几何基础

The geometric thinking in the analysis Liman, on the basis of mathematics and physics it focuses on the two areas of the far-reaching implications.

本文在分析黎曼的几何思想的基础上，着重论述了它对数学和物理学两个领域所产生的深远影响。

By the aid of a example, the parameters were solved with the tangent line of a circle, the intersection point of tangent and thecoordinates defined by the geometrical relationship of the image based on two propositions proposed in the paper.

借助实例，在文中建立的2个命题的基础上，通过对圆的切线、切线交点及所成像的几何关系确定的的坐标进行参数求解，得到确定模型的二维像和三维像。

The paper resolves the difficulty of time and space integration through the geometry principle based on the hypothesis of the linear density distribution that is adopted here.

本文在推导过程中采用了稠密车流线性化密度分布的假设，并在此基础上利用几何原理解决了时空积分的困难。

Once more, applys three-dimensional CAD software Pro/Engineer establishing the geometry models of all kinds of parts in the crank link mechanism, then useing the Pro/E software assembling function assembles the components of crank link into the piston module, the connecting rod module and the crank module, then using Pro/E software mechanism analysis module (Pro/Mechanism), establishes the multi-rigid dynamics model of the crank link, and carries on the kinematics analysis and the dynamics analysis simulation, and it studies the piston and the connecting rod movement rule as well as crank link motion gear movement envelopment. The analysis of simulation results shows that those simulation results are meet to true working state of engine.

再次，应用三维CAD软件：Pro/Engineer建立了曲柄连杆机构各零部件的几何模型，在此工作的基础上，利用Pro/E软件的装配功能，将曲柄连杆机构的各组成零件装配成活塞组件、连杆组件和曲轴组件，然后利用Pro/E软件的机构分析模块(Pro/Mechanism)，建立曲柄连杆机构的多刚体动力学模型，进行运动学分析和动力学分析模拟，研究了在不考虑外力作用并使曲轴保持匀速转动的情况下，活塞和连杆的运动规律以及曲柄连杆机构的运动包络。

Web-based application system of geometric error compensation aims to broaden error compensation technology by using network. SMART-CNC machine tool has been chosen as the object of experiment. Based on the kinematics of multi-body system, the movement equation for SMART-CNC machine tool has been built.Furthermore, web-based error compensation system has been implemented.

基于Web的数控曲面磨床几何误差补偿技术：以误差补偿技术的网络化应用为目的展开研究，选取SMART-CNC 数控曲面磨床为研究对象，运用多体理论，建立了磨床的运动模型，获得了与精密刀具轨迹相对应的逆变刀具路线或逆变数控指令的求解方法，在此基础开发了基于网络的误差补偿软件，构建了网络化误差补偿服务系统。

MANDER constructive model is used to simulate stress-strain relationship of confined concrete; three sensitive parameters (pier height, confined index and concrete strength) are analyzed and the effect rule that how non-linear constructive model of reinforced concrete affects load of high pier is obtained.

由于高桥墩的几何非线性及材料非线性本构关系所导致的二次效应非常显著，因此采用传统的以弹性理论为基础的设计计算方法求算高柔桥墩的内力和变形会引起较大偏差。

In Chapter 2, equalization is described as a space mapping in the geometry space with the view of mathematics, which establishes the base for the application of Neural Networks.

第二章用数学的观点将均衡问题表述为几何空间的区域划分判决问题，为神经网络的应用奠定基础。

Then, the equation was changed into the standard form of the Mathieu equation using Galerkin method.

首先在载流薄板的磁弹性非线性运动方程、物理方程、几何方程、洛仑兹力表达式及电动力学方程的基础上，导出了载流薄板在电磁场与机械荷载共同作用下的磁弹性动力稳定方程，然后应用Galerkin方法将稳定方程整理为Mathieu方程的标准形式，并将薄板的动力稳定性问题归结为对Mathieu方程的求解。

Accurately considering the axial extension and first order transverse shearing deformation, the geo metrically nonlinear governing equations for functionally graded Timoshenko beam subjected to mechanical as well as thermal loads were established. In the analysis it was assumed that the material properties of the beam vary continuously as a power function of the thickness.

在精确考虑轴线伸长和墓于－阶横向剪切变形理论的基础上建立了功能梯度Timoshenko梁受热－机载荷作用时的几何非线性控制方程，其中功能梯度梁的材料性质采用了沿厚度方向按照幂函数连续变化的形式。

Geodesic, which was initially proposed by Bernoulli and ever demonstrated by Gauss, is as a foundational concept in the modern differential geometry and has been used as one of the foundations of all the general relativity. However, it implicates lots of logic paradoxes.

作为构造整个"广义相对论"的形式基础之一，现代微分几何中由Bernoulli最初提出并经过Gauss论证的"测地线"概念隐含大量逻辑悖论。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。