函数的微分法

To discuss deeply, this article use indirect means to research by difference differential equation, that is: using the Liyapnof function to discuss the time delay stability of one-dimensionality force telepresence system in order to determine the time delay limits which could ensue the system work normal.

为了进一步深入讨论，本文还从差分微分方程入手，采用间接法进行进一步讨论，即：利用李亚普诺夫函数对一维力觉临场感系统的时延稳定性进行讨论，确定保障系统正常工作的时延界限。

The fracture problem can be solved by calculating the boundary value of a partial differential equation. By the methods of complex variable function and undetermined coefficients, the formulae for deflection, displacement, bending moment, torque, stress and strains near the crack tip are derived.

该断裂同题可化为求解一个偏微分方程的边值问题，借助复变函数方法和待定系数法，推出了裂纹尖端附近的挠度、位移、弯矩、扭矩、应力和应变的计算公式。

The functional by variational calculus leads to a set of elliptic partial differential equations,in particular,Poisson equations,which is possibly solved by numerical methods.

利用变分法可以从这个二次误差指标函数导出一组椭圆形偏微分方程泊松方程，这类方程有相当成熟的数值解法。

Using DF in determining the limit cycle number of differential equation is a significant analysis try.

将描述函数法用于确定微分方程极限环个数的问题是一个有意义的理论探索。

This paper, by means of Rolle theorem, introduces constant method to demonstrate mean value theorem for differential calculus and attains the corresponding supplementary function of the demonstrating method.

借助于Rolle定理，用待定常数法证明了微分中值定理，得到了该证明方法的辅助函数簇，这种证明方法对解决同类问题有很好的推广应用价值。

The first part gives some basic introduction to the meshless methods of Partial Differential equation.

第一部分给出了偏微分方程数值解的无网格方法，特别介绍了以径向基函数插值为基础的配置点法。

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。

For the models by MMFI is a nonlinear differential equation with variable coefficients and the 'nonlinearity' brings discommodiousness to analyse the nature and quantification of a control system, it applies brim linearization method to better MMFI. By transforming 'triangle wave' membership functions of the base elements into 'rectangle wave' membership functions, we get three models which represent different aspect respectively. By simulating second order system and analysing the errors of the results, a conclusion is drawn, that is, the model obtained by brim linearization method has a good precision in contrast with the real model.

由于模糊推理建模法得到的模型是变系数非线性微分方程，这种&非线性&对该控制系统的某些定性或定量分析带来不便，因此应用边缘线性化方法对模糊推理建模法进行改进，将基元的隶属函数由&三角波&改成&矩形波&，从而得到了三个模型，这三个模型各有侧重，通过对二阶系统进行仿真，分析仿真结果，从而给出了关于边缘线性化方法的结论，即由边缘线性化方法得到的系统模型对该系统的真实模型有较高的逼近精度。

The topics covered in this course include: unconstrained optimization methods, constrained optimization methods, convex analysis, Lagrangian relaxation, nondifferentiable optimization, and applications in integer programming.

这门课程的主题包括：无限制最适化方法，限制最适化方法，凸分析，拉格朗日松弛法，不可微分函数最适化，以及在整数规划上的应用。

Nonlinear partial differential dynamic equations of bending vibration of a tilting stepped drive shaft with two supports were built under non-inertia movement coordinate system by theorem of the motion of mass center and Heaviside function. According to the condition of equal displacement in an adjoining plane of the shaft, an equivalent shaft and its equation were obtained. A motion equation of the equivalent shaft was obtained by method of Galerkin. An approximate steady-state solution of the main resonance was obtained by method of multiple scales. The influence factors, motion stability, amplitude jump of main resonance of a stepped drive shaft and so on were analyzed.

用质心运动定理、Heaviside函数建立了非惯性系下倾料两端支承阶梯传动轴的非线性弯曲振动偏微分动力学方程，并根据相邻轴段的衔接面处位移相等的条件，得到阶梯轴的当量轴及其动力学方程；用Galerkin法得到当量轴的弯曲运动方程，用多尺度法求得稳态下当量轴的主共振的一次近似定常解，分析了影响阶梯传动轴主共振的因素、运动稳定性、振幅突变性等。

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 。