❯▼❆ ❍❊❯❘❮❙❚■❈❆ ❇❆❙❊❆❉❆ ❊▼ ❈❖▲Ô◆■❆ ❉❊
❋❖❘▼■●❆❙ P❆❘❆ ❖ P❘❖❇▲❊▼❆ ❉❖ ❈❆❘❚❊■❘❖
❏❆■❘❖✳ ❱■❆◆❆ ❏❘✳
❯▼❆ ❍❊❯❘❮❙❚■❈❆ ❇❆❙❊❆❉❆ ❊▼ ❈❖▲Ô◆■❆ ❉❊
❋❖❘▼■●❆❙ P❆❘❆ ❖ P❘❖❇▲❊▼❆ ❉❖ ❈❆❘❚❊■❘❖
❈❍■◆✃❙ ▼■❙❚❖
❉✐ss❡rt❛çã♦ ❛♣r❡s❡♥t❛❞❛ ❛♦ Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❈✐ê♥❝✐❛ ❞❛ ❈♦♠♣✉t❛çã♦ ❞♦ ■♥st✐t✉t♦ ❞❡ ❈✐ê♥❝✐❛s ❊①❛t❛s ❞❛ ❯♥✐✈❡r✲ s✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ▼✐♥❛s ●❡r❛✐s✳ ❉❡♣❛rt❛✲ ♠❡♥t♦ ❞❡ ❈✐ê♥❝✐❛ ❞❛ ❈♦♠♣✉t❛çã♦✳ ❝♦♠♦ r❡q✉✐s✐t♦ ♣❛r❝✐❛❧ ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞♦ ❣r❛✉ ❞❡ ▼❡str❡ ❡♠ ❈✐ê♥❝✐❛ ❞❛ ❈♦♠♣✉t❛çã♦✳
❖r✐❡♥t❛❞♦r✿ Pr♦❢✳ ❙❡❜❛st✐á♥ ❆❧❜❡rt♦ ❯rr✉t✐❛
❝
✷✵✶✵✱ ❏❛✐r♦✳ ❱✐❛♥❛ ❏r✳✳
❚♦❞♦s ♦s ❞✐r❡✐t♦s r❡s❡r✈❛❞♦s✳
❱✐❛♥❛ ❏r✳✱ ❏❛✐r♦✳
❱✻✶✹❤ ❯♠❛ ❤❡✉ríst✐❝❛ ❜❛s❡❛❞❛ ❡♠ ❝♦❧ô♥✐❛ ❞❡ ❢♦r♠✐❣❛s ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞♦ ❈❛rt❡✐r♦ ❈❤✐♥ês ▼✐st♦ ✴ ❏❛✐r♦✳ ❱✐❛♥❛ ❏r✳✳ ✖ ❇❡❧♦ ❍♦r✐③♦♥t❡✱ ✷✵✶✵
①✈✐✐✐✱ ✹✻ ❢✳ ✿ ✐❧✳ ❀ ✷✾❝♠
❉✐ss❡rt❛çã♦ ✭♠❡str❛❞♦✮ ✖ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ▼✐♥❛s ●❡r❛✐s✳ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❈✐ê♥❝✐❛ ❞❛
❈♦♠♣✉t❛çã♦✳
❖r✐❡♥t❛❞♦r✿ Pr♦❢✳ ❙❡❜❛st✐á♥ ❆❧❜❡rt♦ ❯rr✉t✐❛ ✶✳ ❚❡♦r✐❛ ❞♦s ●r❛❢♦s ✲ ❚❡s❡✳ ✷✳ ❖t✐♠✐③❛çã♦ ✲ ❚❡s❡✳ ✸✳ ❈♦❧ô♥✐❛ ❞❡ ❋♦r♠✐❣❛s ✲ ❚❡s❡✳ ✹✳ Pr♦❜❧❡♠❛ ❞♦ ❝❛rt❡✐r♦ ❝❤✐♥ês ♠✐st♦ ✲ ❚❡s❡✳ ■✳ ❖r✐❡♥t❛❞♦r ■■✳ ❚ít✉❧♦✳
❆❣r❛❞❡❝✐♠❡♥t♦s
▼❡✉s ❛❣r❛❞❡❝✐♠❡♥t♦s ✈ã♦ ♣❛r❛ t♦❞❛s ❛s ♣❡ss♦❛s q✉❡ ❝♦♥tr✐❜✉ír❛♠ ♣❛r❛ ❝♦♥❝❧✉sã♦ ❞❡st❡ tr❛❜❛❧❤♦✳ ❆❣r❛❞❡ç♦ ❡s♣❡❝✐❛❧♠❡♥t❡ ❛ ♠✐♥❤❛ ♠ã❡✱ ♠✐♥❤❛s ✐r♠ãs ❡ ♠✐♥❤❛ ♥♦✐✈❛✱ ▼♦❡♠❛ ●♦♠❡s ▲✐♥❤❛r❡s✱ ♣♦r t♦❞♦ ♦ ❛♠♦r✱ ♣❛❝✐ê♥❝✐❛ ❡ ✐♥❝❡♥t✐✈♦ ♥♦s ♠♦♠❡♥t♦s ❡♠ q✉❡ ♠❛✐s ♣r❡✲ ❝✐s❡✐✳ ❆❣r❛❞❡ç♦ ❛♦ ♠❡✉ ♦r✐❡♥t❛❞♦r✱ Pr♦❢❡ss♦r ❙❡❜❛st✐á♥ ❆❧❜❡rt♦ ❯rr✉t✐❛✱ ♣❡❧❛ ♣❛❝✐ê♥❝✐❛ ❡ ❝♦♠♣r❡❡♥sã♦✱ ❛ss✐♠ ❝♦♠♦ ❛s ✈❡r❞❛❞❡✐r❛s ❧✐çõ❡s s♦❜r❡ ❝♦♠♣✉t❛çã♦ ❝✐❡♥tí✜❝❛ ❡ ♣❡sq✉✐s❛ ❡♠ ❝♦♠♣✉t❛çã♦✳ ❆❧é♠ ❞✐ss♦✱ ✉♠ ❛❣r❛❞❡❝✐♠❡♥t♦ ❛ ♠❡✉s ❝♦♠♣❛♥❤❡✐r♦s ❞❡ tr❛❜❛❧❤♦ ♥❛ ▲í❞❡r ❆✈✐❛çã♦✱ ♣❡❧♦ ✐♥❝❡♥t✐✈♦ ❡ ❝♦♠♣❛♥❤❡✐r✐s♠♦✱ ❡ ♣r✐♥❝✐♣❛❧♠❡♥t❡✱ ❛ ❏♦ã♦ ❈❛r❧♦s P❡r❡✐r❛ ❈❛♠♣♦s ❡ ❊❞❣❛r❞ ❞❡ ❆r❛ú❥♦ ▼✐tr❡✳ ❆❣r❛❞❡ç♦ t❛♠❜é♠ áq✉❡❧❛s ♣❡ss♦❛s q✉❡✱ ♠❡s♠♦ ❞✉r❛♥t❡ ❛s ♣✐♦r❡s ✈❡♥t❛♥✐❛s✱ ♥ã♦ ♠❡ ❞❡✐①❛r❛♠ ❞❡s✐st✐r ♦✉ ❢r❛q✉❡❥❛r ❡ s❡♠♣r❡ t✐✈❡r❛♠ ✉♠❛ ♣❛❧❛✈r❛ ❞❡ ✐♥❝❡♥t✐✈♦✳ ◆❡ss❡ í♥t❡r✐♠✱ ❛❧é♠ ❞♦s ❥á ❝✐t❛❞♦s✱ ❛❣r❛❞❡ç♦ ❛ P❛trí✲ ❝✐❛ ❈♦rrê❛✱ ♠❡✉s s♦❜r✐♥❤♦s ❡ ❝✉♥❤❛❞♦s ❡ ❛ ❘❡♥❛t♦ ❡ ❈â♥❞✐❞❛ ▲✐♥❤❛r❡s✳ ◗✉❡ ♣♦ss❛♠♦s ❝♦♥q✉✐st❛r ❝❛❞❛ ✈❡③ ♠❛✐s✳
❘❡s✉♠♦
❖ Pr♦❜❧❡♠❛ ❞♦ ❈❛rt❡✐r♦ ❈❤✐♥ês ✭❈❤✐♥❡s❡ P♦st♠❛♥ Pr♦❜❧❡♠✱ ❡♠ ✐♥❣❧ês✮ é ✉♠ ❞♦s ❞❡s❛✜♦s ❝❧áss✐❝♦s ❡♠ ❈✐ê♥❝✐❛ ❞❛ ❈♦♠♣✉t❛çã♦✱ ❡s♣❡❝✐✜❝❛♠❡♥t❡ ♥❛ ár❡❛ ❞❡ ❣r❛❢♦s✳ ➱ ✉♠ ♣r♦❜❧❡♠❛ ❞❡ ♦t✐♠✐③❛çã♦ ❝♦♠❜✐♥❛tór✐❛ ❜❡♠ ❝♦♥❤❡❝✐❞♦ ❝♦♠ ✉♠❛ ✐♥✜♥✐❞❛❞❡ ❞❡ ❛♣❧✐❝❛çõ❡s ♣rát✐❝❛s✳ ●r❛♥❞❡ ♣❛rt❡ ❞♦s ♣r♦❜❧❡♠❛s ❞♦ ♠✉♥❞♦ r❡❛❧ ♦♥❞❡ s❡❥❛ ♣r❡❝✐s♦ ♣❡r❝♦rr❡r ✉♠❛ ❝✐❞❛❞❡✱ ✉♠ tr❡❝❤♦ ❞❡ ♠❛♣❛ ♦✉ ✉♠❛ r❡❞❡ ❞❡ r❡❝✉rs♦s✱ t❛✐s ❝♦♠♦ ❝♦❧❡t❛ ❞❡ ❧✐①♦ ✉r❜❛♥♦✱ ✐♥s♣❡çã♦ ❡♠ ✜♦s✱ r❡t✐r❛❞❛ ❞❡ ❣❡❧♦ ♦✉ ❡♥tr❡❣❛ ❞❡ ❝❛rt❛s✱ ♣♦❞❡♠ s❡r ♠♦❞❡❧❛❞♦s ❛tr❛✈és ❞♦ ❈❤✐♥❡s❡ P♦st♠❛♥ ♣r♦❜❧❡♠ ✭❈PP✮ ♦✉ ❞❡ s✉❛s ✈❛r✐❛çõ❡s✳ ❇❛s✐❝❛♠❡♥t❡✱ ♣r♦❝✉r❛✲s❡ ✉♠ ❝❛♠✐♥❤♦ ❞❡ ❝✉st♦ ♠í♥✐♠♦ ❡♠ ✉♠ ❣r❛❢♦✱ ❞❡ ❢♦r♠❛ q✉❡ ♦ ❝❛♠✐♥❤♦ ❝♦♥t❡♠♣❧❡ t♦❞❛s ❛s ❛r❡st❛s ❡ ❛r❝♦s ❞♦ ❣r❛❢♦ ♣❡❧♦ ♠❡♥♦s ✉♠❛ ✈❡③✳ ❊st❡ ♣r♦❜❧❡♠❛ ♣♦ss✉✐ s♦❧✉çã♦ ❡♠ t❡♠♣♦ ♣♦❧✐♥♦♠✐❛❧ t❛♥t♦ ♣❛r❛ ❛ ✈❡rsã♦ ♦r✐❡♥t❛❞❛ q✉❛♥t♦ ♣❛r❛ ❛ ✈❡rsã♦ ♥ã♦✲♦r✐❡♥t❛❞❛✳ ❖ ♦❜❥❡t♦ ❞❡ ❡st✉❞♦ ❞❡st❡ tr❛❜❛❧❤♦ é ❛ ✈❛r✐❛çã♦ ❞♦ ❈PP ❝♦♥❤❡❝✐❞❛ ❝♦♠♦ Pr♦❜❧❡♠❛ ❞♦ ❝❛rt❡✐r♦ ❝❤✐♥ês ♠✐st♦✱ ♦♥❞❡ ❝♦✲❡①✐st❡♠ ❡♠ ✉♠ ❣r❛❢♦ ❛r❡st❛s ✭♥ã♦✲❞✐r❡❝✐♦♥❛❞❛s✮ ❡ ❛r❝♦s✳ ❊st❛ ✈❛r✐❛çã♦ ❞♦ ❈PP é ✉♠ ♣r♦❜❧❡♠❛ ◆P✲❈♦♠♣❧❡t♦ ❬P❛♣❛❞✐♠✐tr✐♦✉✱ ✶✾✼✻❪✳ ➱ ♣r♦♣♦st❛ ✉♠❛ ❤❡✉ríst✐❝❛ ❜❛s❡❛❞❛ ❡♠ ❝♦❧ô♥✐❛s ❞❡ ❢♦r♠✐❣❛s ♣❛r❛ ♦ ▼❈PP ✭Pr♦❜❧❡♠❛ ❞♦ ❈❛rt❡✐r♦ ❈❤✐♥ês ▼✐st♦✮✱ ❛ss✐♠ ❝♦♠♦ ✉♠ ♣r♦❝❡❞✐♠❡♥t♦ ❞❡ ♠❡❧❤♦r❛ ❝♦♥tí♥✉❛ ❞❛ s♦❧✉çã♦✳
P❛❧❛✈r❛s✲❝❤❛✈❡✿ ❖t✐♠✐③❛çã♦✱ ❈♦❧ô♥✐❛ ❞❡ ❋♦r♠✐❣❛s✱ ❈❛rt❡✐r♦ ❈❤✐♥ês ▼✐st♦✳
▲✐st❛ ❞❡ ❋✐❣✉r❛s
✶✳✶ ❊①❡♠♣❧♦ ❞❡ ✉♠ ❣r❛❢♦ ♠✐st♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸ ✸✳✶ ❈❛♠✐♥❤♦s ❞❡ t❛♠❛♥❤♦s ✐❣✉❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸ ✸✳✷ ❈❛♠✐♥❤♦s ❞❡ t❛♠❛♥❤♦s ❞✐❢❡r❡♥t❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹ ✸✳✸ ❊①❡♠♣❧♦ ♣❛r❛ ❛ ♣r♦✈❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻ ✸✳✹ ❊①❡♠♣❧♦s ❞❡ ❝✐r❝✉✐t♦s ❞❡ t❛♠❛♥❤♦ ✷✭❛✮✱✸✭❜✮✱✹✭❝✮ ❡ ✺✭❞✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✸✳✺ ❊①❡♠♣❧♦s ❞❡ ❝✐r❝✉✐t♦s ❣❡r❛❞♦s ♣♦r ❉✐❥❦str❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✹✳✶ ❊①❡❝✉çã♦ ♥❛ ✐♥stâ♥❝✐❛ ▼❆✵✺✸✷ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✹✳✷ ❉❡t❛❧❤❛♠❡♥t♦ ❞❛ ❡①❡❝✉çã♦ ♥♦s ❥❛r❞✐♥s ❞❡ ★ ✶✵✵ ❛ ✷✵✵ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ✹✳✸ ❆♣r♦✈❡✐t❛♠❡♥t♦ ❞♦ ❏❛r❞✐♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✹✳✹ ❊✈❛♣♦r❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻
▲✐st❛ ❞❡ ❚❛❜❡❧❛s
✸✳✶ ❆♥á❧✐s❡ ❞❡ ❝✐r❝✉✐t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸ ✹✳✶ ■♥stâ♥❝✐❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ✹✳✷ ●❡r❛çã♦ ❞❡ ❝✐r❝✉✐t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼ ✹✳✸ ❈♦❧ô♥✐❛ ❞❡ ❢♦r♠✐❣❛s ✲ ❘❡s✉❧t❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾
❙✉♠ár✐♦
❆❣r❛❞❡❝✐♠❡♥t♦s ✈✐✐
❘❡s✉♠♦ ①✐
▲✐st❛ ❞❡ ❋✐❣✉r❛s ①✐✐✐
▲✐st❛ ❞❡ ❚❛❜❡❧❛s ①✈
✶ ■♥tr♦❞✉çã♦ ✶
✶✳✶ ❖❜❥❡t✐✈♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷ ✶✳✷ ❆❧❣✉♥s ❝♦♥❝❡✐t♦s ✐♠♣♦rt❛♥t❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷ ✶✳✸ ❉❡✜♥✐çã♦ ❞♦ ♣r♦❜❧❡♠❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸ ✶✳✸✳✶ ❈♦♥t❡①t♦ t❡ór✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹
✷ ❘❡✈✐sã♦ ❜✐❜❧✐♦❣rá✜❝❛ ✼
✷✳✶ ❱❛r✐❛çõ❡s ❞♦ ♣r♦❜❧❡♠❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼ ✷✳✷ ❈❛rt❡✐r♦ ❈❤✐♥ês ▼✐st♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽
✸ ❆ ❤❡✉ríst✐❝❛ ♣r♦♣♦st❛ ✶✶
✸✳✶ ❈♦❧ô♥✐❛s ❞❡ ❋♦r♠✐❣❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶ ✸✳✶✳✶ ❯♠ ❡①❡♠♣❧♦ ✲ ❖ ♣r♦❜❧❡♠❛ ❞♦ ❝❛✐①❡✐r♦ ✈✐❛❥❛♥t❡ ✭P❈❱✮ ✳ ✳ ✳ ✳ ✳ ✶✷ ✸✳✶✳✷ ❆ ✐♥s♣✐r❛çã♦ ♥❛ ♥❛t✉r❡③❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸ ✸✳✷ ❋✉♥❞❛♠❡♥t❛çã♦ t❡ór✐❝❛ ❞❛ ❝♦❜❡rt✉r❛ ❞❡ ✉♠ ❣r❛❢♦ ♣♦r ❝✐r❝✉✐t♦s ✳ ✳ ✳ ✳ ✳ ✶✹ ✸✳✸ ❈♦♥str✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼ ✸✳✸✳✶ ❈✐r❝✉✐t♦s ❞❡ t❛♠❛♥❤♦ ❞❡✜♥✐❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼ ✸✳✸✳✷ ❈✐r❝✉✐t♦s ❛❧❡❛tór✐♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✸✳✸✳✸ ❈✐r❝✉✐t♦s ♣♦r ❉✐❥❦str❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ✸✳✸✳✹ ❚r❛t❛♠❡♥t♦ ❞♦ ❜❛♥❝♦ ❞❡ ❞❛❞♦s ❞❡ ❝✐r❝✉✐t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✸✳✹ ▼❡❧❤♦r✐❛ ✲ ❖t✐♠✐③❛çã♦ ♣♦r ❈♦❧ô♥✐❛ ❞❡ ❋♦r♠✐❣❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹
✸✳✹✳✶ ■♥✐❝✐❛❧✐③❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹ ✸✳✹✳✷ ●❡r❛♥❞♦ ✉♠ ❏❛r❞✐♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✸✳✹✳✸ ❆♣❧✐❝❛♥❞♦ ❢❡r♦♠ô♥✐♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✹ ❘❡s✉❧t❛❞♦s ❝♦♠♣✉t❛❝✐♦♥❛✐s ✸✶ ✹✳✶ ▼❡t♦❞♦❧♦❣✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✹✳✷ ■♥stâ♥❝✐❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✹✳✸ ❈♦♥✈❡r❣ê♥❝✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✹✳✹ ❆♣r♦✈❡✐t❛♠❡♥t♦ ❞❡ ❢♦r♠✐❣❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✹✳✺ ❊✈❛♣♦r❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✹✳✻ ●❡r❛çã♦ ❞❡ ❝✐r❝✉✐t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼ ✹✳✼ ❚❡♠♣♦s ❞❡ ❡①❡❝✉çã♦ ❡ q✉❛❧✐❞❛❞❡ ❞❛ s♦❧✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽
✺ ❈♦♥❝❧✉sã♦ ✹✶
✺✳✶ ❚r❛❜❛❧❤♦s ❋✉t✉r♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ❘❡❢❡rê♥❝✐❛s ❇✐❜❧✐♦❣rá✜❝❛s ✹✸
❈❛♣ít✉❧♦ ✶
■♥tr♦❞✉çã♦
❖ ♣r♦❜❧❡♠❛ ❞♦ ❈❛rt❡✐r♦ ❈❤✐♥ês✱ ♦✉ ❈❤✐♥❡s❡ P♦st♠❛♥ Pr♦❜❧❡♠ ✭❈PP✮ ❢♦✐ ✐♥tr♦❞✉③✐❞♦ ♣♦r ▼❡✐❣✉ ●✉❛♥ ✶ ❬▼❡✐❣✉✱ ✶✾✻✷❪✳ ❯♠❛ ❞❛s ❛♣❧✐❝❛çõ❡s ❞♦ ❈PP ♣♦❞❡ s❡r ❞❡s❝r✐t❛ ❝♦♠♦
✉♠ ❝❛rt❡✐r♦ q✉❡ ♣❛rt❡ ❞❡ ✉♠ ♣♦st♦ ❞♦s ❈♦rr❡✐♦s✱ ❡♥tr❡❣❛ ❝❛rt❛s ❡♠ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ r✉❛s ❡ ✈♦❧t❛ ❛♦ ♣♦st♦ ❞♦s ❝♦rr❡✐♦s ♦r✐❣✐♥❛❧✳ ❖ ♣r♦❜❧❡♠❛ ❞♦ ❈❛rt❡✐r♦ ❈❤✐♥ês ❡ s✉❛s ✈❛r✐❛çõ❡s ❢♦r♠❛♠ ✉♠❛ ❝❧❛ss❡ ❞❡♥tr♦ ❞♦s ♣r♦❜❧❡♠❛s ❞❡ r♦t❡❛♠❡♥t♦ ❡♠ ❛r❝♦s✳ ❖ ♦❜❥❡t✐✈♦ é ❡♥❝♦♥tr❛r ✉♠ ❝❛♠✐♥❤♦ q✉❡ s❛✐❛ ❞❡ ✉♠ ❝❡rt♦ ✈ért✐❝❡✲♦r✐❣❡♠✱ ♣❡r❝♦rr❛ t♦❞♦s ♦s ❛r❝♦s ❞❡ ✉♠ ❞❡t❡r♠✐♥❛❞♦ ❣r❛❢♦ ❞❛ ❢♦r♠❛ ♠❛✐s ❡❝♦♥ô♠✐❝❛ ♣♦ssí✈❡❧✱ r❡t♦r♥❛♥❞♦ ❛♦ ✈ért✐❝❡✲♦r✐❣❡♠✱ ❝r✐❛♥❞♦ ✉♠ ❝✐r❝✉✐t♦ q✉❡ ❝♦♠❡❝❡ ❡ t❡r♠✐♥❡ ❡♠ ✉♠ ♠❡s♠♦ ✈ért✐❝❡✳
