O problema da partição

❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❘✉r❛❧ ❞❡ P❡r♥❛♠❜✉❝♦

Pr♦❥❡t♦ ❡ ❆♥á❧✐s❡ ❞❡ ❆❧❣♦r✐t♠♦s

❇r❛♥❝❤ ❛♥❞ ❇♦✉♥❞

Pr♦❢✳ ❚✐❛❣♦ ❇✉❛rq✉❡ ❆ss✉♥çã♦ ❞❡ ❈❛r✈❛❧❤♦

❯♥✐❞❛❞❡ ❆❝❛❞ê♠✐❝❛ ❞❡ ●❛r❛♥❤✉♥s ✕ ❯❋❘P❊ ❇❛❝❤❛r❡❧❛❞♦ ❡♠ ❈✐ê♥❝✐❛s ❞❛ ❈♦♠♣✉t❛çã♦

✼ ❞❡ ❞❡③❡♠❜r♦ ❞❡ ✷✵✶✽

❘♦t❡✐r♦

✶ ❖ ♣r♦❜❧❡♠❛ ❞❛ ♣❛rt✐çã♦

✷ Pr♦❜❧❡♠❛s ❞❡ ♦t✐♠✐③❛çã♦

✸ ❇✉s❝❛ ❡①❛✉st✐✈❛

✹ ❇r❛♥❝❤ ❛♥❞ ❇♦✉♥❞

✺ ❊①❡r❝í❝✐♦

❖ ♣r♦❜❧❡♠❛ ❞❛ ♣❛rt✐çã♦

• _{❯♠ ❝♦♥❥✉♥t♦ ❞❡ ♦❜❥❡t♦s✳} • _{❈❛❞❛ ♦❜❥❡t♦ t❡♠ ✉♠ ♣❡s♦✳}

• _{❉✐✈✐❞✐r ♦s ♦❜❥❡t♦s ❡♠ ❞♦✐s ❣r✉♣♦s s❡♥❞♦ q✉❡ ❝❛❞❛ ❣r✉♣♦ t❡♠ ♦}

♠❡s♠♦ ♣❡s♦✳

• _{P❛r❛ ✉♠ ❝♦♥❥✉♥t♦ ❝♦♠} n ❣r✉♣♦s sã♦2n ♣♦ssí✈❡✐s ♣❛rt✐çõ❡s✳

• _{❊①❡♠♣❧♦✿} p=_{2_,4_,1_,1_}✳ ❙♦❧✉çã♦ _G1 =_{4_}✱ _G2 =_{2_,1_,1_}✱ ✶✻ ✭= 24✮ ♣❛rt✐çõ❡s ❡ ❛♣❡♥❛s ✷ s♦❧✉çõ❡s✳

• _{P❛r❛ ✺✵ ✐t❡♥s sã♦} 250 ♥ós ❡ ❛♣r♦①✐♠❛❞❛♠❡♥t❡₁

,13_×1015 s♦❧✉çõ❡s✳

➪r✈♦r❡ ❞❡ ❜✉s❝❛

• k✲és✐♠♦ ♥í✈❡❧ ❞❛ ár✈♦r❡ ❝♦rr❡s♣♦♥❞❡ ❛♦ k✲és✐♠♦ ✐t❡♠✳

• _{❖ r❛♠♦ ♣❛r❛ ❡sq✉❡r❞❛ ✐♥❞✐❝❛ q✉❡ ♦ ✐t❡♠} k ❢♦✐ ✐♥s❡r✐❞♦ ♥♦ ❣r✉♣♦ ✶✱ ♣❛r❛ ❛ ❞✐r❡✐t❛ ♥♦ ❣r✉♣♦ ✷✳

• _{❊①❡♠♣❧♦✿} p=_{2_,4_,1_,1_}✱ ✶✻ ✭= 24✮ ❢♦❧❤❛s ❡ ❛♣❡♥❛s ❞✉❛s s♦❧✉çõ❡s✳

Pr♦❜❧❡♠❛s ❞❡ ♦t✐♠✐③❛çã♦

• _{❉✉❛s ❢♦r♠❛s ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❛ ♣❛rt✐çã♦✳} • _{Pr♦❜❧❡♠❛ ❞❡ s❛t✐s❢❛çã♦ ❞❡ r❡str✐çõ❡s✳}

