We consider a space of infinite signals composed of finite-alphabet letters. Each signal generates a sequence of empirical measures on the alphabet and a limit set corresponding to this sequence. The space of signals is partitioned into narrow basins consisting of signals with identical limit sets for the empirical measures, and the packing dimension is computed for each narrow basin.

The necessary conditions of the center at the singular point O (0, 0) for the kolmogorov system with fourth-degree homogeneous nonlinearities are found in the work of B. Ferenc, J. Dzheny, W. Liu, V. G. Romanovsky. For all these cases, with the exception of two, sufficiency is also proved. In the present article, sufficiency is proved for two cases of the center that were not proved in the above-mentioned work. In addition, the sufficiency of two other conditions of the center is proved in another way.

The phase-structural composition of a silica film grown on Si substrate implanted with Zn ions at room temperature with different fluences has been studied using transmission electron microscopy and electron diffraction. The small clusters (1–2 nm) and the large clusters (5–7 nm) have been formed in as-implanted silica films with the Zn concentration of 6–7 at % and 16–18 at %, respectively. Furnace annealing at 750 °С for two hours results both in the formation of the orthorhombic Zn₂SiO₄ phase (space group R-3) in the case of low fluence (5 · 10¹⁶ cm^–2) and in the formation of the cubic ZnO phase (space group F-43m) in the case of high fluence (1 · 10¹⁷ cm^–2). It has been shown that impurity loss during implantation and subsequent annealing increase with fluence of implanted ions. The fraction of Zn atoms in clusters has been estimated to be 15 % and 18 % for fluences (5 · 10¹⁶ cm^–2) and (1 · 10¹⁷ cm^–2), respectively. It has been shown that residual Zn impurities dissolved in silica matrix noticeably suppress the light-emitting properties of silica with embedded Zn₂SiO₄ and ZnO nanocrystals.

We considered the two-dimensional theoretical field model of interaction of scalar and fermion fields with the Higgs potential. Contribution of instanton effects to total fermion propagator is calculated. Mass correction to the propagator in the presence of an instanton field is determined. The obtained results can be interpreted as confinement.

Microspheres comparable with yeast cells in size were obtained by the glutaraldehyde crosslinking of polyvinyl alcohol (PVA), whose 25 g/l water solution containing magnetite particles was dispersed in the isooctane/Span 85/Tween 85 medium. yeast cell walls were partially hydrolysed by sonication in formic acid near the boiling point. The microspheres were made targets for phagocytosis by the addition of yeast lysate to the crosslinkable PVA solution and a subsequent treatment of the freshly crosslinked microspheres with diluted yeast lysate. The microspheres were also made fluorescent when the emulsification medium saturated with fluorescent 2-aminopyrimidine derivatives was used. A protocol for phagocytosis assay using the thus modified microspheres was developed.

The swelling kinetics of cross-linked polyacrylamide was studied depending on the composition of the external solution. It was shown that the polymer gel swelling during the transition from water to a potassium or sodium chloride solution and vice versa sharply decreases, then gradually increases. The swelling of gel in a solution of sodium chloride is higher than that of potassium chloride. In the equilibrium swollen gel, the concentration of salts in the gel phase is higher than in the external solution and increases with the transition from potassium chloride to sodium chloride.

Polyampholytes, containing aminodiacetic functional groups, on the base of polyacrylonitrile fiber Nitron C were obtained by the amination reaction of nitrile groups with polyamines (number of repeating units from 1 to 5) and subsequent alkylation with monochloroacetic acid. The experimental results of potentiometric titration and sorption of supporting electrolyte (kCl) ions by synthesized ion exchangers were obtained, which made it possible to determine the acidity parameters of functional groups: the presence of four types of cation exchange and two types of anion exchange groups was detected in polyampholytes, the sequence of their neutralization in the titration process was established.

To find small-molecule compounds that can simulate the structural and functional properties of the high affinity X77 ligand of the main protease of SARS-CoV-2 - etiologic agent of COVID-19, the virtual screening of 9 molecular libraries of the Pharmit web server containing over 213.5 million chemical structures was performed. Using molecular modeling, the neutralizing activity of the identified molecules was evaluated, resulting in 5 leader compounds promising for synthesis and testing for antiviral activity. The data obtained indicate that these compounds may be used as basic structures for the development of effective drugs to treat the novel coronavirus infection.

