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MIZUTANI Akira  水谷 明

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MIZITANI Akira  水谷 明

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Researcher Number 80011716
Other IDs
Affiliation (based on the past Project Information) *help 2011: 学習院大学, 理学部, 教授
2009: 学習院大学, 理学部, 教授
1994 – 2007: 学習院大学, 理学部, 教授
1987 – 1994: 学習院大学, 理学部, 助教授
Review Section/Research Field
Principal Investigator
解析学
Except Principal Investigator
解析学 / Basic analysis / Basic analysis / Algebra / Science education / 代数学・幾何学 / Science education / Geometry / General mathematics (including Probability theory/Statistical mathematics)
Keywords
Principal Investigator
有限要素法 / 逆反復法 / 変分原理 / 不安定解 / 準線形楕円型境界値問題
Except Principal Investigator
量子力学 / 経路積分 / Schrodinger equation / Stationary phase method / 停留位相法 … More / Quantum mechanics / Selfajoint operator / Oscillatory integrals / Feynman path integrals / WKB法 / Feynman経路積分 / Schrodinger方程式 / スペクトル理論 / path integrals / WKB-method / Stationary phase / 振動積分 / シュレーディンガー方程式 / 固有値の数値計算 / Scrodinger方程式 / Feynman path integral / HIGH-SCHOOL MATHEMATICS / NATIONAL CURRICULUM / MATHEMATICAL EDUCATION / 高等学校数学 / 教育課程 / 数学教育 / 数学基礎 / 学習指導要領 / Spectral theory / 非線形偏微分方程式 / シュレーディンガー作用素 / 代数的独立性 / 超越数 / 散乱理論 / シュレ-ディンガ-作用素 / Navier-Stokes / Maxwell / 自己共役作用素 / FUNDAMENTALS OF MATHEMATICS / CURRICULUM GUIDELINES / BASIC / 準古典近似 / ファインマン積分 / 非線形方程式 / 分散型評価 / 偏微分方程式 / 数理物理学 / 特異性伝播 / 小平次元 / ファインマン経路積分 / 不定方程式 / 極値的長さ / FUNDAMENTALS OF MATH / CURRICULUM / 教育過程 / Dissipative / Bi-harmonic / Besov space / Singular Perturbation / Self-adjoint / Shrodinger / Wiener空間 / 最大関数 / 消散型 / 消散方 / 重調和 / Besov空間 / 特異摂動 / Schrodinger / Random system / Microlocal singularities / Time periodic system / Scattering theory / Nonlinear differential equations / Partial differential equations / Mathematical Physics / 状態密度関数 / ランダムシュレーディンガー作用素 / phase space tunnenling / 量子電磁力学 / 漸近展開 / 断熱近似 / ランダム磁場 / レゾナンス / ネルソンモデル / 平滑化作用 / スペクトル / 散乱の波動作用素 / ランダム系 / 超局所特異性 / 時間周期系 / MATHEMATICS ACTIVITIES / 教育ソフト / 数学的活動 / Scridinger方程式 / Statuinary phase method / EKB法 / Foureir積分作用素 / 汎関数解析 / 位相停留法 / シュレーディングー方程式 / シュレーディレガー方程式 / 中等教育 / 情報教育 / コンピュータ / 高校数学 / Covering surface of the unit disc / Nonlinear PDE / Zeros of Polynomials / Feynman integral / 代数方程式の数値解法 / 点相互作用 / 特異相互作用 / 単位円板の被覆面 / 多項式の零点 / 停留位相の方法 / precise graphic image / triply periodic minimal surface / crystallographic group / minimal surface / 精密画像 / 結晶群 / 3重周期的極小曲面 / 極小曲面 / Lie-Trotter product formula / Feynman-Kac formula / Perturbation / Schridinger方程式 / Feru man経路積分 / sfationary phare methos / path integral / Feynman 経路積分 / ハミルトニアン / stationary phrse aruthod / puth integral / Functional equations / Diophantine equations / Algebraic independence / Transcendental numbers / 関数等式 / Finite element approximation / Explicit method / Degenerate non-linear parabolic equations / Pass integral / Feynmann integral / Semi-linear elliptic boundary value problem / マンデルブロ-集合 / 有限要素法近似 / 漸近解析 / 陽解法 / 有限要素近似 / 退化放物型方程式 / 準線形線形楕円形境界値問題 / シュレ-ディンガー方程式 / Diophantine Approximation / Transcendental Numbers / パデ近似 / マ-ラ-関数 / ディオファンタス近似 / extremal length / 平面曲線 / 代数多様体 / Black-Scholls方程式 / HWW方程式 / 極限の可視化 / default-risk system / オプション / 多倍長計算 / フラクタル次元 / アトラクター / 漸近挙動 / blow up time / Default risk / 金融工学 / 相分離 / 数理モデル / 特異性伝播問題 / 量子物理学 / 基本解 / 関数解析学 / 線形偏微分方程式 / 実解析 / 関数解析 / 関数方程式 / フーリエ積分作用 / Feynman path integrate / Feynman / フーリエ積分作用素 / Schnodinger方程式 / Feynman path mlegrals / クレモナ変換 / 代数曲線 / 種数 / 微分型式 / 極小モデル / 双有理 / 代数幾何 / フーリェ積分作用素 / シンV-ディンガー方程式 / 汎関数 / 数値計算 / 積公式 / 逆スペクトル問題 / 共鳴レヴェル / 調和測度 / 等角容量 / 極値的距離 / ポテンシャル / ネットワ-ク / 倉持境界 / リ-マン面 / レンズ空間 / プロログ / 高速フ-リエ変換 Less
  • Research Projects