• _{❱❡r✐✜❝❛r s❡ ❡①✐st❡ ✉♠❛ s♦❧✉çã♦✿ ❡①✐st❡ ❛❧❣✉♠❛ ❢♦r♠❛ ❞❡}

❞✐✈✐❞✐r ♦s ❡❧❡♠❡♥t♦s ♣❛r❛ q✉❡ ❝❛❞❛ ♣❛rt✐çã♦ t❡♥❤❛ ♦ ♠❡s♠♦ ♣❡s♦❄

• _{❘❡s♣♦st❛ ❜♦♦❧❡❛♥❛✱ ❡①✐st❡ ♦✉ ♥ã♦ ❛ s♦❧✉çã♦} • _{Pr♦❜❧❡♠❛ ❞❡ ♦t✐♠✐③❛çã♦✳}

• _{❊♥❝♦♥tr❛r ❛ ♠❡❧❤♦r s♦❧✉çã♦ ♣♦ssí✈❡❧✿ ❡♥❝♦♥tr❛r ❛ s♦❧✉çã♦}

❝♦♠ ❛ ♠❡♥♦r ❞✐❢❡r❡♥ç❛ ❞❡ ♣❡s♦s ❡♥tr❡ ♦s ❞♦✐s ❝♦♥❥✉♥t♦s✳

• _{❘❡s♣♦♥t❛ ✐♥t❡✐r❛✳}

❱❛♥t❛❣❡♥s ❞♦ ♣r♦❜❧❡♠❛ ❞❡ ♦t✐♠✐③❛çã♦

• _{❆ r❡s♣♦st❛ ♣♦❞❡ s❡r ❝♦♥✈❡rt✐❞❛ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❡ s❛t✐s❢❛çã♦ ❞❡}

r❡str✐çõ❡s ✭❞✐❢❡r❡♥ç❛ ❂ ✵✮✳

• _{▼❛✐s ✢❡①í✈❡❧ ✭r❡❧❛①❛çã♦ ❞♦ ♣r♦❜❧❡♠❛✮✿ ♣♦❞❡ ❛❝❤❛r ❛❧❣✉♠❛}

s♦❧✉çã♦ ❛♣r♦①✐♠❛❞❛ q✉❛♥❞♦ ♥ã♦ ❡①✐st❡ ❛ s♦❧✉çã♦ ✐❞❡❛❧✳

• _{❖ ♣r♦❜❧❡♠❛ ❞❡ s❛t✐s❢❛çã♦ ❞❡ r❡str✐çõ❡s ♣♦❞❡ ❞❡♠♦r❛r ❞❡♠❛✐s ❡}

❝♦♥t✐♥✉❛r ❡①❡❝✉t❛♥❞♦ s❡♠ ❞❛r ❝❡rt❡③❛ ❞❡ q✉❡ ❡①✐st❡ ❛ ♠❡❧❤♦r r❡s♣♦st❛✳

• _{❖ ♣r♦❜❧❡♠❛ ❞❡ ♦t✐♠✐③❛çã♦ ♣♦❞❡ ❞❛r ✉♠ ❜♦❛ r❡s♣♦st❛ ❡♠ ✉♠}

t❡♠♣♦ r❛③♦á✈❡❧ ❡ ❝♦♥t✐♥✉❛r ♣r♦❝✉r❛♥❞♦ ♣♦r ✉♠❛ r❡s♣♦st❛ ♠❡❧❤♦r✳

❇✉s❝❛ ❡①❛✉st✐✈❛

• _{❱✐s✐t❛ t♦❞♦s ♦s ♣♦ssí✈❡✐s ♥ós✳}

• _{P♦❞❡ s❡r ✐♠♣❧❡♠❡♥t❛❞❛ ✉t✐❧✐③❛♥❞♦ r❡❝✉rsã♦✳}

• _{❆ r❡❝✉rsã♦ ♠❛♥té♠ ♦ r❡❣✐str♦ ❡♠ q✉❡ ♥í✈❡❧ ❞❛ ár✈♦r❡ ❡stá✳} • _{❆❧❣♦r✐t♠♦ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❛ ♣❛rt✐çã♦✱ ❞✐✈✐❞✐❞♦ ❡♠ ❞✉❛s}

