In the class of discrete control actions a linear control problem of a dynamic object under conditions of constantly acting disturbances is considered. A method is suggested to construct guaranteeing disclosable and closable loops in the real-time mode. 

For special linear and symplectic groups of not too small ranks with respect to p over a field of an odd characteristic p and p-restricted irreducible representations of а general form, lower estimates for the number of Jordan blocks of size >ps in the images of unipotent elements of order ps+1 > p in such representations are obtained. These estimates depend upon the group rank, the characteristic and the value of the highest weight of the representation on the maximal root of the group. These results are aimed at searching “rare” classes of unipotent elements that can be useful for solving recognition problems for representations and linear groups. 

The mixed problem for the one-dimensional Klein–Gordon–Fock equation with nonlocal conditions in a halfstrip is considered. Solving this problem reduces to solving the systems of the second-type Volterra equations. The theorems of existence and uniqueness of a solution in the class of twice continuously differentiable functions were proved for these equations, when initial functions are smooth enough. It is proved that fulfillment of the matching conditions for given functions is necessary and sufficient for the existence of a unique smooth solution when initial functions are smooth enough. The method of characteristics is used for the problem analysis. This method reduces to splitting the original area of the definition into subdomains. The solution of the subproblem can be constructed with in each subdomain, the help of the initial and nonlocal conditions. The obtained solutions are then glued at common points, and these gluing conditions are the matching conditions.

This approach can be used in constructing both an analytical solution, when the solution of the systems of integral equations can be found explicitly, and an approximate solution. Moreover, approximate solutions can be constructed numerically and analytically. When the numerical solution is constructed, matching conditions are essential and need to be considered while developing numerical methods. 

This article deals with the problem of optimal control of a linear dynamical object subject to unknown bounded disturbances with the control requiring to robustly steer an object to a given target set while minimizing a total impulse of a multidimensional sampled-data input. We define an optimal control strategy, which takes into account one future state of an object, and propose an efficient numerical method to construct it. The optimal strategy performance is compared to an optimal open-loop worst-case input, and some estimates for cost improvement are provided. 

The surface morphology and optical properties of Si coatings formed by magnetron sputtering were studied using atomic force microscopy, scanning electron microscopy, and spectrophotometry methods. The possibility to influence the surface morphology of coating (filamentous structures and/or round holes) and the location of maxima and minima in reflectance and transmittance via a controllable variation of magnetron sputtering regimes (substrate temperature and bias potential) is shown. 

Simulation of tunneling of electrons excited by the sunlight to TiO2 surface states is performed. The surface states appear due to absorption of impurities and organic compounds on the TiO2 nanocomposite in the gas environment. Interference of transmitted and reflected waves, overbarrier and reflected waves under the conditions of the complex potential relief is taken into account. 

It was obtained that liposomal streptokinase (SK) with a hydrodynamic diameter of ~70 nm and a zeta-potential of –6.2 mV contains 14.1 % wt of drug. The complex formulations based on liposomal SK include “associated” and “free” SK in the ratios of 20/80, 40/60 and 50/50. The in vivo experiments on rats showed an increase in the elimination half-time from 1.8 to 31.9 min and in the time to reach the maximum concentration of streptokinase from 15 to 45 min. The decrease in the elimination rate constant by a factor of 18 compared with SK was also found. The optimal ratio of “associated” and “free” SK in the complex formulation was 40 and 60 % respectively. It was used to obtain liposomal fibrin-specific form of thrombolytic with similar physico-chemical and pharmacokinetic parameters. 

The genetic variability of sad and fad desaturase genes of linseed was analyzed according to sequencing data. The impact assessment of various allelic variants of these genes on the fatty acid composition of linseed oil was given. The obtained data for the structure and polymorphism of desaturase genes can be used in developing marker systems for markerassisted selection of linseed and in creating varieties with an improved fatty acid composition of oil. 

