Reduced anisotropic unitary Whitehead groups of henselian division algebras, which are either unramified or tamely ramified with commutative residue algebra, are computed.

In the present article, the approximation of the function |sin x| s by the partial sums of the rational trigonometric Fourier series is considered. An integral representation, uniform and point estimates for the above-mentioned approximation were obtained. Based on them, several special cases of the selection of poles were studied. In the case of the approximation by the partial sums of the polynomial trigonometric Fourier series, an asymptotic equality was found. A detailed study is made of a fixed number of geometrically different poles.

In terms of matrix observability, the necessary and sufficient conditions are obtained for the linear timevarying observation system to have stationary orbits with respect to the linear time-varying transformation group of class C1 . The full invariant of the action of a transformation group is described. It is proved that for any matrix function A c C(T, Rn×n ), there exists such an n-vector function c(t), t c T, that the pair (A, c) is uniformly observable. The algorithm for constructing a stationary system is described.

In this paper, we consider the compact difference approximation of the fourth and second-order schemes on a three-point stencil for Klein–Gordon equations with variable coefficients. Despite the linearity of the differential and difference problems, it is not possible in this case to apply the well-known results on the theory of stability of three-layer operator-difference schemes by A. A. Samarskii. The main purpose is to prove the stability with respect to the initial data and the right-hand side of compact difference schemes in the grid norms L₂(W_h), W¹₂ (W_h), C (W_h). Using the method of energy inequalities, the corresponding a priori estimates, expressing the stability and convergence of the solution to the difference problem with the assumption h ≤ = h_0,  h₀ = const, τ≥h is obtained. The conducted numerical experiment shows how Runge rule is used to determine the different orders of the convergence rate of the difference scheme in the case of two independent variables.

The circular quantum dots localized in the double heterostructures are simulated by means of the axially symmetric smooth confinement potential of finite depth. For the proposed potential of new type, the exact wave functions and the energy levels of electron are found. The dependence of energy spectrum on potential parameters is investigated.

The possibilities and conditions for modifying the band gap and the behavior of interband transitions under compressive and tensile strains in the crystal lattice of a molybdenum disulfide monolayer have been determined by theoretical modeling. It is shown that depending on the value and direction of the strains the compound may be a direct-gap or indirect-gap semiconductor, and the conditions for such transformations are determined. The results demonstrate a potential use of the molybdenum disulfide monolayer in nanoelectronic devices of new generation in which controlled transport of charge carriers is possible

A Fe, Mn-oxide catalyst was obtained by impregnation of thermally activated dolomite granules with aqueous solutions of Fe(III) and Mn(II) sulfates followed by heat treatment. Its physicochemical properties were studied using differential thermal analysis, X-ray diffraction, low-temperature adsorption-desorption of nitrogen, and scanning electron microscopy. The high efficiency of Fe(II) ion oxidation in aqueous media in a flow-type catalytic reactor was shown, which makes the obtained catalyst promising for the deironization of artesian waters.

The objective of the study was to analyze the genomic structure and allelic composition of the dwarfing Rht-B1, Rht-D1 and Rht8 genes in 37 varieties and breeding samples of soft winter wheat in connection with breeding for lodging resistance in the Republic of Belarus. The molecular cytogenetic marking (C-banding) and DNA typing of genotypes were used. As a result, the analysis of the chromosomal composition of the breeding material showed that 21 winter wheat samples are characterized by the standard karyotype with the genomic structure AABBDD (2n = 42). Five variants of translocations affecting the chromosomes 1B, 3B, 5B, 6B, and 7B were revealed in the karyotypes of the remaining samples. It was found that the chromosomes of the 2nd and 4th homologous groups, in which the main dwarfing genes (Rht-B1, Rht-D1, and Rht8) are localized, did not undergo structural changes. Genotyping showed that 45.9 % of the samples contain one of the dwarfing alleles (Rht-B1b, Rht-D1b, Rht8c) in their genotype. A combination of two commercially significant alleles (Rht-B1b and Rht8c) in the genotype were identified in one of the winter wheat samples. The genotype with a combination of the Rht-B1a, Rht-D1a and Rht8b alleles occurred with the highest frequency (37.8 %) in the analysed breeding material. The Rht-B1b, Rht-D1a, Rht8b; Rht-B1a, Rht-D1a, Rht8a genotypes showed the frequency of 16.2 %. The Rht-B1a, Rht-D1a, Rht8c; Rht-B1a, Rht-D1b, Rht8b; Rht-B1a, Rht-D1b, Rht8j genotypes were identified in 5.4 % of the samples; the Rht-B1a, Rht-D1b, Rht8а genotypes – in 8.1 % of the samples. The analysis of the plant height, taking into account the karyotyping and genotyping data showed that the targeted selection of the most efficient allelic combinations of dwarfing genes is important for the cultivation region. The studies carried out allow us to suggest that the selection by the overwintering level can contribute to the fixation of the Rht8b allele in the breeding material, which is apparently associated with better winter hardiness in the conditions of Belarus.

