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Rigidity and prolongability of differential equations and the study of global structure

Research Project

Project/Area Number 21340038
Research Category

Grant-in-Aid for Scientific Research (B)

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

Principal Investigator

HARAOKA Yoshishige  熊本大学, 自然科学研究科, 教授 (30208665)

Co-Investigator(Renkei-kenkyūsha) YOKOYAMA Toshiaki  千葉工業大学, 工学部, 教授 (30210636)
KATO Mitsuo  琉球大学, 教育学部, 教授 (50045043)
OSHIMA Toshio  城西大学, 理学部, 教授 (50011721)
TANABE Susumu  Galatasaray 大学, 教授 (90432997)
KIMURA Hironobu  熊本大学, 大学院・自然科学研究科, 教授 (40161575)
SHIMENO Nobukazu  関西学院大学, 理工学部, 教授 (60254140)
SADAHIRO Taizo  津田塾大学, 学芸学部, 准教授 (00280454)
MIMACHI Katsuhisa  東京工業大学, 大学院・理工学研究科, 教授 (40211594)
KATO Fumiharu  熊本大学, 大学院・自然科学研究科, 教授 (50294880)
Project Period (FY) 2009-04-01 – 2014-03-31
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥16,250,000 (Direct Cost: ¥12,500,000、Indirect Cost: ¥3,750,000)
Fiscal Year 2013: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2012: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2011: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2010: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2009: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Keywords大域解析 / 複素領域における微分方程式 / モノドロミー / 完全積分可能系 / アクセサリー・パラメーター / 超曲面 / rigid局所系 / 接続係数 / middle convolution / 解析学 / 微分方程式
Research Abstract

We constructed a framework for the global study of linear ordinary differential equations and holonomic systems in several variables by using the notion of rigidity and spectral types and the operation called middle convolution. We succeeded to define the middle convolution for holonomic systems, which brings a new structure on the moduli space of holonomic systems. In some cases, middle convolution connects an ordinary differential equation to a holonomic system, and then we can compare various structures among ODEs and holonomic systems.

Report

(6 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Annual Research Report
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • Research Products

    (145 results)

All 2014 2013 2012 2011 2010 2009 Other

All Journal Article (51 results) (of which Peer Reviewed: 43 results) Presentation (83 results) (of which Invited: 13 results) Book (5 results) Remarks (6 results)

  • [Journal Article] Recursive calculation of connection formulas for systems of differential equations of Okubo normal form2014

    • Author(s)
      Toshiaki Yokoyama
    • Journal Title

      Journal of Dynamical and Control Systems

      Volume: 20 Pages: 241-292

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] UNIFORMIZATION SYSTEMS OF EQUATIONS WITH SINGULARITIES ALONG THE DISCRIMINANT SETS OF COMPLEX REFLECTION GROUPS OF RANK THREE2014

    • Author(s)
      Mitsuo Kato and Jiro Sekiguchi
    • Journal Title

      Kyushu Journal of Mathematics

      Volume: 68 Issue: 1 Pages: 181-221

    • DOI

      10.2206/kyushujm.68.181

    • NAID

      130004941524

    • ISSN
      1340-6116, 1883-2032
    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] A generalization of carries processes and Eulerian numbers2014

    • Author(s)
      Nakano, F., Sadahiro, T
    • Journal Title

      Adv. in Appl. Math

      Volume: 53 Pages: 28-43

    • DOI

      10.1016/j.aam.2013.09.005

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Prolongability of ordinary differential equations2013

    • Author(s)
      Yoshishige Haraoka
    • Journal Title

      Journal of Nonlinear Mathematical Physics

      Volume: 20 Supplement 1 Issue: Supplement 1 Pages: 70-84

    • DOI

      10.1080/14029251.2013.862435

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Classification of Fuchsian systems and their connection problem2013

    • Author(s)
      Toshio Oshima
    • Journal Title

      RIMS Kokyuroku Bessatsu

      Volume: 37 Pages: 163-192

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] The connection problem associated with a Selberg type integral and the q-Racah polynomials2013

    • Author(s)
      Katsuhisa Mimachi
    • Journal Title

      Forum Math

      Volume: 25 Pages: 1127-1179

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] The densest lattices in PGL3(Q2)2013

    • Author(s)
      Daniel Allcock, Fumiharu Kato
    • Journal Title

      Adv. Math.

      Volume: 242 Pages: 102-115

    • DOI

      10.1016/j.aim.2013.04.003

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Hitting matrix and domino tiling with diagonal impurities2013

    • Author(s)
      Nakano, F., Sadahiro, T
    • Journal Title

      J. Stat. Phys

      Volume: 151(no. 6) Issue: 6 Pages: 1035-1055

    • DOI

      10.1007/s10955-013-0744-6

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Regular coordinates and deformation equations for Fuchsian systems2012

    • Author(s)
      Yoshishige Haraoka
    • Journal Title

      Banach Center Publications

      Volume: 97 Pages: 39-58

    • DOI

      10.4064/bc97-0-3

    • Related Report
      2013 Final Research Report 2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A classification of roots of symmetric Kac- Moody root systems and its application2012

    • Author(s)
      Kazuki Hiroe and Toshio Oshima
    • Journal Title

      Springer Proceedings in Mathematics and Statistics

      Volume: 40 Pages: 195-241

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] CONNECTION FORMULAS AND IRREDUCIBILITY CONDITIONS FOR APPELL&rsquo;S <i>F</i><sub>2</sub>2012

