●✐♦✈❛♥✐ ➶♥❣❡❧♦ ❙✐❧✈❛ ❞❛ ◆ó❜r❡❣❛
■♥t❡❣r❛✐s ❞❡ ▲✐♥❤❛ ■♥t❡r✈❛❧❛r❡s✿
❋✉♥❞❛♠❡♥t♦s ❡ ❆♣❧✐❝❛çõ❡s
●✐♦✈❛♥✐ ➶♥❣❡❧♦ ❙✐❧✈❛ ❞❛ ◆ó❜r❡❣❛
■♥t❡❣r❛✐s ❞❡ ▲✐♥❤❛ ■♥t❡r✈❛❧❛r❡s✿
❋✉♥❞❛♠❡♥t♦s ❡ ❆♣❧✐❝❛çõ❡s
❉✐ss❡rt❛çã♦ ❛♣r❡s❡♥t❛❞❛ ❝♦♠♦ r❡q✉✐s✐t♦ ♣❛r❛ ❛♣r♦✈❛çã♦ ♥❛ ❞✐s❝✐♣❧✐♥❛ ❉✐ss❡rt❛çã♦ ❞❡ ▼❡str❛❞♦ ♥♦ ♣❡rí♦❞♦ ✷✵✶✵✳✶✳
❖r✐❡♥t❛❞♦r✿
Pr♦❢✳ ❉r✳ ❇❡♥❥❛♠✐♥ ❘❡♥❡ ❈❛❧❧❡❥❛s ❇❡❞r❡❣❛❧
❈♦✲♦r✐❡♥t❛❞♦r✿
Pr♦❢✳ ❉r✳ ❘♦❜❡rt♦ ❈❛❧❧❡❥❛s ❇❡❞r❡❣❛❧
●r✉♣♦ ❞❡ ▲ó❣✐❝❛✱ ▲✐♥❣✉❛❣❡♠ ■♥❢♦r♠❛❧✱ ❚❡♦r✐❛ ❡ ❆♣❧✐❝❛çã♦ ✕ ▲♦▲■❚❆ Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❙✐st❡♠❛s ❡ ❚❡♦r✐❛ ❞❛ ❈♦♠♣✉t❛çã♦
❉❡♣❛rt❛♠❡♥t♦ ❞❡ ■♥❢♦r♠át✐❝❛ ❡ ▼❛t❡♠át✐❝❛ ❆♣❧✐❝❛❞❛ ❈❡♥tr♦ ❞❡ ❈✐ê♥❝✐❛s ❊①❛t❛s ❡ ❞❛ ❚❡rr❛
❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ ❘✐♦ ●r❛♥❞❡ ❞♦ ◆♦rt❡
❆❣r❛❞❡❝✐♠❡♥t♦s
❘❡s✉♠♦
❆ ♥❡❝❡ss✐❞❛❞❡ ❞❡ ✉♠❛ ♣r❡❝✐sã♦ ❡ ❞❡ ✉♠❛ ❛♣r♦①✐♠❛çã♦ ❞♦s r❡s✉❧t❛❞♦s ♥✉♠ér✐❝♦s
✜③❡r❛♠ ❝♦♠ q✉❡ ❞✐✈❡rs❛s t❡♦r✐❛s s✉r❣✐ss❡♠✿ ❞❡♥tr❡ ❡❧❛s✱ ❞❡st❛❝❛♠♦s ❛ ▼❛t❡♠át✐❝❛ ■♥✲
t❡r✈❛❧❛r✳ ❆ ▼❛t❡♠át✐❝❛ ■♥t❡r✈❛❧❛r s✉r❣✐✉ ♥❛ ❞é❝❛❞❛ ❞❡ ✻✵ ❝♦♠ ♦s tr❛❜❛❧❤♦s ❞❡ ♣❡sq✉✐s❛
❞❡ ▼♦♦r❡ ✭▼❖❖❘❊✱ ✶✾✺✾✮ ✱ ❡♠ q✉❡ ❡❧❡ ♣r♦♣ôs tr❛❜❛❧❤❛r ❝♦♠ ✉♠❛ ▼❛t❡♠át✐❝❛ ❜❛s❡❛❞❛
♥❛ ♥♦çã♦ ❞❡ ✐♥t❡r✈❛❧♦ r❡❛❧ ❡ ♥ã♦ ♠❛✐s ❝♦♠ ✉♠ ♥ú♠❡r♦ ❝♦♠♦ ❛♣r♦①✐♠❛çã♦✳ ❈♦♠ ✐ss♦✱
s✉r❣✐✉ ❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ r❡✈✐s✐t❛r ❡ r❡❢♦r♠✉❧❛r ♦s ❝♦♥❝❡✐t♦s ❡ r❡s✉❧t❛❞♦s ❞❛ ▼❛t❡♠át✐❝❛
❈❧áss✐❝❛ ✉t✐❧✐③❛♥❞♦ ❝♦♠♦ ❜❛s❡ ❛ ♥♦çã♦ ❞❡ ✐♥t❡r✈❛❧♦ ❞❡ ▼♦♦r❡✳ ❯♠❛ ❞❛s ár❡❛s ❞❛ ▼❛t❡✲
♠át✐❝❛ ❈❧áss✐❝❛ q✉❡ t❡♠ t✐❞♦ ♠✉✐t❛s ❛♣❧✐❝❛çõ❡s ❡♠ ❡♥❣❡♥❤❛r✐❛s ❡ ❝✐ê♥❝✐❛s é ❛ ❆♥á❧✐s❡s
◆✉♠ér✐❝❛✱ ♦♥❞❡ ✉♠ ❞♦s s❡✉s ♣✐❧❛r❡s é ♦ ❈á❧❝✉❧♦ ■♥t❡❣r❛❧ ❡ ❡♠ ♣❛rt✐❝✉❧❛r ❛s ✐♥t❡❣r❛✐s ❞❡
❧✐♥❤❛✳ ❆ss✐♠✱ é ♠✉✐t♦ ❞❡s❡❥á✈❡❧ s❡ t❡r ✉♠ ❝á❧❝✉❧♦ ✐♥t❡❣r❛❧ ❞❡♥tr♦ ❞❛ ♣ró♣r✐❛ ▼❛t❡♠át✐❝❛
■♥t❡r✈❛❧❛r✳
◆♦ ♣r❡s❡♥t❡ tr❛❜❛❧❤♦ ❛♣r❡s❡♥t❛✲s❡ ✉♠❛ ♥♦çã♦ ❞❡ ■♥t❡❣r❛❧ ❞❡ ▲✐♥❤❛ ■♥t❡r✈❛❧❛r ❜❛s❡✲
❛❞❛ ♥❛ ❡①t❡♥sã♦ ❞❡ ✐♥t❡❣r❛çã♦ ♣r♦♣♦st❛ ♣♦r ❇❡❞r❡❣❛❧ ❡♠ ✭❇❊❉❘❊●❆▲❀ ❇❊❉❘❊●❆▲✱
✷✵✶✵✮✳ P❛r❛ ❛ ❢✉♥❞❛♠❡♥t❛çã♦ ❛♣r❡s❡♥t❛✲s❡ ✐♥❝✐❛❧♠❡♥t❡ ✉♠❛ ✐♥tr♦❞✉çã♦ s♦❜r❡ ❛ ♣❡s♣❡❝✲
t✐✈❛ ❡♠ q✉❡ ♦ tr❛❜❛❧❤♦ ❢♦✐ r❡❛❧✐③❛❞♦✱ ❝♦♥s✐❞❡r❛♥❞♦ ❛❧❣✉♥s ❛s♣❡❝t♦s ❤✐stór✐❝♦✲❡✈♦❧✉t✐✈♦s
❞❛ ▼❛t❡♠át✐❝❛ ❈❧áss✐❝❛✳ ❖s ❝♦♥❝❡✐t♦s ❞❡ ■♥t❡❣r❛✐s ❞❡ ▲✐♥❤❛ ❈❧áss✐❝❛✱ ❜❡♠ ❝♦♠♦ ❛❧❣✉✲
♠❛s ❞❛s s✉❛s ❛♣❧✐❝❛çõ❡s ♠❛✐s ✐♠♣♦rt❛♥t❡s✳ ❆❧❣✉♥s ❝♦♥❝❡✐t♦s ❞❡ ▼❛t❡♠át✐❝❛ ■♥t❡r✈❛❧❛r
♥❡❝❡ssár✐♦s ♣❛r❛ ♦ ❡♥t❡♥❞✐♠❡♥t♦ ❞♦ tr❛❜❛❧❤♦✳ P❛r❛ ✜♥❛❧✐③❛r ♣r♦♣♦♠♦s ✉♠❛ ❛♣❧✐❝❛çã♦
❞❛ ✐♥t❡❣r❛❧ ❞❡ ❧✐♥❤❛ ❡♠ ✉♠ ❡①♣❡r✐♠ê♥t♦ ❝❧áss✐❝♦ ❞❛ ♠❡❝â♥✐❝❛ q✉â♥t✐❝❛ ✭❛ ❞✐❢r❛çã♦ ❞❡
✉♠ ❡❧étr♦♥ ❡♠ ✉♠❛ ❢❡♥❞❛✮ q✉❡ ❣r❛ç❛s ❛♦ ❢❛t♦ ❞❡ s❡r ❛ ▼❛t❡♠át✐❝❛ ■♥t❡r✈❛❧❛r ✉t✐❧✐③❛❞❛✱
P❛❧❛✈r❛s✲❝❤❛✈❡✿ ▼❛t❡♠át✐❝❛ ■♥t❡r✈❛❧❛r✱ ❆♥á❧✐s❡ ■♥t❡r✈❛❧❛r✱ ■♥t❡❣r❛❧ ❞❡ ▲✐♥❤❛ ❡
❆❜str❛❝t
❚❤❡ r❡q✉✐r❡♠❡♥t ♦❢ ❛ ❣r❡❛t❡r ♣r❡❝✐s✐♦♥ ❛♥❞ ❛♣♣r♦①✐♠❛t✐♦♥ ♦❢ ♥✉♠❡r✐❝❛❧ r❡s✉❧ts ❣❛✈❡
r✐s❡ t♦ ✈❛r✐♦✉s t❤❡♦r✐❡s✿ ❛♠♦♥❣ t❤❡♠✱ ✇❡ ❝❛♥ ❤✐❣❤❧✐❣❤t t❤❡ ♠❛t❤❡♠❛t✐❝s ♦❢ ✐♥t❡r✈❛❧s✳
❚❤❡ ♠❛t❤❡♠❛t✐❝s ♦❢ ✐♥t❡r✈❛❧s ❛♣♣❡❛r❡❞ ✐♥ t❤❡ ✻✵s ✇✐t❤ t❤❡ r❡s❡❛r❝❤ ✇♦r❦s ❜② ▼♦♦r❡✱ ✐♥
✇❤✐❝❤ ❤❡ ♣r♦♣♦s❡❞ t♦ ✇♦r❦ ✇✐t❤ ♠❛t❤❡♠❛t✐❝s ❜❛s❡❞ ♦♥ t❤❡ ♥♦t✐♦♥ ♦❢ r❡❛❧ ✐♥t❡r✈❛❧ ✐♥st❡❛❞
♦❢ ♣♦✐♥t❡❞ ♥✉♠❜❡rs✳ ❙♦✱ ❛ ♥❡❝❡ss✐t② ♦❢ r❡✈✐s✐t✐♥❣ ❛♥❞ r❡❢♦r♠✉❧❛t✐♥❣ t❤❡ ❝♦♥❝❡♣ts ❛♥❞
r❡s✉❧ts ♦❢ ❝❧❛ss✐❝ ♠❛t❤❡♠❛t✐❝s ❛♣♣❡❛r❡❞✱ ✉s✐♥❣ ▼♦♦r❡✬s ♥♦t✐♦♥ ♦❢ ✐♥t❡r✈❛❧s ❛s ❜❛s✐s✳ ❖♥❡
♦❢ t❤❡ ✜❡❧❞s ✐♥ ❝❧❛ss✐❝ ♠❛t❤❡♠❛t✐❝s ✇❤✐❝❤ ❤❛s ❤❛❞ ♣❧❡♥t② ♦❢ ❛♣♣❧✐❝❛t✐♦♥ ✐♥ ❡♥❣✐♥❡❡r✐♥❣
❛♥❞ s❝✐❡♥❝❡s ✐s t❤❡ ♥✉♠❡r✐❝❛❧ ❛♥❛❧②s✐s✱ ✇❤♦s❡ ♦♥❡ ✐♠♣♦rt❛♥t ❜❛s✐s ✐s t❤❡ ❢✉❧❧ ❞✐✛❡r❡♥t✐❛❧
❝❛❧❝✉❧✉s ❛♥❞✱ ✐♥ ♣❛rt✐❝✉❧❛r✱ t❤❡ ❧✐♥❡ ✐♥t❡❣r❛❧s✳ ❚❤❡r❡❢♦r❡✱ ✐t ✐s r❡❛❧❧② ❞❡s✐r❛❜❧❡ t♦ ❤❛✈❡ ❛
❞✐✛❡r❡♥t✐❛❧ ❛♥❞ ❢✉❧❧ ❝❛❧❝✉❧✉s ✐♥s✐❞❡ t❤❡ ♠❛t❤❡♠❛t✐❝s ♦❢ ✐♥t❡r✈❛❧s ✐ts❡❧❢✳ ❍♦✇❡✈❡r✱ s❝✐❡♥t✐✲
✜❝ ✇♦r❦ r❡❛s♦♥❛❜❧② ❜❛s❡❞ ✐♥ s✉❝❤ t❤❡♦r② ❝❛♥♥♦t ❜❡ ❢♦✉♥❞ ✐♥ t❤❡ ❧✐t❡r❛t✉r❡✱ t❤❛t ♠❡❛♥s✱
✇♦r❦s ✇❤✐❝❤ ❝♦♥t❛✐♥ ❛ ♥♦t✐♦♥ ♦❢ ✐♥t❡❣r❛❧s ❛♥❞ ❞❡r✐✈❛t✐✈❡s ❢♦r ❢✉♥❝t✐♦♥s ♦❢ ✐♥t❡r✈❛❧ t❤❛t
❢✉❧✜❧❧ ❛ s✐♠✐❧❛r r❡s✉❧t t♦ t❤❡ ❢✉♥❞❛♠❡♥t❛❧ ❝❛❧❝✉❧✉s t❤❡♦r❡♠✳ ❚❤✐s ✇♦r❦ ♣r❡s❡♥ts ❛ ♥♦t✐♦♥
♦❢ ✐♥t❡❣r❛❧ ♦❢ ❧✐♥❡ ♦❢ ✐♥t❡r✈❛❧s ❜❛s❡❞ ♦♥ t❤❡ ✐♥t❡❣r❛t✐♦♥ ❡①t❡♥s✐♦♥ ♣r♦♣♦s❡❞ ❜② ❇❡❞r❡❣❛❧✳
❆s ❢✉♥❞❛♠❡♥t❛❧s✱ t❤✐s ✇♦r❦ ♣r❡s❡♥ts✱ ❛t ✜rst✱ ❛♥ ✐♥tr♦❞✉❝t✐♦♥ ❛❜♦✉t t❤❡ ♣❡rs♣❡❝t✐✈❡
