Maq ele unifacs lista AV2

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❉✐s❝✐♣❧✐♥❛✿ ▼áq✉✐♥❛s ❡❧étr✐❝❛s
❉♦❝❡♥t❡✿ ❊✉❞❡♠❛r✐♦ ❙♦✉③❛ ❞❡ ❙❛♥t❛♥❛
❯♥✐❢❛❝s
❚❡ór✐❝❛s
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❱♦❝ê ❡s♣❡r❛r✐❛ q✉❡ ✉♠ ❣❡r❛❞♦r ❞❡ ✹✵✵ ❍③ ❢♦ss❡ ♠❛✐♦r ♦✉ ♠❡♥♦r q✉❡ ✉♠ ❣❡r❛❞♦r
❞❡ ✻✵ ❍③ ❝♦♠ ❛s ♠❡s♠❛s ❝❛r❛❝t❡ríst✐❝❛s ♥♦♠✐♥❛✐s ❞❡ ♣♦tê♥❝✐❛ ❡ t❡♥sã♦❄
❏✉st✐✜q✉❡
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❆♦ ❝♦❧♦❝❛r ❡♠ ♣❛r❛❧❡❧♦ ✉♠ ❣❡r❛❞♦r sí♥❝r♦♥♦ ❝♦♠ ❛ r❡❞❡ ♣❡r❝❡❜❡✉✲s❡ q✉❡ ❛s três
❧â♠♣❛❞❛s ❡♥tr❡ ♦ ❣❡r❛❞♦r ❡ ❛ r❡❞❡ ❡st❛✈❛♠ ♣✐s❝❛♥❞♦ s✐♠✉❧t❛♥❡❛♠❡♥t❡ ❝♦♠ ❛
♠❡s♠❛ ❧✉♠✐♥♦s✐❞❛❞❡ ❡ ❢♦✐ s✉❣❡r✐❞♦ ♣❡❧♦ ❡♥❣❡♥❤❡✐r♦ q✉❡ ❛ ❡①❝✐t❛çã♦ ❢♦ss❡
❛✉♠❡♥t❛❞❛✳ ❉❡s❝r❡✈❛ ♦ q✉❡ ❡st❛✈❛ ♦❝♦rr❡♥❞♦ ♣❛r❛ ❛s ❧â♠♣❛❞❛s ❡st❛r❡♠
♣✐s❝❛♥❞♦ ❡ ♦ q✉❡ ♦❝♦rr❡rá ♥❛ s❡q✉ê♥❝✐❛ ❛♣ós ❛ ❡①❝✐t❛çã♦ s❡r ❛✉♠❡♥t❛❞❛✳ ❋❛ç❛
✉♠ ❞✐❛❣r❛♠❛ ❢❛s♦r✐❛❧ ❝♦♠♣❛r❛♥❞♦ ♦s ❢❛s♦r❡s ❞❡ t❡♥sõ❡s ❞♦ ❣❡r❛❞♦r ❡ ❞❛ r❡❞❡
❛♥t❡s ❡ ❞❡♣♦✐s ❞❛ ❡①❝✐t❛çã♦ s❡r ❛✉♠❡♥t❛❞❛✳
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❉❡s❝r❡✈❛ ❝♦♠♦ s❡ ♦❜té♠ ❛s ❝✉r✈❛s ❱ ❡ ♣❛r❛ q✉❡ ❡❧❛s s❡r✈❡♠✳
Pr♦❜❧❡♠❛s
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◆✉♠❛ ❢á❜r✐❝❛ ❤á ❛s s❡❣✉✐♥t❡s ❝❛r❣❛s✿ ♠♦t♦r ❞❡ ✐♥❞✉çã♦ ❡♠ ❣❛✐♦❧❛ ❞❡ ✶✵✵✵ ❤♣✱
✵✱✼ ❞❡ ❢❛t♦r ❞❡ ♣♦tê♥❝✐❛ ♠é❞✐♦ ❡ ❡✜❝✐ê♥❝✐❛ ♠é❞✐❛ ❞❡ ✵✱✽✺❀ ❝❛r❣❛s ❞❡ ✐❧✉♠✐♥❛çã♦
✐♥❝❛♥❞❡s❝❡♥t❡ ❡ ❛q✉❡❝✐♠❡♥t♦ ❞❡ ✶✵✵ ❦❲✳
