Related papers: Non-commutative Laurent phenomenon for two variabl…
Using the Berezin-Marinov pseudoclassical formulation of spin particle we propose a classical model of spin noncommutativity. In the nonrelativistic case, the Poisson brackets between the coordinates are proportional to the spin angular…
Non-alternating Hamiltonian Lie algebras in three variables over a perfect field of characteristic 2 are considered. A classification of non-alternating Hamiltonian forms over an algebra of divided powers in three variables and of the…
We establish several bifurcation results for the singular Lane-Emden-Fowler equation.
We derive the Euler-Lagrange equation corresponding to a variant of non-Euclidean constrained von Karman theories.
Let $p$ be a polynomial in the non-commuting variables $(a,x)=(a_1,...,a_{g_a},x_1,...,x_{g_x})$. If $p$ is convex in the variables $x$, then $p$ has degree two in $x$ and moreover, $p$ has the form $p = L + \Lambda ^T \Lambda,$ where $L$…
We are proving a Bernstein type inequality in the shift-invariant spaces of $L_2(R)$.
We consider the $*$-Markov equation for the symmetric Laurent polynomials in three variables with integer coefficients, which is an equivariant analog of the classical Markov equation for integers. We study how the properties of the Markov…
In the present study, we analyze in combination the principles of special relativity and the phenomenon of the aberration of light, deriving a system of equations that allows establishing the relationship between the angles commonly…
We derive bilateral asymptotic as well as non-asymptotic estimates for the multivariate Laplace integrals. Possible applications: Tauberian theorems for random vectors.
In this paper, we establish an extension of a noncommutative Bennett inequality with a parameter $1\leq r\leq2$ and use it together with some noncommutative techniques to establish a Rosenthal inequality. We also present a noncommutative…
The "Modularity Conjecture" is the assertion that the join of two nonmodular varieties is nonmodular. We establish the veracity of this conjecture for the case of linear idempotent varieties. We also establish analogous results concerning…
We report in this survey some new results concerning noncommutative Chern characters: construction and the cases when they are exactly computed. The major result indicates some clear relation of these noncommutative objects and their…
We approach the convergence of the Magnus, Wilcox, and symmetric Wilcox expansions by a non-commutative heat equation derived from the Maurer-Cartan equation.
Two examples of the situation when the classical observables should be described by a noncommutative probability space are investigated. Possible experimental approach to find quantum-like correlations for classical disordered systems is…
We propose two methods for obtaining the dual of non-linear relativity as previously formulated in momentum space. In the first we allow for the (dual) position space to acquire a non-linear representation of the Lorentz group independently…
We show that the L^2-torsion and the von Neumann rho-invariant give rise to commensurability invariants of knots.
By using Laurent graph polynomials instead of the usual ones, i.e. by allowing negative powers of the variables, we simplify an existing method of determining the Alon-Tarsi numbers of planar graphs.
The problem as to when two noncommuting observables are considered to have the same value arises commonly, but shows a nontrivial difficulty. Here, an answer is given by establishing the notion of perfect correlations between noncommuting…
We propose a simple low-energy classical experiment in which the effects of noncommutativity can be clearly separated from commutative physics. The ensuing bound on the noncommutative scale is remarkable, especially in view of its…
The goal of this paper is to introduce and study noncommutative Catalan numbers $C_n$ which belong to the free Laurent polynomial algebra in $n$ generators. Our noncommutative numbers admit interesting (commutative and noncommutative)…