一类核具有连续横截面变换半群的秩

设X_n={1,2,…,n}并赋予自然数序,MCK_n是X_n上核具有连续横截面保序或反序变换所构成的半群.K_n是MCK_n的最大正则子半群.本文将考虑K_n的理想K(n,r)={α∈K_n:|im(α)|≤r}(3≤r≤n-1).证明了K(n,r)的秩为(n-r+1)(n-r+2)(n-r+3)/6.     

全相似保序变换半群H(SPO_n,r)的秩

设自然数n≥5,X_n={1,2,…,n},并赋予自然数的大小顺序,令H(SPO_n,r)=SPO_n∪L(n,r)(5≤n,2≤r≤n-3)是X_n上的全相似部分保序变换半群.得到全相似保序变换半群H(SPO_n,r)的秩为■.     

半群P_n(k)的正则性和Green关系

设P_n是X_n={1,…,n}上的部分变换半群.对任意1≤k≤n,令P_n(k)={α∈P_n:(x∈dom(α)x≤k■xα≤k},则易验证P_n(k)是P_n的子半群.刻画了半群P_n(k)的正则元的特征,并且描述了这个半群上的Green关系.     

OI_n的理想K(n,r)的极大逆子半群

Xn为n元有限集,OIn为Xn上的一切保序严格部分一一变换半群.记K(n,r)={α∈OIn∶|Tmα|≤r}(0≤r≤n-1)则K(n,r)(0≤r≤n-1)是OIn的理想.我们刻划了K(n,r)(1≤r≤n-1)的极大逆子半群.     

半群CDO_n的每个星理想的秩和相关秩

研究的CDOn是自然序集X_n={1,2,3,…,n}(n≥4)上的保序且保压缩或保反序且保压缩有限奇异变换半群,记K_D~*(n,r)={α∈CDO_n:|Imα|≤r}为半群CDOn的双边星理想.对1≤r≤n一1,刻划了K_D~*(n,r)是由秩为r的元素生成的且当r=1时,rank(K_D~*(n,r))=n;当2≤r≤n一1时,rank(K_D~*(n,r))=C_(n-1)~(r-1).进一步证明了当l=r时,r(K_D~*(n,r),K_D~*(n,l))=0且当1≤lr时,r(K_D~*(n,r),K_D~*(n,l))=C_(n-1)~(r-1)     

半群PO_(n,r)的秩

设POn为Xn上的保序部分变换半群.对任意的2≤r≤n一1,考虑半群PO_(n,r)={α∈PO_n:Im(α)■[r]}([r]={1,2,…,r}),证明了PO_(n,r)的秩为Σn-1k=r(nk)((k-1)(r-1))+r-1.     

半群CSPO_n中星理想的秩和相关秩

设自然数n≥4,CSPO_n是有限链[n]上的严格部分保序且压缩奇异变换半群.对任意的r(0≤r≤n-1),记N_P~*(n,r)={α∈CSPO_n:|Im(α)|≤r}为半群CSPO_n的双边星理想.通过对秩为r的元素和星格林关系的分析,分别获得了半群N_P~*(n,r)的极小生成集和秩.进一步确定了当0≤l≤r时,半群N_P~*(n,r)关于其星理想N_P~*(n,l)的相关秩.     

半群OF_n(Y)的幂等元秩

设OT(X_n)是X_n={1,2,…,n}上的保序变换半群.Y是X_n的非空真子集且|Y|=r,令OT(X_n,Y)={α∈OT(X_n):X_nα?Y},OF(X_n,Y)={α∈OT(X_n,Y):X_nα=Yα}.考虑半群OF_n(Y)={α∈OF(X_n,Y):|im(α)|≤r-1},证明了半群OF_n(Y)是由幂等元生成,并得到了OF_n(Y)的幂等元秩.     