Infection of tomato plants with Fusarium oxysporum causes activation of lipid peroxidation processes (LPO) and significant changes in the structural and functional state of photosynthetic membranes, which is reflected in a decrease in Chl a, Chl a / Chl b ratio, disturbances in the absorption and utilization of light energy in PS II of photosynthesis. Pretreatment of plants with β-1,3-glucan contributes to the LPO stabilization and normalizes the course of photochemical processes in chloroplasts of infected leaves, which indicates the protective activity of the drug. 

In the present article, we studied a correlation between an increased resistance of winter wheat seedlings of different varieties to powdery mildew and high levels of constitutive expression of genes encoding one of two pathogenesisrelated proteins: thaumatin-like protein (Tlp) or oxalate oxidase (OxOxid). Highly resistant varieties have shown either high Tlp expression and low OxOxid expression or high OxOxid expression and low Tlp expression. We propose to use a combination of both Tlp and OxOxid gene expression levels as a marker for resistance of winter wheat breeding material to powdery mildew. 

Geodocumentating and selection estimation of 23 taxa of the lilac genus collection (Syringa L.) were conducted in the Central Botanical Gardens of NAS of Belarus (hereinafter – CBG). The obtained data were used to document the taxa of the named collection on the basis of the geographic information system ArcGIS. This allowed us to determine the characteristics of the location of the investigated lilac species and serves as the basis for carrying out a large number of studies, combining the data of the researchers of different generations. The following parameters were defined: coordinates of the location within CBG, percentage proportion syringin, bark proportion in relation to the timber, dry matter content in the crust. Integrated productivity was calculated in the studied taxa. On this basis, each taxon is added to particular selection categories: category 1 – shrubs with high productivity (1.80 and more kg/t of raw material); category 2 – shrubs with average productivity (0.80– 1.80 kg/t of raw material); category 3 – shrubs with low productivity (0.80 and below kg/t of raw materials). 

The experiments on rats and rabbits using modern physiological, biochemical methods of research and pharmacological approach have shown that arginine of blood plasma and liquor participates in central neurochemical mechanisms of thermoregulation during endotoxin fever, changing the chemoreactive properties of cerebral neurons and the impulsive activity of heat-sensitive neurons brain thermoregulatory structures. It has been established that the administration of L-arginine hydrochloride into the brain ventricles at a dose of 100 μg per animal or into the blood stream at a dose of 20 mg/ kg causes the pronounced antipyretic effect. In 30 minutes after the intravenous administration of carbon-labeled arginine hydrochloride (25 μCi/kg) at the height of endotoxin fever (60 minutes after the injection of endotoxine E. coli), the radioac tivity level in the blood plasma decreases and significantly increases in cerebrospinal fluid and hypothalamus tissue in rabbits. It has been revealed that although the content and speed of norepinephrine turnover in the hypothalamus after the introduction of L-arginine hydrochloride (100 μg) into the ventricles of the rats does not change in comparison with control animals, however, the chemoreactive properties of the thermoregulatory structures of the brain change, which manifests itself in a change in the expression and duration of thermoregulatory effects of the central action of norepinephrine and acetylcholine. It has been found that L-arginine hydrochloride (100 μg) after being introduced into the brain ventricles stimulates the growth of the impulse activity of heat-sensitive neurons of the medial preoptic region of the anterior hypothalamus in rabbits, caused by an increase in the brain temperature when the animal body is overheated. Apparently, the basis of one of the mechanisms of the antipyretic action of arginine under endotoxin fever conditions is the change in adreno- and cholinoreactive properties of cerebral neurons and, in particular, the increase in the sensitivity of brain adrenoretseptors to noradrenaline. 

