In this article we study the extremal properties of the Hermite–Padé approximations of type I for the exponential system {e^λpz}^k_p=0 with different arbitrary real and complexes λ₀, λ₁, …, λ_k. The theorems proved complement the known results of P. Borwein, F. Wielonsky, K. Driver.

The Jordan block structure of images of regular unipotent elements from subsystem subgroups of type C₂ in irreducible representations of groups of type C_n in characteristic p ≥ 11 with locally small highest weights is determined. These results can be applied for investigating the behaviour of unipotent elements in modular representations of simple algebraic groups and recognizing representations and linear groups.

The article deals with the problem of integrability of the product of integrable functions in the Kurzweil–Henstock sense. The classical theorem states here that the product of an integrable function and a function of bounded variation is also integrable. In the article it is proved that the product of a function with the primitive satisfying the Hölder condition with the exponent α or with the module φ and a function satisfying the Hölder condition with the exponent β or with the module ψ such that α + β > 1  or t^–2φ(t)ψ(t) is integrable. Similar results for functions with generalized (Winer, Young, Waterman, Schramm) bounded variations are stated.

It is proved that the spectra of the upper characteristic frequency of zeros and the frequency of signs (also called as the upper Sergeev frequencies) of the linear differential equations are the Suslin sets of the nonnegative semi-axis of the extended number straight line. The inverse claim is obtained under the assumption that the spectra contain zero. It is also proved that the upper Sergeev frequency of zeros and the frequency of signs, considered as the functions of initial values, are the functions of the third and second Baire classes, respectively.

Laser-induced breakdown spectroscopy has been applied for a rapid determination of the main components in flooding cement. Spectra of the erosion plume formed under the action of dual laser pulses were recorded. We used the calibration-free approach based on the detailed diagnostic of the laser ablation plasma, without using standard samples of known composition. The accuracy of determining the basic elements for such an analytical approach was ~4 %.

The methods of liquid impact forging and electron beam welding of the parts of superconducting niobium cavities were investigated. The manufacturing technology of single-cell 1.3 GHz niobium cavities was developed. The test results of the fabricated cavities indicate the preservation of superconducting properties of cavity material and the compliance of the cavity geometry with assigned sizes. The cavities comply with the requirements of modern particle accelerators.

The quasi-Newtonian model of the reci ci procal invariant Hamil il tonian dynamics of gravitating masses, which obeys the Gibson maximum tension principle, is proposed. The symmetry of the model is defined by the Lorentz complex group with real metric. The mass of a model object is the only ly free parameter that defines space-time momentum-energy scales as well ll as frequency characteristics of the model. In the case of small masses there appears the classical analog of the Schrödinger "bouncing" (Zitterbewegung). In the limiting case of the Universe mass the model reproduces the "cyclic" variant of traditional cosmology. The availability of Gibbon’s limit results both in a universal relationship between energy density and cosmological expansion rate, as well as in the existence of the upper and lower limits of these quantities.

Polythermic dependences of the phase transformation degree during Sr₂FeMoO_6–d crystallization by the solid phase method have been studied for powders synthesized from the stoichiometric mixture of the oxides SrCO₃ Fe₂O₃, MoO₃ and from the partially reduced precursors SrFeO_3–x and SrMoO_4–y. It is found that the general rule for all samples is a transition from the kinetic mode of interaction to the diffusion one. In this case, the reaction product layer is formed and is increased with its blocking action. However, it should be mentioned that for the samples synthesized from a mixture of simple oxides, the kinetic stage of solid-phase interactions is mixed with the presence of some fraction of the diffusion part due to the formation of intermediate reaction products. When α is increased, the fraction of the diffusion part grows. The use of the partially reduced precursors SrFeO_3–x and SrMoO_4–y with submicron grains allows one to synthesize the single-phase compound Sr₂FeMoO_6–d with the superstructure ordering of Fe³⁺/Mo⁺⁵ cations. In this case, the kinetic difficulties of the Sr₂FeMoO_6–d phase formation are significantly reduced by increase in the diffusion mobility of Fe³⁺ and Mo⁺⁵ cations and by decrease in the distance of their motion to the reaction zone.

The transformation of the intermolecular complex of chromium (III)–polymer into the intramolecular one was revealed to be the main reason for degradation of polyelectrolyte hydrogels based on sulfonated and carboxylated polyacrylamides crosslinked by chromium (III) acetate during thermal aging, while the mineralized water addition caused polymer salts to precipitate. Hydrogel destruction occurred at a relatively high content of carboxylate groups formed due to the hydrolysis of amide or substituted amide groups. NMR ¹³C and NMR ¹H spectroscopy showed that the hydrolysis of the functional groups in polyelectrolyte hydrogel containing a sulfo group proceeded slowly, thus resulting in a higher resistance to thermal aging as compared to that based on carboxylated polyacrylamide.

The tribological behavior of Langmuir–Blodgett composite monolayers of triacontanoic acid (TA) with carbon nanotubes (CNT) was studied. It was found that the highest wear stability against the mechanical influence of steel indenter was observed for the composite coating formed from the suspension of CNT and TA in the weight ratio 1.0 : 1.0.

