❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ●♦✐ás
■♥st✐t✉t♦ ❞❡ ▼❛t❡♠át✐❝❛ ❡ ❊st❛tíst✐❝❛
Pr♦❣r❛♠❛ ❞❡ ▼❡str❛❞♦ Pr♦✜ss✐♦♥❛❧ ❡♠
▼❛t❡♠át✐❝❛ ❡♠ ❘❡❞❡ ◆❛❝✐♦♥❛❧
❘❡♣r❡s❡♥t❛çõ❡s ❡♠ ▼❛t❡♠át✐❝❛✿
❖❜s❡r✈❛çõ❡s ♣❛r❛ ♦ ❊♥s✐♥♦ ❡ ❛ ❆♣r❡♥❞✐③❛❣❡♠
❡♠ ●❡♦♠❡tr✐❛
❈❤❛r❧❡s ▲♦✉r❡♥ç♦ ❞❡ ❇❛st♦s
●♦✐â♥✐❛
❈❤❛r❧❡s ▲♦✉r❡♥ç♦ ❞❡ ❇❛st♦s
❘❡♣r❡s❡♥t❛çõ❡s ❡♠ ▼❛t❡♠át✐❝❛✿
❖❜s❡r✈❛çõ❡s ♣❛r❛ ♦ ❊♥s✐♥♦ ❡ ❛ ❆♣r❡♥❞✐③❛❣❡♠
❡♠ ●❡♦♠❡tr✐❛
❉✐ss❡rt❛çã♦ ❛♣r❡s❡♥t❛❞❛ ❛♦ Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❞♦ ■♥st✐t✉t♦ ❞❡ ▼❛t❡♠át✐❝❛ ❡ ❊st❛tíst✐❝❛ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ●♦✐ás✱ ❝♦♠♦ r❡q✉✐s✐t♦ ♣❛r❛ ♦❜t❡♥çã♦ ❞♦ tít✉❧♦ ❞❡ ▼❡str❡ ❡♠ ▼❡str❛❞♦ Pr♦✜ss✐♦♥❛❧ ❡♠ ▼❛t❡♠át✐❝❛✳ ➪r❡❛ ❞❡ ❈♦♥❝❡♥tr❛çã♦✿ ▼❛t❡♠át✐❝❛ ❞♦ ❊♥s✐♥♦ ❇ás✐❝♦✳ ❖r✐❡♥t❛❞♦r❛✿ Pr♦❢❛✳ ❉r❛✳ ■✈♦♥✐❧❞❡s ❘✐❜❡✐r♦ ▼❛rt✐♥s ❉✐❛s✳
●♦✐â♥✐❛
❚♦❞♦s ♦s ❞✐r❡✐t♦s r❡s❡r✈❛❞♦s✳ ➱ ♣r♦✐❜✐❞❛ ❛ r❡♣r♦❞✉çã♦ t♦t❛❧ ♦✉ ♣❛r❝✐❛❧ ❞❡st❡ tr❛❜❛❧❤♦ s❡♠ ❛ ❛✉t♦r✐③❛çã♦ ❞❛ ✉♥✐✈❡rs✐❞❛❞❡✱ ❞♦ ❛✉t♦r ❡ ❞❛ ♦r✐❡♥t❛❞♦r❛✳
❆❣r❛❞❡❝✐♠❡♥t♦s
➚ ♠✐♥❤❛ ♠ã❡✱ q✉❡ ❢❛③ ❞❡ t✉❞♦ ❛ s❡✉ ❛❧❝❛♥❝❡ ❡♠ ♠❡✉ ❢❛✈♦r✳ ◗✉❡ ❡stá s❡♠♣r❡ ♣r❡s❡♥t❡ ♠❡ ❛♣♦✐❛♥❞♦ ❡♠ t✉❞♦ ♦ q✉❡ t❡♥❤♦ ❝♦♥q✉✐st❛❞♦✳
❆♦s ♠❡✉s ❝♦❧❡❣❛s ❞❡ ♠❡str❛❞♦ q✉❡ ♣✉❞❡ ❝♦♥❤❡❝❡r✱ q✉❡ ♠❡ ❛❥✉❞❛r❛♠ ❝♦♠♣❛rt✐❧❤❛♥❞♦ s❡✉s ❝♦♥❤❡❝✐♠❡♥t♦s ❡ q✉❡ ♠❡ ❛❝♦♠♣❛♥❤❛r❛♠ ♥❡st❡s q✉❛s❡ ❞♦✐s ❛♥♦s✳
❆♦ ❝♦❧❡❣❛ ❍✉♠❜❡rt♦ ❆❧✈❡s ❞❡ ❈❛str♦✱ q✉❡ ❡st❡✈❡ ❝♦♠✐❣♦ ❡♠ q✉❛s❡ t♦❞❛s ❛s ✈✐❛❣❡♥s ❛♦s ❡♥❝♦♥tr♦s ❞♦ ❝✉rs♦❀ ♣❡ss♦❛ ❝♦♠ q✉❡♠ ♣❛rt✐❧❤❡✐ ♠✉✐t♦ ❞♦ q✉❡ ✈✐✈✐ ❡ q✉❡ s♦✉❜❡ ♠❡ ♦✉✈✐r✳
❆♦s ✐❞❡❛❧✐③❛❞♦r❡s ❞♦ P❘❖❋▼❆❚✱ q✉❡ ♠❡ ♣r♦♣♦r❝✐♦♥❛r❛♠ ❡st❛ ♦♣♦rt✉♥✐❞❛❞❡ ❞❡ ❛♣❡r❢❡✐ç♦❛♠❡♥t♦✱ q✉❡ ♠✉✐t♦ ❛❝r❡s❝❡♥t❛ ❛♦ ♠❡✉ ❛♣r❡♥❞✐③❛❞♦ ❡ ❝❡rt❛♠❡♥t❡ à ♠✐♥❤❛ ♣r♦✲ ✜ssã♦✳
➚ ✉♥✐❞❛❞❡ ❡s❝♦❧❛r ❡ s❡❝r❡t❛r✐❛ ♠✉♥✐❝✐♣❛❧ ✭❯r✉❛♥❛✮✱ q✉❡ ♠❡ ❝♦♥❝❡❞❡r❛♠ q✉❛s❡ ❞♦✐s ❛♥♦s ❞❡ ❛❢❛st❛♠❡♥t♦✱ ❡ ❛ss✐♠ ♣✉❞❡ ❞✐s♣♦r ♠❛✐♦r t❡♠♣♦ ♣❛r❛ ♦s ❡st✉❞♦s✳
➚ ❈❆P❊❙ ♣❡❧❛ ♦❢❡rt❛ ❞❛ ❜♦❧s❛✱ q✉❡ ❝♦♥tr✐❜✉✐✉ ♣❛r❛ ♦ ❝✉st❡✐♦ ❞❡ ✈✐❛❣❡♥s ❡ ♠❛t❡r✐❛✐s ❞♦ ❝✉rs♦✳
❆ t♦❞♦s ♦s ♣r♦❢❡ss♦r❡s q✉❡ ❛ s❡✉ ♠♦❞♦ ❝♦❧❛❜♦r❛r❛♠ ♣❛r❛ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞♦ ❝✉rs♦✱ tr❛♥s♠✐t✐♥❞♦ ❝♦♥❤❡❝✐♠❡♥t♦s ✐♠♣♦rt❛♥t❡s à ♠✐♥❤❛ ❢♦r♠❛çã♦✳
➚ ♣r♦❢❡ss♦r❛ ❉r❛✳ ■✈♦♥✐❧❞❡s ❘✐❜❡✐r♦ ▼❛rt✐♥s ❉✐❛s✱ q✉❡ ♠❡ ♦r✐❡♥t♦✉ ❞✉r❛♥t❡ ♦ ❞❡✲
s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡st❛ ❞✐ss❡rt❛çã♦✳
❆♦s ♣r♦❢❡ss♦r❡s ❉r✳ ▼ár✐♦ ❏♦sé ❞❡ ❙♦✉③❛ ❡ ❉r❛✳ ❊✉♥✐❝❡ ❈â♥❞✐❞❛ P❡r❡✐r❛ ❘♦❞r✐❣✉❡s✱
♣❡❧❛ ♣❛rt✐❝✐♣❛çã♦ ❞❛ ❇❛♥❝❛ ❊①❛♠✐♥❛❞♦r❛ ❡ ♣❡❧❛s ♣❡rt✐♥❡♥t❡s ♦❜s❡r✈❛çõ❡s✳
❘❡s✉♠♦
◆❡st❡ tr❛❜❛❧❤♦ sã♦ ❢❡✐t❛s ♦❜s❡r✈❛çõ❡s s♦❜r❡ ❛❧❣✉♠❛s ❢♦r♠❛s ❡♠ q✉❡ s❡ é ♣♦ssí✈❡❧ ❡♥s✐✲ ♥❛r ❡ ❛♣r❡♥❞❡r ❣❡♦♠❡tr✐❛ ❛tr❛✈és ❞❛s r❡♣r❡s❡♥t❛çõ❡s✳ P❛r❛ ✐ss♦✱ tr❛t❛♠♦s ❞❛ ❧✐♥❣✉❛❣❡♠ ♠❛t❡♠át✐❝❛✱ ❞♦ ❡♥t❡♥❞✐♠❡♥t♦ ❞♦s ♠♦❞♦s ❞❡ r❡♣r❡s❡♥t❛çã♦ ❡ ❞♦ ❡♥s✐♥♦ ❞❡ ❣❡♦♠❡tr✐❛ ❛❧✐❛❞♦ ❛ ♦✉tr❛s ár❡❛s ❞❛ ▼❛t❡♠át✐❝❛ ♥♦ ❊♥s✐♥♦ ❇ás✐❝♦✳ ❆ ♣❡sq✉✐s❛ ❜✐❜❧✐♦❣rá✜❝❛ ❝♦♥✲ t❡♠♣❧♦✉ ✉♠ ❜r❡✈❡ ❡st✉❞♦ s♦❜r❡ ♦ ❡♥s✐♥♦ ❞❡ ❣❡♦♠❡tr✐❛ ♥❛s ❡s❝♦❧❛s ♣ú❜❧✐❝❛s✱ ❡①♣❧♦r❛♥❞♦ ❛ ♣r❡s❡♥ç❛ ❡♠ ❧✐✈r♦s ❞✐❞át✐❝♦s ❞❛ ❤✐stór✐❛ ❞❛ ♠❛t❡♠át✐❝❛✱ ❞❛ r❡s♦❧✉çã♦ ❞❡ ♣r♦❜❧❡♠❛s ❡ ❞❛s r❡♣r❡s❡♥t❛çõ❡s✳ ■♥❞✐❝❛♠♦s t❛♠❜é♠✱ ❛❧❣✉♠❛s ❞❛s ♠✐♥❤❛s ♣rát✐❝❛s ❞❡ ❡♥s✐♥♦ q✉❡ r❡❧❛❝✐♦♥❛♠ ❞✐❢❡r❡♥t❡s ❢♦r♠❛s ❞❡ r❡♣r❡s❡♥t❛r ❡ ❞❡ r❡♣r❡s❡♥t❛çõ❡s ❛tr❛✈és ❞❡ ♦❜❥❡t♦s r❡❛✐s ❡ ❞❡ r❡❝✉rs♦s ❝♦♠♣✉t❛❝✐♦♥❛✐s✳
P❛❧❛✈r❛s✲❝❤❛✈❡
●❡♦♠❡tr✐❛✳ ▲✐♥❣✉❛❣❡♠ ♠❛t❡♠át✐❝❛✳ ▲✐✈r♦ ❞✐❞át✐❝♦✳ Prát✐❝❛s ❞❡ ❡♥s✐♥♦ ❡ ❛♣r❡♥❞✐✲ ③❛❣❡♠✳ ❘❡♣r❡s❡♥t❛çõ❡s✳
❆❜str❛❝t
❚❤✐s ✇♦r❦ ♦❜s❡r✈❛t✐♦♥s ❛r❡ ♠❛❞❡ ❛❜♦✉t s♦♠❡ ✇❛②s ✐♥ ✇❤✐❝❤ ✐t ✐s ♣♦ss✐❜❧❡ t♦ t❡❛❝❤ ❛♥❞ ❧❡❛r♥ ❣❡♦♠❡tr② t❤r♦✉❣❤ t❤❡ r❡♣r❡s❡♥t❛t✐♦♥s✳ ❋♦r t❤✐s✱ ✇❡ tr❡❛t t❤❡ ♠❛t❤❡♠❛t✐❝❛❧ ❧❛♥❣✉❛❣❡✱ ✉♥❞❡rst❛♥❞✐♥❣ ♦❢ t❤❡ ♠♦❞❡s ♦❢ r❡♣r❡s❡♥t❛t✐♦♥ ❛♥❞ t❤❡ t❡❛❝❤✐♥❣ ♦❢ ❣❡♦♠❡tr② ❝♦♠❜✐♥❡❞ ✇✐t❤ ♦t❤❡r ❛r❡❛s ♦❢ ▼❛t❤❡♠❛t✐❝s ✐♥ ❇❛s✐❝ ❊❞✉❝❛t✐♦♥✳ ❚❤❡ ❧✐t❡r❛t✉r❡ s❡❛r❝❤ ✐♥❝❧✉❞❡❞ ❛ ❜r✐❡❢ st✉❞② ♦❢ ❣❡♦♠❡tr② t❡❛❝❤✐♥❣ ✐♥ t❤❡ ♣✉❜❧✐❝ s❝❤♦♦❧s✱ ❡①♣❧♦r✐♥❣ t❤❡ ♣r❡s❡♥❝❡ ✐♥ t❡①t❜♦♦❦s ♦❢ ❤✐st♦r② ♦❢ ♠❛t❤❡♠❛t✐❝s✱ ♣r♦❜❧❡♠ s♦❧✈✐♥❣ ❛♥❞ r❡♣r❡s❡♥t❛t✐♦♥s✳ ❲❡ ♥♦t❡ ❛❧s♦✱ s♦♠❡ ♦❢ ♠② t❡❛❝❤✐♥❣ ♣r❛❝t✐❝❡s t❤❛t r❡❧❛t❡ ❞✐✛❡r❡♥t ✇❛②s ♦❢ r❡♣r❡s❡♥t✐♥❣ ❛♥❞ r❡♣r❡s❡♥t❛t✐♦♥s t❤r♦✉❣❤ r❡❛❧ ♦❜❥❡❝ts ❛♥❞ ❝♦♠♣✉t✐♥❣ r❡s♦✉r❝❡s✳
❑❡②✇♦r❞s
●❡♦♠❡tr②✳ ▼❛t❤❡♠❛t✐❝❛❧ ❧❛♥❣✉❛❣❡✳ Pr❛❝t✐❝❡s ♦❢ t❡❛❝❤✐♥❣ ❛♥❞ ❧❡❛r♥✐♥❣✳ ❘❡♣r❡s❡♥✲ t❛t✐♦♥s✳ ❚❡①t❜♦♦❦✳
▲✐st❛ ❞❡ ❋✐❣✉r❛s
✶✳✶ ❈♦♥t❛❣❡♠ ❡ ♦ r❡❣✐str♦ ❞❡ q✉❛♥t✐❞❛❞❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹ ✷✳✶ ❚❛❜❡❧❛ ❞❡s❝r✐t✐✈❛ ❞♦s ❝♦♥t❡ú❞♦s ❞❡ ♠❛t❡♠át✐❝❛ ♥♦ ❊♥s✐♥♦ ▼é❞✐♦✳ ✳ ✳ ✳ ✳ ✶✸ ✸✳✶ ❘❡♣r❡s❡♥t❛çã♦ ❛❧❣é❜r✐❝❛ ❡ r❡♣r❡s❡♥t❛çã♦ ❣❡♦♠étr✐❝❛ ❞❡ ✉♠❛ ❢✉♥çã♦✳ ✳ ✳ ✷✵ ✸✳✷ ▼♦❞♦s ❞❡ r❡♣r❡s❡♥t❛çã♦✱ ❬✸✱ ❇♦❛✈✐❞❛✱ ♣✳✼✷❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹ ✸✳✸ ❊st✉❞❛♥t❡s ❞♦ ✼♦ ❛♥♦ ✭✷✵✶✸✮✱ ❡♠ ✉♠❛ ❛✉❧❛ s♦❜r❡ ♣♦❧✐❡❞r♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵
