❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ●♦✐ás
■♥st✐t✉t♦ ❞❡ ▼❛t❡♠át✐❝❛ ❡ ❊st❛tíst✐❝❛
Pr♦❣r❛♠❛ ❞❡ ▼❡str❛❞♦ Pr♦✜ss✐♦♥❛❧ ❡♠
▼❛t❡♠át✐❝❛ ❡♠ ❘❡❞❡ ◆❛❝✐♦♥❛❧
❆ ▼❛t❡♠át✐❝❛ ❞❛ ❊❞✉❝❛çã♦ ❋✐♥❛♥❝❡✐r❛
❆❧❡ss❛♥❞r♦ ❆♥❞r❡❛t✐♥✐ ◆❡t♦
●♦✐â♥✐❛
❆❧❡ss❛♥❞r♦ ❆♥❞r❡❛t✐♥✐ ◆❡t♦
❆ ▼❛t❡♠át✐❝❛ ❞❛ ❊❞✉❝❛çã♦ ❋✐♥❛♥❝❡✐r❛
❚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✳ ▼❛r✐♦ ❏♦sé ❞❡ ❙♦✉③❛
❚♦❞♦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✉♠♦
❊st❡ tr❛❜❛❧❤♦ t❡♠ ♣♦r ♦❜❥❡t✐✈♦ ♣r♦♠♦✈❡r ✉♠❛ r❡✢❡①ã♦ ❛❝❡r❝❛ ❞❛s ♣♦t❡♥❝✐❛✐s ✐♥t❡r✲ ❢❛❝❡s ❞✐❞át✐❝❛s ❡♥tr❡ ❛ ❡❞✉❝❛çã♦ ✜♥❛♥❝❡✐r❛ ❡ ♦s ❝♦♥t❡ú❞♦s ❞❡ ♠❛t❡♠át✐❝❛ ❛❜♦r❞❛❞♦s ♥♦ ❡♥s✐♥♦ ♠é❞✐♦ ❛tr❛✈és ❞❡ ✉♠ ❝✉rs♦ ❞❡ ❡❞✉❝❛çã♦ ✜♥❛♥❝❡✐r❛✳ ➱ ❛♣r❡s❡♥t❛❞❛ ✉♠❛ ❢❡r✲ r❛♠❡♥t❛ ♣❛r❛ ♦r❣❛♥✐③❛r ❡ ❝❧❛ss✐✜❝❛r ♦s ❣❛st♦s ❞❡ ♠❛♥❡✐r❛ s✐st❡♠át✐❝❛✳ ❊♠ s❡❣✉✐❞❛ sã♦ ❛❜♦r❞❛❞❛s ❛s ♦♣❡r❛çõ❡s ✜♥❛♥❝❡✐r❛s ❞❡ ❝ré❞✐t♦ ❝♦♠♦ ❝❤❡q✉❡ ❡s♣❡❝✐❛❧✱ ♦ ❝ré❞✐✐t♦ ❞✐r❡t♦ ❛♦ ❝♦♥s✉♠✐❞♦r ❡ ❛ ❛♥t❡❝✐♣❛çã♦ ❞❡ ❞é❝✐♠♦ t❡r❝❡✐r♦ s❛❧ár✐♦✳ ◆♦ t❡r❝❡✐r♦✱ ❛ ❝❛❞❡r♥❡t❛ ❞❡ ♣♦✉♣❛♥ç❛ ❡ ♦ r❡❝✐❜♦ ❞❡ ❞❡♣ós✐t♦ ❜❛♥❝ár✐♦✱ q✉❡ sã♦ ❛s ❛♣❧✐❝❛çõ❡s ❞❡ r❡♥❞❛ ✜①❛ ♠❛✐s ❝♦♠✉♥s r❡❛❧✐③❛❞❛s ♣♦r ♣❡ss♦❛s ❢ís✐❝❛s✳
P❛❧❛✈r❛s✲❝❤❛✈❡
▼❛t❡♠át✐❝❛ ❊♥s✐♥♦ ❇ás✐❝♦✱ ❡❞✉❝❛çã♦ ✜♥❛♥❝❡✐r❛✱ ❛♣❧✐❝❛çõ❡s ✜♥❛♥❝❡✐r❛s✳
❆❜str❛❝t
❚❤✐s ♣❛♣❡r ❛✐♠s t♦ ♣r♦♠♦t❡ ❛ r❡✢❡❝t✐♦♥ ❛❜♦✉t t❤❡ ❞✐❞❛❝t✐❝ ♣♦t❡♥t✐❛❧ ✐♥t❡r❢❛❝❡s ❜❡t✇❡❡♥ ✜♥❛♥❝✐❛❧ ❡❞✉❝❛t✐♦♥ ❛♥❞ ♠❛t❤ ❝♦♥t❡♥t ❝♦✈❡r❡❞ ✐♥ ❤✐❣❤ s❝❤♦♦❧ t❤r♦✉❣❤ ❛ ❝♦✉rs❡ ♦❢ ✜♥❛♥❝✐❛❧ ❡❞✉❝❛t✐♦♥✳ ❖ ✜rst ❝♦✉rs❡ ♠♦❞✉❧❡ ♣r❡s❡♥ts ❛ t♦♦❧ t♦ ♦r❣❛♥✐③❡ s♣❡♥❞✐♥❣ s♦ s②st❡♠❛t✐❝ ✳ ■♥ t❤❡ s❡❝♦♥❞ ♠♦❞✉❧❡ ❞✐s❝✉ss❡s t❤❡ ❞✐✛❡r❡♥t t②♣❡s ♦❢ ❧♦❛♥ ❛♥❞ ❝r❡❞✐t✳ ❚❤❡ t❤✐r❞ ♠♦❞✉❧❡ ❤❛s ❜❡❡♥ t❤❡ ♠♦st ❝♦♠♠♦♥ ✐♥✈❡st♠❡♥ts ❛♥❞ ❤♦✇ t❤❡② ✇♦r❦
❑❡②✇♦r❞s
♠❛t❤ ❤✐❣❤ s❝❤♦♦❧✱✜♥❛♥❝✐❛❧ ❡❞✉❝❛t✐♦♥✱❧♦❛♥s✱ ✐♥✈❡st♠❡♥ts✳
▲✐st❛ ❞❡ ❋✐❣✉r❛s
✶ ❖r❣❛♥✐③❛♥❞♦ ♦s r❡❝❡❜✐♠❡♥t♦s ❡ ♦s ❣❛st♦s ♠❡♥s❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽ ✷ ❘❡❝❡❜✐♠❡♥t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✸ ❉❡s♣❡s❛s ❋✐①❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✹ ❉❡s♣❡s❛s ❋✐①❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✺ ❉❡✜♥❛ s❡✉s ♦❜❥❡t✐✈♦s ♠❡♥s❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ✻ ◗✉❛♥t♦ q✉❡r ❡❝♦♥♦♠✐③❛r❄ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ✼ ●❛st♦s s❡♠❛♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✽ ❋✐♠ ❞♦ ♠ês ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸ ✾ ❉✐❛❣r❛♠❛ ❞♦ ✢✉①♦ ❞❡ ❝❛✐①❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✶✵ ❙❛❧❞♦s ❈♦♥t❛ ❈♦rr❡♥t❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✶✶ ❏✉r♦s ❈♦♥t❛ ❈♦rr❡♥t❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷ ✶✷ ■❖❋ ❈♦♥t❛ ❈♦rr❡♥t❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✶✸ ◗✉❛❞r♦ ❞❡ ❆♠♦rt✐③❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ✶✹ ◗✉❛❞r♦ ❞❡ ❆♠♦rt✐③❛çã♦ ❡ ❝á❧❝✉❧♦ ❞♦ ■❖❋ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵
❙✉♠ár✐♦
✶ ■♥tr♦❞✉çã♦ ✶✹
✶✳✶ P♦r q✉❡ ❞❡✈❡♠♦s ✐♥❝❧✉✐r ❛ ❊❞✉❝❛çã♦ ❋✐♥❛♥❝❡✐r❛ ♥❛s ❡s❝♦❧❛s❄ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹ ✶✳✷ ❖❜❥❡t✐✈♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻
✷ ❖ ❈✉rs♦ ✶✼
✷✳✶ ❆ss✉♠✐♥❞♦ ♦ ❝♦♥trô❧❡ ❞❛s ❞❡s♣❡s❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼ ✷✳✷ ❆ss✉♠✐♥❞♦ ♦ ❝♦♥tr♦❧❡ ❞❛s ❞❡s♣❡s❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽ ✷✳✸ P❧❛♥✐❧❤❛ ✷ ✲ P♦♥❞♦ ❡♠ ❞✐❛ ♦s ❣❛st♦s s❡♠❛♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✷✳✹ P❧❛♥✐❧❤❛ ✸ ✲ ❋✐♠ ❞♦ ▼ês ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✷✳✺ ◗✉❡st✐♦♥ár✐♦ ❋✐♥❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶
✸ ▼❛t❡♠át✐❝❛ ❋✐♥❛♥❝❡✐r❛ ✷✺
✸✳✶ ❈❛♣✐t❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✸✳✷ ❋❧✉①♦ ❞❡ ❈❛✐①❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✸✳✸ ❏✉r♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✸✳✹ ❚❛①❛ ❞❡ ❏✉r♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✸✳✺ ❘❡❣✐♠❡s ❞❡ ❈❛♣✐t❛❧✐③❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✸✳✺✳✶ ❘❡❣✐♠❡s ❞❡ ❝❛♣✐t❛❧✐③❛çã♦ ❞✐s❝r❡t❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✸✳✺✳✶✳✶ ❘❡❣✐♠❡ ❞❡ ❝❛♣✐t❛❧✐③❛çã♦ s✐♠♣❧❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✸✳✺✳✶✳✷ ❘❡❣✐♠❡ ❞❡ ❝❛♣✐t❛❧✐③❛çã♦ ❝♦♠♣♦st❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾ ✸✳✺✳✷ ❘❡❣✐♠❡s ❞❡ ❝❛♣✐t❛❧✐③❛çã♦ ❝♦♥tí♥✉❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵
✹ ❚❛①❛s ✸✶
✹✳✶ ❚❛①❛s Pr♦♣♦r❝✐♦♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✹✳✷ ❚❛①❛s ❊q✉✐✈❛❧❡♥t❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ✹✳✷✳✶ ❚❛①❛s ❊q✉✐✈❛❧❡♥t❡s ❡♠ r❡❣✐♠❡ ❞❡ ❈❛♣✐t❛❧✐③❛çã♦ ❙✐♠♣❧❡s ✳ ✳ ✳ ✳ ✳ ✸✷ ✹✳✷✳✷ ❚❛①❛s ❡q✉✐✈❛❧❡♥t❡s ❡♠ r❡❣✐♠❡ ❞❡ ❝❛♣✐t❛❧✐③❛çã♦ ❝♦♠♣♦st❛ ✳ ✳ ✳ ✳ ✸✸ ✹✳✸ ❚❛①❛ ❊❢❡t✐✈❛ ❡ ❚❛①❛ ◆♦♠✐♥❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ✹✳✹ ❚❛①❛ ❖✈❡r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ✹✳✺ ❚❛①❛ ❘❡❛❧ ❡ ❚❛①❛ ❆♣❛r❡♥t❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺
✺ ■♠♣♦st♦s ✸✼
✻ ❋✐♥❛♥❝✐❛♠❡♥t♦s ✸✽ ✻✳✶ ❈✉st♦ ❊❢❡t✐✈♦ ❚♦t❛❧ ✭❈❊❚✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✻✳✷ ❈❤❡q✉❡ ❊s♣❡❝✐❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ✻✳✷✳✶ ▼❡t♦❞♦❧♦❣✐❛ ❞❡ ❝á❧❝✉❧♦ ❛tr❛✈és ❞❡ ✉♠ ❡①❡♠♣❧♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ✻✳✸ ❆♥t❡❝✐♣❛çã♦ ❉é❝✐♠♦ ❚❡r❝❡✐r♦ ❙❛❧ár✐♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹ ✻✳✹ ❈ré❞✐t♦ ❉✐r❡t♦ ❛♦ ❈♦♥s✉♠✐❞♦r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺ ✻✳✹✳✶ ❱❛❧♦r ❞❛ P❛r❝❡❧❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺ ✻✳✹✳✷ ❈á❧❝✉❧♦ ❞♦ ■❖❋ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽
✼ ❆♣❧✐❝❛çõ❡s ✹✾
✼✳✶ ❈❡rt✐✜❝❛❞♦ ❞❡ ❉❡♣ós✐t♦ ❇❛♥❝ár✐♦ ❡ ❘❡❝✐❜♦ ❞❡ ❉❡♣ós✐t♦ ❇❛♥❝ár✐♦ ✳ ✳ ✳ ✳ ✺✵ ✼✳✶✳✶ ❈❉❇ ❡ ❘❉❇ ❝♦♠ t❛①❛s ♣r❡✜①❛❞❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶ ✼✳✶✳✷ ❈❉❇ ❡ ❘❉❇ ❝♦♠ t❛①❛s ♣ós✲✜①❛❞❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ✼✳✶✳✸ ❈♦♥❢r♦♥t♦ ❚❛①❛ ♣r❡✜①❛❞❛ ❡ ♣ós✲✜①❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹ ✼✳✷ ❈❛❞❡r♥❡t❛ ❞❡ P♦✉♣❛♥ç❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹
✽ ❈♦♥s✐❞❡r❛çõ❡s ❋✐♥❛✐s ✺✼
✶ ■♥tr♦❞✉çã♦
✶✳✶ P♦r q✉❡ ❞❡✈❡♠♦s ✐♥❝❧✉✐r ❛ ❊❞✉❝❛çã♦ ❋✐♥❛♥❝❡✐r❛ ♥❛s ❡s❝♦❧❛s❄
❖ ❇r❛s✐❧ t❡♠ ✈✐✈✐❞♦ ❣r❛♥❞❡s tr❛♥s❢♦r♠❛çõ❡s s♦❝✐❛✐s ❡ ❡❝♦♥ô♠✐❝❛s ♥❛s ú❧t✐♠❛s ❞é❝❛✲ ❞❛s✱ ❡s♣❡❝✐❛❧♠❡♥t❡ ♥♦ q✉❡ ❞✐③ r❡s♣❡✐t♦ ❛ ♠♦❡❞❛✳ ❉❡ ✶✾✻✾ ❛ ✶✾✾✹ ♦ ♥♦ss♦ ♣❛ís tr♦❝♦✉ ❞❡ ♠♦❡❞❛ s❡t❡ ✈❡③❡s✳ ❖ ❈r✉③❡✐r♦ ♥♦✈♦ ❝✐r❝✉❧♦✉ ❞❡ ✶✾✻✼ ❛ ✶✾✼✵✳ ❊♠ s❡❣✉✐t❡ ❛ ♠♦❡❞❛ ✈♦❧t❛ ❛ s❡ ❝❤❛♠❛r ❈r✉③❡✐r♦✱ q✉❡ ❝✐r❝✉❧♦✉ ❞❡ ✶✾✼✵ ❛té ✶✾✽✻ s❡♥❞♦ s✉❜st✐t✉í❞♦ ♣❡❧♦ ❈r✉③❛❞♦ ❡♠ ✶✾✽✻✱ ❡♠ s❡❣✉✐❞❛ tr♦❝❛❞♦ ♣❡❧♦ ❈r✉③❛❞♦ ◆♦✈♦ ❡♠ ✶✾✽✾✳ ❖ ❈r✉③❡✐r♦ ❢♦✐ r❡ss✉❝✐t❛❞♦ ❡♠ ✶✾✾✵ ❡ ❞✉r♦✉ ❛té ✶✾✾✸✱ q✉❛♥❞♦ s✉r❣❡ ♦ ❈r✉③❡✐r♦ ❘❡❛❧✳ q✉❡ ♥ã♦ s♦❜r❡✈✐✈❡✉ ♠✉✐t♦ t❡♠♣♦✳ ❊♠ ✶✾✾✹✱ ❝♦♠ ❛ ❝r✐❛çã♦ ❞♦ P❧❛♥♦ ❘❡❛❧✱ ❛❞♦t❛♠♦s ✉♠❛ ♥♦✈❛ ♠♦❡❞❛✱ ♦ ❘❡❛❧✱ q✉❡ ❝✐r❝✉❧❛ ❛t✉❛❧♠❡♥t❡ ♥♦ ♣❛ís✳
❈♦♠ ♦ P❧❛♥♦ ❘❡❛❧ ✈❡✐♦ ❛ ❡st❛❜✐❧✐③❛çã♦ ♠♦♥❡tár✐❛✱ ❛ ♠✉❞❛♥ç❛ ❞❡ ❝♦♠♦ ❛s ♣❡ss♦❛s s❡ r❡❧❛❝✐♦♥❛♠ ❝♦♠ ♦ ❞✐♥❤❡✐r♦✱ ❛❧é♠ ❞❡ ♥♦✈♦s ❤á❜✐t♦s ❞❡ ❝♦♥s✉♠♦✳ ❆ ❡❝♦♥♦♠✐❛ ❡stá✲ ✈❡❧ ♣r♦♠♦✈❡✉ ♦ ❛✉♠❡♥t♦ ❞❛ ♣❛r❝❡❧❛ ❞❛ ♣♦♣✉❧❛çã♦ ❜r❛s✐❧❡✐r❛ ❝♦♠ ❝♦♥t❛ ❜❛♥❝❛r✐❛✱ q✉❡ ♣❛ss♦✉ ❞❡ ✶✵✪ ❡♠ ✶✾✻✾ ♣❛r❛ ✻✵✪ ❡♠ ✷✵✶✶✱ s❡❣✉♥❞♦ ♦ ■P❊❆ ✲ ■♥st✐t✉t♦ ❞❡ P❡sq✉✐s❛ ❊❝♦ô♠✐❝❛ ❆♣❧✐❝❛❞❛ ✳ ❚❛❧ ❢❛t♦✱ ♣r♦♠♦✈❡✉ ❣r❛♥❞❡s tr❛♥s❢♦r♠❛çõ❡s ♥♦ s✐st❡♠❛ ✜♥❛♥❝❡✐r♦ ❡ ❜❛♥❝ár✐♦ ❜r❛s✐❧❡✐r♦✳ ❈r✐❛r❛♠✲s❡ ♥♦✈❛s ♠♦❞❛❧✐❞❛❞❡s ❞❡ ❝ré❞✐t♦✱ ❞❡ ✐♥✈❡st✐♠❡♥t♦ ❡ ❞❡ tr❛♥s❛çõ❡s ✜♥❛❝❡✐r❛s✳ ❈♦♠♦ ❡ ♦♥❞❡ ✐♥✈❡st✐r❄ ❈♦♠♦ ❡ ♦♥❞❡ t♦♠❛r ❞✐♥❤❡✐r♦ ❡♠♣r❡st❛❞♦❄ ❊ss❛s sã♦ ❞❡❝✐sõ❡s q✉❡ ❞❡♠❛♥❞❛♠ ❝♦♥❤❡❝✐♠❡♥t♦✳
❍♦✉✈❡ ✉♠ ❛✉♠❡♥t♦ ♣❡❧❛ ♣r♦❝✉r❛ ❞❡ ❜❡♥s ❞❡ ❝♦♥s✉♠♦✱ q✉❡ ✉❧tr❛♣❛ss❛♠ ❛s ♥❡❝❡s✲ s✐❞❛❞❡s ✐♥❞✐✈✐❞✉❛✐s ❞❡ s✉❜s✐stê♥❝✐❛✳ ❖ ❝✐❝❧♦ ❞❡ ✈✐❞❛ ❞♦s ♣r♦❞✉t♦s é ❝❛❞❛ ✈❡③ ♠❡♥♦r ❡ ❛ ♣r❡ssã♦ ♣❡❧♦ ❝♦♥s✉♠♦ é ❝❛❞❛ ✈❡③ ♠❛✐♦r✳ ❆ss✐♠✱ ❛ ❞❡❝✐sã♦ ❞❡ ❝♦♥s✉♠✐r ❛❣♦r❛ ♦✉ ♣♦st❡r❣❛r ✉♠❛ ❝♦♠♣r❛ é ✉♠❛ ❞❡❝✐sã♦ q✉❡ ♥ã♦ ❞❡✈❡ s❡r ❢❡✐t❛ ♣♦r ✐♠♣✉❧s♦✳ ❱✐✈❡r ♦ ❛❣♦r❛ ♣❡♥s❛♥❞♦ t❛♠❜é♠ ♥♦ ❢✉t✉r♦ ♥ã♦ é tã♦ ❞✐❢í❝✐❧ q✉❛♥t♦ ♣❛r❡❝❡✳ ❖ s❡❣r❡❞♦ é r❡✢❡t✐r ❡ t♦✲ ♠❛r ❞❡❝✐sõ❡s ❝♦♥s❝✐❡♥t❡s ❛ ❝❛❞❛ ❝♦♠♣r❛✱ ❡✈✐t❛♥❞♦ ❝♦♥s✉♠✐r ♣♦r ✐♠♣✉❧s♦✳ ■ss♦ ❞❡♠❛♥❞❛ ❝♦♥❤❡❝✐♠❡♥t♦✳
❉✐❛r✐❛♠❡♥t❡ ♦✉✈✐♠♦s r❡❧❛t♦s ♥♦s ♠❡✐♦s ❞❡ ❝♦♠✉♥✐❝❛çã♦ s♦❜r❡ ♦ ❞❡✜❝✐t ❞♦ s✐st❡♠❛ ♣r❡✈✐❞❡♥❝✐ár✐♦ ♦✜❝✐❛❧✳ ❙❡ ❤♦❥❡ ♦ ❜❡♥❡❢í❝✐♦ q✉❡ ✉♠❛ ♣❡ss♦❛ ♣♦❞❡ ❡s♣❡r❛r ❞❡ ✉♠❛ ❛♣♦✲ s❡♥t❛❞♦r✐❛ ❣♦✈❡r♥❛♠❡♥t❛❧ é ♣❡q✉❡♥♦✱ ♥✉♠ ❢✉t✉r♦ ♣ró①✐♠♦ é ❞❡ s❡ ❡s♣❡r❛r q✉❡ ❡ss❡s ❜❡♥❡❢í❝✐♦s s❡❥❛♠ ❞✐r❡❝✐♦♥❛❞♦s ❛♦s ♠❛✐s ♥❡❝❡ss✐t❛❞♦s✳ ■ss♦ s✐❣♥✐✜❝❛ q✉❡ ♦s ✐♥❞✐✈í❞✉♦s