It is shown that the intragastric administration of 1,2- and 1,3-diacylglycerphosphate fludarabine derivatives to Wistar rats and ICR outbred mice leads to a prolonged circulation of fludarabine in animal serum in comparison with the analogous administration of equimolar fludarabine phosphate. The investigated compounds can be regarded as oral fludarabine prodrugs. It is found that the oral bioavalability of fludarabine from its 1,2-dimyristoylglycerophosphate derivative is close to its oral bioavalability from equimolar fludarabine phosphate. Based on the data of the model in vitro experiments, we can suppose that fludarabine can release from its diacylglycerphosphate prodrugs under the action of phospholipases A and D and phosphodiesterases.

Primary male-goats Lac-1 (human lactoferrin gene construction hLF5) and Lac-2 (human lactoferrin gene construction hLF3) with a genome containing a human lactoferrin gene were bred and the sperm bank of primary male-goats was created within the framework of Belarus-Russia Union State programs. The herd of goats that produced recombinant human lactoferrin (rhLF) in their milk was obtained. Human lactoferrin (rhLF) from the milk of transgenic goats, natural human lactoferrin (nhLf) from the woman milk, and natural goat lactoferrin (gLf) from the milk of non-transgenic goats were purified using cation-exchange chromatography. Physicochemical characteristics of rhLF were similar to those of nhLf as revealed by different analytical methods including mass spectrometry and peptide mapping. g. Oral supplementation with rhLF activated lipid metabolism and steroidogenesis, promoted favorable changes in the gut microflor composition as well as the enhancement of the functional activity and the fine structure of the rat liver and gut.

The aim of the present research was to study the frequency of the distribution of variants of gene polymorphism of aromatase (СYP19A1) in Belarusian patients with serous ovarian cancer. This population established the influence of gene polymorphism rs10046 with the risk of serous ovarian cancer in women older than 50 years: CT genotype in a group of patients with serous ovarian cancer was met significantly less than in the control group (OR = 0.58; 95 % CI: 0.37–0.91; p = 0.023).

The results of chemical analysis of soil samples taken near Mount Vechernyaya (Enderby Land, East Antarctica) during the 4th, 5th, and 7th Belarusian Antarctic expeditions are given. For the first time, in this region the chemical, grain size and mineralogical composition of the soil is characterized. The content of water-soluble compounds, macro- and microelements, mineral oil is defined. The connection of elevated concentrations of heavy metals and hydrocarbons with the previous human activity in Mount Vechernyaya region is shown.

It is shown that the factors of activity, fugacity, as well as the osmotic, isotonic compressibility are a special case of the associative-ionized non-ideality factor i_as = 1 – α_as + α_i(v – 1) suitable for describing associated solutions of nonelectrolytes and electrolytes with the use of the classical equations. Here i_as is the association degree, α_i is the dissociation degree, ν is the number of the ionized particles, into which the electrolyte molecule breaks. At the same time, i_as is a special case of the generalized non-ideality factor of systems (GNF) g = 1 – β_ord + α_nord that binds the ideal and real models of any systems. (β_ord ≡ α_as is the fraction of the ordered elements of the system, α_nord ≡ α_i(v – 1) is the fraction of the disordered elements of the system).

Characteristic features of the structure and mechanical properties of nanocomposites based on polyethylene terephtalate (PET) and layered clay silicates (LCS) were studied. Na⁺-montmorillonite (not treated) and organoclay Cloisite 30B were used as LCS. The materials were compounded by means of the extrusion technology using a twin-screw extruder (the diameter of screws was equal to 35 mm, L / D = 40. The temperature of the main compounding zones was above the PET melting temperature for melt extrusion, and ≈50 °С and ≈100 °С below that temperature for low-temperature extrusion. It was found that the change from the regime of melt extrusion to that of low-temperature extrusion promoted the increase in the deformation-strength properties of the PET/clay nanocomposites. The X-ray diffraction analysis showed that the degree of nanoclay intercalation in the PET matrix increased with changing to the low-temperature extrusion regimes. The nanoclays appeared to cause a nucleating effect on the PET crystallization; this effect became stronger with higher degrees of polymer overcooling in the material cylinder of the extruder.

The limiting case of operation of an adsorption refrigerator, in which the temperature and concentration are uniform over the cross-section due to a uniform distribution of heat transfer fluid within an adsorber and a high rate of heat exchange between sorbent and heat transfer fluid, is examined. The influence of various parameters on the efficiency of the considered device is investigated and their optimum values are found.

The article proposes a method of identifying the most promising export product groups from the viewpoint of evaluation of their export profitability and the degree of technological proximity in relation to the goods in the trade of which the country has a comparative advantage. The article presents a methodology of placing the country to potential importing countries for Belarusian goods based on the determination of the country’s position on the level of its macro-economic development, the degree of country risk, and the level of development of foreign trade. The proposals for the commodity and geographic diversification of the Belarusian export are proposed.

The results of studying the influence of some factors on the efficiency of the cattle pick-up are presented in the article. It is established that the level of recoverability of the oocyte-cumulus complexes from the number of punctured follicles is 68.7%. The yield of oocytes per one aspiration is 2.7, including per one positive aspiration for extraction – 3.3. Most acceptable for aspiration is the 17G dia needle regardless of the vacuum level. The greatest number of aspirated follicles (6.2 and 8.0) and picked-up oocytes (4.0 to 5.5) is observed when for simulation the follicle-stimulating Pluset hormone is used at a dose of 750 I. E. with or without the use of the progestagen drug Crestar during the stimulation process.