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It can be shown that the base function for the optimal analysis of PSV data is HSV eigen-function deduced from the proper or thogonal decomposition of the geomagnetic model data instead of the lower degree spherical harmonic function in common use.

统计学意义上最优的分析方法不是直接对PSV数据作低阶轴对称球谐分析，而是通过对地磁场模型数据的特征正交分析，得到表征HSV的特征函数，再用它们去分析PSV形式的数据。

In section 2.7, according to the complex expression of the horizontal gradient of spherical harmonic, the spherical orthogonal function family needed for the description of the earth's gravity potential up to 2 degree horizontal gradients is defined and proved directly.

在§2.7中，直接由体球谐函数水平梯度的复表示定义并证明了描述地球引力位直到二阶水平梯度所需的球面正交函数系。

This paper has investigated the expression on rotational motion of earth's surface and Earth's deformation fields with complex vector surface spherical harmonic function, theoretical definition of the crust-fixed reference frames and the terrestrial reference system, and theoretical substantiating to the consistency between them.

徐州师范大学国土信息与测绘工程系，徐州 221116；2。中国科学院测量与地球物理研究所，武汉 430077摘要：本文研究了内核地球模型下的地球表面的旋转运动和地球形变场的复数矢量球函数表示，以及外壳固定参考架、地球参考系的理论定义和它们之间等价性的理论证明。

In this paper, a new numerical method, the coupling method of spherical harmonic function spectral and streamline diffusion finite element method for unsteady Boltzmann equation in the neutron logging field is discussed, and the convegrence and error estimations of this scheme are proved.

针对中子测井问题，研究非定常Boltamann中子输运方程的确定型数值求解方法，给出了求解Boltzmann方程的球谐函数展开和流线扩散有限元耦合方法，证明了这种耦合方法的收敛性和误差估计·实际算例表明此方法是有效

Based on the current continuity equation, using spherical harmonic function expansion, where lower boundary condition is the surface atmospheric electric potential, upper boundary condition is the electric potential of the bottom of the ionosphere, and non-homogeneous current source function of the vertical dipole assumptions is used for the charging of thunderstorms, the state analytical solution of global atmospheric electricity model in lower atmosphere is gotten.

本文从电流连续方程出发，采用球谐函数展开法，边界条件采用下边界为地表大气电势，上边界为电离层底部电势，非齐次电流源函数项采用垂直偶极子假设。

Spherical harmonics is of importance for spherical signal analysis. This paper matches shape similarity among images by a spherical harmonic descriptor.

摘要球面调和分析是球面信号分析的重要工具，本文采用球面调和描述子对图像进行形状匹配。

In this paper, a sort of recursive formulas of spherical harmonics integrals, which often appear in the gravitational gradient harmonic analysis, are deduced according to the recursive formulas between every other order of spherical harmonics and the trigonometric functions＇properties. And the calculated formulas on the recursive initialization also are brought forward.

本文根据球谐函数的跨次递推公式和三角函数的性质，详细推导了在重力梯度调和分析中出现的一类球楷函数积分的跨次递推公式和递推初始值的计算公式。

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。

The numerical solutions of neutral atoms with attractive interaction in a harmonic trap and a spherically symmetric well potential of depth infinite are calculated.

根据最近的BEC的动力学模型和主方程，用母函数方法求得玻色凝聚体主方程的解，并计算了凝聚体形成的增率与起伏，增率曲线存在一平台，而平台的粒子数起伏则是超泊松分布的。

In the study of radial sphygmogram on the patients with ischemia heart disease, Our analysis of the harmonic C4 of left Cun showed significant difference between the two groups (p=0.0039). And the optimal contact pressure of left Cun was smaller than others (p=0.013). The result was approval for the TCM theory "Left cun correspond to heart".

在缺血性心脏病患者的脉波图研究中，以观察组与对照组相比，频域分析的结果显示在仅左寸脉波的C4有显著差异(p=0.0039)，两组最佳取脉压力的比较，也显示仅在左寸有显著差异(p=0.013)。

Now she was hungry and angry.She began to smoulder.

现在她又饿又气，她开始流露难以抑制的怒火。

You have placed our iniquities before You, Our secret sins in the light of Your presence.

诗90：8 你将我们的罪孽摆在你面前、将我们的隐恶摆在你面光之中。