❖ ♣r♦❜❧❡♠❛ ❞♦ ❝❛rt❡✐r♦ ❝❤✐♥ês é ✉♠ ♣r♦❜❧❡♠❛ ❞❡ ♦t✐♠✐③❛çã♦ ❝♦♠❜✐♥❛tór✐❛ ❝❧ásss✐❝♦ ❝♦♠ ✉♠❛ ❣r❛♥t❡ q✉❛♥t✐❞❛❞❡ ❞❡ ❛♣❧✐❝❛çõ❡s ♣rát✐❝❛s✱ t❛✐s ❝♦♠♦ ❝♦❧❡t❛ ❞❡ ❧✐①♦ ✉r❜❛♥♦✱ ✐♥s♣❡çã♦ ❡♠ ✜♦s✱ r❡t✐r❛❞❛ ❞❡ ❣❡❧♦✱ ❡♥tr❡❣❛ ❞❡ ❝❛rt❛s ♦✉ ♣r♦❜❧❡♠❛s s❡♠❡❧❤❛♥t❡s ♦♥❞❡ s❡❥❛ ♣r❡❝✐s♦ ♣❡r❝♦rr❡r ✉♠❛ ❝✐❞❛❞❡✱ ✉♠ tr❡❝❤♦ ❞❡ ♠❛♣❛ ♦✉ ✉♠❛ r❡❞❡ ❞❡ r❡❝✉rs♦s✳ ❚❛✐s ❛♣❧✐❝❛çõ❡s s❡ ❜❡♥❡✜❝✐❛♠ ❞❛s ❡❝♦♥♦♠✐❛s ♣r♦♣♦r❝✐♦♥❛❞❛s ♣♦r ✉♠ ♠❡❧❤♦r ✉s♦ ❞♦ r❡❝✉rs♦ ❡♠ q✉❡stã♦✱ s❡❥❛ ❡❧❡ ✉♠❛ ♣❡ss♦❛✱ ✉♠❛ ❡s❝❛✈❛❞❡✐r❛ ♦✉ ✉♠ ❝❛♠✐♥❤ã♦ ❞❡ ❧✐①♦✳ ❯♠❛ r♦t❛ ♦t✐♠✐③❛❞❛✱ ♥❛ ❝♦❧❡t❛ ❞❡ ❧✐①♦ ✉r❜❛♥♦ ♣♦r ❡①❡♠♣❧♦✱ ♣❡r♠✐t❡ ❞✐♠✐♥✉✐r ❛s ❥❛♥❡❧❛s ❞❡ ❝♦❧❡t❛✷✱ ❡❝♦♥♦♠✐③❛♥❞♦ ❝♦♠❜✉stí✈❡❧✱ r❡❝✉rs♦s ❤✉♠❛♥♦s ❡ ♠❡❧❤♦r❛♥❞♦ ❛ q✉❛❧✐❞❛❞❡
❞♦s s❡r✈✐ç♦s✳
◆❛ ✈❡rsã♦ ❝❧áss✐❝❛ ❞♦ ❈PP ❬▼❡✐❣✉✱ ✶✾✻✷❪✱ ❞❛❞♦ ✉♠ ●r❛❢♦ ● ❂ ✭❱✱❊✮✱ ♦♥❞❡ ❱ é ♦ ❝♦♥❥✉♥t♦ ❞❡ ✈ért✐❝❡s ❡ ❊ é ♦ ❝♦♥❥✉♥t♦ ❞❡ ❛r❡st❛s✱ ♦ ♦❜❥❡t✐✈♦ é ❡♥❝♦♥tr❛r ✉♠ ❝✐r❝✉✐t♦
✶❊st❡ ❛✉t♦r é r❡❢❡r❡♥❝✐❛❞♦ ❡♠ ♦✉tr♦s t❡①t♦s ❝♦♠♦ ▼❡✐✲❑✉ ❑✉❛♥✱ ❑✇❛♥ ▼❡✐❦✉✱ ❛❧é♠ ❞❡ ♦✉tr❛s
✈❛r✐❛çõ❡s✳ ❊st❛s ❞✐❢❡r❡♥ç❛s ♥❛ ❣r❛✜❛ ❞♦ ♥♦♠❡ ❞♦ ❛✉t♦r ✈❡♠ ❞♦ ❢❛t♦ ❞❡ s❡✉ tr❛❜❛❧❤♦ t❡r s✐❞♦ ♣✉❜❧✐❝❛❞♦ ❛♣❡♥❛s ❡♠ ❝❤✐♥ês ❡ q✉❡ ❛ tr❛♥s❧✐t❡r❛çã♦ ❞❡ s❡✉ ♥♦♠❡ ❛♦ ❛❧❢❛❜❡t♦ ❧❛t✐♥♦ ❛❝❡✐t❡ ✈ár✐❛s ✐♥t❡r♣r❡t❛çõ❡s✳ ❆ ❣r❛✜❛ ▼❡✐❣✉ ●✉❛♥ é ❝✐t❛❞❛ ❡♠ ❬❆♠✐♥✉ ✫ ❊❣❧❡s❡✱ ✷✵✵✻❪
✷❏❛♥❡❧❛ ❞❡ ❈♦❧❡t❛ é ♦ t❡♠♣♦ q✉❡ ✉♠ ❝❛♠✐♥❤ã♦ ❞❡ ❧✐①♦ ❣❛st❛ ♣❡r❝♦rr❡♥❞♦ ❛s r✉❛s ❝♦❧❡t❛♥❞♦ ❧✐①♦
✷ ❈❛♣ít✉❧♦ ✶✳ ■♥tr♦❞✉çã♦
❞❡ ❝✉st♦ ♠í♥✐♠♦✱ q✉❡ ♣❛ss❡ ♣❡❧♦ ♠❡♥♦s ✉♠❛ ✈❡③ ♣♦r ❝❛❞❛ ❛r❡st❛ ❞❡ ●✳ ❆s ❛r❡st❛s sã♦ ♣❡r❝♦rr✐❞❛s✱ ❝♦♠❡ç❛♥❞♦ ❡ t❡r♠✐♥❛♥❞♦ ❡♠ ✉♠ ♠❡s♠♦ ✈ért✐❝❡✳ ❊①✐st❡♠ ✈❡rsõ❡s ♦♥❞❡ ❛s ❛r❡st❛s sã♦ ❞✐r❡❝✐♦♥❛❞❛s ✭❬P❡❛r♥ ❡t ❛❧✳✱ ✶✾✽✼❪✱ ❬❊❞♠♦♥❞s ✫ ❏♦♥❤s♦♥✱ ✶✾✼✸❪✱ ❬▼❛❧❛♥❞r❛❦✐ ✫ ❉❛s❦✐♥✱ ✶✾✾✸❪✮✱ ♥ã♦✲❞✐r❡❝✐♦♥❛❞❛s ✭❬❆♠✐♥✉ ✫ ❊❣❧❡s❡✱ ✷✵✵✻❪✱ ❬P❡❛r♥ ❡t ❛❧✳✱ ✶✾✽✼❪✱ ❬❲❛♥❣ ✫ ❲❡♥✱ ✷✵✵✷❪✱ ❬❇❡♥❛✈❡♥t ❡t ❛❧✳✱ ✶✾✽✼❪✮ ♦✉ ♠✐st❛s ✭❬❇❡♥❛✈❡♥t ❡t ❛❧✳✱ ✶✾✽✼❪✱ ❬❙❜✐❤✐ ✫ ❊❣❧❡s❡✱ ✷✵✵✼❪✮✳
◆❡st❡ tr❛❜❛❧❤♦✱ s❡rá ❛❜♦r❞❛❞❛ ❛ ✈❡rsã♦ ♠✐st❛ ❞♦ ❈PP ✭▼❈PP✮✱ ♦♥❞❡ ❡①✐st❡♠ ♥♦ ❣r❛❢♦ ❆r❡st❛s ✭q✉❡ ♥ã♦ sã♦ ❞✐r❡❝✐♦♥❛❞❛s✮ ❡ ❆r❝♦s ✭q✉❡ ✢✉❡♠ ❡♠ ❛♣❡♥❛s ✉♠❛ ❞✐r❡çã♦✮✳ ◆♦ ▼❈PP✱ t❡♠♦s ✉♠ ●r❛❢♦ ● ❂ ✭❱✱❊✱❆✮✱ ♦♥❞❡ ❱ é ♥♦✈❛♠❡♥t❡ ♦ ❝♦♥❥✉♥t♦ ❞❡ ✈ér✲ t✐❝❡s✱ ❊ sã♦ ❛s ❛r❡st❛s ❡ ❆ sã♦ ♦s ❛r❝♦s✱ q✉❡ sã♦ ❞✐r❡❝✐♦♥❛❞♦s✳ ❖ ❝❛s♦ ♦♥❞❡ ♦ ❣r❛❢♦ é ❝♦♠♣❧❡t❛♠❡♥t❡ ❜✐❞✐r❡❝✐♦♥❛❧ ✭❆ ❂ ∅✮✱ ❝♦♠ ❛♣❡♥❛s r✉❛s ❞❡ ♠ã♦ ❞✉♣❧❛ ♣♦r ❡①❡♠♣❧♦✱ ❢♦✐
❡st✉❞❛❞♦ ❡♠ ❞❡t❛❧❤❡s ❡ ♣♦❞❡ s❡r r❡s♦❧✈✐❞♦ ❡✜❝✐❡♥t❡♠❡♥t❡ ❬❊❞♠♦♥❞s✱ ✶✾✻✺❪✳ ❖ ♦✉tr♦ ❝❛s♦ ❡s♣❡❝✐❛❧ ♦♥❞❡ ♦ ❣r❛❢♦ ♣♦ss✉✐ ❛♣❡♥❛s ❛r❝♦s ✭❊ ❂∅✮ t❛♠❜é♠ s❡ ♣r♦✈♦✉ s❡r ❞❡ ❢á❝✐❧
r❡s♦❧✉çã♦✱ ❡♠ t❡♠♣♦ ♣♦❧✐♥♦♠✐❛❧ ❬❊❞♠♦♥❞s ✫ ❏♦♥❤s♦♥✱ ✶✾✼✸❪✳ ❖ Pr♦❜❧❡♠❛ ❞♦ ❈❛rt❡✐r♦ ❈❤✐♥ês ♠✐st♦ ❢♦✐ ♣r♦✈❛❞♦ ❝♦♠♦ ◆P✲❈♦♠♣❧❡t♦ ❡♠ ❬P❛♣❛❞✐♠✐tr✐♦✉✱ ✶✾✼✻❪✳
✶✳✶ ❖❜❥❡t✐✈♦
❖ ♦❜❥❡t✐✈♦ ❞❡ss❛ ❞✐ss❡rt❛çã♦ é ♣r♦❞✉③✐r ✉♠ ❛❧❣♦r✐t♠♦ ❤❡✉ríst✐❝♦ ❞❡ q✉❛❧✐❞❛❞❡ ❝♦♠✲ ♣❛rá✈❡❧ ❛♦s ❛❧❣♦r✐t♠♦s ❤❡✉ríst✐❝♦s ❞❡ ✈❛♥❣✉❛r❞❛ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛✱ t❛♥t♦ ❡♠ t❡♠♣♦ ❞❡ ❡①❡❝✉çã♦ q✉❛♥t♦ ❛♦ ❝✉st♦ ❞❛ s♦❧✉çã♦✱ ♣❛r❛ ❛ ✈❡rsã♦ ♠✐st❛ ❞♦ ❈PP✳ ➱ ♣r♦♣♦st❛ ❛ ❝♦♥✲ str✉çã♦ ❞❡ ✉♠❛ ❤❡✉ríst✐❝❛ ❜❛s❡❛❞❛ ❡♠ ❝♦❧ô♥✐❛ ❞❡ ❢♦r♠✐❣❛s✳ ❊♠❜♦r❛ ♦✉tr❛s ❤❡✉ríst✐❝❛s t❡♥❤❛♠ s✐❞♦ ♣r♦♣♦st❛s✱ t❛✐s tr❛❜❛❧❤♦s ❢♦❝❛r❛♠ ❡♠ ♥❡❝❡ss✐❞❛❞❡s ❡s♣❡❝í✜❝❛s✱ ❝♦♠♦ ❝♦❧❡t❛ ❞❡ ❧✐①♦ ❡♠ ✉♠❛ ❞❡t❡r♠✐♥❛❞❛ ❝✐❞❛❞❡ ✭❇❛r❝❡❧♦♥❛✱ ❡♠ ❬❇❛✉t✐st❛ ❡t ❛❧✳✱ ✷✵✵✽❪✮ ♦✉ ♦✉tr♦s t✐♣♦s ❞❡ ❤❡✉ríst✐❝❛s ✭❬❈♦r❜❡rá♥ ❡t ❛❧✳✱ ✷✵✵✷❜❪✱ ❬❇❡♥❛✈❡♥t ❡t ❛❧✳✱ ✶✾✽✼❪✱ ❬❨❛♦②✉❡♥②♦♥❣ ✫ ❈❤❛r♥s❡t❤✐❦✉❧✱ ✷✵✵✷❪✮✳ ❙❡rã♦ ✉s❛❞❛s ♥❡st❡ tr❛❜❛❧❤♦ ❛s ✐♥stâ♥❝✐❛s ✉t✐❧✐③❛❞❛s ❡♠ ❬❈♦r✲ ❜❡rá♥ ❡t ❛❧✳✱ ✷✵✵✼❪✱ ♦♥❞❡ ♦s ✈❛❧♦r❡s ót✐♠♦s ❡stã♦ ❛ss✐♥❛❧❛❞♦s✱ ♣❡r♠✐t✐♥❞♦ ✉♠❛ ❛♥á❧✐s❡ s♦❜r❡ ❛ q✉❛❧✐❞❛❞❡ ❞❛ s♦❧✉çã♦✳
✶✳✷ ❆❧❣✉♥s ❝♦♥❝❡✐t♦s ✐♠♣♦rt❛♥t❡s
✶✳✸✳ ❉❡❢✐♥✐çã♦ ❞♦ ♣r♦❜❧❡♠❛ ✸
❖s ❡❧❡♠❡♥t♦s ❞❡ ❆ sã♦ ❝❤❛♠❛❞♦s ❞❡ ❛r❝♦s✳ ❆r❝♦s sã♦ ❝♦♠♦ ❛r❡st❛s✱ ❝♦♠ ❡①❝❡çã♦ ❞❡ q✉❡ ❛ ❝♦♥❡①ã♦ ❡♥tr❡ s❡✉s ❞♦✐s ✈ért✐❝❡s t❡r♠✐♥❛✐s é ❢❡✐t❛ ❛♣❡♥❛s ❡♠ ✉♠❛ ❞✐r❡çã♦✱ ❛tr❛✈és ❞❡ ✉♠ ♣❛r ♦r❞❡♥❛❞♦✱ ❞♦ ✈ért✐❝❡ ♦r✐❣❡♠ ❛♦ ✈ért✐❝❡ ❞❡st✐♥♦✳
❙❡ ♦ ❝♦♥❥✉♥t♦ ❆ é ✈❛③✐♦✱ ● é ✉♠ ❣r❛❢♦ ♥ã♦✲❞✐r❡❝✐♦♥❛❞♦✳ ❙❡ ♦ ❝♦♥❥✉♥t♦ ❊ é ✈❛③✐♦✱ ● é ✉♠ ❣r❛❢♦ ❞✐r❡❝✐♦♥❛❞♦✳ ❙❡ ♦s ❞♦✐s ❝♦♥❥✉♥t♦s ❢♦r❡♠ ♥ã♦✲✈❛③✐♦s✱ t❡♠♦s ✉♠ ❣r❛❢♦ ♠✐st♦✳ ❯♠ ❡①❡♠♣❧♦ ❞❡st❡ t✐♣♦ ❞❡ ❣r❛❢♦ ❡stá ♥❛ ✜❣✉r❛ ✶✳✶✳ ◆❡ss❡ tr❛❜❛❧❤♦✱ s❡rá ✉s❛❞♦ ♦ t❡r♠♦ ❧✐❣❛çã♦ ♣❛r❛ ❛r❡st❛s ♦✉ ❛r❝♦s✱ ✐♥❞✐s❝r✐♠✐♥❛❞❛♠❡♥t❡✳ ❚❛♠❜é♠ é ❝♦♠✉♠ ♦ ✉s♦ ❞♦ t❡r♠♦ ❡♥❧❛❝❡ ♥❛ ❧✐t❡r❛t✉r❛✱ s❡♥❞♦ ❛♠❜♦s tr❛❞✉çõ❡s ❞♦ t❡r♠♦ ✐♥❣❧ês ❧✐♥❦✳
❋✐❣✉r❛ ✶✳✶✳ ❊①❡♠♣❧♦ ❞❡ ✉♠ ❣r❛❢♦ ♠✐st♦