✸✳✹ ❈❛♣❛ ❞♦ ❧✐✈r♦ ▼❛t❡♠át✐❝❛✿ t❡♦r✐❛ ❡ ❝♦♥t❡①t♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✸✳✺ ❈❛♣❛ ❡ s✉♠ár✐♦ ❞❡ ✉♠❛ ❞❛s ✉♥✐❞❛❞❡s ❞♦ ❧✐✈r♦ ❞♦ Pr♦❥❡t♦ ❱❡❧❡❛r✳ ✳ ✳ ✳ ✳ ✸✻ ✹✳✶ ❉❡♠♦♥str❛çã♦ ❞♦ t❡♦r❡♠❛ ♣✐t❛❣ór✐❝♦✱ s❡❣✉♥❞♦ ❊✉❝❧✐❞❡s ✭❈á❧❝✉❧♦ ❞❡ ár❡❛s✮✳ ✹✷ ✹✳✷ ❉❡♠♦♥str❛çã♦ ❞♦ t❡♦r❡♠❛ ♣✐t❛❣ór✐❝♦✱ s❡❣✉♥❞♦ ❇❤❛s❦❛r❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✹✳✸ ❉❡♠♦♥str❛çã♦ ❞♦ t❡♦r❡♠❛ ♣✐t❛❣ór✐❝♦✱ s❡❣✉♥❞♦ ❇❤❛s❦❛r❛ ✲ ♣❛ss♦s ❞❛ ❞❡✲
❝♦♠♣♦s✐çã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✹✳✹ Pr♦♣r✐❡❞❛❞❡ ❛ss♦❝✐❛t✐✈❛ ❞❛ ❛❞✐çã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹ ✹✳✺ Pr♦♣r✐❡❞❛❞❡ ❝♦♠✉t❛t✐✈❛ ❞❛ ❛❞✐çã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺ ✹✳✻ Pr♦♣r✐❡❞❛❞❡ ❞✐str✐❜✉t✐✈❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻ ✹✳✼ Pr♦♣r✐❡❞❛❞❡ ❝♦♠✉t❛t✐✈❛ ❞❡ ♠✉❧t✐♣❧✐❝❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻ ✹✳✽ ◗✉❛❞r❛❞♦ ❞❛ s♦♠❛ ❞❡ ❞♦✐s t❡r♠♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ✹✳✾ ◗✉❛❞r❛❞♦ ❞❛ ❞✐❢❡r❡♥ç❛ ❞❡ ❞♦✐s t❡r♠♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ✹✳✶✵ ❖s q✉❛tr♦ r❡tâ♥❣✉❧♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵ ✹✳✶✶ ❙♦❧✉çã♦ ✲ ◗✉❛tr♦ r❡tâ♥❣✉❧♦s ❞❡ ♣❛♣❡❧ ✭✈❡rsã♦ ❖❇▼❊P✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶ ✹✳✶✷ ❚❡♦r❡♠❛ ❋✉♥❞❛♠❡♥t❛❧ ❞❛ Pr♦♣♦r❝✐♦♥❛❧✐❞❛❞❡✱ ❛♣❧✐❝❛❞♦ ❡♠ f(x) =ax✳ ✳ ✺✷
✹✳✶✸ ❘❛í③❡s ❞❛ ❡q✉❛çã♦ ❞♦ t✐♣♦ x2−sx+p2 = 0✱ ❝♦♠ s >2p✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹
✹✳✶✹ ❘❡tâ♥❣✉❧♦ R✱ q✉❡ ❡①♣r❡ss❛ ♦ mdc ❡ ♦ mmc ❡♥tr❡ ❞♦✐s ♥ú♠❡r♦s✳ ✳ ✳ ✳ ✳ ✺✻
✹✳✶✺ Pr♦❝❡❞✐♠❡♥t♦ ♣❛r❛ ❡♥❝♦♥tr❛r ♦ mdc ❡ ♦ mmc✱ ❛♠♣❧❛♠❡♥t❡ ✉t✐❧✐③❛❞♦ ♥♦
❊♥s✐♥♦ ❇ás✐❝♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽ ✹✳✶✻ ❈♦♥str✉çã♦ q✉❡ ❡①♣r❡ss❛ ❡♠ s❡❣♠❡♥t♦s ❛❧❣✉♠❛s ♠é❞✐❛s ❡♥tr❡ ❞♦✐s ♥ú✲
♠❡r♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ✹✳✶✼ ▼ét♦❞♦ ❣rá✜❝♦ ♣❛r❛ ❝❛❧❝✉❧❛r ❛ r❛✐③ q✉❛❞r❛❞❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✹✳✶✽ ❈♦♥str✉çã♦ ❣❡♦♠étr✐❝❛ ♣❛r❛ ♦❜t❡r ❛ r❛✐③ q✉❛❞r❛❞❛ ❞❡ ✉♠ ♥ú♠❡r♦ ✭❆♣♣❧❡t
❘❛✐③ ◗✉❛❞r❛❞❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷ ✺✳✶ Pr♦t♦❝♦❧♦ ❞❡ ❝♦♥str✉çã♦ ❞♦ ❆♣♣❧❡t ❘❛✐③ ◗✉❛❞r❛❞❛✱ ❣❡r❛❞♦ ♥♦ ●❡♦●❡❜r❛✳ ✻✸ ✺✳✷ P♦❧✐❡❞r♦s✿ ❚❡tr❛❡❞r♦✱ ❍❡①❛❡❞r♦✱ ❖❝t❛❡❞r♦✱ ❉♦❞❡❝❛❡❞r♦ ❡ ■❝♦s❛❡❞r♦✳ ✳ ✳ ✳ ✻✹ ✺✳✸ P♦❧✐❡❞r♦ ❞♦❞❡❝❛❡❞r♦ ❡ s✉❛ ♣❧❛♥✐✜❝❛çã♦ ❡♠ ❞✉❛s ✈✐st❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹ ✺✳✹ ❘❡❣✐ã♦ ❡♥tr❡ ❝✉r✈❛s ❡ s❡❣♠❡♥t♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺ ✺✳✺ ❘❡❢❡rê♥❝✐❛ à ♦❜r❛ ❖s ❊❧❡♠❡♥t♦s✱ ❞❡ ❊✉❝❧✐❞❡s ❬✷✱ ❇✐❣♦❞❡✱ ♣✳✽✶❪✳ ✳ ✳ ✳ ✳ ✳ ✻✻ ✺✳✻ ▼♦❞♦s ❞❡ r❡♣r❡s❡♥t❛çã♦ ❬✻✱ ❈❡♥t✉r✐ó♥✱ ♣✳✻✶❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼
❙✉♠ár✐♦
■♥tr♦❞✉çã♦ ✶
✶ ◆♦t❛s s♦❜r❡ r❡♣r❡s❡♥t❛çõ❡s ❡ ❣❡♦♠❡tr✐❛ ♥❛ ❤✐stór✐❛ ❞❛ ♠❛t❡♠át✐❝❛ ✸ ✷ ❖ ❡♥s✐♥♦ ❞❡ ❣❡♦♠❡tr✐❛ ❡♠ ❡s❝♦❧❛s ♣ú❜❧✐❝❛s ✽
✸ ❘❡♣r❡s❡♥t❛çõ❡s ✶✾
✸✳✶ ▲í♥❣✉❛ ❡ ❧✐♥❣✉❛❣❡♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✸✳✷ ❋♦r♠❛s ❞❡ r❡♣r❡s❡♥t❛çõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✸✳✸ ❊♥s✐♥♦ ❡ ❛♣r❡♥❞✐③❛❣❡♠ ❝♦♠ ♦❜❥❡t♦s ❡❞✉❝❛❝✐♦♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✸✳✹ ●❡♦●❡❜r❛✿ ❡①❡♠♣❧♦ ❞❡ r❡❝✉rs♦ ❝♦♠♣✉t❛❝✐♦♥❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✸✳✺ ❈♦♥❡①õ❡s ❡♥tr❡ ❛s ár❡❛s ❞❛ ❞✐s❝✐♣❧✐♥❛ ▼❛t❡♠át✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹
✹ ❊①❡♠♣❧♦s ❡ ♣r♦❜❧❡♠❛s ✸✾
✹✳✶ ❖ t❡♦r❡♠❛ ♣✐t❛❣ór✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ✹✳✷ ❘❡♣r❡s❡♥t❛çõ❡s ❞❡ ❛❧❣✉♥s ❝♦♥❝❡✐t♦s ❛❧❣é❜r✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹ ✹✳✷✳✶ ❆❧❣✉♠❛s ♣r♦♣r✐❡❞❛❞❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹ ✹✳✷✳✷ Pr♦❞✉t♦s ♥♦tá✈❡✐s✿ (a+b)2 ❡ (a−b)2 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽
✹✳✸ ◗✉❛tr♦ r❡tâ♥❣✉❧♦s ❞❡ ♣❛♣❡❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵ ✹✳✹ ❚❡♦r❡♠❛ ❋✉♥❞❛♠❡♥t❛❧ ❞❛ Pr♦♣♦r❝✐♦♥❛❧✐❞❛❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷ ✹✳✺ ❘❛í③❡s ❞❛ ❡q✉❛çã♦x2−Sx+P = 0 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸
✹✳✻ ▼á①✐♠♦ ❞✐✈✐s♦r ❝♦♠✉♠ ✭mdc✮ ❡ ♠í♥✐♠♦ ♠ú❧t✐♣❧♦ ❝♦♠✉♠ ✭mmc✮ ✳ ✳ ✳ ✳ ✺✺
