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Mathematical Analysis of Stochastic and Dynamic Systems

Research Project

Project/Area Number 01460007
Research Category

Grant-in-Aid for General Scientific Research (B)

Allocation TypeSingle-year Grants
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionHiroshima University

Principal Investigator

FUJIKOSHI Yasunori (1990)  Department of Mathematics, Professor, 理学部, 教授 (40033849)

十時 東生 (1989)  広島大学, 理学部, 教授 (70027366)

Co-Investigator(Kenkyū-buntansha) MATSUMOTO Takao  Department of Mathematics, Associate Professor, 理学部, 助教授 (50025467)
MAEDA Fumi-yuki  Department of Mathematics, Professor, 理学部, 教授 (10033804)
KUSANO Takasi  Department of Mathematics, Professor, 理学部, 教授 (70033868)
MIMURA Masayasu  Department of Mathematics, Professor., 理学部, 教授 (50068128)
TAKENAKA Shigeo  Department of Mathematics, Associate Professor, 理学部, 助教授 (80022680)
大春 愼之助  広島大学, 理学部, 教授 (40063721)
藤越 康祝  広島大学, 理学部, 教授 (40033849)
谷口 礼偉  広島大学, 理学部, 助手 (40157970)
Project Period (FY) 1989 – 1990
Project Status Completed (Fiscal Year 1990)
Budget Amount *help
¥6,800,000 (Direct Cost: ¥6,800,000)
Fiscal Year 1990: ¥3,100,000 (Direct Cost: ¥3,100,000)
Fiscal Year 1989: ¥3,700,000 (Direct Cost: ¥3,700,000)
KeywordsStochastic 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 / 摂動論
Research Abstract

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.

Report

(3 results)
  • 1990 Annual Research Report   Final Research Report Summary
  • 1989 Annual Research Report
  • Research Products

    (23 results)

All Other

All Publications (23 results)

  • [Publications] Y.Fujikoshi: "Error bounds for asymptotic expansions of the maximums of the multivariate tー and Fー variables with common denominator" Hiroshima Math.J.19. 319-327 (1989)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] M.Mimura: "Global bifurcation phenomena of traveling wave solutions for some bistable reactionーdiffusion systems" Nonlinear Analysis;Theory,Methods and Appl.13. 507-526 (1989)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] T.Kusano: "Existence theorems for elliptic MongeーAmpere equations in the plane" Differential and Integral Equations. 3. 487-493 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] S.Oharu: "Characterization of nonlinear semigroups associated with semilinear evolution equations" Trans.Amer.Math.Soc.311. 593-619 (1989)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] K.Okamoto: "KirillovーKostant theory and Feynman path integrals on coadjoint orbits I" Hokkaido Math.J. (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] 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)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] H. Totoki: "A Remark on Random Fractals" Hiroshima Math. J.19. 563-566 (1989)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] M. Mimura: "Global Bifurcation Phenomena of Traveling Wave Solutions for Some Bistable Reaction - Diffusion Systems" Nonlinear Analysis ; Theory, Methods and Appl.13. 507-526 (1989)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] T. Kusano: "Existence Theorems for Elliptic Monge - Ampere Equations in the Plane" Differential and Integral Equations. 3. 487-493 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] S. Oharu: "Characterization of Nonlinear Semigroups Associated with Semilinear Evolution Equations" Trans. Amer. Math. Soc.311-2. 593-619 (1989)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] K. Okamoto: "Kirillov-Kostant Theory and Feyman path Integrals on Coadjoint Orbits I" Hokkaido Math. J.(1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] Y.Fujikoshi: "The growth curve model with an autoregressive covariance structure" Ann.Inst.Statist.Math.42. 533-542 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] S.Takenaka: "On determinisms of symmetric α stable processes of generalized Chentsov type" preprint. (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] M.Mimura: "Pattern dynamics in excitable reactionーdiffusion media,in “Formation dynamics and statistics of patterns"" World Scientific Press. 55-112 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] T.Kusano: "Existence theorems for elliptic MongeーAmpe^^`re equations in the plane" Differential and Integral Equations. 3. 487-493 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] F.ーY.Maeda: "Martin boundary of a harmonic space with adjoint structure and its applications" Hiroshima Mathematical Journal. 21. 163-186 (1991)

    • Related Report
      1990 Annual Research Report
  • [Publications] T.Matsumoto: "LusternikーSchnirelmann category and knot complement" J.Fac.Sci.Univ.Tokyo. 37. 103-107 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] H.Totoki: "A remark on random fractals" Hiroshima Mathematical Journal. 19. 563-566 (1989)

    • Related Report
      1989 Annual Research Report
  • [Publications] H.Yaguchi: "Entropy analysis of a nearest neighbor attractive/repulsive exclusion process on one-dimensional lattices" Annals of Probability. 18. (1990)

    • Related Report
      1989 Annual Research Report
  • [Publications] Y.Fujikoshi: "Error bounds for asymptotic expansions of the maximums of the multivariate t- and F- variables with common denominator" Hiroshima Mathematical Journal. 19. 319-327 (1989)

    • Related Report
      1989 Annual Research Report
  • [Publications] Y.Nishiura: "Layer oscillations in reaction-diffusion systems" Siam Journal of Applied Mathematics. 49. 481-514 (1989)

    • Related Report
      1989 Annual Research Report
  • [Publications] J.Jaros: "Sufficient conditions for oscillations in higher order linear functional differential equations of neutral type" Japanese Journal of Mathematics. 15. 415-432 (1989)

    • Related Report
      1989 Annual Research Report
  • [Publications] S.Oharu: "Characterization of nonlinear semigroups associated with semilinear evolution equations" Transaction of American Mathematical Society. 311. 593-619 (1989)

    • Related Report
      1989 Annual Research Report

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Published: 1989-04-01   Modified: 2016-04-21  

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