Dirichlet零边值问题的正解存在性

由于一些本质困难,N=3被称为具Sobolev临界指数2*的Dirichlet问题-△u=λu+|u|2*-2u,x∈ΩRN;u(x)0,x∈Ω;u=0,x∈Ω的临界维数.众所周知,N=3时,上述问题存在古典(正)解的一个充分条件是Ω为R3上的小球以及14λ1λλ1.本文考虑Ω是R3中更一般的有界光滑区域,得出了一正解存在性结论,从而肯定了沈尧天在文中提及的一个未解决的问题.     

非扩张映像不动点新的简单逼近算法

提出了一个简单的非扩张映像不动点的逼近算法,该算法通过非迭代的逼近序列来实现.从算法的复杂性来看,提出的算法比经典的Mann迭代算法、Ishikawa迭代算法和Halpern迭代算法更简单.提出的算法紧密联系着非扩张映像不动点的存在性,因此,还得到了非扩张映像的新不动点定理, 拓展和改进了经典的Goebel-Kirk,Kim-Xu等作者的结果.     

围长为2的偶数阶本原极小强连通有向图的1一指数集

本文研究了围长为2的n阶本原极小强连通有向图的1-指数集,证明了：当n（≥4）为偶数时,E（1）={4,5,6,7,…,2n-4）,无缺数段。     

具有非局部时滞的扩散Nicholson苍蝇方程的波前解

研究了具有非局部时滞的扩散Nicholson苍蝇方程,其中时滞由一个定义在所有过去时间和整个一维空间区域上的积分卷积表示.当时滞核是强生成核时,根据线性链式技巧和几何奇异扰动理论,获得了小时滞时波前解的存在性.     

Asymptotically optimal neighbour sum distinguishing colourings of graphs

Consider a simple graph G = (V,E) and its proper edge colouring c with the elements of the set {1,2,…,k}. The colouring c is said to be neighbour sum distinguishing if for every pair of vertices u, v adjacent in G, the sum of colours of the edges incident with u is distinct from the corresponding sum for v. The smallest integer k for which such colouring exists is known as the neighbour sum distinguishing index of a graph and denoted by . The definition of this parameter, which makes sense for graphs containing no isolated edges, immediately implies that , where Δ is the maximum degree of G. On the other hand, it was conjectured by Flandrin et al. that for all those graphs, except for C₅. We prove this bound to be asymptotically correct by showing that . The main idea of our argument relays on a random assignment of the colours, where the choice for every edge is biased by so called attractors, randomly assigned to the vertices. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 776–791, 2015     

Estimation of rating classes and default probabilities in credit risk models with dependencies

Let Y = m(X) + ε be a regression model with a dichotomous output Y and a one‐step regression function m . In the literature, estimators for the three parameters of m , that is, the breakpoint θ and the levels a and b , are proposed for independent and identically distributed (i.i.d.) observations. We show that these standard estimators also work in a non‐i.i.d. framework, that is, that they are strongly consistent under mild conditions. For that purpose, we use a linear one‐factor model for the input X and a Bernoulli mixture model for the output Y . The estimators for the split point and the risk levels are applied to a problem arising in credit rating systems. In particular, we divide the range of individuals' creditworthiness into two groups. The first group has a higher probability of default and the second group has a lower one. We also stress connections between the standard estimator for the cutoff θ and concepts prevalent in credit risk modeling, for example, receiver operating characteristic. Copyright © 2014 John Wiley & Sons, Ltd.     

Neighbor Distinguishing Edge Colorings Via the Combinatorial Nullstellensatz Revisited

Consider a simple graph and its proper edge coloring c with the elements of the set . We say that c is neighbor set distinguishing (or adjacent strong) if for every edge , the set of colors incident with u is distinct from the set of colors incident with v. Let us then consider a stronger requirement and suppose we wish to distinguishing adjacent vertices by sums of their incident colors. In both problems the challenging conjectures presume that such colorings exist for any graph G containing no isolated edges if only . We prove that in both problems is sufficient. The proof is based on the Combinatorial Nullstellensatz, applied in the “sum environment.” In fact the identical bound also holds if we use any set of k real numbers instead of as edge colors, and the same is true in list versions of the both concepts. In particular, we therefore obtain that lists of length ( in fact) are sufficient for planar graphs.     

END样本最近邻密度估计的强相合速度

本文研究了扩展负相依(END)样本最近邻密度估计的强相合性问题.利用END序列的Bernstein型不等式和截尾的方法,获得了END样本最近邻密度估计的强相合速度,推广了NA样本和ND样本最近邻密度估计的相应结果.     

一些图的Mycielski图的均匀邻强边染色

如果图G的一个正常边染色满足相邻点的色集不同,且任意两种颜色所染边数目相差不超过1,则称为均匀邻强边染色,其所用最少染色数称为均匀邻强边色数.本文得到了路、圈、星和扇的Mycielski图的均匀邻强边色数.     

三维Boussinesq方程组大解的全局L~2稳定性

对三维有界及无界区域上的Boussinesq方程的全局L~2稳定性进行了讨论.在解满足适当的条件下,证明了此解为稳定的,并得出此稳定性条件的等价性条件,最后得出了二维Boussinesq方程组在三维扰动下的解的全局存在性和稳定性.