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Using two new methods, this paper prores one pertubation theorem on the finite Hilbert space of 2×2 operator matrices, and gereralizes this theorem to the infinite Hilbert space of selfadjoint operators.

给出了有限维Hilbert空间中2×2算子矩阵的数值域扰动定理的两种证明方法，并且将该定理推广到无限维Hilbert空间上的自伴算子。

Finally we also study some operators in spinor QED which give gauge independent matrixelements when acting on some specific states.

最后我们还研究了旋量电动力学中的一些算符，这些算符作用到某些特定态上时也给出规范无关的矩阵元。

For the uniformly ergodic Markov processes, which is a classic framwork established by Deuschel-Stroock for studying the LDP for empirical measures, the LDP of f_n~* in the weak topology and the uniform weak*-LDP in the strong topology ||·||_1 for f_n~* are established. Furthermore, we prove that f_n~* is asymptotic optimal in the sense of Bahadur. These results are obtained for the first time in the dependent case. For this generalization from the i.i.d.

在此框架下，我们建立了f_n~*在弱拓扑下的大偏差原理以及在L~1-拓扑下对初始点一致的弱*大偏差原理，另外，我们还证明了f_n~*在Bahadur意义下是渐近最优的，这些结果在相依情形下是全新的，为了做这样本质性的推广，我们需要克服许(来源：ABC论文6d网www.abclunwen.com)多技术上的困难和应用不少特殊的工具，诸如Harnack型不等式，Cramèr型偏差不等式，一致可积算子，线性算子的扰动理论，Bishop-Phelps定理等等(它们都是首次用于处理这样的问题)。

In constructing new solutions of Feigenbaum renor- malization group equation, it is important to know which operator commute s with the iterative operator,This paper presents a theorem about the structure of the ab.

本文揭示了与迭代算子对易的算子集合在构造Feigenbaum重整化群方程新解中的重要性。

An example of these maximal monotone operators is the subdifferential of a closed convex function.

这种多值极大单调算子的一个特殊例子是闭凸函数的下微分算子，所以本文考虑的多值随机微分方程包含了在凸区域内具有反射边界的随机微分方程。

Significant progress has been made by Dalibard,Dupont-Roc and Cohen-Tannoudji in 1982,who argued that there exists a symmetric operator ordering between the operators of atom and field that renders the distinct contributions of vacuum fluctuations and radiation reaction to the atom\'s spontaneous emission and energy shift separately Hermitian.

这种不确定性的根源来自于相互作用哈密顿量中原子和场算符的排序问题。1982年，法国物理学家Dalibard，Dupont-Roc和Cohen-Tannoudji提出原子和场算符对称排序的方法，从而消除了这种不确定性，使得真空涨落和辐射反作用对原子自发辐射和能级移动的贡献都是厄米的。

Based on the theory of dimensions chain, with an illustration of machining, the process of establishing, searching and resolving of process dimension formula equation is analyzed in detailed; And then leading-in the basic dimension matrix equation and tolerance matrix equation, a program in Matlab language is made.

王战中，王为杰，韩彦军，程林章，李辉，基于矩阵的工艺尺寸链分析与解算文章基于尺寸链原理，借助一个机械加工实例，详细分析了工艺尺寸式方程的建立、查找及解算过程；并在此基础上引入基本尺寸矩阵方程和公差矩阵方程，采用Matlab语言编写计算机程序。

The article offerred the morphology Top-Hat operator that a kind of genetic algorithm optimizes on foundation of traditional morphology functor.

本文在传统形态学算子基础上提出了一种遗传算法优化的形态学Top-Hat算子。

It investigates mainly infinite matrix conver-gence、infinite matrix transformations、the automatic continuity and boundedness of infinitematrix operators、infinite matrix topological algebras、invariant theory、infinite matrix meth-ods、compact operators series and Eberlein-Smulian theorem,etc.

主要研究了无穷矩阵收敛、无穷矩阵变换、无穷矩阵算子的自连续性和自有界性、无穷矩阵拓扑代数、不变性理论、无穷矩阵方法、紧算子级数与Eberlein-Smulian定理等。

USES AND LITMITATIONS OF THE TRIAL BALANCE. The trial balance provide proofthat the ledger is in balance.

试算表的使用及其局限性试算表提供了证明分类账是否平衡的证据。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。