This article presents the classical solution with mixed boundary conditions in the quarter of the plane for the wave equation in the analytical form. The boundary of the region consists of two perpendicular half-straight lines. On one of them, Cauchy’s boundary conditions are assigned. The second half-straight line is divided into two parts. Dirichlet’s condition is assigned on the straight line and Neumann’s conditions – on the half-straight line. The classical solution of the considered problem is defined in the class of double continuous differentiable functions in the quarter of the plane. To build this solution, the partial solution of the initial wave equation is written. For the assigned functions of the problem, the matching conditions are written, which are necessary and enough so that the solution of the problem would be classical and unique.

The article is devoted to the problem of creation of high-speed neural networks (NN) for calculation of interval-index characteristics of a minimally redundant modular code. The functional base of the proposed solution is an advanced class of neural networks of a final ring. These neural networks perform position-modular code transformations of scalable numbers using a modified reduction technology. A developed neural network has a uniform parallel structure, easy to implement and requires the time expenditures of the order (3[log₂b]+ [log₂k]+6t_sum  close to the lower theoretical estimate. Here b and k is the average bit capacity and the number of modules respectively; t _sum is the duration of the two-place operation of adding integers. The refusal from a normalization of the numbers of the modular code leads to a reduction of the required set of NN of the finite ring on the (k – 1) component. At the same time, the abnormal configuration of minimally redundant modular coding requires an average k-fold increase in the interval index module (relative to the rest of the bases of the modular number system). It leads to an adequate increase in hardware expenses on this module. Besides, the transition from normalized to unregulated coding reduces the level of homogeneity of the structure of the NN for calculating intervalindex characteristics. The possibility of reducing the structural complexity of the proposed NN by using abnormal intervalindex characteristics is investigated.

In the article, using the Gelfand–Yaglom general approach, a new 20-component wave equation for spin 1/2 fermion that is characterized by three mass parameters is derived. Based on the 20-component wave function three auxiliary bispinors are determined, in the absence of an external field, these bispinors obey three separate Dirac-like equations with different masses M₁ , M₂ , M₃ . In the presence of external electromagnetic fields, the main equation is not split into the separated equations; instead quite definite mixing of three Dirac-like equations arises. The model is extended to the curved space-time background. If the scalar space curvature differs from zero, then additional terms of geometrical interaction occur between three bispinor components. The model for fermion with three mass parameters allows for the restriction to the case of the neutral Majorana particle.

The method of calculation of redshift of light from a point-like source that moves in the gravitational field of the Kerr black hole as a function of time of observation is developed. The widely presented in literature methods for solving the boundary problem are based on a numerical selection of parameters of geodesics. In contrast, the proposed method is based on approximate analytical expressions for isotropic geodesics in the Kerr metric. The proposed method is illustrated by the example of a model problem with parameters corresponding to real stars moving in the immediate vicinity of a supermassive black hole located in the Center of our Galaxy. The same example shows the efficiency and good accuracy of this method.

The effect of ultrasound oscillations (USO) on the heat transfer conditions between a specimen and environment is examined using a specially developed experimental facility. The influence of the USO amplitude on the combustion temperature and velocity as well as on the phase composition and crystal lattice parameters of the synthesized compounds is studied for the self-propagating high-temperature synthesis (SHS) in Ti–С(Si,B) systems. The heat transfer coefficient on the surface of a specimen during its oscillations with an ultrasound frequency is assessed. Possible mechanisms of the effect of USO on the SHS process are considered. It is demonstrated that a decrease in the SHS temperature is connected with cooling the specimen due to forced convection of a surrounding gas, while a change in a phase composition of the synthesized material and the crystallographic parameters of the phases occurs due to changes in the conditions of high-temperature heterogeneous interactions in the SHS wave.

It is known that during the process of carbon nanomaterials synthesis, gaseous products and various unknown hydrocarbons are formed. Thus, the production of carbon nanomaterials could damage the environment. A detailed analysis of all gaseous products during the pyrolysis process is needed in order to clarify the nature of the formed substances and to control the technological characteristics of the catalyst. The chemical composition study of exhaust gases was made on the facility of propane-butane mixture pyrolysis for the carbon nanomaterial synthesis. The analysis of 16 polycyclic aromatic hydrocarbons (PAHs) of the extracts is made using a gas chromatography-mass spectrometry method. A quantitative analysis of gases was made by gas chromatography coupled with a heat conduction detector and a flame ionization detector. It was established that the concentrations of some PAHs exceed 14, 20, 90 and 100 times much as a maximum permissible concentration in the air. It was found that the appropriate devices of carbon nanomaterial production should be used in order to eliminate the PAHs that are formed.

