中文摘要：

该文首次研究以0为飞射壁的生灭过程爆发前的若干性质，通过引入线性方程组和推移算子，得到了多种情况下此类过程在爆发前从状态i出发运动到状态n（i≤n≤∞或n≤i）的概率和平均时间的精确表达式．同时，我们还定义了mi，ei，Ni，R等一系列特征数，并表明了这些特征数的概率意义。

英文摘要：

This paper first deals with some properties of birth and death processes with state 0 as their leap-reflecting barriers before explosion. By proposing a system of linear equations and shift operator, the authors obtain some precise expressions of both probability and average time when the processes move from state i to state n （i≤n≤∞ or n ≤ i） in several cases. On the other hand, the authors not only give a new definition of the characteristic numbers such as mi, Ni, R, ei etc, but also show their probability meanings.