界

Applying the De Caen"s inequality of sum of the squares of the degree and Cauchy"s inequality, we obtain a strict lower bound and a strict upper bound of the largest Laplace eigenvalues only in terms of vertex number of a unicycle graph. Applying the Laplace matrix theorem of trees, we obtain an upper bound of the second smallest Laplace eigenvalues of a unicycle. Extremal graph whose second smallest Laplace eigenvalues reach the obtained upper bound is determined. We also obtain an upper bound of the second largest Laplace eigenvalues in terms of vertex number of the largest connected branch of unicycle graph, and obtain a theoretical method to calculate the second largest Laplace eigenvalues of unicycle graph. We obtain an upper bound of any Laplace eigenvalues in terms of vertex number of a unicycle graph. We also obtain the distribution of Laplace eigenvalues in the inter [0,n] in terms of the matching number.

本文得到了以下几个方面的结果： 1、利用图度平方和的De Caen不等式和Cauchy不等式给出单圈图的最大Laplace特征值仅依赖于顶点数的严格的上下界；利用树的Laplace理论给出了单圈图次小Laplace特征值的一个上界，并刻画了达到该上界的极图；利用子图的连通分支的顶点个数给出了单圈图次大Laplace特征值的一个上界，并给出了单圈图次大Laplace特征值一个理论上的一个求法；利用单圈图的阶数给出了其一般Laplace特征值的一个上界；利用单圈图的匹配数给出其Laplace矩阵谱在区间[0，n]上的分布情况。

At last the results have been applied to the tracking problem of a class of mechanical systems with discontinuous friction term. Chapter 3 mainly deals with uniformly ultimate boundedness of a class of nonautonomous systems with discontinuous right-hand sides and corresponding perturbed systems (in the sense of Filippov solutions). The definitions of globally uniformly strongly ultimate boundedness and globally uniformly weakly ultimate boundedness of discontinuous systems and the definition of globally equiuniformly strongly ultimate boundedness of corresponding perturbed systems are presented firstly.

首次给出不连续系统全局强一致最终有界、全局弱一致最终有界的定义，以及针对于扰动系统的全局强等度一致最终有界性的定义，并基于非光滑的Lyapunov函数得到了不连续系统全局一致强、弱最终有界的Lyapunov定理和扰动系统全局强等度一致最终有界性的Lyapunov定理。

Fri particular, the Wittmann-type strong law of larg numbers for independent random variables is generalized to the case of NA random variables. We also present the sufficient and necessary condition of the laws of logarithm, and we extend Teicher-type strong law of the large numbers for sequence of NA random variables. Some of the laws of iterated logarithm of Teicher-type, Egorov-type arid Wittmann-type for sequence of NA random variables are obtained. Then we investigate the rate3f ionvergcll( fbr series of NA randonl variables, we obtain soIne results fbr tl1e Iaws of theiterated logarithttl, the laws of logarithm and decreasing order fOr the tail sum.Risk itllttlysis tlleory is a sigIlifica11t part of insurance InatheInatics.

Wittmann（1985a）关于实独立随机变量列的结果，并给出了NA列强大数律成立的若干条件，特别建立了一般NA列对数律成立的充分必要条件，在二阶矩存在的条件下完整的解决了一般NA列对数律的问题，中文摘要2而已有的一些NA列对数律的结果可以由它推出，给出了NA列的Teiclier型强大数律，表明lbiChCI·（1979）给出的实独立随机变量列的强大数律可以减弱其条件等；建立厂不问分布NA列的Teicfl仪；Egorov，Petrov型有界重对数律，以及加权同分布NA列的有界重对数律，进一步推广了NA列的Kolmogory有界重对数律等，特别对NA列建立了Wittm洲型有界重对数律，而其证明方法与独立情形有很大不同，同时通过反例表明在与独立场合类似的条件下，独立列的Wittmann有界重对数律不能完美的推广到NA歹小惰形；最后研究了NA随机变量级数的收敛速度，给出了尾和下降的阶；尾和的有界重对数律，及尾和对数律成立的充要条件等，并通过反例说明 NA随机变量级数与独立随机变量级数在收敛速度方面存在的差异。

First of all this article discusses the scientific definition and appellation of transnational ethnic groups at the angle of political anthropology, then focuses attention on the restrictions and influence upon transnational ethnic groups imposed by the theories, principles and ideas such as 'the unchangeableness of the existing political boundaries',' the supremeness of state sovereignty',' competitions of the overall strength among nation-states',etc.;the author holds that these theories, prin...

文章首先从政治人类学的角度探讨了跨界民族的科学界定和称谓，随后集中探讨了"现行政治疆界不变"、"国家主权高于一切"、"综合国力较量"等理论、准则、理念对跨界民族的制约和影响。笔者认为，在一般情况下，它们不仅决定着跨界民族的民族过程取向，而且已成为解决跨界民族问题的前提，并成为目前国际关系中的一些基本原则。文章最后以非洲大陆为例，就如何正确解决跨界民族问题提出了一些对策。

The precipitation of SiO〓 from ZrSiO〓 grains and the isopachous strip were revealed by TEM micrographs as the microstructural characteristics of TZ30 sample fabricated at 1500℃/lhr.

