Repositório UFAL: Teorema de Decomposição de Cheeger-Gromoll.

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❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❆❧❛❣♦❛s ■♥st✐t✉t♦ ❞❡ ▼❛t❡♠át✐❝❛

❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❆❧❛❣♦❛s ■♥st✐t✉t♦ ❞❡ ▼❛t❡♠át✐❝❛Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ▼❛t❡♠át✐❝❛ ❉✐ss❡rt❛çã♦ ❞❡ ▼❡str❛❞♦ ❚❡♦r❡♠❛ ❞❡ ❉❡❝♦♠♣♦s✐çã♦ ❞❡ ❈❤❡❡❣❡r✲●r♦♠♦❧❧▼❛r❝✐✉s P❡trú❝✐♦ ❞❡ ❆❧♠❡✐❞❛ ❈❛✈❛❧❝❛♥t❡ ▼❛❝❡✐ó✱ ❇r❛s✐❧ ✶✹ ❞❡ ❉❡③❡♠❜r♦ ✷✵✵✼ ❆♦s ♠❡✉s ♣❛✐s ❋r❛♥❝✐s❝♦ P❡trú❝✐♦ ❈❛✈❛❧❝❛♥t❡❡ ▼❛r✐❛ ❞❛s ◆❡✈❡s ❞❡ ❆❧♠❡✐❞❛ ❈❛✈❛❧❝❛♥t❡✳ ❖ ❝❛♠✐♥❤♦ ❞♦ ❛♠♦r ♥✉♥❝❛ é s✉❛✈❡✱♠❛s ❡❧❡ ♣♦❞❡ s❡r ❝♦♥tí♥✉♦✳✳✳ ❆❣r❛❞❡❝✐♠❡♥t♦s ❆❣r❛❞❡ç♦ ❛♦ ♣r♦❢❡ss♦r ❍✐❧ár✐♦ ❆❧❡♥❝❛r✱ ♠❡✉ ♦r✐❡♥t❛❞♦r✱ ♣♦r ❡ss❡s ❛♥♦s ❞❡♦r✐❡♥t❛çã♦ ❛❝❛❞ê♠✐❝❛ ❡ ♦♣♦rt✉♥✐❞❛❞❡s ❞❛❞❛s✳ ❆♦ ♣r♦❢❡ss♦r ❆❞á♥ ❈♦r❝❤♦✱ ♣❡❧❛ ♦r✐❡♥t❛çã♦ ❡ ❛♠✐③❛❞❡ ❢♦r♥❡❝✐❞❛s ❞❡ s✉❛♣❛rt❡ ❞✉r❛♥t❡ ♦s ❛♥♦s ❞❡ ❣r❛❞✉❛çã♦ ❡ ♠❡str❛❞♦✳ ❆♦ ♠❡✉ ✐r♠ã♦ ❡ ♣r♦❢❡ss♦r ▼❛r❝♦s P❡trú❝✐♦✱ ♣❡❧♦ ❝✉rs♦ ❞❡ ■♥tr♦❞✉çã♦ à●❡♦♠❡tr✐❛ ❘✐❡♠❛♥♥✐❛♥❛ ❞❛❞♦ ♥♦ ♣r✐♠❡✐r♦ s❡♠❡str❡ ❞❡ ✷✵✵✼✱ ♣❡❧❛ ♠♦r❛❞✐❛♣r♦♣♦r❝✐♦♥❛❞❛ ♥❡st❡s ❞♦✐s ú❧t✐♠♦s ❛♥♦s✱ ♣❡❧❛ ♣❛❝✐ê♥❝✐❛✱ ❡t❝✳ ❆♦s ♣r♦❢❡ss♦r❡s ❊♥❛❧❞♦ ❱❡r❣❛st❛ ❡ ❋❡r♥❛♥❞♦ ❈♦❞á ▼❛rq✉❡s ♣❡❧❛s ✈❛❧✐♦s❛s❝♦rr❡çõ❡s ❡ s✉❣❡stõ❡s ❞❛❞❛s ♣❛r❛ ♠❡❧❤♦r✐❛ ❞❡st❛ ❞✐ss❡rt❛çã♦✳ ❆♦s ♠❡✉s ❛♠✐❣♦s ❞♦ Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ▼❛t❡♠át✐❝❛ ❞❛❯❋❆▲✱ ❞❡ ❢♦r♠❛ ❡s♣❡❝✐❛❧ ❛ ❆♥❞ré P✐③③❛✐❛✱ ❆r❧②s♦♥ ❆❧✈❡s ❡ ❊✈❡rs♦♥ ❋❡r♥❛♥❞♦✳ ❆♦s ♠❡✉s ❛♠✐❣♦s ❆s❦❡r② ❆❧❡①❛♥❞r❡✱ ❈❛✐♦ ❡ ▼❛♥♦❡❧ ❞♦ ■♥st✐t✉t♦ ❞❡ ❋ís✐❝❛❞❛ ❯❋❆▲ ♣❡❧❛ ❢♦rç❛ ❞❛❞❛✱ ❛ss✐♠ ❝♦♠♦ t❛♠❜é♠ ❛❣r❛❞❡ç♦ ❛ ❉❛r❧✐t♦♥ ❈❡③ár✐♦✱●❡❧s✐✈â♥✐♦ ❙♦✉③❛ ❡ ❏♦sé ❊❞✉❛r❞♦✳ ❆♦ ♠❡✉ ❛♠✐❣♦ ▼ár❝✐♦ ❍❡♥r✐q✉❡✱ ✉♠ ❛❣r❛❞❡❝✐♠❡♥t♦ t♦❞♦ ❡s♣❡❝✐❛❧ ♣❡❧❛s✐♠♣♦rt❛♥t❡s ❞ú✈✐❞❛s ❡s❝❧❛r❡❝✐❞❛s✱ ❛s q✉❛✐s ❞❡r❛♠ ✜r♠❡③❛ ❛ ✈ár✐♦s ❛r❣✉♠❡♥t♦s♠❛t❡♠át✐❝♦s ❞❡st❛ ❞✐ss❡rt❛çã♦✳ ❙♦✉ ♠✉✐t♦ ❣r❛t♦ ❛♦s ♣r♦❢❡ss♦r❡s ❆❞r✐❛♥♦ ❆❣✉✐❛r ❡ ❊❞✉❛r❞♦ P❡r❞✐❣ã♦♣❡❧♦s s❡♠✐♥ár✐♦s ❞❡ ❊s♣❛ç♦s ▼étr✐❝♦s ❡ ■♥tr♦❞✉çã♦ à ❆♥á❧✐s❡ ❋✉♥❝✐♦♥❛❧♠✐♥✐str❛❞♦s✳ ❆♦ ♣r♦❢❡ss♦r ❆❞❡❧❛í❧s♦♥ P❡✐①♦t♦ ❡ s❡✉s ♦r✐❡♥t❛♥❞♦s ♣❡❧❛ ❛♠✐③❛❞❡ ❡ ❛♣♦✐♦♥❡st❛ ❞✐ss❡rt❛çã♦✱ ✐st♦ ✐♥❝❧✉✐ ❈❧❛r✐ss❛ ❈♦❞á ❡ ❈❧❛✉❞❡♠✐r ❙✐❧✈✐♥♦✳ ❆ t♦❞♦s ♦s ♣r♦❢❡ss♦r❡s ❞♦ ■♥st✐t✉t♦ ❞❡ ▼❛t❡♠át✐❝❛ ❞❛ ❯❋❆▲ q✉❡❝♦❧❛❜♦r❛r❛♠ ❝♦♠ ♠✐♥❤❛ ❢♦r♠❛çã♦ ♠❛t❡♠át✐❝❛✳ ❆♦ ❈♦♥s❡❧❤♦ ◆❛❝✐♦♥❛❧ ❞❡ ❉❡s❡♥✈♦❧✈✐♠❡♥t♦ ❈✐❡♥tí✜❝♦ ❡ ❚❡❝♥♦❧ó❣✐❝♦ ✲❈◆Pq ✲ ♣❡❧♦ ❛♣♦✐♦ ✜♥❛♥❝❡✐r♦✳ ❆ ❉❡✉s ♣♦r t✉❞♦✳✳✳ ❘❡s✉♠♦ ❉❡♠♦♥str❛♠♦s ♦ ❚❡♦r❡♠❛ ❞❡ ❉❡❝♦♠♣♦s✐çã♦ ❞❡ ❈❤❡❡❣❡r✲●r♦♠♦❧❧✱♦ q✉❛❧ ❣❛r❛♥t❡ q✉❡ ✉♠❛ ✈❛r✐❡❞❛❞❡ ❘✐❡♠❛♥♥✐❛♥❛ ❝♦♠♣❧❡t❛ ♥✲❞✐♠❡♥s✐♦♥❛❧✱ ❝♦♠ ❝✉r✈❛t✉r❛ ❞❡ ❘✐❝❝✐ ♥ã♦✲♥❡❣❛t✐✈❛✱ q✉❡ ♣♦ss✉✐✉♠❛ ❧✐♥❤❛✱ ♣♦❞❡ s❡r ❞❡❝♦♠♣♦st❛ ✐s♦♠❡tr✐❝❛♠❡♥t❡ ♥✉♠ ♣r♦❞✉t♦❘✐❡♠❛♥♥✐❛♥♦ ❞❡ ✉♠❛ ✈❛r✐❡❞❛❞❡ ✭♥✲✶ ✮✲❞✐♠❡♥s✐♦♥❛❧ ❝♦♠ ♦ ❝♦♥❥✉♥t♦❞♦s r❡❛✐s✳P❛❧❛✈r❛s✲❝❤❛✈❡✿ ■s♦♠❡tr✐❛✱ ❋ór♠✉❧❛ ❞❡ ❲❡✐t③❡♥❜ö❝❦✱ ▲❛♣❧❛❝✐❛♥♦✱❉❡❝♦♠♣♦s✐çã♦ ❞❡ ❈❤❡❡❣❡r✲●r♦♠♦❧❧✱ ❋✉♥çõ❡s ❞❡ ❇✉s❡♠❛♥♥✳ ❆❜str❛❝t ❲❡ ❞❡♠♦♥str❛t❡ t❤❡ ❙♣❧✐tt✐♥❣ ❚❤❡♦r❡♠ ❞✉❡ t♦ ❈❤❡❡❣❡r ❛♥❞●r♦♠♦❧❧✱ ✇❤✐❝❤ ❡♥s✉r❡s t❤❛t ❛ ❝♦♠♣❧❡t❡ ❘✐❡♠❛♥♥✐❛♥ ♥✲♠❛♥✐❢♦❧❞✇❤✐❝❤ ❤❛s ♥♦♥♥❡❣❛t✐✈❡ ❘✐❝❝✐ ❝✉r✈❛t✉r❡ ❛♥❞ ❛ ❧✐♥❡✱ ❝❛♥ ❜❡ s♣❧✐t✐s♦♠❡tr✐❝❛❧❧② ✐♥t♦ t❤❡ ❘✐❡♠❛♥♥✐❛♥ ♣r♦❞✉❝t ♦❢ r❡❛❧ ✇✐t❤ ❛ ✭♥✲✶ ✮✲♠❛♥✐❢♦❧❞✳❑❡② ✇♦r❞s✿ ■s♦♠❡tr②✱ ❲❡✐t③❡♥❜ö❝❦✬s ❋♦r♠✉❧❛✱ ▲❛♣❧❛❝✐❛♥✱❙♣❧✐tt✐♥❣ ❚❤❡♦r❡♠ ♦❢ ❈❤❡❡❣❡r✲●r♦♠♦❧❧✱ ❇✉s❡♠❛♥♥ ❋✉♥❝t✐♦♥s✳ ❙✉♠ár✐♦ ■♥tr♦❞✉çã♦✾ ✶ ❈♦♥❝❡✐t♦s ❇ás✐❝♦s ❞❛ ●❡♦♠❡tr✐❛ ❘✐❡♠❛♥♥✐❛♥❛ ✶✷✶✳✶ ❱❛r✐❡❞❛❞❡s ❡ ▼étr✐❝❛s ❘✐❡♠❛♥♥✐❛♥❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✶✳✷ ❆ ❈♦♥❡①ã♦ ❞❡ ▲❡✈✐✲❈✐✈✐t❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻✶✳✸ ❆♣❧✐❝❛çã♦ ❊①♣♦♥❡♥❝✐❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽✶✳✹ ❱❛r✐❡❞❛❞❡s ❈♦♠♣❧❡t❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾✶✳✺ ❈✉r✈❛t✉r❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✷ ❘❡s✉❧t❛❞♦s Pr❡❧✐♠✐♥❛r❡s✷✹ ✷✳✶ ❋ór♠✉❧❛ ❞❡ ❲❡✐t③❡♥❜ö❝❦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹✷✳✷ ❆ ❍❡ss✐❛♥❛ ❞❛ ❋✉♥çã♦ ❉✐stâ♥❝✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽✷✳✸ ❚❡♦r❡♠❛ ❞❡ ❈♦♠♣❛r❛çã♦ ❞♦ ▲❛♣❧❛❝✐❛♥♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✸ ❖ ❚❡♦r❡♠❛ ❞❡ ❉❡❝♦♠♣♦s✐çã♦ ❞❡ ❈❤❡❡❣❡r✲●r♦♠♦❧❧ ✸✾✸✳✶ ❋✉♥çõ❡s ❞❡ ❇✉s❡♠❛♥♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾✸✳✷ ❚❡♦r❡♠❛ ❞❡ ❈❤❡❡❣❡r✲●r♦♠♦❧❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ❘❡❢❡rê♥❝✐❛s ❇✐❜❧✐♦❣rá✜❝❛s✹✽ ❮♥❞✐❝❡ ❘❡♠✐ss✐✈♦✺✵ ■♥tr♦❞✉çã♦ ❖ ❚❡♦r❡♠❛ ❞❡ ❉❡❝♦♠♣♦s✐çã♦ ❞❡ ❈❤❡❡❣❡r✲●r♦♠♦❧❧ é ❞❡ ❢✉♥❞❛♠❡♥t❛❧✐♠♣♦rtâ♥❝✐❛ ❡♠ ●❡♦♠❡tr✐❛ ❘✐❡♠❛♥♥✐❛♥❛ ❡✱ ❛❧é♠ ❞✐ss♦✱ ♣♦ss✉✐ ♠✉✐t❛s❛♣❧✐❝❛çõ❡s✳ ■♥✐❝✐❛❧♠❡♥t❡✱ ❡st❡ t❡♦r❡♠❛ ❢♦✐ ♣r♦✈❛❞♦ ♣♦r ❈♦❤♥✲❱♦ss❡♥✱ ❡♠ ✸ ✶✾✸✻✱ ♣❛r❛ s✉♣❡r❢í❝✐❡s ♥♦ ❡s♣❛ç♦ ❊✉❝❧✐❞✐❛♥♦ ❘ ❡✱ ❡♠ s❡❣✉✐❞❛✱ ♣♦r ❚♦♣♦♥♦❣♦✈❡♠ ✶✾✻✹✱ ♣❛r❛ ✈❛r✐❡❞❛❞❡s ❝♦♠♣❧❡t❛s ♥✲❞✐♠❡♥s✐♦♥❛✐s✱ ❝♦♠ ❛ ❤✐♣ót❡s❡ ❞❡❝✉r✈❛t✉r❛ s❡❝❝✐♦♥❛❧ ♥ã♦✲♥❡❣❛t✐✈❛✳ ❆ ✈❡rsã♦ q✉❡ ❛♣r❡s❡♥t❛♠♦s ❛q✉✐✱ ❞❡✈✐❞❛ ❛❈❤❡❡❣❡r ❡ ●r♦♠♦❧❧✱ ❣❡♥❡r❛❧✐③❛ ♦ ❚❡♦r❡♠❛ ❞❡ ❉❡❝♦♠♣♦s✐çã♦ ♣❛r❛ ✈❛r✐❡❞❛❞❡s❘✐❡♠❛♥♥✐❛♥❛s ❝♦♠♣❧❡t❛s ❝♦♠ ❝✉r✈❛t✉r❛ ❞❡ ❘✐❝❝✐ ♥ã♦✲♥❡❣❛t✐✈❛✱ ❝✉❥♦ r❡s✉❧t❛❞♦❢♦✐ ♣✉❜❧✐❝❛❞♦ ❡♠ ✶✾✼✶ ♥♦ ❏♦✉r♥❛❧ ♦❢ ❉✐✛❡r❡♥t✐❛❧ ●❡♦♠❡tr② ❝♦♠ ♦ s❡❣✉✐♥t❡❡♥✉♥❝✐❛❞♦✿ ♥ ❚❡♦r❡♠❛ ✵✳✶✳ ❙❡❥❛ ✭▼ ❀ ❣✮ ✉♠❛ ✈❛r✐❡❞❛❞❡ ❘✐❡♠❛♥♥✐❛♥❛ ❝♦♠♣❧❡t❛ ❝♦♠❝✉r✈❛t✉r❛ ❞❡ ❘✐❝❝✐ ♥ã♦✲♥❡❣❛t✐✈❛✳ ❊♥tã♦ ▼ é ✐s♦♠étr✐❝❛ ❛ ✉♠ ♣r♦❞✉t♦ ❦❦ ❘✐❡♠❛♥♥✐❛♥♦ ❞❛ ❢♦r♠❛ ❘ ✂ ◆✱ ♦♥❞❡ ◆ ♥ã♦ ❝♦♥té♠ ❧✐♥❤❛s ❡ ❘ ♣♦ss✉✐❛ ♠étr✐❝❛ ❝❛♥ô♥✐❝❛✳ ◆♦ ❡♥t❛♥t♦✱ ❝♦♠ ✉♠ ❛r❣✉♠❡♥t♦ ❞❡ ✐♥❞✉çã♦ ✜♥✐t❛✱ é s✉✜❝✐❡♥t❡ ♣r♦✈❛r q✉❡ ♥ s❡ ✭▼ ❀ ❣✮ é ✉♠❛ ✈❛r✐❡❞❛❞❡ ❘✐❡♠❛♥♥✐❛♥❛ ❝♦♠♣❧❡t❛✱ ❛ q✉❛❧ ❝♦♥té♠ ✉♠❛ ❧✐♥❤❛❡ ❘✐❝✭▼✮ ✕ ✵✱ ❡♥tã♦ ▼ é ✐s♦♠étr✐❝❛ ❛ ✉♠ ♣r♦❞✉t♦ ❘✐❡♠❛♥♥✐❛♥♦ ❞❛ ❢♦r♠❛❘ ✂ ◆✳ P♦✐s✱ t❡r❡♠♦s ❘✐❝✭◆✮ ✕ ✵ ❡ ◆ ❝♦♠♣❧❡t❛✳ ❊st❛ ❞✐ss❡rt❛çã♦ ❡stá ❞✐✈✐❞✐❞❛ ❞❛ s❡❣✉✐♥t❡ ♠❛♥❡✐r❛✳◆♦ ♣r✐♠❡✐r♦ ❝❛♣ít✉❧♦ ❛♣r❡s❡♥t❛♠♦s ❝♦♥❝❡✐t♦s ❜ás✐❝♦s ❞❡ ●❡♦♠❡tr✐❛ ❘✐❡♠❛♥♥✐❛♥❛ ❡ ♣r♦❝✉r❛♠♦s ✜①❛r ❛s ♥♦t❛çõ❡s✳◆♦ s❡❣✉♥❞♦ ❝❛♣ít✉❧♦✱ ❛❧❣✉♥s r❡s✉❧t❛❞♦s ♣r❡❧✐♠✐♥❛r❡s sã♦ ❞❡♠♦♥str❛❞♦s✱ ❛ s❛❜❡r✱ ♣♦r ❡①❡♠♣❧♦✱ ❛ ❋ór♠✉❧❛ ❞❡ ❲❡✐t③❡♥❜ö❝❦✳ ✸ Pr♦♣♦s✐çã♦ ✵✳✶✳ ❙❡❥❛ ❢ ✷ ❈ ✉♠❛ ❢✉♥çã♦ ❞❡✜♥✐❞❛ ❡♠ ▼✳ ❊♥tã♦✁ ✶ ✷ ✷ ✁ ❥ ❣r❛❞ ❢❥ ❂ ❥ ❍❡ss ❢❥ ✰ ❤❣r❛❞ ❢❀ ❣r❛❞✭✁❢✮✐ ✰ ❘✐❝ ✭❣r❛❞ ❢❀ ❣r❛❞ ❢✮ ✿✷ ❆♣r❡s❡♥t❛♠♦s t❛♠❜é♠ r❡s✉❧t❛❞♦s s♦❜r❡ ❛ ❍❡ss✐❛♥❛ ❞❛ ❢✉♥çã♦ ❞✐stâ♥❝✐❛ ❡❝♦♥❝❧✉í♠♦s ♦ ❝❛♣ít✉❧♦ ❝♦♠ ♦ ❚❡♦r❡♠❛ ❞❡ ❈♦♠♣❛r❛çã♦ ❞♦ ▲❛♣❧❛❝✐❛♥♦✿ ♥ ❚❡♦r❡♠❛ ✵✳✷✳ ❙❡❥❛ ✭▼ ❀ ❣✮ ✉♠❛ ✈❛r✐❡❞❛❞❡ ❘✐❡♠❛♥♥✐❛♥❛ ❝♦♠♣❧❡t❛✳ ❙✉♣♦✲♥❤❛♠♦s q✉❡ ❛ ❝✉r✈❛t✉r❛ ❞❡ ❘✐❝❝✐ ❞❡ ▼ s❛t✐s❢❛③ ❘✐❝✭▼✮ ✕ ✭♥ ✶✮❦❣✳ ❙❡❥❛ r❛ ❞✐stâ♥❝✐❛ ❣❡♦❞és✐❝❛ ❛♦ ♣♦♥t♦ ♣ ✷ ▼✳ ❙✉♣♦♥❤❛♠♦s ❛✐♥❞❛ q✉❡ ❛ ❢✉♥çã♦ r é❞✐❢❡r❡♥❝✐á✈❡❧ ♥♦ ♣♦♥t♦ ①✳ ❊♥tã♦ ✁r✭①✮ ✔ ✁r ❦ ✭⑦①✮❀ ✙ ♣ ♦♥❞❡ r ❦ ✭⑦①✮ ❂ r✭①✮ ❂ r ✵ ❡ r ✵ ❁ s❡ ❦ ❃ ✵✳ ❦ ❋✐♥❛❧♠❡♥t❡✱ ♥♦ t❡r❝❡✐r♦ ❝❛♣ít✉❧♦ ❞❡st❛ ❞✐ss❡rt❛çã♦✱ ❞❡♠♦♥str❛♠♦s ♦ ❚❡♦✲ r❡♠❛ ❞❡ ❉❡❝♦♠♣♦s✐çã♦ ❞❡ ❈❤❡❡❣❡r✲●r♦♠♦❧❧✳ ❆♥t❡s✱ ♣♦ré♠✱ ❛✐♥❞❛ ❞❡♠♦♥s✲tr❛♠♦s ❛❧❣✉♥s r❡s✉❧t❛❞♦s ❝♦♠ ♦ ✐♥t✉✐t♦ ❞❡ ❛♣r❡s❡♥t❛r♠♦s ♦ t❡♦r❡♠❛ ✜♥❛❧❝♦♠ ✉♠❛ ❜♦❛ ♦❜❥❡t✐✈✐❞❛❞❡✳ ❉❡♥tr❡ t❛✐s r❡s✉❧t❛❞♦s✱ ♠♦str❛♠♦s q✉❡ ❛ ❢✉♥çã♦ ✰ ❞❡ ❇✉s❡♠❛♥♥ ❜ ❛ss♦❝✐❛❞❛ ❛ ✉♠ r❛✐♦ ✌ é s✉♣❡r✲❤❛r♠ô♥✐❝❛ ♥♦ s❡♥t✐❞♦ ❞❛s❞✐str✐❜✉✐çõ❡s ❡ ♦ ❚❡♦r❡♠❛ ❞❡ ❈♦♠♣❛r❛çã♦ ❞♦ ▲❛♣❧❛❝✐❛♥♦ ♥♦ s❡♥t✐❞♦ ❞❛s❞✐str✐❜✉✐çõ❡s✳ ❘❡ss❛❧t❛♠♦s q✉❡ ❛ ❞❡♠♦♥str❛çã♦ ❢❡✐t❛ ♥❡st❛ ❞✐ss❡rt❛çã♦ é ❜❛s❡❛❞❛ ♥♦ s❡❣✉✐♥t❡ ❛rt✐❣♦✿❊s❝❤❡♥❜✉r❣✱ ❏✳✲❍✳✱ ❍❡✐♥t③❡✱ ❊✳✱ ❆♥ ❡❧❡♠❡♥t❛r② ♣r♦♦❢ ♦❢ t❤❡ ❈❤❡❡❣❡r✲ ●r♦♠♦❧❧ s♣❧✐tt✐♥❣ t❤❡♦r❡♠✱ ❆♥♥✳ ●❧♦❜✳ ❆♥❛❧②s✐s ❛♥❞ ●❡♦♠❡tr②✱ ✈♦❧✳ ✷✱✭✶✾✽✹✮✱ ✶✹✶✕✶✺✶✳ ❖ q✉❛❧ ❛♣r❡s❡♥t❛ ♥♦✈❛s té❝♥✐❝❛s ❞❡ ❝♦♠♦ ❛t❛❝❛r t❡♦r❡♠❛s ❞❡❞❡❝♦♠♣♦s✐çã♦✳ ❱❛❧❡ ♦❜s❡r✈❛r q✉❡ ♦ t❡♦r❡♠❛ ♥ã♦ é ✈á❧✐❞♦ ♣❛r❛ ✈❛r✐❡❞❛❞❡s q✉❡ ♣♦ss✉❡♠❝✉r✈❛t✉r❛ ❡s❝❛❧❛r ♥ã♦ ♥❡❣❛t✐✈❛✳ ❈♦♠♦ ❝♦♥tr❛✲❡①❡♠♣❧♦✱ ♣♦❞❡♠♦s ❝✐t❛r ❛ ✈❛✲ ✷ ✷ r✐❡❞❛❞❡ ❘ ✂ ❙ ❝♦♠ ❛ ♠étr✐❝❛ ❞❡ ❙❝❤✇❛r③s❝❤✐❧❞✳ ❈❛♣ít✉❧♦ ✶ ❈♦♥❝❡✐t♦s ❇ás✐❝♦s ❞❛ ●❡♦♠❡tr✐❛❘✐❡♠❛♥♥✐❛♥❛ ◆❡st❡ ❝❛♣ít✉❧♦ ✐♥tr♦❞✉③✐♠♦s ❝♦♥❝❡✐t♦s ❡ r❡s✉❧t❛❞♦s ❜ás✐❝♦s ❞❡ ●❡♦♠❡tr✐❛❘✐❡♠❛♥♥✐❛♥❛✱ t❛✐s ❝♦♠♦ ✈❛r✐❡❞❛❞❡s ❡ ♠étr✐❝❛s ❘✐❡♠❛♥♥✐❛♥❛s✱ ❛ ❝♦♥❡①ã♦ ❞❡▲❡✈✐✲❈✐✈✐t❛✱ ❝✉r✈❛t✉r❛s✱ ✈❛r✐❡❞❛❞❡s ❝♦♠♣❧❡t❛s ❡ ♦✉tr♦s ❝♦♥❝❡✐t♦s q✉❡ ♣r❡❝✐✲ s❛r❡♠♦s ♣❛r❛ ♦s ♣ró①✐♠♦s ❝❛♣ít✉❧♦s ❞❡st❛ ❞✐ss❡rt❛çã♦✳ ✶✳✶ ❱❛r✐❡❞❛❞❡s ❡ ▼étr✐❝❛s ❘✐❡♠❛♥♥✐❛♥❛s♥ ❙❛❜❡♠♦s q✉❡ ❞❛❞❛ ✉♠❛ ✈❛r✐❡❞❛❞❡ ❞✐❢❡r❡♥❝✐á✈❡❧ ▼ ✱ ✉♠ ❝❛♠♣♦ ❞❡ ✈❡t♦r❡s❳ ❡♠ ▼ é ✉♠❛ ❛♣❧✐❝❛çã♦ q✉❡ ❛ ❝❛❞❛ ♣♦♥t♦ ♣ ✷ ▼ ❛ss♦❝✐❛ ✉♠ ✈❡t♦r ❳✭♣✮ ♣ ♣❡rt❡❝❡♥t❡ ❛♦ ❡s♣❛ç♦ t❛♥❣❡♥t❡ ❚ ▼✳ ♥ ❈♦♥s✐❞❡r❛♥❞♦ ✉♠❛ ♣❛r❛♠❡tr✐③❛çã♦ ① ✿ ❯ ✚ ❘ ✦ ▼✱ ♣♦❞❡♠♦s ❡s❝r❡✈❡r✱♣❛r❛ ❝❛❞❛ ♣ ✷ ①✭❯✮✱ ♥ ❳❅ ❳✭♣✮ ❂ ☛ ✐ ✭♣✮ ✭♣✮❀❅① ✐ ✐❂✶ ❅ ❅ ♦♥❞❡ ❢ ✭♣✮❀ ✿ ✿ ✿ ❀ ✭♣✮❣ é ❛ ❜❛s❡ ❞❡ ✈❡t♦r❡s t❛♥❣❡♥t❡s ❡♠ ♣ ✷ ▼ ❛ss♦❝✐❛❞❛ ❅① ❅① ✶ ♥ à ①✱ ❡ ☛ ✶ ❀ ✿ ✿ ✿ ❀ ☛ ♥ sã♦ ❢✉♥çõ❡s ❞✐❢❡r❡♥❝✐á✈❡✐s ❡♠ ❯✳ ❈♦♠ ❛❜✉s♦ ❞❡ ♥♦t❛çã♦✱❡s❝r❡✈❡♥❞♦ ❢ ❛♦ ✐♥✈és ❞❡ ❢ ✍ ①✱ ♣♦❞❡♠♦s t❛♠❜é♠ ♣❡♥s❛r ❡♠ ✉♠ ❝❛♠♣♦❞❡ ✈❡t♦r❡s ❝♦♠♦ ✉♠❛ ❛♣❧✐❝❛çã♦ ❳ ✿ ❉ ✦ ❋ ❞♦ ❝♦♥❥✉♥t♦ ❉ ❞❛s ❢✉♥çõ❡s ❞✐❢❡r❡♥❝✐á✈❡✐s ❡♠ ▼ ♥♦ ❝♦♥❥✉♥t♦ ❋ ❞❛s ❢✉♥çõ❡s ❡♠ ▼✱ ❞❡✜♥✐❞❛ ♣♦r❳✭❢✮✭♣✮ ❂ ❅❜ ❥ ❜ ✐ ❛ ✐ ❳ ❥ ✰❳ ❅❢❅① ❥ ❅① ✐✓ ❥ ✐ ✷ ✒❛ ✐ ❳ ❥ ❳ ✓❂ ❥ ❅① ✐ ❢❅① ✷ ❅ ❢❅① ✐ ❅① ❥ ❥ ✷ ❅① ✐✿ ✓❅❢ ❜ ❥❅❛ ✐❅① ❥ ❅❜ ❥❅① ✐ ✒❛ ✐ ✐ ❳ ❥ ❳❨ ✭❢✮ ❨ ❳✭❢✮ ❂❳ ✿❉❛í✱ ✉s❛♥❞♦ ♦ t❡♦r❡♠❛ ❞❡ ❙❝❤✇❛rt③✱ ♦❜t❡♠♦s ❢❅① ❥ ❅① ✐ ❜ ❥ ❛ ✐❅ ✿❆♥❛❧♦❣❛♠❡♥t❡✱ ✈❡♠♦s q✉❡ ❥ ❳ ✐ ❳ ❅① ✐✰ ✓❅❢ ❅❛ ✐❅① ❥ ✒❜ ❥ ❥ ❳ ✐ ❨ ❳✭❢✮ ❂❳ ❅ ✰ ❜ ♥ ♣❡rt❡♥❝❡♥t❡s ❛ ❳ ✭▼✮✳❊♥tã♦ ❬❳❀ ❨ ❪ ✿❂ ❳❨ ❨ ❳ ♣❡rt❡♥❝❡ ❛ ❳ ✭▼✮✳ ❳✒ ❥ ❳ ✦❂ ❥ ❅❢❅① ❥ ❜ ❥ ✥❳ ❉❡ ❢❛t♦✱❳❨ ✭❢✮ ❂ ❳ ❥ ❅❅① ❥ ❥ ❜ ❥ ❡ ❨ ❂P ✐ ❅❅① ✐ ❛ ✐ ❊①❡♠♣❧♦ ✶✳✶✳ ❙❡❥❛♠ ❳ ❂P ❖ ❝♦♥❥✉♥t♦ ❞❡ t♦❞♦s ♦s ❝❛♠♣♦s ❞❡ ✈❡t♦r❡s ❡♠ ▼ s❡rá ❞❡♥♦t❛❞♦ ♣♦r ❳ ✭▼✮✳❆ s❡❣✉✐r✱ ❛♣r❡s❡♥t❛r❡♠♦s ♦ ❝♦❧❝❤❡t❡ ❞❡ ▲✐❡ ❞❡ ❞♦✐s ❝❛♠♣♦s✳ ❅① ✐✭♣✮✿ ☛ ✐ ✭♣✮❅❢ ✐❂✶ ❳ ❜ ❅❢❅① ❥ ✓❂ ❅❢❅① ✐ ❅① ❥ ✒❅❜ ✐ ❛ ✐ ❳ ❥ ❳ ❥ ❥ ❅❢❅① ❥ ✒❜ ✐ ❅❅① ✐ ❛ ✐ ❳ ❥ ❳ ✓❂ ■ss♦ ♠♦str❛ q✉❡ ❬❳❀ ❨ ❪ é ✉♠ ❝❛♠♣♦ ❞❡ ✈❡t♦r❡s✳❉❡♥♦♠✐♥❛♠♦s ❬❳❀ ❨ ❪ ♦ ❝♦❧❝❤❡t❡ ❞❡ ▲✐❡ ❞♦s ❝❛♠♣♦s ❳ ❡ ❨ ✳ P❛ss❡♠♦s ❛❣♦r❛ à s❡❣✉✐♥t❡ ❞❡✜♥✐çã♦✿ ♥ ❯♠❛ ♠étr✐❝❛ ❘✐❡♠❛♥♥✐❛♥❛ ❡♠ ✉♠❛ ✈❛r✐❡❞❛❞❡ ❞✐❢❡r❡♥❝✐á✈❡❧ ▼ é ✉♠❛❝♦rr❡s♣♦♥❞ê♥❝✐❛ q✉❡ ❛ss♦❝✐❛ ❛ ❝❛❞❛ ♣♦♥t♦ ♣ ✷ ▼ ✉♠ ♣r♦❞✉t♦ ✐♥t❡r♥♦ ❤✁❀ ✁✐ ❂ ♣ ♥ ❣ ♣ ✭✁❀ ✁✮ ♥♦ ❡s♣❛ç♦ t❛♥❣❡♥t❡ ❚ ♣ ▼✱ t❛❧ q✉❡✿ s❡ ① ✿ ❯ ✚ ❘ ✦ ▼ é ✉♠ s✐st❡♠❛❞❡ ❝♦♦r❞❡♥❛❞❛s ❧♦❝❛✐s ❡♠ t♦r♥♦ ❞❡ ♣✱ ❡♥tã♦ ♣❛r❛ ❝❛❞❛ ✐❀ ❥ ✷ ❢✶❀ ✿ ✿ ✿ ❀ ♥❣✱❉ ❊ ❅ ❅ ✭q✮❀ ✭q✮ é ✉♠❛ ❢✉♥çã♦ ❞✐❢❡r❡♥❝✐á✈❡❧ ❡♠ ❯✳ ❅① ❅① ✐ ❥ q ❉ ❊ ❅ ❅ ✐❥ ❆s ❢✉♥çõ❡s ❣ ✿❂ ❀ sã♦ ❝❤❛♠❛❞❛s ❝♦♠♣♦♥❡♥t❡s ❞❛ ♠étr✐❝❛ ❅① ❅① ✐ ❥ ♥ ♥ ❘✐❡♠❛♥♥✐❛♥❛ ♥♦ s✐st❡♠❛ ❞❡ ❝♦♦r❞❡♥❛❞❛s ① ✿ ❯ ✚ ❘ ✦ ▼ ✳ ❯♠❛✈❛r✐❡❞❛❞❡ ❞✐❢❡r❡♥❝✐á✈❡❧ ❝♦♠ ✉♠❛ ♠étr✐❝❛ ❘✐❡♠❛♥♥✐❛♥❛ é ❝❤❛♠❛❞❛ ✈❛r✐❡❞❛❞❡ ♥ ❘✐❡♠❛♥♥✐❛♥❛✳ ❉❡♥♦t❛r❡♠♦s ♣♦r ✭▼ ❀ ❣✮ ✉♠❛ ✈❛r✐❡❞❛❞❡ ❘✐❡♠❛♥♥✐❛♥❛ ❞❡❞✐♠❡♥sã♦ ♥ ❝♦♠ ✉♠❛ ♠étr✐❝❛ ❣✳ ♥ ✶ ♥ ❊①❡♠♣❧♦ ✶✳✷✳ ❆ ❡s❢❡r❛ ✉♥✐tár✐❛ ❙ ✭✶✮ ❂ ❢① ❂ ✭① ✶ ❀ ✿ ✿ ✿ ❀ ① ♥ ✮ ✷ ❘ ❀ ❥①❥ ❂ ✶❣é ✉♠❛ ✈❛r✐❡❞❛❞❡ ❘✐❡♠❛♥♥✐❛♥❛✳ ❈♦♠ ❡❢❡✐t♦✱ ❜❛st❛ ❞❡✜♥✐r♠♦s ❛ ♠étr✐❝❛ ❣ ♣♦r♥ ♥ ✶ ❣✭✉❀ ✈✮ ♣ ❂ ❤✉❀ ✈✐ ✱ ♦♥❞❡ ✉❀ ✈ ✷ ❚ ♣ ❙ ✳ ❘ ♥ ❊①❡♠♣❧♦ ✶✳✸✳ ❖ ❡s♣❛ç♦ ❤✐♣❡r❜ó❧✐❝♦ ❍ ✳ ♥ ♥ ❈♦♥s✐❞❡r❡ ❛ ✈❛r✐❡❞❛❞❡ ❞✐❢❡r❡♥❝✐á✈❡❧ ❯ ❂ ❘ ❂ ❢✭① ✶ ❀ ✿ ✿ ✿ ❀ ① ♥ ✮ ✷ ❘ ❀ ① ♥ ❃ ✵❣✱ ✰ ♥ ❝♦♠ ❛ ❝❛rt❛ ✐❞ ✿ ❯ ✚ ❘ ✦ ❯✳ ❉❛❞♦ ♣ ✷ ❯✱ ♣ ❂ ✭① ✶ ❀ ✿ ✿ ✿ ❀ ① ♥ ✮✱ s❡❥❛♠ ♥ ♣ ✈❀ ✇ ✷ ❚ ❯ ❂ ❘ ✳❉❡✜♥✐♠♦s ✶ ♥❤ ♣ ✭✈❀ ✇✮ ❂ ❤✈❀ ✇✐ ✿ ❘ ✷ ① ♥ ♥ ❱ê✲s❡ q✉❡ ✭❯❀ ❤✮ ✿❂ ❍ é ✉♠❛ ✈❛r✐❡❞❛❞❡ ❘✐❡♠❛♥♥✐❛♥❛✱ ❞❡♥♦♠✐♥❛❞❛❡s♣❛ç♦ ❤✐♣❡r❜ó❧✐❝♦✳❊①❡♠♣❧♦ ✶✳✹✳ ❱❛r✐❡❞❛❞❡s ■♠❡rs❛s✳ ♥ ♥✰❦ ❙❡❥❛ ❢ ✿ ▼ ✦ ◆ ✉♠❛ ✐♠❡rsã♦✱ ✐st♦ é✱ ❢ é ✉♠❛ ❛♣❧✐❝❛çã♦ ❞✐❢❡r❡♥❝✐á✈❡❧ ♣ ♣ ❢✭♣✮ ❡ ❞❢ ✿ ❚ ▼ ✦ ❚ ◆ é ✐♥❥❡t✐✈❛ ♣❛r❛ t♦❞♦ ♣ ✷ ▼✳ ❙❡ ◆ t❡♠ ✉♠❛ ♠étr✐❝❛❘✐❡♠❛♥♥✐❛♥❛✱ ❢ ✐♥❞✉③ ✉♠❛ ♠étr✐❝❛ ❘✐❡♠❛♥♥✐❛♥❛ ❡♠ ▼✱ ❞❛❞❛ ♣♦r ♣ ♣ ♣ ❤✉❀ ✈✐ ❂ ❤❞❢ ✭✉✮❀ ❞❢ ✭✈✮✐ ❀ ✉❀ ✈ ✷ ❚ ▼✿ ♣ ❢✭♣✮ ❈♦♠ ❡❢❡✐t♦✱ ❝♦♠♦ ❞❢ ♣ é ✐♥❥❡t✐✈❛✱ ❤✁❀ ✁✐ é ♣♦s✐t✐✈♦ ❞❡✜♥✐❞♦✳ ❆s ❞❡♠❛✐s❝♦♥❞✐çõ❡s ❞❛ ❞❡✜♥✐çã♦ ❞❡ ♠étr✐❝❛ ❘✐❡♠❛♥♥✐❛♥❛ ♣♦❞❡♠ s❡r ❢❛❝✐❧♠❡♥t❡ ✈❡r✐✜❝❛❞❛s✳❆ ♠étr✐❝❛ ❞❡ ▼ é ❡♥tã♦ ❝❤❛♠❛❞❛ ❛ ♠étr✐❝❛ ✐♥❞✉③✐❞❛ ♣♦r ❢ ❡ ❢ é ✉♠❛ ✐♠❡rsã♦ ✐s♦♠étr✐❝❛✳ ♥ ♥✰❦ ◗✉❛♥❞♦ ❢ ✿ ▼ ✦ ◆ é ✉♠❛ ✐♠❡rsã♦ ❡✱ ❛❧é♠ ❞✐ss♦✱ ❢ é ✉♠❤♦♠❡♦♠♦r✜s♠♦ s♦❜r❡ ❢✭▼✮ ✚ ◆✱ ♦♥❞❡ ❢✭▼✮ t❡♠ ❛ t♦♣♦❧♦❣✐❛ ✐♥❞✉③✐❞❛ ♣♦r◆✱ ❞✐③✲s❡ q✉❡ ❢ é ✉♠ ♠❡r❣✉❧❤♦✳ ❙❡ ▼ ✚ ◆ ❡ ❛ ✐♥❝❧✉sã♦ ✐ ✿ ▼ ✱✦ ◆ é ✉♠♠❡r❣✉❧❤♦✱ ❞✐③✲s❡ q✉❡ ▼ é ✉♠❛ s✉❜✈❛r✐❡❞❛❞❡ ❞❡ ◆✳ ❯♠❛ ❝❧❛ss❡ ✐♠♣♦rt❛♥t❡ ❞❡ ✈❛r✐❡❞❛❞❡s ❘✐❡♠❛♥♥✐❛♥❛s é ❞❛❞❛ ♥♦ ❡①❡♠♣❧♦ s❡❣✉✐♥t❡✳❊①❡♠♣❧♦ ✶✳✺✳ ▼étr✐❝❛ Pr♦❞✉t♦✳ ♥ ♥ ✶ ✷ ✶ ✷ ❙❡❥❛♠ ✭▼ ✶ ❀ ❣ ✮ ❡ ✭▼ ✷ ❀ ❣ ✮ ✈❛r✐❡❞❛❞❡s ❘✐❡♠❛♥♥✐❛♥❛s ❡ ❝♦♥s✐❞❡r❡ ♦ ♣r♦❞✉t♦ ✶ ✷ ❝❛rt❡s✐❛♥♦ ▼ ❂ ▼ ✂ ▼ ❝♦♠ ❛ ❡str✉t✉r❛ ❞✐❢❡r❡♥❝✐á✈❡❧ ♣r♦❞✉t♦✳ ❙❡❥❛♠ ✶ ✶ ✷ ✶ ✷ ✶ ✷ ✷ ✙ ✿ ▼ ✂ ▼ ✦ ▼ ❡ ✙ ✿ ▼ ✂ ▼ ✦ ▼ ❛s ♣r♦❥❡çõ❡s ♥❛t✉r❛✐s✳P♦❞❡♠♦s ✐♥tr♦❞✉③✐r ❡♠ ▼ ✶ ✂ ▼ ✷ ✉♠❛ ♠étr✐❝❛ ❘✐❡♠❛♥♥✐❛♥❛ ♣♦♥❞♦✱ ♣❛r❛❝❛❞❛ ✭♣❀ q✮ ✷ ▼ ✶ ✂ ▼ ✷ ❡ ✉❀ ✈ ✷ ❚ ✭♣❀q✮ ✭▼ ✶ ✂ ▼ ✷ ✮✱ ❤✉❀ ✈✐ ❂ ❤❞✙ ✶ ✁ ✉❀ ❞✙ ✶ ✁ ✈✐ ✰ ❤❞✙ ✷ ✁ ✉❀ ❞✙ ✷ ✁ ✈✐ ✿ ✭♣❀q✮ ♣ q ✶ ✶ ✷ ❈♦♠♦ ❝❛s♦s ♣❛rt✐❝✉❧❛r❡s t❡♠♦s✱ ♣♦r ❡①❡♠♣❧♦✱ ❙ ✂ ❙ ❂ ❚ ♦✉✱ ♠❛✐s ✶ ✶ ♥ ❣❡r❛❧♠❡♥t❡✱ ❙ ✂ ✁ ✁ ✁ ✂ ❙ ❂ ❚ ✱ ♦s q✉❛✐s tê♠ ✉♠❛ ❡str✉t✉r❛ ❘✐❡♠❛♥♥✐❛♥❛ ✶ ✷ ♦❜t✐❞❛ q✉❛♥❞♦ ❡s❝♦❧❤❡♠♦s ♥♦ ❝ír❝✉❧♦ ❙ ✚ ❘ ❛ ♠étr✐❝❛ ❘✐❡♠❛♥♥✐❛♥❛ ✷♥ ✐♥❞✉③✐❞❛ ♣♦r ❘ ❡✱ ❡♠ s❡❣✉✐❞❛✱ t♦♠❛♠♦s ❛ ♠étr✐❝❛ ♣r♦❞✉t♦ ❡♠ ❚ ✳ ❖ t♦r♦ ♥ ❚ ❝♦♠ ❡st❛ ♠étr✐❝❛ ❘✐❡♠❛♥♥✐❛♥❛ é ❝❤❛♠❛❞♦ t♦r♦ ♣❧❛♥♦ ♦✉ t♦r♦ ✢❛t✳❚❡♦r❡♠❛ ✶✳✶✳ ❚♦❞❛ ✈❛r✐❡❞❛❞❡ ❝♦♠ ❜❛s❡ ❡♥✉♠❡rá✈❡❧✱ ❞✐❢❡r❡♥❝✐á✈❡❧ ❡ ❞❡❍❛✉s❞♦r✛ ♣♦ss✉✐ ✉♠❛ ♠étr✐❝❛ ❘✐❡♠❛♥♥✐❛♥❛✳❉❡♠♦♥str❛çã♦✳ ❱❡r ❬✸❪✱ ♣á❣✐♥❛ ✹✼✳ ♥ ♥ ❉❡✜♥✐çã♦ ✶✳✶✳ ❙❡❥❛♠ ✭▼ ❀ ❣✮ ❡ ✭▼ ❀ ❣✮ ✈❛r✐❡❞❛❞❡s ❘✐❡♠❛♥♥✐❛♥❛s✳ ❯♠❞✐❢❡♦♠♦r✜s♠♦ ✬ ✿ ▼ ✦ ▼ é ❞✐t♦ ✉♠❛ ✐s♦♠❡tr✐❛ s❡ ❣ ✭❞✬ ♣ ✭✈✮❀ ❞✬ ♣ ✭✇✮✮ ❂ ❣ ♣ ✭✈❀ ✇✮❀ ✽ ♣ ✷ ▼❀ ✽ ✈❀ ✇ ✷ ❚ ♣ ▼✿ ✬✭♣✮ ✶✳✷ ❆ ❈♦♥❡①ã♦ ❞❡ ▲❡✈✐✲❈✐✈✐t❛ ❯♠❛ ❝♦♥❡①ã♦ ❛✜♠ r ❡♠ ✉♠❛ ✈❛r✐❡❞❛❞❡ ❞✐❢❡r❡♥❝✐á✈❡❧ ▼ é ✉♠❛ ❛♣❧✐❝❛çã♦ r ✿ ❳ ✭▼✮ ✂ ❳ ✭▼✮ ✦ ❳ ✭▼✮t❛❧ q✉❡✱ ✽ ❳❀ ❨❀ ❩ ✷ ❳ ✭▼✮ ❡ ✽ ❢❀ ❣ ✷ ❉✭▼✮✱ t❡♠✲s❡ ✭✐✮ r ❢❳✰❣❨ ❩ ❂ ❢r ❳ ❩ ✰ ❣r ❳ ❩✭✐✐✮ r ❳ ✭❨ ✰ ❩✮ ❂ r ❳ ❨ ✰ r ❳ ❩ ❳ ❳ ✭✐✐✐✮ r ❢❨ ❂ ❢r ❨ ✰ ❳✭❢✮❨ ✳ ❅ ✐ ❊♠ ❝♦♦r❞❡♥❛❞❛s ❧♦❝❛✐s✱ ❳ ❂ ✱ ♣♦❞❡✲s❡ ❢❛❝✐❧♠❡♥t❡ ✈❡r✱ ♣❛r❛ ❳ ❂ ❅① ✐ P P ✐ ✐ ✐ ✐ ① ❳ ❡ ❨ ❂ ② ❨ ✱ q✉❡ ✐ ✐ ✥ ✦❳ ❳ ❦ r ❳ ❨ ❂ ① ✐ ② ❥ ✰ ❳✭② ❦ ✮ ❳ ❦ ✿ ✐❥ ❦ ✐❀❥ P ❦ ❦ ❖s ❝♦❡✜❝✐❡♥t❡s ✱ ❞❡✜♥✐❞♦s ♣♦r r ❳ ❳ ❥ ❂ ❳ ❦ ✱ sã♦ ❝❤❛♠❛❞♦s ✐❥ ✐ ✐❥ ❦ sí♠❜♦❧♦s ❞❡ ❈❤r✐st♦✛❡❧ ❞❛ ❝♦♥❡①ã♦✳❊♠ t❡r♠♦s ❞♦s ❝♦❡✜❝✐❡♥t❡s ❞❛ ♠étr✐❝❛ ❘✐❡♠❛♥♥✐❛♥❛✱ ♦s sí♠❜♦❧♦s ❞❡ ❈❤r✐st♦✛❡❧ ♣♦ss✉❡♠ ❛ s❡❣✉✐♥t❡ ❡①♣r❡ssã♦✿✚ ✛ ❳✶ ❅ ❅ ❅ ♠❦♠ ❥❦ ❦✐ ✐❥ ✐❥ ❂ ❣ ✰ ❣ ❣ ❣ ❀ ✐ ❥ ❦ ✷ ❅① ❅① ❅① ❦ ❦♠❦♠ ♦♥❞❡ ✭❣ ✮ é ❛ ♠❛tr✐③ ✐♥✈❡rs❛ ❞❡ ✭❣ ✮✱ ✈❡r ❬✸❪✱ ♣á❣✐♥❛ ✻✷✳❉❛❞❛ ✉♠❛ ❝✉r✈❛ ❞✐❢❡r❡♥❝✐á✈❡❧ ☛ ✿ ■ ✚ ❘ ✦ ▼✱ ✉♠ ❝❛♠♣♦ ❛♦ ❧♦♥❣♦ ❞❡ ☛ é ✉♠❛ ❢✉♥çã♦ ❱ ✿ ■ ✦ ❚ ▼ t❛❧ q✉❡ ❱ ✭t✮ ✷ ❚ ☛✭t✮ ▼✱ ♦♥❞❡❚ ▼ ❂ ❢✭♣❀ ✈✮❥♣ ✷ ▼❀ ✈ ✷ ❚ ♣ ▼❣ é ♦ ✜❜r❛❞♦ t❛♥❣❡♥t❡ ❞❡ ▼✳ ❞ ❙❡❥❛ t ✷ ■✳ ❊♠ ❝♦♦r❞❡♥❛❞❛s✱ t❡♠♦s ❛ ❜❛s❡ ❢ ❣ ❡♠ ❚ t ■ ❂ ❘✳ P♦r ❞t ❞✵ ❞❡✜♥✐çã♦✱ ☛ ✭ ✮ é ♦ ✈❡t♦r t❛♥❣❡♥t❡ à ❝✉r✈❛ ☛ ❡♠ ☛✭t✮✳ ❯s❛r❡♠♦s ❛ ♥♦t❛çã♦✿ t ❞t ✁ ❞ ✵ ❞☛ ❂ ☛ ✭t✮✳ ❞t ❉❱ ❛♦ ❧♦♥❣♦ ❞❡ ☛✱ ❡①✐st❡ ✉♠ ú♥✐❝♦ ❝❛♠♣♦ ❞❡♥♦t❛❞♦ ♣♦r t❛❧ q✉❡ ❞t ❉ ❉❱ ❉❲ ✭❛✮ ✭❱ ✰ ❲ ✮ ❂ ✰ ❀ ❞t ❞t ❞t ❞❢❉ ❉❱ ✭❜✮ ✭❢❱ ✮ ❂ ❱ ✰ ❢ ❀ ❞t ❞t ❞t ✭❝✮ ❙❡ ❱ ✭t✮ é ❛ r❡str✐çã♦ ❞❡ ✉♠ ❝❛♠♣♦ ❨ ❞❡✜♥✐❞♦ ♥✉♠❛ ✈✐③✐♥❤❛♥ç❛ ❞❡ ❉❱ ✵ ☛✭■✮✱ ❡♥tã♦ ❂ r ☛ ✭t✮ ❨ ✳ ❞t ❉❡♠♦♥str❛çã♦✳ ❱❡r ❬✸❪✱ ♣á❣✐♥❛ ✺✼✳❉✐③❡♠♦s q✉❡ ✉♠❛ ❝♦♥❡①ã♦ ❛✜♠ r ❡♠ ✉♠❛ ✈❛r✐❡❞❛❞❡ ❞✐❢❡r❡♥❝✐á✈❡❧ ▼ é s✐♠étr✐❝❛ s❡ ❳ ❨ r ❨ r ❳ ❂ ❬❳❀ ❨ ❪❀ ✽ ❳❀ ❨ ✷ ❳ ✭▼✮✿❆ ❥✉st✐✜❝❛t✐✈❛ ♣❛r❛ t❛❧ ♥♦♠❡♥❝❧❛t✉r❛ ✈❡♠ ❞♦ s❡❣✉✐♥t❡ ❢❛t♦✿ ✽ ✐❀ ❥ ✷ ❢✶❀ ✁ ✁ ✁ ❀ ♥❣✱ r ❳ ❳ ❥ r ❳ ❳ ✐ ❂ ❬❳ ✐ ❀ ❳ ❥ ❪ ❂ ✵❀✐ ❥ ❦ ❦ ♦ q✉❡ é ❡q✉✐✈❛❧❡♥t❡ ❛ ❂ ✳ ✐❥ ❥✐ ❉✐③❡♠♦s q✉❡ ✉♠❛ ❝♦♥❡①ã♦ ❛✜♠ r ❡♠ ✉♠❛ ✈❛r✐❡❞❛❞❡ ❘✐❡♠❛♥♥✐❛♥❛ ▼ é❝♦♠♣❛tí✈❡❧ ❝♦♠ ❛ ♠étr✐❝❛ s❡ ❳ ❤❨❀ ❩✐ ❂ ❤r ❳ ❨❀ ❩✐ ✰ ❤❨❀ r ❳ ❩✐ ❀ ✽ ❳❀ ❨❀ ❩ ✷ ❳ ✭▼✮✿❖ ♣ró①✐♠♦ t❡♦r❡♠❛ é ❢✉♥❞❛♠❡♥t❛❧ ❡♠ ●❡♦♠❡tr✐❛ ❘✐❡♠❛♥♥✐❛♥❛✳ ❚❡♦r❡♠❛ ✶✳✷ ✭▲❡✈✐✲❈✐✈✐t❛✮✳ ❉❛❞❛ ✉♠❛ ✈❛r✐❡❞❛❞❡ ❘✐❡♠❛♥♥✐❛♥❛ ▼✱ ❡①✐st❡✉♠❛ ú♥✐❝❛ ❝♦♥❡①ã♦ ❛✜♠ r ❡♠ ▼ q✉❡ é s✐♠étr✐❝❛ ❡ ❝♦♠♣❛tí✈❡❧ ❝♦♠ ❛ ♠étr✐❝❛❘✐❡♠❛♥♥✐❛♥❛✳❉❡♠♦♥str❛çã♦✳ ❱❡r ❬✸❪✱ ♣á❣✐♥❛ ✻✶✳ ❚❛❧ ❝♦♥❡①ã♦ é ❞❡♥♦♠✐♥❛❞❛ ❝♦♥❡①ã♦ ❞❡ ▲❡✈✐✲❈✐✈✐t❛ ✭♦✉ ❘✐❡♠❛♥♥✐❛♥❛✮ ❞❡▼✳ ❆ ♣❛rt✐r ❞❛q✉✐ ❡st❛r❡♠♦s s❡♠♣r❡ ❝♦♥s✐❞❡r❛♥❞♦ ✈❛r✐❡❞❛❞❡s ❘✐❡♠❛♥♥✐❛♥❛s❝♦♠ s✉❛s r❡s♣❡❝t✐✈❛s ❝♦♥❡①õ❡s ❞❡ ▲❡✈✐✲❈✐✈✐t❛✳ ✶✳✸ ❆♣❧✐❝❛çã♦ ❊①♣♦♥❡♥❝✐❛❧❉ ✵ ❯♠❛ ❝✉r✈❛ ☛ ❡♠ ▼ é ✉♠❛ ❣❡♦❞és✐❝❛ ❡♠ t ✷ ■ s❡ ☛ ✭t✮ ❂ ✵✳ ❞t ♣ ✵ ✵ ◆❡st❡ ❝❛s♦✱ s❡ ✈✭t✮ ❂ ❤☛ ✭t✮❀ ☛ ✭t✮✐ é ❛ ✈❡❧♦❝✐❞❛❞❡ ❞❡ ☛✱ t❡♠♦s q✉❡❞ ❞ ✷ ✵ ✵ ✭✈ ✭t✮✮ ❂ ❤☛ ✭t✮❀ ☛ ✭t✮✐❞t ❞t ✜ ✢❉ ✵ ✵ ❂ ✷ ☛ ✭t✮❀ ☛ ✭t✮❞t ❂ ✵✿P♦rt❛♥t♦✱ s❡ ☛ é ❣❡♦❞és✐❝❛✱ ❡♥tã♦ ♦ ✈❡t♦r ✈❡❧♦❝✐❞❛❞❡ ❞❡ ☛ ♣♦ss✉✐ ♥♦r♠❛ ❝♦♥st❛♥t❡✳❉❡✜♥✐çã♦ ✶✳✷✳ ❯♠ ❝❛♠♣♦ ❱ ❛♦ ❧♦♥❣♦ ❞❡ ✉♠❛ ❝✉r✈❛ ☛ é ❞✐t♦ ♣❛r❛❧❡❧♦ s❡ ❉❱ ❂ ✵✳ ❞t Pr♦♣♦s✐çã♦ ✶✳✷✳ ❙❡❥❛♠ ☛ ✿ ■ ✦ ▼ ❞✐❢❡r❡♥❝✐á✈❡❧ ❡ ❱ ✵ ✷ ❚ ☛✭t ✮ ▼✳ ❊♥tã♦ ✵ ✵ ✵ ❡①✐st❡ ✉♠ ú♥✐❝♦ ❝❛♠♣♦ ♣❛r❛❧❡❧♦ ❱ ✱ ❛♦ ❧♦♥❣♦ ❞❡ ☛✱ t❛❧ q✉❡ ❱ ✭t ✮ ❂ ❱ ✳❉❡♠♦♥str❛çã♦✳ ❱❡r ❬✸❪✱ ♣á❣✐♥❛ ✺✽✳ ❈♦♠♦ ❝♦♥s❡q✉ê♥❝✐❛ ❞♦ t❡♦r❡♠❛ ❞❡ ❡①✐stê♥❝✐❛ ❡ ✉♥✐❝✐❞❛❞❡ ❞❡ s♦❧✉çõ❡s ❞❡❡q✉❛çõ❡s ❞✐❢❡r❡♥❝✐❛✐s ♦r❞✐♥ár✐❛s✱ ♦❜t❡♠♦s ♦ s❡❣✉✐♥t❡ r❡s✉❧t❛❞♦✿ ♣ Pr♦♣♦s✐çã♦ ✶✳✸✳ ❉❛❞♦s ♣ ✷ ▼ ❡ ✈ ✷ ❚ ▼✱ ❡①✐st❡ ✉♠❛ ú♥✐❝❛ ❣❡♦❞és✐❝❛ ✵ ☛ ✿ ■ ✦ ▼ t❛❧ q✉❡ ☛✭✵✮ ❂ ♣ ❡ ☛ ✭✵✮ ❂ ✈✳❙❡ ✈ ✷ ❚ ♣ ▼✱ ✈❛♠♦s ❞❡♥♦t❛r ♣♦r ✌ ✈ ❛ ú♥✐❝❛ ❣❡♦❞és✐❝❛ ❞❡ ▼ q✉❡ ♣❛ss❛ ♣♦r ♣ ✷ ▼ ❝♦♠ ✈❡❧♦❝✐❞❛❞❡ ✈ ✷ ❚ ♣ ▼✳❙❡❥❛ ✝ ♣ ❂ ❢✈ ✷ ❚ ♣ ▼❀ ✌ ✈ ❡stá ❞❡✜♥✐❞❛ ♥✉♠ ✐♥t❡r✈❛❧♦ ❝♦♥t❡♥❞♦ ❬✵❀ ✶❪❣✳ ❉❡✜♥✐çã♦ ✶✳✸✳ ❆ ❛♣❧✐❝❛çã♦ ❡①♣ ✿ ✝ ♣ ✦ ▼✱ ❞❡✜♥✐❞❛ ♣♦r ❡①♣ ✭✈✮ ❂ ✌ ✈ ✭✶✮✱ ♣ ♣ é ❞❡♥♦♠✐♥❛❞❛ ❛♣❧✐❝❛çã♦ ❡①♣♦♥❡♥❝✐❛❧✳Pr♦♣♦s✐çã♦ ✶✳✹✳ ❆s s❡❣✉✐♥t❡s ♣r♦♣r✐❡❞❛❞❡s sã♦ s❛t✐s❢❡✐t❛s✿ ♣ ♣ ✶✳ ❝❛❞❛ ❝♦♥❥✉♥t♦ ✝ ✚ ❚ ▼ é ❡str❡❧❛❞♦ ❡♠ r❡❧❛çã♦ ❛ ♣❀ ✷✳ ♣❛r❛ ❝❛❞❛ ✈ ✷ ❚ ♣ ▼✱ ❛ ❣❡♦❞és✐❝❛ ✌ ✈ é ❞❛❞❛ ♣♦r ✌ ✈ ✭t✮ ❂ ❡①♣ ✭t✈✮✱ ♣❛r❛ ♣ t♦❞♦ t ✷ ❘ ♦♥❞❡ ♦s ❞♦✐s ❧❛❞♦s ❡stã♦ ❞❡✜♥✐❞♦s❀✸✳ ❛ ❛♣❧✐❝❛çã♦ ❡①♣ é ❞✐❢❡r❡♥❝✐á✈❡❧✳ ♣ ❉❡♠♦♥str❛çã♦✳ ❱❡r ❬✸❪✱ ♣á❣✐♥❛ ✼✶✳➱ ♣♦ssí✈❡❧ ❛✉♠❡♥t❛r ❛ ✈❡❧♦❝✐❞❛❞❡ ❞❡ ✉♠❛ ❣❡♦❞és✐❝❛ ❞✐♠✐♥✉✐♥❞♦ ♦ s❡✉ ✐♥t❡r✈❛❧♦ ❞❡ ❞❡✜♥✐çã♦ ❡ ✈✐❝❡✲✈❡rs❛✳ ■ss♦ s❡❣✉❡ ❞❡ ✉♠❛ ♣r♦♣r✐❡❞❛❞❡ ❝♦♥❤❡❝✐❞❛✱ ❝❤❛♠❛❞❛ ❤♦♠♦❣❡♥❡✐❞❛❞❡ ❞❛s ❣❡♦❞és✐❝❛s✳ ❊♠ t❡r♠♦s ♠❛t❡♠á✲ t✐❝♦s✱ ❡①♣r❡ss❛♠♦s ✐ss♦ ❞❛ s❡❣✉✐♥t❡ ❢♦r♠❛✿ ✕✈ ✈ ♣ ✌ ✭t✮ ❂ ✌ ✭✕t✮❀ ✽ ✈ ✷ ❚ ▼ ❡ ✽ ✕❀ t ✷ ❘✿Pr♦♣♦s✐çã♦ ✶✳✺✳ P❛r❛ t♦❞♦ ♣ ✷ ▼✱ ❡①✐st❡♠ ✉♠❛ ✈✐③✐♥❤❛♥ç❛ ❱ ❞❛ ♦r✐❣❡♠ ❞❡❚ ♣ ▼ ❡ ✉♠❛ ✈✐③✐♥❤❛♥ç❛ ❯ ❞❡ ♣✱ t❛✐s q✉❡ ❡①♣ ✿ ❱ ✦ ❯ é ✉♠ ❞✐❢❡♦♠♦r✜s♠♦✳ ♣ ❉❡♠♦♥str❛çã♦✳ ❉❡ ❢❛t♦✱❞ ☞☞ ✵ ❞✭❡①♣ ♣ ✮ ✭✈✮ ❂ ✭❡①♣ ♣ ✭t✈✮✮ t❂✵ ❞t❞ ☞☞❂ ✭✌ ✈ ✭t✮✮ t❂✵ ❞t ✵ ❂ ✌ ✭✵✮ ✈ ❂ ✈✿ ✵ ♣ ▲♦❣♦✱ ❞✭❡①♣ ✮ é ❛ ✐❞❡♥t✐❞❛❞❡ ❞❡ ❚ ▼✱ s❡❣✉❡✲s❡ ❡♥tã♦ ❞♦ t❡♦r❡♠❛ ❞❛ ♣ ❢✉♥çã♦ ✐♥✈❡rs❛ q✉❡ ❡①♣ ♣ é ✉♠ ❞✐❢❡♦♠♦r✜s♠♦ ❧♦❝❛❧ ♥✉♠❛ ✈✐③✐♥❤❛♥ç❛ ❞❡ ✵ ❡♠ ♣ ❚ ▼✳❖ ❛❜❡rt♦ ❯ ❞❛❞♦ ♣❡❧❛ ♣r♦♣♦s✐çã♦ ❛♥t❡r✐♦r é ❝❤❛♠❛❞♦ ✈✐③✐♥❤❛♥ç❛ ♥♦r♠❛❧ ❞❡ ♣✳ ✶✳✹ ❱❛r✐❡❞❛❞❡s ❈♦♠♣❧❡t❛s ◗✉❛♥❞♦ s❡ ❡stá ✐♥t❡r❡ss❛❞♦ ❡♠ ❡st✉❞❛r ♣r♦♣r✐❡❞❛❞❡s ❣❧♦❜❛✐s ❞❡ ✉♠❛ ✈❛✲ r✐❡❞❛❞❡ ❘✐❡♠❛♥♥✐❛♥❛✱ ✜❝❛ ❝♦♥✈❡♥✐❡♥t❡ ❝♦♥s✐❞❡r❛r♠♦s ✈❛r✐❡❞❛❞❡s ❝♦♠♣❧❡t❛s✳ ❉❡✜♥✐çã♦ ✶✳✹✳ ❯♠❛ ✈❛r✐❡❞❛❞❡ ❘✐❛♠❛♥♥✐❛♥❛ ▼ é ✭❣❡♦❞❡s✐❝❛♠❡♥t❡✮❝♦♠♣❧❡t❛ s❡✱ ♣❛r❛ t♦❞♦ ♣ ✷ ▼✱ ❛ ❛♣❧✐❝❛çã♦ ❡①♣♦♥❡♥❝✐❛❧ ❡①♣ ❡stá ❞❡✜♥✐❞❛ ♣ ♣❛r❛ t♦❞♦ ✈ ✷ ❚ ♣ ▼✱ ✐st♦ é✱ ❛s ❣❡♦❞és✐❝❛s ✌✭t✮ q✉❡ ♣❛rt❡♠ ❞❡ ♣ ❡stã♦ ❞❡✜♥✐❞❛s♣❛r❛ t♦❞♦s ♦s ✈❛❧♦r❡s ❞♦ ♣❛râ♠❡tr♦ t ✷ ❘✳ P♦❞❡♠♦s ❞❡✜♥✐r ✉♠❛ ❞✐stâ♥❝✐❛ ❞✭♣❀ q✮ ♥✉♠❛ ✈❛r✐❡❞❛❞❡ ❘✐❡♠❛♥♥✐❛♥❛✱ ❛ q✉❛❧ ❡st❛r❡♠♦s s❡♠♣r❡ s✉♣♦♥❞♦ ❝♦♥❡①❛✱ ❞❛ s❡❣✉✐♥t❡ ♠❛♥❡✐r❛✿ ❞✭♣❀ q✮ ❂ í♥✜♠♦❞♦s ❝♦♠♣r✐♠❡♥t♦s ❞❡ t♦❞❛s ❛s ❝✉r✈❛s ☛ ♣❀q ✱ ♦♥❞❡ ☛ ♣❀q é ✉♠❛ ❝✉r✈❛ ❞✐❢❡r❡♥❝✐á✈❡❧♣♦r ♣❛rt❡s ❧✐❣❛♥❞♦ ♣ ❛ q✳ ◆ã♦ é ❞✐❢í❝✐❧ ✈❡r q✉❡ ✭▼❀ ❞✮ é ✉♠ ❡s♣❛ç♦ ♠étr✐❝♦✳❚❡♦r❡♠❛ ✶✳✸ ✭❍♦♣❢✲❘✐♥♦✇✮✳ ❯♠❛ ✈❛r✐❡❞❛❞❡ ❘✐❡♠❛♥♥✐❛♥❛ é ❝♦♠♣❧❡t❛ s❡✱ ❡ s♦♠❡♥t❡ s❡✱ é ❝♦♠♣❧❡t❛ ❝♦♠♦ ✉♠ ❡s♣❛ç♦ ♠étr✐❝♦✳❉❡♠♦♥str❛çã♦✳ ❱❡r ❬✽❪✱ ♣á❣✐♥❛ ✶✵✽✳ ❖ ❚❡♦r❡♠❛ ✭✶✳✸✮ ♣♦ss✉✐ ✈ár✐❛s ❝♦♥s❡qüê♥❝✐❛s✱ ♣♦r ❡①❡♠♣❧♦✿✭✐✮ s❡ ▼ é ❝♦♠♣❧❡t❛✱ ❡♥tã♦ ❞♦✐s ♣♦♥t♦s q✉❛✐sq✉❡r ❞❡ ▼ ♣♦❞❡♠ s❡r ❧✐❣❛❞♦s ♣♦r ✉♠ s❡❣♠❡♥t♦ ❞❡ ❣❡♦❞és✐❝❛ ♠✐♥✐♠✐③❛♥t❡❀✭✐✐✮ s❡ ▼ é ❝♦♠♣❛❝t❛✱ ❡♥tã♦ ▼ é ❝♦♠♣❧❡t❛✳ ✶✳✺ ❈✉r✈❛t✉r❛s ◆❡st❛ s❡çã♦✱ ✐♥tr♦❞✉③✐♠♦s ♦ ❝♦♥❝❡✐t♦ ❞❡ ❝✉r✈❛t✉r❛ ♥✉♠❛ ✈❛r✐❡❞❛❞❡❘✐❡♠❛♥♥✐❛♥❛✱ ❝✉❧♠✐♥❛♥❞♦ ❝♦♠ ❛s ❞❡✜♥✐çõ❡s ❞❡ ❝✉r✈❛t✉r❛ ❞❡ ❘✐❝❝✐ ❡❝✉r✈❛t✉r❛ ❡s❝❛❧❛r✳ ▼❛✐s ❝♦♥s✐❞❡r❛çõ❡s s♦❜r❡ ❝✉r✈❛t✉r❛s ♣♦❞❡♠ s❡r ✈✐st❛s✱♣♦r ❡①❡♠♣❧♦✱ ❡♠ ❬✽❪✱ ❝❛♣ít✉❧♦ ✼✳ ❆ ❝✉r✈❛t✉r❛ ❘ ❞❡ ✉♠❛ ✈❛r✐❡❞❛❞❡ ❘✐❡♠❛♥♥✐❛♥❛ é ❛ ❛♣❧✐❝❛çã♦ q✉❡ ❛ ❝❛❞❛♣❛r ❳❀ ❨ ✷ ❳ ✭▼✮ ❛ss♦❝✐❛ ❛ ❝♦rr❡s♣♦♥❞ê♥❝✐❛ ❘✭❳❀ ❨ ✮ ✿ ❳ ✭▼✮ ✦ ❳ ✭▼✮❞❛❞❛ ♣♦r ❘✭❳❀ ❨ ✮❩ ❂ r ❳ r ❨ ❩ r ❨ r ❳ ❩ r ❬❳❀❨ ❪ ❩✿ ✷ ✷ ✷ ❥① ❫ ②❥ ❂ ❥①❥ ❥②❥ ❤①❀ ②✐é ❛ ár❡❛ ❞♦ ♣❛r❛❧❡❧♦❣r❛♠♦ ❣❡r❛❞♦ ♣♦r ❢①❀ ②❣✳ ♣ P♦❞❡✲s❡ ✈❡r✐✜❝❛r q✉❡✱ s❡ ✛ ✚ ❚ ▼ é ✉♠ s✉❜❡s♣❛ç♦ ❞❡ ❞✐♠❡♥sã♦ ✷ ❝♦♠❜❛s❡ ❢①❀ ②❣✱ ❡♥tã♦ ❤❘✭①❀ ②✮②❀ ①✐❑✭①❀ ②✮ ❂ ✷ ❥① ❫ ②❥♥ã♦ ❞❡♣❡♥❞❡ ❞❛ ❡s❝♦❧❤❛ ❞❛ ❜❛s❡ ❞❡ ✛✳ ❋✐❝❛ ❡♥tã♦ ❜❡♠ ❞❡✜♥✐❞❛ ❛ ❝✉r✈❛t✉r❛ s❡❝❝✐♦♥❛❧ ❞❡ ✛ ❡♠ ▼ ♥♦ ♣♦♥t♦ ♣❝♦♠♦ s❡♥❞♦ ♦ ♥ú♠❡r♦ r❡❛❧ ❞❛❞♦ ♣♦r ❑✭✛✮ ✿❂ ❑✭①❀ ②✮✳ ♥ ♣ ❙❡❥❛ ① ❂ ③ ✉♠ ✈❡t♦r ✉♥✐tár✐♦ ❡♠ ❚ ▼✱ t♦♠❡♠♦s ✉♠❛ ❜❛s❡ ♦rt♦♥♦r♠❛❧ ✶ ♥ ✶ ♣ ❇ ❂ ❢③ ❀ ✿ ✿ ✿ ❀ ③ ❣ ❞♦ ❤✐♣❡r♣❧❛♥♦ ❞❡ ❚ ▼ ♦rt♦❣♦♥❛❧ ❛ ① ❡ ❝♦♥s✐❞❡r❡♠♦s ❛s s❡❣✉✐♥t❡s ♠é❞✐❛s✿❉❡✜♥✐çã♦ ✶✳✺✳ ❈✉r✈❛t✉r❛ ❞❡ ❘✐❝❝✐ ❳✶ ❘✐❝ ♣ ✭①✮ ❂ ❤❘✭①❀ ③ ✐ ✮③ ✐ ❀ ①✐ ❀ ✐ ❂ ✶❀ ✿ ✿ ✿ ❀ ♥ ✶✿♥ ✶ ✐ ❉❡✜♥✐çã♦ ✶✳✻✳ ❈✉r✈❛t✉r❛ ❊s❝❛❧❛r❳ ✶❙✭♣✮ ❂ ❘✐❝ ♣ ✭③ ❥ ✮✿ ♥ ❥ ❊♠ ❬✸❪✱ ♣á❣✐♥❛ ✶✵✽✱ é ❞❡♠♦♥str❛❞♦ q✉❡ ❛ ❝✉r✈❛t✉r❛ ❞❡ ❘✐❝❝✐ ❡ ❛ ❝✉r✈❛t✉r❛❡s❝❛❧❛r ♥ã♦ ❞❡♣❡♥❞❡♠ ❞❛s ❝♦rr❡s♣♦♥❞❡♥t❡s ❜❛s❡s ♦rt♦♥♦r♠❛✐s✱ ♣♦rt❛♥t♦ ❡stã♦❜❡♠ ❞❡✜♥✐❞❛s✳ ❆✐♥❞❛ ❝♦♥s✐❞❡r❛♥❞♦ ❛ ❜❛s❡ ♦rt♦♥♦r♠❛❧ ❇✱ ♦❜s❡r✈❛♠♦s q✉❡ ♥ ✶ ❳✶ ♣ ✐ ❘✐❝ ✭①✮ ❂ ❑✭①❀ ③ ✮✿♥ ✶ ✐❂✶ P♦rt❛♥t♦✱ s❡ ▼ é ✉♠❛ ✈❛r✐❡❞❛❞❡ ❘✐❡♠❛♥♥✐❛♥❛ ❝♦♠ ❝✉r✈❛t✉r❛ s❡❝❝✐♦♥❛❧ ♥ã♦✲♥❡❣❛t✐✈❛ ❡♠ t♦❞♦s ♦s ♣♦♥t♦s✱ ❡♥tã♦ ♦ ♠❡s♠♦ ❛❝♦♥t❡❝❡ ❝♦♠ ❛ ❝✉r✈❛t✉r❛❞❡ ❘✐❝❝✐✱ ✐st♦ é✱ ❘✐❝✭▼✮ ✕ ✵✳❖❜s❡r✈❛çã♦ ✶✳✶✳ ❆❧❣✉♠❛s ✈❡③❡s ✉s❛r❡♠♦s ❛ ♥♦t❛çã♦ ❞❡ ❊✐♥st❡✐♥✱ ♦✉ s❡❥❛✱♦♠✐t✐r❡♠♦s ♦ s✐♥❛❧ ❞❡ s♦♠❛tór✐♦ ❡♠ s♦♠❛s q✉❡ ❛♣❛r❡❝❡♠ í♥❞✐❝❡s r❡♣❡t✐❞♦s✱♣♦r ❡①❡♠♣❧♦ ❳ ❦ ❦ ❦ ❦ ❳ ❂ ❳ ✿ ✐❥ ✐❥ ❦ ❙❡❥❛ ❢❡ ✶ ❀ ✿ ✿ ✿ ❀ ❡ ♥ ❣ ✉♠❛ ❜❛s❡ ♦rt♦♥♦r♠❛❧ ❞❡ ❝❛♠♣♦s ❞❡ ✈❡t♦r❡s ❡♠ t♦r♥♦ ❞❡ ❧ ✉♠ ♣♦♥t♦ ♣ ✷ ▼✳ ❖s ❝♦❡✜❝✐❡♥t❡s ❘ ✱ ❞❡✜♥✐❞♦s ♣♦r ✐❥❦ ❳ ❧ ✐ ❥ ❦ ❧ ❘✭❡ ❀ ❡ ✮❡ ❂ ❘ ✐❥❦ ❡ ❧ ❧ ❂ ❘ ❡ ❧ ❀ ✭✶✳✶✮ ✐❥❦ sã♦ ❞❡♥♦♠✐♥❛❞♦s ❝♦♠♣♦♥❡♥t❡s ❞♦ t❡♥s♦r ❝✉r✈❛t✉r❛✳❚❡♠♦s ❛✐♥❞❛ q✉❡ ✯ ✰❳ ❧ ❤❘✭❡ ✐ ❀ ❡ ❥ ✮❡ ❦ ❀ ❡ s ✐ ❂ ❘ ❡ ❧ ❀ ❡ s ✐❥❦ ❧ ❳ ❧ ❂ ❘ ✍ ❧s ✐❥❦ ❧s ❂ ❘ ✐❥❦ ✐❥❦s ✿❂ ❘ ✿❖s ❝♦❡✜❝✐❡♥t❡s ❘ ✐❥❦s sã♦ ❞❡♥♦♠✐♥❛❞♦s ❝♦❡✜❝✐❡♥t❡s ❞❡ ❘✐❝❝✐✳❖✉tr❛ ♥♦t❛çã♦ q✉❡ ✉t✐❧✐③❛r❡♠♦s é ❛ s❡❣✉✐♥t❡✿ ❳❘✐❝✭✈❀ ✇✮ ❂ ❤❘✭✈❀ ❡ ✐ ✮❡ ✐ ❀ ✇✮✐ ❂ ❤❘✭✈❀ ❡ ✐ ✮❡ ✐ ❀ ✇✮✐ ✿ ✐ ❖s ❝♦❡✜❝✐❡♥t❡s ❞❡ ❘✐❝❝✐ tê♠ ✉♠❛ ❡①♣r❡ssã♦ ❡♠ t❡r♠♦s ❞♦s sí♠❜♦❧♦s ❞❡ ❈❤r✐st♦✛❡❧ ❞❛❞❛ ♣♦r❘ ❀ ✭✶✳✷✮❛ q✉❛❧✱ ♥❛ ♥♦t❛çã♦ ❞❡ ❊✐♥st❡✐♥✱ s❡ ❡①♣r❡ss❛ ❝♦♠♦ s ✐❦ ❅❅❡ ❥ s ❥❦ ❅❡ ✐ ✰❅ ❧ ✐❦s ❥❧ ❧ ❥❦s ✐❧ ❂ s ✐❥❦ ❘ s ✐❦ s ✐❥❦ ❅❅❡ ❥ s ❥❦ ❅❡ ✐ ✰❅ ❥❧ ❧ ❧✐❦ s ❳ ✐❧ ❧ ❧❥❦ s ❂❳ ✿❆ ❡①♣r❡ssã♦ ✭✶✳✷✮ ♣♦❞❡ s❡r ❡♥❝♦♥tr❛❞❛✱ ♣♦r ❡①❡♠♣❧♦✱ ❡♠ ❬✸❪✱ ♣á❣✐♥❛ ✶✵✸✳ ❈❛♣ít✉❧♦ ✷ ❘❡s✉❧t❛❞♦s Pr❡❧✐♠✐♥❛r❡s ❖s r❡s✉❧t❛❞♦s ❞❡st❡ ❝❛♣ít✉❧♦ ❢♦r♠❛rã♦ ✉♠❛ ❜❛s❡ ♣❛r❛ ♦ ♣ró①✐♠♦ ❡ ú❧t✐♠♦❝❛♣ít✉❧♦ ❞❡st❛ ❞✐ss❡rt❛çã♦✳ ✷✳✶ ❋ór♠✉❧❛ ❞❡ ❲❡✐t③❡♥❜ö❝❦ ❆♣r❡s❡♥t❛r❡♠♦s ❛ s❡❣✉✐r ✉♠ r❡s✉❧t❛❞♦ ❞❡ ❣r❛♥❞❡ ✐♠♣♦rtâ♥❝✐❛✱ ❛ s❛❜❡r✿ ❛❢ór♠✉❧❛ ❞❡ ❲❡✐t③❡♥❜ö❝❦✳ ❆♥t❡s✱ ♣♦ré♠✱ ♠♦str❛r❡♠♦s ❛ ✐❞❡♥t✐❞❛❞❡ ❞❡ ❘✐❝❝✐✱❛ ✜♠ ❞❡ ❢❛③❡r♠♦s ✉s♦ ❛❞✐❛♥t❡✳ ✸ ▲❡♠❛ ✷✳✶ ✭■❞❡♥t✐❞❛❞❡ ❞❡ ❘✐❝❝✐✮✳ ❉❛❞❛ ❢ ✷ ❈ ✭▼✮✱ ♣❛r❛ q✉❛✐sq✉❡r ✶ ✔✐❀ ❥❀ ❦ ✔ ♥✱ ✈❛❧❡ ❛ ✐❣✉❛❧❞❛❞❡✿ ❢ ✐❦❧ ❂ ❢ ✐❧❦ ✰ ❘ ❦❧s✐ ❢ s ❀♦♥❞❡ ❘ ❦❧s✐ sã♦ ♦s ❝♦❡✜❝✐❡♥t❡s ❞❡ ❘✐❝❝✐✳❉❡♠♦♥str❛çã♦✳ ❚❡♠♦s q✉❡ ❅❢ ❅✭ ✮ ❅❡ ❅❢ ✐ ✉ ❢ ✐❦ ❂ ❦✐ ❅❡ ❦ ❅❡ ✉ ✷ ❅ ❢ ❅❢ ✉ ❂ ❦✐ ✿ ✐ ❦ ✉ ❅❡ ❅❡ ❅❡ ❉❛í✱❢ ✐❦❧ ❂ ❢❅❡ ❧ ❅❡ ✉ ❅❡ ❧✭ ✉ ✐❦ ✮❅❢ ❅❡ ✉ ✉ ✐❦ ❅ ✷ ✰❅ ✿❆♣❧✐❝❛♥❞♦ ❡ss❛ ú❧t✐♠❛ ❡q✉❛çã♦ ❛ ✭✷✳✶✮✱ ♦❜t❡♠♦s ❅❡ ❦✭ ✉ ✐❧ ✮❅❢ ❅❡ ✉✰ ✉ ✐❧ ❅ ✷ ❢ ✐❦❧ ❢ ✐❧❦ ❂❅ ❢❅❡ ❦ ❅❡ ✉ ✉ ❧✐ ❅ ❅❡ ❦❂ ❅❅❡ ❧ ✭ ✉ ✐❦ ✮❅❢ ❅❡ ✉ ✉ ✐❦ ✷ ✷ ❢❅❡ ❧ ❅❡ ✉ ✰❅ ❅❡ ❦✭ ✉ ✐❧ ✮❅❢ ❅❡ ✉✰ ✉ ✐❧ ❅ ❢❅❡ ❦ ❅❡ ✉ ❢ ✉❦ ✰ ❅❡ ❧❅❢ ✓✰ ✷ ❢❅❡ ✉ ❅❡ ❦ s✉❦ ❅❢❅❡ s ✉ ❦✐ ✉ ❧✐ ✒❅ ✷ ❢❅❡ ✉ ❅❡ ❧ s✉❧ ❅❢❅❡ s ✒❅ ❢❅❡ ❦ ❅❡ ✉ ✉ ❦✐ ❅ ❢ ✉❧❂ ❅❅❡ ❧ ✭ ✉ ✐❦ ✮❅❢ ❅❡ ✉ ✉ ✐❦ ✷ ✷ ❢❅❡ ❧ ❅❡ ✉ ✰❅ ❅❡ ❦✭ ✉ ✐❧ ✮❅❢ ❅❡ ✉✰ ✉ ✐❧ ❅ ✐❧ ✐❦ ❅❢ ✿ ✭✷✳✶✮▼❛s ✉❦ ❅❢ ✐❧ ❅❡ ❦✰ ✉ ❦✐ ❢ ✉❧ ❅❢ ✉ ❧✐ ✐❦ ❅❡ ❧ ❂❅ ❅❡ ❧ ✒❅ ✷ ❢ ❅❡ ❧ ✐ ❦ ✉❦✐ ✐❦ ❅❡ ❧ ✉ ❧✐ ❢ ✉❦ ✉ ❧❦ ❢ ✉✐ ❀❡ ❢ ✐❧❦ ❂❅❢ ✐❧❅❡ ❢ ✉❧ ✐❦ ✉ ❦❧ ❢ ✉✐ ✿❈♦♠♦ ✉ ❧❦ ❂✉ ❦❧ ✱ s❡❣✉❡✲s❡ q✉❡ ❢ ✐❦❧ ❢ ✐❧❦ ❂❅❢ ❢❅❡ ❡ ❅❢ ❅❅❡ ❦ ❅❡ ✉ ❡❅❢ ✐❧ ❅❡ ❦❂ ❅ ✸ ❢❅❡ ❦ ❅❡ ✐ ❅❡ ❧ ✭ ❢❅❡ ✉ ✐❧ ✮❅❢ ❅❡ ✉ ✉ ✐❧ ❅ ✷ ❢❅❡ ❦ ❅❡ ✉ ✿❆ss✐♠✱ ❧ ✷ ❦ ✉✐❦ ❅❡ ❅❢❅❡ ✉ ✓❂ ❅ ✸ ❢❅❡ ❧ ✐ ❅ ❅❡ ❦ ❅❅❡ ❧ ✭ ✉ ✐❦ ✮ ❅❢❅❡ ✉ ✉✐❦ ✓✿ ❯s❛♥❞♦ ♠❛✐s ✉♠❛ ✈❡③ ❛ s✐♠❡tr✐❛ ❞♦s sí♠❜♦❧♦s ❞❡ ❈❤r✐st♦✛❡❧✱ ✈❡♠♦s q✉❡✒ ✓ ❅ ❅ ❅❢ ✉ s ✉ s s s ✐❦❧ ✐❧❦ ❢ ❢ ❂ ✰ ✭ ✮ ✭ ✮ ❧✐ ✉❦ ❦✐ ✉❧ ✐❧ ✐❦ ❅❡ ❦ ❅❡ ❧ ❅❡ s ❦❧s✐ s ❂ ❘ ❢ ✿ ✸ Pr♦♣♦s✐çã♦ ✷✳✶ ✭❋ór♠✉❧❛ ❞❡ ❲❡✐t③❡♥❜ö❝❦✮✳ ❙❡❥❛ ❢ ✷ ❈ ✉♠❛ ❢✉♥çã♦❞❡✜♥✐❞❛ ❡♠ ▼✳ ❊♥tã♦ ✁✶ ✷ ✷ ✁ ❥ ❣r❛❞ ❢❥ ❂ ❥ ❍❡ss ❢❥ ✰ ❤❣r❛❞ ❢❀ ❣r❛❞✭✁❢✮✐ ✰ ❘✐❝ ✭❣r❛❞ ❢❀ ❣r❛❞ ❢✮ ✿✷ ✶ ♥ ❉❡♠♦♥str❛çã♦✳ ❙❡❥❛ ❢❊ ❀ ✿✿✿❀ ❊ ❣ ✉♠❛ ❜❛s❡ ♦rt♦♥♦r♠❛❧ ❡♠ t♦r♥♦ ❞❡ ✉♠ ♣♦♥t♦P ♥ ✷ ✷ ♣ ✷ ▼✳ ❆✜r♠❛♠♦s q✉❡ ❥ ❣r❛❞ ❢❥ ❂ ❢ ✐ ✳ ❉❡ ❢❛t♦✱ ❡♠ ♣ ✷ ▼✱ ✐❂✶ ✶ ♥ ♦ ❝❛♠♣♦ ❣r❛❞ ❢ ♣♦❞❡ s❡r ❡s❝r✐t♦ ♥❛ ❜❛s❡ ❢❊ ❀ ✿✿✿❀ ❊ ❣ ❝♦♠♦ ❣r❛❞ ❢✭♣✮ ❂P ♥ ✐ ✐ ✐ ☛ ✭♣✮❊ ✭♣✮✱ ♦♥❞❡ ❝❛❞❛ ☛ ✿ ❯ ✦ ❘ é ✉♠❛ ❛♣❧✐❝❛çã♦ ❞✐❢❡r❡♥❝✐á✈❡❧ ❡♠ ✐❂✶ ❯✳❱✐st♦ q✉❡ ❢ ✐ ❂ ❊ ✐ ✭❢✮❂ ❤❊ ✐ ❀ ❣r❛❞ ❢✐❂ ☛ ✐ ❀ P ♥ ✐ ✐ t❡♠♦s q✉❡ ❣r❛❞ ❢ ❂ ❢ ❊ ❡✱ ♣♦rt❛♥t♦✱ ✐❂✶ ✷ ❥ ❣r❛❞ ❢❥ ❂ ❤❣r❛❞ ❢❀ ❣r❛❞ ❢✐✯ ✰ ♥ ♥ ❳ ❳❂ ❢ ✐ ❊ ✐ ❀ ❢ ✐ ❊ ✐ ✐❂✶ ✐❂✶ ♥ ❳ ✷ ❂ ❢ ✿ ✐ ✐❂✶ ■st♦ ♣r♦✈❛ ❛ ❛✜r♠❛çã♦✳ ❆❣♦r❛✱❳ ✷ ✷ ✭❥ ❣r❛❞ ❢❥ ✮ ❥ ❂ ✭ ❢ ✮ ❥ ✐ ✐ ❳ ✐ ✐❥ ❂ ✷❢ ❢ ❀ ✐ ♦✉ s❡❥❛✱❳ ✶ ✷ ❥ ✐ ✐❥ ✭❥ ❣r❛❞ ❢❥ ✮ ❂ ❢ ❢ ✿✷ ✐ ❚❡♠♦s t❛♠❜é♠ q✉❡❳ ✶ ✷ ✷ ❥❥ ✐ ✐❥❥ ✭❥ ❣r❛❞ ❢❥ ✮ ❂ ✭❢ ✰ ❢ ❢ ✮❀ ✐❥ ✷ ✐ ❞♦♥❞❡✥ ✦ ❳ ❳✁ ✶ ✷ ✷ ✐ ✐❥❥ ✁ ❥ ❣r❛❞ ❢❥ ❂ ✭❢ ✐❥ ✰ ❢ ❢ ✮✷ ❥ ✐ ❳ ✷ ✐ ✐❥❥ ❂ ✭❢ ✰ ❢ ❢ ✮✿ ✭✷✳✷✮ ✐❥ ✐❀❥ ❆❣♦r❛✱ ❝♦♠♦ ❛ ❍❡ss✐❛♥❛ ❞❡ ✉♠❛ ❢✉♥çã♦ é ✉♠ ✷✲t❡♥s♦r s✐♠étr✐❝♦✱ t❡♠♦s q✉❡ ❢ ✐❥❥ ❂ ❢ ❥✐❥ ✳ ❯s❛♥❞♦ ❡st❡ ❢❛t♦ ❥✉♥t❛♠❡♥t❡ ❝♦♠ ❛ ✐❞❡♥t✐❞❛❞❡ ❞❡ ❘✐❝❝✐✱♦❜t❡♠♦s q✉❡ ❢ ✐❥❥ ❂ ❢ ❥✐❥ ❂ ❢ ❥❥✐ ✰ ❘ ✐❥s❥ ❢ s ✿❆♣❧✐❝❛♥❞♦ ❡st❛ ú❧t✐♠❛ ✐❣✉❛❧❞❛❞❡ ❛ ✭✷✳✷✮✱ ✈❡♠♦s q✉❡ ❳✁ ✶ ✷ ✷ ✐ ❥❥✐ ✐❥s❥ s ✁ ❥ ❣r❛❞ ❢❥ ❂ ✭❢ ✰ ❢ ✭❢ ✰ ❘ ❢ ✮✮✿ ✐❥ ✷ ✐❀❥ ❋✐♥❛❧♠❡♥t❡✱ ♦❜t❡♠♦s q✉❡❳ ❳ ❳ ✁✶ ✷ ✷ ✁ ❥ ❣r❛❞ ❢❥ ❂ ❢ ✰ ❢ ✐ ❢ ❥❥✐ ✰ ❘ ✐❥s❥ ❢ s ❢ ✐ ✐❥ ✷ ✐❀❥ ✐❀❥ ✐❀❥ ❳ ✷ ❂ ❥ ❍❡ss ❢❥ ✰ ❤❣r❛❞ ❢❀ ❣r❛❞✭✁❢✮✐ ✰ ❘✐❝✭❊ s ❀ ❊ ✐ ✮❢ s ❢ ✐ ✐❀s ❳ ❳ ✷ s s ✐ ✐ ❂ ❥ ❍❡ss ❢❥ ✰ ❤❣r❛❞ ❢❀ ❣r❛❞✭✁❢✮✐ ✰ ❘✐❝✭ ❢ ❊ ❀ ❢ ❊ ✮ s ✐ ✷ ❂ ❥ ❍❡ss ❢❥ ✰ ❤❣r❛❞ ❢❀ ❣r❛❞✭✁❢✮✐ ✰ ❘✐❝✭❣r❛❞ ❢❀ ❣r❛❞ ❢✮✿ ✷✳✷ ❆ ❍❡ss✐❛♥❛ ❞❛ ❋✉♥çã♦ ❉✐stâ♥❝✐❛ ◆❡st❛ s❡çã♦✱ ♦❜t❡r❡♠♦s ❞♦✐s r❡s✉❧t❛❞♦s s♦❜r❡ ❛ ❍❡ss✐❛♥❛ ❞❛ ❢✉♥çã♦❞✐stâ♥❝✐❛✳ ❚❛✐s r❡s✉❧t❛❞♦s s❡rã♦ ✐♠♣♦rt❛♥t❡s ♣❛r❛ ❛ ❞❡♠♦♥str❛çã♦ ❞♦❚❡♦r❡♠❛ ❞❡ ❈♦♠♣❛r❛çã♦ ❞♦ ▲❛♣❧❛❝✐❛♥♦ ♥❛ ♣ró①✐♠❛ s❡çã♦✳Pr♦♣♦s✐çã♦ ✷✳✷✳ ❙❡❥❛ r ✿ ▼ ✦ ❘ ❞❡✜♥✐❞❛ ♣♦r r✭①✮ ❂ ❞✭①❀ ♣✮✱ ♦♥❞❡ ❞ é ❛ ❅ ❅ ❅ ❢✉♥çã♦ ❞✐stâ♥❝✐❛✳ ❊♥tã♦ ❍❡ss r✭ ❀ ✮ ❂ ✵✳ ❆❧é♠ ❞✐ss♦✱ s❡ ✽ ❳ ❄ ✱ ✈❛❧❡ ❅r ❅r ❅r ❅ ❅ ❍❡ss r✭ ❀ ❳✮ ❂ ✵✱ ♦♥❞❡ é ♦ ✈❡t♦r ✈❡❧♦❝✐❞❛❞❡✳ ❅r ❅r ❉❡♠♦♥str❛çã♦✳ ❯s❛♥❞♦ ❛ ❞❡✜♥✐çã♦ ❞❡ ❍❡ss✐❛♥❛ ♣❛r❛ ❛ ❢✉♥çã♦ r ❡ ♦ ❢❛t♦ q✉❡ ❅ ❛s ❝✉r✈❛s r ✼ ✦ r✇✱ ♣❛r❛ ✇ ✜①❛❞♦✱ sã♦ ❣❡♦❞és✐❝❛s ❝♦♠ ✈❡t♦r ✈❡❧♦❝✐❞❛❞❡ ✱ ❅r t❡♠♦s q✉❡✒ ✓ ❅ ❅ ❅ ❅ ❅ ❅❍❡ss r ❀ ❂ r r r ❅r ❅r ❅r ❅r ❅r ❅r❅ ❂ ✭✶✮❅r ❂ ✵✿❆❣♦r❛✱ ♣❡❧♦ ▲❡♠❛ ❞❡ ●❛✉ss✱ ✈❡r ❬✽❪✱ ♣á❣✐♥❛ ✶✵✷✱ t❡♠♦s q✉❡ ❅❣r❛❞ r ❂ ✿ ❅r ❅ P♦rt❛♥t♦✱ s❡ ❳ ❄ ✱ ♦❜t❡♠♦s ❅r ❅ ❅❍❡ss r✭ ❀ ❳✮ ❂ ❍❡ss r✭❳❀ ✮ ❅r ❅r❅ ❅ ❂ ❳ r ✭r ❳ ✮r❅r ❅r✜ ✢ ❅ ❅ ❳ ❂ r ❀ ❀❅r ❅r ❅ ♣♦✐s ❳✭ ✮r ❂ ❳✭✶✮ ❂ ✵✳ ❅r ❯s❛♥❞♦ ❛ ❝♦♠♣❛t✐❜✐❧✐❞❛❞❡ ❞❛ ♠étr✐❝❛✱ ♦❜t❡♠♦s✜ ✢ ❅ ✶ ❅ ❅❍❡ss r✭ ❀ ❳✮ ❂ ❳ ❀ ✿ ❅r ✷ ❅r ❅r❋✐♥❛❧♠❡♥t❡✱ ❝♦♠♦ ❛s ❣❡♦❞és✐❝❛s r❛❞✐❛✐s sã♦ ♣❛r❛♠❡tr✐③❛❞❛s ♣♦r ❝♦♠♣r✐♠❡♥t♦ ❞❡ ❛r❝♦✱❅ ✶ ❍❡ss r✭ ❀ ❳✮ ❂ ❳✭✶✮ ❂ ✵✿❅r ✷ ♥ Pr♦♣♦s✐çã♦ ✷✳✸✳ ❈♦♥s✐❞❡r❡♠♦s ❘ ♠✉♥✐❞♦ ❝♦♠ ❛ ♠étr✐❝❛ ❣✱ ❡s❝r✐t❛ ❡♠ ✷ ✷ ✷ ✷ ❝♦♦r❞❡♥❛❞❛s ♣♦❧❛r❡s ❝♦♠♦ ❞r ✰ ❢ ✭r✮❞✇ ✱ ♦♥❞❡ ❞✇ r❡♣r❡s❡♥t❛ ❛ ♠étr✐❝❛ ♥ ✶ ❝❛♥ô♥✐❝❛ ❡♠ ❙ ✳ ❙❡❥❛ r✭①✮ ❂ ❞✭①❀ ♣✮✱ ♦♥❞❡ ❞ é ❛ ❢✉♥çã♦ ❞✐stâ♥❝✐❛✳ ❊♥tã♦✱ ♥ ✶ ❅ s❡ ① ❂ r✇✱ r ❃ ✵✱ ✇ ✷ ❙ ✱ ♣❛r❛ q✉❛✐sq✉❡r ❳❀ ❨ ♦rt♦❣♦♥❛✐s ❛ ✱ ❅r ✵ ❢ ✭r✮❍❡ss r✭❳❀ ❨ ✮ ❂ ❣✭❳❀ ❨ ✮✿ ❢✭r✮❆❧é♠ ❞✐ss♦✱ ✵ ❢ ✭r✮✁r✭①✮ ❂ ✭♥ ✶✮ ✿ ❢✭r✮❉❡♠♦♥str❛çã♦✳ ❙❡❥❛♠ ❳❀ ❨ ❝❛♠♣♦s ❞❡ ✈❡t♦r❡s t❛♥❣❡♥t❡s ❛♦ ❝♦♥❥✉♥t♦ ❞❡ ♥í✈❡❧ ✜ ✢ ✜ ✢❅ ❅ ❂ ❨ ❳❀ r ❨ ❳❀❅r ❅r ✜ ✢ ✜ ✢ ✜ ✢❅ ❅ ❅ ❂ r ❨ ❳❀ ✰ ❳❀ r ❨ r ❨ ❳❀❅r ❅r ❅r ✜ ✢❅ ❨ ❂ ❳❀ r❅r ✜ ✢❅ ❂ ❨❀ r ❳ ✿❅r ◆❛ ú❧t✐♠❛ ✐❣✉❛❧❞❛❞❡ ✉s❛♠♦s ❛ s✐♠❡tr✐❛ ❞❛ ❍❡ss✐❛♥❛✳ ❅ ❅❅ ❆❣♦r❛✱ s❡❥❛♠ ❂ ♦ ❝❛♠♣♦ ♥♦r♠❛❧ ❛ ❤✐♣❡rs✉♣❡r❢í❝✐❡ r ❂ ❝ ❡ ❀ ✿ ✿ ✿ ❀ ❅① ❅r ♥❅① ✶ ❅ ♥ ✶ ✱ ♦s ❝❛♠♣♦s ❝♦♦r❞❡♥❛❞♦s ❡♠ ❙ ✳ ❅① ♥ ✶ ❆ss✐♠✱ ♣❛r❛ ✶ ✔ ✐❀ ❥ ✔ ♥ ✶✱ t❡♠♦s q✉❡✒ ✓ ✜ ✢ ❅ ❅ ❅ ❅ ❅❍❡ss r ❀ ❂ ❀ r ❅①✐ ❅① ✐ ❅① ❥ ❅① ❥ ❅① ♥✜ ✢ ❅ ❅ ❦ ❂ ❀ ♥✐ ❅① ❦ ❅① ❥ ❦ ❂ ❣ ❦❥ ♥✐ ❯s❛♥❞♦ ❛ ❢ór♠✉❧❛ ❞♦s sí♠❜♦❧♦s ❞❡ ❈❤r✐st♦✛❡❧ ❡♠ t❡r♠♦s ❞♦s ❝♦❡✜❝✐❡♥t❡s❉ ❊ ❅ ❅ ♥✐ ❞❛ ♠étr✐❝❛ ❡ ✉s❛♥❞♦ ♦ ❢❛t♦ q✉❡ ❣ ❂ ❀ ❂ ✵❀ ✽ ✐ ❂ ✶❀ ✿ ✿ ✿ ❀ ♥ ✶✱ ❅r ❅① ✐ ❡♥❝♦♥tr❛♠♦s✒ ✓ ❳✶ ❅❣ ❧♥ ❅❣ ❧✐ ❅❣ ♥✐ ❦ ❦❧ ❂ ❣ ✰ ♥✐ ✐ ♥ ❧ ✷ ❅① ❅① ❅① ❧ ❳✶ ❅❣ ❧✐ ❦❧ ❂ ❣ ✿✷ ❅r ❧ ▼❛s✱ ♣♦r ♦✉tr♦ ❧❛❞♦✱❅❣ ❧✐ ✵ ✷ ❦❧ ✷ ✷ ❦❧ ❂ ✷❢❢ ✭❞✇ ✮ ❧✐ ❡ ❣ ❂ ❢ ✭❞✇ ✮ ✿❅r ❉❛í✱❳ ✶ ❦ ✷ ✷ ❦❧ ✵ ✷ ❂ ❢ ✭❞✇ ✮ ✷❢❢ ✭❞✇ ✮ ❧✐ ♥✐ ✷ ❧ ✵ ❢❂ ✍ ✐❦ ✿ ❢P♦rt❛♥t♦✱ ✒ ✓ ✵ ❅ ❅ ❢ ✐❦ ❦❥ ❍❡ss r ❀ ❂ ✍ ❣ ✐ ❥ ❅① ❅① ❢✒ ✓ ✵ ❢ ❅ ❅❂ ❣ ❀ ✿ ✐ ❥ ❢ ❅① ❅① ❅ ▲♦❣♦✱ s❡ ❳ ❡ ❨ sã♦ ♦rt♦❣♦♥❛✐s ❛ ✱ ❡♥tã♦ ❅r ✵ ❢❍❡ss r✭❳❀ ❨ ✮ ❂ ❣✭❳❀ ❨ ✮✿ ❢❆❣♦r❛✱ s❛❜❡♠♦s q✉❡ ❡①✐st❡ ❆ ✿ ❚ ❙ ✦ ❚ ❙ t❛❧ q✉❡ tr ❍❡ss r ❂ tr❆ ❡ ✐❥ ❍❡ss r✭❳❀ ❨ ✮ ❂ ❤❆❳❀ ❨ ✐✱ ✽ ❳❀ ❨ ✷ ❚ ❙✳ ❖r❛✱ ❆✭❳ ✐ ✮ ❂ ❛ ❳ ❥ ✳ ■st♦ ✐♠♣❧✐❝❛ ✐❥ ✐❥ ❥❦ q✉❡ ❤❆✭❳ ✐ ✮❀ ❳ ❦ ✐ ❂ ❛ ❣ ❥❦ ✱ ♦✉ s❡❥❛✱ ❛ ❂ ❣ ❍❡ss r✭❳ ✐ ❀ ❳ ❦ ✮✳❆ss✐♠✱ ✁r ❂ tr ❍❡ss r ❂ tr❆ ✵ ❳❢ ✐❦ ❂ ❣ ❣✭❳ ✐ ❀ ❳ ❦ ✮❢ ✐ ✵ ❢❂ ✭♥ ✶✮ ✿ ❢❊①❡♠♣❧♦ ✷✳✶✳ ❈❛❧❝✉❧❛r❡♠♦s ♦ ▲❛♣❧❛❝✐❛♥♦ ❞❛ ❢✉♥çã♦ ❞✐stâ♥❝✐❛ r ❦ ✱ ❝♦♠ r❡s✲♣❡✐t♦ ❛ ♠étr✐❝❛ ✷ ✷ ✷ ❞r ✰ ❢ ❦ ❞✇ ❀ ♦♥❞❡✽ ♣✶ ❃❃ ♣ s✐♥✭ ❦r✮❀ s❡ ❦ ❃ ✵❃❃❁ ❦❢ ❦ ✭r✮ ❂ r❀ s❡ ❦ ❂ ✵ ❃❃ ♣✶ ❃❃ ♣✿ s✐♥❤✭ ❦r✮❀ s❡ ❦ ❁ ✵✿ ❦ ♥ ✶ ✷ ❖❜s❡r✈❛♠♦s q✉❡✱ q✉❛♥❞♦ ❦ ❃ ✵✱ ♦❜t❡♠♦s ❛ ♠étr✐❝❛ ❞❛ ❡s❢❡r❛ ❙ ❞❡ r❛✐♦ ❦ q✉❡ t❡♠ ❝✉r✈❛t✉r❛ s❡❝❝✐♦♥❛❧ ❝♦♥st❛♥t❡ ❦✳ ◗✉❛♥❞♦ ❦ ❁ ✵✱ ♦❜t❡♠♦s ❛ ♠étr✐❝❛ ♥ ❞♦ ❡s♣❛ç♦ ❤✐♣❡r❜ó❧✐❝♦ ❍ ✱ t❛♠❜é♠ ❝♦♠ ❝✉r✈❛t✉r❛ s❡❝❝✐♦♥❛❧ ❝♦♥st❛♥t❡ ✐❣✉❛❧ ❛ ♥ ❦✳ ◗✉❛♥❞♦ ❦ ❂ ✵✱ ♦❜❡t♠♦s ❛ ♠étr✐❝❛ ❝❛♥ô♥✐❝❛ ❞♦ ❘ ❡♠ ❝♦♦r❞❡♥❛❞❛s ♣♦❧❛r❡s✳➱ ❢á❝✐❧ ✈❡r q✉❡ ✽ ♣❃ ❝♦s✭ ❦r✮❀ s❡ ❦ ❃ ✵❁ ✵ ❢ ✭r✮ ❂ ❦ ✶❀ s❡ ❦ ❂ ✵ ❃♣ ✿❝♦s❤✭ ❦r✮❀ s❡ ❦ ❁ ✵✿ ❆ss✐♠✱ ♣❛r❛ ❦ ❃ ✵✱ t❡♠♦s♣ ♣ ❦ ❝♦s✭ ❦r✮❍❡ss r ❦ ❂ ♣ ❣ s✐♥✭ ❦r✮ ♣ ♣❂ ❦ ❝♦t✭ ❦r✮❣✿ ◗✉❛♥❞♦ ❦ ❂ ✵✱✶ ❍❡ss r ❂ ❣✿ r❊ ♣ ♣❦ ❝♦s❤✭ ❦r✮ ❍❡ss r ❦ ❂ ♣ ❣ s✐♥❤✭ ❦r✮♣ ♣ ❂ ❦ ❝♦t❤✭ ❦r✮❣❀ s❡ ❦ ❁ ✵✳ ♣ ♣❃ ❦ ❝♦t✭ ❦r✮❀ s❡ ❦ ❃ ✵❃❃❁ ✶ ✶ ✁r ❦ ❂❀ s❡ ❦ ❂ ✵ r ♥ ✶ ❃❃❃ ♣ ♣✿ ❦ ❝♦t❤✭ ❦r✮❀ s❡ ❦ ❁ ✵✿ ✷✳✸ ❚❡♦r❡♠❛ ❞❡ ❈♦♠♣❛r❛çã♦ ❞♦ ▲❛♣❧❛❝✐❛♥♦ P❛rt✐♠♦s ❛❣♦r❛ ♣❛r❛ ♦ t❡♦r❡♠❛ ❞❡ ❈♦♠♣❛r❛çã♦ ❞♦ ▲❛♣❧❛❝✐❛♥♦✱ ♦ q✉❛❧ s❡rá❞❡♠♦♥str❛❞♦ ❝♦♠ ♦ ✉s♦ ❞❛ ❢ór♠✉❧❛ ❞❡ ❲❡✐t③❡♥❜ö❝❦✳ ♥ ❚❡♦r❡♠❛ ✷✳✶✳ ❙❡❥❛ ✭▼ ❀ ❣✮ ✉♠❛ ✈❛r✐❡❞❛❞❡ ❘✐❡♠❛♥♥✐❛♥❛ ❝♦♠♣❧❡t❛✳ ❙✉♣♦✲♥❤❛♠♦s q✉❡ ❛ ❝✉r✈❛t✉r❛ ❞❡ ❘✐❝❝✐ ❞❡ ▼ s❛t✐s❢❛③ ❘✐❝✭▼✮ ✕ ✭♥ ✶✮❦❣✳ ❙❡❥❛ r❛ ❞✐stâ♥❝✐❛ ❣❡♦❞és✐❝❛ ❛♦ ♣♦♥t♦ ♣ ✷ ▼✳ ❙✉♣♦♥❤❛♠♦s ❛✐♥❞❛ q✉❡ ❛ ❢✉♥çã♦ r é❞✐❢❡r❡♥❝✐á✈❡❧ ♥♦ ♣♦♥t♦ ①✳ ❊♥tã♦ ✁r✭①✮ ✔ ✁r ❦ ✭⑦①✮❀ ✭✷✳✸✮ ✙ ♣❦ ✵ ✵ ♦♥❞❡ r ✭⑦①✮ ❂ r✭①✮ ❂ r ❡ r ❁ s❡ ❦ ❃ ✵✳ ❙❡ ❛ ✐❣✉❛❧❞❛❞❡ é s❛t✐s❢❡✐t❛✱ ❦ ❡♥tã♦ ❛ ❝✉r✈❛t✉r❛ s❡❝❝✐♦♥❛❧ ❞❡ q✉❛❧q✉❡r ♣❧❛♥♦ q✉❡ ❝♦♥t❡♥❤❛ ♦ ✈❡t♦r r❛❞✐❛❧✱❛♦ ❧♦♥❣♦ ❞❡ ❣❡♦❞és✐❝❛s ❧✐❣❛♥❞♦ ♣ ❡ ①✱ é ❝♦♥st❛♥t❡ ❡ ✐❣✉❛❧ ❛ ❦✳❉❡♠♦♥str❛çã♦✳ ❆ ❍❡ss✐❛♥❛ ❞❛ ❢✉♥çã♦ r ♣♦ss✉✐ ✉♠ ❛✉t♦✈❛❧♦r ✐❣✉❛❧ ❛ ③❡r♦✱ ♣♦✐s ✁ ❅ ❅ ❅ ❅ ❍❡ss r ❀ ❂ ✵ ❡ ❍❡ss r✭ ❀ ❳✮ ❂ ✵❀ ✽ ❳❄ ✳ ❊ss❡ ❢❛t♦ ❡ ❛ ❞❡s✐❣✉❛❧❞❛❞❡ ❅r ❅r ❅r ❅r ❞❡ ❈❛✉❝❤②✲❙❝❤✇❛r③ ❛♣❧✐❝❛❞❛ às ♠❛tr✐③❡s ❍❡ss✐❛♥❛ ❞❡ r ❡ ■❞❡♥t✐❞❛❞❡ ♥♦s ❞ã♦ ✷ ✭✁r✮ ✷ ❥ ❍❡ss r❥ ✕ ✿ ✭✷✳✹✮♥ ✶ ❯s❛♥❞♦ ❛ ❢ór♠✉❧❛ ❞❡ ❲❡✐t③❡♥❜ö❝❦ ❡ ♦ ❢❛t♦ ❞❡ q✉❡ ❥ ❣r❛❞ r❥ ❂ ✶✱ ♦❜t❡♠♦s✒ ✓ ❅ ❅ ✷ ✵ ❂ ❥ ❍❡ss r❥ ✰ ❤❣r❛❞ r❀ ❣r❛❞✭✁r✮✐ ✰ ❘✐❝ ❀❅r ❅r ✜ ✢ ✒ ✓❅ ❅ ❅ ✷ ❂ ❥ ❍❡ss r❥ ✰ ❀ ❣r❛❞✭✁r✮ ✰ ❘✐❝ ❀❅r ❅r ❅r ✒ ✓❅ ❅ ❅ ✷ ❂ ❥ ❍❡ss r❥ ✰ ✁r ✰ ❘✐❝ ❀❅r ❅r ❅r ✒ ✓❅ ❅ ✷ ✵ ❂ ❥ ❍❡ss r❥ ✰ ✭✁r✮ ✰ ❘✐❝ ❀ ✿❅r ❅r ❙❡❥❛ ✬ ❂ ✁r✳ ❯s❛♥❞♦ ❛ ❤✐♣ót❡s❡ s♦❜r❡ ❛ ❝✉r✈❛t✉r❛ ❞❡ ❘✐❝❝✐ ❡ ❛❞❡s✐❣✉❛❧❞❛❞❡ ✭✷✳✹✮✱ ✈❡♠♦s q✉❡ ✷ ✬ ✵ ✬ ✰ ✰ ✭♥ ✶✮❦ ✔ ✵✿♥ ✶ ✵ ❢ ❦ ❊st✉❞❛♥❞♦ ♦ ❝❛s♦ ❞❛ ✐❣✉❛❧❞❛❞❡✱ ♦❜s❡r✈❛♠♦s q✉❡ ✥ ❂ ✁r ❦ ❂ ✭♥ ✶✮ s❛✲ ❢ ❦ ❦ t✐s❢❛③ ❛ ✐❣✉❛❧❞❛❞❡✱ ♦♥❞❡ r é ❛ ❢✉♥çã♦ ❞✐stâ♥❝✐❛ s♦❜r❡ ❛ ✈❛r✐❡❞❛❞❡ ❞❡ ❝✉r✈❛t✉r❛ s❡❝❝✐♦♥❛❧ ❝♦♥s✲t❛♥t❡ ❦ ❡✽ ♣✶ ❃❃ ♣ s✐♥✭ ❦r✮❀ s❡ ❦ ❃ ✵❃❃❁ ❦ ❦ ❢ ✭r✮ ❂ r❀ s❡ ❦ ❂ ✵❃❃ ♣✶ ❃❃ ♣ s✐♥❤✭ ❦r✮❀ s❡ ❦ ❁ ✵✿✿ ❦❱✐st♦ q✉❡ ✥ é ✐♥❥❡t✐✈❛ ❡♠ s❡✉s r❡s♣❡❝t✐✈♦s ❞♦♠í♥✐♦s✱ ♣♦❞❡♠♦s ❡s❝♦❧❤❡r ✉♠❛ ❢✉♥çã♦ ✒✭t✮✱ ❞❡✜♥✐❞❛ ❡♠ ❬✵❀ r ✵ ✮✱ s❛t✐s❢❛③❡♥❞♦✒✭✵✮ ❂ ✵❀ ✥✭✒✭t✮✮ ❂ ✬✭t✮✿ ❆❣♦r❛✱ ❝♦♠♦ ✷ ✷ ✬ ✭t✮ ✥ ✭✒✭t✮✮ ✵ ✵ ✬ ✭t✮ ✰ ✰ ✭♥ ✶✮❦ ✔ ✵ ❂ ✥ ✭✒✭t✮✮ ✰ ✰ ✭♥ ✶✮❦❀♥ ✶ ♥ ✶ ✵ ♥ ✶❡ ❥ ✿ ❉❡ss❛s ❞✉❛s ú❧t✐♠❛s ✐❣✉❛❧❞❛❞❡s✱ s❡❣✉❡✲s❡ q✉❡ ✕ ❂ ✥ ♥ ✶ ✳ ❆❣♦r❛✱❝♦♥s✐❞❡r❡♠♦s ❛ ❜❛s❡ ❇ ❂ ✟❡ ✶ ❀ ✿ ✿ ✿ ❀ ❡ ♥ ✶ ❀ ❅ ❅r ✠❞❡ ✈❡t♦r❡s ♦rt♦♥♦r♠❛✐s q✉❡ ❞✐❛❣♦♥❛❧✐③❛ ❛ ❍❡ss✐❛♥❛ ❞❡ r✳❆✜r♠❛♠♦s q✉❡ r ❡❥ ❅❅r ❂✥ ❉❡ ❢❛t♦✱ ❡s❝r❡✈❡♥❞♦ r ❡ ❥ ✷ ❅ ❅r ♥❛ ❜❛s❡ ❇✱ t❡♠♦s r ❡ ❥ ❅❅r ❂ ♥ ✶ ❳ ❦❂✶ ☛ ❦ ❡ ❦ ✰ ❛❅ ♥ ✶✿ ❂✥ ✭t✮ ✔ ✥ ✭✒✭t✮✮✿❈♦♠♦ ✥ ✵ ✭✒✭t✮✮✿▼❛s ✬ ✵ ✭t✮ ❂ ✥ ✵ ✭✒✭t✮✮✒ ✵ ✭t✮ ❡✱ ♣♦rt❛♥t♦✱✥ ✵ ✭✒✭t✮✮✒ ✵ ✭t✮ ✔ ✥ ✵ ✵ ✷ ✭t✮ ❁ ✵✱ t❡♠♦s ✒ ✵ ✭t✮ ✕ ✶✳ ■♥t❡❣r❛♥❞♦ ❡st❛ ú❧t✐♠❛ ❞❡s✐❣✉❛❧❞❛❞❡ s❡❣✉❡✲s❡ q✉❡ ✒✭t✮ ✕ t✱ ❞♦♥❞❡✬✭t✮ ❂ ✥✭✒✭t✮✮ ✔ ✥✭t✮❀ ♣♦✐s ❛ ❢✉♥çã♦ ✥ é ❞❡❝r❡s❝❡♥t❡✳ ■st♦ é✱ ✈❛❧❡ ❛ ❞❡s✐❣✉❛❧❞❛❞❡ ✭✷✳✸✮✳◗✉❛♥t♦ à ✐❣✉❛❧❞❛❞❡ ❡♠ ✭✷✳✸✮✱ s❛❜❡♠♦s q✉❡ ❛ ♠❡s♠❛ ♦❝♦rr❡ s❡✱ ❡ s♦♠❡♥t❡ s❡✱ ❛ ❍❡ss✐❛♥❛ é ♠ú❧t✐♣❧❛ ❞❛ ✐❞❡♥t✐❞❛❞❡✱ ♦✉ s❡❥❛✱ ❍❡ss r ❂ ✕■✱ ♣❛r❛ ❛❧❣✉♠❛ ❝♦♥st❛♥t❡ ✕✳ ▼❛s ♦ ❢❛t♦ ❞❡ ❍❡ss r ❅ ❅r ❀ ❅ ❅r ✁❂ ✵ ✐♠♣❧✐❝❛✱ ♥❡st❡ ❝❛s♦✱ q✉❡ ♦ t❡r♠♦ ❛ ♥♥ ❞❛ ♠❛tr✐③ ❍❡ss✐❛♥❛ ❞❡ r é ♥✉❧♦ ❡✱ ♣♦rt❛♥t♦✱ ❥ ❍❡ss r❥ ✷ ❂ ✭♥ ✶✮✕ ✷ ✳P♦r ♦✉tr♦ ❧❛❞♦✱ ❥ ❍❡ss r❥ ❅r✿ ❉❛í✱✡ r ❡❥ ❥ ✢❂ ❥ ❀ ❡ ❅❅r ❬❡ ❥ ❀ ❅ ❅r ❪ ❅❅r r ❅❅r r❅ ❅r r❡ ✥♥ ✶ ❡ ❥ r ❅ ❅r ❂✜ r ❀ ❡ ❥✓ ❅❅r ❅r❀ ❡ ❥ ❀❅ ❂ ❘✒ ✜ r❅ ❅r✒ ✓❡ ❥ ❀ ❡ ❥ ☞☞☞ ♥ ✶❉ r❅ ❅r ❡ ❥ ❀ ❡ ❥ ♥ ✶✓ ✷ ✰✥ ✵ ✒✥ ✶♥ ✶ ❊❂ ♥ ✶✥ ✢❂ ✵ ✥ ✢❂ ✥♥ ✶ r❅ ❅r ❡ ❥ ❀ ❡ ❥ ♥ ✶❡ ❥ ✰ ✵ ✜✥ ① ❅r✓ ☞☞ ❅ ❅r ❅❅r ❅ ❅r P❛r❛ ✐ ✻❂ ❥✱ t❡♠♦s✡ r ❡❥ ✢❂ ❛✿ ❅❅r ❅r❀ ✜ r ❡❥❅ ✢❂ ❅r❀ ❂ ❍❡ss r✭❡ ❥ ❀ ❡ ✐ ✮ ❂ ✵✱ ♦✉ s❡❥❛✱ ☛ ✐ ❂ ✵ ♣❛r❛ t♦❞♦ ✐ ✻❂ ❥✳❆ss✐♠✱ ♦❜t❡♠♦s q✉❡ r ✜❅ ❥ ❡ ✵ ❂✶✷ ☛❂ ❛ ❂ ✵✱ ♣♦✐s ❅ ❅r ❀ ❀ ❡ ✐☛ ❡ ❥ ❡ ❥ ❀❅ ❂ ❍❡ss r✭❡ ❥ ❀ ❡ ❥ ✮ ❂ ✕✱ t❡♠♦s r ❑✒ ✿❊ ❛ ❛✜r♠❛çã♦ ❡stá ♣r♦✈❛❞❛✳❚❡♠♦s ❡♥tã♦ ❥ ♥ ✶❡ ❂✥ ❅❅r ❡ ❥ ❀ ❡ ❥☛ ❅❅r ❅ ❅r ✡ r ❡❥ ✿❈♦♠♦ ☛ ❥ ❂ ❥ ❡ ❥ ❂ ☛ ❂ ❦✿ ❉❡✜♥✐çã♦ ✷✳✶✳ ❉✐③❡♠♦s q✉❡ ✁r ✔ ❢ ♥♦ s❡♥t✐❞♦ ❞❛s ❞✐str✐❜✉✐çõ❡s✱ s❡❩ ❩ ✶ r✁ ✬ ✔ ✬❢❀ ✽ ✬ ✕ ✵❀ ✬ ✷ ❈ ✭▼✮✿ ✵ ▼ ▼ ❖ ❚❡♦r❡♠❛ ❞❡ ❈♦♠♣❛r❛çã♦ ❞♦ ▲❛♣❧❛❝✐❛♥♦ t❛♠❜é♠ é ✈á❧✐❞♦ ♥♦ s❡♥t✐❞♦❞❛s ❞✐str✐❜✉✐çõ❡s✳ ♥ ❚❡♦r❡♠❛ ✷✳✷✳ ❙❡❥❛♠ ✭▼ ❀ ❣✮ ✉♠❛ ✈❛r✐❡❞❛❞❡ ❘✐❡♠❛♥♥✐❛♥❛ ❝♦♠♣❧❡t❛ ❡ r ❛❢✉♥çã♦ ❞✐stâ♥❝✐❛ ❣❡♦❞és✐❝❛✳ ❙✉♣♦♥❤❛♠♦s q✉❡ ❛ ❝✉r✈❛t✉r❛ ❞❡ ❘✐❝❝✐ ❞❡ ❣ s❛✲ t✐s❢❛③ ❘✐❝✭▼✮ ✕ ✭♥ ✶✮❦❣✳ ❊♥tã♦ ✁r✭①✮ ✔ ✁r ❦ ♥♦ s❡♥t✐❞♦ ❞❛s ❞✐str✐❜✉✐çõ❡s✳ P❉❡♠♦♥str❛çã♦✳ ❙❡❥❛ ♣ ✷ ▼ ❡ ❝♦♥s✐❞❡r❡♠♦s ♦ ♠❡r❣✉❧❤♦ ❡①♣ ✿ ✦ ▼✳ ♣ ♣ ❈♦♥s✐❞❡r❡♠♦s t❛♠❜é♠ ✉♠❛ ❢❛♠í❧✐❛ ❞❡ ❛❜❡rt♦s ❡str❡❧❛❞♦s ❢✡ ✧ ❀ ✧ ❃ ✵❣ t❛❧P q✉❡✱ q✉❛♥❞♦ ✧ ✦ ✵✱ ✡ ✧ ✦ ✳ P❡❧♦ ❚❡♦r❡♠❛ ❞❡ ❈♦♠♣❛r❛çã♦ ❞♦ ▲❛♣❧❛❝✐❛♥♦✱ ♣ ❩ ❩✁r✬ ✔ ✁r ❦ ✬❀ ✬ ✕ ✵✿ ✭✷✳✺✮ ✡ ✡ ✧ ✧ ❆❣♦r❛✱ ❛ ♣r✐♠❡✐r❛ ✐❞❡♥t✐❞❛❞❡ ❞❡ ●r❡❡♥ ♥♦s ❞á❩ ❩ ❩ ❅r✁r✬ ❂ ❤❣r❛❞ r❀ ❣r❛❞ ✬✐ ✰ ✬✿ ✡ ✡ ❅✡ ❅✑ ✧ ✧ ✎ ✎✎ ❈♦♠♦ ✬ ✕ ✵ ❡ ✡ é ❡str❡❧❛❞♦✱ t❡♠♦s q✉❡ ❛ ✐♥t❡❣r❛❧ s♦❜r❡ ✡ é ♠❛✐♦r ♦✉✐❣✉❛❧ ❛ ③❡r♦✳ ❉❛í ❩ ❩✁r✬ ✕ ❤❣r❛❞ r❀ ❣r❛❞ ✬✐ ✿ ✡ ✡ ✧ ✧ ❋❛③❡♥❞♦ ✧ ✦ ✵ ❡ ✉s❛♥❞♦ ❛ ❞❡s✐❣✉❛❧❞❛❞❡ ✭✷✳✺✮✱ ♦❜t❡♠♦s❩ ❩ ❦ ❤❣r❛❞ r❀ ❣r❛❞ ✬✐ ✔ ✁r ✬✿ P P ♣ ♣ ❈♦♠♦ ❛ ❢✉♥çã♦ ❞✐stâ♥❝✐❛ é ▲✐♣s❝❤✐t③✐❛♥❛✱ ❝♦♥s❡qü❡♥t❡♠❡♥t❡ é q✿t✿♣✿ ❞✐❢❡✲ ✶ r❡♥❝✐á✈❡❧ ❡✱ ♣♦rt❛♥t♦✱ s✉❛ ❞❡r✐✈❛❞❛ ❝♦✐♥❝✐❞❡ ❝♦♠ ❛ ❞❡r✐✈❛❞❛ ❢r❛❝❛ ❡♠ ❍ ✱ ✈❡r❬✻❪✱ ♣á❣✐♥❛s ✽✶ ❡ ✷✸✺✳ P♦r ♦✉tr♦ ❧❛❞♦✱ ❛ ❞❡✜♥✐çã♦ ❞❡ ❞❡r✐✈❛❞❛ ❢r❛❝❛ ❡♠ ❍ ✶ ♥♦s ❞✐③ q✉❡❩ ▼ ❤❣r❛❞ r❀ ❣r❛❞ ✬✐ ❂❩ ▼ r✁✬❀ ✽ ✬ ✕ ✵❀ ✬ ✷ ❈ ✶ ✵ ✭▼✮✿P♦rt❛♥t♦ ❩ ▼ r✁✬ ✔❩ ▼ ✁r ❦ ✬❀ ✽ ✬ ✕ ✵❀ ✬ ✷ ❈ ✶ ✵ ✭▼✮✿ ❈❛♣ít✉❧♦ ✸ ❖ ❚❡♦r❡♠❛ ❞❡ ❉❡❝♦♠♣♦s✐çã♦ ❞❡❈❤❡❡❣❡r✲●r♦♠♦❧❧ ◆❡st❡ ❝❛♣ít✉❧♦ ❡st❛r❡♠♦s s❡♠♣r❡ ♥♦s ❞✐r❡❝✐♦♥❛♥❞♦ ❛♦ ❚❡♦r❡♠❛ ❞❡❉❡❝♦♠♣♦s✐çã♦ ❞❡ ❈❤❡❡❣❡r✲●r♦♠♦❧❧✱ ♦❜t❡♥❞♦ ❛♥t❡s ✐♠♣♦rt❛♥t❡s r❡s✉❧t❛❞♦s q✉❡ ❢❛r❡♠♦s ✉s♦ ❡♠ s✉❛ ❞❡♠♦♥str❛çã♦✳ ✸✳✶ ❋✉♥çõ❡s ❞❡ ❇✉s❡♠❛♥♥ ❆s ❢✉♥çõ❡s ❞❡ ❇✉s❡♠❛♥♥ ❞❡s❡♠♣❡♥❤❛♠ ✉♠ ♣❛♣❡❧ ✐♠♣♦rt❛♥t❡ ♥❛ ❞❡♠♦♥s✲ tr❛çã♦ q✉❡ ❞❛r❡♠♦s ❞♦ ❚❡♦r❡♠❛ ❞❡ ❈❤❡❡❣❡r✲●r♦♠♦❧❧ s♦❜r❡ ❞❡❝♦♠♣♦s✐çã♦ ❞❡✈❛r✐❡❞❛❞❡s ❘✐❡♠❛♥♥✐❛♥❛s ❝♦♠ ❝✉r✈❛t✉r❛ ❞❡ ❘✐❝❝✐ ♥ã♦✲♥❡❣❛t✐✈❛✳❉❡✜♥✐çã♦ ✸✳✶✳ ❯♠❛ ❣❡♦❞és✐❝❛ ✌ ✿ ✭ ✶❀ ✶✮ ✦ ▼✱ ♣❛r❛♠❡tr✐③❛❞❛ ♣❡❧♦ ✶ ✷ ✶ ✷ ❝♦♠♣r✐♠❡♥t♦ ❞❡ ❛r❝♦✱ é ❝❤❛♠❛❞❛ ✉♠❛ ❧✐♥❤❛✱ s❡ ❞✭✌✭t ✮❀ ✌✭t ✮✮ ❂ ❥t t ❥✱ ✶ ✷ ✽ t ❀ t ✷ ✭ ✶❀ ✶✮✳❉❡✜♥✐çã♦ ✸✳✷✳ ❯♠❛ ❣❡♦❞és✐❝❛ ✌ ✿ ❬✵❀ ✶✮ ✦ ▼✱ ♣❛r❛♠❡tr✐③❛❞❛ ♣❡❧♦❝♦♠♣r✐♠❡♥t♦ ❞❡ ❛r❝♦✱ é ❝❤❛♠❛❞❛ ✉♠ r❛✐♦✱ s❡ ❞✭✌✭t ✶ ✮❀ ✌✭t ✷ ✮✮ ❂ ❥t ✶ t ✷ ❥✱✽ t ✶ ❀ t ✷ ✷ ❬✵❀ ✶✮✳ ❖❜s❡r✈❛♠♦s q✉❡ s❡ ▼ é ❝♦♠♣❧❡t❛ ❡ ♥ã♦ ❝♦♠♣❛❝t❛✱ ❡♥tã♦✱ ♣❛r❛ t♦❞♦♣ ✷ ▼✱ ❡①✐st❡ ✉♠ r❛✐♦ ✌ t❛❧ q✉❡ ✌✭✵✮ ❂ ♣✱ ✈❡r ❬✷❪✱ ♣á❣✐♥❛ ✹✵✺✳ P♦ré♠♥❡♠ t♦❞❛ ✈❛r✐❡❞❛❞❡ ❝♦♠♣❧❡t❛ ❡ ♥ã♦ ❝♦♠♣❛❝t❛ ♣♦ss✉✐ ✉♠❛ ❧✐♥❤❛✱ ❝♦♠♦ é ✸ ✷ ✷ ♦ ❝❛s♦ ❞♦ ♣❛r❛❜♦❧ó✐❞❡ ❞❡ r❡✈♦❧✉çã♦ ❢✭①❀ ②❀ ③✮ ✷ ❘ ❥ ③ ❂ ① ✰ ② ❣✳ ❯♠❛❞❡♠♦♥str❛çã♦ ❞❡st❡ ú❧t✐♠♦ ❢❛t♦ ♣♦❞❡ s❡r ❡♥❝♦♥tr❛❞❛ ❡♠ ❬✷❪✱ ♣á❣✐♥❛s ✸✵✾ ❡✸✻✸✳❉❡✜♥✐çã♦ ✸✳✸✳ ❉❛❞♦ ✉♠ r❛✐♦ ✌✱ ❛ ❢✉♥çã♦ ❞❡ ❇✉s❡♠❛♥♥ ❛ss♦❝✐❛❞❛ ❛ ❡ss❡ r❛✐♦✱ ❜ ✌ ✱ é ❞❡✜♥✐❞❛ ♣♦r ✌ ❜ ✭①✮ ❂ ❧✐♠ ✭❞✭①❀ ✌✭t✮✮ t✮✿ t✦✶ ❉❛❞❛ ✉♠❛ ❧✐♥❤❛ ✌ ✿ ✭ ✶❀ ✶✮ ✦ ▼✱ ♣♦❞❡♠♦s ❛ss♦❝✐❛r ❛ ❡❧❛ ❞✉❛s ❢✉♥çõ❡s❞❡ ❇✉s❡♠❛♥♥✱ ❛ s❛❜❡r✿ ✰ ❜ ✭①✮ ❂ ❧✐♠ ❞✭①❀ ✌✭t✮✮ t❀ t✦✶ ❡❜ ✭①✮ ❂ ❧✐♠ ❞✭①❀ ✌✭ t✮✮ t✿ t✦✶ ❉❡✜♥✐♥❞♦ ✰ ❜ ✭①✮ ✿❂ ❞✭①❀ ✌✭t✮✮ t❀ t t❡♠♦s✱ ♣❡❧❛ ❞❡s✐❣✉❛❧❞❛❞❡ tr✐❛♥❣✉❧❛r✱ q✉❡ ✰ ❜ t ✭①✮ ✔ ❞✭①❀ ✌✭✵✮✮ ✰ ❞✭✌✭✵✮❀ ✌✭t✮✮ t❂ ❞✭①❀ ✌✭✵✮✮✿ ✰ P♦rt❛♥t♦✱ ❛ ❢❛♠í❧✐❛ ❞❡ ❢✉♥çõ❡s ❢❜ ❣ t✕✵ é ✉♥✐❢♦r♠❡♠❡♥t❡ ❧✐♠✐t❛❞❛ ♥♦s t ❝♦♠♣❛❝t♦s ❞❡ ▼✳ ❆✜r♠❛♠♦s ❛❣♦r❛ q✉❡ ❡st❛ ❢❛♠í❧✐❛ é ♥ã♦✲❝r❡s❝❡♥t❡✳❉❡ ❢❛t♦✱ s❡ t ✶ ❁ t ✷ ✱ ♣❡❧❛ ❞❡s✐❣✉❛❧❞❛❞❡ tr✐❛♥❣✉❧❛r✱ t❡♠♦s ✰ ❜ ✭①✮ ❂ ❞✭①❀ ✌✭t ✷ ✮✮ t ✷ t ✷ ✶ ✶ ✷ ✷ ✔ ❞✭①❀ ✌✭t ✮✮ ✰ ❞✭✌✭t ✮❀ ✌✭t ✮✮ t ✶ ✷ ✶ ✷ ❂ ❞✭①❀ ✌✭t ✮✮ ✰ t t t ✰ ❂ ❜ t ✭①✮✿ ✶ ✰✰ ✰ ❆ ❢❛♠í❧✐❛ t ✼✦ ❜ t é✱ ♣♦rt❛♥t♦✱ ♠♦♥ót♦♥❛ ♥ã♦✲❝r❡s❝❡♥t❡✳ ❆ss✐♠✱ ❜ t ✦ ❜ ✰ ✉♥✐❢♦r♠❡♠❡♥t❡ ♥♦s ❝♦♠♣❛❝t♦s ❞❡ ▼ ❡ ❜ ❡stá ❜❡♠ ❞❡✜♥✐❞❛✳❖❜s❡r✈❛♠♦s ❛✐♥❞❛ q✉❡✱ ❝♦♠♦ ✰ ✰ ❜ ✭①✮ ❜ ✭②✮ ❂ ❞✭①❀ ✌✭t✮✮ ❞✭②❀ ✌✭t✮✮ t t ✔ ❞✭①❀ ②✮ ✰ ❞✭②❀ ✌✭t✮✮ ❞✭②❀ ✌✭t✮✮❂ ❞✭①❀ ②✮❀ ✰ ❛s ❢✉♥çõ❡s ❜ t sã♦ ▲✐♣s❝❤✐t③✐❛♥❛s ♣❛r❛ t ❃ ✵✱ ❝♦♠ ❝♦♥st❛♥t❡ ❞❡ ▲✐♣s❝❤✐t③ ✐❣✉❛❧ ✰ ❛ ✶✱ ❝❧❛r♦ q✉❡ ❛ ❢✉♥çã♦ ❜ t❛♠❜é♠ é ▲✐♣s❝❤✐t③✐❛♥❛✱ s❡♥❞♦✱ ♣♦rt❛♥t♦✱ q✿t✿♣✿❞✐❢❡r❡♥❝✐á✈❡❧✱ ✈❡r ❬✻❪✱ ♣á❣✐♥❛ ✽✶✳ ✸✳✷ ❚❡♦r❡♠❛ ❞❡ ❈❤❡❡❣❡r✲●r♦♠♦❧❧ ❆ ✐❞é✐❛ ❞❛ ♣r♦✈❛ ❝♦♥s✐st❡ ❡♠ ❝♦♥str✉✐r ✉♠❛ ❢✉♥çã♦ ❤ s✉❛✈❡ ❡ ❤❛r♠ô♥✐❝❛✱❞❡✜♥✐❞❛ ❡♠ ▼✱ t❛❧ q✉❡ ❥ ❣r❛❞ ❤❥ ❂ ✶✳ ❊♥tã♦✱ ❝♦♠ ♦ ❛✉①í❧✐♦ ❞❛ ❢ór♠✉❧❛ ❞❡❲❡✐t③❡♥❜ö❝❦✱ ♠♦str❛♠♦s q✉❡ ♦s ❝♦♥❥✉♥t♦s ❞❡ ♥í✈❡❧ ❞❡ ❤ sã♦ s✉❜✈❛r✐❡❞❛❞❡s ✶ t♦t❛❧♠❡♥t❡ ❣❡♦❞és✐❝❛s ❞❡ ▼✳ ❉❡✜♥✐♠♦s ❡♥tã♦ ◆ ❂ ❤ ✭✵✮✳ P❛r❛ t❛❧ ❝♦♥s✲ ✰ tr✉çã♦✱ ❝♦♥t❛r❡♠♦s ❝♦♠ ❛s ❢✉♥çõ❡s ❞❡ ❇✉s❡♠❛♥♥ ❜ ❡ ❜ ❛ss♦❝✐❛❞❛s à ❧✐♥❤❛✌✳ ♥ Pr♦♣♦s✐çã♦ ✸✳✶ ✭❉❡s✐❣✉❛❧❞❛❞❡ ❞♦ ❱❛❧♦r ▼é❞✐♦✮✳ ❙❡❥❛ ✭▼ ❀ ❣✮ ✉♠❛✈❛r✐❡❞❛❞❡ ❘✐❡♠❛♥♥✐❛♥❛ ❝♦♠♣❧❡t❛ ❝♦♠ ❘✐❝✭▼✮ ✕ ✵✳ ❙❡❥❛ ❢ ✕ ✵ ✉♠❛ ❢✉♥çã♦▲✐♣s❝❤✐t③✐❛♥❛ t❛❧ q✉❡ ✁❢ ✔ ✵ ♥♦ s❡♥t✐❞♦ ❞❛s ❞✐str✐❜✉✐çõ❡s✳ ❊♥tã♦ ❩✶ ❢✭①✮ ✕ ❢✿ ♥ ♥ ✇ ❘ ❇ ✭①✮ ❘❉❡♠♦♥str❛çã♦✳ ➱ s✉✜❝✐❡♥t❡ ♠♦str❛r q✉❡ ❛ ❢✉♥çã♦ ❤ ✿ ✭✵❀ ✶✮ ✦ ✭✵❀ ✶✮✱❞❡✜♥✐❞❛ ♣♦r ❩✶ ❤✭❘✮ ❂ ❢❀ ♥ ✇ ♥ ❘ ❇ ✭①✮ ❘é ♥ã♦ ❝r❡s❝❡♥t❡✳ P♦✐s✱ ❝♦♠♦ ❩✶ ❧✐♠ ❢ ❂ ❢✭①✮❀ ♥ ❘✦✵ ✇ ♥ ❘ ❇ ✭①✮ ❘ ✉♠❛ ✈❡③ ♠♦str❛❞♦ q✉❡ ❤ é ♥ã♦ ❝r❡s❝❡♥t❡✱ t❡r❡♠♦s ♦ s❡❣✉✐♥t❡✿ s❡ ❘ ❃ ❘ ✶ ❃✁ ✁ ✁ ❃ ❘ ♥ ❃ ✁ ✁ ✁ ❃ ✵✱ ❡♥tã♦ ❤✭❘✮ ✔ ❤✭❘ ✶ ✮ ✔ ✁ ✁ ✁ ✔ ❤✭❘ ♥ ✮ ✔ ✁ ✁ ✁ ✔ ❢✭①✮✳ ❇ ❘ ❢✁r ❡①♣ ♣ ✭❇ ❘ ✭✵✮❭✡ ✧ ✮ ❩ ✧✦✵ ❂ ❧✐♠ ✷ ❢✁r ❩ ❂ ❧✐♠ ✐♥t❡❣r❛❧ ❞❛ ❡sq✉❡r❞❛ ❡ ♦ ❡❧❡♠❡♥t♦ ❞❡ ✈♦❧✉♠❡ ❞❛ ✐♥t❡❣r❛❧ ❞♦ ❧❛❞♦ ❞✐r❡✐t♦✳❆❣♦r❛✱ ❢✿ ✭✸✳✶✮❱❛❧❡ ♦❜s❡r✈❛r q✉❡ ❡st❛♠♦s ♦♠✐t✐♥❞♦ ❡♠ ✭✸✳✶✮ ♦ ❡❧❡♠❡♥t♦ ❞❡ ár❡❛ ♥❛ ❇ ❘ ❢ ✔ ♥❩ ❙ ✵ ❘ ❘❩ ✮✮✳Pr❡❝✐s❛♠♦s ❡♥tã♦ ♠♦str❛r q✉❡ ✷ ✧✦✵ ❭P ❅✑✦ ❙ ✵ ❘ ❩ ☛✰ ✷❘ ✷ ✡❣r❛❞ ❢❀ ❣r❛❞ r ❇ ❘ ✕❩ ✷ ✥ ❩ ❢❅r ❅ ❡①♣ ♣ ✭❇ ❘ ✭✵✮❭✡ ✧ ✮ ❩ ☛✰ ✷ ✡❣r❛❞ ❢❀ ❣r❛❞ r ❡①♣ ♣ ✭❇ ❘ ✭✵✮❭✡ ✧ ✮ ♣ ✵ ❘ ❂ ❡①♣ ♣ ✭✐♥t✭❙❘ ❖❜s❡r✈❡♠♦s q✉❡ ❤ é ❧♦❝❛❧♠❡♥t❡ ▲✐♣s❝❤✐t③✐❛♥❛✱ ♣♦rt❛♥t♦✱ ❤ é q✿t✿♣✿ ❞✐❢❡✲ r❡♥❝✐á✈❡❧✳❚❡♠♦s q✉❡ ♥✇ ♥ ❘ ❢✓ ❇ ❘ ✭①✮ ✒❩ ❢ ✔ ✵✱ ❇ ❘ ✭①✮ ❩ ♥✰✶ ❢✓ ✵ ✔♥ ❇ ❘ ✭①✮ ✒❩ ♥ ✇ ♥ ❘ ✭❘✮ ✔ ✵ ✱✶ ✵ ❤ ✵ ❘❩ ❢❞✛ ❣ ❀♦♥❞❡ ❙ ❢♣ ❙ ✵ ❘ ❩ ❞❡t❣❞✛❂ ❢♣ ✐♥t✭❙ ❘ ❭ P♣ ✮ ✔❩ ❞❡t❣ ❞①✧ ❇ ❘ ❭ P♣ ❇ ❘ ✭①✮ ❞❡t❣ ❞①❘ ❢♣ ❇ ✭❘✰✧✮ ❭ P♣ ❘ ✧✦✵ ❧✐♠ s✉♣ ❢❆✐♥❞❛✱ ❢❀ ♦✉ s❡❥❛✱❩ ❩ ❩ ✡ ☛ ✷ ✷ ✷❘ ❢ ❣r❛❞ ❢❀ ❣r❛❞ r ✔ ❢✁r ✿ ✵ ❙ ❇ ❇ ❘ ❘ ❘ ❖r❛✱ ♣❡❧♦ ❚❡♦r❡♠❛ ❞❡ ❈♦♠♣❛r❛çã♦ ❞♦ ▲❛♣❧❛❝✐❛♥♦ ♥♦ s❡♥t✐❞♦ ❞❛s❞✐str✐❜✉✐çõ❡s✱ ✷ ✁r ❂ ✷r✁r ✰ ✷ ❤❣r❛❞ r❀ ❣r❛❞ r✐✔ ✷✭♥ ✶✮ ✰ ✷ ❂ ✷♥✿ P♦rt❛♥t♦✱❩ ❩ ❩ ✡ ☛ ✷ ✷❘ ❢ ❣r❛❞ ❢❀ ❣r❛❞ r ✔ ✷♥ ❢✿ ✭✸✳✷✮ ✵ ❙ ❇ ❇ ❘ ❘ ❘ ❚❡♠♦s t❛♠❜é♠ q✉❡❩ ❩ ✡ ☛ ✡ ☛ ✷ ✷ ✷ ❣r❛❞ ❢❀ ❣r❛❞ r ❂ ❣r❛❞ ❢❀ ❣r❛❞✭r ❘ ✮ ❇ ❇ ❘ ❘ ❩ ✷ ✷ ❂ ✁❢✭r ❘ ✮ ❇ ❘ ✕ ✵❀ ✭✸✳✸✮ ✷ ✷ ♣♦✐s ✁❢ ✔ ✵ ❡ r ✭①✮ ❘ ✔ ✵❀ ✽ ① ✷ ❇ ❘ ✳❆ ❞❡s✐❣✉❛❧❞❛❞❡ ✭✸✳✸✮ ❛♣❧✐❝❛❞❛ ❛ ✭✸✳✷✮ ♥♦s ❢♦r♥❡❝❡ ❩ ❩✷❘ ❢ ✔ ✷♥ ❢✿ ✵ ❙ ❇ ❘ ❘ ♥ ❈♦r♦❧ár✐♦ ✸✳✶✳ ❙❡❥❛♠ ✭▼ ❀ ❣✮ ✉♠❛ ✈❛r✐❡❞❛❞❡ ❘✐❡♠❛♥♥✐❛♥❛ ❝♦♠♣❧❡t❛ ❝♦♠❘✐❝✭▼✮ ✕ ✵ ❡ ❢ ✿ ▼ ✦ ❘ ✉♠❛ ❢✉♥çã♦ ♥ã♦✲♥❡❣❛t✐✈❛ ❝♦♠ ✁❢ ✔ ✵✳❙✉♣♦♥❤❛♠♦s q✉❡ ❡①✐st❡ ① ✵ ✷ ▼ t❛❧ q✉❡ ❢✭① ✵ ✮ ❂ ✵✳ ❊♥tã♦ ❢ ✑ ✵✳❉❡♠♦♥str❛çã♦✳ ❉❡ ❢❛t♦✱ ❩✵ ✕ ❢❀ ✽ ❘✿ ❇ ✭① ✮ ❘ ✵ ♥ ▲❡♠❛ ✸✳✶✳ ❙❡❥❛ ✭▼ ❀ ❣✮ ✉♠❛ ✈❛r✐❡❞❛❞❡ ❘✐❡♠❛♥♥✐❛♥❛ ❝♦♠♣❧❡t❛ ❝♦♠ ✰ ❝✉r✈❛t✉r❛ ❞❡ ❘✐❝❝✐ ♥ã♦✲♥❡❣❛t✐✈❛✳ ❆ ❢✉♥çã♦ ❜ ✿ ▼ ✦ ❘✱ é s✉♣❡r✲❤❛r♠ô♥✐❝❛ ✰ ♥♦ s❡♥t✐❞♦ ❞❛s ❞✐str✐❜✉✐çõ❡s✱ ✐st♦ é✱ ✁❜ ✔ ✵ ♥♦ s❡♥t✐❞♦ ❞❛s ❞✐str✐❜✉✐çõ❡s✳ ✶ ❉❡♠♦♥str❛çã♦✳ ❖ ❚❡♦r❡♠❛ ✷✿✷ ✐♠♣❧✐❝❛✱ ♣❛r❛ t♦❞♦ t ❃ ✵ ❡ ♣❛r❛ t♦❞❛ ✬ ✷ ❈ ✱ ✵ ✬ ✕ ✵✱ q✉❡❩ ❩ ✰ ✰ ❜ ✁✬ ❂ ✬✁❜ t t ▼ ▼ ❩❂ ❞✭①❀ ✌✭t✮✮✁✬ ▼ ❩✶ ✔ ✭♥ ✶✮ ✬ ✿ ▼ ❞✭①❀ ✌✭t✮✮ ❖r❛✱❞✭①❀ ✌✭t✮✮ ✕ ❞✭✌✭t✮❀ ✌✭✵✮✮ ❞✭✌✭✵✮❀ ①✮✿ ❚❡♠♦s ❡♥tã♦ q✉❡✱ ✜①❛❞❛ ❛ ❢✉♥çã♦ ✬ ❞✐❢❡r❡♥❝✐á✈❡❧✱ ♥ã♦✲♥❡❣❛t✐✈❛ ❡ ❞❡ s✉♣♦rt❡ ❝♦♠♣❛❝t♦✱❩ ✶❧✐♠ ✬ ❂ ✵✿ t ✦✶ ▼ ❞✭①❀ ✌✭t✮✮ ▲♦❣♦✱ ♦❜t❡♠♦s❩ ✰ ❜ ✁✬ ✔ ✵✿ ▼ ❱❛❧❡ ♦❜s❡r✈❛r q✉❡✱ ❛♥❛❧♦❣❛♠❡♥t❡✱ ♣♦❞❡♠♦s ♣r♦✈❛r q✉❡ ❜ t❛♠❜é♠ é s✉♣❡r✲❤❛r♠ô♥✐❝❛ ♥♦ s❡♥t✐❞♦ ❞❛s ❞✐str✐❜✉✐çõ❡s✳❊st❛♠♦s ❛❣♦r❛ ❡♠ ❝♦♥❞✐çõ❡s ❞❡ ❞❡♠♦♥str❛r ♦ ♣r✐♥❝✐♣❛❧ r❡s✉❧t❛❞♦ ❞❡st❛ ♠♦♥♦❣r❛✜❛✱ ♦ ❚❡♦r❡♠❛ ❞❡ ❉❡❝♦♠♣♦s✐çã♦ ❞❡ ❈❤❡❡❣❡r✲●r♦♠♦❧❧✳ ♥ ❚❡♦r❡♠❛ ✸✳✶✳ ❙❡❥❛ ✭▼ ❀ ❣✮ ✉♠❛ ✈❛r✐❡❞❛❞❡ ❘✐❡♠❛♥♥✐❛♥❛ ❝♦♠♣❧❡t❛ ❝♦♠❝✉r✈❛t✉r❛ ❞❡ ❘✐❝❝✐ ♥ã♦✲♥❡❣❛t✐✈❛✳ ❙❡ ▼ ♣♦ss✉✐ ✉♠❛ ❧✐♥❤❛✳ ❊♥tã♦ ▼ é✐s♦♠étr✐❝❛ ❛ ◆ ✂ ❘ ♠✉♥✐❞❛ ❞❛ ♠étr✐❝❛ ♣r♦❞✉t♦✱ ♦♥❞❡ ◆ é ✉♠❛ ✈❛r✐❡❞❛❞❡❘✐❡♠❛♥♥✐❛♥❛ ❞❡ ❞✐♠❡♥sã♦ ✭♥ ✶✮ ❝♦♠ ❘✐❝✭◆✮ ✕ ✵✳❉❡♠♦♥str❛çã♦✳ ■♥✐❝✐❛❧♠❡♥t❡✱ ✉s❛♥❞♦ ❛ ❞❡s✐❣✉❛❧❞❛❞❡ tr✐❛♥❣✉❧❛r✱ ✈❡♠♦s q✉❡ ✰ ❛ ❢✉♥çã♦ ❢✭①✮ ❂ ❜ ✭①✮ ✰ ❜ ✭①✮ é ♥ã♦✲♥❡❣❛t✐✈❛✳ ❆❧é♠ ❞✐ss♦✱ ❢✭①✮ ❂ ✵ ♣❛r❛① ❂ ✌✭t✮✳ P❡❧♦ ▲❡♠❛ ✸✳✶✱ ❛ ❢✉♥çã♦ ❢ é s✉♣❡r✲❤❛r♠ô♥✐❝❛ ♥♦ s❡♥t✐❞♦ ❞❛s❞✐str✐❜✉✐çõ❡s✱ ✉♠❛ ✈❡③ q✉❡ ❢ é s♦♠❛ ❞❡ ❢✉♥çõ❡s s✉♣❡r✲❤❛r♠ô♥✐❝❛s✳ ❙❡❣✉❡❡♥tã♦ ❞♦ ❈♦r♦❧ár✐♦ ❞❛ Pr♦♣♦s✐çã♦ ✸✳✶ q✉❡ ❢ ❂ ✵ ❡♠ ▼✳ P♦rt❛♥t♦✱ ✁❢ ❂ ✵✱ ✰ ✰ ✐st♦ é✱ ✁❜ ✰ ✁❜ ❂ ✵✳ ■st♦ ✐♠♣❧✐❝❛ q✉❡ ✁❜ ❂ ✁❜ ❂ ✵ ♥♦ s❡♥t✐❞♦ ✰ ❞❛s ❞✐str✐❜✉✐çõ❡s✱ ♣♦✐s ✁❜ ✔ ✵ ❡ ✁❜ ✔ ✵✳ ■st♦ ❣❛r❛♥t❡ ❛ s✉❛✈✐❞❛❞❡ ❞❛s❢✉♥çõ❡s ❞❡ ❇✉s❡♠❛♥♥✱ ♣❡❧♦ ▲❡♠❛ ❞❡ ❲❡②❧✳ ❆✜r♠❛♠♦s ❛❣♦r❛ q✉❡ ❛ ❢✉♥çã♦ ✰✷ ❤ ✿❂ ❜ s❛t✐s❢❛③ ❥ ❣r❛❞ ❤❥ ❂ ✶✳ ❉❡ ❢❛t♦✱ ❥ ❣r❛❞ ❤❥ ✔ ✶✱ ♣♦✐s ❥á ✈✐♠♦s q✉❡❤ é ▲✐♣s❝❤✐t✐③✐❛♥❛ ❝♦♠ ❝♦♥st❛♥t❡ ❞❡ ▲✐♣s❝❤✐t③ ✐❣✉❛❧ ❛ ✶✳ ▲♦❣♦ ❛ ❢✉♥çã♦ ✷ ❋ ✿❂ ✶ ❥ ❣r❛❞ ❤❥ é ♥ã♦✲♥❡❣❛t✐✈❛✳❯s❛♥❞♦ ❛ ❢ór♠✉❧❛ ❞❡ ❲❡✐t③❡♥❜ö❝❦✱ t❡♠♦s ✁✶ ✷ ✷ ✁ ❥ ❣r❛❞ ❤❥ ❂ ❥ ❍❡ss ❤❥ ✰ ❤❣r❛❞ ❤❀ ❣r❛❞✭✁❤✮✐ ✰ ❘✐❝ ✭❣r❛❞ ❤❀ ❣r❛❞ ❤✮✷ ✷ ✕ ❥ ❍❡ss ❤❥ ✕ ✵✿ ❞ ❙❡❣✉❡✲s❡ ❡♥tã♦ q✉❡ ✁❋ ✔ ✵✳ P♦r s✉❛ ✈❡③✱ t❡♠♦s q✉❡ ❤✭✌✭s✮✮ ❂ ✶ ✭✐ss♦ ❞s ✰ ✵ s❡❣✉❡ ❞❛ ❞❡✜♥✐çã♦ ❞❡ ❜ ✮ ❡✱ ♣♦rt❛♥t♦✱ ❤❣r❛❞ ❤❀ ✌ ✭s✮✐ ❂ ✶✳ ❆ ❞❡s✐❣✉❛❧❞❛❞❡❞❡ ❈❛✉❝❤②✲❙❝❤✇❛r③ ✐♠♣❧✐❝❛ ✵ ✵ ✶ ❂ ❥ ❤❣r❛❞ ❤❀ ✌ ✭s✮✐ ❥ ✔ ❥ ❣r❛❞ ❤❥❥✌ ✭s✮❥ ✔ ✶❀ ✵ ❞♦♥❞❡ ❣r❛❞ ❤ ❂ ✌ ✳ ❉❛í✱ ♦❜t❡♠♦s q✉❡ ❋ ✭✌✭s✮✮ ❂ ✵✳ ❋✐♥❛❧♠❡♥t❡✱ ✉s❛♥❞♦ ♦❈♦r♦❧ár✐♦ ✭✸✳✶✮✱ t❡♠♦s ❋ ✑ ✵✳ ■st♦ ♣r♦✈❛ ❛ ❛✜r♠❛çã♦✱ ♦✉ s❡❥❛✱ ❥ ❣r❛❞ ❤❥ ❂ ✶✳❈♦♠♦ ❝♦♥s❡qüê♥❝✐❛ ❞✐ss♦✱ ❛✐♥❞❛ ♦❜t❡♠♦s q✉❡ ❥ ❍❡ss ❤❥ ❂ ✵✳ P♦rt❛♥t♦ ❣r❛❞ ❤é ♣❛r❛❧❡❧♦✳ ✶ P♦❞❡♠♦s ❡♥tã♦ ❞❡✜♥✐r ✉♠❛ ✐s♦♠❡tr✐❛ ❡♥tr❡ ❘ ❝❛rt❡s✐❛♥♦ ◆ ✿❂ ❤ ✭✵✮ ❡ ▼ ❞❛ s❡❣✉✐♥t❡ ♠❛♥❡✐r❛✿✬ ✿ ❘ ✂ ◆ ✦ ▼ ✭t❀ ①✮ ✦ ❡①♣ ✭t ❣r❛❞ ❤✭①✮✮❀ ① ❈♦♠ ❡❢❡✐t♦✱ ♣❛r❛ ✈❡t♦r❡s ✈❡rt✐❝❛✐s ❜❛st❛ ♦❜s❡r✈❛r♠♦s q✉❡✜ ✒ ✓ ✒ ✓✢ ❅ ❅❞✬ ✭t❀①✮ ❀ ❞✬ ✭t❀①✮ ❂ ❤❣r❛❞ ❤❀ ❣r❛❞ ❤✐ ❅t ❅t❂ ✶ ✜ ✢❅ ❅ ❂ ❀ ✿❅t ❅t ◗✉❛♥❞♦ t❡♠♦s ✉♠ ✈❡t♦r ✈❡rt✐❝❛❧ ❡ ♦✉tr♦ ❤♦r✐③♦♥t❛❧✱ ♦ r❡s✉❧t❛❞♦ s❡❣✉❡ ❞♦▲❡♠❛ ❞❡ ●❛✉ss✳ ❋✐♥❛❧♠❡♥t❡✱ ♥♦ ❝❛s♦ ❡♠ q✉❡ t❡♠♦s ✉ ❡ ✈✱ ✈❡t♦r❡s ❤♦r✐③♦♥t❛✐s✱ ❛ ❢✉♥çã♦✡ ☛ ❢✭t✮ ✿❂ ❞✬ ✭t❀①✮ ✭✉✮❀ ❞✬ ✭t❀①✮ ✭✈✮ ❀é ❝♦♥st❛♥t❡ ❡♠ t✳ ❈♦♠ ❡❢❡✐t♦✱ ♣❡❧♦ ▲❡♠❛ ❞❡ ❙✐♠❡tr✐❛✱ ✈❡r ❬✸❪✱ ♣á❣✐♥❛ ✼✻✱ ❡♣♦r ❣r❛❞ ❤ s❡r ✉♠ ❝❛♠♣♦ ♣❛r❛❧❡❧♦✱ ♦❜t❡♠♦s ✡ ☛ ✡ ☛ ✵ ❣r❛❞ ❤ ✭t❀①✮ ✭t❀①✮ ✭t❀①✮ ❣r❛❞ ❤ ✭t❀①✮ ❢ ✭t✮ ❂ r ❞✬ ✭✉✮❀ ❞✬ ✭✈✮ ✰ ❞✬ ✭✉✮❀ r ❞✬ ✭✈✮❉ ❊ ❉ ❊ ❞✬ ✭✉✮ ✭t❀①✮ ✭t❀①✮ ❞✬ ✭✈✮ ❂ r ❣r❛❞ ❤❀ ❞✬ ✭✈✮ ✰ ❞✬ ✭✉✮❀ r ❣r❛❞ ❤ ✭t❀①✮ ✭t❀①✮❂ ✵✿ P♦rt❛♥t♦✱✡ ☛ ❞✬ ✭t❀①✮ ✭✉✮❀ ❞✬ ✭t❀①✮ ✭✈✮ ❂ ❤❞✬ ✵ ✭✉✮❀ ❞✬ ✵ ✭✈✮✐❂ ❤✉❀ ✈✐ ❀ ♣❛r❛ q✉❛✐sq✉❡r ✉❀ ✈ ✷ ❚ ✭t❀①✮ ❘ ✂ ◆✳ ❈♦r♦❧ár✐♦ ✸✳✷✳ ❙❡❥❛ ▼ ✉♠❛ ✈❛r✐❡❞❛❞❡ ❘✐❡♠❛♥♥✐❛♥❛ ❝♦♠♣❧❡t❛ ❝♦♠ ❦ ❝✉r✈❛t✉r❛ ❞❡ ❘✐❝❝✐ ♥ã♦✲♥❡❣❛t✐✈❛✳ ❊♥tã♦ ▼ é ✐s♦♠étr✐❝❛ ❛ ✉♠ ♣r♦❞✉t♦ ◆ ✂❘ ✱ ❦ ♦♥❞❡ ◆ ♥ã♦ ❝♦♥té♠ ❧✐♥❤❛s ❡ ❘ ♣♦ss✉✐ ❛ ♠étr✐❝❛ ❝❛♥ô♥✐❝❛✳ ♥ ❉❡♠♦♥str❛çã♦✳ ❉❡ ❢❛t♦✱ s❡ ▼ ♣♦ss✉✐r ✉♠❛ ❧✐♥❤❛✱ ❡♥tã♦ ♣❡❧♦ t❡♦r❡♠❛ ♥ ✶ ❛♥t❡r✐♦r✱ ▼ é ✐s♦♠étr✐❝❛ ❛ ✉♠ ♣r♦❞✉t♦ ❘ ✂ ◆ ✳ ❙❡✱ ❛❧é♠ ❞✐ss♦✱ ◆ ♣♦ss✉✐r✉♠❛ ❧✐♥❤❛✱ ❡♥tã♦ ✉s❛♠♦s ♦ t❡♦r❡♠❛ ♠❛✐s ✉♠❛ ✈❡③✱ ❥á q✉❡ ❘✐❝✭◆✮ ✕ ✵ ❡ ◆ é❝♦♠♣❧❡t❛✳ ❖ r❡s✉❧t❛❞♦ s❡❣✉❡ ♣♦r ✐♥❞✉çã♦✳ ❘❡❢❡rê♥❝✐❛s ❇✐❜❧✐♦❣rá✜❝❛s ❬✶❪ ❈❤❡❡❣❡r✱ ❏✳✱ ●r♦♠♦❧❧✱ ❉✳✱ ❚❤❡ ❙♣❧✐tt✐♥❣ ❚❤❡♦r❡♠ ❢♦r ▼❛♥✐❢♦❧❞s ♦❢◆♦♥♥❡❣❛t✐✈❡ ❘✐❝❝✐ ❈✉r✈❛t✉r❡✱ ❏✳ ❉✐✛❡r❡♥t✐❛❧ ●❡♦♠❡tr②✱ ✭✶✾✼✶✮✱ ✶✶✾✕✶✷✽✳ ❬✷❪ ❞♦ ❈❛r♠♦✱ ▼✳ P✳✱ ●❡♦♠❡tr✐❛ ❉✐❢❡r❡♥❝✐❛❧ ❞❡ ❈✉r✈❛s ❡ ❙✉♣❡r❢í❝✐❡s✱ ❚❡①t♦s❯♥✐✈❡rs✐tár✐♦s✱ ❙❇▼✱ ❘✐♦ ❞❡ ❏❛♥❡✐r♦✱ ✷ ❛ ❡❞✐çã♦✱ ✷✵✵✺✳❬✸❪ ❞♦ ❈❛r♠♦✱ ▼✳ P✳✱ ●❡♦♠❡tr✐❛ ❘✐❡♠❛♥♥✐❛♥❛✱ Pr♦❥❡t♦ ❊✉❝❧✐❞❡s✱ ❘✐♦ ❞❡ ❏❛♥❡✐r♦✱ ✸ ❛ ❡❞✐çã♦✱ ✷✵✵✺✳❬✹❪ ❊s❝❤❡♥❜✉r❣✱ ❏✳✲❍✳✱ ❍❡✐♥t③❡✱ ❊✳✱ ❆♥ ❡❧❡♠❡♥t❛r② ♣r♦♦❢ ♦❢ t❤❡ ❈❤❡❡❣❡r✲ ●r♦♠♦❧❧ s♣❧✐tt✐♥❣ t❤❡♦r❡♠✱ ❆♥♥✳ ●❧♦❜✳ ❆♥❛❧②s✐s ❛♥❞ ●❡♦♠❡tr②✱ ✈♦❧✳ ✷✱✭✶✾✽✹✮✱ ✶✹✶✕✶✺✶✳ ❬✺❪ ❊s❝♦❜❛r✱ ❏✳ ❋✳✱ ❚♦♣✐❝s ✐♥ P❉❊✬❙ ❛♥❞ ❉✐✛❡r❡♥t✐❛❧ ●❡♦♠❡tr②✱ ❳■■ ❊s❝♦❧❛❞❡ ●❡♦♠❡tr✐❛ ❉✐❢❡r❡♥❝✐❛❧✱ ✷✵✵✷✳ ❬✻❪ ❊✈❛♥s✱ ▲✳ ❈✳✱ ●❛r✐❡♣②✱ ❘✳ ❋✳✱ ▼❡❛s✉r❡ ❚❤❡♦r② ❛♥❞ ❋✐♥❡ Pr♦♣❡rt✐❡s ♦❢❋✉♥❝t✐♦♥s✱ ❈❘❈ Pr❡ss✱ ✶✾✾✷✳ ❬✼❪ ❊✈❛♥s✱ ▲✳ ❈✳✱ P❛rt✐❛❧ ❉✐✛❡r❡♥t✐❛❧ ❊q✉❛t✐♦♥s✱ ●r❛❞✉❛t❡ ❙t✉❞✐❡s ✐♥▼❛t❤❡♠❛t✐❝s✱ ❱♦❧✉♠❡ ✶✾✱ ✷✵✵✷✳ ❬✽❪ ▲❡❡✱ ❏✳ ▼✳✱ ❘✐❡♠❛♥♥✐❛♥ ▼❛♥✐❢♦❧❞s ✲ ❆♥ ■♥tr♦❞✉❝t✐♦♥ t♦ ❈✉r✈❛t✉r❡✱❙♣r✐♥❣❡r✱ ✶✾✾✼✳ ❬✾❪ ❙❝❤♦❡♥✱ ❘✳✱ ❨❛✉✱ ❙✳ ❚✳✱ ▲❡❝t✉r❡s ♦♥ ❉✐✛❡r❡♥t✐❛❧ ●❡♦♠❡tr②✱ ■♥t❡r♥❛t✐♦♥❛❧Pr❡ss ■♥❝✱ ❇♦st♦♥✱ ✈♦❧✳ ✶✱ ✶✾✾✹✳ ❬✶✵❪ ❙♣✐✈❛❦✱ ▼✳✱ ❆ ❈♦♠♣r❡❤❡♥s✐✈❡ ■♥tr♦❞✉❝t✐♦♥ t♦ ❉✐✛❡r❡♥t✐❛❧ ●❡♦♠❡tr②✱P✉❜❧✐s❤ ♦r P❡r✐s❤✱ ■◆❈✳ ❍♦✉st♦♥✱ ❚❡①❛s ✭❯✳❙✳❆✳✮✱ ❱♦❧✉♠❡ ■■✱ ✶✾✼✵✳ ❮♥❞✐❝❡ ❘❡♠✐ss✐✈♦ ❛♣❧✐❝❛çã♦ ❡①♣♦♥❡♥❝✐❛❧✱ ✶✺✱ ✶✼❝❛♠♣♦ ❞❡ ✈❡t♦r❡s✱ ✾✱ ✶✵✱ ✶✾❞❡ ✈❡t♦r❡s t❛♥❣❡♥t❡s✱ ✷✻♣❛r❛❧❡❧♦✱ ✶✺✱ ✹✷ ❝♦❡✜❝✐❡♥t❡s❞❛ ♠étr✐❝❛✱ ✶✸✱ ✷✼❞❡ ❘✐❝❝✐✱ ✶✾✱ ✷✶ ❝♦♥❡①ã♦✱ ✾✱ ✶✸❛✜♠✱ ✶✸✱ ✶✹❝♦♠♣❛tí✈❡❧✱ ✶✹❞❡ ▲❡✈✐✲❈✐✈✐t❛✱ ✶✹ s✐♠étr✐❝❛✱ ✶✹ ❝♦♥❥✉♥t♦❞♦s ❝❛♠♣♦s ❞❡ ✈❡t♦r❡s✱ ✶✵ ❝✉r✈❛t✉r❛✱ ✶✼❞❡ ❘✐❝❝✐✱ ✶✽✱ ✶✾✱ ✸✵✱ ✸✶✱ ✸✹✱ ✸✻✱ ✹✶✱ ✹✸❡s❝❛❧❛r✱ ✶✽ s❡❝❝✐♦♥❛❧✱ ✶✽✱ ✷✾✱ ✸✶ ❞✐❢❡♦♠♦r✜s♠♦✱ ✶✷✱ ✶✻❡s❢❡r❛ ✉♥✐tár✐❛✱ ✶✶❡s♣❛ç♦ ❤✐♣❡r❜ó❧✐❝♦✱ ✶✶✱ ✷✾♠étr✐❝♦✱ ✶✼ t❛♥❣❡♥t❡✱ ✾ ❋ór♠✉❧❛ ❞❡ ❲❡✐t③❡♥❜ö❝❦✱ ✷✸✜❜r❛❞♦ t❛♥❣❡♥t❡✱ ✶✸❢✉♥çã♦ ❞❡ ❇✉s❡♠❛♥♥✱ ✸✺❣❡♦❞és✐❝❛✱ ✽✱ ✶✺✕✶✼✱ ✷✺✱ ✷✻✱ ✸✵✱ ✸✹✱ ✸✻■❞❡♥t✐❞❛❞❡ ❞❡ ❘✐❝❝✐✱ ✷✶✐♠❡rsã♦✱ ✶✶✱ ✶✷ ✐s♦♠étr✐❝❛✱ ✶✷✐s♦♠❡tr✐❛✱ ✶✷✱ ✹✷▲❡♠❛ ❞❡ ●❛✉ss✱ ✷✺❞❡ ❙✐♠❡tr✐❛✱ ✹✷ ❧✐♥❤❛✱ ✸✹✱ ✹✶♠étr✐❝❛ ❝❛♥ô♥✐❝❛✱ ✷✻✱ ✹✸❞❛ ❡s❢❡r❛✱ ✷✾❞♦ ❡s♣❛ç♦ ❤✐♣❡r❜ó❧✐❝♦✱ ✷✾✐♥❞✉③✐❞❛✱ ✶✷♣r♦❞✉t♦✱ ✶✷✱ ✹✶❘✐❡♠❛♥♥✐❛♥❛✱ ✶✶✕✶✹ ♠❡r❣✉❧❤♦✱ ✶✷♥♦t❛çã♦ ❞❡ ❊✐♥st❡✐♥✱ ✶✾♣❛r❛♠❡tr✐③❛çã♦✱ ✾ ♣r♦❞✉t♦ ✐♥t❡r♥♦✱ ✶✶✱ ✶✽ r❛✐♦✱ ✸✹sí♠❜♦❧♦s ❞❡ ❈❤r✐st♦✛❡❧✱ ✶✸✱ ✶✾✱ ✷✸✱ ✷✼ s✉❜✈❛r✐❡❞❛❞❡✱ ✶✷✱ ✸✻❚❡♦r❡♠❛

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