    • Author(s)
      Mitsuo Kato
    • Journal Title

      Kyushu Journal of Mathematics

      Volume: 66 Issue: 2 Pages: 325-363

    • DOI

      10.2206/kyushujm.66.325

    • NAID

      130002543079

    • ISSN
      1340-6116, 1883-2032
    • Related Report
      2013 Final Research Report 2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Topological theory for Selberg type integral associated with rigid Fuchsian systems2012

    • Author(s)
      Yoshishige Haraoka and Sho Hamaguchi
    • Journal Title

      Math. Ann

      Volume: 353 Issue: 4 Pages: 1239-1271

    • DOI

      10.1007/s00208-011-0717-5

    • Related Report
      2013 Final Research Report 2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Middle convolution for completely integrable systems with logarithmic singularities along hyperplane arrangement2012

    • Author(s)
      Yoshishige Haraoka
    • Journal Title

      Adv. Stud. Pure Math

      Volume: 62 Pages: 109-136

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Solutions for some families of Fuchsian differential equations free from accessory parameters in terms of the integral of Euler type2012

    • Author(s)
      Katsuhisa Mimachi
    • Journal Title

      Adv. Stud. Pure Math

      Volume: 62 Pages: 233-260

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] MONODROMY REPRESENTATIONS ASSOCIATED WITH THE GAUSS HYPERGEOMETRIC FUNCTION USING INTEGRALS OF A MULTIVALUED FUNCTION2012

    • Author(s)
      Katsuhisa Mimachi
    • Journal Title

      Kyushu Journal of Mathematics

      Volume: 66 Issue: 1 Pages: 35-60

    • DOI

      10.2206/kyushujm.66.35

    • NAID

      130002543071

    • ISSN
      1340-6116, 1883-2032
    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] IRREDUCIBILITY AND REDUCIBILITY OF LAURICELLA' S SYSTEM OF DIFFERENTIAL EQUATIONS <i>E</i><sub>D</sub> AND THE JORDAN-POCHHAMMER DIFFERENTIAL EQUATION <i>E</i><sub>JP</sub>2012

    • Author(s)
      Katsuhisa Mimachi
    • Journal Title

      Kyushu Journal of Mathematics

      Volume: 66 Issue: 1 Pages: 61-87

    • DOI

      10.2206/kyushujm.66.61

    • NAID

      130002543072

    • ISSN
      1340-6116, 1883-2032
    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] MONODROMY REPRESENTATIONS ASSOCIATED WITH APPELL' S HYPERGEOMETRIC FUNCTION <i>F</i><sub>1</sub> USING INTEGRALS OF A MULTIVALUED FUNCTION2012

    • Author(s)
      Katsuhisa Mimachi
    • Journal Title

      Kyushu Journal of Mathematics

      Volume: 66 Issue: 1 Pages: 89-114

    • DOI

      10.2206/kyushujm.66.89

    • NAID

      130002543073

    • ISSN
      1340-6116, 1883-2032
    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Un anneau de deformation universel et conducteur superieur2012

    • Author(s)
      Kato, F.
    • Journal Title

      Proc. Japan. Acad. Ser. A Math. Sci.

      Volume: 88 Issue: 2 Pages: 25-27

    • DOI

      10.3792/pjaa.88.25

    • Related Report
      2012 Annual Research Report 2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Middle convolution for completely integrable systems with logarithmic singularities along hyperplane arrangement2012

    • Author(s)
      Yoshishie Haraoka
    • Journal Title

      Advanced Studies in Pure Mathematics

      Volume: 62 Pages: 109-136

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A (-β)-expansion associated to Sturmian sequences2012

    • Author(s)
      Nakano, F., Sadahiro, T
    • Journal Title

      Integers

      Volume: 12(no. 4) Issue: 4 Pages: 571-599

    • DOI

      10.1515/integers-2011-0123

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On a problem of arrangements related to the hypergeometric integrals of confluent type2012

    • Author(s)
      Hironobu Kimura
    • Journal Title

      Advanced Studies in Pure Mathematics

      Volume: 62 Pages: 137-155

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Solutions for some families of Fuchsian differential equations free from accessory parameters in terms of the integral of Euler type2012

    • Author(s)
      Katsuhisa Mimachi
    • Journal Title

      Advanced Studies in Pure Mathematics

      Volume: 62 Pages: 233-260

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A connection problem for Simpson's even family of rank four2011

    • Author(s)
      Yoshishige Haraoka and Katsuhisa Mimachi
    • Journal Title

      Funk. Ekvac

      Volume: 54 Pages: 495-515

    • NAID

      130001271656

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] 大域解析可能なFuchs 型方程式2011

    • Author(s)
      原岡喜重
    • Journal Title

      数学

      Volume: 63 Pages: 257-280

    • NAID

      10029849848

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] On Wronskian determinant formulas of the general hypergeometric functions2011

    • Author(s)
      Hironobu Kimura
    • Journal Title

      Tokyo J. Math

      Volume: 34 Pages: 507-524

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] A connection problem for Simpson's even family of rank four2011

    • Author(s)
      Yoshishige Haraoka
    • Journal Title

      Funkcialaj Ekvacioj

      Volume: 54 Pages: 495-515

    • NAID

      130001271656

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 大域解析可能なFuchs型方程式2011

    • Author(s)
      原岡喜重
    • Journal Title

      数学

      Volume: 63 Pages: 257-280

    • NAID

      10029849848

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] THE HYPERGEOMETRIC DIFFERENTIAL EQUATION 3E2 WITH CUBIC CURVES AS SCHWARZ IMAGES2011

