In certain scientific domains, there is a need for tensor operations. To facilitate tensor computations, computer algebra systems are employed. In our research, we have been using …
To construct realistic mathematical models from the first principles, the authors suggest using the stochastization method. In a number of works different approaches to …
A series of theoretical and experimental works is known which investigated the magnetic properties of graphene structures. This is due, among other things, to the prospects of …
Ability to calculate integrals of rapidly oscillating functions is crucial for solving many problems in optics, electrodynamics, quantum mechanics, nuclear physics, and many other …
When modeling such phenomena as population dynamics, controllable flows, etc., a problem arises of adapting the existing models to a phenomenon under study. For this purpose, we …
Self-oscillating modes in control systems of computer networks quite negatively affect the characteristics of these networks. The problem of finding the areas of self-oscillations …
Spinors are more special objects than tensor. Therefore possess more properties than the more generic objects such as tensors. Thus, the group of Lorentz two-spinors is the …
For the study and verification of our mathematical model of telecommunication systems a discrete simulation model and a continuous analytical model were developed. However, for …
The mathematical model of light propagation in a planar gradient optical waveguide consists of the Maxwell's equations supplemented by the matter equations and boundary conditions. …
Representing a probability density function (PDF) and other quantities describing a solution of stochastic differential equations by a functional integral is considered in this …
To synthesize Maxwell optics systems, the mathematical apparatus of tensor and vector analysis is generally employed. This mathematical apparatus implies executing a great number …
Background Spinors are more special objects than tensor. Therefore possess more properties than the more generic objects such as tensors. Group of Lorentz two-spinors is the …
Background. Presentation of probability as an intrinsic property of the nature leads researchers to switch from deterministic to stochastic description of the phenomena. On the …
Background. Presentation of probability as an intrinsic property of the nature leads researchers to switch from deterministic to stochastic description of the phenomena. On the …
In a planar regular optical waveguide, propagation of polarized monochromatic electromagnetic radiation obeys a law following from the Maxwell equations. The Maxwell equations in …
During development of methods for stochastization of one-step processes the attention was focused on obtaining the stochastic equations in the form of the Langevin, since this form …
In the study of a phenomenon it is necessary to construct a model of this phenomenon. The models differ in their expressive properties, degree of maturity, requirements. We need …
It is assumed that the introduction of stochastic in mathematical model makes it more adequate. But there is virtually no methods of coordinated (depended on structure of the …
This paper considers three types of tensor computations. On their basis, we attempt to formulate criteria that must be satisfied by a computer algebra system dealing with tensors. …
The article is devoted to application of tensorial formalism for derivation of different types of Maxwell's equations. The Maxwell's equations are written in the covariant …