Nakai Isao 中居功

… Alternative Names

Researcher Number	90207704
External Links
Affiliation (Current)	2022: お茶の水女子大学, , 名誉教授 2022: お茶の水女子大学, 基幹研究院, 教授
Affiliation (based on the past Project Information) *help	2015 – 2018: お茶の水女子大学, 基幹研究院, 教授 2011 – 2013: お茶の水女子大学, 大学院人間文化創成科学研究科, 教授 2009 – 2010: お茶の水女子大学, 理学部, 教授 2002 – 2006: お茶の水女子大学, 理学部, 教授 1999 – 2000: お茶の水女子大学, 理学部, 教授 … More
Review Section/Research Field	Principal Investigator Geometry / Global analysis / Geometry Except Principal Investigator Geometry / 代数学・幾何学 / Geometry / Algebra / Global analysis / Global analysis
Keywords	Principal Investigator 常微分方程式 / WEB / 葉層 / Web / WEB幾何学 / 複素力学系 / 可積分系 / 一階偏微分方程式 / 関係式 / CHERN接続 … More Except Principal Investigator 接触変換 / 特異葉層構造 / 接触幾何学 / 葉層 / 葉層構造 / 特異点集合 / 単純階別リー環 / 局所同値問題 / Web / 留数 / 定性論 / 相似変換擬群 / foliation / qualitative theory / similarity pseudogroup / ルジャンドル特異点 / ラグランジュ特異点 / 接触幾何 / Monge-Ampere equation / モンジュ・アンペール方程式 / 可積分系 / 複素力学系 / 可微分写像の位相 / Jet空間の層化 / 写像図式 / 完全積分可能な微分方程式 / 合成写像の位相 / Baum-Bottの留数 / Lehmannの留数 / 微分式系(difefrential system) / ハミルトン-ヤコビ-ベルマン / 保存則 / クレロー型方程式 / 複素解析的特異葉層構造 / 不変部分多様体 / Cech-de Rham cohomology / 特性類の留数 / 微分式系(differential system) / ハミルトン-ヤコビ方程式 / 特異性 / ラグランジュ特異部分多様体 / 平均曲率の発展方程式 / 位相幾何 / トポロジー / 多様体 / 群 / 結び目 / シンプレクティック幾何 / トーリックトポロジー / 微分式系 / 階別単純リー環 / 包合系 / 高次ジェット空間 / 有限型微分方程式系 / 複素解析幾何学 / 特異点理論 / 開折理論 / 特異点の留数 / 時異葉層構造 / 開析理論 / 解複体 / 特性多様体 / Complex analytic geometry / Singularity theory / Singular foliation / Unfolding theory / Singular set / 3次元3次超曲面 / C^3のcompact化 / ベクトル場の留数 / 準線形微分方程式 / Whiteneyの開いた傘 / Lagrange安定 / 複素多様体 / 3次超曲面 / ファノ多様体 / A cubic threefold / Compactifications of C^3 / Foliation / Residue of a vector field / Open Whitney umbrella / Quasi-linear differential equation / Lagrange stable / Wed / ベクトル場 / 指数と留数 / 局所化 / 特性類 / 特異多様体 / ベットル場 / 正則ベクトル場 / vector fields / singular foliations / indices and residues / localization / characteristic classes / singular varieties / 正則葉層 / 織構造 / 葉層バンドル / PL同相群 / 横断的幾何構造 / 複素葉層 / 同相群 / holomerphic foliation / wob / foliated bundle / residue / PL homeomorphism group / 可展開面 / モンジュアンペ-ル方程式 / 笠 / 平面三角曲線 / 擬直線配置 / ヒルベルト16問題 / ヒルベルト化問題 / 射影幾何 / 特異点論 / 空間曲線 / Web幾何 / symplectic幾何 / 特異葉層 / フロント写像 / Legendre singularity / Lagrange singularity / Tangent developable / Open umbrella / Plane trigonometric curve / Pseudo-line arrangement / Hilbert's 16th problem / 接触交換 / 超幾何方程式系 / 準線形二階偏微分方程式 / 超性解の分岐 / 可積分測地流 / ラフランシュ安定性 / 超楕円写像類群 / 準線形一階偏微分方程式 / 例外形単純リー環 / 二階の過剰決定系 / 二階偏微分方程式系 / 例外単純リー環 / 同値問題 / 超幾何微分方程式系 / Contact Transformation / Hypergeometric Systems / Quasi-linear First Order PDE / Viscosity Solution / Integrable geodesic flow / Lagrange Stability / Hyperelliptic mopping class groups / 単純特異点 / シンプレクティック欠損 / グラスマン幾何 / ガウス写像 / 双対多様体 / 可展部分多様体 / シンプレクティック・モデュライ / 接触同値 / ギベンタル予想 / 非ホロノーム横断性定理 / 非ホロノームホモトピー原理 / 可展面 / 等径超曲面 / 極小曲面 / 接触構造 / ケーリー8元数体 / 可展超曲面 / 射影構造 / 等質空間 / ケーレー8元体 / 射影微分幾何 / simple singularity / symplectic defect / contact geometry / Grassmannian geometry / Gauss mapping / dual variety / developable submanifold / サックスティーダーの定理 / 例外的極小集合 / 留数理論 / ミルナー数 / 非ユニモデュラーリー群 / 指数公式 / ウエッブ / ブラシュケ接続 / 区分線形同相群 / Sacksteder's Theorem / exceptional minimal set / 高階有限型微分方程式系 / 調和写像と可積分系 / 測地流と可積分系 / Gauss-Schwarz理論 / Gaup.Schwary理論 / 解の特異点 / 調和写像 / 高階有限型微分方程式 / 射影部分多様体論 / 過剰決定系 / Contact transformations / Monge-Ampere equations / Systems of higher order partial differential equations of finite type / Harmonic mappings and Integrable systems / Geodesic flows and Integrade systems / Gauss-Schwarz theory / ハミルトン力学系 / ゼータ関数 / コシレイ指数 / 変分法 / シンプレクティック幾何学 / 力学系ゼータ関数 / コンレイ指数 / Hamiltonian system / integrable system / variational method / zeta function / Conley index / complex dynamical system / symplectic geometry / 局所自由リー群作用 / 葉層コホモロジー / パラメータ剛性 / ホロサイクル流 / Ruelle不変量 / 一意エルゴード性 / 極小集合 / ルエル不変量 / 一竜エルゴート性 / foliations / locally free lie group actions / foliated cohomology / parameter rigidity / horocycle flow / Ruelle invariant / unique ergodicity / minimal set / カオス / フラクタル / 分岐 / ジュリア集合 / 力学系 / くりこみ / タイヒミュラー空間 / マンデルブロート集合 / 分岐理論 / 超越整関数 / 放物型不動点 / タイヒミュラー空間論 / Complex Dynamics / Chaos / Fractal / Bifurcation / Julia set / Dynamical System / Renormalization / Teichmuller space Less

