In this article, linear operators satisfying anti-commutation relations are considered. It is proven that an anti-commutative type of the Glimm-Jaffe-Nelson commutator theorem follows.

We study a connection between the isochronicity of a center of a polynomial vector field and the existence of a polynomial commuting system. We demonstrate an isochronous system of degree 4 which does not commute with any polynomial system. We prove that among the Newton polynomial systems only the Lienard and Abel systems may commute with transversal polynomial fields. We give a full and const...

For truncated Toeplitz operators, which are compressions of multiplication operators to model subspaces of the Hardy space H2 , we obtain criteria for commutation relations. The results show an analogy to the case of Toeplitz matrices, and they extend the theory of Sedlock algebras. Mathematics subject classification (2010): 47B32, 47B35, 47B37.

1.1 This paper is a part of a much broader project which aims to establish, for a typical ’co-ordinate algebra’ A in the sense of non-commutative geometry, or a scheme, a geometric counterpart VA. Here “geometric” should also be understood in some broad but well-defined sense. We believe this is possible in the setting of model theory, where a crucial new experience in generalisation of semanti...

We study the dynamical features of Maggiore’s generalised commutation relations. We focus on their generality and, in particular, their dependence on the Hamiltonian H . We derive the generalisation of the Planck’s law for black body spectrum, study the statistical mechanics of free particles, and study the early universe evolution which now exhibits non trivial features. We find that the dynam...

High switching frequency associated with soft commutation techniques is a new trend in switching converters. Following this trend, the authors present a buck pulsewidth modulation converter, where the dc voltage conversion ratio has a quadratic dependence on duty cycle, providing a large step-down. By introducing two resonant networks, soft switching is attained, providing highly efficient oper...

A class of representations of the canonical commutation relations is investigated. These representations, which are called exponential representations, are given by explicit formulas. Exponential representations are thus comparable to tensor product representations in the sense that they provide the possibility of computing useful criteria concerning various properties. In particular, they are ...

In High Voltage Direct Current (HVDC) transmission system applications, the control and protection plays an essential role in overall performance. This paper aims to give solutions some performance problems that can occur HVDC link. this paper, ways mitigate serious malfunction of commutation failure process operation converters are studied functions like Commutation Failure Prevention (CFPREV)...