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Urtenov Makhamet Khuseyevich
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Articles count: 43
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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

01.00.00 Physicalmathematical sciences
DescriptionIn the article we have derived mathematical models of nonstationary 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 NernstPlanck. 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

Description
This article analyzes the boundary problem model of transport of binary electrolyte membrane systems in the approximation of Ohm's law. Different methods of solution are proposed

ANALYSIS OF METHODS OF GENERATION OF TIME SERIES WITH LONGTERM CORRELATION STRUCTURE
01.00.00 Physicalmathematical sciences
DescriptionThis 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

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

Description
This article is a continuation of [1] devoted to the definition of a system of indicators to assess the creditworthiness of Russian regions, obtaining the minimum and the optimal number of clusters for the regions dependent credit index, the construction ofdiscriminant models to assess the creditworthiness of the regions, with the reliability of recognition of 91% and 96%. However, adequate and effective assessment of the state of the region, the model of multivariate statistical analysis is necessary to supplement and use them in conjunction with other models of assessment of the region, such as fuzzy are the production, hybrid systems, neural networks, i.e., create a representative group of methods. Development of fuzzy and fuzzy hybrid (neurofuzzy) systems for the credit assessment of regions subject of this article

RESEARCH OF CREDIT STATUS OF REGIONS BY METHODS OF THE MULTIVARIATE STATISTICAL ANALYSIS
DescriptionThe review of the basic techniques of rating agencies of the Russian Federation and the algorithm of own technique of an estimation of credit status and investment appeal of regions Russian Federations with use of the device of the multivariate statistical analysis is described in this article

01.00.00 Physicalmathematical sciences
DescriptionThis work is a continuation of [1], which was devoted to the investigation of the hydrodynamics of the experimental electrochemical cell with rotating disk cation exchange membrane. This article focuses on the transport of salt ions in a closed cell at different initial experimentation with modes of exact current regimes. The main regularities of transport of salt ions and membrane equal accessible surface were set