This paper deals with an optimal control problem for a linear discrete system subject to unknown bounded disturbances with the control goal being to steer the system with guarantees to a given target set while minimizing a given cost function. We define an optimal control strategy with one correction time instant, meaning taking into account information about one future state of the object, and propose an efficient numerical method for constructing it.

In this paper, we consider compact difference approximation of the fourth-order schemes for linear, semi-linear, and quasilinear Klein-Gordon equations. with respect to a small perturbation of initial conditions, right-hand side, and coefficients of the linear equations the strong stability of difference schemes is proved. The conducted numerical experiment shows how Runge rule is used to determine the orders of convergence of the difference scheme in the case of two independent variables.

Nanostructured TiZrSiN coatings were formed on various types of substrates in regimes with a lack and stoichiometric nitrogen concentration using reactive magnetron sputtering. Using the methods of scanning electron microscopy and X-ray diffraction, the structural-phase state of the initial coatings, their thickness, and morphology were investigated. Nanoindentation tests according to the methods of Oliver and Farr, as well as tribomechanical tests were performed to determine hardness, Young's modulus and friction coefficient of the TiZrSiN coatings. The TiZrSiN coatings were irradiated with hydrogen ions H⁺ with an energy of 500 keV in the fluence range from 1 • 10¹⁶ to 1 • 10¹⁷ ions/cm² on the AN 2500 accelerator complex. It was found that TiZrSiN nanostructured coatings deposited in nitrogen deficiency and stoichiometry regimes are radiation-resistant and potentially promising for use as protective on the bodies of small aircraft in orbit of the Earth and in open space.

Silica with ordered nanostructured morphology characteristic of mesoporous molecular sieves with cubic packing of cylindrical pores and a three-dimensional porous structure is obtained from natural quartz sand. It was shown by X-ray diffraction, scanning electron microscopy, and low-temperature nitrogen adsorption-desorption that the obtained silica material is thermally stable, amorphous, consists of submicron grains, has a high specific surface area of 1396 m²/g, a pore volume of 0.780 cm³/g and an average diameter of 2.2 nm with a narrow size distribution of mesopores.

The effect of sodium dodecyl sulfate and sodium oleate on the structural-rheological properties of a dispersed hydrogel based on polyacrylic acid was studied. It was shown that the viscosity of hydrogel compositions with surfactants is higher than the viscosity of the individual components and increases with increasing temperature from 20 to 40 °C. Compositions with sodium oleate are non-Newton liquids and exhibit thixotropic properties.

In silico analysis of “protein-ligand” complexes of human CYP7 enzymes with modified borondipyrrome-tene (BODIPY) and steroids, containing photo-activated crosslinking groups, wasperformed in order to identify structural peculiarities of their interaction. It was found that BODIPY molecules and DHEA derivative with diazirine group are able to bind tightly with human steroid-hydroxylases. Binding affinity is comparable with corresponding values for essential ligands of the enzymes. Binding mode of the modified steroid corresponds to the binding mode of essential CYP7 ligands, so formation of hydroxylated products is possible. It was found that presence of both diazirine and NBD groups in a molecule significantly increases affinity of the compound in case of CYP7A1 and, especially, CYP7B1. Amino acid residues, located in a close proximity with photo-activated groups were detected, that can form covalent adducts with them. The obtained results can shed light on the mechanism of interaction of the compounds with recombinant human CYP7 enzymes in vitro. The results can also be used for the identification of modified amino acids of the proteins that are formed under photoactivation of the compounds in vitro.

A metagenomic analysis of the endophytic microflora of Vaccinium corymbosum L. and Vaccinium myrtillus L. root systems was carried out. Two dominant species of micromycetes forming ericoid mycorrhiza were identified - Phialocephala fortinii C. J. K. Wang & H. E. Wilcox and Pezicula sp. Tul. & C. Tul. Pure cultures of mycorrhizal fungi were prepared, a comprehensive morphological and genetic assay of the strains was carried out. Based on the results of genetic-taxonomic analysis, the assumption of the polyphyletic origin of species belonging to Phialocephala and Pezicula is confirmed.

