系数函数

By using the expansion of spherical wave functions for a cylindrical wave function and with the help of the theory of hypergeometric functions, the Sommerfeld type integral contained in the electromagnetic fields is expressed as a rapidly and absolutely convergent series of spherical wave functions; and the coefficients of the series are the Legender Polynomials with the complex argument for the constitutive parameter.

应用圆柱波函数的球面波展开式和超几何函数理论，场分量中的索末菲尔德型积分被表示成快速、绝对收敛的球面波函数系展开式；展开系数是以物性参数为复宗量的勒让德多项式。

By using the expansion of spherical wave functions for a cylindrical wave function and with the help of the theory of hypergeometric functions, the Sommerfeld type integral contained in the electromagnetic fields is expressed as a rapidly and absolutely convergent series of spherical wave functions; and the coefficients of the series are the Legender Polyno...

应用圆柱波函数的球面波展开式和超几何函数理论，场分量中的索末菲尔德型积分被表示成快速、绝对收敛的球面波函数系展开式；展开系数是以物性参数为复宗量的勒让德多项式。

The potential functions of incident and scattered waves were expanded into Fourier-Bessel series, and the coefficients of scattering waves field were determined by imposing continuity conditions of stress and displacement at the soil-pile interfaces with the help of a set of cylindrical coordinate systems and in accordance with the Graff's addition theorem.

将倾斜入射波和散射坡的势函数展开成Fourier-Bessel函数的无穷级数的形式，利用一组圆柱坐标系统和Graff加法转换定理，通过施加桩土界面处的应力和位移连续的边界条件，求解出散射波势函数的待定系数，进而得到饱和土体中任意点的位移和应力。

Content: In this thesis, we investigate properties and coefficients maximum problem of some analytic functions in function theory, the research center is univalent function.

中文摘要：本文研究了函数论中几类解析函数族的性质和系数的最值问题，主要以单叶函数为研究对象，不仅对一些结果进行了推广，同时也获得了一些新结果。

For non-Kolmogorov turbulence, the anisoplanatiam error, the angular correlation function of Zernike polynomials, the residual phase structure function and the long-exposure OTF after low-order modes correction are analyzed.

分析了非科尔莫戈罗夫湍流情况下，自适应光学系统低阶模式校正时的非等晕误差、泽尼克系数角相关函数、残余相位结构函数以及长曝光光学传递函数，并定义了一个新变量模式校正因子，用来有效评价目标非等晕误差对低阶模式校正自适应光学系统补偿效果的影响。

Using the continued fraction method other than the traditional recurrence methods to generate the Bessel function, we built an accurate code for calculating the Mie scattering.

2利用Mie散射模式计算气溶胶散射相函数的展开式系数，直接提供逐次散射计算中所需要的立体角积分网格上的相函数，避免为获得相函数而进行内插。

The optimal collocated positions of secondary source with two microphones are studied and the separate of transfer function method that reduce the influence of acoustic feedback are developed based on plane wave transmission theory of sound and concept of transfer function in a duct. After, In order to identify the variation of the signals and find out individual correlation coefficient, cross correlation function analysis between primary noise signal and reference input signal is processed.

本文根据管道声场的平面波传递理论，进行第二声源与两个感测麦克风之间的位置配置研究，配合数位讯号处理的技术，发展出转移函数分离法，以消除声场回授的影响，之后，再将使用和未使用转移函数分离法的讯号个别与主要噪音源讯号做交互相关函数的运算处理，辨识讯号之间的差异，找出个别的相关性系数。

The authors studied carefully two numerical differential methods, finite difference method and rational polynomial technique, and pointed that FDM is the special ease of RPT when the limit state function is linear. Accordingly, FDM3 can be used for the continuous linear limit state function and RPT5 for the continuous nonlinear limit state function. For the discontinuous limit state function, RPT should be used because of the large error of FDM.

对于可靠度分析中常用的有限差分法及有理多项式法这两种数值微分方法，本文详细研究了二者间的异同及其求导结果与步长的关系，指出了对于相同的步长控制系数及取样方式，FDM是RPT在线性情况下的特例；对于连续的线性功能函数，可直接用3点FDM求导；对于连续的非线性功能函数，可用5点RPT求导；对于非连续的功能函数，应采用RPT求导。

The results show that, the chloride concentrations and diffusion coefficients are both a one-humped function of elevations (can also be the time scale of seawater infiltration), they increase with the increase of elevation until they get to the peak value, and then decrease with the increase of elevation; an evident relationship is being between the surface chloride concentrations and the wave forces acted on the concrete surface, while there is no much difference among the diffusion coefficients; the diffusion coefficients get to bigger as the depth from the concrete surface increase in the influence of the capillary structures evolution and chloride concentration, but this tendency of change was alleviated with the increase of depth.

研究结果表明：氯离子侵蚀混凝土设施的竖向分布规律为氯离子浓度、扩散系数与标高之间同为单峰函数分布，先随高程变大而变大，达到峰值后，随高程变大而减小；氯离子侵蚀混凝土设施的环向分布规律为混凝土构件表面氯离子浓度、氯离子通量与波浪力之间有明显的对应关系，波浪力越大，则表面氯离子浓度和氯离子通量越高，而扩散系数在各方位角差别不明显；由于混凝土长期服役过程中内部毛细孔隙结构演化以及氯离子浓度的影响，氯离子扩散系数随混凝土深度变大而变大，但这种变化趋势随深度逐渐趋缓。

The theories proposed by Wilson (1994) were adopted to describe the fundamental behaviors of temperature and variation of suction of soil. The Darcy's law and Pick's law described the flows and evaporation of water respectively. Some proposed assumptions including the characteristic curve of volumetric water content and hydraulic conductivity were only related to the suction of unsaturated soil. The coefficient of latent heat for water was a linear function of temperature; and the heat conductivity was calculated according to the equation proposed by De Vries.

对于土体的温度和吸力变化特征，采用Wilson提出的理论加以描述，在此理论中，分别利用Darcy和Fick定律描述水和蒸汽的流动规律，土水特征曲线和水力传导系数假定仅仅相关于非饱和土吸力，水的潜热系数是温度的线性函数，温度传导系数采用De Vries建议方程加以计算。

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。