№ 131(7), September, 2017
Public date: 29.09.2017
Archive of journal: Articles count 124, 307 kb
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01.00.00 Physical-mathematical sciences
THE RATIONALE FOR THE USE OF ELECTROMAGNETIC FIELD IN THE PRODUCTION OF SUNFLOWER OIL
01.00.00 Physical-mathematical sciences
DescriptionIn some works, the feasibility of the use of fixed and variable electromagnetic fields of different frequencies and tension in the production technology of sunflower oil are shown, but there is no theoretical justification. The possibility of electromagnetic effects is associated with the presence of polar molecules specific to organic systems. Without prejudice to the role of polar groups of terrestrial circuits, this work tries to address this challenge more comprehensively. The reason for this is the distinctive feature of the behavior of sunflower during its flowering. This characteristic is that the sunflower hat during the day changes its direction in accordance with the direction of movement of the Sun across the sky; so called "magnetism" of their attraction. To justify this effect, we have analyzed the essence of emitted photons, the Sun chemical composition and structure arrangement of seeds in a sunflower hat. Particles of light from the Sun represent a stream of photons - a wide range of electromagnetic waves of frequencies that exhibit and magnetic properties. The article shows principal macro- and micronutrients of sunflower raw materials and divides them into groups of para- , dia- , and ferromagnetic materials. In sunflower seeds, there are chemical elements: diamagnetism-C, H, N, P, S, B, Cu, Zn, J; paramagnetism-O, K, Ca, Mg, Mo, As and ferromagnetic-iron (Fe). As there is resultant force of the magnetic attraction between the sunflower hat and magnetic flow of photons from the Sun, this effect dominates the action of paramagnetics K2O ( -28.4 24.5%), CaO (7.6-17.0)%, MgO (12.3-17.9%), magnetized in an external magnetic field in the direction of the field. The presence of evident effect demonstrates that it is possible to improve a number of technological operations in the manufacture of sunflower oil using electrical, magnetic or electromagnetic fields
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SIMULATION OF A STEPPED LIGHTNING LEADER
01.00.00 Physical-mathematical sciences
DescriptionIn this work, a model is developed that describes the formation of a stepped lightning leader in a conducting medium. To describe the contribution of the conductivity currents, we modified the standard electrostatic equation taking into account the vortex component of the electric field. As a result of this generalization, a system of parabolic-type nonlinear equations is formulated that describes the formation of streamers and the lightning channel. Numerical simulation of the propagation of ionization waves in a region with a ratio of 1/100, 1/200 allows us to identify two types of stepped streamers in the form of waves of compression and rarefaction, respectively. It was previously established that there are three streamer branching mechanisms. The first mechanism is related to the instability of the front, which leads to the separation of the head of the streamer into two parts. The second mechanism is associated with 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. In numerical experiments, the third branching mechanism observed in experiments connected with closing the space charge to the anode through the streamer system was observed. These branching mechanisms are also revealed when the leader is propagated. The obtained results, as well as the data of numerical experiments confirm the hypothesis of the universality of the minimal model of the streamer, as well as its expansion in the form proposed by the author. Known phenomena of nature associated with the electrical discharge - streamer, plasmoid, ball lightning and stepped leader can be described within the framework of the minimal model
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ASYMPTOTICS OF ESTIMATES OF PROBABILITY DISTRIBUTION DENSITY
01.00.00 Physical-mathematical sciences
DescriptionNonparametric estimates of the probability distribution density in spaces of arbitrary nature are one of the main tools of non-numerical statistics. Their particular cases are considered - kernel density estimates in spaces of arbitrary nature, histogram estimations and Fix-Hodges-type estimates. The purpose of this article is the completion of a series of papers devoted to the mathematical study of the asymptotic properties of various types of nonparametric estimates of the probability distribution density in spaces of general nature. Thus, a mathematical foundation is applied to the application of such estimates in non-numerical statistics. We begin by considering the mean square error of the kernel density estimate and, in order to maximize the order of its decrease, the choice of the kernel function and the sequence of the blur indicators. The basic concepts are the circular distribution function and the circular density. The order of convergence in the general case is the same as in estimating the density of a numerical random variable, but the main conditions are imposed not on the density of a random variable, but on the circular density. Next, we consider other types of nonparametric density estimates - histogram estimates and Fix-Hodges-type estimates. Then we study nonparametric regression estimates and their application to solve discriminant analysis problems in a general nature space
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THE REALIZATION OF GALOIS GROUPS BY TRINOMIALS OVER THE FIELD OF RATIONAL NUMBERS Q
01.00.00 Physical-mathematical sciences
DescriptionIt is known that not every finite group can be realized over the field of rational numbers as a Galois group of some binomial. In this connection, a more general question arises: suppose that there is given a finite transitive subgroup G of the symmetric group S on n symbols; Can this group G be realized as a Galois group of some trinomial of degree n over the field of rational numbers? In this paper we prove that every transitive subgroup of the group S can be realized in the form of the Galois group of a certain trinomial of the degree n, for the values n = 2, 3, 4. For n = 5 , 6 we give examples that realize concrete Galois groups. In the case n = 7, all the transitive subgroups of the group S are realized, except possibly one group of the isomorphic dihedral group D. Further calculations will be directed to the realization of specific Galois groups for n = 8, 9 ..., however, the number of transitive subgroups of the group S for n = 8, 9 ... grows very fast, so the larger the value of n, the more difficult it is to realize not just everything but the specific subgroup of the group S in the form of a trinomial over Q