Functional methods for time series prediction: a nonparametric approach

The problem of prediction in time series using nonparametric functional techniques is considered. An extension of the local linear method to regression with functional explanatory variable is proposed. This forecasting method is compared with the functional Nadaraya–Watson method and with finite‐dimensional nonparametric predictors for several real‐time series. Prediction intervals based on the bootstrap and conditional distribution estimation for those nonparametric methods are also compared. Copyright © 2010 John Wiley & Sons, Ltd.     

随机Dirichlet级数表示的整函数的增长性

系统地研究了全平面上收敛的随机Dirichlet级数的增长性 .得到了类似于Dirchlet级数所表示的整函数的增长性的结果     

徐有壬的幂级数代数符号系统研究

介绍并研究徐有壬的幂级数代数符号系统的方法和特点。     

上下极限的概念在极限教学中的作用

讨论在《数学分析》课程中引入上、下极限概念的教学的意义 .指明了它对提高学生分析能力的作用     

Identification of asymmetric prediction intervals through causal forces

When causal forces are specified, the expected direction of the trend can be compared with the trend based on extrapolation. Series in which the expected trend conflicts with the extrapolated trend are called contrary series. We hypothesized that contrary series would have asymmetric forecast errors, with larger errors in the direction of the expected trend. Using annual series that contained minimal information about causality, we examined 671 contrary forecasts. As expected, most (81%) of the errors were in the direction of the causal forces. Also as expected, the asymmetries were more likely for longer forecast horizons; for six‐year‐ahead forecasts, 89% of the forecasts were in the expected direction. The asymmetries were often substantial. Contrary series should be flagged and treated separately when prediction intervals are estimated, perhaps by shifting the interval in the direction of the causal forces. Copyright © 2001 John Wiley & Sons, Ltd.     

关于Diophantine方程x~3+1=3py~2

设p是奇素数,证明了当p=108 s2+1,其中s是正整数时,方程x 3+1=3py2无正整数解(x,y).     

关于Hilbert不等式的一个改进(英文)

证明了重组数的经典Hilbert重不等式通过引入一个适当的形如π－θ／（θ＞0）的权函数可以把两个单独的和都得到改进。借助于Euler—Maclaurin求和公式得到了一个非常强的结果。     

汉江安康站最大径流量的动态预测模型研究

用平稳时间序列的ARMA( p ,q)模型分析法 ,分析了汉江安康站 1 943年到1 995年共 5 3年最大径流量的水文资料 ,建立了陕南汉江安康站最大径流量的中短期动态预测数学模型 .经对 1 996年和 1 997年的最大径流量进行预测 ,结果与实际相吻合     

正项级数敛散性判别法的推广

以正项级数∑1lnn(lnlnn)~β(β>0)为标准建立了比Gauss判别法更为精细的两种判别法,并推广到一般情况,从而得到了正项级数敛散性判别法的推广形式.     

石油测井时域电磁响应的数值计算

本文在圆柱坐标系中,用传输线矩阵法对电磁测井问题进行了时域计算.计算中采用横向三层油井模型,即井筒层、渗透层和真地层,并考虑上下围岩的影响.井筒层参数为σ=0.5、ε_r=80;渗透层σ=0.1、ε_r=20;真地层σ=0.025、ε_r=5,上下围岩σ=0.2、ε_y=30,收发点相距0.3m,计算电场 z 分量的时域响应.并讨论了当收发天线间的距离增大,去除围岩效应和真地层的电参数发生变化时的波形变化情况,证明了电磁测井仪器的可行性.