✹✳✼ ▼é❞✐❛s ❡♥tr❡ ❞♦✐s ♥ú♠❡r♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽ ✹✳✽ ■♥t❡r♣r❡t❛çã♦ ❣❡♦♠étr✐❝❛ ❞❡ ✉♠❛ r❛✐③ q✉❛❞r❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵
✺ ❈♦♠♣❧❡♠❡♥t♦s ✻✸
✺✳✶ ❊①❡♠♣❧♦ ❞❡ ✉♠ ♣r♦t♦❝♦❧♦ ❞❡ ❝♦♥str✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸ ✺✳✷ ❈♦♥str✉çõ❡s ♥♦ ●❡♦●❡❜r❛ ❝♦♠ ✈✐s✉❛❧✐③❛çã♦ ✸❉ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹ ✺✳✸ ❖s ❊❧❡♠❡♥t♦s ❞❡ ❊✉❝❧✐❞❡s ❞❡ ❆❧❡①❛♥❞r✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻ ✺✳✹ ❊①❡♠♣❧♦ ❞❡ r❡♣r❡s❡♥t❛çõ❡s ❡♠ ✉♠ ❧✐✈r♦ ❞✐❞át✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼ ✺✳✺ ❆ ●❡♦♠❡tr✐❛ ❝♦♠♦ t❡♥❞ê♥❝✐❛ ❛t✉❛❧ ♥♦ ❡♥s✐♥♦ ❞❡ ▼❛t❡♠át✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾
❈♦♥s✐❞❡r❛çõ❡s ✜♥❛✐s ✼✵
❘❡❢❡rê♥❝✐❛s ❜✐❜❧✐♦❣rá✜❝❛s ✼✸
■♥tr♦❞✉çã♦
❆s r❡♣r❡s❡♥t❛çõ❡s ♣♦ss✉❡♠ s✐❣♥✐✜❝❛t✐✈❛ ✐♠♣♦rtâ♥❝✐❛ ♣❛r❛ ♦ ❝♦♥❤❡❝✐♠❡♥t♦✱ ❡❧❛s ♣❡r✲ ♠✐t❡♠ q✉❡ s❡ ♣♦ss❛ s❛✐r ❞♦ ✐♠❛❣✐♥ár✐♦✱ ❞♦ ✐♥t❡r✐♦r ❞♦ s❡r✱ ♣❛r❛ ♦ ❡①t❡r✐♦r✱ ♣r♦♠♦✈❡♥❞♦ s✉❛ ❞✐ss❡♠✐♥❛çã♦✳ ▼❡s♠♦ ❛♣ós ❛♥♦s ❝♦♠♦ ❡st✉❞❛♥t❡ ❡ ❛❧❣✉♥s ❛♥♦s ❝♦♠♦ ♣r♦❢❡ss♦r✱ ❛♣❡✲ s❛r ❞❡ ✉t✐❧✐③❛r ❡ t❡r ❝❡rt❛ ♣r♦①✐♠✐❞❛❞❡ ❝♦♠ ❛s r❡♣r❡s❡♥t❛çõ❡s✱ ♥ã♦ ❤❛✈✐❛ t♦♠❛❞♦ ❝✐ê♥❝✐❛ ❞♦ q✉❛♥t♦ ❛s r❡♣r❡s❡♥t❛çõ❡s ❡stã♦ ♣r❡s❡♥t❡s ♥❛ ♠❛t❡♠át✐❝❛✱ ❡ q✉❡ ❡❧❛s sã♦ ♣r♦♣í❝✐❛s à ❛♣r❡♥❞✐③❛❣❡♠✳
❖ ❞❡s♣❡rt❛r s✉r❣✐✉ ♥❛ ♦♣♦rt✉♥✐❞❛❞❡ ❞❡ ♥♦✈♦s ❡ ♠❛✐s ❛♣r♦❢✉♥❞❛❞♦s ❡st✉❞♦s ❞❡ ❛❧✲ ❣✉♠❛s ár❡❛s ❞❛ ▼❛t❡♠át✐❝❛✱ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ❛ ❣❡♦♠❡tr✐❛✳ ❆ ♣❡r❝❡♣çã♦ ❞❡ q✉❡ ❡st❛s ár❡❛s s❡ ❝♦♠✉♥✐❝❛✈❛♠ ❡ ❛ ♣r♦❝✉r❛ ♣♦r r❡s♦❧✈❡r ♦ ♠á①✐♠♦ ❞❡ ♣r♦❜❧❡♠❛s ❡ ♦❜s❡r✈á✲❧♦s s♦❜ ❞✐❢❡r❡♥t❡s s♦❧✉çõ❡s✱ ❝✉❧♠✐♥♦✉ ♥❡st❡ tr❛❜❛❧❤♦✳
◆♦ ❈❛♣ít✉❧♦ ✶✱ ❞❡st❛❝❛♠♦s ❜r❡✈❡s ❢❛t♦s ❤✐stór✐❝♦s s♦❜r❡ ❣❡♦♠❡tr✐❛ ❡ r❡♣r❡s❡♥t❛çã♦✱ ❝♦♠ ♦❜❥❡t✐✈♦ ❞❡ s✐t✉❛r ❡ ❡✈✐❞❡♥❝✐❛r ❛ ♣r❡s❡♥ç❛ ❞❛s r❡♣r❡s❡♥t❛çõ❡s ♥♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❛ ▼❛t❡♠át✐❝❛✳ ❉✐s❝♦rr❡✉✲s❡ s♦❜r❡ r❡❣✐str♦s ♠❛t❡♠át✐❝♦s ❡♠ ♣❛r❡❞❡s✱ ♠❛❞❡✐r❛✱ ♣❛♣✐r♦s ❡t❝✳ ❡ ❛ ❝♦♥str✉çã♦ ❞❛ ▼❛t❡♠át✐❝❛ ❜❛s❡❛❞❛ ♥♦ ❝♦t✐❞✐❛♥♦ ❡ ♥❛ r❡s♦❧✉çã♦ ❞❡ ♣r♦❜❧❡♠❛s✱ ♣❛r❛ ❡♥tã♦ ❞✐s♣♦r s♦❜r❡ ❛ ❡str✉t✉r❛çã♦ ❞♦ ❝♦♥❤❡❝✐♠❡♥t♦ ♠❛t❡♠át✐❝♦✳
◆♦ ❈❛♣ít✉❧♦ ✷✱ s❡❣✉❡♠ ❝❛r❛❝t❡ríst✐❝❛s ❞♦ ❡♥s✐♥♦ ❡♠ ❡s❝♦❧❛s ♣ú❜❧✐❝❛s✱ ♦❜s❡r✈❛♥❞♦ ♦ ❡♥s✐♥❛r ❡ ❛♣r❡♥❞❡r ❡♠ ❣❡♦♠❡tr✐❛✳ ❉❡st❛❝❛♠♦s ❛s ♣♦❧ít✐❝❛s ❡♠♣r❡❣❛❞❛s ♥♦ ❡♥s✐♥♦ ✭P❈◆s✱ ▲❉❇ ❡ ♦✉tr♦s✮✱ ♦s ❧✐✈r♦s ❞✐❞át✐❝♦s✱ ❛ ❢♦r♠❛çã♦ ❞♦ ♣r♦❢❡ss♦r ❡ s✉❛s ♣rát✐❝❛s✳
❆s r❡♣r❡s❡♥t❛çõ❡s t✐✈❡r❛♠ ❝♦♥s✐❞❡rá✈❡❧ ❞❡st❛q✉❡ ♥♦ t❡r❝❡✐r♦ ❝❛♣ít✉❧♦❀ ❝❛r❛❝t❡r✐✲ ③❛♥❞♦ ♦ q✉❡ sã♦ ❡ ❛❧❣✉♠❛s ❞✐❢❡r❡♥t❡s ❢♦r♠❛s ❞❡ r❡♣r❡s❡♥t❛çõ❡s✱ s✐t✉❛♠♦s ❡st❛s ❢♦r♠❛s ❞❡ r❡♣r❡s❡♥t❛çã♦ s❡❣✉♥❞♦ ♦❜❥❡t♦s ♠❛t❡♠át✐❝♦s✱ ❡♥❢❛t✐③❛♥❞♦ ❛ ✐♠♣♦rtâ♥❝✐❛ ❞♦ tr❛t❛✲
♠❡♥t♦ ❡ ❞❛ ❝♦♥✈❡rsã♦ ❡♥tr❡ r❡♣r❡s❡♥t❛çõ❡s ❡ ✐♥❞✐❝❛♥❞♦ ♦s ♠♦❞♦s ❞❡ r❡♣r❡s❡♥t❛çã♦✳ ❋♦r❛♠ ♦❜s❡r✈❛❞♦s ❛ ❧í♥❣✉❛✱ ❛ ❧✐♥❣✉❛❣❡♠ ♠❛t❡♠át✐❝❛✱ ❛❧❣✉♠❛s ❢♦r♠❛s ❞❡ r❡♣r❡s❡♥t❛✲ çõ❡s✱ ♦ ❡♥s✐♥♦ ❡ ❛ ❛♣r❡♥❞✐③❛❣❡♠ ✉t✐❧✐③❛♥❞♦ ♦❜❥❡t♦s ❡❞✉❝❛❝✐♦♥❛✐s ❡ ❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ r❡❧❛❝✐♦♥❛r ❞✐❢❡r❡♥t❡s ár❡❛s ❞❛ ▼❛t❡♠át✐❝❛✳
◆♦ ♣❡♥ú❧t✐♠♦ ❝❛♣ít✉❧♦✱ ❡stã♦ ✐♥❞✐❝❛❞♦s ❛❧❣✉♥s ❡①❡♠♣❧♦s q✉❡ ❝❛r❛❝t❡r✐③❛♠ ❡ r❡❢♦r✲ ç❛♠ ❛s ♦❜s❡r✈❛çõ❡s s♦❜r❡ r❡♣r❡s❡♥t❛çõ❡s ❡ s♦❜r❡ ❣❡♦♠❡tr✐❛ ♣r❡s❡♥t❡s ♥❡st❡ tr❛❜❛❧❤♦✱ ✐♥❢❡r✐♥❞♦ ❛❧❣✉♠❛s r❡✢❡①õ❡s s♦❜r❡ ♦s ♦❜❥❡t♦s ♣r✐♥❝✐♣❛✐s ❞❡st❡ ❡st✉❞♦ ❡ s♦❜r❡ ❡♥s✐♥❛r ❡ ❛♣r❡♥❞❡r ❡♠ ▼❛t❡♠át✐❝❛✳
❘❡❢♦rç❛♠♦s✱ ♥♦ ❝❛♣ít✉❧♦ ✹✱ ❛❧❣✉♠❛s ❝♦♥s✐❞❡r❛çõ❡s s♦❜r❡ ♦ ❡♥s✐♥♦ ❡ ❛ ❛♣r❡♥❞✐③❛❣❡♠ ♥❛ ❞✐s❝✐♣❧✐♥❛ ❞❡ ♠❛t❡♠át✐❝❛ ❡ r❡ss❛❧t❛♠♦s ❛ ✐♠♣♦rtâ♥❝✐❛ ❞❡ t❡r ♥❛s r❡♣r❡s❡♥t❛çõ❡s ✉♠❛ ♣♦ss✐❜✐❧✐❞❛❞❡ ❞❡ ❛♠♣❧✐❛r ❛s ♣rát✐❝❛s ❞♦ ♣r♦❢❡ss♦r✳
❈❛♣ít✉❧♦ ✶
◆♦t❛s s♦❜r❡ r❡♣r❡s❡♥t❛çõ❡s ❡
❣❡♦♠❡tr✐❛ ♥❛ ❤✐stór✐❛ ❞❛ ♠❛t❡♠át✐❝❛
◗✉❡♠ ❝♦♥t❛ ✉♠❛ ❤✐stór✐❛ ♣r♦❝✉r❛ ❢✉♥❞❛♠❡♥tá✲❧❛ ❡♠ ❞♦❝✉♠❡♥t♦s ❡ ❢❛t♦s✱ ✐♥❢❡r✐♥❞♦ ✐♥t❡r♣r❡t❛çõ❡s s♦❜r❡ ❛q✉✐❧♦ q✉❡ t♦♠❛ ❝♦♠♦ ❜❛s❡ ❡ ❡♥tã♦ ❛♠♣❧✐❛ ♦s r❡❣✐str♦s ❛❝❡r❝❛ ❞♦ ❛ss✉♥t♦ ❛ q✉❡ s❡ ♣r♦♣ôs ❞❡s❡♥✈♦❧✈❡r✳ ❇❛s❡❛❞♦ ❡♠ r❡❢❡rê♥❝✐❛s ❜✐❜❧✐♦❣rá✜❝❛s✱ ♣r♦❝✉r♦✉✲ s❡ ❞❡s❝r❡✈❡r ❛ r❡s♣❡✐t♦ ❞❡ ❢❛t♦s ❡ r❡❣✐str♦s ❞❡ r❡♣r❡s❡♥t❛çõ❡s✱ ♠❛✐s ❡s♣❡❝✐✜❝❛♠❡♥t❡ ❡♠ ❣❡♦♠❡tr✐❛ ♥❛ ❤✐stór✐❛ ❞❛ ♠❛t❡♠át✐❝❛✳
❆ ❣❡♦♠❡tr✐❛ ♥❛s❝❡✉ ❝♦♠♦ ✉♠❛ ❝✐ê♥❝✐❛ ❡♠♣ír✐❝❛ ♦✉ ❡①♣❡r✐♠❡♥t❛❧✳ ◆❛ ✏❝♦♥❢r♦♥t❛çã♦✑ ❝♦♠ ♦ s❡✉ ♠❡✐♦ ❛♠❜✐❡♥t❡ ♦ ❍♦♠❡♠ ❞❛ ❆♥t✐❣❛ ■❞❛❞❡ ❞❛ P❡❞r❛ ❝❤❡❣♦✉ ❛♦s ♣r✐♠❡✐r♦s ❝♦♥❤❡❝✐♠❡♥t♦s ❣❡♦♠étr✐❝♦s✳ ❖ ♣r♦❝❡ss♦ ❞❛ ❛q✉✐s✐çã♦ ♣❡❧♦ tr❛❜❛❧❤♦ ❞❡ ✐♠❛❣❡♥s ❛❜str❛t❛s ❞❛s r❡❧❛çõ❡s ❡s♣❛❝✐❛✐s ❡♥tr❡ ♦s ♦❜❥❡t♦s ❢ís✐❝♦s ❡ ❛s s✉❛s ♣❛rt❡s ❞❡❝♦rr❡✉✱ ♣r✐♠❡✐r♦✱ ❞❡ ✉♠❛ ❢♦r♠❛ ❡①tr❡♠❛♠❡♥t❡ ❧❡♥t❛✳ ❉❡♣♦✐s ❞❡ t❡r s✐❞♦ r❡✉♥✐❞♦ s✉✜❝✐❡♥t❡ ♠❛t❡r✐❛❧ ❢❛❝t✉❛❧ r❡s♣❡✐t❛♥t❡ às ❢♦r♠❛s ❡s♣❛❝✐❛✐s ♠❛✐s s✐♠♣❧❡s✱ t♦r♥♦✉✲s❡ ♣♦ssí✈❡❧✱ s♦❜ ❝♦♥❞✐çõ❡s s♦❝✐❛✐s ❡s♣❡❝✐❛✐s✱ ❝♦♠♦✱ ♣♦r ❡①❡♠♣❧♦✱ ♥♦ ❊❣✐t♦ ❛♥t✐❣♦✱ ▼❡s♦♣♦tâ♠✐❛ ❡ ❈❤✐♥❛✱ s✐st❡✲ ♠❛t✐③❛r ❝♦♥s✐❞❡r❛✈❡❧♠❡♥t❡ ♦ ♠❛t❡r✐❛❧ ❢❛❝t✉❛❧ r❡❝♦❧❤✐❞♦✳ ❈♦♠ ✐ss♦ ❝♦♠❡ç♦✉ ❛ tr❛♥s❢♦r♠❛çã♦ ❞❛ ❣❡♦♠❡tr✐❛ ❞❡ ✉♠❛ ❝✐ê♥❝✐❛ ❡♠♣ír✐❝❛ ♥✉♠❛ ❝✐ê♥❝✐❛ ♠❛t❡♠át✐❝❛ ✭✳✳✳✮✳ ❬✶✹✱ ●❡r❞❡s✱ ♣✳✷✾❪
