必要条件

Let R be a ring with identity. Then R is a division ring if and only if every unitary module over R is a free module.

R 是有单位元的环，它是除环的充分必要条件是其上的所有幺模都是自由模。

First we give some necessary and sufficient conditions for the oscillation of(1) by Lebesguge s dominated convergence theorem and Schauder — Tychonoff fixed point theorem.

这篇文章中，我们首先利用Lebesgue控制收敛定理，以及Schauder-Tychonoff不动点定理给出了方程(1)振动的若干充分必要条件。

In this paper, the authors consider the even-order neutral difference equations with continuous arguments. By using Lebesgue' dominated convergence theorem, a necessary and sufficient condition for the existence of eventually positive and bounded solutions is obtained.

研究一类具连续变量偶数阶中立型时滞差分方程，利用Lebesgue控制收敛定理给出这类方程存在最终有界正解的一个充分必要条件，得到相应新的比较定理。

In this paper,a necessary condition that a cut vertex belongs to every γ s set of G is discussed,and a necessary and sufficient condition of existing indepedent set dominating set in G is given.

本文讨论了割点属于G的任一最小集控制集的必要条件，并且给出了G有独立集控制集的充要条件。

As a consequence, we make a conclusion that the dual Toeplitz operator is normal if and only if the range of the symbol lies on a line.

在此基础上研究了对偶Toeplitz算子的正规性，得到了对偶Toeplitz算子是正规算子的充分必要条件。

Hydrogen gas, as a refrigerant of the dynamotor, can increase the efficiency of generating electricity.

氢气作为发电机的冷却剂可以有效地提高其发电效率，而氢气参数处于正常范围内更是保证发电机高效、安全正常工作的必要条件，所以对发电机系统氢气参数的实时监测可以实现对发电机运行的必要而且有效的实时状态评估。

This loss of the form of the word represents a great easement for the thought-processes and may be a necessary condition for the existence of science, but art could never be satisfied with this eroded word.

这个词的损失的形式代表，伟大的缓和进程的思想和科学可能是存在的必要条件，但艺术是永远不会满足于这个词的侵蚀。

This is a necessary condition for the electric field to be zero .

这是使电场为0的一个必要条件。

The requirements were respectively investigated in terms of the criterions of Gibbs function and electromotive force.

根据吉布斯函数和电动势判据，讨论了反应进行的必要条件。

Think:" The tension between the elephantine " outside resembling " and " elephant like " and " condition "," is the requirement that artistic conception makes.

认为："象"和"境"、"象"和"象外之象"之间的张力是意境生成的必要条件。

Recall that, in the Kolmogorov axiomatization, measurable sets are the sets which have a probability or, in other words, the sets corresponding to yes/no questions that have a probabilistic answer.

延期开工的Kolmogorov宣布要衡量所有套职能有限许多坐标限制在于衡量子寅。换句话说，如果是/否的问题回答f可看的价值观念在许多最有限坐标，然后它有一个概率的答案。

The experimental results showed that the algorithm can filter singular points and remain fixity of the target edge.

实验表明：基于模糊理论的图像智能滤波方法比常规图像滤波方法运算量小，它既能去除奇异点，又能保持图像中目标的边缘不变性，具有很好的滤波效果。