系数函数

The Airy function is used to calculate the plasma impedance and the grill-plasma scattering matrix is deduced, then the coupling properties of the HT-7 LHCD MJ launcher are studied with the antenna scattering matrix and the grill-plasma scattering matrix based on the liner coupling theory. The average power reflection coefficient, directivity, power spectrum are obtained for different edge plasma densities and for different phasings between main waveguides.

采用线型耦合理论，用艾黎函数计算了等离子体阻抗，推导出常规波导阵对等离子体的散射矩阵，并利用它和天线自身的散射矩阵研究了HT-7装置低杂波多结波导阵天线的耦合特性；计算了其平均功率反射系数、方向性系数和功率谱与等离子体边缘密度和主波导相位差等参数的关系。

With the method, tendency of measured value was analyzed, harmonic mode was checked by using autocorrelation function, the relation between spectrum parameters was analyzed and Fourier coefficient was calculated based on the theory of Fourier series. Finally, the significance of every period was tested and dominant period determined so as to establish the prediction model.

首先对实测序列进行趋势项分析；其次用自相关函数进行谐波模式检验；然后根据函数的傅立叶级数展开理论，分析谱参数之间的函数关系，计算傅氏系数；最后采用F分布检验法对周期进行显著性检验，确定主要周期，从而建立预报模型。

The thesis demonstrated the function dependency and the greatest lower bound ofλ-spiral function and proved the inclusion relation of the two functions.

对λ-螺旋形函数的从属性及星函数实部的精确下界给出了证明，并证明了两族函数的包含关系，给出了特殊情况的系数估计。

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。

This article makes use of the approximation property of Laguerre orthogonal function series to present a Laguerre function approxima te model of linear dynamic systems.The model eliminates the need for assumption of the plant order and the time delay and approaches unknown systems via estimat ing the Laguerre coefficients on-line.

蒋中摘要：利用Laguerre正交函数序列对空间函数的良好逼近特性，建立了线性动态系统的Laguerre函数近似模型，该模型不需要对象的阶次和时延等结构知识，通过在线辨识对象的 Laguerre系数矩阵，能较好地逼近结构未知系统。

Furthermore, buckling effect factors and their influence law are exploited. Finally, combining the character of piles foundation with high bridge piers with engineering practice, four optimal mathematic models are proposed and flow diagram of optimization analysis is fulfilled by the computer optimum program. A numerical example is analyzed to get optimal solution by using this program. Meanwhile based on the optimal model with buckling coefficient as the objective function, parameter variables are discussed about their effect rule toward the optimal value of objective function.

最后，针对高桥墩桩基础的特点，在基本优化模型的基础上，根据不同的目标函数建立了相应的优化模型，给出优化设计算法流程图，编制了相应的优化计算程序；并根据高桥墩桩基的工程实际设计了一个数值算例，采用本文编制的优化计算程序对该结构进行优化，得到了优化后的最优解；同时，采用高桥墩桩基屈曲系数作为目标函数的优化模型进行因素分析，初步探讨了参数变量对目标函数最优值的影响规律和程度。

How to easily and reasonably determine the value of principal stress in the direction of plane strain is the key point.

基于弹塑性理论及土的试验规律，在平面应变的简单加载条件下，假定主应力之间的关系为双线性函数，并利用一维固结和破坏时的主应力状态，确定双线性函数的系数，得到平面应变方向上主应力计算公式的一个较合理形式，为应力状态和材料性质的函数。

The wavelet function corresponding to a certain scale can be regarded as the transfer function of a band-pass filter according to the definition of CWT, thus, sampling the signal and the wavelet function respectively, the wavelet coefficients at this scale can be obtained by convolving the two time series.

根据CWT的定义，可将某一尺度下的小波函数看作一带通滤波器的传递函数，于是对信号和小波函数分别进行采样后，再利用快速傅里叶变换实现两个序列的线性卷积，便能求出相应尺度下的小波系数。

The research of lift-off velocity distribution function of saltating sand grain would redound to solve the random problem of single lift-off sand grain from sand bed and promote the combination between microcosmic researches and macroscopical researches of Aeolian sand movement.

沙粒起跳初速度分布函数的研究成果将有助于解决在错综复杂的沙床面上单颗沙粒运动的随机性问题，初步实现微观与宏观研究的结合；跃移沙粒降落速度分布函数对于反演跃移沙粒与沙床面碰撞的恢复系数，深入理解碰撞过程具有十分重要的意义，同时也将促进击溅函数的修正工作。

An explicit analytical solution of the threshold pump power of the laser has been derived based on rate equations which contain the attenuation coefficients of the pump and laser radiations as well as the major contribution of the re-emission of the upper level atoms to the pump wave by using the analytical solutions. An analytical solution of the minimum fiber length required for the onset of the oscillation is presented. In addition, the analytical solutions describing the variations of the density of the pump radiation and upper laser level population along the fiber length have also been given.

从速率方程组出发，在不忽略光纤损耗系数和保留再发射项主导部分的近似条件下推导出了双包层光纤激光器阈值泵浦功率的显函数解析表达式，得到了光纤激光器产生振荡所需的最小光纤长度的显函数解析解；还给出了泵浦光子数密度和上能级粒子数密度沿光纤方向随光纤长度变化的显函数解析解。

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。