Asymptotic distributions of non-central studentized statistics

Let X1,...,Xn be independent and identically distributed random variables and Wn = Wn(X1,...,Xn) be an estimator of parameter θ.Denote Tn =(Wn - θ0)/sn,where sn2 is a variance estimator of Wn.In this paper a general result on the limiting distributions of the non-central studen-tized statistic Tn is given.Especially,when s2n is the jacknife estimate of variance,it is shown that the limit could be normal,a weighted χ2 distribution,a stable distribution,or a mixture of normal and stable distribution.Applicati...     

逻辑系统(W)、W、Wn中的广义矛盾式及一种降级算法

研究了多值逻辑系统(W)、W、Wn中的广义矛盾式,并对这些多值逻辑系统中的广义矛盾式进行了分划,强调了这种分划的不重不漏.在(W)、W、Wn中给出了一种降级算法,但(W)、W中的矛盾式并不能由对非矛盾式进行降级得到.而在Wn中,矛盾式可由非矛盾式经过有限次降级得到.     

一类Cayley图的可扩性

设 Sn是那个对称群 .让〈n〉 ={ 1,2 ,… ,n} ,B*表示 Sn中所有对换的集合和 B B* .关于 B的对换图 Wn 被定义为 V(Wn) =〈n〉,E(Wn) ={ [uv]:(uv)∈ B} .如果 Wn是一棵树 ,则这个对换图称为一棵对换树 Tn.Tn 是 Sn 的一个极小生成集 .在这篇文章里 ,我们研究了 Cayley图 Cay(Sn,Tn)的性质 .证明了Cay(Sn,Tn)是 (n - 2 ) -可扩的 ,即 ,Cay(Sn,Tn)的可扩性达到最大 .     

On Some Cycles in Wenger Graphs

Let p be a prime,q be a power of p,and let Fq be the field of q elements.For any positive integer n,the Wenger graph Wn(q)is defined as follows:it is a bipartite graph with the vertex partitions being two copies of the(n+1)-dimensional vector space Fq^n+1,and two vertices p=(p(1),…,p(n+1))and l=[l(1),…,l(n+1)]being adjacent if p(i)+l(i)=p(1)l(1)i-1,for all i=2,3,…,n+1.In 2008,Shao,He and Shan showed that for n≥2,Wn(q)contains a cycle of length 2 k where 4≤k≤2 p and k≠5.In this paper we extend their results by showing that(i)for n≥2 and p≥3,Wn(q)contains cycles of length 2k,where 4≤k≤4 p+1 and k≠5;(ii)for q≥5,0相似文献   

形式系统L*(n)的完备性

模糊逻辑命题演算形式系统 L*自 1 997年被提出以来 ,在模糊逻辑与模糊推理的理论与应用中发挥了重要的作用 .系统 L* 的完备性直到最近才由作者给出证明 .本文进一步研究系统 L*的扩张在 n元 R0 链 Wn 上的完备性问题 ,通过构造公式列 ,得到系统 L*的扩张列 { L* (n) } ,使用代数方法证明了对于任何n≥ 3 ,系统 L* (n)关于 Wn 是完备的     

关于任意随机变量序列配重和的一类强偏差定理

设{Xn,n≥1}是在E={0，1)中取值的二值随机序列，{an，n≥1}是[0，1]中取值的一列常数，Wn(ω)=n∑i=1aiXi(ω)，本文利用区间剖分法[1],[2]构造单调函数，研究任意二值随机序列配重和Wn(ω)的一类用不等式表示的定理，即强偏差定理．     

形式系统T^*(n)的完备性

模糊逻辑命题演算形式系统T ^*自1997年被提出以来,在模糊逻辑与模糊推理的理论与应用发挥了重要的作用,系统T^*的完备性直到最近才由作者给出证明,本文进一步研究系统T^*的扩张在n元R0链Wn上的完备性问题,通过构造公式列,得到系统T^*的扩张到｛T^*(n)｝,使用代数方法证明了对于任何n≥3,系统T^*(n)关于Wn是完备的。     

Asymptotic properties of supercritical branching processes in random environments

We consider a supercritical branching process （Zn） in an independent and identically distributed random environment ξ, and present some recent results on the asymptotic properties of the limit variable W of the natural martingale Wn = Zn/E[Zn｜ξ], the convergence rates of W - Wn （by considering the convergence in law with a suitable norming, the almost sure convergence, the convergence in Lp, and the convergence in probability）, and limit theorems （such as central limit theorems, moderate and large deviations principles） on （log Zn）.     

一类混合Ramsey数

设a(G)表示图G的点荫度,m为正整数,H为连通图,混合Ramsey数v(a;m;H)被定义的为最小的正整数P,使得对任意P阶图G则有a(G)≥m或者H包括于G^-。本文给出了v(a;m;H)的一种计算方法,并对图Cn和轮Wn确定了v(a;n;Cn)和v(a;m;Wn)的值。     

Ⅱ-凝聚环中的对偶性

通过π-凝聚环上的f.g.模的自反性引进了WQF-环和GIF-环,给出了QF-环一个新的刻画.并研究了π-凝聚环上的Wn模上的自反性的特征性质.     

