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本文主要研究了单位球笛卡尔积作为约束的优化问题,给出了此类问题的最优性条件.同时将求解此问题的一些经典的梯度算法推广到了更加一般的形式,并证明了新算法的收敛性.随机二次规划问题和求解图像变分去噪模型的数值结果表明新算法并不弱于一些经典的算法,特别是在精度要求较高的情形下.
We prove global regularity of solutions of Oldroyd-B equations in 2 spatial dimensions with spatial di usion of the polymeric stresses.
We give an example of a well posed, nite energy, 2D incompressible active scalar equation with the same scaling as the surface quasi-geostrophic equation and prove that it can produce nite time sing...
This paper considers the three dimensional Muskat problem in the stable regime.We obtain a conservation law which provides an L2 maximum principle for the uid interface. We also show global in time ex...
用Schauder不动点定理研究分数阶三点边值问题:〖FC(〗Dα0+u(t)+f(t,u(t))+e(t)=0,0
We consider mixed integer linear programs defined by two equations involving two integer variables and non-negative continuous variables. The non-trivial facet-defining inequalities of such problems c...
The problem of spin-0 and spin-1 bosons in the background of a general mixing of minimal and nonminimal vector inversely linear potentials is explored in a unified way in the context of the Duffin-Ke...
BGG-equations are geometric overdetermined systems of PDEs on parabolic geometries. Normal solutions of BGG-equations are particularly interesting and we give a simple formula for the necessary and su...
We use geometric methods to study two natural two-component generalizations of the periodic Camassa–Holm and Degasperis–Procesi equations.
分形几何学     分形几何学  维数  分形理论       2005/8/25
分形几何学的基本思想是:客观事物具有自相似的层次结构,局部与整体在形态、功能、信息、时间、空间等方面具有统计意义上的相似性,成为自相似性。例如,一块磁铁中的每一部分都像整体一样具有南北两极,不断分割下去,每一部分都具有和整体磁铁相同的磁场。这种自相似的层次结构,适当的放大或缩小几何尺寸,整个结构不变。

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