t❡♥❤❛♠ q✉❡ s❡ ♣r❡♣❛r❛r✱ ♣♦✉♣❛♥❞♦ ❛♦ ❧♦♥❣♦ ❞❛ ✈✐❞❛✳ ❈♦♠♦ ♣♦✉♣❛r❄ ❖♥❞❡ ✐♥✈❡st✐r❄ ❊ss❛s sã♦ ❞❡❝✐sõ❡s q✉❡ ❞❡♠❛♥❞❛♠ ❝♦♥❤❡❝✐♠❡♥t♦✳ ❋✐❝❛ ❡♥tã♦ ❛ ♣❡r❣✉♥t❛✱ q✉❡♠ ❞❡✈❡ ♣r♦✈❡r ❡ss❡ t✐♣♦ ❞❡ ❝♦♥❤❡❝✐♠❡♥t♦❄
❖ ♣r✐♥❝✐♣❛❧ ♣❛tr♦❝✐♥❛❞♦r ❡ ❛rt✐❝✉❧❛❞♦r ❞❡✈❡ s❡r ♦ ●♦✈❡r♥♦✳ ■♥✐❝✐❛❧♠❡♥t❡ ❛tr❛✈és ❞❛ ❊s❝♦❧❛✱ q✉❡ ❞❡✈❡ tr❛t❛r ♦ ❛ss✉♥t♦ ❝♦♠♦ ✉♠ t❡♠❛ tr❛♥s✈❡rs❛❧ q✉❡ ❛❜r❛♥❣❡ t♦❞❛s ❛s ❞✐s❝✐♣❧✐♥❛s ❞❛ ❊❞✉❝❛çã♦ ❇ás✐❝❛ ❡ ♣♦st❡r✐♦r♠❡♥t❡✱ ❛tr❛✈és ❞❡ s❡✉s ♦r❣ã♦s r❡❣✉❧❛❞♦r❡s ❞♦ s✐t❡♠❛ ✜♥❛♥❝❡✐r♦✱ ♦✉ s❡❥❛✱ ♦ ❇❛♥❝♦ ❈❡♥tr❛❧ ❡ ❛ ❈♦♠✐ssã♦ ❞❡ ❱❛❧♦r❡s ▼♦❜✐❧✐ár✐♦s✳ P♦r ♦✉tr♦ ❧❛❞♦ t❡♠♦s ❛s ✐♥st✐t✉✐çõ❡s ✜♥❛♥❝❡✐r❛s✱ ♣♦✐s ❝❧✐❡♥t❡s ❝♦♥❝✐❡♥t❡s t❡rã♦ r❡❧❛❝✐♦✲ ♥❛♠❡♥t♦s ❞✉r❛❞♦✉r♦s✱ ❛✜♥❛❧ ❞❡ ❝♦♥t❛s✱ ♦s ✐♥❛❞✐♠♣❧❡♥t❡s ♥ã♦ tr❛③❡♠ ❧✉❝r♦ ♣❛r❛ ❡ss❛s ❡♠♣r❡s❛s✳ ❚❡♠♦s ❛✐♥❞❛ ❛s ❡♥t✐❞❛❞❡s r❡♣r❡s❡♥t❛t✐✈❛s ❞❛ s♦❝✐❡❞❛❞❡✱ ❝♦♠♦ ♦s ♦r❣ã♦s ❞❡ ❝❧❛ss❡ ❡ ♦s s✐♥❞✐❝❛t♦s✳
❚❡r ❛s ✜♥❛♥ç❛s s♦❜ ❝♦♥tr♦❧❡ ❞❡✈❡ s❡r ✉♠ ❞♦s ♦❜❥❡t✐✈♦s ❢✉♥❞❛♠❡♥t❛✐s ❞❛s ♣❡ss♦❛s ❡ ❞❛s ❢❛♠í❧✐❛s✳ ❆ ❡❞✉❝❛çã♦ ✜♥❛♥❝❡✐r❛✱ ❡♥t❡♥❞✐❞❛ ❝♦♠♦ ✉♠ t❡♠❛ tr❛♥s✈❡rs❛❧ q✉❡ ❞✐❛❧♦❣❛ ❝♦♠ ❛s ❞✐✈❡rs❛s ❞✐s❝✐♣❧✐♥❛s ❞♦ ❝✉rrí❝✉❧♦ ❞♦ ❊♥s✐♥♦ ▼é❞✐♦ ❡ ❋✉♥❞❛♠❡♥t❛❧✱ ♣r♦♣✐❝✐❛ ❛♦ ❡st✉❞❛♥t❡ ❝♦♠♣r❡❡♥❞❡r ❝♦♠♦ ❝♦♥❝r❡t✐③❛r s❡✉s s♦♥❤♦s✱ s✉❛s ❛s♣✐r❛çõ❡s ❡ ❝♦♠♦ s❡ ♣r❡✲ ♣❛r❛r ♣❛r❛ ❛s ❞✐✈❡rs❛s ❢❛s❡s ❞❛ ✈✐❞❛✳
❊st❡ tr❛❜❛❧❤♦ é ❢r✉t♦ ❞❛ ❡①♣❡r✐ê♥❝✐❛✿
✲ ❉❡ ♠❛✐s ❞❡ ✶✺ ❛♥♦s ❡♠ ✉♠❛ ✐♥st✐t✉✐çã♦ ✜♥❛♥❝❡✐r❛ ❡st❛t❛❧✱ ♠✉✐t♦ ❞♦s q✉❛✐s ♥❛ r❡❞❡ ❞❡ ❛❣ê♥❝✐❛s✱ ♦♥❞❡ t✐✈❡ ❛ ♦♣♦rt✉♥✐❞❛❞❡ ❞❡ ❝♦♥❤❡❝❡r ♦s ❤á❜✐t♦s ✜♥❛♥❝❡✐r♦s ❞♦s ❝❧✐❡♥t❡s❀
✲ ❞❛ ✈✐✈ê♥❝✐❛ ❞♦s ♣❧❛♥♦s ❡❝♦♥ô♠✐❝♦s✿ ❈r✉③❛❞♦✭✶✾✽✻✮✱ ❇r❡ss❡r ✭✶✾✽✼✮✱ ❱❡rã♦ ✭✶✾✽✾✮ ❈♦❧❧♦r ■ ✭✶✾✾✵✮✱ ❈♦❧❧♦r ■■ ✭✶✾✾✶✮ ❡ r❡❛❧ ✭✶✾✾✹✮✳
✲ ❉❛ ❡①♣❡r✐ê♥❝✐❛ ❞♦❝❡♥t❡ ♥❛ ❊❞✉❝❛çã♦ ❇ás✐❝❛ ❞❛ r❡❞❡ ♣ú❜❧✐❝❛ ❡ ♣r✐✈❛❞❛ ❞♦ ❉✐str✐t♦ ❋❡❞❡r❛❧ ♦♥❞❡ ♣✉❞❡ ♦❜s❡r✈❛r ❝♦♠♦ ♦s ❛❞♦❧❡s❝❡♥t❡s s❡ r❡❧❛❝✐♦♥❛♠ ❝♦♠ ♦ ❞✐♥❤❡✐r♦ ❡ ❝♦♠♦ sã♦ s✉❛s ❡①♣❡❝t❛t✐✈❛s ❞❡ ❝♦♥s✉♠♦ ❡ s❡✉s ♣❛❧♥♦s ❞❡ ❢✉t✉r♦✳
✶✳✷ ❖❜❥❡t✐✈♦
❊st❡ tr❛❜❛❧❤♦ t❡♠ ♣♦r ♦❜❥❡t✐✈♦ ♣r♦♠♦✈❡r ✉♠❛ r❡✢❡①ã♦ ❛❝❡r❝❛ ❞❛s ♣♦t❡♥❝✐❛✐s ✐♥t❡r✲ ❢❛❝❡s ❞✐❞át✐❝❛s ❡♥tr❡ ❛ ❡❞✉❝❛çã♦ ✜♥❛♥❝❡✐r❛ ❡ ♦s ❝♦♥t❡ú❞♦s ❞❡ ♠❛t❡♠át✐❝❛ ❛❜♦r❞❛❞♦s ♥♦ ❡♥s✐♥♦ ♠é❞✐♦ ❛tr❛✈és ❞❡ ✉♠ ❝✉rs♦ ❡♠ ♣❛r❛❧❡❧♦ ❛♦ ❞❡ ▼❛t❡♠át✐❝❛✳ ❖s ❝♦♥❤❡❝✐♠❡♥t♦s ♣ré✈✐♦s ♥❡❝❡ssár✐♦s sã♦✿ ♣♦t❡♥❝✐❛çã♦❀ r❛❞✐❝❛çã♦❀ sér✐❡s❀ ♣r♦❣r❡ssã♦ ❛r✐t♠ét✐❝❛ ❡ ♣r♦❣r❡s✲ sã♦ ❣❡♦♠étr✐❝❛✳ ❉❡ss❛ ♠❛♥❡✐r❛✱ r❡❝♦♠❡♥❞❛✲s❡ ✐♥✐❝✐❛r ❛ ♣❛rt✐r ❞♦ s❡❣✉♥❞♦ s❡♠❡str❡ ❞♦ ♣r✐♠❡✐r♦ ❛♥♦ ❞♦ ❊♥s✐♥♦ ▼é❞✐♦✳
❆ s✉❣❡stã♦✱ é q✉❡ ♦ ❝✉rs♦ s❡❥❛ ✐♥❝❧✉í❞♦ ♥❛ ❣r❛❞❡ ❝✉rr✐❝✉❧❛r ❡ q✉❡ ❛s ❛✉❧❛s s❡❥❛♠ ♠✐♥✐str❛❞❛s ♣♦r ❞✐✈❡rs♦s ♣r♦❢❡ss♦r❡s✳ ❆ss✐♠ ❛ ♣❛rt❡ ❤✐stót✐❝❛ ❞♦ ❉✐♥❤❡✐r♦ é ♠✐♥✐str❛❞❛ ♣❡❧♦ ♣r♦❢❡ss♦r ❞❡ ❍✐stór✐❛✳ ❖s ❛s♣❡❝t♦s s♦❝✐❛s ✜❝❛♠ ❛ ❝❛r❣♦ ❞♦ ♣r♦❢❡ss♦r ❞❡ s♦❝✐♦❧♦❣✐❛✱ ❛s ❝♦♥s❡q✉ê♥❝✐❛s ❡❝♦♥ô♠✐❝❛s ❞♦s ❞✐✈❡rs♦s ♣❧❛♥♦s ✜❝❛♠ ❝♦♠ ♦ ♣r♦❢❡ss♦r ❞❡ ❣❡♦❣r❛✜❛ ❡ ❛ss✐♠ ♣♦r ❞✐❛♥t❡✳ Pr♦❝❡❞❡♥❞♦ ❞❡ss❛ ❢♦r♠❛✱ é ♣♦ssí✈❡❧ ❡str✉t✉r❛r t❡♠♣♦r❛❧♠❡♥t❡ ♦ ❝✉rs♦ ❡ ❞❛r✲❧❤❡ ✉♠❛ ❧✐♥❤❛ ❞❡ ❝♦♥t✐♥✉✐❞❛❞❡✱ ❝♦♠♦ é ❢❡✐t♦ ❝♦♠ ❛s ❞❡♠❛✐s ❞✐s❝✐♣❧✐♥❛s✳
❆ s❡❣✉✐r sã♦ ❡❧❡♥❝❛❞♦s ♦s três ♠ó❞✉❧♦s ❞♦ ❝✉rs♦✱ ♦❜❥❡t♦ ❞❡ss❡ tr❛❜❛❧❤♦✱ r❡❝♦♠❡♥✲ ❞❛❞♦s ♣❛r❛ ♦ ♣r♦❢❡ss♦r ❞❡ ▼❛t❡♠át✐❝❛✳ ❖ ♣r✐♠❡✐r♦ ♠ó❞✉❧♦ s❡ r❡❢❡r❡ ❛♦ ❝♦♥❤❡❝✐♠❡♥t♦ ❞♦s ❣❛st♦s ♠❡♥s❛✐s ❡ s❡♠❛♥❛✐s✱ ❞♦ ❝♦♥tr♦❧❡ ❞♦ ❝♦♥s✉♠♦ ❞✐ár✐♦ ❡ ❞❛ ❛♥á❧✐s❡ ❞♦s r❡s✉❧✲ t❛❞♦s ♠ês ❛ ♠ês✳ ❋❡✐t♦ ✐ss♦✱ ♣❛ss❛✲s❡ ❛ ♣r✐♦r✐③❛r ❡ ❛ ❝❛t❡❣♦r✐③❛r ♦s ❣❛st♦s✱ ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛s ♥❡❝❡ss✐❞❛❞❡s ❞✐ár✐❛s✳ ❈✉❧♠✐♥❛♥❞♦ ❝♦♠ ♣r❡✈✐sã♦ ♣❛r❛ ♦s ♣ró①✐♠♦s ♠❡s❡s✳ ❊ss❛s ❛t✐✈✐❞❛❞❡s sã♦ ❢❡✐t❛s ❛tr❛✈és ❞❡ ✉♠ ♣r❡❡♥❝❤✐♠❡♥t♦ ♠❡tó❞✐❝♦ ❡ s✐st❡♠át✐❝♦ ❞❡ ♣❧❛♥✐❧❤❛s✳ ❋✐♥❛❧♠❡♥t❡✱ ❢❡❝❤❛✲s❡ ❡ss❡ ♠ó❞✉❧♦ ❝♦♠ ✉♠ ❜❛❧❛♥ç♦ ❛♥✉❛❧✱ ♥♦ q✉❛❧ ❝❛❞❛ ❛❧✉♥♦ ❡❧❛❜♦r❛ ♦s ❣rá✜❝♦s ❞❡ r❡❝❡✐t❛s ❡ ❞❡s♣❡s❛s ❛♦ ❧♦♥❣♦ ❞♦ ❛♥♦✱ ❡ ♣r❡❡♥❝❤❡ ✉♠ q✉❡st✐♦♥ár✐♦ q✉❡ t❡♠ ♣♦r ✜♥❛❧✐❞❛❞❡ ♣r♦♠♦✈❡r ❛ ❛♥á❧✐s❡ ❝rít✐❝❛ ❞♦s ❡s❢♦rç♦s ❡ r❡s✉❧t❛❞♦s ♣❡ss♦❛✐s ♦❜t✐❞♦s✳
❖ s❡❣✉♥❞♦ ♠ó❞✉❧♦✱ ❛❜♦r❞❛ ❛ ▼❛t❡♠át✐❝❛ ❡♥✈♦❧✈✐❞❛ ♥❛s ❢♦♥t❡s ♠❛✐s ❝♦♠✉♥s ❞❡ ✜♥❛♥❝✐❛♠❡♥t♦✱ t❛✐s ❝♦♠♦ ❈ré❞✐t♦ ❉✐r❡t♦ ❛♦ ❈♦♥s✉♠✐❞♦r❀ ❈❤❡q✉❡ ❊s♣❡❝✐❛❧ ❡ ❆♥t❡❝✐♣❛✲ çã♦ ❞❡ ❉é❝✐♠♦ t❡r❝❡✐r♦ ❙❛❧ár✐♦✳ ❙ã♦ ❛♥❛❧✐s❛❞♦s ♦s ✐♠♣❛❝t♦s ❞♦s ✐♠♣♦st♦s ❡ ❛s t❛①❛s ❝♦❜r❛❞❛s ♣❡❧♦s ❛❣❡♥t❡s ✜♥❛♥❝❡✐r♦s✳
