Computable analysis on the nonnegative real line-Walsh-Fourier transform and computability of distributions-

• Project/Area Number: 21540152
• 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: Kyoto Sangyo University
• Principal Investigator: MORI Takakazu 京都産業大学, 理学部, 教授 (00065880)
• 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)
• Project Period (FY): 2009 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥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)
• 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

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.

Research Products

• [Journal Article] Sequential computability of a function-limiting recursion versus effective uniformity- (2010)
  • Author(s): Mariko Yasugi, Masako Washihara
  • Journal Title: Scientiae Mathematicae Japonicae Volume: Vol.71 Pages: 331-341
  • Peer Reviewed
• [Journal Article] Fine convergence of functions and its effectivization (2010)
  • Author(s): Takakazu Mori, Mariko Yasugi, Yoshiki Tsujii
  • Journal Title: Automata, Formal Languages and Algebraic Systems(World Scientific) Pages: 139-162
  • Peer Reviewed
• [Journal Article] Fine convergence of functions and its effectivization (2010)
  • Author(s): T.Mori, M.Yasugi, Y.Tsujii
  • Journal Title: Automata, Formal Languages and Algebraic Systems (World Scientific) Pages: 139-162
  • Peer Reviewed
• [Journal Article] Fine computability of probability distribution functions and computability of probability distributions on the real line (2010)
  • Author(s): T.Mori, Y.Tsujii, M.Yasugi
  • Journal Title: University of Cape Town (Abstract集) Pages: 17-17
  • NAID: 110009995243
  • Peer Reviewed
• [Journal Article] Fine-computable functions on the unit square and their integral (2009)
  • Author(s): Takakazu Mori, Mariko Yasugi, Yoshiki Tsujii
  • Journal Title: Journal of Universal Computer Science Volume: Vol.15 Pages: 1264-1279
  • URL: http://www.jucs.org/jucs_15_6/fine_computable_functions_on
  • Peer Reviewed
• [Journal Article] Fine continuous functions and fractals defined by infinite systems of contractions (2009)
  • Author(s): Yoshiki Tsujii, Takakazu Mori, Mariko Yasugi, Hideki Tsuiki
  • Journal Title: Lecture Notes in Artificial Intelligence Volume: Vol.5489 Pages: 1264-1279
  • Peer Reviewed
• [Journal Article] Random iteration algorithm for graph-directed sets, Proceedings of the Sixth International Conference on Computability and Complexity in Analysis (2009)
  • Author(s): Yoshiki Tsujii, Takakazu Mori, Mariko Yasugi, Hideki Tsuiki
  • Journal Title: Dagstuhl Research Online Publication Volume: 2275 Pages: 245-256
  • URL: http://drops.dagstuhl.de/opus/volltexte/2009/2275/pdf/Tsujii.2275.pdf
  • Peer Reviewed
• [Journal Article] Computability of probability distribution, Proceedings of the Sixth International Conference on Computability and Complexity in Analysis (2009)
  • Author(s): Takakazu Mori, Yoshiki Tsujii, Mariko Yasugi
  • Journal Title: Dagstuhl Research Online Publication Volume: 2270 Pages: 185-196
  • URL: http://drops.dagstuhl.de/opus/volltexte/2009/2270/pdf/Mori.2270.pdf
  • Peer Reviewed
• [Journal Article] Fine-computable functions on the unit square and their integral (2009)
  • Author(s): T.Mori, M.Yasugi, Y.Tsujii
  • Journal Title: Journal of Universal Computer Science 15 Pages: 1264-1279
  • Peer Reviewed
• [Journal Article] Fine continuous functions and fractals defined by infinite systems of contractions (2009)
  • Author(s): Y.Tsujii, T.Mori, M.Yasugi, H.Tsuiki
  • Journal Title: Lecture Notes in Artificial Intelligence Vol.5489 Pages: 109-125
  • Peer Reviewed
• [Journal Article] Computability of probability distribution (2009)
  • Author(s): T.Mori, Y.Tsujii, M.Yasugi
  • Journal Title: Proceedings of the Sixth International Conference on Computability and Complexity in Analysis DROPS 2009/2270 Pages: 185-196
  • Peer Reviewed
• [Journal Article] Random iteration algorithm for graph-directed sets (2009)
  • Author(s): Y.Tsujii, T.Mori, M.Yasugi, H.Tsuiki
  • Journal Title: Proceedings of the Sixth International Conference on Computability and Complexity in Analysis DROPS 20 2009/2275 Pages: 245-256
  • Peer Reviewed
• [Presentation] Fine computability of probability distribution functions and computability of probability distributions on the real line (2011)
  • Author(s): Takakazu Mori, Yoshiki Tsujii, Mariko Yasugi
  • Organizer: Computability and Complexity in Analysis(CCA2011)
  • Place of Presentation: University of Cape Town, South Africa
  • Year and Date: 2011-02-04
• [Presentation] Fine computability of probability distribution functions and computability of probability distributions on the real line (2011)
  • Author(s): T.Mori, Y.Tsujii, M.Yasugi
  • Organizer: CCA2011
  • Place of Presentation: Cape Town, 南アフリカ
  • Year and Date: 2011-02-04
• [Presentation] 極限再帰性という計算概念の基礎 (2010)
  • Author(s): 八杉満利子
  • Organizer: 科学基礎論学会
  • Place of Presentation: 専修大学生田キャンパス
  • Year and Date: 2010-06-13
• [Presentation] On sequential computability of a function (2010)
  • Author(s): Mariko Yasugi, Masako Washihara
  • Organizer: Workshop on Constructive Aspects of Logic and Mathematics
  • Place of Presentation: 金沢エクセルホテル東急
  • Year and Date: 2010-03-10
• [Presentation] Computation in the limit-its image and philosophy behind- (2009)
  • Author(s): Mariko Yasugi
  • Place of Presentation: 筑波大学
  • Year and Date: 2009-08-29
• [Presentation] Random iteration algorithm for graph directed sets (2009)
  • Author(s): Yoshiki Tsujii, Takakazu Mori, Mariko Yasugi, Hideki Tsuiki
  • Organizer: CCA2009
  • Place of Presentation: University of Ljubljana, Slovenia
  • Year and Date: 2009-08-21
• [Presentation] Computability of Probability Distributions and Distribution Functions on the Real Line (2009)
  • Author(s): Takakazu Mori, Yoshiki Tsujii, Mariko Yasugi
  • Organizer: CCA2009
  • Place of Presentation: University of Ljubljana, Slovenia
  • Year and Date: 2009-08-21
• [Presentation] Random iteration algorithm for graph-directed sets (2009)
  • Author(s): Y.Tsujii, T.Mori, M.Yasugi, H.Tsuiki
  • Organizer: CCA2009
  • Place of Presentation: University of Ljubljana, Slovenia
  • Year and Date: 2009-08-21
• [Presentation] Computability of probability distributions (2009)
  • Author(s): T.Mori, Y.Tsujii, M.Yasugi
  • Organizer: CCA2009
  • Place of Presentation: University of Ljubljana, Slovenia
  • Year and Date: 2009-08-20
• [Presentation] Cognition of computation by limiting recursion (2009)
  • Author(s): Mariko Yasugi
  • Organizer: TF4-E Workshop
  • Place of Presentation: 京都産業大学
  • Year and Date: 2009-03-23