❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❖✉r♦ Pr❡t♦ ■♥st✐t✉t♦ ❞❡ ❈✐ê♥❝✐❛s ❊①❛t❛s ❡ ❇✐♦❧ó❣✐❝❛s
❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❈♦♠♣✉t❛çã♦
Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❈✐ê♥❝✐❛ ❞❛ ❈♦♠♣✉t❛çã♦
❆❧❣♦r✐t♠♦s ▼✉❧t✐♦❜❥❡t✐✈♦s ♣❛r❛ ♦ Pr♦❜❧❡♠❛ ❞❡ ❙❡q✉❡♥❝✐❛♠❡♥t♦ ❞❡ ❚❛r❡❢❛s ❡♠ ❯♠❛ ▼áq✉✐♥❛ ❝♦♠ ❚❡♠♣♦ ❞❡ Pr❡♣❛r❛çã♦ ❉❡♣❡♥❞❡♥t❡ ❞❛
❙❡q✉ê♥❝✐❛ ❡ ❞❛ ❋❛♠í❧✐❛
❉✐ss❡rt❛çã♦ ❞❡ ▼❡str❛❞♦ s✉❜♠❡t✐❞❛ ❛♦ Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❈✐ê♥❝✐❛ ❞❛ ❈♦♠♣✉t❛çã♦ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❖✉r♦ Pr❡t♦✱ ❝♦♠♦ ♣❛rt❡ ❞♦s r❡q✉✐s✐t♦s ❡①✐❣✐❞♦s ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞♦ tít✉❧♦ ❞❡ ▼❡str❡ ❡♠ ❈✐ê♥❝✐❛ ❞❛ ❈♦♠♣✉t❛çã♦✳
❆❧✉♥♦✿ ▼❛r❝❡❧♦ ❋❡rr❡✐r❛ ❘❡❣♦
❖r✐❡♥t❛❞♦r✿ ▼❛r❝♦♥❡ ❏❛♠✐❧s♦♥ ❋r❡✐t❛s ❙♦✉③❛ ❈♦✲♦r✐❡♥t❛❞♦r✿ ❏♦sé ❊❧✐❛s ❈❧❛✉❞✐♦ ❆rr♦②♦
❆❣r❛❞❡❝✐♠❡♥t♦s
Pr✐♠❡✐r❛♠❡♥t❡✱ ❛❣r❛❞❡ç♦ à ❉❡✉s ♣❡❧❛ ✈✐❞❛ ❡ ♣♦r t✉❞♦ ❞❡ ❜♦♠ q✉❡ t❡♠ ♠❡ ♣r♦✲ ♣♦r❝✐♦♥❛❞♦✳
➚ ♠✐♥❤❛ ♠ã❡✱ ♠❡✉ ✐r♠ã♦✱ ♠✐♥❤❛ ✐r♠ã✱ ♠✐♥❤❛ ❛✈ó✱ ❡ à t♦❞❛ ❛ ♠✐♥❤❛ ❢❛♠í❧✐❛ q✉❡ é ✉♠ r❡❝❛♥t♦ ❞❡ ❛♠♦r✱ ♣❡❧♦ ❛♣♦✐♦ ❡ ♦ ✐♥❝❡♥t✐✈♦ ❡♠ t♦❞❛ ❛ ♠✐♥❤❛ ✈✐❞❛✳
➚ ♠✐♥❤❛ ♥❛♠♦r❛❞❛ ❈❛r♦❧✐♥❡✱ ♣❡ss♦❛ q✉❡ ❛♠♦ ❡ q✉❡ ♠❡ ❛❝♦♠♣❛♥❤♦✉ ♣♦r t♦❞♦ ❡ss❡ ♣❡r❝✉rs♦✱ s❡♠♣r❡ ❞✐s♣♦st❛ ❛ ♠❡ ❛❥✉❞❛r✳
❆♦ ♣r♦❢❡ss♦r ▼❛r❝♦♥❡ ♣❡❧❛ ❡①❝❡❧❡♥t❡ ♦r✐❡♥t❛çã♦ ♣❛r❛ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡st❡ tr❛❜❛❧❤♦✱ ♣❡❧❛ ❛♠✐③❛❞❡ ❡ ✐♥❝❡♥t✐✈♦✱ ❡ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ♣❡❧♦s ❡♥s✐♥❛♠❡♥t♦s ❞❡ ✈✐❞❛✳
❆♦ ♣r♦❢❡ss♦r ❏♦sé ❊❧✐❛s ❈❧❛✉❞✐♦ ❆rr♦②♦ ♣❡❧❛ s✉❛ ✈❛❧✐♦s❛ ♦r✐❡♥t❛çã♦ q✉❡ ❡♥r✐q✉❡❝❡✉ ♠✉✐t♦ ♦ tr❛❜❛❧❤♦✳
❆♦ ❘✐❝❛r❞♦ ❇r❛s✐❧✱ ♣r♦❢❡ss♦r ❱❛❧t❡r ❈❛r✈❛❧❤♦ ❡ ♦s ❝♦❧❡❣❛s ❞❛ ❉✐✈✐sã♦ ❞❡ ❚❡❝♥♦❧♦✲ ❣✐❛ ❞❛ ■♥❢♦r♠❛çã♦ ❞❛ ❯❋❱❏▼ q✉❡ ♠❡ ❛❥✉❞❛r❛♠ ❛ ❝♦♥s❡❣✉✐r ♦ ❛❢❛st❛♠❡♥t♦ ❞♦ ♠❡✉ tr❛❜❛❧❤♦✳
➚ ❯❋❱❏▼ q✉❡ ♠❡ ❝♦♥❝❡❞❡✉ ✉♠ ♣❡rí♦❞♦ ❞❡ ❛❢❛st❛♠❡♥t♦ ♣❛r❛ q✉❡ ❡✉ ♣✉❞❡ss❡ ❝♦♥❝r❡t✐③❛r ♠❛✐s ❡ss❡ ♦❜❥❡t✐✈♦ ❡♠ ♠✐♥❤❛ ✈✐❞❛✳
➚ ❯❋❖P ❡ ❛♦ ♣r♦❣r❛♠❛ ❞❡ ♣ós✲❣r❛❞✉❛çã♦ ❡♠ ❈✐ê♥❝✐❛ ❞❛ ❈♦♠♣✉t❛çã♦ ♣❡❧❛ ♦♣♦r✲ t✉♥✐❞❛❞❡ ❞❡ ♠❡ q✉❛❧✐✜❝❛r✳
❆♦s ót✐♠♦s ♣r♦❢❡ss♦r❡s ❞♦ ❉❊❈❖▼ q✉❡ ❝♦♥tr✐❜✉ír❛♠ ♠✉✐t♦ ♣❛r❛ ❛ ♠✐♥❤❛ ❢♦r✲ ♠❛çã♦ ❡ ❢♦r❛♠ ❛ ❜❛s❡ ♣❛r❛ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡st❡ tr❛❜❛❧❤♦✳
❆♦s ❝♦❧❡❣❛s ❞♦ ♠❡str❛❞♦ ♣❡❧♦ ❝♦♠♣❛♥❤❡✐r✐s♠♦✳
➚ ❞♦♥❛ ❍❡r❝í❧✐❛ q✉❡ ♠❡ ♣r♦♣♦r❝✐♦♥♦✉ ✉♠ ❧❛r ❡♠ ❖✉r♦ Pr❡t♦✳ ❆♦ ♠❡✉ ❛♠✐❣♦ ❘❛❢❛❡❧ ♣♦r s❡♠♣r❡ ♠❡ ✐♥❝❡♥t✐✈❛r✳
❘❡s✉♠♦
❊st❡ tr❛❜❛❧❤♦ tr❛t❛ ❞♦ Pr♦❜❧❡♠❛ ❞❡ ❙❡q✉❡♥❝✐❛♠❡♥t♦ ❞❡ ❚❛r❡❢❛s ❡♠ ❯♠❛ ▼áq✉✐♥❛ ❝♦♠ ❚❡♠♣♦ ❞❡ Pr❡♣❛r❛çã♦ ❉❡♣❡♥❞❡♥t❡ ❞❛ ❙❡q✉ê♥❝✐❛ ❡ ❞❛ ❋❛♠í❧✐❛✳ ◆❡ss❡ ♣r♦❜❧❡♠❛✱ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ t❛r❡❢❛s ❞❡✈❡♠ s❡r ♣r♦❝❡ss❛❞❛s ♣♦r ✉♠❛ ♠áq✉✐♥❛✱ s❡♥❞♦ q✉❡ ❛♥t❡s ❞❛ ❡①❡❝✉çã♦ ❞❡ ❝❛❞❛ t❛r❡❢❛ é ♥❡❝❡ssár✐♦ ✉♠ t❡♠♣♦ ♣❛r❛ ♣r❡♣❛r❛r ❛ ♠áq✉✐♥❛✱ ♦ q✉❛❧ é ❞❡✜♥✐❞♦ ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛ s❡q✉ê♥❝✐❛ ❡ ❛ ❢❛♠í❧✐❛ ❞❛ t❛r❡❢❛✳ ❉❡st❛ ❢♦r♠❛✱ ♦ t❡♠♣♦ ❞❡ ♣r❡♣❛r❛çã♦ ❞❛ ♠áq✉✐♥❛ é r❡q✉❡r✐❞♦✱ ❛♣❡♥❛s✱ ♣❛r❛ ❡①❡❝✉t❛r ❞✉❛s t❛r❡❢❛s ❝♦♥s❡❝✉t✐✈❛s q✉❡ ♣❡rt❡♥❝❡♠ ❛ ❢❛♠í❧✐❛s ❞✐❢❡r❡♥t❡s✳ ❈♦♥s✐❞❡r❛♠✲s❡ ♦s ♦❜❥❡t✐✈♦s ❞❡ ♠✐♥✐♠✐③❛r ♦ ♠❛✲ ❦❡s♣❛♥ ❡ ♦ ❛tr❛s♦ t♦t❛❧ ♣♦♥❞❡r❛❞♦✳ P❛r❛ r❡s♦❧✈ê✲❧♦✱ ❢♦r❛♠ ❛♥❛❧✐s❛❞♦s s❡t❡ ❛❧❣♦r✐t♠♦s ❞❡ ♦t✐♠✐③❛çã♦ ♠✉❧t✐♦❜❥❡t✐✈♦✳ ❖ ♣r✐♠❡✐r♦ é ♦ ▼✉❧t✐✲♦❜❥❡❝t✐✈❡ ❱❛r✐❛❜❧❡ ◆❡✐❣❤❜♦r❤♦♦❞ ❙❡❛r❝❤ ✭▼❖❱◆❙✮✱ q✉❡ é ✉♠ ♠ét♦❞♦ ❞❡ ♦t✐♠✐③❛çã♦ ♠✉❧t✐♦❜❥❡t✐✈♦ ❜❛s❡❛❞♦ ♥❛ ♠❡✲ t❛❤❡✉ríst✐❝❛ ❱❛r✐❛❜❧❡ ◆❡✐❣❤❜♦r❤♦♦❞ ❙❡❛r❝❤ ✭❱◆❙✮✳ ❖ s❡❣✉♥❞♦ ❡ ♦ t❡r❝❡✐r♦ sã♦ ❞✉❛s ✈❛r✐❛♥t❡s ❞♦ ▼❖❱◆❙ ❡♥❝♦♥tr❛❞❛s ♥❛ ❧✐t❡r❛t✉r❛✱ ❞❡♥♦♠✐♥❛❞❛s ▼❖❱◆❙❴❖tt♦♥✐ ❡ ▼❖❱◆❙❴❆rr♦②♦✱ q✉❡ ❝♦♥s✐st❡♠ ❡♠ ❛❞✐❝✐♦♥❛r ✉♠ ♣r♦❝❡❞✐♠❡♥t♦ ❞❡ ✐♥t❡♥s✐✜❝❛çã♦ ♥♦ ▼❖❱◆❙✳ ❖ q✉❛rt♦ é ♦ P❛r❡t♦ ■t❡r❛t❡❞ ▲♦❝❛❧ ❙❡❛r❝❤ ✭P■▲❙✮✱ q✉❡ é ✉♠ ❛❧❣♦r✐t♠♦ ♠✉❧t✐♦❜❥❡t✐✈♦ ❞❡ ❜✉s❝❛ ❧♦❝❛❧ ❝♦♠ ❝❛r❛❝t❡ríst✐❝❛s s❡♠❡❧❤❛♥t❡s à ♠❡t❛❤❡✉ríst✐❝❛ ■t❡✲ r❛t❡❞ ▲♦❝❛❧ ❙❡❛r❝❤ ✭■▲❙✮✳ ❖ q✉✐♥t♦ é ✉♠❛ ✈❛r✐❛♥t❡ ❞♦ P■▲❙ ♣r♦♣♦st❛ ♥❡st❡ tr❛❜❛❧❤♦✱ ❞❡♥♦♠✐♥❛❞❛ P■▲❙✶✱ ❡♠ q✉❡ ✉♠ ♥♦✈♦ ♣r♦❝❡❞✐♠❡♥t♦ ❞❡ ♣❡rt✉r❜❛çã♦ é ❞❡s❡♥✈♦❧✈✐❞♦✳ ❖ s❡①t♦ ❡ ♦ sét✐♠♦ sã♦ ♦ ◆♦♥❞♦♠✐♥❛t❡❞ ❙♦rt✐♥❣ ●❡♥❡t✐❝ ❆❧❣♦r✐t❤♠ ■■ ✭◆❙●❆✲■■✮ ❡ ♦ ❙tr❡♥❣t❤ P❛r❡t♦ ❊✈♦❧✉t✐♦♥❛r② ❆❧❣♦r✐t❤♠ ✷ ✭❙P❊❆✷✮✱ ♦s q✉❛✐s sã♦ ♠ét♦❞♦s ❞❡ ♦t✐♠✐③❛çã♦ ❜❛s❡❛❞♦s ♥♦ ♣r♦❝❡ss♦ ❞❡ ❡✈♦❧✉çã♦ ♥❛t✉r❛❧ ♣❛r❛ ♣r♦❜❧❡♠❛s ♠✉❧t✐♦❜❥❡t✐✲ ✈♦s✳ ❊♥tr❡ ♦s s❡t❡ ❛❧❣♦r✐t♠♦s✱ ❝✐♥❝♦ sã♦ ❞❡ ❜✉s❝❛ ❧♦❝❛❧✿ ▼❖❱◆❙✱ ▼❖❱◆❙❴❖tt♦♥✐✱ ▼❖❱◆❙❴❆rr♦②♦✱ P■▲❙ ❡ P■▲❙✶✱ ❡ ♦✉tr♦s ❞♦✐s sã♦ ❞❡ ❜✉s❝❛ ♣♦♣✉❧❛❝✐♦♥❛❧✿ ◆❙●❆✲■■ ❡ ❙P❊❆✷✳ ❊ss❡s ❛❧❣♦r✐t♠♦s ❢♦r❛♠ ❝♦♠♣❛r❛❞♦s ❡♠ r❡❧❛çã♦ às ♠étr✐❝❛s ❞❡ ❝❛r❞✐✲ ♥❛❧✐❞❛❞❡✱ ❞✐stâ♥❝✐❛ ♠é❞✐❛✱ ❞✐stâ♥❝✐❛ ♠á①✐♠❛✱ ❞✐❢❡r❡♥ç❛ ❞❡ ❤✐♣❡r✈♦❧✉♠❡ ❡ ❡♣s✐❧♦♥✳ ❖s r❡s✉❧t❛❞♦s ❝♦♠♣✉t❛❝✐♦♥❛✐s r❡❛❧✐③❛❞♦s ❡♠ ✐♥stâ♥❝✐❛s✲t❡st❡ ❣❡r❛❞❛s ❛❧❡❛t♦r✐❛♠❡♥t❡ ♠♦str❛r❛♠ q✉❡ ♦ ❛❧❣♦r✐t♠♦ P■▲❙✶ é ❡st❛t✐st✐❝❛♠❡♥t❡ s✉♣❡r✐♦r ❛ t♦❞♦s ♦s ♦✉tr♦s ❛❧❣♦r✐t♠♦s ❡♠ r❡❧❛çã♦ às ♠étr✐❝❛s ❝❛r❞✐♥❛❧✐❞❛❞❡✱ ❞✐stâ♥❝✐❛ ♠é❞✐❛✱ ❞✐❢❡r❡♥ç❛ ❞❡ ❤✐✲ ♣❡r✈♦❧✉♠❡ ❡ ♠étr✐❝❛ ❡♣s✐❧♦♥✱ ❡♠ t❡r♠♦s ❞❡ r❡s✉❧t❛❞♦s ♠é❞✐♦s✳ ❖ P■▲❙✶ ❝♦♥s❡❣✉✐✉ t❛♠❜é♠ ♦ ♠❡❧❤♦r r❡s✉❧t❛❞♦ ♠é❞✐♦ ♣❛r❛ ❛ ♠étr✐❝❛ ❞✐stâ♥❝✐❛ ♠á①✐♠❛❀ ❡♥tr❡t❛♥t♦✱ ❛ ♣❛rt✐r ❞❛ ❛♥á❧✐s❡ ❡st❛tíst✐❝❛ ♥ã♦ ❢♦✐ ♣♦ssí✈❡❧ ❛✜r♠❛r q✉❡ ❛ ❞✐❢❡r❡♥ç❛ ♦❜s❡r✈❛❞❛ ❡♥tr❡ ❡❧❡ ♦ ◆❙●❆✲■■ ❡r❛ s✐❣♥✐✜❝❛t✐✈❛✳
