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并指出高阶电多极子电象的求解方法。Furthermore this, papet points the solution method of the image of higher multipole.

推导出了用多极场空间谐波函数表示的磁矢位的通项表达式。General expressions of the magnetic vector potential for multipole fields are derived.

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研究了多极透镜与旋转对称透镜组合系统的基本性质。The elementary properties of the system combining a multipole len with a round len are studied.

我们开发了一套利用多极组合测井分析岩石力学特征的软件。We have developed a software package for rock mechanical analysis with multipole array sonic logs.

几年来，多极组合声波测井仪已广泛应用于中国各油田。Multipole array sonic logging tools have widely been employed in Chinese oilfields in recent years.

第三章，超短激光脉冲在光子晶体光纤中传输的理论研究。The dispersion and losses properties of photonic crystal fibers are investigated using the multipole method in chapter two.

通过分析实例，揭示了多极透镜加非对称电压后的某些新特性。Some novel features of multipole lens are shown through several examples, in which unsymmetric voltages are applied to the lens.

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分层快速多极算法被用来加速用迭代法求解线性方程组时的矩阵向量乘积的运算。Multilevel fast multipole method is used to fast calculate the matrix-vector product when we solve the linear system by iterative method.

计算了几个静电电子透镜的例子，给出了不同电极缺陷的电位分布和微扰多极场分布。The potential distribution and the perturbation multipole field of the different electrode defects in some electrostatic lenses were given.

多层快速非均匀平面波算法的计算复杂度等同于多层快速多极子方法，因此可用于电大尺寸问题的求解。The computational complexity of MLFIPWA is the same as the multilevel fast multipole algorithm, so it can be used to solve large-scale problems.

用多极方法数值研究构成六重对称全内反射型光子晶体光纤各种结构参数对基模零色散点的调节。Zero dispersion point adjusted by structural parameters of TIR-PCF with sixfold rotation symmetry is studied numerically with a multipole method.

使用平均原子模型研究了电四极及更高阶跃迁对高温稠密金等离子体辐射不透明度的贡献。The contributions of the multipole transitions to the opacity of hot and dense plasmas of gold are taken into account by using an average-atom model.

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为精确模拟该结构的应力状况，该文提出一种三维高阶快速多极边界元法。The stress fields of such structure around the opening were predicted using a three-dimensional, higher-order fast multipole boundary element method.

应用静磁场理论分析了高分辨磁旋转编码器磁鼓的表露磁场，通过数值计算得到磁鼓表露场分布的直观曲线。Based on the theory of static magnetic field, the surface magnetic field on the high-resolution multipole magnetic drum for a magnetic rotary encoder was analyzed.

研究结果表明，高阶快速多极边界元法易于分析此类大规模问题，并具有很高的数值计算精度，满足工程设计的要求。The results show that the higher-order, fast multipole boundary element method can be applied to large problems with high numerical accuracy for engineering designs.

基于曲面RWG基函数结合多层快速多极子方法计算电大尺寸目标的电磁散射。The present paper applies fast multipole method and multilevel fast multipole algorithm based on the curve RWG moment of method to solve scattering from complex target.

快速多极算法作为边界元法的求解算法，从而使边界元法能够对含有大量随机分布颗粒的复合材料进行大规模模拟。Fast multipole method is used as a fast solver for BEM, making BEM applicable for large scale simulation of composites with a large number of randomly distributed particles.

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本文证明任意阶次磁多极子场力线方程总可以用有限形式解析地表示，并对偶极族和四极族磁多极子场力线的位形给予注记。In this paper it is pointed out that the equation of field lines of a magnetic multipole with any order and degree can always be analytically expressed in term of finite form.

中性粒子的静磁囚禁依赖于非均匀电磁场与粒子的磁多极矩之间的相互作用，能提供这种非均匀场的电流结构被称为静磁阱。The magnetostatic trapping of neutral particles is based on the interaction between the magnetic multipole moments of the particles and the non-uniform electromagnetic fields.

这些多极子又产生电磁振荡，向各个方向发射电磁波，形成粒子的散射过程，即电磁辐射。Then this multipole electromagnetic oscillations occur again, electromagnetic wave was shot off in all directions, form particle scattering process-----Electromagnetic radiation.