❆ ❝♦♠❜✐♥❛çã♦ ❞♦s ♠ét♦❞♦s ❞❡ ❜❛rr❡✐r❛ ❡ ❞❡ ❜❛rr❡✐r❛
♠♦❞✐✜❝❛❞❛ ♥❛ r❡s♦❧✉çã♦ ❞♦ Pr♦❜❧❡♠❛ ❞❡ ❋❧✉①♦ ❞❡
P♦tê♥❝✐❛ Ót✐♠♦ ❘❡❛t✐✈♦
❏éss✐❝❛ ❆♥t♦♥✐♦ ❉❡❧❣❛❞♦
❆ ❝♦♠❜✐♥❛çã♦ ❞♦s ♠ét♦❞♦s ❞❡ ❜❛rr❡✐r❛ ❡ ❞❡ ❜❛rr❡✐r❛ ♠♦❞✐✜❝❛❞❛
♥❛ r❡s♦❧✉çã♦ ❞♦ Pr♦❜❧❡♠❛ ❞❡ ❋❧✉①♦ ❞❡ P♦tê♥❝✐❛ Ót✐♠♦ ❘❡❛t✐✈♦
❏éss✐❝❛ ❆♥t♦♥✐♦ ❉❡❧❣❛❞♦
❖r✐❡♥t❛❞♦r❛✿ Pr♦❢❛ ❆❞❥✳ ❊❞♠é❛ ❈áss✐❛ ❇❛♣t✐st❛
❉✐ss❡rt❛çã♦ ❞❡ ▼❡str❛❞♦ ❛♣r❡s❡♥t❛❞❛ ❛♦ Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❊♥❣❡♥❤❛r✐❛ ❊❧étr✐❝❛✱ ❞❛ ❋❛✲ ❝✉❧❞❛❞❡ ❞❡ ❊♥❣❡♥❤❛r✐❛ ❞❡ ❇❛✉r✉✱ ❞❛ ❯♥✐✈❡rs✐✲ ❞❛❞❡ ❊st❛❞✉❛❧ P❛✉❧✐st❛ ✏❏ú❧✐♦ ❞❡ ▼❡sq✉✐t❛ ❋✐❧❤♦✑
− ❈❛♠♣✉s ❞❡ ❇❛✉r✉✱ ♣❛r❛ ♦❜t❡♥çã♦ ❞♦ tít✉❧♦ ❞❡
▼❡str❡ ❡♠ ❊♥❣❡♥❤❛r✐❛ ❊❧étr✐❝❛✳
Delgado, Jéssica Antonio.
A combinação dos métodos de barreira e de barreira modificada na resolução do problema de fluxo de potência ótimo reativo / Jéssica Antonio Delgado, 2016 184 f.
Orientador: Edméa Cássia Baptista
Dissertação (Mestrado)–Universidade Estadual Paulista. Faculdade de Engenharia, Bauru, 2016
1. Método de barreira logarítmica. 2. Método de barreira logarítmica modificada. 3. Fluxo de potência ótimo reativo. I. Universidade Estadual Paulista. Faculdade de Engenharia. II. Título.
Pr✐♠❡✐r❛♠❡♥t❡✱ à ❉❡✉s ❛❝✐♠❛ ❞❡ t✉❞♦ ❡ ❞❡ t♦❞♦s✳
➚ ♠✐♥❤❛ ❢❛♠í❧✐❛✱ ❙❛♥②✱ ❘❡♥❛t♦✱ ❏✉♥✐♦r ❡ ▲❛r❛✱ ♣♦r s❡♠♣r❡ ♠❡ ❛♣♦✐❛r❡♠✱ ✐♥❝❡♥t✐✈❛r❡♠ ❡ ❝♦♠♣r❡❡♥❞❡r❡♠ ♠❡✉s ♠♦♠❡♥t♦s ❞❡ ❛✉sê♥❝✐❛✳
➚ ♣r♦❢❡ss♦r❛ ❊❞♠é❛ ❈áss✐❛ ❇❛♣t✐st❛✱ ♣❡❧❛ ♦r✐❡♥t❛çã♦ ❡ ❡♥s✐♥❛♠❡♥t♦s tr❛♥s♠✐t✐❞♦s✱ ❡ ♣♦r t♦❞♦ ❛♣♦✐♦✱ ❛♠✐③❛❞❡ ❡ ❝♦♠♣r❡❡♥sã♦✳ ❯♠❛ ♣❛❧❛✈r❛ ❝❡rt❛✱ ❞✐t❛ ♥♦ ♠♦♠❡♥t♦ ❝❡rt♦✱ ❢❛③ t♦❞❛ ❛ ❞✐❢❡r❡♥ç❛✳
➚ ♣r♦❢❡ss♦r❛ ❙❛♥❞r❛ ❋✐♦r❡❧❧✐ ❞❡ ❆❧♠❡✐❞❛ P❡♥t❡❛❞♦ ❙✐♠❡ã♦✱ ♣♦r ♠❡ ✐♥❝❡♥t✐✈❛r ❞❡s❞❡ ❛ ❣r❛❞✉❛çã♦ ❡ t❛♠❜é♠ ♣♦r ❛❝❡✐t❛r ♦ ❝♦♥✈✐t❡ ♣❛r❛ ♣❛rt✐❝✐♣❛r ❞❛ ❜❛♥❝❛ ❞❡ ❛✈❛❧✐❛çã♦ ❡ ♣❡❧❛s ❝♦♥tr✐❜✉✐çõ❡s ❞❛❞❛s ❛ ❡st❡ tr❛❜❛❧❤♦✳
➚ ♣r♦❢❡ss♦r❛ ❊❞✐❧❛✐♥❡ ▼❛rt✐♥s ❙♦❧❡r ❡ ❛♦ ♣r♦❢❡ss♦r ●❡r❛❧❞♦ ▼❛rt✐♥s ❞❛ ❈♦st❛✱ ♣♦r ❛❝❡✐t❛r❡♠ ♦ ❝♦♥✈✐t❡ ♣❛r❛ ♣❛rt✐❝✐♣❛r ❞❛ ❜❛♥❝❛ ❞❡ ❛✈❛❧✐❛çã♦ ❡ ♣❡❧❛s ❝♦♥tr✐❜✉✐çõ❡s ❞❛❞❛s ❛ ❡st❡ tr❛❜❛❧❤♦✳
❆♦s ♣r♦❢❡ss♦r❡s ▲❡♦♥❛r❞♦ ◆❡♣♦♠✉❝❡♥♦ ❡ ❆♥t♦♥✐♦ ❘♦❜❡rt♦ ❇❛❧❜♦ ♣❡❧♦s ❡♥s✐♥❛♠❡♥t♦s tr❛♥s♠✐t✐❞♦s✱ ♣♦r t♦❞♦ ❛♣♦✐♦✱ ❛♠✐③❛❞❡ ❡ ❝♦♠♣r❡❡♥sã♦✳
❆♦ ♠❡✉ ❣r❛♥❞❡ ❛♠✐❣♦ ❘❛❢❛❡❧ ❖rt✐③✱ ♣❡❧♦ ❝♦♠♣❛♥❤❡✐r✐s♠♦ ♥❛ ✈✐❞❛✳
❆♦s ♣r♦❢❡ss♦r❡s ❞♦ Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❊♥❣❡♥❤❛r✐❛ ❊❧étr✐❝❛✱ ❢✉♥❝✐♦♥ár✐♦s ❞❛ ❙❡çã♦ ❚é❝♥✐❝❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❞❛ ❋❛❝✉❧❞❛❞❡ ❞❡ ❊♥❣❡♥❤❛r✐❛ ❡ ❝♦❧❡❣❛s ❞♦ ▲❖❊❊❙P✳ ➚ ❈♦♦r❞❡♥❛çã♦ ❞❡ ❆♣❡r❢❡✐ç♦❛♠❡♥t♦ ❞❡ P❡ss♦❛❧ ❞❡ ◆í✈❡❧ ❙✉♣❡r✐♦r ✭❈❛♣❡s✮✱ ♣❡❧♦ ❛♣♦✐♦ ✜♥❛♥❝❡✐r♦✳
❆ t♦❞♦s ♦s q✉❡✱ ❞✐r❡t❛ ♦✉ ✐♥❞✐r❡t❛♠❡♥t❡✱ ❡st✐✈❡r❛♠ ❝♦♠✐❣♦ ♥❡st❛ ❝❛♠✐♥❤❛❞❛✳
q✉❡ t❡♠ q✉❡ s❡r✧
❈❤✐❝♦ ❳❛✈✐❡r
❉❊▲●❆❉❖✱❏✳❆✳ ❆ ❈❖▼❇■◆❆➬➹❖ ❉❖❙ ▼➱❚❖❉❖❙ ❉❊ ❇❆❘❘❊■❘❆ ❊ ❉❊ ❇❆❘✲ ❘❊■❘❆ ▼❖❉■❋■❈❆❉❆ ◆❆ ❘❊❙❖▲❯➬➹❖ ❉❖ P❘❖❇▲❊▼❆ ❉❊ ❋▲❯❳❖ ❉❊ P❖❚✃◆✲ ❈■❆ Ó❚■▼❖ ❘❊❆❚■❱❖✳ ✷✵✶✻ ❋❛❝✉❧❞❛❞❡ ❞❡ ❊♥❣❡♥❤❛r✐❛ ❞❡ ❇❛✉r✉✱ ❯◆❊❙P✲❯♥✐✈❡rs✐❞❛❞❡ ❊st❛❞✉❛❧ P❛✉❧✐st❛ ✧❏ú❧✐♦ ❞❡ ▼❡sq✉✐t❛ ❋✐❧❤♦✧✱ ❇❛✉r✉✳
❊st❡ tr❛❜❛❧❤♦ ♣r♦♣õ❡ ✉♠❛ ❛❜♦r❞❛❣❡♠ q✉❡ ✉t✐❧✐③❛ ✉♠❛ ❝♦♠❜✐♥❛çã♦ ❞❡ ♠ét♦❞♦s ❜❛s❡✲ ❛❞♦s ♥❛ ❢✉♥çã♦ ❜❛rr❡✐r❛ ❧♦❣❛rít♠✐❝❛ ❡ ❜❛rr❡✐r❛ ❧♦❣❛rít♠✐❝❛ ♠♦❞✐✜❝❛❞❛ ♣❛r❛ ❛ r❡s♦❧✉çã♦ ❞♦ ♣r♦❜❧❡♠❛ ❞❡ ❋❧✉①♦ ❞❡ P♦tê♥❝✐❛ Ót✐♠♦ ❘❡❛t✐✈♦✳ ◆❛ ❛❜♦r❞❛❣❡♠ ♣r♦♣♦st❛ ❛s r❡str✐çõ❡s ❞❡ ❞❡s✐❣✉❛❧❞❛❞❡ sã♦ tr❛♥s❢♦r♠❛❞❛s ❡♠ ✐❣✉❛❧❞❛❞❡ ✐♥tr♦❞✉③✐♥❞♦ ❛s ✈❛r✐á✈❡✐s ❞❡ ❢♦❧❣❛✱ ❛s q✉❛✐s sã♦ tr❛t❛❞❛s ♣❡❧❛ ❢✉♥çã♦ ❜❛rr❡✐r❛ ❧♦❣❛rít♠✐❝❛ ♦✉ ♣❡❧❛ ❢✉♥çã♦ ❜❛rr❡✐r❛ ❧♦❣❛rít♠✐❝❛ ♠♦❞✐✜❝❛❞❛ ❡ ❛s r❡str✐çõ❡s ❞❡ ✐❣✉❛❧❞❛❞❡ sã♦ tr❛t❛❞❛s ♣❡❧♦s ♠✉❧t✐♣❧✐❝❛❞♦r❡s ❞❡ ▲❛❣r❛♥❣❡✳ ❊st❡s ♠ét♦❞♦s sã♦ ✉t✐❧✐③❛❞♦s ❡♠ ❞✉❛s ❡t❛♣❛s✳ ■♥✐❝✐❛❧♠❡♥t❡ ❛♣❧✐❝❛✲s❡ ♦ ♠ét♦❞♦ ❜❛s❡❛❞♦ ♥❛ ❢✉♥çã♦ ❜❛rr❡✐r❛ ❧♦❣❛rít♠✐❝❛ ❛té q✉❡ ✉♠ ❝r✐tér✐♦ ❞❡ tr❛♥s✐çã♦ s❡❥❛ s❛t✐s❢❡✐t❛✳ ❉❡♣♦✐s ❛♣❧✐❝❛✲s❡ ♦ ♠ét♦❞♦ ❜❛s❡❛❞♦ ♥❛ ❢✉♥çã♦ ❜❛rr❡✐r❛ ❧♦❣❛rít♠✐❝❛ ♠♦❞✐✜❝❛❞❛ ❛té q✉❡ ❛ ❝♦♥❞✐✲ çã♦ ❞❡ ❝♦♥✈❡r❣ê♥❝✐❛ s❡❥❛ s❛t✐s❢❡✐t❛✳ ❚❡st❡s ♥✉♠ér✐❝♦s ✉t✐❧✐③❛♥❞♦ ♦s s✐st❡♠❛s ❡❧étr✐❝♦s ❞❡ ✸ ❜❛rr❛s ❡ ■❊❊❊ ✶✹✱ ✸✵✱ ✺✼ ❡ ✶✶✽ ❜❛rr❛s ✐♥❞✐❝❛♠ q✉❡ ♦ ♠ét♦❞♦ é ❡✜❝✐❡♥t❡ ♥❛ r❡s♦❧✉çã♦ ❞♦ ♣r♦❜❧❡♠❛ ❋❧✉①♦ ❞❡ P♦tê♥❝✐❛ Ót✐♠♦ ❘❡❛t✐✈♦✳ ❯♠❛ ❝♦♠♣❛r❛çã♦ ❞♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ♣❡❧❛ ❛❜♦r❞❛❣❡♠ ♣r♦♣♦st❛ ❝♦♠ ♦s ❞♦s ♠ét♦❞♦s ❞❡ ❜❛rr❡✐r❛ ❧♦❣❛rít♠✐❝❛ ❡ ❞❡ ❜❛rr❡✐r❛ ❧♦❣❛rít♠✐❝❛ ♠♦❞✐✜❝❛❞❛ s❡♣❛r❛❞❛♠❡♥t❡ é r❡❛❧✐③❛❞❛✳
P❛❧❛✈r❛s✲❝❤❛✈❡✿ ♠ét♦❞♦ ❞❡ ❜❛rr❡✐r❛ ❧♦❣❛rít♠✐❝❛❀ ♠ét♦❞♦ ❞❡ ❜❛rr❡✐r❛ ❧♦❣❛rít♠✐❝❛ ♠♦❞✐✜❝❛❞❛❀ ❋❧✉①♦ ❞❡ P♦tê♥❝✐❛ Ót✐♠♦ ❘❡❛t✐✈♦❀ ❙✐st❡♠❛s ❊❧étr✐❝♦s ❞❡ P♦tê♥❝✐❛✳
