关于Mori整环的$w$-全局变换环的注记

Let R be a domain and let Rwg be the w-global transform of R. In this note it is shown that if R is a Mori domain, then the t-dimension formula t-dim（Rwg） = t-dim（R） - 1 holds.     

平环和的Heegaard亏格的一个下界

Let Mi, i = 1,2, be a compact orientable 3-manifold, and Ai an incompressible annulus on a component Fi of OMi. Suppose A1 is separating on F1 and A2 is non-separating on F2. Let M be the annulus sum of M1 and M2 along A1 and A2. In the present paper, we give a lower bound for the genus of the annulus sum M in the condition of the Heegaard distances of the submanifolds M1 and M2     

非双倍测度下的Marcinkiewicz积分的加权估计

Let μ be a nonnegative Radon measure on R d which satisfies the growth condition μ(B(x,r)) ≤ C0rn for all x ∈Rd and r >0,where C0 is a fixed constant and 0相似文献   

用拉普拉斯谱半径定序给定阶和匹配数的树

Let T（n,i） be the set of all trees with order n and matching number i.We determine the third to sixth trees in T（2i ＋ 1,i） and the third to fifth trees in T（n,i） for n ≥ 2i ＋ 2 with the largest Laplacian spectral radius.     

沿着不连通曲面的Heegaard分解的不可稳定化的融合积

Let M be a 3-manifold, F= {F1 , F2 , . . . , Fn } be a collection of essential closed surfaces in M (for any i, j ∈ {1, ..., n}, ifi≠j, Fi is not parallel to Fj and Fi ∩Fj = φ) and0 M be a collection of components of M. Suppose M-UFi ∈FFi×(-1, 1) contains k components M1 , M2 , . . . , Mk . If each M i has a Heegaard splitting ViUSiWi with d(Si) > 4(g(M1 ) + ··· + g(Mk )), then any minimal Heegaard splitting of M relative to 0M is obtained by doing amalgamations and self-amalgamations from minimal Heegaard splittings or -stabilization of minimal Heegaard splittings of M1 , M2 , . . . , Mk .     

辛代数的极大幂零子代数的保李括积零的线性映射

Let F be a field with char F = 2, l a maximal nilpotent subalgebra of the symplectic algebra sp（2m,F）. In this paper, we characterize linear maps of l which preserve zero Lie brackets in both directions. It is shown that for m ≥ 4, a map φ of l preserves zero Lie brackets in both directions if and only if φ = ψcσT0λαφdηf, where ψc,σT0,λα,φd,ηf are the standard maps preserving zero Lie brackets in both directions.     

von Neumann代数交叉积的注记

设A是B(H)中的极大交换*-子代数, G是离散群,在不要求G自由地作用在A的情况下,得到了交叉积A×αG是因子的充分且必要条件.     

代数自由积上的线性泛函的延拓

本文研究了C^＊-代数及其＊-稠子代数的＊-代数自由积．利用自由积的性质，得到了这两类自由积上的线性泛函到C^＊-代数（泛）自由积上的态延拓的充要条件，从而证明了这类延拓对于一般的C^＊-代数也是成立的．     

半覆盖远离性质与有限群的结构

In this paper,the so-called π-cover-avoiding properties of subgroups are defined and investigated.In terms of this property,we characterize the π-solvability of finite groups.Some other new results are also obtained based on the assumption that some subgroups have the semi cover-avoiding properties in a finite group.     

固定悬挂点的三圈图的无号拉普拉斯谱半径

In this paper,we determine the unique graph with the largest signless Laplacian spectral radius among all the tricyclic graphs with n vertices and k pendant vertices.     

关于核型$C^{*}$代数单调积的注记

Given two nuclear C^＊-algebras A1 and A2 with states φ1 and φ2, we show that the monotone product C^＊-algebra A1 △→ A2 is still nuclear. Furthermore, if both the states φ1 and φ2 are faithful, then the monotone product ,A1 △→ A2 is nuclear if and only if the C^＊-algebras ,A1 and A2 both are nuclear.     

给定最大度的树的最大谱半径

In this paper, we characterize the trees with the largest Laplacian and adjacency spectral radii among all trees with fixed number of vertices and fixed maximal degree, respectively.     

图的无符号拉普拉斯和距离无符号拉普拉斯特征值

Let G be a simple graph. We first show that ■, where δiand di denote the i-th signless Laplacian eigenvalue and the i-th degree of vertex in G, respectively.Suppose G is a simple and connected graph, then some inequalities on the distance signless Laplacian eigenvalues are obtained by deleting some vertices and some edges from G. In addition, for the distance signless Laplacian spectral radius ρQ(G), we determine the extremal graphs with the minimum ρQ(G) among the trees with given diameter, the unicyclic and bicyclic graphs with given girth, respectively.     

二次极大子群皆是$PSC^{*}$-群的有限群

This paper discusses the influence of minimal subgroups on the structure of finite groups and gives the structures of finite groups all of whose second maximal subgroups are PSC^＊-groups.     

图的距离无符号拉普拉斯谱半径的关于色数的下界

Let G be a connected graph on n vertices with chromatic number k, and let ρ(G)be the distance signless Laplacian spectral radius of G. We show that ρ(G) ≥ 2n + 2「n k」- 4,with equality if and only if G is a regular Tur′an graph.     

A Note on Maximal Inequality for Stochastic Convolutions

Using unitary dilations we give a very simple proof of the maximal inequality for a stochastic convolution

极大非独立集可削去的因子临界图

如果对一个简单图G的每一个与G的顶点数同奇偶的独立集I，都有G-I有完美匹配，则称G是独立集可削去的因子临界图．如果图G不是独立集可削去的因子临界图，而对任意两个小相邻的顶点x与y，G xy足独立集可削去的因子临界图，则称G足极大非独立集可削去的因子临界图，本刻画了极大非独立集可削去的因子临界图。     

$C^*$-代数上可加Jordan左$*$-导子的刻画

设$\delta$是一个$*$-代数$\mathcal A$到其左$\mathcal A$-模$\mathcal M$的可加映射, 如果对任意$A\in\mathcal A$, 有$\delta(A^2)=A\delta(A)+A^*\delta(A)$, 则称$\delta$~是一个可加Jordan左$*$-导子. 在本文中, 我们证明了复的单位$C^*$- 代数到其Banach左模的每个可加Jordan左$*$-导子都恒等于零. 设$G\in\mathcal A$, 如果对任意$A,B\in \mathcal A$, 当$AB=G$时, 有$\delta(AB)=A\delta(B)+B^*\delta(A)$, 则称$\delta$在$G$处左$*$-可导. 我们证明了复的单位$C^*$-代数到其Banach左模的在单位点处左$*$-可导的连续可加映射恒等于零.