Study on Multifractal and its Applications to the Digital Sum Problems

多重分形及其在数字和问题中的应用研究

基本信息

批准号：
12640135
负责人：
OKADA Tatsuya
金额：
$ 0.45万
依托单位：
Fukushima Medical University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2000
资助国家：
日本
起止时间：
2000 至 2001
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12640135/
关键词：
Fractal Multifractal Digital Sum Problems Multinomial Measure 多項測度

项目摘要

The purpose of this research project is to study a system of infinitely many difference equations and functional equation with respect to the multinomial measure, which is a typical multifractal measure, and to apply this study to the digital sum problems expanded in the p-adic number. We investigated the digital sum problems systematic by using the multinomial measure. Each investigator considered his subject positively and made usefulcontribution. We enumerate the results in the following.1. Usual digital sum problems were solved by using the multinomial measures.2. We introduced a generalization of the power and the exponential sums, which contained information per digit, and gave explicit formulas of them by using the multinomial measure.3. As an application of the formula obtained above, we gave an explicit formula of the number of occurrences of subblock in the p-adic expansion.4. By generalizing the distribution function of multinomial measure with complex coefficients, we gave another explicit formula of Coquet's summation formula related to the binary digits in the multiple of three.Above complexity is only one instance of a generalization of the multinomial measure. In the process of this study, we found that new classes of measures, which contain the multinomial measures, are still more effective for the digital sum problems. We should prepare an effective theory of these measures for applications of the digital sum problems.

该研究项目的目的是研究相对于多项式措施的无限多个差异方程式和功能方程的系统，这是一种典型的多重措施，并将这项研究应用于P-ADIC数字中扩展的数字总和问题。我们通过使用多项式措施研究了数字总和问题系统性。每个调查人员都对他的主题进行了积极的考虑，并进行了有用的贡献。我们在下文中列举结果1。通常使用多项式措施解决了通常的数字总和问题。2。我们介绍了功率和指数总和的概括，其中包含每个数字的信息，并通过使用多项式度量给出了它们的明确公式。3。作为上述公式的应用，我们给出了p-Adic扩展中子块发生数量的明确公式。4。通过概括具有复杂系数的多项式度量的分布函数，我们给出了与三个倍数中二进制数字有关的Coquet求和公式的另一个明确的公式。Above复杂性只是多项式度量概括的一个实例。在这项研究的过程中，我们发现包含多项式措施的新措施对于数字总和问题仍然更有效。我们应该为这些措施的有效理论准备数字总和问题的应用。