一类特殊分布纪录值之和的中心极限定理

摘要：设{X，Xn,n≥1)为独立同分布的服从某连续分布F的随机变量序列，X^(1)=X1，X^(2),X^(3),…为其纪录值序列．令ψ(u)=F^-1(1-e^-u)．其中F^-1是F的反函数．本文研究当ψ(u)=log^pu时Tn=∑k=1^nX^(k)=^dn∑k=1^nψ(Sn)的极限性质．解决了户为所有正整数时Tn的中心极限定理．     

Hermite-Fejer Interpolation With Moved End Points

Let Z_n={z_(kn)=cosθ_(kn):θ_(kn)=(2k-1)/(2n)π,k=1,2…,n}be the zeros of T_n(x)=cosnθ(x=cosθ,θ∈[0,π]).For 0≤ε≤1,let α_n=:α_n(ε)=:cos(1-ε)/(2n)π,β_n=:β_n(ε)=:cos(2n-1+ε)/(2n)π=-α_n,X_n~(1)=(Z_n-{z_(1z)})∪{α_n},X_n~(2)=(Zn-{z_(nn)})∪{β_n},X_n~(3)=(Z_n-{z_(1n),z_(nn)})∪{α_n,β_n},Y_n~(1)=Z_n∪{α_n},Y_n~(2)=Z_n∪{β_n},Y_n~(3)=Z_n∪{α_nβ_n}.     

最大最小次序统计量的联合分布

X1,X2,…,Xn是来自总体X的简单随机样本,Nk=min1≤i≤k{Xi},Mk=max1≤i≤k{Xi}(k=1,2,…,n),本文给出了最小次序统计量与最大次序统计量的联合分布函数.     

ON CHOVER''''S LIL FOR THE WEIGHTED SUMS OF STABLE RANDOM VARIABLES

Let {Xn,n ≥ 1} be a sequence of α-stable random variables(0 < α < 2), {ani,1 ≤ i≤ n, n≥1} be an array of constant real numbers. Under some restriction of {ani,1 ≤ i ≤ n,n≥1}, the authors discuss the integral test for the weighted partial sums {Σi=1naniXi,n ≥ 1}, and obtain the Chover's laws of iterated logarithm(LIL) as corollaries.     

一个新的Smarandache函数及其均值

对任意正整数n≥3,我们定义算术函数C(n)为最大的正整数m≤n-2使得n |Cnm=n!/m!·(n-m)!.即就是C(n)=max{m:m≤n-2,n|Cnm},并规定C(1)=C(2)=1.本文的主要目的是利用初等及解析方法研究这一函数的均值分布问题,并给出几个有趣的均值公式及渐近式.     

Context-free grammars for triangular arrays

We consider context-free grammars of the form G = {f → fb1+b2+1ga1+a2, g → fb1 ga1+1},where ai and bi are integers sub ject to certain positivity conditions. Such a grammar G gives rise to triangular arrays {T(n, k)}0≤k≤n satisfying a three-term recurrence relation. Many combinatorial sequences can be generated in this way. Let Tn (x) =∑nk=0T(n, k)xk. Based on the differential operator with respect to G, we define a sequence of linear operators Pn such that Tn+1(x) = Pn(Tn(x)). Applying the characterization of real stability preserving linear operators on the multivariate polynomials due to Borcea and Br?ndén, we obtain a necessary and sufficient condition for the operator Pn to be real stability preserving for any n. As a consequence, we are led to a sufficient condition for the real-rootedness of the polynomials defined by certain triangular arrays, obtained by Wang and Yeh.Moreover, as special cases we obtain grammars that lead to identities involving the Whitney numbers and the Bessel numbers.     

