离散问题

The sufficient and necessary conditions of positive definitiveness of a covariance matrix from multivariate discrete data are obtained.

本论文通过引入p-向量配、I-线性组合及它们的性质，研究离散型样本协方差矩阵的正定性问题。

Detectability of Discrete Event Systems based on automata/languages is studied.

讨论基于自动机/形式语言模型的离散事件系统的可测性问题。

It is known theoretically that to the variational problem with weak constraints in cost functional J, its Euler equation can be discreted into difference format, by using matrix theory and difference method of partial differential equation we know that there exists optimal selection of weight factors in the cost functional under the condition of minimal variance between analysis field and ideal field.

从理论上可知，对于目标泛函J带有约束条件的变分问题，将其Euler方程离散成差分形式，利用矩阵理论和偏微分方程的差分方法，则目标泛函的权重因子，在分析场和理想场的最小方差意义下存在最优选取。

Using the directional derivative formula, the governing equation is discreted in the physical domain in which a nonorthogonal grid system is used. Two kinds of AF2 schemes, i. e. AF2-plane relaxation and full implicit AF2, for the TSD equation are proposed. Numerical results show that the full implicit AF2 scheme converges faster than AF2plane relaxation scheme. For the rectangular wing and swept wing, the results of the present method are compared with FP results, and the agreement is good.

采用适合于梯形机翼和后掠机翼的斜网格，利用方向导数公式直接在物理空间对主管方程进行离散；将近似因式分解方法应用于绕机翼的跨音速小扰动势流问题，提出AF2—面松弛和AF2全隐式两种迭代格式，并对它们的收敛速度进行比较，结果表明后者明显快于前者；直机翼和后掠机翼的算例表明，本文方法的结果与精确势流方法的结果吻合良好。

A scalable parallel algorithm of block tridiagonal systems for solving the initial boundary value problem of 3D-parabolic equation with the Dirichlet boundary condition is discussed.

对三维抛物型方程带Dirichlet边界条件初边值问题的离散系统使用块三对角可扩展并行算法求解。

A scalable parallel algorithm of block tridiagonal systems for solving the boundary value problem of 2D Poisson equation with the Dirichlet boundary condition is discussed.

对二维Poisson方程带Dirichlet边界条件边值问题的离散系统使用块三对角可扩展并行算法求解。

In spite of the granular nature, soil has traditionally been modeled as a continuum. This continuum mechanics cannot get the precise solution while soil\'s nonlinear, discontinuous, large deformation, and strain localization behavior are considered. The discrete element method is based on discontinuum theory, and is pioneered by Cundall.

土是由多相介质组成的离散颗粒集合体，尽管研究者早已在土的散粒状属性上达成共识，但关于土体力学性质的研究还经常沿用连续介质力学方法，这种基于连续体小变形假设的方法在求解实际土体非线性、非连续、大变形、应变局部化问题时往往无法得到精确解答。

The CSD algorithm is shown to be efficient design method for complex system in parallel, and can search out better design for mixed continuous/discrete system in very reasonable number of system analysis compared to traditional optimization method, and is able to deal with the issue of dynamic design requirements.

并行子空间设计算法不仅有效地实现了并行设计思想，而且与传统的优化算法相比，CSD算法降低飞机系统分析的次数，找到系统全局最优解的概率也较高。另外，它还能成功地解决含有离散/连续混合变量的设计优化问题，以及具有处理工程设计中设计要求动态变化的能力。

The method solves the low efficiency problem of contact detection algorithm in wide size distribution particle discrete element numerical calculation in some extent.

改进方法在很大程度上解决了大尺寸分布颗粒离散元中接触检测算法效率低下的问题。

By studying the relationships between the sub-problems of distribution system, a model of distribution network designing with inventory control in competitive environment is proposed, which based on discrete model of two-echelons distribution network.

深入分析了在竞争环境下分销网络中各子问题之间的关系，建立完全竞争环境下两级分销网络的设计模型，该模型是在两级分销网络离散模型的基础上，将市场竞争因素考虑在内，进一步完善分销网络的设计模型。

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。