❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❙ã♦ P❛✉❧♦
❊s❝♦❧❛ ❙✉♣❡r✐♦r ❞❡ ❆❣r✐❝✉❧t✉r❛ ✏▲✉✐③ ❞❡ ◗✉❡✐r♦③✑
▼♦❞❡❧♦s ❞❡ ❞♦s❡✲r❡s♣♦st❛ ❝♦♠ ❝❡♥s✉r❛ ✐♥t❡r✈❛❧❛r ❛♣❧✐❝❛❞♦s ❛
❞❛❞♦s ❞❡ ❣❡r♠✐♥❛çã♦ ❞❡ s❡♠❡♥t❡s
■á❜✐t❛ ❋❛❜✐❛♥❛ ❙♦✉s❛ ❆③❡✈❡❞♦
❚❡s❡ ❛♣r❡s❡♥t❛❞❛ ♣❛r❛ ♦❜t❡♥çã♦ ❞♦ tít✉❧♦ ❞❡ ❉♦✉t♦r❛ ❡♠ ❈✐ê♥❝✐❛s✳ ➪r❡❛ ❞❡ ❝♦♥❝❡♥tr❛çã♦✿ ❊st❛tíst✐❝❛ ❡ ❊①♣❡r✐♠❡♥t❛çã♦ ❆❣r♦♥ô♠✐❝❛
■á❜✐t❛ ❋❛❜✐❛♥❛ ❙♦✉s❛ ❆③❡✈❡❞♦ ▲✐❝❡♥❝✐❛❞❛ ❡♠ ▼❛t❡♠át✐❝❛
▼♦❞❡❧♦s ❞❡ ❞♦s❡✲r❡s♣♦st❛ ❝♦♠ ❝❡♥s✉r❛ ✐♥t❡r✈❛❧❛r ❛♣❧✐❝❛❞♦s ❛ ❞❛❞♦s ❞❡ ❣❡r♠✐♥❛çã♦ ❞❡ s❡♠❡♥t❡s
✈❡rsã♦ r❡✈✐s❛❞❛ ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛ r❡s♦❧✉çã♦ ❈♦P●r ✻✵✶✽ ❞❡ ✷✵✶✶
❖r✐❡♥t❛❞♦r✿
Pr♦❢✳ ❉r✳ ❈➱❙❆❘ ●❖◆➬❆▲❱❊❙ ❉❊ ▲■▼❆ ❈♦♦r✐❡♥t❛❞♦r✿
Pr♦❢✳ ❉r✳ ❏❯❱✃◆❈■❖ ❙❆◆❚❖❙ ◆❖❇❘❊
❚❡s❡ ❛♣r❡s❡♥t❛❞❛ ♣❛r❛ ♦❜t❡♥çã♦ ❞♦ tít✉❧♦ ❞❡ ❉♦✉t♦r❛ ❡♠ ❈✐ê♥❝✐❛s✳ ➪r❡❛ ❞❡ ❝♦♥❝❡♥tr❛çã♦✿ ❊st❛tíst✐❝❛ ❡ ❊①♣❡r✐♠❡♥t❛çã♦ ❆❣r♦♥ô♠✐❝❛
Dados Internacionais de Catalogação na Publicação DIVISÃO DE BIBLIOTECA - DIBD/ESALQ/USP
Azevedo, Iábita Fabiana Sousa
Modelos de dose-resposta com censura intervalar aplicados a dados de germinação de sementes / Iábita Fabiana Sousa Azevedo. - - versão revisada de acordo com a resolução CoPGr 6018 de 2011. - - Piracicaba, 2016.
74 p. : il.
Tese (Doutorado) - - Escola Superior de Agricultura “Luiz de Queiroz”.
1. Análise de sobrevivência 2. Germinação de sementes 3. Modelos de dose-resposta 4. Censura intervalar 5. Pacote drc I. Título
CDD 519.546 A994m
✸
❉❡❞✐❝❛tór✐❛
✺
❆●❘❆❉❊❈■▼❊◆❚❖❙
❊ss❛ t❡s❡ ♥ã♦ t❡r✐❛ s✐❞♦ ❡s❝r✐t❛ s❡♠ ❛ ❝♦❧❛❜♦r❛çã♦ ❞❡ ✈ár✐❛s ♣❡ss♦❛s q✉❡ ♥ã♦ só ♠❡ ❛❥✉❞❛r❛♠✱ ♠❛s t❛♠❜é♠ ❢♦r❛♠ ❡①❡♠♣❧♦s ❞❡ ❝♦♠♦ ❡♥❢r❡♥t❛r ❛s ❛❞✈❡rs✐❞❛❞❡s q✉❛♥❞♦ s❡ ❜✉s❝❛ ✉♠ s♦♥❤♦✳ ◗✉❡r♦ ❡①♣r❡ss❛r ❞❡ ❝♦r❛çã♦ ♦s ♠❡✉s ❛❣r❛❞❡❝✐♠❡♥t♦s às s❡❣✉✐♥t❡s ♣❡ss♦❛s ❡ ✐♥st✐t✉✐çõ❡s✿
➚ ❉❡✉s✱ ♣❡❧♦s ♠♦♠❡♥t♦s ❞✐❢í❝❡✐s q✉❡ ♠❡ ❧❡♠❜r♦✉ q✉❡ ❞❡✈❡r✐❛ ♠❡ ❡s❢♦rç❛r ❡ t❡r ❜♦♠ â♥✐♠♦✱ ♠♦❧❞❛♥❞♦ ❛ss✐♠ ♦ ♠❡✉ ❝❛rát❡r ❛ ❡①❡♠♣❧♦ ❞❡ ❈r✐st♦✱ ❡ ♣❡❧♦s ♠♦♠❡♥t♦s ❢❡❧✐③❡s q✉❡ ♠❡ ❞❡r❛♠ ❢♦rç❛ ♣❛r❛ ♣r♦ss❡❣✉✐r✳
➚ ♠✐♥❤❛ ❣r❛♥❞❡ ❢❛♠í❧✐❛ ❛ q✉❛❧ ❡✉ s♦✉ ♠✉✐t♦ ❢❡❧✐③ ❞❡ ♣❡rt❡♥❝❡r✿ ♠✐♥❤❛ ♠ã❡✱ ✐r♠ã✱ ✐r♠ã♦s✱ ❛✈ós✱ t✐♦s✱ t✐❛s✱ ♣r✐♠♦s✱ ♣r✐♠❛s✱ ❝✉♥❤❛❞♦s✱ ❝✉♥❤❛❞❛s✱ ♠❡✉s s♦❣r♦s ♣❡❧♦ ❝✉✐❞❛❞♦✱ ♣❡❧❛ ❢♦rç❛✱ ❞❡❞✐❝❛çã♦✱ ❛♠♦r ❡ ♣❡❧♦ ❛♣♦✐♦ ♥♦s ♠♦♠❡♥t♦s ❞✐❢í❝❡✐s q✉❡ ♥ã♦ ❢♦r❛♠ ♣♦✉❝♦s ❡ ♣❡❧❛s ✐♥q✉✐❡t❛♥t❡s ❞❡❝✐sõ❡s✱ ♣♦r ❝❛❞❛ ♦r❛çã♦✱ ♣♦r ❡st❛r❡♠ ❛♦ ♠❡✉ ❧❛❞♦ ❛ ❝❛❞❛ ❝♦♥q✉✐st❛ ❡ s❡ ❛❧❡❣r❛r❡♠ ❝♦♠✐❣♦ ❛ ❝❛❞❛ r❡❛❧✐③❛çã♦✳
❆♦ ♠❡✉ ♠❛r✐❞♦ ❋❛❜✐♦ ❆③❡✈❡❞♦✱ q✉❡ ♥♦ ♠❡✐♦ ❞❡ss❛ ❝❛♠✐♥❤❛❞❛ r❡❛♣❛r❡❝❡✉ ❡♠ ♠✐♥❤❛ ✈✐❞❛ ❞❡ ✉♠❛ ♠❛♥❡✐r❛ ❜❡❧❛ ❡ ❡ss❡♥❝✐❛❧ ♣❛r❛ q✉❡ ♣✉❞❡ss❡ ❝❤❡❣❛r ❛té ❛q✉✐✳
❆♦ Pr♦❢❡ss♦r ❏♦❡❧ ❆✉❣✉st♦ ▼✉♥✐③ ❡ ❛ ♣r♦❢❡ss♦r❛ ❚❛❝✐❛♥❛ ❙❛✈✐❛♥ ♣❡❧♦ ✐♥❝❡♥t✐✈♦ ❛ ❝♦♠❡ç❛r ❡st❛ ♥♦✈❛ ❡t❛♣❛✳
❆♦ ♣r♦❢❡ss♦r ❈és❛r ●♦♥ç❛❧✈❡s ❞❡ ▲✐♠❛ ♣♦r s❡r ♠❛✐s q✉❡ ✉♠ ♦r✐❡♥t❛❞♦r✱ ♣♦r s✉❛s ❝♦♥tr✐❜✉✐çõ❡s✱ ♣♦r ❛❝r❡❞✐t❛r ❡♠ ♠✐♠ ❡ ♥♦ ♠❡✉ ❝r❡s❝✐♠❡♥t♦✱ ♣❡❧♦ s❡✉ ❛♣♦✐♦ ❢✉♥❞❛♠❡♥t❛❧ ❡ ♣♦r ♠❡ ❡♥s✐♥❛r t❛♥t♦ ❝♦♠ ♦ s❡✉ ❡①❡♠♣❧♦ ❞❡ ❣❡♥❡r♦s✐❞❛❞❡ ❡ ♣❛❝✐ê♥❝✐❛✳
❆♦ ♣r♦❢❡ss♦r ❏✉✈ê♥❝✐♦ ❙❛♥t♦s ◆♦❜r❡✱ ♣♦r s✉❛s ❝♦♥tr✐❜✉✐çõ❡s ♣❛r❛ ♠❡❧❤♦r✐❛ ❞❡st❡ tr❛❜❛❧❤♦✳
❆♦ Pr♦❢❡ss♦r❡s ❈❤r✐st✐❛♥ ❘✐t③ ❡ ❲❛❧♠❡s ❩❡✈✐❛♥❡✱ ♣❡❧❛ ❞✐s♣♦s✐çã♦ ❛ ❛❥✉✲ ❞❛r✱ ♣♦r ❝♦♠♣❛rt✐❧❤❛r s❡✉s ❝♦♥❤❡❝✐♠❡♥t♦s ❞❡ ♠❛♥❡✐r❛ tã♦ ♥♦❜r❡✱ ♠✐♥❤❛ ❛❞♠✐r❛çã♦ ❡ ♠❡✉ ♦❜r✐❣❛❞❛✳
❆ PP●❊❆✴❊❙❆▲◗ ♣♦r t❡r ♠❡ r❡❝❡❜✐❞♦ ♥♦ ❝✉rs♦ ❞❡ ❞♦✉t♦r❛❞♦✱ ❛♦s ♣r♦✲ ❢❡ss♦r❡s ❞♦ ❞❡♣❛rt❛♠❡♥t♦ ♣♦r ❝♦♠♣❛rt✐❧❤❛r❡♠ ♦s s❡✉s ❝♦♥❤❡❝✐♠❡♥t♦s ❡ ❡♠ ❡s♣❡❝✐❛❧ ❛♦ ♣r♦❢❡ss♦r ❈❛r❧♦s ❚❛❞❡✉ ❡ ❛ Pr♦❢❡ss♦r❛ ❘♦s❡❧✐ ▲❡❛♥❞r♦ ♣♦r t♦❞♦ ❛♣♦✐♦ ♥❡ss❛ ❥♦r♥❛❞❛✳
✻
❣❛tt♦✳
➚ ❆❞r✐❡❧❡ ❇✐❛s❡✱ q✉❡ ♥❡ss❡s ❛♥♦s s❡ t♦r♥♦✉ ✉♠❛ ❣r❛♥❞❡ ❛♠✐❣❛✱ q✉❡ ❧❡✈❡✲ ♠♦s ❡ss❛ ❛♠✐③❛❞❡ ♣♦r t♦❞❛ ❛ ✈✐❞❛✱ s❡♠♣r❡ ♠❡ ✐♥❝❡♥t✐✈❛♥❞♦ ❛ ♣r♦ss❡❣✉✐r✳
❆♦s ❛❧✉♥♦s ❞♦ PP●❊❆✱ ♠❡✉s ❛♠✐❣♦s ❞❛ ✈✐❞❛ ❛❝❛❞ê♠✐❝❛✱ ♦ ♠❡✉ ♠✉✐t♦ ♦❜r✐❣❛❞❛✱ ❡♠ ❡s♣❡❝✐❛❧ ❱❛❧✐❛♥❛✱ ❑✉❛♥❣✱ ▼❛r✐s♦❧✱ ◆✐❧t♦♥✱ ❙❡r❣✐♦✱ ❚✐❛❣♦ ❱✐❛♥❛✱ ■③❛❜❡❧❛✱ ❉❥❛✐r✱ ❏♦s✐❛♥❡✱ ❆❧t❡♠✐r✱ ❘❛❢❛❡❧ ▼♦r❛❧✳
❆ ♠✐♥❤❛ ❝❛s❛ ❡♠ P✐r❛❝✐❝❛❜❛✱ ❛ ❝❛❞❛ ✐r♠ã q✉❡ ❛❥✉❞♦✉ ❛ ♠✐♥✐♠✐③❛r ❛ s❛✉❞❛❞❡ ❞❡ ❝❛s❛✱ ❡ ❛ ❝❛❞❛ ❛♠✐❣❛ q✉❡ ❝♦♥❤❡❝✐ ❞✉r❛♥t❡ ❡ss❡s ❛♥♦s✱ ❞✐✈✐❞✐♥❞♦ ❛❧❡❣r✐❛s✱ ❞ú✈✐❞❛s ❡ ❛♥s❡✐♦s✳
❆♦ ♠❡✉ ♣❛✐✱ q✉❡ ♥ã♦ ♣♦❞❡ ✈❡r ❛ ❝♦♥❝❧✉sã♦ ❞❡st❡ tr❛❜❛❧❤♦✱ ♠❛s q✉❡ ❢♦✐ ✉♠ ❣r❛♥❞❡ ❡①❡♠♣❧♦ ♣❛r❛ ♠✐♠ ❞❡ ❛♠♦r✱ ❛❧❡❣r✐❛✱ ❣❡♥❡r♦s✐❞❛❞❡ ❡ ❢♦rç❛✳
