Four periods of research activity of professor G.V. Rimskiy in 1960–2000 are presented. The main research results of these periods are shown.

A method of optically visualized block watermarking the images based on the proposed models of embedded message, marked image and robust textural correlation message extracting is developed. The results of computer modeling are presented.

At high problem dimension the Kalman filter becomes difficult to realize in real time due to the high computational costs. Alternatively, a technique of filter synthesis on the basis of the extended least square method with extended square discrepancy is given. The technique allows to reduce the computation costs for the search of filter gain coefficients, but it increases the variance of the filtering error in comparison with Kalman filter. The degree of this increase in case of prior information is not taken into account is shown on example.

A method of analytical solution of the boundary-value problem of electromagnetic field penetration of point magnetic dipole through the infinite planar leans (screen) from the focusing metamaterials is suggested. It is demonstrated, that for the lenses with special combinations of material parameters in layers the series of focuses are formed: one is over the screen and three is in front of the screen in the half-space of point source of the excitation field. The summary field of focuses in front of the lens is equal to the sum of fields of magnetic and electric dipoles.

A Mathematical model of filtering consolidation in the body of soil dam with conduit and
washout zone in two-dimensional case is considered. The impact of such technogenic factors as temperature, salt concentration, subsidence of upper boundary and interior points of the dam with time is taken into account. The software to automate the calculation of numerical solution of the boundary problem by radial basis functions has been created, which enables to conduct numerical experiments by varying the input parameters and shape. The influence of the presence of conduit and washout zone on the pressure, temperature and concentration of salts in the dam body at different time intervals is
investigated. A number of numerical experiments is conducted and the analysis of dam accidents is performed.

Some problems of the finite element modeling of electromagnetic field distribution in the
nearest zone of spherical metallic and dielectric nanoparticles caused by a plane wave are considered. The appropriate mathematical models, algorithms and software were developed, its verification is carried out. The discrepancy between the results of research of the mathematical model and the existing results of calculations using analytical formulas does not exceed 10 %.

Investigation of the 4th power dynamic systems behavior in conditions of the interval parameter variations is carried out on the basis of root locus portraits. Investigation of the system dynamics is carried out and the behavior regularities at the system stability bound are determined for root locus portraits of the 4th power systems with interval parametric uncertainties. On this basis the stability conditions are derived and expressions are determined for calculating intervals of parameter variation ensuring the system robust stability.

Computer aided research method on the basis of general theory of root trajectories is considered in the frame of study of multi-channel control systems with varying parameters included as cofactors with arbitrary exponents in coefficients of the characteristic equation of the system. Possibilities of the method are demonstrated on the example of constructing stability regions projections on the plane of varying parameters of dual-channel pulse system with cross-connections.

The article covers the use of perseptron, Hopfild artificial neural network and semantic network for classification of text information. Network training algorithms are studied. An algorithm of inverse mistake spreading for perceptron network and convergence algorithm for Hopfild network are implemented. On the basis of the offered models and algorithms automatic text classification software is developed and its operation results are evaluated.

In the article the comparison of traditional routing algorithms with content based routing algorithms is performed. Investigation of source and sink locations influence on energy consumption, delays and data transfer reliability is made as well. It is proved, that this kind of routing may increase the efficiency of sensor networks operating in a large range of conditions.

The supply chain management method for manufacture scheduling and planning based
on APS-algorithm is offered. It . Logistics solutions and inventory management problems are discussed. The structure of automated control system of enterprise is designed and its tasks are described.