01.00.00 Physical-mathematical sciences
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THEORY OF PHYSICAL CONSTANTS AND SUPERGRAVITY IN 112D
01.00.00 Physical-mathematical sciences
DescriptionIn this article we discuss a version of the metric theory of the fundamental interactions in which it is assumed that the physical constants due to the presence of extra dimensions of space-time. The estimation of the number of physical constants based on the theory of supergravity in 112D is that the minimum number of constants is equal to 222, and the maximum number - 1404928. At present, the number of parameters that characterize the elementary particles, isotopes and chemical elements is about 150920. This number is 9.3 less than the maximum possible number of parameters that indicate still great potential of modern science. Functions describing the area and volume of a unit hypersphere, embedded in a Riemannian space of arbitrary dimension, were used to find the fundamental physical constants. A satisfactory agreement with a relative error of 0.03% calculated and experimental values of the fine structure constant found out. For the ratio of the average mass of a nucleon to the electron mass is obtained coincidence with the experimental value with an accuracy of 0.002%. The proposed theory of physical constants different from that Bartini theory that established the optimal dimension of the space is a hypersphere 5 and 7, rather than 6 as in Bartini theory. The problems of the compactification of extra dimensions in describing the motion in fourdimensional space-time are discussed
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A NUMERICAL ALGORITHM IN THE PROBLEM OF SELF-ORGANIZATION OF LABOR RESOURCES
01.00.00 Physical-mathematical sciences
DescriptionIn this article, there is a numerical method of solving the problem of self-organization of the labor resources. The problem deals with finding probabilities of hiring and the layoffs of specialists from the sectors of the labor market. A mathematical model of labor resources dynamics is used to solve this problem. The initial problem is incorrect, because number of equations of the descriptive system is less than number of unknown variables. A special algorithm is designed for guaranteed finding the normal solution in finite number of iterations. The algorithm is separated into two key stages. Initially, unconditional normal solution of the problem is found by applying the modified method of Gauss for underdetermined systems. Later, this solution is projected in the subspace of permissible values. After that, the normal solution of the problem with consideration of non-negativity of the desired values is being found by using the gradient projection method. The proposed algorithm has been successfully used to develop application in programming environment C++. This application is focused on solving of the problem of selforganization of the labor resources. Comparative analysis of speed of the application and add-ins MS Excel "Solver" showed that the same problem is solved much faster in the application designed by the author than in a table processor MS Excel when using the add-in "Solver". This demonstrates the high efficiency of the proposed method
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01.00.00 Physical-mathematical sciences
DescriptionThe article deals with the solution of the NavierStokes equations describing turbulent flows over rough surfaces. 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. It is shown, that in threedimensional flows over a rough surface turbulent viscosity increases proportionally to the square of the distance from the wall. The models of the flow, taking into account the properties of the turbulent environment are considered. A modification of the continuity equation taking into account the limiting magnitude of pressure fluctuations is proposed. It is shown, that due to the pressure pulsation, the incompressibility condition may be violated even for flows with low Mach numbers. Modification of the continuity equation taking into account turbulent fluctuations leads to a system of nonlinear equations of parabolic type. Modification of continuity equation in the system of Navier-Stokes by the introduction of turbulent viscosity allows the regularization of the Navier-Stokes equations to solve the problems with rapidly changing dynamic parameters. The main result of which is obtained by numerical simulation of the modified system of equations is the stability of the numerical algorithm at a large Reynolds number, which can be explained, first, a system of parabolic type, and a large quantity of turbulent viscosity. A numerical model of flow around plates with the rapid change in angle of attack has been verified. We have discovered the type of instability of the turbulent boundary layer associated with the rapid changes in dynamic parameters. It is shown, that the fluctuations of the boundary layer to cause generation of sound at a frequency of 100 Hz to 1 kHz
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01.00.00 Physical-mathematical sciences
DescriptionClassical combinatorial formula to calculate the number of combinations from n on m: C(n,m)=n!/(m!(nm)!) involves the intermediate calculation of factorials, which is often impossible when n>170, due to limitations in the capacity of numbers that are used in programming languages and created through these systems. However, in some cases it is necessary to calculate the number of combinations for n and m much larger than this limit, such as when a value greater than 10000. In such cases, there is a definite problem, which manifests itself, for example in the fact that many on-line services meant to calculate the number of combinations with these parameters do not work properly. In this article, we present its solution in the form of an algorithm and software implementation. The essence of the approach is to first decompose the factorials into prime factors and reduce them, and then to produce multiplication. This approach differs from those cited in the Internet
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APPLIED STATISTICS – THE STATE AND THE PROSPECTS
01.00.00 Physical-mathematical sciences
DescriptionApplied 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
DescriptionFuzzy 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
DescriptionOne 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
DescriptionThis 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
DescriptionThe 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
DescriptionThe 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