Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
Annales UMCS sectio A publishes original works research papers in pure and applied mathematics, especially complex analysis, differential equations, functional analysis, differential geometry and probability theory. Punkty MEiN: 20 ISSN: 0365-1029 e-ISSN:2083-7402 Submitted articles rejection rate : approx. 30%
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Special bihyperbolic numbers and their connections with triangular tables and matrices
In this paper we express special bihyperbolic numbers as paradeterminants and parapermanents of some triangular matrices. Moreover, by applying the connections between these parameters of triangular tables and the determinants and permanents of lower Hessenberg matrices, we obtain another expressions of these numbers, using matrices which are not triangular.
Copyright (c) 2025 Paweł Bednarz, Anna Kosiorowska, Adrian Michalski http://creativecommons.org/licenses/by/4.0
The existence of solutions to the nonhomogeneous degenerate nonlinear elliptic equations
In this paper we are interested in the existence and uniqueness of solutions for Dirichlet problem associated with the degenerate nonlinear elliptic equations \begin{align*}&- \mathrm{div}\big[{\mathcal{A}}(x, {\nabla}u)\, {\omega}_2(x) + {\mathcal{B}}(x, {\nabla}u)\, {\nu}_1(x)\big] + {\mathcal{H}}(x,u,{\nabla}u){\nu}_2 + {\vert u \vert}^{p-2}u\,{\omega}_1\\ &= {\rho}_0 - \sum_{j=1}^nD_j{\rho}_j,\\ & u - {\psi}\, {\in}\, W_0^{1,p}(\Omega , {\omega}_1 , {\omega}_2),\end{align*} in the setting of the weighted Sobolev spaces.
Copyright (c) 2025 Albo Carlos Cavalheiro http://creativecommons.org/licenses/by/4.0
The general theorem of Necas admits a simple proof
In this note, we shall study a new, short proof of the general theorem of Necas about the solvability of linear partial differential equations in the Banach space setting. The complexity of this proof does not seem to be greater than that of the Lax-Milgram theorem, and since the theorem of Necas is strictly stronger than the Lax-Milgram theorem, the author hopes that his new proof will help the theorem of Necas to gain prominence in PDE and functional analysis lectures.
Copyright (c) 2025 Adrian Fellhauer http://creativecommons.org/licenses/by/4.0
On third-order Jacobsthal numbers and their bihyperbolic generalizations
In this paper, we introduce bihyperbolic third-order Jacobsthal and third-order Jacobsthal--Lucas numbers. In other words, bihyperbolic numbers whose coefficients are consecutive third-order Jacobsthal and third-order Jacobsthal--Lucas numbers. Furthermore, we study one parameter generalizations of bihyperbolic third-order Jacobsthal and third-order Jacobsthal--Lucas numbers and relations between them.
Copyright (c) 2025 Gamaliel Morales http://creativecommons.org/licenses/by/4.0
A simple spatial model of population dynamics
A mathematical model is presented that describes the dynamics of a spatially distributed population, incorporating the effects of external migration. The evolution of the population density is governed by a simple integro-differential equation. In the spatially homogeneous case, the model isreduced to the classical logistic equation with an additional constant term and its behavior is fully characterized. In the inhomogeneous case, the dynamics is examined through numerical simulations and typical long-term behavior is illustrated.
Copyright (c) 2025 Krzysztof Pilorz http://creativecommons.org/licenses/by/4.0
In this article we introduce and analyze the concept of (involutive) bounded BRK-algebras. Additionally, we observe some of the substructures of (involutive) bounded BRK-algebras and find their mutual connections.
Copyright (c) 2025 Daniel Abraham Romano http://creativecommons.org/licenses/by/4.0