    • Author(s)
      Mitsuo Kato
    • Journal Title

      Kyushu Journal of Mathematics

      Volume: 65 Issue: 1 Pages: 55-74

    • DOI

      10.2206/kyushujm.65.55

    • NAID

      130000884045

    • ISSN
      1340-6116, 1883-2032
    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] SCHWARZ IMAGES OF ALGEBRAIC 3F22011

    • Author(s)
      Mitsuo Kato
    • Journal Title

      Kyushu Journal of Mathematics

      Volume: 65 Issue: 2 Pages: 299-333

    • DOI

      10.2206/kyushujm.65.299

    • NAID

      130001444149

    • ISSN
      1340-6116, 1883-2032
    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On Hausdorff completions of commutative rings in rigid geometry2011

    • Author(s)
      Kazuhiro Fujiwara
    • Journal Title

      Journal of Algebra

      Volume: 322 Issue: 1 Pages: 293-321

    • DOI

      10.1016/j.jalgebra.2011.02.001

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Topological rings in rigid geometry2011

    • Author(s)
      Fumiharu Kato
    • Journal Title

      LMS Lecture Notes series, Cambridge University Press

      Volume: 383 Pages: 103-144

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Broadcastings and digit tilings on three-dimensional torus networks2011

    • Author(s)
      Ryotaro Okazaki
    • Journal Title

      Theoretical Computer Science

      Volume: 412 Pages: 307-319

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] (-β)-展開の性質について2011

    • Author(s)
      中野史彦
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 1725 Pages: 92-105

    • Related Report
      2010 Annual Research Report
  • [Journal Article] Generating systems for finite irreducible complex reflection groups2010

    • Author(s)
      Yoshishige Haraoka and Mitsuo Kato
    • Journal Title

      Funk. Ekvac

      Volume: 53 Pages: 435-488

    • NAID

      130000419153

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Heckman-Opdam hypergeometric functions and their specializations2010

    • Author(s)
      Toshio Oshima and Nobukazu Shimeno
    • Journal Title

      RIMS Kokyuroku Bessatsu

      Volume: B20 Pages: 129-162

    • Related Report
      2013 Final Research Report 2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Generating systems for finite irreducible complex reflection groups2010

    • Author(s)
      Yoshishige Haraoka
    • Journal Title

      Funkcialaj Ekvacioj

      Volume: 53 Pages: 435-488

    • NAID

      130000419153

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Reflection subgroups of the monodromy groups of Appell's F_42010

    • Author(s)
      Mitsuo Kato
    • Journal Title

      Kyushu Journal of Mathematics

      Volume: 64 Pages: 281-296

    • NAID

      130000441861

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] (概)自由因子を定める大波面について2010

    • Author(s)
      田邊晋
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 1707 Pages: 76-93

    • Related Report
      2010 Annual Research Report
  • [Journal Article] Local move connectedness of domino tilings with diagonal impurities2010

    • Author(s)
      Fumihiko Nakano
    • Journal Title

      Discrete Mathematics 310

      Pages: 1918-1931

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A bijection theorem for domino tiling's with diagonal impurities2010

    • Author(s)
      Fumihiko Nakano
    • Journal Title

      Journal of Statistical Physics (掲載決定)

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 微分方程式の延長とmiddle convolution2009

    • Author(s)
      原岡喜重
    • Journal Title

      数理解析研究所講究録

      Volume: 1662 Pages: 88-94

    • Related Report
      2013 Final Research Report
  • [Journal Article] Hypergeometric groups for complete intersections associated to Calabi-Yau varieties in weighted projective spaces2009

    • Author(s)
      田邊晋
    • Journal Title

      数理解析研究所講究録

      Volume: 1662 Pages: 1-19

    • Related Report
      2013 Final Research Report
  • [Journal Article] 微分方程式の延長と middle convolution2009

    • Author(s)
      原岡喜重
    • Journal Title

      数理解析研究所講究録 1662

      Pages: 88-94

    • Related Report
      2009 Annual Research Report
  • [Journal Article] General Schlesinger systems and their hypergeometric type solutions2009

    • Author(s)
      木村弘信
    • Journal Title

      数理解析研究所講究録 1662

      Pages: 218-230

    • Related Report
      2009 Annual Research Report
  • [Journal Article] Hypergeometric groups for complete intersections associated to Calabi-Yau varieties in weighted projective spaces2009

    • Author(s)
      田邊晋
    • Journal Title

      数理解析研究所講究録 1662

      Pages: 158-175

    • Related Report
      2009 Annual Research Report
  • [Journal Article] Wave front propagation and the discriminant of a tame polynomial2009

    • Author(s)
      田邊晋
    • Journal Title

      数理解析研究所講究録 1664

      Pages: 1-19

    • Related Report
      2009 Annual Research Report
  • [Journal Article] Middle convolution for completely integrable systems with logarithmic singularities along hyperplane arrangement

    • Author(s)
      Yoshishige Haraoka
    • Journal Title

      Advanced Studies in Pure Mathematics "Proceedings of MSJ-SI 2009"

      Volume: (未定 掲載決定)

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A connection problem for Simpson's even family of rank four

    • Author(s)
      Yoshishige Haraoka
    • Journal Title

      Funkcialaj Ekvacioj

      Volume: (未定 掲載決定)

    • NAID

      130001271656

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On Wronskian determinant formulas of the general hypergeometric functions

    • Author(s)
      Hironobu Kimura
    • Journal Title

      Tokyo Journal of Mathematics

      Volume: (未定 掲載決定)

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On a problem of arrangements related to the hypergeometric integrals of confluent type

    • Author(s)
      Hironobu Kimura
    • Journal Title

      Advanced Studies in Pure Mathematics "Proceedings of MSJ-SI 2009"

      Volume: (未定 掲載決定)

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Reflection subgroups of the monodromy groups of Appell's F_4

    • Author(s)
      Mitsuo Kato
    • Journal Title

      Kyushu Journal of Mathematics (掲載決定)

    • NAID

      130000441861

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Presentation] ゲージ理論とアクセサリー・パラメーター2014

    • Author(s)
      原岡喜重
    • Organizer
      研究集会「アクセサリー・パラメーター研究会」
    • Place of Presentation
      熊本大学理学部
    • Year and Date
      2014-03-08
    • Related Report
      2013 Annual Research Report 2013 Final Research Report
  • [Presentation] Rigid holonomic systems2014

    • Author(s)
      原岡喜重
    • Organizer
      研究集会「第9回代数・解析・幾何学セミナー」
    • Place of Presentation
      鹿児島大学理学部
    • Year and Date
      2014-02-17
    • Related Report
      2013 Final Research Report
  • [Presentation] 多項式係数の線型常微分方程式2013

    • Author(s)
      大島利雄
    • Organizer
      日本数学会秋期総合分科会総合講演
    • Place of Presentation
      愛媛大学
    • Year and Date
      2013-09-25
    • Related Report
      2013 Final Research Report
  • [Presentation] Rigidity of local systems over complement spaces2013

    • Author(s)
      Yoshishige Haraoka
    • Organizer
      研究集会「Moduli Theory in Algebraic Geometry and Integrable Systems」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2013-09-20
    • Related Report
      2013 Annual Research Report 2013 Final Research Report
  • [Presentation] Holonomic 系に対するmiddle convolution2013

    • Author(s)
      原岡喜重
    • Organizer
      研究集会「アクセサリー・パラメーター研究会」
    • Place of Presentation
      東京大学玉原国際セミナーハウス
    • Year and Date
      2013-09-17
    • Related Report
      2013 Final Research Report
  • [Presentation] On construction of holonomic systems2013

    • Author(s)
      Yoshishige Haraoka
    • Organizer
      研究集会「Global Study of Differential Equations in the Complex Domain, Polish-Japanese research group」
    • Place of Presentation
      Banach Center, Warsaw, Poland
    • Year and Date
      2013-09-02
    • Related Report
      2013 Annual Research Report 2013 Final Research Report
  • [Presentation] Rigidity of holonomic systems in several variables2013

    • Author(s)
      Yoshishige Haraoka
    • Organizer
      研究集会「Formal and Analytic Solutions of Differential, Difference and Discrete Equations 」
    • Place of Presentation
      Mathematical Research and Conference Center, Bedlewo, Poland
    • Year and Date
      2013-08-27
    • Related Report
      2013 Final Research Report
  • [Presentation] 完全積分可能系と超曲面の補空間の幾何2013

    • Author(s)
      原岡喜重
    • Organizer
      研究集会「代数多様体のトポロジーとその周辺」
    • Place of Presentation
      北海道大学理学部
    • Year and Date
      2013-08-21
    • Related Report
      2013 Annual Research Report 2013 Final Research Report
  • [Presentation] Rigidity of local systems on P^nhypersurface2012

    • Author(s)
      Yoshishige Haraoka
    • Organizer
      研究集会「Workshop on Free Divisors and Differential Equations」
    • Place of Presentation
      東京農工大学
    • Year and Date
      2012-11-06
    • Related Report
      2013 Final Research Report
  • [Presentation] Accessory parameters in degenerations2012

    • Author(s)
      加藤文元
    • Organizer
      研究集会「Symposium on Arithmetic & Geometry」
    • Place of Presentation
      九州大学
    • Year and Date
      2012-06-02
    • Related Report
      2013 Final Research Report
  • [Presentation] Riemann球面上の代数的線型常微分法停止医2012

    • Author(s)
      大島利雄
    • Organizer
      日本数学会、特別講演
    • Place of Presentation
      東京理科大学(招待講演)
    • Year and Date
      2012-03-28
    • Related Report
      2011 Annual Research Report
  • [Presentation] アクセサリー・パラメーターと退化2012

    • Author(s)
      加藤文元
    • Organizer
      研究集会「アクセサリー・パラメーター研究会」
    • Place of Presentation
      熊本大学理学部
    • Year and Date
      2012-03-15
    • Related Report
      2013 Final Research Report
  • [Presentation] アクセサリー・パラメーターと退化2012

    • Author(s)
      加藤文元
    • Organizer
      アクセサリー・パラメーター研究会
    • Place of Presentation
      熊本大学理学部(招待講演)
    • Year and Date
      2012-03-15
    • Related Report
      2011 Annual Research Report
  • [Presentation] Ordinary differential equations and Kac-Moody root systems2012

    • Author(s)
      Toshio Oshima
    • Organizer
      Conference-Lie groups : structure, actions and representations
    • Place of Presentation
      Bochum, Germany(招待講演)
    • Year and Date
      2012-01-12
    • Related Report
      2011 Annual Research Report
  • [Presentation] 多項式係数の線型常微分方程式と特殊関数2012

    • Author(s)
      大島利雄
    • Organizer
      研究集会「微分方程式の総合的研究」
    • Place of Presentation
      京都大学理学部
    • Related Report
      2013 Final Research Report
  • [Presentation] Fuchs 型方程式の接続問題I, II2012

    • Author(s)
      原岡喜重
    • Organizer
      研究集会「ボレル総和法と接続問題」
    • Place of Presentation
      広島大学理学部
    • Related Report
      2013 Final Research Report
  • [Presentation] Fuchs型方程式の接続問題I、II2012

