无公害害虫治理策略的数学研究

首先应用状态脉冲反馈控制的理论,建立了无公害害虫治理中的数学模型,并且对所建的模型进行定性分析,利用微分方程几何理论中后续函数法得到系统的阶一周期解存在的充分条件,证明该周期解是轨道渐近稳定的,同时利用数值模拟的手段讨论了系统在害虫治理中的应用意义.  

A note on the rate of returns in random walks

For one-dimensional simple symmetric random walks, we prove that the irregular set associated with the rate of returns to the origin is residual.  

Optimal partial regularity of second order parabolic systems under controllable growth condition

We consider the regularity for weak solutions of second order nonlinear parabolic systems under controllable growth condition, and obtain a general criterion for a weak solution to be regular in the neighborhood of a given point. In particular, we get the optimal regularity by the method of A-caloric approximation introduced by Duzaar and Mingione.  

The Vietoris topology on rectifiable spaces

A topological space G is said to be a rectifiable space provided that there are a surjective homeomorphism φ:G×G→G×G and an element e∈G such that π ₁°φ=π ₁ and for every x∈G we have φ(x,x)=(x,e), where π ₁:G×G→G is the projection to the first coordinate. Let G be a rectifiable space and C(G) be the family of all non-empty compact subsets of G. In this paper, we study the Vietoris topology on C(G), and show that if G is a locally compact rectifiable space, then (C(G),?) together with the Vietoris topology is a topological semi-right loop.  

Eigenvalue problems on Riemannian manifolds with a modified Ricci tensor

In this paper, we study the eigenvalue problems on a Riemannian manifold with a modified Ricci tensor. We obtain some sharp lower bound estimates for the first eigenvalue of Laplacian. We also prove some rigidity theorems for the Riemannian manifold with some suitable conditions.  

On the Laplacian, signless Laplacian and normalized Laplacian characteristic polynomials of a graph

The Laplacian, signless Laplacian and normalized Laplacian characteristic polynomials of a graph are the characteristic polynomials of its Laplacian matrix, signless Laplacian matrix and normalized Laplacian matrix, respectively. In this paper, we mainly derive six reduction procedures on the Laplacian, signless Laplacian and normalized Laplacian characteristic polynomials of a graph which can be used to construct larger Laplacian, signless Laplacian and normalized Laplacian cospectral graphs, respectively.  

置换性很好的一类群

主要研究子群置换性质对有限群结构的影响.通过子群的置换性得到一类群，即B 群.B群是全可置换群的扩展，利用全可置换群的p次中心扩张和子群的阶得到B群的一些性质并对B 群的结构进行一些刻画.应用B 群的结构得到有限p （p〉2）群为二元生成的B 群的充要条件.  

Fault-free Hamiltonian cycles passing through a prescribed linear forest in 3-ary n-cube with faulty edges

The k-ary n-cube Qkn （n ≥2 and k ≥3） is one of the most popular interconnection networks. In this paper, we consider the problem of a fault- free Hamiltonian cycle passing through a prescribed linear forest （i.e., pairwise vertex-disjoint paths） in the 3-ary n-cube Qn^3 with faulty edges. The following result is obtained. Let E0 （≠θ） be a linear forest and F （≠θ） be a set of faulty edges in Q3 such that E0∩ F = 0 and ｜E0｜ ＋｜F｜ ≤ 2n - 2. Then all edges of E0 lie on a Hamiltonian cycle in Qn^3- F, and the upper bound 2n - 2 is sharp.  

γ-klee-图的Hamilton-连通性和着色

一个r-klee-图递归定义为一个r＋1阶完全图或者通过用一个r阶完全图替换已知的r-klee-图G′中的一个顶点所得到的图.本文主要研究了r-klee-图的Hamilton-连通性和着色问题.我们证明了：每一个r-klee-图是Hamilton-连通的和它的色数是r;如果r是奇数,则它的边色数是r;如果r是偶数,则它的边色数是r＋1.  

单圈图上Abelian沙堆模型的雪崩大小（英文）

研究图上Abelian沙堆模型问题.首先给出关于沙堆模型常返构型的极大雪崩序列,然后刻画了一些雪崩性质.基于这些性质,我们确定了单圈图的基本雪崩中每个顶点的topplings数及它的雪崩多项式,推广了R.Cori的结果.