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This paper studys the stability of nonlinear systems in two particular critical cases. In a case, the linear systems at the equilibrium point of interest is assumed to possess a simple zero eigenvalue. In the other case, it is assumed to possess a complex conjugate pair of simple pure imaginary eigenvalue.

本文基于中心流形定理研究了非线性系统在两种特殊临界情形下的稳定性问题，一种是与它相应的线性系统在平衡点仅有零特征根，另一种是与它相应的线性系统在平衡点仅有一对共轭的纯虚数特征根。

For example, one of our conclusions is that a nonsingular QSIC has one affinely finite component if and only if the characteristic equation of the two quadrics has two distinct real roots and a pair of complex conjugate roots.

由于两二次曲面的特征方程实根个数及其重数可用精确的计算方法得到，本文分类结果可用于实现对任意两二次曲面的非平面交线拓扑形态的判断。

Generally speaking, this resulting univariate equation has three real roots or has a real root and a pair of conjugate complex roots.

但根据参数化的过程是平面与拼接曲面相截获得交线后，再用平面与所得交线相截。

It has a pair of compound eyes that composed of 28000 small eyes.

它有由28000只小眼睛组成的一个对复眼。

The head was a kind of shield with a pair of compound eyes, often with thousands of lenses.

下文讲的是化石使我们了解了这些生物的形态。

There are a pair of compound eyes

昆虫的头有一双眼睛

They have a pair of big compound eyes on the head.

它们头部有一对大复眼，它们有三对脚

The head was a kind of shield with a pair of compound eyes,often with thousands of lenses.

头部是一个甲片，上面有一对复眼，由上千个晶状体组成。

The head were a kind of shield with a pair of compound eyes, frequently with tho北美nds of lenses.

下文讲的是化石使咱们了解了这一些生物的形态。

The head was a kind of shield with a pair of compound eyes, often with thousands of lenses. They were usually an inch or two long but some were 2 feet.

虽然这些动物中有一些是现今活着的各种动物的祖先，但是另一些动物现在已经灭绝了，即他们现在已经没有活着的后代了。

In the United States, chronic alcoholism and hepatitis C are the most common ones.

在美国，慢性酒精中毒，肝炎是最常见的。

If you have any questions, you can contact me anytime.

如果有任何问题，你可以随时联系我。