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Application of Hilbert's 13th problem to lower dimensional decomposition of higher dimensional numerical tables

Research Project

Project/Area Number 26400189
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Foundations of mathematics/Applied mathematics
Research InstitutionTokyo University of Science

Principal Investigator

Akashi Shigeo  東京理科大学, 理工学部情報科学科, 教授 (30202518)

Co-Investigator(Kenkyū-buntansha) 児玉 賢史  東京理科大学, 理工学部情報科学科, 助教 (60632552)
Project Period (FY) 2014-04-01 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywordsヒルベルトの第13問題 / 高次元データ / シンプソン公式 / DHCPスヌーピング / ネットワークセキュリティ / エントロピー / 多変数関数 / εーエントロピー / 数値データ圧縮 / ネットワーク犯罪 / DHCP / ロンゲストマッチングルール / 数値計算高速化 / Collatz予想 / 再生核Hilbert空間 / 不動点定理 / 離散力学系 / 数値表データ / データ圧縮 / 標本化定理 / 埋蔵問題 / 集合値解析 / エントロピー解析 / 再生核Hilbert空間論
Outline of Final Research Achievements

It is well known that the the theory of higher dimensional data compression is closely related to the theory of functions of several variables, because the 13th problem formulated by Hilbert in 1900 pointed out the way of decomposing functions of several variables into some functions of less several variables in the way of keeping reproducible would play important roles in the theory of nomographs, namely, graphs which are used to make numerical calculation without calculators much easier. The first result is to give a negative solution to the infinitely differentiable function version of the Hilbert's 13th problem and the second result is to develop a numerical-integration-oriented higher dimensional data decomposition. which can accelerate Simpson'approximate integration.

Report

(4 results)
  • 2016 Annual Research Report   Final Research Report ( PDF )
  • 2015 Research-status Report
  • 2014 Research-status Report
  • Research Products

    (33 results)

All 2017 2016 2015 2014 Other

All Int'l Joint Research (8 results) Journal Article (7 results) (of which Int'l Joint Research: 3 results,  Peer Reviewed: 6 results,  Open Access: 6 results) Presentation (11 results) (of which Int'l Joint Research: 4 results,  Invited: 7 results) Book (1 results) Remarks (4 results) Funded Workshop (2 results)

  • [Int'l Joint Research] National Taiwan Normal University(Taiwan)

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research] Pukyong National University(韓国)

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research] Chiang Mai University(Thailand)

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research] National Taiwan Normal University(Taiwan)

    • Related Report
      2015 Research-status Report
  • [Int'l Joint Research] Pukyong National University/Donr-A University(韓国)

    • Related Report
      2015 Research-status Report
  • [Int'l Joint Research] Catania University(Italy)

    • Related Report
      2015 Research-status Report
  • [Int'l Joint Research] Chiang Mai University/Nareuan University(Thailand)

    • Related Report
      2015 Research-status Report
  • [Int'l Joint Research] Uniwersytet Marii Curie-Sklodowskiej(Poland)

    • Related Report
      2015 Research-status Report
  • [Journal Article] TCP 接続回線切断時点での logout 機能とセッションハイジャック持続性2016

    • Author(s)
      明石重男、藤枝俊輔、松澤智史、田内俊充
    • Journal Title

      シスコネットワーキングアカデミー全国大会NAIM2016講究録

      Volume: http://tcj.jp/

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Weak convergence theorem for an infinite family of demimetric mappings in a Hilbert space2016

    • Author(s)
      Shigeo Akashi and Wataru Takahashi
    • Journal Title

      Journal of Nonlinear and Convex Analysis

      Volume: 17 Pages: 2159-2169

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Strong convergent relative methods for generalized split feasibility problems in Hibert spaces2015

    • Author(s)
      Shigeo Akashi, Yasunori Kimura and Wataru Takahashi
    • Journal Title

      Journal of Convex Analysis

      Volume: 22 Pages: 917-938

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] The embedding problem of the ranges of a Hilbert space under the compact positive operators2015

    • Author(s)
      Satoshi Kodama and Shigeo Akashi
    • Journal Title

      Journal of Nonlinear and Convex Analysis

      Volume: 16 Pages: 2297-2300

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] パーセプトロン収束定理とハーン・バナッハの定理の関係について2015

    • Author(s)
      児玉賢史,水谷友哉,明石重男
    • Journal Title

      数理解析研究所講究録

      Volume: 1963 Pages: 231-234

    • Related Report
      2015 Research-status Report
  • [Journal Article] The homeomorphism problem of the ranges of a Hilbert space under the compact positive operators2014

    • Author(s)
      Shigeo Akashi and Satoshi Kodama
    • Journal Title

      Proceedings of the Third Asian Conference on Nonlinear Analysis and Optimization

      Volume: 3 Pages: 1-5

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] 逆問題的視点からみたFourier解析2014

    • Author(s)
      水谷友哉, 児玉賢史, 明石重男
    • Journal Title

      京都大学数理解析研究所講究録「非線形解析学と凸解析学の研究」

      Volume: 1923 Pages: 105-109

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access
  • [Presentation] Mathematics-oriented skills which may be abused for cybercrimes related to the networking systems2017

    • Author(s)
      Shigeo Akashi
    • Organizer
      International conference for leading and young computer scientists 2017
    • Place of Presentation
      Okinawa Convention Center
    • Year and Date
      2017-03-25
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 空間上に配置された複数レーザー光を用いたユーザーインターフェースの提案2016

