独立重尾随机变量随机和的大偏差估计

本文研究了一类独立重尾随机变量随机和S（t)∧=∑k=1^N(t)Xk,t≥0的大偏差概率，其中{N(t),t≥0}是一放大晨负整数值随机变量；{Xn,n≥1}是非负，独立随机变量序列，并与{N(t),t≥０}独立。本文的结果将{Xn,n≥１}为独立同分布情形推广到了独立不同分布情形。     

可列非齐次马氏链泛函的一类强大数定律

本文用分析方法研究可列非齐次马氏链的泛函的极限性质，得到了一类不同形式的强大数定律，在其中通常形式的强大数定律中的数学期望被条件期望所代替，关于独立随机变量序列的若干经典强大数定律是本文结果的推论．     

右删失数据下的时间序列数据分析

当平稳时间序列{Xn}被另外的平稳序列{Yn}删失后,我们研究{Xn}的协方差,相关系数的估计问题．特别当{Xn}是AR(p)序列时,我们研究AR(p)的参数估计和一步预测问题．给出的估计量是强相合的．计算机模拟结果说明所提供的方法是适用的．     

齐次Moran集的Bouligand维数

设m({nk}k≥1,{Ck}k≥1是由{nk}k≥1,{Ck}k≥1所确定的齐次Moran集类，其中{nk}k≥1是正整数序列，{Ck}k≥1是正实数列。本文确定了m中元素的上（下）Bouligand维数的最大、小值之间的数s，存在m中的元素使其上（下）Bouligand维数值为s。还讨论了齐次Cantor集与偏齐次Cantor集的Bouligand维数存在性之间的关系。     

稳定随机游动重点集的离散豪斯道夫维数

设是ｄ维格子点上的严格α－稳定的随机游动，称为的Ｐ重点集（Ｐ１），本文讨论了的离散豪斯道夫维数，并对，（ａ＜ｄ），证明了Ｐ重点集的维数都等于ａ，即     

An Adaptive Mesh-Refining Algorithm Allowing for an <Emphasis Type="Italic">H</Emphasis><Superscript>1</Superscript> Stable <Emphasis Type="Italic">L</Emphasis><Superscript>2</Superscript> Projection onto Courant Finite Element Spaces

Suppose $\cal{S}^1({\cal T})\subset H^1(\Omega)$ is the $P_1$-finite element space of $\cal{T}$-piecewise affine functions based on a regular triangulation $\cal{T}$ of a two-dimensional surface $\Omega$ into triangles. The $L^2$ projection $\Pi$ onto $\cal{S}^1(\cal{T})$ is $H^1$ stable if $\norm{\Pi v}{H^1(\Omega)}\le C\norm{v}{H^1(\Omega)}$ for all $v$ in the Sobolev space $H^1(\Omega)$ and if the bound $C$ does not depend on the mesh-size in $\cal{T}$ or on the dimension of $\cal{S}^1(\cal{T})$. \hskip 1em A red–green–blue refining adaptive algorithm is designed which refines a coarse mesh $\cal{T}_0$ successively such that each triangle is divided into one, two, three, or four subtriangles. This is the newest vertex bisection supplemented with possible red refinements based on a careful initialization. The resulting finite element space allows for an $H^1$ stable $L^2$ projection. The stability bound $C$ depends only on the coarse mesh $\cal{T}_0$ through the number of unknowns, the shapes of the triangles in $\cal{T}_0$, and possible Dirichlet boundary conditions. Our arguments also provide a discrete version $\norm{h_\cal{T}^{-1}\,\Pi v}{L^2(\Omega)}\le C\norm{h_\cal{T}^{-1}\,v}{L^2(\Omega)}$ in $L^2$ norms weighted with the mesh-size $h_\T$.     

