具有卷积的中心自反环

本文研究了具有卷积的中心自反环的性质,定义并引入了中心-自反环,显然,中心-自反环是自反环、中心自反环和-自反环的推广.给出了这类环的一些特征,研究了相关的环扩张,包括平凡扩张,Dorroh扩张和多项式扩张.     

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.     

相伴随机变量序列的泛函型几乎处处中心极限定理

对于均值为零的平稳相伴随机变量序列,首先证明了在L(n)=EX_1~2 2 sum from n to j=2 Cov(X_1,X_j)是一个缓变函数的条件下的泛函型几乎处处中心极限定理.另外还给出了正则化部分和函数的对数平均几乎处处收敛性.     

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.     

国家级弱磁实验室高精度中央空调设计

弱磁计量实验室对磁环境、温度控制精度均有严格要求.普通恒温恒湿空调器虽然能达到温度控制精度要求,但由于含铁磁物质,不能在该环境下使用;常规中央空调系统虽然可以满足磁环境要求,但难以满足温度波动小于0.2℃/h的温控精度要求.本项目设计采用中央空调加分区控温的方式较好地解决了该难题,设计中采用高效能热隔离、小温差送风、孔...     

Large Deviations Behavior for the Quadratic Error of Density Estimate

For a projection estimator f_n of an unknown density f we investigate the behavior of large deviations probability P{T_n > r_n} when r_n , where T_n is appropriately centered and normed quadratic error f_n-f)².     

Aberration-corrected catadioptric magnifiers useful for simple microfiche readers

The present paper considers the magnifying power and aberration properties of three different catadioptric magnifying systems useful for application as simple hand-held microfiche readers. These are in the form of a plano-convex lens, a meniscus lens and an achromatic doublet lens and all their outer surfaces have been coated with a semi-reflecting film so that they behave like catadioptric elements. These can be designed to give magnification in the range of 15 × to 25 × with sufficient eye relief. Using such magnifiers, it is possible to read microfiche having frame sizes of 16 × 12 mm and 12 × 9 mm. The cemented achromatic doublet coated on the outer surfaces seems to give a very good image for use in microfiche reader.     

Estimation of vector ARMAX models

The asymptotic properties of maximum likelihood estimates of a vector ARMAX system are considered under general conditions, relating to the nature of the exogenous variables and the innovation sequence and to the form of the parameterization of the rational transfer functions, from exogenous variables and innovations to the output vector. The exogenous variables are assumed to be such that the sample serial covariances converge to limits. The innovations are assumed to be martingale differences and to be nondeterministic in a fairly weak sense. Stronger conditions ensure that the asymptotic distribution of the estimates has the same covariance matrix as for Gaussian innovations but these stronger conditions are somewhat implausible. With each ARMAX structure may be associated an integer (the McMillan degree) and all structures for a given value of this integer may be topologised as an analytic manifold. Other parameterizations and topologisations of spaces of structures as analytic manifolds may also be considered and the presentation is sufficiently general to cover a wide range of these. Greater generality is also achieved by allowing for general forms of constraints.     

Central limit theorem and weak law of large numbers with rates for martingales in Banach spaces

This paper is concerned with large-$\text{O}$ error estimates concerning convergence in distribution as well as norm convergence for Banach space-valued martingale difference sequences. Indeed, two general limit theorems equipped with rates of convergence for such difference sequences are established. Applications of these lead to the central limit theorem and the weak law of large numbers with rates for Banach space-valued martingales.