The non-local boundary value problem for the second order mixed parabolo-hyperbolic equation with the non-smooth conditions of conjugation has been examined. The uniqueness and the existence of the solution for this problem have been proved
Theorems of the value distribution of the sums of Abelian Group’s characters and short exponentail triginimetric sums are proved in this article. Asymptotic formulas of these sums’ fractional moments are proved
The article discusses the question of the essence of radiation of electromagnetic waves of different sources and questioned the reliability of its description by J.Maxwell in the form of alternating electric and magnetic fields. It justifies the formation of an electromagnetic wave in the form of a wave of compression-decompression in surrounding electromagnetic photon field with a flux of photons of different frequencies emitted by different sources or antenna
The probabilistic model of grouping data (including multidimensional data) is described. We have also generalized Euler-Maclaurin’s formulas. With its help Sheppard’s corrections and corrections on
grouping for correlation coefficient are received. We have found and studied asymptotical corrections on grouping data generally. Accuracy of approach has been estimated
The article analyses well-known approaches to the explanations of Kolmogorov's conditions for probabilities studied in applications. It discusses better-founded explanations, offers and looks into new
approaches to the explanations of connectedness of the conditions
In this article we consider a model of the structure of matter, in which elementary particles, atoms and molecules are composed of gravitational waves. A model of interaction of light and particle beams with macroscopic gravitational waves has been proposed.
The protocols of experiments to test the theory are considered
The solution of the problem of the displacement of the perihelion of Mercury in Einstein's theory of gravitation, taking into account the mechanism of formation of matter from dark energy, has been
obtained. It is shown that the observed value of the precession imposes a restriction on the equation of state of dark energy in the case of static fields
In this paper, we investigated solutions of the Navier-Stokes equations associated with the solutions of Einstein's equations for empty space. There exists a metric in which the Navier-Stokes equations are integrated exactly. We demonstrate that the solution of the Navier-Stokes equations of general form consistent metrics describing in general relativity space with nonzero curvature
In the article we have considered A. N. Kolmogorov and N. V. Smirnov papers dedicated to one-sided and two-sided goodness-of-fit and homogeneity tests. It has been shown that the term "Kolmogorov - Smirnov test" used incorrectly. We have also given the recommendations on use of the terms "Kolmogorov test", "Smirnov test", "test of Kolmogorov-Smirnov type" and discussed omega-square test (Cramer-von Mises–Smirnov test). Typical errors in the application of these criterions have been considered, in particular to test for normality of the distribution of measurement results
Is it possible to automate the study of the properties of numbers and their relationship so that the results of this study can be formulated in the form of statements, indicating the specific quantity of information stored in them? To answer this question it is offered to apply the same method that is widely tested and proved in studies of real objects and their relations in various fields to study the properties of numbers in the theory of numbers namely - the automated system-cognitive analysis (A.S.C. analysis), based on information theory