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Halos de matéria escura e campos escalares

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✣✤✁✑☛✦✥✧✄✝✥✧✚★✥✩✖✪✍☎✞✬✫✮✭✢☛✌✄✢✯✰✏

✱✲✞✡✳✴✏✵✠✧✥✧✏✛✶✷✞✸✁✹✥✧✖✷✍☎✞✺✫✮✭✢☛✌✄✎✯✻✏✽✼✿✾❀✏❁✥✩✞❂✶✷❃❁✥✧✄✢✯✰✏

❄ ❅❇❆✡❈✷❉ ❊●❋ ❍ ❅✺■❑❏▼▲❖◆✸❅ ❋P❉❘◗❚❙●▲❖❅ ❋ ◗❚❅❯❍ ❱ ❈✷❉

❋▼❉❘◗❚❅❯❆✸❅❇▲❑❋P❉

❲❨❳❬❩✤❳❬❭✕❪❚❲❴❫❛❵❜❭✕❫❞❝❢❡ ❣❯❝✽❳✐❤✙❥✙❦❬❡

❧✴♠♦♥q♣❛r✦s✉t✤✈☞✇✤♠②①✟③✵♠♦✇✤④✢⑤✟⑥☎♠②⑤✛⑦✸⑧☞⑨q⑩★❶❷t✤⑧☞❸✡❹❺♣②❻❼♣②♠★❽✑❻✩♠❾t✤❿➀✇

➁☞➂➄➃✦➅✉➃✤➆➈➇➊➉➋➃➍➌❼➂❾➎✉➏➐➎➍➑➊➒➓➃✦➔✌➉➋➃✌➉✑→❞➑✩➏➍➒↔➣↕➒➛➙✧➒✝➉

➔✌➎✑➜✟➝q➏➍➣➓➞♦➃➀➔✦➃❺➟❂➑➊➣↕➠✤➎➍➂❾➏➍➣➛➔✦➃✦➔✌➎❬➔✌➎✑➡✻➢✌➉

➤➥➃✤➙✧➆q➉➦➌✩➃✤➂➄➃➧➉✤➅②➒✢➎➍➑➩➨➫➢✌➉➭➔✌➉❑➒➛➝↕➒➛➙✧➆q➉➯➔✌➎

➲❺➎✉➏➍➒➛➂❾➎➳➎➍➵➺➸❁➣➓➻➍➑✰➞➍➣➛➃✿➏②➼

➽➚➾➊➪➹➶➘➾❺➴✦➷✸➾➊➬➱➮↔➪❂➾➊✃❂❐❼❒➫➾✡❮

③✵♠♦✇✤④✢⑤✛⑥✑♠❛⑤✟⑦❂⑧✩⑨q⑩❷❶☎t❰⑧☞❸✰❹❺♣②❻❼♣②♠★❽✑❻☞♠♦t✤❿➀✇➭ÏÑÐ✢Ò➹Ó✢Ô✑Õ✩③✛Ö

③✵♠♦✇✤④✢⑤✛⑥✑♠❛⑤✟×✟❸ÙØ②♥Ù✇➀❽☎❻✻✈☞t✤❸q❸qt❘Ï➛Ð✢Ò➹Ó✝Ô✴Õ✩③✛Ö

③✵♠♦✇✤④✢⑤✛⑥✑♠❛⑤✟Ú☎⑧☞Û➘✇➦Ü✴♥ÙØ②♣❛rÝs♦♣✐Þ➥t✤ß✻♣❛❸àt❰s♦✇❑Ï➛Ð✢á☎③✛â✛Ö

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③✽t❰♠❾t➦⑩♦♣②♠★Û➘♠♦t✤r☞✈☞♣❰ç➊⑩♦è❬♥qr✦s♦♣②♥q♠➄✇☞①❁r➊t❰✈➊t

é

♣②⑧❑♣➍ê✩t✤Û➘♣❛♠❾t➦✇➘⑧❖♣❞ê✧Ø②❸q⑧✩♥➓⑤

Õ✧èës❾✇✌✈☞✇➦♣②❿ìØít✤✈➊t➦Ø②✇✤♥q⑩❾t✧⑤✵③❢î✌♣❬ï✌⑧☞t✤r✦s❾✇✮ð❛⑩

á☎✇➦❿➀⑨qr☞♥Ù❿ñ✇òï✌⑧✩♣❬④➛t❰ó②♣②⑩❛⑤

❽✑⑩➄⑩♦♥Ù❿❴♣②❿❴Ø②t✤✈➊t➦❸àt✤Û✤✇➳t➀❸Ù⑧➊tòs❾✇✌✈➊t

ô

♠➄♥q❸qõ☞t✩ç✩ß❼✇➘♠♦ïÝ⑧☞♣➋t✤❸ös✉tò÷✌♥Ù÷✤♣✤⑤

(3)

â✵⑩➄s❾t➋ð★❿➚⑧☞♥ös❾✇ëß☞♠➄✇➐÷✤tí÷✤♣②❸q❿➀♣②r✦s♦♣✑tëß➊t✤♠✎s❾♣★❿ñt✤♥q⑩❁♣❛⑩♦ß❼♣②♠♦t✤✈➊t❬♣❷❿ñt✤♥Ù⑩✵ß☞♠❾t✤ó❛♣②♠➄✇➘⑩❾t❬✈☞♣★⑩♦♣❛♠✛♣❛⑩♦Ø❛♠♦♥Ùs❾t

✈☞♣❛rÝs♦♠♦✇➳✈☞✇➳ß✩♠♦✇✌Ø②♣②⑩➄⑩♦✇➳✈☞♣✑♣②❸àt❰❻✻✇➘♠♦t✤ûíã❰✇ò✈➊t➚✈☞♥Ù⑩♦⑩➄♣②♠➄s❾t✤ûíã❰✇☞⑤✛ü✴⑧☞♣②❿✺ý♦þ➚t✤Ø❛✇➘❿ñß☞t✤r☞õ☞✇➘⑧✮✈☞♣✴ß❼♣②♠➄s♦✇

⑧☞❿ÿß☞♠♦✇✌Ø②♣❛⑩♦⑩♦✇➦✈☞♣❛⑩♦⑩➄♣❬s♦♥qß❼✇➚⑩❾t❰❻✻♣ë✈➊t❰⑩➥✈☞♥✁☞Ø②⑧☞❸Ù✈➊t✤✈☞♣❛⑩➥ïÝ⑧☞♣➋t✤ß➊t✤♠➄♣②Ø②♣❛❿ì♣✴ß✩♠♦✇➐÷❰t➐÷✤♣②❸Ù❿ñ♣❛rÝs♦♣ë⑩♦♣❛♠❾þ

Øít❰ß➊t✤ó➦✈☞♣➀♣②r✦s❾♣❛r☞✈☞♣②♠➋✇❑ß✻✇➘♠➄ïÝ⑧☞èñ✈✩♣②⑩♦⑩♦t❖Û➘♥ÙÛ✦t✤r✦s❾♣❛⑩♦Ø②t❘÷✤✇➘r✦s✉t✤✈✩♣✮✈☞♣➦♥qr✩Ø②❸q⑧✩♥q♠✴❿➚⑧✩♥Ùs✉t❰⑩ëß✻♣❛⑩♦⑩♦✇➘t✤⑩

t✤ïÝ⑧☞♥✸r☞♣❛⑩♦⑩♦t✤⑩☎❸Ù♥qr☞õ☞t✤⑩②⑤

③✽t✤♠♦t✮Ø②✇✤❿ñ♣❛ûít✤♠❛ç✡t✤Û➘♠♦t✤✈☞♣❛û②✇✄✂✮✈✩♥Ù÷✌♥qr☞✈☞t✤✈☞♣➋❿✮þ✿ê✧♥Ù❿✮t➦✈☞✇ ❿➀♣②⑧➯Ø❛♠♦♣❛✈☞✇☞ç✰ß❼♣②❸qtñ♥Ù❸q⑧☞❿➀♥qr➊t❰ûíã✤✇

✈☞♣✛⑧☞❿ Øít❰❿ñ♥Ùr☞õ☞✇★ïÝ⑧☞♣✹r✩♣②❿ ⑩♦♣❛❿ñß✩♠♦♣✛ß➊t✤♠♦♣❛Ø②♣❛⑧✐s✉ã❰✇☎Ø❛❸àt✤♠➄✇☎ïÝ⑧➊t✤r✦s♦✇☎♣❛⑧òÛ➘✇➘⑩✎s✉t✤♠➄♥àt✩⑤➹⑥✑♣❛♥öê✧✇✑❿➀♣②⑧✩⑩

Ø②⑧✩❿ñß☞♠➄♥q❿➀♣②r✦s❾✇✤⑩➋✈✩♣✮Û➘♠♦t❰s❾♥Ù✈➊ã✤✇❘s✉t✤❿ò❻✻ð❛❿➺t✤✇➯③✵♠➄✇✤④✢⑤❘⑥✑♠❛⑤✙❶☎t✤⑧✩❸✛❽☎❻☞♠❾t❰❿ñ✇☞ç➹ß❼♣②❸àt✙ß➊t✤Ø❛♥qè❛r☞Ø②♥qt

♣➚❻❼✇✦t✿Ó➓÷➘✇➘r✦s✉t❰✈☞♣➳Ø②✇➘❿ ïÝ⑧☞♣➳❿➀♣➚✇➘♠♦♥Ù♣②r✦s❾✇✤⑧✡ç✡Ø②✇✤r☞✈☞⑧☞ó❛♥q⑧❜✇❘ß☞♠➄✇➘❻☞❸q♣❛❿✮tñ❿ñ♣✐♣②r☞⑩➄♥qr➊t✤r✩✈☞✇❘s✉t✤r✦s✉t❰⑩

Ø②✇✤♥q⑩❾t❰⑩➥♣✑s❾✇✤♠♦r☞✇➘⑧❘ß❼✇➘⑩➄⑩♦⑨Ù÷✤♣②❸✸t➚♠➄♣ít✤❸Ù♥qó②t✤ûíã✤✇✐✈☞♣②⑩➄⑩❾t➳✇➘❻☞♠♦t✩⑤✵❽✑Û✤♠❾t✤✈☞♣❛û②✇➦t✤♥Ùr☞✈➊t➚t❰✇➘⑩➥❿➀♣②⑧☞⑩ ④➛t❰❿ñ♥Ù❸öÓ

♥àt❰♠♦♣②⑩❂ïÝ⑧☞♣❰ç✤✈☞♣✟⑧☞❿ñt★④Ñ✇✤♠♦❿ñt➥✇➘⑧✐✈✩♣✹✇➘⑧✧s❾♠❾t✧ç✿④Ñ✇➘♠♦t✤❿✬Ø②t✤ß➊t✤ó❛♣②⑩❢✈☞♣✟✈➊t✤♠❂⑩♦⑧☞ß❼✇➘♠✎s❾♣✛♣②❿➀✇✧Ø❛♥q✇➘r➊t❰❸✤ß➊t✤♠♦t

ïÝ⑧☞♣ë✇➚s❾♠♦t✤❻➊t✤❸Ùõ☞✇ò④Ñ✇➘⑩➄⑩♦♣ëØ❛✇➘r☞Ø②♠➄♣❛s♦♥qóít❰✈☞✇☞⑤✟á✑ã❰✇➳❿ñ♣❛r☞✇➘⑩✕♥q❿➀ß❼✇➘♠➄s❾t✤r✦s❾♣✤ç✌⑧☞❿ÿt✤Û➘♠♦t✤✈☞♣②Ø❛♥q❿➀♣②r✦s❾✇➚t✤✇

Þ➥á✑③✵ï❘ß❼♣②❸Ù✇➦t✤ß✻✇✤♥q✇☎➊r➊t❰r☞Ø②♣❛♥q♠♦✇✩ç➊Ø②♣②♠✎s✉t✤❿➀♣②r✦s♦♣➋♥Ùr☞✈☞♥Ù⑩♦ß❼♣②r☞⑩♦þ➐÷✤♣②❸↔⑤

Ô☎❿✝✆✢❿ò⑧☞♥Ùs♦✇➀✇✤❻☞♠♦♥ÙÛ✦t✤✈☞✇✟✞✴♣②⑩➄ß✻♣❛Ø②♥àt❰❸➹÷❰t✤♥❂ß➊t✤♠♦tñ✇ñß✻♣❛⑩♦⑩♦✇➘t✤❸❢✈✩✇✮Û➘♠➄⑧☞ß✻✇ñØ✡✠➘⑩➄❿ñ♥ÙØ②✇☞①✟Ü✴♥Ùr☞⑨qØ❛♥q⑧☞⑩

Ò➊♣②♠➄r➊t✤r☞✈☞♣❛⑩☎ÏÑÜ✴♥Ùr☞♥↕Ö❞ç

é

õ☞♥qt✤Û➘✇➋③❢♣❛♠♦♣②♥Ù♠❾t✩çÝ❶★✇➘r➊t❰❸q✈☞✇

ô

t❰s♦♥q⑩✎s✉t➦Ï☞☛❬t✍✌☞Ø✉õ✩✇ÝÖ✽♣★Ð ÷✤t❰r✏✎✹t✤⑩➄⑧☞✈➊t✩çÝß❼♣②❸Ù✇

Ø②✇✤rÝ÷✌⑨ö÷✧♥Ù✇✙✈☞♥Ù÷✤♣②♠➄s♦♥q✈☞⑨Ù⑩♦⑩➄♥q❿➀✇ ♣➦ß✻♣❛❸àt✤⑩ë♥Ùr✑✌✩❿ñ♣❛♠❾t✤⑩ë✈☞♥Ù⑩♦Ø❛⑧☞⑩♦⑩➄î✧♣❛⑩❬④Ñ♠➄⑧✩s❾⑨ö④Ñ♣②♠♦t✤⑩ër➊t❘❸q✇➘⑧✩⑩❾t❘✈➊t❘r☞✇➘⑩➄⑩❾t