❋❛ç♦ q✉❡stã♦ ❞❡ ❛❣r❛❞❡❝❡r ❛ t♦❞❛s ❛s ♣❡ss♦❛s q✉❡ t♦r❝❡r❛♠ ♦✉ ✐♥t❡r❝❡❞❡✲ r❛♠ ♣♦r ♠✐♠✱ ♠❡s♠♦ q✉❡ ❞❡ ❢♦r♠❛ ❛♥ô♥✐♠❛✳ ❆❧❜❛✱ ❘✐❝❛r❞♦✱ ❙❛♠❛r❛✱ ▲✉❝❛s✱ P❛trí❝✐❛✱ ❆♥❛ ❈❧❛ú❞✐❛✱ ❙✐❧✈✐❛✱ ❑❡✐t❡✱ ❛♠✐❣♦s ❞❡ ▲❛✈r❛s✳ ❆ t♦❞♦s ❡ss❡s ❛♠✐❣♦s ❡ ♠✉✐t♦s ♦✉tr♦s ❛q✉✐ ♥ã♦ ❝✐t❛❞♦s✱ ♠❡✉ ♠✉✐t♦ ♦❜r✐❣❛❞❛✳
✼
✧▲❡✈❛♥t❛r❡✐ ♦s ♠❡✉s ♦❧❤♦s ♣❛r❛ ♦s ♠♦♥t❡s✱ ❞❡ ♦♥❞❡ ✈❡♠ ♦ ♠❡✉ s♦❝♦rr♦✳ ❖ ♠❡✉ s♦❝♦rr♦ ✈❡♠ ❞♦ ❙❡♥❤♦r q✉❡ ❢❡③ ♦ ❝é✉ ❡ ❛ t❡rr❛✳✧
✽
✾
❙❯▼➪❘■❖
✶✶
❘❊❙❯▼❖
▼♦❞❡❧♦s ❞❡ ❞♦s❡✲r❡s♣♦st❛ ❝♦♠ ❝❡♥s✉r❛ ✐♥t❡r✈❛❧❛r ❛♣❧✐❝❛❞♦s ❛ ❞❛❞♦s ❞❡ ❣❡r♠✐♥❛çã♦ ❞❡ s❡♠❡♥t❡s
❖ ❝r❡s❝✐♠❡♥t♦ ❞❡ ✐♥✈❡st✐♠❡♥t♦s ❡♠ ❜✐♦t❡❝♥♦❧♦❣✐❛ ♥❛ ❛❣r✐❝✉❧t✉r❛ t❡♠ s✐❞♦ ✉♠ ❡❧❡♠❡♥t♦ ♣r✐♠♦r❞✐❛❧ ♣❛r❛ ❛ s❡❣✉r❛♥ç❛ ❛❧✐♠❡♥t❛r ❣❧♦❜❛❧✳ ■ss♦ t❡♠ ❧❡✈❛❞♦ ❛ ✉♠❛ r❡♦r❣❛♥✐③❛çã♦ ❞❛ ✐♥❞ústr✐❛ ♠✉♥❞✐❛❧ ❞❡ s❡♠❡♥t❡s ♥❛ ❜✉s❝❛ ♣♦r té❝♥✐❝❛s ♠❛✐s ❛❞❡q✉❛❞❛s ❞❡ ❝✉❧t✐✈♦✱ ♠❡❝❛♥✐③❛çã♦✱ ✉s♦ ❞❡ ❢❡rt✐❧✐③❛♥t❡s✱ ❞❡❢❡♥s✐✈♦s ❛❣rí❝♦❧❛s ❡ ❛ ✉t✐❧✐③❛çã♦ ❞❡ s❡♠❡♥t❡s✳ ❖ ❇r❛s✐❧ ♣♦r s❡r ✉♠ ❞♦s ❛♠❜✐❡♥t❡s ♠❛✐s só❧✐❞♦s ♥❡ss❡ ❝♦♥t❡①t♦ t❡♠ ❝♦♥tr✐❜✉í❞♦ ❝♦♠ ♦ ❝r❡s❝✐♠❡♥t♦ ❡ ❛ ❞✐✈❡rs✐✜❝❛çã♦ ❞❛ ♣r♦❞✉çã♦ ❞❡ s❡♠❡♥t❡s ❧❡✈❛♥❞♦ ❛s ❧❛✈♦✉r❛s ❜r❛s✐❧❡✐r❛s ❛ ❛t✐♥❣✐r❡♠ ✉♠ ♥♦✈♦ ♣❛t❛♠❛r ❞❡ ♣r♦❞✉t✐✈✐❞❛❞❡✳ ❉✐❢❡r❡♥t❡s ♠❡t♦❞♦❧♦❣✐❛s ❡st❛tíst✐❝❛s tê♠ s✐❞♦ ✉t✐❧✐③❛❞❛s ♣❛r❛ ❛♥❛❧✐s❛r ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞❛ ❣❡r♠✐♥❛çã♦ ❞❡ ✉♠❛ ♣♦♣✉❧❛çã♦ ❞❡ s❡♠❡♥t❡s✳ ❊♥tr❡t❛♥t♦✱ ✉s❛r ❛❜♦r❞❛❣❡♥s ❡st❛tíst✐❝❛s q✉❡ ❛♥❛❧✐s❛♠ ♦s ❞❛❞♦s ❞❡ ❣❡r♠✐♥❛çã♦ ❞❛ ♠❡❧❤♦r ♠❛♥❡✐r❛ ♣♦ssí✈❡❧ ♣❡r♠✐t✐rá ✉♠❛ ♠❛✐♦r ❝♦♥✜❛❜✐❧✐❞❛❞❡ ❞♦s r❡s✉❧t❛❞♦s✱ ❜❡♠ ❝♦♠♦✱ ❣❛♥❤♦ ❞❡ ✐♥❢♦r♠❛çõ❡s ♣❡rt✐♥❡♥t❡s✳ ❈♦♠♦ ❡♠ t❡st❡s ❞❡ ❣❡r♠✐♥❛çã♦ ❞❡ s❡♠❡♥t❡s ❡st✉❞❛✲s❡ ♦ t❡♠♣♦ ❛té ❛ ♦❝♦rrê♥❝✐❛ ❞♦ ❡✈❡♥t♦✱ q✉❡ ❡♥✈♦❧✈❡ ♠❡❞✐❞❛s r❡♣❡t✐❞❛s ❢❡✐t❛s ♥♦ ♠❡s♠♦ ❧♦t❡ ❡ ♥ã♦ s❡ ❝♦♥❤❡❝❡ ♦ t❡♠♣♦ ❡①❛t♦ ❞❛ ❣❡r♠✐♥❛çã♦ ❞❛ s❡♠❡♥t❡✱ ♣r♦♣õ❡✲s❡ ♦ ✉s♦ ❞❡ ♠♦❞❡❧♦s ❞❡ ❞♦s❡✲r❡s♣♦st❛ ❝♦♠ ❝❡♥s✉r❛ ✐♥t❡r✈❛❧❛r✱ q✉❡ ♣❡r♠✐t❡♠ ❛ ✐♥t❡r♣r❡t❛çã♦ ❜✐♦❧ó❣✐❝❛ ❞♦s ♣❛râ♠❡tr♦s ✉s❛❞♦s ♣❛r❛ ♠❡❞✐r ♦ ♣r♦❝❡ss♦ ❣❡r♠✐♥❛t✐✈♦ ❡ r❡✢❡t❡♠ ♦ ❞❡s❡♥❤♦ ❡①♣❡r✐♠❡♥t❛❧ ❞♦s ❞❛❞♦s✳ ◆❡st❡ tr❛❜❛❧❤♦ ❢♦r❛♠ ✉t✐❧✐③❛❞❛s ❞✉❛s ♠❡t♦❞♦❧♦❣✐❛s ❡st❛tíst✐❝❛s ✉s✉❛✐s ♥❛ ❛♥á❧✐s❡ ❞❡ ❞❛❞♦s ❞❡ ❣❡r♠✐♥❛✲ çã♦ ❞❡ s❡♠❡♥t❡s ❡ s❡✉s r❡s✉❧t❛❞♦s ❢♦r❛♠ ❝♦♠♣❛r❛❞♦s ❝♦♠ ♦s ❞❛ ❛❜♦r❞❛❣❡♠ ❞❡ ♠♦❞❡❧♦s ❞♦s❡✲r❡s♣♦st❛ ❝♦♠ ❝❡♥s✉r❛ ✐♥t❡r✈❛❧❛r✳ ❋♦r❛♠ ✉t✐❧✐③❛❞♦s ♦s ♠♦❞❡❧♦s ❞❡ ❞♦s❡✲r❡s♣♦st❛ ❲❡✐❜✉❧❧ ✷ ❡ ❧♦❣✲❧♦❣íst✐❝♦ ♣❛r❛ ❡①♣❧✐❝❛r ♦ ♣r♦❝❡ss♦ ❣❡r♠✐♥❛t✐✈♦ ❞❡ s❡♠❡♥t❡s ❞❡ ❇r❛❝❤✐✲ ❛r✐❛ ❡ ❈✐tr✉♠❡❧♦ ❙✇✐♥❣❧❡ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ ❝♦♠ ❞✐❢❡r❡♥t❡s t❡♠♣♦s ❞❡ ♦❜s❡r✈❛çã♦✳ ❖s ❡①♣❡r✐♠❡♥t♦s ❢♦r❛♠ r❡❛❧✐③❛❞♦s ❡♠ ❞❡❧✐♥❡❛♠❡♥t♦ ✐♥t❡✐r❛♠❡♥t❡ ❛❧❡❛t♦r✐③❛❞♦ ❡ ♦s ♣r♦❝❡✲ ❞✐♠❡♥t♦s ❞♦s t❡st❡s ❞❡ ❣❡r♠✐♥❛çã♦ ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛s ❘❡❣r❛s ♣❛r❛ ❆♥á❧✐s❡ ❞❡ ❙❡♠❡♥t❡s ✭❘❆❙✮✳ ❆s ❝♦♥❝❧✉sõ❡s ♦❜t✐❞❛s ❛ ♣❛rt✐r ❞❛ ❛♥á❧✐s❡ ❞♦s ❞❛❞♦s ♣♦r ♠❡✐♦ ❞❛ ♠❡t♦❞♦❧♦❣✐❛ ♣r♦♣♦st❛✱ ❡♠ ❣❡r❛❧✱ ❞✐✈❡r❣✐r❛♠ ❞❛s ❝♦♥❝❧✉sõ❡s ♦❜t✐❞❛s ♣♦r ❛❜♦r❞❛❣❡♥s tr❛❞✐❝✐♦♥❛✐s ✭♠♦❞❡❧♦s ❞❡ r❡❣r❡ssã♦ ♥ã♦✲❧✐♥❡❛r ❝♦♥s✐❞❡r❛♥❞♦ ❛ ❞✐str✐❜✉✐çã♦ ♥♦r♠❛❧ ❡ í♥❞✐❝❡s ❞❡ ❣❡r♠✐♥❛çã♦ ❝♦♠ ♦ ✉s♦ ❞❛ ❛♥á❧✐s❡ ❞❡ ✈❛r✐â♥❝✐❛✮ ✉t✐❧✐③❛❞❛s ♣❛r❛ ❛♥❛❧✐s❛r ❞❛❞♦s ❞❡ ❣❡r♠✐♥❛çã♦✳ ❖s ♠♦❞❡❧♦s ❞❡ ❞♦s❡✲r❡s♣♦st❛ ❝♦♠ ❝❡♥s✉r❛ ✐♥t❡r✈❛❧❛r ❛♣r❡s❡♥t❛r❛♠ ❛❥✉s✲ t❡s s❛t✐s❢❛tór✐♦s ❡ s❡♥❞♦ ♣♦rt❛♥t♦ ✉♠❛ ❛♥á❧✐s❡ ♠❛✐s ❛❞❡q✉❛❞❛ q✉❡ ❛s ❛❜♦r❞❛❣❡♥s ✉s✉❛✐s✳
✶✸
❆❇❙❚❘❆❈❚
❉♦s❡✲r❡s♣♦♥s❡ ♠♦❞❡❧s ✇✐t❤ ✐♥t❡r✈❛❧✲❝❡♥s♦r❡❞ ❛♣♣❧✐❡❞ t♦ s❡❡❞ ❣❡r♠✐♥❛t✐♦♥ ❞❛t❛
❚❤❡ ❣r♦✇t❤ ♦❢ ✐♥✈❡st♠❡♥t ✐♥ ❜✐♦t❡❝❤♥♦❧♦❣② ✐♥ ❛❣r✐❝✉❧t✉r❡ ❤❛s ❜❡❡♥ ❛ ✈✐t❛❧ ❡❧❡♠❡♥t ❢♦r ❣❧♦❜❛❧ ❢♦♦❞ s❡❝✉r✐t②✳ ❚❤✐s ❤❛s ❧❡❞ t♦ ❛ r❡♦r❣❛♥✐③❛t✐♦♥ ♦❢ t❤❡ ✇♦r❧❞ s❡❡❞ ✐♥✲ ❞✉str② ✐♥ t❤❡ s❡❡❦✐♥❣ ♦❢ t❤❡ ♠♦st ❛♣♣r♦♣r✐❛t❡ t❡❝❤♥✐q✉❡s ♦❢ ❝✉❧t✐✈❛t✐♦♥✱ ♠❡❝❤❛♥✐③❛t✐♦♥✱ ✉s❡ ♦❢ ❢❡rt✐❧✐③❡rs✱ ♣❡st✐❝✐❞❡s ❛♥❞ s❡❡❞s✳ ❚❤❡ ❇r❛③✐❧ ❢♦r ❜❡✐♥❣ ♦♥❡ ♦❢ t❤❡ ♠♦st s♦❧✐❞ ✐♥ t❤❡ ✇♦r❧❞ ❝♦♥t❡①t ♦❢ t❤❡ s❡❡❞ ✐♥❞✉str② ❤❛s ❝♦♥tr✐❜✉t❡❞ t♦ t❤❡ ❣r♦✇t❤ ❛♥❞ ❞✐✈❡rs✐✜❝❛t✐♦♥ ♦❢ s❡❡❞ ♣r♦❞✉❝t✐♦♥✱ ❧❡❛❞✐♥❣ ❇r❛③✐❧✐❛♥ ❝r♦♣s t♦ ❛ ♥❡✇ ❧❡✈❡❧ ♦❢ ♣r♦❞✉❝t✐✈✐t②✳ ❉✐✛❡r❡♥t st❛t✐st✐❝❛❧ ♠❡t❤♦❞♦❧♦❣✐❡s ❤❛✈❡ ❜❡❡♥ ✉s❡❞ t♦ ❛♥❛❧②③❡ t❤❡ ❣❡r♠✐♥❛t✐♦♥ ❜❡❤❛✈✐♦r✳ ❍♦✇❡✲ ✈❡r✱ ✉s✐♥❣ st❛t✐st✐❝❛❧ ❛♣♣r♦❛❝❤❡s t❤❛t ❛♥❛❧②③❡ ❣❡r♠✐♥❛t✐♦♥ ❞❛t❛ ❛s ❡✣❝✐❡♥t❧② ❛s ♣♦ss✐❜❧❡ ✇✐❧❧ ❛❧❧♦✇ ❛ ❣r❡❛t❡r r❡❧✐❛❜✐❧✐t② ♦❢ t❤❡ r❡s✉❧ts✱ ❛s ✇❡❧❧ ❛s r❡❧❡✈❛♥t ✐♥❢♦r♠❛t✐♦♥ ❣❛✐♥✳ ❆s ✐♥ s❡❡❞ ❣❡r♠✐♥❛t✐♦♥ t❡st st✉❞✐❡s t❤❡ t✐♠❡ ✉♥t✐❧ t❤❡ ♦❝❝✉rr❡♥❝❡ ♦❢ t❤❡ ❡✈❡♥t✱ ✐♥✈♦❧✈❡s r❡♣❡❛t❡❞ ♠❡❛s✉r❡♠❡♥ts ♦♥ t❤❡ s❛♠❡ ❡①♣❡r✐♠❡♥t❛❧ ✉♥✐t ❛♥❞ ❞♦ ♥♦t ❦♥♦✇ t❤❡ ❡①❛❝t t✐♠❡ ♦❢ ❣❡r♠✐♥❛t✐♦♥✱ ✇❡ ♣r♦♣♦s❡ t❤❡ ✉s❡ ♦❢ ❞♦s❡✲r❡s♣♦♥s❡ ♠♦❞❡❧s ✇✐t❤ ✐♥t❡r✈❛❧ ❝❡♥s✉r❡❞ t❤❛t ❛❧❧♦✇ ❜✐♦❧♦❣✐❝❛❧ ✐♥t❡r♣r❡t❛t✐♦♥ ♦❢ ♣❛r❛♠❡t❡rs ✉s❡❞ t♦ ♠❡❛s✉r❡ t❤❡ ❣❡r♠✐♥❛t✐♦♥ ♣r♦❝❡ss ❛♥❞ r❡✢❡❝t t❤❡ ❡①♣❡r✐♠❡♥t❛❧ ❞❡s✐❣♥ ♦❢ t❤❡ ❣❡r♠✐♥❛t✐♦♥ ❞❛t❛✳ ■♥ t❤✐s ✇♦r❦ ✇❡ ✉s❡❞ t✇♦ ♠❡t❤♦❞♦❧♦❣✐❡s ♦❢ ✉s✉❛❧ st❛t✐st✐❝❛❧ ❛♥❛❧②s✐s ❛♥❞ t❤❡✐r r❡s✉❧ts ✇❡r❡ ❝♦♠♣❛r❡❞ ✇✐t❤ t❤♦s❡ ♦❢ t❤❡ ❛♣♣r♦❛❝❤ t❤❛t ✉s❡s t❤❡ ❞♦s❡✲r❡s♣♦♥s❡ ♠♦❞❡❧s ✇✐t❤ ✐♥t❡r✈❛❧ ❝❡♥s✉r❡❞✳ ❲❡ ✉s❡❞ t❤❡ ❞♦s❡ r❡s♣♦♥s❡ ♠♦❞❡❧s ❲❡✐❜✉❧❧ ✷ ❛♥❞ ❧♦❣✲❧♦❣✐st✐❝ t♦ ❡①♣❧❛✐♥ t❤❡ ♣r♦❝❡ss ♦❢ s❡❡❞ ❣❡r✲ ♠✐♥❛t✐♦♥ ♦❢ ❇r❛❝❤✐❛r✐❛ ❛♥❞ ❈✐tr✉♠❡❧♦ ❙✇✐♥❣❧❡ ✇✐t❤ ❞✐✛❡r❡♥t ♦❜s❡r✈❛t✐♦♥ t✐♠❡s✳ ❚❤❡ ❡①♣❡r✐♠❡♥ts ✇❡r❡ ❝❛rr✐❡❞ ♦✉t ✐♥ ❝♦♠♣❧❡t❡❧② r❛♥❞♦♠✐③❡❞ ❞❡s✐❣♥ ❛♥❞ t❡st✐♥❣ ♣r♦❝❡❞✉✲ r❡s ❛❝❝♦r❞✐♥❣ t♦ t❤❡ r✉❧❡s ❢♦r s❡❡❞ ❛♥❛❧②s✐s ✭❘❆❙✮✳ ❚❤❡ ❝♦♥❝❧✉s✐♦♥s ♦❜t❛✐♥❡❞ ❢r♦♠ t❤❡ ❛♥❛❧②s✐s ♦❢ t❤❡ ❞❛t❛ ❜② t❤❡ ♣r♦♣♦s❡❞ ♠❡t❤♦❞♦❧♦❣② ✐♥ ❣❡♥❡r❛❧ ❞✐✈❡r❣❡❞ ❢r♦♠ t❤❡ ❝♦♥✲ ❝❧✉s✐♦♥s ♦❜t❛✐♥❡❞ ❜② tr❛❞✐t✐♦♥❛❧ ❛♣♣r♦❛❝❤❡s ✭r❡❣r❡ss✐♦♥ ♠♦❞❡❧s ♥♦♥❧✐♥❡❛r ❝♦♥s✐❞❡r✐♥❣ ♥♦r♠❛❧ ❞✐str✐❜✉t✐♦♥ ❛♥❞ ❣❡r♠✐♥❛t✐♦♥ ✐♥❞✐❝❡s ✉s✐♥❣ ❛♥❛❧②s✐s ♦❢ ✈❛r✐❛♥❝❡✮ ✉s❡❞ t♦ ❛♥❛❧②③❡ ❞❛t❛ ❣❡r♠✐♥❛t✐♦♥✳ ❚❤❡ ❞♦s❡✲r❡s♣♦♥s❡ ♠♦❞❡❧s ✇✐t❤ ✐♥t❡r✈❛❧✲❝❡♥s♦r❡❞ s❤♦✇❡❞ s❛t✐s❢❛❝✲ t♦r② ❛❞❥✉st♠❡♥ts ❛♥❞ t❤❡r❡❢♦r❡ ❛ ♠♦r❡ ❛❝❝✉r❛t❡ ❛♥❛❧②s✐s t❤❛♥ t❤❡ ✉s✉❛❧ ❛♣♣r♦❛❝❤❡s✳
✶✺
▲■❙❚❆ ❉❊ ❋■●❯❘❆❙
❋✐❣✉r❛ ✶ ✲ ❈✉r✈❛s ❞❡ ❣❡r♠✐♥❛çã♦ ❛♦ ❧♦♥❣♦ ❞♦ t❡♠♣♦ ✭❛✮✱ ❞✐str✐❜✉✐çõ❡s ❞♦ t❡♠♣♦ ❞❡ ❣❡r♠✐♥❛çã♦ ✭❜✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ❋✐❣✉r❛ ✷ ✲ ❊st✐♠❛❞♦r❡s ❞❡ ❝✉r✈❛s ❞❡ ❑✲▼ ❞❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ♣❛r❛ ❞❛❞♦s
✜❝tí❝✐♦s ❞❡ ❣❡r♠✐♥❛çã♦✱ ❥✉♥t❛♠❡♥t❡ ❝♦♠ ✐♥t❡r✈❛❧♦s ❞❡ ❝♦♥✜❛♥ç❛ ✭✾✺✪✮ ✭❧✐♥❤❛s tr❛❝❡❥❛❞❛s✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ❋✐❣✉r❛ ✸ ✲ ❊st✐♠❛t✐✈❛ ❞❡ ❑❛♣❧❛♥✲▼❡✐❡r ♣❛r❛ ♦s ❧♦t❡s ❞❡ s❡♠❡♥t❡s ❞❡ ❇r❛❝❤✐❛r✐❛ ✹✼ ❋✐❣✉r❛ ✹ ✲ ❈✉r✈❛s ♠é❞✐❛s ❞❡ ❣❡r♠✐♥❛çã♦ ❞❡ s❡♠❡♥t❡s ❞❡ ❇r❛❝❤✐❛r✐❛✱ ♣♦r tr❛t❛✲
♠❡♥t♦✱ ❛❥✉st❛❞❛s ♣❡❧♦ ♠♦❞❡❧♦ ❲✷ ✉s❛♥❞♦ ✉s❛♥❞♦ ❛s ❛❜♦r❞❛❣❡♥s ✶ ❡ ✷ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶ ❋✐❣✉r❛ ✺ ✲ ●rá✜❝♦s ♥♦r♠❛✐s ❝♦♠ ❡♥✈❡❧♦♣❡ s✐♠✉❧❛❞♦ ♣❛r❛ ♦s r❡sí❞✉♦s ❞♦s ❛❥✉st❡s
❞♦ ♠♦❞❡❧♦ ❲✷ ✉s❛♥❞♦ ❛s ❛❜♦r❞❛❣❡♥s ✶ ❡ ✷ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶ ❋✐❣✉r❛ ✼ ✲ ❈✉r✈❛s ♠é❞✐❛s ❞❡ ❣❡r♠✐♥❛çã♦ ❞❡ s❡♠❡♥t❡s ❞❡ ❝✐tr✉♠❡❧♦ ❙✇✐♥❣❧❡✱ ♣♦r
tr❛t❛♠❡♥t♦✱ ❛❥✉st❛❞❛s ♣❡❧♦ ♠♦❞❡❧♦ ▲▲ ✉s❛♥❞♦ ❛s ❞✉❛s ❛❜♦r❞❛❣❡♥s ✳ ✺✼ ❋✐❣✉r❛ ✽ ✲ ●rá✜❝♦s ♥♦r♠❛✐s ❝♦♠ ❡♥✈❡❧♦♣❡ s✐♠✉❧❛❞♦ ♣❛r❛ ♦s r❡sí❞✉♦s ❞♦s ❛❥✉st❡s
✶✻
✶✼
▲■❙❚❆ ❉❊ ❚❆❇❊▲❆❙
❚❛❜❡❧❛ ✶ ✲ ▲✐st❛ ❞❡ ♠♦❞❡❧♦s ❞❡ ❞♦s❡✲r❡s♣♦st❛ ❡ ❢✉♥çõ❡s ❝♦rr❡s♣♦♥❞❡♥t❡s ✳ ✳ ✳ ✳ ✳ ✸✺ ❚❛❜❡❧❛ ✷ ✲ ❋♦r♠❛t♦ ❞❡ ✉♠ ❛rq✉✐✈♦ ❞❡ ❞❛❞♦s ♣❛r❛ ❛♥á❧✐s❡ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛✱ ❝♦♠
❞♦✐s ❧♦t❡s✱ ❞✉❛s r❡♣❡t✐çõ❡s ❡ q✉❛tr♦ s❡♠❡♥t❡s ♣♦r r❡♣❡t✐çã♦✱♦❜s❡r✈❛❞❛s ❞✉r❛♥t❡ três ❞✐❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹ ❚❛❜❡❧❛ ✸ ✲ ❉❛❞♦s ❞❡ s❡♠❡♥t❡s ❞❡ ❇r❛❝❤✐❛r✐❛✱ ♣♦r tr❛t❛♠❡♥t♦✱ ❝♦♠ ♦s ✐♥t❡r✈❛❧♦
❞❡ ♦❜s❡r✈❛çõ❡s ❡ ♦ ♥ú♠❡r♦ ❞❡ s❡♠❡♥t❡s ❣❡r♠✐♥❛❞❛s ❡♠ ❝❛❞❛ ❞✐❛ ✳ ✳ ✳ ✹✻ ❚❛❜❡❧❛ ✹ ✲ ❊st✐♠❛t✐✈❛s ❞❡ ❑❛♣❧❛♥✲▼❡✐❡r ♣❛r❛ ♦ ❡♥s❛✐♦ ❞❡ ❣❡r♠✐♥❛çã♦ ❞❛s s❡♠❡♥✲
t❡s ❞❡ ❇r❛❝❤✐❛r✐❛✱ ♣♦r tr❛t❛♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ❚❛❜❡❧❛ ✺ ✲ ▼♦❞❡❧♦s ♣r♦♣♦st♦s ♣❛r❛ ❞❡s❝r✐çã♦ ❞♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❣❡r♠✐♥❛t✐✈♦ ❞❡ s❡✲
♠❡♥t❡s ❞❡ ❇r❛❝❤✐❛r✐❛✱ ❆■❈ ❡ ❇■❈ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ❚❛❜❡❧❛ ✻ ✲ ❊st✐♠❛t✐✈❛s ❞♦s ♣❛râ♠❡tr♦s ✭❡rr♦s ♣❛❞rã♦ ❡♥tr❡ ♣❛rê♥t❡s❡s ❡ ✐♥t❡r✈❛✲
❧♦s ❝♦♠ ✾✺✪ ❞❡ ❝♦♥✜❛♥ç❛ ❡♥tr❡ ❝♦❧❝❤❡t❡s✮ ❞♦ ♠♦❞❡❧♦ ❲✷ ♣♦r ❛❜♦r❞❛❣❡♥s ✹✾ ❚❛❜❡❧❛ ✼ ✲ ❊st✐♠❛t✐✈❛s ❞♦ ♣❛râ♠❡tr♦ t50 ♣❛r❛ ❝❛❞❛ tr❛t❛♠❡♥t♦ ✭❞♦s❡✮✱ ❝♦♠ r❡s✲
♣❡❝t✐✈♦s ❡rr♦s ♣❛❞rã♦ ❡ ✐♥t❡r✈❛❧♦s ❞❡ ❝♦♥✜❛♥ç❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷ ❚❛❜❡❧❛ ✽ ✲ ❊st✐♠❛t✐✈❛s ❞❛s ❞✐❢❡r❡♥ç❛s ❡♥tr❡ ❛s ❝✉r✈❛s ❛❥✉st❛❞❛s ♣❛r❛ ❝❛❞❛ ❞♦s❡
❝♦♠ r❡❧❛çã♦ ❛♦ ♣❛râ♠❡tr♦ ❞❡ ♣♦r❝❡♥t❛❣❡♠ ♠á①✐♠❛ ✭d✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸
❚❛❜❡❧❛ ✾ ✲ ❊st✐♠❛t✐✈❛s ❞❛s ❞✐❢❡r❡♥ç❛s ❡♥tr❡ ❛s ❝✉r✈❛s ❛❥✉st❛❞❛s ♣❛r❛ ❝❛❞❛ ❞♦s❡ ❝♦♠ r❡❧❛çã♦ ❛♦ ♣❛râ♠❡tr♦ ❞❡ ✐♥❝❧✐♥❛çã♦ ❞❛ ❝✉r✈❛ ✭b✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹
❚❛❜❡❧❛ ✶✵ ✲❆♥á❧✐s❡s ❞❡ ✈❛r✐â♥❝✐❛ ♣❛r❛ ❛s ❡st✐♠❛t✐✈❛s ❞♦s í♥❞✐❝❡s ❞❡ ❣❡r♠✐♥❛çã♦ ✳ ✺✹ ❚❛❜❡❧❛ ✶✶ ✲❊st✐♠❛t✐✈❛s ❞❡ ❑❛♣❧❛♥✲▼❡✐❡r ♣❛r❛ ♦ ❡♥s❛✐♦ ❞❡ ❣❡r♠✐♥❛çã♦ ❞❛s s❡♠❡♥✲
t❡s ❞❡ ❝✐tr✉♠❡❧♦ ❙✇✐♥❣❧❡ ♣♦r tr❛t❛♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻ ❚❛❜❡❧❛ ✶✷ ✲▼♦❞❡❧♦s ♣r♦♣♦st♦s ♣❛r❛ ❞❡s❝r✐çã♦ ❞❛ ❣❡r♠✐♥❛çã♦ ❞❛s s❡♠❡♥t❡s ❞❡ ❈r✐tr✉✲