The effect of the precipitation value (PV) of mixtures of strong and weak non-solvent additives (NSA) on the phase state and viscosity of polyethersulfone(PES)/dimethylacetamide(DMAc)/non-solvent solutions and on the structure and performance of PES membranes were studied. Polyethylene glycol 400 (PEG-400, PV > 1000), water (PV = 10.6), 85 % phosphoric acid (PV = 13.0), glycerol (Gly, PV = 27.8) and mixtures thereof were used as NSA for PES-DMAc solutions. Using Gly/PEG-400 mixtures it was established that the increase in PV of NSA leads to the increase of a miscibility gap on the phase diagram. At a constant concentration of Gly/PEG-400 mixture, the viscosity of the solutions decreases. For a constant ratio (0.94–0.95) of the NSA amount added to the polymer-solvent system to the NSA amount causes a phase separation of the casting solution (coagulation value) increase in PV of NSA Gly/PEG-400 leads to an increase of the membrane pure water flux (PWF) from 13 up to 150 l/m2 h at 1 bar. The most dramatic increase in PWF occurs in the range of PV 39.7–125 g/dL. The results of SEM study don’t show significant differences in the cross-section morphology of membranes for different PV of NSA. However, the thickness of the selective membrane layer increases from 1 up to 4.5 μm when PV increased from 39.7 up to 750 g/dL. Thus, these studies allow us to conclude that the structure and properties of ultrafiltration membranes depend not only on the coagulation value of the casting solution, but also on the precipitation value of NSA.

Bovine pericardium samples modified with ethylene glycol diglycidyl ether, designed for surgical correction of congenital heart defects and large blood vessels, were studied by scanning electron microscopy, X-ray diffraction, IR spectroscopy, and differential thermal analysis. It was found that the initial samples of pericardium, before implantation, contain sites of disorganization of the collagen matrix, fragile fracture of collagen fibrils and destruction of the interstitial membranes promoting the penetration of immunocytes into the deep layers of the pericardium. Ossifying calcification with amorphized hydroxyapatite deposition and bone tissue formation as well as multiple erosions and hypertrophic proliferation in the endothelial membrane were detected in the implantation pericardium samples.

Related wild and cultural wheat species are regularly involved for expanding T. aestivum genetic diversity because they contain many valuable genes. We evaluated the effect of the genetic material of tetraploid species of the genus Triticum (T. dicoccoides, T. dicoccum) on the grain quality of introgression lines of spring bread wheat. The composition of the high molecular weight glutenin subunits which play an essential role in the formation of wheat baking properties was identified in the introgression lines of bread wheat and their parental forms. The traits of grain quality (hardness, protein and gluten content, gluten quality) were also evaluated. The lines with Glu-1 loci alleles from wheat relatives T. dicoccoides and Т. dicoccum were selected. It was found that the introgression of alien genetic material into the common wheat genome had a positive effect on the parameters of grain quality such as hardness, protein and gluten content. The lines with Glu-A1 loci alleles from T. dicoccoides and Glu-B1 from T. dicoccum were at the level of a parent wheat variety or of a higher gluten quality. As a result of the research, the new lines of bread soft wheat with high grain quality were found and can be used in the crop breeding.

The efficiency of the treatment of dry eye disease patients with keratopathy at a subconjunctival injection of 1 % sodium hyaluronate was studied. This review describes the functions of hyaluronic acid depending on its molecular weight. The performed study shows the necessity of using the injection form of sodium hyaluronate in the treatment of patients with dry eye disease.