❖ t❡r❝❡✐r♦ ♠ó❞✉❧♦ ❛❜♦r❞❛ ♦s ❛s♣❡❝t♦s ♠❛t❡♠át✐❝♦s r❡❧❛t✐✈♦s ❛♦s ✐♥✈❡st✐♠❡♥t♦s ♠❛✐s ❝♦♠✉♥s ❡①✐st❡♥t❡s ❛t✉❛❧♠❡♥t❡ ♥♦ ▼❡r❝❛❞♦ ❋✐♥❛♥❝❡✐r♦✱ ❛ ❝❛❞❡r♥❡t❛ ❞❡ ♣♦✉♣❛♥ç❛ ❡ ♦s ❝❡rt✐✜❝❛❞♦s ❞❡ ❞❡♣ós✐t♦ ❜❛♥❝ár✐♦s ✭❈❉❇✮✳
✷ ❖ ❈✉rs♦
✷✳✶ ❆ss✉♠✐♥❞♦ ♦ ❝♦♥trô❧❡ ❞❛s ❞❡s♣❡s❛s
❆ ♣r✐♠❡✐r❛ ♣❛rt❡ ❞♦ ❝✉rs♦ é ❞❡❞✐❝❛❞❛ ❛♦ ❝♦♥❤❡❝✐♠❡♥t♦ ❞♦s ❤á❜✐t♦s ✜♥❛♥❝❡✐r♦s ❡ ❞❡ ❝♦♠♦ ♦r❣❛♥✐③❛r ❛s ✜♥❛♥ç❛s ♣❡ss♦❛✐s ❞❡ ♠❛♥❡✐r❛ s✐st❡♠át✐❝❛✳ P❛r❛ ✐ss♦ ❧❛♥ç❛✲s❡ ♠ã♦ ❞❡ três ♣❧❛♥✐❧❤❛s q✉❡ ❛❥✉❞❛♠ ❛✿
✲ ❖r❣❛♥✐③❛r ♦s ❣❛st♦s ❞❡ ♠❛♥❡✐r❛ s✐st❡♠át✐❝❛❀
✲ ❖❜s❡r✈❛r ♦ ❝♦♥s✉♠♦ ❞✐ár✐♦❀
✲ ❆♥❛❧✐s❛r ♦s r❡s✉❧t❛❞♦s ♠ês ❛ ♠ês❀
✲ Pr✐♦r✐③❛r ❡ ❝❛t❡❣♦r✐③❛r ♦s ❣❛st♦s ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛s ♥❡❝❡ss✐❞❛❞❡s ❞✐ár✐❛s❀
✲ ❘❡✢❡t✐r s♦❜r❡ ♦s ❣❛st♦s ❞❡ ♠❛♥❡✐r❛ ♦❜❥❡t✐✈❛ ♣❛r❛ ♣♦❞❡r s✉❜st✐t✉✐r ♦s ♠❛✉s ❤á❜✐t♦s ✜♥❛♥❝❡✐r♦s
❍♦❥❡ ❡♠ ❞✐❛✱ ❝♦♥s✉♠✐r é ✉♠ ❛t♦ q✉❡ ♠✉✐t❛s ✈❡③❡s ❛t❡♥❞❡ ♠❛✐s ❛♦s ❞❡s❡❥♦s q✉❡ ❛ ✈❡r❞❛❞❡✐r❛ ♥❡❝❡ss✐❞❛❞❡✳ ❖ ❛t♦ ❞❡ ❝♦♠♣r❛r ❡①✐❣❡ ✉♠❛ r❡✢❡①ã♦ s♦❜r❡ s✉❛s ❝♦♥s❡q✉ê♥❝✐❛s q✉❡ ♣♦✉❝❛s ✈❡③❡s é ❢❡✐t❛✳ ➱ ✉♠❛ ❛çã♦ ❛✉t♦♠át✐❝❛ ❡ ♠✉✐t❛s ✈❡③❡s ✐rr❛❝✐♦♥❛❧✳ P♦r ❛❝❛s♦ s❛❜❡✲s❡ ♦♥❞❡ s❡ ♣r♦❞✉③ t✉❞♦ q✉❡ ❝❤❡❣❛ às ♥♦ss❛s ♠ã♦s❄ ◗✉❡♠ ❢❛❜r✐❝❛❄ ❊♠ q✉❡ ❝♦♥✲ ❞✐çõ❡s❄ ❈♦♠♣r❛✲s❡ ♣r♦❞✉t♦s ♦✉ ♠❛r❝❛s❄ P❡♥s❛♠♦s r❡❛❧♠❡♥t❡ s❡ ♣r❡❝✐s❛♠♦s ❞❡ t✉❞♦ q✉❡ ❝♦♠♣r❛♠♦s❄ ❆s ❝♦✐s❛s r❡❛❧♠❡♥t❡ ✈❛❧❡♠ ♦ ♣r❡ç♦ q✉❡ ❡st❛ ♥❛ ❡t✐q✉❡t❛❄ ❖ ♠✉♥❞♦ ♠❛t❡r✐❛❧ t❡♠ ❝♦✐s❛s ❜♦❛s✱ ♠❛s t❛❧✈❡③ ❡st❡❥❛♠♦s ♣❡r❞❡♥❞♦ ❛ ❝❛♣❛❝✐❞❛❞❡ ❞❡ ❞❛r ❛q✉✐❧♦ q✉❡ ♥♦s ❝❡r❝❛ ♦ ✈❛❧♦r q✉❡ ♠❡r❡❝❡✱ ❡ ❞❡ ❝♦♠♣❛rt✐❧❤❛r ❝♦♠ ♦s ♦✉tr♦s ♦ q✉❡ t❡♠♦s✳ ❚✉❞♦ t❡♠ ♦ ✈❛❧♦r q✉❡ q✉✐s❡r♠♦s ❞❛r✳
P❛r❛ ❝♦♥❤❡❝❡r♠♦s ♦s ❤á❜✐t♦s ✜♥❛♥❝❡✐r♦s✱ ♣r✐♠❡✐r♦ é ♣r❡❝✐s♦ ❝♦❧♦❝❛r t✉❞♦ às ❝❧❛r❛s✱ ❡ ♣❛r❛ ✐ss♦✱ ❧❛♥ç❛✲s❡ ♠ã♦ ❞❡ três ♣❧❛♥✐❧❤❛s✳ ◆❛ ♣r✐♠❡✐r❛ ♣❧❛♥✐❧❤❛✱ ❡st❛❜❡❧❡❝❡✲s❡ ✉♠❛ ❡st✐♠❛t✐✈❛ ♠❡♥s❛❧ ❞♦ ❞✐♥❤❡✐r♦ ❞✐s♣♦♥í✈❡❧ ✭❣❛♥❤♦s ♠❡♥♦s ❣❛st♦s ✜①♦s✮ ❡ ♦s ♦❜❥❡t✐✈♦s ❛ s❡r❡♠ ❛❧❝❛ç❛❞♦s✳ ◆❛ s❡❣✉♥❞❛✱ ❛♥♦t❛✲s❡ ♦s ❣❛st♦s ❞✐ár✐♦s ❡♠ ❝❛❞❛ s❡♠❛♥❛✱ ❞✐✈✐❞✐❞♦s ♣♦r ❝❛t❡❣♦r✐❛s✳ ◆❛ ú❧t✐♠❛✱ ❢❛③✲s❡ ♦ ❝á❧❝✉❧♦ ❞❡ t✉❞♦ ♦ q✉❡ ❢♦✐ ❣❛st♦ ♥♦ ♠ês ❡ ✉♠❛ ❛✉✲ t♦❛✈❛❧✐❛çã♦ ❡♠ r❡❧❛çã♦ ❛♦s ♦❜❥❡t✐✈♦s ❡st❛❜❡❧❡❝✐❞♦s✳
◆♦ ✜♥❛❧ ❞❡ ❞♦③❡ ♠❡s❡s✱ ♥ã♦ é ♣r❡❝✐s♦ ❝♦♠❡ç❛r ♦❜r✐❣❛t♦r✐❛♠❡♥t❡ ❡♠ ❏❛♥❡✐r♦✱ sã♦ ❢❡✐t♦s ♦s ❣rá✜❝♦s ❞♦ ❜❛❧❛♥ç♦ ❛♥✉❛❧ ❡ é r❡s♣♦♥❞✐❞♦ ✉♠ q✉❡st✐♦♥ár✐♦ ♣❛r❛ s❡ ❛✈❛❧✐❛r ❡ r❡✢❡t✐r s♦❜r❡ r❡s✉❧t❛❞♦s ❡ ❛✈❛♥ç♦s ♦❜t✐❞♦s✳
✷✳✷ ❆ss✉♠✐♥❞♦ ♦ ❝♦♥tr♦❧❡ ❞❛s ❞❡s♣❡s❛s
❆ P❧❛♥✐❧❤❛ ✶ t❡♠ ❝♦♠♦ ♦❜❥❡t✐✈♦ ❡st✐♠❛r ♦ ❞✐♥❤❡✐r♦ ❞✐s♣♦♥í✈❡❧ ♣❛r❛ ♦ ♠ês✳
❋✐❣✉r❛ ✶✿ ❖r❣❛♥✐③❛♥❞♦ ♦s r❡❝❡❜✐♠❡♥t♦s ❡ ♦s ❣❛st♦s ♠❡♥s❛✐s
❆ ❝❛❞❛ ✐♥í❝✐♦ ❞❡ ♠ês✱ ❞❡t❡r♠✐♥❛✲s❡ q✉❛✐s sã♦ ♦s r❡❝❡❜✐♠❡♥t♦s ❡ ❛s ❞❡s♣❡s❛s ✜①❛s✳ ❆ ❞✐❢❡r❡♥ç❛ ❡♥tr❡ ❛♠❜♦s ♣❡r♠✐t❡ s❛❜❡r q✉❛❧ ❛ ❞✐s♣♦♥✐❜✐❧✐❞❛❞❡ ♣❛r❛ ♦ ♠ês✳
❈♦♠♦ ♣r❡❡♥❝❤❡r ❛ ♣❧❛♥✐❧❤❛❄ ◗✉❛❞r♦ ✶ ✲ ❘❡❝❡❜✐♠❡♥t♦s ✿
◆❡st❡ q✉❛❞r♦ r❡❣✐str❛✲s❡ ❛ ❞❛t❛✱ ♦ ✈❛❧♦r ❡ tít✉❧♦ ❞♦s r❡❝❡❜✐♠❡♥t♦s ❡ ❝❛❧❝✉❧❛✲s❡ ♦ t♦t❛❧✳
❋✐❣✉r❛ ✷✿ ❘❡❝❡❜✐♠❡♥t♦s
◗✉❛❞r♦ ✷ ❉❡s♣❡s❛s ❋✐①❛s✿
❙ã♦ t♦❞♦s ❛q✉❡❧❡s ❣❛st♦s q✉❡ ♦❝♦rr❡♠ ❞❡ ♠❛♥❡✐r❛ r❡❣✉❧❛r ♠ês ❛ ♠ês✳ ❍á ♦s ✐♥✈❛r✐á✲ ✈❡✐s✱ ♣♦r ❡①❡♠♣❧♦✿ ❛❧✉❣✉❡❧✱ ✜♥❛♥❝✐❛♠❡♥t♦s✱ ♣❧❛♥♦ ❞❡ ✐♥t❡r♥❡t✱ ❛❝❛❞❡♠✐❛✳ ❍á t❛♠❜é♠ ♦s ❡st✐♠❛❞♦s✱ q✉❡ sã♦ ❛q✉❡❧❡s ❝✉❥♦ ✈❛❧♦r ✈❛r✐❛ ❝♦♠ ♦ ❝♦♥s✉♠♦✱ ♣♦r ❡①❡♠♣❧♦ ❝❡❧✉❧❛r✱ tr❛♥s♣♦rt❡✱ ❧✉③✳ ◗✉❛♥❞♦ é ❢❡✐t❛ ❛ ❡st✐♠❛t✐✈❛ ❞❡ ❝❛❞❛ ✉♠ ❞❡ss❡s ❣❛st♦s ♣♦❞❡✲s❡ ❜❛s❡❛r ♥❛s ❝♦♥t❛s ❛♥t❡r✐♦r❡s ❡ ✉t✐❧✐③❛r ♦ ✈❛❧♦r ♠é❞✐♦✳
◆❛ ♣❛rt❡ ✐♥❢❡r✐♦r✱ ❡❢❡t✉❛r ❛ ❞✐❢❡r❡♥ç❛✱ ❢❛t✉r❛♠❡♥t♦ ♠❡♥♦s ❞❡s♣❡s❛s ✜①❛s✳ ❊st❡ é ♦ ✈❛❧♦r ❞✐s♣♦♥í✈❡❧ ♣❛r❛ ♦ ♠ês✳
❈❛❞❛ ✈❡③ q✉❡ ❝♦♠❡ç❛r ✉♠ ♥♦✈♦ ♠ês✱ ❡st❛❜❡❧❡❝❡✲s❡ ✉♠ ♦✉ ♠❛✐s ♦❜❥❡t✐✈♦s ❛ s❡r❡♠ ❛❧❝❛♥ç❛❞♦s✱ s❡❥❛ ❛ ❝✉rt♦ ♦✉ ❧♦♥❣♦ ♣r❛③♦✱ ♣♦r ❡①❡♠♣❧♦✿ ❡❝♦♥♦♠✐③❛r ❝❡rt♦ ✈❛❧♦r ♠❡♥s❛❧✲ ♠❡♥t❡ ♣❛r❛ ❢❛③❡r ✉♠❛ ✈✐❛❣❡♠ ♥❛s ❢ér✐❛s✳ P❡♥s❡ t❛♠❜é♠ ❡♠ ♣❡q✉❡♥♦s ❣❡st♦s ❞✐ár✐♦s q✉❡ ♣♦❞❡♠ ❛❥✉❞❛r ❛ ❝♦rr✐❣✐r ♦s ❡①❝❡ss♦s ❡ ♦s ♠❛✉s ❤á❜✐t♦s ❞❡ ❝♦♥s✉♠♦✳ ❆♥♦t❡✲s❡ ❛s ♣r♦♠❡ss❛s q✉❡ s❡ ❞❡s❡❥❛r✳ ❊st❛❜❡❧❡❝❡r ✉♠ ✈❛❧♦r ❡st✐♠❛❞♦ ❞❡ ❡❝♦♥♦♠✐❛ ❡♠ ❢✉♥çã♦ ❞♦s ♦❜❥❡t✐✈♦s✳ ✭❋✐❣✉r❛ ✻✮
❋✐❣✉r❛ ✸✿ ❉❡s♣❡s❛s ❋✐①❛s
❋✐❣✉r❛ ✹✿ ❉❡s♣❡s❛s ❋✐①❛s
✷✳✸ P❧❛♥✐❧❤❛ ✷ ✲ P♦♥❞♦ ❡♠ ❞✐❛ ♦s ❣❛st♦s s❡♠❛♥❛✐s
❖ ❞❡s♠❡♠❜r❛♠❡♥t♦ ❞♦s ❣❛st♦s s❡♠❛♥❛✐s é ❛ ♣❛rt❡ q✉❡ r❡q✉❡r ♠❛✐♦r ❝♦♥stâ♥❝✐❛✳ ➱ ♦♥❞❡ ✜❝❛♠ r❡❣✐str❛❞❛s ❛s ❝♦♠♣r❛s ❞✐ár✐❛s✳ ❘❡s❡r✈❛✲s❡ ✉♠ ♣❡rí♦❞♦ ❞♦ ❞✐❛ ♣❛r❛ r❡❣✐str❛r ❛s ❡ss❛s ❞❡s♣❡s❛s✳ ◆ã♦ ❞❡✐①❛r ♣❛ss❛r ♠❛✐s q✉❡ ✉♠ ❞✐❛ ♣❛r❛ ❡❢❡t✉❛r ♦ r❡❣✐str♦✳
