Multifractal and it's application
Project/Area Number  10640184 
Research Category 
GrantinAid for Scientific Research (C).

Section  一般 
Research Field 
Basic analysis

Research Institution  Tohoku Gakuin University 
Principal Investigator 
SEKIGUCHI Takeshi Tohoku Gakuin Univ, Faculty of Liberal Arts, Professor, 教養学部, 教授 (30004485)

CoInvestigator(Kenkyūbuntansha) 
SHIOTA Yasunobu Tohoku Gakuin Univ, Faculty of Liberal Arts, Professor, 教養学部, 教授 (00154170)

Project Fiscal Year 
1998 – 1999

Project Status 
Completed(Fiscal Year 1999)

Budget Amount *help 
¥1,300,000 (Direct Cost : ¥1,300,000)
Fiscal Year 1999 : ¥500,000 (Direct Cost : ¥500,000)
Fiscal Year 1998 : ¥800,000 (Direct Cost : ¥800,000)

Keywords  fractal / multinomial measure / Gray code / フラクタル / 多項速度 / グレー符号 / 多項測度 / マルチノミアル測度 / 特異点スペクトル 
Research Abstract 
The purpose of this research project is to make the singular point spectrum, which is a characteristic of fractal, clear mathematically strictly, and prepare an effective theory for the application to other fields. Our research was began based on our previous two results: A generalization of HataYamaguti's results on Takagi function II: Multinomial case, Japan J. Indust. Appl. Math., 13(1996),435463 and Multifractal spectrum of multinomial measures,Proc.Japan Acad,73,Ser.A( 1997), 123125 with Okada, Sekiguchi and Shiota. Earch investigator considered his subject and made usefule contribution. And we had several results. We enumerate some of that in the following. 1. Digital sum problem expanded in the padic number was solved by using the multinomial measures. 2. As an application of the above result we obtained the explicit representation of subblock occurrences for the padic expansion. 3. We characterized a kind of Gray code with a property like selfsimilarity. In the process of the above study we found the new class of selfsimilar measures, which contains the multinomial measures. These measures are characterize with the system of infintely many difference equations as same as the multinomial measures. We should investigate the singular point spectrum of thsese measures for the next subject.

Report
(4results)
Research Output
(15results)