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✣❸■ ❍➴❈ ❚❍⑩■ ◆●❯❨➊◆ ❚❘×❮◆● ✣❸■ ❍➴❈ ❑❍❖❆ ❍➴❈ ✖✖✖✖✖✖✖✖✖✖✖✖✖✖✖✖✖ ◆●❯❨➍◆ ❚❍➚ ❑❍❯❨➊◆ ❇⑨■ ❚❖⑩◆ ❙❚■❈❑✲❙▲■P ❱⑨ ▼❐❚ ❙➮ P❍×❒◆● P❍⑩P ❚➐▼ ◆●❍■➏▼ ●❺◆ ✣Ó◆● ▲❯❾◆ ❱❿◆ ❚❍❸❈ ❙➒ ❚❖⑩◆ ❍➴❈ ❚❤→✐ ◆❣✉②➯♥ ✲ ◆➠♠ ✷✵✶✺ download by : skknchat@gmail.com ✣❸■ ❍➴❈ ❚❍⑩■ ◆●❯❨➊◆ ❚❘×❮◆● ✣❸■ ❍➴❈ ❑❍❖❆ ❍➴❈ ✖✖✖✖✖✖✖✖✖✖✖✖✖✖✖✖✖ ◆●❯❨➍◆ ❚❍➚ ❑❍❯❨➊◆ ❇⑨■ ❚❖⑩◆ ❙❚■❈❑✲❙▲■P ❱⑨ ▼❐❚ ❙➮ P❍×❒◆● P❍⑩P ❚➐▼ ◆●❍■➏▼ ●❺◆ ✣Ĩ◆● ❈❤✉②➯♥ ♥❣➔♥❤✿ ❚❖⑩◆ Ù◆● ❉Ư◆● ▼➣ sè✿ ✻✵✳✹✻✳✵✶✳✶✷ ▲❯❾◆ ❱❿◆ ❚❍❸❈ ❙➒ ❚❖⑩◆ ❍➴❈ ◆❣÷í✐ ữợ ễ ✲ ◆➠♠ ✷✵✶✺ download by : skknchat@gmail.com ✐ ❳→❝ ♥❤➟♥ trữ ổ ữớ ữợ ❞➝♥ ❦❤♦❛ ❤å❝ ❚❙✳ ❱ô ❱✐♥❤ ◗✉❛♥❣ download by : skknchat@gmail.com ✐✐ ▲í✐ ❝↔♠ ì♥ ✣➸ ❤♦➔♥ t❤➔♥❤ ✤÷đ❝ ❧✉➟♥ ✈➠♥ ♠ët ❝→❝❤ ❤♦➔♥ ❝❤➾♥❤✱ tỉ✐ ❧✉ỉ♥ ♥❤➟♥ ✤÷đ❝ sü ữợ ú ù t t P ụ ❱✐♥❤ ◗✉❛♥❣ ✭❚r÷í♥❣ ✣↕✐ ❤å❝ ❑❤♦❛ ❍å❝✮✳ ❚ỉ✐ ①✐♥ ❝❤➙♥ t❤➔♥❤ ❜➔② tä ❧á♥❣ ❜✐➳t ì♥ s➙✉ s➢❝ ✤➳♥ t❤➛② ✈➔ ①✐♥ ❣û✐ ❧í✐ tr✐ ➙♥ ♥❤➜t ❝õ❛ tỉ✐ ✤è✐ ✈ỵ✐ ♥❤ú♥❣ ✤✐➲✉ t❤➛② ✤➣ ❞➔♥❤ ❝❤♦ tỉ✐✳ ❚ỉ✐ ①✐♥ ❝❤➙♥ t❤➔♥❤ ❝↔♠ ì♥ ❜❛♥ ❧➣♥❤ ✤↕♦ ♣❤á♥❣ s❛✉ ✣↕✐ qỵ t ổ ợ ✭✷✵✶✹✲ ✷✵✶✻✮ ❚r÷í♥❣ ✣↕✐ ❤å❝ ❑❤♦❛ ❍å❝ ✲ ✣↕✐ ❤å❝ ❚❤→✐ ◆❣✉②➯♥ ✤➣ t➟♥ t➻♥❤ tr✉②➲♥ ✤↕t ♥❤ú♥❣ ❦✐➳♥ t❤ù❝ qỵ ụ ữ t tổ t❤➔♥❤ ❦❤â❛ ❤å❝✳ ❚ỉ✐ ①✐♥ ❣û✐ ❧í✐ ❝↔♠ ì♥ ❝❤➙♥ t t tợ ỳ ữớ ❧✉ỉ♥ ✤ë♥❣ ✈✐➯♥✱ ❤é trđ ✈➔ t↕♦ ♠å✐ ✤✐➲✉ ❦✐➺♥ ❝❤♦ tæ✐ tr♦♥❣ s✉èt q✉→ tr➻♥❤ ❤å❝ t➟♣ ✈➔ t❤ü❝ ❤✐➺♥ ❧✉➟♥ ✈➠♥✳ ❳✐♥ tr➙♥ trå♥❣ ❝↔♠ ì♥✦ ❚❤→✐ ♥❣✉②➯♥✱ t❤→♥❣ ✶✷ ♥➠♠ ✷✵✶✺ ◆❣÷í✐ ✈✐➳t ❧✉➟♥ ✈➠♥ ◆❣✉②➵♥ ❚❤à ❑❤✉②➯♥ download by : skknchat@gmail.com ✐✐✐ ▼ư❝ ❧ư❝ ▲í✐ ❝↔♠ ì♥ ✐✐ ▼ö❝ ❧ö❝ ✐✐✐ ▼ð ✤➛✉ ✶ ▼ët sè ❦➼ ❤✐➺✉ ✈✐➳t t➢t ✹ ✶ ❑■➌◆ ❚❍Ù❈ ❈❍❯❽◆ ❇➚ ✺ ✶✳✶ ✶✳✷ ❑❤æ♥❣ ❣✐❛♥ ❙♦❜♦❧❡✈✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺ ✶✳✶✳✶ ¯ ❑❤æ♥❣ ❣✐❛♥ C k Ω ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺ ✶✳✶✳✷ ❑❤æ♥❣ ❣✐❛♥ Lp (Ω) ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻ ✶✳✶✳✸ ❑❤æ♥❣ ❣✐❛♥ ❲ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻ ✶✳✶✳✹ ❑❤æ♥❣ ❣✐❛♥ H01 (Ω) ✈➔ ❦❤→✐ ♥✐➺♠ ✈➳t ❝õ❛ ❤➔♠ ✳ ✳ ✼ ✶✳✶✳✺ ❈æ♥❣ t❤ù❝ ●r❡❡♥✱ ❜➜t ✤➥♥❣ t❤ù❝ P♦✐♥❝❛r❡ ✳ ✳ ✳ ✳ ✾ ✶✳✶✳✻ ❑❤ỉ♥❣ ❣✐❛♥ ❙♦❜♦❧❡✈ ✈ỵ✐ ❝❤➾ sè ➙♠ H −1 (Ω) ✈➔ H − (∂Ω) ✶✵ 1,p (Ω) P❤÷ì♥❣ tr➻♥❤ ❊❧❧✐♣t✐❝ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶ ✶✳✷✳✶ ❑❤→✐ ♥✐➺♠ ♥❣❤✐➺♠ ②➳✉ ❝õ❛ ♣❤÷ì♥❣ tr➻♥❤ ✳ ✳ ✳ ✳ ✳ ✶✶ ✶✳✷✳✷ ✣à♥❤ ♥❣❤➽❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷ download by : skknchat@gmail.com ✐✈ ✶✳✷✳✸ ✶✳✸ ✶✳✹ ▼➺♥❤ ✤➲ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷ ❑✐➳♥ tự sỡ ỗ ỡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ữủ ỗ ợ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ữủ ỗ ứ ỵ ỡ sỹ tử ♣❤÷ì♥❣ ♣❤→♣ ❧➦♣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ỵ tt s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹ ✶✳✹✳✶ P❤÷ì♥❣ ữợ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹ ✶✳✹✳✷ ❇➔✐ t♦→♥ s❛✐ ♣❤➙♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺ ✶✳✹✳✸ ❑➳t ❧✉➟♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻ ✷ ❇➔✐ t♦→♥ st✐❝❦✲s❧✐♣ ✈➔ ♣❤÷ì♥❣ ♣❤→♣ t➻♠ ♥❣❤✐➺♠ ❞↕♥❣ t✐➺♠ ❝➟♥ ✶✼ ✷✳✶ ▼æ ❤➻♥❤ ❜➔✐ t♦→♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼ ✷✳✷ ▼ët sè ♣❤÷ì♥❣ ♣❤→♣ t➻♠ ♥❣❤✐➺♠ ❞↕♥❣ ❦❤❛✐ tr✐➸♥ ✳ ✳ ✳ ✳ ✶✾ ✷✳✸ P❤÷ì♥❣ ♣❤→♣ ❙❋❇■▼ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ❑➳t ❧✉➟♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✷✳✸✳✶ ✸ P❤÷ì♥❣ ♣❤→♣ ❧➦♣ ❣✐↔✐ ❜➔✐ t♦→♥ st✐❝❦ ✕ s❧✐♣ tê♥❣ q✉→t ỡ s ỵ tt ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✸✳✶✳✶ ❈ì sð ♣❤÷ì♥❣ ♣❤→♣ ❝❤✐❛ ♠✐➲♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✸✳✶✳✷ ỡ ỗ t tỷ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✸✳✷ ỡ ỗ t ủ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ✸✳✸ ▼ët sè ❦➳t q✉↔ t❤ü❝ ♥❣❤✐➺♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ❑➳t ❧✉➟♥ download by : skknchat@gmail.com ✸✼ ✈ ❚➔✐ ❧✐➺✉ t❤❛♠ ❦❤↔♦ ✸✽ P❍❺◆ P❍Ö ▲Ö❈ ✹✵ download by : skknchat@gmail.com ✶ ▼ð ✤➛✉ ❇➔✐ t♦→♥ ❙t✐❝❦✲❙❧✐♣ ❧➔ ♠ët ❞↕♥❣ ❜➔✐ t♦→♥ ♠➝✉ ♠ü❝ ❝õ❛ ♣❤÷ì♥❣ tr➻♥❤ s♦♥❣ ✤✐➲✉ ❤á❛ ✈ỵ✐ ✈➳ ♣❤↔✐ t❤✉➛♥ ♥❤➜t✳ ✣✐➸♠ ✤➦❝ ❜✐➺t ❝õ❛ ❜➔✐ t♦→♥ ♥➔② ❧➔ ❤➺ ✤✐➲✉ ❦✐➺♥ ❜✐➯♥ ❝õ❛ ❜➔✐ t♦→♥ ❧➔ ❞↕♥❣ ❦➻ ❞à tù❝ ❧➔ tr➯♥ ♠ët ✤♦↕♥ ❜✐➯♥ trì♥ ♥↔② s✐♥❤ ❤✐➺♥ t÷đ♥❣ t❤✐➳✉ ✤✐➲✉ ❦✐➺♥ ố ợ ỗ tớ t s✐♥❤ ♥❤ú♥❣ ✤✐➸♠ ❦➻ ❞à ❧➔ ❝→❝ ✤✐➸♠ ❣✐❛♦ ❣✐ú❛ ✤✐➲✉ ❦✐➺♥ ❤➔♠ ✈➔ ✤✐➲✉ ❦✐➺♥ ✤↕♦ ❤➔♠✳ ✣➙② ❧➔ ♠ët ♠æ ❤➻♥❤ ♠æ t↔ sü ❞❛♦ ✤ë♥❣ ❝õ❛ ❝→❝ t ỗ õ q ❜✐➯♥ ❞↕♥❣ ♥❣➔♠✱ ❣è✐ tü❛ ✈➔ ❜✐➯♥ tü ❞♦ ❤é♥ ❤đ♣✳ ✣➙② ❧➔ ♠ët ♠ỉ ❤➻♥❤ ❜➔✐ t♦→♥ ✤÷đ❝ ❝→❝ t→❝ ❣✐↔ tr➯♥ t❤➳ ❣✐ỵ✐ r➜t q✉❛♥ t➙♠✱ ❝â t➼♥❤ ù♥❣ ❞ö♥❣ ❝→♦✳ ❱➻ t➼♥❤ ❝❤➜t ❦➻ ❞à ♥➯♥ ✈✐➺❝ t➻♠ ♥❣❤✐➺♠ ❝õ❛ ❜➔✐ t♦→♥ ❦❤æ♥❣ t❤➸ t❤ü❝ ❤✐➺♥ ❜➡♥❣ ❝→❝ ♣❤÷ì♥❣ ♣❤→♣ t❤ỉ♥❣ t❤÷í♥❣✳ ❍✐➺♥ ♥❛② ❝→❝ t→❝ ❣✐↔ tr t ợ tữớ t t t ữợ s t t tứ ✤✐➸♠ ❦➻ ❞à ❧➔ ✤✐➸♠ ❣✐❛♦ ❣✐ú❛ ❝→❝ ❧♦↕✐ ✤✐➲♥ ❦✐➺♥ ❜✐➯♥✱ ♥❣÷í✐ t❛ t➻♠ ❝→❝❤ ①➙② ❞ü♥❣ ❝→❝ ❤➺ r ữợ tồ ỹ tọ ❦✐➺♥ ❝õ❛ ❜➔✐ t♦→♥ ✈➔ tø ✤â ♥❣❤✐➺♠ ①➜♣ ①➾ ❝õ❛ ❜➔✐ t♦→♥ ✤÷đ❝ ①→❝ ✤à♥❤ ❜➡♥❣ ❝→❝ ❝ỉ♥❣ t❤ù❝ ❦❤❛✐ tr✐➸♥ ❞↕♥❣ ❝❤✉é✐ ❤➔♠ t❤æ♥❣ q✉❛ ❝→❝ ❤➺ ❤➔♠ r✐➯♥❣✳ ❚ø ✤â ❜➔✐ t♦→♥ ✤÷❛ ✈➲ ✈✐➺❝ ①→❝ ✤à♥❤ ❝→❝ ❤➺ sè ❝õ❛ ❦❤❛✐ tr✐➸♥ ❜➡♥❣ ❝→❝ ♣❤÷ì♥❣ ♣❤→♣ số ỷ ỵ tt t tỷ ỹ sỡ ỗ ❝→❝ ❣✐→ trà t❤✐➳✉ tr➯♥ ❜✐➯♥ ✤➸ ❝❤✉②➸♥ ❜➔✐ t♦→♥ ❝â ❝❤ù❛ ❝→❝ ✤✐➸♠ ❦➻ ❞à ✈➲ ❝→❝ ❜➔✐ t♦→♥ ổ ự t ủ ợ ữỡ download by : skknchat@gmail.com ✷ ♣❤→♣ ♣❤➙♥ r➣ ♣❤÷ì♥❣ tr➻♥❤ ❝➜♣ ❜è♥ ✈➲ ❤❛✐ ♣❤÷ì♥❣ tr➻♥❤ ❝➜♣ ❤❛✐✳ ❚ø ✤â →♣ ❞ư♥❣ ❝→❝ ♣❤÷ì♥❣ ♣❤→♣ s❛✐ ♣❤➙♥ ✤➸ ❣✐↔✐ q✉②➳t ❝→❝ ❜➔✐ t♦→♥ ❝♦♥ q✉❛ ✤â ①➙② ❞ü♥❣ ♥❣❤✐➺♠ ❝õ❛ ❜➔✐ t♦→♥ ❣è❝ ❜❛♥ ✤➛✉✳ ❳✉➜t ♣❤→t tø ♣❤➙♥ t➼❝❤ ✤â✱ ♠ö❝ t✐➯✉ ♥❣❤✐➯♥ ❝ù✉ ❝❤➼♥❤ ❝õ❛ ❧✉➟♥ ✈➠♥ ❧➔ t➻♠ ❤✐➸✉ ✈➲ ♠æ ❤➻♥❤ ❜➔✐ t♦→♥ ❙t✐❝❦✲❙❧✐♣✱ ♥❣❤✐➯♥ ❝ù✉ ❝ì sð ❝õ❛ ♣❤÷ì♥❣ ♣❤→♣ ❦❤❛✐ tr✐➸♥ t➻♠ ♥❣❤✐➺♠ ①➜♣ t t ỗ tớ ự ỡ s ỵ tt t tỷ ũ ữỡ ♣❤➙♥ r➣ ❝❤✉②➸♥ ❜➔✐ t♦→♥ ❙t✐❝❦✲❙❧✐♣ ✈➲ ❝→❝ ❜➔✐ t♦→♥ ❡❧❧✐♣t✐❝ ❝➜♣ ❤❛✐✱ sû ❞ư♥❣ ♣❤÷ì♥❣ ♣❤→♣ s❛✐ ♣❤➙♥ ✤➸ ①→❝ ✤à♥❤ ♥❣❤✐➺♠ ❝õ❛ ❜➔✐ t♦→♥ ❣è❝✳ ❙♦ s→♥❤ ❦➳t q✉↔ t❤ü❝ ♥❣❤✐➺♠ ❝õ❛ ❝→❝ ♣❤÷ì♥❣ ♣❤→♣✳ ❈→❝ ❦➳t q✉↔ t❤ü❝ ♥❣❤✐➺♠ ✤÷đ❝ t❤ü❝ ❤✐➺♥ tr➯♥ ♠→② t➼♥❤ ✤✐➺♥ tû✳ ◆ë✐ ❞✉♥❣ ❝õ❛ ❜↔♥ ❧✉➟♥ ✈➠♥ ✤÷đ❝ tr➻♥❤ ❜➔② tr♦♥❣ ✸ ❝❤÷ì♥❣✳ ❈❤÷ì♥❣ ✶✿ ❚r➻♥❤ ❜➔② ♥❤ú♥❣ ❦✐➳♥ t❤ù❝ ❝ì sð ✈➲ ❝→❝ ❦❤ỉ♥❣ ❣✐❛♥ ❤➔♠✱ ❧➼ t❤✉②➳t ♣❤÷ì♥❣ tr➻♥❤ s ỏ ỵ tt t tỷ sỡ ỗ t tỷ sỹ tử tt s ổ ữợ ❝→❝ ♣❤÷ì♥❣ ♣❤→♣ s❛✐ ♣❤➙♥ ✤↕♦ ❤➔♠✱ ❤➺ ♣❤÷ì♥❣ tr➻♥❤ ữợ ữỡ r ổ t t ♣❤÷ì♥❣ ♣❤→♣ ❦❤❛✐ tr✐➸♥ t❤ỉ♥❣ q✉❛ ❝→❝ ❤➺ ❤➔♠ r✐➯♥❣✱ ♣❤÷ì♥❣ ♣❤→♣ ❧➦♣ t➻♠ ♥❣❤✐➺♠ ①➜♣ ①➾✳ ❈❤÷ì♥❣ ✸ ❚r➻♥❤ ❜➔② ♠ët sè ❦➳t