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Urtenov Makhamet Khuseyevich
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Articles count: 43
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05.13.18 Mathematical modeling, numerical methods and software complexes
DescriptionThe article presents ways to estimate the socioeconomic condition of the subjects of the Russian Federation using fuzzy production systems, discriminant analysis and neural networks. This study is based on the thirteen indicators of the socioeconomic condition of the regions of the Russian Federation identified by RIA Rating rating agency. The goal of the work is to develop a software package combining the estimation methods above and allowing to get three alternative estimation options for a subject of the Russian Federation, using these thirteen indicators. The developed program assigns each region an estimation from the following set: AAA– the highest socioeconomic condition, AA  very high, A– high, BBB– above average, BB– average, B– below average, CCC– low, CC– very low, C– the lowest indicators of the socioeconomic conditions in the region of the Russian Federation. The software package is developed in Matlab and has an intuitive interface. The results can be used as an alternative to current methods of estimation of the socioeconomic indicators

FINANCIAL RISK WARNING AT OIL PRODUCTION COMPANIES
08.00.13 Mathematical and instrumental methods of Economics
DescriptionThis article is devoted to a problem of effective management of a financial and economic condition of companies on the example of the enterprises of oil products supply. We consider questions of support of adoption of management decisions which concern stabilization of a financial condition of the company and as a result of decrease in financial risks. The article also provides a description of the program complex called FESP_ON developed by the authors allowing to carry out the profound complex assessment of a financial and economic condition of Societies of oil products supply

01.00.00 Physicalmathematical sciences
DescriptionAn analysis of the experimental data obtained by the authors, as well as reference books, allowed to hypothesize about the essential role of gravitational convection in electromembrane systems with ampholytes even in underlimiting current regimes. The article is devoted to the development of the mathematical model of ion transport in a flow elecrtomembrane system during electrodialysis of ampholytecontaining solutions with taking into account a possible appearance of gravitational convection, in particular, due to nonisothermal protonation–deprotonation reactions of ampholytes. The article presents the boundary value problem that is the new mathematical model for diffusion, convection and electromigration of four components of the solution (ions of sodium, dihydrogen phosphate and hydrogen, as well as molecules of orthophosphoric acid) in a half of an electrodialysis desalination channel, adjacent to an anionexchange membrane. The membrane is considered as ideally selective and homogeneous. The system of partial differential equations, that is the base of the model, also includes equations of NavierStokes, material balance, convective heat conduction and the electroneutrality condition. The system of equations is supplemented by a number of natural and original boundary conditions. A distinctive feature of this study is the absence of assumptions about the equilibrium of chemical reactions in a diffusion layer. The results of the study can be used for the development of environmentally rational and resource saving membrane technologies for a processing of products of agroindustrial complex

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
DescriptionThe influence of dissociation / recombination of water molecules is important for understanding electroconvection processes, as some authors believe that the emergence of new carriers + H and − OH , and can lead to a reduction in the spacecharge and, consequently, to electroconvection disappearance. However, as shown in [5], the dissociation of water molecules, although it reduces the space charge and increases the threshold fall potential jump at which begins electroconvection, yet it persists and effectively mixes the solution. This article is devoted to mathematical modeling of electrodiffusion of four types of ions at the same time (two salt ions as well as + H and − OH ions) in the diffusion layer in electromembrane systems with perfectly selective membrane under the joint influence of violation of electrical neutrality, and the reaction of dissociation / recombination of water molecules, development of mathematical models of these processes, building efficient algorithms asymptotic and numerical analysis for different types of electrolytes. The work proposes a new mathematical model of the process of transfer of salt ions in view of the space charge and the dissociation / recombination of water in the form of a boundary value problem for a system of ordinary differential equations. This system is reduced to a form convenient for numerical solution. We have calculated the required additional boundary conditions for the electric field. Numerical and asymptotic solution of the boundary value problem and physicochemical analysis of the influence of dissociation / recombination on the transfer of salt ions is expected to devote the next part of the work