❛❞♦♣t❡❞ ❜② ✐t✱ ❝♦♥s✐❞❡r✐♥❣ s♦♠❡ ❤✐st♦r✐❝❛❧✲❡✈♦❧✉t✐♦♥❛r② ❛s♣❡❝ts ♦❢ ❝❧❛ss✐❝ ♠❛t❤❡♠❛t✐❝s✳
❚❤❡ ❝❧❛ss✐❝❛❧ ❝♦♥❝❡♣ts ♦❢ ✐♥t❡❣r❛❧s ♦❢ ❧✐♥❡✱ ❛s ✇❡❧❧ ❛s s♦♠❡ ♦❢ t❤❡✐r ♠♦st ✐♠♣♦rt❛♥t ❛♣♣❧✐✲
❝❛t✐♦♥s✳ ❋✐♥❛❧❧②✱ ❛♥ ❛♣♣❧✐❝❛t✐♦♥ ♦❢ ❛ ❧✐♥❡ ♦❢ ✐♥t❡❣r❛❧ ✐♥ ❛ ❝❧❛ss✐❝❛❧ ❡①♣❡r✐♠❡♥t ♦♥ q✉❛♥t✉♠
♠❡❝❤❛♥✐❝s ✭❛ ❞✐✛r❛❝t✐♦♥ ♦❢ ❛♥ ❡❧❡❝tr♦♥ ✐♥t♦ ❛ ❝r❛❝❦✮ ✐s ♣r♦♣♦s❡❞✱ ✇❤✐❝❤✱ ❞✉❡ t♦ t❤❡ ❢❛❝t
♦❢ t❤❡ ✉s❛❣❡ ♦❢ t❤❡ ♠❛t❤❡♠❛t✐❝s ♦❢ ✐♥t❡r✈❛❧s✱ ♣r♦✈✐❞❡s ❛ ♠♦r❡ ❞❡t❛✐❧❡❞ ❢♦❝✉s✱ ❝❧♦s❡r t♦
❙✉♠ár✐♦
▲✐st❛ ❞❡ ❋✐❣✉r❛s
▲✐st❛ ❞❡ ❙í♠❜♦❧♦s
✶ ■♥tr♦❞✉çã♦ ♣✳ ✶✶
✶✳✶ ❈á❧❝✉❧♦ ■♥t❡❣r❛❧ ❈❧áss✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✷
✶✳✷ ❈á❧❝✉❧♦ ■♥t❡❣r❛❧ ■♥t❡r✈❛❧❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✸
✷ ■♥t❡❣r❛❧ ❞❡ ▲✐♥❤❛ ❈❧áss✐❝❛ ♣✳ ✶✺
✷✳✶ ❈❛r❛❝t❡r✐③❛çã♦ ❞❛ ■♥t❡❣r❛❧ ❞❡ ▲✐♥❤❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✺
✷✳✷ Pr♦♣r✐❡❞❛❞❡s ❞❡ ■♥t❡❣r❛✐s ❞❡ ▲✐♥❤❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✼
✷✳✸ ❆♣❧✐❝❛çõ❡s ❞❡ ■♥t❡❣r❛✐s ❞❡ ▲✐♥❤❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✽
✷✳✸✳✶ ❉❡♥s✐❞❛❞❡ ▲✐♥❡❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✽
✷✳✸✳✷ ▲❡✐ ❞❡ ❇✐♦t✲❙❛✈❛rt ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✽
✷✳✸✳✸ ▼❡r❝❛❞♦ ❋✐♥❛♥❝❡✐r♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✾
✸ ❋✉♥❞❛♠❡♥t♦s ❞❡ ▼❛t❡♠át✐❝❛ ■♥t❡r✈❛❧❛r ♣✳ ✷✷
✸✳✶ ❈♦♥❝❡✐t♦s ❢✉♥❞❛♠❡♥t❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✷
✸✳✷ Pr♦♣r✐❡❞❛❞❡s ❆❧❣é❜r✐❝❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✹
✸✳✸ ❘❡❧❛çã♦ ❞❡ ❖r❞❡♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✹
✸✳✹ ❚♦♣♦❧♦❣✐❛ ♥♦ ■✭❘✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✺
✸✳✺✳✶ ■♥t❡❣r❛❧ ❞❡ ▼♦♦r❡ ❡ ❨❛♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✽
✸✳✺✳✷ ■♥t❡❣r❛❧ ❞❡ ❇❡❞r❡❣❛❧✲❇❡❞r❡❣❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✾
✹ ■♥t❡❣r❛❧ ❞❡ ▲✐♥❤❛ ■♥t❡r✈❛❧❛r ♣✳ ✸✵
✺ ❆♣❧✐❝❛çã♦ ❞❛ ■♥t❡❣r❛❧ ■♥t❡r✈❛❧❛r ❞❡ ▲✐♥❤❛ ■♥t❡r✈❛❧❛r ♣✳ ✸✾
✺✳✶ ❉✐❢r❛çã♦ ❞❡ ✉♠❛ P❛rtí❝✉❧❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✵
✺✳✷ ❊①♣❡r✐♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✶
✺✳✸ ▼♦❞❡❧❛❣❡♠ ■♥t❡r✈❛❧❛r ❞♦ ❊①♣❡r✐♠❡♥t♦ ❞❡ ❉✐❢r❛çã♦ ❞❡ ✉♠❛ P❛rtí❝✉❧❛ ✳ ♣✳ ✹✸
✺✳✸✳✶ ❈♦♥s✐❞❡r❛çõ❡s ❋✐♥❛✐s s♦❜r❡ ♦ ❊①♣❡r✐♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✸
✻ ❈♦♥❝❧✉sõ❡s ❡ ❚r❛❜❛❧❤♦s ❋✉t✉r♦s ♣✳ ✺✺
✻✳✶ ❈♦♥❝❧✉sõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✺
✻✳✷ ❚r❛❜❛❧❤♦s ❋✉t✉r♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✻
▲✐st❛ ❞❡ ❋✐❣✉r❛s
✷✳✶ ❱❛r✐❛çã♦ ❞♦s í♥❞✐❝❡s ❉♦✇ ❏♦♥❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✵
✺✳✶ ▼♦❞❡❧♦ ❞❡ ❉✐❢r❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✷
✺✳✷ ▼♦❞❡❧♦ ❞❛ ❉✐❢r❛çã♦ ■♥t❡r✈❛❧❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✸
✺✳✸ ❘❡♣r❡s❡♥t❛çã♦ ❣❡♦♠étr✐❝❛ ❞♦s át♦♠♦s ❡ s✉❛s ❞✐stâ♥❝✐❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✹
✺✳✹ ❋♦rç❛ ❣❡r❛❞❛ ♣❡❧♦ ❝❛♠♣♦ ❡❧étr✐❝♦ ❞❛ ❢❡♥❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✼
✺✳✺ ❋✉♥çã♦ ❢♦rç❛ ✐♥t❡r✈❛❧❛r r❡s✉❧t❛♥t❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✾
✺✳✻ ●rá✜❝♦ ❞♦ ❚r❛❜❛❧❤♦ ❞♦ ▼♦✈✐♠❡♥t♦ ✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✷
▲✐st❛ ❞❡ ❙í♠❜♦❧♦s
■ ✐♥t❡r✈❛❧♦ r❡❛❧
P✭■ ✮ ❝♦♥❥✉♥t♦ ❞❡ ♣❛rt✐çõ❡s ❞♦ ✐♥t❡r✈❛❧♦ ■
P P❛rt✐çã♦
✡ ❙✉❜❝♦♥❥✉♥t♦ ❛❜❡rt♦ ❞♦ ❘♥
■✭❘✮ ❊①t❡♥sã♦ ❞♦s r❡❛✐s ✐♥t❡r✈❛❧❛r ■ ❙✉❜❝♦♥❥✉♥t♦ ❞❡ ✐♥t❡r✈❛❧♦s ❞❡ ■❘ ❞✐❛♠✭❆✮ ❉✐stâ♥❝✐❛ ❞♦s ❡①tr❡♠♦s ❞♦ ✐♥t❡r✈❛❧♦
❋
❆ ❙✉♣r❡♠♦ ❞❡ ❆
d❆ ■♥✜♠♦ ❞❡ ❆
❥ ❥ ❖♣❡r❛❞♦r ❞❡ ♠ó❞✉❧♦
❦ ❦ ❖♣❡r❛❞♦r ❞❡ ♥♦r♠❛
♠❛①✭❳✮ ❱❛❧♦r ♠á①✐♠♦ r❡❛❧ ❞♦ ❝♦♥❥✉♥t♦ ❳ ♠✐♥✭❳✮ ❱❛❧♦r ♠í♥✐♠♦ r❡❛❧ ❞♦ ❝♦♥❥✉♥t♦ ❳ ❉♦♠✭❢✮ ❉♦♠í♥✐♦ ❞❛ ❢✉♥çã♦ ❢
✛✭❋❀✕❀P✮ ❙♦♠❛tór✐♦ ✐♥❢❡r✐♦r ❞❡ ❘✐❡♠❛♥♥
P
✭❋❀✕❀P✮ ❙♦♠❛tór✐♦ s✉♣❡r✐♦r ❞❡ ❘✐❡♠❛♥♥
❘❇
❆ ❋ ✭❳✮❞❳ ■♥t❡❣r❛❧ ✐♥t❡r✈❛❧❛r ❞❡ ❋
❘
✕❋ ✭❳✮❞❙ ■♥t❡❣r❛❧ ❞❡ ▲✐♥❤❛ ■♥t❡r✈❛❧❛r ❞❡ ❋ s♦❜r❡ ✕
✶✶
✶ ■♥tr♦❞✉çã♦
✶✳✶ ❈á❧❝✉❧♦ ■♥t❡❣r❛❧ ❈❧áss✐❝♦ ✶✷
