Current Issue : April - June Volume : 2020 Issue Number : 2 Articles : 6 Articles
The rational canonical form theorem is very essential basic result of\nmatrix theory, which has been proved by different methods in the\nliterature. In this note, we provide an efficient direct proof, from\nwhich the minimality for the decomposition of the rational canonical\nform can be found....
The flow and heat transfer of the basalt melt in the boundary layer on a flat\nplate is considered. The conditions of formation of the layer and the intensity\nof heat transfer are determined. A self-similar analysis using the symmetry\nmethod was used. A system of ordinary differential equations in self-similar\nform is obtained. The fluid flow and heat transfer of molten basalt at a laminar\nsteady-state flow in the feeder furnaces are numerically researched. The\nterm â??protective layerâ? on the interface â??basalt melt-liningâ? is introduced.\nThe dependences for the calculation of dimensionless shear stresses and the\nNusselt number on the lining surface are obtained. The conditions of rational\norganization of the technological process of basalt melt feeding in the furnace\nfeeder are formulated....
Let b greater then or equal to 2 be a numeration base. A b-weak additive Ramanujan-Hardy (or\nb-wARH) number N is a non-negative integer for which there exists at least\none non-negative integer A, such that the sum of A and the sum of base b digits\nof N, added to the reversal of the sum, give N. We say that a pair of such\nnumbers are related of degrees d greater then or equal to 0 if their difference is d. We show for all\nnumeration bases an infinity of degrees d for which there exists an infinity of\npairs of b-wARH numbers related of degree d....
This article deals with a numerical approach based on the symmetric space-time Chebyshev\nspectral collocation method for solving different types of Burgers equations with Dirichlet boundary\nconditions. In this method, the variables of the equation are first approximated by interpolating\npolynomials and then discretized at the Chebyshevâ??Gaussâ??Lobatto points. Thus, we get a system of\nalgebraic equations whose solution is the set of unknown coefficients of the approximate solution of\nthe main problem. We investigate the convergence of the suggested numerical scheme and compare\nthe proposed method with several recent approaches through examining some test problems....
This article studied the principles of movements in the horizontal part of the\nnewly constructed ginning camera, which is created by the authors, of the\ncotton particles. During the movement, the cotton particles get affected by\npressing to various surface and forceful turbulent and horizontal movements\nof the surface. Some foreign mixtures and additional unnecessary objects get\nseparated by the turbulence of the various surfaces and movement of the paneled\nstripes. Ginning efficiency and the quality of the cotton will be improved\nas the defects of the cotton particles are removed. â??Cotton particle + net surfaceâ?\nmovement principle of the Cartesian coordinate system was examined\nbased on the rows of Cartesian coordinate system, by dividing all sides of the\nsystem by m weight and has the following second ordered multiple gender\ndifferential formula....
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