❯♠ ♣❛ss❡✐♦ é ✉♠❛ s❡q✉❡♥❝✐❛ ❞❡ ❛r❡st❛s ❡ ❛r❝♦s q✉❡ ❝♦♠❡ç❛ ❡♠ ✉♠ ✈ért✐❝❡ q✉❛❧✲ q✉❡r✱ ♣❡r❝♦rr❛ ✉♠❛ ❞❛s ❧✐❣❛çõ❡s ❞❡ss❡ ✈ért✐❝❡ ❛té ♦ ♣ró①✐♠♦ ✈ért✐❝❡✱ ❡ ❛tr❛✈és ❞❛ s✉❝❡ssã♦ ❞❡ ♣❡r❝✉rs♦s✱ r❡t♦r♥❛ ❛♦ ✈ért✐❝❡ ♦r✐❣✐♥❛❧✳ ❊st❡ ♣❛ss❡✐♦ ♣♦❞❡rá s❡r ❝❤❛♠❛❞♦ t❛♠❜é♠ ❞❡ ❝✐❝❧♦ ♦✉ ❝✐r❝✉✐t♦✳ ❖s ❛r❝♦s sã♦ ♣❡r❝♦rr✐❞♦s ❡♠ ♦❜❡❞✐ê♥❝✐❛ ❛ s✉❛s ♦r✐❡♥✲ t❛çõ❡s✱ ♦✉ s❡❥❛✱ ❛r❝♦s sã♦ s❡♠♣r❡ ♣❡r❝♦rr✐❞♦s ❞♦ ✈ért✐❝❡ ♦r✐❣❡♠ ❛♦ ✈ért✐❝❡ ❞❡st✐♥♦✳ ❖✉tr♦s ❝♦♥❝❡✐t♦s ✐♠♣♦rt❛♥t❡s ❡♠ ❣r❛❢♦s ♣♦❞❡♠ s❡r ❡♥❝♦♥tr❛❞♦s ❡♠ ❬●r♦ss ✫ ❨❡❧❧❡♥✱ ✷✵✵✸❪✳
✶✳✸ ❉❡✜♥✐çã♦ ❞♦ ♣r♦❜❧❡♠❛
❙❡❥❛ ✉♠ ❣r❛❢♦ ♠✐st♦ ● ❂ ✭❱✱❊✱❆✮✱ ♦♥❞❡ ❱ é ♦ ❝♦♥❥✉♥t♦ ❞❡ ✈ért✐❝❡s✱ ❊ é ♦ ❝♦♥❥✉♥t♦ ❞❛s ❛r❡st❛s ❡ ❆✱ é ♦ ❝♦♥❥✉♥t♦ ❞♦s ❛r❝♦s ✳ ❈❛❞❛ ❛r❡st❛ eij ∈E ✈❛✐ ❞♦ ✈ért✐❝❡ ✐ ❛té ♦ ✈ért✐❝❡
❥ ❡ ✈✐❝❡✲✈❡rs❛✳ ❈❛❞❛ aij ∈A ✈❛✐ ❛♣❡♥❛s ❞♦ ✈ért✐❝❡ ✐ ♣❛r❛ ♦ ✈ért✐❝❡ ❥✳ ❚♦❞❛s ❛s ❛r❡st❛s ❡
✹ ❈❛♣ít✉❧♦ ✶✳ ■♥tr♦❞✉çã♦
é ♦ ♣r♦❜❧❡♠❛ ❞❡ ❣❡r❛r ❡st❡ ♣❛ss❡✐♦ ♣❛ss❛♥❞♦ ♣❡❧♦ ♠❡♥♦s ✉♠❛ ✈❡③ ❡♠ ❝❛❞❛ ❛r❡st❛ ❡ ❛r❝♦ ❞❡ ● ❞❡ ❢♦r♠❛ ❛ ♠✐♥✐♠✐③❛r ♦ ❝✉st♦ t♦t❛❧ ❞❡ ♣❡r❝✉rs♦ ❞♦ ♣❛ss❡✐♦ q✉❡ ❝♦♠❡❝❡ ❡ t❡r♠✐♥❡ ♥♦ ♠❡s♠♦ ✈ért✐❝❡✳
◆❡st❡ tr❛❜❛❧❤♦✱ s❡rã♦ ✉s❛❞❛s ❛s s❡❣✉✐♥t❡s ♥♦t❛çõ❡s✿
• Ei ✿ ❞❡♥♦t❛♠ ♦ ❝♦♥❥✉♥t♦ ❞❡ ❛r❡st❛s ❧✐❣❛❞❛s ❛♦ ✈ért✐❝❡ ✐✳ • A+
i ✿ ❞❡♥♦t❛♠ ♦ ❝♦♥❥✉♥t♦ ❞❡ ❛r❝♦s ❝✉❥♦ ✈ért✐❝❡ ✐ s❡❥❛ ♦ ✈ért✐❝❡ ❞❡ ❞❡st✐♥♦✳ • A−i ✿ ❞❡♥♦t❛♠ ♦ ❝♦♥❥✉♥t♦ ❞❡ ❛r❝♦s ❝✉❥♦ ✈ért✐❝❡ ✐ s❡❥❛ ♦ ✈ért✐❝❡ ❞❡ ♦r✐❣❡♠✳ • D+
i ✿ é ♦ ❣r❛✉ ❞❡ ❡♥tr❛❞❛ ❞♦ ✈ért✐❝❡ ✐✱ q✉❡ é ❛ s♦♠❛ ❞❛s ❛r❡st❛s ❧✐❣❛❞❛s ❛♦ ✈ért✐❝❡
♠❛✐s ♦s ❛r❝♦s q✉❡ ❝❤❡❣❛♠ ❛ ❡st❡ ✈ért✐❝❡ ✭ Ei S A+ i ✮✳
• D−i ✿ é ♦ ❣r❛✉ ❞❡ s❛í❞❛ ❞♦ ✈ért✐❝❡ ✐✱ q✉❡ é ❛ s♦♠❛ ❞❛s ❛r❡st❛s ❧✐❣❛❞❛s ❛♦ ✈ért✐❝❡
♠❛✐s ♦s ❛r❝♦s q✉❡ s❛❡♠ ❞❡st❡ ✈ért✐❝❡ ✭ Ei
S
A−i
✮✳ • Di ✿ é ♦ ❣r❛✉ ❞♦ ✈ért✐❝❡ ✐ ✭
Ei S A+ i S
A−i
✮✳
• δij ✿ é ♦ ❝✉st♦✱ ♦✉ ❞✐stâ♥❝✐❛✱ ♣❛r❛ ♣❡r❝♦rr❡r ❛ ❧✐❣❛çã♦ ❡♥tr❡ ♦s ✈ért✐❝❡s ✐ ❡ ❥✳ ❙❡
❡st❛ ❧✐❣❛çã♦ ♥ã♦ ❡①✐st✐r✱ s❡✉ ✈❛❧♦r é ∞✳
✶✳✸✳✶ ❈♦♥t❡①t♦ t❡ór✐❝♦
✶✳✸✳✶✳✶ ❚❡♦r❡♠❛ ❞❡ ❊✉❧❡r
❖ t❡♦r❡♠❛ ❞❡ ❊✉❧❡r ❞✐③ q✉❡ ✉♠ ❣r❛❢♦ ❝♦♥❡①♦ ❡ ♥ã♦✲❞✐r❡❝✐♦♥❛❞♦ ● ❂ ✭❱✱❊✮ ❝♦♥té♠ ✉♠ ❝✐r❝✉✐t♦ ❊✉❧❡r✐❛♥♦ s❡ ❡ s♦♠❡♥t❡ s❡ Di é ♣❛r ♣❛r❛ t♦❞♦s ♦s ✈ért✐❝❡s i ∈ V✳ ❊❞♠♦♥❞s
❡ ❏♦❤♥s♦♥ ❬❊❞♠♦♥❞s ✫ ❏♦♥❤s♦♥✱ ✶✾✼✸❪ ♠♦str❛r❛♠ q✉❡ é ♣♦ssí✈❡❧ ❝♦♥✈❡rt❡r ✉♠ ❣r❛❢♦ ● ❡♠ ❡✉❧❡r✐❛♥♦ tr❛♥s❢♦r♠❛♥❞♦ t♦❞♦s ♦s ✈ért✐❝❡s ❞❡ ❣r❛✉ í♠♣❛r ❡♠ ✈ért✐❝❡s ❞❡ ❣r❛✉ ♣❛r r❡♣❡t✐♥❞♦ ❛❧❣✉♠❛s ❛r❡st❛s ❞❡ ❊ ❝♦♠ ❝✉st♦ ♠í♥✐♠♦ ❡♠ t❡♠♣♦ ♣♦❧✐♥♦♠✐❛❧✳ ❈♦♠ ❡ss❡ ♥♦✈♦ ❣r❛❢♦ s❡♥❞♦ ❡✉❧❡r✐❛♥♦✱ é ♣♦ssí✈❡❧ ❡♥❝♦♥tr❛r t❛♠❜é♠ ❡♠ t❡♠♣♦ ♣♦❧✐♥♦♠✐❛❧ ♦ ❝✐r❝✉✐t♦ ❡✉❧❡r✐❛♥♦ r❡❧❛❝✐♦♥❛❞♦ ❛ ❡st❡ ❣r❛❢♦✳ ❊♠ ❢✉♥çã♦ ❞✐ss♦✱ ♦ ♣r♦❜❧❡♠❛ ❞♦ ❝❛rt❡✐r♦ ❝❤✐♥ês ❝❧áss✐❝♦ é ♣♦❧✐♥♦♠✐❛❧✳
✶✳✸✳✶✳✷ ❚❡♦r❡♠❛ ❞❡ ❊❞♠♦♥❞s ❡ ❏♦❤♥s♦♥ ❬❊❞♠♦♥❞s ✫ ❏♦♥❤s♦♥✱ ✶✾✼✸❪
❯♠ ❣r❛❢♦ ❞✐r❡❝✐♦♥❛❞♦ ❢♦rt❡♠❡♥t❡ ❝♦♥❡①♦ ● ❂ ✭❱✱❆✮ ❝♦♥té♠ ✉♠ ❝✐r❝✉✐t♦ ❡✉❧❡r✐❛♥♦✱ s❡ ❡ s♦♠❡♥t❡ s❡✱ ♣❛r❛ t♦❞♦s ♦s ✈ért✐❝❡s i ∈ V✱ D+
i = Di−✳ ❖✉ s❡❥❛✱ s❡ ♦ ❣r❛✉ ❞❡ ❡♥tr❛❞❛
✶✳✸✳ ❉❡❢✐♥✐çã♦ ❞♦ ♣r♦❜❧❡♠❛ ✺
❯♠ ❣r❛❢♦ ❞✐r❡❝✐♦♥❛❞♦ é ❢♦rt❡♠❡♥t❡ ❝♦♥❡①♦ s❡ ❡①✐st❡ ✉♠ ❝❛♠✐♥❤♦ ❞✐r❡❝✐♦♥❛❞♦ ❞♦ ✈ért✐❝❡ ✐ ❛té q✉❛❧q✉❡r ♦✉tr♦ ✈ért✐❝❡ ♣❡rt❡♥❝❡♥t❡ ❛ ❱✳ ❊❞♠♦♥❞s ❡ ❏♦❤♥s♦♥ ❬❊❞♠♦♥❞s ✫ ❏♦♥❤s♦♥✱ ✶✾✼✸❪ t❛♠❜é♠ ❛♣r❡s❡♥t❛r❛♠ ✉♠ ❛❧❣♦r✐t♠♦ ♣♦❧✐♥♦♠✐❛❧ q✉❡ ❡q✉✐❧✐❜r❛ t♦❞♦s ♦s ✈ért✐❝❡s ❛❞✐❝✐♦♥❛♥❞♦ ❛❧❣✉♥s ❛r❝♦s ❛ ● ❝♦♠ ❝✉st♦ ♠í♥✐♠♦✱ ❣❡r❛♥❞♦ ✉♠ ♥♦✈♦ ❣r❛❢♦ ❡✉❧❡r✐❛♥♦✳ ❈♦♠♦ ❡♥❝♦♥tr❛r ♦ ❝✐r❝✉✐t♦ ❡✉❧❡r✐❛♥♦ ❞❡st❡ ❣r❛❢♦ é ✉♠ ♣r♦❜❧❡♠❛ ♣♦❧✐♥♦♠✐❛❧✱ ♦ ♣r♦❜❧❡♠❛ ❞♦ ❝❛rt❡✐r♦ ❝❤✐♥ês ❞✐r❡❝✐♦♥❛❞♦ t❡♠ s♦❧✉çã♦ ♣♦❧✐♥♦♠✐❛❧✳
✶✳✸✳✶✳✸ ❚❡♦r❡♠❛ ❞❡ ❋♦r❞ ❡ ❋✉❧❦❡rs♦♥ ❬❋♦r❞ ✫ ❋✉❧❦❡rs♦♥✱ ✶✾✻✷❪
❋♦r❞ ❡ ❋✉❧❦❡rs♦♥ ♣r♦✈❛r❛♠ q✉❡ ✉♠ ❣r❛❢♦ ● ❂ ✭❱✱❊✱❆✮ ♠✐st♦ ❡ ❢♦rt❡♠❡♥t❡ ❝♦♥❡①♦ ❝♦♥té♠ ✉♠ ❝✐r❝✉✐t♦ ❡✉❧❡r✐❛♥♦ s❡ ❡ s♦♠❡♥t❡ s❡✱ s❛t✐s❢❛③ ❞✉❛s ❝♦♥❞✐çõ❡s✿
• P❛r❛ t♦❞♦ ✈ért✐❝❡ i∈V✱ Di é ♣❛r✳
• P❛r❛ t♦❞♦ s✉❜❝♦♥❥✉♥t♦ ❞❡ ✈ért✐❝❡s ❙ ⊆ ❱✱ ❛ ❞✐❢❡r❡♥ç❛ ❡♥tr❡ ♦ ♥ú♠❡r♦ ❞❡ ❛r❝♦s
♦r✐❣✐♥ár✐♦s ❡♠ ❙ ❡ ❝♦♠ ❞❡st✐♥♦ ❡♠ ✈ért✐❝❡s ❞❡ ❱✴❙ ❡ ♦ ♥ú♠❡r♦ ❞❡ ❛r❝♦s ♦r✐❣✐♥ár✐♦s ❡♠ ❱✴❙ ❝♦♠ ❞❡st✐♥♦ ❡♠ ✈ért✐❝❡s ❞❡ ❙ é ♠❡♥♦r ♦✉ ✐❣✉❛❧ ❛♦ ♥ú♠❡r♦ ❞❡ ❛r❡st❛s ✉♥✐♥❞♦ ✈ért✐❝❡s ❡♠ ❙ ❡ ❱✴❙
❈❛♣ít✉❧♦ ✷
❘❡✈✐sã♦ ❜✐❜❧✐♦❣rá✜❝❛
◆❡st❡ ❝❛♣ít✉❧♦✱ s❡rá r❡✈✐st❛ ❜♦❛ ♣❛rt❡ ❞❛ ❧✐t❡r❛t✉r❛ s♦❜r❡ ♦ Pr♦❜❧❡♠❛ ❞♦ ❈❛rt❡✐r♦ ❈❤✐♥ês✱ t❛♥t♦ ♥❛ ❢♦r♠❛ ❞❡ ❧✐✈r♦s q✉❛♥t♦ ❡♠ ❛rt✐❣♦s q✉❡ ❡①♣❧♦r❛♠ s❡✉s ❞✐✈❡rs♦s ❛s♣❡❝t♦s ❡ ✈❛r✐❛çõ❡s✳ ❊♠ ♣❛rt✐❝✉❧❛r✱ ♦ ♣r♦❜❧❡♠❛ ❞♦ ❈❛rt❡✐r♦ ❈❤✐♥ês ▼✐st♦ ✭▼❈PP✮✱ ♣♦r s✉❛ ❝♦♠♣❧❡①✐❞❛❞❡✱ ♣♦ss✉✐ ❡①t❡♥s❛ ❜✐❜❧✐♦❣r❛✜❛✱ q✉❡ s❡rá r❡✈✐st❛ ❡♠ s❡✉s ♣♦♥t♦s ♠❛✐s ✐♠♣♦rt❛♥t❡s✳