The human genetic phenotyping is one of the most intensely developing area of forensic genetics. Externally visible traits, including eye color, can be predicted by analyzing single nucleotide polymorphisms with a high predictive rate. We studied the polymorphisms rs12913832 and rs1800407 in the HERC2 and OCA2 genes, respectively, to evaluate its prognostic availability in relation to the iris pigmentation of the Belarusian population. For this, both eye images and DNA samples were collected from 314 individuals to analyze the key polymorphisms by the TaqMan assay. Our data confirmed a relevance of rs12913832:A>G and rs1800407:G>A in the prediction context. The highest values of the sensitivity (SE = 0.94) and the specificity (SP = 0.90) were obtained for rs12913832, demonstrating the high efficiency of this marker as a classifier of phenotypic groups. The presence of the ancestral dominant allele rs12913832-A causes a dark (brown) iris pigmentation, how- ever, the heterozygous state rs12913832:GA includes a range of mixed variants. The predictive value of rs1800407 for the genetic phenotyping is highly significant (SE = 0.98), but has a low specificity (SP = 0.14), thus rs1800407, not being an effective classifier, can be used as an auxiliary in the eye color predictive model. The analysis of a cumulative impact of the both poly- morphisms on the iris color variation shows their high prospects for the genetic phenotyping of the Belarusian population.

In this study, we presented a panel of 14 microsatellite loci (MFW1, MFW2, MFW6, MFW9, MFW10, MFW11, MFW13, MFW16, MFW20, MFW24, MFW26, MFW28, MFW29 and Cid0909), with which we studied the genetic structure of Cyprinus carpio carpio of the breed “Izobelinsky” in the Republic of Belarus. Four offshoots of carp were included in the study: two mirrory (“Smes’ zerkal’naya”, “Tri prim”) and two scaly (“Smes’ cheshujchataya”, “Stolin XVIII”).

As a result, it was found that the carp breed “Izobelinsky” exhibits a high level of in-breed genetic variability. In the studied microsatellite loci, 231 alleles were identified, 62 % of the total number of alleles were rare alleles with a frequency of occurrence of less than 5.0 %. The number of effective alleles (Ne) at the loci ranged from 3.082 (MFW10) to 9.754 (MFW26). The Shannon biodiversity index (I) was 2.082 ± 0.075. The highest value of the expected heterozygosity index (He) was noted for the MFW26 locus (0.897), the lowest – for the MFW10 locus (0.676).

The greatest genetic diversity is characteristic of the scaly carp “Smes’ cheshujchataya” and “Stolin XVIII”. The highest total percentage of rare alleles was determined for fishes from “Stolin XVIII”. The minimum values of this parameter were found for specimens of the carp “Smes’ zerkal’naya” and “Tri prim”.

The results of this study indicate a fairly high genetic diversity of four offshoots of the carp breed “Izobelinsky”, which was established using the marker loci optimally selected for analysis. This makes it possible to differentiate the layering among themselves.