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❯♠ ♠♦t♦r sí♥❝r♦♥♦ ❢♦✐ ✐♥st❛❧❛❞♦ ♣❛r❛ ♣r♦✈❡r ✸✵✵ ❤♣ ♣❛r❛ ✉♠ ♥♦✈♦
♣r♦❝❡ss♦✳ ❖ ♠♦t♦r sí♥❝r♦♥♦ ♦♣❡r❛ ❝♦♠ ✾✷✪ ❞❡ ❡✜❝✐ê♥❝✐❛✳ ❉❡t❡r♠✐♥❡ ❛
♣♦tê♥❝✐❛ ❛♣❛r❡♥t❡ ❞♦ ♠♦t♦r sí♥❝r♦♥♦ s❡ ♦ ❢❛t♦r ❞❡ ♣♦tê♥❝✐❛ ❣❧♦❜❛❧ ❞❛
❢á❜r✐❝❛ ❡stá ❡♠ ✵✱✾✺✳ ❉❡t❡r♠✐♥❡ t❛♠❜é♠ ♦ ❢❛t♦r ❞❡ ♣♦tê♥❝✐❛ ❞♦ ♠♦t♦r
sí♥❝r♦♥♦✳
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❘❡s♣✿ ✺✹✽✱✷✹ ❦❱❆✱ ✵✱✹✵✽✷ ❛❞✐❛♥t❛❞♦
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❯♠❛ ❢♦♥t❡ tr✐❢ás✐❝❛ ❞❡ ✻✵ ❍③ ❡stá ❞✐s♣♦♥í✈❡❧ ♣❛r❛ ❛❝✐♦♥❛r ♠♦t♦r❡s✳ ❍á ❞✉❛s
♠áq✉✐♥❛s sí♥❝r♦♥❛s ❞✐s♣♦♥í✈❡✐s✱ q✉❡ ♣♦❞❡♠ t❡r s❡✉s ❡✐①♦s ❝♦♥❡❝t❛❞♦s ♣❛r❛ q✉❡
✉♠❛ ❞❡❧❛s ♦♣❡r❡ ❝♦♠♦ ♠♦t♦r ❡ ♦✉tr❛ ❝♦♠♦ ❣❡r❛❞♦r✳ ■❞❡♥t✐✜q✉❡ ❛ ✈❡❧♦❝✐❞❛❞❡ ❡ ♦
♥ú♠❡r♦ ❞❡ ♣♦❧♦s ❞❡s❡❥❛❞♦s ❞❡ ❝❛❞❛ ✉♠❛ ❞❛s ♠áq✉✐♥❛s ♣❛r❛ s❡ ♦❜t❡r ✈✐❛ ❛
♠áq✉✐♥❛ q✉❡ ♦♣❡r❛ ❝♦♠♦ ❣❡r❛❞♦r ✉♠❛ t❡♥sã♦ ❞❡✿
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✶✽✵ ❍③
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✺✵✵ ❍③
Pr♦❜❧❡♠❛s
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❖s ❞❛❞♦s ❞♦s ❡♥s❛✐♦s ❞❛ ♠áq✉✐♥❛ sí♥❝r♦♥❛ ❝♦♥❡❝t❛❞❛ ❡♠ ❨✱ ✷✺ ❦❱✱ ✼✺✵ ❦❱❆✱ ✻✵
❍③ ❡ ✸✻✵✵ r♣♠ ❡stã♦ ♠♦str❛❞♦s ♥❛ t❛❜❡❧❛ ❛❜❛✐①♦✳ ❯s❛♥❞♦ ❡st❡s ❞❛❞♦s ❢❛ç❛ ♦
q✉❡ é s♦❧✐❝✐t❛❞♦✿
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❉❡t❡r♠✐♥❡ ♦ ♥ú♠❡r♦ ❞❡ ♣♦❧♦s ❞❛ ♠áq✉✐♥❛
