高校应用数学学报第15卷(2000年)B辑(英文版)第4期目次和提要

无环多重图的最大亏格的下界李德明 (首都师大数学系 )　刘彦佩 (北方交通大学数学系 )依照无环多重图的连通度 ,得到了它们的最大亏格的下界 .这不仅回答了 Chen,Archdeacon和 Gross的问题 ,也推广了现有结果 .这样 ,无环多重图的最大亏格的下界问题便有了完满的结论 .3 -连通无环多重图的最大亏格的紧下界李德明 (首都师大数学系 )　刘彦佩 (北方交通大学数学系 )证明了如果圈秩大于等于 1 0 ,3 -连通无环多重图的最大亏格至少是三分之一圈秩加一 ,有无限多个 3 -连通无环多重图的最大亏格取到这一下界 .具分段常变元的时滞微分方程的振…     

关于除环的伪理想

M.K.Sen于1976年推广环的理想概念,定义了伪理想,并用依理想来研究除环、域和正则环。侯国荣1983年又推广伪理想,建立n—伪理想,得到了更好的结果。本文则证明了:非交换除环和有限域无真伪理想,因而文关于除环的几乎全部结果都是平凡的。我们还证明了非交换除环无真n—伪理想,给出了有限域无真n—伪理想的充分必要条件。文中讨论了无限域的伪理想,得到了关于除环结构的几个有用结果。     

流的Birkhoff中心及Ω稳定性条件

首先对紧度量空间上的连续流论证了滤子的存在性与无环性的关系,并给出了Birkhoff中心是非游荡集的一个充分条件;然后对流形上的C1流证明了:Birkhoff中心双曲+无环条件公理A+无环条件,因而它是Ω稳定的.     

Amitsur定理和Regev定理的推广

本文将PI一环论中关于恒等式和中心多项式的Amitsur定理和Regev定理同时由域推广到无零因子环,得到无零因子环上全矩阵环的两个相应定理。     

关于RC-正则环（英文）

我们利用related单位正则无刻画了正则环的比较结构，进而把文[2]定理中的related单位元推广到了related单位正则无，并给出了RC－正则环的一个局部特征．     

有根无环平面地图节点剖分计数方程

一个平面地图,如果无有边是环,则称为是无环的.有根的意义与[1]中的相同.在那里对于此类地图的一些计数问题作了研究,但从未触及到节点剖分.这篇文章的主要目的在于研究这类地图的依节点剖分的计数.求出了有根无环平面地图依节点剖分计数的母函数所满足的一个泛函方程.并且,作为这一方程的一种应用,求出了一类在节点的最大次给定情况下的有根无环平面地图依节点剖分计数的一些结果.     

半环上保持矩阵{1}-逆的线性算子

刻画了某类特殊可换无零因子反环上保持矩阵{1}一逆的可逆线性算子,并将此结果推广到此类无零因子反环的任意直积上．推广了某些文献的一些结果．     

Г-环的单位元与其算子环的单位元之间的关系

г—环的单位元是其算子环中的元素.本文探讨Г—的单位与其算子环的单位元之间的关系.举例表明存在Г—环(Г_N—环)M,它的左、右算子环均有单位元,而M既无左单位元,又无右单位元.那么在什么条件下,Г—环(Г_N—环)的左、右算子环具有单位元时,其本身必定具有左、右单位元呢?对Г—环和Г_N—环分别探讨了此问题,并给出了了解答此问题的充要条件.     

环并半环

称环的无交并组成的半环为环并半环. 环并半环的全体形成一个簇B, 它包含了环和幂等元半环. 特别地, 它包含了分配格簇. 给出了环并半环的若干结构定理, 进一步, 借此揭示了B的子簇格的结构.     

仅有局部单位元环上的范畴对偶

［１］讨论了在无单位元环上的范畴等价，本文讨论无单位无环上的范畴对偶。     

数有根近2-正则平面地图

The number of rooted nearly 2-regular maps with the valency of root-vertex, the number of non-rooted vertices and the valency of root-face as three parameters is obtained. Furthermore, the explicit expressions of the special cases including loopless nearly 2-regular maps and simple nearly 2-regular maps in terms of the above three parameters are derived.     

Multigraph realizations of degree sequences: Maximization is easy, minimization is hard

The following minimization problem is shown to be NP-hard: Given a graphic degree sequence, find a realization of this degree sequence as loopless multigraph that minimizes the number of edges in the underlying support graph. The corresponding maximization problem is known to be solvable in polynomial time.     

Maximum k-colorable subgraphs

A lower bound is established on the number of edges in a maximum k-colorable subgraph of a loopless graph G. For the special case of 3-regular graphs, lower bounds are also determined on the maximum number of edges in a bipartite subgraph whose color classes are of equal size.     

LOWER BOUNDS ON THE MAXIMUM GENUS OF LOOPLESS MULTIGRAPHS

§ 1　IntroductionThe maximum genusγM(G) of a graph G is the maximum among the genera,which Ghas a cellularembedding on a sphere with k handles.Since any embedding of G has atleastone face,by Euler polyhedral equation,itcan be obtained thatγM(G)≤β(G) / 2 ,whereβ(G) is the Betti number of G.A graph G is called up-embeddable ifγM(G) =β(G) / 2 .[1 ] has showed that thereare atleasttwo edge-disjointspanning trees in G if G is 4 -edge connected.Let T be a span-ning tree of G.An odd …     

Generating a Gray Code for P-Sequences

P-sequences are used for coding binary trees and they are also an alternative representation for well-formed parentheses strings. We present here the first Gray code and loopless generating algorithm for P-sequences, and extend them in a Gray code and a new loopless generating algorithm for well-formed parentheses strings. Ranking and unranking algorithms are also discussed.     

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.     

3-连通无环多重图的最大亏格的紧下界

It is proved that every 3-connected loopless multigraph has maximum genus at least one-third of its cycle rank plus one if its cycle rank is not less than ten, and if its cycle rank is less than ten,it is upper-embeddable. This lower bound is tight. There are infinitely many 3-connected loopless multigraphs attaining this bound.     

A TIGHT LOWER BOUND ON THE MAXIMUM GENUS OF A 3-CONNECTED LOOPLESS MULTIGRAPH

§ 1　 IntroductionA loopless multigraph is a graph having multiple edges but no loops.A multiple ver-tex is a vertex incident with multiple edges.A cubic graph is a graph,each of whose ver-tices is3-valent.A cut-vertex is a vertex of G which will disconnect the graph G if itis re-moved from G.A vertex set C with k vertices is a k-vertex cut setif G-C is disconnectedwhen C is removed.A graph G is k-connected if for any h相似文献   

Enumeration of loopless maps on the projective plane

In this paper we study the rooted loopless maps on the sphere and the projective plane with the valency of root-face and the number of edges as parameters. Explicit expression of enumerating function is obtained for such maps on the sphere and the projective plane. A parametric expression of the generating function is obtained for such maps on the projective plane, from which asymptotic evaluations are derived.     

Loopless Generation of Linear Extensions of a Poset

Canfield and Williamson gave the first loopless algorithm for generating all linear extensions of a poset. It elegantly generates all signed extensions, resulting in each extension appearing somewhere with each sign, but retains only every other one independent of its sign. It uses an array for the extension. In this paper we give another loopless algorithm for generating all the linear extensions. It generates each extension only once and uses a list for the extensions.