函数的微分法

Two types of new Abel differential equation are structured by method of variation replacement, variation position transformation and compound function derivation law.

借助变量替换法、交换变量位置法及复合函数求导法则，构造出两类新的 Abel型微分方程，论证它们的可积性，提供可积的判据，从而推广有关文献的结论，扩大微分方程的可积范围。

Put the discrete algebraic equations of initial derivative conditions and algebraic equation system of governing differential equation together to form a new algebraic system.

采用重心Lagrange插值近似未知函数，推导了未知函数各阶导数微分矩阵的显式表达式，建立了求解二阶常微分方程初值问题的重心Lagrange插值配点法。

By adopting the asymptotic expansion method, the higher order partial differential equation was transformed into the system of ordinary differential equations.

采用渐近展开法，将该控制方程——高阶偏微分方程转化为常微分方程组，求解该方程组获得应力函数，进而得到功能梯度材料中裂纹尖端应力高阶渐近场的解析式。

The authors studied carefully two numerical differential methods, finite difference method and rational polynomial technique, and pointed that FDM is the special ease of RPT when the limit state function is linear. Accordingly, FDM3 can be used for the continuous linear limit state function and RPT5 for the continuous nonlinear limit state function. For the discontinuous limit state function, RPT should be used because of the large error of FDM.

对于可靠度分析中常用的有限差分法及有理多项式法这两种数值微分方法，本文详细研究了二者间的异同及其求导结果与步长的关系，指出了对于相同的步长控制系数及取样方式，FDM是RPT在线性情况下的特例；对于连续的线性功能函数，可直接用3点FDM求导；对于连续的非线性功能函数，可用5点RPT求导；对于非连续的功能函数，应采用RPT求导。

This paper is a report of a light frequency equation of inflexion on Planck function we have deduced in light of Planck formula.

基于普朗克公式，利用微分方法导出了普朗克函数的拐点光频率方程，并通过牛顿迭代法求出了这个方程的两个根，进而找到了可求任意温度下两个拐点光频率的普遍公式，为研制热辐射测温仪工作波长的选择提供了技术参考。

Secondly, point out that meshless method is different from finite element method in handling boundary condition and numerical integral because the approximation function of meshless method is not inserted function, it have itself special methods. Deduces meshless Galerkin essential equation of parabolic partial differential equation with the method ofweighted residuals------Galerkin. Furthermore, discusses the main factors which may effectthe calculation precision and give some suggestion with which can get the best result.

其次，由于无网格法的近似函数不是插值函数，所以无网格Galerkin法在处理边界条件和对区域积分时是不同于有限元的，它有其独特的处理方法，从加权残量法——Galerkin出发，推导出抛物型偏微分方程无网格Galerkin法的基本方程，并对影响无网格Galerkin法的主要因素进行探讨，给出了取得最佳效果的相应建议。

Fundamental concepts in power system differential-algebraic equations model, like singular point and multiple energy function sheets defined on constraint manifolds, are studied.

所得研究成果揭示了微分代数模型与奇异扰动模型的本质区别、奇异性与系统模型和系统负载的联系、结构保持能量函数法可能具有的内在保守性等，这对深入理解电力系统微分代数方程模型的拓扑结构、结构保持能量函数法和暂态电压稳定及其与功角稳定的关系具有一定的价值。

For overcome nonlinear terms of any degree in the equation, we made a proper transformation according to the structure of the equation at first, make the equations into ordinary differential equation. Then solve the ordinary differential equation exactly, by auxiliary functions method and undetermined the coefficient method and algebraic computer system Mathematica.

为了克服方程中非线性项的任意次幂，我们采用的方法是首先根据方程的特点，做适当的变换，使原问题转化为常微分方程的问题，其次对该常微分方程再进行各类变换，如辅助函数法以及待定系数法……。

According the experiential formulas of headbox to design the stepped diffuser headbox's geometry parameters. Supposing Paper suspension flow as potential flow and basing on hydrokinetic and computational fluid dynamics theories, we can solve the elliptoid partial differential equations which are followed by the flow functions and the potential functions by finite element method and simulate the flow's speed distribution with pde toolbox of matlab software. The simulate results and the flow analysis have good precision.

按照流浆箱的经验设计公式，设计阶梯扩散式流浆箱的各组件几何参数，以流体动力学、计算流体力学等理论为基础，假定浆流的流动为势流，采用有限元法求解浆流流动时其流函数和速度势函数所符合的椭圆型偏微分方程，应用matlab软件的偏微分方程工具包pde toolbox，模拟出所设计的流浆箱各组件内的浆流的流场流速分布，模拟结果与数值计算流动分析结果吻合。

In this paper the rocket of 122mm, 20km is exampled, CADET is used in random ballistics system with the action of random wind by use of sharping filter when the differential equations of sharping filter and angle motion equations of ballistics are allied.

以某火箭弹为例，在随机风场作用下，利用纵风作用下的随机弹道系统成形滤波器，把成形滤波器的微分方程和外弹道角运动方程联立，对此系统采用协方差分析描述函数法，对火箭弹的散布进行了计算。

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 。