21 citations · 200 across the 33 of their papers we have counts for
34 papers
Applications of certain probability distributions on positive integers
Symon Serbenyuk
The main goal of this research is to model and investigate generalizations of functions from [31]. Arguments of modeled functions are presented by the representation $π_{\mathfrak…
Minkowski type functions on probability distributions
Symon Serbenyuk
In this research, Minkowski type functions which are constructed on certain probability distributions, are introduced. There are investigated differential, integral, and other prop…
The Engel--Minkowski question-mark function
Symon Serbenyuk
The present article deals with properties of a certain function of the Minkowski type with arguments defined by Engel series. Differential, integral, and other properties of the fu…
On one map between singular expansions
Symon Serbenyuk
The present article deals with properties of one map between two expansions of real numbers of the Salem type. Differential, integral, and other properties of the function were con…
Systems of functional equations, the generalized shift, and modelling pathological functions
Symon Serbenyuk
The present article is devoted to one class of generalizations of the Salem functions. To construct such functions by systems of functional equations, the generalized shift operato…
On one class of modifications of the Salem function
Symon Serbenyuk
The present article deals with properties of one class of functions with complicated local structure. These functions can be modeled by certain operators of digits. Such operators…
One example of singular representations of real numbers from the unit interval
Symon Serbenyuk
In this article, for modelling numeral systems, the operator approach, which is introduced in [25], is generalized for a certain case. An example of such numeral systems is introdu…
One modification of the Salem function
Symon Serbenyuk
The present article is devoted to one example which related to the Salem function. The main attention is given to properties of one type of functions including items related to fun…
One class of functions with arguments in negative bases
Symon Serbenyuk
The present research deals with generalizations of the Salem function with arguments defined in terms of certain alternating expansions of real numbers. The special attention is gi…
A note on rational numbers and certain operators
Symon Serbenyuk
This paper is devoted to conditions defined in terms of the generalized shift operator for a rational number to be representable by certain positive generalizations of -ary expa…
Rational numbers represented by sign-variable Cantor series
Symon Serbenyuk
The present article is devoted to representations of rational numbers in terms sign-variable Cantor expansions. The main attention is given to one of the discussions given by J. Ga…
Certain singular distributions and fractals
Symon Serbenyuk
In the present article, the main attention is given to fractal sets whose elements have certain restrictions on using digits or combinations of digits in own nega-P-representation.…
On certain maps defined by infinite sums
Symon Serbenyuk
The present article is devoted to some examples of functions whose arguments represented in terms of certain series of the Cantor type.
On certain generalizations of one function and related problems (Systems of functional equations and generalizations of certain functions)
Symon Serbenyuk
The present article is devoted to the generalized Salem functions, the generailed shift operator, and certain related problems. A description of further investigations of the autho…
Generalized shift operator of certain encodings of real numbers
Symon Serbenyuk
The present article is devoted to the investigation of some properties of the generalized shift operator of numbers represented in terms of numeral systems with a variable alphabet…
On certain functions and related problems
Symon Serbenyuk
The present article is devoted to the description of further investigations of the author of this article. These investigations (in terms of various representations of real numbers…
On one approach to modeling numeral systems
Symon Serbenyuk
In this article, the operator approach to modeling numeral systems is introduced. This approach can be useful for coding information and providing computer protection. Certain exam…
Certain functions defined in terms of Cantor series
Symon Serbenyuk
The present article is devoted to certain examples of functions whose argument represented in terms of Cantor series.
Modeling rational numbers by Cantor series
Symon Serbenyuk
In the present article, modeling certain rational numbers, that are represented in terms of Cantor series, are described. The statements on relations between digits in the represen…
One distribution function on the Moran sets
Symon Serbenyuk
In the present article, topological, metric, and fractal properties of certain sets are investigated. These sets are images of sets whose elements have restrictions on using digits…
Generalizations of certain representations of real numbers
Symon Serbenyuk
In the present article, real number representations, that are generalizations of classical positive and alternating representations of numbers, are introduced and investigated. The…
Cantor series expansions of rational numbers
Symon Serbenyuk
This survey is devoted to necessary and suffcient conditions for a rational number to be representable by a Cantor series. Necessary and suffcient conditions are formulated for the…
More on one class of fractals
Symon Serbenyuk
This article is devoted to sets having the Moran structure. The main attention is given to topological, metric, and fractal properties of certain sets whose elements have restricti…
Non-differentiable functions defined in terms of classical representations of real numbers
Symon Serbenyuk
The present article is devoted to functions from a certain subclass of non-differentiable functions. The arguments and values of considered functions represented by the s-adic repr…