❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❇r❛sí❧✐❛
■♥st✐t✉t♦ ❞❡ ❈✐ê♥❝✐❛s ❊①❛t❛s
❉❡♣❛rt❛♠❡♥t♦ ❞❡ ▼❛t❡♠át✐❝❛
Pr♦❣r❛♠❛ ❞❡ ▼❡str❛❞♦ Pr♦✜ss✐♦♥❛❧ ❡♠
▼❛t❡♠át✐❝❛ ❡♠ ❘❡❞❡ ◆❛❝✐♦♥❛❧
▲ó❣✐❝❛ ❇ás✐❝❛ ❡ ♦ ▼ét♦❞♦ ❆①✐♦♠át✐❝♦✿ ❯♠❛
■♥tr♦❞✉çã♦ ❆tr❛✈és ❞❛ ❚❡♦r✐❛ ❞♦s ❈♦♥❥✉♥t♦s
❆♥❞ré ❆♥❞❡rs♦♥ ❞❛ ❙✐❧✈❛ ◆✉♥❡s
❇r❛sí❧✐❛
◆❛ q✉❛❧✐❞❛❞❡ ❞❡ t✐t✉❧❛r ❞♦s ❞✐r❡✐t♦s ❞❡ ❛✉t♦r ❞❛ ♣✉❜❧✐❝❛çã♦✱ ❛✉t♦r✐③♦ ❛ ❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❇r❛sí❧✐❛ ❛ ❞✐s♣♦♥✐❜✐❧✐③❛r ♣♦r ♠❡✐♦ ❞♦ s✐t❡ ✇✇✇✳❜❝❡✳✉♥❜✳❜r s❡♠ r❡ss❛r❝✐♠❡♥t♦ ❞♦s ❞✐r❡✐t♦s ❛✉t♦r❛✐s✱ ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛ ▲❡✐ ♥♦ ✾✻✶✵✴✾✽✱ ♦ t❡①t♦ ✐♥t❡❣r❛❧ ❞❡st❛ ♦❜r❛✱ ❝♦♥❢♦r♠❡
❆♥❞ré ❆♥❞❡rs♦♥ ❞❛ ❙✐❧✈❛ ◆✉♥❡s
▲ó❣✐❝❛ ❇ás✐❝❛ ❡ ♦ ▼ét♦❞♦ ❆①✐♦♠át✐❝♦✿ ❯♠❛
■♥tr♦❞✉çã♦ ❆tr❛✈és ❞❛ ❚❡♦r✐❛ ❞♦s ❈♦♥❥✉♥t♦s
❚r❛❜❛❧❤♦ ❞❡ ❈♦♥❝❧✉sã♦ ❞❡ ❈✉rs♦ ❛♣r❡s❡♥t❛❞♦ ❛♦ ❉❡♣❛rt❛♠❡♥t♦ ❞❡
▼❛t❡♠át✐❝❛ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❇r❛sí❧✐❛✱ ❝♦♠♦ ♣❛rt❡ ❞♦s r❡q✉✐s✐t♦s ♣❛r❛ ♦❜t❡♥çã♦ ❞♦ ❣r❛✉ ❞❡ ▼❡str❡✳
❖r✐❡♥t❛❞♦r✿ Pr♦❢✳ ❉r✳ ❍❡❧❞❡r ❞❡ ❈❛r✈❛❧❤♦ ▼❛t♦s✳
❇r❛sí❧✐❛
Ficha catalográfica elaborada automaticamente, com os dados fornecidos pelo(a) autor(a)
972l
Nunes, André Anderson da Silva
Lógica Básica e o Método Axiomático: Uma Introdução Através da Teoria dos Conjuntos / André Anderson da Silva Nunes; orientador Helder de Carvalho Matos. - Brasília, 2015.
134 p.
❚♦❞♦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
❈❤❡❣♦ ❛♦ ✜♠ ❞❡ ♠❛✐s ✉♠ ❝✐❝❧♦ ❞❛ ♠✐♥❤❛ ✈✐❞❛ ❛❝❛❞ê♠✐❝❛ ❝♦♠ ♠❛✐s ❝ré❞✐t♦s ❛ ❞❛r ❞♦ q✉❡ ♦s q✉❡ ❝✉rs❡✐✳ ❋♦r❛♠ ♠✉✐t♦s ♦s ✐♥❝❡♥t✐✈❛❞♦r❡s ❞❡ss❛ ❥♦r♥❛❞❛ q✉❡ s❡ ❡♥❝❡rr❛✱ ❡ ♦ ❡s♣❛ç♦ ❛q✉✐ é ♣❡q✉❡♥♦ ♣❛r❛ ❧❡♠❜r❛r ❞❡ t♦❞♦s ❡❧❡s✳
❆❣r❛❞❡ç♦ ❡♠ ♣r✐♠❡✐r♦ ❧✉❣❛r ❛♦ ♠❡✉ ❙❡♥❤♦r✱ ❏❡s✉s ❈r✐st♦✱ ❛✉t♦r ❡ ❝♦♥s✉♠❛❞♦r ❞❛ ♠✐♥❤❛ ❢é✳ ❊s♣❡r♦ q✉❡ ♦ ❙❡♥❤♦r ♠❡ ♣❡r❞♦❡ ♣❡❧♦s ♠♦♠❡♥t♦s ❡♠ q✉❡ ❞✐✈✐❞✐ ♦s ❛ss✉♥t♦s ❞♦ ❘❡✐♥♦ ❞♦s ❈é✉s ❝♦♠ ❛s ❛t✐✈✐❞❛❞❡s ❛❝❛❞ê♠✐❝❛s✳ ❖ ❛❣r❛❞❡ç♦ ♣♦r s❡r ♦ ú♥✐❝♦ ❛ ❡st❛r ❝♦♠✐❣♦ ❡♠ t♦❞♦s ♦s ♠♦♠❡♥t♦s ❞❡ss❛ ❝❛♠✐♥❤❛❞❛✳ ❊ t❛♠❜é♠ ♣❡❧♦s ♣❛✐s q✉❡ ♠❡ ❞❡st❡✱ ♣♦rq✉❡ ❝♦♠ ♠✉✐t❛s ❣♦t❛s ❞❡ s✉♦r ♠❡ ✐♠♣✉❧s✐♦♥❛r❛♠ ♣❛r❛ ♦ ❝❛♠✐♥❤♦ ❞♦ ❝♦♥❤❡❝✐♠❡♥t♦✳ ➚ ♠✐♥❤❛ ❡s♣♦s❛ ❡ ✜❧❤❛s✱ q✉❡ ❛❜r✐r❛♠ ♠ã♦ ❞❛ ♠✐♥❤❛ ♣r❡s❡♥ç❛ ❡♠ ♠✉✐t♦s ♠♦♠❡♥t♦s ✐♠♣♦rt❛♥t❡s ❡ ❛t✉r❛r❛♠ ♦ ♠❡✉ ♠❛✉ ❤✉♠♦r ♥♦s ✜♥❛✐s ❞❡ s❡♠❡str❡s ❧❡t✐✈♦s✳ ❙❡♠♣r❡ ❢♦✐ ♣♦r ✈♦❝ês✳ ❊s♣❡r♦ t❡r s✐❞♦ ✉♠ ❜♦♠ r❡♣r❡s❡♥t❛♥t❡ ❞❡ss❛ ❢❛♠í❧✐❛ ♣♦r ♦♥❞❡ ♣❛ss❡✐✳
❆❣r❛❞❡ç♦ ❛♦ ♠❡✉ ♣❛ís ❡ ❛♦s ❜r❛s✐❧❡✐r♦s q✉❡ ❝✉st❡❛r❛♠ ♦s ♠❡✉s ❡st✉❞♦s✳ ❊✉ t❡♥❤♦ ✉♠❛ ❞í✈✐❞❛ ❝♦♠ ❡st❡ ♣♦✈♦ ❡ ❡♥✈✐❞❛r❡✐ ❡s❢♦rç♦s ♣❛r❛ q✉✐tá✲❧❛ ❛té ♦ ú❧t✐♠♦ ❝❡♥t❛✈♦✳ ❊s♣❡r♦ ❛❥✉❞❛r ♠✉✐t♦s ♥♦✈♦s ❜r❛s✐❧❡✐r♦s q✉❡ ♣❛ss❛rã♦ ♣❡❧♦ ♠❡✉ ❝❛♠✐♥❤♦ ♥❛s ❡s❝♦❧❛s ❞♦ ❉✐str✐t♦ ❋❡❞❡r❛❧ ❞❛ ♠❡s♠❛ ❢♦r♠❛ q✉❡ ❢✉✐ ❛❥✉❞❛❞♦ ❡♥q✉❛♥t♦ ❛❧✉♥♦✳
●♦st❛r✐❛ ❞❡ ❞❡♠♦♥str❛r ❡♠ ❡s♣❡❝✐❛❧ ♠✐♥❤❛ ❡♥♦r♠❡ ❣r❛t✐❞ã♦ ❛♦s ♣r♦❢❡ss♦r❡s ▲✐♥❡✉ ◆❡t♦✱ ❘✉✐ ❙❡✐♠❡t③✱ ❘❛q✉❡❧ ❈❛r♥❡✐r♦ ❉örr ❡ ▼❛r✐❛ ❚❡r❡③✐♥❤❛ ●❛s♣❛r q✉❡ ❡♠ ♠✉✐t♦ ❝♦♥tr✐❜✉ír❛♠ ♣❛r❛ ♦ ♠❡✉ ✐♥t❡r❡ss❡ ♣❡❧❛ ❘❛✐♥❤❛ ❞❛s ❈✐ê♥❝✐❛s✳ ❉✉r❛♥t❡ ♦s ❛♥♦s ❞❡ ❣r❛❞✉❛çã♦ ❡ ♠❡str❛❞♦✱ ❡ ❛❣♦r❛ ♥❛ ♠✐♥❤❛ ✈✐❞❛ ♣r♦✜ss✐♦♥❛❧✱ ♦s s❡♥❤♦r❡s ❝♦♥t✐♥✉❛rã♦ s❡♥❞♦ ✉♠❛ ❣r❛♥❞❡ ✐♥s♣✐r❛çã♦✳
➚ ❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❇r❛sí❧✐❛ q✉❡ ♠❡ ❛❝♦❧❤❡✉ ❡ ♣❡❧❛ q✉❛❧ t❡♥❤♦ ❡♥♦r♠❡ ❝❛r✐♥❤♦✳ ❈❛r✲ r❡❣♦ ❝♦♠✐❣♦ ❛ ❧✐çã♦ ♠❛✐s ✈❛❧✐♦s❛ q✉❡ ✉♠ ❞✐♣❧♦♠❛ ❞❛ ❯♥❇ ♣♦❞❡ ♦❢❡r❡❝❡r✿ ❡st♦✉ ♣r♦♥t♦ ♣❛r❛ ❝♦♥t✐♥✉❛r ❛♣r❡♥❞❡♥❞♦✳ ❚❡r❡✐ s❛✉❞❛❞❡s✳
✏❆♣r❡♥❞✐ ❛ ♥ã♦ t❡♥t❛r ❝♦♥✈❡♥❝❡r ♥✐♥❣✉é♠✳ ❖ tr❛❜❛❧❤♦ ❞❡ ❝♦♥✈❡♥❝❡r é ❢❛❧t❛ ❞❡ r❡s♣❡✐t♦✱ é ✉♠❛ t❡♥t❛t✐✈❛ ❞❡ ❝♦✲ ❧♦♥✐③❛çã♦ ❞♦ ♦✉tr♦✳✑
❘❡s✉♠♦
❆ ❡s❝♦❧❤❛ ❞♦ t❡♠❛ ✈✐s❛ ✐♥tr♦❞✉③✐r ❞❡ ❢♦r♠❛ s✐♠♣❧✐✜❝❛❞❛ ♦s ♣r✐♥❝í♣✐♦s ❞♦ ♠ét♦❞♦ ❛①✐♦♠át✐❝♦✱ ❜❡♠ ❝♦♠♦ ❛ ❢♦r♠❛ ♦r❣❛♥✐③❛❞❛ ❞❡ ♣❡♥s❛r ❡ ❛r❣✉♠❡♥t❛r✱ ❛♠❜♦s ❛♣❧✐❝❛❞♦s à ❚❡♦r✐❛ ❞♦s ❈♦♥❥✉♥t♦s✳ ❈♦♥✈✐❞❛♠♦s ♦ ❧❡✐t♦r✱ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ♦ ♣r♦❢❡ss♦r ❞❡ ❡♥s✐♥♦ ❜ás✐❝♦✱ ❛ ❜✉s❝❛r ♦ ❛♣❡r❢❡✐ç♦❛♠❡♥t♦ ❞❡ s✉❛ ❢♦r♠❛ ❞❡ ❛r❣✉♠❡♥t❛r ❛tr❛✈és ❞❡ r❡❣r❛s ❝♦♥✈❡♥❝✐♦✲ ♥❛❧♠❡♥t❡ ❛❝❡✐t❛s ❡ ❜❡♠ ❞❡✜♥✐❞❛s ❞❛ ▲ó❣✐❝❛ ❇ás✐❝❛✳ ❚❛❧ ❝♦♠♣❡tê♥❝✐❛ ❛r❣✉♠❡♥t❛t✐✈❛ é ❢✉♥❞❛♠❡♥t❛❧ ♥❛ ár❞✉❛ t❛r❡❢❛ ❞❡ ❝♦♥❞✉③✐r ♦s ❞✐s❝❡♥t❡s ❛ ❡✈♦❧✉✐r ❞❡ ✉♠ ♠♦❞♦ ✐♥❢♦r♠❛❧ ✭♥♦ ❊♥s✐♥♦ ❋✉♥❞❛♠❡♥t❛❧✮ ❛ ✉♠ s♦✜st✐❝❛❞♦ ♠ét♦❞♦ ❞❡ ♦r❣❛♥✐③❛çã♦ ❞❡ ❞❡♠♦♥str❛çõ❡s✱ ❢✉♥❞❛♠❡♥t❛❞♦ ❡♠ ✉♠ s✐st❡♠❛ ❞❡❞✉t✐✈♦ ❝♦♠♣❧❡t♦✳ ❖ ♠♦❞❡❧♦ ❛①✐♦♠át✐❝♦ ✉t✐❧✐③❛❞♦ ♥♦ ❡♥s✐♥♦ ❜ás✐❝♦ é ♦ ❞❛ ●❡♦♠❡tr✐❛ ❊✉❝❧✐❞✐❛♥❛ P❧❛♥❛✳ ◆❡st❡ tr❛❜❛❧❤♦✱ ❡♥tr❡t❛♥t♦✱ ♦ ✐♥✲ ✈❡st✐♠❡♥t♦ ❢♦✐ ♥♦ tr❛t❛♠❡♥t♦ ❞❛ ❚❡♦r✐❛ ❞♦s ❈♦♥❥✉♥t♦s✱ ❞❛❞❛ s✉❛ ❣r❛♥❞❡ ✐♠♣♦rtâ♥❝✐❛ ❞❡♥tr♦ ❞❡ t♦❞♦s ♦s ♦✉tr♦s r❛♠♦s ❞❛ ▼❛t❡♠át✐❝❛✳
