For finite π-solvable absolutely irreducible linear groups of degree n < 2 | H| over a field of zero characteristic with a π-Hall TI-subgroup H of a nonprimary odd order that is not normal, the existence of certain factorizations is proved.

Построены монотонные схемы для параболических уравнений со смешанными условиями. Кроме того, для них устанавливается важное следствие принципа максимума, на основании которого можно сделать вывод об устойчивости алгоритма в равномерной норме. В основе конструкции лежит идея использования полуцелых узлов в граничных точках задания краевых условий второго или третьего рода. Полученные результаты обобщаются на построенные аналогичные алгоритмы для одномерных уравнений пороупругости.

In this paper, for parabolic equations with mixed boundary conditions monotone schemes are constructed. Moreover we establish an important corollary of the maximum principle for them. On the basis of this corollary one can make a conclusion about the stability of the algorithm in the uniform norm. The idea is to use half-integer nodes at boundary points of the boundary conditions with the second or third order. The obtained results are generalized to construct the similar algorithm for equations of poroelasticity in the one-dimensional case.

In the paper we construct a Lobatto-type quadrature formulas on the segment [−1,1] by weight 1 /√1− x 2 by using quasi-Hermite-type rational interpolation with nodes Chebyshev–Markov. The coefficients of quadrature formulas of Lobatto-type were calculated and estimation of their error in particular. We give example of the use of these quadrature formula and compare the rate of approximation of various types of quadrature formulas.

In this paper we consider the following problem. Let A₀ be some quasi-periodic subalgebra of the algebra of almost periodic functions on Rm and a : R^m → R^m, a(x) = Mx, is a linear map defined by a square matrix of size m. There exists the smallest closed subalgebra A⁺, containing A₀ and invariant under α, and there exists the smallest closed subalgebra A, containing A₀, invariant under α and α^–1. We obtain conditions on the linear map α when these subalgebras are quasi-periodic.

Ti-Al-N films were synthesized by a reactive magnetron sputtering to investigate the effects of sputtering conditions on the microstructure and mechanical properties. The deposited coatings were characterised by RBS (Rutherford backscattering spectroscopy), scanning electron microscopy and microindentation. Results show that deposition parameters have a large influence on the hardness of deposited coatings and their microstructure. It was revealed that the high hardness and low friction coefficient are corresponded to films with globular microstructure.

The separation of variables in the Laplace–Beltrami operator (Hamiltonian for a free quantum mechanical particle) of three-dimensional Lobachevsky space in the horospherical and quasi Cartesian coordinates provides an opportunity to introduce standard (conventional) coherent states. We consider problems, (oscillator, quantum mechanical particle in the uniform magnetic field) for which introduced coherent states are the adequate method of investigation.

We have considered a one-dimensional Kronig–Penney-like model of coherent electron transport. The model represents a curved channel with scattering centers which is subjected to an external uniform electric field. We have shown that the transmission coefficient of the channel is exponentially sensitive to both transverse and longitudinal field magnitudes.

The fluorescence excitation spectra of jet-cooled oxalyl halides (COF)₂ and (COCl)₂ are measured and compared with their absorption spectra in the gas phase. High efficiency fluorescence of oxalyl fluoride molecules excited to the single vibronic levels of b_g symmetry and high efficiency of nonradiative transitions for molecules excited to the single vibronic levels of α_g symmetry are observed. High intensity hot band 7₀² 8₀¹ is detected in the spectrum of oxalyl chloride. These results are compared with data for glyoxal (COH)₂, obtained earlier.

The formation enthalpies of tautomeric forms of C-alkoxy-1,2,4-triazoles (alkoxy = OCH₃, OC₂H₅, Oi-C₃H₇, Ot-C₄H₉) and isomeric N-methyl-C-methoxy-1,2,4-triazoles have been calculated by means of designed isodesmic and isomerisation reactions. The relative Gibbs energies for their tautomeric forms and isomers in aqueous solution have been calculated. N₂-tautomers and isomers of C-alkoxy-1,2,4-triazoles wеre found to have the smallest values of formation enthalpy whereas N₄-forms are less stable in gaseous phase. Increasing of electron donor properties of substituent leads to the stabilization of N₂-tautomers in comparison with N₁-tautomers. N₁- and N₂-tautomers and isomers have similar values of Gibbs free energy in aqueous solution. In contrast to gaseous phase, N₁-derivatives of C-methoxy- and C-ethoxy-1,2,4-triazoles as well as N-methyl-C-methoxy-1,2,4-triazoles are more stable than corresponding N₂-derivatives. This is due to higher polarity of N₁-isomers in comparison with N₂-ones. N₄-derivatives are less stable in gaseous phase as well as in aqueous solution.