    • Author(s)
      小瀨木悠佳、亀山眞也、児玉賢史、明石重男
    • Organizer
      第15回情報科学技術フォーラム
    • Place of Presentation
      富山大学
    • Year and Date
      2016-09-07
    • Related Report
      2016 Annual Research Report
  • [Presentation] The asymptotic behavior of iterated expansive-mapping systems2016

    • Author(s)
      Shigeo Akashi and Yasushi Kikuchi
    • Organizer
      International Workshop on Nonlinear Analysis and Convex Analysis
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2016-08-31
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] ウェブ経由によるサーバサイト攻撃のネットワーク構造論的解析2016

    • Author(s)
      明石重男、藤枝俊輔
    • Organizer
      シスコネットワーキングアカデミー全国大会2016
    • Place of Presentation
      石川ハイテク交流センター
    • Year and Date
      2016-08-18
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] Inequality theoretic relations of the variance of a probability distribution and the gradient vectorscharacterized by the density functions2015

    • Author(s)
      Satoshi Kodama, Shin-ya Kameyama, Yuka Ozeki and Shigeo Akashi
    • Organizer
      京都大学数理解析研究所共同研究集会「Nonlinear Analysis and Convex Analysis」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2015-09-07
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] ブロードキャストフレーム解析とDHCPサーバMACアドレス認証突破法2015

    • Author(s)
      明石重男,藤枝俊輔,児玉賢史,田内俊充
    • Organizer
      シスコネットワーキングアカデミー全国大会NAIM2015
    • Place of Presentation
      学校法人KBC学園 国際電子ビジネス専門学校(沖縄県那覇市)
    • Year and Date
      2015-08-20
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] The embedding problems of reproducing kernel Hilbert spaces included by L2[0,1]2015

    • Author(s)
      Shigeo Akashi
    • Organizer
      International Conference on Fixed Pointh Theory and its Applications
    • Place of Presentation
      Galatasaray University at Istanbul inTurkey
    • Year and Date
      2015-07-20
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] A relation between the orbital structure and the topological one of an ε-expansive dynamical systems2015

    • Author(s)
      Satoshi Kodama and Shigeo Akashi
    • Organizer
      The Ninth International Conference on Nonlinear Analysis and Convex Analysis
    • Place of Presentation
      Naresuan University (Thailand)
    • Year and Date
      2015-01-21 – 2015-01-25
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] OSPFv3等コストマルチパス問題とtraceroute機能の非整合性2014

    • Author(s)
      明石重男、木下稔雅、藤枝俊輔
    • Organizer
      シスコネットサーキングアカデミーNAIMI2014
    • Place of Presentation
      ソラシティカンファレンスセンター (東京都千代田区)
    • Year and Date
      2014-08-21 – 2014-08-22
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Simplification of Kolmogorov-Arnold representation related to Hilbert's 13th problem2014

    • Author(s)
      Tomoya Mizutani, Yusuke Goto, Yasushi Kikuchi, Satoshi Kodama and Shigeo Akashi
    • Organizer
      京都大学数理解析研究所共同研究集会「非線形解析学と凸解析学の研究」
    • Place of Presentation
      京都大学数理解析研究所 (京都府京都市)
    • Year and Date
      2014-08-19 – 2014-08-21
    • Related Report
      2014 Research-status Report
  • [Presentation] Application of fixed point theory and dynamical system theory to Collatz conjecture2014

    • Author(s)
      Shigeo Akashi and Satoshi Kodama
    • Organizer
      The Fourth Asian Conference on Nonlinear Analysis and Optimization
    • Place of Presentation
      National Taiwan Normal University (Taiwan)
    • Year and Date
      2014-08-05 – 2014-08-09
    • Related Report
      2014 Research-status Report
    • Invited
  • [Book] 数理解析研究所講究録「非線形解析学と凸解析学の研究」2015

    • Author(s)
      高橋渉,明石重男,児玉賢史
    • Total Pages
      234
    • Publisher
      京都大学数理解析研究所
    • Related Report
      2015 Research-status Report
  • [Remarks] 第5回非線形解析学と最適化理論アジア会議

    • URL

      http://mathweb.sc.niigata-u.ac.jp/~nao2016/

    • Related Report
      2016 Annual Research Report
  • [Remarks] 第10回非線形解析学と凸解析学国際会議

    • URL

      http://www.rs.tus.ac.jp/naca2017/

    • Related Report
      2016 Annual Research Report
  • [Remarks] シスコネットワーキングアカデミー全国大会NAIM2015

    • URL

      http://tcj.jp/news/2015/150701.php

    • Related Report
      2015 Research-status Report
  • [Remarks] Nonlinear Analysis and Convex Analysis

    • URL

      https://sites.google.com/site/fixedpointthailand/home/naca2015

    • Related Report
      2015 Research-status Report
  • [Funded Workshop] International Workshop on Nonlinear Analysis and Convex Analysis2016

    • Place of Presentation
      Research Institute for Mathematical Sciences attached to Kyoto University
    • Year and Date
      2016-08-31
    • Related Report
      2016 Annual Research Report
  • [Funded Workshop] Asian Conference on Nonlinear Analysis and Optimization2016

    • Place of Presentation
      Toki Messe, Niigata city, Niigata prefecture, Japan
    • Year and Date
      2016-08-01
    • Related Report
      2016 Annual Research Report

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Published: 2014-04-04   Modified: 2022-02-28  

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