P❛❧❛✈r❛s✲❝❤❛✈❡
❚❡♦r✐❛ ❞♦s ❈♦♥❥✉♥t♦s✱ ▼ét♦❞♦ ❆①✐♦♠át✐❝♦✱ ▲ó❣✐❝❛ ❇ás✐❝❛✳
❆❜str❛❝t
❚❤❡ ❝❤♦✐❝❡ ♦❢ t❤❡♠❡ ✐s t♦ ♣r♦✈✐❞❡ ❛ s✐♠♣❧❡ ✇❛② ♦❢ ✐♥tr♦❞✉❝t✐♦♥ t♦ t❤❡ ♣r✐♥❝✐♣❧❡s ♦❢ ❛①✐♦♠❛t✐❝ ♠❡t❤♦❞ ❛♥❞ ❛♥ ♦r❣❛♥✐③❡❞ ✇❛② ♦❢ t❤✐♥❦✐♥❣ ❛♥❞ ❛r❣✉✐♥❣✱ ❜♦t❤ ❛♣♣❧✐❡❞ t♦ ❙❡t ❚❤❡♦r②✳ ❲❡ ✐♥✈✐t❡ t❤❡ r❡❛❞❡r✱ ❡s♣❡❝✐❛❧❧② t❤❡ t❡❛❝❤❡r ♦❢ ❡❧❡♠❡♥t❛r② ❡❞✉❝❛t✐♦♥✱ t♦ s❡❡❦ t❤❡ ✐♠♣r♦✈❡♠❡♥t ♦❢ t❤❡✐r ✇❛② t♦ ❛r❣✉❡ t❤r♦✉❣❤ ❝♦♥✈❡♥t✐♦♥❛❧❧② ❛❝❝❡♣t❡❞ ❛♥❞ ✇❡❧❧✲ ❞❡✜♥❡❞ r✉❧❡s ♦❢ t❤❡ ❇❛s✐❝ ▲♦❣✐❝✳ ❚❤✐s ❛r❣✉♠❡♥t❛t✐✈❡ ❝♦♠♣❡t❡♥❝❡ ✐s ❢✉♥❞❛♠❡♥t❛❧ ✐♥ t❤❡ ❛r❞✉♦✉s t❛s❦ ♦❢ ❧❡❛❞✐♥❣ t❤❡ st✉❞❡♥ts t♦ ❡✈♦❧✈❡ ✐♥ ❛♥ ✐♥❢♦r♠❛❧ ✇❛② ✭✐♥ ❡❧❡♠❡♥t❛r② s❝❤♦♦❧✮ t♦ ❛ s♦♣❤✐st✐❝❛t❡❞ ♠❡t❤♦❞ ♦❢ ♦r❣❛♥✐③✐♥❣ ♣r♦♦❢s✱ ❜❛s❡❞ ♦♥ ❛ ❝♦♠♣❧❡t❡ ❞❡❞✉❝t✐✈❡ s②st❡♠✳ ❚❤❡ ❛①✐♦♠❛t✐❝ ♠♦❞❡❧ ✉s❡❞ ✐♥ ❜❛s✐❝ ❡❞✉❝❛t✐♦♥ ✐s t❤❡ ❊✉❝❧✐❞❡❛♥ ❣❡♦♠❡tr②✳ ■♥ t❤✐s ✇♦r❦✱ ❤♦✇❡✈❡r✱ t❤❡ ✐♥✈❡st♠❡♥t ✇❛s ✐♥ t❤❡ tr❡❛t♠❡♥t ♦❢ ❙❡t ❚❤❡♦r②✱ ❣✐✈❡♥ ✐ts ❣r❡❛t ✐♠♣♦rt❛♥❝❡ ✐♥ ❛❧❧ ♦t❤❡r ❜r❛♥❝❤❡s ♦❢ ♠❛t❤❡♠❛t✐❝s✳
❑❡②✇♦r❞s
❙❡t ❚❤❡♦r②✱ ❆①✐♦♠❛t✐❝ ▼❡t❤♦❞✱ ❇❛s✐❝ ▲♦❣✐❝✳
▲✐st❛ ❞❡ ❋✐❣✉r❛s
✶✳✶ ❉✐❛❣r❛♠❛ ❞❡ ❱❡♥♥ ✲ ■❣✉❛❧❞❛❞❡ ❞❡ ❝♦♥❥✉♥t♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✶✳✷ ❉✐❛❣r❛♠❛ ❞❡ ❱❡♥♥ ✲ ■♥❝❧✉sã♦ ♣ró♣r✐❛ ❞❡ ❝♦♥❥✉♥t♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✶✳✸ ❉✐❛❣r❛♠❛ ✲ ❊①❡♠♣❧♦ ✶✳✶✹ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✶✳✹ ❉✐❛❣r❛♠❛ ❞❡ ❱❡♥♥ ✲ ■♥t❡rs❡❝çã♦ ❞❡ ❝♦♥❥✉♥t♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✶✳✺ ❉✐❛❣r❛♠❛ ❞❡ ❱❡♥♥ ✲ ❯♥✐ã♦ ❉✐s❥✉♥t❛ ❞❡ ❝♦♥❥✉♥t♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ✶✳✻ ❉✐❛❣r❛♠❛ ❞❡ ❱❡♥♥ ✲ ❯♥✐ã♦ ❞❡ ❝♦♥❥✉♥t♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ✶✳✼ ❉✐❛❣r❛♠❛ ✲ ❊①❡♠♣❧♦ ✶✳✶✼ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ✶✳✽ ❉✐❛❣r❛♠❛ ❞❡ ❱❡♥♥ ✲ ❉✐❢❡r❡♥ç❛ ❞❡ ❈♦♥❥✉♥t♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✶✳✾ ❉✐❛❣r❛♠❛ ❞❡ ❱❡♥♥ ✲ ❉✐❢❡r❡♥ç❛ ❙✐♠étr✐❝❛ ❞❡ ❈♦♥❥✉♥t♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✶✳✶✵ ❉✐❛❣r❛♠❛ ❞❡ ❱❡♥♥ ✲ ❈♦♠♣❧❡♠❡♥t❛r ❞❡ ❝♦♥❥✉♥t♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻
✷✳✶ ◗✉❛❧ ❞♦s s❡❣♠❡♥t♦s é ♦ ♠❛✐♦r❄ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶ ✷✳✷ ❆s r❡t❛s ❤♦r✐③♦♥t❛✐s sã♦ ♣❛r❛❧❡❧❛s❄ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶ ✷✳✸ ◗✉❛♥t♦s ♣♦♥t♦s ❝✐♥③❛s ❡①✐st❡♠ ♥❛ ✜❣✉r❛❄ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷ ✷✳✹ ❆s r❡t❛s ✈❡rt✐❝❛✐s sã♦ ♣❛r❛❧❡❧❛s❄ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷
✸✳✶ ●❡♦r❣ ❈❛♥t♦r ✭✶✽✹✺ ❛ ✶✾✶✽✮✱ ❢✉♥❞❛❞♦r ❞❛ t❡♦r✐❛ ❞♦s ❝♦♥❥✉♥t♦s✳ ✳ ✳ ✳ ✳ ✳ ✽✵
✹✳✶ ❊①❡♠♣❧♦ ✹✳✶✵ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✺ ✹✳✷ ❊①❡♠♣❧♦ ✹✳✷✸ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✾ ✹✳✸ ❊①❡♠♣❧♦ ✹✳✷✼ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✶ ✹✳✹ ●rá✜❝♦ ❞❡ ❤✭①✮ ❂ x
a2
−x2 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✶
❆✳✶ ❇✐❥❡çã♦ ❡♥tr❡N ❡ ✉♠ s✉❜❝♦♥❥✉♥t♦ ♣ró♣r✐♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✾
❆✳✷ N × N é ❡♥✉♠❡rá✈❡❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✵
❆✳✸ ❆r❣✉♠❡♥t♦ ❞❛ ❞✐❛❣♦♥❛❧ ❞❡ ❈❛♥t♦r✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✶
▲✐st❛ ❞❡ ❚❛❜❡❧❛s
✷✳✶ ❚❛❜❡❧❛ ❱❡r❞❛❞❡ ✲ ◆❡❣❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✷✳✷ ❚❛❜❡❧❛ ❱❡r❞❛❞❡ ✲ ❈♦♥❥✉♥çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✷✳✸ ❚❛❜❡❧❛ ❱❡r❞❛❞❡ ✲ ◆❡❣❛çã♦ ❞❛ ❈♦♥❥✉♥çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷ ✷✳✹ ❚❛❜❡❧❛ ❱❡r❞❛❞❡ ✲ ❈♦♥❥✉♥çã♦ ❡♥tr❡ ✉♠❛ s❡♥t❡♥ç❛ ❡ s✉❛ ♥❡❣❛çã♦ ✳ ✳ ✳ ✳ ✳ ✻✸ ✷✳✺ ❚❛❜❡❧❛ ❱❡r❞❛❞❡ ✲ ❉✐s❥✉♥çã♦ ❊①❝❧✉s✐✈❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺ ✷✳✻ ❚❛❜❡❧❛ ❱❡r❞❛❞❡ ✲ ❉✐s❥✉♥çã♦ ■♥❝❧✉s✐✈❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻ ✷✳✼ ❚❛❜❡❧❛ ❱❡r❞❛❞❡ ✲ ◆❡❣❛çã♦ ❞❛ ❉✐s❥✉♥çã♦ ■♥❝❧✉s✐✈❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻ ✷✳✽ ❚❛❜❡❧❛ ❱❡r❞❛❞❡ ✲ ❉✐s❥✉♥çã♦ ❡♥tr❡ ✉♠❛ s❡♥t❡♥ç❛ ❡ s✉❛ ♥❡❣❛çã♦✳ ✳ ✳ ✳ ✳ ✳ ✻✼ ✷✳✾ ❚❛❜❡❧❛ ❱❡r❞❛❞❡ ✲ ❈♦♥❞✐❝✐♦♥❛❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽ ✷✳✶✵ ❚❛❜❡❧❛ ❱❡r❞❛❞❡ ✲ ◆❡❣❛çã♦ ❞❛ ❈♦♥❞✐❝✐♦♥❛❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵ ✷✳✶✶ ❚❛❜❡❧❛ ❱❡r❞❛❞❡ ✲ ❇✐❝♦♥❞✐❝✐♦♥❛❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶ ✷✳✶✷ ❘❡❣r❛s ❞❡ ■♥❢❡rê♥❝✐❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺ ✷✳✶✸ ❱❛❧✐❞❛çã♦ ✲ ▼♦❞✉♥s ♣♦♥❡♥s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻ ✷✳✶✹ ❱❛❧✐❞❛çã♦ ✲ ▼♦❞✉♥s t♦❧❧❡♥s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻ ✷✳✶✺ ❱❛❧✐❞❛çã♦ ✲ ❙✐❧♦❣✐s♠♦ ❞✐s❥✉♥t✐✈♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻ ✷✳✶✻ ❱❛❧✐❞❛çã♦ ✲ ❊①❡♠♣❧♦ ✷✳✽✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✼ ✷✳✶✼ ❱❛❧✐❞❛çã♦ ✲ ❊①❡♠♣❧♦ ✷✳✾✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✼