⑩❾t❰❸àt✩ç✻Ø②⑧✿ý➄✇➘⑩✑✈☞♣②⑩➄✈☞✇➘❻☞♠♦t✤❿ñ♣❛r✦s❾✇➘⑩✴Ø❛♣②♠✎s✉t✤❿➀♣②r✦s❾♣➚④➛t❰ó②♣②❿ ß➊t✤♠✎s❾♣➚✈✩♣②⑩♦⑩➄♣➚s❾♣❞ê✧s♦✇☞⑤✓✒❖⑧☞♥ös✉t✤⑩☎ß➊t✤❸Ù❿✮t✤⑩

÷❰ã✤✇➦t✤ïÝ⑧☞♥❼s✉t✤❿➚❻❼ð②❿ ß➊t✤♠♦t✕✔✤✇✦ã✤✇➳❽☎⑩♦⑩➄♥q♠❾t✿s❾♥➓ç✌Û➘♠♦t✤r☞✈☞♣✴Û✤⑧☞♠♦⑧❘♥ÙrÝs♦♣②❸Ù♣②Ø❛s♦⑧➊t✤❸✻r☞✇➳ïÝ⑧☞♣ë✈☞♥qó☎♠♦♣❛⑩♦ß❼♣②♥Ùs♦✇

t✤✇➳⑧☞r✩♥Ù÷➘♣❛♠♦⑩➄✇➀✈☞tò④Ñ⑨q⑩♦♥ÙØítò♣ë✈✩✇➘⑩✕Ø②✇➘❿➀ß☞⑧✩s❾t✤✈☞✇➘♠➄♣②⑩➋ÏÑ♣✴ß☞♠♦✇➐÷❰tí÷➘♣❛❸q❿➀♣②r✦s❾♣❬✈☞♣✴÷❰þ✤♠➄♥q✇➘⑩✹✇➘⑧✩s❾♠➄✇➘⑩➥s✖✠✤ß☞♥öÓ

Ø②✇✤⑩✉Ö➍⑤✑❧✴⑧✩s❾♠➄✇➘⑩✑ïÝ⑧☞♣òØ②♣②♠✎s✉t✤❿➀♣②r✦s♦♣✐s❾è❛❿❨÷➘♣②ó➦t❰ï✌⑧✩♥❢⑩♦ã✤✇❘Þ➥t✤♠➄❸q✇➘⑩✗✒❖✇➘❸Ù♥qr➊t➦♣✕✒❖þ✤♠♦♥Ù✇ ô t✤❸Ù✈☞♥q✇❰s♦s❾♥↔ç

t✤r✦s❾♥ÙÛ➘✇➘⑩✑÷✌♥Ùó②♥qr✩õ☞✇➘⑩ë✈☞♣➦⑩❾t❰❸àt ♣➦ïÝ⑧☞♣➦♥qr✦÷❰t✤♠♦♥qt➐÷✤♣②❸Ù❿ñ♣❛rÝs♦♣➳t✤ß➊t❰♠♦♣②Ø❛♥àt✤❿ r➊t✤⑩❬✈☞♥Ù⑩♦Ø❛⑧☞⑩♦⑩➄î✧♣❛⑩✐✈➊t✙✘

ä✑✚

ß➊t✤♠♦t➚✈➊t✤♠➥⑧✩❿✪ê✧♣②ïÝ⑧☞♣❞Ó✝❿ñt❰s❾♣ër✩✇➳ß☞♠♦✇➘❻✩❸q♣②❿ñt✩⑤❢❽✑Û➘♠♦t✤✈☞♣②û❛✇➦t✤♥qr✩✈➊t➚t✤✇➦❶★✇✧✈✩♠♦♥qÛ✤✇➚Ò➊♠♦♣❛⑩♦r☞♣❛✈➊t➚ß✻✇✤♠

❿➀♣❷♣❛r☞⑩♦♥Ùr➊t✤♠✛r➊ã✤✇✐t✤ß❼♣②r➊t✤⑩✛⑧☞❿✘❿➚⑧✩♥Ùs❾✇❬✈☞♣★s❾♣❛✇➘♠♦♥qt➋✈✩♣☎Ø②t✤❿ñß❼✇➘⑩✟❿ñt✤⑩✵s✉t✤❿➚❻❼ð②❿✘ïÝ⑧☞♣❷✇➘⑩ ✚✜✛✓✢ ❿

ïÝ⑧☞♣ò⑩➄♣②ß➊t❰♠❾t✤❿ t➀Ô✴Õ✩③P✈✩♣ò❿➀♥qr☞õ➊t➳Ø②t✤⑩❾t➀ß✻✇✌✈☞♣②❿ì⑩♦♥q❿❨⑩➄♣②♠★÷➘♣❛r☞Ø②♥Ù✈☞✇➘⑩✑✈✩♣✐❻☞♥ÙØ②♥ÙØ②❸q♣➍s✉t✩⑤✣✒➭t✤r✩✈☞✇

t✤♥Ùr☞✈➊t✑⑧☞❿ t✤❸✁✤✴♣②⑩➄ß✻♣❛Ø②♥qt✤❸✧ß☞t✤♠❾tët✤⑩❢❿ñ✇✌ûít❰⑩✽✈➊t✴⑩➄♣②Ø②♠➄♣❛s❾t✤♠♦♥qt✑✈➊tëÒ✽⑨Ù⑩♦♥qØ②t✿Ó✥✒❖t❰s❾♣❛❿✮þ❰s♦♥qØ②t✩①✸Õ✧♥Ù❿ñ✇✤r☞♣✤ç

❽✑❿➀ð②❸Ù♥àtò♣ ô ♣➍s❾õ❑ïÝ⑧☞♣✐ïÝ⑧☞♣❛❻☞♠❾t❰♠❾t✤❿❴❿ò⑧☞♥Ùs♦✇➘⑩➥♣❬❿➚⑧☞♥ös❾✇➘⑩✕Û✦t❰❸qõ☞✇➘⑩❛⑤

❧✒♣❛⑩♦ß➊t❰û②✇➳ð✑Ø❛⑧☞♠➄s♦✇☞ç✩❿ñt✤⑩ t➚t✤⑧☞⑩➄è②r☞Ø❛♥àt➚✈☞♣✴r✩✇➘❿ñ♣❛⑩ r➊ã❰✇ò÷❰t✤♥✻✇❰④Ñ⑧☞⑩♦Ø②t✤♠➥✇➚❻☞♠➄♥q❸Ùõ☞✇ò✈☞♣☎s✉t✤r✦s❾✇✤⑩

❿➀♣②♠♦♣❛Ø②♣❛✈☞✇➘♠♦♣❛⑩☎✈✩♣òt✤Û✤♠❾t✤✈☞♣❛Ø②♥Ù❿ñ♣❛rÝs♦✇➳ß✻✇✤♠❷⑧✩❿✮t➳♠❾t❰óíã✤✇➀r➊ã✤✇➦❿➀♣②r☞✇➘⑩★Û➘♠♦t✤r☞✈☞♥Ù✇➘⑩❾t➳ïÝ⑧☞♣✐t✤⑩❷t✤r✦s❾♣❞Ó

♠♦♥Ù✇➘♠♦♣❛⑩②①✵⑧☞❿ñt➚♥qr✩Ø②✇➘❿➀♣②r☞⑩➄⑧☞♠❾þí÷✤♣②❸❂t✤❿➀♥qó②t✤✈☞♣✤⑤❁â✟r✦s♦♠❾t✤❿❨t❰ï✌⑧✩♥✡✇➦ß✻♣❛⑩♦⑩♦✇➘t✤❸✸✈☞✇➘⑩ é þ ✢ ♥q✇✤r☞⑩②ç✩÷❰þ✤♠➄♥q✇➘⑩

t✤❿➀♥qÛ➘✇✤⑩☎♣➦t✤❿➀♥qÛ➘t✤⑩✑♥Ùr☞Ø②♠➄⑨Ù÷➘♣❛♥q⑩☎✈☞♣②⑩➄✈☞♣➦✇➘⑩✑s❾♣❛❿ñß❼✇➘⑩✴✈✩♣➳Û➘♠❾t✤✈✩⑧➊t✤ûíã❰✇☞⑤

é

t✤❿➚❻❼ð②❿ ④➛t✤ó❛♣②❿ ß☞t✤♠➄s♦♣

✈☞♣❛⑩♦⑩♦♣✐s❾♥q❿➀♣➋✇ñs❾♥Ù❿ñ♣❬✈☞♣➋④Ñ⑧✩s❾⑩♦t✤❸➹♣✐s❾✇✌✈➊tñt➀s❾⑧✩♠♦❿ñt✮t✤ïÝ⑧☞♥➹✈➊t✮Ò❢⑨q⑩♦♥ÙØít➦ïÝ⑧☞♣➚Ø②⑧✩♠➄s❾♥Ù⑧➭❻➊t✿s❾♣②♠☎⑧☞❿ñt

❻❼✇➘❸àt✑r✩✇➋Þ ♣②ß❼è✕r➊t✤⑩❁õ☞✇✤♠❾t✤⑩✵✈☞♣✹④Ñ✇➘❸qÛ✦t✧ç✤♣②r✦s♦♠♦♣✕⑧☞❿ñt✑♥qr✦s♦♣②Û➘♠♦t✤❸✩♣➥✇✤⑧✩s❾♠♦t✩⑤❁⑦✸♣ít❰r☞✈☞♠♦✇✓✦ë♠♦⑧✩Û☞ç✤÷✌⑧☞❸qÛ✤✇

(4)

ß❼♣②❸q✇✤⑩✕♥qr✧✌☞❿➀♣②♠♦✇✤⑩✕Ø②✇➘r☞⑩➄♣②❸Ùõ☞✇➘⑩★♣❬♥qr✦s❾♣❛♠♦⑧☞♠➄❻➊t✤r☞✇➘⑩❛⑤Ù⑤ö⑤

③❢✇➘♠☎☞❿❖ç✟Û➘✇➘⑩✎s✉t✤♠➄♥àt➭✈✩♣✙t✤Û➘♠❾t❰✈☞♣②Ø❛♣②♠➦t➯ß➊t✤♠➄Ø②♣❛♥q♠❾t➯♣ s❾t✤❿➚❻❼ð②❿ Û➘♠❾t❰r☞✈☞♣✙t✤❿➀♥qÛ✦t❑❽✑♠➄♥àt✤✈☞r✩♣

❧✴❸q⑨Ù❿ñß☞♥Ù✇❬ß✻♣❛❸q✇➳Ø②✇✤❸q✇☞ç✌ß✻♣❛❸àt✤⑩ ♥qr✧✌☞❿➀♣②♠❾t❰⑩➥ß➊t✤❸qt➐÷✌♠♦t✤⑩ ✈☞♣❬t❰ß✻✇➘♥Ù✇ò♣ëØ②t✤♠♦♥Ùr☞õ☞✇☞ç✩t✤❸qð❛❿ ✈✩♣ë⑩♦♣②⑧✙Ø❛✇➘❿➦Ó

(5)
(6)

Þ ♣②♠➄Øít➳✈☞♣

ä➘æ✍✶

✈✩✇➚Ø②✇➘r✦s♦♣✡✌☞✈☞✇➦♣❛r☞♣②♠➄Û➘ð❛s♦♥qØ②✇ò✈☞✇➚⑧☞r☞♥ö÷➘♣❛♠♦⑩♦✇➦⑩➄♣✴♣②r☞Ø❛✇➘r✦s❾♠♦t➚⑩♦✇➘❻❘⑧☞❿ñt➋④Ñ✇✤♠♦❿ñt

✈☞♣✐r➊t❰s❾⑧✩♠♦♣②ó②t t✤♥Ùr☞✈➊tñr☞ã✤✇✮✈☞♣➍s❾♣❛♠♦❿➀♥qr➊t✤✈☞tñ♣òð➋Ø②✇✤r☞õ☞♣②Ø❛♥q✈➊tñß✻♣❛❸q✇✮r✩✇➘❿ñ♣➋✈☞♣✐❿✮t❰s♦ð②♠➄♥àt➦♣②⑩♦Ø❛⑧☞♠❾t✧⑤

⑥✑♣❛⑩♦✈☞♣✑t✤⑩✟ß☞♠♦♥Ù❿ñ♣❛♥q♠❾t❰⑩❁♣②⑩➄ß✻♣❛Ø②⑧☞❸qt✤û②î✌♣②⑩✹t✤Ø②♣❛♠♦Ø②t➋✈☞♣❷⑩♦⑧☞t➋♣❞ê✩♥Ù⑩➄s♦è②r☞Ø❛♥àtñÏ☞✷✹✸★♥qØ

