In the article a strengthened version of the ’Fundamental Theorem of Asset Pricing’ for a one-period market model is proven. The principal role in this result is played by total and nonanihilating cones.

Titanium aluminium nitride (TiAlN) is a promising material for space application as protective, radiation-resistance coatings. During the operation in space such coatings are exposed to the flux of energetic particles. We present the results of the proton irradiation effect on the mechanical, structural, and optical properties of the TiAlN coating deposited by reactive magnetron sputtering. The irradiation with fluence of 5 · 1016 ion/cm² results in an increase of Young՚s modulus and nanohardness above the superhard level, while a further fluence increase (up to 2 · 1017 ion/cm² ) results in a decrease of these parameters. Surface smoothing after proton irradiation has been demonstrated by profilometry. It is shown that irradiation with protons results in an increase of specular reflectance. Diffuse reflectance increases to a lesser extent and only after irradiation with relatively low proton fluences ((2–5)· 1016 ion/cm² ).

The effect of plasmonic films containing gold nanoparticles of different shape (nanospheres and nanorods) on the photostability of InP/ZnSe/ZnSeS/ZnS and CdSe/ZnCdS/ZnS quantum dots with core/shell structure has been determined. Gold nanospheres increase the photostability of InP/ZnSe/ZnSeS/ZnS quantum dots when excited by blue LED radiation when reducing the average lifetime of the excited state of quantum dots and, accordingly, when reducing the probability of Auger processes. An increase in the average lifetime of the excited state of CdSe/ZnCdS/ZnS quantum dots in complexes with gold nanorods leads to a decrease in the photostability upon excitation at 449 and 532 nm.

A virtual library of biologically active molecules has been formed and in silico screening has been carried out for identification of small-molecule chemical compounds – potential SARS-CoV-2 inhibitors able to bind to the HR1 trimer of the protein S and to block the formation of a six-helix bundle 6-HB, which is critical for the virus-cell fusion and viral infectivity. Molecular modeling methods were used to evaluate the binding affinity of the identified compounds to the HR1 trimer of the protein S. As a result, 12 molecules exhibiting the high binding affinity to this functionally important region of the virus were found. The data obtained indicate the promise of using these compounds in the development of new antiviral drugs presenting SARS-CoV-2 fusion inhibitors that can block the virus entry into the host cell.

The synthesis of Zr-Ca-Mg and Ti-Ca-Mg phosphates of different composition was carried out and their sorption properties to Sr(II) ions were studied. The effect of pH of aqueous solutions, as well as of background electrolytes NaCl, CaCl2 , the seawater solution on the sorption-selective properties of phosphate sorbents was studied. The sorption isotherms and kinetic regularities of the Sr(II) ion removal were studied, the mathematical modeling of the experimental data using various models was carried out. It was found that Ti-containing sorbents had the greatest selectivity to Sr(II) ions. The maximum sorption capacity for the Ti-2 sample reached 196.5 mg/g (2.2 mmol/g). Samples of Zr-Ca-Mg and Ti-Ca-Mg phosphates had a high sorption capacity in the 0.1 M NaCl solution and in seawater. The sorption kinetics for all sorbents with a high degree of confidence (R² ≥ 0.99) was described by a pseudo-second-order equation, due to the chemical interaction during the Sr(II) ions sorption. The study of the phase composition of sorption products indicated the ion exchange and chemisorption mechanism of the Sr(II) ions sorption.

Cytochrome P450 3A4 (3A4) is highly expressed in the human liver cells and plays a decisive role in the metabolism of xenobiotics, including more than 50 % of medical products. The activity of this enzyme can be regulated at the expression level of genes, as well as at the conformation level of the structure of the protein itself, due to changes in the molecular environment, including due to the interaction with high-molecular effectors. The understanding of the structure changes and the 3A4 dynamics in response to the environmental changes is necessary to predict the changes in the level of its activity that to a considerable extent regulates the body’s homeostasis. To perform in vitro experiments on the structure, dynamics, and protein-ligand/protein interactions of the enzymes by the modern spectral methods, the approach is used, in which the target protein is selectively added with cysteine residues in the given polypeptide chain loci by the protein engineering methods for subsequent labeling with specialized molecular labels. To do this, the human mutant form of membrane-bound (full length) recombinant cytochrome P450 3A4 C58A/C64M/C98A/C239T/C377A/C468S/S291C was obtained. According to the circular dichroism spectroscopy data we established that the introduced mutations do not cause significant changes in the secondary structure of the obtained form 3A4, which shows the preservation of the folding of the peptide chain. The spectral photometric measurements were made to comparatively analyze the changes in the affinity to the ligands of the active center. Moreover, we showed that the testosterone hydroxylase activity in the in vitro reconstructed system for a given mutation form of 3A4 increases many times with respect to the wild form of the enzyme.

