Scientific Journal of KubSAU

An 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 ampholyte-containing 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 anion-exchange 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 Navier-Stokes, 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 agro-industrial complex

The article’s conclusion is that for adequate and effective inflation modeling in Russia by means of modern neuronet technologies it is necessary to consider tendencies of economic development. For training and forecast, it is necessary to use only those periods of time within the limits of which identical economic tendencies work. The article uses modern tool means, such as neuronet, which is offered to technology, for approximation and forecasting of rates of inflation

In this article, a mathematical model of the dynamics of the efficiency of arbitration courts of Russian Federation in the form of the Cauchy problem for systems of difference and differential equations is built. The main regularities of the dynamics of the efficiency of arbitration courts are found

In this article, the author's approach for research of financial and economic crisis of the enterprises with use of canonical catastrophe of a fold and assemblage is offered. Mathematical models of development of crisis at the enterprise at different levels of detailed elaboration: 1) at an estimation of liquidity and solvency, financial stability, business activity, profitability; 2) at an estimation of the general financial and economic condition of the enterprise; 3) for construction of potential of development of enterprise are offered

This article continues the works [1,2], devoted to the theoretical study of the basic laws of electroconvection caused by natural or artificial inhomogeneous conductivity of ion-exchange membranes in a smooth rectangular channel electrodialysis desalination unit. For this purpose, a mathematical model was created for a binary electrolyte electroconvection at overlimiting current modes in the form of a boundary value problem for a coupled system of the Nernst-Planck-Poisson and Navier-Stokes equations. We have studied the influence of heterogeneity on the ion-exchange membranes and ion transport electroconvection salt, calculated currentvoltage characteristic. The possibility of intensification of mass transfer due to the surface modification of ion exchange membranes was also shown

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 (neuro-fuzzy) systems for the credit assessment of regions subject of this article

This article analyzes the changes in the number of cases of various clients of the pyramid and the establishment of the basic rules of the pyramid schemes based on discrete models. The article is also a continuation of previous work [1], which had formulas to simulate the amount collected by the pyramid scheme

This article is devoted to the analysis of different cases of changing the number of customers of the financial pyramid and the establishment of the basic rules of the pyramid schemes on the basis of continuous models, and it is a continuation of works [1, 2], which had formulas to simulate the amount collected by the pyramid scheme and it considers the discrete models

The article analyzes the various approaches to the mathematical modeling of financial pyramids. It considered “economically rational subject”, game approach and the approach of Dubovsky. In this article, the mathematical models of the unproblematic approaches examined; we also analyzed their characteristics, including the dependence of the lifetime of the pyramid of accrued interest and the number of clients, the maximum possible profit of the founders of the pyramid, etc. This work analyzes the various options of the campaign, including whether the implicit advertising company, which arises from the spread of the financial company clients and rumors about their income

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