❉❊▲●❆❉❖✱ ❏✳❆✳ ❚❍❊ ❈❖▼❇■◆❆❚■❖◆ ❖❋ ▼❊❚❍❖❉❙ ❇❆❘❘■❊❘ ❆◆❉ ▼❖❉■✲ ❋■❊❉ ❇❆❘❘■❊❘ ■◆ ❘❊❙❖▲❯❚■❖◆ ❖❋ ❘❊❆❈❚■❱❊ ❖P❚▼❆▲ P❖❲❊❘ ❋▲❖❲ P❘❖✲ ❇▲❊▼✳❋❛❝✉❧❞❛❞❡ ❞❡ ❊♥❣❡♥❤❛r✐❛ ❞❡ ❇❛✉r✉✱ ❯◆❊❙P✲❯♥✐✈❡rs✐❞❛❞❡ ❊st❛❞✉❛❧ P❛✉❧✐st❛ ✧❏ú✲ ❧✐♦ ❞❡ ▼❡sq✉✐t❛ ❋✐❧❤♦✧✱ ❇❛✉r✉✳
❚❤✐s ✇♦r❦ ♣r♦♣♦s❡s ❛♥ ❛♣♣r♦❛❝❤ t❤❛t ✉s❡s ❛ ❝♦♠❜✐♥❛t✐♦♥ ♦❢ ♠❡t❤♦❞s ❜❛s❡❞ ♦♥ ❧♦❣❛✲ r✐t❤♠✐❝ ❜❛rr✐❡r ❢✉♥❝t✐♦♥ ❛♥❞ ♠♦❞✐✜❡❞ ❧♦❣❛r✐t❤♠✐❝ ❜❛rr✐❡r ❢✉♥❝t✐♦♥ ❢♦r t❤❡ r❡s♦❧✉t✐♦♥ ♦❢ t❤❡ r❡❛❝t✐✈❡ ♦♣t✐♠❛❧ ♣♦✇❡r ✢♦✇ ♣r♦❜❧❡♠✳ ■♥ t❤✐s ♣r♦♣♦s❡❞ ❛♣♣r♦❛❝❤ t❤❡ ✐♥❡q✉❛❧✐t② ❝♦♥s✲ tr❛✐♥ts ❛r❡ tr❛♥s❢♦r♠❡❞ ✐♥t♦ ❡q✉❛❧✐t✐❡s ❜② ❛❞❞✐♥❣ t❤❡ s❧❛❝❦ ✈❛r✐❛❜❧❡s✱ ✇❤✐❝❤ ❛r❡ ❤❛♥❞❧❡❞ ❜② ❧♦❣❛r✐t❤♠✐❝ ❜❛rr✐❡r ❢✉♥❝t✐♦♥ ♦r ♠♦❞✐✜❡❞ ❧♦❣❛r✐t❤♠✐❝ ❜❛rr✐❡r ❢✉♥❝t✐♦♥✱ ❛♥❞ t❤❡ ❡q✉❛❧✐t② ❝♦♥str❛✐♥ts ❛r❡ ❤❛♥❞❧❡❞ ❜② ♠❡❛♥s ♦❢ ▲❛❣r❛♥❣❡ ♠✉❧t✐♣❧✐❡rs✳ ❚❤❡s❡ ♠❡t❤♦❞s ❛r❡ ✉s❡❞ ✐♥ t✇♦ st❡♣s✳ ■♥✐t✐❛❧❧②✱ t❤❡ ♠❡t❤♦❞ ❜❛s❡❞ ♦♥ t❤❡ ❧♦❣❛r✐t❤♠✐❝ ❜❛rr✐❡r ❢✉♥❝t✐♦♥ ✐s ❛♣♣❧✐❡❞ ✉♥t✐❧ t❤❡ st♦♣ ❝♦♥❞✐t✐♦♥ ✐s s❛t✐s✜❡❞✳ ❆❢t❡r t❤❡ ♠❡t❤♦❞ ❜❛s❡❞ ♦♥ ♠♦❞✐✜❡❞ ❧♦❣❛r✐t❤♠✐❝ ❜❛rr✐❡r ❢✉♥❝t✐♦♥ ✐s ✉s❡❞ ✉♥t✐❧ t❤❡ ❝♦♥✈❡r❣❡♥❝❡ ❝♦♥❞✐t✐♦♥ ✐s s❛t✐s✜❡❞✳ ◆✉♠❡r✐❝❛❧ t❡sts ❝❛rr✐❡❞ ♦✉t ✇✐t❤ t❤❡ ✸ ❜✉s✱ ■❊❊❊ ✶✹✱ ✸✵✱ ✺✼ ❛♥❞ ✶✶✽ ❜✉s ❡❧❡❝tr✐❝❛❧ s②st❡♠s ✐♥❞✐❝❛t❡ t❤❛t t❤❡ ♣r♦♣♦s❡❞ ❛♣♣r♦❛❝❤ ✐s ❡✣❝✐❡♥t ✐♥ t❤❡ r❡s♦❧✉t✐♦♥ ♦❢ t❤❡ r❡❛❝t✐✈❡ ♦♣t✐♠❛❧ ♣♦✇❡r ✢♦✇ ♣r♦❜❧❡♠✳ ❚❤❡ r❡s✉❧ts ♦❜t❛✐♥❡❞ ❜② t❤❡ ♣r♦♣♦s❡❞ ❛♣♣r♦❛❝❤ ✇❡r❡ ❝♦♠♣❛r❡❞ ✇✐t❤ t❤❡ ❧♦❣❛r✐t❤♠✐❝ ❜❛rr✐❡r ♠❡t❤♦❞ ❛♥❞ t❤❡ ❧♦❣❛r✐t❤♠✐❝ ❜❛rr✐❡r ♠❡t❤♦❞ ♠♦❞✐✜❡❞✱ s❡♣❛r❛t❡❧②✳
❑❡②✲✇♦r❞s✿ ❧♦❣❛r✐t❤♠✐❝ ❜❛rr✐❡r ♠❡t❤♦❞❀ ♠♦❞✐✜❡❞ ❧♦❣❛r✐t❤♠✐❝ ❜❛rr✐❡r ♠❡t❤♦❞❀ ❖♣t✐✲ ♠❛❧ P♦✇❡r ❋❧♦✇ ❘❡❛❝t✐✈❡❀ ❊❧❡❝tr✐❝❛❧ P♦✇❡r ❙②st❡♠✳
f(x)✿ ❢✉♥çã♦ ♦❜❥❡t✐✈♦❀
g(x)✿ ✈❡t♦r ❞❛s r❡str✐çõ❡s ❞❡ ✐❣✉❛❧❞❛❞❡❀
h(x)✿ ✈❡t♦r ❞❛s r❡str✐çõ❡s ❞❡ ❞❡s✐❣✉❛❧❞❛❞❡❀
x✿ ✈❛r✐á✈❡❧ ♣r✐♠❛❧❀
R✿ ❝♦♥❥✉♥t♦s ❞♦s ♥ú♠❡r♦s r❡❛✐s❀ ▲✿ ❢✉♥çã♦ ▲❛❣r❛♥❣✐❛♥❛❀
π e λ✿ ♠✉❧t✐♣❧✐❝❛❞♦r❡s ❞❡ ▲❛❣r❛♥❣❡❀
β✿ ❛t✉❛❧✐③❛❞♦r ❞♦ ♣❛râ♠❡tr♦ ❞❡ ❜❛rr❡✐r❛ ❧♦❣❛rít♠✐❝❛❀
❋▲❇▲▼✿ ❢✉♥çã♦ ▲❛❣r❛♥❣✐❛♥❛ ❜❛rr❡✐r❛ ❧♦❣❛rít♠✐❝❛ ♠♦❞✐✜❝❛❞❛❀ ❋▲❇▲✿ ❢✉♥çã♦ ▲❛❣r❛♥❣✐❛♥❛ ❜❛rr❡✐r❛ ❧♦❣❛rít♠✐❝❛❀
s1, s2, s3✿ ✈❛r✐á✈❡✐s ❞❡ ❢♦❧❣❛❀
∇✿ ✈❡t♦r ❣r❛❞✐❡♥t❡❀
∇x✿ ✈❡t♦r ❣r❛❞✐❡♥t❡ ❡♠ r❡❧❛çã♦ à ①❀
∈✿ ♣❡rt❡♥❝❡ à❀
min✿ ♠✐♥✐♠✐③❛r❀
∆d✿ ✈❡t♦r ❞❛s ❞✐r❡çõ❡s❀ B(x)✿ ❢✉♥çã♦ ❜❛rr❡✐r❛❀
ψ✿ ❢✉♥çã♦ ❞❡ ✉♠❛ ✈❛r✐á✈❡❧ r❡❧❛❝✐♦♥❛❞❛ à ❢✉♥çã♦ ❜❛rr❡✐r❛❀
f(x)✿ ❢✉♥çã♦ ♦❜❥❡t✐✈♦❀
❋❇❆✿ ❢✉♥çã♦ ❛✉①✐❧✐❛r r❡❧❛❝✐♦♥❛❞❛ à ❜❛rr❡✐r❛❀
µ✿ ♣❛râ♠❡tr♦ ❞❡ ❜❛rr❡✐r❛❀ ω✿ ❢✉♥çã♦ ❜❛rr❡✐r❛ ❧♦❣❛rít♠✐❝❛❀
Γ✿ ❢✉♥çã♦ ❜❛rr❡✐r❛ ❧♦❣❛rít♠✐❝❛ ♠♦❞✐✜❝❛❞❛❀
Jg(x)✿ ♠❛tr✐③❡s ❏❛❝♦❜✐❛♥❛s ❞❛s r❡str✐çõ❡s ❞❡ ✐❣✉❛❧❞❛❞❡❀
Jh(x)✿ ♠❛tr✐③❡s ❏❛❝♦❜✐❛♥❛s ❞❛s r❡str✐çõ❡s ❞❡ ❞❡s✐❣✉❛❧❞❛❞❡❀
❲✿ ♠❛tr✐③ ❍❡ss✐❛♥❛ ❞❛ ❢✉♥çã♦ ❜❛rr❡✐r❛ ❧♦❣❛rít♠✐❝❛❀
W1✿ ♠❛tr✐③ ❍❡ss✐❛♥❛ ❞❛ ❢✉♥çã♦ ❜❛rr❡✐r❛ ❧♦❣❛rít♠✐❝❛ ♠♦❞✐✜❝❛❞❛❀
αp✿ ♣❛ss♦ ♣r✐♠❛❧❀
αd✿ ♣❛ss♦ ❞✉❛❧❀
u✿ ✈❡t♦r ❞♦s ❡st✐♠❛❞♦r❡s ❞♦s ♠✉❧t✐♣❧✐❝❛❞♦r❡s ❞❡ ▲❛❣r❛♥❣❡❀ ε✿ t♦❧❡râ♥❝✐❛❀
❱✿ ✈❡t♦r ❞❛s ♠❛❣♥✐t✉❞❡s ❞❛s t❡♥sõ❡s❀t♦❧❡râ♥❝✐❛❀
θ✿ ✈❡t♦r ❞♦s â♥❣✉❧♦s ❞❛s t❡♥sõ❡s❀
t❛♣✿ ✈❡t♦r ❞♦s t❛♣s ❞♦s tr❛♥s❢♦r♠❛❞♦r❡s❀
P✿ ♣♦tê♥❝✐❛ ❛t✐✈❛❀
◗✿ ♣♦tê♥❝✐❛ r❡❛t✐✈❛❀
Qmin
l ✿ ❧✐♠✐t❡s ♠í♥✐♠♦s ❞❡ ❣❡r❛çã♦ ❞❡ ♣♦tê♥❝✐❛ r❡❛t✐✈❛ ♥❛ ❜❛rr❛ l❀
Qmax
l ✿ ❧✐♠✐t❡s ♠á①✐♠♦s ❞❡ ❣❡r❛çã♦ ❞❡ ♣♦tê♥❝✐❛ r❡❛t✐✈❛ ♥❛ ❜❛rr❛l❀
Vmin
k ✿ ❧✐♠✐t❡s ♠í♥✐♠♦s ❞❛s ♠❛❣♥✐t✉❞❡s ❞❛ t❡♥sã♦ ♥❛ ❜❛rr❛k❀
Vmax
k ✿ ❧✐♠✐t❡s ♠á①✐♠♦s ❞❛s ♠❛❣♥✐t✉❞❡s ❞❛ t❡♥sã♦ ♥❛ ❜❛rr❛ k❀
tapmin
o ✿ ❧✐♠✐t❡s ♠í♥✐♠♦s ❞♦s t❛♣s ❞♦ tr❛♥s❢♦r♠❛❞♦r ♥❛ ❜❛rr❛o❀
tapmax
o ✿ ❧✐♠✐t❡s ♠á①✐♠♦s ❞♦s t❛♣s ❞♦ tr❛♥s❢♦r♠❛❞♦r ♥❛ ❜❛rr❛ o❀
PC
i ✿ ♣♦tê♥❝✐❛ ❛t✐✈❛ ❝♦♥s✉♠✐❞❛ ♥❛ ❜❛rr❛ i❀
PG
i ✿ ♣♦tê♥❝✐❛ ❛t✐✈❛ ❣❡r❛❞❛ ♥❛ ❜❛rr❛ i❀
bim✿ ❛ s✉s❝❡♣tâ♥❝✐❛ ❞❛ ❧✐♥❤❛ im❀
gim✿ é ❛ ❝♦♥❞✉tâ♥❝✐❛ ❞❛ ❧✐♥❤❛ im❀
QC
j ✿ ❛ ♣♦tê♥❝✐❛ r❡❛t✐✈❛ ❝♦♥s✉♠✐❞❛ ♥❛ ❜❛rr❛ j❀
QG
j ✿ ❛ ♣♦tê♥❝✐❛ r❡❛t✐✈❛ ❣❡r❛❞❛ ♥❛ ❜❛rr❛ j❀
bsh
jm✿ ❛ s✉s❝❡♣tâ♥❝✐❛ s❤✉♥t ❞❛ ❧✐♥❤❛ jm❀
bsh
j ✿ ❛ s✉s❝❡♣tâ♥❝✐❛ s❤✉♥t ❞❛ ❜❛rr❛ j❀
ϑi✿ é ♦ ❝♦♥❥✉♥t♦ ❞❛s ❜❛rr❛s ✈✐③✐♥❤❛s ❛ ❜❛rr❛ i✳
❋P❖✿ ❋❧✉①♦ ❞❡ P♦tê♥❝✐❛ Ót✐♠♦❀
❋P❖❘✿ ❋❧✉①♦ ❞❡ P♦tê♥❝✐❛ Ót✐♠♦ ❘❡❛t✐✈♦❀ ▼❇▲✿ ♠ét♦❞♦ ❞❡ ❜❛rr❡✐r❛ ❧♦❣❛rít♠✐❝❛❀
▼❇▲▼✿ ♠ét♦❞♦ ❞❡ ❜❛rr❡✐r❛ ❧♦❣❛rít♠✐❝❛ ♠♦❞✐✜❝❛❞❛❀ ❑❑❚✿ ❑r✉s❤✲❑✉❤♥✲❚✉❝❦❡r❀
■P❖P❚✿ ■♥t❡r✐♦r P♦✐♥t ❖♣t✐♠❡③❡r ▼P■✿ ♠ét♦❞♦ ❞❡ ♣♦♥t♦s ✐♥t❡r✐♦r❡s❀ P◗✿ ♣r♦❣r❛♠❛çã♦ q✉❛❞rát✐❝❛❀ P▲✿ ♣r♦❣r❛♠❛çã♦ ❧✐♥❡❛r❀
❈❖P❙✿ ❝♦♥str❛✐♥❡❞ ♦♣t✐♠✐③❛t✐♦♥ ♣r♦❜❧❡♠s❀
❈❯❚❊✿ ❝♦♥str❛✐♥❡❞ ❛♥❞ ✉♥❝♦♥str❛✐♥❡❞ t❡st✐♥❣ ❡♥✈✐r♦♥♠❡♥t❀
❈❯❚❊❘✿ ❝♦♥str❛✐♥❡❞ ❛♥❞ ✉♥❝♦♥str❛✐♥❡❞ t❡st✐♥❣ ❡♥✈✐r♦♥♠❡♥t r❡✈✐s✐t❡❞❀ ▼❇▼✿ ♠ét♦❞♦ ❞❡ ❜❛rr❡✐r❛ ♠♦❞✐✜❝❛❞❛❀
