Bøger af Tamara G Stryzhak

The book "Analytical functions of Matrices" continues the series "Modern Mathematics for Engineers". This project is addressed to upper-course university students in Mathematics specialties, to graduate students, and to researchers who apply Mathematics in different spheres. The project team was inspired by the positive experience of the researchers of the University of California who published the monograph "Modern Mathematics for Engineers" in 1956. The impulse for starting the Project "Modern Mathematics for Engineers" was the fact that 2008 was announced "The Year of Mathematics in Germany".

The reduction principle is a common idea which states that while researching the stability of solutions of the dynamic system (the system of differential, difference, differential-difference equations) the order of the researched system can be decreased. As the main obstacle in researching a dynamic system is a big dimension of the system, decreasing the order significantly simplifies the stability of the research process.This work contains some ways of decreasing the system order. The author aimed to keep the details to a minimum, to facilitate a better understanding of the main ideas, and the rigor of explanations is replaced by examples and references to the original works.The project Modern Mathematics for Engineers is addressed to upper-course University students in Mathematics specialties, to graduate students and to researchers who apply Mathematics in different spheres.

Tamara G. Stryzhak researches the stability of solutions of the system of linear difference equations with random Markovian coefficients. She also deals with Lyapunov functions which were used to receive the necessary and sufficient conditions of the stability of the solutions in the average quadratic mean.As an example, Stryzhak discusses the stability of solutions of a single difference equation with one random Markovian coefficient which takes on two values.The series on Modern Mathematics for Engineers is addressed to upper-course University students in Mathematics specialties, to graduate students and to researchers who apply Mathematics in different spheres.