The convergence of Cesaro averages for certain nonstationary Markov chains

If P is a stochastic matrix corresponding to a stationary, irreducible, positive persistent Markov chain of period d>1, the powers Pⁿ will not converge as n → ∞. However, the subsequences P^nd+k for k=0,1,...d-1, and hence Cesaro averages Σⁿ_k-1 P^k/n, will converge. In this paper we determine classes of nonstationary Markov chains for which the analogous subsequences and/or Cesaro averages converge and consider the rates of convergence. The results obtained are then applied to the analysis of expected average cost.     

超曲面上具有非光滑密度之测度的Fourier变换

设Ｓ是Ｒ~ｎ中具有非零Ｇａｕｓｓ曲率的光滑闭曲面,ｄσ是Ｓ上的Ｌｅｂｅｓｇｕｅ诱导测度．若密度函数Ψ∈Ｃ∞（Ｓ） 则测度 ｄμψ＝ψｄσ的 Ｆｏｕｒｉｅｒ变换│d　　　　　　　 本文证明,若ψ非光滑则上述结论一般不成立;但对于ψ∈Ｌ~p（S,dσ）ｐ≥２在适当条件下, ｄμψ 仍有相应的衰减估计．应用所得结论可获得球面 Ｓ~（ｎ－１）上一种加权极大平均算子的有界性．     

Construction of polynomial matrix using block coefficient matrix representation auto-regressive moving average model for actively controlled structures

The polynomial matrix using the block coefficient matrix representation auto-regressive moving average (referred to as the PM-ARMA) model is constructed in this paper for actively controlled multi-degree-of-freedom (MDOF) structures with time-delay through equivalently transforming the preliminary state space realization into the new state space realization. The PM-ARMA model is a more general formulation with respect to the polynomial using the coefficient representation auto-regressive moving average (ARMA) model due to its capability to cope with actively controlled structures with any given structural degrees of freedom and any chosen number of sensors and actuators. (The sensors and actuators are required to maintain the identical number.) under any dimensional stationary stochastic excitation. The project supported by the National Natural Science Foundation of China (50278054)     

Comparison of the cuscore, GLRT and cusum control charts for detecting a dynamic mean change

Although statistical process control (SPC) techniques have been focused mostly on detecting constant mean shifts, dynamic and time-varying process changes frequently occur in the monitoring of feedback-controlled and autocorrelated processes. In this research, the performances of cumulative score (Cuscore), generalized likelihood ratio test (GLRT), and cumulative sum (CUSUM) charts in detecting a dynamic mean change that finally approaches a steady-state value are compared. Theoretical results in average run length (ARL) comparison are provided. From the theretical study we find that, when the steady-state value is greater or less than a critical value,Rδ/2+δ/2, the Cuscore and CUSUM charts have a different performance in detecting the mean change. We prove also that the GLRT has the best performance among the three charts in detecting any mean change for which the steady-state value is not equal to δ or δR, when the in-control ARL is large.     

Some Mean Values Related to Average Multiplicative Orders of Elements in Finite Fields

For any positive integer n let α(n) denote the average order of elements in the cyclic group Z_n. In this note, we investigate the functions α(n)/n and α(n)/φ(n) when n ranges through numbers of the form p−1 with p prime, and when n ranges through numbers of the form 2^m−1 with m a positive integer. In particular, we show that such functions have limiting distributions, and we compute their average values, and their minimal and maximal orders.To Jean-Louis Nicolas at his 60th birthday2000 Mathematics Subject Classification: Primary—11N45; Secondary—05A16, 11N37This work was supported in part by Grant SEP-CONACYT 37259-E.     

积分球的光功率波形变换理论

分析说明了积分存在一次反射短时平均等照度性质，提出了积分球的几个概念：平均反射程λ、平均反射时间μ、平均反射率ρ^-、平均出射程η、平均出射时间τ（等于积分球的时间常数）。用分析方法推导了积分球时间常数的一般表达式、积分球对δ函数形式的功率波形的变换表达式、积分球对任意光功率波形的变换表达及其反变换表达式。     

一种积分数据的函数重构及其误差估计

本文考虑了一种基于函数积分平均值的函数重构方法,在定义了一个插值算子之后建立了误差估计.从理论分析结果可以看出这种方法得到的解是适定的,因此我们不需要选择正则化参数,这样就简化了算法,而且最后一系列的数值结果很好的验证了这种方法的有效性.     

基于加权减影的非等厚工件的X射线检测

针对X射线对厚度不均匀工件进行DR(DigitalRadiography)缺陷检测需要两次成像的问题,以实现一次成像全方位检测缺陷为目的,提出了减影和加权的处理方法。运用这种方法,恰当地提取每个像素点中的背景因素,把像素点之间相互影响的程度用合理的权重表达,最终改善了灰度显示的动态范围,降低了噪声对图像的污染、保护了缺陷的边缘和细节。     

公路沿线基准地价评估的数学模型

从投资将导致地价增值的观点出发，建立了新建成改建公路沿线基准地价评估的分段指数递减的数学模型，采用“四三二一”法则建立了公路两侧不同纵深土地的基准地价评估的数学模型，并应用于宁波市江北区公路的基准地价评估，取得了较为满意的效果。