❋❇❈✿ ❢✉♥çã♦ ❜❛rr❡✐r❛ ❝❧áss✐❝❛❀ ❋❇▼✿ ❢✉♥çã♦ ❜❛rr❡✐r❛ ♠♦❞✐✜❝❛❞❛❀ ❋▲❈✿ ❢✉♥çã♦ ▲❛❣r❛♥❣✐❛♥❛ ❝❧áss✐❝❛❀
P❉P❊✿ ♠ét♦❞♦ ♣r✐♠❛❧✲❞✉❛❧ ❞❡ ♣♦♥t♦ ❡①t❡r✐♦r❀ ▼P❊✿ ♠ét♦❞♦ ❞❡ ♣♦♥t♦ ❡①t❡r✐♦r❀
❚▲✿ tr❛♥s❢♦r♠❛çã♦ ▲❛❣r❛♥❣✐❛♥❛❀ ▼❉❊■✿ ♠ét♦❞♦ ❞✉❛❧ ❞❡ ❡❧✐♣só✐❞❡ ✐♥t❡r✐♦r❀ ❉❊✿ ❞❡s♣❛❝❤♦ ❡❝♦♥ô♠✐❝♦❀
▼❈❈✿ ♠ú❧t✐♣❧❛s ❝♦rr❡çõ❡s ❝❡♥tr❛❧✐③❛❞❛s❀ P❉P✿ ♣r✐♠❛❧✲❞✉❛❧ ♣✉r♦❀
P❉P❈✿ ♣r✐♠❛❧✲❞✉❛❧ ♣r❡✈✐s♦r✲❝♦rr❡t♦r❀
■❊❊❊✿ ■♥st✐t✉t❡ ♦❢ ❊❧❡❝tr✐❝❛❧ ❛♥❞ ❊❧❡❝tr♦♥✐❝s ❊♥❣✐♥❡❡rs❀ ❇▼P❈✿ ❜❛rr❡✐r❛ ♠♦❞✐✜❝❛❞❛ ♣r❡✈✐s♦r✲❝♦rr❡t♦r❀
❆●❆▲✿ ❛❧❣♦r✐t♠♦ ❣❡♥ét✐❝♦ ❛❞❛♣t❛t✐✈♦ ❧✐♥❡❛r❀ P❉❇▲✿ ♣r✐♠❛❧✲❞✉❛❧ ❜❛rr❡✐r❛ ❧♦❣❛rít♠✐❝❛❀
❋▲❇▲▼✿ ❢✉♥çã♦ ▲❛❣r❛♥❣✐❛♥❛ ❜❛rr❡✐r❛ ❧♦❣❛rít♠✐❝❛ ♠♦❞✐✜❝❛❞❛❀
▲❖❊❙P✿ ❧❛❜♦r❛tór✐♦ ❞❡ ♦t✐♠✐③❛çã♦ ❞❡ ❡st✉❞♦s ❡❝♦♥ô♠✐❝♦s ❡ ❞❡ ♣♦tê♥❝✐❛❀
▼❲✿ ♠❡❣❛✇❛tts❀
P❉❇▲❇▲▼✿ ♦ ♠ét♦❞♦ ♣r✐♠❛❧✲❞✉❛❧ ❜❛rr❡✐r❛ ❧♦❣❛rít♠✐❝❛ ❡ ❜❛rr❡✐r❛ ❧♦❣❛rít♠✐❝❛ ♠♦❞✐✜✲ ❝❛❞❛✳
✶ ■♥tr♦❞✉çã♦ ✶
✷ ❍✐stór✐❝♦ ✺
✷✳✶ ❍✐stór✐❝♦ ❞♦ ♠ét♦❞♦ ❞❡ ❜❛rr❡✐r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺ ✷✳✷ ❍✐stór✐❝♦ ❞♦ ♠ét♦❞♦ ❜❛rr❡✐r❛ ♠♦❞✐✜❝❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸ ✷✳✸ ❍✐stór✐❝♦ ❞♦ ♣r♦❜❧❡♠❛ ❞❡ ✢✉①♦ ❞❡ ♣♦tê♥❝✐❛ ót✐♠♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺
✸ ❘❡✈✐sã♦ ❞❡ ♠ét♦❞♦s ❞❡ ♦t✐♠✐③❛çã♦ ✷✺
✸✳✶ ❖ ♠ét♦❞♦ ❞✉❛❧✲▲❛❣r❛♥❣✐❛♥♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✸✳✶✳✶ ❆❧❣♦r✐t♠♦ ❞✉❛❧✲▲❛❣r❛♥❣✐❛♥♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✸✳✶✳✷ ❉✐✜❝✉❧❞❛❞❡s ❝♦♠♣✉t❛❝✐♦♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✸✳✷ ❖ ♠ét♦❞♦ ❞❡ ❜❛rr❡✐r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✸✳✷✳✶ ❆❧❣♦r✐t♠♦ ❞♦ ♠ét♦❞♦ ❞❡ ❜❛rr❡✐r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾ ✸✳✷✳✷ ❖ ♠ét♦❞♦ ♣r✐♠❛❧✲❞✉❛❧ ❜❛rr❡✐r❛ ❧♦❣❛rít♠✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾ ✸✳✷✳✸ ❆❧❣♦r✐t♠♦ ♣r✐♠❛❧✲❞✉❛❧ ❜❛rr❡✐r❛ ❧♦❣❛rít♠✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✸✳✷✳✹ ❉✐✜❝✉❧❞❛❞❡s ❝♦♠♣✉t❛❝✐♦♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✸✳✸ ❖ ♠ét♦❞♦ ❞❡ ❜❛rr❡✐r❛ ♠♦❞✐✜❝❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ✸✳✸✳✶ ❆❧❣♦r✐t♠♦ ❞♦ ♠ét♦❞♦ ❞❡ ❜❛rr❡✐r❛ ♠♦❞✐✜❝❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✸✳✸✳✷ ❖ ♠ét♦❞♦ ❞❛ ❢✉♥çã♦ ▲❛❣r❛♥❣✐❛♥❛ ❜❛rr❡✐r❛ ❧♦❣❛rít♠✐❝❛ ♠♦❞✐✜❝❛❞❛ ✳ ✸✼ ✸✳✸✳✸ ❖ ❆❧❣♦r✐t♠♦ ❞♦ ♠ét♦❞♦ ❞❛ ❢✉♥çã♦ ▲❛❣r❛♥❣✐❛♥❛ ❜❛rr❡✐r❛ ❧♦❣❛rít♠✐❝❛
♠♦❞✐✜❝❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✸✳✸✳✹ ❉✐✜❝✉❧❞❛❞❡s ❝♦♠♣✉t❛❝✐♦♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷
✹ ❖ ♠ét♦❞♦ ♣r✐♠❛❧✲❞✉❛❧ ❜❛rr❡✐r❛ ❧♦❣❛rít♠✐❝❛ ❡ ❜❛rr❡✐r❛ ❧♦❣❛rít♠✐❝❛ ♠♦✲
❞✐✜❝❛❞❛ ✹✸
✹✳✶ ■♥tr♦❞✉çã♦ ❡ ♠♦t✐✈❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✹✳✷ ❖ ❛❧❣♦r✐t♠♦ ❞♦ ♠ét♦❞♦ P❉❇▲❇▲▼ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹ ✹✳✸ ❖ ❡①❡♠♣❧♦ ♥✉♠ér✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺ ✹✳✸✳✶ ❘❡s♦❧✉çã♦ ❞♦ ❡①❡♠♣❧♦ ♥✉♠ér✐❝♦ ❝♦♠ ♦ ♠ét♦❞♦ P❉❇▲ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻ ✹✳✸✳✷ ❘❡s♦❧✉çã♦ ❞♦ ❡①❡♠♣❧♦ ♥✉♠ér✐❝♦ ❝♦♠ ♦ ♠ét♦❞♦ ❞❛ ❋▲❇▲▼ ✳ ✳ ✳ ✳ ✳ ✹✽ ✹✳✸✳✸ ❘❡s♦❧✉çã♦ ❞♦ ❡①❡♠♣❧♦ ♥✉♠ér✐❝♦ ❝♦♠ ♦ ♠ét♦❞♦ P❉❇▲❇▲▼ ✳ ✳ ✳ ✳ ✳ ✺✶
✺ ❖ ♣r♦❜❧❡♠❛ ❞❡ ❋❧✉①♦ ❞❡ P♦tê♥❝✐❛ Ót✐♠♦ ❘❡❛t✐✈♦ ✺✺
✺✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺ ✺✳✷ ❋♦r♠✉❧❛çã♦ ♠❛t❡♠át✐❝❛ ❞♦ ♣r♦❜❧❡♠❛ ❋P❖❘ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻ ✺✳✸ ❋✉♥çã♦ ♦❜❥❡t✐✈♦ ❞♦ ❋P❖❘ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽ ✺✳✹ ❘❡str✐çõ❡s ❞❡ ✐❣✉❛❧❞❛❞❡ ❞♦ ❋P❖❘ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽ ✺✳✺ ❘❡str✐çõ❡s ❞❡ ❞❡s✐❣✉❛❧❞❛❞❡ ❞♦ ❋P❖❘ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵ ✺✳✻ ❆ ❢✉♥çã♦ ▲❛❣r❛♥❣✐❛♥❛ ❜❛rr❡✐r❛ ❧♦❣❛rít♠✐❝❛ ❛ss♦❝✐❛❞❛ ❛♦ ♣r♦❜❧❡♠❛ ❞❡ ❋P❖❘ ✻✵ ✺✳✼ ❆ ❢✉♥çã♦ ▲❛❣r❛♥❣✐❛♥❛ ❜❛rr❡✐r❛ ❧♦❣❛rít♠✐❝❛ ♠♦❞✐✜❝❛❞❛ ❛ss♦❝✐❛❞❛ ❛♦ ♣r♦✲
❜❧❡♠❛ ❞❡ ❋P❖❘ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷ ✺✳✽ ❖ ♠ét♦❞♦ ♣r✐♠❛❧✲❞✉❛❧ ❜❛rr❡✐r❛ ❧♦❣❛rít♠✐❝❛ ❛♣❧✐❝❛❞♦ ❛♦ ♣r♦❜❧❡♠❛ ❞❡ ❋P❖❘ ✻✹ ✺✳✾ ❖ ♠ét♦❞♦ ❞❛ ❢✉♥çã♦ ▲❛❣r❛♥❣✐❛♥❛ ❜❛rr❡✐r❛ ❧♦❣❛rít♠✐❝❛ ♠♦❞✐✜❝❛❞❛ ❛♣❧✐❝❛❞♦
❛♦ ♣r♦❜❧❡♠❛ ❞❡ ❋P❖❘ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺ ✺✳✶✵ ❖ ♠ét♦❞♦ P❉❇▲❇▲▼ ❛♣❧✐❝❛❞♦ ❛♦ Pr♦❜❧❡♠❛ ❞❡ ❋P❖❘ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺
✻ ❘❡s✉❧t❛❞♦s ♥✉♠ér✐❝♦s ✻✼
