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31.
An analytical function f(A) of an arbitrary n×n constant matrix A is determined and expressed by the “fundamental formula”, the linear combination of constituent matrices. The constituent matrices Zkh, which depend on A but not on the function f(s), are computed from the given matrix A, that may have repeated eigenvalues. The associated companion matrix C and Jordan matrix J are then expressed when all the eigenvalues with multiplicities are known. Several other related matrices, such as Vandermonde matrix V, modal matrix W, Krylov matrix K and their inverses, are also derived and depicted as in a 2-D or 3-D mapping diagram. The constituent matrices Zkh of A are thus obtained by these matrices through similarity matrix transformations. Alternatively, efficient and direct approaches for Zkh can be found by the linear combination of matrices, that may be further simplified by writing them in “super column matrix” forms. Finally, a typical example is provided to show the merit of several approaches for the constituent matrices of a given matrix A.  相似文献   
32.
The Lie group method is applied to make a group classification of the PDE governs the dispersion of gaseous pollutants in the presence of a temperature inversion and obtained on a great varity of analytical solutions. The pollutants are assumed to be spread in the layer bounded by the ground surface and the inversion level and they are driven by wind in the horizontal direction. The general solution has been specified for two cases; (i) the ground absorbs all the gaseous pollutants and (ii) the ground does not absorb any pollutant.  相似文献   
33.
A simple and efficient approximate numerical technique is presented to obtain solutions to a wide class of two-point boundary value similarity problems in fluid mechanics. This technique is based on the common finite difference method with central differencing, a tridiagonal matrix manipulation and an iterative procedure. The technique described in this paper has been successfully applied to three different representative similarity problems of fluid mechanics. Each one of these problems is described by a coupled, non-linear system of three ordinary differential equations and has already been solved elsewhere using a different numerical method. So, the obtained numerical results, by our efficient numerical technique, permit a comparative study and show the accuracy and the effectiveness of this technique.  相似文献   
34.
35.
Based on three physicochemical properties of amino acid side chains, we proposed a novel unique 3D graphical representation of protein sequences. Then, we constructed two vectors of three components as mathematical objects to characterize protein sequences numerically. The similarity/dissimilarity analysis among nine ND5 protein sequences proved the utility of our approach. A correlation and significance analysis have been provided to compare our results and the sequence homology.  相似文献   
36.
两四元数相似当且仅当它们有相同的实部和模,两四元数合相似当且仅当它们有相同的模.应用四维Clifford代数的矩阵表示,得到了四维Clifford代数中两元素相似或合相似的充分必要条件.  相似文献   
37.
The steady laminar boundary layer flow over a permeable flat plate in a uniform free stream, with the bottom surface of the plate is heated by convection from a hot fluid is considered. Similarity solutions for the flow and thermal fields are possible if the mass transpiration rate at the surface and the convective heat transfer from the hot fluid on the lower surface of the plate vary like x−1/2, where x is the distance from the leading edge of the solid surface. The governing partial differential equations are first transformed into ordinary differential equations, before being solved numerically. The effects of the governing parameters on the flow and thermal fields are thoroughly examined and discussed.  相似文献   
38.
The simultaneous effects of suction and injection on tangential movement of a nonlinear power-law stretching surface governed by laminar boundary layer flow of a viscous and incompressible fluid beneath a non-uniform free with stream pressure gradient is considered. The self-similar flow is governed by Falkner-Skan equation, with transpiration parameter γ, wall slip velocity λ and stretching sheet (or pressure gradient) parameter β. The exact solution for β = −1 and three closed form asymptotic solutions for β large, large suction γ, and λ → 1 have also been presented. Dual solutions are found for β = −1 for each value of the transpiration parameter, including the non-permeable surface, for each prescribed value of the wall slip velocity λ. The large β asymptotic solution also dual with respect to wall slip velocity λ, but do not depend on suction and blowing. The critical values of γ, β and λ are obtained and their significance on the skin friction and velocity profiles is discussed. An approximate solution by integral method for a trial velocity profile is presented and results are compared with the exact solutions.  相似文献   
39.
The variable-coefficient Kadomtsev-Petviashvili (KP) equation is hereby under investigation. Painlevé analysis is given out, and an auto-Bäcklund transformation is presented via the truncated Painlevé expansion. Based on the auto-Bäcklund transformation, new analytic solutions are given, including the soliton-like and periodic solutions. It is also reduced to a (1+1)-dimensional partial differential equation via classical Lie group method and the Painlevé I equation by CK direct method.  相似文献   
40.
We introduce an approach that combines a similarity method with several transformations to find analytical solitary wave solutions for a generalized space- and time-variable coefficients of nonlinear Schrödinger equation with higher-order terms with consideration of varying dispersion, higher nonlinearities, gain/loss and external potential. One of these transformations is constructed in such a way that allows study of the width of localized solutions. Solitary-like wave solutions for front, bright and dark are given. The precise expressions of the soliton?s width, peak, and the trajectory of its mass center and the external potential which are symbol of dynamic behavior of these solutions, are investigated analytically. In addition, the dynamical behavior of moving, periodic, quasi-periodic of breathing, and resonant are discussed. Stability of the obtained solutions is analyzed both analytically and numerically.  相似文献   
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