2 citations · 2 across the 7 of their papers we have counts for
7 papers
From Dimension Drop to Aperiodic Order
Natalia Jurga, Dmytro Karvatskyi
We consider the parametrised family of sets for $(x,y) \in…
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…
Topological, metric and fractal properties of one family of self-similar sets
Dmytro Karvatskyi
Depending on a natural parameter , we study the topological, metric, and fractal properties of the homogeneous self-similar set $$K_{l}=\left\{\sum_{i=1}^{\infty} \frac{\varepsi…
On the Lebesgue measure of one generalised set of subsums of geometric series
Oleg Makarchuk, Dmytro Karvatskyi
In the present paper, we study a set that can be treated as a generalised set of subsums for a geometric series. This object was discovered independently in various mathematical as…
Fractal analysis of Guthrie-Nymann's set and its generalisations
Mykola Pratsiovytyi, Dmytro Karvatskyi
In this paper, we study the fractal properties of the boundary of the Cantorval connected with Guthrie-Nymann's series. In particular, we prove that such a Cantorval can be represe…
The achievement set of generalized multigeometric sequences
Dmytro Karvatskyi, Aniceto Murillo, Antonio Viruel
We study the topology of all possible subsums of the generalized multigeometric series where $k_1, k_2, \do…
Cantorvals as sets of subsums for a series connected with trigonometric functions
Mykola Pratsiovytyi, Dmytro Karvatskyi
We study properties of the set of subsums for a convergent series , where $k_1, k_2, k_3,\dots…