The homeomorphism Problem of families of functions of several variables and the data compression problem of multidimensional numerical tables

• Project/Area Number: 19540148
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Tokyo University of Science
• Principal Investigator: AKASHI Shigeo Tokyo University of Science, 理工学部, 教授 (30202518)
• Project Period (FY): 2007 – 2009
• Project Status: Completed (Fiscal Year 2009)
• Budget Amount: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000); Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2007: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
• Keywords: Hilbertの第13問題 / ε-entropy / データ圧縮問題 / 多次元数値表ε-拡大的力学系 / 完全不連結空間 / 同型問題 / 埋蔵問題 / ε-エントロピー / 重ねあわせ表現 / Kolmogorov-Arnoldの表現定理 / Vituskinの定理 / 強(弱)表現可能性 / 強(弱)表現不可能性 / 記号力学系 / データ圧縮 / Kolmogorov-Arnoldの定理 / Cauchyの積分定理 / ベクトルの外積 / 形状認識 / 隣接点判定法 / Jordanの閉曲線定理 / 2次元数値表

Research Abstract

A series of my interdisciplinary research papers are mainly situated on the boundary between mathematics and computer science, because I think that mutual application of each other's good quality is important. More exactly speaking, my research papers can be divided into the following two parts :
1. Unsolved problems derived from the 13^<th> problem formulated by D. Hilbert.
2. Homeomorphism problems of ε-expansive dynamical systems on totally disconnected compact Hausdorff metric spaces.

