调和的

FENG Kang, YU De-hao and some other scholars of our country are the first ones to create the natural boundary element method, and they have successfully studied the natural boundary reduction method for the boundary value problems of harmonic equation and biharmonic equation.

我国学者冯康、余德浩等首创自然边界元法，并已成功地研究了调和方程及双调和方程边值问题的自然边界归化方法。

The other is the difference of the original wind and the harmonic part, which is the solution of Poisson equation with homogeneous boundary condition and can be expanded into double Fourierism cosine series.

第一部分是Laplace方程在给定边界条件下的解，由于Laplace方程的解是调和函数，这个部分可称为调和部分，又因为其与区域内部值无关，也称外部部分。

It is the first time to have the theorem of orthogonal decomposition, a theoretical kernel in inverse gravimetric problem, realized in practice.

文章针对物理大地测量学反问题研究中的拟调和性重力场源及重调和性重力场源，将该研究中的理论核心——正交分解定理予以具体实现。

In this paper, we extend the A-harmonic e equation from the constant differential form which values in zero to any differential form, that is p-harmonic type equation.

在本文中，我们主要是把A-调和方程从取特殊值0的常微分形式推广到任意给定的微分形式，即p-调和类型方程。

As known, using the porential theory Green's tormulae and the fundamental solutions wecan reduce the harmonic and biharmonic elliptic boundary value problems to integral equationson the boundary.

我们熟知，利用位势理论或由Green公式及基本解出发区域内调和及重调和边值问题可归化为边界上的积分方程。

We research the spherical harmonics express of Lambert re- flection and propose a pure image based rendering method to synthesis image under arbitrary illumination condition based on spherical harmonics.

研究了朗伯反射的球调和表示，提出了一种基于球调和函数的任意光照目标图像生成方法。

The main results are:(1) the L1 boundedness of the Cesaro means operator of the harmonic expansions on the unit sphere with reflection-invariant measures is proved, and the characterization of the convergence index is given; for the points not in the planes with singularities, the pointwise convergence is also proved; these results are the generalizations of those both for the classical spherical harmonic expansions and for the Jacobi expansions;(2) Using the differential-reflection operators of Dunkl type, the uncertainty principle of a class of Sturm-Liouville operators is established, and as consequences, the uncertainty principles of some well-known classical orthogonal expansions such as Jacobi, Hermite and Laguerre expansions are obtained;(3) by introducing the Cauchy-Riemann equations in terms of the differential-reflection operators of two variables, the harmonic analysis of the extended Jacobi expansions is studied; the results include the Lp boundedness and the weak-L1 boundedness of the conjugate extended Jacobi expansions; specially, for some indexes p smaller than 1, the basic theory of the related Hardy spaces is established.

主要成果有：（1）证明了带有反射不变测度的球面调和展开蔡沙罗平均算子的L1有界性，给出了收敛指标的特征刻划，对不在奇性平面上的点，还证明了点态收敛性，这些成果同时推广了经典球面调和展开和雅可比展开的结果；（2）利用Dunkl型的微分-反射算子建立了一类斯特姆-刘威尔算子的测不准原理，并由此得到一些著名的经典正交展开如雅克比展开、赫米特展开和拉盖尔展开的测不准原理；（3）利用由两个变量的微分-反射算子定义的柯西-黎曼方程组来研究扩展雅克比展开的调和分析，证明了共轭扩展雅克比展开的Lp有界性和弱L1有界性，特别是对小于1的一些指标p，建立了相应的哈代空间的基本理论。

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。

We first show that the multiple harmonic Ritz values have only one harmonic Ritz vector associated with them in algebra.

用代数方法证明对每个重调和Ritz值，只有一个线性无关的调和Ritz向量与之对应。

In a word,the value of reconciliation should be admitted and put to a proper use.

长期以来，调和是被纳入反对之列的，其原因就在于把它视为调和主义。

Chrysanthemum of 10 thousand birthday is lax to edaphic requirement, with the arenaceous qualitative loam with fecund, good drainage had better.

万寿菊对土壤要求不严，以肥沃。排水良好的砂质壤土为好。

He unstepped the mast and furled the sail and tied it.

他拔下桅杆，把帆卷起，系住。