✸✳✶ ❈♦♥tr❛❞✐çã♦ ✲ ❇✐❝♦♥❞✐❝✐♦♥❛❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✸
✺✳✶ ❚❛❜❡❧❛ ❱❡r❞❛❞❡ ✲ ❚♦❞♦s ♦s ❈♦♥❡❝t✐✈♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✹ ✺✳✷ Pr♦♣r✐❡❞❛❞❡s ❞♦s ❈♦♥❡❝t✐✈♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✹ ✺✳✸ Pr♦❜❧❡♠❛ ✹ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✻
❙✉♠ár✐♦
✶ ❈♦♥❝❡✐t♦s ■♥✐❝✐❛✐s ❡ ❛ ❚❡♦r✐❛ ❞♦s ❈♦♥❥✉♥t♦s ❞❡ ❈❛♥t♦r ✶✽ ✶✳✶ ❈♦♥❥✉♥t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✶✳✷ ❖♣❡r❛çõ❡s ❙♦❜r❡ ❈♦♥❥✉♥t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ✶✳✷✳✶ Pr✐♥❝í♣✐♦ ❞❛ ❆❜str❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✶✳✷✳✷ ■❣✉❛❧❞❛❞❡ ❞❡ ❈♦♥❥✉♥t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✶✳✷✳✸ ■♥❝❧✉sã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✶✳✷✳✹ ■♥t❡rs❡❝çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✶✳✷✳✺ ❯♥✐ã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✶✳✷✳✻ ❉✐❢❡r❡♥ç❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ✶✳✷✳✼ ❈♦♠♣❧❡♠❡♥t❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✶✳✸ ❘❡❧❛çõ❡s ❡ ❋✉♥çõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✶✳✸✳✶ P❛r❡s ❖r❞❡♥❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼ ✶✳✸✳✷ Pr♦❞✉t♦ ❈❛rt❡s✐❛♥♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✶✳✸✳✸ ❘❡❧❛çõ❡s ❞❡ ❊q✉✐✈❛❧ê♥❝✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✶✳✸✳✹ P❛rt✐çõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾ ✶✳✸✳✺ ❋✉♥çõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷ ✶✳✹ ◆ú♠❡r♦s ◆❛t✉r❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹
✷ ❆ ▲ó❣✐❝❛ ❇✐✈❛❧❡♥t❡ ✹✻
✷✳✶ P♦r q✉❡ ❡st✉❞❛r ♣r✐♥❝í♣✐♦s ❞❡ ▲ó❣✐❝❛❄ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼ ✷✳✷ ❖ ▼ét♦❞♦ ❆①✐♦♠át✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ✷✳✷✳✶ ❖ ♠ét♦❞♦ ❞❛ ❚❡♥t❛t✐✈❛ ❡ ❊rr♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ✷✳✷✳✷ ❖ ❛✉①í❧✐♦ ❞♦s ❘❡❝✉rs♦s ❈♦♠♣✉t❛❝✐♦♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵ ✷✳✷✳✸ ❆ ❈♦♥✜❛❜✐❧✐❞❛❞❡ ♥♦ ❯s♦ ❞❡ ❉✐❛❣r❛♠❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵ ✷✳✸ ❖ q✉❡ sã♦ ❙❡♥t❡♥ç❛s❄ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸
✷✳✹ ❆ ◆♦çã♦ ❞❡ ❱❡r❞❛❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼ ✷✳✹✳✶ ❖ ♠ét♦❞♦ ❊♠♣ír✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼ ✷✳✹✳✷ ❖ ♠ét♦❞♦ ❉❡❞✉t✐✈♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽ ✷✳✹✳✸ ❖ ♠ét♦❞♦ ■♥❞✉t✐✈♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽ ✷✳✹✳✹ ❈♦♥❡t✐✈♦s ❧ó❣✐❝♦s ❡ t❛❜❡❧❛s ✈❡r❞❛❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ✷✳✹✳✺ ◆❡❣❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵ ✷✳✹✳✻ ❈♦♥❥✉♥çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✷✳✹✳✼ ❉✐s❥✉♥çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸ ✷✳✹✳✽ ❈♦♥❞✐❝✐♦♥❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼ ✷✳✹✳✾ ❇✐❝♦♥❞✐❝✐♦♥❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵ ✷✳✺ ❆r❣✉♠❡♥t❛çã♦ ▲ó❣✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶
✸ ❆ ❚❡♦r✐❛ ❞♦s ❈♦♥❥✉♥t♦s ❆①✐♦♠❛t✐③❛❞❛ ✼✾ ✸✳✶ ❖s ♣❛r❛❞♦①♦s ❞❛ t❡♦r✐❛ ❞♦s ❈♦♥❥✉♥t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✶ ✸✳✷ ❆①✐♦♠❛ ❞❛ ❊①t❡♥sã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✹ ✸✳✸ ❆①✐♦♠❛ ❞❛ ❊s♣❡❝✐✜❝❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✺ ✸✳✹ ❆①✐♦♠❛ ❞❛ ❯♥✐ã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✺ ✸✳✺ ❆①✐♦♠❛ ❞♦ P❛r❡❛♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✻ ✸✳✻ ❆①✐♦♠❛ ❞❛ ❙♦♠❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✻ ✸✳✼ ❆①✐♦♠❛ ❞❛ P♦tê♥❝✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✼ ✸✳✽ ❆①✐♦♠❛ ❞❛ ❘❡❣✉❧❛r✐❞❛❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✼ ✸✳✾ ❆①✐♦♠❛ ❞♦s ❈❛r❞✐♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✽ ✸✳✶✵ ❆①✐♦♠❛ ❞❛ ■♥✜♥✐t✉❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✽ ✸✳✶✶ ❆①✐♦♠❛ ❞❛ ❊s❝♦❧❤❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✽
