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 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 nonlinear equation of aircraft is linearized by state transforming differential relationship between input and a new input, and the nonlinear system is decoupled to a one order linear system and a two order linear system.
中文: 通过状态变换输出与新输入间的线性微分关系使非线性飞机方程反馈线性化，将原非线性系统解耦为一个一阶和一个二阶线性系统。
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英文: This paper is to develop a model on synthesis reaction of methanol using material and thermodynamics balance, and to utilize MATLAB to solve multielement nonlinear equation set on proposed model, so calculate balance composition of reactions, parameters o
中文: 摘要通过物料平衡与势力学平衡对甲醇合成反应过程进行建模，并采用matlab工具对所建模型进行多元非线性方程组的求解，以根据给定操作条件来计算反应平衡组成、各股物料参数、各主要工艺指标如甲醇産量、消耗等，并继而定量分析各种操作条件对工艺指标的影响，以便指导实际化工生産操作，从而帮助确定最佳的合成操作工况条件，并可以根据给定的原料条件等参数预测合成産量与消耗等指标。
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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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