An Application of Polya's Enumeration Theorem to Partitions of Subsets of Positive Integers

Let S be a non-empty subset of positive integers. A partition of a positive integer n into S is a finite nondecreasing sequence of positive integers a ₁, a ₂,...,a _r in S with repetitions allowed such that . Here we apply Polya's enumeration theorem to find the number P(n; S) of partitions of n into S, and the number DP(n; S) of distinct partitions of n into S. We also present recursive formulas for computing P(n; S) and DP(n; S).     

关于整数和集的定理的推广

本文主要利用加性数论的理论考察整数和集,稚广了Vscvolod F．Lev的关于整数和的定理：设n≥1,B增包含[1,n],｜B｜〉n/4,k=｜B｜＋1,则 （1）当1≤n≤2k-3时,有ia^s能写成两个不同B中元之和。 （2）当2k-2≤,1〈3k-3时,有ia^s能写成最多四个B中元之和。 （3）当3k-3≤n〈4k-4时,有ia^s能写成最多2h个B中元之和。 其中h=max[2k/4k-4-n],i=1,2,3,4,6     

Relating Subsets of a Poset,and a Partition Theorem for WQOs

We point out some basic properties of the partial ordering which a poset P induces on its power set, defining AB to mean that every element of A lies below some element of B. One result is that if P is a WQO then P decomposes uniquely into finitely many indivisible sets A ₁,...,A _n (that are essential parts of P in the sense that PP\A _i ).     

随机弱内向映射的多个随机不动点定理

利用随机不动点指数理论及Banach常微分方程理论的随机结果,证明了关于随机弱内向映射一个随机三解定理.     

一个随机偏差定理

设{Xn，n≥0}是可列非齐次马尔可夫链，Sn（i0，i1，…，im-1，ω）表示m元状态序组（i0，i1，…，im-1）在序列（X0，X1，…，Xm-1），（X1，X2，…，Xm），…，（Xn-1，Xn，…，Xn＋m-2）中出现的次数.本文给出了关于Sn（i0，i1，…，im-1，ω）的一个对任意可列非齐次马尔可夫链普遍成立的随机偏差定理，即用不等式表示的一个强极限定理.     

一个随机偏差定理

设{Xn,n≥0}是可列非齐次马尔可夫链,Sn(i0,i1,…,im-1,ω)表示m元状态序组(i0,i1,…,im-1)在序列(X0,X1,…,Xm-1),(X1,X2,…,Xm),…,(Xn-1,Xn,…,Xn+m-2)中出现的次数.本文给出了关于Sn(i0,i1,…,im-1,ω)的一个对任意可列非齐次马尔可夫链普遍成立的随机偏差定理,即用不等式表示的一个强极限定理.     

Erdős–Ko–Rado and Hilton–Milner theorems for two-forms

The celebrated Erd?s–Ko–Rado theorem about the maximal size of an intersecting family of r-element subsets of $\{1,\dots ,n\}$ was extended to the setting of exterior algebra in [5, Theorem 2.3] and in [6, Theorem 1.4]. However, the equality case has not been settled yet. In this short note, we show that the extension of the Erd?s–Ko–Rado theorem and the characterization of the equality case therein, as well as those of the Hilton–Milner theorem to the setting of exterior algebra in the simplest non-trivial case of two-forms follow from a folklore puzzle about possible arrangements of an intersecting family of lines.     

随机自反随机赋范模上的平均遍历定理(英文)

本文对随机自反随机赋范模上的几乎处处幂有界的随机线性算子证明了一个平均遍历定理,这一定理推广和改进了几个已知的重要的结果.     

NA及LNQD随机变量列的几乎处处中心极限定理

本文在二阶矩存在的条件下,证明了NA及LNQD随机变量列的几乎处处中心极限定理,使主要结果成立,其中W为[0,1]上标准Brown运动。     

The p-adic Approach to Wolstenholme's Theorem

The p-adic Approach to Wolstenholme's Theorem@孙琦@洪绍方&&     

A Central Limit Theorem for Random Fields of Negatively Associated Processes

A central limit theorem for negatively associated random fields is established under the fairly general conditions. We use the finite second moment condition instead of the finite (2+)th moment condition used by Roussas.⁽¹⁵⁾ A similar result is also given for positively associated sequences.     

关于完备随机内积模中的Lax-Milgram定理的注记

设(S,X)为数域K上以σ-有限测度空间(Ω,A,μ)为基的完备的RIP-模,而且α:S×S→L(μ,K)满足如下条件:(A)存在ξ∈L (μ),使得a(p,q)ξ·X~p·X~q,p,q∈S;(B)a是coercive(即,存在η∈L (μ),使得a(p,p)η·X~p2,p∈S且μ({ωη(ω)=0})=0);(C)对每个q∈S,a(·,q):S→L(μ,K)是模同态,且对每个p∈S,a(p,ξq1 ηq2)=ξ-a(p,q1) η-a(p,q2),q1,q2∈S及ξ,η∈L(μ,K).则存在唯一的连续模同态A:S→S使A-1存在且μ-a.s.有界,还满足:(1)a(p,q)=XA(p),q,p,q∈S;(2)X~A-1(p)1ηX~p,p∈S.     

An Asymptotic Behavior of the Remainder in the Central Limit Theorem for Moments of Sums of Independent Random Variables

The objective of the paper is to study the asymptotic behavior of the reminder in the central limit theorem for moments of sums of independent random variables.     

Central Limit Theorem for a Class of Nonhomogeneous Random Walks

A spatially nonhomogeneous random walk _t on the grid =^m X ⁿ is considered. Let _t ⁰ be a random walk homogeneous in time and space, and let _t be obtained from it by changing transition probabilities on the set A= X ⁿ, || < , so that the walk remains homogeneous only with respect to the subgroup ⁿ of the group . It is shown that if >m 2 or the drift is distinct from zero, then the central limit theorem holds for _t.     

有限子集系的一个结果

１９８７年，黄国泰推广了Ｋｌｅｉｔｍａｎ和Ｋａｔｏｎａ定理。但是，若对某个正整数ｔ（１≤ｔ≤ｋ－１）不存在Ｆ中的两个元Ａ，Ｂ满足：存在某ｔ个Ｓｉ，使得Ｓｉ∩Ａ－Ｓｉ∩Ｂ，而对其余的ｋ－ｔ个Ｓｊ都有Ａ∩Ｓｊ     

Extension of a Theorem of Kiming and Olsson for the Partition Function

Some congruence properties of the partition function are proved.     

关于随机选择的一个强极限定理

本文利用似然比和区间剖分法研究相依Ｎ值随机变量序列选择的极限性质,得到关于赌博方法的一个强极限定理的若干推广。     

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??The local limit theorems for the minimum of a random walk with Markovian increments is given, with using Presman's factorization theory. This result implies the asymptotic behaviour of the survival probability for a critical branching process in Markovian depended random environment.     

不连续随机算子随机不动点定理及其应用

该文利用半序理论和随机压缩映象原理,得到了一类不连续随机增算子随机不动点的唯一存在定理.作为应用,考虑了R~n中含间断项的一阶随机微分积分方程初值问题.