01.00.00 Physical-mathematical sciences
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01.00.00 Physical-mathematical sciences
DescriptionIn the article, we have suggested a general mathematical model of non-stationary and non-isothermal process of a binary electrolyte transfer in dilute solutions in an electro-membrane system (EMS), taking into account the joint action of gravitational convection, forced convection and electro convection in potential dynamic mode. This model is a boundary problem for a system of two-dimensional quasi-linear Navier-Stokes equation and Nernst-Planck-Poisson in partial derivatives equation. We have developed a theory of similarity of the process of heat and mass transfer in electro-membrane systems, specifically, in a desalting channel of electro dialysis apparatus, taking into account joint actions of concentration polarization, space charge, gravity convection, forced convection and electro convection. It is shown that the criterion of electro convection does not directly depend on the initial concentration, and, therefore, electro convection occurs at any initial concentration. At the same time, the criterion of concentration convection linearly dependents on the initial concentration, and, therefore, at high concentrations, concentration convection prevails, while at lower concentrations, the role of gravitational convection begins to fall whereas the role of electro convection increases. The theory of similarity of the process of heat and mass transfer in the desalting channel of electro dialysis apparatus built in this work taking into account the joint action of concentration polarization, space charge, gravity convection, forced convection and electro convection is important for engineering calculations, for scaling the results of experiments in an electro-membrane cell for industrial electro dialysis water desalting apparatus
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GENERAL RELATIVITY AND DYNAMICAL MODEL OF ELECTROMAGNETIC DRIVE
01.00.00 Physical-mathematical sciences
DescriptionThe article discusses the dynamic model of the rocket motor electromagnetic type, consisting of a source of electromagnetic waves of radio frequency band and a conical cavity in which electromagnetic waves are excited. The processes of excitation of electromagnetic oscillations in a cavity with conducting walls, as well as the waves of the YangMills field are investigated. The multi-dimensional transient numerical model describing the processes of electromagnetic oscillations in a cavity with conducting wall created. Separately, the case of standing waves in the cavity with conducting walls considered. It is shown that the oscillations mode in the conducting resonator different from that in an ideal resonator, both in steady and unsteady processes. The mechanism of formation of traction for the changes in the space-time metric, the contribution of particle currents, the Yang-Mills and electromagnetic field proposed. It is shown that the Yang-Mills field calls the change of the dielectric constant, which leads to a change in the capacitance of the resonator. Thus, the parametric resonance occurs in the system, which leads to a strengthening of the Yang-Mills amplitude, and to the emergence of traction. We have developed a dynamic model, which enables optimal traction on a significant number of parameters. It was found that the thrust increases in the Yang-Mills field near the main resonance frequency. A model describing the excitation and emission of nonlinear waves of the Yang-Mills field was proposed. It is shown that nonlinear waves of the Yang-Mills field more effectively carry the momentum from the system in comparison with electromagnetic waves, and it explains the significant increase by several orders of thrust in the engines of the electromagnetic type, compared with the photon rocket
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FUZZY SETS THEORY AS THE PART OF PROBABILITY THEORY
01.00.00 Physical-mathematical sciences
DescriptionOne of the key provisions of the system fuzzy interval mathematics - the claim that the theory of fuzzy sets is the part of the theory of random sets, thus, part of the probability theory. The article is devoted to the justification of this statement. Proved number of theorems that show that the fuzzy sets and the results of operations on them can be viewed as the projections of random sets and the results of the corresponding operations on them
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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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THEORY AND CONSTANTS OF WALL TURBULENCE
01.00.00 Physical-mathematical sciences
DescriptionThe completely closed model of wall turbulence was derived directly from the Navier-Stokes equation. The fundamental constants of wall turbulence including the Karman constant have been calculated within a theory. This model has been developed also for the accelerated and non-isothermal turbulent boundary layer flows. The estimated mean velocity, temperature and impurity concentration profiles as well as the spectral characteristics of the streamwise velocity component are to be shown in a good agreement with the experimental data
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THEORY OF ELECTROMAGNETIC DRIVE WITH ELEMENTARY PARTICLES CURRENT AND VACUUM POLARIZATION
01.00.00 Physical-mathematical sciences
DescriptionThe article discusses a model of rocket motor of electromagnetic type, consisting of a source of electromagnetic radio frequency oscillations and the conical cavity, in which electromagnetic waves are excited. We have created a multi-dimensional transient numerical model describing the process of establishing electromagnetic oscillations in the resonator, taking into account the finite conductivity of the walls. Separately, the standing waves in the cavity with conducting walls have been simulated. It is shown that the oscillations mode in the conducting resonator different from that in an ideal resonator, both in a case of steady and unsteady waves. We have built a dynamic model taking into account the thermal conductivity and electrical conductivity of the walls, waves and particles emission and vacuum polarization. We have also developed a dynamic model enables to optimize a thrust force on a considerable number of parameters without the involvement of the hypotheses about the physics of the phenomenon. We run the optimization of the operating parameters of the device, namely by the excitation frequency, the frequency of the modulating signal, the magnitude of heat losses of electromagnetic energy by thermal radiation in the IR spectrum, the parameters of forced heat transfer and the temperature dependence of the resistance of the material of the cavity walls. It is found that the pulse modulation greatly improves the efficiency of conversion of electromagnetic energy into thrust. The mechanism of formation of traction, adjusting the metrics of space-time, the current contribution of elementary particles, the Yang-Mills and electromagnetic fields is proposed. It is shown that the contribution of the elementary particles in the thrust force is proportional to the electrical conductivity of the system multiplied by Abraham force
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01.00.00 Physical-mathematical sciences
DescriptionThe work presents the calculation on the basis of magnetic circuits of magnetic field induction in the "water" gaps of the device for activation of water with alternating magnetic field of industrial frequency. We have executed the calculations of magnetic inductance of the coil of the device taking into account the thickness of layers of winding current-carrying wires. This allowed experimentally determining - with reasonable accuracy - the value of the relative permeability of the steel used, housing, necessary for the specified calculation of the device in general
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THEORETICAL TOOLS OF STATISTICAL METHODS
01.00.00 Physical-mathematical sciences
DescriptionWe have considered the basic mathematical tools (theorems, methods) which are used regularly in the justification of new results in the field of statistical methods: rules of large numbers, central limit theorems, the necessary and sufficient conditions for the inheritance of convergence, the linearization method, the invariance principle
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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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01.00.00 Physical-mathematical sciences
DescriptionIn the study we consider the problem of determining the motion and similarity parameter to the system of worlds in a Riemannian space 112D with a common field of gravity. Centrally symmetric metric, depending on the 110 angle coordinates and the radial coordinate and time was investigated. It is assumed that there are intelligent beings in every world, striving for self-knowledge. By virtue of the presence of the world hierarchy in one of them there is a system of complete identification of each characteristic of the individual being with macroparameters his world. If sentient beings in all the world to create a device to simulate their own history in the form of a network of computers using the available material and the physical laws of his world, and the loss of information when displaying one world to another is 1%, then 37- th world played only 68.9449%. For Earthlings, it was found that the average similarity parameter of professional group in recognition by using astronomical parameters is 68.75%. Therefore, we can assume that the world system, including Earth, contains 37 "floors." Assuming that each "floor" takes three space dimensions, and all the "floors" connected by a single time, we find here that the number of dimensions of space-time of the whole system is 112. In the article the angular motion in a Riemannian space is considered. The effect of the separate worlds on other worlds is simulated. It has been shown that the physical laws in all worlds represent a single movement covering the markers in the form of the motion of atoms and elementary particles in a gravitational field in the 112D