Banach空间中有限族渐进伪压缩映象的迭代程序

Let E be a real Banach space and K be a nonempty closed convex and bounded subset of E. Let Ti ： K→ K, i=1, 2,... ,N, be N uniformly L-Lipschitzian, uniformly asymptotically regular with sequences {ε^（i）n} and asymptotically pseudocontractive mappings with sequences {κ^（i）n}, where {κ^（i）n} and {ε^（i）n}, i = 1, 2,... ,N, satisfy certain mild conditions. Let a sequence {xn} be generated from x1 ∈ K by zn：= （1-μn）xn＋μnT^nnxn, xn＋1 ：= λnθnx1＋ [1 - λn（1 ＋ θn）]xn ＋ λnT^nnzn for all integer n ≥ 1, where Tn = Tn（mod N）, and {λn}, {θn} and {μn} are three real sequences in [0, 1] satisfying appropriate conditions. Then ｜｜xn- Tixn｜｜→ 0 as n→∞ for each l ∈ {1, 2,..., N}. The results presented in this paper generalize and improve the corresponding results of Chidume and Zegeye, Reinermann, Rhoades and Schu.     

重截断和的渐近分布

设{X_n,n≥1}是i.i.d.随机变量序列,X_n,1≤…≤X_(n,n)是X_1,…,X_n的次序统计量。又设k_(n,1,) k_(n,2)是满足条件1≤k_(n,1)相似文献   

三步投影算法的收敛性及其在变分不等式组中的应用

First a general model for a three-step projection method is introduced, and second it has been applied to the approximation solvability of a system of nonlinear variational inequality problems in a Hilbert space setting. Let H be a real Hilbert space and K be a nonempty closed convex subset of H. For arbitrarily chosen initial points x0, y0, z0 ∈ K,compute sequences xn, yxn, zxn such that { xn+1=(1-αn-rn)xn+αxPk[yn-ρTyn]+rnun,yn=(1-β-δn)xn+βnPk[zn-ηTxn]+δnun,zn=(1-an-λn)xn+akPk[xn-γTxn]+λnwn.For η, ρ,γ>0 are constants,{αn}, {βn}, {an}, {rn}, {δn}, {λn} C [0,1], {un}, {vn}, {wn} are sequences in K, and 0≤n + rn ≤ 1,0 ≤βn + δn ≤ 1,0 ≤ an + λn ≤ 1,(A)n ≥ 0, where T : K → H is a nonlinear mapping onto K. At last three-step models are applied to some variational inequality problems.     

关于k阶记录时间与k阶记录值的联合分布

设独立同分布随机变量序列{x_nj n≥1}的分布函数F(x)=p(x₁(k)(n);n≥1},{X^(k)(n);n≥1} 分别为{x_nj n≥1}的K阶记录时间序列和k阶记录值序列.本文我们用直接方法求出了{U^(k)(i),X^(k)(i);1≤i≤n}的联合分布，从而证明了k阶记录时间序列及k阶记录值序列的马氏性，并导出了它们之间的一     

非平稳高斯序列超过数点过程与部分和的联合渐近分布

设$\{X_{i}\}^{\infty}_{i=1}$是标准化非平稳高斯序列, $N_{n}$为$X_{1},X_{2},\cdots,X_{n}$对水平$\mu_{n}(x)$的超过数形成的点过程, $r_{ij}=\ep X_{i}X_{j}$, $S_{n}=\tsm_{i=1}^{n}X_{i}$. 在$r_{ij}$满足一定条件时, 本文得到了$N_{n}$与$S_{n}$的渐近独立性.     

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 .     

负相协随机变量非随机和的差的精确大偏差

In this paper,we study precise large deviation for the non-random difference sum from j=1 to n_1(t) X_(1j)-sum from j=1 to n_2(t) X_(2j),where sum from j=1 to n_1(t) X_(1j) is the non-random sum of {X_(1j),j≥1} which is a sequence of negatively associated random variables with common distribution F_1(x),and sum from j=1 to n_2(t) X_(2j) is the non-random sum of {X_(2j),j≥1} which is a sequence of independent and identically distributed random variables,n_1(t) and n_2(t) are two positive integer functions.Under some other mild conditions,we establish the following uniformly asymptotic relation lim t→∞ sup x≥r(n_1(t))~(p+1)|(P(∑~(n_1(t)_(j=1)X_(1j)-∑~(n_2(t)_(j=1)X_(2j)-(μ_1n_1(t)-μ_2n_2(t)x))/(n_1(t)F_1(x))-1|=0.     

