01.00.00 Physical-mathematical sciences
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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
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LOGARITHMIC LAW AND EMERGENCE PARAMETER OF CLASSICAL AND QUANTUM SYSTEMS
01.00.00 Physical-mathematical sciences
DescriptionThe work discusses various examples of physical systems which state is determined by the logarithmic law - quantum and classical statistical systems and relativistic motion in multidimensional spaces. It was established that the Fermi-Dirac statistics and BoseEinstein-Maxwell-Boltzmann distribution could be described by a single equation, which follows from Einstein's equations for systems with central symmetry. We have built the rate of emergence of classical and quantum systems. The interrelation between statistical and dynamic parameters in supergravity theory in spaces of arbitrary dimension was established. It is shown that the description of the motion of a large number of particles can be reduced to the problem of motion on a hypersphere. Radial motion in this model is reduced to the known distributions of quantum and classical statistics. The model of angular movement is reduced to a system of nonlinear equations describing the interaction of a test particle with sources logarithmic type. The HamiltonJacobi equation was integrated under the most general assumptions in the case of centrally-symmetric metric. The dependence of actions on the system parameters and metrics was found out. It is shown that in the case of fermions the action reaches extremum in fourdimensional space. In the case of bosons there is a local extremum of action in spaces of any dimension
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01.00.00 Physical-mathematical sciences
DescriptionThe creation of artificial intelligence systems is one of important and perspective directions of development of modern information technology. Since there are many alternatives of mathematical models of systems of artificial intelligence, there is a need to assess the quality of these models, which requires their comparison. To achieve this goal we require free access to the source data and methodology, which allows to convert these data into a form needed for processing in artificial intelligence. A good choice for these purposes is a database of test problems for systems of artificial intelligence of repository of UCI. In this work we used the database "Iris Data Set" from the bank's original task of artificial intelligence – UCI repository, which solved the problem of formalization of the subject area (development of classification and descriptive dials and graduations and the encoding of the source data, resulting training sample, essentially representing a normalized source data), synthesis and verification statistical and system-cognitive models of the subject area, identify colors with classes, which serve varieties of Iris, as well as studies of the subject area by studying its model. To solve these problems we used the automated system-cognitive analysis (ASC-analysis) and its programmatic Toolkit – intellectual system called "Eidos"
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01.00.00 Physical-mathematical sciences
DescriptionAn analysis of the experimental data obtained by the authors, as well as reference books, allowed to hypothesize about the essential role of gravitational convection in electromembrane systems with ampholytes even in underlimiting current regimes. The article is devoted to the development of the mathematical model of ion transport in a flow elecrtomembrane system during electrodialysis of ampholyte-containing solutions with taking into account a possible appearance of gravitational convection, in particular, due to nonisothermal protonation–deprotonation reactions of ampholytes. The article presents the boundary value problem that is the new mathematical model for diffusion, convection and electromigration of four components of the solution (ions of sodium, dihydrogen phosphate and hydrogen, as well as molecules of orthophosphoric acid) in a half of an electrodialysis desalination channel, adjacent to an anion-exchange membrane. The membrane is considered as ideally selective and homogeneous. The system of partial differential equations, that is the base of the model, also includes equations of Navier-Stokes, material balance, convective heat conduction and the electroneutrality condition. The system of equations is supplemented by a number of natural and original boundary conditions. A distinctive feature of this study is the absence of assumptions about the equilibrium of chemical reactions in a diffusion layer. The results of the study can be used for the development of environmentally rational and resource saving membrane technologies for a processing of products of agro-industrial complex
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SIMULATION OF A PLASMA CHANNEL AND TRACK IN MOTION OF PLASMA SOURCE IN CONDUCTIVE ENVIRONMENT
01.00.00 Physical-mathematical sciences
DescriptionA model is developed that describes the formation of the plasma channel and the trace when moving in a conducting medium of various objects that are sources of plasma - ball lightning, plasmoids, charged particles, and so on. To describe the contribution of conduction currents, we modified the standard electrostatic equation considering the vortex component of the electric field. As a result of this generalization, a system of parabolictype nonlinear equations is formulated that describes the formation of the plasma channel and the track behind the moving object. In this formulation, the problem of the formation of the lightning channel in weak electric fields, characteristic for atmospheric discharges of cloudearth, is solved. Numerical simulation of the motion of plasma sources in a region with a ratio of the sizes 1/100, 1/200 makes it possible to find the shape of the channel and the total length of the track, as well as the branching regimes. It was previously established that there are three streamer branching mechanisms. The first mechanism is associated with the instability of the front, which leads to the separation of the head of the streamer into two parts. The second mechanism is related to the instability of the streamer in the base region, which leads to the branching of the streamer with the formation of a large number of lateral streamers closing the main channel of the streamer to the cathode. The third branching mechanism, observed in experiments, is associated with the closure of the space charge to the anode through the streamer system. These branching mechanisms are also revealed when the leader is spread. Numerical experiments have revealed a new channel branching mechanism and a trace behind a moving plasma object, caused by the conductivity of the medium
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01.00.00 Physical-mathematical sciences