✹ ❈❛r❛❝t❡r✐③❛çõ❡s ❖r❞✐♥❛❧ ❡ ❈❛r❞✐♥❛❧ ❞♦ ❝♦♥❥✉♥t♦ N ✾✵
✹✳✶ ❆①✐♦♠❛s ❞❡ P❡❛♥♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✶ ✹✳✷ ❖r❞❡♠ ❡ ♦ Pr✐♥❝í♣✐♦ ❞❛ ❇♦❛ ❖r❞❡♥❛çã♦ ❡♠ N ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✷
✹✳✸ ❈♦♥❥✉♥t♦s ❋✐♥✐t♦s ❡ ■♥✜♥✐t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✸ ✹✳✹ ❈♦♥❥✉♥t♦s ❊♥✉♠❡rá✈❡✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✺ ✹✳✺ ❈♦♥❥✉♥t♦s ◆ã♦ ❊♥✉♠❡rá✈❡✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✾
✺ ❆♣❧✐❝❛çõ❡s ❛♦ ❊♥s✐♥♦ ▼é❞✐♦ ✶✵✷ ✺✳✶ Pr♦❜❧❡♠❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✹
❆ ❙♦❧✉çõ❡s ❛♦s Pr♦❜❧❡♠❛s ❞♦ ❈❛♣ít✉❧♦ ✺ ✶✶✺
■♥tr♦❞✉çã♦
◆♦ ♣r♦❝❡ss♦ ❞❡ ❡♥s✐♥♦✲❛♣r❡♥❞✐③❛❣❡♠ ♣❛r❡❝❡ s❡r ❞✐❢í❝✐❧ ✉s❛r ▼❛t❡♠át✐❝❛ ♣❛r❛ tr❡✐♥❛r ♦ r❛❝✐♦❝í♥✐♦ ❧ó❣✐❝♦ ❞♦s ❛❧✉♥♦s s❡♠ ❢❛③❡r ❝♦♠ q✉❡ ❡❧❡s ❡♥t❡♥❞❛♠ ❛ ♥♦çã♦ ❞❡ ❞❡♠♦♥str❛✲ çã♦✳ ❈♦♥s❡❣✉✐r ✉♠❛ ❥✉st✐✜❝❛t✐✈❛ ❞❡ ❛❝♦r❞♦ ❝♦♠ ❝❡rt❛s r❡❣r❛s ❞❡ ✐♥❢❡rê♥❝✐❛ ♣❛r❛ ♠♦str❛r q✉❡ ✉♠❛ ♣r♦♣♦s✐çã♦ é ❝♦♥s❡q✉ê♥❝✐❛ ❞❡ ♦✉tr❛s ♣r♦♣♦s✐çõ❡s✱ ♣r❡✈✐❛♠❡♥t❡ ❛❞♠✐t✐❞❛s ❝♦♠♦ ✈❡r❞❛❞❡✐r❛s✱ é ✉♠ ♣r♦❝❡ss♦ ❝♦♥str✉t✐✈♦ ❢✉♥❞❛♠❡♥t❛❧ ❞❡ t❡♦r✐❛s ❞❡♥tr♦ ❞❡ ✈ár✐♦s r❛♠♦s ❞♦ ❝♦♥❤❡❝✐♠❡♥t♦ ❝✐❡♥tí✜❝♦✱ ❝❛r❛❝t❡r✐③❛♥❞♦ ♦ r❛❝✐♦❝í♥✐♦ ❞❡❞✉t✐✈♦✳ ❊♥tr❡t❛♥t♦ é ❝♦♠✉♠ ❡♥❝♦♥tr❛r ✉♠ ♣r♦❢❡ss♦r ❞❛ ár❡❛ q✉❡ ❥á ♦✉✈✐✉ ❛ ♣❡r❣✉♥t❛✿ ✏P❛r❛ q✉❡ s❡r✈❡ ▼❛t❡♠át✐❝❛❄✑ ▼❡s♠♦ ♥ã♦ s❡♥❞♦ ♣♦ssí✈❡❧ r❡s♣♦♥❞❡r ❡♠ ♣♦✉❝❛s ♣❛❧❛✈r❛s ❛ ❡st❛ ♣❡r❣✉♥t❛✱ é ❢✉♥❞❛✲ ♠❡♥t❛❧ ♥ã♦ ❞❡✐①❛r ♦s ❛❧✉♥♦s s❡♠ ✉♠❛ r❡s♣♦st❛ r❛③♦á✈❡❧✳ ❊ ♦ ♠❛✐s ❛♣r♦♣r✐❛❞♦ t❛❧✈❡③ s❡❥❛ ❛♣♦♥t❛r ❛ ♣r✐♥❝✐♣❛❧ q✉❛❧✐❞❛❞❡ ❞❛ ▼❛t❡♠át✐❝❛✿ ❡❧❛ ❡st❛❜❡❧❡❝❡ ✈❡r❞❛❞❡s ✐♠✉tá✈❡✐s✳ ❆ ♥♦çã♦ ❞❡ ✈❡r❞❛❞❡ q✉❡ ♣❡r♠❡✐❛ ✉♠ t❡♦r❡♠❛ ❞❡♠♦♥str❛❞♦ ❝♦rr❡t❛♠❡♥t❡ ♣r❡✈❛❧❡❝❡ ♣❛r❛ s❡♠♣r❡✳ ❊ é ❥✉st❛♠❡♥t❡ ♦ ❡♥t❡♥❞✐♠❡♥t♦ ❞♦ r✐❣♦r ❛♣r❡s❡♥t❛❞♦ ♥❛s ❞❡❞✉çõ❡s q✉❡ ♥♦s ❧❡✈❛♠ ❛ ❛♣r❡❝✐❛r ❡ss❛ q✉❛❧✐❞❛❞❡ í♠♣❛r q✉❡ só ❛ ▼❛t❡♠át✐❝❛ ♦❢❡r❡❝❡✳ ◆❡st❡ ❝♦♥t❡①t♦ ✐♥✲ s❡r✐♠♦s ♦ ♦❜❥❡t✐✈♦ ❣❡r❛❧ ❞❡st❡ tr❛❜❛❧❤♦✿ ❛♣r❡s❡♥t❛r ❛ ❞✐♥â♠✐❝❛ ❞❡ s✐st❡♠❛s ❛①✐♦♠át✐❝♦s ♣♦r ♠❡✐♦ ❞♦ ♠ét♦❞♦ ❞❡❞✉t✐✈♦✳
❯♠ ❛r❣✉♠❡♥t♦ ❞❡❞✉t✐✈♦ é ✉♠❛ s❡q✉ê♥❝✐❛ ❞❡ ❛✜r♠❛çõ❡s q✉❡✱ ♣❛rt✐♥❞♦ ❞❡ ❛①✐♦♠❛s✱ ♣r❡♠✐ss❛s ♦✉ ❝♦♥❥❡❝t✉r❛s✱ ♥♦s ❧❡✈❛ ❛ ❝♦♥❝❧✉sõ❡s ❞❡ ❛❝♦r❞♦ ❝♦♠ r❡❣r❛s ❞❡ ✐♥❢❡rê♥❝✐❛ ✈á❧✐❞❛s✳ ➱ ❛tr❛✈és ❞❡st❛ ♠❡t♦❞♦❧♦❣✐❛ q✉❡ ❛♥❛❧✐s❛♠♦s ❡ ❞❡s❝♦❜r✐♠♦s ❛s ❝♦♥s❡q✉ê♥❝✐❛s ❞❡ ❛✜r♠❛çõ❡s ❛ss✉♠✐❞❛s ❝♦♠♦ ✈❡r❞❛❞❡✐r❛s✳ ■✈❛♥ ❙t❡✇❛rt✱ ♠❛t❡♠át✐❝♦ ✐♥❣❧ês✱ ❡s❝r❡✈❡✉ ❡♠ ❬✷✹❪✿
✏◆✐♥❣✉é♠ t❡ ♣❡❞❡ ♣❛r❛ ❛❝r❡❞✐t❛r ❡♠ ❛①✐♦♠❛s✳ ❆❧✐ás✱ ❛❝r❡❞✐t❛r ♥❡❧❡s ♦✉ ❞✉✈✐❞❛r ❞❡❧❡s é ✐♥út✐❧✱ ♣♦✐s ❞❡ ♠♦❞♦ ♥❡♥❤✉♠ ❝♦rr❡s♣♦♥✲
❞❡♠ à r❡❛❧✐❞❛❞❡✳✑
❊①♣❧✐❝♦✿ ♥ã♦ ✐♠♣♦rt❛ s❡ ❛s ✈❡r❞❛❞❡s ❞❛s q✉❛✐s ♣❛rt✐♠♦s sã♦ ♦✉ ♥ã♦ ❛❝❡✐t❛s ✉♥✐✈❡r✲ s❛❧♠❡♥t❡✳ ❉❡ ❢❛t♦✱ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❤✐stór✐❝♦ ❞❛ ▼❛t❡♠át✐❝❛ ♥♦s tr❛③ ✉♠ ❡①❡♠♣❧♦ ✐♥str✉t✐✈♦ ❞❡ss❡ ♣♦♥t♦ ❞❡ ✈✐st❛✿ ❛ ♥❡❣❛çã♦ ❞♦ ❛①✐♦♠❛ ❞❛s ♣❛r❛❧❡❧❛s ❞❡ ❊✉❝❧✐❞❡s ✲ q✉❡ ♣♦st✉❧❛ q✉❡ ♣♦r ✉♠ ♣♦♥t♦ ❡①t❡r✐♦r ❛ ✉♠❛ r❡t❛ ♣❛ss❛ ❡①❛t❛♠❡♥t❡ ✉♠❛ r❡t❛ ♣❛r❛❧❡❧❛ à ✐♥✐❝✐❛❧ ✲ ❧❡✈♦✉ à ❞❡s❝♦❜❡rt❛ ❞❛s ❣❡♦♠❡tr✐❛s ♥ã♦ ❡✉❝❧✐❞✐❛♥❛s✳ ❊♠❜♦r❛ ♠❛✐s ❛ ❢r❡♥t❡ ❞✐s❝✉t❛♠♦s ❛ ♥♦çã♦ ❞❡ ✈❡r❞❛❞❡✱ ❞❡✈❡✲s❡ ❡♥t❡♥❞❡r q✉❡ ♦ ✐♥t❡r❡ss❛♥t❡ ❞♦ ♠ét♦❞♦ ❛①✐♦♠á✲ t✐❝♦ é ♦r❣❛♥✐③❛r ❛s ❝♦♥❝❧✉sõ❡s q✉❡ ❞❡❝♦rr❡♠ ❧♦❣✐❝❛♠❡♥t❡ ❞❡ss❛s ✏✈❡r❞❛❞❡s✑ ❡s❝♦❧❤✐❞❛s✳
❆ss✐♠✱ ♥♦ss♦ ❢♦❝♦ é s❡♠♣r❡ ♦ q✉❡ ♣♦❞❡♠♦s ❝♦♥❝❧✉✐r ❞❡ ❢♦r♠❛ ✈á❧✐❞❛✱ ❡ ♥ã♦ s❡ ♦ ♣♦♥t♦ ❞❡ ♣❛rt✐❞❛ é ♦✉ ♥ã♦ ❛❝❡✐t♦ ♣♦r t♦❞♦s ❝♦♠♦ ✈❡r❞❛❞❡✳
P❛r❛ ❛t✐♥❣✐r ♦ ♦❜❥❡t✐✈♦ ❣❡r❛❧ ❞❡st❡ tr❛❜❛❧❤♦✱ ❢❛r❡♠♦s ✉♠❛ ❜r❡✈❡ ❡①♣♦s✐çã♦ ❞❛ t❡♦r✐❛ ❞♦s ❝♦♥❥✉♥t♦s✱ ❝♦♠ ❛❧❣✉♥s ❞♦s r❡s✉❧t❛❞♦s ♠❛✐s ✉s❛❞♦s ♥❛ ❡❞✉❝❛çã♦ ❜ás✐❝❛✳ ▼❛✐s q✉❡ ✐ss♦✿ q✉❡r❡♠♦s ❛♣r❡s❡♥t❛r ✉♠ ♣♦✉❝♦ ❞❛ ❤✐stór✐❛ q✉❡ ❧❡✈♦✉ à ❝r✐❛çã♦ ❞❡ss❛ t❡♦r✐❛ ♣♦r ❈❛♥t♦r✱ ✐♥❝❧✉✐♥❞♦ ❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ ✉♠❛ ❡str✉t✉r❛ ❛①✐♦♠át✐❝❛ ♠❛✐s r❡✜♥❛❞❛ ♣❛r❛ ❞❛r ✉♠❛ ❜❛s❡ ✜r♠❡ à t❡♦r✐❛ ❝r✐❛❞❛ ♣♦r ❈❛♥t♦r✳ ❊ ✐ss♦ ❢♦✐ ♣❡r❝❡❜✐❞♦ ❛ ♣❛rt✐r ❞♦ s✉r❣✐♠❡♥t♦ ❞❡ ❛❧❣✉♥s ♣❛r❛❞♦①♦s✱ ❛s ✈❡③❡s tã♦ s✐♠♣❧❡s q✉❡ ♣♦❞❡♠ s❡r ❞✐s❝✉t✐❞♦s s❡♠ ❞✐✜❝✉❧❞❛✲ ❞❡s ❝♦♠ ♦s ❛❧✉♥♦s ♥♦ ✐♥í❝✐♦ ❞♦ ❊♥s✐♥♦ ▼é❞✐♦✳ ❊ss❛s ❝♦♥tr❛❞✐çõ❡s ❛♣❛r❡♥t❡s ❛❧é♠ ❞❡ ❛♣r❡s❡♥t❛❞❛s✱ s❡r✈❡♠ ❞❡ ❥✉st✐✜❝❛t✐✈❛ ♣❛r❛ ♦ ✉s♦ ❞❛ ❧✐♥❣✉❛❣❡♠ ♠❛t❡♠át✐❝❛ ♠❛✐s ❢♦r♠❛❧ q✉❡ ❡❧✐♠✐♥❛ ❛ s✉❛ ♦❝♦rrê♥❝✐❛✳ ❆ t❡♦r✐❛ ❛q✉✐ ❛♣r❡s❡♥t❛❞❛ ♥ã♦ s❡rá r✐❣♦r♦s❛✱ ♠❛s s✐♠ ✏✐♥❣ê♥✉❛✑❀ ♦ ✐♥t✉✐t♦ é ❛♣❡♥❛s tr❛♥s♠✐t✐r ❛s ✐❞❡✐❛s ♣♦r trás ❞♦ ♠ét♦❞♦ ❛①✐♦♠át✐❝♦✳ ❆ ❡①♣♦s✐çã♦ ❢❡✐t❛ ♥♦ ❝❛♣ít✉❧♦ ✸ ❝♦♥s✐st❡ ♥❛ ❛❞❛♣t❛çã♦ ❞❛ ❛①✐♦♠át✐❝❛ ❞❡ ❩❡r♠❡❧♦✲❋r❛❡♥❦❡❧ ♣❛r❛ ❛ t❡♦r✐❛ ❞♦s ❝♦♥❥✉♥t♦s✳ Pr♦ss❡❣✉✐r❡♠♦s ❛♣r❡s❡♥t❛♥❞♦ ♦s ❢✉♥❞❛♠❡♥t♦s ❞❛ ❧ó❣✐❝❛ ❜✐✈❛❧❡♥t❡✱ ❛ ✜♠ ❞❡ ❡s❝❧❛r❡❝❡r ♦ ❝♦♥❝❡✐t♦ ❞❡ ❛r❣✉♠❡♥t♦ ✈á❧✐❞♦✳ ❆❧❣✉♥s ❡①❡♠♣❧♦s ✐♥✲ t❡r❡ss❛♥t❡s ❢♦r❛ ❞❛ ♠❛t❡♠át✐❝❛ ♣✉r❛ sã♦ ❛♣r❡s❡♥t❛❞♦s✱ ❥á q✉❡ ❛❧❝❛♥ç❛♠ ♦s ❡❞✐t❛✐s ❞❡ ❝♦♥❝✉rs♦s ♣ú❜❧✐❝♦s ❞❡ ♥í✈❡❧ ♠é❞✐♦ ❞❡♥tr♦ ❞❛ ár❡❛ ❞❡ r❛❝✐♦❝í♥✐♦ ❧ó❣✐❝♦✳ ❋✐♥❛❧✐③❛✲s❡ ❡st❛ ❡①♣♦s✐çã♦ ♣❡rt✐♥❡♥t❡ ❛♦s ❢✉♥❞❛♠❡♥t♦s ❞❛ ♠❛t❡♠át✐❝❛ ❞❡❧✐♥❡❛♥❞♦ ❞✉❛s ❞❡s❝r✐çõ❡s ♣❛r❛ ♦ ❝♦♥❝❡✐t♦ ❞❡ ♥ú♠❡r♦✳ Pr✐♠❡✐r♦✱ ✉♠❛ ❜r❡✈❡ ❛♣r❡s❡♥t❛çã♦ ❞♦s ❆①✐♦♠❛s ❞❡ P❡❛♥♦ é ❢❡✐t❛ ❝♦♠ ✐♥t✉✐t♦ ❞❡ ❞❡s❝r❡✈❡r ♦r❞✐♥❛❧♠❡♥t❡ ♦ ❝♦♥❥✉♥t♦ ❞♦s ♥ú♠❡r♦s ♥❛t✉r❛✐s✳ ❆ s❡✲ ❣✉✐r é ❢❡✐t❛ ❝❛r❛❝t❡r✐③❛çã♦ ❞❛ ✐❞❡✐❛ ❞❡ ❝❛r❞✐♥❛❧✐❞❛❞❡✱ ✈✐t❛❧ ♣❛r❛ ❞❡s❝r❡✈❡r ❛ q✉❛♥t✐❞❛❞❡ r❡♣r❡s❡♥t❛❞❛ ♣♦r ✉♠ ♥ú♠❡r♦ ♥❛t✉r❛❧✳
❊st❡ tr❛❜❛❧❤♦ ❢♦✐ ❞❡s❡♥✈♦❧✈✐❞♦ ❛ ♣❛rt✐r ❞❛ ♣❡sq✉✐s❛ ❜✐❜❧✐♦❣rá✜❝❛ ❞❛s ♦❜r❛s ♠❡♥❝✐♦✲ ♥❛❞❛s ♥♦ ❝❛♠♣♦ ❘❡❢❡rê♥❝✐❛s✱ ❞❛ q✉❛❧ s❡ ♣r♦❝✉r♦✉ ❡①tr❛✐r ❛s ✐❞❡✐❛s ♠❛✐s ✐♥t❡r❡ss❛♥t❡s ❡ ❛♣❧✐❝á✈❡✐s ❛♦ ❊♥s✐♥♦ ▼é❞✐♦ ❛❝❡r❝❛ ❞♦ t❡♠❛ ❞❡s❡♥✈♦❧✈✐❞♦✳ ❍♦✉✈❡ ❛ ♣r❡t❡♥sã♦ ❞❡ s❡ ❢❛③❡r ❛ tr❛♥s♣♦s✐çã♦ ♣❛r❛ ✉♠❛ ❧✐♥❣✉❛❣❡♠ ♠❛✐s ❛❝❡ssí✈❡❧ ❞♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❛①✐♦♠át✐❝♦ ❞❛ t❡♦r✐❛ ❞♦s ❝♦♥❥✉♥t♦s❀ ✉♠ ❡s❢♦rç♦ ❢♦✐ ❢❡✐t♦ ♥♦ s❡♥t✐❞♦ ❞❡ ♥ã♦ s❡ ❛❜r✐r ♠ã♦✱ ♣♦ré♠✱ ❞❛ ♣r❡❝✐sã♦ ♠í♥✐♠❛ ♥❡❝❡ssár✐❛ ♣❛r❛ ❡♥❝♦r❛❥❛r ♦ ❧❡✐t♦r ❛ ❛♣❡r❢❡✐ç♦❛r s❡✉s ♠ét♦❞♦s ❞❡ ❛r❣✉♠❡♥t❛çã♦ ❛❝❡r❝❛ ❞❡ ♣r♦♣♦s✐çõ❡s ♥♦ ❝♦♥t❡①t♦ ❞❡ ✉♠❛ t❡♦r✐❛ ❞❡ ♣r✐♠❡✐r❛ ♦r❞❡♠✳ ❊♠ ♣❛rt✐❝✉❧❛r✱ ❢♦✐ ❡①♣♦st❛ ❛ ✐❞❡✐❛ ❢✉♥❞❛♠❡♥t❛❧ ❞♦ ♠ét♦❞♦ ❛①✐♦♠át✐❝♦✿ ❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ s❡ ♦❜t❡r ✉♠ s✐st❡♠❛ ❧ó❣✐❝♦ ❡ ❢✉♥❞❛♠❡♥t❛❞♦ ❛ ♣❛rt✐r ❞❡ ✉♠ ❝♦♥❥✉♥t♦ ♠í♥✐♠♦ ❞❡ ♣r♦♣♦s✐çõ❡s✱ ❛ ♣❛rt✐r ❞❛s q✉❛✐s s❡ ♣♦❞❡ ❡①tr❛✐r ♥♦✈❛s ♣r♦♣♦s✐çõ❡s ♦✉ ❝♦♥❥❡❝t✉r❛s✳
❈❛♣ít✉❧♦ ✶
❈♦♥❝❡✐t♦s ■♥✐❝✐❛✐s ❡ ❛ ❚❡♦r✐❛ ❞♦s
❈♦♥❥✉♥t♦s ❞❡ ❈❛♥t♦r
■♠❛❣✐♥❡ q✉❡ ✈♦❝ê q✉❡✐r❛ ❡①♣❧✐❝❛r ❛ ✉♠ ❛❧✉♥♦ ❞♦ ❡♥s✐♥♦ ❢✉♥❞❛♠❡♥t❛❧ ♦ q✉❡ sã♦ ❝♦♥✲ ❥✉♥t♦s✳ P♦❞❡r✐❛ ❝♦♠❡ç❛r ❞✐③❡♥❞♦ q✉❡ ❝♦♥❥✉♥t♦s sã♦ ❝♦❧❡çõ❡s ❞❡ ♦❜❥❡t♦s✳ ❯♠ ❛❧✉♥♦ ♠❛✐s ✐♥❞❛❣❛❞♦r ♣♦❞❡r✐❛ ♣❡r❣✉♥t❛r✿ ✏❖ q✉❡ sã♦ ❡ss❡s ♦❜❥❡t♦s❄✑ ❆ r❡s♣♦st❛ ❛ ❡ss❛ ♣❡r❣✉♥t❛ ♣❛r❡❝❡ s❡r s✐♠♣❧❡s✿ ♦s ♦❜❥❡t♦s ♣♦❞❡♠ t❡r q✉❛❧q✉❡r ♥❛t✉r❡③❛✱ ♦✉ s❡❥❛✱ ♣♦❞❡♠♦s ❢❛❧❛r ❡♠ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ♣❡ss♦❛s✱ ❞♦s át♦♠♦s ❞❡ ♦①✐❣ê♥✐♦ ♥❛ ❛t♠♦s❢❡r❛ t❡rr❡str❡✱ ❞♦s ♥ú♠❡r♦s q✉❡ ✉s❛♠♦s ♣❛r❛ ❝♦♥t❛❣❡♠✱ ❞❛s ♣❡ç❛s ❞❡ r♦✉♣❛ ❡♠ ✉♠❛ ❧♦❥❛✳ ◆♦✈♦s q✉❡st✐♦♥❛♠❡♥t♦s ♣♦❞❡r✐❛♠ s❡r ❧❡✈❛♥t❛❞♦s ❛ ♣❛rt✐r ❞❛í✿ ❊ s❡ ❡✉ ❢♦r♠❛r ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❝♦♥❥✉♥t♦s✱ ♦ q✉❡ s❡r✐❛ ✐ss♦❄ ❊①✐st❡ ✉♠ ❝♦♥❥✉♥t♦ s❡♠ ♦❜❥❡t♦ ♥❡♥❤✉♠❄
❯♠ ♦✉tr♦ q✉❡st✐♦♥❛♠❡♥t♦ r❡❢❡r❡♥t❡ à ❡①♣❧✐❝❛çã♦ ❛♥t❡r✐♦r q✉❡ ♣♦❞❡r✐❛ s✉r❣✐r✿ ✏❖ q✉❡ sã♦ ❝♦❧❡çõ❡s❄✑ P♦❞❡rí❛♠♦s ❛❜r✐r ❡♥tã♦ ✉♠ ❞✐❝✐♦♥ár✐♦ ❡ ❡♥❝♦♥tr❛r ✈ár✐❛s ♣❛❧❛✈r❛s q✉❡ ♥♦s ♣❡r♠✐t✐ss❡♠ ❡①♣r❡ss❛r ❛ ✐❞❡✐❛ ❞❡ ❝♦❧❡çã♦ ♥❡st❡ ❝♦♥t❡①t♦✿ ❆❥✉♥t❛♠❡♥t♦✱ r❡✉♥✐ã♦ ❞❡ ♦❜❥❡t♦s✳ ❖ ❛❧✉♥♦✱ ✐♥s✐st❡♥t❡✱ ♣♦❞❡r✐❛ ❡♥tã♦ ♣❡r❣✉♥t❛r ♦ q✉❡ é ✏❛❥✉♥t❛♠❡♥t♦✑✳ ◆♦s ❡♥✈♦❧✈❡rí❛♠♦s ❡♥tã♦ ❡♠ ✉♠❛ ❞✐s❝✉ssã♦ q✉❡ ♣♦❞❡r✐❛ s❡ ❡st❡♥❞❡r ♣♦r ♠✉✐t♦ t❡♠♣♦✳
❖ ♣♦♥t♦ ❝❡♥tr❛❧ ❞❡ss❡ ♣r♦❝❡ss♦ ❞❡ ❝♦♥✈❡♥❝✐♠❡♥t♦ ❞♦ ❛❧✉♥♦ é ♦ s❡❣✉✐♥t❡✿ t❡♠♦s q✉❡ ❡♥❝♦♥tr❛r ❛❧❣✉♠❛ s❡♥t❡♥ç❛ q✉❡ s❡❥❛ ❛❝❡✐t❛ ♣♦r ❡❧❡ s❡♠ q✉❡st✐♦♥❛♠❡♥t♦ ♣❛r❛ ❡①♣❧✐❝❛r ♦ s✐❣♥✐✜❝❛❞♦ ❞❡ ❝♦♥❥✉♥t♦✳ ❯♠❛ r❡✢❡①ã♦ s❡♠❡❧❤❛♥t❡ t❛♠❜é♠ ♣♦❞❡r✐❛ s❡r ❧❡✈❛♥t❛❞❛ ❞❡♥tr♦ ❞❛ ❣❡♦♠❡tr✐❛ ♥❛ t❡♥t❛t✐✈❛ ❞❡ ❡①♣❧✐❝❛r ♦ q✉❡ é ✉♠❛ r❡t❛✳ ❉❡ ❛❝♦r❞♦ ❝♦♠ ❬✻❪✱ t❡♠✲s❡✿
s❢ ✭❞❡ r❡t♦✮ ✶ ●❡♦♠ ▲✐♥❤❛ q✉❡ ❡st❛❜❡❧❡❝❡ ❛ ♠❛✐s ❝✉rt❛ ❞✐stâ♥❝✐❛ ❡♥tr❡ ❞♦✐s ♣♦♥t♦s❀ ❧✐♥❤❛ r❡t❛✳ ✷ ❚r❛ç♦ ❞✐r❡✐t♦✳ ✸ ▲❛♥ç♦ ❞❡ ❡str❛❞❛ r❡t✐❧í♥❡♦✳
P♦❞❡rí❛♠♦s ❡♥tã♦ ♥♦✈❛♠❡♥t❡ ❡♥tr❛r ❡♠ ✉♠ ♣r♦❝❡ss♦ ❞❡ ❝♦♥✈❡♥❝✐♠❡♥t♦ ❜✉s❝❛♥❞♦ ✉♠❛ s❡♥t❡♥ç❛ q✉❡ ♠❡❧❤♦r ❞❡s❝r❡✈❡ss❡ ♣❛r❛ ❝❛❞❛ ❛❧✉♥♦ ♦ s❡♥t✐❞♦ ❞❡ r❡t❛✳ ❊ ❝❛❞❛ ❡s❝♦❧❤❛✱ ♣♦r ♠❛✐s ❡❧✉❝✐❞❛t✐✈❛ q✉❡ ❢♦ss❡ tr❛r✐❛ ❧✐♠✐t❛çõ❡s✳ P♦r ❡①❡♠♣❧♦✱ s❡ ❡s❝♦❧❤êss❡♠♦s ♦ s✐❣♥✐✜❝❛❞♦ ✶ ❛❝✐♠❛✱ ♣♦❞❡rí❛♠♦s ❡♥tã♦ q✉❡st✐♦♥❛r s♦❜r❡ ♦ q✉❡ s❡r✐❛♠ r❡t❛s ♥❛ s✉♣❡r❢í❝✐❡ t❡rr❡str❡✱ q✉❡ s❛❜❡♠♦s s❡r ✏❝✉r✈❛✑✳ ❈❡rt❛♠❡♥t❡ ✉♠❛ r❡t❛ ❝✉r✈❛ ♣❛r❡❝❡r✐❛ ❡str❛♥❤♦ ❛ ❛❧❣✉é♠ q✉❡ ♥ã♦ t❡✈❡ ❝♦♥t❛t♦ ❝♦♠ ❛s ❣❡♦♠❡tr✐❛s ♥ã♦ ❡✉❝❧✐❞✐❛♥❛s✳
