The article describes the relations between spectral radius of transfer operators and topological pressure. The key role is played by new dynamical characteristics – rami-rate and forward entropy.

In the present paper, we have developed the theory of a massless spin 2 particle. We apply the matrix equation in Minkowski space-time, specifying it in cylindrical coordinates t, r, φ, z and tetrad. By diagonalizing energy operators, the third projection of total angular momentum, and the third projection of linear momentum, we derive the system of 39 differential equations in a polar coordinate r. In order to resolve this system, we apply the Fedorov–Gronskiy method based on the projective operator method. In accordance with this method, the dependence of all 39 functions is determined only by five different functions of the polar variable r that in the considered case are expressed in terms of Bessel functions. We find the explicit form of six independent solutions of the basic matrix equation. In order to eliminate gauge degrees of freedom, we use the general structure of gauge solutions according to the Pauli-Fierz approach, when the gauge solutions for the spin 2 field are constructed on the basis of the exact solution for a massless spin 1 field (in Bessel functions as well). In this way, we find the explicit form of two independent gauge solutions for the spin 2 field. In the end, we derive the explicit form of two gauge-free solutions for the massless spin 2 field, as should be expected by physical reason.

We studied the kinetic features of fibrin clot destruction in vitro under the action of ultrasonic cavitation generated by low-frequency (36 kHz) ultrasound (US) with the intensity I₀  of 4.4–51.2 W/cm², using a flexible waveguide concentrator. It was established that the rate of US destruction of clots immersed in saline at the initial stage of the process is proportional to I₀ in the range of 12–51 W/cm², corresponds to first-order kinetics, and is determined by the erosive processes without the formation of D-dimers and other fibrinolysis products at a minimum contribution of sonochemical reactions. The clot destruction rate is maximum at the initial time moment and decreases with increasing the US exposure duration (by 35 % in 1 min and by 72 % by the end of the second minute at I₀ = 51.2 W/cm²). It was shown that in order to increase the completeness of clot destruction at a minimum administered US dose, it is advisable to minimize the US exposure time when using the highest values of the US intensity limited by the level of safe cavitation exposure to the vascular wall, hemostasis, and blood cells.

Stoichiometric C : N : P ratios were compared between primary producers in littoral and pelagic ecosystems of mesotrophic relatively shallow lake Obsterno and shallow macrophyte covered low trophic lake Nobisto from May to October over the next two years. Elemental seston ratios of lake Obsterno revealed smaller differences between littoral and pelagic zones in comparison with lake Nobisto in 2017. During the studied period, in the both lakes, the seston C : N and C : P ratios were higher than the Redfield ratio (106 : 16 : 1 C : N : P) on most dates and N : P was always more than 16. Pelagic C : P and N : P ratios in lake Obsterno were the highest in May in 2017, July and September in 2018 with significant differences between littoral and pelagic zones. N : P ratios decreased in October but there were no significant differences among habitats. In lake Nobisto in 2018, seston C : P and N : P ratios increased from May to July in littoral and pelagic zones but then decreased in September to October. Our research shows differences in stoichiometric ratios in littoral and pelagic zones of these two lakes, which indicates food quality (seston C : N : P ratios) differences for zooplankton species depending on season and location.

This study determined the effect of exogenously applied hydroxycinnamic acids and their chitosan-based conjugates on growth and biochemical parameters of microclone potato plants (Solanum tuberosum L.) in vitro under optimal conditions. The findings of the present investigation confirm applying of chitosan-caffeic acid and chitosan-ferulic acid conjugates on microclone potato plants to improve growth and development. A significant growth-stimulating effect was found in caffeic acid and its chitosan-based conjugate. Chitosan behaved like a general elicitor inducing oxidative stress in plant cells. In turn, hydroxycinnamic acids acted as antioxidants to scavenge reactive oxygen species. The chitosan-caffeic acid conjugate can be considered as a low stress factor that activates metabolism and adaptation processes of microclonal potato plants.

The growth factor genes VEGF and TGFB1 are involved in the normal functioning of the kidneys, and some polymorphic loci of these genes determine a genetic predisposition to the autoimmune diseases, including systemic lupus erythematosus (SLE) and its dangerous complication, lupus nephritis (LN). The products of these genes, in particular, the vascular endothelial growth factor protein and the transforming growth factor β1 protein are used in clinical practice as markers of endothelial dysfunction for early diagnosis of kidney pathology. However, the relationship between the expression of these proteins and the genotypes/alleles of the polymorphic loci of these genes has not been studied enough, which requires clarification of this issue for the child population of Belarus. In this work, we analyzed the associations of the TGFB1 (rs1800469) and VEGF (rs699947 and rs2010963) gene genotypes with the concentration of their products in the blood serum of patients with LN during exacerbation and remission of the disease. The study did not find a significant relationship between polymorphic variants of the TGFB1 gene (rs1800469) and levels of its product in the blood. An association has been established between the rs699947 and rs2010963 polymorphic variants of the VEGF gene and the serum concentration of the gene product in pediatric patients with LN during exacerbation. It was found that the homozygous minor genotype AA of the polymorphic locus rs699947 and the group of genotypes GC + CC containing at least one minor allele of the locus rs2010963 are associated with higher levels of the gene product in the blood serum of children with LN during disease exacerbation (p < 0.001 and p = 0.036, respectively). Thus, VEGF polymorphic variants associated with an increased concentration of the gene product in the blood serum during disease exacerbation can be considered as markers of the risk of disease exacerbation in patients with LN.

The article presents the results of study of the modern water-erosion processes in the Central Belarus territory. The mechanisms of sheet, gully and river erosion are considered. The areas of development of these processes are established and the parameters of annual erosion drift are calculated. The contribution of each process to the dynamics of the earth's surface relief of the region under study is determined. It is shown that the development of water-erosion processes lead to noticeable negative consequences for environment, disruption (up to destruction) of natural and natural-technogenic objects, and significant economic damage.

The updated provisions of the basing theory and the updated composition of the bases are given: installation, guide, support, double guide, double support, and triple support. Base combinations form five sets, each of which can be implemented using explicit or hidden bases or their combinations. It is shown that basing an object with sets of hidden bases causes the greatest difficulties, and a feature of basing an object with hidden bases is determining the position of reference points using the contact points of the object, implemented by the installation elements. When basing an object with a hidden base, the position of the reference point is determined by a self-centering mechanism using the points of contact with the basing object. Various schemes of constructive solutions for basing and fixing objects in sets of hidden bases in self-centering mechanisms are considered.

The article presents the data of electret-thermal analysis of ultrahigh molecular weight polyethylene as a polymer material promising for medicine and technology, polyvinyl alcohol as a biocompatible gel-forming polymer, blood as a system with coordinatively bound polarizable components, synovial fluid as a component of the lubricating medium of joints containing giauloronates and cholesterol esters, starch-containing polymer biodegradable compositions, chitosan as a natural electret biopolymer, vegetable oils as systems with supramolecular formations in the form of fatty acid triglyceride associates. The variants of interpretation of the thermally stimulated current spectra obtained during the analysis are proposed, which are based on the fundamental concepts of dielectric physics, condensed matter physics, and related natural science disciplines. It is concluded that the addition of the content of curricula in individual academic disciplines with information about this method will contribute to improving the effectiveness of specialists training by institutions of higher education.