Bài viết nghiên cứu cá chốt bông giai đoạn sau nở chịu đựng những yếu tố bất lợi của môi trường tốt hơn giai đoạn phôi. Kết quả nghiên cứu là cơ sở khoa học quan trọng cho các nghiên cứu về sản xuất giống và bảo tồn loài cá này trong tương lai.
rữớ ổ P ỗ ■❞❡♥t✐❢✐❝❛t✐♦♥ ♦❢ t❤❡ t♦❧❡r❛♥t ❝❛♣❛❝✐t② t♦ ❛q✉❛t✐❝ ❡♥✈✐r♦♥♠❡♥t ❢❛❝t♦rs ✭t❡♠♣❡r❛t✉r❡✱ ♣❍ ❛♥❞ ❞✐ss♦❧✈❡❞ ♦①②❣❡♥✮ ♦❢ ❆s✐❛♥ ❜✉♠❜❧❡❜❡❡ ❝❛t❢✐s❤ ✭Ps❡✉❞♦♠②st✉s s✐❛♠❡♥s✐s ❘❡❣❛♥✱ ✶✾✶✸✮ ❇✐♥❤ ❚✳ ❚✳ ❱♦∗ ✱ ❈❤❛✉ ▼✳ P❤❛♠✱ ❚r✉❝ ❚✳ ❚✳ ◆❣✉②❡♥✱ ❚✉❛♥ ❱✳ ❱♦✱ ✫ ❚✉ ❱✳ ◆❣✉②❡♥ ❋❛❝✉❧t② ♦❢ ❋✐s❤❡r✐❡s✱ ◆♦♥❣ ▲❛♠ ❯♥✐✈❡rs✐t②✱ ❍♦ ❈❤✐ ▼✐♥❤ ❈✐t②✱ ❱✐❡t♥❛♠ ❆❘❚■❈▲❊ ■◆❋❖ ❘❡s❡❛r❝❤ P❛♣❡r ❘❡❝❡✐✈❡❞✿ ▼❛② ✵✼✱ ✷✵✶✾ ❘❡✈✐s❡❞✿ ❙❡♣t❡♠❜❡r ✵✾✱ ✷✵✶✾ ❆❝❝❡♣t❡❞✿ ❙❡♣t❡♠❜❡r ✷✹✱ ✷✵✶✾ ❑❡②✇♦r❞s ❆s✐❛♥ ❜✉♠❜❧❡❜❡❡ ❝❛t❢✐s❤ ❉✐ss♦❧✈❡❞ ♦①②❣❡♥ ♣❍✱ t❡♠♣❡r❛t✉r❡ ❚♦❧❡r❛♥t ❝❛♣❛❝✐t② ∗ ❈♦rr❡s♣♦♥❞✐♥❣ ❛✉t❤♦r ❱♦ ❚❤✐ ❚❤❛♥❤ ❇✐♥❤ ❊♠❛✐❧✿ ✈t❜✐♥❤✶✾✼✺❅②❛❤♦♦✳❝♦♠ ❆❇❙❚❘❆❈❚ ❆s✐❛♥ ❜✉♠❜❧❡❜❡❡ ❝❛t❢✐s❤ ✭Ps❡✉❞♦♠②st✉s s✐❛♠❡♥s✐s ✮ ❜❡❧♦♥❣s t♦ ❇❛❣r✐❞❛❡ ❢❛♠✐❧② ❛♥❞ ✐s ❛♥ ❡❝♦♥♦♠✐❝ ✈❛❧✉❡ ♦r♥❛♠❡♥t❛❧ s♣❡❝✐❡s✳ ❍♦✇❡✈❡r✱ ❜✐♦❧♦❣✐❝❛❧ ❝❤❛r❛❝t❡r✐st✐❝s ♦❢ t❤✐s ❢✐s❤ s♣❡❝✐❡s ❤❛✈❡ ❜❡❡♥ r❛r❡❧② r❡♣♦rt❡❞ ✐♥ t❤❡ ❧✐t❡r✲ ❛t✉r❡✳ ❆ st✉❞② t♦ ✐❞❡♥t✐❢② t♦❧❡r❛♥t ❝❛♣❛❝✐t② t♦ ❛q✉❛t✐❝ ❡♥✈✐r♦♥♠❡♥t ❢❛❝✲ t♦rs ✭✐♥❝✐♣✐❡♥t ❧❡t❤❛❧ t❡♠♣❡r❛t✉r❡ ✭■▲❚✮ ❛♥❞ ✐♥❝✐♣✐❡♥t ❧❡t❤❛❧ ♣❍ ✭■▲♣❍✮ ❛♥❞ ♦①②❣❡♥ t❤r❡s❤♦❧❞✮ ♦❢ ❆s✐❛♥ ❜✉♠❜❧❡❜❡❡ ❝❛t❢✐s❤ ❛t t❤r❡❡ ❞❡✈❡❧♦♣♠❡♥✲ t❛❧ st❛❣❡s ♥❛♠❡❧② ❡♠❜r②♦✱ ❤❛t❝❤❧✐♥❣ ❛♥❞ t❡♥✲❞❛② ♣♦st ❤❛t❝❤✐♥❣ ✭❞♣❤✮ ✇❛s ❝❛rr✐❡❞ ♦✉t ❢r♦♠ ❏✉❧② ✷✵✶✽ t♦ ❏❛♥✉❛r② ✷✵✶✾ ❛t t❤❡ ❊①♣❡r✐♠❡♥t❛❧ ❋❛r♠ ❢♦r ❆q✉❛❝✉❧t✉r❡ ♦❢ ❋✐s❤❡r✐❡s ❋❛❝✉❧t② ✲ ◆♦♥❣ ▲❛♠ ❯♥✐✈❡rs✐t② ✐♥ ❍❈▼ ❈✐t②✳ ❚❤❡ r❡s✉❧ts s❤♦✇❡❞ t❤❛t t❤❡ ✐♥❝✐♣✐❡♥t ✉♣♣❡r ❛♥❞ ❧♦✇❡r ❧❡t❤❛❧ t❡♠♣❡r❛t✉r❡s ✭■❯▲❚ ❛♥❞ ■▲▲❚✮ ✇❡r❡ ✸✷✳✺0 ❈ ❛♥❞ ✷✷✳✸0 ❈ ❢♦r ❡♠❜r②♦s✱ ✸✻✳✼0 ❈ ❛♥❞ ✶✽✳✼0 ❈ ❢♦r ❤❛t❝❤❧✐♥❣s✱ ❛♥❞ ✸✽✳✻0 ❈ ❛♥❞ ✶✺✳✾0 ❈ ❢♦r ✶✵ ❞♣❤ ❢✐s❤✱ r❡s♣❡❝t✐✈❡❧②✳ ❚❤❡ ✐♥❝✐♣✐❡♥t ✉♣♣❡r ❛♥❞ ❧♦✇❡r ❧❡t❤❛❧ ♣❍s ✭■❯▲♣❍ ❛♥❞ ■▲▲♣❍✮ ✇❡r❡ ✶✵✳✼ ❛♥❞ ✹✳✹ ❢♦r ❡♠❜r②♦s✱ ✶✵✳✷ ❛♥❞ ✸✳✼ ❢♦r ❤❛t❝❤❧✐♥❣s✱ ❛♥❞ ✶✵✳✷ ❛♥❞ ✸✳✽ ❢♦r ✶✵ ❞♣❤ ❢✐s❤✱ r❡s♣❡❝t✐✈❡❧②✳ ❚❤❡ ♦①②❣❡♥ t❤r❡s❤♦❧❞s ♦❢ t❤❡ ❝❛t❢✐s❤ ❛t t❤❡ t❤r❡❡ st❛❣❡s ✇❡r❡ ✹✳✼✱ ✶✳✶ ❛♥❞ ✶✳✵ ♠❣ ❖2 ✴▲✱ r❡s♣❡❝t✐✈❡❧②✳ ❚❤❡ ❆s✐❛♥ ❜✉♠❜❧❡❜❡❡ ❝❛t❢✐s❤ ❛t ♣♦st ❤❛t❝❤✐♥❣ st❛❣❡s ❛♣♣❡❛rs t♦ t♦❧❡r✲ ❛t❡ t♦ ✉♥❢❛✈♦r❛❜❧❡ ❡♥✈✐r♦♥♠❡♥t❛❧ ❢❛❝t♦rs ❝♦♠♣❛r❡❞ t♦ ❡♠❜r②♦♥✐❝ ♦♥❡✳ ❚❤❡ st✉❞② r❡s✉❧ts ✇♦✉❧❞ ❜❡ ❛♥ ✐♠♣♦rt❛♥t s❝✐❡♥t✐❢✐❝ ❜❛s❡ ❢♦r r❡s❡❛r❝❤❡s ♦♥ s❡❡❞ ♣r♦❞✉❝t✐♦♥ ❛♥❞ ❝♦♥s❡r✈❛t✐♦♥ ♦❢ t❤❡ ❢✐s❤ ✐♥ t❤❡ ❢✉t✉r❡✳ ❈✐t❡❞ ❛s✿ ❱♦✱ ❇✳ ❚✳ ❚✳✱ P❤❛♠✱ ❈✳ ▼✳✱ ◆❣✉②❡♥✱ ❚✳ ❚✳ ❚✳✱ ❱♦✱ ❚✳ ❱✳✱ ✫ ◆❣✉②❡♥✱ ❚✳ ❱✳ ✭✷✵✶✾✮✳ ■❞❡♥t✐❢✐❝❛t✐♦♥ ♦❢ t❤❡ t♦❧❡r❛♥t ❝❛♣❛❝✐t② t♦ ❛q✉❛t✐❝ ❡♥✈✐r♦♥♠❡♥t ❢❛❝t♦rs ✭t❡♠♣❡r❛t✉r❡✱ ♣❍ ❛♥❞ ❞✐s✲ s♦❧✈❡❞ ♦①②❣❡♥✮ ♦❢ ❆s✐❛♥ ❜✉♠❜❧❡❜❡❡ ❝❛t❢✐s❤ ✭Ps❡✉❞♦♠②st✉s s✐❛♠❡♥s✐s ❘❡❣❛♥✱ ✶✾✶✸✮✳ ❚❤❡ ❏♦✉r♥❛❧ ♦❢ ❆❣r✐❝✉❧t✉r❡ ❛♥❞ ❉❡✈❡❧♦♣♠❡♥t ✶✽✭✺✮✱ ✹✸✲✺✶✳ ✇✇✇✳❥❛❞✳❤❝♠✉❛❢✳❡❞✉✳✈♥ ❚↕♣ ❝❤➼ ◆ỉ♥❣ ♥❣❤✐➺♣ ✈➔ P❤→t tr✐➸♥ ✶✽✭✺✮ ✹✹ ❚r÷í♥❣ ✣↕✐ ổ P ỗ ỹ ởt số tố ổ trữớ ữợ ✭♥❤✐➺t ✤ë✱ ♣❍ ✈➔ æ①② ❤á❛ t❛♥✮ ❝õ❛ ❝→ ❝❤èt ❜æ♥❣ ✭Ps❡✉❞♦♠②st✉s s✐❛♠❡♥s✐s ❘❡❣❛♥✱ ✶✾✶✸✮ ❱ã ❚❤à ❚❤❛♥❤ ❇➻♥❤∗ ✱ P❤↕♠ ▼✐♥❤ ❈❤➙✉✱ ◆❣✉②➵♥ ❚❤à ❚❤❛♥❤ ❚ró❝✱ ❱ã ❱➠♥ ❚✉➜♥ ✫ ◆❣✉②➵♥ ❱➠♥ ❚÷ ❑❤♦❛ ❚❤õ② ❙↔♥✱ ❚r÷í♥❣ ✣↕✐ ❍å❝ ổ P P ỗ ❇⑩❖ ❇➔✐ ❜→♦ ❦❤♦❛ ❤å❝ ◆❣➔② ♥❤➟♥✿ ✵✼✴✵✺✴✷✵✶✾ ◆❣➔② ❝❤➾♥❤ sû❛✿ ✵✾✴✵✾✴✷✵✶✾ ◆❣➔② ❝❤➜♣ ♥❤➟♥✿ ✷✹✴✵✾✴✷✵✶✾ ❚ø ❦❤â❛ ❈→ ❝❤èt ❜æ♥❣ ❑❤↔ ♥➠♥❣ ❝❤à✉ ❞ü♥❣ ◆❤✐➺t ✤ë ➷①② ❤á❛ t❛♥ ♣❍ ∗ ❚→❝ ❣✐↔ ❧✐➯♥ ❤➺ ❚➶▼ ❚➁❚ ❈→ ❝❤èt ❜æ♥❣ ✭Ps❡✉❞♦♠②st✉s s✐❛♠❡♥s✐s ✮ t❤✉ë❝ ❤å ❝→ ♥❣↕♥❤ ❇❛❣r✐❞❛❡ ✈➔ ❧➔ ❧♦➔✐ ❝→ ❝↔♥❤ ❝â ❣✐→ trà ❦✐♥❤ t➳✳ ❚✉② ♥❤✐➯♥ ❝❤♦ ✤➳♥ ♥❛② ❝→❝ ❝æ♥❣ ❜è ✈➲ ✤➦❝ ✤✐➸♠ s✐♥❤ ❤å❝ ❝õ❛ ❧♦➔✐ ❝→ ♥➔② ❝á♥ r➜t ❤↕♥ ❝❤➳✳ ◆❣❤✐➯♥ ❝ù✉ ✈➲ ❦❤↔ ♥➠♥❣ ❝❤à✉ ✤ü♥❣ ♠ët sè ②➳✉ tố ổ trữớ ữợ t ổ ỏ t❛♥✮ ❝õ❛ ❝→ ❝❤èt ❜æ♥❣ ð ❝→❝ ❣✐❛✐ ✤♦↕♥ ♣❤æ✐✱ ợ tờ ữủ t❤ü❝ ❤✐➺♥ tø t❤→♥❣ ✼✴✷✵✶✽ ✤➳♥ t❤→♥❣ ✶✴✷✵✶✾ t↕✐ ❑❤♦❛ ❚❤õ② ❙↔♥ ✲ ❚r÷í♥❣ ✣↕✐ ❤å❝ ◆ỉ♥❣ ▲➙♠ ❚P✳❍❈▼✳ ❈→❝ ❦➳t q✉↔ ♥❣❤✐➯♥ ❝ù✉ ❝❤♦ t❤➜② ♥❣÷ï♥❣ ♥❤✐➺t ✤ë ❝❛♦ ✈➔ t❤➜♣ ❝õ❛ ♣❤æ✐ ❧➔ ✸✷✱✺0 ❈ ✈➔ ✷✷✱✸0 ❈❀ ❝→ ♠ỵ✐ ♥ð ❧➔ ✸✻✱✼0 ❈ ✈➔ ✶✽✱✼0 ❈❀ ❝→ ✶✵ ♥❣➔② t✉ê✐ ❧➔ ✸✽✱✻0 ❈ ✈➔ ✶✺✱✾0 ❈✳ ◆❣÷ï♥❣ ♣❍ ❝❛♦ ✈➔ t❤➜♣ ð ❣✐❛✐ ✤♦↕♥ ♣❤æ✐ ❧➔ ✶✵✱✼ ✈➔ ✹✱✹❀ ❝→ ♠ỵ✐ ♥ð ❧➔ ✶✵✱✷ ✈➔ ✸✱✼❀ ❝→ ✶✵ ♥❣➔② t✉ê✐ ❧➔ ✶✵✱✷ ✈➔ ✸✱✽✳ ◆❣÷ï♥❣ ỉ①② ❝õ❛ ❝→ ❝❤èt ❜ỉ♥❣ ❣✐❛✐ ✤♦↕♥ ♣❤ỉ✐✱ ❝→ ♠ỵ✐ ♥ð ✈➔ ❝→ ✶✵ ♥❣➔② t✉ê✐ ❧➛♥ ❧÷đt ❧➔ ✹✱✼❀ ✶✱✶❀ ✶✱✵ ♠❣ ❖2 ✴▲✳ ❈→ ❝❤èt ❜æ♥❣ ❣✐❛✐ ✤♦↕♥ s❛✉ ♥ð ❝❤à✉ ✤ü♥❣ ♥❤ú♥❣ ②➳✉ tè ❜➜t ❧đ✐ ❝õ❛ ♠ỉ✐ tr÷í♥❣ tèt ❤ì♥ ❣✐❛✐ ✤♦↕♥ ♣❤ỉ✐✳ ❑➳t q✉↔ ♥❣❤✐➯♥ ❝ù✉ ❧➔ ❝ì sð ❦❤♦❛ ❤å❝ q✉❛♥ trå♥❣ ❝❤♦ ❝→❝ ♥❣❤✐➯♥ ❝ù✉ s t ố tỗ tr♦♥❣ t÷ì♥❣ ❧❛✐✳ ❱ã ❚❤à ❚❤❛♥❤ ❇➻♥❤ ❊♠❛✐❧✿ ✈t❜✐♥❤✶✾✼✺❅②❛❤♦♦✳❝♦♠ ✶✳ ✣➦t ❱➜♥ ✣➲ ❈→ ❝❤èt ❜æ♥❣ ✭Ps❡✉❞♦♠②st✉s s✐❛♠❡♥s✐s ❘❡❣❛♥✱ ✶✾✶✸✮ t❤✉ë❝ ❣✐è♥❣ ❝→ ❝❤èt Ps❡✉❞♦♠②st✉s✱ ❤å ❝→ ♥❣↕♥❤ ❇❛❣r✐❞❛❡✳ ❇❛❣r✐❞❛❡ ❧➔ ♠ët tr♦♥❣ ♥❤ú♥❣ ❤å ❧ỵ♥ ✈ỵ✐ ❝→❝ t❤➔♥❤ ✈✐➯♥ ❝â t❤➸ t➻♠ t❤➜② ❦❤➢♣ ❝❤➙✉ ⑩✱ ❝❤➙✉ P❤✐ ✈➔ ❚r✉♥❣ ✣æ♥❣✳ Ð ❝❤➙✉ ⑩✱ ❝→ ❝❤èt ❜æ♥❣ ♣❤➙♥ ❜è ð ❧÷✉ ✈ü❝ ❝→❝ sỉ♥❣ ▼❡❦♦♥❣ ✈➔ ❈❤❛♦ P❤r❛②❛✱ ✈➔ ❜→♥ ✤↔♦ ❚❤→✐ ▲❛♥✳ ◆❤â♠ ❝→ ♥❣↕♥❤ ♥➔② ✤÷đ❝ q✉❛♥ t➙♠ ✤➦❝ ❜✐➺t ❞♦ ❝â ♥❤✐➲✉ ❧♦➔✐ ❝→ ❝â ❣✐→ trà ❧➔♠ ❝→ ❝↔♥❤ s♦ ✈ỵ✐ ❝→❝ ❤å ❝→ ❞❛ trì♥ ✭❝❛t❢✐s❤✮ ❝❤➙✉ ⑩ ❦❤→❝✳ ◆❣➔② ♥❛②✱ ♣❤➛♥ ❧ỵ♥ ❝→❝ ❧♦➔✐ ❞ò♥❣ ❧➔♠ ❝→ ❝↔♥❤ t❤✉ë❝ ❣✐è♥❣ Ps❡✉✲ ❞♦♠②st✉s ❞♦ ❝❤ó♥❣ sð ❤ú✉ sü ✤❛ ❞↕♥❣ ✈➲ ♠➔✉ s➢❝✱ ❝â tữỡ t ợ ✈➺t ♠➔✉ t÷ì♥❣ ♣❤↔♥ ♥➡♠ tr➯♥ t❤➙♥ ✈➔ ✈➙②✳ ❚r♦♥❣ sè ❝→❝ ❧♦➔✐ ❝→ ❝↔♥❤ t❤✉ë❝ ❣✐è♥❣ Ps❡✉❞♦♠②s✲ t✉s t❤➻ ❝→ ❝❤èt ❜ỉ♥❣ ✤÷đ❝ ÷❛ ❝❤✉ë♥❣ ❤ì♥ ❝↔ ✈➔ ✤÷đ❝ ①✉➜t✴♥❤➟♣ ❦❤➞✉ ✈ỵ✐ t➯♥ ❣å✐ ❵❜✉♠❜❧❡❜❡❡ ❝❛t✲ ❢✐s❤✬ ✭▲✐♥❞❡r✱ ✷✵✵✵❛ ✫ ❜✮✳ ❚✉② ♥❤✐➯♥✱ ❧♦➔✐ ❝→ ♥➔② ❚↕♣ ❝❤➼ ◆æ♥❣ ♥❣❤✐➺♣ ✈➔ P❤→t tr✐➸♥ ✶✽✭✺✮ ❝❤➾ ✤÷đ❝ ❦❤❛✐ t❤→❝ tø tỹ số ữủ õ ợ t tử ỗ ỡ tữỡ ố tợ t q✉→ ♠ù❝ ❧♦➔✐ ❝→ ♥➔② ♥❣♦➔✐ tü ♥❤✐➯♥✳ Ð ❱✐➺t ◆❛♠✱ ❝→ ❝❤èt ❜ỉ♥❣ ✤÷đ❝ ♥❣÷í✐ ❞➙♥ ❦❤❛✐ t❤→❝ ♥❤✐➲✉ ð ✈ò♥❣ ❚➙♥ ❈❤➙✉✱ ❚❤♦↕✐ ❙ì♥ ✭❆♥ ●✐✲ ❛♥❣✮ ✈➔ ỗ r r ỗ ♥❣❤✐➺♠ ❝õ❛ ♥❣÷í✐ ❞➙♥ t❤➻ ❝→ ❝❤èt ❜ỉ♥❣ ð ❝→❝ ✤à❛ ♣❤÷ì♥❣ ♥➔② t❤÷í♥❣ ❜➢t ❣➦♣ ✈➔♦ ✤➛✉ ♠ò❛ ♠÷❛ ✈➔ ✤÷đ❝ ✤→♥❤ ❜➢t✱ ❦❤❛✐ t❤→❝ ❝❤õ ②➳✉ ✈➔♦ ❝→❝ t❤→♥❣ ✶✵✱ ✶✶ ❤➡♥❣ ♥➠♠ ✭❱♦✱ ✷✵✶✺✮✳ ◆❣♦➔✐ ♥❣❤✐➯♥ ❝ù✉ ✤à♥❤ ❧♦↕✐ ✭❱♦✱ ✷✵✶✺✮✱ ❝❤♦ ✤➳♥ ♥❛② ❝â r➜t ➼t ♥❣❤✐➯♥ ❝ù✉ ✈➲ ✤➦❝ ✤✐➸♠ s✐♥❤ ❤å❝ tr➯♥ ❧♦➔✐ ❝→ ♥➔②✳ ❱➻ ✈➟②✱ ✈✐➺❝ t✐➳♥ ❤➔♥❤ ♥❣❤✐➯♥ ❝ù✉ ①→❝ ✤à♥❤ ❦❤↔ ♥➠♥❣ ❝❤à✉ ✤ü♥❣ ❝→❝ ②➳✉ tè ♠ỉ✐ tr÷í♥❣ ❝❤➼♥❤ ✭♥❤✐➺t ✤ë✱ ♣❍✱ æ①② ❤á❛ t❛♥✮ ❝õ❛ ❝→ ❝❤èt ❜æ♥❣ ❧➔ ❤➳t sù❝ ❝➛♥ t❤✐➳t ✤➸ ❧➔♠ ❝ì sð ❦❤♦❛ ❤å❝ ✈✐➺❝ t❤✉➛♥ ❞÷ï♥❣✱ s↔♥ ①✉➜t ❣✐è♥❣✱ ♣❤→t tr✐➸♥ ♥✉ỉ✐ ỗ ủ tỹ ố tữủ rữớ ổ P ỗ tr tữỡ ữợ tr ❜➻♥❤ t❤➼ ♥❣❤✐➺♠ ✈ỵ✐ ❞✉♥❣ ❞à❝❤ ◆❛❖❍ ✵✱✶◆ ✤➸ t➠♥❣ ♣❍ ✷✳ ❱➟t ▲✐➺✉ ✈➔ P❤÷ì♥❣ P❤→♣ ◆❣❤✐➯♥ ❈ù✉ ✭①→❝ ✤à♥❤ ♣❍ ❝❛♦ ❣➙② ❝❤➳t ✭■❯✭♣♣❡r✮▲♣❍✮✮ ✈➔ ❍2 ❙❖4 ✵✱✶◆ ✤➸ ❣✐↔♠ ♣❍ ✭①→❝ ✤à♥❤ ♣❍ t❤➜♣ ❣➙② ◆❣❤✐➯♥ ❝ù✉ ✤÷đ❝ t✐➳♥ ❤➔♥❤ tø t❤→♥❣ ✼✴✷✵✶✽ ❝❤➳t ✭■▲✭♦✇❡r✮▲♣❍✮✮ ✤➸ ❝â ❣✐→ trà ♣❍ t❤❡♦ ②➯✉ ❝➛✉ ✤➳♥ t❤→♥❣ ✶✴✷✵✶✾ t↕✐ ❚r↕✐ t❤ü❝ ♥❣❤✐➺♠ ❑❤♦❛ ✈ỵ✐ ♠ù❝ ✶ ❣✐→ trà ♣❍ ð ♠é✐ ❧➛♥ t➠♥❣ ❤❛② ❣✐↔♠✳ ❙❛✉ ❚❤õ② ❙↔♥✱ ❚r÷í♥❣ ✣↕✐ ❤å❝ ◆æ♥❣ ▲➙♠ ❚P✳❍❈▼✳ ❦❤✐ ✤↕t ♣❍ ♠♦♥❣ ♠✉è♥✱ ♣❍ tr♦♥❣ ❜➻♥❤ ✤÷đ❝ ❣✐ú ❈→ ❝❤èt ❜ỉ♥❣ ❜è ♠➭ ✤÷đ❝ t✉②➸♥ ❝❤å♥ tø ✤➔♥ ❝→ ê♥ ✤à♥❤ ✈➔ ❣❤✐ ♥❤➟♥ sè ♠➝✉ ✈➟t ❜à ❝❤➳t ❧✐➯♥ tư❝ ❝❤èt ❜ỉ♥❣ tü ♥❤✐➯♥ t❤✉ tø ❝→❝ t➾♥❤ ♠✐➲♥ ❚➙② ✈➔ tr♦♥❣ ✷✹ ❣✐í✳ ❚r♦♥❣ ❝↔ ✷ t❤➼ ♥❣❤✐➺♠ tr➯♥✱ ❝→❝ ❜➻♥❤ ✤÷đ❝ sư❝ ✣ỉ♥❣ ◆❛♠ ❇ë✳ ❈→ ❜è ♠➭ ✤÷đ❝ ♥✉ỉ✐ ✈é tr♦♥❣ ❛♦ ❦❤➼ ♥❤➭ ✤➸ ✤↔♠ ❜↔♦ æ①② ❤á❛ t❛♥ ✤➛② ✤õ✳ ❈→❝ ♠➝✉ ❧ât ❜↕t ✈➔ ✤÷đ❝ ❦➼❝❤ t s s ợ s ữủ ÷ì♥❣ ♥✉ỉ✐ ✈ỵ✐ t❤ù❝ ➠♥ ❧➔ ▼♦✐♥❛ ✈➟t ❝❤➳t ✤÷đ❝ ợt ọ tr ữ t ữủ ữợ tr t trũ ❝❤➾ ▲✐♠♥♦❞r✐❧✉s ❤♦❢❢♠❡✐st❡r②✳ ❝❛♦ ✈➔ t❤➜♣ ❣➙② ❝❤➳t ♠➝✉ ✈➟t ✤÷đ❝ t➼♥❤ t♦→♥ ❞ü❛ ✷✳✶✳ ❚❤➼ ♥❣❤✐➺♠ ①→❝ ✤à♥❤ ♥❣÷ï♥❣ t tr t ỗ q t t ❝õ❛ t✛ ❧➺ ❝❤➳t ð ❝→ ❝❤èt ❜ỉ♥❣ ✷✹ ❣✐í t❤❡♦ ♥❤✐➺t ✤ë ❤❛② ♣❍✳ ❚❤➼ ♥❣❤✐➺♠ ①→❝ ✤à♥❤ ♥❤✐➺t ✤ë ❜➢t ✤➛✉ ❣➙② ❝❤➳t ✭✐♥❝✐♣✐❡♥t ❧❡t❤❛❧ t❡♠♣❡r❛t✉r❡✱ ■▲❚✮ ✲ ♥❤✐➺t ✤ë ❣➙② ❝❤➳t ✺✵✪ ✤è✐ t÷đ♥❣ t❤➼ ♥❣❤✐➺♠ ❦❤✐ ữủ ỷ ỵ ợ ởt t t t ❤❛② ❣✐↔♠ ð ❦❤♦↔♥❣ t❤í✐ ❣✐❛♥ ✷✹ ❣✐í ✭❇❡✐t✐♥❣❡r ✫ ❝t✈✳✱ ✷✵✵✵✮ ✲ ✤÷đ❝ ❜è tr➼ t❤❡♦ ❦✐➸✉ ❤♦➔♥ t♦➔♥ ợ ố tữủ ❝ù✉ ✭♣❤ỉ✐ ✤➣ ♣❤→t tr✐➸♥ ①❛ ❤ì♥ ❣✐❛✐ ✤♦↕♥ ♣❤ỉ✐ ợ tờ ữủ ự tr ỹ õ t ữợ ợ ♠➟t ✤ë ✷✵ ♠➝✉✴❜➻♥❤✳ ❈→❝ ❜➻♥❤ t❤➼ ♥❣❤✐➺♠ ✤÷đ❝ ✤➦t tr ởt tũ ố õ ự ữợ ũ ữợ õ t t r ữợ ❧↕♥❤ ✭①→❝ ✤à♥❤ ♥❤✐➺t ✤ë t❤➜♣ ❣➙② ❝❤➳t ✭■▲✭♦✇❡r✮▲❚✮✮ t❤➯♠ ữợ tr tũ ố t t t ữợ ự t ợ ♠ù❝ ✶0 ❈ ð ♠é✐ ❧➛♥ t➠♥❣ ❤❛② ❣✐↔♠✳ ✣➦t ♥❤✐➺t ❦➳ tr♦♥❣ ❜➻♥❤ t❤➼ ♥❣❤✐➺♠ ✤➸ t❤❡♦ ❞ã✐ ♥❤✐➺t ✤ë ✈➔ ✤↔♠ ❜↔♦ ♥❤✐➺t ✤ë tr♦♥❣ ❜➻♥❤ t➠♥❣ ❤❛② ❣✐↔♠ ❦❤ỉ♥❣ q✉→ ✵✱✷0 ❈✴❣✐í✳ ❙❛✉ ❦❤✐ ✤↕t ♥❤✐➺t ✤ë ♠♦♥❣ ♠✉è♥✱ ♥❤✐➺t ✤ë tr♦♥❣ ❜➻♥❤ ✤÷đ❝ ❣✐ú ê♥ ✤à♥❤ ✈➔ ❣❤✐ ♥❤➟♥ sè ♠➝✉ ✈➟t ❜à ❝❤➳t ❧✐➯♥ tö❝ tr♦♥❣ ✷✹ ❣✐í✳ ❇✐➸✉ ❤✐➺♥ ❝õ❛ ♣❤ỉ✐ ❝❤➳t ❧➔ sü ❜✐➳♥ ✤ê✐ ♠➔✉ ✈➔ trð ♥➯♥ ♠í ✤ư❝✱ ❝õ❛ ❝→ ♠ỵ✐ ♥ð ❧➔ sü ♥❣ø♥❣ ✈➟♥ ✤ë♥❣ ✈➔ ❝õ❛ ❝→ ✶✵ ♥❣➔② t✉ê✐ ❧➔ sü ♥❣ø♥❣ ❝û ✤ë♥❣ ❝õ❛ ♥➢♣ ♠❛♥❣✳ ✷✳✸✳ ❚❤➼ ♥❣❤✐➺♠ ①→❝ ✤à♥❤ ♥❣÷ï♥❣ ỉ①② ❝õ❛ ❝→ ❝❤èt ❜ỉ♥❣ ◆❣÷ï♥❣ ỉ①② ❝õ❛ ❝→ ✤÷đ❝ ①→❝ ✤à♥❤ ❜➡♥❣ ữỡ r ữợ ✈➔♦ ✤➛② ❜➻♥❤ t❤õ② t✐♥❤ ✺✵✵ ♠▲✱ t❤↔ ♠➝✉ ♠➟t ✤ë ✷✵ ❝♦♥ ♥❤➭ ♥❤➔♥❣ ✈➔♦ ❜➻♥❤ ✈➔ ✤➟② ♥➢♣ t❤➟t ❦➼♥ ✭tr→♥❤ ❦❤ỉ♥❣ ❝â ❜åt ❦❤➼✮✳ ❚✐➳♣ tư❝ t❤❡♦ ❞ã✐ ✤➳♥ ❦❤✐ ♥➔♦ > ✺✵✪ ♣❤ỉ✐ trð ♥➯♥ ♠í ✤ư❝ ❤❛② ❝→ ❦❤ỉ♥❣ ❝á♥ ❤♦↕t ✤ë♥❣ ♥ú❛ t❤➻ ❧➜② r ởt ữợ ổ ỏ t ✲ ✤÷đ❝ ①❡♠ ♥❤÷ ♥❣÷ï♥❣ ỉ①② ❝õ❛ ♣❤ỉ✐ ❤❛② ❝→ t ữủ ợ t từ ữủ ợ ♠❡t❡r ❤✐➺✉ ❍❆◆◆❆ ✈➔ ỉ①② ❤á❛ t❛♥ ✤÷đ❝ ①→❝ ✤à♥❤ ợ ữỡ r ỷ ỵ sè ❧✐➺✉ ❚➜t ❝↔ sè ❧✐➺✉ ✈➲ t✛ ❧➺ ❝❤➳t ✤÷đ❝ ❝❤✉②➸♥ ✤ê✐ √ t❤➔♥❤ ❛r❝s✐♥ ✈➔ ✤÷đ❝ ♣❤➙♥ t➼❝❤ ❆◆❖❱❆ ♠ët ②➳✉ tè ✭❖♥❡✲✇❛② ❆◆❖❱❆✮ ✈ỵ✐ ♣❤➨♣ t❤û ❉❯❈❆◆ P P t ỗ q t t ❝õ❛ t✛ ❧➺ ❝❤➳t ✭✤÷đ❝ ❝❤✉②➸♥ ✤ê✐ t❤➔♥❤ ♣r♦❜✐t✮ ð ✷✹ ❣✐í t❤❡♦ ♥❤✐➺t ✤ë ❤❛② ♣❍ ✭✤÷đ❝ ❝❤✉②➸♥ ✤ê✐ t❤➔♥❤ ▲♦❣✶✵✮ sû ❞ö♥❣ ♣❤➛♥ ♠➲♠ ❊①❝❡❧✳ ✷✳✷✳ ❚❤➼ ♥❣❤✐➺♠ ①→❝ ✤à♥❤ ♥❣÷ï♥❣ ♣❍ ❝õ❛ ❝→ ❝❤èt ❜ỉ♥❣ ✸✳ ❑➳t ◗✉↔ ✈➔ ❚❤↔♦ ▲✉➟♥ ❚❤➼ ♥❣❤✐➺♠ ①→❝ ✤à♥❤ ♣❍ ❜➢t ✤➛✉ ❣➙② ❝❤➳t ✭✐♥✲ ✸✳✶✳ ◆❣÷ï♥❣ ♥❤✐➺t ✤ë ❝õ❛ ❝→ ❝❤èt ❜æ♥❣ ❝✐♣✐❡♥t ❧❡t❤❛❧ ♣❍✱ ■▲♣❍✮ ✲ ♣❍ ❣➙② ❝❤➳t ố tữủ t ữủ ỷ ỵ ợ ♠ët ❧♦↕t ❝→❝ ✸✳✶✳✶✳ ●✐❛✐ ✤♦↕♥ ♣❤æ✐ ♣❍ t➠♥❣ ❤❛② ❣✐↔♠ ð ❦❤♦↔♥❣ t❤í✐ ❣✐❛♥ ✷✹ ❣✐í ✲ ❝ơ♥❣ ✤÷đ❝ ố tr t t ữù ♥❤✐➺t ✤ë ❝❛♦ ❣➙② ❝❤➳t ✭■❯▲❚✮ ✈ỵ✐ ✸ ❧➛♥ ❧➦♣ ❧↕✐✳ ✣è✐ t÷đ♥❣ ♥❣❤✐➯♥ ❝ù✉ ✤÷đ❝ ❝❤ù❛ P❤ỉ✐ ❦❤ỉ♥❣ ❝❤➳t ð ❝→❝ ♥❤✐➺t ✤ë ✸✵ ✈➔ ✸✶0 ❈✳ tr♦♥❣ ❝→❝ ỹ õ t ữợ ợ t ❍✐➺♥ t÷đ♥❣ ♣❤ỉ✐ ❝❤➳t ①↔② r❛ ð ❝→❝ ♥❣❤✐➺♠ t❤ù❝ ✇✇✇✳❥❛❞✳❤❝♠✉❛❢✳❡❞✉✳✈♥ ❚↕♣ ❝❤➼ ◆æ♥❣ ♥❣❤✐➺♣ ✈➔ P❤→t tr✐➸♥ ✶✽✭✺✮ ✹✻ ❝â ❣✐→ trà ♥❤✐➺t ✤ë tø ✸✷ ✲ ✸✾0 ❈✳ ❚✛ ❧➺ ♣❤ỉ✐ ❝❤➳t t➼❝❤ ❧ơ② ð ✷✹ ❣✐í ð ♥❣❤✐➺♠ t❤ù❝ ✸✷0 ❈ ❧➔ ✸✽✱✸✪✱ t➠♥❣ ❧➯♥ ✾✵✪ ð ✸✸0 ❈ ✈➔ ð ❝→❝ ♥❤✐➺t ✤ë ❝❛♦ ❤ì♥ ✭✸✹ ✲ ✸✾0 ❈✮ ❝â t✛ ❧➺ ♣❤æ✐ ❝❤➳t ✶✵✵✪ s❛✉ ✶ ❣✐í t❤➼ ♥❣❤✐➺♠✳ ❚✛ ❧➺ ♣❤ỉ✐ ❝❤➳t t➼❝❤ ❧ơ② ð ✷✹ ❣✐í ð ✸✸0 ❈ ❧➔ ❦❤→❝ ❜✐➺t ❝â þ ♥❣❤➽❛ t❤è♥❣ ❦➯ ✭P < ✵✱✵✺✮ s♦ ✈ỵ✐ t✛ t t Pữỡ tr ỗ q✉✐ t✉②➳♥ t➼♥❤ ❝õ❛ t✛ ❧➺ ♣❤æ✐ ❝❤➳t ✭②✮ t❤❡♦ ♥❤✐➺t ✤ë ❝❛♦ ✭①✮ ❧➔ ② ❂ ✷✵✼✱✾✶① ✕ ✸✵✾✱✸✻ ✭❘2 ❂ ✵✱✾✺✸✺✮✳ ◆❤÷ ✈➟②✱ tr♦♥❣ t❤➼ ♥❣❤✐➺♠ ♥➔②✱ ♥❤✐➺t ✤ë ❝❛♦ ❣➙② ❝❤➳t ✭■❯▲❚✮ ❝→ ❝❤èt ❜æ♥❣ ❣✐❛✐ ✤♦↕♥ ổ ữủ ◆❣÷ï♥❣ ♥❤✐➺t ✤ë t❤➜♣ ❣➙② ❝❤➳t ✭■▲▲❚✮ ❚÷ì♥❣ tü ♥❤÷ ð t❤➼ ♥❣❤✐➺♠ ♥❤✐➺t ✤ë ❝❛♦✱ ♣❤æ✐ ❦❤æ♥❣ ❝❤➳t ð ❝→❝ ♥❤✐➺t ✤ë tø ✷✻ ✲ ✷✹0 ❈✳ ❍✐➺♥ t÷đ♥❣ ♣❤æ✐ ❝❤➳t ①↔② r❛ ð ❝→❝ ♥❣❤✐➺♠ t❤ù❝ ❝â ❣✐→ trà ♥❤✐➺t ✤ë tø ✷✸✱✺ ✲ ✶✹➸❈✳ ❚✛ ❧➺ ♣❤æ✐ ❝❤➳t t➼❝❤ ❧ơ② ð ✷✹ ❣✐í ð ♥❣❤✐➺♠ t❤ù❝ ✷✸✱✺0 ❈ ❧➔ ✺✻✱✻✪✱ t➠♥❣ ❧➯♥ ✻✽✱✸✪ ð ✷✸0 ❈✱ ✼✺✪ ð ✷✶➸❈ ✈➔ ✼✻✱✻✪ ð ✷✷0 ❈❀ ❝á♥ ð ❝→❝ ♥❤✐➺t ✤ë t❤➜♣ ❤ì♥ ✭✷✵ ✲ ✶✹0 ❈✮✱ t✛ ❧➺ ♣❤ỉ✐ ❝❤➳t ❧➔ ✶✵✵✪ s❛✉ ✶ ❣✐í t❤➼ ♥❣❤✐➺♠✳ ❚✛ ❧➺ ♣❤ỉ✐ ❝❤➳t t➼❝❤ ❧ơ② ð ✷✹ ❣✐í ð ✷✶ t ổ õ ỵ tố P > ữ t õ ỵ ♥❣❤➽❛ t❤è♥❣ ❦➯ ✭P < ✵✱✵✺✮ s♦ ✈ỵ✐ t✛ ❧➺ t t Pữỡ tr ỗ q t✉②➳♥ t➼♥❤ ❝õ❛ t✛ ❧➺ ♣❤æ✐ ❝❤➳t ✭②✮ t❤❡♦ ♥❤✐➺t ✤ë t❤➜♣ ✭①✮ ❧➔ ② ❂ ✲ ✼✹✱✹✶✶① ✰ ✶✵✺✱✸✷ ✭❘2 ❂ ✵✱✻✹✸✺✮✳ ❚r♦♥❣ t❤➼ ♥❣❤✐➺♠ ♥➔②✱ ♥❤✐➺t ✤ë t❤➜♣ ❣➙② ❝❤➳t ✭■▲▲❚✮ ❝→ ❝❤èt ❜ỉ♥❣ ❣✐❛✐ ✤♦↕♥ ♣❤ỉ✐ ✤÷đ❝ ①→❝ ✤à♥❤ ❧➔ ✷✷✱✸0 ❈ ✭❍➻♥❤ ✶✮✳ ✸✳✶✳✷✳ ●✐❛✐ ✤♦↕♥ ợ ữù t t ✭■❯▲❚✮ ❈→ ❦❤æ♥❣ ❝❤➳t ð ❝→❝ ♥❤✐➺t ✤ë tø ✸✵ ✲ ✸✹0 ❈✳ ❍✐➺♥ t÷đ♥❣ ❝→ ❝❤➳t ①↔② r❛ ð ❝→❝ ♥❣❤✐➺♠ t❤ù❝ ❝â ❣✐→ trà ♥❤✐➺t ✤ë tø ✸✺ ✲ ✸✾0 ❈✳ ❚✛ ❧➺ ❝→ ❝❤➳t t➼❝❤ ❧ô② ð ✷✹ ❣✐í ð ♥❣❤✐➺♠ t❤ù❝ ✸✺0 ❈ ❧➔ ✷✶✱✻✪✱ t➠♥❣ ❧➯♥ ✺✺✪ ð ♥❤✐➺t ✤ë ✸✼➸❈ ✈➔ ✼✶✱✻✪ ð ♥❤✐➺t ✤ë ✸✽➸❈❀ ð ♥❤✐➺t ✤ë ❝❛♦ ❤ì♥ ✭✸✾0 ❈✮✱ t✛ ❧➺ ❝→ ❝❤➳t ❧➔ ✶✵✵✪ s❛✉ ✶ ❣✐í t❤➼ ♥❣❤✐➺♠✳ ❚✛ ❧➺ ❝→ ❝❤➳t t➼❝❤ ❧ơ② ð ✷✹ ❣✐í ð ❝→❝ ♥❤✐➺t ✤ë ✸✺ ✲ ✸✽0 ❈ ❧➔ ❦❤→❝ ❜✐➺t õ ỵ tố P < ụ ❦❤→❝ ❜✐➺t s♦ ✈ỵ✐ t✛ ❧➺ ❝❤➳t ð ❝→❝ ♥❤✐➺t Pữỡ tr ỗ q t t t ❧➺ ❝→ ❝❤➳t ✭②✮ t❤❡♦ ♥❤✐➺t ✤ë ❝❛♦ ✭①✮ ❧➔ ② ❂ ✶✶✼✱✶✾① ✕ ✶✼✽✱✹✷ ✭❘2 ❂ ✵✱✽✺✺✷✮✳ ◆❤÷ ✈➟② tr♦♥❣ t❤➼ ♥❣❤✐➺♠ ♥➔②✱ ♥❤✐➺t ✤ë ❝❛♦ ❣➙② ❝❤➳t ✭■❯▲❚✮ ốt ổ ợ ữủ ữù t t ❣➙② ❝❤➳t ✭■▲▲❚✮ ❚↕♣ ❝❤➼ ◆æ♥❣ ♥❣❤✐➺♣ ✈➔ P❤→t tr✐➸♥ rữớ ổ P ỗ ❈→ ❦❤æ♥❣ ❝❤➳t ð ❝→❝ ♥❤✐➺t ✤ë tø ✷✻ ✲ ✷✶0 ❈✳ ❍✐➺♥ t÷đ♥❣ ❝→ ❝❤➳t ①↔② r❛ ð ❝→❝ ♥❣❤✐➺♠ t❤ù❝ ❝â ❣✐→ trà ♥❤✐➺t ✤ë tø ✷✵ ✲ ✶✹0 ❈✳ ❚✛ ❧➺ ❝→ ❝❤➳t t➼❝❤ ❧ô② ð ✷✹ ❣✐í ð ♥❣❤✐➺♠ t❤ù❝ ✷✵0 ❈ ❧➔ ✶✸✱✸✪✱ t➠♥❣ ❧➯♥ ✺✸✱✸✪ ð ✶✾0 ❈ ✈➔ ✻✵✱✵✪ ð ✶✽0 ❈❀ ❝á♥ ð ❝→❝ ♥❤✐➺t ✤ë t❤➜♣ ❤ì♥ ✭✶✼ ✲ ✶✹0 ❈✮✱ t✛ ❧➺ ❝→ ❝❤➳t ❧➔ ✶✵✵✪ s❛✉ ✶ ❣✐í t❤➼ ♥❣❤✐➺♠✳ ❚✛ ❧➺ ❝→ ❝❤➳t t➼❝❤ ❧ơ② ð ✷✹ ❣✐í ð ❝→❝ ♥❤✐➺t ✤ë ✷✵ ✲ ✶✽0 ❈ ❧➔ ❦❤→❝ t õ ỵ tố P < ❝ơ♥❣ ❦❤→❝ ❜✐➺t s♦ ✈ỵ✐ t✛ ❧➺ ❝❤➳t ð ❝→❝ t Pữỡ tr ỗ q t t t✛ ❧➺ ❝→ ❝❤➳t ✭②✮ t❤❡♦ ♥❤✐➺t ✤ë t❤➜♣ ✭①✮ ❧➔ ② ❂ ✲ ✽✶✱✼✸✾① ✰ ✶✵✾✱✵✶ ✭❘2 ❂ ✵✱✽✾✹✾✮✳ ❚r♦♥❣ t❤➼ ♥❣❤✐➺♠ ♥➔②✱ ♥❤✐➺t ✤ë t❤➜♣ ❣➙② ❝❤➳t ✭■▲▲❚✮ ốt ổ ợ ữủ ❧➔ ✶✽✱✼0 ❈ ✭❍➻♥❤ ✷✮✳ ✸✳✶✳✸✳ ●✐❛✐ ✤♦↕♥ ❝→ ✶✵ tờ ữù t t ❈→ ❦❤æ♥❣ ❝❤➳t ð ❝→❝ ♥❤✐➺t ✤ë tø ✸✵ ✲ ✸✼0 ❈✳ ❍✐➺♥ t÷đ♥❣ ❝→ ❝❤➳t ①↔② r❛ ð ❝→❝ ♥❣❤✐➺♠ t❤ù❝ ❝â ❣✐→ trà ♥❤✐➺t ✤ë tø ✸✽ ✲ ✸✾0 ❈✳ ❚✛ ❧➺ ❝→ ❝❤➳t t➼❝❤ ❧ô② ð ✷✹ ❣✐í ð ♥❣❤✐➺♠ t❤ù❝ ✸✽0 ❈ ❧➔ ✹✻✱✻✪ ✈➔ t➠♥❣ ❧➯♥ ✺✺✱✵✪ ð ♥❤✐➺t ✤ë ✸✾0 ❈✳ ❚✛ ❧➺ ❝→ ❝❤➳t t➼❝❤ ❧ơ② ð ✷✹ ❣✐í ð ✸✽ ✈➔ ✸✾0 t õ ỵ tố P < ✵✱✵✺✮ ✈➔ ❝ơ♥❣ ❦❤→❝ ❜✐➺t s♦ ✈ỵ✐ t✛ ❧➺ t t Pữỡ tr ỗ q t✉②➳♥ t➼♥❤ ❝õ❛ t✛ ❧➺ ❝→ ❝❤➳t ✭②✮ t❤❡♦ ♥❤✐➺t ✤ë ❝❛♦ ✭①✮ ❧➔ ② ❂ ✷✷✺✱✵✽① ✲ ✸✺✷✱✷✶ ✭❘2 ❂ ✵✱✼✽✼✶✮✳ ◆❤✐➺t ✤ë ❝❛♦ ❣➙② ❝❤➳t ✭■❯▲❚✮ ❝→ ❝❤èt ❜ỉ♥❣ ❣✐❛✐ ✤♦↕♥ ✶✵ ♥❣➔② t✉ê✐ ✤÷đ❝ ①→❝ ✤à♥❤ ❧➔ ữù t t ❝❤➳t ✭■▲▲❚✮ ❈→ ❦❤æ♥❣ ❝❤➳t ð ❝→❝ ♥❤✐➺t ✤ë tø ✷✻ ✲ ✶✽0 ❈✳ ❍✐➺♥ t÷đ♥❣ ❝→ ❝❤➳t ①↔② r❛ ð ❝→❝ ♥❣❤✐➺♠ t❤ù❝ ❝â ❣✐→ trà ♥❤✐➺t ✤ë tø ✶✼ ✲ ✶✹0 ❈❀ tr♦♥❣ ✤â✱ ð ♥❤✐➺t ✤ë ✶✹0 ❈ t✛ ❧➺ ❝→ ❝❤➳t ❧➔ ✶✵✵✪ s❛✉ ✶ ❣✐í t❤➼ ♥❣❤✐➺♠✳ Ð ❝→❝ ♥❣❤✐➺♠ t❤ù❝ ✶✼✱ ✶✻ ✈➔ ✶✺0 ❈✱ t✛ ❧➺ ❝→ ❝❤➳t t➼❝❤ ❧ơ② s❛✉ ✷✹ ❣✐í tữỡ ữỡ t õ ỵ t❤è♥❣ ❦➯ s♦ ✈ỵ✐ ❝→❝ ♥❣❤✐➺♠ t❤ù❝ ❝á♥ ❧↕✐ ✭P < Pữỡ tr ỗ q t t t ❧➺ ❝→ ❝❤➳t ✭②✮ t❤❡♦ ♥❤✐➺t ✤ë t❤➜♣ ✭①✮ ❧➔ ② ❂ ✲ ✻✸✱✸✸✷① ✰ ✽✶✱✵✼✸ ✭❘2 ❂ ✵✱✼✻✹✸✮✳ ◆❤✐➺t ✤ë t❤➜♣ ❣➙② ❝❤➳t ✭■▲▲❚✮ ❝→ ❝❤èt ❜æ♥❣ ❣✐❛✐ ✤♦↕♥ ✶✵ ♥❣➔② t✉ê✐ ✤÷đ❝ ①→❝ ✤à♥❤ ❧➔ ✶✺✱✾0 ❈ ✭❍➻♥❤ ✸✮✳ ❍➛✉ ❤➳t ❝→❝ ❧♦➔✐ ❝→ ♥✉æ✐ ♣❤➙♥ ❜è tü ỗ sổ ỷ ỳ ✈ò♥❣ ♣❤➙♥ ❜è ❝â ✈➽ ✤ë t❤➜♣ t❤➻ ♥❤✐➺t ✤ë t❤➼❝❤ ❤đ♣ ❝❤♦ ♣❤ỉ✐ ♣❤→t tr✐➸♥ tø ✷✼ ✲ ✸✶0 ❈ ✭P❤❛♠ ✫ ◆❣✉②❡♥✱ ✷✵✵✾✮✳ ❚r♦♥❣ s✉èt q✉→ tr➻♥❤ ♣❤→t tr rữớ ổ P ỗ Pữỡ tr ỗ q t t ❝õ❛ t✛ ❧➺ ❝❤➳t ♣❤æ✐ ❝→ ❝❤èt ❜æ♥❣ t❤❡♦ ♥❤✐➺t ✤ë ❝❛♦ ✭tr→✐✮ ✈➔ t❤➜♣ ✭♣❤↔✐✮ ❍➻♥❤ ✷✳ P❤÷ì♥❣ tr➻♥❤ ỗ q t t t t ốt ❜ỉ♥❣ ❣✐❛✐ ✤♦↕♥ ♠ỵ✐ ♥ð t❤❡♦ ♥❤✐➺t ✤ë ❝❛♦ ✭tr→✐✮ t Pữỡ tr ỗ q t t➼♥❤ ❝õ❛ t✛ ❧➺ ❝❤➳t ❝→ ❝❤èt ❜æ♥❣ ❣✐❛✐ ✤♦↕♥ ✶✵ ♥❣➔② t✉ê✐ t❤❡♦ ♥❤✐➺t ✤ë ❝❛♦ ✭tr→✐✮ ✈➔ t❤➜♣ ✭♣❤↔✐✮✳ ♣❤ỉ✐ ❝â ❤❛✐ t❤í✐ ❦ý ♥❤↕② ❝↔♠ ♥❤➜t ✈ỵ✐ ❝→❝ ②➳✉ tè ♠ỉ✐ tr÷í♥❣✳ ✣â ❧➔ t❤í✐ ❦ý ♣❤ỉ✐ ✈à ✈➔ t❤í✐ ❦ý ♣❤➛♥ ✤✉ỉ✐ t→❝❤ ❦❤ä✐ ♥♦➣♥ ❤♦➔♥❣✳ ❑❤✐ ♥❤✐➺t ✤ë ✸✵ ✲ ✸✶0 ❈ t➾ ❧➺ ❞à ❤➻♥❤ ❝õ❛ ♣❤æ✐ ✻✵ ✲ ✼✵✪ ✈➔ t➾ ❧➺ ♣❤æ✐ t trữợ ❚❤❡♦ ❚r✉♦♥❣ ✭✷✵✵✸✮✱ ♥❤✐➺t ✤ë t❤➼❝❤ ❤ñ♣ ❝❤♦ ✤❛ sè ổ ữợ ồt tứ ❈✱ ❣✐ỵ✐ ❤↕♥ ♥❤✐➺t ✤ë ❝❤♦ ♣❤➨♣ ❧➔ ✶✵ ✲ ✹✵0 ❈✳ ❚❤❡♦ ❋✐s❤✲ ❜❛s❡ ✭❤tt♣s✿✴✴✇✇✇✳❢✐s❤❜❛s❡✳s❡✴s✉♠♠❛r②✴✶✶✾✽✼✮✱ ❝→ ❝❤èt ❜æ♥❣ ❧➔ ❧♦➔✐ ❝→ sè♥❣ ð ✈ò♥❣ ♥❤✐➺t ✤ỵ✐✱ ❚↕♣ ❝❤➼ ◆ỉ♥❣ ♥❣❤✐➺♣ ✈➔ P❤→t tr✐➸♥ ✶✽✭✺✮ ✹✽ t❤➼❝❤ ❤ñ♣ ♣❤→t tr✐➸♥ ð ♥❤✐➺t ✤ë tø ✷✵✲✷✻0 ❈✳ ❚r♦♥❣ ♥❣❤✐➯♥ ❝ù✉ ♥➔② ♥❤✐➺t ✤ë ❝❛♦ ❣➙② ❝❤➳t ✭■❯▲❚✮ ❝→ ❝❤èt ❜æ♥❣ ❣✐❛✐ ✤♦↕♥ ✶✵ ♥❣➔② t✉ê✐ ✭✸✽✱✻0 ❈✮ ❧➔ ❝❛♦ ❤ì♥ ❣✐❛✐ ✤♦↕♥ ♠ỵ✐ ♥ð ✭✸✻✱✼0 ❈✮ ✈➔ ❝õ❛ ❣✐❛✐ ✤♦↕♥ ♠ỵ✐ ♥ð ❧➔ ❝❛♦ ❤ì♥ ❣✐❛✐ ✤♦↕♥ ♣❤ỉ✐ ✭✸✷✱✺0 ❈✮✳ ◆❣÷đ❝ ❧↕✐✱ ♥❤✐➺t ✤ë t❤➜♣ ❣➙② ❝❤➳t ✭■▲▲❚✮ ❝→ ❝❤èt ❜æ♥❣ ❣✐❛✐ ✤♦↕♥ ✶✵ ♥❣➔② t✉ê✐ ✭✶✺✱✾0 ❈✮ ❧➔ t❤➜♣ ❤ì♥ ❣✐❛✐ ✤♦↕♥ ♠ỵ✐ ♥ð ✭✶✽✱✼0 ❈✮ ✈➔ ❝õ❛ ❣✐❛✐ ✤♦↕♥ ♠ỵ✐ ♥ð t❤➜♣ ❤ì♥ ❣✐❛✐ ✤♦↕♥ ♣❤ỉ✐ ✭✷✷✱✸0 ❈✮✳ ✣✐➲✉ ♥➔② ❝â t❤➸ ❦➳t ❧✉➟♥ r➡♥❣ ❦❤↔ ♥➠♥❣ ❝❤à✉ ✤ü♥❣ ♥❤✐➺t ✤ë ❜➜t ❧đ✐ ❝õ❛ ❝→ ❝❤èt ❜ỉ♥❣ t➠♥❣ ❞➛♥ t❤❡♦ sü ♣❤→t tr✐➸♥ ✈➔ t✉ê✐ ❝→✳ ❑❤✐ ❝ì t❤➸ ❝→ ♥❣➔② ❝➔♥❣ ❤♦➔♥ ❝❤➾♥❤ t❤➻ ❝❤à✉ ✤ü♥❣ ✤✐➲✉ ❦✐➺♥ ❜➜t ❧đ✐ ❝õ❛ ♠ỉ✐ tr÷í♥❣ tèt ❤ì♥✳ ◆❤➻♥ ❝❤✉♥❣✱ ❜✐➯♥ ✤ë ♥❤✐➺t ✤ë ❣➙② ❝❤➳t ❝→ ❝❤èt ❜æ♥❣ ❧➔ ❤➭♣ ❤ì♥ s♦ ✈ỵ✐ ♠ët sè ❧♦➔✐ ❝→ ♥✉ỉ✐ ð ✣❇✲ ❙❈▲✳ ❙♦ ✈ỵ✐ ❝→ ❝❤➨♣ ❈②♣r✐♥✉s ❝❛r♣✐♦ ✈➔ ❝→ t❤→❝ ❧→❝ ❝á♠ ❈❤✐t❛❧❛ ❝❤✐t❛❧❛ t❤➻ ♥❤✐➺t ✤ë ❝❛♦ ❣➙② ❝❤➳t ❝→ ❝❤èt ❜ỉ♥❣ t❤➜♣ ❤ì♥ ♥❤÷♥❣ ♥❤✐➺t ✤ë t❤➜♣ ❣➙② ❝❤➳t ❝❛♦ ❤ì♥✳ ◆❣÷ï♥❣ ♥❤✐➺t ✤ë ❝❛♦ ✈➔ t❤➜♣ ❝õ❛ ❝→ ❝❤➨♣ ❧➛♥ ❧÷đt ❧➔ ✹✶✱✶0 ❈ ✈➔ ✹✱✺ ✲ ✾✱✷0 ❈ ✭◆❣✉②❡♥✱ ✷✵✵✹✮ ✈➔ ❝õ❛ ❝→ t❤→t ❧→t ❝á♠ ❧➔ ✹✶ ✲ ✹✶✱✼0 ❈ ✈➔ ✶✵✱✶ ✲ ✶✶0 ❈ ✭▲❛✱ ✷✵✶✷✮✳ ◆❤✐➺t ✤ë ❝❛♦ ❣➙② ❝❤➳t ❝→ ❝❤èt ❜æ♥❣ ❝ơ♥❣ t❤➜♣ ❤ì♥ ❝→ tr❛ P❛♥❣❛s✐❛♥♦❞♦♥ ❤②♣♦♣❤t❤❛❧♠✉s ✭✹✵✱✽0 ❈✮ ✈➔ ❝→ ❜❛s❛ P❛♥❣❛s✐✉s ❜♦✲ ❝♦✉rt✐ ✭✹✵✱✸0 ❈✮ ♥❤÷♥❣ ♥❤✐➺t ✤ë t❤➜♣ ❣➙② ❝❤➳t ❧➔ t÷ì♥❣ ✤÷ì♥❣ ❝→ tr❛ ✭✶✻✱✼0 ❈✮ ð ❣✐❛✐ ✤♦↕♥ ❣✐è♥❣ ✭❉✉♦♥❣✱ ✷✵✵✸✮✳ ❙ü ❦❤→❝ ❜✐➺t ♥➔② ❝â t❤➸ ❞♦ sü ❦❤→❝ ♥❤❛✉ ✈➲ ♣❤÷ì♥❣ ♣❤→♣ ♥❣❤✐➯♥ ❝ù✉ ❝ơ♥❣ ♥❤÷ ❦❤↔ ♥➠♥❣ ❝❤à✉ ✤ü♥❣ ❝õ❛ ❧♦➔✐✳ ✸✳✷✳ ◆❣÷ï♥❣ ♣❍ ❝õ❛ ❝→ ❝❤èt ❜ỉ♥❣ ✸✳✷✳✶✳ ●✐❛✐ ✤♦↕♥ ♣❤ỉ✐ • ◆❣÷ï♥❣ ♣❍ ❝❛♦ ❣➙② ❝❤➳t ✭■❯▲♣❍✮ P❤ỉ✐ ❦❤ỉ♥❣ ❝❤➳t ð ❝→❝ ♣❍ tø ✼ ✲ ✾✳ ❍✐➺♥ t÷đ♥❣ ♣❤ỉ✐ ❝❤➳t ①↔② r❛ ð ❝→❝ ♥❣❤✐➺♠ t❤ù❝ ❝â ❣✐→ trà ♣❍ tø ✶✵ ✲ ✶✶❀ tr♦♥❣ ✤â✱ t✛ ❧➺ ♣❤æ✐ ❝❤➳t t➼❝❤ ❧ơ② ð ✷✹ ❣✐í ð ♣❍ ❂ ✶✵ ❧➔ ✷✶✱✸✪ ✈➔ t➠♥❣ ❧➯♥ ✺✷✱✸✪ ð ♣❍ ❂ ✶✶✳ ❚✛ ❧➺ ♣❤ỉ✐ ❝❤➳t t➼❝❤ ❧ơ② ð ✷✹ ❣✐í ð t õ ỵ ♥❣❤➽❛ t❤è♥❣ ❦➯ ✭P < ✵✱✵✺✮ ✈➔ ❝ô♥❣ ❦❤→❝ ❜✐➺t s ợ t t Pữỡ tr ỗ q t t t ổ t ✭②✮ t❤❡♦ ♣❍ ❝❛♦ ✭①✮ ❧➔ ② ❂ ✺✽✱✻✷✼① ✕ ✺✺✱✹✺✺ ✭❘2 ❂ ✵✱✽✾✶✶✮✳ ◆❤÷ ✈➟②✱ tr♦♥❣ t❤➼ ♥❣❤✐➺♠ ♥➔②✱ ♣❍ ❝❛♦ ❣➙② ❝❤➳t ✭■❯▲♣❍✮ ❝→ ❝❤èt ❜æ♥❣ ❣✐❛✐ ✤♦↕♥ ổ ữủ ữù ♣❍ t❤➜♣ ❣➙② ❝❤➳t ✭■▲▲♣❍✮ P❤æ✐ ❦❤æ♥❣ ❝❤➳t ð ♣❍ ❂ ✼✳ ❍✐➺♥ t÷đ♥❣ ♣❤ỉ✐ ❝❤➳t ①↔② r❛ ð ❝→❝ ♥❣❤✐➺♠ t❤ù❝ ❝â ❣✐→ trà ♣❍ tø ❚↕♣ ❝❤➼ ◆æ♥❣ ♥❣❤✐➺♣ ✈➔ P❤→t tr✐➸♥ ✶✽✭✺✮ ❚r÷í♥❣ ✣↕✐ ❤å❝ ◆ỉ♥❣ ▲➙♠ P ỗ ổ ❝❤➳t t➼❝❤ ❧ơ② ð ✷✹ ❣✐í ð ♥❣❤✐➺♠ t❤ù❝ ♣❍ ❂ ✻✱ ✼ ✈➔ ✽ ❧➔ t÷ì♥❣ ✤÷ì♥❣ ♥❤❛✉ ✭✷✵✱✸ ✲ ✷✶✱✸✪✮✱ ✈➔ t✛ ❧➺ ♣❤æ✐ ❝❤➳t ❧➔ ✶✵✵✪ s❛✉ ✼ ❣✐í t❤➼ ♥❣❤✐➺♠ ð ♣❍ ❂ ✸✳ ❚✛ ❧➺ ♣❤ỉ✐ ❝❤➳t t➼❝❤ ❧ơ② ð ✷✹ ❣✐í ð ❝→ ♣❍ ❂ ✻✱ ✼ ✈➔ ✽ ❧➔ ❦❤→❝ ❜✐➺t ❦❤æ♥❣ ❝â þ ♥❣❤➽❛ t❤è♥❣ ❦➯ ✭P > ✵✱✵✺✮ ♥❤÷♥❣ ❦❤→❝ ❜✐➺t õ ỵ tố P < s ợ t t Pữỡ tr ỗ q✉✐ t✉②➳♥ t➼♥❤ ❝õ❛ t✛ ❧➺ ♣❤æ✐ ❝❤➳t ✭②✮ t❤❡♦ ♣❍ t❤➜♣ ✭①✮ ❧➔ ② ❂ ✲ ✶✾✱✵✾✾① ✰ ✶✼✱✷✺✷ ✭❘2 ❂ ✵✱✽✶✮✳ ❚r♦♥❣ t❤➼ ♥❣❤✐➺♠ ♥➔②✱ ♣❍ t❤➜♣ ❣➙② ❝❤➳t ✭■▲▲♣❍✮ ❝→ ❝❤èt ❜ỉ♥❣ ❣✐❛✐ ✤♦↕♥ ♣❤ỉ✐ ✤÷đ❝ ①→❝ ✤à♥❤ ❧➔ ✹✱✹ ✭❍➻♥❤ ✹✮✳ ✸✳✷✳✷✳ ●✐❛✐ ✤♦↕♥ ❝→ ♠ỵ✐ ữù t t q ❝❤♦ t❤➜② ❝→ ❦❤æ♥❣ ❝❤➳t ð ❝→❝ ♣❍ tø ✼ ✲ ✾✳ ❍✐➺♥ t÷đ♥❣ ❝→ ❝❤➳t ①↔② r❛ ð ❝→❝ ♥❣❤✐➺♠ t❤ù❝ ❝â ❣✐→ trà ♣❍ tø ✶✵ ✲ ✶✶✳ ❚✛ ❧➺ ❝→ ❝❤➳t t➼❝❤ ❧ơ② ð ✷✹ ❣✐í ð ♥❣❤✐➺♠ t❤ù❝ ♣❍ ❂ ✶✵ ❧➔ ✸✽✱✵✪✱ t➠♥❣ ❧➯♥ ✺✺✱✸✪ ð ♣❍ ❂ ✶✵✱✺❀ ð ♣❍ ❝❛♦ ❤ì♥ ✭♣❍ ❂ ✶✶✮✱ t✛ ❧➺ ❝→ ❝❤➳t ❧➔ ✶✵✵✪ s❛✉ ✶ ❣✐í t❤➼ ♥❣❤✐➺♠✳ ❚✛ ❧➺ ❝→ ❝❤➳t t➼❝❤ ❧ô② ð ✷✹ ❣✐í ð ♣❍ ❂ ✶✵ ✈➔ ✶✵✱✺ ❧➔ ❦❤→❝ ❜✐➺t õ ỵ tố P < ụ ❦❤→❝ ❜✐➺t s♦ ✈ỵ✐ t✛ ❧➺ ❝❤➳t ð ❝→❝ ♣❍ Pữỡ tr ỗ q t t t ❝→ ❝❤➳t ✭②✮ t❤❡♦ ♣❍ ❝❛♦ ✭①✮ ❧➔ ② ❂ ✾✸✱✺✽① ✕ ✽✾✱✸✸✼ ✭❘2 ❂ ✵✱✾✻✶✼✮✳ ◆❤÷ ✈➟② tr♦♥❣ t❤➼ ♥❣❤✐➺♠ ♥➔②✱ ♣❍ ❝❛♦ ❣➙② ❝❤➳t ✭■❯▲♣❍✮ ❝→ ❝❤èt ❜æ♥❣ ợ ữủ ữù t t ữỡ tỹ ❝→ ❦❤æ♥❣ ❝❤➳t ð ❝→❝ ♣❍ tø ✼ ✲ ✺✳ ❍✐➺♥ t÷đ♥❣ ❝→ ❝❤➳t ①↔② r❛ ð ❝→❝ ♥❣❤✐➺♠ t❤ù❝ ❝â ❣✐→ trà ♣❍ tø ✹ ✲ ✸✳ ❚✛ ❧➺ ❝→ ❝❤➳t t➼❝❤ ❧ơ② ð ✷✹ ❣✐í ð ♥❣❤✐➺♠ t❤ù❝ ♣❍ ❂ ✹ ❧➔ ✸✶✱✻✪✱ t➠♥❣ ❧➯♥ ✺✶✱✻✪ ð ♣❍ ❂ ✸✱✺❀ ð ♣❍ t❤➜♣ ❤ì♥ ✭♣❍ ❂ ✸✮✱ t✛ ❧➺ ❝→ ❝❤➳t ❧➔ ✶✵✵✪ s❛✉ ✷ ❣✐í t❤➼ ♥❣❤✐➺♠✳ ❚✛ ❧➺ ❝→ ❝❤➳t t➼❝❤ ❧ơ② ð ✷✹ ❣✐í ð t õ ỵ ♥❣❤➽❛ t❤è♥❣ ❦➯ ✭P < ✵✱✵✺✮ ✈➔ ❝ô♥❣ ❦❤→❝ ❜✐➺t s ợ t t Pữỡ tr ỗ q t t t t ✭②✮ t❤❡♦ ♣❍ t❤➜♣ ✭①✮ ❧➔ ② ❂ ✲ ✸✼✱✷✽✷① ✰ ✷✻✱✷✶✹ ✭❘2 ❂ ✵✱✾✻✶✼✮✳ ❚r♦♥❣ t❤➼ ♥❣❤✐➺♠ ♥➔②✱ ♣❍ t❤➜♣ ❣➙② ❝❤➳t ✭■▲▲♣❍✮ ❝→ ❝❤èt ❜ỉ♥❣ ❣✐❛✐ ✤♦↕♥ ♠ỵ✐ ♥ð ✤÷đ❝ ①→❝ ✤à♥❤ ❧➔ ✸✱✼ ✭❍➻♥❤ ✺✮✳ ✸✳✷✳✸✳ ●✐❛✐ tờ ữù ❝❤➳t ✭■❯▲♣❍✮ ❚÷ì♥❣ tü t❤➼ ♥❣❤✐➺♠ tr➯♥✱ ❝→ ❦❤ỉ♥❣ ❝❤➳t ð ❝→❝ ♣❍ tø ✼ ✲ ✾✳ ❍✐➺♥ t÷đ♥❣ ❝→ ❝❤➳t ①↔② r❛ ð ❝→❝ ✇✇✇✳❥❛❞✳❤❝♠✉❛❢✳❡❞✉✳✈♥ ✹✾ ❚r÷í♥❣ ✣↕✐ ❤å❝ ổ P ỗ Pữỡ tr ỗ q t t t t ổ ❝❤èt ❜æ♥❣ t❤❡♦ ♣❍ ❝❛♦ ✭tr→✐✮ ✈➔ t❤➜♣ ✭♣❤↔✐✮✳ ❍➻♥❤ Pữỡ tr ỗ q t t t ❝❤➳t ❝→ ❝❤èt ❜ỉ♥❣ ❣✐❛✐ ✤♦↕♥ ♠ỵ✐ ♥ð t❤❡♦ ♣❍ tr t Pữỡ tr ỗ q✉✐ t✉②➳♥ t➼♥❤ ❝õ❛ t✛ ❧➺ ❝❤➳t ❝→ ❝❤èt ❜æ♥❣ ❣✐❛✐ ✤♦↕♥ ✶✵ ♥❣➔② t✉ê✐ t❤❡♦ ♣❍ ❝❛♦ ✭tr→✐✮ ✈➔ t❤➜♣ ✭♣❤↔✐✮✳ ♥❣❤✐➺♠ t❤ù❝ ❝â ❣✐→ trà ♣❍ tø ✶✵ ✲ ✶✶✳ ❚✛ ❧➺ ❝→ ❝❤➳t t➼❝❤ ❧ô② ð ✷✹ ❣✐í ð ♥❣❤✐➺♠ t❤ù❝ ♣❍ ❂ ✶✵ ❧➔ ✷✵✱✵✪✱ t➠♥❣ ❧➯♥ ✺✻✱✸✪ ð ♣❍ ❂ ✶✵✱✺ ✈➔ t✛ ❧➺ ❝→ ❝❤➳t ❧➔ ✶✵✵✪ s❛✉ ✶ ❣✐í t❤➼ ♥❣❤✐➺♠ ð ♣❍ ❂ ✶✶✳ ❚✛ ❧➺ ❝→ ❝❤➳t t➼❝❤ ❧ô② ð ✷✹ ❣✐í ð ♣❍ ❂ ✶✵ ✈➔ ✶✵✱✺ ❧➔ ❦❤→❝ ❜✐➺t õ ỵ tố P < ụ ✇✇✇✳❥❛❞✳❤❝♠✉❛❢✳❡❞✉✳✈♥ ❦❤→❝ ❜✐➺t s♦ ✈ỵ✐ t✛ ❧➺ ❝❤➳t ð ❝→❝ Pữỡ tr ỗ q t t t ❧➺ ❝→ ❝❤➳t ✭②✮ t❤❡♦ ♣❍ ❝❛♦ ✭①✮ ❧➔ ② ❂ ✾✹✱✷✷✷① ✕ ✾✵✱✶✵✾ ✭❘2 ❂ ✵✱✾✻✷✻✮✳ ♣❍ ❝❛♦ ❣➙② ❝❤➳t ✭■❯▲♣❍✮ ❝→ ❝❤èt ❜æ♥❣ ❣✐❛✐ ✤♦↕♥ ✶✵ ♥❣➔② t✉ê✐ ✤÷đ❝ ①→❝ ✤à♥❤ ❧➔ ✶✵✱✷ ✭❍➻♥❤ ✻✮✳ ❚↕♣ ❝❤➼ ◆ỉ♥❣ ♥❣❤✐➺♣ ✈➔ P❤→t tr✐➸♥ ✶✽✭✺✮ ✺✵ ❚r÷í♥❣ ✣↕✐ ❤å❝ ◆ỉ♥❣ P ỗ ữù ổ ỏ t❛♥ ✭♠❣ ❖2 ✴▲✮ ❝õ❛ ❝→ ❝❤èt ❜æ♥❣ ð ❝→❝ ❣✐❛✐ ✤♦↕♥ ♣❤→t tr✐➸♥ ❦❤→❝ ▲➛♥ ❧➦♣ ❧↕✐ ✶ ✷ ✸ ❚r✉♥❣ ❜➻♥❤ ●✐❛✐ ✤♦↕♥ ♣❤æ✐ ✹✱✽ ✹✱✸ ✺✱✷ ✹✱✼ ➧ ✵✱✺ ●✐❛✐ ✤♦↕♥ ♠ỵ✐ ♥ð ✵✱✾ ✶✱✵ ✶✱✸ ✶✱✶ ➧ ✵✱✷ ●✐❛✐ ✤♦↕♥ ✶✵ ♥❣➔② t✉ê✐ ✶✱✷ ✵✱✽ ✶✱✵ ✶✱✵ ➧ ✵✱✷ ❧đ✐ ❝õ❛ ❝→ ❝❤èt ❜ỉ♥❣ s❛✉ ♥ð ❧➔ ❦➨♠ ❤ì♥ ♣❤ỉ✐ ✤è✐ ❈→ ❦❤ỉ♥❣ ❝❤➳t ð ❝→❝ tứ tữủ ợ ✈➔ tèt ❤ì♥ ✤è✐ ✈ỵ✐ ♣❍ t❤➜♣✳ ❝→ ❝❤➳t ①↔② r❛ ð ❝→❝ ♥❣❤✐➺♠ t❤ù❝ ❝â ❣✐→ trà ♣❍ tø ◆❤➻♥ ❝❤✉♥❣✱ ♣❍ ❝❛♦ ❣➙② ❝❤➳t ♣❤æ✐ ❝→ ❝❤èt ❜æ♥❣ ✹ ✲ ✸✳ ❚✛ ❧➺ ❝→ ❝❤➳t t➼❝❤ ❧ô② ð ✷✹ ❣✐í ❝õ❛ ♥❣❤✐➺♠ ❧➔ t❤➜♣ ❤ì♥ s♦ ✈ỵ✐ ♣❤ỉ✐ rổ ỗ s tự ✻✶✱✻✪ ✈➔ ❝õ❛ ♣❍ ❂ ✸✱✺ ❧➔ ✺✷✱✸✪❀ t❡st✉❞✐♥❡✉s ✭♣❍ ❂ ✶✶✮ ✈➔ ❝→ s➦❝ r➡♥ ❚r✐❝❤♦❣❛st❡r t✛ ❧➺ ❝→ ❝❤➳t t➼❝❤ ❧ô② ❝õ❛ ♥❣❤✐➺♠ t❤ù❝ ♣❍ ❂ ✸ ❧➔ ♣❡❝t♦r❛❧✐s ✭♣❍ ❂ ✶✶✱✽✮ ✭▲❡✱ ✷✵✶✵✮✳ ♣❍ ❝❛♦ ❣➙② ❝❤➳t ✶✵✵✪ s❛✉ ✷ ❣✐í t❤➼ ♥❣❤✐➺♠✳ ❚✛ ❧➺ ❝→ ❝❤➳t t ụ ốt ổ tữỡ ữỡ ợ ❝❤➨♣ ✭✾✱✺ ✲ ð ✷✹ ❣✐í ð ♣❍ ❂ ✹ t õ ỵ ✷✵✵✹✮✱ ❝→ t❛✐ t÷đ♥❣ ❖s♣❤r♦♥❡♠✉s t❤è♥❣ ❦➯ ✭P < ✵✱✵✺✮ ✈➔ ❝ơ♥❣ ❦❤→❝ ❜✐➺t s♦ ✈ỵ✐ t✛ ❣♦r❛♠② ✭✾✱✺ ✲ ✶✶✮ ✭❚r❛♥❣✱ ✷✵✶✵✮✳ ♣❍ t❤➜♣ ❣➙② ❝❤➳t ❝→ ❝❤èt ❜æ♥❣ tữỡ ữỡ s ợ tt t Pữỡ tr ỗ q t t t✛ ❧➺ ❝→ ❧→t ❝á♠ ◆♦t♦♣t❡r✉s ❝❤✐t❛❧❛ ✭✸✱✺ ✲ ✹✱✺✮ ✭▲❛✱ ✷✵✶✷✮✱ ❝❤➳t ✭②✮ t❤❡♦ ♣❍ t❤➜♣ ✭①✮ ❧➔ ② ❂ ✲ ✸✻✱✻✼✽① ✰ t❤➜♣ ❤ì♥ s♦ ✈ỵ✐ ❝→ ❝❤➨♣ ✭✹✱✷ ✲ ✹✱✺✮ ✭◆❣✉②❡♥✱ ✷✵✵✹✮ ✷✻✱✵✻✷ ✭❘2 ❂ ✵✱✾✷✶✻✮✳ ♣❍ t❤➜♣ ❣➙② ❝❤➳t ✭■▲▲♣❍✮ ✈➔ ❝→ t❛✐ t÷đ♥❣ ✭✹✱✵ ✲ ✹✱✺✮ ✭❚r❛♥❣✱ ✷✵✶✵✮✱ ✈➔ ❝❛♦ ❝→ ❝❤èt ❜æ♥❣ ❣✐❛✐ ✤♦↕♥ tờ ữủ ỡ s ợ s➦❝ r➡♥✭✷✱✹✮ ✭▲❡✱ ✷✵✶✵✮✳ ❙ü ❦❤→❝ ❜✐➺t ♥➔② ❝ô♥❣ ❝â t❤➸ ❞♦ sü ❦❤→❝ ♥❤❛✉ ✈➲ ♣❤÷ì♥❣ ❧➔ ✸✱✽ ✭❍➻♥❤ ✻✮✳ ♣❤→♣ ♥❣❤✐➯♥ ❝ù✉ ❝ơ♥❣ ♥❤÷ ❦❤↔ ♥➠♥❣ ❝❤à✉ ✤ü♥❣ ❚❤❡♦ ❚r✉♦♥❣ ✭✷✵✵✸✮✱ ♣❍ ❧➔ ♠ët tr♦♥❣ ♥❤ú♥❣ ❝õ❛ ❧♦➔✐✳ tố ổ trữớ ữ rt ợ sè♥❣ ❝→✳ ♣❍ ❝â ↔♥❤ ❤÷ð♥❣ trü❝ t✐➳♣ ✤➳♥ ❝→❝ ❣✐❛✐ ✤♦↕♥ ✸✳✸✳ ◆❣÷ï♥❣ ỉ①② ❤á❛ t❛♥ ✭❉❖✮ ❝õ❛ ❝→ ❝❤èt ♣❤→t tr✐➸♥ ❜❛♥ ✤➛✉ ❝õ❛ ❝→✳ ✣❛ sè ❝→❝ ❧♦➔✐ ❝→ ❝â ❜ỉ♥❣ t❤➸ ❝❤à✉ ✤ü♥❣ ♠ët ❣✐ỵ✐ ❤↕♥ rë♥❣ ❝õ❛ ♣❍✱ tø ✺✲ ✾✳ ❚r♦♥❣ ♥❣❤✐➯♥ ❝ù✉ ✈➲ ↔♥❤ ❤÷ð♥❣ ❝õ❛ ♣❍ tr➯♥ ❑➳t q✉↔ t❤➼ ♥❣❤✐➺♠ ①→❝ ✤à♥❤ ♥❣÷ï♥❣ ỉ①② ð ❝→❝ ❝→ Pr♦❝❤✐❧♦❞✉s ❧✐♥❡❛t✉s✱ ❘❡②♥❛❧t❡✲❚❛t❛❥❡ ✫ ❝t✈✳ ❣✐❛✐ ✤♦↕♥ ♣❤→t tr✐➸♥ ❦❤→❝ ♥❤❛✉ ❝õ❛ ❝→ ❝❤èt ❜æ♥❣ ✭✷✵✶✺✮ ✤➣ t➻♠ t❤➜② ð ♣❍ ✺✱✵ t♦➔♥ ❜ë trù♥❣ ❜à ❝❤➳t ✤÷đ❝ tr➻♥❤ ❜➔② ð ❇↔♥❣ ✶✳ s❛✉ ✹ ❣✐í✳ ❚rù♥❣ ✤÷đ❝ ➜♣ ð ♣❍ tø ✻✱✵ ✲ ✽✱✺ ❝â t➾ ❧➺ ❚❤❡♦ ◆❣✉②❡♥ ✭✷✵✵✺✮✱ ❤➔♠ ❧÷đ♥❣ ỉ①② ❤á❛ t❛♥ t❤ư t✐♥❤ ✈➔ t➾ ❧➺ sè♥❣ t÷ì♥❣ tü ữ tr ữợ t ủ ❤♦↕t ✤ë♥❣ s✐♥❤ ✻✱✵ trù♥❣ ❝â ✤÷í♥❣ ❦➼♥❤ ♥❤ä ❤ì♥ ✈➔ ➜✉ trò♥❣ ❝→ tr÷ð♥❣ ✈➔ ♣❤→t tr✐➸♥✱ ✤➸ ✤↔♠ ❜↔♦ ❝❤♦ ♣❤ỉ✐ ♣❤→t ❝â ❝❤✐➲✉ ❞➔✐ ♥❣➢♥ ❤ì♥ s♦ ợ trự ữủ ổ tr tữớ ✸✲✺ ♠❣✴▲✳ ❚r♦♥❣ ❤➛✉ ❤➳t tr÷í♥❣ tr✉♥❣ t➼♥❤ ❤❛② ❦✐➲♠✳ ❚r♦♥❣ ❣✐❛✐ ✤♦↕♥ ÷ì♥❣ tr÷í♥❣ ❤đ♣✱ ❤➔♠ ❧÷đ♥❣ ỉ①② ❤á❛ t tr ữợ ổ trũ t số ❤➟✉ ➜✉ trò♥❣ ❝❛♦ t❤➜♣ ❤ì♥ ✷ ♠❣✴▲ t❤➻ ♣❤ỉ✐ s➩ ❝❤➳t ♥❣↕t✳ ●✐❛✐ ✤♦↕♥ ♥❤➜t ð ♣❍ ✼✱✵✳ ❏❡❧❧②♠❛♥ ✫ ❍❛r❞✐♥❣ ✭✷✵✶✹✮ ♥❣❤✐➯♥ ❝á♥ ♥❤ä✱ ❝→ ❝♦♥ ❝â ♥❣÷ï♥❣ æ①② ❝❛♦✱ ❝❛♦ ♥❤➜t ✤â ❧➔ ❝ù✉ tr➯♥ ✺ ❧♦➔✐ ữợ ồt t ổ tü ❞♦ ✈➔ ❝→ ❜ët ✭P❤❛♠ ✫ ◆❣✉②❡♥✱ t❤➜② t➜t t ữợ < ✹ ✷✵✵✾✮✳ ♥❤÷♥❣ ❝→ tr÷ð♥❣ t❤➔♥❤ ❝â t❤➸ sè♥❣ ð ♣❍ ✹✱✺ ✈➔ ◆❣÷ï♥❣ ỉ①② ❝õ❛ ❝→ ❝❤èt ❜ỉ♥❣ ❧➔ t❤➜♣ ❤ì♥ r➜t ❝→ tr÷ð♥❣ t❤➔♥❤ ❝❤à✉ ✤ü♥❣ ♣❍ t❤➜♣ tốt ỡ s ợ ổ ữù ổ ❝õ❛ ❝→ ❝❤èt ❝♦♥✳ ❜ỉ♥❣ ❝❛♦ ❤ì♥ s♦ ✈ỵ✐ ❝→ ❝❤➨♣ ✭✵✱✷✷ ✲ ✵✱✶✶ ♠❣ ❑➳t q✉↔ ❝→❝ t❤➼ ♥❣❤✐➺♠ tr➯♥ ❝❤♦ t❤➜② ♣❍ ❝❛♦ ❖2 ✴▲✮✱ ❝→ tr➢♠ ❝ä ❈t❡♥♦♣❤❛r②♥❣♦❞♦♥ ✐❞❡❧❧❛ ✭✵✱✹✾ ❣➙② ❝❤➳t ✭■❯▲♣❍✮ ❝→ ❝❤èt ❜æ♥❣ ❣✐❛✐ ✤♦↕♥ ✶✵ ♥❣➔② ✲ ✵✱✷✷ ♠❣ ❖2 ✴▲✮✱ ❝→ ♠➧ tr➢♥❣ ❍②♣♦♣❤t❤❛❧♠✐❝❤t❤②s t✉ê✐ ✭✶✵✱✷✮ ❧➔ ❜➡♥❣ ❣✐❛✐ ✤♦↕♥ ♠ỵ✐ ♥ð ✭✶✵✱✷✮ ✈➔ ❤❛r♠❛♥❞✐ ✭✵✱✽✾ ✲ ✵✱✺✺ ♠❣ ❖2 ✴▲✮ ✈➔ ❝→ trỉ✐ ▲❛❜❡♦ t❤➜♣ ❤ì♥ ❣✐❛✐ ✤♦↕♥ ♣❤ỉ✐ ✭✶✵✱✼✮✳ ◆❣÷đ❝ ❧↕✐✱ ♣❍ r♦❤✐t❛ ✭✵✱✾✼ ✲ ✵✱✻✻ ♠❣ ❖2 ✴▲✮ ✭◆❣✉②❡♥✱ ✷✵✵✹❀ t❤➜♣ ❣➙② ❝❤➳t ✭■▲▲♣❍✮ ❝→ ❝❤èt ❜æ♥❣ ❣✐❛✐ ✤♦↕♥ ✶✵ ❚r❛♥✱ ✷✵✵✼✮✳ ♥❣➔② t✉ê✐ ✭✸✱✽✮ ❧➔ t÷ì♥❣ ✤÷ì♥❣ ❣✐❛✐ ✤♦↕♥ ♠ỵ✐ ♥ð ✭✸✱✼✮ ✈➔ t❤➜♣ ❤ì♥ ❣✐❛✐ ✤♦↕♥ ♣❤ỉ✐ ✭✹✱✹✮✳ ✣✐➲✉ ♥➔② ❝â t❤➸ ❦➳t ❧✉➟♥ r➡♥❣ ❦❤↔ ♥➠♥❣ ỹ t ữù t t ✭■▲▲♣❍✮ ❚↕♣ ❝❤➼ ◆æ♥❣ ♥❣❤✐➺♣ ✈➔ P❤→t tr✐➸♥ ✶✽✭✺✮ ✇✇✇✳❥❛❞✳❤❝♠✉❛❢✳❡❞✉✳✈♥ rữớ ổ P ỗ ❑➳t ▲✉➟♥ ✈➔ ❑✐➳♥ ◆❣❤à ✹✳✶✳ ❑➳t ❧✉➟♥ ◆❣÷ï♥❣ ♥❤✐➺t ✤ë ❝❛♦ ✈➔ t❤➜♣ ❝õ❛ ♣❤æ✐ ❧➔ ✸✷✱✺0 ❈ ✈➔ ✷✷✱✸0 ❈❀ ❝→ ♠ỵ✐ ♥ð ❧➔ ✸✻✱✼0 ❈ ✈➔ ✶✽✱✼0 ❈❀ ❝→ ✶✵ ♥❣➔② t✉ê✐ ❧➔ ✸✽✱✻0 ❈ ✈➔ ✶✺✱✾0 ❈✳ ◆❣÷ï♥❣ ♣❍ ❝❛♦ ✈➔ t❤➜♣ ð ❣✐❛✐ ✤♦↕♥ ♣❤ỉ✐ ❧➔ ✶✵✱✼ ✈➔ ✹✱✹❀ ❝→ ♠ỵ✐ ♥ð ❧➔ ✶✵✱✷ ✈➔ ✸✱✼ ❝→ ✶✵ ♥❣➔② t✉ê✐ ❧➔ ✶✵✱✷ ✈➔ ✸✱✽✳ ◆❣÷ï♥❣ ỉ①② ❝õ❛ ❝→ ❝❤èt ❜ỉ♥❣ ❣✐❛✐ ✤♦↕♥ ♣❤ỉ✐✱ ❝→ ♠ỵ✐ ♥ð ✈➔ ❝→ ✶✵ ♥❣➔② t✉ê✐ ❧➛♥ ❧÷đt ❧➔ ✹✱✼❀ ✶✱✶❀ ✶✱✵ ♠❣ ❖2 ✴▲✳ ✹✳✷✳ ❑✐➳♥ ◆❣❤à ❈➛♥ ♥❣❤✐➯♥ ❝ù✉ ↔♥❤ ❤÷ð♥❣ ❝õ❛ ♥❤✐➺t ✤ë✱ ♣❍ ✈➔ ỉ①② ❤á❛ t❛♥ ✤➳♥ q✉→ tr➻♥❤ t❤➔♥❤ t❤ö❝ s✐♥❤ ❞ö❝ ✈➔ s✐♥❤ s↔♥ ❝õ❛ ❝→ ❝❤èt ❜æ♥❣✳ ❈➛♥ t✐➳♥ ❤➔♥❤ t❤➯♠ ❝→❝ ♥❣❤✐➯♥ ❝ù✉ ✤➸ ①→❝ ✤à♥❤ ❝→❝ ♥❣÷ï♥❣ ❝õ❛ ❝→❝ ②➳✉ tè ♠ỉ✐ tr÷í♥❣ ❦❤→❝ ❝õ❛ ❝→ ❝❤èt ❜ỉ♥❣ ♥❤÷ ✤ë ♠➦♥✱ ❛♠♠♦♥✐❛✱ ♥✐tr✐t❡✱✳✳✳ ❚➔✐ ▲✐➺✉ ❚❤❛♠ ❑❤↔♦ ✭❘❡❢❡r❡♥❝❡s✮ ❇❡✐t✐♥❣❡r✱ ❚✳ ▲✳✱ ❇❡♥♥❡tt✱ ❲✳ ❆✳✱ ✫ ▼❝❈❛✉❧❡②✱ ❘✳ ❲✳ ✭✷✵✵✵✮✳ ❚❡♠♣❡r❛t✉r❡ t♦❧❡r❛♥❝❡s ♦❢ ◆♦rt❤ ❆♠❡r✐❝❛♥ ❢r❡s❤✇❛t❡r ❢✐s❤❡s ❡①♣♦s❡❞ t♦ ❞②♥❛♠✐❝ ❝❤❛♥❣❡s ✐♥ t❡♠✲ ♣❡r❛t✉r❡✳ ❊♥✈✐r♦♥♠❡♥t❛❧ ❇✐♦❧♦❣② ♦❢ ❋✐s❤❡s ✺✽✱ ✷✸✼✲ ✷✼✺✳ ❉✉♦♥❣✱ ❨✳ ❚✳ ✭✷✵✵✸✮✳ ❙t✉❞② ♦♥ s♦♠❡ ♠♦r♣❤♦❧♦❣✐❝❛❧✱ ❣r♦✇t❤ ❛♥❞ ♣❤②s✐♦❧♦❣✐❝❛❧ ❝❤❛r❛❝t❡r✐st✐❝s ♦❢ ❜❛s❛ ✭P❛♥✲ ❣❛s✐✉s ❜♦❝♦✉rt✐✮✱ tr❛ ✭P❛♥❣❛s✐✉s ❤②♣♦♣❤t❤❛❧♠✉s✮ ❛♥❞ t❤❡✐r ❤②❜r✐❞✳ ✭❯♥♣✉❜❧✐s❤❡❞ ♠❛st❡r✬s t❤❡s✐s✮✳ ❈❛♥ ❚❤♦ ❯♥✐✈❡rs✐t②✱ ❈❛♥ ❚❤♦✱ ❱✐❡t♥❛♠✳ ❏❡❧❧②♠❛♥✱ P✳ ●✳✱ ✫ ❍❛r❞✐♥❣✱ ❏✳ ❙✳ ✭✷✵✶✹✮✳ ❱❛r✐❛❜❧❡ s✉r✲ ✈✐✈❛❧ ❛❝r♦ss ❧♦✇ ♣❍ ❣r❛❞✐❡♥ts ✐♥ ❢r❡s❤✇❛t❡r ❢✐s❤ s♣❡❝✐❡s✳ ❏♦✉r♥❛❧ ♦❢ ❋✐s❤ ❇✐♦❧♦❣② ✽✺✱ ✶✼✹✻✕✶✼✺✷✳ ▲❛✱ ◆✳ ❆✳ ✭✷✵✶✷✮✳ ❙t✉❞② ♦♥ s♦♠❡ ❜✐♦❧♦❣✐❝❛❧ ❝❤❛r❛❝t❡r✐s✲ t✐❝s ♦❢ ❦♥✐❢❡ ❢✐s❤ ✭❈❤✐t❛❧❛ ❝❤✐t❛❧❛ ✮ ❛t ❡♠❜r②♦♥✐❝✱ ❧❛r✈❛❧ ❛♥❞ ❢✐♥❣❡r❧✐♥❣ st❛❣❡s✳ ❈❛♥ ❚❤♦ ❯♥✐✈❡rs✐t② ❏♦✉r♥❛❧ ♦❢ ❙❝✐❡♥❝❡ ✷✶❜✱ ✻✷✲✻✼✳ ▲❡✱ ❑✳ P✳ ✭✷✵✶✵✮✳ ❊❢❢❡❝ts ♦❢ s❛❧✐♥✐t② ❛♥❞ ♣❍ ♦♥ t❤❡ ❣r♦✇t❤ ♦❢ ❡♠❜r②♦ ❛♥❞ ❧❛r✈❛❡ ♦❢ ❝❧✐♠❜✐♥❣ ♣❡r❝❤✳ ✭❯♥♣✉❜❧✐s❤❡❞ ♠❛st❡r✬s t❤❡s✐s✮✳ ❈❛♥ ❚❤♦ ❯♥✐✈❡rs✐t②✱ ❈❛♥ ❚❤♦✱ ❱✐❡t✲ ♥❛♠✳ ✺✶ ▲✐♥❞❡r✱ ❘✳ ❙✳ ✭✷✵✵✵❜✮✳ ❚❤❡ ❝❛t❢✐s❤❡s ♦❢ ❆s✐❛ ❢❛♠✐❧② ❜❛❣r✐✲ ❞❛❡✳ ✭P❛rt ♦♥❡✮✳ ❈❛t ❈❤❛t ✶✳ ❘❡tr✐❡✈❡❞ ❆♣r✐❧ ✶✱ ✷✵✶✾✱ ❢r♦♠ ❤tt♣s✿✴✴✇✇✇✳♣❧❛♥❡t❝❛t❢✐s❤✳❝♦♠✴s❤❛♥❡s✇♦r❧❞✴ s❤❛♥❡s✇♦r❧❞✳♣❤♣❄❛rt✐❝❧❡❴✐❞❂✶✽✻✳ ◆❣✉②❡♥✱ ❑✳ ❱✳ ✭✷✵✵✹✮✳ ❙♦♠❡ ♠♦r♣❤♦❧♦❣✐❝❛❧✱ ❡❝♦❧♦❣✐❝❛❧✱ ❜✐♦❝❤❡♠✐❝❛❧ ❛♥❞ ❣❡♥❡t✐❝ ❝❤❛r❛❝t❡r✐st✐❝s ♦❢ t❤r❡❡ ❝♦♠✲ ♠♦♥ ❝❛r♣ str❛✐♥s ✭②❡❧❧♦✇✱ ✇❤✐t❡ ❛♥❞ ❍✉♥❣❛r②✮ ✐♥ ▼❡❦♦♥❣ r✐✈❡r ❞❡❧t❛✳ ✭❯♥♣✉❜❧✐s❤❡❞ ❞♦❝t♦r❛❧ ❞✐ss❡rt❛✲ t✐♦♥✮✳ ◆❤❛ ❚r❛♥❣ ❋✐s❤❡r✐❡s ❯♥✐✈❡rs✐t②✱ ◆❤❛ ❚r❛♥❣✱ ❱✐❡t♥❛♠✳ ◆❣✉②❡♥✱ ❑✳ ❱✳ ✭✷✵✵✺✮✳ ❚❡①t❜♦♦❦ ♦♥ ❢✐s❤ s❡❡❞ ♣r♦❞✉❝t✐♦♥✳ ❈❛♥ ❚❤♦ ❯♥✐✈❡rs✐t②✱ ❈❛♥ ❚❤♦✱ ❱✐❡t♥❛♠✳ ◆❣✉②❡♥✱ ❚✳ ❱✳ ✭✷✵✵✺✮✳ ▲❡❝t✉r❡ ♦♥ ♣❤②s✐♦❧♦❣② ♦❢ ❢✐s❤ ❛♥❞ ❝r✉st❛❝❡❛♥✳ ◆♦♥❣ ▲❛♠ ❯♥✐✈❡rs✐t②✱ ❍♦ ❈❤✐ ▼✐♥❤ ❈✐t②✱ ❱✐❡t♥❛♠✳ P❤❛♠ ❚✳ ▼✳✱ ✫ ◆❣✉②❡♥ ❑✳ ❱✳ ✭✷✵✵✾✮✳ ❙❝✐❡♥t✐❢✐❝ ❜❛s✐s ❛♥❞ t❡❝❤♥✐q✉❡ ♦❢ ❢✐s❤ s❡❡❞ ♣r♦❞✉❝t✐♦♥✳ ❍♦ ❈❤✐ ▼✐♥❤ ❈✐t②✱ ❱✐❡t♥❛♠✿ ❆❣r✐❝✉❧t✉r❛❧ P✉❜❧✐s❤✐♥❣ ❍♦✉s❡✳ ❘❡②♥❛❧t❡✲❚❛t❛❥❡✱ ❉✳ ❆✳✱ ❇❛❧❞✐ss❡r♦tt♦✱ ❇✳✱ ✫ ❩❛♥✐❜♦♥✐✲ ❋✐❧❤♦✱ ❊✳ ✭✷✵✶✺✮✳ ❚❤❡ ❡❢❢❡❝t ♦❢ ✇❛t❡r ♣❍ ♦♥ t❤❡ ✐♥❝✉✲ ❜❛t✐♦♥ ❛♥❞ ❧❛r✈✐❝✉❧t✉r❡ ♦❢ ❝✉r✐♠❜❛t→ Pr♦❝❤✐❧♦❞✉s ❧✐♥❡❛✲ t✉s ✭❱❛❧❡♥❝✐❡♥♥❡s✱ ✶✽✸✼✮ ✭❈❤❛r❛❝✐❢♦r♠❡s✿ Pr♦❝❤✐❧♦❞♦♥✲ t✐❞❛❡✮✳ ◆❡♦tr♦♣✐❝❛❧ ■❝❤t❤②♦❧♦❣② ✶✸✭✶✮✱ ✶✼✾✲✶✽✻✳ ❚r❛♥✱ ❱✳ ❱✳ ✭✷✵✵✼✮✳ ❚❡①t❜♦♦❦ ♦♥ ❋✐s❤❡r✐❡s✳ ❍❛ ◆♦✐✱ ❱✐❡t✲ ♥❛♠✿ ❯♥✐✈❡rs✐t② ♦❢ ❊❞✉❝❛t✐♦♥ P✉❜❧✐s❤✐♥❣ ❍♦✉s❡✳ ❚r❛♥❣✱ P✳ ❱✳ ✭✷✵✶✵✮✳ ❙t✉❞② ♦♥ ❡❢❢❡❝ts ♦❢ s❛❧✐♥✐t② ♦♥ ❣r♦✇t❤ ❛♥❞ ♦s♠♦t✐❝ r❡❣✉❧❛t✐♦♥ ♦❢ s♥❛❦❡✲s❦✐♥ ❣♦✉r❛♠② ✭❚r✐✲ ❝❤♦❣❛st❡r ♣❡❝t♦r❛❧✐s ❘❡❣❛♥✱ ✶✾✶✵✮✳ ✭❯♥♣✉❜❧✐s❤❡❞ ♠❛s✲ t❡r✬s t❤❡s✐s✮✳ ❈❛♥ ❚❤♦ ❯♥✐✈❡rs✐t②✱ ❈❛♥ ❚❤♦✱ ❱✐❡t♥❛♠✳ ❚r✉♦♥❣✱ P✳ ◗✳ ✭✷✵✵✸✮✳ ❲❛t❡r q✉❛❧✐t② ♠❛♥❛❣❡♠❡♥t ♦❢ ❢r❡s❤✲ ✇❛t❡r ❢✐s❤ ♣♦♥❞✳ ❍♦ ❈❤✐ ▼✐♥❤ ❈✐t②✱ ❱✐❡t♥❛♠✿ ❆❣r✐❝✉❧✲ t✉r❛❧ P✉❜❧✐s❤✐♥❣ ❍♦✉s❡✳ ❱♦✱ ❇✳ ❚✳ ❚✳ ✭✷✵✶✺✮✳ ❙t✉❞② ♦♥ s♦♠❡ ❜✐♦❧♦❣✐❝❛❧ ❝❤❛r❛❝t❡r✲ ✐st✐❝s ♦❢ ❆s✐❛♥ ❜✉♠❜❧❡❜❡❡ ❝❛t❢✐s❤ ✭Ps❡✉❞♦♠②st✉s s✐❛✲ ♠❡♥s✐s ❘❡❣❛♥✱ ✶✾✶✸✮✳ ❘❡♣♦rt ♦❢ s❝✐❡♥t✐❢✐❝ r❡s❡❛r❝❤✳ ◆♦♥❣ ▲❛♠ ❯♥✐✈❡rs✐t②✱ ❍♦ ❈❤✐ ▼✐♥❤ ❈✐t②✱ ❱✐❡t♥❛♠✳ ❲♦❦♦♠❛✱ ❑✳✱ ✫ ▼❛r✐♦❣❤❛❡✱ ■✳ ❊✳ ✭✶✾✾✻✮✳ ❙✉r✈✐✈❛❧ ♦❢ ❚✐❧❛♣✐❛ ❣✉✐♥❡❡♥s✐s ✉♥❞❡r ❝♦♥❞✐t✐♦♥s ♦❢ ❧♦✇ ❞✐ss♦❧✈❡❞ ♦①②❣❡♥ ❛♥❞ ❧♦✇ ♣❍✳ ■♥ P✉❧❧✐♥✱ ❘✳ ❙✳ ❱✳✱ ▲❛③❛r❞✱ ❏✳✱ ▲❡❣❡♥❞r❡✱ ▼✳✱ ❆♠♦♥ ❑♦t❤❧❛s✱ ❏✳ ❇✳✱ ✫ P❛✉❧②✱ ❉✳ ✭❊❞s✳✮✳ ■❈▲❆❘▼ ❈♦♥❢❡r❡♥❝ ✹✶✿ ❚❤❡ ❚❤✐r❞ ■♥t❡r♥❛✲ t✐♦♥❛❧ ❙②♠♣♦s✐✉♠ ♦♥ ❚✐❧❛♣✐❛ ✐♥ ❆q✉❛❝✉❧t✉r❡ ✭✹✹✷✲ ✹✹✽✮✳ ▼❛❦❛t✐ ❈✐t②✱ P❤✐❧✐♣♣✐♥❡s✳ ▲✐♥❞❡r✱ ❘✳ ❙✳ ✭✷✵✵✵❛✮✳ ❚❤❡ ❝❛t❢✐s❤❡s ♦❢ ❆s✐❛ ❢❛♠✐❧② ❜❛❣r✐✲ ❞❛❡✳ ✭P❛rt ♦♥❡✮✳ ❈❛t ❈❤❛t ✶✳ ❘❡tr✐❡✈❡❞ ❆♣r✐❧ ✶✱ ✷✵✶✾✱ ❢r♦♠ ❤tt♣s✿✴✴✇✇✇✳♣❧❛♥❡t❝❛t❢✐s❤✳❝♦♠✴s❤❛♥❡s✇♦r❧❞✴ s❤❛♥❡s✇♦r❧❞✳♣❤♣❄❛rt✐❝❧❡❴✐❞❂✶✽✺✳ ✇✇✇✳❥❛❞✳❤❝♠✉❛❢✳❡❞✉✳✈♥ ❚↕♣ ❝❤➼ ◆æ♥❣ ♥❣❤✐➺♣ ✈➔ P❤→t tr✐➸♥ ✶✽✭✺✮ ... ✤♦ ✈ỵ✐ ♣❍ ♠❡t❡r ❤✐➺✉ ❍❆◆◆❆ ✈➔ ỉ①② ❤á❛ t❛♥ ữủ ợ ữỡ r ỷ ỵ số t số t✛ ❧➺ ❝❤➳t ✤÷đ❝ ❝❤✉②➸♥ ✤ê✐ √ t❤➔♥❤ ❛r❝s✐♥ ✈➔ ữủ t ởt tố ợ tỷ P P t ỗ q✉✐ t✉②➳♥ t➼♥❤ ❝õ❛ t✛ ❧➺ ❝❤➳t ✭✤÷đ❝ ❝❤✉②➸♥... ❜è ✈➲ ✤➦❝ ✤✐➸♠ s✐♥❤ ❤å❝ ❝õ❛ ❧♦➔✐ ❝→ ♥➔② ❝á♥ r➜t ❤↕♥ ❝❤➳✳ ◆❣❤✐➯♥ ❝ù✉ ✈➲ ❦❤↔ ♥➠♥❣ ❝❤à✉ ✤ü♥❣ ởt số tố ổ trữớ ữợ t ✈➔ æ①② ❤á❛ t❛♥✮ ❝õ❛ ❝→ ❝❤èt ❜æ♥❣ ð ❝→❝ ❣✐❛✐ ✤♦↕♥ ♣❤ỉ✐✱ ❝→ ♠ỵ✐ ♥ð ✈➔ ❝→ ✶✵ ♥❣➔②... ❣✐í t❤➼ ♥❣❤✐➺♠✳ ❚✛ ❧➺ ♣❤ỉ✐ ❝❤➳t t➼❝❤ ❧ơ② ð ✷✹ ❣✐í ð ✷✶ ✈➔ ✷✷0 ❈ ❧➔ ❦❤→❝ ❜✐➺t ❦❤ỉ♥❣ õ ỵ tố P > ữ t õ ỵ tố P < s ợ t t t Pữỡ tr ỗ q t t t ổ t ✭②✮ t❤❡♦ ♥❤✐➺t ✤ë t❤➜♣ ✭①✮ ❧➔ ② ❂ ✲ ✼✹✱✹✶✶①