级数解

Smarandache function ; Asymptotic formula ; Equation ; Positive integer solutions ; Infinity series

Smarandache函数；渐近公式；方程；正整数解；无穷级数

A periodic oscillation analytic solution for the system at bifurcation point was obtained by using the method of series.

利用级数法求出了系统在分歧点处的时间周期振荡解的解析表达式。

By transforming the interlace series type linear differential equation with coefficient containing binomial coefficients and arrangement number into the linear differential equation of successive integral,the theory and method for solving this kind of equation are determined.

通过把系数含有二项式系数与排列数的交错级数型线性微分方程化为可逐次积分的线性微分方程，找出了求这类方程通解的方法与理论，把所得定理给出了严格的证明，并通过实例介绍了它的应用。

In 2D eddy current field 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, and solves several real engineering examples of 2D eddy current field boundary-value problems by the MT.

本文从电磁理论和有关数学定理出发，通过引入内极、外极、内交角的概念，建立一种新的电磁场计算体系——电磁场分析中的多极理论；从理论上证明，在电磁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。

The decomposition method provides the solution in a rapidly convergent series with components that are elegantly computed.

分解方法的特点在于所得到的解为级数形式，不仅具有很好的收敛性而且容易计算。

The MHD equilibrium solutions of a toroidal plasma with non-circular cross-section and linear current distribution are written in terms of a fast convergent series.

用一个收敛很快的级数构造了非圆截面、线性电流分布环形等离子体的磁流体平衡解。

Based on wave function expansion method, the potential functions of scattered waves are expanded into Fourier-Bessel series; and a set of cylindrical coordinate systems is utilized in such a way that it allows to solve the problem of multiple scattering; the solution is determined by imposing continuity and equilibrium conditions at the soil-pile interfaces.

采用波函数展开法，将散射波的势函数展开成Fourier-Bessel级数的形式，利用一组可以求解多散射问题的圆柱坐标系统和桩土界面处位移连续的条件，以及刚性桩的动力平衡条件，得到问题的理论解。

The paper presents a linear transient solution for the solitary wave generated by a piston-type paddle in a finite flume based on the boundary condition derived by Dean and Dalrymple (1991). The wavemaker problem is simplified by decomposing the wave potential into two parts. One is the evanescent wave and the other is progressive wave. The possible solution for the evanescent wave is expressed in form of the Fourier series.

本文根据Dean与Dalrymple（1991）描述造波水槽内部之线性边界条件，将水槽内部之流速势分为振荡波与前进波以简化问题，再以Fourier级数展开，可将问题化为二非齐次常微分方程式，在给定造波初始条件的情况下即可解析有限长度造波水槽自静止开始造波一段时间后停止之线性暂态解。

The vehicle loads are considered as rectangular harmonic moving loads,and the analytical solution of the pavement and layered ground interaction is deduced with Lame decomposition theorem of displacement field and Fourier transform method.

首先，考虑车辆荷载的多轮性质，利用三角级数、Fourier变换及叠加原理等方法推导获得了粘弹性地基上连续配筋混凝土路面在多轮荷载作用下的稳态响应解；另外考虑基底剪切阻尼作用，详细分析了荷载参数、路面参数和地基参数对路面动力响应的影响。

A new approach based on operator decomposition method has been developed to solve nonlinear Helmholtz equation.The approach is applied to compute the magnetic field and eddy current in nonlinear ferromagnetic materials and it provides an analytical solution.

根据算子分裂法的基本思想提出了一种有效的求解非线性亥姆霍兹方程的逼近解析法，对非线性铁磁材料中的磁场和涡流进行了求解，获得了级数形式的解析解。

However, as the name（read－only memory）implies, CD disks cannot be written onorchanged in any way.

然而，正如其名字所指出的那样，CD盘不能写，也不能用任何方式改变其内容。

Galvanizes steel pallet is mainly export which suits standard packing of European Union, the North America. galvanizes steel pallet is suitable to heavy rack. Pallet surface can design plate type, corrugated and the gap form, satisfies the different requirements.

镀锌钢托盘多用于出口，替代木托盘，免薰蒸，符合欧盟、北美各国对出口货物包装材料的法令要求；喷涂钢托盘适用于重载上货架之用，托盘表面根据需要制作成平板状、波纹状及间隔形式，满足不同的使用要求。