    • Author(s)
      原岡喜重
    • Organizer
      ボレル総和法と接続問題
    • Place of Presentation
      広島大学理学部(招待講演)
    • Related Report
      2011 Annual Research Report
  • [Presentation] Adic formal algebraic spaces of finite ideal type and rigid GAGA on algebraic spaces2011

    • Author(s)
      Fumiharu Kato
    • Organizer
      2011 Taiwan-Japan Workshop on Arithmetic Algebraic Geometry and Related Topics
    • Place of Presentation
      Institute of Mathematics, Academia Sinica,台湾(招待講演)
    • Year and Date
      2011-11-18
    • Related Report
      2011 Annual Research Report
  • [Presentation] 代数的線形常微分方程式とKac-Moodyルート系2011

    • Author(s)
      大島利雄
    • Organizer
      2011年表現論シンポジウム
    • Place of Presentation
      みなべ町、和歌山(招待講演)
    • Year and Date
      2011-11-09
    • Related Report
      2011 Annual Research Report
  • [Presentation] Regular coordinates and reduction of deformation equations for Fuchsian systems2011

    • Author(s)
      Yoshishige Haraoka
    • Organizer
      研究集会「Formal and Analytic Solutions of Differential Equations II」
    • Place of Presentation
      Mathematical Research and Conference Center, Bedlewo, Poland
    • Year and Date
      2011-08-11
    • Related Report
      2013 Final Research Report
  • [Presentation] Regular coordinate and reduction of deformation equations for Fuchsian systems2011

    • Author(s)
      Yoshishige Haraoka
    • Organizer
      Formal and Analytic Solutions of Differential Equations II
    • Place of Presentation
      Mathematical Resarch and Conference Center, Bedlewo, Poland(招待講演)
    • Year and Date
      2011-08-11
    • Related Report
      2011 Annual Research Report
  • [Presentation] Fuchsian systemのregular coorcinateと変形方程式のreduction2011

    • Author(s)
      原岡喜重
    • Organizer
      大岡山談話会
    • Place of Presentation
      東京工業大学理学部(招待講演)
    • Year and Date
      2011-06-22
    • Related Report
      2011 Annual Research Report
  • [Presentation] Monodromy of rank 3 completely integrable systems singular along free divisors2011

    • Author(s)
      Yoshishige Haraoka
    • Organizer
      研究集会「Workshop on Free Divisors」
    • Place of Presentation
      University of Warwick, Coventry, UK
    • Year and Date
      2011-05-31
    • Related Report
      2013 Final Research Report
  • [Presentation] Monodromy of rank 3 completely integrable systems singular along free divisors2011

    • Author(s)
      Yoshishige Haraoka
    • Organizer
      Workshop on Free Divisors
    • Place of Presentation
      University of Warwick, Coventry, UK(招待講演)
    • Year and Date
      2011-05-31
    • Related Report
      2011 Annual Research Report
  • [Presentation] On lattices in PGL (Q2)2011

    • Author(s)
      加藤文元
    • Organizer
      九州大学代数学セミナー
    • Place of Presentation
      九州大学伊都図書館(招待講演)
    • Year and Date
      2011-05-20
    • Related Report
      2011 Annual Research Report
  • [Presentation] Ordinary differential equations and Kac-Moody root systems2011

    • Author(s)
      Toshio Oshima
    • Organizer
      Recent Developments in Harmonic Analysis and their Applications
    • Place of Presentation
      Marrakech, Morocco(招待講演)
    • Year and Date
      2011-04-29
    • Related Report
      2011 Annual Research Report
  • [Presentation] Rank 3のuniformization equationsのモノドロミー表現2011

    • Author(s)
      加藤満生
    • Organizer
      アクセサリー・パラメーター研究会
    • Place of Presentation
      熊本大学理学部(招待講演)
    • Year and Date
      2011-03-19
    • Related Report
      2010 Annual Research Report
  • [Presentation] Fuchsian systemのアクセサリー・パラメーターと変形方程式のreduction2011

    • Author(s)
      原岡喜重
    • Organizer
      アクセサリー・パラメーター研究会
    • Place of Presentation
      熊本大学理学部(招待講演)
    • Year and Date
      2011-03-17
    • Related Report
      2010 Annual Research Report
  • [Presentation] Monodromy representations of uniformization equations of rank three2011

    • Author(s)
      加藤満生
    • Organizer
      研究集会「Workshop on Geometry and Analysis of Discriminants」
    • Place of Presentation
      東京大学数物連携宇宙研究機構
    • Year and Date
      2011-02-08
    • Related Report
      2013 Final Research Report
  • [Presentation] Monodromy representations of uniformization equations of rank three2011

    • Author(s)
      加藤満生
    • Organizer
      Workshop on Geometry and Analysis of Discriminants
    • Place of Presentation
      東京大学数物連携宇宙研究機構(招待講演)
    • Year and Date
      2011-02-08
    • Related Report
      2010 Annual Research Report
  • [Presentation] Kashiwara-Malgrange filtration on oscillating and period integrals2011

    • Author(s)
      Susumu Tanabe
    • Organizer
      Workshop on Geometry and Analysis of Discriminants
    • Place of Presentation
      東京大学数物連携宇宙研究機構(招待講演)
    • Year and Date
      2011-02-08
    • Related Report
      2010 Annual Research Report
  • [Presentation] 常微分方程式と特殊関数の計算2011

    • Author(s)
      大島利雄
    • Organizer
      計算による数理科学の展開
    • Place of Presentation
      神戸大学理学部(招待講演)
    • Year and Date
      2011-01-08
    • Related Report
      2010 Annual Research Report
  • [Presentation] Fuchs型方程式の解析2011

