On the spatially periodic ordering in the system of electrons above the surface of liquid helium in an external electric field

A theory of equilibrium states of electrons above a liquid helium surface in the presence of an external clamping field is built based on the first principles of quantum statistics for the system of many identical Fermi-particles. The approach is based on the variation principle modified for the considered system and on Thomas-Fermi model. In terms of the developed theory we obtain the self-consistency equations that connect the parameters of the system description, i.e., the potential of a static electric field, the distribution function of electrons and the surface profile of a liquid dielectric. The equations are used to study the phase transition of the system to a spatially periodic state. To demonstrate the capabilities of the proposed method, the characteristics of the phase transition of the system to a spatially periodic state of a trough type are analyzed.Comment: 11 pages, 2 figures, 1 tabl

Analysis of image segmentation methods

В даній роботі розглянуті методи сегментації зображень. Проведений їх порівняльний аналіз.In this work reviewed the methods of image segmentation. Their comparative analysis was carried out

Analysis of Fracture Characteristic of a Gas Main Pipe on the Basis of the Additive Mathematical Model of the Cyclic Random Process and Polynomial Function

The use of a mathematical model to describe the phenomenon of dynamic fracture of the gas main in a broad range of crack propagation rates is substantiated, taking into account the stochastic and cyclic nature of this process. Particular attention is paid to the reliability of the proposed approach, which is evaluated based on comparison with known natural experiments

Diagnostic features of relief formations on the nanostructured titanium VT1-0 surface after laser shock-wave treatment

A new class of diagnostic features for conducting morphological analysis of relief formations induced by laser shock-wave treatment on the surface of the nanostructured titanium VT1-0 alloy is proposed. They are the coefficients of series expansions of statistical estimates for the orthogonal basis of Chebyshev, Laguerre, Kravchuk discrete polynomials and trigonometric functions. Based on the criterion of the minimum number of the diagnostic features in the above-mentioned bases, the Chebyshev one was selected as the most appropriate to solve this problem