| 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 |