Geometry of Planar 3-websPrincipal Investigator
- Principal Investigator
  
  Nakai Isao
- Project Period (FY)
  2015 – 2018
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Geometry
- Research Institution
  Ochanomizu University
Relations of formal power series of one variable and coding of space curves by iterated path integralsPrincipal Investigator
- Principal Investigator
  
  NAKAI Isao
- Project Period (FY)
  2011 – 2013
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Global analysis
- Research Institution
  Ochanomizu University
Overall study of topology
- Principal Investigator
  
  MASUDA Mikiya
- Project Period (FY)
  2007 – 2009
- Research Category
  
  Grant-in-Aid for Scientific Research (A)
- Research Field
  
  Geometry
- Research Institution
  Osaka City University
Research on the differential sysytems and geometric structures associated with simple graded Lie algebras
- Principal Investigator
  
  YAMAGUCHI Keizo
- Project Period (FY)
  2007 – 2010
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Research Field
  
  Geometry
- Research Institution
  Hokkaido University
Research on Complex Dynamics
- Principal Investigator
  
  UEDA Tetsuo, 宍倉光広
- Project Period (FY)
  2003 – 2006
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Research Field
  
  Global analysis
- Research Institution
  Kyoto University
Topology of Solutions of 1st order PDEs and web gPrincipal Investigator
- Principal Investigator
  
  NAKAI Isao
- Project Period (FY)
  2002 – 2005
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Research Field
  
  Geometry
- Research Institution
  Ochanomizu University
Synthetic studies of foliations and discrete group actions
- Principal Investigator
  
