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of differential equations
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  微分方程
     On the Complex Oscillation of Differential Equations f″+e~(az)f′+Q(z)f=F(z)
     微分方程f″+e~(az)f′+Q(z)f=F(z)的复振荡
短句来源
     Some necessary and sufficient conditions for the oscillation for all solutions of the class of differential equations:x'(t) +P/tx(αt) =0,t≥t0 >0,其中p∈R,α>0 are obtained, where p∈R,α>0, is constant number.
     考虑微分方程:x′(t)+(p/t)x(αt)=0,t≥t_0>0,其中p∈R,α>0为常数,获得了该方程一切解振动的必要充分条件。
短句来源
     Weak Carathodory Solution of Differential Equations in Banach Spaces
     Banach空间中微分方程的弱Carathodory解
短句来源
     EXISTENCE OF THE INFINITE LIMIT CYCLES OF DIFFERENTIAL EQUATIONS =H (Y)-F(X), =-G(X)
     微分方程=H(Y)-F(X),=-G(X)无限多个极限环的存在性
短句来源
     The Numerical Solution to Boundary Value Problems of Differential Equations in Hilbert Space-W_2~2(*)
     W_2~2(*)空间微分方程边值问题数值解
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  微分方程组
     A STUDY ON LIMIT CYCLES OF DIFFERENTIAL EQUATIONS (dx)/(dt)=y+μxF_1(x,y),(dy)/(dt)=-x+μyF_2(x,y) (1)_μ
     微分方程组(dx)/(dt)=y+μxF_1(x,y),(dy)/(dt)=-x+μyF_2(x,y) (1)_μ极限环之研究
短句来源
     SOME RESEARCHES ABOUT THE SYSTEM OF DIFFERENTIAL EQUATIONS (dpξ)/(dtp)=Aξ
     关于微分方程组dpξ/(dp_t)=Aξ的一些探讨
短句来源
     Theory of Operator metrices and Solution to the Linear systems of Differential Equations with Constant Coefficients(Ⅰ)
     算子矩阵理论与常系数线性微分方程组求解(Ⅰ)
短句来源
     The nonlinear differential equations are reduced by the travelling wave solution and similarity reductions, then the ordinary differential equations are obtained and the equations are discussed by Painleve analysis. An example of differential equations with ' weak Painleve property is given.
     对一类非线性偏微分方程组进行行波约化和相似约化,使原来的偏微分方程约化为常微分方程,并对此常微分方程进行Painleve分析,进一步给出此类非线性偏微分方程约化后的常微分方程组只有“弱”Painleve性质,还给出微分方程具有“弱”Painleve性质的一个例证。
短句来源
     Eigenvalue Estimation of a Certain System of Differential Equations
     某类微分方程组的特征值估计
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  型微分方程
     Sufficient Conditions of Oscillation of Differential Equations
     中立型微分方程振动的充分条件
短句来源
     In this paper, by using the continuity theorem in coincidence degree theory and Lyapunov functional method, we deal with the existence and the uniqueness of the the periodic solutions of a class of differential equations with delays.