❡s❜❛rr❛ ❡♠ ❛❧❣✉♥s ♣r♦❜❧❡♠❛s q✉❡✱ s❡❣✉♥❞♦ ✭❚❘■◆❉❆❉❊✱ ✷✵✵✾✮✱ ❡stã♦ ❝♦♥❝❡♥tr❛❞♦s ♥❛ ❡s❝♦❧❤❛ ❞❛ t♦♣♦❧♦❣✐❛ ♣❛r❛ ❛ ❞❡✜♥✐çã♦ ❞♦s ❡s♣❛ç♦s ✐♥t❡r✈❛❧❛r❡s✳ ❈♦♥t✉❞♦✱ ♠❡s♠♦ ❝♦♠ ❡ss❡s ♣r♦❜❧❡♠❛s✱ ❛❧❣✉♠❛s t❡♦r✐❛s ❞❛ ♠❛t❡♠át✐❝❛ ❝❧áss✐❝❛ t❡♠ s✐❞♦ ❡st❡♥❞✐❞❛s ♣❛r❛ ❛ ♠❛✲ t❡♠át✐❝❛ ✐♥t❡r✈❛❧❛r✱ ♣♦ré♠✱ ♥♦ ❝❛s♦ ❞❛ ✐♥t❡❣r❛❧ ❞❡ ❧✐♥❤❛ ♥ã♦ ❡♥❝♦♥tr❛♠♦s ♥❛ ❧✐t❡r❛t✉r❛ q✉❛❧q✉❡r ❡①t❡♥sã♦ ✐♥t❡r✈❛❧❛r ❞❛ ♠❡s♠❛✳ ❊st❡ tr❛❜❛❧❤♦ t❡♠ ❝♦♠♦ ♦❜❥❡t✐✈♦ ❞❡s❡♥✈♦❧✈❡r t❛❧ ❡①t❡♥sã♦ ❞❡ ❢♦r♠❛ ♠❛t❡♠❛t✐❝❛♠❡♥t❡ ❢✉♥❞❛♠❡♥t❛❞❛✳
✶✳✶ ❈á❧❝✉❧♦ ■♥t❡❣r❛❧ ❈❧áss✐❝♦
✶✳✷ ❈á❧❝✉❧♦ ■♥t❡❣r❛❧ ■♥t❡r✈❛❧❛r ✶✸
s❛♠❡♥t♦ ❞✐❣✐t❛❧ ❞❡ ✐♠❛❣❡♥s ✭❙❯◆❉◗❯■❙❚✱ ✷✵✵✸✮❀ ♥❛ ❢ís✐❝❛ q✉â♥t✐❝❛✱ ♥❛ ❡st❛tíst✐❝❛ ❡ ♥❛ ♠❛t❡♠át✐❝❛ ✜♥❛♥❝❡✐r❛ ✭❑▲❊■◆❊❘❚✱ ✷✵✵✹✮✳
✶✳✷ ❈á❧❝✉❧♦ ■♥t❡❣r❛❧ ■♥t❡r✈❛❧❛r
❈♦♠ ♦ s✉❝❡ss♦ ❞❛ ♠❛t❡♠át✐❝❛ ✐♥t❡r✈❛❧❛r✱ ♥❛t✉r❛❧♠❡♥t❡✱ r❡♣r♦❞✉③✐r ❛s t❡♦r✐❛s ❝♦♥s✲ tr✉✐❞❛s ♥❛ ♠❛t❡♠át✐❝❛ ❝❧áss✐❝❛ ♣❛r❛ ❛ ♠❛t❡♠át✐❝❛ ✐♥t❡r✈❛❧❛r ✈❡✐♦ ❛ s❡r ✉♠ ❞♦s ♣r✐♥❝✐♣❛✐s ❢♦❝♦s ❞♦s ♣❡sq✉✐s❛❞♦r❡s ❞❛ ár❡❛✳ ❖ ❝á❧❝✉❧♦ ✐♥t❡❣r❛❧ ❢♦✐ ✉♠❛ ❞❡ss❛s t❡♦r✐❛s✱ ♦♥❞❡ ❞❡st❛✲ ❝❛♠♦s ♦ tr❛❜❛❧❤♦ ✭❙❯◆❆●❆✱ ✶✾✺✽✮ q✉❡ ❛♣r❡s❡♥t❛ ❛ ✉t✐❧✐③❛çã♦ ❞♦ ▼ét♦❞♦ ❞❡ ❙✐♠♣s♦♥✶
❝♦♠ ♦ ❛❥✉st❡ ❞♦ ❡rr♦ ❜❛s❡❛❞♦ ♥❛s ♦♣❡r❛çõ❡s ❡♠ ✐♥t❡r✈❛❧♦s✳ ❏á ❡♠ ✭▼❖❖❘❊❀ ❨❆◆●✱ ✶✾✺✾✮ ❢♦✐ ❛♣r❡s❡♥t❛❞♦ ✉♠❛ ❢✉♥❞❛♠❡♥t❛çã♦ t❡ór✐❝❛ ❞♦ q✉❡ s❡r✐❛ ✉♠❛ ✐♥t❡❣r❛çã♦ ✐♥t❡r✈❛✲ ❧❛r ❞❡ ✉♠❛ ❢✉♥çã♦ ✐♥t❡r✈❛❧❛r✳ ❖ tr❛❜❛❧❤♦ ✭❆❈■❖▲❨✱ ✶✾✾✶✮ ❛♣r❡s❡♥t❛ ✉♠❛ ✐♥t❡❣r❛çã♦ ❞❡ ❢✉♥çõ❡s ✐♥t❡r✈❛❧❛r❡s ❞❡✜♥✐❞❛s s♦❜ ❛ t♦♣♦❧♦❣✐❛ ❞❡ ❙❝♦tt✳ ❊♥❝♦♥tr❛✲s❡ ♥♦ tr❛❜❛❧❤♦ ✭❇❊❉❘❊●❆▲❀ ❇❊❉❘❊●❆▲✱ ✷✵✶✵✮ ❛ ❢✉♥❞❛♠❡♥t❛çã♦ ❞❡ ✉♠ ♥♦✈♦ ♠♦❞❡❧♦ ❞❡ ✐♥t❡❣r❛çã♦ q✉❡ ♣♦❞❡ s❡r ❞❡✜♥✐❞♦ ❡♥tr❡ ✐♥t❡r✈❛❧♦s✱ ❞✐❢❡r❡♥t❡♠❡♥t❡ ❞❛ ✐♥t❡❣r❛❧ ❞❡ ▼♦♦r❡ q✉❡ ❡r❛ ❞❡✜♥✐❞❛ ❡♥tr❡ ♥ú♠❡r♦s r❡❛✐s✳ ❙♦❜ ❛ ❧✉③ ❞❡ss❛ ❡✈♦❧✉çã♦ ♣r♦♣♦♠♦s ♥♦ ♣r❡s❡♥t❡ tr❛❜❛❧❤♦ ✉♠❛ ❢✉♥❞❛♠❡♥t❛çã♦ ❞❡ ✉♠ ♠♦❞❡❧♦ ❞❡ ✐♥t❡❣r❛❧ ❞❡ ❧✐♥❤❛ ✐♥t❡r✈❛❧❛r ❝♦♠♦ ✉♠❛ ❡①t❡♥sã♦ ❞❛ ✐♥t❡❣r❛❧ ♣r♦♣♦st❛ ❡♠ ✭❇❊❉❘❊●❆▲❀ ❇❊❉❘❊●❆▲✱ ✷✵✶✵✮✳
❆ss✐♠✱ ❡st❡ tr❛❜❛❧❤♦ s❡ ❡♥❝♦♥tr❛ ❡str✉t✉r❛❞♦ ♥♦s s❡❣✉✐♥t❡s ❝❛♣ít✉❧♦s✿
❖ ❝❛♣ít✉❧♦ ✷✱ ❛♣r❡s❡♥t❛ ✉♠ r❡s✉♠♦ s♦❜r❡ ❛s ✐♥t❡❣r❛✐s ❞❡ ❧✐♥❤❛ ❝❧áss✐❝❛s✱ ❛ s❛❜❡r✿ ❛ ❞❡✜♥✐çã♦✱ ♦ t❡♦r❡♠❛ ❞❡ ❝❛r❛❝t❡r✐③❛çã♦✱ ❛❧❣✉♠❛s ❞❛s ♣r✐♥❝✐♣❛✐s ♣r♦♣r✐❡❞❛❞❡s ❡ ❛♣❧✐❝❛çõ❡s✳
❖ ❝❛♣ít✉❧♦ ✸✱ ❛♣r❡s❡♥t❛ ✉♠ ❡st✉❞♦ ❞❛s ♣r✐♥❝✐♣❛✐s ♣r♦♣r✐❡❞❛❞❡s ❡ ❛r✐t♠ét✐❝❛ ✐♥t❡r✲ ✈❛❧❛r ❜ás✐❝❛ ✭♦♣❡r❛çõ❡s ❜ás✐❝❛s✮❀ ❛ t♦♣♦❧♦❣✐❛ ❞❡ ▼♦♦r❡ ♥♦ ■✭❘✮❀ ❢✉♥çõ❡s ✐♥t❡r✈❛❧❛r❡s✱ ✐♥t❡❣r❛çõ❡s ✐♥t❡r✈❛❧❛r❡s ❡ r❡❧❛çõ❡s ❞❡ ♣ré✲♦r❞❡♠ ♥♦ ❝♦♥❥✉♥t♦ ■✭❘✮✳
❖ ❝❛♣ít✉❧♦ ✹✱ ❞❡s❡♥✈♦❧✈❡ ❛ ♣r♦♣♦st❛ ❞❛ ❞✐ss❡rt❛çã♦✳ ❆♣r❡s❡♥t❛♠♦s ❛ ❞❡✜♥✐çã♦ ❡ ❛ ❢✉♥❞❛♠❡♥t❛çã♦ ❞❡ ✉♠❛ ✐♥t❡❣r❛❧ ❞❡ ❧✐♥❤❛ ❜❛s❡❛❞❛ ♥❛ ✐♥t❡❣r❛❧ ❢✉♥❞❛♠❡♥t❛❞❛ ❡♠ ✭❇❊✲ ❉❘❊●❆▲❀ ❇❊❉❘❊●❆▲✱ ✷✵✶✵✮✳
❖ ❝❛♣ít✉❧♦ ✺✱ ❛♣r❡s❡♥t❛ ✉♠ ❡①♣❡r✐♠❡♥t♦ ❝❧áss✐❝♦ ❞❛ ♠❡❝â♥✐❝❛ q✉â♥t✐❝❛✱ ❛ ❞✐❢r❛çã♦ ❞❡ ❡❧étr♦♥ ❡♠ ✉♠❛ ❢❡♥❞❛✳ ◆❡st❡ ❡①♣❡r✐♠❡♥t♦ ♣❛ss❛♠♦s ❛ ❝♦♥s✐❞❡r❛r ✉♠❛ ❞❛s ❝♦♦r❞❡♥❛❞❛s
✶✳✷ ❈á❧❝✉❧♦ ■♥t❡❣r❛❧ ■♥t❡r✈❛❧❛r ✶✹
✶✺
✷ ■♥t❡❣r❛❧ ❞❡ ▲✐♥❤❛ ❈❧áss✐❝❛
■♥t✉✐t✐✈❛♠❡♥t❡ ♣♦❞❡♠♦s ♣❡♥s❛r ❡♠ ✉♠ ❝❛♠✐♥❤♦ ❝♦♠♦ ✉♠ ❧✉❣❛r ❣❡♦♠étr✐❝♦✱ ♦✉ s❡❥❛✱ ❝♦♠♦ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ♣♦♥t♦s ❝♦♠ ✉♠❛ ❞❡t❡r♠✐♥❛❞❛ ♣r♦♣r✐❡❞❛❞❡✳ ❚❛♠❜é♠ é ❜❡♠ ♣♦ssí✈❡❧ ♣❡♥s❛r ♥♦ ❝❛♠✐♥❤♦ ❝♦♠♦ ✉♠❛ tr❛❥❡tór✐❛ ❞❡ ✉♠❛ ♣❛rtí❝✉❧❛ ❡♠ ♠♦✈✐♠❡♥t♦ ❡♠ q✉❡ ❛s ❝♦♦r❞❡♥❛❞❛s sã♦ ❢✉♥çõ❡s ❞❡ ✉♠ ♣❛râ♠❡tr♦ q✉❡ é r❡❣✐❞♦ ♣❡❧♦ t❡♠♣♦✳ ❊st❛ ❛❜♦r❞❛❣❡♠ é ❛ ♠❛✐s ✉s❛❞❛✱ ♣♦✐s ✉s❛ ❝♦♠♦ ❧✐♥❣✉❛❣❡♠ ❛s ❢✉♥çõ❡s q✉❡ ♣❡r♠✐t❡♠ ❡①♣❧♦r❛r ♠❡❧❤♦r ❛s ❝❛r❛❝t❡ríst✐❝❛s ❞♦ ❝❛♠✐♥❤♦✳
✷✳✶ ❈❛r❛❝t❡r✐③❛çã♦ ❞❛ ■♥t❡❣r❛❧ ❞❡ ▲✐♥❤❛
❉❡✜♥✐çã♦ ✷✳✶✳ ❯♠❛ ♣❛rt✐çã♦ ❞❡ ✉♠ ✐♥t❡r✈❛❧♦ r❡❛❧ ■ ❂ ❬❛❀❜❪ é ✉♠❛ s❡q✉ê♥❝✐❛ P ❂ ❢❛ ❂ ①✵❀①✶❀✿✿✿❀①♥❂ ❜❣ t❛❧ q✉❡ ♣❛r❛ ❝❛❞❛ ✐ ❂ ✵❀✿✿✿❀♥ ✶✱ ①✐❁ ①✐✰✶✳ P✭■✮ é ♦ ❝♦♥❥✉♥t♦
❞❛s ♣❛rt✐çõ❡s ❞❡ ■✳
❉❡✜♥✐çã♦ ✷✳✷✳ ❆ ♣❛rt✐çã♦ P✶ ❞❡ ■ é ♠❛✐s ✜♥❛ q✉❡ ❛ ♣❛rt✐çã♦ P✷ ❞❡ ■✱ ❞❡♥♦t❛❞❛
♣♦r P✶✖ P✷✱ s❡ P✷✒ P✶✳
❉❡✜♥✐çã♦ ✷✳✸✳ ❯♠ ❝❛♠✐♥❤♦ ❡♠ ✉♠ ❛❜❡rt♦ ✡ ✒ ❘♥ é ✉♠❛ ❛♣❧✐❝❛çã♦ ✌ ✿ ■ ✦ ✡ ❝✉❥♦
❞♦♠í♥✐♦ é ✉♠ ✐♥t❡r✈❛❧♦ ■ ✒ ❘✳
◗✉❛♥❞♦ ♦ ❝❛♠✐♥❤♦ ✌ ✿ ■ ✦ ❘♥ é ❞✐❢❡r❡♥❝✐á✈❡❧ ❡♠ t♦❞♦s ♦s ♣♦♥t♦ ❞❡ ■ ❞✐③❡♠♦s q✉❡ ♦ ❝❛♠✐♥❤♦ é ❞✐❢❡r❡♥❝✐á✈❡❧ ❡♠ ■✳ ❆ ❞❡r✐✈❛❞❛ ♥♦s ❞á ✉♠❛ ❛♣❧✐❝❛çã♦ ✌✵✿ ■ ✦ ❘♥✳ ◗✉❛♥❞♦
❛ ❛♣❧✐❝❛çã♦ ✌✵ é ❝♦♥tí♥✉❛ ❞✐③❡♠♦s q✉❡ ✌ é ❞❡ ❝❧❛ss❡ ❈✶
