谱定理

The last two parts contain the four basic principles in Banach space, and the theory on the spectrum of operators.

最后两部分，Banach空间的四个基本定理和谱的一些基本性质和分类等。

In this thesis,using the Bernstein polynomial approximation,Stieltjes transform method and the central limit theorem of martingale,under suitable moment conditions,we prove the CLT of LSS G_n with a generalized regular class C4 of the kernel functions for large dimensional sample covariance matrices.

在适当的矩条件下，当核函数f属于C4时，我们证明了大维随机协方差矩阵的线性谱统计量的中心极限定理。

Combination of 〓P MAS NMR with the binomial theorem calculation suggests that a restricted random distribution of Mg is present in the molecular sieves.

结合〓P MAS谱和二项式定理计算表明镁在磷酸铝分子筛上的分布是随机的。

Based on Brune ω~2 source spectrum ,Hanks and McGuire deduced a simplified formula of RMS accelera- tion by stationary random vibration theory and Parseval theorem.

Hanks 和 McGuire 基于 Brune 的ω~2震源谱，借助平稳随机振动理论和 Parseval 定理给出了估计均方根加速度衰减关系的表达式。

In the present work,the existence and uniqueness results aboutperiodic boundary value problems for different kinds of the nonlin-ear periodically perturbed nonconservative systems are establishedthrough the discretization technique,under suitable assumptions,by using global inverse function theorem and result about the ex-istence and uniqueness of periodic solution for nonhomogeneouslyfirst order linear periodic boundary value problem.

本文的第一章概述了在讨论原问题解的存在唯一性过程中以及构造和分析相关的数值求解方法时将要用到的全局反函数定理、有关矩阵特征值的若干重要引理、线性常微分方程非齐次周期问题解的存在唯一性定理和单参数影射方法及有关结论，并简单回顾了已有的证明非线性微分方程周期边值问题解的存在唯一性的方法，其中包括谱理论、最大最小化形式方法、摄动技术和全局反函数理论方法，最后，介绍了两类数值求解非线性微分方程问题的方法。

The conventional numerical simulation of a reverberant field as a launch acoustic environment was introduced. Following the reciprocity theorem used in the coupled FE-BE model, the structural response due to reverberant acoustic excitation was substituted by the sound pressure caused by force excitation on the structure, then the output response power spectrum density of the coupled model subjected to reverberant environment was evaluated based on the stochastic analysis principle.

首先介绍了传统的构建混响声场的数值模拟方法；其后利用声振耦合中的互易定理，将混响声场的激励问题转化为结构模型上力激励引起的场点声压响应问题，并采用随机分析原理，用谱分析方法推导了结构在混响声场激励下的响应计算公式；最后建立了航天器典型结构的声振耦合模型，并分别用传统方法和利用互易定理的方法进行了数值模拟。

The multi-degree-freedom equivalent model of INS bracket is also given and analyzed to improve the analysis precision. The dynamic response spectrum of this model is achieved by modal analysis and spectrum theory. The numeric formulas of time-domain response are deduced by residue theorem.

对于惯导减振支架的多自由度系统等效分析模型，则运用模态叠加法和谱分析理论得到响应的功率谱，根据留数定理推导了系统时域加速度动力响应的数值计算公式。

In the second part,we gave the theorem of inhomogeneous spectral inclusion regions of partitioned matrices,so some relevant researches have been improved in this field.

第二部分给出了分块矩阵的非齐次谱包含域定理。从而把有关矩阵非齐次谱包含域的研究工作做了一定改进。

In this thesis, we mainly study problems on global geometry and geometricanalysis of Riemannian submanifolds, including vanishing theorem for homologygroups, topological sphere theorem, L~2 harmonic 1-forms, finiteness of end andthe spectrum of the Laplacian. In 1973, by using the Federer-Fleming existence theorem and the techniquesfrom the calculus of variations in the geometric measure theory, H.

本文着重研究黎曼子流形上整体几何与几何分析的若干问题，主要内容包括子流形的同调群消没定理、拓扑球面定理、L~2调和1-形式、端的有限性和Laplace算子谱等问题。

We prove the relativistic virial theorem, which gives simple criteria for the absence of embedded eigenvalues in certain regions of the continuous spectrum.

我们证明相对论维里定理，这定理对于连续谱空间里本征值的缺乏给出了简单的标准。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。