Riemann boundary value problem for harmonic functions in Clifford analysis

In this article, we mainly deal with the boundary value problem for harmonic function with values in Clifford algebra: where is a Liapunov surface in , the Dirac operator , are unknown functions with values in a universal Clifford algebra Under some assumptions, we show that the boundary value problem is solvable.     

Fast structured LU factorization for nonsymmetric matrices

In this paper, an approximate LU factorization algorithm is developed for nonsymmetric matrices based on the hierarchically semiseparable matrix techniques. It utilizes a technique involving orthogonal transformations and approximations to avoid the explicit computation of the Schur complement in each factorization step. A modified compression method is further developed for the case when some diagonal blocks have small singular values. The complexity of the methods proposed in this paper is analyzed and shown to be $O(N^2k)$ , where $N$ is the dimension of matrix and $k$ is the maximum off-diagonal (numerical) rank. Depending on the accuracy and efficiency requirements in the approximation, this factorization can be used either as a direct solver or a preconditioner. Numerical results from applications are included to show the efficiency of our method.     

基于模糊TOPSIS法的职业选择定量分析

由于职业选择受多种因素的影响,且许多因素又具有模糊不确定性,单纯地从定性的角度无法准确清晰地进行选择判断.为解决这一问题,本文运用模糊TOPSIS法对职业选择问题进行定量分析.首先,从个人兴趣爱好、单位的工资收入水平、地理位置、单位性质、发展前景、继续深造的条件和机会、发展机会等,建立职业选择的评价指标体系;然后,采用模糊集理论与专家综合评判相结合的方法求出模糊评价指标的概率并给出所有评价指标的权数;接着,以模糊数学和传统TOPSIS(逼近理想解的排序法)法为基础,建立职业选择评价方法;最后,以某大学生职业选择为例,验证该评价方法的有效性.结果表明,运用模糊TOPSIS法对职业选择定量分析是可行的.     

Congruences for broken 3-diamond and 7 dots bracelet partitions

Andrews and Paule introduced broken k-diamond partitions by using MacMahon’s partition analysis. Later, Fu found a generalization which he called k dots bracelet partitions. In this paper, with the aid of Farkas and Kra’s partition theorem and a p-dissection identity of f(?q), we derive many congruences for broken 3-diamond partitions and 7 dots bracelet partitions.     

Geometric and topological rigidity for compact submanifolds of odd dimension

We investigate rigidity problems for odd-dimensional compact submanifolds.We show that if Mn(n 5)is an odd-dimensional compact submanifold with parallel mean curvature in Sn+p,and if RicM(n-2-1n)(1+H2)and Hδn,whereδn is an explicit positive constant depending only on n,then M is a totally umbilical sphere.Here H is the mean curvature of M.Moreover,we prove that if Mn(n 5)is an odd-dimensional compact submanifold in the space form Fn+p(c)with c 0,and if RicM(n-2-εn)(c+H2),whereεn is an explicit positive constant depending only on n,then M is homeomorphic to a sphere.     

Morrey global bounds and quasilinear Riccati type equations below the natural exponent

We obtain global bounds in Lorentz–Morrey spaces for gradients of solutions to a class of quasilinear elliptic equations with low integrability data. The results are then applied to obtain sharp existence results in the framework of Morrey spaces for Riccati type equations with a gradient source term having growths below the natural exponent of the operator involved. A special feature of our results is that they hold under a very general assumption on the nonlinear structure, and under a mild natural restriction on the boundary of the ground domain.     

Characterizations of Strength Extremal Graphs

With graphs considered as natural models for many network design problems, edge connectivity κ′(G) and maximum number of edge-disjoint spanning trees τ(G) of a graph G have been used as measures for reliability and strength in communication networks modeled as graph G (see Cunningham, in J ACM 32:549–561, 1985; Matula, in Proceedings of 28th Symposium Foundations of Computer Science, pp 249–251, 1987, among others). Mader (Math Ann 191:21–28, 1971) and Matula (J Appl Math 22:459–480, 1972) introduced the maximum subgraph edge connectivity \({\overline{\kappa'}(G) = {\rm max} \{\kappa'(H) : H {\rm is} \, {\rm a} \, {\rm subgraph} \, {\rm of} G \}}\) . Motivated by their applications in network design and by the established inequalities $$\overline{\kappa'}(G) \ge \kappa'(G) \ge \tau(G),$$ we present the following in this paper:

1. For each integer k > 0, a characterization for graphs G with the property that \({\overline{\kappa'}(G) \le k}\) but for any edge e not in G, \({\overline{\kappa'}(G + e) \ge k+1}\) .
2. For any integer n > 0, a characterization for graphs G with |V(G)| = n such that κ′(G) = τ(G) with |E(G)| minimized.

     

On the O(1/t) convergence rate of the projection and contraction methods for variational inequalities with Lipschitz continuous monotone operators

Nemirovski’s analysis (SIAM J. Optim. 15:229–251, 2005) indicates that the extragradient method has the O(1/t) convergence rate for variational inequalities with Lipschitz continuous monotone operators. For the same problems, in the last decades, a class of Fejér monotone projection and contraction methods is developed. Until now, only convergence results are available to these projection and contraction methods, though the numerical experiments indicate that they always outperform the extragradient method. The reason is that the former benefits from the ‘optimal’ step size in the contraction sense. In this paper, we prove the convergence rate under a unified conceptual framework, which includes the projection and contraction methods as special cases and thus perfects the theory of the existing projection and contraction methods. Preliminary numerical results demonstrate that the projection and contraction methods converge twice faster than the extragradient method.     

Customized proximal point algorithms for linearly constrained convex minimization and saddle-point problems: a unified approach

This paper focuses on some customized applications of the proximal point algorithm (PPA) to two classes of problems: the convex minimization problem with linear constraints and a generic or separable objective function, and a saddle-point problem. We treat these two classes of problems uniformly by a mixed variational inequality, and show how the application of PPA with customized metric proximal parameters can yield favorable algorithms which are able to make use of the models’ structures effectively. Our customized PPA revisit turns out to unify some algorithms including some existing ones in the literature and some new ones to be proposed. From the PPA perspective, we establish the global convergence and a worst-case O(1/t) convergence rate for this series of algorithms in a unified way.     

基于系数相关性的自适应水印算法

根据人类视觉特征提出了一种基于小波系数相关性的自适应水印嵌入算法.该算法先对原始图像进行的小波分解,选取水印所要嵌入的子带并将所选取的子带划分成2×2大小的块,同时利用每一个小波块中相邻的4个系数之间具有一定的相关性与所要嵌入的水印图像来构造该小波块的水印系数,利用人类视觉模型调整水印的嵌入强度,从而在保证水印不可见性的基础上最大限度的保证水印的鲁棒性.选取不同特点的两幅图片进行实验,实验结果表明,该算法对高斯噪声、椒盐噪声、JPEG压缩、剪切、中值滤波等攻击都具有较好的鲁棒性,对旋转几何攻击具有一定的鲁棒性.