01.00.00 Physical-mathematical sciences
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FUNDAMENTAL THEOREM OF ARITHMETIC AND SOME OF ITS ASPECTS
01.00.00 Physical-mathematical sciences
DescriptionIn this article, we present the fundamental theorem of arithmetic and its role. We consider various rings for its performance
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BASIC IDEAS OF INTERVAL DATA STATISTICS
01.00.00 Physical-mathematical sciences
DescriptionIn the article we have considered the basic idea of asymptotic mathematical statistics of interval data, in which the elements of a sample are not the numbers, but the intervals. Algorithms and conclusions of interval data statistics fundamentally different from the classical ones. The results related to the basic concepts of notna and rational sample sizes are listed. Interval data statistics as an integral part of the system of fuzzy interval mathematics is shown
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MAIN FEATURES OF THE NEW PARADIGM OF MATHEMATICAL STATISTICS
01.00.00 Physical-mathematical sciences
DescriptionThe new paradigm of mathematical statistics is based on the transition from parametric to nonparametric statistical methods, the numerical data - to non-numeric, on the intensive use of information technology. Its distinctive features are revealed in comparison with the old paradigm of mathematical statistics in the mid-twentieth century
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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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BASES FOR DESIGN OF PARAMETERS OF ELECTROACTIVATOR FOR WATER SOLU-TIONS
01.00.00 Physical-mathematical sciences
DescriptionIn the article below the following items are represented: existing methods for design of electroactivator for water solutions, processes within an electroactivator are examined, the new formulas for calculation of the main characteristics of electroactivator are proposed, dependences of the parameters upon the factors which influence on device functioning are plotted, conclusions regard processes and proposals for design and operating are made
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PECULIARITIES OF GROWING NOMINALLY PURE AND NEODYMIUM DOPED STRONTIUM TUNGSTATE SINGLE CRYSTALS
01.00.00 Physical-mathematical sciences
DescriptionThe Nd3+ doped and nominally pure SrWO4 single crystals have been grown by modified Czochralski method. The nature of thermo physical behavior of the growth system with an additional afterheater for crystals with different light transmission was shown. The distribution of Nd3+ ions along the obtained crystals was investigated, the effective distribution coefficient was equal to 0.71
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PECULIARITIES OF PHOTOCHEMICAL PROCESSES UNDER SPLITTING OF ISOTOPES IN WATER SOLUTION
01.00.00 Physical-mathematical sciences
DescriptionFundamental task of photochemical splitting of isotopes of neutralizing metals in water solution is considered. It was shown that the coefficient of splitting is limited by such processes as electrical migration and isotope exchange. Equation of regression for isotope splitting coefficient value was casted.
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RUSSIAN SCIENTIFIC SCHOOL IN THE ECONOMETRICS FIELD
01.00.00 Physical-mathematical sciences
DescriptionWe have considered the formation of the Russian scientific school in the field of econometrics, obtained its obtained scientific results, the possibilities of their use in solving problems of the economy, the organization of production and controlling of industrial companies and organizations, as well as in teaching. As econometrics we consider a scientific and an academic discipline devoted to the development and application of statistical methods to study economic phenomena and processes, in short, statistical methods in economics. Therefore, we can say that a lot of domestic books and articles, in particular, the works by the author of this publication from the beginning of the 70s, are the parts of econometrics. However, in this article we consider only the works, in the titles of which we can see the word of "econometrics". In our country the term "econometrics" has become popular since the mid 90s. However, many publications and training courses are still developed in the western outdated paradigm. They do not conform to the new paradigm of mathematical methods of economics, the new paradigm of applied statistics and mathematical statistics, mathematical methods of research. Russian science school in the field of econometrics operates within the scientific school in the field of probability theory and mathematical statistics based by A.N. Kolmogorov. Russian science school is developed in accordance with the new paradigm of mathematical methods. It is necessary to examine the main results of Russian scientific schools in the field of econometrics. We present the information on the institutional design of national scientific schools in econometrics, in particular, on the activities of the Institute of High Technologies statistics and econometrics
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01.00.00 Physical-mathematical sciences
DescriptionAccording to the new paradigm of applied mathematical statistics one should prefer non-parametric methods and models. However, in applied statistics we currently use a variety of parametric models. The term "parametric" means that the probabilistic-statistical model is fully described by a finite-dimensional vector of fixed dimension, and this dimension does not depend on the size of the sample. In parametric statistics the estimation problem is to estimate the unknown value (for statistician) of parameter by means of the best (in some sense) method. In the statistical problems of standardization and quality control we use a three-parameter family of gamma distributions. In this article, it is considered as an example of the parametric distribution family. We compare the methods for estimating the parameters. The method of moments is universal. However, the estimates obtained with the help of method of moments have optimal properties only in rare cases. Maximum likelihood estimation (MLE) belongs to the class of the best asymptotically normal estimates. In most cases, analytical solutions do not exist; therefore, to find MLE it is necessary to apply numerical methods. However, the use of numerical methods creates numerous problems. Convergence of iterative algorithms requires justification. In a number of examples of the analysis of real data, the likelihood function has many local maxima, and because of that natural iterative procedures do not converge. We suggest the use of one-step estimates (OS-estimates). They have equally good asymptotic properties as the maximum likelihood estimators, under the same conditions of regularity that MLE. One-step estimates are written in the form of explicit formulas. In this article it is proved that the one-step estimates are the best asymptotically normal estimates (under natural conditions). We have found OS-estimates for the gamma distribution and given the results of calculations using data on operating time to limit state for incisors
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ESTIMATION OF VIRUSES DISTRIBUTION AREA DIAMETER USING MODELS ON PREFRACTAL GRAPHS
01.00.00 Physical-mathematical sciences
DescriptionThe article investigates the problem of estimation of diameters of prefractal graphs with priming stars and with full priming which contiguity of old edges in a trajectory isn't broken on spectra