格林函数

While calculating tensor Green's functions, the algorithm of secondary division is adopted to solve the singular problem. The Gaussian quadrature and continued fraction is adopted to calculate the integral with Bessel function. This method not only can ensure the right calculation of tensor Green's functions but also can get high precision.

求取张量格林函数积分时，采用二次剖分算法解决计算中奇异值问题，对于含有贝塞尔函数的积分项，利用结合连分式展开的高斯求积代替常规的快速汉克尔变换方法，确保了张量格林函数的正确计算并提高了计算精度。

The Green's tensor in frequency domain for cylindrical layered media was deduced from the 3-D Green dyadic for homogeneous media according to the propagation laws of waves in layered media,then the Green's tensor in spatial domain can be achieved with Fourier transformation ,which is a singular integral of wave-number.

根据分层介质中波的传播规律，由均匀介质中的三维张量格林函数得到频率域中柱状分层介质的张量格林函数表达式，经过傅立叶变换，可以得到空间域的格林函数，它是一个关于波数的奇异积分。

The Green's tensor in frequency domain for cylindrical layered media was deduced from the3-D Green dyadic for homogeneous media according to the propagation laws of waves in layered media,then the Green's tensor in spatial domain can be achieved with Fourier transformation,which is a singular integral of wave-number.

摘要根据分层介质中波的传播规律，由均匀介质中的三维张量格林函数得到频率域中柱状分层介质的张量格林函数表达式，经过傅立叶变换，可以得到空间域的格林函数，它是一个关于波数的奇异积分。

The research on the improvement for the convergent quality of"the Nodal Green's Function Method For Cylindrical Geometry on Neumann Boundary Condition Based on Green's Functions on slab geometry"is an original work.

在本论文中，"基于贝塞尔函数的第二类边界条件圆柱几何格林函数节块法"在中子扩散方程求解方法研究领域中是首创的，属创新成果；关于改善"基于平板几何格林函数的第二类边界条件圆柱几何格林函数节块法"的收敛性能的研究也属创新成果。

The Green's function in Cartesian geometry can be used to replace the complex Green's function in cylindrical geometry when solving the neutron diffusion equation in cylindrical geometry.

用格林函数节块法求解圆柱几何中子扩散方程时，可用平板几何格林函数代替复杂的圆柱几何格林函数。

In chapter two, the lattice Green's function is introduced, especially recursive Green's function method.

在第二章中，我们介绍了格点格林函数方法，特别是递归格林函数方法。

Derivations of Green's functions, Green's function for the Laplacian operator, Green's function for the diffusion operator, Green's function for the wave operator.

格林函数：格林函数推导，广义格林函数，拉普拉斯运算子的格林函数，扩散运算子的格林函数，波运算子的格林函数。

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。

In the path integral formalism, we represent the generating functional and Green functions of Φ〓 theory by taking account of that the partial and the functional derivatives commute. Also we discuss the effective action for noncommutative scalar fields, and show how the noncommutative phase factors appear in path integral formalism. We realize that the two approaches (path integral and canonical quantizations) are completely equivalent each other.

在用路径积分方法对非对易标量场进行研究时，我们利用偏微商和泛函微商的可交换性，给出了Φ〓场格林函数和格林函数生成泛函的具体表达形式，得出了非对易相因子在路径积分方法中的具体表现形式，并对连通格林函数和有效作用量等问题做了讨论。

For acquiring relations between the eigenfunctions of waveguides and tensor Green function, we first take the Fourier transform of Green function. In isotropic media the simplest image function can be expressed in dyadic form, and in anisotropic media in the form of ABA+-ikz0,where A is the coordinate matrix.

为了得到波导管的本征函数和格林张量函数的一些关系，我们首先对格林函数作富氏变换，它的象函数在各向同性介质波导中以并矢形式作为最简单的表达方法，而在充有各向异性介质波导中可以表为ABA~+e~的形式，这里A是坐标矩阵。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。