This article is aimed at constructing a solution to the first mixed problem for the one-dimensional wave equation in the form convenient for numerical implementation with the help of the characteristic parallelogram. The derivation of the formula for numerical solution is based on the representation of the classical solution of the considered problem. This problem is formulated as follows. The one-dimensional wave equation is given in the half-strip on the plane of the two independent variables. Cauchy conditions assigned on the basis of the half-strip are related to the equation. Values of the sought solution are set by the given functions on the lateral half-line side of the area. The parallelogram method can be extended to other equations and problems.

In the article we present an improvement to the lemma on the order of zero approximation by irreducible divisors of integer polynomials from A. O. Gelfond’s monograph “Transcendental and algebraic numbers”. The lemma says that if a polynomial P(x)∈Z[x] of degree not exceeding n and of height not exceeding Q satisfies inequality P(x) < Q−w, w > 6n, for some transcendental point x∈Z, then there exists a divisor d(x)∈Z[x] of P(x) that can be written as a degree of some polynomial irreducible over the field of rational numbers satisfying d(x) < Q−w+6n. Gelfond’s lemma and similar results have important applications to many problems of the metric theory of Diophantine approximation. One of such applications is the result of V. Bernik (1983) on the upper bound for the Hausdorff dimension of the set of real numbers with specified order of zero approximation by the values of integer polynomials. This result along with the result of A. Baker and W. Schmidt (1970) on the lower bound of the Hausdorff dimension of the set mentioned above gives the exact formula. In order to prove the upper bound V. Bernik improved and extended Gelfond’s lemma by using a weaker condition w > 3n and obtaining a better estimate d(x) < Q−w+n, as well as by considering the values of polynomials on an interval. However, the condition on w is still restrictive and limits the range of problems this result could be applied to. In our work, we improve the existing results by obtaining the estimate d(x) < Q−w+n−1 on some interval for any w. The result is obtained using the methods of the theory of transcendental numbers.

Recently it has been shown that the Lobachevsky geometry simulates an ideal mirror distributed in the space. Since the Lobachevsky model enters some cosmological models of the Universe, using theses models we need to take into account the presence of the «cosmological mirror». The earlier analysis assumed a static character of the space-time geometry. In this article, the generalization of the cosmological reflection effect to the oscillating de Sitter Universe is given for the scalar field. It is shown that the vanishing factor  cos² t in the metric of space-time does not lead to a singular behavior of solutions of the wave equation for the scalar field; instead, the solutions have a simple phase factor behavior in the time variable t, so the squared modulus of the wave function at cos  t → 0 turns to be 1.

By the method of melting special powder amounts of cobalt antimonide and cobalt telluride in vacuum, the solid solutions alloys of the CoSb_1–x Te_x system were synthesized with the NiAs structure. X-ray analysis results of the alloys confirmed the formation of a continuous series of solid solutions with a nickel-arsenide-type structure in the system. The constants a of the initial CoSb and CoTe compounds are close in values, which determines the course of the dependence a = f(x) that is practically parallel to the concentration axis. The dependence of the constant c on the concentration increases smoothly from 5.181 Å in CoSb to 5.371 Å in CoTe with a slight deflection to the concentration axis. The alloy density, determined by the hydrostatic weighing in carbon tetrachloride, has a linear dependence on the concentration. The concentration dependence of the micro hardness of the CoSb_1–x Te_x alloys passes through a weakly expressed maximum in the range of average compositions. Specific magnetization and magnetic susceptibility of the alloys are measured by the ponderomotive method in a magnetic field of 6.8 · 10⁵ A/m in the temperature range 80–1200 K. At the temperature of liquid nitrogen, the value of specific magnetization is maximum (~6,0–6,5 Гс · см³ · г^–1) in CoTe and solid solutions based on it. Solid solutions of compositions x = 0.4–0.9 have a magnetic transition temperature exceeding 1200 K. 

For the first time, a semiconductor p⁺n⁺-diode is considered, which is completely compensated with the point irradiationinduced defects (rt-defects) of one kind in three charge states (−1, 0, +1 in elementary charge units) on the background of the crystalline matrix. Each rt-defect introduces two energy levels into the semiconductor band gap. Such a diode, in which electrons in the conduction band and holes in the valence band are absent, is called a ζ-diode. The charge transport in the ζ-diode is performed by electron hopping via rt-defects only. In the drift-diffusion approximation, a system of nonlinear differential equations, which describes the hopping migration of electrons via rt-defects, is solved numerically. The distribution of the electric potential and the charge states along the ζ-diode, as well as its static current-voltage characteristics are calculated for a temperature of 78 K. The possibility of hopping current rectification in the ζ-diode based on crystalline silicon, partially disordered by the point irradiation-induced defects, is shown. 

