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The integral equation can be simplified by means of Laplace transforms methods.

最后对所得的积分方程进行数值求解得到桩的剪力、弯矩和位移。

The integral equation can be simplified by means of Laplace transform.

对所得的积分方程进行Laplace变换，得到变换域内的积分方程。

The human heart is the center of the cardiovascular system. Integrated with mechanical, electrical, neural and biochemical properties, the heart is difficult to model, and there is no ideal integral model now. The developed electrical models haven't considered the mechanical properties and blood flow process in the heart; while the mechanical ones have normally deal with the heart in the diastole period, and the electrical activity was simplified too much although some mechanical models have investigated the heart during systole.

心脏是循环系统的核心，它集机、电、神经和生化控制于一体，建模难度很大，目前尚无较理想的统一模型；心脏电生理模型未与心脏的机械动力过程和血液流动过程联系起来；而心脏力学模型大都只研究舒张期的力学特性，即使研究收缩期心脏的力学问题，也往往对心电兴奋做了许多简化假设。

In the case of simply supported ends, the Galerkin method is used to simplify the integro-partial-differential equation into an integro -differential equation. The equation is further simplified into a set of ordinary differential equations by introducing an additional variable. Finally, the numerical methods in modern nonlinear dynamics such as phase plane trajectory, power spectrum and Lyapunov exponents are adopted to investigate the dynamical behavior of the beam.

对于两端简支的情形，采用Galerkin方法简化为常微分－积分方程；然后通过引进附加变量的方法进一步简化为常微分方程；最后利用相平面图、功率谱和Lyapunov指数等非线性动力学中的数值方法识别梁的动力学行为。

He says the two-stage interceptor is a simplified version of the three-stage version used above the Pacific.

他说欧洲的两阶段防御是太平洋三阶段防御的简化版本。

A formula of rock resistant coefficient is derived based on unified strength theory, which can be adopted to obtain rock resistant coefficient in other situations or strength thoeries simplified by assuming the parameter value in the formula. The strength differential effect, intermediate principal stress effect and the ground water permeation effect are considered in the formula.

基于统一强度理论，将巷道围岩视为多孔介质，考虑地下水渗流作用的影响，推导出了巷道围岩抗力系数计算统一公式，改变公式中的参数可以退化为其他围岩条件或者其他强度理论条件下的围岩抗力系数计算公式。

The Turing test is often simplified to one in which a machine attempts to convince a human interrogator that it is a human.

图灵测试通常被简化为这样一种形式：机器试图让人类询问者相信它是人类。

This algorithm simplified the calculational methods of point of intersection and improved system speed.

该算法生成的真实感图形显示效果好，接近光线追踪生成的真实感图形。

As an accurate analysis seems to be intractable, part of our analysis is based on a simplified model.

由于准确分析难以实现，本文的部分分析基于一个简化的模型。

Presents the design of longitudinal control for ASTOVL lift-fan aircraft, a multi-variable, strong-coupling, complicated nonlinear system to make the system nonlinear offset and decouple, and the method used for linear system in designing the system to gain expectant flying qualities and the combination of aerodynamic control surfaces with thrust vectors to delay the control surfaces getting into saturation, and the minimum N-norm generalized inverse theorem of weighted generalized inverse adopted to apportion the moments commands, which make the control surfaces gain appropriate deflection and the simulation results to verify the dynamic inverse control laws designed really make the system nonlinear offset and decouple; when one command is given, only this output will response, and others do not response; when all commands are given together, the responses will be just the linear superpose of the response of each command, therefore the operation of the pilot will be simplified greatly.

摘 要： ASTOVL升力风扇飞机是多变量、强耦合、复杂的非线性系统，采用非线性动态逆理论设计控制律以实现系统的非线性对消及解耦，然后，采用线性系统的设计方法对系统进行设计，以使系统获得期望的飞行品质。同时，考虑到ASTOVL升力风扇飞机是由气动舵面和推力矢量融合作用的，为了延缓各舵面进入饱和的时间，采用加权广义逆中的极小N-范数广义逆定理分配力矩指令，从而使各舵面达到适当的偏转角。并将所设计的控制律进行了仿真，结果验证了所设计的动态逆控制律使系统实现了非线性对消和解耦，单个指令作用时，只有该项响应，其余不受影响；所有指令作用时，其结果就等于单个指令作用时的线性叠加，这样使驾驶员的操纵大大简化而易于控制，从而大大降低了飞行事故率。

My father is over 60 years old, and he lifts weights every day.

我爸爸六十多岁了，他每天都练习举重。

Then in a serious tone she declared:"It doesn't pay, dear boy, to look like a ninny with one's wife the first night."

两眼湿润了，她把身子蜷得很小，这样似乎可以更好地闻闻自己。