以下为句子列表：
英文: A nonlinear equation of fluid-solid coupling for vibration of hydraulic-turbines was developed based on finite element method.
中文: 文中基于有限元法建立水力机组流固耦合振动的控制方程。
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英文: By the method, the two-dimensional implicit method can be induced in soluting tridiagonal linear equation group.
中文: 这种方法可以将二维隐式方法归结为求解三对角线性方程组。
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英文: By using a nonlinear equation satisfied the charge operator, the spectrum is calculated exactly in energy basis for each cell.
中文: 根据电荷算符满足的非线性运动方程，在各单元能量基上，精确地计算了能谱。
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英文: The complex pressure distribution in the model makes the fluid flow computation of horizontal well be fairly complicated, so the non-linear equation describing fluid flow performance has been applied for space iterative computation followed by time iterat
中文: 由于所用气藏模型压力分布较为复杂，使得水平井的流动计算变得相当复杂，应用表征流动特性的非线性方程对空间进行迭代计算，再向时间推进。
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英文: Bifurcation phenomenon of the nonlinear equation f(x,λ)=(x x +λx +λ ,-x -x ) T=0 near the origin is studied by using LS reduction and Newton′s diagram,three branches bifur cating equilibrium point is obtained.
中文: 利用LS简约和Newton图研究了非线性方程 f(x ,λ) =(xx +λx +λ ,-x-x ) T =0 在原点附近的分岔现象 ,得到了从平衡点分枝出来的全部实的三个解枝 .
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