✢✻✺

✚✜✼

✘✽✘✦Ö❞ç➘÷✤þ❰♠♦♥q✇✤⑩

❿➀✇✧✈☞♣❛❸q✇➘⑩❂④Ñ✇➘♠♦t✤❿✒ß☞♠♦✇➘ß❼✇➘⑩✎s❾✇➘⑩❁r☞t☎s❾♣❛rÝs❾t❰s❾♥ö÷❰t✑✈☞♣➹ý➄⑧☞⑩✎s❾♥✾➊Øít✤♠❢✇➘⑩✽✈☞t✤✈☞✇➘⑩❁✇✤❻☞⑩♦♣❛♠➄÷❰t✤Ø②♥Ù✇➘r➊t✤♥Ù⑩✽♣❛r☞Ø②✇➘r✌Ó

s❾♠♦t✤✈☞✇➘⑩❷❿ñt✤⑩②ç❼t❰s♦ð✐õ☞✇➫ý➄♣✤ç❼r☞♣②r☞õÝ⑧☞❿ ✈☞♣❛❸q♣②⑩★④Ñ✇➘♥❂Øít❰ß➊t✤ó➋✈☞♣òØ❛⑧☞❿ñß✩♠♦♥q♠★♣❛⑩♦⑩❾t➀s✉t✤♠➄♣❛④➛t➀tñØ②✇✤rÝs♦♣②r✦s❾✇✩⑤

á☎♣❛⑩➄s❾tñ✈☞♥Ù⑩♦⑩♦♣❛♠➄s❾t✤ûíã✤✇✩ç✻t❰ß☞♠♦♣❛⑩♦♣②r✦s❾t✤♠♦♣❛❿ñ✇➘⑩❷⑧☞❿ñt➀❻✩♠♦♣❛÷✤♣ò✈☞♥Ù⑩♦Ø❛⑧☞⑩♦⑩♦ã✤✇✮✈☞♣❛⑩♦⑩➄♣②⑩✑❿➀✇✌✈☞♣②❸Ù✇➘⑩②ç➩t✤❸Ùð②❿ÿ✈☞♣

ß☞♠➄✇➘ß✻✇✤♠❁⑧☞❿✷r☞✇➐÷✤✇☞çÝ❻➊t✤⑩♦♣②t✤✈☞✇❬r➊të♥q✈✩ð②♥àt✴✈✩♣✕ï✌⑧✩♣★s❾t✤r✦s❾✇➋të❿✮t✿s❾ð②♠➄♥àt✑♣❛⑩♦Ø❛⑧☞♠❾t❬ïÝ⑧➊t✤r✦s❾✇✐të♣②r☞♣❛♠♦Û➘♥qt

(7)

☛✦✥✧✠✩✏✟✯❼✥

á☎♣②t✤♠♦❸

s❂✸✹♣②r✦s

☞÷➘♣➥ß❼♣②♠➄Ø②♣❛rÝs✽✇✤④➊s❾õ✩♣ ♣②r✩♣②♠♦Û✤♣❛s❾♥ÙØ✹Ø❛✇➘r✦s❾♣❛rÝs❁✇✤④☞s❾õ✩♣➥⑧☞r☞♥ö÷➘♣②♠➄⑩♦♣ t✤ß☞ß❼♣ít✤♠➄⑩✽♥qròt

④Ñ✇➘♠➄❿❯s❾õ➊t✿s✹♥Ù⑩✟⑩➄s❾♥Ù❸q❸✧⑧☞r

r☞✇✱✸★r❘t✤r☞✈ñ♥q⑩✵r➊t❰❿ñ♣❛✈ñ✈➊t❰♠

❿ñt❰s♦s♦♣②♠②⑤❁Õ✧♥qr✩Ø②♣✕s❾õ☞♣✬➊♠➄⑩➄s✛⑩♦ß❼♣②Ø❛⑧☞❸àt❰s♦♥q✇➘r✩⑩

t✤❻❼✇➘⑧✩s ♥Ùs❾⑩✹♣➍ê✧♥q⑩✎s❾♣❛r☞Ø②♣➀Ï❃✷✹✸★♥qØ

✢✻✺

✚✱✼

✘✍✘✦Ö➍ç✌❿✮t❰r

❿➀✇✧✈✩♣②❸q⑩✹õ➊tí÷➘♣✴❻❼♣②♣❛r✙ß☞♠♦✇➘ß❼✇➘⑩➄♣②✈✮s♦♠

♥qr☞Û✐s❾✇

ý➄⑧☞⑩✎s❾♥Ù④

t✤❸q❸❼s❾õ☞♣❬✇➘❻✩⑩♦♣②♠✎÷➘♣❛✈➭✈➊t❰s❾t➳❻☞⑧✩síç➊⑧✩rÝs♦♥q❸✡r✩✇❄✸❬ç➊r✩✇➘r☞♣❬✇✤④❂s❾õ☞♣❛❿❴õ➊t✤⑩★❻❼♣②♣❛r➭t✤❻✩❸q♣✴s❾✇➦⑩➄✇➘❸Ù÷✤♣

s❾õ✩♥q⑩✕ß☞♠➄✇➘❻☞❸q♣❛❿❖⑤✽Ð✝r❑s♦õ☞♥q⑩✕❿➀✇➘r☞✇➘Û✤♠❾t✤ß☞õ

ç❅✸✹♣✓✸★♥Ù❸q❸✰ß✩♠♦♣②⑩➄♣②r✦s✑t➦❻✩♠♦♥q♣➍④➹✈☞♥q⑩➄Ø②⑧☞⑩➄⑩♦♥q✇✤r➭t✤❻❼✇➘⑧✩s✕s♦õ☞♣②⑩➄♣

❿➀✇✧✈☞♣❛❸q⑩òt✤r☞✈❚ß☞♠♦✇✤ß✻✇➘⑩➄♣✙t➯r☞♣❆✸ì✇➘r☞♣❰ç✛❻☞t✤⑩♦♣❛✈ ✇➘r s♦õ☞♣❘♥q✈✩♣ít➭s❾õ☞t❰s➦❻✻✇❰s❾õ ✈➊t✤♠

❿ñt❰s♦s♦♣②♠➳t❰r☞✈

✈➊t✤♠

♣②r✩♣②♠♦Û

(8)

Ò✽♥ÙÛ➘⑧☞♠♦t

(9)

❣ ❤ ➪❥✐➐❒➫❐✸✃❧❦♥♠✽♦☞❐ ❣

♣ q

❐✸✃➹➴✑rÑ❐❁s✐❐❥tí➬➱❐❥r❭✉✇✈❼➮➛➶➘❐②①➹➾➊✃❂❒❄♦☞❐ ③

ä

Þ ✇➘r☞⑩✎s❾♠♦⑧✩ûíã✤✇➀✈☞✇➦❿ñ✇✌✈☞♣❛❸q✇ ⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤❬⑤✐⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤➋⑤➋⑤➋⑤✐⑤➋⑤✐⑤

ä

ä

â❁÷➘✇➘❸Ù⑧☞ûíã✤✇➦✈☞✇➦④➛t❰s♦✇➘♠➥✈☞♣❬♣②⑩➄Øít✤❸qt

a

(

t

)

⑤➋⑤❬⑤✐⑤➋⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤❬⑤✐⑤➋⑤✐⑤➋⑤➋⑤ ✚✽✚

ä ⑤④✘ Þ ♣②r☞⑩➄✇ñ✈✩✇ñ⑧☞r✩♥Ù÷➘♣❛♠♦⑩➄✇❑⑤➋⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤❬⑤✐⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤➋⑤➋⑤➋⑤✐⑤➋⑤✐⑤ ✚ ✘

ä ⑤④✘✩⑤✚ Ð✝✈☞t✤✈☞♣❬✈☞✇➦⑧☞r☞♥ö÷➘♣②♠➄⑩♦✇✂⑤✐⑤➋⑤➋⑤✐⑤➋⑤❬⑤✐⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤➋⑤➋⑤➋⑤✐⑤➋⑤✐⑤ ✚➫æ

ä

⑥✑♥q⑩✎s❵⑤✤r✩Ø②♥àt❰⑩✕♣②❿ Þ ✇➘⑩➄❿ñ✇✤❸q✇➘Û➘♥qt ⑤➋⑤➋⑤✐⑤➋⑤❬⑤✐⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤➋⑤➋⑤➋⑤✐⑤➋⑤✐⑤

✚➫æ

ä

æ

á☎⑧☞Ø❛❸q♣❛✇➘⑩♦⑩➄⑨qr✦s❾♣❛⑩♦♣➋ß☞♠♦♥Ù❿ñ✇➘♠➄✈☞♥àt❰❸❼♣➋t➳♠❾t❰✈☞♥àt✤û②ã✤✇➦Ø✡✠➘⑩➄❿ñ♥ÙØít➚✈☞♣ë④Ñ⑧☞r✩✈☞✇ ⑤➋⑤✐⑤➋⑤✐⑤

✚❄⑥

ä

æ

â✵♠♦t➦✈☞t➀♠♦t✤✈☞♥àt❰ûíã✤✇ ⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤❬⑤✐⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤➋⑤➋⑤➋⑤✐⑤➋⑤✐⑤

✚✱✼

ä

æ

ä

â✵♠♦t➦✈☞t➀❿ñt❰s❾ð❛♠♦♥qt ⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤❬⑤✐⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤➋⑤➋⑤➋⑤✐⑤➋⑤✐⑤

ä✤å

ä

æ

⑤❛✘ ❶❷t✤✈☞♥qt✤ûíã❰✇➳Ø✡✠➘⑩➄❿ñ♥ÙØít➚✈☞♣ë④Ñ⑧☞r☞✈✩✇ ⑤❬⑤✐⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤➋⑤➋⑤➋⑤✐⑤➋⑤✐⑤

ä✤å

ä

⑤④⑦ ❶❷♣❛⑩♦⑧☞❿➀✇ ⑤➋⑤✐⑤➋⑤➋⑤➋⑤➋⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤❬⑤✐⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤➋⑤➋⑤➋⑤✐⑤➋⑤✐⑤

ä❅✚

⑧ q

➾⑨✐✱⑩Ý❒✿➮➛➾ ➴✑tí➶✻❦❂❒✿➾

♣✇⑧

✘✩⑤

â❁÷✧♥Ù✈☞è②r✩Ø②♥àt❰⑩✕✈➊t➀r✩♣②Ø②♣❛⑩♦⑩➄♥q✈➊t✤✈✩♣✐✈➊t➦♣➍ê✧♥Ù⑩➄s❾è❛r☞Ø②♥qt➳✈☞♣❬❿✮t❰s♦ð②♠➄♥àt➚♣②⑩➄Ø②⑧☞♠♦t ⑤✐⑤➋⑤✐⑤

ä✟✛

✘✩⑤

ä

Þ ⑧☞♠➄÷❰t✤⑩★✈☞♣❬♠➄✇✤s✉t✤û②ã✤✇➭⑤➋⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤❬⑤✐⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤➋⑤➋⑤➋⑤✐⑤➋⑤✐⑤

ä

✘✩⑤ä ⑤✚ Ô❷❿❴ß❼✇➘⑧☞Ø②✇➦⑩➄✇➘❻☞♠♦♣➋t➦♣②ïÝ⑧➊t✤û②ã✤✇ñt✤Ø②✇➘❸Ù♥q⑩➄♥q✇➘r➊t❰❸✻✈☞♣ ô ✇✤❸Ùs❾ó❛❿✮t❰r☞r ⑤➋⑤✐⑤ ä✍❶

✘✩⑤④✘ ③❢♣❛♠✪➊⑩❷✈☞♣❬✈☞♣②r✩⑩♦♥q✈☞t✤✈☞♣❨⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤❬⑤✐⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤➋⑤➋⑤➋⑤✐⑤➋⑤✐⑤

ä✍✼

✘✩⑤④✘✩⑤

❽☎❸qÛ➘⑧✩r☞⑩✕ß✻♣❛♠✪➊⑩★ß❼✇➘ß☞⑧☞❸qt✤♠♦♣❛⑩❬⑤✐⑤➋⑤❬⑤✐⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤➋⑤➋⑤➋⑤✐⑤➋⑤✐⑤ ✘

✘✧⑤❛✘✩⑤✚ ⑤✚ ③➹♣②♠✥➊❸❂á✐⑤Ò ⑤❹✒⑤❘⑤✐⑤➋⑤❬⑤✐⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤➋⑤➋⑤➋⑤✐⑤➋⑤✐⑤ ✘ ✚

✘✧⑤❛✘✩⑤

ä

③➹♣②♠✥➊❸♥✒❖✇✌✇➘♠♦♣❬♣❛s❷t❰❸➓⑤ ⑤✐⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤➋⑤➋⑤➋⑤✐⑤➋⑤✐⑤ ✘✽✘

✘✧⑤❛✘✩⑤

⑤④✘ Ú☎t✤❸q✇➳ß✩⑩♦♣②⑧✩✈☞✇❰Ó✝♥Ù⑩♦✇✤s♦ð②♠➄❿ñ♥ÙØ②✇➦⑤✐⑤➋⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤➋⑤➋⑤➋⑤✐⑤➋⑤✐⑤ ✘✽✘