P❆▲❆❱❘❆❙✲❈❍❆❱❊✿ Pr♦❜❧❡♠❛ ❞❡ s❡q✉❡♥❝✐❛♠❡♥t♦ ❡♠ ú♥✐❝❛ ♠áq✉✐♥❛✱ ❖t✐♠✐✲ ③❛çã♦ ♠✉❧t✐♦❜❥❡t✐✈♦✱ P❛r❡t♦ ■t❡r❛t❡❞ ▲♦❝❛❧ ❙❡❛r❝❤✱ ▼✉❧t✐✲♦❜❥❡❝t✐✈❡ ❱❛r✐❛❜❧❡ ◆❡✐❣❤✲ ❜♦r❤♦♦❞ ❙❡❛r❝❤✱ ◆♦♥❞♦♠✐♥❛t❡❞ ❙♦rt✐♥❣ ●❡♥❡t✐❝ ❆❧❣♦r✐t❤♠✱ ❙tr❡♥❣t❤ P❛r❡t♦ ❊✈♦❧✉✲ t✐♦♥❛r② ❆❧❣♦r✐t❤♠
❆❜str❛❝t
❚❤✐s ✇♦r❦ ❛❞❞r❡ss❡s t❤❡ ❙✐♥❣❧❡ ▼❛❝❤✐♥❡ ❙❝❤❡❞✉❧✐♥❣ Pr♦❜❧❡♠ ✇✐t❤ ❙❡q✉❡♥❝❡ ❉❡✲ ♣❡♥❞❡♥t ❋❛♠✐❧② ❙❡t✉♣ ❚✐♠❡s✳ ■♥ t❤✐s ♣r♦❜❧❡♠✱ t❤❡r❡ ✐s ❛ s❡t ♦❢ ❥♦❜s t♦ ❜❡ ♣r♦✲ ❝❡ss❡❞ ❜② ❛ s✐♥❣❧❡ ♠❛❝❤✐♥❡✱ ❛♥❞ ❜❡❢♦r❡ t❤❡ ❡①❡❝✉t✐♦♥ ♦❢ ❡❛❝❤ ❥♦❜ ❛ t✐♠❡ t♦ ♣r❡✲ ♣❛r❡ t❤❡ ♠❛❝❤✐♥❡ ✐s r❡q✉✐r❡❞✱ ✇❤✐❝❤ ✐s ❞❡✜♥❡❞ ❛❝❝♦r❞✐♥❣ t♦ t❤❡ s❡q✉❡♥❝❡ ❛♥❞ t❤❡ ❢❛♠✐❧② ♦❢ t❤❡ ❥♦❜✳ ❚❤✉s✱ t❤❡ s❡t✉♣ t✐♠❡ ✐s r❡q✉✐r❡❞ ♦♥❧② t♦ ♣❡r❢♦r♠ t✇♦ ❝♦♥s❡✲ ❝✉t✐✈❡ ❥♦❜s ❜❡❧♦♥❣✐♥❣ t♦ ❞✐✛❡r❡♥t ❢❛♠✐❧✐❡s✳ ❚✇♦ ♦❜❥❡❝t✐✈❡s ✇❡r❡ ❝♦♥s✐❞❡r❡❞✿ t❤❡ ♠✐♥✐♠✐③❛t✐♦♥ ♦❢ t❤❡ ♠❛❦❡s♣❛♥ ❛♥❞ t❤❡ t♦t❛❧ ✇❡✐❣❤t❡❞ t❛r❞✐♥❡ss✳ ■♥ ♦r❞❡r t♦ s♦❧✈❡ t❤✐s ♣r♦❜❧❡♠✱ s❡✈❡♥ ♠✉❧t✐✲♦❜❥❡❝t✐✈❡ ❛❧❣♦r✐t❤♠s ✇❡r❡ ❛♥❛❧②③❡❞✳ ❚❤❡ ✜rst ♦♥❡ ✐s t❤❡ ▼✉❧t✐✲♦❜❥❡❝t✐✈❡ ❱❛r✐❛❜❧❡ ◆❡✐❣❤❜♦r❤♦♦❞ ❙❡❛r❝❤ ✭▼❖❱◆❙✮✱ ✇❤✐❝❤ ✐s ❛ ♠✉❧t✐✲♦❜❥❡❝t✐✈❡ ♦♣t✐♠✐③❛t✐♦♥ ♠❡t❤♦❞ ❜❛s❡❞ ♦♥ ❱❛r✐❛❜❧❡ ◆❡✐❣❤❜♦r❤♦♦❞ ❙❡❛r❝❤ ✭❱◆❙✮✳ ❚❤❡ s❡❝♦♥❞ ❛♥❞ t❤✐r❞ ♦♥❡s ❛r❡ t✇♦ ✈❛r✐❛♥ts ♦❢ ▼❖❱◆❙ ❢♦✉♥❞ ✐♥ t❤❡ ❧✐t❡r❛t✉r❡✱ ❤❡r❡ ♥❛♠❡❞ ▼❖❱◆❙❴❖tt♦♥✐ ❛♥❞ ▼❖❱◆❙❴❆rr♦②♦✱ ✇❤✐❝❤ ❝♦♥s✐sts ✐♥ ❛❞❞✐♥❣ ❛♥ ✐♥t❡♥s✐✜❝❛t✐♦♥ ♣r♦❝❡❞✉r❡ ✐♥ t❤❡ ▼❖❱◆❙✳ ❚❤❡ ❢♦✉rt❤ ♦♥❡ ✐s t❤❡ P❛r❡t♦ ■t❡r❛t❡❞ ▲♦❝❛❧ ❙❡❛r❝❤ ✭P■▲❙✮✱ ✇❤✐❝❤ ✐s ❛ ♠✉❧t✐✲♦❜❥❡❝t✐✈❡ ❧♦❝❛❧ s❡❛r❝❤ ❛❧❣♦r✐t❤♠ ✇✐t❤ s✐♠✐❧❛r ❢❡❛t✉r❡s t♦ t❤❡ ♠❡t❛✲ ❤❡✉r✐st✐❝s ■t❡r❛t❡❞ ▲♦❝❛❧ ❙❡❛r❝❤ ✭■▲❙✮✳ ❚❤❡ ✜❢t❤ ♦♥❡ ✐s ❛ ✈❛r✐❛♥t ♦❢ P■▲❙ ♣r♦♣♦s❡❞ ✐♥ t❤✐s ✇♦r❦✱ ❝❛❧❧❡❞ P■▲❙✶✱ ✐♥ ✇❤✐❝❤ ❛ ♥❡✇ ♣❡rt✉r❜❛t✐♦♥ ♣r♦❝❡❞✉r❡ ✐s ❞❡✈❡❧♦♣❡❞✳ ❚❤❡ s✐①t❤ ❛♥❞ s❡✈❡♥t❤ ♦♥❡s ❛r❡ t❤❡ ◆♦♥❞♦♠✐♥❛t❡❞ ❙♦rt✐♥❣ ●❡♥❡t✐❝ ❆❧❣♦r✐t❤♠ ■■ ✭◆❙●❆✲■■✮ ❛♥❞ t❤❡ ❙tr❡♥❣t❤ P❛r❡t♦ ❊✈♦❧✉t✐♦♥❛r② ❆❧❣♦r✐t❤♠ ✷ ✭❙P❊❆✷✮✱ ✇❤✐❝❤ ❛r❡ ♦♣t✐♠✐③❛t✐♦♥ ♠❡t❤♦❞s ❜❛s❡❞ ♦♥ t❤❡ ♣r♦❝❡ss ♦❢ ♥❛t✉r❛❧ ❡✈♦❧✉t✐♦♥ ❢♦r ♠✉❧t✐✲♦❜❥❡❝t✐✈❡ ♣r♦❜❧❡♠s✳ ❆♠♦♥❣ t❤❡ s❡✈❡♥ ❛❧❣♦r✐t❤♠s✱ ✜✈❡ ❛r❡ ❜❛s❡❞ ♦♥ ❧♦❝❛❧ s❡❛r❝❤✿ ▼❖❱◆❙✱ ▼❖❱◆❙❴❖tt♦♥✐✱ ▼❖❱◆❙❴❆rr♦②♦✱ P■▲❙ ❛♥❞ P■▲❙✶✱ ❛♥❞ t✇♦ ♦t❤❡r ❛r❡ ♣♦♣✉❧❛t✐♦♥✲ ❜❛s❡❞✿ ◆❙●❆✲■■ ❛♥❞ ❙P❊❆✷✳ ❚❤❡s❡ ❛❧❣♦r✐t❤♠s ✇❡r❡ ❝♦♠♣❛r❡❞ ❛❝❝♦r❞✐♥❣ t♦ ❝❛r✲ ❞✐♥❛❧✐t②✱ ❛✈❡r❛❣❡ ❞✐st❛♥❝❡✱ ♠❛①✐♠✉♠ ❞✐st❛♥❝❡✱ ❤②♣❡r✈♦❧✉♠❡ ❞✐✛❡r❡♥❝❡ ❛♥❞ ❡♣s✐❧♦♥ ♠❡tr✐❝s✳ ❚❤❡ ❈♦♠♣✉t❛t✐♦♥❛❧ r❡s✉❧ts r❡❛❧✐③❡❞ ♦✈❡r t❡st ✐♥st❛♥❝❡s r❛♥❞♦♠❧② ❣❡♥❡r❛✲ t❡❞ s❤♦✇ t❤❛t P■▲❙✶ ✐s st❛t✐st✐❝❛❧❧② ❜❡tt❡r t❤❛♥ ❛❧❧ ♦t❤❡r ❛❧❣♦r✐t❤♠s ✐♥ r❡❧❛t✐♦♥ t♦ t❤❡ ❝❛r❞✐♥❛❧✐t②✱ ❛✈❡r❛❣❡ ❞✐st❛♥❝❡✱ ❞✐✛❡r❡♥❝❡ ♦❢ ❤②♣❡r✈♦❧✉♠❡ ❛♥❞ ❡♣s✐❧♦♥ ♠❡tr✐❝s✱ ✐♥ t❡r♠s ♦❢ ❛✈❡r❛❣❡ r❡s✉❧ts✳ ❚❤❡ P■▲❙✶ ♣r♦❞✉❝❡❞ ❛❧s♦ t❤❡ ❜❡st ❛✈❡r❛❣❡ r❡s✉❧t ❢♦r t❤❡ ♠❡tr✐❝ ♠❛①✐♠✉♠ ❞✐st❛♥❝❡❀ ❤♦✇❡✈❡r✱ ❢r♦♠ t❤❡ st❛t✐st✐❝❛❧ ❛♥❛❧②s✐s ✐s ♥♦t ♣♦ss✐❜❧❡ t♦ ❛✣r♠ t❤❛t t❤❡ ❞✐✛❡r❡♥❝❡ ❜❡t✇❡❡♥ ✐t ❛♥❞ t❤❡ ◆❙●❆✲■■ ✐s s✐❣♥✐✜❝❛♥t✳
❑❡②✇♦r❞s✿ ❙✐♥❣❧❡ ♠❛❝❤✐♥❡ s❝❤❡❞✉❧✐♥❣✱ ▼✉❧t✐✲♦❜❥❡❝t✐✈❡ ♦♣t✐♠✐③❛t✐♦♥✱ P❛r❡t♦ ■t❡✲ r❛t❡❞ ▲♦❝❛❧ ❙❡❛r❝❤✱ ▼✉❧t✐✲♦❜❥❡❝t✐✈❡ ❱❛r✐❛❜❧❡ ◆❡✐❣❤❜♦r❤♦♦❞ ❙❡❛r❝❤✱ ◆♦♥❞♦♠✐♥❛t❡❞ ❙♦rt✐♥❣ ●❡♥❡t✐❝ ❆❧❣♦r✐t❤♠✱ ❙tr❡♥❣t❤ P❛r❡t♦ ❊✈♦❧✉t✐♦♥❛r② ❆❧❣♦r✐t❤♠
❙✉♠ár✐♦
▲✐st❛ ❞❡ ❋✐❣✉r❛s ✐①
▲✐st❛ ❞❡ ❆❧❣♦r✐t♠♦s ①
▲✐st❛ ❞❡ ❚❛❜❡❧❛s ①✐
▲✐st❛ ❞❡ ❆❜r❡✈✐❛t✉r❛s ❡ ❙✐❣❧❛s ①✐✐
✶ ■♥tr♦❞✉çã♦ ✶
✶✳✶ ❖❜❥❡t✐✈♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸ ✶✳✶✳✶ ❖❜❥❡t✐✈♦ ●❡r❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸ ✶✳✶✳✷ ❖❜❥❡t✐✈♦s ❊s♣❡❝í✜❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸ ✶✳✷ ▼♦t✐✈❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹ ✶✳✸ ❊str✉t✉r❛ ❞♦ ❚r❛❜❛❧❤♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹
✷ ❈❛r❛❝t❡r✐③❛çã♦ ❞♦ Pr♦❜❧❡♠❛ ✺
✸ ❘❡✈✐sã♦ ❇✐❜❧✐♦❣rá✜❝❛ ✼