    (29 results)
  • Research Products

    (10 results)
  • Co-Researchers

    (29 People)
  •  Mathematical analysis of the nonlinear systems arising in the industry.

    • Principal Investigator
      NAKAMURA Masaaki
    • Project Period (FY)
      2009 – 2011
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      General mathematics (including Probability theory/Statistical mathematics)
    • Research Institution
      Nihon University
  •  Mathematical Analysis of Quantum Physics

    • Principal Investigator
      YAJIMA Kenji (KENJI Yajima)
    • Project Period (FY)
      2006 – 2009
    • Research Category
      Grant-in-Aid for Scientific Research (B)
    • Research Field
      Basic analysis
    • Research Institution
      Gakushuin University
  •  Research on Functional Analysis and Mathematical theory of Feynman path integrals

    • Principal Investigator
      FUJIWARA Daisuke
    • Project Period (FY)
      2005 – 2007
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Basic analysis
    • Research Institution
      Gakushuin University
  •  Study of developing firm ability in Mathematics.

    • Principal Investigator
      IITAKA Shigeru
    • Project Period (FY)
      2004 – 2006
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Science education
    • Research Institution
      Gakushuin University
  •  Research on Functional Analysis and Mathematical theory of Feynman path integrals.

    • Principal Investigator
      FUJIWARA Daisuke
    • Project Period (FY)
      2003 – 2004
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Basic analysis
    • Research Institution
      Gakushuin University.
  •  Mathematical Analysis of Quantum Physics

    • Principal Investigator
      YAJIMA Kenji
    • Project Period (FY)
      2002 – 2005
    • Research Category
      Grant-in-Aid for Scientific Research (B)
    • Research Field
      Basic analysis
    • Research Institution
      Gakushuin University
      The University of Tokyo
  •  On the scattering theory and the singular perturbations for the self-adjoint operators

    • Principal Investigator
      WATANABE Kazuo
    • Project Period (FY)
      2002 – 2003
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Basic analysis
    • Research Institution
      Gakushuin University
  •  Research in Functional Analsys and Mathematical theory of Feynman path integrals

    • Principal Investigator
      FUJIWARA Daisuke
    • Project Period (FY)
      2001 – 2002
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Basic analysis
    • Research Institution
      Gakushuin University
  •  THE PROMTION OF ABILITY OF MATHEMATICS LEARNING

    • Principal Investigator
      SHIGERU Iitaka
    • Project Period (FY)
      2001 – 2003
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Science education
    • Research Institution
      GAKUSHUIN UNIVERSITY
  •  Research in Functional Analsys and Mathematical theory of Feynman path integrals.

