❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ●♦✐ás
■♥st✐t✉t♦ ❞❡ ▼❛t❡♠át✐❝❛ ❡ ❊st❛tíst✐❝❛
Pr♦❣r❛♠❛ ❞❡ ▼❡str❛❞♦ Pr♦✜ss✐♦♥❛❧ ❡♠
▼❛t❡♠át✐❝❛ ❡♠ ❘❡❞❡ ◆❛❝✐♦♥❛❧
❆ ❯t✐❧✐③❛çã♦ ❞♦ ▼✉❧t✐♣❧❛♥♦ ♥♦ ❊♥s✐♥♦ ❞❡
●❡♦♠❡tr✐❛ ♣❛r❛ ❆❧✉♥♦s ❞♦ ❊♥s✐♥♦
❋✉♥❞❛♠❡♥t❛❧ ❝♦♠ ❉❡✜❝✐ê♥❝✐❛ ❱✐s✉❛❧
❍✉❣❧❡✐❜s♦♥ ❇❡r♥❛r❞♦ ❞❛ ❙✐❧✈❛
●♦✐â♥✐❛
❍✉❣❧❡✐❜s♦♥ ❇❡r♥❛r❞♦ ❞❛ ❙✐❧✈❛
❆ ❯t✐❧✐③❛çã♦ ❞♦ ▼✉❧t✐♣❧❛♥♦ ♥♦ ❊♥s✐♥♦ ❞❡
●❡♦♠❡tr✐❛ ♣❛r❛ ❆❧✉♥♦s ❞♦ ❊♥s✐♥♦
❋✉♥❞❛♠❡♥t❛❧ ❝♦♠ ❉❡✜❝✐ê♥❝✐❛ ❱✐s✉❛❧
❚r❛❜❛❧❤♦ ❞❡ ❈♦♥❝❧✉sã♦ ❞❡ ❈✉rs♦ ❛♣r❡s❡♥t❛❞♦ ❛♦ ■♥st✐t✉t♦ ❞❡ ▼❛t❡♠át✐❝❛ ❡ ❊st❛tíst✐❝❛ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ●♦✐ás✱ ❝♦♠♦ ♣❛rt❡ ❞♦s r❡q✉✐s✐t♦s ♣❛r❛ ♦❜t❡♥çã♦ ❞♦ ❣r❛✉ ❞❡ ▼❡str❡ ❡♠ ▼❛t❡♠át✐❝❛✳
➪r❡❛ ❞❡ ❈♦♥❝❡♥tr❛çã♦✿ ▼❛t❡♠át✐❝❛ ❞♦ ❊♥s✐♥♦ ❇ás✐❝♦
❖r✐❡♥t❛❞♦r✿ Pr♦❢✳ ❉r✳ ❋❛❜✐❛♥♦ ❋♦rt✉♥❛t♦ ❚❡✐①❡✐r❛ ❞♦s ❙❛♥t♦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
❆❣r❛❞❡ç♦ ❛ ❉❡✉s✱ ♣♦r t❡r ♠❡ ♣❡r♠✐t✐❞♦ ❝♦♥❝❧✉✐r ♠❛✐s ✉♠❛ ❡t❛♣❛ ✐♠♣♦rt❛♥t❡ ❞❛ ♠✐♥❤❛ ✈✐❞❛✱ t❡r ♠❡ ❞❛❞♦ ❢♦rç❛ ♣❛r❛ ✈❡♥❝❡r ❞❡s❛✜♦s ❡ s✉♣❡r❛r ♦❜stá❝✉❧♦s✱ ♠❡ ♣❡r♠✐t✐❞♦ ❝❤❡❣❛r ❛té ❛q✉✐ ❡ ❛❜❡rt♦ ❝❛♠✐♥❤♦s ♣❛r❛ q✉❡ ❡✉ ♣♦ss❛ ✐r ♠❛✐s ❧♦♥❣❡✳
❆♦s ♠❡✉s ♣❛✐s✱ ❩❡♥❛✐❞❡ ❘♦❞r✐❣✉❡s ❞❛ ❙✐❧✈❛ ❡ ❖❧✐✈✐♦ ❇❡r♥❛r❞♦ ❞❛ ❙✐❧✈❛✱ ❡ às ♠✐♥❤❛s ✐r♠ãs✱ ❙❡r❣✐❛♥❛ ❘♦❞r✐❣✉❡s ❞❛ ❙✐❧✈❛ ❡ ❏♦✐s❡ ❘♦❞r✐❣✉❡s ❞❛ ❙✐❧✈❛✱ q✉❡ ♠❡ ❞❡r❛♠ ❢♦rç❛✱ ❛❝r❡❞✐t❛r❛♠ ♥❛ ♠✐♥❤❛ ❝❛♣❛❝✐❞❛❞❡ ❡ ♠❡ ❛♣♦✐❛r❛♠ ❞❛s ♠❛✐s ❞✐❢❡r❡♥t❡s ❢♦r♠❛s ♣❛r❛ ❝♦♥❝❧✉✐r ❡st❛ ❡t❛♣❛✳
❆♦s ♠❡✉s ❝♦♠♣❛♥❤❡✐r♦s ❞❡ ❝✉rs♦ ♣❡❧❛ ❛❥✉❞❛ ❡ ♣❡❧❛ ❣❡♥❡r♦s✐❞❛❞❡ ❡♠ ❝♦♠♣❛rt✐❧❤❛r s❡✉s ❝♦♥❤❡❝✐♠❡♥t♦s✳
❆♦ ♠❡✉ ♦r✐❡♥t❛❞♦r✱ Pr♦❢❡ss♦r ❉r✳ ❋❛❜✐❛♥♦ ❋♦rt✉♥❛t♦ ❚❡✐①❡✐r❛ ❞♦s ❙❛♥t♦s✱ ♣❡❧❛ ♦♣♦rt✉♥✐❞❛❞❡ ❡ ♣❡❧❛ ❝♦♥✜❛♥ç❛ ❞❡♣♦s✐t❛❞❛ ❡♠ ♠✐♠✳
❆ t♦❞♦s ♦s ♣r♦❢❡ss♦r❡s ❞♦ P❘❖❋▼❆❚✲❯❋● q✉❡ ❞❡❞✐❝❛r❛♠ ♦ s❡✉ t❡♠♣♦ ♣r❡❝✐♦s♦ ❡ tr❛♥s♠✐t✐r❛♠ ❝♦♥❤❡❝✐♠❡♥t♦s ✐♠♣♦rt❛♥tíss✐♠♦s ♣❛r❛ ❛ ♥♦ss❛ ❢♦r♠❛çã♦✳
➚ ❙❡❝r❡t❛r✐❛ ▼✉♥✐❝✐♣❛❧ ❞❡ ❊❞✉❝❛çã♦ ❞❡ ●♦✐â♥✐❛ q✉❡ ♠❡ ❝♦♥❝❡❞❡✉ ▲✐❝❡♥ç❛ ♣❛r❛ ❆♣r✐♠♦r❛♠❡♥t♦ ♠❡ ♣♦ss✐❜✐❧✐t❛♥❞♦ ✉♠ ♠❛✐♦r ❡♥✈♦❧✈✐♠❡♥t♦ ❝♦♠ ♦ ❝✉rs♦✳
❘❡s✉♠♦
◆❛ ♠❛t❡♠át✐❝❛✱ q✉❛♥❞♦ s❡ ❝♦♥s❡❣✉❡ ❛ss♦❝✐❛r ♦ ❝♦♥❝r❡t♦ ❝♦♠ ♦ ❛❜str❛t♦✱ ❝♦❧❤❡♠✲s❡ ♠✉✐t♦s ❢r✉t♦s✳ Pr✐♥❝✐♣❛❧♠❡♥t❡ s❡ ♥❛s t✉r♠❛s ❡stã♦ ♣r❡s❡♥t❡s ❛❧✉♥♦s ❝♦♠ ❞❡✜❝✐ê♥❝✐❛ ✈✐s✉❛❧✳ ❉❛❞❛ ❛s ❞✐✜❝✉❧❞❛❞❡s ❡♥❝♦♥tr❛❞❛s ♣❛r❛ ❡♥s✐♥❛r ●❡♦♠❡tr✐❛ P❧❛♥❛ ♥♦ ❊♥s✐♥♦ ❋✉♥❞❛♠❡♥t❛❧✱ ❡st❡ tr❛❜❛❧❤♦ t❡♠ ❝♦♠♦ ♦❜❥❡t✐✈♦ ♣r✐♥❝✐♣❛❧ ❛♣r❡s❡♥t❛r ♦ ▼✉❧t✐♣❧❛♥♦ ❝♦♠♦ ❛❧t❡r♥❛t✐✈❛ ❞❡ ❡♥s✐♥♦ ❞❡ ●❡♦♠❡tr✐❛ P❧❛♥❛✱ ♥ã♦ só ♣❛r❛ ♣♦rt❛❞♦r❡s ❞❡ ❞❡✜❝✐ê♥❝✐❛ ✈✐s✉❛❧✱ ❡ s✐♠ ♣❛r❛ t♦❞♦s ♦s ❛❧✉♥♦s✱ ✈✐s❛♥❞♦ ♠❡❧❤♦r❛r ❛ ❛♣r❡♥❞✐③❛❣❡♠ ❜❡♠ ❝♦♠♦ ❛✉♠❡♥t❛r ♦ ✐♥t❡r❡ss❡ ❞♦s ♠❡s♠♦s ♥❛s ❛✉❧❛s✳ ❆ ♣❡sq✉✐s❛ ❝♦♥t❡♠♣❧♦✉✱ t❛♠❜é♠✱ ✉♠ ❜r❡✈❡ ❡st✉❞♦ s♦✲ ❜r❡ ❛ ❞❡✜❝✐ê♥❝✐❛ ✈✐s✉❛❧✱ ♦s ❛✈❛♥ç♦s ♥❛ ❧❡❣✐s❧❛çã♦ ♣❛r❛ ✐♥❝❧✉sã♦ ❞❡ ❞❡✜❝✐❡♥t❡s ♥♦ s✐st❡♠❛ ❞❡ ❡♥s✐♥♦ ❡ ♦ ❝ó❞✐❣♦ ❇r❛✐❧❧❡✳ ❋♦r❛♠ t❛♠❜é♠ s✉❣❡r✐❞❛s ❛❧❣✉♠❛s ❛t✐✈✐❞❛❞❡s✱ ❛❞❛♣t❛❞❛s ♣❛r❛ ♦ ▼✉❧t✐♣❧❛♥♦✳
P❛❧❛✈r❛s✲❝❤❛✈❡
❉❡✜❝✐ê♥❝✐❛ ✈✐s✉❛❧✱ ●❡♦♠❡tr✐❛ ♣❧❛♥❛✱ ▼✉❧t✐♣❧❛♥♦✱ ■♥❝❧✉sã♦✱ ❈ó❞✐❣♦ ❇r❛✐❧❧❡
❆❜str❛❝t
■♥ ♠❛t❤❡♠❛t✐❝s✱ ✇❤❡♥ ②♦✉ ❝❛♥ ❛ss♦❝✐❛t❡ t❤❡ ❝♦♥❝r❡t❡ ✇✐t❤ t❤❡ ❛❜str❛❝t✱ r❡❛♣ ♠❛♥② ❢r✉✐ts✳ ❊s♣❡❝✐❛❧❧② ✐❢ ✐♥ t❤❡ ❝❧❛ss❡s ❛r❡ ♣r❡s❡♥t st✉❞❡♥ts ✇✐t❤ ✈✐s✉❛❧ ✐♠♣❛✐r♠❡♥t✳ ●✐✈❡♥ t❤❡ ❞✐✣❝✉❧t✐❡s ❡♥❝♦✉♥t❡r❡❞ t♦ t❡❛❝❤ P❧❛♥❡ ●❡♦♠❡tr② ♦♥ ❊❧❡♠❡♥t❛r② ❙❝❤♦♦❧✱ t❤✐s ✇♦r❦ ❤❛s ❛s ✐ts ♠❛✐♥ ♦❜❥❡❝t✐✈❡ t♦ ✐♥tr♦❞✉❝❡ t❤❡ ▼✉❧t✐♣❧❛♥❡ ❛s ❛♥ ❛❧t❡r♥❛t✐✈❡ t❡❛❝❤✐♥❣ ♦❢ P❧❛♥❡ ●❡♦♠❡tr②✱ ♥♦t ♦♥❧② ❢♦r ♣❡♦♣❧❡ ✇✐t❤ ✈✐s✉❛❧ ✐♠♣❛✐r♠❡♥t✱ ❜✉t ❢♦r ❛❧❧ st✉❞❡♥ts✱ t♦ ✐♠♣r♦✈❡ ❧❡❛r♥✐♥❣ ❛s ✇❡❧❧ ❛s ✐♥❝r❡❛s❡ t❤❡✐r ✐♥t❡r❡st ♦♥ ❝❧❛ss❡s✳ ❚❤❡ r❡s❡❛r❝❤ ❛❧s♦ ✐♥❝❧✉❞❡❞ ❛ ❜r✐❡❢ st✉❞② ♦♥ ✈✐s✉❛❧ ✐♠♣❛✐r♠❡♥t✱ ❛❞✈❛♥❝❡s ✐♥ ❧❡❣✐s❧❛t✐♦♥ ❢♦r ✐♥❝❧✉s✐♦♥ ♦❢ ♣❡♦♣❧❡ ✇✐t❤ ❞✐s❛❜✐❧✐t✐❡s ✐♥ t❤❡ ❡❞✉❝❛t✐♦♥ s②st❡♠ ❛♥❞ t❤❡ ❇r❛✐❧❧❡ ❝♦❞❡✳ ❲❡r❡ ❛❧s♦ s✉❣❣❡st❡❞ s♦♠❡ ❛❝t✐✈✐t✐❡s✱ ❛❞❛♣t❡❞ t♦ t❤❡ ▼✉❧t✐♣❧❛♥❡✳
❑❡②✇♦r❞s
❱✐s✉❛❧ ✐♠♣❛✐r♠❡♥t✱ P❧❛♥❡ ●❡♦♠❡tr②✱ ▼✉❧t✐♣❧❛♥❡✱ ■♥❝❧✉s✐♦♥✱ ❇r❛✐❧❧❡ ❝♦❞❡
▲✐st❛ ❞❡ ❋✐❣✉r❛s
✶ ❈❡❧❛ ❇r❛✐❧❧❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵
✷ ❘❡❣❧❡t❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶
✸ ▼áq✉✐♥❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶
✹ ❉✐s♣♦s✐çã♦ ❯♥✐✈❡rs❛❧ ❞♦s ✻✸ ❙✐♥❛✐s ❙✐♠♣❧❡s ❞♦ ❙✐st❡♠❛ ❇r❛✐❧❧❡ ✳ ✳ ✳ ✳ ✳ ✷✷
✺ P♦♥t♦ P ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽
✻ ❘❡t❛ q✉❡ ♣❛ss❛ ♣♦r ❆ ❡ ❇ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽
✼ P❧❛♥♦ α ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽
✽ ❙❡❣♠❡♥t♦ ❆❇ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾
✾ ❙❡♠✐rr❡t❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾
✶✵ ➶♥❣✉❧♦ABCˆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾
