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However, the second associated Legendre function is too complicated to compute, so a simple and practical ellipsoidal harmonic series expansion is introduced, and the series solution and integral solution of the Dirichlet boundary value problem and the Neumann boundary value problem under ellipsoidal boundary are given.

鉴于展开式中第二类缔合勒让德函数的计算较为复杂，接着引入一种形式简单、实用的椭球谐级数展开，介绍了椭球界面下Dirichlet边值问题和Neumann边值问题的级数解和积分解。

Pre-stressed composite space truss is one of the new kind of space structure systems developed on the basis of prestress and space truss, which consists of steel and reinforced concrete. At present the study in this field is just being begun in our country. Therefore, in this paper static and dynamic performances of pre-stressed composite space truss associated with a practical engineering are studied, in addition, dynamic test on construction site and model experiment are done. Finally, we conclude this structure is well in stress and stiffness and dynamic characteristics.

预应力组合网架是一种基于网架和预应力技术发展起来的由钢和钢筋混凝土组合而成的新型预应力空间结构体系，目前国内在此领域的研究和应用都较少，为此，本文结合实际工程对预应力组合网架进行了静力和动力的分析研究，并作了施工现场的动力测试及模型试验，总结出预应力组合网架受力比较合理，刚度、动力特性好，是值得推广的一种空间结构形式。

During the previous analysis of asphalt pavement structure with cracks, the stress intensity factors were usually calculated approximatively using plane strain model for some limitation. However, the assumptive load of this model is not coincident to the practical load.

在以往分析含裂缝的沥青路面结构时，由于条件的限制，通常是假设沥青路面结构近似为一平面应变模型，但是这种模型所假设的荷载与实际作用的荷载有较大的区别。

Features of a practical asymmetric electrode system were studied.

设计了一种非对称电极，这种非对称电极的阳极是Chang电极或Ernst电极，阴极是由直线和圆弧构成的简单电极。

Hence we first propose a globally optimized random search algorithm and prove its asymptotic global convergence; then to improve its convergence velocity and reduce implementation complexity, we propose a practical sub-optimal random search algorithm and analyze its implementation complexity.

为此本文首先给出了一种用于OFDM符号估计的全局最优随机搜索方法，并证明了其渐进全局收敛特性；同时为了改进全局最优的随机搜索算法的收敛速度和实现复杂度，提出了一种可实现的次优的随机搜索算法，并结合实现分析了所提的次优随机算法的计算复杂度。

Chapter 9: We report a large quantity of numerical experiments of 13 different algebraic multigrid algorithms for solving the Poisson equation, anisotropic equation, equation with cross-derivative terms, general matrix problems with large off-diagonal positive entries, biharmonic equation, Toeplity matrix, elasticity systems, finite element discretization of the Laplacian and even 3D problems. Particular attention is focused on asymptotic convergence factors and CPU-time consumed. Numerical results for many different types of practical problems demonstrate the efficiency and robustness of the proposed algebraic multigrid methods.

第九章：在各种代数多重网格算法的基础上，进行了大量的数值试验，具体给出了十三种不同的代数多重网格方法求解泊松方程，各向异性方程，带混合导数项的方程，带有大的非对角正元素的一般矩阵问题，重调和方程，托普利兹矩阵，弹性力学方程组，拉普拉斯算子的有限元离散，甚至三维问题的较为丰富的数值结果，重点关注它们的渐近收敛因子和所需的CPU时间，来源于不同类型问题的计算结果既为代数多重网格理论分析和算法的改进提供了很实用的资料，同时也证实了本文给出的代数多重网格算法的效绩和稳健性。

To make our approach to be practical, we also discuss the asymptotic expansion of the operator in chapter 6 which is based on the non-abelian Stokes theorem.

但是由于格点上的算符是path-order变量的乘积，并且其构成非常复杂，按照正常的方式展开实际上是不可能的，为了使我们的算法实际可行，本文接着讨论了格点上算符的渐近展开问题，并且给出了基于non-abelStokes定理的方法，这种方法克服了以前各种办法的缺点，并且简单可行，适用于任意的Wilson算符。

The new method has advantage of asymptotic solution, numerical solution and BVT method. It is useful and efficient in practical application.

混合算法结合了渐近解、数值解和BVT法的优势，是一个实用、有效的算法。

In many practical applications, we have adopted a software standard RS232 asynchronous serial communication, the result proved very stable and reliable.

在很多实际应用中，我们已经采用了软件实现RS232标准的异步串行通信，结果证明工作非常稳定可靠。

The foundation of this system provides a good reference to promote the standardization and intelligence of the overhaul and maintenance of vacuum switches. This paper develops a special HF pulse power supply for internal pressure estimation, which achieves the output of HF-HV sinusoidal pulse wave whose frequency and amplitude can be modified respectively, and meets the design requirements according to the results of Simulink simulation and practical experiments. With the help of AT89S52, this paper designs an I~2C serial bus based signal detection system for peak value signal acquisition of HF pulse currents, which communicates with the upper computer by asynchronous serial communication for uploading the data. In the upper computer, a human computer interface is developed by Matlab software, whose functions are to do some computation and graphic display, such as calibrating the relation curve of vacuum degree and peak value of HF pulse currents, vacuum degree computation, and vacuum lifetime evaluation analysis basing on grey forecasting model as well as making relative suggestions.

本文研制了用于真空度检测的高频脉冲电源，通过Simulink仿真和试验检验其满足设计要求，实现了电压幅值和频率独立可调的正弦波高频高压脉冲输出；利用以AT89S52为核心基于I~2C串行总线的信号检测系统实现高频脉冲电流峰值信号的采集，通过异步串行通信实现单片机与计算机之间的数据通信，将检测数据传至上位机；在上位机利用Matlab开发人机交互界面，实现相关数据处理和图形显示，包括真空度——高频脉冲电流峰值关系曲线标定、真空度数值计算、基于灰色预测模型的真空寿命评估分析和提出相应决策建议。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。