     本文将运用重合度理论中的延拓定理和Lyapunov泛函方法讨论一类时滞微分方程周期解存在性和唯一性,应用指数二分性和Krasnoselskii不动点定理研究了一类中立型微分方程周期解存在的充分条件。
短句来源
     Existence of Periodic Solutions of A Class of Differential Equations with Continuons Distribution
     一类具连续分布型微分方程的周期解的存在性
短句来源
     A method of minimization to a class of boundary-value problems of differential equations with convolution is given by using potential operator defined in a real Banach space, separating coupled variable; the transformed minimum principle on Laplace transformation and the weighted minimum principle in original place-time domain are established.
     通过定义在一个实Banach空间上的有势算子对耦合变量的分离,对一类卷积型微分方程边值问题给出了极小化方法.建立了关于Laplace变换的转换最小值原理和在原空间-时间域的加权最小值原理.
短句来源
     Combining with the measure of nonlinear operator, they research the dissipativity of differential equations with delay and give some sufficient conditions for the uniformly dissipativity of Hopfield neural networks with delay.
     利用连续Lipschitz算子的测度研究了滞后型微分方程的耗散性. 并应用于时滞Hopfield神经网络,获得了其一致耗散性及平衡点全局一致渐近稳定的充分条件.
短句来源
  “of differential equations”译为未确定词的双语例句
     MIXED BOUNDARY VALUE PROBLEM FOR SECOND ORDER SYSTEM OF DIFFERENTIAL EQUATIONS OF THE ELLIPTIC TYPE
     MIXED BOUNDARY VALUE PROBLEM FOR SECOND ORDER SYSTEM OF DIFFERENTIAL EQUATIONS OF THE ELLIPTIC TYPE
短句来源
     WIDE SENSE STABILITY OF COMPLEX SYSTEMS OF DIFFERENTIAL EQUATIONS OF ARBITRARY DIMENSION
     WIDE SENSE STABILITY OF COMPLEX SYSTEMS OF DIFFERENTIAL EQUATIONS OF ARBITRARY DIMENSION
短句来源
     The θ-Methods in Numerical Solution of Systems of Differential Equations with Two Delay Terms
     The θ-Methods in Numerical Solution of Systems of Differential Equations with Two Delay Terms
短句来源
     A COMPARISON THEOREM FOR THE OSCILLATION OF DIFFERENTIAL EQUATIONS WITH ADVANCED ARGUMENT
     A COMPARISON THEOREM FOR THE OSCILLATION OF DIFFERENTIAL EQUATIONS WITH ADVANCED ARGUMENT
短句来源
     ON THE LOCAL SOLVABILITY OF DIFFERENTIAL EQUATIONS ASSOCIATED TO UNSOLVABLE INHOMOGENEOUS LEFT INVARIANT DIFFERENTIAL OPERATORS ON THE HEISENBERG GROUP
     ON THE LOCAL SOLVABILITY OF DIFFERENTIAL EQUATIONS ASSOCIATED TO UNSOLVABLE INHOMOGENEOUS LEFT INVARIANT DIFFERENTIAL OPERATORS ON THE HEISENBERG GROUP
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  of differential equations
Symmetries and group-invariant solutions of differential equations
      
