### 博碩士論文 92221022 完整後設資料紀錄

 DC 欄位 值 語言 DC.contributor 數學系 zh_TW DC.creator 黎右強 zh_TW DC.creator You-Chiang Li en_US dc.date.accessioned 2006-7-2T07:39:07Z dc.date.available 2006-7-2T07:39:07Z dc.date.issued 2006 dc.identifier.uri http://ir.lib.ncu.edu.tw:88/thesis/view_etd.asp?URN=92221022 dc.contributor.department 數學系 zh_TW DC.description 國立中央大學 zh_TW DC.description National Central University en_US dc.description.abstract 對於實數\$xi\$我們定義\$||xi||\$為最接近\$xi\$整數。我的論文主要是探討\$V={liminf_{qin mathbb{N}}q|q xi |:xi in mathbb{R} setminusmathbb{Q}}.\$ 這個集合。此篇論文裡面有三個重要定理，分別是Dirichlet、Hurwitz和Markoff的定理。由Dirichlet的定理我們可證得 \$Vsubset[0,1]\$。而由Hurwitz的定理，我們更進一步推得 \$Vsubset[0,1/sqrt{5}]\$，並且\$1/sqrt{5}\$ 將不能再更小。Markoff的定理則是一個重要的結果，他清楚的說明了集合\$V\$在 \$(1/3, 1/sqrt{5}]\$ 這個區間上分布的情形。 zh_TW dc.description.abstract For raal \$xi\$, we define \$||xi||\$ be the nearest integer. We are interested in the set \$V={liminf_{qin mathbb{N}}q|q xi |:xi in mathbb{R} setminusmathbb{Q}}.\$ . Our main theorems are the Dirichlet’’s theorem, the Hurwitz’’s theorem and the Markoff’’s theorem. From Dirichlet’s theorem, we may prove that \$Vsubset[0,1]\$. And from Hurwitz’s theorem, we may obtain that \$Vsubset[0,1/sqrt{5}]\$ and \$1/sqrt{5}\$ cannot be improved. Markoff’’s theorem is an important result. He explained how \$V\$ distributes over the interval \$(1/3, 1/sqrt{5}]\$ en_US DC.subject 馬可夫鏈 zh_TW DC.subject Markoff chain en_US DC.subject Diophantine approximation en_US DC.title Diophantine approximation and the Markoff chain en_US dc.language.iso en_US en_US DC.type 博碩士論文 zh_TW DC.type thesis en_US DC.publisher National Central University en_US