级数解

Expanding the unknown function in a small perturbation parameter and using a successive expansion in a Taylor series for the water particle path and the period of a particle motion, the third order asymptotic expressions for the Lagrangian particle trajectories and the period of particle motion can be derived directly in Lagrangian form.

藉由一系列连续的Taylor级数展开，於考量波动场中各流体质点之运动轨迹与运动周期下，将已知的Eulerian解转换成完全未知的Lagrangian形式解。

It is shown that the leading term of interior asymptotic solutions is exactly the solution of Kirchhoff plate theory.

结果表明，内域解渐近级数的首项正是熟知的Kirchhoff板理论解。

In 3D scalar Helmholtz equation computation, for the first time, this dissertation proves that there is an analytical solution of infinite series convegence for the problems satisfying the MT expansion condition, derives the MT general solution formula and the using laws, proves or explains the using rules that are used in the GMT and but they can't be proven or explained by The GMT.

首次从理论上证明，在三维静电场分析中，存在一种无穷级数收敛，且有一定普遍性的解析解；推导出三维静电场分析的多极理论通解及其使用规则，证明或解释广义多极技术不能证明或解释的若干使用规则，用多极理论求解工程实际中的三维静电场边值问题。

As a result, it shows thatthe static or dynamic subsystem optimum alone is not equal to the system optimum. Three initial value problems met in the optimal design of flying vehicle are studied andconclusions are derived that: orthogonal test method can be adopted to decide the initial valueof static optimization problem, some mathematical techniques can be used to deal with thecostate variables of Maximum Principle and decide the initial value of the costate variable,the indirect method can be used to get the analytical solution under ideal case to guide thechoice of the initial control curve in the direct method. With some numerical examples oftrajectory optimization, it shows that all these methods are useful not only in accelerating theconvergence but also in converging to the global optimum.

针对飞行器优化设计中的三种初始值问题进行了研究，以远程弹道导弹弹道的工程优化为例说明，对于静态优化问题，采用正交试验法选取初始值，不仅可以大大加快收敛的速度，而且更有可能收敛到全局最优解；以气动力辅助变轨问题为例说明，用共态变量的一阶泰勒级数展开可以解决极大值原理中共态变量初值难于确定的问题；以二级弹道导弹的主动段弹道优化为例说明，利用间接法在理想情况下得到的解析解来指导直接法初始控制曲线的选择，将大大有利于提高直接法的收敛速度。

Since the multiple scattering should be considered, the scattering problem of many-cylinders is more complicated than single cylinder. By using scattering matrix method to solve the scattering problem of many-cylinders, first we have to express the incident fieldand scattered field by special function（for example, Bessel function and Hankel function）under cylindrical coordinate, then use the addition theorem of special function to get a linear system of equations to relate the incident field coefficients and scattered field coefficients. The incident and scattered field coefficients for every cylinder can be solved from the linear equations by matching electromagnetic boundary condition pointwisely.

单颗圆柱散射体的散射场解析解很早就被解出，而多个圆柱阵列的散射场问题因为涉及到入射光在圆柱与圆柱间的多重散射，故散射行为较单颗圆柱的散射复杂，因此圆柱阵列的多重散射问题需要利用加法定理来处理；散射矩阵法的主要精神即是先用圆柱座标下的特殊函数对平面波和圆柱散射体的内外域电磁场做无穷级数展开，再藉由特殊函数的加法定理将所有圆柱散射体的展开中心移到同一个展开中心，最后可以得到一组连结整个散射系统的入射电磁场系数及散射电磁场系数的线性方程组，将该组线性方程配合电磁场在散射体边界的连续条件，便可分别求出圆柱阵列中各个圆柱体的内部电磁场与外部散射场，再利用线性叠加原理即可求得整个圆柱系统的全域电磁场分布。

We also use the Schr〓der transformation, Abel transformation, power series and Dirichlet series theory to discuss the existence and uniquness of analytic solutions for an extensive class of nonlinear iterative equations.

进而还利用Schr〓der变换、Abel变换以及幂级数与Dirichlet级数理论研究一类具有相当广泛性的非线性迭代函数方程解析解的存在性和唯一性问题。

In order to solve the problem of chart projection transformation among all projections in shiphandling simulator,using the theory of power series spreading out and the method of trigonometric power series calculating back, a direct and reverse solving algorithm models of meridian arc length , and Gauss projection and Mercator projection transforming algorithm are introduced in this paper.

为了解决船舶操纵模拟器中不同投影方式海图的投影变换问题，应用幂级数展开理论和三角级数回求方法，给出了子午线弧长、等量纬度的直接正反解算法模型及高斯投影与墨卡托投影的相互转化算法。这些算法具有非常高的计算精度，避免了迭代运算，在船舶操纵模拟器中得到广泛应

Based on the linear elastic theory, the piezoelectric theory and magnetostrictive theory, using the power series expansion series method, a three-dimensional resolution of the natural frequencies of a simply supported rectangular laminate is investigated.

基于线弹性理论、压电理论和磁致伸缩理论，使用幂级数和傅立叶级数解法，得到了四边可移简支、磁电复合材料层合板的固有频率的三维精确解。

A practicable analytic solusion is obtained for any sector by means of Fourier series with singular items.

从位移场带奇性分离的Fourier级数表达式着手，得到扇形问题可实际操作的解析解，可以证明此级数解法与Wiliams分离变量法等价。

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。

I'm strongly against the death penalty — it's an eye for an eye.

我不赞成死刑——这是以牙还牙的报复行为。

And to get you the support you need, we're enlisting all elements of our national power: our diplomacy and development, our economic might and our moral suasion, so that you and the rest of our military do not bear the burden of our security alone.

并给你们所须的支援，我们正徵召国家所有各种的力量：我们的外交及发展，我们的经济力量与道德劝说，所以你们与其他军人不须要孤独地负起国家安全的责任。