The effect of exogenous 5-aminolevulinic acid (ALA) on the activity of dihydroflavonol-4-reductase (DFR), the expression of the dfr gene and the hy5 gene of the transcription factor Hy5 and the light effect of different intensities in combination with the ALA action on the accumulation of anthocyanins in cotyledonous leaves of winter rape (Brassica napus L.) were studied. It was shown that the stimulation of the accumulation of anthocyanins under the exogenous ALA action at the molecular level was provided by increasing the expression level of the dfr and hy5 genes and the activity of the DFR enzyme. Increasing the light intensity from 40.5 to 66.2 μmol photons/m²·s enhanced the ability of plants to accumulate anthocyanins on average by 35 %. The ALA action at concentrations of 50, 100, 150 and 200 mg/L led to an additional increase in the accumulation of anthocyanins at the two used levels of illumination, and in a dose-dependent manner. The stimulating effect of ALA under high light intensity was much higher than in the case of lower illumination. Thus, the stimulation of the anthocyanin accumulation under illumination of 40.5 μmol photons/m²·s was 106 % when using 50 mg/L ALA, 165 % – when using 100 mg/L ALA, 222 % – in the case of 150 mg/L ALA and 350 % – under the action of 200 mg/L ALA compared with light control without of ALA treatment. At an illumination of 66.2 μmol photons/m²·s, these indicators were 164, 262, 359 and 583 % respectively. Thus, it was demonstrated that the stimulation of the accumulation of anthocyanins under the action of ALA in winter rape plants was due to its positive effect on the transcription of the dfr and hy5 genes at the molecular level.

Antimicrobial peptide MsrA1 is a synthetic hybrid molecule based on cecropin A from giant silk moth larvae and on melittin from melliferous bee venom. Transgenic potato plants of the Belarusian variety Odyssey with the constitutive expressiоn of msrA1 gene are shown to exhibit increased resistance to fungal pathogens Phytophthora infestans and Alternaria solani. Peroxidase genes expression studies using cDNA-PCR and DNA sequencing revealed the activation of the POX peroxidase gene in transgenic plants in the absence of pathogens. This may be indirect evidence of the increased formation of reactive oxygen species, which may explain special resistance to fungal pathogens. The data obtained also confirm a possible role of intracellular antimicrobial peptide in making the plants more resistant to oxidative stress by the way of activation of the host plant defense system.

Modern medicine faces the problem of the growth of cardiovascular pathology. Given the high medical and social significance of the problem of treating patients with coronary heart disease and acute myocardial infarction, the search for new effective methods to prevent or weaken ischemic myocardial damage and mechanisms for their implementation is an urgent task of modern experimental and clinical medicine. The aim of the study was to determine the significance of hyperlactatemia in the realization of the infarct-limiting effect of remote ischemic postconditioning (RIPostC) in rat myocardial ischemia-reperfusion in the experiment. The study revealed that after 15-minute RIPostC, which was performed 10 minutes after 30-minute acute myocardial ischemia followed by 120-minute reperfusion, the plasma lactate level in rats increased 1.87 times (87.7 %, p < 0.05) compared with intact animals. It was established that the introduction of L-lactate into the left common jugular vein at a dose of 10 μg/kg, which was carried out 25 minutes after the onset of reperfusion under the conditions of myocardial ischemia (30 minutes) and next reperfusion (120 minutes) and RIPostC (10 minutes after the onset of reperfusion), which was reproduced by ischemia of these limbs, have a heart attack-limiting effect. The increase of the level of blood lactate (hyperlactatemia) after RIPostC in myocardial ischemia-reperfusion is of significance in the implementation of its infarct-limiting effect.

Using the electromyography data, the functional state of the maxillofacial region muscles of dental patients with bruxism signs and obstructive sleep apnea syndrome was defined. After dental treatment, 122 patients aged 25–47 with bruxism signs and obstructive sleep apnea syndrome and without it were examined. The disease duration was about 5 years. All patients were divided into two groups. The first group consisted of 41 patients, whose bruxism signs were not combined with the obstructive sleep apnea syndrome. The second group included 81 patients with the bruxism signs and the obstructive sleep apnea syndrome. When performing surface electromyography of the maxillofacial region muscles (temporal, chewing, medial digastric) of the both-group patients at rest without load the differences in the bioelectric activity indicators were not observed. The indicator difference between the comparison groups appeared when conducting functional load tests that were expressed through the amplitude difference during tooth compression under the functional activity of the temporal and digastric muscles. Such data illustrate that the patients of the first group have bigger functional compensation than the patients of the second group. There also occurs cross compensation of temporal and digastric muscles. It is expressed symmetrically.

