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一阶微分     
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  first order differential
     F(x)∈C′,G≠0.Then first order differential equationdydx-G′(x)G(x)y=Q(x)Ф(y+F(x)G(x))+G′(x)G(x)F(x)-F′(x)is integrable and possesses parameter formal general solution.
     F(x)∈C′,G≠0,则一阶微分方程dydx-G′(x)G(x)y=Q(x)Ф(y+F(x)G(x))+G′(x)G(x)F(x)-F′(x)可积,且具有参数形式的通解.
短句来源
     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
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     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
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     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
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     The exponential algorithm between chlorophyll-a concentration and the first order differential of the reflectance at 695.5 nm is good(R~2=0.76).
     利用695.5 nm一阶微分建立的指数模型精度进一步提高,其R2达到了0.76;
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  first-order differential
     Existence of solutions of terminal value problems for first-order differential equations in Banach space
     Banach空间一阶微分方程终值问题解的存在性
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     Analysis of First-order Differential Equation in More Second Order Circuits
     高阶电路的一阶微分方程分析
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     The second-order N-dimensional radial Schrdinger differential equation with the isotropic harmonic oscillator is reduced to a first-order differential equation by means of the Laplace transform, and then, its solutions are directly obtained by means of making use of an integral.
     用Laplace变换把二阶N维各向同性谐振子的径向Schr dinger微分方程退化为一阶微分方程,然后用直接积分法求出一阶微分方程的解.
短句来源
     The second-order one-dimensional Schrdinger differential equation for the harmonic oscillator is reduced to a first-order differential equation by means of the Laplace transform,and then,its solutions are obtained by means of directly making use of an integral.
     用Laplace变换把二阶一维谐振子的Schr dinger微分方程退化为一阶微分方程,用直接积分法求出一阶微分方程的解.
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     Master equations which normally appear as an infinite set of first-order differential equations coupled with each other are simplified to 4 independent equations, leading to Bloch equations for dressed atoms through which all the coherent interactions of atoms with light can be extended to the case of dressed atoms.
     把无限多个互相耦合的一阶微分方程(主方程)简化为四个独立的方程,从而得到Dressed原子与探测光相互作用的Bloch方程,可以把普通原子与光相干相互作用的全部过程推广到Dressed原子。
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  one order differential
     For one order differential equation M(x,y)dx+N(x,y)dy=0, the method of seeking an integrating factor is a valid way of finding the solution.
     对于一阶微分方程M(x,y)dx+N(x,y)dy=0,求积分因子是一种有效的求解途径.
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     In this paper comparisons of the two methods in settlement prediction is presented, and it is proved that their one order differential equation is strict consistent, which it is important for the application of Grey Model Theory in settlement prediction.
     本文对两种方法的一阶微分方程作了比较 ,证明在一定条件下 ,灰色模型理论和 Asaoka法两者的一阶微分方程是严格一致的 ,这对灰色模型理论在地基沉降预测中的推广应用具有重要意义
短句来源
     The chaotic motions of axial compressed nonlinear elastic beam subjected to transverse load were studied. Considering material and geometric nonlinearity, nonlinear partial differential equation of the system was derived. Under ideal displacement conditions,one order differential equations were devived and solved.
     研究了非线性弹性梁的混沌运动 ,梁受到轴向载荷的作用 ,计及材料非线性和几何非线性 ,建立了该动力系统的非线性偏微分方程 ,并在理想的位移模态条件下得出了一阶微分方程组 ,求解该动力系统后发现 ,当载荷 P0 和 f 满足一定条件时 ,系统将发生混沌运动 ,且混沌运动的区域呈现带状。
短句来源
     But PID controller only concerns error's one order differential only, does not concern the second and high order of error's differential, thus the PID controller can't depict dynamical behavior perfectly.
     但PID控制器仅涉及到误差一阶微分,却未涉及到误差的二阶以及高阶微分,因此PID控制器不能完全刻画系统的动态行为。
短句来源
     A new mathematical model of unsteady aerodynamics of airplane at high angles of attack is developed, with employment of a one order differential equation to describe the aerodynamic increment caused by nonlinear unsteady effects.
     采用一阶微分方程描述由非线性非定常效应引起的气动力增量 ,从而建立了一种新的飞机大攻角非定常气动力数学模型。
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  one-order differential
     The thesis states the high order differentiator (HOD) that does not depend on the model of the controlled plant. The HOD can extract high quality one-order differential signal and high-order differential signals of the given signal.
     本文论述了不依赖被控对象模型的高阶微分器(High order differentiator-HOD),该HOD能高品质的提取信号的一阶微分及高阶微分信号。
短句来源
     Research on one-order differential coefficient estimation based on Kalman filtering
     基于Kalman滤波的一阶微分参量估计方法的研究
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     A Scalar wave equation with an aix direction variate z is used to describe a single-mode taper fiber, and the scalar wave equation is changed to one-order differential equations group by a Simple transform.
     本文采用含有轴向坐标参变量的标量波动方程来描写锥体光纤,通过一种简单的变换,将标量波动方程化为一阶微分方程组。
短句来源
     The governor dynamics equation was expressed by two one-order differential equations, and a continuous function - function sigmoid was used as a substitute of function sign. So the dynamics equation can be solved conveniently by applying numerical integral methods, and the oscillation of the result within a small range can be avoided.
     调速器动力学方程用2个一阶微分方程表示,引入了连续性函数sigmoid函数代替非连续性函数sign函数,使调速器动力学方程能够方便地应用数值积分方法求解,并且避免了计算结果的小范围振荡。
短句来源
     Setting out from various solution methods for a one-order differential equation, some techniques of solution differential equation are given, and from here what should be noticed are explains.
     本文从一个一阶微分方程的多种解法出发,展示解微分方程的某些技巧,并由此说明几点应注意的问题.
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  first order differential
As the order is 1, the result here is simplified to that of first order differential equation.
      
The method used to derive the energy functions of nets from first order differential equations is valid for all first order continuous autonomous systems.
      
The applications of infinite systems of linear first order differential equations with 2L+1-term recursion formulas are discussed.
      
In this formulation the Schr?dinger equation is a system of two first order differential equations for two component wave functions.
      
On the oscillation of solutions of first order differential equations with deviating arguments
      
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  first-order differential
In the present paper we obtain an approximate first-order differential equation for the frequency squared, using the filling level as the independent variable.
      
An ordinary first-order differential equation is obtained for the velocity distribution along the profile in [2].
      
In the present study, the solution of this type of equation is reduced to the integration of a chain of linear first-order differential equations.
      
The system of three non-linear first-order differential equations has kinetic energy and circulation integrals representing two ellipsoids with displaced centers in parameter space.
      
The problem is reduced to two essentially nonlinear first-order differential equations for the velocity and concentration of ions.
      
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