❖ ❝❛♠✐♥❤♦ ♠❛✐s ♦❜❥❡t✐✈♦ ❞❡♥tr♦ ❞♦ ❡♥s✐♥♦ ❜ás✐❝♦ ♣❛r❡❝❡ s❡r ❡♥tã♦ ❛♣r❡s❡♥t❛r ❛♦s ❛❧✉♥♦s ♠♦❞❡❧♦s q✉❡ s❡r✈❡♠ ❞❡ ✐♥t❡r♣r❡t❛çã♦ ♣❛r❛ ♦s ❝♦♥❝❡✐t♦s q✉❡ ❞❡s❡❥❛♠♦s ❡①♣❧✐❝❛r✳ ❆ ✜♥❛❧✐❞❛❞❡ é ❞❡s❡♥✈♦❧✈❡r ❛❧❣✉♠ ❝r✐tér✐♦ ✐♥t✉✐t✐✈♦ ❛ s❡r ✉t✐❧✐③❛❞♦ ♣♦st❡r✐♦r♠❡♥t❡ ♣❛r❛ s❡ ❞❡❝✐❞✐r s❡ ♦✉tr♦s ♠♦❞❡❧♦s s❛t✐s❢❛③❡♠ ♦✉ ♥ã♦ ❡ss❡ ❝r✐tér✐♦✳ ❊♠ ❝❛s♦ ❛✜r♠❛t✐✈♦✱ ♦ ❝♦♥❝❡✐t♦ s❡ ❛♣❧✐❝❛✳ ❈❛s♦ ❝♦♥trár✐♦✱ ♦ ♠♦❞❡❧♦ é r❡❥❡✐t❛❞♦ ❝♦♠♦ ✐♥t❡r♣r❡t❛çã♦✳ ❖ ✐♥t❡r❡ss❛♥t❡ ❛q✉✐ é q✉❡ ♦s ♠♦❞❡❧♦s r❡❥❡✐t❛❞♦s ❛❥✉❞❛♠ ♥❛ ❝♦♠♣r❡❡♥sã♦ ❞♦ ❝♦♥❝❡✐t♦ t❛♥t♦ q✉❛♥t♦ ♦s ♠♦❞❡❧♦s ❛❝❡✐t♦s✳ ❉❡ ❢❛t♦✱ ✉♠ ❜♦♠ ♣♦♥t♦ ❞❡ ♣❛rt✐❞❛ ♣❛r❛ s❡ s❛❜❡r ♦ q✉❡ ❛❧❣✉♠❛ ❝♦✐s❛ é ♣♦❞❡ s❡r ❞❡❝✐❞✐r ❛♥t❡s ♦ q✉❡ ❡st❛ ♥ã♦ é✳
❆ ❞✐✜❝✉❧❞❛❞❡ q✉❡ ❡♥❝♦♥tr❛♠♦s ♥❛ ❡①♣♦s✐çã♦ ❛♥t❡r✐♦r s❡rá s❛♥❛❞❛ ❞❡♥tr♦ ❞♦ ♠ét♦❞♦ ❛①✐♦♠át✐❝♦ ❞❛ s❡❣✉✐♥t❡ ❢♦r♠❛✿ ❛❞♠✐t❡✲s❡ q✉❡ ❛❧❣✉♥s t❡r♠♦s sã♦ ✐♥❞❡✜♥✐❞♦s✱ ✐st♦ é✱ sã♦ ❛❝❡✐t♦s s❡♠ ♠❛✐♦r❡s ❡①♣❧✐❝❛çõ❡s✳ ➱ ♦ ❝❛s♦ ❞❡ r❡t❛s✱ ♥♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❛①✐♦♠át✐❝♦ ❞❛ ❣❡♦♠❡tr✐❛✱ ❡ ❞❡ ❝♦♥❥✉♥t♦s✱ ❞❡♥tr♦ ❞❛ ❚❡♦r✐❛ ❞♦s ❈♦♥❥✉♥t♦s✳ ❖✉tr♦ t❡r♠♦ ✐♥❞❡✜♥✐❞♦ ❞✐③ r❡s♣❡✐t♦ ❛ r❡❧❛çã♦ ❞❡ ♣❡rt✐♥ê♥❝✐❛✱ q✉❡ tr❛❞✉③ ♦ ❢❛t♦ ❞❡ ✉♠ ❡❧❡♠❡♥t♦ s❡r ♦✉ ♥ã♦ ♠❡♠❜r♦ ❞❡ ✉♠ ❝♦♥❥✉♥t♦✳ ❖s t❡r♠♦s ✐♥❞❡✜♥✐❞♦s s❡rã♦ ❡♥tã♦ ♦ ♣♦♥t♦ ❞❡ ♣❛rt✐❞❛ ❞❛ t❡♦r✐❛✱ ❢✉♥❝✐♦♥❛♥❞♦ ❝♦♠♦ ✉♠ ♣♦♥t♦ ❞❡ ❝♦♥❝♦r❞â♥❝✐❛ q✉❡ ❡✈✐t❛ r❡❣r❡ssõ❡s ✐♥✜♥✐t❛s ♥❛ t❡♥t❛t✐✈❛ ❞❡ ❡①♣❧✐❝á✲❧♦s✳
❖❝♦rr❡ q✉❡✱ ♥ã♦ s❛❜❡♥❞♦ ❡①❛t❛♠❡♥t❡ q✉❛❧ ❛ ✐❞❡✐❛ q✉❡ ❝❛❞❛ ♣❡ss♦❛ tr❛③ ❞♦s t❡r♠♦s ✐♥❞❡✜♥✐❞♦s✱ é ♥❡❝❡ssár✐♦ ❡st❛❜❡❧❡❝❡r r❡❣r❛s q✉❡ ❞❡❧✐♠✐t❛♠ ♦s ✉s♦s ❞❡ss❡s t❡r♠♦s✳ ❆ss✐♠ s✉r❣❡ ❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ ❛❞♦t❛r ❛❧❣✉♠❛s s❡♥t❡♥ç❛s s♦❜r❡ ❡ss❡s t❡r♠♦s ✐♥❞❡✜♥✐❞♦s✱ ❝❤❛♠❛✲ ❞♦s ❞❡ ❛①✐♦♠❛s ♦✉ ♣♦st✉❧❛❞♦s✱ t❛♠❜é♠ s❡♠ ♠❛✐♦r❡s ❥✉st✐✜❝❛t✐✈❛s✳ ❖s ❛①✐♦♠❛s r❡❣❡♠ ♦ ✉s♦ ❞♦s t❡r♠♦s ✐♥❞❡✜♥✐❞♦s✳ ❖ s❡♥t✐❞♦ ❞❡ ✏s❡♥t❡♥ç❛s✑ é ♦ ♠❡s♠♦ ❞❡ ✏♣r♦♣♦s✐çõ❡s✑✱ ❡ s❡rá ❡①♣❧✐❝❛❞♦ ♥♦ ❝❛♣ít✉❧♦ ✷✳
❉❡ ♣♦ss❡ ❞♦s ❛①✐♦♠❛s✱ ♦ ♣r♦❜❧❡♠❛ q✉❡ s❡ ❡st❛❜❡❧❡❝❡ é ♦ ❞❡ ❝♦♥✈❡♥❝❡r ❛❧❣✉é♠ ♣♦r ♠ét♦❞♦s ♣✉r❛♠❡♥t❡ ❞❡❞✉t✐✈♦s q✉❡ ✉♠❛ ♣r♦♣♦s✐çã♦ ❞❡❝♦rr❡ ❧♦❣✐❝❛♠❡♥t❡ ❞❡ ♦✉tr❛s✳ ❆s✲ s✐♠ ❛ t❡♦r✐❛ ❝♦♠❡ç❛ ❛ ❣❛♥❤❛r ❝♦r♣♦ ❛ ♣❛rt✐r ❞❛ ❡s❝♦❧❤❛ ❞❡ ❝❡rt♦s t❡r♠♦s ✐♥❞❡✜♥✐❞♦s ❡
❞❛ ❛❞♦çã♦ ❞❡ ❛①✐♦♠❛s q✉❡ ❞✐t❛♠ ❝♦♠♦ ❡ss❡s t❡r♠♦s ♣♦❞❡♠ s❡r ✉s❛❞♦s✳ ❉❡ss❡s ❛①✐♦✲ ♠❛s ❞❡✈❡♠♦s ♦❜t❡r ♥♦✈❛s ❝♦♥❝❧✉sõ❡s✱ ♦✉ s❡❥❛✱ ♥♦✈❛s s❡♥t❡♥ç❛s✳ ❊ss❛s s❡♥t❡♥ç❛s ❞❡✈❡♠ ❞❡❝♦rr❡r ❧♦❣✐❝❛♠❡♥t❡ ❞♦s ❛①✐♦♠❛s ✭♦✉ ❞❡ s❡♥t❡♥ç❛s ♣r❡✈✐❛♠❡♥t❡ ❞❡♠♦♥str❛❞❛s✮ ♣♦r ♠❡✐♦ ❞❡ ♣r✐♥❝í♣✐♦s q✉❡ s❡❥❛♠ ❛❝❡✐t♦s t❛♥t♦ ♣♦r q✉❡♠ ❛s ♦❜t❡✈❡ q✉❛♥t♦ ♣♦r q✉❡♠ ❞❡s❡❥❛ s❡r ❝♦♥✈❡♥❝✐❞♦ ❞❡ q✉❡ ❡❧❛s sã♦ ✈❡r❞❛❞❡✐r❛s✳ ❊ss❡s ❝r✐tér✐♦s ♥❡❝❡ssár✐♦s ♣❛r❛ s❡ ❞❡❝✐❞✐r q✉❛♥❞♦ ✉♠ s❡♥t❡♥ç❛ ❞❡❝♦rr❡ ❧♦❣✐❝❛♠❡♥t❡ ❞❡ ♦✉tr❛s ❞ã♦ ♦ ❝♦♥t❡①t♦ ❡♠ q✉❡ s❡ ✐♥s❡r❡♠ ♦s ♣r✐♥❝í♣✐♦s ❞❡ ❧ó❣✐❝❛✱ ❝✉❥❛ ❝✉❧♠✐♥â♥❝✐❛ é ❛ ♥♦çã♦ ❞❡ ❛r❣✉♠❡♥t❛çã♦ ❛♣r❡s❡♥t❛❞❛ ♥❛ s❡❝çã♦ ✷✳✺✳
✶✳✶ ❈♦♥❥✉♥t♦s
❈♦♥❢♦r♠❡ ❞✐s❝✉t✐❞♦ ♥❛ ✐♥tr♦❞✉çã♦ ❞❡st❡ ❝❛♣ít✉❧♦✱ ♦ t❡r♠♦ ❝♦♥❥✉♥t♦ s❡rá t♦♠❛❞♦ ❝♦♠♦ ✐♥❞❡✜♥✐❞♦✱ ♣♦rt❛♥t♦✱ s❡♠ ❞❡✜♥✐çã♦✳ ❯♠ ❝r✐tér✐♦ ♣❛r❛ ❛ ♥♦t❛çã♦ s❡r✐❛ ❛❞♦t❛r ♥❛ ✐♥❞✐❝❛çã♦ ❞❡ ❝♦♥❥✉♥t♦s ❛♣❡♥❛s ❧❡tr❛s ♠❛✐ús❝✉❧❛s✿ ❆✱ ❇✱ ❈✱ ❡t❝✳✱ ✜❝❛♥❞♦ r❡s❡r✈❛❞♦ ♣❛r❛ s❡✉s ❡❧❡♠❡♥t♦s ❛s ❧❡tr❛s ♠✐♥ús❝✉❧❛s✱ ①✱ ②✱ ③✱ ❡t❝✳✳ ■st♦ é ❢❡✐t♦ ♥❡st❡ tr❛❜❛❧❤♦ ❝♦♠ ❛ s❡❣✉✐♥t❡ r❡ss❛❧✈❛✿ ❡①✐st❡♠ ❝♦♥❥✉♥t♦s q✉❡ sã♦ ❡❧❡♠❡♥t♦s ❞❡ ♦✉tr♦s ❝♦♥❥✉♥t♦s✱ ❡♥tã♦ ❡st❛ ♥♦t❛çã♦ ❛♣r❡s❡♥t❛rá ✉♠❛ ✐♥❝♦♥s✐stê♥❝✐❛ ♥♦s ❝♦♥t❡①t♦s ❡♠ q✉❡ ♥♦s r❡❢❡r✐r♠♦s ❛ ✉♠ ❝♦♥❥✉♥t♦ q✉❡ é t❛♠❜é♠ ♠❡♠❜r♦ ❞❡ ✉♠ ❝♦♥❥✉♥t♦ ✏♠❛✐♦r✑✳ ❉❡✈❡ ✜❝❛r ❝❧❛r♦ q✉❡ q✉❛♥❞♦ ♦ ❝♦♥t❡①t♦ s✉❣❡r✐r q✉❡ ✉♠ ❡❧❡♠❡♥t♦ ♣♦❞❡ s❡r t❛♥t♦ ✉♠ ❝♦♥❥✉♥t♦ ❝♦♠♦ ♠❡♠❜r♦ ❞❡ ♦✉tr♦ ❝♦♥❥✉♥t♦✱ s❡rã♦ ✉s❛❞❛s ❧❡tr❛s ♠✐♥ús❝✉❧❛s✳
❚❛♠❜é♠ ❛ss✉♠✐r❡♠♦s✱ ❝♦♠♦ ❢♦✐ ❞✐t♦✱ ❛ r❡❧❛çã♦ ❞❡ ♣❡rt✐♥ê♥❝✐❛ ❡♥tr❡ ❞♦✐s ♦❜❥❡t♦s✱ q✉❡ ❢❛③ r❡❢❡rê♥❝✐❛ ❛♦ ❢❛t♦ ❞❡ ✉♠ ❡❧❡♠❡♥t♦ s❡r ♠❡♠❜r♦ ✭♦✉ ♥ã♦✮ ❞❡ ✉♠ ❝♦♥❥✉♥t♦✳ ❆ ♥♦çã♦ ❞❡ ❝♦♥❥✉♥t♦ q✉❡ ❞❛ q✉❛❧ s❡rá ❢❡✐t♦ ✉s♦ ❛q✉✐ é ❛ s❡❣✉✐♥t❡✿
❙ é ✉♠ ❝♦♥❥✉♥t♦ s❡ ❡①✐st❡ ❛❧❣✉♠ ❡❧❡♠❡♥t♦ ♣❡rt❡♥❝❡♥t❡ ❛ ❙ ♦✉ s❡ ❙ é ✈❛③✐♦✳
❆ s❡♥t❡♥ç❛ ❛❝✐♠❛ ♥ã♦ é ✉♠❛ ❞❡✜♥✐çã♦ ❞❡ ❝♦♥❥✉♥t♦✱ ♠❛s ❛♣❡♥❛s ✉♠❛ ✐❞❡✐❛ ❞♦ q✉❡ s✐❣♥✐✜❝❛rá ❛ ❛✜r♠❛çã♦ ✏❙ é ✉♠ ❝♦♥❥✉♥t♦✑✳ ■♥t✉✐t✐✈❛♠❡♥t❡ ✉♠ ❝♦♥❥✉♥t♦ é ✉♠❛ ❝♦❧❡çã♦ ❞❡ ♦❜❥❡t♦s ❞✐st✐♥❣✉í✈❡✐s ❢r✉t♦ ❞❡ ♥♦ss♦ ✐♥t❡❧❡❝t♦✱ ❝♦♥❝❡❜✐❞♦ ❝♦♠♦ ✉♠❛ ❡♥t✐❞❛❞❡ ú♥✐❝❛✳ ❖s ♠❡♠❜r♦s q✉❡ ❝♦♠♣õ❡ ♦ ❝♦♥❥✉♥t♦ sã♦ ❝❤❛♠❛❞♦s ❞❡ ❡❧❡♠❡♥t♦s ❞❡ss❡ ❝♦♥❥✉♥t♦✳ ❋❛r❡♠♦s ✉s♦ ❞♦s t❡r♠♦s ❝❧❛ss❡✱ ❝♦❧❡çã♦ ♦✉ ❢❛♠í❧✐❛ ❞❡ ❝♦♥❥✉♥t♦s q✉❛♥❞♦ ❡st✐✈❡r♠♦s tr❛t❛♥❞♦ ❞❡ ✉♠ ❝♦♥❥✉♥t♦ ❝✉❥♦s ❡❧❡♠❡♥t♦s t❛♠❜é♠ sã♦ ❝♦♥❥✉♥t♦s✳
❋❛③❡♥❞♦ r❡❢❡rê♥❝✐❛ à r❡❧❛çã♦ ❞❡ ♣❡rt✐♥ê♥❝✐❛✱ ❛❞♦t❛r❡♠♦s ♦ sí♠❜♦❧♦ ✏∈✑ ♣❛r❛ ❝♦♥s✲
tr✉✐r s❡♥t❡♥ç❛s ❞♦ t✐♣♦✿
❛ ∈ ❙
q✉❡ ✐♥❞✐❝❛ q✉❡ ❛ é ❡❧❡♠❡♥t♦ ❞♦ ❝♦♥❥✉♥t♦ ❙✳ ❆ ♥♦t❛çã♦ ❡st❛❜❡❧❡❝✐❞❛ ♥ã♦ r❡tr❛t❛ s❡ ❛ é s✐♠♣❧❡s♠❡♥t❡ ❡❧❡♠❡♥t♦ ♦✉ s❡ t❛♠❜é♠ é ✉♠ ❝♦♥❥✉♥t♦✱ ♠❛s ❡st❛❜❡❧❡❝❡ q✉❡ ❙ é ❝♦♥❥✉♥t♦✳ ❆ ♥❡❣❛çã♦ ❞❛ ❛✜r♠❛çã♦ ❛❝✐♠❛ é ❝♦♥str✉í❞❛ ❝♦♠ ✉s♦ ❞♦ s✐♠❜♦❧♦ ✏∈/✑✿