高分辨电镜研究表明，在两晶粒晶界（包括ZrO〓/ZrO〓晶界和ZrO〓/ZrSiO〓晶界）以及三晶粒晶界上均无残留的SiO〓玻璃相；这种晶界构型对高温力学性能是极为有利的。

In Chapter 2, we consider the error bound and the auxiliary problem algorithm for the generalized linear complementarity problem over a polyhedral cone: First, we give an absolute and a relative global error bound for GLCP and nondegenerate GLCP, respectively, and then we explore the properties of the solution set of the problem, based on which we establish another absolute and relative error bound for GLCP which is much exacter compared with the result above.

第二章主要研究了闭凸锥上广义线性互补问题的误差界及基于其上的一个求解GLCP的辅助问题算法：(1)给出了GLCP的全局绝对误差界和在有非退化解时的全局绝对误差界及其相对误差界；(2)对GLCP的解集结构进行了探讨，并利用得到的结果给出了GLCP的另一个全局绝对误差界和相对误差界估计；(3)我们提出了一个求解GLCP的辅助问题算法，并证明在适当条件下该算法具有全局收敛性。

A simplified model was proposed to simulate material microstructure according that metal solidification is a Monte Carlo process. First, use the point of"putting randomly, growing uniformly"to generate grain boundary, then recognize grain boundary trifurcate points, eliminate bad trifurcate points, and distinguish the connections among these points, thus obtain straight grain boundary picture.

根据金属凝固过程是—Monte Carlo过程，建立了金属材料显微组织的简化Monte Carlo方法，采用&随机投放，等速生长&的方法形成矩齿形晶界图，并通过逐点判断法识别出晶界三重点，剔除奇异三重点，并识别出晶界及晶界间相邻关系，从而获得晶界结构的直线近似形态图，为细观组织短裂纹的数值模拟作好准备。

Next, after analyzing the nets′relationship in three layer channel routing, setting up the objective function toward channel area minimization, we propose some new terms, for example, the withstand bound columns, valid complete cover net sets, TRACK valid routing, etc.. The conceptions and natures of static bound of nets, dynamic bound of unrouted net set and the lower bound value of the horizontal tracks are discussed; and the methods of calculating static bound, dynamic bound and lower bound are put forward.

文章接着分析了线网在三层通道区布线中的相互关系，为了以完成布线所需通道区面积最小化为目标解决三层通道区布线问题，提出了柱界列、完全有效覆盖线网集、TRACK有效布线等一些新的概念，讨论了三层通道区布线问题中线网定界、未布线网集动界和水平通道数Lower-Bound等概念和它们的性质，给出了定界、动界、Lower-Bound值的计算方法。

The main creating aspects are finding and clarify such a fundamental physical process that the grain boundaries emit vacancies under compressive stress to induce solute non-equilibrium grain boundary dilution and absorb vacancies under tensile stress to induce non-equilibrium grain boundary segregation, formulizing the structural equations and the composition equations in force equilibrium in grain bounary region to describe this physical processes and the kinetic equations for non-equilibrium grain boundary segregation under tensile stress, calculating the modulus in grain boundary region from the expermental data of grain bounday segregation using the structure and coposition equations and calculating the diffusion coefficients of vacancy-solute atom complexes using the kinetic equation simulating the experimental results of grain boundary segregation.

本项目的主要创新点是，发现并阐明了弹性应力场作用下空位与晶界交互作用的基本物理过程：在张应力作用下，晶界会吸收空位，引起溶质非平衡晶界偏聚；压应力作用下，晶界会发射空位，引起非平衡晶界贫化。建立了描述此物理过程的晶界区力学平衡的结构方程和成分方程；？建立了张应力引起的非平衡晶界偏聚动力学方程？；用晶界区力学平衡的结构方程和成分方程？，首次通过实验测量计算出多晶材料晶界区的弹性模量；通过建立的动力学方程模拟实验结果，首次获得溶质原子－空位形成的复合体的扩散系数。

This article discusses the theoretical questions such as 'the transnational ethnic groups' connotation, classification, the differences between transnational ethnic groups and problems of these groups, then analyses the conditions and causes that give rise to problems of transnational ethnic groups, the evolution trend of transnational ethnic groups' influence upon geographic politics and the enlightening significance for us in the course to resolving problems of transnational eth...

本文对跨界民族的内涵、分类、跨界民族和跨界民族问题的区别等理论问题进行了探讨，在此基础上，分析了造成跨界民族问题的条件和原因、跨界民族对地缘政治的影响会沿着什么样的趋势进行演变及跨界民族问题在解决过程中所带给我们的启示

They weren't aggressive, but I yelled and threw a rock in their direction to get them off the trail and away from me, just in case.

他们没有侵略性，但我大喊，并在他们的方向扔石头让他们过的线索，远离我，以防万一。

In slot 2 in your bag put wrapping paper, quantity does not matter in this case.

在你的书包里槽2把包装纸、数量无关紧要。