✶✶ ▼♦❞❡❧♦ ❞❡ tr❛♥s❢❡r✐❞♦r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✶✷ ▼❡❞✐♥❞♦ ➶♥❣✉❧♦ ♥♦ ▼✉❧t✐♣❧❛♥♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✶✸ ❚✐♣♦s ❞❡ â♥❣✉❧♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶
✶✹ r ks ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷
✶✺ r ⊥s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷
✶✻ ❚r✐â♥❣✉❧♦ ❆❇❈ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ✶✼ ❊q✉✐❧át❡r♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✶✽ ■sós❝❡❧❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✶✾ ❊s❝❛❧❡♥♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✷✵ ❆❝✉tâ♥❣✉❧♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✷✶ ❘❡tâ♥❣✉❧♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✷✷ ❖❜t✉sâ♥❣✉❧♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸
✷✸ ❈❛s♦ ❆▲❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹
✷✹ ❈❛s♦ ▲❆▲ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ✷✺ ❈❛s♦ ▲▲▲ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ✷✻ ❈❛s♦ ❍❈ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✷✼ ❈❛s♦ ❍❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✷✽ ➶♥❣✉❧♦s ❡♥tr❡ ♣❛r❛❧❡❧❛s ❡ ✉♠ tr❛♥s✈❡rs❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✷✾ ➶♥❣✉❧♦s ❛❧t❡r♥♦s ✐♥t❡r♥♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✸✵ ❙♦♠❛ ❞♦s â♥❣✉❧♦s ✐♥t❡r♥♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼ ✸✶ ◗✉❛❞r✐❧át❡r♦ ❆❇❈❉ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✸✷ ❘❡tâ♥❣✉❧♦ ❆❇❈❉ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✸✸ ◗✉❛❞r❛❞♦ ❆❇❈❉ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽
✸✹ P♦❧í❣♦♥♦ s✐♠♣❧❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾ ✸✺ P♦❧í❣♦♥♦s ♥ã♦ s✐♠♣❧❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾ ✸✻ P♦❧í❣♦♥♦ ❝♦♥✈❡①♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ✸✼ P♦❧í❣♦♥♦ ♥ã♦ ❝♦♥✈❡①♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ✸✽ ❉✐❛❣♦♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ✸✾ ➶♥❣✉❧♦s ✐♥t❡r♥♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✹✵ ❯♥✐❞❛❞❡s ❞❡ ❝♦♠♣r✐♠❡♥t♦ ❡ ❞❡ ár❡❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷
✹✶ ❘❡tâ♥❣✉❧♦ ❞❡ ❧❛❞♦s a ❡b ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷
✹✷ P❛r❛❧❡❧♦❣r❛♠♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✹✸ P❛r❛❧❡❧♦❣r❛♠♦ ❞❡❝♦♠♣♦st♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✹✹ P❛r❛❧❡❧♦❣r❛♠♦ ❞✐✈✐❞✐❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✹✺ ❚❛♣é③✐♦ ❞❡❝♦♠♣♦st♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹ ✹✻ ▲♦s❛♥❣♦ ❞❡❝♦♠♣♦st♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺
✹✼ P♦❧í❣♦♥♦ABCDEF ❞❡❝♦♠♣♦st♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺
✹✽ ❊①❡♠♣❧♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻ ✹✾ ❚r✐â♥❣✉❧♦ ❢✉♥❞❛♠❡♥t❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼ ✺✵ ❉❡❝♦♠♣♦s✐çã♦ ❡♠ tr✐â♥❣✉❧♦s ❢✉♥❞❛♠❡♥t❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ✺✶ ❚r✐â♥❣✉❧♦ r❡tâ♥❣✉❧♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽
✺✷ ◗✉❛❞r❛❞♦ ❞❡ ❧❛❞♦ a+b ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾
✺✸ ◗✉❛❞r❛❞♦ ❞❡ ❧❛❞♦ a+b ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾
✺✹ ❋❡✐①❡ ❞❡ ♣❛r❛❧❡❧❛s ❝♦♥t❛❞❛s ♣♦r tr❛♥s✈❡rs❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶ ✺✺ ❚r❛♥s✈❡rs❛✐s ❝♦♠ s❡❣♠❡♥t♦s ❝♦♥❣r✉❡♥t❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶ ✺✻ ❯♥✐❞❛❞❡ ❞❡ ár❡❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻ ✺✼ ❙✉❣❡stõ❡s ♣❛r❛ ♦s ♣♦❧í❣♦♥♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽ ✺✽ ❊①❡♠♣❧♦ ❞♦ ❏♦❣♦ ❞♦s ❙❡❣♠❡♥t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾
▲✐st❛ ❞❡ ❚❛❜❡❧❛s
✶ ◆ú♠❡r♦s ■♥❞♦✲❛rá❜✐❝♦s ♥♦ ❈ó❞✐❣♦ ❇r❛✐❧❧❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸
✷ ❖♣❡r❛çõ❡s ❢✉♥❞❛♠❡♥t❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸
✸ ❈♦♥❥✉♥t♦s ◆✉♠ér✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹
✹ ◆ú♠❡r♦s ♥❡❣❛t✐✈♦s✱ ♥ú♠❡r♦s ❞❡❝✐♠❛✐s✱ ♣♦tê♥❝✐❛ ❡ r❛✐③ q✉❛❞r❛❞❛ ✳ ✳ ✳ ✳ ✷✹
✺ ◆♦t❛çõ❡s ●❡♦♠étr✐❝❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺
✻ ❋✐❣✉r❛s P❧❛♥❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺
✼ ❑✐t ▼✉❧t✐♣❧❛♥♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼
✽ ◗✉❛❞r✐❧át❡r♦s ◆♦tá✈❡✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾
✾ ■♥✈❡st✐❣❛çã♦ ❞❛ q✉❛♥t✐❞❛❞❡ ❞❡ ❞✐❛❣♦♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸
✶✵ ■♥✈❡st✐❣❛çã♦ ❞❛ s♦♠❛ ❞♦s â♥❣✉❧♦s ✐♥t❡r♥♦s ❞❡ ✉♠ ♣♦❧í❣♦♥♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹ ✶✶ ✽ P♦♥t♦s ❞❡ ❋r♦♥t❡✐r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼ ✶✷ ✾ P♦♥t♦s ❞❡ ❋r♦♥t❡✐r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽ ✶✸ ✶✵ P♦♥t♦s ❞❡ ❋r♦♥t❡✐r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽ ✶✹ ■♥✈❡st✐❣❛çã♦ ❞❛ r❡❣r❛ ❣❡r❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽
❙✉♠ár✐♦
✶ ■♥tr♦❞✉çã♦ ✶✺
✷ ❉❡✜♥✐çã♦ ❞❡ ❉❡✜❝✐ê♥❝✐❛ ❱✐s✉❛❧ ✶✻
✸ ❆✈❛♥ç♦s ♥❛ ▲❡❣✐s❧❛çã♦ ■♥❝❧✉s✐✈❛ ❉❡s❞❡ ❛ ❈♦♥st✐t✉✐çã♦ ❞❡ ✶✾✽✽ ✶✼
✹ ❖ ❙✐st❡♠❛ ❇r❛✐❧❧❡ ✶✾
✺ ❆❧❣✉♠❛s ❘❡♣r❡s❡♥t❛çõ❡s ▼❛t❡♠át✐❝❛s ❡♠ ❇r❛✐❧❧❡ ✷✸
✻ ❖ ▼✉❧t✐♣❧❛♥♦ ✷✺
✼ ❈♦♥❝❡✐t♦s ❇ás✐❝♦s ❞❡ ●❡♦♠❡tr✐❛ P❧❛♥❛ ✷✽
✽ ❚r✐â♥❣✉❧♦ ✸✷
✾ ◗✉❛❞r✐❧át❡r♦s ✸✼
✶✵ P♦❧í❣♦♥♦s ✸✾
✶✶ ❈á❧❝✉❧♦ ❞❡ ➪r❡❛s ✹✶
✶✷ ❚❡♦r❡♠❛ ❞❡ P✐tá❣♦r❛s ✹✽
✶✸ ❚❡♦r❡♠❛ ❞❡ ❚❛❧❡s ✺✵
✶✹ ❙✉❣❡stã♦ ❞❡ ❆t✐✈✐❞❛❞❡s ✺✷
✶ ■♥tr♦❞✉çã♦
❆♦ ❧♦♥❣♦ ❞❛ ❝❛rr❡✐r❛ ❞❡ ♣r♦❢❡ss♦r ❞❡ ▼❛t❡♠át✐❝❛✱ ♣❡r❝❡❜❡♠♦s q✉❡ ❤á ✉♠❛ ❣r❛♥❞❡ ❞✐✜❝✉❧❞❛❞❡✱ ♣♦r ♣❛rt❡ ❞♦s ❛❧✉♥♦s ❞♦ ❊♥s✐♥♦ ❋✉♥❞❛♠❡♥t❛❧✱ ❡♠ ❛♣r❡♥❞❡r ●❡♦♠❡tr✐❛✳ ❉✐✜❝✉❧❞❛❞❡ q✉❡ ♣♦❞❡ s❡r ❛❣r❛✈❛❞❛ s❡ ♦ ❛❧✉♥♦ ❢♦r ♣♦rt❛❞♦r ❞❡ ❞❡✜❝✐ê♥❝✐❛ ✈✐s✉❛❧✳
❆ ✐♥❝❧✉sã♦ ❞♦ ❛❧✉♥♦ ♣♦rt❛❞♦r ❞❡ ❞❡✜❝✐ê♥❝✐❛ ✈✐s✉❛❧ ❡stá ❣❛r❛♥t✐❞❛ ♣♦r ❧❡✐✱ ♠❛s ♣❛r❛ q✉❡ ❡❧❡ r❡❛❧♠❡♥t❡ ♣♦ss❛ s❡r ✐♥❝❧✉í❞♦ ♥♦ ❛♠❜✐❡♥t❡ ❞❡ ❡♥s✐♥♦✱ ❝♦♠♦ q✉❛❧q✉❡r ♦✉tr♦ ❛❧✉♥♦✱ ❝❛❜❡ ❛♦ ♣r♦❢❡ss♦r ❜✉s❝❛r ❛❧t❡r♥❛t✐✈❛s ♥❛ t❡♥t❛t✐✈❛ ❞❡ ♠❡❧❤♦r❛r ❛ ❛♣r❡♥❞✐③❛❣❡♠ ❡ ❢❛❝✐✲ ❧✐t❛r ♦ ❡♥s✐♥♦ ❞❡ ❣❡♦♠❡tr✐❛✳
❖ ▼✉❧t✐♣❧❛♥♦ é ✉♠❛ ❢❡rr❛♠❡♥t❛ q✉❡ ♣♦ss✐❜✐❧✐t❛ ❛♦ ♣r♦❢❡ss♦r ❝r✐❛r✱ ❡♠ s❛❧❛ ❞❡ ❛✉❧❛✱ ✉♠ ❛♠❜✐❡♥t❡ ❞❡ ♠❛♥✐♣✉❧❛çã♦ ❡ ✐♥✈❡st✐❣❛çã♦✱ ♦♥❞❡ ♦ ❛❧✉♥♦✱ ❞❡✜❝✐❡♥t❡ ✈✐s✉❛❧ ♦✉ ♥ã♦✱ ♣♦ss❛ ❡♥❝♦♥tr❛r ❝♦♥❞✐çõ❡s ♣❛r❛ ♣r♦❞✉③✐r ♦ ❝♦♥❤❡❝✐♠❡♥t♦✳ ❊ ♦ ♣r✐♥❝✐♣❛❧ ♦❜❥❡t✐✈♦ ❞❡st❡ tr❛❜❛❧❤♦ é ♣r♦♣♦r ✉♠❛ ❛❜♦r❞❛❣❡♠ ❞❛ ●❡♦♠❡tr✐❛ P❧❛♥❛✱ ❛tr❛✈és ❞♦ ▼✉❧t✐♣❧❛♥♦✳
◆♦ ❈❛♣ít✉❧♦ ✷ ❢♦✐ ❛♣r❡s❡♥t❛❞❛ ❛ ❞❡✜♥✐çã♦ ❡ ❛ ❝❧❛ss✐✜❝❛çã♦ ❞❡ ❞❡✜❝✐ê♥❝✐❛ ✈✐s✉❛❧✳ ◆♦ ❈❛♣ít✉❧♦ ✸ ❢♦r❛♠ ❛♣r❡s❡♥t❛❞❛s ❛❧❣✉♠❛s ❧❡✐s✱ ❞✐r❡tr✐③❡s✱ ❞❡❝r❡t♦s ❡ ♣♦rt❛r✐❛✱ q✉❡ ♥♦rt❡✐❛♠ ❛ ✐♥❝❧✉sã♦ ❜r❛s✐❧❡✐r❛✳
◆♦s ❈❛♣ít✉❧♦s ✹ ❡ ✺ tr❛t❛♠♦s s♦❜r❡ ♦ ❙✐st❡♠❛ ❇r❛✐❧❧❡✱ s❡✉ s✉r❣✐♠❡♥t♦✱ s❡✉ ❝r✐❛❞♦r✱ ❛ ❝❤❡❣❛❞❛ ❛♦ ❇r❛s✐❧✱ ♦ ❛❧❢❛❜❡t♦ ❇r❛✐❧❧❡ ❡ ❛s r❡♣r❡s❡♥t❛çã♦ ♠❛t❡♠át✐❝❛s ♥♦ ❝ó❞✐❣♦ ❇r❛✐❧❧❡ ✉s❛❞❛s ♥❡st❡ tr❛❜❛❧❤♦✳
◆♦s ❈❛♣ít✉❧♦s ✻ ❢♦✐ ❛♣r❡s❡♥t❛❞♦ ♦ ▼✉❧t✐♣❧❛♥♦✱ ❞❡s❞❡ ♦ q✉❡ ♠♦t✐✈♦✉ ❛ s✉❛ ❝r✐❛çã♦ ❛té ♦ s❡✉ ❢♦r♠❛t♦ ✐♥❞✉str✐❛❧✐③❛❞♦ ❞❡ ❤♦❥❡✳
◆♦s ❈❛♣ít✉❧♦s ✼✱ ✽✱ ✾✱ ✶✵✱ ✶✶✱ ✶✷ ❡ ✶✸ ❢♦r❛♠ ❛♣r❡s❡♥t❛❞♦s ❞✐✈❡rs♦s ❝♦♥t❡ú❞♦s ❞❡ ●❡♦♠❡tr✐❛ ❛tr❛✈és ❞♦ ▼✉❧t✐♣❧❛♥♦✳
◆♦ ❈❛♣ít✉❧♦ ✶✹ ❢♦r❛♠ ♣r♦♣♦st❛s ❛❧❣✉♠❛s ❛t✐✈✐❞❛❞❡s ❛❞❛♣t❛❞❛s ♣❛r❛ ♦ ▼✉❧t✐♣❧❛♥♦✳
✷ ❉❡✜♥✐çã♦ ❞❡ ❉❡✜❝✐ê♥❝✐❛ ❱✐s✉❛❧
❆ ✈✐sã♦ é ✉♠ ❞♦s s❡♥t✐❞♦s q✉❡ ♥♦s ❛❥✉❞❛ ❛ ❝♦♠♣r❡❡♥❞❡r ♦ ♠✉♥❞♦ à ♥♦ss❛ ✈♦❧t❛✱ ❛♦ ♠❡s♠♦ t❡♠♣♦ q✉❡ ❞á s✐❣♥✐✜❝❛❞♦ ♣❛r❛ ♦s ♦❜❥❡t♦s✱ ❝♦♥❝❡✐t♦s ❡ ✐❞❡✐❛s✳ ➱ t❛♠❜é♠ ✉♠ ❞♦s ❝❛♥❛✐s ♠❛✐s ✐♠♣♦rt❛♥t❡ ❞❡ r❡❧❛❝✐♦♥❛♠❡♥t♦ ❞♦ ✐♥❞✐✈í❞✉♦ ❝♦♠ ♦ ♠✉♥❞♦ ❡①t❡r✐♦r✳
❙❡❣✉♥❞♦ ❝❧❛ss✐✜❝❛çã♦ ❞❛ ❖r❣❛♥✐③❛çã♦ ▼✉♥❞✐❛❧ ❞❛ ❙❛ú❞❡✱ ❛ ❞❡✜❝✐ê♥❝✐❛ ✈✐s✉❛❧ ❡stá ❞✐✈✐❞✐❞❛ ❡♠✿ ❇❛✐①❛ ❱✐sã♦ ✲ ◗✉❡ é ❛ ❛❧t❡r❛çã♦ ❞❛ ❝❛♣❛❝✐❞❛❞❡ ❢✉♥❝✐♦♥❛❧ ❞❛ ✈✐sã♦✱ ❞❡✲ ❝♦rr❡♥t❡ ❞❡ ✐♥ú♠❡r♦s ❢❛t♦r❡s ✐s♦❧❛❞♦s ♦✉ ❛ss♦❝✐❛❞♦s t❛✐s ❝♦♠♦ ❜❛✐①❛ ❛❝✉✐❞❛❞❡ ✈✐s✉❛❧ s✐❣♥✐✜❝❛t✐✈❛✱ r❡❞✉çã♦ ✐♠♣♦rt❛♥t❡ ❞♦ ❝❛♠♣♦ ✈✐s✉❛❧✱ ❛❧t❡r❛çõ❡s ❝♦rt✐❝❛✐s ❡✴♦✉ ❞❡ s❡♥s✐✲ ❜✐❧✐❞❛❞❡ ❛♦s ❝♦♥tr❛st❡s q✉❡ ✐♥t❡r❢❡r❡♠ ♦✉ ❧✐♠✐t❛♠ ♦ ❞❡s❡♠♣❡♥❤♦ ✈✐s✉❛❧ ❞♦ ✐♥❞✐✈í❞✉♦✳ ❆ ♣❡r❞❛ ❞❛ ❢✉♥çã♦ ✈✐s✉❛❧ ♣♦❞❡ s❡r ❡♠ ♥í✈❡❧ s❡✈❡r♦✱ ♠♦❞❡r❛❞♦ ♦✉ ❧❡✈❡✱ ♣♦❞❡♥❞♦ s❡r ✐♥✢✉❡♥❝✐❛❞❛ t❛♠❜é♠ ♣♦r ❢❛t♦r❡s ❛♠❜✐❡♥t❛✐s ✐♥❛❞❡q✉❛❞♦s✳ ❈❡❣✉❡✐r❛ ✲ ◗✉❡ é ❛ ♣❡r❞❛ t♦t❛❧ ❞❛ ✈✐sã♦ ❛té ❛ ❛✉sê♥❝✐❛ ❞❡ ♣r♦❥❡çã♦ ❞❡ ❧✉③✳ ❆s ♣❡ss♦❛s ❝❡❣❛s ♣♦❞❡♠ ✉t✐❧✐③❛r ♦s ♦✉tr♦s s❡♥t✐❞♦s ♣❛r❛ s✉❛ ❛♣r❡♥❞✐③❛❣❡♠ ❡ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦
P❛r❛ ♦ ♣r♦❢❡ss♦r ❆♥tô♥✐♦ ❏♦ã♦ ❈♦♥❞❡✱ ❞♦ ■♥st✐t✉t♦ ❇❡♥❥❛♠✐♥ ❈♦♥st❛♥t✱ ✉♠❛ ♣❡ss♦❛ é ❝♦♥s✐❞❡r❛❞❛ ❝❡❣❛ s❡ ❛ ✈✐sã♦ ❝♦rr✐❣✐❞❛ ❞♦ ♠❡❧❤♦r ❞♦s s❡✉s ♦❧❤♦s é ❞❡ ✷✵✴✷✵✵ ♦✉ ♠❡♥♦s✱ ✐st♦ é✱ s❡ ❡❧❛ ♣♦❞❡ ✈❡r ❛ ✷✵ ♣és ✭✻ ♠❡tr♦s✮ ♦ q✉❡ ✉♠❛ ♣❡ss♦❛ ❞❡ ✈✐sã♦ ♥♦r♠❛❧ ♣♦❞❡ ✈❡r ❛ ✷✵✵ ♣és ✭✻✵ ♠❡tr♦s✮✱ ♦✉ s❡ ♦ ❞✐â♠❡tr♦ ♠❛✐s ❧❛r❣♦ ❞♦ s❡✉ ❝❛♠♣♦ ✈✐s✉❛❧ s✉❜❡♥t❡♥❞❡ ✉♠ ❛r❝♦ ♥ã♦ ♠❛✐♦r ❞❡ ✷✵ ❣r❛✉s✱ ❛✐♥❞❛ q✉❡ s✉❛ ❛❝✉✐❞❛❞❡ ✈✐s✉❛❧ ♥❡ss❡ ❡str❡✐t♦ ❝❛♠♣♦ ♣♦ss❛ s❡r s✉♣❡r✐♦r ❛ ✷✵✴✷✵✵ ✭❈❖◆❉❊✱ ✷✵✵✺✮✳
❉♦ ♣♦♥t♦ ❞❡ ✈✐st❛ ❧❡❣❛❧✱ ♦ ❉❡❝r❡t♦ ✺✳✷✾✻✴✵✹ q✉❡ r❡❣✉❧❛♠❡♥t❛ ❛s ❧❡✐s ✶✵✳✵✹✽✴✵✵ ❡ ✶✵✳✵✾✽✴✵✵ q✉❡ ❡st❛❜❡❧❡❝❡♠ ❝♦♥❞✐çõ❡s ♣❛r❛ ❛ ✐♠♣❧❡♠❡♥t❛çã♦ ❞❡ ✉♠❛ ♣♦❧ít✐❝❛ ♥❛❝✐♦♥❛❧ ❞❡ ❛❝❡ss✐❜✐❧✐❞❛❞❡✱ tr❛③❡♥❞♦ ❝♦♥s❡q✉ê♥❝✐❛s ♣rát✐❝❛s q✉❡ ✐♥❞✉③❡♠ ❛ ✉♠❛ ♠✉❞❛♥ç❛ ❞❡ ♣♦st✉r❛ ♥❛ s♦❝✐❡❞❛❞❡ ♣❛r❛ ❛ ❣❛r❛♥t✐❛ ❞❛ ❛❝❡ss✐❜✐❧✐❞❛❞❡ ❛s ♣❡ss♦❛s ❝♦♠ ❞❡✜❝✐ê♥❝✐❛ ♦✉ ❝♦♠ ♠♦❜✐❧✐❞❛❞❡ r❡❞✉③✐❞❛ ❞❡✜♥❡ ❈❡❣✉❡✐r❛✱ ❝♦♠♦ ❞❡✜❝✐ê♥❝✐❛ ♥❛ q✉❛❧ ❛ ❛❝✉✐❞❛❞❡ ✈✐s✉❛❧ é ✐❣✉❛❧ ♦✉ ♠❡♥♦r q✉❡ ✵✱✵✺ ♥♦ ♠❡❧❤♦r ♦❧❤♦✱ ❝♦♠ ❛ ♠❡❧❤♦r ❝♦rr❡çã♦ ó♣t✐❝❛ ❡ ❇❛✐①❛ ❱✐sã♦✱ s✐❣♥✐✜❝❛ ❛❝✉✐❞❛❞❡ ✈✐s✉❛❧ ❡♥tr❡ ✵✱✸ ❡ ✵✱✵✺ ♥♦ ♠❡❧❤♦r ♦❧❤♦✱ ❝♦♠ ❛ ♠❡❧❤♦r ❝♦rr❡çã♦ ó♣t✐❝❛❀ ♦s ❝❛s♦s ♥♦s q✉❛✐s ❛ s♦♠❛tór✐❛ ❞❛ ♠❡❞✐❞❛ ❞♦ ❝❛♠♣♦ ✈✐s✉❛❧ ❡♠ ❛♠❜♦s ♦s ♦❧❤♦s ❢♦r ✐❣✉❛❧
