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Urtenov Makhamet Khuseyevich
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professor
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Articles count: 43
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01.00.00 Physicalmathematical sciences
DescriptionMicro 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 twodimensional Stokes equation to calculate the flow of the electrolyte, and onedimensional equations of NernstPlanck 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 twodimensional 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 twodimensional mathematical models of ion transport of salt and electroosmosis in micro and nanochannels formed by selective ionexchange membranes

NUMERICAL SOLUTION TRANSPORT MODEL BINARY ELECTROLYTE IN APPROXIMATION OF OHM'S LAW
DescriptionThe article is devoted to the numerical solution of boundary value problem of the binaryelectrolyte model of transport in membrane systems in the approximation of Ohm's law. Different numerical methods are offered. The main regularities of transfer are established

01.00.00 Physicalmathematical sciences
DescriptionThe phenomenon of electro convection in membrane systems is of considerable interest, because it is, according to many authors, the main mechanism of overlimiting mass transfer. A great number of theoretical and experimental works, in which, as a rule, dimensional values were used, are devoted to electro convection study. Because of that, in actual fact, there is investigated the influence of individual factors on the transfer process. For example, the influence of voltage jumps, the average speed of a forced stream of the solution, the geometric characteristics of the channel, the initial concentration, etc. However, the influence of these factors appears not separately, at the same time. Thus, there is the problem of introducing dimensionless complexes of dimensional values that have a physical meaning and that allow to evaluate the inner links of the process. As it is known, for solving that problem, there is applied a theory of similarity, based on the transition towards dimensionless parameters in equations and formulas describing the process, and using values, typical of the system under study. This work is devoted to the determining of physical meaning of similarity criteria of salt ions processes, taking into account electro convection in the desalting channel of electro dialysis apparatus. The channel is bounded with perfectly selective, homogeneous anionexchange and cationexchange membranes. The introduced similarity criteria are used so as to conduct the theoretical study of the effect of a number of parameters of a desalting process on electro convection

01.00.00 Physicalmathematical sciences
DescriptionIn the article, we have suggested a general mathematical model of nonstationary and nonisothermal process of a binary electrolyte transfer in dilute solutions in an electromembrane system (EMS), taking into account the joint action of gravitational convection, forced convection and electro convection in potential dynamic mode. This model is a boundary problem for a system of twodimensional quasilinear NavierStokes equation and NernstPlanckPoisson in partial derivatives equation. We have developed a theory of similarity of the process of heat and mass transfer in electromembrane systems, specifically, in a desalting channel of electro dialysis apparatus, taking into account joint actions of concentration polarization, space charge, gravity convection, forced convection and electro convection. It is shown that the criterion of electro convection does not directly depend on the initial concentration, and, therefore, electro convection occurs at any initial concentration. At the same time, the criterion of concentration convection linearly dependents on the initial concentration, and, therefore, at high concentrations, concentration convection prevails, while at lower concentrations, the role of gravitational convection begins to fall whereas the role of electro convection increases. The theory of similarity of the process of heat and mass transfer in the desalting channel of electro dialysis apparatus built in this work taking into account the joint action of concentration polarization, space charge, gravity convection, forced convection and electro convection is important for engineering calculations, for scaling the results of experiments in an electromembrane cell for industrial electro dialysis water desalting apparatus

COMPARATIVE ANALYSIS OF METHODS OF ESTIMATION OF THE INCONSISTENCY OF AGRICULTURAL ENTERPRISES
DescriptionIn 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

Description
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 KarachaevoCircassian Republic

Description
The article provides an overview of the basic rating methodologies, describes an algorithm of the own methodology for estimation the creditworthiness and investment attractiveness of the agricultural enterprises of Krasnodar region, using modern mathematical models. The rating of 30 agricultural enterprises of various patterns of ownership and scale is presented. The rating of 30 agricultural enterprises of various patterns of ownership and scale is presented

CALCULATION AND ANALYSIS OF TIME BEHAVIOR OF ELECTROCONVECTION IN MEMBRANE SYSTEMS
01.00.00 Physicalmathematical sciences
DescriptionThe 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 currentvoltage 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 cationexchange membranes. The Hurst numbers for different parts of the currentvoltage curve were calculated in order to determine whether the parts were persistent. The Fourieranalysis of the oscillating term of the currentvoltage 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 crosssection 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 crosssection of the desalting channel. The oscillations of the currentvoltage curve were physically interpreted. Namely, it was shown that the main frequency of oscillations of the currentvoltage 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 crosssection of the desalting channel

THE DEVELOPMENT OF COUNTRIES' CREDIT RATING ASSESSMENT SYSTEM
01.00.00 Physicalmathematical sciences
DescriptionThis work presents a new approach to the countries’ credit rating definition, based on the advanced mathematical models, such as neural network model, multiple regression, cluster analysis and discriminant analysis. A range of the analyses such as discriminant, cluster, multiple regression models and a neural network were performed on the following economic figures: GDP per capita, GDP value, annual growth rate of GDP, FDI  foreign investment, rate of unemployment, consumer price inflation index, the size of government debt in percentage of GDP. The results, obtained for each model were combined in the countries’ credit rating estimation system called "7M"

01.00.00 Physicalmathematical sciences
DescriptionIn 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