♠❡❧♦ s✇✐♥❣✱ ❆■❈ ❡ ❇■❈ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻ ❚❛❜❡❧❛ ✶✸ ✲❊st✐♠❛t✐✈❛s ❞♦s ♣❛râ♠❡tr♦s ✭❡rr♦s ♣❛❞rã♦ ❡♥tr❡ ♣❛rê♥t❡s❡s ❡ ✐♥t❡r✈❛✲
❧♦s ❝♦♠ ✾✺✪ ❞❡ ❝♦♥✜❛♥ç❛ ❡♥tr❡ ❝♦❧❝❤❡t❡s✮ ❞♦ ♠♦❞❡❧♦ ▲▲ ♦❜t✐❞❛s ♣♦r ♠❡✐♦ ❞♦ ❛❥✉st❡ ❞❛s ❛❜♦r❞❛❣❡♥s ✶ ❡ ✷ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼ ❚❛❜❡❧❛ ✶✹ ✲❊st✐♠❛t✐✈❛s ❞❛s ❞✐❢❡r❡♥ç❛s ❡♥tr❡ ❛s ❝✉r✈❛s ❞❡ ❣❡r♠✐♥❛çã♦ ♣❛r❛ ❝❛❞❛
❧♦t❡ ♣♦r ♠❡✐♦ ❞♦ ❛❥✉st❡ ❞❛s ❛❜♦r❞❛❣❡♥s ✶ ❡ ✷✱ ❞❡ ❛❝♦r❞♦ ❝♦♠ ♦s ♣❛râ♠❡tr♦sd✱ t50 ❡b ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ❚❛❜❡❧❛ ✶✺ ✲❆♥á❧✐s❡s ❞❡ ✈❛r✐â♥❝✐❛ ♣❛r❛ ❛s ❡st✐♠❛t✐✈❛s ❞♦s í♥❞✐❝❡s ❞❡ ❣❡r♠✐♥❛çã♦
✶✽
✶✾
✶ ■◆❚❘❖❉❯➬➹❖
❊st✐♠❛✲s❡ q✉❡ ❛té ✷✵✸✵ ❛ ♣♦♣✉❧❛çã♦ ♠✉♥❞✐❛❧ ❝❤❡❣✉❡ ❛ ✽✱✸ ❜✐❧❤õ❡s ❞❡ ♣❡s✲ s♦❛s✱ ♦ q✉❡ ❧❡✈❛rá ❛ ✉♠ ❝r❡s❝✐♠❡♥t♦ ❞❛ ❞❡♠❛♥❞❛ ♠✉♥❞✐❛❧ ♣♦r ❛❧✐♠❡♥t♦s ❡♠ t♦r♥♦ ❞❡ ✸✺✪✳ ❙❡ ❛ss♦❝✐❛❞♦ ❛ ❡ss❡ ❝r❡s❝✐♠❡♥t♦ ♣♦♣✉❧❛❝✐♦♥❛❧ ❛s ♠✉❞❛♥ç❛s ❝❧✐♠át✐❝❛s✱ ♥♦ ❢✉t✉r♦ ❛ ❡s❝❛ss❡③ ❞❡ ❛❧✐♠❡♥t♦s ♣♦❞❡rá s❡r ✐♠♣✉❧s✐♦♥❛❞❛✱ ♣❡r♠✐t✐♥❞♦ q✉❡ ❡st❛❞♦s ♥❛ ➪❢r✐❝❛✱ ❖r✐❡♥t❡ ▼é❞✐♦✱ ❈❤✐♥❛ ❡ ❮♥❞✐❛ s❡❥❛♠ ♠❛✐s ✈✉❧♥❡rá✈❡✐s ❛ ❡ss❡ t✐♣♦ ❞❡ ♣r♦❜❧❡♠❛ ✭❘❖❈❑✲ ❋❊▲▲❊❘ ❋❖❯◆❉❆❚■❖◆❀ ●▲❖❇❆▲ ❇❯❙■◆❊❙❙ ◆❊❚❲❖❘❑✲●❇◆✱ ✷✵✶✵❀ ❯◆■❚❊❉ ❙❚❆❚❊❙✱ ✷✵✶✷❛❀ ■◆❙❚■❚❯❚❖ ❉❊ P❊❙◗❯■❙❆ ❊❈❖◆Ô▼■❈❆ ❊ ❆P▲■❈❆❉❆ ✲■P❊❆✱ ✷✵✶✺✮✳
❊♠ ✉♠❛ ♣❡rs♣❡❝t✐✈❛ t❡❝♥♦❧ó❣✐❝❛✱ ♦ ❝r❡s❝✐♠❡♥t♦ ❞❡ ✐♥✈❡st✐♠❡♥t♦s ❡♠ ❜✐✲ ♦t❡❝♥♦❧♦❣✐❛ ♥❛ ❛❣r✐❝✉❧t✉r❛ ♣♦r ♠❡✐♦ ❞❡ ❝✉❧t✐✈❛r❡s ❣❡♥❡t✐❝❛♠❡♥t❡ ♠♦❞✐✜❝❛❞❛s✱ t❡♠ s✐❞♦ ❝♦♥s✐❞❡r❛❞♦ ✉♠ ❢❛t♦r✲❝❤❛✈❡ ♣❛r❛ ❣❛r❛♥t✐r ❛ s❡❣✉r❛♥ç❛ ❛❧✐♠❡♥t❛r ❣❧♦❜❛❧✳ ■ss♦ t❛♠❜é♠ t❡♠ ❧❡✈❛❞♦ ❛ ✉♠❛ r❡❡str✉t✉r❛çã♦ ♥❛ ✐♥❞ústr✐❛ ❞❡ s❡♠❡♥t❡s✱ ✉♠❛ ✈❡③ q✉❡ ✐♥✈❡st✐♠❡♥t♦s t❡❝♥♦❧ó❣✐❝♦s ✈♦❧t❛❞♦s ♣❛r❛ ❛ s✉st❡♥t❛❜✐❧✐❞❛❞❡ ❞❛ ♣r♦❞✉çã♦ ❛❣rí❝♦❧❛ ♣❡r♠✐t❡ ❛❧✐♥❤❛r ♣❡s✲ q✉✐s❛s ❡♠ ❡♥❣❡♥❤❛r✐❛ ❣❡♥ét✐❝❛✱ s❡♠❡♥t❡s✱ ♦ ✉s♦ ❛❞❡q✉❛❞♦ ❞❡ ♥♦✈❛s t❡❝♥♦❧♦❣✐❛s ❛❣rí❝♦❧❛s ❡ ❢❡rt✐❧✐③❛♥t❡s ✭❯◆■❚❊❉ ❙❚❆❚❊❙✱ ✷✵✶✷❛❀ ■P❊❆✱ ✷✵✶✺✮✳
❖ ❇r❛s✐❧ t❡♠ s✐❞♦ ❝♦♥s✐❞❡r❛❞♦ ✉♠ ❞♦s ❛♠❜✐❡♥t❡s ♠❛✐s só❧✐❞♦s ♣❛r❛ ♥❡❣ó✲ ❝✐♦s ♥♦ ❝♦♥t❡①t♦ ❣❧♦❜❛❧ ❞❛ ✐♥❞ústr✐❛ ❞❡ s❡♠❡♥t❡s✱ s❡❥❛ ♣♦r s❡✉ s✐st❡♠❛ r❡❣✉❧❛tór✐♦ ♦✉ ♣♦r ❝❛r❛❝t❡ríst✐❝❛s ❝♦♥t✐♥❡♥t❛✐s q✉❡ ❢❛✈♦r❡❝❡♠ s❡♠❡♥t❡s ❞❡ ❛❧t❛ q✉❛❧✐❞❛❞❡✱ ❞❡ ❞✐❢❡r❡♥t❡s ❡s♣é❝✐❡s✱ ❡♠ ❞✐❢❡r❡♥t❡s ❝♦♥❞✐çõ❡s ❡❞❛❢♦❝❧✐♠át✐❝❛s✶✳ ❆ ✐♥t❡♥s✐✜❝❛çã♦ ❞♦ ✉s♦ ❞❡ s❡♠❡♥t❡s
♠❡❧❤♦r❛❞❛s t❡♠ ❧❡✈❛❞♦ ❛♦ ❝r❡s❝✐♠❡♥t♦ ❡ à ❞✐✈❡rs✐✜❝❛çã♦ ❞❛ ♣r♦❞✉çã♦ ❞❡ s❡♠❡♥t❡s✱ ♦ q✉❡ ❝♦♥tr✐❜✉✐✉ ♣❛r❛ ❛t✐♥❣✐r ✉♠ ♥♦✈♦ ♣❛t❛♠❛r ❞❡ ♣r♦❞✉t✐✈✐❞❛❞❡ ♣❡❧❛s ❧❛✈♦✉r❛s ❜r❛s✐❧❡✐r❛s ✭❙❆◆❚❖❙ ❡t ❛❧✳✱ ✷✵✶✹✮✳
❊st✉❞♦s ❡♥✈♦❧✈❡♥❞♦ ❡①♣❡r✐♠❡♥t♦s ❞❡ ❣❡r♠✐♥❛çã♦ ❞❡ s❡♠❡♥t❡s ❡stã♦ ♣r❡✲ s❡♥t❡s ❡♠ ♠✉✐t❛s ❧✐♥❤❛s ❞❡ ♣❡sq✉✐s❛ ❡ sã♦ ❝♦♥❞✉③✐❞♦s ❡♠ ✉♠❛ ❛♠♣❧❛ ✈❛r✐❡❞❛❞❡ ❞❡ s✐t✉❛çõ❡s ❜✐♦❧ó❣✐❝❛s✱ t❛✐s ❝♦♠♦✿ ✜s✐♦❧♦❣✐❛ ❞❡ s❡♠❡♥t❡s✱ t✐♣♦s ❡ ❝♦♥tr♦❧❡s ❞❡ ❞♦r♠ê♥❝✐❛✱ ❣❡♥ét✐❝❛ ❡ ❞✐❢❡r❡♥ç❛s ✐♥❞✉③✐❞❛s ♣♦r ❢❛t♦r❡s ❛♠❜✐❡♥t❛✐s ❡♥tr❡ ♣♦♣✉❧❛çõ❡s ❝♦✲❡s♣❡❝í✜❝❛s✱ ♦ ❛r♠❛③❡♥❛♠❡♥t♦ ❞❛s s❡♠❡♥t❡s ♦✉ ♠ét♦❞♦s ❞❡ ♣r❡♣❛r❛çã♦ q✉❡ ♠❛①✐♠✐③❛♠ ♦ ♣❡r❝❡♥t✉❛❧ ❞❡ ❣❡r♠✐♥❛çã♦ ❡ ♣ós✲s❡♠❡❛❞✉r❛ ❞❡ ❢❛t♦r❡s ❛♠❜✐❡♥t❛✐s✱ ❢ís✐❝♦s ❡ q✉í♠✐❝♦s ✭❇❆❙❑■◆❀ ❇❆❙❑■◆✱ ✷✵✵✶✮✳
✶❈♦♥❞✐çõ❡s ❡❞❛❢♦❝❧✐♠át✐❝❛s✿ sã♦ ❢❛t♦r❡s ❢ís✐❝♦s✲q✉í♠✐❝♦s ❞♦ s♦❧♦ ❡ ♠❛✐s ❢❛t♦r❡s ❞❡ ❝❧✐♠❛✱ ❞❡♥tr❡
✷✵
❖s ❡①♣❡r✐♠❡♥t♦s ❞❡ ❣❡r♠✐♥❛çã♦ ❞❡ s❡♠❡♥t❡s ♣♦❞❡♠ s❡r ❞✐✈✐❞✐❞♦s ❡♠ ❞♦✐s ❣r✉♣♦s✿ ♦s ❡♥s❛✐♦s ♦♥❞❡ ♥♦✈♦s ❧♦t❡s ❞❡ s❡♠❡♥t❡s sã♦ ✉t✐❧✐③❛❞♦s ♣❛r❛ ❝❛❞❛ t❡♠♣♦ ❞❡ ✐♥s♣❡çã♦✱ ❣❡r❛❧♠❡♥t❡ ✉t✐❧✐③❛❞♦s ❡♠ ❡st✉❞♦s s♦❜r❡ ♦ ✐♠♣❛❝t♦ ❞♦ ❛r♠❛③❡♥❛♠❡♥t♦ ♥❛ ✈✐❛❜✐❧✐❞❛❞❡ ❞❛s s❡♠❡♥t❡s ❡ ♦s ❡♥s❛✐♦s ♠❛✐s ♣♦♣✉❧❛r❡s✱ ♦♥❞❡ ❛s s❡♠❡♥t❡s ❞❡ ✉♠ ♠❡s♠♦ ❧♦t❡ sã♦ ♦❜s❡r✈❛❞❛s s✉❝❡ss✐✈❛♠❡♥t❡ ❛♦ ❧♦♥❣♦ ❞❡ ✉♠ ✐♥t❡r✈❛❧♦ ❞❡ t❡♠♣♦✳
❍❛②✱ ▼❡❛❞ ❡ ❇❧♦♦♠❜❡r❣ ✭✷✵✶✹✮ ❛❧❡rt❛♠ q✉❡ ❡st❡s ❞♦✐s ❝❡♥ár✐♦s ♥ã♦ ♣♦✲ ❞❡♠ s❡r ❝♦♥s✐❞❡r❛❞♦s ❝♦♠♦ ❣❡r❛❞♦r❡s ❞❡ ❞❛❞♦s s❡♠❡❧❤❛♥t❡s✱ ❡ ♥❡♠ q✉❡ ♦s ❞❛❞♦s s❡❥❛♠ tr❛t❛❞♦s ❝♦♠♦ s❡ ❢♦ss❡♠ ♦s ♠❡s♠♦s✱ ♣♦✐s ♦s ❞❛❞♦s ❣❡r❛❞♦s ❛ ♣❛rt✐r ❞❡ ✉♠ ❡①♣❡r✐♠❡♥t♦ ❞❡ ❛r♠❛③❡♥❛❣❡♠ sã♦ ♣r♦✈❡♥✐❡♥t❡s ❞❡ ❛♠♦str❛s ✐♥❞❡♣❡♥❞❡♥t❡s ❡♠ ♠♦♠❡♥t♦s ❞✐❢❡r❡♥✲ t❡s ❡ ♣♦❞❡♠ s❡r ❛♥❛❧✐s❛❞♦s ♣♦r ♠❡✐♦ ❞❡ ♠♦❞❡❧♦s ❧✐♥❡❛r❡s ❣❡♥❡r❛❧✐③❛❞♦s ♣❛r❛ ❞❛❞♦s ❜✐♥♦♠✐❛✐s✱ ❝♦♠♦ r❡❣r❡ssã♦ ❧♦❣íst✐❝❛✱ ♣♦r ❡①❡♠♣❧♦✳ ❊♥tr❡t❛♥t♦✱ ❛s ❝♦♥t❛❣❡♥s ❝✉♠✉❧❛t✐✲ ✈❛s r❡❣✐str❛❞❛s ❞✉r❛♥t❡ ♦ ♣r♦❣r❡ss♦ ❞❛ ❣❡r♠✐♥❛çã♦ ♥ã♦ sã♦ ✐♥❞❡♣❡♥❞❡♥t❡s✱ ✐♥❞✐❝❛♥❞♦ q✉❡ ✉♠❛ ❛❜♦r❞❛❣❡♠ ❛❧t❡r♥❛t✐✈❛ ❞❡ ❛♥á❧✐s❡ ❞❡✈❛ s❡r ✉t✐❧✐③❛❞❛ ♣❛r❛ ❞❡s❝r❡✈❡r ❛ ✈❛r✐á✈❡❧ r❡s♣♦st❛ ❜✐♥ár✐❛✱ ❝♦♠♦ ♣♦r ❡①❡♠♣❧♦✱ ❛♥á❧✐s❡ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛✳
❉✐❢❡r❡♥t❡s ♠❡t♦❞♦❧♦❣✐❛s ❡st❛tíst✐❝❛s tê♠ s✐❞♦ ✉t✐❧✐③❛❞❛s ♣❛r❛ ❛♥❛❧✐s❛r ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞❡ ✉♠❛ ♣♦♣✉❧❛çã♦ ❞❡ s❡♠❡♥t❡s ♥♦ q✉❡ ❞✐③ r❡s♣❡✐t♦ à ❣❡r♠✐♥❛çã♦✿ ♦s í♥❞✐❝❡s ❞❡ ❣❡r♠✐♥❛çã♦✱ ♣r♦♣♦st♦s ❡ ❞✐s❝✉t✐❞♦s ♣♦r ❞✐✈❡rs♦s ♣❡sq✉✐s❛❞♦r❡s ❛♦ ❧♦♥❣♦ ❞♦ t❡♠♣♦ ✭❆◆❏❯▼❀ ❇❆❏❲❆✱ ✷✵✵✺❀ ❘❆◆❆▲ ❡t ❛❧✳✱ ✷✵✵✾❀ ❚❍❖▼❙❖◆❀ ❊▲✲❑❆❙❙❆❇❨✱ ✶✾✾✸✮✱ ♦s ♠ét♦❞♦s ❞❡ r❡❣r❡ssã♦ ❝❧áss✐❝❛ ✭❆◆❖❱❆✱ r❡❣r❡ssã♦ ❧✐♥❡❛r ♦✉ ♥ã♦✲❧✐♥❡❛r✮ ✭❙❆◆✲ ❚❖❙ ❡t ❛❧✳✱ ✷✵✶✸❀ ❙❖❯❙❆ ❡t ❛❧✳✱ ✷✵✶✹✮✱ t❡st❡s ♥ã♦✲♣❛r❛♠étr✐❝♦s✱ ♠♦❞❡❧♦s ❧✐♥❡❛r❡s ❣❡✲ ♥❡r❛❧✐③❛❞♦s ✭❖✬◆❊■▲▲ ❡t ❛❧✳✱ ✷✵✵✹✱ ❙❆❆❚❑❆▼P ❡t ❛❧✳✱ ✷✵✶✶✮ ❡ té❝♥✐❝❛s ❞❡ ❛♥á❧✐s❡ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ✭▼❆◆❙❖ ❡t ❛❧✳✱ ✷✵✶✸✮✳
❖s í♥❞✐❝❡s ❞❡ ❣❡r♠✐♥❛çã♦ ✭❆❚❆❮❉❊ ❡t ❛❧✳✱ ✷✵✶✺❀ ❇■◆❙❋❊▲❉ ❡t ❛❧✳✱ ✷✵✶✹❀ ▼❖❚❆ ❡t ❛❧✳✱ ✷✵✶✺❀ ❙■▲❱❆ ❏❯◆■❖❘ ❡t ❛❧✳✱ ✷✵✶✺✮ ❛✐♥❞❛ sã♦ ❛♠♣❧❛♠❡♥t❡ ✉t✐❧✐③❛❞♦s✳ ❊♥✲ tr❡t❛♥t♦✱ ❡①✐st❡♠ ❛❞✈❡rtê♥❝✐❛s q✉❛♥t♦ ❛ ♣r♦❜❧❡♠❛s ❡st❛tíst✐❝♦s ♣♦t❡♥❝✐❛❧♠❡♥t❡ ❣r❛✈❡s ❡♠ s❡✉ ✉s♦✱ ✐♥❞✐❝❛♥❞♦ q✉❡ ❡❧❡s ♥ã♦ ❢♦r♥❡❝❡♠ ✉♠❛ ❜❛s❡ ❛❞❡q✉❛❞❛ ♣❛r❛ ❝❛r❛❝t❡r✐③❛r ♦ ♣❛❞rã♦ t❡♠♣♦r❛❧ ❞❡ ❣❡r♠✐♥❛çã♦✱ ♥❡♠ sã♦ ❛❞❡q✉❛❞♦s ♣❛r❛ ❝♦♠♣❛r❛r ❣r✉♣♦s ❞❡ s❡♠❡♥t❡s ♦✉ ❛✈❛❧✐❛r ♦s ❡❢❡✐t♦s ❞❡ tr❛t❛♠❡♥t♦s ✭❇❘❖❲◆❀ ▼❆❨❊❘✱ ✶✾✽✽❛❀ ▼❝◆❆■❘ ❡t ❛❧✳✱ ✷✵✶✷❀ ❙❈❖❚❚❀ ❏❖◆❊❙❀ ❲■▲▲■❆▼❙✱ ✶✾✽✹✮✳
✷✶
❞❡ s❡♠❡♥t❡s ❛❣r✉♣❛❞❛s ❡♠ ✉♥✐❞❛❞❡s ❡①♣❡r✐♠❡♥t❛✐s ♦❜s❡r✈❛❞❛s ❧♦♥❣✐t✉❞✐♥❛❧♠❡♥t❡ ❡ ♥❛ ♠❡s♠❛ ✉♥✐❞❛❞❡ ❞❡ ❛❧❡❛t♦r✐③❛çã♦❀ ❛ ❛ss✐♥❝r♦♥✐❛ ❞❛s ❣❡r♠✐♥❛çõ❡s✱ ♣♦✐s ❛ ❣r❛♥❞❡ ♣❛rt❡ ❞❛ ❣❡r♠✐♥❛çã♦ s❡ ♣r♦❝❡ss❛ ❡♠ t❡♠♣♦ ✐♥t❡r♠❡❞✐ár✐♦ ❡ ✉♠❛ ♣❡q✉❡♥❛ ♣❛rt❡ ❡♠ t❡♠♣♦ ♣r❡❝♦❝❡ ♦✉ t❛r❞✐❛♠❡♥t❡✱ ❛❧é♠ ❞❛ ❛ss✐♠❡tr✐❛ ♣♦s✐t✐✈❛ ❞❛s r❡s♣♦st❛s✱ ✉♠❛ ✈❡③ q✉❡ ❛ t❛①❛ ❞❡ ❛✉♠❡♥t♦ ❞❛ ❣❡r♠✐♥❛çã♦ ❝✉♠✉❧❛t✐✈❛ ❞✐♠✐♥✉✐ ❛♦ ❧♦♥❣♦ ❞♦ t❡♠♣♦ ✭❍❆❨❀ ▼❊❆❉❀ ❇▲❖❖▼❇❊❘●✱ ✷✵✶✹✮✳
❯s❛r ❛❜♦r❞❛❣❡♥s ❡st❛tíst✐❝❛s q✉❡ ❛♥❛❧✐s❛♠ ♦s ❞❛❞♦s ❞❡ ❣❡r♠✐♥❛çã♦ ❞❛ ♠❡❧❤♦r ❢♦r♠❛ ♣♦ssí✈❡❧ ♣❡r♠✐t✐rá ✉♠❛ ♠❛✐♦r ❝♦♥✜❛❜✐❧✐❞❛❞❡ ❞♦s r❡s✉❧t❛❞♦s✱ ❜❡♠ ❝♦♠♦ ✉♠ ♠❛✐♦r ❣❛♥❤♦ ❞❡ ✐♥❢♦r♠❛çõ❡s ♦✉ ❞❡ ✐♥t❡r♣r❡t❛çõ❡s ♣❡rt✐♥❡♥t❡s✳
❖ ♦❜❥❡t✐✈♦ ❞❡st❡ ❡st✉❞♦ é ❛♣r❡s❡♥t❛r ✉♠❛ ♠❡t♦❞♦❧♦❣✐❛ ❞❡ ❛♥á❧✐s❡ ♥❛ ❞❡s❝r✐çã♦ ❞♦ ♣r♦❝❡ss♦ ❣❡r♠✐♥❛t✐✈♦ q✉❡ ✉t✐❧✐③❛ ♠♦❞❡❧♦s ❞❡ ❞♦s❡✲r❡s♣♦st❛ ❝♦♠ ❝❡♥s✉r❛ ✐♥t❡r✈❛❧❛r ❡ ❝♦♠♣❛r❛r s❡✉s r❡s✉❧t❛❞♦s ❝♦♠ ♦s ♦❜t✐❞♦s ❝♦♠ ❞✉❛s ❛❜♦r❞❛❣❡♥s ✉s✉❛✐s ❡♠ t❡st❡s ❞❡ ❣❡r♠✐♥❛çã♦✿ ♠♦❞❡❧♦s ❞❡ r❡❣r❡ssã♦ ♥ã♦✲❧✐♥❡❛r ❡ í♥❞✐❝❡s ❞❡ ❣❡r♠✐♥❛çã♦✳
✷✷
✷✸
✷ ❉❊❙❊◆❱❖▲❱■▼❊◆❚❖
▼♦r❢♦❧♦❣✐❝❛♠❡♥t❡ ❛ s❡♠❡♥t❡ é s❡♠❡❧❤❛♥t❡ ❛♦ ❣rã♦ ❝♦♠❡r❝✐❛❧✱ ♣♦ré♠ ❡❧❛ é ♣r♦❞✉③✐❞❛ ❝♦♠ ❛ ✜♥❛❧✐❞❛❞❡ ❞❡ s❡♠❡❛❞✉r❛ s♦❜ ❝✉✐❞❛❞♦s ❡s♣❡❝✐❛✐s✳ ❉❡♥tr❡ ♦s ❛tr✐❜✉t♦s q✉❡ ✐♥✢✉❡♥❝✐❛♠ ♥❛ q✉❛❧✐❞❛❞❡ ❞❡ ✉♠ ❧♦t❡ ❞❡ s❡♠❡♥t❡s✱ ❡stã♦ ❛❧é♠ ❞❛s q✉❛❧✐❞❛❞❡s ❣❡✲ ♥ét✐❝❛s ❝♦♠♦ r❡s✐stê♥❝✐❛ ❛ ❞♦❡♥ç❛s✱ ❛s q✉❛❧✐❞❛❞❡s ❢ís✐❝❛s ✭❛✉sê♥❝✐❛ ❞❡ ♠❛t❡r✐❛❧ ✐♥❡rt❡ ❡ s❡♠❡♥t❡s ❞❡ ♦✉tr❛s ❝✉❧t✉r❛s ♦✉ ❝✉❧t✐✈❛r❡s✮✱ ✜s✐♦❧ó❣✐❝❛s ✭❣❡r♠✐♥❛çã♦ ❡ ✈✐❣♦r✮ ❡ s❛♥✐tár✐❛s ✭ ❛✉sê♥❝✐❛ ❞❡ ❢✉♥❣♦s✱ ❜❛❝tér✐❛s✱ ✈✐r✉s✮✭▲❖P❊❙❀ ◆❆❙❈■▼❊◆❚❖✱ ✷✵✵✾✮✳
❊ss❛s ❝❛r❛❝t❡ríst✐❝❛s ❛❢❡t❛♠ ❞✐r❡t❛♠❡♥t❡ ♦ s✐st❡♠❛ ♣r♦❞✉t✐✈♦ ❞❛s ❧❛✈♦✉✲ r❛s ♥❛ ♠❡❞✐❞❛ q✉❡ ♣♦❞❡♠ r❡❞✉③✐r ❝✉st♦s✱ ❞❡t❡r♠✐♥❛r ❛ ♣♦♣✉❧❛çã♦ ❛❞❡q✉❛❞❛ ❞❡ ♣❧❛♥t❛s ❡ ❞✐♠✐♥✉✐r ♦ ✉s♦ ❞❡ ❤❡r❜✐❝✐❞❛s ❡ ❢❡rt✐❧✐③❛♥t❡s✳
❊str❛té❣✐❛s ❡ té❝♥✐❝❛s ❞❡ ❛✈❛❧✐❛çã♦ ❞❛ ❣❡r♠✐♥❛çã♦ ✈❛r✐❛♠✱ ❞❡♣❡♥❞❡♥❞♦ ❞♦ q✉❡ s❡ ❜✉s❝❛✿ ❛✈❛❧✐❛r ❛ ✈✐❛❜✐❧✐❞❛❞❡ ❡ ♦ ✈✐❣♦r ❞❡ ✉♠ ❧♦t❡ ❞❡ s❡♠❡♥t❡s ♦✉ ❞❡s❝r❡✈❡r ✉♠❛ ♣♦♣✉❧❛çã♦ ❛ ♣❛rt✐r ❞❛ ♣❡rs♣❡❝t✐✈❛ ❡❝♦❧ó❣✐❝❛✱ ✜s✐♦❧ó❣✐❝❛ ♦✉ ❣❡♥ét✐❝❛✳ ◆❡ss❡ ❝♦♥t❡①t♦✱ tr❛t❛♠❡♥t♦s ♣❛❞rõ❡s ❡ ♠ét♦❞♦s ❞❡ ❣❡r♠✐♥❛çã♦ tê♠ s✐❞♦ ❞❡s❡♥✈♦❧✈✐❞♦s ♣❛r❛ ❞✐❢❡r❡♥t❡s ❡s♣é❝✐❡s ❛❣rí❝♦❧❛s✱ ❝♦♠♦ ♦s ❜✐♦❡♥s❛✐♦s ❡♠ ❣❡r♠✐♥❛çã♦✱ q✉❡ ❞♦ ♣♦♥t♦ ❞❡ ✈✐st❛ ❡st❛tíst✐❝♦✱ sã♦ ❡①♣❡r✐♠❡♥t♦s ♣❧❛♥❡❥❛❞♦s ♣❛r❛ ❡st✐♠❛r ♦ ♣♦t❡♥❝✐❛❧ ❞❡ ✉♠ ♦✉ ♠❛✐s ❡stí♠✉❧♦s r❡❧❛t✐✈♦s ❛ ✉♠ ♣❛❞rã♦✱ ✉s❛♥❞♦ ❛ ✐♥❢♦r♠❛çã♦ ♣r♦♣♦r❝✐♦♥❛❞❛ ♣❡❧❛ r❡s♣♦st❛ ♠❡♥s✉r❛❞❛ s♦❜r❡ ♦ ♠❛t❡r✐❛❧ ❜✐♦❧ó❣✐❝♦ ✭❋■◆◆❊❨✱ ✶✾✼✾❀ ❙❖❯❩❆ ❡t ❛❧✳✱ ✷✵✵✵✮✳
❊♠ ❜✐♦❡♥s❛✐♦s ❞❡ ❣❡r♠✐♥❛çã♦✱ ❛ ✈❡r✐✜❝❛çã♦ ❞❛ ♦❝♦rrê♥❝✐❛ ❞❡ ❡❢❡✐t♦s ✐♥✐✲ ❜✐tór✐♦s ♦✉ ❡st✐♠✉❧❛♥t❡s ♥❛ ❣❡r♠✐♥❛çã♦ ❡ ♥♦ ❝r❡s❝✐♠❡♥t♦ ❞❛s s❡♠❡♥t❡s✱ ♦s ♣❛râ♠❡tr♦s ❞❡ ❣❡r♠✐♥❛❜✐❧✐❞❛❞❡✱ t❡♠♣♦ ♠é❞✐♦ ❞❡ ❣❡r♠✐♥❛çã♦ ❡ ❝r❡s❝✐♠❡♥t♦ ✐♥✐❝✐❛❧ sã♦ ❡st✉❞❛❞♦s ✭❈❖◆❉❊❙❙❆ ❡t ❛❧✳✱ ✷✵✶✸❀ ❙■▲❱❊■❘❆ ❡t ❛❧✳✱ ✷✵✶✹❀ ❋❊■❚❖❙❆ ❡t ❛❧✳✱ ✷✵✶✺✮✳
✷✳✶ ❈❛r❛❝t❡ríst✐❝❛s ❞♦s ❞❛❞♦s ❞❡ ❣❡r♠✐♥❛çã♦ ❞❡ s❡♠❡♥t❡s
❊♠ ❡st✉❞♦s ❞❡ ❣❡r♠✐♥❛çã♦ ❞❡ s❡♠❡♥t❡s ❛ ✐♥t❡r♣r❡t❛çã♦ ❞♦s ❞❛❞♦s ♣♦❞❡ ✈❛r✐❛r ✐♥✐❝✐❛❧♠❡♥t❡ ❞❡ ❛❝♦r❞♦ ❝♦♠ ♦ ❝r✐tér✐♦ ❛❞♦t❛❞♦✱ ♦✉ s❡❥❛✱ q✉❛❧ ✐♥❢♦r♠❛çã♦ ❡stá s❡ ❜✉s❝❛♥❞♦ ❡ ❡♠ q✉❛❧ ❝♦♥t❡①t♦ ❛ ✐♥❢♦r♠❛çã♦ ❡stá ✐♥s❡r✐❞❛✳
