导出方程

From the motion equation of the bar which vibrates one-dimensionally and longitudinally, the model of mechanical four-terminal network and the transfer equations are set up, and the natural frequency equation of coniform horn and the ratio of speed of vibration are derived.

从变截面杆作一维纵振动的运动方程出发，建立机械四端网络的数学模型及传输特性方程，导出了圆锥形变幅杆的频率方程和振速比。

On the basis of the thermal balance equation,specific inner work equation,cyclic heat absorption equation of a thermal system and the standard coal-consumption calculation formulae of power generation,derived was a general calculation model featuring the influence of lower terminal temperature difference of a heater on the coal consumption of a power plant.

根据热力系统热平衡方程、比内功方程、循环吸热量方程及发电标准煤耗率计算公式，导出了加热器下端差对机组煤耗影响的通用计算模型；并且在考虑到加热器下端差的影响的基础上，改进了以往的建模方法，得到了更为完善的加热器上端差对机组煤耗影响的通用计算模型。

The forward kinematics is analyzed by choosing one of the mechanisms which have one, two,three or zero angle constraint.Wherein,3-CCC is a new parallel mechanism which has three angle constraints and three distance constraints, Calay\'s formular and direction cosine matrix are used to describe the rotation matrix respectively.By setting Dixon\'s and Sylvester\'s resultant with the three angle constraint equations respectively and using parameters replacement to deal with the distance constraint equations,the 64 order input-output equation of the forward kinematics is obtained under both of the methods.Numerical example confirms these theretical results and the motion simulation is shown in VC++ by integrating OpenGL.

3对高小山提出的广义并联机构进行了研究，以其中具有角度约束的并联机构进行了分析，选取具有一个、两个、三个和零个角度约束类型中各一个机构进行了运动学正解求解，其中3-CCC是一种全部由圆柱副构成的具有三个线线角度和三个距离约束的新型并联机构，文中分别用Calay公式和方向余弦两种旋转矩阵建模方法对其位置正解进行了分析，通过对三个角度约束方程分别构造Dixon结式和Sylvester结式，以及对三个距离约束方程进行变量代换分别导出了位置正解输入输(来源：4040ABC论文网www.abclunwen.com)出方程，得出64组位置正解，并使用数值算例验证了其全部根。

Based on Crank-Nicoson's technique, and a new approach for the numerical simulation of the model is raised. The truncation error of the one step difference method reaches O (△t^2+△x^2) and of quite good stability condition.

基于Coriolis加速度和Lagrangian应力公式，利用Newton第二定律导出轴向加速度运动弦线横向振动的动力学模型；通过线性变换将方程化为一阶无量纲的非线性微分方程组；并利用Crank-Nicoson的中点离散技巧，给出运动方程的单步二阶差分方法；算法把对运动方程和本构方程分别离散，使之可以用于不同本构的运动弦线的数值仿真。

Firstly, the author establish the functions of stability on the basis of the spline function method ,according to the theory of geometrical nonlinear and the theory of stability, educe the stability equation of structure based on variational principle, then carry through the flexuosity analysis of CFST arch.The big distortion geometrical nonlinear was considered by the stability equation,the author simplified the problem of geometrical nonlinear through ignored quadratic term and reserve the simple term, at last boiled down to solve the linear stability equation of eigenvalue .

利用样条函数方法、根据几何非线性变形理论和结构稳定性理论，先建立起结构稳定的泛函，再由变分原理导出结构的稳定方程，进行钢管混凝土拱屈曲分析；本文所建立的稳定方程考虑了几何非线性的大变形效应，通过忽略几何非线性的二次项，保留一次项，将几何非线性问题简化，最后归结为求解线性稳定问题的特征值稳定方程，建立了结构非线性静力稳定性问题的新算法及失稳类型判别准则。

The functional by variational calculus leads to a set of elliptic partial differential equations,in particular,Poisson equations,which is possibly solved by numerical methods.

利用变分法可以从这个二次误差指标函数导出一组椭圆形偏微分方程泊松方程，这类方程有相当成熟的数值解法。

An inhomogeneous Benjamin-Davis-Ono-Burgers equation including topographic forcing and turbulent dissipation is derived in terms of the quasi-geostrophic vorticity equation, an approximate analytic solution of the BDO-Burgers equation with a small dissipation is obtained, the time variations of mass and energy of the algebraic solitary waves are discussed, and finally, the forced BDO-Burgers equation is integrated numerically and the numerical solutions are given for a given basic flow with a weak shear and a localized topographic forcing.

利用包括地形外源和湍流耗散的准地转涡度方程导出了包含强迫项和湍流耗散项的非齐次强迫BDO-Burgers方程，求出了小耗散存在情况下BDO-Burgers方程的近似解析解，讨论了代数孤立波的质量和能量的守恒关系，最后，对给定的弱切变基本气流和局地地形强迫，数值积分强迫BDO-Burgers方程，求得了不同参数下的数值解。

At first,the limitation of the general heat conduction equation is discussed and then,nonlinear heat conduction equations are derived,when we consider that thermal conductivity,specific heat capacity and density are dependent of temperature.

研究了线性情形中热传导方程的局限性，在此基础上考虑到热传导方程中导热系数、比热容、密度与温度的关系，导出了非线性热传导方程，并求出了几类非线性热传导方程的孤波解。

Considering that thermodynarmic irreversibility and hydrodynamic equations can not be derived rigorously and unifiedly from the Liouville equations, the anomalous Langevin equation in the Liouville space is proposed as a fundamental equation of statistical physics.

考虑到热力学不可逆性和流体力学方程不能严格统一地从刘维方程推导出，本文提出了刘维空间的反常朗之万方程作为统计物理的基本方程。

An algorithm called initial function method for the solution of differential equation with tension is also given.

推导出了不考虑拉伸和考虑拉伸情况的弹性环形变微分方程，导出了求解不考虑拉伸情况的弹性环形变微分方程的差分方程和算法，还给出了可谓之初参数法的求解考虑拉伸情况的弹性环形变微分方程的算法。

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。