№ 119(5), May, 2016
Public date: 31.05.2016
Archive of journal: Articles count 97, 232 kb
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01.00.00 Physical-mathematical sciences
APPLIED STATISTICS – THE STATE AND THE PROSPECTS
01.00.00 Physical-mathematical sciences
Description
Applied Statistics - the science of how to analyze the statistical data. As an independent scientificpractical area it develops very quickly. It includes numerous widely and deeply developed scientific directions. Those who use the applied statistics and other statistical methods, usually focused on specific areas of study, ie, are not specialists in applied statistics. Therefore, it is useful to make a critical analysis of the current state of applied statistics and discuss trends in the development of statistical methods. Most of the practical importance of applied statistics justifies the usefulness of the work on the development of its methodology, in which the field of scientific and applied activities would be considered as a whole. We have given some brief information about the history of applied statistics. Based on Scientometrics of Applied Statistics we state that each expert has only a small part of accumulated knowledge in this area. We discuss five topical areas in which modern applied statistics develops, ie five "points of growth": nonparametric, robustness, bootstrap, statistics of interval data, and statistics of non-numerical data. We discuss some details of the basic ideas of a non-numerical statistics. In the last more than 60 years in Russia, there has been a huge gap between official statistics and the scientific community of experts on statistical methods
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01.00.00 Physical-mathematical sciences
Description
Fuzzy sets are the special form of objects of nonnumeric nature. Therefore, in the processing of the sample, the elements of which are fuzzy sets, a variety of methods for the analysis of statistical data of any nature can be used - the calculation of the average, non-parametric density estimators, construction of diagnostic rules, etc. We have told about the development of our work on the theory of fuzziness (1975 - 2015). In the first of our work on fuzzy sets (1975), the theory of random sets is regarded as a generalization of the theory of fuzzy sets. In non-fiction series "Mathematics. Cybernetics" (publishing house "Knowledge") in 1980 the first book by a Soviet author fuzzy sets is published - our brochure "Optimization problems and fuzzy variables". This book is essentially a "squeeze" our research of 70-ies, ie, the research on the theory of stability and in particular on the statistics of objects of non-numeric nature, with a bias in the methodology. The book includes the main results of the fuzzy theory and its note to the random set theory, as well as new results (first publication!) of statistics of fuzzy sets. On the basis of further experience, you can expect that the theory of fuzzy sets will be more actively applied in organizational and economic modeling of industry management processes. We discuss the concept of the average value of a fuzzy set. We have considered a number of statements of problems of testing statistical hypotheses on fuzzy sets. We have also proposed and justified some algorithms for restore relationships between fuzzy variables; we have given the representation of various variants of fuzzy cluster analysis of data and variables and described some methods of collection and description of fuzzy data
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METHODS OF REDUCING SPACE DIMENSION OF STATISTICAL DATA
01.00.00 Physical-mathematical sciences
Description
One of the "points of growth" of applied statistics is methods of reducing the dimension of statistical data. They are increasingly used in the analysis of data in specific applied research, such as sociology. We investigate the most promising methods to reduce the dimensionality. The principal components are one of the most commonly used methods to reduce the dimensionality. For visual analysis of data are often used the projections of original vectors on the plane of the first two principal components. Usually the data structure is clearly visible, highlighted compact clusters of objects and separately allocated vectors. The principal components are one method of factor analysis. The new idea of factor analysis in comparison with the method of principal components is that, based on loads, the factors breaks up into groups. In one group of factors, new factor is combined with a similar impact on the elements of the new basis. Then each group is recommended to leave one representative. Sometimes, instead of the choice of representative by calculation, a new factor that is central to the group in question. Reduced dimension occurs during the transition to the system factors, which are representatives of groups. Other factors are discarded. On the use of distance (proximity measures, indicators of differences) between features and extensive class are based methods of multidimensional scaling. The basic idea of this class of methods is to present each object as point of the geometric space (usually of dimension 1, 2, or 3) whose coordinates are the values of the hidden (latent) factors which combine to adequately describe the object. As an example of the application of probabilistic and statistical modeling and the results of statistics of non-numeric data, we justify the consistency of estimators of the dimension of the data in multidimensional scaling, which are proposed previously by Kruskal from heuristic considerations. We have considered a number of consistent estimations of dimension of models (in regression analysis and in theory of classification). We also give some information about the algorithms for reduce the dimensionality in the automated system-cognitive analysis
