The aim of the presented article is to prove that any unitary involution of involutory central simple algebra A over a global field or over a field of cohomological dimension not greater than 2 is decomposable with respect to the decomposition of A into primary components.

In this article, for any non-crossing perfect matching a disjoint compatible spanning tree with a maximum vertex degree no more than 4 is constructed with the complexity O(n4 log n) The criterion of existence of a non-crossing perfect matching in the complement of a star of the order less than 2n in K2n has been obtained. It has been proved that there exists a noncrossing perfect matching in the complement of a tree of the order (n + 1) in K2n with the number of inner vertices no more than (n – 1).

A graph is called 1-triangle if for each maximal independent set I, each edge of this graph with both end vertices not belonging to I forms exactly one triangle with a vertex from the set I. We have obtained a structural characterization of 1-triangle graphs which implies a polynomial time recognition algorithm for this class of graphs.

The article presents the methods of analysis of the Markov queueing networks with incomes that are used in forecasting expected incomes of logistics transportation systems.

Using nondeterministic polynomial time Turing machines, a recursive presentation of the complexity class NP ∩ coNP has been constructed for the first time.

In this article we found the value of the Hausdorff dimension of a set of points in the space of real, complex and p-adic numbers that are approximated with a given order by algebraic numbers. The proof is based both on the metric theorem on the exact order of a simultaneous approximation of zero in this space and on the construction of a regular system of real algebraic numbers, complex algebraic numbers and p-adic algebraic numbers of p

The formation of gold nanorods as well as thin films prepared via electrostatic deposition of gold nanorods has been investigated. The obtained gold nanorods films have been used as substrates for the surface-enhanced Raman scattering analysis of sulfur-free organic molecules mitoxantrone and malachite green as well as inorganic malachite microcrystals for the first time. The additional modification of films with L-cysteine allows one to significantly extend the use of gold nanorods for the surface-enhanced Raman scattering analysis.

The electronic band spectra and the optical properties of 2D crystals of tin sulfide (SnS) were investigated by means of ab initio simulation. Low-temperature (α-SnS) and high-temperature (β- SnS) phases in the form of 2D crystals were considered. All compounds were found to be semiconductors. Their band gaps decrease upon increasing the number of monolayers approaching the values of bulk materials. Calculated reflection coefficients of the structures studied are lower than in bulk materials, and the light absorption coefficient has the same order of magnitude as in bulk SnS and GaAs.

А new type of resonant excitation of surface plasmons is proposed and investigated which is characterized by the equality of the phase velocities and attenuation coefficients of the plasmons and an excitation field. It has been shown that this type of resonance can be realized by means of the modified Otto scheme. The peculiarity of this scheme is the presence in a transition layer of the periodic system of wedges allowing one to form an inclined evanescent wave. The calculation shows that the modified scheme can provide a local power gain of two orders greater as compared with the standard Otto scheme.

A thermodynamic analysis of the after-effects of low temperatures on the structural characteristics of membranes of peripheral blood lymphocytes of human was made. Structure changes in membranes are outlined using the theory of secondkind phase transitions. Based on the analysis made, the trend in raising the immunological status of the body of athletes after a whole-body cryotherapy course is explained from the viewpoint of decreasing a value of Young’s modulus of peripheral blood lymphocytes, reducing the microviscosity of annular lipid of peripheral blood and of occurring processes similar to second-kind phase transitions in plasmic membranes of lymphocytes.

The Dirac equation for spin 1/2 particle with anomalous magnetic moment is solved in presence of the external uniform magnetic field. After separation of the variables, the problem is reduced to a 4-order ordinary differential equation, which is solved exactly with the use of the factorization method. A generalized formulas for Landau energy levels are found. Solutions are expressed in terms of confluent hypergeometric functions.

The synthesis of new 2-acylcyclopentane-1,3-diones with a saturated С9–С12 acyl chain was described. The compounds were synthesized by the O-acylation of cyclopentane-1,3-dione with appropriate acyl chlorides in the presence of pyridine in chloroform, followed by the O–C- isomerization of the prepared enol acylates under the action of acetone cyanohydrin in acetonitrile in the presence of triethylamine.

The possibility of solvothermal deposition of mixed oxide of molybdenum-vanadium on an inert silica carrier (mesoporous grains, nanoparticles) via the polycondensation of mixed molybdenum- vanadium acid under controlled conditions has been demonstrated. It is shown that the obtained catalysts representing the solid V2O5 : MoO3 solution exhisit the high activity in the reaction of thiophene oxidation at 250 °С and can be used for desulphation of hydrocarbons.

