Scientific Journal of KubSAU

The 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 space-charge 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 physico-chemical analysis of the influence of dissociation / recombination on the transfer of salt ions is expected to devote the next part of the work

This 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"

This 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 Nernst-Planck-Poisson and Navier-Stokes 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

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

We propose a mathematical model of ion transport binary salt in electroosmotic flow in a capillary. The capillary is open on one side and immersed in a vessel of large volume, in which the concentration of the solution is maintained constant, and the other side closed ion exchange membrane. The walls are considered wettable, i.e. the solution adheres to the walls. This means that the mathematical modeling used to rate the condition of sticking. We study the boundary value problem for a coupled system of equations Nernst, Planck, Poisson and Navier-Stokes equations. Used boundary conditions of general form. The mathematical model is based on the general laws of transport and contains no adjustable parameters. Using this model, the basic laws of ion transport salt solution liquid flow, the emergence and development electroconvection, distribution of concentration of salt ions in the capillary with a small change in time, ie, in the initial (transitional) regime. We have identified the presence of ion-exchange membrane surface electroconvective vortices and their influence on the mechanisms of ion transport of salt and fluid movement in different areas of the capillary. A feature of the capillary transport is to the right of the vortex region stagnant areas with a higher concentration of ions

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

For effective management of economic and financial activity of a modern enterprise it is required to have information – software supply for its separate components: branches, divisions, services. Automation of the account allows accelerating significantly the process of granting, processing and the analysis of information necessary for the purposes of management. An important aspect on introduction of a program complex is the concept on its realization, i.e. the head of the company should define the way of development of automation of business - processes, what type of introduction is more preferable to the enterprise, what documents will formalize each of the stages. The article generalizes the data obtained by practical consideration on the basis of the realized projects on introduction of the automated systems in the companies from various fields of activity. The main stages of the design direction in the sphere of automation of business – processes are presented in this work, as well as the features of the subject and the characteristics of each stage, documentary objects for realization of each of them. Also on the basis of the carried-out analysis, the authors described a number of the existing shortcomings on realization of the design direction. In view of the data specified in article, the companies will be able to begin the project on automation of their own business effectively and quickly

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

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