问题求解

To solve the difficulties of digital integral that exist in global optimization of redundant manipulators, this paper discussed how to build up dynamic equation, the inner relation between constraints and unconstraint optimum control problems, then a digital method solving optimum control problems is deeply analyzed.

为了解决冗余度机器人全局法优化中数值求解的困难，本文讨论了动力学方程的建立、无约束和有约束最优控制问题之间的内在联系，重点分析了求解最优控制问题的数值方法。

The problem of solving linear equations changed equivalently into the problem of searching the minimum of unconstrained optimizations of function by variation principle in the paper.

首先通过变分原理将求解线性方程组的问题转化为等价的求解无约束函数最优化问题的极小值。

In the sense of Von Karman large displacement, the governing equation of nonlinear dynamic response of the clamped circular plates under impact of a mass is established by using the virtual displacement principle and Galerkin's method in this paper. The effect of coupling between the impact load and the displacement of. the circular plates is considered. The governing equation is solved by applying the time increment method and the singular perturbation theory, and the asymptotic solutions of nonlinear dyna...

本文在Von Kármán大位移的意义上，利用虚位移原理伽辽金方法建立了圆板在物体撞击下的非线性动力响应的控制微分方程，在研究响应问题时，考虑了冲击载荷与圆板位移响应之间的耦合影响，文中使用时间增量法和奇异摄动理论求解问题的控制方程，获得了固支圆板非线性动力响应的近似解，并且求解了具体算例，绘出了圆板位移、应力响应曲线以及冲击力随时间的变化曲线。

And by using the initial conditions as well as the end conditions, the dynamic problem is then transferred to a second kind Volterra integral equation about the function of the axial strain with respect to time which can also be solved successfully by the interpolation method. For piezoelectric and pyroelectric hollow cylinders, by following the solving procedure for elastic hollow cylinder and by using the electric boundary conditions, the dynamic problems are transferred to two Volterra integral equations about two functions of time, one is axial strain and the other is related to electric displacement, which can also be solved efficiently and quickly by employing interpolation method. The elastodynamic solutions of hollow spheres, which are made of elastic, piezoelectric and pyroelectric materials, respectively, for spherically symmetric problems are also obtained.

对于弹性空心圆柱，通过引入一特定函数将非齐次边界条件化为齐次边界条件，然后利用正交展开技术，导出关于时间函数的方程，再结合初始条件和端部边界条件，将原问题转化为关于一个时间函数的第二类Volterra积分方程，运用插值法可给出此积分方程的解；对于压电和热释电空心圆柱，利用求解弹性空心圆柱相似的方法，再结合电学边界条件，原问题转化为关于两个时间函数（轴向应变和与电位移有关的函数）的第二类Volterra积分方程组，同样可用插值法来构造相应的递推公式高效地求解此积分方程组。

The Ant Colony Optimization is a kind of bionic optimization based on swarm intelligence,which provides new methods for complex combinatory optimization.

蚁群算法是一种用于求解优化问题的新型模拟进化算法，该算法在许多相当困难的优化问题的求解中体现了极强的寻优能力和较好的性质。

Unfortunately, just the lack of design model to guide software design process of EC brings many issues in practices of EC. It is difficult to design reusable EC software based on the basic structure of EC. For example, the EC software aimed to solve function optimization can't be used to solve combinatory optimization without an overall modification.

由于缺少一个软件设计模型来指导演化算法的软件设计过程，仅从演化计算的基本结构出发设计出的软件很难用来求解不同种类的问题，比如针对函数优化而设计的演化算法不经大幅度的修改就不能够用来求解组合优化问题。

The one is Pagano method which has been proven effective to static problems, but it is very complicate for the three-dimension dynamic problems of finitely long piezoelectric laminated plates.

同时，指出Pagano方法求解动态问题所遇到的困难，为克服这些困难，提出了一种求解压电层合板动态问题三维精确解的幂级数展开方法。

Based on the Hertzian contact theory, the pressure distribution on balls of a pair of angular contact ball bearing under three dimensional loading conditions was analyzed.

本文首先介绍了Hertz接触理论的基本特点与求解过程，对于实际存在的有限长线接触问题进行了详细讨论并完成了对该问题基本积分方程的一维数值求解。。。

By using active set strategy, the authors need only to solve a reduced trust region subproblem which is solved inexactly by the truncated conjugate gradient method.

作者利用有效集策略，在每次迭代中只需求解一个低维的信赖域子问题，该信赖域子问题是通过截断共轭梯度法来近似求解的。

The ultimate goal of the algorithm is to transfer the equilibria of sequential games into the linear program,and it is very easy to solve the equilibria of games through using ready-made linear programming software such as LINDO/LINGO software.

该算法的目的是把序贯型博弈纳什均衡求解问题转化为线性规划问题，然后通过使用现成的线性规划软件（比如LINDO/LINGO软件）进行求解。

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。