等价的

Let a =∈〓. Then corresponding to 62 equivalence classes in χ for ～, we have 144polynomial elements in one variable in canonical basis, each of them also cor-responds to a region which consists of six independent inequalities.

定理。设a=∈〓。那么与χ关于～的62个等价类对应，在典范基中有144个单变量多项式元素，每个单变量多项式元素也对应一个由六个独立不等式构成的区域。

It is a crucial issue to establish a unified canonical description form for different design levels with low complexity.

该方法可以用来有效判断不同设计层次的描述是否等价，从而可以实现跨设计层次的模块重用、综合和验证。

In view of cellular automaton, the classes are treated as states of the automaton.

从元胞自动机的观点来看，这些等价类可以被当作自动机的状态。

This paper includes five parts. Part one is an introduction which introduces the definition of the circular chromatic number and its equal definition, and then it presents theories and conclusions cited later.

本文一共分为五个部分，第一部分为引言，介绍了圈色数的定义及其等价定义，还总结了后面常会引用的定理和结论。

Several criteria are given for judging whether ideal class number of a realquadratic function field to be one.

研究了实二次函数域的理想类数为1的一些必要条件以及等价条件。

In this paper, infinitesimal classification is given and theorem condition of equivalent infinitesimal replacement is simplified,thus,this theorem is easy to operate.

对无穷小提出了新的分类法，并对等价无穷小替换定理的条件进行了简化，从而使得该定理应用更加方便。

X→Y has a closed graph are provided,and the classical closed-graph theorem is generalized.

本文给出了算子T具有闭图象的一些等价条件，并推广了经典的闭图象定理。

In chapter 2, we introduce weak hopf π coalgebra and two kinds of special subalgebra over it.Some basic properties are studied to make a basis for the following chapter.

第三章主要是在弱Hopf群余代数上建立Yetter-Drinfeld模，探讨其性质并给出它的等价条件，从而对其结构有更本质的认识。

Aiming at the problem of equivalent conversion from conjunctive normal form to disjunctive normal form, an effective algorithm was proposed to construct reduction tree based on discernibility matrix.

针对差别矩阵求约简过程中合取范式向析取范式等价转换的难题，提出一种基于差别矩阵构造约简树的有效方法。

To see this note that the contrapositive is false only when is false and is true.that is only when p is true and q is false.we now show that neither the converse ,,nor the inverse ,has the same truth value as for all possible truth values of p and q.

当两个复合命题含有相同的真值的时候，我们称之为等价命题，（为什么是复合命题因为如果不是符合命题的话那么就是同一个命题了。

And Pharaoh spoke to Joseph, saying, Your father and your brothers have come to you.

47：5 法老对约瑟说，你父亲和你弟兄们到你这里来了。

Additionally, the approximate flattening of surface strip using lines linking midpoints on perpendicular lines between geodesic curves and the unconditional extreme value method are discussed.

提出了用测地线方程、曲面上两点间短程线来计算膜结构曲面测地线的方法，同时，采用测地线间垂线的中点连线和用无约束极值法进行空间条状曲面近似展开的分析。