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2005 Fiscal Year Final Research Report Summary

Analysis on a fractal set and Iteration dynamical systems of discrete Laplacians

Research Project

Project/Area Number 16540122
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionNihon University

Principal Investigator

SUZUKI Osamu  Nihon University, College of Humanities and Sciences, Professor, 文理学部, 教授 (10096844)

Co-Investigator(Kenkyū-buntansha) NONO Kiyoharu  Fukuoka University of Education, Faculty of Education, Professor, 教育学部, 教授 (10117046)
MORI Makoto  Nihon University, College of Humanities and Sciences, Professor, 文理学部, 教授 (60092532)
Project Period (FY) 2004 – 2005
Keywordsdiscrete Laplacian / iteration dynamical system / fractal set / organization and evolution
Research Abstract

System analysis is performed in the case of (1)Iteration dynamical systems of discrete Laplacian and (2)Differential and integral calculus on a fractal sets. Details can be described in the cases separately :
(1)Iteration dynamical systems of discrete Laplacian
The laplacian operator plays a very important role in mathematical physics. We may say that we can describe nothing without the Laplacian operator. Hence we may try to discretize Laplacian operators and consider the iteration dynamical systems. In this research we propose the idea on the description of the organizations and evolutions. In fact, we can give a systematic description of the designs of carpets, laces and embroideries. Also we can describe the evolutions of the extinct animals. Here we want to make a stress on the fact that we can describe the mass extinctions quite well.
(2)Differential and integral calculus on a fractal set.
We have a quite natural invariant measure on a fractal set and we can develop the integral theory with respect to the measure. In this research we could introduce derivations on a fractal set and then we can develop the differential and integral calculus on a fractal set.

  • Research Products

    (5 results)

All 2005 Other

All Journal Article (5 results)

  • [Journal Article] Periodicity theorems for graded fractal bundles related to Clifford structure2005

    • Author(s)
      Osamu SUZUKI
    • Journal Title

      International Journal of Pure and Applied Mathematics 24-2

      Pages: 181-209

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Dynamical systems defined by iterations of discrete Laplacians and their computer simulations2005

    • Author(s)
      Osamu SUZUKI
    • Journal Title

      Proceedings of the 12^th International Conference on finite or infinite dimensional complex analysis and applications 1

      Pages: 1-8

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Dynamical systems, fractal sets and fluctuations2005

    • Author(s)
      Osamu SUZUKI
    • Journal Title

      Proceedings of the 12^th International Conference on finite or infinite dimensional complex analysis and applications 1

      Pages: 253-260

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Periodicity theorems for graded fractal bundles related to Clifford structures2005

    • Author(s)
      Osamu SUZUKI
    • Journal Title

      International Journal of Pure and Applied Mathematics Vol.24-2

      Pages: 181-209

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Differential and integral calculus on fractal sets (Schauder basis 80years after)

    • Author(s)
      Osamu SUZUKI
    • Journal Title

      Proceeding of the international conference on Livov school in Poland (To appear in)

    • Description
      「研究成果報告書概要(和文)」より

URL: 

Published: 2007-12-13  

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