❆ t❛❜❡❧❛ ❞❛ ✜❣✉r❛ ✼ ♣❡r♠✐t❡ ♦ ❝á❧❝✉❧♦ ❞♦ ❣❛st♦ s❡♠❛♥❛❧ ♣♦r ❝❛t❡❣♦r✐❛✱ t♦r♥❛♥❞♦ ♣♦ssí✈❡❧ ✈✐s✉❛❧✐③❛r ♦♥❞❡ é ❣❛st♦ ♦ ❞✐♥❤❡✐r♦ ❡ q✉❛❧ ♦ ✐♠♣❛❝t♦ ❞❡ ❝❛❞❛ ❝♦♥t❛ ♥♦s ❣❛st♦s ♠❡♥s❛✐s ❡ s❡♠❛♥❛✐s✳
✷✳✹ P❧❛♥✐❧❤❛ ✸ ✲ ❋✐♠ ❞♦ ▼ês
◆♦ ✜♥❛❧ ❞♦ ♠ês✱ ♦ t♦t❛❧ ❞❡ ❝❛❞❛ s❡♠❛♥❛ é tr❛♥s❝r✐t♦ ♥❛ P❧❛♥✐❧❤❛ ✸✱ ❛♣✉r❛♥❞♦✲s❡ ❡♠ s❡❣✉✐❞❛✱ ♦ t♦t❛❧ ♠❡♥s❛❧✳ ❆♦ ✜♥❛❧ ❞❡ ❝❛❞❛ ♠ês✱ ❞❡✈❡✲s❡ ❢❛③❡r ✉♠❛ r❡✈✐sã♦ ❞♦s ♦❜❥❡t✐✈♦s
❋✐❣✉r❛ ✺✿ ❉❡✜♥❛ s❡✉s ♦❜❥❡t✐✈♦s ♠❡♥s❛✐s
❋✐❣✉r❛ ✻✿ ◗✉❛♥t♦ q✉❡r ❡❝♦♥♦♠✐③❛r❄
❡ ♣r♦♠❡ss❛s✳ ❘❡✢❡t✐r s♦❜r❡ ♦s ♦❜❥❡t✐✈♦s ❡ ♣r♦♠❡ss❛s ❞❛rá ❝♦♥✜❛♥ç❛ ♣❛r❛ ❝♦♠❡ç❛r ♦ ♠ês s❡❣✉✐♥t❡✳
❋✐♥❛❧♠❡♥t❡✱ ❢❛③✲s❡ ✉♠❛ ❝♦♠♣❛r❛çã♦ ❡♥tr❡ ❛ ♣r❡✈✐sã♦ ✐♥✐❝✐❛❧ ❞❡ ❡❝♦♥♦♠✐❛ ❡ ♦ r❡s✉❧✲ t❛❞♦ ♦❜t✐❞♦ ♥♦ ♠ês ✭✜❣✉r❛ ✽✮✳
✷✳✺ ◗✉❡st✐♦♥ár✐♦ ❋✐♥❛❧
◆♦ ✜♠ ❞❡ ❞♦③❡ ♠❡s❡s✱ é ✐♠♣♦rtâ♥t❡ ❢❛③❡r ✉♠❛ ❛✈❛❧✐❛çã♦ ❞❡ t♦❞♦ ♦ ♣r♦❝❡ss♦✳ ❆ ❢❡r✲ r❛♠❡♥t❛ ✉t✐❧✐③❛❞❛ é ✉♠ q✉❡st✐♦♥ár✐♦ q✉❡ ❛❧é♠ ❞❡ ❛✈❛❧✐❛r✱ t❡♠ ❛ ✐♥t❡♥çã♦ ❞❡ ♣r♦✈♦❝❛r
❋✐❣✉r❛ ✼✿ ●❛st♦s s❡♠❛♥❛✐s
✉♠❛ r❡✢❡①ã♦ ❛❝❡r❝❛ ❞❛s ♠✉❞❛♥ç❛s ♥♦s ❤á❜✐t♦s ❞❡ ❝♦♥s✉♠♦✳
◗✉❡st✐♦♥ár✐♦ ✲ ❈♦♠♦ ❢♦r❛♠ ❡ss❡s ú❧t✐♠♦s ❞♦③❡ ♠❡s❡s❄
✶✳ ❉♦ q✉❡ ♠❛✐s s❡♥t✐ ❢❛❧t❛ ❞✉r❛♥t❡ ❡ss❡s ✶✷ ♠❡s❡s❄
✷✳ ◗✉❛✐s ❤á❜✐t♦s ❞❡ ❝♦♥s✉♠♦ ❢♦r❛♠ ❛❜❛♥❞♦♥❛❞♦s❄
✸✳ ◗✉❛✐s ❤á❜✐t♦s ❞❡ ❝♦♥s✉♠♦ ✐♥❝♦r♣♦r❡✐ à ♠✐♥❤❛ ✈✐❞❛ ❞✐ár✐❛❄
✹✳ ◗✉❛❧ ❢♦✐ ♦ ♠ês ♠❛✐s ❞✐❢í❝✐❧❄
P♦r q✉ê❄
✲ ❚✐✈❡ ♠✉✐t♦s ❣❛st♦s ✐♥❡s♣❡r❛❞♦s❀
❋✐❣✉r❛ ✽✿ ❋✐♠ ❞♦ ♠ês
✲ ❊①❛❣❡r❡✐ ❡♠ ❧❛③❡r❀
✲ ❉❡s❝✉✐❞❡✐✲♠❡ ❝♦♠ ♠❡✉s ❣❛st♦s ❞✐ár✐♦s❀ ✲ ❋✉✐ ❞❡s♣❡❞✐❞♦❀
✲ ❘❡❝❡❜✐ ❝♦♠ ♠✉✐t♦ ❛tr❛s♦❀ ✲ ❖✉tr♦s✳
✺✳ ◗✉❛❧ ♠ês ❢♦✐ ♠❛✐s ❢á❝✐❧❄ P♦r q✉ê❄
✲ ❈♦♥s❡❣✉✐ ❝❤❡❣❛r ❛ ♠✐♥❤❛ ♣r❡✈✐sã♦ ❞❡ ❡❝♦♥♦♠✐❛❀ ✲ ❈✉♠♣r✐ t♦❞❛s ❛s ♠✐♥❤❛s ♣♦r♠❡ss❛s❀
✲ ❆t✐♥❣✐ ♠❡✉s ♦❜❥❡t✐✈♦s❀
✲ ◆♦t❡✐ ✉♠❛ ♠❡❧❤♦r❛ ♥❛ ♠✐♥❤❛ ❡❝♦♥♦♠✐❛❀
✲ ●❛♥❤❡✐ ✉♠ ❞✐♥❤❡✐r♦ ❡①tr❛❀ ✲ ❖✉tr♦s✳
✻✳ ❈✉♠♣r✐ ❛ ♠❛✐♦r✐❛ ❞❡ ♠✐♥❤❛s ♣r♦♠❡ss❛s❄
✲ ❙✐♠ ✲ ◆ã♦
✲ P♦❞❡r✐❛ t❡r ❢❡✐t♦ ♠❡❧❤♦r
✼✳ ◗✉❡ ♣r♦♠❡ss❛s ❢♦r❛♠ ❛s ♠❛✐s ❞✐❢í❝❡✐s ❞❡ ❝✉♠♣r✐r❄
P♦r q✉ê❄
✲ ▼✐♥❤❛ r♦t✐♥❛ ❞✐ár✐❛ ❞✐✜❝✉❧t♦✉❀
✲ ▼❡✉s ❤♦rár✐♦s ❞❡ tr❛❜❛❧❤♦ ♥ã♦ ♠❡ ♣❡r♠✐t✐r❛♠❀ ✲ ❋❛❧t♦✉✲♠❡ ❞✐s❝✐♣❧✐♥❛❀
✲ ❖✉tr♦s✳
✽✳ ❊ ♠❡✉s ♦❜❥❡t✐✈♦s❄ ◗✉❛✐s ✜❝❛r❛♠ ♣❡♥❞❡♥t❡s❄
P♦r q✉ê❄
✲ Pr❡❝✐s❡✐ ❞❡ ♠❛✐s t❡♠♣♦ ♣❛r❛ ❛t✐♥❣í✲❧♦s❀
✲ ◆ã♦ ♣✉❞❡ ❡❝♦♥♦♠✐③❛r ❞✐♥❤❡✐r♦ s✉✜❝✐❡♥t❡ ♣❛r❛ ❛t✐♥❣í✲❧♦s❀ ✲ ❊r❛♠ ♣♦✉❝♦ r❡❛❧✐st❛s❀
✲ ❋✉✐ ♣♦✉❝♦ ❞✐s❝✐♣❧✐♥❛❞♦✱ ❛ ♠❡❞✐❞❛ q✉❡ ♦s ✐❛ ❞❡✐①❛♥❞♦ ♣❡❧♦ ❝❛♠✐♥❤♦✱ ♣✉❧❛✈❛ ♣❛r❛ ♦ s❡❣✉✐♥t❡ ❝♦♠ ♦ ♠❡s♠♦ r❡s✉❧t❛❞♦❀
✲ ❖✉tr♦s✳
✾✳ ◆♦t❡✐ ❛❧❣✉♠❛ ♠✉❞❛♥ç❛ s✉❜stâ♥❝✐❛❧ ♥♦s ❣❛st♦s ❡♠ ❛❧❣✉♠❛ ❞❛s ❝❛t❡❣♦r✐❛s ❞✉r❛♥t❡ ❡ss❡s t❡♠♣♦❄
✲ ❙♦❜r❡✈✐❝ê♥❝✐❛❀ ✲ ▲❛③❡r❀
✲ ❈✉❧t✉r❛❀
✲ ❊①tr❛s✳
✶✵✳ ❊♠ q✉❛❧ ❡✉ ❣❛st❛✈❛ ♠❛✐s ❛♥t❡s ❞❡ ❝♦♠❡ç❛r❄ ❊ ❛❣♦r❛❄
• ◆♦ ✐♥í❝✐♦
✲ ❙♦❜r❡✈✐✈ê♥❝✐❛❀ ✲ ▲❛③❡r❀
✲ ❈✉❧t✉r❛❀ ✲ ❊①tr❛s✳
• ◆♦ ✜♥❛❧
✲ ❙♦❜r❡✈✐✈ê♥❝✐❛❀ ✲ ▲❛③❡r❀
✲ ❈✉❧t✉r❛❀ ✲ ❊①tr❛s✳
• ❖ q✉❡ ♠❡ ❢❡③ ♠❛✐s ❢❡❧✐③ ♥❡ss❡s ú❧t✐♠♦s ✶✷ ♠❡s❡s❄
• ❆ r❡s♣❡✐t♦ ❞♦ ❞✐♥❤❡✐r♦ ❡ ❞♦ ❝♦♥s✉♠♦✱ ❛♣r❡♥❞✐✿
✲ ❉✐✈✐❞í✲❧♦ ❝♦♠ ♦s ♦✉tr♦s❀
✲ ◗✉❡ ♦ ❞✐♥❤❡✐r♦ é ✉♠ ♠❡✐♦✱ ♥ã♦ ✉♠ ✜♠❀
✲ ❆ s❡r ❝♦♥s❝✐❡♥t❡ ❞❛ r❡♣❡r❝✉ssã♦ ❞❡ ♠❡✉s ❛t♦s ❞❡ ❝♦♥s✉♠♦❀ ✲ ❖✉tr♦s✳
✸ ▼❛t❡♠át✐❝❛ ❋✐♥❛♥❝❡✐r❛
◆❡st❡ ❝❛♣ít✉❧♦ sã♦ ❛♣r❡s❡♥t❛❞♦s ♦s ♣r✐♥❝✐♣❛✐s ❝♦♥❝❡✐t♦s ❡ ♠♦❞❡❧♦s ❞❛ ▼❛t❡♠át✐❝❛ ❋✐♥❛♥❝❡✐r❛✳ ❖ ❡st❛❜❡❧❡❝✐♠❡♥t♦ ❞❡ss❡s ❝♦♥❝❡✐t♦s s❡r✈❡♠ ❞❡ ♣♦♥t♦ ❞❡ ♣❛rt✐❞❛ ♣❛r❛ ❛ ❛❜♦r❞❛❣❡♠ ❞♦s ♣r♦❞✉t♦s ✜♥❛♥❝❡✐r♦s ❛♥❛❧✐s❛❞♦s ♥❡st❡ tr❛❜❛❧❤♦✳
✸✳✶ ❈❛♣✐t❛❧
❉♦ ♣♦♥t♦ ❞❡ ✈✐st❛ ❡❝♦♥ô♠✐❝♦ ♦ ❝❛♣✐t❛❧ ♣♦❞❡ s❡r ✈✐st♦ ❝♦♠♦ ✉♠ ❞♦s ❢❛t♦r❡s ❞❡ ♣r♦❞✉çã♦✳ ➱ ❝♦♥s✐❞❡r❛❞♦✱ t❛♠❜é♠✱ ❛ ❡①♣r❡ssã♦ ♠♦♥❡tár✐❛ ❞❡ ✉♠ ❜❡♠ ♦✉ s❡r✈✐ç♦✳
●❡♥❡r✐❝❛♠❡♥t❡ ✐♥❞✐❝❛♠♦s ♦ ❝❛♣✐t❛❧ ♣❡❧❛ ❧❡tr❛C✳ ◗✉❛♥❞♦ ❢♦r ✐♥t❡r❡ss❛♥t❡ ❡✈✐❞❡♥❝✐❛r ❛ ❞❛t❛t✱ à q✉❛❧ ♦ ❝❛♣✐t❛❧ s❡ r❡❢❡r❡✱ ❧❛♥ç❛✲s❡ ♠ã♦ ❞❛ ♥♦t❛çã♦ Ct✳
✸✳✷ ❋❧✉①♦ ❞❡ ❈❛✐①❛
❋❧✉①♦ ❞❡ ❝❛✐①❛ ❞❡ ✉♠ ♣r♦❥❡t♦ ♦✉ ✐♥✈❡st✐♠❡♥t♦ é ♦ ❝♦♥❥✉♥t♦ ❞❡ ❡♥tr❛❞❛s ❡ s❛í❞❛s ❞❡ ❝❛♣✐t❛❧ ❛♦ ❧♦♥❣♦ ❞♦ t❡♠♣♦✳
❈♦♥✈❡♥❝✐♦♥❛✲s❡ q✉❡ ❛s ❡♥tr❛❞❛s ❞❡ ❝❛✐①❛ ♦✉ ❝ré❞✐t♦s sã♦ ✈❛❧♦r❡s ♣♦s✐t✐✈♦s ❞❡ ❝❛♣✐t❛❧ ❡ q✉❡ ❛s s❛í❞❛s ❞❡ ❝❛✐①❛ ♦✉ ❞é❜✐t♦s sã♦ ✈❛❧♦r❡s ♥❡❣❛t✐✈♦s ❞❡ ❝❛♣✐t❛❧✳
❖ ✢✉①♦ ❞❡ ❝❛✐①❛ ♣♦❞❡ s❡r ❛♣r❡s❡♥t❛❞♦ ❡sq✉❡♠❛t✐❝❛♠❡♥t❡ ❛tr❛✈és ❞♦s s❡❣✉✐♥t❡s ❞✐❛❣r❛♠❛s✿
❋✐❣✉r❛ ✾✿ ❉✐❛❣r❛♠❛ ❞♦ ✢✉①♦ ❞❡ ❝❛✐①❛
❉❡ ✉♠ ♠♦❞♦ ❣❡r❛❧✱ ♣♦❞❡✲s❡ ❞✐③❡r ❞♦ ♣♦♥t♦ ❞❡ ✈✐st❛ ✜♥❛❝❡✐r♦✱ q✉❡ ♦s ❡✈❡♥t♦s ❡❝♦♥ô✲ ♠✐❝♦s ♣♦❞❡♠ s❡r s✐♥t❡t✐③❛❞♦s ❛tr❛✈és ❞❡ ✢✉①♦s ❞❡ ❝❛✐①❛✳
✸✳✸ ❏✉r♦s
❖ ❝♦♥❝❡✐t♦ ❞❡ ❥✉r♦s ♣♦❞❡ s❡r ❛♣r❡s❡♥t❛❞♦ ❝♦♠♦ s❡♥❞♦ ❛ r❡♠✉♥❡r❛çã♦ ♣❡❧♦ ✉s♦ ❞♦ ❝❛♣✐t❛❧✳
