The proposed methods are based on the modal coordinate equations, to avoid the tedious mathematical manipulation.
该方法建立在模态方程的基础上，避免了繁杂的数学过程。
Additionally, a mathematical manipulation is adopted to remove the second-order spacial derivatives in the body surface boundary condition.
对二阶物面边界条件采用数学手段，推导出一个没有二阶空间导数的表达式，以便于计算。
A model for optimizing fault diagnosis for power systems is formulated as a 0-1 integer programming problem. The fault equipment can be determined by means of refined mathematical manipulation.
电网故障诊断优化模型可将诊断问题表示成求极值的0-1整数规划问题，从而可通过严密的数学运算来确知故障设备。
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