01.00.00 Physical-mathematical sciences
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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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GENERAL RELATIVITY AND METRIC OF LOCAL SUPERCLUSTER
01.00.00 Physical-mathematical sciences
DescriptionIt is shown that the metric of clusters of galaxies should be universal, depending only on the fundamental constants and compatible with the metric of the universe. There are examples of universal metrics obtained in Einstein's theory of gravitation. On the basis of axisymmetric solutions of Einstein’s equation proposed universal metric describing the properties of galaxies, groups and clusters of galaxies
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01.00.00 Physical-mathematical sciences
DescriptionThis article briefly reviews the classical concept of functional dependence in mathematics, determines the limitations of this concept for adequate modeling of reality and formulates the problem, consisting in search of such generalization of the concept of func-tions, which is more suitable for the adequate reflec-tion of causal relationships in the real domain. Also, it discusses theoretical and practical solving the prob-lem, consisting in: (a) we suggest the universal method of calculating the amount of information in the value of argument about the meaning of the function, i.e. cognitive functions which is independent from the subject area; b) we offer software tools: Eidos intelli-gent system, allowing in practice to carry out these calculations, i.e. to build cognitive functions based on a fragmented noisy empirical data of high dimension. We also offer the concepts of nonreducing, partially and completely reduced direct and inverse, positive and negative cognitive functions and the method of formation of reduced cognitive function, which is a generalization of known weighted least-squares meth-od on the basis of observation the amount of infor-mation in the values of the argument about the values of the functions accounting
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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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GENERAL RELATIVITY AND METRICS OF INHOMOGENEOUS ROTATING UNIVERSE
01.00.00 Physical-mathematical sciences
DescriptionThe metric of inhomogeneous rotating Universe is discussed. There are examples of universal metrics obtained in Einstein's theory of gravitation. On the basis of solutions of Einstein’s equation we have proposed universal metric describing the properties of galaxies, groups and clusters of galaxies in inhomogeneous rotating Universe
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COSMOLOGY OF INHOMOGENEOUS ROTATING UNIVERSE AND REALITY SHOW
01.00.00 Physical-mathematical sciences
DescriptionOn the basis of the solutions of Einstein we have proposed universal metric describing the properties of an inhomogeneous rotating universe. It is shown that in the case of space-time metric of negative curvature, the field equations are hyperbolic, parabolic or elliptic type, depending on the equation of state. An equation for the general state of the species, describing the emergence of matter, as the aggregate state of dark energy proposed
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HEEDING OF HETEROGENEITY OF ENVIRONMENT WHEN CALCULATING A MAGNETIC FIELD
01.00.00 Physical-mathematical sciences
DescriptionThe formula for definition of magnitude and direction of secondary sources of a field as surface currents for the registration of heterogeneity of environment is found. We have shown that it is possible to solve non-linear field problems, using the mathematical deduc-tions shown in this article
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QUANTUM GRAVITY AND YANG-MILLS THEORY
01.00.00 Physical-mathematical sciences
DescriptionIn this paper, we consider Einstein's theory of gravitation in connection with Yang-Mills theory. The model of the metric satisfying the basic requirements of quantum theory is proposed. The mechanism of generation of baryonic matter of dark energy is discussed
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01.00.00 Physical-mathematical sciences
DescriptionThis work deals with the numerical method of solution of integral equation with the kernel, which has the first order singularities by two variables. The solution is approximated by piecewise linear functions by every variable. The coefficients are determined by the collocation method. The singular integrals of basic functions are calculated exact
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QUANTUM GRAVITY AND REALITY SHOW
01.00.00 Physical-mathematical sciences
DescriptionIn this article, we consider quantum gravity in multidimensional space. The model of the metric satisfying the basic requirements of quantum theory is proposed. It is shown that gravitational waves are described by the Liouville equation, and matter waves associated with gravitational waves by a simple equation. The mechanism of generation of baryonic matter of dark energy is discussed