01.00.00 Physical-mathematical sciences
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01.00.00 Physical-mathematical sciences
DescriptionThe influence of dissociation / recombination of water molecules is important for understanding electroconvection processes, as some authors believe that the emergence of new carriers + H and − OH , and can lead to a reduction in the space-charge and, consequently, to electroconvection disappearance. However, as shown in [5], the dissociation of water molecules, although it reduces the space charge and increases the threshold fall potential jump at which begins electroconvection, yet it persists and effectively mixes the solution. This article is devoted to mathematical modeling of electrodiffusion of four types of ions at the same time (two salt ions as well as + H and − OH ions) in the diffusion layer in electromembrane systems with perfectly selective membrane under the joint influence of violation of electrical neutrality, and the reaction of dissociation / recombination of water molecules, development of mathematical models of these processes, building efficient algorithms asymptotic and numerical analysis for different types of electrolytes. The work proposes a new mathematical model of the process of transfer of salt ions in view of the space charge and the dissociation / recombination of water in the form of a boundary value problem for a system of ordinary differential equations. This system is reduced to a form convenient for numerical solution. We have calculated the required additional boundary conditions for the electric field. Numerical and asymptotic solution of the boundary value problem and physico-chemical analysis of the influence of dissociation / recombination on the transfer of salt ions is expected to devote the next part of the work
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RESTRICTED MANY-BODY PROBLEM IN THE RICCI FLOWS IN GENERAL RELATIVITY
01.00.00 Physical-mathematical sciences
DescriptionIn this article, the restricted problem of three and more bodies in the Ricci flow in the general theory of relativity considered. A system of non-linear parabolic equations describing the evolution of the axially symmetric metrics in the Ricci flow proposed. A model describing the motion of particles in the Ricci flow derived. It is shown that the theory describing the Ricci flow in the many-body problem is consistent with the Einstein-Infeld theory, which describes the dynamics of the material particles provided by the singularities of the gravitational field. As an example, consider the metric having axial symmetry and contains two singularities simulating particles of finite mass. It is shown that the static metric with two singularities corresponds to Newton's theory of the two centers of gravity, moving around the center of mass in circular orbits in a noninertial frame of reference, rotating with a period of bodies. We consider the statement of the problem of many bodies distributed at the initial time on the axis of symmetry of the system. In numerical calculations, we studied the properties of the gravitational potential in the problem of establishing a static condition in which multiple singularities retain the initial position on the axis of the system. This is achieved due to relativistic effects, which have no analogues in Newton's theory of gravitation. Using the properties of relativistic potentials we have justified transition from the relativistic motion of the particles to the dynamic equations in the classic theory
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THE DEVELOPMENT OF COUNTRIES' CREDIT RATING ASSESSMENT SYSTEM
01.00.00 Physical-mathematical sciences
DescriptionThis work presents a new approach to the countries’ credit rating definition, based on the advanced mathematical models, such as neural network model, multiple regression, cluster analysis and discriminant analysis. A range of the analyses such as discriminant, cluster, multiple regression models and a neural network were performed on the following economic figures: GDP per capita, GDP value, annual growth rate of GDP, FDI - foreign investment, rate of unemployment, consumer price inflation index, the size of government debt in percentage of GDP. The results, obtained for each model were combined in the countries’ credit rating estimation system called "7M"
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ABOUT RECONNECTION PHENOMENON IN THE LOWER LAYERS OF A MAGNETIC TUBE. THEORY
01.00.00 Physical-mathematical sciences
DescriptionIt was shown before [1,2], that variants of intensity of γ-quantas of axion origin, induced by the variants of the magnetic field in the the tacho wedge through the termomagnetic Ettinshausen-Nernst effect, cause variations of solar luminance and ultimately characterise the changes of active and calm state of the Sun. It is shown in the article in which way the areas of sunspots are generated by the action of global dynamo in the convective zone, or in other words, which fundamental processes connect the sunspots and solar cycles with the large-scaled magnetic field of the Sun
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TO THE RESEARCH METHODS OF FAULTS UNDER THE VIBRATION IMPACTS
01.00.00 Physical-mathematical sciences
DescriptionWe propose an approach to the modeling of stressstrain state of lithospheric structures near faults by modeling them as Kirchhoff plates on threedimensional elastic foundation. We describe an efficient method of solving problems for plates with rectilinear fractures, based on the transformation of the differential operator, which allows us to analyze the solutions obtained for different contact conditions in the area of the fracture. The method is presented on the example of the vibration problem of two elongated plates on the surface of the elastic layer under the effect of concentrated surface load. The results of numerical implementation of the developed algorithm make it possible to identify the influence of the substrate properties, characteristics of the plates and the nature of their border interactions on the picture of wave process in the test structure. At the same time obtained configurations of the harmonic signal passage through the fracture can serve as an indicator of its type. The proposed approach should be used to determine the presence and type of fractures based on measurements of signals from vibration sources in cases when geophysical environment can be modeled by the previously described structure. The problems of studying objects we reviewed in this paper also occur in various areas of technology, and, therefore we can apply the proposed method for their solution
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DYNAMICS OF THE GEOMAGNETIC FIELD AND REVERSALS IN THE SATELLITE MODEL
01.00.00 Physical-mathematical sciences
