完整後設資料紀錄
DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.author | 施建興 | en_US |
dc.contributor.author | Shih, Chien-Hsin | en_US |
dc.contributor.author | 李榮耀 | en_US |
dc.contributor.author | Lee, Jong-Eao | en_US |
dc.date.accessioned | 2014-12-12T01:30:22Z | - |
dc.date.available | 2014-12-12T01:30:22Z | - |
dc.date.issued | 2010 | en_US |
dc.identifier.uri | http://140.113.39.130/cdrfb3/record/nctu/#GT079622529 | en_US |
dc.identifier.uri | http://hdl.handle.net/11536/42516 | - |
dc.description.abstract | 假設 P(u) 是一個 u 的多項式函數且 f(u)=Sqrt{P(u)}。 在 complex plane 上 f 是一個多值函數。在 extended complex plane 上我們利用適合的 cut-structure 建立 f 的 Riemann surface R 。則 f 是一個定義在 R 上的單值函數。接著我們在 f 的代數結構上面做積分的運算。特別地,我們主要針對兩種特別的路徑來積分,分別為 a-cycle 及 b-cycle 。運用 principle of deformation of paths 來計算這些積分。此外,我們將以上的方法應用在微分方程上。 | zh_TW |
dc.description.abstract | Let P(u) be a polynomial of u and let f(u)=Sqrt{P(u)}. f is a 2-valued function defined on the complex plane C. We construct the Riemann surface R by a proper cut-structure on the extended complex plane. Then f is a single-valued function on R. Then we do evaluations of path integrals on R with its algebraic structure for f. In particular, we evaluate integrals along two special paths, a-cycle and b-cycle, respectively. We apply the principle of deformation of paths to evaluate those integrals. Furthermore, we apply the above argument to differential equations. | en_US |
dc.language.iso | en_US | en_US |
dc.subject | 黎曼空間 | zh_TW |
dc.subject | 代數結構 | zh_TW |
dc.subject | 幾何結構 | zh_TW |
dc.subject | 路徑積分 | zh_TW |
dc.subject | Riemann Surface | en_US |
dc.subject | algebraic structure | en_US |
dc.subject | geometry structure | en_US |
dc.subject | path integrals | en_US |
dc.title | N相黎曼面上的路徑積分及微分方程上之應用 | zh_TW |
dc.title | Path Integrals on Riemann Surfaces of Genus N and Its Applications on Differential Equations | en_US |
dc.type | Thesis | en_US |
dc.contributor.department | 應用數學系所 | zh_TW |
顯示於類別: | 畢業論文 |