Bauman Moscow State Technical University
Author list of organization
List of articles written by the authors of the organization
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MATHEMATICAL METHODS OF CLASSIFICATION THEORY
01.00.00 Physical-mathematical sciences
DescriptionThis article gives a review of mathematical methods of construction and using of classifications. The main approaches to solving the problems of cluster analysis and grouping are discussed. We have also proposed global and local natural classification criteria. The methods of discriminant analysis (diagnosis, pattern recognition with the teacher) are discussed in connection with the construction of generalized indicators (ratings)
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ABOUT THE METHODOLOGY OF STATISTICAL METHODS
01.00.00 Physical-mathematical sciences
DescriptionThe purpose of the article - to justify the need to develop the methodology of statistical methods as an independent scientific direction. The models of mathematician and applied specialist are presented. We have obtained the conclusions on teaching and research and discussed five major unsolved problems of statistical methods: the effect of deviations from the traditional prerequisites; use asymptotic results for finite sample sizes; selecting one of the many specific tests for the hypothesis; organization of theoretical work in the field of statistical methods; conduct applied research and teaching of statistical methods
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01.00.00 Physical-mathematical sciences
DescriptionLusian - dichotomous data model as a finite sequence of independent Bernoulli trials with, generally speaking, different probabilities of success. The tasks of statistical hypothesis testing, classification, averaging lusians are discussed. In accordance with the requirements of practice the problems are considered primarily in the asymptotic behavior of increasing dimension, in which the number of unknown parameters increases in proportion to the size of data. The method of testing hypotheses on set of small samples and the theory of unbiased statistical estimates were proved to be useful
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PROBABILISTIC-STATISTICAL METHODS IN GNEDENKO’S RESEARCHES
01.00.00 Physical-mathematical sciences
DescriptionWe analyze the probabilistic-statistical methods in the researches of Boris Vladimirovich Gnedenko – the academician of Ukrainian Academy of Science, which are very important for the XXI century. We have also discussed the limit theorems of probability theory, mathematical statistics, reliability theory, statistical methods of quality control and queuing theory. We give some information about the main stages of scientific career of B.V. Gnedenko, his views on the history of mathematics and teaching
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ORGANIZATIONAL-ECONOMIC SUPPORT OF INNOVATION
DescriptionIn the article we have analyzed the way of scientific and technical ideas creation to mass production. Particular attention is paid to the organization of commercialization of innovative projects using modern information technologies, especially Internet auctions. To adequately describe the actual processes, we have highlighted 13 stages in the development of the innovative project and put into consideration the diversity of its trajectories. We have also identified the need for specialized structures (innovation centers), providing organizational-economic support to innovative projects, especially in the organization of expert estimates, conducting market research, developing business plans
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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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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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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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THEORY OF EXPERT ESTIMATES IN OUR COUNTRY
01.00.00 Physical-mathematical sciences
DescriptionIs given the analysis of the development of expert estimates in our country after the war. Are presented a diversity of expert technologies, the main ideas and publications that help identify the driving forces of development in this promising scientific and practical field
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DISTANCES IN THE SPACES OF STATISTICAL DATA
01.00.00 Physical-mathematical sciences
DescriptionThe core of applied statistics is statistics in spaces of arbitrary nature, based on the use of distances and optimization problems. This article discusses the various distances in spaces of statistical data, in particular, their conclusions on the basis of appropriate systems of axioms. The conditions and proofs of theorems first published in scientific periodicals