A new algorithm for measuring the vectors of harmonic signals by nonuniform frequency-dependent sampling of the signals and algebraic summation of sets of sampled readouts, invariant to an arbitrary number of additive forms of periodic interference, is proposed. The algorithm ensures effective suppression of the interference in an extremely simple way and is intended for use in instruments for measuring active and passive ac quantities

Consideration was given to the model obeying a system of ordinary differential equations where the subsystems are systems of autonomous ordinary differential equations. If the coupling parameter ε = 0, then the model falls apart into decoupled subsystems. For a model consisting of coupled subsystems, considered was the main mode for which the problems of oscillations, bifurcation, and stability were solved, and the results obtained before for the case of two second-order subsystems were generalized.

We introduce a generalization of equilibrium in secure strategies, which takes into account inhomogeneous attitudes of players to security in noncooperative games. In the proposed Asymmetric Equilibrium in Secure Strategies players are divided into classes that unequally related to each other threats. Namely, a player in his behavior takes into account threats posed by players of his own or higher class, and ignores threats of lower-class players. We provide illustrative examples of these equilibria in matrix and continuous games, which have neither Nash-Cournot equilibrium no equilibrium in secure strategies. The proposed concept provides theoretical framework for studying games in which asymmetric and hierarchical logic plays an important role in the interaction of players.

Abstract: This paper analyzes the routing problem in order to design automatic train operation in a station. The authors consider the routing problem for the receipt-departure of trains and their shunting movements. It is noted that, in the case of stations with a branched track infrastructure, the number of all admissible routes becomes large, leading to bulky computations in the search procedure. A certain method is proposed to partition stations into zones for reducing the amount of computations. And finally, the authors pose the graph cutting problem of a railway station network with due account of track infrastructure features and present its solution algorithm.