❛ ∈/ ❙
❉♦ ♣♦♥t♦ ❞❡ ✈✐st❛ ❞♦s ❢✉♥❞❛♠❡♥t♦s ❞❛ ♠❛t❡♠át✐❝❛ ❛ ✐♥♦✈❛çã♦ ♣r♦✈♦❝❛❞❛ ♣❡❧♦ tr❛✲ ❜❛❧❤♦ ❞❡ ❈❛♥t♦r ❢♦✐ ❛ s✉❛ ✐♥s✐stê♥❝✐❛ ♥❛ ❡①✐stê♥❝✐❛ ❞❡ ❝♦♥❥✉♥t♦s ✐♥✜♥✐t♦s ❝♦♠♦ ♦❜❥❡t♦s ♠❛t❡♠át✐❝♦s ❡q✉✐✈❛❧❡♥t❡s ❛ ♥ú♠❡r♦s ❡ ❛ ❝♦♥❥✉♥t♦s ✜♥✐t♦s✳ ❯♠ r❡❧❛t♦ ❤✐stór✐❝♦ ❞❛ ✈✐❞❛ ❞❡st❡ ♠❛t❡♠át✐❝♦ ♣♦❞❡ s❡r ♦❜t✐❞♦ ❡♠ ❬✶✼❪✳ ❖ ❝♦♥❝❡✐t♦ ❞❡ ✐♥✜♥✐t♦ ♣♦r ❡❧❡ ❞❡s❡♥✈♦❧✈✐❞♦ t❡♠ ❞❡s❡♠♣❡♥❤❛❞♦ ✉♠ ♣❛♣❡❧ ✐♠♣♦rt❛♥t❡ ❞❡♥tr♦ ❞❛ ▼❛t❡♠át✐❝❛✱ s❡♥❞♦ tã♦ ✐♠♣♦rt❛♥t❡ q✉❛♥t♦ ♦ ❝♦♥❝❡✐t♦ ❞❡ ♥ú♠❡r♦✳
✶✳✷ ❖♣❡r❛çõ❡s ❙♦❜r❡ ❈♦♥❥✉♥t♦s
❙❡rá ✐♥tr♦❞✉③✐❞❛ ♥❛ ♣ró①✐♠❛ s❡❝çã♦ ♦s sí♠❜♦❧♦s ❧ó❣✐❝♦s q✉❡ s❡rã♦ ✉s❛❞♦s ♥❛ ❢♦r♠❛✲ çã♦ ❞❡ s❡♥t❡♥ç❛s ❝♦♠♣♦st❛s ❛♦ ❧♦♥❣♦ ❞❡st❡ tr❛❜❛❧❤♦✳ ❊♠ s❛❧❛ ❞❡ ❛✉❧❛✱ ✐st♦ ♣♦❞❡ s❡r ❢❡✐t♦ ❡♠ ♣❛r❛❧❡❧♦ ❝♦♠ ♦ ❡st✉❞♦ ❞❛s ♦♣❡r❛çõ❡s s♦❜r❡ ❝♦♥❥✉♥t♦s✳ ❊ss❛s ♦♣❡r❛çõ❡s sã♦ ❣❡r❛❧♠❡♥t❡ tr❛t❛❞❛s ❝♦♠ ♠❛✐s ❞❡t❛❧❤❡s ♥♦ ♣r✐♠❡✐r♦ ❛♥♦ ❞♦ ❊♥s✐♥♦ ▼é❞✐♦✱ ♣r❡❝❡❞❡♥❞♦ ♦ ❡st✉❞♦ ❞❛s ❢✉♥çõ❡s✳ P♦r ✐ss♦ ❡♥t❡♥❞❡♠♦s ♥ã♦ s❡r ❝♦♠♣❧❡t❛♠❡♥t❡ ❢♦r❛ ❞❡ ❝♦♥t❡①t♦ ❛♣r♦✈❡✐t❛r ❡ss❡ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ♣r❡✈✐st♦ ♥♦ ❝✉rrí❝✉❧♦ ❞❛ ❊❞✉❝❛çã♦ ❇ás✐❝❛ ♣❛r❛ ❡❧✉❝✐✲ ❞❛r ♠❡❧❤♦r ♦ ✉s♦ ❞♦s ❝♦♥❡❝t✐✈♦s ❧ó❣✐❝♦s ❞❛ ❢♦r♠❛ q✉❡ s❡rá ❛♣r❡s❡♥t❛❞❛ ♥❡st❛ s❡❝çã♦✳ ❖s ❞❡t❛❧❤❡s ❛❝❡r❝❛ ❞♦ ✉s♦ ❞❡ ❝❛❞❛ ✉♠ ❞❡ss❡s ❝♦♥❡❝t✐✈♦s s❡rã♦ ❞❛❞♦s ♥♦ ♣ró①✐♠♦ ❝❛♣í✲ t✉❧♦✳ P♦r ❡♥q✉❛♥t♦ ✉s❛r❡♠♦s t❛✐s sí♠❜♦❧♦s ❛♣❡♥❛s ❝♦♠♦ ❢♦r♠❛ ❞❡ ❛❜r❡✈✐❛r ❛ ❡s❝r✐t❛ ❞❡ ❛❧❣✉♠❛s s❡♥t❡♥ç❛s✳ ❖ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❛q✉✐ ♥ã♦ é ❛①✐♦♠át✐❝♦✱ ✜❝❛♥❞♦ ❛ ❡①✐❜✐çã♦ ❞♦s ❛①✐♦♠❛s r❡s❡r✈❛❞❛ ♣❛r❛ ♦ ❝❛♣ít✉❧♦ ✸✳
✶✳✷✳✶ Pr✐♥❝í♣✐♦ ❞❛ ❆❜str❛çã♦
❆ ♦r✐❣❡♠ ❞❛ ❚❡♦r✐❛ ❞♦s ❝♦♥❥✉♥t♦s ♣♦❞❡ s❡r ❡♥❝♦♥tr❛❞❛ ♥♦s tr❛❜❛❧❤♦s ❞♦ ♠❛t❡♠át✐❝♦ r✉ss♦ ●❡♦r❣ ❈❛♥t♦r ✭✶✽✹✺✲✶✾✶✽✮✱ ♦s q✉❛✐s ❜✉s❝❛✈❛♠ ❛ ♠❛✐s ♣r✐♠✐t✐✈❛ ❡ s✐♥tét✐❝❛ ❞❡✜✲ ♥✐çã♦ ❞❡ ❝♦♥❥✉♥t♦✳ ❆❞♠✐t✐♥❞♦ ❛ ♥♦çã♦ ♣r✐♠✐t✐✈❛ ❞❡ q✉❡ ✉♠ ❝♦♥❥✉♥t♦ é ❛❧❣♦ q✉❡ ♣♦ss✉✐ ❡❧❡♠❡♥t♦s✱ ♣❛ss❛✲s❡ ❛ ♣r♦❝✉r❛r ✉♠❛ ❢♦r♠❛ ❞❡ ❝♦♥str✉✐r ❝♦♥❥✉♥t♦s✳ ❯♠❛ ✈❡③ q✉❡ ❝♦♥✲ ❥✉♥t♦s sã♦ ❢r✉t♦s ❞❡ ♥♦ss♦ ✐♥t❡❧❡❝t♦✱ ✉♠❛ ♠❛♥❡✐r❛ ❞❡ ❢♦r♠á✲❧♦s ♣♦❞❡ s❡r s✐♠♣❧❡s♠❡♥t❡ ❧✐st❛♥❞♦ s❡✉s ❡❧❡♠❡♥t♦s✱ ✉♠ ❛ ✉♠✱ ❝♦♠♦ ♥♦s ❡①❡♠♣❧♦s ❛ s❡❣✉✐r✳
❊①❡♠♣❧♦ ✶✳✶✳ ❖ ❝♦♥❥✉♥t♦N ❂ ④✵✱ ✶✱ ✷✱ ✸✱✳✳✳⑥ é ♦ ❝♦♥❥✉♥t♦ ❞♦s ♥ú♠❡r♦s ♥❛t✉r❛✐s✳
❈♦♠❡♥tár✐♦✿ ◗✉❛♥❞♦ ✜③❡r♠♦s ❛ ♦♣çã♦ ❞❡ ❧✐st❛r ♦s ❡❧❡♠❡♥t♦s ❞❡ ✉♠ ❝♦♥❥✉♥t♦ ❡s❝r❡✲ ✈❡r❡♠♦s ❡st❡s ❡❧❡♠❡♥t♦s ❡♥tr❡ ❝❤❛✈❡s✳ ❙❡ ♦ ❝♦♥❥✉♥t♦ t✐✈❡r ✐♥✜♥✐t♦s ❡❧❡♠❡♥t♦s ♠❛s ❢♦r ❡✈✐❞❡♥t❡ ♦ ♣❛❞rã♦ q✉❡ ♥♦s ♣❡r♠✐t❡ ♣❡r❝❡❜❡r q✉❛❧ ♦ ❡❧❡♠❡♥t♦ s❡❣✉✐♥t❡ ❛ q✉❛❧q✉❡r ❡❧❡✲ ♠❡♥t♦ ❞❛❞♦✱ ✉s❛r❡♠♦s r❡t✐❝ê♥❝✐❛s ♣❛r❛ ✐♥❞✐❝❛r q✉❡ ❛ s❡q✉ê♥❝✐❛ ♣r♦ss❡❣✉❡ ♥❡st❡ ♣❛❞rã♦✳ ❆♣r❡s❡♥t❛r❡♠♦s ❛ ♣❛rt✐r ❞♦s ❛①✐♦♠❛s ❞❛ t❡♦r✐❛ ❞♦s ❝♦♥❥✉♥t♦s ✉♠❛ ✐♥t❡r♣r❡t❛çã♦ ♣❛r❛ ❛ ♥❛t✉r❡③❛ ❝❛r❞✐♥❛❧ ❞♦s ♥ú♠❡r♦s ♥❛t✉r❛✐s✳ ❆ ♥❛t✉r❡③❛ ♦r❞✐♥❛❧ ❞❡ss❡s ♥ú♠❡r♦s ♣♦❞❡ s❡r ❞❡s❡♥✈♦❧✈✐❞❛ ❛tr❛✈és ❞♦s ❛①✐♦♠❛s ❞❡ P❡❛♥♦✳
❊①❡♠♣❧♦ ✶✳✷✳ ❖ ❝♦♥❥✉♥t♦ Z ❂ ④✳✳✳✱ ✲ ✷✱ ✲✶✱ ✵✱ ✶✱ ✷✱ ✸✱✳✳✳⑥ é ♦ ❝♦♥❥✉♥t♦ ❞♦s ♥ú♠❡r♦s
✐♥t❡✐r♦s✳
❈♦♠❡♥tár✐♦✿ ◆❡st❡ ❝❛s♦✱ ♥♦t❛♠♦s q✉❡ ♦ ❝♦♥❥✉♥t♦ t❡♠ s❡✉ ♣❛❞rã♦ ❞❡ ✏✐♥✜♥✐t✉❞❡✑ ❡♠ ❞✉❛s ❞✐r❡çõ❡s✿ ❛ ❡sq✉❡r❞❛ ❡ ❛ ❞✐r❡✐t❛ ❞❡ ③❡r♦✳ ❖ sí♠❜♦❧♦Z é ❛❞♦t❛❞♦ ♣❛r❛ ♥ú♠❡r♦s
✐♥t❡✐r♦s ♣♦rq✉❡ ❡ss❛ é ❛ ♣r✐♠❡✐r❛ ❧❡tr❛ ❞❛ ♣❛❧❛✈r❛ ❛❧❡♠ã ❩❛❤❧✱ q✉❡ s✐❣♥✐✜❝❛ ♥ú♠❡r♦✳ P♦❞❡♠♦s ♦❜t❡r ♦s ♥ú♠❡r♦s ✐♥t❡✐r♦s ❛ ♣❛rt✐r ❞♦s ♥ú♠❡r♦s ♥❛t✉r❛✐s✱ ♣♦r ❡①❡♠♣❧♦✱ ♣♦r ♠❡✐♦ ❞❛ ✐♥tr♦❞✉çã♦ ❞❡ s❡❣♠❡♥t♦s ♦r✐❡♥t❛❞♦s✳
❖ ♠ét♦❞♦ ❞❡ ❧✐st❛❣❡♠ ❞♦s ❝♦♥❥✉♥t♦s t❡♠ ✉♠❛ ❧✐♠✐t❛çã♦✿ ❝♦♠♦ ♣♦❞❡rí❛♠♦s ❡s❝r❡✈❡r✱ ♣♦r ❡①❡♠♣❧♦✱ ♦ ❝♦♥❥✉♥t♦ ❞❡ t♦❞♦s ♦s ♥ú♠❡r♦s r❡❛✐s❄ ◆❡st❡ ❝❛s♦ ♥ã♦ ❤á ❛♣❛r❡♥t❡♠❡♥t❡ ✉♠ ✏♣❛❞rã♦✑ q✉❡ ♥♦s ♣❡r♠✐t❛ ❞❡s❝r❡✈❡r t♦❞♦s ♦s ♥ú♠❡r♦s r❡❛✐s ❡♠ ✉♠❛ ❧✐st❛✳ ■st♦ ♣♦rq✉❡✱ s❡ t❡♥t❛r♠♦s ❡s❝r❡✈❡r ♦s ♥ú♠❡r♦s r❡❛✐s ❡♠ ♦r❞❡♠ ❝r❡s❝❡♥t❡✱ ♣♦r ❡①❡♠♣❧♦✱ ❡♥tr❡ ❞♦✐s ♥ú♠❡r♦s r❡❛✐s q✉❛✐sq✉❡r q✉❡ ❝♦❧♦❝❛r♠♦s ♥❛ ❧✐st❛ s❡♠♣r❡ ❤❛✈❡rá ✉♠ ♦✉tr♦ r❡❛❧ ❡♥tr❡ ❡❧❡s q✉❡ ♥ã♦ ❛♣❛r❡❝❡rá ♥❛ ❧✐st❛✳ ❖ ❛r❣✉♠❡♥t♦ ❞❛ ❞✐❛❣♦♥❛❧✐③❛çã♦✱ ❞❛❞♦ ♣♦r ❈❛♥t♦r ❡♠ ✶✽✼✹✱ é ✉♠❛ ♣r♦✈❛ ♠❛t❡♠át✐❝❛ ❞❡ q✉❡ ❡①✐st❡♠ ❝♦♥❥✉♥t♦s ✐♥✜♥✐t♦s q✉❡ ♥ã♦ ♣♦❞❡♠ s❡r ♣♦st♦s ❡♠ ❝♦rr❡s♣♦♥❞ê♥❝✐❛ ❜✐✉♥í✈♦❝❛ ❝♦♠ ♦ ❝♦♥❥✉♥t♦ ❞♦s ♥ú♠❡r♦s ♥❛t✉r❛✐s✳ ■st♦ ❡q✉✐✈❛❧❡ ❛ ❞✐③❡r q✉❡ ♥ã♦ s❡ ♣♦❞❡r ❢❛③❡r ❛ ❡♥✉♠❡r❛çã♦ ❞❡s❡❥❛❞❛ ♣❛r❛ ❛❧❣✉♥s ❝♦♥❥✉♥t♦s ✐♥✜♥✐t♦s✱ ❝♦♠♦ é ♦ ❝❛s♦ ❞♦ ❝♦♥❥✉♥t♦ ❞♦s ♥ú♠❡r♦s r❡❛✐s✳ ❉❡ ❢❛t♦✱ ♦ ❛r❣✉♠❡♥t♦ ❞❛