✸✳✶ ❖t✐♠✐③❛çã♦ ▼✉❧t✐♦❜❥❡t✐✈♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼ ✸✳✶✳✶ ❉❡✜♥✐çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼ ✸✳✶✳✷ ▼ét♦❞♦s ❈❧áss✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾ ✸✳✷ ▼étr✐❝❛s ❞❡ ❆✈❛❧✐❛çã♦ ❞❡ ❉❡s❡♠♣❡♥❤♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶ ✸✳✷✳✶ ▼étr✐❝❛ ❞❡ ❈❛r❞✐♥❛❧✐❞❛❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶ ✸✳✷✳✷ ▼étr✐❝❛s ❞❡ ❉✐stâ♥❝✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷ ✸✳✷✳✸ ▼étr✐❝❛ ❤✐♣❡r✈♦❧✉♠❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷ ✸✳✷✳✹ ▼étr✐❝❛ ❡♣s✐❧♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸ ✸✳✸ ❆❧❣♦r✐t♠♦s ▼✉❧t✐♦❜❥❡t✐✈♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹ ✸✳✸✳✶ ▼❖❱◆❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺ ✸✳✸✳✷ ▼❖❱◆❙❴❖tt♦♥✐ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻ ✸✳✸✳✸ ▼❖❱◆❙❴❆rr♦②♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻ ✸✳✸✳✹ P■▲❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽ ✸✳✸✳✺ ◆❙●❆✲■■ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✸✳✸✳✻ ❙P❊❆✷ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✸✳✹ ❚r❛❜❛❧❤♦s ❘❡❧❛❝✐♦♥❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✸✳✹✳✶ ▼❛❦❡s♣❛♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✸✳✹✳✷ ❆tr❛s♦ ❚♦t❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✸✳✹✳✸ ❋❛♠í❧✐❛s ❞❡ ❚❛r❡❢❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✸✳✹✳✹ Pr♦❜❧❡♠❛s ❞❡ ❖t✐♠✐③❛çã♦ ▼✉❧t✐♦❜❥❡t✐✈♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽
✹ ▼❡t♦❞♦❧♦❣✐❛ ✷✾ ✹✳✶ ❘❡♣r❡s❡♥t❛çã♦ ❞❛ ❙♦❧✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾ ✹✳✷ ●❡r❛çã♦ ❞❛ ❙♦❧✉çã♦ ■♥✐❝✐❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾ ✹✳✸ ❊str✉t✉r❛s ❞❡ ❱✐③✐♥❤❛♥ç❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✹✳✸✳✶ ❱✐③✐♥❤❛♥ç❛ ❞❡ ■♥s❡rçã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✹✳✸✳✷ ❱✐③✐♥❤❛♥ç❛ ❞❡ ❚r♦❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✹✳✹ P❡rt✉r❜❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✹✳✺ ❙❡❧❡çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✹✳✺✳✶ ❙❡❧❡çã♦ ♣❛r❛ ❘❡♣r♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✹✳✺✳✷ ❙❡❧❡çã♦ P♦♣✉❧❛❝✐♦♥❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✹✳✻ ❘❡♣r♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✹✳✻✳✶ ❈r✉③❛♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✹✳✻✳✷ ▼✉t❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾ ✹✳✼ ❆❧❣♦r✐t♠♦s ■♠♣❧❡♠❡♥t❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ✹✳✼✳✶ ▼❖❱◆❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ✹✳✼✳✷ ▼❖❱◆❙❴❖tt♦♥✐ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✹✳✼✳✸ ▼❖❱◆❙❴❆rr♦②♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✹✳✼✳✹ P■▲❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✹✳✼✳✺ P■▲❙✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✹✳✼✳✻ ◆❙●❆✲■■ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷ ✹✳✼✳✼ ❙P❊❆✷ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✹✳✽ ◆♦r♠❛❧✐③❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✹✳✾ P❛râ♠❡tr♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹
✺ ❘❡s✉❧t❛❞♦s ❈♦♠♣✉t❛❝✐♦♥❛✐s ✹✺
✺✳✶ ■♥stâ♥❝✐❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺ ✺✳✷ ❊①♣❡r✐♠❡♥t♦s ❈♦♠♣✉t❛❝✐♦♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻ ✺✳✸ ❆♥á❧✐s❡ ❊st❛tíst✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶
✻ ❈♦♥❝❧✉sõ❡s ❡ ❚r❛❜❛❧❤♦s ❋✉t✉r♦s ✺✻
❆ P✉❜❧✐❝❛çõ❡s ✺✽
❇ ❘❡s✉❧t❛❞♦s ❈♦♠♣❧❡t♦s ✺✾
❘❡❢❡rê♥❝✐❛s ✻✵
▲✐st❛ ❞❡ ❋✐❣✉r❛s
✶✳✶ Pr♦❞✉t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷ ✷✳✶ ❙❡q✉ê♥❝✐❛ r❡❧❛t✐✈❛ ❛♦ ❡①❡♠♣❧♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻ ✸✳✶ ▼❛♣❡❛♠❡♥t♦ ❞❛s ❱❛r✐á✈❡✐s ❞❡ ❉❡❝✐sã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽ ✸✳✷ ❋✉♥çã♦ P♦♥❞❡r❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵ ✸✳✸ ❍✐♣❡r✈♦❧✉♠❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸ ✸✳✹ ❉✐❢❡r❡♥ç❛ ❞♦ ❍✐♣❡r✈♦❧✉♠❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸ ✸✳✺ ❊♣s✐❧♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹ ✸✳✻ P❡rt✉r❜❛çã♦ ❖r✐❣✐♥❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✹✳✶ ❘❡♣r❡s❡♥t❛çã♦ ❞❛ ❙♦❧✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾ ✹✳✷ ▼♦✈✐♠❡♥t♦ ❞❡ ✐♥s❡rçã♦ ♣❛r❛x < y ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵
✹✳✸ ▼♦✈✐♠❡♥t♦ ❞❡ ✐♥s❡rçã♦ ♣❛r❛x > y ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶
✹✳✹ ▼♦✈✐♠❡♥t♦ ❞❡ tr♦❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✹✳✺ ◆í✈❡❧ ✶ ❞❛ P❡rt✉r❜❛çã♦ Pr♦♣♦st❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ✹✳✻ ◆í✈❡❧ ✷ ❞❛ P❡rt✉r❜❛çã♦ Pr♦♣♦st❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ✹✳✼ ◆í✈❡❧p ❞❛ P❡rt✉r❜❛çã♦ Pr♦♣♦st❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷
