For each failure mode, an explicit formula is derived for the prediction of shear strength.
对于每一种破坏模式，给出了受剪承载力计算公式。
The normwise structured backward error of an approximate eigen-pair is defined and its explicit formula is given.
给出一类周期特征值问题的向后误差分析，定义了特征对的范数型结构向后误差，并给出了显式表达式。
For critical state model, the author derives an explicit formula of matrix h, which is used in implicit computation scheme.
对临界状态模型推导了用于隐式计算格式的H矩阵的显式表达式。
For Bingham type plastic fluid modal, the explicit formula for calculating the pumping pressure is obtained, which can be used to choose the pump type.
对于宾汉型塑性流体模型，得到了计算驱动压力的显式计算公式，据此可进行污泥泵型选择。
A two-strain SIR epidemic model is discussed and an explicit formula for the basic reproductive number is derived by analyzing the local stability of the trivial equilibrium.
讨论了一类由两种不同病毒导致的SIR流行病模型，分析了平凡平衡点的局部稳定性，得到了基本再生数的数学表达式；
When a inverse function of monotone function can not show the explicit formula, the distribution density curve of continuous randon variable can be gained with a parametric equation.
当单调函数的反函数不能显性表示时，连续型随机变量的分布密度曲线仍可通过参数方程的形式获得。
At each iteration, a master direction is obtained by solving one direction finding subproblem which always possesses a solution, and an auxiliary direction is yielded by an explicit formula.
在每次迭代中，主方向是通过求解一个总有解的寻找方向子问题产生，而辅助方向是由一显式公式计算产生。
This thesis also presents an explicit formula that converts a triangular SBGB patch of degree n to a degenerate rectangular SBGB patch of degree nxn by reparametrization and the SBGB dual bases.
利用SBGB型基函数的对偶泛函，推导出SBGB三角曲面片到退化矩形曲面片的顶点转化公式。
This thesis also presents an explicit formula that converts a triangular SBGB patch of degree n to a degenerate rectangular SBGB patch of degree nxn by reparametrization and the SBGB dual bases.
利用SBGB型基函数的对偶泛函，推导出SBGB三角曲面片到退化矩形曲面片的顶点转化公式。
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