Scientific Journal of KubSAU

The article presents a new approach to 2D modeling of transport of salt ions in EMC (electro systems: electrodialysis devices, electro-cells, etc.) under the condition of electrical neutrality with limiting and overlimiting current density. For definiteness as seen half of EMS channel EDA desalting (electrodialysis apparatus), the right border, which serves as a CEM (cation exchange membrane). The new approach in the use of partial differential equations of the first order, instead of equations of convective diffusion. A common method of transport modeling binary electrolyte in the EMS under the condition of electrical neutrality, is to use the equation of convective diffusion (partial differential equations of the second order). The article presents a new approach to modeling 2D transfer binary electrolyte in EMS under the same conditions, using partial differential equation of the first order for the decision, which does not require a boundary condition for concentration on the membrane surface. This allows you to simulate the transport of salt ions, as in prelimit and exorbitant current density and to determine the boundaries of the field of electrical neutrality

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

In the article an effective system of an estimation of a financial and economic status of the factories of a building sector of Krasnodar region (Armavir district), based on use of methods of the multidimensional statistical analysis is introduced. The programmatic complex "FAP-stroi", including MS Excel plug-in, macros of «Statistica 6» and exterior processing of «1С: Enterprise 8» is built

The modern Russian companies have realized the need of automation of document flow not only as a mean of keeping documents in order, but also as a tool of optimization of expenses, as an assistant in adoption of administrative decisions. The Russian market of information systems for long time had no software products intended for educational institutions. The majority of the automated systems are intended for the enterprises with an activity in the sphere of trade and production. In comparison with the above companies, the list of software products for commercial training centers is small. Even considering the developed line of programs it is impossible to speak about meeting all the requirements for companies of such activity. At creation of the automated system for training center, the analysis of the existing software products intended for automation of training centers and adjacent institutes was carried out; a number of features of activity are revealed. The article is devoted to the description of the developed automated information system of document flow of a commercial educational institution, namely the developed configuration of "Training center" on a platform of "1C: Enterprise 8.2". The developed program complex serving as the administrative tool for the analysis of economic activity of training center, scheduling of the educational equipment and teaching structure, payroll calculation taking into account specifics of branch has been presented in the article

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

The article provides a comparative analysis of assessments of the socio-economic development of the Krasnodar region from such well-known rating agencies as Standard & Poors, Moody’s, Fitch Ratings, which belong to the United States of America. The studied ratings are compared with the ratings of the national agency of the Russian Federation called “Expert RA”. The values of the established ratings are examined, as well as number of possible reasons why the ratings of the United States of America differ from the ratings of the Russian Federation, for example, economic and political reasons, and, subsequently, how these ratings affect the investment attractiveness of the Krasnodar region. The article explains positive and negative aspects of the integrated methodology used by international rating agencies, consisting of software and expert opinion, the level of access to it for study and analysis. We study another (local) source of information on the investment attractiveness of the Krasnodar region, which is a state institution, namely the Department of Investments and Development of Small and Medium Enterprises of the Krasnodar region. Options are proposed for improving the system of analysis of statistical data through methods that are based on a clear mathematical approach to provide an adequate assessment of the region and municipalities without the influence of subjective expert opinion