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first order differential equation
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  一阶微分方程
     We shall show sufficient and necessary condition that first order differential equation M(x,y)dx+N(x,y)dy=0 have 1,μ(x,y)=F(ax+by),2,μ(x,y)-G(xy), 3,μ(x,y)=exp[∫f(x)dx+∫g(y)dy] three forms integrating factors. 
     给出了一阶微分方程M (x ,y)dx +N(x ,y)dy =0 ,具有1.μ(x ,y) =F(ax +by) ,  2 .μ(x ,y) =G(xy) ,3.μ(x ,y) =exp[∫f(x)dx +∫g(y)dy]三种形式的积分因子的充要条件
短句来源
     The necessary and sufficient condition of existence of integrating factor for the first order differential equation M(x,y)dx+N(x,y)dy=0 and the calculating formula of integrating factor are obtained.
     给出了一阶微分方程M(x,y)dx+N(x,y)dy=0具有形如μ(x,y)=φ(f(x)g(y))的一类积分因子的充分必要条件以及积分因子的计算公式.
短句来源
     Problems about the Integrating Factor of First Order Differential Equation
     关于一阶微分方程的积分因子问题
短句来源
     The application of th integrating factor of first order differential equation
     一阶微分方程积分因子的应用
短句来源
     Taking the superstructure as elastomer and the simulating the time delay with a first order differential equation, the state equations of motion for this system were developed, the controllable friction force of sliding structure was calculated by using instantaneous optimal control method.
     考虑上部结构的刚度和阻尼,采用一阶微分方程模拟时滞的影响,与结构的振动微分方程一起作为整个系统的状态方程,使用瞬态最优控制算法计算基底摩擦力的大小,通过计算实例对这种摩擦力可控的滑移隔震半主动控制方案进行了分析.
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  “first order differential equation”译为未确定词的双语例句
     Existence of the solutions of terminal value problems for first order differential equation on infinite interval in Banach spaces
     无穷区间上Banach空间常微分方程终值问题解的存在性
短句来源
     Let Q(x), F(·) 6 C, f(x), h = h(x) 6 C' and f ≠ 0, then first order differential equation is integrable. This result indicates a series of new pracrical integrable types. Some classical and moden integrable results are derived.
     证明了若F,Q C,而f,hC’且f≠0(其中C表示连续函数的集合C’表示可导函数的集合),则一阶常微分方程可积.并由此结果引出了非线性微分方程一系列新的实用的可积类型,推广了古典的和近代的可积性结果,扩大了微分方程封闭求积的范围。
短句来源
     The covergency and stability of numerical solution in first order differential equation are studied in this paper. The optimal coefficients are determined, and 3 trongly stable formulas in two-step linear method are got.
     本文研究一阶常微分方程数值解的收敛性与稳定性,利用最优化方法,确定最优系数,得到三个强稳定的线性两步公式.
短句来源
     The equations of motion of the system are derived by means of analytical dynamies. Using Bogoliubov-Mitropolskii asymptotic method, they are reduced to a set of first order differential equation which can be solved with numerical integration.
     文章依据分析动力学导出运动方程,再使用Bogoliubov-Mitropolskii渐近法,将它们化简为一阶微分方程组,进而数值积分求解.
短句来源
     The numerical methods in first order difference equation and the convergence and stability of numerical solution in first order differential equation are studied in this paper. Accordin to Runge-kutta method,the optimal coefficients are determined by optimal technology,at the same time,the optimal algorithm of strongly stable Runge-kutta in three-step orderare got.
     本文利用最优化思想,根据一阶常微分方程数值解的收敛性和稳定性,引进最优化技术,确定最优系数,得到强稳定的三阶Runge-Kutta最优算法.
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  first order differential equation
The quasi-cylindrical problem is reduced to solving a phase-plane first order differential equation.
      
With the M-C model we arrive at a single first order differential equation, while for the D-P solid an algebraic constraint supplements the governing differential equation.
      
It is shown that the governing field equations can be reduced to a single first order differential equation from which the stress concentration factor is obtained by a standard numerical method.
      