✷✹
◆♦ ❡♥t❛♥t♦✱ ❋❡rr❡✐r❛ ❡ ❇♦r❣❤❡tt✐ ✭✷✵✵✹✮ s✉❜❞✐✈✐❞❡♠ ❛ ❞❡✜♥✐çã♦ ❞❛ ❣❡r✲ ♠✐♥❛çã♦ ❡♠ ✉♠ ❝r✐tér✐♦ ♣❛r❛ ✧t❡❝♥♦❧♦❣✐st❛ ❞❡ s❡♠❡♥t❡s ❡ ❛❣rô♥♦♠♦s✧ ❡♠ q✉❡ ❛ ❣❡r✲ ♠✐♥❛çã♦ é ❛ ❡♠❡r❣ê♥❝✐❛ ❞❛ ♣❧❛♥t❛ ♥♦ s♦❧♦ ♦✉ ❛ ❢♦r♠❛çã♦ ❞❡ ✉♠❛ ♣❧â♥t✉❧❛ ✈✐❣♦r♦s❛ ♥♦ s✉❜str❛t♦ ✉t✐❧✐③❛❞♦ ❡ ❡♠ ✉♠ ✧❝r✐tér✐♦ ❜♦tâ♥✐❝♦ ♦✉ ♠♦r❢♦❧ó❣✐❝♦✧ ❡♠ q✉❡ ❛ ❣❡r♠✐♥❛çã♦ é ❝♦♥s✐❞❡r❛❞❛ ❝♦♠♦ ❛ ♣r♦t✉sã♦ ❞❡ ✉♠❛ ❞❛s ♣❛rt❡s ❞♦ ❡♠❜r✐ã♦ ❞❡ ❞❡♥tr♦ ❞♦s ❡♥✈♦❧tó✲ r✐♦s ✭✐st♦ é✱ q✉❛♥❞♦ ❛ r❛❞í❝✉❧❛ t❡♠ ❝r❡s❝✐❞♦ ♣❡❧♦ ♠❡♥♦s 1mm ❢♦r❛ ❞♦ r❡✈❡st✐♠❡♥t♦ ❞❛
s❡♠❡♥t❡✮✳
P❛r❛ q✉❡ ❛ ❣❡r♠✐♥❛çã♦ ❞❡ ✉♠❛ s❡♠❡♥t❡ ♦❝♦rr❛ ❞❡t❡r♠✐♥❛❞❛s ❝♦♥❞✐çõ❡s ❞❡✈❡♠ ❛❝♦♥t❡❝❡r✿ ❡❧❛ ♣r❡❝✐s❛ s❡r ✈✐á✈❡❧✱ s✉❛s ❝♦♥❞✐çõ❡s ✐♥t❡r♥❛s ❡ ❛s ❝♦♥❞✐çõ❡s ❛♠❜✐❡♥✲ t❛✐s ❞❡✈❡♠ s❡r ❢❛✈♦rá✈❡✐s ✭á❣✉❛✱ t❡♠♣❡r❛t✉r❛✱ ♦①✐❣ê♥✐♦ ❡ ❧✉③✮✱ ❡ ❛s ❝♦♥❞✐çõ❡s ❞❡ s❛♥✐❞❛❞❡ ❞❡✈❡♠ s❡r s❛t✐s❢❛tór✐❛s ✭❛✉sê♥❝✐❛ ❞❡ ❛❣❡♥t❡s ♣❛t♦❣ê♥✐❝♦s✮ ✭P❖P■◆■◆●❙✱ ✶✾✽✺✮✳
❆ ❣❡r♠✐♥❛çã♦ ❡stá ❛ss♦❝✐❛❞❛ à ❞♦r♠ê♥❝✐❛ ❞❛s s❡♠❡♥t❡s✱ ♥♦ s❡♥t✐❞♦ q✉❡ ✉♠❛ s❡♠❡♥t❡ é ❞♦r♠❡♥t❡ q✉❛♥❞♦ ♥ã♦ t❡♠ ❛ ❝❛♣❛❝✐❞❛❞❡ ♣❛r❛ ❣❡r♠✐♥❛r ❡♠ ✉♠ ♣❡rí♦❞♦ ❞❡ t❡♠♣♦ ❡s♣❡❝í✜❝♦ s♦❜ q✉❛❧q✉❡r ❝♦♠❜✐♥❛çã♦ ❞❡ ❢❛t♦r❡s ❛♠❜✐❡♥t❛✐s ❡ ❢ís✐❝♦s ♥♦r♠❛✐s q✉❡ ❞❡ ♦✉tr❛ ❢♦r♠❛ s❡r✐❛♠ ❢❛✈♦rá✈❡✐s ♣❛r❛ ❛ s✉❛ ❣❡r♠✐♥❛çã♦ ✭❇❆❙❑■◆❀ ❇❆❙❑■◆✱ ✷✵✵✹✮✳ ❉❡♥tr♦ ❞❡ss❡ ❝♦♥t❡①t♦✱ ❞❡✜♥❡✲s❡ ❛ ❞♦r♠ê♥❝✐❛ ♠♦r❢♦❧ó❣✐❝❛ ❝♦♠♦ ✉♠ ❛tr❛s♦ ❞❛ ❣❡r♠✐♥❛çã♦ ❞❡✈✐❞♦ ❛♦ t❡♠♣♦ ♥❡❝❡ssár✐♦ ❞❡ ❝r❡s❝✐♠❡♥t♦ ❞♦ ❡♠❜r✐ã♦ ❡ ❡♠❡r❣ê♥❝✐❛ ❞❛ r❛❞í❝✉❧❛✱ ❛♣ós ❛ s❡♠❡♥t❡ t❡r ❛t✐♥❣✐❞♦ ❛ ♠❛t✉r✐❞❛❞❡✳
❯s✉❛❧♠❡♥t❡✱ ♦ ✐♥t❡r❡ss❡ ❡♥tr❡ ♦s ♣❡sq✉✐s❛❞♦r❡s ❞❡ s❡♠❡♥t❡s ♥ã♦ ❡stá ♥❛ ❣❡r♠✐♥❛çã♦ ❞❡ ✉♠❛ s❡♠❡♥t❡ ❡♠ s✐✱ ♠❛s ❡♠ s❡❣✉✐r ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❣❡r♠✐♥❛t✐✈♦ ❞❡ ✉♠❛ ❞❡t❡r♠✐♥❛❞❛ q✉❛♥t✐❞❛❞❡ ❞❡ s❡♠❡♥t❡s✱ ❞❡♥♦♠✐♥❛❞❛ ❛♠♦str❛✳
✷✺
❆ ❛♠♦str❛❣❡♠ ❞❡ s❡♠❡♥t❡s ❜✉s❝❛ ♦❜t❡r ✉♠❛ ❛♠♦str❛ ❞❡ t❛♠❛♥❤♦ ❛❞❡✲ q✉❛❞♦ ♣❛r❛ ♦s t❡st❡s✱ q✉❡ ❡st❡❥❛ ❡♠ ❝♦♥❢♦r♠✐❞❛❞❡ ❝♦♠ ♦s ❧♦t❡s ❞❡ s❡♠❡♥t❡s ❡ ❡♠ ♣r♦♣♦rçõ❡s s❡♠❡❧❤❛♥t❡s✳ ❆ q✉❛♥t✐❞❛❞❡ ❞❡ s❡♠❡♥t❡s ❛♥❛❧✐s❛❞❛s é✱ ❡♠ ❣❡r❛❧✱ ♠✉✐t♦ ♣❡✲ q✉❡♥❛ ❡♠ r❡❧❛çã♦ ❛♦ t❛♠❛♥❤♦ ❞♦ ❧♦t❡ q✉❡ r❡♣r❡s❡♥t❛✱ ✈❛r✐❛ ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛ ❡s♣é❝✐❡ ❡ sã♦ ❡s♣❡❝✐✜❝❛❞❛s ♣❡❧❛s ❘❆❙ ✭❇❘❆❙■▲✱ ✷✵✵✾✱ ♣✳ ✹✺✮✳
❆ ❣❡r♠✐♥❛çã♦ ❞❡ s❡♠❡♥t❡s ❞❡ ✉♠ ❧♦t❡ é ✉s✉❛❧♠❡♥t❡ ❞❡s❝r✐t❛ ❧✐st❛♥❞♦ ♦ ♥ú✲ ♠❡r♦ ♦✉ ❛ ♣♦r❝❡♥t❛❣❡♠ ❞❡ s❡♠❡♥t❡s q✉❡ ❛t✐♥❣❡♠ ✉♠ ❝❡rt♦ ❡stá❣✐♦ ❞❡ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ♣♦r ✉♠ ❞❡t❡r♠✐♥❛❞♦ t❡♠♣♦ ❞❡ ❡♠❜❡❜✐çã♦✳ ❯♠❛ ❞❡s❝r✐çã♦ ❝♦♠♣❧❡t❛ ❞❛ ❣❡r♠✐♥❛çã♦ ❞❡✈❡ ✐♥❝❧✉✐r ♦ ♣❡r❝❡♥t✉❛❧ ♠á①✐♠♦ ❞❡ ❣❡r♠✐♥❛çã♦✱ ❛ ✈❡❧♦❝✐❞❛❞❡ ♠é❞✐❛ ❞❡ ❣❡r♠✐♥❛çã♦ ❡ ❛ ✈❛r✐❛çã♦ ❧♦♥❣✐t✉❞✐♥❛❧ ❞❡ss❛ ✈❡❧♦❝✐❞❛❞❡ ♠é❞✐❛ ✭❏❆◆❙❙❊◆✱ ✶✾✼✸✮✳
✷✳✷ ▼❡❞✐❞❛s ❞❡ ❣❡r♠✐♥❛çã♦ ❞❡ s❡♠❡♥t❡s
❉✐❢❡r❡♥t❡s ❢♦r♠❛s ❞❡ ♠❡❞✐r ❛ ❣❡r♠✐♥❛çã♦ ❢♦r❛♠ ❞❡s❡♥✈♦❧✈✐❞❛s ❛♦ ❧♦♥❣♦ ❞♦ t❡♠♣♦✱ ❡♠ q✉❡ ♦s r❡s✉❧t❛❞♦s ❞♦ ♣r♦❝❡ss♦ ❣❡r♠✐♥❛t✐✈♦ tê♠ s✐❞♦ ❡①♣r❡ss♦s ♣♦r ♠❡✐♦ ❞❡ í♥❞✐❝❡s ♦✉ ♣❡❧❛s ❝✉r✈❛s ❛❥✉st❛❞❛s ❞❡ ♠♦❞❡❧♦s ✈❛r✐❛❞♦s✳ ❘❛♥❛❧ ❡ ❙❛♥t❛♥❛ ✭✷✵✵✻✮ ❛♣r❡s❡♥t❛♠ ♣❡❧♦ ♠❡♥♦s tr✐♥t❛ ❞❡ss❛s ♠❡❞✐❞❛s✳
❈❛♠♣❜❡❧❧ ❡ ❙♦r❡♥s❡♥ ✭✶✾✼✾✮✱ ❝♦♠ ♦❜❥❡t✐✈♦ ❞❡ ❞❡✜♥✐r ✉♠❛ ♥♦✈❛ ❜❛s❡ ♣❛r❛ ❣❡r♠✐♥❛çã♦✱ ❛❧❡rt❛♠ q✉❡ ♠❡❞✐❞❛s ♣❛r❛ ❝❛r❛❝t❡r✐③❛r ❧♦t❡s ❞❡ s❡♠❡♥t❡s sã♦ ❝♦♠♣❧✐❝❛✲ ❞❛s✱ ♣♦✐s ❛ ❢r❡q✉ê♥❝✐❛ ❞♦s ❞✐❛s ♣❛r❛ ❣❡r♠✐♥❛çã♦ ♥ã♦ t❡♠ ✉♠❛ ❞✐str✐❜✉✐çã♦ ♥♦r♠❛❧✳ ❊❧✲❑❛ss❛❜② ❡t ❛❧✳ ✭✷✵✵✽✮ ❛♦ ❛♣r❡s❡♥t❛r❡♠ ✉♠ ❡st✉❞♦ s♦❜r❡ ♠♦❞❡❧❛❣❡♠ ♠❛t❡♠át✐❝❛ ❞❛ ❣❡r♠✐♥❛çã♦ ❞❡ s❡♠❡♥t❡s✱ ✐❞❡♥t✐✜❝❛r❛♠ q✉❡ ❛ ❞❡♣❡♥❞ê♥❝✐❛ ❞❡ ✉♠ ú♥✐❝♦ í♥❞✐❝❡ ❞❡ ❣❡r♠✐♥❛çã♦ ❝♦♠♦ ❣❡r♠✐♥❛❜✐❧✐❞❛❞❡✱ ✈❛❧♦r ❞❡ ♣✐❝♦✱ í♥❞✐❝❡ ❞❡ ✈❡❧♦❝✐❞❛❞❡ ❞❡ ❣❡r♠✐♥❛çã♦ ♦✉ ♠❡s♠♦ q✉❛❧q✉❡r ❞♦s s❡✉s ❝♦♠♣♦♥❡♥t❡s ✐♥❞✐✈✐❞✉❛✐s✱ é ✐♥❛❞❡q✉❛❞❛✳ ❆ r❛③ã♦ ♣❛r❛ ❛ ✐♥❛❞❡q✉❛çã♦ ❞❡st❛s ♠❡❞✐❞❛s é ❛ s✉❛ ❢❛❧t❛ ❞❡ ❛ss♦❝✐❛çã♦ ❝♦♠ ♦ t❡♠♣♦ ❛♦ ❧♦♥❣♦ ❞♦ ❝✉rs♦ ❞❡ ❣❡r♠✐♥❛çã♦✱ ♠❡s♠♦ q✉❡ ♦ t❡♠♣♦ s❡❥❛ ✉s❛❞♦ ♣❛r❛ ❝❛❧❝✉❧❛r ❝❛❞❛ ✉♠ ❞♦s ❝♦♠♣♦♥❡♥✲ t❡s ❞♦ í♥❞✐❝❡✳ ❖ s❡✉ ✉s♦ ❡①❝❧✉s✐✈♦ ♥ã♦ ♣❡r♠✐t❡ t✐r❛r ❝♦♥❝❧✉sõ❡s ✐♥❢♦r♠❛t✐✈❛s s♦❜r❡ ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❣❡r♠✐♥❛t✐✈♦ ❞❡ ✉♠ ❧♦t❡ ❞❡ s❡♠❡♥t❡s✳
✷✻
s❡♠❡♥t❡s ❣❡r♠✐♥❛❞❛s✱ ❛❧t❡r❛çõ❡s ❧♦♥❣✐t✉❞✐♥❛✐s ♥❛ t❛①❛ ❞❡ ❣❡r♠✐♥❛çã♦ ❡ ♦ ❡st❛❞♦ ❞❛s s❡♠❡♥t❡s ♥ã♦ ❣❡r♠✐♥❛❞❛s ✭❋❆▼❊❘✱ ✶✾✾✼✮✳
