Arabian Journal of Mathematics最新文献

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.

Sierpiński graphs are frequently related to fractals, and fractals apply in several fields of science, i.e., in chemical graph theory, computer networking, biology, and physical sciences. Functions and polynomials are powerful tools in computer mathematics for predicting the features of networks. Topological descriptors, frequently graph constraints, are absolute values that characterize the topology of a computer network. In this essay, Firstly, we compute the M-polynomials for Sierpiński-type fractals. We derive some degree-dependent topological invariants after applying algebraic operations on these M-polynomials.

This paper aims to study the existence and stability results concerning a fractional partial differential equation with variable exponent source functions. The local existence result for (alpha in (0,1)) is established with the help of the (alpha )-resolvent kernel and the Schauder-fixed point theorem. The non-continuation theorem is proved by the fixed point technique and accordingly the global existence of solution is achieved. The uniqueness of the solution is obtained using the contraction principle and the stability results are discussed by means of Ulam-Hyers and generalized Ulam-Hyers-Rassias stability concepts via the Picard operator. Examples are provided to illustrate the results.

Fourth order extended Fisher Kolmogorov reaction diffusion equation has been solved numerically using a hybrid technique. The temporal direction has been discretized using Crank Nicolson technique. The space direction has been split into second order equation using twice continuously differentiable function. The space splitting results into a system of equations with linear heat equation and non linear reaction diffusion equation. Quintic Hermite interpolating polynomials have been implemented to discretize the space direction which gives a system of collocation equations to be solved numerically. The hybrid technique ensures the fourth order convergence in space and second order in time direction. Unconditional stability has been obtained by plotting the eigen values of the matrix of iterations. Travelling wave behaviour of dependent variable has been obtained and the computed numerical values are shown by surfaces and curves for analyzing the behaviour of the numerical solution in both space and time directions.

The aim of this paper is twofold: first, we obtain various curvature inequalities which involve the Ricci and scalar curvatures of horizontal and vertical distributions of anti-invariant Riemannian submersion defined from conformal Kenmotsu space form onto a Riemannian manifold. Second, we obtain the Chen–Ricci inequality for the said Riemannian submersion. The equality cases of all the inequalities are studied. Moreover, these curvature inequalities are studied under two different cases: the structure vector field (xi ) being vertical or horizontal.

We prove that any homogeneous local representation (varphi :B_n rightarrow GL_n(mathbb {C})) of type 1 or 2 of dimension (nge 6) is reducible. Then, we prove that any representation (varphi :B_n rightarrow GL_n(mathbb {C})) of type 3 is equivalent to a complex specialization of the standard representation (tau _n). Also, we study the irreducibility of all local linear representations of the braid group (B_3) of degree 3. We prove that any local representation of type 1 of (B_3) is reducible to a Burau type representation and that any local representation of type 2 of (B_3) is equivalent to a complex specialization of the standard representation. Moreover, we construct a representation of (B_3) of degree 6 using the tensor product of local representations of type 2. Let (u_i), (i=1,2), be non-zero complex numbers on the unit circle. We determine a necessary and sufficient condition that guarantees the irreducibility of the obtained representation.