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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.
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     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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  “阶微分”译为未确定词的双语例句
     THE PROBLEM OF BOUNDEDNESS OF SOLUTIONS OF LINEAR DIFFERENTAL EQUATION OF SECOND ORDER
     关于线性二阶微分方程有界解问题
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     THE BOUNDNESS OF SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS y"+A(t)y=0
     关于二阶微分方程y″+A(t)y=0的解的有界性
短句来源
     GEOMETRICAL PROPERTIES OF THE INTEGRAL SURFACES OF DIFFERENTIAL EQUATIONS OF THE FIRST ORDER IN THE COMPLEX DOMAIN
     复数域内一阶微分方程的积分曲面的几何性质
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     The Method of Matched Asymptotic, Expansions for the solution of a Non-Linear Second order Differential Equation
     求一类非线性二阶微分方程解的匹配渐近展开方法
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     NECESSARY AND SUFFICIENT CONDITIONS FOR GLOBAL ASYMPTOTIC STABILITY OF SECOND ORDER DIFFERENTIAL EQUATIONS
     二阶微分方程全局渐近稳定性的充要条件
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  相似匹配句对
     The nth-order Linear Differential Subordination
     n线性微分从属
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     The First-order Differential Subordinations
     一微分从属
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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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In this paper the general synthesis problem of optimal control systems with the criterion of transient responses as a positive integral functional (3) is discussed.In the first part it is assumed that the motion of controlled object is described by a system of ordinary differential equations and that the final states of the system form a bounded and closed convex region in n-dimentional euclidian phase space. A method is proposed for finding all optimal control functions which lead any starting state into the...

In this paper the general synthesis problem of optimal control systems with the criterion of transient responses as a positive integral functional (3) is discussed.In the first part it is assumed that the motion of controlled object is described by a system of ordinary differential equations and that the final states of the system form a bounded and closed convex region in n-dimentional euclidian phase space. A method is proposed for finding all optimal control functions which lead any starting state into the given final region of states. Some conclusions are obtained from the maximum principle by using transversal conditions of optimal trajectories in terminal points, and the particular properties of the stated problem are pointed out. The case of linear dif-ferential equations with integral quadratic functional criterion is investigated in detail.Further, in the second part the fundamental properties of isoloss regions, the rela-tions between the isoloss region and optimal control functions are indicated. As a direct result a partial differential equation determining the optimal loss-function J (x) is found and the connection between function J (x)and optimal vector control function u (x) is also stated. The methods proposed are practically the extension of the me-thods used by us for designing time optimal control systems as seen in [5, 6 ,7].Finally, an example is illustrated with optimal trajectories shown in phase plane.The necessary numerical data is calculated by an analog computer with high accuracy.

文中研究了具有公式(3)表示的一般正积分泛函的最优控制系统的综合问题.在第一部分中研究了具有控制参数的一阶微分方程组.控制系统的终点状态为n维相空间内的某一逐段光滑边界的闭性区域Ω.文中指出了根据极大值原理和轨道终点的横截条件寻找引到Ω的所有最优轨迹的方法.这里详细地研究了具有二次泛函和被积函数中不明显含有控制参数的质量指标泛函的线性方程情况.在文中第二部分研究了等损耗区的主要特性.指出了等损耗区与最优控制函数之间的关系.导出了求算最优损耗函数J(x)的偏微分方程,以及这一函数与最优控制函数u(x)的关系.上述方法是我们曾在文献[5,6,7]中用过的最优快速系统的综合方法的推广.文章最后举有例证.

In this paper, the problem of the antisymctrical small deflection of isotropic sandwich plates (in the theory of E. Reissner[1]) is reduced to the solution of two displacement-functions w and f, where to satisfies a differential equation of fourth order, and f satisfies a differential equation of second order. For a simply supported polygonal sandwich plates, it is proved that / vanishes identically, and the relation between w and the deflection w0 of a similar single-layered thin plates is established. By this...

In this paper, the problem of the antisymctrical small deflection of isotropic sandwich plates (in the theory of E. Reissner[1]) is reduced to the solution of two displacement-functions w and f, where to satisfies a differential equation of fourth order, and f satisfies a differential equation of second order. For a simply supported polygonal sandwich plates, it is proved that / vanishes identically, and the relation between w and the deflection w0 of a similar single-layered thin plates is established. By this relation, the solutions of a class of problems of sandwich plates may be derived from the corresponding solutions of single-layered thin plates.

本文首先把各向同性夹层板的反对称小挠度問題(E.Reissner的理論)归結为求解两个位移函数ω和f。这里ω满足一个四阶微分方程,而f滿足一个两阶微分方程。接着証明,对于周边簡支的多角形夹层板,f恆等于零,并进一步指出ω与同样形状的单层薄板的挠度w_0的关系。利用这个关系使人有可能从許多单层薄板的已知解答导出相应的夹层板問題的解答。

Experiments on the dynamics of fast fluidization were carried out in a 100mm-diameter plexiglas column, 8 meters in height, on FCC catalyst, alumina powder, iron ore concentrate and fine pyrites cinder. Based on the rapid formation and dissolution of dense strands or clusters of solids dispersed in a continuum of dilute phase, a physical flow model of fast fluidization has been proposed leading to a first-order differatial equation, the solution of which yields a four-parameter equation of voidage distribution...

Experiments on the dynamics of fast fluidization were carried out in a 100mm-diameter plexiglas column, 8 meters in height, on FCC catalyst, alumina powder, iron ore concentrate and fine pyrites cinder. Based on the rapid formation and dissolution of dense strands or clusters of solids dispersed in a continuum of dilute phase, a physical flow model of fast fluidization has been proposed leading to a first-order differatial equation, the solution of which yields a four-parameter equation of voidage distribution along the bed height z

在外径100mm,高8m的有机玻璃的装置上,对FCC催化剂、三氧化二铝粉料、铁精矿和细粒黄铁矿烧渣进行了快速流态化的流动实验。基于分布在稀薄连续相中颗粒密集体的不断形成和解体的现象,提出了快速流态化的分相流动的物理模型,并用一个一阶微分方程加以描述。其解为 In((ε-ε_a)/(ε'-ε))=-(z-z_i)/Z_o 四个模型参数,即ε_a、ε'、Z_o、和z_i由实验确定。

 
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