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In this thesis, we study two problems: the existence results of solutions for generalized vector quasi-equilibrium problems and Hlder continuity of solutions to generalized vector equilibrium problems. The detailed contents are listed as following:In Hausdorff topological vector space, we discuss the existence results of solutions for three types of generalized vector quasi-equilibrium problem (GVQEP1,(GVQEP2) and (GVQEP3), for short respectively.

本文主要研究了两类问题：广义向量拟平衡问题解的存在性以及广义向量平衡问题解的Hlder连续性，具体内容如下：在Hausdorff向量拓扑空间中，讨论了三类广义向量拟平衡问题(GVQEP1)，(GVQEP2)和(GVQEP3)解的存在性定理。

Generalized Linear Models are an extension of the linear modeling process that allows models to be fit to data that follow probability distributions other than the Normal distribution, such as the Poisson, Binomial, Multinomial, and etc.. Generalized Linear Models also relax the requirement of equality or constancy of variances that is required for hypothesis tests in traditional linear models. Hypothesis tests applied to the Generalized Linear Model do not require normality of the response variable, nor do they require homogeneity of variances.

广义线性模型是线性模型的扩展，对数据的要求不必局限于服从正态分布，同时放松了对"方差一致性"的要求，这在传统的一般线性模型假设检验中是必不可少的，而在广义线性模型假设检验中，响应变量也可以服从其它分布（如：泊松分布，二项分布及多项分布等）。

Subsequently, we discuss the generalized derivable mappings at zero point on standard operator algebras and show that every generalized derivable mapping at zero point on standard operator algebras is a generalized inner derivation.

其次又对标准算子代数上的在零点广义可导的线性映射进行了讨论，证明了标准算子代数上的在零点广义可导的线性映射是广义内导子。

Then,by using the algebraic method which was introduced by Yang L.and Zhang J.Z.,and the generalized isometric embedding theory,the generalized concept of metric addition is brought forward,a geometric inequality about the generalized metric addition is given,and the main result of Ya...

然后利用杨路和张景中引进的代数方法，应用广义等距嵌入定理，提出了关于两组两个完全同向的n维单形"广义度量加"的概念，并且证明了涉及"广义度量加"的一个几何不等式，它推广了杨路和张景中关于Alexander猜想的结果。

Generalized linear models, which can model a large variety of data, have a wide area of application. The class of GLMs includes, as special cases, linear regression, analysis-of-variance models, log-linear models for the analysis of contingency tables, logistic models for binary data in the form of proportions and many others. Usually, the parameters in the generalized linear models are estimated by the method of maximum likelihood . But, in the literature, the nonrobustness of the maximum likelihood estimator forβhas been studied extensively. The quasi-likelihood estimator of the parameter of the generalized linear model shares the same non-robustness properties.

广义线性模型，可用于对多种类型的数据进行建模，是应用非常广泛的模型，线性回归模型、方差分析模型、用于列联表分析的对数线性模型和逻辑斯谛模型等都是广义线性模型的特例，通常，我们用极大似然的方法估计广义线性模型中的参数，但是，在文献中，对参数β的极大似然估计的非稳健性已经有了广泛的研究，广义线性模型的拟似然估计也显示了非稳健性。

Two application methods of Lagrangian equation and bond graphs in the dynam-ics of electro-mechanical systems are discussed with stress laid on the AFS methodsuch that:1.the relation between the non-conservative generalized force(orgeneralized electromotive force)E_i and bond graph is clearly illustrated and 2.theimproved method for calculating the generalized force(or generalized electromotiveforce)E_i for the electro-mechanical system is presented.

本文首先讨论并对比了拉氏方程与键图在机电系统动力学上应用的两种不同形式。并提出了：①关于运用 AFS 形式时非保守广义力 E_i 与键图间的关系；②机电综合系统中计算广义力E_的改进方法。

Based on the existing generalized synchronization, a new synchronization the full-state generalized synchronization is proposed for nonidentical chaotic systems. The controller with a unified structure is designed for this new synchronization. This simple and adaptive controller can be applied to a wide range of generalized synchronizations.

在已有的广义同步定义基础上，提出了一种新的概念—-非恒同混沌系统的全状态广义同步，给出了实现全状态广义同步的统一的控制器形式，该控制器适用范围大，结构相对简单，并且是自适应的。

By applying these two tools,we mainly discuss the problems as follows:1 Perturbation identities for the generalized polar decomposition:By applying singular value decomposition, we study the perturbation bounds of the generalized polar decomposition under unitary invariant norms when A is perturbed by addition or multiplication,respectively and give our bounds in identities.2 A class of new unitary invariant metrics: This paper generalized a class of new unitarily invariant metrics and give the upper-bounds and lower-bounds by C-S decomposition.

利用这两个强有力的工具，本文主要讨论了如下问题：1 矩阵广义极分解的扰动等式：利用奇异值分解，本文分别讨论了加法扰动和乘法扰动下矩阵广义极分解在任意酉不变范数下的扰动界，并首次以恒等式的形式给出了酉极因子和半正定因子的扰动界。2 一类新的酉不变度量：本文推广了文[22] 中的结论，定义了一类新的酉不变度量。

Generalized way ; graph analysis ; prime number distribution ; Kronecher function ; Hanavan model ; generalized coordinate ; generalized inertia force ; technical movement.

国家自然科学基金；高等学校博士学科点专项科研基金广义路径；线图分析；素数分布；卷和函数； Kronecher函数； Hanavan模型；广义坐标；广义惯性力；动作技术

Using operator-theoretic-methods, we give some characterizations for a dual generalized frame of a generalized frame in a separable Hilbert space H. We also prove a result concerning two strongly disjiont generalized frames.

本文研究了可分的Hilbert空间H中的广义框架，运用算子理论方法，研究了可分的Hilbert空间H中广义框架的性质，给出了广义框架的对偶广义框架的一些刻画，并且证明了两个广义框架是强非交的一个充分必要条件。

The system can be widely used in belt weighing and batching process control,etc.

介绍了基于智能模糊控制的嵌入式配料系统的设计方法，对模糊PID控制过程和系统调零作了重点的讨论，同时给出了PID控制的程序流程图和系统定长调零子程序。

"I dunno," she answered,"but if you show me aroun', I'll recognize it from the lighthouse just outside the porthole."

"我不知道，"她回答说，"如果你能带我转转，我能认出来的，因为灯塔就在舷窗外。"