以下为句子列表：
英文: By constructing the geometrical model of a certain underground single arm type pantograph and applying the translation of pantograph-head balancing bar and the perpendicular displacement of pantograph in the direction of the movement of locomotive while r
中文: 摘要在建立某地铁单臂受电弓简化几何模型的基础上，根据列车平稳受流对受电弓提出的各项要求，以受电弓升弓时机车前进方向上的纵向偏移量和弓头平衡杆的平动为目标，以受电弓正常升弓所需升弓转矩等为约束，运用基于遗传算法的多目标优化技术，对该型受电弓机构进行了优化，得到了使受电弓运动性能达到最优的几何参数。
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英文: The aim of this paper is to investigate the asymptotically mean square stability (MS-stable) of the analytical solution and the numerical method (the continuous θ-method) for a linear stochastic pantograph equation.
中文: 摘要本文目的是研究线性随机比例方程解析解和数值方法（连续θ-方法）的渐近均方稳定性。
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英文: The optimum geometric parameters, which could improve the pantograph performance, could be obtained successfully.
中文: 并运用虚拟样机技术对弓头升弓轨迹、升弓转矩和平衡杆摆动角度等优化所得参数进行了仿真验证。
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