❖ ❛rt✐❣♦ ❞❡ ▼❡✐❣✉ ●✉❛♥ ❬▼❡✐❣✉✱ ✶✾✻✷❪✱ ♠❛r❝❛ ❛ ✐♥tr♦❞✉çã♦ ❞♦ Pr♦❜❧❡♠❛ ❞♦ ❈❛rt❡✐r♦ ❈❤✐♥ês ♥❛ ❧✐t❡r❛t✉r❛ ❞❡ Pr♦❣r❛♠❛çã♦ ▼❛t❡♠át✐❝❛✳ ❊st❡ ❛rt✐❣♦ ❞❡✜♥❡ ♦ ♣r♦❜❧❡♠❛ ❡ ♣r♦♣õ❡ ✉♠ ♣r✐♠❡✐r♦ ♠♦❞❡❧♦ ❜❛s❡❛❞♦ ❡♠ r❡str✐çõ❡s ♣❛r❛ ♦ ❈PP✳ ❆s r❡str✐çõ❡s ♣r♦♣♦st❛s ♥♦ ♠♦❞❡❧♦ ❡st❛✈❛♠ r❡❧❛❝✐♦♥❛❞❛s á ♣r♦✐❜✐çã♦ ❞❡ ✉♠❛ ❞❡t❡r♠✐♥❛❞❛ ♦r✐❡♥t❛çã♦ ❡♠ ❛❧❣✉♠❛s ❛r❡st❛s✱ ❛ss✐♠ ❝♦♠♦ ❛ ♦❜r✐❣❛t♦r✐❡❞❛❞❡ ❞❡ ✉♠ ❞❡t❡r♠✐♥❛❞❛ ❞✐r❡çã♦ ❡♠ ♦✉tr❛s✱ ❝♦♥❢♦r♠❡ ✉♠ ♠♦❞❡❧♦ ❞❡ ❡s❝♦❧❤❛s ❜❛s❡❛❞❛s ♥♦ ❣r❛✉ ❞❡ ❝❛❞❛ ✈ért✐❝❡✳ ❆ ❝♦♥tr✐❜✉✐çã♦ s❡❣✉✐♥t❡ ✈❡✐♦ ❡♠ ✶✾✼✸ ❛tr❛✈és ❞♦ ❛rt✐❣♦ ❞❡ ❊❞♠♦♥❞s ❡ ❏♦❤♥s♦♥ ❬❊❞♠♦♥❞s ✫ ❏♦♥❤s♦♥✱ ✶✾✼✸❪✳ ❆q✉✐✱ ♦s ❛✉t♦r❡s ❢❛③❡♠ ❛s ♣r✐♠❡✐r❛s r❡❧❛çõ❡s ❡♥tr❡ ♠♦❞❡❧♦s ✉t✐❧✐③❛❞♦s ♥❛ ❣❡r❛çã♦ ❞❡ ♣❛ss❡✐♦s ❡✉❧❡r✐❛♥♦s ❡ ❈PP✱ ❛❧é♠ ❞❛ ❞❡✜♥✐çã♦ ❞♦ ♣♦❧✐❡❞r♦ ❞❡ s♦❧✉çõ❡s ✈✐á✈❡✐s ♣❛r❛ ❡st❛ ❝❧❛ss❡ ❞❡ ♣r♦❜❧❡♠❛s✳ ❊st❛❜❡❧❡❝❡♠ t❛♠❜é♠ ❝❡rt❛s ❞❡✜♥✐çõ❡s s♦❜r❡ ❣r❛❢♦s ❞✐r❡❝✐♦♥❛❞♦s✱ ♥ã♦✲❞✐r❡❝✐♦♥❛❞❛s ❡ ♠✐st♦s ❡ ❝♦♠♦ ❡st❡s ❛❢❡t❛♠ ❛ s♦❧✉çã♦ ❞♦ ♣r♦❜❧❡♠❛✳ ➱ s✉❣❡r✐❞♦ ♦ ✉s♦ ❞♦s ♠♦❞❡❧♦s ❡ ❛❧❣♦r✐t♠♦s ❞❡ ♣❛ss❡✐♦s ❡✉❧❡r✐❛♥♦s ♣❛r❛ r❡s♦❧✉çã♦ ❞♦ ❈PP✳
✷✳✶ ❱❛r✐❛çõ❡s ❞♦ ♣r♦❜❧❡♠❛
❊♠ ✶✾✽✼✱ ❇❡♥❛✈❡♥t ❡t ❛❧✳ ❬❇❡♥❛✈❡♥t ❡t ❛❧✳✱ ✶✾✽✼❪ ❢❛③❡♠ ♦ ♣r✐♠❡✐r♦ ✉s♦ ❞❡ ❤❡✉ríst✐❝❛s ♣❛r❛ r❡s♦❧✉çã♦ ❞❡ ❈PP✱ ♥❛ ✈❡rsã♦ ♦♥❞❡ ♦ ❛❣❡♥t❡ ♣♦ss✉✐ ❝❡rt❛ ❝❛♣❛❝✐❞❛❞❡ ❞❡ tr❛♥s♣♦rt❡
✽ ❈❛♣ít✉❧♦ ✷✳ ❘❡✈✐sã♦ ❜✐❜❧✐♦❣rá❢✐❝❛
❡ ❞❡✈❡ r❡t♦r♥❛r ❛♦ ❞❡♣ós✐t♦ ❡♠ ❜✉s❝❛ ❞❡ ♥♦✈♦ ♠❛t❡r✐❛❧ ❞❡ ❞✐str✐❜✉✐çã♦✳
❆ ♣r✐♠❡✐r❛ ♠❡♥çã♦ ❛♦ ❈PP ❝♦♠ ♦r❞❡♥❛çã♦ ❞❛s ❛r❡st❛s é ❢❡✐t❛ ❡♠ ❬❉❡sr♦❝❤❡rs ❡t ❛❧✳✱ ✶✾✾✶❪✳ ❊st❡ ❛rt✐❣♦ ♣r♦♣õ❡ ✉♠ ♠♦❞❡❧♦ ♦♥❞❡ ❝❡rt❛s ❛r❡st❛s ❞❡✈❡♠ s❡r ✈✐s✐t❛❞❛s ❛♥t❡s ❞❛s ♦✉tr❛s✱ ♣♦r ✉♠❛ r❡❧❛çã♦ ❞❡ ♣r❡❝❡❞ê♥❝✐❛✳ P♦❞❡♠♦s ♣❡♥s❛r ❡♠ r❡❧❛çõ❡s ❞❡ ♣r❡❝❡❞ê♥❝✐❛ ❝♦♠♦ ✉♠ ♣r✐♠❡✐r❛ t❡♥t❛t✐✈❛ ❞❡ ♣r♦❞✉çã♦ ❞❡ ❥❛♥❡❧❛s ❞❡ t❡♠♣♦✳
❯♠ ❞♦s tr❛❜❛❧❤♦s ♠❛✐s ✐♠♣♦rt❛♥t❡s ❞❡st❛ ❝❧❛ss❡ ❞❡ ♣r♦❜❧❡♠❛s ✈❡♠ ❞❡ ▼❛❧❛♥✲ ❞r❛❦✐ ❡ ❉❛s❦✐♥ ❬▼❛❧❛♥❞r❛❦✐ ✫ ❉❛s❦✐♥✱ ✶✾✾✸❪✱ ❡♠ ✶✾✾✸✱ ♦♥❞❡ é ♣r♦♣♦st♦ ♦ ▼❛①✐♠✉♠ ❜❡♥❡✜t ❈❤✐♥❡s❡ P♦st♠❛♥ Pr♦❜❧❡♠✳ ◆♦ ❈PP ❝❧áss✐❝♦✱ ♦ ♦❜❥❡t✐✈♦ ❞♦ ♣r♦❜❧❡♠❛ ❡r❛ ❛ ♠✐♥✐♠✐③❛çã♦ ❞❡ ❝✉st♦s ♣❛r❛ ♦ ♣❛ss❡✐♦✳ ◆❡st❡ ❛rt✐❣♦✱ ❛ r❡str✐çã♦ ❞❡ q✉❡ t♦❞❛s ❛s ❛r❡st❛s ❞❡✈❡♠ s❡r ♣❡r❝♦rr✐❞❛s é r❡❧❛①❛❞❛ ❡ ❝❛❞❛ ❛r❡st❛ ♣♦ss✉✐ ✉♠ ❝✉st♦ ❡ ✉♠ ❧✉❝r♦ ❛♦ ❛tr❛✈❡ssá✲❧❛ ❡ ✉♠❛ ♣❡♥❛❧✐❞❛❞❡ s❡ ❛ ❛r❡st❛ ♥ã♦ ❢♦r ❛tr❛✈❡ss❛❞❛ ♥♦ ♣❛ss❡✐♦ ✜♥❛❧✳ ❊ss❡ ♣r♦❜❧❡♠❛ é ❢♦r♠✉❧❛❞♦ ❝♦♠♦ ✉♠ ♣r♦❜❧❡♠❛ ❞❡ Pr♦❣r❛♠❛çã♦ ▲✐♥❡❛r ■♥t❡✐r❛✳
✷✳✷ ❈❛rt❡✐r♦ ❈❤✐♥ês ▼✐st♦
❊♠ ❬P❛♣❛❞✐♠✐tr✐♦✉✱ ✶✾✼✻❪✱ ❞❡♠♦♥str♦✉✲s❡ q✉❡ ♦ ▼❈PP é ◆P✲❈♦♠♣❧❡t♦✳ ❆❧❣✉♥s ❛♥♦s ❞❡♣♦✐s✱ ❋r❡❞❡r✐❝❦s♦♥ ❬❋r❡❞❡r✐❝❦s♦♥ ❡t ❛❧✳✱ ✶✾✼✻❪ s✉❣❡r✐✉ ✉♠ ❛❧❣♦r✐t♠♦ ❛♣r♦①✐♠❛t✐✈♦ ♣❛r❛ ♦ ▼❈PP✱ ❝♦♠ ♦ ♥♦♠❡ ❞❡ ▼✐st♦✱ ❡♠ ❣r❛❢♦s ❣❡♥ér✐❝♦s q✉❡ ❛♠♣❧✐❛ ❛s té❝♥✐❝❛s ✉s❛❞❛s ♣❛r❛ ❣r❛❢♦s ♣❛r❡s ✭❝♦♠ t♦❞♦s ♦s ✈ért✐❝❡s ❞❡ ❣r❛✉ ♣❛r✮✳ ❋r❡❞❡r✐❝❦s♦♥ t❛♠❜é♠ ♠♦str♦✉ q✉❡ ♦s ❛❧❣♦r✐t♠♦s ✉s❛❞♦s ❛té ❛❧✐ t❡♠ ✉♠ ♣✐♦r ❝❛s♦ ❞❡ ✷ ✈❡③❡s ❛ s♦❧✉çã♦ ót✐♠❛✳ ❊♥✲ tr❡t❛♥t♦✱ ❛♣❧✐❝❛♥❞♦ ❛s ❤❡✉ríst✐❝❛s ❡ s❡❧❡❝✐♦♥❛♥❞♦ ❛ ♠❡❧❤♦r s♦❧✉çã♦✱ ♦ ♣✐♦r ❝❛s♦ ✈❛✐ ❛ ✺✴✸✳
✷✳✷✳ ❈❛rt❡✐r♦ ❈❤✐♥ês ▼✐st♦ ✾
❜❡♠ ❞❡t❛❧❤❛❞❛ ❞❡ss❡ ♣r♦❝❡❞✐♠❡♥t♦ ♣♦❞❡ s❡r ❡♥❝♦♥tr❛❞❛ ❡♠ ❬◆❡❣r❡✐r♦s ❡t ❛❧✳✱ ✷✵✵✾❪✳ ❊♠ ✶✾✾✾✱ ❘❛❣❤❛✈❛❝❤❛r✐ ❡ ❱❡❡r❛s❛♠② ❬❘❛❣❤❛✈❛❝❤❛r✐ ✫ ❱❡❡r❛s❛♠②✱ ✶✾✾✾❪ ♣r♦✲ ♣✉s❡r❛♠ ✉♠❛ ♠♦❞✐✜❝❛çã♦ ❞♦ ❛❧❣♦r✐t♠♦ ❞❡ ❋r❡❞❡r✐❝❦s♦♥ ❬❋r❡❞❡r✐❝❦s♦♥ ❡t ❛❧✳✱ ✶✾✼✻❪ ❝♦♠ ✉♠ ♣✐♦r ❝❛s♦ ❞❡ ✸✴✷✳ ▼❛✐s ❛✐♥❞❛✱ ❛❧é♠ ❞❡ s❡✉ ❜♦♠ ❞❡s❡♠♣❡♥❤♦ t❡ór✐❝♦✱ ♦ ❆❧❣♦r✐t♠♦ ▼✐st♦ ▼♦❞✐✜❝❛❞♦ ♣r♦♣♦st♦ é t❛♠❜é♠ ❝♦♠♣❡t✐t✐✈♦ ♥❛ ♣rát✐❝❛✱ ❡s♣❡❝✐❛❧♠❡♥t❡ ❡♠ ❣r❛❢♦s ❝♦♠ ♠é❞✐❛ ❛ ❛❧t❛ ♣♦r❝❡♥t❛❣❡♠ ❞❡ ❛r❝♦s✱ ❝♦♠♦ ❞❡♠♦♥str❛❞♦ ❡♠ ❈♦r❜❡rá♥ ❡t ❛❧ ❬❈♦r✲ ❜❡rá♥ ❡t ❛❧✳✱ ✷✵✵✷❜❪✱ ♥♦ q✉❛❧ ✉♠❛ ❤❡✉ríst✐❝❛ ●❘❆❙P ♣❛r❛ ♦ ▼❈PP t❛♠❜é♠ é ♣r♦♣♦st❛✳ P❡❛r♥ ❡ ▲✐✉ ❬P❡❛r♥ ✫ ▲✐✉✱ ✶✾✾✺❪ ♣r♦♣✉s❡r❛♠ ✉♠❛ ❤❡✉ríst✐❝❛ ❜❛s❡❛❞❛ ♥♦ ♣r♦❝❡❞✲ ✐♠❡♥t♦ ♣r♦♣♦st♦ ♣♦r ❊❞♠♦♥❞s ❡ ❏♦❤♥s♦♥✱ ❝♦♠ ❡①❝❡❧❡♥t❡s r❡s✉❧t❛❞♦s ❝♦♠♣✉t❛❝✐♦♥❛✐s ❡♠ r❡❧❛çã♦ ❛♦ t❡♠♣♦✳ P❡❛r♥ ❡ ❈❤♦✉ ❬P❡❛r♥ ✫ ❈❤♦✉✱ ✶✾✾✾❪ ❡✈♦❧✉ír❛♠ ♦ ❛rt✐❣♦ ❛♥t❡r✐♦r✱ ❝♦♠ ❛❧t❡r❛çõ❡s ♥❛s ❤❡✉ríst✐❝❛s ♣r♦♣♦st❛s q✉❡ ♠❡❧❤♦r❛r❛♠ ❛s ✐♠♣❧❡♠❡♥t❛çõ❡s✱ ❣❛♥❤❛♥❞♦ ❞❡s❡♠♣❡♥❤♦✳ ❊♠ ❬▲❛♣♦rt❡✱ ✶✾✾✼❪✱ ❛s tr❛♥s❢♦r♠❛çõ❡s ♣r♦♣♦st❛s ♣♦r ❬❉r♦r✱ ✷✵✵✵❪ sã♦ ✉t✐❧✐③❛❞❛s✱ ❝♦♥✈❡rt❡♥❞♦ ♣r♦❜❧❡♠❛s ❞❡ r♦t❡❛♠❡♥t♦ ❡♠ ❛r❝♦s ❡♠ ♣r♦❜❧❡♠❛s ❞❡ r♦t❡❛♠❡♥t♦s ❡♠ ✈ért✐❝❡s ❡q✉✐✈❛❧❡♥t❡s✱ ❝♦♠♦ ♦ Pr♦❜❧❡♠❛ ❞♦ ❈❛✐①❡✐r♦ ❱✐❛❥❛♥t❡✳
❆♥❣❡❧ ❈♦r❜❡rá♥ ❡ s❡✉s ❛❧✉♥♦s ✜③❡r❛♠ ♠✉✐t❛s ❝♦♥tr✐❜✉✐çõ❡s r❡❧❡✈❛♥t❡s ❛♦ ▼❈PP✱ ❝♦♠♣❛r❛♥❞♦ ❞✐❢❡r❡♥t❡s ❢♦r♠✉❧❛çõ❡s ♠❛t❡♠át✐❝❛s ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❬❈♦r❜❡rá♥ ❡t ❛❧✳✱ ✷✵✵✻❪ ❡ ❡st✉❞❛♥❞♦ ❛ ✈❡rsã♦ r✉r❛❧ ❞♦ ♣r♦❜❧❡♠❛ ❬❈♦r❜❡rá♥ ❡t ❛❧✳✱ ✷✵✵✷❛❪✱ ❡♥tr❡ ♦✉tr❛s ❝♦♥tr✐❜✉✐çõ❡s ✐♠♣♦rt❛♥t❡s✳ ❈♦r❜❡rá♥ t❛♠❜é♠ ❣❡r♦✉ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ✐♥stâ♥❝✐❛s ❞❡ t❡st❡ ❡♠ ❬❈♦r❜❡rá♥ ❡t ❛❧✳✱ ✷✵✵✼❪✱ ✉t✐❧✐③❛❞❛s ❡♠ ✈ár✐♦s ❛rt✐❣♦s ♣♦st❡r✐♦r❡s✱ ❛ss✐♠ ❝♦♠♦ ♥❡st❡ tr❛❜❛❧❤♦✳