DescriptionThe article deals with the problem of changing the polarity of the geomagnetic field in the satellite model. It is assumed that the central core of the earth magnetized and surrounded by a number of satellites, each of which has a magnetic moment. Satellites interact with a central core and one another by means of gravity and through a magnetic field. It is shown that satellites distributed in orbit around a central core in such a system. It displays two models, one of which on the outer orbit satellites interact with each other and with a central body - the core and satellites, located on the inner orbit. The central body can make sudden upheavals in the fall at the core of one or more satellites, which leads to the excitation of vibrations in the satellite system, located on the outer orbit. It is shown that the duration of phase with constant polarity and upheaval time depends on the magnitude of the disturbance torque and core asymmetry. The second model contains two magnets subsystems and the central core. The rapid change of the geomagnetic field polarity detected on the basis of paleomagnetic data is modeled based on the Euler theory describing the rigid body rotation. In this model, there are modes with a quick flip of the body while maintaining the angular momentum. If the body has a magnetic moment, when there is a change coup magnetic field polarity. This leads to the excitation of vibrations in the satellite subsystems that are on the inner and outer orbits. Numerical simulation of the dynamics of the system consisting of the core and 10-13 satellites was run to determine the period of constant polarity magnetic field
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01.00.00 Physical-mathematical sciences
DescriptionIn the present article, we investigate the metric of the crystal space in the general theory of relativity and in the Yang-Mills theory. It is shown that the presence of a lattice of gravitational ether has observable macroscopic consequences. Earlier, the influence of the gravity of the celestial bodies of the solar system on the electrical conductivity, inductance, the rate of radioactive decay of atomic nuclei, on seismic activity, the magnetic field and the motion of the pole of our planet, and on the rate of biochemical reactions was established. In all cases, a similar behavior of the physicochemical characteristics of materials and processes is observed, depending on the universal parameters characterizing the seasonal variations of the gravitational field of the solar system. The relationship between lattice parameters and the properties of materials, elements, atomic nuclei, and elementary particles is discussed. Possible metrics of the crystal space are constructed: a metric that depends on the Weierstrass function, derived in the Yang-Mills theory and analogous metrics found in Einstein's theory. Such metrics, which have a central symmetry, can be used to justify the structure of elementary particles, the properties of atomic nuclei, atoms and matter. Periodic metrics are constructed that admit an electromagnetic field, as well as metrics associated with the assumed structure of the crystal space. These metrics are of particular interest, since the properties of the substance are related to the metric parameters. We proposed the model of electron beam as a streamer of preons
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ELECTRON STRUCTURE AND THE YANGMILLS THEORY
01.00.00 Physical-mathematical sciences
DescriptionWe have studied the question of the electromagnetic structure of a relativistic electron in connection with the Yang-Mills theory. From the Lorentz electrodynamics equations of and Dirac electron theory derived an equation describing nonlinear waves of the scalar potential. It is shown that this equation is similar to the equation describing the dynamics of the condensate in the Yang-Mills theory. There is also the connection to the Schrödinger equation: the scalar potential is a complex function, similar to the wave function in the Schrödinger theory. The model discussed electron is a solitary wave that occurs in the electromagnetic field. This wave has the properties of charged particles, able to interact with the external electric and magnetic field. An analytical solution describing solitary electromagnetic waves traveling at a speed less than the speed of light has been obtained. The existence of solitary electromagnetic waves consistent with the Hertz's hypothesis that suggested that cathode rays are a form of wave motion in an electromagnetic field. The proposed model of the electromagnetic structure of the electron thus solves the problem of duality wave-particle, which historically arose in the interpretation of experiments with cathode rays. Numerical modeling of electromagnetic electron structure shows that the initial state such as a spherical shell is unstable and disintegrates into a pair of nonlinear waves that leave the system with the speed of light. In the decay of the initial state concentrated in the neighborhood of the origin, waves of complex part of potential disappear with time, but a real part of the potential it tends to equilibrium
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MANY-BODY PROBLEM IN THE METRIC OF CIRCULAR DISTRIBUTED SOURSES
01.00.00 Physical-mathematical sciences
DescriptionIn this article we consider the many-body problem in general relativity in the case of the distribution of N singularities on the circle. It specifies the exact solution of the problem for an arbitrary distribution of singularities. It is shown that the static metric of N singularities corresponds to Newton's theory of N centers of gravity, moving around the central body in a circular orbit in a non-inertial frame of reference, rotating with a period of bodies revolving. We consider the statement of the problem of many bodies distributed at the initial time on the circle. In numerical calculations, we studied the properties of the gravitational potential in the problem of establishing a static condition in which multiple singularities retain the initial position on the circle. This is achieved due to relativistic effects, which have no analogues in Newton's theory of gravitation. Using the properties of relativistic potentials justified transition from the relativistic motion of the particles to the dynamic equations in the classical theory. A system of non-linear parabolic equations describing the evolution of the metric in the Ricci flow proposed. The problem of the calculation of the potentials in the Ricci flow formulated. The application of the theory to describe the ring galaxy, planetary rings and the asteroid belt considered
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PROBABILISTIC MODEL OF THE PROCESS OF REDUCTION OF THE PRICE FOR PLANNED ACTIONS
01.00.00 Physical-mathematical sciences
DescriptionThe soil fertility increase issues are very relevant now. Intensive development of agriculture cannot be made effectively without complex actions for farmlands protection from different types of degradations. On the one hand, it is necessary to ensure the maximum harvest of crops, and to preserve and increase the fertility of the soil and prevent negative anthropogenic impact on the environment on the other. For an extended reproduction of soil fertility, a system of measures is necessary for introduction of mineral and organic fertilizers into the soil, agrotechnical and reclamation methods, stimulation of humus formation processes, and so on. Therefore, methods are important that allow us to estimate the planned measures in advance to improve soil fertility and to eliminate environmental damage. In the article, the estimated parameters are treated by random variables. This allows us to consider the uncertainty in terms of probability distributions. It is offered a probabilistic model of the process of reducing the price of the proposed activity. Mathematical expectation, variance, distribution density of the considered random variable probabilities as the main characteristics of the object state price are calculated. The model can be used to address issues of rational use of land, scientifically based land management organization, when drafting land reclamation project