等价变换

A multivariable equality constraint condition is hidden in switching functions through different equivalent transformations.

通过将一个由设备状态信息确定的多变量等式约束条件，经不同的等价变换，隐含于开关函数中，建立一个新的故障诊断数学模型。

By equivalent transformation, the interval system is transformed to an uncertain system with matrix norm bounds.

通过等价变换，将区间系统转换为对应的矩阵范数不确定系统，并据此导出区间系统的鲁棒滤波算法。

Firstly, by constructing the Lyapunov function with a special structure, a prior estimate is obtained. Secondly, with the help of Green\'s function, the original problem is transformed into an equivalent operator equation, and the fixed point theory of contraction mapping in a Banach space guarantees the existence and uniqueness of the global solution.

首先，构造具有特殊结构的Lyapunov函数，得到解的先验估计；其次，借助Green函数将原方程等价变换成算子方程，Banach压缩映射的不动点定理保证了全局解的存在唯一性；最后通过常微分方程的定解，证明了主要结论，即平凡解全局渐近稳定。

An equivalent transformation is made for the original system by the Leibniz Newton formula. By applying Lyapunov stability theory and associating with Moon's inequality, the delay dependent robust stability condition for the Markov jumping neural networks is established.

利用Leibniz-Newton公式对原系统进行等价变换，基于Lyapunov稳定性理论，并结合Moon不等式得到了此类Markov跳变神经网络时滞相关均方鲁棒稳定性的判别条件。

A method of mapping E-R representations onto corresponding XDD representation is proposed, which naturally combines together the conceptual model and the structural model of XML document.

提出了根据关系代数表达式构造查询子句的方法，关系代数表达式可以用若干个XML子句描述，并通过等价变换得到查询结果，证明了该方法的正确性。

The traditional query tree optimization methods,parallel database optimization methods based on left linear trees and right linear trees,bushy trees,and operation of the forest,have their own pros and cons,they have been more in-depth and maturity of the study.The query optimization method based on multiple weighted tree has studied its model of parallel query plan,its complexity model of parallel query plan and query optimization algorithms.The semantic query method transforms an inquiry into one or several semantic equivalence inquiries then has to find and implement a strategy to achieve a better query.Agent-based parallel database query optimization using Multi-Agent technology to automatically search the integrity constraint conditions which are related to the determined query,there for,the efficiency between several relations' joins has been greatly improved.The parallel optimization algorithm,based on genetic algorithm which is suitable for multi-joins of cluster environment,has deeply studied the relations storage options,multi-joins query optimization and query processing and other key technologies based on cluster parallel database.

传统的查询树优化方法，即基于左线性树、右线性树、浓密树、操作森林的并行数据库查询优化方法，各有优劣，对其的研究比较深入、成熟；基于多重加权树的查询优化方法，研究了其并行查询计划模型、并行查询计划的复杂性模型和查询优化算法；语义查询优化方法将一个查询变换成一个或数个语义等价的查询，进而寻找并执行这些等价查询中具有较好实现策略的一个；基于Agent的并行数据库查询优化采用Multi-Agent技术自动查找与给定查询有关的完整性约束条件，使得多个关系间连接操作的效率得到很大的提高；基于遗传算法的并行优化算法，深入研究了基于机群并行数据库中关系存储的选择、多连接查询优化和查询处理等关键技术。

As an application of continuous wavelet transform,we discuss the relationsbetween some differemtial equaltions and the integral equations by using thecontinuous wavelet transform in 〓,vector function space andabstract function space respectively;prove that they are equivalent not only in theweak topology but also in the strong topology.

作为连续小波变换的应用，分别利用〓上的，多元函数空间上的，向量函数空间上的和抽象函数空间上的连续小波变换分别得到了某些线性微分方程，某些线性偏微分方程，某些向量线性微分方程和某些抽象函数的微分方程分别等价于其相应的积分方程，证明了它们不仅在弱收敛意义下而且在范数收敛意义下是等价的。

Based on the propagation and transformation law of Wigner distribution function through a general axially nonsymmetrical optical system,investigated is the transform relationship of WDF between the input and the output planes of a pair of cylindrical lenses system which is used widely in optical signal processing .

基于维格纳分布函数在一般非轴对称系统的传播和变换规律，讨论了在光学信息处理系统中常用的双柱透镜系统输入和输出面WDF之间的变换关系，在直角坐标中给出了联系该系统相空间坐标的维格纳分布函数的坐标变换关系式和等价的矩阵表示。

In Chapter 4, we not only give a new definition of fuzzy finite automata, of which the state transition accords with a compound fuzzy transition, but also present an important conclusion that the coarsest respecting compound fuzzy transition partition of states is same with the coarsest equivalent partition. In the discussion of coarsest partition, we give an algorithm respecting compound fuzzy transition which would be applied to get the coarsest respecting compound fuzzy transition partition.

第四章根据分明自动机的等价分类，通过重新定义模糊自动机识别过程，使得模糊自动机的识别过程与一个合成模糊变换一致，而且得到了尊重合成模糊变换的最粗分类即为状态集的最粗等价分类这一重要结论。

Furthermore we introduce the concepts of coverings and lattice-valued homomorphisms,we prove that the L-valued fuzzy transformation semigroups in which the multiplication is fuzzy transformation semigroup inducible is equivelent to usual faithful transformation semigroups in the sence of lattice-valued strong homomorphism.

若格半群中的乘法是格值变换半群可诱导的，在格值强同态下证明了格值可诱导变换半群和一般有效变换半群是等价的。

Finally, according to market conditions and market products this article paper analyzes the trends in the development of camera technology, and designs a color night vision camera.

最后根据市场情况和市面上产品的情况分析了摄像机技术的发展趋势，并设计了一款彩色夜视摄像机。

Only person height weeds and the fierce looks stone idles were there.

只有半人深的荒草和龇牙咧嘴的神像。