✘✩⑤④✘✩⑤ä Þ ✇✤r☞⑩♦♥Ù✈☞♣②♠♦t✤û②î✌♣②⑩★⑩♦✇✤❻☞♠♦♣❬✇➘⑩★ß❼♣②♠✪☞⑩❷✈✩♣➋✈✩♣②r☞⑩➄♥q✈➊t✤✈✩♣ ⑤➋⑤➋⑤➋⑤➋⑤➋⑤✐⑤➋⑤✐⑤ ✘ ✛

✘✩⑤

Þ ♠♦♥Ù⑩♦♣✛r☞✇✴❿➀✇✧✈☞♣❛❸q✇☎Þ➥⑥❷✒ì✈☞♣➍÷✌♥q✈☞✇✑t✤✇✑ß❼♣②♠✥➊❸✧✈✩♣ ✈☞♣❛r☞⑩♦♥Ù✈➊t✤✈☞♣❛⑩❁✈☞♣ õ☞t✤❸q✇➘⑩❂♣❛⑩♦Ø②⑧✩♠♦✇➘⑩❸✘

æ

✘✩⑤

æ

á✑t❰s♦⑧☞♠♦♣❛óít➳✈➊t➦❿✮t✿s❾ð②♠➄♥àt➚♣❛⑩♦Ø②⑧✩♠❾t ⑤➋⑤✐⑤➋⑤❬⑤✐⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤➋⑤➋⑤➋⑤✐⑤➋⑤✐⑤ ✘✽⑦

③ q ❐✸✃➹➴✑rÑ➾❹✈➩➴✌➬ ✃❂❐❥t❻❺❂➾❼rÑ❐❥t ⑧✇❽

✒❖✇✌✈☞♣②❸Ù✇➘⑩✕Ø②✇➘❿ì❿✮t❰s♦ð②♠➄♥àtò♣❛⑩♦Ø②⑧✩♠❾t➀④Ñ♠➄♥àt ⑤➋⑤❬⑤✐⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤➋⑤➋⑤➋⑤✐⑤➋⑤✐⑤ ✘

✛ ⑤✚ ⑤✚ ❧✒❿ñ✇✌✈☞♣❛❸q✇➳✈☞✇➦Ø②✇✤❸àt✤ß☞⑩➄✇➦♣②⑩➄④Ñð❛♠♦♥ÙØ②✇➀⑤✐⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤➋⑤➋⑤➋⑤✐⑤➋⑤✐⑤ ✘ ❶

ä

Þ➥þ❰❸qØ②⑧✩❸q✇➘⑩➥✈✩✇ñ❿➀✇✧✈✩♣②❸q✇ ⑤➋⑤➋⑤✐⑤➋⑤❬⑤✐⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤➋⑤➋⑤➋⑤✐⑤➋⑤✐⑤ ✘

ä

✒❖✇✌✈☞♣②❸Ù✇➘⑩✕Ø②✇➘❿ìØít✤❿➀ß✻✇✤⑩✕♣②⑩♦Ø②t✤❸àt❰♠♦♣②⑩ò⑤✐⑤➋⑤❬⑤✐⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤➋⑤➋⑤➋⑤✐⑤➋⑤✐⑤

✛✧⑥

(10)

ä

ä

✒❑✇✧✈☞♣❛❸q✇➀Þ➥⑥❷✒➉➈➊✒❖✇✧✈✩♣②❸q✇ñÕ✩Ò✽⑥❷✒ ⑤✐⑤➋⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤➋⑤➋⑤➋⑤✐⑤➋⑤✐⑤

✛✧⑥

✛ ⑤ä ⑤❛✘ ✒❑✇✧✈☞♣❛❸q✇➘⑩➋✒❖t❰s♦s♦✇➘⑩★♣❛s❷t✤❸➍➌❳➎✽➏↔ç❋➌❳➎✽➏ ⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤➋⑤➋⑤➋⑤✐⑤➋⑤✐⑤ ✛✻✼

ä

✒❑✇✧✈☞♣❛❸q✇➳❽☎♠♦❻❼♣

♣❛s❷t❰❸➍➌➐➎✍➏➓ç➑➌❳➎✽➏ñ⑤❬⑤✐⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤➋⑤➋⑤➋⑤✐⑤➋⑤✐⑤

æ➘ä

ä

æ

Þ ✇✤r☞⑩♦♥Ù✈☞♣②♠♦t✤û②î✌♣②⑩★Û➘♣❛♠❾t✤♥Ù⑩ ⑤➋⑤✐⑤➋⑤❬⑤✐⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤➋⑤➋⑤➋⑤✐⑤➋⑤✐⑤

æ

✛ ⑤ä ⑤❛⑦ Þ ✇✤❿ñ✇➳⑧☞❿ìØít✤❿➀ß✻✇➦♣❛⑩♦Øít❰❸àt✤♠✕ß❼✇✧✈✩♣➋⑩➄♥q❿➚⑧✩❸àt✤♠ t➦❿ñt❰s♦ð②♠♦♥qt➚♣②⑩➄Ø②⑧☞♠♦t ⑤ æ ✘

ä

⑥☎♥q⑩♦Ø❛⑧☞⑩♦⑩➄î✧♣❛⑩☎Û✤♣②♠❾t❰♥q⑩ ⑤✐⑤➋⑤➋⑤✐⑤➋⑤❬⑤✐⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤➋⑤➋⑤➋⑤✐⑤➋⑤✐⑤

æ✽⑥

➒ s✐➾➊➬❸①✵❐ ➴✑tí➶➘➾❼rÑ➾☞❒✮✃➹➴❜➽➚❐➩❒✿➪❬➓ ❤ ➪♥➔➓➴❅r➛✃ →✹➣

→ ↔❖➾❼rÑ❐❥t➦✃➹➴❜➽➚❐➩❒✿➪❬➓

➪♥➔➓➴❅r➛✃ ➣

⑦✩⑤

Õ✧♥q❿➀ß☞❸Ù♥✁➊Ø②t✤ûíã✤✇✐✈➊t➦❿ñð➍s❾♠♦♥ÙØít ⑤✐⑤➋⑤➋⑤✐⑤➋⑤❬⑤✐⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤➋⑤➋⑤➋⑤✐⑤➋⑤✐⑤

⑥➘æ

⑦✩⑤

ä

⑦✸♥q❻❼♣②♠♦✈☞t✤✈☞♣ë✈☞♣❬Û✦t✤⑧✩Û➘♣P⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤❬⑤✐⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤➋⑤➋⑤➋⑤✐⑤➋⑤✐⑤

⑦✩⑤④✘ ❽✑r☞⑩♦t❰s❾ó❬ß➊t❰♠❾t➳✇➦Øít✤❿➀ß✻✇✬⑤✐⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤❬⑤✐⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤➋⑤➋⑤➋⑤✐⑤➋⑤✐⑤

⑥✽⑥

⑦✩⑤✛ á✑t❰s♦⑧☞♠♦♣❛óít➳✈➊t✤⑩★♣❛ï✌⑧☞t✤û②î✌♣②⑩❷✈☞♥Ù④Ñ♣❛♠♦♣❛r☞Ø②♥qt✤♥q⑩ ⑤✐⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤➋⑤➋⑤➋⑤✐⑤➋⑤✐⑤ ⑥✽⑥

⑦✩⑤

æ

â✵⑩➄s❾⑧✩✈☞✇ñ✈✩✇➀Ø②t✤⑩♦✇➀✈☞♣➋t✤❸ÙÛ➘⑧☞r☞⑩✕ß❼✇✤s❾♣❛r☞Ø②♥qt✤♥q⑩✕✈✩✇➦s♦♥qß❼✇

U

=

U

Φ

,

Φ

⑤✐⑤➋⑤✐⑤

⑥✍✼

⑦✩⑤

æ

③➹✇✤s❾♣❛r☞Ø②♥qt✤❸✡✈☞✇➦s❾♥Ùß✻✇

U

Φ

,

Φ

=

K

Φ

p

⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤➋⑤➋⑤➋⑤✐⑤➋⑤✐⑤

❶➘å

⑦✩⑤

æ

ä

③➹✇✤s❾♣❛r☞Ø②♥qt✤❸✡✈☞✇➦s❾♥Ùß✻✇

U

Φ

,

Φ

=

e

β

|

Φ

|

⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤➋⑤➋⑤➋⑤✐⑤➋⑤✐⑤ ❶✍✛

⑦✩⑤

æ

⑤❛✘ ③➹✇✤s❾♣❛r☞Ø②♥qt✤❸✡✈☞✇➦s❾♥Ùß✻✇

U

Φ

,

Φ

=

e

β

|

Φ

|

2

⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤➋⑤➋⑤➋⑤✐⑤➋⑤✐⑤

⑦✩⑤æ ⑤✛ ③➹✇✤s❾♣❛r☞Ø②♥qt✤❸✡✈☞✇➦s❾♥Ùß✻✇

U

Φ

,

Φ

=

e

β

|

Φ

|

3

⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤➋⑤➋⑤➋⑤✐⑤➋⑤✐⑤ ❶✻⑥ ⑦✩⑤④⑦ Þ ✇➘r☞⑩➄♥q✈☞♣❛♠❾t✤û❛î✧♣❛⑩✬☞r➊t✤♥q⑩❷⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤❬⑤✐⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤➋⑤➋⑤➋⑤✐⑤➋⑤✐⑤

✼➘å

➣ s✐❐✻➪➹➶✻r❭❦❧t✡↕✰➴❅t➦➴➙①✵➴Ý❒✮t✡①✵➴✌➶✍✐➫➮➜➛☞➾❼t ➝ ♣

➞ ➟ t✡①➹➾❼♠➘❐❹➓➠✐í➴✧➬➡①✵❐ ➴✑t✡➔ ➴Ý❒✿➮↔➶➘➾➊➬❺➴✧➪❥✐➐➴➙t②➮↔➬❸⑩✻✐➐❒✿➮➛➶➘❐ ➝❹③

➽ ➢✙➪❢➮➜➛❼➴✌❒✮t②❐➱✃➹➴ ➟ ➮↔➪♥t❆✐➐➴✌➮➛➪❋➓❾✃❂➴➥➤✡➮✴✐✡✐➐➴Ý❒ ➝✹➣

s ➞➧➦ ❐➩❒❰✃❂➾❹✈➩➴✌➬ ➛✸➮➛➾➨✐➐➴Ý❐➩❒✿➮➛➾➥r➛➮↔➪❂➴Ý➾☞❒ñ✃➹➴➩①✵➴Ý❒✱✐❄❦❂❒ ➦ ➾❼♠✽↕✰➴❅t ➝✇➝

➫ ➭ ➾ ➦ ➴✑rÑ➾➱➶➘❐❼➬ ➾❼t➀➶➘❐❼➪➹➴✦➷❋↕✡➴✑t ❣✑➯❥♣

➟ ➲ ❐❼✐➐➴✌➮➛❒➫❐②①❢➾✩❒✿➾❺➶➘❐❼➪✹✐➫➮➛➪❬❦❂➾❼♠✽♦☞❐ ✃❂❐❸✐➐❒➫➾ ➦ ➾❼r❭❺➹❐ ❣✑➯❥⑧

â✕⑤

③❢✇➘⑩➄⑩♦♥Ù❻☞♥q❸Ù♥q✈➊t✤✈✩♣②⑩➥Ø❛✇➘❿❴⑧☞❿❴ß❼✇✤s♦♣②r☞Ø❛♥àt✤❸✡✈✩✇➦s♦♥qß❼✇➳♣➍ê✧ß❼✇➘r☞♣②r✩Ø②♥àt❰❸❀⑤➋⑤➋⑤➋⑤✐⑤➋⑤✐⑤

✚➐å

â✕⑤

ä

Þ ✇➘❿➀✇❘♠♦♣②❸qt✤Ø②♥Ù✇➘r➊t✤♠✑✇➘⑩❬❿ñ✇✌✈☞♣②❸Ù✇➘⑩✴Ø❛✇➘❿●Øít❰❿ñß❼✇➘⑩✴♣❛⑩♦Øít❰❸àt✤♠➄♣②⑩❬Ø②✇➘❿ ✇➘⑩❬✈➊t✤✈☞✇➘⑩

(11)

❈❋❊✪●❄❍☞❊✪■❃❊✥❏✡❑☞▲❆▼✥◆P❖➺❊✪■☞◗✡❘❄❊✥❙❯❚❵❑☞❱❛❲✪▲➺❨✮▲❩■❬●✮▲❩❍❭❑☞❊✪■❋❨✱❊❉❘❄❙❯▲✣❪❆▲❩❫❛❚P❴✱❱❛▲❜❑❃❝❛●❄❱❳❲✥▲❄❞✴⑤➋⑤➋⑤➋⑤➋⑤✐⑤➋⑤✐⑤ ÷✧♥Ù♥q♥

ä ⑤✚ ➻ ❱❛▲❩❪❩❍➼▲P❙❯▲❧❖❩❍☞❱④❪❆❱④❏✮▲❩❫✱❨✱❊➑➽➑❘❄➾✮➾❄❫④❊❜➚➶➪❩➹✮❊❋❘✮❙②❍☞❊✪■❃❘❄❫➘❑➼▲❩❨✱❖❉❨✱❖❉➴❥❍❃❖❩➷✴❊➬❑❃❖❉➽➱➮✱✃❐➚❒➪❆➹✮❘❄❑❃❱❛❫④❱❛❮✪▲❩❏✮❨✱❖