❖ ❛❧❣♦r✐t♠♦ ❞❡ ❇r❛♥❝❤✲❛♥❞✲❈✉t ♣r♦♣♦st♦ ❡♠ ❬❈♦r❜❡rá♥ ❡t ❛❧✳✱ ✷✵✵✼❪ é ❝❛♣❛③ ❞❡ r❡s♦❧✈❡r ✐♥stâ♥❝✐❛s ❞❡ ▼❈PP✳ ✶✼ ❞❡ ✷✹ ✐♥stâ♥❝✐❛s ❝♦♠ ✸✵✵✵ ✈ért✐❝❡s ❡ ♠❛✐s ❞❡ ✾✵✵✵ ❧✐❣❛çõ❡s ❢♦r❛♠ r❡s♦❧✈✐❞❛s ❛té ❛ ♦t✐♠❛❧✐❞❛❞❡ s❡♠ ♦ ✉s♦ ❞❡ ❤❡✉ríst✐❝❛s q✉❡ ♣r♦❞✉③❛♠ ✉♣♣❡r ❜♦✉♥❞s ✐♥✐❝✐❛✐s✳
✶✵ ❈❛♣ít✉❧♦ ✷✳ ❘❡✈✐sã♦ ❜✐❜❧✐♦❣rá❢✐❝❛
❖s ❛rt✐❣♦s ❞❡ ❬❇❡♥❛✈❡♥t ❡t ❛❧✳✱ ✶✾✾✷❪ ❡ ❬❇♦❞✐♥ ❡t ❛❧✳✱ ✶✾✽✸❪ ✐❧✉str❛♠ ❛ q✉❛♥t✐❞❛❞❡ ❞❡ ❝♦♥❤❡❝✐♠❡♥t♦ ❝♦♥str✉í❞❛ ♥❛ ❛ré❛ ❞❡ r♦t❡❛♠❡♥t♦ ❡♠ ❛r❝♦s ♥♦s ú❧t✐♠♦s ✷✼ ❛♥♦s✳ ❬◆❡❣r❡✐r♦s ❡t ❛❧✳✱ ✷✵✵✾❪ é ❛ ❝♦♠♣✐❧❛çã♦ ♠❛✐s r❡❝❡♥t❡ s♦❜r❡ ♦ ❛ss✉♥t♦✱ ❢♦❝❛♥❞♦ ♥❛s ✈❡rsõ❡s ❞✐r❡❝✐♦♥❛❞❛✱ ♥ã♦ ❞✐r❡❝✐♦♥❛❞❛ ❡ ♠✐st❛ ❞♦ ❈PP✱ ❛♣r❡s❡♥t❛♥❞♦ ♦ s♦❢t✇❛r❡ ❳◆✃❙✱ q✉❡ ✐♥❝❧✉✐ ✉♠ ❣❡r❛❞♦r ❞❡ ❣r❛❢♦s ♣❛r❛ ❛s ✈❡rsõ❡s ❝✐t❛❞❛s✱ ♦ ❛❧❣♦r✐t♠♦ ❞❡ ❬❙❤❡r❛❢❛t✱ ✶✾✽✽❪✱ ❡ ✉♠ ❛❧❣♦r✐t♠♦ ●❘❆❙P ❝❤❛♠❛❞♦ ❈♦♠❜✐♥❛❞♦✫❍í❜r✐❞♦✳
❈❛♣ít✉❧♦ ✸
❆ ❤❡✉ríst✐❝❛ ♣r♦♣♦st❛
◆❡st❡ ❝❛♣ít✉❧♦✱ s❡rá ♣r♦♣♦st❛ ❛ ❤❡✉ríst✐❝❛ ✉s❛❞❛ ♣❛r❛ ❛ s♦❧✉çã♦ ❞♦ ♣r♦❜❧❡♠❛ ❞♦ ❝❛rt❡✐r♦ ❝❤✐♥ês ❡ ♦s ❢✉♥❞❛♠❡♥t♦s ❞❡st❛ ❤❡✉ríst✐❝❛✳ ❆ ❤❡✉ríst✐❝❛ ♣r♦♣♦st❛ s❡ ❜❛s❡✐❛ ♥❛ ♠❡t❛✲❤❡✉ríst✐❝❛ ❞❡ ❝♦❧ô♥✐❛s ❞❡ ❢♦r♠✐❣❛s✳ ❈♦♠♣✉t❛❝✐♦♥❛❧♠❡♥t❡✱ ❛ ♠❡t❛✲❤❡✉ríst✐❝❛ ❝r✐❛ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❡❧❡♠❡♥t♦s✱ ✉♠ ❜❛♥❝♦ ❞❡ ❝✐r❝✉✐t♦s✱ q✉❡ s❡rã♦ ✉s❛❞♦s ♥❛ ❝♦♥str✉çã♦ ❞❡ s♦❧✉çõ❡s s❡♠✐✲❛❧❡❛tór✐❛s✱ ♦✉ s❡❥❛✱ q✉❡ ♣♦ss✉❡♠ ✉♠ ❝❛rát❡r ❛❧❡❛tór✐♦ ❣✉✐❛❞♦ ♣♦r ✉♠ ♣❛râ♠❡tr♦ ❞❡ ❞✐str✐❜✉✐çã♦✱ ❡♠ ❜✉s❝❛ ❞❛ ♠❡❧❤♦r✐❛ ❞❛ s♦❧✉çã♦ ❝♦rr❡♥t❡ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛✳ ❊ss❛s s♦❧✉çõ❡s sã♦ ❛♥❛❧✐s❛❞❛s ❡ s✉❛ q✉❛❧✐❞❛❞❡ é ❧❡✈❛❞❛ ❡♠ ❝♦♥s✐❞❡r❛çã♦ ♥❛ ❣❡r❛çã♦ ❞❡ ♥♦✈❛s s♦❧✉çõ❡s✱ ❛tr❛✈és ❞❡ ♣❛râ♠❡tr♦s ♣r♦❜❛❜✐❧íst✐❝♦s✱ ❣❡r❛❞♦s ♣❡❧❛ q✉❛❧✐❞❛❞❡ ❞❛s s♦❧✉çõ❡s ❛♥t❡r✐♦r❡s✳ ❊ss❛s ❢❛s❡s s❡ r❡♣❡t❡♠ ❛té q✉❡ ✉♠ ❝r✐tér✐♦ ❞❡ ♣❛r❛❞❛ ✭❞❡ t❡♠♣♦ ♦✉ q✉❛❧✐❞❛❞❡ ❞❛ s♦❧✉çã♦✮ s❡❥❛ ❛t✐♥❣✐❞♦✳
P❛r❛ ♠❡❧❤♦r ❡♥t❡♥❞✐♠❡♥t♦✱ s❡rá ❢❡✐t❛ ✉♠❛ ❜r❡✈❡ ✐♥tr♦❞✉çã♦ ás ❤❡✉ríst✐❝❛s ❜❛s❡❛❞❛s ❡♠ ❝♦❧ô♥✐❛s ❞❡ ❢♦r♠✐❣❛s ❡ ❡♠ s❡❣✉✐❞❛✱ ❛ ❛♣❧✐❝❛çã♦ ❞❡st❛s ❛♦ ♣r♦❜❧❡♠❛ ❞♦ ❝❛rt❡✐r♦ ❝❤✐♥ês✳
✸✳✶ ❈♦❧ô♥✐❛s ❞❡ ❋♦r♠✐❣❛s
❖t✐♠✐③❛çã♦ ♣♦r ❝♦❧ô♥✐❛ ❞❡ ❢♦r♠✐❣❛s ✭❖❈❋ ♦✉ ❆❈❖✱ ❞♦ ✐♥❣❧ês ❆♥t ❈♦❧♦♥② ❖♣t✐♠✐③❛✲ t✐♦♥✮ é ✉♠❛ ♠❡t❛✲❤❡✉ríst✐❝❛ ❜❛s❡❛❞❛ ❡♠ ♣♦♣✉❧❛çã♦ q✉❡ ♣♦❞❡ s❡r ✉s❛❞❛ ♣❛r❛ ❡♥❝♦♥tr❛r s♦❧✉çõ❡s ❛♣r♦①✐♠❛❞❛s ♣❛r❛ ♣r♦❜❧❡♠❛s ❞✐❢í❝❡✐s ❞❡ ♦t✐♠✐③❛çã♦✳
❊♠ ❖❈❋✱ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❛❣❡♥t❡s ✭❢♦r♠✐❣❛s ❛rt✐✜❝✐❛✐s✮ ♣r♦❝✉r❛♠ ♣♦r s♦❧✉çõ❡s ♣❛r❛ ✉♠ ❝❡rt♦ ♣r♦❜❧❡♠❛ ❞❡ ♦t✐♠✐③❛çã♦✳ ❆s ❢♦r♠✐❣❛s ❛rt✐✜❝✐❛✐s ❝♦♥str♦❡♠ ❞❡ ❢♦r♠❛ ✐♥❝r❡♠❡♥t❛❧ s♦❧✉çõ❡s ❛tr❛✈és ❞❛ ❛❣r❡❣❛çã♦ ❞❡ ❡❧❡♠❡♥t♦s ♦✉ ❝♦♥❥✉♥t♦s ❞❡ ❡❧❡♠❡♥t♦s ❞♦ ❣r❛❢♦✳ ❖ ♣r♦❝❡ss♦ ❞❡ ❝♦♥str✉çã♦ ❞❛s s♦❧✉çõ❡s é ❡st♦❝ást✐❝♦ ❡ ❣✉✐❛❞♦ ♣❡❧♦ ♠♦❞❡❧♦ ❞❡
✶✷ ❈❛♣ít✉❧♦ ✸✳ ❆ ❤❡✉ríst✐❝❛ ♣r♦♣♦st❛
❢❡r♦♠ô♥✐♦s✱ q✉❡ é ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ✈❛❧♦r❡s ❛ss♦❝✐❛❞♦s ❝♦♠ ❛s ❝♦♠♣♦♥❡♥t❡s ❞♦ ❣r❛❢♦✱ s❡❥❛♠ ✈ért✐❝❡s ♦✉ ❛r❡st❛s✱ ❡ q✉❡ s♦❢r❡♠ ❛❧t❡r❛çã♦ ❞✉r❛♥t❡ ♦ tr❛❜❛❧❤♦ ❞❛s ❢♦r♠✐❣❛s ❛rt✐✜❝✐❛✐s✳
✸✳✶✳✶ ❯♠ ❡①❡♠♣❧♦ ✲ ❖ ♣r♦❜❧❡♠❛ ❞♦ ❝❛✐①❡✐r♦ ✈✐❛❥❛♥t❡ ✭P❈❱✮
❆ ❢♦r♠❛ ♠❛✐s ❢á❝✐❧ ❞❡ s❡ ❡♥t❡♥❞❡r ❝♦♠♦ ✉♠❛ ❖❈❋ ❢✉♥❝✐♦♥❛ é ❛tr❛✈és ❞❡ ✉♠ ❡①❡♠♣❧♦✱ ✉t✐❧✐③❛❞♦ ❡♠ ❬❉♦r✐❣♦✱ ✶✾✾✷❪✱ ❛ t❡s❡ ❞❡ ❞♦✉t♦r❛❞♦ ❞❡ ▼❛r❝♦ ❉♦r✐❣♦ q✉❡ ♣r♦♣ôs ✐♥✐❝✐❛❧♠❡♥t❡ ❡st❛ ♠❡t❛✲❤❡✉ríst✐❝❛✳ ❈♦♥s✐❞❡r❡ ♦ ♣r♦❜❧❡♠❛ ❞♦ ❈❛✐①❡✐r♦ ❱✐❛❥❛♥t❡✳ ◆♦ P❈❱✱ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❝✐❞❛❞❡s ❡ ❞✐stâ♥❝✐❛s ❡♥tr❡ ❡st❛s sã♦ ❞❛❞♦s✳ ❖ ♣r♦❜❧❡♠❛ ❝♦♥s✐st❡ ❡♠ ❛❝❤❛r ✉♠ ❝✐r❝✉✐t♦ ❞❡ ❝✉st♦ ♠í♥✐♠♦ q✉❡ ✈✐s✐t❡ ❝❛❞❛ ❝✐❞❛❞❡ ❛♣❡♥❛s ✉♠❛ ✈❡③✳
P❛r❛ q✉❡ s❡ ❛♣❧✐q✉❡ ❖❈❋ ♥♦ P❈❱✱ ❛ss♦❝✐❡ ♦s ✈ért✐❝❡s ❞❡ ✉♠ ❣r❛❢♦ ❝♦♠ ♦ ❝♦♥❥✉♥t♦ ❞❡ ❝✐❞❛❞❡s✳ ❊st❡ ❣r❛❢♦ é ❝❤❛♠❛❞♦ ●r❛❢♦ ❞❡ ❝♦♥str✉çã♦✳ ❈♦♥s✐❞❡r❡ t❛♠❜é♠ q✉❡ ❛s ❞✐stâ♥❝✐❛s ❡♥tr❡ ❛s ❝✐❞❛❞❡s ❡stã♦ r❡♣r❡s❡♥t❛❞❛s ♣♦r ❛r❡st❛s ❡ q✉❡ ❡st❛s ❛r❡st❛s t❡♠ ✈❛❧♦r❡s ❤❡✉ríst✐❝♦s ❡ ❢❡r♦♠ô♥✐❝♦s ❛ss♦❝✐❛❞♦s✳ ❖s ✈❛❧♦r❡s ❞❡ ❢❡rô♠♦♥✐♦s sã♦ ❛t✉❛❧✐③❛❞♦s ❡♠ t❡♠♣♦ ❞❡ ❡①❡❝✉çã♦ ❡ r❡♣r❡s❡♥t❛♠ ❛ ❡①♣❡r✐ê♥❝✐❛ ❛❝✉♠✉❧❛❞❛ ❞❛ ❝♦❧ô♥✐❛ ❞❡ ❢♦r♠✐❣❛s✱ ❡♥q✉❛♥t♦ ✈❛❧♦r❡s ❤❡✉ríst✐❝♦s sã♦ ❞❡♣❡♥❞❡♥t❡s ❞♦ ♣r♦❜❧❡♠❛ ❡ q✉❡ ♥♦ ❝❛s♦ ❞♦ P❈❱✱ sã♦ ✐♥✐❝✐❛❧✐③❛❞♦s ❝♦♠ ♦ ✈❛❧♦r ❞♦ ✐♥✈❡rs♦ ❞❛s ❞✐stâ♥❝✐❛s ✭1
δij✮✳
