虚

By spectral analysis of the system, we find that 0 is the uniquespectral point of system on the imaginary axis.

同时通过研究系统算子的谱特征，证明了系统算子的谱点均位于复平面的左半平面且虚轴上除0外无谱，进而得到系统的渐近稳定性，特别在范数意义下系统的动态解收敛到稳态解。

Non-condition stability means the radixes of character equations couldn't reach the imaginary axis while the increasing of τ from 0 to+∞.

无条件稳定意味着τ从0增加到+∞的整个过程中，特征方程的零点不能达到虚轴。

Because it can pull the loci, or parts thereof, away from the imaginary axis,deeper into the left-half plane.

对根轨迹或部分根轨迹有拉的作用，使根轨迹远离虚轴，向更左的左半平面移动。

The vertical axis is therefore called the imaginary axis.

因而纵轴称为虚轴。

A zero can improve relative stability because it can pull the loci, or parts thereof, away from the imaginary axis, deeper into the left-half plane.

零点可以提高系统的相关稳定性，因为零点对根轨迹或部分根轨迹有拉的作用，使根轨迹远离虚轴，向更左的左半平面移动。

The symmetric values about the imaginary axis of zero-poles which the unstable process lies in the open and closed right-half plane are defined as their mirror-injection.

非稳定过程在开右半平面的零极点关于虚轴的对称值称为该零极点的镜像映射。

Secondly, a conjecture about the stability for these systems is proposed based on the sufficient and necessary condition of the isolated transfer function being positive real. When the zeros and poles of the transfer functions lie in the imaginary axis, a known conclusion is derived from the conjecture; while the zeros and poles are on the real axis, a new result is obtained and is proved in this note. Finally, according to the conjecture, an example with poles existing on the complex plane is presented, which is not only interesting but also challenging.

然后， 基于所有孤立部分传递函数都正实的充分必要条件给出了上述系统为稳定的一个猜想，当传递函数的零极点都位于虚轴上时，由这一猜想得到了一个已知的结论；当传递函数的零极点都位于实轴上时，由这一猜想得到了一个新的结论，本文证明该结论是正确的；最后，根据这一猜想，给出了传递函数极点位于复平面的一个例子，它涉及到一类系数矩阵为时变正定矩阵的振动方程的稳定性问题，值得去深入研究。

Based on two algebra Riccati equation method especially the structure of the system Hamilton matrix and system observability theory, the role of invariant zeros in constructing system reduced order controllers was given. That is, by the suitable selection of free parameters of the system H(subscript ∞) controller, some points which were symmetry with the unstable invariant zeros about the imaginary axis became the stable poles of the system controller which were not observable and could be reduced from the system, thus could get further reduced order controller.

基于2代数黎卡提方程方法，特别是系统Hamilton矩阵的结构特点和系统可观测性理论，论述了不变零点在构造系统降阶控制器中所起的作用，即通过选择控制器的自由参量，使某些不稳定的不变零点关于虚轴对称的点构成系统控制器不可观的稳定极点，从而实现了控制器进一步降阶。

The transcendental characteristic equation is converted into a polynomial equation at the imaginary axis without any substitutions. This method needs less computation than the CTCR method.

该方法将含有指数项的特征方程在虚轴上转化为多项式方程进行研究，无需任何中间变量代换，处理方法简单，计算量小。

It is proved by the analytical and numerical method that the modulus of the Z transform of a finite impulse response sequence has no extreme values at poles (with maximums along imaginary axis and no extreme values along real axis), and the negative second order derivative of the modulus normalized along frequency axis with respect to angular frequency has maximums at the poles.

根据实测瞬态电磁脉冲响应，较好地反演了导体球和导体长椭球的冲激响应，测得了它们的雷达截面和谐振频率。用解析与数值相结合的方法证明了有限冲激响应序列Z变换的模在极点无极值（沿虚轴有极大值，沿实轴无极值），而沿频率轴的归一化值对角频率的负二阶导数在极点有极大值。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。