Multilayer films (chitosan/dextran)_n , (chitosan/pectin)_n , (chitosan/carboxymethylcellulose)_n , (polyethyleneimine/dextran)_n , (polyethyleneimine/pectin)_n , (polyethyleneimine/carboxymethylcellulose)_n (n = 4; 4.5) with a thickness of 8.5 to 396.3 nm have been obtained. The relationship between the physicochemical characteristics of the films and the adhesion of mesenchymal stem cells to them has been determined. It has been shown that the mesenchymal stem cells effectively adhere to defect-free ultrathin multilayer viscoelastic chitosan-containing films and form on their surface a monolayer culture of fibroblast-like cells with high viability. 

In silico design of novel HIV-1 entry inhibitors able to mimic the primary receptor CD4 of the viral envelope gp120 protein was carried out using the click-chemistry methodology. The neutralizing activity of the designed molecules was evaluated by molecular docking, resulting in the discovery of 6 top compounds promising for synthesis and biological trials. The designed compounds may be used as basic structures for the development of novel, potent, and safe antiviral drugs with broad HIV-1 neutralization.

The state-of the-art in antibiotics modification is the development of acid resistant dosage forms for per oral treatment. This article is about the synthesis of complexes of ceftriaxone and cefotaxime, 3rd generation antibiotics of cephalosporines family, with new water-soluble cellulose derivative – acetate sulfate sodium salt. The composition of complexes was established by UV- and FTIR-spectroscopy. Stable in acid media tablet dosage form of antibiotics was prepared by the immobilization of complexes on activated carbon. Release of the major quantity of antibiotics was proved by HPLC method to be in alkaline media modeling the intestine.

The case report of the Danon disease firstly diagnosed in Belarus is presented. The targeted Next-Generation Sequencing (tNGS) was used to search for mutations in 46 genes associated with cardiomyopathy of different genesis in a patient suffered from dilated cardiomyopathy, peripheral muscle disorders and mild dementia. Hemizygous deletion c.864+3_864+6delGAGT (rs397516751, NM_002294.2) in the LAMP2 gene affecting the natural splice site was detected. The LAMP2 gene (Lysosomal Associated Membrane Protein 2, Xq24) encodes a membrane glycoprotein essential for the adhesion of lysosomes. Mutations in LAMP2 lead to the distortion of the autophagy by lysosomes and glycogen accumulation in the cells. Clinically, they manifest in the Danon disease: hypertrophic or dilated cardiomyopathy, skeletal myopathy, and mental retardation. The metabolic reason of cardiomyopathy has not been recognized in the present case. The tNGS has allowed one to correct the diagnosis. The early exact diagnosis for such patients is essential to slow down the disease progression. The Danon disease can proceed asymptomatically before puberty and then develops rapidly with sudden mortality. 

The comparative study of the processes of growth, organ formation and physiological and biochemical responses of plants in experiences in vitro and in vivo are carried out under influence steroid glycosides and plant hormones (auxins, gibberellins and cytokinins). The common and specific properties of these connections are revealed. On the strength of these properties, the steroid glycosides are referred to new group steroid phytohormones. The general properties of steroid glycosides are optimization of all the known processes of growth and morphogenesis (intensification of the growth of stems, leaves and roots of wheat, apical dominance in barley and wheat, accelerating germination of freshly harvested potato tubers, the increase of pigment content in the cereals leaves, the cotyledons of pumpkin and amaranth seedlings, the accumulation of biomass in clover plants), attraversa ability and regulation of physiological and biochemical processes of plants. The new plant hormones are hydrophilic conjugate that activates juvenile and volumetric growth, with prolonged activity, high stability and transportability in plants.

The objective of the present work is to study the effects of fat and propranolol adrenoblocker on changes in the potentials of smooth muscles (PSM) of the stomach and the colon, impulsion of sympathetic fibres (ISF). Acute experiments on rats (anaestesia – 70 mg/kg of thiopental sodium, intraperitoneally) have been carried. It is found that a single introduction of olive oil into the duodenum (0.5 ml) results in a long increase of the amplitude of the PSM of pilorus and reciprocne – to falling in the colon. Simultaneously, the sympathetic inhibitory reaction occurs and the ISF in the mesenteric nerves of the candal part of the intestines is depressed. The preliminary hypodermic introduction of propranolol eliminates both those answers. After a long addition of olive oil (1 ml/day) to the feed, in 30 days the amplitude of the background PSMs of the pilorus considerably grows and there are no effects of the PSM increase on the action of propranolol and fat regularly arising in the control, but the colon potentials decrease for sure as in the case of a single introduction of the β-blocker. These data show that both single and long actions of the fat on interoceptors cause a stable suppression of the activity of β-adrenoreceptors of the stomach and intestines, thereof the tonic electric activity of the smooth muscles of these organs rises. It is supposed that the adrenoblocking effects of the fat consumed in large quantities on the motor function of the intestines are an important part of the peripheral mechanisms associated with the obesity.