♦✉ ♠❡♥♦r q✉❡60o❀ ♦✉ ❛ ♦❝♦rrê♥❝✐❛ s✐♠✉❧tâ♥❡❛ ❞❡ q✉❛✐sq✉❡r ❞❛s ❝♦♥❞✐çõ❡s ❛♥t❡r✐♦r❡s✳
◆♦ ❡♥t❛♥t♦✱ t♦❞❛s ❡ss❛s ❞❡✜♥✐çõ❡s✱ ❛✐♥❞❛ q✉❡ ❣❡r❛❧♠❡♥t❡ ❛❝❡✐t❛s ♥♦ ♠❡✐♦ ❝✐❡♥tí✜❝♦✱ ♥ã♦ ✐♠♣❧✐❝❛♠ q✉❡ ❛ ♣❡ss♦❛ ❝♦♠ ❞❡✜❝✐ê♥❝✐❛ ✈✐s✉❛❧ t❡♥❤❛ ✉♠ ♣♦t❡♥❝✐❛❧ ✐♥❛❞❡q✉❛❞♦ ❞❡ ❛♣r❡♥❞✐③❛❣❡♠✳ ❊ ❛ ♣❛❧❛✈r❛ ❞❡✜❝✐ê♥❝✐❛ ♥ã♦ ❞❡✈❡r✐❛ ❣❡r❛r r❡✢❡①♦s ♥❡❣❛t✐✈♦s✱ ♣♦✐s ❞❡✜✲ ❝✐ê♥❝✐❛ ♥ã♦ é ♦ ❝♦♥trár✐♦ ❞❡ ❡✜❝✐ê♥❝✐❛✳ ❆ ❞❡✜❝✐ê♥❝✐❛ ♥❡st❡ ❝❛s♦✱ ✐♥❞✐❝❛ ❢❛❧t❛✱ ❧✐♠✐t❛çã♦✳ ■♥❞✐❝❛ q✉❡ ❛❧❣✉é♠ ♥ã♦ t❡♠ ❝❡rt♦s ❛tr✐❜✉t♦s ❢ís✐❝♦s✱ s❡♥s♦r✐❛✐s ♦✉ ♠❡♥t❛✐s✳
❆ ✐♥❝❧✉sã♦ ✈❡♠ ❛❝♦♥t❡❝❡♥❞♦ ❛♦s ♣♦✉❝♦s✱ ✐♥✢✉❡♥❝✐❛❞❛ ♣❡❧❛ ❝♦♥s❝✐❡♥t✐③❛çã♦ ❞❛s ❢❛✲
♠í❧✐❛s✱ ❞❛s ❡♠♣r❡s❛s ❡ ♣❡❧❛ ✐♠♣❧❡♠❡♥t❛çã♦ ❞❡ ❞❡❝r❡t♦s ❡ ❧❡✐s q✉❡ ❛ ❣❛r❛♥t❡♠✳
✸ ❆✈❛♥ç♦s ♥❛ ▲❡❣✐s❧❛çã♦ ■♥❝❧✉s✐✈❛ ❉❡s❞❡ ❛ ❈♦♥st✐t✉✐✲
çã♦ ❞❡ ✶✾✽✽
▼✉✐t❛s sã♦ ❛s ❧❡✐s q✉❡ ❛ ♣❛rt✐r ❞❛ ❈♦♥st✐t✉✐çã♦ ❋❡❞❡r❛❧ ❞❡ ✶✾✽✽ ❬✶❪✱ ❝♦♥s✐❞❡r❛❞❛ ✉♠ ♠❛r❝♦ ♥❛ ❧❡❣✐s❧❛çã♦ ✐♥❝❧✉s✐✈❛✱ ♣r❡t❡♥❞❡♠ ♣r♦♠♦✈❡r ❡✜❝❛③♠❡♥t❡ ❛ ✐♥❝❧✉sã♦ ❞❛s ♣❡ss♦❛s ♣♦rt❛❞♦r❛s ❞❡ ❞❡✜❝✐ê♥❝✐❛ ♥❛ ❡s❝♦❧❤❛✱ ♥❛ ❢❛♠í❧✐❛ ❡ ♥❛ s♦❝✐❡❞❛❞❡✳
❆ ♣ró♣r✐❛ ❈♦♥st✐t✉✐çã♦ ❞❡ ✶✾✽✽✱ ♥♦ ❛rt✐❣♦ ✸ ✐♥❝✐s♦ ■❱✱ ❡st❛❜❡❧❡❝❡ ✏♣r♦♠♦✈❡r ♦ ❜❡♠ ❞❡ t♦❞♦s✱ s❡♠ ♣r❡❝♦♥❝❡✐t♦s ❞❡ ♦r✐❣❡♠✱ r❛ç❛✱ s❡①♦✱ ❝♦r✱ ✐❞❛❞❡ ❡ q✉❛✐sq✉❡r ♦✉tr❛s ❢♦r♠❛s ❞❡ ❞✐s❝r✐♠✐♥❛çã♦✑✳ ❉❡✜♥❡✱ ❛✐♥❞❛✱ ♥♦ ❛rt✐❣♦ ✷✵✺✱ ❛ ❡❞✉❝❛çã♦ ❝♦♠♦ ✉♠ ❞✐r❡✐t♦ ❞❡ t♦❞♦s✱ ❣❛r❛♥t✐♥❞♦ ♦ ♣❧❡♥♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❛ ♣❡ss♦❛✱ ♦ ❡①❡r❝í❝✐♦ ❞❛ ❝✐❞❛❞❛♥✐❛ ❡ ❛ q✉❛❧✐✜❝❛çã♦ ♣❛r❛ ♦ tr❛❜❛❧❤♦✳ ◆♦ ❛rt✐❣♦ ✷✵✻✱ ✐♥❝✐s♦ ■✱ ❡st❛❜❡❧❡❝❡ ❛ ✏✐❣✉❛❧❞❛❞❡ ❞❡ ❝♦♥❞✐çõ❡s ❞❡ ❛❝❡ss♦ ❡ ♣❡r♠❛♥ê♥❝✐❛ ♥❛ ❡s❝♦❧❛✑ ❝♦♠♦ ✉♠ ❞♦s ♣r✐♥❝í♣✐♦s ♣❛r❛ ♦ ❡♥s✐♥♦ ❡ ❣❛r❛♥t❡✱ ♥♦ s❡✉ ❛rt✐❣♦ ✷✵✽✱ ❝♦♠♦ ❞❡✈❡r ❞♦ ❊st❛❞♦✱ ❛ ♦❢❡rt❛ ❞♦ ❛t❡♥❞✐♠❡♥t♦ ❡❞✉❝❛❝✐♦♥❛❧ ❡s♣❡❝✐❛❧✐③❛❞♦✱ ♣r❡❢❡r❡♥❝✐❛❧♠❡♥t❡ ♥❛ r❡❞❡ r❡❣✉❧❛r ❞❡ ❡♥s✐♥♦✳
❆ ❧❡✐ n◦ ✼✳✽✺✸✱ ❞❡ ✷✹ ❞❡ ♦✉t✉❜r♦ ❞❡ ✶✾✽✾ ❬✼❪✱ r❡❣✉❧❛♠❡♥t❛❞❛ ♣❡❧♦ ❞❡❝r❡t♦ n◦ ✸✷✾✽✱
❞❡ ✷✵ ❞❡ ❞❡③❡♠❜r♦ ❞❡ ✶✾✾✾✱ ♣r❡✈ê ❛ ✐♥❝❧✉sã♦ ❞❡ ♣♦rt❛❞♦r❡s ❞❡ ❞❡✜❝✐ê♥❝✐❛s ♥♦ s✐st❡♠❛ ❡❞✉❝❛❝✐♦♥❛❧ ❞❡s❞❡ ❛ ♣ré✲❡s❝♦❧❛✱ ✐♥❝❧✉✐♥❞♦ t♦❞❛s ❛s ❡t❛♣❛s ❞❛ ❡❞✉❝❛çã♦✱ s❡❥❛♠ ❛s ❡s❝♦❧❛s ♣ú❜❧✐❝❛s✱ ♣r✐✈❛❞❛s ♦✉ ❡s♣❡❝✐❛✐s✳ ❊st❛ ❧❡✐ ❣❛r❛♥t❡ ❛✐♥❞❛ ❊❞✉❝❛çã♦ ❊s♣❡❝✐❛❧✱ ♦❜r✐❣❛tór✐❛ ❡ ❣r❛t✉✐t❛ ❡♠ ❡st❛❜❡❧❡❝✐♠❡♥t♦ ♣ú❜❧✐❝♦ ❞❡ ❡♥s✐♥♦✱ ♣❡r♠✐t✐♥❞♦ ❛❝❡ss♦ ❞❡ ❛❧✉♥♦s ♣♦rt❛❞♦r❡s ❞❡ ❞❡✜❝✐ê♥❝✐❛ ❛♦s ♠❡s♠♦s ❜❡♥❡❢í❝✐♦s ❞♦s ❞❡♠❛✐s ❡❞✉❝❛♥❞♦s✳
❖ ❊st❛t✉t♦ ❞❛ ❈r✐❛♥ç❛ ❡ ❞♦ ❆❞♦❧❡s❝❡♥t❡ ✭❊❈❆✮ ❬✻❪ ✲ ▲❡✐n◦ ✽✳✵✻✾✱ ❞❡ ✶✸ ❞❡ ❥✉❧❤♦ ❞❡
✶✾✾✵ ✲ q✉❡✱ ❡♥tr❡ ♦✉tr♦s✱ ❣❛r❛♥t❡ ♦ ❛t❡♥❞✐♠❡♥t♦ ❡❞✉❝❛❝✐♦♥❛❧ ❡s♣❡❝✐❛❧✐③❛❞♦ às ❝r✐❛♥ç❛s ❝♦♠ ❞❡✜❝✐ê♥❝✐❛ ♣r❡❢❡r❡♥❝✐❛❧♠❡♥t❡ ♥❛ r❡❞❡ r❡❣✉❧❛r ❞❡ ❡♥s✐♥♦❀ ♦ tr❛❜❛❧❤♦ ♣r♦t❡❣✐❞♦ ❛♦ ❛❞♦❧❡s❝❡♥t❡ ❝♦♠ ❞❡✜❝✐ê♥❝✐❛ ❡ ♣r✐♦r✐❞❛❞❡ ❞❡ ❛t❡♥❞✐♠❡♥t♦ ♥❛s ❛çõ❡s ❡ ♣♦❧ít✐❝❛s ♣ú❜❧✐❝❛s ❞❡ ♣r❡✈❡♥çã♦ ❡ ♣r♦t❡çã♦ ♣❛r❛ ❢❛♠í❧✐❛s ❝♦♠ ❝r✐❛♥ç❛s ❡ ❛❞♦❧❡s❝❡♥t❡s ♥❡ss❛ ❝♦♥❞✐çã♦✳
❆ ▲❡✐ ❞❡ ❉✐r❡tr✐③❡s ❡ ❇❛s❡s ❞❛ ❊❞✉❝❛çã♦ ◆❛❝✐♦♥❛❧ ✭▲❉❇✮ ❬✹❪✱ ❧❡✐ n◦ ✾✸✾✹✱ ❞❡ ✷✵ ❞❡
❞❡③❡♠❜r♦ ❞❡ ✶✾✾✻✱ q✉❡ r❡s❡r✈❛ ❝❛♣ít✉❧♦ ❡s♣❡❝í✜❝♦ ♣❛r❛ ❛ ❊❞✉❝❛çã♦ ❊s♣❡❝✐❛❧✱ ❛ss❡❣✉r❛ ❛♦s ❡❞✉❝❛♥❞♦s ❝♦♠ ♥❡❝❡ss✐❞❛❞❡s ❡s♣❡❝✐❛✐s r❡❝✉rs♦s ❡❞✉❝❛t✐✈♦s✱ ♣r♦❢❡ss♦r❡s ❡s♣❡❝✐❛❧✐✲ ③❛❞♦s✱ ❜❡♠ ❝♦♠♦ ♣r♦❢❡ss♦r❡s ❞♦ ❡♥s✐♥♦ r❡❣✉❧❛r✱ ❝❛♣❛❝✐t❛❞♦s ♣❛r❛ ❛ ✐♥t❡❣r❛çã♦ ❞❡ss❡s ❡❞✉❝❛♥❞♦s ❡♠ ❝❧❛ss❡s ❝♦♠✉♥s✳
❖ ■ P❧❛♥♦ ◆❛❝✐♦♥❛❧ ❞❡ ❊❞✉❝❛çã♦ ✭P◆❊✮ ✷✵✵✶✴✷✵✶✵✱ ❧❡✐ n◦ ✶✵✳✶✼✷✱ ❞❡ ✾ ❞❡ ❥❛♥❡✐r♦
❞❡ ✷✵✵✶✱ ❝♦♥t❡♥❞♦ ✷✽ ♠❡t❛s ❡ ♦❜❥❡t✐✈♦s ♣❛r❛ ❛s ❝r✐❛♥ç❛s ❡ ❥♦✈❡♥s ❝♦♠ ❞❡✜❝✐ê♥❝✐❛✳ ❊♥tr❡ ❡❧❛s✱ ❛✜r♠❛✈❛ q✉❡ ❛ ❊❞✉❝❛çã♦ ❊s♣❡❝✐❛❧✱ ✏❝♦♠♦ ♠♦❞❛❧✐❞❛❞❡ ❞❡ ❡❞✉❝❛çã♦ ❡s❝♦❧❛r✑✱ ❞❡✈❡r✐❛ s❡r ♣r♦♠♦✈✐❞❛ ❡♠ t♦❞♦s ♦s ❞✐❢❡r❡♥t❡s ♥í✈❡✐s ❞❡ ❡♥s✐♥♦ ❡ q✉❡ ✏❛ ❣❛r❛♥t✐❛ ❞❡ ✈❛❣❛s ♥♦ ❡♥s✐♥♦ r❡❣✉❧❛r ♣❛r❛ ♦s ❞✐✈❡rs♦s ❣r❛✉s ❡ t✐♣♦s ❞❡ ❞❡✜❝✐ê♥❝✐❛✑ ❡r❛ ✉♠❛ ♠❡❞✐❞❛ ✐♠♣♦rt❛♥t❡✳
❆s ❉✐r❡tr✐③❡s ◆❛❝✐♦♥❛✐s ♣❛r❛ ❛ ❊❞✉❝❛çã♦ ❊s♣❡❝✐❛❧ ♥❛ ❊❞✉❝❛çã♦ ❬✷❪✱ ❘❡s♦❧✉çã♦ n◦
✷✴✷✵✵✶✱ ✐♥st✐t✉í❞❛ ♣❡❧♦ ❈♦♥s❡❧❤♦ ◆❛❝✐♦♥❛❧ ❞❡ ❊❞✉❝❛çã♦ ✭❈◆❊✮✱ ❡♥tr❡ ♦s ♣r✐♥❝✐♣❛✐s ♣♦♥t♦s✱ ❛✜r♠❛ q✉❡ ✏♦s s✐st❡♠❛s ❞❡ ❡♥s✐♥♦ ❞❡✈❡♠ ♠❛tr✐❝✉❧❛r t♦❞♦s ♦s ❛❧✉♥♦s✱ ❝❛❜❡♥❞♦ às ❡s❝♦❧❛s ♦r❣❛♥✐③❛r✲s❡ ♣❛r❛ ♦ ❛t❡♥❞✐♠❡♥t♦ ❛♦s ❡❞✉❝❛♥❞♦s ❝♦♠ ♥❡❝❡ss✐❞❛❞❡s ❡❞✉❝❛❝✐♦♥❛✐s ❡s♣❡❝✐❛✐s✱ ❛ss❡❣✉r❛♥❞♦ ❛s ❝♦♥❞✐çõ❡s ♥❡❝❡ssár✐❛s ♣❛r❛ ✉♠❛ ❡❞✉❝❛çã♦ ❞❡ q✉❛❧✐❞❛❞❡ ♣❛r❛ t♦❞♦s✑✳ P♦ré♠✱ ♦ ❞♦❝✉♠❡♥t♦ ❝♦❧♦❝❛ ❝♦♠♦ ♣♦ss✐❜✐❧✐❞❛❞❡ ❛ s✉❜st✐t✉✐çã♦ ❞♦ ❡♥s✐♥♦ r❡❣✉❧❛r ♣❡❧♦ ❛t❡♥❞✐♠❡♥t♦ ❡s♣❡❝✐❛❧✐③❛❞♦ ✳
❆ ▲❡✐n◦ ✶✵✳✹✸✻✱ ❞❡ ✷✹ ❞❡ ❛❜r✐❧ ❞❡ ✷✵✵✷ ❬✸❪✱ r❡❣✉❧❛♠❡♥t❛❞❛ ♣❡❧♦ ❉❡❝r❡t♦n◦ ✺✳✻✷✻✱ ❞❡
