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Rok 2024
  • Graphs with isolation number equal to one third of the order


    A set D of vertices of a graph G is isolating if the set of vertices not in D and with no neighbor in D is independent. The isolation number of G, denoted by \iota(G) , is the minimum cardinality of an isolating set of G. It is known that \iota(G) \leq n/3 , if G is a connected graph of order n, , distinct from C_5 . The main result of this work is the characterisation of unicyclic and block graphs of order n with isolating number...

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  • On the Fenchel–Moreau conjugate of G-function and the second derivative of the modular in anisotropic Orlicz spaces

    In this paper, we investigate the properties of the Fenchel–Moreau conjugate of G-function with respect to the coupling function c(x, A) = |A[x]2 |. We provide conditions that guarantee that the conjugate is also a G-function. We also show that if a G-function G is twice differentiable and its second derivative belongs to the Orlicz space generated by the Fenchel–Moreau conjugate of G then the modular generated by G is twice differentiable...

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  • Rotating rod and ball

    We consider a mechanical system consisting of an infinite rod (a straight line) and a ball (a massless point) on the plane. The rod rotates uniformly around one of its points. The ball is reflected elastically when colliding with the rod and moves freely between consecutive hits. A sliding motion along the rod is also allowed. We prove the existence and uniqueness of the motion with a given position and velocity at a certain time...

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Rok 2023
Rok 2022
Rok 2021
  • Equivalence of equicontinuity concepts for Markov operators derived from a Schur-like property for spaces of measures
    • S. C. Hille
    • T. Szarek
    • D. Worm
    • M. Ziemlańska


    Various equicontinuity properties for families of Markov operators have been – and still are – used in the study of existence and uniqueness of invariant probability for these operators, and of asymptotic stability. We prove a general result on equivalence of equicontinuity concepts. It allows comparing results in the literature and switching from one view on equicontinuity to another, which is technically convenient in proofs....

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  • Isolation Number versus Domination Number of Trees
    • M. Lemańska
    • M. J. Souto-Salorio
    • A. Dapena
    • F. Vazquez-Araujo

    - Mathematics - Rok 2021

    If G=(VG,EG) is a graph of order n, we call S⊆VG an isolating set if the graph induced by VG−NG[S] contains no edges. The minimum cardinality of an isolating set of G is called the isolation number of G, and it is denoted by ι(G). It is known that ι(G)≤n3 and the bound is sharp. A subset S⊆VG is called dominating in G if NG[S]=VG. The minimum cardinality of a dominating set of G is the domination number, and it is denoted by γ(G)....

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  • Matematyka na zajęciach z arkuszy kalkulacyjnych

    Na zajęciach, zarówno w szkole, jak i na uczelni, do pokazania technicznej strony użycia arkusza kalkulacyjnego, tj.dostępnych funkcjonalności oraz organizacji danych, często wykorzystuje się proste zadania matematyczne. W naszym artykule zwracamy uwagę na potrzebę rozumienia przez użytkowników arkuszy kalkulacyjnych pojęć matematycznych, które umożliwiają odpowiednie przygotowanie danych oraz zinterpretowanie uzyskanych za pomocą...

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  • On asymptotic periodicity of kernel double Markovian operators

    It is proved that a kernel, doubly Markovian operator T is asymptotically periodic if and only if its deterministic σ-field Σd(T)(equivalently Σd(T∗)) is finite. It follows that kernel doubly Markovian operator T is asymptotically periodic if and only if T∗ is asymptotically periodic.

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  • Parseval Wavelet Frames on Riemannian Manifold

    We construct Parseval wavelet frames in L 2 (M) for a general Riemannian manifold M and we show the existence of wavelet unconditional frames in L p (M) for 1 < p < ∞. This is made possible thanks to smooth orthogonal projection decomposition of the identity operator on L 2 (M), which was recently proven by Bownik et al. (Potential Anal 54:41–94, 2021). We also show a characterization of Triebel–Lizorkin F sp,q (M) and Besov B...

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  • Polish Adaptation of the Pregnancy-Related Anxiety Questionnaire—Revised 2 for All Pregnant Women
    • A. Michalik
    • L. Wójcicka
    • A. Zdun-Ryżewska
    • A. Czerwińska-Osipiak
    • M. Krzemiński
    • J. Olszewska
    • D. Klasa-Mazurkiewicz
    • A. Huizink

    - Healthcare - Rok 2021

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  • Secure Italian domination in graphs


    An Italian dominating function (IDF) on a graph G is a function f:V(G)→{0,1,2} such that for every vertex v with f(v)=0, the total weight of f assigned to the neighbours of v is at least two, i.e., ∑u∈NG(v)f(u)≥2. For any function f:V(G)→{0,1,2} and any pair of adjacent vertices with f(v)=0 and u with f(u)>0, the function fu→v is defined by fu→v(v)=1, fu→v(u)=f(u)−1 and fu→v(x)=f(x) whenever x∈V(G)∖{u,v}. A secure Italian dominating...

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  • Smooth Orthogonal Projections on Riemannian Manifold


    We construct a decomposition of the identity operator on a Riemannian manifold M as a sum of smooth orthogonal projections subordinate to an open cover of M. This extends a decomposition on the real line by smooth orthogonal projection due to Coifman and Meyer (C. R. Acad. Sci. Paris, S´er. I Math., 312(3), 259–261 1991) and Auscher, Weiss, Wickerhauser (1992), and a similar decomposition when M is the sphere by Bownik and Dziedziul (Const....

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Rok 2020
Rok 2019