❉❡✜♥✐çã♦ ✷✳✹✳ ❙❡❥❛ ❢ ✿ ❬❛❀❜❪ ✦ ✡ ✉♠ ❝❛♠✐♥❤♦ ❝♦♠ ✐♠❛❣❡♠ ❞❡✜♥✐❞❛ ♥♦ ❛❜❡rt♦ ✡ ✚ ❘✱ ✐st♦ é✱ ✉♠❛ ❛♣❧✐❝❛çã♦ ❝✉❥♦ ❞♦♠í♥✐♦ é ✉♠ ✐♥t❡r✈❛❧♦ ❞❛ r❡t❛✳ ❉✐③✲s❡ q✉❡ ♦ ❝❛♠✐♥❤♦ ❢ ✿ ❬❛❀❜❪ ✦ ✡ é ❞✐❢❡r❡♥❝✐á✈❡❧ ♥♦ ♣♦♥t♦ t✵✷ ❬❛❀❜❪ s❡ ❡①✐st❡✿
✷✳✶ ❈❛r❛❝t❡r✐③❛çã♦ ❞❛ ■♥t❡❣r❛❧ ❞❡ ▲✐♥❤❛ ✶✻
❝❤❛♠❛❞♦ ❛ ❞❡r✐✈❛❞❛ ❞❡ ❢ ♥♦ ♣♦♥t♦ t✵ ✳
❉❡✜♥✐çã♦ ✷✳✺✳ ❙❡❥❛ ❛ ❢✉♥çã♦ ❢ ✿ ✡ ✒ ❘♥ ✦ ❘ ❡ ♦ ❝❛♠✐♥❤♦ ✌ ✿ ■ ✦ ✡✱ ❛ ✐♥t❡❣r❛❧
❞❡ ❧✐♥❤❛ ❞❡ ❢ s♦❜ ♦ ❝❛♠✐♥❤♦ ✌ é ❞❡✜♥✐❞❛ ❝♦♠♦
❩
✌❢❞❙ ❂ ❧✐♠✁✦✵ ♠
❳
✐❂✵❢✭✌✭t✐✮✮✁✌✭t✐✮
❖♥❞❡ ❞❙ é ♦ ❝♦♠♣r✐♠❡♥t♦ ✐♥✜♥✐t❡s✐♠❛❧ ❞♦ ❝❛♠✐♥❤♦ ❣❡r❛❞♦ ♣❡❧♦ ❝❛♠✐♥❤♦ ✌✳
❚❡♦r❡♠❛ ✷✳✶✳ ✭❋❯▲❑❙✱ ✶✾✻✾✮ ❈♦♥s✐❞❡r❡ ✉♠❛ ❢✉♥çã♦ ❢ ✿ ✡ ✚ ❘♥ ✦ ❘ ❞❡✜♥✐❞❛ ♥♦ ❛❜❡rt♦ ✡✳ ❚♦♠❡♠♦s ✉♠❛ ❢✉♥çã♦ ✌ ✿ ❬❛❀❜❪ ✦ ✡ ❝♦♠♦ ✉♠❛ ❢✉♥çã♦ ❝❛♠✐♥❤♦✳ ❊♥tã♦
❩
✌❢❞❙ ❂
❩
❛ ❜
❢✭✌✭t✮✮❦✌✵✭t✮❦❞t
❉❡♠♦♥str❛çã♦✳ ❈♦♥s✐❞❡r❡ ✉♠❛ ♣❛rt✐çã♦ P ❂ ❢❛ ❂ t✵❁ t✶❁ t✷ ❁ t✸❁ ✿✿✿ ❁ t♠❂ ❜❣ ❞❡
✉♠ ✐♥t❡r✈❛❧♦ ■✱ ♦♥❞❡ q✉❛❧q✉❡r ♣❛rt✐çã♦ P✵❂ ❢❛ ❂ t✵✵ ❁ t✵✶❁ t✵✷❁ t✵✸ ❁ ✿✿✿ ❁ t✵❦ ❂ ❜❣ q✉❡
s❛t✐s❢❛ç❛ P ✚ P✵✳ ❈❧❛r❛♠❡♥t❡ s❡ ✈❡r✐✜❝❛ q✉❡
♠
❳
✐❂✵
❢✭✌✭t✐✮✮❦✌✭t✐✮ ✌✭t✐ ✶✮❦ ✻ ❦
❳
✐❂✵
❢✭✌✭t✵✐✮✮❦✌✭t✵✐✮ ✌✭t✵✐ ✶✮❦
❙❛❜❡♥❞♦ q✉❡ ❛ ❢✉♥çã♦ é ❝♦♥tí♥✉❛✿
❦✌✵✭t✮ ✌✵✭t✐✮❦ ✻ ✧ ✽t ✷ ❬t✐ ✶❀t✐❪❀✐ ❂ ✵❀✶❀✿✿✿❀♠
❖♥❞❡ ✧ é ✉♠❛ ❝♦♥st❛♥t❡ r❡❧❛t✐✈❛♠❡♥t❡ ♣❡q✉❡♥❛✱ ❊♥tã♦✿
♠
❳
✐❂✵
❢✭✌✭t✐✮✮❦✌✭t✐✮ ✌✭t✐ ✶✮❦ ❂ ♠
❳
✐❂✵
❢✭✌✭t✮✮✌✌✌✌✌❩ t✐
t✐ ✶✌
✵✭t✮❞t✌✌✌✌
✌
▼❛s ✌✌
✌✌ ✌
❩ t✐
t✐ ✶✌
✵✭t ✐✮❞t ✌✌ ✌✌ ✌ ✌✌ ✌✌ ✌
❩ t✐
t✐ ✶✭✌
✵✭t✮ ✌✵✭t ✐✮✮❞t ✌✌ ✌✌ ✌✻ ✌✌ ✌✌ ✌
❩ t✐
t✐ ✶✌
✵✭t✮❞t✌✌✌✌
✌
❊ ✌✌
✌✌ ✌
❩ t✐
t✐ ✶✌
✵✭t✮❞t✌✌✌✌
✌✻ ✌✌ ✌✌ ✌
❩ t✐
t✐ ✶✌
✵✭t ✐✮❞t ✌✌ ✌✌ ✌✰ ✌✌ ✌✌ ✌
❩ t✐
t✐ ✶✭✌
✵✭t✮ ✌✵✭t ✐✮✮❞t ✌✌ ✌✌ ✌ ❆❧é♠ ❞✐ss♦ ✌✌ ✌✌ ✌
❩ t✐
t✐ ✶✭✌
✵✭t✮ ✌✵✭t ✐✮✮❞t
✌✌ ✌✌ ✌✻
❩ t✐
t✐ ✶❦✭✌
✵✭t✮ ✌✵✭t
✷✳✷ Pr♦♣r✐❡❞❛❞❡s ❞❡ ■♥t❡❣r❛✐s ❞❡ ▲✐♥❤❛ ✶✼
▲♦❣♦
♠
❳
✐❂✵
❢✭✌✭t✐✮✮❦✌✭t✐✮ ✌✭t✐ ✶✮❦ ✻ ♠
❳
✐❂✵
✭❢✭✌✭t✐✮✮❦✌✵✭t✐✮❦✭t✐ t✐ ✶✮ ✰ ✧✭t✐ t✐ ✶✮✮ ✻
❯✭❢✭✌✭t✮✮❦✌✵❦❀P ✮ ✰ ❢✭✌✭t✮✮✧✭❜ ❛✮
♠
❳
✐❂✵❢✭✌✭t✐✮✮❦✌✭t✐✮ ✌✭t✐ ✶✮❦ ❃ ♠
❳
✐❂✵✭❢✭✌✭t✐✮✮❦✌ ✵✭t
✐✮❦✭t✐ t✐ ✶✮ ✧✭t✐ t✐ ✶✮✮ ❃
▲✭❢✭✌✭t✮✮❦✌✵❦❀P ✮ ❢✭✌✭t✮✮✧✭❜ ❛✮
❚♦♠❛♥❞♦ ♣❛rt✐çõ❡s ❛r❜✐tr❛r✐❛♠❡♥t❡ ✜♥❛s✱ ❝♦♥❝❧✉✐✲s❡ q✉❡✿
❩
❛ ❜
❢✭✌✭t✮✮❦✌✵✭t✮❦❞t ❢✭✌✭t✮✮✧✭❜ ❛✮ ✻❩
❛ ❜
❢✭✌✭t✮✮❦✌✵✭t✮❦❞t
❡ ❩
❛ ❜
❢✭✌✭t✮✮❦✌✵✭t✮❦❞t ✻❩
❛ ❜
❢✭✌✭t✮✮❦✌✵✭t✮❦❞t ✰ ❢✭✌✭t✮✮✧✭❜ ❛✮
❙❡♥❞♦ ✉♠ ✧ s✉✜❝✐❡♥t❡♠❡♥t❡ ♣❡q✉❡♥♦✳
✷✳✷ Pr♦♣r✐❡❞❛❞❡s ❞❡ ■♥t❡❣r❛✐s ❞❡ ▲✐♥❤❛
Pr♦♣♦s✐çã♦ ✷✳✶✳ ❙❡❥❛ ❢ ✿ ✡ ✚ ❘♥ ✦ ❘ ❡ ❣ ✿ ✡ ✚ ❘♥ ✦ ❘ ❢✉♥çõ❡s ❞❡✜♥✐❞❛s ♥♦
❛❜❡rt♦ ✡✱ ✌ ✿ ❬❛❀❜❪ ✦ ✡ ❛ ❢✉♥çã♦ q✉❡ ❞❡s❝r❡✈❡ ♦ ♠♦✈✐♠❡♥t♦ ❞❡ ✉♠❛ ♣❛rtí❝✉❧❛ ❡♠ ✡ ♠❡❞✐❞♦ ❡♠ t✳
✶✳ ❙❡ ❛ ❡ ❜ sã♦ ♥ú♠❡r♦s r❡❛✐s q✉❛✐sq✉❡r t❡♠✲s❡
❩ ✌✭❛❢ ✰ ❜❣✮❞❙ ❂ ❛ ❩ ✌❢❞❙ ✰ ❜ ❩ ✌❣❞❙
✷✳ ❙❡ ❛ ❝✉r✈❛ ✕ é ❞❡ ❝❧❛ss ❈✶ ♣♦r ♣❛rt❡s✱ s❡ ❢♦r ❝♦♥tí♥✉❛ ❡ s❡ ❡①✐st✐r❡♠ ✉♠❛ ♣❛rt✐çã♦ ❛ ❂ t✵❁ t✶❁ ✿✿✿ ❁ t♥❂ ❜ ❡ ❝✉r✈❛s ✌✐✿ ❬t✐ ✶❀t✐❪ ✦ ✡✱ ✐ ❂ ✶❀✷❀✸❀✹❀✿✿✿❀♥✱
❞❡ ❝❧❛ss❡ ❈✶✳
✷✳✸ ❆♣❧✐❝❛çõ❡s ❞❡ ■♥t❡❣r❛✐s ❞❡ ▲✐♥❤❛ ✶✽
✷✳✸ ❆♣❧✐❝❛çõ❡s ❞❡ ■♥t❡❣r❛✐s ❞❡ ▲✐♥❤❛
✷✳✸✳✶ ❉❡♥s✐❞❛❞❡ ▲✐♥❡❛r
❆ ✐♥t❡❣r❛❧ ❞❡ ❧✐♥❤❛✱ r❡❧❛t✐✈❛ ❛♦ ❝♦♠♣r✐♠❡♥t♦ ❞❡ ❛r❝♦✱ ♣♦❞❡ s❡r ❛♣❧✐❝❛❞❛ ♥♦ ❝á❧❝✉❧♦ ❞❛ ♠❛ss❛ ❞❡ ✉♠ ✜♦ ❞❡❧❣❛❞♦✱ ❝✉❥❛ ❞❡♥s✐❞❛❞❡ ❧✐♥❡❛r s❡❥❛ ❝♦♥❤❡❝✐❞❛ ❞❡ ❛❧❣✉♠❛ ♠❛♥❡✐r❛ ✭✈❛❧♦r ❡s❝❛❧❛r ♦✉ ❛❧❣✉♠❛ ❢✉♥çã♦ ❝♦♠ ♦s ♣❛râ♠❡tr♦s ❞❡ ❡♥tr❛❞❛s ❝♦♥❤❡❝✐❞❛s ♦✉ ❡st✐♣✉❧á✈❡✐s✮✳ ❙❡♥❞♦ ❛ss✐♠✿ ❉❛❞♦ ❛ ❢✉♥çã♦ ✌ ✿ ❬❛❀❜❪ ✦ ✡ ✚ ❘♥✱ q✉❡ r❡♣r❡s❡♥t❛ ❛ ❢♦r♠❛ ❞♦ ✜♦✱ ❡ ❛
❢✉♥çã♦ ✍ ✿ ❘♥ ✦ ❘ ❛ ❢✉♥çã♦ ❞❡♥s✐❞❛❞❡ ❞♦ ✜♦✱ ❛ ♠❛ss❛ é ❞❛❞❛ ❢♦r✿
❩
✌✍❞❙ ❂
❩ ❜
❛ ✍✭✌✭t✮✮❦✌ ✵✭t✮❦❞t
✷✳✸✳✷ ▲❡✐ ❞❡ ❇✐♦t✲❙❛✈❛rt
❉❛❞❛ ✉♠❛ ❝❛r❣❛ ♣♦s✐t✐✈❛ q✱ ♠♦✈❡♥❞♦✲s❡ ❛ ✉♠❛ ✈❡❧♦❝✐❞❛❞❡ ✦✈ ✳ ❊ss❛ ❝❛r❣❛ ❡♠ ♠♦✲ ✈✐♠❡♥t♦ ♦r✐❣✐♥❛ ✉♠ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦✱ ❝✉❥❛ ❛ ✐♥t❡♥s✐❞❛❞❡ ❡♠ ✉♠ ♣♦♥t♦ P q✉❛❧q✉❡r é ❞❛❞❛ ♣♦r✿
❇q ❂❦ q ✈ s❡♥✭✒✮r✷
♦♥❞❡✱ r é ❛ ❞✐stâ♥❝✐❛ ❡♥tr❡ ❛ ❝❛r❣❛ ❡ P ✱ ❡ ✒ é ♦ â♥❣✉❧♦ ❢♦r♠❛❞♦ ❡♥tr❡ ✦✈ ✱✦r ❡ ❦ é ❛ ❝♦♥st❛♥t❡ ❡❧❡tr♦stát✐❝❛ ♥♦ ✈á❝✉♦ ❞❡ ✈❛❧♦r ✽❀✾✽✽ ✂ ✶✵✾◆♠✷
❈✷
✷✳✸ ❆♣❧✐❝❛çõ❡s ❞❡ ■♥t❡❣r❛✐s ❞❡ ▲✐♥❤❛ ✶✾
✉♠❛ ❝✉r✈❛ ❈✳ ❉✐✈✐❞✐♥❞♦ ♦ ❝♦♥❞✉t♦r ❡♠ ♣❡q✉❡♥♦s s❡❣♠❡♥t♦s ❞❡ ❞✐♠❡♥sã♦ ❞s ❡ ❛❞♠✐t✐♥❞♦ q✉❡ ❛ ár❡❛ ❞❡ s✉❛ s❡çã♦ r❡t❛ é ❆✱ ♣♦❞❡♠♦s ❞✐③❡r q✉❡ ♦ ✈♦❧✉♠❡ ♣♦❞❡ s❡r ❝❛❧❝✉❧❛❞♦ ♣♦r ❆❞s✳ ❙❡♥❞♦✱ ♥ ♣♦rt❛❞♦r❡s ❞❡ ❝❛r❣❛ ♣❛r❛ ❝❛❞❛ ✉♥✐❞❛❞❡ ❞❡ ✈♦❧✉♠❡ ❡ ❝❛❞❛ ✉♠ ❞❡ ❝❛r❣❛ q✱ ❡♥tã♦ ❛ ❝❛r❣❛ t♦t❛❧ é✿
❞◗ ❂ ♥ q ❆ ❞s ✭✷✳✶✮
