函数的振荡

It is found that:(1) the variation of dFM may lead to two different features for the IEC,one is the oscillatory behavior of IEC with the spacer thickness,the other is the exponential behavior in the most spacer thickness.(2)As a oscillatory function of dFM ,the IEC exhibits multiple periods and a negative non-oscillatory term.(3)The Fermi energy of the conduction electrons has a little variation as the magnetization of the two FMs changes from parallel to antiparallel alignment,furthermore,this variation is correlated with the IEC to some extent.

结果发现：（1）dFM的变化会导致层间交换耦合出现两种不同的特征，一种是随着中间层厚度的增加，IEC有振荡行为；另一种是其指数衰减行为；（2）作为dFM的振荡函数，IEC表现出多个周期和一个负的非振荡项；（3）传导电子的费密能会随着两铁磁体的磁化排列变化而稍有变化，进一步地，这种变化与IEC有着某种程度的关联。

In this paper, we study the oscillations of the eigenfunction of Sturm-Liouville problem with indefinite coefficients and general separated boundary conditions on (0,l).

本文研究了定义在有限区间上的具有一般分离型边条件的左定Sturm-Liouville算子的特征函数的振荡问题。

It is difficult to compute directly the coefficients from the integral formula, since the integral function in the formula of the ideal digital fractional differentiator is a high-order oscillating function.

从理想数字分数微分器系数计算公式的特点考虑，利用变量代换把积分函数中的振荡因子转换成积分上限，避免高阶振荡函数积分计算，给出了计算分数微分器系数的递推公式。

However, due to the oscillation and singularity of the integrand of Green's function and that integral interval is infinite, it is difficult to compute the function and to control the accuracy.

而格林函数中被积函数的振荡性，奇异性和积分区间为无穷使得该函数的计算较为困难，精度不易控制。

A series of theoretical and experimental studies on the microstrip patch antennas with dielectric superstrates is carried out systematically. Firstly, a comprehensive survey of the microstrip antenna technology and its theories are presented. Then, two analysis techniques, named as the spectral domain Green's function method and the spectral domain integral equation method are developed. The SDGF method is a simplified analysis technique, which takes advantage of the spectral domain immittance approach to find the dyadic Green's function for the stratified media, and obtains the complete closed-form formulas for radiation patterns, directivity, efficiency, gain etc. Some interesting calculated results are presented. The SDIE method is capable of determining resonant frequency, radiation characteristics, input impedance etc, for the covered microstrip patch antennas. Comparing with other full-wave analyses it reduced computation and mathematical labour remarkably. The singularities near the pole location of the surface-wave modes and the difficulty of the integral computation over infinite range of oscillating integrands are dealt with actively and documented well. Results predicted by the SDIE method agree extremely well with our experimental results for resonant frequencies of various superstrates. The superstrate effects on impedance and radiation characteristics also have been investigated experimentally so that the gap due to lack of measured data and computed results for multi-layered superstrate has been filled to some degrees and two useful observations have been achieved for weakening the resonant frequency shift and optimizing the microstrip antenna gain. As a meaningful application, the design and analysis of a 4×4 patch array are introduced.

实用微带天线普遍加介质覆盖层来防护热，物理损伤和环境影响，也可能在飞行或严酷气候条件下自然形成覆盖层本论文对带介质覆盖层的微带贴片天线系统地作了一系列理论和实验研究首先，对微带天线技术和理论作了全面的综述然后，发展了两种分析方法，称为谱域格林函数法和谱域积分方程法SDGF法是一种简化的分析技术，它利用谱域导抗法来求得分层媒质的并矢格林函数，并得出方向图、方向性系数、增益等参数的完整的闭式公式，给出了一些令人感兴趣的计算结果SDIE法能确定介质覆盖微带天线的谐振频率、辐射特性和输入阻抗等与其它全波分析方法相比，它明显减小了计算量和数学工作量已有效地处理了表面波模极点附近的奇异性和对振荡的被积函数的无限区间积分计算的困难对于不同覆盖层情况下的谐振频率，由SDIE法所预示的结果与我们的实验结果吻合得很好对于覆盖层对阻抗和辐射特性的影响也已作了实验研究这在某种程度上填补了缺少实验数据和计算结果之间的间隙，并得出了缓解谐振频率偏移和优化天线增益的两点有用的结论作为有意义的应用，介绍了一个4×4元矩形贴片天线阵的设计和分析。

Secondly, oscillation energy function of inter-area mode oscillation is defined which can be regarded as a measure of the deflection away from the steady state position during dynamic oscillation period.

分析了功率振荡过程中能量函数的变化，提出了衰减振荡能量的阻尼控制策略，目的是使系统暂态能量以最快的速度归零，即回到故障后的稳定平衡点。

The NEF method is potential in developing new efficient tools for on-line security analysis and control. In study of the method of damping system low-frequency oscillations, this project has proposed the control strategy of oscillation energy function descent.

项目研究中还应用归一化暂态能量函数对电力系统振荡机理进行分析，设计了增加阻尼平抑电力系统振荡的方法，提出了振荡能量函数的概念，得出"振荡能量函数下降法"的控制策略。

The main results are as following: A A new demonstration to optical theorem is constructed B The scattering amplitude function for small particles, which is more accurate than that in classical RGB, is gained using electrostatics approximation, C Through a δ transform to the high frequent oscillation function, a concise deduction of the EG-type scattering amplitude function has been achieved.

主要结果如下： A给出了光学定理的一个新证法； B利用静场近似，得到了比经典RGB更精确的小粒子散射振幅函数； C通过一个高频振荡函数的δ变换，给出了一种EG散射振幅表达式的简明推导，并做了小角度散射简化，参照ADT，对EG近似又做了相位修正； D定义了一个新的函数—消光函数，并得到了组合散射体消光函数的平均定理。

Based on the idea, this paper develops a new performance index of detecting the oscillatory feedback control loops.

本文利用这个思想，在现有评价控制回路振荡方法的基础上，提出了一种新的回路振荡评价方法，通过找出系统可接受的振荡程度和被控变量的自相关函数的关系，得到评价反馈控制回路振荡的性能指标。

In the optimization iteration, the levelset function values of nodes are considered as design variables. To computedifferences normally, the Heaviside function is handled for smoothing, theregularized Heaviside function is selected to avoid the oscillation inhomogenizations method, and the results can converge smoothly.

在优化迭代过程中，节点上的Level Set函数值被看作是设计变量，并且为了便于微分计算能够正常进行，对Heaviside函数及其导函数做了光滑化处理，选取了一种正则化的Heaviside函数，避免了均匀化方法中出现的振荡现象，可以平稳地收敛到最终结果。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。