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kolmogorov equation
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  kolmogorov方程
     First, a backward Kolmogorov equation for the conditional reliability function and a generalized Pontryagin equation for the conditional moment of the first-passage time are established.
     首先给出了条件可靠性函数满足的后向Kolmogorov方程以及首次穿越时间条件矩满足的广义Pontryagin方程.
短句来源
     First, the backward Kolmogorov equation for the conditional reliability function and the Pontryagin equation for mean first-passage time and then- associated boundary and initial conditions are derived based on the stochastic averaging methods for quasi non-integrable, quasi integrable and quasi partially integrable Hamiltonian systems, respectively.
     首先利用拟不可积、拟可积非共振及拟部分可积非共振Hamilton系统的随机平均法分别给出了研究该系统首次穿越问题的提法,包括计算条件可靠性函数的后向Kolmogorov方程及计算平均首次穿越时间的Pontryagin方程及其边值条件。
短句来源
     Then the stationary joint probability density, the conditional reliability function, the mean first-passage time of the optimally controlled system are obtained from solving the reduced FPK equation, the backward Kolmogorov equation and the Pontryagin equation, respectively of fully averaged systems.
     求解与之相应的后向Kolmogorov方程得最优控制系统的条件可靠性函数,进而求得首次穿越时间的条件概率密度; 求解与之相应的Pontryagin方程得最优控制系统的平均首次穿越时间(寿命)。
短句来源
     Then the FPK equation governing the joint probability density of amplitude and phase, the backward Kolmogorov equation governing the conditional reliability function, and the Pontryagin equation governing the mean first passage time are established, respectively. The stationary joint probability density of amplitude and phase, the conditional reliability function and the conditional probability density function of the first passage time, and the mean first passage time are obtained by solving these equations.
     在此基础上,建立联合概率密度满足的Fokker-Planck-Kolmogorov(FPK)方程、条件可靠性函数满足的后向Kolmogorov方程以及平均首次穿越时间满足的Pontryagin方程,分别求解这些方程得到联合概率密度、条件可靠性函数以及平均首次穿越时间(寿命)。
短句来源
     The motion equations is reduced to averaged stochastic differential equations,and a backward Kolmogorov equation governing the conditional reliability function and a generalized Pontrayagin equation governing the conditional monments of first-passage time are established.
     首先利用随机平均法给出了系统随机平均It^o微分方程,对平均方程的稳态概率密度做了数值分析; 然后建立了条件可靠性函数的后向Kolmogorov方程及首次穿越时间条件矩的Pontragin方程;
短句来源
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  k方程
     The exact stationary solution of a class of nonlinear dynamic problems subjected to Gaussian white noise has been obtained by solving its corresponding Fokker Planck Kolmogorov equation.
     一类受高斯白噪声激励的非线性动力学方程能通过求解对应的 F P K 方程得到精确稳态解。
短句来源
  “kolmogorov equation”译为未确定词的双语例句
     By the method of stochastic averaging of energy envelope the analytical expression of the moments of the first snapthrough time for shallow curved structures under random loading is drived. The probability density of the first snapthrough time is obtained by using implicit finite difference method to solve the backward Kolmogorov equation satisfied by conditional reliability function.
     本文用能量包线随机平均法,导出了随机载荷作用下浅曲结构首次发生突变的时间的各阶矩的解析表达式,并通过用臆式差分法数字求解条件可靠性函数所满足的后向柯尔英哥洛夫方程,给出了发生首次突变的时间的概率密度.
短句来源
     The first-order linear streamflow model is studied to develop stochastic analysis model, based on Markovian process, for the probability of streamflow forecasting. First, the parameters in model are expanded to include stochastic terms. Second, an analytical solution for the probability density function are produced by using FokkerplanckKolmogorov equation.
     以流域一阶线性径流模型为例,将模型中各参数扩展为随机变量,推导出基于马尔柯夫过程的可用于流域径流趋势分析的随机模型,并由Fokker-Planck-Kolmogorov(简写FPK)方程产生径流概率密度函数.模型应用于洵河柴坪流域的经济趋势分析,验证了该方法的实用性.
短句来源
     The Kolmogorov equation is presented and solved under reflecting -boundary condition in one- dimension half infinite space. The result conforms to the experiment data obtained at present.
     在一维半无限空间和反射边界条件下求解了该方程,结果与现有的实验事实相吻合。
短句来源
     By using the kolmogorov equation,this article analysed the survivability of some tank in defensive combat in three stages.
     运用柯尔莫哥洛夫方程,分三个阶段分析了某式坦克在防御战斗中的生存能力问题。
短句来源
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  kolmogorov equation
the fundamental solution of the heat equation, or the Kolmogorov equation), since the above principles no longer hold in this situation.
      
Three approaches to the problem of 1-D wave propagation in media with random elastic and mass properties are studied: (i) method of integral spectral decomposition, (ii) the Fokker-Plank-Kolmogorov equation, and (iii) the Dyson integral equation.
      
In the second stage, the random fluctuating terms exciting the averaged system are evaluated, leading to a Fokker-Planck-Kolmogorov equation governing the probability density function of the energy and phase variables.
      
Phase transformation of crystalline films does not follow the Johnson-Mehl-Avrami-Kolmogorov equation for nucleation and growth transformation.
      
