一类双参共振的梁方程边值问题解的存在性

本文讨论了和四阶梁方程的两参数特征值问题u（4）－αu十＝0，u（O）＝u（1）＝u″（1）＝u（1）＝0相对应的非线性双参共振梁方程边值问题u（4）－α1u十βu十g（x，u，u″）＝h（x），u（0）＝u（1）＝u″（0）＝u（1）＝0其中（α1，β1）为特征值对）的解的存在性．应用Lyapunav－Schmidt过程和Leray－Schauder连续定理，得到了该问题的一个存在性结果．推广了Gupta在文［3］中的工作．     

非齐次对称特征值问题

引言 用SR~(n×n)表示所有。n×n实对称矩阵的集合。R~n表示n维线性空间。||·||_2表示向量的Euclid范数或矩阵的谱范数。 本文研究如下问题: 问题ISEP 给定矩阵A∈SR~n×n和向量b∈R~n,求实数λ和向量X∈R~n使得 AX=λX+b, (1) ||X||_2=1. (2) 若b=0,则问题ISEP就是通常的实对称矩阵特征值问题,若b≠0,则问题ISEP称为非齐次对称特征值问题,使(1)和(2)式成立的数λ和向量X分别称为非齐次特征值和相应的非齐     

Applications of parametric programming and eigenvalue maximization to the quadratic assignment problem

We investigate new bounding strategies based on different relaxations of the quadratic assignment problem. In particular, we improve the lower bound found by using an eigenvalue decomposition of the quadratic part and by solving a linear program for the linear part. The improvement is accomplished by applying a steepest ascent algorithm to the sum of the two bounds.Both authors would like to thank the Natural Sciences and Engineering Research Council Canada and the Austrian Government for their support.This author would like to acknowledge partial support from the Department of Combinatorics and Optimization at the University of Waterloo.Research partially supported by Natural Sciences and Engineering Research Council Canada.     

一类非线性四阶椭圆型方程的极值原理及其特征值问题

主要应用 Hopf极值原理 ,对一类非线性四阶椭圆型方程Δ2 u +h( x,u,Δu) =0进行研究 ,得到解的泛函的极值原理 .类似的文章结果也有许多 ,其方法均为构造适当的“P-泛函”,但是以前的结果都对方程有较强的要求限制 .本文通过构造新的泛函 ,减弱了要求限制 .同时对方程Δ2 u +λh( x,u,Δu) =0的特征值给出了估计 .     

相依回归系统的主成分改进估计

对两个相依方程组成的回归系统,当设计矩阵呈病态时,提出了回归系数的一个主成分估计β_1**(k)及其相应的两步估计β_1**(k,T),并在均方误差意义下研究了它们的优良性质。     

Multilevel regularization of wavelet based fitting of scattered data – some experiments

In [6], an adaptive method to approximate unorganized clouds of points by smooth surfaces based on wavelets has been described. The general fitting algorithm operates on a coarse-to-fine basis. It selects on each refinement level in a first step a reduced number of wavelets which are appropriate to represent the features of the data set. In a second step, the fitting surface is constructed as the linear combination of the wavelets which minimizes the distance to the data in a least squares sense. This is followed by a thresholding procedure on the wavelet coefficients to discard those which are too small to contribute much to the surface representation. In this paper, we firstly generalize this strategy to a classically regularized least squares functional by adding a Sobolev norm, taking advantage of the capability of wavelets to characterize Sobolev spaces of even fractional order. After recalling the usual cross-validation technique to determine the involved smoothing parameters, some examples of fitting severely irregularly distributed data, synthetically produced and of geophysical origin, are presented. In order to reduce computational costs, we then introduce a multilevel generalized cross-validation technique which goes beyond the Sobolev formulation and exploits the hierarchical setting based on wavelets. We illustrate the performance of the new strategy on some geophysical data. AMS subject classification 65T60, 62G09, 93E14, 93E24We gratefully acknowledge the support by the Deutsche Forschungsgemeinschaft (KU 1028/7 1 and SFB 611) and by the Basque Government.     

求常系数线性齐次差分方程组通解的一种方法

给出了求常系数线性齐次差分方程组通解的一种方法 ,用一个例子说明所给方法 .     

矩阵特征值、特征向量的确定

首先对由 A的特征值、特征向量求 A- 1 ,AT,A* ( A的伴随矩阵 )、P- 1 AP以及 A的多项式φ( A)的特征值和特征向量的结论作了个归纳 ;对相反的情形 ,我们给出了部分已有的结果 ,并通过四道例题着重讨论了如何由 φ( A)的特征值来求 A的特征值 .     

紧流形上的第一特征值

This paper discusses the first eigenvalue on a compact Riemann manifold with the negative lower bound Ricci curvature. Let M be a compact Riemann manifold with the Ricci curvature≥-R, R=const. ≥0 and d is the diameter of M. Our main result is that the first eigenvalue λ1 of M satisfies λ1≥π^2/d^2-0.518R.     

一类幂零群上的特征值问题及估计

本文对幂零Lie群H_n×R^k上的Laplace算子,利用酉表示理论证明了它在全空间上无特征值存在,通过推广Friedrichs方法证明了在有界域上存在一列离散特征值,最后通过建立不变向量场之间的关系给出了特征值之差的估计.