❰ ❚P❍☞❱❛❖❆■⑨❙❇Ï➬❑❃❖✱❨✱❖✡■✇❨✱❱④ÐÑ❊✥❍☞❊✥❏✡❑❃❊➠■❼❨✱❊❋❙❇❊✪❨✱❱❳❨❄▲❉❨✱❊➑❨❄❱❛■❭❑☞Ò❩❏✮❲➬❱❳▲❄❞❼Ó✹❖❩❏✱ÐÑ❖❆❍❃❙❇❊❬●✟❖✱❨✱❊❧■❭❊❬❖❩➾✟■❭❊✪❍ ❰ ▲P❍➠Ô ❖❯❙❇❊✥❫❛Õ❄❖❆❍♥▲❵➷✴❘✮■❭❑❃❊➍▲P❑❃❘✮▲❩❫✧●✮▲❩❍☞▲✣❖❆■♥❨❄▲❩❨✱❖✡■➑❲➬❖❆❍❃❍☞❊✪■❃●✍❖❩❏✮❨✱❊❉▲❇❘❄❙❯▲❯❲✥❖❩❏✮■❭❑☞▲❩❏❆❑☞❊➍❨✱❊❜➽♥❘❄➾❄➾❄❫❛❊ Ö

H0

× ❨✱❊➍▲P●✮❍❃❖✖❴✱❱❛❙❇▲❆❨❄▲P❙❇❊✪❏❆❑☞❊

72

km.M pc

1

.s

1

❞ ⑤✐⑤➋⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤➋⑤➋⑤➋⑤✐⑤➋⑤✐⑤ ⑥

ä ⑤ ä Ø ❱④❏❄Õ✟▲➋❨✱❊➺❙❜❘❄❏✮❨❄❖ Ö ❊✪❙ ❰ ❊✪❍❃❙❇❊✥❫❛Õ❄❖ × ●✮▲❩❍☞▲❯❖Ù❖❩➾✮■❃❊✥❍ ❰ ▲❩❨✱❖❆❍➱Ú➡❊❜●✟▲P❍➼▲✬▲✬❪✡▲P❫❳❚❵❴✱❱❛▲ÙÛ✣❞✍Ü❧■ ❫❛❱④❏✮Õ✮▲❩■❋▲❩❮✥❘❄❱❳■❬❍❃❊✪●❄❍☞❊✪■❃❊✥❏✡❑☞▲❩❙Ý▲❜❑☞❍☞▲P➷✴❊➬❑☞Þ❩❍☞❱❛▲✣❨✱❖❆■❬❍➼▲P❱❛❖❆■❬❨✱❊➀❫❛❘❄❮❩❞ ⑤➋⑤✐⑤➋⑤➋⑤➋⑤➋⑤➋⑤✐⑤➋⑤✐⑤ ❶

ä ⑤④✘ ß✇▲❩❫④❖❆❍❃❊➠■❅●✍❊✥❍☞❙❇❱➘❑☞❱❛❨❄❖❆■❼●✮▲❩❍☞▲

m

DM

0

+ Ω

B

0

Λ

Ô❩❊✥❴✡❑☞❍☞▲❩❝❛❨❄❖➀❨❄❊❉➚➶➪❩➹à❞❥Ú➱■ ❰ ❝❛❏✮❲✥❘❄❫④❖✡■ ❨✱❱❛❮✥❊✪❙❁❍☞❊✪■❃●✍❊✥❱④❑❃❖➋▲Ù❨❄▲❩❨✱❖✡■➑❨✱❖✡■➑❊➬❴✱●✍❊✥❍☞❱④❙❇❊✪❏❆❑☞❖❆■➱➮✜❫④❖✡▲P❏ ➻ ❱④❪❆❱➘❑➼▲P❫❹➮✜á✜â❷➮✱❘❄❍ ❰ ❊✥â Ö ➮ ➻ ➮❄➮ × ❊ ã✙ä Ü♥➴❹Ô✟▲P❫❛Ï✥❙❁❨✱❊➀❍❃❊➠■✴❑☞❍❃❱❳▼➬å✜❊✪■æ●❄❍☞❖ ❰ ❊✪❏❄❱❛❊✥❏✡❑❃❊➠■æ❨❄❊❉❖❩➾✮■❃❊✥❍ ❰ ▲❩▼➬å✜❊➠■✹❨✱❊➍■❃❘❄●✍❊✥❍☞❏❄❖ ❰ ▲❩■✪❞✪⑤➋⑤✐⑤ ✚✜✛

✘✩⑤✚ ç ❴✜❑☞❍☞▲❩❝❛❨✱❖➍❨✮▲❉❍❃❊✥ÐÑ❊✥❍☞è✥❏✮❲✥❱❛▲✣➚❒➪❩➹éÔ✜▲P●✮❍❃❊➠■❭❊✪❏❆❑➼▲➀❙❯▲P❱❳■✇❨✱❊➍ê➠ë❩ë❉❲➬❘✮❍

❰ ▲❩■❥❨✱❊➑❍☞❖P❑☞▲❆▼✥◆❩❖➀❨❄❱➘ÐÑ❊✪❍❃❊✪❏❆❑☞❊✪■✪Ô ■❃❘❄❪❩❊✪❍❃❱❛❏✮❨✱❖➺ÐÑ❖❩❍❃❑❃❊✪❙❇❊✥❏✡❑❃❊➀❘❄❙❁●✟❊✪❍❭ì✮❫✑●❄❫❛▲❩❏❄❖❇●✮▲P❍➼▲➺❫④❖❆❏❄❪❆▲❆■æ❨❄❱❛■❭❑☞Ò❩❏✮❲➬❱❳▲❩■✪❞ ⑤➋⑤➋⑤➋⑤➋⑤✐⑤➋⑤✐⑤ ä✍❶ ✛ ⑤ ✚ ❈❋❊✪●❄❍☞❊✪■❃❊✥❏✡❑☞▲❆▼✥◆P❖❜❊✪■☞◗❆❘✮❊✥❙❯❚❵❑☞❱❛❲✪▲ Ö ➾❄❱❛❨❄❱④❙❇❊✥❏✟■❭❱❛❖❩❏✮▲❩❫ × ❨❄▲✣❊ ❰ ❖❩❫❛❘✮▼✪◆P❖➺❨✮▲❩■❬❲✥▲❩❙❇▲❆❨❄▲❩■✪❞❹Ü♥■❋❲✥▲Pí ❙❯▲❩❨✮▲❩■❋▲P❮✪❘❄❱❳■⑨➷❭❚➺●✟▲❩■☞■❃▲❩❍☞▲❩❙î●✟❊✪❫④❖❇❑☞❘❄❍❃❏❄íà▲❩❍❃❖❆❘❄❏✮❨✬❊➍▲❩❪❩❖❆❍☞▲✣▲P●✍❊✥❏✮▲❆■❋❨✱❱❛❙✣❱❛❏✜❘❄❊✥❙ï■❭❊✪❘ ❰ ❖❩❫④í ❘❄❙❇❊❆Ô✮❖✬❲➬❖❆❏✡❑❃❍➼❚P❍☞❱④❖ ❰ ▲P❫❛❊✥❏✮❨✱❖❯●✟▲P❍➼▲❯▲❩■ ❰ ❊✥❍➼❨✱❊✪■✪❞✹Ü➥❲✪▲P❙❯▲❩❨✮▲ ❰ ❊✥❍☞❙❇❊✥❫❛Õ✮▲❄Ô❄❱❛❏✮❨✱❱❳❲✥▲❆❨❄▲❇●✍❖❩❍❼➷ ❏❄❖❯❨✱❊➠■❭❊✪❏❄Õ❄❖✟Ô❄▲P●✮▲❩❍❃❊➠❲➬❊➱❏❄❖❇❊➬❴❄▲❵❑☞❖✣❙❇❖❆❙✣❊✪❏✡❑❃❖❇❊✥❙ï◗❆❘✮❊➀▲P❑❃❱❛❏❄❪❩❊

r

max

❞✒⑤➋⑤➋⑤➋⑤➋⑤✐⑤➋⑤✐⑤ ✛Ýä ✛ ⑤ ä ç ■❃●✍❊✪❲❂❑☞❍❃❖➑❨✮▲❩■✻●✍❖❆■☞■❭❝ ❰ ❊✪❱❛■✻❲✥❖❩❏✮❨❄❱❛▼✥å✡❊➠■✻❱❛❏❄❱❛❲✥❱❛▲❩❱❛■✑◗❆❘✮❊❼❫④❊ ❰ ▲❩❙➃▲❬❘❄❙➩❨✱❊➠❲✥▲P❱❛❙❇❊✥❏✡❑❃❖➑❨✮▲❋■❭❖❆❫④❘✮▼✪◆P❖ ●✮▲❩❍☞▲❯▲➋❙❇Ï➬❑❃❍☞❱❳❲✥▲

u

(

x

)

❏❄❖➋❱❛❏✱ì✮❏❄❱④❑❃❖✟❞➀Ú➱■♥●❄❱❛❲✥❖❆■➱■❭❊❜❍❃❊✥ÐÑ❊✥❍☞❊✥❙ñð✬❲➬❖❆❏✮❨✱❱❳▼➬å✜❊✪■♥❱④❏✮❱❛❲✥❱❛▲❩❱❛■❧◗❆❘✮❊ ❫❛❊ ❰ ▲P❙òð✗■❃❖❩❫❛❘✮▼➬å✜❊✪■➀❲✥❖❩❙ò❲➬❖❆❙❇●✟❖❆❍❭❑➼▲P❙❇❊✥❏✡❑❃❖✗▲❩■☞■❭❱❛❏✡❑❃Þ❩❑❃❱❳❲➬❖Ù❨❄❊✪❲➬❍☞❊✪■☞❲➬❊✪❏✡❑❃❊✣●✮▲P❍➼▲➋▲❆■➱❲✥❘❄❍ ❰ ▲❆■

❨✱❊➀❍☞❖P❑➼▲❩▼✥◆❩❖✮❞ ⑤✐⑤➋⑤➋⑤➋⑤➋⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤❬⑤✐⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤➋⑤➋⑤➋⑤✐⑤➋⑤✐⑤ ⑦

✛ ✛ ⑤④✘ Ó✹❘❄❍ ❰ ▲❩■❬❨✱❊❉❍☞❖P❑➼▲❩▼✥◆❩❖❜●✮▲❩❍☞▲✣❖✡■æ▲❩❘✱❑❃❖ ❰

▲❩❫④❖❆❍❃❊➠■✹❏✽ó➱ë❜❊❉❏✍ó➺ê❆❞ ⑤✐⑤➋⑤✐⑤➋⑤➋⑤➋⑤➋⑤➋⑤✐⑤➋⑤✐⑤ ⑦

✛ ✛ ⑤ ✛ Ó✹❘❄❍ ❰ ▲❩■❬❨✱❊❉❍☞❖P❑➼▲❩▼✥◆❩❖❜●✮▲❩❍☞▲✣❖✡■æ▲❩❘✱❑❃❖ ❰ ▲❩❫④❖❆❍❃❊➠■✹❏✽ó➀ô➍❊❉❏✍ó➱õ✮❞➋⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤➋⑤➋⑤➋⑤✐⑤➋⑤✐⑤ ⑦ æ

✛ ⑤æ Ó✹❘❄❍

▲❩■❬❨✱❊❉❍☞❖P❑➼▲❩▼✥◆❩❖❜●✮▲❩❍☞▲✣❖✡■æ▲❩❘✱❑❃❖

▲❩❫④❖❆❍❃❊➠■æ▲❩❘✱❑❃❖

▲❩❫④❖❆❍❃❊➠■❥❏✍ó➀ö➺❊➀❏✍ó➺ê➠ë❄❞❢⑤➋⑤➋⑤➋⑤✐⑤➋⑤✐⑤ ⑦ æ

✛ ⑤④⑦ Ó✹❘❄❍ ❰ ▲❇❨✱❊➀❍❃❖❩❑☞▲❩▼✪◆P❖✣●✮▲P❍➼▲➺❖❇▲❩❘✱❑❃❖ ❰ ▲❩❫④❖❆❍æ❏✽ó

❞ ⑤✐⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤➋⑤➋⑤➋⑤✐⑤➋⑤✐⑤ ⑦✽⑦

æ ⑤✚ Û➱❍➼❚❵ì✟❲✥❖❋❨✱❊

σ

(

x

)

❏❄❖➑❲✥▲❆■❭❖❋❨✱❊❼❘❄❙➙●✍❖P❑❃❊✪❏✮❲➬❱❳▲P❫

U

,

Φ

)

❲✥❖❩❏✮■❭❑☞▲❩❏✡❑❃❊❹●✮▲P❍➼▲❬❨✱❘✮▲❆■✧❲➬❖❆❏✮❨✱❱❳▼➬å✜❊✪■ ❱❛❏❄❱❳❲➬❱❳▲P❱❳■✑❍☞❊✥●❄❍☞❊✪■❃❊✥❏✡❑➼▲❵❑❃❱ ❰ ▲❩■❅❨✱❖❧❲✥❖❩❙❇●✟❖❆❍❭❑➼▲P❙❇❊✥❏✡❑☞❖❧❨❄▲➑ÐÑ❘❄❏✮▼✥◆❩❖✮❞❹÷➑❙❯▲➑●✟▲P❍➼▲➑❘❄❙❯▲➱❲➬❖❩❏✟❨✱❱❛▼✪◆P❖ ❱❛❏❄❱❳❲➬❱❳▲P❫✡●❄❍❃Þ✖❴✱❱❛❙❯▲➑❨✱❊❬ë❄Ô✖❖❩❘✱❑☞❍☞▲♥●❄❍☞Þ✖❴✜❱❛❙❯▲➑❨✱❊➱ê❩❞ ç ❙➥▲P❙➺➾✟❖✡■✑❖✡■❅❲✪▲❩■❃❖❆■✪Ô

˜

σ

(0)

ÐÑ❖❩❱✱■❃❘❄●✟❖✡■✴❑☞❖ ❏✜❘❄❫❛❖✮❞ ç ❙ñ❲✥▲❆❨❄▲❇❪❩❍➼❚❵ì✍❲➬❖✮Ô✱●✮❫④❖❩❑❃❖❩❘❄íà■❃❊➀❑☞▲❩❙❜➾✍Ï✥❙ø❘❄❙❯▲✬❲➬❘✮❍ ❰ ▲❯❨✱❖❯❑☞❱④●✍❖

σ

(0)

sin(

x

x

)

(12)

ù æ ⑤ ä Û➱❍➼❚❵ì✟❲✥❖❆■❋●✟▲P❍➼▲❯▲✬❨✱❊✥❏✟■❭❱❳❨❄▲❩❨❄❊❜❨✱❊❜❊✪❏❄❊✥❍☞❪❩❱❳▲❇❊➍●❄❍☞❊✪■☞■❃å✡❊➠■➑❨✱❖➋❲✪▲P❙❇●✍❖✮❞✄✂➑❖✗❲✥▲❆■❭❖✬▲❩●❄❍❃❊➠■❭❊✪❏✱í ❑➼▲❩❨✱❖✟Ô✪ÐÑ❖❆❱✜❘✱❑❃❱❛❫④❱❛❮✪▲❆❨✱❖➱❘❄❙

e

σ

(0) = 0

.

