01.00.00 Physical-mathematical sciences
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TWO-SAMPLE WILCOXON TEST - ANALYSIS OF TWO MYTHS
01.00.00 Physical-mathematical sciences
DescriptionIt was established that the two-sample Wilcoxon test (Mann-Whitney test) was designed to test the hypothesis H0: P(X
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GRAVITATIONAL WAVES AND STATIONARY STATES OF QUANTUM AND CLASSICAL SYSTEMS
01.00.00 Physical-mathematical sciences
DescriptionIn this paper, we consider gravitation theory 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 the Schrodinger equation as well. The solutions of the Einstein equations describing the stationary states of arbitrary quantum and classical systems with central symmetry have been obtained. Thus, it is proved that atoms and atomic nuclei can be represented as standing gravitational waves
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GRAVITATIONAL WAVES AND EMERGENCE PARAMETER OF CLASSICAL AND QUANTUM SYSTEMS
01.00.00 Physical-mathematical sciences
DescriptionIt was established that the Fermi-Dirac statistics, Bose-Einstein and Maxwell-Boltzmann distribution can be described by a single equation, which follows from Einstein's equations for systems with central symmetry. Emergence parameter of classical and quantum systems composed by the rays of gravitational waves interacting with gravitational field of the universe has been computed
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GRAVITATIONAL WAVES AND SCHRODINGER QUANTUM THEORY
01.00.00 Physical-mathematical sciences
DescriptionIn this paper, we consider gravitation theory 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. Conjecture about the Schrödinger wave function due to gravitational waves was proved. Solutions of the gravitational field equations similar to the de Broglie waves have been constructed.
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GRAVITATIONAL WAVES AND QUANTUM THEORY
01.00.00 Physical-mathematical sciences
DescriptionIn this article we consider gravitation theory 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. Schrödinger conjecture about the Schrödinger wave function and gravitational waves has been proved
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GRAVITATIONAL WAVES IN THE RICCI FLOW FROM SINGULARITIES MERGER
01.00.00 Physical-mathematical sciences
DescriptionIn this study, we investigate the problem of the emission of gravitational waves produced in collisions of particles submitted to the singularities of the gravitational field. A system of non-linear parabolic equations describing the evolution of the axially symmetric metrics in the Ricci flow derived. A model describing the emission of gravitational waves in the collision and merger of the particles in the Ricci flow proposed. It is shown that the theory of the Ricci flow describes the problem of black holes merge, consistent with Einstein-Infeld theory, which describes the dynamics of the material particles provided by the singularities of the gravitational field. As an example, we consider the metric having axial symmetry and comprising two singularities simulating particles of finite mass. We have numerically investigated the change of the metric in the collision and merger of the particles. The initial and boundary conditions using the exact solution of the static problem, so the collision persist particularly metrics caused by the presence of particles. In numerical experiments determined that the collision of the particles in the Ricci flow leads to the formation of gravitational waves, similar in structure to the waves, registered in the LIGO experiment. Consequently, we can assume that the observed gravity waves caused mainly by transients associated with the change in the metric of a system. The influence of the parameters of the problem - the speed and mass of the particles, on the amplitude and intensity of the emission of gravitational waves was numerically simulated. We have found chaotic behavior of gravitational potentials at the merger of the singularities in the Ricci flow
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GRAVITY FIELD IN THE VICINITY OF STARS AND GEOMETRIC TURBULENCE
01.00.00 Physical-mathematical sciences
DescriptionIn this article, the solutions of Einstein's equations for empty space, describing the gravitational field near the Sunlike star have been investigated. We have accounted the own field of the star, the motion of the star around the galactic center, the motion of the galaxy relative to the center of the local supercluster and the expansion of the Universe. The resulting gravitational field near the star has a complex structure, which leads to large-scale geometric turbulence linking large and small scales in this problem
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GEOMETRIC TURBULENCE AND STELLAR EVOLUTION
01.00.00 Physical-mathematical sciences
DescriptionIn this article we consider Einstein's theory of gravity in relation to the Yang-Mills theory. It is shown that in Einstein's theory there exists a metric together with the Yang-Mills theory, in which the field equations are reduced to the Liouville equation describing the evolution of stars. The mechanism of generation of stellar energy of dark energy in the processes of geometric turbulence is discussed
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GEOMETRIC TURBULENCE AND QUANTUM THEORY
01.00.00 Physical-mathematical sciences
DescriptionThe parabolic equation describing the evolution of the gravitational field is derived from Einstein equation. The instability of metric leads to a geometric pattern of turbulence. Microscopic turbulent pulsations generate two kinds of matter with positive and negative energy density, respectively. It is shown that in the case of negative energy density parabolic equation leads to an equation of Schrödinger type
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GEOMETRIC TURBULENCE IN GENERAL RELATIVITY
01.00.00 Physical-mathematical sciences
DescriptionThe article presents the simulation results of the metric of elementary particles, atoms, stars and galaxies in the general theory of relativity and Yang-Mills theory. We have shown metrics and field equations describing the transition to turbulence. The problems of a unified field theory with the turbulent fluctuations of the metric are considered. A transition from the Einstein equations to the diffusion equation and the Schrödinger equation in quantum mechanics is shown. Ther are examples of metrics in which the field equations are reduced to a single equation, it changes type depending on the equation of state. These examples can be seen as a transition to the geometric turbulence. It is shown that the field equations in general relativity can be reduced to a hyperbolic, elliptic or parabolic type. The equation of parabolic type describing the perturbations of the gravitational field on the scale of stars, galaxies and clusters of galaxies, which is a generalization of the theory of gravitation Newton-Poisson in case of Riemannian geometry, taking into account the curvature of space-time has been derived. It was found that the geometric turbulence leads to an exchange between regions of different scale. Under turbulent exchange material formed of two types of clusters, having positive and negative energy density that corresponds to the classical and quantum particle motion respectively. These results allow us to answer the question about the origin of the quantum theory