Central limit theorem for quadratic forms for sparse tables

Sufficient conditions for asymptotic normality for quadratic forms in {n_t − np_t} are given, where {n_t} are the observed counts with expected cell means {np_t}. The main result is used to derive asymptotic distributions of many statistics including the Pearson's chi-square.     

NSD序列加权和的中心极限定理及其在EV回归模型中的应用

基于负超可加相依(简称为NSD)随机序列的性质及其一些不等式,利用随机变量的截断方法建立了NSD随机序列加权和的中心极限定理,从而推广了负相协NA随机序列的相应结论.并将其应用到变系数EV回归模型,得到了未知参数LS估计的渐近正态性.     

浑水中非均匀光场探测图像方法

分析了传统的水下观测和激光观测技术在能见度约为0.5~1.5 m的浑浊水域和0.2 m的特浑水域观测遇到的理论和技术上的局限性.叙述了一种非均匀光场集束光水下目标图像探测方法和系统,并在各种浑浊水质中进行其特性的试验.试验结果表明该系统基本上解决了浑浊水中的观测问题.     

激光干涉法测引力常量

在扭摆法测量引力常量的基础上,提出利用激光干涉法测扭转偏角,并采用磁感应力来消减周围环境的噪声干扰,能使引力常量G的测量精度有很大提高.     

大尺度有效引力的E(2)规范理论模型

微波背景辐射的低l极矩的各向异性可能不能用微波背景辐射静止系boost到本动参考系来解释,我们推断boost对称性在宇宙学尺度上缺失,又由于单纯结合广义相对论和物质结构的标准模型不能解释星系以上尺度的引力现象,需要引入暗物质和暗能量.而迄今为止所有寻找暗物质粒子的实验给出的都是否定结果,暗能量的本质更是一个谜.因此,我们假设洛伦兹对称性是从星系以上尺度开始部分破缺,以非常狭义相对论对称群E(2)为例,用E(2)规范理论来构造大尺度有效引力理论,并分析了此规范理论的自洽性.从这些讨论中发现,当物质源即使为普通标量物质时,contortion也一般非零,非零contortion的存在会贡献一个等效能量动量张量的分布,它可能对暗物质效应给出至少部分的贡献.我们从对称性出发修改引力,有别于其他的修改引力理论.     

Existence, uniqueness, and convergence of the regularized primal-dual central path

In a recent work [J. Castro, J. Cuesta, Quadratic regularizations in an interior-point method for primal block-angular problems, Mathematical Programming, in press (doi:10.1007/s10107-010-0341-2)] the authors improved one of the most efficient interior-point approaches for some classes of block-angular problems. This was achieved by adding a quadratic regularization to the logarithmic barrier. This regularized barrier was shown to be self-concordant, thus fitting the general structural optimization interior-point framework. In practice, however, most codes implement primal-dual path-following algorithms. This short paper shows that the primal-dual regularized central path is well defined, i.e., it exists, it is unique, and it converges to a strictly complementary primal-dual solution.     

Estimating the spectral measure of an extreme value distribution

Let (X₁, Y₁), (X₂, Y₂),…, (X_n, Y_n) be a random sample from a bivariate distribution function F which is in the domain of attraction of a bivariate extreme value distribution function G. This G is characterized by the extreme value indices and its spectral measure or angular measure. The extreme value indices determine both the marginals and the spectral measure determines the dependence structure. In this paper, we construct an empirical measure, based on the sample, which is a consistent estimator of the spectral measure. We also show for positive extreme value indices the asymptotic normality of the estimator under a suitable 2nd order strengthening of the bivariate domain of attraction condition.     

MASSIVE SCALAR PARTICLE IN THE GRAVITATIONAL FIELD OF A MICROCOSMIC BLACK HOLE

The finite motion of a massive scalar particle in the gravitational field of a microcosmic black hole with weak relativistic approximation is discussed. In the Schwarzschild field, using the condition for balance σ=0, we obtain the relation between the produced and captured amplitudes for particles. In the Kerr field we show that the attenuation depends on the moment of the black hole and the attenuation process becomes an exciting one when ωh.     

Estimates of commutators for multilinear operators on Herz-type spaces

In this paper, the boundedness of mulitilinear commutator [b,T] on Herz-type space is considered, where T is a standard Calderón-Zygmund singular operator and b ∈ (BMO(Rn))m.