Opuscula Mathematica
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ISSN 1232-9274
e-ISSN: 2300-6919
Issue Date
2023
Volume
Vol. 43
Number
No. 2
Description
Journal Volume
Opuscula Mathematica
Vol. 43 (2023)
Projects
Pages
Articles
Global attractivity of a higher order nonlinear difference equation with unimodal terms
(Wydawnictwa AGH, 2023) Almaslokh, Abdulaziz; Qian, Chuanxi
In the present paper, we study the asymptotic behavior of the following higher order nonlinear difference equation with unimodal terms $x(n+1)= ax(n)+ bx(n)g(x(n)) + cx(n-k)g(x(n-k)), \quad n=0, 1, \ldots,$ where $a$, $b$ and $c$ are constants with $0 \lt a \lt 1$, $0 \leq b \lt 1$, $0 \leq c \lt 1$ and $a+b+c=1$, $g \in C[[0,\infty), [0,\infty)]$ is decreasing, and $k$ is a positive integer. We obtain some new sufficient conditions for the global attractivity of positive solutions of the equation. Applications to some population models are also given.
Square-root boundaries for Bessel processes and the hitting times of radial Ornstein-Uhlenbeck processes
(Wydawnictwa AGH, 2023) Hamana, Yuji
This article deals with the first hitting times of a Bessel process to a square-root boundary. We obtain the explicit form of the distribution function of the hitting time by means of zeros of the confluent hypergeometric function with respect to the first parameter. In deducing the distribution function, the time that a radial Ornstein-Uhlenbeck process reaches a certain point is very useful and plays an important role. We also give its distribution function in the case that the starting point is closer to the origin than the arrival site.
Self-coalition graphs
(Wydawnictwa AGH, 2023) Haynes, Teresa W.; Hedetniemi, Jason T.; Hedetniemi, Stephen T.; McRae, Alice A.; Mohan, Raghuveer
A coalition in a graph $G=(V,E)$ consists of two disjoint sets $V_1$ and $V_2$ of vertices, such that neither $V_1$ nor $V_2$ is a dominating set, but the union $V_1 \cup V_2$ is a dominating set of $G$. A coalition partition in a graph $G$ of order $n=|V|$ is a vertex partition $\pi = \{V_1, V_2, \ldots, V_k\}$ such that every set $V_i$ either is a dominating set consisting of a single vertex of degree $n-1$, or is not a dominating set but forms a coalition with another set $V_j$ which is not a dominating set. Associated with every coalition partition $\pi$ of a graph $G$ is a graph called the coalition graph of $G$ with respect to $\pi$, denoted $CG(G,\pi)$, the vertices of which correspond one-to-one with the sets $V_1, V_2, \ldots, V_k$ of $\pi$ and two vertices are adjacent in $CG(G,\pi)$ if and only if their corresponding sets in $\pi$ form a coalition. The singleton partition $\pi_1$ of the vertex set of $G$ is a partition of order $|V|$, that is, each vertex of $G$ is in a singleton set of the partition. A graph $G$ is called a self-coalition graph if $G$ is isomorphic to its coalition graph $CG(G,\pi_{1})$, where $\pi_1$ is the singleton partition of $G$. In this paper, we characterize self-coalition graphs.
Lower density operators. Φf versus Φd
(Wydawnictwa AGH, 2023) Ivanova, Gertruda; Wagner-Bojakowska, Elżbieta; Wilczyński, Władysław
Using the new method of the construction of lower density operator introduced in the earlier paper of the first two authors, we study how much the new operator can be different from the classical one. The aim of this paper is to show that if $f$ is a good adjusted measure-preserving bijection then the lower density operator generated by $f$ can be really different from the classical density operator.
Asymptotic analysis of the steady advection-diffusion problem in axial domains
(Wydawnictwa AGH, 2023) Morales, Fernando A.
We present the asymptotic analysis of the steady advection-diffusion equation in a thin tube. The problem is modeled in a mixed-type variational formulation, in order to separate the phenomenon in the axial direction and a transverse one. Such formulation makes visible the natural separation of scales within the problem and permits a successful asymptotic analysis, delivering a limiting form, free from the initial geometric singularity and suitable for approximating the original one. Furthermore, it is shown that the limiting problem can be simplified to a significantly simpler structure.