The study of the supramolecular complex of fatty acid with hemoglobin as an indicator of phospholipolysis at different stages of experimental acute necrotizing pancreatitis was carried out. It is found that the amplitude of the differential spectrum of hemoglobin in the presence of myristic, oleic and palmitic acids or mixtures thereof depends on the length of hydrocarbon chains of fatty acids and on the presence of double bonds. Full compliance of the dynamics of changes in the phospholipase A2 activity with a pathomorphological picture of the development of pathology of the pancreas and its treatment is found. It is shown that the test system for determining the activity of phospholipase A2 through the measurement of the differential spectrum of hemoglobin in the wavelength range 403–423 nm during the formation of the supramolecular complex of hemoglobin with fatty acids can be used for the diagnosis of severe forms of necrotizing pancreatitis as an informative laboratory test.

At present, the complex of alien species of sucking phythophagous arthropods in the fauna of Belarus includes 61 species of insects and mates from 35 genera, 12 families and 4 orders. The majority of them have the European (19 species) origin, and а smaller number is due to the Mediterranean (12), North American (11) origin. Seven invasive species are cryptogenic.

A collection of tomato genotypes was tested by functional PCR markers for the genes determining a carotenoid content and a period of fruit preservation. Identified as a result of DNA-typing sources of breeding the valuable genes were used for high carotene content line crossing and long-storage testers according to the top-cross scheme. The combining ability of lines and testers on the basis of “mass concentration of β-carotene” features was studied and the specimens with a high concentration of β-carotene and lycopene were selected.

We used a high-throughput array to evaluate the diversity of hexaploid wheat growing in Belarus under the breeding program through 384 gene-associated SNPs. The gene pool of winter and spring varieties are significantly different in frequency of 248 variants from 174 SNPs. The genetic structure of the Belarusian population of wheat has appeared similar to the Russian and Ukrainian varieties and is essentially different from west-European varieties. But it has a high variability 
and, consequently, a good genetic potential for the improvement through breeding.

It was shown that the butyrylcholinesterase activity in the blood of women with non-malignant breast cancer was lower as compared to patients with malignant breast cancer (P < 0,001). Using two dimensional gel-electrophoresis method it was found that blood plasma proteomic maps are different for patients with various molecular subtypes of breast cancer. Identified differences consist in the appearance of additional new proteins and changes in the expression of proteins present in norm. Current data provide an advance to develop supplemental methods of breast cancer diagnosis and prognosis of the therapy outcomes.

The content of a number of metals in some fruticose lichens from East Antarctica has been studied. The influence of various sources on the formation of their composition has been estimated. It has been shown that long-distance atmospheric transfer of such elements as Zn, Mn, Cu, Pb, Ti, Sr, Rb, Y, Ba has an essential impact on their accumulation in lichens. Accumulation of aluminium and iron in lichens is associated with their lithogenic origin. Comparing to other lichens, Pseudephebe pubescens is characterized by a significant accumulation of the above-noted metals, and this species can therefore be used as an indicator of atmospheric transfer of pollutants in the air.

In this article the mechanisms of the labor market adjustment to structural changes in economy are analyzed. It is revealed that the mechanisms for quantitative adjustment are connected with the preservation of unnecessary labor, weaken competition for workplaces; the mechanisms for qualitative adjustment don’t provide the reaction of the educational services market to structural changes in economy; the mechanisms for wages don’t stimulate the labor transition into new spheres in economy; the mechanisms for institutional adjustment don’t promote the coordination of the named mechanisms action. For successful adaptation of the labor market to structural changes in economy the following is necessary: reduction of inefficient workplaces, socially responsible restructuring (including over retraining and modern methods of personnel work), coordination of the educational services market and the labor market, realization by wages of the function stimulating workers to productive and qualitative work, increase of labor market institutional flexibility.

The article is devoted to the study of the influence of different factors on the productive longevity and the lifetime milk production of the Belarusian black-motley cows. It was found that among the factors contributing to the many-year productive use of cows it is possible to identify the causes of both hereditary and paratypic nature that need to be taken into account in animal husbandry. The most powerful influence of genetic factors on the period of the productive use is set by the factor of “linear affiliation” (h2 = 10.3 %), and from paratypic factors – “the yield of milk in the first lactation” (h2 = 11.78 %).