Related papers: Nonsymmetric generic matrix equations

The matrix semigroup membership problem asks, given square matrices $M,M_1,\ldots,M_k$ of the same dimension, whether $M$ lies in the semigroup generated by $M_1,\ldots,M_k$. It is classical that this problem is undecidable in general but…

In this paper we prove that points in the space $X(k,n)$ of configurations of $n$ points in $\mathbb{CP}^{k-1}$ which are fixed under a certain cyclic action are the solutions to the generalized scattering equations on planar kinematics…

We consider two basic algorithmic problems concerning tuples of (skew-)symmetric matrices. The first problem asks to decide, given two tuples of (skew-)symmetric matrices $(B_1, \dots, B_m)$ and $(C_1, \dots, C_m)$, whether there exists an…

A hypersurface $H$ in $\mathbb{P}^r$ of degree $n$ is called determinantal if it is the zero locus of a polynomial of the form $\operatorname{det}(x_0 A_0 + \ldots + x_r A_r)$ for some $(r+1)$-tuple of $n \times n$ matrices $A = (A_0,…

Although the conjugacy classes of the general linear group are known, it is not obvious (from the canonic form of matrices) that two permutation matrices are similar if and only if they are conjugate as permutations in the symmetric group,…

Two families of certain nonsymmetric generalized Jacobi polynomials with negative integer indexes are used for solving third- and fifth-order two point boundary value problems subject to homogeneous and nonhomogeneous boundary conditions…

For any rank 2 of simple Lie algebra, the relativistic Chern-Simons system has the following form: \begin{equation}\label{e001} \left\{\begin{array}{c} \Delta u_1+(\sum_{i=1}^2K_{1i}e^{u_i}…

We study orbits and reachable sets of generic couples of Hamiltonians $H_1, H_2$ on a symplectic manifold $N$. We prove that, $C^k$-generically for $k$ large enough, orbits coincide with the whole of $N$, and that the same is true for…

We give a new proof of universality properties in the bulk of spectrum of the hermitian matrix models, assuming that the potential that determines the model is globally $C^{2}$ and locally $C^{3}$ function (see Theorem \ref{t:U.t1}). The…

We obtain a generic regularity result for stationary integral $n$-varifolds with only strongly isolated singularities inside $N$-dimensional Riemannian manifolds, in absence of any restriction on the dimension ($n\geq 2$) and codimension.…

Let $e_{1},\dots, e_{k}$ be complex $n\times n$ matrices such that $e_{i}e_{j}=-e_{j}e_{i}$ whenever $i\not=j$. We conjecture that $\hbox{rk}(e_{1}^{2})+\hbox{rk}(e_{2}^{2})+\cdots+\hbox{rk}(e_{k}^{2})\leq O(n\log n)$, and prove some…

Let $g$ and $n$ be nonnegative integers and $\mathcal A=(a_0,\dots,a_n)$ a sequence of $n+1$ integers summing up to $d$. Let $\overline{\mathcal M}_{g,n+1}$ be the moduli space of $(n+1)$-pointed stable curves of genus $g$ and…

We show that every entire solution to the Bernoulli (or one-phase) free boundary problem with finite Morse index in $\mathbb{R}^3$ is axially symmetric. In fact, we additionally prove that the same result would follow in any dimension $4…

A systematic investigation of the skew-symmetric solutions of the three-dimensional Jacobi equations is presented. As a result, three disjoint and complementary new families of solutions are characterized. Such families are very general,…

In this paper, we study a class of generalized extensible beam equations with a superlinear nonlinearity \begin{equation*} \left\{ \begin{array}{ll} \Delta ^{2}u-M\left( \Vert \nabla u\Vert _{L^{2}}^{2}\right) \Delta u+\lambda V(x) u=f(…

Let A be an n by n matrix with determinant 1. We show that for all n > 2 there exist dimensional strictly positive constants C_n such that the average over the orthogonal group of log rho(A X) d X > C_n log ||A||, where ||A|| denotes the…

In this paper we analyzed solutions of some complex matrix equations related to pseudoinverses using the concept of reproductivity. Especially for matrix equation AXB=C it is shown that Penrose's general solution is actually the case of the…

The nonlinear supersymmetry of one-dimensional systems is investigated in the context of the quantum anomaly problem. Any classical supersymmetric system characterized by the nonlinear in the Hamiltonian superalgebra is symplectomorphic to…

Let $\mathbf{k}$ be an algebraically closed field of characteristic $\geq 7$ or zero. Let $\mathcal{A}$ be a tame order of global dimension $2$ over a normal surface $X$ over $\mathbf{k}$ such that…

It is shown that the correlation functions of the random variables $\det(\lambda - X)$, in which $X$ is a real symmetric $ N\times N$ random matrix, exhibit universal local statistics in the large $N$ limit. The derivation relies on an…