❆ ♠❡❞✐❞❛ ❞♦s ❥✉r♦s✱ ♥✉♠ ❞❡t❡r♠✐♥❛❞♦ ✐♥t❡r✈❛❧♦ ❞❡ t❡♠♣♦✱ é ♦❜t✐❞❛ ♣❡❧❛ ❞✐❢❡r❡♥ç❛ ❡♥tr❡ ♦ ❝❛♣✐t❛❧ ♥♦ ✜♥❛❧ ❞♦ ✐♥t❡r✈❛❧♦ ❡ ♦ ❝❛♣✐t❛❧ ♥♦ ✐♥í❝✐♦ ❞♦ ✐♥t❡r✈❛❧♦✳
J =F −P ✭✶✮
♦♥❞❡✿ J ❂ ❏✉r♦s❀F ❂ ❈❛♣✐t❛❧ ✜♥❛❧ ♦✉ ▼♦♥t❛♥t❡❀ P ❂ Pr✐♥❝✐❛♣❛❧ ❈♦♥s❡q✉❡♥t❡♠❡♥t❡✿
F =P +J ✭✷✮
✸✳✹ ❚❛①❛ ❞❡ ❏✉r♦s
◆❛ ♣rát✐❝❛✱ ❛ ❞❡t❡r♠✐♥❛çã♦ ❞♦ ❥✉r♦ q✉❡ é ❝♦❜r❛❞♦ ❡♠ q✉❛❧q✉❡r tr❛♥s❛çã♦ ✜♥❛♥❝❡✐r❛ é ❡❢❡t✉❛❞❛ ♠❡❞✐❛♥t❡ ❛ ❝♦♥s✐❞❡r❛çã♦ ❞❡ ✉♠ ❝♦❡✜❝✐❡♥t❡ ❞❡♥♦♠✐♥❛❞♦ t❛①❛ ❞❡ ❥✉r♦s✳ ❆ t❛①❛ ❞❡ ❥✉r♦s✱ q✉❡ s❡♠♣r❡ é r❡❢❡r✐❞❛ ❛ ✉♠ ❝❡rt♦ ♣❡rí♦❞♦ ❞❡ t❡♠♣♦✱ q✉❡ ♣♦❞❡ s❡r ♠ês✱ s❡♠❡str❡✱ ❛♥♦✱ ❡t❝✳✱ ♥❛❞❛ ♠❛✐s é ❞♦ q✉❡ ❛ r❡♠✉♥❡r❛çã♦ ♣❡❧❛ ✉t✐❧✐③❛çã♦ ❞❛ ✉♥✐❞❛❞❡ ❞❡ ❝❛♣✐t❛❧ ❞✉r❛♥t❡ ♦ ♣❡rí♦❞♦ ❛ q✉❡ ❡❧❛ s❡ r❡❢❡r❡✳ ❖✉ s❡❥❛✱ ❛ t❛①❛ ❞❡ ❥✉r♦s ♣♦❞❡ s❡r ✐♥t❡r♣r❡t❛❞❛ ❝♦♠♦ s❡♥❞♦ ♦ ♣r❡ç♦ ❝♦❜r❛❞♦ ♣❡❧❛ ✉t✐❧✐③❛çã♦ ❞❛ ✉♥✐❞❛❞❡ ❞❡ ❝❛♣✐t❛❧ ❞✉r❛♥t❡ ♦ ♣❡rí♦❞♦ ❝♦♥s✐❞❡r❛❞♦✱ ♦✉ ❛✐♥❞❛ ❞❡ ♠❛♥❡✐r❛ ♠❛✐s ❧✐✈r❡✱ ♦ ♣r❡ç♦ ❞♦ ❞✐♥❤❡✐r♦✳ ❆s t❛①❛s ❞❡ ❥✉r♦s ❝♦st✉♠❛♠ s❡r ❛♣r❡s❡♥t❛❞❛s✱ ♦✉ s♦❜ ❢♦r♠❛ ✉♥✐tár✐❛ ♦✉ s♦❜ ❢♦r♠❛ ♣❡r❝❡♥t✉❛❧✳ ❆ss✐♠✱ s❡ ♣❡❧♦ ❡♠♣rést✐♠♦ ❞❡ ❘✩ ✶✱✵✵ ♣❡❧♦ ♣r❛③♦ ❞❡ ✉♠ ♠ês✱ ❢♦✐ ❝♦❜r❛❞♦ ♦ ❥✉r♦ ❞❡ ❘✩ ✵✱✶✵✱ ❞✐③ q✉❡ ❛ t❛①❛ ❞❡ ❥✉r♦ ❝♦♥s✐❞❡r❛❞❛ ❢♦✐ ❞❡ ❘✩ ✵✱✶✵ ✴ ❘✩ ✶✱✵✵ ❂ ✵✱✶✵ ❛♦ ♠ês ✭❢♦r♠❛ ✉♥✐tár✐❛✮ ♦✉ ✶✵✪ ❛♦ ♠ês ✭❢♦r♠❛ ♣❡r❝❡♥t✉❛❧✮✳
■♥❞✐❝❛✲s❡ ❛ t❛①❛ ❞❡ ❥✉r♦s ♣❡❧❛ ❧❡tr❛ i
i= J
P ✭✸✮
❈♦♥s❡q✉❡♥t❡♠❡♥t❡✿
J =P ·i ✭✹✮
➱ ❢✉♥❞❛♠❡♥t❛❧ ❡①♣r❡ss❛r ❝❧❛r❛♠❡♥t❡ ❛ ✉♥✐❞❛❞❡ ❞❡ t❡♠♣♦ ❞❛ t❛①❛ ❞❡ ❥✉r♦s ❛♦ ✉t✐❧✐③❛r ❛ ❡①♣r❡ssã♦ ✭✸✮✳ P♦r ❡①❡♠♣❧♦✱ ✉♠❛ ♦♣❡r❛çã♦ ❝♦♠ ♣r❛③♦ ❞❡ ✉♠ ❛♥♦ ♣♦❞❡ s❡r ❡①♣r❡ss❛ ❡♠ ♠❡s❡s ✭✶✷✮✱ ❞✐❛s ✭✸✻✵ ♦✉ ✸✻✺✮ ❡ tr✐♠❡str❡s✭✹✮✳
◆❛ ❡①♣r❡ssã♦ ✭✹✮✱ J ✐♥❞✐❝❛ ♦s ❥✉r♦s r❡❝❡❜✐❞♦s ♥♦ ♣❡rí♦❞♦ ❞❡ t❡♠♣♦ ❛ q✉❡ s❡ r❡❢❡r❡ ❛ t❛①❛✳
✸✳✺ ❘❡❣✐♠❡s ❞❡ ❈❛♣✐t❛❧✐③❛çã♦
❘❡❣✐♠❡ ❞❡ ❝❛♣✐t❛❧✐③❛çã♦ é ♦ ♥♦♠❡ ❞❛❞♦ ❛♦ ♣r♦❝❡ss♦ ❞❡ ❢♦r♠❛çã♦ ❞❡ ❝❛♣✐t❛❧ ❛♦ ❧♦♥❣♦ ❞♦ t❡♠♣♦✳
❉♦ ♣♦♥t♦ ❞❡ ✈✐st❛ ❢♦r♠❛❧ ❡①✐st❡♠ ❜❛s✐❝❛♠❡♥t❡✱ ❞♦✐s t✐♣♦s ❞❡ r❡❣✐♠❡s ❞❡ ❝❛♣✐t❛❧✐③❛✲ çã♦✿ ♦s r❡❣✐♠❡s ❞❡ ❝❛♣✐t❛❧✐③❛çã♦ ❞✐s❝r❡t❛ ❡ ♦s r❡❣✐♠❡ ❞❡ ❝❛♣✐t❛❧✐③❛çã♦ ❝♦♥tí♥✉❛✳
✸✳✺✳✶ ❘❡❣✐♠❡s ❞❡ ❝❛♣✐t❛❧✐③❛çã♦ ❞✐s❝r❡t❛
◗✉❛♥❞♦ ♦♣❡r❛✲s❡ ❝♦♠ r❡❣✐♠❡s ❞❡ ❝❛♣✐t❛❧✐③❛çã♦ ❞✐s❝r❡t❛✱ ♦s ❥✉r♦s ❣❡r❛❞♦s✱ sã♦ ✐♥✲ ❝♦r♣♦r❛❞♦s s♦♠❡♥t❡ ♥♦ ✜♥❛❧ ❞❡ ❝❛❞❛ ✐♥t❡r✈❛❧♦ ❞❡ t❡♠♣♦ ❛ q✉❡ s❡ r❡❢❡r❡ ❛ t❛①❛ ❞❡ ❥✉r♦s ❝♦♥s✐❞❡r❛❞❛✳
❖s r❡❣✐♠❡s ❞❡ ❝❛♣✐t❛❧✐③❛çã♦ ❞✐s❝r❡t❛ ✉s✉❛✐s ❡♠ ✜♥❛♥ç❛s sã♦✿ r❡❣✐♠❡ ❞❡ ❝❛♣✐t❛❧✐③❛çã♦ s✐♠♣❧❡s ❡ r❡❣✐♠❡ ❞❡ ❝❛♣✐t❛❧✐③❛çã♦ ❝♦♠♣♦st❛
✸✳✺✳✶✳✶ ❘❡❣✐♠❡ ❞❡ ❝❛♣✐t❛❧✐③❛çã♦ s✐♠♣❧❡s ✳
◆♦ r❡❣✐♠❡ ❞❡ ❝❛♣✐t❛❧✐③❛çã♦ s✐♠♣❧❡s ♦s ❥✉r♦s sã♦ ❣❡r❛❞♦s ❡①❝❧✉s✐✈❛♠❡♥t❡ ♣❡❧♦ ❝❛♣✐t❛❧ P ✐♥✐❝✐❛❧♠❡♥t❡ ✐♥✈❡st✐❞♦✳
❖s ❥✉r♦sJ ❢♦r♠❛❞♦s ❛♦ ✜♥❛❧ ❞❡ ❝❛❞❛ ✐♥t❡r✈❛❧♦ ✉♥✐tár✐♦ ❞❡ t❡♠♣♦✱ ❡①♣r❡ss♦s ♥❛ t❛①❛ ❞❡ ❥✉r♦si✱ sã♦ ❝❛❧❝✉❧❛❞♦s ♣♦r
J =P ·i
❧♦❣♦✱
❏✉r♦s ❣❡r❛❞♦s ❞✉r❛♥t❡ ♦ ✶♦ ✐♥t❡✈❛❧♦ ❞❡ t❡♠♣♦✿ J1 =P
❏✉r♦s ❣❡r❛❞♦s ❞✉r❛♥t❡ ♦ ✷♦ ✐♥t❡✈❛❧♦ ❞❡ t❡♠♣♦✿ J2 =P
❏✉r♦s ❣❡r❛❞♦s ❞✉r❛♥t❡ ♦ ✸♦ ✐♥t❡✈❛❧♦ ❞❡ t❡♠♣♦✿ J3 =P
❏✉r♦s ❣❡r❛❞♦s ❞✉r❛♥t❡ ♦ ❡♥és✐♠♦ ✐♥t❡✈❛❧♦ ❞❡ t❡♠♣♦✿ Jn=P
❖s ❥✉r♦s t♦t❛✐s ❛♦ ✜♥❛❧ ❞♦sn ✐♥t❡r✈❛❧♦s ✉♥✐tár✐♦s ❞❡ t❡♠♣♦
J =J1 +J2+· · ·+Jn
J =P +P +· · ·+P ✭n ♣❛r❝❡❧❛s✮
♦✉
J =n·P ·i ✭✺✮
❝♦♠♦ ♣❡❧❛ ❡①♣r❡ssã♦ ✭✷✮
F =P +J ❞❡❝♦rr❡ q✉❡✱
F =P +n·P ·i
❡
F =P(1 +n·i) ✭✻✮
❖❜s❡r✈❛çõ❡s✿
✭❛✮ ❆ ❡①♣r❡ssã♦ ✭✺✮ ✐♥❞✐❝❛ q✉❡ ♦s ❥✉r♦s s✐♠♣❧❡sJ sã♦ ❞✐r❡t❛♠❡♥t❡ ♣♦r♣♦r❝✐♦♥❛✐s ❛♦ ❝❛♣✐t❛❧ ✐♥✐❝✐❛❧ P✱ ❛♦ ♥ú♠❡♠r♦n ❞❡ ✐♥t❡r✈❛❧♦s ✉♥✐tár✐♦s ❞❡ t❡♠♣♦ ❡ à t❛①❛ ❞❡ ❥✉r♦si
✭❜✮ ❖ ❞♦♠í♥✐♦ ❞❛ ❢✉♥çã♦ ❡①♣❡r❡ss❛ ♥❛ r❡❧❛çã♦ ✭✻✮ é ♦ ❝♦♥❥✉♥t♦ ❞♦s ■♥t❡r✐♦s ♥ã♦ ♥❡❣❛t✐✈♦s✳ P♦❞❡✲s❡✱ s❡♠ ♣r❡❥✉í③♦ ❞❛ ♣r❡❝✐sã♦ ❞❡ ❝♦♥❝❡✐t♦s✱ ❡st❡♥❞ê✲❧♦s ❛♦ ❝♦♥❥✉♥t♦ ❞♦s ❘❡❛✐s ♥ã♦ ♥❡❣❛t✐✈♦s✳
✸✳✺✳✶✳✷ ❘❡❣✐♠❡ ❞❡ ❝❛♣✐t❛❧✐③❛çã♦ ❝♦♠♣♦st❛ ✳
❖ r❡❣✐♠❡ ❞❡ ❝❛♣✐t❛❧✐③❛çã♦ ❝♦♠♣♦st❛ é ❛ ❢♦r♠❛ ❞❡ ❝❛♣✐t❛❧✐③❛çã♦ ♠❛✐s ✉t✐❧✐③❛❞❛ ♥❛s ♣rát✐❝❛s ✜♥❛♥❝❡✐r❛s ♥♦ ❇r❛s✐❧✳
◆♦ r❡❣✐♠❡ ❞❡ ❝❛♣✐t❛❧✐③❛çã♦ ❝♦♠♣♦st❛✱ ♦s ❥✉r♦s ✭❢♦r♠❛❞♦s ❛♦ ✜♥❛❧ ❞❡ ❝❛❞❛ ✐♥t❡r✈❛❧♦ ❞❡ t❡♠♣♦✮ sã♦ ❣❡r❛❞♦s ♣❡❧♦ ♠♦♥t❛♥t❡ ❡①✐st❡♥t❡ ♥♦ ✐♥í❝✐♦ ❞❡ ❝❛❞❛ ✐♥t❡r✈❛❧♦✳ ❖✉ s❡❥❛✱ ♦s ❥✉r♦s sã♦ ❣❡r❛❞♦s ♣❡❧❛ s♦♠❛ ❞♦ ❝❛♣✐t❛❧ P✱ ✐♥✐❝✐❛❧♠❡♥t❡ ✐♥✈❡st✐❞♦✱ ❝♦♠ ♦s ❥✉r♦s ❛❝✉♠✉❧❛❞♦s ❛té ♦ ✜♠ ❞♦ ✐♥t❡r✈❛❧♦ ✐♠❡❞✐❛t❡♠❡♥t❡ ❛♥t❡r✐♦r✳
❖ ♠♦❞❡❧♦ ♠❛t❡♠át✐❝♦ ❛ss♦❝✐❛❞♦ ❛♦ r❡❣✐♠❡ ❞❡ ❝❛♣✐t❛❧✐③❛çã♦ ❝♦♠♣♦st❛ ❝♦♥s✐❞❡r❛ ✉♠❛ ❝❡rt❛ t❛①❛ ❞❡ ❥✉r♦s✱ ❝♦♥st❛♥t❡✱ ❡♠ q✉❡ ❡st❛ ❡①♣r❡ss❛ ♦ ✐♥t❡r✈❛❧♦ ✉♥✐tár✐♦ ❞❡ t❡♠♣♦✱ ❛♦ ✜♠ ❞♦ q✉❛❧ ♦s ❥✉r♦s ❢♦r♠❛❞♦s sã♦✐♥♦r♣♦r❛❞♦s ❛♦ ❝❛♣✐t❛❧✳
