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total: 378
Catalog Publications
Year 2024
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Graphs with isolation number equal to one third of the order
PublicationA 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
PublicationIn 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
PublicationWe 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...
Year 2023
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Attractors of dissipative homeomorphisms of the infinite surface homeomorphic to a punctured sphere
PublicationA class of dissipative orientation preserving homeomorphisms of the infinite annulus,pairs of pants, or generally any infinite surface homeomorphic to a punctured sphere isconsidered. We prove that in some isotopy classes the local behavior of such homeomor-phisms at a fixed point, namely the existence of so-called inverse saddle, impacts thetopology of the attractor — it cannot be arcwise connected
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Between therapy effect and false-positive result in animal experimentation
PublicationDespite the animal models’ complexity, researchers tend to reduce the number of animals in experiments for expenses and ethical concerns. This tendency makes the risk of false-positive results, as statistical significance, the primary criterion to validate findings, often fails if testing small samples. This study aims to highlight such risks using an example from experimental regenerative therapy and propose a machine-learning...
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Distortion in the group of circle homeomorphisms
PublicationLet G be the group PAff+(R/Z) of piecewise affine circle homeomorphisms or the group Diff∞(R/Z) of smooth circle diffeomorphisms. A constructive proof that all irrational rotations are distorted in G is given.
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Restrained differential of a graph
PublicationGiven a graph $G=(V(G), E(G))$ and a vertex $v\in V(G)$, the {open neighbourhood} of $v$ is defined to be $N(v)=\{u\in V(G) :\, uv\in E(G)\}$. The {external neighbourhood} of a set $S\subseteq V(G)$ is defined as $S_e=\left(\cup_{v\in S}N(v)\right)\setminus S$, while the \emph{restrained external neighbourhood} of $S$ is defined as $S_r=\{v\in S_e : N(v)\cap S_e\neq \varnothing\}$. The restrained differential of a graph $G$ is...
Year 2022
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Marcinkiewicz Averages of Smooth Orthogonal Projections on Sphere
PublicationWe construct a single smooth orthogonal projection with desired localization whose average under a group action yields the decomposition of the identity operator. For any full rank lattice \Gamma ⊂ R^d , a smooth projection is localized in a neighborhood of an arbitrary precompact fundamental domain R^d / \Gamma. We also show the existence of a highly localized smooth orthogonal projection, whose Marcinkiewicz average under the...
Year 2021
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Equivalence of equicontinuity concepts for Markov operators derived from a Schur-like property for spaces of measures
PublicationVarious 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
PublicationIf 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
PublicationNa 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
PublicationIt 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
PublicationWe 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
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Secure Italian domination in graphs
PublicationAn 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
PublicationWe 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....
Year 2020
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A space-efficient algorithm for computing the minimum cycle mean in a directed graph
PublicationAn algorithm is introduced for computing the minimum cycle mean in a strongly connected directed graph with n vertices and m arcs that requires O(n) working space. This is a considerable improvement for sparse graphs in comparison to the classical algorithms that require O(n^2) working space. The time complexity of the algorithm is still O(nm). An implementation in C++ is made publicly available at http://www.pawelpilarczyk.com/cymealg/.
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Association of Genes Related to Oxidative Stress with the Extent of Coronary Atherosclerosis
PublicationOxidative stress is believed to play a critical role in atherosclerosis initiation and progression. In line with this, in a group of 1099 subjects, we determined eight single nucleotide polymorphisms (SNPs) related to oxidative stress (PON1 c.575A>G, MPO c.463G>A, SOD2 c.47T>C, GCLM c.590C>T, NOS3 c.894G>T, NOS3 c.786T>C, CYBA c.214C>T, and CYBA c.932A>G) and assessed the extent of atherosclerosis in coronary arteries based on...
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Bounded solutions of odd nonautonomous ODE
PublicationBorsuk-Ulam type argument is used in order to prove exstence of nontrivial bounded solutions to some nonautonomous differential euations which are odd with respect to the spatial variable. A Poincare compactification trick is also applied.
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Certified domination
PublicationImagine that we are given a set D of officials and a set W of civils. For each civil x ∈ W, there must be an official v ∈ D that can serve x, and whenever any such v is serving x, there must also be another civil w ∈ W that observes v, that is, w may act as a kind of witness, to avoid any abuse from v. What is the minimum number of officials to guarantee such a service, assuming a given social network? In this paper, we introduce...