This paper concerns the automated simpliication of expressions which involve non-commuting variables. The technology has been applied to the simpliication of matrix and operator theory expressions which arise in engineering applications. The non-commutative variant of the Grr obner Basis Algorithm is used to generate rewrite rules. We will also look at the phenomenon of innnite bases and implic...

We prove an implicit function theorem for non-commutative functions. We use this to show that if p(X, Y ) is a generic non-commuting polynomial in two variables, and X is a generic matrix, then all solutions Y of p(X, Y ) = 0 will commute with X.

We define four 3×3 commuting contractions which do not dilate to commuting isometries. However they do satisfy the scalar von Neumann inequality. These matrices are all nilpotent of order 2. We also show that any three 3×3 commuting contractions which are scalar plus nilpotent of order 2 do dilate to commuting isometries.

The aim of this study was to verify the prevalence of physical inactivity and associated factors among adolescents commuting to school. This was an epidemiological study based on secondary data from a sample of 4,207 adolescents (14-19 years). Data were collected through a previously validated questionnaire (GSHS-WHO). Adolescents were classified as "inactive in commuting" when they reported no...

Tensor networks are a central tool in condensed matter physics. In this paper, we initiate the study of tensor network non-zero testing (TNZ): Given a tensor network T , does T represent a non-zero vector? We show that TNZ is not in the Polynomial-Time Hierarchy unless the hierarchy collapses. We next show (among other results) that the special cases of TNZ on nonnegative and injective tensor n...

In papers on primary state diffusion (Percival 1994, 1995), numerical estimates suggested that fluctuations in the space-time metric on the scale of the Planck time (≈ 10s) could be detected using atom interferometers. In this paper we first specify a stochastic metric obtained from fluctuations that propagate with the velocity of light, and then develop the non-Markovian quantum state diffusio...

We describe a method for simulating the dynamics of an S3 cosmic string network. We use a lattice Monte Carlo to generate initial conditions for the network, which subsequently is allowed to relax continuously according to a simplified model of string dynamics. The dynamics incorporates some novel features which, to our knowledge, have not been studied in previous numerical simulations: The exi...

The components of the position operator, at a fixed time, for a massless and spinning particle with given helicity λ described in terms of bosonic degrees of freedom have an anomalous commutator proportional to λ. The position operator generates translations in momentum space. We show that a ray-representation for these translations emerges due to the non-commuting components of the position op...

Our previous " exotic " particle, together with the more recent anomalous anyon model (which has arbitrary gyromagnetic factor g) are reviewed. The non-relativistic limit of the anyon generalizes the exotic particle which has g = 0 to any g. When put into planar electric and magnetic fields, the Hall effect becomes mandatory for all g = 2, when the field takes some critical value.

Let G be a non-abelian group and Z(G) be its center. The non-commuting graph AG of G is the graph whose vertex set is G\Z(G) and two vertices are joined by an edge if they do not commute. Let SL(2, q) be the special linear group of degree 2 over the finite field of order q. In this paper we prove that if G is a group such that AG ∼= ASL(2,q) for some prime power q ≥ 2, then G ∼= SL(2, q). MSC 2...