Computable analysis on the nonnegative real line-Walsh-Fourier transform and computability of distributions-
| Project/Area Number |
21540152
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Kyoto Sangyo University |
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Principal Investigator |
MORI Takakazu 京都産業大学, 理学部, 教授 (00065880)
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| Co-Investigator(Renkei-kenkyūsha) |
TSUJII Yoshiki 京都産業大学, 理学部, 教授 (90065871)
YASUGI Mariko 京都産業大学, 名誉教授 (90022277)
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| Project Period (FY) |
2009 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2009: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Keywords | 計算可能解析 / 計算可能関数 / 実効的連続性 / 実効的収束関数列 / 計算可能確率分布 / 実効的収束確率分布列 / 実効的ウォルシュ・フーリエ解析 / ファイン計算可能実数列 / ファイン計算可能関数 / 確率分布の実効的収束 / 分布関数 / 列計算可能性 / 特性関数 / 実効的中心極限定理 / 2進無理数 / 離散分布 / ファイン位相 / ファイン連続関数 / 計算可能分布 / 分布の実効的収束 / フラクタル / ランダムな反復アルゴリズム |
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| Research Abstract |
We formulated the Fine computability and prove the effectivization of Fubini's Theorem on the unit square. We defined computability and effective convergence of probability distributions, and investigated the relations to Fine computability and effective Fine convergence of the corresponding probability distribution functions. We also investigated the relation to computability and effective convergence of the corresponding characteristic functions. We proved an effectivization of Bochner's Theorem.
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Report
(4 results)
Research Products
(22 results)