Research Products

• [Journal Article] Compressibility of multidimensional numerical data constructed from smooth functions (2009)
  • Author(s): S. Kodama, S. Akashi
  • Journal Title: Proceedings of the 1st Asian Conference on Nonlinear Analysis and Optimization vol.1 Pages: 173-176
• [Journal Article] The homeomorphism problem of symmetricε-expansive dynamical systems (2009)
  • Author(s): S. Akashi, S. Kodama
  • Journal Title: Proceedings of the 5th International Conference on Nonlinear Analysis and Convex Analysis vol.5 Pages: 1-6
• [Journal Article] Compressibility of multidimensional numerical data constructed from smooth functions of one variable (2009)
  • Author(s): S.Kodama, S.Akashi
  • Journal Title: Proceedings of the First Asian Conference on Nonlinear Analysis and Optimization 第1巻 Pages: 173-176
  • Peer Reviewed
• [Journal Article] The homeomorphism problem of symmetric ε-expansive dynamical systems (2009)
  • Author(s): S.Akashi, S.Kodama
  • Journal Title: Proceedings of the 5^<th> International Conference on Nonlinear Analysis and Convex Analysis 第5巻 Pages: 1-6
  • Peer Reviewed
• [Journal Article] A Version of Hilbert's 13th problem for entire functions (2008)
  • Author(s): S. Akashi
  • Journal Title: Taiwanese Math. Journal vol.38 Pages: 15-27
• [Journal Article] The homeomorphism problem of symmetric ε-dynamical systems (2008)
  • Author(s): Shigeo Akashi, Satoshi Kodama
  • Journal Title: Proceedings of the 5th International Conference on Nonlinear Analysis and convex Analysis 5 Pages: 1-6
  • Peer Reviewed
• [Journal Article] Compressibility of multidimensional numerical data constructed from smooth functions of one variable
  • Author(s): Satoshi Kodama, Shigeo Akashi
  • Journal Title: Proceedings of the 1st Asian Conference on Nonlinear Analysis and Optimization 掲載確定
  • Peer Reviewed
• [Journal Article] A version of Hilbert's 13th problem for infinitely differentiable functions
  • Author(s): Shigeo Akashi, Satoshi Kodama
  • Journal Title: Nonlinear Analysis Series a : Theory, Methods & Applications 掲載確定
  • Peer Reviewed
• [Presentation] Topological classification of compact-set-valued and upper-semi-continuous mappings (Keynote talk) (2009)
  • Author(s): S. Akashi
  • Organizer: The 9th International Conference on Fixed Point Theory and Its Applications
  • Place of Presentation: 國立彰化師範大学(中華民国)
  • Year and Date: 2009-07-19
• [Presentation] Topological classification of compact-set-valued and upper-semi-continuous mappings(Keynote speech) (2009)
  • Author(s): S.Akashi
  • Organizer: The 9^<th> International Conference on Fixed Point Theory and Its Applications
  • Place of Presentation: 國立彰化師範大学(中華民国)
  • Year and Date: 2009-07-17
• [Presentation] Entropy theoretic approximation of nonlinear numerical data (Invited talk) (2009)
  • Author(s): S. Akashi, S. Kodama
  • Organizer: The 6th International Conference on Nonlinear Analysis and Convex Analysis
  • Place of Presentation: 東京工業大学(日本)
  • Year and Date: 2009-03-27
• [Presentation] Entropy theoretic approximation of nonlinear numerical data(Invited talk) (2009)
  • Author(s): S.Akashi, S.Kodama
  • Organizer: The 6^<th> International Conference on Nonlinear Analysis and Convex Analysis
  • Place of Presentation: 東京工業大学(日本)
  • Year and Date: 2009-03-27
• [Presentation] Fixed point theoretic aspects of functional Banach algebra (2008)
  • Author(s): S. Akashi
  • Organizer: The 5th World Congress of Nonlinear Analysts
  • Place of Presentation: Hyatt Grand Cypress Resort Hotel, Orlando Florida, USA
  • Year and Date: 2008-07-02
• [Presentation] Fixed point theoretic aspects of functional Banach algebras (2008)
  • Author(s): Shigeo Akashi
  • Organizer: The 5th World congress of Nonlinear Analysis
  • Place of Presentation: Hyatt Grand Cypress Resort, Orlando FL, USA
  • Year and Date: 2008-07-02
• [Presentation] Fixed point theoretic classification ofε-expansive dynamical systems on compact and totally disconnected metric spaces (Keynote talk) (2007)
  • Author(s): S.Akashi
  • Organizer: The Eighth International Conference on Fixed Point Theory and Its Applications
  • Place of Presentation: Chiang-Mai University(Thailand)
  • Year and Date: 2007-07-19
• [Presentation] Fixed point theoretic classification of ε-expansive dynamical systems on compact and totally disconnected metric spaces (2007)
  • Author(s): Shigeo Akashi
  • Organizer: The Eighth International Conference on Fixed Point Theory and Its Applications
  • Place of Presentation: Chiang Mai University(Thailandでの基調講演)
  • Year and Date: 2007-07-19
• [Presentation] Computation thoeretical classification of Hilbert's 13th problem (2007)
  • Author(s): S. Akashi
  • Organizer: The Fifth International Conference on Nonlinear Analysis and Convex Analysis (Invited talk)
  • Place of Presentation: 清華大学(中華民国)
  • Year and Date: 2007-06-03
• [Presentation] Computation thoeretical classification of Hilbert's 13th problem (2007)
  • Author(s): Shigeo Akashi
  • Organizer: The Fifth International Conference on Nonlinear Analysis and Convex Analysis
  • Place of Presentation: 清華大学(中華民国での招待講演)
  • Year and Date: 2007-06-03
• [Book] Proceedings of the First Asian Conference on Nonlinear Analysis and Optimization (2009)
  • Author(s): S.Akashi, W.Takahashi, T.Tanaka
  • Total Pages: 387
  • Publisher: Yokohama Publishers
• [Book] 圧縮伸長技術, 日経SYSTEM 8 (2008)
  • Author(s): 明石重男, 奥村晴彦, 他3名
  • Publisher: 日経BP社
• [Book] 非線形解析学と凸解析学の研究, 京都大学数理解析研究所講究録 1611 (2008)
  • Author(s): 明石重男編
  • Total Pages: 220
• [Book] 日経SYSTEMS 8月号 (2008)
  • Author(s): 明石, 井上, 奥村, 桑内, 千葉, 中川, 中野, 藤原, 宮本(五十音順)
  • Publisher: 絵で見るテクノロジ「圧縮伸長技術」
• [Remarks] 本研究課題に基づいて得られたデータ圧縮関係の研究成果が、平成21年3月16日の日刊工業新聞1面で『大規模数値表を処理する数値列可逆圧縮技術』として紹介された。また本研究課題に基づいて得られた複雑形状認識システム関係の研究成果が、経済産業省産学連携プロジェクトにおける優れた研究成果としての評価を得たとして、平成19年5月16日に理化工業株式会社から技術表彰を受けた
• [Remarks] ウェブページではないが、本研究課題に基づいて得られた研究成果が、平成21年3月16日の日刊工業新聞1面で『大規模数値表を処理する数値列可逆圧縮技術』として紹介された
• [Patent(Industrial Property Rights)] 図形に関する内点判別法 (2007)
  • Inventor(s): 明石重男, 村田徹也, 付思, 佐々木愛子
  • Industrial Property Rights Holder: 理化工業株式会社
  • Filing Date: 2007-05-16
• [Patent(Industrial Property Rights)] 図形に対する内点判別方法 (2007)
  • Inventor(s): 明石, 村田, 付, 佐々木
  • Industrial Property Rights Holder: 理化工業株式会社
  • Filing Date: 2007-05-16