集合的

Let G be a finite group, and S a subset of G not containing theidentity element 1. The Cayley digraph Cay on G with respect to S is definedas a directed graph with vertex set G and edge set {|g∈G, s∈S}. IfS~(-1)=S, then Cay is undirected and in this case, we view two directededges and as an undirected edge {u, v}. Obviously, the right regularrepresentation R of G, the acting group of G by right multiplication, is asubgroup of the full automorphism group AutCay(G, S of Cay.

给定有限群G，设S是G的不含单位元1的子集，群G关于子集S的Cayley有向图Cay是一个以G顶点集合，而以｛|g∈G，s∈S｝为边集合的有向图，特别地，若S~(-1)=S，则X=Cay是无向的，此时我们把一条无向边｛u，v｝等同于两条有向边和，易见，群G的右正则表示R，即G在G上的右乘作用，为图Cay的全自同构群AutCay

By the combinatorial proof or combinatorial interpretation, the identity is equipped with certain count meaning. The most general way in the combinatorial proof is to count two sides of the identity by two different methods. Generaly, through building a bijection from one set to another one, the number of the two sets respectively represents the two sides of the identity.

恒等式的组合证明或组合解释赋予了恒等式一定的计数意义，组合证明最常用的方法是分别用两种不同的方法对恒等式的两端进行计数，一般通过构造两个集合之间的双射，这两个集合的个数分别表示恒等式的两端，从而根据双射的一一对应性证明恒等式。

Moreover, by the combinatorial proof or combinatorial interpretation, the identity is equipped with certain count meaning. The most general way in the combinatorial proofs is to count two sides of the identity by two different methods. Generaly, through building a bijection from one set to another one, the number of the two sets respectively represents the two sides of the identity. Because of the 1-1 property of bijection, the identity is proved.

此外，恒等式的组合证明或组合解释赋予了恒等式一定的计数意义，组合证明最常用的方法是分别用两种不同的方法对恒等式的两端进行计数，一般通过构造两个集合之间的双射，这两个集合的个数分别表示恒等式的两端，从而根据双射的一一对应性证明恒等式。

Based on a formal analysis of lifting decomposition, the hierarchical structure concept of the decomposition set, as well as the lifting decomposition technique of the polyphase matrix' greatest mth-order common divisor, is proposed to conquer the difficulties in the practical computation of and the optimal search in the huge decomposition set.

本文在形式化分析Lifting分解原理的基础上，提出了分解集合的分级结构概念以及多相矩阵的m阶最大公因子Lifling分解技术，克服了分解集合求解问题的高复杂性所带来的实际计算与搜索困难；进一步地，从数值稳定性及计算代价两方面研究了分解的评价问题，设计出两种实用的分解稳定性准则；最后，结合分级结构技术提出一种最优分解算法。

We generalize the concept of the set of variability defined in the unit diskby K.Strebel to general Riemann surfaces and prove that the set of variablity withrespect to the modulo homotopic class of a quasiconformal mapping between twoRiemann surfaces is a compact and connected subset.Consequently the num-ber of the extremal mappings in the modulo homotopic class of a quasiconformalmapping between two general Riemann surfaces is either one or infinity.

Strebel的定义在单位圆上的可变性集合的概念推广到一般Riemann曲面上去，并且证明了Riemann曲面之间的拟共形映射的模边同伦类所确定的可变性集合是一个连通的紧子集，从而得出一般Riemann曲面之间拟共形映射的模边同伦类中的极值映射要么唯一，要么有无穷多个。

Firstly,the classification of probability rule is analyzed on the base of classic rough set concepts and extended to the equal relation of set in the indefinite system,namely,the upper and lower approximation space of research set is expressed in the form of conditional probability;then,according to the measure of probability rule,the attributes reduction is carried out and the classification rule is extracted by using the related parameters of condition attributes' impend precision from the angle of conditional probability;Finally,the related simulation test result is given and the result shows the classification rules with probability measures is more rational.

首先在经典粗糙集概念的基础上分析概率规则的分类，并将其推广到不确定系统的集合等价关系中，即用条件概率的形式表示研究集合的上下近似空间；然后根据概率规则的测度从条件概率的角度利用条件属性的逼近精度的相关参数进行属性集的约简进而提取分类规则；最后给出了相关的仿真实验结果，结果表明带有概率测度的分类规则更合理。

Some statistical properties of product assembly are obtained on the basis of industrial investigation of assembly procedure and analysis of assembly operations of typical products; concept of fuzzy quotient set is introduced to the study of assembly sequence planning and a theoretical frame and algorithm for assembly sequence planning based on product fuzzy quotient set is presented; theory and method of fuzzy automata and fuzzy decision are used in the investigation of sensor based assembly sequence planning and a theoretical frame and algorithm for assembly sequence planning based on information sensing of assembly process are presented; an assembly model for product is put forward; study of product disassemblability is carried on.

论文通过对产品装配工艺的工厂调研及典型产品的装配作业分析得到了有关产品装配的一些统计特征；将模糊商集合的概念引入装配顺序规划的研究中，提出了基于产品模糊商集合的装配顺序规划的理论框架和算法；将模糊自动机及模糊决策的理论和方法应用到基于感知的装配顺序规划的研究中，提出了基于装配过程信息感知的装配顺序规划的理论框架和算法；提出了一种产品装配模型；进行了产品可拆卸性的研究。

In aim at the complicity and high-dimensional state-space for the controlled system, it simplifies the calculation of geometric polytope by optimize with ellipsoidal approximate techniques, and the robust control effectiveness near to the optimal.

本论文所提示的基于几何理论的约束非线性控制算法是建立在最大输出允许集合的基础上，运用状态空间的有界子集表达鲁棒时优离散时间控制问题的价值函数，通过逆序计算该价值函数的水平集合，求得其所需的控制量，针对被控系统的复杂性及高维状态空间问题，运用椭球近似技术予以优化，使得几何多面体的计算得以简化，且鲁棒控制效果接近最优。

Patent pool refers to two or more patentees put the patents owned by their respective which belong production of a product or production process required to complete together, and through the establishment of an independent entity or through the entity by patentees authorized to conduct a management agreement.

中文摘要：所谓专利池，是指两个或两个以上的专利权人将其各自拥有的对生产某一产品或完成某一生产流程所需的专利集合到一起，并通过建立一个独立的实体或经由权利人授权的主体，对该专利集合的专利许可行为进行管理的一种协议。

In order to distinguish these two types of transitions, a state recognition method is introduced. We firstly propose a variable contact set in which the contact points on the robot body are defined to represent the alternation of the contact states logically. Then, by predefining thresholds for the contact forces, the state transition can be well recognized.3 As another research topic, the local tracking control according to the pre-acquired state transition trajectories plays an important role in realizing the non-regular motion for the humanoid robot.

在状态转换识别方法上，本文提出了接触点集合的概念，对接触状态的变化进行逻辑上的表达；再结合接触点集合的变化情况，通过设定接触力阀值来实现对状态转换的识别。3根据给定的状态转换轨迹进行局部的跟踪控制，是本文实现类人机器人非规则运动的另一个重要研究内容。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。