无环多重图的最大亏格的下界

The lower bounds on the maximum genus of loopless graphs are obtained according to the connectivity of these graphs. This not only answers a question of Chen, Archdeacon and Gross, but also generalizes the previous known results. Thus, a picture of the lower bounds on the maximum genus of loopless multigraphs is presented.     

7个经典Ramsey数R(k,l)的新下界

利用构造性的方法,得到7个经典Ramsey数的新下界R(3,29)≥174,R(4,23)≥272,R(5,24)≥488,R(7,12)≥312,R(8,18)≥728,R(8,20)≥860,R(9,21)≥1278.     

A lower bound for linear forms in values of a continued fraction

Let y = y(x) be a function defined by a continued fraction. A lower bound for |Λ| = |β ₁ y ₁ + β ₂ y ₂ + α| is given, where y ₁ = y(x ₁), y ₂ = y(x ₂), x ₁ and x ₂ are positive integers, α, β ₁ and β ₂ are algebraic irrational numbers.     

On the Clique-Transversal Number in （Claw,K4）-Free 4-Regular Graphs

A clique-transversal set D of a graph G is a set of vertices of G such that D meets all cliques of G.The clique-transversal number,denoted by τC(G),is the minimum cardinality of a clique-transversal set in G.In this paper,we first present a lower bound on τC(G) and characterize the extremal graphs achieving the lower bound for a connected(claw,K4)-free 4-regular graph G.Furthermore,we show that for any 2-connected(claw,K4)-free 4-regular graph G of order n,its clique-transversal number equals to [n/3].     

锥中调和函数的下界及其应用

本文首先给出锥中一类调和函数的下界,所得结果推广了张艳慧、邓冠铁和高洁欣在半空间中的相关结论;作为应用,接着证明了锥中的Levin型定理;最后,给出了锥中Dirichlet问题解积分表示形式的唯一性定理.     

Roper-Suffridge算子上的偏差定理下界估计的简单证明

Liczberski-Starkov first found a lower bound for ||D(f)|| near the origin, where is the Roper-Suffridge operator on the unit ball Bn in Cn and F is a normalized convex function on the unit disk. Later, Liczberski-Starkov and Hamada-Kohr proved the lower bound holds on the whole unit ball using a complex computation. Here we provide a rather short and easy proof for the lower bound. Similarly, when F is a normalized starlike function on the unit disk, a lower bound of ||D(f)|| is obtained again.     

Lower bounds of the topological entropy for nonautonomous dynamical systems

In this paper, lower bounds of the topological entropy for nonautonomous dynamical systems are given via the growths of topological complexity in fundamental group and in degree.     

图的最大亏格、支配数和围长

一个连图G的最大亏格γM（G）=（β（G）-ξ（G）/2,其中β（G）=E（G）-V（G 1是G的圈秩,ξ（G）是G的Betti亏数,本文利用G的支配数和围长给出了G的Betti亏数ξ（G）的一个上界,从而也给出了最大亏格γ（M（G）的一个下界,而且它是可达的,对于某些图类,该下界比黄元秋（2000）所给下界更好。     

一类拟线性抛物型方程解的爆破时间的下界

本文巧妙应用广义Sobolev不等式,研究了一类拟线性抛物型方程解的爆破时间的下界,该结果推广了文献[1]中的定理2.1和定理3.1的结论,同样完善了文献[2]中的模型(4.1)的结论.     

一类反应扩散方程的爆破时间下界估计

该文讨论了一类反应项为非线性非局部热源且热汇具有时间系数的反应扩散方程,分别在Dirichlet、Neumann或Robin边界条件下,在有界区域中的爆破行为.若解可能在有限时间发生爆破,通过构造合适的辅助函数,对时间系数给出适当的条件,利用Sobolev、H?lder不等式及Payne和Schaefer积分不等式等技巧,得出了解的爆破时间下界的估计.