❆s ❢♦r♠✐❣❛s ❝♦♥str♦❡♠ ❛s s♦❧✉çõ❡s ❞❛ s❡❣✉✐♥t❡ ❢♦r♠❛✿ ❈❛❞❛ ❢♦r♠✐❣❛ ❝♦♠❡ç❛ ❡♠ ✉♠❛ ❝✐❞❛❞❡ ❛❧❡❛tór✐❛ ✭✉♠ ✈ért✐❝❡ ❞♦ ❣r❛❢♦ ❞❡ ❝♦♥str✉çã♦✮ ❡ ❛ ❝❛❞❛ ♣❛ss♦ ❞❛ ❝♦♥str✉çã♦✱ s❡ ♠♦✈❡ ♣❡❧❛s ❛r❡st❛s✳ ❈❛❞❛ ❢♦r♠✐❣❛ ♠❛♥té♠ ❛ ♠❡♠ór✐❛ ❞❡ s❡✉ ❝❛♠✐♥❤♦ ❡✱ ♥♦s ♣ró①✲ ✐♠♦s ♣❛ss♦s✱ ❡✈✐t❛ ❝✐❞❛❞❡s ❥á ✈✐s✐t❛❞❛s✳ ❯♠❛ ❢♦r♠✐❣❛ ❛❝❛❜♦✉ ❛ ❝♦♥str✉çã♦ ❞❡ ✉♠❛ s♦❧✉çã♦ ✉♠❛ ✈❡③ q✉❡ t❡♥❤❛ ✈✐s✐t❛❞♦ t♦❞♦s ♦s ✈ért✐❝❡s ❞♦ ❣r❛❢♦✳ ❆ ❝❛❞❛ ♣❛ss♦ ❞❛ ❝♦♥✲ str✉çã♦✱ ❛ ❢♦r♠✐❣❛ s♦rt❡✐❛✱ ❞❡♥tr♦ ❞❡ ✉♠❛ ❞✐str✐❜✉✐çã♦ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡s✱ ❛ ❛r❡st❛ ❛ s❡r s❡❣✉✐❞❛ ❞❡♥tr❡ ❛q✉❡❧❛s q✉❡ ❧❡✈❛♠ ❛ ✈ért✐❝❡s ♥ã♦✲✈✐s✐t❛❞♦s✳ ❆ ❞✐str✐❜✉✐çã♦ ♣r♦❜❛✲ ❜✐❧íst✐❝❛ é ❣✉✐❛❞❛ ♣❡❧♦s ✈❛❧♦r❡s ❢❡rô♠♦♥✐❝♦s ❡ ♣❡❧❛ ✐♥❢♦r♠❛çã♦ ❤❡✉ríst✐❝❛✿ ◗✉❛♥t♦ ♠❛✐s ❢❡rô♠♦♥✐♦ ❡ ♠❛✐♦r ♦ ✈❛❧♦r ❤❡✉ríst✐❝♦ ❛ss♦❝✐❛❞♦ á ❛r❡st❛ ✭ 1
Dij✮✱ ♠❛✐♦r ❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡
✸✳✶✳ ❈♦❧ô♥✐❛s ❞❡ ❋♦r♠✐❣❛s ✶✸
✸✳✶✳✷ ❆ ✐♥s♣✐r❛çã♦ ♥❛ ♥❛t✉r❡③❛
◆♦ ❡①♣❡r✐♠❡♥t♦ ❞❛ ♣♦♥t❡ ❞✉♣❧❛✱ ✉♠ ❢♦r♠✐❣✉❡✐r♦ é ❝♦♥❡❝t❛❞❛ ❛ ✉♠❛ ❢♦♥t❡ ❞❡ ❛❧✐♠❡♥t♦ ♣♦r ❞✉❛s ♣♦♥t❡s✳ ❆s ❢♦r♠✐❣❛s ♣♦❞❡♠ ❛t✐♥❣✐r ❛ ❝♦♠✐❞❛ ❡ tr❛③ê✲❧❛ ❛♦ ♥✐♥❤♦ ❛tr❛✈és ❞❛s ❞✉❛s ♣♦♥t❡s✳ ❖ ♦❜❥❡t✐✈♦ ❞♦ ❡①♣❡r✐♠❡♥t♦ é ♦❜s❡r✈❛r ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞❛ ❝♦❧ô♥✐❛✳ ❖❜s❡r✈❛✲s❡ q✉❡ s❡ ❛s ❞✉❛s ♣♦♥t❡s t❡♠ ♦ ♠❡s♠♦ t❛♠❛♥❤♦✒ ❛s ❢♦r♠✐❣❛s t❡♥❞❡♠ ❛ ❝♦♥✈❡r❣✐r ❛♦ ✉s♦ ❞❡ ❛♣❡♥❛s ✉♠❛✳ ❙❡ ♦ ❡①♣❡r✐♠❡♥t♦ é r❡♣❡t✐❞♦ ✉♠ ❝❡rt♦ ♥ú♠❡r♦ ❞❡ ✈❡③❡s✱ ♥♦t❛✲s❡ q✉❡ ❝❛❞❛ ♣♦♥t❡ é ✉s❛❞❛ ❡♠ ✺✵✪ ❞❛s ✈❡③❡s✳ ❊st❡s r❡s✉❧t❛❞♦s ❡①♣❧✐❝❛♠✲s❡ ♣❡❧♦ ❢❛t♦ ❞❡ q✉❡ ❛s ❢♦r♠✐❣❛s✱ ❛♦ s❡ ♠♦✈✐♠❡♥t❛r❡♠✱ ❞❡♣♦s✐t❛♠ ❢❡r♦♠ô♥✐♦s ♥♦ s♦❧♦✱ ❡ ✐♥❞❡♣❡♥❞❡♥t❡♠❡♥t❡ ❞♦ ❝❛♠✐♥❤♦ s❡❣✉✐❞♦✱ s✉❛ ❡s❝♦❧❤❛ é ❣✉✐❛❞❛ ♣❡❧♦s ❢❡rô♠♦♥✐♦s ❞❡✐①❛❞♦s ♣❡❧❛s ♦✉tr❛s ❢♦r♠✐❣❛s✿q✉❛♥t♦ ♠❛✐s ❢❡r♦♠ô♥✐♦ ❡♠ ✉♠ ❝❛♠✐♥❤♦ ❡♠ ♣❛rt✐❝✉❧❛r✱ ♠❛✐♦r ❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ q✉❡ ❛q✉❡❧❡ ❝❛♠✐♥❤♦ s❡❥❛ ❡s❝♦❧❤✐❞♦✳
❈♦♥s✐❞❡r❡ ♦ ❝❛s♦ ❡♠ q✉❡ ❛s ❞✉❛s ♣♦♥t❡s t❡♠ ♦ ♠❡s♠♦ t❛♠❛♥❤♦✳ ❆ ✜❣✉r❛ ✸✳✶ ♣♦❞❡ s❡r ✉s❛❞❛ ♣❛r❛ ✐❧✉str❛r ♦ ❡①♣❡r✐♠❡♥t♦✳
❋✐❣✉r❛ ✸✳✶✳ ❈❛♠✐♥❤♦s ❞❡ t❛♠❛♥❤♦s ✐❣✉❛✐s
✶✹ ❈❛♣ít✉❧♦ ✸✳ ❆ ❤❡✉ríst✐❝❛ ♣r♦♣♦st❛
❞❡ ❞❡❝✐sã♦ ✷ ✭❋✐❣✉r❛ ✷✮✱ ❡♥❝♦♥tr❛♠ ✉♠ ♥í✈❡❧ ♠❛✐s ❛❧t♦ ❞❡ ❢❡r♦♠ô♥✐♦s ♥❛ ♣♦♥t❡ ♠❛✐s ❝✉rt❛✱ q✉❡ ❡♥tã♦ é ❡s❝♦❧❤✐❞❛ ❝♦♠ ♠❛✐♦r ♣r♦❜❛❜✐❧✐❞❛❞❡ ❡ r❡❝❡❜❡ ♥♦✈❛♠❡♥t❡ ❢❡r♦♠ô♥✐♦ ❛❞✐❝✐♦♥❛❧✳ ❊st❡ ❢❛t♦ ❛✉♠❡♥t❛ ❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ q✉❡ ❛s ♣ró①✐♠❛s ❢♦r♠✐❣❛s ❡s❝♦❧❤❛♠ ❡st❡ ❝❛♠✐♥❤♦ ❡♠ ❞❡tr✐♠❡♥t♦ ❞♦ ♦✉tr♦✳
❊①✐st❡ ✉♠ ♠♦❞❡❧♦ ❞❡s❡♥✈♦❧✈✐❞♦ ♣♦r ❬●♦ss ❡t ❛❧✳✱ ✶✾✽✾❪ ♣❛r❛ ❡st❡ ❝♦♠♣♦rt❛♠❡♥t♦✳ ❆ss✉♠✐♥❞♦ q✉❡ ❡♠ ✉♠ ❞❛❞♦ ♠♦♠❡♥t♦✱fi ❢♦r♠✐❣❛s ♣❛ss❛r❛♠ ♣❡❧❛ ✐✲és✐♠❛ ♣♦♥t❡ ✱❛
♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ q✉❡ ✉♠❛ ❢♦r♠✐❣❛ ❡s❝♦❧❤❛ ❛ ♣♦♥t❡ ✐ é✿
pi =
mi+kh B
X
j=1
mj +kh
✭✸✳✶✮
♦♥❞❡ ❇ é ♦ ♥ú♠❡r♦ ❞❡ ♣♦♥t❡s ❡ ♦s ♣❛râ♠❡tr♦s ❦ ❡ ❤ sã♦ ♣ró♣r✐♦s ❞❡ ❝❛❞❛ ❡①♣❡r✲ ✐♠❡♥t♦✳ ❙✐♠✉❧❛çõ❡s ❞❡ ▼♦♥t❡ ❈❛r❧♦ ❡♥❝♦♥tr❛r❛♠ ❝♦♠♦ ✈❛❧♦r❡s ❛❞❡q✉❛❞♦s k ≈ 20 ❡
h≈2✳
❊st❛ ❡q✉❛çã♦ ✐♥s♣✐r♦✉ ❛ ❡q✉❛çã♦ ✉s❛❞❛ ♥♦ ♣r✐♠❡✐r♦ ❛❧❣♦r✐t♠♦ ❞❡ ❖❈❋ ✭❬❉♦r✐❣♦✱ ✶✾✾✷❪✮✳
❋✐❣✉r❛ ✸✳✷✳ ❈❛♠✐♥❤♦s ❞❡ t❛♠❛♥❤♦s ❞✐❢❡r❡♥t❡s
✸✳✷ ❋✉♥❞❛♠❡♥t❛çã♦ t❡ór✐❝❛ ❞❛ ❝♦❜❡rt✉r❛ ❞❡ ✉♠
❣r❛❢♦ ♣♦r ❝✐r❝✉✐t♦s
✸✳✷✳ ❋✉♥❞❛♠❡♥t❛çã♦ t❡ór✐❝❛ ❞❛ ❝♦❜❡rt✉r❛ ❞❡ ✉♠ ❣r❛❢♦ ♣♦r ❝✐r❝✉✐t♦s✶✺
▲❡♠❛ ✸✳✷✳✶ P❛r❛ t♦❞♦ ❣r❛❢♦ ● ♠✐st♦ ♥ã♦✲❡✉❧❡r✐❛♥♦ ❡ ❢♦rt❡♠❡♥t❡ ❝♦♥❡①♦✱ t♦❞♦ ❝✐r❝✉✐t♦ ❈ ❞❡ ● ❝♦♥té♠ ♣❡❧♦ ♠❡♥♦s ✉♠ ✈ért✐❝❡ ✈ ❝♦♠ ✉♠❛ ❛r❡st❛ ✐♥❝✐❞❡♥t❡ ♥ã♦ ❝♦♥t✐❞❛ ❡♠ ❈ ♦✉ ✉♠ ❛r❝♦ ❝♦♠ ♦r✐❣❡♠ ❡♠ ✈ ❡ ♥ã♦ ❝♦♥t✐❞❛ ❡♠ ❈✳
Pr♦✈❛ ❙❡❥❛ ❈ ✉♠ ❝✐r❝✉✐t♦ ❛r❜✐trár✐♦✳ ❈♦♠♦ ● é ♥ã♦✲❡✉❧❡r✐❛♥♦✱ ❡①✐st❡ ✉♠❛ ❧✐❣❛çã♦ ℓ /∈
❈✳ ❙❡ ❈ ♣❛ss❛ ♣♦r t♦❞♦s ♦s ✈ért✐❝❡s ❞❡ ●✱ ℓ é ✐♥❝✐❞❡♥t❡ ♦✉ t❡♠ ♦r✐❣❡♠ ❡♠ ✉♠ ✈ért✐❝❡
❞❡ ❈ ❡ ♦ t❡♦r❡♠❛ ❡stá ♣r♦✈❛❞♦✳ ❈❛s♦ ❝♦♥trár✐♦✱ s❡❥❛ ✈ ✉♠ ✈ért✐❝❡ ❛r❜✐trár✐♦ t❛❧ q✉❡ ✈ ♥ã♦ s❡❥❛ ✈✐s✐t❛❞♦ ♣♦r ❈✳ ❈♦♥s✐❞❡r❡ ✉♠ ❝❛♠✐♥❤♦ ❞❡ ✉♠ ✈ért✐❝❡ ❛r❜✐trár✐♦ ✉ ✈✐s✐t❛❞♦ ♣♦r ❈ ♣❛r❛ ✈✱ ❝✉❥❛ ❡①✐stê♥❝✐❛ é ❣❛r❛♥t✐❞❛ ♣❡❧♦ ❢❛t♦ ❞❡ q✉❡ ● é ❢♦rt❡♠❡♥t❡ ❝♦♥❡①♦✳ ❆ ú❧t✐♠❛ ❧✐❣❛çã♦ ❞♦ ❝❛♠✐♥❤♦ ✉ → ✈ ♥ã♦ ♣❡rt❡♥❝❡ ❛ ❈✱ ♣♦✐s ✈ ♥ã♦ é ✈✐s✐t❛❞♦ ♣♦r ❈✳ ❆
♣r✐♠❡✐r❛ ❧✐❣❛çã♦ ❞❡st❡ ❝❛♠✐♥❤♦ ✉→✈ ♥ã♦ ♣❡rt❡♥❝❡♥t❡ ❛ ❈ é ❡✈✐❞❡♥t❡♠❡♥t❡ ✉♠❛ ❛r❡st❛
✐♥❝✐❞❡♥t❡ ♦✉ ✉♠ ❛r❝♦ ❝♦♠ ♦r✐❣❡♠ ❡♠ ✉✱ ♣r♦✈❛♥❞♦ ♦ t❡♦r❡♠❛✳