❘❡t♦♠❛♥❞♦ ♦ ❝♦♥❝❡✐t♦ ❞❡ t❛①❛ ❞❡ ❥✉r♦s✱ t❡♠✲s❡✿
i= J
P ❉❡❝♦rr❡ ❡♥tã♦✱
J =P ·i
❆♦ ✜♥❛❧ ❞♦ ✶♦ ✐♥t❡r✈❛❧♦ ✉♥✐tár✐♦ ❞❡ t❡♠♣♦
J1 =P ·i ❡ F1 =P +J1 =P(1 +i)
❆♦ ✜♥❛❧ ❞♦ ✷♦ ✐♥t❡r✈❛❧♦ ✉♥✐tár✐♦ ❞❡ t❡♠♣♦
J2 =F1·i ❡F2 =F1+J2 =P(1 +i)2
❆♦ ✜♥❛❧ ❞♦ ✸♦ ✐♥t❡r✈❛❧♦ ✉♥✐tár✐♦ ❞❡ t❡♠♣♦
J3 =F2·i ❡F3 =F2+J3 =P(1 +i)3
●❡♥❡r❛❧✐③❛♥❞♦ ♣❛r❛ ♦ ❡✲♥és✐♠♦ ✐♥t❡r✈❛❧♦ ✉♥✐tár✐♦ ❞❡ t❡♠♣♦✱
F =P(1 +i)n ✭✼✮
❖❜s❡r✈❛çã♦✿
❖ ❞♦♠í♥✐♦ ❞❛ ❢✉♥çã♦ ❡①♣r❡ss❛ ♥❛ r❡❧❛çã♦ ✭✼✮ é ♦ ❝♦♥❥✉♥t♦ ❞♦s ■♥t❡✐r♦s ♥ã♦ ♥❡❣❛t✐✈♦s✳ P♦❞❡✲s❡ ❡st❡♥❞ê✲❧♦s ✐❣✉❛❧♠❡♥t❡ ❛♦ ❝♦♥❥✉♥t♦ ❞♦s ❘❡❛✐s ♥ã♦ ♥❡❣❛t✐✈♦s✳
✸✳✺✳✷ ❘❡❣✐♠❡s ❞❡ ❝❛♣✐t❛❧✐③❛çã♦ ❝♦♥tí♥✉❛
◆♦ r❡❣✐♠❡ ❞❡ ❝❛♣✐t❛❧✐③❛çã♦ ❝♦♥tí♥✉❛ ❝♦♥s✐❞❡r❛✲s❡ ✉♠❛ t❛①❛ ❞❡ ❥✉r♦sI ❞✐t❛ ✐♥st❛♥tâ✲ ♥❡❛✱ r❡❢❡r✐❞❛ ❛ ✉♠ ✐♥t❡r✈❛❧♦ ❞❡ t❡♠♣♦ ✐♥✜♥✐t❡s✐♠❛❧✱ ❛♦ ✜♥❛❧ ❞♦ q✉❛❧ ♦s ❥✉r♦s ❢♦r♠❛❞♦s s❡ ✐♥❝♦r♣♦r❛♠ ❛♦ ❝❛♣✐t❛❧
❖ ♠♦❞❡❧♦ ♠❛t❡♠át✐❝♦ ❛ss♦❝✐❛❞♦ ❛♦ r❡❣✐♠❡ ❞❡ ❝❛♣✐t❛❧✐③❛çã♦ ❝♦♥tí♥✉❛ ❛ss✉♠❡ q✉❡ ♦s ❥✉r♦s✱ ♦✉ ❛❝rés❝✐♠♦s ❞❡ ❝❛♣✐t❛❧dPt sã♦ ❞✐r❡t❛♠❡♥t❡ ♣r♦♣♦r❝✐♦♥❛✐s ❛♦ ❝❛♣✐t❛❧ Pt✱ ❛♦
✐♥t❡r✈❛❧♦ ✐♥✜♥✐t❡s✐♠❛❧ ❞❡ t❡♠♣♦dt❡ à t❛①❛I✱ s✉♣♦st❛ ❝♦♥st❛♥t❡ ❞✉r❛♥t❡ ❛ ❝❛♣✐t❛❧✐③❛çã♦✳ ❆ss✐♠✱
dPt=Pt·dt·I
dPt
Pt =I·dt
♦✉ Z
dPt
Pt
=
Z I·dt
❞❡❝♦rr❡ q✉❡
ln Pt=I·t+k
♦♥❞❡ k é ✉♠❛ ❝♦♥st❛♥t❡ ❞❡ ✐♥t❡❣r❛çã♦✳P♦rt❛♥t♦✱
Pt =eI·t
+k=eI·t·ek
❈♦♠♦ ♣❛r❛ t ❂ ✵ t❡♠✲s❡ P0 =P =ek ❡♥tã♦
Pt=P ·eI·t ✭✽✮
✹ ❚❛①❛s
❈♦♠♦ ♦ ❝✉rs♦ ❢♦❝❛ ❛❧❣✉♥s ♣r♦❞✉t♦s ✜♥❛♥❝❡✐r♦s ♠❛✐s ❝♦♠✉♥s ♦❢❡r❡❝✐❞♦s ♣❡❧♦ ♠❡r❝❛❞♦ às ♣❡ss♦❛s ❢ís✐❝❛s✱ ✈❛❧❡ ❞✐s❝♦rr❡r s♦❜r❡ ♦s ❞✐❢❡r❡♥t❡s t✐♣♦s ❞❡ t❛①❛s ❞❡ ❥✉r♦s q✉❡ sã♦ ✉t✐❧✐③❛❞♦s ♥❛s ♦♣❡r❛çõ❡s ✜♥❛♥❝❡✐r❛s✿
✲ t❛①❛s ♣r♦♣♦r❝✐♦♥❛✐s❀ ✲ t❛①❛s ❡q✉✐✈❛❧❡♥t❡s❀ ✲ t❛①❛s ❡❢❡t✐✈❛s❀ ✲ t❛①❛s ♥♦♠✐♥❛✐s❀ ✲ t❛①❛ ♦✈❡r❀
✲ t❛①❛ r❡❛❧ ❡ t❛①❛ ❛♣❛r❡♥t❡✳
✹✳✶ ❚❛①❛s Pr♦♣♦r❝✐♦♥❛✐s
❉✉❛s t❛①❛s ❞❡ ❥✉r♦s i1 ❡ i2✱ ❡①♣r❡ss❛s ❡♠ ✉♥✐❞❛❞❡s ❞❡ t❡♠♣♦ ❞✐st✐♥t❛s t1 ❡ t2✱ sã♦ ❞✐t❛s ♣r♦♣♦r❝✐♦♥❛✐s q✉❛♥❞♦✱ ✐♥❝✐❞✐♥❞♦ s♦❜r❡ ✉♠ ♠❡s♠♦ ❝❛♣✐t❛❧✱ ❞✉r❛♥t❡ ✉♠ ♠❡s♠♦ ♣❡rí♦❞♦✱ ♣r♦❞✉③❡♠ ♦ ♠❡s♠♦ ♠♦♥t❛♥t❡✳ P❛r❛ t❛①❛s ♣r♦♣♦r❝✐♦♥❛✐s ✈❡r✐✜❝❛✲s❡ ❛ s❡❣✉✐♥t❡ r❡❧❛çã♦✿
i1 i2 =
t1
t2. ✭✾✮
◆❛ r❡❧❛çã♦(9)✱ ❛s t❛①❛si1 ❡i2 ♣♦❞❡♠ ❡st❛r ♦✉ s♦❜ ❛ ❢♦r♠❛ ✉♥✐tár✐❛ ♦✉ s♦❜ ❛ ❢♦r♠❛ ♣❡r❝❡♥t✉❛❧✱ ♣♦ré♠ é ♥❡❝❡ssár✐❛ q✉❡ ❛♠❜❛s ❡st❡❥❛♠ s♦❜ ❛ ♠❡s♠❛ ❢♦r♠❛✳
❆ss✐♠ ❛s t❛①❛si1 ❂ ✹✪ ❛♦ tr✐♠❡str❡ ❡ i2❂✶✻✪ ❛♦ ❛♥♦ sã♦ ♣r♦♣♦r❝✐♦♥❛✐s✱ ✐st♦ é✱
i1 i2 = t1 t2 ⇒ 4 16 = 3 12 ♦✉
0,04 0,16 =
3 12.
❙❡❥❛i1 ✉♠❛ t❛①❛ r❡❧❛t✐✈❛ ❛ ✉♠ ❝❡rt♦ ♣❡rí♦❞♦t1✳ ❉❡ ❛❝♦r❞♦ ❝♦♠ ❛ r❡❧❛çã♦ (9)✱ ♣❛r❛
q✉❡ ❛ t❛①❛i2 r❡❧❛t✐✈❛ ❛ ✉♠ ❝❡rt♦ ♣❡rí♦❞♦t2 q✉❡ ❝♦rr❡s♣♦♥❞❡ ❛ ✉♠❛ ❢r❛çã♦ 1
k ❞♦ ♣❡rí♦❞♦ t1 ✱ s❡❥❛ ♣r♦♣♦r❝✐♦♥❛❧ ❛ t❛①❛i1✱ ❞❡✈❡♠♦s t❡r✱ ♦❜s❡r✈❛♥❞♦ q✉❡ t2 = t1
k✿
i1 i2 = t1 t2 ⇒ i1 i2 = t1 t1 k ♦✉ i1 i2 = t1 1 · k t1. ♦✉
i2 = i1
k✳ ✭✶✵✮
❆ r❡❧❛çã♦ (2) ♣❡r♠✐t❡✱ ❞❡ ♠❛♥❡✐r❛ rá♣✐❞❛✱ ❞❡t❡r♠✐♥❛r ❛ t❛①❛ q✉❡✱ r❡❧❛t✐✈❛♠❡♥t❡
❛ ❢r❛çã♦ 1
k ❞♦ ♣❡rí♦❞♦ ❛ q✉❡ s❡ r❡❢❡r❡ ✉♠❛ ❞❛❞❛ ♦✉tr❛ t❛①❛✱ s❡❥❛ ♣r♦♣♦r❝✐♦♥❛❧ ❛ ❡ss❛ ú❧t✐♠❛✳ ❆ss✐♠ ❛ t❛①❛ ❛♥✉❛❧ q✉❡ é ♣r♦♣♦r❝✐♦♥❛❧ ❛ t❛①❛ ❞❡ ❥✉r♦s ❞❡ ✷✪ ❛♦ ♠ês é✿
i2 = i1
k ⇒0,02 = i1
12 ⇒i1 = 0,24♦✉ i1 = 24%.
✹✳✷ ❚❛①❛s ❊q✉✐✈❛❧❡♥t❡s
❙❡❥❛♠ ❞✉❛s t❛①❛s ❞❡ ❥✉r♦s i1 ❡ i2✱ r❡s♣❡❝t✐✈❛♠❡♥t❡ r❡❧❛t✐✈❛ ❛♦s ♣❡rí♦❞♦s t1 ❡ t2✳ ❊st❛s ❞✉❛s t❛①❛s sã♦ ❞✐t❛s ❡q✉✐✈❛❧❡♥t❡s s❡✱ ♣❛r❛ ✉♠ ♠❡s♠♦ ♣r❛③♦ ❞❡ ❛♣❧✐❝❛çã♦✱ ❢♦r ✐♥❞✐❢❡r❡♥t❡ ❝♦❧♦❝❛r ♥♦ss♦ ❝❛♣✐t❛❧ ❛ r❡♥❞❡r ❥✉r♦s ❛ t❛①❛ i1 ♦✉ ❛ t❛①❛ i2✳ ❈♦♠♦ ❛ ❢♦r✲ ♠❛çã♦ ❞♦ ♠♦♥t❛♥t❡ ❞❡♣❡♥❞❡ ❞♦ r❡❣✐♠❡ ❞❡ ❝❛♣✐t❛❧✐③❛çã♦ ❞♦s ❥✉r♦s✱ t♦r♥❛✲s❡ ♥❡❝❡ssár✐♦ ❡s♣❡❝✐✜❝❛r ❡♠ q✉❛❧ r❡❣✐♠❡ ❛s t❛①❛s sã♦ ❡q✉✐✈❛❧❡♥t❡s✳
❙❡♥❞♦ P ♦ ❝❛♣✐t❛❧ ✐♥✐❝✐❛❧ ❡ t♦♠❛♥❞♦✲s❡✱ ♣♦r ❡①❡♠♣❧♦✱ ♦ ♣❡rí♦❞♦ ❛ q✉❡ s❡ r❡❢❡r❡ ❛ t❛①❛i1 ❝♦♠♦ ♣r❛③♦ ❞❡ ❛♣❧✐❝❛çã♦✳ P❛r❛ q✉❡ ❛s t❛①❛si1 ❡i2 s❡❥❛♠ ❡q✉✐✈❛❧❡♥t❡s✱ ❞❡✈❡♠♦s t❡r q✉❡ ♦s ♠♦♥t❛♥t❡s ♣r♦❞✉③✐❞♦s ♣❡❧❛s ❞✉❛s t❛①❛s ♥♦ ♠❡s♠♦ ♣❡rí♦❞♦✱ s❡❥❛♠ ✐❣✉❛✐s✳ ❙❡ s✉♣♦r♠♦s q✉❡ ♦ ♣❡rí♦❞♦ ❞❛ t❛①❛ i2 s❡❥❛ k ✈❡③❡s ♠❡♥♦r q✉❡ ♦ ♣❡rí♦❞♦ ❞❛ i1 ♣♦❞❡♠♦s ❞✐③❡r q✉❡ ♦ ♠♦♥t❛♥t❡ ♣r♦❞✉③✐❞♦ ♣❡❧❛ t❛①❛i1 ❡♠ ✉♠ ♣❡rí♦❞♦ ❞❡ t❛①❛i1✱ ❞❡✈❡ s❡r ✐❣✉❛❧ ❛♦ ♠♦♥t❛♥t❡ ♣r♦❞✉③✐❞♦ ♣❡❧❛ t❛①❛i2 ❡♠ k ♣❡rí♦❞♦s ❞❡ t❛①❛ i2✳
✹✳✷✳✶ ❚❛①❛s ❊q✉✐✈❛❧❡♥t❡s ❡♠ r❡❣✐♠❡ ❞❡ ❈❛♣✐t❛❧✐③❛çã♦ ❙✐♠♣❧❡s
◆♦ r❡❣✐♠❡ ❞❡ ❝❛♣✐t❛❧✐③❛çã♦ s✐♠♣❧❡s✱ t❡♠✲s❡
P(1 +i1·1) =P(1 +i2·k)
♦✉
i2 = i1
k ♦✉i1 =k·i2 ✳ ✭✶✶✮
❈♦♥❝❧✉✐✲s❡ q✉❡ ♥♦ r❡❣✐♠❡ ❞❡ ❝❛♣✐t❛❧✐③❛çã♦ s✐♠♣❧❡s✱ ❞✉❛s t❛①❛s sã♦ ❡q✉✐✈❛❧❡♥t❡s s❡ sã♦ ♣r♦♣♦r❝✐♦♥❛✐s✳
