离散问题

The Frechet derivative of the cost function is determined via the solution of an adjoint partial differential equation, and the boundary shape is then modified in a direction of descent. This process is repeated until an optimum solution is approached. The advantage is that the cost function variation is independent of the flow field variation, with the result that the gradient of cost function with respect to arbitrary number of design variables can be determined without the need for additional flow-field evaluations. So each design cycle requires the numerical solution of both the flow and the adjoint equations leading to a computational cost roughly equal to the cost of two flow solutions.

虽然他们的研究成果大多数都可以在公开性文献上看到，但是其中一些具体的细节问题的处理方法却没有透露，比如：伴随方程如何离散求解才能减小最终梯度计算中的误差，使得设计过程有效地进行；伴随方程与流动方程的边界条件是不同的，如何合理地处理伴随方程的边界条件，才能推动设计过程朝着设计目标而发展；在减阻问题中目标函数如何定义，求解梯度的具体数学公式如何推导，如何通过数值方法来实现它们等。

In this project, we have tackled the robust fault detection and diagnosis problem for affine nonlinear sampled-data systems based on nonlinear H∞ filtering theory,and focused on the design of robust fault dtetction filter. The main contribution of this project is that we (1)present design methods of robust fault estimator for nonlinear discrete-time systems based on least square estimation and linear matrix inequality;(2)improve the bounded real lemma of systems with finite discrete jumps;(3)develop the robust fault detection filters for affine nonlinear sampled-data systems with parameter uncertainties based on the improved bounded real lemma.

本项目以提高故障的正确检测率为目的，以非线性H∞滤波理论为基础，对不确定仿射非线性采样系统的鲁棒故障检测与诊断问题进行了研究，重点研究了不确定仿射非线性采样系统的鲁棒故障检测滤波器设计问题，取得了一些新的成果，主要成果有：(1)基于最小二乘估计和线性矩阵不等式，给出了非线性离散系统的鲁棒故障估计器设计方法；(2)改进了有限跳跃点系统的有界实引理；（3）基于改进的有界实引理，给出了不确定仿射非线性采样系统的鲁棒故障检测滤波器的设计方法。

The displacement of each strip is interpolated in nodal line displacements.Then the problem is east into ODLS problem by variational principle,and solved byNDTFM.

将位移离散模型代入问题的变分关系中，通过积分、变分等过程将问题转化为一个一维问题，这样就可以应用数值传递函数求解。

To obtain quadratical convergence, however, strict complementarity condition at the Danskin point was used. The condition is too strict to be satisfied in many practical problems such as discrete semi-infinite minimax problem. Another kind of Newton method for finite minimax problems was presented by E. Polak and, without strict complementarity at the Danskin point, superlinear convergence (of order 3/2) was proven.

Polak等人提出了一种直接求解极大极小问题的二阶收敛的牛顿法，但是为获得二阶收敛速度要求在Danskin点处满足严格互补条件，这个条件太强，很多实际问题尤其是半无限极大极小问题的离散化不满足该条件；他们又给出另外一种牛顿法，在不假设严格互补条件成立的情况下，证明了它的超线性（3/2阶）收敛性。

The essence idea of restoration based on Total Variation is that translate the problem into minimum of energy functional with TV regularization, then the Partial Differential Equations are got from the principle of variation, finally after discretization the optimal resolution with the numerical methods is obtained.

基于整体变分的图像恢复概括的说就是把图像恢复问题形式化为带有整体变分正则化项的图像能量泛函极值问题，采用变分原理将其中的最小化问题转为所要求解的偏微分方程，即Euler-Lagrange方程，利用数字图像本身的离散特征使用适当的数值方法来求它的最优解，最后达到逼近原始图像的目的。

The nonlinear equations are dealt by the quasi linear iteration equation,at last,by the orthogonal discrete method,the solutions of the initial problem are obtained.

本文建立的载流板壳二维磁弹性问题的数值计算方法——差分正交离散法不仅对二维问题有效，同样也为三维磁弹性的边值问题的解决奠定了理论基础。

Although the disperse model is beautiful and sententiously, the problem is NP-hard problem, when the number of aminophenol is very huge, the style of the difficulty of settle the problem is exponential, solving the problem is impossible.

离散模型固然很简洁优美，但是蛋白质结构的预测问题是NP-HARD问题，当蛋白质一维氨基酸序列的链长n很大的时候，计算时间随着问题规模的增加呈指数方式增长，求解将变得非常困难。

The variational problem of semi-discrete problem is given, the well-posedness of the variational problem is proved, and some error estimates are presented.

给出半离散化问题的变分问题，证明了变分问题的适定性，并给出了误差估计。

In orde to obtain system optimization in high efficiency production and operation safety, the microcosmic problem of goaf treatment was brought into the creative design of mining method and the synergism of two problems was studied. Firstly, in view of the occurrence characteristics and mining conditions of catacalstic ore section of orebody No. 105 in Gaofeng mine in Guangxi province, considering the adaptability to different scale goafs in the ore section, based on mining environment reconstructing idea and continuous mining mode, a new mining method (mining environment reconstructing non-pillar sublevel-strip continuous mining method) was put forward. Then, some repr, esentative goafs were selected and their stabilities were calculated by discrete element method on the basis of differences of goaf scale, surrounding conditions and situ stress field. At last, the mining layout was adjusted on the basis of goafs stability analysis and the goafs were adjusted as a part of cutting engineering, blasting space or stope, so as to determine all kinds of goafs treatment schemes.

摘 要：为在生产高效和作业安全上取得系统整体最优，将碎裂矿段的空区处理微观问题纳入采矿方法创新设计宏观问题中，开展2种问题的协同研究：首先，针对广西高峰矿105号矿体碎裂矿段的赋存特点和开采技术条件，考虑对各种规模空区适应性，基于采矿环境再造和连续采矿理论，提出采矿环境再造无底柱分段分条连续采矿法；然后，根据采空区规模、围岩状况和原岩应力场等条件的差异，在所有采空区中选择具有代表性的空区，运用离散元程序对其稳定性进行计算分析；最后，在稳定性分析的基础上，灵活调整开采布局，将采空区调整为部分切割工程、自由爆破空间或采场，从而确定出各种规模空区的处理方案。

On the one hand, the paper theoretically develops the relations between online public opinion and public decision-making as well as its background connotation of rights and powers and their complicated linkages, based on which the"should-be"state of the relations between the foregoing two is proposed, on the other, it also analyzes, in the light of the states quo, the"is-being"state of the contradictions between the two sides.

一是从理论上梳理网络民意和公共决策的关系，****其背后的权利和权力意蕴和复杂纠葛，提出网络民意和公共决策关系的&应然&状态；二是从现实出发，对两者间的矛盾的&实然&情形进行分析，具体考察了网民结构、网络自由离散特征、网络情绪化表达等问题同公共决策民主、科学、理性要求的冲突，以及公共决策中对待网络民意的消极态度、&自利&倾向和技术方法上的被动和偏差等问题同网络民意的正当性、利益性、自主性要求之间的矛盾，并提出对各问题的反向思考和意见。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。