在详细的数学推导之后，给出了金属疲劳断裂几率即一个变上限复杂积分的近似解析函数表达式，并与计算机的数值曲线进行了比较。
Following a detailed mathematical derivation a new approximate algorithm for the fatigue fracture of metals is given namely a complicate integral having a changing upper limit.
在柱坐标系中，求出了绝对零度情况下近理想玻色气体涡旋态的波函数和能量的近似解析形式。
Approximate analytical solutions of wave function and energy of vortex in the cylindrical coordinates system are obtained for the near-ideal Bose gases at zero temperature.
以高斯光束的变换为例，推导出了一个表示为初等函数之和的近似解析传输公式。
The transformation of Gaussian beams is taken as an example, an approximate analytical propagation expression in terms of a sum of elementary functions is derived.
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