Updated view of genetic features of schizophrenia based on rare SNPs/CNVs with a huge influence on a disease and common SNPs with a small effect of each allele is presented. Altogether these genetic factors are acting to create neuropathophysiological disturbances observed in schizophrenia. Association of five polymorphisms MIR137 rs1625579, DRD2/ANKK1 rs1800497, MTHFR rs1801133, DNMT3B rs2424913, СОМТ rs4680 with the risk of schizophrenia in the Belarusian population, the level of symptoms of schizophrenia patients assessed by PANSS in the acute stage and remission, cognitive impairments, and treatment trajectory of schizophrenia patients during antipsychotic treatment were analyzed. The A/A-genotype of СОМТ rs4680 (р = 0.008) and the С/С-genotype of MTHFR rs1801133 (р = 0.02) are associated with the risk of schizophrenia among Belarusians. The T-allele of MTHFR rs1801133 is a risk factor of positive symptoms (р = 0.02). Combining the C/C-genotype (DNMT3B rs2424913) and the G-allele (COMT rs4680) is associated with a significant difference in negative symptoms level between men and women. The polymorphism of СОМТ rs4680 (р < 0.05) and the combination of СОМТ rs4680 + DRD2/ANKK1 rs1800497 (р = 0.005) as well as MTHFR rs1801133 + DNMT3B rs2424913 (р = 0.006) are related to the cognitive parameters measured by the WCST and Stroop test respectively. Schizophrenia patients who are the G-allele carriers of MIR137 rs1625579 demonstrated a more favorable negative symptom trajectory in comparison to Т/Тhomozygotes (F = 2.2, p = 0.03). The trajectory of negative symptoms (F = 2.2, p = 0.03) and general psychopathological symptoms (F = 4.3, p = 0.0001) is different between men and women under antipsychotic treatment. These differences are associated with a minor amount of alleles of MIR137 rs1625579, DRD2/ANKK1 rs1800497, MTHFR rs1801133 polymorphic sites.

Scotch pine (Pinus sylvestris L.) is one of the main forest forming species in Belarus, which cover 49.2 % of the country’s forested area. The aim of the study was to investigate spatial distribution of microsatellite (SSR) alleles (chloroplast DNA) and identify the features of the genetic structure and genogeographic differentiation of P. sylvestris populations in Belarus. Molecular genetic analysis of six SSR loci of Scotch pine cpDNA in samples form 73 naturally originated stands was carried out. 35 allelic variants of loci PCP1289, PCP4507, PCP83314, PCP71987, PCP26106, PCP30277 were identified. The analysis of the geographic distribution of the dominant allelic variants showed that the population structure of the pine forest is rather homogeneous. Certain regional differences in a number of cases were found for less common, but also widespread variants. One group of alleles is characterized by an increase or decrease in the frequency of occurrence in the direction from the southwest to the northeast. Another group includes allelic variants which share is maximal in the zone covering the Grodno region, the southwestern part of the Minsk region and the Gomel region, while to southwest and to northeast from this zone their frequency of occurrence decreases or is absent. A number of alleles were found only in one of the analyzed stands or in a limited area, which may indicate their local origin as a result of spontaneous mutations. The obtained results are important both from a general biological point of view in studying the evolution and formation of the genetic structure of P. sylvestris in Belarus, and from a practical point of view, since they allow to improve the forest seed zoning of the species.

The morphological changes in the gastric mucosa in the presence of duodenogastric reflux and refluxesophagitis and their connection with the presence of Helicobacter pylori (HP) infection are studied. The endoscopic and histological examination of the stomach antral part was performed in 1251 patients with different gastroduodenal pathologies. HP was diagnosed by histological and real-time PCR methods. Among patients with different gastroduodenal pathologies the frequency of H. pylori infection was 77.9 %. Duodenogastric reflux was detected in 23.9 % of patients. In the presence of duodenogastric reflux, we have found a decrease in the risk of duodenal ulcer by a factor of 2.5, thus duodenogastric reflux may protect against the development of duodenal ulcer. In patients with duodenogastric reflux in the presence of H. pylori infection, significant differences from the group uninfected of Helicobacter pylori were found in the metaplasia frequency. A significant increase in the frequency of foveolar hyperplasia among patients with duodenogastric reflux was revealed. The prevalence of reflux-esophagitis in the study group was 8.3 %. No increased risk in reflux-esophagitis was observed either in the HP-positive or HP-negative cases. According to our finding, duodenogastric reflux was characterized by foveolar hyperplasia and metaplasia. We suggest that the presence or absence of H. pylori does not affect reflux-esophagitis.

