Arabian Journal of Mathematics最新文献

Let (mathbb {F}_{d}) ((din mathbb {N})) be the group with d generators (called the free two-step nilpotent Lie group) and (K:=SO(d)) is the rotation group on (mathbb {R}^d.) Under the action of K on (mathbb {F}_d,) one can form the semidirect product (G:=Kltimes mathbb {F}_d.) It is well-known in representation theory that (widehat{G}) is a topological space (endowed with the Fell topology, see Fell in Can J Math 14:237–268, 1962). In the present work, we have described partially the convergence in the unitary dual (widehat{G}) of G and we have shown that this description enables us to determine the cortex, cor(G) of G,  that is the set of all irreducible unitary representations in (widehat{G},) that cannot be Hausdorff separated from the trivial representation (1_G) of G.

In this paper we attempt to generalize some classical results from Artinian/Noetherian ring theory to hereditary torsion theories. It is worthwhile noticing that the investigation of Artinian and Noetherian rings is an abundant source of findings, primarily related to the structure of rings and modules. By extending the concept of S-Noetherian rings, we explore totally Artinian and totally Noetherian rings. The primary goal of this note is to establish connections between totally Artinian and totally Noetherian rings, and to characterize the former, initially through localization at maximal ideals and later, as a result, by demonstrating that the ring A is totally Artinian if, and only if, it has an Artinian homomorphic image with a totally torsion kernel. The theory is further developed by addressing several open problems and presenting illustrative examples. The central aim of this paper is to offer examples of these types of rings by exploring their underlying structure.

This paper investigates a class of nonlinear elliptic Dirichlet boundary value problems governed by a logarithmic double-phase operator and involving a convection term dependent on the gradient. Under suitable growth conditions on the convection term, we establish the existence of weak solutions by leveraging the framework of Young measures and the Galerkin approximation method. Our analysis is conducted within the setting of Musielak–Orlicz Sobolev spaces with variable exponent, specifically in the space (mathscr {Y}_{0}^{1, mathscr {H}_{log }}(mathscr {D})). To the best of our knowledge, this is the first study addressing such problems in this functional framework. Our results provide new insights into the interplay between logarithmic double-phase structures and gradient-dependent convection effects, paving the way for further investigations in this direction.

This article presents a study on the King-type modification of Bernstein–Durrmeyer-type operators introduced by Páltănea [25]. For the new King-type operators, we estimate the moments, convergence rate for continuous functions and establish a Korovkin-type theorem and a Voronovskaya-type theorem to demonstrate uniform and pointwise convergence. Moreover, we also provide an interval in which the order of approximation of the new King-type operators is better than the Páltănea operators. The Ditzian–Totik modulus of continuity and the classical modulus of continuity are used to prove quantitative convergence theorems.

The present paper focuses on the characterization of invariant submanifolds of hyperbolic Kenmotsu manifolds. First, we prove that an invariant submanifold of a hyperbolic Kenmotsu manifold is again a hyperbolic Kenmotsu manifold and is minimal. Next, the conditions for the invariant submanifold to be totally geodesic are obtained. Also, it is shown that a 3-dimensional submanifolds is totally geodesic if and only if it is invariant. Moreover, an invariant submanifold of a hyperbolic Kenmotsu manifold admitting (eta )-Ricci–Bourguignon soliton is examined and constructed an example to verify the results.

By Rosenthal’s inequality for negatively dependent random variables under sub-linear expectations, we study complete moment convergence and integral convergence for NA dependent random variables. The results in the paper extend some convergence properties under independent assumption from probability space to the sub-linear expectation space.

We study some arithmetic properties on the set of (beta )-polynomials. Firstly, we give a sufficient condition for the finiteness of (L_{odot }) which represent the maximal finite shift after the comma for the product of two beta-polynomials. Secondly, we give explicit values of (L_{odot }) for families of Pisot basis.

In this article, we investigate the stability of a high-density wave oscillating on a ring equipped with an internal dynamic controller. At the ring boundaries, the wave vanishes on the lower boundary and releases significant kinetic energy on the upper one. The analysis begins with a proof of the existence and uniqueness of the solution using the semigroup method, along with a demonstration of the total energy decay over time. Then, using Nakao’s method, we establish that this energy decay is exponential under a specific condition on the internal controller parameter. Finally, numerical experiments based on the finite difference method are conducted to illustrate and confirm the exponential stability.

The contraction mapping principle (CMP, i.e. the fixed point technique of Banach–Caccioppoli) is used to show existence and uniqueness of (L^p)-solutions of Itô-type stochastic neutral integro-differential equations with infinite memory, driven by a standard Wiener process. For this purpose, we study several properties of an associated integral-type map ({mathbb {H}}), which is a contraction on the strong Banach space ({mathbb {S}}) of adapted, stochastic processes with finite supremum moments and appropriate contraction constant. As a side-product, the (L^p)-error of appropriate successive iterations is estimated and simulation-results of a numerical example are given. Properties of the (L^p)-solutions such as (L^p)- and a.s. Hölder-continuity, and (L^p)-boundedness are investigated.

This paper presents an efficient numerical approach for solving the time-fractional fourth-order reaction–diffusion model involving a distributed-order operator. To discretize the fractional Caputo operator in time, quadratic and linear interpolation approximations are applied. For spatial discretization of the derivative operator, a direct meshless local Petrov–Galerkin scheme is used on the computational domain, which includes complex shapes. Stability and convergence analyses of the proposed numerical approach are presented and discussed. To evaluate the efficiency and performance of the method, several numerical examples are provided. Charts and tables are included to better illustrate the accuracy of the proposed method.