This article is devoted to the statistical analysis of multivariate binary time series. For solving this problem a parsimonious neural network model of Markov’s ergodic chain of order s was determined. Consistent statistical estimators for model parameters and estimation algorithms of parameters and forecasting algorithms of future states of time series were developed. The results of computer experiments on simulated and real data are presented.

In the article it is proven that once polynomials f and g possess a common root w of multiplicity s for f and multiplicity p for g, the Taylor series expansion for their resultant R = R (f , g)(g , b) in variables b (coefficients g) starts with the summand of order s, and the Taylor series expansion for R = R (f , g)(g , b) in variables a (coefficients f) starts with the summand of order p; and the explicit formulas for the corresponding summands of the Taylor series are obtained. Based on this, a number of results linking higher derivatives of resultants and multiple common roots of polynomials, which differ in ideas from the well-known ones, are obtained.

The analogy used in nanophotonics with radiophysics, on the basis of which the notion of an optical nanoantenna was introduced and fruitfully used, is extended to the case of two-step processes with optical excitation of a quantum emitter (scatterer) and subsequent emission of secondary photons and the concept of an “optical nanotransceiver” (transceiver), i. e. a device receiving primary and generating secondary photons is introduced. The nanotransceiver efficiency parameter is introduced, which is defined by the product of the primary radiation intensity factor and the local density of photonic states at the secondary radiation frequency. This nanotransceiver parameter determines scattered radiation intensity enhancement and a maximum possible value of photoluminescence enhancement. The latter is achieved for emitters with low intrinsic quantum yield.

The chemical composition of high-viscosity heavy oil has been studied by IR spectroscopy and X-ray fluorescence spectrometry. It is found that characteristic absorption bands are available and characterize aliphatic structures and aromatic cycles, sulfur- and organophosphorus compounds, and the presence of compounds containing heteroatoms P, V, Ca, Pd, Ni, Ru, Mo, Fe, Cu and Zn in its composition is found. The method of rotational viscometry has established the Newtonian nature of the oil flow in the studied range of the velocity up to 300 s^–1. At the same time, according to the densitometry results (ρ = 0.954 g/cm³ ), studied heavy oil belongs to the bituminous type characterized by a complex rheological behavior under long- and high-term deformation conditions. In order to regulate the studied oil viscosity properties, composite additives based on amphiphilic reagents of cationic and amphoteric type and organic solvents have been developed, their influence on dynamic and kinematic viscosity has been examined. It has been established that compositions with surfactants simultaneously containing a large amount of amino and phosphate groups dissolved in a non-polar aromatic solvent (toluene) or an organic mixture (catalytic reforming gasoline) have a maximum modifying effect of the colloidal structure of bituminous oil. The interaction of functional groups of amphiphilic reagents with oil heteroatoms leads to the dispersion of resinous-asphaltene substances, a decrease in the structural and mechanical strength of the system, an increase in the molecular mobility of aggregates, which results in improving the investigated oil quality and viscosity characteristics by 7.0 and 12.6 % according to the composition efficiency index.

Tris-dibenzoylmethanate ([V(dbm)₃ ]) and tris-benzoylacetonate vanadium ([V(bac)₃ ]) were obtained by electrochemical synthesis. The composition of chelates was determined using elemental analysis and IR spectral data. It was shown that the formation of a quasi-aromatic metallocycle, the main structural element of chelate, occurred as a result of electrolysis. At the same time, the batachromic shift of absorption bands of carbonyl groups was more than 100 cm^–1. The overwhelming majority of absorption bands in the IR spectra of both compounds had mixed nature. For ([V(dbm)₃ ] the characteristic of absorption bands did not exceed 13.5 %, and for [V(bac)₃ ] – 10.3 %. The peripheral groups of ligands (phenyl and methyl) did not undergo transformation when influenced by electric current.

Aluminosilicate nanotubes (ANT) with a length of 600–1000 nm and a diameter of 15–25 nm were obtained by successive intercalation of kaolin with dimethyl sulfoxide and methanol followed by treatment with a cetyltrimethylammonium chloride solution. It is shown for the first time that the treatment of ANT with a mixture of H₂SO₄ –H₂O₂ leads to removing organic impurities from them and appearing catalytic activity in the α-pinene epoxide isomerization, the products of whicn are campholenic (41.4 %) and iso-campholenic (22.7 %) aldehydes in cyclohexane and trans-carveol (up to 56.0 %) in dimethyl sulfoxide.

