Bauman Moscow State Technical University
Author list of organization
List of articles written by the authors of the organization
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SOME PROBLEMS OF SOCIALECOLOGICAL MANAGEMENT IN MODERN ECONOMY
DescriptionClassical economic textbooks assume that the effect of a particular company on the environment is infinitely small, in particular, that resources required for an industrial firm are available, and it's only the price to be paid for their involvement. For a large corporation, the situation is quite different. It converts the environment by means of its activity. Objectively existing resource limits are become important. The effects are increased when we consider the economy as a whole thing. Therefore, we have the obvious need for careful consideration of management problems in the real process of interaction between the economy, society and environment. This article is devoted to some approaches to this consideration. We have demonstrated that the economy is the servant of society. In all the economical developed countries in the twentieth century the role of the state in the economy has been increased in 3-5 times. We have discussed the influence of the modern ecological situation on the economy and management. In particular, we predict the end of private enterprise in the classical meaning. We examined the social-ecological aspects of management of the state and personnel of the firm. Discussion of Russian problems we begin with an analysis of the dynamics of the main economic and demographic indicators of Russia, including the total fertility rate in Russia. The system of scenarios of population projections for the period up to 2050 shows the inevitability of significant reduction in the Russian population (in the absence of intensive management actions). We describe two basic scenarios of solving socio-ecological conflicts
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AVERAGE VALUES AND RULES OF LARGE NUMBERS IN THE SPACES OF ARBITRARY ORIGIN
01.00.00 Physical-mathematical sciences
DescriptionThe new results of the sample average values in different spaces and rules of large numbers for them are given in the article. We also introduced the weighted average values of type I corresponding to the sample, and type II, corresponding to the set of order statistics. The evolution of ideas about the Kemeny distance and the Kemeny median is traced. The modified Kemeny median, convenient for computation and avoiding the effect of the "center of the bagel hole" is proposed. As a generalization of the Kemeny median, we introduced and studied the empirical and theoretical values in the spaces of arbitrary origin. For them, we proved the rules of large numbers
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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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NON-NUMERICAL DATA STATISTICS IS A CENTRAL PART OF MODERN APPLIED STATISTICS
08.00.13 Mathematical and instrumental methods of Economics
DescriptionIn 1979, non-numerical data statistics was singled out as an independent area of applied statistics. Initially, the term "statistics of objects of non-numerical nature" was used to denote this area of mathematical methods of economics. Our basic non-numeric statistics textbook is called "Non-Numeric Statistics". Non-numerical data statistics is one of the four main areas of applied statistics (along with number statistics, multidimensional statistical analysis, statistics of time series and random processes). Statistics of non-numerical data are divided into statistics in spaces of a general nature and sections devoted to specific types of non-numerical data (statistics of interval data, statistics of fuzzy sets, statistics of binary relations, etc.). Currently, statistics in spaces of a general nature is the central part of applied statistics, and non-numeric data statistics including it is the main area of applied statistics. This statement is confirmed, in particular, by the analysis of publications in the section "Mathematical Research Methods" of the journal "Industrial Laboratory. Diagnostics of Materials" - the main place of publication of russian studies on applied statistics. This article is devoted to the analysis of the basic ideas of non-numerical data statistics against the background of the development of applied statistics from the perspective of a new paradigm of mathematical research methods. Various types of non-numeric data are described. The historical path of statistical science is analyzed. We have discussed the development of statistics of non-numerical data. The article analyzes basic ideas of statistics in spaces of a general nature: average values, laws of large numbers, extreme statistical problems, nonparametric estimates of the probability density, classification methods (diagnostics and cluster analysis), statistics of the integral type. Some statistical methods for analyzing data lying in specific spaces of non-numeric nature are briefly considered: non-parametric statistics (real distributions usually differ significantly from normal), statistics of fuzzy sets, theory of expert estimates (the Kemeny median is a sample average of expert orderings), etc. We have also discussed some unsolved problems in statistics of nonnumeric data
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STATISTICAL METHODS IN HISTORY
01.00.00 Physical-mathematical sciences
DescriptionWe have given a critical analysis of statistical models and methods for processing text information in historical records to establish the times when there were certain events, ie, to build science-based chronology. There are three main kinds of sources of knowledge of ancient history: ancient texts, the remains of material culture and traditions. The specific date of the extracted by archaeologists objects in most cases can not be found. The group of Academician A.T. Fomenko has developed and applied new statistical methods for analysis of historical texts (Chronicle), based on the intensive use of computer technology. Two major scientific results were: the majority of historical records that we know now, are duplicated (in particular, chronicles, describing the so-called "Ancient Rome" and "Middle Ages", talking about the same events); the known historical chronicles tell us about real events, separated from the present time for not more than 1000 years. It was found that chronicles describing the history of "ancient times" and "Middle Ages" and the chronicle of Chinese history and the history of various European countries do not talk about different, but about the same events. We have the attempt of a new dating of historical events and restoring the true history of human society based on new data. From the standpoint of statistical methods of historical records and images of their fragments – they are special cases of non-numeric objects of nature. Therefore, developed by the group of A.T. Fomenko computer-statistical methods are the part of non-numerical statistics. We have considered some methods of statistical analysis of chronicles applied by the group of A.T. Fomenko: correlation method of maximums; dynasties method; the method of attenuation frequency; questionnaire method codes. New chronology allows us to understand much of the battle of ideas in modern science and mass consciousness. It becomes clear the root cause of cautious attitude of the West towards Russia
