离散问题

By solving the simultaneous equations of discrete BIEs and friction law, spontaneous rupture can be calculated.

摩擦准则和本文建立的离散化边界积分方程联立，即可求解半空间的断层上的自发破裂传播问题。

Fundamental study on numerical computation for singular integrals withHilbert kernel and discrete Hilbert bo...

本文对带Hilbert核的奇异积分的数值计算和离散Hilbert边值问题作了一些基础性研究。

Secondly, we discuss the uncertain discrete-time singular system with control input matrix perturbation.

摘要研究了具有圆盘区域极点约束的一类不确定离散广义系统的鲁棒控制问题。

In this thesis, I summarize the theoretical calculation method, applied scope and notice of siphonic drainage system, and point out the advantage of siphonic drainage system compared with gravitation drainage system. In the archetype experiment study of siphonic drainage tube, I adopt different tube diameter and different structural height to survey the drainage volume and press in different place. I observe various kinds of flow state, and get chief factors which influence hydraulic peculiarity of system as the tube diameter or structural height, and find out the relevance of factor to flux. I apply CFD Fluent software and adopt standard k-ε model and RNG k-ε model, then use finite volume method and second-order upwind scheme to discrete numerical model, while coupling numeration of velocity field and press is based on SIMPLE. In the numerical simulation of curved part of tube, siphonic drainage tube experiment system and multi-outlet siphonic drainage system, I make research on internal velocity and press of system in different project condition by changing the tube diameter of curved part, negative press value in tube export and improving the quantity of water gutter. This thesis first adopts a method of combining archetype experiment and numerical simulation to study the siphonic drainage system, test and verify the validity of experiment and numerical simulation, and makefurther study on system, it solves the problems of limited testing conditions, and has a logical results, it can provide a valid method for optimizing and designing the drainage tube-net system. The conclusion have referring value for study and design of siphonic drainage system.

本文首先对虹吸式排水系统理论计算方法、适用范围以及注意事项做出总结，并分析了虹吸式排水系统的优势；再对虹吸式排水管道进行原型试验研究，采用不同管径不同立管高度，对系统流量、管道压强进行量测，观察了各种工况下的流态，对其水力特性进行研究分析，找出影响水力特性的落差、管径主要因素以及与排水量的关系；进一步应用计算流体力学Fluent软件，采用标准κ-ε模型与RNGκ-ε模型，计算过程应用有限体积法和二阶迎风格式对数值模型进行离散，速度和压力的耦合采用SIMPLE算法，分别对系统弯管段、虹吸排水管道试验系统、多斗虹吸式排水系统进行数值模拟分析，通过改变管段弯头处半径、管段出口负压值、增加雨水斗数对不同工况下系统内部的速度和压力进行研究；本文首次采用结合原型试验与数值模拟相结合的方法，对虹吸式屋面雨水排水系统进行研究，试验与模拟相互验证，并进行拓展，很好地解决了虹吸式屋面雨水排水系统由于试验条件限制问题，结果正确合理，为排水管网系统设计和优化研究提供了有效的方法，对工程设计有较好的参考价值。

By introducing a slack variable, the stabilization problem of discrete T-S fuzzy systems is converted into an LMI feasibility problem, and an LMI based design method for output feedback H(subscript ∞) controller is presented.

通过引入松弛变量，将离散T-S模糊系统的输出反馈镇定问题归结为求解一组线性矩阵不等式，进而给出基于LMI的输出反馈H控制器的设计方法。

Thedissertation discusses in detail on the implementation of the algorithm, and applies it toanalyze the scattering from the conductor objects, dielectric objects, and microstrip patchantenna. The solenoidal basis functions are adopted in the scattering analysis of dielectricobjects, which lead to a less number of unknowns for the same mesh as in the traditionalSchaubert-Wilton-Glisson basis functions.

第三种快速方法是多层快速多极子加速电磁分析算法，它应用在时谐电磁场问题时将存储量及计算复杂度都降低到O，并且适用于任意形状的网格离散，具有很强的灵活性，文中将这一加速算法应用到金属体、介质体、以及无限大底板的微带结构的电磁散射特性分析中。

Combination optimization problem has many extensive application backgrounds, and its objective is to find the optimal combinations of discrete status in the solution space.

组合优化问题具有广泛的应用背景，它的目标是寻找解空间中离散状态的最优组合。

We use the boundary integral method to simulate the spherically symmetric collapse of a cavitation bubble, a free-surface potential problem having analytical solution. Evolving error curves are given in the thesis, and the influences of various discretization methods on the accuracy and the stability are compared.

我们使用边界积分法模拟空化气泡的球对称溃灭，一个具有分析解的自由面势流问题，给出了计算误差的演化曲线，比较了各种数值离散法对精度和稳定性的影响。

It was supposed that the dynamic moving process of the stock price and the return was driven by Geometry Brownian Motion and the lognormal distribution respectively. Takinginto account the riskneutral environment, we got a closedform analytical formula for deferred arithmetic asian options by the method of Taylor expansion of the stochastic integral formula within the terminal payoff. Furthermore, with the series definition of the definite integral, we transferred the continuous problem into a discrete one which is simpleenough to figure out. Meanwhile we tested the accuracy of the formula with the Monte Carlo simulation as a benchmark and the result shows that the formula can be utilized to price the related financial derivatives.

在标的价格服从几何布朗运动、收益服从对数正态分布的前提下，通过风险中性定价原理，对到期损益中的随机积分进行任意次Taylor近似，并由级数定义将此连续问题离散化，给出了延期算术平均亚式期权封闭形式的解析定价公式，并与Monte Carlo模拟得到的价格作为标尺对得到的公式进行精确性检验，结果表明，所得公式可以应用到金融实务中对此类衍生品定价中。

According to the concept of strain energy of cracked materials, the orientation tensor of crack was defined. Considering the crack-closing and friction between crack surface under compression, The damage tensor, damage strain and effective elastic modulus were formulated. A method for discrete description of damage mechanism was given, and the evolution equation of discrete orientation density of crack was obtained. The relationship of micromechanism and the macro-representation of concrete failure were studied.

从含裂纹材料的变形能出发，引出了裂纹的方位张量；在考虑裂纹受压闭合与滑动摩擦的基础上，给出了损伤张量、损伤应变和有效弹性系数的表达式，在损伤机构离散化方法的基础上，给出了方位密度的演化方程；将上述损伤理论应用于混凝土的损伤分析，研究了混凝土破坏的微观机制与宏观表现的关系及Griffith准则和Mohr-Coulomb准则的相似性问题，对修正的Griffith准则进行了改进。

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。