01.00.00 Physical-mathematical sciences
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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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01.00.00 Physical-mathematical sciences
DescriptionThe article presents a project of the Yang-Mills amplifier. Amplifier model is a multilayer spherical shell with increasing density towards the center. In the center of the amplifier is the core of high-density material. It is shown that in such a system, the amplitude of the Yang-Mills waves rises from the periphery to the center of several orders of magnitude. The role of the Yang-Mills field in the processes occurring in the nuclei of galaxies, stars and planets is discussed. The data modeling to strengthen the Yang-Mills field in the bowels of the planet, with an atomic explosion, and in some special devices such as the voltaic pile. To describe the mechanism of amplification chromodynamics field used as accurate results in Yang-Mills theory and numerical models developed based on an average and the exact equations as well. Among the exact solutions of the special role played by the centralsymmetric metric describing the contribution of the Yang-Mills field in the speed of recession of galaxies. Among the approximate numerical models can be noted the eight-scalar model we have developed for the simulation of non-linear color oscillations and chaos in the Yang-Mills theory. Earlier models were investigated spatio-temporal oscillations of the YangMills theory in the case of three and eight colors. The results of numerical simulation show that the nonlinear interaction does not lead to a spatial mixing of colors as it might be in the case of turbulent diffusion. Depending on the system parameters there is a suppression of the amplitude of the oscillations the first three by five colors or vice versa. The kinetic energy fluctuations or shared equally between the color components, or dominated by the kinetic energy of repressed groups of colors. In the present study, we found that amplification chromodynamic field leads to a sharp increase in the amplitude of the suppressed color, which can lead to an increase in entropy, excitation of nuclear reactions and decays particles
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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
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EXITATION OF ELECTROMAGNETIC RADIATION, NUCLEAR REACTION AND PARTICLES DECAY BY THE ACCELERATION
01.00.00 Physical-mathematical sciences
DescriptionThe article discusses the excitation of electromagnetic radiation, nuclear reactions and decays of particles by the acceleration of charges, atomic nuclei and the macroscopic volumes of matter. The motion of charged particles in a magnetic trap used for plasma confinement was computed. We propose a model of the electromagnetic radiation of a charge moving in a non-inertial reference frame in general relativity. We have also constructed a theory of perturbation with using a wave equation with small parameters, taking into account a characteristic radius of the trajectory of the electrons as they move in a magnetic field. It was found that in the first approximation, the radiation back-reaction force depends on the acceleration of the charge. For the simulating of processes in hadrons and nuclei we used Yang-Mills theory and the metric, describes the acceleration and rotating reference frame in general relativity. We consider the scalar glueball model for an arbitrary dependence of acceleration and angular velocity of the system on time. The numerical model of wave propagation in non-inertial reference frame for the geometry of system of one, two or three spatial dimensions was tested. In the numerical experiments shown that the acceleration of the system leads to instability, leading to an unlimited increase in the amplitude of waves, which is interpreted as a decay of system. It was found that there are critical values of acceleration above which the instability develops
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ANALYTICAL METHOD OF THE RESEARCH OF KINETICS FOR THE PROCESS OF DROPLET DISPERSION
01.00.00 Physical-mathematical sciences
DescriptionIn the article we have concerned the researched mathematical method for the process of droplet dispersion on a horizontal surface. On the basis of the asymptotical method and the method of the division of variables we have found the approximate analytical solution of the problem
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FRACTAL AND PREEFACTAL GRAPHS, BASIC DEFINITIONS AND SYMBOLS
01.00.00 Physical-mathematical sciences
DescriptionThe fractal and prefractal graph are described in the article. The basic definitions and notation are proposed, the procedure for constructing prefractal graph, the operation of replacement vertex by seed is given
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01.00.00 Physical-mathematical sciences
DescriptionThe article presents the theorem of Chebyshev on the distribution of primes, considering functions that approximated prime numbers. We have also considered a new function, which is quite good for approximation of prime numbers. A review of the known results on distribution of prime numbers is given as well
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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
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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