Mesh-dependent stability for finite element approximations of parabolic equations with mass lumping

In this paper, based on some mesh-dependent estimates on the extreme eigenvalues of a general finite element system defined on a simplicial mesh, novel and sharp bounds on the permissible time step size are derived for the mass lumping finite element approximations of parabolic equations. The bounds are dependent not only on the mesh size but also on the mesh shape. These results provide guidance to the stability of numerical solutions of parabolic problems in relation to the unstructured geometric meshing. Numerical experiments on both uniform meshes and adaptive meshes are presented to validate the theoretical analysis.     

基于方向信息测度的图像边缘检测

边缘检测是图像处理中—个重要的研究课题．针对传统图像边缘检测算法对噪声敏感的问题,本文在分析图像像素灰度信息的基础上,建立了—个改进的确定方向信息测度的方法,并利用震动滤波对边缘检测图像进行增强,该方法在滤除噪声的同时,能有效地保留图像的基本目标信息,正确提取图像的边缘．     

Equitable edge‐colorings of simple graphs

An edge‐coloring of a graph G is equitable if, for each v∈V(G), the number of edges colored with any one color incident with v differs from the number of edges colored with any other color incident with v by at most one. A new sufficient condition for equitable edge‐colorings of simple graphs is obtained. This result covers the previous results, which are due to Hilton and de Werra, verifies a conjecture made by Hilton recently, and substantially extends it to a more general class of graphs. © 2010 Wiley Periodicals, Inc. J Graph Theory 66:175‐197, 2011     

The existence of a 2‐factor in K1, n‐free graphs with large connectivity and large edge‐connectivity

In this article, we study the existence of a 2‐factor in a K_{1, n}‐free graph. Sumner [J London Math Soc 13 (1976), 351–359] proved that for n?4, an (n?1)‐connected K_{1, n}‐free graph of even order has a 1‐factor. On the other hand, for every pair of integers m and n with m?n?4, there exist infinitely many (n?2)‐connected K_{1, n}‐free graphs of even order and minimum degree at least m which have no 1‐factor. This implies that the connectivity condition of Sumner's result is sharp, and we cannot guarantee the existence of a 1‐factor by imposing a large minimum degree. On the other hand, Ota and Tokuda [J Graph Theory 22 (1996), 59–64] proved that for n?3, every K_{1, n}‐free graph of minimum degree at least 2n?2 has a 2‐factor, regardless of its connectivity. They also gave examples showing that their minimum degree condition is sharp. But all of them have bridges. These suggest that the effects of connectivity, edge‐connectivity and minimum degree to the existence of a 2‐factor in a K_{1, n}‐free graph are more complicated than those to the existence of a 1‐factor. In this article, we clarify these effects by giving sharp minimum degree conditions for a K_{1, n}‐free graph with a given connectivity or edge‐connectivity to have a 2‐factor. Copyright © 2010 Wiley Periodicals, Inc. J Graph Theory 68:77‐89, 2011     

Finding Δ(Σ) for a surface σ of characteristic χ(Σ) = −5

For each surface Σ, we define Δ(Σ) = max{Δ(G)|Gis a class two graph of maximum degree Δ(G) that can be embedded in Σ}. Hence, Vizing's Planar Graph Conjecture can be restated as Δ(Σ) = 5 if Σ is a plane. In this paper, we show that Δ(Σ) = 9 if Σ is a surface of characteristic χ(Σ) = ?5. © 2010 Wiley Periodicals, Inc. J Graph Theory 68:148‐168, 2011     

Linear restrictions and two step least squares with applications

In this paper we consider the full rank regression model with arbitrary covariance matrix: Y = Xß + ε. It is shown that the effect of restricting the information Y to T = A′Y may be analyzed through an associatedi regression problem which is amenable to solution by two step least squares. The results are applied to the important case of missing observations, where some classical results are rederived.     

对称群上Cayley图的连通性

本文研究限制性边连通度的λ′-原子．运用所得结果可以证明Cayley图C(Sn,S)是最优超-λ的．这里Sn是n次对称群,S是若干由奇置换构成的共轭类的并，另外，我们还证明了C(Sn，S)是Vosperian的．除非它是完全二部图．     

秩协方差分析及应用

吴占鹏．秩协方差分析及应用．数理统计与管理，１９９８，１７（３），７～１０．在随机区组试验中，区组内往往存在土壤梯度差异，使试验误差增大。为此，本文提出秩协方差分析方法，即把土壤差异εｉｊ分解成Δ·ｘｉｊ和δｉｊ两个成份，从中剔除土壤梯度差异Δ·ｘｉｊ对试验精度的影响，以提高试验结果的可靠性     

后台阶流动的数值模拟

访述了大涡模拟的基本思想，指出大涡模拟的效率主要取决于四个因素，即流动中须有大尺度涡存在、合理的计算格式、合适的滤波器和亚格子应力模型。在深入考虑粘性不可压缩流Navier—Stokes方程各个子项作用的基础上，提出二阶全展开Euler—Taylor—Galerkin有限元方法作为大涡模拟的离散格式，并采用Gauss滤波器，对典型算例——后台阶处的流动进行大涡模拟，计算结果与相关文献符合的很好。从计算结果还可以看出大涡模拟与二阶全展开ETG有限元方法的结合在捕捉涡系及反映涡动时变过程方面具有明显的优势，说明大涡模拟适合于边界几何形状复杂区域流动的模拟。同时应用二阶全展开ETG有限元方法对低雷诺数粘性不可压缩后台阶流动进行了计算，得到与相关文献符合良好的计算结果，即该方法也可独立用于对低雷诺数粘性不可压缩流动的计算。