数值函数

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。

The model was solved by the Ritz method, and the orthogonal polynomials generated by the Gram-Schmidt process were employed as admissible function for both disk and blades. With this approach, the matrix derived from kinetic energies becomes diagonal and numerical manipulation can become easy and stable.

采用Gram-Schmidt方法生成正交多项式作为李兹容许函数进行模型的离散化，简化了所得到的频率方程求解过程，有利於求解过程的数值稳定性，并可方便地通过对方程系数性质的分析了解结构振动模态的性质。

And then, after establishing the optimization model in accordance with the principle of optimal design of shape formulas, we could obtain the numerical optimization aerofoil on the basis of NACA0018 master pattern solved by the Fluent console, and discuss the reasons of improvement of power coefficient.

然后按照形函数的优化设计原理，建立了优化模型，用Fluent平台求解，在NACA0018母型基础上得到数值优化翼型，并探讨了能量利用率提高的原因。

The main characteristics of seismic source function in underground explosion are studied by seismological method and numerical method.

结合地震反演方法和数值计算方法，研究了地下爆炸震源函数的特征以及介质特性对震源函数的影响。

In this paper, we contribute an evolutionary heterogeneous beliefs model byusing t distribution to replace traditional standard normal to describe fundamen-tal price process and adding risk-adjusted market fraction function in classicaltwo types traders scheme. And then we utilizedifference equation stability and bifurcation theory and numerical simulation tostudy the system. It is found that the system has some styled facts (high kurto-sis、fat tali and long memory) of the actual financial market, and this indicatesthat the simulation model can reflect well the true financial market.

本文通过引入t分布代替原有的正态分布描述基础价格过程，引入经风险调整的投资者市场分数维函数取代原有的无风险调整的市场分数维函数，在经典的两类投资者(自主投资者和图表分析者)模拟模型框架下，建立了新的异质预期资产定价模型，利用差分方程稳定性和分支理论及数值模拟的方法对该系统进行理论分析和实证研究，发现模型具有真实金融市场的程式化事实(尖峰厚尾性，长记忆性等)，模拟效果较好。

By observing the constructed membership functions, we learn that the human preference is not consistent with equal-weighted, equal-spaced numerical evaluations. Nor is it consistent with simplified, symmetric triangular or trapezoidal membership functions.

由观察所建构的归属函数显示：人类的偏好当转成模糊评估尺度时，与等权重、等间隔的数值评估或对称的简化型归属函数是不一致的。

New factorized quasi-Newton equation not only uses the gradient information of the objection function ,but also uses the function information .

本文利用二次函数近似梯度的方法构造新分解拟牛顿方程，不仅利用到了目标函数的梯度信息，而且用到了目标函数值的信息，比传统的分解拟牛顿方程具有更高的二阶曲率逼近。

The residual parts are surface integrations whose integrands are the products of the scalar Green's function and fields or their derivatives. The high order singularity of integrands in the integral equation is reduced to one order, making for program implementation.

剩下的部分是关於标量Green函数与场强值或与它们的一阶导数值乘积的面积分，这样积分方程的被积函数高阶奇异性被降到一阶，有利於计算机的程序实现。

Based on these, an improving μ-synthesis is presented, with which the high-purity distillation is designed well. 2. The robust performance problem of MIMO plant is explained with the plant direction angle, which shows that the robust performance varies with different input uncertainties and the μ-synthesis should be applied correctly according to the uncertainty structure. 3. Condition number and bandwidth are the important items for robust performance design in MIMO system. The H〓 two-block problems can not deal with the robust performance design of MIMO system because of the condition number cancellation. A general μ-synthesis procedure for MIMO system with uncertainties is presented. 4. For the SISO system, the object function in robust performance is amplified by at most 〓 than that of H〓 two-block problems in value: So the robust performance of SISO system can be done with the H〓 two-block problems to avoid the complicated μ-synthesis procedure. 5. All the conclusions and methods presented in this paper are demonstrated by some typical design examples.

从而形成一种改进的μ综合方去，并对精馏塔病态对象进行了鲁棒性能设计，得到令人满意的结果；（2）利用对象的方向角解释了MIMO对象鲁棒性能设计出现问题的原因，并提出不同输入摄动形式下系统的鲁棒性能问题也并不相同，因此利用μ综合处理鲁棒性能设计时，应根据不同的摄动情况采用不同的结构进行设计：（3）条件数问题和带宽问题是MIMO系统鲁棒性能设计的两个主要问题，指出由于条件数对消的存在使得一般H〓两块问题无法处理MIMO系统的鲁棒性能设计，而μ综合方法则是处理MIMO系统鲁棒性能设计的有效方法，并给出了其处理MIMO系统鲁棒性能设计的一般性方法；（4）提出对于SISO系统H〓两块问题（S/T问题、S/KS问题）的设计指标函数与鲁棒性能设计的μ指标函数在数值上最大差〓倍，因此对于一般SISO系统的鲁棒性能设计可以简单地用一般的H〓的两块问题处理，而避免μ综合设计的复杂过程；（5）本文中提出的结论和算法都利用H〓/μ发展中的典型例子：Doyle-Stein问题，Safonov的战斗机模型，精馏塔对象等进行了设计验证。

A recursive matrix method is adopted for computing the magnetic-current-source dyadic Green′s function in anisotropic media. The response of multi-component induction logging in layered and deviated anisotropic formation is simulated by using the obtained dyadic Green′s function. The influence of coil spacing, bed thickness, deviation angle and shoulder bed on the response is analyzed.

采用递推矩阵方法计算各向异性介质的磁流源并矢Green函数，并利用上述并矢Green函数对层状各向异性倾斜地层中多分量感应测井的响应进行数值模拟，分析了线圈距、层厚、倾角和围岩对多分量感应测井响应的影响。

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。