离散问题

To date, most research on DTCNNs has restricted to the stability of a system[17-19,37,38].Few papers consider the existence and attractability of periodic so-lutions.

迄今为止，大多数文献局限于研究离散细胞神经网络模型的稳定性，很少考虑离散时间细胞神经网络周期解的存在性及吸引性问题。

The many exact solutions, such as, trigonometric function, solitary pattern solutions, solitary wave solutions, Jacobi and Weierstrass elliptic function solutions are given by the auxiliary equation method.

近来，随着计算机技术的发展，关于孤立波的研究越来越多的依赖于计算机软件的应用，随之产生了一系列求解非线性波动方程的新方法，并且这些方法逐渐的被应用到离散的非线性微分—差分系统中来研究离散系统的孤立波问题。

It is true that the discrete version of Korn's second inequality does not hold in the standard Crouziex-Raviart 1 element space. In [24] , the strain tensor was modified, at the same time, the bilinear form changed, as a result the modified discrete version of Korn's second inequality holding in the standard Crouziex-Raviart 1 element space.

我们知道，在标准的Crouziex-Raviart 1元空间中第二Korn不等式的离散形式是不成立，Falk在[24]中修改了应变张量，相应的弹性问题的双线性型也被修改，这样，修改后的第二Korn不等式的离散形式在标准的Crouziex-Raviart 1元空间中成立。

In point of the physical characters,it is better to differentiate the time derivative in the characteristic direction than intime direction.

1.4中针对流体的流动以对流为主的物理特性，采用特征线法去对时间导数项离散，使截断因子比通常的时间方向离散小得多，更好地反映了问题的物理特性。

Spectral element methods for partial differencial equation is introduced in this study from viewpoint of the collocation approximation of Chebyshev polynomial. Wave Equation and its space discretization are deduced. Two time integral methods, central difference method and implicit Newmark method, are introduced, and their stability and applicability are also discussed in some details. The significance of absorbing boundary conditions in spectral element methods for Aeroacoustics is explained, and Clayton-Engquist-Majda absorbing boundary conditions is emphasized and introduced, then the discrete scheme of this boundary conditions is deduced and applied to spectral element methods for wave equation.

本文从Chebyshev多项式逼近理论出发，详细介绍了谱元方法求解偏微分方程的过程；推导了流体中的声波动方程并在空间上对其进行了谱元离散；详细讨论了两种时间积分方法──中心差分法和Newmark方法，分析了它们的稳定性条件，并从理论上对比了两种方法的优缺点和适用范围；将吸收边界条件推广应用于谱元方法求解气动声学问题中，重点介绍了Clayton-Engquist-Majda吸收边界条件的原理和公式，推导了该吸收边界条件的变分形式，并将其引入波动方程的离散形式中。

The examples indicate that the algorithm has strong pertinence and high efficiency, hi the discrete variable optimization, the problem is solved in the relative quotient method On the base of analyzing the relative quotient method, the conjugate gradient direction is used to modify the old search directions, the iterative matrix of the algorithm, and the method to resolve the discrete variable optimization, the relative conjugate difference quotient algorithm is presented.

离散变量优化算法是从相对差商法开始的，在详细分析相对差上法的基础上，用共轭梯度方向修正原有的搜索方向，并对算法的迭代矩阵进行相关的修改，最终形成一种用于求解离散变量优化问题的RCDQ法。

The controller makes the closed-loop systems internally stable and minimizes the H2 norm of the transfer matrix Tzw from w to z. Two Riccati formulae based on 8 operator is deduced. The H2 problems for continuous time systems, Z operator models and 8 operator models are investigated respectively.The guaranteed cost control problem of robust stabilization and robust performance for uncertain systems which is described by 8 operator is discussed in this paper.

采用Riccati方程处理方法讨论了基于Delta算子描述下的离散系统存在输出反馈控制器的问题，得到了两个基于Delta算子的Riccati方程，设计了Delta域的输出反馈控制器，使得闭环系统内稳定，且满足从w到z的传递矩阵T_的H_2范数最小，设计了基于Delta算子描述下的离散系统的最优控制器，并与S域和Z域的H_2控制器进行了比较。

The discrete element method and the finite element method have their own advantages and weaknesses. Basically, the DEM was developed for predicting the failure problems accompanying with the transition from continuum to non-continuum media. However, it is not accurate to calculate the problem of continuum media. The FEM may forecast the failure area of the material reasonably, while it is hard to calculate the failure process in brittle media. Therefore it becomes a good choice to combine the two methods to construct a hybrid model.

离散元法和有限元法等数值计算方法各有其优势，同时也都存在不足之处：离散元法适于处理由连续介质向非连续介质转化的破坏问题，但对于连续体计算结果精度不高；有限元法适于预测材料破坏的区域，但难以直接用于计算脆性材料破坏过程，因此将两种方法结合可以形成一种较好的混合模型。

Since the decimation of discrete time signals is similar to the sampling of continuous signals, it is also studied in the thesis.

鉴于对离散信号的抽取和对连续信号的采样非常相似，本文还把研究范围拓展到了对离散信号的抽取问题。

And then the spatial predicates,possibly used in SDMKD from GIS,are analyzed and listed.Subsequently,the formal expression of spatial assoc...

从G IS数据库中挖掘空间关联规则的主要问题是多层、多关系的规则挖掘问题，不同专题图层不同空间对象之间空间谓词的高效计算与存储表达是解决问题的关键；把空间关系非空间化，将连续数据离散化，从而把求解问题转换成布尔型关联规则问题进行讨论，基于此而探讨了一种通过SJI-P表组织空间谓词，然后根据目标对象的概念层级自顶向下、逐层细化的空间关联规则挖掘方法。

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。