若干圈的广义冠图的2-强边染色

本文研究了圈的广义冠图CmFn,CmWn,CmCn的2-强边染色(D(2)-点可区别边染色).利用穷染、递推的方法得到了CmFn,CmWn,CmCn的2-强边色数(D(2)-点可区别边色数),并给出一种染色方案,推广了参考文献[6,7]的相应结果.     

The maximum and minimum degrees of random bipartite multigraphs

In this paper the authors generalize the classic random bipartite graph model, and define a model of the random bipartite multigraphs as follows:let m = m（n） be a positive integer-valued function on n and ζ（n,m;{pk}） the probability space consisting of all the labeled bipartite multigraphs with two vertex sets A ={a₁,a₂,...,a_n} and B = {b₁,b₂,...,b_m}, in which the numbers t_ai,b_j of the edges between any two vertices a_i∈A and b_j∈ B are identically distributed independent random variables with distribution P{t_ai,b_j=k}=pk,k=0,1,2,...,where pk ≥0 and ∞Σk=0 pk=1. They obtain that X_c,d,A, the number of vertices in A with degree between c and d of G_n,m∈ζ（n, m;{pk}） has asymptotically Poisson distribution, and answer the following two questions about the space ζ（n,m;{pk}） with {pk} having geometric distribution, binomial distribution and Poisson distribution, respectively. Under which condition for {pk} can there be a function D（n） such that almost every random multigraph G_n,m∈ζ（n,m;{pk}） has maximum degree D（n）in A? under which condition for {pk} has almost every multigraph G（n,m）∈ζ（n,m;{pk}） a unique vertex of maximum degree in A?     

一类具有非局部扩散的时滞Lotka-Volterra竞争模型的行波解

本文研究一类具有非局部扩散的时滞Lotka-Volterra竞争模型{(δ)/(δ)t u1(x,t)=d1 [(J1*u1)(x,t)-u1(x,t)]+r1u1(x,t)[1 - a1u1(x,t)- b1u1(x,t-Τ1)-c1u2(x,t-Τ2)],(δ)/(δ)tu2(x,t)=d2[(J2*u2)(x,t)-u2(x,t)]+r2u2(x,t)[1 - a2u2(x,t)- b2u2(x,t -Τ3)-c2u1(x,t-Τ4)]行波解的存在性问题.通过利用交叉迭代技巧,我们可以把行波解的存在性转化为寻找一对适当的上下解,这篇文章中的结果推广了已有的一些结果.     

半线性抛物方程在L2p空间中全局吸引子的存在性

本文研究了半线性抛物方程所生成的半群{S（t）}t≥0的吸引子的存在性.利用文献[1]中证明吸引子正则性的思想,分别得到半群{S（t）}t≥0在L^2p（Ω）空间中具有一个有界吸收集和一个全局吸引子.     

利用分裂Bregman方法的图像恢复组合模型

ROF模型是图像恢复中的经典模型,具有保留图像边缘的优点,但同时也存在梯子现象.而利用二次范数fΩ｜▽u｜2 dxdy的模型可以避免梯子现象,但容易使图像变得模糊.针对两种方法的优缺点,提出了一种新的通过设置边缘检测开关函数的组合模型,在图像平坦区利用二次范数模型处理,而在强边缘处利用ROF模型处理,而且应用分裂的Br...     

集值映射的对称向量拟均衡问题

研究向量集值映射的拟均衡问题的有效解,利用数值化方法与不动点定理,得到解的存在性定理.作为应用,得到广义向量鞍点,向量变分不等式与向量互补问题的存在性定理.     

A NOTE ON GENERALIZED ABSOLUTE SUMMABILITY FACTORS FOR A TRIANGULAR MATRIX

In this paper, a general theorem on | A, δ |k -summability factors of infinite series is proved under different conditions.     

SOME EXACT SOLUTIONS OF 3-DIMENSIONAL ZERO-PRESSURE GAS DYNAMICS SYSTEM

The 3-dimensional zero-pressure gas dynamics system appears in the modeling for the large scale structure formation in the universe. The aim of this paper is to construct spherically symmetric solutions to the system. The radial component of the velocity and density satisfy a simpler one dimensional problem. First we construct explicit solutions of this one dimensional case with initial and boundary conditions. Then we get special radial solutions with different behaviours at the origin.     

The ergodicity of stochastic generalized porous media equations with lévy jump

In this article,we first prove the existence and uniqueness of the solution to the stochastic generalized porous medium equation perturbed by Lévy process,and then show the exponential convergence of(pt)t≥0 to equilibrium uniform on any bounded subset in H.     

基于GARCH类模型和SV类模型的沪深两市波动性研究

以CSMAR数据库2007年2月27日至2008年5月14日共297个交易日的上证综指和深证综指的收盘价数据为研究对象,通过比较5类GARCH模型和两类SV模型对上证综指和深证综指样本内(2007年2月27日至2008年2月27日)收益率波动特征的描述能力以及样本外(2008年2月28日至2008年5月14日)收益率波动的预测能力,得出GARCH类模型相比SV类模型更适合描述中国证券市场的波动性.