✷ ❞❡ ❞❡③❡♠❜r♦ ❞❡ ✷✵✵✹✱ q✉❡ ♣r❡✈ê ❛ ▲í♥❣✉❛ ❇r❛s✐❧❡✐r❛ ❞❡ ❙✐♥❛✐s ✭▲■❇❘❆❙✮✱ ❝♦♠♦ ♠❡✐♦ ❧❡❣❛❧ ❞❡ ❝♦♠✉♥✐❝❛çã♦ ❡ ❡①♣r❡ssã♦ ❞❡ ❝♦♠✉♥✐❞❛❞❡ ❞❡ ♣❡ss♦❛s s✉r❞❛s✳❉✐s♣õ❡✱ ❛✐♥❞❛✱ s♦❜r❡ ❛ ✐♥❝❧✉sã♦ ❞❛ ▲■❇❘❆❙ ❝♦♠♦ ❞✐s❝✐♣❧✐♥❛ ❝✉rr✐❝✉❧❛r ❡ s♦❜r❡ ❛ ❢♦r♠❛çã♦ ❡ ❛ ❝❡rt✐✜❝❛çã♦ ❞❡ ♣r♦❢❡ss♦r✱ ✐♥str✉t♦r ❡ tr❛❞✉t♦r✴✐♥tér♣r❡t❡ ❞❡ss❡ ♥♦✈♦ ♠❡✐♦ ❧❡❣❛❧ ❞❡ ❝♦♠✉♥✐❝❛çã♦ ❡ ❡①♣r❡ssã♦✳
❊♠ ✷✵✵✻✱ ❛ ❙❡❝r❡t❛r✐❛ ❊s♣❡❝✐❛❧ ❞♦s ❉✐r❡✐t♦s ❍✉♠❛♥♦s✱ ♦ ▼✐♥✐stér✐♦ ❞❛ ❊❞✉❝❛çã♦✱ ♦ ▼✐♥✐stér✐♦ ❞❛ ❏✉st✐ç❛✱ ❡ ❛ ❯◆❊❙❈❖ ❧❛♥ç❛♠ ♦ P❧❛♥♦ ◆❛❝✐♦♥❛❧ ❞❡ ❊❞✉❝❛çã♦ ❡♠ ❉✐✲ r❡✐t♦s ❍✉♠❛♥♦s ❬✺❪✱ ✐♥s❡r✐♥❞♦ ♦ ❇r❛s✐❧ ♥❛ ❉é❝❛❞❛ ❞❛ ❊❞✉❝❛çã♦ ❡♠ ❉✐r❡✐t♦s ❍✉♠❛♥♦s ♣r❡✈✐st❛ ♥♦ Pr♦❣r❛♠❛ ▼✉♥❞✐❛❧ ❞❡ ❊❞✉❝❛çã♦ ❡♠ ❉✐r❡✐t♦s ❍✉♠❛♥♦s✳ ❖ P❧❛♥♦ ❞❡✜♥❡ ❛çõ❡s ♣❛r❛ ❢♦♠❡♥t❛r ♥♦ ❝✉rrí❝✉❧♦ ❞❛ ❡❞✉❝❛çã♦ ❜ás✐❝❛ ❛s t❡♠át✐❝❛s r❡❧❛t✐✈❛s às ♣❡ss♦❛s ❝♦♠ ❞❡✜❝✐ê♥❝✐❛ ❡ ♣❛r❛ ❞❡s❡♥✈♦❧✈❡r ❛çõ❡s ❛✜r♠❛t✐✈❛s q✉❡ ♣♦ss✐❜✐❧✐t❡♠ ❛ ✐♥❝❧✉sã♦✳
■♥st✐t✉í❞❛ ♣❡❧❛ P♦rt❛r✐❛ ♥♦ ✸✶✾ ❞♦ ▼✐♥✐stér✐♦ ❞❛ ❊❞✉❝❛çã♦ ❡♠ ✷✻ ❞❡ ❢❡✈❡r❡✐r♦ ❞❡
✶✾✾✾✱ ❛ ❈♦♠✐ssã♦ ❇r❛s✐❧❡✐r❛ ❞❡ ❇r❛✐❧❧❡ ✭❈❇❇✮ ✈✐s❛✈❛ ❛ ✉♠❛ ♣♦❧ít✐❝❛ q✉❡ ❡st❛❜❡❧❡❝❡ ❉✐r❡✲ tr✐③❡s ❡ ◆♦r♠❛s ♣❛r❛ ♦ ✉s♦✱ ♦ ❡♥s✐♥♦✱ ❛ ♣r♦❞✉çã♦ ❡ ❛ ❞✐❢✉sã♦ ❞♦ ❙✐st❡♠❛ ❇r❛✐❧❧❡✱ ❛♣❧✐❝❛❞❛ à ▲í♥❣✉❛ P♦rt✉❣✉❡s❛✱ à ▼❛t❡♠át✐❝❛ ❡ ❛ ♦✉tr❛s ❈✐ê♥❝✐❛s✱ à ▼ús✐❝❛ ❡ à ■♥❢♦r♠át✐❝❛✳
❈♦♠♦ ✈✐♠♦s✱ ♦ ❇r❛s✐❧ é r✐q✉íss✐♠♦ ❡♠ ❧❡✐s q✉❡ ❣❛r❛♥t❡♠ ❛ ✐♥❝❧✉sã♦✳ ▼❛s✱ ❞✐r❡✐t♦s ❛ss❡❣✉r❛❞♦s✱ ♣♦r s✐ só✱ ♥ã♦ ❣❛r❛♥t❡♠ ❜❡♠ ❡st❛r ✐♥t❡r✐♦r✳ ❋❛③✲s❡ ♥❡❝❡ssár✐♦ ♣♦❧ít✐❝❛s ♣ú❜❧✐❝❛s ❡✜❝✐❡♥t❡s ❡ ♠✉✐t♦ ❡st✉❞♦✱ ♣❡sq✉✐s❛ ♣❛r❛ ❛♠♣❧✐❛r ♦ ❝♦♥❤❡❝✐♠❡♥t♦✱ ❞❡s❡♥✈♦❧✈❡r ❡ t❡st❛r ❢♦r♠❛s q✉❡ ✈✐❛❜✐❧✐③❡♠ ❛ ✈❡r❞❛❞❡✐r❛ ✐♥❝❧✉sã♦✳ ❆❧é♠ ❞✐ss♦✱ é ♣r❡❝✐s♦ ✉❧tr❛♣❛ss❛r ♦✉tr❛s ❜❛rr❡✐r❛s ❝♦♠♦ ♦ ♣r❡❝♦♥❝❡✐t♦ ❡ ❛ ❞✐s❝r✐♠✐♥❛çã♦✱ r❡s✉❧t❛❞♦ ❞❛ ❢❛❧t❛ ❞❡ ✐♥❢♦r♠❛çã♦ ❞❛ s♦❝✐❡❞❛❞❡✳
✹ ❖ ❙✐st❡♠❛ ❇r❛✐❧❧❡
❙❡❣✉♥❞♦ ❛ r❡✈✐st❛ ❇❡♥❥❛♠✐♠ ❈♦♥st❛♥t ❬✽❪✱ ❡♠ ✶✼✽✹✱ ♥❛ ❝✐❞❛❞❡ ❞❡ P❛r✐s✱ ❱❛❧❡♥t✐♥ ❍❛ü② ❢✉♥❞♦✉ ❛ ♣r✐♠❡✐r❛ ❡s❝♦❧❛ ♣❛r❛ ❝❡❣♦s ❞♦ ♠✉♥❞♦✱ ❞❡♥♦♠✐♥❛❞❛ ■♥st✐t✉t♦ ❘❡❛❧ ❞♦s ❏♦✈❡♥s ❈❡❣♦s✳ ◆❡❧❛ ❱❛❧❡♥t✐♥ ❞❡s❡♥✈♦❧✈❡✉ ✉♠ s✐st❡♠❛ q✉❡ ♣r♦♣♦r❝✐♦♥❛✈❛✱ ❛♦s ❡st✉❞❛♥✲ t❡s✱ ❛ ❧❡✐t✉r❛ ❛tr❛✈és ❞❛ r❡♣r❡s❡♥t❛çã♦ ❞❡ ❝❛r❛❝t❡r❡s ❡♠ ❛❧t♦✲r❡❧❡✈♦✳
❊♠ ✶✽✷✸✱ ♦ ♦✜❝✐❛❧ ❞♦ ❡①ér❝✐t♦ ❢r❛♥❝ês ❈❤❛r❧❡s ❇❛r❜✐❡r ✈✐s✐t♦✉ ♦ ■♥st✐t✉t♦ ◆❛❝✐♦♥❛❧ ❞♦s ❏♦✈❡♥s ❈❡❣♦s ❡♠ P❛r✐s✱ ♦♥❞❡ ❛♣r❡s❡♥t♦✉ ✉♠ s✐st❡♠❛ ❞❡ ❝♦♠✉♥✐❝❛çã♦ ❜❛s❡❛❞♦ ❡♠ ❞♦③❡ s✐♥❛✐s✱ ❝♦♠♣r❡❡♥❞✐❞♦s ❡♥tr❡ ❧✐♥❤❛s ❡ ♣♦♥t♦s s❛❧✐❡♥t❡s✱ ❞❡♥♦♠✐♥❛❞♦ ❙♦♥♦❣r❛✜❛✳ ❖ s✐st❡♠❛ ♦❜❥❡t✐✈❛✈❛ ❛ ❝♦♠✉♥✐❝❛çã♦ ♥♦t✉r♥❛ ❡♥tr❡ ♦s s♦❧❞❛❞♦s ❞❛ ❧✐♥❤❛ ❞❡ ❜❛t❛❧❤❛ s✐❧❡♥❝✐♦s❛♠❡♥t❡ ❡ s❡♠ ❛ ♣r❡s❡♥ç❛ ❞❡ ❧✉③✳ ◆ã♦ ♦❜t❡✈❡ ♦ r❡s✉❧t❛❞♦ ❡s♣❡r❛❞♦✱ ♣♦✐s ♦s s♦❧❞❛❞♦s ❛❝❤❛r❛♠ ♦ s✐st❡♠❛ ♠✉✐t♦ ❝♦♠♣❧✐❝❛❞♦✳ ❈♦♥t✉❞♦✱ s❡✉ s✐st❡♠❛ ❢♦✐ ❜❡♠ r❡❝❡❜✐❞♦ ♣❡❧♦s ❛❧✉♥♦s ❞♦ ■♥st✐t✉t♦✳
❊♥tr❡ ♦s ❛❧✉♥♦s ❞♦ ■♥st✐t✉t♦ ❡♥❝♦♥tr❛✈❛✲s❡ ▲♦✉✐s ❇r❛✐❧❧❡✱ ❝❡❣♦ ❞❡s❞❡ ♦s três ❛♥♦s✱ ❡♥tã♦ ❝♦♠ q✉❛t♦r③❡ ❛♥♦s✱ q✉❡ s❡ ✐♥t❡r❡ss♦✉ ♣❡❧♦ s✐st❡♠❛ ❡ ❛♣r❡s❡♥t♦✉ ❛❧❣✉♠❛s s✉❣❡s✲ tõ❡s ❝♦♠ ✈✐st❛ ❛♦ s❡✉ ❛♣❡r❢❡✐ç♦❛♠❡♥t♦✳ ❋❛❝❡ à r❡❝✉s❛ ❞❡ ❇❛r❜✐❡r ❡♠ ❢❛③❡r q✉❛✐sq✉❡r ❛❧t❡r❛çõ❡s ❛♦ s❡✉ s✐st❡♠❛✱ ▲♦✉✐s ❇r❛✐❧❧❡ ♠♦❞✐✜❝♦✉ ❡ ❛♣r❡s❡♥t♦✉✱ ❡♠ ✶✽✷✺✱ ✉♠ s✐st❡♠❛ ❞❡ ❡s❝r✐t❛ ♣❛❞rã♦ ♣❛r❛ ❞❡✜❝✐❡♥t❡s ✈✐s✉❛✐s ✉s❛❞♦ ❛té ❛♦s ❞✐❛s ❞❡ ❤♦❥❡✱ q✉❡ ❢♦✐✱ s❡❣✉♥❞♦ ❈❡rq✉❡✐r❛✱ ✏❛ ❤❡r❛♥ç❛ ♠❛✐s s✐❣♥✐✜❝❛t✐✈❛ ❞❡✐①❛❞❛ s♦❜r❡ ❛ ❚❡rr❛ ♣♦r ▲♦✉✐s ❇r❛✐❧❧❡✱ ♥❛ q✉❛❧ ♣❡r♠❛♥❡❝❡✉ ♣♦r ❛♣❡♥❛s ✹✸ ❛♥♦s✱ é ♦ ❤♦❥❡ ❝❤❛♠❛❞♦ ❙✐st❡♠❛ ❇r❛✐❧❧❡✱ ✐♥✈❡♥t♦ q✉❡ ♦ ❡t❡r♥✐③♦✉ ♥❛ ❤✐stór✐❛ ❞❛ ❤✉♠❛♥✐❞❛❞❡✑✭❈❡rq✉❡✐r♦✱ ✷✵✵✾✮✳
❖ ❙✐st❡♠❛ ❝❤❡❣♦✉ ❛♦ ❇r❛s✐❧ ❛tr❛✈és ❞❡ ❏♦sé ➪❧✈❛r❡s ❞❡ ❆③❡✈❡❞♦ ❛♣ós r❡❣r❡ss❛r ❞❡ s❡✉s ❡st✉❞♦s ❡♠ P❛r✐s✱ ♥♦ ■♥st✐t✉t♦ ❘❡❛❧ ❞♦s ❏♦✈❡♥s ❈❡❣♦s✳ ❏♦sé ➪❧✈❛r❡s ❞❡ ❆③❡✈❡❞♦ ❡♥s✐♥♦✉ ♦ ❙✐st❡♠❛ ❇r❛✐❧❧❡ ❛ ❆❞è❧❡ ❙✐❣❛✉❞✱ ✜❧❤❛ ❞♦ ❉r✳ ❳❛✈✐❡r ❙✐❣❛✉❞✱ ♠é❞✐❝♦ ❞♦ P❛ç♦✳ ▲♦❣♦ ❢♦✐ ❛♣r❡s❡♥t❛❞♦ ❛ ❉✳ P❡❞r♦ ■■ ♣❡❧♦ ❉r✳ ❙✐❣❛✉❞ ♣❛r❛ ❛♣r❡s❡♥t❛r s✉❛s ✐❞❡✐❛s ❞❡ t❡r✲s❡ ♥♦ ❇r❛s✐❧ ✉♠ ❝♦❧é❣✐♦ ♦♥❞❡ ❛s ♣❡ss♦❛s ❝❡❣❛s ♣✉❞❡ss❡♠ ❡st✉❞❛r✳ ❊ ❢♦✐ ❛ss✐♠ q✉❡ ❡♠ ✶✷ ❞❡
s❡t❡♠❜r♦ ❞❡ ✶✽✺✹ ♥❛s❝❡✉✱ ❛tr❛✈és ❞♦ ❉❡❝r❡t♦ ■♠♣❡r✐❛❧ ♥♦✶✳✹✷✽✱ ♦ ■♠♣❡r✐❛❧ ■♥st✐t✉t♦ ❞♦s
▼❡♥✐♥♦s ❈❡❣♦s✱ ❤♦❥❡ ❞❡♥♦♠✐♥❛❞♦ ■♥st✐t✉t♦ ❇❡♥❥❛♠✐♥ ❈♦♥st❛♥t✱ ♦ ♣r✐♠❡✐r♦ ❡❞✉❝❛♥❞ár✐♦ ♣❛r❛ ❝❡❣♦s ❞❛ ❆♠ér✐❝❛ ▲❛t✐♥❛✳
❖ s✐st❡♠❛ ❝♦♥st❛ ❞❛ ❝♦♠❜✐♥❛çã♦ ❞❡ s❡✐s ♣♦♥t♦s ❡♠ r❡❧❡✈♦✱ ❞✐s♣♦st♦s ♥❛ ✈❡rt✐❝❛❧ ❡♠ ❞✉❛s ❝♦❧✉♥❛s ❡ três ♣♦♥t♦s ❝❛❞❛✳ ❖s s❡✐s ♣♦♥t♦s ❢♦r♠❛♠ ♦ q✉❡ s❡ ❝♦♥✈❡♥❝✐♦♥♦✉ ❝❤❛♠❛r ✏❝❡❧❛ ❜r❛✐❧❡✑✳ P❛r❛ ❢❛❝✐❧✐t❛r ❛ ✐❞❡♥t✐✜❝❛çã♦✱ ♦s ♣♦♥t♦s sã♦ ♥✉♠❡r❛❞♦s ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛ ✜❣✉r❛ ✶✳
❉❡✈✐❞♦ ❛ ❡ss❡ t✐♣♦ ❞❡ ❝♦♥✜❣✉r❛çã♦✱ ♦ ♠ét♦❞♦ ❛❞♠✐t❡ ✉♠ ♥ú♠❡r♦ ✜♥✐t♦ ❞❡ ❝❛r❛❝t❡r❡s✱ ♣♦✐s ♦s ♣♦♥t♦s ❡♠ r❡❧❡✈♦ sã♦ ♣♦s✐❝✐♦♥❛❞♦s ❡♠ ❞✐❢❡r❡♥t❡s ❧✉❣❛r❡s✱ ❞❛♥❞♦ ❛ ✐❞❡✐❛ ❞❛s
❋✐❣✉r❛ ✶✿ ❈❡❧❛ ❇r❛✐❧❧❡
s❡❣✉✐♥t❡s ❝♦♠❜✐♥❛çõ❡s✿
• ❈♦♠❜✐♥❛çã♦ ❞❡ s❡✐s ♣♦♥t♦s ❛❣r✉♣❛❞♦s ✉♠ ❛ ✉♠❀
C6,1 =
6!
