Applied Geometry

应用几何

• 批准号: 07404002
• 负责人: MATUMOTO Takao
• 金额: $ 16.38万
• 依托单位: HIROSHIMA UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (A)
• 财政年份: 1995
• 资助国家: 日本
• 起止时间: 1995 至 1998
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-07404002/
• 关键词: Visible geometry; 3- amd 4-manifolds; Information geomtry; Comutational geometry; Boundary surface; Deformation of surfaces; 2-dimensional knot; 見える 幾何学; 3次元空間; 曲線・曲面; 情報幾何; 計算幾何; 力学系; 4次元空間; 幾何学センター; 境界面の構造; 曲線の曲面

We are seeking how to study the applied geometry, by organizing the applied geometry seminar and symposium "Visible Geometry". The new topics and methods in the study of curves and surfaces in 3-space, the structure of the boundary surface and its move, the structure of 3-dimensional or 4-dimensional manifolds, dynamical approach, algebraic and algorithmic approach to geometry, information geometric aspect are the main contents of our recent study.Matumoto investigates the deformation of generic surfaces in 3-space by the visible geometric methods with applications to the study of surfaces in 4-space especially of the 2-dimensionza1 knots, besides the study of information and computational geometry. Agaoka classified the tilings of the sphere by the rectangle triangles. Saeki is interested in the global study of the manifolds and mappings from the view point of singularity theory, and found a new topological meaning of curvature and tangential developping surface of the curve in 3-spac … More e. Yoshida found a relation between the boundary and characteristic classes. Nakayama extends the notion of Lyapunov function and studied the space of orbits. Doi handles the counting problem of plane curves. Harada defined the curvature for the discrete data to approximate efficiently by a polygonal curve and proposed a method to remove the unnecessary data. Tabata is working on the finite element analysis with some geometric considerations. Nishiura improves the softwear to pursue the branching solutions and studies the self-replicating dynamics. Irie studies the time evolution of space-structure and strategy for a population dynamics. Muta investigated the quantum theoretic phase structures in the curved spacetime. Tanisaki studied the geometric structure of quantum group by D-module. Imaoka studies some algorithms for the various invariants in topology. In information geometric aspects Matumoto characterized the statistical manifold by two point function and Fujikoshi studies the asymptotic expansions and error estimates in statistics. Less

我们正在寻求如何研究应用几何，通过组织应用几何研讨会和专题讨论会“可见几何”。介绍了三维空间中曲线曲面研究的新课题和新方法，边界曲面的结构及其移动，三维或四维流形的结构，动力学方法，几何的代数和算法方法，Matumoto研究了三维空间中一般曲面的变形问题，空间的可视化几何方法，并应用于研究曲面在4-空间，特别是2-dimensionza1结，除了研究信息和计算几何。阿高卡用矩形三角形对球面的镶嵌进行了分类。Saeki从奇点理论的角度对流形和映射的整体性进行了研究，发现了三维空间中曲线的曲率和切向展曲面的新的拓扑意义， ...更多信息 e.吉田发现了边界和特征类之间的关系。Nakayama扩展了李雅普诺夫函数的概念，并研究了轨道空间。Doi处理平面曲线的计数问题。Harada定义了离散数据的曲率，并提出了一种去除不必要数据的方法。Tabata正在进行有限元分析，并考虑一些几何因素。Nishiura改进了软件以寻求分支解决方案，并研究了自复制动力学。入江研究了种群动力学的空间结构和策略的时间演化。穆塔研究了弯曲时空中的量子理论相结构。谷崎用D-模研究了量子群的几何结构。Imaoka研究了拓扑学中各种不变量的一些算法。在信息几何方面，Matumoto用两点函数刻画了统计流形，Fujikoshi研究了统计流形的渐近展开和误差估计。少

项目成果

Mitsunori Imaoka: "A solution of Sylvester's matrix equation" Intern.J.Math.Edu.in Sci.& Tech.27. 471-473 (1996)

Mitsunori Imaoka：“西尔维斯特矩阵方程的解”Intern.J.Math.Edu.in Sci。

藤越 康祝: "Sharp error bounds for asymptotic expansion of the distribution functions of scale mixture" Ann.Inst.Statist.Math.49. 285-297 (1997)

Yasuyuki Fujikoshi：“尺度混合分布函数的渐近展开的锐误差界”Ann.Inst.Statist.Math.49 (1997)。

牟田泰三: "電磁力学" 岩波書店, 206 (1993)

牟田泰三：《电动力学》岩波书店，206（1993）

原田耕一: "Approximation polygonal curves in two and three dimensions" Graphical Models and Image Processing. 60. 222-225 (1998)

Koichi Harada：“二维和三维近似多边形曲线”图形模型和图像处理。60. 222-225 (1998)。

松本 尭生: "Classification of closed oriented 4-manifolds modulo connected sum with simply connected manifolds" Hiroshima Mathematical Journal. 28. 207-212 (1998)

Takao Matsumoto：“具有简单连通流形的闭向 4 流形模连通和的分类”广岛数学杂志 28. 207-212 (1998)。