The article deals with asymptotic properties of diagonal Hermite–Pade’s approximants of type I for the exponential system {e^{λ j z}}^k _{j  = 0} with arbitrary real λ₀, λ₁, ..., λ_k. The proved theorems complement the known results of P. Borwein, F. Wielonsky, and A. P. Starovoitov.

The existence of 2D linear differential systems with bounded piecewise continuous coefficients and a negative senior general exponent, such that the higher central exponent of the corresponding singular system is positive on a countable set of values of the positive parameter under derivative, is proved. Also, the existence of 2D linear singular differential systems with the effect of sign changing of the higher central exponent and the higher general exponent under small linear perturbations at an infinite number of small positive values for a parameter under derivative is proved. The result can be generalized to the case of systems of arbitrary dimension, and can be stated in the class of linear systems with infinitely differentiable coefficients.

We obtained a sharp lower bound for the number of polynomials with the discriminants divisible by a large power of prime number.

In the 30-component first-order wave equation (Fedorov, 1951) for a massive spin 2 particle, a non-relativistic approximation is performed. The quantum-mechanical equation of Pauli type for a spin 2 particle in the presence of an external electromagnetic field is derived. The non-relativistic wave function is a symmetric irreducible 2-rank tensor with five independent components.

It is shown that the equations of intensity transfer can be used for describing the stimulated Raman scattering (SRS) in solids in a wide range of pump radiation intensities, and that the effect of the stimulated Raman scattering on the population of vibrational transition levels, on which SRS occurs, can be considered negligible. A simple method is developed for taking into account this effect in the region where it must not be neglected.

We have found an exact solution to the task of determination of the energies of the non-perturbed states ai and vibronic coupling matrix elements bi that describe the vibronic analogue of the complex Fermi resonance, using the experimental data represented by the energies e_k ^(obs) and the transition intensities I_k ^(obs) (k = 1, 2, …, n) in an observed absorption spectrum. The algorithm consists of two stages. At the first stage, the Jacobi rotations are used to construct a similarity transformation X with the requirement (X_1k)² = I_k ^(obs) that corresponds to the condition that there is only one non-perturbed «bright» state. At the second stage, the algebraic eigenvalue problem for the matrix Xdiag({e_k ^(obs)})X ^–1 is employed to find ai and bi values.

By acylation of biphenyl and naphthalene 4,5-dichloroisothiazol-3-carbonyl chloride under Friedel-Crafts reaction conditions p-biphenyl- and 1-naphthyl-(4,5-dichloroisothiazol-3-yl) ketones, respectively, were synthesized. It was found that acylation of biphenyl in the dichloromethane medium proceeds nonselectively and leads to a mixture of para- and meta-isomers but in the nitrobenzene solution only the para-isomer is formed. By the reaction of p-biphenyl-(4,5 dichlorisothiazol-3-yl) ketone with sodium phenolate p-biphenyl (5-phenylthio-4-chlorisothiazol-3-yl) ketone was obtained.

The possibility of synthesis of metal-matrix composites via coprecipitation of nickel with the particles of МоО₃ (core)–WO₃(shell) structure was demonstrated. It has been shown that the deposition of WO₃ shell permits one to stabilize the dispersed molybdenum trioxide in the nickel plating bath, with the particles of second phase retaining the redox activity that facilitates their overgrowing with matrix metal and ensures large oxide loading in the nickel deposit at a low concentration of oxide in the electrolyte. It is shown that due to the lamellar structure inherent in the MoO₃ core the Ni–MoO₃/WO₃ composites exhibit enhanced wear resistance that is more than 3 times as high as that of bare galvanic nickel.

Young’s modulus and Poisson’s ratio for graphene sheet models have been calculated in the framework of the finite element method as well as using semi-empirical PM6 and ab initio and DFT approaches. All three groups of the methods predict a monotonic increase of Young’s modulus with increasing a sample size with turning the curves to asymptote for bulk samples. Young’s modulus value calculated using quantum-chemical method PM6 converges to 1.01 TPa, reaching this value for the 9 × 15 model (C₃₀₄H₅₀). This value is in a good agreement with the literature data obtained both experimentally and theoretically for a bulk sample of graphene.

The possibility of hydrogen bond formation between the silanol group and the oxygen atom of the ether group or the terminal hydroxyl group of polyethylene glycol (M_n = 400 g · mol^–1, PEG-400) in the silica (aerosil) dispersions in PEG-400 was proved by quantum chemical simulation and IR-spectroscopy. The silica dispersions in PEG-400 over the concentration range of 0.5–3 % were found to be sols, but with increasing the silica concentration the sol–gel transition was shown to occur that yields different thermocoagulation stability of the dispersions depending on the silica concentration.

