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This dissertation is devoted to a very important equation system among differential equation systems------quasi-linear equation system, as is a important topic of equation system(especially when discussed shock wave solution), Often appear in such research fields as Hydrokinetics, the semiconductor establishes in physical theory ,Chemical reaction theory , project, Biology , Communication and Ecology etc.

中文摘要:本论文主要研究了微分方程中的一类很重要的方程组——拟线性方程组,它是微分方程的一个重要的课题,常常出现在流体动力学、半导体设置的物理理论、化学反应理论、工程、生物、通信和生态等研究领域中。

In this paper, we used the regularization method and the best disturbed iteration to solve such more extensive equations: every kind of positive problems and inverse problems of the hyperbolic partial differential equation and parabolic equation. We give homologous methods to solve the positive problems and inverse problems of nonlinear Burgers equation and Boussinesq equation.

本文应用正则化方法和最佳摄动量法,解决了一类更广泛的双曲型和抛物型偏微分方程的各类正问题及反问题,对非线性的Burgers方程及Boussinesq方程的正问题及反问题,也给出了相应的求解方法。

Afterwards, we propose a new constant coefficients measurement method in dynamic equation of robot manipulators, this measurement method includes three groups of experiments: group one, let each joint of robot manipulator keep static to measure the constant coefficients in gravity term of dynamic equation and Coulomb frictional torque, group two: let only one joint of robot manipulator move at a constant velocity to measure the viscous frictional coefficient and constant coefficients in effective inertia of dynamic equation, group three: let only one joint of robot manipulator move at constant acceleration at a time to measure constant coefficients in Coriolis and centrifugal term and coupling inertia of dynamic equation.

让操作器单个关节恒速运动,在对驱动系统中传动机构,减速装置和电感系数综合考虑的基础上,这组实验对粘滞摩擦系数及有效惯量中常数系数进行测量。这种测量方法只要求旋转关节的驱动电机施加恒定电压,回转关节驱动电机施加正弦波电压。3。让操作器单个关节恒加速运动,这组实验测量动力学方程中哥氏力、离心力项和耦合惯量项中的常数系数,这种测量方法只要求单个关节匀加速运动,而其它各关节保持静止,这种测量方法虽然要求关节匀加速运动,但不必进行关节角加速度检测,而只需进行关节角位移和角速度检测即可,输入量直接给定为输入电压。

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。

Because the workpiece is in dynamic balance, the resultant moment acting on it should be zero. Introducing the moment from lapping tool and press head a moving differential equation is built. In this equation only workpiece rotating speed is unknown. It means that workpiece rotating speed can be got by this equation. Since there is a transcendental function in integral function of the equation an analytic result can not be got, only digital result can be got by a computer. Thus a change rule of workpiece rotating speed with lapping parameters is known, e.g. the radius of press disc ball socket, radius of press head ball, the distance between the workpiece rotating axis and lapping tool rotating axis, workpiece radius, modulus of elasticity of the press head and press disc, friction coefficients between the lapping tool and workpiece, and between the head and disc, pressure between the lapping tool and workpiece and pressure between the press head and press disc.

因工件处于动态平衡状态,其上所受到的来自于磨具和压头的力矩应相等,将二力矩表达式联立,建立工件运动微分方程,该方程中只有工件的旋转角速度是未知量,因此可以求出工件旋转角速度,但该方程积分式中含有超越函数,得不出解析解,只能通过计算机求出数值解,得出工件旋转角速度随各研磨参数的变化规律,如压盖球座半径、压头的球头半径、工件回转中心相对磨具回转中心的偏心距、工件半径、压头和压盖材料的弹性模量、磨具与工件间的摩擦系数、压头压盖间的摩擦系数、磨具与工件间的压强、压头压盖间的压力等。

Results There was a linear trend between logarithmic X and Y, the equation of logarithmic curve was able to be fitted, There was a linear trend between logarithmic Y and X, the equation of exponential curve was able to be fitted, There was a linear trend between logarithmic X and logarithmic Y, the equation of power curve can be fitted. There is a parabola pattern between X and Y, the equation of parabola was able to be fitted.

结果 X取自然对数与Y作散点图有直线趋势,拟合对数曲线方程;Y取自然对数与X作散点图有直线趋势,拟合指数曲线方程;X取自然对数与Y取自然对数作散点图有直线趋势,拟合幂函数曲线方程;原始数据X和Y成抛物线关系,拟合抛物线方程。

Field data of pedestrian flow was collected in Chinese comprehensive passenger transport terminal—Xizhimen underground station using video recording, and then selected and analyzed by statistic analysis software SPSS. Parameters relation models for pedestrian flow on different terminal facilities were established based on data statistics. The results show that the pedestrian flow-density relation model is quadratic equation in corridor; the flow-space relation model is quadratic equation when space is below a certain value and is logarithmic equation when space is above the value; the speed-density relation model is linear equation. The models on stairs show the similar characteristics, but the eigenvalue is different.

对国内综合交通客运枢纽——北京西直门地铁站行人流数据进行视频采集,采用统计分析软件SPSS对行人流参数数据进行筛选及拟合分析,建立了不同设施的行人流参数关系曲线及函数模型,研究结果表明,水平通道处行人流量与密度呈二次函数关系、流量与空间在某一临界点两侧分别呈二次函数及对数函数关系、速度与密度呈线性关系,楼梯处与之相似但特征点数值存在差异。

Dinger equation is achieved, but also the resistance phase problem in the equation is skillfully solved. With a unitary transformation, the finite-differenced Schr?dinger equation becomes a standard Mathieu equation in p?

通过合适选取系统哈密顿的形式,不仅能够实现介观含源RLC电路的量子化,给出该电路的瞬态薛定谔方程,还可以解决电阻给薛定谔方程的求解带来的困难。

Based on the magnetic-elasticity nonlinear kinetic equations, physical equations, electrical kinetic equations and the expression of Lorentz forces, the magnetic-elasticity kinetic buckling equation of a current-carrying plate applied mechanical load in a magnet field were derived. The equation was transformed into the standard Mathieu equation by using Galerkin method. Thus, the magnetic-elasticity kinetic problem was changed into a problem of solving the Mathieu equation.

在载流薄板的磁弹性非线性运动方程、物理方程、洛仑兹力表达式及电动力学方程的基础上,导出了载流薄板磁弹性动力屈曲方程,并应用Galerkin原理把屈曲方程整理为Mathieu方程的标准形式,将载流矩形薄板在电磁场与机械荷载共同作用下的磁弹性屈曲问题归结为对Mathieu方程的求解问题。

Based on the magneticelasticity nonlinear kinetic equations, physical equations, electrical kinetic equations and the expression of Lorentz forces, the magneticelasticity kinetic buckling equation of a currentcarrying plate applied mechanical load in a magnet field were derived. The equation was transformed into the standard Mathieu equation by using Galerkin method. Thus, the magneticelasticity kinetic problem was changed into a problem of solving the Mathieu equation.

在载流薄板的磁弹性非线性运动方程、物理方程、洛仑兹力表达式及电动力学方程的基础上,导出了载流薄板磁弹性动力屈曲方程,并应用Galerkin原理把屈曲方程整理为Mathieu方程的标准形式,将载流矩形薄板在电磁场与机械荷载共同作用下的磁弹性屈曲问题归结为对Mathieu方程的求解问题。

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