Such an approach permits us to combine the features of the mass balance (solute continuity in a Chromatographie column), of the mass transfer phenomenon, and of the adsorption isotherm into a single first order differential equation.
      
It will be shown briefly, that the build-up of the junction admittance from the bulk semiconductor to the junction interface can be given in terms of a first order differential equation.
      
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Recently, digital computers are gradually used to replace analog or hybrid computations for implement of continuous-system simulations. Digital continuous-system simulation has significant advantages: better man-machine interaction, higher accuracy and reproducibility, more convenient programming and report generation, etc.The simulation user would like to have a more convenient and flexible simulation language, in order to be as free as possible from the details of computer programming and concentrate...

Recently, digital computers are gradually used to replace analog or hybrid computations for implement of continuous-system simulations. Digital continuous-system simulation has significant advantages: better man-machine interaction, higher accuracy and reproducibility, more convenient programming and report generation, etc.The simulation user would like to have a more convenient and flexible simulation language, in order to be as free as possible from the details of computer programming and concentrate on his system simulations. An equation-oriented BASIC simulation language which permits the user to enter first-order differential equations in essentially unchanged mathematical form is introduced in this paper. It may run on any machine which supports BASIC. The user does not even have to be familiar with BASIC so long as he follows the simple format specified. A computing example is given to illustrate its application.

近年来,已逐渐用数字计算机代替模拟计算机或混合计算机来实现连续系统的仿真。连续系统的数字仿真的显著特点是:便于人机对话,求解精度高和重复性好,容易编排程序和输出计算结果。但是,为了避开编程序的细节和把精力集中在系统仿真上,系统仿真者希望有一个方便和灵活的仿真语言。本文介绍一种面向方程的BASIC仿真语言,它允许用户直接用一阶微分方程组的数学表达式写入,并能在任何一台配置BASIC语言的数字机上运算。使用时只要遵循规定的简单格式而不用去熟悉BASIC语言的细节。文中附有阐述用法的计算实例。

In this paper the differential equationis discussed and conditions are found which the functions P1(x), P2(y), Q1(x) and Q2(y) must satisfy for the equation to be integrable. It shows that Bernolli's equation is only a special case of this equation, so that a class of first order differential equations can be reduced to integrable cases and can be solved conveniently by elementary methods.

本文讨论了微分方程 dy/dx+P_1(x)P_2(y)=Q_1(x)Q_2(y)在P_1(x),P_2(y),Q_1(x),Q_2(y)满足什么条件下可化为可积类型;并得出了Bernoulli方程仅仅是此种方程的一个特例;从而使一类一阶微分方程能较方便的用初等解法化为求积分问题。

In this paper, starting from the equations of the nonlinear inertio-internal1 gravity waves in stratified shear fluid, and considering the flow about a class of the progressive waves, the autonomous dynamic systems of the first-order differential equations in two variables are derived. Using the qualitative theory of the differential equations, we analyze qualitatively the topological structure of the integral curves in the neighbourhood of the origin on a phase planewith...

In this paper, starting from the equations of the nonlinear inertio-internal1 gravity waves in stratified shear fluid, and considering the flow about a class of the progressive waves, the autonomous dynamic systems of the first-order differential equations in two variables are derived. Using the qualitative theory of the differential equations, we analyze qualitatively the topological structure of the integral curves in the neighbourhood of the origin on a phase planewith cartesian axes u, v. On the du/dz (the velocity shear), L2-L02 (L is thehorizontal scale, L0 is the Rossby radius of deformation) plane, the integral curves divide the plane into some domains of different stability.

本文从层结切变流体的非线性惯性重力内波的方程组出发,设解为行波的形式并将非线性项在平衡点附近作Taylor展开,导得了两个变量的一阶自治动力系统的常微分方程组。应用常微分方程的稳定性理论,讨论了惯性重力内波的稳定性。分析指出:在考虑了速度垂直切变和非线性作用后,惯性重力内波的稳定性发生了变化,当LL_0时是稳定的结论只是在时才是正确的,当时,L_0~2<0和L>L_0成为不稳定的条件。 本文还讨论了某些条件下非线性惯性重力内波的解析解。

 
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