Разработка и анализ редуцированной вычислительной схемы
The paper discusses a novel approach to solving large systems of linear ordinary differential equations of the first order. This paper describes the introduction of a new reduced computational scheme based on the Euler methods. Given the nuances of the algorithmic construction of the computational scheme. The estimated error of this scheme in comparison with the implicit Euler method. Calculated time implementation costs reduced computational schemes. The study was implemented in the framework of the Basic Research Program at the National Research University Higher School of Economics (HSE) in 2014.
A method based on the spectral analysis of thermowave oscillations formed under the effect of radiation of lasers operated in a periodic pulsed mode is developed for investigating the state of the interface of multilayered systems. The method is based on high sensitivity of the shape of the oscillating component of the pyrometric signal to adhesion characteristics of the phase interface. The shape of the signal is quantitatively estimated using the correlation coefficient (for a film–interface system) and the transfer function (for multilayered specimens).
Let G be a semisimple algebraic group whose decomposition into the product of simple components does not contain simple groups of type A, and P⊆G be a parabolic subgroup. Extending the results of Popov , we enumerate all triples (G, P, n) such that (a) there exists an open G-orbit on the multiple flag variety G/P × G/P × . . . × G/P (n factors), (b) the number of G-orbits on the multiple flag variety is finite.
I give the explicit formula for the (set-theoretical) system of Resultants of m+1 homogeneous polynomials in n+1 variables