Thin-film coatings efficiently (to 51 %) scattering light in the visible spectrum were obtained from particles of titanium dioxide by roll-to-roll technology on the rotating cylinder with glass substrate which separates the Langmuir–Blodjett trough into two compartmens with linear barriers.

A new photosensitive optical materials based on methylmethacrylate, modified organic acids, and phenanthrenequinone is obtained and investigated. The possibility of the recording of holographic gratings in this material is shown. Chemical conditions for the formation of holograms are discussed. Thermal and adhesive properties were improved with the aim of expanding the range of polymer application and generating of diffractive elements with long term stability and high optical quality.

The prediction efficiency of white cabbage F₁ hybrid performance based on ISSR and RAPD markers was carried out. In result molecular-genetics evaluation of white cabbage collection, five divergent lines were selected and tested by full diallel (5×5) mating design. Through analysis relationship genetic divergence of parental lines and F₁ hybrid performance the significant correlations (r > 0.5) were found for the main yield components. Yield potential of half-diallel F₁ hybrids was predetermined total GD by 67.2 % (R = r2), whereas no significant associations were found for reciprocal F₁. Consequently, heterotic response does not simply result from the overall genetic diversity within a hybrid, but is likely only diversity at some specific loci causing the formation of superior F1 genotype with high expression of the traits.

The results of the genetic structure’s study of the spruce formation of Belarus is according to mitochondrial DNA polymorphism (locus mt15-D02). The formation of the genetic structure of plants with particularly Picea abies (L.) Karst. is various due to their historical origin – Carpathian and Boreal. It’s revealed that Boreal mitotype occurs almost throughout the territory of Belarus, while the Carpathian is concentrated in the south-western part. Firstly, using DNA markers it’s shown the existence of the overlapping area of migration flows P. abies in the south-west of the country. The most probable way of their distribution on the territory of Belarus is in the postglacial period, as well as modern trends in migration in the investigated region.

Genetic diversity of the 50 plum accessions (species and varieties) cultivated in Belarus was studied by the SSR analysis using 20 markers. On the average 17.7 and 13.3 alleles were identified among domestic and diploid plum accessions respectively. Percentage of the unique genotypes were 0.681 and 0.552 and discrimination power levels were 0.811 and 0.741 for domestic and diploid plum accessions respectively. Cluster analysis allowed division of almost all accessions into two big groups according to their ploidy level. Genetic distances between the diploid plum varieties belonging to different species or interspecific hybrids were similar to the distances between intraspecific ones that indicates on low interspecific differentiation of diploid plum.

In experiments on rats, it was found that hyperthyrosis is accompanied by activation of the detoxication processes and a rise in body temperature. Inhibition of the NO-synthase activity by methyl ester N^G-nitro-L-arginine diminishes the typical changes in detoxication processes and body temperature induced by the action of exogenous triiodothyronine.

For reduced pressure 60–300 Torr experimental results and theoretical estimates of electrostatic deposition of femtoliter droplets, containing inside nanoparticles, from the gas stream on substrate-electrode are presented. It is shown that the corona discharge with a stream of droplets is stable in a limited range of currents and voltages. Similarity criterion of the process of electrostatic deposition is obtained. It was found that the use a thin dielectric substrate, covering the electrodes, significantly reduces agglomeration of charged droplets due to Coulomb repulsion.

Analysis of thermal-hydrodynamic instability of plane filtration combustion front of solid fuel is performed. The boundaries of stable region for co-flow combustion wave are determined by numerical modeling. Possible scenarios of plane combustion front evolution o new steady-state or oscillating structures are investigated. The results are expressed in terms of dimensionless parameters.

Different ontological and epistemological principles of understanding the source text form the basis of religious literature translations in the Grand Duchy of Lithuania. In the community of religious freethinkers they were the subject of analysis, individual interpretation and exemplary retelling based on a variety of sources. Striving of the representatives of official religious denominations (Maciej X, deacon Fyodor) who understood the translated text as revelatory for a consistent explanation of the truths contained therein embodied in the translation into Church Slavonic and other Slavic languages. Representatives of the major currents of Reformation used the canonical texts as a means of confirming their theories and propaganda and resorted to simplified translations. Abundance and imperfections of the texts arising in the XVI century pushed A. Kurbsky, K. Ostrozhsky and other Orthodox translators to search and attempt to revive the translation tradition of Cyril and Methodius which was substantially updated and developed in the XV century by Maxim the Greek.

The article is devoted to the evolution of historiography of the USA and Great Britain concerning the history of Belorussia during the Great Patriotic War. The most important subjects in English-speaking researches are shown. The scientific and extra scientific factors which influenced on the western scientific works are noted. The author analyzed approaches of various scientific schools, their strong and weak sides.