    • Author(s)
      大島利雄
    • Organizer
      アクセサリー・パラメーター研究会
    • Place of Presentation
      熊本大学理学部(招待講演)
    • Related Report
      2010 Annual Research Report
  • [Presentation] Fuchs型常微分方程式とKac-Moody root系2010

    • Author(s)
      大島利雄
    • Organizer
      表現論シンポジウム
    • Place of Presentation
      静岡県伊豆の国市おおとり荘(招待講演)
    • Year and Date
      2010-11-11
    • Related Report
      2010 Annual Research Report
  • [Presentation] 微分方程式サイドから見た共形場理論2010

    • Author(s)
      原岡喜重
    • Organizer
      研究集会「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
      2010-10-10
    • Related Report
      2013 Final Research Report
  • [Presentation] 微分方程式サイドから見た共形場理論2010

    • Author(s)
      原岡喜重
    • Organizer
      Workshop on Accessory Parameters
    • Place of Presentation
      東京大学玉原国際セミナーハウス(群馬県)(招待講演)
    • Year and Date
      2010-10-10
    • Related Report
      2010 Annual Research Report
  • [Presentation] Local move connectedness of matchings of lattices with extra edges2010

    • Author(s)
      Fumihiko Nakano
    • Organizer
      7^<th> International Conference on Lattice Path Combinatorics and Applications
    • Place of Presentation
      シエナ大学(イタリア)
    • Year and Date
      2010-07-05
    • Related Report
      2010 Annual Research Report
  • [Presentation] Kac-Moody root systems and linear algebraic differential equations2010

    • Author(s)
      Toshio Oshima
    • Organizer
      International Workshop on Representation Theory and Harmonic Analysis
    • Place of Presentation
      天津,南開研究所(中華人民共和国)(招待講演)
    • Year and Date
      2010-06-07
    • Related Report
      2010 Annual Research Report
  • [Presentation] Looking for "good" Fuchsian differential equations2010

    • Author(s)
      原岡喜重
    • Organizer
      Festcolloquium-in honor of Professor Dr.Donald A.Lutz on the occasion of his 70^<th> birthday
    • Place of Presentation
      San Diego State Univ.(USA)
    • Year and Date
      2010-03-29
    • Related Report
      2009 Annual Research Report
  • [Presentation] 特殊関数と代数的常微分方程式2010

    • Author(s)
      大島利雄
    • Organizer
      日本数学会年会企画特別講演
    • Place of Presentation
      慶應義塾大学理工学部
    • Year and Date
      2010-03-27
    • Related Report
      2013 Final Research Report
  • [Presentation] Simpson の Even 4 の接続問題2010

    • Author(s)
      原岡喜重
    • Organizer
      日本数学会年会(一般講演)
    • Place of Presentation
      慶應義塾大学理工学部
    • Year and Date
      2010-03-27
    • Related Report
      2009 Annual Research Report
  • [Presentation] 特殊関数と代数的常微分方程式2010

    • Author(s)
      大島利雄
    • Organizer
      日本数学会年会(企画特別講演)
    • Place of Presentation
      慶應義塾大学理工学部
    • Year and Date
      2010-03-27
    • Related Report
      2009 Annual Research Report
  • [Presentation] 完全交叉孤立特異点に付随したGauss-Manin 系と齋藤自由因子2010

    • Author(s)
      田邊晋
    • Organizer
      研究集会「アクセサリー・パラメーター研究会」
    • Place of Presentation
      熊本大学理学部
    • Year and Date
      2010-03-17
    • Related Report
      2013 Final Research Report
  • [Presentation] 完全交叉孤立特異点に付随した Gauss-Manin 系と齋藤自由因子2010

    • Author(s)
      田邊晋
    • Organizer
      アクセサリー・パラメーター研究会
    • Place of Presentation
      熊本大学理学部
    • Year and Date
      2010-03-17
    • Related Report
      2009 Annual Research Report
  • [Presentation] 複素鏡映群のdiscriminant から決まる微分方程式2010

    • Author(s)
      加藤満生
    • Organizer
      研究集会「アクセサリー・パラメーター研究会」
    • Place of Presentation
      熊本大学理学部
    • Year and Date
      2010-03-16
    • Related Report
      2013 Final Research Report
  • [Presentation] 複素鏡映群の discriminant から決まる微分方程式2010

    • Author(s)
      加藤満生
    • Organizer
      アクセサリー・パラメーター研究会
    • Place of Presentation
      熊本大学理学部
    • Year and Date
      2010-03-16
    • Related Report
      2009 Annual Research Report
  • [Presentation] アクセサリー・パラメーターの個数を変える操作について2010

    • Author(s)
      原岡喜重
    • Organizer
      アクセサリー・パラメーター研究会
    • Place of Presentation
      熊本大学理学部
    • Year and Date
      2010-03-15
    • Related Report
      2009 Annual Research Report
  • [Presentation] On Horn-Kapranov uniformisation of the discriminantal loci2010

    • Author(s)
      田邊晋
    • Organizer
      Application of the singularity theory to the computer science
    • Place of Presentation
      Univ.of Athens, Greece
    • Year and Date
      2010-03-10
    • Related Report
      2009 Annual Research Report
  • [Presentation] 特殊関数とFuchs型常微分方程式2010

    • Author(s)
      大島利雄
    • Organizer
      東大数理談話会
    • Place of Presentation
      東京大学数理科学研究科
    • Year and Date
      2010-01-08
    • Related Report
      2009 Annual Research Report
  • [Presentation] Universal model of Fuchsian differential equations2010

