#### Name

Urtenov Makhamet Khuseyevich

#### Scholastic degree

•

#### Academic rank

professor

#### Honorary rank

â€”

#### Organization, job position

Kuban State University

#### Web site url

â€”

## Articles count: 43

There is a 2D mathematical model of ion transport
binary salt with the main conjugate effects of
concentration polarization in the overlimiting current
mode: the bulk charge and the dissociation/
recombination of water, gravity and electroconvection
and Joule heating the solution in the form of a
boundary value problem for systems of differential
equations with partial derivatives in the article. This
system is presented in a form convenient for numerical
solution. We describe the necessary boundary
conditions. This article presents a theoretical study of
the interaction of forced, gravitational and
electroconvection, the dissociation / recombination of
water molecules, and Joule heating of the solution and
heat transport through membranes. We have
constructed a mathematical model of two-dimensional
non-stationary ion transport binary salt in a smooth
rectangular channel desalting electrodialysis device
using equations Nernst-Planck-Poisson, heat
conduction and Navier-Stokes equations and the
natural boundary conditions. For numerical solution
we use the finite element method, with the splitting of
task at each new time layer into three subtasks:
electrochemical, thermal conductivity, hydrodynamic.
Such approach to the development of numerical
methods is the original and can solve arising in
modeling boundary-value problems for a nonlinear system of partial differential equations

In the article we have derived mathematical models of non-stationary transport binary electrolyte in EMS (electromembrane systems: electrodialysis apparatus, electromembrane cell, etc.) for the galvanostatic mode. To be specific, as EMS viewed channel of desalting of EDA (electrodialysis apparatus) and EMS with RMD (rotating membrane disk). We present a formula expressing the intensity of the electric field through the current density and concentration. Also, we have received the differential equation for the current density. The fundamental point here is derived new equation for the unknown vector function of current density of the initial system of equations of Nernst-Planck. In addition, the article shows the output equation for the current density in three dimensions; we have proposed various methods for solving the equation of the current density and the boundary conditions for the current density. The proposed mathematical models of transport binary electrolyte are easy to be generalized to an arbitrary electrolyte. However, the corresponding equations are cumbersome. It should be also noted that the boundary conditions can be varied and depend on the purpose of a particular study in this regard, in this work are just the equation having the general form

This article gives a comparative analysis of six modeling techniques of fractal differential noise, including: direct definition method, the method of Hosking, the method of Davis and Hart's, the circulant embedding method, Paxson method and method of spectral simulation. Furthermore, the algorithms are given for the analysis and the method of estimation of Hurst`s parameter is selected, this method is the main criterion of quality when comparing the above mentioned methods of fractal differential noise

The aim of this work is to carry out numerical analysis of time behavior of electroconvection in membrane systems, such as a desalting channel of electrodialysis apparatus. The current-voltage curve and the solution flaw were analyzed theoretically using mathematical models of ions transfer taking into account electroconvection in smooth desalting channel consisting of ideally selective anion- and cation-exchange membranes. The Hurst numbers for different parts of the current-voltage curve were calculated in order to determine whether the parts were persistent. The Fourier-analysis of the oscillating term of the current-voltage curve was carried out for the first time so as to determine predominant frequencies in the signal. Frequencies of passing of complexes of vortexes through the cross-section of the desalting channel were calculated. Frequencies of oscillations of concentration profiles were determined. It was found that the frequencies of oscillations of the concentration profiles coincide with the frequencies of passing of complexes of vortexes through the cross-section of the desalting channel. The oscillations of the current-voltage curve were physically interpreted. Namely, it was shown that the main frequency of oscillations of the current-voltage curve corresponds to the frequency of oscillations of the concentration profiles. The oscillations of the concentration profiles, produced by the passing of complexes of vortexes, cause oscillations of conductivity and, consequently, cause oscillations of resistance and of the current density. It was shown that the main frequency of the signal corresponds to the frequency of passing of complexes of vortexes through the cross-section of the desalting channel

The article is devoted to the use of methods of cluster analysis, such as multivariate statistical, indistinct and neuronet, for an estimation of financial and economic condition of middle and small enterprises of building branch of Krasnodar region, and also to revealing of the reasons and laws of occurrence and development of crisis at these enterprises

The results of cluster analysis of the operational functioning of the Russian arbitration courts of various instances are shown, and the new mathematical model of discriminant analysis to measure the efficiency of arbitration courts are presented

The article is devoted to a problem of the analysis of economic and financial activity of region, an estimation and diagnostics of its social condition, to the analysis of investment appeal, credit status and potential of development by means of modern mathematical methods, models, tools, means and intellectual systems, on an example of Karachaevo-Circassian Republic

In the article, the analysis of inconsistency of agricultural enterprise is carried out by various methods. The hypothesis about absence of a universal method of an estimation of the inconsistency, yielding authentic result is proved

In this article, we describe a modification of the design pattern of "Strategy", which informs customers about the different types of algorithms (strategies) without disclosing the features of their implementation, as well as allows you to control compliance with the algorithms and methods. In addition, the architecture of the algorithms and methods that use the above modification is described in details

Micro and nanofluidics are the new multidisciplinary
sciences. One of the tasks of which is creation and
management of flow of fluid in the thin channels size
of a few nano- or micrometer which exposed the
external electric field, where the walls are the ion
exchange membrane. Electroosmosis
(electroconvection) plays an important role in these
tasks. A large number of articless were devoted to
electroosmosis. One of the first, Dukhin S.S.,
Mishchuk N.A. and Rubinstein I. gave a theoretical
explanation of the overlimiting current by
electroosmosis. They used two-dimensional Stokes
equation to calculate the flow of the electrolyte, and
one-dimensional equations of Nernst-Planck and
Poisson to calculate the electric power. These
researches have multiple limitations because of the
computational complexity the mathematical
simulation. Thus, there is an actual problem of the
asymptotic solution of boundary value problems for
the two-dimensional systems of equations of NernstPlanck
and Poisson without these restrictions. These
researches we derived in simplified models of
electroosmosis in galvanic dynamical mode using the
decomposition method. We have created a hierarchical
system of two-dimensional mathematical models of
ion transport of salt and electroosmosis in micro- and
nanochannels formed by selective ion-exchange
membranes