一类线性互补问题解存在性判断的区间方法

利用目标函数的区间斜量,以Miranda定理为理论依据,将Moore-Kioustelidis定理推广到不可微情况,提出了一类线性互补问题解存在性判断的区间方法,给出了具体实例,表明这种判断方法是有效的.     

N-环Von-Neumann正则性

环R称为N-环,如果R的素根N(R)=｛r∈R｜存在自然数n使rⁿ=0}.本文不仅对N-环进行了刻划,而且还研究了N-环的VonNeumann正则性.特别证明了：对于N-环R,如下条件是等价的：(1)R是强正则环;(2)R是正则环;(3)R是左SP-环;(4)R是右SF-环;(5)R是MELT,左p-V-环;(6)R是MERT,右p-V-环.因此推广了文献[4]中几乎所有的重要结果,同时也改进或推广了其它某些有关正则环的有用结果.     

受迫Li\''{e}nard方程周期解的存在唯一性

本文利用整体反函数理论证明了受迫Li\'{e}nard方程$x'+f(x)x'+g(t,x)=e(t)$周期解的存在唯一性，推广和改进了现有的结果.     

Volterra型积分微分方程非线性边值问题

本文首先利用上、下解方法研究了一类Ｖｏｌｔｅｒｔａ型积分微分方程Ｄｉｒｉｃｈｌｅｔ问题和非线性边值问题的解的存在性；然后，利用所得到的微分不等式理论考虑一类相应的奇摄动非线性边值问题，获得包括边界层在内的一致有效渐近解的存在性。     

DECIMAL SET WITH ZERO MEASURE AND FULL HAUSDORFF DIMENSION

Let Fκ = {χ ε (0,1)｜{2^nχ} ≥ 1/2^κ,n ε Z }, Z = {0,1,2,3}, κ ε N;F = Uκ^∞=1Fκ be a decimal set in (0, 1), where {2^nχ} is the fractional part of a number 2^nχ. In this note, we prove that dimHF = 1 and H^1(F) =0, where dimH is Hausdr off dimension, and H^1(F) is the Hausdorff measure of F.     

广义IP-内射环

对环R,令ip(R_R)={a∈R：任意一个从R的右理想到R且象为aR的模同态能开拓到R}。众所周知,R为右IP-内射环当且仅当R=ip(R_R),R为右单-内射环当且仅当{a∈R：aR is simple)(?)ip(R_R)。对环R的一个子集S,我们引进了S-IP-内射环的概念,即满足S(?)ip(R_R)的环。并得到了这种环的一些性质。     

AN ITERATED-SUBSPACE MINIMIZATION METHODS WITH SYMMETRIC RANK-ONE UPDATING

We consider an Iterated-Subspace Minimization(ISM) method for solving large-scale unconstrained minimization problems.At each major iteration of the method, a two-dimensional manifold, the iterated subspace, is constructed and an approximate minimizer of the objective function in this manifold then determined, and a symmetric rank-one updating is used to solve the inner minimization problem.     

Hardy空间的等价刻画

设Ｇ为局部域Ｋ上的２ｎ＋１维Ｈｅｉｓｅｎｂｅｒｇ群．本文证明了通过各种极大函数定义的Ｈａｒｄｙ空间的等价性，给出了Ｈａｒｄｙ空间的原子分解．利用这些等价定义及一些卷积算子定理，给出了Ｈａｒｄｙ空间的平方函数刻画——Ｌｕｚｉｎ面积函数刻画与Ｌｉｔｌｅｗｏｏｄ－Ｐａｌｅｙ平方函数刻画     

拟相似集的Hausdorff测度的特征

Siegfried GRAF在文献［1］中给出了自相似集上的Hausdorff测度(简称H-测度)的特征.John McLaughlin在文献［2］中引入了拟相似集的概念,K.J.Falconer又在文献［3］中讨论了拟相似集上H-测度和维数的性质.本文研究拟相似集上的H-测度的特征,并得出在一定条件下支撑于其上满足一定条件的测度与H-测度的等价性条件.     

SCORE LISTS IN （h, k）-BIPARTITE HYPERTOURNAMENTS

Given non-negative integers m,n,h and k with m ≥ h ＞ 1 and n ≥ k ＞ 1, an (h, k)-bipartite hypertournament on m n vertices is a triple (U, V, A), where U and V are two sets of vertices with |U| = m and |V| = n, and A is a set of (h k)-tuples of vertices,called arcs, with at most h vertices from U and at most k vertices from V, such that for any h k subsets U1 ∪ V1 of U ∪ V, A contains exactly one of the (h k)! (h k)-tuples whose entries belong to U1 ∪ V1. Necessary and sufficient conditions for a pair of non-decreasing sequences of non-negative integers to be the losing score lists or score lists of some(h, k)-bipartite hypertournament are obtained.