Arabian Journal of Mathematics最新文献

We investigate and characterize several kinds of elements such as units, idempotents, von Neumann regular, (pi )-regular and clean elements for skew PBW extensions over weak compatible rings. We also study the notions of Gelfand and Harmonic rings for these families of algebras. The results presented here extend those corresponding in the literature for commutative and noncommutative rings of polynomial type.

We aim to introduce the concept of centrally-extended left derivations and prove some related results to this new concept. The first part is devoted to prove that a centrally extended left derivation preserves the center of semiprime rings. The second part deals with equivalence between left derivations and our new concept. Finally we provide some results regarding commutativity.

Kim (Ramanujan Math Soc Lect Notes Ser 14:157–163, 2010) introduced the overcubic partition function (overline{a}(n)), which represents the number of all the overlined versions of the cubic partition counted by a(n). Let ( overline{b}_r(n)) denote the number of overcubic partitions of n with r-tuples. Several authors established many particular and infinite families of congruences for ( overline{b}_2(n)). In this paper, we show that ( overline{b}_{2^beta m+t}(n)equiv overline{b}_{t}(n) ,(mod ,2^{beta +1}), ) where (beta ge 1), (mge 0), and (tge 1) are integers. We also prove some new congruences modulo 8, 16 and 32 for (overline{b}_{4m+2}(n)), (overline{b}_{4m+3}(n)), (overline{b}_{8m+2}(n)), (overline{b}_{8m+4}(n)) and (overline{b}_{16m+4}(n)), where m is any non-negative integer.

In this paper, we present novel transcendence results for the certain Rosen continued fractions by using the Subspace Theorem.

In this paper, we investigate the highly dispersive perturbed nonlinear Schrödinger equation (NLSE) with (beta )-fractional derivatives, generalized nonlocal laws and sextic-power law refractive index. This equation is crucial for modeling complex phenomena in nonlinear optics, such as soliton formation, light pulse propagation in optical fibers, and light wave control, with potential applications in designing efficient optical communication devices. Furthermore, it provides a framework for understanding the intricate interactions between high dispersion, nonlocality, and complex nonlinearity, contributing to the development of new theories in wave physics. To accomplish this, we use the modified extended direct algebraic method. A variety of distinct traveling wave solutions are furnished. The obtained solutions comprise dark, bright, combo bright-dark and singular soliton solutions. Additionally, singular periodic solutions, rational and exponential solutions. Furthermore, graphical simulations are presented that highlight the distinctive characteristics of these solutions. Compared to Nofal et al. (Optik 228:166120, 2021), the proposed technique produced novel and diversified results. The results showcase the significant influence of fractional derivatives in shaping the characteristics of the soliton solutions, which is crucial for accurately modeling the dispersive and nonlocal effects in optical fibers. The extracted solutions confirmed the efficacy and strength of the current approach. The parameter constraints ensure the existence of the obtained soliton solutions. It is worth noting that the proposed method, being effective, consistent, and influential, can be applied to solve various other physical models and related disciplines.

In the present article, we introduce a novel generalization of modified Bernstein operators which is again a positive linear operator. We show the necessary and sufficient condition for the convergence of these operators. We also study some other approximation properties of these operators using standard tools of approximation theory.

In this paper, we investigate the generalization of Hermite-Hadamard-type orthogonality within skew structures. Moslehian and Rassias (Commun Math Anal 8:16–21, 2010) characterized inner product spaces by employing the parallelogram law for skew structures in their research. We introduce the concept of skew orthogonality by integrating the parallelogram law of skew structures with Hermite-Hadamard-type orthogonality and discuss its properties. Finally, we characterize inner product spaces using mappings that preserve skew orthogonality.

The different systems of Sylvester quaternion matrix equations have prolific functions in system and control. This paper considers a Hermitian solution of a system of Sylvester quaternion matrix equations over a quaternion algebra (mathbb {H}). If some necessary and sufficient conditions are fulfilled, the general solution to these quaternion matrix equations is expressed by explicit representation formulas in terms of generalized inverses. We provide an algorithm and a numerical example based on the original direct method using determinantal representations of the quaternion Moore–Penrose inverse.

In this article, we study one, two and three-dimensional nonlinear elastic wave equations using quadratically nonlinear Murnaghan potential. We employ two effective methods for obtaining approximate series solutions the Adomian decomposition and the variational iteration method. These methods have the advantage of not requiring any physical parametric assumptions in the problem. Finally, these methods can generate expansion solutions for linear and nonlinear differential equations without perturbation, linearization, or discretization. The results obtained using the adopted methods along various initial and boundary conditions are in excellent agreement with the numerical results on MATLAB, which show the reliability of our methods to these problems. We came to the conclusion that our methods are accurate and simple to use.

A balancing-like sequence is a binary recurrence sequence which generalizes the balancing sequence and the sequence of nonnegative integers. This sequence, under certain assumptions, may be used to describe the growth of fortune of a person engaged in some business or profession. Since, in any business or profession, the growth is influenced by many uncertainties, it is more natural to induce some sort of randomness in the balancing-like sequences. If, in a balancing-like sequence, the growth rate is assumed to be a random variable, the resulting sequence will be a stochastic process and the sequence of expectations, in many cases, cannot be described as a binary recurrence sequence. In some cases, the growth rate of expectations increases without limit while, in some cases, it remains finite.