For stochastic discrete external actions stationary in a broad sense, the problem of forming correlation matrices of state vectors and outputs of multichannel linear discrete systems is solved. Three methods for calculating the scalar correlation functions of the output of multichannel systems are presented. The first one allows to calculate the correlation function of an output, which depends on the scalar stochastic effect on a particular input; the second is used to calculate the correlation functions of each output of the system under the vector stochastic action; the third one forms the minorant and the majorant of the correlation func-tions of the system in the space of its outputs by means of singular expansion of the correlation matrix. It is shown that the problem of forming correlation matrices and functions can be solved based on using the fundamental matrices of the system under the condition that the matrix of dispersions of the state vector is known. The state space method allows calculation of the dispersions matrix of the system state vector using the discrete Lyapunov matrix equation in the case of an exogenous stochastic effect of the discrete "white noise" type. The developed procedures for formation of correlation matrices of vector variables of discrete multichannel systems are illustrated by examples.  

The classical treatment of motion of a point (the center of masses – translation motion) and the motion around a point (around the center of mass - the spinor motion) is supplemented by the simultaneous torsion of an equilateral hyperbola around two orthogonal axes, called the two-torsion thin field. The spaces of possible states of binary two-torsion fields in the scalar field generated by the thin field, make up three spatial hollow resonators described by pseudo-spheres inscribed one into the other in Lobachevsky geometry. The introduced concepts are illustrated by the example of a pair of the biospherethe noosphere of V. I. Vernadsky, interpreted by a kind of "matrioshka" of a dipole with alternating pseudospherical resonators and spherical protective domes.

Stochastic control systems are considered under pulsed input entrance influence generated Poisson streams of events; examples are systems such as devices using ionizing radiation, the systems of mass service etc. A given nonlinear functional of the Poisson flow intensity with time limitation is synthesized. The proposed method employs a probabilistic form of the mathematical description of Poisson process. Calculations of nonlinear functionals use an estimate of stream intensity as an argument, the estimate is based on calculation of random number of events for the fixed quantization interval. An analytical solution of the problem of setting calculating device with the account for Poisson distribution of input signal is presented. Calculation formulas are given that make it possible to find a concrete solution of the problem for several typical nonlinearities. The results are confirmed by modeling the process of formation of a nonlinear functional described by a third order polynomial using the applied mathematical programs package Scilab. It is anticipated that the proposed algorithm for calculating the tuning function of a computing device for reproducing a given analytically nonlinear functional can be used to solve practical problems in stochastic systems with Poisson input signal.

During operation, the transmission line supports (OHL towers) are mechanically deformed due to wind and ice congestion, this is the cause of numerous accidents. The existing methods of monitoring preemergency regimes have not been widely adopted, and therefore development of new principles for the operation of devices for monitoring force loads seems necessary. Indirect manifestations of the existing mechanical loads are deflections of the pillars of linear supports. This phenomenon is observed on "flexible" power transmission lines with an asymmetric arrangement of phases. The method of high-precision deflection measurement allows estimating the degree of glaciation of phase wires. A variant of the technical implementation of this diagnostic method with the use of a video camera is proposed. The procedure for calculating the deflection of the apex of the support under the influence of ice and wind is described. The perspectives of diagnostics of an OHL condition using information on support deflection is discussed.

The problem of analysis of the effect of temperature variations on parameters of optical systems is considered. Relations which determine position and size of the image under the influence of changes in temperature and pressure on the refractive index of the lens material are derived. It is shown that when the lens spherical surface rests on the base surface of the end frame or housing, the changes in the diameter of the contact circle of the contacting parts caused by the temperature fluctuations have a much greater effect than changes in the shape of the surface of the optical element. It is demonstrated that recalculation of the refractive index of the lens material in development of optical systems for instruments designed for the use in outer space is necessary.

A gated-viewing device intended for detection of optical devices conducting counter observation, by their reflection of probing radiation, is developed. Description of the instrument design and results of its experimental testing are presented. The range-gated viewing method is realized on an interline transfer CCD image sensor.

The psychophysiological state of a person when observing visual scenes depends, among other things, on the visual complexity of the images. Images of laser graphics are used to create visual content for the rooms of psychological relief. To increase the effectiveness of such rooms, it is necessary to be able to assess the visual complexity of the images of the laser graphics, as well as its range, in which the images will have a relaxing effect. For these purposes, a method for determining the degree of self-similarity of images based on a pyramid of oriented gradients is proposed.

Peculiarities of synthesis of broadband coatings for separation of achromatic light in the spectral range of 1,5—25 microns to be used in Fourier spectrophotometers of intermediate and far IR, are considered. Methods for the synthesis of multilayer coatings and the stability analysis of coatings are developed. The films are created from materials based on Ge and ZnS, the optical constants of Ge and ZnS films are determined in the spectral range from spectrophotometerс data with the use of correction of optical spectra for absorption. Two synthesized multilayer coatings with 4 and 5 layers are tested. The both coatings meet the requirements and are recommended for the use as coatings for separation of achromatic light for Fourier spectrophotometers of intermediate and far IR. Comparison of the coatings in the required spectral range demonstrate a higher resistance of the 4-layer coating to errors in the layers, has the smaller criterion of stability and feature quality, and is easy to manufacture. intermediate and far IR.

Results of development and testing of small-sized high-sensitive sensor of deformations on the base of piezo-optical transducer are presented. The sensor sensitivity to absolute deformation reaches values of the order of Δx=10–7 mm, which corresponds to a sensitivity to the relative deformation of the order of Δx/x ==10–9. Such a high sensitivity opens new possibilities in controlling various mechanisms, for example, lifts, both after their installation before starting up, and directly during the current operation. The sensor capabilities are demonstrated by the example of monitoring the movement parameters of the elevator carried out in accordance with the International Standard ISO 18738-1: 2012 (E): acceleration and braking, jerking, friction along the guides, vibration. The proposed sensor and monitoring methods with its use allow organizing feedback for engine control aimed at wear reduction, energy saving, prevention of overloads and emergency situations.

The influence of temperature on the error of incremental optoelectronic encoders of linear displacements based on raster structures, is considered. Basic principles of optoelectronic encoders of linear displacements are described. The performed theoretical analysis of additional error because of ambient temperature fluctuations demonstrates that the greatest influence is exerted by changes in the linear dimensions of the raster structures caused by linear expansion of the raster material. Results of experimental studies of the error of the LIR-14 encoder caused by changes in the ambient temperature are presented, and an estimate is given of the degree of influence of the error components due to this phenomenon.

The possibility of using waterjet cutting equipment for gear crowns manufacturing is considered. According to performed investigations, water-jet cutting with NC3015S equipment can replace only the roughing. Results of measurements of crowns working surfaces are presented and the accuracy of manufacturing is evaluated.