Abundant semigroups whose idempotents satisfy permutation identities

The aim of this paper is to study abundant semigroups whose idempotents satisfy permutation identities. After some properties are obtained, the quasi-spined product structure of such semigroups is established while some special cases are investigated. In particular, the structure ofPI-abundant semigroups is obtained.  

EXISTENCE RESULTS FOR SEMIPOSITONE BOUNDARY VALUE PROBLEMS

1 IntroductionWe consider the existence of positive solutions for the Sturm-Liouville boundary vaueproblemwhere f and e: [r, R x [0, oo) - R are two continuous functions satisfying:(H1) f(t, u) 2 0, for (t, u) 6 [r, R x [0, oo);(H2) There exists M > 0 such thatThe boundary value problem (l.1)-(1.2) arises iu a variety of different applied mathematicsand physics. We note that the well-known Proudmau equation(whicli was established by Proudman in 1926, see J. Proudman, Proc. London Math. …  

On congruence lattices of regular semigroups with Q-inverse transversals

Communicated by F. Pastijn  

图的邻点可区别全色数的一个上界

Let G = （V, E） be a simple connected graph, and ｜V（G）｜ ≥ 2. Let f be a mapping from V（G） ∪ E（G） to {1,2…, k}. If arbitary uv ∈ E（G）,f（u） ≠ f（v）,f（u） ≠ f（uv）,f（v） ≠ f（uv）; arbitary uv, uw ∈ E（G）（v ≠ w）, f（uv） ≠ f（uw）;arbitary uv ∈ E（G） and u ≠ v, C（u） ≠ C（v）, where
C（u）={f（u）}∪{f（uv）｜uv∈E（G）}.
Then f is called a k-adjacent-vertex-distinguishing-proper-total coloring of the graph G（k-AVDTC of G for short）. The number min{k｜k-AVDTC of G} is called the adjacent vertex-distinguishing total chromatic number and denoted by χat（G）. In this paper we prove that if △（G） is at least a particular constant and δ ≥32√△ln△, then χat（G） ≤ △（G） ＋ 10^26 ＋ 2√△ln△.  

最大度不小于5的外平面图的邻强边染色

图G(V,E)的一k-正常边染色叫做k-邻强边染色当且仅当对任意uv∈E(G)有,f[u]≠f[v],其中f[u]={f(uw)|uw∈E(G)},f(uw)表示边uw的染色.并且x'as(G)=min{k|存在k-图G的邻强边染色}叫做图G的图的邻强边色数.本文证明了对最大度不小于5的外平面图有△≤x'as(G)≤△ 1,且x'as(G)=△ 1当且仅当存在相邻的最大度点.  

Halin-图的邻强边染色

图G(V,E)的正常κ-边染色f叫做图G(V,E)的κ-邻强边染色当且仅当任意uv∈E(G)满足f[u]≠f[v],其中,f[u]={f(uw)|uw∈E(G)},称f是G的κ-临强边染色,简记为κ-ASEC.并且x′_as(G)=min{k|κ-ASEC of G}叫做G(V,E)的邻强边色数.本文研究了△(G)≥5的Halin-图的邻强边色数.  

一类连通无三角形图线图的共色数的下界

Erd(o)s,Gimbel and Straight (1990) conjectured that if ω(G)＜5 and z(G)＞3,then z(G)≥χ(G)-2. But by using the concept of edge cochromatic number it is proved that if G is the line graph of a connected triangle-free graph with ω(G)＜5 and G≠K4, then z(G)≥χ(G)-2.  

若干倍图的均匀全染色(英文)

如果图G的一个正常全染色满足任意两种颜色所染元素(点或边)数目相差不超过1,则称为G的均匀全染色,其所用最少染色数称为均匀全色数.本文得到了星、扇和轮的倍图的均匀全色数.  

Controllability of Semilinear Differential Systems with Nonlocal Initial Conditions in Banach Spaces

In this note, we establish a sufficient condition for the controllability of a first-order semilinear differential system with nonlocal initial conditions in Banach spaces. The approach used is the Sadovskii fixed-point theorem combined with operator semigroups. Particularly, the compactness of the operator semigroups is not needed in this article. Y.K. Chang was supported by Tianyuan Youth Fund of Mathematics in China (10826063), NNSF of China (10801065), the Scientific Research Fund of Gansu Provincial Education Department (20868), and Qing Lan Talent Engineering Funds (QL-05-16A) of Lanzhou Jiaotong University. J.J. Nieto was supported by Ministerio de Educacion y Ciencia-FEDER Project MTM2007-61724, and by Xunta de Galicia-FEDER Project PGIDIT05PXIC20702PN.  

齐次Morrey-Herz空间上粗糙核高阶交换子的有界性

在齐次Morrey-Herz空间上建立了由粗糙核算子T与BMO(R~n)函数生成的高阶交换子T_(b,m)的有界性.同时对Hardy-Littlewood极大粗糙算子和相应的分数次极大粗糙算子所生成的高阶交换子也得到了相应的结果.