半群OI_n(k)的秩

设OI_n是[n]上的保序严格部分一一变换半群.对任意1≤k≤n-1,研究半群OI_n(k)={α∈OI_n:(■x∈dom(α))x≤k■xα≤k}的秩,证明了半群OI_n(k)的秩为n+1.     

半群O_n(k)的秩

设O_n是有限链[n]上的保序变换半群.对任意1≤k≤n-1,研究半群O_n(k)={α∈O_n:(x∈[n]x≤k→xα≤k}的秩和幂等元秩,证明了半群O_n(k)的秩为2n-3.进一步,得到了半群O_n(k)(2≤k≤n-1)的幂等元秩为n和半群O_n(1)的幂等元秩为n-1.     

稳定随机变量序列几何加权和的Chover重对数律

设｛Ｘｎ,ｎ≥ ０｝是独立同分布的随机变量序列,其分布函数是一个对称的指数为 ａ（０＜ ａ＜ ２）的稳定分布·本文证明了依概率 １有 ｌｉｍ ｓｕｐβ－ｌ－｜（ ｌ－βα）１／α∑∞ ｎ＝０βｎＸｎ＝ｅｘｐ（１／α）·     

A note on maximal regular subsemigroups of the finite transformation semigroups \mathcal{T}(n,r)

Let $\mathcal{T}_{n}$ be the semigroup of all full transformations on the finite set X _n ={1,2,…,n}. For 1≤r≤n, set $\mathcal {T}(n, r)=\{ \alpha\in\mathcal{T}_{n} | \operatorname{rank}(\alpha)\leq r\}$ . In this note we show that, for 2≤r≤n?2, any maximal regular subsemigroup of the semigroup $\mathcal{T} (n,r)$ is idempotent generated, but this may not happen in the semigroup $\mathcal{T}(n, n-1)$ .     

强收敛与弱收敛的微小区别

对于独立同分布随机变量序列{Xn,n≥1},证明了其满足弱大数律的一个必要条件是:对于任何r∈(0,1),E|X|r<∞都成立.另外我们还举例说明了这样的条件不是充分的.     

Non-group Ranks in Finite Full Transformation Semigroups

T _n be the full transformation semigroup on a finite set. Both rank and idempotent rank of the semigroup K(n,r) = {α∈T _n : | im α | ≤r, 2 ≤ r ≤ n - 1. In this paper we prove that the non-group rank, defined as the cardinality of a minimal generating set of non-group elements, of K(n,r) is S(n,r) , the Stirling number of the second kind.     

Bipartite Graphs Kn,n+r- A (|A| ≤ 3) Determined by Their Cycle Length Distributions

The cycle length distribution of a graph G of order n is a sequence (c1 (G),..., cn (G)), where ci(G) is the number of cycles of length i in G. In general, the graphs with cycle length distribution (c1(G),...,cn(G)) are not unique. A graph G is determined by its cycle length distribution if the graph with cycle length distribution (c1 (G),..., cn (G)) is unique. Let Kn,n+r be a complete bipartite graph and A(∈)E(Kn,n+r). In this paper, we obtain: Let s > 1 be an integer. (1) If r = 2s, n > s(s - 1) + 2|A|, then Kn,n+r - A (A(∈)E(Kn,n+r),|A| ≤ 3) is determined by its cycle length distribution; (2) If r = 2s + 1,n > s2 + 2|A|, Kn,n+r - A (A(∈)E(Kn,n+r), |A| ≤ 3) is determined by its cycle length distribution.     

L~p INEQUALITIES AND ADMISSIBLE OPERATOR FOR POLYNOMIALS

Let p(z) be a polynomial of degree at most n. In this paper we obtain some new results about the dependence of p(Rz)-βp(rz) + α (R+1/r+1)n-|β | p(rz) s on p(z) s for every α, β∈ C with |α|≤ 1, |β | ≤ 1, R > r 1, and s > 0. Our results not only generalize some well known inequalities, but also are variety of interesting results deduced from them by a fairly uniform procedure.