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1·A necessary and sufficient condition of the existence of prime model is proved.

研究了主型的有关性质，证明了一个素模型存在的充分必要条件。

2·In this paper we give a necessary and sufficient condition on diagonalization matrix.

本文给出矩阵可对角化的一个充要条件。

3·In this note, a necessary and sufficient condition of diagonalization for square matrix is considering.

方阵是否可以对角化，是矩阵的一条很重要的性质。

4·It is obtained that a necessary and sufficient condition for a closed fuzzy set to be a convex fuzzy set.

引入线性拓扑空间中的凸闭模糊集概念，得到闭模糊集是凸模糊集的充分必要条件。

5·The question as to whether binarity is a necessary and sufficient condition to produce barium star is addressed.

讨论了双星是否是产生钡星的必要和充分条件，因为已知道的钡星系统全是双星。

6·A necessary and sufficient condition for an ideal of an integral table algebra being self-orthogonal is obtained.

本文给出了整表代数的单边理想是自正交理想的必要充分条件。

7·In this section, we also establish a necessary and sufficient condition for the algorithm of the mixed scheduling.

在这一部分里，我们同样得到了一个任务集可以用混合调度算法调度的一个充分必要条件。

8·In this paper, We give a necessary and sufficient condition that closed decomposable operator, is strongly decomposable.

本文给出了封闭可分解算子是强可分解的一个充分必要条件。

9·A necessary and sufficient condition for an inner set space with three critical sets which can be weighted is also given.

给出了具有三个临界集的内集空间可以赋权的一个充分和必要条件。

10·Finally, the necessary and sufficient condition is shown for similarity and consimilarity of matrices over quaternion field.

同时得到一些关于四元数矩阵的性质，以及体上矩阵相似和合相似的充要条件。

充要条件

1·In this paper we give a necessary and sufficient condition on diagonalization matrix.

本文给出矩阵可对角化的一个充要条件。

2·The author discusses a class of general of singular boundary value problems by using the first integral method, and the necessary and sufficient condition of positive solutions was obtained.

运用首次积分法讨论了较广泛的一类常微分方程边值问题，得到了正解存在的充要条件。

3·This paper studies the necessary and sufficient condition of uniformly convergent difference scheme for the elliptic-parabolic partial differential equation with a small parameter.

本文研究小参数椭圆-抛物偏微分方程一致收敛差分格式的充要条件。