查询词典 spherical function

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。

Besides, in the new spectral dynamical framework the calculation amount firstly is decreased to half by properly using the complex conjugate relation of spectral coefficients and the symmetric and anti-symmetric character of spherical function.

另外，新方案中的纬向谱系数计算式，合理利用谱系数的复共轭性质及球函数关于赤道对称或反对称特性，使计算量减半。

The solution of spherical function is given in the paper,and it is applied reasonably in the problem of eigenvalue of angular momentum square operator.

本文对球函数方程进行了求解，并将球函数方程的解合理地应用于角动量平方算符的本征值问题中。

In addition, the study on ionic liquid being used as the electrolyte of EDLC was carried out extraneously, a good result of 310F/g was obtained. That the possibility of spherical active carbon used as the electrode materials was also investigated for the convenient preparation of electrode, the specific capacitance of spherical active carbon was 188F/g, having directive function for the preparation from powder SAC to spherical active carbon.

另外，本项目也额外进行了离子液体作为电解液性能的研究，获得了比电容高达310F/g好结果；考虑到电极制作，又研究了活性炭微球作为电极的可能性，得到了比电容为188F/g的结果，为下一步将粉状的超级活性炭制作为球状的活性炭提供了指导与借鉴作用。

This project studies the scale-dependent deformation behavior of the metal matrix composite, the void nucleation and void growth mechanisms at the micron/submicron scale. The main results are:(1) In prophase, growth and coalescence of the void embedded in the graded matrix are analyzed in detailed;(2) Based on the infinite solid model containing a micro-void, coupling effects of the void shape and the void size on the void growth are studied carefully, the results show that it seems to exist a critical equivalent void radius, which is associated with the material length. When radius of a microvoid is close to or smaller than the critical void radius, the micro-void growth rate is essentially eliminated;(3) The coupling effects of the particle shape and size on the mesoscopic stress fields within the particle and matrix are also investigated by introducing the conception of inclusion/matrix interfacial energy. The results show that the stress concentration factors within the particle and on the matrix/particle interface are also strongly size-dependent,so the void nucleation mechanism is size-dependent.(4) By employing a specific orthogonal curve coordinate frame and a 'kernel function' conception, a 'unified method'solving the spheriodal and spherical void problems is suggested; by this unified method, size-dependent plastic potentials of the porous materials containing the spheriodal or spherical voids are obtained, which extend the traditional Gurson model for the spherical void and GLD model for the spheriodal voids to the micron scale.(5) Based on the RVE model containing the spheriodal or spherical particles, the influences of the particle shape and size on the size-dependent mechanical behavior of metal matrix composite are studied.

中文摘要：本项目对金属基复合材料在微细观尺度下的尺度相关变形行为、孔洞形核及长大的机理和模型进行了研究，取得了如下主要结果：1）在前期研究中，探讨了基体的梯度分布对孔洞长大和聚合的影响；2）基于含孔洞的无限大体模型，探讨了孔洞形状和孔洞尺寸对其长大的耦合作用，结果表明：可能存在一个与材料特征长度相关的临界孔洞尺寸，当椭球孔洞的等效半径小于临界孔洞半径时，孔洞的长大受到明显抑制；3）通过引入基体/夹杂界面能的概念，分析了夹杂尺寸、夹杂形状对材料细观应力场的耦合影响，结果表明：颗粒内部和界面上的应力集中因子强烈地依赖于夹杂的尺寸和形状，因此，孔洞的形核机理是尺寸相关的；4）采用一种特殊的正交曲线坐标系和引入"核函数"的概念，"统一"地得到了含椭球和球形孔洞的材料的尺寸相关塑性势，它将传统的Gurson球形孔洞模型和GLD椭球孔洞模型推广到微尺度范围；5）基于含椭球和球形夹杂的体胞模型，初步研究了夹杂形状、夹杂尺寸对金属基复合材料尺寸相关力学行为的影响。

Results show that salt content in farmlands meet to normal distribution and its spatial structure meet to a penta spherical function.

结果表明，该地区在微咸水灌溉条件下，土壤含盐量服从正态分布，其空间结构符合 5次球状函数；地下水含盐量服从对数正态分布，其空间结构符合 3次球状函数。

Meanwhile, salt content in groundwater meet log normal distribution and its spatial structure meet to a cubic spherical function....

利用 GSLIB软件，绘制了该县土壤含盐量和地下水含盐量等值线图，为该地区水土管理，防止土壤盐渍化提供了决策依据

The formula for computing the 3-dimensional axially symmetrical steady magnetic field for vectorpotential is derived by the spherical function expansion.

本文用球函数展开法推导出计算轴对称三维稳恒磁场矢势的公式，应用该公式既能计算电流分布区域外部的磁场，又能计算电流分布区域内部的磁场。

Using the properties of the harmonic function and the theories of the expansion of the spherical harmonics,the equivalence between Moritz analytical continuation and Bjerhammar s virtual spherical solution is proved according to the power series expanded form of the real number field function,the differences in meaning between the two solutions are analyzed.

利用调和函数的性质以及球谐函数展开理论，并根据实数域上函数的幂级数展开式证明了Moritz解析延拓解与Bjerhammar虚拟球面解的等价性，同时分析了两种解的内在区别。

Second, based on the spherical vector wave function in uniaxial anisotropic medium, and the first, second, third and fourth spherical Bessel functions satisfy the same differential equation and recursive formula. The scattering fields in terms of spherical vector wave function from a uniaxial anisotropic spherical shell and an anisotropic uniaxial-coated conducting sphere by a plane wave are derived. The electromagnetic fields in uniaxial anisotropic medium and free space can be expressed in terms of spherical vector wave functions in uniaxial anisotropic media and isotropic medium.

二、在建立均匀各向异性单轴介质球矢量波函数理论的基础上，利用二阶线性偏微分方程的性质和第一、第二、第三和第四类球Bessel函数满足相同的微分方程和递推关系，我们分别研究了单轴介质球壳和单轴介质涂覆导体球对平面波的电磁散射特性，首先给出了各个区域的电磁场用球矢量波函数来表示的解析表达式，进而利用电磁场在边界上满足电磁场切向连续的边界条件和球谐函数的正交性，得出了各向异性单轴介质球结构中电磁场用球矢量波函数表示的系数所满足的矩阵方程。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。