◆❛s r❡❢❡rê♥❝✐❛s s♦❜r❡ ❛ ❤✐stór✐❛ ❞❛ ♠❛t❡♠át✐❝❛ ♣❡r❝❡❜❡✲s❡ ❛ ❢❛❧t❛ ❞❡ r❡❣✐str♦s q✉❡ ❝♦♠♣r♦✈❡♠ ❛ ♦r✐❣❡♠ ❞❡ ✐♥ú♠❡r♦s ❝♦♥❤❡❝✐♠❡♥t♦s✱ ❤á t❛♠❜é♠ ❛ ❜✉s❝❛ ♣♦r ❢✉♥❞❛♠❡♥t❛r
❡ r❡❧❛❝✐♦♥❛r ❢❛t♦s ♦❝♦rr✐❞♦s ❡♠ ✈ár✐❛s ♣❛rt❡s ❞♦ ♠✉♥❞♦✳ ❖s r❡❣✐str♦s ♠❛t❡♠át✐❝♦s ❞♦ ❝♦♥❝r❡t♦ ♦❝♦rr✐❛♠ ❡♠ ❞✐✈❡rs♦s ♠❛t❡r✐❛✐s ✭♣❛r❡❞❡s✱ ♣❡❞r❛s✱ ♣❛♣✐r♦s✱ ✜❜r❛s ❞❡ ár✈♦r❡s✱ tá❜✉❧❛s ❞❡ ❛r❣✐❧❛ ❡t❝✳✮ ❡ ❛❝r❡❞✐t❛✲s❡ q✉❡ ♠✉✐t♦ ❞✐ss♦ s❡ ♣❡r❞❡✉ ❥✉st❛♠❡♥t❡ ♣♦r ❝♦♥t❛ ❞❛ q✉❛❧✐❞❛❞❡ ❞♦ ♠❛t❡r✐❛❧ ✉t✐❧✐③❛❞♦✳
❆ ♠❛t❡♠át✐❝❛ ❢♦✐ s❡♥❞♦ ❝♦♥str✉í❞❛ ❡♠ ❞✐✈❡rs❛s ♣❛rt❡s ❞♦ ♠✉♥❞♦✱ r❡♠❡t❡♥❞♦ ✉♠ ❧♦♥❣♦ ♣❡rí♦❞♦ ❞❡s❞❡ ❛♥t❡s ❞♦s ♣r✐♠❡✐r♦s r❡❣✐str♦s ❛té ❛ s✉❛ ❡str✉t✉r❛ ❛t✉❛❧✳ P❡r❝❡❜❡✲s❡ q✉❡ ♥ã♦ ❤á ✉♠❛ ❝♦♥t✐♥✉✐❞❛❞❡ ú♥✐❝❛ ❞❡ ❡✈♦❧✉çã♦❀ ✉♠ ❞❡t❡r♠✐♥❛❞♦ ❝♦♥❤❡❝✐♠❡♥t♦ ♣❛r❛ ❛ ♠❛t❡♠át✐❝❛ s✉r❣✐❛ ❡♥tr❡ ✈ár✐♦s ♣♦✈♦s ❝♦♠ ❞✐❢❡r❡♥t❡s ✜♥❛❧✐❞❛❞❡s ❡ ♣♦r ✈❡③❡s✱ ❛♦ ♠❡s♠♦ t❡♠♣♦✳
➱ ❝❡rt♦ q✉❡ q✉❛♥❞♦ ✈✐❡r❛♠ ❛s ♣r✐♠❡✐r❛s r❡♣r❡s❡♥t❛çõ❡s✱ ❛♥t❡s ❥á ❤❛✈✐❛♠ ❛♦ ❤♦♠❡♠ ♦✉tr♦s ❝♦♥❤❡❝✐♠❡♥t♦s ♣r♦✈✐❞♦s ♣♦ss✐✈❡❧♠❡♥t❡ ♣❡❧♦ ✉s♦ ❞♦s s❡♥t✐❞♦s ❢r❡♥t❡ ❛♦ q✉❡ ❧❤❡ ❡r❛ ♣ró①✐♠♦✱ ❝♦♠♦ ❛ ❛ss♦❝✐❛çã♦ ❛ ♦❜❥❡t♦s r❡❛✐s✱ ❞❡ ❝♦♥❝❡✐t♦s ❡ ♦✉tr❛s q✉❛❧✐✜❝❛çõ❡s ❞❡ ✉s♦✱ ❢♦r♠❛ ❡ t❛♠❛♥❤♦✳ ❚❛✐s ❛ss♦❝✐❛çõ❡s ❛♣r❡s❡♥t❛✈❛♠ ✈❛r✐❛çõ❡s ♣♦r ❝♦♥t❛✱ ❡♥tr❡ ♦✉tr♦s✱ ❞❡ ❢❛t♦r❡s ❧✐❣❛❞♦s às ❝❛r❛❝t❡ríst✐❝❛s ♣ró♣r✐❛s ❞♦s ❞✐❢❡r❡♥t❡s ♣♦✈♦s✳
❋✐❣✉r❛ ✶✳✶✿ ❈♦♥t❛❣❡♠ ❡ ♦ r❡❣✐str♦ ❞❡ q✉❛♥t✐❞❛❞❡s✳
❈♦♥t❛✲s❡ q✉❡ ❛ ♠❛t❡♠át✐❝❛ ❡ s❡✉s ❞✐✈❡rs♦s ❝❛♠♣♦s ❢♦r❛♠ s✉r❣✐♥❞♦ ❞❡✈✐❞♦ às ❝♦♥✲ ❞✐çõ❡s ❡ ♥❡❝❡ss✐❞❛❞❡s ❤✉♠❛♥❛s✳ ❍♦✇❛r❞ ❊✈❡s✱ ❬✶✷✱ ♣✳✶❪ r❡❧❛t❛ q✉❡ ✏✐♥ú♠❡r❛s ❝✐r❝✉♥s✲ tâ♥❝✐❛s ❞❛ ✈✐❞❛✱ ❛té ♠❡s♠♦ ❞♦ ❤♦♠❡♠ ♠❛✐s ♣r✐♠✐t✐✈♦✱ ❧❡✈❛✈❛♠ ❛ ✉♠ ❝❡rt♦ ♠♦♥t❛♥t❡ ❞❡ ❞❡s❝♦❜❡rt❛s ❣❡♦♠étr✐❝❛s s✉❜❝♦♥s❝✐❡♥t❡s✑ ❡ ❡①❡♠♣❧✐✜❝❛ ✉♠❛ sér✐❡ ❞❡ ♦✉tr♦s ❝♦♥❝❡✐t♦s ♣♦ss✐✈❡❧♠❡♥t❡ ❛❞✈✐♥❞♦s ❞❛ ♦❜s❡r✈❛çã♦ ❞❛ ♥❛t✉r❡③❛✱ ❞❡ s✐t✉❛çõ❡s ❝r✐❛❞❛s ♦✉ ❞❛ ♣ró♣r✐❛
❡✈♦❧✉çã♦ ❤✉♠❛♥❛✱ ♣❛r❛ ❡st❡ ❝❡♥ár✐♦ ♥♦♠❡♦✉✲s❡ ✏❣❡♦♠❡tr✐❛ s✉❜❝♦♥s❝✐❡♥t❡✑✳ ◆♦ ❡♥s✐♥♦ ❞❡ ♠❛t❡♠át✐❝❛✱ ✉♠❛ ❞❛s r❡❢❡rê♥❝✐❛s ❤✐stór✐❝❛s ♠❛✐s r❡❝♦rr❡♥t❡s é ❛ ❞❡ ❝♦♥t❛❣❡♠ ❝♦♠ ❛ ❛ss♦❝✐❛çã♦ 1 ♣❛r❛ 1 ❞❡ ✉♠ ❛♥✐♠❛❧ ❡ ❛❧❣✉♠❛ r❡♣r❡s❡♥t❛çã♦ ♦✉ ❛ss♦❝✐❛çã♦ ✭s❡❥❛ ❝♦♠
♣❡❞r❛s✱ ❣r❛✈❡t♦s✱ ♠❛r❝❛s ♦✉ ♥ós✮✱ ❝♦♠♦ ♥❛ ❋✐❣✉r❛ ✶✳✶✱ ♣r❡s❡♥t❡ ❡♠ ❉❛♥t❡ ❬✽✱ ♣✳✶✸❪✱ ❧✐✈r♦ ❞✐❞át✐❝♦ ❞❛ ✺❛ sér✐❡ ❞♦ ❊♥s✐♥♦ ❋✉♥❞❛♠❡♥t❛❧✳
❯♠ ❢❛t♦ ✐♠♣♦rt❛♥t❡ ❛ r❡s♣❡✐t♦ ❞❛ ❡✈♦❧✉çã♦ ♠❛t❡♠át✐❝❛✱ ❡stá ❧✐❣❛❞♦ ❛♦ q✉❡ ❞❡st❛❝❛ ▼♦❧ ❬✷✸✱ ♣✳✶✻❪✱ ❞❡ q✉❡ ✏♦ ♠❛✐♦r ❧❡❣❛❞♦ ❞❡ss❛ ❝✐✈✐❧✐③❛çã♦ ❬▼❡s♦♣♦tâ♠✐❛❪ ❢♦✐ ♦ ❞❡s❡♥✈♦❧✲ ✈✐♠❡♥t♦ ✭. . .✮ ❞❛ ❢♦r♠❛ ❞❡ ❝♦♠✉♥✐❝❛çã♦ ❡s❝r✐t❛ ♠❛✐s ❛♥t✐❣❛ ❞❛ ❤✉♠❛♥✐❞❛❞❡✿ ❛ ❡s❝r✐t❛
❝✉♥❡✐❢♦r♠❡✑✳ ❘❡♣r❡s❡♥t❛r ❛tr❛✈és ❞❛ ❡s❝r✐t❛✱ ❡♠ ♣❧❛❝❛s ❞❡ ❛r❣✐❧❛✱ ❞❡✉ à ❤✉♠❛♥✐❞❛❞❡ ❛ ♣♦ss✐❜✐❧✐❞❛❞❡ ❞❡ s❡ r❡❝♦♥❤❡❝❡r✱ ❞❡ r❡❝♦♥❤❡❝❡r ❡ ♣❛rt✐❝✐♣❛r ❞❛ ❡✈♦❧✉çã♦ ❞♦ ❝♦♥❤❡❝✐♠❡♥t♦ ♠❛t❡♠át✐❝♦✳
▼✉✐t♦ t❡♠♣♦ ❞❡♣♦✐s✱ ❥á ❝♦♠ ♣♦ss❡ ❞❡ ♠❛✐♦r ❝♦♥❥✉♥t♦ ❞❡ ❢❡rr❛♠❡♥t❛s ♣❡r❝❡❜❡✲s❡ q✉❡ ❛s r❡♣r❡s❡♥t❛çõ❡s ❞❡✐①❛r✐❛♠ ❞❡ s❡r ❛♣❡♥❛s s♦❜r❡ ♦ r❡❛❧✱ ♠❛s ❢r✉t♦ ❞❡ ✉♠❛ ❝♦♠❜✐♥❛çã♦ ❡♥tr❡ ♦ r❡❛❧ ❡ ❛ ✐♠❛❣✐♥❛çã♦✳ ◆ã♦ ❤❛✈✐❛♠ ♠❛✐s ❛♣❡♥❛s ♣r♦❜❧❡♠❛s s♦❧t♦s ❛ r❡s♣❡✐t♦ ❞❛s ♥❡❝❡ss✐❞❛❞❡s ❤✉♠❛♥❛s✱ ♠❛s ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❝❛r❛❝t❡ríst✐❝❛s q✉❡ ♣❡r♠✐t✐❛♠ ❡str✉t✉r❛r ❝♦♥❤❡❝✐♠❡♥t♦s ❣❡r❛✐s s♦❜r❡ ❣❡♦♠❡tr✐❛✳ ❆ ♠❛t❡♠át✐❝❛ t✐♥❤❛ ❛❣♦r❛ ♦✉tr♦ ❝❛♠♣♦✱ ❝♦♠ ❧✐♥❣✉❛❣❡♠ ♣ró♣r✐❛ q✉❡ tr❛t❛✈❛ ❞❡ ♠❡❞✐❞❛s ❡ ❢♦r♠❛s✱ ♥ã♦ ❞❡✐①❛♥❞♦ ❞❡ ❛t❡♥❞❡r ❡ ❞❡ s❡ ♥✉tr✐r ❞❛s ♣❡r❝❡♣çõ❡s ❡ ✈✐✈ê♥❝✐❛s ❞♦s ♣♦✈♦s✱ ♠❛s✱ ❛tr❛✈és ❞❡st❡s ❝♦♥❤❡❝✐♠❡♥t♦s✱ ♣❛ss❛♥❞♦ ❛ ✐♥❢❡r✐r s♦❜r❡ ♦ ♠❡✐♦✱ ❡♠ q✉❡ ❍♦✇❛r❞ ❊✈❡s ❬✶✷✱ ♣✳✷✼❪ ✐♥❞✐❝❛ ♣♦r ✏❣❡♦♠❡tr✐❛ ❝✐❡♥tí✜❝❛✑✳
❍♦✇❛r❞ ❊✈❡s ❬✶✷✱ ♣✳✷✼❪✱ ❡✈✐❞❡♥❝✐❛ ❛✐♥❞❛ q✉❡ ✏P♦r ✈♦❧t❛ ❞♦ ❛♥♦ ✻✵✵ ❛✳❈✳✱ ♦s ❣r❡❣♦s ❝♦✲ ♠❡ç❛r❛♠ ❛ ✐♥tr♦❞✉③✐r ❞❡❞✉çã♦ ♥❛ ❣❡♦♠❡tr✐❛✑✱ ♦r✐❣✐♥❛♥❞♦ ❛ ✏❣❡♦♠❡tr✐❛ ❞❡♠♦♥str❛t✐✈❛✑ ❡ q✉❡ ♣♦r ✉♠ ❧♦♥❣♦ ♣❡rí♦❞♦✱ ❝♦♥s✐❞❡r❛✈❛✲s❡ ❛♣❡♥❛s ✉♠❛ ❣❡♦♠❡tr✐❛✱ ❡♠ q✉❡ ♦ ❡s♣❛ç♦ ❡r❛ ❝♦♥❝❡❜✐❞♦ ✏❝♦♠♦ ✉♠ ❞♦♠í♥✐♦ ♦✉ ❧✉❣❛r ♥♦ q✉❛❧ ♦s ♦❜❥❡t♦s ♣♦❞✐❛♠ s❡ ❞❡s❧♦❝❛r ❧✐✈r❡♠❡♥t❡ ❡ s❡r ❝♦♠♣❛r❛❞♦s ✉♥s ❝♦♠ ♦s ♦✉tr♦s✑✳
◆ã♦ ❢♦✐ ❛ ♣r✐♠❡✐r❛ ❡str✉t✉r❛çã♦ ❞♦ ❝♦♥❤❡❝✐♠❡♥t♦ ♠❛t❡♠át✐❝♦ ❡♠ ❢♦r♠❛ ❞❡ ❧✐✈r♦✱ ♠❛s ✉♠❛ ❝♦❧❡çã♦ ♠❛t❡♠át✐❝❛ ❞❡ ❣r❛♥❞❡ ✐♠♣♦rtâ♥❝✐❛ ❢♦✐ ❊❧❡♠❡♥t♦s✱ ❡♠ q✉❡ ❊✉❝❧✐❞❡s ❡ ❝❡rt❛♠❡♥t❡ ♦✉tr♦s✱ ❝♦♥tr✐❜✉ír❛♠ ❣r❛♥❞❡♠❡♥t❡ ♣❛r❛ ❛ ❡✈♦❧✉çã♦ ❞♦ ❝♦♥❤❡❝✐♠❡♥t♦ ♠❛✲
