01.00.00 Physical-mathematical sciences
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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
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ASYMPTOTICS OF ESTIMATES OF PROBABILITY DISTRIBUTION DENSITY
01.00.00 Physical-mathematical sciences
DescriptionNonparametric estimates of the probability distribution density in spaces of arbitrary nature are one of the main tools of non-numerical statistics. Their particular cases are considered - kernel density estimates in spaces of arbitrary nature, histogram estimations and Fix-Hodges-type estimates. The purpose of this article is the completion of a series of papers devoted to the mathematical study of the asymptotic properties of various types of nonparametric estimates of the probability distribution density in spaces of general nature. Thus, a mathematical foundation is applied to the application of such estimates in non-numerical statistics. We begin by considering the mean square error of the kernel density estimate and, in order to maximize the order of its decrease, the choice of the kernel function and the sequence of the blur indicators. The basic concepts are the circular distribution function and the circular density. The order of convergence in the general case is the same as in estimating the density of a numerical random variable, but the main conditions are imposed not on the density of a random variable, but on the circular density. Next, we consider other types of nonparametric density estimates - histogram estimates and Fix-Hodges-type estimates. Then we study nonparametric regression estimates and their application to solve discriminant analysis problems in a general nature space
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01.00.00 Physical-mathematical sciences
DescriptionWe consider an approach to the transition from continuous to discrete scale which was defined by means of step of quantization (i.e. interval of grouping). Applied purpose is selecting the number of gradations in sociological questionnaires. In accordance with the methodology of the general stability theory, we offer to choose a step so that the errors, generated by the quantization, were of the same order as the errors inherent in the answers of respondents. At a finite length of interval of the measured value change of the scale this step of quantization uniquely determines the number of gradations. It turns out that for many issues gated it is enough to point 3 - 6 answers gradations (hints). On the basis of the probabilistic model we have proved three theorems of quantization. They are allowed to develop recommendations on the choice of the number of gradations in sociological questionnaires. The idea of "quantization" has applications not only in sociology. We have noted, that it can be used not only to select the number of gradations. So, there are two very interesting applications of the idea of "quantization" in inventory management theory - in the two-level model and in the classical Wilson model taking into account deviations from it (shows that "quantization" can use as a way to improve stability). For the two-level inventory management model we proved three theorems. We have abandoned the assumption of Poisson demand, which is rarely carried out in practice, and we give generally fairly simple formulas for finding the optimal values of the control parameters, simultaneously correcting the mistakes of predecessors. Once again we see the interpenetration of statistical methods that have arisen to analyze data from a variety of subject areas, in this case, from sociology and logistics. We have another proof that the statistical methods - single scientificpractical area that is inappropriate to share by areas of applications
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ON THE NUMERATIONS OF THE FINITE PARTIALLY ORDERED SETS
01.00.00 Physical-mathematical sciences
DescriptionIn this article, we discuss various issues related to the formulas approximating the distribution function of prime numbers pi(x). This question has occupied many scholars, but the exact function is well approximated function pi(x) over the number of positive integers not. Based on certain hypotheses, we present a new function s(x) is very well approximated pi(x). The above article hypotheses are so important that their numerical validation and refinement for the lengths of the segments more in 1014 - one of the main areas related to the problem of approximation of the function pi(x) throughout the series of natural numbers. After analyzing the behaviors and constructs many functions, we are building the basis of the function s(x), which is well approximates the function pi(x) throughout the series of natural numbers. We also present a table of values for x, less or equal 1022 for the difference of s(x) - pi(x)
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ORBIT ABNORMAL MOVEMENT IN GENERAL RELATIVITY
01.00.00 Physical-mathematical sciences
DescriptionThe solution of the problem of the displacement of the perihelion of Mercury in Einstein's theory of gravitation, taking into account the mechanism of formation of matter from dark energy, has been obtained. It is shown that the observed value of the precession imposes a restriction on the equation of state of dark energy in the case of static fields
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ANALYTICAL METHOD OF THE RESEARCH OF KINETICS FOR THE PROCESS OF DROPLET DISPERSION
01.00.00 Physical-mathematical sciences
DescriptionIn the article we have concerned the researched mathematical method for the process of droplet dispersion on a horizontal surface. On the basis of the asymptotical method and the method of the division of variables we have found the approximate analytical solution of the problem
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01.00.00 Physical-mathematical sciences
DescriptionIn various applications it is necessary to analyze some expert orderings, ie clustered rankings of examination objects. These areas include technical studies, ecology, management, economics, sociology, forecasting, etc. The objects may make samples of the products, technologies, mathematical models, projects, job applicants and others. We obtain clustered rankings which can be both with the help of experts and objective way, for example, by comparing the mathematical models with experimental data using a particular quality criterion. The method described in this article was developed in connection with the problems of chemical safety and environmental security of the biosphere. We propose a new method for constructing a clustered ranking which can be average (in the sense, discussed in this work) for all clustered rankings under our consideration. Then the contradictions between the individual initial rankings are contained within clusters average (coordinated) ranking. As a result, ordered clusters reflects the general opinion of the experts, more precisely, the total that is contained simultaneously in all the original rankings. Newly built clustered ranking is often called the matching (coordinated) ranking with respect to the original clustered rankings. The clusters are enclosed objects about which some of the initial rankings are contradictory. For these objects is necessary to conduct the new studies. These studies can be formal mathematics (calculation of the Kemeny median, orderings by means of the averages and medians of ranks, etc.) or these studies require involvement of new information from the relevant application area, it may be necessary conduct additional scientific research. In this article we introduce the necessary concepts and we formulate the new algorithm of construct the coordinated ranking for some cluster rankings in general terms, and its properties are discussed
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01.00.00 Physical-mathematical sciences
DescriptionIn the article an effective system of an estimation of a financial and economic status of the factories of a building sector of Krasnodar region (Armavir district), based on use of methods of the multidimensional statistical analysis is introduced. The programmatic complex "FAP-stroi", including MS Excel plug-in, macros of «Statistica 6» and exterior processing of «1С: Enterprise 8» is built
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ANALYSIS OF APPLICATION CONDITIONS OF KOLMOGOROV’ PROBABILITY THEORY
01.00.00 Physical-mathematical sciences
DescriptionThe article analyses well-known approaches to the explanations of Kolmogorov's conditions for probabilities studied in applications. It discusses better-founded explanations, offers and looks into new approaches to the explanations of connectedness of the conditions
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WATER STRUCTURE AND DILUTE WATER SYSTEM PROPERTIES ANALYSIS
01.00.00 Physical-mathematical sciences
DescriptionThe cluster structure in pure water (distilled) and water salt solution was considered. The experimental methods of the structural units’ registration in water were analyzed. It is shown that the clusters influence on water properties is insignificant by salt concentration more than 10-5 mole