The respiratory distress syndrome (RDS) and the bronchopulmonary dysplasia (BPD) are the lung diseases that occur mainly in preterm infants. Polymorphic variants of surfactant protein genes are considered as candidates contributing to the pathogenesis of RDS and BPD. The association of 5 polymorphic variants of the SFTPB gene (rs2077079, rs1130866, D2S388, D2S2232, VNTR 4 introns) and 3 polymorphic substitutions of the SFTPC gene (rs4715, rs1124, rs2070687) in newborns with the development risk and severity of RDS and BPD was studied. 555 newborns were included in the study, among which 313 premature babies with a gestational age of 28–36 weeks. Genotyping was performed by the Sanger sequencing, the microsatellite analysis, and the real-time PCR. All premature newborns were characterized by the presence of RDS of different severity and BPD was detected in 36 newborns. The microsatellite marker D2S388 of the SFTPB gene contributes to the etiology of RDS and may serve as a gene for its predisposition. Allele 256 bp increases the risk of developing severe RDS. At the same time, the –18AA rs2077079 genotype of the SFTPB gene is associated with a reduced risk of developing severe RDS. The polymorphic variant c.413C>A p. T138N (rs4715) of the SFTPC gene is associated with BPD: the 413CC genotype increases, and the 413CA genotype reduces the risk of developing the disease.

The relationship between the birthrate and biomass of different-group phytoplankton was analyzed during the summer for Daphnia cucullata and Bosmina logirostris in the mesotrophic Drysviaty Lake. The high cross-correlation coefficients were obtained for the birthrate and phytoplankton with a size from 5 to 20 µm. There is no correlation between the birthrate and seston with a size of ≤50 µm. Our results suggest that the total biomass of phytoplankton and seston do not reflect the food availability of cladocerans.

The dependence of the protective effect of brassinosteroids (BS) in a wide range of concentrations on the growth of the root system of fiber flax (Linum usitatissimum L.) and spring barley (Hordeum vulgare L.) seedlings under salt stress was studied. A narrow range of BS concentrations was revealed, in which they cause a weakening of the inhibitory effect of salinity on the root system of seedlings. An almost complete coincidence of the BS concentration ranges was noted, in which the maximum stress-protective effect of phytohormones was observed for the both crops (6,9 ⋅ 10–7–5,9 ⋅ 10–8 М for fiber flax and 2,8 ⋅ 10–7–2,4 ⋅ 10–8 М for spring barley). In the experiment with winter wheat (Triticum aestivum L.), which lasted 19 days, already on the 6th day before the seedlings were placed under stress conditions, the elongation of the seedlings treated with exogenous brassinosteroids was noted. By the end of the experiment (in the second leaf unfolding phase), all brassinosteroids showed a pronounced protective-stimulating effect under the salinity conditions that depended on the chemical structure of the hormone and changed in the brassinolide > homobrassinolide > homocastasterone > epibrassinolide series.

Cardiovascular diseases are the main cause of death and disability in the economically developed countries of the world. Taking into account the high medical, social, and economic importance of the problem of treating patients with coronary heart disease and acute myocardial infarction, the search for new effective methods how to prevent or weaken the unfavorable effects of ischemic and reperfusion myocardial injury and to find out the mechanisms of their implementation is an urgent task of modern experimental and clinical medicine. The aim of the study was to elucidate the participation of nitric oxide (NO) in the mechanisms of realization of the infarct-limiting effect of post-conditioning (PostC) with lactate during myocardial ischemia-reperfusion in young and old rats. According to the study results, it was found that PostC with lactate (10 mg/kg), carried out at the 25th minute of myocardial reperfusion after 30-minute acute coronary occlusion, has an infarction-limiting effect in both young and old rats. However, in the animals under the conditions of systemic action of an inhibitor of NO-synthase of NG-nitro-L-arginine methyl ester at a dose of 25 mg/kg (intravenous administration 5 minutes before the start of reperfusion and 30 minutes before PostC), the cardioprotective effect of PostC with lactate was preserved only partially in young rats. The infarction-limiting effect of PostC with lactate was fully preserved in old rats. The data obtained suggest that the activity of NO-synthase and the NO level in the blood are significant in the mechanisms of implementation of the infarct-limiting effect of PostC with lactate in young, but not in old rats.

The aim of the study is to analyze the changes in the elastic fibers and the expression features of elastinbinding protein-1, lysyl oxidase-1, and tetraspanin CD151 in the invasive ductal breast cancer tissues before and after chemotherapy courses. The study included 34 patients with invasive ductal breast cancer. The patients were divided into two groups: the first group had surgical resection of the tumor before chemotherapy, and the second group had surgical resection of the residual tumor after neoadjuvant chemotherapy. The frequency of elastic fibers accumulations around the ducts in patients without chemotherapy was significantly higher (61.1 %) than that in patients after neoadjuvant chemotherapy (25.0 %). After chemotherapy, the expression of elastin-binding protein-1 changed: the proportion of patients with a strong expression of this protein in tumor cells after chemotherapy increased (62.5 %) in comparison to patients without chemotherapy (16.8 %). The combined cytoplasmic and/or membrane expression of elastin-binding protein-1 in the tumor cells predominated in the second group compared with diffuse cytoplasmic expression (55.0 %) in tumor cells of patients of the first group.