DescriptionThe time-optimal diagram of movement of the executive body of the precision DC drive with elastic shafting with constrains of maximum current and the fifth derivative of the speed has been designed. The algorithm has been developed to determine the parameters of the time-optimal diagram of movement of the executive body of the precision DC drive with elastic shafting with constrains of maximum current and the fifth derivative of the speed. The region of existence of the time-optimal diagram of movement of the executive body of the precision DC drive with elastic shafting with constrains of maximum current and the fifth derivative of the speed has been set. According to the results of the numeral experiment, the dependences of the duration of the cycle of movement of the executive body of the drive from prescribed displacement (rotation angle) for different values of the fifth derivative of the speed have been plotted
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SIMULATION OF ATMOSPHERIC VORTEX FLOWS ON JUPIER AND SATURN
01.00.00 Physical-mathematical sciences
DescriptionAtmospheric currents on Jupiter and Saturn are characterized by turbulence and complex vortex structure, which is caused by a large angular speed of the gas giants. In this paper we consider two types of eddy currents - for hexagonal in the northern polar region of Saturn and the Great Red Spot in the equatorial region of Jupiter. For the numerical simulation of turbulent flows of this type the model of the planetary boundary layer was developed by the author. In both cases, the main strengthening mechanism is associated with geostrophic flow of small amplitude interacting with the planetary turbulent boundary layer. For hexagonal Saturn with its characteristic length scales and speed - 120 m / s and 14,500 km, respectively, there are more than 35 years data of observation. We have found that a small axial symmetry violation geostrophic flow in the shear causes the development of a hexagonal pattern in a turbulent boundary layer. In addition, under the influence of the Coriolis force and the eddy viscosity gradient in the turbulent boundary layer there is the jet formed, pressed against the lower edge of the layer. Great Red Spot on Jupiter has the characteristic velocity and length scales - 150 m / s, 14,000 km from north to south and 24000-40000 km from west to east, there are already more than 350 years data. It identified another mechanism of formation of vortex flow, coupled with the strengthening of small amplitude zonal flow in a turbulent boundary layer with the eddy viscosity gradient and the volume turbulent viscosity on a rotating planet. Both mechanisms are confirmed by numerical calculations of non-stationary planetary boundary layer
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THEORY OF PHYSICAL CONSTANTS AND SUPERGRAVITY IN 112D
01.00.00 Physical-mathematical sciences
DescriptionIn this article we discuss a version of the metric theory of the fundamental interactions in which it is assumed that the physical constants due to the presence of extra dimensions of space-time. The estimation of the number of physical constants based on the theory of supergravity in 112D is that the minimum number of constants is equal to 222, and the maximum number - 1404928. At present, the number of parameters that characterize the elementary particles, isotopes and chemical elements is about 150920. This number is 9.3 less than the maximum possible number of parameters that indicate still great potential of modern science. Functions describing the area and volume of a unit hypersphere, embedded in a Riemannian space of arbitrary dimension, were used to find the fundamental physical constants. A satisfactory agreement with a relative error of 0.03% calculated and experimental values of the fine structure constant found out. For the ratio of the average mass of a nucleon to the electron mass is obtained coincidence with the experimental value with an accuracy of 0.002%. The proposed theory of physical constants different from that Bartini theory that established the optimal dimension of the space is a hypersphere 5 and 7, rather than 6 as in Bartini theory. The problems of the compactification of extra dimensions in describing the motion in fourdimensional space-time are discussed
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01.00.00 Physical-mathematical sciences
DescriptionThe problem of establishing of the factorization of irreducible polynomials with integer coefficients on prime modules p has been long of interest to mathematicians. The quadratic and cubic reciprocity laws solve this problem for quadratic polynomials and binomials of the form x3-a . More general reciprocity laws solve the formulated problem for some classes of polynomials, for example, with Abelian Galois group, but for polynomials with non-Abelian Galois group, the problem is far from its complete solution. Our study shows how using the results of Voronov G.F., Hasse H. and Stickelberger L., one can find conditions that must satisfy prime number p. Gauss received a similar result for binomial x3-2. Specific examples are given, for instance, for the polynomial x3-x - I, also conditions arc formulated for which a quadratic field is immersed in non-Abelian Galois extension of degree 6. Also, conditions are given under which a Diophantine equation: а12a22-4a22-4a13a3- 27a32+18a1a2a3=D has a solution for integer values of D
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CHARACTERIZATION OF AVERAGE VALUES BY MEANS OF MEASUREMENT SCALES
01.00.00 Physical-mathematical sciences
DescriptionAccording to measurement theory, statistical data are measured in various scales. The most widely used ordinal scale, scales of intervals and relations. Statistical methods of data analysis should correspond to the scales in which the data is measured. The term "correspondence" is specified with the help of the concepts of an adequate function and an allowable scale transformation. The main content of the article is a description of the average values that can be used to analyze data measured in the ordinal scale, interval and relationship scales, and some others. The main attention is paid to the means for Cauchy and the means for Kolmogorov. In addition to the mean, from this point of view, polynomials and correlation indices are also analyzed. Detailed mathematical proofs of characterization theorems are given for the first time in scientific periodicals. It is shown that in the ordinal scale there are exactly n average values, that can be used, namely, n order statistics. The proof is represented as a chain of 9 lemmas. In the scale of intervals from all Kolmogorov means, only the arithmetic mean can be used. In the scale of relations from all the Kolmogorov means, only the power means and the geometric mean are permissible. The kind of adequate polynomials in the relationship scale is indicated