Topology, its Applications to Mathematical Physics and Numerical Computations

拓扑及其在数学物理和数值计算中的应用

• 批准号: 09640096
• 负责人: YAMAGUCHI K.
• 金额: $ 1.86万
• 依托单位: THE UNIVERSITY OF ELECTRO COMMUN.
• 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-09640096/
• 关键词: topology; homotopy; harmonic map; configuration space; valuation; differential equation; space; numerical analysis; ケージ理論; 多項式; コホモロジー; 常微分方程式; 応用解析学

The main purpose of K.Yamaguchi is to study the topologies of labelled configuration spaces, which are recently well studied from the point of view of harmonic maps and is to investigate the topologies of several mapping spaces. The former study is mainly based on the joint work with M.Guest (Univ. Rochester, USA) and with A.Kozlowski (Toyama Internaitinal Univ.). First, recently we considered the homotopy type of the space SP^d_n(C) consisting of all monic complex polynomials of degree d and determined it explicitely. Next, he investigated its generalization, which is related to well-known Gromov's Smale-Hirsh principle. In particular1 he found some typical examples of it and published its result. Moreover, he and A.Kozlowski found its relations to the recent work of Vassiliev and submitted the preprint with respect to this work. Finally, concerning to the latter subject, he noticed the group structure of the group of self-homotopy equivalences of SO(4) and submitted it. M.Misawa studied the valation principle related to harmonic maps from the point of view of partial differential equation. In particular, he found the existence and regurality of p-harmonic maps and its gradient flows, whose paper is soon appeared. M.Fukuhara considered the domain decomposition and its applications to numerical computations.

K.Yamaguchi的主要目的是研究标号构形空间的拓扑，这是最近从调和映射的角度研究得很好的，并且是研究几个映射空间的拓扑。前者主要是与美国罗切斯特大学的M.Guest和富山国际大学的A.Kozlowski合作完成的。首先，最近我们研究了由所有d次一元复多项式组成的空间SP^d_n（C）的同伦型，并明确地确定了它的同伦型。接下来，他研究了它的推广，这与著名的格罗莫夫的Smal-Hirsh原理有关。特别是他发现了一些典型的例子，并发表了他的结果。此外，他和A.Kozlowski发现它与Vassiliev最近的工作有关，并提交了关于这项工作的预印本。最后，关于后一个主题，他注意到组结构的自同伦等价的SO（4），并提交了它。M.三泽研究了valation原则有关调和映射的角度来看，偏微分方程。特别是，他发现的存在性和regurality的p-调和映射及其梯度流，其文件很快出现。M.Fukuhara考虑了区域分解及其在数值计算中的应用。

项目成果

M.Guest, A.Kozlowski and K.Yamaguchi: "The homological stability of oriented configuration spaces" J.Math.Kyoto Univ.36,No4. 809-814 (1996)

M.Guest、A.Kozlowski 和 K.Yamaguchi：“定向构型空间的同调稳定性”J.Math.Kyoto Univ.36，No4。

H.Fujita, M.Fukuhara and N.Saito: "On the rate of convergence of iterations in the domain decomposition methods" Proc.third China-Japan Seminar on Numerical Anal.30-43. 1998

H.Fujita、M.Fukuhara 和 N.Saito：“论域分解方法中迭代的收敛速度”Proc.第三届中日数值分析研讨会.30-43。

H.Fujita, M.Fukuhara and N.Saito: "On the rate of convergence of iterations in the domain decomposition methods" Proc.third China-Japan Seminar on Numerical Analysis. 30-43 (1998)

H.Fujita、M.Fukuhara 和 N.Saito：“论域分解方法中迭代的收敛速度”Proc.第三届中日数值分析研讨会。

M.Guest, A.Kozlowski and K.Yamaguchi: "Stable splitting of the space of polynomials with roots of bounded multiplicity" J.Math.Kyoto Univ.38-2. 351-366 (1998)

M.Guest、A.Kozlowski 和 K.Yamaguchi：“具有有界重数根的多项式空间的稳定分裂”J.Math.Kyoto Univ.38-2。

H.Fujita, M.Fukuhara and N.Saito: "On the rate of convergence of itevations in the domain decompoition" Proc.third Japan-China joint seminar of numerical Math.予定. (1997)

H.Fujita、M.Fukuhara 和 N.Saito：“论域分解中的迭代收敛率”，第三届中日数值数学联合研讨会（1997 年）。