This study is devoted to investigating the association of intelligence with a person’s genotype. Comparative psychological and molecular genetic testing was carried out on a representative sample of Belarusian population representatives numbering 746 people. Intelligence quotient (IQ) was determined using D. Wechsler’s test. It was established that the distribution of general intelligence values among the Belarusian population representatives was shifted towards higher results. The persons were divided into low and high IQ groups using the quartile method. The association of intelligence level with genotype was determined using a panel of genetic markers consisting of 18 gene polymorphic variants of neurogenesis, synaptic plasticity and neurotransmitter systems. Molecular genetic testing was carried out using real-time PCR. To automate a search for informative gene combinations associated with cognitive abilities, we used a special computer program that we had previously developed, taking into account the gene interaction effects. 15 most informative combinations of polymorphic gene variants associated with a high intelligence level were identified. These gene variants can be used to assess a genetic predisposition to the formation of high-level intelligence, which will allow assessing the abilities of candidates for extreme activities.

The hanging birch pollen collected in the period April – May 2020, 2021 in the territory of six regions of the Republic of Belarus was studied. Recombinant plasmid DNA was obtained. A nucleotide sequence of cloned fragments was determined. The results on the spectrum of isoforms of the Bet v 1 protein were analyzed. The obtained sequences corresponded to one degree or another to 11 genetic variants of the studied allergen. There were 7 isoforms of Bet v 1 defined within one tree. The predominant isoform of the birch pollen allergen Bet v 1 in the territory of the Republic of Belarus was Bet v 1.0101 (Bet v 1a, X15877.1). The identified variants were analyzed for their potential allergenicity by screening amino acids that according to the literature data were identified as affecting IgE-binding. The analysis of amino acid residues included in the IgE-binding conformational epitopes revealed amino acid substitutions exhibiting the multidirectional (high or low) IgE-binding activity in positions 31, 58, 113, 114, 126. The structure of dominant epitopes recognized by the T-cell receptor was studied. It was found that the C-terminal immunodominant T-cell epitope Bet v 1_143–157 is highly conserved among various isoforms of the allergen in contrast to the epitope Bet v 1_78–93 located in the central region. The revealed amino acid substitutions of the studied sites can affect the activation of T-cells, cross-reactivity and significantly increase the variability of the expected IgE-mediated reaction.

The present study deals with the analysis of the frequency and recurrence of extreme deflation phenomena in the territory of Belarus. The deflation intensity was estimated using meteorological data. 810 cases of dust storms and drifting snow were recorded in the country in the period of 1961–2022, of which 238 had low intensity, 213 – medium intensity and 359 – high intensity. The deflation phenomenon dynamics was analyzed: in the period of 1961–2000 the number of cases decreased gradually, but after 2000 there was an increase in dust storms. The growth of deflation repeatability corresponds to ongoing current climate changes. The spatial zoning of the country by deflation intensity was conducted based on the relief, the composition and structure of cover deposits, and the conditions of economic development of the area. The zones are presented as follows: with low deflation intensity (central Belarusian hills and ridges, northern and eastern regions of the country), medium (central regions of the country) and high (Belarusian Polesie, Grodno, Volkovysk and Slonim uplands with adjacent plains and lowlands).

The article presents the results on energy characteristics and the thermophysical state in the vapor-gas shell formation stage during electrolyte-plasma treatment. The vapor-gas shell formation stage is characterized by intense heating of the anode layer, a transition to undeveloped bubble boiling with high heat release capacity, boiling crisis emergence, and by a transition to the film mode with low heat release capacity. At the same time, a traditional electrochemical process occurs on the anode, which is accompanied by dissolving the surface layer. Dependences characterizing the influence of electrolyte-plasma treatment parameters on the specific power and specific energy of the vapor-gas shell formation stage are established. The obtained results allow optimizing the parameters of new effective processes of electrolyte-plasma treatment in controlled pulse modes, at which both electrochemical (vapor-gas shell formation) and electrolyte-plasma stages are realized within one pulse of millisecond duration.