Fundamentals of metric theory of real numbers in their $\overline{Q_3}$-representation

Q3 Mathematics
I. Zamrii, V. Shkapa, H. Vlasyk
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引用次数: 0

Abstract

In the paper we were studied encoding of fractional part of a real number with an infinite alphabet (set of digits) coinciding with the set of non-negative integers. The geometry of this encoding is generated by $Q_3$-representation of real numbers, which is a generalization of the classical ternary representation. The new representation has infinite alphabet, zero surfeit and can be efficiently used for specifying mathematical objects with fractal properties. We have been studied the functions that store the "tails" of $\overline{Q_3}$-representation of numbers and the set of such functions,some metric problems and some problems of probability theory are connected with $\overline{Q_3}$-representation.
实数度量理论的基本原理及其$\overline{Q_3}$-表示
本文研究了与非负整数集重合的无穷字母(数字集)实数小数部分的编码问题。这种编码的几何形式是由实数的$Q_3$-表示生成的,它是经典三元表示的推广。该表示具有无穷字母、零过剩的特点,可以有效地表示具有分形性质的数学对象。研究了$\overline{Q_3}$-表示的“尾”函数及其集合,并讨论了与$\overline{Q_3}$-表示有关的度量问题和概率论中的一些问题。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Matematychni Studii
Matematychni Studii Mathematics-Mathematics (all)
CiteScore
1.00
自引率
0.00%
发文量
38
期刊介绍: Journal is devoted to research in all fields of mathematics.
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