    • Principal Investigator
      FUJIWARA Daisuke
    • Project Period (FY)
      1999 – 2000
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Basic analysis
    • Research Institution
      Gakushuin University
  •  Mathematics of Schrodinger Equations

    • Principal Investigator
      KURODA Shige toshi
    • Project Period (FY)
      1998 – 1999
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Basic analysis
    • Research Institution
      Gakushuin University
  •  THE STUDY OF HIGH-SCHOOL MATH AND ITS NEIGHBORHOODS

    • Principal Investigator
      IITAKA Shigeru
    • Project Period (FY)
      1998 – 2000
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Science education
    • Research Institution
      GAKUSHUIN UNIVERSITY
  •  Research in Functional Analsys.

    • Principal Investigator
      FUJIWARA Daisuke
    • Project Period (FY)
      1997 – 1998
    • Research Category
      Grant-in-Aid for Scientific Research (B)
    • Research Field
      解析学
    • Research Institution
      Department of Mathematics, Faculty of Sciences, Gakushuin University
  •  Precise Graphic Images of Minimal Surfaces Using Computer

    • Principal Investigator
      KAWASAKI Tetsuro
    • Project Period (FY)
      1997 – 1998
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Geometry
    • Research Institution
      Gakushuin University
  •  汎関数解析

    • Principal Investigator
      藤原 大輔
    • Project Period (FY)
      1996
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      解析学
    • Research Institution
      Gakushuin University
  •  Algebraic and Analytic Research of Transcendental Numbers

    • Principal Investigator
      IITAKA Shigeru, 三井 孝美
    • Project Period (FY)
      1996 – 1997
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Algebra
    • Research Institution
      Gakushuin University
  •  汎関数解析

    • Principal Investigator
      藤原 大輔
    • Project Period (FY)
      1995
    • Research Category
      Grant-in-Aid for General Scientific Research (C)
    • Research Field
      解析学
    • Research Institution
      Gakushuin University
  •  Functional Analysis and Partial Differential Equations

    • Principal Investigator
      KURODA Shigetoshi
    • Project Period (FY)
      1995 – 1996
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      解析学
    • Research Institution
      Gakushuin University, Faculty of Science
  •  汎関数解析

    • Principal Investigator
      藤原 大輔
    • Project Period (FY)
      1994
    • Research Category
      Grant-in-Aid for General Scientific Research (C)
    • Research Field
      解析学
    • Research Institution
      Gakushuin University
  •  代数多様体の双有理不変構造の研究

    • Principal Investigator
      飯高 茂
    • Project Period (FY)
      1994
    • Research Category
      Grant-in-Aid for General Scientific Research (C)
    • Research Field
      Algebra
    • Research Institution
      Gakushuin University
  •  超越数の代数的・解析的研究

    • Principal Investigator
      三井 孝美
    • Project Period (FY)
      1993
    • Research Category
      Grant-in-Aid for General Scientific Research (C)
    • Research Field
      Algebra
    • Research Institution
      Gakushuin University
  •  偏微分方程式の近似解法Principal Investigator

    • Principal Investigator
      水谷 明
    • Project Period (FY)
      1993
    • Research Category
      Grant-in-Aid for General Scientific Research (C)
    • Research Field
      解析学
    • Research Institution
      Gakushuin University
  •  関数解析・偏微分方程式の研究