强相依高斯序列对高水平超过的弱收敛

设{Xn}为标准化非平稳高期序列，rij=cov(Xi,Xj),Nn为{Xn}对水平un=x/an bn的超过数形成的点过程。当rijlog(j-i)→r∈（0，∞),(j-i→ ∞),且n→∞时，点过程Nn依分布收敛到Cox-过程。     

Estimates of Dirichlet Eigenvalues for One-Dimensional Fractal Drums

Let $\Omega$, with finite Lebesgue measure $|\Omega|$, be a non-empty open subset of $\mathbb{R}$, and $\Omega=\bigcup_{j=1}^\infty\Omega_j$, where the open sets $\Omega_j$ are pairwise disjoint and the boundary $\Gamma=\partial\Omega$ has Minkowski dimension $D\in (0,1)$. In this paper we study the Dirichlet eigenvalues problem on the domain $\Omega$ and give the exact second asymptotic term for the eigenvalues, which is related to the Minkowski dimension $D$. Meanwhile, we give sharp lower bound estimates for Dirichlet eigenvalues for such one-dimensional fractal domains.     

Asymptotic cones and Assouad-Nagata dimension

We prove that the dimension of any asymptotic cone over a metric space does not exceed the asymptotic Assouad-Nagata dimension of . This improves a result of Dranishnikov and Smith (2007), who showed for all separable subsets of special asymptotic cones , where is an exponential ultrafilter on natural numbers.

We also show that the Assouad-Nagata dimension of the discrete Heisenberg group equals its asymptotic dimension.

     

任意信源与马氏信源比较及小偏差定理

设{X_n,n≥0}是在S={1,2,…N}中取值的可测函数列,P、Q是测度空间上的两个概率测度,其中Q关于{X_n,n≥0}是马氏测度.本文引进了P关于Q的样本散度率距离的概念,并利用这个概念得到了任意信源二元函数一类平均值的小偏差定理,作为推论得到了任意信源熵密度的小偏差定理.最后我们将Shannon-McMillan定理推广到非齐次马氏信源情形.     

Dimension Results for Space-anisotropic Gaussian Random Fields

Let X = {X(t) ∈ R~d, t ∈ R~N} be a centered space-anisotropic Gaussian random field whose components satisfy some mild conditions. By introducing a new anisotropic metric in R~d, we obtain the Hausdorff and packing dimension in the new metric for the image of X. Moreover, the Hausdorff dimension in the new metric for the image of X has a uniform version.     

LIMIT THEOREM FOR A CLASS OF SEQUENCE OF WEAKLY DEPENDENT RANDOM VARIABLES

In this paper, we consider a central limit theorem for the sequence of stationary m-dependent random variables, the variance of which is possibly infinite. Theorem. Let {Xn, n=l, 2,...} be a sequence of stationary m-dependent random variables with means zero. The following conditions are satisfied. (i) \[{M^2}\int_{{\text{|}}{X_1}| > M} {dP} /\int_{{X_1}| < M} {X_1^2} dP \to 0{\kern 1pt} {\kern 1pt} {\kern 1pt} (M \to \infty )\] (ii) \[\int_{\{ {X_1}| < M,|{X_i}| < M} {X_1^{}} {X_i}dP/\int_{|{X_1}| < M} {X_1^2} dP \to 0{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} (M \to \infty )\] then there are constants Bsubsub>0, such that \[\frac{1}{{{B_n}}}\sum\limits_{i = 1}^n {{X_1}} \] converges in distribution N(0,1).     

一个关于马尔可夫链的极限定理

给出一个关于可列非齐次马尔可夫链M元状态序组出现频率的新形式的强极限定理,所得结论对任意可列非齐次马尔可夫链普遍成立.     

最优布尔函数的一个性质

Walsh谱只有3个值:0,±2m+2,且同时达到代数次数上界n-m-1和非线性度上界2n-1-2m+1的n元m阶弹性布尔函数(m>n/2-2)称为饱和最优函数(saturatedbest简写为SB).本文将给出关于SB函数非零谱值位置分布的一个性质,利用这一性质我们给出构造非线性度为56的4次7兀2阶弹性布尔函数的一种方法.     

ASYMPTOTIC NORMALITY OF KERNEL ESTIMATES OF A DENSITY FUNCTION UNDER ASSOCIATION DEPENDENCE

Let {X_n, n≥1} be a strictly stationary sequence of random variables, whichare either associated or negatively associated, f(·) be their common density. In this paper,the author shows a central limit theorem for a kernel estimate of f(·) under certain regularconditions.     