On the model of Achilles tendon injury in rats, the antinociceptive and regenerative effect of allogeneic transplantation of various doses of adipose-derived mesenchymal stem cells (ADMSCs) into the lesion area was studied. It was found that netiher of tested regimens of allogeneic transplantation of ADMSCs contributed to a decrease in the edema of the injured limb. Among the studied regimens, only a twofold administration of 0.25 • 10⁶ ADMSCs exhibited an antinociceptive effect. Administration of 0.50 • 10⁶ ADMSCs promoted the accelerated onset of neovascularization of tendon tissue, while enhancing inflammation and the formation of granulation tissue. Double transplantation of 0.25 • 10⁶ ADMSCs led to accelerated reorganization of collagen fibers, later neovascularization, however, there was an absence of inflammatory infiltrate, lipomatosis, and massive formation of granulation tissue in the lesion area.

The article substantiates the mechanisms and significance of the increased contents of blood plasma cholesterol and high density lipoproteins (HDLP) under acute exposure to stress factors leading to activation of metabolism. To a great extent, these changes reflect the adaptation rearrangements in cell membranes that are predominantly haracterized by a decreased content of free cholesterol in their composition due to its efflux to HDLP particles . The changes in HDLP fatty acid composition also contribute to this process resulting in a reduction of membrane microviscosity so that to intensify the intracellular metabolism and to enhance cellular functional activity.

In the development of neurotechnologies, the search for applications for invasive neuroelectronic devices is relevant. One of the promising areas can be the development of ways of influencing intercellular communication, that is, not by acting on pre-, post- and extrasynaptic receptors, but on the extracellular matrix surrounding neurons and glia. For the development of bioelectronic pharmaceuticals, it is important to search for stimulation parameters at which a controlled change in the structural and functional parameters of the nervous tissue is possible. We considered one of the actual mechanisms of the molecular pathogenesis of SARS-CoV-2 infection - the induction of glycosaminoglycan metabolism. It is assumed that, getting into the olfactory epithelium and the olfactory bulbs of the brain, the virus is able to reach the structures of the central nervous system. When modeling changes in the enzymatic activity of hyaluronidase (0.1; 1.0; 10.0 U/ml) for 5 minutes in one of the key structures of the limbic system - the hippocampus (3-4-week-old ratpups, n = 64), the conditions for the transformation of intercellular contacts were revealed and evoked electrical activity of populations of CA1 region. The recorded development of synaptic plasticity processes has an adaptive potential at hyaluronidase concentrations not exceeding 1.0 U/ml.
The in vitro method proposed in this work and a reasonable target for exposure - elements of the extracellular matrix, make it possible to simulate one of the mechanisms of the development of viral infection, optimize the process of preliminary screening of new medicinal substances that can minimize the risk of developing neuroinflammatory processes, and also substantiate the conditions for safe and/or therapeutic effects and electrical impulses on the elements of the nervous tissue.

For the first time, the authors determined lateral-temporal series of magmatic complexes of the Late Frasnian-Early Famennian Pripyat-Dnieper Magmatic Area according to the results of petrological and geochemical study of rocks of the Pripyat-Dnieper Magmatic Area (north-western part of the Pripyat-Dnieper-Donetsk Magmatic Province) in the southwest of the East European Platform using the principles of structural-material analysis and taking into account previous studies. The series consists of four complexes, formed during stages of magmatic activity, separated by time intervals: Zhlobin Complex (Rechitsa Time, the beginning of the Late Frasnian), Uvarovichi complex (Late Voronezh Time, the middle of the Late Frasnian), Pripyat Complex (Skolodin (Skolodin-Chernin?) Time, the end of the Late Frasnian) and Loev complex (Yelets (Yelets- Petrikov?) Time, Early Famennian). The rocks of the Zhlobin Complex belong to the alkaline-ultramafic (carbonatite-kimberlite-nephelinite) formation; Uvarovichi Complex - to the alkaline-mafic formation (basaltoids and phonolites); Pripyat Complex - to the alkaline-mafic-salic formation (trachyandesites); Loev Complex - to the alkaline-ultramafic (nepheline) formation.