The cases in which (1) time-changes in oil saturation can be neglected and (2) pressure and oil saturation distributions in time and space described by a common system of differential equations are studied separately.
      
A two-dimensional system of differential equations in a cone and a sufficient condition for the existence of its periodic solution are investigated.
      
The introduced concepts are used for solving the problem on periodic oscillations of controlled objects described by the system of differential equations and by the system of differential inclusions.
      
Stability of solutions of differential equations under generalized pulse perturbations
      
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A more general mathematical analysis of the kinetics of polycondensation-depolycondensation reactions is given in the article. Three different types of reactions are considered, namely, (1) reactions between molecules AB and AB, (2) reactions between molecules AA and BB, (3) reactions between molecules AA and BC. One of the condensation products is assumed (without loss of generality) to be water.For reactions of the first type, [p_n], the number of molecules of the n-mer (AB)_n, obeys the following Flory distribution:...

A more general mathematical analysis of the kinetics of polycondensation-depolycondensation reactions is given in the article. Three different types of reactions are considered, namely, (1) reactions between molecules AB and AB, (2) reactions between molecules AA and BB, (3) reactions between molecules AA and BC. One of the condensation products is assumed (without loss of generality) to be water.For reactions of the first type, [p_n], the number of molecules of the n-mer (AB)_n, obeys the following Flory distribution: [p_n]=N_0p~(n-1)(1-p)~2 where N_0 denotes the total number of AB segments (including the unreacted monomers). and p, as defined by is a measure of the degree of condensation. It is shown that p is the solution of the following differential equation: dp/dt=k/2N_0(1-p)~2-k_(-1)p[H_2O] where K and k_(-1) are velocity constants of condensation and hydrolysis respectively, and [H_2O] denotes the number of water molecules. Three special cases are discussed.For reactions of the second type, three different types of condensation products are possible besides water; they obey the following distributions: [p_(2n)]=2N′_0r~(n-1)p~(2n-1)(1-p)(1-rp) [p′_(2n-1)]=N′_0r~(n-1)p~(2n-2)(1-p)~2 [p″_(2n-1)]=N′_0r~(n-2)p~(2n-2)(1-rp)~2 where N′_0 and N″_0 denote the total number of segments AA and BB respectively, r denotes the ratio N′_0/N″_0, and p, as defined by is the solution of the following differential equation: dp/dt=kn′_0/r(1-p)(1-rp)-k_(-1)P[H_2O]For reactions of the third type, six different types of condensation products are possible besides water; they obey the following distributions: [P′_(2n)]=NP~(n-1)q~n(1-p/2-q/2)(1-p) [p″_(2n)]=Np~nq~(n-1)(1-p/2-q/2_(?))(1-q) [p_(2n-1)=Np~(n-1)q~(n-1)(1-p/2-q/2)~2 [p′_(2n-1)]=N/4p~(n-2)q~n(1-p)~2 [p″_(2n-1)]=N/4p~nq~(n-2)(1-p)~2 [p′″_(2n-n)]=∈(n)N/4p~(n-1)q~(n-1)(1-p)(1-q),where N denotes either the total number of segments AA or that of BC, while p and q, as defined by satisfy the following set of differential equations: dp/dt=k′N/2(1-p)(2-p-q)-k′_(-1)p[H_O] dq/dt=k″N/2(1-q)(2-p-q)-k″_(-1)q[H_2O]

本文討論AB型,AA和BB型以及AA和BC型分子间的缩聚-裂解反應,由動力学方程出發,得到这三种类型反應过程中高聚分子的分佈情况,并求得几种不同反應條件下的缩聚度p和q是何种時间的函数,利用它们和实验数值比較,可以求得縮聚反應速度常数K和水解反應速度常数k_(-1),并在AA和BC型分子间的反應中,可以求得K'和K″的此值,藉以比较官能團B和C的活潑度。还討論了三种平均分子量的表示式、数值以及它们相互的比值,後者僅在没有水解作用的情况下,才和Flory的结果相同。

This is a critical exposition and analysis of the modern developments in the theory of turbulent motion of an incompressible fluid. We begin with the review of the mixture length theories based upon Reynolds' equations of mean motion. Secondly, we analyze the principal contributions to the theory of homogeneous isotropic turbulence. Thirdly, we discuss the treatment of the general turbulent shear flow by means of Reynolds' equations of mean motion and the dynamical equations of velocity correlations which are...

This is a critical exposition and analysis of the modern developments in the theory of turbulent motion of an incompressible fluid. We begin with the review of the mixture length theories based upon Reynolds' equations of mean motion. Secondly, we analyze the principal contributions to the theory of homogeneous isotropic turbulence. Thirdly, we discuss the treatment of the general turbulent shear flow by means of Reynolds' equations of mean motion and the dynamical equations of velocity correlations which are derived from the equations of turbulent velocity fluctuation. We also point out at the same time that although this method yields theoretical results which are in better agreement with experiment than the results of the mixture length theories and furthermore the theory also leads to the theoretical distributions ot the mean squares of velocity fluctuation, on account of the presence of the higher order velocity correlations in the equations, it continuously leads to unclosed systems of differential equations and hence meets difficulties which are difficult to overcome. Therefore, based upon the above retrospect of the developments of the theory of turbulence and the recent work on the vorticity structure of the homogeneous isotropic turbulence in its final period of decay, we finally propose a new approach to the turbulence problem: The basic component motion of turbulence is vortex motion due to the action of viscosity of the fluid. The dynamical equations which govern the vortex motion of turbulence are Reynolds' equations of mean motion and the equations of velocity fluctuation derived from the Navier-Stokes equations by the averaging process. We also emphasize the importance of Reynolds' recognition that the turbulent motion of a fluid can be separated into the mean motion and fluctuation. The future theoretical investigation is to look for the vortex motions which are solutions of these two sets of equations. In order to make the solutions of the problem unique and comparable with experimental measurements, they should also satisfy statistical conditions on the distribution of vortices analogous to Kol-mogoroffs condition in his statistical theory of locally isotropic turbulence at high Reynolds number turbulent flows.