t❡♠át✐❝♦✳ ▼✉♥✐③ ◆❡t♦ ❬✷✻✱ ♣✳✷❪ ❞✐③ q✉❡ ✏❆ ✐♠♣♦rtâ♥❝✐❛ ❞♦s ❊❧❡♠❡♥t♦s s❡ ❞❡✈❡ ❛♦ ❢❛t♦ ❞❡ s❡r ❛ ♣r✐♠❡✐r❛ ♦❜r❛ ❡♠ q✉❡ s❡ ❝♦♥s✐❞❡r❛ ✉♠ ❝♦r♣♦ ❞❡ ❝♦♥❤❡❝✐♠❡♥t♦ ♠❛t❡♠át✐❝♦ ❝♦♠♦ ♣❛rt❡ ❞❡ ✉♠ s✐st❡♠❛ ❧ó❣✐❝♦ ❞❡❞✉t✐✈♦ ❜❡♠ ❞❡✜♥✐❞♦✑ ❡ ▼♦❧ ❬✷✸✱ ♣✳✹✺✲✺✷❪ r❡tr❛t❛✱ r❡s✉♠✐❞❛♠❡♥t❡✱ ❝❛❞❛ ✉♠ ❞♦s ❧✐✈r♦s q✉❡ ❝♦♠♣✉♥❤❛♠ ❛ ❝♦❧❡çã♦✿
❖s ♣r✐♠❡✐r♦s q✉❛tr♦ ❧✐✈r♦s tr❛t❛♠ ❞❡ ❣❡♦♠❡tr✐❛ ♣❧❛♥❛ ❡❧❡♠❡♥t❛r ❡ ❡st✉❞❛♠ ♣r♦♣r✐❡❞❛❞❡s ❞❡ ✜❣✉r❛s r❡t✐❧í♥❡❛s ❡ ❞♦ ❝ír❝✉❧♦✱ ❛❜♦r❞❛♥❞♦ ♣r♦❜❧❡♠❛s ❝✉❥❛ s♦❧✉çã♦ s❡ ❢❛③ ❝♦♠ ré❣✉❛ ❡ ❝♦♠♣❛ss♦✳ ❖ ❧✐✈r♦ ❱ ❛❜♦r❞❛ ❛ t❡♦r✐❛ ❞❡ ♣r♦♣♦rçõ❡s ❡ ♦ ❧✐✈r♦ ❱■ ❛♣❧✐❝❛ ❡ss❛ t❡♦r✐❛ ❛♦ ❡st✉❞♦ ❞❡ ❣❡♦♠❡tr✐❛✳ ❖s ❧✐✈r♦s ❱■■✱ ❱■■■ ❡ ■❳ ✈❡rs❛♠ s♦❜r❡ ❛ t❡♦r✐❛ ❞♦s ♥ú♠❡r♦s✳ ❖ ❧✐✈r♦ ❳ tr❛t❛ ❞♦s ✐♥❝♦♠❡♥s✉rá✈❡✐s ❡ ♦s ❧✐✈r♦s ❳■✱ ❳■■ ❡ ❳■■■ ❞✐s❝♦rr❡♠ s♦❜r❡ ❣❡♦♠❡tr✐❛ só❧✐❞❛✳ ❬✷✸✱ ▼♦❧✱ ♣✳✹✻❪
P♦r ✉♠ ❧♦♥❣♦ ♣❡rí♦❞♦✱ ❛ ❣❡♦♠❡tr✐❛ ❡st❡✈❡ ❜❛s❡❛❞❛ ♥♦ ❧✐✈r♦ ❖s ❊❧❡♠❡♥t♦s ❞❡ ❊✉❝❧✐✲ ❞❡s✳ ❘♦q✉❡ ❡ ❈❛r✈❛❧❤♦✱ ❬✸✸✱ ♣✳✶✷✷✲✶✷✹❪ r❡tr❛t❛♠ s♦❜r❡ ❛❧❣✉♠❛s ❞❛s ♠✉✐t❛s tr❛❞✉çõ❡s ❞❡ ❊❧❡♠❡♥t♦s ❡ ❞❡ q✉❡ ❛♣❡♥❛s ❡♠ ✷✵✵✾ ❤♦✉✈❡ ❛ ♣r✐♠❡✐r❛ ❡❞✐çã♦ ❝♦♠♣❧❡t❛ ♥❛ ❧í♥❣✉❛ ♣♦rt✉❣✉❡s❛✱ ♣♦r ■r✐♥❡✉ ❇✐❝✉❞♦✳ ❆ ❋✐❣✉r❛ ✺✳✺✱ ✉♠❛ ❢♦t♦ ❞❛ ♣á❣✐♥❛ ✽✶ ❞❡ ❧✐✈r♦ ❞✐❞át✐❝♦ ❞♦ ✾♦ ❛♥♦ r❡❢❡r❡✲s❡ ❛ ❡st❡ ❢❛t♦ ❞❛ ♦❜r❛ ❞❡ ❊✉❝❧✐❞❡s ✭❛♥❡①♦ ✺✳✸✮✳
▼❛s✱ ❛♦s ♣♦✉❝♦s ❛ ❣❡♦♠❡tr✐❛ ❣❛♥❤❛✈❛ ❝♦♥❤❡❝✐♠❡♥t♦s ❡ ❡st✉❞♦s ✈♦❧t❛❞♦s ♥ã♦ só ♣❛r❛ ♦ q✉❡ s❡ ❞❡s❝r❡✈❡✉ ❝♦♠♦ ✏❣❡♦♠❡tr✐❛ ♣r✐♠✐t✐✈❛✑✱ ♠❛s ❞❡♥tr♦ ❞❡ s❡✉ ♣ró♣r✐♦ ❝❛♠♣♦ ❞❡ ❝♦♥❤❡❝✐♠❡♥t♦❀ s✉r❣✐❛♠ ♥♦✈❛s r❡❣r❛s✱ ♥♦✈♦s ♠♦❞♦s ❞❡ ♣❡♥s❛r s♦❜r❡ ♦ ❡s♣❛ç♦✱ ❡ ❝♦♠ ♦ t❡♠♣♦✱ ❝♦♥s✐❞❡r♦✉✲s❡ ❛ ❡①✐stê♥❝✐❛ ❞❡ ♠❛✐s ❞❡ ✉♠❛ ❣❡♦♠❡tr✐❛✳ P♦r ❝♦♥t❛✱ ♣♦r ❡①❡♠♣❧♦✱ ❞♦ ❡s♣❛ç♦ ❛❣♦r❛ s❡r ✏❝♦♥s✐❞❡r❛❞♦ ✉♠❛ ❝♦❧❡çã♦ ❞❡ ♣♦♥t♦s✑✱ ❛s ❛t❡♥çõ❡s s❡ ✈♦❧t❛r❛♠ ♣❛r❛ ✏✉♠ ❣r✉♣♦ ❞❡ tr❛♥s❢♦r♠❛çõ❡s ❝♦♥❣r✉❡♥t❡s ❞♦ ❡s♣❛ç♦ ❡♠ s✐ ♠❡s♠♦✑✱ ❛ ❣❡♦♠❡tr✐❛ s❡ ❝♦♥✜❣✉r❛ ❝♦♠♦ ✏♦ ❡st✉❞♦ ❞❛s ♣r♦♣r✐❡❞❛❞❡s ❞❛s ❝♦♥✜❣✉r❛çõ❡s ❞❡ ♣♦♥t♦s q✉❡ ♣❡r♠❛♥❡❝❡♠ ✐♥❛❧t❡r❛❞❛s q✉❛♥❞♦ ♦ ❡s♣❛ç♦ ❝✐r❝✉♥❞❛♥t❡ é s✉❥❡✐t♦ ❛ ❡ss❛s tr❛♥s❢♦r♠❛çõ❡s✑✳ ❬✶✷✱ ❍♦✇❛r❞ ❊✈❡s✱ ♣✳✷✼❪
❈♦♠ ♦ t❡♠♣♦✱ ❛ ❣❡♦♠❡tr✐❛ ♣❛ss♦✉ ❛ t❡r ♦✉tr❛s ❞❡✜♥✐çõ❡s✱ ♦✉ s❡❥❛✱ ❛♠♣❧✐♦✉✲s❡ ❡♠ ♥♦✈♦s ❝❛♠♣♦s ❛ ♣♦♥t♦ ❞❡ ♣r♦♣✐❝✐❛r ♥♦✈❛s ❣❡♦♠❡tr✐❛s✱ ❝❛❞❛ ✉♠❛ ❝♦♠ ❧✐♥❣✉❛❣❡♠ ♣ró♣r✐❛ ❡ ♥♦ ✜♥❛❧ ❞♦ sé❝✉❧♦ ❳■❳✱ ♦ ❝♦♥❝❡✐t♦ ❞❡ ❛①✐♦♠át✐❝❛ ❢♦r♠❛❧ ♣❡r♠✐t✐✉ q✉❡ ❝❛❞❛ ✉♠❛ ❞❡ss❛s ❣❡♦♠❡tr✐❛s s❡ t♦r♥❛ss❡♠ ✉♠❛ s✉❜ár❡❛ ❡s♣❡❝í✜❝❛ ❞❛ ♠❛t❡♠át✐❝❛✳ ❆s r❡♣r❡s❡♥t❛çõ❡s
❡♠ ♠❛t❡♠át✐❝❛✱ ♣♦ss✐❜✐❧✐t❛r❛♠ ❛❧é♠ ❞❛ ❡str✉t✉r❛çã♦✱ ✉♠❛ ♥♦✈❛ ❢♦r♠❛ ❞❡ ❡st✉❞❛r ♦ ❝♦♥❤❡❝✐♠❡♥t♦✱ ♣♦❞❡♥❞♦ ❛♠♣❧✐á✲❧♦ ❡ ❛té ❢✉♥❞❛♠❡♥t❛r✱ ♣♦r ❡①❡♠♣❧♦✱ ♥♦✈❛s ár❡❛s ❡♠ ❣❡♦♠❡tr✐❛✳
❆s r❡♣r❡s❡♥t❛çõ❡s ❝♦♠❡ç❛♠ ❛ ❣❛♥❤❛r ❡s♣❛ç♦ ❝♦♠ ♦ ❘❡♥❛s❝✐♠❡♥t♦✳ ❋❧♦r❡s ✐♥❞✐❝❛ q✉❡
❛♥t❡r✐♦r♠❡♥t❡ ♦ ❝♦♥❤❡❝✐♠❡♥t♦ ❞♦ ♠✉♥❞♦ ❡ ❞♦s ❤♦♠❡♥s ❡s✲ t❛✈❛ s♦❜ ♦ ♣♦❞❡r ❞❛s ❡♥t✐❞❛❞❡s r❡❧✐❣✐♦s❛s✱ ✭✳✳✳✮ ❝♦♠ ❛ ❞❡s❝♦✲ ❜❡rt❛ ❞❛ r❛③ã♦ ♦ s✉❥❡✐t♦ ❞♦ ❝♦♥❤❡❝✐♠❡♥t♦ ♣❛ss❛ ❛ ❝♦♥❤❡❝❡r ❡ ❛ r❡♣r❡s❡♥t❛r ♦s ♦❜❥❡t♦s ❞♦ ❝♦♥❤❡❝✐♠❡♥t♦✳ ❆ q✉❡stã♦ ❞❛ r❡♣r❡s❡♥t❛çã♦ ♣❛ss❛✱ ❡♥tã♦✱ ❛ s❡r ♣r♦❜❧❡♠❛t✐③❛❞❛ ❡♥q✉❛♥t♦ ❡①♣r❡ssã♦ ✐❝♦♥♦❣rá✜❝❛ ❞❛ r❡❧❛çã♦ ❡♥tr❡ ♦ s✉❥❡✐t♦ ❞♦ ❝♦♥❤❡✲ ❝✐♠❡♥t♦ ❡ ♦ ♦❜❥❡t♦ ❞❛❞♦ ❛ ❝♦♥❤❡❝❡r✱ ❝r✐❛♥❞♦ ♣r✐♥❝í♣✐♦s ❞❛ r❡♣r❡s❡♥t❛çã♦ s♦❜ ♦ ❛s♣❡❝t♦ ❞❡ ❢✉♥❞❛♠❡♥t♦ t❡ór✐❝♦✱ ❡♣✐st❡✲ ♠♦❧ó❣✐❝♦✳ ❬✶✸✱ ❋❧♦r❡s✱ ♣✳✶✶✻❪
❍á ♣♦rt❛♥t♦✱ ✉♠❛ ♥♦✈❛ ✈✐sã♦ ❞❡ ♠✉♥❞♦ ❛♦ ♣♦♥t♦ q✉❡ ❛s ❝✐ê♥❝✐❛s s❡ ♣r♦♣õ❡♠ ❛ ❝♦♥str✉✐r ♠❛✐s ❝♦♥❤❡❝✐♠❡♥t♦s s♦❜r❡ ❡❧❡✱ ❛ ❡①♣❧✐❝á✲❧♦ ❡ ❡♥tã♦ r❡♣r❡s❡♥t❛r✳ ❆ ♣ró♣r✐❛ r❡♣r❡s❡♥t❛çã♦ ♣❛ss❛ ❛ t❡r ♠❛✐♦r ♦✉ ♥♦✈♦ ❞❡st❛q✉❡ ❡♠ ✈ár✐❛s ár❡❛s✳ ◆❛ ♠❛t❡♠át✐❝❛✱ ❞❡✐①❛ ❞❡ s❡r ❛ ✐♥t✉✐çã♦ ❣❡♦♠étr✐❝❛ ❡ ♦ ❞✐s❝✉rs♦✱ r❡❢❡rê♥❝✐❛s ♣❛r❛ ♦ ❝♦♥❤❡❝✐♠❡♥t♦❀ ♦ q✉❡ s❡ ♣❡r❝❡❜❡ é ❛ ♣r❡s❡♥ç❛ ❞❡ ✉♠❛ ♦r❣❛♥✐③❛çã♦ ❞❡ s✐❣♥♦s q✉❡ trás ♣❛r❛ ♦ s❛❜❡r ♦ q✉❡ s❡r✐❛ ✉♠❛ ❧✐♥❣✉❛❣❡♠❀ ♦s ❞✐s❝✉rs♦s ❡ ❞❡s❝r✐çõ❡s ❡♠ ❞✐❢❡r❡♥t❡s ❧í♥❣✉❛s ✭♣♦r ❝♦♥t❛ ❞❡ ✐♥ú♠❡r♦s ♣♦✈♦s ❡ ❝✉❧t✉r❛s✮ sã♦ tr❛❞✉③✐❞♦s ♣♦r ✉♠❛ ✉♥✐❢♦r♠✐❞❛❞❡ ❞❡ sí♠❜♦❧♦s ❡ ♦♣❡r❛çõ❡s✳
❈❛♣ít✉❧♦ ✷
❖ ❡♥s✐♥♦ ❞❡ ❣❡♦♠❡tr✐❛ ❡♠ ❡s❝♦❧❛s
♣ú❜❧✐❝❛s
❆♦ ♥❛s❝❡r✱ ❛ ❝r✐❛♥ç❛ ♣❛ss❛ ❛ t❡r s✉❛s ♣r✐♠❡✐r❛s ✐♥t❡r❛çõ❡s ❝♦♠ ♦ ❡s♣❛ç♦✳ ❚✉❞♦ ❛✐♥❞❛ é ❞❡s❝♦♥❤❡❝✐❞♦✱ ❡♠ ♥❛❞❛ ❤á s✐❣♥✐✜❝❛❞♦✳ ❆s ♣r✐♠❡✐r❛s s❡♥s❛çõ❡s✱ ❛s r❡♣❡t✐çõ❡s✱ ❛s ❡①♣❡r✐ê♥❝✐❛s✱ sã♦ ✐♥ú♠❡r♦s ❡stí♠✉❧♦s q✉❡ ❛♦s ♣♦✉❝♦s ❞ã♦ ❛♦ s✉❥❡✐t♦ ✉♠ s❡♥t✐❞♦ ❞❡ ❡s♣❛ç♦✳ ❖ ❧✐✈r♦ ❞❡ ❑♦❜❛②❛s❤✐ ❬✶✽❪ ✲ ✏❆ ❝♦♥str✉çã♦ ❞❛ ❣❡♦♠❡tr✐❛ ♣❡❧❛ ❝r✐❛♥ç❛✑✱ ❛♣r❡s❡♥t❛ ❝❛r❛❝t❡ríst✐❝❛s r❡❧❡✈❛♥t❡s s♦❜r❡ ❛ ❣❡♦♠❡tr✐❛ ✐♥❢❛♥t✐❧✱ q✉❡ ♥ã♦ é ❛ss✉♥t♦ ❞❡st❛ ❞✐ss❡rt❛çã♦✱ ♠❛s q✉❡ ❝♦♥tr✐❜✉✐ ♣❛r❛ ♦ ❡♥t❡♥❞✐♠❡♥t♦ ❞❛ ❝♦♥str✉çã♦ ❞♦ ❝♦♥❤❡❝✐♠❡♥t♦ ✭❡♠ ❡s♣❡❝í✜❝♦✱ ❛ ❣❡♦♠❡tr✐❛✮ ♣❡❧♦ s✉❥❡✐t♦ ❡♠ s❡✉s ♣r✐♠❡✐r♦s ✼ ❛♥♦s✳
◆♦s P❛râ♠❡tr♦s ❈✉rr✐❝✉❧❛r❡s ◆❛❝✐♦♥❛✐s ✲ P❈◆ ❬✺✱ ♣✳✹✼❪✱ ❛♦ s❡r❡♠ ❞❡s❝r✐t♦s ♦s ♦❜✲ ❥❡t✐✈♦s ♣r♦♣♦st♦s ♥♦ ❞♦❝✉♠❡♥t♦✱ ❤á ✉♠ ❞❡st❛q✉❡ ♣❛r❛ ❛s ✏❝❛♣❛❝✐❞❛❞❡s q✉❡ ❞❡✈❡♠ s❡r ❞❡s❡♥✈♦❧✈✐❞❛s ♣❡❧♦s ❛❧✉♥♦s ❛♦ ❧♦♥❣♦ ❞❛ ❡s❝♦❧❛r✐❞❛❞❡✑ ❡ ❛ r❡s♣❡✐t♦ ❞❛ ❝❛♣❛❝✐❞❛❞❡ ❝♦❣♥✐✲ t✐✈❛✱ ✐♥❞✐❝❛♠ q✉❡ ❡❧❛