星扇轮联图的邻点可约边染色

对简单图G(V,E),若存在自然数κ(1≤κ≤Δ(G))和映射f:E(G)→{1,2,…,κ}使得对任意相邻两点u,v∈V(G),uv∈E(G),当d(u)=d(v)时,有C(u)=C(u),则f为G的κ-邻点可约边染色(简记为κ-AVREC of G),而x′_(aur)(G)=max{κ|κ-AVREC of G}称为G的邻点可约边染色数.其中C(u)={f(uv)|uv∈E(G)}.证明了联图在若干情况下的邻点可约边染色定理,得到了S_n+S_n,F_n+F_n,W_n+W_n,S_n+F_n,S_n+W_n和F_n+W_n的邻点可约边色数.     

一类变换半群的秩

设自然数n≥4,X_n={1,2,…,n},证明了X_n上的保序压缩全变换半群W_n的秩为n-1.     

The reverse order law for theW-weighted Drazin inverse of multiple matrices product

By using the rank methods of matrix, a necessary and sufficient condition is established for reverse order law $$\begin{gathered} WA_{d,W} W = (W_n (A_n )_{d,W_n } W_n )(W_{n - 1} (A_{n - 1} )_{d,W_{n - 1} } W_{n - 1} ) \hfill \\ ... (W_1 (A_1 )_{d,W_1 } W_1 ) \hfill \\ \end{gathered} $$ to hold for the W-weighted Drazin inverses, whereA =A ₁ A ₂ … A _n andW =W _n W _n-1 …W ₁. This result is the extension of the result proposed by [Linear Algebra Appl., 348(2002)265-272] and the result proposed by [J. Math. Research and Exposition. 19(1999)355-358].     

关于图的一般邻点可区别边染色

给出了轮图W_n、扇图F_n、风车图K_2~t、图D_(m,4)、图D_(m,n)、齿轮图W_n的一般邻点可区别色指标.     

关于轮网络的一簇猜想

轮网络是由Cayley图模型设计出来的一种新型互连网络模型.星网络、冒泡排序网络、修正冒泡排序网络可嵌入轮网络.为了揭示它的整体结构,对轮网络提出如下一簇猜想:轮网络是边不交的i个Hamilton圈及2(n-i)-2个完美匹配的并,其中1≤i≤(n-1);并证明了当n=4,5,6,1≤i≤3时,猜想成立.     

几何测度空间基的研究

研究了几何测度空间中的基本对称函数μ_0,μ_1,…,μ_n和内蕴体积函数V_0,V_1,…,V_n,证明了Lⁿ上连续不变赋值函数空间中由基本对称函数构成的基{μ_0,μ_1,…,μ_n}和由内蕴体积函数构成的基{V_0,V_1,…V_n}(或均质积分构成的基{W_0,W_1,…,W_n})等价.     

On Some Ramsey Numbers for Quadrilaterals Versus Wheels

For given graphs G ₁ and G ₂, the Ramsey number R(G ₁, G ₂) is the least integer n such that every 2-coloring of the edges of K _n contains a subgraph isomorphic to G ₁ in the first color or a subgraph isomorphic to G ₂ in the second color. Surahmat et al. proved that the Ramsey number ${R(C_4, W_n) \leq n + \lceil (n-1)/3\rceil}$ . By using asymptotic methods one can obtain the following property: ${R(C_4, W_n) \leq n + \sqrt{n}+o(1)}$ . In this paper we show that in fact ${R(C_4, W_n) \leq n + \sqrt{n-2}+1}$ for n ≥ 11. Moreover, by modification of the Erd?s-Rényi graph we obtain an exact value ${R(C_4, W_{q^2+1}) = q^2 + q + 1}$ with q ≥ 4 being a prime power. In addition, we provide exact values for Ramsey numbers R(C ₄, W _n ) for 14 ≤ n ≤ 17.     

Central limit theorems for empirical product densities of stationary point processes

We prove the asymptotic normality of kernel estimators of second- and higher-order product densities (and of the pair correlation function) for spatially homogeneous (and isotropic) point processes observed on a sampling window \(W_n\) , which is assumed to expand unboundedly in all directions as \(n \rightarrow \infty \,\) . We first study the asymptotic behavior of the covariances of the empirical product densities under minimal moment and weak dependence assumptions. The proof of the main results is based on the Brillinger-mixing property of the underlying point process and certain smoothness conditions on the higher-order reduced cumulant measures. Finally, the obtained limit theorems enable us to construct \(\chi ^2\) -goodness-of-fit tests for hypothetical product densities.     

条件经验随机过程的渐近性质

设(Xi,Yi)(i=1,2,…,n)是来自总体(X,Y)的样本(独立同分布),其中X∈R1,Y∈Rq.M(x y)是Y=y时X的条件分布,Mnkn(x y)为M(x y)的第kn个最近邻域的经验分布估计量,讨论条件经验过程Sn(t,x,y)=kn12(Mnkn(x y)-M(x y))的渐近性质,得出在适当条件下,对固定的y,Sn(t,x,y)(x,t为参数)弱收敛于某一G aussian过程S(.).