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THE DEVELOPMENT OF COUNTRIES' CREDIT RATING ASSESSMENT SYSTEM
01.00.00 Physical-mathematical sciences
Description
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"
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MATHEMATICAL MODELS OF MEDICALECONOMIC CONTROL OF DRUGS PRESCRIPTION
01.00.00 Physical-mathematical sciences
Description
The federal program on essential drugs provision (EDP) is one of the most significant and socially important state projects; it is directed to the reduction of morbidity and mortality together with the improvement of life quality of the society and its social climate. In accordance with the federal law “On social state assistance” from 17.07.1999 №178- FL, the essence of the program is that medical recipes are dispensed for preferential medicines to be received by federal program participants. The medical-economic control (MEC) of the drugs designation and provision of federal benefit recipients is performed basing on the automated registries examination of released drugs. The number of passed and failed examination recipes is determined according to the registers processing results. A certain percentage of the accepted for payment prescriptions is a subject for MEC. For the purpose of the recipes selection for testing, the paper proposes the mathematical models of criteria application and MEC-planning. The game model of organization and MEC performance in health care organizations is build basing on the theory of games. The considered play model suggests that the health services quality examination need to be adjusted and some strategies are to be improved. The solution on the planning of checked recipes number allows to perform the inspection of all the health care organizations, involved in EDP program
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SIMULATION OF TURBULENT FLOW IN A CAVITY ON THE NAVIER-STOKES EQUATIONS
01.00.00 Physical-mathematical sciences
Description
The article deals with the numerical solution of the Navier-Stokes equations describing turbulent flow in a rectangle cavity or in a cuboid with one open face at high Reynolds numbers. It is known, that there is a mechanism of turbulent mixing in natural systems, leading to an increase in the viscosity of the continuous medium. In this regard, we suggest methods of regularization of the Navier-Stokes equations, similar to the natural mechanisms of mixing. We proposed the models based on the properties of the turbulent environment. For this we modified the continuity equation taking into account the pressure fluctuations. It is shown that the incompressibility condition is can be violated due to pressure fluctuation even for flows with low Mach numbers. Modification of continuity equation by the introduction of turbulent viscosity allows the regularization of the Navier-Stokes equations to solve the problems with rapidly changing dynamic parameters. It was shown that the modification of the continuity equation taking into account turbulent fluctuations leads to a system of nonlinear equations of parabolic type. A numerical model of turbulent flow in the cavity with the rapid change in the parameters of the main flow developed. Discovered type of instability of the turbulent flow associated with the rapid changes in the main flow velocity. In numerical simulations found that due to the acceleration of the main flow there is the unsteady vortex flow in the cavity, which is characterized by the integral of energy not vanishing with time, vibrations that have a certain period, depending on the turbulent viscosity
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THE UNIFIED FIELD THEORY AND SUPERGRAVITY IN 112D
01.00.00 Physical-mathematical sciences
Description
In the paper the problem of constructing a unified field theory based on the theory of supergravity in the 112D is discussed. It is assumed that in the 112-dimensional Riemann space there are 37 three-dimensional worlds coexist having a single time and associated gravity. Investigated centrally symmetric metric depends on the radial coordinate in the observable physical space of one of the worlds. It is assumed that in the 112D performed the wave equation of the general form, describing the dynamics of the scalar field. From this equation, the wave equation is displayed in the fourdimensional space-time, containing terms describing the contribution of extra dimensions. It is shown that the quantum numbers of the problem allow us to describe the structure of the atom and the atomic nucleus on the assumption that given the total mass of the central body. The problem on the dynamics of the scalar field in the 112D in a centrally symmetric metric has been described. Built of field quantization theory in general, and in the particular case of metrics depending on the Weierstrass elliptic functions. It is shown that in this case there are bounded periodic potentials and corresponding periodic solutions that depend on the energy and angular momentum projection, and on the invariants of the Weierstrass function. It is found that in an excited state with a sufficiently large magnitude of the angular momentum of the projection portion of the radial wave function is periodic in a limited range, while the ground state allowed waves on all axes of the radial coordinate. The connection of the solutions to the Yang-Mills theories discussed