❉✐❛❣♦♥❛❧ ❞❡ ❈❛♥t♦r ✲ ❛♣r❡s❡♥t❛❞♦ ❝♦♠ ♠❛✐s ❞❡t❛❧❤❡s ❡♠ ❬✷✶❪ ❡ ♥❛ s♦❧✉çã♦ ❞❛❞❛ ❛♦ Pr♦❜❧❡♠❛ ✷✵ ❝♦♠♦ ❛♣❧✐❝❛çã♦ ❞♦ ❚❡♦r❡♠❛ ✹✳✷✹✱ ♥♦ ❛♣ê♥❞✐❝❡ ❆ ✲ ♣♦ss✐❜✐❧✐t❛ ❡①♣❧✐❝❛r ♣♦rq✉❡ é ✐♠♣♦ssí✈❡❧ ❝♦❧♦❝❛r t♦❞♦s ♦s ♥ú♠❡r♦s r❡❛✐s ❡♠ ✉♠❛ ❧✐st❛ ❡♥✉♠❡rá✈❡❧✱ ✐st♦ é✱ ✉♠❛ ❧✐st❛ ♥❛ q✉❛❧ ♣♦❞❡♠♦s ✏❝♦♥t❛r✑ ♦s ❡❧❡♠❡♥t♦s✳ ■st♦ ♣♦❞❡ s❡r ❡♥t❡♥❞✐❞♦ ❛ ♣❛rt✐r ❞❛ ❛✜r♠❛çã♦ ❞❡ q✉❡ t♦❞♦ ♥ú♠❡r♦ r❡❛❧ ❛❞♠✐t❡ ✉♠❛ r❡♣r❡s❡♥t❛çã♦ ❞❡❝✐♠❛❧ ✐♥✜♥✐t❛✳ ❊s♣❡r❛✲ s❡ q✉❡ ✉♠ ❛❧✉♥♦ ❞❡ ❊♥s✐♥♦ ▼é❞✐♦ ❥á ❡st❡❥❛ ❝♦♥✈❡♥❝✐❞♦ ❞❡st❛ ❛✜r♠❛çã♦ ♣❛r❛ ♦s ♥ú♠❡r♦s ✐rr❛❝✐♦♥❛✐s ❡ t❛♠❜é♠ ♣❛r❛ ❞í③✐♠❛s ♣❡r✐ó❞✐❝❛s ✭❞❡❝✐♠❛✐s ❝♦♠ r❡♣r❡s❡♥t❛çã♦ ✐♥✜♥✐t❛✮✳ P♦r ✐ss♦ ✈❡❥❛♠♦s ❝♦♠♦ ♣♦❞❡♠♦s ♦❜t❡r ❛ r❡♣r❡s❡♥t❛çã♦ ✐♥✜♥✐t❛ ❞❡ ♥ú♠❡r♦s ❞❡❝✐♠❛✐s ✜♥✐t♦s✳
❊①❡♠♣❧♦ ✶✳✸✳ ▼♦str❡ q✉❡ ✵✱✠✾ é ✐❣✉❛❧ ❛ ✶✱ ♦♥❞❡ ✵✱✠✾ ❂ ✵✱✾✾✾✳✳✳✳
❙♦❧✉çã♦✳ ❋❛③❡♥❞♦✲s❡ ① ❂ ✵✱✠✾✱ t❡♠✲s❡ ✶✵ ① ❂ ✾✱✠✾✱ ❞❡ ♦♥❞❡ s✉❜tr❛✐♥❞♦ ❛ s❡❣✉♥❞❛ ❡q✉❛çã♦ ❞❛ ♣r✐♠❡✐r❛ ♦❜t❡♠♦s ✾ ① ❂ ✾✱ ♦✉ s❡❥❛✱ ① ❂ ✶✳ ❱❡♠♦s ❛ss✐♠ q✉❡ ♦ ♥ú♠❡r♦ ✶ ❛❞♠✐t❡ r❡♣r❡s❡♥t❛çã♦ ❞❡❝✐♠❛❧ ✐♥✜♥✐t❛ ✵✱✠✾✳
❊①❡♠♣❧♦ ✶✳✹✳ ❖❜t❡♥❤❛ ✉♠❛ r❡♣r❡s❡♥t❛çã♦ ❞❡❝✐♠❛❧ ✐♥✜♥✐t❛ ♣❛r❛ ♦ ♥ú♠❡r♦ r❛❝✐♦♥❛❧ 3 4✳
❙♦❧✉çã♦✳ ❙❛❜❡✲s❡ q✉❡ ❛ ❞✐✈✐sã♦ ❞❡ ✸ ♣♦r ✹ é ✵✱✼✺✳ ❊st❛ r❡♣r❡s❡♥t❛çã♦✱ ❡♥tr❡t❛♥t♦✱ é ✜♥✐t❛✳ P❛r❛ ♦❜t❡r ❛ r❡♣r❡s❡♥t❛çã♦ ❞❡❝✐♠❛❧ ✐♥✜♥✐t❛✱ ♣♦❞❡♠♦s ❢❛③❡r ✉s♦ ❞♦ ♠❡s♠♦ r❛❝✐♦❝í♥✐♦ ❛♣❧✐❝❛❞♦ ♥♦ ❡①❡♠♣❧♦ ❛♥t❡r✐♦r ♣❛r❛ ❡s❝r❡✈❡r ✵✱✵✺ ❂ ✵✱✵✹✠✾✳ ❙❡♥❞♦ ① ❂ ✵✱✵✹✠✾ ♦❜t❡♠♦s✱ s✉❝❡ss✐✈❛♠❡♥t❡✱ ❛♦ s❡ ♠✉❧t✐♣❧✐❝❛r ❛ ✐❣✉❛❧❞❛❞❡ ❛♥t❡r✐♦r ♣♦r ✶✵✵ ❡ ♣♦r ✶✵✵✵✱ ✶✵✵ ① ❂ ✹✱✠✾ ❡ ✶✵✵✵ ① ❂ ✹✾✱✠✾✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ❙✉❜tr❛✐♥❞♦ ❛s ❞✉❛s ú❧t✐♠❛s ✐❣✉❛❧❞❛❞❡s ❝❤❡❣❛♠♦s ❛ ✾✵✵ ① ❂ ✹✺✱ ♦✉ s❡❥❛✱ ① ❂ 1
20 ❂ ✵✱✵✺✳ ❆ss✐♠✱ ❛ ❞❡❝✐♠❛❧ ✵✱✼✺ ♣♦❞❡ s❡r r❡❡s❝r✐t❛
❝♦♠♦ ✵✱✼ ✰ ✵✱✵✺ ❂ ✵✱✼ ✰ ✵✱✵✹✠✾ ❂ ✵✱✼✹✠✾✳
❊①❡♠♣❧♦ ✶✳✺✳ ▼♦str❡ q✉❡ é ✐♠♣♦ssí✈❡❧ ❡♥✉♠❡r❛r ✉♠❛ ❧✐st❛ ❝♦♥t❡♠♣❧❛♥❞♦ t♦❞♦s ♦s ♥ú✲ ♠❡r♦s r❡❛✐s✳ ❊st❡ ❡①❡♠♣❧♦ t❡rá ❝♦♠♦ ❝♦♥s❡q✉ê♥❝✐❛ ❛ ♥ã♦ ❡♥✉♠❡r❛❜✐❧✐❞❛❞❡ ❞♦ ❝♦♥❥✉♥t♦ ❞♦s ♥ú♠❡r♦s r❡❛✐s✱ ❝♦♥❢♦r♠❡ ❛♣r❡s❡♥t❛❞♦ ♥♦ ❈❛♣ít✉❧♦ ✹✳
❙♦❧✉çã♦✳ ❖ ❛r❣✉♠❡♥t♦ ✉s❛❞♦ ❛q✉✐ é ❞❡♥♦♠✐♥❛❞♦ ✏♠ét♦❞♦ ❞❛ ❞✐❛❣♦♥❛❧ ❞❡ ❈❛♥t♦r✑✱ ❡ ♥♦s ♠♦str❛ q✉❡ ✐♥❞❡♣❡♥❞❡♥t❡♠❡♥t❡ ❞❛ ❧✐st❛ ❞❡ ♥ú♠❡r♦s r❡❛✐s q✉❡ ♠♦♥t❡♠♦s✱ s❡♠♣r❡ ❞❡✐①❛r❡♠♦s ❛❧❣✉♠ ♥ú♠❡r♦ ❞❡ ❢♦r❛✳ ❱❛♠♦s ❝♦♥s✐❞❡r❛r ❛♣❡♥❛s ♦s ♥ú♠❡r♦s r❡❛✐s ♥♦ ✐♥t❡r✈❛❧♦ ❬✵✱ ✶❪✳ ❙✉♣♦♥❤❛ ❡♥tã♦ q✉❡ ❡①✐st❛ ✉♠❛ ❧✐st❛ ❝♦♠♣❧❡t❛ ❞❡ ♥ú♠❡r♦s r❡❛✐s ♥❡st❡ ✐♥t❡r✈❛❧♦✱ ❝❛❞❛ ♥ú♠❡r♦ ❝♦♠ s✉❛ r❡♣r❡s❡♥t❛çã♦ ❞❡❝✐♠❛❧ ✐♥✜♥✐t❛✿ x1✱ x2, x3, ✳✳✳✱ ♦♥❞❡ s❡
t❡♠ xi ❂ 0, bi1bi2bi3bi4... ♣❛r❛ ❝❛❞❛ ✐ ♥❛t✉r❛❧✳ ❙❡❥❛ ♦ ♥ú♠❡r♦ ✇ ❂ 0, a1a2a3a4...✱ ♦♥❞❡
ai ❂ ✵ s❡ bii 6= ✵ ❡ ai ❂ ✶ s❡ bii ❂ ✵✳ ❖❜s❡r✈❡ q✉❡ ✇ é ✉♠ ♥ú♠❡r♦ r❡❛❧ ♣❡rt❡♥❝❡♥t❡
❛♦ ✐♥t❡r✈❛❧♦✱ ❝♦♠ r❡♣r❡s❡♥t❛çã♦ ❞❡❝✐♠❛❧ ✐♥✜♥✐t❛ ❡ é ❞✐❢❡r❡♥t❡ ❞❡ ❝❛❞❛ xi ♣♦✐s ai 6= bii
♣❛r❛ t♦❞♦ ✐✳ ❊♠ ♣❛rt✐❝✉❧❛r✱ ✇6= x1 ♣♦✐s ♦ ♣r✐♠❡✐r♦ ❛❧❣❛r✐s♠♦ ❞❡❝✐♠❛❧ ❞❡ ✇✱ q✉❡ é a1✱
é ❞✐❢❡r❡♥t❡ ❞♦ ♣r✐♠❡✐r♦ ❛❧❣❛r✐s♠♦ ❞❡❝✐♠❛❧ ❞❡ x1✱ q✉❡ é b11✳ ▲♦❣♦✱ q✉❛❧q✉❡r q✉❡ s❡❥❛
❛ ❧✐st❛ ✐♥✜♥✐t❛ ❞❡ ♥ú♠❡r♦s r❡❛✐s ♥♦ ✐♥t❡r✈❛❧♦ ❬✵✱ ✶❪ ♥ã♦ s❡rá s✉✜❝✐❡♥t❡ ♣❛r❛ ❞❡s❝r❡✈❡r t♦❞♦s ♦s ♥ú♠❡r♦s r❡❛✐s✱ ❥á q✉❡ ✇ ❝♦♠♦ ❝♦♥str✉í❞♦ ♥❡st❡ ❡①❡♠♣❧♦ ♥ã♦ ❢❛rá ♣❛rt❡ ❞❡st❛ ❧✐st❛✳
❉✐❛♥t❡ ❞♦ ♣r♦❜❧❡♠❛ ❞❛ ✐♥❡✜❝✐ê♥❝✐❛ ❡♠ ❞❡s❝r❡✈❡r ❝♦♥❥✉♥t♦s ✐♥✜♥✐t♦s ✏♠✉✐t♦ ❣r❛♥✲ ❞❡s✑ ❧✐st❛♥❞♦ s❡✉s ❡❧❡♠❡♥t♦s✱ ❝♦♠♦ é ♦ ❝❛s♦ ❞♦ ❝♦♥❥✉♥t♦ ❞♦s ♥ú♠❡r♦s r❡❛✐s✱ ❛ s❛í❞❛ ❡♥❝♦♥tr❛❞❛ ♣♦r ❈❛♥t♦r ❢♦✐ ❡st❛❜❡❧❡❝❡r ♦ ❝♦♥❝❡✐t♦ ❞❡ ✏❢ór♠✉❧❛ ❞❡ ①✑✳ ❯♠❛ ♥♦çã♦ ♠❛✐s ❞❡t❛❧❤❛❞❛ s♦❜r❡ ❡ss❛s ❢ór♠✉❧❛s s❡rá ❞❛❞❛ ♥♦ ❝❛♣ít✉❧♦ ✷✳ P♦r ❡♥q✉❛♥t♦✱ ❛✜r♠❛r❡♠♦s q✉❡ ✉♠❛ ❢ór♠✉❧❛ ❡♠ ① é ✉♠❛ s❡♥t❡♥ç❛ ❞❡❝❧❛r❛t✐✈❛ s♦❜r❡ ① ❛ q✉❛❧ ♣♦❞❡ s❡r ❝❧❛ss✐✜❝❛❞❛ ❝♦♠♦ ✈❡r❞❛❞❡✐r❛ ♦✉ ❢❛❧s❛✳ ❆ss✐♠✱ ✉♠❛ ❢ór♠✉❧❛✱ ♦✉ s❡♥t❡♥ç❛✱ ♦✉ ❛✐♥❞❛ ♣r♦♣♦s✐çã♦ s♦❜r❡ ① é ✉♠❛ s❡q✉ê♥❝✐❛ ✜♥✐t❛ ❞❡ ♣❛❧❛✈r❛s ✭♦✉ sí♠❜♦❧♦s✮✱ ✐♥❝❧✉✐♥❞♦ ♦ ♣ró♣r✐♦ ① ❡ r❡♣r❡s❡♥✲ t❛❞❛ ♣♦r P✭①✮✱ ♦♥❞❡ ♣♦❞❡♠♦s s✉❜st✐t✉✐r ❛ ♦❝♦rrê♥❝✐❛ ❞❡ ① ♣♦r ✉♠ ♦❜❥❡t♦ ❞❡ ♥❛t✉r❡③❛ ❛❞❡q✉❛❞❛ à ❢♦r♠✉❧❛✳
❊①❡♠♣❧♦ ✶✳✻✳ ❯♠ ❡①❡♠♣❧♦ ❞❡ ❢ór♠✉❧❛ s❡r✐❛✱ ❞❛❞♦ ♦ ❝♦♥❥✉♥t♦ ❆ ❂ ④✶✱ ✷✱ ✸⑥✱ ❛ s❡♥t❡♥ç❛ ① ∈ ❆✳ ◆❡st❡ ❝❛s♦✱ P✭✶✮✱ P✭✷✮ ❡ P✭✸✮ sã♦ ✈❡r❞❛❞❡✐r❛s ❡ P✭✺✮ é ❢❛❧s❛✳
P❛r❛ ❞❡s❝r❡✈❡r ❝♦♥❥✉♥t♦s ❛tr❛✈és ❞♦ ✉s♦ ❞❡ ❢ór♠✉❧❛s✱ ❢❛r❡♠♦s ✉s♦ ❞♦ s❡❣✉✐♥t❡ ♣r✐♥✲ ❝í♣✐♦✿
Pr✐♥❝í♣✐♦ ❞❛ ❆❜str❛çã♦✿ ❯♠❛ ❢ór♠✉❧❛ P✭①✮ ❞❡✜♥❡ ✉♠ ❝♦♥❥✉♥t♦ ❆ s❡ ❡ s♦♠❡♥t❡ s❡ ❛ ∈ ❆ ←→ P✭❛✮✱ ♦✉ s❡❥❛✱ ♦s ❛ ∈ ❆ sã♦ ♦s ú♥✐❝♦s ♣❛r❛ ♦s q✉❛✐s P✭❛✮ é ✈❡r❞❛❞❡✐r❛✳
❈♦♥❢♦r♠❡ ✈❡r❡♠♦s ♥❛ ♣ró①✐♠❛ s❡❝çã♦✱ ✉♠ ❝♦♥❥✉♥t♦ ✜❝❛rá ✉♥✐❝❛♠❡♥t❡ ❞❡t❡r♠✐♥❛❞♦ ♣❡❧♦s s❡✉s ❡❧❡♠❡♥t♦s✱ ❞❡ ❢♦r♠❛ q✉❡ s❡ ❞♦✐s ❝♦♥❥✉♥t♦s ♣♦ss✉❡♠ ❡①❛t❛♠❡♥t❡ ♦s ♠❡s♠♦s ❡❧❡♠❡♥t♦s ❡♥tã♦ ❡❧❡s sã♦ ✐❣✉❛✐s✳ ❆ss✐♠✱ ❛♦ ❛♣❧✐❝❛r♠♦s ♦ Pr✐♥❝í♣✐♦ ❞❛ ❆❜str❛çã♦ ♣❛r❛ ❞❡s❝r❡✈❡r ✉♠ ❝♦♥❥✉♥t♦✱ ❡st❡ ❝♦♥❥✉♥t♦ s❡rá ú♥✐❝♦✳ ◆❛ ♥♦t❛çã♦ ❛ s❡❣✉✐r✱ ❛ ❜❛rr❛ ✏✴✑ é ❧✐❞❛ ❝♦♠♦ ✏t❛❧ q✉❡✑ ❡ ❡s❝r❡✈❡✲s❡
❆ ❂ ④① ✴ P✭①✮⑥