q✉↔ t❤ü❝ ♥❣❤✐➺♠ ✤è✐ ✈ỵ✐ ❜➔✐ t t ữủ t ữợ sỹ ữợ t t ụ ①✐♥ ❜➔② tä ❧á♥❣ ❜✐➳t ì♥ ❝❤➙♥ t❤➔♥❤ ❝õ❛ ♠➻♥❤ ✤è✐ ✈ỵ✐ t❤➛②✳ ❊♠ ①✐♥ ❝❤➙♥ t❤➔♥❤ ❝↔♠ ì♥ ❝→❝ t❤➛②✱ ❝æ ❣✐→♦ ✣↕✐ ❤å❝ ❑❤♦❛ ❤å❝ ✲ ✣↕✐ ❤å❝ ❚❤→✐ ♥❣✉②➯♥ ✤➣ t❤❛♠ ❣✐❛ ❣✐↔♥❣ ❞↕②✱ ❣✐ó♣ ✤ï ❡♠ tr♦♥❣ s✉èt q✉→ tr➻♥❤ ❤å❝ t➟♣ ♥➙♥❣ ❝❛♦ tr➻♥❤ ✤ë ❦✐➳♥ t❤ù❝✳ ❚✉② ♥❤✐➯♥ ✈➻ ✤✐➲✉ ❦✐➺♥ t❤í✐ ❣✐❛♥ ✈➔ ❦❤↔ ♥➠♥❣ ❝â ❤↕♥ ♥➯♥ ❧✉➟♥ ✈➠♥ ❦❤æ♥❣ t❤➸ tr→♥❤ ❦❤ä✐ ♥❤ú♥❣ t❤✐➳✉ sât✳ ❊♠ ❦➼♥❤ ♠♦♥❣ ❝→❝ t❤➛② ❝æ õ õ ỵ download by : skknchat@gmail.com ✸ ✤➸ ❧✉➟♥ ✈➠♥ ✤÷đ❝ ❤♦➔♥ t❤✐➺♥ ❤ì♥✳ download by : skknchat@gmail.com ✸✾ ❬✹❪ ❉❛♥❣ ◗✉❛♥❣ ❆✱ ❚r✉♦♥❣ ❍❛ ❍❛✐✱ ❱✉ ❱✐♥❤ ◗✉❛♥❣✱ ■♥t❡r❛t✐✈❡ ▼❡t❤♦❞ ❢♦r ❛ ❇✐❤❛r♠♦♥✐❝ Pr♦❜❧❡♠ ✇✐t❤ ❈r❛❝❦ ❙✐♥❣❣✉❧❛r✐t✐❡s✱ ❆♣♣❧✐❡❞ ▼❛t❤✲ ❡♠❛t✐❝❛❧ ❙❝✐❡♥❝❡s✱ ❱♦❧✳ ✻✱ ✷✵✶✷✱ ♥♦✳ ✻✷✱ ✸✵✾✺✲✸✵✶✽✳ ❬✺❪ ❋✉♥❛r♦ ❉✳✱ ◗✉❛rt❡r♦♥✐ ❆✳✱ ❩❛♥♦❧❧✐ P✳ ✭✶✾✾✽✮✱ ✧ ❆♥ ✐t❡r❛t✐✈❡ ♣r♦❝❡✲ ❞✉r❡ ✇✐t❤ ✐♥t❡r❢❛❝❡ r❡❧❛①❛t✐♦♥ ❢♦r ❞♦♠❛✐♥ ❞❡❝♦♠♣♦s✐t✐♦♥ ♠❡t❤♦❞✧✱ ❙■❆▼ ❏✳ ◆✉♠❜❡r✳ ❆♥❛❧✳ ✷✺✭✻✮✱ ♣♣✳ ✶✷✶✸ ✲ ✶✷✸✻✳ ❬✻❪ ▼✳ ❊❧❧✐♦t✐s✱ ●✳ ●❡♦r❣✐♦✉ ❛♥❞ ❈✳ ❳❡♥♦♣❤♦♥t♦s✱ ❙♦❧✉t✐♦♥ ♦❢ t❤❡ ♣❧❛♥❛r ◆❡✇t♦♥✐❛♥ st✐❝❦✲s❧✐♣ ♣r♦❜❧❡♠ ✇✐t❤ t❤❡ s✐♥❣✉❧❛r ❢✉♥❝t✐♦♥ ❜♦✉♥❞❛r② ✐♥t❡❣r❛❧ ♠❡t❤♦❞✱ ✐♥t✳ ❏✳ ◆✉♠❡r✳ ▼❡t❤✳ ❋❧✉✐❞s ✷✵✵✺❀ ✹✽✿✶✵✵✶✲✶✵✷✶✳ ❬✼❪ ▼❛r❝❤✉❦ ●✳■✳ ✭✶✾✽✷✮✱ ▼❡t❤♦❞s ♦❢ ◆✉♠❡r✐❝❛❧ ▼❛t❤❡♠❛t✐❝s✱ ❙♣r✐♥❣❡r✱ ◆❡✇ ❨♦r❦✳ ❬✽❪ ❙❛♠❛rs❦✐❥ ❆✳ ❛♥❞ ◆✐❦♦❧❛❡✈ ❊✳✱ ◆✉♠❡r✐❝❛❧ ♠❡t❤♦❞s ❢♦r ●r✐❞ ❊q✉❛✲ t✐♦♥s✱ ✈♦❧✳ ✷✱ ❇✐r❦❤❛✉s❡r✱ ❜❛s❡❧✱ ✶✾✽✾✳ download by : skknchat@gmail.com ✹✵ P❍❺◆ P❍Ư ▲Ư❈ ✭❈→❝ ❝❤÷ì♥❣ tr ỗ tr ổ trữớ t ữỡ tr tr❛ ❜➔✐ t♦→♥ ❙t✐❝❦✲❧✐♣ ✪ ❈❤✉♦♥❣ tr✐♥❤ ❣✐❛✐ ❜❛✐ t♦→♥ st✐❝❦✲s❧✐♣ ✪ ❚r✉♦♥❣ ❤♦♣ ❦❤♦♥❣ ❜✐❡t tr✉♦❝ ♥❣❤✐❡♠ ❞✉♥❣ ✪ ♣❤✐ ❧❛ ❤❛♠ ✈❡ ♣❤❛✐ ✪ ❜✶✱❜✷✱❜✸✱❜✹✿ ❧❛ ❝❛❝ ❣✐❛ tr✐ tr❡♥ ❜✐❡♥ tr❛✐✱♣❤❛✐✱❞✉♦✐✱tr❡♥ ✪ ◆❣❛② ❧❛♣ ✷✺✴✶✶✴✷✵✶✺ ✪ ❉❛ ❦✐❡♠ tr❛ ❝❤➼♥❤ ①❛❝ ❝❧❡❛r ❛❧❧ ❝❧❝ t❡t❛❂✵✳✺❀✪t❤❛♠ s♦ ❧❛♣ ❝❤✐❛ ♠✐❡♥ t♦❂✵✳✾✺❀✪t❤❛♠ s♦ ❧❛♣ s♦♥❣ ❞✐❡✉ ❤♦❛ ❛❂✶❀ ❡✶❂✵✳✺❀ ❜❂✶❀ ❦✶❂✶❀❦✷❂✶❀ ❝❝❂✵❀ ❝♦✉♥t❂✲✶❀ ❡♣①✐❧♦♥❂✶✵ ✂✭✲✹✮❀s❛✐s♦❂✶✵❀ ♥❂✻❀ ◆❂✷✂ ♥❀ download by : skknchat@gmail.com ✹✶ ▼❂◆❀ ♣✶❂✶❀♣✷❂▼✰✶❀♣✸❂✷✯▼✰✶❀♣✹❂✸✯▼✰✶❀♣✺❂✹✯▼✰✶❀♣✻❂✺✯▼✰✶❀q✶❂✶❀q✷❂◆✰✶❀q ❢♦r ❥❂✵✿◆❀ ❝s✐✶✭❥✰✶✮❂✵❀✪❦❤♦✐ t❛♦ ❣✐❛ tr✐ ❧❛♣ ❝❤✐❛ ♠✐❡♥ ❡t❛✶✭❥✰✶✮❂✵❀ ❡♥❞❀ ❢♦r ✐❂✵✿▼❀ ♣❤✐✶✭✐✰✶✮❂✵❀ ✪❑❤♦✐ t❛♦ ❝❤♦ ❞❛② ❧❛♣ s♦♥❣ ❞✐❡✉ ❤♦❛ ♣❤✐✸✭✐✰✶✮❂✵❀ ❡♥❞❀ ❤✶✶❂❡✶✴▼❀❤✷✶❂✭❛✲❡✶✮✴▼❀ ❤✶✷❂❜✴◆❀❤✷✷❂❜✴◆❀ ❢♦r ✐❂✵✿✷✯▼❀ ❢♦r ❥❂✵✿◆❀ ✉❧✉✉✭✐✰✶✱❥✰✶✮❂✵❀ ❡♥❞❀ ❡♥❞❀ t❤♦✐❣✐❛♥❂❝♣✉t✐♠❡❀ ✇❤✐❧❡ ❛♥❞✭❝♦✉♥t❁✹✵✵✱s❛✐s♦❃❡♣①✐❧♦♥✮❀ ❝♦✉♥t❂❝♦✉♥t✰✶❀ ✪❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂●✐❛✐ ♠✐❡♥ ✷❂❂❂❂❂❂❂❂❂❂❂❂❂ ✪ ●✐❛✐ ❜❛✐ t♦❛♥ ✈♦✐ ✈✷ ❧✶❂❛✲❡✶❀❧✷❂❜❀▼✷❂▼❀◆✷❂◆❀♥✷❂♥❀ ✪ ●✐❛ tr✐ ✈❡ ♣❤❛✐ ✈➔ ♥❣❤✐❡♠ ❞✉♥❣ ❢♦r ✐❂✵✿▼✷❀ download by : skknchat@gmail.com ✹✷ ❢♦r ❥❂✵✿◆✷❀ ♣❤✐✭✐✰✶✱❥✰✶✮❂✵❀✪ ❍❛♠ ✈❡ ♣❤❛✐ ❡♥❞❀ ❡♥❞❀ ✪ ❉✐❡✉ ❦✐❡♥ tr❡♥ ❝❛♥❤ tr❛✐ ✈❛ ♣❤❛✐ ❢♦r ❥❂✵✿◆✷❀ ❜✶✭❥✰✶✮❂❝s✐✶✭❥✰✶✮❀ ❜✷✭❥✰✶✮❂✵❀ ❡♥❞❀ ✪ ❉✐❡✉ ❦✐❡♥ tr❡♥ ❝❛♥❤ ❞✉♦✐ ✈❛ tr❡♥ ❢♦r ✐❂✵✿▼✷❀ ❜✸✭✐✰✶✮❂✵❀ ❜✹✭✐✰✶✮❂✵❀ ❡♥❞❀ ✈✷❂✉✶✶✵✵✭♣❤✐✱❜✶✱❜✷✱❜✸✱❜✹✱❧✶✱❧✷✱❦✶✱❦✷✱❝❝✱▼✷✱◆✷✱♥✷✱♣✷✱♣✸✱q✶✱q✷✮❀ ✪ ●✐❛✐ ❜❛✐ t♦❛♥ ✈♦✐ ✉✷ ✪ ●✐❛ tr✐ ✈❡ ♣❤❛✐ ❢♦r ✐❂✵✿▼✷❀ ❢♦r ❥❂✵✿◆✷❀ ♣❤✐✭✐✰✶✱❥✰✶✮❂✲✈✷✭♣✷✰✐✱q✶✰❥✮❀ ✪ ❍❛♠ ✈❡ ♣❤❛✐ ❡♥❞❀ ❡♥❞❀ ✪ ❉✐❡✉ ❦✐❡♥ tr❡♥ ❝❛♥❤ tr❛✐ ✈❛ ♣❤❛✐ ❢♦r ❥❂✵✿◆✷❀ download by : skknchat@gmail.com ✹✸ ❜✶✭❥✰✶✮❂❡t❛✶✭❥✰✶✮❀ ❜✷✭❥✰✶✮❂✵❀ ❡♥❞❀ ✪ ❉✐❡✉ ❦✐❡♥ tr❡♥ ❝❛♥❤ ❞✉♦✐ ✈❛ tr❡♥ ❢♦r ✐❂✵✿▼✷❀ ❜✸✭✐✰✶✮❂✲✶❀ ❜✹✭✐✰✶✮❂✵❀ ❡♥❞❀ ✉✷❂✉✶✶✵✵✭♣❤✐✱❜✶✱❜✷✱❜✸✱❜✹✱❧✶✱❧✷✱✶✱✶✱✵✱▼✷✱◆✷✱♥✷✱♣✷✱♣✸✱q✶✱q✷✮❀ ✪ ●✐❛✐ ❜❛✐ t♦❛♥ ✈♦✐ ✈✶ ❧✶❂❡✶❀❧✷❂❜❀▼✶❂▼❀◆✶❂◆❀♥✶❂♥❀ ❤✶✶❂❧✶✴▼✶❀ ❤✶✷❂❧✷✴◆✶❀ ✪ ●✐❛ tr✐ ✈❡ ♣❤❛✐ ❢♦r ✐❂✵✿▼✶❀ ❢♦r ❥❂✵✿◆✶❀ ♣❤✐✭✐✰✶✱❥✰✶✮❂✵❀ ✪ ❍❛♠ ✈❡ ♣❤❛✐ ❡♥❞❀ ❡♥❞❀ ✪ ❉✐❡✉ ❦✐❡♥ tr❡♥ ❝❛♥❤ tr❛✐ ✈❛ ♣❤❛✐ ❢♦r ❥❂✵✿◆✶❀ ❜✶✭❥✰✶✮❂♣❤✐✶✭❥✰✶✮❀ ❜✷✭❥✰✶✮❂✈✷✭♣✷✱q✶✰❥✮❀ ❡♥❞❀ ✪ ❉✐❡✉ ❦✐❡♥ tr❡♥ ❝❛♥❤ ❞✉♦✐ ✈❛ tr❡♥ download by : skknchat@gmail.com ✹✹ ❢♦r ✐❂✵✿▼✶❀ ❜✸✭✐✰✶✮❂✵❀ ❜✹✭✐✰✶✮❂♣❤✐✸✭✐✰✶✮❀ ❡♥❞❀ ✈✶❂✉✵✵✵✵✭♣❤✐✱❜✶✱❜✷✱❜✸✱❜✹✱❧✶✱❧✷✱❦✶✱❦✷✱❝❝✱▼✶✱◆✶✱♥✶✱♣✶✱♣✷✱q✶✱q✷✮❀ ✪ ●✐❛✐ ❜❛✐ t♦❛♥ ✈♦✐ ✉✶ ✪ ●✐❛ tr✐ ✈❡ ♣❤❛✐ ❢♦r ✐❂✵✿▼✶❀ ❢♦r ❥❂✵✿◆✶❀ ♣❤✐✭✐✰✶✱❥✰✶✮❂✲✈✶✭♣✶✰✐✱q✶✰❥✮❀ ✪ ❍❛♠ ✈❡ ♣❤❛✐ ❡♥❞❀ ❡♥❞❀ ✪ ❉✐❡✉ ❦✐❡♥ tr❡♥ ❝❛♥❤ tr❛✐ ✈❛ ♣❤❛✐ ❢♦r ❥❂✵✿◆✶❀ ①✷❂✵✰❥✯❤✶✷❀ ❜✶✭❥✰✶✮❂✶✴✷✯①✷✯✭✸✲①✷✂ ✷✮✲✶❀ ❜✷✭❥✰✶✮❂✉✷✭♣✷✱q✶✰❥✮❀ ❡♥❞❀ ✪ ❉✐❡✉ ❦✐❡♥ tr❡♥ ❝❛♥❤ ❞✉♦✐ ✈❛ tr❡♥ ❢♦r ✐❂✵✿▼✶❀ ❜✸✭✐✰✶✮❂✲✶❀ ❜✹✭✐✰✶✮❂✵❀ ❡♥❞❀ ✉✶❂✉✵✵✵✵✭♣❤✐✱❜✶✱❜✷✱❜✸✱❜✹✱❧✶✱❧✷✱✶✱✶✱✵✱▼✶✱◆✶✱♥✶✱♣✶✱♣✷✱q✶✱q✷✮❀ ✪❂❂❂❂❂❂❂❂❂❂❂❂❂❂ download by : skknchat@gmail.com ✹✺ ✪ ❍✐❡✉ ❝❤✐♥❤ ❣✐❛ tr✐ ❝s✐✶ tr❡♥ ❜✐❡♥ ❝❤✐❛ ✷ ♠✐❡♥ ✶✲✷ ❢♦r ❥❂✵✿◆✶❀ ♣❤✵✶✭❥✰✶✮❂✵❀ ❡♥❞❀ ❞✈✶❂❞①✭q✶✱q✷✱♣✷✱♣❤✵✶✱✈✶✱❤✶✶✱❤✶✷✱❦✶✱❦✷✱▼✶✱✲✶✮❀ ❝s✐✶❂t❡t❛✯❝s✐✶✲✭✶✲t❡t❛✮✯❞✈✶❀ ✪ ❍✐❡✉ ❝❤✐♥❤ ❣✐❛ tr✐ ❡t❛✶ tr❡♥ ❜✐❡♥ ❝❤✐❛ ✷ ♠✐❡♥ ✶✲✷ ❢♦r ❥❂✵✿◆✶❀ ♣❤✵✶✭❥✰✶✮❂✲✈✶✭♣✷✱q✶✰❥✮❀ ❡♥❞❀ ❞✉✶❂❞①✭q✶✱q✷✱♣✷✱♣❤✵✶✱✉✶✱❤✶✶✱❤✶✷✱✶✱✶✱▼✶✱✲✶✮❀ ❡t❛✶❂t❡t❛✯❡t❛✶✲✭✶✲t❡t❛✮✯❞✉✶❀ ✪❍✐❡✉ ❝❤✐♥❤ ❣✐❛ tr✐ ♣❤✐✶ ❢♦r ❥❂✵✿◆✷❀ ①✷❂✵✰❥✯❤✶✷❀ ❞❤✷✷✭❥✰✶✮❂✵❀ ♣❤✵✵✸✭❥✰✶✮❂✲✈✶✭♣✶✱q✶✰❥✮❀ ❡♥❞❀ ❞✉✶❂❞①✭q✶✱q✷✱♣✶✱♣❤✵✵✸✱✉✶✱❤✶✶✱❤✶✷✱✶✱✶✱◆✱✶✮❀ ♣❤✐✶❂♣❤✐✶✰t♦✯✭❞✉✶✲❞❤✷✷✮❀ ✪❍✐❡✉ ❝❤✐♥❤ ❣✐❛ tr✐ ♣❤✐✸ ❢♦r ✐❂✵✿▼✶❀ ♣❤✵✵✹✸✭✐✰✶✮❂✲✈✶✭♣✶✰✐✱q✷✮❀ ❡♥❞❀ ❞✉✸❂❞②✭♣✶✱♣✷✱q✷✱♣❤✵✵✹✸✱✉✶✱❤✶✶✱❤✶✷✱✶✱✶✱▼✱✲✶✮❀ ♣❤✐✸❂♣❤✐✸✰t♦✯❞✉✸❀ ❢♦r ✐❂✵✿▼❀ download by : skknchat@gmail.com ✹✻ ❢♦r ❥❂✵✿◆❀ ✉①①✭♣✶✰✐✱q✶✰❥✮❂✉✶✭♣✶✰✐✱q✶✰❥✮❀✪◆❣❤✐❡♠ ①❛♣ ①✐ tr❡♥ ♠✐❡♥ ✶ ✉①①✭♣✷✰✐✱q✶✰❥✮❂✉✷✭♣✷✰✐✱q✶✰❥✮❀✪◆❣❤✐❡♠ ①❛♣ ①✐ tr❡♥ ♠✐❡♥ ✷ ❡♥❞❀ ❡♥❞❀ s❛✐s♦❂❝❤✉❛♥✭✉❧✉✉✲✉①①✮ ✉❧✉✉❂✉①①❀ ❡♥❞❀ ✪❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂ t❤♦✐❣✐❛♥❂❝♣✉t✐♠❡✲t❤♦✐❣✐❛♥ ❝♦✉♥t ✪❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂ ❱❡ ❞♦ t❤✐ tr❡♥ t♦❛♥ ♠✐❡♥ ❢♦r ✐❂✵✿▼❀ ①✶❂✵✰✐✯❤✶✶❀ ①①✭♣✶✰✐✮❂①✶❀ ①✶❂❡✶✰✐✯❤✷✶❀ ①①✭♣✷✰✐✮❂①✶❀ ❡♥❞❀ ❢♦r ❥❂✵✿◆❀ ①✷❂✵✰❥✯❤✶✷❀ ②②✭q✶✰❥✮❂①✷❀ ❡♥❞❀ [X, Y ]❂♠❡s❤❣r✐❞✭①①✱②②✮❀ ♠❡s❤✭❳✱❨✱✉①①✬✮❀ download by : skknchat@gmail.com ✹✼ t✐t❧❡✭✬❉❡❢❧❡❝t✐♦♥ s✉r❢❛❝❡s✬✮ ①❧❛❜❡❧✭✬①✬✮ ②❧❛❜❡❧✭✬②✬✮ ✷✳ ❈❤÷ì♥❣ tr➻♥❤ ❙t✐❝❦❴❧✐♣ tê♥❣ q✉→t ✪ ❈❤✉♦♥❣ tr✐♥❤ ❣✐❛✐ ❜❛✐ t♦→♥ st✐❝❦❴s❧✐♣❴❝① ✪ ❚r✉♦♥❣ ❤♦♣ ❜✐❡t tr✉♦❝ ♥❣❤✐❡♠ ❞✉♥❣ ✪ ♣❤✐ ❧❛ ❤❛♠ ✈❡ ♣❤❛✐ ✪ ❜✶✱❜✷✱❜✸✱❜✹✿ ❧❛ ❝❛❝ ❣✐❛ tr✐ tr❡♥ ❜✐❡♥ tr❛✐✱♣❤❛✐✱❞✉♦✐✱tr❡♥ ✪ ✉❞❞ ❧❛ ♥❣❤✐❡♠ ❜❛✐ t♦❛♥✿ ✪ ◆❣❛② ❧❛♣ ✷✹✴✶✶✴✷✵✶✺ ✪ ❉❛ ❦✐❡♠ tr❛ ❝❤➼♥❤ ①❛❝ ❝❧❡❛r ❛❧❧ ❝❧❝ t❡t❛❂✵✳✺❀✪t❤❛♠ s♦ ❧❛♣ ❝❤✐❛ ♠✐❡♥ t♦❂✵✳✾✺❀✪t❤❛♠ s♦ ❧❛♣ s♦♥❣ ❞✐❡✉ ❤♦❛ ❛❂✶❀ ❡✶❂✵✳✺❀ ❜❂✶❀ ❦✶❂✶❀❦✷❂✶❀ ❝❝❂✵❀ ❝♦✉♥t❂✲✶❀ ❡♣①✐❧♦♥❂✶✵✂✭✲✹✮❀s❛✐s♦❂✶✵❀ ♥❂✻❀ ◆❂✷✂ ♥❀ ▼❂◆❀ ♣✶❂✶❀♣✷❂▼✰✶❀♣✸❂✷✯▼✰✶❀♣✹❂✸✯▼✰✶❀♣✺❂✹✯▼✰✶❀♣✻❂✺✯▼✰✶❀q✶❂✶❀q✷❂◆✰✶❀q ❢♦r ❥❂✵✿◆❀ ❝s✐✶✭❥✰✶✮❂✵❀✪❦❤♦✐ t❛♦ ❣✐❛ tr✐ ❧❛♣ ❝❤✐❛ ♠✐❡♥ download by : skknchat@gmail.com ✹✽ ❡t❛✶✭❥✰✶✮❂✵❀ ❡♥❞❀ ❢♦r ✐❂✵✿▼❀ ♣❤✐✶✭✐✰✶✮❂✵❀ ✪❑❤♦✐ t❛♦ ❝❤♦ ❞❛② ❧❛♣ s♦♥❣ ❞✐❡✉ ❤♦❛ ♣❤✐✸✭✐✰✶✮❂✵❀ ❡♥❞❀ ❤✶✶❂❡✶✴▼❀❤✷✶❂✭❛✲❡✶✮✴▼❀ ❤✶✷❂❜✴◆❀❤✷✷❂❜✴◆❀ ❢♦r ✐❂✵✿▼❀ ❢♦r ❥❂✵✿◆❀ ①✶❂✵✰✐✯❤✶✶❀ ①✷❂✵✰❥✯❤✶✷❀ ✉❞✭♣✶✰✐✱q✶✰❥✮❂✉✭①✶✱①✷✮❀✪◆❣❤✐❡♠ ❞✉♥❣ tr❡♥ ▼✐❡♥ ✶ ①✶❂❡✶✰✐✯❤✷✶❀ ①✷❂✵✰❥✯❤✷✷❀ ✉❞✭♣✷✰✐✱q✶✰❥✮❂✉✭①✶✱①✷✮❀✪◆❣❤✐❡♠ ❞✉♥❣ tr❡♥ ▼✐❡♥ ✷ ❡♥❞❀ ❡♥❞❀ t❤♦✐❣✐❛♥❂❝♣✉t✐♠❡❀ ✇❤✐❧❡ ❛♥❞✭❝♦✉♥t❁✹✵✵✱s❛✐s♦❃❡♣①✐❧♦♥✮❀ ❝♦✉♥t❂❝♦✉♥t✰✶❀ ✪❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂●✐❛✐ ♠✐❡♥ ✷❂❂❂❂❂❂❂❂❂❂❂❂❂ ✪ ●✐❛✐ ❜❛✐ t♦❛♥ ✈♦✐ ✈✷ ❧✶❂❛✲❡✶❀❧✷❂❜❀▼✷❂▼❀◆✷❂◆❀♥✷❂♥❀ ✪ ●✐❛ tr✐ ✈❡ ♣❤❛✐ ✈➔ ♥❣❤✐❡♠ ❞✉♥❣ ❢♦r ✐❂✵✿▼✷❀ download by : skknchat@gmail.com ✹✾ ❢♦r ❥❂✵✿◆✷❀ ①✶❂❡✶✰✐✯❤✷✶❀ ①✷❂✵✰❥✯❤✷✷❀ ♣❤✐✭✐✰✶✱❥✰✶✮❂✈♣✶✭①✶✱①✷✱❝❝✱❦✶✱❦✷✮❀✪ ❍❛♠ ✈❡ ♣❤❛✐ ❡♥❞❀ ❡♥❞❀ ✪ ❉✐❡✉ ❦✐❡♥ tr❡♥ ❝❛♥❤ tr❛✐ ✈❛ ♣❤❛✐ ❢♦r ❥❂✵✿◆✷❀ ①✷❂✵✰❥✯❤✷✷❀ ❜✶✭❥✰✶✮❂❝s✐✶✭❥✰✶✮❀ ❜✷✭❥✰✶✮❂❞❤✸①✭❛✱①✷✮❀ ❡♥❞❀ ✪ ❉✐❡✉ ❦✐❡♥ tr❡♥ ❝❛♥❤ ❞✉♦✐ ✈❛ tr❡♥ ❢♦r ✐❂✵✿▼✷❀ ①✶❂❡✶✰✐✯❤✷✶❀ ❜✸✭✐✰✶✮❂❞❡❧t❛✭①✶✱✵✮❀ ❜✹✭✐✰✶✮❂❞❡❧t❛✭①✶✱❜✮❀ ❡♥❞❀ ✈✷❂✉✶✶✵✵✭♣❤✐✱❜✶✱❜✷✱❜✸✱❜✹✱❧✶✱❧✷✱❦✶✱❦✷✱❝❝✱▼✷✱◆✷✱♥✷✱♣✷✱♣✸✱q✶✱q✷✮❀ ✪ ●✐❛✐ ❜❛✐ t♦❛♥ ✈♦✐ ✉✷ ✪ ●✐❛ tr✐ ✈❡ ♣❤❛✐ ❢♦r ✐❂✵✿▼✷❀ ❢♦r ❥❂✵✿◆✷❀ ♣❤✐✭✐✰✶✱❥✰✶✮❂✲✈✷✭♣✷✰✐✱q✶✰❥✮❀ ✪ ❍❛♠ ✈❡ ♣❤❛✐ ❡♥❞❀ download by : skknchat@gmail.com ✺✵ ❡♥❞❀ ✪ ❉✐❡✉ ❦✐❡♥ tr❡♥ ❝❛♥❤ tr❛✐ ✈❛ ♣❤❛✐ ❢♦r ❥❂✵✿◆✷❀ ①✷❂✵✰❥✯❤✷✷❀ ❜✶✭❥✰✶✮❂❡t❛✶✭❥✰✶✮❀ ❜✷✭❥✰✶✮❂❞❤①✭❛✱①✷✮❀ ❡♥❞❀ ✪ ❉✐❡✉ ❦✐❡♥ tr❡♥ ❝❛♥❤ ❞✉♦✐ ✈❛ tr❡♥ ❢♦r ✐❂✵✿▼✷❀ ①✶❂❡✶✰✐✯❤✷✶❀ ❜✸✭✐✰✶✮❂✉✭①✶✱✵✮❀ ❜✹✭✐✰✶✮❂✉✭①✶✱❜✮❀ ❡♥❞❀ ✉✷❂✉✶✶✵✵✭♣❤✐✱❜✶✱❜✷✱❜✸✱❜✹✱❧✶✱❧✷✱✶✱✶✱✵✱▼✷✱◆✷✱♥✷✱♣✷✱♣✸✱q✶✱q✷✮❀ ✪ ●✐❛✐ ❜❛✐ t♦❛♥ ✈♦✐ ✈✶ ❧✶❂❡✶❀❧✷❂❜❀▼✶❂▼❀◆✶❂◆❀♥✶❂♥❀ ❤✶✶❂❧✶✴▼✶❀ ❤✶✷❂❧✷✴◆✶❀ ✪ ●✐❛ tr✐ ✈❡ ♣❤❛✐ ❢♦r ✐❂✵✿▼✶❀ ❢♦r ❥❂✵✿◆✶❀ ①✶❂✵✰✐✯❤✶✶❀ ①✷❂✵✰❥✯❤✶✷❀ ♣❤✐✭✐✰✶✱❥✰✶✮❂✈♣✶✭①✶✱①✷✱❝❝✱❦✶✱❦✷✮❀ ✪ ❍❛♠ ✈❡ ♣❤❛✐ ❡♥❞❀ ❡♥❞❀ download by : skknchat@gmail.com ✺✶ ✪ ❉✐❡✉ ❦✐❡♥ tr❡♥ ❝❛♥❤ tr❛✐ ✈❛ ♣❤❛✐ ❢♦r ❥❂✵✿◆✶❀ ①✷❂✵✰❥✯❤✶✷❀ ✪❜✶✭❥✰✶✮❂❞❡❧t❛✭✵✱①✷✮❀ ❜✶✭❥✰✶✮❂♣❤✐✶✭❥✰✶✮❀ ❜✷✭❥✰✶✮❂✈✷✭♣✷✱q✶✰❥✮❀ ❡♥❞❀ ✪ ❉✐❡✉ ❦✐❡♥ tr❡♥ ❝❛♥❤ ❞✉♦✐ ✈❛ tr❡♥ ❢♦r ✐❂✵✿▼✶❀ ①✶❂✵✰✐✯❤✶✶❀ ❜✸✭✐✰✶✮❂❞❡❧t❛✭①✶✱✵✮❀ ❜✹✭✐✰✶✮❂♣❤✐✸✭✐✰✶✮❀ ❡♥❞❀ ✈✶❂✉✵✵✵✵✭♣❤✐✱❜✶✱❜✷✱❜✸✱❜✹✱❧✶✱❧✷✱❦✶✱❦✷✱❝❝✱▼✶✱◆✶✱♥✶✱♣✶✱♣✷✱q✶✱q✷✮❀ ✪ ●✐❛✐ ❜❛✐ t♦❛♥ ✈♦✐ ✉✶ ✪ ●✐❛ tr✐ ✈❡ ♣❤❛✐ ❢♦r ✐❂✵✿▼✶❀ ❢♦r ❥❂✵✿◆✶❀ ♣❤✐✭✐✰✶✱❥✰✶✮❂✲✈✶✭♣✶✰✐✱q✶✰❥✮❀ ✪ ❍❛♠ ✈❡ ♣❤❛✐ ❡♥❞❀ ❡♥❞❀ ✪ ❉✐❡✉ ❦✐❡♥ tr❡♥ ❝❛♥❤ tr❛✐ ✈❛ ♣❤❛✐ ❢♦r ❥❂✵✿◆✶❀ ①✷❂✵✰❥✯❤✶✷❀ ❜✶✭❥✰✶✮❂✉✭✵✱①✷✮❀ download by : skknchat@gmail.com ✺✷ ❜✷✭❥✰✶✮❂✉✷✭♣✷✱q✶✰❥✮❀ ❡♥❞❀ ✪ ❉✐❡✉ ❦✐❡♥ tr❡♥ ❝❛♥❤ ❞✉♦✐ ✈❛ tr❡♥ ❢♦r ✐❂✵✿▼✶❀ ①✶❂✵✰✐✯❤✶✶❀ ❜✸✭✐✰✶✮❂✉✭①✶✱✵✮❀ ❜✹✭✐✰✶✮❂✉✭①✶✱❜✮❀ ❡♥❞❀ ✉✶❂✉✵✵✵✵✭♣❤✐✱❜✶✱❜✷✱❜✸✱❜✹✱❧✶✱❧✷✱✶✱✶✱✵✱▼✶✱◆✶✱♥✶✱♣✶✱♣✷✱q✶✱q✷✮❀ ✪❂❂❂❂❂❂❂❂❂❂❂❂❂❂ ✪ ❍✐❡✉ ❝❤✐♥❤ ❣✐❛ tr✐ ❝s✐✶ ❢♦r ❥❂✵✿◆✶❀ ①✷❂✵✰❥✯❤✶✷❀ ♣❤✵✶✭❥✰✶✮❂✈♣✶✭❡✶✱①✷✱❝❝✱❦✶✱❦✷✮❀ ❡♥❞❀ ❞✈✶❂❞①✭q✶✱q✷✱♣✷✱♣❤✵✶✱✈✶✱❤✶✶✱❤✶✷✱❦✶✱❦✷✱▼✶✱✲✶✮❀ ❝s✐✶❂t❡t❛✯❝s✐✶✲✭✶✲t❡t❛✮✯❞✈✶❀ ✪ ❍✐❡✉ ❝❤✐♥❤ ❣✐❛ tr✐ ❡t❛✶ ❢♦r ❥❂✵✿◆✶❀ ♣❤✵✶✭❥✰✶✮❂✲✈✶✭♣✷✱q✶✰❥✮❀ ❡♥❞❀ ❞✉✶❂❞①✭q✶✱q✷✱♣✷✱♣❤✵✶✱✉✶✱❤✶✶✱❤✶✷✱✶✱✶✱▼✶✱✲✶✮❀ ❡t❛✶❂t❡t❛✯❡t❛✶✲✭✶✲t❡t❛✮✯❞✉✶❀ ✪❍✐❡✉ ❝❤✐♥❤ ❣✐❛ tr✐ ♣❤✐✶ ❢♦r ❥❂✵✿◆✷❀ ①✷❂✵✰❥✯❤✶✷❀ download by : skknchat@gmail.com ✺✸ ❞❤✷✷✭❥✰✶✮❂❞❤①✭✵✱①✷✮❀ ♣❤✵✵✸✭❥✰✶✮❂✲✈✶✭♣✶✱q✶✰❥✮❀ ❡♥❞❀ ❞✉✶❂❞①✭q✶✱q✷✱♣✶✱♣❤✵✵✸✱✉✶✱❤✶✶✱❤✶✷✱✶✱✶✱◆✱✶✮❀ ♣❤✐✶❂♣❤✐✶✰t♦✯✭❞✉✶✲❞❤✷✷✮❀ ✪❍✐❡✉ ❝❤✐♥❤ ❣✐❛ tr✐ ♣❤✐✸ ❢♦r ✐❂✵✿▼✶❀ ①✶❂✵✰✐✯❤✶✶❀ ❞❤✸✸✭✐✰✶✮❂❞❤②✭①✶✱❜✮❀ ♣❤✵✵✹✸✭✐✰✶✮❂✲✈✶✭♣✶✰✐✱q✷✮❀ ❡♥❞❀ ❞✉✸❂❞②✭♣✶✱♣✷✱q✷✱♣❤✵✵✹✸✱✉✶✱❤✶✶✱❤✶✷✱✶✱✶✱▼✱✲✶✮❀ ♣❤✐✸❂♣❤✐✸✰t♦✯✭❞✉✸✰❞❤✸✸✮❀ ❢♦r ✐❂✵✿▼❀ ❢♦r ❥❂✵✿◆❀ ✉①①✭♣✶✰✐✱q✶✰❥✮❂✉✶✭♣✶✰✐✱q✶✰❥✮❀✪◆❣❤✐❡♠ ①❛♣ ①✐ tr❡♥ ♠✐❡♥ ✶ ✉①①✭♣✷✰✐✱q✶✰❥✮❂✉✷✭♣✷✰✐✱q✶✰❥✮❀✪◆❣❤✐❡♠ ①❛♣ ①✐ tr❡♥ ♠✐❡♥ ✷ ❡♥❞❀ ❡♥❞❀ s❛✐s♦❂❝❤✉❛♥✭✉❞✲✉①①✮ ❡♥❞❀ ✪❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂ t❤♦✐❣✐❛♥❂❝♣✉t✐♠❡✲t❤♦✐❣✐❛♥ ❝♦✉♥t ✪❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂❂ download by : skknchat@gmail.com ... ❤➺ ❤➔♠ r✐➯♥❣✳ ❚ø ✤â ❜➔✐ t♦→♥ ✤÷❛ ✈➲ ✈✐➺❝ ①→❝ ✤à♥❤ ❝→❝ ❤➺ sè ❝õ❛ ❦❤❛✐ tr✐➸♥ ❜➡♥❣ ❝→❝ ♣❤÷ì♥❣ ♣❤→♣ số ỷ ỵ tt t tỷ ỹ sỡ ỗ ❝→❝ ❣✐→ trà t❤✐➳✉ tr➯♥ ❜✐➯♥ ✤➸ ❝❤✉②➸♥ ❜➔✐ t♦→♥ ❝â ❝❤ù❛ ❝→❝ ✤✐➸♠ ❦➻... () ỗ t ởt ①↕ t✉②➳♥ t➼♥❤ ❧✐➯♥ tö❝✿ (∂Ω)✳ g ∈ H (∂Ω) → ug ∈ H (Ω) ❱ỵ✐ γ (ug ) = g ✈➔ tỗ t ởt số C1 () tở ♠✐➲♥ Ω s❛♦ ❝❤♦✿ ug ✶✳✶✳✺ H (Ω) C1 (Ω) g 1 H (∂Ω) , ∀g ∈ H (Ω) ❈æ♥❣ t❤ù❝ ●r❡❡♥✱ ❜➜t... ▲✐♣s❝❤✐t③✱ ∂Ω = Γ1 ∪ Γ2✱ tr♦♥❣ ✤â Γ1, Γ2 ❧➔ ❝→❝ t➟♣ ✤â♥❣✱ rí✐ ♥❤❛✉✱ Γ1 ❝â ✤ë ✤♦ ❞÷ì♥❣✳ õ tỗ t số C () s ✿ u ∀u ∈ H (Ω) , γ (u) = ✶✳✶✳✻ CΩ ∇u L2 (Ω) L2 (Ω) , tr➯♥ Γ1 ❑❤ỉ♥❣ ❣✐❛♥ ❙♦❜♦❧❡✈ ✈ỵ✐ ❝❤➾

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