The article presents the results of study of the effect of additives of an ultrafine powder of the Ti–46Al–8Cr system obtained by MASHS on the tribotechnical properties of a friction material based on BrO6 bronze. It is shown that in the range of powder additive concentrations 0.5–1.5 wt. %, the dynamic coefficient of friction increases from 0.04 to 0.055, in the range of 1.5–2.5 % – to 0.055–0.058. The introduction of the 0.5–1.0 % Ti–46Al–8Cr powder permitted to reduce the wear rate of the friction material from 4.0 to 3.7 μm/km. An increase in the additive to 2.5 % led to an increase in the material wear rate up to 6 μm/km.

The formation of nickel silicide layers on (111)-Si substrates during rapid thermal annealing in the heat balance mode was studied by the Rutherford backscattering method, X-ray diffraction, transmission electron microscopy, and electrophysical measurements. Nickel films of about 70 nm thickness were deposited by magnetron sputtering at room temperature. The rapid thermal treatment was carried out in a heat balance mode by irradiating the substrates backside with a non-coherent light flux of quartz halogen lamps in the nitrogen medium for 7 seconds up to the temperature range of 200 to 550 °C. The redistribution of nickel and silicon atoms to monosilicide NiSi composition starts already at a temperature of 300 °С and almost ends at a temperature of 400 °С. In the same temperature range, the orthorhombic NiSi phase with an average grain size of about 0.05–0.1 μm is formed. At a rapid thermal treatment temperature of 300 °C, two phases of silicides (Ni2 Si and NiSi) are formed, while a thin layer of unreacted Ni is retained on the surface. This fact can be explained by the high heating rate at the initial annealing stage, at which the temperature conditions of the NiSi phase formation occur earlier than the entire Ni layer manages to turn into the Ni2 Si phase. The layers with a simultaneous presence of three phases are characterized by a high roughness of the silicide-silicon interface. The dependence of the specific resistivity of nickel silicide layers shows an increase to the values of 26–30 μOhm · cm in the range of rapid thermal treatment temperatures of 200–250 °C and a subsequent decrease to the values of about 15 μOhm · cm at a rapid thermal treatment temperature of 400 °C. This value of specific resistivity is characteristic of the high conductivity of the NiSi phase and correlates well with the results of structure studies.

The aim of the present work is to study the influence of the technological parameters of the ion-plasma treatment (IPT) on the functional properties of a TiNi shape memory alloy and its biocompatibility. The object of the study was the Ti–50.8 at. % Ni alloy, widely applied in medical devices. IPT was carried out by vacuum-arc evaporation of a titanium cathode at different values of the bias potential (0, –100, and –500 V), followed by TiN deposition. The functional properties of the TiNi alloy after IPT were investigated using differential scanning calorimetry. The biocompatible properties were evaluated using atomic emission spectrometry to measure a nickel concentration after one year holding TiN-coated TiNi samples in the 0.9 % NaCl solution. It has been determined that by setting the temperature regime of heating of Ti–50.8 at. % Ni alloy samples due to the technological parameters of the IPT process, it is possible to change the interval of realization of thermoelastic martensitic transformations, and, consequently, the temperature response of devices made of this alloy, i. e. to set the necessary functional properties. The comparative analysis of the characteristic temperatures after heat and ion-plasma treatments allow us to conclude that the proposed method for calculation of the TiNi substrate temperature is correct at IPT. The calculated temperature of the TiNi samples was ~275 °C at the zero potential, which is sufficient to shift the characteristic temperatures of the alloy. The substrate temperature during deposition was ~400 °C at a – 100 V bias and above 600 °C at a – 500 V bias, respectively. The Ni concentration in the model solution did not exceed 0.14 mg/l after one year holding, which indicates the high biocompatibility of the TiN-coated TiNi samples.