A Robust Algorithm for Blind Total Variation Restoration

Image restoration is a fundamental problem in image processing. Blind image restoration has a great value in its practical application. However, it is not an easy problem to solve due to its complexity and difficulty. In this paper, we combine our robust algorithm for known blur operator with an alternating minimization implicit iterative scheme to deal with blind deconvolution problem, recover the image and identify the point spread function（PSF）. The only assumption needed is satisfy the practical physical sense. Numerical experiments demonstrate that this minimization algorithm is efficient and robust over a wide range of PSF and have almost the same results compared with known PSF algorithm.     

Classical Risk Model with Threshold Dividend Strategy

In this article, a threshold dividend strategy is used for classical risk model. Under this dividend strategy, certain probability of ruin, which occurs in case of constant barrier strategy, is avoided. Using the strong Markov property of the surplus process and the distribution of the deficit in classical risk model, the survival probability for this model is derived, which is more direct than that in Asmussen（2000, P195, Proposition 1.10）. The occupation time of non-dividend of this model is also discussed by means of Martingale method.     

解析Toeplitz算子的强不可约性

本文得到解析Toeplitz算子的强不可约性的一个充分条件，并且刻画了换位代数的k0-群．     

粗糙集代数与MV代数

讨论粗糙集代数与MV代数的关系以及由粗糙集代数构造MV代数的方法.粗糙集代数本身具有格结构,证明了在适当选取蕴涵及乘积运算之后,粗糙集代数就成为MV代数.     

（n-3）-Filiform李代数的极大环面

求出了（n-3）-filiform李代数的极大环面，并证明了（n-3）-filiform李代数是可完备化的．     

中立型延迟微分方程一般线性方法的非线性稳定性

本文研究一类非线性中立型延迟微分方程一般线性方法的数值稳定性.证明了一般线性方法为(k,p,O)-代数稳定时,在一定的约束条件下,其数值解保持微分方程理论解的稳定性质,特别是证明了在约束网格情形代数靛的-般线性方法能无条件保持解析解的稳定性.     

线性中立型单延迟系统李代数稳定性判据

研究了线性中立型单延迟微分系统的稳定性.从矩阵李代数可解性角度,推导出新的简单的延迟独立稳定性判据.该新判据的重要意义和优越性在于首次突破了以往大多数相关文献的稳定性判据在应用上受条件‖C‖<1,ρ(|C|)<1或ρ(|N|)<1的限制,从而首次成功确定了在‖C‖≥,ρ(|C|)≥1和ρ(|N|)≥1的情形下中立型延迟微分系统渐近稳定性.最后,通过两个例子显示了新判据的优越性.     

空间向量、夹角与距离

1．重、难点分析 引入向量研究几何是几何代数化的需要．它一方面能使我们了解一些近代数学知识．开拓视野；另一方面，为解决立体几何中某些用传统的纯几何方法解决时技巧性大、随机性强的问题提供一些通法，降低了解题难度．     

(h,ψ)-广义单调与(h,ψ)-广义凸

本文定义了几种(h,ψ)-广义凸性及(h,ψ)-广义单调性,讨论了广义(h,ψ)-方向导数与Clarke方向导数,广义(h,ψ)-梯度集与Clarke梯度集等的相关关系.利用此关系证明了这些广义凸性与广义单调性之间的相关关系,同时还揭示了这些广义凸性、单调性与通常广义凸性、单调性存在的内在联系.