等价的

The equivalenceof the adjunction for the grey-scale morphological dilation and erosion, and for thefuzzy conjunction and implication has been proved. A series of properties ofgery-scale morphological operators are discussed.

证明了灰度形态学膨胀和腐蚀算子之间的伴随关系与模糊逻辑合取和蕴涵算子之间的伴随关系的等价性。

For the sake of getting more economic or effective controllers, a mapping law is proposed that the sub-systems in a space are mapped algebraic equally into another space to reduce differences by optimal theory. No any restrictions are added to the controlled systems, and without need to solve coupled Lyapunove or Riccati equalities.

2考虑了各子系统之间的层次差异，提出了变换规则，通过代数等价变换将各子系统映射到另一空间，借助优化理论，消除各子系统之间的差异，从而获得更经济、更有效的控制器。

Analytic functions of complex variable function is the main object of study, and the five equivalent conditions of analytic functions penetrate the whole process of learning of complex function.

解析函数是复变函数论主要的研究对象，而解析函数的五个等价条件又贯穿了我们对复变函数论学习的全过程。

Qu. The regulated state is guaranteed to enter and remain in a given arbitrarily small neighborhood of origin within a finite time interval. proposing two new tracking control strategies for robot.

Qu等价匹配条件的非线性鲁棒控制方案，它能够保证状态在有限时间内收缩到原点的预先指定的任意小邻域。

Regular sets: finite automata, regular expressions, equivalences among notations, methods of proving a language not to be regular.

正则集：有限自动机，正则表达式，符号表示法中的等价，证明一种语言不是正则的方法。

Isometries and equivalences of quantum codes also are researched.

深入研究了量子码的等价性问题，给出了若干基本结论，特别地，证明了MacWilliams的一个著名定理在量子情形不成立。

Under Z-condition and strict pseudomonotonicity assumptions, we establish the equivalences among the equilibrium problem, the least element problem of the feasible set, and a related optimization problem.

在Z-条件及严格单调性假设下，我们得到：均衡问题、均衡问题可行集的最小元问题以及一个相关的优化问题等价。

For the single agent case, a fixed-point semantics which can be translated to the answer set semantics of the general logic program is given and is proved equivalent to the complete Bonatti stable set.

对于单主体的情形，给出了一种不动点语义，证明了它和完全Bonatti稳定集等价，并可以转化为扩展逻辑程序的回答集语义。

Also a totally topological transitive system is topologically double ergodic if the regular minimal points are dense in it.

还证明了正规极小点稠密的完全拓扑传递系统是双重拓扑遍历的，从而对有限型子转移而言，拓扑强混合与完全拓扑传递等价。

Aiming at the problem of Markova chain state transition prediction, this paper presents equivalent prediction method and models based on Discrete Process Neural Networks. According to the description of system state transition problems in a certain condition, we discuss the equivalence relation between DPNN and Markov models.

针对Markov链状态转移预测，提出一种基于离散过程神经元网络的等效状态转移预测方法和模型，探讨DPNN与Markov模型在一定条件下对于系统状态转移特性描述的等价性问题。

The concept of equivalent rotationally rigidity is offered and the formula of rotationally rigidity is obtained.

主要做了如下几个方面的工作：对伸臂位于顶部的单层框架—筒体模型进行分析，提出了等效转动约束的概念和转动约束刚度的表达式。

Male cats normally do not need aftercare with the exception of the night after the anesthetic.

男猫通常不需要善后除了晚上的麻醉。