微分

For composite foundation with compressible piles, based on displacement harmony condition, and combining with load transfer method and approximate solution of differential equation, analysis methods of linear and nonlinear interaction between piles and surrounding soil were suggested.

对柔性桩复合地基，是基于位移协调条件，并结合荷载传递法与微分方程的近似解法——子域法，提出了变截面自由单桩与地基土、刚性承台下柔性单桩和变截面柔性单桩与地基土、刚性承台下柔性群桩与地基土线性及非线性相互作用的分析方法，并得到有效桩长、桩与基土的荷载分配及刚性承台下各桩桩项荷载分配、荷载—沉降关系、荷载传递规律等有意义的结果。

This section presents two kinds of characteristic schemes, one is the natural use of the usual backward Euler characteristic difference scheme ( [60] ) onto the triangular mesh, the other replaces the backward Euler's method by modified Euler formula to approximate the characteristic differential equation, so that the discretization for characteristic curve can get up to second order accuracy.

本节给出了两种三角形网格上的特征差分格式，第一种是通常的向后Euler型特征差分格式（[60]）在三角形网格上的自然运用，第二种采用§3.3、§3.4的离散思想，使用改进的Euler公式代替向后Euler公式来近似特征微分方程，使其对特征线的离散达到了二阶精度。

Without presuming the activation functions to be continuous, bounded and monotone nondecreasing, by utilizing linear matrix inequality and Cellina approximate selection theory in differential inclusion, a sufficient condition is provided to ensure existence of periodic solutions for that recurrent neural networks.

在并不要求激励函数连续、有界及单调非减的情况下，通过利用线性矩阵不等式和微分包含中的Cellina近似选择定理，得到了该神经网络模型存在周期解的充分条件。

The basic concept in these sections is replacing backward Euler's method by modified backward Eulers's method to approximate the characteristic differential equation and discretizing the convection-diffusion equation at the middle point of the approximate characteristic curve, which will make the convective term get up to second order accuracy.

这三节的基本离散方法是用改进的Euler公式代替向后Euler公式来近似特征微分方程，并且将近似特征线的中点作为离散节点，使得对流项的离散精度提高到二阶，对于扩散项，将其转移到待求时间层进行离散。

Firstly, the isotropic difference templates were introduced to approximate the differential in the ADI-FDTD method, and the weighting coefficients of difference terms were determined for implementing isotropic numerical dispersion; Then the permittivity and permeability were adjusted manually to reduce the numerical dispersion error in any directions. Therefore the simulation accuracy and efficiency can be improved effectively for time domain problems with some finite bandwidths.

该方法在ADI-FDTD方法的差分近似微分中引入各向同性差分模板，并通过确定各向同性差分的加权系数来近似实现各向同性，然后人为修正空间的介质参数来减少各个方向上的数值色散误差，因此在模拟一定带宽的时域问题时可有效提高计算精度和计算效率。

Homotopy perturbation method; MOL method; nonlinear partial differential equation; approximate solution

基础科学，数学，数学分析同伦摄动法；直线法；非线性偏微分方程；近似解

For composite foundation with compressible piles, based on displacement harmony condition, and combining with load transfer method and approximate solution of differential equation, analysis methods of linear and nonlinear interaction between piles and surrounding soil were suggested. A lot of significative results, for example availability pile length, load distribution between piles and surrounding soil, load distribution among all piles under rigidity pile-cap, load-settlement relation etc, were obtained.

对柔性桩复合地基，是基于位移协调条件，并结合荷载传递法与微分方程的近似解法—子域法，提出了变截面自由单桩与地基土、刚性承台下柔性单桩和变截面柔性单桩与地基土、刚性承台下柔性群桩与地基土线性及非线性相互作用的分析方法，并得到有效桩长、桩与基土的荷载分配及刚性承台下各桩桩顶荷载分配、荷载一沉降关系、荷载传递规律等有意义的结果。

The basic idea is to set a continuous solution of the region with a finite number of discrete points instead of a grid consisting of, these discrete points called grid nodes the solution of a continuous area on a given function of continuous variables used in the definition of discrete grid variable function approximation the original equation and boundary conditions in the micro-business operators to approximate differential, integral with the points and to approximate, so the original differential equations and boundary conditions are replaced by algebraic equations near Side, that is, finite difference equations , solve this equation group can get the original problem in discrete points on the approximate solution.

基本思想是把连续的定解区域用有限个离散点构成的网格来代替，这些离散点称作网格的节点；把连续定解区域上的连续变量的函数用在网格上定义的离散变量函数来近似；把原方程和定解条件中的微商用差商来近似，积分用积分和来近似，于是原微分方程和定解条件就近似地代之以代数方程组，即有限差分方程组，解此方程组就可以得到原问题在离散点上的近似解。

Considering the pitch deviation, pitch accumulative deviation, flank angle deviation and their combined influence on the pitch diameter, the authors present a complete differential optimal approximate model in this paper and use the ideal thread to approximate the actual thread radially and axially.

本文建立的螺纹中径当量全微分优化逼近模型，考虑了螺距偏差、螺距累积偏差和半角偏差本身及其相互间对中径的综合影响，并用理想螺纹在径向和轴向二维逼近实际螺纹。

In this paper, we study an approximate solution of the second-order linear ordinary differential equations with variable coefficients .

本文研究了二阶变系数线性常微分方程的一种近似求解方法。

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。