Mathematical Analysis of Stochastic and Dynamic Systems

随机和动态系统的数学分析

• 批准号: 01460007
• 负责人: FUJIKOSHI Yasunori
• 金额: $ 4.35万
• 依托单位: Hiroshima University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (B)
• 财政年份: 1989
• 资助国家: 日本
• 起止时间: 1989 至 1990
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-01460007/
• 关键词: Stochastic System and Dynamic System; Growth Curve Model; Fractal Set; Hausdorff Dimension; Reaction Diffusion System; Monge-Ampere Equation; Martin Boundary; Knot; エルゴ-ド理論; 自己相似性; 安定過程; ランダムフラクタル; 多粒子モデル; 分布の漸近展開; ホップ分岐; 中立型方程式; 非線形半群; 摂

We have investigated about stochastic systems and dynamic systems related to various fields of natural science and technology. We used mathematical tools from several fields, for instance, theory of probability, statistics, differential equation, functional analysis, geometry, numerical analysis and so on. We also applied our results to statistical physics and biological physics.1. Stochastic System :(1) Y. Fujikoshi : Asymptotic Expansions in Mathematical Statistics, Statistical Testing of the Growth Curve Model.(2) H. Totoki : Hausdorff Dimension of Random Fractals, Cross Product of Random Dynamics.2. Mathematical and Numerical Analysis of Dymanical Systems :(1) M. Mimura etc : Stability and Bifurcations in Bistable Reaction Diffusion Systems.(2) T. Kusano : Existence Theorem of Solutions for Monge-Ampere Equation.(3) S. Oharu : Non-linear Perturbation of Semi-groups.(4) F.-Y. Maeda : Martin Boundary of Harmonic Space.3. Geometric Approach of Dynamic Systems :(1) T. Matsumoto : Condition of Triviality for Knots of a Certain Kind.(2) K. Okamoto : Kirillov-Kostant Theory and Feymnann's path integral. These results are closely related to applied mathematics, for example, mathematical physics and biophysics.

我们已经研究了与自然科学和技术各个领域有关的随机系统和动态系统。我们使用了来自几个领域的数学工具，例如概率理论，统计，微分方程，功能分析，几何，数值分析等。我们还将结果应用于统计物理学和生物物理学1。随机系统：（1）Y. Fujikoshi：数学统计数据中的渐近扩展，生长曲线模型的统计测试。（2）H。Totoki：随机分形的Hausdorff尺寸，随机动力学的交叉产物。2。染色体系统的数学和数值分析：（1）M。mimura等：Bissable反应扩散系统中的稳定性和分叉。（2）T。Kusano：Monge-Ampere方程溶液的存在定理。 MAEDA：谐波空间的马丁边界3。动态系统的几何方法：（1）T。Matsumoto：某种结的琐事状况。（2）K。Okamoto：Kirillov-Kostant理论和Feymnann的路径积分。这些结果与应用数学密切相关，例如数学物理学和生物物理学。

项目成果

T.Matsumoto: "LusternikーSchnirelmann category and knot complement" J.Fac.Sci.Univ.Tokyo. 37. 103-107 (1990)

T.Matsumoto：“Lusternik-Schnirelmann 类别和结补”J.Fac.Sci.Univ.Tokyo 37. 103-107 (1990)。

H.Totoki: "A remark on random fractals" Hiroshima Mathematical Journal. 19. 563-566 (1989)

H.Totoki：“关于随机分形的评论”广岛数学杂志。

H. Totoki: "A Remark on Random Fractals" Hiroshima Math. J.19. 563-566 (1989)

H. Totoki：“随机分形的评论”广岛数学。

Y. Fujikoshi: "Error Bounds for Asymptotic Expansions of the Maximums of the Multivariatet - and f- Variables with Common Denominator" Hiroshima Math. J.19-2. 319-327 (1989)

Y. Fujikoshi：“具有公分母的多元变量和 f 变量的最大值渐近展开的误差界”广岛数学。

K. Okamoto: "Kirillov-Kostant Theory and Feyman path Integrals on Coadjoint Orbits I" Hokkaido Math. J.(1991)

K. Okamoto：“基里洛夫-科斯坦特理论和共伴轨道上的费曼路径积分 I”北海道数学。