两两PQD序列的一个收敛性质

研究了一类广泛的随机变量序列两两PQD列的收敛性质,得到了与PA序列相类似的完全收敛性和强大数定律的结果.     

Some Convergence Properties for ψ-Mixing Sequences

In this paper,we extend the Kolmogorov-type inequality to the case of ψ-mixing sequences.Moreover,we study the strong limit theorems for partial sums of ψ-mixing random variables.As a result,we extend the Khintchine-Kolmogorov-type convergence theorem,the three series theorem,Marcinkiewicz strong law of large number to the case of ψ-mixing sequences.     

Riordan阵与Cauchy多项式

给出了Cauchy多项式c_n~α(z)的定义,并导出它的生成函数.再利用Riordan阵方法得到包含Cauchy多项式的一些恒等式,获得它与广义调和多项式H_n~((r))(z),广义Stirling多项式P_(n,r)(z)的关系式.     

随机变量阵列加权和最大值的收敛性

本文研究了形如maxun≤j≤un｜∑ji=un aniXni｜的弱大数律和Lr收敛性,其中0＜r≤p,0＜p≤2,{ani,un≤i≤vn,n≥1}是实数阵列,{Xni,un≤i≤vn,n≥1}当0＜p＜1时是任意随机变量阵列,当1≤p≤2时是均值为零的行为NA的随机变量阵列.所得结果丰富和推广了许多已知的结果.     

A Fourier transform Raman spectrometer with visible laser excitation

We present the development and performance of a Fourier transformation (FT)‐based Raman spectrometer working with visible laser (532 nm) excitation. It is generally thought that FT‐Raman spectrometers are not viable in the visible range where shot noise limits the detector performance and therein they are outperformed by grating based, dispersive ones. We show that contrary to this common belief, the recent advances of high‐performance interference filters makes the FT‐Raman design a valid alternative to dispersive Raman spectrometers for samples which do not luminesce. We critically compare the performance of our spectrometer to two dispersive ones: a home‐built single channel and a state‐of‐the‐art charge coupled device‐based instruments. We demonstrate a similar or even better sensitivity than the charge coupled device‐based dispersive spectrometer particularly when the laser power density is considered. The instrument possesses all the known advantages of the FT principle of spectral accuracy, high throughput, and economic design. We also discuss the general considerations, which helps the community reassess the utility of the different Raman spectrometer designs. Copyright © 2015 John Wiley & Sons, Ltd.     

纠正一道习题的解答

针对《近世代数习题解》中一道习题的错解,深入分析了错误的原因,利用一个概率问题的解答给出了正确的解答,并得到了第二类Stirling数的解析表达式.