✻✳✶ ❖ s✐st❡♠❛ ✸ ❜❛rr❛s ✭♣❛rt❡ ✶✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽ ✻✳✷ ❖ s✐st❡♠❛ ✸ ❜❛rr❛s ✭♣❛rt❡ ✷✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹ ✻✳✸ ❖ s✐st❡♠❛ ■❊❊❊ ✶✹ ❜❛rr❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✾ ✻✳✹ ❖ s✐st❡♠❛ ■❊❊❊ ✸✵ ❜❛rr❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✺ ✻✳✺ ❖ s✐st❡♠❛ ■❊❊❊ ✺✼ ❜❛rr❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✶ ✻✳✻ ❖ s✐st❡♠❛ ■❊❊❊ ✶✶✽ ❜❛rr❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✼
✼ ❈♦♥❝❧✉sõ❡s ✶✵✺
✼✳✶ ❚r❛❜❛❧❤♦s ❢✉t✉r♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✻ ✼✳✷ ❚r❛❜❛❧❤♦s ♣✉❜❧✐❝❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✻
❇✐❜❧✐♦❣r❛✜❛ ✶✵✼
❆ ❙♦❧✉çõ❡s ót✐♠❛s ♣❛r❛ ♦s s✐st❡♠❛s ❡❧étr✐❝♦s ✶✶✾
❆✳✶ ❙♦❧✉çõ❡s ót✐♠❛s ♣❛r❛ ♦ s✐st❡♠❛ ✸ ❜❛rr❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✾ ❆✳✶✳✶ ❙♦❧✉çõ❡s ót✐♠❛s ♣❛r❛ ♦ s✐st❡♠❛ ✸ ❜❛rr❛s ✭♣❛rt❡ ✶✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✾ ❆✳✶✳✷ ❙♦❧✉çõ❡s ót✐♠❛s ♣❛r❛ ♦ s✐st❡♠❛ ✸ ❜❛rr❛s ✭♣❛rt❡ ✷✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✵ ❆✳✷ ❙♦❧✉çõ❡s ót✐♠❛s ♣❛r❛ ♦ s✐st❡♠❛ ❡❧étr✐❝♦ ■❊❊❊ ✶✹ ❜❛rr❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✶ ❆✳✸ ❙♦❧✉çõ❡s ót✐♠❛s ♣❛r❛ ♦ s✐st❡♠❛ ❡❧étr✐❝♦ ■❊❊❊ ✸✵ ❜❛rr❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✹ ❆✳✹ ❙♦❧✉çõ❡s ót✐♠❛s ♣❛r❛ ♦ s✐st❡♠❛ ❡❧étr✐❝♦ ■❊❊❊ ✺✼ ❜❛rr❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✽ ❆✳✺ ❙♦❧✉çõ❡s ót✐♠❛s ♣❛r❛ ♦ s✐st❡♠❛ ❡❧étr✐❝♦ ■❊❊❊ ✶✶✽ ❜❛rr❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✻
✹✳✶ ❆ ❝♦♥✈❡r❣ê♥❝✐❛ ❞♦ ❡①❡♠♣❧♦ ♥✉♠ér✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷ ✹✳✷ ❆♠♣❧✐❛çã♦ ❞❛ ❝♦♥✈❡r❣ê♥❝✐❛ ❞♦ ❡①❡♠♣❧♦ ♥✉♠ér✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ✻✳✶ ❖ ❙✐st❡♠❛ ✸ ❜❛rr❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽ ✻✳✷ ▼❛❣♥✐t✉❞❡s ❞❛s t❡♥sõ❡s ✜♥❛✐s ♥❛s ✸ ❜❛rr❛s ✭♣❛rt❡✶✮ ❞♦ s✐st❡♠❛ ♣❛r❛ ♦
♠ét♦❞♦ P❉❇▲ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸ ✻✳✸ ▼❛❣♥✐t✉❞❡s ❞❛s t❡♥sõ❡s ✜♥❛✐s ♥❛s ✸ ❜❛rr❛s ✭♣❛rt❡✶✮ ❞♦ s✐st❡♠❛ ♣❛r❛ ♦
♠ét♦❞♦ ❞❛ ❋▲❇▲▼ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸ ✻✳✹ ▼❛❣♥✐t✉❞❡s ❞❛s t❡♥sõ❡s ✜♥❛✐s ♥❛s ✸ ❜❛rr❛s ✭♣❛rt❡✶✮ ❞♦ s✐st❡♠❛ ♣❛r❛ ♦
♠ét♦❞♦ P❉❇▲❇▲▼ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹ ✻✳✺ ▼❛❣♥✐t✉❞❡s ❞❛s t❡♥sõ❡s ✜♥❛✐s ♥❛s ✸ ❜❛rr❛s ✭♣❛rt❡✷✮ ❞♦ s✐st❡♠❛ ♣❛r❛ ♦
♠ét♦❞♦ P❉❇▲ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✼ ✻✳✻ ▼❛❣♥✐t✉❞❡s ❞❛s t❡♥sõ❡s ✜♥❛✐s ♥❛s ✸ ❜❛rr❛s ✭♣❛rt❡✷✮ ❞♦ s✐st❡♠❛ ♣❛r❛ ♦
♠ét♦❞♦ ❞❛ ❋▲❇▲▼ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✼ ✻✳✼ ▼❛❣♥✐t✉❞❡s ❞❛s t❡♥sõ❡s ✜♥❛✐s ♥❛s ✸ ❜❛rr❛s ✭♣❛rt❡✷✮ ❞♦ s✐st❡♠❛ ♣❛r❛ ♦
♠ét♦❞♦ P❉❇▲❇▲▼ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✽ ✻✳✽ ❖ s✐st❡♠❛ ❡❧étr✐❝♦ ■❊❊❊ ✶✹ ❜❛rr❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✾ ✻✳✾ ▼❛❣♥✐t✉❞❡s ❞❛s t❡♥sõ❡s ✜♥❛✐s ♥❛s ✶✹ ❜❛rr❛s ❞♦ s✐st❡♠❛ ♣❛r❛ ♦ ♠ét♦❞♦ P❉❇▲ ✽✸ ✻✳✶✵ ▼❛❣♥✐t✉❞❡s ❞❛s t❡♥sõ❡s ✜♥❛✐s ♥❛s ✶✹ ❜❛rr❛s ❞♦ s✐st❡♠❛ ♣❛r❛ ♦ ♠ét♦❞♦ ❞❛
❋▲❇▲▼ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✸ ✻✳✶✶ ▼❛❣♥✐t✉❞❡s ❞❛s t❡♥sõ❡s ✜♥❛✐s ♥❛s ✶✹ ❜❛rr❛s ❞♦ s✐st❡♠❛ ♣❛r❛ ♦ ♠ét♦❞♦
P❉❇▲❇▲▼ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✹ ✻✳✶✷ ❖ s✐st❡♠❛ ■❊❊❊ ✸✵ ❜❛rr❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✺
✻✳✶✸ ▼❛❣♥✐t✉❞❡s ❞❛s t❡♥sõ❡s ✜♥❛✐s ♥❛s ✸✵ ❜❛rr❛s ❞♦ s✐st❡♠❛ ♣❛r❛ ♦ ♠ét♦❞♦ P❉❇▲ ✽✾ ✻✳✶✹ ▼❛❣♥✐t✉❞❡s ❞❛s t❡♥sõ❡s ✜♥❛✐s ♥❛s ✸✵ ❜❛rr❛s ❞♦ s✐st❡♠❛ ♣❛r❛ ♦ ♠ét♦❞♦ ❞❛
❋▲❇▲▼ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✾ ✻✳✶✺ ▼❛❣♥✐t✉❞❡s ❞❛s t❡♥sõ❡s ✜♥❛✐s ♥❛s ✸✵ ❜❛rr❛s ❞♦ s✐st❡♠❛ ♣❛r❛ ♦ ♠ét♦❞♦
P❉❇▲❇▲▼ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✵ ✻✳✶✻ ❖ s✐st❡♠❛ ■❊❊❊ ✺✼ ❜❛rr❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✶ ✻✳✶✼ ▼❛❣♥✐t✉❞❡s ❞❛s t❡♥sõ❡s ✜♥❛✐s ♥❛s ✺✼ ❜❛rr❛s ❞♦ s✐st❡♠❛ ♣❛r❛ ♦ ♠ét♦❞♦ P❉❇▲ ✾✺ ✻✳✶✽ ▼❛❣♥✐t✉❞❡s ❞❛s t❡♥sõ❡s ✜♥❛✐s ♥❛s ✺✼ ❜❛rr❛s ❞♦ s✐st❡♠❛ ♣❛r❛ ♦ ♠ét♦❞♦ ❞❛
❋▲❇▲▼ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✺ ✻✳✶✾ ▼❛❣♥✐t✉❞❡s ❞❛s t❡♥sõ❡s ✜♥❛✐s ♥❛s ✺✼ ❜❛rr❛s ❞♦ s✐st❡♠❛ ♣❛r❛ ♦ ♠ét♦❞♦
P❉❇▲❇▲▼ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✻ ✻✳✷✵ ❖ s✐st❡♠❛ ■❊❊❊ ✶✶✽ ❜❛rr❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✽ ✻✳✷✶ ▼❛❣♥✐t✉❞❡s ❞❛s t❡♥sõ❡s ✜♥❛✐s ♥❛s ✶✶✽ ❜❛rr❛s ❞♦ s✐st❡♠❛ ♣❛r❛ ♦ ♠ét♦❞♦
P❉❇▲ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✷ ✻✳✷✷ ▼❛❣♥✐t✉❞❡s ❞❛s t❡♥sõ❡s ✜♥❛✐s ♥❛s ✶✶✽ ❜❛rr❛s ❞♦ s✐st❡♠❛ ♣❛r❛ ♦ ♠ét♦❞♦ ❞❛