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STATISTICAL MODELS IN MEDICINE
01.00.00 Physical-mathematical sciences
DescriptionThe article is devoted to the discussion of the organization of clinical-statistical studies and experiments. We have considered the examples of the application of statistical methods in scientific medical research. Under the clinical-statistical research we understand specially organized collection and analysis of medical data about the course of disease in patients, research of the dynamics of objective and subjective indicators of the state of reaction to these or other therapeutic effects. We study one, two or more groups of individuals (patients or healthy), conclusions are drawn on the whole group, but not for each individual patient. The purpose of research - to transfer the conclusions reached for the sample to the general population, i.e., clinical and statistical study focused on the production of useful recommendations concerning those patients who fall into the field of view of doctors after the end of the study. There are two main types of research - prospective and retrospective. The first related to the analysis of the last patients, the second - to monitoring the course of their disease in the future. We have considered typical mistakes in the organization of clinical-statistical studies. When planning a research, we usually distinguish the experimental and control groups, which are identical or similar in all respects except for the studied factors (exposure). We discuss the various options for blind methods and consider the application of statistical models and methods in scientific medical research. We have analyzed examples of confidence estimation of proportion (probability) and the homogeneity test of probabilities. For statistical modeling we use the Poisson distribution in the case of small probability. With its help, we analyze statistical data on the opisthorchiasis
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STATISTICAL ESTIMATION FOR THE GROUPED DATA
01.00.00 Physical-mathematical sciences
DescriptionThe probabilistic model of grouping data (including multidimensional data) is described. We have also generalized Euler-Maclaurin’s formulas. With its help Sheppard’s corrections and corrections on grouping for correlation coefficient are received. We have found and studied asymptotical corrections on grouping data generally. Accuracy of approach has been estimated
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STRATEGY OF RETRO INNOVATIONS IN IMPORT SUBSTITUTION
08.00.13 Mathematical and instrumental methods of Economics
DescriptionUnfavorable changes in exchange rates, sanctions restrictions on the supply to Russia of spare parts necessary for the repair and maintenance of previously imported equipment have led to a significant reduction in the service life of imported machinery and equipment. For the solution, the authors propose to implement the strategy of retro-innovations providing the development of new technologies maintaining in working condition of machinery and equipment in conditions of shortage of spare parts and consumables. To do this, it is necessary to develop technologies for the restoration of complex technical devices in order to extend their service life under the restrictions created by the financial market and sanctions policy. The study of the problem was carried out on the example of the operation of trucks of foreign production, the evaluation of engine life and analyzed the structure of the market. On the basis of the obtained results, a model was proposed, on the basis of which it is possible to form a plan for the production of spare parts for high-quality engine repair by domestic enterprises. The strategy of retro-innovations does not solve all the problems of import substitution, but it allows to increase the level of economic security of strategically important economic activities, it creates jobs and provides an opportunity to significantly extend the life of expensive and complex technical devices
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EXISTENCE OF ASYMPTOTICALLY OPTIMAL PLANS IN DISCRETE PROBLEMS OF DYNAMIC PROGRAMMING
08.00.13 Mathematical and instrumental methods of Economics
DescriptionDynamic programming is designed to solve discrete optimal control problems. According to this method, the optimal solution in a multidimensional problem is found by decomposing it into stages, each of which represents a subproblem with respect to one variable. In economic problems, the number of stages is the planning horizon. The choice of a planning horizon is necessary for a rigorous statement of the applied problem in the field of economics and management, but it is often difficult to justify. We see a way out in the use of asymptotically optimal plans for which the values of the optimization criterion differ little from its values for optimal plans for all sufficiently large planning horizons. The main result of the paper is the existence of an asymptotically optimal plan. The proof is carried out in several statements. If the sum of the maximums of the transition functions tends to 0, the existence of an asymptotically optimal plan is obtained in Theorem 1. A special case is models with a discount at a discount coefficient less than 1. The main part of the article is devoted to models with a discount coefficient equal to 1. Theorem 2 on the highway is proved for base set of a finite number of elements. In Theorem 3, a statement is obtained on the approximation of an arbitrary set by a finite one. In the final Theorem 4, the existence of an asymptotically optimal plan is proved in the general case. The term “magistral” is associated with a well-known recommendation to drivers: in order to get from point A to point B, it is advisable to go to the highway (magistral) at the initial section of the road, and then exit the highway and get to point B. The recommendation for choosing the optimal one is similar trajectories using the Pontryagin maximum principle in the model of the optimal distribution of time between obtaining knowledge and developing skills. This fact underlines the methodological proximity of dynamic programming and the Pontryagin maximum principle
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THEORETICAL TOOLS OF STATISTICAL METHODS
01.00.00 Physical-mathematical sciences
DescriptionWe have considered the basic mathematical tools (theorems, methods) which are used regularly in the justification of new results in the field of statistical methods: rules of large numbers, central limit theorems, the necessary and sufficient conditions for the inheritance of convergence, the linearization method, the invariance principle