✹✳✷✳✷ ❚❛①❛s ❡q✉✐✈❛❧❡♥t❡s ❡♠ r❡❣✐♠❡ ❞❡ ❝❛♣✐t❛❧✐③❛çã♦ ❝♦♠♣♦st❛
◆♦ r❡❣✐♠❡ ❞❡ ❝❛♣✐t❛❧✐③❛çã♦ ❝♦♠♣♦st❛✱ t❡♠✲s❡
P(1 +i1)1
=P(1 +i2)k ✳
P♦rt❛♥t♦✱
i1 = (1 +i2)k−1 ✭✶✷✮
♦✉
i2 = (1 +i1)1k −1 ✳ ✭✶✸✮
❈♦♥s✐❞❡r❛♥❞♦ ♦s ♣r✐♥❝✐♣❛✐s s✉❜♣❡rí♦❞♦s ✉t✐❧✐③❛❞♦s ♥♦ ♠❡r❝❛❞♦ ✜♥❛♥❝❡✐r♦✱ ♣♦❞❡✲s❡ ❡st❛❜❡❧❡❝❡r ❛s s❡❣✉✐♥t❡s r❡❧❛çõ❡s ❡♥tr❡ ❛s t❛①❛s ❡q✉✐✈❛❧❡♥t❡s✱ ♥♦ r❡❣✐♠❡ ❞❡ ❝❛♣✐t❛❧✐③❛çã♦ ❝♦♠♣♦st❛✿
(1 +ia) = (1 +is)2 = (1 +iq)3 = (1 +it)4 = (1 +ib)6 = (1 +im)12= (1 +id)360
♦♥❞❡
✲ ia ❞❡♥♦t❛ ✉♠❛ t❛①❛ ❛♥✉❛❧❀
✲ is ❞❡♥♦t❛ ✉♠❛ t❛①❛ s❡♠❡str❛❧ ❡q✉✐✈❛❧❡♥t❡❀
✲ iq ❞❡♥♦t❛ ✉♠❛ t❛①❛ q✉❛❞r✐♠❡str❛❧ ❡q✉✐✈❛❧❡♥t❡❀
✲ it ❞❡♥♦t❛ ✉♠❛ t❛①❛ tr✐♠❡str❛❧ ❡q✉✐✈❛❧❡♥t❡❀
✲ ib ❞❡♥♦t❛ ✉♠❛ t❛①❛ ❜✐♠❡str❛❧ ❡q✉✐✈❛❧❡♥t❡❀
✲ im ❞❡♥♦t❛ ✉♠❛ t❛①❛ ♠❡♥s❛❧ ❡q✉✐✈❛❧❡♥t❡❀ ✲ id ❞❡♥♦t❛ ✉♠❛ t❛①❛ ❞✐❛r✐❛ ❡q✉✐✈❛❧❡♥t❡✳
✹✳✸ ❚❛①❛ ❊❢❡t✐✈❛ ❡ ❚❛①❛ ◆♦♠✐♥❛❧
◆♦ ♠❡r❝❛❞♦ ✐♠♦❜✐❧✐ár✐♦ é ❝♦♠✉♠ ❞✐✈✉❧❣❛r ✉♠❛ t❛①❛ ❞❡ ✶✷✪ ❛♦ ❛♥♦ ❝♦♠ ❝❛♣✐t❛❧✐✲ ③❛çã♦ ♠❡♥s❛❧✱ ✐st♦ é✱ ❛ t❛①❛ ❡①♣r❡ss❛ é ❛♥✉❛❧✱ ♠❛s ♦s ❥✉r♦s sã♦ ✐♥❝♦r♣♦r❛❞♦s ❛♦ ✜♥❛❧ ❞❡ ❝❛❞❛ ♠ês ❡ ♥ã♦ ❛♣❡♥❛s ♥♦ ✜♥❛❧ ❞♦ ❛♥♦✳ ❉❛ ♠❡s♠❛ ❢♦r♠❛ t❡♠✲s❡ ❛ ❝❛❞❡r♥❡t❛ ❞❡ ♣♦✉♣❛♥ç❛✱ ❝✉❥❛ t❛①❛ é ❞❡ ✻✪ ❛♦ ❛♥♦✱ ❝♦♠ ❝❛♣✐t❛❧✐③❛çã♦ ♠❡♥s❛❧✳ ❊st❡s ❡①❡♠♣❧♦s ❛♣r❡✲ s❡♥t❛♠ ✉♠❛ ✐♥❝♦❡rê♥❝✐❛✱ ♣♦✐s s❡♥❞♦ ✉♠❛ t❛①❛ ❛♥✉❛❧✱ ♦s ❥✉r♦s só s❡rã♦ ❢♦r♠❛❞♦s ❛♦ ✜♠ ❞❡ ❝❛❞❛ ❛♥♦✳ ❊♠❜♦r❛ ❡①❡♠♣❧♦s ❝♦♠♦ ❡st❡s✱ s❡ ❡♥t❡♥❞✐❞♦s ❛♦ ♣é ❞❛ ❧❡tr❛ s❡❥❛♠ ❛❜s✉r❞♦s✱ sã♦ ❢r❡q✉❡♥t❡s ♥❛ ♣rát✐❝❛ ❡ ❝❛r❛❝t❡r✐③❛♠ ♦ q✉❡ s❡ ❝♦♥✈❡♥❝✐♦♥♦✉ ❝❤❛♠❛r ❞❡ t❛①❛s ♥♦♠✐♥❛✐s✳ ❆ss✐♠ ✉♠❛ t❛①❛ ♥♦♠✐♥❛❧ é ❛q✉❡❧❛ ❝✉❥♦ ♣❡rí♦❞♦ ❞❡ ❝❛♣✐t❛❧✐③❛çã♦ ♥ã♦ ❝♦✐♥❝✐❞❡ ❝♦♠ ❛q✉❡❧❡ ❛ q✉❡ ❡❧❛ s❡ r❡❢❡r❡✳ ❏á ❛ t❛①❛ ❡❢❡t✐✈❛ é ❛q✉❡❧❛ ❡①♣r❡ss❛ ♥✉♠❛ ✉♥✐✲ ❞❛❞❡ ❞❡ t❡♠♣♦ ❝♦✐♥❝✐❞❡♥t❡ ❝♦♠ ♦ ♣❡rí♦❞♦ ❞❡ t❡♠♣♦ ❡♠ q✉❡ ♦s ❥✉r♦s sã♦ ❝❛♣✐t❛❧✐③❛❞♦s✳ P♦r ❝♦♥✈❡♥çã♦✱ ❞❛❞❛ ✉♠❛ t❛①❛ ♥♦♠✐♥❛❧ in ❛ t❛①❛ ❡❢❡t✐✈❛ ❝♦rr❡s♣♦♥❞❡♥t❡✱ r❡❧❛t✐✈❛ ❛♦
♣❡rí♦❞♦ ❞❡ ❝❛♣✐t❛❧✐③❛çã♦✱ s❡rá ❛ t❛①❛ie q✉❡ ❧❤❡ s❡❥❛ ♣r♦♣♦r❝✐♦♥❛❧
ie=
in
k ✱ ✭✶✹✮
♦♥❞❡ k é ♦ ♥ú♠❡r♦ ❞❡ ♣❡rí♦❞♦s ❞❡ ❝❛♣✐t❛❧✐③❛çã♦ ❝♦♥t✐❞♦s ♥❛ ✉♥✐❞❛❞❡ ❞❡ t❡♠♣♦ ❡♠ q✉❡ ❛ t❛①❛ ♥♦♠✐♥❛❧ é ❡①♣r❡ss❛✳
❈♦♠♦ ❡①❡♠♣❧♦✱ ♣♦❞❡♠♦s ❝✐t❛r ❛ t❛①❛ ♥♦♠✐♥❛❧ ❞❛ ❝❛❞❡r♥❡t❛ ❞❡ ♣♦✉♣❛♥ç❛ q✉❡ é ❞❡ ✻✪ ❛♦ ❛♥♦✱ ❝❛♣✐t❛❧✐③❛❞♦s ♠❡♥s❛❧♠❡♥t❡✳ ❆ss✐♠✱ ❛ t❛①❛ ❡❢❡t✐✈❛ ❛♥✉❛❧ ❞❛ ❝❛❞❡r♥❡t❛ ❞❡ ♣♦✉♣❛♥ç❛ é ✻✱✶✼✪✱ ♣♦✐s
ie=
in
k =
0,06
12 = 0,005ou0,5%
❆ t❛①❛ ❡❢❡t✐✈❛ ❛♥✉❛❧ é ❛ t❛①❛ ❡q✉✐✈❛❧❡♥t❡ à t❛①❛ ❡❢❡t✐✈❛ ♠❡♥s❛❧✳ ■st♦ é✱
(1 +ia)1 = (1 +im)12⇒ia = (1 +im)12−1
ia= (1 + 0,005)
12
−1⇒ia = 0,0617 ♦✉6,17% t❛①❛ ❡❢❡t✐✈❛ ❛♥✉❛❧✳✮
✹✳✹ ❚❛①❛ ❖✈❡r
❖ ♠❡r❝❛❞♦ ✜♥❛♥❝❡✐r♦ ❜r❛s✐❧❡✐r♦✱ ♣❡rt✉r❜❛❞♦ ♣♦r ❞✐st♦rçõ❡s ❝❛✉s❛❞❛s ♣❡❧♦s ❡❧❡✈❛❞♦s í♥❞✐❝❡s ✐♥✢❛❝✐♦♥ár✐♦s ♥♦ ♣❛ss❛❞♦✱ ❧❛♥ç♦✉ ♠ã♦ ❞❡ ✉♠ ❝♦♥❝❡✐t♦ ✐♥t❡r❡ss❛♥t❡ ♣❛r❛ ♠❡❞✐r
♦ ❞❡s❡♠♣❡♥❤♦ ❞❛s ♦♣❡r❛çõ❡s ✜♥❛♥❝❡✐r❛s✳ ❚r❛t❛✲s❡ ❞❛ ❝❛♣✐t❛❧✐③❛çã♦ ♣♦r ❞✐❛ út✐❧✳ ❊♠ ❧✐♥❤❛s ❣❡r❛✐s✱ ❛ ❛♥á❧✐s❡ ❞❛s ♦♣❡r❛çõ❡s é ❢❡✐t❛ ❞❛ s❡❣✉✐♥t❡ ♠❛♥❡✐r❛✿
✲ ❉❡t❡r♠✐♥❛✲s❡✱ ✐♥✐❝✐❛❧♠❡♥t❡✱ ❛ t❛①❛ ❡❢❡t✐✈❛ ❞❡ ✉♠❛ ❞❛❞❛ ♦♣❡r❛çã♦ ♥✉♠ ❞❡t❡r♠✐♥❛❞♦ ♣❡rí♦❞♦✳
✲ ❊♠ s❡❣✉✐❞❛✱ ♦❜té♠✲s❡ ❛ t❛①❛ ❡q✉✐✈❛❧❡♥t❡ ♣♦r ❞✐❛ út✐❧✱ ❝♦♥s✐❞❡r❛♥❞♦✲s❡ ♦ ♥ú♠❡r♦ ❞❡ ❞✐❛s ✉t❡✐s ❝♦♥t✐❞♦s ♥♦ ♣❡rí♦❞♦ ❡♠ q✉❡stã♦✳
❊ss❛ t❛①❛ ❛♦ ❞✐❛ út✐❧ é ❝❤❛♠❛❞❛ t❛①❛ ♦✈❡r✳
❊ss❛ ♠❡t♦❞♦❧♦❣✐❛ é ❛❞♦t❛❞❛ ❛♣❡♥❛s ♥♦ ❇r❛s✐❧ ❡ ❛ t❛①❛ ♦✈❡r é ✉t✐❧✐③❛❞❛ ❡♠ ❡♠♣rés✲ t✐♠♦s ❡♥tr❡ ✐♥st✐t✉✐çõ❡s ✜♥❛♥❝❡✐r❛s✳ ❆ r❡❧❛çã♦ ❡♥tr❡ ❛ t❛①❛ ♦✈❡r ♠❡♥s❛❧ ❡ ❛ t❛①❛ ❡❢❡t✐✈❛ ♠❡♥s❛❧ é ❞❛❞❛ ♣♦r✿
ie =
1 + iover 30
du
−1 ✭✶✺✮
♦✉
iover = [(1 +ie) 1
du −1]·30✱ ✭✶✻✮
♦♥❞❡✿
✲ ie❂t❛①❛ ❡❢❡t✐✈❛ ♠❡♥s❛❧❀
✲ iover ❂t❛①❛ ♦✈❡r ♠❡♥s❛❧❀
✲ du ❂ ♥ú♠❡r♦ ❞❡ ❞✐❛s út❡✐s ♥♦ ♠ês✳
✹✳✺ ❚❛①❛ ❘❡❛❧ ❡ ❚❛①❛ ❆♣❛r❡♥t❡
❉❡ ♠❛♥❡✐r❛ s✐♠♣❧✐st❛✱ ♦ ♣r♦❝❡ss♦ ✐♥✢❛❝✐♦♥ár✐♦ ❞❡ ✉♠❛ ❡❝♦♥♦♠✐❛ ♣♦❞❡ s❡r ❡♥t❡♥❞✐❞♦ ♣❡❧❛ ❡❧❡✈❛çã♦ ❣❡♥❡r❛❧✐③❛❞❛ ❞♦s ♣r❡ç♦s ❞❡ ❜❡♥s ❡ s❡r✈✐ç♦s✳ ❆ ✐♥✢❛çã♦ ❝❛✉s❛ ♦ ❢❡♥ô♠❡♥♦ ❞❛ ✐❧✉sã♦ ♠♦♥❡tár✐❛ ♥❛s ♣rát✐❝❛s ✜♥❛♥❝❡✐r❛s✱ ❛ss✐♠ ♣❛r❛ ❛♣✉r❛r♠♦s ❛ t❛①❛ r❡❛❧ ❞❡ ❥✉r♦s✱ ❞❡✈❡♠♦s ❡①♣✉r❣❛r ♦s ❡❢❡✐t♦s ❞❛s t❛①❛s ✐♥✢❛❝✐♦♥ár✐❛s✳
(1 +iaparente) = (1 +iinf la)(1 +ireal)
ireal=
(1 +iaparente) (1 +iinf la)
−1 ✭✶✼✮
❆ss✐♠✱ ✉♠❛ ♣❡ss♦❛ q✉❡ ✐♥✈❡st✐✉ ♥♦ ♠❡r❝❛❞♦ ✜♥❛♥❝❡✐r♦ ♥✉♠ ❞❛❞♦ ♣❡rí♦❞♦ ❡ ♦❜t❡✈❡ ✉♠❛ r❡♥t❛❜✐❧✐❞❛❞❡ ❡❢❡t✐✈❛ ❞❡ ✷✵✪✱ s❡ ♥❡ss❡ ♠❡s♠♦ ♣❡rí♦❞♦ ❛ t❛①❛ ❞❡ ✐♥✢❛çã♦ ❢♦✐ ❞❡ ✾✪✱ ❛ t❛①❛ r❡❛❧ ♣r♦♣✐❝✐❛❞❛ ♣♦r ❡st❡ ✐♥✈❡st✐♠❡♥t♦ ❢♦✐ ❞❡
ireal=
(1 + 0,20)
(1 + 0,09) −1 = 0,1009 ♦✉ 10,09%
