Application of Hilbert's 13th problem to lower dimensional decomposition of higher dimensional numerical tables
| Project/Area Number |
26400189
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | Tokyo University of Science |
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Principal Investigator |
Akashi Shigeo 東京理科大学, 理工学部情報科学科, 教授 (30202518)
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| 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)
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| 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)
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| 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 |
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| 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.
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Report
(4 results)
Research Products
(33 results)