❋▲❇▲▼ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✸ ✻✳✷✸ ▼❛❣♥✐t✉❞❡s ❞❛s t❡♥sõ❡s ✜♥❛✐s ♥❛s ✶✶✽ ❜❛rr❛s ❞♦ s✐st❡♠❛ ♣❛r❛ ♦ ♠ét♦❞♦
P❉❇▲❇▲▼ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✹
✹✳✶ ❈♦♥✈❡r❣ê♥❝✐❛ ❞♦ ♠ét♦❞♦ P❉❇▲ ♣❛r❛ ♣r♦❜❧❡♠❛ ✹✳✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ✹✳✷ ❈♦♥✈❡r❣ê♥❝✐❛ ❞♦ ♠ét♦❞♦ ❞❛ ❋▲❇▲▼ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ✹✳✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶ ✹✳✸ ❈♦♥✈❡r❣ê♥❝✐❛ ❞♦ ♠ét♦❞♦ P❉❇▲❇▲▼ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ✹✳✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶
✻✳✶ Pr♦❝❡ss♦ ❞❡ ❝♦♥✈❡r❣ê♥❝✐❛ ❞♦ ♠ét♦❞♦ P❉❇▲ ♣❛r❛ ♦ s✐st❡♠❛ ✸ ❜❛rr❛s ✭♣❛rt❡✶✮✳ ✼✶ ✻✳✷ Pr♦❝❡ss♦ ❞❡ ❝♦♥✈❡r❣ê♥❝✐❛ ❞♦ ♠ét♦❞♦ ❞❛ ❋▲❇▲▼ ♣❛r❛ ♦ s✐st❡♠❛ ✸ ❜❛rr❛s
✭♣❛rt❡✶✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶ ✻✳✸ Pr♦❝❡ss♦ ❞❡ ❝♦♥✈❡r❣ê♥❝✐❛ ❞♦ ♠ét♦❞♦ P❉❇▲❇▲▼ ♣❛r❛ ♦ s✐st❡♠❛ ✸ ❜❛rr❛s
✭♣❛rt❡✶✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷ ✻✳✹ Pr♦❝❡ss♦ ❞❡ ❝♦♥✈❡r❣ê♥❝✐❛ ❞♦ ♠ét♦❞♦ P❉❇▲ ♣❛r❛ ♦ s✐st❡♠❛ ✸ ❜❛rr❛s ✭♣❛rt❡✷✮✳ ✼✺ ✻✳✺ Pr♦❝❡ss♦ ❞❡ ❝♦♥✈❡r❣ê♥❝✐❛ ❞♦ ♠ét♦❞♦ ❞❛ ❋▲❇▲▼ ♣❛r❛ ♦ s✐st❡♠❛ ✸ ❜❛rr❛s
✭♣❛rt❡✷✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺ ✻✳✻ Pr♦❝❡ss♦ ❞❡ ❝♦♥✈❡r❣ê♥❝✐❛ ❞♦ ♠ét♦❞♦ P❉❇▲❇▲▼ ♣❛r❛ ♦ s✐st❡♠❛ ✸ ❜❛rr❛s
✭♣❛rt❡✷✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻ ✻✳✼ Pr♦❝❡ss♦ ❞❡ ❝♦♥✈❡r❣ê♥❝✐❛ ❞♦ ♠ét♦❞♦ P❉❇▲ ♣❛r❛ ♦ s✐st❡♠❛ ■❊❊❊ ✶✹ ❜❛rr❛s✳ ✽✵ ✻✳✽ Pr♦❝❡ss♦ ❞❡ ❝♦♥✈❡r❣ê♥❝✐❛ ❞♦ ♠ét♦❞♦ ❞❛ ❋▲❇▲▼ ♣❛r❛ ♦ s✐st❡♠❛ ■❊❊❊ ✶✹
❜❛rr❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✶ ✻✳✾ Pr♦❝❡ss♦ ❞❡ ❝♦♥✈❡r❣ê♥❝✐❛ ❞♦ ♠ét♦❞♦ P❉❇▲❇▲▼ ♣❛r❛ ♦ s✐st❡♠❛ ■❊❊❊ ✶✹
❜❛rr❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✷ ✻✳✶✵ Pr♦❝❡ss♦ ❞❡ ❝♦♥✈❡r❣ê♥❝✐❛ ❞♦ ♠ét♦❞♦ P❉❇▲ ♣❛r❛ ♦ s✐st❡♠❛ ■❊❊❊ ✸✵ ❜❛rr❛s✳ ✽✻ ✻✳✶✶ Pr♦❝❡ss♦ ❞❡ ❝♦♥✈❡r❣ê♥❝✐❛ ❞♦ ♠ét♦❞♦ ❞❛ ❋▲❇▲▼ ♣❛r❛ ♦ s✐st❡♠❛ ■❊❊❊ ✸✵
✻✳✶✷ Pr♦❝❡ss♦ ❞❡ ❝♦♥✈❡r❣ê♥❝✐❛ ❞♦ ♠ét♦❞♦ P❉❇▲❇▲▼ ♣❛r❛ ♦ s✐st❡♠❛ ■❊❊❊ ✸✵ ❜❛rr❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✽ ✻✳✶✸ Pr♦❝❡ss♦ ❞❡ ❝♦♥✈❡r❣ê♥❝✐❛ ❞♦ ♠ét♦❞♦ P❉❇▲ ♣❛r❛ ♦ s✐st❡♠❛ ■❊❊❊ ✺✼ ❜❛rr❛s✳ ✾✷ ✻✳✶✹ Pr♦❝❡ss♦ ❞❡ ❝♦♥✈❡r❣ê♥❝✐❛ ❞♦ ♠ét♦❞♦ ❞❛ ❋▲❇▲▼ ♣❛r❛ ♦ s✐st❡♠❛ ■❊❊❊ ✺✼
❜❛rr❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✸ ✻✳✶✺ Pr♦❝❡ss♦ ❞❡ ❝♦♥✈❡r❣ê♥❝✐❛ ❞♦ ♠ét♦❞♦ P❉❇▲❇▲▼ ♣❛r❛ ♦ s✐st❡♠❛ ■❊❊❊ ✺✼
❜❛rr❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✹ ✻✳✶✻ Pr♦❝❡ss♦ ❞❡ ❝♦♥✈❡r❣ê♥❝✐❛ ❞♦ ♠ét♦❞♦ P❉❇▲ ♣❛r❛ ♦ s✐st❡♠❛ ■❊❊❊ ✶✶✽ ❜❛r✲
r❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✾ ✻✳✶✼ Pr♦❝❡ss♦ ❞❡ ❝♦♥✈❡r❣ê♥❝✐❛ ❞♦ ♠ét♦❞♦ ❞❛ ❋▲❇▲▼ ♣❛r❛ ♦ s✐st❡♠❛ ■❊❊❊ ✶✶✽
❜❛rr❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✵ ✻✳✶✽ Pr♦❝❡ss♦ ❞❡ ❝♦♥✈❡r❣ê♥❝✐❛ ❞♦ ♠ét♦❞♦ P❉❇▲❇▲▼ ♣❛r❛ ♦ s✐st❡♠❛ ■❊❊❊ ✶✶✽
❜❛rr❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✶ ❆✳✶ ❙♦❧✉çõ❡s ót✐♠❛s ❞♦ ♠ét♦❞♦ P❉❇▲ ♣❛r❛ ♦ s✐st❡♠❛ ❡❧étr✐❝♦ ✸ ❜❛rr❛s ✭♣❛rt❡ ✶✮ ✶✶✾ ❆✳✷ ❙♦❧✉çõ❡s ót✐♠❛s ❞♦ ♠ét♦❞♦ ❞❛ ❋▲❇▲▼ ♣❛r❛ ♦ s✐st❡♠❛ s✐st❡♠❛ ❡❧étr✐❝♦ ✸
❜❛rr❛s ✭♣❛rt❡ ✶✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✾ ❆✳✸ ❙♦❧✉çõ❡s ót✐♠❛s ❞♦ ♠ét♦❞♦ P❉❇▲❇▲▼ ♣❛r❛ ♦ s✐st❡♠❛ ❡❧étr✐❝♦ ✸ ❜❛rr❛s
✭♣❛rt❡ ✶✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✵ ❆✳✹ ❙♦❧✉çõ❡s ót✐♠❛s ❞♦ ♠ét♦❞♦ P❉❇▲ ♣❛r❛ ♦ s✐st❡♠❛ ❡❧étr✐❝♦ ✸ ❜❛rr❛s ✭♣❛rt❡ ✷✮ ✶✷✵ ❆✳✺ ❙♦❧✉çõ❡s ót✐♠❛s ❞♦ ♠ét♦❞♦ ❞❛ ❋▲❇▲▼ ♣❛r❛ ♦ s✐st❡♠❛ s✐st❡♠❛ ❡❧étr✐❝♦ ✸
❜❛rr❛s ✭♣❛rt❡ ✷✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✵ ❆✳✻ ❙♦❧✉çõ❡s ót✐♠❛s ❞♦ ♠ét♦❞♦ P❉❇▲❇▲▼ ♣❛r❛ ♦ s✐st❡♠❛ ❡❧étr✐❝♦ ✸ ❜❛rr❛s
✭♣❛rt❡ ✷✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✵ ❆✳✼ ❙♦❧✉çõ❡s ót✐♠❛s ❞❛s ♠❛❣♥✐t✉❞❡s ❞❛ t❡♥sã♦ ❡ ♦s â♥❣✉❧♦s ❞♦ ♠ét♦❞♦ P❉❇▲
♣❛r❛ ♦ s✐st❡♠❛ ❡❧étr✐❝♦ ■❊❊❊ ✶✹ ❜❛rr❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✶ ❆✳✽ ❙♦❧✉çõ❡s ót✐♠❛s ❞♦s ❚❛♣s ❞♦ ♠ét♦❞♦ P❉❇▲ ♦ s✐st❡♠❛ ❡❧étr✐❝♦ ■❊❊❊ ✶✹ ❜❛rr❛s✶✷✶ ❆✳✾ ❙♦❧✉çõ❡s ót✐♠❛s ❞❛s ♠❛❣♥✐t✉❞❡s ❞❛ t❡♥sã♦ ❡ ♦s â♥❣✉❧♦s ❞♦ ♠ét♦❞♦ ❞❛ ❋▲✲
❇▲▼ ♣❛r❛ ♦ s✐st❡♠❛ ❡❧étr✐❝♦ ■❊❊❊ ✶✹ ❜❛rr❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✷ ❆✳✶✵ ❙♦❧✉çõ❡s ót✐♠❛s ❞♦s ❚❛♣s ❞♦ ♠ét♦❞♦ ❞❛ ❋▲❇▲▼ ♦ s✐st❡♠❛ ❡❧étr✐❝♦ ■❊❊❊
✶✹ ❜❛rr❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✷ ❆✳✶✶ ❙♦❧✉çõ❡s ót✐♠❛s ❞❛s ♠❛❣♥✐t✉❞❡s ❞❛ t❡♥sã♦ ❡ ♦s â♥❣✉❧♦s ❞♦ ♠ét♦❞♦ P❉❇▲✲
