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Rok 2024
  • An absorbing set for the Chialvo map

    The classical Chialvo model, introduced in 1995, is one of the most important models that describe single neuron dynamics. In order to conduct effective numerical analysis of this model, it is necessary to obtain a rigorous estimate for the maximal bounded invariant set. We discuss this problem, and we correct and improve the results obtained by Courbage and Nekorkin (2010). In particular, we provide an explicit formula for an...

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  • Linear Time-Varying Dynamic-Algebraic Equations of Index One on Time Scales
    Publikacja

    - Rok 2024

    In this paper, we introduce a class of linear time-varying dynamic-algebraic equations (LTVDAE) of tractability index one on ar- bitrary time scales. We propose a procedure for the decoupling of the considered class LTVDAE. Explicit formulae are written down both for transfer operator and the obtained decoupled system. A projector ap- proach is used to prove the main statement of the paper and sufficient conditions of decoupling...

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Rok 2023
Rok 2022
  • A convergence result for mountain pass periodic solutions of perturbed Hamiltonian systems

    In this work, we study second-order Hamiltonian systems under small perturbations. We assume that the main term of the system has a mountain pass structure, but do not suppose any condition on the perturbation. We prove the existence of a periodic solution. Moreover, we show that periodic solutions of perturbed systems converge to periodic solutions of the unperturbed systems if the perturbation tends to zero. The assumption on...

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  • A NUMERICAL STUDY ON THE DYNAMICS OF DENGUE DISEASE MODEL WITH FRACTIONAL PIECEWISE DERIVATIVE
    Publikacja
    • J. Khan
    • M. Ur Rahman
    • M. Riaz
    • J. Awrejcewicz

    - FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY - Rok 2022

    The aim of this paper is to study the dynamics of Dengue disease model using a novel piecewise derivative approach in the sense of singular and non-singular kernels. The singular kernel operator is in the sense of Caputo, whereas the non-singular kernel operator is the Atangana–Baleanu Caputo operator. The existence and uniqueness of a solution with piecewise derivative are examined for the aforementioned problem. The suggested...

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  • Application of Doubly Connected Dominating Sets to Safe Rectangular Smart Grids
    Publikacja

    - ENERGIES - Rok 2022

    Smart grids, together with the Internet of Things, are considered to be the future of the electric energy world. This is possible through a two-way communication between nodes of the grids and computer processing. It is necessary that the communication is easy and safe, and the distance between a point of demand and supply is short, to reduce the electricity loss. All these requirements should be met at the lowest possible cost....

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  • Constructive Controllability for Incompressible Vector Fields
    Publikacja

    - Rok 2022

    We give a constructive proof of a global controllability result for an autonomous system of ODEs guided by bounded locally Lipschitz and divergence free (i.e. incompressible) vector field, when the phase space is the whole Euclidean space and the vector field satisfies so-called vanishing mean drift condition. For the case when the ODE is defined over some smooth compact connected Riemannian manifold, we significantly strengthen...

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  • Curlicues generated by circle homeomorphisms

    We investigate the curves in the complex plane which are generated by sequences of real numbers being the lifts of the points on the orbit of an orientation preserving circle homeomorphism. Geometrical properties of these curves such as boundedness, superficiality, local discrete radius of curvature are linked with dynamical properties of the circle homeomorphism which generates them: rotation number and its continued fraction...

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  • Generalized Dold sequences on partially-ordered sets
    Publikacja

    - ELECTRONIC JOURNAL OF COMBINATORICS - Rok 2022

    Dold sequences constitute an important class of integer sequences that play an important role in combinatorics, number theory, topology and dynamical systems. We generalize the notion of Dold sequence for the case of partially ordered sets and describe their properties. In particular we give two alternative descriptions of generalized Dold sequences: by some class of elementary sequences as well as by different...

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  • Hydrological Dry Periods versus Atmospheric Circulations in the Lower Vistula Basin (Poland) in 1954–2018
    Publikacja

    - Quaestiones Geographicae - Rok 2022

    The paper discusses the impact of atmospheric circulation on the occurrence of droughts. The research in-cludes mean monthly discharges for 7 rivers in 1954-2018. Dry periods were determined with Standardised Streamflow Indices (SSI-12). Additionally, the circulation type calendar for Central Poland was used to determine the atmospheric circulation indices: western zonal (W), southern meridional (S) and cyclonicity (C). The analyses...

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  • Limits Theorems for Random Walks on Homeo(S1)
    Publikacja

    - JOURNAL OF STATISTICAL PHYSICS - Rok 2022

    The central limit theorem and law of the iterated logarithm for Markov chains corresponding to random walks on the space Homeo(S1) of circle homeomorphisms for centered Lipschitz functions and every starting point are proved.