❖ ❝♦♥❥✉♥t♦ ❞❡ ❝❛r❣❛s ❡♠ ♠♦✈✐♠❡♥t♦ é ❡q✉✐✈❛❧❡♥t❡ ❛ ✉♠❛ ú♥✐❝❛ ❝❛r❣❛ ❞◗✱ ♠♦✈❡♥❞♦ ❡♠ ✈❡❧♦❝✐❞❛❞❡ ✦✈ ✱ ❧♦❣♦ ❡♠ ✉♠ ♣♦♥t♦ q✉❛❧q✉❡r P ✱ ♦ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❞✦❇ ♣r♦❞✉③✐❞♦ ♣❡❧❛s ❝❛r❣❛s ❞❡ ✐♥t❡♥s✐❞❛❞❡ ❞❇ ❞❛❞❛ ♣♦r✿
❞❇ ❂❦ ❞◗ ✈ s❡♥✭✒✮r✷ ✭✷✳✷✮
❙✉❜st✐t✉✐♥❞♦ ❛ ❡q✉❛çã♦ ✷✳✶ ❡♠ ✷✳✷ t❡r❡♠♦s
❞❇ ❂ ❦ ♥ q ✈ ❆ ❞s s❡♥✭✒✮
r✷ ✭✷✳✸✮
❡ s❡♥❞♦ ♥ q ✈ ❆ ❛ ✐♥t❡♥s✐❞❛❞❡ ❞❛ ❝♦rr❡♥t❡ ✐✱ ❞❡st❡ ♠♦❞♦✿
❞❇ ❂ ❦ ✐ ❞s s❡♥✭✒✮r✷ ✭✷✳✹✮
❆ ❡①♣r❡ssã♦ ✷✳✹ é ❝♦♥❤❡❝✐❞❛ ❝♦♠♦ ▲❡✐ ❞❡ ❇✐♦t✲❙❛✈❛rt✳ ❊❧❛ ❢♦r♥❡❝❡ ❛ ✐♥t❡♥s✐❞❛❞❡ ❞♦ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❇ ❣❡r❛❞♦ ♣❡❧❛ ❝♦rr❡♥t❡ ✐ ❡♠ q✉❛❧q✉❡r ♣♦♥t♦ ❞❛ ❝✉r✈❛ ❞❡ ❝♦♠♣r✐♠❡♥t♦ ❞s✳ ❆ ✐♥t❡♥s✐❞❛❞❡ ❞♦ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ r❡s✉❧t❛♥t❡ ✦❇ ❡♠ ✉♠ ♣♦♥t♦ P q✉❛❧q✉❡r é ❞❛❞♦ ♣❡❧❛ ✐♥t❡❣r❛❧ ❞❡ ❧✐♥❤❛✳
❇ ❂ ❦❩
❈
✐ s❡♥✭✒✮ r✷ ❞s
✷✳✸✳✸ ▼❡r❝❛❞♦ ❋✐♥❛♥❝❡✐r♦
✷✳✸ ❆♣❧✐❝❛çõ❡s ❞❡ ■♥t❡❣r❛✐s ❞❡ ▲✐♥❤❛ ✷✵
✐♥❢♦r♠❛çõ❡s ♣❡rt✐♥❡♥t❡s ❛♦ ♠❡r❝❛❞♦✳
❋❧✉t✉❛çã♦ ❞❡ Pr♦♣r✐❡❞❛❞❡s ❞♦s ❱❛❧♦r❡s ❋✐♥❛♥❝❡✐r♦s
❙❡❥❛ ❙✭t✮ ♦ ❡st♦q✉❡ ♠♦♥❡tár✐♦ ❞❡ ✉♠❛ ❛çã♦ ♦✉ ♦✉tr♦ ✈❛❧♦r ✜♥❛♥❝❡✐r♦✳ ❆♥❛❧✐s❛♥❞♦ ❛ ♠é❞✐❛ ❞♦s ♣r❡ç♦s ❞❛s ❛çõ❡s ✭♦✉ ❞❡ ❛❧❣✉♠ ✈❛❧♦r ♠♦♥❡tár✐♦✮ ❡♠ ❧♦♥❣♦s ♣❡rí♦❞♦s ❞❡ t❡♠♣♦✱ s❡❣✉♥❞♦ ✭❉❖❘❖●❖❱❚❙❊❱✱ ✶✾✾✺✮✱ ♣♦❞❡ s❡r ❛♣r♦①✐♠❛❞♦ ❡①♣♦♥❡♥❝✐❛❧♠❡♥t❡ ✐ss♦ ♣♦rq✉❡ ❣❡r❛❧♠❡♥t❡ é ✉t✐❧✐③❛❞❛ ✉♠❛ ❡s❝❛❧❛ ❡①♣♦♥❡♥❝✐❛❧ ♣❛r❛ ❛ ♣❧♦t❛❣❡♠✳ ■st♦ é ♠❡❧❤♦r r❡♣r❡s❡♥t❛❞♦ ❡♠ ✷✳✶✳
❋✐❣✉r❛ ✷✳✶✿ ●rá✜❝♦ ❞♦ ❝r❡s❝✐♠❡♥t♦ ❞♦s í♥❞✐❝❡s ❝❛❧❝✉❧❛❞♦s s♦❜r❡ ❣r❛♥❞❡s ✉♥✐❞❛❞❡s ✐♥❞✉str✐❛✐s ♥♦s ❊st❛❞♦s ❯♥✐❞♦s ♥♦s ú❧t✐♠♦s ✻✵ ❛♥♦s
❖ ❡st♦q✉❡ ♠♦♥❡tár✐♦ s❛t✐s❢❛③ ❛ ❡q✉❛çã♦ ❞✐❢❡r❡♥❝✐❛❧ ❡st♦❝ást✐❝❛ ♣❛r❛ ♦ ❝r❡s❝✐♠❡♥t♦ ❡①♣♦♥❡♥❝✐❛❧✳
❙✵✭t✮
❙✭t✮ ❂ rs✰ ✑✭t✮ ✭✷✳✺✮
❖♥❞❡ ❙❙✭t✮✵✭t✮ é ❝❤❛♠❛❞♦ ❞❡ ✈❛❧♦r ❞❡ r❡t♦r♥♦✱ rs✱ é ❛ t❛①❛ ❞❡ ❝r❡s❝✐♠❡♥t♦ ❡ ✑✭t✮ é ♦
r✉✐❞♦ ❜r❛♥❝♦ ❞❡✜♥✐❞♦ ♣❡❧❛ ❝♦rr❡❧❛çã♦ ❞❛ ❢✉♥çã♦✿
❤✑✭t✮✐ ❂ ✵ ❤✑✭t✮✑✵✭t✮✐ ❂ ✛✷✍✭t t✵✮ ✭✷✳✻✮
✷✳✸ ❆♣❧✐❝❛çõ❡s ❞❡ ■♥t❡❣r❛✐s ❞❡ ▲✐♥❤❛ ✷✶
❞❛ ✈♦❧❛t✐❧✐❞❛❞❡ ❞♦ ♣r❡ç♦ ❞❛s ❛çõ❡s ✈ ❂ ✛✳ ❖ r❡t♦r♥♦ ❞✐ár✐♦ é ❝❛❧❝✉❧❛❞♦ ❝♦♠♦✿
✁❙✭t✮ ❂ ❬❙✭t♥✰✶✮ ❙✭t♥✮❪
❖ ❝♦♥❥✉♥t♦ ❞❡ t♦❞♦s ♦s ✈❛❧♦r❡s ❞❡ ❙✭t♥✮ é ❝❤❛♠❛❞♦ ❞❡ sér✐❡ ❞❡ ♣r❡ç♦s ♣❡❧♦ t❡♠♣♦✳ ❉❡✈✐❞♦
❛♦s ✈❛❧♦r❡s s❡r❡♠ ♠✉✐t♦ ❣r❛♥❞❡s✱ ❢❛r❡♠♦s ♦ ❧♦❣❛r✐t♠♦ ❞❛ ❡q✉❛çã♦ ✈❛❧♦r ❞❡ r❡t♦r♥♦✱
①✭t✮ ✑ ❧♦❣❙✭t✮
❞❛í ♣♦❞❡♠♦s ❡s❝r❡✈❡r ❛ ❡q✉❛çã♦ ❞✐❢❡r❡♥❝✐❛❧ ❞❡ ❝r❡s❝✐♠❡♥t♦ ❝♦♠♦✿
①✵✭t✮ ❂ ❙✵ ❙
✶
✷✛✷❂ r①✰ ✑✭t✮
❉❛í t✐r❛♠♦s q✉❡
r①✑ rs ✶✷✛✷
❆ ❞✐❢❡r❡♥❝✐❛çã♦ ✜♥✐t❛ ❞❡ ✁①✭t♥✮ ❂ ①✭t♥✰✶✮ ①✭t♥✮ q✉❡ ❝♦rr❡s♣♦♥❞❡ ❛ ❞✐❢❡r❡♥❝✐❛çã♦ ❞①
❡stá r❡❧❛❝✐♦♥❛❞❛ ❛♦ r❡t♦r♥♦ ❙✭t✮ ❝♦♥t✉❞♦ é ✉♠❛ ✈❛r✐❛çã♦ ❞♦ ❧♦❣❙✭t✮✳ ❈♦♥t✉❞♦ ♣❡❧❛ ❡①♣❛♥sã♦ ❞❛ ❞❡r✐✈❛❞❛ ♣♦❞❡♠♦s t❡r✿
❞① ❂ ❞❙❞①❞❙✭t✮ ✶✷❞❙❞✷①✷❞❙✷✭t✮ ✰ ✿✿✿
❞① ❂ ❙❙✭t✮✵✭t✮❞t ✶✷
✧
❙✵✭t✮ ❙✭t✮
★✷
❞t ✰ ✿✿✿
❆s ♣♦tê♥❝✐❛s ❞❡ ♦r❞❡♠ ♠✉✐t♦ ❡❧❡✈❛❞❛ ♥ã♦ ✐♥❢♦r♠❛♠ s♦❜r❡ ❛ ♦s❝✐❧❛çã♦ ❞❛ ♣♦tê♥❝✐❛ ❣❛✉s✲ s✐❛♥❛✳ ■ss♦ ♥♦s ❢❛③ ❞✐③❡r q✉❡✿
✧
❙✵✭t✮
❙✭t✮
★✷
❞t ❂ ①✵✷✭t✮❞t
▲♦❣♦✱ é ♣♦ssí✈❡❧ ❞❡✜♥✐r ❛ ♠é❞✐❛ ❞♦ ❡st♦q✉❡ ♠♦♥❡tár✐♦ ❡♠ ✉♠ ♣❡rí♦❞♦ ❞❡ t❡♠♣♦ ❞❡t❡r✲ ♠✐♥❛❞♦ ♣❡❧❛ ✐♥t❡❣r❛❧ ❞❡ ❧✐♥❤❛✱
✶ ❜ ❛
❩ ❜
❛ ❦①
✵✭t✮❦❞t✿
✷✷
✸ ❋✉♥❞❛♠❡♥t♦s ❞❡ ▼❛t❡♠át✐❝❛
■♥t❡r✈❛❧❛r
❆♣r❡s❡♥t❛r❡♠♦s ♥❡st❡ ❝❛♣ít✉❧♦ ❛❧❣✉♥s ❝♦♥❝❡✐t♦s ❡ ❞❡✜♥✐çõ❡s ❜ás✐❝❛s ❞❛ ♠❛t❡♠át✐❝❛ ✐♥t❡r✈❛❧❛r q✉❡ s❡rã♦ ❛ ❜❛s❡ ♣❛r❛ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞♦s ❧❡♠❛s✱ t❡♦r❡♠❛s✱ ♣r♦♣♦s✐çõ❡s ❡ ❝♦r♦❧ár✐♦s q✉❡ s❡rã♦ ❛♣r❡s❡♥t❛❞♦s ♥♦ ❝❛♣ít✉❧♦ ✹✳ ❊st❡ ❝❛♣ít✉❧♦ ❡stá ❜❛s❡❛❞♦ ♥♦s tr❛✲ ❜❛❧❤♦s ❞❡ ✭❙❯◆❆●❆✱ ✶✾✺✽✮✱ ✭▼❖❖❘❊✱ ✶✾✺✾✮✱ ✭▼❖❖❘❊✱ ✶✾✻✻✮✱ ✭▼❖❖❘❊✱ ✶✾✼✾✮ ❡ ✭❇❊❉❘❊●❆▲❀ ❇❊❉❘❊●❆▲✱ ✷✵✶✵✮✳
✸✳✶ ❈♦♥❝❡✐t♦s ❢✉♥❞❛♠❡♥t❛✐s
❉❡✜♥✐çã♦ ✸✳✶✳ ❉✐③❡♠♦s q✉❡ ✉♠ ✐♥t❡r✈❛❧♦ é ✉♠ ❝♦♥❥✉♥t♦ ❢❡❝❤❛❞♦ ❞❡ ♥ú♠❡r♦s r❡❛✐s r❡♣r❡s❡♥t❛❞♦ ♣❡❧♦ ♣❛r ❝♦♠♣♦st♦ ♣❡❧♦ ❧✐♠✐t❡ ✐♥❢❡r✐♦r ❡ ♦ ❧✐♠✐t❡ s✉♣❡r✐♦r ❞♦ ✐♥t❡r✈❛❧♦✳ ❆ss✐♠ ♣❛r❛ t♦❞♦ ❛❀❜ ✷ ❘ t❛❧ q✉❡ ❛ ✔ ❜✱ ♦ ♣❛r ❬❛❀❜❪ r❡♣r❡s❡♥t❛ ♦ ✐♥t❡r✈❛❧♦✳
❬❛❀❜❪ ❂ ❢① ✷ ❘ ❥ ❛ ✻ ① ✻ ❜❣ ✭✸✳✶✮
◗✉❛♥❞♦ t✐✈❡r♠♦s ♦ ❝❛s♦ ❞❡ ❛ ❂ ❜ ♦ ✐♥t❡r✈❛❧♦ ❬❛❀❜❪ r❡❝❡❜❡ ♦ ♥♦♠❡ ❞❡ ✐♥t❡r✈❛❧♦ ❞❡❣❡♥❡r❛❞♦✳ ❖ ❝♦♥❥✉♥t♦ ❞♦s ✐♥t❡r✈❛❧♦s ❞❡ ❡①tr❡♠♦s r❡❛✐s ❘ é ❞❡♥♦♠✐♥❛❞♦ ❞❡ ■✭❘✮✳
❉❡✜♥✐çã♦ ✸✳✷✳ ❖ ❝♦♥❥✉♥t♦ ■✭❘✮ t❡♠ ❛ss♦❝✐❛❞♦ ❞✉❛s ♣r♦❥❡çõ❡s✿
✙✶❀✙✷✿ ■✭❘✮ ✦ ❘
✙✶✭❬①❀①❪✮ ✼✦ ①
✙✷✭❬①❀①❪✮ ✼✦ ①
P♦r ❝♦♥✈❡♥çã♦✱ ♣❛r❛ t♦❞♦ ❳ ✷ ■✭❘✮✱ ❞❡♥♦t❛r❡♠♦s s✉❛s ♣r♦❥❡çõ❡s✱ ✙✶✭❳✮ ❡ ✙✷✭❳✮✱
✸✳✶ ❈♦♥❝❡✐t♦s ❢✉♥❞❛♠❡♥t❛✐s ✷✸