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❉❡t❡r♠✐♥❡ ♦s ✈❛❧♦r❡s ❞❛s r❡❛tâ♥❝✐❛s ♥ã♦✲s❛t✉r❛❞❛ ❡ s❛t✉r❛❞❛ ❡♠ ♦❤♠s ❡
❡♠ ♣♦r ✉♥✐❞❛❞❡
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❖ t❡st❡ ❞❡ ❝✉rt♦✲❝✐r❝✉✐t♦ ❢♦✐ r❡❛❧✐③❛❞♦ ❝♦♠ ❝♦rr❡♥t❡ ❞❡ ❝❛♠♣♦ ❝♦♥st❛♥t❡
✭✶✺✵✵❆✮✱ ♠❛s ❡♠ ❞✐❢❡r❡♥t❡s ✈❡❧♦❝✐❞❛❞❡s ✭✶✵✵✵r♣♠✱ ✷✵✵✵r♣♠✱ ✸✵✵✵r♣♠ ❡
✸✻✵✵r♣♠✮✳ ❉❡t❡r♠✐♥❡ ❛ ❝♦rr❡♥t❡ ❞❡ ❝✉rt♦ ❝✐r❝✉✐t♦ ♥❡ss❛s ✈❡❧♦❝✐❞❛❞❡s
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❉❡t❡r♠✐♥❡ ❛ ❝♦rr❡♥t❡ ❞❡ ❝❛♠♣♦ s❡ ❛ ♠áq✉✐♥❛s sí♥❝r♦♥❛ ❡♥tr❡❢❛ ♣♦tê♥❝✐❛
❛♣❛r❡♥t❡ ♥♦♠✐♥❛❧ ❛♦ ❜❛rr❛♠❡♥t♦ ✐♥✜♥✐t♦ ❝♦♠ ❢❛t♦r ❞❡ ♣♦tê♥❝✐❛ ✵✱✾
❛tr❛s❛❞♦
If ✭❆✮ VLL ✭❦❱✮ Ia ✭❆✮ VLL ✭❦❱✮
❝✐r❝✉✐t♦ ❛❜❡rt♦ ❝✉rt♦✲❝✐r❝✉✐t♦ ❧✐♥❤❛ ❞❡ ❡♥tr❡❢❡rr♦
✶✺✵✵ ✷✺ ✶✵✳✵✵✵ ✸✵
Pr♦❜❧❡♠❛s
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❯♠❛ ♠áq✉✐♥❛ sí♥❝r♦♥❛ tr✐❢ás✐❝❛ ❡♠ ❨✱ ❞❡ ✶✵ ▼❱❆ ❡ ✶✹ ❦❱ é ❝♦♥❡❝t❛❞❛ ❛ ✉♠❛
r❡❞❡ tr✐❢ás✐❝❛ ❞❡ ✶✹ ❦❱ ❡ ✻✵ ❍③✳ ❊❧❛ ❞r❡♥❛ ✺ ▼❲ ❝♦♠ ✉♠ ❢❛t♦r ❞❡ ♣♦tê♥❝✐❛
❛❞✐❛♥t❛❞♦✳
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❉❡t❡r♠✐♥❡ ♦s ✈❛❧♦r❡s ❞❛ ❝♦rr❡♥t❡ ❞❡ ❛r♠❛❞✉r❛✱ t❡♥sã♦ ✐♥t❡r♥❛ ❞❡
❛r♠❛❞✉r❛ ✭t❡♥sã♦ ❞❡ ❡①❝✐t❛çã♦✮ ❡ ❛ ❝♦rr❡♥t❡ ❞❡ ❝❛♠♣♦✳ ❉❡s❡♥❤❡ ♦
❞✐❛❣r❛♠❛ ❢❛s♦r✐❛❧✳ ❘❡s♣✳✿ ✵, ✺✽✽ ✸✶, ✽➦♣✉✱ ✶, ✸✷✼✷ −✶✽, ✺
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♣✉ ❡ ✷✻✺✱✹✹ ❆
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❖❜s✶✿ ❱❡❥❛ ❡①❡♠♣❧♦ ✻✳✷ ❞♦ P✳ ❈✳ ❙❡♥
