查询词典 ordinary differential equation

By transforming the interlace series type linear differential equation with coefficients containing negative second order power function and arrangement number into the linear differential equation of successive integral,the theory and method for the general solution of this kind of equation are determined.

通过把系数含有负二次幂函数与排列数的交错级数型线性微分方程化为可逐次积分的线性微分方程，找出了求这类方程通解的方法与理论，所得定理给出了严格的证明，并通过实例介绍了它的应用

Pass the interlace series type linear differential equation that coefficient contains power function and arrangement number change into the linear differential equation of successive integral, have found out the theory and method that begs this kind of equation to know to untie.

通过把系数含有幂函数与排列数的交错级数型线性微分方程化为可逐次积分的线性微分方程，找出了求这类方程通解的方法与理论，把所得定理给出了严格的证明，并通过实例介绍了它的应用。

By transforming high - grade gentle lack one type linear differential equation into the linear differential equation of successive integral, the theory and method for the general solutions of this kind of equation are determined.

方程'+=f是高阶线性微分方程，(约定尹0)=刃，是两项和的形式，其特征是含有相同的底，导数的次数相差一阶，因此不妨定义该方程为：高阶和式次数差一型线性微分方程。

Two basic theorems are given by researching Hamilton's two steps linear differential equations of bender equations which provide widespread application methods of normal differential operator correspond to ladder operators,then the solutions of general equations are obtained by taking advantage of the two above theorems: The energy eigenvalue equation of one-dimensional oscillator; the common state of ; the radial equation of a bondage state of hydrogen atom; the radial equation isotropic three-dimensional harmonic oscillator; the infinity deep potential well of ball

本文通过研究束缚态本征方程里的哈密顿算符的二阶线性常微分形式，给出两个基本定理并证明，提供构造二阶线性常微分算符相应的阶梯算符的普遍实用的方法，然后利用这两个定理构造量子力学中常见力学量的阶梯算符，并用以计算其能量本征值和对应本征函数：一维谐振子的能量本征方程；共同本征态；氢原子束缚态径向方程；三维各向同性谐振子的径向方程；无限深球势阱。

Based on the given results of second order boundary value problem, the existence of solutions of nonlinear differential-difference equation and unique of solutions of Hammerstein type integro-differential-difference linear equation were established because Hammerstein linear equation featured only one solution.

以二阶边值问题的已知结果为基础，建立了微分差分非线性方程解的存在性，以及Hammerstein型线性方程解的唯一性。

Neutral equation; stochastic functional differential equation; stochastic differential equation with delay; infinite delay; asymptotic propertie; semimartingale convergence theorem; Markovian switching; moment stability; moment boundedness

基础科学，数学，概率论、数理统计中立型方程；随机泛函微分方程；随机延迟微分方程；无限时滞；渐近性质；半鞅收敛定理； Markov调制；矩稳定性；矩有界性

Studying from dynamic hydraulics, in consideration of the friction impact, differential equation of motion and equation of continuity have been established, from which transient velocity equation and pressure fluctuation equation describing viscous fluid micro-vibration inside of a string have been deduced out.

从动态水力学的角度出发，建立了考虑摩擦力影响的流体运动微分方程和连续性方程，得到了具有粘滞性流体在管柱内微振动时的瞬态速度和压力波动方程。

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。

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。

Now she was hungry and angry.She began to smoulder.

现在她又饿又气，她开始流露难以抑制的怒火。

You have placed our iniquities before You, Our secret sins in the light of Your presence.

诗90：8 你将我们的罪孽摆在你面前、将我们的隐恶摆在你面光之中。