不满足交换律(x1+x2+…+xm)n系数的性质

本文给出了当x1,x2,…,xi满足(x1 x2 … xi-1)xi=a(x1 x2 … xi-1)2 qxi(x1 x2 … xi-1) bx2i时,(x1 x2 … xm)n的展开式,以及当a=0、b=0特殊情况时系数的性质。     

求自然数方幂和的简单方法

讨论了利用二项式公式求自然数的方幂和的简单、实用方法。     

复合二项风险模型破产概率的鞅方法证明

讨论一般情形的复合二项风险模型，首先构造一个离散鞅，应用可选抽样定理和收敛定理，给出该风险模型的最终破产概率公式的简洁证明，并得出最终破产概率一个易于计算的上界表达式．     

与级联三能级原子相互作用的二项式光场的熵压缩

运用量子熵理论并借助于数值计算方法。研究与级联三能级原子相互作用的二项式光场的熵压缩性质．光场的初始参量对光场熵压缩的影响．当初始光场处于相干态时．在较短时间内光场出现熵压缩效应；当初始光场处于中间态时。光场熵压缩的深度和持续时间增加；当初始光场过渡到数态时．光场熵压缩明显减弱直到消失．研究结果表明：在与原子相互作用过程中。从相干态到数态过渡的中间态光场具有较好的熵压缩性质．     

二项分布可靠度的Bayes估计

在二项分布的可靠度的先验分布为幂分布时给出了其在熵损失函数下的E—Bayes估计公式和多层Bayes估计公式．通过实例验证,这两种估计公式都是稳定的,并进一步表明了在熵损失函数下计算出的二项分布可靠度的E—Bayes估计比多层Bayes估计的精度更高,稳定性更好,计算简单,便于应用．     

Modeling citation behavior in Management Science journals

Citation rates are becoming increasingly important in judging the research quality of journals, institutions and departments, and individual faculty. This paper looks at the pattern of citations across different management science journals and over time. A stochastic model is proposed which views the generating mechanism of citations as a gamma mixture of Poisson processes generating overall a negative binomial distribution. This is tested empirically with a large sample of papers published in 1990 from six management science journals and found to fit well. The model is extended to include obsolescence, i.e., that the citation rate for a paper varies over its cited lifetime. This leads to the additional citations distribution which shows that future citations are a linear function of past citations with a time-dependent and decreasing slope. This is also verified empirically in a way that allows different obsolescence functions to be fitted to the data. Conclusions concerning the predictability of future citations, and future research in this area are discussed.     

词偏序集上反演公式的推广

在客斥原理和Gould—Hsu反演公式的基础上,提出了新词(word)偏序集上的广义二项式系数的性质,并结出了一个反演公式。     

泊松分布与负二项分布在风险管理中的应用

讨论了泊松分布与负二项分布的优良特性及相互关系,以便在风险管理中更好地运用它们.