  MATSUMOTO Shigenori
- Project Period (FY)
  2001 – 2003
- Research Category
  
  Grant-in-Aid for Scientific Research (A)
- Research Field
  
  Geometry
- Research Institution
  Nihon University
Research of Systems of Partial Differential Equations from the view point of Contact Geometry
- Principal Investigator
  
  YAMAGUCHI Keizo
- Project Period (FY)
  1999 – 2002
- Research Category
  
  Grant-in-Aid for Scientific Research (A)
- Research Field
  
  Geometry
- Research Institution
  HOKKAIDO UNIVERSITY
Analysis of dynamical systems and related topics in geometry
- Principal Investigator
  
  ITO Hidekazu
- Project Period (FY)
  1999 – 2000
- Research Category
  
  Grant-in-Aid for Scientific Research (B).
- Research Field
  
  Global analysis
- Research Institution
  Tokyo Institute of Technology
Projective contact geometry and singularity theory
- Principal Investigator
  
  ISHIKAWA Goo
- Project Period (FY)
  1998 – 2001
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Research Field
  
  Geometry
- Research Institution
  HOKKAIDOUNIVERSITY
Geometry of webs, Hamiltonian systems and complex dynamicsPrincipal Investigator
- Principal Investigator
  
  NAKAI Isao
- Project Period (FY)
  1998 – 2000
- Research Category
  
  Grant-in-Aid for Scientific Research (B).
- Research Field
  
  Geometry
- Research Institution
  Ochanomizu University
  Hokkaido University
Many-sided Research of Foliations
- Principal Investigator
  
  NISHIMORI Toshiyuki
- Project Period (FY)
  1998 – 2000
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Geometry
- Research Institution
  HOKKAIDO UNIVERSITY
可積分系の幾何学とWeb幾何学Principal Investigator
- Principal Investigator
  
  中居功
- Project Period (FY)
  1996
- Research Category
  
  Grant-in-Aid for Scientific Research on Priority Areas
- Research Institution
  Hokkaido University
Contact Geometry of Second Order
- Principal Investigator
  
  YAMAGUCHI Keizo
- Project Period (FY)
  1996 – 1998
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Research Field
  
  Geometry
- Research Institution
  Hokkaido Univ.
First Order Partial Differential Equation and WEB GeometryPrincipal Investigator
- Principal Investigator
  
  NAKAI Isao
- Project Period (FY)
  1996 – 1997
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Geometry
- Research Institution
  HOKKAIDO UNIVERSITY
Research on Complex Analytic Geometry and Singularity Theory
- Principal Investigator
  
  SUWA Tatsuo
- Project Period (FY)
  1995 – 1996
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Research Field
  
  Geometry
- Research Institution
  Hokkaido University
Foliation Theory
- Principal Investigator
  
  NISHIMORI Toshiyuki
- Project Period (FY)
  1995 – 1996
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Geometry
- Research Institution
  Hokkaido University
Contact geometric singularity theory of projective varieties.
- Principal Investigator
  
  ISHIKAWA Go-o
- Project Period (FY)
  1995 – 1996
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Geometry
- Research Institution
  HOKKAIDO UNIVERSITY
複素解析的葉層構造の特異点の研究
- Principal Investigator
  
  諏訪立雄
- Project Period (FY)
  1994
- Research Category
  
  Grant-in-Aid for Scientific Research on Priority Areas
- Research Institution
  Hokkaido University
二階の接触幾何学
- Principal Investigator
  
  山口佳三
- Project Period (FY)
  1994
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  Geometry
- Research Institution
  Hokkaido University
偏微分方程式の幾何と解析
- Principal Investigator
  
  泉屋周一
- Project Period (FY)
  1994
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  Geometry
- Research Institution
  Hokkaido University
Study on Complex Manifolds
- Principal Investigator
  
  NAKAMURA Iku
- Project Period (FY)
  1994 – 1995
- Research Category
  
  Grant-in-Aid for General Scientific Research (B)
- Research Field
  
  Algebra
- Research Institution
  Hokkaido University
偏微分方程式の幾何学的理論と特異点
- Principal Investigator
  
  泉屋周一
- Project Period (FY)
  1993
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  Geometry
- Research Institution
  Hokkaido University
複素解析的葉層構造の特異点の研究
- Principal Investigator
  
  SUWA Tatsuo
- Project Period (FY)
  1992
- Research Category
  
  Grant-in-Aid for Scientific Research on Priority Areas
- Research Institution
  Hokkaido University
二階の接触幾何学
- Principal Investigator
  
