As a powerful tool in scientific computation, Mathematica offers us algebraic computation, but it does not provide functions to directly calculate commutators in quantum mechanics. Different from present software packets to deal with noncommutative algebra, such as NCAlgebra and NCComAlgebra, one simple method of calculating the commutator in quantum mechanics is put forward and is demonstrated...

We revisit the question of microcausality violations in quantum field theory on noncommutative spacetime, taking O(x) =: φ⋆φ : (x) as a sample observable. Using methods of the theory of distributions, we precisely describe the support properties of the commutator [O(x),O(y)] and prove that, in the case of spacespace noncommutativity, it does not vanish at spacelike separation in the noncommutin...

Abstract. Non-uniform filtering of the Navier-Stokes equations expresses itself, next to the turbulent stresses, in additional closure terms known as commutator errors. These terms require explicit subgrid modeling if the non-uniformity of the filter is sufficiently pronounced. We derive expressions for the magnitude of the mean flux, the turbulent stress flux and the commutator error for indiv...

RKMK methods and Crouch-Grossman methods are two classes of Lie group methods. The former is using flows and commutators of a Lie algebra of vector fields as a part of the method definition. The latter uses only compositions of flows of such vector fields, but the number of flows which needs to be computed is much higher than in the RKMK methods. We present a new type of methods which avoids th...

let g be a fixed element of a finite group g. we introduce the g-noncommuting graph of g whose vertex set is whole elements of the group g and two vertices x,y are adjacent whenever [x,y] g  and  [y,x] g. we denote this graph by . in this paper, we present some graph theoretical properties of g-noncommuting graph. specially, we investigate about its planarity and regularity, its clique number a...

We study the ramifications of Schur’s theorem that, if G is a group such that G/ZG is finite, then G′ is finite, if we restrict attention to nilpotent group. Here ZG is the center of G, and G′ is the commutator subgroup. We use localization methods and obtain relativized versions of the main theorems. 2000 Mathematics Subject Classification. 20B07, 20D15.

It is shown that product BMO of S.-Y.A.Chang and R. Fefferman, defined on the space R1 ⊗ · · ·⊗Rdt , can be characterized by the multiparameter commutators of Riesz transforms. This extends a classical one-parameter result of R. Coifman, R. Rochberg, and G. Weiss [8], and at the same time extends the work of M. Lacey and S. Ferguson [12] and M. Lacey and E. Terwilleger [19], on multiparameter c...

Article history: Received 25 July 2008 Accepted 16 December 2008 Available online 30 January 2009 Submitted by R.A. Brualdi AMS classification: 47A30 47A63 47B10 47B15 47B47

In this survey paper we show how character methods can be used to solve a wide range of seemingly unrelated problems. These include commutators, powers of conjugacy classes and related random walks, as well as word maps and Waring type problems. In particular we describe recent progress made on conjectures of Ore, of Thompson, and of Lulov and Pak. New open problems and conjectures are also sta...