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In modern geometry, the study of the geometries of maximal mobility is of great importance. Some of these geometries are well studied (for example, the Euclidean and Lobachevsky geometries, pseudo-Euclidean, symplectic, spherical geometry, etc.), while others (for example, Helmholtz and pseudo-Helmholtz geometries) have not yet attracted active attention of researchers. There is still no complete classification of the geometries of maximal mobility. In this work, we present some results concerning the classification problem for two- and three-dimensional geometries of local maximal mobility. This problem is reduced to functional equations of a special form and is solved by the embedding method in the class of analytic functions.
In the conditions of a scientific and economic experiment, morphological and biochemical blood parameters of broiler chickens were studied when they were fed gamma-aminobutyric acid (GABA), fumaric acid, and their combination under industrial housing conditions. The experiment was conducted at a broiler poultry farm in the Kemerovo region. The research subject was broiler chickens of the Ross 308 cross. The control group birds were fed a complete balanced feed (CBF). The 1st experimental group received CBF + GABA at a dose of 25 g/t of feed. The 2nd experimental group received CBF + fumaric acid at a dose of 200 g/t of feed. The 3rd experimental group received CBF + GABA at a dose of 25 g/t of feed + fumaric acid at a dose of 200 g/t of feed. Blood for analysis was collected on the 1st, 21st, and 42nd days of bird rearing. The research results showed that the introduction of the studied feed additives into the diet of broiler chickens had a positive effect on their morphobiochemical blood parameters. For instance, the number of erythrocytes at 21 days of age in the blood of broilers from all experimental groups exceeded the control value by 8.9–14.9 %, and at 42 days of age, by 10.8–15.8 %. Hemoglobin content was higher than the control by 23.9–28.3 % and 5.3–7.1 %, respectively. At 42 days of age, the number of eosinophils in the blood of chickens in the 1st, 2nd, and 3rd experimental groups decreased by 6.7 % (p < 0.01), 4.5 % (p < 0.05), and 3.0 %. Protein metabolism indicators in birds from all experimental groups at 21 days of age surpassed the control values for total protein by 5.6–10.9 %, for albumin by 3.7–12.3 %, and for globulin by 7.0–12.7 %. Aspartate aminotransferase activity in the blood of broilers in the 2nd and 3rd experimental groups at 21 days of life was higher than in the control group by 39.6 % (p < 0.05) and 43.4 %, respectively. At 42 days of age, it was higher by 37.3 % (p < 0.01) and 25.0 %, respectively. Therefore, the introduction of gamma-aminobutyric acid, fumaric acid, and their complex into the diet of broiler chickens contributes to an increase in anabolic processes in the birds’ bodies. All the digital data obtained during the experiment were processed by methods of variational statistics (calculation of M±SEM, Student’s criterion).
In this paper, we consider the problem of finding all locally boundedly exactly doubly transitive extensions of the parallel translation group of a four-dimensional space. Groups with decomposable Lie algebras are found.
We investigate the independence of axioms defining a quandle – an algebraic structure important in knot theory and combinatorial algebra. It is proved that all four axioms included in the standard definition of a quandle are independent. For finite quandles, one of the solvability axioms turns out to be a consequence of the others, owing to which it is possible to construct a minimal system of three axioms. An example of a right-distributive left quasigroup is constructed. As an application, for the constructed right-distributive systems, set-theoretic solutions to the Yang–Baxter equations and the corresponding associated groups are indicated.
