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The investigations on the geometric structures on differentiable manifolds.

Research Project

Project/Area Number 62540040
Research Category

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

Allocation TypeSingle-year Grants
Research Field 代数学・幾何学
Research InstitutionKyoto University

Principal Investigator

TANDAI Kouichi  Kyoto University Yoshida College, Professor, 教養部, 教授 (90026732)

Co-Investigator(Kenkyū-buntansha) KASAHARA Koji  Kyoto University Yoshida College, Professor, 教養部, 教授 (70026748)
DATE Eturo  Kyoto University Yoshida College, Assistant Professor, 教養部, 助教授 (00107062)
KONO Norio  Kyoto University Yoshida College, Assistant Professor, 教養部, 助教授 (90028134)
ASANO Kiyoshi  Kyoto University Yoshida College, Professor, 教養部, 教授 (90026774)
宮本 宗実  京都大学, 教養部, 助教授 (00026775)
今西 英器  京都大学, 教養部, 助教授 (90025411)
Project Period (FY) 1987 – 1988
Project Status Completed (Fiscal Year 1988)
Budget Amount *help
¥2,200,000 (Direct Cost: ¥2,200,000)
Fiscal Year 1988: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 1987: ¥1,300,000 (Direct Cost: ¥1,300,000)
KeywordsCauchy-Kowalewski theorem / Nash-Moser theorem / Boltzmann equation / Arithmetic-geometric mean / Central limit theorem / Log-log law / 高木関数 / ガウス過程 / 自己相似関数 / 分布尾の限界
Research Abstract

Our research consists of the unfied study of geometry and analysis, in connection with the geometric structure on a differentiable manifold. Below we state the summary of the results obtained. In the fluid dynamics,which play fundamental role in physics as well as in technology, we view the fluid as continuum, for the equation of the fluid flow as well as its solutions their asymptotic behavior were clarified[1]. When the initial data is sufficiently close to an equilibrium state, it is shown that the Boltzmann equation has a unique global solution[4]. An extention of the non-linear Cauchy-Lowalewski theorem is obtained with a simplified proof[2]. An simplified and elegant treatment of Nash-Moser implict function theorem was given[3]. An alternate proof of Cox-Geppert theorem on arithmetic-geometric mean was obtaind[5]. As for the investigations relating to the probability theory, for the multiplicative system of random variables, functional central limit theorem and log-log law were proved[6]. Generalized Takagi functions are investigated[7],a necessary and sufficient condition for an self-affine function is absolutely continuous with respect to lebesgues measure and surface filling functions, defined by two self-affine functions, are discussed[8]. In connection with the statistical mechnics, the local height probabilities of certain integrable SOS-modelzare obtained in terms of modular forms[9]. The local height probabilities of certain solvable SOS-model are calculated in terms of modular functions[10]. The startriangle relations and some combinatorial identities[11]. As stated above, not only the contents of our research cover a vast variety of mathematical science, but also they are excellent results on the topics of up-to-date. The research is continued now inceantly, and therefore, further developments can be expected.

Report

(2 results)
  • 1988 Annual Research Report   Final Research Report Summary
  • Research Products

    (20 results)

All Other

All Publications (20 results)

  • [Publications] 浅野潔: Proc.Japan Acad.64. 102-105 (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] 浅野潔: Proc.Japan Acad.64. 139-142 (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] 浅野潔: T.T.S.P.16. 735-761 (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] 河野敬雄: Acta Math.Acad.Sci.Hungaricae.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] 河野敬雄: Acta Math.Acad.Sci.Hungaricae. 49. 315-324 (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] 河野敬雄: Japan J.Applied Math.5. 441-454 (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] 伊達悦朗: Phy.Rev.B.35. 2106-2108 (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] 伊達悦朗: Nucl.Rev.B.16. 231-273 (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] 伊達悦朗: Advsnced Studies Pure Math.16. 17-122 (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Asano, Kiyoshi: "A note on the abstract Cauchy-Kowaleuski theorem" Proc. Japan Acad.64. 102-105 (1988)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Asano, Kiyoshi: "A note on the Nash-Moser implict function theorem" Proc. Japan Acad.64. 139-142 (1988)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Asano, Kiyoshi: "On the gloval solutions of the initial boundary value problem for the Boltzmann equation with an external fouse" T.T.S.P.16. 735-761 (1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Kono, Norio: "Functional central limit and log log law for multiplicative" Acta Math. Acad. Sci. Hungaricae.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Kono, Norio: "On generalized Takagi functions" Acta Math. Acad. Sci. Hungaricae. 49. 315-324 (1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Kono, Norio: "On self-affine functions 11" Japan J. Applied Math.5. 441-454 (1988)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Date, Eturo: "Automorphic properties of local height probabilities for integrable solid-on-solid models" Phy. Rev. B.35. 2106-2108 (1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Date, Eturo: "Exactely solvable SOS models: Local height probabilities and theta functions identities" Nucl. Rev. B.16. 231-273 (1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Date, Eturo: "Exactly solvable SOS models 11 Proof of the star-triangle relation and combinatorial identities" Advanced Studies Pure Math.16. 17-122 (1988)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] 河野敬雄: Annals of Prof.(1987)

    • Related Report
      1988 Annual Research Report
  • [Publications] 河野敬雄: Japan Journal of Applied Mathematics.

    • Related Report
      1988 Annual Research Report

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Published: 1987-04-01   Modified: 2016-04-21  

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