Opuscula Mathematica
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ISSN 1232-9274
e-ISSN: 2300-6919
Issue Date
2020
Volume
Vol. 40
Number
No. 2
Description
Journal Volume
Opuscula Mathematica
Vol. 40 (2020)
Projects
Pages
Articles
On the deformed Besov-Hankel spaces
(Wydawnictwa AGH, 2020) Saïd, Salem Ben; Boubatra, Mohamed Amine; Sifi, Mohamed
In this paper we introduce function spaces denoted by $BH_{\kappa,\beta}^{p,r}$ ($0\lt\beta\lt 1$, $1\leq p, r \leq +\infty$) as subspaces of $L^p$ that we call deformed Besov-Hankel spaces. We provide characterizations of these spaces in terms of Bochner-Riesz means in the case $1\leq p\leq +\infty$ and in terms of partial Hankel integrals in the case $1\lt p\lt +\infty$ associated to the deformed Hankel operator by a parameter $\kappa\gt 0$. For $p=r=+\infty$, we obtain an approximation result involving partial Hankel integrals.
Maximum packings of the λ-fold complete 3-uniform hypergraph with loose 3-cycles
(Wydawnictwa AGH, 2020) Bunge, Ryan C.; Collins, Dontez; Conko-Camel, Daryl; El-Zanati, Saad I.; Liebrecht, Rachel; Vasquez, Alexander
It is known that the 3-uniform loose 3-cycle decomposes the complete 3-uniform hypergraph of order $v$ if and only if $v \equiv 0, 1,\text{ or }2\ (\operatorname{mod} 9)$. For all positive integers $\lambda$ and $v$, we find a maximum packing with loose 3-cycles of the $\lambda$-fold complete 3-uniform hypergraph of order $v$. We show that, if $v \geq 6$, such a packing has a leave of two or fewer edges.
On the asymptotic behavior of nonoscillatory solutions of certain fractional differential equations with positive and negative terms
(Wydawnictwa AGH, 2020) Graef, John R.; Grace, Said R.; Tunç, Ercan
This paper is concerned with the asymptotic behavior of the nonoscillatory solutions of the forced fractional differential equation with positive and negative terms of the form $^{C}D_{c}^{\alpha}y(t)+f(t,x(t))=e(t)+k(t)x^{\eta}(t)+h(t,x(t)),$ where $t\geq c \geq 1$, $\alpha \in (0,1)$, $\eta \geq 1$ is the ratio of positive odd integers, and $^{C}D_{c}^{\alpha}y$ denotes the Caputo fractional derivative of $y$ of order $\alpha$. The cases $y(t)=(a(t)(x^{\prime}(t))^{\eta})^{\prime} \quad \text{and} \quad y(t)=a(t)(x^{\prime}(t))^{\eta}$ are considered. The approach taken here can be applied to other related fractional differential equations. Examples are provided to illustrate the relevance of the results obtained.
Asymptotic expansion of large eigenvalues for a class of unbounded Jacobi matrices
(Wydawnictwa AGH, 2020) Harrat, Ayoub; Zerouali, El Hassan; Zieliński, Lech
We investigate a class of infinite tridiagonal matrices which define unbounded self-adjoint operators with discrete spectrum. Our purpose is to establish the asymptotic expansion of large eigenvalues and to compute two correction terms explicitly.
Subdivision of hypergraphs and their colorings
(Wydawnictwa AGH, 2020) Iradmusa, Moharram N.
In this paper we introduce the subdivision of hypergraphs, study their properties and parameters and investigate their weak and strong chromatic numbers in various cases.