For locating the critical failure surface, the particle swarm or the harmony method is used, which is an upper bound approach.
而搜索临界滑裂面的过程，采用粒子群法或和声法搜索最危险滑动面。
The paper forword a mathematical model of stream function for sinkings with no internal mandrel and applies the upper bound approach principle to make further deduction and calculation.
对无芯棒缩管提出了流函数的数学模型，应用上限原理加以推导和数值运算。
The differential and integral equation for survival probability and a upper bound of ruin probability are given by using renewal theory and stochastic process approach.
利用更新理论和随机过程等方法，给出了模型生存概率所满足的微积分方程关系式和破产概率的一个上界估计。
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