    • Author(s)
      大島利雄
    • Organizer
      超幾何方程式研究会2010
    • Place of Presentation
      神戸大学理学部
    • Year and Date
      2010-01-07
    • Related Report
      2009 Annual Research Report
  • [Presentation] スペクトルタイプからみたFuchs型微分方程式2010

    • Author(s)
      大島利雄
    • Organizer
      微分作用素と剛性
    • Place of Presentation
      九州大学数理学研究院(招待講演)
    • Related Report
      2010 Annual Research Report
  • [Presentation] Fuchs型常微分方程式についての最新の結果の概説2010

    • Author(s)
      大島利雄
    • Organizer
      Workshop on Accessory Parameters
    • Place of Presentation
      東京大学玉原国際セミナーハウス(群馬県)(招待講演)
    • Related Report
      2010 Annual Research Report
  • [Presentation] (概)自由因子を定める大波面について2009

    • Author(s)
      田邊晋
    • Organizer
      カビ分社増の特異点論とそれに関連する幾何学
    • Place of Presentation
      日本大学文理学部
    • Year and Date
      2009-12-08
    • Related Report
      2009 Annual Research Report
  • [Presentation] Arrangement of hyperplanes arising from sections of rigid local systems2009

    • Author(s)
      Yoshishige Haraoka
    • Organizer
      研究集会「MSJ-SI 2009 on Arrangements of Hyperplanes」
    • Place of Presentation
      北海道大学学術交流会館
    • Year and Date
      2009-08-11
    • Related Report
      2013 Final Research Report
  • [Presentation] Arrangement of hyperplanes arising from sections of rigid local systems2009

    • Author(s)
      原岡喜重
    • Organizer
      MSJ-SI 2009 on Arrangements of Hyperplanes
    • Place of Presentation
      北海道大学学術交流会館
    • Year and Date
      2009-08-11
    • Related Report
      2009 Annual Research Report
  • [Presentation] On a problem of arrangements related to the hypergeometric integrals of confluent type2009

    • Author(s)
      Hironobu Kimura
    • Organizer
      MSJ-SI 2009 on Arrangements of Hyperplanes
    • Place of Presentation
      北海道大学学術交流会館
    • Year and Date
      2009-08-11
    • Related Report
      2009 Annual Research Report
  • [Presentation] Fractional calculus of Weyl algebra and its applications2009

    • Author(s)
      大島利雄
    • Organizer
      Workshop of Integral Geometry and Group Representations
    • Place of Presentation
      東京大学玉原国際セミナーハウス
    • Year and Date
      2009-08-09
    • Related Report
      2009 Annual Research Report
  • [Presentation] Fractional calculus of Weyl algebra and its application2009

    • Author(s)
      Toshio Oshima
    • Organizer
      研究集会「Representation Theory of Real Reductive Groups 」
    • Place of Presentation
      The University of Uta, USA
    • Year and Date
      2009-07-30
    • Related Report
      2013 Final Research Report
  • [Presentation] Fractional calculus of Weyl algebra and its applications2009

    • Author(s)
      大島利雄
    • Organizer
      Representation Theory of Real Reductive Groups
    • Place of Presentation
      The University of Uta, USA
    • Year and Date
      2009-07-30
    • Related Report
      2009 Annual Research Report
  • [Presentation] Prolongation and middle convolution of Fuchsian systems2009

    • Author(s)
      Yoshishige Haraoka
    • Organizer
      研究集会「Non-abelian Hodge Theory and Geoemtry of Twister Structure」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2009-07-13
    • Related Report
      2013 Final Research Report
  • [Presentation] Prolongation and middle convolution of Fuchsian systems2009

    • Author(s)
      原岡喜重
    • Organizer
      Non-abelian Hodge theory and geometry of twister structure
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2009-07-13
    • Related Report
      2009 Annual Research Report
  • [Presentation] Domino tilings with diagonal impurities2009

    • Author(s)
      Taizo Sadahiro
    • Organizer
      研究集会「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
      2009-06-19
    • Related Report
      2013 Final Research Report
  • [Presentation] Prolongation and middle convolution of Fuchsian systems2009

    • Author(s)
      原岡喜重
    • 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
      2009-06-19
    • Related Report
      2009 Annual Research Report
  • [Presentation] Domino tilings with diagonal impurities2009

    • Author(s)
      貞廣泰造
    • 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
      2009-06-19
    • Related Report
      2009 Annual Research Report
  • [Presentation] Fractional calculus of Weyl algebra and its applications2009

    • Author(s)
      大島利雄
    • Organizer
      群の表現と非可換調和解析の新展開
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2009-06-04
    • Related Report
      2009 Annual Research Report
  • [Presentation] Pattern frequencies in tilings of strips2009

    • Author(s)
      貞廣泰造
    • Organizer
      準周期タイルと言語理論の周辺
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2009-06-01
    • Related Report
      2009 Annual Research Report
  • [Presentation] Fractional calculus of Weyl algebra and its applications I, II2009

    • Author(s)
      大島利雄
    • Organizer
      Workshop on Accessory Parameters
    • Place of Presentation
      東京大学玉原国際セミナーハウス
    • Related Report
      2009 Annual Research Report
  • [Presentation] Rigidity for holonomic systems in several variables'

    • Author(s)
      Yoshishige Haraoka
    • Organizer
      研究集会「Formal and Analytic Solutions of Differential, Difference and Discrete Equations」
    • Place of Presentation
      Mathematical Research and Conference Center, Bedlewo, Poland
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Holonomic系に対するmiddle convolution'

    • Author(s)
      原岡喜重
    • Organizer
      研究集会「アクセサリー・パラメーター研究会」
    • Place of Presentation
      東京大学玉原国際セミナーハウス
    • Related Report
      2013 Annual Research Report
  • [Presentation] Rigid holonomic systems'