❉❡✜♥✐çã♦ ✸✳✸ ✭■❣✉❛❧❞❛❞❡ ❡♥tr❡ ■♥t❡r✈❛❧♦s✮✳ ❙❡❥❛♠ ❳ ❡ ❨ ❞♦✐s ✐♥t❡r✈❛❧♦s ❞❡ ■✭❘✮✳ ❉✐③✲s❡ q✉❡ ❳ ❂ ❨ s❡✱ ❡ s♦♠❡♥t❡ s❡ ① ❂ ② ❡ ① ❂ ②✳
❉❡✜♥✐çã♦ ✸✳✹ ✭❆❞✐çã♦✮✳ ❙❡❥❛♠ ❳❀❨ ✷ ■✭❘✮✳ ❆ s♦♠❛ ❞❡ ❳ ❝♦♠ ❨ ✱ ❞❡♥♦t❛❞❛ ♣♦r ❳ ✰ ❨ ✱ é ♦ ❝♦♥❥✉♥t♦ ❢① ✰ ② ❥ ① ✷ ❳ ❡ ② ✷ ❨ ❣
❙✉♥❛❣❛ ❡♠ ✭❙❯◆❆●❆✱ ✶✾✺✽✮ ♣r♦✈♦✉ q✉❡ ❳ ✰ ❨ ❂ ❬① ✰ ②❀① ✰ ②❪✳
❉❡✜♥✐çã♦ ✸✳✺ ✭Ps❡✉❞♦ ■♥✈❡rs♦ ❆❞✐t✐✈♦✮✳ ❉❛❞♦ ❳ ❂ ❬①❀①❪ ✷ ■✭❘✮✳ ❳ ❂ ❬ ①❀ ①❪ ✷ ■✭❘✮ é ❝❤❛♠❛❞♦ ❞❡ ♣s❡✉❞♦ ✐♥✈❡rs♦ ❛❞✐t✐✈♦ ❞❡ ❳✳ ❖❜s❡r✈❡ q✉❡ ❳ ❂ ❢ ① ❥ ① ✷ ❳❣
❖ ♣s❡✉❞♦ ✐♥✈❡rs♦ ❛❞✐t✐✈♦ ♥ã♦ é ♦ ✐♥✈❡rs♦ ❛❞✐t✐✈♦✱ ♣♦✐s ❛ s♦♠❛ ❞♦ ♣s❡✉❞♦ ✐♥✈❡rs♦ ❝♦♠ ♦ ✐♥t❡r✈❛❧♦ ♥❡♠ s❡♠♣r❡ é ❬✵❀✵❪ ✭q✉❡ s❡r✐❛ ♦ ✐♥t❡r✈❛❧♦ ♥❡✉tr♦ ❞❛ s♦♠❛✮✳ P♦✐s✱ s❡❥❛ ❳ ❂ ❬✵❀❛❪ ✿ ♣❛r❛ t♦❞♦ ❛ ✷ ❘ ❢✵❣✱ ❧♦❣♦ ♦ s❡✉ ♣s❡✉❞♦ ✐♥✈❡rs♦ s❡r✐❛ ❳ ❂ ❬ ❛❀✵❪ ♣♦rt❛♥t♦ ❳ ✰ ✭ ❳✮ ❂ ❬ ❛❀❛❪ ✻❂ ❬✵❀✵❪✳ ◆♦ ❡♥t❛♥t♦✱ ♣♦❞❡♠♦s ❛✜r♠❛r q✉❡ ✵ ✷ ❳ ❳
❉❡✜♥✐çã♦ ✸✳✻ ✭❙✉❜tr❛çã♦✮✳ ❙❡❥❛♠ ❳❀ ❨ ✷ ■✭❘✮✳ ❆ s✉❜tr❛çã♦ ❞❡ ❨ ❡♠ ❳✱ ❞❡♥♦t❛❞❛ ♣♦r ❳ ❨ ✱ é ♦ ❝♦♥❥✉♥t♦ ❢① ② ❥ ① ✷ ❳ ❡ ② ✷ ❨ ❣
➱ ❢á❝✐❧ ✈❡r q✉❡ ♣❡❧❛ ❞❡✜♥✐çã♦ ❞❡ ♣s❡✉❞♦ ✐♥✈❡rs♦ ❛❞✐t✐✈♦ q✉❡ ❨ ❂ ❬②❀②❪ ❂ ❬ ②❀ ②❪ ♣♦rt❛♥t♦ ❳ ❨ ❂ ❬① ②❀① ②❪ ❂ ❳ ✰ ✭ ❨ ✮✳ ❊st❡ r❡s✉❧t❛❞♦ ❢♦✐ ❞❡✈✐❞❛♠❡♥t❡ ♣r♦✈❛❞♦ ♣♦r ❙✉♥❛❣❛ ✭❙❯◆❆●❆✱ ✶✾✺✽✮
❉❡✜♥✐çã♦ ✸✳✼ ✭▼✉❧t✐♣❧✐❝❛çã♦✮✳ ❙❡❥❛♠ ❳❀ ❨ ✷ ■✭❘✮✳ ❆ ♠✉❧t✐♣❧✐❝❛çã♦ ❞❡ ❳ ❡ ❨ ✱ ❞❡♥♦t❛❞❛ ♣♦r ❳ ✁ ❨ ✱ é ♦ ❝♦♥❥✉♥t♦ ❢① ✁ ② ❥ ① ✷ ❳ ❡ ② ✷ ❨ ❣
❙✉♥❛❣❛ ❡♠ ✭❙❯◆❆●❆✱ ✶✾✺✽✮ ♣r♦✈❛ q✉❡ ❳ ✁ ❨ ❂ ❬♠✐♥✭① ✁ ②❀① ✁ ②❀① ✁ ②❀① ✁ ②✮❀♠❛①✭① ✁ ②❀① ✁ ②❀① ✁ ②❀① ✁ ②✮❪
❉❡✜♥✐çã♦ ✸✳✽ ✭Ps❡✉❞♦ ■♥✈❡rs♦ ▼✉❧t✐♣❧✐❝❛t✐✈♦✮✳ ❙❡❥❛♠ ♦ ✐♥t❡r✈❛❧♦ ❳✳ ❖ ♣s❡✉❞♦ ✐♥✈❡rs♦ ♠✉❧t✐♣❧✐❝❛t✐✈♦ ❞❡ ❳ é ❞❛❞♦ ♣♦r ✶
❳ ❂
♥
✶
① ❥ ① ✷ ❳
♦
✳ P❡❧♦ ❢❛t♦ ❞❡ ✶
❳ ❂
♥
✶
① ❥ ① ✷ ❳
♦
✱ ✵ ❂✷ ❳✳
◆♦t❡ q✉❡ ❳✶ ❂❤✶①❀①✶✐✳
❉❡✜♥✐çã♦ ✸✳✾ ✭❉✐✈✐sã♦✮✳ ❙❡❥❛ ♦s ✐♥t❡r✈❛❧♦s ❳ ❡ ❨ ✳ ❆ ❞✐✈✐sã♦ ❞❡ ❳ ♣♦r ❨ ✱ ❞❡♥♦t❛❞❛ ♣♦r ❳❨✱ é ❞❛❞❛ ♣♦r ❳❨ ❂♥①② ❥ ① ✷ ❳ ❡ ② ✷ ❨♦P❡❧♦ ❢❛t♦ ❞❡ ❳❨ ❂♥① ✁✶② ❥ ① ✷ ❳ ❡ ② ✷ ❨♦✱ ③❡r♦ ♥ã♦ ♣♦❞❡ ♣❡rt❡♥❝❡r ❛ ❨ ✳
✸✳✷ Pr♦♣r✐❡❞❛❞❡s ❆❧❣é❜r✐❝❛s ✷✹
✸✳✷ Pr♦♣r✐❡❞❛❞❡s ❆❧❣é❜r✐❝❛s
❆s ♣r♦♣r✐❡❞❛❞❡s ❛❧❣é❜r✐❝❛s ❞❛ ❛r✐t♠ét✐❝❛ ✐♥t❡r✈❛❧❛r sã♦ ❝♦♥s❡q✉ê♥❝✐❛s ✐♠❡❞✐❛t❛s ❞♦ ❝♦♥❥✉♥t♦ ❞❡ ❞❡✜♥✐çõ❡s ❞❛s ♦♣❡r❛çõ❡s ❞❛ ❛r✐t♠ét✐❝❛ ✐♥t❡r✈❛❧❛r✳
Pr♦♣♦s✐çã♦ ✸✳✶✳ ❙❡❥❛ ❳✱❨ ❡ ❩ ✷ ■✭❘✮✱ ✈❛❧❡✿
❆ss♦❝✐❛t✐✈✐❞❛❞❡ ♥❛ ❛❞✐çã♦✿ ❳ ✰ ✭❨ ✰ ❩✮ ❂ ✭❳ ✰ ❨ ✮ ✰ ❩
❆ss♦❝✐❛t✐✈✐❞❛❞❡ ♥❛ ♠✉❧t✐♣❧✐❝❛çã♦✿ ❳ ✁ ✭❨ ✁ ❩✮ ❂ ✭❳ ✁ ❨ ✮ ✁ ❩
❈♦♠✉t❛t✐✈✐❞❛❞❡ ♥❛ ❛❞✐çã♦✿ ❳ ✰ ❨ ❂ ❨ ✰ ❳
❈♦♠✉t❛t✐✈✐❞❛❞❡ ♥❛ ♠✉❧t✐♣❧✐❝❛çã♦ ❳ ✁ ❨ ❂ ❨ ✁ ❳
■❞❡♥t✐❞❛❞❡ ♥❛ ❛❞✐çã♦✿ ❊①✐st❡ ✵ ❂ ❬✵❀✵❪ ❡♠ ■✭❘✮ t❛❧ q✉❡ ✵ ✰ ❳ ❂ ❳ ✰ ✵ ❂ ❳
■❞❡♥t✐❞❛❞❡ ♥❛ ♠✉❧t✐♣❧✐❝❛çã♦✿ ❊①✐st❡ ✶ ❂ ❬✶❀✶❪ ❡♠ ■✭❘✮ t❛❧ q✉❡ ✶ ✁ ❳ ❂ ❳ ✁ ✶ ❂ ❳
❙✉❜❞✐str✐❜✉t✐✈✐❞❛❞❡✿ ❳ ✁ ✭❨ ✰ ❩✮ ✒ ❳ ✁ ❨ ✰ ❳ ✁ ❩
❉❡♠♦♥str❛çã♦✳ ❱❡❥❛ ✭▼❖❖❘❊✱ ✶✾✺✾✮
✸✳✸ ❘❡❧❛çã♦ ❞❡ ❖r❞❡♠
❖s ✐♥t❡r✈❛❧♦s ❡♠ ■✭❘✮✱ ♣♦❞❡♠ ❛ss✉♠✐r ❞✐✈❡rs❛s s❡♠â♥t✐❝❛s ❞✐❢❡r❡♥t❡s✳ ❯♠ ✐♥t❡r✈❛❧♦ ♣♦❞❡ s❡r ✈✐st♦ ❝♦♠♦ ❝♦♥❥✉♥t♦❀ ❝♦♠♦ ✉♠ ✐♥t❡r✈❛❧♦❀ ❝♦♠♦ ✉♠❛ ✐♥❢♦r♠❛çã♦❀ ❝♦♠♦ ✉♠❛ r❡♣r❡s❡♥t❛çã♦ ♦✉ ❝♦♠♦ ✉♠ ♣❛r ♦r❞❡♥❛❞♦✳ ➱ ♣♦ssí✈❡❧ ❞❡✜♥✐r ❞✐✈❡rs❛s ♦r❞❡♥s ♥❛t✉r❛✐s s♦❜r❡ ♦ ❝♦♥❥✉♥t♦ ■✭❘✮ r❡s♣❡✐t❛♥❞♦ ✉♠❛ s❡♠â♥t✐❝❛ s♦❜r❡ ■✭❘✮ ✳
❉❡✜♥✐çã♦ ✸✳✶✵ ✭❖r❞❡♠ ❞❡ ✐♥❝❧✉sã♦✱ ✭▼❖❖❘❊✱ ✶✾✼✾✮✮✳ ❙❡❥❛♠ ♦s ✐♥t❡r✈❛❧♦s ❳ ❡ ❨ ❛ ♦r❞❡♠ ❞❛ ■♥❝❧✉sã♦ ❞❡✜♥❡ q✉❡ ❳ ✒ ❨ ✱ ② ✔ ① ❡ ① ✔ ②✳
❉❡✜♥✐çã♦ ✸✳✶✶ ✭◗✉❛s❡✲♦r❞❡♠ ❞❡ ▼♦♦r❡✱ ✭▼❖❖❘❊✱ ✶✾✼✾✮✮✳ ❙❡❥❛♠ ♦s ✐♥t❡r✈❛❧♦s ❳ ❡ ❨ ❛ ♦r❞❡♠ ❞❛ ▼♦♦r❡ ❞✐③ q✉❡ ❳ ❁▼ ❨ ✱ ✽① ✷ ❳ ❡ ✽② ✷ ❨❀① ❁ ② ✱ ① ❁ ②✳
❖❜s❡r✈❡ q✉❡ ❛ q✉❛s❡✲♦r❞❡♠✶ ❞❡ ▼♦♦r❡ ♥ã♦ é ✉♠❛ ♦r❞❡♠✷✱ ♣♦✐s ♥ã♦ s❛t✐s❢❛③ ❛ r❡✢❡✲
①✐✈✐❞❛❞❡✳
✶➱ ✉♠❛ r❡❧❛çã♦ q✉❡ ♣♦ss✉✐ ❛s ♣r♦♣r✐❡❞❛❞❡s✿ ❛♥t✐✲r❡✢❡①✐✈❛ ❡ tr❛♥s✐t✐✈❛
✸✳✹ ❚♦♣♦❧♦❣✐❛ ♥♦ ■✭❘✮ ✷✺
❉❡✜♥✐çã♦ ✸✳✶✷ ✭❖r❞❡♠ ❞❡ ❑✉❧✐s❝❤✲▼✐r❛♥❦❡r✱ ✭❑❯▲■❙❈❍❀ ▼■❘❆◆❑❊❘✱ ✶✾✽✻✮✮✳ ❙❡❥❛♠ ♦s ✐♥t❡r✈❛❧♦s ❳ ❡ ❨ ❛ ♦r❞❡♠ ❞❡ ❑✉❧✐s❝❤✲▼✐r❛♥❦❡r ❞✐③ q✉❡ ❳ ✔❑❨ ✱ ① ✔ ② ❡ ① ✔ ②✳
Pr♦♣♦s✐çã♦ ✸✳✷ ✭■♥❝❧✉sã♦ ▼♦♥♦tô♥✐❝❛✱ ✭▼❖❖❘❊✱ ✶✾✻✻✮✮✳ ❙❡❥❛♠ ❳❀❨❀❩❀❲ ✐♥t❡r✈❛✲ ❧♦s✱ t❛✐s q✉❡ ❳ ✒ ❩ ❡ ❨ ✒ ❲ ✳ ❊♥tã♦ ❛s s❡❣✉✐♥t❡s r❡❧❛çõ❡s sã♦ ✈á❧✐❞❛s✿
❼ ❳ ✰ ❨ ✒ ❲ ✰ ❩
❼ ❳ ✒ ❩
❼ ❳ ❨ ✒ ❩ ❲
❼ ❳ ✁ ❨ ✒ ❩ ✁ ❲
❼ ❳✶ ✒ ❩✶ ❞❡s❞❡ q✉❡ ✵ ❂✷ ❩❀❳
❼ ❳❨ ✒ ❲❩ ❞❡s❞❡ q✉❡ ✵ ❂✷ ❲❀❨
❉❡♠♦♥str❛çã♦✳ ❆ ♣r♦✈❛ é ✉♠❛ ❝♦♥s❡q✉ê♥❝✐❛ ❞✐r❡t❛ ❞❛s ♦♣❡r❛çõ❡s ❛r✐t♠ét✐❝❛s✳