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DYNAMICS OF THE GEOMAGNETIC FIELD AND SUPERGRAVITY IN 112D
01.00.00 Physical-mathematical sciences
Description
The paper deals with the problem of changing the polarity of the geomagnetic field as a problem of a unified field theory and supergravity in the 112D. Investigated centrally symmetric metric depends on the radial coordinate in the observable physical space of one of the worlds. The equation that relates the magnetic field of the planet with a gravitational field in 5D has been derived. The problem of changing the polarity of the magnetic field of the Earth discussed. The rapid change of the geomagnetic field polarity detected on the basis of paleomagnetic data is modeled as a movement on a hypersphere in the 112D, which corresponds to 110 corners. The simplest example of such a movement in the case of the three angles is the Euler model that describes the rigid body rotation. In this model, there are modes with a quick flip of the body while conservation of the angular momentum. If the body has a magnetic moment, when such a change occurs flip of the magnetic field. It is assumed that the central core of the earth is magnetized and surrounded by a number of satellites, each of which has a magnetic moment. Satellites interact with a central core and one another by means of gravity and through a magnetic field. The central core may sudden flip, as in the Euler model. It is shown that the duration of phase with constant polarity and upheaval time depends on the magnitude of the disturbance torque and core asymmetry. We discuss Einstein's hypothesis about the origin of the magnetic field when rotating the neutral masses. It is shown that the motion on a hypersphere in the 112D has the effect of a magnetic field due to the interaction of nucleons in nuclei. Such magnetic field is most evident for iron, cobalt and nickel - elements are consisting of the Earth's core
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INVESTIGATION OF ASCORBIC ACID ADSORPTION ON KSMG SILICA GEL
Description
The article studies adsorption of ascorbic acid on KSMG silicagel. The experimental results, the basic thermodynamic characteristics of ascorbic acid adsorption on oxide silicon have been used for treatment of adsorption mechanism of ascorbic acid on silica KSMG. Results of the study ascorbic acid adsorption on silica gel KSMG may be used for further identification of it in the various objects
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DETERMINATION OF ACUTE TOXICITY OF BIO HUMATES
Description
In the work, we present the results of the investigation of acute toxicity of bio humates obtained by the method vermicultivation on laboratory animals. In the diets of farm animals and Pets to fill in the missing nutrients in the past years, we had an extensive use of various feed additives. Among them, mineral (macro - and micronutrients), protein and fat supplements, vitamins, biostimulants, complex natural compounds (sapropel, peat), synthetic products (enzymes, hormones, antibiotics, adaptogens, antioxidants). The search for new ways of improvement and increase of efficiency of agricultural animals using feed additives with high demands on ecology of meat and dairy foods naturally led to increased studies on the use in livestock farming of water-soluble alkaline salts of natural humic acids - humates. Their environmental safety and the unique ability to improve metabolism and increase energy cells very positively manifested in living organisms. Numerous studies Russian and foreign scientists installed a high efficiency natural humates as biostimulators and immunomodulators in animal husbandry and veterinary medicine. Accumulated extensive experimental material, proving that the use of humates leads to faster growth of animals, reducing morbidity and mortality, increase the body's resistance to toxins in feed and resistance to adverse environmental conditions. Improving with the help of humates ecological purity of the ecosystems "water — soil — plant", as well as the health of birds, animals and fish will ultimately lead to strengthen health and to prolong human life as a consumer of agricultural products. Currently, the livestock market is intensively increasing the humates produced in Russia and abroad from brown coal, peat, sapropel. A special place among them has been occupied by the newest formulations because of a unique combination of safety, efficiency, and value, which, thanks to its amazing properties to increase energy cells, stimulate vital processes and to enhance the beneficial effects of other substances called energine. They are harmless to animals and humans; do not have allergologie, anaphylactogenic, teratogenic, embryotoxic and carcinogenic properties when used in recommended doses. This allows you to create on their basis organic natural feed additives and veterinary medicines for agricultural animals, birds, fish, fur animals and Pets, and preventive and therapeutic drugs for humans
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