Several norm equalities are proved by norm inequality and mathematics induction.

运用范数不等式，使用数学归纳法，证明了几个范数等式。

The paper get some rank equalities of scalar-involutory matrices by elementary operation.

运用初等变换方法探讨了数量对合矩阵的若干秩等式。

So far, all of the samples have shown constraints as equalities, but this is only part of the story.

到目前为止，所有示例中的约束都是等式，但是这只是一部分。

If you want strict equalities in approximations means that we replace the function by its tangent approximation.

如果你想要严格的近似等式,那就意味着我们要用切线逼近来取代原函数。

In this paper, an improved paramodulation method is also presented, that prohibits the paramodulation between equalities .

文中还提出了一种改进的调解方法，其中禁止等词之间的调解。

It is held that women's liberation can not be realized by claiming one or two equalities in rights between men and women but by changing the patriarchal culture.

笔者认为，寻求妇女解放之路不能只靠谋求一两个与男性平等的权利来实现，而是要通过改变男权制文化来寻求解决办法。