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2007 Fiscal Year Final Research Report Summary

Analytic study of Painleve equations and a nelated clans of equation

Research Project

Project/Area Number 17340050
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Global analysis
Research InstitutionKeio University

Principal Investigator

SHIMOMURA Shun  Keio University, Facualry of Science and Technlogy, Prof. (00154328)

Co-Investigator(Kenkyū-buntansha) TANI Atusi  Keio University, Faculty of Science and Technology, Prof (90118969)
SHIOKAWA Iekata  Keio University, Faculty of Science and Technology, Honorary Prof (00015835)
KIMURA Hironobu  Kumamoto University, Faculty of Science and Technology, Professor (40161575)
HANAOKA Yoshishige  Kumamoto University, Faculty of Science and Technology, Professor (30208665)
ISHIGAKI Katsuya  Nippon Insitute of Technology, Faculty of Engineering, Associate Professor (60202991)
Project Period (FY) 2005 – 2007
KeywordsPainleve equations / Ganier system / quasi-Painleve property / Fibonacci numbers
Research Abstract

1. We found a class of nonlinear ordinary differential equations containing the first Painleve equation such that each equation admits the quasi-Painleve property, and discussed the global multi-valuedness of their solutions. We also found a similar clean of equations containing the second Painleve equation.
2. For solutions of the fifth Painleve equation, we examined value distribution in a sectonial domain. Under a certain condition, we proved the equi-distribution of values.
3. For a degenerate Garnier system corresponding to the first Painleve equation, we obtain an asymptotic solution around a singular locus.
4. We examined algebraic independence and algebraic relations for reciprocal rums of Fibonacci numbers. We also discussed their relation to zeta values.

  • Research Products

    (8 results)

All 2008 2007

All Journal Article (6 results) (of which Peer Reviewed: 3 results) Presentation (2 results)

  • [Journal Article] A Class of diffecestial equationd of PI-type toith the guasi-painleup propcity2007

    • Author(s)
      Shun Shimomura
    • Journal Title

      Aun.Mat.Pusa Appl 186

      Pages: 267-280

    • Description
      「研究成果報告書概要(和文)」より
    • Peer Reviewed
  • [Journal Article] Aiymptotic solntions of a degeneiate Gasnies oystem of the finst Poai leve type2007

    • Author(s)
      Shun Shimomura
    • Journal Title

      RIMS Kokyuroku Beisatsu B2

      Pages: 227-237

    • Description
      「研究成果報告書概要(和文)」より
    • Peer Reviewed
  • [Journal Article] Algelraic nelationg for reciprocal rums of Fibonacci numbeis2007

    • Author(s)
      Caisten Elsnes, Shun Shimomura Iehata Seriokawa
    • Journal Title

      Acta Arith 130

      Pages: 37-60

    • Description
      「研究成果報告書概要(和文)」より
    • Peer Reviewed
  • [Journal Article] A class of differential equations of PI-type with the quasi-Painleve property2007

    • Author(s)
      Shun, Shimomura
    • Journal Title

      Ann. Mat. Pma Appl 186

      Pages: 267-280

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Asymptotic solutions of a degemenate Gannier system of the tinst Painleve type2007

    • Author(s)
      Shun, Shimomura
    • Journal Title

      RIMS Kokyuroku Bessatsu B2

      Pages: 227-237

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Algelraic nelations for recipnocal rums of Fibonacci numbers2007

    • Author(s)
      Cansten Elsner, Shun Shimomura, Iekata Shiokawa
    • Journal Title

      Acta Arith 130

      Pages: 37-60

    • Description
      「研究成果報告書概要(欧文)」より
  • [Presentation] 角領域における値分布論とその応用2008

    • Author(s)
      下村 俊
    • Organizer
      日本数学会(函数論分科会特別講演)
    • Place of Presentation
      近畿大学
    • Year and Date
      2008-03-24
    • Description
      「研究成果報告書概要(和文)」より
  • [Presentation] Shun, Shimomura2008

    • Author(s)
      Shun, Shimomura
    • Organizer
      Annual Mectiny The Mathematical Society of Japan
    • Place of Presentation
      Kinki University
    • Year and Date
      2008-03-24
    • Description
      「研究成果報告書概要(欧文)」より

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Published: 2010-02-04  

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