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

Local inhomogeneity of the magnetic field as a possible factor of influence on the human

The results of expeditionary studies in August 2013 at the Chui region of the earthquake epicenter (2003), in the area, characterized by an abnormal performance of the spatial distribution of the geomagnetic field vector values are presented. The adaptive response of the human body by analyzing the variability of the cardiovascular system activity in a short stay in the area of natural character geomagnetic anomalies is investigated. It is shown that a person entering the zone with abnormal magnetic field gradient levels can disrupt adaptive human body reaction that is accompanied by an increased level of the cardiovascular system functioning after visiting zone and increasing the power spectral density of oscillations several RR intervals of heart rate in the range of 0,04 -0,15 Hz and 0,5-1 Hz while in a zone. © (2016) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only

Nonreciprocal transmission of microwaves through a long Josephson junction

Nonreciprocal microwave transmission through a long Josephson junction in the flux-flow regime is studied analytically and numerically within the framework of the perturbed sine-Gordon model. We demonstrate that the maximum attenuation of the transmitted power occurs when the direction of the flux flow is opposite to the direction of the microwave propagation. This attenuation is nonreciprocal with respect to the flux-flow direction and can be enhanced by increasing the system length and proper impedance matching of the junction ends to external transmission line.Comment: 5 pages, 5 figure