这篇论文的内容是关於不可压缩流体的湍流理论近代发展的综合性介绍舆分析。我们首先评述了根据Reynolds的平均运动方程所建立的混合长度理论。其次,分析关於均匀各向同性湍流的主要理论工作。第三,讨论了运用Reynolds的平均运动方程和根据速度涨落方程求得的速度关联函数的动力学方程来处理具有Reynolds剪应力的普通湍流运动问题。同时说明这个方法虽然能够给出比混合长度理论舆实验较为接近的理论结果并能提出速度涨落平方平均值的理论分布,但是由於在求出的速度关联的动力学方程中出现高次元的速度关联,它继续地导致不封闭的微分方程组因而遇到不易克服的困难。因此,从以上湍流理论发展的回顾和最近关於均匀各向同性湍流在后期衰变运动的涡性结构工作,我们在最后提出了对今后湍流理论研究工作的新看法:湍流运动的基本组成部分是流体粘性作用所引起的涡旋运动;这个涡旋运动的动力学根据是用平均的方法后Navier-Stokes方程所导出的Reyonlds的平均运动方程典带度涨落方程。我们并着重说明Reynolds认识到湍流运动可分作平均运动与涨落运动的重要性。今后的理论工作则在於求这两组动力学方程的涡旋运动解,而这种类型的解并须满足像在高Re...

这篇论文的内容是关於不可压缩流体的湍流理论近代发展的综合性介绍舆分析。我们首先评述了根据Reynolds的平均运动方程所建立的混合长度理论。其次,分析关於均匀各向同性湍流的主要理论工作。第三,讨论了运用Reynolds的平均运动方程和根据速度涨落方程求得的速度关联函数的动力学方程来处理具有Reynolds剪应力的普通湍流运动问题。同时说明这个方法虽然能够给出比混合长度理论舆实验较为接近的理论结果并能提出速度涨落平方平均值的理论分布,但是由於在求出的速度关联的动力学方程中出现高次元的速度关联,它继续地导致不封闭的微分方程组因而遇到不易克服的困难。因此,从以上湍流理论发展的回顾和最近关於均匀各向同性湍流在后期衰变运动的涡性结构工作,我们在最后提出了对今后湍流理论研究工作的新看法:湍流运动的基本组成部分是流体粘性作用所引起的涡旋运动;这个涡旋运动的动力学根据是用平均的方法后Navier-Stokes方程所导出的Reyonlds的平均运动方程典带度涨落方程。我们并着重说明Reynolds认识到湍流运动可分作平均运动与涨落运动的重要性。今后的理论工作则在於求这两组动力学方程的涡旋运动解,而这种类型的解并须满足像在高Reynolds数运动的局部各向同性湍流理论中所提出的统计条件,方能使解满

A mathematical analysis of the kinetics of free radical addition polymerizations with various types of initiation mochanism (catalysed, thermalchemical and photochemical initiations) is given by solving the systems of differential equations and therefore, we obtain the theoritical distritutions for various kinds of polymer which have been yielded in the chemical reactions of free radical addition polymerizations and also the three kinds of average molecular weight. As to the assumption of stationary state,...

A mathematical analysis of the kinetics of free radical addition polymerizations with various types of initiation mochanism (catalysed, thermalchemical and photochemical initiations) is given by solving the systems of differential equations and therefore, we obtain the theoritical distritutions for various kinds of polymer which have been yielded in the chemical reactions of free radical addition polymerizations and also the three kinds of average molecular weight. As to the assumption of stationary state, we know that it has been widely used to investigate the kinetics of polymerizations, but there is still lack of rigorous analysis of the assumption. In this article, the basic condition for the validity of stationary state is derived and it is readily proved that, for the reactions of free radical addition polymerizations, the stationary state method is applicable.

我们讨论了热、光和催化剂分解引发的加聚反应动力学,结合自由基型加聚反应的特性,得到了动力学方程粗的解,推导出链段分布和平均分子量公式,证实稳定态假定对于自由基型加聚反应是可以应用的.

 
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