On the total mean curvature of non-rigid surfaces

Using Green's theorem we reduce the variation of the total mean curvature of a smooth surface in the Euclidean 3-space to a line integral of a special vector field and obtain the following well-known theorem as an immediate consequence: the total mean curvature of a closed smooth surface in the Euclidean 3-space is stationary under an infinitesimal flex.Comment: 4 page

An infinitesimally nonrigid polyhedron with nonstationary volume in the Lobachevsky 3-space

We give an example of an infinitesimally nonrigid polyhedron in the Lobachevsky 3-space and construct an infinitesimal flex of that polyhedron such that the volume of the polyhedron isn't stationary under the flex.Comment: 10 pages, 2 Postscript figure

Volumes of polytopes in spaces of constant curvature

We overview the volume calculations for polyhedra in Euclidean, spherical and hyperbolic spaces. We prove the Sforza formula for the volume of an arbitrary tetrahedron in $H^3$ and $S^3$. We also present some results, which provide a solution for Seidel problem on the volume of non-Euclidean tetrahedron. Finally, we consider a convex hyperbolic quadrilateral inscribed in a circle, horocycle or one branch of equidistant curve. This is a natural hyperbolic analog of the cyclic quadrilateral in the Euclidean plane. We find a few versions of the Brahmagupta formula for the area of such quadrilateral. We also present a formula for the area of a hyperbolic trapezoid.Comment: 22 pages, 9 figures, 58 reference

Volume formula for a Z2\mathbb{Z}_2-symmetric spherical tetrahedron through its edge lengths

The present paper considers volume formulae, as well as trigonometric identities, that hold for a tetrahedron in 3-dimensional spherical space of constant sectional curvature +1. The tetrahedron possesses a certain symmetry: namely rotation through angle $\pi$ in the middle points of a certain pair of its skew edges.Comment: 27 pages, 2 figures; enhanced and improved exposition, typos corrected; Arkiv foer Matematik, 201

ВЛИЯНИЕ УСЛОВИЙ РОСТА НА СТРУКТУРНОЕ СОВЕРШЕНСТВО СЛОЕВ AlN, ПОЛУЧЕННЫХ МЕТОДОМ МОС–ГИДРИДНОЙ ЭПИТАКСИИ

In present work the influence of growth conditions on structural quality of AlN layers grown by МОСVD have been investigated. The influence of buffer layers grown with different temperatures and V/III ratio on crystalline quality of AlN were explored. We have reported that the high temperature buffer layer with low V/III ratio is most efficient way to improve the structural quality of AlN. Further improvement was achieved by minimizing the parasitic reactions between NH3 and TMAl. It was carried out by optimization the total flow through the reactor. Applying these methods, it was possible to obtain a high-quality AlN layers (FWHM for (0002), (0004) and (101–3) reflections were 50, 97 and 202 arc seconds respectively) with good root-mean-square roughness of surface 0.7 nm.Рассмотрено влияние буферных слоев, формируемых при различных температурах и отношениях элементов V и III групп (V/III), на кристаллическое совершенство эпитаксиальных слоев AlN, выращенных методом МОС-гидридной эпитаксии на подложках a-Al2O3. Показано, что наиболее эффективным способом повышения структурного совершенства эпитаксиальных слоев является использование высокотемпературного буферного слоя при низком отношении V/III. Дальнейшее улучшение качества слоев AlN возможно благодаря снижению паразитных реакций между аммиаком и триметилалюминием в газовой фазе путем оптимизации потока газа через реактор. Установленные значения ростовых параметров, позволили получить слои AlN высокого кристаллического совершенства (полуширина рентгеновских кривых качания для отражений (0002), (0004) и (101-3) составила 50, 97 и 202 угл. с соответственно) с хорошей среднеквадратической шероховатостью поверхности 0,7 нм, пригодные для создания приборов на их основе

ИССЛЕДОВАНИЕ ПРОЦЕССА ТЕРМИЧЕСКОЙ АКТИВАЦИИ АКЦЕПТОРНОЙ ПРИМЕСИ В ЭПИТАКСИАЛЬНЫХ СЛОЯХ GaN : Mg

The effect of thermal annealing of GaN:Mg layers on acceptor impurity activation has been investigated. Hole concentration increased and mobility decreased with an increase in thermal annealing temperature. The sample annealed at 1000 oC demonstrated the lowest value of resistivity. Rapid thermal annealing (annealing with high heating speed) considerably improved the efficiency of Mg activation in the GaN layers. The optimum time of annealing at 1000 oC has been determined. The hole concentration increased by up to 4 times compared to specimens after conventional annealing.Исследовано влияние условий термического отжига эпитаксиальных слоев GaN : Mg на активацию атомов акцепторной примеси. По результатам измерений методом Холла установлено, что с увеличением температуры отжига концентрация дырок возрастает, а подвижность уменьшается. Наименьшее значение удельного электрического сопротивления получено на образцах, отожженных при температуре 1000 oC. Быстрый термический отжиг (отжиг с высокой скоростью нагрева) позволяет существенно повысить эффективность процесса активации атомов магния в эпитаксиальных слоях GaN. Оптимальное время указанного процесса при температуре 1000 oC составило 1 мин. Показано, что концентрация дырок возросла в 4 раза по сравнению с образцами, подвергнутыми стандартному термическому отжигу

THE DEGREE OF POLYMERIZATION OF POWER TRANSFORMERS’ PAPER INSULATION

The paper presents the results of research and analysis of literature data on the paper insulation's thermal aging. An exponential decrease in the degree of polymerization of paper insulation from the aging time is established, at the starting time of transformers’ operation the aging rate of paper insulation is maximal and after that its slowing down. It was found out that the degree of polymerization at the starting time of the transformer's operation can be in the range of 900 units, this is due to its drying during the manufacturing process