We have developed the method for evaluation of the arterial vessel “biological age” (BA) through arterial wall stiffness. Stiffness is determined using a new index, which is independent of blood pressure and heart rate. These features of the used index allow neutralizing the effect of blood pressure and heart rate on arterial stiffness. Therefore, the evaluation of BA based on the proposed method is reasonably accurate. It gives the possibility of a highly reliable detection of the arterial system accelerated aging. The method is implemented in detail for the common carotid artery. We have established the formulas determining its BA index through stiffness index and heart rate values.

There is a big uncertainty of the assessments of the effect of “small” climate formative factor (solar and geomagnetic activity, geophysical parameters of the Earth, planetary effects, etc.) on the climate. The objective of the article is to assess global climate changes and their causes. For the first time, when analyzing the character and closeness of solar-atmospheric connections, the approach based on the simplified 22-year cycle model of the solar activity and running trends of temperature anomalies is applied. The obtained results are verified with a wide use of various methods for assessment of their statistical significance. The analysis of the changes in the linear trends of global temperature anomalies has shown a distinct and statistically significant manifestation of a 22-year magnetic solar cycle in the space-temporal changes of trend values. The closeness of the connection of 22-year solar cycles and the values of the linear trends of the temperature anomalies appeared to be somewhat higher in the winter than in other year seasons. The alternative scenario of Globe climate changes in the near future, assuming a decrease in the values of the Globe temperature anomalies in 2017–2019 (2020) by 0.1–0.2 °С in comparison with the previous period (2014–2016), is offered.

The high degree of correlation and genetic communications between radon volume activities (RVO), main types of crystalline basement rocks, geophysical fields, and main tectonic elements has been detected. Taking into account this correlation, a map of the radon activity of the basement was designed with three types of territory marking: with RVO more than 78200 Bq/m³ , 50000–72900 Bq/m³ and 25700–44000 Bq/m³ . The particular composition of rocks, as well as structural elements of zoning of the basemenet appeared in the RVO distribution. 

The article presents results of analytical and experimental study of neutronics of the accelerator driven subcritical systems by the “Yalina-Booster” example. Zero power subcritical assembly “Yalina-Booster” with fast and thermal spectrum represents a model of subcritical nuclear system driven by external neutron source (Accelerator Driven Systems – ADS). Accelerator of the hydrogen ions (the neutron generator NG-12-1) is used as an external neutron source. The assembly design allows to vary the material content of the core and long half-life radionuclide samples (long lived minor actinides and some fission products) placed in the experimental channels aimed to study the effect of neutron flux density in thermal and fast neutron energy ranges. The objective of the research was to search the ways of keeping the main neutronics at the appropriate level by gradual reducing of nuclear fuel enrichment in the fast zone. Principal estimating criteria of the neutronics variation by such fuel conversion were: subcriticality levels, spatial distributions of neutron flux density, time behavior of neutron flux density for pulsed mode of the external neutron source operation in terms of different ion pulses durations etc.

In recent times, researchers are interested in ultra and nanopowders of oxide ceramics and functional materials based on them. This article describes the results of obtaining an aluminum hydroxide powder – boehmite produced by the method of hydrothermal oxidation of aluminum. Boehmite obtained by this technology is characterized by high phase purity (according to the XRD-analysis there is well-crystallized boehmite). It is found that the hydrothermal synthesis, carried out by combustion in pre- and supercritical water, can be considered as an effective method of obtaining extra pure nanocrystalline hydroxides (boehmite) and oxides of aluminum (corrundum). In the case of realization of oxides and hydroxides of aluminum and also the technology of obtaining hydrogen and heat energy, this process can be considered to be highly profitable.

The structure phase composition and properties of silicon carbide and boron carbide ceramics obtained by reactive sintering have been investigated. It has been found that they essentially depend on the charge composition and the parameters of carbide skeleton infiltrated with silicon (total and open porosity, pore shape and size) and on the free silicon content. It is shown that the density, bending strength, hardness of silicon carbide and boron carbide ceramics obtained by reactive sintering, increase with high the compacting pressure of carbide skeleton. The boron carbide and boron carbide with 50 % silicon carbide infiltrated with silicon exhibited the highest properties.

This article summarizes and systematizes the processes of plasma plating (metallization) of refractory powders (including self-plating combined with amorphization, pulse division of spheroids and chemical interaction of an ionized gas with a particle surface). Plasma coatings having no analogs in composition, structure and properties: abrasion, shock, heat-resistant composites are made of these materials.