The non-abelian tensor product of groups which has its origins in algebraic K-theory as well as inhomotopy theory, was introduced by Brown and Loday in 1987. Group theoretical aspects of non-abelian tensor products have been studied extensively. In particular, some studies focused on the relationship between the exponent of a group and exponent of its tensor square. On the other hand, com...

In this article, the notions of non-abelian tensor and exterior products of two normal crossed submodules of a given crossed module of groups are introduced and some of their basic properties are established. In particular, we investigate some common properties between normal crossed modules and their tensor products, and present some bounds on the nilpotency class and solvability length of the...

A molecular field theory of the cholesteric ordering in nematic nanocomposites doped with chiral nanoparticles was developed taking into consideration dispersion interaction between rod-like nanoparticles. It shown that inverse pitch helical structure is proportional to anisotropy effective polarizability and gyration tensor a nanoparticle host. The enables one predict sense inversion induced b...

The deployment of high power radio frequency waves in the ion cyclotron range constitutes an important operational facility in many plasma devices, including ITER. Not only for pure heating of the plasma, i.e. Ion Cyclotron Resonant Heating (ICRH), but also for the generation of non-inductive current through Ion Cyclotron Current Drive (ICCD). We concentrate on minority species heating scenario...

Interaction of charged particles with each other and/or with external fields results in emission of electromagnetic radiation. This article considers the emission arising as fast (nonthermal) particles move through media with random inhomogeneities. The nature of these inhomogeneities might be rather arbitrary. One of the simplest examples of inhomogeneities is a distribution of the microscopic...

The problem of constructing and justifying the discrete algorithms support operator method for numerical modeling differential repeated rotational operations vector analysis (curlcurl) in application to problems magnetohydrodynamics is considered. Difference schemes on unstructured meshes do not approximate equations local sense. Therefore, it necessary prove convergence these exact solution, w...