❢✉♥çõ❡s✳

• _{❋✉♥çã♦ ❞❡ ✐♥✐❝✐❛❧✐③❛çã♦✳} • _{❋✉♥çã♦ r❡❝✉rs✐✈❛✳}

❆❧❣♦r✐t♠♦ ❞❡ ❜✉s❝❛ ❡①❛✉st✐✈❛

• _{◆ã♦ ✐♥t❡rr♦♠♣❡ ♦ ❛❧❣♦r✐t♠♦ ❛♥t❡s ❞❡ ♣❡r❝♦rr❡r ❡①❛t❛♠❡♥t❡}

t♦❞♦s ♦s ❝❛♠✐♥❤♦s✳

• _{❋✉♥çã♦ ❞❡ ■♥✐❝✐❛❧✐③❛çã♦}

• _{■♥✐❝✐❛❧✐③❛ ❛ ♠❡❧❤♦r s♦❧✉çã♦✳} • _{❋❛③ ❛ ❝❤❛♠❛❞❛ r❡❝✉rs✐✈❛ ✐♥✐❝✐❛❧✳} • _{❋✉♥çã♦ r❡❝✉rs✐✈❛}

• _{❈❛s♦ ❜❛s❡✿ ✈❡r✐✜❝❛ s❡ t♦❞♦s ♦s ✐t❡♥s ❢♦r❛♠ ❛❧♦❝❛❞♦s✳} • _{◆♦ ❝❛s♦ ❜❛s❡ ❛ ♠❡❧❤♦r s♦❧✉çã♦ ♣♦❞❡ s❡r ❛t✉❛❧✐③❛❞❛✳} • _{❋❛③ ❞✉❛s ❝❤❛♠❛❞❛s r❡❝✉rs✐✈❛s✿}

• _{❛tr✐❜✉✐♥❞♦ ♦ ✐t❡♠ ❛♦ ❣r✉♣♦ ✶❀} • _{❛tr✐❜✉✐♥❞♦ ♦ ✐t❡♠ ❛♦ ❣r✉♣♦ ✷✳}

❋✉♥çã♦ ❞❡ ■♥✐❝✐❛❧✐③❛çã♦

• _{■♥✐❝✐❛❧✐③❛ ❛ ♠❡❧❤♦r s♦❧✉çã♦✳} • _{❋❛③ ❛ ❝❤❛♠❛❞❛ r❡❝✉rs✐✈❛ ✐♥✐❝✐❛❧✳}

• _{❖ ✈❛❧♦r ③❡r♦ ❝♦♠♦ ♣❛râ♠❡tr♦ ❞❛ ❝❤❛♠❛❞❛ r❡❝✉rs✐✈❛ ✐♥❞✐❝❛}

q✉❛♥t♦s ✐t❡♥s ❢♦r❛♠ ❛❧♦❝❛❞♦s ✭♣r♦❢✉♥❞✐❞❛❞❡ ❞❛ ár✈♦r❡✮✳

• _{❖❜s❡r✈❡ q✉❡ ♥ã♦ ❡①✐st❡ r❡t♦r♥♦ ❞❡ r❡s♣♦st❛✳}

• _{❆ ♠❡❧❤♦r s♦❧✉çã♦ é ❛r♠❛③❡♥❛❞❛ ❡♠ ✉♠❛ ✈❛r✐á✈❡❧ ❡①t❡r♥❛✳} • _{❖ ❛❧❣♦r✐t♠♦ só ♣❛r❛ ❞❡♣♦✐s ❞❡ ❡s❣♦t❛r ✭❡①❛✉r✐r✮ t♦❞♦s ♦s}

❝❛♠✐♥❤♦s ❞❛ ár✈♦r❡ ❞❡ ❜✉s❝❛✳

❆ ♠❡❧❤♦r s♦❧✉çã♦ ❛té ♦ ♠♦♠❡♥t♦

• _{✭❜❡st s♦❧✉t✐♦♥✮}

• _{P♦❞❡ s❛❧✈❛r ❛♣❡♥❛s ♦ ✈❛❧♦r ✭❞❛ ❛✈❛❧✐❛çã♦✮ ❞❛ s♦❧✉çã♦✳} • _{P♦❞❡ ❛❞✐❝✐♦♥❛❧♠❡♥t❡ s❛❧✈❛r ❛ s♦❧✉çã♦ ✭q✉❛✐s ✐t❡♥s ♥♦ ❣r✉♣♦}