✹✳✽ ❖♣❡r❛❞♦r ❖❳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✹✳✾ ❖♣❡r❛❞♦r ▲❖❳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼ ✹✳✶✵ ▼❛♣❡❛♠❡♥t♦ ❞♦ ♣r✐♠❡✐r♦ ❡❧❡♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✹✳✶✶ ▼❛♣❡❛♠❡♥t♦ ❞♦ s❡❣✉♥❞♦ ❡❧❡♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾
▲✐st❛ ❞❡ ❆❧❣♦r✐t♠♦s
✶ ▼❖❱◆❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺ ✷ ■♥t❡♥s✐✜❝❛çã♦ ❞❡ ❖tt♦♥✐ ❡t ❛❧✳ ✭✷✵✶✶✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼ ✸ ■♥t❡♥s✐✜❝❛çã♦ ❞❡ ❆rr♦②♦ ❡t ❛❧✳ ✭✷✵✶✶✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽ ✹ P■▲❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✺ ❋❛st ◆♦♥✲❉♦♠✐♥❛t❡❞ ❙♦rt✐♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ✻ ❝r♦✇❞✐♥❣ ❞✐st❛♥❝❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✼ ◆❙●❆✲■■ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸ ✽ ❙P❊❆✷ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹ ✾ P■▲❙✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷
▲✐st❛ ❞❡ ❚❛❜❡❧❛s
✷✳✶ ■♥stâ♥❝✐❛ ❞♦ ♣r♦❜❧❡♠❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻ ✷✳✷ ❚❡♠♣♦ ❞❡ Pr❡♣❛r❛çã♦ ❡♥tr❡ ❛s ❋❛♠í❧✐❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻ ✸✳✶ ❘❡❧❛çõ❡s ❞❡ ❉♦♠✐♥â♥❝✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾ ✹✳✶ ❱❛❧♦r❡s ❞♦s ♠❡❧❤♦r❡s ♣❛râ♠❡tr♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹ ✺✳✶ ◆ú♠❡r♦ ❞❡ s♦❧✉çõ❡s ♥ã♦✲❞♦♠✐♥❛❞❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻ ✺✳✷ ❈♦♠♣❛r❛çã♦ ❞♦s ❛❧❣♦r✐t♠♦s ❝♦♠ r❡❧❛çã♦ à ♠étr✐❝❛ ❞❡ ❈❛r❞✐♥❛❧✐❞❛❞❡
✭C1R✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼
✺✳✸ ❈♦♠♣❛r❛çã♦ ❞♦s ❛❧❣♦r✐t♠♦s ❝♦♠ r❡❧❛çã♦ à ♠étr✐❝❛ ❉✐stâ♥❝✐❛ ▼é❞✐❛ ✭D1R✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽
✺✳✹ ❈♦♠♣❛r❛çã♦ ❞♦s ❛❧❣♦r✐t♠♦s ❝♦♠ r❡❧❛çã♦ à ♠étr✐❝❛ ❉✐stâ♥❝✐❛ ▼á①✐♠❛ ✭Dmax✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽
✺✳✺ ❈♦♠♣❛r❛çã♦ ❞♦s ❛❧❣♦r✐t♠♦s ❝♦♠ r❡❧❛çã♦ à ♠étr✐❝❛ ❉✐❢❡r❡♥ç❛ ❞❡ ❍✐✲ ♣❡r✈♦❧✉♠❡ ✭H−✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ✺✳✻ ❈♦♠♣❛r❛çã♦ ❞♦s ❛❧❣♦r✐t♠♦s ❝♦♠ r❡❧❛çã♦ à ♠étr✐❝❛ ❊♣s✐❧♦♥✭I1
ǫ✮ ✳ ✳ ✳ ✳ ✺✵
✺✳✼ ❘❡s✉♠♦ ❞❛ ❝♦♠♣❛r❛çã♦ ❞♦s ❛❧❣♦r✐t♠♦s ♣♦r ♠étr✐❝❛ ❡♠ r❡❧❛çã♦ ❛♦s r❡s✉❧t❛❞♦s ♠é❞✐♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵ ✺✳✽ ❘❡s✉♠♦ ❞❛ ❝♦♠♣❛r❛çã♦ ❞♦s ❛❧❣♦r✐t♠♦s ♣♦r ♠étr✐❝❛ ❡♠ r❡❧❛çã♦ ❛♦s
♠❡❧❤♦r❡s r❡s✉❧t❛❞♦s ❡♥❝♦♥tr❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶ ✺✳✾ ❚❡st❡ ❑r✉s❦❛❧✲❲❛❧❧✐s✿ ❝❛r❞✐♥❛❧✐❞❛❞❡ ✭C1R✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷
✺✳✶✵ ❚❡st❡ ❑r✉s❦❛❧✲❲❛❧❧✐s✿ ❞✐stâ♥❝✐❛ ♠é❞✐❛ ✭D1R✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷
✺✳✶✶ ❚❡st❡ ❑r✉s❦❛❧✲❲❛❧❧✐s✿ ❞✐stâ♥❝✐❛ ♠á①✐♠❛ ✭Dmax✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸
✺✳✶✷ ❚❡st❡ ❑r✉s❦❛❧✲❲❛❧❧✐s✿ ❞✐❢❡r❡♥ç❛ ❞❡ ❤✐♣❡r✈♦❧✉♠❡ ✭H−✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ✺✳✶✸ ❚❡st❡ ❑r✉s❦❛❧✲❲❛❧❧✐s✿ ♠étr✐❝❛ ❡♣s✐❧♦♥ ✭I1
ǫ✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹
✺✳✶✹ ❚❡st❡ ❑r✉s❦❛❧✲❲❛❧❧✐s ❞❡ ❝♦♠♣❛r❛çã♦ ♠ú❧t✐♣❧❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺
▲✐st❛ ❞❡ ❆❜r❡✈✐❛t✉r❛s ❡ ❙✐❣❧❛s
■▲❙ ■t❡r❛t❡❞ ▲♦❝❛❧ ❙❡❛r❝❤ ▲❖❳ ▲✐♥❡❛r ❖r❞❡r ❈r♦ss♦✈❡r
▼❖❱◆❙ ▼✉❧t✐✲♦❜❥❡❝t✐✈❡ ❱❛r✐❛❜❧❡ ◆❡✐❣❤❜♦r❤♦♦❞ ❙❡❛r❝❤ ◆❙●❆✲■■ ◆♦♥❞♦♠✐♥❛t❡❞ ❙♦rt✐♥❣ ●❡♥❡t✐❝ ❆❧❣♦r✐t❤♠ ■■ ❖❳ ❖r❞❡r ❈r♦ss♦✈❡r
P▼❳ P❛rt✐❛❧ ▼❛♣♣❡❞ ❈r♦ss♦✈❡r P■▲❙ P❛r❡t♦ ■t❡r❛t❡❞ ▲♦❝❛❧ ❙❡❛r❝❤
❙P❊❆✷ ❙tr❡♥❣t❤ P❛r❡t♦ ❊✈♦❧✉t✐♦♥❛r② ❆❧❣♦r✐t❤♠ ✷ ❱◆❙ ❱❛r✐❛❜❧❡ ◆❡✐❣❤❜♦r❤♦♦❞ ❙❡❛r❝❤
❈❛♣ít✉❧♦ ✶
■♥tr♦❞✉çã♦
◆♦ ❛t✉❛❧ ❛♠❜✐❡♥t❡ ❝♦♠♣❡t✐t✐✈♦ ✐♥❞✉str✐❛❧✱ ❡♠ q✉❡ ♥♦t❛✲s❡ ✉♠ ❛✉♠❡♥t♦ ❞❛ ❝♦♥❝♦rrê♥✲ ❝✐❛ ❡♥tr❡ ❛s ❡♠♣r❡s❛s✱ ❝♦❧♦❝❛✲s❡ ♦ s✐st❡♠❛ ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦✱ ♣r♦❣r❛♠❛çã♦ ❡ ❝♦♥tr♦❧❡ ❞❛ ♣r♦❞✉çã♦ ❝♦♠♦ ✉♠❛ ár❡❛ ❞❡ ❞❡❝✐sã♦ ♣r✐♦r✐tár✐❛ ♣❛r❛ ❛s ♦r❣❛♥✐③❛çõ❡s ✭P❡❞r♦s♦ ❡ ❈♦rrê❛✱ ✶✾✾✻✮✳ ◆❡st❡ ❝♦♥t❡①t♦✱ r❡❛❧✐③❛r ♦ ♣❧❛♥❡❥❛♠❡♥t♦ ❞♦ s❡q✉❡♥❝✐❛♠❡♥t♦ ❞❡ t❛r❡❢❛s ✐♠♣❧✐❝❛ ❡♠ ♠❡❧❤♦r❛r ♦ ❝♦♥tr♦❧❡ ❞♦ ✢✉①♦ ❞❛ ❝❛❞❡✐❛ ♣r♦❞✉t✐✈❛✳ ❊ss❡ ♣❧❛♥❡❥❛♠❡♥t♦ ❞❡ t❛r❡❢❛s ❞❡✈❡ s❡r ❢❡✐t♦ ❞❡ ♠♦❞♦ ❛ ♣❡r♠✐t✐r q✉❡ ❛ ❡♠♣r❡s❛ ❝♦♥s✐❣❛ ❝✉♠♣r✐r ♦s ♣r❛③♦s ❞❡ ❡♥tr❡❣❛ q✉❡ ❢♦r❛♠ ❛❝♦r❞❛❞♦s✱ s♦❜ ♦ r✐s❝♦ ❞❡ ♣❡r❞❡r ❝❧✐❡♥t❡s ❡♠ ❝❛s♦ ❞❡ ❞❡s❝✉♠✲ ♣r✐♠❡♥t♦✳ ❆❧é♠ ❞✐ss♦✱ ❞❡s❡❥❛✲s❡ ♣r♦❣r❛♠❛r ❛s ❛t✐✈✐❞❛❞❡s ❞❡ t❛❧ ♠❛♥❡✐r❛ ❛ ✉t✐❧✐③❛r ♦s r❡❝✉rs♦s ❞✐s♣♦♥í✈❡✐s ❞❡ ✉♠❛ ❢♦r♠❛ ♠❛✐s ❡✜❝✐❡♥t❡ ♣♦ssí✈❡❧✳ ❖s ❜❡♥❡❢í❝✐♦s ❞❡ ✉♠ ❜♦♠ ♣❧❛♥❡❥❛♠❡♥t♦ sã♦ ♦ ❛✉♠❡♥t♦ ❞❛ ♣r♦❞✉t✐✈✐❞❛❞❡ ♦r❣❛♥✐③❛❝✐♦♥❛❧✱ r❡❞✉çã♦ ❞♦s ❝✉st♦s ❞❡ ♣r♦❞✉çã♦✱ ❛❣✐❧✐❞❛❞❡ ♥♦ ♣r♦❝❡ss♦ ❞❡ t♦♠❛❞❛ ❞❡ ❞❡❝✐sã♦ ❡ ❛✉♠❡♥t♦ ❞❛ ❡✜❝✐ê♥❝✐❛ ♦r❣❛♥✐③❛❝✐♦♥❛❧✳