We consider a mixed problem for a nonlinear ultraparabolic equation that is a nonlinear generalization of the diffusion equation with inertia and the special cases of which are the Fokker-Planck equation and the Kolmogorov equation.
      
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The Fokker-Planck-Kolmogorov equation plays an important role infinding the probabilistic structures of systems response. The FPK equationwill be exactly solvable only in the linear systems and in a few special cases ofnonlinear systems in stationary state. In this paper an approximate method offinding the transition probability density is proposed. On the basis of theexpansion of orthogonal function, the part-operator of the FPK equation isselected as an expansion function of solution, and the relationship...

The Fokker-Planck-Kolmogorov equation plays an important role infinding the probabilistic structures of systems response. The FPK equationwill be exactly solvable only in the linear systems and in a few special cases ofnonlinear systems in stationary state. In this paper an approximate method offinding the transition probability density is proposed. On the basis of theexpansion of orthogonal function, the part-operator of the FPK equation isselected as an expansion function of solution, and the relationship between theinitial and eigenvalue problems of the least coupling coefficients is established.Finally, as an example, the procedure for solving the FPK equation of a non-linear system-Duffin's equation-in nonstationary state is presented. Itsresults show that the Matrix Continued-Fraction Method proposed in this paperis of fast covergence, high accuracy and regular in calculating patterns. Thusit can be available in various nonlinear potential fields.

FPK方程是求解系统响应概率结构的关键方程,目前其解析解还只限于线性系统响应和少数几种特殊情况非线性系统的平稳响应过程。本文以正交函数展开法为基础,选择了FPK方程的部分算子作为解的展开函数系,同时根据系数方程最小耦合关系式的初始值问题和特征值问题及其两者的关系,提出了求解振动系统转移概率密度函数的近似方法。最后,以Duffin方程为例给出了非线性系统非平稳过程FPK方程的求解过程。计算结果表明,矩阵连分法收敛快、方法规则且精度高,能适用于各种非线性势场。

The exact solutions for stationary responses of one class of the second order and three classes of higher order nonlinear systems to parametric and/or external white noise excitation are constructed by using Fokker-Planck-Kolmogorov equation approach. The conditions for the existence and uniqueness and the behavior of the solutions are discussed. All the systems under Consideration are characterized by the dependence of nonconservative forces on the first integrals of the corresponding conservative systems...

The exact solutions for stationary responses of one class of the second order and three classes of higher order nonlinear systems to parametric and/or external white noise excitation are constructed by using Fokker-Planck-Kolmogorov equation approach. The conditions for the existence and uniqueness and the behavior of the solutions are discussed. All the systems under Consideration are characterized by the dependence of nonconservative forces on the first integrals of the corresponding conservative systems and are called generalized-energy-dependent (G. E. D.) systems. It is shown that for each of the four classes of G. E. D. nonlinear stochastic systems there is a family of non-G. E. D. systems which are equivalent to the G. E. D. system in the sense of having identical stationary solution. The way to find the equivalent stochastic systems for a given G. E. D. system is indicated and, as an example, the equivalent stochastic systems for the second order G. E. D. nonlinear stochastic system are given. It is pointed out and illustrated with example that the exact stationary solutions for many. non-G. E. D. nonlinear stochastic systems may be found by searching the equivalent G. E. D. systems.

用福克-普朗克-柯尔莫哥洛夫方程方法构造了一类二阶、三类高阶非线性系统对白噪声参激与/或外激的平稳响应的精确解.讨论了解的存在与唯一性及解的性态.所考虑的系统的共同特点是非保守力依赖于相应保守系统的首次积分,因此可称为广义能量依赖系统.文中指出,对每个广义能量依赖系统,存在一族与之随机等价的非广义能量依赖系统,它们有相同的平稳概率密度.并指出对一给定广义能量依赖系统,如何找到其等价随机系统.作为例子,给出了二阶广义能量依赖随机系统的等价随机系统.最后指出并用例子说明,许多非广义能量依赖非线性随机系统的精确平稳解可通过寻求其等价广义能量依赖系统而找到.

By the method of stochastic averaging of energy envelope the analytical expression of the moments of the first snapthrough time for shallow curved structures under random loading is drived. The probability density of the first snapthrough time is obtained by using implicit finite difference method to solve the backward Kolmogorov equation satisfied by conditional reliability function. By comparing with the result of digital simulation, we can see that this method yields satisfactory results in the case...

By the method of stochastic averaging of energy envelope the analytical expression of the moments of the first snapthrough time for shallow curved structures under random loading is drived. The probability density of the first snapthrough time is obtained by using implicit finite difference method to solve the backward Kolmogorov equation satisfied by conditional reliability function. By comparing with the result of digital simulation, we can see that this method yields satisfactory results in the case of light damping. The influences of various parameters on the first snap-through time are also analysed.

本文用能量包线随机平均法,导出了随机载荷作用下浅曲结构首次发生突变的时间的各阶矩的解析表达式,并通过用臆式差分法数字求解条件可靠性函数所满足的后向柯尔英哥洛夫方程,给出了发生首次突变的时间的概率密度.与数字模拟结果比较表明,在结构阻尼不大时该法给出令人满意的结果.文中还研究了各种参数对结构首次发生突变的时间统计量的影响.

 
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