Grigorieva T. Mathematical modeling of channels, signals and systems of communication with use of tensor methods

Dissertation is devoted to development of uniform methodology of construction of mathematical models of channels, signals and systems of communication with the help of the device of the tensor analysis expanding opportunity of the analysis and synthesis of these models. Using methods of the theory of models we show that metric tensor of Riemann's space is strictly proved mathematical model of telecommunication system. The essentially new procedure of transformation of a nonlinear signal to a linear kind in the Riemann's space with the help of concept by covariant derivative is developed. The opportunity using the theory of simplexes in a combination with the device of the tensor analysis for effective research of structural and functional properties of communication system is shown. The adaptation of a task of multipach routing to data - networks is offered with application of tensor methods of research.