❉❡✜♥✐çã♦ ✸✳✶✸ ✭❖r❞❡♠ ❞❛ ■♥❢♦r♠❛çã♦✱ ✭❆❈■❖▲❨✱ ✶✾✾✶✮✮✳ ❙❡❥❛♠ ♦s ✐♥t❡r✈❛❧♦s ❳ ❡ ❨ ❛ ♦r❞❡♠ ❞❛ ✐♥❢♦r♠❛çã♦ ❞✐③ q✉❡ ❳ ✈ ❨ ✱ ❳ ✒ ❨ ✱ ① ✔ ① ❡ ② ✔ ②✳
✸✳✹ ❚♦♣♦❧♦❣✐❛ ♥♦ ■✭❘✮
❆♣r❡s❡♥t❛♠♦s ♥❡ss❛ s❡çã♦✱ ❛❧❣✉♠❛s ♣r♦♣r✐❡❞❛❞❡s ❧✐❣❛❞❛s ❛♦s ❡st✉❞♦s ❞❡ ❆♥á❧✐s❡ ■♥t❡r✈❛❧❛r ❝♦♠♦ ❛ ♥♦çã♦ ❞❡ ❝♦♥❥✉♥t♦✱ ♣❛rt✐çã♦✱ ♠étr✐❝❛ ❡ ❡s♣❛ç♦ ♠étr✐❝♦✳
❉❡✜♥✐çã♦ ✸✳✶✹✳ ❯♠❛ ♣❛rt✐çã♦ ❞❡ ❈ ✷ ■✭❘✮ é ✉♠❛ s❡q✉ê♥❝✐❛ P ❂ ❢❝ ❂ ①✵❀①✶❀①✷❀✿✿✿❀①♥❂❝❣✳
❚❛❧ q✉❡ ♣❛r❛ ❝❛❞❛ ✐ ❂ ✵❀✶❀✿✿✿❀♥ ✶✱ ①✐❁ ①✐✰✶✳ P✭❈✮ é ♦ ❝♦♥❥✉♥t♦ ❞❛s ♣❛rt✐çõ❡s ❞❡
❈
❉❡✜♥✐çã♦ ✸✳✶✺✳ ❆ ♣❛rt✐çã♦ P✶ ❞❡ ❈ é ♠❛✐s ✜♥❛ q✉❡ ❛ ♣❛rt✐çã♦ P✷ ❞❡ ❈✱ ❞❡♥♦t❛❞❛
♣♦r P✶✹ P✷✱ s❡ P✷✒ P✶
Pr♦♣♦s✐çã♦ ✸✳✸✳ ❙❡❥❛ ❈ ✷ ■✭❘✮✳ ❤P✭❈✮❀✹✐✱ é ✉♠ r❡t✐❝✉❧❛❞♦ ❝♦♠ ♠❛✐♦r ❡❧❡♠❡♥t♦
✭❢❝❀❝❣✮✳
✸✳✹ ❚♦♣♦❧♦❣✐❛ ♥♦ ■✭❘✮ ✷✻
❉❡✜♥✐çã♦ ✸✳✶✻✳ ❙❡❥❛♠ ❆ ❡ ❇ ❞♦✐s ✐♥t❡r✈❛❧♦s r❡❛✐s ❞✐st✐♥t♦s t❛❧ q✉❡ ❆ ✔❦ ❇✳ ❉❡✜✲
♥✐♠♦s
■❬❆❀❇❪❂ ❢❳ ✷ ■✭❘✮❥ ❆ ✔❦ ❳ ✔❦❇❣ ✭✸✳✷✮
❉❡✜♥✐çã♦ ✸✳✶✼ ✭❉✐stâ♥❝✐❛ ❡♥tr❡ ❞♦✐s ✐♥t❡r✈❛❧♦s✮✳ ❙❡❥❛♠ ❳❀❨ ✷ ■✭❘✮✳ ❆ ❞✐stâ♥❝✐❛ ❡♥tr❡ ❳ ❡ ❨ ✱ ❞❡♥♦t❛❞♦ ♣♦r ❞▼✭❳❀❨ ✮✱ é ❞❛❞❛ ♣❡❧♦ ♥ú♠❡r♦ r❡❛❧ ♥ã♦ ♥❡❣❛t✐✈♦
❞▼✭❳❀❨ ✮ ❂ ♠❛①❢❥❜ ❛❥❀❥❜ ❛❥❣
Pr♦♣♦s✐çã♦ ✸✳✹✳ ❙❡❥❛ ■ ✉♠ s✉❜❝♦♥❥✉♥t♦ ♥ã♦ ✈❛③✐♦ ❞❡ ■✭❘✮✳ ❆ ❢✉♥çã♦ ❞▼ ✿ ■ ✂■ ✦
❘✰ é ✉♠❛ ♠étr✐❝❛ ❞❡ ■ ♣♦✐s s❛t✐s❢❛③ ❛s s❡❣✉✐♥t❡s ♣r♦♣r✐❡❞❛❞❡s✿
❼ ❞▼✭❳❀❨ ✮ ❂ ✵ ss❡ ❳ ❂ ❨
❼ ❞▼✭❳❀❨ ✮ ❂ ❞▼✭❨❀❳✮ ✽ ❳❀❨ ✷ ■
❼ ❞▼✭❳❀❨ ✮ ✔ ❞▼✭❳❀❩✮ ✰ ❞▼✭❩❀❨ ✮ ✽ ❩❀❳❀❨ ✷ ■
❉❡♠♦♥str❛çã♦✳ ❱❡❥❛ ❡♠ ✭▼❖❖❘❊✱ ✶✾✼✾✮
❈♦♥t✉❞♦✱ ✉♠❛ ✈❡③ q✉❡ ■ é ♥ã♦ ✈❛③✐♦ ❡ ❛ ❢✉♥çã♦ ❞▼ ❡stá ❞❡✜♥✐❞❛ s♦❜r❡ ■✱ ❡♥tã♦ ♦
♣❛r ✭■❀❞▼✮ é ✉♠ ❡s♣❛ç♦ ♠étr✐❝♦✳
❯♠❛ ✈❡③ q✉❡ ❆ ✻❂ ❇✱ ❡♥tã♦ ❛ ❁ ❜ ♦✉ ❛ ❁ ❜✳ ❉❡ss❛ ♠❛♥❡✐r❛✱ s❡♠ ♣❡r❞❛ ❞❡ ❣❡♥❡r❛❧✐❞❛❞❡✱ ✈❛♠♦s s✉♣♦r q✉❡ ❛ ❁ ❜ ✭♥♦ ♦✉tr♦ ❝❛s♦ é ❞✉❛❧✮✳
❉❛❞♦ ♦ ❡s♣❛ç♦ ♠étr✐❝♦ ✭■❀❞▼✮ ❡ ✉♠ s✉❜❝♦♥❥✉♥t♦ ❍ ✒ ■✱ ❞❡✜♥✐♠♦s ♦ ❞✐❛♠❡tr♦ ❞❡
❍✱ ❞❡♥♦t❛❞♦ ♣♦r ❞✐❛♠✭❍✮✱ ❝♦♠♦
❞✐❛♠✭❍✮ ❂●❢❞▼✭❳❀❨ ✮ ❥ ❳❀❨ ✷ ❍❣❀ ✭✸✳✸✮
♦♥❞❡ ❋ ❞❡♥♦t❛ ♦ s✉♣r❡♠♦ ❝♦♠ r❡s♣❡✐t♦ à ♦r❞❡♠ ✉s✉❛❧ ❞❛ r❡t❛ ❡ ❞▼ é ❛ ❞✐stâ♥❝✐❛ ❞❡
▼♦♦r❡✳ ❉❡✈❡♠♦s ♦❜s❡r✈❛r q✉❡ ❞✐❛♠✭❍✮ ♣♦❞❡ s❡r ✐♥✜♥✐t♦ ❡♠ ❛❧❣✉♥s ❝❛s♦s✳
❉❡✜♥✐çã♦ ✸✳✶✽✳ ❯♠ s✉❜❝♦♥❥✉♥t♦ ❳ ❞❡ ✉♠ ❡s♣❛ç♦ ♠étr✐❝♦ ✭■❀❞▼✮ é ❧✐♠✐t❛❞♦ s❡
❞✐❛♠✭❳✮ ✷ ❘✄ ✰ ✳
✸✳✹ ❚♦♣♦❧♦❣✐❛ ♥♦ ■✭❘✮ ✷✼
▲❡♠❛ ✸✳✶ ✭▲❡♠❛ ❞❛ ❈♦♠♣❧❡t✉❞❡✮✳ ❙❡❥❛ ❍ ✉♠ s✉❜❝♦♥❥✉♥t♦ ❧✐♠✐t❛❞♦ ❞❡ ■✭❘✮✳ ❉❡✜✲ ♥✐♠♦s ❍ ❂ ❢❝ ❥ ❈ ✷ ❍❣ ❡ ❍ ❂ ❢❝ ❥ ❈ ✷ ❍❣✳ ❊♥tã♦✱ ♦ s✉♣r❡♠♦ ❡ ♦ í♥✜♠♦ ❞❡ ❍ ❝♦♠ r❡s♣❡✐t♦ à ♦r❞❡♠ ❞❡ ❑✉❧✐s❝❤✲▼✐r❛♥❦❡r✱ r❡♣r❡s❡♥t❛❞♦ ♣♦r ❋❍ ❡ d❍✱ sã♦ ♦s ✐♥t❡r✈❛❧♦s ❬❋❍❀❋❍❪ ❡ ❬d❍❀d❍❪✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳
❉❡♠♦♥str❛çã♦✳ ✈❡r ✭❇❊❉❘❊●❆▲❀ ❇❊❉❘❊●❆▲✱ ✷✵✶✵✮
▲❡♠❛ ✸✳✷✳ ❙❡❥❛♠ ■ ❡ ❏ s✉❜❝♦♥❥✉♥t♦s ❧✐♠✐t❛❞♦s ❞❡ ■✭❘✮ ❡
■ ✰ ❏ ❂ ❢ ❳ ✰ ❨ ❥ ❳ ✷ ■❀ ❨ ✷ ❏ ❣✿
❊♥tã♦✱
l
✭■ ✰ ❏ ✮ ❂l■ ✰l❏ ❡ ●✭■ ✰ ❏ ✮ ❂●■ ✰●❏
❉❡♠♦♥str❛çã♦✳ ✈❡❥❛ ✭❇❊❉❘❊●❆▲❀ ❇❊❉❘❊●❆▲✱ ✷✵✶✵✮
❉❡✜♥✐çã♦ ✸✳✶✾✳ ❙❡❥❛ ❳ ✷ ■✭❘✮✳ ❖ ♠ó❞✉❧♦ ❞❡ ❳ é ✉♠ ♥ú♠❡r♦ r❡❛❧ ♥ã♦ ♥❡❣❛t✐✈♦ ❞❛❞♦ ♣♦r✿
❥❳❥ ❂ ♠❛①❢❥①❥❀❥①❥❣ ✕ ✵ ✭✸✳✹✮
●❡♦♠❡tr✐❝❛♠❡♥t❡✱ ♦ ♠ó❞✉❧♦ ❞♦ ✐♥t❡r✈❛❧♦ ❝♦rr❡s♣♦♥❞❡ à ♠❛✐♦r ❞✐stâ♥❝✐❛ ❞♦ ❝❡♥tr♦ ❞❛ r❡t❛ ❞♦s r❡❛✐s ✭ ♣♦♥t♦ ✵✮ ❛té ✉♠ ❞♦s ❡①tr❡♠♦s✳
❚❡♦r❡♠❛ ✸✳✶✳ ❙❡❥❛♠ ❳❀❨ ✷ ■✭❘✮✳ ❆s s❡❣✉✐♥t❡s ♣r♦♣r✐❡❞❛❞❡s s❡ ✈❡r✐✜❝❛♠✿
✶✳ ❥❳❥ ❂ ✵ ✱ ❳ ❂ ❬✵❀✵❪
✷✳ ❥❳ ✰ ❨ ❥ ✔ ❥❳❥ ✰ ❥❨ ❥
✸✳ ❥❳ ✁ ❨ ❥ ❂ ❥❳❥ ✁ ❥❨ ❥
❉❡♠♦♥str❛çã♦✳ ❱❡❥❛ ❡♠ ✭❙❆◆❚❖❙✱ ✷✵✵✶✮
❉❡✜♥✐çã♦ ✸✳✷✵ ✭❉❡✜♥✐çã♦ ❞❡ ❋✉♥çã♦ ■♥t❡r✈❛❧❛r✮✳ ❯♠❛ ❢✉♥çã♦ ❋ é ❝❤❛♠❛❞❛ ❞❡ ❢✉♥✲ çã♦ ✐♥t❡r✈❛❧❛r s❡ ♦ s❡✉ ❞♦♠í♥✐♦ ❡ ♦ ❝♦♥tr❛❞♦♠í♥✐♦ sã♦ s✉❜❝♦♥❥✉♥t♦s ❞❡ ■✭❘✮✳
✸✳✺ ■♥t❡❣r❛çã♦ ■♥t❡r✈❛❧❛r ✷✽
❉❡✜♥✐çã♦ ✸✳✷✷✳ ❯♠❛ ❢✉♥çã♦ ✐♥t❡r✈❛❧❛r ❋ é ❞✐t❛ ❧✐♠✐t❛❞❛ s❡✱ ❛ ✐♠❛❣❡♠ ❞❡ ❋ ❢♦r ❧✐♠✐t❛❞❛✱ ♦✉ s❡❥❛✱ ❡stá ❝♦♥t✐❞❛ ❡♠ ■❬❆❀❇❪ ♣❛r❛ ❛❧❣✉♠ ❆❀❇ ✷ ■✭❘✮✳ ◆❡st❡ ❝❛s♦✱
❆ ✔❦❋ ✭❳✮ ✔❦❇✱ ♣❛r❛ t♦❞♦ ❳ ♣❡rt❡♥❝❡♥t❡ ❛♦ ❞♦♠í♥✐♦ ❞❡ ❋ ✳
❈♦♠♦ ♥♦t❛çã♦✱ s❡♥❞♦ ❛ ❢✉♥çã♦ ❋ ✿ ■ ✦ ■✭❘✮✱ ❞❡✜♥✐♠♦s ❛s ❢✉♥çõ❡s ❋ ✿ ■ ✦ ❘ ❡ ❋ ✿ ■ ✦ ❘ ♣♦r ❋ ✭❳✮ ❂ ❋ ✭❳✮ ❡ ❋ ✭❳✮ ❂ ❋ ✭❳✮✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳
❈♦r♦❧ár✐♦ ✸✳✶✳ ❙❡❥❛ ■ ✚ ■✭❘✮ ❡ ❋ ✿ ■ ✦ ■✭❘✮ ✉♠❛ ❢✉♥çã♦ ✐♥t❡r✈❛❧❛r ❧✐♠✐t❛❞❛✳ ❊♥tã♦ ♦ s✉❜❝♦♥❥✉♥t♦ ❋ ✭■✮ ❂ ❢❋ ✭❳✮ ✷ ■✭❘✮ ❥ ❳ ✷ ■❣ t❡♠ s✉♣r❡♠♦ ❡ ✐♥✜♠♦ ❝♦♠ r❡s♣❡✐t♦ à ♦r❞❡♠ ❞❡ ❑✉❧✐s❝❤✲▼✐r❛♥❦❡r✳ ❉❡ ❢❛t♦✿
●
❋ ✭■✮ ❂ ❬●❋ ✭■✮❀●❋ ✭■✮❪
l
❋ ✭■✮ ❂ ❬l❋ ✭■✮❀l❋ ✭■✮❪
❉❡♠♦♥str❛çã♦✳ ✈❡❥❛ ❡♠ ✭❇❊❉❘❊●❆▲❀ ❇❊❉❘❊●❆▲✱ ✷✵✶✵✮
✸✳✺ ■♥t❡❣r❛çã♦ ■♥t❡r✈❛❧❛r
✸✳✺✳✶ ■♥t❡❣r❛❧ ❞❡ ▼♦♦r❡ ❡ ❨❛♥❣
