01.00.00 Physical-mathematical sciences
-
01.00.00 Physical-mathematical sciences
DescriptionThis article proposes a generalized principle of relativity, similar to Galileo's principle of relativity Ein-stein, but for all kinds of real and virtual systems, not just the physical, hypothesis about his relationship with the theorem of Emmy Noether and laws of con-servation of energy, momentum and angular momen-tum in the socio-economic and psychological systems. On the basis of the information theory of time and information theory of value (E.V. Lutsenko, 1980), the conclusions about the non-uniformity of the course of time in social systems, inhomogeneity and anisotropy's of a bench economic space and violations of the laws of conservation of energy, momentum and angular momentum in social systems, and accordingly, of a failure to comply or only partial implementation for them the generalized principle of relativity have been made in the article
-
01.00.00 Physical-mathematical sciences
DescriptionCriterions of the choice of electronic blocks of calculate technique means, that require special (higher) attention in point of view of their diagnostic and technical state prognosing, are offered in this article; an example of using of the hierarchies analysis method to determine such elements is considered
-
01.00.00 Physical-mathematical sciences
DescriptionThe article presents a technique of short-term forecasting of water level in the river bed of a mountain type using Markov’s chains
-
LIMIT THEORY OF NONPARAMETRIC STATISTICS
01.00.00 Physical-mathematical sciences
DescriptionWe have studied the asymptotic behavior of a broad class of nonparametric statistics, which includes statistics of omega-square type and Kolmogorov-Smirnov type. Limit theorems have been proved. We have also developed the method of approximation with step functions. With the help of this method we have obtained a number of necessary and sufficient conditions
-
THE LIMIT THEORY OF THE SOLUTIONS OF EXTREMAL STATISTICAL PROBLEMS
01.00.00 Physical-mathematical sciences
DescriptionMany procedures of applied mathematical statistics are based on the solution of extreme problems. As examples it is enough to name methods of least squares, maximum likelihood, minimal contrast, main components. In accordance with the new paradigm of applied mathematical statistics, the central part of this scientific and practical discipline is the statistics of non-numerical data (it is also called the statistics of objects of non-numerical nature or non-numeric statistics) in which the empirical and theoretical averages are determined by solving extreme problems. As shown in this paper, the laws of large numbers are valid, according to which empirical averages approach the theoretical ones with increasing sample size. Of great importance are limit theorems describing the asymptotic behavior of solutions of extremal statistical problems. For example, in the method of least squares, selective estimates of the parameters of the dependence approach the theoretical values, the maximum likelihood estimates tend to the estimated parameters, etc. It is quite natural to seek to study the asymptotic behavior of solutions of extremal statistical problems in the general case. The corresponding results can be used in various special cases. This is the theoretical and practical use of the limiting results obtained under the weakest assumptions. The present article is devoted to a series of limit theorems concerning the asymptotics of solutions of extremal statistical problems in the most general formulations. Along with the results of probability theory, the apparatus of general topology is used. The main differences between the results of this article and numerous studies on related topics are: we consider spaces of a general nature; the behavior of solutions is studied for extremal statistical problems of general form; it is possible to weaken ordinary requirements of bicompactness type by introducing conditions of the type of asymptotic uniform divisibility
-
LIMIT THEOREMS IN STATISTICAL CONTROL
01.00.00 Physical-mathematical sciences
DescriptionThe article analyzes the development of the theory of statistical control (from the XVIII century to the present). Prof. M.V. Ostrogradskii (1846) clearly describes the practical needs (ie, arising from the quality assurance of large quantities of bags of flour or pieces of cloth), to meet whom he spent his research. At the same time Simpson was among the ideas of probability theory XVIII century. Therefore prof. M.V. Ostrogradskii may be regarded as the founder of the theory of statistical process control (not only in our country but all over the world). Limit theorems of probability theory and mathematical statistics have provided a number of asymptotic results in problems of statistical quality control, offer based on these best practices. However, we must find out how much interest among specialists characteristics are different from limit for finite sample sizes. Such research for the synthesis algorithm control plan on the basis of the limit average output level of defects is made in this article, and for the synthesis algorithm control plan on the basis of the acceptance and the rejection levels of defects - not yet (clarification of the conditions of applicability of this algorithm - unsolved problem of applied mathematics). We have briefly reviewed the development of our researches on the statistical control. Control units can be not only some units of production, but also documents (with internal and external audit), and standard units of air, water and soil in the environmental monitoring. One of the achievements can be regarded as the transfer of statistical control of production for environmental monitoring
-
LIMIT THEOREMS FOR KERNEL DENSITY ESTIMATORS IN SPACES OF ARBITRARY NATURE
01.00.00 Physical-mathematical sciences
DescriptionSome estimators of the probability density function in spaces of arbitrary nature are used for various tasks in statistics of non-numerical data. Systematic exposition of the theory of such estimators had a start in our work [2]. This article is a direct continuation of the article [2]. We will regularly use references to conditions and theorems of the article [2], in which we introduced several types of nonparametric estimators of the probability density. We studied more linear estimators. In this article we consider particular cases - kernel density estimates in spaces of arbitrary nature. When estimating the density of the one-dimensional random variable, kernel estimators become the Parzen-Rosenblatt estimators. Asymptotic behavior of kernel density estimators in the general case of an arbitrary nature spaces are devoted to Theorem 1 - 8. Under different conditions we prove the consistency and asymptotic normality of kernel density estimators. We have studied uniform convergence. We have introduced the concept of "preferred rate differences" and studied nuclear density estimators based on it. We have also introduced and studied natural affinity measures which are used in the analysis of the asymptotic behavior of kernel density estimators. We have found the asymptotic behavior of dispersions of kernel density estimators and considered the examples including kernel density estimators in finite-dimensional spaces and in the space of square-integrable functions
-
THE PROPOSED AXIOMS OF THE GENERAL THEORY OF CYCLES
01.00.00 Physical-mathematical sciences
DescriptionIn this article, we consider the task of systematizing the axioms and postulates, directly or indirectly connected with the study of the cycles of varying length and nature, which constitute the absolute of the general theory of cycles
-
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
-
01.00.00 Physical-mathematical sciences
DescriptionIn the article with the help of a technique, based on discretization initial problem of time variable and the method of basic potentials, is constructed the approximate solution of the second two-dimensional problem for the equation of diffusion with depending on concentration coefficients and source function. The general view of the approximate solution of this problem is reduced. On concrete example convergence of the approximate solution of the problem to the exact is shown