Header Page of 128 ✣❸■ ❍➴❈ ◗❯➮❈ ●■❆ ❍⑨ ◆❐■ ❚❘×❮◆● ✣❸■ ❍➴❈ ❑❍❖❆ ❍➴❈ ❚Ü ◆❍■➊◆ ✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲✲ P❤↕♠ ▼✐♥❤ ❚✐➳♥ P❍➆P ❇■➌◆ ✣✃■ ▲❆P▲❆❈❊ ❘❮■ ❘❸❈ ❱❰■ P❍×❒◆● ❚❘➐◆❍ ❙❆■ P❍❹◆ ▲❯❾◆ ❱❿◆ ❚❍❸❈ ❙➒ ❈❤✉②➯♥ ♥❣➔♥❤✿ P❍×❒◆● PP P số ữớ ữợ ❦❤♦❛ ❤å❝ P●❙✳❚❙✳ ◆●❯❨➍◆ ❚❍Õ❨ ❚❍❆◆❍ ❍⑨ ◆❐■✲ ✷✵✶✹ luan van thac si - luan van kinh te - khoa luan - tai lieu -Footer Page of 128 Header Page of 128 ✶ ▼ư❝ ❧ư❝ ▼ð ✤➛✉ ▲í✐ ❝↔♠ ì♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶ ❈⑩❈ ❑❍⑩■ ◆■➏▼ ❇✃ ❚❘Ñ ✶✳✶ ❑❤→✐ ♥✐➺♠ s❛✐ ♣❤➙♥ ❤ú✉ ❤↕♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✳✶✳✶ ✣à♥❤ ♥❣❤➽❛ ✈➔ ✈➼ ❞ö ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✳✶✳✷ ▼ët sè t➼♥❤ ❝❤➜t ❝õ❛ s❛✐ ♣❤➙♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✳✷ ❈→❝ ❦❤→✐ ♥✐➺♠ ❝ì ❜↔♥ ✈➲ ♣❤÷ì♥❣ tr➻♥❤ s❛✐ ♣❤➙♥ ✈➔ ♥❣❤✐➺♠ ❝õ❛ ♥â ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✳✷✳✶ P❤÷ì♥❣ tr➻♥❤ s❛✐ ♣❤➙♥ t✉②➳♥ t➼♥❤ ✈ỵ✐ ❤➺ sè ❤➡♥❣ ✈➔ ❞↕♥❣ ❜✐➸✉ ❞✐➵♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✳✷✳✷ ❈→❝ ✤à♥❤ ♥❣❤➽❛ ✈➔ ❝→❝ ❦❤→✐ ♥✐➺♠ ❧✐➯♥ q✉❛♥ ✤➳♥ ♣❤÷ì♥❣ tr➻♥❤ s❛✐ ♣❤➙♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✳✸ P❤÷ì♥❣ ♣❤→♣ t♦→♥ tû ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✳✸✳✶ ▼ët sè ❦✐➳♥ t❤ù❝ ✈➲ ♣❤➨♣ ❜✐➳♥ ✤ê✐ ▲❛♣❧❛❝❡ rí✐ r↕❝ ✳ ✶✳✸✳✷ ❈→❝ ✤à♥❤ ỵ ổ tự tữớ ũ ố tữỡ ự ợ trữợ P❤ư ❧ư❝ ❝❤÷ì♥❣ ■ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✳✹✳✶ ❇↔♥❣ ✤è✐ ❝❤✐➳✉ ❣è❝ ↔♥❤✿ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✳✹✳✷ ❇➔✐ t➟♣ ❝❤÷ì♥❣ ■ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸ ✹ ✻ ✻ ✻ ✽ ✾ ✾ ✶✶ ✶✷ ✶✷ ✶✹ ✶✺ ✷✶ ✷✶ ✷✺ ✷ P❍×❒◆● P❍⑩P Pì P Pữỡ tr s ♣❤➙♥ t✉②➳♥ t➼♥❤ ❝➜♣ ✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✳✶✳✶ ✣à♥❤ ♥❣❤➽❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✳✶✳✷ ●✐↔✐ ♣❤÷ì♥❣ tr➻♥❤ s❛✐ ♣❤➙♥ t✉②➳♥ t➼♥❤ ❝➜♣ ✶ t❤✉➛♥ ♥❤➜t ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✳✶✳✸ ●✐↔✐ ♣❤÷ì♥❣ tr➻♥❤ s❛✐ ♣❤➙♥ t✉②➳♥ t➼♥❤ ❦❤ỉ♥❣ t❤✉➛♥ ♥❤➜t ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✳✶✳✹ P❤÷ì♥❣ ♣❤→♣ ❜✐➳♥ t❤✐➯♥ ❤➡♥❣ sè t➻♠ ♥❣❤✐➺♠ r✐➯♥❣ f ∗ (n) ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ luan van thac si - luan van kinh te - khoa luan - tai lieu -Footer Page of 128 ✷✼ ✷✼ ✷✽ ✷✽ ✷✽ Header Page of 128 ✷ ✷✳✶✳✺ P❤÷ì♥❣ ♣❤→♣ ❝❤å♥ ✭ P❤÷ì♥❣ ♣❤→♣ ❤➺ sè ❜➜t ✤à♥❤ ✮ ✷✳✷ P❤÷ì♥❣ tr➻♥❤ s❛✐ ♣❤➙♥ t✉②➳♥ t➼♥❤ ❝➜♣ ✷ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✳✷✳✶ ✣à♥❤ ♥❣❤➽❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✳✷✳✷ ●✐↔✐ ♣❤÷ì♥❣ tr➻♥❤ s❛✐ ♣❤➙♥ t✉②➳♥ t➼♥❤ ❝➜♣ ❤❛✐ t❤✉➛♥ ♥❤➜t ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✳✷✳✸ ●✐↔✐ ♣❤÷ì♥❣ tr➻♥❤ s❛✐ ♣❤➙♥ t✉②➳♥ t➼♥❤ ❝➜♣ ❤❛✐ ❦❤ỉ♥❣ t❤✉➛♥ ♥❤➜t ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✳✷✳✹ ❈→❝ ♣❤÷ì♥❣ ♣❤→♣ t➻♠ ♥❣❤✐➺♠ r✐➯♥❣ ❝õ❛ ♣❤÷ì♥❣ tr➻♥❤ s❛✐ ♣❤➙♥ t✉②➳♥ t➼♥❤ ❝➜♣ ❤❛✐ ❦❤æ♥❣ t❤✉➛♥ ♥❤➜t ✳ ✳ ✳ ✷✳✸ ❑❤→✐ q✉→t ✈➲ ♣❤÷ì♥❣ tr➻♥❤ s❛✐ ♣❤➙♥ t✉②➳♥ t➼♥❤ ❝➜♣ ❝❛♦ ✳ ✷✳✸✳✶ ✣à♥❤ ♥❣❤➽❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✳✸✳✷ ❈→❝❤ ❣✐↔✐ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✳✹ ●✐↔✐ ♣❤÷ì♥❣ tr➻♥❤ s❛✐ ♣❤➙♥ t✉②➳♥ t➼♥❤ ❜➡♥❣ ♣❤÷ì♥❣ ♣❤→♣ t♦→♥ tû ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ỵ ổ tự tữớ ❞ò♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✳✹✳✷ ▲÷đ❝ ỗ ữỡ tr s ữỡ t tû ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✳✹✳✸ ❈→❝ ✈➼ ❞ö ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ✸✽ ✸✽ ✸✾ ✹✶ ✹✶ ✹✽ ✹✽ ✹✾ ✺✶ ✺✶ ✺✹ ✺✺ ✸ ▼❐❚ ❙➮ Ù◆● ❉Ö◆● ❈Õ❆ ❙❆■ P❍❹◆ ❱⑨ P❍➆P ❇■➌◆ ✣✃■ ▲❆P▲❆❈❊ ❘❮■ ❘❸❈ ❚❘❖◆● ●■❷■ ❚❖⑩◆ P❍✃ ❚❍➷◆● ✻✸ ✸✳✶ ❚➻♠ sè ❤↕♥❣ tê♥❣ q✉→t ❝õ❛ ❞➣② sè ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✳✷ ❚➼♥❤ tê♥❣ ❝õ❛ ♥ sè ❤↕♥❣ ✤➛✉ tr♦♥❣ ♠ët ❞➣② sè ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✳✸ ❙❛✐ ♣❤➙♥ ✈ỵ✐ ✈✐➺❝ ①→❝ ✤à♥❤ ✤❛ t❤ù❝ ❤♦➦❝ ❣✐↔✐ ♣❤÷ì♥❣ tr➻♥❤ ❤➔♠✿ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✳✹ ❇➔✐ t➟♣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ❑➳t ❧✉➟♥ ❚➔✐ ❧✐➺✉ t❤❛♠ ❦❤↔♦ luan van thac si - luan van kinh te - khoa luan - tai lieu -Footer Page of 128 ✻✸ ✻✻ ✻✾ ✼✷ ✼✸ ✼✹ ✸ Header Page of 128 ▼ð ✤➛✉ ❈â ♥❤✐➲✉ ❜➔✐ t♦→♥ ✈➲ ❞➣② sè ❤♦➦❝ ❤➔♠ sè ♠➔ ❣✐↔ t❤✐➳t ❤♦➦❝ ❧í✐ ú õ t t tr ỗ ữ t ❝æ♥❣ t❤ù❝ sè ❤↕♥❣ tê♥❣ q✉→t ❝õ❛ ♠ët ❞➣② sè ổ tự tr ỗ t tờ số ❤↕♥❣ ✤➛✉ ❝õ❛ ♠ët ❞➣② sè✱ ❣✐↔✐ ♣❤÷ì♥❣ tr➻♥❤ ❤➔♠✳ ✳ ✳ ◆❤ú♥❣ ❜➔✐ t♦→♥ ✤â ❞➝♥ tỵ✐ ✈✐➺❝ ♣❤↔✐ ❣✐↔✐ ❝→❝ ♣❤÷ì♥❣ tr➻♥❤ s❛✐ ♣❤➙♥✳ ❈→❝❤ t❤ỉ♥❣ t❤÷í♥❣ ❣✐↔✐ ♣❤÷ì♥❣ tr➻♥❤ s❛✐ ♣❤➙♥ ❧➔ ❞ü❛ tr➯♥ ✈✐➺❝ ❣✐↔✐ ♣❤÷ì♥❣ tr➻♥❤ ✤➦❝ tr÷♥❣ ✈➔ t➻♠ ♥❣❤✐➺♠ r✐➯♥❣✳ ▼é✐ ♣❤÷ì♥❣ tr➻♥❤ s❛✐ ♣❤➙♥ ❦❤→❝ ♥❤❛✉ ❧↕✐ ❝â ❝→❝❤ ❝❤å♥ ♥❣❤✐➺♠ r✐➯♥❣ ❦❤→❝ ♥❤❛✉✳ ❚❛ ❜✐➳t r➡♥❣ ✈✐➺❝ ❣✐↔✐ ♣❤÷ì♥❣ tr➻♥❤ ✤➦❝ tr÷♥❣ tø ❜➟❝ ❜❛ trð ❧➯♥ ❣➦♣ ❦❤ỉ♥❣ ➼t ❦❤â ❦❤➠♥✳ ▼➦t ❦❤→❝✱ ♥➳✉ ❝♦✐ ♠é✐ ❞➣② sè ♥❤÷ ❣✐→ trà ❝õ❛ ♠ët ❤➔♠ sè t↕✐ ❝→❝ ✤è✐ sè ♥❣✉②➯♥ t❤➻ ✈✐➺❝ ❣✐↔✐ ♣❤÷ì♥❣ tr➻♥❤ s❛✐ ♣❤➙♥ ❝â t❤➸ ❞ü❛ tr➯♥ ❝→❝ ♣❤➨♣ t♦→♥ ❝õ❛ ❤➔♠ sè✳ ❚♦→♥ tû ▲❛♣❧❛❝❡ rí✐ r↕❝ ❧➔ ♠ët tr♦♥❣ ♥❤ú♥❣ ❝ỉ♥❣ ❝ư ❣✐ó♣ ❣✐↔✐ ♣❤÷ì♥❣ tr➻♥❤ s❛✐ ♣❤➙♥ ❝â ❤✐➺✉ q✉↔✳ ❙ü ❦❤→❝ ❜✐➺t ❦❤✐ t❛ sû ❞ư♥❣ t♦→♥ tû ▲❛♣❧❛❝❡ ❧➔ t❛ ❦❤ỉ♥❣ ❝➛♥ ❣✐↔✐ ♣❤÷ì♥❣ tr➻♥❤ ✤➦❝ tr÷♥❣✳ ✣➸ ❝â t❤➸ tâ♠ t➢t ❝→❝❤ ❣✐↔✐ ♣❤÷ì♥❣ tr➻♥❤ s❛✐ ♣❤➙♥ t❤❡♦ ❝→❝❤ t❤ỉ♥❣ t❤÷í♥❣ ✈➔ ❜ê s✉♥❣ ♣❤÷ì♥❣ ♣❤→♣ t♦→♥ tû ▲❛♣❧❛❝❡ rí✐ r t ữợ P ❣✐❛♦ ❝❤♦ tæ✐ ✤➲ t➔✐ ✧ P❤➨♣ ❜✐➳♥ ✤ê✐ ▲❛♣❧❛❝❡ rớ r ợ ữỡ tr s ✤÷đ❝ ❝❤✐❛ ❧➔♠ ❜❛ ❝❤÷ì♥❣✳ ❈❤÷ì♥❣ ■✳❈→❝ ❦❤→✐ ♥✐➺♠ ❜ê trđ ◆ë✐ ❞✉♥❣ ❝❤➼♥❤ ❝õ❛ ❝❤÷ì♥❣ ♥➔② ❧➔ ❝✉♥❣ ❝➜♣ ❝→❝ ❦❤→✐ ♥✐➺♠ ❝ì ❜↔♥ ✈➲ s❛✐ ♣❤➙♥✱ ♣❤÷ì♥❣ tr➻♥❤ s❛✐ ♣❤➙♥ t✉②➳♥ t➼♥❤✱ ✤à♥❤ ♥❣❤➽❛ ✈➔ ♠ët sè t➼♥❤ ❝❤➜t ❝õ❛ ♣❤➨♣ ❜✐➳♥ ✤ê✐ ▲❛♣❧❛❝❡ rí✐ r↕❝✳ ❈❤÷ì♥❣ ■■✳ P❤÷ì♥❣ ♣❤→♣ ❣✐↔✐ ♣❤÷ì♥❣ tr➻♥❤ s❛✐ ♣❤➙♥ t✉②➳♥ t➼♥❤ ✳ ◆ë✐ ❞✉♥❣ ❝❤➼♥❤ ❝õ❛ ❝❤÷ì♥❣ ♥➔② ❧➔ tr➻♥❤ ❜➛② ❝→❝❤ ❣✐↔✐ ♣❤÷ì♥❣ tr➻♥❤ s❛✐ ♣❤➙♥ t✉②➳♥ t➼♥❤ ❝➜♣ ♠ët✱ ❝➜♣ ❤❛✐✱ ❝→❝ ♣❤÷ì♥❣ ♣❤→♣ ❝❤å♥ ♥❣❤✐➺♠ r✐➯♥❣ tò② t❤❡♦ ❞↕♥❣ ố ỡ ợ t ữỡ ♣❤→♣ ❣✐↔✐ ♣❤÷ì♥❣ tr➻♥❤ s❛✐ ♣❤➙♥ ❜➡♥❣ ❝→❝❤ ❝❤✉②➸♥ q✉❛ ❜✐➳♥ ✤ê✐ ▲❛♣❧❛❝❡ rí✐ r↕❝✳ ✳ luan van thac si - luan van kinh te - khoa luan - tai lieu -Footer Page of 128 Header Page of 128 ✹ ❈❤÷ì♥❣ ■■■✳ ▼ët sè ù♥❣ ❞ư♥❣ ❝õ❛ s❛✐ ♣❤➙♥ ✈➔ ♣❤➨♣ ❜✐➳♥ ✤ê✐ ▲❛♣❧❛❝❡ rí✐ r↕❝ tr♦♥❣ ❣✐↔✐ t♦→♥ ♣❤ê t❤ỉ♥❣✳ ◆ë✐ ❞✉♥❣ ❝❤➼♥❤ ❝õ❛ ❝❤÷ì♥❣ ♥➔② ❧➔ ✤÷❛ r❛ ♠ët sè ù♥❣ ❞ư♥❣ ❝õ❛ s❛✐ ♣❤➙♥ tr♦♥❣ ❣✐↔✐ t♦→♥ ♣❤ê t❤ỉ♥❣ ♥❤÷ ①→❝ ✤à♥❤ ❝ỉ♥❣ t❤ù❝ sè ❤↕♥❣ tê♥❣ q✉→t ❝õ❛ ❞➣② sè✱ t➼♥❤ tê♥❣ ❝õ❛ ♥ sè ❤↕♥❣ ✤➛✉ ❝õ❛ ♠ët ❞➣② sè✱ ù♥❣ ❞ö♥❣ s❛✐ ♣❤➙♥ tr♦♥❣ ①→❝ ✤à♥❤ ✤❛ t❤ù❝✱ ù♥❣ ❞ö♥❣ s❛✐ ♣❤➙♥ ❣✐↔✐ ♣❤÷ì♥❣ tr➻♥❤ ❤➔♠✳✳✳ ❉♦ t❤í✐ ❣✐❛♥ t❤ü❝ ❤✐➺♥ ❧✉➟♥ ✈➠♥ ❦❤æ♥❣ ♥❤✐➲✉✱ ❦✐➳♥ t❤ù❝ ❝á♥ ❤↕♥ ❝❤➳ ♥➯♥ ❦❤✐ ❧➔♠ ❧✉➟♥ ✈➠♥ ❦❤æ♥❣ tr→♥❤ ❦❤ä✐ ♥❤ú♥❣ ❤↕♥ ❝❤➳ ✈➔ s sõt ữủ sỹ õ ỵ ỳ ỵ qỵ t ổ ✈➔ ❜↕♥ ✤å❝✳ luan van thac si - luan van kinh te - khoa luan - tai lieu -Footer Page of 128 Header Page of 128 ▲í✐ ❝↔♠ ì♥ ❍♦➔♥ t❤➔♥❤ ✤÷đ❝ ❧✉➟♥ ✈➠♥ ♥➔②✱ ♥❣♦➔✐ sü ♥é ❧ü❝ ❝õ❛ ❜↔♥ t❤➙♥✱ tỉ✐ ✤➣ ♥❤➟♥ ✤÷đ❝ sü ❝❤➾ ❜↔♦✱ ❣✐ó♣ ✤ï tø ♥❤✐➲✉ ♣❤➼❛ ❝õ❛ ❝→❝ t❤➛②✱ ❝ỉ ❣✐→♦✱ ❣✐❛ ✤➻♥❤ ✈➔ ❜↕♥ ❜➧✳ ❚æ✐ ①✐♥ ❜➔② tä ỏ t ỡ s s tợ ữớ t ✱ ♥❣÷í✐ ✤➣ trü❝ t✐➳♣ tr✉②➲♥ t❤ư ❦✐➳♥ t❤ù❝✱ q✉②➳t ữợ ự t t ữợ tæ✐ ❤♦➔♥ t❤➔♥❤ ❜↔♥ ❧✉➟♥ ✈➠♥✳ ❚æ✐ ①✐♥ ❝❤➙♥ t❤➔♥❤ ❝↔♠ ì♥ ❝→❝ t❤➛②✱ ❝ỉ ❣✐→♦ ❦❤♦❛ ❚♦→♥ ✲ ❈ì ✲ ❚✐♥ ❤å❝✱ ❚r÷í♥❣ ✣↕✐ ❤å❝ ❑❤♦❛ ❤å❝ tü ♥❤✐➯♥ ✲ ✣↕✐ ❤å❝ ◗✉è❝ ❣✐❛ ❍➔ ◆ë✐✱ ♥❤ú♥❣ ♥❣÷í✐ ✤➣ trü❝ t✐➳♣ ❣✐↔♥❣ ❞↕② ✈➔ ❣✐ó♣ ✤ï tỉ✐ tr♦♥❣ q✉→ tr➻♥❤ ❤å❝ t➟♣ t↕✐ tr÷í♥❣ ❝ò♥❣ t♦➔♥ t❤➸ ❜↕♥ ❜➧ ữớ t õ õ ỵ ú ù ✤ë♥❣ ✈✐➯♥ tæ✐ tr♦♥❣ q✉→ tr➻♥❤ ❤å❝ t➟♣✱ ♥❣❤✐➯♥ ❝ù✉ ✈➔ ❤♦➔♥ t❤➔♥❤ ❧✉➟♥ ✈➠♥ ♥➔②✳ ❉♦ t❤í✐ ❣✐❛♥ t❤ü❝ ❤✐➺♥ ❧✉➟♥ ✈➠♥ ❦❤æ♥❣ ♥❤✐➲✉✱ ❦✐➳♥ t❤ù❝ ❝á♥ ❤↕♥ ❝❤➳ ♥➯♥ ❦❤✐ ❧➔♠ ❧✉➟♥ ✈➠♥ ❦❤æ♥❣ tr→♥❤ ❦❤ä✐ ♥❤ú♥❣ ❤↕♥ s sõt ữủ ỵ õ õ t ổ ỗ ♥❣❤✐➺♣ ✤➸ ❜↔♥ ❧✉➟♥ ✈➠♥ ✤÷đ❝ ❤♦➔♥ ❝❤➾♥❤ ❤ì♥✳ ❳✐♥ ❝❤➙♥ t❤➔♥❤ ❝↔♠ ì♥✳ P●❙✳❚❙✳ ◆❣✉②➵♥ ❚❤õ② ❚❤❛♥❤ ❍➔ ◆ë✐✱ ♥❣➔② ✷✵ t❤→♥❣ ✶✶ ♥➠♠ ✷✵✶✹ ❍å❝ ✈✐➯♥ P❤↕♠ ▼✐♥❤ ❚✐➳♥ luan van thac si - luan van kinh te - khoa luan - tai lieu -Footer Page of 128 ✻ Header Page of 128 ❈❤÷ì♥❣ ✶ ❈⑩❈ ❑❍⑩■ ◆■➏▼ ❇✃ ❚❘Ñ ✶✳✶ ❑❤→✐ ♥✐➺♠ s❛✐ ♣❤➙♥ ❤ú✉ ❤↕♥ ✶✳✶✳✶ ✣à♥❤ ♥❣❤➽❛ ✈➔ ✈➼ ❞ư ❱ỵ✐ ❤➡♥❣ sè h = 0✱ ❤➔♠ sè y = f (x) ❝â ❣✐→ trà t↕✐ ❝→❝ ✤✐➸♠ x0 , x1 = x0 + h, x2 = x0 + 2h, , xn = x0 + nh, (n ∈ N) t÷ì♥❣ ù♥❣ ❧➔ y0 , y1 , , yn , ♥❣❤➽❛ ❧➔ y0 =f (x0 ) = f0 ; y1 =f (x1 ) = f (x0 + h) = f1 ; y2 =f (x2 ) = f (x1 + h) = f2 ; ②♥ =f (xn ) = f (xn−1 + h) = fn ; ❑➼ ❤✐➺✉ ∆y = f (x + h) − f (x) = ∆f (x) ❧➔ s❛✐ ♣❤➙♥ ❝➜♣ ♠ët ❝õ❛ ❤➔♠ sè f (x) t↕✐ ✤✐➸♠ x.