  YAMAGUCHI Keizo
- Project Period (FY)
  1992
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  代数学・幾何学
- Research Institution
  Hokkaido University
河微分写像の位相
- Principal Investigator
  
  森川良三
- Project Period (FY)
  1990
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  代数学・幾何学
- Research Institution
  Nagasaki University
Research on Complex Analytic Geometry and Singularity Theory
- Principal Investigator
  
  SUWA Tatsuo
- Project Period (FY)
  1990 – 1991
- Research Category
  
  Grant-in-Aid for General Scientific Research (B)
- Research Field
  
  代数学・幾何学
- Research Institution
  Hokkaido University

All 2018 2016 2015 2014 2013 2012 2011 2005

All Journal Article Presentation

[Journal Article] Web geometry of solutions of first order ODEs2018
- Author(s)
  Isao Nakai
- Journal Title
  
  Natural Science Report, Ochanomizu University
  
  Volume: 68 Pages: 1-5
- NAID
  40021527760
- Open Access
- Data Source
  KAKENHI-PROJECT-15K04838
[Journal Article] Finding roots by a simple origami2016
- Author(s)
  ISAO NAKAI
- Journal Title
  
  Ochanomizu University Natural Science Report
  
  Volume: 66,no.1 Pages: 1-17
- NAID
  120005860185
- Peer Reviewed / Open Access
- Data Source
  KAKENHI-PROJECT-15K04838
[Journal Article] Webs and Singularities2014
- Author(s)
  NAKAI, Isao
- Journal Title
  
  Journal of Singularities
  
  Volume: Vol 9(掲載ページ未定)
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-23540236
[Journal Article] Relations of formal diffeomorphisms2005
- Author(s)
  Isao Nakai, Kana Yanai
- Journal Title
  
  RIMS Koukyuroku 1447
  
  Pages: 145-163
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-14340022
[Journal Article] Relations of formal diffeomorphisms2005
- Author(s)
  中居功
- Journal Title
  
  数理解析研究所講究録 1447
  
  Pages: 145-163
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-14340022
[Presentation] Web geometriy from the view point of rigidity and curvature2018
- Author(s)
  Isao Nakai
- Organizer
  Seminaire de Geometrie, IMB, Universite de Bordeaux I
- Invited
- Data Source
  KAKENHI-PROJECT-15K04838
[Presentation] Some topics in web geometry2015
- Author(s)
  Isao Nakai
- Organizer
  日本数学会秋季会
- Place of Presentation
  京都産業大学
- Year and Date
  2015-09-15
- Invited / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-15K04838
[Presentation] Relation of germs of diffeomorphisms of (C,0) and Geometry of path group2013
- Author(s)
  Isao Nakai
- Organizer
  Seminar on Geometry and Topology in Weizman institute
- Place of Presentation
  Rehovot, Israel
- Invited
- Data Source
  KAKENHI-PROJECT-23540236
[Presentation] Geometry of Path group Feuilletages et equations differentielles complexes2012
- Author(s)
  NAKAI, Isao
- Organizer
  国際議
- Place of Presentation
  フランス, マルセイユ CIRM 研究所
- Year and Date
  2012-10-16
- Data Source
  KAKENHI-PROJECT-23540236
[Presentation] Relation of germs of diffeomorphisms of (C,0) and Geometry of path group2012
- Author(s)
  Isao Nakai
- Organizer
  Feuilletages et équations différentielles complexes
- Place of Presentation
  Luminy, France
- Invited
- Data Source
  KAKENHI-PROJECT-23540236
[Presentation] Topology of Cubic maps2011
- Author(s)
  中居功
- Organizer
  Journees Textiles(招待講演)
- Place of Presentation
  Rennes, France
- Data Source
  KAKENHI-PROJECT-23540236
[Presentation] Webs and Singularities Resolution of singularities and related topics2011
- Author(s)
  NAKAI, Isao
- Organizer
  国際会議
- Place of Presentation
  Tordesillas, スペイン
- Year and Date
  2011-09-22
- Data Source
  KAKENHI-PROJECT-23540236
[Presentation] Topology of Cubic maps2011
- Author(s)
  中居功
- Organizer
  Congreso Hironaka 80(招待講演)
- Place of Presentation
  Tordesillas, SPEIN
- Data Source
  KAKENHI-PROJECT-23540236
[Presentation] Webs and Singularities Les Jornees textiles2011
- Author(s)
  NAKAI, Isao
- Organizer
  国際会議
- Place of Presentation
  Universite de Rennes 1, フランス, レンヌ
- Year and Date
  2011-11-23
- Data Source
  KAKENHI-PROJECT-23540236

