Kuban State University
Author list of organization
List of articles written by the authors of the organization
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01.00.00 Physical-mathematical sciences
DescriptionThis article investigates hydrodynamic of experimental electrochemical cell with rotating disk in the cation exchange membrane. We have also investigated the flow in open, with the free surface of the solution and in hermetically closed cells. The main regularities of the hydrodynamics of the experimental cell at its real size were set
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01.00.00 Physical-mathematical sciences
DescriptionIn the article we build a mathematical model of elec-tro-diffusion of ions in the diffusion layer of a mem-brane system complicated by the occurrence of the previous slow homogeneous chemical reaction with the condition of electrical neutrality of the solution. We have set a two-point boundary value problem and developed a method to solve it; we have given an algorithm and a numerical method for solving it in Comsol 3.5 environment. The formula for limiting kinetic current was derived. Some of the model’s capabilities to describe the properties of the system are given
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MATHEMATICAL MODELING OF ANTIBACTERIAL IMMUNE REACTION
DescriptionThe work describes the mathematical model of an antibacterial immune reaction, which is presented as a system of integral-differential equations. The global characteristics of the adequacy of the model to the real process are studied
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01.00.00 Physical-mathematical sciences
DescriptionThe article presents a mathematical model of the effect on ion transport electro convection salt in non-smooth camera channel desalting electro dialysis apparatus in the presence of forced convection. The basic rules of process of electro convection are revealed
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Description
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
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Description
The models of the estimation advertising effectiveness are reviewed and analyzed in the paper. The algorithm and example of the program’s work, which determines financial performance of the company with taking into account advertising investments is described and the mostly important results are discussed
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MATHEMATICAL MODELING OF ELECTROCONVECTION IN THE CAPILLARIES. TRANSIENT BEHAVIOR
01.00.00 Physical-mathematical sciences
DescriptionWe 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
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01.00.00 Physical-mathematical sciences
DescriptionIn 1893, the French mathematician J. Adamar raised the question: given a matrix of fixed order with coefficients not exceeding modulo this value, then what is the maximum modulo value can take the determinant of this matrix? Adamar fully decided this question in the case when the coefficients of the matrix are complex numbers and put forward the corresponding hypothesis in the case when the matrix coefficients are real numbers modulo equal to one. Such matrices satisfying the Hadamard conjecture were called Hadamard matrices, their order is four and it is unknown whether this condition is sufficient for their existence. The article examines a natural generalization of the Hadamard matrices over the field of real numbers, they are there for any order. This paper proposes an algorithm for the construction of generalized Hadamard matrices, and it is illustrated by numerical examples. Also introduces the concept of constants for the natural numbers are computed values of this constant for some natural numbers and shown some applications of Hadamard constants for estimates on the top and bottom of the module of the determinant of this order with arbitrary real coefficients, and these estimates are in some cases better than the known estimates of Hadamard. The results of the article are associated with the results of the con on the value of determinants of matrices with real coefficients, not exceeding modulo units
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Description
In this article, we examine questions about realization of interdisciplinary connections in the process of teaching of mathematics the students of economic specialties. Taking into account the circumstance that economic specialties are integrating information from mathematical, natural, humanitarian and socioeconomic disciplines, going near the selection of maintenance of course of mathematics must be oriented to the mathematical apparatus for all cycles forming certain abilities and skills. Thus, in the process of teaching mathematics we have to emphasize the necessity of maintenance of "vertical" connections in a course mathematics, marking that maintenance of flat rate of mathematics can not be certain from the cleanly pragmatic point of view, based only on the specific of future specialty of studying, without the account of internal logic of mathematics, id est., from a course mathematicians we must not eliminate questions and divisions, not having a direct professional orientation, but providing internal subject connections or the logic of the discipline. Accordance to the criterion of internal subject integrity means, that maintenance of the course of mathematics will not grow into totality of fragmentary information necessary for the special preparation, and will possess necessary plenitude, logical uncontradiction and sequence. On the other hand, it is necessary to accent attention on the study of the different processes and phenomena, lighted up in general professional disciplines, as studying of all these questions must be of the ponderable use in the professional becoming of future specialist, i.e. the special importance is acquired by interdisciplinary integration connections at the level of which the applied professional orientation of the studied material comes true
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Description
The article points to the fact that the structurization of the meso-environment has debatable character, and instruments of its investigating are not developed. Because of this reason the following hypothesis of a research is formulated: basis system approach which is connected with expert approach, with methods of processing of diverse qualitative information and transition to measurement of factors in metric system in items of information in bits determines objectivity of the analysis and increases of reliability of a research of the external environment of corporation. The offered model structure of the meso-environment contains: regional legislation, specifics of regional economy, regional community and human capital, regional resources, regional communication environment, features of regional commodity market and services, infrastructure of the regional market, development of small business, etc. Features of its investigating are considered. The method of MesoOT analysis of the regional environment is offered. Application of numerical score of factors and involvement of experts to its development during the analysis is proved. The need to develop of the scale for measuring of diverse regional factors in information units using the well-known intellectual system "Eidos-X ++" is discussed in this article. The version of the analysis of the regional environment (meso-environment) is developed and presented in matrix form of MesoOT analysis in the adapted structure of "researches" to features of the agrarian and industrial region