№ 122(8), October, 2016
Public date: 31.10.2016
Archive of journal: Articles count 85, 207 kb

01.00.00 Physicalmathematical sciences
01.00.00 Physicalmathematical sciences
DescriptionAdequate 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 online 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 wellknown 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 informationanalytical 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 socalled "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 systemcognitive 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 online access to the RSCI

01.00.00 Physicalmathematical sciences
DescriptionThis article is devoted to the asymptotic analysis of boundary value problem for a system of equations of NernstPlanck 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 electromembrane 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

THE PROBLEM OF RESEARCH OF FINAL RANKING FOR GROUP OF EXPERTS BY MEANS OF KEMENY MEDIAN
01.00.00 Physicalmathematical sciences
DescriptionIn 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

ABOUT THE NEW PARADIGM OF MATHEMATICAL METHODS OF RESEARCH
01.00.00 Physicalmathematical sciences
DescriptionIn 2011 – 2015, the scientific community was represented by a new paradigm of mathematical methods of research in the field of organizational and economic modeling, econometrics and statistics. There was a talk about a new paradigm of applied statistics, mathematical statistics, mathematical methods of economics, the analysis of statistical and expert data in problems of economics and management. We consider it necessary to develop organizational and economic support for solving specific application area, such as the space industry, start with a new paradigm of mathematical methods. The same requirements apply to the teaching of the respective disciplines. In the development of curricula and working programs, we must be based on a new paradigm of mathematical methods of research. In this study, we present the basic information about a new paradigm of mathematical methods of research. We start with a brief formulation of a new paradigm. The presentation in this article focuses primarily on the scientific field of "Mathematical and instrumental methods of economy", including organizational and economic and economicmathematical modeling, econometrics and statistics, and decision theory, systems analysis, cybernetics, operations research. We discuss the basic concepts. We talk about the development of a new paradigm. We carry out a detailed comparison of the old and the new paradigms of mathematical methods of research. We give information about the educational literature, prepared in accordance with the new paradigm of mathematical methods of researches

NONPARAMETRIC KERNEL ESTIMATORS OF PROBABILITY DENSITY IN THE DISCRETE SPACES
01.00.00 Physicalmathematical sciences
DescriptionSome estimators of the probability density function in spaces of arbitrary nature are used for various tasks in statistics of nonnumerical data. Systematic exposition of the theory of such estimators has been started in our articles [3, 4]. This article is a direct continuation of these works [3, 4]. We will regularly use references to conditions and theorems of the articles [3, 4], in which introduced several types of nonparametric estimators of the probability density. We have studied linear estimators. In this article, we consider particular cases  kernel density estimates in discrete spaces. When estimating the density of the onedimensional random variable, kernel estimators become the ParzenRosenblatt estimators. Under different conditions, we prove the consistency and asymptotic normality of kernel density estimators. We have introduced the concept of "preferred rate differences" and are studied nuclear density estimators based on it. We have introduced and studied natural affinity measures which are used in the analysis of the asymptotic behavior of kernel density estimators. Kernel density estimates are considered for sequences of spaces with measures. We give the conditions under which the difference between the densities of probability distributions and of the mathematical expectations of their nuclear estimates uniformly tends to 0. Is established the uniform convergence of the variances. We find the conditions on the kernel functions, in which take place these theorems about uniform convergence. As examples, there are considered the spaces of fuzzy subsets of finite sets and the spaces of all subsets of finite sets. We give the condition to support the use of kernel density estimation in finite spaces. We discuss the counterexample of space of rankings in which the application of kernel density estimators can not be correct

MATTER GENERATION FROM SINGULARITIES COLLIDING IN THE RICCI FLOWS
01.00.00 Physicalmathematical sciences
DescriptionIn this article, we investigate the problem of creation of matter in the collision of particles, presented by singularities of the gravitational field. A system of nonlinear parabolic equations describing the evolution of the axially symmetric metrics in the Ricci flow derived. A model describing the creation of matter in the collision and merger of the particles in the Ricci flow proposed. It is shown that the theory that describes the Ricci flow in the collision of black holes is consistent with EinsteinInfeld theory, which describes the dynamics of the material particles provided by the singularities of the gravitational field. As an example, we consider the metric having axial symmetry and which contains two singularities simulating particles of finite mass. It is shown that the static metric with two singularities corresponding to in Newton's theory of gravity two particles moving around the center of mass in circular orbits in a noninertial frame of reference, rotating with a period of twobody system rotation. We have numerically investigated the change of the metric in the collision of particles with subsequent expansion. In numerical experiments, we have determined that the collision of the particles in the Ricci flow leads to the formation of two types of matter with positive and negative energy density, respectively. When moving singularities towards each other in the area between the particles the matter is formed with negative energy density, and in the region behind the particles  with positive density. In the recession of the singularities, the matter with positive energy density is formed in the area between the particles. The question of the nature of baryonic matter in the expanding universe is discussed

