Abstract: In this paper, we define and study the notion of hereditary class on nearly μ-Lindelöf space. Moreover, we study the effects of some types of continuity of hereditary class on nearly μ-Lindelöf space by properties of the function. Also, more variations between these spaces and some known spaces are investigated. PubDate: Fri, 09 Feb 2024 00:00:00 GMT

Abstract: New sufficient conditions for oscillation of a second-order nonlinear differential equation with some sublinear neutral terms are established via canonical transform and integral averaging method. Examples are provided to illustrate the significance and novelty of the presented results. PubDate: Mon, 18 Dec 2023 00:00:00 GMT

Abstract: In this paper, we introduce novel methods for computing middle surfaces between various 3D data sets such as point clouds and/or discrete surfaces. Traditionally the middle surface is obtained by detecting singularities in computed distance function such as ridges, triple junctions, etc. It requires to compute second order differential characteristics, and also some kinds of heuristics must be applied. Opposite to that, we determine the middle surface just from computing the distance function itself which is a fast and simple approach. We present and compare the results of the fast sweeping method, the vector distance transform algorithm, the fast marching method, and the Dijkstra-Pythagoras method in finding the middle surface between 3D data sets. PubDate: Mon, 18 Dec 2023 00:00:00 GMT

Abstract: The authors present some new criteria for the oscillation of second order nonlinear differential equations with mixed nonlinear neutral terms and mixed deviating arguments. The approach used is to linearize the equation under consideration and then to deduce the oscillation from that of the linear form. In so doing, the authors obtain new oscillation criteria via a comparison with the first order equations whose oscillatory behaviors are known. They illustrate their results with some examples. PubDate: Mon, 18 Dec 2023 00:00:00 GMT

Abstract: Polybius cipher is a special substitution system widely used during history. In our research, we found several Polybius-like ciphers used in Czecho-slovakia and in the Slovak State from the first half of the 20th century. Various types of this cipher are described in the first Czechoslovak cryptanalysis manual “šifrovací systémy a návod k luštění kryptogramů” by plk. Josef Růžek. It can be also found in the official cryptology directive called G–VII–8 “šifrování” (encryption) from 1938, and another variant in the new version of the same directive from 1946. In this work, we focus on a special Polybius-like cipher inspired by three real ciphers used in Czechoslovakia and in the Slovak State. Two were used during WW2 and one right after the war. We will show how these ciphers were used and how they can be solved with a modern heuristic approach on a personal computer. We evaluate the effectiveness of the Hill-Climbing heuristic methods with restarts. We also investigated several different fitness functions and language models. PubDate: Sat, 09 Dec 2023 00:00:00 GMT

Abstract: In this article, we use the notion of ideals to study open covers and related selection principles, and thus, we extend some results in (Caserta et al. 2012; Chandra et al. 2020) where open covers and related selection principles have been investigated using the idea of strong uniform convergence (Beer and Levi, 2009) on a bornology. We introduce the notions of ℐ-γℬ s -cover, ℐ-strong-ℬ-Hurewicz and ℐ-strong-ℬ-groupable cover. Also, in (C(X),τsℬ), some properties like ℐ-strictly Frèchet Urysohn, ℐ-Reznichenko property are investigated. PubDate: Thu, 16 Nov 2023 00:00:00 GMT

Abstract: This paper deals with density on the set of natural numbers and its connections to the distribution of sequences. Under the assumption of independence, some formulas are derived. PubDate: Thu, 16 Nov 2023 00:00:00 GMT

Abstract: The aim of this paper is to give necessary and sufficient conditions in terms of the Fourier Laguerre-Bessel transform 𝒲LBf of the function f to ensure that f belongs to the generalized Lipschitz classes Hαk (X) and hkα (X), where X =[0, +∞) × [0, +∞). PubDate: Thu, 16 Nov 2023 00:00:00 GMT

Abstract: The paper deals with the strong porosity of some families of real functions continuous with respect to a given topology 𝒯 or 𝒜-continuous (i.e., continuous with respect to some special family 𝒜 of sets of the real line). Particularly, porosity of those families is investigated in space of the Baire 1 functions or in the space of the Baire 1 and Darboux functions. PubDate: Thu, 16 Nov 2023 00:00:00 GMT

Abstract: The purpose of this paper is to introduce a few variants of generalized quasi-continuity of functions defined on a bitopological space and to study their mutual relationship. Moreover, some characterization of sectional quasi-continuous function and its continuity points are investigated. PubDate: Thu, 16 Nov 2023 00:00:00 GMT

Abstract: In the present paper, we introduce new types of generalized closed sets called ij -pre-generalized closed sets and study some of their properties in bi-topological spaces. Also, we use them to construct new types of separation axioms. Further, we introduce and study the concepts of pairwise operation pc-open sets and pairwise operation pc-separation axioms in bitopological spaces. Several interesting characterizations of different spaces are discussed. The relationships between these spaces are given. PubDate: Thu, 16 Nov 2023 00:00:00 GMT

Abstract: The direct calculation of the generalized operator entropy proves to be difficult due to the appearance of rational exponents of matrices. The main motivation of this work is to overcome these difficulties and to present a practical and efficient method for this calculation using its representation by the matrix continued fraction. At the end of our work, we deduce a continued fraction expansion of the Bregman operator divergence. Some numerical examples illustrating the theoretical result are discussed. PubDate: Thu, 16 Nov 2023 00:00:00 GMT

