黎曼流形上的一般Sobolev型不等式

给出了流形上与一般Sobolev型不等式等价的等周不等式和热核上界条件,推广了经典Sobolev不等式的相应结果.     

一类双切Nevanlinna-Pick 插值问题的可解条件

用基本矩阵不等式方法给出Cm(T,2π-T)函数类中m×m的矩阵函数双切Nevanlinna-Pick插值问题的可解条件.     

利用Arnold对称性变换的图像信息隐藏算法

提出了一种利用Arnold对称性变换的图像信息隐藏算法.待隐藏的秘密信息以及公开的承载信息均为灰度级静止图像.首先使用图像置乱技术将秘图变换成无意义的图像,同时用一个数值控制置乱的次数,并在嵌入和提取时作为密钥.在此基础上,将密图嵌入到承载图像的DCT域系数中.该算法实现的隐藏图像透明性好,并具有较高的保密性和一定的稳健性.     

Orlicz空间上的Markov-Bernstein型不等式

借助D.S. Lubinsky & P. Nevai的方法,推广了D.S. Lubinsky & P. Nevai的结果,并用它证明了Orlicz空间上带权的 Markov-Bernstein型不等式.为得到Orlicz空间上多项式逼近的逆定理提供了理论基础.     

关于Steffensen型不等式

将众所周知的Steffensen积分不等式推广到Stieltjes积分的情形.     

研究性学习在线性变换教学中的应用

研究性学习是数学教学中一种重要的教学方式,通过考虑两个线性映射的值域与核之间的关系,得到了Sylvester不等式和Frobenius不等式的证明,并且给出这两个不等式中等号成立的充分必要条件,为研究性学习提供了一个教学案例.     

The usefulness of heuristic N(E)RLS algorithms for combining forecasts

There exists theoretical and empirical evidence on the efficiency and robustness of Non-negativity Restricted Least Squares combinations of forecasts. However, the computational complexity of the method hinders its widespread use in practice. We examine various optimizing and heuristic computational algorithms for estimating NRLS combination models and provide certain CPU-time reducing implementations. We empirically compare the combination weights identified by the alternative algorithms and their computational demands based on a total of more than 66,000 models estimated to combine the forecasts of 37 firm-specific accounting earnings series. The ex ante prediction accuracies of combined forecasts from the optimizing versus heuristic algorithms are compared. The effects of fit sample size, model specification, multicollinearity, correlations of forecast errors, and series and forecast variances on the relative accuracy of the optimizing versus heuristic algorithms are analysed. The results reveal that, in general, the computationally simple heuristic algorithms perform as well as the optimizing algorithms. No generalizable conclusions could be reached, however, about which algorithm should be used based on series and forecast characteristics. © 1997 John Wiley & Sons, Ltd.     

一个加性混合幂丢番图不等式

证明了如果η是实数, λ1,μ1,μ2,μ3,μ4,θ1,θ2是非零实数,并且不同一符号,至少有一个λ1/μj (i=1,2,3,4)是无理数, 那么对任意0<σ<1/30,不等式|λ1x21+μ1x32+μ2x33+μ3x34+μ4x35+θ1x46+θ2x57+η|<(max|xi|)-σ有无穷多整数解x1,...,x7.     

积分不等式性质的推广

推广了定积分不等式性质。通过讨论定积分不等式中不等号严格成立的充分必要条件,给出了不等号严格成立的一些判别方法,并通过举例说明了结论的应用。     

离散型随机变量的分布律与Toeplitz矩阵

本文分别利用对数分布的随机变量分布律和负二项分布的随机变量的分布律构造出两类Tocplitz矩阵,并讨论其特征,得到了一些较好的结果.