❆ ❋✐❣✉r❛ ✶ ♠♦str❛ ❛❧❣✉♥s ❡①❡♠♣❧♦s ❞❡ ❝✉r✈❛s ❞❡ ❣❡r♠✐♥❛çã♦✱ s♦❜r❡ ♦s q✉❛✐s ❞❡✈❡♠ s❡r ❢❡✐t❛s ❛❧❣✉♠❛s ♦❜s❡r✈❛çõ❡s ❣❡r❛✐s✳ ❆s ❝✉r✈❛s ❞❡ ❣❡r♠✐♥❛çã♦ ❣❡r❛❧✲ ♠❡♥t❡ sã♦ s✐❣♠♦✐❞❛✐s✱ q✉❡ é r❡s✉❧t❛❞♦ ❞❛ ❛ss✐♥❝r♦♥✐❛ ❞❛ ❣❡r♠✐♥❛çã♦ ❞❛s s❡♠❡♥t❡s✱ ❡♠ q✉❡ ✉♠❛ ♣❡q✉❡♥❛ ♣❛rt❡ ❞❡ ❣❡r♠✐♥❛çõ❡s ❛❝♦♥t❡❝❡ ♣r❡❝♦❝❡ ♦✉ t❛r❞✐❛♠❡♥t❡ ❡ ✉♠❛ ❣r❛♥❞❡ q✉❛♥t✐❞❛❞❡ ❞❛s ❣❡r♠✐♥❛çõ❡s ❡♠ t❡♠♣♦ ✐♥t❡r♠❡❞✐ár✐♦✳ ●❡r❛❧♠❡♥t❡✱ ❛s ❝✉r✈❛s sã♦ ❛s✲ s✐♠étr✐❝❛s ♣♦s✐t✐✈❛s ♣♦rq✉❡ ✉♠❛ ♠❛✐♦r ♣♦r❝❡♥t❛❣❡♠ ❞❡ s❡♠❡♥t❡s ❣❡r♠✐♥❛ ♥❛ ♣r✐♠❡✐r❛ ♠❡t❛❞❡ ❞♦ ♣❡rí♦❞♦ ❞❡ ❣❡r♠✐♥❛çã♦ ❛♦ ✐♥✈és ❞♦ s❡❣✉♥❞♦✳
❈♦♥s✐❞❡r❛çõ❡s ❛ r❡s♣❡✐t♦ ❞❛s ❝✉r✈❛s ❞❡ ❣❡r♠✐♥❛çã♦ sã♦ ❛♣r❡s❡♥t❛❞❛s ♣♦r ❇❡✇❧❡② ❡ ❇❧❛❝❦ ✭✶✾✾✹✮✱ ♦♥❞❡ ✐❞❡♥t✐✜❝❛♠ ✐♠♣♦rt❛♥t❡s ❞✐❢❡r❡♥ç❛s ❡♥tr❡ ❛s ♣♦♣✉❧❛çõ❡s ❞❡ s❡♠❡♥t❡s✳ ❆ ❢♦r♠❛ ❞❛s ❝✉r✈❛s ❞❡♣❡♥❞❡ ❞❛ ✉♥✐❢♦r♠✐❞❛❞❡ ❞❛ ♣♦♣✉❧❛çã♦✱ ✐st♦ é✱ ❞♦ ❣r❛✉ ❞❡ s✐♠✉❧t❛♥❡✐❞❛❞❡ ♦✉ s✐♥❝r♦♥✐❛ ❞❛ ❣❡r♠✐♥❛çã♦✳ ■st♦ ♣♦❞❡ s❡r ♥♦t♦r✐❛♠❡♥t❡ ♦❜s❡r✈❛❞♦ ❡♥tr❡ ❛s ♣♦♣✉❧❛çõ❡s ❞❡ s❡♠❡♥t❡s r❡♣r❡s❡♥t❛❞❛s ♣❡❧❛s ❝✉r✈❛s ✭❞✮ ❡ ✭❢✮ ❞❛ ❋✐❣✉r❛ ✶✭❛✮✱ ❡♠ q✉❡ ❛ ❝✉r✈❛ ✭❢✮ ♥❡❝❡ss✐t❛ ❞❡ ✉♥✐❢♦r♠✐❞❛❞❡ ❞❡ s❡♠❡♥t❡s ✐♥❞✐✈✐❞✉❛✐s ♣❛r❛ ❝♦♠♣❧❡t❛r ❛ s✉❛ ❣❡r♠✐♥❛çã♦ ❡♠ ❞✐❢❡r❡♥t❡s ♣❡rí♦❞♦s ❞❡ t❡♠♣♦ ❡ ❛ ❝✉r✈❛ ✭❞✮ ❥á ❛♣r❡s❡♥t❛ ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❛❧t❛♠❡♥t❡ ✉♥✐❢♦r♠❡ ❞❛s s❡♠❡♥t❡s✳ ❆ ✐♥❝❧✐♥❛çã♦ ♠❛✐s ❛❝❡♥t✉❛❞❛ ❞❛ ❝✉r✈❛ ✭❞✮ ❋✐❣✉r❛ ✶✭❛✮ ❡♠ r❡❧❛çã♦ ❛s ❞❡♠❛✐s é ❞❡❝♦rr❡♥t❡ ❞♦ ❢❛t♦ ❞❡ q✉❡ ❛ ♠❛✐♦r✐❛ ❞❛s s❡♠❡♥t❡s ❝♦♠♣❧❡t♦✉ ♦ ♣r♦❝❡ss♦ ❞❡ ❣❡r♠✐♥❛çã♦ ❡♠ ✉♠ ♣❡rí♦❞♦ ❞❡ t❡♠♣♦ r❡❧❛t✐✈❛♠❡♥t❡ ♠❡♥♦r q✉❡ ♦s ❞❡♠❛✐s ❧♦t❡s ✭❋✐❣✉r❛ ✶✭❜✮✮✳
❆ ❞❡✜♥✐çã♦ ❞❡ t❛①❛ ❞❡ ❣❡r♠✐♥❛çã♦ ❡♥tr❡ ♦s ♣❡sq✉✐s❛❞♦r❡s ❞❡ s❡♠❡♥t❡s é ✉t✐❧✐③❛❞❛ ❡♠ ❞♦✐s s❡♥t✐❞♦s✿ ❝♦♠♦ ✉♠❛ ♠❡❞✐❞❛ ❞❡ ✉♥✐❢♦r♠✐❞❛❞❡✱ ✐st♦ é✱ q✉❛♥t♦ ♠❛✐s ❛❝❡♥t✉❛❞❛ ❢♦r ❛ ✐♥❝❧✐♥❛çã♦ ❞❛ ❝✉r✈❛✱ ♠❛✐s ✉♥✐❢♦r♠❡ s❡rá ♦ t❡♠♣♦ ♥❡❝❡ssár✐♦ ♣❛r❛ ❛ ❣❡r♠✐♥❛çã♦✱ ♦✉ ♥♦ s❡♥t✐❞♦ ❞❡ ❞❡s❝r❡✈❡r ❛ ✈❡❧♦❝✐❞❛❞❡ ❞❡ ❣❡r♠✐♥❛çã♦✱ ❞❡✜♥✐❞❛ ❝♦♠♦ ♦ ✐♥✈❡rs♦ ❞♦ t❡♠♣♦ ♥❡❝❡ssár✐♦ ♣❛r❛ ❣❡r♠✐♥❛çã♦ ♦❝♦rr❡r ✭❘❖❇❊❘❚❙✱ ✶✾✼✷✮✳ ❊ss❛s ❞❡✜♥✐çõ❡s ♣♦❞❡♠ s❡r ❝❧❛r❛♠❡♥t❡ ♦❜s❡r✈❛❞❛s ♣❡❧❛s ❝✉r✈❛s ✭❝✮ ❡ ✭❞✮ ❛♣r❡s❡♥t❛❞❛s ♥❛s ❋✐❣✉r❛s ✶✭❛✮ ❡ ✶✭❜✮✳
✷✼
0 25 50 75 100
0 5 10 15 20 25
Tempo (dias)
(%) Ger
minação acum
ulada
curvas de germinação ab cd ef
✭❛✮
0 20 40
0 5 10 15 20 25
Tempo (dias)
(%) sementes ger
minadas/unidade de tempo
curvas de germinação ab cd ef
✭❜✮
❋✐❣✉r❛ ✶ ✕ ❈✉r✈❛s ❞❡ ❣❡r♠✐♥❛çã♦ ❛♦ ❧♦♥❣♦ ❞♦ t❡♠♣♦ ✭❛✮✱ ❞✐str✐❜✉✐çõ❡s ❞♦ t❡♠♣♦ ❞❡ ❣❡r♠✐♥❛çã♦ ✭❜✮
❆s ❝✉r✈❛s ✭❛✮ ❡ ✭❡✮ ♥❛ ❋✐❣✉r❛ ✶✭❛✮ ❡①✐❜❡♠ ♣♦♣✉❧❛çõ❡s ❡♠ q✉❡ ❛ ♣r♦♣♦rçã♦ ❞❡ s❡♠❡♥t❡s ❝❛♣❛③❡s ❞❡ ❝♦♠♣❧❡t❛r ❛ ❣❡r♠✐♥❛çã♦ é ♠❛✐s ❜❛✐①❛✳ ❆ ❛ss✐♠❡tr✐❛ ♣♦s✐t✐✈❛ t❛♠❜é♠ é ✉♠❛ ✐♠♣♦rt❛♥t❡ ♦❜s❡r✈❛çã♦ ♥❛s ❝✉r✈❛s ❞❡ ❞✐str✐❜✉✐çã♦ ♠♦str❛❞❛s ♥❛ ❋✐❣✉r❛ ✶✭❜✮✳
✷✳✸ ❆♥á❧✐s❡ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛
❆ ❣❡r♠✐♥❛çã♦ ❞❛s s❡♠❡♥t❡s é ✉♠ ❞♦s ♣r♦❝❡ss♦s ❞❛ ❛❣r✐❝✉❧t✉r❛ q✉❡ ❡stá ✐♥tr✐♥s❡❝❛♠❡♥t❡ ❛ss♦❝✐❛❞♦ ❝♦♠ ♦ t❡♠♣♦✳ ❋❛t♦ ❡ss❡ q✉❡ r❡❝❡♥t❡♠❡♥t❡ t❡♠ ❧❡✈❛❞♦ ❞✐✈❡r✲ s♦s ♣❡sq✉✐s❛❞♦r❡s ❛ ❡♥❢❛t✐③❛r ❛ ♥❡❝❡ss✐❞❛❞❡ ❞❛ ✉t✐❧✐③❛çã♦ ❞❡ ♠❡t♦❞♦❧♦❣✐❛s ❡st❛tíst✐❝❛s ♠❛✐s ❛❞❡q✉❛❞❛s ♣❛r❛ ♠❡❧❤♦r ❞❡s❝r❡✈❡r ❡st❡ ♣r♦❝❡ss♦✳
❆s té❝♥✐❝❛s ❞❡ ❛♥á❧✐s❡ ❡st❛tíst✐❝❛ ♣r❡♦❝✉♣❛❞❛s ❡♠ ❡st✉❞❛r ♦ t❡♠♣♦ ❛té ❛ ♦❝♦rrê♥❝✐❛ ❞❡ ✉♠ ❞❡t❡r♠✐♥❛❞♦ ❡✈❡♥t♦✱ ❝♦♥❤❡❝✐❞❛s ❝♦♠♦ ❛♥á❧✐s❡ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛✱ ♦❢❡r❡❝❡♠ ♦ ❝♦♥❥✉♥t♦ ♠❛✐s ❛❞❡q✉❛❞♦ ❡ ♣♦❞❡r♦s♦ ❞❡ ❛♥á❧✐s❡ ❞❡ ❞❛❞♦s ❞❡ ❣❡r♠✐♥❛çã♦ ✭▼❝◆❆■❘❀ ❙❯◆❑❆❘❆❀ ❋❖❘❇■❙❍✱ ✷✵✶✷✮✱ ❡♠❜♦r❛ t❡♥❤❛♠ s✐❞♦ ♣♦✉❝♦ ✉s❛❞❛s ♣❛r❛ ❡st❛ ✜♥❛❧✐❞❛❞❡ ✭❆▼❆❚❀ ❱❆❘●❆❙❀ ●❖▼➱❩✱ ✷✵✶✹❀ ▼❆◆❙❖ ❡t ❛❧✳✱ ✷✵✶✸❀ ❖◆❖❋❘■ ❡t ❛❧✳✱ ✷✵✶✵❀ ❙❈❖❚❚❀ ❏❖◆❊❙❀ ❲■▲▲■❆▼❙✱ ✶✾✽✹✮✳
✷✽
❞♦r♠ê♥❝✐❛ ♠♦r❢♦❧ó❣✐❝❛ ♠❛✐♦r q✉❡ ❛ ❞✉r❛çã♦ ❞♦ ❡①♣❡r✐♠❡♥t♦✱ ❧❡✈❛♥❞♦ ❛ ♦❜s❡r✈❛çõ❡s ✐♥❝♦♠♣❧❡t❛s✳ ❆ss✐♠✱ ♣❛r❛ ❛s s❡♠❡♥t❡s q✉❡ ♥ã♦ ❣❡r♠✐♥❛r❛♠ ❛té ♦ ✜♥❛❧ ❞♦ ❡①♣❡r✐♠❡♥t♦ ♦❜s❡r✈❛✲s❡ ♦ t❡♠♣♦ ❝❡♥s✉r❛❞♦✱ q✉❡ ❝♦rr❡s♣♦♥❞❡ ❛♦ ♣❡rí♦❞♦ ❞❡ t❡♠♣♦ ♦❜s❡r✈❛❞♦ ❞❡s❞❡ ♦ ✐♥í❝✐♦ ❞♦ ❡①♣❡r✐♠❡♥t♦ ❛té ♦ s❡✉ tér♠✐♥♦✳ ❊ss❡s r❡s✉❧t❛❞♦s sã♦ r❡❢❡r✐❞♦s ❝♦♠♦ ♦❜s❡r✲ ✈❛çõ❡s ❝❡♥s✉r❛❞❛s à ❞✐r❡✐t❛✳ ❈❡♥s✉r❛ à ❡sq✉❡r❞❛ ❡ ❝❡♥s✉r❛ ✐♥t❡r✈❛❧❛r t❛♠❜é♠ ❡stã♦ ♣r❡s❡♥t❡s ❡♠ ❡♥s❛✐♦s ❞❡ ❣❡r♠✐♥❛çã♦✱ r❡s♣❡❝t✐✈❛♠❡♥t❡ q✉❛♥❞♦ ❛ ❣❡r♠✐♥❛çã♦ ❥á ♦❝♦rr❡✉ ❛♥t❡s ❞❛ ♣r✐♠❡✐r❛ ❛✈❛❧✐❛çã♦ ♦✉ q✉❛♥❞♦ ♦ t❡♠♣♦ ❡①❛t♦ ❞❡ ❣❡r♠✐♥❛çã♦ ♦❝♦rr❡ ❡♠ ❛❧❣✉♠ ✐♥st❛♥t❡ ❡♥tr❡ ❞✉❛s ❞❛t❛s s✉❝❡ss✐✈❛s ❞❡ ♠♦♥✐t♦r❛♠❡♥t♦ ✭❖◆❖❋❘■ ❡t ❛❧✳✱ ✷✵✶✶✮✳
❖s ❞❛❞♦s ♥❛ ❛♥á❧✐s❡ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ♣♦❞❡♠ s❡r ❡s❝r✐t♦s ❝♦♠♦ ✉♠ ♣❛r ♦r❞❡♥❛❞♦ (ti, δi)❡♠ q✉❡ti é ♦ t❡♠♣♦ ❞❡ ❢❛❧❤❛ ♦✉ ❝❡♥s✉r❛ ❡δi é ♦ ✐♥❞✐❝❛❞♦r ❞❡ ❝❡♥s✉r❛✱
t❛❧ q✉❡✱
δi =
1, s❡ ti é ✉♠ t❡♠♣♦ ❞❡ ❢❛❧❤❛, 0, s❡ ti é ✉♠ t❡♠♣♦ ❞❡ ❝❡♥s✉r❛.
