离散问题

The experimental results, show that the RBF neural network is suitable for solving the problem of scattered data interpolation on a surface, and is more efficient than traditional methods. Furthermore, it can be easily generalized to solve the scattered data interpolation problem in higher dimensions.

从应用结果来看，RBF网络适合于解决曲面离散点集的光滑插值问题，比传统的样条方法更有效、更方便，具有较好的使用价值，并且可以很容易地推广到求解高维散乱数据插值问题之中。

According to the special structure of the coefficient matrix arising from the SUPG discretization of convection-diffusion problem, or the MAC discretization of the Oseen problem, we use Kronecker product approximation to design the preconditioner.

第一章讨论预条件技术，针对对流扩散问题和 Oseen 问题离散后系数矩阵所具有的特殊结构，用近似 Kronecker 积构造预条件子。

Based on the elliptic curve cryptosystem, a multi-key sharing scheme in which the Lagrange interpolation polynomial is used and the cheaters can be detected is presented.

文章利用拉格朗日插值的思想，提出了一种基于椭圆曲线的可防欺诈的动态多密钥共享方案；方案中每个参与者的子密钥可以不受限制的重复使用，因此在更新主密钥的时候，无需更改参与者的子密钥，从而减少了可信中心与参与者之间的通信量；方案可灵活地增删参与者，且安全性是基于椭圆曲线离散对数问题的难解性，因而其安全性比在有限域上更高；方案实现过程中解决了检验子密钥真伪的问题。

Especially,occurrence of Lie group method s associated with wants of the dynamics,it can be used to discretion of the equations in spaces of curvature,and it cann t have the drift off the manifold of solution.

特别是所谓的的李群方法是在动力学问题的需求下诞生的，它能在弯曲的空间中进行离散化，根本不会出现'违约问题'。

The basic idea was to discrete the structure and find the load function according to the energy criterion of buckling and the principle of random displacement method. As the critical load is the minimum of the load function, a problem of frame buckling can be transformed into an optimization problem. Therefore, the critical load can be found through solving the optimization problem.

先将结构离散为一个有限自由度系统；然后根据有限自由度系统平衡稳定性的能量准则和随机位移法的基本原理，建立符合能量准则的载荷函数，该函数不为零的最小值即为临界载荷，由此将稳定问题转化为无约束的多维优化问题；最后应用遗传算法求出相应于最优解的目标函数值。

The unbalance forces due to the lumped eccentric mass are treated as general forces. Meanwhile, the potential energy expression about gravity based on finite element method is presented for convenience. Based on the variational inequalities principle, the finite element is used to determine the film forces produced by fluid film bearing and damper at any moment and its Jacobian matrix with respect to location and velocity of journal and bearing house.

在第二部分中，主要应用有限元方法及Hamilton原理对所研究系统进行了建模分析，着重对质量偏心问题进行了分析处理，并对此提出了两种处理方法：一、转化为对系统动能的影响；二、将其产生的离心惯性力视为非保守的广义力，并对其表达式进行了推导，同时为分析问题方便，基于有限元离散化方法，推导了重力的势能表达式。

The quadratic optimal control problem of delay discrete-time linear system is proposed with quadratic performance index. It is transformed intoanother problem by using the Principle of Optimality. The direct expressions of theoptimal control sequence and performance index sequence are given by mathematicalinduction.

针对给定的二次型性能指标，提出了时滞离散系统线性二次最优控制问题，并利用最优性原理将该问题进行了转化，进而利用数学归纳法推出最优有记忆饱和控制序列及最优性能指标序列的直观表达式。

In recent years, Feng Kang has advanced a more natural and direct redu-ction, i. e. the reduction via Green's formula and Green's function.

近年来冯康又提出一种更自然而直接的归化，即从Green公式及Green函数出发将微分方程边值问题化为边界上的含有广义函数意义下发散积分有限部分的奇异积分方程，这种归化在各种边界归化中占有特殊地位，被称为正则边界归化，本文将这一理论应用于重调和椭圆边值问题，研究了其正则归化的性质，并通过利用Green函数、Fourier分析及复变函数论方法等不同途径求出了在上半平面、单位圆内部、单位圆外部三种区域的Poisson积分公式及正则积分方程，其离散化可用于实际计算。

While from fault detection aspect this method can detect abrupt and incipient faults effectively and is more robust than the methods where the thresholds are determined by statistical properties of residual errors.

第二类问题为在状态空间模型下带有未知但有界噪声的非线性离散时间系统传感器故障的检测与隔离问题。

It is shown that some problems of this new class, together with a suitable time discretization ,represent the schematization of the original problem corresponding to well known numerical integration schemes.

它被显示这个新的班级一些问题，连同一个适当的时间离散化一起，表现对广为人知数字的整合方案符合的最初问题的 schematization 。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。