❖ ♣r♦❜❧❡♠❛ ❞❛ ❝♦❜❡rt✉r❛ ❞❡ ✉♠ ❣r❛❢♦ ♣♦r ❝✐r❝✉✐t♦s ✭P❈❈✮ é ◆P✲❉í✜❝✐❧ ❡ ❞❡✜♥✐❞♦ ❝♦♠♦✿ ❉❛❞♦ ✉♠ ❣r❛❢♦ ♠✐st♦ ● ❢♦rt❡♠❡♥t❡ ❝♦♥❡①♦✱ ❞❡✈❡ s❡r ❡♥❝♦♥tr❛❞♦ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❝✐r❝✉✐t♦s ❞❡ ❝✉st♦ ♠í♥✐♠♦ t❛❧ q✉❡ ❝❛❞❛ ❛r❡st❛ ❡ ❛r❝♦ ❞❡ ● ❡st❡❥❛ ♣r❡s❡♥t❡ ❡♠ ♣❡❧♦ ♠❡♥♦s ✉♠ ❝✐r❝✉✐t♦✳ ❊♠ ❬▲❡❡ ✫ ❲❛❦❛❜❛②❛s❤✐✱ ✷✵✵✷❪✱ ❛ r❡❧❛çã♦ ❡♥tr❡ ♦ ♣r♦❜❧❡♠❛ ❞♦ ❝❛rt❡✐r♦ ❝❤✐♥ês ❡ ❛ ❝♦❜❡rt✉r❛ ❞❡ ✉♠ ❣r❛❢♦ ♣♦r ❝✐r❝✉✐t♦s é ❞✐s❝✉t✐❞❛ ❛tr❛✈és ❞❡ ✉♠❛ r❡✈✐sã♦ ❞❛ ❧✐t❡r❛t✉r❛ s♦❜r❡ ♦ ♣r♦❜❧❡♠❛✳ ➱ ♣r♦✈❛❞♦ q✉❡ ♦s ♣r♦❜❧❡♠❛s sã♦ ❡q✉✐✈❛❧❡♥t❡s ❡ ♣♦ss✉❡♠ s♦❧✉çã♦ ❝♦♠✉♠ ❡ ❜✐❥❡t✐✈❛✳ ❉❡ ❢❛t♦✱ ❛ ❝♦♥❝❧✉sã♦ ❞❡ q✉❡ ♦s ♣r♦❜❧❡♠❛s sã♦ r❡❧❛❝✐♦♥❛❞♦s é ❜❡♠ ✐♥st✐♥t✐✈❛ ❡ ❞❡r✐✈❛ ❞❡ ✉♠ s❡♥s♦ ❝♦♠✉♠✿ ❛ s♦❧✉çã♦ ❡s♣❡r❛❞❛ ♣❛r❛ ♦ ▼❈PP é ✉♠ ♣❛ss❡✐♦ ♣❡❧♦ ❣r❛❢♦✱ q✉❡ ❝♦♥t❡♥❤❛ t♦❞❛s ❛s ❛r❡st❛s ❡ ❛r❝♦s ❡ q✉❡ ❝♦♠❡❝❡ ❡ t❡r♠✐♥❡ ♥♦ ♠❡s♠♦ ✈ért✐❝❡✳ ❉❡ ❢♦r♠❛ r✐❣♦r♦s❛✱ é ♥❡❝❡ssár✐♦ ♣r♦✈❛r q✉❡ ❡st❛ ❝♦❜❡rt✉r❛ ♣♦r ❝✐r❝✉✐t♦s ❝♦♠ ❞✉♣❧✐❝❛çõ❡s ❞❡ ❢❛t♦ ❣❡r❛ ✉♠❛ s♦❧✉çã♦ ♣❛r❛ ♦ ▼❈PP✳
❚❡♦r❡♠❛ ✸✳✷✳✷ ❆ s♦❧✉çã♦ ❞❛ ❝♦❜❡rt✉r❛ ❞❛s ❧✐❣❛çõ❡s ♠í♥✐♠❛ ❞❡ ✉♠ ❣r❛❢♦ ♠✐st♦ ♣♦r ❝✐r❝✉✐t♦s é ❡q✉✐✈❛❧❡♥t❡ ❛ s♦❧✉çã♦ ❞♦ ♣r♦❜❧❡♠❛ ❞♦ ❈❛rt❡✐r♦ ❈❤✐♥ês ▼✐st♦✱ ❡♠ ✉♠ ❣r❛❢♦ ❢♦rt❡♠❡♥t❡ ❝♦♥❡①♦✳
Pr♦✈❛ ➱ ♣r❡❝✐s♦ ♣r♦✈❛r q✉❡ ♣♦❞❡♠♦s tr❛♥s❢♦r♠❛r ❛ s♦❧✉çã♦ ❞❡ ✉♠ ▼❈PP ❡♠ ✉♠ ♣r♦❜❧❡♠❛ ❞❡ ❝♦❜❡rt✉r❛ ♣♦r ❝✐r❝✉✐t♦s ❡ ✈✐❝❡✲✈❡rs❛✳
▼❈PP → P❈❈
✶✻ ❈❛♣ít✉❧♦ ✸✳ ❆ ❤❡✉ríst✐❝❛ ♣r♦♣♦st❛
P❈❈ → ▼❈PP
❆ s♦❧✉çã♦ ❞♦ ♣r♦❜❧❡♠❛ ❞❡ ❝♦❜❡rt✉r❛ é ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❝✐r❝✉✐t♦s ❞❡ ❝✉st♦ ♠í♥✐♠♦✳ ➱ ♥❡❝❡ssár✐♦ ♣r♦✈❛r q✉❡ ❡st❡s ❝✐r❝✉✐t♦s ♣♦❞❡♠ s❡r ♣❡r❝♦rr✐❞♦s ❞❡ ❢♦r♠❛ ❛ ❝r✐❛r ✉♠ ú♥✐❝♦ ❝✐r❝✉✐t♦✳ ❆ss✐♠✱ ✉♠ ❝✐r❝✉✐t♦C1 é ❡s❝♦❧❤✐❞♦ ❞❡st❡ ❝♦♥❥✉♥t♦✳ ❉♦ ❝✐r❝✉✐t♦ C1✱ ✉♠ ✈ért✐❝❡ v12 é ❡s❝♦❧❤✐❞♦✱ ❞❡ ❢♦r♠❛ t❛❧ q✉❡v12 ❡st❡❥❛ ❝♦♥t✐❞♦ ❡♠ ♦✉tr♦ ❝✐r❝✉✐t♦✱ C2✳ ❯♥✐♥❞♦ ❡ss❡s
❞♦✐s ❝✐r❝✉✐t♦s✱ é ♣♦ssí✈❡❧ ✐♠❛❣✐♥á✲❧♦s ❝♦♠♦ ✉♠ só✱ ♣♦✐s ♣❛rt✐♥❞♦ ❞❡ ✉♠ ✈ért✐❝❡ q✉❛❧q✉❡r ❞❡C1✱ ❡st❡ é ♣❡r❝♦rr✐❞♦ ❛té ♦ ✈ért✐❝❡V12 ❞❡ ✐♥t❡r❝❡ssã♦✱ ❞❛í ❞✉r❛♥t❡ ♦ ❝✐r❝✉✐t♦C2 ❛té ♦
✈ért✐❝❡ ❞❡ ✐♥t❡r❝❡ssã♦ ❡ ✜♥❛❧♠❡♥t❡✱ ❞❡ ✈♦❧t❛ ❛♦ ✈ért✐❝❡ ❞❡ ♦r✐❣❡♠ ♣❡❧♦ ❝✐r❝✉✐t♦C1✳ ❊st❡
♣r♦❝❡ss♦ ♣♦❞❡ s❡r r❡♣❡t✐❞♦ ❛té q✉❡ ♥ã♦ ❤❛❥❛♠ ♠❛✐s ❝✐r❝✉✐t♦s ♥ã♦ ✐♥❝❧✉s♦s ♥❛ s♦❧✉çã♦✳ ❊st❡ ♣r♦❝❡ss♦ ❡stá ❡①❡♠♣❧✐✜❝❛❞♦ ♥❛ ✜❣✉r❛ ✸✳✸✳
✸✳✸✳ ❈♦♥str✉çã♦ ✶✼
❆ ✜❣✉r❛ ✸✳✸❛ ❝♦♥té♠ ✸ ❝✐r❝✉✐t♦s✱ ✉♠❛ s♦❧✉çã♦ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❡ ❝♦❜❡rt✉r❛✳ ❆ ✜❣✉r❛ ✸✳✸❜ ♠♦str❛ ♦s ♠❡s♠♦s ✸ ❝✐r❝✉✐t♦s✱ ♣♦ré♠ ❞❡st❛❝❛❞♦s ❡ ♠♦str❛♥❞♦ s❡✉s ♣♦♥t♦s ❞❡ ✐♥t❡r❝❡ssã♦✳ P❛rt✐♥❞♦ ❞♦ ✈ért✐❝❡ ✾ ❞♦ ❝✐r❝✉✐t♦ C1✱ ♣♦r ❡①❡♠♣❧♦✱ é ♣♦ssí✈❡❧ ❣❡r❛r ♦
❝✐r❝✉✐t♦ ❜❛s❡❛❞♦ ❡♠ ✈ért✐❝❡s ✾✲✶✲✸✲✷✲✺✲✻✲✼✲✾✲✹✲✺✲✻✲✽✲✼✲✾✲✶✲✸✲✹✲✺✲✻✲✽✲✾✳
✸✳✸ ❈♦♥str✉çã♦
❆ ❤❡✉ríst✐❝❛ ❝♦♠❡ç❛ ❝♦♠ ❛ ❣❡r❛çã♦ ❞❡ ✉♠ ❜❛♥❝♦ ❞❡ ❞❛❞♦s ❞❡ ❝✐r❝✉✐t♦s✱ ♥ã♦✲❡①❛✉st✐✈♦✱ ♦♥❞❡ ❝❛❞❛ ❧✐❣❛çã♦ ✭❛r❡st❛ ♦✉ ❛r❝♦✮ ❡st❡❥❛ ♣r❡s❡♥t❡ ❡♠ ♣❡❧♦ ♠❡♥♦s ✉♠ ❝✐r❝✉✐t♦✳ ❊st❡ ❜❛♥❝♦ ❞❡ ❞❛❞♦s ♣♦❞❡ s❡r ❣❡r❛❞♦ ❞❡ q✉❛❧q✉❡r ❢♦r♠❛✱ ❞❡s❞❡ q✉❡ s❡❥❛ ♣♦ssí✈❡❧ ❝♦♥❤❡❝❡r t♦❞❛s ❛s ❧✐❣❛çõ❡s q✉❡ ♣❡rt❡♥❝❡♠ ❛ ✉♠ ❝✐r❝✉✐t♦ ❡ s❡✉ ❝✉st♦ t♦t❛❧✳
◆❡ss❡ tr❛❜❛❧❤♦✱ ♦ ❜❛♥❝♦ ❞❡ ❞❛❞♦s ❢♦✐ ❣❡r❛❞♦ ♣♦r três ♠ét♦❞♦s✱ ❞❡t❛❧❤❛❞♦s ❛❜❛✐①♦✱ s❡♠♣r❡ ❝♦♠ ♦ ♦❜❥❡t✐✈♦ ❞❡ ❝♦♥t❡♠♣❧❛r ❝❛❞❛ ❧✐❣❛çã♦ ❝♦♠ ✉♠❛ ❞✐✈❡rs✐❞❛❞❡ ♠í♥✐♠❛✱ q✉❡ ♣❡r♠✐t❛ ✉♠❛ ❡①❡❝✉çã♦ ♣r♦❞✉t✐✈❛ ❞❛ ♦t✐♠✐③❛çã♦ ❞❛ ❝♦❧ô♥✐❛ ❞❡ ❢♦r♠✐❣❛s✳
✸✳✸✳✶ ❈✐r❝✉✐t♦s ❞❡ t❛♠❛♥❤♦ ❞❡✜♥✐❞♦
✶✽ ❈❛♣ít✉❧♦ ✸✳ ❆ ❤❡✉ríst✐❝❛ ♣r♦♣♦st❛
◆♦ ❛❧❣♦r✐t♠♦ ✶✱L é ♦ ❝♦♥❥✉♥t♦ ❞❡ ❧✐❣❛çõ❡s ❡ N é ♦ ❝♦♥❥✉♥t♦ ❞❡ ✈ért✐❝❡s ❞❡ ●✳
✶ Pr♦❝❡❞✐♠❡♥t♦ ❈✐r❝✉✐t♦s❚❛♠❛♥❤♦❑ ✭❚❛♠❛♥❤♦❑✮ ❀ ✷ ♣❛r❛ ❝❛❞❛ni ∈N ❢❛ç❛
✸ ❉❋❙✭ni✱ni✱ ❚❛♠❛♥❤♦❑✱✶✱ ✲✶✱ ❬❧✐st❛ ✈❛③✐❛❪✮❀
✹ ✜♠ ♣❛r❛ ❝❛❞❛
✺ Pr♦❝❡❞✐♠❡♥t♦ ❉❋❙ ✭◆♦❆t✉❛❧✱ ◆♦Pr♦❝✉r❛❞♦✱ ❚❛♠❛♥❤♦✱ ◆✐✈❡❧✱
❆r❡st❛❖r✐❣❡♠✱ ❈✐r❝✉✐t♦✮ ❀
✻ ♣❛r❛ ❝❛❞❛l ∈L ✐♥❝✐❞❡♥t❡ ❛ N oAtual ❢❛ç❛
✼ s❡ ✭l ✦❂ ❆r❡st❛❖r✐❣❡♠✮ ❡♥tã♦
✽ ❈♦❧♦q✉❡ l ♥♦ ❢✉♥❞♦ ❞❛ ❧✐st❛ ❈✐r❝✉✐t♦❀ ❀
✾ s❡ ✭◆✐✈❡❧ ❂ ❚❛♠❛♥❤♦✮ ❡ ✭◆♦❉❡st✐♥♦✭l✮ ❂ ◆♦Pr♦❝✉r❛❞♦✮ ❡♥tã♦
✶✵ ❆r♠❛③❡♥❡ ❈✐r❝✉✐t♦ ♥♦ ❜❛♥❝♦ ❞❡ ❞❛❞♦s ❡ r❡t♦r♥❡❀ ✶✶ ✜♠ s❡
✶✷ s❡ ◆✐✈❡❧ ❁ ❚❛♠❛♥❤♦ ❡♥tã♦
✶✸ ❉❋❙✭◆♦❉❡st✐♥♦✭l✮✱◆♦Pr♦❝✉r❛❞♦✱ ❚❛♠❛♥❤♦✱◆✐✈❡❧✰✶✱l✱ ❈✐r❝✉✐t♦✮❀
✶✹ ✜♠ s❡ ✶✺ ✜♠ s❡ ✶✻ ✜♠ ♣❛r❛ ❝❛❞❛ ✶✼ ❘❡t♦r♥❡ ❀
❆❧❣♦r✐t♠♦ ✶✿ ❈✐r❝✉✐t♦s ❞❡ t❛♠❛♥❤♦ ❞❡✜♥✐❞♦ ❑
✸✳✸✳ ❈♦♥str✉çã♦ ✶✾
❋✐❣✉r❛ ✸✳✹✳ ❊①❡♠♣❧♦s ❞❡ ❝✐r❝✉✐t♦s ❞❡ t❛♠❛♥❤♦ ✷✭❛✮✱✸✭❜✮✱✹✭❝✮ ❡ ✺✭❞✮
✸✳✸✳✷ ❈✐r❝✉✐t♦s ❛❧❡❛tór✐♦s
❊st❡ ♠ét♦❞♦ t❛♠❜é♠ s❡ ❜❛s❡✐❛ ❡♠ ✉♠❛ ❜✉s❝❛ ❡♠ ♣r♦❢✉♥❞✐❞❛❞❡ ♠♦❞✐✜❝❛❞❛✳ ❯♠❛ ❧✐❣❛çã♦ é ❡s❝♦❧❤✐❞❛ ♣♦r ♥ã♦ ♣❡rt❡♥❝❡r ❛ ♥❡♥❤✉♠ ❝✐r❝✉✐t♦ ♦✉ ❛♣❡♥❛s ❛❧❡❛t♦r✐❛♠❡♥t❡✱ ❝♦♠ ✜♥s ❞❡ ❞✐✈❡rs✐❞❛❞❡✳ ❊ss❛ ❧✐❣❛çã♦ é ♣❡r❝♦rr✐❞❛✱ ❛t✐♥❣✐♥❞♦ ✉♠ ✈ért✐❝❡✳ ❊st❡ ✈ért✐❝❡ r❡❝❡❜❡ ✉♠ ♥ú♠❡r♦✱ q✉❡ é ♦ ♣❛ss♦ ❛t✉❛❧ ❞♦ ❉❋❙ ❡ ✉♠❛ ❧✐❣❛çã♦ ✐♥❝✐❞❡♥t❡ é s♦rt❡❛❞❛ ❡ ♣❡r❝♦rr✐❞❛✳