❖ ♣r♦❜❧❡♠❛ ❞❡ r❡❛❧✐③❛r ♦ s❡q✉❡♥❝✐❛♠❡♥t♦ ❞❡ t❛r❡❢❛s ❡stá ♣r❡s❡♥t❡ ❡♠ ❞✐✈❡rs❛s ár❡❛s✱ ❝♦♠♦ ♥❛ ✐♥❞ústr✐❛✱ ♥❛ ♠❛♥✉❢❛t✉r❛✱ ♥♦ ❣❡r❡♥❝✐❛♠❡♥t♦ ❞❡ ♣r♦❝❡ss♦s ❞❡ ✉♠ ❝♦♠♣✉t❛❞♦r✱ ❞❡♥tr❡ ♦✉tr❛s✳
❖s ♣r✐♠❡✐r♦s ❡st✉❞♦s✱ ❞❡ ♠❛✐♦r r❡❧❡✈â♥❝✐❛✱ ❢❡✐t♦s ❛❝❡r❝❛ ❞❡ss❡s ♣r♦❜❧❡♠❛s sã♦ ❞❛ ❞é❝❛❞❛ ❞❡ ✺✵ ❡✱ ❞❡s❞❡ ❡♥tã♦✱ ❛s ❛❜♦r❞❛❣❡♥s s❡ ❛♣r♦①✐♠❛r❛♠ ❝❛❞❛ ✈❡③ ♠❛✐s ❞❡ ❛♣❧✐✲ ❝❛çõ❡s ✐♥❞✉str✐❛✐s✱ ❛✉♠❡♥t❛♥❞♦ ❛ss✐♠ ❛ ❝♦♠♣❧❡①✐❞❛❞❡ ❞♦s ♣r♦❜❧❡♠❛s✳ ◆❡ss❛ é♣♦❝❛✱ ♦s ❡st✉❞♦s ❡r❛♠ ❢❡✐t♦s ❝♦♠ ♣r♦❜❧❡♠❛s r❡❧❛t✐✈❛♠❡♥t❡ s✐♠♣❧❡s✱ ♦ q✉❡ ♣♦ss✐❜✐❧✐t♦✉ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ❛❧❣♦r✐t♠♦s ❝❛♣❛③❡s ❞❡ ❢♦r♥❡❝❡r ✉♠❛ s♦❧✉çã♦ ót✐♠❛✳ ❈♦♠ ♦ ♣❛s✲ s❛r ❞♦ t❡♠♣♦ ❛s ❛❜♦r❞❛❣❡♥s ❢♦r❛♠ s❡ t♦r♥❛♥❞♦ ♠❛✐s s♦✜st✐❝❛❞❛s ❡ ♥❛ ❞é❝❛❞❛ ❞❡ ✼✵ ♠✉✐t♦s ♣r♦❜❧❡♠❛s ❢♦r❛♠ ♣r♦✈❛❞♦s s❡r ◆P✲❞✐❢í❝❡✐s✳ ❆♣ós ♦s ❛♥♦s ✽✵✱ ♦s ❡st✉❞♦s t♦♠❛r❛♠ ❞✉❛s ❞✐r❡çõ❡s✱ ❞❡ ✉♠ ❧❛❞♦ ❛❜♦r❞❛❣❡♥s ✉t✐❧✐③❛♥❞♦ ❛❧❣♦r✐t♠♦s ❛♣r♦①✐♠❛❞♦s ❡ ❞♦ ♦✉tr♦✱ ❡st✉❞♦s ❞❡ ♠ét♦❞♦s ❤❡✉ríst✐❝♦s ✭▲❡✉♥❣✱ ✷✵✵✹✮✳
◆♦ ♣r♦❝❡ss♦ ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦ ❡ ♦♣❡r❛çã♦ ✐♥❞✉str✐❛❧✱ é ✉s✉❛❧ q✉❡ ♠❛✐s ❞❡ ✉♠❛ ❢✉♥çã♦ ♦❜❥❡t✐✈♦ s❡❥❛ ❞❡s❡❥á✈❡❧ ❡ ❡ss❡♥❝✐❛❧ ♣❛r❛ ✉♠❛ ❛♥á❧✐s❡ ♠❛✐s ♣r❡❝✐s❛ ❞♦ ♣r♦❜❧❡♠❛✳ ◆♦ ❡♥t❛♥t♦✱ ♣♦r ✉♠❛ q✉❡stã♦ ❞❡ s✐♠♣❧✐❝✐❞❛❞❡ ❛ ♠❛✐♦r✐❛ ❞❛s ❛❜♦r❞❛❣❡♥s ♠♦❞❡❧❛♠ ♦ ♣r♦❜❧❡♠❛ ❝♦♠ ✉♠ ú♥✐❝♦ ♦❜❥❡t✐✈♦✳
❖❜s❡r✈❛✲s❡ q✉❡ ❡♠ ♣r♦❜❧❡♠❛s ❞❡ s❡q✉❡♥❝✐❛♠❡♥t♦✱ ❡①✐st❡♠ ♠✉✐t♦s ♦❜❥❡t✐✈♦s ❞✐✲ ❢❡r❡♥t❡s ❡ ❝♦♥✢✐t❛♥t❡s✱ ❞♦s q✉❛✐s✱ s❡❣✉♥❞♦ P✐♥❡❞♦ ✭✷✵✵✽✮✱ ♣♦❞❡✲s❡ ❞❡st❛❝❛r✿
• ▼❛❦❡s♣❛♥✱ q✉❡ ❝♦♥s✐st❡ ❡♠ ♠✐♥✐♠✐③❛r ♦ ♠❛✐♦r t❡♠♣♦ ❞❡ tér♠✐♥♦ ❞❡ ✉♠ ❝♦♥✲
❥✉♥t♦ ❞❡ t❛r❡❢❛s✳ ❆ ♠✐♥✐♠✐③❛çã♦ ❞♦ ♠❛❦❡s♣❛♥ ✐♠♣❧✐❝❛ ❡♠ ✉♠❛ ❜♦❛ ✉t✐❧✐③❛çã♦ ❞❛ ♠áq✉✐♥❛❀
✶✳✵ ■♥tr♦❞✉çã♦ ✷
• ❙♦♠❛ ♣♦♥❞❡r❛❞❛ ❞♦s t❡♠♣♦s ❞❡ tér♠✐♥♦ ❞❡ ❝❛❞❛ t❛r❡❢❛ ♦✉ ✢✉①♦ t♦t❛❧ ♣♦♥❞❡✲
r❛❞♦✱ q✉❡ ♠❡❞❡ ♦ ❡st♦q✉❡ ❡♠ ♣r♦❝❡ss❛♠❡♥t♦❀
• ❆tr❛s♦ t♦t❛❧ ♣♦♥❞❡r❛❞♦✱ q✉❡ ❝♦♥s✐st❡ ❡♠ ❞❡t❡r♠✐♥❛r ✉♠ s❡q✉❡♥❝✐❛♠❡♥t♦ ❝✉❥❛
s♦♠❛ ♣♦♥❞❡r❛❞❛ ❞♦s ❛tr❛s♦s ❞❛s t❛r❡❢❛s s❡❥❛ ♠í♥✐♠❛❀
• ❆❞✐❛♥t❛♠❡♥t♦ t♦t❛❧ ♣♦♥❞❡r❛❞♦✱ q✉❡ ❝♦♥s✐st❡ ❡♠ ❞❡t❡r♠✐♥❛r ✉♠ s❡q✉❡♥❝✐❛✲
♠❡♥t♦ ❝♦♠ ♦ ♠❡♥♦r ✈❛❧♦r ♣❛r❛ ❛❞✐❛♥t❛♠❡♥t♦ t♦t❛❧ ♣♦♥❞❡r❛❞♦❀
• ❙♦♠❛ ♣♦♥❞❡r❛❞❛ ❞❡ ❛tr❛s♦s ❡ ❛❞✐❛♥t❛♠❡♥t♦s✱ q✉❡ ❝♦♥s✐st❡ ❡♠ ❞❡t❡r♠✐♥❛r ✉♠
s❡q✉❡♥❝✐❛♠❡♥t♦ ❝♦♠ ✉♠ ✈❛❧♦r ♠í♥✐♠♦ ♣❛r❛ ♦ ❛❞✐❛♥t❛♠❡♥t♦ ❡ ❛tr❛s♦ ❞❛s t❛✲ r❡❢❛s✳ ❊ss❡ ♦❜❥❡t✐✈♦ ❡stá r❡❧❛❝✐♦♥❛❞♦ à ✜❧♦s♦✜❛ ❏✉st✲■♥✲❚✐♠❡ ❞❡ ♣r♦❞✉çã♦✱ ♥❛ q✉❛❧ ✉♠❛ t❛r❡❢❛ ❞❡✈❡ s❡r ✜♥❛❧✐③❛❞❛ ♥❛ s✉❛ ❞❛t❛ ❞❡ ❡♥tr❡❣❛✳
• ▲❛t❡♥❡ss ♠á①✐♠♦✱ q✉❡ ❝♦♥s✐st❡ ❡♠ ♠✐♥✐♠✐③❛r ❛ ♠❛✐♦r ❞✐❢❡r❡♥ç❛ ❡♥tr❡ ♦ t❡♠♣♦
❞❡ tér♠✐♥♦ ❡ ❛ ❞❛t❛ ❞❡ ❡♥tr❡❣❛ ❞❛s t❛r❡❢❛s✳ ❆ ❞✐❢❡r❡♥ç❛ ❡♥tr❡ ♦ ▲❛t❡♥❡ss ❡ ♦ ❛tr❛s♦ é q✉❡ ❛q✉❡❧❡ ♣♦❞❡ ❛ss✉♠✐r ✈❛❧♦r❡s ♥❡❣❛t✐✈♦s ❡♥q✉❛♥t♦ q✉❡ ❡ss❡ ♥ã♦✳ ◆❡st❡ tr❛❜❛❧❤♦ ❞✐s❝✉t❡✲s❡ ♦ ♣r♦❜❧❡♠❛ ❞❡ s❡q✉❡♥❝✐❛♠❡♥t♦ ❡♠ ✉♠❛ ♠áq✉✐♥❛ ❡♠ q✉❡ ♦ t❡♠♣♦ ❞❡ ♣r❡♣❛r❛çã♦ ❞❛ ♠áq✉✐♥❛ ❞❡♣❡♥❞❡♥t❡ ❞❛ s❡q✉ê♥❝✐❛ ❡ ❞❛ ❢❛♠í❧✐❛ ❞❛s t❛r❡❢❛s✳ ❖ ❛❣r✉♣❛♠❡♥t♦ ❞❡ t❛r❡❢❛s ❡♠ ❢❛♠í❧✐❛s ♦❝♦rr❡✱ ♣♦r ❡①❡♠♣❧♦✱ ♥❛ s✐❞❡r✉r❣✐❛✳ ❊♠ ❇✉st❛♠❛♥t❡ ✭✷✵✵✼✮✱ ♦ ❛✉t♦r ♠♦str❛ ✉♠ ♣r♦❝❡ss♦ ❞❡ ❢❛❜r✐❝❛çã♦ ❞❡ ♣r♦❞✉t♦s s✐❞❡rúr❣✐❝♦s ✭❝❛♥t♦♥❡✐r❛✱ ✈❡r❣❛❧❤ã♦✱ ❜❛rr❛ ❝❤❛t❛ ❡t❝✳✮ ♥♦ s❡t♦r ❞❡ ❧❛♠✐♥❛çã♦✱ ❡♠ q✉❡ ❛s t❛r❡❢❛s sã♦ ❛❣r✉♣❛❞❛s ❡♠ ❢❛♠í❧✐❛s ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛s s❡♠❡❧❤❛♥ç❛s ❞♦s ♣r♦❞✉t♦s✳ ◆♦ ❝❛s♦✱ ♦s ♣r♦❞✉t♦s ❞❛ ♠❡s♠❛ ❢❛♠í❧✐❛ sã♦ ❛q✉❡❧❡s q✉❡ ❞✐❢❡r❡♥❝✐❛♠ ❡♥tr❡ s✐ ❛♣❡♥❛s ♣❡❧❛ ❡s♣❡ss✉r❛✳ ❊♠ t❛✐s ❝✐r❝✉♥stâ♥❝✐❛s✱ ♦ t❡♠♣♦ ❞❡ ♣r❡♣❛r❛çã♦ é tã♦ ♣❡q✉❡♥♦ ❡ ✐♥s✐❣♥✐✜❝❛♥t❡ ❡♠ r❡❧❛çã♦ ❛♦ t❡♠♣♦ ❞❡ ♣r♦❝❡ss❛♠❡♥t♦ ❞❛s t❛r❡❢❛s✱ q✉❡ é ❝♦♠✉♠ ❝♦♥s✐❞❡rá✲❧♦ ✐❣✉❛❧ ❛ ③❡r♦✳ ❆ ✈❛♥t❛❣❡♠✱ ♣♦rt❛♥t♦✱ ❞❡ s❡ ❢❛③❡r ❡ss❡ ❛❣r✉♣❛♠❡♥t♦✱ é q✉❡ ❛s t❛r❡❢❛s ♣❡rt❡♥❝❡♥t❡s ❛ ✉♠❛ ♠❡s♠❛ ❢❛♠í❧✐❛✱ q✉❛♥❞♦ ♣r♦❝❡ss❛❞❛s ❡♠ s❡q✉ê♥❝✐❛✱ ♥ã♦ r❡q✉❡r❡♠ t❡♠♣♦ ❞❡ ♣r❡♣❛r❛çã♦✳
◆❛ ❋✐❣✉r❛ ✶✳✶ ❛♣r❡s❡♥t❛✲s❡ ✉♠❛ ❛♣❧✐❝❛çã♦ ♣rát✐❝❛ ❞♦ ♣r♦❜❧❡♠❛ ❞❡ s❡q✉❡♥❝✐❛✲ ♠❡♥t♦ ❝♦♠ ❢❛♠í❧✐❛s ❞❡ t❛r❡❢❛s✳ ◆❡st❡ ❝❛s♦✱ ❡①✐st❡♠ ❞✐✈❡rs♦s ♣r♦❞✉t♦s✱ ❝❛❞❛ ✉♠ ❝♦♠ t❛♠❛♥❤♦✱ ❡s♣❡ss✉r❛ ❡ s❡çã♦ ❞✐❢❡r❡♥t❡s✳ Pr♦❞✉t♦s q✉❡ ♣❡rt❡♥❝❡♠ ❛ ✉♠❛ ♠❡s♠❛ ❢❛♠í❧✐❛ ♣♦ss✉❡♠ ❛ ♠❡s♠❛ s❡çã♦ ❡ ♦ ♠❡s♠♦ t❛♠❛♥❤♦✱ ♦✉ s❡❥❛✱ ❡❧❡s s❡ ❞✐❢❡r❡♥❝✐❛♠ ❛♣❡♥❛s ♣❡❧❛ ❡s♣❡ss✉r❛✳
❋✐❣✉r❛ ✶✳✶✿ Pr♦❞✉t♦s
✶✳✶ ❖❜❥❡t✐✈♦s ✸ ♦❜❥❡t✐✈♦ ✐s♦❧❛❞❛♠❡♥t❡✱ ❛ ♠❡t❛✱ ♥❡st❡ ❝❛s♦✱ é ♦❜t❡r ✉♠ ❝♦♥❥✉♥t♦ ❞❡ s♦❧✉çõ❡s ♥ã♦✲ ❞♦♠✐♥❛❞❛s✱ ❞❡ ♠♦❞♦ q✉❡ ❝❛❞❛ s♦❧✉çã♦ ♣❡rt❡♥❝❡♥t❡ ❛ ❡ss❡ ❝♦♥❥✉♥t♦ ♥ã♦ s❡❥❛ ♣✐♦r q✉❡ ♥❡♥❤✉♠❛ ♦✉tr❛ ♥♦s ❞♦✐s ♦❜❥❡t✐✈♦s s✐♠✉❧t❛♥❡❛♠❡♥t❡✳