We have established the relationships of quasicyclic components in changes of air temperature and precipitation in Belarus with large-scale modes of general variability of the atmosphere and ocean in the Atlantic-European region. When the summer air temperature changes in Belarus and in Eastern Europe, a quasi-60-year oscillation is identified, which coincides in phase with the Atlantic multi-decadal oscillation. It is shown that the time series of winter air temperature in Belarus contain a quasi-8-year component synchronized with a similar component of the North Atlantic Oscillation. Moreover, the periods of acceleration and deceleration of winter warming in Belarus coincide with the upward and downward quasi-30-year phases of the North Atlantic Oscillation, respectively. The latter are also consistent with fluctuations in moisture content in Belarus and Europe. Based on the established patterns, we have concluded that the rapid rise in winter temperatures, slowing down of summer warming and deterioration in water supply in the southern regions of Belarus observed in the last decade are part of a natural cycle lasting about 30 years, developing against the background of a long-term trend of anthropogenic global warming.

It is proposed that the design and production of individual elements of parts and products as a whole be carried out from the standpoint of operation and monitoring of its condition, both in traditional and additive manufacturing using the modular principle in engineering and technology. The way of unification of design decisions for the design of the product, equipment and technological and metrological equipment during its manufacture is discussed, to ensure, regardless of the type of production (single, serial, mass), the transition from standard and group to modular technologies. The basics of basing theory are updated taking into account the revision of the existing description from theoretical mechanics by means of the position of three coordinate points; to go to a new description from the theory of machines and mechanisms by depriving a subject of basing degrees of freedom (mobility) in a technical system (design, technological, measuring). It is shown how the design of the technology for manufacturing the product and measuring its characteristics is carried out in a system that includes equipment and equipment as mechanisms, the closing link of which are basing objects.

From an interdisciplinary point of view, on the basis of a systematic approach, the concept of transferring control to a driver in highly automated vehicles was first formulated, which allows one to determine the potential possibility of regaining control of a highly automated car based on its awareness of the situational situation along the route of movement and monitoring of the current functional state, including readiness for emergency actions, and individual features of the driver. The classification of cross-modal information flows in highly automated and autonomous cars is presented. The definition of cross-modal interaction in highly automated vehicles is given, and the goal of analyzing heterogeneous information flows in on-board vehicle systems is formulated, where automatic analysis of heterogeneous information flows gives a synergistic effect. Examples of relevant driver information are provided.

Traditional notions on the Belarusian-Lithuanian borderlands and the earlier Lithuania of the 10-13th c. are quite sketchy. In the public consciousness of a population of the historical Lithuania (“Lithuania in the narrow sense”) is significantly inferior in terms of its civilization development of neighboring Rus' and Poland. But already in the 13th century new impulses of state formation began from Lithuania at a time when the entire of the East Slavic region of Europe was in a deep crisis. The article analyzes the results of the latest archaeological and historical research of the four centers of the Belarusian-Lithuanian borderlands and the historical Lithuania in the 10-13th c.: Kreva, Halsany, Kemaй (Kernave), Vilnia (Vilnius). The significant presence of Slavic settlers influenced the existence of urban settlements with a clear administrative and sacred function among the Baltic pagan population of Lithuania in the 12th-14th centuries. On the example of Kreva and Kernave we can see the emergence of regional centers of Lithuania, the first of which is already in the 14th century it will be the domain of Alhierd (Olgierd) and Jagiello, and the second in the late 13th - early 14th centuries it will be the main residence of the Duke Trojdzien and perhaps of Vicien. Halsany become generic possession of the Halsanski princes and early modern town as and Kreva will develop in accordance with the process of urbanization (16-18th cc.). Kreva, Kernave and Vilnius can be described as the sacred center of the Balts. These observations allow us to consider the emergence of a new state, the Grand Duchy of Lithuania, as a result of the influence of the Slavic ethnos on the corresponding development of political and economic interests of Lithuanian elites, as well as ethno-cultural interaction.