2018
Том 70
№ 8

All Issues

Makarchuk O. P.

Articles: 2
Article (Ukrainian)

Frequency of a Digit in the Representation of a Number and the Asymptotic Mean Value of the Digits

Klymchuk S. O., Makarchuk O. P., Pratsiovytyi M. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2014. - 66, № 3. - pp. 302–310

We study the relationship between the frequency of a ternary digit in a number and the asymptotic mean value of the digits. The conditions for the existence of the asymptotic mean of digits in a ternary number are established. We indicate an infinite everywhere dense set of numbers without frequency of digits but with the asymptotic mean of the digits.

Article (Ukrainian)

Distribution of Random Variable Represented by a Binary Fraction with Three Identically Distributed Redundant Digits

Makarchuk O. P., Pratsiovytyi M. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2014. - 66, № 1. - pp. 79–88

We present the complete solution of the problem of pure Lebesgue type of the distribution of random variable χ represented by a binary fraction with three identically distributed redundant digits.