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❖❜s✷✿ ❱❡r ❣rá✜❝♦s ❞❛s ❝✉r✈❛s ♥♦ ♣ró①✐♠♦ s❧✐❞❡✳
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❖❜s✸✿ ❉❡s♣r❡③❡ ❛ r❡s✐stê♥❝✐❛ ❞❡ ❛r♠❛❞✉r❛✳ ❆ r❡❛tâ♥❝✐❛ ❞❛
❛r♠❛❞✉r❛ ❞❛ ♠áq✉✐♥❛ ❞❡✈❡ s❡r ♦❜t✐❞❛ ❛ ♣❛rt✐r ❞❡ ❡♥s❛✐♦ ♣ré✈✐♦ ❝✉❥♦s
❞❛❞♦s sã♦ ♠♦str❛❞♦s ❛❜❛✐①♦✿
If ✭❆✮ VLL ✭❦❱✮ Ia ✭❆✮ VLL ✭❦❱✮
❝✐r❝✉✐t♦ ❛❜❡rt♦ ❝✉rt♦✲❝✐r❝✉✐t♦ ❧✐♥❤❛ ❞❡ ❡♥tr❡❢❡rr♦
✶✵✵ ✾
✶✽ ✹✾✵
✶✺✵ ✶✷
✷✵✵ ✶✹
✷✺✵ ✶✺✱✸
✸✵✵ ✶✺✱✾
✸✺✵ ✶✻✱✹
Pr♦❜❧❡♠❛s
Pr♦❜❧❡♠❛s
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❯♠ ♠♦t♦r sí♥❝r♦♥♦ ❝♦♠ r♦t♦r ❝✐❧✐♥❞r✐❝♦ ❞❡ ✷✺✵ ❤♣✱ ✷✸✵✵ ❱✱ ✻✵ ❍③ ❡ ❝♦♥❡❝t❛❞♦
❡♠ ❨ ♣♦ss✉✐ r❡❛tâ♥❝✐❛ sí♥❝r♦♥❛ ♣♦r ❢❛s❡ ❞❡ ✶✶Ω✳ ◗✉❛♥❞♦ ❡❧❡ ♦♣❡r❛ ❞r❡♥❛♥❞♦
✶✻✺✱✽❦❲ ❡stá ❝♦♠ â♥❣✉❧♦ ❞❡ ♣♦tê♥❝✐❛ ❞❡ ✶✺➦ ❡❧étr✐❝♦s✳ ❊♥❝♦♥tr❡ ♦ q✉❡ é
s♦❧✐❝✐t❛❞♦✿
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❉❡t❡r♠✐♥❡ ❛ t❡♥sã♦ ❞❡ ❡①❝✐t❛çã♦ ✭t❡♥sã♦ ✐♥t❡r♥❛ ❞❡ ❛r♠❛❞✉r❛✮ ♣♦r ❢❛s❡
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❉❡t❡r♠✐♥❡ ❛ ❝♦rr❡♥t❡ ❞❡ ❧✐♥❤❛ ❞❛ ❢♦♥t❡
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❉❡t❡r♠✐♥❡ ♦ ❢❛t♦r ❞❡ ♣♦tê♥❝✐❛ ❞❛ ❢♦♥t❡
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❙❡ ❛ ❝❛r❣❛ ♠❡❝â♥✐❝❛ é r❡t✐r❛❞❛ ❡ t♦❞❛s ❛s ♣❡r❞❛s sã♦ ❞❡s♣r❡③í✈❡✐s✿
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❉❡t❡r♠✐♥❡ ❛ ♥♦✈❛ ❝♦rr❡♥t❡ ❞❡ ❧✐♥❤❛ ❡ ♦ ❢❛t♦r ❞❡ ♣♦tê♥❝✐❛ ❞❛ ❢♦♥t❡
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❉❡s❡♥❤❡ ♦ ❞✐❛❣r❛♠❛ ❢❛s♦r✐❛❧ ♣❛r❛ ❛ ❝♦♥❞✐çã♦ ❛♥t❡r✐♦r
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P♦r q✉❡ ✈❛❧♦r ♣♦r❝❡♥t✉❛❧ ❞❡✈❡ s❡r ❞✐♠✐♥✉✐❞❛ ❛ ❝♦r❡♥t❡ ❞❡ ❝❛♠♣♦
♣❛r❛ ♠✐♥✐♠✐③❛r ❛ ❝♦rr❡♥t❡ ❞❡ ❧✐♥❤❛❄ ❈♦♥s✐❞❡r❛r q✉❡ ♥ã♦ ❤á
s❛t✉r❛çã♦ ♠❛❣♥ét✐❝❛
Pr♦❜❧❡♠❛s
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❯♠❛ ♠áq✉✐♥❛ sí♥❝r♦♥❛ tr✐❢ás✐❝❛ ❞❡ ♣♦❧♦s s❛❧✐❡♥t❡s✱ ✶✵✵ ▼❱❆✱ ✶✷ ❦❱✱ ✻✵ ❍③
♣♦ss✉✐ r❡❛tâ♥❝✐❛s ❞❡ ❡✐①♦s ❞✐r❡t♦ ❡ ❡♠ q✉❛❞r❛t✉r❛ ❞❡ r❡s♣❡❝t✐✈❛♠❡♥t❡ ✶ ♣✉ ❡ ✵✱✼
♣✉✳ ❆ ♠áq✉✐♥❛ ♦♣❡r❛ ❝♦♥❡❝t❛❞❛ ❛ ✉♠ ❜❛rr❛♠❡♥♦ ✐♥✜♥✐t♦ ❡ ❡♥tr❡❣❛ ✼✷ ▼❲ ❝♦♠
❢❛t♦r ❞❡ ♣♦tê♥❝✐❛ ❞❡ ✵✱✾ ❛tr❛s❛❞♦✳ ❆ r❡s✐stê♥❝✐❛ ❡ ❛r♠❛❞✉r❛ ♣♦❞❡ s❡r ❞❡s♣r❡③❛❞❛✳
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❉❡t❡r♠✐♥❡ ❛ t❡♥sã♦ ❞❡ ❡①❝✐t❛çã♦ ❡ ♦ â♥❣✉❧♦ ❞❡ ♣♦tê♥❝✐❛✳ ❉❡s❡♥❤❡ ♦
❞✐❛❣r❛♠❛ ❢❛s♦r✐❛❧ ❝♦♠ ❛ t❡♥sã♦ t❡r♠✐♥❛❧ ❝♦♠♦ s❡♥❞♦ ❛ r❡❢❡rê♥❝✐❛✳
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❉❡t❡r♠✐♥❡ ❛ ♠á①✐♠❛ ♣♦tê♥❝✐❛ q✉❡ ♦ ❣❡r❛❞♦r sí♥❝r♦♥♦ ♣♦❞❡ ❢♦r♥❡❝❡r s❡ ❛
❝♦rr❡♥t❡ ❞❡ ❝❛♠♣♦ é ③❡r❛❞❛✳ ❉❡t❡r♠✐♥❡ ❛ ❝♦rr❡♥t❡ ❞❡ ❛r♠❛❞✉r❛ ❡ ♦ ❢❛t♦r
❞❡ ♣♦tê♥❝✐❛ ♣❛r❛ ❡st❛ ❝♦♥❞✐çã♦✳ ❉❡s❡♥❤❡ ♦ ❞✐❛❣r❛♠❛ ❢❛s♦r✐❛❧
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❖❜s✳✿ ✈❡❥❛ ❡①❡♠♣❧♦s ✻✳✼ ❡ ✻✳✽ ❞♦ P✳ ❈✳ ❙❡♥
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❘❡s♣✳✿ ✶, ✺✷✵✹ ♣✉✱ ✷✷, ✵✺✷➦❀ ✷✶✱✹✸ ▼❲✱ ✶✱✷✸✸ ♣✉✱ ❋P❂✵✱✶✼✸✻ ✭❛❞✐❛♥t❛❞♦✮