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first order differential equations
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  一阶微分方程
     Existence and uniqueness of periodic solutions for first order differential equations in Banach spaces
     Banach空间一阶微分方程周期解的存在唯一性
短句来源
     Unique Existence of the Solutions for the First Order Differential Equations in Banach Spaces
     Banach空间一阶微分方程解的存在唯一性
短句来源
     PERIODIC BOUNDARY VALUE PROBLEMS OF FIRST ORDER DIFFERENTIAL EQUATIONS
     一阶微分方程的周期边值问题
短句来源
     Using the topological degree theory, the author proves several existence theorems of solutions between lower and upper solutions for periodic boundary value problems of first order differential equations, where the lower and upper solutions \$α(t)\$ and \$β(t)\$ need not satisfy relations \$α(0)≤α(2π),β(0)≥β(2π).
     该文用拓扑度理论证明了一阶微分方程周期边值问题关于下解与上解之间解的存在性的两个定理 ,这里下解 α( t)与上解 β( t)可以不满足关系 α( 0 )≤ α( 2 π) ,β( 0 )≥ β( 2 π)。
短句来源
     Solution-Seeking Formula for Three Kinds of First Order Differential Equations
     三类一阶微分方程的求解公式
短句来源
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  一阶微分方程组
     The design can directly solve the first order differential equations which include a mixture of scalar equations, vector equations and matrix equations, so the design can provide some helpful references for project.
     该设计为工程实现中直接求解含标量、向量和矩阵等混合形式的一阶微分方程组的数值解提供了一定的参考价值;
短句来源
     Vibration is one of the essential factors that affected the working quality of cutter. Proposes a mathematical model to technology system of assembled cutter,and transforms the model into the first order differential equations in order to make the solution convenient. The occurrence frequency of vibration in technology system is analyzed.
     加工中振动是影响切刀工作性能和工件质量的主要因素,通过分析建立了装配式车刀工艺系统的数学模型,为使问题求解方便,将模型转换为一阶微分方程组(代数方程),具体分析工艺系统元件振动的发生频率,以C6140车床装配式切刀工艺系统为例,进行了实验研究,绘制了幅频特性曲线,得出了切断刀产生振动的频率范围,便于生产实践中选择。
短句来源
     In this paper,We make an elementary transfomation to some special Riccati equations,get the second order differential equation or first order differential equations,after that get the special solution of the Riccati equation with the help of special solution of the second order differential equation or first order differential equations,or formula method and observation trial method.
     通过对一般Riccati方程进行初等变换,使之变为特殊的Riccati方程,然后利用公式、观察实验,或利用二阶微分方程的特解,或利用一阶微分方程组的特解等方法,求得这些Riccati方程的特解.
短句来源
     In this paper, by applying the Schauder fixed point theorem, the existence of solutions of infinite boundary value systems is proved for first order differential equations in a Banach space .
     本文利用Schauder不动点原理得出了下列Banach空间中一阶微分方程组的无穷边值问题解存在的判定定理.
短句来源
     First, the method presented by Hojman for finding the conserved quantity of the system of second order differential equations is generalized and applied to the system of first order differential equations, particularly to the odd-dimensional system for finding the integral in this paper.
     首先,将Hojman用于求解二阶微分方程组守恒量的方法推广并应用于一阶微分方程组,特别是奇数维微分方程组的积分问题.
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  “first order differential equations”译为未确定词的双语例句
     The classical method for determining reaction mechanism was used and Gaus-Newton-Marquardt nonlinear fitting program and Runge-Kutta program for solving the first order differential equations were used for treating the data and a good result was obtained.
     采用经典确定反应机理的方法及Gauss-Newton-Marquardt非线性拟合和Runge-Kutta解一次微分方程组程序处理数据并获得了良好的结果。
短句来源
     With regard to the kmcl of differential equation y″+py′qy=f(Χ),the author gives the special solution formula as r_1≠r_2.Only finding out the special solutions to two linear first order differential equations and using the formula,we can obtain the corresponding special solution to nonhomogeneous linear ordinary differential equation of the second order.
     对于二阶常系数非齐次线性微分方程:y~″+py′+gy=f(x),给出了当特征根 r_1与 r_2不等时的特解公式。 利用该公式,只需求出两个一阶线性微分方程的特解,就可以得到相应二阶常系数非齐次线性微分方程的特解。
短句来源
     With regard to the kind of differential equation y″+py′+qy=f(x) , the author gives the special solution formula as r 1≠r 2 . Only finding out the special solutions to two linear first order differential equations and using the formula, we can obtain the corresponding special solution to nonhomogeneous linear ordinary differential equation of the second order.
     对于二阶常系数非齐次线性微分方程:y″+ py′+ qy= f(x),给出了当特征根r1 与r2不等时的特解公式。 利用该公式,只需求出两个一阶线性微分方程的特解,就可以得到相应二阶常系数非齐次线性微分方程的特解。
短句来源
     The existence of solutions for general initial value problems of first order differential equations
     一阶常微分方程广义初值问题解的存在性
短句来源
     Infinite Boundary Value Problems for First Order Differential Equations in a Banach Space
     Banach空间中一阶脉冲微分方程的无穷边值
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  first order differential equations
For reflection free amplification the solution of the complete system of equations differs only slightly from the solution of the approximate first order differential equations [2], even for very high nonlinearities.
      
An explicit fourth order Runge-Kutta Fehlberg method for the numerical solution of first order differential equations having oscillating solutions is developed in this paper.
      
Solution and stability of a system of two linear homogeneous first order differential equations with variable coefficients
      
A system of three ordinary non-linear first order differential equations is proposed for the computation of the geometrical spreading of the wave front of a seismic body wave in a three-dimensional medium.
      
A system of three ordinary non-linear first order differential equations is proposed for the computation of the geometrical spreading of the wave front of a seismic body wave in a three-dimensional medium.
      
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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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