    • Principal Investigator
      黒田 成俊
    • Project Period (FY)
      1992
    • Research Category
      Grant-in-Aid for General Scientific Research (C)
    • Research Field
      解析学
    • Research Institution
      Gakushuin University
  •  解析多様体の研究

    • Principal Investigator
      大津賀 信
    • Project Period (FY)
      1991
    • Research Category
      Grant-in-Aid for General Scientific Research (C)
    • Research Field
      解析学
    • Research Institution
      Gakushuin University
  •  解析多様体の研究

    • Principal Investigator
      大津賀 信
    • Project Period (FY)
      1990
    • Research Category
      Grant-in-Aid for General Scientific Research (C)
    • Research Field
      解析学
    • Research Institution
      Gakushuin University
  •  関数解析・偏微分方程式の研究

    • Principal Investigator
      KURODA Shigetoshi
    • Project Period (FY)
      1989
    • Research Category
      Grant-in-Aid for General Scientific Research (C)
    • Research Field
      解析学
    • Research Institution
      Gakushuin University
  •  Study of Algebraic and Analytic Theory of Transcendental Numbers

    • Principal Investigator
      MITSUI Takayoshi
    • Project Period (FY)
      1989 – 1990
    • Research Category
      Grant-in-Aid for General Scientific Research (C)
    • Research Field
      代数学・幾何学
    • Research Institution
      Gakushuin University
  •  偏微分方程式と関数解析・数値解析の研究

    • Principal Investigator
      黒田 成俊
    • Project Period (FY)
      1988
    • Research Category
      Grant-in-Aid for General Scientific Research (C)
    • Research Field
      解析学
    • Research Institution
      Gakushuin University
  •  代数多様体の研究

    • Principal Investigator
      飯高 茂
    • Project Period (FY)
      1987
    • Research Category
      Grant-in-Aid for General Scientific Research (C)
    • Research Field
      代数学・幾何学
    • Research Institution
      Gakushuin University

All 2007 2005

All Journal Article Presentation

  • [Journal Article] Finite element approximation to degenerate parabolic equations, an application of nonlinear semi-group theory2005

    • Author(s)
      A.Mizutani
    • Journal Title

      ESAIM Mathematical modeling and Numerical Analysis vol.39

      Pages: 755-780

    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-14340039
  • [Journal Article] Finite element approximation to degenerate parabolic equations, an application of nonlinear semi-group theory2005

    • Author(s)
      A.Mizutani
    • Journal Title

      ESAIM Mathematical modeling and Numerical Analysis 39

      Pages: 755-780

    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-14340039
  • [Journal Article] On finite element method for the biharminic Dirichlet problem in the polygonal domains, On the quasi-optimal rate of convergence2005

    • Author(s)
      A.Mizutani
    • Journal Title

      Japan J. indust. Appl. Math. 22

      Pages: 45-56

    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-14340039
  • [Journal Article] On finite element method for the biharminic Dirichlet problem in the polygonal domains, On the quasi-optimal rate of convergence2005

    • Author(s)
      A.Mizutani
    • Journal Title

      Japan J.Indust.Appl.Math. Vol.22

      Pages: 45-56

    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-14340039
  • [Journal Article] Finite element approximation for degenerate parabolic equations.An application of nonlinear semigroup theory2005

    • Author(s)
      A.Mizutani, N.Saito and T.Suzuki
    • Journal Title

      M2AN Math.Model.Numer.Anal 39

      Pages: 755-780

    • Description
      「研究成果報告書概要(和文)」より
    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-17540170
  • [Journal Article] Finite element approximation for degenerate parabolic equations, An application of nonlinear semigroup theory2005

    • Author(s)
      Akira Mizutani
    • Journal Title

      M2NA Mathematical Modelling and Numerical Analysis 39

      Pages: 755-780

    • Data Source
      KAKENHI-PROJECT-14340039
  • [Journal Article] Finite element approx-imation for degenerate parabolic equations. An application of nonlinear semigroup theor2005

