ON THE RAYLEIGH QUOTIENT FOR SINGULAR VALUES

In this paper, the theoretical analysis for the Rayleigh quotient matrix is studied, some results of the Rayleigh quotient （matrix） of Hermitian matrices are extended to those for arbitrary matrix on one hand. On the other hand, some unitarily invariant norm bounds for singular values are presented for Rayleigh quotient matrices. Our results improve the existing bounds.     

具有时滞的Rayleigh方程周期解的存在性与唯一性

本文研究了具有偏差变元的Rayleigh方程周期解的存在性和唯一性.利用Mawhin连续性定理,得到了该方程周期解存在性和唯一性的新结果,改进了一些已有结果.     

关于Rayleigh商矩阵

§1.预备知识 在不加注明的情况下,本文沿用[3]中的记号. 设A为n×n矩阵,Q及?为n×m矩阵,而且m相似文献   

ON TRAVELING WAVES OF A GENERALIZED BISTABLE EQUATION

1. IntroductionConsider the initial value problem for the bistable equationwhere f(u) = u(1-u)(u-a) and 0 < 2a < 1. Let us examine the critical points of f. Sincethe critical points are given by ρ±(a)=1/3(1 a± √1-a a~2),which are functions of theparameter a and satisfy ρ(a) ρ-(a) =2 2a/3 andρ p (a)ρ-(a)= a/3. Sinceone can obtain the ranges of the critical points 0 < ρ-(a) <1/4, 2/3 <ρ (a) <4/5. For anyconstant w with f(ρ-(a)) < w < f(ρ (a)), suppose that f(u) - w = -(u - A)(u …     

半直线上的Hammerstein积分方程的有限截段逼近

在半直线上线性积分方程:的数值求解中,用方程(0.1)相应的有限截段方程的解、x_m(s)逼近原方程的解x(s)的方法得到x_m对x在有限区间上的一致收敛性结果.用这种方法研究方程(0.1)的数值解日见增多,特别是在[1]中,Anselone与Sloan提出所谓点列的“严格收敛性”概念来研究方程(0.1)与(0.2)的关系,显著地改