| 1. | Some notes about harmonic functions on riemannian manifolds
流形上调和函数的一些注记 |
| 2. | Positive harmonic functions on a class of complete riemannian manifolds
流形的正调和函数 |
| 3. | An extension form of liouville ' s theorem about analytic functions for general harmonic functions is proved
摘要证明复变函数中的刘维尔定理在调和函数中的一种推广。 |
| 4. | The north border of the basement , extended from west to east along the north latitude 38 , this latitude structure zone is part of the zone in the middle of ordos basin along the north latitude 38 , this is caused by the rate of earth rotation , according with the condition of global harmonic function
压陷北界沿北纬38带东西向展布，该纬向构造是沿鄂尔多斯盆地中部38带分布的纬向构造带的一部分，是由地球自转速率变化引起，符合全球协和函数的条件。 |
| 5. | In chapter 3 , we will estimate the first eigenvalue of laplacian from below on manifolds with a little negative curvature . in chapter 4 , we will prove the existence of bounded nontrivial harmonic functions on some classes of complete manifolds which will generalize the results of s . y . cheng ' s
在第三章，我们将给出具有小负曲率的流形上laplace算子的第一特征值的下界估计；第四章，我们会给出一类完备非紧流形上非平凡的有界调和函数的存在性，推广了s . y . cheng的结果。 |
| 6. | Through the analysis of the deduction process of harmonic function model , it is illustrated that some hypotheses in the deduction process are unreasonable and the harmonic function can not reflect the objective regularity of the vertical crust movement , so that it isnt an effective method to compile isoline map of the vertical crust movement rate
对有关文献提出的“地壳垂直运动调和分析”模型的建立过程作了全面分析，指出：该模型建立过程中所做的一些处理是不合理的，由此建立的模型不是地壳垂直运动规律的客观反映，因而尚不足以成为编制地壳垂直运动速率面等值线图的可靠手段。 |
| 7. | Firstly , in spherical coordinate system , the sovp formulation for the time - harmonic electromagnetic fields of the current dipole in conductive infinite - space is derived , using reciprocity theorem and transforming relations between special functions . then , selecting appropriate coordinate system , using superposition principle , the boundary - value problem of modified magnetic vector potential on the problem of a time - harmonic current dipole in spherical conductor is solved and analytical solution is obtained . finally , by means of the addition formulas of legendre polynomial and spherical harmonics function of degree n and order 1 , the analytical solution in spherical coordinate system specially located is transformed into that in spherical coordinate system arbitrarily located
首先利用特殊函数间的转化关系和互易定理推导得到了无限大导体空间中球坐标下时谐电流元电磁场的二阶矢量位形式：然后利用叠加原理，选择合适坐标系，求解了导体球中时谐电流元的修正磁矢量位边值问题，得到了问题的解析解；最后依据不同坐标系下电磁场解的转化原理，借助勒让德多项式和n次1阶球谐函数的加法公式，将坐标系特殊安放时的电磁场解析解变换到坐标系一般安放时的解析解，给出了球内电场和球外磁场的并矢格林函数。 |
| 8. | The addition formula of spherical harmonics function of degree n and order 1 is derived using the relations between coordinate varieties after coordinate rotating and the property of the associated legendre polynomial . the relations among the magnetic vector potential , the modified magnetic vector potential and the second - order vector potential ( sovp ) are shown going forward one by one . it is explained that the solutions of electromagnetic fields in different coordinate systems can be transformed and an example having analytical solution is given
利用坐标旋转后球坐标变量间的关系和连带勒让德多项式的性质推导得到了n次1阶球谐函数的加法公式；以递进的方式说明磁矢量位、修正磁矢量位与二阶矢量位的关系，写出了引入二阶矢量位的过程；以时谐场矢量边值问题为例，阐明了不同坐标系下电磁场解的相互转化原理，给出了一个解析解的转化例子；在球坐标下，引入了较球矢量波函数更普遍的两类矢量函数，给出了其在球面上的正交关系。 |
| 9. | The article stated here will give some remarks to the following equation in two cases : for the case > 0 , the equation expresses the eigenvalue of the laplacian while for the case = 0 , it is the existence of nontriv - ial bounded harmonic functions on complete noncompact manifolds
本文中我们主要分两种情况来讨论了关于laplace算子的方程： u + u = 0 ， r ~ + { 0 }对应于0 ，是riemann流形上laplace算子的特征值问题，而对应于= 0则是完备非紧流形上非平凡的有界调和函数的存在性问题。 |
| 10. | After introducing the conventional edge detection operator and multiscale wavelet edge detection operator , we discussed the well quality of b - spline function > n - class derivative of gauss function n harmonic function and hermite function in wavelet theory and their concrete application in the image edge detection
在对单尺度下的传统边缘检测算子和多尺度小波边缘检测算子介绍的基础上，讨论了b样条、 gauss函数的n阶导数、谐波函数以及hermite函数在小波理论中所具有的良好性质，以及它们在图像边缘检测中的具体应用。 |