Abstract: We study measurable real valued multipliers of variationally McShane (resp. McShane) integrable functions defined on a σ-finite outer regular quasi-Radon measure space and taking values in a complete locally convex topological vector space X. We also show: in case X is representable by semi-norm then essentially bounded real measurable functions are multipliers of functions which are Pettis integrable as well as integrable by semi-norm. The space of real valued measurable and essentially bounded functions turn out to be precisely the multipliers of variationally McShane (resp. McShane) integrable functions in case X is representable by semi-norm. PubDate: Thu, 16 Nov 2023 00:00:00 GMT

Abstract: This paper presents a general unified approach to the notions of generalized closedness in topological spaces. The research concerning the notion of generalized closed sets in topological spaces was initiated by Norman Levine in 1970. In the succeeding years, the concepts of this type of generalizations have been investigated in many versions using the standard generalizations of topologies which has resulted in a large body of literature. However, the methods and results in the past years have become standard and lacking in innovation.The basic notion used in this conception is the closure operator designated by a family ℬ ⊆ 𝒫(X), which need not be a Kuratowski operator. Here, we introduce a general conception of natural extensions of families ℬ ⊆ 𝒫 (X), denoted by ℬ ᐊ 𝒦, which are determined by other families 𝒦 ⊆ 𝒫(X). Precisely,ℬ⊲𝒦={ A⊆X:A¯ℬ⊆A¯𝒦 },\mathcal{B} \triangleleft \mathcal{K} = \left\{ {A \subseteq X:{{\bar A}^\mathcal{B}} \subseteq {{\bar A}^\mathcal{K}}} \right\},where (…)¯𝒜{\overline {\left( \ldots \right)} ^\mathcal{A}} denotes the closure operator designated by 𝒜 ⊆ 𝒫(X).We prove that the collection of all generalizations ℬ ᐊ 𝒦, where ℬ, 𝒦 ⊆ 𝒫 (X), forms a Boolean algebra. In this theory, the family of all generalized closed sets in a topological space X(𝒯 )is equal to 𝒞 ᐊ 𝒯, where 𝒞 is the family of all closed subsets of X. This concept gives tools that enable the systemizing and developing of the current research area of this topic. The results obtained in this general conception easily extend and imply well-known theorems as obvious corollaries. Moreover, they also give many new results concerning relationships between various types of generalized closedness studied so far in a topological space. In particular, we prove and demonstrate in a graph that in a topological space X(𝒯) there exist only nine different generalizations determined by the standard generalizations of topologies. The tools introduced in this paper enabled us to show that many generalizations studied in the literature are improper. PubDate: Thu, 16 Nov 2023 00:00:00 GMT

Abstract: In this paper, we introduce strongly star g-compactness as a topological covering property and compare its structure to other topological properties that have analogous structures. The characteristics of a strongly star g-compact subset and strongly star g-compact subspace are looked at. Finally, some finite intersection-like characteristics that will result in some situations akin to strongly star g-compactness are presented. PubDate: Thu, 16 Nov 2023 00:00:00 GMT

Abstract: We study two particular modifications of the P-property of ideals and related cardinal invariants cof𝒥 (ℐ)and cov+(ℐ). We give some results on the existence of P (𝒥)-ideals or non-P (𝒥)-ideals regarding specific classes of ideals, particularly meager ideals on ω. We also provide values of the cardinal invariant cof𝒥 (ℐ) describing the smallest families ensuring P(𝒥) for particular critical ideals. Moreover, we obtain a simple way of proving strict inequalities Fin <K 〈𝒜 〉 <K Fin × Fin for any MAD family 𝒜 using the weak P-ideal notion. PubDate: Thu, 16 Nov 2023 00:00:00 GMT

Abstract: When analyzing cell trajectories, we often have to deal with noisy data due to the random motion of the cells and possible imperfections in cell center detection. To smooth these trajectories, we present a mathematical model and numerical method based on evolving open-plane curve approach in the Lagrangian formulation. The model contains two terms: the first is the smoothing term given by the influence of local curvature, while the other attracts the curve to the original trajectory. We use the flowing finite volume method to discretize the advection-diffusion partial differential equation. The PDE includes the asymptotically uniform tangential redistribution of curve grid points. We present results for macrophage trajectory smoothing and define a method to compute the cell velocity for the discrete points on the smoothed curve. PubDate: Tue, 31 Oct 2023 00:00:00 GMT

Abstract: We investigate a discrete analogue of the polylogarithm function. Difference and summation relations are obtained, as well as its connection to the discrete hypergeometric series. PubDate: Wed, 28 Jun 2023 00:00:00 GMT

Abstract: We study the Volterra integro-differential equation on time scales and provide sufficient conditions for boundness of all solutions of considered equation. Using that result, we present the conditions for exponential stability of considered equation. All the results proved on the general time scale include results for both integral and discrete Volterra equations. PubDate: Wed, 28 Jun 2023 00:00:00 GMT

Abstract: We provide sufficient criteria for the existence of solutions for fourth-order nonlinear dynamic equations on time scales(a(t)xΔ2(t))Δ2=b(t)f(x(t))+c(t),{\left( {a\left( t \right){x^{{\Delta ^2}}}\left( t \right)} \right)^{{\Delta ^2}}} = b\left( t \right)f\left( {x\left( t \right)} \right) + c\left( t \right),such that for a given function y : 𝕋 → ℝ there exists a solution x : 𝕋 → ℝ to considered equation with asymptotic behaviour x(t)=y(t)+o(1tβ)x\left( t \right) = y\left( t \right) + o\left( {{1 \over {{t^\beta }}}} \right). The presented result is applied to the study of solutions to the classical Euler–Bernoulli beam equation, which means that it covers the case 𝕋 = ℝ. PubDate: Wed, 28 Jun 2023 00:00:00 GMT