Abstract:
Waves of finite amplitude on a thin layer of non-Newtonian fluid modelled as a power-law fluid are considered. In the long wave approximation, the system of equations taking into account the viscous and nonlinear effects has the hyper- bolic type. For the two-parameter family of periodic waves in the film flow on a vertical wall the modulation equations for nonlinear wave trains are derived and investigated. The stability criterium for roll waves based on the hyperbolicity of the modulation equations is suggested. It is shown that the evolution of stable roll waves can be described by self-similar solutions of the modulation equations.

Abstract:
A hierarchy of mathematical models describing viscosity-stratified flow in a Hele-Shaw cell is constructed. Numerical modelling of jet flow and development of viscous fingers with the influence of inertia and friction is carried out. One-dimensional multi-layer flows are studied. In the framework of three-layer flow the interpretation of the Saffman--Taylor instability is given. Two kinematic-wave models of viscous fingering are proposed. The first one includes friction between the fluid layers. The second model takes into account the formation of the intermediate mixing layer. Comparison with calculations on the basis of two-dimensional equations shows that these models allow to determine the velocity of propagation and the thickness of the viscous fingers.

Abstract:
The evolution of breaking waves propagating towards the shore and more specifically the run-up phase over the swash-zone for surface as well as for internal waves is considered. The study is based on a) laboratory run up experiments for surface waves ; b) laboratory stratified flow experiments and c) on field data describing the internal wave run up. The presentation is focused on the breaking and energy transfer mechanisms common to surface and internal waves in the swash-zone. The mathematical model taking into account turbulent mixing and dispersion effects is discussed.

Observations and numeric modeling of internal wave
generation and transformationin the
shelf zone of sea show that the main part of tidal energy is transported to
shores in form of internal gravitational waves. Long-term measurements of
temperature and current velocity fluctuations at many levels in the near-bottom
thermocline were carried out during the periods when stable seasonal
thermocline was present. Analysis of the measurements permits us to understand
mechanisms of internal wave destruction with turbulent motion generation and
corresponding rebuilding of velocity and density mean fields in the stratified
near-bottom layer. Spectral analysis of temperature fluctuations shows that in
shoaling internal waves the low-frequency maxima disappear, maxima at higher frequencies
appear, and the spectra slope in the high frequency range changes with depth.
Taking into account the concurrent analysis of near-bottom pressure
fluctuations and current velocity fluctuations from surface till bottom we come
to the conclusion that breaking internal waves in a near-bottom thermocline
generate not only small-scale three-dimensional turbulence, but also quasi-horizontal
turbulence of larger scales, which considerably contributes into mixing and
sediments, alluvium, and nutrients transport in the shelf zone of sea.

This article should not be considered
as a full review of current methods for non-destructive testing of surface layers.
Rather, it is a subjective in this area. However, the article provides some
review of the challenges posed by the current state of surface layers treatment
techniques on the area of Non-Destructive materials evaluation: enhancement of the sensitivity to the
type of defects, increasing resolution to submicron values, the requirement to
diagnose the surface layers with depth resolution of properties, diagnosis of multilayer
multicomponent surface layers and coatings, treated with concentrated energy.

Abstract:
The evolution of large amplitude internal waves propagating towards the shore and more specifically the run up phase over the "swash" zone is considered. The mathematical model describing the generation, interaction, and decaying of solitary internal waves of the second mode in the interlayer is proposed. The exact solution specifying the shape of solitary waves symmetric with respect to the unperturbed interface is constructed. It is shown that, taking into account the friction on interfaces in the mathematical model, it is possible to describe adequately the change in the phase and amplitude characteristics of two solitary waves moving towards each other before and after their interaction. It is demonstrated that propagation of large amplitude solitary internal waves of depression over a shelf could be simulated in laboratory experiments by internal symmetric solitary waves of the second mode.

Abstract:
Dynamics of large amplitude internal waves in two-layers of shallow water is considered. It is demonstrated that in laboratory experiments the subsurface waves of depression over a shelf may be simulated by internal symmetric solitary waves of the mode 2 ("lump-like" waves). The mathematical model describing the propagation and decaying of large internal waves in two-layer fluid is introduced. It is a variant of Choi-Camassa equations with hydrostatic pressure distribution in one of the layers. It is shown that the numerical scheme developed for the Green-Naghdi equations in open channel flows may be applied for the description of large amplitude internal waves over a shelf.

Abstract:
In order to neutralize a drastic pollution of the environment (technogenic catastrophe) it is suggested to use technogenic technologies of chemical compound decontamination. One in such technologies can be the technology using metal oxide solid aerosols which are active in removal of pollutant compounds and obtainable by combustion under ambient air of appropriate metal particles, for example, aluminum, magnesium, titanium and etc. It is shown that the titanium dioxide out of an solid aerosol, obtained by pyrotechnic mixture combustion containing titanium microparticles has optic, chemical and photocatalytic properties close to properties of titanium dioxide produced by a different way. The production of such aerosol in direct place of a technogenic catastrophe can be made for the cleaning of atmosphere near a pollution source.

Abstract:
Under study is the problem of optimum allocation of a resource. The following is proposed: the algorithm of dynamic programming in which on each step we only use the set of Pareto-optimal points, from which unpromising points are in addition excluded. For this purpose, initial approximations and bilateral prognostic evaluations of optimum are used. These evaluations are obtained by the method of branch and bound. A new algorithm “descent-ascent” is proposed to find upper and lower limits of the optimum. It repeatedly allows to increase the efficiency of the algorithm in the comparison with the well known methods. The results of calculations are included.

Abstract:
Superposition of signals in DNA molecule is a sufficiently general principle of information coding. The necessary re-quirement for such superposition is the degeneracy of the code, which allows placing different messages on the same DNA fragment. Code words that are equivalent in the informational sense (i.e., synonyms) form synonymous group and the entire set of code words is partitioned into synonymous groups. This paper is dedicated to constructing and analyzing the model of synonymous coding. We evaluate some characteristics of synonymous coding as applied to code words of length two although many definitions may be extended for words of arbitrary length.