Computer-based screening of small-molecule HIV-1 entry inhibitors presenting potential peptidomimetics of broadly neutralizing monoclonal antibody 10E8 is carried out. Eight chemical compounds able to block the HIV-1 gp41 segment critical for fusion of the virus membrane with a target cell were identified using molecular modeling. These compounds
are considered as promising basic structures for the design of novel broad anti-HIV drugs

The leaf rust resistance genes Lr1 was revealed in cultivars Fasan, Koksa, Munk, Verbena; the gene Lr10 – in cultivar Vasilisa; the locus linked with the gene Lr20 – in cultivars Banti, Bombona, Korynta, Quattro, Fasan, Triso, Vasilisa, Viza, Darja, Laska, Lubava, Passvet, Sabina. The loci linked with the gene resistance genes Lr9, Lr12, Lr19, Lr21, Lr22a, Lr24, Lr25, Lr26, Lr28, Lr29, Lr34, Lr35, Lr37, Lr42, Lr46, Lr47 and Lr48 were not identified in the investigated varieties.

We have studied the foraging activity and stomach contents of YOY fish in 2 different habitat types: in the bare littoral zone with a sandy or slightly silty bottom and in the littoral zone with reed stands (Schoenoplectus lacustris) of mesoeutrophic Lake Obsterno (north-west of Belarus). The gut content in 5 species of YOY fish (bleak, bream, roach, rudd and sunbleak) during the first decade of July was analyzed and the food selectivity was estimated by Ivlev Selectivity Index. It has been shown that the high food selectivity pointed out for tichoplanktonic species of Cladocera (Chydoridae family) in contrast with euplanktonic species. The overlap trophic niches for 3 studied species (YOY’s bleak, roach and rudd) were welldefined in the bare littoral zone to compare with the littoral zone with reed stands. We also speculate that the rarity and low density in some Chydoridae family species may be coupled with high YOY pressure.

The substitution of cyanocobalamine for lipoic acid in the composition of immunotropic anti-stressin B (B₁+B₆+B₁₂), which was successfully tested in clinical sepsisology, resulted in the development of neurovasotropin, an antidiabetic drug with enhanced antioxidant capacity. During incubation of myoglobin in the presence of hydroperoxide, components of neurovasotropin (thiamine, lipoic acid, and to a lesser extent pyridoxal phosphate) inhibited the production of dimers of paracetamol and tyrosine, markers of oxidative stress indicating the level of free radical formation in the system in vitro. Further modification of neurovasotropin due to its incorporation in tyrosine (or substitution of the pyridoxine constituents for tyrosine) will result in the development of a new drug «homestasin» with probably more pronounced antioxidant properties, which is necessary for correction of different pathologies related to oxidative stress (myocardial infarction, cerebral stroke, etc).

It was established that the response of tumor cells to the action of the redox-active compound is regulated by the intracellular redox state quantitatively characterized by the effective redox potential and the redox buffer capacity. Phenolic antioxidant 3,5-dimethyl-4-hydroxybenzyl thioetanoate (BEP-11-K) was found to stimulate the proliferation in culture and an increase of the redox buffer capacity. Phenolic antioxidant 3-(3’-tert-butyl-4’ hydroxyphenyl)propyl thiosulfonate (TS-13) inhibits the growth of tumor cells in culture. The action of TS-13 results in a decrease of the redox buffer capacity and an increase of the effective redox potential. The toxic effect of TC-13 is reduced by an increase of the cellular redox buffer capacity.

In experiments on 22 sexually mature male rats it was found that short-term hypobaric hypoxia is accompanied by restructuring the integrative activity of the brain and the mechanisms of learning and memory that are vulnerable to the oxygen tension in the tissues of the brain. The oxygen tension reduction during 5 minutes contributes to a two-fold increase of the safety period of the conditioned reflex of active avoidance. The preconditioning effect of 5 minute hypoxia is revealed in 7 days after repeated more prolonged 10 minute hypoxia. The decrease in the total motor activity (an average of 60 %) and the increase in the latency period of nociceptive reflexes (an average of 51 per cent) were accompanied in a test of the hot plate. A similar nature of passive-defensive reflex signals is indicative of the shift of the organism to the endogenous resources saving that allows us to save energy resources, including for brain cells, and to survive under the conditions of lower oxygen tension.

Associations between the static arterial distensibility and the arterial distensibility obtained with regard to a 24-hour ambulatory heart rate are established.

This work presents the data on the existing stock, quality indicators of brown coal and oil shale in Belarus, as well as the most appropriate and cost-effective technologies of their deep and complex processing.

It is shown that the possibility of using the smart grid technology for organizing a water supply system, which will ensure the future sustainable development of society, is described by the mathematical model.

The authors offer to get a mathematical model of degradation of a functional parameter in the form of the conditional density of its distribution for a given operating time on the basis of the three-parameter Weibull-Gnedenko distribution. This provides prediction errors of reliability for samples of electronic devices, which are smaller than the errors after using the degradation model on the basis of a normal distribution of the functional parameter.

The highest values of the associative combining ability on reproductive traits were typical for maternal forms of Belarusian Large white breed of pigs (12.3) and Belarusian Meat breed of pigs (9.8). On fattening and meat traits the highest values of the associative combining ability and the resulting parameter were typical for the paternal forms of Duroc breed (2.78).