1!(6−1)! = 6
• ❈♦♠❜✐♥❛çã♦ ❞❡ s❡✐s ♣♦♥t♦s ❛❣r✉♣❛❞♦s ❞♦✐s ❛ ❞♦✐s❀
C6,2 =
6!
1!(6−2)! = 15
• ❈♦♠❜✐♥❛çã♦ ❞❡ s❡✐s ♣♦♥t♦s ❛❣r✉♣❛❞♦s três ❛ três❀
C6,3 =
6!
1!(6−3)! = 20
• ❈♦♠❜✐♥❛çã♦ ❞❡ s❡✐s ♣♦♥t♦s ❛❣r✉♣❛❞♦s q✉❛tr♦ ❛ q✉❛tr♦❀
C6,4 =
6!
1!(6−4)! = 15
• ❈♦♠❜✐♥❛çã♦ ❞❡ s❡✐s ♣♦♥t♦s ❛❣r✉♣❛❞♦s ❝✐♥❝♦ ❛ ❝✐♥❝♦❀
C6,5 =
6!
1!(6−6)! = 6
• ❈♦♠❜✐♥❛çã♦ ❞❡ s❡✐s ♣♦♥t♦s ❛❣r✉♣❛❞♦s s❡✐s ❛ s❡✐s❀
C6,6 =
6!
1!(6−6)! = 1
❆ss✐♠✱ ♦ ♥ú♠❡r♦ ❞❡ ❝❛r❛❝t❡r❡s q✉❡ ♣♦❞❡♠ s❡r r❡♣r❡s❡♥t❛❞♦s ♣❡❧♦ ❙✐st❡♠❛ ❇r❛✐❧❧❡ ✭❋✐❣✉r❛ ✹✮ é ❛ s♦♠❛ ❞❛s ❝♦♠❜✐♥❛çõ❡sC6,1+C6,2+C6,3+C6,4+C6,5+C6,6 = 6 + 15 +
20 + 15 + 6 + 1 = 63✳
❯♠ t❡①t♦ ❡s❝r✐t♦ ♣♦❞❡ s❡r ❡❧❛❜♦r❛❞♦ ♣♦r ♠❡✐♦ ❞❡ ✉♠❛ r❡❣❧❡t❡ ❡ ♣✉♥çã♦ ✭❋✐❣✉r❛ ✷✮ ♦✉ ❞❡ ✉♠❛ ♠áq✉✐♥❛ ❞❡ ❡s❝r❡✈❡r ❜r❛✐❧❧❡ ✭❋✐❣✉r❛ ✸✮✳
❆ r❡❣❧❡t❡ é ✉♠❛ ré❣✉❛ ❞❡ ♠❛❞❡✐r❛✱ ♠❡t❛❧ ♦✉ ♣❧ást✐❝♦ ❝♦♠ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❝❡❧❛s ❜r❛✐❧❧❡ ❞✐s♣♦st❛s ❡♠ ❧✐♥❤❛s ❤♦r✐③♦♥t❛✐s s♦❜r❡ ✉♠❛ ❜❛s❡ ♣❧❛♥❛✳
❖ ♣✉♥çã♦ é ✉♠ ✐♥str✉♠❡♥t♦ ❡♠ ♠❛❞❡✐r❛ ♦✉ ♣❧ást✐❝♦ ♥♦ ❢♦r♠❛t♦ ❞❡ ♣❡r❛ ♦✉ ❛♥❛tô✲ ♠✐❝♦✱ ❝♦♠ ♣♦♥t❛ ♠❡tá❧✐❝❛✱ ✉t✐❧✐③❛❞♦ ♣❛r❛ ❛ ♣❡r❢✉r❛çã♦ ❞♦s ♣♦♥t♦s ♥❛ ❝❡❧❛ ❜r❛✐❧❧❡✳
❆ ♠áq✉✐♥❛ ❞❡ ❡s❝r❡✈❡r ❇r❛✐❧❧❡ é ✉♠ ❡q✉✐♣❛♠❡♥t♦ ♠❡❝â♥✐❝♦ ♦✉ ❡❧étr✐❝♦ ❝♦♠ ✉♠ ❣r✉♣♦ ❞❡ três t❡❝❧❛s ♣❛r❛❧❡❧❛s ❞❡ ❝❛❞❛ ❧❛❞♦ ♣❛r❛ r❡♣r❡s❡♥t❛r ❛ ❝❡❧❛ ❇r❛✐❧❧❡✱ ✉♠❛ ❜❛rr❛ ❞❡ ❡s♣❛ç♦ ♥♦ ❝❡♥tr♦ ❡ ✉♠ ❞✐s♣♦s✐t✐✈♦ ♣❛r❛ ❛❥✉st❛r ❛ ❢♦❧❤❛ ❞❡ ♣❛♣❡❧✳
❋✐❣✉r❛ ✷✿ ❘❡❣❧❡t❡ ❋✐❣✉r❛ ✸✿ ▼áq✉✐♥❛
a b c d e f g h i j
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❋✐❣✉r❛ ✹✿ ❉✐s♣♦s✐çã♦ ❯♥✐✈❡rs❛❧ ❞♦s ✻✸ ❙✐♥❛✐s ❙✐♠♣❧❡s ❞♦ ❙✐st❡♠❛ ❇r❛✐❧❧❡
✺ ❆❧❣✉♠❛s ❘❡♣r❡s❡♥t❛çõ❡s ▼❛t❡♠át✐❝❛s ❡♠ ❇r❛✐❧❧❡
P❛r❛ r❡♣r❡s❡♥t❛r ♦s ♥ú♠❡r♦s ♥♦ ❝ó❞✐❣♦ ❇r❛✐❧❧❡ ✉s❛✲s❡ ❛ ❝♦♠❜✐♥❛çã♦ ✭✸✹✺✻✮ ❛♥t❡❝❡✲ ❞❡♥❞♦ ♦s ♠❡s♠♦s sí♠❜♦❧♦s q✉❡ r❡♣r❡s❡♥t❛♠ ❛s ❧❡tr❛s ❞❡ ❛ ❛té ❥ ✭❚❛❜❡❧❛ ✶✮✳
❚❛❜❡❧❛ ✶✿ ◆ú♠❡r♦s ■♥❞♦✲❛rá❜✐❝♦s ♥♦ ❈ó❞✐❣♦ ❇r❛✐❧❧❡
❆s ♦♣❡r❛çõ❡s ❢✉♥❞❛♠❡♥t❛✐s ❞❡ ❛❞✐çã♦✱ s✉❜tr❛çã♦✱ ♠✉❧t✐♣❧✐❝❛çã♦ ❡ ❞✐✈✐sã♦ ❡stã♦ r❡✲ ♣r❡s❡♥t❛❞❛s ♥❛ t❛❜❡❧❛ ✷✳
❚❛❜❡❧❛ ✷✿ ❖♣❡r❛çõ❡s ❢✉♥❞❛♠❡♥t❛✐s
P❛r❛ ✐♥❞✐❝❛r ♦s ❝♦♥❥✉♥t♦s ♥✉♠ér✐❝♦s ✉t✐❧✐③❛✲s❡ ❛ ❝♦♠❜✐♥❛çã♦ ❞❡ ✭✹✺✻✮ ❛♥t❡s ❞❛ ❧❡tr❛ q✉❡ r❡♣r❡s❡♥t❛ ♦ ❝♦♥❥✉♥t♦ ✭❚❛❜❡❧❛ ✸✮✳
❚❛❜❡❧❛ ✸✿ ❈♦♥❥✉♥t♦s ◆✉♠ér✐❝♦s
P❛r❛ r❡♣r❡s❡♥t❛r ♥ú♠❡r♦s ♥❡❣❛t✐✈♦s ❜❛st❛ ✉s❛r ❛ ❝♦♠❜✐♥❛çã♦ ❞❡ ♣♦♥t♦s ✭✸✻✮ à ❡sq✉❡r❞❛ ❞♦ ♥ú♠❡r♦✳ ❆ ✐♥❞✐❝❛çã♦ ❞❡ ♥ú♠❡r♦s ❞❡❝✐♠❛✐s é ❢❡✐t❛ ✉s❛♥❞♦ ♦ ♣♦♥t♦ ✭✷✮ ♣❛r❛ s❡♣❛r❛r ❛ ♣❛rt❡ ✐♥t❡✐r❛ ❞❛ ♣❛rt❡ ❞❡❝✐♠❛❧✳ P❛r❛ r❡♣r❡s❡♥t❛r ♣♦tê♥❝✐❛✱ ❛♣ós ❛ ❡s❝r✐t❛ ❞♦ ❛❧❣❛r✐s♠♦ ❞❛ ❜❛s❡ ❡s❝r❡✈❡✲s❡ ♦s ♣♦♥t♦s ✭✶✷✮ ❡ ❧♦❣♦ ❡♠ s❡❣✉✐❞❛ ♦ ❛❧❣❛r✐s♠♦ ❞♦ ❡①♣♦❡♥t❡✳ ❆ ❝♦♠❜✐♥❛çã♦ q✉❡ r❡♣r❡s❡♥t❛ ❛ r❛✐③ q✉❛❞r❛❞❛ é ✭✶✷✹✻✮✭✶✺✻✮ ❝♦❧♦❝❛❞❛ à ❡sq✉❡r❞❛ ❞♦ ♥ú♠❡r♦ ✭❚❛❜❡❧❛ ✹✮✳
❚❛❜❡❧❛ ✹✿ ◆ú♠❡r♦s ♥❡❣❛t✐✈♦s✱ ♥ú♠❡r♦s ❞❡❝✐♠❛✐s✱ ♣♦tê♥❝✐❛ ❡ r❛✐③ q✉❛❞r❛❞❛
◆♦ ❝ó❞✐❣♦ ❇r❛✐❧❧❡ t❛♠❜é♠ ♣♦❞❡♠♦s r❡♣r❡s❡♥t❛r ❛❧❣✉♠❛s ♥♦t❛çõ❡s ❞❡ ❣❡♦♠❡tr✐❛ ✭❚❛❜❡❧❛ ✺✮ ❡ ✉s❛r t❛♠❜é♠ ❛❧❣✉♠❛s ❝♦♠❜✐♥❛çõ❡s ♣❛r❛ r❡♣r❡s❡♥t❛r ❢♦r♠❛s ❣❡♦♠étr✐❝❛s ♣❧❛♥❛s ✭❚❛❜❡❧❛ ✻✮✳
❚❛❜❡❧❛ ✺✿ ◆♦t❛çõ❡s ●❡♦♠étr✐❝❛s
❚❛❜❡❧❛ ✻✿ ❋✐❣✉r❛s P❧❛♥❛s
✻ ❖ ▼✉❧t✐♣❧❛♥♦
❖ ▼✉❧t✐♣❧❛♥♦ é ✉♠❛ ❢❡rr❛♠❡♥t❛ ❝r✐❛❞❛ ♣❡❧♦ ♣r♦❢❡ss♦r ❘✉❜❡♥s ❋❡rr♦♥❛t♦✱ ♠❡str❡ ♣❡❧❛ ❯❋❙❈✱ ❡♠ ❞❡❝♦rrê♥❝✐❛ ❞❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ ✉♠ ❛❧✉♥♦ ❝❡❣♦✱ ■✳ ❏✳ ❞❡ P✳ ✭✷✷ ❛♥♦s ❝❡❣♦ ❞❡s❞❡ ♦s ✽✮ q✉❡ ❡st❛✈❛ ❡st✉❞❛♥❞♦ ❈á❧❝✉❧♦ ❉✐❢❡r❡♥❝✐❛❧ ❡ ■♥t❡❣r❛❧ ♥♦ ❛♥♦ ✷✵✵✵ ♥❛ ❯◆■P❆◆ ✭❯♥✐✈❡rs✐❞❛❞❡ P❛♥✲❆♠❡r✐❝❛♥❛ ❞❛ ❝✐❞❛❞❡ ❞❡ ❈❛s❝❛✈❡❧ ✲ P❛r❛♥á✮✳
❙❡❣✉♥❞♦ ❞❡s❝r✐çã♦ ❞♦ ♣r♦❢❡ss♦r ❋❡rr♦♥❛t♦✿
❖ ♠❛t❡r✐❛❧ ❝♦♥❝r❡t♦ ❞❡♥♦♠✐♥❛❞♦ ▼✉❧t✐♣❧❛♥♦ ❝♦♥s✐st❡✱ ❜❛s✐❝❛✲ ♠❡♥t❡✱ ❡♠ ✉♠❛ ♣❧❛❝❛ ♣❡r❢✉r❛❞❛ ❞❡ ❧✐♥❤❛s ❡ ❝♦❧✉♥❛s ♣❡r♣❡♥❞✐✲ ❝✉❧❛r❡s✱ ♦♥❞❡ ♦s ❢✉r♦s sã♦ ❡q✉✐❞✐st❛♥t❡s✳ ❖ t❛♠❛♥❤♦ ❞❛ ♣❧❛❝❛ ❡ ❛ ❞✐stâ♥❝✐❛ ❡♥tr❡ ♦s ❢✉r♦s ♣♦❞❡ ✈❛r✐❛r ❝♦♥s♦❛♥t❡ ❛ ♥❡❝❡ss✐❞❛❞❡ ✭❋❊❘❘❖◆❆❚❖✱ ✷✵✵✷✱ ♣✳✺✼✮✳
