Related papers: Sufficient conditions for the unique solvability o…
In this paper, we have obtained a necessary and suffcient condition for the series.
We give two conditions that are necessary and sufficient for the uniqueness of Filippov solutions of scalar, autonomous ordinary differential equations with discontinuous velocity fields. When only one of the two conditions is satisfied, we…
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…
The SOR-like iteration method for solving the absolute value equations~(AVE) of finding a vector $x$ such that $Ax - |x| - b = 0$ with $\nu = \|A^{-1}\|_2 < 1$ is investigated. The convergence conditions of the SOR-like iteration method…
In this paper, we derive some necessary and sufficient solvability conditions for some systems of one sided coupled Sylvester-type real quaternion matrix equations in terms of ranks and generalized inverses of matrices. We also give the…
The system of generalized absolute value equations (GAVE) has attracted more and more attention in the optimization community. In this paper, by introducing a smoothing function, we develop a smoothing Newton algorithm with non-monotone…
Exactly solvable variable parametric Burgers type equations in one-dimension are introduced, and two different approaches for solving the corresponding initial value problems are given. The first one is using the relationship between the…
For positive semidefinite $n\times n$ matrices $A$ and $B$, the singular value inequality $(2+t)s_{j}(A^{r}B^{2-r}+A^{2-r}B^{r})\leq 2s_{j}(A^{2}+tAB+B^{2})$ is shown to hold for $r=\frac{1}{2}, 1, \frac{3}{2}$ and all $-2<t\leq 2$.
Using first and second order supersymmetry formalism we obtain a class of exactly solvable potentials subject to moving boundary conditions.
A counter-example to lower bounds for the singular values of the sum of two matrices in [1] and [2] is given. Correct forms of the bounds are pointed out.
Given the matrix equation ${\bf A X} + {\bf X B} + f({\bf X }) {\bf C} ={\bf D}$ in the unknown $n\times m$ matrix ${\bf X }$, we analyze existence and uniqueness conditions, together with computational solution strategies for $f \,:…
We are interested in the uniqueness of solutions to Maxwell's equations when the magnetic permeability $\mu$ and the permittivity $\varepsilon$ are symmetric positive definite matrix-valued functions in $\mathbb{R}^{3}$. We show that a…
Let $A$ be an $n\times n$ random matrix with independent, identically distributed mean 0, variance 1 subgaussian entries. We prove that $$ \mathbb{P}(A\text{ has distinct singular values})\geq 1-e^{-cn} $$ for some $c>0$, confirming a…
We obtain sufficient conditions for solutions of the $m$th-order differential inequality $$ \sum_{|\alpha| = m} \partial^\alpha a_\alpha (x, u) \ge f (x) g (|u|) \quad \mbox{in } B_1 \setminus \{ 0 \} $$ to have a removable singularity at…
In this paper, which is a follow-up to [A. Borobia, R. Canogar, F. De Ter\'an, Mediterr. J. Math. 18, 40 (2021)], we provide a necessary and sufficient condition for the matrix equation $X^\top AX=B$ to be consistent when $B$ is symmetric.…
In this paper, for the first time in the literature, we study the stability of solutions of two classes of feasibility (i.e., split equality and split feasibility) problems by set-valued and variational analysis techniques. Our idea is to…
We present a new approach to compute selected eigenvalues and eigenvectors of the two-parameter eigenvalue problem. Our method requires computing generalized eigenvalue problems of the same size as the matrices of the initial two-parameter…
We identify many new solvable subcases of the general dynamical system characterized by two autonomous first-order ordinary differential equations with purely quadratic right-hand sides; the solvable character of these dynamical systems…
Let $S$ be a real $n\times n$ matrix, $z,\hat c\in \mathbb R^n$, and $| z|$ the componentwise modulus of $z$. Then the piecewise linear equation system $$z-S| z| = \hat c$$ is called an \textit{absolute value equation} (AVE). It has been…
It is well known that if $A\in\mathbb{C}^{N\times N}$ and $B\in\mathbb{C}^{N\times M}$ form a controllable pair (in the sense that the Kalman matrix $[B\ |\ AB\ | \ \dots\ |\ A^{N-1}B]$ has full rank) then, there exists…