• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Substitution and its Application

Research Project

Project/Area Number 09640291
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 InstitutionTsuda College

Principal Investigator

ITO Shunji  Tsuda College, Dep. Liberal Arts, Professor, 学芸学部, 教授 (30055321)

Co-Investigator(Kenkyū-buntansha) OTUKI Makoto  Tsuda College, Dep. Liberal Arts, Professor, 学芸学部, 教授 (20110348)
NIWA Toshio  Tsuda College, Dep. Liberal Arts, Professor, 学芸学部, 教授 (70025419)
KASAHARA Kenkichi  Tsuda College, Dep. Liberal Arts, Professor, 学芸学部, 教授 (40012330)
TACHII Hiroko  Tsuda College, Dep. Liberal Arts, Assistant, 学芸学部, 研究助手 (20286959)
TANAKA Shigeru  Tsuda College, Dep. Liberal Arts, Professor, 学芸学部, 教授 (70055317)
Project Period (FY) 1997 – 1999
Project Status Completed (Fiscal Year 1999)
Budget Amount *help
¥2,600,000 (Direct Cost: ¥2,600,000)
Fiscal Year 1999: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 1998: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 1997: ¥1,000,000 (Direct Cost: ¥1,000,000)
Keywordssubstitution / fractal / titling / atomic surface / stepped surfaces / multi-dim continued fraction / Substitution / Dynamical system / Diophantine近似 / discrepancy / Markov partition / フラクタル / タイリング / ディオファンタス近似 / Markov変換 / アディング マシーン / Tiling / 多次元連分数変換
Research Abstract

On substitutions and related topics we success
(1) to give the decomposition theorem of 2 states invertible substitutions,
(2) to construct the tiling substitution of plane by using the idea of dual substitution,
(3) to study uniformity of orbit of 2 dimentional rotation on TィイD12ィエD1,
(4) to study the fractal structure of atomic surface from unimodular substitution.

Report

(4 results)
  • 1999 Annual Research Report   Final Research Report Summary
  • 1998 Annual Research Report
  • 1997 Annual Research Report
  • Research Products

    (9 results)

All Other

All Publications (9 results)

  • [Publications] Shunji ITO: "Symbolical and geometrical characterizations of Kronecker sequences by using the accelerated bran's algorithm"J. Math. Sei. Univ. Tokyo. 7. 163-193 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Shunji ITO: "Decomposition theorem on invertible substitutions"Osala J. Math. 35. 821-834 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Shunji ITO: "Symbolical and geometrical characterizations of Kronecker sequences by using the accelerated Brun's algorithm"J. Math. Sei. Univ. Tokyo. 7. 163-193 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Shunji ITO: "Decomposition theorem on invertible substitutions"Osaka J. Math. 35. 821-834 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Ei Hiromi: "Decomposition the theorem on invertible substitutions"Osaka J. Math.. 35. 821-834 (1998)

    • Related Report
      1999 Annual Research Report
  • [Publications] Maki Furukado: "The quasi-periodic tiling of the plane and Markov subshifts"Japanese Journal of Math.. 24. 1-42 (1998)

    • Related Report
      1999 Annual Research Report
  • [Publications] Maki FURUKADO: "The quasi-periodic tiling of the plane and Markovsubshifts" JAPANESE JOURNAL OF MATHEMATICS. Vo1・24,No.1. 1-42 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Hiromi EI: "Decomposition theorem on invertible substitutions" Osaka J・Math.35. 821-834 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 古門・麻貴: "The quasi-periodic Tiling of the Plane" Japanese Jarnal of Mathematics. 24-1. (1998)

    • Related Report
      1997 Annual Research Report

URL: 

Published: 1997-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi