Related papers: The Unique Solvability Conditions for the Generali…
We consider matrix Riccati inequality arising in the theory of absolute stability, $H_\infty$ control problem, $LQ$ problem, and optimal estimation problem. In the case of sign definite frequency domain function, the solvability of Riccati…
By a result of Horv\'ath the equation solvability problem over finite nilpotent groups and rings is in P. We generalize his result, showing that the equation solvability over every finite supernilpotent Mal'cev algebra is in P. We also give…
We study the removability of a singular set for elliptic equations involving weight functions and variable exponents. We consider the case where the singular set satisfies conditions related to some generalization of upper Minkowski content…
Consider a linear system of equations with interval coefficients, and each interval coefficient is associated with either a universal or an existential quantifier. The AE solution set and AE solvability of the system is defined by…
We consider the convolution equation $F*X=B$, where $F\in\mathbb{R}^{3\times 3}$ and $B\in\mathbb{R}^{m\times n}$ are given, and $X\in\mathbb{R}^{m\times n}$ is to be determined. The convolution equation can be regarded as a linear system…
In the present paper, a robust approach to a special class of convex feasibility problems is considered. By techniques of convex and variational analysis, conditions for the existence of robust feasible solutions and related error bounds…
We investigate the conditions under which systems of two differential eigenvalue equations are quasi exactly solvable. These systems reveal a rich set of algebraic structures. Some of them are explicitely described. An exemple of quasi…
We investigate singularly perturbed nonlinear complex differential systems of the form $\hbar \partial_x f = F (x, \hbar, f)$ where $\hbar$ is a small complex perturbation parameter. Under a geometric assumption on the eigenvalues of the…
For given non-consistent initial conditions, we study the stability of a class of generalised linear systems of difference equations with constant coefficients and taking into account that the leading coefficient can be a singular matrix.…
We establish the existence of smooth vacuum Gowdy solutions, which are asymptotically velocity term dominated (AVTD) and have T3-spatial topology, in an infinite dimensional family of generalized wave gauges. These results show that the…
The system of Einstein-Maxwell equations for fields mentioned in the title is simplified. Known pure radiation solutions are systematized and new solutions are given by separating the variables.
This paper is concerned with solving some structured multi-linear systems, which are called tensor absolute value equations. This kind of absolute value equations is closely related to tensor complementarity problems and is a generalization…
In this paper we prove uniqueness for an inverse boundary value problem (IBVP) arising in electrodynamics. We assume that the electromagnetic properties of the medium, namely the magnetic permeability, the electric permittivity and the…
In this work we continue our study initiated in \cite{GFGP} on the uniqueness properties of real solutions to the IVP associated to the Benjamin-Ono (BO) equation. In particular, we shall show that the uniqueness results established in…
An inverse-free neural network model with mixed delays is proposed for solving the absolute value equation (AVE) $Ax -|x| - b =0$, which includes an inverse-free neural network model with discrete delay as a special case. By using the…
Classic reachability games on graphs are zero-sum games, where the goal of one player, Eve, is to visit a vertex from a given target set, and that of other player, Adam, is to prevent this. Generalised reachability games, studied by…
Solving a singular linear system for an individual vector solution is an ill-posed problem with a condition number infinity. From an alternative perspective, however, the general solution of a singular system is of a bounded sensitivity as…
Strict mathematics reveals that the strict solution of a Vlasov-Maxwell equation set cannot be of a zero-temperature mathematical form. This universal property of Vlasov-Maxwell system can lead to a closed equation set of three macroscopic…
This paper explores some sufficient conditions for the enhanced solvability of strong vector equilibrium problems, which can be established via a variational approach. Enhanced solvability here means existence of solutions, which are strong…
Consider the nonlinear matrix equation X-sum_{i=1}^{m}A_{i}^{*}X^{-1}A_{i}=Q. This paper shows that there exists a unique positive definite solution to the equation without any restriction on A_{i}. Three perturbation bounds for the unique…