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The computation of generalized inverses of quaternion matrices is a fundamental problem in quaternion linear algebra, with wide-ranging applications in signal processing, image restoration, and multidimensional data analysis. This paper…
Drake and Szekeres have extended the Newman-Janis algorithm to produce stationary axisymmetric spacetimes from general static spherically symmetric solutions of the Einstein equations. The algorithm mathematically generates an…
This paper deals with the class of Q-tensors, that is, a Q-tensor is a real tensor $\mathcal{A}$ such that the tensor complementarity problem $(\q, \mathcal{A})$: $$\mbox{ finding } \x \in \mathbb{R}^n\mbox{ such that }\x \geq \0, \q +…
We rigorously construct a family of smooth self-similar solutions to the isentropic gravitational Euler-Poisson system with a polytropic equation of state for polytropic indices lying in the full energy-supercritical range,…
We present a circulant and skew-circulant splitting (CSCS) iterative method for solving large sparse continuous Sylvester equations $AX + XB = C$, where the coefficient matrices $A$ and $B$ are Toeplitz matrices. A theoretical study shows…
We show the existence of positive solutions for a class of singular elliptic systems with convection term. The approach combines pseudomonotone operator theory, sub and supersolution method and perturbation arguments involving singular…
This paper uses the Noether symmetry approach to examine the viable and stable traversable wormhole solutions in the framework of $f(\mathcal{R,}\mathcal{T}^{2})$ theory, where $\mathcal{R}$ is the Ricci scalar and…
We give an overview of recent advances in analysis of equations of electrodynamics with the aid of biquaternionic technique. We discuss both models with constant and variable coefficients, integral representations of solutions, a numerical…
Two inverse-free iterative methods are developed for solving Sylvester matrix equations when the spectra of the coefficient matrices are on, or near, known disjoint subintervals of the real axis. Both methods use the recently-introduced…
The integrability conditions for the existence of Killing-Yano tensors or, equivalently, covariantly closed conformal Killing-Yano tensors, in the presence of torsion are worked out. As an application, all metrics and torsions compatible…
The following document presents a possible solution and a brief stability analysis for a nonlinear system, which is obtained by studying the possibility of building a hybrid solar receiver; It is necessary to mention that the solution of…
We present a general strategy to solve the stationary Schr\"odinger-Poisson (SP) system of equations for multistates with axial symmetry. The approach allows us to obtain the well known single and multistate solutions with spherical…
Finding a Z-eigenpair of a symmetric tensor is equivalent to finding a KKT point of a sphere constrained minimization problem. Based on this equivalency, in this paper, we first propose a class of iterative methods to get a Z-eigenpair of a…
In this paper, we give a necessary and sufficient condition for an even order three dimensional strongly symmetric circulant tensor to be positive semi-definite. In some cases, we show that this condition is also sufficient for this tensor…
We provide a nontrivial bound on the rank of any tensor $T$ over the quaternions $\mathbb{H}$ in the $n_1\times n_2\times n_3$ cases where $2\leq n_i\leq 3$. We describe a decomposition of $T$ into $3$ simple tensors in the $2\times 2\times…
Multilinear systems of equations arise in various applications, such as numerical partial differential equations, data mining, and tensor complementarity problems. In this paper, we propose a homotopy method for finding the unique positive…
We examine various well known exact solutions available in the literature to investigate the recent criterion obtained in ref. [20] which should be fulfilled by any static and spherically symmetric solution in the state of hydrostatic…
N-fold supersymmetry is an extension of the ordinary supersymmetry in one-dimensional quantum mechanics. One of its major property is quasi-solvability, which means that energy eigenvalues can be obtained for a portion of the spectra. We…
In this paper, the author studies quaternionic Monge-Amp\`ere equations and obtain the existence of the solutions to the Dirichlet problem for such equations in strictly pesudoconvex domains in quaternionic space. The stability and…
A common optimization problem is the minimization of a symmetric positive definite quadratic form $< x,Tx >$ under linear constrains. The solution to this problem may be given using the Moore-Penrose inverse matrix. In this work we extend…