✶ ❡ ✷✮✳

• _{■♥✐❝✐❛❧✐③❛çã♦}

• _{❚♦❞♦s ♦s ✐t❡♥s ❡♠ ✉♠ ú♥✐❝♦ ❣r✉♣♦✳}

• _{❆ ❢✉♥çã♦ ♦❜❥❡t✐✈♦ é ❛ ❞✐❢❡r❡♥ç❛ ❡♥tr❡ ♦s ♣❡s♦s ❞❡ ❝❛❞❛}

❣r✉♣♦✳

• _{❙♦♠❛ ❞❡ t♦❞♦s ♦s ♣❡s♦s✳}

• _{❆t✉❛❧✐③❛çã♦ é r❡❛❧✐③❛❞❛ ❝❛❞❛ ✈❡③ q✉❡ ❛ ❢✉♥çã♦ r❡❝✉rs✐✈❛ ❡♥❝♦♥tr❛}

✉♠ ♠❡❧❤♦r r❡s✉❧t❛❞♦✳

❋✉♥çã♦ r❡❝✉rs✐✈❛ ■

• _{❈❛s♦ ❜❛s❡✿ ✈❡r✐✜❝❛ s❡ t♦❞♦s ♦s ✐t❡♥s ❢♦r❛♠ ❛❧♦❝❛❞♦s✳} • _{◆♦ ❝❛s♦ ❜❛s❡ ❛ ♠❡❧❤♦r s♦❧✉çã♦ ♣♦❞❡ s❡r ❛t✉❛❧✐③❛❞❛✳} • _{❋❛③ ❞✉❛s ❝❤❛♠❛❞❛s r❡❝✉rs✐✈❛s✿}

• _{❛tr✐❜✉✐♥❞♦ ♦ ✐t❡♠ ❛♦ ❣r✉♣♦ ✶❀} • _{❛tr✐❜✉✐♥❞♦ ♦ ✐t❡♠ ❛♦ ❣r✉♣♦ ✷✳}

• _{◆ã♦ ✐♥t❡rr♦♠♣❡ ❛ ❡①❡❝✉çã♦ s♦❜ ♥❡♥❤✉♠❛ ❝♦♥❞✐çã♦✳}

• _{❋❛③ s❡♠♣r❡ ❛s ❞✉❛s ❝❤❛♠❛❞❛s r❡❝✉rs✐✈❛s ✭❛✈❛❧✐❛♥❞♦ ♦s ❞♦✐s}

❝❛s♦s ♣♦ssí✈❡✐s✮✳

• _{❊①❤❛✉st✐✈❡❙❡❛r❝❤✭■♥t❡❣❡r✿ ♥❡①t❴✐♥❞❡①✮}

• _{♥❡①t❴✐♥❞❡① é ❛ ♣r♦❢✉♥❞✐❞❛❞❡ ❞❛ ár✈♦r❡ ✭♦ í♥❞✐❝❡ ❞♦ ♣ró①✐♠♦}

♥ú♠❡r♦ q✉❡ s❡ q✉❡r ❛❞✐❝✐♦♥❛r✮✳

• _{♠❛①❴✐♥❞❡① é ♦ t♦t❛❧ ❞❡ ✐t❡♥s ❞♦ ♣r♦❜❧❡♠❛✳}

❋✉♥çã♦ r❡❝✉rs✐✈❛ ■■

❋✉♥çã♦ r❡❝✉rs✐✈❛ ■■■

✶✳ ♥❡①t❴✐♥❞❡① ❃ ♠❛①❴✐♥❞❡①

• _{❙ó é tr✉❡ s❡ q✉✐s❡r ❛❞✐❝✐♦♥❛r ✉♠ ✐t❡♠ ❛ ♠❛✐s q✉❡ ♦ t♦t❛❧✱} • _{✐st♦ é✱ t♦❞♦s ♦s ✐t❡♥s ❥á ❢♦r❛♠ ❛❧♦❝❛❞♦s✳}

✷✳ ❯♠❛ ✈❡③ q✉❡ s❡ t❡♠ ✉♠❛ ❛❧♦❝❛çã♦ ❝♦♠♣❧❡t❛✱ ♣♦❞❡✲s❡ ❛✈❛❧✐❛r ❛ s♦❧✉çã♦ ❡✱ s❡ ❢♦r ♦ ❝❛s♦✱ s✉❜st✐t✉✐r ❛ ♠❡❧❤♦r s♦❧✉çã♦✳

