一阶导数

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

In this paper, one corollary has been derived, i. e., the Frechet derivative which is necessary to the resistivity inversion, is the first order of Zhang's integrated geometric factor.

针对阵列电位电极系测井正演与反演研究，我们得到另一结论：反演过程中必然用到的Frechet导数为张氏一阶积分几何因子。

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。

For the first-order ordinary differential equation system, the coefficient matrix of variables with derivative is decomposed into the triangular factor form and transformed into unit matrix.

对于一阶常微分方程组，将具有导数变量的系数矩阵作三角化分解，使其简化成单位矩阵。

Theorem(Stokes's Theorem) Let be a piecewise smooth oriented curve in three-space, be a piecewise smooth oriented surface with boundary curve .The surface and the curve are related by a right-hand relationship, i.e., if the fingers of the right hand are cupped in the direction of ,then the thumbpoints in the direction of orientation of .,, have continuous first partial derivatives on and ,then

定理 设为分段光滑的空间有向闭曲线，是以为边界的分片光滑的有向曲面，的正向与的侧符合右手规则(即如果右手大拇指表示曲面的方向，则弯曲四指表示曲线的方向)，函数，，在曲面上具有一阶连续偏导数，则有下述公式成立

Let be a vector field, where ,,have continuous first derivatives.

设是一向量场，，，有一阶连续偏导数。

The canonic OC expansion of the first-order Boolean partial derivative of the OC type logic function was discussed.

讨论了OC型逻辑函数一阶布尔偏导数的规范OC展开式。

With the frequency and mode shape being regarded as functions of damage parameters, the overdetermined algebraic equations with damage parameters as unknowns can then be constructed by differentiating frequency and mode function on the basis of structure mode finite element formula, the damage parameters of which are obtained via Taylor expansion.

本方法从结构模态有限元算式出发，把频率和振型看作损伤参数的函数，经过泰勒展开获得频率、振型对损伤参数的一阶偏导数，然后构造以损伤参数为未知量的超定线代方程组，求解得到全部损伤参数值。

With the frequency and mode shape being regarded as functions of damage parameters, the overdetermined algebraic equations with damage parameters as unknowns can then be constructed by differentiating frequency and mode function on the basis of structure mode finite element formula, the damage parameters of which are obtained via Taylor expansion. The whole damage parameters can be found via solving the algebraic equations.

本方法从结构模态有限元算式出发，把频率和振型看作损伤参数的函数，经过泰勒展开获得频率、振型对损伤参数的一阶偏导数，然后构造以损伤参数为未知量的超定线代方程组，求解得到全部损伤参数值。

Then based on SURE unbias estimation, LMS algorithm and the new threshold function, this paper proposes a speech enhancement method called adaptive wavelet coefficients subtraction.

在小波阈值去噪的方法中，为满足时变信号的实时处理要求，本文首先提出一种新的阈值函数，新阈值函数克服了传统阈值函数的缺点，具有无穷阶连续导数。

We will see more and more activist government policies that distinguish economic activities according to the nationality of the actors.

我们将看到越来越多激进的政府政策，这些政策根据企业的国籍来区分经济活动。

If we can prove the independence of an axiomatic system, then we can guarantee the conciseness of this system, ie.

如果能够证明某个一阶谓词系统的独立性，那么就能够保证该系统的建立是精炼的，即没有任何一条公理或推理规则是多余的。