Table of contents

In this article is developed a calculus which reflects the most general group-theoretic properties of flows and which is based on an exponential representation of flows defined by nonstationary differential equations. Problems of optimization and control have had the greatest influence on the development of this calculus, and the results are intended mainly to treat these problems. Bibliography: 11 titles.

The asymptotics of relaxation oscillations are considered. Figures: 7. Bibliography: 7 titles.

Certain control problems under conditions of undetermined information for systems described by differential equations can be formalized within the framework of differential games. The present paper is devoted to one such formalization developed by the author and his collaborators. Bibliography: 22 titles.

In this paper functions satisfying the inequality in a domain are studied. Here is a linear second order elliptic operator with positive definite characteristic form, , and is defined in an interval , in which , and . Bibliography: 13 titles.

This paper studies the approximation of functions of two variables by functions whose graphs in 3-space are continuous surfaces which are piecewise flat. By analogy with the case of functions of one variable, we naturally call such approximating functions polygonal. Bibliography: 8 titles.

A necessary optimality condition in the form of Pontrjagin's maximum principle and the existence of the optimal process are proved for optimal systems containing variable time lags in the phase coordinates and variable commensurable time lags in the controls. Bibliography: 10 titles.