❊♠ t❡r♠♦s ❞❡ ❛❧❣♦r✐t♠♦s ♣❛r❛ s♦❧✉çã♦ ❞❡ ♣r♦❜❧❡♠❛s ❞❡ ♦t✐♠✐③❛çã♦ ♠✉❧t✐♦❜❥❡t✐✈♦✱ ❢♦✐ ❛♣❡♥❛s ❡♠ ♠❡❛❞♦s ❞♦s ❛♥♦s ✽✵ q✉❡ ✉♠❛ q✉❛♥t✐❞❛❞❡ ❝♦♥s✐❞❡rá✈❡❧ ❞❡ ♣❡sq✉✐s❛s ♥❡st❡ ❝❛♠♣♦ ❝♦♠❡ç❛r❛♠ ❛ s❡r ❢❡✐t❛s✳ ❆ ♣❛rt✐r ❞❛í✱ s✉r❣✐r❛♠ ♦s ♣r✐♠❡✐r♦s ❛❧❣♦r✐t♠♦s ♠✉❧t✐♦❜❥❡t✐✈♦s✱ ❛ ♠❛✐♦r✐❛ ❞❡❧❡s ❜❛s❡❛❞♦s ❡♠ ❛❧❣♦r✐t♠♦s ❡✈♦❧✉t✐✈♦s✳ ❆t✉❛❧♠❡♥t❡✱ ❡①✐st❡♠ ❞✐✈❡rs♦s ❛❧❣♦r✐t♠♦s ♠✉❧t✐♦❜❥❡t✐✈♦s ♣r♦♣♦st♦s ♥❛ ❧✐t❡r❛t✉r❛ ✭❈♦❡❧❧♦ ❡ ▲❛♠♦♥t✱ ✷✵✵✹✮✳
❚❡♥❞♦ ❡♠ ✈✐st❛ ❛ ❝♦♠♣❧❡①✐❞❛❞❡ ❝♦♠♣✉t❛❝✐♦♥❛❧ ❞♦s ♣r♦❜❧❡♠❛s ❞❡ s❡q✉❡♥❝✐❛♠❡♥t♦✱ ♦s ♠ét♦❞♦s ♠❛✐s ✉t✐❧✐③❛❞♦s ♣❛r❛ r❡s♦❧✈ê✲❧♦s sã♦ ♦s ♠❡t❛❤❡✉ríst✐❝♦s✳ ❘❡✈✐sõ❡s ❞❛ ❧✐t❡✲ r❛t✉r❛ tê♠ ♠♦str❛❞♦ q✉❡ ♠ét♦❞♦s ✐♥s♣✐r❛❞♦s ❡♠ ♣r♦❝❡❞✐♠❡♥t♦s ❡✈♦❧✉t✐✈♦s✱ t❛✐s ❝♦♠♦ ♦s ❛❧❣♦r✐t♠♦s ◆♦♥❞♦♠✐♥❛t❡❞ ❙♦rt✐♥❣ ●❡♥❡t✐❝ ❆❧❣♦r✐t❤♠ ■■ ✲ ◆❙●❆✲■■ ✭❉❡❜ ❡t ❛❧✳✱ ✷✵✵✷✮ ❡ ❙tr❡♥❣t❤ P❛r❡t♦ ❆♣♣r♦❛❝❤ ✕ ❙P❊❆✷ ✭❩✐t③❧❡r ❡ ❚❤✐❡❧❡✱ ✶✾✾✾✮✱ ❡stã♦ ❡♥tr❡ ♦s ♠❛✐s ✉t✐❧✐③❛❞♦s ❡♠ ♦t✐♠✐③❛çã♦ ♠✉❧t✐♦❜❥❡t✐✈♦✳ ❊♥tr❡t❛♥t♦✱ r❡❝❡♥t❡♠❡♥t❡ s✉r❣✐r❛♠ ♥❛ ❧✐t❡r❛t✉r❛ r❡❧❛t♦s ❞❡ ❛♣❧✐❝❛çõ❡s ❜❡♠ s✉❝❡❞✐❞❛s ❞❡ ♠ét♦❞♦s ♠✉❧t✐♦❜❥❡t✐✈♦s ❜❛s❡❛❞♦s ❡♠ ❜✉s❝❛ ❧♦❝❛❧✱ t❛✐s ❝♦♠♦ ▼✉❧t✐✲♦❜❥❡❝t✐✈❡ ❱❛r✐❛❜❧❡ ◆❡✐❣❤❜♦r❤♦♦❞ ❙❡❛r❝❤ ✕ ▼❖❱◆❙ ✭●❡✐❣❡r✱ ✷✵✵✹✮ ❡ P❛r❡t♦ ■t❡r❛t❡❞ ▲♦❝❛❧ ❙❡❛r❝❤ ✕ P■▲❙ ✭●❡✐❣❡r✱ ✷✵✵✾✮✱ ❝♦♥❢♦r♠❡ ♠♦s✲ tr❛♠ ♦s tr❛❜❛❧❤♦s ❞❡ ❆rr♦②♦ ❡t ❛❧✳ ✭✷✵✶✶✮✱ ❖tt♦♥✐ ❡t ❛❧✳ ✭✷✵✶✶✮ ❡ ▼✐♥❡❧❧❛ ❡t ❛❧✳ ✭✷✵✶✵✮✳ ◆❡st❡ ú❧t✐♠♦✱ ♣♦r ❡①❡♠♣❧♦✱ ♠♦str❛✲s❡ ❛ s✉♣❡r✐♦r✐❞❛❞❡ ❞♦ P■▲❙ s♦❜r❡ ♦ ❙P❊❆✷✳
❊♠ ✈✐st❛ ❞❡ss❡ ❜♦♠ ❞❡s❡♠♣❡♥❤♦ ❞❡ ❛❧❣♦r✐t♠♦s ❜❛s❡❛❞♦s ❡♠ ❜✉s❝❛ ❧♦❝❛❧ ♥❛ s♦✲ ❧✉çã♦ ❞❡ ♣r♦❜❧❡♠❛s s✐♠✐❧❛r❡s ❛♦ ❛❜♦r❞❛❞♦✱ ♥♦ ♣r❡s❡♥t❡ tr❛❜❛❧❤♦ sã♦ ✐♠♣❧❡♠❡♥t❛❞❛s ❛❞❛♣t❛çõ❡s ❞♦s ❛❧❣♦r✐t♠♦s ♠✉❧t✐♦❜❥❡t✐✈♦s ▼❖❱◆❙ ❡ P■▲❙ ♥❛ s♦❧✉çã♦ ❞♦ ♣r♦❜❧❡♠❛ ❞❡ s❡q✉❡♥❝✐❛♠❡♥t♦ ❡♠ ❡st✉❞♦✳ ❖s ❛❧❣♦r✐t♠♦s ▼❖❱◆❙ ❞❡ ❆rr♦②♦ ❡t ❛❧✳ ✭✷✵✶✶✮ ❡ ❖tt♦♥✐ ❡t ❛❧✳ ✭✷✵✶✶✮ ❢♦r❛♠ ❛❞❛♣t❛❞♦s ♣❛r❛ r❡s♦❧✈❡r ♦ ♣r♦❜❧❡♠❛✱ ❞❛♥❞♦ ♦r✐❣❡♠ às ✈❛r✐❛♥t❡s ▼❖❱◆❙❴❖tt♦♥✐ ❡ ▼❖❱◆❙❴❆rr♦②♦❀ ❡♥q✉❛♥t♦ q✉❡ ✉♠ ♥♦✈❛ ✈❛r✐❛♥t❡✱ ❞❡✲ ♥♦♠✐♥❛❞❛ P▲❙✶✱ ❢♦✐ ❞❡s❡♥✈♦❧✈✐❞❛ ❛ ♣❛rt✐r ❞❛ ♣r♦♣♦s✐çã♦ ❞❡ ✉♠ ♥♦✈♦ ♣r♦❝❡❞✐♠❡♥t♦ ❞❡ ♣❡rt✉r❜❛çã♦ ♣❛r❛ ♦ P■▲❙✳ P❛r❛ ✈❡r✐✜❝❛r ❛ ❡✜❝✐ê♥❝✐❛ ❞❡ss❡s ❛❧❣♦r✐t♠♦s ❞❡ ❜✉s❝❛ ❧♦❝❛❧✱ t❛♠❜é♠ ❢♦r❛♠ ❛❞❛♣t❛❞♦s ❛♦ ♣r♦❜❧❡♠❛ ♦s ❛❧❣♦r✐t♠♦s ❡✈♦❧✉t✐✈♦s ◆❙●❆✲■■ ❡ ❙P❊❆✷✳
✶✳✶ ❖❜❥❡t✐✈♦s
◆❡st❛ s❡çã♦ sã♦ ❛♣r❡s❡♥t❛❞♦s ♦s ♣r✐♥❝✐♣❛✐s ♦❜❥❡t✐✈♦s ❞❡st❡ tr❛❜❛❧❤♦✳
✶✳✶✳✶ ❖❜❥❡t✐✈♦ ●❡r❛❧
❖ ♦❜❥❡t✐✈♦ ❞♦ ♣r❡s❡♥t❡ tr❛❜❛❧❤♦ é ❞❡s❡♥✈♦❧✈❡r ✉♠ ❛❧❣♦r✐t♠♦ ♠✉❧t✐♦❜❥❡t✐✈♦ ❡✜❝✐❡♥t❡ ♣❛r❛ r❡s♦❧✈❡r ♦ Pr♦❜❧❡♠❛ ❞❡ ❙❡q✉❡♥❝✐❛♠❡♥t♦ ❞❡ ❚❛r❡❢❛s ❡♠ ✉♠❛ ▼áq✉✐♥❛ ❝♦♠ ❚❡♠♣♦ ❞❡ Pr❡♣❛r❛çã♦ ❉❡♣❡♥❞❡♥t❡ ❞❛ ❙❡q✉ê♥❝✐❛ ❡ ❞❛ ❋❛♠í❧✐❛✱ t❡♥❞♦ ❝♦♠♦ ♦❜❥❡t✐✈♦s ❛ ♠✐♥✐♠✐③❛çã♦ ❞♦ ♠❛❦❡s♣❛♥ ❡ ❞♦ ❛tr❛s♦ t♦t❛❧ ♣♦♥❞❡r❛❞♦✳
✶✳✶✳✷ ❖❜❥❡t✐✈♦s ❊s♣❡❝í✜❝♦s
✶✳✸ ▼♦t✐✈❛çã♦ ✹
• ■♥✈❡st✐❣❛r ♦s ♣r✐♥❝✐♣❛✐s tr❛❜❛❧❤♦s ❞❛ ❧✐t❡r❛t✉r❛ q✉❡ tr❛t❛♠ ❞❡ ❛❧❣♦r✐t♠♦s ♠✉❧✲
t✐♦❜❥❡t✐✈♦s✱ ❛ss✐♠ ❝♦♠♦ ❛q✉❡❧❡s q✉❡ tr❛t❛♠ ♣r♦❜❧❡♠❛s ❝♦rr❡❧❛t♦s ❛♦ ❛❜♦r❞❛❞♦✳
• ■♠♣❧❡♠❡♥t❛r ❛❧❣♦r✐t♠♦s ♠✉❧t✐♦❜❥❡t✐✈♦s ❜❛s❡❛❞♦s ❡♠ ❜✉s❝❛ ❧♦❝❛❧ ❡ ❡♠ ❜✉s❝❛
♣♦♣✉❧❛❝✐♦♥❛❧ ♣❛r❛ r❡s♦❧✈❡r ♦ ♣r♦❜❧❡♠❛ tr❛t❛❞♦✳
• ❈r✐❛r ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ✐♥stâ♥❝✐❛s ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❛❜♦r❞❛❞♦✳ • ❘❡❛❧✐③❛r ❡①♣❡r✐♠❡♥t♦s ❝♦♠ ♦s ❛❧❣♦r✐t♠♦s ✐♠♣❧❡♠❡♥t❛❞♦s✳
• ❈♦♠♣❛r❛r ♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ♣♦r ❝❛❞❛ ❛❧❣♦r✐t♠♦✱ s❡❣✉♥❞♦ ❛s ♠étr✐❝❛s ❞❡
❝❛r❞✐♥❛❧✐❞❛❞❡✱ ❞✐stâ♥❝✐❛ ♠é❞✐❛✱ ❞✐stâ♥❝✐❛ ♠á①✐♠❛✱ ❤✐♣❡r✈♦❧✉♠❡ ❡ ❡♣s✐❧♦♥✳
• ❱❡r✐✜❝❛r ❛ ❞✐❢❡r❡♥ç❛ ❡♥tr❡ ♦s r❡s✉❧t❛❞♦s ❞♦s ❛❧❣♦r✐t♠♦s ✐♠♣❧❡♠❡♥t❛❞♦s ❛ ♣❛rt✐r
❞♦ ✉s♦ ❞❡ t❡st❡s ❡st❛tíst✐❝♦s✳
• P✉❜❧✐❝❛r ♦s r❡s✉❧t❛❞♦s ❞❛ ♣❡sq✉✐s❛ ❡♠ ❡✈❡♥t♦s ❡ ♣❡r✐ó❞✐❝♦s✳
✶✳✷ ▼♦t✐✈❛çã♦
❖ ✐♥t❡r❡ss❡ ♥♦ ❡st✉❞♦ ❞❡ ♣r♦❜❧❡♠❛s ❞❡ s❡q✉❡♥❝✐❛♠❡♥t♦ ❞❡ t❛r❡❢❛s ♦❝♦rr❡ ❞❡✈✐❞♦ ❛ ♣❡❧♦ ♠❡♥♦s ❞♦✐s ❛s♣❡❝t♦s✳ ❖ ♣r✐♠❡✐r♦ é ♦ ✐♥t❡r❡ss❡ ♣rát✐❝♦✱ ✉♠❛ ✈❡③ q✉❡ ❤á ❞✐✈❡rs❛s ❛♣❧✐❝❛çõ❡s ❞❡ss❛ ❝❧❛ss❡ ❞❡ ♣r♦❜❧❡♠❛s ♥❛ ✐♥❞ústr✐❛✱ ❝♦♠♦✱ ♣♦r ❡①❡♠♣❧♦✱ ♥❛s ár❡❛s tê①t✐❧ ✭●❡♥❞r❡❛✉ ❡t ❛❧✳✱ ✷✵✵✶✮✱ ❡❧❡trô♥✐❝❛ ✭❑✐♠ ❡t ❛❧✳✱ ✷✵✵✷✮ ❡ s✐❞❡rúr❣✐❝❛ ✭❚❛♥❣ ❡ ❲❛♥❣✱ ✷✵✵✾✮✳ ❖✉tr♦ ❛s♣❡❝t♦ q✉❡ r❡❧❡✈❛ ♦ ❡st✉❞♦ ❞❡ss❡ t✐♣♦ ❞❡ ♣r♦❜❧❡♠❛✱ é ♦ ✐♥t❡r❡ss❡ t❡ór✐❝♦✱ ✈✐st♦ q✉❡ ❛ ♠❛✐♦r✐❛ ❞♦s ♣r♦❜❧❡♠❛s ❞❡ s❡q✉❡♥❝✐❛♠❡♥t♦ ♣❡rt❡♥❝❡♠ à ❝❧❛ss❡ ◆P✲❞✐❢í❝✐❧ ✭❇r✉❝❦❡r✱ ✷✵✵✼✮✳
❉❡ ♥♦ss♦ ❝♦♥❤❡❝✐♠❡♥t♦✱ ♥ã♦ ❢♦r❛♠ ❡♥❝♦♥tr❛❞❛s r❡❢❡rê♥❝✐❛s ♥❛ ❧✐t❡r❛t✉r❛ s♦❜r❡ ♦ ❡st✉❞♦ ❞♦ ♣r♦❜❧❡♠❛ ❛❜♦r❞❛❞♦✳ P♦r ♦✉tr♦ ❧❛❞♦✱ ♣r♦❜❧❡♠❛s ❞❡ s❡q✉❡♥❝✐❛♠❡♥t♦ ❞❡ t❛r❡❢❛s ♣♦❞❡♠ ❡♥✈♦❧✈❡r ❞✐✈❡rs♦s ♦❜❥❡t✐✈♦s✱ ♥♦ ❡♥t❛♥t♦✱ ❣r❛♥❞❡ ♣❛rt❡ ❞❛s ♣❡sq✉✐s❛s ♥❡ss❡ ❝❛♠♣♦ ❝♦♥s✐❞❡r❛♠ ❛♣❡♥❛s ✉♠ ú♥✐❝♦ ♦❜❥❡t✐✈♦✱ ♦✉ q✉❛♥❞♦ ♠❛✐s ❞❡ ✉♠ é ❝♦♥s✐❞❡✲ r❛❞♦✱ ❣❡r❛❧♠❡♥t❡✱ ❞❡✜♥❡✲s❡ ✉♠ ú♥✐❝♦ ♦❜❥❡t✐✈♦ r❡♣r❡s❡♥t❛❞♦ ♣❡❧❛ ❝♦♠❜✐♥❛çã♦ ❧✐♥❡❛r ❞♦s ♦❜❥❡t✐✈♦s ❡♥✈♦❧✈✐❞♦s✱ ♦✉ s❡❥❛✱ ♦ ♣r♦❜❧❡♠❛ é tr❛t❛❞♦ ♥♦r♠❛❧♠❡♥t❡ ❡♠ ✉♠❛ ❛❜♦r✲ ❞❛❣❡♠ ♠♦♥♦✲♦❜❥❡t✐✈♦✳ ❆♦ ❝♦♥trár✐♦ ❞❡ss❡ ♣r♦❝❡❞✐♠❡♥t♦ ❝♦♠✉♠✱ ♥❡st❡ tr❛❜❛❧❤♦ ♦ ♣r♦❜❧❡♠❛ é tr❛t❛❞♦ ❝♦♠ ❛❧❣♦r✐t♠♦s ❞❡ ♦t✐♠✐③❛çã♦ ♠✉❧t✐♦❜❥❡t✐✈♦✳ ❖❜s❡r✈♦✉✲s❡ q✉❡ ❣❡r❛❧♠❡♥t❡ ♦s ♣r♦❜❧❡♠❛s ♠✉❧t✐♦❜❥❡t✐✈♦s sã♦ tr❛t❛❞♦s ♣♦r ♠❡✐♦ ❞❡ ❛❧❣♦r✐t♠♦s ❜❛s❡✲ ❛❞♦s ❡♠ ❜✉s❝❛ ♣♦♣✉❧❛❝✐♦♥❛❧❀ ❡♥tr❡t❛♥t♦✱ ❤á r❡❧❛t♦s ♥❛ ❧✐t❡r❛t✉r❛ ❞❡ ❛♣❧✐❝❛çõ❡s ❜❡♠ s✉❝❡❞✐❞❛s ❞❡ ❛❧❣♦r✐t♠♦s ❜❛s❡❛❞♦s ❡♠ ❜✉s❝❛ ❧♦❝❛❧✱ ♣♦r ✐ss♦✱ ♦♣t♦✉✲s❡✱ ♥❡st❡ tr❛❜❛❧❤♦✱ ♣♦r ❞❡s❡♥✈♦❧✈❡r ❡ ❝♦♠♣❛r❛r ♦ ❞❡s❡♠♣❡♥❤♦ ❞❡ss❛s ❞✉❛s ❝❧❛ss❡s ❞❡ ❛❧❣♦r✐t♠♦s✳