✸✳ ❊♥tr❛ ♥♦ ❊❧s❡ s❡ ♥ã♦ ❝♦♠♣❧❡t♦✉ ✉♠❛ ❛❧♦❝❛çã♦✳

✹✳ ❆❧♦❝❛ ♦ ✐t❡♠ ❛t✉❛❧ ♥♦ ❣✉♣♦ ✵❀ ❢❛③ ❛ ❝❤❛♠❛❞❛ r❡❝✉rs✐✈❛❀ ❞❡s❛❧♦❝❛ ♦ ✐t❡♠✳

✺✳ ❆❧♦❝❛ ♦ ✐t❡♠ ❛t✉❛❧ ♥♦ ❣✉♣♦ ✶❀ ❢❛③ ❛ ❝❤❛♠❛❞❛ r❡❝✉rs✐✈❛❀ ❞❡s❛❧♦❝❛ ♦ ✐t❡♠✳

◗✉❡stõ❡s ❞❡ ✐♠♣❧❡♠❡♥t❛çã♦

• _{❆✈❛❧✐❛çã♦ ❞❛ s♦❧✉çã♦✿ s♦♠❛r t♦❞♦s ♦s ♣❡s♦s ❞❡ ❝❛❞❛ ❣r✉♣♦ ❡}

❝❛❧❝✉❧❛r ♦ ✈❛❧♦r ❛❜s♦❧✉t♦ ❞❛ ❞✐❢❡r❡♥ç❛ ❞❡st❛s s♦♠❛s✳

• _{❘❡♣r❡s❡♥t❛çã♦ ❞❛s s♦❧✉çõ❡s}

• _{P❛r❛ ❛ s♦❧✉çã♦ ♣❛r❝✐❛❧ ❡ ♣❛r❛ ♠❡❧❤♦r s♦❧✉çã♦ ❛té ♦ ♠♦♠❡♥t♦✳} • _{❆ ❛✈❛❧✐❛çã♦ ❞❛ s♦❧✉çã♦ é ✉♠ ❡s❝❛❧❛r ✭✐♥t❡✐r♦ ♦✉ ♣♦♥t♦ ✢✉t✉❛♥t❡✱}

❞❡♣❡♥❞❡♥❞♦ ❞❡ ❝♦♠♦ sã♦ r❡♣r❡s❡♥t❛❞♦s ♦s ♣❡s♦s✮✳

• _{❆ s♦❧✉çã♦ é ✉♠ ✈❡t♦r✱ ❛}k✲és✐♠❛ ♣♦s✐çã♦ é ♦ ♥ú♠❡r♦ ❞♦ ❣r✉♣♦

♥♦ q✉❛❧ ❢♦✐ ❛❧♦❝❛❞♦ ❛q✉❡❧❡ ✐t❡♠✳

• _{▼❡❧❤♦r❛♠❡♥t♦✿ ✏❝✉rt♦ ❝✐r❝✉✐t♦✑ ✭s❤♦rt ❝✐r❝✉✐t✮} • _{❆ ♠❡♥♦r ❞✐❢❡r❡♥ç❛ ♣♦ssí✈❡❧ é ③❡r♦✳}

• _{■♥t❡rr♦♠♣❡r ♦ ❛❧❣♦r✐t♠♦ tã♦ ❧♦❣♦ ❡♥❝♦♥tr❡ ❛ ♠❡❧❤♦r s♦❧✉çã♦} ♣♦ssí✈❡❧✳

• _{❊①❡♠♣❧♦✿ ✷✵ ✐t❡♥s✱ ✷✳✵✾✼✳✶✺✵ ♥ós❀ ❡♥❝♦♥tr❛ ❛ s♦❧✉çã♦ ✈✐s✐t❛♥❞♦} ❛♣❡♥❛s ✹✳✵✾✽ ♥ós ✭♦s r❡s✉❧t❛❞♦s ✈❛r✐❛♠ ❞❡♣❡♥❞❡♥❞♦ ❞♦ ❝♦♥❥✉♥t♦ ❞❡ ♣❡s♦s✮✳

❇r❛♥❝❤ ❛♥❞ ❇♦✉♥❞

• _{❯♠❛ té❝♥✐❝❛ ❞❡ ❜✉s❝❛ ♠❛✐s ❡✜❝✐❡♥t❡ q✉❡ ❛ ❜✉s❝❛ ❡①❛✉st✐✈❛✳} • _{❆✈❛❧✐❛ ♣r❡✈✐❛♠❡♥t❡ q✉❛❧ ♦ ♠❡❧❤♦r r❡s✉❧t❛❞♦ q✉❡ ❝♦♥s❡❣✉✐rá}

