Kiuchi Isao 木内功

… Alternative Names

木内功キウチイサオ

KIUCHI Isao 木内功

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Researcher Number	30271076
Other IDs
External Links
Affiliation (Current)	2025: 山口大学, その他部局等 , 名誉教授
Affiliation (based on the past Project Information) *help	2021 – 2023: 山口大学, 大学院創成科学研究科, 教授 2013: 山口大学, 大学院理工学研究科, 教授 2011 – 2013: 山口大学, 理工学研究科, 教授 2011: 山口大学, 大学院・理工学研究科, 教授 2008 – 2009: 山口大学, 大学院・理工学研究科, 教授 … More 2007: Yamaguchi University, Graduate School of Science and Engineeritng, Associate Professor 2006: 山口大学, 大学院理工学研究科, 助教授 2006: 山口大学, 理工学研究科, 助教授 2004 – 2005: 山口大学, 理学部, 助教授 1997 – 2002: 山口大学, 理学部, 助教授 1995: 山口大学, 教養部, 助教授 Less
Review Section/Research Field	Principal Investigator Algebra / Basic Section 11010:Algebra-related Except Principal Investigator Algebra / Basic analysis / Geometry / Basic analysis / Algebra / Global analysis
Keywords	Principal Investigator 数論的関数 / 乗法的関数 / リーマン・ゼータ関数 / cube-full numbers / squarefull numbers / gcd和関数 / リーマンゼータ関数 / gcd / Mean value theorems / Multiplicative functions … More / Omega results / Riemann-Siegel formula / Divisor function / Riemann zeta-function / Voronoiの公式 / Ω-結果 / short intervals / 平均値公式 / 平均値定理 / 平均的定理 / オメガ結果 / リーマン・ジィーゲル公式 / 約数関数 / 近似関数等式 … More Except Principal Investigator リーマン面 / 多重ゼータ関数 / 代数曲線 / 解析接続 / gonality / 平均値定理 / 極値的長さ / 等角写像 / 正則写像 / generalized relative projectivity / lifting module / extending module / Skew-Matrix ring / Harada ring / Nakayama ring / モジュラー関係式 / Analytic continuation / Ramanujan formula / Modular relation / 近似関数等式 / Ramanujan公式 / modular relation / 擬等角写像 / Universality / ゼータ関数 / universality / Rankin-Selberg L関数 / 漸近展開 / 二乗平均 / Riemannゼータ関数 / 閉リーマン面 / Weierstrass 点 / 特性類 / ジェット空間 / 安定ホモトピー群 / 折り目写像 / ホモトピー / 特異点 / 数論的関数 / 約数問題 / 穴あきトーラス / unimndnlar Lie noun / surface / left invariant metric / Liegroup / submanifold / homogeneous space / Grassmann geometry / リー郡 / ユニモジュラーリー群 / 曲面 / 左不変計量 / リー群 / 部分多様体 / 等質空間 / グラスマン幾何 / zeta-function associated with polynomial / exponential sum / double zeta-function / Mellin-Barnes integral / H-function / functional equation / オーダー評価 / ダブルゼータ関数 / 部分分数展開 / ワイル変換 / メリンーバーンズ積分 / 多項式ゼータ関数 / 指数和 / 2重ゼータ関数 / メリン-バーンズ積分 / H-関数 / モデュラー関係式 / 関数等式 / homotopy / Thom polynomial / jet space / singularity / smooth map / 分類空間 / ホモトピー型 / ホモトピー群 / 多様体 / 微分可能写像 / トム多項式 / 写像の特異点 / generalized relative injectivity / OF-ring / Nakayama自己同型 / Nakayama置換 / Harada環 / CS-加群 / Nakayama環 / QF-環 / Artin環 / Nakayama -automorphism / Nakayama-permutation / sjkew-matrix ring / Quasi-Frobenius ring / Artinian ring / generalized relative inectity / QF-ring / Von-Neumann regular rings / Self-duality of rings / Extending modules / Quasi-Frobenius rings / Ring theory / 多元環 / ノイマン正則環 / 環の自己双対性 / Extending module / 準フロベニウス環 / 環論 / quasi order / fundamental domain / properly discontinuous group / extremal length / conformal mapping / Riemann surface / 双曲的長さ / タイヒミュラー空間 / アールフォース関数 / ランキンの卵 / 線形誤り訂正符号 / フェルマー曲線 / ペアノ曲線 / マルチン境界 / 擬順序 / 基本領域 / 真性不連続群 / Automorphic L-function / Ramanujan's formula / Hurwitx zeta-function / Euler-Zagier sum / Multiple zeta-function / 実二次体 / 普遍性 / 多重ガンマ関数 / Mellin-Barnes formula / 保型L関数 / 普遍性定理 / Hurwitzゼータ関数 / Euler-Zagier和 / Multiple zeta function / Elliptic curve / Arithmetical function / Mean value formula / Dirichlet series / Rankin-Selberg 級数 / Bernoulli数 / 楕円曲線 / Dirichlet級数 / global solutions / growth estimate / distortion estimate / Bloch functions / Beltrami differential / variational formula / quasiconformal mapping / singular integral / 大域解 / 増大度評価 / 歪曲評価 / Bloch函数 / Beltrami微分 / 変分公式 / 特異積分作用素 / Weierstrass point / normal generation / Brill-Noether theory / meromorphic function / algebraic curve / compact Riemann surface / ブリル・ネーター理論 / Weierstrass点 / 正規生成性 / Brill-Noether 理論 / 有理型函数 / Rankin-Selberg L-function / Asymptotic expansion / Mean square / Divisor problem / Voronoi's formula / Dirichlet L-function / Riemann zeta-function / 二重ガンマ関数 / Pisot数 / L関数 / Lerchゼータ関数 / Voronoiの公式 / Voronoi公式 / Dirichlet L関数 / 閉 Riemann 面 / ２葉被覆 / bielliptic / 閉 Riemann面 / gonality 列 / 関数論 / 解析学 / 写像 / K-軌道 / J-image / 球面の安定ホモトピー群 / Pontrjagin類 / Thom多項式 / コボルディズム. / 折り目 / 可微分写像 / ヴォロノイ公式 / 2乗平均 / 数論敵関数 / スターリング数 / ラマヌジャン / 離散和と連続和 / ランキン-セルバーグ級数 / ガウスの円問題 / ディリクレの約数問題 / リーマンゼータ関数 / ベルヌーイ多項式 / チャウラ-ワールムの和 / 数論的誤差項 / 円問題 / 極値截線写像 / 単葉関数 / 共形幾何構造 / 変分問題 / p-調和写像 / n-調和写像 / conformal geometric structure / n-harmonic map Less