In the present study, the obtained data on the previously unknown behaviors of radon migration in the near-surface atmospheric and soil layers were validated experimentally. The experiment finds two earth origins of radon concentrations occurred in the air in the pores of the near-surface dispersive soil, intragenic and hypogenic, with a considerable atmospheric impact of the liquid forms of precipitation transporting radon from the atmosphere to the ground. The equations were used to establish the mathematical relation between the amounts of precipitation and atmospheric radon. We also assessed a relative contribution of the atmospheric and earth sources to the total radon concentration in the air in the soil pores. The atmospheric source was found to have a sporadically higher impact on the radon levels in the air in the soil pores as against the earth source, depending on the amounts of precipitation and radon concentrations in them. A close correlation was established between the radon concentrations in the soil and the effect of lunisolar gravitational forces on the earth’s crust. The findings of the radon levels in near-surface soils are expected to be applied as one of the criteria for environmental assessment of radon concentrations and associated threats.

The main shortcomings of modern technological machine-tool complexes are shown. They are: the lack of consideration of individual consumer needs and their insufficient flexibility that do not take into account the trend of rapid changes in the production program. A concept for the development of metal-cutting machine tools based on the principles of the modular technology is proposed. The created machine tool complexes are designed to satisfy the individual needs of consumers, while the flexibility of production equipment should ensure the transition to the manufacture of new parts and the replacement of the technological processing scheme by changing the processing modes, readjustment and reconfiguration of machines; the development of machine tools should be carried out simultaneously with the improvement of the technology of processing parts. Technological complexes should be created by the layout synthesis using the element base that should contain two groups of functional modules, technological and service, and the service purpose of the machine should include the range of both the manufactured surface modules with their characteristics and the modules of technological support.

The purpose of this study is an analysis of the numerical simulation results of the magnetic-pulsed processing (MPP) of axis cutting tools using ANSYS. Practical recommendations for the choice of optimal MPP modes are developed on the basis of this analysis. The induction current distribution on the surface of a drill placed in an inductor was obtained using the Ansys Electronics Desktop (Maxwell) module. The time realization of the current pulse in the inductor corresponds to the shape of the experimentally measured pulse waveform. The magnetic pulse is generated by the unit MIU-2. According to the calculation, the magnetic field strength reaches the value h0,1 = 1.247 · 107 [A/m] at a depth of 0.1 mm from the drill surface. Two cases of drill positioning in the inductor are considered: full loading of the drill (the drill is installed on the inductor entire length) and half loading of the drill (the cutting edges are situated in the inductor center). The analysis results show that the density of the induction current has the highest value in the grove of the drill at full loading and in the region of cutting during the discharging in the inductor for the MPP cycle and drill cooling during the charging of the capacitor bank for the repeated MPP cycle) using the Ansys Transient Thermal module. The temperature distribution was obtained for the both options for the location of the drill inside the inductor. The result is that for reinforcing the side surface of the cutting tool (cutting band) the full loading option must be used. For reinforcing the cutting edges the half loading option is more efficient.

The Belarusian Large White breed of pigs is characterized by high maternal performance, resistance, livability of young animals, their fattening and meat productivity. The breed is effectively used for commercial cross breeding with Yorkshire and Landrace pigs. The article contains the results of a comprehensive assessment of the Belarusian Large White breed pigs in terms of development and productivity. The subject of research was the active part of purebred herds of pigs of this breed raised at the following breeding enterprises: agricultural branch “SGC “Zadneprovsky” of JSC “Orsha bread products company”, JSC “SGC “Zarechye”, JSC “Breeding plant “Timonovo”, JSC “Krasnaya Buda”. The main method of working with the breed was the purebred line breeding. Individual selection of animals was carried out according to the main indicators of productivity, development and conformation. The group matching of boars and sows of the breed by reproductive performance was carried out on the basis of the valuation data of breeding enterprises. A comprehensive assessment of development and productivity of the Belarusian Large White pigs showed that on average, intrabreed adult boars aged 36 months had a live weight of 313.0 kg, a body length of 182.0 cm, and sows had a body length of 250.0 kg and 164.0 cm, respectively. Productivity indicators of sows from all controlled breeding herds were as follows: prolificacy – 10.2 heads, milkability (litter weight on the 21st day) – 52.1 kg, number of piglets at weaning – 9.5 heads. Based on a set of indicators, the progeny of boars of Drachun 90685 and Smyk 46706 lines (“SGC “Zadneprovsky”) have the best fattening and meat quality traits. On the basis of the research results obtained, the schemes of interlinear group matching of sows and boars of the Belarusian Large White breed at the breeding enterprises of the Republic were developed.