Jian Shen

collaborators

2 papers

math.CO2009

A bound on the scrambling index of a primitive matrix using Boolean rank

Mahmud Akelbek, Sandra Fital, Jian Shen

The scrambling index of an $n \times n$ primitive matrix $A$ is the smallest positive integer $k$ such that $A^{k} (A^{t})^{k} = J$ , where $A^{t}$ denotes the transpose of $A$ and $J$ denote…

math.PR2009

On the Borel-Cantelli Lemma and its Generalization

Chunrong Feng, Liangpan Li, Jian Shen

Let ${A_{n}}_{n = 1}^{\infty}$ be a sequence of events on a probability space $(Ω, F, P)$ . We show that if $lim_{m \to \infty} \sum_{n = 1}^{m} w_{n} P (A_{n}) = \infty$ …