等价的

As for a given automata,there exists three cases:for some state which did not being visited, for some state itself indeed being not reachable although it has been visited,for some state it is equivalent to other states though it can be reached to, in these three cases it is obviously redundant to construct these automata, and the only way for us is to delete,integrate and reduct these useless states in order to minimize the number of states.

对于一个给定的自动机，它的状态中有一些根本没有被访问过，有一些尽管被访问过，但是本身是不可达的，有一些状态尽管是可达的，但是在功能上却与另一些状态等价，这样的自动机在设计和应用中显然很累赘，可以将一些无用的状态删掉，将另外一些等价状态进行整合和约简，使之状态数达到极小。

This article compared the integrand of infinite integral and unbounded function integral by comparing the infinitesimal with the infinity, obtained the corresponding equivalence theorem of criterion of convergence of abnormal integral, and gave out the proof.

将无穷积分及无界函数积分的被积函数运用无穷小和无穷大比较的方法进行比较，得到了相应的反常积分敛散性极限审敛法的等价定理，并给予证明，从而可运用等价定理灵活的判断反常积分的敛散性。

Secondly, the invertible assignment problem are studied. At last, we explored the conditions on the invertible completion of part matrix Mx and obtained the characterizations of the relovent operator of invertible completion.

利用构造分块初等矩阵、算子广义逆、极分解、谱分解为工具，深入地研究了算子对的逆补Mxy、算子逆配置的一系列等价刻画及一般性结论、缺项算子矩阵存在逆补Mx的等价刻画，并获得了逆补的预解集的性质刻画。

Secondly,it is proved that monotonicity is equivalent to the law of proof by contradiction,and a simpler equivalent condition to monotonicity is given.

首先，讨论了择优逻辑的若干基本性质，并给出了单调性的一个充要条件；其次，证明了单调性与反证律等价，并给出了单调性的一个更为简洁的充要条件；最后，讨论了解释集合是归纳集时的单调性，证明了单调性与择优蕴涵的退化等价。

In Chapter 3,we classify a binary-coded individual space equivalently withthe help of the ideals of Boolean algebra and analyze the search capabilitiesof a new kind of algebraic crossover operator in these equivalence classes,thenprovide the algebraic representation of a type of genetic algorithms by usingthe permutation group,therefore we can derive a lot of new forms of geneticalgorithms.

第三章运用Boole代数的理想将二进制编码的个体空间进行等价分类，分析了一类代数杂交算子在这些等价类上的搜索能力；然后利用置换群给出一类遗传算法的代数表示，由此导出多种新形式的遗传算法，并给出其中两类算法形式的收敛性结果。

Ricardian equivalence, is an economic theory which suggests that it does not matter whether a government finances its spending with debt or tax increase, total level of interest rate, private investment, and consumption will remain unchanged.

李嘉图等价定理认为，政府的财政收入形式的选择，不会引起人们经济行为的调整摘要：李嘉图等价定理认为，政府的财政收入形式的选择，不会引起人们经济行为的调整。

Transversality condition is used to characterize the stability of such equivariant bifurcation problems.

本文第五章利用奇点理论中光滑映射芽的左右等价关系，考虑在左右等价群的一个子群的作用下，分歧参数具有对称性的等变分歧问题的开折问题，得到了相应的通用开折定理。

To gain an ideal algorithm, based on the theories of rough set and granular computing, the basic algorithms of indiscernibility relation and computing positive region were designed, in which dynamic SQL was used to directly get the sorted object sets so that the sort algorithm was left out.

摘 要：为获取高效算法，结合Rough集和粒计算理论，基于知识颗粒设计出获取等价类的算法及计算正区域的等价算法，使用动态SQL语句直接获取已排序的对象集，省略类似算法必需的排序算法，降低了实现的复杂度。

The invariant V (A , [1〓] that we used for unital case is the semigroup of Murry-von Neumann equivalence classes of projections in matrices over C〓-algebras together with the class of the unit.

我们用来分类的不变量（V，[1〓]）是A的矩阵代数中所有投影的Murry-von Neumann等价类所成的半群及单位元所在的等价类。

Then the self-recurrent neural network structure, one kind of simplified structure of internal recurrent network, and the leaming algorithm, dynamic backpropogation algorithm of self-recurrent neural network, is proposed.

本文将神经网络作为传统的线性模型的非线性推广进行了分析，证实了多层前向神经网络与非线性自回归模型的等价意义，及带有反馈的循环神经网络与非线性自回归移动平均模型的等价意义。

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。