查询词典 variation derivative

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。

We re-examine a problem about action principle which may be easily ignored in the end. After some detailed study, we find that it is correct to do variation of the action with respect to scale factors for Bianchi IX model up to some higher derivative Lagrangian corrections.

我们最后重新检验了在变分法里头容易被忽略的一个问题，最后我们发现，在Lagrangian放入一些高阶修正项的Bianchi II， VIII， IX模型都可以直接对尺度因子变分而得到正确的场方程式。

First of all, modeling image by fractional-order derivative and negative Sobolev space, this paper presents a fractional-order multi-scale variation PDE model, and the proposes the adaptive parameter selection method and obtains the field and scale adaptively algorithm for SAR image denoising.

首先利用分数阶导数以及负指数Sobolev 空间对图像进行建模，建立了分数阶多尺度变分PDE 模型，然后给出了模型参数自适应选择方法，并在此基础上提出了区域、尺度自适应的SAR 图像去噪算法。

The following results are made from this research: Assessing data quality and band combination of different bands in line with geo-target features in desertification areas, and determining basic bands for desertification monitoring. And understanding and studying the spectral features and variation rules of geo-targets in the experimental area, raising that it is the basis of geo-targets information collection with imaging spectrometer data to understand spectral features and variation rules of geo-targets, realizing that in a great extent spectral-integrated-form-based classification method can remove the phenomenon of "different spectrum with same objects" resulted from reflection ratio curve translation because of the angle change among sensor, targets and observation direction, and the average and variance images can be introduced to solve the problem of two kinds of geo-target with similar spectral forms and much different values of whole reflectionratio. It is suggested that "red edge" range bands of vegetation, which has close relationship with vegetation cover and biomass, is the main characteristic bands and important basis for careful vegetation classification and quantitative retrieval, and pixel-based derivative spectral analysis is very useful for removing the effects of soil background values and quantitatively retrieving vegetation biomass and cover. The remote sense quantitative retrieval model is developed for main appraisable factors of desertification monitoring assessment with imaging spectrometer data and then the applicability of model is analyzed.

研究结果如下：首先针对荒漠化地区的地物特征，对高光谱数据不同波段的数据质量、波段组合进行了评价，提出了适用于荒漠化监测的基本波段选择集；初步了解和掌握了研究地区的地物光谱特性及变异规律，进一步明确了掌握地物光谱特征和变异规律是用成像光谱仪数据提取地物信息的基础；发现了基于光谱整体形状的分类方法在很大程度上能够消除由于传感器、地物目标观测方向之间的角度变化引起的反射率曲线整体平移的"同物异谱"现象，对于谱形相似而整体反射率的值相差较大的两类地物，通过引入均值和方差图像参与分类得到解决；研究还表明在植被"红边"范围内的波段是进行荒漠化监测的主要特征波段，这些波段与植被生物量和盖度都有密切的关系，是开展精细植被分类研究和植被定量反演的重要基础；像元的导数光谱分析可以消除土壤背景的影响，是进行植被生物量和盖度定量反演的有力工具；建立了荒漠化监测主要评价因子的定量反演模型，并分析了模型的适用性。

The results showed that both the break point on the Ia-c curve and the minimum of the derivative variation corresponding to the λa-c curve agreed very well with the critical micelle concentration of the surfactant in aqueous solution as measured by surface tension technique.

以对二甲氨基苯甲腈为探针，测定它在表面活性剂(C12TABr、SDS、C12E23、C12-3-12·2Br)水溶液中的第二重荧光强度和对应的特征波长对表面活性剂浓度曲线，由Ia-c 曲线的转折点或λa-c曲线对应的一阶导数极小点可以获得临界胶团浓度。

The part of calculus that deals with the variation of a function with respect to changes in the independent variable by means of the concepts of derivative and differential.

微积分学中有关用导数与微分的观念讨论函数随独立变量改变的部分。

The following results are made from this research: Assessing data quality and band combination of different bands in line with geo-target features in desertification areas, and determining basic bands for desertification monitoring. And understanding and studying the spectral features and variation rules of geo-targets in the experimental area, raising that it is the basis of geo-targets information collection with imaging spectrometer data to understand spectral features and variation rules of geo-targets, realizing that in a great extent spectral-integrated-form-based classification method can remove the phenomenon of "different spectrum with same objects" resulted from reflection ratio curve translation because of the angle change among sensor, targets and observation direction, and the average and variance images can be introduced to solve the problem of two kinds of geo-target with similar spectral forms and much different values of whole reflectionratio. It is suggested that "red edge" range bands of vegetation, which has close relationship with vegetation cover and biomass, is the main characteristic bands and important basis for careful vegetation classification and quantitative retrieval, and pixel-based derivative spectral analysis is very useful for removing the effects of soil background values and quantitatively retrieving vegetation biomass and cover. The remote sense quantitative retrieval model is developed for main appraisable factors of desertification monitoring assessment with imaging spectrometer data and then the applicability of model is analyzed.

研究结果如下：首先针对荒漠化地区的地物特征，对高光谱数据不同波段的数据质量、波段组合进行了评价，提出了适用于荒漠化监测的基本波段选择集；初步了解和掌握了研究地区的地物光谱特性及变异规律，进一步明确了掌握地物光谱特征和变异规律是用成像光谱仪数据提取地物信息的基础；发现了基于光谱整体形状的分类方法在很大程度上能够消除由于传感器、地物目标观测方向之间的角度变化引起的反射率曲线整体平移的&同物异谱&现象，对于谱形相似而整体反射率的值相差较大的两类地物，通过引入均值和方差图像参与分类得到解决；研究还表明在植被&红边&范围内的波段是进行荒漠化监测的主要特征波段，这些波段与植被生物量和盖度都有密切的关系，是开展精细植被分类研究和植被定量反演的重要基础；像元的导数光谱分析可以消除土壤背景的影响，是进行植被生物量和盖度定量反演的有力工具；建立了荒漠化监测主要评价因子的定量反演模型，并分析了模型的适用性。

Assuming slow time variation (for large λ), expand in the powers of the time derivative

假 设时间是慢变的（对大λ，以时间导数的指数形式展开至最低阶，结果便是描述自旋1/2的单位矢量n的路径积

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。