✳ ❱➟② ∆y0 = ∆f (x0 ) = y1 − y0 ; ∆y1 = ∆f (x1 ) = f (x1 + h) − f (x1 ) = y2 − y1 ; ∆yn−1 = ∆f (xn−1 ) = yn − yn−1 ∆yn = yn+1 − yn tữớ t ũ ủ ợ ✈✐➺❝ ♥❣❤✐➯♥ ❝ù✉ ❞➣② sè ✈➻ ♠é✐ sè ❤↕♥❣ tr♦♥❣ ❞➣② sè ✤÷đ❝ ❝♦✐ ❧➔ ❣✐→ trà ❝õ❛ ♠ët ❤➔♠ sè ♥➔♦ ✤â t↕✐ ❝→❝ ✤è✐ sè ♥❣✉②➯♥✳ ✣à♥❤ ♥❣❤➽❛ ✶✳✶✳ ●✐↔ sû ❤➔♠ sè y = f (x) ✤÷đ❝ ❝❤♦ t↕✐ ❝→❝ ✤✐➸♠ xk = x0 + k, k ∈ N✳ ❑❤✐ ✤â ∆yk = ∆fk = f (xk+1 ) − f (xk ) luan van thac si - luan van kinh te - khoa luan - tai lieu -Footer Page of 128 ✼ Header Page of 128 ✤÷đ❝ ❣å✐ ❧➔ s❛✐ ♣❤➙♥ ✭ ❤ú✉ ❤↕♥ ✮ ❝➜♣ ♠ët ❝õ❛ ❤➔♠ sè f (x) t↕✐ ✤✐➸♠ xk ✳ ❱➼ ❞ö ✶✳✶✳ ❚➻♠ t➜t ❝↔ ❝→❝ ✤❛ t❤ù❝ f (x) ∈ R[x] t❤ä❛ ♠➣♥ ❝→❝ ✤✐➲✉ ❦✐➺♥ s❛✉ ❛✮f (x + 1) − f (x) = ∀x ❜✮(x + 1) − f (x) = x ∀x ●✐↔✐✳ ❛✮ ❈❤♦ x = 0, 1, n t❛ ✤÷đ❝ ♣❤÷ì♥❣ tr➻♥❤ f (x) = f (0) ❝â ✈æ sè ♥❣❤✐➺♠✳ ▼➦t ❦❤→❝✱ f (x) ❧➔ ✤❛ t❤ù❝ ♥➯♥ f (x) = f (0) ∀x ❚❤û ❧↕✐ t❛ t❤➜② ✤ó♥❣✳ ✭ ❚❤❡♦ ✤à♥❤ ♥❣❤➽❛ s❛✐ ♣❤➙♥ ✈➔ ❦➳t q✉↔ ♣❤➛♥ ❛✮ t❤➻ ∆f (x) = ∀x ❞➝♥ tỵ✐ f (x) ❧➔ ❤➡♥❣ sè✳ ✮ ❜✮ ❈❤å♥ g(x) s❛♦ ❝❤♦ g(x + 1) − g(x) = x ∀x ❚❛ ❝❤å♥ g(x) = ax2 + bx t õ ú ỵ a(x + 1)2 + b(x + 1) − ax2 − bx = x ∀x ⇔ 2ax + a + b = x ❙✉② r❛ a = 21 , b = −1 ✱ ✈➟② g(x) = x − x ❉♦ ✤â (f (x + 1) − g(x + 1)) − (f (x) − g(x)) = ∀x✱✈✐➳t t❤❡♦ s❛✐ ♣❤➙♥ ❝➜♣ ♠ët ❧➔ ∆(f (x) − g(x)) = ❚❤❡♦ ❝➙✉ ❛✮ t❤➻ f (x) − g(x) = C ✭❈ ❧➔ ❤➡♥❣ sè ✮ ♥➯♥ f (x) = 21 x2 − 12 x + C ✣à♥❤ ♥❣❤➽❛ ✶✳✷✳ ❚❛ ❣å✐ s❛✐ ♣❤➙♥ ❝➜♣ ❤❛✐ ❝õ❛ ❤➔♠ sè f (x) ❧➔ s❛✐ ♣❤➙♥ ❝õ❛ s❛✐ ♣❤➙♥ ❝➜♣ ♠ët ❝õ❛ ❤➔♠ sè f (x)✳ ❙❛✐ ♣❤➙♥ ❝õ❛ s❛✐ ♣❤➙♥ ❝➜♣ ♥✲✶ ❣å✐ ❧➔ s❛✐ ♣❤➙♥ ❝➜♣ ♥ ❝õ❛ ❤➔♠ sè f (x)✳ ❑➼ ❤✐➯✉ ∆n f (xk ) ❧➔ s❛✐ ♣❤➙♥ ❝➜♣ ♥ ❝õ❛ ❤➔♠ sè f (x) t↕✐ ✤✐➸♠ xk ∆n yk = ∆n f (xk ) = ∆(∆n−1 f (xk )) = ∆n−1 f (xk+1 ) − ∆n−1 f (xk ) ❉♦ ✤â ∆2 yk = ∆2 fk = ∆f (xk+1 ) − ∆f (xk ) = f (xk+2 ) − 2f (xk+1 ) + f (xk ) ❱ỵ✐ ❤➔♠ sè y = f (x) s❛✐ ♣❤➙♥ ❝→❝ ❝➜♣ ❝õ❛ ♥â t↕✐ ❝→❝ ✤✐➸♠ xk ✤÷đ❝ s➢♣ ①➳♣ t❤❡♦ ❜↔♥❣ s❛✉✿ x = xk yk = f (xk ) ∆yk ∆2 yk x0 x1 x2 x3 x4 y0 y1 y2 y3 y4 ✳ ✳ ✳ ∆y0 ∆y1 ∆y2 ∆y3 2 ∆ y0 ∆ y1 ∆ y3 luan van thac si - luan van kinh te - khoa luan - tai lieu -Footer Page of 128 ✽ Header Page of 128 ❱➼ ❞ö ✶✳✷✳ ❳→❝ ✤à♥❤ ❝æ♥❣ t❤ù❝ sè ❤↕♥❣ tê♥❣ q✉→t ❝õ❛ ❞➣② sè ❜✐➳t ❝→❝ sè ❤↕♥❣ tr♦♥❣ ❞➣② ❧➔ ✲✶✱ ✷✱ ✶✸✱ ✹✹✱ ✶✵✼✱ ✷✶✹ ✳✳✳ ●✐↔✐✳ ●å✐ f (n) ❧➔ sè ❤↕♥❣ tê♥❣ q✉→t ❝õ❛ ❞➣② sè ✤➣ ❝❤♦✳ ❇↔♥❣ s❛✐ ♣❤➙♥ ❝→❝ ❝➜♣ ❝õ❛ f (n) ❧➔ n f (n) −1 13 44 107 214✳ ✳ ✳ ∆f (n) 11 31 63 107 ∆ f (n) 20 32 44 ∆ f (n) 12 12 12 ∆ f (n) 0 ❚❤❡♦ ❜↔♥❣ s❛✐ ♣❤➙♥ tr➯♥✱ f (n) ❧➔ ♠ët ❤➔♠ sè ❜➟❝ ✸ ❝õ❛ ♥ ♥➯♥ t❛ ✤➦t f (n) = an3 + bn2 + cn + d (a = 0) ❉♦ f (0) = −1, f (1) = 2, f (2) = 13, f (3) = 44 ♥➯♥ t❛ ❝â ❤➺ d = −1 a+b+c+d=2 8a + 4b + 2c + d = 13 27a + 9b + 3c + d = 44 ●✐↔✐ ❤➺ ♥➔② t❛ ✤÷đ❝ a = 2, b = −2, c = 3, d = −1✳ ❱➟② sè ❤↕♥❣ tê♥❣ q✉→t ❝õ❛ ❞➣② sè ✤➣ ❝❤♦ ❧➔ f (n) = 2n3 − 2n2 + 3n − ✶✳✶✳✷ ▼ët sè t➼♥❤ ❝❤➜t ❝õ❛ s❛✐ ♣❤➙♥ ❚➼♥❤ ❝❤➜t ✶✳✶✳ ❙❛✐ ♣❤➙♥ ❝õ❛ ❤➡♥❣ sè ❜➡♥❣ ✵ ✭ ❈ ❧➔ ❤➡♥❣ sè✮✳ ∆C = 0, ❚➼♥❤ ❝❤➜t ✶✳✷✳ ❙❛✐ ♣❤➙♥ ♠å✐ ❝➜♣ ❝â t❤➸ ❜✐➸✉ ❞✐➵♥ ❧↕✐ t❤❡♦ ❝→❝ ❣✐→ trà ❝õ❛ ❤➔♠ sè k (−1)i Cki yn+k−i k ∆ yn = i=0 ❚➼♥❤ ❝❤➜t ✶✳✸✳ ❙❛✐ ♣❤➙♥ ♠å✐ ❝➜♣ ❧➔ ♠ët t♦→♥ tû t✉②➳♥ t➼♥❤ ∆k (αf + βg) = α∆k f + β∆k g ❱ỵ✐ α, β ❧➔ số tũ ỵ f, g sè ❝õ❛ ❜✐➳♥ sè x luan van thac