必要条件

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。

The trick is to grow the middle class and keep reducing the number of poor people.

在全球经济的背景下，相当数量的富裕人口是一个社会成功的必要条件之一。

Then it proves a necessary and sufficient condition for anamalgamation of two 3-manifolds with toms boundary with no new incompressible surfaces.Lastly, with the help of the condition and the theorem about the classification of allautomorphisms of a torus, it is proveed that there exists infinitely many 3-manifolds each ofwhich contains no incompressible surfaces besides a torus.

最后，文章给出了以环面作为边界的两个3维流形在作融合积时不产生新的不可压缩曲面的一个充分必要条件，并将这个结果与关于环面到自身的自同胚类的分类的结果相结合，证明了本文的一个核心结论，即存在无穷多个互不同胚的3维流形满足除了一个环面以外不含有其他的不可压缩曲面。

It sounds like a cliche, but that's the real necessity

这听起来像一句老生常谈，但它却是真正的必要条件。

In this paper, a sufficient and necessary condition such that the Ricci form of continuous loop group s is closed is given.

本文给出了连续环群的Ricci形式是闭的充分必要条件。

Patience is a very necessary for coastguard skippers the commanders appear to have patience of job .

耐心是海岸警卫队船长们的必要条件，指挥官们似乎都有极大的耐心。

Patience is a very necessary qualification for coastguard skippers;the commanders appear to have patience of job.

耐心是海岸警卫队船长们的必要条件，指挥官们似乎都有极大的耐心。

If is cyclic, then for every codeword the word is also a codeword.

必要条件：如果是循环码，那么仍然是码字，故线性码是理想。a是多项式，码字也看成是多项式。

As a second year graduate textbook, Cohomology of Groups introduces students to cohomology theory (involving a rich interplay between algebra and topology) with a minimum of prerequisites.

作为第2本年毕业生教科书，组的Cohomology有最少的必要条件向学生介绍cohomology 理论(与在代数和拓扑之间的丰富的相关作用有关)。

In particular, we compute Hochschild homology and cohomology groups of infinitedimensional path algebras and some of their quotient algebras, and we prove that for a general monomial algebra (not necessary finite-dimensional), all Hochschild cohomology groups of positive degrees vanish if and only if its Gabriel quiver is a finite tree.

特别地，我们计算了无限维路代数以及某些商代数的Hochschild同调群和上同调群，而且给出了一般单项代数的各正次Hochschild上同调群为零的充分必要条件，即它的Gabriel箭图是有限树。

If you are unfortunate enough to the lovelorn, please tell me, I will help you out, really, please contact me!

如果你不幸失恋了，请告诉我，我会帮助你摆脱困境，真的，请联系我啦！

China's plan to cut energy intensity by 20 percent and pollutant discharges by 10 percent between 2006 and 2010 is a case in point.

中国计划在2006年到2010间降低20%的能源强度和减少10%的主要污染物排放，就是一个这样的例子。