On sums of arithmetic functions involving gcd-sum functionsPrincipal Investigator
- Principal Investigator
  
  木内功
- Project Period (FY)
  2021 – 2024
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Review Section
  
  Basic Section 11010:Algebra-related
- Research Institution
  Yamaguchi University
Studies on special linear series and Weierstrass points on compact Riemann surfaces
- Principal Investigator
  
  KATO Takao
- Project Period (FY)
  2011 – 2013
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Basic analysis
- Research Institution
  Yamaguchi University
Research on holomorphic mappings of Riemann surfaces----roles of handles played in the existence problem of holomorphic mappings
- Principal Investigator
  
  MASUMOTO Makoto
- Project Period (FY)
  2010 – 2013
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Basic analysis
- Research Institution
  Yamaguchi University
Analytic properties of the error term arising from the arithmetical problems
- Principal Investigator
  
  TANIGAWA Yoshio
- Project Period (FY)
  2009 – 2011
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Nagoya University
Homotopy theory on singularities of differentiable maps and K-invariant spaces of the jet spaces
- Principal Investigator
  
  ANDO Yoshifumi
- Project Period (FY)
  2009 – 2011
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Geometry
- Research Institution
  Yamaguchi University
Holomorphic mappings of Riemann surfaces with handles
- Principal Investigator
  
  MASUMOTO Makoto
- Project Period (FY)
  2007 – 2009
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Basic analysis
- Research Institution
  Yamaguchi University
n-harmonic maps and conformal structures on Riemannian manifolds
- Principal Investigator
  