Nowadays, the infection recurrence rate in osteomyelitis is still high. New hardware not only allowing one to stabilize bone fragments, but also having antibacterial activity seems to be an extremely useful and promising task. The goal of the study was to assess the effectiveness of use of an antibacterial coating based on polymethylmethacrylate cement in experiment and in infected nonunions of long tubular bones of the lower limbs. Bone cement-based coatings impregnated with antibiotics were formed on titanium plates. A plate rinse was carried out; antibiotic concentrations in the rinsed solutions were estimated by a serial broth microdilution method. The antibacterial activity of control and rinsed samples against the antibiotic-sensitive and multiple-antibiotic-resistant Staphylococcus aureus and Pseudomonas aeruginosa strains was estimated by a bilayer agar method. Clinical part. The study included 70 patients divided into 2 groups: osteosynthesis with antibacterial-coated interlocking nail (40 patients, main group) and osteosynthesis with an external fixation device (30 patients, control group) comparable in age, sex and disease duration. The effectiveness of the antibacterial coating was analyzed by the duration of systemic use of antibiotics and infection recurrence rate. The concentrations of meropenem and phosphomycin in the rinsed solutions obtained at one-fold and two-fold treatments were sufficient to suppress the growth of control strains. Vancomycin-containing samples possessed sufficient antibacterial activity against both methicillin-sensitive (MSSA) and methicillin-resistant (MRSA) S. aureus strains, double rinse of the samples eliminated their bactericidal properties. The duration of systemic antibacterial therapy in the main group was statistically significantly lower than in the control group (U = 77.5, p < 0.001), and in the main group the infection recurrence rate was lower than 32.5 % vs. 86.7 % (χ² = 20.39, p < 0.001). The PMMA-based coating impregnated with phosphomycin, meropenem or vancomycin possesses sufficient and long-lasting antibacterial activity, mainly against antibiotic-sensitive strains. An adequate use of such a coating in clinical practice allows one to obtain the desired result of treatment.

The aim of the work was to improve the results of surgical treatment of patients having fractures of the proximal shoulder with the use of the approaches, including the reposition of bone fragments with adequate osteosynthesis and prevention of impingement syndrome, the reconstruction of all damaged structures of the rotator-bicipitale complex. A score assessment of the treatment results of 512 patients aged from 18 to 87 years old was performed, operated from 2004 to 2018 for the treatment of which the tactical approaches and the methods of surgical treatment developed by the authors aimed at restoring the rotator and bicipital elements were used. The use of the developed tactical approaches and methods made it possible to achieve a favorable outcome of treatment in 503 (98.2 %) patients. Thus, the reconstruction of injuries of the rotatory-bicipital complex is a promising way to improve the results of treatment in patients with fractures of the proximal shoulder.

A medium-scale map of iodine deficiency in the territory of the Republic of Belarus was created for the first time. The map characterizes in detail a spatial variation of iodine concentration in soils of Belarus. The article analyzes a spatial specificity of the ecological situation formed as a result of heterogeneity of the iodine content in soils. Using the means of a specialized GIS, the area of high iodine deficiency was identified at the level of administrative regions. The identified area was further differentiated in terms of different level of ecological risk due to a natural soil iodine deficiency. As a result of such geoinformation analysis, the areas of moderate, significant and greatest risks were established in the territory of Belarus. These regions should become the objects of high priority monitoring and are directly in need of targeted preventive measures.

This article investigates the causes and mechanism of change in the climatic pause from 1998 to 2014. In particular, based on the satellite data and the meteorological reanalysis we found a relationship between the temperature of the tropical region of the Pacific Ocean, the speed of the surface wind, and the total content of water vapor in the atmosphere. We also showed that the climatic pause can be explained by a decrease in the water vapor content in the atmosphere and evaluated how this decrease affected the radiation balance of the ground surface. The observed dynamics of water vapor is shown to lead to a decrease in the incoming part of the radiation balance of the ground surface by an amount, which is more than one order of magnitude larger than that caused by the increase in anthropogenic carbon dioxide. It was demonstrated that a decrease in the cloud cover optical thickness could also lead to the stabilization of the global temperature by means of radiative heating of the underlying surface.

We studied numerically and experimentally convective heat transfer and drag of two side-by-side tubes in different arrangements in the narrow channel at the Reynolds number ranging from 8000 to 40000 in comparison with circular tubes. The visualization results of the flow structure in the wake behind the arrangements of the investigated tubes are presented. It is shown that the thermal and hydraulic performance of side-by-side drop-shaped tubes is by a factor of 1.2–2 higher than that of circular tubes due to a lower drag of drop-shaped tubes.

In the article, using subsequent transformations of the structure and mathematical model of a classic gradient jammer canceller, the mathematical model and the structure of a gradient jammer canceller with a pre-processor are obtained. A new structure provides that the adaptation speed of a canceller does not depend on the spread of the eigenvalues of the input signal correlation matrix. An intermediate model provides the analysis of weight misadjustment of the classic gradient jammer canceller. The aim of the new mathematical model is a subsequent analysis of weight misadjustment of the jammer canceller with a stable adaptation speed.