999

Ô

˜

σ

(0) = 0

❊✹❖❧●✟❖❩❑❃❊✪❏✮❲➬❱❳▲P❫

U

,

Φ

)

ÔP■❃❘❄●✍❖❆■❭❑❃❖ ❲✥❖❩❏✮■❭❑☞▲❩❏❆❑☞❊❩Ô✡ÐÑ❖❩❱✑❏❄❖❩❍☞❙❯▲P❫❛❱④❮➠▲❩❨✱❖➺●✮▲P❍➼▲✗ê❩❞ ⑤✐⑤➋⑤❬⑤✐⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤➋⑤➋⑤➋⑤✐⑤➋⑤✐⑤ ⑥➘ä æ ⑤④✘ Û➱❍➼❚❵ì✟❲✥❖❉❫④❖❆❪Píà❫④❖❆❪➍❨❄▲❜❨❄❊✥❏✮■❃❱❛❨✮▲❩❨✱❊♥❨❄❊♥❊✥❏✮❊✥❍☞❪❩❱❳▲❉●✮▲P❍➼▲ ❰ ❚P❍☞❱❛▲❆■❥❲✥❖❩❏✮❨✱❱❳▼➬å✜❊➠■✇❱❛❏❄❱❛❲✥❱❛▲❩❱❛■✹❨✱❱④ÐÑ❊✥❍☞❊✥❏✡❑❃❊➠■♥❞ ⑥ ✘

æ ⑤✛ Û➱❍➼❚❵ì✟❲✥❖❆■➺●✮▲P❍➼▲

x

2

ρ

(

x

)

●✮▲❩❍☞▲ ❘❄❙❯▲ ❲➬❖❩❏✟❨✱❱❛▼✪◆P❖ ❱④❏✮❱❛❲✥❱❛▲❩❫❬◗✡❘✮▲❩❫❛◗✡❘❄❊✪❍❇❍❃❊✪●❄❍❃❊➠■❭❊✪❏✡❑☞▲❵❑☞❱

▲ ❨✱❖

❲✥❖❩❙❇●✟❖❆❍❭❑➼▲P❙❇❊✥❏✡❑☞❖✓❨❄▲❷ÐÑ❘✮❏✮▼✥◆❩❖

Ö

σ

(0) = 0

.

50

Ô

σ

(0) = 0

× ❞ Ú➱■❜❪❆❍☞❚Pì✟❲➬❖✡■❉❙❇❖❆■❭❑❃❍➼▲P❙ ❍☞❊✥❪❆❱④å✜❊✪■❜❨✱❱❛■❭❑❃❱❛❏✡❑☞▲❆■➺❨✱❖✓❊✪■❃●✮▲❩▼✥❖ Ö ●❄❍☞Þ✖❴✱❱④❙❯▲➅❖❆❘❻❨✱❱❳■✴❑➼▲P❏✡❑❃❊✗❨❄▲❷❖❩❍☞❱❛❪❩❊✥❙ × ❊✗▲❩■➺❨✱❱➘ÐÑ❊✪❍❃❊✪❏✮▼✥▲❆■ ❊✪❏✮❲➬❖❆❏❆❑☞❍☞▲❆❨❄▲❩■æ◗✡❘✮▲P❏✟❨✱❖❇Ï➀❨❄❊✪■☞❲➬❖❩❏✡❑➼▲❩❨✱❖ Ö ❊➠■❃◗✡❘❄❊✪❍☞❨❄▲ ×

❖❩❘➅❏✮◆P❖✣❖✣ÐÑ❘❄❏✮❨✱❖✟❞ ⑤➋⑤➋⑤➋⑤✐⑤➋⑤✐⑤ ⑥✟✛

⑦✩⑤

Û➱❍➼❚❵ì✟❲✥❖❆■❇●✮▲❩❍☞▲✕▲❻▲P❏✮❚❩❫④❱❳■❭❊ ❨❄❖✏❙❇❖✜❨❄❊✥❫❛❖❻❨✱❊✏➚❒➪✟Ô❬➪❩➹❉▲P●❄❍☞❊✪■❃❊✥❏✡❑➼▲❩❨✱❖☎❏❄❖ Óæ▲❩●✧❞✆☎✮❞✆✂➑❖✡■

❪❆❍☞❚Pì✟❲➬❖✡■✥Ô✡▲❩■æ■❭❊✪❪❩❘❄❱❛❏✡❑❃❊✪■✹❲➬❖❆❏✮❨✱❱❳▼➬å✜❊✪■✹❱④❏✮❱❛❲✥❱❛▲❩❱❛■❥ÐÑ❖❩❍➼▲P❙ ❘✱❑☞❱④❫❛❱④❮➠▲❩❨❄▲❆■✞✝

σ

(0) = 1

Ô

σ

(0) = 0

Ô

u

(0) =

1

.

3437

Ô

u

(0) = 0

Ö

❲✥▲❆■❭❖

n

= 2

×

σ

(0) = 1

Ô

σ

(0) = 0

Ô

u

(0) =

1

.

6831

u

(0) = 0

Ö

❲✥▲❆■❭❖

n

= 10

×

❞❘⑤➋⑤✐⑤❬⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤✐⑤❬⑤➋⑤✐⑤➋⑤✐⑤➋⑤

⑥✍❶

⑦✩⑤

ä

Û➱❍➼❚❵ì✟❲✥❖❉❑❃❍☞❱❳❨✱❱④❙❇❊✪❏✮■❭❱❛❖❩❏✟▲P❫✟▲❩●❄❍☞❊✪■❃❊✥❏✡❑☞▲❩❏✮❨✱❖❉❘❄❙ ❑☞❍❃❊➠❲➼Õ❄❖❜❨✱❖➺❊✪■❃●✮▲❩▼✥❖❜❨✱❊➱●✮▲P❍➼ÒP❙❇❊➬❑☞❍❃❖✡■❼●✮▲❩❍☞▲

u

(

x

)

p

❞ ⑤➋⑤➋⑤✐⑤➋⑤❬⑤✐⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤✐⑤➋⑤❬⑤✐⑤➋⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤❬⑤✐⑤➋⑤✐⑤➋⑤➋⑤ ❶⑨✚

⑦✩⑤④✘ Û➱❍➼❚❵ì✟❲✥❖❆■❬●✮▲❩❍☞▲❇▲❩❫④❪❆❘❄❏✮■

▲P❫❛❖❩❍☞❊✪■❋❨❄❖✬●✮▲P❍➼ÒP❙❇❊✥❑❃❍☞❖➺●

Ö

p

= 0

,

1

,

2

×

❨❄❖✬●✟❖❩❑❃❊✪❏✮❲➬❱❳▲P❫✧●✟▲P❍➼▲❇❖ ❲✪▲P❙❇●✟❖✟❞✠✟➨❱❛❙✣❊➠❨✱❱❳▲❵❑❃❖➅❏❄❖❩❑☞▲❩❍❜◗✡❘❄❊✬✃❅Ü ➻ ➮☎■❃Þ❷■❭❊❇❑☞❖❩❍☞❏✮▲✗❏❄❊✥❪✡▲❵❑☞❱ ❰ ❖ Ö ❖ ◗✡❘❄❊❯●✟❊✪❍❃❙❇❱④❑❃❱❛❍❃❱❳▲

❘❄❙ý❲➬❖❩❙❇●✍❖❩❍❃❑☞▲❩❙✣❊✪❏✡❑❃❖ ❨❄❖ ❑☞❱④●✍❖☎❊➬❴✱●✍❖❩❏❄❊✪❏✮❲➬❱❳▲P❫❬●✮▲❩❍☞▲ ❖ ❲✪▲P❙❇●✍❖

× ●✮▲P❍➼▲ ❰ ▲❩❫④❖❆❍❃❊➠■❜❙➺❘❄❱➘❑☞❖ ❪❆❍☞▲❩❏✮❨✱❊✪■æ❊➀●✍❖❆■❃❱➘❑☞❱ ❰ ❖❆■❋❨✱❊➀❘

(

x

)

❞ ⑤➋⑤✐⑤➋⑤✐⑤➋⑤❬⑤✐⑤➋⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤❬⑤✐⑤➋⑤✐⑤➋⑤➋⑤ ❶✦ä ⑦✩⑤ ✛ Û➱❍➼❚❵ì✟❲✥❖❆■➀❨❄▲❷■❃❖❩❫❛❘✮▼✥◆❩❖➅●✮▲P❍➼▲✗❖ ❲✥▲P❙❇●✍❖❷❊✬❨❄▲❷❨✱❊✪❏✮■❭❱❳❨❄▲❆❨✱❊❯❊➬ÐÑ❊✥❑❃❱ ❰

▲ ●✮▲P❍➼▲➅❲✥▲❩❨✮▲Ù❘✮❙ ❨✱❖✡■

❲✪▲❩■❃❖❆■✪❞➑Ú➱■♥●✮▲P❍➼ÒP❙❇❊✥❑❃❍☞❖❆■❬❘✱❑☞❱④❫❛❱④❮➠▲❩❨✱❖✡■❋ÐÑ❖❆❍☞▲❩❙

u

(0) =

0

.

01

Ô

u

(0) = 0

Ô

σ

(0) = 0

.

2

Ô

σ

(0) = 0

❊❉❖

▲P❫❛❖❩❍❬●✮▲❩❍☞▲

8

πG

ω

2

K

= 10

5

❞ ⑤❬⑤✐⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤➋⑤➋⑤➋⑤✐⑤➋⑤✐⑤ ❶ ✘ ⑦✩⑤ æ Ó✹❘❄❍ ❰ ▲❩■➑❨❄❊❜❍☞❖P❑☞▲❆▼✥◆❩❖✣●✟▲P❍➼▲✬▲❩■♥●✮▲P❍❃❑❃❝❳❲➬❘❄❫❳▲❩■❭íé❑❃❊✪■❭❑❃❊❆❞❋Ü♥■➱❲➬❘❄❍ ❰ ▲❩■❋ÐÑ❖❆❍☞▲❩❙ ÐÑ❊✪❱➘❑➼▲❩■♥●✮▲P❍➼▲❯❘❄❙❯▲ ❍☞❊✥❪❆❱❛◆❩❖❧❖❆❏✮❨✱❊❋▲❉▲P●❄❍☞❖✖❴✱❱④❙❯▲❆▼✥◆P❖❧❏❄❊✞✡❬❑☞❖❩❏❄❱❳▲P❏✟▲❧●✟▲P❍➼▲

u

(

x

)

▲❩❱④❏✟❨❄▲➱Ï ❰ ❚❩❫④❱❳❨❄▲➱❊❋❖❆■✇●✮▲P❍➼ÒP❙❇❊➬❑❃í ❍☞❖❆■✹❘✱❑❃❱❛❫❛❱④❮➠▲❩❨✱❖✡■❥ÐÑ❖❆❍☞▲❩❙î❖❆■æ❙❇❊✪■❃❙❇❖❆■❬❨✱❖❇❪❩❍➼❚❵ì✟❲✥❖ Ö☞☛ ❞☎ × ❞❥Ú➙●✟▲P❱❛❏❄❊✥❫✻❱❛❏✱ÐÑ❊✥❍☞❱❛❖❩❍❋▲P●❄❍☞❊✪■❃❊✥❏✡❑➼▲❜▲ ❊ ❰ ❖❩❫❛❘✮▼✪◆P❖➺❨❄❖✣●✟▲P❍➼ÒP❙❇❊➬❑☞❍❃❖

u

ef f

(

x

)

