Abstract. In the present paper, using a modification of the LJ-potential and the continuum approach, we define С60-H2 (He) potentials, as well as interaction energy of two fullerene particles. The proposed approach allows to calculate interactions between carbon structures of any character (wavy graphenes, nanotubes, etc.). The obtained results allowed to localize global sorption zones both inside the particle and on the outer surface of the fullerene.
Quasi-hyperbolic spaces are projective spaces with decaying absolute. This work is a continuation of the author's work [7], in which surfaces in one of these spaces are examined by methods of external forms and a moving frame. The semi-Chebyshev and Chebyshev networks of lines on the surface in quasi-hyperbolic space are considered. In this paper we use the definition of parallel transfer adopted in [6]. By analogy with Euclidean geometry, the semi-Chebyshev network of lines on the surface is the network in which the tangents to the lines of one family are carried parallel along the lines of another family. A Chebyshev network is a network in which tangents to the lines of each family are carried parallel along the lines of another family. We proved three theorems. In Theorem 1, we obtain a natural equation for non-geodesic lines that are part of a conjugate semi-Chebyshev network on the surface so that tangents to lines of another family are transferred in parallel along them. In Theorem 2, the natural equation of non-geodesic lines in the Chebyshev network is obtained. In Theorem 3 we prove that conjugate Chebyshev networks, one family of which is neither geodesic lines, nor Euclidean sections, exist on surfaces with the latitude of four functions of one argument.
Квазигиперболические пространства являются проективными пространствами с распадающимся абсолютом. В работе рассмотрены поверхности в одном из таких пространств методами внешних форм и подвижного репера. Найдены геометрические характеристики для инвариантов линии на поверхности. Получены аналоги поверхностей Фосса.
Сибирский физико-технический институт Пл. Новособорная, 1 634050 Томск В работе предложены вычислительная технология, реализующая задачи линейной теории упругости в цилиндрических координатах. Особое внимание уделяется зоне контакта двух тел. Для ее раскрытия предложено использовать сетки с экспоненциальным расположением узлов по каждому из трех координатных направлений. Расчетами установлено существенное влияние формы сдавливающего элемента на распределение напряжений в зоне контакта. Ключевые слова: контактное воздействие, упругие перемещения точек, обобщенный закон Гука, касательные и нормальные напряжения, рекуррентные формулы, метод простой итерации.
Abstract. The present paper reviews pressure-gravitational movement of a gas and liquid medium in a vertical isotropic bed of a canonical rectangular shape with two permeability windows on the side borders. The work proposes a simple computing technology based on symmetric approximation of differential members and the Gauss-Seidel linearization which allows to significantly expand the range of the model's applicability from the standpoint of moisture saturation compared to traditional numerical.
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