实轴

The final result indicates that in the expression of the completeness relation,the integral path is along the real axis from -∞ to ∞ but runs over near the origin,which is contrary to the Cauchy principal value appearing in previous works.

同时得到展开式中的积分是沿实轴从-∞到∞，但在原点附近将从上方绕过。这不同于过去所得的C auchy主值积分。为最明确显示这一差别，在单孤子情况下又用平方Jost函数的显式，直接作了验证。

To extend this idea to the computation of the measure of fractal sets built on the real axis, it can be seen immediately that the fractional integral (1) does not work as it fails to be additive because of its non-trivial kernel.

延长 这一想法，以计算该措施的分形集的建立在实轴上，可以看到马上说，分数次积分（ 1 ）是行不通的，因为它未能被添加剂的，因为它不平凡的内核。

The second chapter is the main part of this paper, in which the formulation of the Riemann boundary value problem of non-normal type on the real axis, the solution method of homogeneous problem, the relation between the two kinds of different derivatives and the inhomogeneous problem will be thoroughly given. In this paper, the solution and the solvability of the Riemann boundary value problem of non-normal type on the real axis will be given. Furthermore, it is shown that the twokinds of derivatives of the function Ψ are existing and equivalent in the case ofthe solution about the original problem, therefore, we get uniformly Hermite interpolatory polynomial. The relation between the two kinds of different derivativesof the function Ψ are similar for smooth closed contours by means of the same proof.

第二章是本文的主要部分，分别给出了实轴上一类非正则型Riemann边值问题的提法、齐次问题的解法、两种导数的关系及非齐次问题的求解，本文运用杜金元教授[11]的方法获得了实轴上非正则型Riemann边值问题的封闭解及可解性条件，且在问题可解的情况下论证了函数Ψ的非切向极限导数和Peano导数存在且相等，从而获得了统一的Hermite插值多项式，同样关于封闭曲线上非正则型Riemann边值问题，采用本文论证方法证得了函数Ψ的非切向极限导数和Peano导数存在且相等，从而较好地统一了[10]、[11]中的Hermite插值多项式。

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。

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。

This article discusses the use of the theorem of the residues to calculate Cauchy's Principal values of the improper integral, where auxiliary function has poles of higher order on the real axis and proposes a new theorem of culcuation.

在复函中应用留数定理计算广义积分的科希主值时，许多著作仅讨论了辅助函数在实轴上有一阶极点的情形[1-3]，有的则认为：辅助函数"在实轴上的奇点不能是二阶或二阶以上的极点["4，5]。

Applying this new theorem, one can easily find the auxiliary function and solve many problems of Cauchy's principal values of improper integral as well, the original theorem being unable to do so.

由于这个条件的限制，在寻找辅助函数时往往碰到困难，甚至找不到在实轴上只有一阶极点的辅助函数。

Finally, A class of inverse Riemann boundary value problem for bianalytic functions on the real axis is proposed.

先消去参变未知函数，再采用易于推广的矩阵形式记法，可把该问题转化为两个实轴上的解析函数Riemann边值问题。

To reconstruct the state variables precisely, the observer s pole is placed on the negative real-axis in the complex plane, and in the flat range on the curves ofobservation time vs.

为了使观测器精确重构状态变量，将观测器的极点配置在复平面负实轴上，观测器极点分布与观测时间关系曲线的平缓变化区域。

We consider an auxiliary function related to the Cauchy transform of the measure μ,, and get that it preserves sign on negative real axis. The property play a role in the study of the transform.

我们考虑了与测度μ的Cauchy变换相关的一个辅助函数，得到了它在负实轴上具有保号性，此性质对研究该变换的一些有趣的分形性质起作用。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。