t❡♠ ❣r❛♥❞❡ ✐♥✢✉ê♥❝✐❛ ♥❛ ♣♦st✉r❛ ❞♦ ✐♥❞✐✈í❞✉♦ ❡♠ r❡❧❛çã♦ às ♠❡t❛s q✉❡ q✉❡r ❛t✐♥❣✐r ♥❛s ♠❛✐s ❞✐✈❡rs❛s s✐t✉❛çõ❡s ❞❛ ✈✐❞❛✱ ✈✐♥❝✉❧❛♥❞♦✲s❡ ❞✐r❡t❛♠❡♥t❡ ❛♦ ✉s♦ ❞❡ ❢♦r♠❛s ❞❡ r❡♣r❡s❡♥t❛çã♦ ❡ ❞❡ ❝♦♠✉♥✐❝❛çã♦✱ ❡♥✈♦❧✈❡♥❞♦ ❛ r❡s♦❧✉çã♦ ❞❡ ♣r♦❜❧❡♠❛s✱ ❞❡ ♠❛♥❡✐r❛ ❝♦♥s❝✐❡♥t❡ ♦✉ ♥ã♦✳ ❆ ❛q✉✐s✐çã♦ ♣r♦❣r❡ss✐✈❛ ❞❡ ❝ó❞✐❣♦s ❞❡ r❡♣r❡s❡♥t❛çã♦ ❡ ❛ ♣♦ss✐✲ ❜✐❧✐❞❛❞❡ ❞❡ ♦♣❡r❛r ❝♦♠ ❡❧❡s ✐♥t❡r❢❡r❡ ❞✐r❡t❛♠❡♥t❡ ♥❛ ❛♣r❡♥❞✐③❛❣❡♠ ❞❛ ❧í♥❣✉❛✱ ❞❛ ♠❛t❡♠át✐❝❛✱ ❞❛ r❡♣r❡s❡♥t❛çã♦ ❡s♣❛❝✐❛❧✱ t❡♠♣♦r❛❧ ❡ ❣rá✜❝❛ ❡ ♥❛ ❧❡✐t✉r❛ ❞❡ ✐♠❛❣❡♥s✳ ❬✺✱ P❈◆✱ ♣✳✹✼❪
❖s ♣r✐♠❡✐r♦s ❛♥♦s ❞❡ ✉♠❛ ❝r✐❛♥ç❛ sã♦ ❝❛rr❡❣❛❞♦s ❞❡ ♥♦✈❛s ❡①♣❡r✐ê♥❝✐❛s✱ q✉❡ ♠❛✐s t❛r❞❡ s❡ t♦r♥❛♠ ❞❡t❡r♠✐♥❛♥t❡s ♣❛r❛ ♦ ♠♦❞♦ ❝♦♠♦ ❡❧❛ s❡ ♣❡r❝❡❜❡rá ❡ ♣❡r❝❡❜❡rá ♦ q✉❡ ❡stá ❛ s✉❛ ✈♦❧t❛✳ ❊st❡ ♣❡rí♦❞♦ ✐♥✐❝✐❛❧✱ ❡♠ q✉❡ ♦s s❡♥t✐❞♦s✱ ❛s ❢♦r♠❛s✱ ♦s ❝♦♥❝❡✐t♦s ❡ t✉❞♦ ♠❛✐s sã♦ ✈✐✈❡♥❝✐❛❞♦s ❡ ✈ã♦ ❞❛♥❞♦ s✐❣♥✐✜❝❛❞♦ às ❝♦✐s❛s✱ é ❡①♣❧♦r❛❞♦ ♣♦r ❑♦❜❛②❛s❤✐ ❬✶✽❪✱ q✉❡ ♣r♦♣õ❡ ❛✐♥❞❛ ✉♠ ❛♣❛♥❤❛❞♦ s♦❜r❡ ♦ ❡♥s✐♥♦ ❞❡ ❣❡♦♠❡tr✐❛ às ❝r✐❛♥ç❛s✳ ❇❛s❡❛❞❛s ❡♠ ❉❡❧ ●r❛♥❞❡ ❬✾❪✱ P❛ss♦s ❡ ◆❛❝❛r❛t♦ ❞✐③❡♠ q✉❡✿
❛ ♥❛t✉r❡③❛ ❞❛s ❛t✐✈✐❞❛❞❡s ♠❛t❡♠át✐❝❛s r❡❧❛❝✐♦♥❛❞❛s ❝♦♠ ❛ ❣❡✲ ♦♠❡tr✐❛ ♥❛ ❡s❝♦❧❛ ❜ás✐❝❛ ♣❡r♠✐t❡ ❛ ❛q✉✐s✐çã♦ ❞❡ ❡①♣❡r✐ê♥❝✐❛s ❞❡ ♣❡r❝❡♣çã♦ ✈✐s✉❛❧ ❞❛♥❞♦ ❛♦s ♣r♦❢❡ss♦r❡s ♦♣♦rt✉♥✐❞❛❞❡ ❞❡ ♦❜s❡r✈❛r ❡ ❞❡t❡❝t❛r✱ ❞❡s❞❡ ❝❡❞♦✱ ❝♦♠♦ ♦ ♣❡♥s❛♠❡♥t♦ ❣❡♦♠étr✐❝♦ ❞❛s ❝r✐❛♥ç❛s ✈❛✐ s❡♥❞♦ ❝♦♥str✉í❞♦✳ ✭✳✳✳✮ ❡ss❛ ♣❡r❝❡♣çã♦ ✐♥✐❝✐❛❧ ❞❛s ❤❛❜✐❧✐❞❛❞❡s ❞❡ ♣❡r❝❡♣çã♦ ✈✐s✉❛❧ s❡rá ❢✉♥❞❛♠❡♥t❛❧ ♣❛r❛ ♦ ♣❧❛♥❡❥❛♠❡♥t♦ ❞❡ t❛✲ r❡❢❛s ❞❡ ❣❡♦♠❡tr✐❛ ❛ s❡r❡♠ ♣r♦♣♦st❛s ♣❡❧♦ ♣r♦❢❡ss♦r✳ ❬✷✾✱ P❛ss♦s✱ ♣✳✶✶✹✾❪
▲✐♠✐t❛r✲s❡✲á ❛ ❞❡s❝r❡✈❡r ❛❧❣✉♠❛s ❝❛r❛❝t❡ríst✐❝❛s ❞♦ ❡♥s✐♥♦ ❞❡ ❣❡♦♠❡tr✐❛ ♥♦ ❊♥s✐♥♦ ❇ás✐❝♦✱ ♦❜s❡r✈❛❞❛s ❡♠ r❡❢❡rê♥❝✐❛s q✉❡ ✈ã♦ ❞♦ ❊♥s✐♥♦ ❋✉♥❞❛♠❡♥t❛❧ ■ ✭✶♦ ❛♦ ✺♦ ❛♥♦✮✱
♣❛ss❛♥❞♦ ♣❡❧♦ ❊♥s✐♥♦ ❋✉♥❞❛♠❡♥t❛❧ ■■ ✭✻♦ ❛♦ ✾♦ ❛♥♦✮ ❛té ♦ ❊♥s✐♥♦ ▼é❞✐♦❀ ♣r✐♥❝✐♣❛❧✲
♠❡♥t❡ ❛ ♣❛rt✐r ❞❛ r❡❢♦r♠❛ ❞♦ ❡♥s✐♥♦ ❞❡ ▼❛t❡♠át✐❝❛✱ q✉❡ s❡❣✉♥❞♦ ➪✈✐❧❛ ❬✶✱ ♣✳✸✲✻❪ ✜❝♦✉ ❝♦♥❤❡❝✐❞❛ ❝♦♠♦ ✏▼❛t❡♠át✐❝❛ ▼♦❞❡r♥❛✑✳ P❛✈❛♥❡❧❧♦ ❬✸✵✱ ♣✳✶✸❪✱ ❞✐③ q✉❡ ❛ ✐❞❡✐❛ ❝❡♥tr❛❧ ❞♦ ♠♦✈✐♠❡♥t♦ ✭▼❛t❡♠át✐❝❛ ▼♦❞❡r♥❛✮ ✏é ❛❞❛♣t❛r ♦ ❡♥s✐♥♦ ❞❛ ♠❛t❡♠át✐❝❛ às ♥♦✈❛s ❝♦♥❝❡♣çõ❡s s✉r❣✐❞❛s ❝♦♠ ❛ ❡✈♦❧✉çã♦ ❞❡st❡ r❛♠♦ ❞♦ ❝♦♥❤❡❝✐♠❡♥t♦✳✑
◆♦ ❇r❛s✐❧✱ ❞❡ ❛❝♦r❞♦ ❝♦♠ ❉✉tr❛ ❏ú♥✐♦r ❬✶✻✱ ♣✳✶✹✲✶✺❪✱ ♦ ❡♥s✐♥♦ ❞❡ ❣❡♦♠❡tr✐❛ t❡✈❡ ♣♦✉❝♦ ❞❡st❛q✉❡ ❛té ♦ sé❝✉❧♦ ❳❱■■■✱ ♣♦r ❝♦♥t❛ ❞❡ ❢❛❧t❛ ❞❡ q✉❛❧✐✜❝❛çã♦ ❡ ♣♦r s❡r ❝♦♥s✐❞❡✲ r❛❞♦ ❞❡ ♣♦✉❝❛ ♥❡❝❡ss✐❞❛❞❡ à ❢♦r♠❛çã♦✳ ■♥✐❝✐❛❧♠❡♥t❡✱ ♣♦r ❝♦♥t❛ ❞❡ ✜♥❛❧✐❞❛❞❡s ♠✐❧✐t❛r❡s✱
❛ ●❡♦♠❡tr✐❛ ❡ ♦ ❉❡s❡♥❤♦ ●❡♦♠étr✐❝♦ s✉r❣❡♠ ❡♠ ❛❧❣✉♠❛s ❡s❝♦❧❛s❀ ♠❛s q✉❛♥❞♦ ❛ ❣❡✲ ♦♠❡tr✐❛ ❢♦✐ t♦♠❛❞❛ ❝♦♠♦ ♣ré✲r❡q✉✐s✐t♦ ❞❡ ✐♥❣r❡ss♦ ❡♠ ❝✉rs♦s s✉♣❡r✐♦r❡s é q✉❡ ♦ s❡✉ ❡♥s✐♥♦ ❢♦✐ ❢♦r♠❛❧✐③❛❞♦ ❡ ♣❛ss♦✉ ❛ s❡r ♣❡r♠❛♥❡♥t❡ ♥♦ ❡♥s✐♥♦ s❡❝✉♥❞ár✐♦✳
❆ r❡❢♦r♠❛✱ ❡♥tr❡ ♦✉tr♦s✱ ❛❧t❡r♦✉ ♦ ❝✉rrí❝✉❧♦ ❞❡ ♠❛t❡♠át✐❝❛ ❛❞✐❝✐♦♥❛♥❞♦ ♥♦✈♦s ❝♦♥✲ t❡ú❞♦s✱ ♠♦❞✐✜❝♦✉ t❛♠❜é♠ ❛ ❧✐♥❣✉❛❣❡♠ ❡ ❛ ♥♦t❛çã♦ ❡♠♣r❡❣❛❞❛ ♣❛ss♦✉ ❛ s❡r ❛ ❞❡ ❝♦♥❥✉♥t♦s✳ ▼✉✐t♦s ♣r♦♣✉s❡r❛♠ ✉♠❛ r❡❞✉çã♦ ❞♦ ❝✉rrí❝✉❧♦ ❞❡ ❣❡♦♠❡tr✐❛ ♦✉ ♠❡s♠♦ q✉❡ ❡❧❛ ♥ã♦ ✜③❡ss❡ ♣❛rt❡ ❞♦ ❡♥s✐♥♦ ❞❡ ♠❛t❡♠át✐❝❛✳ ❊s♣❡❝✐✜❝❛♠❡♥t❡ ❛ r❡s♣❡✐t♦ ❞❛ ❣❡♦♠❡tr✐❛ ❡♠ ❧✐✈r♦s ❞✐❞át✐❝♦s✱ ♣♦r ❝♦♥t❛ ❞❛ ▼❛t❡♠át✐❝❛ ▼♦❞❡r♥❛✱ P❛✈❛♥❡❧❧♦ ✐♥❞✐❝❛ q✉❡✿
♦♣t❛✲s❡✱ ♥✉♠ ♣r✐♠❡✐r♦ ♠♦♠❡♥t♦✱ ♣♦r ❛❝❡♥t✉❛r ♥❡ss❡s ❧✐✈r♦s ❛s ♥♦çõ❡s ❞❡ ✜❣✉r❛ ❣❡♦♠étr✐❝❛ ❡ ❞❡ ✐♥t❡rs❡❝çã♦ ❞❡ ✜❣✉r❛s ❝♦♠♦ ❝♦♥✲ ❥✉♥t♦s ❞❡ ♣♦♥t♦s ❞♦ ♣❧❛♥♦✱ ❛❞♦t❛♥❞♦✲s❡✱ ♣❛r❛ s✉❛ r❡♣r❡s❡♥t❛çã♦✱ ❛ ❧✐♥❣✉❛❣❡♠ ❞❛ t❡♦r✐❛ ❞♦s ❝♦♥❥✉♥t♦s✳ Pr♦❝✉r❛✲s❡ tr❛❜❛❧❤á✲❧❛ s❡✲ ❣✉♥❞♦ ✉♠❛ ❛❜♦r❞❛❣❡♠ ✏✐♥t✉✐t✐✈❛✑ q✉❡ s❡ ❝♦♥❝r❡t✐③❛✱ ♥♦s ❧✐✈r♦s ❞✐✲ ❞át✐❝♦s✱ ♣❡❧❛ ✉t✐❧✐③❛çã♦ ❞♦s t❡♦r❡♠❛s ❝♦♠♦ ♣♦st✉❧❛❞♦s✱ ♠❡❞✐❛♥t❡ ♦s q✉❛✐s ♣♦❞❡✲s❡ r❡s♦❧✈❡r ❛❧❣✉♥s ♣r♦❜❧❡♠❛s✳ ◆ã♦ ❡①✐st❡ q✉❛❧q✉❡r ♣r❡♦❝✉♣❛çã♦ ❝♦♠ ❛ ❝♦♥str✉çã♦ ❞❡ ✉♠❛ s✐st❡♠❛t✐③❛çã♦ ❛ ♣❛rt✐r ❞❛s ♥♦çõ❡s ♣r✐♠✐t✐✈❛s ❡ ❡♠♣✐r✐❝❛♠❡♥t❡ ❡❧❛❜♦r❛❞❛s✳ ❬✸✵✱ P❛✈❛♥❡❧❧♦✱ ♣✳✶✸❪
P❛✈❛♥❡❧❧♦ ❬✸✵✱ ♣✳✼❪ ❛♣♦♥t❛ ❞♦✐s ♠♦t✐✈♦s ♣❛r❛ ♦ ❛❜❛♥❞♦♥♦ ❞♦ ❡♥s✐♥♦ ❞❡ ❣❡♦♠❡tr✐❛ ♥♦ ❇r❛s✐❧✿ ❛ ✐♥s❡❣✉r❛♥ç❛ ❞♦s ♣r♦❢❡ss♦r❡s ❞❡ ♠❛t❡♠át✐❝❛ ❡♠ tr❛❜❛❧❤❛r ❝♦♠ ❣❡♦♠❡tr✐❛ ❡ ♣r✐♥❝✐♣❛❧♠❡♥t❡✱ ♦ ♠♦❞♦ ❝♦♠♦ s❡ ♣r♦❝❡❞❡✉ ❛ ❡❞✉❝❛çã♦ ♥♦ ❇r❛s✐❧❀ ✐♥❞✐❝❛♥❞♦ ❛✐♥❞❛ q✉❡ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❛ ♠❛t❡♠át✐❝❛ ♥ã♦ ❢♦✐ ♠♦t✐✈♦ ♣❛r❛ q✉❡ ❛ ❣❡♦♠❡tr✐❛ ❝❡❞❡ss❡ ❡s♣❛ç♦ ♣❛r❛ ♦✉tr❛s ár❡❛s✳ P❛ss♦s ❡ ◆❛❝❛r❛t♦ ❬✷✾✱ ♣✳✶✶✹✽❪ ❝✐t❛♠ q✉❡ ❛ ❣❡♦♠❡tr✐❛ ♥ã♦ é ✏❛ss✉♠✐❞❛ ❝♦♠♦ ♣r✐♦r✐❞❛❞❡ ❢r❡♥t❡ ❛♦s ❞❡♠❛✐s ❝♦♥t❡ú❞♦s ❞❡ ♠❛t❡♠át✐❝❛✱ ♣♦✐s ♥✐♥❣✉é♠ ❡♥s✐♥❛ ❛q✉✐❧♦ q✉❡ ♥ã♦ t❡♠ ❞♦♠í♥✐♦ ❝♦♥❝❡✐t✉❛❧✑✳
