函数的微分法

By level function,ε-subdifferential, normal cone and dual function, global optimal solutions for a convex function in locally convex topological vector space and a few of equivalent forms on it are obtained. Maximum points are characterized.

讨论局部凸拓扑向量空间中凸函数的全局最优解，用水平函数、ε-次微分及法向锥和共轭函数等工具刻画其最大值点，得到最优解的几个等价形式。

Half penalty method and optimism design of ten connecting bar mechanism of plunger slide in double action drawing press;2. The essential boundary condition is imposed by employing a penalty method .

将选择施加在"虚结构"控制点上的虚载荷作为形状优化的设计变量，并将它与无网格Galerkin法相结合来开展结构形状优化研究，采用罚函数法来施加边界条件，通过直接微分法建立了结构形状优化的离散型灵敏度分析算法，利用无网格法研究了节点坐标关于设计变量导数的计算。

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。

On the whole, we do as follows: Firstly, we list some conceptions and lemmas for later use. Secondly, we define δ-fine partitions for infinite interval and integral of vector-valued functions on infinite interval, and discuss the properties of integral, and characterize its primitives...

主要包括以下五部分内容：在第一部分中，我们介绍了本文所用到的基本概念和引理；在第二部分中，通过定义无穷区间上δ-精细的分法，我们给出了无穷区间上向量值函数的积分的定义，并讨论其性质，还给出了原函数的刻划；在本文的第三部分中，我们着重讨论了无穷区间上向量值函数积分的收敛定理；在本文的在第四部分中，我们首先应用无穷区间上向量值函数积分的收敛定理给出了常微分方程整体广义解的存在性定理，其次应用强积分对Banach空间常微分方程广义解进行了讨论；最后，在第五部分中，我们将模糊积分推广到无穷区间上并给出了其数值计算方法。

In the proof,the tools of the conditional moment generating function and the differentiation on a net for the study on strong limit theorems in the random selection system are applied.

在证明中采用了一种把网微分法与条件矩母函数相结合应用于随机选择系统强极限定理研究的一种途径。

In the numerical differentiation matlab, useful midpoint formula, adaptive method, Richardson extrapolation methods such as France seek the derivative of the function, the algorithm of the program implementation in the document have been given.

详细说明： matlab中的数值微分，有用中点公式，自适应法，理查森外推算法等方法求函数的导数，算法的程序实现在文件中都已经给出了。

In order to solve the derivation of power exponent function,this paper has studied the derivation regulations on power function from the perspective of the differentiation of multi-variable function and in accordance with the derivation laws on multi-variable complex function.

为解决幂指函数的求导问题，从多元函数微分法的角度出发，根据多元复合函数的求导法则，探索幂指函数求导的规律，并揭示了幂指函数与幂函数及指数函数导数间的关系，给出了幂指函数求导的另一种方法。

In the POPF model, wind farm is modeled by the probabilistic wind farm model considering the reactive power-slip characteristic, and the inequality constraints include not only the unit output constraints, the ratio constraints, the voltage constraints and the line current constraints but also the reactive compensation capacity constraints in wind farm and the system climbing capacity constraints per minute. By introducing the NCP function, the KKT conditions of POPF system are transformed equivalently. Based on the transformed nonsmooth nonlinear algebraic equations, the FOSMM is used to determine the POPF model expressed by the numerical characteristic of variables. The model includes nonsmooth functions, so it can be solved by a semismooth Newton-type method based on the subdifferential.

概率最优潮流模型中，风电场采用考虑无功功率—滑加热器差特性的风电概率模型，不等式约束中除了机组出力约束、有载调压变压器变比约束、电压约束和支路电流约束，也考虑了风电场无功补偿容量约束、系统的分钟级爬坡能力约束；使用非线性互补函数将概率最优潮流的KKT条件转化为一组包含有不光滑函数的非线性代数方程组，然后基于一次二阶矩法确定了以待求量的数字特征表示的POPF模型，由于该模型包含不光滑函数，因此采用基于次微分的半光滑牛顿型方加热器法求解。

Half penalty method and optimism design of ten connecting bar mechanism of plunger slide in double action drawing press;2. The essential boundary condition is imposed by employing a penalty method .

将选择施加在&虚结构&控制点上的虚载荷作为形状优化的设计变量，并将它与无网格Galerkin法相结合来开展结构形状优化研究，采用罚函数法来施加边界条件，通过直接微分法建立了结构形状优化的离散型灵敏度分析算法，利用无网格法研究了节点坐标关于设计变量导数的计算。

The type of the limit state function is set up according to the Mohr-Coulomb yield criterion which can consider the direction of the slip surface; and the derivatives of the stress to the basic stochastic variables of the slope are computed by using partial differential method based on the incremental tangent stiffness method and the accelerating convergence method of Aitken.

其中功能函数的形式是以考虑滑面方向的Mohr-Coulomb屈服准则来建立的；导数的求解采用的是基于增量切线刚度法及Aitken加速算法的偏微分法；边坡整体可靠指标取的是所有可能滑面的可靠指标的最小值。

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 。