Analysis on Riemann surfaces and manifolds to gether with contributions to physics and engineeing

黎曼曲面和流形分析以及对物理学和工程学的贡献

• 批准号: 09640193
• 负责人: SHIBA Masakazu
• 金额: $ 1.98万
• 依托单位: Hiroshima University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1997
• 资助国家: 日本
• 起止时间: 1997 至 1998
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640193/
• 关键词: Riemann surfaces; Ideal fluid flow; Conformal mapping; Energy integral; Univalent functions; Potential flow; Rankine ovoids; Analytic functions; エネルギー積分; ランキンの卵形

We used the function-theoretic methods to obtain a new insight into the various fluid-dynamical phenomena on surfaces and manifolds. Specifically, we have been interested in Rankine ovoids on plane and Riemann surfaces. We use the function-theoretic technique (initiated by the head investigator) to study the phenomenon physically as well as mathematically. The physical investigation is based on the notions of sink and source, vortex, energy, moment and so on, while the mathematical investigation is based on our own results which have been so far obtained. Of the most importance among them is the study of compact Riemann surfaces into which a prescribed noncompact Riemann surface can be conformally embedded. We have proved that any Rankine ovoid can be realized by a univalent meromorphic function on a simply connected plane domain and that the area of the Rankine ovoid is surprisingly close to the possible maximum area which will be attained in a certain family of competing functions. The result was announced at the International Conference "Computational Methods and Function Theory (CMFT'97)" held in Nicosia, Cyprus, and will be included in the Proceedings.

我们利用泛函理论方法对曲面和流形上的各种流体力学现象有了新的认识。具体来说，我们对平面和黎曼曲面上的朗肯卵泡很感兴趣。我们使用泛函理论技术（由首席研究员发起）从物理和数学上研究这一现象。物理研究是基于汇源、涡旋、能量、力矩等概念，而数学研究是基于我们自己迄今为止得到的结果。其中最重要的是紧致黎曼曲面的研究，其中规定的非紧致黎曼曲面可以共形嵌入其中。我们证明了在单连通平面上任何朗金卵圆都可以用一个一元亚纯函数来实现，并且该朗金卵圆的面积惊人地接近于在某一竞争函数族中可能得到的最大面积。这一结果在塞浦路斯尼科西亚举行的“计算方法和函数理论”国际会议（CMFT'97）上公布，并将被纳入《论文集》。

项目成果

Aizawa,K.: "Quadtree adjoining grammar" Int.J,Pattern Recognition & Art.Intelligence. 近刊. (1999)

Aizawa, K.：“四叉树邻接语法”Int.J，模式识别与艺术智能（1999 年）。

Y.Ohta: "Determinant and Pfaffian Solutions for Discrete Soliton Equa-tions" Proceedings of the SIDE III Meeting, CRM Proceedings and Lec-ture Notes Series. (to appear.).

Y.Ohta：“离散孤子方程的行列式和普法夫解”SIDE III 会议论文集、CRM 论文集和讲座笔记系列。

Ito, M.: "Area theorems for conformal mapping and Rankine ovhlvids" Computational Methods and Function Theory. 近刊. 275-283 (1998)

Ito, M.：“共形映射和兰金 ovhlvids 的面积定理”，计算方法和函数理论，即将出版。

Aizawa, K.: "Quadtrees adgorning grammar" Int.J.Pattern Recognihim & Art : Intelligence. 近刊. (1999)

Aizawa, K.：“四叉树装饰语法”Int.J.Pattern Recognihim & Art：即将出版。

Ramani, A.: "Selfauclty and Schlesuzer chrins for the assymmetric cl-PII and q-PIII equations" Comm,Math.Phys.192. 67-76 (1998)

Ramani, A.：“不对称 cl-PII 和 q-PIII 方程的 Selfauclty 和 Schlesuzer chrins”Comm，Math.Phys.192。