# Researches

## New method of computer-aided screening and diagnosis of oncological diseases of mammary and thyroid gland

New computer-aided diagnosis of breast cancer and fibroadenomatosis based on the effect of deviation of morphometrical and cytospectrophotometrical indecies of interphase nuclei of sick patients’ oral mucous from those of healthy individuals (malignancy associated changes) is proposed. At the first stage, we take scrapes from oral mucous of patients. Then, we obtain investigated indecies on the basis of DNA scanogramm…

## Numerical method for complex fluid dynamics with phase transitions

Method of direct numerical modeling for some heterogeneous fluid dynamics is presented. It is supposed that the fluids are compressible and inviscid (non-viscous). Heterogeneities of the fluids are considered as small drops or particles of one fluid within other fluid. Total number of the drops may be large enough and the drops may have phase transitions. Thus simulations of the…

## Vanishing viscosity asymptotics for Stokes equations.

This paper deals with the properties of solutions to initial–boundary value problems for the nonstationary Stokes equations with vanishing viscosity in a bounded three-dimensional domain. We determine the initial terms in asymptotic expansions of solutions at vanishing viscosity and give error estimates for such approximate expansions. The study of the properties of solutions to fluid dynamics problems with vanishing viscosity…

## Homogenization of Navier-Stokes equations with oscillating data.

We consider initial boundary value problems for unsteady Navier- Stokes equations with periodic data rapidly oscillating with respect to the spatial variables, when the oscillations are zero in mean. The problems are stated in bounded domains that are three-dimensional, for example. The period of data oscillations is specified by a positive small parameter ?and a viscosity coefficient ?in equations of…