❉❡✜♥✐çã♦ ✸✳✷✸✳ ❙❡❥❛ ❆ ✉♠ ✐♥t❡r✈❛❧♦ ❡ ❋ ❢✉♥çã♦ ✐♥t❡r✈❛❧❛r ❝♦♥tí♥✉❛✸ ❡ ✉♠❛ ✐♥✲
❝❧✉sã♦ ♠♦♥♦tô♥✐❝❛ ❝♦♠ r❡s♣❡✐t♦ ❛ ❞▼✳ ❆ ❙♦♠❛ ❞❡ ❘✐❡♠❛♥♥ ❞❛ ❢✉♥çã♦ ❋ ♣❛r❛
✉♠❛ ♣❛rt✐çã♦ P ❞❡ ❆ é ❞❡✜♥✐❞❛ ❝♦♠♦✿
❳
✭❋❀P✮ ❂♥ ✶❳
❦❂✵
❋ ✭❬①❦❀①❦ ✶❪✮❞✭①❦❀①❦ ✶✮
❖♥❞❡ ❞ é ❛ ♠étr✐❝❛ ✉s✉❛❧ s♦❜r❡ ♥ú♠❡r♦s r❡❛✐s ❞✭①❀②✮ ❂ ❥② ①❥✳ ❆ ✐♥t❡❣r❛❧ ❞❡ ▼♦♦r❡ ❡ ❨❛♥❣ ♥♦ ✐♥t❡r✈❛❧♦ ❆ é ❞❡✜♥✐❞❛ ❝♦♠♦✿
❩
❆❋ ✭❳✮❞❳ ❂
❭
P✷P✭❆✮
❳
✭❋❀P✮
❚❡♦r❡♠❛ ✸✳✷ ✭❚❡♦r❡♠❛ ❞❡ ❈❛r❛❝t❡r✐③❛çã♦✮✳ ❙❡❥❛ ❆ ✉♠ ✐♥t❡r✈❛❧♦✱ ❋ ✉♠❛ ❢✉♥çã♦ ✐♥t❡r✈❛❧❛r ❝♦♥tí♥✉❛ ❡ ✐♥❝❧✉sã♦ ♠♦♥♦tô♥✐❝❛✳ ❊♥tã♦
❩
❆❋ ✭❳✮❞❳ ❂
✧❩ ❛
❛ ❢❧✭①✮❞①❀
❩ ❛
❛ ❢r✭①✮❞①
★
✸✳✺ ■♥t❡❣r❛çã♦ ■♥t❡r✈❛❧❛r ✷✾
♦♥❞❡ ❢❧✭①✮ ❂ ✙✶✭❋ ❬①❀①❪✮ ❡ ❢r✭①✮ ❂ ✙✷✭❋ ❬①❀①❪✮
❉❡♠♦♥str❛çã♦✳ ❱❡❥❛ ❡♠ ✭▼❖❖❘❊❀ ❙❚❘❖❚❍❊❘❀ ❨❆◆●✱ ✶✾✻✵✮
✸✳✺✳✷ ■♥t❡❣r❛❧ ❞❡ ❇❡❞r❡❣❛❧✲❇❡❞r❡❣❛❧
❉❡✜♥✐çã♦ ✸✳✷✹✳ ❙❡❥❛ ❋ ✿ ■❬❆❀❇❪ ✦ ■✭❘✮ ✉♠❛ ❢✉♥çã♦ ✐♥t❡r✈❛❧❛r ❝♦♥tí♥✉❛✳ ❉❛❞❛ ✉♠❛
♣❛rt✐çã♦ P ❞❡ ■❬❆❀❇❪✳ ◆ós ❞❡✜♥✐♠♦s ♦s s❡❣✉✐♥t❡s ❙♦♠❛tór✐♦s ❞❡ ❘✐❡♠❛♥♥ ❞❡ ❋
❝♦♠ r❡s♣❡✐t♦ ❛ P
❼ ❙♦♠❛ ❞❡ ❘✐❡♠❛♥♥ ■♥❢❡r✐♦r
✛✭❋❀P✮ ❂❳♥
❦❂✶
l
❋ ✭■❬❳❦ ✶❀❳❦❪✮❞▼✭❳❦ ✶❀❳❦✮
❼ ❙♦♠❛ ❞❡ ❘✐❡♠❛♥♥ ❙✉♣❡r✐♦r
❳
✭❋❀P✮ ❂ ❳♥
❦❂✶
●
❋ ✭■❬❳❦ ✶❀❳❦❪✮❞▼✭❳❦ ✶❀❳❦✮
❖♥❞❡ ❋ ✭■❬❳❦ ✶❀❳❦❪✮ ❂ ❢❋ ✭❳✮ ❥ ❳ ✷ ■❬❳❦ ✶❀❳❦❪❣
❉❡✜♥✐çã♦ ✸✳✷✺✳ ❙❡❥❛ ❋ ✿ ■❬❆❀❇❪ ✦ ■✭❘✮ ✉♠❛ ❢✉♥çã♦ ✐♥t❡r✈❛❧❛r ❝♦♥tí♥✉❛✳ ◆ós ❞❡✜♥✐✲
♠♦s ❝♦♠♦ ❛ ✐♥t❡❣r❛❧ ✐♥❢❡r✐♦r ❞❛ ❢✉♥çã♦ ❋ ❞❡ ❆ ❛té ❇✱ ❞❡♥♦t❛❞❛ ❝♦♠♦❘❆❇❋ ✭❳✮❞❳✱
♣♦r ❩
❇
❆ ❋ ✭❳✮❞❳ ❂
●
P✷P❬❆❀❇❪
✛✭❋❀P✮
❡ ❛ ❞❡✜♥✐çã♦ ❞❛ ✐♥t❡❣r❛❧ s✉♣❡r✐♦r ❞❛ ❢✉♥çã♦ ❋ ❞❡ ❆ ❛té ❇✱ ❞❡♥♦t❛❞❛ ❝♦♠♦
❘❇
❆❋ ✭❳✮❞❳✱ ❝♦♠♦ s❡♥❞♦✿
❩ ❇
❆ ❋ ✭❳✮❞❳ ❂
l
P✷P❬❆❀❇❪
❳
✭❋❀P✮
❚❡♦r❡♠❛ ✸✳✸ ✭❚❡♦r❡♠❛ ❞❡ ❈❛r❛❝t❡r✐③❛çã♦✮✳ ❙❡❥❛ ❋ ✿ ■❬❆❀❇❪ ✦ ■✭❘✮ ✉♠❛ ❢✉♥çã♦ ✐♥✲
t❡r✈❛❧❛r ❝♦♥tí♥✉❛✱ ❡♥tã♦ ❋ é ✉♠❛ ❢✉♥çã♦ ✐♥t❡❣rá✈❡❧ ❡
❩ ❇
❆ ❋ ✭❳✮❞❳ ❂
✧❩ ❜
❛ ❋❧✭①✮❞①❀
❩ ❜
❛ ❋r✭①✮❞①
★
❞▼✭❆❀❇✮
❜ ❛
✸✵
✹ ■♥t❡❣r❛❧ ❞❡ ▲✐♥❤❛ ■♥t❡r✈❛❧❛r
◆❡ss❛ s❡çã♦ ❛♣r❡s❡♥t❛r❡♠♦s ❛ ♥♦çã♦ ❞❡ ✐♥t❡❣r❛❧ ❞❡ ❧✐♥❤❛ ✐♥t❡r✈❛❧❛r✱ ❜❡♠ ❝♦♠♦ ❛s ❞❡✜♥✐çõ❡s✱ t❡♦r❡♠❛s✱ ❝♦r♦❧ár✐♦s✱ ♣r♦♣♦s✐çõ❡s ❡ ❧❡♠❛s ♥❡❝❡ssár✐♦s ♣❛r❛ ❛ ❢✉♥❞❛♠❡♥t❛çã♦✳
❉❡✜♥✐çã♦ ✹✳✶✳ ❯♠ ❝❛♠✐♥❤♦ ❡♠ ■✭❘✮ é ✉♠❛ ❛♣❧✐❝❛çã♦ ✕ ✿ ■ ✦ ■✭❘✮✱ ❝✉❥♦ ❞♦♠í♥✐♦ é ✉♠ ✐♥t❡r✈❛❧♦ ■ ❂ ❬❝❀❞❪ ✒ ❘✳
❈♦♠♦ ♥♦t❛çã♦✱ s❡♥❞♦ ❛ ❢✉♥çã♦ ✕ ✿ ■ ✦ ■✭❘✮✱ ❞❡✜♥✐♠♦s ❛s ❢✉♥çõ❡s ✕ ✿ ■ ✦ ❘ ❡ ✕ ✿ ■ ✦ ❘ ♣♦r ✕✭①✮ ❂ ✕✭①✮ ❡ ✕✭①✮ ❂ ✕✭①✮✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ❆ss✐♠ ♣❛r❛ ❝❛❞❛ t ✷ ■ t❡♠♦s q✉❡ ✕✭t✮ ❂ ❬✕✭t✮❀✕✭t✮❪✳
❉❡✜♥✐çã♦ ✹✳✷✳ ❖ ❝❛♠✐♥❤♦ ✕ é ❝♦♥tí♥✉♦ ✭r❡s♣✳ ❞✐❢❡r❡♥❝✐á✈❡❧✮ ♥♦ ♣♦♥t♦ ❛ ✷ ■ s❡ ❝❛❞❛ ✉♠❛ ❞❛s ❢✉♥çõ❡s ✕✭t✮ ❡ ✕✭t✮ ❢♦r❡♠ ❝♦♥tí♥✉❛s ✭r❡s♣✳ ❞✐❢❡r❡♥❝✐á✈❡✐s✮ ❡♠ ❛✿ ❙❡ ✕ ❢♦r ❞✐❢❡r❡♥❝✐á✈❡❧ ❡♠ ❛ ❞❡✜♥❡✲s❡ ❛ ❞❡r✐✈❛❞❛ ❞♦ ❝❛♠✐♥❤♦ ✕ ♥♦ ♣♦♥t♦ ❛ ♣♦r ✕✵✭❛✮ ❂ ✭✕✵✭❛✮❀✕✵✭❛✮✮ ✷ ❘✷✿ ❆ ♥♦r♠❛ ❦ ✕✵✭❛✮ ❦❂ ▼❛①❢❥ ✕✵✭❛✮ ❥❀❥ ✕✵✭❛✮ ❥❣ ❝❤❛♠❛✲s❡ ✈❛❧♦r ❛❜s♦❧✉t♦ ❞❛ ✈❛r✐❛çã♦ ❞❡ ✕ ❡♠ ❛✿
❉❡✜♥✐çã♦ ✹✳✸✳ ❙❡❥❛ ❋ ✿ ■❬❆❀❇❪ ✦ ■✭❘✮ ✉♠❛ ❢✉♥çã♦ ✐♥t❡r✈❛❧❛r ❧✐♠✐t❛❞❛ ❡ ✕ ✿ ❬❝❀❞❪ ✦
■❬❆❀❇❪ ✉♠ ❝❛♠✐♥❤♦ ❞❡ ❝❧❛ss❡ ❈✶✳ ❉❛❞❛ ❛ ♣❛rt✐çã♦ P ❞❡ ❬❝❀❞❪✱ ❞❡✜♥✐♠♦s ❛s s❡❣✉✐♥t❡s
❙♦♠❛s ❞❡ ❘✐❡♠❛♥♥ ❞❡ ❋ ❝♦♠ r❡s♣❡✐t♦ ❞❡ ✕ ❡ P✿
❙♦♠❛tór✐♦ ✐♥❢❡r✐♦r ❞❡ ❘✐❡♠❛♥♥
✛✭❋❀✕❀P✮ ❂ ❳♥
❦❂✶
l
❋ ✭■❬✕✭①❦ ✶✮❀✕✭①❦✮❪✮❞▼✭✕✭①❦ ✶✮❀✕✭①❦✮✮
❙♦♠❛tór✐♦ s✉♣❡r✐♦r ❞❡ ❘✐❡♠❛♥♥
❳
✭❋❀✕❀P✮ ❂ ❳♥
❦❂✶
●
❋ ✭■❬✕✭①❦ ✶✮❀✕✭①❦✮❪✮❞▼✭✕✭①❦ ✶✮❀✕✭①❦✮✮
✹ ■♥t❡❣r❛❧ ❞❡ ▲✐♥❤❛ ■♥t❡r✈❛❧❛r ✸✶
▲❡♠❛ ✹✳✶✳ ❙❡❥❛ ❋ ✿ ■❬❆❀❇❪ ✦ ■✭❘✮ ✉♠❛ ❢✉♥çã♦ ❧✐♠✐t❛❞❛ ❡ P ✉♠❛ ♣❛rt✐çã♦ ❞❡ ■ ❡
✕ ✿ ❬❝❀❞❪ ✦ ■❬❆❀❇❪ ✉♠ ❝❛♠✐♥❤♦ ❞❡ ❝❧❛ss❡ ❈✶✱ ❡♥tã♦✳
✛✭❋❀✕❀P✮ ✔❳✭❋❀✕❀P✮
❉❡♠♦♥str❛çã♦✳ P❛r❛ t♦❞♦ ❦ ❂ ✵❀✶❀✷❀✿✿✿❀♥ ✶✱l❋ ✭■❬✕✭①✭✐ ✶✮✮❀✕✭①✐✮❪✮ ✔
●
❋ ✭■❬✕✭①✭✐ ✶✮✮❀✕✭①✐✮❪✮
❡ ❞▼✭✕✭✭①✐ ✶✮❀✕✭②✮✮ ❃ ✵✳ ❊♥tã♦ ♣♦❞❡♠♦s ❡s❝r❡✈❡r✳
l
❋ ✭■❬✕✭①✭✐ ✶✮✮❀✕✭①✐✮❪✮ ✔
●
❋ ✭■❬✕✭①✭✐ ✶✮✮❀✕✭①✐✮❪✮
✛✭❋❀✕❀P✮ ✔ ❳✭❋❀✕❀P✮
Pr♦♣♦s✐çã♦ ✹✳✶✳ ❙❡❥❛ ✕ ✿ ❬❝❀❞❪ ✦ ■❬❆❀❇❪ ✉♠ ❝❛♠✐♥❤♦ ❞❡ ❝❧❛ss❡ ❈✶✱ ❋ ✿ ■❬❆❀❇❪ ✦ ■✭❘✮
✉♠❛ ❢✉♥çã♦ ❧✐♠✐t❛❞❛ ❡ s❡❥❛♠ P✵ ❡ P ♣❛rt✐çõ❡s ❞♦ ✐♥t❡r✈❛❧♦ ■ ❂ ❬❝❀❞❪✳ ❙❡ P✵✹ P
❡♥tã♦
✛✭❋❀✕❀P✮ ✔ ✛✭❋❀✕❀P✵✮ ✔❳✭❋❀✕❀P✵✮ ✔❳✭❋❀✕❀P✮✿
❉❡♠♦♥str❛çã♦✳ ❚♦♠❡♠♦s ✉♠❛ ♣❛rt✐çã♦ P ♦♥❞❡ P ❂ ❢❝ ❂ ①✵❀✿✿✿❀①♥❂ ❞❣ ❡ P✵❞❡ ♠❛♥❡✐r❛
q✉❡ P✵❂ ❢❛ ❂ ①✵❀✿✿✿②✿✿✿❀①♥❂ ❜❣ ❙❛❜❡♥❞♦ q✉❡ ❛ ❞✐stâ♥❝✐❛ é✿
❞▼✭✕✭①✐ ✶✮❀✕✭②✮✮ ✰ ❞▼✭✕✭②✮❀✕✭①✐✮✮ ❂ ❞▼✭✕✭①✐ ✶✮❀✕✭①✐✮✮
❚❛♠❜é♠ t❡♠♦s q✉❡✿
l
❋ ✭■❬✕✭①✭✐ ✶✮✮❀✕✭①✐✮❪✮ ✔l❋ ✭■❬✕✭①✭✐ ✶✮✮❀✕✭②✮✮✮
❡ t❛♠❜é♠
l
❋ ✭■❬✕✭①✭✐ ✶✮✮❀✕✭①✐✮✮ ✔
l