❊st❛ ♠❡s♠❛ ❛✉t♦r❛ tr❛ç❛ ✉♠ ♣❡r✜❧ ❞❛ ❡❞✉❝❛çã♦ ♥♦ ❇r❛s✐❧✱ ♥♦ sé❝✉❧♦ ❳❳✱ r❡ss❛❧t❛♥❞♦ ✈ár✐♦s ♣♦♥t♦s✿ s✐t✉❛çã♦ ❡❝♦♥ô♠✐❝❛ ❡ s♦❝✐❛❧ ❞❛ ♣♦♣✉❧❛çã♦✱ ❡♥s✐♥♦ ✈♦❧t❛❞♦ ♣❛r❛ ♥❡❝❡ss✐✲ ❞❛❞❡s ♣rát✐❝❛s ❞❛ ✈✐❞❛✱ ♥❡❝❡ss✐❞❛❞❡ ❞❡ ❢♦r♠❛çã♦ ❞♦s ♣r♦❢❡ss♦r❡s✱ q✉❛♥t✐❞❛❞❡ ❡①❝❡ss✐✈❛ ❞❡ ❝♦♥t❡ú❞♦s ❡♠ r❡❧❛çã♦ ❛♦ t❡♠♣♦ ❞✐s♣♦♥í✈❡❧ ♣❛r❛ s❡r ❞❡s❡♥✈♦❧✈✐❞♦✱ ❛ ❣❡♦♠❡tr✐❛ ♥ã♦ s❡r ♠✐♥✐str❛❞❛ ❡♠ ❛❧❣✉♠❛s sér✐❡s✱ ❛ ❢❛❧t❛ ❞❡ ♣r♦❢❡ss♦r❡s ♣❛r❛ ❛t❡♥❞❡r à ❞❡♠❛♥❞❛ ❝r❡s❝❡♥t❡ ♣❡❧❛ ❜✉s❝❛ ❞♦ ❡♥s✐♥♦✱ ♠á ❝♦♥❞✐çã♦ ❞❡ tr❛❜❛❧❤♦✱ ❢❛❧t❛ ❞❡ ❵✉♥✐❞❛❞❡✬ ♥❛s ❞✐s❝✐♣❧✐♥❛s ❞♦s
❝✉rs♦s ❞❡ ❧✐❝❡♥❝✐❛t✉r❛✱ ✐♠♣❧❛♥t❛çã♦ ❞❛s ✏❧✐❝❡♥❝✐❛t✉r❛s ❝✉rt❛s✑✱ s✉♣❡r❧♦t❛çã♦ ❞❛s ❝❧❛ss❡s✱ ❛✉♠❡♥t♦ ❞❛ ❝❛r❣❛ ❞❡ tr❛❜❛❧❤♦ ❞♦s ♣r♦❢❡ss♦r❡s✱ ❡♥tr❡ ♦✉tr♦s✱ ❝♦♥❝❧✉✐♥❞♦ q✉❡✿
❖ ❛❜❛♥❞♦♥♦ ❞♦ ❡♥s✐♥♦ ❞❡ ❣❡♦♠❡tr✐❛ ❞❡✈❡✱ ♣♦rt❛♥t♦✱ s❡r ❝❛r❛❝t❡✲ r✐③❛❞♦ ❝♦♠♦ ✉♠❛ ❞❡❝✐sã♦ ❡q✉✐✈❛❧❡♥t❡ às ♠❡❞✐❞❛s ❣♦✈❡r♥❛♠❡♥t❛✐s✱ ❡♠ s❡✉s ✈ár✐♦s ♥í✈❡✐s✱ ❝♦♠ r❡❧❛çã♦ à ❡❞✉❝❛çã♦✳ P♦❞❡✲s❡ q✉❡st✐✲ ♦♥❛r ❛s ✈❡r❞❛❞❡✐r❛s ✐♥t❡♥çõ❡s ❡ ❝♦♠♣r♦♠✐ss♦s q✉❡ ❡❧❛s r❡✈❡❧❛♠ ❡♠ r❡❧❛çã♦ ❛♦ ♦❢❡r❡❝✐♠❡♥t♦ ❞❡ ❝♦♥❞✐çõ❡s q✉❡ ✐♠♣❧✐q✉❡ ❡♠ r❡❛✐s ♦♣♦rt✉♥✐❞❛❞❡s ❡❞✉❝❛❝✐♦♥❛✐s ❛ t♦❞♦s ♦s s❡❣♠❡♥t♦s ❞❛ ♣♦♣✉❧❛çã♦ ❜r❛s✐❧❡✐r❛✳ ❬✸✵✱ P❛✈❛♥❡❧❧♦✱ ♣✳✶✻❪
P♦r ♠✉✐t♦ t❡♠♣♦✱ ♦ ❡♥s✐♥♦ ❞❡ ❣❡♦♠❡tr✐❛ ❢♦✐ ♦r❣❛♥✐③❛❞♦ ❡♥tr❡ ♦s ú❧t✐♠♦s ✐t❡♥s ❞♦ ❝✉rrí❝✉❧♦ ❡ ❞❡ ❧✐✈r♦s ❞✐❞át✐❝♦s✱ s❡♠♣r❡ ❝♦♠ ❞✐✈✐sór✐❛s ❡♥tr❡ ♦s ❝♦♥t❡ú❞♦s q✉❡ ♣♦✉❝♦ ♦✉ ♥❛❞❛ s❡ r❡❧❛❝✐♦♥❛✈❛♠✳ ◆♦s ú❧t✐♠♦s ❛♥♦s ♣❡r❝❡❜❡✲s❡ q✉❡ ♦s ❝♦♥t❡ú❞♦s tê♠ s✐❞♦ ♦r❣❛♥✐③❛❞♦s ❞❡ ♠♦❞♦ q✉❡ ❛s ár❡❛s ❡♠ q✉❡ ❛ ♠❛t❡♠át✐❝❛ é ❞✐✈✐❞❛ ♣❛r❛ ♦ ❡♥s✐♥♦ ♥❛s ❡s❝♦❧❛s ❡stã♦ s❡♣❛r❛❞❛s ❡♠ ❜❧♦❝♦s❀ ❛ ❣❡♦♠❡tr✐❛ ♥ã♦ ♠❛✐s ❛♣❛r❡❝❡ ♥♦ ✜♥❛❧✱ ♠❛s ❡♠ ❝❛❞❛ ✉♠ ❞♦s ♣❡rí♦❞♦s✴tr✐♠❡str❡s ❛♦s q✉❛✐s ❛s ❡s❝♦❧❛s ♦r❣❛♥✐③❛♠ s❡✉ ❝❛❧❡♥❞ár✐♦✳
◆♦ ❇r❛s✐❧✱ ❤♦✉✈❡ ✉♠ ♣❡rí♦❞♦ ❡♠ q✉❡ ♦ ❉❡s❡♥❤♦ ✈✐❣♦r♦✉ ❝♦♠♦ ❞✐s❝✐♣❧✐♥❛ ♥♦ q✉❡ ❤♦❥❡ é ♦ ❊♥s✐♥♦ ❋✉♥❞❛♠❡♥t❛❧ ■■✱ ❡ s✉❛ ❜❛s❡ ❡r❛ ♦ ❞❡s❡♥❤♦ ❣❡♦♠étr✐❝♦✳ ❏á ♥❛ ❡t❛♣❛ ❞♦ ❊♥s✐♥♦ ❇ás✐❝♦ ❞❡s✐❣♥❛❞❛ ♣♦r ❊♥s✐♥♦ ▼é❞✐♦✱ ♦ ♣r❡❞♦♠í♥✐♦ ❞❛ ❞✐s❝✐♣❧✐♥❛ ❡r❛ ❛ ❣❡♦♠❡tr✐❛ ❞❡s❝r✐t✐✈❛❀ ♠❛s ❡❧❛✱ ❞❡✐①♦✉ ❞❡ s❡r ❝✉rrí❝✉❧♦ ❜❛s❡ ❡ ❢♦✐ ❛♠♣❧❛♠❡♥t❡ r❡t✐r❛❞❛ ❞♦ ❡♥s✐♥♦ ♣ú❜❧✐❝♦ ♣♦✉❝♦s ❛♥♦s ❛♣ós s✉❛ ♦❜r✐❣❛t♦r✐❡❞❛❞❡ ♣♦r ❧❡✐✳ ❊ ❛ ♣❛rt✐r ❞❛ ▲❉❇ ✺✳✻✾✷✴✼✶ ♦ ❉❡s❡♥❤♦ ❢♦✐ s✉❜st✐t✉í❞♦ ♣♦r ❊❞✉❝❛çã♦ ❆rtíst✐❝❛✳
P❛r❛ ♦ ❊♥s✐♥♦ ▼é❞✐♦✱ ❤á q✉❡ ❞❡st❛❝❛r ♦ ❝♦♥t❡ú❞♦ ❞♦s ❞♦❝✉♠❡♥t♦s ❝♦♠♣❧❡♠❡♥t❛r❡s ❛♦s P❈◆s✳ ◆❡❧❡ é tr❛ç❛❞♦ ✉♠ ♣❡r✜❧ ❞❡st❛ ❡t❛♣❛ ❞♦ ❊♥s✐♥♦ ❇ás✐❝♦✱ s❡❥❛ ❛♣♦♥t❛♥❞♦ ❝❛r❛❝t❡ríst✐❝❛s s♦❝✐❛✐s ❡ ❡❝♦♥ô♠✐❝❛s ♦✉ r❡❢❡r❡♥❝✐❛♥❞♦ ❛ ❧❡❣✐s❧❛çã♦ ❛ r❡s♣❡✐t♦ ❞♦ ❡♥s✐♥♦ ♥♦ ❇r❛s✐❧✱ ♣❛r❛ ♣♦st❡r✐♦r♠❡♥t❡ ❞✐s❝♦rr❡r s♦❜r❡ ❝❛❞❛ ❞✐s❝✐♣❧✐♥❛❀ ♣♦♥t♦ ❡♠ q✉❡ ❝♦❧♦❝❛♠♦s ♣♦r ❡✈✐❞ê♥❝✐❛ ❛s ♦r✐❡♥t❛çõ❡s q✉❛♥t♦ ❛ r❡♣r❡s❡♥t❛çã♦ ♥❛ ♠❛t❡♠át✐❝❛ ✲ q✉❡ t❡rá ♠❛✐♦r ❞❡st❛q✉❡ ♥♦ ♣ró①✐♠♦ ❝❛♣ít✉❧♦✳
❖ ♥♦✈♦ ❡♥s✐♥♦ ♠é❞✐♦✱ ✭✳✳✳✮ ❞❡✐①❛ ❞❡ s❡r✱ ♣♦rt❛♥t♦✱ s✐♠♣❧❡s♠❡♥t❡ ♣r❡♣❛r❛tór✐♦ ♣❛r❛ ♦ ❡♥s✐♥♦ s✉♣❡r✐♦r ♦✉ ❡str✐t❛♠❡♥t❡ ♣r♦✜ss✐♦♥❛❧✐✲ ③❛♥t❡✱ ♣❛r❛ ❛ss✉♠✐r ♥❡❝❡ss❛r✐❛♠❡♥t❡ ❛ r❡s♣♦♥s❛❜✐❧✐❞❛❞❡ ❞❡ ❝♦♠✲ ♣❧❡♠❡♥t❛r ❛ ❡❞✉❝❛çã♦ ❜ás✐❝❛✳ ❬✹✱ ❇r❛s✐❧✱ ♣✳✵✽❪
❆s ✐♥ú♠❡r❛s ❞✐✜❝✉❧❞❛❞❡s r❡❧❛❝✐♦♥❛❞❛s ❛♦ ❡♥s✐♥❛r ❛✐♥❞❛ ♥♦ ♥í✈❡❧ ❢✉♥❞❛♠❡♥t❛❧✱ ✐♥✲ ❢❡❧✐③♠❡♥t❡ r❡✢❡t❡♠ ♠❛✐♦r❡s ❞✐✜❝✉❧❞❛❞❡s ♣❛r❛ ♦s ❡st✉❞❛♥t❡s ❞♦ ❊♥s✐♥♦ ▼é❞✐♦✱ ❡♠ s✉❛ ♠❛✐♦r✐❛ ❛❞♦❧❡s❝❡♥t❡s✳ ➱ ♣❡r❝❡❜✐❞♦ ♦ ❛♣♦♥t❛♠❡♥t♦ ❞♦ ❊♥s✐♥♦ ▼é❞✐♦✱ ♣r✐♥❝✐♣❛❧♠❡♥t❡✱ ❝♦♠♦ ♣r❡♣❛r❛tór✐♦ ♣❛r❛ ♦ ❵✈❡st✐❜✉❧❛r✬ ❡ ❤á ❛ ❜✉s❝❛ ♣♦r r❡s❣❛t❛r ♦ ❡♥s✐♥♦ ♣r♦✜ss✐♦♥❛❧✐✲ ③❛♥t❡ ❡ té❝♥✐❝♦ ❝♦♥❝♦♠✐t❛♥t❡ à ❡t❛♣❛ ❞❡ ❡♥s✐♥♦✳
❖s ❝♦♠♣♦♥❡♥t❡s ❝✉rr✐❝✉❧❛r❡s ✈♦❧t❛r❛♠ ❛♦ ❞❡❜❛t❡ ♥❡st❡s ú❧t✐♠♦s ❛♥♦s✱ ❝♦♠ ❛ ♣r♦✲ ♣♦st❛ ❞❡ ❛♣r♦①✐♠❛r ♦ q✉❡ é ❡♥s✐♥❛❞♦ ♥❛s ❡s❝♦❧❛s ❡♠ t♦❞♦ ♦ t❡rr✐tór✐♦ ❜r❛s✐❧❡✐r♦✳ ❆ ❙♦❝✐❡❞❛❞❡ ❇r❛s✐❧❡✐r❛ ❞❡ ▼❛t❡♠át✐❝❛ ✲ ❙❇▼✱ ❡❧❛❜♦r♦✉ ❞♦❝✉♠❡♥t♦s q✉❡ ♣r♦❝✉r❛♠ ❝♦♥✲ tr✐❜✉✐r ♣❛r❛ ♦ ❞❡❜❛t❡ s♦❜r❡ ♦ ❝✉rrí❝✉❧♦✳ ◆♦ q✉❡ s❡ r❡❢❡r❡ ❛ ❞✐s❝✐♣❧✐♥❛ ♠❛t❡♠át✐❝❛✱ sã♦ ❛♣r❡s❡♥t❛❞♦s ♦s ❝♦♥t❡ú❞♦s ♣r❡s❡♥t❡s ♥❛ ❋✐❣✉r❛ ✷✳✶✱ ♦r❣❛♥✐③❛❞♦s ♣♦r sér✐❡ ❡♠ q✉❛tr♦ ár❡❛s✳ ❊st❛s ár❡❛s sã♦ ❞❡t❛❧❤❛❞❛s✱ ❡s♣❡❝✐✜❝❛♥❞♦✲s❡ ♦s ❝♦♥t❡ú❞♦s✱ ❛s ❤❛❜✐❧✐❞❛❞❡s ❡ ❛❧✲ ❣✉♠❛s ♦❜s❡r✈❛çõ❡s❀ ♣r♦❝✉r❛♥❞♦ ❛✐♥❞❛✱ ❡①♣❧♦r❛r ❛ ❣❡♦♠❡tr✐❛ ❞✉r❛♥t❡ ♦ ❛♥♦ ❧❡t✐✈♦ ❡ ✐♥t❡r❝❛❧❛♥❞♦ ❝♦♠ ♦✉tr♦s ❝♦♥t❡ú❞♦s✳
❯♠❛ ❞❛s q✉❛tr♦ ár❡❛s é ❛ ❣❡♦♠❡tr✐❛✱ ❡ ♣❛r❛ ❡❧❛ ❤á ♦ ❛♣♦♥t❛♠❡♥t♦ ♣❛r❛ ❛ ♥❡❝❡ss✐✲ ❞❛❞❡ ❞❡ r❡❝♦r❞❛r ❡ ❛♣r♦❢✉♥❞❛r ❝♦♥❝❡✐t♦s q✉❡ ❞❡✈❡r✐❛♠ t❡r s✐❞♦ ❛♣r❡s❡♥t❛❞♦s ♥♦ ❊♥s✐♥♦ ❋✉♥❞❛♠❡♥t❛❧ ■■✳ ➱ ✐♥❞✐❝❛❞♦ q✉❡ ♦ ❡♥s✐♥♦ ❡ ❛ ❛♣r❡♥❞✐③❛❣❡♠ ♥❡st❛ ❢❛✐①❛ ❡r❛ ♣❛✉t❛❞♦ ❡♠ ♣r♦♣r✐❡❞❛❞❡s ♣❡r❝❡❜✐❞❛s ♥❛s ✜❣✉r❛s ❡ q✉❡ ♥♦ ❊♥s✐♥♦ ▼é❞✐♦❀ t❛✐s ♣r♦♣r✐❡❞❛❞❡s ♣♦✲ ❞❡♠ s❡r ❞❡♠♦♥str❛❞❛s s❡♠ ❡①❛❣❡r♦ ❛♦ r✐❣♦r ❞❛ ❡s❝r✐t❛ ♣r♦❝✉r❛♥❞♦ ♣r✐✈✐❧❡❣✐❛r ❛❧❣✉♠❛s ✐♥❢♦r♠❛çõ❡s ❝♦♠ ♥♦t❛çã♦ s✐♠♣❧❡s✳ ❘❡❝♦♠❡♥❞❛ ❛ ❛❜♦r❞❛❣❡♠ ✐♥t✉✐t✐✈❛ ❛♦ ❝♦♥❝❡✐t♦ ❞❡ ❧✐♠✐t❡✱ ❛ ❛♣r❡s❡♥t❛çã♦ ❞❡ ❛①✐♦♠❛s✱ ❛ ❞❡♠♦♥str❛çã♦ ❞❡ ❛❧❣✉♥s t❡♦r❡♠❛s ❡ ✐♥❞✐❝❛çã♦ ❞❡ ❞❡✜♥✐çõ❡s r❡❧❛❝✐♦♥❛❞❛s ❛ ❡①❡♠♣❧♦s❀ ❛❧é♠ ❞❡ r❡❧❛❝✐♦♥❛r ✜❣✉r❛s✱ ✐❧✉str❛çõ❡s ❡ ❝♦♥str✉çõ❡s ❞❡ ♣♦❧✐❡❞r♦s ❡ ❝♦r♣♦s r❡❞♦♥❞♦s ❝♦♠ ♦❜❥❡t♦s ❝♦♥❝r❡t♦s✳
