Arabian Journal of Mathematics最新文献

In this paper, we consider the two Hecke groups (G_{4}) and (G_{6}) and we use the Schmidt Subspace Theorem to establish the transcendence of some quasi-periodic Rosen continued fractions in order to get the exact analogues of the results established with the regular continued fractions.

The normalized Ricci flow converges to a constant curvature metric for a connected Kaehlerian slant submanifold in a complex space form if the squared norm of the second fundamental form satisfies certain upper bounds. These bounds include the constant sectional curvature, the slant angle, and the squared norm of the mean curvature vector. Additionally, we demonstrate that the submanifold is diffeomorphic to the sphere (mathbb {S}^{n_1}) under some restriction on the mean curvature. We claim that some of our previous results are rare cases.

In this paper we propose new averaged iterative algorithms designed for solving a split common fixed point problem in the class of demicontractive mappings. The algorithms are obtained by inserting an averaged term into the algorithms used in [Li, R. and He, Z., A new iterative algorithm for split solution problems of quasi-nonexpansive mappings J. Inequal. Appl. 131 (2015), 1–12.] for solving the same problem but in the class of quasi-nonexpansive mappings, which is a subclass of demicontractive mappings. Basically, our investigation is based on the embedding of demicontractive operators in the class of quasi-nonexpansive operators by means of averaged mappings. For the considered algorithms we prove weak and strong convergence theorems in the setting of a real Hilbert space. A numerical example is given to illustrate the results.

In this article, we investigate the asymptotic behavior of the Mindlin–Timoshenko system under the influence of nonlinear dissipation affecting the rotation angle equations. Initially, we provide a concise review of the system’s solution existence. Subsequently, we demonstrate that the energy associated with the solution of the Mindlin–Timoshenko setup follows a dissipation. Furthermore, under the condition of equal wave speeds, we establish a comprehensive decay theorem for the energy, offering explicit insights into its general behavior.

This paper extends the study of the generalized Lorentz spaces to the Lorentz–Herz spaces. The Lorentz–Herz spaces consist of all Lebesgue measurable functions such that theirs non-increasing rearrangements belong to the weighted Herz space. The main result of this paper establishes the mapping properties of the Hardy–Littlewood maximal function on the Lorentz–Herz spaces.

Symmetric spaces arise in wide variety of problems in Mathematics and Physics. They are mostly studied in Representation theory, Harmonic analysis and Differential geometry. As many physical systems have symmetric spaces as their configuration spaces, the study of controllability on symmetric space is quite interesting. In this paper, a driftless control system of type ({dot{x}}= sum _{i=1}^m u_if_i(x)) is considered on a symmetric space. For this we have established global controllability condition which is illustrated by few examples of exponential submanifolds of SE(3) and random matrix ensembles.

Some theorems of Liouville type are given for such P-harmonic maps when target manifold have conformal vector field or convex function or have non-positive sectional curvature.

Valerij G. Bardakov and P. Bellingeri introduced a new linear representation (bar{rho }_F) of degree (n+1) of the braid group (B_n). We study the irreducibility of this representation. We prove that (bar{rho }_F) is reducible to the degree (n-1). Moreover, we give necessary and sufficient conditions for the irreducibility of the complex specialization of its (n-1) degree composition factor (bar{phi }_F).

This study presents the Chebyshev pseudospectral approach in time and space to approximate a solution to the time-fractional multidimensional Burgers equation. The suggested approach utilizes Chebyshev–Gauss–Lobatto (CGL) points in both spatial and temporal directions. To figure out the fractional derivative matrix at CGL points, we use the Caputo fractional derivative formula. Further, the Chebyshev fractional derivative matrix is utilized to reduce the given problem in an algebraic system of equations. The numerical approach known as the Newton–Raphson is implemented to get the desired results for the system. Error analysis for the set of values of ( nu ) is done for various model examples of fractional Burgers equations, where (nu ) represents the fractional order. The computed numerical results are in perfect agreement with the exact solutions.

In the past few decades, the discrete dynamics of difference maps have attained the remarkable attention of researchers owing to their incredible applications in different domains, like cryptography, secure communications, weather forecasting, traffic flow models, neural network models, and population biology. In this article, a generalized chaotic system is proposed, and superior dynamics is disclosed through fixed point analysis, time-series evolution, cobweb representation, period-doubling, period-3 window, and Lyapunov exponent properties. The comparative bifurcation and Lyapunov plots report the superior stability and chaos performance of the generalized system. It is interesting to notice that the generalized system exhibits superior dynamics due to an additional control parameter (beta ). Analytical and numerical simulations are used to explore the superior dynamical characteristics of the generalized system for some specific values of parameter (beta ). Further, it is inferred that the superiority in dynamics of the generalized system may be efficiently used for better future applications.