❛❧❝❛♥ç❛r ❡♠ ✉♠ ❞❡t❡r♠✐♥❛❞♦ ❝❛♠✐♥❤♦✳

• _{❙❡ ❛s ♣❡r❝❡♣t✐✈❛s ♥ã♦ sã♦ ❜♦❛s✱ ❛❜❛♥❞♦♥❛ ❛ ❜✉s❝❛ ♥❛q✉❡❧❛}

s✉❜ár✈♦r❡✳

• _{❊①❡♠♣❧♦ ✭♣r♦❜❧❡♠❛ ❞♦ ♣❛rt✐❝✐♦♥❛♠❡♥t♦✮✿}

• _{❆✈❛❧✐❛çã♦ ❞❛ ♠❡❧❤♦r s♦❧✉çã♦ ❛té ♦ ♠♦♠❡♥t♦✿ ✷✵✳} • _{❙♦♠❛ ❞♦s ♣❡s♦s ❞♦s ✐t❡♥s ❞♦ ❣r✉♣♦ ✶✿ ✶✵✵✳} • _{❙♦♠❛ ❞♦s ♣❡s♦s ❞♦s ✐t❡♥s ❞♦ ❣r✉♣♦ ✷✿ ✺✵✳} • _{❙♦♠❛ ❞♦s ♣❡s♦s ❞♦s ✐t❡♥s ♥ã♦ ❛❧♦❝❛❞♦s✿ ✶✹✳} • _{▼❡❧❤♦r s♦❧✉çã♦ ❛❧❝❛♥çá✈❡❧ ♣❡❧♦ r❛♠♦ ❛t✉❛❧}

|100−(50 + 14)|= 36✳

• _{◆ã♦ é ♣♦ssí✈❡❧ ❡♥❝♦♥tr❛r ✉♠❛ s♦❧✉çã♦ ♠❡❧❤♦r q✉❡ ❛ ❛t✉❛❧✳} • _{❆❜❛♥❞♦♥❡ ❡st❡ r❛♠♦ ❡ ❝♦♥t✐♥✉❡ ❛ ❜✉s❝❛✳}

❆❧❣♦r✐t♠♦

• _{▼✉✐t♦ s❡♠❡❧❤❛♥t❡ ❛♦ ❛❧❣♦r✐t♠♦ ❞❡ ❜✉s❝❛ ❡①❛✉st✐✈❛✳}

• _{Ú♥✐❝❛ ❞✐❢❡r❡♥ç❛✿ ✈❡r✐✜❝❛ s❡ t❡♠ ❝❤❛♥❝❡s ❞❡ ❡♥❝♦♥tr❛r ✉♠❛}

s♦❧✉çã♦ ♠❡❧❤♦r ✭q✉❡ ❛ ♠❡❧❤♦r ❞❡ t♦❞❛s ❛té ♦ ♠♦♠❡♥t♦✮ ❛♥t❡s ❞❡ ❢❛③❡r ❛ ❝❤❛♠❛❞❛ r❡❝✉rs✐✈❛✳

