Scientific Journal of KubSAU

Polythematic online scientific journal
of Kuban State Agrarian University
ISSN 1990-4665
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425 kb

NON-STATIONARY 2D MODEL OF THE GRAVITATIONAL CONVECTION IN ELECTRODIALYSIS OF AMPHOLYTECONTAINING SOLUTIONS

abstract 1231609116 issue 123 pp. 1697 – 1711 30.11.2016 ru 387
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
218 kb

2D SIMULATION OF THE INFLUENCE ON THE MAIN CONJUGATE EFFECTS ON ION TRANSPORT OF A BINARY SALT IN ELECTRO-MEMBRANE SYSTEMS

abstract 1231609117 issue 123 pp. 1712 – 1727 30.11.2016 ru 704
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
3138 kb

IDENTIFICATION OF VARIETIES OF IRISES BY THEIR APPEARANCE WITH THE USE OF ASC-ANALYSIS AND "EIDOS" INTELLECTUAL SYSTEM (REPOSITORY UCI DATA)

abstract 1231609121 issue 123 pp. 1801 – 1835 30.11.2016 ru 375
The creation of artificial intelligence systems is one of important and perspective directions of development of modern information technology. Since there are many alternatives of mathematical models of systems of artificial intelligence, there is a need to assess the quality of these models, which requires their comparison. To achieve this goal we require free access to the source data and methodology, which allows to convert these data into a form needed for processing in artificial intelligence. A good choice for these purposes is a database of test problems for systems of artificial intelligence of repository of UCI. In this work we used the database "Iris Data Set" from the bank's original task of artificial intelligence – UCI repository, which solved the problem of formalization of the subject area (development of classification and descriptive dials and graduations and the encoding of the source data, resulting training sample, essentially representing a normalized source data), synthesis and verification statistical and system-cognitive models of the subject area, identify colors with classes, which serve varieties of Iris, as well as studies of the subject area by studying its model. To solve these problems we used the automated system-cognitive analysis (ASC-analysis) and its programmatic Toolkit – intellectual system called "Eidos"
811 kb

COMBINATORY METHOD OF NUMBERS′ FACTORIZATION

abstract 1231609122 issue 123 pp. 1836 – 1863 30.11.2016 ru 494
Problem having elementary formulation makes us look for its easier solution. So the combinatorial method of positive integer’s factorization is an attempt to do it. The combinatory method possesses simple algorithm, leading immediately to finding out all the factorizations and identification of all prime numbers on any interval of the positive integers. Prime numbers don’t carry any information except their own magnitude. Composite numbers, possessing divisibility properties provide possibility to discover the law of their distribution. The achievement of this purpose also completely solves the problem of finding out the law of prime numbers’ distribution
188 kb

DERIVATION OF THE EQUATIONS OF THE KINETICS OF PLASMA CHEMICAL PROCESSES INVOLVING ISOTOPES IN A MAGNETIC FIELD

abstract 1231609123 issue 123 pp. 1864 – 1877 30.11.2016 ru 433
Specially formed mixtures of isotopes of chemical elements have better consumer properties than their natural counterparts. Therefore, the development of methods for increasing the efficiency of the known methods for producing of isotope materials is relevant. It is known that the chemical bond is formed only in the singlet state of the spins of valence electrons of the reagents. On the basis of the known representations about dispersion of spin projections on the coordinate axes and the molecular-kinetic theory of gases was obtained an expression for the constant of the chemical reaction between the radicals occurring in the magnetic field. This expression allows calculating the reactivity of the isotopic modifications of radicals. Plasma allows to transfer many of the compounds in the gas phase. It is known that a significant part of particles in low temperature plasma is in a radical form. The equations of chemical kinetics for describing the process of oxidation of the carbon isotopes in argon-oxygen plasma occurring in an external permanent magnetic field were written in the work. It was shown that the efficiency of plasma process of isotopes separation can be increased only under insufficient oxygen relative to the stoichiometric value. These equations of chemical kinetics of processes occurring in the plasma process of incomplete oxidation of carbon isotopes needed to find experimental conditions that provide the maximum isotope effect in a magnetic field
329 kb

MANY-BODY PROBLEM IN THE METRIC OF CIRCULAR DISTRIBUTED SOURSES

abstract 1231609132 issue 123 pp. 1985 – 2006 30.11.2016 ru 387
In this article we consider the many-body problem in general relativity in the case of the distribution of N singularities on the circle. It specifies the exact solution of the problem for an arbitrary distribution of singularities. It is shown that the static metric of N singularities corresponds to Newton's theory of N centers of gravity, moving around the central body in a circular orbit in a non-inertial frame of reference, rotating with a period of bodies revolving. We consider the statement of the problem of many bodies distributed at the initial time on the circle. In numerical calculations, we studied the properties of the gravitational potential in the problem of establishing a static condition in which multiple singularities retain the initial position on the circle. This is achieved due to relativistic effects, which have no analogues in Newton's theory of gravitation. Using the properties of relativistic potentials justified transition from the relativistic motion of the particles to the dynamic equations in the classical theory. A system of non-linear parabolic equations describing the evolution of the metric in the Ricci flow proposed. The problem of the calculation of the potentials in the Ricci flow formulated. The application of the theory to describe the ring galaxy, planetary rings and the asteroid belt considered
495 kb

