An overview of the current state of the design and construction processes of the three ground-based extremely large telescopes – the European Extremely Large Telescope (ELT), the Thirty Meter Telescope (TMT), and the Giant Magellan Telescope (GMT) – is presented. Operation of the telescopes is impossible without adaptive optics systems. Modern technologies for the use of adaptive optical systems to be included in the optoelectronic complexes of extremely large telescopes, are considered.

An algorithm for processing spatial objects with the same topological structure on satellite images is considered. The essence of the method is the identification of structures that are stable under topological deformations and distortions. The only thing that does not change when zooming and rotating the object is its shape. The topology does not account for an object coordinates but considers its structure. Experiments with images of several areas carried out using developed algorithm and software product showed that spatial features in the images are recognized with an accuracy of 93 %. According to images comparison performed with the use of three-dimensional barcodes, the topology of objects and their barcodes do not change over time and at different scales. The algorithm for matching three-dimensional barcodes avoids manual processing of images, which reduces the time for searching and matching objects from several hours to several minutes.

The order of formation of preferred pairs of Gordon–Mills–Welch sequences (GMWS) is determined based on the analysis of periodic cross-correlation functions (PCCF) of M-sequences (MS) and GMWS with the period N=511. MS and GMWS with the period N=511 are constructed in the finite fields GF(2S) at S = 9. Application of preferred pairs of GMWS in digital information transmission systems (DITS) is determined by their higher structural secrecy as compared to MS, characterized by an equivalent linear complexity (ELC), numerically equal to the degree of verification polynomials used as the base for sequence data formation. The preferred pairs of GMWS are shown to be formed on the basis of preferred pairs of MS, and each MS acts as a basic sequence in the synthesis of the corresponding GMWS. It is supposed that the results on formation of preferred pairs of GMWS with the period of N=511 can be used in noise protected digital information transmission systems with increased requirements for confidentiality and secrecy, as well as in the synthesis of derived systems of pseudorandom sequences that can be formed in extended finite fields.

The problem of the circuit formalization of decentralized control of complex multidimensional objects using various methods is investigated. A multidimensional object is considered as a dynamic system with discrete time. The spaces of the object states, control actions, goals, observed parameters, and analytical estimates are formalized. Analytical estimates are calculated using the integral indicators. Evaluation of the integral indicators with selectable depth analysis of time series for each of sixteen studied control modes is carried out. For these modes, the optimal field is formed when selecting the optimal control. The formalization of a complex multidimensional object allows to turn from general representation of the system to its subsystems. The problems that can be solved with the proposed formalization of the object and corresponding methods are considered: the Kalman filter, neural network forecast, recurrent equation, and balances.

A software module is proposed for estimating the drying process of the polymer coating of a galvanized strip, characterized by a comprehensive assessment of the basic parameters of the process: temperature condition, solvent vapor concentration, color deviation in the polymer coating. To evaluate these parameters, physical models are constructed accounting for the features of the technological equipment used — a model of heat exchange processes occurring inside the drying furnace, a model of solvent evaporation from the strip surface during the drying of the polymer coating; a model for predicting the color deviation of the polymer coating using machine learning tools, including the "random forest" algorithm. The evaluation of each of the cardinal parameters is represented by a separate block, the totality of which forms the evaluation module. The software implementation of the module is performed, and experimental results are presented.

A method of acousto-optic visualization of spatially inhomogeneous acoustic fields formed by acoustic object is considered. This method is based on Bragg diffraction in a system with a double Fourier transform. Among the advantages of the device that implements this method, there is a high resolution. It is shown analytically that, in contrast to the well-known visualization technique by A. Korpel, the images of acoustic micro-objects obtained with using the proposed a device, are free from astigmatism. As a result of theoretical analysis of the device operation mechanism, equations for calculating the geometric parameters of optical image of acoustic micro-object are derived.

The relevance of the method of reflection spectroscopy for the study of modern dental restoration materials is demonstrated. An automated spectral device "Fluorat-02-panorama" with a developed optical attachment for measuring the reflection spectra of the studied samples is presented. Spectral dependences of the reflection coefficient of composite materials "Estelite Asteria" in “enamel” and “body” shades were obtained, and reflection spectra for samples of both genuine and fake materials were measured. It is shown that for a fake material, the spectral reflection curves are deformed, the maximum values of the reflection coefficient are shifted to the long-wave region of the spectrum, and there is also a significant decrease in the value of the reflection coefficient in the wavelength range of 380...780 nm.

A model of the "Solar Sail" design is presented, in which Cu-Al-Ni single crystals with shape memory properties are used to create power elements of drives that ensure the opening of the sail. The design of the sail mast is considered, and the physical and mechanical characteristics of the drive are presented.