◗✉❛❧q✉❡r ♠ét♦❞♦ ❞❡ ❛♥á❧✐s❡ ❛ss♦❝✐❛❞♦ à ❛♥á❧✐s❡ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ✐♠♣❧✐❝❛ ♥♦ ❡st✉❞♦ ❞❡ ❞✉❛s ❢✉♥çõ❡s✿ ❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ S(t)✱ ❞❡✜♥✐❞❛ ❝♦♠♦ ❛ ♣r♦❜❛❜✐✲
❧✐❞❛❞❡ ❞♦ t❡♠♣♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ T ❞❡ ✉♠ ✐♥❞✐✈í❞✉♦ s❡r s✉♣❡r✐♦r ❛ ✉♠ t❡♠♣♦ t✱ ❡ ❛
❢✉♥çã♦ ❞❡ r✐s❝♦λ(t)✱ ❞❡✜♥✐❞❛ ❝♦♠♦ ♦ r✐s❝♦ ✐♥st❛♥tâ♥❡♦ ❞❡ ♦❝♦rrê♥❝✐❛ ❞❡ ✉♠ ❡✈❡♥t♦✱ ✐st♦
é✱ s❡♠❡♥t❡s ❡♠ r✐s❝♦ ❞❡ ❣❡r♠✐♥❛çã♦ ❡♠ ✉♠ ❞❛❞♦ ✐♥t❡r✈❛❧♦✳
◆♦ ❝♦♥t❡①t♦ ❞❡ ❡st✉❞♦s r❡❧❛❝✐♦♥❛❞♦s à ❣❡r♠✐♥❛çã♦ ❞❡ s❡♠❡♥t❡s✱ ❛ ❢✉♥✲ çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ♣♦❞❡ s❡r s✉❜st✐t✉í❞❛ ♣❡❧❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ ❣❡r♠✐♥❛çã♦✳ ❆ss✐♠✱ ♦s ♦❜❥❡t✐✈♦s ❞❛ ❛♥á❧✐s❡ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ sã♦✿ ❡st✐♠❛r ❡ ✐♥t❡r♣r❡t❛r ❢✉♥çõ❡s ❞❡ r✐s❝♦ ❡✴♦✉ s♦❜r❡✈✐✈ê♥❝✐❛ ❛ ♣❛rt✐r ❞❡ ❞❛❞♦s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛❀ ❝♦♠♣❛r❛r t❛✐s ❢✉♥çõ❡s❀ ❛✈❛❧✐❛r ❛ ✐♥✢✉ê♥❝✐❛ ❞❡ ✈❛r✐á✈❡✐s ❡①♣❧❛♥❛tór✐❛s ♥♦ t❡♠♣♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛✳ ❖s ♠ét♦❞♦s ❞❡ ❛♥á✲ ❧✐s❡ ♣♦❞❡♠ ✈❛r✐❛r ❞❡ ❛❝♦r❞♦ ❝♦♠ ♦ ♦❜❥❡t✐✈♦ ❞♦ ❡st✉❞♦ ✭❈❖▲❖❙■▼❖❀ ●■❖▲❖✱ ✷✵✵✻❀ ❖◆❖❋❘■ ❡t ❛❧✳✱ ✷✵✶✵✮✳
❊♠ t❡r♠♦s ♣r♦❜❛❜✐❧íst✐❝♦s✱ ❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ♣♦❞❡ s❡r ❡①♣r❡ss❛ ❝♦♠♦✿
S(t) =P(T ≥t) =
Z t
∞
f(u)du= 1−F(t), ✭✶✮
❡♠ q✉❡ T é ✉♠❛ ✈❛r✐á✈❡❧ ❛❧❡❛tór✐❛ ♥ã♦ ♥❡❣❛t✐✈❛✱ r❡♣r❡s❡♥t❛♥❞♦ ♦ t❡♠♣♦ ❞❡ ✈✐❞❛✳ ❆
❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❛ss♦❝✐❛❞❛ ❛ ❡ss❛ ✈❛r✐á✈❡❧ ♣♦ss✉✐ ❛s s❡❣✉✐♥t❡s ♣r♦♣r✐❡❞❛❞❡s✿
✷✾
• limt→∞S(t) = 0✱
• S(t)é ♠♦♥ót♦♥❛ ❞❡❝r❡s❝❡♥t❡✳
❊ss❛s ♣r♦♣r✐❡❞❛❞❡s sã♦ ❡♥❝♦♥tr❛❞❛s ❡♠ ❞❛❞♦s ❞❡ ❣❡r♠✐♥❛çã♦✱ ♣♦✐s ♦ t❡♠♣♦ ❞❡ ❣❡r♠✐♥❛çã♦ é s❡♠♣r❡ ♠❛✐♦r q✉❡ ✵✱ ❡♥tã♦ S(0) = 1✳ ❉❡✈✐❞♦ ❛ ❞♦r♠ê♥❝✐❛
♠♦r❢♦❧ó❣✐❝❛✱ ❝♦♠✉♠ ❡♠ ❡①♣❡r✐♠❡♥t♦s ❞❡ ❣❡r♠✐♥❛çã♦✱ S(t) ♣❡r♠❛♥❡❝❡rá ❝♦♥st❛♥t❡ ❡♠
✶ ♣❛r❛ ♣❡q✉❡♥♦s ✈❛❧♦r❡s ❞❡ t ❡ ❡♠ s❡❣✉✐❞❛ ❝♦♠❡ç❛rá ❛ ❞❡❝r❡s❝❡r✳ ◗✉❛♥❞♦ t s❡ t♦r♥❛
❣r❛♥❞❡✱ S(t) ✐rá s❡ ❛♣r♦①✐♠❛r ❞❡ ✉♠ ✈❛❧♦r ❧✐♠✐t❡ ✐❣✉❛❧ ❛ ✵ ✭s❡ t♦❞❛s ❛s s❡♠❡♥t❡s ❣❡r✲
♠✐♥❛r❡♠ ♥❛s ❝♦♥❞✐çõ❡s ❡①♣❡r✐♠❡♥t❛✐s✮ ♦✉ ♠❛✐♦r q✉❡ ③❡r♦ ✭❝❛s♦ ❝♦♥trár✐♦✮ ✭▼❝◆❆■❘❀ ❙❯◆❑❆❘❆❀ ❋❖❘❇■❙❍✱ ✷✵✶✷✮✳
❆ ❢✉♥çã♦ ❞❡ r✐s❝♦✱ λ(t✮✱ ❝♦♥❤❡❝✐❞❛ t❛♠❜é♠ ♣♦r t❛①❛ ❞❡ ❢❛❧❤❛✱ ✐♥❢♦r♠❛
q✉❛❧ ❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❛ ❣❡r♠✐♥❛çã♦ ♦❝♦rr❡r ❡♠ ✉♠ ✐♥t❡r✈❛❧♦ ❞❡ t❡♠♣♦ [t1, t2)✱ ❞❛❞♦ q✉❡ ♥ã♦ ♦❝♦rr❡✉ ❛♥t❡s ❞❡t1✱ ❞✐✈✐❞✐❞❛ ♣❡❧♦ ❝♦♠♣r✐♠❡♥t♦ ❞♦ ✐♥t❡r✈❛❧♦✳
●❡♥❡r❛❧✐③❛♥❞♦ λ(t✮✱ s✐t✉❛❞❛ ♥♦ ✐♥t❡r✈❛❧♦ ✐♥✜♥✐t❡s✐♠❛❧ (t, t+ ∆t]t❡♠✲s❡✿
λ(t) = lim
∆t→0
P(t≤T ≤t+ ∆t |T ≥t) ∆t
= S(t)−S(t+ ∆t) ∆tS(t)
. ✭✷✮
❖✉tr❛ ❢✉♥çã♦ út✐❧ é ❛ ❢✉♥çã♦ ❞❡ r✐s❝♦ ❛❝✉♠✉❧❛❞❛ ❞♦ ✐♥❞✐✈í❞✉♦✱ Λ(t)✱
❞❡✜♥✐❞❛ ❡♠ ✭✸✮✱ q✉❡ ❛♣❡s❛r ❞❡ ♥ã♦ t❡r ✉♠❛ ✐♥t❡r♣r❡t❛çã♦ ❞✐r❡t❛✱ ♣♦❞❡ s❡r ♥❡❝❡ssár✐❛ ♥❛ ❛✈❛❧✐❛çã♦ ❞❡ λ(t)✱ ❝♦♠♦ t❛♠❜é♠ ❡♠ ❡st✐♠❛çõ❡s ♥ã♦ ♣❛r❛♠étr✐❝❛s✳ P♦❞❡ s❡r ❡①♣r❡ss❛
❝♦♠♦✿
Λ(t) =
Z t
0
λ(u)du. ✭✸✮
❆❧❣✉♠❛s r❡❧❛çõ❡s ♠❛t❡♠át✐❝❛s ✐♠♣♦rt❛♥t❡s sã♦ ♦❜t✐❞❛s ♣♦r ♠❡✐♦ ❞❛s ❢✉♥çõ❡s ❞❡✜♥✐❞❛s ❛♥t❡r✐♦r♠❡♥t❡ ❡ ✐♠♣❧✐❝❛ q✉❡ ♦ ❝♦♥❤❡❝✐♠❡♥t♦ ❞❡ ✉♠❛ ❞❛s ❢✉♥çõ❡s ❧❡✈❛ ❛♦ ❝♦♥❤❡❝✐♠❡♥t♦ ❞❛s ❞❡♠❛✐s✿
λ(t) = f(t)
S(t) =−
d
dt(logS(t)),
Λ(t) =
Z t
0
λ(u)du =−logS(t)
❡
S(t) = exp{−Λ(t)}=exp{− Z t
0
✸✵
◆❡st❡ ❝♦♥t❡①t♦✱ ♣❛r❛ ❛♥❛❧✐s❛r ❞❛❞♦s ❞❡ t❡♠♣♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ♥❛ ♣r❡✲ s❡♥ç❛ ❞❡ ❝❡♥s✉r❛✱ ❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ ❣❡r♠✐♥❛çã♦ ♣♦❞❡ s❡r ❡st✐♠❛❞❛ ♣❡❧♦ ❡st✐♠❛❞♦r ♥ã♦✲♣❛r❛♠étr✐❝♦ ❞❡ ❑❛♣❧❛♥✲▼❡✐❡r ✭❑❆P▲❆◆❀ ▼❊■❊❘✱ ✶✾✺✽✮✳ ❖ ❡st✐♠❛❞♦r ❑❛♣❧❛♥✲ ▼❡✐❡r ✭❑✲▼✮ é ✉♠❛ ❞❛s té❝♥✐❝❛s ❞❡ ❛♥á❧✐s❡ ♥ã♦ ♣❛r❛♠étr✐❝❛ ♠❛✐s ✉s❛❞❛s ❡ ❝♦♥s✐st❡ ❡♠ ❞✐✈✐❞✐r ♦ t❡♠♣♦ ❞❡ s❡❣✉✐♠❡♥t♦ ❡♠ ✐♥t❡r✈❛❧♦s✱ ❝✉❥♦s ❧✐♠✐t❡s ❝♦rr❡s♣♦♥❞❡♠ ❛♦ t❡♠♣♦ ❞❡ s❡❣✉✐♠❡♥t♦ ❡♠ q✉❡ ❤♦✉✈❡ ❡✈❡♥t♦s ✭t❡♠♣♦s ❡①❛t♦s ❞❡ ❢❛❧❤❛✮✱ q✉❡ é r❡♣r❡s❡♥t❛❞♦ ♣♦r✿
ˆ
S(t) = Y tj≤t
(nj−dj
nj
), ✭✹✮
❡♠ q✉❡t1, t2,· · ·tksã♦ ♦skt❡♠♣♦s ❞✐st✐♥t♦s ❡♠ q✉❡ ♦❝♦rr❡r❛♠ ♦s ❡✈❡♥t♦s✱djé ♦ ♥ú♠❡r♦
❞❡ s❡♠❡♥t❡s q✉❡ ❣❡r♠✐♥❛r❛♠ ❡♠ tj✱ ❝♦♠ j = 1,2, ..., k✱nj é ♦ ♥ú♠❡r♦ ❞❡ s❡♠❡♥t❡s ❡♠
r✐s❝♦ ❞❡ ❣❡r♠✐♥❛çã♦ s♦❜ ♦ ♠❡s♠♦ ✐♥t❡r✈❛❧♦ tj✳
❙✉❛ ✈❛r✐â♥❝✐❛ é ❝❛❧❝✉❧❛❞❛ ❛ ♣❛rt✐r ❞♦ ❡st✐♠❛❞♦r ❞❡ ●r❡❡♥✇♦♦❞ ✭●❘❊✲ ❊◆❲❖❖❉✱ ✶✾✷✻✮✱ q✉❡ ♣♦❞❡ s❡r ❡①♣r❡ss❛❞❛ ♣♦r✿
ˆ
V( ˆS(t)) = ( ˆS(t))2
d1 n1(n1−d1)
+ d2
n2(n2−d2)
+...+ dj
nj(nj −dj)
, ✭✺✮
♦ ❡st✐♠❛❞♦r ❞♦ ❡rr♦ ♣❛❞rã♦ ❞❡ss❛ ❡st❛tíst✐❝❛✱ Vˆ( ˆS(t))é ❞❛❞♦ ♣♦r✿
ˆ
ephSˆ(t)i=
q
ˆ
V( ˆS(t)), ✭✻✮
❛ ♣❛rt✐r ❞❡ ✭✻✮✱ ✉♠ ✐♥t❡r✈❛❧♦ ❞❡ ❝♦♥✜❛♥ç❛ ❛♣r♦①✐♠❛❞♦ ♣❛r❛S(t)❛ ♥í✈❡❧ ❞❡100(1−α)%
❞❡ ❝♦♥✜❛♥ç❛ ♣♦❞❡ s❡r ❝❛❧❝✉❧❛❞♦ ♣♦r✿
ˆ
S(t)±zα/2 q
ˆ
V( ˆS(t)). ✭✼✮
❊♥tr❡t❛♥t♦✱ ❡st❡ ✐♥t❡r✈❛❧♦ ♣♦❞❡ ❛♣r❡s❡♥t❛r ✈❛❧♦r❡s ♥❡❣❛t✐✈♦s ♦✉ ♠❛✐♦r❡s q✉❡ ✶✱ ♦ q✉❡ é ✐♥❝♦❡r❡♥t❡ ❝♦♠ ❛ ❞❡✜♥✐çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛✳ P♦rt❛♥t♦✱ s✉❣❡r❡✲s❡ ❝♦♥str✉✐r ✉♠ ♥♦✈♦ ✐♥t❡r✈❛❧♦ ❞❡ ❝♦♥✜❛♥ç❛✱ ❝♦♠ ❜❛s❡ ♥❛ tr❛♥s❢♦r♠❛çã♦ Uˆ(t) = ln(−ln(S(t))) ♦❜t❡♥❞♦✲s❡
✉♠ ✐♥t❡r✈❛❧♦ ❛ ♥í✈❡❧ ❞❡100(1−α)% ❞❡ ❝♦♥✜❛♥ç❛✱ ❝♦♠ ✈❛❧♦r❡s ♣♦s✐t✐✈♦s ❡ ♠❡♥♦r❡s q✉❡
✶ ♣❛r❛ S(t)✱ q✉❡ ♣♦❞❡ s❡r ❡①♣r❡ss❛❞♦ ♣♦r✿
ˆ
S(t)exp h
±zα/2
√ˆ
V( ˆU(t))i
✸✶
❡♠ q✉❡ ❛ ✈❛r✐â♥❝✐❛ é ❡st✐♠❛❞❛ ♣♦r✿
ˆ
V( ˆU(t)) = Vˆ[ ˆS(t)]/Sˆ(t)
2
ln
(n1−d1) n1
+ln
(n2−d2) n2
+...+ln
(nj−dj)
nj
. ✭✾✮
❆ ❝✉r✈❛ ❑✲▼ é ✉♠❛ ❢✉♥çã♦ ❞❡❣r❛✉ ❝♦♥tí♥✉❛ à ❞✐r❡✐t❛✱ ❞❡❝r❡s❝❡♥t❡ ❡♠ q✉❡ ♦s ❞❡❣r❛✉s sã♦ ✐♥t❡r✈❛❧♦s ❞❡ t❡♠♣♦ ❡♥tr❡ ❞✉❛s ❢❛❧❤❛s ❞✐st✐♥t❛s ♦❜s❡r✈❛❞❛s✳ ❆ r❡♣r❡s❡♥t❛çã♦ ❣rá✜❝❛ é ♠♦str❛❞❛ ♥❛ ❋✐❣✉r❛ ✷✳
❋✐❣✉r❛ ✷ ✕ ❊st✐♠❛❞♦r❡s ❞❡ ❝✉r✈❛s ❞❡ ❑✲▼ ❞❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ♣❛r❛ ❞❛❞♦s ✜❝tí✲ ❝✐♦s ❞❡ ❣❡r♠✐♥❛çã♦✱ ❥✉♥t❛♠❡♥t❡ ❝♦♠ ✐♥t❡r✈❛❧♦s ❞❡ ❝♦♥✜❛♥ç❛ ✭✾✺✪✮ ✭❧✐♥❤❛s tr❛❝❡❥❛❞❛s✮
❆s ❝✉r✈❛s ❞❡ ❑✲▼ ♥ã♦ ♣❡r♠✐t❡♠ ❛♣❡♥❛s ❝♦♠♣❛r❛r ✈✐s✉❛❧♠❡♥t❡ ♦s tr❛t❛✲ ♠❡♥t♦s✱ ♠❛s t❛♠❜é♠ ❛ ❞❡s❝r✐çã♦ ❞❛s ♣ró♣r✐❛s ❝✉r✈❛s ♣♦r ❡st❛tíst✐❝❛s ❝♦♠♦ ♦ t❡♠♣♦ ♠é❞✐♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛✱ ❛ t❛①❛ ♠é❞✐❛ ❞❡ r✐s❝♦ ❡ ❛ ♠❡❞✐❛♥❛ ❞❛ s♦❜r❡✈✐✈ê♥❝✐❛✱ ✐st♦ é✱ ❡❧❛s ♣♦❞❡♠ s❡r ✉s❛❞❛s ♣❛r❛ ❞❡r✐✈❛r ♦ t❡♠♣♦ ♠❡❞✐❛♥♦ ❞❡ ❣❡r♠✐♥❛çã♦ ✭T50✮ ♦✉ ❚❡♠♣♦ ♠é❞✐♦ ❞❡ ❣❡r♠✐♥❛çã♦ ✭❚▼●✮✱ ❝♦♠ ❡rr♦s ♣❛❞rã♦ ❡✴♦✉ ❧✐♠✐t❡s ❞❡ ❝♦♥✜❛♥ç❛ ✭❖◆❖❋❘■ ❡t ❛❧✳✱ ✷✵✶✵✮✳
