上微分

In the chapter 3,we base on the existence of periodic solution ,using the method of linearization and applying the mean value theorem and the variation-of-constants formula, we get the sufficient condition of the exponential stability of periodic solution of a class of nonlinear functional differential system .

在第三章中，建立在系统周期解存在的基础上，利用线性化的方法，根据微分中值定理和常量变差公式，得到了一类非线性泛函微分系统周期解指数稳定的充分条件。

Based on the existence of the " mean point s"in Differential mean value Theorem,This paper futher studies the problem of the number of the " mean point s" in Differential mean value Theorem.

在微分中值定理"中值点"存在的基础上，进一步研究微分中值定理"中值点"的个数问题。

Multistep method is the first method applied to DAEs.Because of some reasonsin history,all algorighms for DAEs come from those for stiff ODEs,mainly thebackward difference formula.

多步法是最早用于直接求解微分代数方程的方法，由于历史上的原因，长期以来使用的公式都是由刚性常微分方程的求解公式导出的，主要是向后差分公式。

The noise frequency modulation signal was particularly analyzed. The Fokker-Planck equation of noise frequency modulation was presented and the Motion-Group Fourier Transform was used by converting the partial differential equation into the variable coefficient homogenous linear differential equations. Then the solutions were given by using the peano-baker series. So the probability density function of noise frequency modulation in the filter was given. On the basis of the probability density function the stochastic resonance of noise frequency modulation signal is analyzed.

首先建立了噪声调频干扰信号通过脉冲压缩雷达中频滤波器后所满足的福克尔－普朗克方程，然后利用群移傅立叶变换（Motion-Group Fourier Transform，MGFT）将此偏微分方程化成了变系数齐次线性微分方程组，并利用Peano-Baker级数法给出了该方程组的解，最后得到了噪声调频干扰信号通过脉冲压缩雷达中频滤波器后的概率密度函数，在此基础上研究了噪声调频干扰信号造成的随机共振现象。

The paper puts forward a proposal on the basis of its differentiation model to distinguish plumule grains in rice mass.

利用计算机视觉系统，研究大米胚芽的自动识别方法，在分析大米的表面积及轮廓线的二次微分曲线基础上，提出利用大米微分模型识别群体胚芽米的留胚率的设想

The main results are:(1) the L1 boundedness of the Cesaro means operator of the harmonic expansions on the unit sphere with reflection-invariant measures is proved, and the characterization of the convergence index is given; for the points not in the planes with singularities, the pointwise convergence is also proved; these results are the generalizations of those both for the classical spherical harmonic expansions and for the Jacobi expansions;(2) Using the differential-reflection operators of Dunkl type, the uncertainty principle of a class of Sturm-Liouville operators is established, and as consequences, the uncertainty principles of some well-known classical orthogonal expansions such as Jacobi, Hermite and Laguerre expansions are obtained;(3) by introducing the Cauchy-Riemann equations in terms of the differential-reflection operators of two variables, the harmonic analysis of the extended Jacobi expansions is studied; the results include the Lp boundedness and the weak-L1 boundedness of the conjugate extended Jacobi expansions; specially, for some indexes p smaller than 1, the basic theory of the related Hardy spaces is established.

主要成果有：（1）证明了带有反射不变测度的球面调和展开蔡沙罗平均算子的L1有界性，给出了收敛指标的特征刻划，对不在奇性平面上的点，还证明了点态收敛性，这些成果同时推广了经典球面调和展开和雅可比展开的结果；（2）利用Dunkl型的微分-反射算子建立了一类斯特姆-刘威尔算子的测不准原理，并由此得到一些著名的经典正交展开如雅克比展开、赫米特展开和拉盖尔展开的测不准原理；（3）利用由两个变量的微分-反射算子定义的柯西-黎曼方程组来研究扩展雅克比展开的调和分析，证明了共轭扩展雅克比展开的Lp有界性和弱L1有界性，特别是对小于1的一些指标p，建立了相应的哈代空间的基本理论。

Based on structuring a quotient space,consisting of pairs of convex compact sets,this paper discusses the uniqueness of quasidifferential of quasidifferentiable function.

本文在构造凸紧集对商空间的基础上，讨论了拟可微函数拟微分的唯一性，指出拟微分的表示可以不唯一。

Numerical integral method is applied in this paper to study this problem, hoping to provide a reliable, yet simple numerical model for the application in the ocean disposal of waster water.Compared with other numerical model, momentum integral method is simple.

其思想是建立在流动自相似假定的基础上，使流动的控制微分方程简化成常微分方程，并以边界条件使方程封闭，从而结合定解条件来预报浮射流的流动特性，如流速和浓度的分稚规律。

Firstly, we give out a reduction way for quasilinear generalized system A〓=G , and the concept of the index κ geometrically nonsingularity, where A is singular and of smooth kernal space. By using the canonical projection mappings onto the space of ker A , a class singular pointimpasse point only owned by nonlinear generalized system is also studied and we also prove that the regular index κ quasilinear generaized system A〓=G defined on the region W is equivalent with an ODEs 〓 defined on a submanifold W〓 of the W, so we reduce the problem of quasilinear generalized system to the problem of an ODEs.

首先利用投影函数，给出了拟线性广义系统A〓=G的一种归约方法，提出了指数κ几何非奇异的概念，同时对广义系统特有的一类奇点-寂点进行了研究，证明了正则指数κ的拟线性问题A〓=G等价于在其定义域W中某一个子流形W〓上的正常微分方程〓，从而将拟线性广义系统的问题归结为常微分方程问题。

By comparison with some traditional differentiation methods, such as divided differences, by-hand coding and symbolic differentiation, AD is characterized by a lot of virtues, e.g., truncation error free, less running cost and less human labor required.

比起传统意义上的计算微分方法来，自动微分具有计算精度高、计算代价小及投入人力少等优点。

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。