We investigate combinatorial commutation properties for reordering a sequence of two kinds of steps, and for separating wellfoundedness of unions of relations. To that end, we develop the notion of a constricting sequence. These results can be applied, for example, to generic path orderings used in termination proofs. “Loop” as a train destination means that the train enters the Loop elevated s...

To transfer large amount of direct current power having high amplitude voltage over long distance, high voltage direct current (HVDC) transmission system is used. This system was introduced 60 year ago and now it is widely used all over the world. Some examples of HVDC systems are following; Voltage-SourcedConverter (VSC), current commutated converter (CCC) and line commutated converter (LCC) d...

This paper introduces power conversion principles and defines the terminology. The concepts of sources and switches are defined and classified. From the basic laws of source interconnections, a generic method of power converter synthesis is presented. Some examples illustrate this systematic method. Finally, the notions of commutation cell and soft commutation are introduced and discussed.

The differential equations for a local analytic Moufang loop are established. The commutation relations for the infinitesimal translations of the analytic Moufang are found. These commutation relations can be seen as a (minimal) generalization of the Maurer-Cartan equations. 2000 MSC: 20N05, 17D10

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...