№ 134(10), December, 2017
Public date: 29.12.2017
Archive of journal: Articles count 112, 287 kb
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01.00.00 Physical-mathematical sciences
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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VORTEX TURBULENT FLOWS IN ATMOSPHERES OF PLANETS AND ON THE SUN
01.00.00 Physical-mathematical sciences
DescriptionIn this work, we consider two types of vortex currents-cyclones and anticyclones in the Northern and Southern Hemispheres. Numerical modeling of turbulent flows of these types uses the model of the planetary boundary layer developed by the author. The purpose of the study is to test hypotheses about the influence of the Coriolis force on the formation of cyclones and anticyclones in the northern and southern latitudes. The first hypothesis on the direction of circulation in cyclones was verified in the case of axisymmetric radially converging and vertically rising turbulent flows with a natural Coriolis parameter and viscosity. From the obtained data of numerical experiments, it follows that the current in the northern latitudes circulates in a counter clockwise direction, and in the south - in a clockwise direction, in full accordance with the observational data. Thus, we have shown that a cyclonic flow is formed in a turbulent radially converging flow under the influence of the Coriolis force. The second hypothesis on the formation of anticyclones was verified in the case of radially divergent and vertically descending turbulent flows. Because of numerical experiments, it was established that in this case, the current in the northern latitudes circulates clockwise, and in the south - in a counter clockwise direction, which corresponds to observations for anticyclones. To test the effect of the cyclone (anticyclone) center velocity on circulation, a nonstationary 3D model of turbulent flow was developed. Within the framework of this model, flows in cyclones and anticyclones moving at a constant speed, as well as in shear flow, are studied. Some types of loop protuberances on the Sun are explained by the presence of a vortex turbulent flow starting in the bowels of the Sun and encompassing the chromosphere