We obtain a criterion on the commutativity of polynomials in the enveloping algebra of a Lie algebra in terms of an involution condition with respect to the Berezin bracket. As an application, it is shown that the commutativity requirement of missing label operators for reduction chains in the missing label problem can be solved analytically. PACS numbers: 02.20Sv, 21.60Fw

We develop the nth order Fourier-Bessel series expansion of 1-D functions in the interval (0,α). Hence we establish the sampling theorem for a function with α-bandlimited nth order Hankel transform. The latter statement implies that the function is also Fourier transform αbandlimited. The samples’ locations are given by the roots of nth order Bessel functions. In addition, the sampling distance...

We prove an analogue of the magnetic nodal theorem on quantum graphs: the number of zeros of the nth eigenfunction of the Schrödinger operator on a quantum graph is related to the stability of the nth eigenvalue of the perturbation of the operator by magnetic potential. More precisely, we consider the nth eigenvalue as a function of the magnetic perturbation and show that its Morse index at zer...

From Nagumo [10], there have been many accomplishments on the study of the existence of solutions for boundary value problems (BVPs) using the theory of differential inequality (cf. [1–9, 11–17]). However, for the nth-order nonlinear differential equations with the nonlinear boundary conditions, results are very few. The authors made some attempts to solve the nth-order Robin problem [14]. Now ...

We examine magnetic and electric near horizon regions of maximally supersymmetric D– brane and NS5–brane bound states and find transformations between near horizon regions with worldvolume dual magnetic and electric fluxes. These point to dual formulations of NCYM, NCOS and ODp theories in the limit of weak coupling and large spatial or temporal non-commutativity length scale in terms of weakly...

In this paper we study the structure and the commutativity of a ring R, in which for each x,y ? R, there exist two integers depending on x,y such that [x,y]k equals x n or y n.

Abstract The notion of commutativity two normal states on a von Neumann algebra was defined some time ago by means the Pedersen–Takesaki theorem. In this note, we aim at generalising to an arbitrary number states, and obtaining results so joint commutativity. Also relations between broadcastability are investigated.

A new statistical estimation method, Independent Approximates (IAs), is defined and proven to enable closed-form of the parameters heavy-tailed distributions. Given independent, identically distributed samples from a one-dimensional distribution, IAs are formed by partitioning into pairs, triplets, or nth -order groupings retaining median those that approximately equal. The pdf be normalized po...

We calculate the long-range Vanderwaals force and the photoelectric cross section in a noncommutative set up. While we argue that non-commutativity effects could not be discerned for the Vanderwaals interactions, the result for the photoelectric effect shows deviation from the usual commutative one, which in principle can be used to put bounds on the space-space non-commutativity parameter.

We provide here a simple, yet very general framework that allows us to explain several constraint propagation algorithms in a systematic way. In particular, using the notions commutativity and semi-commutativity, we show how the well-known AC-3, PC-2, DAC and DPC algorithms are instances of a single generic algorithm. The work reported here extends and simplifies that of Apt [1].