si - luan van kinh te - khoa luan - tai lieu -Footer Page of 128 ✾ Header Page 10 of 128 ❚➼♥❤ ❝❤➜t ✶✳✹✳ ❍➡♥❣ sè ∀k, m ∈ N, m < k✳ ❚❛ ❝â k−m i Ck−m ∆i f (xm ) yk = f (xk ) = i=0 ❚➼♥❤ ❝❤➜t ✶✳✺✳ ❙❛✐ ♣❤➙♥ ❝➜♣ ❦ ❝õ❛ ✤❛ t❤ù❝ ❜➟❝ ♥ ❝â ❝→❝ t➼♥❤ ❝❤➜t ❛✮ ▲➔ ✤❛ t❤ù❝ ❜➟❝ n − k ✳ ❜✮ ❇➡♥❣ ❤➡♥❣ sè ❦❤✐ n = k ✳ ❝✮ ❇➡♥❣ ✵ ❦❤✐ k > n✳ ❚➼♥❤ ❝❤➜t ✶✳✻✳ ❈æ♥❣ t❤ù❝ s❛✐ ♣❤➙♥ tø♥❣ ♣❤➛♥ ∆(fk gk ) = fk ∆gk + gk+1 ∆fk ❚➼♥❤ ❝❤➜t ✶✳✼✳ ❚ê♥❣ s❛✐ ♣❤➙♥ n ∆yk = yn+1 − y1 k=1 ✶✳✷ ❈→❝ ❦❤→✐ ♥✐➺♠ ❝ì ❜↔♥ ✈➲ ♣❤÷ì♥❣ tr➻♥❤ s❛✐ ♣❤➙♥ ✈➔ ♥❣❤✐➺♠ ❝õ❛ ♥â ✶✳✷✳✶ P❤÷ì♥❣ tr➻♥❤ s❛✐ ♣❤➙♥ t✉②➳♥ t➼♥❤ ✈ỵ✐ ❤➺ sè ❤➡♥❣ ✈➔ ❞↕♥❣ ❜✐➸✉ ❞✐➵♥ P❤÷ì♥❣ tr➻♥❤ ❞↕♥❣ F (n, yn , ∆yn , , ∆k yn ) = ✭✶✳✶✮ F (n, yn , yn+1 , , yn+k ) ✭✶✳✷✮ ❤❛② ✤÷đ❝ ❣å✐ ❧➔ ♣❤÷ì♥❣ tr➻♥❤ s❛✐ ♣❤➙♥ ❝➜♣ ❦✱ tr♦♥❣ ✤â y(n) ❧➔ ➞♥ ❤➔♠✳ ❚❛ ❝â t❤➸ ❜✐➳♥ ✤ê✐ ♣❤÷ì♥❣ tr➻♥❤ ✭✶✳✶✮ ✈➲ ♣❤÷ì♥❣ tr➻♥❤ ✭✶✳✷✮ ✈➔ ♥❣÷đ❝ ❧↕✐✳ ❚❤➟t ✈➟②✱ tø ❝ỉ♥❣ t❤ù❝ k (−1)i Cki yn+k−i k ∆ yn = i=0 s✉② r❛ ∆yn = yn+1 − yn ∆2 yn = yn+2 − C21 yn+1 + yn ∆3 yn = yn+3 − C31 yn+2 + C32 yn+1 − yn luan van thac si - luan van kinh te - khoa luan - tai lieu -Footer Page 10 of 128 Header Page 11 of 128 ✼✹ ❚➔✐ ❧✐➺✉ t❤❛♠ ❦❤↔♦ ❬✶❪ ◆❣✉②➵♥ ❚❤õ② ❚❤❛♥❤✱ ❍➔♠ ❜✐➳♥ ♣❤ù❝ ✈ỵ✐ ♣❤➨♣ ❜✐➳♥ ✤ê✐ ữợ ❣✐↔✐ ❜➔✐ t➟♣ ❤➔♠ ❜✐➳♥ ♣❤ù❝✱ ◆❳❇✣❍◗●❍◆✱ ✷✵✶✶✳ ❬✸❪ ◆❣✉②➵♥ ❱➠♥ ▼➟✉✱ ❚r➛♥ ◆❛♠ ❉ô♥❣✱ ◆❣✉②➵♥ ▼✐♥❤ ❚✉➜♥✱ ❈❤✉②➯♥ ✤➲ ❝❤å♥ ❧å❝ ❞➣② sè ✈➔ →♣ ❞ö♥❣✱ ◆❳❇●❉✱ ✷✵✵✽✳ ❬✹❪ ▲➯ ✣➻♥❤ ✣à♥❤✱ ❇➔✐ t➟♣ ♣❤÷ì♥❣ tr➻♥❤ s❛✐ ♣❤➙♥✱ ◆❳❇✣❍◗●❍◆✱ ✷✵✶✶ ❬✺❪ ◆❣✉②➵♥ ❱➠♥ ▼➟✉✱ ◆❣✉②➵♥ ❱➠♥ ❚✐➳♥✱ ▼ët sè số ỗ ữù s ọ tr ❤å❝ ♣❤ê t❤æ♥❣✱ ◆❳❇●❉✱ ✷✵✶✵ luan van thac si - luan van kinh te - khoa luan - tai lieu -Footer Page 11 of 128