Rock pressure manifestations in the development workings and the bottomhole region of the lower longwalls with the slice pillarless extraction of the Third potash layer of the Starobin potash salt deposit were studied. The stability of the development workings and the bottomhole space of the longwalls and the nature of interaction of the bottomhole lining with the adjoining rocks were studied. The intensity of manifestations of rock pressure in the longwalls and the nature of roof subsidence of the bottomhole region and its fall behind the face support were assessed. The nature of the loading speed distribution of the bottomhole lining for the treatment cycle was clarified. The rate of change of the loading before the heading and during this process and the loading rate of the bottomhole lining are taken as the main load support indicators for the treatment cycle. The cyclical nature of the change in the magnitude of these indicators in the interval of 10–12 treatment cycles is revealed. Their dependence on elastic stresses and creep of roof rocks after the formation of a new face is shown. The presence of the dynamic component of the load of the bottomhole lining due to the factor of the speed of the bottomhole movement was established. The influence of the deformation of rocks in the troughs of displacement on the bottomhole lining has been established. At the same time, it is shown that over a time interval of more than 2 years, the intensity of deformation of the rocks is significantly reduced. The possibility is shown how to determine the mean spacing of the secondary rock subsidence of the main roof and to identify anomalies associated with the boundaries of tectonic dislocations, faults and subsidence troughs by analyzing the dynamics of the accumulated deviations from the average of load support indicators. Recommendations have been developed on rational and safe parameters for maintaining the bottomhole region and the development workings of the lower longwalls with the slice pillarless extraction of the Third potash layer.

The effect of 1.5 wt. % Cloisite 30B organoclay (Cl30B) containing the hydroxyethyl fragments in the surfactant structure on polyamide 6 (PA 6) / functionalized polyolefin (fPO) – a mixture of linear low-density polyethylene and ethylene copolymer with higher olefin – on the structure, mechanical and rheological properties of the materials was studied. The fPO concentration in the blends was varied from 15 to 50 wt. %. The fPO production and the blend compounding were carried out in melt using a twin-screw mixing reactor. The organoclay in the composition of the blends was introduced in two ways: simultaneously with all polymer components (one-step process) and with its preliminary localization in the PA 6 phase (two-step process). It was established that the complex of static and dynamic mechanical and also rheological characteristics of materials and the crystallisability of the components in the blends depend on the way of the Cl30B distribution in the PA6 and fPO phases, as well as on the phase structure of the blends. The organoclay localization mainly in the polyamide phase leads to a 1.3–3.0 time increase of the impact strength of the blends in which fPO forms a dispersed phase and increases their deformation capacity under tension up to 1.2 times regardless of the phase structure. The organoclay blends localized in the PA 6 phase have increased the values of melt flowability and mechanical loss angle tangent at the PA 6 a-relaxation transition and dynamic shear modulus in the temperature range from –100 to 150 °С compared to the materials produced by one-stage technology, which is explained by the blocking of organoclay amide and other polar groups in the structure of PA6 macromolecules in the polyamide phase and by a decrease as a result of this intensity of interfacial interactions with fPO.

Internationalization is one of the most important trends in modern higher education which requires philosophical reflection. The emergence of internationalization is associated with replacing the international influence by international integration. Integration is realized through the convergence of the quality of higher education, which provides the benefits of international participation for different stakeholders operating in various modes of higher education. Accelerating integration processes internationalization is determined by the development of integration processes: there are leaders and outsiders of internationalization. The future of internationalization largely depends on the adaptation of higher education to global development disbalances.

The results of the development of composite polymer materials for processing root systems of seedlings in order to increase the survival rate of forest crops are presented. It has been established that the type of target additives and the concentration of water-soluble polymers in the compositions for processing can significantly affect the physicochemical properties of the composites and moisture loss by root systems of seedlings. The optimal compositions of composite polymer materials for protecting the root systems of a number of conifers from drying out are given.