01.00.00 Physicalmathematical sciences
DescriptionThis article is a continuation of the previous works of the authors [The influence of reaction dissociation / recombination of molecules of water on transportation of electrolyte 1:1 in the membrane systems in the diffusion layer. Part 1. Mathematical model // Scientific journal of Kuban State Agrarian University, 2016. No. 07(121) and The influence of the reaction of dissociation / recombination of molecules of water on transportation of electrolyte 1: 1 in membrane systems in the diffusion layer. Part 2. Asymptotic analysis // Scientific journal of Kuban State Agrarian University, 2016. – №08(122)] and devoted to assessing the possibility of gravitational convection due to the recombination of hydrogen and hydroxyl ions. The article presents the solution of a boundaryvalue problem, which is a mathematical model of electrodiffusion for the four types of ions at the same time (two ions of salts and hydrogen and hydroxyl ions) in the diffusion layer in electromembrane systems with ideal selective membrane, with the heat transfer equation and the NavierStokes equation. The article shows the possibility of the emergence of gravitational convection due to the exothermic reaction of recombination of water molecules in the depth of the solution. The article considered the reaction of recombination of hydrogen ions and hydroxyl, although the main results can be applied, after appropriate modifications, and to amfolitcontaining solutions, such as wine, juices, dairy products, microbiological processing of biomass (amino acids, anions of polybasic carboxylic acids), municipal effluent (anions of phosphoric acid), etc.

01.00.00 Physicalmathematical sciences
DescriptionThis article is devoted to the asymptotic analysis of boundary value problem for a system of equations of NernstPlanck and Poisson for a singularly perturbed system of ordinary differential equations [1], based on two parameters. This boundary value problem simulates electrodiffusion of four kinds of ions at the same time in the diffusion layer in electromembrane systems with perfectly selective membrane, taling into consideration the reaction of recombination of two ions. Meanwhile the other two ions represent ions of a binary salt. As a simple example, we consider the transport of ions sodium, chlorine, hydrogen and hydroxide, moreover, hydrogen and hydroxyl ions recombine in the diffusion layer. A more complex case is the transfer of the products of dissociation of the dihydrogen phosphate of sodium, namely, ions of sodium and dihydrogen phosphate, the latter dissociate at the interface, in turn, hydrogen ions and hydrogen phosphate. Thus, in the solution can simultaneously store three different types of ions: sodium, hydrogen, phosphate. During the transfer, hydrogen ions and ions of hydrogen phosphate recombine to produce phosphoric acid. The article has revealed the structure of the Nernst diffusion layer at currents above Harkatsa current. It is shown, that in the diffusion layer, there are two types of boundary layers: the inner (reaction) boundary layer and boundary layer at the interface solution / membrane

01.00.00 Physicalmathematical sciences
DescriptionThis article describes a mathematical model of transport of salt ions in a cell with a rotating disk cation exchange membrane at transcendent current regimes, taking into account electroconvection. Based on this model, we had a theoretically study of the process of transfer of salt ions and the dependence of the thickness of the diffusion layer from the fall of potential. This article is a continuation of [8] and [9], it conducted a numerical analysis of boundary value problem for a system of equations NernstPlanckPoisson and NavierStokes equations, modeling the transport of salt ions in a cylindrical cell with a rotating disc cation exchange membrane based on electroconvection. It is shown there is an electroconvection vortex in the center of the membrane disc. The solution flows around this vortex and forms a stagnation zone in front of it. With the increase in the size of the fall of potential, the electroconvective vortex decreases and at some value, the electroconvective vortex disappears. The study was conducted in the 1000 s when the angular velocity of 30 turns in a minute and change of the potential difference of 0.2V to 1.4V with a step 0.1. As a result, in this study it is shown that the thickness of the diffusion layer is practically linearly dependent on the fall of potential. The linear dependence of the thickness of diffusion layer from the fall of potential, in the first approximation, is disturbed by a slight deflection curve, the causes of which are needed to be found by means of extra experiments

01.00.00 Physicalmathematical sciences
DescriptionThere 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 twodimensional nonstationary ion transport binary salt in a smooth rectangular channel desalting electrodialysis device using equations NernstPlanckPoisson, heat conduction and NavierStokes 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 boundaryvalue problems for a nonlinear system of partial differential equations

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