✶✳✸ ❊str✉t✉r❛ ❞♦ ❚r❛❜❛❧❤♦
❈❛♣ít✉❧♦ ✷
❈❛r❛❝t❡r✐③❛çã♦ ❞♦ Pr♦❜❧❡♠❛
❖ ♣r♦❜❧❡♠❛ ❛❜♦r❞❛❞♦ ♣♦❞❡ s❡r ❞❡✜♥✐❞♦ ❞❛ s❡❣✉✐♥t❡ ❢♦r♠❛✿ ❡①✐st❡ ✉♠ ❝♦♥❥✉♥t♦
J ={1,2,3, . . . , n}❝♦♠ nt❛r❡❢❛s q✉❡ ❡stã♦ ❞✐s♣♦♥í✈❡✐s ♣❛r❛ s❡r❡♠ s❡q✉❡♥❝✐❛❞❛s ❡♠
✉♠❛ ú♥✐❝❛ ♠áq✉✐♥❛ ❛ ♣❛rt✐r ❞♦ ✐♥st❛♥t❡ ③❡r♦✳ ❈❛❞❛ t❛r❡❢❛ j ∈J ♣♦ss✉✐ ✉♠ t❡♠♣♦
❞❡ ♣r♦❝❡ss❛♠❡♥t♦ pj✱ ✉♠❛ ❞❛t❛ ❞❡ ❡♥tr❡❣❛ dj ❡ ✉♠❛ ♣❡♥❛❧✐❞❛❞❡ ♣♦r ❛tr❛s♦ βj✳ ❆s
t❛r❡❢❛s sã♦ ❛❣r✉♣❛❞❛s ❡♠ f ❢❛♠í❧✐❛s ❞❡ ❛❝♦r❞♦ ❝♦♠ s✉❛s ❝❛r❛❝t❡ríst✐❝❛s✱ s❡♥❞♦ q✉❡
❝❛❞❛ ❢❛♠í❧✐❛ i ♣♦ss✉✐ ni t❛r❡❢❛s✳ ❯♠ t❡♠♣♦ ❞❡ ♣r❡♣❛r❛çã♦ sik é r❡q✉❡r✐❞♦ ❡♥tr❡ ❛
❡①❡❝✉çã♦ ❞❡ ❞✉❛s t❛r❡❢❛s ❝♦♥s❡❝✉t✐✈❛s ❞❡ ❞✐❢❡r❡♥t❡s ❢❛♠í❧✐❛s i ❡ k ❡ ❝❛s♦ ❡❧❛s s❡❥❛♠
❞❛ ♠❡s♠❛ ❢❛♠í❧✐❛ ♥❡♥❤✉♠ t❡♠♣♦ ❞❡ ♣r❡♣❛r❛çã♦ é ♥❡❝❡ssár✐♦✳ ❆ ♣r✐♠❡✐r❛ t❛r❡❢❛ ❛ s❡r ❡①❡❝✉t❛❞❛ ♥ã♦ r❡q✉❡r t❡♠♣♦ ❞❡ ♣r❡♣❛r❛çã♦✳ ❆❧é♠ ❞✐ss♦✱ ♥ã♦ é ♣❡r♠✐t✐❞❛ ♣r❡❡♠♣çã♦✱ ♦✉ s❡❥❛✱ ♦ ♣r♦❝❡ss❛♠❡♥t♦ ❞❡ ✉♠❛ t❛r❡❢❛ ♥ã♦ ♣♦❞❡ s❡r ✐♥t❡rr♦♠♣✐❞♦✳ ❉❛❞❛ ✉♠❛ s❡q✉ê♥❝✐❛ π✱ ❛ ❝❛❞❛ t❛r❡❢❛ j ❡stá ❛ss♦❝✐❛❞♦ ✉♠ ❛tr❛s♦ Tj✳ ❙❡♥❞♦ Cj
♦ ✐♥st❛♥t❡ ❞❡ ❝♦♥❝❧✉sã♦ ✭❝♦♠♣❧❡t✐♦♥ t✐♠❡✮ ❞❛ t❛r❡❢❛ j✱ s❡✉ ❛tr❛s♦ é ❝❛❧❝✉❧❛❞♦ ♣❡❧❛
❡q✉❛çã♦ ✭✷✳✶✮✿
Tj =♠❛①{Cj−dj,0} ✭✷✳✶✮
❖s ♦❜❥❡t✐✈♦s ❞♦ ♣r♦❜❧❡♠❛ ❛❜♦r❞❛❞♦ sã♦ ♠✐♥✐♠✐③❛r✱ s✐♠✉❧t❛♥❡❛♠❡♥t❡✱ ♦ ♠❛❦❡s♣❛♥
f1(π) ❡ ♦ ❛tr❛s♦ t♦t❛❧ ♣♦♥❞❡r❛❞♦f2(π)✳ ❖s ✈❛❧♦r❡s ❞❡ f1(π) ❡ f2(π) sã♦ ❝❛❧❝✉❧❛❞♦s
♣♦r ♠❡✐♦ ❞❛s ❡q✉❛çõ❡s ✭✷✳✷✮ ❡ ✭✷✳✸✮✿
f1(π) = ♠❛①
16j6n{Cj} ✭✷✳✷✮
f2(π) =
X
16j6n
βjTj ✭✷✳✸✮
P❛r❛ ✐❧✉str❛r✱ ❝♦♥s✐❞❡r❡ ❛ ✐♥stâ♥❝✐❛ ❞❛❞❛ ♥❛ ❚❛❜❡❧❛ ✷✳✶✱ q✉❡ ❝♦♥té♠ ✺ t❛r❡❢❛s ✭♥♦♠❡❛❞❛s ❞❡ ✶ ❛ ✺✮ ❡ ❞✉❛s ❢❛♠í❧✐❛s ✭✶ ❡ ✷✮✳ ◆❡ss❛ t❛❜❡❧❛ sã♦ ❛♣r❡s❡♥t❛❞♦s✱ ♣❛r❛ ❝❛❞❛ t❛r❡❢❛ j✱ ❛ ❢❛♠í❧✐❛ià q✉❛❧ ♣❡rt❡♥❝❡✱ ❛ ❞❛t❛ ❞❡ ❡♥tr❡❣❛ dj✱ ♦ t❡♠♣♦ ❞❡ ♣r♦❝❡ss❛♠❡♥t♦
pj ❡ ❛ ♣❡♥❛❧✐❞❛❞❡ ♣♦r ❛tr❛s♦ βj✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✿
❆ ❚❛❜❡❧❛ ✷✳✷ ♠♦str❛ ♦ t❡♠♣♦ ❞❡ ♣r❡♣❛r❛çã♦ ❡♥tr❡ ❛s t❛r❡❢❛s ❞❡ ✉♠❛ ❢❛♠í❧✐❛i ❡
♦✉tr❛ t❛r❡❢❛ ❞❛ ❢❛♠í❧✐❛ k✱ ♥❡st❡ ❝❛s♦ t❡♠✲s❡ ❞✉❛s ❢❛♠í❧✐❛s ✶ ❡ ✷✳
◆❡st❡ ❡①❡♠♣❧♦✱ ♦ t❡♠♣♦ ❞❡ ♣r❡♣❛r❛çã♦ ❡♥tr❡ ✉♠❛ t❛r❡❢❛ ❞❛ ❢❛♠í❧✐❛ ✷ ❡ ♦✉tr❛ t❛r❡❢❛ ❞❛ ❢❛♠í❧✐❛ ✶✱ q✉❡ s❡rã♦ ♣r♦❝❡ss❛❞❛s ❡♠ s❡q✉ê♥❝✐❛✱ é ✐❣✉❛❧ ❛ ✶✱ ❝♦♥❢♦r♠❡ ❛ ❚❛❜❡❧❛ ✷✳✷✳ ➱ ✐♠♣♦rt❛♥t❡ ♦❜s❡r✈❛r q✉❡ ♦ t❡♠♣♦ ❞❡ ♣r❡♣❛r❛çã♦ ❞❡♣❡♥❞❡ ❞❛ s❡q✉ê♥❝✐❛✱
✷✳✵ ❈❛r❛❝t❡r✐③❛çã♦ ❞♦ Pr♦❜❧❡♠❛ ✻
❚❛❜❡❧❛ ✷✳✶✿ ■♥stâ♥❝✐❛ ❞♦ ♣r♦❜❧❡♠❛ ❚❛r❡❢❛ j ❋❛♠í❧✐❛ i dj pj βj
✶ ✷ ✷✷ ✷ ✶✺
✷ ✶ ✶✻ ✹ ✸✼
✸ ✷ ✹ ✻ ✶✷
✹ ✷ ✽ ✶ ✷✶
✺ ✶ ✶✸ ✸ ✶✽
❚❛❜❡❧❛ ✷✳✷✿ ❚❡♠♣♦ ❞❡ Pr❡♣❛r❛çã♦ ❡♥tr❡ ❛s ❋❛♠í❧✐❛s
sik ✶ ✷
✶ ✵ ✸
✷ ✶ ✵
♦✉ s❡❥❛✱ ♦ t❡♠♣♦ ❞❡ ♣r❡♣❛r❛çã♦ ❞❡ i ♣❛r❛ k ♥ã♦ ♥❡❝❡ss❛r✐❛♠❡♥t❡ é ✐❣✉❛❧ ❛♦ t❡♠♣♦
❞❡ ♣r❡♣❛r❛çã♦ ❞❡ k ♣❛r❛ i✳
❈♦♥s✐❞❡r❡ ✉♠❛ s❡q✉ê♥❝✐❛ ❞❡ ❡①❡♠♣❧♦ {3,4,5,2,1}✱ ♥❡ss❡ ❝❛s♦✱ ✈❡r✐✜❝❛✲s❡ q✉❡ ❛
t❛r❡❢❛ 3 é ❛ ♣r✐♠❡✐r❛ ❛ s❡r ❡①❡❝✉t❛❞❛ ❡ ❛ t❛r❡❢❛ 1 é ❛ ú❧t✐♠❛✳ ❉❡ ❛❝♦r❞♦ ❝♦♠ ❛s ❊q✉❛çõ❡s ✭✷✳✷✮ ❡ ✭✷✳✸✮ ❞♦ ♣r♦❜❧❡♠❛✱ ♦s ✈❛❧♦r❡s ❞❛s ❢✉♥çõ❡s ♦❜❥❡t✐✈♦s sã♦✿ f1 = 20 ❡
f2 = 24✳
◆❛ ❋✐❣✉r❛ ✷✳✶ ❛♣r❡s❡♥t❛✲s❡ ♦ ❣rá✜❝♦ ❞❡ ●❛♥tt ❝♦rr❡s♣♦♥❞❡♥t❡ ❛ ❡ss❛ s♦❧✉çã♦✳
3
4
5
2
1
0 2 4 6 8 10 12 14 16 18 20 22
Figura 2.1: Sequência relativa ao exemplo
❈❛♣ít✉❧♦ ✸
❘❡✈✐sã♦ ❇✐❜❧✐♦❣rá✜❝❛
✸✳✶ ❖t✐♠✐③❛çã♦ ▼✉❧t✐♦❜❥❡t✐✈♦
❯♠ ♣r♦❜❧❡♠❛ ❞❡ ♦t✐♠✐③❛çã♦ ♠✉❧t✐♦❜❥❡t✐✈♦ ❡♥✈♦❧✈❡ ❞♦✐s ♦✉ ♠❛✐s ♦❜❥❡t✐✈♦s✱ ♥♦r♠❛❧✲ ♠❡♥t❡ ❝♦♥✢✐t❛♥t❡s✱ q✉❡ ❞❡✈❡♠ s❡r ♦t✐♠✐③❛❞♦s✳ ❆ ♣r✐♥❝✐♣❛❧ ❞✐❢❡r❡♥ç❛✱ ❡♠ r❡❧❛çã♦ à ♦t✐♠✐③❛çã♦ ♠♦♥♦✲♦❜❥❡t✐✈♦✱ é q✉❡ ❡♠ ♣r♦❜❧❡♠❛s ❞❡ ♦t✐♠✐③❛çã♦ ♠✉❧t✐♦❜❥❡t✐✈♦ ♥ã♦ ❡①✐st❡ ✉♠❛ ú♥✐❝❛ s♦❧✉çã♦✱ ♠❛s ❡♠ ✈❡③ ❞✐ss♦✱ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ s♦❧✉çõ❡s ót✐♠❛s✱ ❡ ❝❛❞❛ ✉♠❛ r❡♣r❡s❡♥t❛ ✉♠ ❝♦♠♣r♦♠✐ss♦ ❡♥tr❡ ♦s ♦❜❥❡t✐✈♦s ❞♦ ♣r♦❜❧❡♠❛✳
❯♠❛ ♦♣çã♦ ♣❛r❛ r❡❞✉③✐r ❛ ❝♦♠♣❧❡①✐❞❛❞❡ ❞❡ ✉♠ ♣r♦❜❧❡♠❛ ❞❡ ♦t✐♠✐③❛çã♦ ♠✉❧t✐✲ ♦❜❥❡t✐✈♦ é ❝♦♥✈❡rtê✲❧♦ ♣❛r❛ ✉♠ ♣r♦❜❧❡♠❛ ♠♦♥♦✲♦❜❥❡t✐✈♦ ❛tr✐❜✉✐♥❞♦ ♣❡s♦s ♣❛r❛ ♦s ❞✐❢❡r❡♥t❡s ♦❜❥❡t✐✈♦s✳ ❉❡ss❛ ❢♦r♠❛✱ ✉♠❛ ú♥✐❝❛ ❢✉♥çã♦ ❞❡ ❛✈❛❧✐❛çã♦ é ❝❛❧❝✉❧❛❞❛✳ ❆ ♣r✐♥❝✐♣❛❧ ❞✐✜❝✉❧❞❛❞❡ ❞❡ss❛ ❛❜♦r❞❛❣❡♠ é q✉❡ ♣❡s♦s sã♦ ❛tr✐❜✉í❞♦s ❛♦s ♦❜❥❡t✐✈♦s✱ ❞❡ ❢♦r♠❛ s✉❜❥❡t✐✈❛✱ ❞❡ ❛❝♦r❞♦ ❝♦♠ ✐♠♣♦rtâ♥❝✐❛ ❛tr✐❜✉í❞❛ ♣❡❧♦ t♦♠❛❞♦r ❞❡ ❞❡❝✐sã♦ ✭❞❡✲ ❝✐s✐♦♥ ♠❛❦❡r ✕ ❉▼✮✳ ❊ss❛ ❛❜♦r❞❛❣❡♠ ❛ss✉♠❡ q✉❡ ♦ ❉▼ t❡♠✱ ❛ ♣r✐♦r✐✱ ❝♦♥❤❡❝✐♠❡♥t♦ ❞❛ ✐♠♣♦rtâ♥❝✐❛ ❞♦s ❞✐❢❡r❡♥t❡s ♦❜❥❡t✐✈♦s✱ ♦ q✉❡ é ♠✉✐t♦ ❞✐❢í❝✐❧ ❞❡ ❝♦♥s❡❣✉✐r✳ P♦r ♦✉✲ tr♦ ❧❛❞♦✱ ❡♠ ✉♠❛ ❛❜♦r❞❛❣❡♠ ♠✉❧t✐♦❜❥❡t✐✈♦✱ ❛s s♦❧✉çõ❡s sã♦ ❛✈❛❧✐❛❞❛s ❡ ❝❧❛ss✐✜❝❛❞❛s ❝♦♥❢♦r♠❡ ♦ ❝♦♥❝❡✐t♦ ❞❡ ❞♦♠✐♥â♥❝✐❛✳
