The article was devoted to investigation on the behaviour of solid particles in the transonic 2D-flow through a stationary cascade of airfoils. The mass load of particles is assumed to be very low, so that the inverse effect of the dispersed phase on the carrying gas flow, as well as the interaction between particles are negligible. In this case the simulation of two-phase flow reduces to the consequent solving of two problems: (i) computation of the gas-phase flow field and (ii) calculation of particles' trajectories in it. The present results are useful for prediction of those areas of the airfoils that may be subjected to erosion damage 

The calculation model is designed and the characteristics of heat and mass transfer is numerically studied in laminar and turbulent stabilized gas/steam and droplets flow in a pipe. The mod takes into account the droplets evaporation, vapor diffusion and flow acceleration. Simulation of the heat- and mass transfer is compared with experimental and numerical data. In the whole, vaporization of the droplets leads to essential augmentation of heat transfer in comparison with a single-phase vapor flow 

Современная вероятностная финансовая математика — это обширная область науки, представляющая собой пример успешного применения методов математической физики к анализу динамики рыночных цен активов и хеджированию финансовых обязательств. В статье дается обзор некоторых важнейших результатов в этой области и возможностей их практических применений, использующий в качестве математического аппарата лишь базовое физико-математическое образование 

Basing on the discrete Ahmed–Rao transform, two recurrent sequences of orthogonal bases in a space of discrete periodic signals are constructed. The explicit formulas for the basic signals are presented. The fast algorithm for evaluating the expansion coefficients for stated basis is offered 

The Remez algorithm is a very effective tool for the construction of the Chebyshev best polynomial approximation. In the paper the problem of approximation of a continuous function, defined on an interval, by a continuous piece-wise polynomial function is considered. Our aim is to generalize the Remez algorithm to this case. The Remez algorithm consists of two stages: at the first stage a polynomial is constructed which is the best approximation polynomial for a chosen set of points (basis). At the second stage this basis is adjusted and the best approximation polynomial for this new basis is constructed etc. In the paper only the first stage is discussed: it is shown how to construct a continuous piece-wise polynomial function satisfying the Chebyshev interpolation conditions 

The asymptotic solutions of Maxwell's equations describing electromagnetic waves near the concave, perfectly conducting body are constructed using boundary-layer approach. It is shown that the energy of this wave propagates along the surface rays 

Finite algebraic systems are concerned. Algorithm for generation of set of all identities with specified number of elements and operands produced. It's proved that the cardinal numbers of such sets constitute 2-dimentional non-stationary sequence. An algorithm for generation of algebraic system varieties for specified support and identity set is suggested 

The class of repeated stochastic integrals on martingale, having the usual rules of integration order replacement, is derived. The theorem of integration order replacement is proved. Corollaries and examples of application of this theorem are considered 

The problems of abstract structure optimization for a periodically nonstationary stochastic automaton, connected with its reduced forms construction, are studied. Some special matrix method of construction of reduced form as well as a system of all reduced forms for such automaton is theoretically proved and developed 

Axioms of boolean algebra and boolean ring described in this work. On the basis of application of boolean algebra in fuzzy logic the approach to the decision of the matrix equations over semirings is offered. Booleans of final sets (the set of all their subsets) are used as a rating scale, instead of a traditional fuzzy rating scale [0; 1]. Algorithms of the solution of systems of the equations over boolean algebra are described and successfully applied with use a Stone's duality as a boolean ring