❞✧⑤✐⑤➋⑤✐⑤➋⑤❬⑤✐⑤➋⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤❬⑤✐⑤➋⑤✐⑤➋⑤➋⑤

❶✍✛

⑦✩⑤④⑦ ❈❋❊✪●❄❍☞❊✪■❃❊✥❏✡❑☞▲❆▼✥◆P❖♥❑❃❍☞❱❛❨❄❱④❙❇❊✥❏✟■❭❱❛❖❩❏✮▲❩❫✮❨✱❖❉❊➠■❭●✮▲❆▼➬❖❉❨✱❖➀●✮▲❩❍☞Ò❩❙✣❊✥❑❃❍☞❖

β

❊➑❨❄❖➍❲➬❖✜❊➬ì✟❲✥❱④❊✪❏✡❑❃❊

u

(

x

)

✌ ❨✱❱❛❍❃❊✪❱➘❑➼▲➍Ï➀▲P●❄❍☞❊✪■❃❊✥❏✡❑☞▲❆❨✱❖❉❘❄❙Ý❲✥❖❩❍❃❑❃❊♥●✟▲P❍➼▲➍❘❄❙Ý❲✪▲❩■❃❖➍❍❃❊✪●❄❍☞❊✪■❃❊✥❏✡❑☞▲P❑❃❱

❖✮Ô✡◗✡❘✮▲P❏✮❨❄❖

β

= 1

❞ ✂♥❖ ❰ ▲❩❙❇❊✥❏✡❑❃❊❆Ô❆✃⑨Ü ➻ ➮✬■❃Þ➺■❃❊❋❑❃❖❆❍❃❏✮▲➍❏❄❊✥❪✡▲❵❑❃❱ ❰ ❖❜●✮▲P❍➼▲ ❰ ▲P❫❛❖❩❍☞❊✪■✇❍☞❊✥❫❳▲❵❑☞❱ ❰ ▲❩❙✣❊✪❏✡❑❃❊➑❪❆❍☞▲❩❏✮❨✱❊✪■❥❨✱❊

u

(

x

)

❞ ⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤❬⑤✐⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤✐⑤➋⑤❬⑤✐⑤➋⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤❬⑤✐⑤➋⑤✐⑤➋⑤➋⑤ ❶✦æ

⑦✩⑤ ⑥ Û➱❍➼❚❵ì✟❲✥❖➍❍☞❊✥●❄❍☞❊✪■❃❊✥❏✡❑☞▲P❑❃❱ ❰ ❖➍❨❄▲❜❊ ❰ ❖❩❫❛❘✮▼✥◆❩❖❜❨✱❖❆■✹●✮▲❩❍☞Ò❩❙✣❊✥❑❃❍☞❖❆■✪❞✍✂♥❊✪■☞■❭❊➱❲✥▲❩■❃❖➍❊✪❙î●✮▲P❍❃❑❃❱❳❲➬❘❄❫❳▲P❍➠Ô

β

= 2

❞✟⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤❬⑤✐⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤✐⑤➋⑤❬⑤✐⑤➋⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤❬⑤✐⑤➋⑤✐⑤➋⑤➋⑤

⑦✩⑤❶ ❈❋❊✪●❄❍☞❊✪■❃❊✥❏✡❑☞▲❆▼✥◆P❖✬❨❄❖❆■❧●✟❖✡■❃■❃❝

❰ ❊✥❱❳■ ❰ ▲P❫❛❖❩❍☞❊✪■♥●✮▲P❍➼▲❯❖Ù●✮▲P❍➼ÒP❙❇❊➬❑☞❍❃❖

β

❊➺▲❆■♥●✍❖❆■☞■❭❝ ❰ ❊✪❱❛■♥❱④❙❇●❄❫❛❱④í ❲✪▲❩▼➬å✜❊➠■✇●✮▲❩❍☞▲❉❖✣■❭❱❛❏✮▲❩❫✟❨✱❊➀✃❅Ü ➻ ➮✻❞❄Ú➃❪❆❍☞❚Pì✟❲➬❖➍▲➺❨✱❱❛❍❃❊✪❱➘❑➼▲➍Ï♥❘✮❙î❊➬❴✱❊✥❙❇●❄❫❛❖❜❍☞❊✥●❄❍☞❊✪■❃❊✥❏✡❑➼▲❵❑❃❱ ❰ ❖ ❨❄▲❆■✇❲➬❖❆❏✮❲➬❫❛❘✮■❃å✜❊✪■❹❖❩➾❄❑❃❱❳❨❄▲❩■✪Ô❆◗✡❘❄❊❬❑➼▲P❙❜➾✍Ï✥❙❸❍☞❊✪◗✡❘❄❊✥❍☞❊✥❙②❘❄❙ ❰ ▲❩❫④❖❆❍❥▲P❫④❑❃❖➍❨✱❊

u

(

x

)

●✮▲P❍➼▲➀◗❆❘✮❊

■❃❊➀❖❩➾✱❑☞❊✥❏❄Õ✮▲✣❘❄❙ï✃❅Ü ➻ ➮Ù❏❄❊✪❪❆▲P❑❃❱

❖✮❞ ⑤➋⑤✐⑤➋⑤❬⑤✐⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤➋⑤➋⑤➋⑤✐⑤➋⑤✐⑤ ❶✻⑥

⑦✩⑤

Ú ❪❆❍☞❚Pì✟❲➬❖❧ð♥❊➠■❃◗✡❘❄❊✪❍☞❨❄▲❧▲P●❄❍☞❊✪■❃❊✥❏✡❑➼▲➑▲❧■❃❖❩❫❛❘✮▼✪◆P❖

σ01

Ö

❲➬❘❵➷✴❖➱❙❇Þ✜❨❄❘❄❫④❖❉■❃❊✥❙❇●❄❍☞❊❥Ï

(13)

ù

⑦✩⑤

✘òÓ✹❖❆❙✣●✍❖❩❍❃❑☞▲❩❙❇❊✥❏✡❑❃❖❯●✍❖❆■☞■❭❝

❊✪❫✑●✮▲❩❍☞▲❯▲❆■♥❲✥❘❄❍

▲❆■♥❨✱❊➺❍❃❖❩❑☞▲❩▼✪◆P❖❇❊✥❙ø❘❄❙ñ❲✪▲❩■❃❖➋❨✱❊❜●✍❖P❑☞❊✥❏✮❲✥❱❛▲❩❫

❨✱❖✣❑☞❱④●✍❖❯❫④❊✪❱✧❨✱❊❉●✍❖P❑❃è✪❏✮❲➬❱❳▲❄Ô✟❲➬❖❩❙ ●✍ó➱ë

Ö

●✍❖P❑❃❊✪❏✮❲➬❱❳▲P❫✧❲✥❖❩❏✮■❭❑☞▲❩❏✡❑❃❊

×

❞Ý⑤➋⑤✐⑤➋⑤➋⑤➋⑤➋⑤➋⑤✐⑤➋⑤✐⑤ ✼⑨✚

â✕⑤

Þ➥t✤⑩♦✇

V

(Φ) =

e

β

Φ

2

ç❼Ø②✇✤❿

β

= 0

.

5

ç

σ

(0) = 0

.

02

ç

σ

(0) = 0

ç

u

(0) =

0

.

01

ç

(14)

ä

ß✇▲❩❍❃❱❳▲❩▼✪◆P❖✬❨✱❖❯Ð✾▲P❑❃❖❆❍➱❨✱❊➺❊✪■☞❲✥▲❩❫❛▲❯❲✥❖❩❙ø❖✬❑☞❊✥❙❇●✟❖Ù●✮▲P❍➼▲✬❨✱❱④ÐÑ❊✥❍☞❊✥❏✡❑☞❊✪■♥❲✥❖❩❙❇●✍❖❩❏❄❊✪❏❆❑☞❊✪■➱❨✱❖❩❙❇❱④í

❏✮▲❩❏✡❑❃❊✪■✪❞ÿ⑤✐⑤➋⑤✐⑤➋⑤➋⑤➋⑤➋⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤❬⑤✐⑤➋⑤✐⑤➋⑤➋⑤✐⑤➋⑤✐⑤➋⑤➋⑤➋⑤➋⑤➋⑤✐⑤➋⑤✐⑤ ✚➫ä

✘✩⑤

➴❼▲P❍➼ÒP❙❇❊✥❑❃❍☞❖❆■

Ö

õ✮❞④ê✔✓

×

●✮▲❩❍☞▲❯▲❩❫④❪❆❘❄❏✮■❧❨✱❖❆■♥●✟❊✪❍❭ì✟■♥❙❯▲P❱❳■❋❘✱❑❃❱❛❫❛❱④❮➠▲❩❨✱❖✡■➑●✮▲❩❍☞▲❇❙❇❖✱❨✱❊✥❫❳▲P❪❆❊✥❙ø❨❄▲

❨✱❊✪❏✮■❃❱❛❨❄▲❆❨✱❊✹❨❄❖❆■❅Õ✮▲P❫❛❖❆■❅❊✪■☞❲➬❘❄❍☞❖❆■❅❊✥❙➨❪✡▲P❫❳❚❵❴✱❱❳▲❩■✪❞❅Ú➱■

▲P❫❛❖❩❍☞❊✪■⑨❨✱❊❬❈

Ö

r

m

, r

s

❖❆❘

r

c

×

▲P❍☞❱❛▲❩❙

(15)

✙➳ú✪■✙▲❖❈❨❊➺❙✛✚✢✜ ❈

é ♣②❿➀✇➘⑩✹õ✩✇✿ý➄♣✑❿➚⑧✩♥Ùs❾✇➋❿ñt✤♥q⑩✵♥Ùr✩④Ñ✇➘♠♦❿ñt✤û❛î✧♣❛⑩✹t➋♠♦♣❛⑩♦ß❼♣②♥Ùs♦✇ò✈☞✇✐⑧☞r☞♥ö÷➘♣②♠➄⑩♦✇➚✈✩✇òïÝ⑧☞♣✑ß✩♠♦✇➐÷❰t➐÷✤♣②❸Ù❿ñ♣❛rÝs♦♣

✇❑❿✮t✤♥Ù⑩✴✇✤s♦♥q❿➀♥q⑩➄s❾t✮✈☞✇➘⑩❬Û➘♠➄♣②Û➘✇✤⑩✐t❰rÝs♦♥qÛ➘✇✤⑩ëß✻✇✌✈☞♣②♠➄♥àt ♥Ù❿✮t✤Û✤♥qr➊t✤♠❛⑤ò❽✪Ø②♠➄♣②⑩➄Ø②♣②r✦s♦♣❘tí÷✤t❰❸àt✤r☞Ø✉õ✩♣➳✈☞♣

r☞✇➐÷➘✇✤⑩ñ✈➊t❰✈☞✇➘⑩➀✇➘❻☞⑩♦♣❛♠➄÷❰t✤Ø❛♥q✇➘r➊t❰♥q⑩➳ïÝ⑧☞♣❖÷✤è②❿❀⑩➄⑧☞♠♦Û➘♥Ùr☞✈☞✇❺t➧Ø②t✤✈➊t ✈☞♥àt Ø②✇✤❿ñ♣❛ûít➧t➧ß❼♣②♠➄❿ñ♥ös❾♥q♠òt

❿➀✇➘r✦s✉t✤Û➘♣❛❿✘✈☞♣✑⑧✩❿✮t❷✞ ÷✌♥q⑩♦ã✤✇✐ß☞t✤r☞✇➘♠➠⑤✤❿ñ♥ÙØít✮✞✕✈☞✇➚t✤⑩➄⑩♦⑧☞r✦s♦✇➚ïÝ⑧☞♣ët❰s♦ð✑ß❼✇➘⑧☞Ø②✇➋s❾♣❛❿ñß❼✇➚t❰s♦♠❾þ✤⑩✛♣②♠♦t

⑩♦♥Ù❿ñß✩❸q♣②⑩➄❿ñ♣❛r✦s❾♣❑♥qr☞♥Ù❿✮t✤Û✤♥qr➊þí÷➘♣❛❸➓⑤ ❶❷♣❛⑩♦⑧☞❸ös✉t✤✈✩✇➘⑩✮✈☞♣❑r☞✇➐÷➘✇✤⑩ ♣➍ê✧ß❼♣②♠♦♥Ù❿ñ♣❛r✦s❾✇➘⑩ñ⑩❾ã✤✇❺✈☞♥Ù÷✌⑧☞❸ÙÛ✦t✤✈☞✇➘⑩

Ø②✇✤r☞⑩➄s❾t✤r✦s❾♣②❿➀♣②r✦s♦♣✤ç✡✇ ïÝ⑧☞♣òr☞✇➘⑩✑ß❼♣②♠➄❿ñ♥ös❾♣➋✈☞♣②⑩➄Ø②♠➄♣❛÷➘♣❛♠ëØ②✇➘❿ ♠♦t✤ó②✇✦þí÷✤♣②❸✽♣❛❸q✇✌ï✤✣☞è②r☞Ø❛♥àt➀✇ ïÝ⑧☞♣➚♣②r✌Ó

s❾♣❛r☞✈☞♣❛❿ñ✇➘⑩✛ß❼✇➘♠✟❿ñ✇✌✈☞♣②❸Ù✇ëØ②✇➘⑩➄❿ñ✇✤❸é✠➘Û➘♥ÙØ②✇ëß➊t❰✈☞♠❾ã✤✇✮Ï☞✒➭Þ➥③✹Ö❞⑤✌â✟⑩➄⑩♦♣☎❿ñ✇✌✈☞♣②❸Ù✇☞ç➘ß❼✇➘♠✟⑩♦⑧➊t❬÷➘♣❛ó✤çÝs❾♣②❿

