№ 126(2), February, 2017
Public date: 28.02.2017
Archive of journal: Articles count 63, 153 kb
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01.00.00 Physical-mathematical sciences
01.00.00 Physical-mathematical sciences
DescriptionIn the article we investigate the multicriteria task arising at the organization of distributed calculations in a corporate network. As a mathematical tool to solve the problem we use prefractal graphs, which naturally reflect the structure of relationships in global and corporate networks. The corporate network with the distributed computing system at the solution of a particular task has to be reliable, quickly and qualitatively to make decisions. And every computer in the network should be a part in the solution of the problem, since it is fixed for a certain function. The problem is reduced to cover the prefractal graphs with disjoint simple paths along the edges and vertices. On the set of all admissible coverings we constructed a vector-target function with specific criteria. All these criteria have a specific meaningful interpretation, allowing organizing the calculation of maximum reliability, with minimum time information processing and loading balancing between the network elements. In the article we constructed polynomial algorithms for finding optimal solutions according to specific criteria. For the criteria which are not optimizing the allocated coverings, estimates of the lower and upper bounds are given. For all the algorithms we constructed and substantiated estimation of computational complexity, confirming the advantage of using algorithms on prefractal graphs to classical algorithms on graphs
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INVERSE PROBLEM MODELS OF THE SAMUELSON–HICKS
01.00.00 Physical-mathematical sciences
DescriptionThe article continues the cycle of their studies associated with the formulation and development of methods of construction of nonnegative solutions of inverse problems for dynamic systems. In this article the authors formulated and investigated inverse problems for dynamic systems: model of Samuelsson– Hicks. The technique of constructing non-negative solutions of the studied inverse problems. This method is based on the following scheme of the solution. First, we have to identify the formulation of the direct problem, then the formulation of the inverse. This work investigates how correct the mathematical models describing the dynamic economic system are. Further, in the specified tabular solutions of the direct problem, we have built a system of algebraic equations containing the unknown estimated parameters of the studied model. Then posed inverse problem is reduced to solution of a problem of quadratic programming, the solutions of which are defined in MS Excel. The theoretical material is accompanied by the specific example
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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