣r❡❢❡rê♥❝✐❛s ❞♦ ✉s✉ár✐♦✱ ❞❡s❝r✐t❛ ❡♠ ❈❤✐❝❧❛♥❛ ❡t ❛❧✳ ✭✶✾✾✽✮ ❡ ❈❤✐❝❧❛♥❛ ❡t ❛❧✳ ✭✷✵✵✶✮✱ ❝♦♥s✐st❡ ❡♠ ✉♠❛ ♦r❞❡♥❛çã♦ ✭r❛♥❦✐♥❣✮ ❞❡ t✉♣❧❛s ❞❡✜♥✐❞❛ ♣♦r✿
❉❡✜♥✐çã♦ ✷✳✷✳ ✭❘❛♥❦✐♥❣ ❞❡ ❚✉♣❧❛s✮ ❙❡❥❛ ❘(❆1,❆2, ...,❆❥) ✉♠ ❡sq✉❡♠❛ r❡❧❛❝✐♦♥❛❧ ❡
❚✉♣(❘) ✉♠❛ ❧✐st❛ ❞❡ ♥ t✉♣❧❛s [t1, . . . ,t♥] s♦❜r❡ ❘✳ ❯♠ r❛♥❦✐♥❣ é ✉♠❛ ♣❡r♠✉t❛çã♦ r ❞❡ [1, . . . ,♥]✱ t❛❧ q✉❡✱ ❛ ❧✐st❛ ❞❡ t✉♣❧❛s [t1, . . . ,t♥]❡stá ♦r❞❡♥❛❞❛ ♣♦r ♦r❞❡♠ ❞❡ ♣r❡❢❡rê♥❝✐❛ ❞♦
✉s✉ár✐♦✳
❋✐❣✉r❛ ✷✳✹✿ ❘❛♥❦✐♥❣ ❞❡ ❚✉♣❧❛s
❯♠ ❡①❡♠♣❧♦ ❞❡ r❛♥❦✐♥❣ ❞❡ t✉♣❧❛s é ✐❧✉str❛❞♦ ♥❛ ❋✐❣✉r❛ ✷✳✹❜✳ ◆❡st❡ r❛♥❦✐♥❣✱ ♣♦❞❡✲s❡ ♦❜s❡r✈❛r q✉❡ ❛ t✉♣❧❛ t1 é ♣r❡❢❡rí✈❡❧ ❛ t✉♣❧❛ t2✱ ♣♦✐s t1 ♦❝✉♣❛ ❛ s❡❣✉♥❞❛ ♣♦s✐çã♦ ♥♦ r❛♥❦✐♥❣✱ ❡♥q✉❛♥t♦ t2 ♦❝✉♣❛ ❛ q✉❛rt❛ ♣♦s✐çã♦✳ ❆tr❛✈és ❞♦ r❛♥❦✐♥❣ é ♣♦ssí✈❡❧ ♥♦t❛r t❛♠❜é♠✱ q✉❡ t3 é ❛ t✉♣❧❛ ♠❛✐s ♣r❡❢❡r✐❞❛✱ ♣♦✐s ♦❝✉♣❛ ❛ ♣r✐♠❡✐r❛ ♣♦s✐çã♦ ❞♦ r❛♥❦✐♥❣✱ ❡♥q✉❛♥t♦ t5 é ❛ t✉♣❧❛ ♠❡♥♦s ♣r❡❢❡r✐❞❛ ♦❝✉♣❛♥❞♦ ❛ ú❧t✐♠❛ ♣♦s✐çã♦ ❞♦ r❛♥❦✐♥❣✳
✷✳✷✳✸ ❋✉♥çã♦ ❙❝♦r❡
❘❡♣r❡s❡♥t❛r ♣r❡❢❡rê♥❝✐❛s ❞♦ ✉s✉ár✐♦ ♣♦r ✉♠❛ ❢✉♥çã♦ s❝♦r❡ é s✐♠♣❧❡s♠❡♥t❡ ❛ss♦❝✐❛r ❛ ❝❛❞❛ t✉♣❧❛ ❞♦ ❜❛♥❝♦ ❞❡ ❞❛❞♦s✱ ✉♠ ✈❛❧♦r q✉❡ r❡♣r❡s❡♥t❛ ❛ ♥♦t❛ q✉❡ ✉s✉ár✐♦ ❛✈❛❧✐❛ t❛❧ t✉♣❧❛✳ ❉❡✜♥✐çã♦ ✷✳✸✳ ✭❋✉♥çã♦ ❙❝♦r❡ ✭❈❤✐❝❧❛♥❛ ❡t ❛❧✳✱ ✶✾✾✽✮✮ ❙❡❥❛ ❘(❆1,❆2, ...,❆❥) ✉♠
❡sq✉❡♠❛ r❡❧❛❝✐♦♥❛❧ ❡ ❚✉♣(❘) ✉♠ ❝♦♥❥✉♥t♦ ❞❡ t✉♣❧❛s s♦❜r❡ ❘✳ ❯♠ ✉s✉ár✐♦ ❢♦r♥❡❝❡ s✉❛s
♣r❡❢❡rê♥❝✐❛s s♦❜r❡ ❚✉♣(❘)❛tr❛✈és ❞❡ ✉♠❛ ❢✉♥çã♦ ✉ :❚✉♣(❘)→◆ ✱ q✉❡ ❛ss♦❝✐❛ ♣❛r❛ ❝❛❞❛