❆✳✶✷ ❙♦❧✉çõ❡s ót✐♠❛s ❞♦s ❚❛♣s ❞♦ ♠ét♦❞♦ P❉❇▲❇▲▼ ♦ s✐st❡♠❛ ❡❧étr✐❝♦ ■❊❊❊ ✶✹ ❜❛rr❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✸ ❆✳✶✸ ❙♦❧✉çõ❡s ót✐♠❛s ❞❛s ♠❛❣♥✐t✉❞❡s ❞❛ t❡♥sã♦ ❡ ♦s â♥❣✉❧♦s ❞♦ ♠ét♦❞♦ P❉❇▲
♣❛r❛ ♦ s✐st❡♠❛ ❡❧étr✐❝♦ ■❊❊❊ ✸✵ ❜❛rr❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✹ ❆✳✶✹ ❙♦❧✉çõ❡s ót✐♠❛s ❞♦s ❚❛♣s ❞♦ ♠ét♦❞♦ P❉❇▲ ♣❛r❛ ♦ s✐st❡♠❛ ❡❧étr✐❝♦ ■❊❊❊
✸✵ ❜❛rr❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✺ ❆✳✶✺ ❙♦❧✉çõ❡s ót✐♠❛s ❞❛s ♠❛❣♥✐t✉❞❡s ❞❛ t❡♥sã♦ ❡ ♦s â♥❣✉❧♦s ❞♦ ♠ét♦❞♦ ❞❛ ❋▲✲
❇▲▼ ♣❛r❛ ♦ s✐st❡♠❛ ❡❧étr✐❝♦ ■❊❊❊ ✸✵ ❜❛rr❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✺ ❆✳✶✻ ❙♦❧✉çõ❡s ót✐♠❛s ❞♦s ❚❛♣s ❞♦ ♠ét♦❞♦ ❞❛ ❋▲❇▲▼ ♣❛r❛ ♦ s✐st❡♠❛ ❡❧étr✐❝♦
■❊❊❊ ✸✵ ❜❛rr❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✻ ❆✳✶✼ ❙♦❧✉çõ❡s ót✐♠❛s ❞❛s ♠❛❣♥✐t✉❞❡s ❞❛ t❡♥sã♦ ❡ ♦s â♥❣✉❧♦s ❞♦ ♠ét♦❞♦ P❉❇▲✲
❇▲▼ ♣❛r❛ ♦ s✐st❡♠❛ ❡❧étr✐❝♦ ■❊❊❊ ✸✵ ❜❛rr❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✼ ❆✳✶✽ ❙♦❧✉çõ❡s ót✐♠❛s ❞♦s ❚❛♣s ❞♦ ♠ét♦❞♦ P❉❇▲❇▲▼ ♣❛r❛ ♦ s✐st❡♠❛ ❡❧étr✐❝♦
■❊❊❊ ✸✵ ❜❛rr❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✼ ❆✳✶✾ ❙♦❧✉çõ❡s ót✐♠❛s ❞❛s ♠❛❣♥✐t✉❞❡s ❞❛ t❡♥sã♦ ❡ ♦s â♥❣✉❧♦s ❞♦ ♠ét♦❞♦ P❉❇▲
♣❛r❛ ♦ s✐st❡♠❛ ❡❧étr✐❝♦ ■❊❊❊ ✺✼ ❜❛rr❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✽ ❆✳✶✾ ❙♦❧✉çõ❡s ót✐♠❛s ❞❛s ♠❛❣♥✐t✉❞❡s ❞❛ t❡♥sã♦ ❡ ♦s â♥❣✉❧♦s ❞♦ ♠ét♦❞♦ P❉❇▲
♣❛r❛ ♦ s✐st❡♠❛ ❡❧étr✐❝♦ ■❊❊❊ ✺✼ ❜❛rr❛s✭❝♦♥t✐♥✉❛çã♦✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✾ ❆✳✶✾ ❙♦❧✉çõ❡s ót✐♠❛s ❞❛s ♠❛❣♥✐t✉❞❡s ❞❛ t❡♥sã♦ ❡ ♦s â♥❣✉❧♦s ❞♦ ♠ét♦❞♦ P❉❇▲
♣❛r❛ ♦ s✐st❡♠❛ ❡❧étr✐❝♦ ■❊❊❊ ✺✼ ❜❛rr❛s✭❝♦♥t✐♥✉❛çã♦✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✵ ❆✳✷✵ ❙♦❧✉çõ❡s ót✐♠❛s ❞♦s ❚❛♣s ❞♦ ♠ét♦❞♦ P❉❇▲ ♣❛r❛ ♦ s✐st❡♠❛ ❡❧étr✐❝♦ ■❊❊❊
✺✼ ❜❛rr❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✵ ❆✳✷✶ ❙♦❧✉çõ❡s ót✐♠❛s ❞❛s ♠❛❣♥✐t✉❞❡s ❞❛ t❡♥sã♦ ❡ ♦s â♥❣✉❧♦s ❞♦ ♠ét♦❞♦ ❞❛ ❋▲✲
❇▲▼ ♣❛r❛ ♦ s✐st❡♠❛ ❡❧étr✐❝♦ ■❊❊❊ ✺✼ ❜❛rr❛s✭❝♦♥t✐♥✉❛çã♦✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✶ ❆✳✷✶ ❙♦❧✉çõ❡s ót✐♠❛s ❞❛s ♠❛❣♥✐t✉❞❡s ❞❛ t❡♥sã♦ ❡ ♦s â♥❣✉❧♦s ❞♦ ♠ét♦❞♦ ❞❛ ❋▲✲
❇▲▼ ♣❛r❛ ♦ s✐st❡♠❛ ❡❧étr✐❝♦ ■❊❊❊ ✺✼ ❜❛rr❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✶ ❆✳✷✶ ❙♦❧✉çõ❡s ót✐♠❛s ❞❛s ♠❛❣♥✐t✉❞❡s ❞❛ t❡♥sã♦ ❡ ♦s â♥❣✉❧♦s ❞♦ ♠ét♦❞♦ ❞❛ ❋▲✲
❇▲▼ ♣❛r❛ ♦ s✐st❡♠❛ ❡❧étr✐❝♦ ■❊❊❊ ✺✼ ❜❛rr❛s✭❝♦♥t✐♥✉❛çã♦✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✷ ❆✳✷✶ ❙♦❧✉çõ❡s ót✐♠❛s ❞❛s ♠❛❣♥✐t✉❞❡s ❞❛ t❡♥sã♦ ❡ ♦s â♥❣✉❧♦s ❞♦ ♠ét♦❞♦ ❞❛ ❋▲✲
❇▲▼ ♣❛r❛ ♦ s✐st❡♠❛ ❡❧étr✐❝♦ ■❊❊❊ ✺✼ ❜❛rr❛s✭❝♦♥t✐♥✉❛çã♦✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✸ ❆✳✷✷ ❙♦❧✉çõ❡s ót✐♠❛s ❞♦s ❚❛♣s ❞♦ ♠ét♦❞♦ ❞❛ ❋▲❇▲▼ ♣❛r❛ ♦ s✐st❡♠❛ ❡❧étr✐❝♦
❆✳✷✸ ❙♦❧✉çõ❡s ót✐♠❛s ❞❛s ♠❛❣♥✐t✉❞❡s ❞❛ t❡♥sã♦ ❡ ♦s â♥❣✉❧♦s ❞♦ ♠ét♦❞♦ ❞❛ P❉✲ ❇▲❇▲▼ ♣❛r❛ ♦ s✐st❡♠❛ ❡❧étr✐❝♦ ■❊❊❊ ✺✼ ❜❛rr❛s✭❝♦♥t✐♥✉❛çã♦✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✹ ❆✳✷✸ ❙♦❧✉çõ❡s ót✐♠❛s ❞❛s ♠❛❣♥✐t✉❞❡s ❞❛ t❡♥sã♦ ❡ ♦s â♥❣✉❧♦s ❞♦ ♠ét♦❞♦ ❞❛ P❉✲
❇▲❇▲▼ ♣❛r❛ ♦ s✐st❡♠❛ ❡❧étr✐❝♦ ■❊❊❊ ✺✼ ❜❛rr❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✹ ❆✳✷✸ ❙♦❧✉çõ❡s ót✐♠❛s ❞❛s ♠❛❣♥✐t✉❞❡s ❞❛ t❡♥sã♦ ❡ ♦s â♥❣✉❧♦s ❞♦ ♠ét♦❞♦ ❞❛ P❉✲
❇▲❇▲▼ ♣❛r❛ ♦ s✐st❡♠❛ ❡❧étr✐❝♦ ■❊❊❊ ✺✼ ❜❛rr❛s✭❝♦♥t✐♥✉❛çã♦✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✺ ❆✳✷✸ ❙♦❧✉çõ❡s ót✐♠❛s ❞❛s ♠❛❣♥✐t✉❞❡s ❞❛ t❡♥sã♦ ❡ ♦s â♥❣✉❧♦s ❞♦ ♠ét♦❞♦ ❞❛ P❉✲
❇▲❇▲▼ ♣❛r❛ ♦ s✐st❡♠❛ ❡❧étr✐❝♦ ■❊❊❊ ✺✼ ❜❛rr❛s✭❝♦♥t✐♥✉❛çã♦✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✻ ❆✳✷✹ ❙♦❧✉çõ❡s ót✐♠❛s ❞♦s ❚❛♣s ❞♦ ♠ét♦❞♦ P❉❇▲❇▲▼ ♣❛r❛ ♦ s✐st❡♠❛ ❡❧étr✐❝♦
■❊❊❊ ✺✼ ❜❛rr❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✻ ❆✳✷✺ ❙♦❧✉çõ❡s ót✐♠❛s ❞❛s ♠❛❣♥✐t✉❞❡s ❞❛ t❡♥sã♦ ❡ ♦s â♥❣✉❧♦s ❞♦ ♠ét♦❞♦ ❞❛ P❉❇▲
♣❛r❛ ♦ s✐st❡♠❛ ❡❧étr✐❝♦ ■❊❊❊ ✶✶✽ ❜❛rr❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✼ ❆✳✷✺ ❙♦❧✉çõ❡s ót✐♠❛s ❞❛s ♠❛❣♥✐t✉❞❡s ❞❛ t❡♥sã♦ ❡ ♦s â♥❣✉❧♦s ❞♦ ♠ét♦❞♦ ❞❛ P❉❇▲
♣❛r❛ ♦ s✐st❡♠❛ ❡❧étr✐❝♦ ■❊❊❊ ✶✶✽ ❜❛rr❛s✭❝♦♥t✐♥✉❛çã♦✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✽ ❆✳✷✺ ❙♦❧✉çõ❡s ót✐♠❛s ❞❛s ♠❛❣♥✐t✉❞❡s ❞❛ t❡♥sã♦ ❡ ♦s â♥❣✉❧♦s ❞♦ ♠ét♦❞♦ ❞❛ P❉❇▲
♣❛r❛ ♦ s✐st❡♠❛ ❡❧étr✐❝♦ ■❊❊❊ ✶✶✽ ❜❛rr❛s✭❝♦♥t✐♥✉❛çã♦✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✾ ❆✳✷✺ ❙♦❧✉çõ❡s ót✐♠❛s ❞❛s ♠❛❣♥✐t✉❞❡s ❞❛ t❡♥sã♦ ❡ ♦s â♥❣✉❧♦s ❞♦ ♠ét♦❞♦ ❞❛ P❉❇▲
♣❛r❛ ♦ s✐st❡♠❛ ❡❧étr✐❝♦ ■❊❊❊ ✶✶✽ ❜❛rr❛s✭❝♦♥t✐♥✉❛çã♦✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✵ ❆✳✷✺ ❙♦❧✉çõ❡s ót✐♠❛s ❞❛s ♠❛❣♥✐t✉❞❡s ❞❛ t❡♥sã♦ ❡ ♦s â♥❣✉❧♦s ❞♦ ♠ét♦❞♦ ❞❛ P❉❇▲
♣❛r❛ ♦ s✐st❡♠❛ ❡❧étr✐❝♦ ■❊❊❊ ✶✶✽ ❜❛rr❛s✭❝♦♥t✐♥✉❛çã♦✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✶ ❆✳✷✻ ❙♦❧✉çõ❡s ót✐♠❛s ❞♦s ❚❛♣s ❞♦ ♠ét♦❞♦ P❉❇▲ ♣❛r❛ ♦ s✐st❡♠❛ ❡❧étr✐❝♦ ■❊❊❊
✶✶✽ ❜❛rr❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✶ ❆✳✷✼ ❙♦❧✉çõ❡s ót✐♠❛s ❞❛s ♠❛❣♥✐t✉❞❡s ❞❛ t❡♥sã♦ ❡ ♦s â♥❣✉❧♦s ❞♦ ♠ét♦❞♦ ❞❛ ❋▲✲
❇▲▼ ♣❛r❛ ♦ s✐st❡♠❛ ❡❧étr✐❝♦ ■❊❊❊ ✶✶✽ ❜❛rr❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✶ ❆✳✷✼ ❙♦❧✉çõ❡s ót✐♠❛s ❞❛s ♠❛❣♥✐t✉❞❡s ❞❛ t❡♥sã♦ ❡ ♦s â♥❣✉❧♦s ❞♦ ♠ét♦❞♦ ❞❛ ❋▲✲
❇▲▼ ♣❛r❛ ♦ s✐st❡♠❛ ❡❧étr✐❝♦ ■❊❊❊ ✶✶✽ ❜❛rr❛s✭❝♦♥t✐♥✉❛çã♦✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✷ ❆✳✷✼ ❙♦❧✉çõ❡s ót✐♠❛s ❞❛s ♠❛❣♥✐t✉❞❡s ❞❛ t❡♥sã♦ ❡ ♦s â♥❣✉❧♦s ❞♦ ♠ét♦❞♦ ❞❛ ❋▲✲
❇▲▼ ♣❛r❛ ♦ s✐st❡♠❛ ❡❧étr✐❝♦ ■❊❊❊ ✶✶✽ ❜❛rr❛s✭❝♦♥t✐♥✉❛çã♦✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✸ ❆✳✷✼ ❙♦❧✉çõ❡s ót✐♠❛s ❞❛s ♠❛❣♥✐t✉❞❡s ❞❛ t❡♥sã♦ ❡ ♦s â♥❣✉❧♦s ❞♦ ♠ét♦❞♦ ❞❛ ❋▲✲
❇▲▼ ♣❛r❛ ♦ s✐st❡♠❛ ❡❧étr✐❝♦ ■❊❊❊ ✶✶✽ ❜❛rr❛s✭❝♦♥t✐♥✉❛çã♦✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✹ ❆✳✷✼ ❙♦❧✉çõ❡s ót✐♠❛s ❞❛s ♠❛❣♥✐t✉❞❡s ❞❛ t❡♥sã♦ ❡ ♦s â♥❣✉❧♦s ❞♦ ♠ét♦❞♦ ❞❛ ❋▲✲
❆✳✷✽ ❙♦❧✉çõ❡s ót✐♠❛s ❞♦s ❚❛♣s ❞♦ ♠ét♦❞♦ ❞❛ ❋▲❇▲▼ ♣❛r❛ ♦ s✐st❡♠❛ ❡❧étr✐❝♦ ■❊❊❊ ✶✶✽ ❜❛rr❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✻ ❆✳✷✾ ❙♦❧✉çõ❡s ót✐♠❛s ❞❛s ♠❛❣♥✐t✉❞❡s ❞❛ t❡♥sã♦ ❡ ♦s â♥❣✉❧♦s ❞♦ ♠ét♦❞♦ ❞❛ P❉✲
❇▲❇▲▼ ♣❛r❛ ♦ s✐st❡♠❛ ❡❧étr✐❝♦ ■❊❊❊ ✶✶✽ ❜❛rr❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✻ ❆✳✷✾ ❙♦❧✉çõ❡s ót✐♠❛s ❞❛s ♠❛❣♥✐t✉❞❡s ❞❛ t❡♥sã♦ ❡ ♦s â♥❣✉❧♦s ❞♦ ♠ét♦❞♦ ❞❛ P❉✲
❇▲❇▲▼ ♣❛r❛ ♦ s✐st❡♠❛ ❡❧étr✐❝♦ ■❊❊❊ ✶✶✽ ❜❛rr❛s✭❝♦♥t✐♥✉❛çã♦✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✼ ❆✳✷✾ ❙♦❧✉çõ❡s ót✐♠❛s ❞❛s ♠❛❣♥✐t✉❞❡s ❞❛ t❡♥sã♦ ❡ ♦s â♥❣✉❧♦s ❞♦ ♠ét♦❞♦ ❞❛ P❉✲
❇▲❇▲▼ ♣❛r❛ ♦ s✐st❡♠❛ ❡❧étr✐❝♦ ■❊❊❊ ✶✶✽ ❜❛rr❛s✭❝♦♥t✐♥✉❛çã♦✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✽ ❆✳✷✾ ❙♦❧✉çõ❡s ót✐♠❛s ❞❛s ♠❛❣♥✐t✉❞❡s ❞❛ t❡♥sã♦ ❡ ♦s â♥❣✉❧♦s ❞♦ ♠ét♦❞♦ ❞❛ P❉✲
❇▲❇▲▼ ♣❛r❛ ♦ s✐st❡♠❛ ❡❧étr✐❝♦ ■❊❊❊ ✶✶✽ ❜❛rr❛s✭❝♦♥t✐♥✉❛çã♦✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✾ ❆✳✷✾ ❙♦❧✉çõ❡s ót✐♠❛s ❞❛s ♠❛❣♥✐t✉❞❡s ❞❛ t❡♥sã♦ ❡ ♦s â♥❣✉❧♦s ❞♦ ♠ét♦❞♦ ❞❛ P❉✲
❇▲❇▲▼ ♣❛r❛ ♦ s✐st❡♠❛ ❡❧étr✐❝♦ ■❊❊❊ ✶✶✽ ❜❛rr❛s✭❝♦♥t✐♥✉❛çã♦✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✵ ❆✳✸✵ ❙♦❧✉çõ❡s ót✐♠❛s ❞♦s ❚❛♣s ❞♦ ♠ét♦❞♦ P❉❇▲❇▲▼ ♣❛r❛ ♦ s✐st❡♠❛ ❡❧étr✐❝♦
■❊❊❊ ✶✶✽ ❜❛rr❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✵
■♥tr♦❞✉çã♦
Pr♦❜❧❡♠❛s r❡❛✐s ♣♦❞❡♠ s❡r ♠♦❞❡❧❛❞♦s ♠❛t❡♠❛t✐❝❛♠❡♥t❡ ❝♦♠♦ ♣r♦❜❧❡♠❛s ❞❡ ♦t✐♠✐③❛✲ çã♦✱ ♥❛s ❞✐✈❡rs❛s ár❡❛s ❞♦ ❝♦♥❤❡❝✐♠❡♥t♦✳ ❉❡st❛❝❛✲s❡ ♥❡st❡ tr❛❜❛❧❤♦ ♦ ♣r♦❜❧❡♠❛ ❞❡ ✢✉①♦ ❞❡ ♣♦tê♥❝✐❛ ót✐♠♦ ✭❋P❖✮✱ ❛❜♦r❞❛❞♦ ♥❛ ❡♥❣❡♥❤❛r✐❛ ❡❧étr✐❝❛✱ ♥❛ ár❡❛ ❞❡ s✐st❡♠❛s ❡❧étr✐❝♦s ❞❡ ♣♦tê♥❝✐❛✳ ❖ ♣r♦❜❧❡♠❛ ❞❡ ❋P❖ ❢♦✐ ♣r♦♣♦st♦ ♣♦r ❈❛r♣❡♥t✐❡r ✭✶✾✻✷✮ ✱ ❛ ♣❛rt✐r ❞♦ ♣r♦✲ ❜❧❡♠❛ ❞❡ ❞❡s♣❛❝❤♦ ❡❝♦♥ô♠✐❝♦✳ ❊❧❡ é r❡♣r❡s❡♥t❛❞♦ ♠❛t❡♠❛t✐❝❛♠❡♥t❡ ♣♦r ✉♠ ♣r♦❜❧❡♠❛ ❞❡ ♦t✐♠✐③❛çã♦ ♥ã♦✲❧✐♥❡❛r✱ r❡str✐t♦✱ ♥ã♦ ❝♦♥✈❡①♦✱ ❞❡ ❣r❛♥❞❡ ♣♦rt❡ ❝♦♠ ✈❛r✐á✈❡✐s ❝♦♥tí♥✉❛s ❡ ❞✐s❝r❡t❛s✱ ❡ ❜✉s❝❛ ♦ ♠❡❧❤♦r ♣♦♥t♦ ❞❡ ♦♣❡r❛çã♦ ❞❡ ✉♠ s✐st❡♠❛ ❡❧étr✐❝♦ ❞❡ ♣♦tê♥❝✐❛ ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛❧❣✉♠ ♦❜❥❡t✐✈♦✱ s❛t✐s❢❛③❡♥❞♦ ❛s r❡str✐çõ❡s ❢ís✐❝❛s ❡ ♦♣❡r❛❝✐♦♥❛✐s✳ ❯♠ ❝❛s♦ ♣❛rt✐❝✉❧❛r ❞❡st❡ ♣r♦❜❧❡♠❛✱ ♦ q✉❛❧ é ❡①♣❧♦r❛❞♦ ♥❡st❡ tr❛❜❛❧❤♦✱ é ❞❡♥♦♠✐♥❛❞♦ ❞❡ ❋P❖ ❘❡✲ ❛t✐✈♦ ✭❋P❖❘✮✳ ◆❡st❡ ♣r♦❜❧❡♠❛ ♦s ❝♦♥tr♦❧❡s ❛t✐✈♦s sã♦ ✜①❛❞♦s ❡ ❛s ✈❛r✐á✈❡✐s ❞❡ ❝♦♥tr♦❧❡ r❡❧❛❝✐♦♥❛❞❛s ❝♦♠ ❛ ♣♦tê♥❝✐❛ r❡❛t✐✈❛ ❝♦♠♦✿ ❛s ♠❛❣♥✐t✉❞❡s ❞❛ t❡♥sã♦ ❞♦s ❣❡r❛❞♦r❡s ❡ ❞♦s ❝♦♠♣❡♥s❛❞♦r❡s sí♥❝r♦♥♦s ❡ ❡stát✐❝♦s ❞❡ ♣♦tê♥❝✐❛ r❡❛t✐✈❛ ❡ ♦s t❛♣s ❞♦s tr❛♥s❢♦r♠❛❞♦r❡s sã♦ ♦t✐♠✐③❛❞♦s ❡♠ r❡❧❛çã♦ à ✉♠❛ ❢✉♥çã♦ ♦❜❥❡t✐✈♦✳ ◆❡st❡ tr❛❜❛❧❤♦✱ ❛ ❢✉♥çã♦ ♦❜❥❡t✐✈♦ é r❡♣r❡s❡♥t❛❞❛ ♣❡❧❛s ♣❡r❞❛s ❞❡ ♣♦tê♥❝✐❛ ❛t✐✈❛ ♥❛ tr❛♥s♠✐ssã♦ ❡✱ s❡❣✉♥❞♦ ▼♦♥t✐❝❡❧❧✐ ✫ ▲✐✉ ✭✶✾✾✷✮ ❡ss❛ ❢✉♥çã♦ é ♥ã♦ s❡♣❛rá✈❡❧ ❡ ♥ã♦ ♣❡r♠✐t❡ s✐♠♣❧✐✜❝❛çõ❡s✱ ♦ q✉❡ ❞✐✜❝✉❧t❛ ❛✐♥❞❛ ♠❛✐s ❛ r❡s♦❧✉çã♦ ❞♦ ♣r♦❜❧❡♠❛ ❞❡ ❋P❖✳
