查询词典 if and only if

A string is true if and only if its length is non-zero.

一个字符串当且仅当它的长度不为0是，表达式的值为真。

Let A be a nonsingular nth-order real matrix, then cond_p =||A||_p||A~(-1)||_p =1(p= 1,∞), if and only if A = cpσ, where c is a positive constant, p is a permutation matrix, or is a diagonal mat...

设A为n阶非异实矩阵，则矩阵A的求逆p-范数条件数等于1的充要条件为A=cpσ，其中c为正常数，σ是置换阵，其对角元都等于+1或-1。

Positive semi-definite matrices are positive definite if and only if they are nonsingular.

正半定矩阵是正定的，当且仅当它们是非奇异矩阵。

If and only if p is a minimal prime of a principal ideal.

当且仅当p是一个主理想上的极小素理想。

The existence is affirmed if and only if all principal minor of the matrix composed by the vectors is positive.

本文求得了答案，命题成立的充要条件是由向量组构成的矩阵的每一个主子式为正。

The principal can get the maximum profit by leasing the firm, if and only if the agent is risk-neutral.

有且只有经理是风险中性时，所有者可以通过出租企业得到最大的利润。

We note that any pure elliptic subgroup ofI somis discrete if and only if G is finite group.

最后，我们引入了一种广义非初等群，发现〓变换群经典的离散准则对我们研究的非初等群只是有条件成立，我们找到了充要条件对其建立了离散准则。

The main resul ts show that any pair of pure finite epistemic states are quasi skep tically equivalent if and only if their par-images are similar.

利用有限子语言在原语言上的归约，得到如下的表示定理：任两个纯的有限认知态是拟怀疑等价的，当且仅当它们作用算子 par后结构相似。

Lastly, we study the conditions of linearization for symmetric system, from which we can see that a symmetric system is linearizable on manifold M if and only if this system is linearizable on quotient manifold M/G.

最后讨论了对称非线性系统线性化问题，从中可以看出对于具有对称性的非线性系统只要在商流形M／G上能满足线性化条件即能保证在整个流形M上能线性化。

Since a ring satisfies the related comparability if and only if every regular element is related unit-regular, In Section 2. 3, we first give some equivalent conditions for an arbitrary ring to satisfy the related comparability.

由于环R满足相对可比性当且仅当R的每个正则元是相对幺正则的，§2.2节给出了一般环中给定的正则元是相对幺正则的一些特征刻画，证明了文献[22]（1997）的主要结果在任意环中仍然成立。

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