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 covering group of the Lorentz group. Since the Lorentz group is a symmetry group of Maxwell's equations, it is assumed to reasonable to use when writing the Maxwell equations Lorentz two-spinors and not tensors. We describe in detail the representation of the Maxwell's equations in the form of Lorentz two-spinors. This representation of Maxwell's equations can be of considerable theoretical interest.

EPJ Web of Conferences, open-access proceedings in physics and related sciences

The paper deals with a numerical solution of the problem of waveguide propagation of polarized light in smoothly-irregular transition between closed regular waveguides using the incomplete Galerkin method. This method consists in replacement of variables in the problem of reduction of the Helmholtz equation to the system of differential equations by the Kantorovich method and in formulation of the boundary conditions for the resulting system. The formulation of the boundary problem for the ODE system is realized in computer algebra system Maple. The stated boundary problem is solved using Maples libraries of numerical methods.

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 various reasons, these implementations are not entirely satisfactory. It is necessary to develop a more adequate simulation model, possibly using a different modeling paradigm. In order to modeling of the TCP source it is proposed to use a hybrid (continuous-discrete) approach. For computer implementation of the model the physical modeling language Modelica is used. The hybrid approach allows us to take into account the transitions between different states in the continuous model of the TCP protocol. The considered approach allowed to obtain a simple simulation model of TCP source. This model has great potential for expansion. It is possible to implement different types of TCP.