偏导数

Theorem 2 If has continuous partial derivatives at , then is differentiable at .

定理2如果函数在点的偏导数连续，则函数在该点可微分。

Be differentiable at . Then has first partial derivatives at , and

可微，则复合函数在点的一阶偏导数存在，且有

Now let's discuss the solution of differential equation of the form y=f, and assume the function f has continuous partial derivative.

1现在讨论型如y=f的微分方程的解，这里假设函数f有连续的偏导数。

By using the limits of functions and the exchange limit theorem,we considered the relationship between the double limit of function with two variables and its repeated limit s.

应用函数列的极限与函数的极限交换次序定理，研究了二元函数的二重极限与它的两个累次极限的关系定理，研究了二元函数的两个二阶混合偏导数可交换次序定理。

Theorem1 If has partial derivatives at , and has an extreme value at , then we have

定理 1 设函数在点具有偏导数，且在点处有极值，则有。

In Part 5, the stability of linear large-scale singular dynamic system is investigated by using the method of vector generalized Lyapunov function and the sum type of scalar generalized Lyapunov function, respectively.

首先研究线性广义系统二次型李雅普诺夫函数的存在性；然后建立按线性近似系统决定非线性广义系统稳定性的准则；进而改进广义李雅普诺夫函数法以研究广义系统的稳定性；最后提出利用非线性函数的偏导数矩阵判别非线性微分-代数系统稳定性的若干简便判据。

In addition, after the detailed analysis of those macro-blocks that had no forward motion estimation, the motion information is given approximatively relative to their forward reference frames. And then, a amendatory partial derivative estimation is given for the inconsecutive image blocks when occlusion and cut had happened.

另外对编码过程中未进行前向运动预测的宏块特性进行了详细的分析，给出了这些宏块相对于前向参考帧的运动信息估计方法，并对时域不连续的图像块给出了一种修正的偏导数估计方法，以此解决遮挡、切换等现象。

According to invalidate transform between non-linear constraining function and linear constraining function, and the disable partial differential coefficient of first order for objective function, GA has been chosen for the built mathematic mode, also, the conception of GA, its computing process, features, and operating parameters are introduced irrespectively in this article, meantime, a managerial software for oil pipeline's optimization is programmed.

根据优化模型中的非线性约束函数无法化为线性约束函数，目标函数无法求一阶偏导数的特点，本文从众多优化方法中选择遗传算法对所建立的数学模型进行求解，并对遗传算法的概念、计算步骤、特点、运行参数等逐一进行介绍，并编写了输油管道优化运行管理的软件。

The very important part for wave tomography is to get coefficentmatrix of tomography equations, that is the Jacobin matrix, or deviationderivative matrix of wave field to physical parameters.

波动成像最关键的一步就是求取成像方程的系数矩阵，也就是雅可比系数矩阵，也即波场对物性参数的偏导数矩阵。

In order to find a powerful assistant computation tool for further analysis and design of multilayer optical coatings,an analytical model is mathematically established for accurate calculation of the first and second derivatives of the spectral coefficients of multilayer optical coatings with respect to layer parameters like thickness,real refractive index and extinction coefficient. It is based on the matrix theory of calculating the spectral coefficients of multilayer optical coatings and is achieved by perfectly using the trace operation of matrix.

为了寻找一种膜系深入分析与设计的有力辅助计算工具，从光学薄膜光谱系数的矩阵计算理论出发，基于对矩阵求迹运算的巧妙运用，从数学上建立了准确计算膜系光谱系数关于膜层几何厚度、实际折射率和消光系数等膜层参数的一阶和二阶偏导数的解析模型。

Lugalbanda was a god and shepherd king of Uruk where he was worshipped for over a thousand years.

Lugalbanda 是神和被崇拜了一千年多 Uruk古埃及喜克索王朝国王。

I am coming just now,' and went on perfuming himself with Hunut, then he came and sat.

我来只是现在，'歼灭战perfuming自己与胡努特，那麼，他来到和SAT 。