微分的

The first proposes that any differentiable function defined on an interval has a mean value, at which a tangent line is parallel to the line connecting the endpoints of the function's graph on that interval.

第一个定理指出，定义在一个区间上的任何可微分的函数都有一个平均值，在该点的切线与该区间上函数曲线两端的联机平行。

The calculation of relative variation of the negative feedback amplifier by differential method results in some errors under certain condition, so there was certain limitation in this method.

摘要利用求微分的方法计算负反馈放大器增益的相对变化量，由于在一定的条件下计算出的结果存在一定误差，因而使用这种方法具有一定的局限性。

A relatively direct method is expounded in this paper to prove the termwise differentiation of power series, and a simple method is expressed to calculate the Fourier coefficient.

文摘：用比较直接的方法证明幂级数的和函数在收敛域内可以逐项微分的公式；并得到了计算傅立叶系数的一种简便方法。

In this paper, based on an optimum difference operator for spatial differential given by Holberg, an optimum difference method of modeling crosswell elastic wavefield is put forward, which adopts the staggered-grid technique and calculates the wavefield at different grid points. When the half length of optimum difference operator is taken as four to six points, the required number of grid points per wavelength equals to three, crosshole elastic wavefield numerical modeling can attain satisfied accuracy.

本文以Holberg提出的一种空间微分的最佳差分算子为基础，采用交错网格技术，提出了一种模拟井间弹性波场的最佳差分法，该方法能在大空间网格点上得到精确的波场值，当最佳差分算子的半长度取4～6个点，每个波长只采3个样点时，井间弹性波场的模拟就可以得到满意的精度，其计算速度比常规有限差分法至少快一个数量级。

Using the method of dividing variables , the solution of elastic dynamics can be changed into the eigen value problem of Hamilton's space differential operator matrix , and the total solution of dual variables (modal strain and modal strain rate ) can be obtained by expanding the eigen solutions .

尽管方程的个数增加了1倍(未知量个数增加了1倍)，但方程对时间微分的次数下降到1阶。通过分离变量后，可以将其转变为Hamilton空间算子矩阵的本征值问题，从而使复杂力学问题的解析解成为可能。

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 L-M method based on the subdifferential.

将概率最优潮流表述为随机非线性规划问题后，利用非线性互补函数将该问题的KKT条件进行转化，基于转化后的非线性代数方程组，利用一次二阶矩法确定了以待求量的数字特征表示的概率最优潮流模型，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L-M方法求解。

By introducing the nonlinear complementarity problem function, the Karush-Kuhn-Tucker conditions of OPF model are transformed equivalently into a set of semismooth nonlinear algebraic equations. Then the set of semismooth equations can be solved by a semismooth L-M method based on the subdifferential. The method belongs to Newton-type method. It can ensure the positive defmitiveness of the iterative coefficient matrix by using the L-M parameter, which avoids the ill-conditioning of iterative equations. The method, requiring only the approximate solution of a linear system at each iteration, is quite applicable to the large-scale cases.

在利用非线性互补函数将OPF模型的KKT条件转化为半光滑非线性代数方程组后，采用基于次微分的半光滑L-M法求解，该方法属于牛顿法范畴，可通过对L-M参数的调整保证迭代系数矩阵的正定性，克服了系数矩阵的奇异引起的"病态"，且该方法在确定搜索方向时只需求解线性系统的加热器近似解，适用于大规模系统的求解。

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。

In this paper, we have estabished the closed convexities and connectedness of the cone weak subdiffrerential of limit mapping of set-valued mapping sequence.

在文[，4]基础上，给出了集值映射序列的极限映射的锥弱次微分的闭凸性和连通性。

The algorithm for optimizing parameter is applied and effective,and is much better than that of common Genetic Algorithm,and has good perfectible application future.

文献[2]提出用模糊控制算法整定PID参数，文献[3]将Bang-Bang控制与神经网络自适应控制相结合，利用神经元的学习功能构成了一种自适应PID控制器，文献[4]以蚁群系统和蚁群算法为基础，提出了一种新的具有不完全微分的最优PID控制器的设计方法，文献[5]提出一种利用改进微粒群算法优化PID参数的方法。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。