The aim of the study was to compare the structural and functional parameters of the myocardium in different genotypes of polymorphic markers BsmI (B/b) (rs1544410) and FokI (F/f) (rs2228570) of the vitamin D receptor gene (VDR) in individuals with cardiovascular diseases (CVD). Materials and Methods. We examined 198 patients with CVD. BsmI and FokI of the VDR gene were determined by the polymerase chain reaction. The blood levels of parathyroid hormone, 25(OH)D total, endothelin-1, plasma renin activity were revealed by the method of enzyme immunoassay. The calcium and phosphorus level in the blood was defined by the colorimetric method. Echocardiography was performed by GE Logic P5 Premium (Korea) with a phased sector sensor with a frequency of 2–4 MHz in the modes M-, B-, PW, CW. Results. All participants were divided into groups according to genotypes of FokI and BsmI of the VDR gene. For each polymorphism, the groups were comparable in age, CVD, blood pressure, heart rate, body mass index and levels of the estimated biomarkers. Significant differences (p < 0.05) in the sizes of the aorta and the left atrium (LA), in the sizes and volumes of the left ventricle (LV) and its walls, the diameter of the LV outlet tract and the ejection fraction between the groups with the genotypes of FF and ff were established. In addition, differences (p < 0.05) were found in the aorta size, LA and interventricular septum between the groups with the genotypes of ff and Ff. According to the genotypes of BsmI of the VDR gene, the groups did not differ significantly in the estimated structural and functional parameters of the myocardium and aorta. Hypertrophy of the LV is diagnosed in 78.6 % of participants. Conclusions. Polymorphism of FokI, but not of BsmI of the VDR gene is associated with structural and functional parameters of the myocardium and aorta in individuals with CVD in the Grodno region of Belarus. With the greatest frequency, LV hypertrophy occurs with Ff (37.9 %) and Bb (33.8 %).

The development of sepsis in newborns with congenital malformations of the gastrointestinal tract in the postoperative period depends on the colonization of various biotopes. The starting etiological factors are: the presence of opportunistic and pathogenic microflora in certain biotopes, as well as a quantitative content of microorganisms (the “degree of microbial load”). It has been established that colonization of biotopes with a quantitative assessment of CFU of 104 /g (colony forming unit) and more is one of the factors of the sepsis development in newborns with this pathology. 

The Stefan problem is of extreme importance in investigating many physical processes and technologies. Solving the Stefan problem reduces to calculating a temperature (concentration) profile when an interphase boundary is to be determined. High-accuracy polynomial solutions of the Stefan problem for a semi-infinite medium with Dirichlet/Neumann boundary conditions and general conditions are presented. An initial medium temperature is assumed to be equal to a phase change temperature. With the use of the integral method of boundary characteristics, based on multiple integration of the heat conduction equation, sequences of identical equalities with different boundary conditions are obtained and, as a result, polynomial solutions are constructed. The high efficiency of the approach proposed is illustrated with various examples. The solutions based on the 2nd and 3rd degree polynomials are more exact in comparison to the known solutions. The accuracy of calculating the position of the interphase boundary by means of 4th and 5th degree polynomials is several orders of magnitude higher than that of numerical methods. The solutions obtained can be considered as conditionally exact because of negligibly small errors in determining the interphase boundary and the temperature profile.

Heat transfer in a laminar flow in a gap between rotating and motionless coaxial cylinders has been studied experimentally. The experiment showed that supply of external heat and heating-up of the setup due to dissipation do not practically influence the distribution of excess pressure in a slot gap. The result obtained points to a self-similar mode of temperature variation in a moving air medium. In the course of the experiments, angular points, on passing which the anomalous variation of temperature occurs, were found on the graphs of temperature dependence on time with a variable rotation speed of the inner cylinder. The lambda-type anomalies originate as the rotation speed of the inner cylinder increases. On the contrary, as the speed decreases, a V-shaped turn takes place. The presence of angular points, where the first time derivative of temperature undergoes the first-kind discontinuity, indicates the existence of jumpwise transitions in the laws that govern heat transfer when the rotation speed of the inner cylinder passes through a critical value. According to measurements, as the rotation speed increases or decreases the transition takes place approximately in the range of the same angular speeds 545– 650 s–1. The Reynolds and Taylor numbers that correspond to the indicated rotation speeds are Re = 245–293 and Ta = 22–26, which is much lower than the critical Reynolds number Recr = 3960 for the laminar-to-turbulent flow transition and the critical Taylor number Tacr = 41.3 for the stability loss with origination of Taylor vortices. The appearance of discontinuities is explained by the change in the kinetics of intermolecular interactions caused by a transition from a molecular to phonon mechanism of transfer.