特征值

For the one-dimensional p-Laplacian with indefinite weights, four sequences of periodic and anti-periodic eigenvalues are given by introducing the rotation number function, and these eigenvalues are the endpoints of the preimage intervals of the rotation number function at nonnegative integers.

本文以带变号权函数和带变号势函数的一维p-Laplacian为基本模型，系统地阐述了特征值的旋转数方法、带正权Dirichlet特征值的最佳估计、特征值在正则和奇异渐近半线性方程的可解性中的应用、Fucik谱的旋转数方法以及Fucik谱在周期解的扭转性和多解性中的应用。

Firstly, the eigenvalue problem of a class of second order elliptic equation with critical potential and indefinite weights is considered. Then, using critical point theory, Trudinger-Moser inequality and the properties of the first eigenvalue, we prove the existence of a nontrivial solution for a class of nonlinear elliptic with critical potentialand indefinite weights in R~2. Secondly, we prove the existence of nontrivial solutions for a class of subcritical and critical elliptic systems with indefinite part in R~2 byusing a generalized linking theorem, Trudinger-Moser inequality and concentration-compactness principle.5. The existence of at least three weak solutions for discrete boundary value problem is established by using a three critical point theorem introduced by Ricceri.

首先，讨论了R~2中一类带不定权且含临界位势的二阶椭圆型方程的特征值问题，并借此特征值问题的第一特征值性质，利用山路引理及Trudinger-Moser不等式，证明了R~2中一类带不定权且含临界位势的非线性椭圆型方程非平凡解的存在性；其次，利用广义环绕定理，Trudinger-Moser不等式及集中列紧原理，得到了R~2上一类具有强不定部分的半线性椭圆型方程组在非线性项分别为次临界增长和临界增长情形下非平凡解的存在性。

And in the second part, we consider the following four inverse eigenproblems: the reconstruction of normal five-diagonal matrix by two or three ordered eigenvalues and cor...

第二个部分则讨论四类矩阵逆特征值问题：在考虑给定的两个或三个特征值次序的情况下构造唯一的规范五对角线矩阵：由三个给定的特征值和相应特征向量来构造唯一的实对称三对角线矩阵和不可约实对称三对角线矩阵。

Based on a general parametric eigenstructure assignment result proposed for descriptor linear systems via proportional plus partial derivative state feedback and a result for generalized eigenvalue sensitivity problem of matrix pairs, parametric representation of the closed-loop eigenvalue sensitivities to the perturbed elements in the open-loop system matrices is obtained. An effective algorithm for eigenvalue assignment with minimum sensitivity in descriptor linear systems via proportional plus partial derivative state feedback is then proposed.

摘要基于广义线性系统比例与部分状态导数反馈参数化特征结构配置结果和矩阵对广义特征值灵敏度结果，得到了关于开环系统矩阵中摄动元素的闭环特征值灵敏度的参数表达式，并在此基础上提出了广义线性系统比例与部分状态导数反馈最小灵敏度特征值配置的有效算法。

Sufficient conditions of linear and quadratic feedback stabilizability are obtained for nonlinear systems with uncontrollable critical mode (a single zero eigenvalue, or a pair of pure imaginary eigenvalues), corresponding algorithms are given for constructing stabilizing laws.

结合中心流形方法和范式理论研究了临界情形下非线性系统的稳定性问题，针对临界模态为单零特征值、一对纯虚特征值和一对零特征值的情形，分别获得了渐近稳定或不稳定的充分条件，给出了相应稳定性判据。

Then a fast methodology for calculating the eigenvalues of the structural matrix with interval parameters was put forward, which was based on the Rayleigh quotient and the theories of the interval mathematics.

为提高区间特征值的计算效率，首先分析了区间结构矩阵特征值的设计变量的单调性问题，随后采用区间因子法给出了基于Rayleigh商计算结构广义特征值的一种快速算法。

Based on the stacking of data matrix, real-processing of signal subspace, complex shift invariance equation and joint eigenvalue estimation, an algorithm is presented to solve this problem and handle the estimation jointly.

基于数据矩阵的重新排列、信号子空间的实数化处理、复数移不变方程以及联合特征值估计，推导出联合估计参数的ESPRIT类算法，该算法将参数估计问题转化为3个具有实特征值的实数矩阵的联合特征值估计问题。

In the mobile communication system, the intermediate frequency signal results in the characteristic value is took the appraisal signal quality one kind of standard, how this topic main research is withdraws the intermediate frequency signal the characteristic value,as well as withdraws in the method in each kind to select superiorly withdraws the intermediate frequency signal characteristic value the method.

在移动通信系统中，中频信号得特征值是作为评估信号质量的一种标准，本课题主要研究的是如何来提取中频信号的特征值，以及在各种提取方法中选出最优的提取中频信号特征值的方法。

The time-history velocity response signal of pile can be decomposed by Sym wavelet. The power spectrum value can be extracted from some specified spectrum range. These values from one signal makes up the characteristic vector representing this signal. The relationship between characteristic vector of pile and pile defect type can he established by using BP artificial neural network. Abundant time-history velocity response signals of pile can be acquired by numerical simulation method.

利用Sym小波对基桩速度响应时程曲线进行小波分解，对指定频带上的信号分量进行特征值提取，提取的特征值为反映各频带范围内体现能量分布的功率谱均值，提取的特征值可构成反映信号特征的特征向量，同时利用BP人工神经网络的非线性映射特性建立特征向量和基桩缺陷类别之间的一种对应关系。

Each eigenstate of an observable corresponds to an eigenvector of the operator, and the associated eigenvalue corresponds to the value of the observable in that eigenstate.

每个可见特征值符合操作者一特征向量，而相关的特征值符合特征值里的可见值。

On closer examination, though, this is not a vote for multilateralism but just the opposite.

仔细审视后我们发现，这并非是对多边主义投出的赞成票，而是恰好相反。

Uncovering their weak spots, so I can defeat them.

揭露出他们的弱点，这样我就可以打败他们了。