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Zakład Równań Różniczkowych i Zastosowań Matematyki

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Rok 2023
Rok 2022
  • 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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  • 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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  • 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 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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  • 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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Rok 2021
  • APPLICATION OF ENTROPY-BASED METHODS TO DISTINGUISH HEALTHY INDIVIDUALS WITH NORMAL SINUS RHYTHM FROM PATIENTS WITH CONGESTIVE HEART FAILURE
    Publikacja

    - Rok 2021

    In this paper, we examined whether entropy-based methods are able to differentiate healthy individuals from patients with congestive heart failure. To this aim, we applied two methods: Permutation Entropy and Block Entropy. Long-term ECG recordings (75 000 RR intervals) were analyzed. The results proved that both methods can distinguish those groups on condition that the parameters are appropriately chosen.

  • Common Independence in Graphs
    Publikacja

    - Symmetry-Basel - Rok 2021

    Abstract: The cardinality of a largest independent set of G, denoted by α(G), is called the independence number of G. The independent domination number i(G) of a graph G is the cardinality of a smallest independent dominating set of G. We introduce the concept of the common independence number of a graph G, denoted by αc(G), as the greatest integer r such that every vertex of G belongs to some independent subset X of VG with |X|...

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  • Dold sequences, periodic points, and dynamics
    Publikacja

    - BULLETIN OF THE LONDON MATHEMATICAL SOCIETY - Rok 2021

    In this survey we describe how the so-called Dold congruence arises in topology, and how it relates to periodic point counting in dynamical systems.

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  • Gradient versus proper gradient homotopies
    Publikacja

    - Homology Homotopy and Applications - Rok 2021

    We compare the sets of homotopy classes of gradient and proper gradient vector fields in the plane. Namely, we show that gradient and proper gradient homotopy classi cations are essentially different. We provide a complete description of the sets of homotopy classes of gradient maps from R^n to R^n and proper gradient maps from R^2 to R^2 with the Brouwer degree greater or equal to zero.

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  • High-accuracy computation of hard X-ray focusing and imaging for refractive optics
    Publikacja

    - JOURNAL OF SYNCHROTRON RADIATION - Rok 2021

    A mathematical apparatus for solving problems of X-ray wave propagation through complex optical systems, when the lens thickness can change with jumps, is developed and presented. The developed method is based on the use of the superposition of oriented Gaussian beams, which satisfy the Helmholtz equation with high accuracy. The wave propagation in air and through kinoform and ordinary lenses is considered. Focusing and imaging...

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  • Measured and predicted freeze-thaw days frequencies in climate change conditions in central Poland
    Publikacja

    - PeerJ - Rok 2021

    The rate of progression of geomorphological phenomena is greatly influenced by freeze-thaw processes. In the face of air temperature increasing over the past few decades, a question of the future impact of these processes arises, notably in the temperate and cold climate zones. Using the mean, maximum and minimum daily air temperature data in the period 1951–2018 obtained from three weather stations located in the vicinity of Jeziorsko...

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  • Nilpotent singularities and chaos: Tritrophic food chains
    Publikacja

    - CHAOS SOLITONS & FRACTALS - Rok 2021

    Local bifurcation theory is used to prove the existence of chaotic dynamics in two well-known models of tritrophic food chains. To the best of our knowledge, the simplest technique to guarantee the emergence of strange attractors in a given family of vector fields consists of finding a 3-dimensional nilpotent singularity of codimension 3 and verifying some generic algebraic conditions. We provide the essential background regarding...

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  • Persistent homology as a new method of the assessment of heart rate variability
    Publikacja

    - PLOS ONE - Rok 2021

    Heart rate variability (hrv) is a physiological phenomenon of the variation in the length of the time interval between consecutive heartbeats. In many cases it could be an indicator of the development of pathological states. The classical approach to the analysis of hrv includes time domain methods and frequency domain methods. However, attempts are still being made to define new and more effective hrv assessment tools. Persistent...

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  • Some variants of perfect graphs related to the matching number, the vertex cover and the weakly connected domination number
    Publikacja

    Given two types of graph theoretical parameters ρ and σ, we say that a graph G is (σ, ρ)- perfect if σ(H) = ρ(H) for every non-trivial connected induced subgraph H of G. In this work we characterize (γw, τ )-perfect graphs, (γw, α′)-perfect graphs, and (α′, τ )-perfect graphs, where γw(G), τ (G) and α′(G) denote the weakly connected domination number, the vertex cover number and the matching number of G, respectively. Moreover,...

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Rok 2020