We present an elementary discussion of two basic properties of angular displacements, namely, the anticommutation of finite rotations, and the commutation of infinitesimal rotations, and show how commutation is achieved as the angular displacements get smaller and smaller.

We construct an algebra with twisted commutation relations and equip it with the shift. For appropriate irregularity of the non-local commutation relations we prove that the tracial state is the only translation-invariant state.

The AN−1 (2, 0) superconformal theory has an observable associated with every two-cycle in six dimensions. We make a natural guess for the commutation relations of these operators, which reduces to the commutation relations of Wilson and ’t Hooft lines in four-dimensional SU(N) N = 4 super Yang-Mills theory upon compactification on a two-torus. We then verify these commutation relations by cons...

The commutation relations of the composite fields are studied in the 3, 2 and 1 space dimensions. It is shown that the field of an atom consisting of a nucleus and an electron fields satisfies, in the space-like asymptotic limit, the canonical commutation relations within the sub-Fock-space of the atom. The composite anyon fields are shown to satisfy the proper anyonic commutation relations wit...

We consider the relations between de Vaucouleurs-Ikeuchi diagram and generalized commutation relations among the coordinates and momenta. All physical objects in the Universe ranging from elementary particles to super cluster of galaxies are confined within the Triangle of the de VaucouleursIkeuchi diagram on the matter density versus scale length plane. These three boundaries are characterized...

For brushless motor drives, current control is often used to improve performance and reliability. This tutorial paper analyzes and compares various different schemes of electronic commutation and current control. Starting from a simple 6-step drive without current control, discussion will include bus current control, sinusoidal commutation, phase current control, and synchronous regulator. Rela...

A generalization of the quantum inverse scattering method is proposed replacing the quantum group RLL commutation relations of Lax operators by reflection equation type RLRL commutation relations. Under some natural assumptions the most general algebra of this type allowing to construct the neccessary integrals of ⋆ Supported by the Science and Technology Fellowship Programme for Japan under th...

This article proposes a virtual sensor for piecewise linear systems based on observability analysis that is in function of a commutation law related with the system's outpu. This virtual sensor is also known as a state estimator. Besides, it presents a detector of active mode when the commutation sequences of each linear subsystem are arbitrary and unknown. For the previous, this article propos...