01.00.00 Physical-mathematical sciences
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ABOUT THE NEW PARADIGM OF MATHEMATICAL METHODS OF RESEARCH
01.00.00 Physical-mathematical 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 economic-mathematical 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
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ABOUT NEW PROMISING MATHEMATICAL TOOLS OF CONTROLLING
01.00.00 Physical-mathematical sciences
DescriptionBased on an objective analysis, it must be noted that in the arsenal of managers, especially foreign ones, there is practically no fundamentally new methods and tools. However, promising mathematical and instrumental methods of controlling actively developed in our country. In the XXI century it developed a new paradigm of mathematical methods of economics and produced more than 10 books, developed in accordance with this paradigm. The new paradigm is based on the modern development of mathematics as a whole - on the system interval fuzzy math. The new paradigm offers tools used non-parametric statistics, which suggest that the distribution functions are arbitrary. In 1979 it was allocated one of the four major areas of modern applied statistics - statistics of objects of nonnumeric nature (statistics of non-numeric data, nonnumeric statistics). The other three - statistics of random variables, multivariate statistical analysis, statistics of random processes and time series. Statistics of objects of non-numeric nature is central to the modern mathematical methods of economics. On the basis of modern information-communication technologies we have developed a new economic theory - solidary information economy. New intellectual tools of controlling include an automated system-cognitive analysis (ASA) and its software - the system of "Eidos". The systems approach to solving specific applications often requires going beyond the economy. Very important are the procedures for the introduction of innovative methods and tools
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ON THE NUMERATIONS OF THE FINITE PARTIALLY ORDERED SETS
01.00.00 Physical-mathematical sciences
DescriptionThere is a widely known problem regarding the ordering of the partially ordered sets (Linear Ordering Problem). It boils down to finding the numerations of such sets. The main result of this article is a generalization of one of the known S. S. Kislitsyn's results about finding the number of numerations of finite partially ordered sets
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01.00.00 Physical-mathematical sciences
DescriptionResults of experimental researches of nanoparticles by the method of laser diagnostics were presented. A new algorithm of processing of particle transmission bands was offered at the first time. It was shown, that it was possible to get allocation bar charts according to their sizes with high confidence under high experimental inaccuracy.
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REPRESENTATION OF THE SOLUTIONS OF THE NAVIER-STOKES IN GENERAL RELATIVITY
01.00.00 Physical-mathematical sciences
DescriptionIn this paper, we investigated solutions of the Navier-Stokes equations associated with the solutions of Einstein's equations for empty space. There exists a metric in which the Navier-Stokes equations are integrated exactly. We demonstrate that the solution of the Navier-Stokes equations of general form consistent metrics describing in general relativity space with nonzero curvature
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TESTING OF HOMOGENEITY OF PAIRED SAMPLES
01.00.00 Physical-mathematical sciences
DescriptionThe article begins with the letter of the chief engineer of chemical plant near Moscow. He requests to analyze of data by means of modern statistical methods and give an opinion on the presence (or absence) of the relationship between the two methods of determining the viscosity of the mastic. For each of the batches of mastic It was presented two numbers - the viscosity measurement results of the two methods. These numbers form two paired samples. We want to install, give whether two specific methods similar results. The true values of viscosity in different batches are not equal. Their difference is not allows us to combine the results of the first measurement method in first sample, the results of the second method - in the second sample, as we can do in the case of testing the homogeneity of two independent samples. For solutions to this problem we discuss four statistical criterions, based on a study of the differences between corresponding values in two paired samples. We test the hypothesis of equality 0 of median of these differences (sign test) and of equality 0 of the mathematical expectation of these differences. Hypothesis of testing of equality of the distribution functions of two paired samples is reduced to the hypothesis of symmetry of the distribution function of these differences with respect to 0. In the alternative of the shift is proposed to use the Wilcoxon signed rank criterion. In the total alternative is proposed to use criterion of the omega-square type which is developed by the author of this article
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THE ORIGIN OF INERTIAL MASS OBSEVABLE MATTER
01.00.00 Physical-mathematical sciences
DescriptionWe consider the hypothesis of the origin of mass of the observed matter from electromagnetic field interacting with streams of preons. The interaction between preons and the scalar and vector potentials of the electromagnetic fields acquire mass, which leads to a massive scalar and vector bosons. The described mechanism of mass generation is different from the well-known Higgs mechanism associated with the spontaneous breaking of the electroweak symmetry, for which at the moment is finding a suitable scalar boson
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TO THE QUESTION OF MATHEMATICAL METHODS DEVELOPMENT OF CONTROLLING
01.00.00 Physical-mathematical sciences
DescriptionOn the basis of the objective analysis it must be noted that in the arsenal of managers, especially foreign ones, there is practically no fundamentally new methods and tools of controlling. So says the executive director of Russian Association of Controllers prof. S. G. Falco. However, promising mathematical and instrumental methods of controlling actively developed in our country. It is necessary to implement them. For example, managers should be used techniques which discussed in the book by Orlov AI, Lutsenko EV, Loikaw VI "Advanced mathematical and instrumental methods of controlling" (2015). These methods are based on the modern development of mathematics as a whole - on the system interval fuzzy math (see the same named book by Orlov AI and Lutsenko EV, 2014). Considered methods are developed in accordance with the new paradigm of mathematical methods of research. It includes new paradigms of applied statistics, mathematical statistics, mathematical methods of economics, methods of analysis of statistical and expert data in management and control. In the XXI century there were more than 10 books issued, developed in accordance with the new paradigm of mathematical methods of research. The systems approach to solving specific applications often requires going beyond the economy. Very important are the procedures for the introduction of innovative methods and tools. In this article we consider the above research results in their interconnection
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ABOUT THE DEVELOPMENT OF THE STATISTICS OF NONNUMERICAL OBJECTS
01.00.00 Physical-mathematical sciences
DescriptionAbout thirty-five years ago, the statistics of non-numerical objects was highlighted as an independent field of mathematical statistics. This article analyzes the basic ideas in this area, and relevant publications on the background of the development of applied statistics, and in connection with the system fuzzy interval mathematics
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01.00.00 Physical-mathematical sciences
DescriptionTheorems of the value distribution of the sums of Abelian Group’s characters and short exponentail triginimetric sums are proved in this article. Asymptotic formulas of these sums’ fractional moments are proved