3 citations · 7 across the 17 of their papers we have counts for
18 papers
Infinite continued fractions with a finite alphabet and their applications
Mykola Pratsiovytyi, Sofiia Ratushniak
The paper investigates the topological and metric properties of the set of values of all infinite continued fractions of the form \[0+\frac{1}{a_1+\dfrac{1}{a_2+_{\ddots}}}=1/a…
Fractal random variables defined by probability distributions of digits of their -representation having two bases with different signs
M. Pratsiovytyi, O. Baranovskyi, I. Lysenko +1
In this paper, we study distributions of two random variables \begin{gather*} τ= τ_1 g_{1-τ_1} + \sum_{k=2}^\infty τ_k g_{1-τ_k} \prod_{i=1}^{k-1} g_{τ_i} \equiv Δ^{G_2}_{τ_1τ_2...…
Infinite Bernoulli convolutions generated by multigeometric series and their properties
Mykola Pratsiovytyi, Dmytro Karvatskyi, Oleg Makarchuk
The paper is devoted to infinite Bernoulli convolutions generated by positive multigeometric series and to probability distributions of random variables whose digits in an even int…
On one class of nowhere non-monotonic functions with fractal properties that contains a subclass of singular functions
S. O. Klymchuk, M. V. Pratsiovytyi
We study one class of continuous functions defined on segment by equality $$ f(x)=δ_{α_1(x)1}+\sum^{\infty}_{k=2}\left[δ_{α_k(x)k}\prod^{k-1}_{j=1}g_{α_j (x)j}\right]\e…
Transformations and functions that preserve the asymptotic mean of digits in the ternary representation of a number
M. V. Pratsiovytyi, S. O. Klymchuk, O. P. Makarchuk
In the paper we study transformations of the interval and functions that preserve the asymptotic mean of the digits in the --adic representation of a number , $$r…
Topological, metric and fractal properties of the set of real numbers with a given asymptotic mean of digits in their -adic representation in the case when the digit frequencies exist
M. V. Pratsiovytyi, S. O. Klymchuk
In the paper we describe some properties of function of -adi…