⑩♦♣➀❿➀✇➘⑩➄s♦♠❾t✤✈☞✇✙Ø❛✇➘❿ñ✇✙⑧☞❿ñt✙♣②⑩♦ß❼ð②Ø❛♥q♣➀✈☞♣➦♠❾t✤⑩➄Ø②⑧☞r✩õ☞✇➭✈☞♣➀♥q✈✩ð②♥àt❰⑩ë♣➀Ø❛✇➘r☞⑩✎s✉t❰s❾t✤û②î✌♣②⑩➋ïÝ⑧☞♣➀÷❰t✤♥✵⑩➄♣

t✤ß❼♣②♠✎④Ñ♣②♥qû❛✇✦t✤r☞✈✩✇✙t❑Ø②t✤✈➊t❘r☞✇➐÷➘✇❑♣➍ê✧ß❼♣②♠♦♥Ù❿ñ♣❛r✦s❾✇✙❸àt✤r✩ûít✤✈☞✇✩ç❂t✤❸qû②t✤r☞✈☞✇✙t❑Þ ✇➘⑩➄❿ñ✇➘❸Ù✇➘Û➘♥qt✮✈☞♣➦⑧☞❿ñt

Ø②♥Ùè②r☞Ø❛♥àt✮❻☞t✤⑩➄s❾t✤r✦s❾♣➚♣❛⑩♦ß❼♣②Ø②⑧✩❸àt❰s♦♥Ù÷❰tñß➊t❰♠❾t ⑧☞❿ ♠♦♣❛Ø②✇➘r✩õ☞♣②Ø❛♥q✈☞✇❘⑩✎s✉t❰s♦⑧☞⑩✴✈☞♣òs♦♣②✇➘♠➄♥àt t❰❿ñß☞❸qt✤❿➀♣②r✦s❾♣

t✤❿➀ß➊t✤♠♦t✤✈➊t➚♣②❿ì♠♦♣②⑩➄⑧☞❸Ùs❾t✤✈☞✇➘⑩★✇➘❻✩⑩♦♣②♠✎÷❰t✤Ø②♥Ù✇➘r➊t✤♥Ù⑩②⑤

③❢✇➘♠❑✇➘⑧✩s♦♠♦✇❚❸àt❰✈☞✇☞ç☎s❾t✤❸Ù÷✤♣②ó➧t✤♥Ùr☞✈➊t ❿✮t❰♥q⑩ ♥ÙrÝs♦♣②♠➄♣②⑩♦⑩♦t✤r✦s❾♣❺ï✌⑧✩♣❺✇ Ø②♠➄♣②⑩♦Ø❛♣②r✦s❾♣➧÷➘✇➘❸Ù⑧☞❿➀♣❜✈☞♣

✈➊t✤✈✩✇➘⑩✙Ø②✇➘❸Ù♣❛s✉t❰✈☞✇➘⑩❘ð ïÝ⑧☞♣ ß☞♠❾t❰s♦♥qØ②t✤❿ñ♣❛r✦s❾♣❜r➊t ❿➀♣②⑩♦❿ñt ❿ñ♣❛✈☞♥q✈☞t ♣②❿ ïÝ⑧☞♣ ⑩♦⑧✩♠♦Û➘♣❛❿ r☞✇➐÷❰t✤⑩

♥qr✧④Ñ✇➘♠♦❿ñt✤û②î✌♣②⑩❛ç✟Ø②✇➘❿➀✇ ß✻✇➘♠➳♣❞ê✧♣②❿➀ß☞❸q✇ ❿➀♣②✈☞♥Ù✈➊t✤⑩➳✈➊t ♠❾t✤✈✩♥àt✤û②ã✤✇❜Ø✡✠➘⑩➄❿ñ♥ÙØít❜✈☞♣❘④Ñ⑧☞r☞✈✩✇❺♣✙⑩♦⑧☞t✤⑩

t✤r☞♥Ù⑩♦✇✤s♦♠♦✇➘ß✩♥àt✤⑩✗➌➐➎✍➏➓ç☞✈☞t✤✈☞✇➘⑩✕✈☞♣ë⑩➄⑧☞ß❼♣②♠♦r✩✇➫÷❰t✤⑩✓➌❳➎➊ç✹➎☞ç❥➎☞ç✹➎➊ç✹➎✍➏➓ç✧❿ñ♣❛✈☞♥q✈☞t✤⑩➥ïÝ⑧➊t✤r✦s❾♥ös✉t❰s♦♥Ù÷❰t✤⑩➥✈☞t➚❸q♣②♥

✈☞♣➀Ú☎⑧✩❻☞❻☞❸q♣❐➌❳➎➊ç➱➎☞ç➱➎➊ç➱➎✽➏✟✇✤⑧❺Ø❛⑧☞♠➄÷❰t✤⑩❬✈☞♣➀♠♦✇✤s❾t✤ûíã❰✇❑✈✩♣➀Û➘t✤❸àþ✿ê✧♥qt✤⑩✕➌❳➎✽➏↔ç❢⑧☞❿ ⑩♦♣②❿➳Ó✝r✧✌☞❿➀♣②♠➄✇✙✈☞♣

❿➀✇✧✈☞♣❛❸q✇➘⑩✕ð✐ß☞♠♦✇✤ß✻✇➘⑩✎s❾✇➀ß➊t✤♠♦t➀s❾♣❛r✦s✉t✤♠❷♣➍ê✧ß☞❸Ù♥qØít❰♠☎t❰⑩☎✇➘❻✩⑩♦♣②♠✎÷❰t✤û②î✌♣②⑩➚Ï➛❿ñt❰s❾ð❛♠♦♥àt➳♣❛⑩♦Ø②⑧✩♠❾t✩ç✻♣②r☞♣❛♠♦Û➘♥qt

♣②⑩➄Ø②⑧☞♠♦t✩ç ïÝ⑧☞♥Ùr✦s❾♣②⑩➄⑩♦è❛r☞Ø②♥qt✩ç➥ïÝ⑧➊t✤♠✎s❾♣②⑩➄⑩♦è❛r☞Ø②♥qt✩ç➥Ø②✇✤r☞⑩➄s❾t✤r✦s❾♣❑Ø②✇➘⑩➄❿ñ✇➘❸✁✠➘Û➘♥ÙØít✩ç❁❻✩♠❾t✤r➊t❰⑩②ç ✈✩♥q❿➀♣②r☞⑩➄î✧♣❛⑩

♣➍ê✌s♦♠❾t✤⑩❛ç✽✈☞♣❛rÝs♦♠♦♣➦s✉t✤r✦s♦✇➘⑩✐✇✤⑧✩s❾♠➄✇➘⑩✉Ö❞ç➹✇❑ïÝ⑧☞♣✴ý♦þ✙④Ñ✇➘♠➄r☞♣②Ø❛♣ñ❻❼✇➘r☞⑩➋♥qr✩✈☞⑨qØ❛♥q✇➘⑩✑s❾t✤r✦s❾✇❑✈➊t✙♠♦♥qïÝ⑧☞♣❛óít❑♣

✈➊t➳Ø②✇✤❿ñß☞❸Ù♣➍ê✧♥q✈☞t✤✈☞♣ë✈☞✇➀t✤⑩➄⑩♦⑧☞r✦s❾✇ñïÝ⑧➊t✤r✦s❾✇➀✈☞✇➀❿➚⑧☞♥Ùs♦✇➳ïÝ⑧☞♣➋t✤♥qr☞✈☞t➦ß✩♠♦♣②Ø❛♥q⑩♦t➦⑩➄♣②♠★✈☞♣❛⑩♦Ø②✇✤❻✻♣❛♠➄s❾✇✩⑤

á✑t➋♠♦♣ít❰❸q♥q✈☞t✤✈☞♣✤ç✦♣❛⑩♦⑩♦t✐⑩♦♥ös❾⑧➊t❰ûíã✤✇✐t✤ß➊t✤♠➄♣②r✦s❾♣❛❿ñ♣❛r✦s❾♣❷Ø②✇➘r✩④Ñ⑧✩⑩❾t✐♠➄♣✦✥➊♣➍s❾♣☎✇➋④➛t❰s♦✇❬✈☞♣☎ïÝ⑧☞♣✑t❰s❾⑧☞t✤❸öÓ

❿➀♣②r✦s❾♣➋t➀Þ ✇➘⑩♦❿➀✇➘❸Ù✇➘Û➘♥àt✐⑩♦♣➋♣②r☞Ø❛✇➘r✦s❾♠❾t➦♣②❿ì⑧☞❿❨ß✻♣❛♠♦⑨Ù✇✧✈☞✇➳Ø❛♠♦⑧☞Ø❛♥àt✤❸✰✈☞♣❬⑩♦♣②⑧❖✈☞♣②⑩➄♣②r✦÷➘✇✤❸Ù÷✌♥q❿➀♣②r✦s❾✇✩⑤

Õ✩ã✤✇➀❿➚⑧☞♥ös✉t✤⑩★t❰⑩❷ß❼✇➘⑩➄⑩♦♥q❻✩♥q❸q♥Ù✈➊t✤✈☞♣❛⑩✕t➦⑩♦♣②♠➄♣②❿❨s❾♣❛⑩➄s❾t✤✈➊t✤⑩❷♣❬❿ñ✇✌✈☞♣②❸qt✤✈➊t✤⑩❛⑤✛③❢✇➘♠★♣➍ê✧♣❛❿ñß☞❸Ù✇☞ç☞s❾♣❛❿ñ✇✤⑩

r☞✇➳❿➀✇➘❿➀♣②r✦s❾✇➚❻❼✇✦t✤⑩ ♠❾t✤ó❛î✧♣❛⑩✕ß➊t✤♠❾t➚Ø❛♠♦♣❛♠✕ï✌⑧✩♣ër☞✇➘⑩♦⑩➄✇➦⑧☞r☞♥Ù÷✤♣②♠➄⑩♦✇➦⑩♦♣ë♣❛r☞Ø②✇➘r✦s♦♠❾t➳♣②❿ÿ⑧☞❿ì♣❛⑩➄s✉t❰✈☞✇

✈☞♣✹♣➍ê✧ß➊t✤r☞⑩♦ã✤✇❬t✤Ø❛♣②❸q♣❛♠❾t✤✈☞t☎➌➐➎✍➏➓⑤❁Õ✧✇➘❿➀✇➘⑩➹Øít✤ß➊t❰ó②♣②⑩❢s✉t✤❿➚❻❼ð②❿✒✈☞♣✛s❾♣❛Ø②♣②♠✽Ø②✇➘❿➀♣②r✦s✉þ❰♠♦♥q✇✤⑩❢Ø❛✇✧♣❛♠♦♣②r✦s♦♣②⑩

të♠♦♣❛⑩♦ß❼♣②♥Ùs♦✇✐✈☞t➋t❰❻☞⑧☞r☞✈❼⑤❰r☞Ø②♥qt➋✈☞♣✕÷❰þ✤♠➄♥q✇➘⑩✵♣❛❸q♣②❿➀♣②r✦s♦✇➘⑩✵❸q♣➍÷➘♣②⑩Ù➌❳➎✽➏↔ç✧t❰❸qð②❿❇✈☞♣★ß✻✇✌✈☞♣❛♠♦❿➀✇➘⑩✟t✟➊♠➄❿✮t✤♠

Ø②✇✤❿ ♠➄♣②❸qt❰s❾♥ö÷✤t❘Ø❛✇➘r⑨➩t✤r✩ûít❖ïÝ⑧☞♣ t❖✈☞♣❛r☞⑩♦♥Ù✈➊t✤✈☞♣➀❿ñð❛✈☞♥àt✙✈☞♣ñ♣②r☞♣❛♠♦Û➘♥qt❖r☞✇❖⑧☞r☞♥Ù÷✤♣②♠➄⑩♦✇➯ð➀♥qÛ➘⑧☞t✤❸➍✂

✈☞♣❛r☞⑩♦♥Ù✈➊t✤✈☞♣☎Ø②♠♦⑨ös❾♥ÙØít✩çÝ✇òïÝ⑧☞♣☎✇ò✇➘❻✩♠♦♥qÛ➘t✩çÝr➊t✐❸Ù♥qr☞Û➘⑧☞t✤Û➘♣②❿❯✈➊tò❶★♣②❸qt❰s❾♥ö÷✧♥Ù✈➊t✤✈☞♣➋☛ë♣②♠♦t✤❸➓ç✌t❬s❾♣②♠✹⑧☞❿ñt

⑩♦♣❛ûíã✤✇➀♣②⑩➄ß➊t✤Ø❛♥àt✤❸✸ß☞❸qt✤r➊t✩ç✧Ø②✇➘❿ìØ②⑧☞♠✎÷✤t✿s❾⑧☞♠♦t➀rÝ⑧☞❸qt❐➌❳➎✽➏↔⑤

Referências

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