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Thismethod adopted affine transformation model and a Lie derivative-based analytical algorithm.We introduced the process and characters in extracting information of biological visionsystem, studied the feasibility of the generalized Gabor function used as receptive fieldfunction in extracting information and analyzed affine transformation group and Liederivatives. Finally, we deduced the mathematical denotation for Lie derivatives, i.e. theinfinitesimal generator of the geometric distortion in affine transformation.

对生物视觉信息提取的过程及特点进行了介绍,其中主要研究了广义Gabor函数作为感受野函数提取初级视觉信息的可行性;对仿射变换作为外界图像信息在视觉成像系统上的投影模型的原理进行了初步讨论;对Lie变换群微分算子用于提取仿射变换不变量的分析方法作了剖析,并推导了该方法中关键部分——仿射变换Lie微分算子的具体表达式,也就是几何变形无限小微分算子的计算表达式,使下一步编程实现该方法成为可能。

Its primary coverage includes: Function and limit, derivative and differential, theorem of mean and derivative application, indefinite integral, definite integral and application, space analytic geometry and vector algebra, function of many variables differential method and application, multiple integral and curvilinear integral, infinite series, differential equation and so on.

其主要内容有:函数与极限,导数与微分,中值定理与导数应用,不定积分,定积分及其应用,空间解析几何与矢量代数,多元函数的微分法及其应用,重积分与曲线积分,无穷级数,微分方程等。

Firstly, using strategy of introducing associated auxiliary equation to a givenpartial differential equation without admitting Lagrangian, we make the extendedequations possess a variational principle. Based on this, the concepts of extendedconservation law and extended symmetry to given partial differential equationare put forwarded.

首先,我们给出了引入伴随方程扩充原方程的策略,使给定偏微分方程的扩充方程组具有对应泛函,即称为Lagrange系统的方法,以此为基础提出了作为偏微分方程传统守恒律和对称概念的一种推广—偏微分方程扩充对称和扩充守恒律的概念;其次,先给出以得到的Lagrange系统为基础,利用N?

The differential characteristic set for differential polynomial system maintains the essential character of original differential polynomial system.

微分多项式系统的微分特征列集保留了原微分多项式组的本质特征,具有三角化良序结构等优点,能够克服不同领域问题中的一些困难。

Finally, we put forward the concept of differential characteristic set modulo with respect to a polynomial and present the properties of the characteristic set.

最后,对微分特征列集理论进行了推广,给出了微分多项式系统的模微分特征列集的概念,并研究了其具有的性质。

As an application of continuous wavelet transform,we discuss the relationsbetween some differemtial equaltions and the integral equations by using thecontinuous wavelet transform in 〓,vector function space andabstract function space respectively;prove that they are equivalent not only in theweak topology but also in the strong topology.

作为连续小波变换的应用,分别利用〓上的,多元函数空间上的,向量函数空间上的和抽象函数空间上的连续小波变换分别得到了某些线性微分方程,某些线性偏微分方程,某些向量线性微分方程和某些抽象函数的微分方程分别等价于其相应的积分方程,证明了它们不仅在弱收敛意义下而且在范数收敛意义下是等价的。

By constructing different quotient spaces,using the method of symplectic geometry,the self-adjoint extensions of symmetric differential operators in the direct sum spaces for the different deficiency indices at(2,2)singular points was discussed. The classification and description of complete Lagrangian submanifold that correspond with self-adjoint domains of second order differential operators were given.

由于对称微分算子在端点处的亏指数取值情况不同,当微分算子在端点处的亏指数均取(2, 2)时,通过构造商空间,应用辛几何的方法讨论了直和空间的对称微分算子的自共轭扩张问题,并给出了与二阶微分算子自共轭域相对应的完全Lagrangian子流型的分类与描述。

For the second order inclusion, using the transformation of variable, the existence of nonoscillatory solutions can be reduced to the existence of solutions for a first order inclusion.

在引进了微分包含解的振动性和非振动性的定义之后,通过分析解的单调性给出了一类二阶包含解的渐近性和振动性的判别准则;对于一阶微分包含,首先证明了时滞微分方程的振动性定理,在此基础上给出微分包含的结果。

Our recent works of PDE-based image processing on electronic speckle pattern interferometry are reviewed,including performing contrast enhancement and denoising simultaneously for ESPI fringes,proposing new oriented PDE denoising models for dense ESPI fringes and a nearly preprocessing-free method for skeletonization of gray scale ESPI fringes.

回顾了近几年偏微分方程图像处理技术在电子散斑干涉条纹处理中的应用成果,包括应用偏微分方程图像处理方法同时实现电子散斑干涉条纹图和相位图的滤波和增强处理,提出用于密集电子散斑干涉条纹处理的方向偏微分方程模型及提取电子散斑干涉条纹骨架线的偏微分方程方法。

Based on ODEs and FDEs, some definitions about the stability of delayed differential inclusions are introduced.

这些结果是常微分方程、泛函微分方程以及微分包含稳定性理论的推广和完善,在某种意义下填补了时滞微分包含稳定性理论的一些空白。

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