DYNAMICS OF RELATIVISTIC PARTICLES IN THE RING AND SPIRAL GALAXY METRIC

abstract 1231609143 issue 123 pp. 2136 – 2162 30.11.2016 ru 340
In this work, we examine the dynamics of relativistic particles in the ring or spiral galaxy metric in general relativity. On the basis of the solution of Einstein's equations we have derived metric having axial symmetry, comprising N centers of gravity and a logarithmic singularity. The application received metrics to describe the motion of particles in a spiral and ring galaxy. On the basis of Einstein's equations solutions for vacuum we are explained rotation of matter in spiral galaxies. An expression for gravitation potential in the inner region of spiral galaxies in agreement with experimental data on the rotation of the CO and hydrogen is described. It is established that in the metric with N centers of gravity which are distributed on the circumference, exist as a local motion near the center of gravity, and motion around N gravity center as well. The transition from one mode of motion to another is determined by the initial distance to the circle on which the distributed centers of gravity. A system of non-linear parabolic equations describing the evolution of the metric in the Ricci flow proposed. The boundary problem for the gravitational potentials in the Ricci flow was formulated. There are applications of the theory to describe a spiral and ring galaxy
12261 kb

A SCIENTOMETRIC INTELLIGENT MEASURING SYSTEM OF RSCI DATA BASED UPON THE ASK ANALYSIS AND EIDOS SYSTEM

abstract 1221608014 issue 122 pp. 157 – 212 31.10.2016 ru 588
Adequate and effective assessment of the efficiency, effectiveness and the quality of scientific activities of specific scientists and research teams is crucial for any information society and a society based on knowledge. The solution to this problem is the subject of scientometrics and its purpose. The current stage of development scientometrics differs greatly from his previous appearance in the open as well as paid on-line access to huge amount of detailed data on a large number of indicators on individual authors and on scientific organizations and universities. The world has well-known bibliographic databases: Web of Science, Scopus, Astrophysics Data System, PubMed, MathSciNet, zbMATH, Chemical Abstracts, Springer, Agris, or GeoRef. In Russia, it is primarily the Russian scientific citing index (RSCI). RSCI is a national information-analytical system, accumulating more than 9 million publications of Russian scientists, as well as the information about citation of these publications from more than 6,000 Russian journals. There is too much information; it is so-called "Big data". But the problem is how to make sense of these large data, more precisely, to identify the meaning of scientometric indicators) and thus to convert them into great information ("great information"), and then apply this information to achieve the objective of scientometrics, i.e. to transform it into a lot of knowledge ("great knowledge") about the specific scientists and research teams. The solution to this problem is creating a "Scientific smart metering system" based on the use of the automated system-cognitive analysis and its software tools – an intellectual system called "Eidos". The article provides a numerical example of the creation and application of Scientometric intelligent measurement system based on a small amount of real scientific data that are publicly available using free on-line access to the RSCI
188 kb

THE INFLUENCE OF REACTION OF DISSOCIATION / RECOMBINATION OF MOLECULES OF WATER ON TRANSPORTING ELECTROLYTE 1: 1 IN THE MEMBRANE SYSTEMS IN THE DIFFUSION LAYER. PART 2. ASYMPTOTIC ANALYSIS

abstract 1221608017 issue 122 pp. 241 – 254 31.10.2016 ru 563
This article is devoted to the asymptotic analysis of boundary value problem for a system of equations of Nernst-Planck 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 electro-membrane 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
237 kb

THE PROBLEM OF RESEARCH OF FINAL RANKING FOR GROUP OF EXPERTS BY MEANS OF KEMENY MEDIAN

abstract 1221608055 issue 122 pp. 784 – 805 31.10.2016 ru 502
In various applications, it is necessary to analyze several expert orderings, i.e. clustered rankings objects of examination. These areas include technical studies, ecology, management, economics, sociology, forecasting, etc. The objects can be some samples of products, technologies, mathematical models, projects, job applicants and others. In the construction of the final opinion of the commission of experts, it is important to find clustered ranking that averages responses of experts. This article describes a number of methods for clustered rankings averaging, among which there is the method of Kemeny median calculation, based on the use of Kemeny distance. This article focuses on the computing side of the final ranking among the expert opinions problem by means of median Kemeny calculation. There are currently no exact algorithms for finding the set of all Kemeny medians for a given number of permutations (rankings without connections), only exhaustive search. However, there are various approaches to search for a part or all medians, which are analyzed in this study. Zhikharev's heuristic algorithms serve as a good tool to study the set of all Kemeny medians: identifying any connections in mutual locations of the medians in relation to the aggregated expert opinions set (a variety of expert answers permutations). Litvak offers one precise and one heuristic approaches to calculate the median among all possible sets of solutions. This article introduces the necessary concepts, analyzes the advantages of median Kemeny among other possible searches of expert orderings. It identifies the comparative strengths and weaknesses of examined computational ways
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