  NAKAUCHI Nobumitsu
- Project Period (FY)
  2006 – 2008
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Global analysis
- Research Institution
  Yamaguchi University
Beneath on analytic properties ofvarious zeta-functions
- Principal Investigator
  
  TANIGAWA Yoshio
- Project Period (FY)
  2005 – 2007
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Nagoya University
Study on submanfolds of homogeneous spaces from the view of orbital Grassmann geometry
- Principal Investigator
  
  NAITOH Hiroo
- Project Period (FY)
  2005 – 2007
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Geometry
- Research Institution
  Yamaguchi University
Research of invariants of singularities of smooth mappings
- Principal Investigator
  
  ANDO Yoshifumi
- Project Period (FY)
  2004 – 2005
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Geometry
- Research Institution
  Yamaguchi University
Study on Artinian rings with priority given to Quasi-Frobenius rings
- Principal Investigator
  
  OSHIRO Kiyoichi
- Project Period (FY)
  2001 – 2002
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Yamaguchi University
Studies on the analytic behaviour of number theoretic L-functions
- Principal Investigator
  
  MATSUMOTO Kohji
- Project Period (FY)
  2000 – 2002
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Research Field
  
  Algebra
- Research Institution
  Nagoya University
Holomorphic mappings and moduli of Riemann surfaces
- Principal Investigator
  
  MASUMOTO Makoto
- Project Period (FY)
  2000 – 2002
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Research Field
  
  Basic analysis
- Research Institution
  Yamaguchi University
Research of quasi-Frobenius rings and representation theory
- Principal Investigator
  
  YOSHIMURA Hiroshi
- Project Period (FY)
  2000 – 2001
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Yamaguchi University
Sum formulas for arithmetical functions and mean value theorem for the zeta functions
- Principal Investigator
  
  TANIGAWA Yoshio
- Project Period (FY)
  1999 – 2000
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Nagoya University
Meromorphic functions on Riemann surfaces, Weierstrass points
- Principal Investigator
  
  KATO Takao
- Project Period (FY)
  1998 – 1999
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Research Field
  
  Basic analysis
- Research Institution
  Yamaguchi University
Mean values and Asymptotic Behavior on Arithmetical FunctionsPrincipal Investigator
- Principal Investigator
  
  KIUCHI Isao
- Project Period (FY)
  1998 – 1999
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Yamaguchi University
Variational Formula for Quasiconformal Mappings
- Principal Investigator
  
  YANAGIHARA Hiroshi
- Project Period (FY)
  1998 – 1999
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Basic analysis
- Research Institution
  Yamaguchi University
Behavior of Zeta and L-functions and their arithmetic meaning
- Principal Investigator
  
  MATSUMOTO Kohji
- Project Period (FY)
  1997 – 1999
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Research Field
  
  Algebra
- Research Institution
  Nagoya University
リーマン・ゼータ関数の近似関数等式に関する残余項の研究Principal Investigator
- Principal Investigator
  
  木内功
- Project Period (FY)
  1995
- Research Category
  
  Grant-in-Aid for Encouragement of Young Scientists (A)
- Research Field
  
  Algebra
- Research Institution
  Yamaguchi University

All 2023 2022 2021 2011 2008 2006

All Journal Article Presentation

[Journal Article] On sums of gcd-sum functions2023
- Author(s)
  Inoue Shota、Kiuchi Isao
- Journal Title
  
  International Journal of Number Theory
  
  Volume: 19 Issue: 03 Pages: 593-619
- DOI
  10.1142/s179304212350029x
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22KJ1263, KAKENHI-PROJECT-21K03205
[Journal Article] On a sum involving squarefull numbers, II2023
- Author(s)
  Kiuchi Isao
- Journal Title
  
  Moscow Journal of Combinatorics and Number Theory
  
  Volume: 12 Issue: 3 Pages: 241-246
- DOI
  10.2140/moscow.2023.12.241
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21K03205
[Journal Article] On a sum involving squarefull numbers2022
- Author(s)
  Kiuchi, Isao
- Journal Title
  
