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Original codes and combinatorial-geometrical computational schemes are presented, which are developed and applied for finding exact analytical formulas that describe the probability of error-free readout of random point images recorded by a scanning aperture with a limited number of threshold levels. Combinatorial problems encountered in the course of the study and associated with the new generalization of Catalan numbers are formulated and solved. An attempt is made to find the explicit analytical form of these numbers, which is, on the one hand, a necessary stage of solving the basic research problem and, on the other hand, is an independent self-consistent problem.

Methods are proposed to restore object images and estimate the hardware function in a radiometric system of the millimeter range operating with a large elevation scanning step. These methods generalize the available approaches to image restoration in the spatial and frequency domains with a thinned observation matrix, and incorporate new approaches to estimating the hardware function. The results of experimental studies are given.

This paper considers problems related to measuring the information parameters of the processed signal reflected from the located object under additive non-Gaussian correlated noise. It is shown that in the case of exposure to non-Gaussian correlated noise, an increase in the correlation coefficient promotes the growth in the generalized signal/noise ratio, which, in turn, improves the accuracy of measurement of the signal parameters. These dependences confirm that the measurement error of the information parameters of the signal is affected not only the generalized signal/noise ratio, but also by accounting for the non-Gaussian nature of the additive noise, which leads to a significant improvement in the accuracy of measurement of these parameters.

This paper presents a comparative analysis of the errors of two alternative methods of estimating the central frequency of signals of laser Doppler systems, one of which is based on the maximum likelihood criterion, and the other on the so-called pulse-pair technique. Using computer simulation, the standard of the Doppler signal frequency from its true values are determined for both methods and graphs of these deviations are constructed as a measure of the accuracy gain of one of them. The results will enable developers of appropriate systems to choose an optimal algorithm of signal processing based on a compromise between the accuracy and speed of the systems as well as the labor intensity of calculations.

This paper presents algorithm for controlling an active power filter operating as a fast-response current source, whose practical application significantly improves the quality of the consumed electrical energy in the case of a non-linear load of arbitrary form with a simultaneous possibility of generating reactive power at the fundamental frequency.

A spectral method for determining the signal frequency and readings of a laser ranger with a frequency modulation of the reference channel is proposed based on signal pre-processing with a Gauss window and calculation of the center of mass of its spectral power density. Numerical modeling and experiments with a frequency modulation band of width 5-20 MHz band have shown that this method provides an order of magnitude better accuracy than the conventional methods of spectral analysis.

Specific features of half-plane image formation in a coherent optical spatially noninvariant (aberration-free) system of the 2F-2F telecentric type with a limited aperture of the projection lens (in the absence of the spatial frequency filter) are studied. The dependence of the light intensity behavior at a point corresponding to the half-plane boundary in the image on the object position is found in an analytical form on the basis of approximating the Fresnel functions by analytical functions. As the half-plane approaches the boundary of the field of vision of the system determined by the lens aperture diameter, the light intensity is demonstrated to deviate significantly from that in the case of the axial position of the half-plane, which may lead to noticeable measurement errors in inspecting the geometric parameters of objects by the projection method in transmitted light.

The role of the local field, anharmonicity, and degree of disorder in the formation of the boson peak has been studied. The Raman spectrum of low frequencies of a model crystal of polymethylmethacrylate with disorder elements was calculated using the method of atom-atom potentials taking into account the effect of local fields on the spectrum. The calculations were carried out for a crystal containing rigid molecules of an oligomer of isotactic polymethylmethacrylate and for a structure with flexible molecules.

Results of studying an original method of the modulated optical radiation spectrum analysis and testing a simple detector based on the Fabry-Perot interferometer are reported. The theoretical analysis of detector operation are compared with the results of a model experiment. A possibility of using this analyzer for measuring the characteristics of ultrahigh-frequency modulators of optical radiation operating at modulation frequencies from 10 to 100 GHz and higher is noted.

The aim of the present study is to determine the accumulation of heavy metals in the plankton collected from Kenon Lake. The results of study of the concentration of some heavy metals in the phytoplankton and zooplankton of technogenic-transformed Kenon Lake (Chita, Zabaikalsky Krai) are given. For algae the concentrations of Zn and Sr were high. For zooplankton the concentrations of Ni, Cu, Cd, Hg were less or corresponded to the values obtained for other water bodies. It is shown that the distribution of heavy metals in the water area was varied. The greatest concentration of metals is noted in the plankton from technogenic contaminated sites.