◆❛s ❝♦♥tr✐❜✉✐çõ❡s ❞❛ ❙❇▼ ❬✸✺✱ ❊♥s✐♥♦ ❋✉♥❞❛♠❡♥t❛❧ ■■✱ ♣✳✵✺❪✱ ❤á ❛ ♣r♦♣♦st❛ ❞❡ ✐♥❝❧✉✐r ♥♦ ❊♥s✐♥♦ ❋✉♥❞❛♠❡♥t❛❧ ■■ ❛ ❣❡♦♠❡tr✐❛ ❡s♣❛❝✐❛❧✱ ❝♦♥t❡ú❞♦ ♣r❡s❡♥t❡ ❡♠ ✈ár✐♦s ❧✐✈r♦s ❞✐❞át✐❝♦s ❞❡st❛ ❡t❛♣❛ ❞❡ ❡♥s✐♥♦✱ ♠❛s q✉❡ ♣♦✉❝♦ ♦✉ ♥❛❞❛ é ❡①♣❧♦r❛❞♦✳ ❊ ❛✐♥❞❛✱ ❤á ❛ r❡❝♦♠❡♥❞❛çã♦ ❞❡ q✉❡ s❡ ♠❛♥✐♣✉❧❡ ♠❛t❡r✐❛✐s ❝♦♥❝r❡t♦s✱ ♦❜s❡r✈❡ ❢♦r♠❛s ✸❉ ♣r❡s❡♥t❡s ♥♦ ♠✉♥❞♦ ❡ ✉t✐❧✐③❡ ❛❧❣✉♠ s♦❢t✇❛r❡ ❞❡ ❣❡♦♠❡tr✐❛ ❞✐♥â♠✐❝❛✳ ❚❛✐s r❡❝♦♠❡♥❞❛çõ❡s✱ ♥ã♦ sã♦ ♥♦✈✐❞❛❞❡✱ ♠❛s sã♦ ♣♦✉❝♦ ❡①♣❧♦r❛❞❛s✳
❋✐❣✉r❛ ✷✳✶✿ ❚❛❜❡❧❛ ❞❡s❝r✐t✐✈❛ ❞♦s ❝♦♥t❡ú❞♦s ❞❡ ♠❛t❡♠át✐❝❛ ♥♦ ❊♥s✐♥♦ ▼é❞✐♦✳ ❖s ♣r♦❢❡ss♦r❡s✱ ❛♦ ♣❧❛♥❡❥❛r❡♠ s✉❛s ❛✉❧❛s✱ s❡❣✉✐❛♠ ❛s ❞✐r❡tr✐③❡s ❡ ❛ ♦r❣❛♥✐③❛çã♦ ❞♦s ❧✐✈r♦s ❞✐❞át✐❝♦s✱ ❡ ❛ss✐♠ q✉❛s❡ s❡♠♣r❡ ♦ ❝♦♥t❡ú❞♦ ❞❡ ❣❡♦♠❡tr✐❛ ❡r❛ ♦ ú❧t✐♠♦ ❛ s❡r ❡st✉❞❛❞♦✱ q✉❛♥❞♦ ❡r❛ ❡st✉❞❛❞♦ ❡ q✉❛s❡ ♥✉♥❝❛ ❡st❛✈❛ r❡❧❛❝✐♦♥❛❞♦ ❝♦♠ ♦✉tr❛s ár❡❛s✳ ❖ ❡♥s✐♥♦ ❞❡ ❣❡♦♠❡tr✐❛ ❛✐♥❞❛ é ♠í♥✐♠♦ ❡ s✉♣❡r✜❝✐❛❧✱ ❡ ✐ss♦ s❡ r❡♣❡t❡ sér✐❡ ❛♣ós sér✐❡❀ sã♦ ✈ár✐♦s ❝♦♥❝❡✐t♦s r❡♣❡t✐❞♦s ❡ q✉❛s❡ s❡♠♣r❡ s❡♠ ❢✉♥❞❛♠❡♥t❛çã♦❀ ♦s ❡st✉❞❛♥t❡s t❡r♠✐♥❛♠ ♦ ❊♥s✐♥♦ ❇ás✐❝♦ ❝♦♠ ✐♥ú♠❡r❛s ❞❡✜❝✐ê♥❝✐❛s ❞❡ ❛♣r❡♥❞✐③❛❣❡♠✳ ❑♦❜❛②❛s❤✐ ❬✶✽❪✱ r❡❢❡r❡✲s❡ ❛ ❆r❛ú❥♦ ❛✜r♠❛♥❞♦ q✉❡
. . .♦s ❧✐✈r♦s ❞✐❞át✐❝♦s ❞❡ ▼❛t❡♠át✐❝❛ ♣❛r❛ ♦ ❡♥s✐♥♦ ❢✉♥❞❛♠❡♥t❛❧
✭. . .✮ ♥❛ s✉❛ ♠❛✐♦r✐❛✱ ❡♥❢❛t✐③❛♠ t❡♠❛s ❛r✐t♠ét✐❝♦s ❡♠ ❞❡tr✐♠❡♥t♦
❞♦s ❣❡♦♠étr✐❝♦s✱ q✉❡ sã♦ tr❛t❛❞♦s ❞❡ ❢♦r♠❛ ❛❜str❛t❛✱ ❞❡s❝r✐t✐✈❛ ❡ ❞❡s❛rt✐❝✉❧❛❞❛✱ ♥❛s ú❧t✐♠❛s ♣á❣✐♥❛s ❞❡ ❝❛❞❛ ✈♦❧✉♠❡✳ ❬❆r❛ú❥♦ ♣✳✶✷✲✶✻ ❛♣✉❞ ❑♦❜❛②❛s❤✐✱ ♣✳✶✸✲✶✹❪
❖s ❧✐✈r♦s ❞✐❞át✐❝♦s ❛t✉❛✐s tê♠ ❢✉❣✐❞♦ ❞❛s ❝❛r❛❝t❡ríst✐❝❛s ❛♣♦♥t❛❞❛s ♣♦r ❆r❛ú❥♦✳ ❙ã♦ ✈ár✐❛s ❛s ❞✐s❝✉ssõ❡s ❡ ♣r♦♣♦st❛s ❞❡ ♦r❣❛♥✐③❛çã♦ ❝✉rr✐❝✉❧❛r✱ ♣r♦❝✉r❛♥❞♦ ❛❧t❡r❛r ♦ ♠♦❞♦ ❝♦♠♦ ♦s ❝♦♥t❡ú❞♦s sã♦ ❞✐s♣♦st♦s ♥♦s ❧✐✈r♦s ❞✐❞át✐❝♦s ❡ sã♦ ❡♥s✐♥❛❞♦s ✭tr❛♥s♠✐t✐❞♦s✮ ♥❛s ❡s❝♦❧❛s✳ ◆♦ ❊♥s✐♥♦ ❇ás✐❝♦✱ ♦s ❝♦♥t❡ú❞♦s✱ sér✐❡ ❛♣ós sér✐❡✱ sã♦ ♦r❣❛♥✐③❛❞♦s ❡♠ ❜❧♦❝♦s
t❡♠át✐❝♦s✱ ❡♠ q✉❡ ❛ ❝❛❞❛ sér✐❡ sã♦ ❛❝r❡s❝✐❞♦s ♥♦✈♦s ❝♦♥❝❡✐t♦s✱ ♠❛s ❤á ✉♠❛ t❡♥❞ê♥❝✐❛ ❞♦s ♣r♦❢❡ss♦r❡s ❛✐♥❞❛ ♣r✐♦r✐③❛r❡♠✱ ♣♦r ❡①❡♠♣❧♦✱ ❝♦♥t❡ú❞♦s ❛❧❣é❜r✐❝♦s✱ ❞❡✐①❛♥❞♦ ❞❡ ❧❛❞♦ ❝♦♥t❡ú❞♦s ❣❡♦♠étr✐❝♦s❀ ♦s ♣r♦❜❧❡♠❛s ❡♥✈♦❧✈❡♥❞♦ ❣❡♦♠❡tr✐❛ ♦✉ sã♦ ✐❣♥♦r❛❞♦s ♦✉ ♥ã♦ tê♠ ❛ ❞❡✈✐❞❛ ❛t❡♥çã♦ ❞♦ ♣r♦❢❡ss♦r ❡♠ s✉❛ ♣rát✐❝❛ ♣❡❞❛❣ó❣✐❝❛✳
P❡r❝❡❜❡✲s❡ ♠❛✐♦r ❛t❡♥çã♦ ❛♦s ❧✐✈r♦s ❞✐❞át✐❝♦s ❞❡ ♠❛t❡♠át✐❝❛✱ ♣♦r ❡❧❡s ❡st❛r❡♠ ♠❡✲ ❧❤♦r ❡str✉t✉r❛❞♦s✱ ❝♦♥t❡ú❞♦s r❡❝❤❡❛❞♦s ❞❡ ❞✐❢❡r❡♥t❡s ❢♦r♠❛s ❞❡ r❡♣r❡s❡♥t❛çõ❡s✱ ê♥❢❛s❡ ♥♦ tr❛t❛♠❡♥t♦ ❡ ❝♦♥✈❡rsã♦ ❡♥tr❡ ❛s r❡♣r❡s❡♥t❛çõ❡s❀ ♠❛s ❛ ❞✐st✐♥çã♦ ❡♥tr❡ ♦❜❥❡t♦ ♠❛✲ t❡♠át✐❝♦ ❡ ❛ r❡♣r❡s❡♥t❛çã♦ ❞❡st❡ ♦❜❥❡t♦ ♥ã♦ é ❡✈✐❞❡♥❝✐❛❞❛✳ ◆❡♠ ♠❡s♠♦ ♦ ♣r♦❢❡ss♦r ♣♦ss✉✐ ❝♦♥❤❡❝✐♠❡♥t♦ ❛ r❡s♣❡✐t♦ ♣❛r❛ ♣r♦♣♦r ♣rát✐❝❛s q✉❡ ♣❡r♠✐t❛♠ ❛♦ ❡st✉❞❛♥t❡ ♠❡❧❤♦r ❝♦♠♣r❡❡♥sã♦ ❡♠ ❣❡♦♠❡tr✐❛✳ ❈♦♥❤❡❝❡✲s❡ ❜❛s✐❝❛♠❡♥t❡ ❛ ✜❣✉r❛ ❡ ❛ ❡❧❛ ❛tr✐❜✉✐ ♦ ♦❜❥❡t♦ ❣❡♦♠étr✐❝♦✱ ♠❛s ♣♦✉❝♦ s❡ s❛❜❡ ❞❛s ❝❛r❛❝t❡ríst✐❝❛s ❞♦ ♦❜❥❡t♦ ❣❡♦♠étr✐❝♦ ♣r❡s❡♥t❡s ❡♠ s✉❛ r❡♣r❡s❡♥t❛çã♦✳
➱ ♣r❡❝✐s♦ q✉❡ ❛♦ ♣❧❛♥❡❥❛r ♦ ♣r♦❢❡ss♦r ♣r♦❝✉r❡ ♥ã♦ s❡ ♣r❡♥❞❡r à s❡q✉ê♥❝✐❛ ❛♣r❡s❡♥✲ t❛❞❛ ♥♦s ❧✐✈r♦s✱ ♠❛s ❛ss♦❝✐❛r ✉♠❛ sér✐❡ ❞❡ ❝♦♠♣❡tê♥❝✐❛s ♣❛r❛ ♦ ❛❧❝❛♥❝❡ ❞♦s ♦❜❥❡t✐✈♦s ❡st✐♣✉❧❛❞♦s✳ ❖ ✉s♦ ❞❡ ♣r♦❜❧❡♠❛s t❡♠ s✐❞♦ ✉♠❛ ♣r♦♣♦st❛ q✉❡ ❜✉s❝❛ ✐♥s❡r✐r ❝♦♥t❡ú❞♦s ❞❡ ❣❡♦♠❡tr✐❛ ❡♥tr❡ ♦s ❜❧♦❝♦s ❡s♣❡❝í✜❝♦s ❞❡ á❧❣❡❜r❛ ♦✉ ❛r✐t♠ét✐❝❛✱ ♣♦r ❡①❡♠♣❧♦❀ ❡ é ❛❧❣♦ q✉❡ é ♣❡r❝❡❜✐❞♦ ♥♦s ❧✐✈r♦s ❞✐❞át✐❝♦s ❛t✉❛❧♠❡♥t❡✱ ❝♦♠♦ ♦s ❞❛ ❝♦❧❡çã♦✿ ❆ ❝♦♥q✉✐st❛ ❞❛ ▼❛t❡♠át✐❝❛ ❞❡ ●✐♦✈❛♥♥✐ ❏ú♥✐♦r ❡ ❈❛str✉❝❝✐✱ ❙ã♦ P❛✉❧♦✿ ❋❚❉✱ ✷✵✵✾✳ ▼❛s ❛✐♥❞❛✱ ❢❛❧t❛ ❛té ♠❡s♠♦ ❛♦s ♣r♦❢❡ss♦r❡s✱ ❝♦♥❤❡❝✐♠❡♥t♦ t❡ór✐❝♦ ❡ ❞✐❞át✐❝♦ ♣❛r❛✱ ❛♦ ❡♥s✐♥❛r✱ ❧✐❞❛r ❝♦♠ ♠❡❧❤♦r ❢✉♥❞❛♠❡♥t❛çã♦ ❞❛ ❣❡♦♠❡tr✐❛✳
❆s ❡s❝♦❧❤❛s ❞♦s ❧✐✈r♦s ❞✐❞át✐❝♦s ♣❡❧♦s ♣r♦❢❡ss♦r❡s✱ ♣❛r❡❝❡♠ s❡r ♣♦r ❛q✉❡❧❡s ❧✐✈r♦s ❞❡ ♣♦✉❝❛ ❢✉♥❞❛♠❡♥t❛çã♦✱ ❝♦♠ ❢ór♠✉❧❛s ♣r♦♥t❛s✱ ❜♦❛ ❞✐❛❣r❛♠❛çã♦✱ ♠✉✐t♦s ❡①❡♠♣❧♦s ✭♠♦❞❡❧♦s✮ ❡ ❡①❡r❝í❝✐♦s✳ ❚❡r❡♠ ✉♠❛ ❜♦❛ ❛♣❛rê♥❝✐❛ ❡ ♦r❣❛♥✐③❛çã♦✱ s❡r❡♠ ❜❡♠ ✐❧✉str❛❞♦s✱ t❡r❡♠ ✈ár✐♦s ❡①❡♠♣❧♦s✱ ♣r♦❜❧❡♠❛s ❡ ❡①❡r❝í❝✐♦s sã♦ r❡q✉✐s✐t♦s ♥❡❝❡ssár✐♦s ♣❛r❛ ❡♥s✐♥❛r ❡ ❛♣r❡♥❞❡r✱ ♠❛s é ✐♠♣♦rt❛♥t❡ t❛♠❜é♠ q✉❡ s❡ ❛t❡♥t❡♠ ♣❛r❛ ❛ ❜❛s❡ à q✉❛❧ ❛ ♠❛t❡✲ ♠át✐❝❛ t❡♠ s✐❞♦ ❝♦♥str✉í❞❛❀ q✉❡ ♦s ♣r♦❢❡ss♦r❡s ♥ã♦ ❛❜❛♥❞♦♥❡♠ ❡st❛ ♣❛rt❡ ❞♦ ❡♥s✐♥♦ ♣♦r ❞❡s❝✉❧♣❛ ❞❡ q✉❡ ❛ss✐♠ é ♠❛✐s ❵❢á❝✐❧✬ ❡ ❞❡ q✉❡ é ♣r❡❝✐s♦ ❡♥s✐♥❛r ♣❛r❛ ❛ ✈✐❞❛ ✭❡♥s✐✲ ♥❛r ♦ ❝♦t✐❞✐❛♥♦✮✳ ❆ ♠❛t❡♠át✐❝❛ ♣r❡❝✐s❛ s❡r ❡♥s✐♥❛❞❛ ♣❛r❛ ❛❧é♠ ❞♦ ♣❛❧♣á✈❡❧✱ ❤á q✉❡