  Rocky Mt. J. Math
  
  Volume: 52
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21K03205
[Journal Article] On sums of sums involving cube-full numbers2022
- Author(s)
  Kiuchi, Isao
- Journal Title
  
  Ramanujan J
  
  Volume: 59
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21K03205
[Journal Article] On the weighted average number of subgroups of Zm Zn with mn<x2022
- Author(s)
  Kiuchi Isao, Saad-Eddin.Sumaia
- Journal Title
  
  Inter. J. Number Theory
  
  Volume: 18
- Peer Reviewed / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-21K03205
[Journal Article] On sums of sums involving squarefull numbers2021
- Author(s)
  Kiuchi, Isao
- Journal Title
  
  Acta Arithmetica
  
  Volume: 200 Pages: 197-211
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21K03205
[Journal Article] Analytic properties of double zeta-functions2011
- Author(s)
  I.Kiuchi
- Journal Title
  
  Indagationes Mathematics
  
  Volume: 21 Pages: 16-29
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21540085
[Journal Article] Analytic properties of double zeta-functions2011
- Author(s)
  I. kiuchi, Y. Tanigawa, and W. Zhai
- Journal Title
  
  Indagationes Mathematicae
  
  Volume: 21 Pages: 16-29
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21540085
[Journal Article] Analytic properties of double zeta functions2011
- Author(s)
  I.Kiuchi, Y.Tanigawa, W.Zhai
- Journal Title
  
  Indag.Math.
  
  Volume: 21 Issue: 1-2 Pages: 16-29
- DOI
  10.1016/j.indag.2010.12.001
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21540012
[Journal Article] Analytic properties of double zeta functions2011
- Author(s)
  Kiuchi, Y. Tanigawa, W. Zhai
- Journal Title
  
  Indag. Math.
  
  Volume: 21 Pages: 16-29
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21540012
[Journal Article] Bounds for triple zeta-functions2008
- Author(s)
  Isao Kiuchi
- Journal Title
  
  Indagationes Math, N. S. 19
  
  Pages: 97-114
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18540217
[Journal Article] Bounds for triple zeta-functions2008
- Author(s)
  Isao Kiuchi and Yoshio Tanigawa
- Journal Title
  
  Indagationes Mahem,N.S. 19
  
  Pages: 97-114
- Data Source
  KAKENHI-PROJECT-18540217
[Journal Article] Bounds for triple zetafunctions2008
- Author(s)
  Isao Kiuchi
- Journal Title
  
  Indagonationes Mathematicae 第19巻
  
  Pages: 97-114
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19540187
[Journal Article] Bounds for triple zeta-functions2008
- Author(s)
  I. Kiuchi
- Journal Title
  
  Indagonationes Mathematicae 19
  
  Pages: 97-114
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19540187
[Journal Article] Bounds for double zeta-functions2006
- Author(s)
  Isao Kiuchi
- Journal Title
  
  Annali della Scuola Normale Superiore di Pisa, Classe di Scienze (5) 5・4
  
  Pages: 445-464
- Data Source
  KAKENHI-PROJECT-17540081
[Journal Article] Bounds for double zeta function2006
- Author(s)
  I. Kiuchi and Y. Tanigawa
- Journal Title
  
  Ann. Scoula Norm. Sup. Pisa V
  
  Pages: 445-464
- Description
  「研究成果報告書概要(和文)」より
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-17540022
[Journal Article] Bounds for double geta functions2006
- Author(s)
  I.Kiuchi, Y.Taningawa
- Journal Title
  
  Aun. Scoula Norm. Sup. Pisa V
  
  Pages: 445-464
- Data Source
  KAKENHI-PROJECT-17540022
[Journal Article] Bounds for double zeta-functions2006
- Author(s)
  Isao Kiuchi and Yoshio Tanigawa
- Journal Title
  
  Annali Scuola Normale Superiore di Pisa,Classe di Scienze V.
  