RESTRICTED MANYBODY PROBLEM IN THE RICCI FLOWS IN GENERAL RELATIVITY
01.00.00 Physicalmathematical sciences
DescriptionIn this article, the restricted problem of three and more bodies in the Ricci flow in the general theory of relativity considered. A system of nonlinear parabolic equations describing the evolution of the axially symmetric metrics in the Ricci flow proposed. A model describing the motion of particles in the Ricci flow derived. It is shown that the theory describing the Ricci flow in the manybody problem is consistent with the EinsteinInfeld theory, which describes the dynamics of the material particles provided by the singularities of the gravitational field. As an example, consider the metric having axial symmetry and contains two singularities simulating particles of finite mass. It is shown that the static metric with two singularities corresponds to Newton's theory of the two centers of gravity, moving around the center of mass in circular orbits in a noninertial frame of reference, rotating with a period of bodies. We consider the statement of the problem of many bodies distributed at the initial time on the axis of symmetry of the system. 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 axis of the system. This is achieved due to relativistic effects, which have no analogues in Newton's theory of gravitation. Using the properties of relativistic potentials we have justified transition from the relativistic motion of the particles to the dynamic equations in the classic theory

COLOR MATTER GENERATION IN THE RICCI FLOW IN GENERAL RELATIVITY
01.00.00 Physicalmathematical sciences
DescriptionIn this article, we investigate the restricted problem of many bodies with a logarithmic potential in the general theory of relativity. We consider the metric having axial symmetry and containing a logarithmic singularity. 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 axis of the system. This is achieved due to relativistic effects, which have no analogues in Newton's theory of gravitation. The motion of relativistic particles in a logarithmic potential sources distributed on the surface of a torus simulated. It is shown that the trajectory of the particles in these systems form a torus covered with needles. It was found, that the Ricci flow in the general theory of relativity could be born three kinds of matter  positive and negative energy density, as well as the color of matter, the gravitational potential of which is complex. It has been shown that this type of material is associated with the manifestation of the quantummechanical properties, which is consistent with the hypothesis of the origin of Schrodinger quantum mechanics. It is assumed that the most likely candidate for the role of the color of matter is the system of quarks as to describe the dynamics of quarks using the logarithmic potential, and the quarks themselves are not observed in the free state

SYNTHESIS OF SUBSTITUTED ISOXAZOLO[5,4b]PYRIDINE AND THEIR ANTIDOTE ACTIVITY
DescriptionTo develop the novel herbicide antidotes for the sunflower vegetative plants, the group of chemical compounds, belonging to the derivatives of isoxalopyrazolopyridines was synthesized and their antidote activity both in the laboratory and field experiments was studied. The compounds with a high antidote effect were found

TO THE QUESTION OF PHENOLOGY OF СONVALLARIA MAJALIS L. IN THE CONDITIONS OF THE MIDDLE DON
DescriptionFor the conservation of biodiversity, this study of patterns of biological processes and phases in the development of Convallaria majalis L. that are repeated annually becomes actual. In the article, we have presented an analysis of five years of observations of the rhythm of the development of Convallaria majalis L. in the conditions of the middle Don. There were allocated phenological phases of lily of the valley: vegetative (beginning of sprout growth, deploying of leaves), bud formation, flowering (disclosure of the first flower, mass blossoming, the withering of separate flowers, the ending of flowering), fruitage (the beginning of fruit setting, mass of fruit setting, mass ripening of fruits), the end of the vegetation (appearance of the first changes in color of leaves, the complete drying). We have defined daily average temperature and the appropriate amount of positive temperatures for the passage of various phases of development Convallaria majalis L. By the results of two growing seasons, the optimal daily average temperature for the flowering period is 14,3 ° C (the sum of average daily temperatures 161,3204, 0С)  until 915 days. At higher daily air temperatures flowering begins at lower amount of positive and effective temperatures after 4045 days after the start of the vegetation. At lower daily air temperatures flowering is longer than at higher. In the conditions of the middle Don there were allocated some examples of Convallaria majalis L. which bloom two years in a row