◆♦ ▼✉❧t✐♣❧❛♥♦ ♣♦❞❡✲s❡ tr❛❜❛❧❤❛r ✉♠❛ ❣r❛♥❞❡ ✈❛r✐❡❞❛❞❡ ❞❡ ❝♦♥t❡ú❞♦s✱ t❛✐s ❝♦♠♦✿ ♦♣❡r❛çõ❡s✱ t❛❜✉❛❞❛✱ ❡q✉❛çõ❡s✱ ♣r♦♣♦rçã♦✱ r❡❣r❛ ❞❡ três✱ ❢✉♥çõ❡s✱ ♠❛tr✐③✱ ❞❡t❡r♠✐♥❛♥t❡s✱ s✐st❡♠❛ ❧✐♥❡❛r✱ ❣rá✜❝♦s ❞❡ ❢✉♥çõ❡s✱ ✐♥❡q✉❛çõ❡s✱ ❢✉♥çõ❡s ❡①♣♦♥❡♥❝✐❛✐s ❡ ❧♦❣❛rít♠✐❝❛s✱ tr✐❣♦♥♦♠❡tr✐❛✱ ❣❡♦♠❡tr✐❛ ♣❧❛♥❛ ❡ ❡s♣❛❝✐❛❧✱ ❡st❛tíst✐❝❛✱ ❡♥tr❡ ♦✉tr♦s✳
❖ ♠❛✐s ✐♠♣♦rt❛♥t❡ é q✉❡ ♦ ♠❛t❡r✐❛❧ ♥ã♦ é r❡str✐t♦ ❛♣❡♥❛s às ♣❡ss♦❛s ❝♦♠ ❞❡✜❝✐ê♥❝✐❛ ✈✐s✉❛❧✳ ❙✉r❣❡ ❝♦♠♦ ✉♠❛ ❛❧t❡r♥❛t✐✈❛ ♣❛r❛ q✉❡ ♦ ♣r♦❢❡ss♦r ♣♦ss❛ tr❛❜❛❧❤❛r ❝♦♠ ❡❞✉❝❛♥✲ ❞♦s ❝❡❣♦s s❡♠ r♦t✉❧á✲❧♦s✱ s❡♠ ❝❛✉s❛r✲❧❤❡s ❝♦♥str❛♥❣✐♠❡♥t♦s✱ ♣♦rq✉❡ t❛♠❜é♠ ♣♦❞❡ s❡r ✉t✐❧✐③❛❞♦s ♣♦r ❡❞✉❝❛♥❞♦s q✉❡ ❡♥①❡r❣❛♠ ❝♦♠♦ ❛✜r♠❛ ♦ ♣r♦❢❡ss♦r ❋❡rr♦♥❛t♦✿
❬✳✳✳❪ ❞❡♥tr♦ ❞❡ ✉♠❛ ♠❡s♠❛ ❝❧❛ss❡ ♦s ♠❡s♠♦s ❝♦♥t❡ú❞♦s ♠❛t❡♠át✐✲ ❝♦s ♣♦❞❡♠ s❡r tr❛❜❛❧❤❛❞♦s ❝♦♠ ❛ t✉r♠❛ t♦❞❛✱ s❡♠ ❞✐❢❡r❡♥❝✐❛çõ❡s ❡ ❛tr❛✈és ❞♦s ♠❡s♠♦s ♠ét♦❞♦s ❡ ♣r♦❝❡❞✐♠❡♥t♦s✱ ♣♦✐s ♦ q✉❡ ✈❛✐ ♣r♦♣✐❝✐❛r ❛♦ ❛❧✉♥♦ ❝❡❣♦ ❛ ❧❡✐t✉r❛ ❞♦s ♣✐♥♦s é ♦ t♦q✉❡ ❞❡ s✉❛s ♠ã♦s ♥❛ s✉♣❡r❢í❝✐❡ ❞♦s ♠❡s♠♦s ❡ ❛♦ ❛❧✉♥♦ ✈✐❞❡♥t❡ ❜❛st❛rá ❛ ✈✐s✉❛❧✐✲ ③❛çã♦ ❞♦s ❛❧❣❛r✐s♠♦s ❞❡ q✉❡ ❡❧❡ ♥❡❝❡ss✐t❛ ✭❋❊❘❘❖◆❆❚❖✱ ✷✵✵✷✱ ♣✳✺✽✮✳
❖ ▼✉❧t✐♣❧❛♥♦ s✉r❣✐✉✱ ❞❡ss❛ ❢♦r♠❛✱ ❝♦♠♦ ✉♠ ♠❛t❡r✐❛❧ ❞✐❞át✐❝♦ ♠❡❞✐❛❞♦r ❡♥tr❡ ♦ q✉❡ ♦ ♣r♦❢❡ss♦r ❡①♣❧✐❝❛ ❡ ❝♦♠♦ ♦ ❛❧✉♥♦ ❛♣r❡♥❞❡✱ ♣♦ss✐❜✐❧✐t❛♥❞♦ ❛ ❛♠❜❛s ❛s ♣❛rt❡s s❛t✐s❢❛çã♦ ❡ ✐♥❝❡♥t✐✈♦✳ Pr♦✈❛ ❞❡ss❡ ❢❛t♦ ❡stá ♥♦ r❡❧❛t♦ ❞♦ ❛❧✉♥♦ ■✳ ❏✳ ❞❡ P✳✿
❱♦❝ê ♥ã♦ ✐♥✈❡♥t♦✉ ✉♠ ♠❛t❡r✐❛❧ ♣❛r❛ ♠✐♠✱ ♠❛s ♣❛r❛ t♦❞♦s ♦s ❝❡❣♦s ❞♦ ♠✉♥❞♦✦ ◆❡st❡ ♠♦♠❡♥t♦ ❝♦♠❡❝❡✐ ❛ ❡♥t❡♥❞❡r ♦ q✉❡ ✈♦❝ê q✉✐s ♠❡ ❡①♣❧✐❝❛r✳ ❊st❛ ✐♥✈❡♥çã♦ ❞❡✈❡ s❡r ❞✐✈✉❧❣❛❞❛✦ ✭✳✳✳✮ ❆❣♦r❛ ✈♦✉ ❛♣r❡♥❞❡r ♠❛t❡♠át✐❝❛✳ ✭✳✳✳✮ ➱ ✐ss♦ q✉❡ ♥ós ❝❡❣♦s ♣r❡❝✐s❛♠♦s ♣❛r❛ ❛♣r❡♥❞❡r ♠❛t❡♠át✐❝❛✳ ✭✳✳✳✮ ❆té ❤♦❥❡ t♦❞♦s ✜♥❣✐❛♠ q✉❡ ♠❡ ❡♥s✐♥❛✈❛♠ ❡ ❡✉ ✜♥❣✐❛ q✉❡ ❛♣r❡♥❞✐❛ ✭❋❊❘❘❖◆❆❚❖✱ ✷✵✵✷✱ ♣✳✾✻✮✳
❖ ▼✉❧t✐♣❧❛♥♦✱ ❝♦♠♦ ✐♥str✉♠❡♥t♦ s✐❣♥✐✜❝❛t✐✈♦✱ ❞❡st✐♥❛❞♦ ❛ s❛t✐s❢❛③❡r ❛s ♥❡❝❡ss✐❞❛✲ ❞❡s ❜ás✐❝❛s ❞❡ ❛♣r❡♥❞✐③❛❣❡♠ ❞❛ ♠❛t❡♠át✐❝❛ ❞♦s ❡❞✉❝❛♥❞♦s✱ ♣♦❞❡♥❞♦ s❡ t♦r♥❛r ✉♠❛ ❡✜❝✐❡♥t❡ ❛❧t❡r♥❛t✐✈❛✱ ♣♦✐s ♣♦ss✐❜✐❧✐t❛ ❛ ❝♦♠♣r❡❡♥sã♦ ❞❡ ♠✉✐t♦s ❝♦♥❝❡✐t♦s ❛té ❡♥tã♦ ❞❡✲ ❝♦r❛❞♦s ❡ s❡♠ s❡♥t✐❞♦✱ ♠❛①✐♠✐③❛♥❞♦ ❛s ♦♣♦rt✉♥✐❞❛❞❡s ❞♦s ❞❡✜❝✐❡♥t❡s ✈✐s✉❛✐s✳
❆t✉❛❧♠❡♥t❡✱ ♦ ♠✉❧t✐♣❧❛♥♦ é ✉♠ r❡❝✉rs♦ q✉❡ ❢♦✐ ✐♥❞✉str✐❛❧✐③❛❞♦ ❡♠ ✉♠❛ ✈❡rsã♦ ❡♠
♣❧ást✐❝♦✱ ❝♦♠♦ ♣♦❞❡♠♦s ✈❡r✐✜❝❛r ♥❛ ❚❛❜❡❧❛ ✼✶✳ ❊ é ❛tr❛✈és ❞❡st❡ r❡❝✉rs♦ q✉❡ s❡rã♦
❛♣r❡s❡♥t❛❞♦s✱ ♥♦ ♣ró①✐♠♦ ❈❛♣ít✉❧♦✱ ❛❧❣✉♥s ❝♦♥t❡ú❞♦s ❞❡ ❣❡♦♠❡tr✐❛ ❝♦♠ ❛❧❣✉♠❛s r❡✲ ♣r❡s❡♥t❛çõ❡s ♥♦ ❝ó❞✐❣♦ ❇r❛✐❧❧❡✷✳
✶❖ ▼✉❧t✐♣❧❛♥♦ t❛♠❜é♠ ✈❡♠ ❝♦♠ ✉♠ ❣✉✐❛ ❞❡ ♦r✐❡♥t❛çõ❡s ❞✐❞át✐❝❛s q✉❡ ♥ã♦ ❝♦♥t❡♠♣❧❛ ❣r❛♥❞❡ ♣❛rt❡
❞♦s ❝♦♥t❡ú❞♦s ❛❜♦r❞❛❞♦s ♥❡st❡ tr❛❜❛❧❤♦✳
✷❆ r❡♣r❡s❡♥t❛çã♦ ♥♦ ❝ó❞✐❣♦ ❇r❛✐❧❧❡ ✈✐s❛ ❢❛❝✐❧✐t❛r ♦ tr❛❜❛❧❤♦ ❞♦ ♣r♦❢❡ss♦r ♥❛ ❛♣r❡s❡♥t❛çã♦ ❞♦s ❝♦♥✲
t❡ú❞♦s ❛♦s ❛❧✉♥♦s ♣♦rt❛❞♦r❡s ❞❡ ❞❡✜❝✐ê♥❝✐❛ ✈✐s✉❛❧✳ ❆s ✜❣✉r❛s q✉❡ ♥ã♦ ❛♣r❡s❡♥t❛r❡♠ ❡ss❛ r❡♣r❡s❡♥t❛çã♦ é ♣♦rq✉❡ ❥á ❢♦r❛♠ ❛♣r❡s❡♥t❛❞❛s ❛♥t❡r✐♦r♠❡♥t❡ ♦✉ ♥ã♦ ❡①✐st❡ r❡♣r❡s❡♥t❛çã♦ ❡s♣❡❝í✜❝❛ ♣❛r❛ ❛ ♠❡s♠❛✳
❚❛❜❡❧❛ ✼✿ ❑✐t ▼✉❧t✐♣❧❛♥♦
✼ ❈♦♥❝❡✐t♦s ❇ás✐❝♦s ❞❡ ●❡♦♠❡tr✐❛ P❧❛♥❛
❙❛❜❡♥❞♦ q✉❡ s❡ ❞❡✈❡ ❞❡✜♥✐r ✉♠ ❝♦♥❝❡✐t♦ ♣♦r ♠❡✐♦ ❞❡ ♦✉tr♦s ❥á ❛♥t❡r✐♦r♠❡♥t❡ ❞❡✜✲ ♥✐❞♦s✱ s❡♥❞♦ ❡st❡s t❛♠❜é♠ ❞❡✜♥✐❞♦s ♣♦r ♠❡✐♦ ❞❡ ♦✉tr♦s ❛♥t❡r✐♦r❡s✱ ❡ ❛ss✐♠ s✉❝❡ss✐✈❛✲ ♠❡♥t❡✱ ❝❤❡❣❛r❡♠♦s ❛ ✉♠ ❝♦♥❝❡✐t♦ ♣r✐♠✐t✐✈♦ ❝✉❥❛ ✐♠♣♦ss✐❜✐❧✐❞❛❞❡ ❞❡ ❞❡✜♥✐✲❧♦ é ❡✈✐❞❡♥t❡ ♣♦st♦ q✉❡ ♥ã♦ ❡①✐st❡ ♥❡♥❤✉♠ ♦✉tr♦ ❛♥t❡r✐♦r✳ ❈❤❡❣❛♠♦s✱ ♣♦rt❛♥t♦✱ ❛ ✉♠ ❝♦♥❝❡✐t♦ ♣r✐✲ ♠✐t✐✈♦✳ ❖ ♣♦♥t♦ ✭❋✐❣✉r❛ ✺✮✱ ❛ r❡t❛ ✭❋✐❣✉r❛ ✻✮ ❡ ♦ ♣❧❛♥♦ ✭❋✐❣✉r❛ ✼✮ sã♦ ❝❤❛♠❛❞♦s ❞❡ ♥♦çõ❡s ♣r✐♠✐t✐✈❛s ❞❡ ❣❡♦♠❡tr✐❛✱ ♣♦r s❡r❡♠ ❛❝❡✐t❛s s❡♠ ❞❡✜♥✐çã♦✳
