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991.
Jipu Ma 《Frontiers of Mathematics in China》2008,3(2):305-316
Let E and F be Banach spaces, f: U ⊂ E → F be a map of C
r
(r ⩾ 1), x
0 ∈ U, and ft (x
0) denote the FréLechet differential of f at x
0. Suppose that f′(x
0) is double split, Rank(f′(x
0)) = ∞, dimN(f′(x
0)) > 0 and codimR(f′(x
0)) s> 0. The rank theorem in advanced calculus asks to answer what properties of f ensure that f(x) is conjugate to f′(x
0) near x
0. We have proved that the conclusion of the theorem is equivalent to one kind of singularities for bounded linear operators,
i.e., x
0 is a locally fine point for f′(x) or generalized regular point of f(x); so, a complete rank theorem in advanced calculus is established, i.e., a sufficient and necessary condition such that the
conclusion of the theorem to be held is given.
相似文献
992.
Byung Do Kim 《数学学报(英文版)》2008,24(3):353-372
In this paper, we investigate the stability of functional equation given by the pseudoadditive mappings of the mixed quadratic and Pexider type in the spirit of Hyers, Ulam, Rassias and Gavruta. 相似文献
993.
在Mann的迭代算法基础上,运用Banach空间中的广义投影,使渐进非扩展映像每次迭代生成的序列都投影到一个闭凸的集合中.并证明了该算法的强收敛性. 相似文献
994.
M.T. Darvishi S. Kheybari F. Khani 《Communications in Nonlinear Science & Numerical Simulation》2008,13(10):2091-2103
In this paper, a numerical solution of the generalized Burgers–Huxley equation is presented. This is the application of spectral collocation method. To reduce roundoff error in this method we use Darvishi’s preconditionings. The numerical results obtained by this method have been compared with the exact solution. It can be seen that they are in a good agreement with each other, because errors are very small and figures of exact and numerical solutions are very similar. 相似文献
995.
Hongxia Wu Yunbo Zeng Tianyou Fan 《Communications in Nonlinear Science & Numerical Simulation》2008,13(10):2146-2156
The negative extended KdV equation with self-consistent sources (eKdV−ESCSs) is firstly presented and the associated linear auxiliary equations are derived. The generalized binary Darboux transformation (DT) is applied to construct some new solutions of the eKdV−ESCSs such as singular N-soliton solution, N-soliton solution with finite amplitude, N-positon solution and N-negaton solution. The properties of these solutions are analyzed. Moreover, the interactions of two solitons, positon and negaton, positon and soliton, and two positons are discussed. 相似文献
996.
997.
In this paper, we present an existence result for weak efficient solution for the vector optimization problem. The result is stated for invex strongly compactly Lipschitz functions. 相似文献
998.
999.
1000.
A rotating cylindrical electrochemical cell with a plane ring electrode on its cover containing a binary electrolyte was considered. The equation for the diffusion limiting current density on the ring electrode was derived ignoring the effect of Coriolis force. The solution of transfer equations by the Karman method at the limiting current in the cell allowed us to analyze the effect of Coriolis force on the boundary layer thickness and to determine the conditions, under which the Coriolis force may be ignored. 相似文献