22 citations · 59 across the 20 of their papers we have counts for
28 papers
Sequence spaces of Baire-one functions and their porosity
Marek Balcerzak, Gertruda Ivanova
We consider several families of sequences of Baire-one self-maps of investigated by A. Alikhani-Koopaei. They form a chain of inclusions where each space is closed and nowh…
Linear relations modulo meager sets
Marek Balcerzak, Paolo Leonetti
We prove several topological zero-one laws. First, we show that, if a subset of a Banach space has the Baire property, then admits a somewhere dense set of vectors $x \…
Astrocytes: Arnol'd Tongues Generalization in Dynamical Systems' Parameter Plane
Gonzalo Marcelo Ramírez-Ávila, S. Leo Kingston, Marek Balcerzak +3
We discovered generalized structures, named astrocytes due to their shape, that constitute a defined region characterizing regular behavior within the parameter plane (PP) of dynam…
Electronic Equivalent of a Mechanical Impact Oscillator
Volodymyr Denysenko, Marek Balcerzak, Artur Dabrowski
This paper presents a novel design of an electronic circuit that is equivalent to a mechanical discontinuous impact oscillator exhibiting hard impacts. The governing equations of t…
Master Stability Function for networks of coupled non-smooth oscillators
Volodymyr Denysenko, Marek Balcerzak, Artur Dabrowski
This paper describes extension of the Master Stability Function for arrays of non-smooth oscillators. This extension is based on the previously introduced Jacobi matrix estimation…
Topological complexity of ideal limit points
Marek Balcerzak, Szymon Glab, Paolo Leonetti
Given an ideal on the nonnegative integers and a Polish space , let be the family of subsets such that is the set…
Point-set games and functions with the hereditary small oscillation property
Marek Balcerzak, Tomasz Natkaniec, Piotr Szuca
Given a metric space , we consider certain families of functions having the hereditary oscillation property HSOP and the hereditary continuous restriction pro…
Properties of equi-Baire 1 and equi-Lebesgue families of functions
Marek Balcerzak, Lubica Hola, Dusan Holy
We study several properties of equi-Baire 1 families of functions between metric spaces. We consider the related equi-Lebesgue property for such families. We examine the behaviour…
Optimization of the closed-loop controller of a discontinuous capsule drive using a neural network
Sandra Zarychta, Marek Balcerzak, Volodymyr Denysenko +3
In this paper, construction of a neural-network based, closed-loop control of a discontinuous capsule drive is analyzed. The foundation of the designed controller is an optimized o…
The existence of UFO implies projectively universal morphisms
Marek Balcerzak, Tomasz Kania
Let be a concrete category. We prove that if admits a universally free object , then there is a projectively universal morphism $u\colon \math…
Baire Category Lower Density Operators with Borel Values
Marek Balcerzak, Jacek Hejduk, Artur Wachowicz
We prove that the lower density operator associated with the Baire category density points in the real line has Borel values of class which is analogous to the measure…
Transition to hyperchaos and rare large-intensity pulses in Zeeman laser
S. Leo Kingston, Marek Balcerzak, Syamal K. Dana +1
A discontinuous transition to hyperchaos is observed at discrete critical parameters in the Zeeman laser model for three well known nonlinear sources of instabilities, namely, quas…
Instabilities in quasiperiodic motion lead to intermittent large-intensity events in Zeeman laser
S. Leo Kingston, Arindam Mishra, Marek Balcerzak +2
We report intermittent large-intensity pulses that originate in Zeeman laser due to instabilities in quasiperiodic motion, one route follows torus-doubling to chaos and another goe…
Another characterization of meager ideals
Marek Balcerzak, Szymon Glab, Paolo Leonetti
We show that an ideal on the positive integers is meager if and only if there exists a bounded nonconvergent real sequence such that the set of subsequences [resp…
Games characterizing certain families of functions
Marek Balcerzak, Tomasz Natkaniec, Piotr Szuca
We obtain several game characterizations of Baire 1 functions between Polish spaces X, Y which extends the recent result of V. Kiss. Then we propose similar characterizations for e…
A novel, Fourier series based method of control optimization and its application to a discontinuous capsule drive model
Sandra Zarychta, Tomasz Sagan, Marek Balcerzak +3
This paper presents a novel, Fourier series based numerical method of open-loop control optimization. Due to its flexible assumptions, it can be applied in a large variety of syste…
Cutting sets of continuous functions on the unit interval
Marek Balcerzak, Piotr Nowakowski, Michał Popławski
For a function , we consider the set of points at which cuts the real axis. Given and a Cantor set $D\subset [0,1]…
Convergent subseries of divergent series
Marek Balcerzak, Paolo Leonetti
Let be the set of positive real sequences such that the series is divergent. For each , let be the collectio…
The Baire Category of Subsequences and Permutations which preserve Limit Points
Marek Balcerzak, Paolo Leonetti
Let be a meager ideal on . We show that if is a sequence with values in a separable metric space then the set of subsequences [resp. permutations] of…
Families of feebly continuous functions and their properties
Marek Balcerzak, Tomasz Natkaniec, Małgorzata Terepeta
Let . The notions of feebly continuity and very feebly continuity of at a point were considered by I. Lead…
A Tauberian theorem for ideal statistical convergence
Marek Balcerzak, Paolo Leonetti
Given an ideal on the positive integers, a real sequence is said to be -statistically convergent to provided that $$ \textstyle \left\{n \…
A lower density operator for the Borel algebra
Marek Balcerzak, Szymon Głab
We prove that the existence of a Borel lower density operator (a Borel lifting) with respect to the -ideal of countable sets, for an uncountable Polish space, is equivalent to t…
Ideal convergent subseries in Banach spaces
Marek Balcerzak, Michał Popławski, Artur Wachowicz
Assume that is an ideal on , and is a divergent series in a Banach space . We study the Baire category, and the measure of the set $A(\mat…
On the Relationship between Ideal Cluster Points and Ideal Limit Points
Marek Balcerzak, Paolo Leonetti
Let be a first countable space which admits a non-trivial convergent sequence and let be an analytic P-ideal. First, it is shown that the sets of -li…