Finite Element Approximations of Symmetric Tensors on Simplicial Grids in $\mathbb{R}^n$: The Higher Order Case

The design of mixed finite element methods in linear elasticity with symmetric stress approximations has been a longstanding open problem until Arnold and Winther designed the first family of mixed finite elements where the discrete stress space is the space of $H(div, Ω\;\mathbb{S}) — P_{k+1}$ tensors whose divergence is a $P_{k-1}$ polynomial on each triangle for $k$ ≥ 2. Such a two dimensional family was extended, by Arnold, Awanou and Winther, to a three dimensional family of mixed elements where the discrete stress space is the space of $H(div, Ω\;\mathbb{S}) — P_{k+2}$ tensors, whose divergence is a $P_{k-1}$ polynomial on each tetrahedron for $k$ ≥ 2. In this paper, we are able to construct, in a unified fashion, mixed finite element methods with symmetric stress approximations on an arbitrary simplex in $\mathbb{R}^n$ for any space dimension. On the contrary, the discrete stress space here is the space of $H(div, Ω\;\mathbb{S}) — P_k$ tensors, and the discrete displacement space here is the space of $L²(Ω ; \mathbb{R}^n) — P_{k-1}$ vectors for $k ≥ n$+1. These finite element spaces are defined with respect to an arbitrary simplicial triangulation of the domain, and can be regarded as extensions to any dimension of those in two and three dimensions by Hu and Zhang.     

Inner Product Space and Concept Classes Induced by Bayesian Networks

Bayesian networks have become one of the major models used for statistical inference. In this paper we discuss the properties of the inner product spaces and concept class induced by some special Bayesian networks and the problem whether there exists a Bayesian network such that lower bound on dimensional inner product space just is some positive integer. We focus on two-label classification tasks over the Boolean domain. As main results we show that lower bound on the dimension of the inner product space induced by a class of Bayesian networks without v-structures is where m _i denotes the number of parents for ith variable. As the variable’s number of Bayesian network is n≤5, we also show that for each integer m∈[n+1,2 ⁿ −1] there is a Bayesian network such that VC dimension of concept class and lower bound on dimensional inner product space induced by all are m. This work was supported by National Natural Science Foundation of China (60574075).     

P2r,6图的优美性

Kathiresan KM证实$P_{2r,2m-1}$($r,m$皆为任意正整数)是优美的且猜想:除了$(a,b)=(2r-1,4m-2)$外,所有的$P_{a,b}$都是优美的.杨元生证实$P_{2r+1,2m+1}$是优美的,并且证实了当$r\leq7$, $r=9$时的$P_{2r,2m}$是优美的.严谦泰证实$r$为奇数时$P_{2r,2m}$是优美的.采用回溯和分支限界算法搜索到了一个适合于所有$P_{2r,b}$图($r,b$皆为任意正整数)的优美标号,用函数构造法提取其规律并从数学的严格性进行了证明,使得所有的$P_{2r,b}$图($r,b$ 皆为任意正整数)的优美性得到了证实.     

r模同态的{1}-逆与{2}-逆

本文探讨模同态广义逆在环模理论中的应用．利用模同态的{1}-逆与{2}-逆，分别给出了一类环及一类重要模的特征刻画．     

THE GLOBAL ASYMPTOTICAL STABILITY OF SOLUTION OF ITO RANDOM DIFFERENTIAL EQUATION

In this paper we discuss the stability and global asymptotical stability of the solu- tion of It? random differeirtial equation \[\left\{ \begin{array}{l} d\xi (t) = b(\xi (t),t)dt + \sigma (\xi (t),t)dw(t)\\xi ({t_0}) = {\xi _0} \end{array} \right.\] here \({\xi _0}\) is a bounded random vector. Suffloient conditions for the existence of the two typical stability are given. These conditions are natural extension of Lyapunov function in deterministic system. Our results extend some results due to Friedman, and pinsky (see[l]). We suggest an opinion about definition of asymptotical stability of solution of the following It? random differential equation \[\left\{ \begin{array}{l} d\xi (t) = b(\xi (t)dt + \sigma (\xi (t))dw(t)\\xi ({t_0}) = {x_0} \end{array} \right.\] where \({x_0}\) is a point of n-dimensional Eiiolidian space.