Vol 28, No 1 (2017)

We consider the inverse problem of frequency sounding in a layered medium by a vertical magnetic dipole field. Uniqueness of the inverse problem solution is proved. We apply the method of minimum number of layers to obtain a stable solution of the sounding inverse problem for gradient media.

We consider a linear control problem with a partially known initial condition. Kalman’s observability theory of linear controlled system is applied to derive constructive sufficient conditions under which the control process to attain a terminal set M can be decomposed into the following stages: first collect information on system output, then apply this information to reconstruct the system’s initial state, and finally proceed with active control to attain the terminal set M.

We describe the possibilities of a numerical method based on quasi-gas dynamic (QGD) equations for the numerical simulation of a turbulent boundary layer. A subsonic Couette flow in nitrogen is used as an example, with dynamic Reynolds numbers of 153 and 198. The QGD system differs from the system of Navier–Stokes equations by additional nonlinear dissipative terms with a small parameter as a coefficient. In turbulent flow simulation, these terms describe small-scale effects that are not resolved on the grid. Comparison of our results (velocity profiles and mean-square velocity pulsations) with direct numerical simulation (DNS) results and benchmark experiments show that the QGD algorithm adequately describes the viscous and the logarithmic layers near the wall. Compared with high-accuracy DNS methods, the QGD algorithm permits using a relatively large spatial grid increment in the interior part of the viscous sublayer. Thus, the total number of grid points in the turbulent boundary layer may be relatively small. Unlike various versions of the large-eddy simulation (LES) method, the QGD algorithm does not require introduction of near-wall functions, because the additional terms vanish near the wall. For small Reynolds numbers, the QGD algorithm describes laminar Couette flow.

The article describes the construction of discrete functions which, by some of their values, specify (generate) arbitrary linear functions. The cases of prime and sufficiently large composite k have been considered previously. In the present study we finally solve the problem of existence of such functions for almost all k and n variables. The proof of the probabilistic upper bound and the general approach are due to A. A. Voronenko. The proof for small k has been developed by N. K. Voronova. The proof for k from 21 to 48 is the result of indispensable cooperation of V. P. Il’yutko and A. A. Voronenko.

This paper deals with the numerical analysis of the problem of parabolic quasi-variational inequalities related to impulse control problems. An optimal L^∞-convergence of a piecewise linear finite element method is established using the concept of subsolution.

In this article, we apply two powerful methods, namely the first integral method and a direct algebraic method for constructing many exact solutions for the higher-order nonlinear Schrödinger equation with non-Kerr terms that describes the propagation of femtosecond optical pulses in nonlinear optical fibers. Using a simple transformation, we reduce the given equation to a nonlinear ordinary differential equation (ODE). Various solutions of the resulting nonlinear ODE are obtained by using the above two methods. A comparison between our recent results and the well-known results is given.

The Godunov method of first order accuracy continues to attract the attention of researchers both because of its simple implementation and its sufficiently high numerical accuracy subject to relatively modest resource requirements. However, it is necessary to constantly verify that the method indeed produces acceptable accuracy. We test the method on a number of one- and two-dimensional prototype problems and compare the results with analytical and numerical solutions obtained by higher accuracy schemes. The results for the method tested are quite acceptable. We also compare the solutions of applied problems on flows in supersonic, freely expanding jets and on supersonic flow past blunt bodies. The results for these problems are also positive.

We investigate the properties of multiple linear regression estimators obtained by the Ordinary Least Squares method (OLS) and the Generalized Least Squares method (GLS, Aitken estimator) assuming substantially different errors in input data. We illustrate the mechanism that leads to fallacious conclusions about the quality of OLS and Aitken estimators based on visual graphical analysis of experimental data. Numerical simulation and comparative analysis of the estimators is carried out for simple and parabolic regression models.