1. ISHIKAWA Goo (50176161)

# of Collaborated Projects: 15 results

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2. IZUMIYA Shuichi (80127422)

# of Collaborated Projects: 15 results

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3. YAMAGUCHI Keizo (00113639)

# of Collaborated Projects: 12 results

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4. SUWA Tatsuo (40109418)

# of Collaborated Projects: 11 results

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5. KAWAZUMI Nariya (30214646)

# of Collaborated Projects: 4 results

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6. MINAKAWA Hiroyuki (30241300)

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7. SATO Hajime (30011612)

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8. MATSUMOTO Shigenori (80060143)

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9. ONO Kaoru (20204232)

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10. NAKAMURA Iku (50022687)

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11. KIYOHARA Kazuyoshi (80153245)

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12. TOSE Nobuyuki (00183492)

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13. 田中昇 (80025296)

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14. TSUBOI Takashi (40114566)

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15. MORITA Shigeyuki (70011674)

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16. SASAKI Takeshi (00022682)

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17. NISHIMORI Toshiyuki (50004487)

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18. UEDA Tetsuo (10127053)

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19. 森川良三 (90087081)

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26. MASUDA Mikiya (00143371)

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27. OHSHIKA Ken'ichi (70183225)

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28. KONO Akira (00093237)

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29. KOJIMA Sadayoshi (90117705)

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30. SAKUMA Makoto (30178602)

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31. FUKAYA Kenji (30165261)

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32. SAEKI Osamu (30201510)

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33. KATO Hisao (70152733)

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34. KOHNO Toshitake (80144111)

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35. KANENOBU Taizo (00152819)

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36. KAWAUCHI Akio (00112524)

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37. IWASE Norio (60213287)

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38. MATSUMOTO Keiji (30229546)

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39. HURUHATA Hitoshi (80282036)

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40. YATSUI Tomoaki (00261371)

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41. OZAWA Tetasuya (20169288)

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42. SUZUKI Haruo (80000735)

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43. 日比孝之 (80181113)

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45. OKA Mutsuo (40011697)

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46. HONDA Naofumi (00238817)

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47. 森吉仁志 (00239708)

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48. 森本徹 (80025460)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
49. 神田雄高 (30280861)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
50. YOSHINO Masatomi (00145658)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
51. KIKKAWA Michihika (70032430)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
52. 須川敏幸 (30235858)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
53. TAKAMURA Masashi (60206886)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
54. MORIYAMA Youichi (80210201)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
55. 大仁田義裕 (90183764)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
56. ITO Hidekazu (90159905)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
57. TANAKA Kazunaga (20188288)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
58. KOKUBU Hiroshi (50202057)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
59. MORITA Takehiko (00192782)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
60. 志賀啓成 (10154189)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
61. INABA Takashi (40125901)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
62. KANAI Masahiko (70183035)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
63. NAKAYAMA Hiromichi (30227970)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
64. ASUKE Taro (30294515)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
65. TAKEBE Takashi (60240727)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
66. MAJIMA Hideyuki (50111456)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
67. 伊藤敏和 (60110178)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
68. 大沢健夫 (30115802)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
69. 宍倉光広 (70192606)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
70. USHIKI Shigehiro (10093197)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
71. TANIGUCHI Masahiko (50108974)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
72. TSUJII Masato (20251598)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
73. KISAKA Masashi (70244671)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
74. 稲生啓行 (00362434)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results

Nakai Isao 中居 功

NAKAI Isao 中居 功

中尾 功 ナカオ イワオ

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Geometry of Planar 3-websPrincipal Investigator

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Relations of formal power series of one variable and coding of space curves by iterated path integralsPrincipal Investigator

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Topology of Solutions of 1st order PDEs and web gPrincipal Investigator

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Geometry of webs, Hamiltonian systems and complex dynamicsPrincipal Investigator

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可積分系の幾何学とWeb幾何学Principal Investigator

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Nakai Isao 中居功

NAKAI Isao 中居功

中尾功ナカオイワオ