    • Author(s)
      原岡喜重
    • Organizer
      研究集会「第9回代数・解析・幾何学セミナー」
    • Place of Presentation
      鹿児島大学理学部
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] 大久保型微分方程式の多変数化への試み

    • Author(s)
      加藤満生・眞野智行
    • Organizer
      研究集会「アクセサリー・パラメーター研究会」
    • Place of Presentation
      熊本大学理学部
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Fake projective planes via p-adic uniformisation

    • Author(s)
      Fumiharu Kato
    • Organizer
      Symposium "Combinatorics & arithmetic geometry"
    • Place of Presentation
      Minnaertgebouw, Universiteit Utrecht, Netherlands
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Combinatorial Li-Yau inequality and rational points on curves

    • Author(s)
      Fumiharu Kato
    • Organizer
      Arithmetic and Algebraic Geometry 2014
    • Place of Presentation
      東京大学大学院数理科学研究科大講義室
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] 微分方程式の解の積分表示に関する考察

    • Author(s)
      原岡喜重
    • Organizer
      アクセサリー・パラメーター研究会
    • Place of Presentation
      東京大学玉原国際セミナーハウス
    • Related Report
      2012 Annual Research Report
  • [Presentation] Rigidity of local systems on P^n\hypersurface

    • Author(s)
      Yoshishige Haraoka
    • Organizer
      Workshop on Free Divisors and Differential Equations
    • Place of Presentation
      東京農工大学
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] 超平面配置の補空間に対するrigidity指数

    • Author(s)
      原岡喜重
    • Organizer
      表現論セミナー
    • Place of Presentation
      北海道大学理学部
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] 代数的係数を持つ線形完全積分可能系の構成

    • Author(s)
      原岡喜重
    • Organizer
      アクセサリー・パラメーター研究会
    • Place of Presentation
      熊本大学理学部
    • Related Report
      2012 Annual Research Report
  • [Presentation] 一般超幾何函数{n+1}F_nに付随するモノドロミー表現

    • Author(s)
      三町勝久
    • Organizer
      研究集会「超幾何関数とその周辺」
    • Place of Presentation
      東京大学玉原国際セミナーハウス
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] AppellのF_4超幾何函数に付随するモノドロミー表現

    • Author(s)
      三町勝久
    • Organizer
      超幾何方程式研究会2013
    • Place of Presentation
      神戸大学
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] 古典超幾何函数に付随するモノドロミー表現の既約性・可約性

    • Author(s)
      三町勝久
    • Organizer
      金沢大学数理学談話会
    • Place of Presentation
      金沢大学
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Yet another fake projective plane via p-adic uniformization

    • Author(s)
      加藤文元
    • Organizer
      九州大数的整数論(KANT)2013
    • Place of Presentation
      九州大学
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Yet another fake projective plane via p-adic uniformization

    • Author(s)
      加藤文元
    • Organizer
      Arithmetic and Algebraic Geometry 2013
    • Place of Presentation
      東京大学
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Accessory parameter in degenerations

    • Author(s)
      加藤文元
    • Organizer
      Symposium on ARITHMETIC & GEOMETRY
    • Place of Presentation
      九州大学
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Book] Foundations of rigid geometry2014

    • Author(s)
      Kazuhiro Fujiwara, Fumiharu Kato
    • Total Pages
      728
    • Publisher
      European Mathematical Society Publishing House
    • Related Report
      2013 Annual Research Report
  • [Book] リジッド幾何学入門2013

    • Author(s)
      加藤文元
    • Total Pages
      296
    • Publisher
      岩波書店
    • Related Report
      2012 Annual Research Report
  • [Book] Fractional calculus of Weyl algebra and Fuchsian differential equations, MSJ Memoirs2012

    • Author(s)
      Toshio Oshima
    • Total Pages
      203
    • Publisher
      Mathematical Society of Japan
    • Related Report
      2013 Final Research Report
  • [Book] 特殊関数と代数的線型常微分方程式, 東京大学数理科学レクチャーノート2011

    • Author(s)
      大島利雄
    • Total Pages
      111
    • Publisher
      東京大学大学院数理科学研究科
    • Related Report
      2013 Final Research Report
  • [Book] 特殊関数と代数的線型常微分方程式2011

    • Author(s)
      大島利雄
    • Total Pages
      111
    • Publisher
      東京大学数理科学レクチャーノート
    • Related Report
      2011 Annual Research Report
  • [Remarks] ホームページ :

    • URL

      http://www.sci.kumamoto-u.ac.jp/~haraoka/index-j.html

    • Related Report
      2013 Final Research Report
  • [Remarks] 原岡喜重

    • URL

      http://www.sci.kumamoto-u.ac.jp/~haraoka/index-j.html

    • Related Report
      2013 Annual Research Report
  • [Remarks] 原岡喜重

    • URL

      http://www.sci.kumamoto-u.ac.jp/~haraoka/index-j.html

    • Related Report
      2012 Annual Research Report
  • [Remarks]

    • URL

      http://www.sci.kumamoto-u.ac.jp/~haraoka/index-j.html

    • Related Report
      2011 Annual Research Report
  • [Remarks]

    • URL

      http://www.sci.kumamoto-u.ac.jp/~haraoka/index-j.html

    • Related Report
      2010 Annual Research Report
  • [Remarks]

    • URL

      http://www.sci.kumamoto-u.ac.jp/~haraoka/index-j.html

    • Related Report
      2009 Annual Research Report

URL: 

Published: 2009-04-01   Modified: 2019-07-29  

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