The commutation relation $$KL = LK$$ between finite convolution integral operator K and differential L has implications for spectral properties of K. We characterize all operators admitting this relation. Our analysis places no symmetry constraints on the kernel extending well-known results Morrison real self-adjoint operators.

Given q1, q2 ∈ C \ {0}, we construct a unital Banach algebra Bq1,q2 which contains a universal normalized solution to the (q1, q2)-deformed Heisenberg–Lie commutation relations in the following specific sense: (i) Bq1,q2 contains elements b1, b2, and b3 which satisfy the (q1, q2)-deformed Heisenberg–Lie commutation relations (that is, b1b2 − q1b2b1 = b3, q2b1b3 − b3b1 = 0, and b2b3 − q2b3b2 = 0...

A two-terminal equivalent model of rapidly elongated freeburning arcs in air is presented that is designed to be used in systematic simulations of both existing and new switching concepts of circuit breakers in electric power circuits. The proposed model is based on the combination of a Mayr-type and a Cassie-type differential equation. These are modified in order to take into account the influ...

The interaction of the electric and magnetic dipole moments of a particle with the electromagnetic field is investigated in an approach that deals with four-dimensional (4D) geometric quantities. The new commutation relations for the 4D orbital and intrinsic angular momentums and also for the 4D dipole moments are introduced. The expectation value of the quantum 4-force, which holds in any fram...

We present a generalization of the commutation formula to irregular subdivision schemes and wavelets. We show how, in the noninterpolating case, the divided differences need to be adapted to the subdivision scheme. As an example we include the construction of an entire family of biorthogonal compactly supported irregular knot B-spline wavelets starting from Lagrangian interpolation.

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