广义复合二项风险模型的若干大偏差结果

This paper is a further investigation of large deviation for partial and random sums of random variables, where {Xn,n ≥ 1} is non-negative independent identically distributed random variables with a common heavy-tailed distribution function F on the real line R and finite mean μ∈ R. {N（n）,n ≥ 0} is a binomial process with a parameter p ∈ （0,1） and independent of {Xn,n ≥ 1}; {M（n）,n ≥ 0} is a Poisson process with intensity λ 〉 0, Sn = ΣNn i=1 Xi-cM（n）. Suppose F ∈ C, we futher extend and improve some large deviation results. These results can apply to certain problems in insurance and finance.     

单圈图的最大特征值的上界的改进

Let G（V, E） be a unicyclic graph, Cm be a cycle of length m and Cm G, and ui ∈ V（Cm）. The G - E（Cm） are m trees, denoted by Ti, i = 1, 2,..., m. For i = 1, 2,..., m, let eui be the excentricity of ui in Ti and ec = max{eui ： i = 1, 2 , m}. Let κ = ec＋1. Forj = 1,2,...,k- 1, let δij = max{dv ： dist（v, ui） = j,v ∈ Ti}, δj = max{δij ： i = 1, 2,..., m}, δ0 = max{dui ： ui ∈ V（Cm）}. Then λ1（G）≤max{max 2≤j≤k-2 （√δj-1-1＋√δj-1）,2＋√δ0-2,√δ0-2＋√δ1-1}. If G ≌ Cn, then the equality holds, where λ1 （G） is the largest eigenvalue of the adjacency matrix of G.     

至多一个变点的$\Gamma$分布的统计推断及在金融中的应用

对至多一个变点的Γ分布,即X1,X2…,Xn为一列相互独立的随机变量序列,且X1,X2,…,X[nΥ0]i．i．d～Γ(x;ν1,λ1),X[nΥ0] 1,X[nΥ0] 2,…,Xn i．i．d～Γ(x;ν2,λ2),其中Υ0未知,称Υ0为该序列的变点．在利用第一型极值分布逼近文中提出统计量的分布的基础上,给出了变点Υ0估计(?)的相合性及强弱收敛速度．最后给出了在金融序列上的应用．     

On Factorisations and Generators in Transformation Semigroups

It is shown that the classical decomposition of permutations into disjoint cycles can be extended to more general mappings by means of path-cycles, and an algorithm is given to obtain the decomposition. The device is used to obtain information about generating sets for the semigroup of all singular selfmaps of $X_{n} = \{1, 2, \dots, n\}$. Let $T_{n,r} = S_{n}\cup K_{n,r}$, where $S_{n}$ is the symmetric group and $K_{n,r}$ is the set of maps $\alpha\,:\, X_{n} \to X_{n}$ such that $|im(\alpha)| \le r$. The smallest number of elements of $K_{n,r}$ which, together with $S_{n}$, generate $T_{n,r}$ is $p_{r}(n)$, the number of partitions of $n$ with $r$ terms.     

NA阵列加权乘积和的完全收敛性

设{X_(ni):1≤i≤n,n≥1}为行间NA阵列,g(x)是R~+上指数为α的正则变化函数,r>0,m为正整数,{a_(ni):1≤i≤n,n≥1}为满足条件(?)|a_(ni)|=O((g(n))~1)的实数阵列,本文得到了使sum from n=1 to ∞n~(r-1)Pr(|■multiply from j=1 to m a_(nij) X_(nij)|>ε)<∞,■ε>0成立的条件,推广并改进了Stout及王岳宝和苏淳等的结论。     

Orthogonal sequences constructed from quasi-orthogonal ultraspherical polynomials

Numerical Algorithms - Let $\displaystyle \{x_{k,n-1}\}_{k=1}^{n-1}$ and $\displaystyle \{x_{k,n}\}_{k=1}^{n},$ $n \in \mathbb {N}$ , be two sets of real, distinct points satisfying the interlacing...     

由H\"{o}rmander向量场构成的抛物方程的 $W_{\ast}^{1,p}$ 正则性

设 $X_{1},\cdots ,X_{q}\ (q相似文献