极大3限制边连通二部图的充分条件

设G=(V,E)是一个连通图.称一个边集合S■E是一个k限制边割,如果G-S的每个连通分支至少有k个顶点.称G的所有k限制边割中所含边数最少的边割的基数为G的k限制边连通度,记为λ_k(G).定义ξ_k(G)=min{[X,■]:|X|=k,G[X]连通,■=V(G)\X}.称图G是极大k限制边连通的,如果λ_k(G)=ξ_k(G).本文给出了围长为g>6的极大3限制边连通二部图的充分条件.     

一个R2上含双曲函数核的Hilbert型不等式

通过引入参数，构造了一个全平面上的、含双曲函数的非齐次核函数。利用正切函数的有理分式展开，建立了最佳常数因子与正切函数高阶导数相关联的Hilbert型积分不等式。 作为应用，通过赋予参数不同的值，建立了一些有意义的特殊结果。     

概率语言多属性群决策方法及其在新型智慧城市市民获得感评价中的应用

针对公众参与的语言信息多属性群决策问题，研究了考虑参与者满意度的概率语言多属性群决策方法。首先，根据参与者的语言评价信息确定并规范化概率语言决策矩阵。然后，对大群体进行共识分析，由最大化参与者群体的满意度构建线性规划模型，确定参与者群组的权重；构造正、负理想方案的评价向量，构建多目标规划模型，用拉格朗日乘子法求解属性权重；定义各方案的加权贴近度，并以此对方案进行排序和优选。最后，通过新型智慧城市市民获得感评价案例验证了模型的可行性和有效性。     

On generalized perfect difference sets constructed from Sidon sets

Let $\mathbb{N}$ be the set of positive integers. For a nonempty set A of integers and every integer u, denote by $d_A(u)$ the number of $(a,a^{\prime })$ with $a,a^{\prime }\in A$ such that $u=a-a^{\prime }$. For a sequence S of positive integers, let $S(x)$ be the counting function of S. The set $A\subseteq \mathbb{N}$ is called a perfect difference set if $d_A(u)=1$ for every positive integer u. In 2008, Cilleruelo and Nathanson (2008) [4] constructed dense perfect difference sets from dense Sidon sets. In this paper, as a main result, we prove that: let $f:\mathbb{N}\to \mathbb{N}$ be an increasing function satisfying $f(n)\ge 2$ for any positive integer n, then for every Sidon set B and every function $\omega (x)\to \infty$, there exists a set $A\subseteq \mathbb{N}$ such that $d_A(u)=f(u)$ for every positive integer u and $B(x/3)-\omega (x)\le A(x)\le B(x/3)+\omega (x)$ for all $x\ge C_{f,B,\omega }$.     

Existence of multiple and sign-changing solutions for a second-order nonlinear functional difference equation with periodic coefficients

In the present paper, we apply the method of invariant sets of descending flow to establish a series of criteria to ensure that a second-order nonlinear functional difference equation with periodic boundary conditions possesses at least one trivial solution and three nontrivial solutions. These nontrivial solutions consist of sign-changing solutions, positive solutions and negative solutions. Moreover, as an application of our theoretical results, an example is elaborated. Our results generalize and improve some existing ones.