    • Author(s)
      A., Mizutani, N., Saito, T., Suzuki
    • Journal Title

      M2AN Math. Model. Num. Anal 39

      Pages: 755-780

    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-17540170
  • [Journal Article] Finite element approximation for degenerate parabolic equations. An application of nonlinear semigroup theory.2005

    • Author(s)
      Mizutani, A.
    • Journal Title

      M2AN Math.Model.Numer.Anal. 39 no.4

      Pages: 755-780

    • Data Source
      KAKENHI-PROJECT-17540170
  • [Presentation] 4階非線形2点境界値問題に対する解の精度保証2007

    • Author(s)
      水谷 明
    • Organizer
      日本数学会応用数学分科会
    • Place of Presentation
      埼玉大学,埼玉県
    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-17540170
  • [Presentation] Numerical enclosure of solutions for 4th order nonlinear two-point boundary value problems2007

    • Author(s)
      A., Mizutani
    • Organizer
      Ann. meeting Math. Soc. Japan
    • Place of Presentation
      Saitama Unv. Saitama
    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-17540170
  • 1.  KURODA Shigetoshi (20011463)
    # of Collaborated Projects: 22 results
    # of Collaborated Products: 0 results
  • 2.  FUJIWARA Daisuke (10011561)
    # of Collaborated Projects: 20 results
    # of Collaborated Products: 0 results
  • 3.  IITAKA Shigeru (20011588)
    # of Collaborated Projects: 18 results
    # of Collaborated Products: 0 results
  • 4.  KATASE Kiyoshi (70080489)
    # of Collaborated Projects: 18 results
    # of Collaborated Products: 0 results
  • 5.  MITSUI Takayoshi (20080484)
    # of Collaborated Projects: 11 results
    # of Collaborated Products: 0 results
  • 6.  WATANABE Kazuo (90260851)
    # of Collaborated Projects: 11 results
    # of Collaborated Products: 0 results
  • 7.  KAWASAKI Tetsuro (90107061)
    # of Collaborated Projects: 10 results
    # of Collaborated Products: 0 results
  • 8.  OHTSUKA Makoto (30033765)
    # of Collaborated Projects: 7 results
    # of Collaborated Products: 0 results
  • 9.  SHIMOMURA Akihiro (00365066)
    # of Collaborated Projects: 5 results
    # of Collaborated Products: 0 results
  • 10.  YAJIMA Kenji (80011758)
    # of Collaborated Projects: 4 results
    # of Collaborated Products: 0 results
  • 11.  OKABE Tsuneharu (80087080)
    # of Collaborated Projects: 3 results
    # of Collaborated Products: 0 results
  • 12.  NAKAMURA Shu (50183520)
    # of Collaborated Projects: 2 results
    # of Collaborated Products: 0 results
  • 13.  CHEN Yungang (50217262)
    # of Collaborated Projects: 2 results
    # of Collaborated Products: 0 results
  • 14.  NAKAJIMA Shoichi (90172311)
    # of Collaborated Projects: 2 results
    # of Collaborated Products: 0 results
  • 15.  浅枝 陽 (60080488)
    # of Collaborated Projects: 2 results
    # of Collaborated Products: 0 results
  • 16.  NAKAMURA Masaaki (00017419)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 17.  ISHIMURA Naoyuki (80212934)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 18.  IMAI Hitoshi (80203298)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 19.  NAKANO Shin (40180327)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 20.  ICHINOSE Takashi (20024044)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 21.  JIN Naondo (90206368)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 22.  KURATA Kuzuhiro (10186489)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 23.  SUZUKI Toshio (20020472)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 24.  SUGANO Satoko (50316931)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 25.  KAKEUCHI Shingo (00333021)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 26.  KADOWAKI Mitsuteru (70300548)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 27.  赤尾 和男 (50011698)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 28.  小川 卓克 (20224107)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 29.  田中 仁
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results

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