The model of the position-dependent noncommutativety in quantum mechanics is proposed. We start with a given commutation relations between the operators of coordinatesˆx i , ˆ x j = ω ij (ˆ x), and construct the complete algebra of commutation relations, including the operators of mo-menta. The constructed algebra is a deformation of a standard Heisenberg algebra and obey the Jacobi identity. T...

We consider a few problems connected to the commutation of languages, in particular nite ones. The goal is to emphasize the challenging nature of such simply formulated problems. In doing so we give a survey of results achieved during the last few years, restate several open problems and illustrate some approaches to attack such problems by two simple constructions.

The uncertainty relations and the underlying canonical commutation relations are at the heart of quantum mechanics. In recent years, for various conceptual and technical reasons, there has been renewed interest in the question whether there may exist corrections to the canonical commutation relations which could be significant at extreme scales. Let me start with a brief (and certainly incomple...

The torque ripple of a switched reluctance motor (SRM) limits its application in electric vehicles. This paper proposes DITC system for SRMs based on novel multilevel converter (MLC), which aims at the problem that cannot be effectively suppressed conventional direct instantaneous control (DITC) an SRM due to limitation DC bus voltage asymmetric half-bridge (AHBC) and single strategy formulated...

We present a confluence tool for left-linear term rewrite systems. The tool proves confluence by using Hindley’s commutation theorem together with three commutation criteria, including Church-Rosser modulo associative and/or commutative theories. Despite a small number of its techniques, experiments show that the tool is comparable to recent powerful confluence tools.

We discuss the meaning of renormalization used for deriving quadratic bosonic commutation relations introduced by Accardi [ALV] and find a representation of these relations on an interacting Fock space. Also, we investigate classical stochastic processes which can be constructed from noncommutative quadratic white noise. We postulate quadratic free white noise commutation relations and find the...

Asymptotics of solutions to Schrödinger equations with singular magnetic and electric potentials is investigated. By using a Almgren type monotonicity formula, separation of variables, and an iterative Brezis-Kato type procedure, we describe the exact behavior near the singularity of solutions to linear and semilinear (critical and subcritical) elliptic equations with an inverse square electric...