▼✉✐t♦s tr❛❜❛❧❤♦s ❢♦r❛♠ ❞❡s❡♥✈♦❧✈✐❞♦s ♥❛ t❡♥t❛t✐✈❛ ❞❡ r❡s♦❧✈ê✲❧♦ ✉t✐❧✐③❛♥❞♦ ❞✐❢❡r❡♥t❡s té❝♥✐❝❛s ❞❡ ♦t✐♠✐③❛çã♦✳ ❈✐t❛♠✲s❡✿ ●r❛♥✈✐❧❧❡ ✭✶✾✾✹✮✱ ❲✉ ❡t ❛❧✳ ✭✶✾✾✹✮ ❡ ❚♦rr❡s ✫ ◗✉✐♥✲ t❛♥❛ ✭✶✾✾✽✮ q✉❡ ❛♣❧✐❝❛r❛♠ ✉♠ ❛❧❣♦r✐t♠♦ ♣r✐♠❛❧✲❞✉❛❧ ❜❛rr❡✐r❛ ❧♦❣❛rít♠✐❝❛ ♥❛ r❡s♦❧✉çã♦ ❞♦ ♣r♦❜❧❡♠❛ ❞❡ ❋❧✉①♦ ❞❡ P♦tê♥❝✐❛ Ót✐♠♦❀ ❇❛♣t✐st❛ ❡t ❛❧✳ ✭✷✵✵✹✮✱ ❇❛♣t✐st❛ ❡t ❛❧✳ ✭✷✵✵✺✮ ❡ ❇❛♣t✐st❛ ❡t ❛❧✳ ✭✷✵✵✻✮ q✉❡ r❡s♦❧✈❡r❛♠ ♦ ♣r♦❜❧❡♠❛ ✉t✐❧✐③❛♥❞♦ ✉♠❛ ❢✉♥çã♦ ▲❛❣r❛♥❣✐❛♥❛ ❛✉♠❡♥t❛❞❛✲❜❛rr❡✐r❛ ❧♦❣❛rít♠✐❝❛❀ ❙♦✉s❛ ❡t ❛❧✳ ✭✷✵✵✽✮✱ ❙♦✉s❛ ❡t ❛❧✳ ✭✷✵✵✾✮ ❡ ❙♦✉s❛ ❡t ❛❧✳
✭✷✵✶✷✮ q✉❡ ✉t✐❧✐③❛r❛♠ ✉♠❛ ❢✉♥çã♦ ▲❛❣r❛♥❣✐❛♥❛ ❜❛rr❡✐r❛ ♠♦❞✐✜❝❛❞❛❀ ❈❛♣✐t❛♥❡s❝✉ ❡t ❛❧✳ ✭✷✵✵✼✮ ♦ q✉❛❧ ❛♥❛❧✐s❛ ♦ ❞❡s❡♠♣❡♥❤♦ ❞❡ três ❛❧❣♦r✐t♠♦s ❞❡ ♣♦♥t♦s ✐♥t❡r✐♦r❡s ❡ s✉❛ ❛♣❧✐❝❛✲ çã♦ ❛♦ ❋P❖❀ ❙♦❧❡r ❡t ❛❧✳ ✭✷✵✶✸✮ q✉❡ ✉t✐❧✐③♦✉ ✉♠❛ ♠❡t♦❞♦❧♦❣✐❛ ❞❡t❡r♠✐♥íst✐❝❛ ❞❡ r❡s♦❧✉çã♦ ❞♦ ♣r♦❜❧❡♠❛ ❞❡ ❋P❖ ❝♦♠ ✈❛r✐á✈❡✐s ❞❡ ❝♦♥tr♦❧❡ ❞✐s❝r❡t❛s ❡ P✐♥❤❡✐r♦ ❡t ❛❧✳ ✭✷✵✶✺✮ ♦ q✉❛❧ ✉t✐❧✐③♦✉ ✉♠❛ ❢✉♥çã♦ ❜❛rr❡✐r❛ ♠♦❞✐✜❝❛❞❛ ❝♦♠ ♠ét♦❞♦ ♣r❡✈✐s♦r✲❝♦rr❡t♦r ❡ ❡str❛té❣✐❛ ❞❡ ❝♦♥✈❡r❣ê♥❝✐❛ ❣❧♦❜❛❧✳
❆ss✐♠✱ t❡♥❞♦ ❡♠ ✈✐st❛ ❛ ✐♠♣♦rtâ♥❝✐❛ ❞♦ ❋P❖ ❡ ❛ ❜✉s❝❛ ♣♦r ♠ét♦❞♦s ♠❛✐s ❡✜❝✐❡♥t❡s ❡ r♦❜✉st♦s ❞❡ s♦❧✉çã♦ é ♣r♦♣♦st♦ ♥❡st❡ tr❛❜❛❧❤♦ ✉♠❛ ♥♦✈❛ ❛❜♦r❞❛❣❡♠ q✉❡ ❝♦♠❜✐♥❛ ♦s ♠ét♦❞♦s ❜❛s❡❛❞♦s ♥❛ ❢✉♥çã♦ ❜❛rr❡✐r❛ ❧♦❣❛rít♠✐❝❛ ❡ ♥❛ ❜❛rr❡✐r❛ ❧♦❣❛rít♠✐❝❛ ♠♦❞✐✜❝❛❞❛✳ ❊st❛ ❝♦♠❜✐♥❛çã♦ ❥✉st✐✜❝❛✲s❡ q✉❡ ❡st❡s ❥á s❡ ♠♦str❛r❛♠ ❡✜❝✐❡♥t❡s ♥❛ r❡s♦❧✉çã♦ ❞♦ ❋P❖ s❡♣❛r❛❞❛♠❡♥t❡ ❡ ✉♠❛ ♣r♦♣♦st❛ s✐♠✐❧❛r ❥á t❡r s✐❞♦ ✐♥✈❡st✐❣❛❞❛ ♣♦r ●r✐✈❛ ✭✷✵✵✹✮ ♣❛r❛ r❡s♦❧✉çã♦ ❞❡ ♣r♦❜❧❡♠❛s ❞❡ ♦t✐♠✐③❛çã♦ ♥ã♦ ❧✐♥❡❛r✳
❖ ♠ét♦❞♦ ❞❡ ❜❛rr❡✐r❛ ❧♦❣❛rít♠✐❝❛ ✭▼❇▲✮ é ✉t✐❧✐③❛❞♦ ♣❛r❛ r❡s♦❧✉çã♦ ❞❡ ♣r♦❜❧❡♠❛s ❝♦♠ r❡str✐çõ❡s ❞❡ ❞❡s✐❣✉❛❧❞❛❞❡✱ ❝✉❥♦ ✐♥t❡r✐♦r é ♥ã♦ ✈❛③✐♦✳ P♦❞❡ s❡r ✈✐st♦ ❝♦♠♦ ✉♠ ❝❛s♦ ♣❛rt✐❝✉❧❛r ❞♦ ♠ét♦❞♦ ❞❛s ♣❡♥❛❧✐❞❛❞❡s✱ ♠❛s ❞✐❢❡r❡♥❝✐❛✲s❡ ❞❡st❡ ♣♦r ❡①✐❣✐r ✉♠❛ ♣❡♥❛❧✐③❛✲ çã♦ ✐♥t❡r♥❛✱ ♦✉ s❡❥❛✱ ♣♦r tr❛❜❛❧❤❛r ♥♦ ✐♥t❡r✐♦r ❞❛ r❡❣✐ã♦ ❢❛❝tí✈❡❧✱ ✉t✐❧✐③❛♥❞♦ ✉♠❛ ❢✉♥çã♦ ❛✉①✐❧✐❛r q✉❡ ❝r❡s❝❡ ✐♥❞❡✜♥✐❞❛♠❡♥t❡ ♣ró①✐♠♦ à ❢r♦♥t❡✐r❛ ❡ ✉♠❛ s❡q✉ê♥❝✐❛ ❞❡❝r❡s❝❡♥t❡ ❞❡ ♣❛râ♠❡tr♦s ❞❡ ❜❛rr❡✐r❛✳ ❆ ❢✉♥çã♦ ❜❛rr❡✐r❛ ❧♦❣❛rít♠✐❝❛ ❢♦✐ ❛♣r❡s❡♥t❛❞❛ ♣♦r ❋r✐s❝❤ ✭✶✾✺✺✮ ♣❛r❛ ♣r♦❜❧❡♠❛s ❞❡ ♣r♦❣r❛♠❛çã♦ ❝♦♥✈❡①❛✳ ❊st❡ ♠ét♦❞♦ ❢♦✐ r❡❛❧♠❡♥t❡ ♣♦♣✉❧❛r✐③❛❞♦ ♣♦r ✭❋✐❛❝❝♦ ✫ ▼❝❈♦r♠✐❝❦✱ ✶✾✻✽✮ q✉❡ ❛ss♦❝✐❛r❛♠ ❛ ❢✉♥çã♦ ❜❛rr❡✐r❛ ❡ ❛ ❢✉♥çã♦ ♣❡♥❛❧✐❞❛❞❡ ❡♠ ✉♠❛ ♠❡s♠❛ ❢✉♥çã♦ ❛✉①✐❧✐❛r✳
❖ ♠ét♦❞♦ ❞❡ ❜❛rr❡✐r❛ ❧♦❣❛rít♠✐❝❛ ♠♦❞✐✜❝❛❞❛ ✭▼❇▲▼✮ ❢♦✐ ❛♣r❡s❡♥t❛❞♦ ♣♦r P♦❧②❛❦ ✭✶✾✾✷✮✳ ❊st❡ ♠ét♦❞♦ ❝♦♠❜✐♥❛ ❛s ♠❡❧❤♦r❡s ♣r♦♣r✐❡❞❛❞❡s ❞❛ ❢✉♥çã♦ ▲❛❣r❛♥❣✐❛♥❛ ❝❧áss✐❝❛ ❡ ❞❛ ❢✉♥çã♦ ❜❛rr❡✐r❛ ❝❧áss✐❝❛✱ ❡✈✐t❛♥❞♦ ♦s ♣r♦❜❧❡♠❛s q✉❡ ❛♠❜❛s ❡♥❢r❡♥t❛♠✳ ❙❡❣✉♥❞♦ ♦ ❛✉t♦r✱ ❛ ✜♥❛❧✐❞❛❞❡ q✉❡ ♦ ♠ét♦❞♦ ❜❛rr❡✐r❛ ♠♦❞✐✜❝❛❞❛ t❡♠ ♣❛r❛ ♦s ♠ét♦❞♦s ❞❡ ♣♦♥t♦s ✐♥t❡r✐♦r❡s é ❛ ♠❡s♠❛ ❞❛ ❢✉♥çã♦ ▲❛❣r❛♥❣✐❛♥❛ ❛✉♠❡♥t❛❞❛ t❡♠ ♣❛r❛ ♦s ♠ét♦❞♦s ❞❡ ♣❡♥❛❧✐❞❛❞❡✿ ❛❥✉❞á✲❧♦s ❛ ✏❞r✐❜❧❛r✑ s✉❛s ❞✐✜❝✉❧❞❛❞❡s✳
◆❛ ❛❜♦r❞❛❣❡♠ ♣r♦♣♦st❛ ♥❡st❡ tr❛❜❛❧❤♦✱ ❛s r❡str✐çõ❡s ❞❡ ❞❡s✐❣✉❛❧❞❛❞❡ ❞♦ ♣r♦❜❧❡♠❛ sã♦ tr❛♥s❢♦r♠❛❞❛s ❡♠ ✐❣✉❛❧❞❛❞❡ ♣♦r ♠❡✐♦ ❞❛ ✉t✐❧✐③❛çã♦ ❞❡ ✈❛r✐á✈❡✐s ❞❡ ❢♦❧❣❛ ♥ã♦ ♥❡❣❛t✐✈❛s✳ ❆s ✈❛r✐á✈❡✐s ❞❡ ❢♦❧❣❛ sã♦ tr❛t❛❞❛s ♣❡❧❛s ❢✉♥çõ❡s ❜❛rr❡✐r❛ ❧♦❣❛rít♠✐❝❛ ❡ ❜❛rr❡✐r❛ ❧♦❣❛rít✲ ♠✐❝❛ ♠♦❞✐✜❝❛❞❛✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ ❡ ❛s ❞❡♠❛✐s r❡str✐çõ❡s ♣♦r ♠❡✐♦ ❞❡ ♠✉❧t✐♣❧✐❝❛❞♦r❡s ❞❡ ▲❛❣r❛♥❣❡✳ ❊st❡s ♠ét♦❞♦s s❡rã♦ ✉t✐❧✐③❛❞♦s ❡♠ ❞✉❛s ❡t❛♣❛s✳ ■♥✐❝✐❛❧♠❡♥t❡ ❛♣❧✐❝❛✲s❡ ♦ ▼❇▲
❛té q✉❡ ✉♠❛ ❝♦♥❞✐çã♦ ❞❡ tr❛♥s✐çã♦ s❡❥❛ s❛t✐s❢❡✐t❛✱ ❡♠ s❡❣✉✐❞❛ ❛♣❧✐❝❛✲s❡ ♦ ▼❇▲▼ ❛té q✉❡ ✉♠❛ ❝♦♥❞✐çã♦ ❞❡ ❝♦♥✈❡r❣ê♥❝✐❛ s❡❥❛ s❛t✐s❢❡✐t❛✳
❊st❡ tr❛❜❛❧❤♦ ❡♥❝♦♥tr❛✲s❡ ❞✐✈✐❞✐❞♦ ❡♠ ✼ ❝❛♣ít✉❧♦s✿
◆♦ ❝❛♣ít✉❧♦ ✶✱ ❛♣r❡s❡♥t❛✲s❡ ❛ ♠♦t✐✈❛çã♦ ♣❛r❛ ♦ tr❛❜❛❧❤♦ ❡ s❡✉ ♦❜❥❡t✐✈♦✱ ♥♦ ❝❛♣í✲ t✉❧♦ ✷✱ ❝♦♠ ♦ ♦❜❥❡t✐✈♦ ❞❡ ♣♦s✐❝✐♦♥❛r ♦ tr❛❜❛❧❤♦ ❝r♦♥♦❧♦❣✐❝❛♠❡♥t❡✱ ❛♣r❡s❡♥t❛✲s❡ ✉♠ ❤✐s✲ tór✐❝♦ ❞♦ ♠ét♦❞♦ ❞❡ ❜❛rr❡✐r❛✱ ❞♦ ♠ét♦❞♦ ❜❛rr❡✐r❛ ♠♦❞✐✜❝❛❞❛ ❡ ❞♦ ♣r♦❜❧❡♠❛ ❞❡ ✢✉①♦ ❞❡ ♣♦tê♥❝✐❛ ót✐♠♦✱ ♥♦ ❝❛♣ít✉❧♦ ✸✱ ❛♣r❡s❡♥t❛✲s❡ ✉♠❛ r❡✈✐sã♦ ❞♦s ♠ét♦❞♦s ❞❡ ♦t✐♠✐③❛çã♦✿ ❞✉❛❧✲▲❛❣r❛♥❣✐❛♥♦✱ ♠ét♦❞♦ ❞❡ ❜❛rr❡✐r❛ ❡ ♠ét♦❞♦ ❞❡ ❜❛rr❡✐r❛ ♠♦❞✐✜❝❛❞❛✱ ❝♦♠ ♦❜❥❡t✐✈♦ ❞❡ ❢♦r♥❡❝❡r ✉♠ s✉♣♦rt❡ t❡ór✐❝♦ ♣❛r❛ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞♦ ♥♦✈♦ ♠ét♦❞♦✱ ♥♦ ❝❛♣ít✉❧♦ ✹✱ ❛♣r❡s❡♥t❛✲s❡ ❛ ❛❜♦r❞❛❣❡♠ ♣r♦♣♦st❛✱ s❡✉ ❛❧❣♦r✐t♠♦ ❡ ❛♥❛❧✐s❛✲s❡ ✉♠ ❡①❡♠♣❧♦ ♠❛t❡♠át✐❝♦✱ ♥♦ ❝❛♣ít✉❧♦ ✺✱ ❛♣r❡s❡♥t❛✲s❡ ❛ ❢♦r♠✉❧❛çã♦ ❞♦ ❋P❖❘✱ ❝♦♥str♦❡♠✲s❡ ❛s ❞✉❛s ❢✉♥çõ❡s✿ ❜❛rr❡✐r❛ ❧♦❣❛rít♠✐❝❛ ❡ ❜❛rr❡✐r❛ ❧♦❣❛rít♠✐❝❛ ♠♦❞✐✜❝❛❞❛ ❡ ❛♣❧✐❝❛♠✲s❡ ♦s três ♠ét♦❞♦s ❛♦ ♣r♦❜❧❡♠❛ ❞❡ ❋P❖❘✱ ♥♦ ❝❛♣ít✉❧♦ ✻✱ ❛♣r❡s❡♥t❛♠✲s❡ ♦s r❡s✉❧t❛❞♦s ♥✉♠ér✐❝♦s ♣❛r❛ ♦s s✐st❡♠❛s ❡❧étr✐❝♦s ❞❡ ✸ ❜❛rr❛s ❡ ■❊❊❊ ✶✹✱ ✸✵✱ ✺✼ ❡ ✶✶✽ ❜❛rr❛s ❡ ♥♦ ❝❛♣ít✉❧♦ ✼✱ ❛♣r❡s❡♥t❛♠✲s❡ ❛s ❝♦♥❝❧✉sõ❡s ❞♦ tr❛❜❛❧❤♦✱ ❛s ♣❡rs♣❡❝t✐✈❛s ❞❡ ❝♦♥t✐♥✉✐❞❛❞❡ ❞❡st❡ ❡ ♦s tr❛❜❛❧❤♦s ♣✉❜❧✐❝❛❞♦s✳
