The problem of automated construction of recognizers of anomalies in the behavior of complicated dynamical systems is solved by means of analyzing trajectories obtained from sensors surrounding the system. A specific feature of the problem consists in the fact that, depending on the individual properties of the system and conditions of its operation, trajectories that contain anomalies may significantly differ from each other in amplitude and length. Besides, the training set could be incompletely defined. The algorithm described here is based on the idea of applying an algebraic approach to the labeling of trajectories. It allows to construct recognizers of abnormal behavior of complicated dynamical systems. The training of the algorithm could be done on an incompletely defined training set.

New algorithms for query modifications are proposed. These algorithms involve the lexical optimization based on the mathematical transformations that have never been used for the query optimization before.

In the A. Cordoba and P. Fernandez research of the divergence of greedy algorithms in Lebesgue spaces some maximum operator P*(x) played the key role. This article reviews the assessment P*(x) in Marcinkiewicz spaces.

We consider the estimation of the spike delay induced by external sinaptic influence. We propose a first-order estimation for the latent period of synapse coupled spiking neurons.

We give the mathematical justification of one numerical experiment dealing with the propagation of radio waves through a complicated relief environment.

The asymptotics of spatially inhomogeneous periodic solutions of the complex spatially distributed Hutchinson equation with periodic boundary conditions are presented. It is shown that such solutions are observable in a numerical experiment.

This paper analyzes the well known multiplier-accelerator model from a mathematical point of view. It introduces non-linear components to standard linear models. Using the theory of normal forms, the existence of the stable non-homogeneous invariant torus has been shown.

We consider Bernoulli measures and obtain a closed-form expression of the entropy estimator bias.

Some properties of the dynamics of a differential equation with the linear distributed delay is studied. In critical cases, which all have an infinite dimension, special equations - normal forms - were built.

The chaotic phase synchronization of two cascaded one-ring and two-ring PLL systems in the conditions of additive and phase noise is investigated. A registration technique of the chaotic phase synchronisation on the basis of the continuous wavelet transform is developed. Onset conditions of the steady chaotic phase synchronisation are revealed. Advantages of the two-ring system of PLL over the one-ring system is shown.