❋✐❣✉r❛ ✺✿ P♦♥t♦ P ❋✐❣✉r❛ ✻✿ ❘❡t❛ q✉❡ ♣❛ss❛ ♣♦r ❆ ❡ ❇
❋✐❣✉r❛ ✼✿ P❧❛♥♦α
❆ ♣❛rt✐r ❞❡ss❡s ❝♦♥❝❡✐t♦s ♣r✐♠✐t✐✈♦s ♣♦❞❡♠♦s ❞❡✜♥✐r ♦✉tr♦ ❝♦♠♦✿ s❡❣♠❡♥t♦ ❞❡ r❡t❛✱ s❡♠✐rr❡t❛ ❡ â♥❣✉❧♦✳
• ❉❛❞♦s ❞♦✐s ♣♦♥t♦s ❞✐st✐♥t♦s✱ ❛ r❡✉♥✐ã♦ ❞♦ ❝♦♥❥✉♥t♦ ❞❡ss❡s ❞♦✐s ♣♦♥t♦s ❝♦♠ ♦
❝♦♥❥✉♥t♦ ❞♦s ♣♦♥t♦s q✉❡ ❡stã♦ ❡♥tr❡ ❡❧❡ é ✉♠ s❡❣♠❡♥t♦ ❞❡ r❡t❛ ✭❋✐❣✉r❛ ✽✮✳
❋✐❣✉r❛ ✽✿ ❙❡❣♠❡♥t♦ ❆❇
• ❉❛❞♦s ❞♦✐s ♣♦♥t♦s ❞✐st✐♥t♦ ❆ ❡ ❇✱ ❛ r❡✉♥✐ã♦ ❞♦ s❡❣♠❡♥t♦ ❞❡ r❡t❛ ❆❇ ❝♦♠ ♦
❝♦♥❥✉♥t♦ ❞♦s ♣♦♥t♦s ❳ t❛✐s q✉❡ ❇ ❡stá ❡♥tr❡ ❆ ❡ ❳ é ❛ s❡♠✐rr❡t❛ ❆❇ ✭ ✐♥❞✐❝❛❞❛ ♣♦r−→AB✮
❋✐❣✉r❛ ✾✿ ❙❡♠✐rr❡t❛
• ❉❛❞❛s ❞✉❛s s❡♠✐rr❡t❛s ❞❡ ♠❡s♠❛ ♦r✐❣❡♠✱ ✉♠ â♥❣✉❧♦ ♦✉ r❡❣✐ã♦ ❛♥❣✉❧❛r é ✉♠❛ ❞❛s
❞✉❛s r❡❣✐õ❡s ❞♦ ♣❧❛♥♦ ❧✐♠✐t❛❞❛s ♣❡❧❛s s❡♠✐rr❡t❛s ✭❋✐❣✉r❛ ✶✵✮✳
❋✐❣✉r❛ ✶✵✿ ➶♥❣✉❧♦ABCˆ
❆ ✉♥✐❞❛❞❡ ❞❡ ♠❡❞✐❞❛ ❞❡ â♥❣✉❧♦ ♠❛✐s ✉s❛❞❛ é ♦ ❣r❛✉✱ ✐♥❞✐❝❛❞♦ ♣❡❧♦ sí♠❜♦❧♦ ◦
❝♦❧♦❝❛❞♦ à ❞✐r❡✐t❛ ❞♦ ♥ú♠❡r♦✳ ❯♠ ❣r❛✉ r❡♣r❡s❡♥t❛ 1
360 ❞♦ ❝♦♠♣r✐♠❡♥t♦ ❞❡ ✉♠❛ ❝✐r❝✉♥✲
❢❡rê♥❝✐❛✳ ❊ ♦ ✐♥str✉♠❡♥t♦ ✉s❛❞♦ ♣❛r❛ ♠❡❞✐r â♥❣✉❧♦ é ♦ tr❛♥s❢❡r✐❞♦r ✭❋✐❣✉r❛ ✶✶✮✳
❋✐❣✉r❛ ✶✶✿ ▼♦❞❡❧♦ ❞❡ tr❛♥s❢❡r✐❞♦r
P❛r❛ ♠❡❞✐r â♥❣✉❧♦s ❢❡✐t♦s ♥♦ ▼✉❧t✐♣❧❛♥♦ ❘❡t❛♥❣✉❧❛r✱ ✉s❛r❡♠♦s ♦ ▼✉❧t✐♣❧❛♥♦ ❈✐r✲ ❝✉❧❛r ❡ ❛ ❤❛st❡ tr✐❣♦♥♦♠étr✐❝❛ ❞❡ ♠❛✐♦r ♠❡❞✐❞❛ q✉❡ ❢✉♥❝✐♦♥❛rã♦ ❝♦♠♦ ✉♠ tr❛♥s❢❡r✐❞♦r ✭❋✐❣✉r❛ ✶✷✮✳
✶✳ ❈♦♠ três ♣✐♥♦s ❡ ❞♦✐s ❡❧ást✐❝♦s ❞❡✈❡♠♦s ❢❛③❡r ✉♠ â♥❣✉❧♦ ♥♦ ▼✉❧t✐♣❧❛♥♦ r❡t❛♥❣✉✲ ❧❛r❀
✷✳ ❈♦♠ ♦s ✜①❛❞♦r❡s ♣❛r❛ ❝✐♠❛✱ ❡♥❝❛✐①❡ ❛ ❤❛st❡ tr✐❣♦♥♦♠étr✐❝❛ ♥♦ ❝❡♥tr♦ ❞♦ ▼✉❧t✐✲ ♣❧❛♥♦ ❝✐r❝✉❧❛r✳ ❆❧✐♥❤❡ ❛ ❤❛st❡ ❝♦♠ q✉❛❧q✉❡r ✉♠ ❞♦s q✉❛tr♦ ❣r✉♣♦s ❞❡ três ❢✉r♦s ✐♥t❡r♥♦s ❡ ♣r❡♥❞❛ ♦ ♣✐♥♦ ♠❡♥♦r ♥♦ ❢✉r♦ ❞❛ ❜♦r❞❛❀
✸✳ ❘❡♠♦✈❛ ♦ ♣✐♥♦ ❞♦ ✈ért✐❝❡ ❡ ❡♥❝❛✐①❡ ♦ ❝❡♥tr♦ ❞♦ ▼✉❧t✐♣❧❛♥♦ ❝✐r❝✉❧❛r❀
✹✳ ❆❧✐♥❤❡ ❛ ❤❛st❡ ❝♦♠ ✉♠ ❞♦s ♦✉tr♦s ♣✐♥♦s❀
✺✳ ▼♦✈❛ ❛ ❤❛st❡✱ ❝♦♥t❛♥❞♦ ♦s ❢✉r♦s ❞❛ ❜♦r❞❛✱ ❛té ❛❧✐♥❤❛r ❝♦♠ ♦ ♦✉tr♦ ♣✐♥♦✳ ❈❛❞❛
❢✉r♦ ❝♦♥t❛❞♦ ❝♦rr❡s♣♦♥❞❡ ❛ 5◦✳ ❙❡✱ ♣❛r❛ ❛❧✐♥❤❛r ❝♦♠ ♦ ♦✉tr♦ ♣✐♥♦✱ ❛ ❤❛st❡ ✜❝❛r
❡♥tr❡ ❞♦✐s ❢✉r♦s✱ ❛rr❡❞♦♥❞❛r❡♠♦s ♣❛r❛ 3◦✳
❋✐❣✉r❛ ✶✷✿ ▼❡❞✐♥❞♦ ➶♥❣✉❧♦ ♥♦ ▼✉❧t✐♣❧❛♥♦
❯♠ â♥❣✉❧♦ s❡rá✿ â♥❣✉❧♦ r❡t♦✱ s❡ s✉❛ ♠❡❞✐❞❛ ❢♦r ✐❣✉❛❧ ❛ 90◦❀ â♥❣✉❧♦ ❛❣✉❞♦ s❡
s✉❛ ♠❡❞✐❛ ❢♦r ♠❡♥♦r q✉❡ 90◦❀ ❡ â♥❣✉❧♦ ♦❜t✉s♦ s❡ s✉❛ ♠❡❞✐❞❛ ❢♦r ♠❛✐♦r q✉❡ 90◦ ❡
♠❡♥♦r q✉❡ 180◦ ✭❋✐❣✉r❛ ✶✸✮✳
❋✐❣✉r❛ ✶✸✿ ❚✐♣♦s ❞❡ â♥❣✉❧♦
◆♦ ▼✉❧t✐♣❧❛♥♦✱ ♣❛r❛ s❡ r❡♣r❡s❡♥t❛r ✉♠ â♥❣✉❧♦ r❡t♦✱ ❜❛st❛ ❝♦❧♦❝❛r ❞♦✐s ♣✐♥♦s ❡♠ ✉♠❛ ♠❡s♠❛ ❧✐♥❤❛✱ ❡ ✉♠ ♦✉tr♦ ♣✐♥♦ ❡♠ q✉❛❧q✉❡r ♣♦♥t♦ ❞❛ ❝♦❧✉♥❛ q✉❡ ❥á ♣♦ss✉✐ ✉♠ ♣✐♥♦ ❝♦❧♦❝❛❞♦ ❛♥t❡r✐♦r♠❡♥t❡ q✉❡ s❡rá ♦ ✈ért✐❝❡ ❞♦ â♥❣✉❧♦✳
❉✉❛s r❡t❛s ❞✐st✐♥t❛s✱ ❡♠ ✉♠ ♠❡s♠♦ ♣❧❛♥♦✱ ♣♦❞❡♠ s❡r✿ ♣❛r❛❧❡❧❛s ✭❋✐❣✉r❛ ✶✹✮ s❡ ♥ã♦ t✐✈❡r❡♠ ♥❡♠ ✉♠ ♣♦♥t♦ ❡♠ ❝♦♠✉♠❀ ❝♦♥❝♦rr❡♥t❡s s❡ t✐✈❡r❡♠ ✉♠ ♣♦♥t♦ ❡♠ ❝♦♠✉♠✳ ❆s r❡t❛s ❝♦♥❝♦rr❡♥t❡s ♣♦❞❡♠ s❡r✿ ♣❡r♣❡♥❞✐❝✉❧❛r❡s ✭❋✐❣✉r❛ ✶✺✮ s❡ ❢♦r♠❛r❡♠ q✉❛tr♦ â♥❣✉❧♦s r❡t♦s❀ ♦❜❧✐q✉❛s s❡ ❢♦r♠❛r❡♠ ❞♦✐s â♥❣✉❧♦s ❛❣✉❞♦s ❡ ❞♦✐s â♥❣✉❧♦s ♦❜t✉s♦s✳
❋✐❣✉r❛ ✶✹✿ rks ❋✐❣✉r❛ ✶✺✿ r⊥s
❆ s❡❣✉✐r s❡rá ❛♣r❡s❡♥t❛❞♦ ♦ tr✐â♥❣✉❧♦✱ ✉♠❛ ✜❣✉r❛ ❞❡ ❣r❛♥❞❡ ✐♠♣♦rtâ♥❝✐❛ ♥❛ ❣❡♦✲ ♠❡tr✐❛ ❞❡✈✐❞♦ à s✉❛ ❣r❛♥❞❡ ❛♣❧✐❝❛❜✐❧✐❞❛❞❡✳ ❚❛♥t♦ é q✉❡ s❡✉ ❡st✉❞♦ ❣❡r♦✉ ✉♠ r❛♠♦ ♥❛ ♠❛t❡♠át✐❝❛✿ ❛ tr✐❣♦♥♦♠❡tr✐❛✳
✽ ❚r✐â♥❣✉❧♦
❉❛❞♦s três ♣♦♥t♦s ❆✱ ❇ ❡ ❈ ♥ã♦ ❝♦❧✐♥❡❛r❡s✱ à r❡✉♥✐ã♦ ❞♦s s❡❣♠❡♥t♦sAB ✱AB ❡ AC
❝❤❛♠❛✲s❡ tr✐â♥❣✉❧♦ ❆❇❈ ✭❋✐❣✉r❛ ✶✻✮✳
❋✐❣✉r❛ ✶✻✿ ❚r✐â♥❣✉❧♦ ❆❇❈
• ❱ért✐❝❡s✿ A✱ B ❡C❀
• ▲❛❞♦s✿ AB ✱ AB ❡ AC❀
• ➶♥❣✉❧♦s✿ ABCˆ ✱ BCAˆ ❡CABˆ ✳
◗✉❛♥t♦ ❛♦s ❧❛❞♦s ✉♠ tr✐â♥❣✉❧♦ ♣♦❞❡ s❡r✿
• ❊q✉✐❧át❡r♦✿ s❡ ♣♦ss✉✐r ♦s três ❧❛❞♦s ❝♦♥❣r✉❡♥t❡s ✭❋✐❣✉r❛ ✶✼✮✳
• ■sós❝❡❧❡s✿ s❡ ♣♦ss✉✐r ❛♣❡♥❛s ❞♦✐s ❧❛❞♦s ❝♦♥❣r✉❡♥t❡s ✭❋✐❣✉r❛ ✶✽✮✳
• ❊s❝❛❧❡♥♦✿ s❡ ♣♦ss✉✐r ♦s três ❧❛❞♦s ❞✐❢❡r❡♥t❡s ✭❋✐❣✉r❛ ✶✾✮✳