✸✳✶✳✶ ❉❡✜♥✐çã♦
●❡r❛❧♠❡♥t❡✱ ❡♠ ♣r♦❜❧❡♠❛s ❞❡ ♦t✐♠✐③❛çã♦ ♠✉❧t✐♦❜❥❡t✐✈♦✱ t❡♠✲s❡ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ m
✈❛r✐á✈❡✐s ❞❡ ❞❡❝✐sã♦ ❡ ✉♠ ❝♦♥❥✉♥t♦ ❞❡n ❢✉♥çõ❡s ♦❜❥❡t✐✈♦s✳ ❯♠ ✈❡t♦r ❞❡ ❞❡❝✐sã♦x∈
X ❞♦ ♣r♦❜❧❡♠❛ ❡s♣❡❝✐✜❝❛ ✉♠ ✈❛❧♦r ♣❛r❛ ❝❛❞❛ ✉♠❛s ❞❛sm ✈❛r✐á✈❡✐s ❞❡ ❞❡❝✐sã♦✳ X é
❞❡♥♦t❛❞♦ ❝♦♠♦ ♦ ❡s♣❛ç♦ ❞❡ ❞❡❝✐sã♦✳ ❖s n ♦❜❥❡t✐✈♦s✱ ♥♦r♠❛❧♠❡♥t❡✱ sã♦ ❝♦♥✢✐t❛♥t❡s✳
❖ r❡s✉❧t❛❞♦ ♣❛r❛ ❛s n❢✉♥çõ❡s ♦❜❥❡t✐✈♦s ❞❡✜♥❡ ♦ ❡s♣❛ç♦ ❞❡ ♦❜❥❡t✐✈♦sY ❞❡ ❞✐♠❡♥sã♦ n✱ t❛♠❜é♠ ❝❤❛♠❛❞♦ ❞❡ ❡s♣❛ç♦ ❞❡ s♦❧✉çõ❡s✳ ❆ss✐♠✱ ❛n✲és✐♠❛ ❢✉♥çã♦ ♦❜❥❡t✐✈♦fn(x)é
❞❡s❝r✐t❛ ♣♦rfn(x) :Rm →R❡ ♦ ✈❡t♦r ❞❡ ❢✉♥çõ❡sf(x)❞❡✜♥✐❞❛ ♣♦rf(x) :Rm →Rn✳
❆ r❡❣✐ã♦ ❢❛❝tí✈❡❧ ❞♦ ♣r♦❜❧❡♠❛ Xf é ✉♠ s✉❜❝♦♥❥✉♥t♦ ❞❡ X ❞❡✜♥✐❞♦ ♣❡❧❛s r❡str✐çõ❡s
❞♦ ♣r♦❜❧❡♠❛✳ ❆ss✐♠✱ ♦ ♣r♦❜❧❡♠❛ ❞❡ ♦t✐♠✐③❛çã♦ ♠✉❧t✐♦❜❥❡t✐✈♦ ♣♦❞❡ s❡r ❢♦r♠✉❧❛❞♦ ❞❛ s❡❣✉✐♥t❡ ♠❛♥❡✐r❛✿
▼✐♥✐♠✐③❛r f(x) = (f1(x), f2(x), . . . , fn(x))
s✉❥❡✐t♦ ❛ gj(x)≥0 j = 1,2, . . . , J
hk(x) = 0 k = 1,2, . . . , K ✭✸✳✶✮
✸✳✶ ❖t✐♠✐③❛çã♦ ▼✉❧t✐♦❜❥❡t✐✈♦ ✽ ❆ r❡❣✐ã♦ ❢❛❝tí✈❡❧ ❝♦♠ ♦ ❡s♣❛ç♦ ❞❡ ♦❜❥❡t✐✈♦sYf ♣♦❞❡ s❡r ❞❡s❝r✐t❛ ♣♦rYf =f(Xf)✳
❆ ❢✉♥çã♦ ❞❡ ❛✈❛❧✐❛çã♦ ♠✉❧t✐♦❜❥❡t✐✈♦ f : X → Y ♠❛♣❡✐❛ ❛s ✈❛r✐á✈❡✐s ❞❡ ❞❡❝✐sã♦ x={x1, x2,· · · , xm} ♣❛r❛ ♦ ✈❡t♦r ❞❡ ♦❜❥❡t✐✈♦sy={y1, y2,· · · , yn}✳ ❊ss❛ s✐t✉❛çã♦ é
r❡♣r❡s❡♥t❛❞❛ ♥❛ ❋✐❣✉r❛ ✸✳✶✱ q✉❡ ❝♦♥s✐❞❡r❛ m= 2 ❡n = 3✳
X ={x∈Rm} Y ={y∈R
n}
x2
x1
f1
f2
f3
f
❊s♣❛ç♦ ❞❡ ❉❡❝✐sã♦ ❊s♣❛ç♦ ❞❡ ❖❜❥❡t✐✈♦s
❋✐❣✉r❛ ✸✳✶✿ ▼❛♣❡❛♠❡♥t♦ ❞❛s ❱❛r✐á✈❡✐s ❞❡ ❉❡❝✐sã♦
❆❧❣✉♥s ❝♦♥❝❡✐t♦s ❞❡ ♦t✐♠✐③❛çã♦ ♠✉❧t✐♦❜❥❡t✐✈♦ ✭❆rr♦②♦✱ ✷✵✵✷❀ ❈♦❡❧❧♦ ❡t ❛❧✳✱ ✷✵✵✼❀ ❚❛❦❛❤❛s❤✐✱ ✷✵✵✹✮ sã♦ ♥❡❝❡ssár✐♦s ♣❛r❛ ♦ ♠❡❧❤♦r ❡♥t❡♥❞✐♠❡♥t♦ ❞♦s ❛❧❣♦r✐t♠♦s ♣r♦✲ ♣♦st♦s✿
❉❡✜♥✐çã♦ ✶ ✭P❛r❡t♦ ❉♦♠✐♥â♥❝✐❛✮ P❛r❛ q✉❛✐sq✉❡r ❞✉❛s s♦❧✉çõ❡s x1, x2 ∈ Xf✱
s❡♥❞♦ Xf ♦ ❝♦♥❥✉♥t♦ ❞❡ s♦❧✉çõ❡s ❢❛❝tí✈❡✐s✱ ❡ ♣❛r❛ ✉♠❛ ❢✉♥çã♦ ✈❡t♦r✐❛❧ f(x) =
(f1(x), f2(x), ..., fn(x)) : X → Z✱ t❡♠✲s❡ q✉❡✱ x1 ❞♦♠✐♥❛ x2 s❡ ❛ ✐♠❛❣❡♠ ❞❡ x1
❞♦♠✐♥❛ ❛ ✐♠❛❣❡♠ ❞❡ x2✱ ✐st♦ é✱ f(x1)6 f(x2) ❡ f(x1) 6=f(x2)✳ ❖ ❝♦♥❝❡✐t♦ ❞❡ P❛✲
r❡t♦ ❞♦♠✐♥â♥❝✐❛ ❡st❛❜❡❧❡❝❡ ❛ r❡❧❛çã♦≺❡♥tr❡ ❞♦✐s ✈❡t♦r❡s ❞❡ ❞❡❝✐sã♦✳ ❆ss✐♠✱x1 ≺x2
❞❡♥♦t❛ q✉❡ ♦ ✈❡t♦r ❞❡ ❞❡❝✐sã♦ x1 ❞♦♠✐♥❛ ♦ ✈❡t♦r ❞❡ ❞❡❝✐sã♦ x2✳
❉❡✜♥✐çã♦ ✷ ✭❙♦❧✉çõ❡s ◆ã♦✲❈♦♠♣❛rá✈❡✐s✮ P❛r❛ q✉❛✐sq✉❡r ❞✉❛s s♦❧✉çõ❡s x1, x2
∈Xf✱ s❡♥❞♦ Xf ♦ ❝♦♥❥✉♥t♦ ❞❡ s♦❧✉çõ❡s ❢❛❝tí✈❡✐s✱ ❡ ♣❛r❛ ✉♠❛ ❢✉♥çã♦ ✈❡t♦r✐❛❧f(x) =
(f1(x), f2(x), ..., fn) : X → Z✱ ❞✐③✲s❡ q✉❡ x1 ❡ x2 sã♦ ♥ã♦ ❝♦♠♣❛rá✈❡✐s s❡ ♥❡♠ x1
❞♦♠✐♥❛ x2 ❡ ♥❡♠x2 ❞♦♠✐♥❛ x1✳
❉❡✜♥✐çã♦ ✸ ✭❙♦❧✉çã♦ P❛r❡t♦✲ót✐♠❛✮ ❯♠❛ s♦❧✉çã♦ x∗ ∈ X
f é ✉♠❛ s♦❧✉çã♦
P❛r❡t♦✲ót✐♠❛ s❡ ♥ã♦ ❡①✐st❡ q✉❛❧q✉❡r ♦✉tr❛ s♦❧✉çã♦ x ∈ Xf✱ t❛❧ q✉❡ x ❞♦♠✐♥❡ x∗❀
z∗ =f(x∗) é ❝❤❛♠❛❞♦ ❞❡ ♣♦♥t♦ ❡✜❝✐❡♥t❡ ♦✉ ♣♦♥t♦ P❛r❡t♦✲ót✐♠♦✳
❉❡✜♥✐çã♦ ✹ ✭❈♦♥❥✉♥t♦ P❛r❡t♦✲ót✐♠♦✮ ❖ ❝♦♥❥✉♥t♦ P❛r❡t♦✲ót✐♠♦P✱ ♦✉ ❝♦♥❥✉♥t♦
P❛r❡t♦✲ót✐♠♦ ❣❧♦❜❛❧ ♣❛r❛ ✉♠ ♣r♦❜❧❡♠❛ ❞❡ ♦t✐♠✐③❛çã♦ ♠✉❧t✐♦❜❥❡t✐✈♦ é ❞❡✜♥✐❞♦ ❝♦♠♦✿
P ={x∗
✸✳✶ ❖t✐♠✐③❛çã♦ ▼✉❧t✐♦❜❥❡t✐✈♦ ✾ ❉❡✜♥✐çã♦ ✺ ✭❋r♦♥t❡✐r❛ P❛r❡t♦✲ót✐♠❛✮ ❆ ❢r♦♥t❡✐r❛ P❛r❡t♦✲ót✐♠❛F✱ ♦✉ ❢r♦♥t❡✐r❛
P❛r❡t♦✲ót✐♠❛ ❣❧♦❜❛❧ ♣❛r❛ ✉♠ ♣r♦❜❧❡♠❛ ❞❡ ♦t✐♠✐③❛çã♦ ♠✉❧t✐♦❜❥❡t✐✈♦ ❝♦rr❡s♣♦♥❞❡ à ✐♠❛❣❡♠ ❞♦ ❝♦♥❥✉♥t♦ P❛r❡t♦✲ót✐♠♦✱ s❡♥❞♦ ❞❡✜♥✐❞❛ ❝♦♠♦✿
F ={y =f(x) :x∈ P} ✭✸✳✸✮
❊①✐st❡♠ ❞✐✈❡rs❛s r❡❧❛çõ❡s ❞❡ ♦r❞❡♠ ❡♥tr❡ ❞✉❛s s♦❧✉çõ❡s x1, x2 ∈Xf✳ ❯♠❛ ❧✐st❛
❞❛s ♠❛✐s ❝♦♠✉♥s é ❛♣r❡s❡♥t❛ ♥❛ ❚❛❜❡❧❛ ✸✳✶
❚❛❜❡❧❛ ✸✳✶✿ ❘❡❧❛çõ❡s ❞❡ ❉♦♠✐♥â♥❝✐❛
r❡❧❛çã♦ ♥♦t❛çã♦ ✐♥t❡r♣r❡t❛çã♦
❞♦♠✐♥❛ ❡str✐t❛♠❡♥t❡ x1 ≺≺x2 fn(x1)< fn(x2)∀n
❞♦♠✐♥❛ x1 ≺x2 fn(x1)≤fn(x2) ∀n∧ ∃i:fi(x1)< fi(x2)
❞♦♠✐♥❛ ❢r❛❝❛♠❡♥t❡ x1 x2 fn(x1)≤fn(x2) ∀n
♥ã♦✲❝♦♠♣❛rá✈❡✐s x1 kx2 ¬(x1 x2)∧ ¬(x2 x1)
✐♥❞✐❢❡r❡♥t❡ x1 ∼x2 fn(x1) = fn(x2)∀n
✸✳✶✳✷ ▼ét♦❞♦s ❈❧áss✐❝♦s
◆❡st❛ s❡çã♦ sã♦ ❛♣r❡s❡♥t❛❞♦s ♦s ♠ét♦❞♦s tr❛❞✐❝✐♦♥❛✐s ♣❛r❛ r❡s♦❧✈❡r ♣r♦❜❧❡♠❛s ❞❡ ♦t✐♠✐③❛çã♦ ♠✉❧t✐♦❜❥❡t✐✈♦✳
✸✳✶✳✷✳✶ ▼ét♦❞♦ ❞❛ ❙♦♠❛ P♦♥❞❡r❛❞❛
❊st❡ ♠ét♦❞♦ ❝♦♥s✐st❡ ❡♠ ❝r✐❛r ✉♠ ♠♦❞❡❧♦ ♠♦♥♦✲♦❜❥❡t✐✈♦ ❛ ♣❛rt✐r ❞❛ ♣♦♥❞❡r❛çã♦ ❞❛s
n ❢✉♥çõ❡s ♦❜❥❡t✐✈♦s ❛tr❛✈és ❞❛ ❛tr✐❜✉✐çã♦ ❞❡ ♣❡s♦s ♣❛r❛ ❝❛❞❛ ❢✉♥çã♦✳ ❉❡ss❛ ❢♦r♠❛✱
♦ ♠ét♦❞♦ ❞❡ s♦♠❛ ♣♦♥❞❡r❛❞❛ ♣❛r❛ ✉♠ ♣r♦❜❧❡♠❛ ❞❡ ♦t✐♠✐③❛çã♦ ♠✉❧t✐♦❜❥❡t✐✈♦ ♣♦❞❡ s❡r ❞❡✜♥✐❞♦ ❞❛ s❡❣✉✐♥t❡ ❢♦r♠❛✿
f(x) =
n
X
i=1
wifi(x) ✭✸✳✹✮
♦✉ s❡❥❛✱ ❝❛❞❛ ❢✉♥çã♦ ♦❜❥❡t✐✈♦ fi é ♠✉❧t✐♣❧✐❝❛❞❛ ♣♦r ✉♠ ♣❡s♦ wi✱ ❝♦♠ wi ≥0✳ ❆❧é♠
❞✐ss♦✱ ❣❡r❛❧♠❡♥t❡ ❛ s♦♠❛ ❞♦s ♣❡s♦s é ♥♦r♠❛❧✐③❛❞❛✿
n
X
i=i
wi = 1 ✭✸✳✺✮
❆♥❛❧✐s❛♥❞♦ ❛ ❢✉♥çã♦f(x) ♦❜t✐❞❛ ♣❡❧❛ ❝♦♠❜✐♥❛çã♦ ❧✐♥❡❛r ❞❛s ❢✉♥çõ❡sfi✱ ♣♦❞❡✲s❡
❛✜r♠❛r q✉❡ ❛ s♦❧✉çã♦ ❢♦r♥❡❝✐❞❛ ♣♦r ❡ss❡ ♠ét♦❞♦ s❡rá ✉♠ ♣♦♥t♦ ❞❛ ❢r❡♥t❡ P❛r❡t♦✲ ót✐♠❛✳ ❆ ❞❡✜♥✐çã♦ ❞❡ q✉❛❧ é ♦ ♣♦♥t♦ ❞❛ ❢r♦♥t❡✐r❛ P❛r❡t♦✲ót✐♠❛ ❞❡♣❡♥❞❡ ❞❛ ❛tr✐❜✉✐çã♦ ❞♦s ♣❡s♦s ♣❛r❛ ❝❛❞❛ ❢✉♥çã♦ ♦❜❥❡t✐✈♦✳
