Related papers: A Simple Proof of the Classification of Normal Toe…
In this paper, we present sufficient conditions to guarantee the invertibility of rational circulant matrices with any given size. These sufficient conditions consist of linear combinations of the entries in the first row with integer…
The Neumann--Zagier matrices of an ideal triangulation are integer matrices with symplectic properties whose entries encode the number of tetrahedra that wind around each edge of the triangulation. They can be used as input data for the…
Given a lower-triangular matrix of real numbers, one can ask the following four total-positivity questions: total positivity of the triangle itself; total positivity of its row-reversal; Toeplitz-total positivity of its row sequences…
We present a classification of the so-called "additive symmetric 2-cocycles" of arbitrary degree and dimension over Z/p, along with a partial result and some conjectures for m-cocycles over Z/p, m > 2. This expands greatly on a result…
In this paper we investigate Toeplitz and symmetric Toeplitz determinants of inverse functions for some classes of univalent functions and improve some previous results.
Several classes of systems of evolution equations with one or two vector unknowns are considered. We investigate also systems with one vector and one scalar unknown. For these classes all equations having the simplest higher symmetry are…
We study matrix integration over the classical Lie groups $U(N),Sp(2N),O(2N)$ and $O(2N+1)$, using symmetric function theory and the equivalent formulation in terms of determinants and minors of Toeplitz$\pm$Hankel matrices. We establish a…
In the context of applying the Lorentz group theory to polarization optics in the frames of Stokes-Mueller formalism, some properties of the Lorentz group are investigated. We start with the factorized form of arbitrary Lorentz matrix as a…
We present an alternative account of the problem of classifying and finding normal forms for arbitrary bilinear forms. Beginning from basic results developed by Riehm, our solution to this problem hinges on the classification of…
Using calculus we show how to prove some combinatorial inequalities of the type log-concavity or log-convexity. It is shown by this method that binomial coefficients and Stirling numbers of the first and second kinds are log-concave, and…
We find a recursive algorithm for computing the precise centralizers of the complex orthogonal and symplectic groups, and hence the isotropy groups, with respect to the similarity transformation on the spaces of skew-symmetric and…
We search for rational, four-dimensional maps of standard type (x_{n+1} - 2x_n + x_{n-1} = eps f(x,eps)) possessing one or two polynomial integrals. There are no non-trivial maps corresponding to cubic oscillators, but we find a…
In this paper we study some basic problems about Toeplitz subshifts of finite topological rank. We define the notion of a strong Toeplitz subshift of finite rank $K$ by combining the characterizations of Toeplitz-ness and of finite…
Denote by $w(T)$ the numerical radius of a matrix $T$. An elementary proof is given to the fact that $w(AB) \leq w(A)w(B)$ for a pair of commuting matrices of order two, and characterization is given for the matrix pairs that attain the…
Starting from the spectral analysis of g-circulant matrices, we consider a new multigrid method for circulant and Toeplitz matrices with given generating function. We assume that the size n of the coefficient matrix is divisible by g \geq 2…
In this paper, two kinds of generalizations of ideal matrices, generalized ideal matrices and double ideal matrices. are obtained and studied, The concepts of generalized ideal matrices and double ideal matrices are proposed, and their…
The properties common to the Lorenz and Chen attractors, as well as their fundamental differences, have been studied for many years in a vast number of works and remain a topic far from a rigorous and complete description. In this paper we…
We prove that if $A$ is a regular graded skew Clifford algebra and is a twist of a regular graded Clifford algebra $B$ by an automorphism, then the subalgebra of $A$ generated by a certain normalizing sequence of homogeneous degree-two…
Given a trigonometric polynomial f:[0,1]\to[0,1] of degree m, one can define a corresponding stationary process {X_i}_{i\in Z} via determinants of the Toeplitz matrix for f. We show that for m=1 this process, which is trivially…
A recent paper of A.~Connes and W.D.~van Suijlekom identifies the operator system of $n\times n$ Toeplitz matrices with the dual of the space of all trigonometric polynomials of degree less than $n$. The present paper examines this…