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  • Matematyczny świat wirusów i bakterii
    Publikacja

    - Rok 2022

    Kiedyś, mówiąc o zastosowaniach matematyki, przychodziła nam na myśl głównie fizyka. Dziś wiemy, że matematyka ma ważne zastosowania również w biologii i medycynie. To, jak szybko rozwijają się bakterie i wirusy oraz jak szybko odpowiada na ich obecność nasz układ odpornościowy, można opisać językiem matematyki. Głównym narzędziem służącym do opisu tempa zmiany interesującej nas wielkości jest pochodna. Dzięki pochodnej możemy przewidzieć...

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  • MEMORY EFFECT ANALYSIS USING PIECEWISE CUBIC B-SPLINE OF TIME FRACTIONAL DIFFUSION EQUATION
    Publikacja
    • M. Shafiq
    • F. A. Abdullah
    • M. Abbas
    • A. Sm Alzaidi
    • M. Riaz

    - FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY - Rok 2022

    The purpose of this work is to study the memory effect analysis of Caputo–Fabrizio time fractional diffusion equation by means of cubic B-spline functions. The Caputo–Fabrizio interpretation of fractional derivative involves a non-singular kernel that permits to describe some class of material heterogeneities and the effect of memory more effectively. The proposed numerical technique relies on finite difference approach and cubic...

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  • Minimal Sets of Lefschetz Periods for Morse-Smale Diffeomorphisms of a Connected Sum of g Real Projective Planes
    Publikacja

    - Rok 2022

    The dataset titled Database of the minimal sets of Lefschetz periods for Morse-Smale diffeomorphisms of a connected sum of g real projective planes contains all of the values of the topological invariant called the minimal set of Lefschetz periods, computed for Morse-Smale diffeomorphisms of a non-orientable compact surface without boundary of genus g (i.e. a connected sum of g real projective planes), where g varies from 1 to...

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  • On a comparison principle and the uniqueness of spectral flow
    Publikacja

    - MATHEMATISCHE NACHRICHTEN - Rok 2022

    The spectral flow is a well-known quantity in spectral theory that measures the variation of spectra about 0 along paths of selfadjoint Fredholm operators. The aim of this work is twofold. Firstly, we consider homotopy invariance properties of the spectral flow and establish a simple formula which comprises its classical homotopy invariance and yields a comparison theorem for the spectral flow under compact perturbations. We apply...

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  • On Computing Curlicues Generated by Circle Homeomorphisms
    Publikacja

    The dataset entitled Computing dynamical curlicues contains values of consecutive points on a curlicue generated, respectively, by rotation on the circle by different angles, the Arnold circle map (with various parameter values) and an exemplary sequence as well as corresponding diameters and Birkhoff averages of these curves. We additionally provide source codes of the Matlab programs which can be used to generate and plot the...

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  • On proper (1,2)‐dominating sets in graphs
    Publikacja

    In 2008, Hedetniemi et al. introduced the concept of (1,)-domination and obtained some interesting results for (1,2) -domination. Obviously every (1,1) -dominating set of a graph (known as 2-dominating set) is (1,2) -dominating; to distinguish these concepts, we define a proper (1,2) -dominating set of a graph as follows: a subset is a proper (1,2) -dominating set of a graph if is (1,2) -dominating and it is not a (1,1) -dominating...

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  • Paired domination versus domination and packing number in graphs
    Publikacja

    Given a graph G = (V(G), E(G)), the size of a minimum dominating set, minimum paired dominating set, and a minimum total dominating set of a graph G are denoted by γ (G), γpr(G), and γt(G), respectively. For a positive integer k, a k-packing in G is a set S ⊆ V(G) such that for every pair of distinct vertices u and v in S, the distance between u and v is at least k + 1. The k-packing number is the order of a largest kpacking and...

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  • Straightened characteristics of McKendrick-von Foerster equation
    Publikacja

    - JOURNAL OF DIFFERENTIAL EQUATIONS - Rok 2022

    We study the McKendrick-von Foerster equation with renewal (that is the age-structured model, with total population dependent coefficient and nonlinearity). By using a change of variables, the model is then transformed to a standard age-structured model in which the total population dependent coefficient of the transport term reduces to a constant 1. We use this transformation to get existence, uniqueness of solutions of the problem...

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  • t-SNE Highlights Phylogenetic and Temporal Patterns of SARS-CoV-2 Spike and Nucleocapsid Protein Evolution
    Publikacja
    • G. Tamazian
    • A. Komissarov
    • D. Kobak
    • D. Polyakov
    • E. Andronov
    • S. Nechaev
    • S. Kryzhevich
    • Y. Porozov
    • E. Stepanov

    - Rok 2022

    We propose applying t-distributed stochastic neighbor embedding to protein sequences of SARS-CoV-2 to construct, visualize and study the evolutionary space of the coronavirus. The basic idea is to explore the COVID-19 evolution space by using modern manifold learning techniques applied to evolutionary distances between variants. Evolutionary distances have been calculated based on the structures of the nucleocapsid and spike proteins.

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Rok 2021