近似微分

The method of address mapping used by CMAC is adopted in the new network.

由于高阶接收域函数的引入，使其可以获得较CMAC连续性强且有解析微分的复杂函数近似。

Unfortunately, most of the analytical solution for fractional differential equation are complicated owing to complex series or special functions.

然而大多数分数阶微分方程的解析解含有复杂的级数或特殊函数，不利于近似计算。

To solve the B-Ss pricing formulas,there are many popular methods now,such as partial differential equation,analytical approximation,binomial tree methods,finite difference method and Monte-Carlo simulation.

对于Black-Scholes期权定价模型，如今比较流行的定价方法有偏微分方程、解析近似方法、二叉树方法、有限差分方法和Monte-Carlo模拟等。

Based on the modem FEM with the dynamic substructure method, itd dynamic equation is established with almost no limits to DOFs of the system, in which the left side is the first approach of the nonlinear system and the right side is the excitation and coupling nonlinear pseudo forces. The modal analysis method is used to get the eigen solution to the reduced linear homogeneous dynamic differential equation. When the system is excited by the harmonic excitation at the right side of the equation, the nonlinear dynamic response can be calculated by the numerical method to give quantitative analysis.

基于近代有限元和子结构模态综合法的动力学建模方法，获得非线性系统动力学微分方程，其自由度几乎没有限制，对左端首次近似齐次方程进行模态分析，选取对响应有贡献的部分本征对，同样对右端激励和非线性伪力作模态变换，得到减缩后非线性系统耦合动力学微分方程。

However, the solutions of the Cauchy problem of the nonlinear hyperbolic system generally develop singularities in finite time even if the initial data are small and smooth.For this reason, solutions must be found in the space of discontinuous functions. Therefore, one can not directly use the classical analytic techniques that predominate in the theory of partial differential equations of other types. Instead, we construct approximate solutions via the singular perturbation methods. By using the compactness of the approximate solutions, we can obtain the existence of the solutions of original system.

然而一般而言，即使是在初值很小且光滑的情况下，非线性双曲型守恒律的Cauchy问题的解在有限时间内也会出现奇异性，为此，我们必须在不连续函数空间中寻找上述问题的解，因此对这类问题的研究，我们也不可能直接利用在其它类型的偏微分方程中占主导地位的解析方法来解决问题，而是通过奇异扰动法构造近似解，由近似解的紧性得到原问题解的存在性。

Integral of one variable functions, improper integral and its convergence properties.

本课程的主要内容包括：1 各种极限运算，其中包括数列极限、函数极限以及上、下极限；2 一元函数的微分学，包括微分和导数的运算法则、微分中值定理及其应用等；3 一元函数的积分和广义积分及其收敛性；4 级数及其收敛性，包括数值级数的收敛性和函数项级数的各种运算和性质；5 多元函数的微分学及其应用，其中很多方面与一元函数的微分学近似，需要注意它们之间的区别；6 多元函数的积分学，包括多重积分的性质与计算，多重积分的的应用等；7 曲线、曲面积分及其应用；8 含参变量积分的计算与性质；9 Fourier 级数及其应用，等等。

Secondly, the effectiveness and limitation of the classical perturbation, such as the method of multiple scales and the Poincare-Lindstedt method, are discussed in detail through a Duffing oscillator with delayed velocity feedback. It is shown that the two perturbation methods are effective only in solving the approximate solution of the first two orders. An ambiguity or paradox will be encountered when they are used to seeking for the third or higher order approximation of solution.

其次，以一具有时滞速度反馈的Duffing系统为例，研究了经典摄动法如多尺度法，Poincaré-Lindstedt法等在求解时滞微分方程级数解时的适用性和局限性问题，指出利用这些方法只能有效求得系统的前两阶近似解，而在求系统的三次以上近似解时会出现矛盾或二义性。

A program based on four kinds of methods in thermal analysis is designed for finding out the mechanism of decomposition reaction of explosives and calculating their kinetic parameters. Compared with the Kissinger's method, the program here adopted has the advantage of exploring the reaction mechanism besieds a calculation of the kinetic parameters. Mechanism of decomposition of the explosive PYX was determined applying this program. The kinetic parameters of PYX calculated by non-isothermal integral meth...

以热分析理论为依据，摒弃了以往仅用一种热分析法进行反应动力学研究和近似假设─—炸药的热分解反应机理f＝（1—α）n所带来的弊病，采取4种热分析方法（等温积分法、等温微分法、非等温微分法、非等温积分法）相结合的方法，编制了计算程序，首先判断反应机理，然后求取动力学参数，用所编程序对PYX炸药的反应动力学进行了研究，用非等温法判断了PYX炸药的反应机理，并求得动力学参数，所求参数与Kissinger法求得的结果十分接近。

The finite difference time-domain method is stable and easy to be used, but due to the fact that it approximates the space derivatives in Maxwells curlequations by central difference, FDTD usually requires more than 20 grids perwavelength to achieve acceptable accuracy. As a contrast, pseudospectraltime-domain method approximates the space derivatives by pseudospectralmethod, which guarantees the accuracy, theoretically requiting only 2 grids perwavelength.

传统的电磁场数值算法——时域有限差分法稳定而易于实现，但由于FDTD采用中心差分近似Maxwell旋度方程的微分，每个波长上需要取的网格数通常较多，而时域伪谱法采用伪谱法求微分，理论上每个波长只需要取两个网格便可以达到较高的精度。

They are differentiated twice with approximate ideal differentiators to obtain the corrected accelerogram.

本文通过对数字强震仪系统使用的力平衡加速度计的仪器响应误差进行分析，提出了一个校正仪器响应失真的处理方法，即对未校正记录做低通滤波后运用近似理想微分器做两次微分得到校正加速度记录。

Do you know, i need you to come back

你知道吗，我需要你回来

Yang yinshu、Wang xiangsheng、Li decang,The first discovery of haemaphysalis conicinna.

1〕 杨银书，王祥生，李德昌。安徽省首次发现嗜群血蜱。