Акимов А. А., Абдуллина Р. И. Построение функции Римана-Грина для одного случая // Международный научный журнал "Интернаука". — 2017. — №10.

Summary. The paper deals with a problem with initial conditions for a beam equation with embedded ends. The problem was solved in two ways: as a sum of the Fourier series in the system of eigenfunctions of a one-dimensional spectral problem, and using finite-difference approximations, a numerical solution was obtained. The quantitative coincidence of the results of numerical and analytical calculations of beam deformation is obtained.

Key words: oscillations of a beam, the Euler equation, the initial-boundary conditions.

Summary. In work the analysis of a risk degree of bankruptcy of Gazprombank Open joint stock company is provided by the method based on use of the device of the theory of fuzzy logic. This method allows to consider quantitative and qualitative indexes which can be both normalized, and not normalized; to consider the level of acceptable risk for the organization and its feature; to beforehand distinguish a possibility of approach of risk of bankruptcy. Using annual accounting records of bank input parameters for carrying out this analysis were chosen. On the basis of the carried-out analysis conclusions are drawn on a financial condition of bank and on its risk degree of bankruptcy.

Keywords. Fuzzy logic, indicator, bankruptcy, risk degree.

Summary: In this paper it is shown that under specified conditions on the initial data a certain infinite coupled system of ordinary differential equations has a solution satisfying an auxiliary convergence condition. The infinite system discussed is essentially the Galerkin expansion of the solution to a given quasi-linear e equation. The results obtained suffice to prove the existence of a solution to this equation of oscillations of a beam.

Keywords: quasi-linear wave equation, method of energy inequalities, equation of oscillations of a beam.

Summary. In this paper  we consider the Tricomi problem in a mixed domain for the Chaplygin equation. Frankl was first which  showed that the problem of the expiry of a supersonic jet from a vessel with plane walls (inside subsonic speed of the vessel) in the hodograph plane is reduced to the Tricomi problem for Chaplygin equation. In the method of auxiliary functions we received a new theorem of uniqueness of the solution of this problem with the Frankl condition in a new domain, without any restrictions, except  the smoothness on the elliptical part of the border domain.

Keywords: method of auxiliary functions, Chaplygin equation of the Tricomi problem, an equation of mixed type.

Summary: The paper deals with the history of the Riemann-Green's function. The article presents a method first used by Riemann in solving some boundary value problems for partial differential equations of hyperbolic type by comparing the two solutions, constructed in different ways.

Keywords: problem of Cauchy, Riemann-Green function, Fouier cosine transform.