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2012 Fiscal Year Final Research Report

Complementary study on monodromy preserving deformations and new special functions with integral representation

Research Project

  • PDF
Project/Area Number 21740118
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Global analysis
Research InstitutionUniversity of the Ryukyus

Principal Investigator

MANO Toshiyuki  琉球大学, 理学部, 准教授 (60378594)

Project Period (FY) 2009 – 2012
Keywordsモノドロミ / 積分表示 / 楕円曲線
Research Abstract

We studied properties of the Wirtinger integral which is represented in terms of a definite integral of a power product of theta functions. Moreover, we obtained research results regarding global behaviors of solutions to linear differential equations and detailed properties of monodromy preserving deformations.

  • Research Products

    (16 results)

All 2013 2012 2011 2010 2009

All Journal Article (6 results) (of which Peer Reviewed: 6 results) Presentation (10 results)

  • [Journal Article] On a generalization of Wirtinger's integral2012

    • Author(s)
      Toshiyuki Mano
    • Journal Title

      Kyushu Journal of Mathematics

      Volume: Vol.66 Pages: 435-447

    • Peer Reviewed
  • [Journal Article] Twisted cohomology and homology groups associated to the Riemann-Wirtinger integral2012

    • Author(s)
      Toshiyuki Mano and Humihiko Watanabe
    • Journal Title

      Proceedings of the American Mathematical Society

      Volume: Vol.140 Pages: 3867-3881

    • Peer Reviewed
  • [Journal Article] Determinant formula for solutions of the Garnier system and Pade approximation2012

    • Author(s)
      Tohiyuki Mano
    • Journal Title

      Journal of Physics A: Mathmatical and Theoretical

      Volume: Vol.45

    • DOI

      DOI:10.1088/1751-8113/45/13/135206

    • Peer Reviewed
  • [Journal Article] Monodromy preserving deformation of linear differential equations on a rational nodal curve2011

    • Author(s)
      Tohiyuki Mano
    • Journal Title

      Kumamoto Journal of Mathematics

      Volume: Vol.24 Pages: 1-32

    • Peer Reviewed
  • [Journal Article] Asymptotic behavior around a boundary point of the q-Painleve VI equation and its connection problem2010

    • Author(s)
      Tohiyuki Mano
    • Journal Title

      Nonlinearity

      Volume: Vol.23 Pages: 1585-1608

    • Peer Reviewed
  • [Journal Article] Studies on monodromy preserving deformation of linear differential equations on elliptic curves2009

    • Author(s)
      Toshiyuki Mano
    • Journal Title

      Journal of Mathematical Physics

      Volume: Vol.50

    • DOI

      DOI:10.1063/1.3204973

    • Peer Reviewed
  • [Presentation] Algebraic Painleve VI solutions derived from differential equations on C32013

    • Author(s)
      眞野智行、加藤満生
    • Organizer
      超幾何方程式研究会 2013
    • Place of Presentation
      神戸大学
    • Year and Date
      2013-01-06
  • [Presentation] Algebraic Painleve VI solutions derived from free divisors in C3 II2012

    • Author(s)
      眞 野 智 行
    • Organizer
      Workshop on Free Divisors and Differential Equations
    • Place of Presentation
      東京農工大学
    • Year and Date
      2012-11-09
  • [Presentation] ガルニエ系の解の行列式公式とパデ近似2011

    • Author(s)
      眞野智行
    • Organizer
      ガルニエ系の解の行列式公式とパデ近似
    • Place of Presentation
      信州大学
    • Year and Date
      2011-09-30
  • [Presentation] モノドロミ保存変形とパデ近似2011

    • Author(s)
      眞野智行
    • Organizer
      南九州代数系集会
    • Place of Presentation
      鹿児島大学
    • Year and Date
      2011-08-26
  • [Presentation] 高階線形微分方程式の合流操作とモノドロミ保存変形の退化2010

    • Author(s)
      眞野智行、川向洋之
    • Organizer
      Workshop on Accessory Parameters
    • Place of Presentation
      東京大学玉原国際セミナーハウス
    • Year and Date
      2010-10-11
  • [Presentation] 高階線形微分方程式の豪州操作とモノドロミ保存変形の退化2010

    • Author(s)
      眞野智行、川向洋之
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      名古屋大学
    • Year and Date
      2010-09-24
  • [Presentation] 一般 Wirtinger 積分から得られるフックス型方程式のスペクトルデータについて2010

    • Author(s)
      眞野智行
    • Organizer
      アクセサリー・パラメーター研究会
    • Place of Presentation
      熊本大学
    • Year and Date
      2010-03-17
  • [Presentation] Riemann-Wirtinger 積分とその応用2009

    • Author(s)
      眞野智行
    • Organizer
      微分方程式の総合的研究
    • Place of Presentation
      東京大学
    • Year and Date
      2009-12-18
  • [Presentation] q-PVI 系の境界点における漸近挙動と接続問題2009

    • Author(s)
      眞野智行
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      大阪大学
    • Year and Date
      2009-09-25
  • [Presentation] he Riemann-Wirtinger integral and its application2009

    • Author(s)
      Toshiyuki Mano
    • Organizer
      Third International Conference on Geometry and Quantization GEOQUANT
    • Place of Presentation
      University of Luxembourg
    • Year and Date
      2009-09-11

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Published: 2014-08-29  

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