微分

In Chapter Ⅲ, by considering functions H k that may not have nonpositive partial derivative on s and employing integral averaging technique and Hardy inequality, the oscillation for a class of high order nonlinear differential equations and high order nonlinear damped differential equations is discussed, new oscillation criteria are established.

第二章利用广义Riccati技巧、积分平均技巧以及微分不等式理论，讨论了一类二阶非线性常微分方程的振动性，得到了若干新的振动准则，并讨论了该方程具有强迫项时解的渐近性态。

Of the fundamental matrix in (2) satisfies the differential equation =A , it follows that the matrix = itself satisfies the matrix differential equation Because its column vectors are linearly independent, it also follows that the fundamental matrix is nonsingular, and therefore has inverse matrix .

基本矩阵的求解由于（2）中的基本矩阵的列向量满足微分方程A，进而这个矩阵本身就满足矩阵微分方程。

But most of these papers only considered the nonsingular case...

本章主要内容包括：在§1.1中，我们考虑了如下奇异四阶微分边值问题到目前为止，有关四阶微分边值问题已有不少文献，但大多数文献中作者只讨论了非线性项是非奇异的情形，很少有文献讨论奇异的情形。

A important result is the one-order expression of AR Yt = DYt-1 + E, from paralleling a high-order differential equation transformation into a one-order differential equation system, the one-order expression exposes that the AR is only a certain more-multivariable power series processAnd, if a process is described as an AR, the sufficient and necessary condition is the spectrum norm A of the coefficient matrix D less than one.

作者用高阶微分方程化一阶微分方程组的方法，获得多元弱平稳序列p阶自回归模型的一步滑动平均表达式，证明了AR的是一个更高维的幂级数的线性过程，从而，说明了AR关于序列依概率成立的充要条件是：该模型更高维的幂级数的线性过程的表达式中系数矩阵D的谱范数λ＜1。

Direct difference is sensitive to noisy data, so a threshold limitation is given, which can not only filter the result from noisy data but also pick edge points up according men's desire. On the other hand, artificial intelligence is used for segmentation in reverse engineering. Because the essence of segmentation is clustering similar characteristics and self-organizing feature mapping is one function of neural network, SOFM network is used for segmentation in the thesis, coordinates and normal of data points is took as the characteristics vector.

第二种方法，基于双向角度微分的边点提取法，针对三维正交模型采用基于截面线的方式组织数据，此方法比基于曲率半径方法更简洁，不用进行曲面拟合，大大提高了计算速度；计算过程中由数据点的直接差分逼近微分，但直接差分对数据误差敏感，为此，本文提出了阈值过滤的方法，一方面过滤了数据误差在计算结果中引起的噪音，另一方面可以按照设计意图控制边点的提取；来决定是否提取光滑交接的边点。

And the spectrum was divided into three regions, which were 430~100 nm, 1 000~1 800 nm, 430~1 800 nm, respectively. Four methods of spectrum data preprocessing were used, which were multiplicative scattering correction, standard normal variate, first derivative and second derivative.

应用多元散射校正，标准正态变量变换，一阶微分和二阶微分四种不同预处理方法，分别在430~1 000 nm、1 000~1 800 nm和430~1 800 nm三个光谱范围内建立识别脐橙污染程度的偏最小二乘法数学模型。

Character of solution of stochastic differential equation in dual of nuclear space was studied.

研究核空间的对偶空间的随机微分方程解的性质，得到微分方程组解 L 2收敛的条件，及在一定条件下解过程导出的测度{ Pn}为胎

IDFwas proposed recently to solve the problem in control.In this paper,we study the frequency characteristics of IDF,and then compare it with that of numerical differentiation and typical differentiator.

研究了IDF的频率特性，并与数值微分频率特性、典型微分环节的频率特性进行了比较，然后对其进行了误差分析。

The closed-form expressions are derived so that all required differentiations are obtained in closed form and numerical differentiation can be avoided.

特别是对微带和缝隙混合结构的空域MoM分析，旋度算子的微分在谱域进行，并可以给出它们的解析表达式，其对应的空域格林函数可通过高阶的Sommerfeld恒等式获得，从而避免了数值微分。

Therefore, numerical analysis has been duly noted and come up with a variety of numerical integration, numerical differentiation, as well as the numerical solution of differential equations, the calculation of the volume comes down to basic computing, which laid the foundation of modern computer based on the numerical algorithm.

于是，数值分析受到了重视，研究出各种数值积分，数值微分，以及微分方程数值解法，把计算过程归结为巨量的基本运算，从而奠定了现代计算机的数值算法基础。

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。