01.00.00 Physical-mathematical sciences
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KEY STAGES OF STATISTICAL METHODS DEVELOPMENT
01.00.00 Physical-mathematical sciences
DescriptionThe first statistical publication – the Fourth Book of Moses, “Numbers” in the Old Testament. We trace the development of ideas about the statistics until the twentieth century. The present stage of statistical methods began with parametric statistics by Pearson, Student, Fisher. Scientometrics of statistical researches provides an indication of the accumulated results. Nonparametric statistics appeared in the 1930s, applied statistics in our country - at the turn of 1970-80. We have discussed what gives applied statistics to national economy. Also we have told briefly about the history of statistical methods in Russia (until Kolmogorov's time)
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01.00.00 Physical-mathematical sciences
DescriptionThe drawbacks of the existing ontology languages and problems of their practical application are discussed in this paper. The requirements for the process of ontologies creating are laid down. A simplified method of constructing the ontological domain model on the basis of the original language SXML is proposed
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MATHEMATICAL THEORY OF RATINGS
01.00.00 Physical-mathematical sciences
DescriptionWhen developing management solutions with the aim of joint consideration and comparison of various factors, partial removal of uncertainty is widely used ratings. In the theory of decisionmaking in almost the same sense, we use the terms "composite index" or "integrated indicator". The article is devoted to the mathematical theory of ratings as tools for studying socio-economic systems. We considered, primarily, linear ratings which is a linear function from a single (private) indicators (factors, criteria), constructed using the coefficients of importance (weightiness, importance). The study discusses the factors affecting the magnitude of the ratings. Three groups of causes affect the value of a line ranking: the ways of measurement of individual indicators, the choice of the set of indicators; the values of the coefficients of importance. We considered binary ratings when the rating takes two values. To compare the proposed rankings we use a new indicator of the quality of diagnostics and prognostic power. Significantly, in many managerial situations, significant differences between objects are identified using any rating. According to the fundamental results of stability theory, the same source data should be processed in several ways. Matching findings, obtained using multiple methods, likely reflect the properties of reality. The difference is the result of a subjective selection method. When using the results of the comparison of objects according to several indicators (criteria ratings), including in dynamics, very useful is the selection of the Pareto set. We discuss the examples of the application of the decision theory, expert evaluations and rankings when developing complex technical systems
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01.00.00 Physical-mathematical sciences
DescriptionThe article investigates the first boundary problem for the partial differential equations of the second order with deviating argument. The method of separation of variables is used to prove the solubility of the boundary problem in the desired class of functions
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PREONS SHELLS AND ATOMIC STRUCTURE
01.00.00 Physical-mathematical sciences
DescriptionWe consider the model of the structure of electrons and quarks, in which these particles are presented consisting of elementary particles preons. From this model, the theory of electron shells, as a continuation of the quark nuclear shells has been proposed
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DYNAMICS OF QUARKS IN THE HADRONS METRICS WITH APPLICATION TO THE BARYON STRUCTURE
01.00.00 Physical-mathematical sciences
DescriptionThe dynamics of quarks in hadrons metric is investigated. A model of baryons in the case of a stationary metric formulated. The magnetic moments of the proton, neutron and lambda baryon calculated. The metric of hadrons is determined from the Yang-Mills theory. The result is a bubble metric containing only the time and angular coordinates. We find that there may be a spherical particle, which expand in sync with the space of the universe. Therefore, they appear to the outside observer static entities having spherical symmetry, such as protons. We have shown that the quarks in the hadrons metric can be described on the basis of the Dirac equation and the equations of quantum electrodynamics. The closure model formulated and the magnetic moments of hadrons (uud), (udd) and (sdu) at given energy and given electric charge are calculated. The investigated region corresponds to the resonance energy of the quarks system, in which, apparently, pi mesons can be generated.
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HADRONS MASS SPECTRUM AND THE GLUON THERMODYNAMICS
01.00.00 Physical-mathematical sciences
DescriptionIt is shown, that the hadron mass spectrum can be associated with the energy of the excited states of gluon condensate. Gluon thermodynamics is built on the basis of this concept. The transition temperature of hadronic matter to the quark-gluon plasma calculated on the basis of this model is about 175,856 MeV, which is consistent with experimental data and calculations based on lattice quantum chromodynamics (LQCD)
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MATHEMATICAL MODELING OF FINANCIAL PYRAMID SCHEME. PART 2. CONTINUOUS MODELS
01.00.00 Physical-mathematical sciences
DescriptionThis article is devoted to the analysis of different cases of changing the number of customers of the financial pyramid and the establishment of the basic rules of the pyramid schemes on the basis of continuous models, and it is a continuation of works [1, 2], which had formulas to simulate the amount collected by the pyramid scheme and it considers the discrete models
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QUANTUM ELECTRODYNAMICS OF PREONS, QUARKS AND LEPTONS
01.00.00 Physical-mathematical sciences
DescriptionIn this article we consider the system of equations of electrodynamics of continuous media molecules consisting of preons, including quarks and electrons
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ASYMPTOTIC METHODS OF STATISTICAL CONTROL
01.00.00 Physical-mathematical sciences
DescriptionStatistical control is a sampling control based on the probability theory and mathematical statistics. The article presents the development of the methods of statistical control in our country. It discussed the basics of the theory of statistical control – the plans of statistical control and their operational characteristics, the risks of the supplier and the consumer, the acceptance level of defectiveness and the rejection level of defectiveness. We have obtained the asymptotic method of synthesis of control plans based on the limit average output level of defectiveness. We have also developed the asymptotic theory of single sampling plans and formulated some unsolved mathematical problems of the theory of statistical control