Algebras with ternary law of composition and their realization by cubic matrices

We study partially and totally associative ternary algebras of first and second kind. Assuming the vector space underlying a ternary algebra to be a topological space and a triple product to be continuous mapping we consider the trivial vector bundle over a ternary algebra and show that a triple product induces a structure of binary algebra in each fiber of this vector bundle. We find the sufficient and necessary condition for a ternary multiplication to induce a structure of associative binary algebra in each fiber of this vector bundle. Given two modules over the algebras with involutions we construct a ternary algebra which is used as a building block for a Lie algebra. We construct ternary algebras of cubic matrices and find four different totally associative ternary multiplications of second kind of cubic matrices. It is proved that these are the only totally associative ternary multiplications of second kind in the case of cubic matrices. We describe a ternary analog of Lie algebra of cubic matrices of second order which is based on a notion of j-commutator and find all commutation relations of generators of this algebra.Comment: 17 pages, 1 figure, to appear in "Journal of Generalized Lie Theory and Applications

Photo- and Cathodoluminescence MG-doped Alumina Ceramics

This work was financially supported by the Russian Science Foundation (RSF), project No. 1872-10082

Nash equilibrium design in the interaction model of entities in the customs service system

The urgency of the analyzed issue is due to the importance of the use of economic-mathematical tools in the course of modeling the interaction of the entities in the customs service system that is necessary for the development of foreign economic activity (FEA) of any state. The purpose of the article is to identify effective strategies for the interaction between the participants of foreign trade activities with customs brokers. The leading method to the study of this issue is economic-mathematical modeling, allowing studying the process of making decisions while choosing the strategy of cooperation between the customs broker and his client. Results: the article suggests the mathematical model to optimize the management mechanisms of interaction between enterprises, engaged in foreign trade, and customs dealers. The data of this article may be useful in modeling interaction of the entities in the customs service system using the methods of game theory. The model of “customer - customs broker” is implemented as a bimatrix game. Assuming the noncooperativegame the authors solve the problem of finding Nash equilibrium in mixed strategies. © 2016 Fedorenko et al

Corrosion resistance of alloys of Hastelloy in chloroaluminate melts

The corrosion of Hastelloy S, Hastelloy X, Haynes 230, Hastelloy N, Hastelloy G35 and Hastelloy C2000 alloys was studied in KCl-AlCl3 melts at 550°С. The rates and the mechanisms of corrosion of the studied materials were determined. The processes taking place during the interaction between alloys and chloroaluminate melts were investigated

Joule Heating and Current-Induced Instabilities in Magnetic Nanocontacts

We consider the electrical current through a magnetic point contact in the limit of a strong inelastic scattering of electrons. In this limit local Joule heating of the contact region plays a decisive role in determining the transport properties of the point contact. We show that if an applied constant bias voltage exceeds a critical value, the stationary state of the system is unstable, and that periodic, non-harmonic oscillations in time of both the electrical current through the contact and the local temperature in the contact region develop spontaneously. Our estimations show that the necessary experimental conditions for observing such oscillations with characteristic frequencies in the range $10^8 \div 10^9$ Hz can easily be met. We also show a possibility to manipulate upon the magnetization direction of a magnetic grain coupled through a point contact to a bulk ferromagnetic by exciting the above-mentioned thermal-electric oscillations.Comment: 9 pages, 6 figures, submitted to Physical Review