• _{Pr♦ss❡❣✉❡ ❝♦♠ ❛ ❝❤❛♠❛❞❛ r❡❝✉rs✐✈❛ ❛♣❡♥❛s s❡ ❡①✐st✐r ❛}

♣♦ss✐❜✐❧✐❞❛❞❡✳

❆❧❣♦r✐t♠♦

❙♦❜r❡ ♦ ❛❧❣♦r✐t♠♦

• _{❱❛♥t❛❣❡♥s✿}

• _{❙❡♠♣r❡ ❡♥❝♦♥tr❛ ❛ ♠❡❧❤♦r s♦❧✉çã♦✳} • _{❘❡❞✉③ ♦ ♥ú♠❡r♦ ❞❡ ♥ós ♥❛ ❜✉s❝❛✳}

• _{❉❡s✈❛♥t❛❣❡♠✿ ❛✐♥❞❛ ❢❛③ ♠✉✐t❛s ❜✉s❝❛s✳ ❆✐♥❞❛ é ❧❡♥t♦ ♣❛r❛ ❝❛s♦s}

♠❛✐♦r❡s✳

• _{❊①❡♠♣❧♦✿ ✷✵ ✐t❡♥s}

• _{❊①❛✉st✐✈♦✿ ✭✈✐s✐t❛✮ ✷✳✵✾✼✳✶✺✵ ♥ós❀ ❇r❛♥❝❤✲❛♥❞✲❇♦✉♥❞✿ ✼✼✹✳✻✺✵✳} • _{❈♦♠ ❝✉rt♦ ❝✐r❝✉✐t♦✱ ❊①❛✉st✐✈♦✿ ✹✱✵✽✷ ♥ós❀ ❇r❛♥❝❤✲❛♥❞✲❇♦✉♥❞✿}

✷✾✽✳

• _{❊①❡♠♣❧♦✿ ✷✺ ✐t❡♥s✳}

• _{❊①❛✉st✐✈♦✿ ✻✳✻ s❡❣✉♥❞♦s✱ ❇r❛♥❝❤✲❛♥❞✲❇♦✉♥❞✿ ✷s✳} • _{❇r❛♥❝❤✲❛♥❞✲❇♦✉♥❞✿ ✷✻ ✐t❡♥s ✹s✱ ✶✼ ✐t❡♥s ✼✳✾ s❡❣✉♥❞♦s✳}

❊①❡r❝í❝✐♦

✶✳ ❋❛ç❛ ✉♠ ❛❧❣♦r✐t♠♦ ❇r❛♥❝❤ ❛♥❞ ❇♦✉♥❞ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❛ ♠♦❝❤✐❧❛ ✵✲✶ ✭❡♥❝♦♥tr❛r ❛ ♠❛✐♦r s♦♠❛ ❞♦s ✈❛❧♦r ❞♦s ✐t❡♥s r❡str✐t♦ ❛♦ ❧✐♠✐t❡ ♠á①✐♠♦ ❞❡ ♣❡s♦ ❞❛ ♠♦❝❤✐❧❛✮✳

✷✳ ❊①❡❝✉t❡ s❡✉ ❛❧❣♦r✐t♠♦ ♣❛r❛ ✉♠ ♠♦❝❤✐❧❛ q✉❡ s✉♣♦rt❛ ♦ ♣❡s♦ ♠á①✐♠♦ ✶✵ ♣❛r❛ ♦s ✐t❡♥s ❛❜❛✐①♦✿

■t❡♠ P❡s♦ ❱❛❧♦r

❆ ✷ ✹✵

❇ ✸✱✶✹ ✺✵

❈ ✶✱✾✽ ✶✵✵

❉ ✺ ✾✺

❊ ✸ ✸✵

❊①❡r❝í❝✐♦✿ ✉♠❛ ♣♦ssí✈❡❧ s♦❧✉çã♦

❘❡❢❡rê♥❝✐❛

• _{❙t❡♣❤❡♥s✱ ❘♦❞✳ ❊ss❡♥t✐❛❧ ❆❧❣♦r✐t❤♠s ✿ ❆ Pr❛❝t✐❝❛❧ ❆♣♣r♦❛❝❤ t♦} ❈♦♠♣✉t❡r ❆❧❣♦r✐t❤♠s✱ ❏♦❤♥ ❲✐❧❡② ✫ ❙♦♥s✱ ■♥❝♦r♣♦r❛t❡❞✱ ✷✵✶✸✳ Pr♦◗✉❡st ❊❜♦♦❦ ❈❡♥tr❛❧✱ ❁❤tt♣s✿✴✴❡❜♦♦❦❝❡♥tr❛❧✳♣r♦q✉❡st✳❝♦♠✴❧✐❜✴ ✉❢r♣❡✲❡❜♦♦❦s✴❞❡t❛✐❧✳❛❝t✐♦♥❄❞♦❝■❉❂✶✸✷✹✹✻✷❃✳ ✭◆❡st❛ ❛✉❧❛✿ ❈❛♣ít✉❧♦ ✶✷✱ ♣á❣✐♥❛s ✸✵✺✲✸✶✵✮✳

• _{❁❤tt♣s✿✴✴✇✇✇✳❣❡❡❦s❢♦r❣❡❡❦s✳♦r❣✴❜r❛♥❝❤✲❛♥❞✲❜♦✉♥❞✲❛❧❣♦r✐t❤♠✴❃}