  Pages: 445-464
- Data Source
  KAKENHI-PROJECT-18540217
[Journal Article] Bounds for double zeta functions2006
- Author(s)
  I. Kiuchi, Y. Tanigawa
- Journal Title
  
  Ann. Scoula Norm. Sup. Pisa, V
  
  Pages: 445-464
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-17540022
[Presentation] ゼータ関数の性質2008
- Author(s)
  木内功
- Organizer
  平成19年度日本数学会中国・四国支部例会
- Place of Presentation
  山口大学
- Year and Date
  2008-01-27
- Data Source
  KAKENHI-PROJECT-19540187

1. MASUMOTO Makoto (50173761)

# of Collaborated Projects: 7 results

# of Collaborated Products: 0 results
2. YANAGIHARA Hiroshi (30200538)

# of Collaborated Projects: 7 results

# of Collaborated Products: 0 results
3. TANIGAWA Yoshio (50109261)

# of Collaborated Projects: 6 results

# of Collaborated Products: 4 results
4. KATO Takao (10016157)

# of Collaborated Projects: 5 results

# of Collaborated Products: 0 results
5. KOMIYA Katsuhiro (00034744)

# of Collaborated Projects: 4 results

# of Collaborated Products: 0 results
6. SHIBA Masakazu (70025469)

# of Collaborated Projects: 4 results

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7. YAMADA Akira (60126331)

# of Collaborated Projects: 4 results

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8. MATSUMOTO Kohji (60192754)

# of Collaborated Projects: 4 results

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9. AKIYAMA Shigeki (60212445)

# of Collaborated Projects: 4 results

# of Collaborated Products: 0 results
10. WATANABE Tadashi (10107724)

# of Collaborated Projects: 3 results

# of Collaborated Products: 0 results
11. KIKUMASA Isao (70234200)

# of Collaborated Projects: 3 results

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12. NAITOH Hiroo (10127772)

# of Collaborated Projects: 3 results

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13. SATO Yoshihisa (90231349)

# of Collaborated Projects: 3 results

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14. KANEMITSU Shigeru (60117091)

# of Collaborated Projects: 3 results

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15. ANDO Yoshifumi (80001840)

# of Collaborated Projects: 3 results

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16. KITAOKA Yoshiyuki (40022686)

# of Collaborated Projects: 3 results

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17. MIYAZAWA Yasuyuki (60263761)

# of Collaborated Projects: 2 results

# of Collaborated Products: 0 results
18. YOSHIMURA Hiroshi (00182824)

# of Collaborated Projects: 2 results

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19. KATAYAMA Hisao (00043860)

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20. NAKAUCHI Nobumitsu (50180237)

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21. KAWAI Shigeo (30186043)

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22. TAKEUCHI Hiroshi (20197271)

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23. HATAYA Yasushi (20294621)

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24. IIYORI Nobuyasu (00241779)

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25. OHBUCHI Akira (10211111)

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26. KATSURADA Masanori (90224485)

# of Collaborated Projects: 2 results

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27. OSHIRO Kiyoichi (90034727)

# of Collaborated Projects: 2 results

# of Collaborated Products: 0 results
28. KUTAMI Mamoru (80034734)

# of Collaborated Projects: 2 results

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29. TAKAKUWA Shoichiro (10183435)

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30. OKADA Mari (40201389)

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31. FURUYA Jun (10413890)

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32. KAJI Shizuo (00509656)

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33. KOMEDA Jiryou (90162065)

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34. ITO Hiroshi (30168372)

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35. HOMMA Masaaki (80145523)

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36. KURIYAMA Ken (10116717)

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37. GOUMA Tomomi (70253135)

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38. SUZUKI Noriaki (50154563)

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39. KADO Jiro (10117939)

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40. TSUKADA Haruo (00257990)

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41. 松野好雅 (30190490)

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42. 柳研二郎 (90108267)

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43. 金銅誠之 (50186847)

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44. 瀬川重男 (80105634)

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45. 河津清 (70037258)

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46. 馬場良始 (10201724)

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47. 植田玲 (70213345)

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Kiuchi Isao 木内 功

木内 功 キウチ イサオ

KIUCHI Isao 木内 功

Research Projects

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Kiuchi Isao 木内功

木内功キウチイサオ

KIUCHI Isao 木内功