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龙格现象    
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  runge phenomenon
    Because of these reasons,putting forward Runge phenomenon,designing a principal-agent range model. On base of this model,to make consignor and agent aim same,to increase corporate value,put forward two ways of reducing contract effective angle,including executive stock options and construction of independent director.
    由此提出了龙格现象,设计了委托———代理区间化模型,并相应地提出了减小契约效力角,使委托人与代理人目标趋于一致,增加公司价值的两种方法:经理股票期权激励和加强独立董事建设。
短句来源
  runge phenomenon
    Because of these reasons,putting forward Runge phenomenon,designing a principal-agent range model. On base of this model,to make consignor and agent aim same,to increase corporate value,put forward two ways of reducing contract effective angle,including executive stock options and construction of independent director.
    由此提出了龙格现象,设计了委托———代理区间化模型,并相应地提出了减小契约效力角,使委托人与代理人目标趋于一致,增加公司价值的两种方法:经理股票期权激励和加强独立董事建设。
短句来源
  runge phenomenon
    Because of these reasons,putting forward Runge phenomenon,designing a principal-agent range model. On base of this model,to make consignor and agent aim same,to increase corporate value,put forward two ways of reducing contract effective angle,including executive stock options and construction of independent director.
    由此提出了龙格现象,设计了委托———代理区间化模型,并相应地提出了减小契约效力角,使委托人与代理人目标趋于一致,增加公司价值的两种方法:经理股票期权激励和加强独立董事建设。
短句来源
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  runge phenomenon
No filtering is done; with ten coarse grid points in the front, the Runge phenomenon was not observed.
      
This so-called Runge phenomenon is not a problem with the barycentric formula, but is intrinsic in the underlying interpolation problem.
      
Thus, an important issue in high-order AMR is dealing with the potential for the Runge phenomenon associated with interpolation on uniform grids.
      
  runge phenomenon
No filtering is done; with ten coarse grid points in the front, the Runge phenomenon was not observed.
      
This so-called Runge phenomenon is not a problem with the barycentric formula, but is intrinsic in the underlying interpolation problem.
      
Thus, an important issue in high-order AMR is dealing with the potential for the Runge phenomenon associated with interpolation on uniform grids.
      
  runge phenomenon
No filtering is done; with ten coarse grid points in the front, the Runge phenomenon was not observed.
      
This so-called Runge phenomenon is not a problem with the barycentric formula, but is intrinsic in the underlying interpolation problem.
      
Thus, an important issue in high-order AMR is dealing with the potential for the Runge phenomenon associated with interpolation on uniform grids.
      
  其他


In the present paper the convergence and validity of the results of boundary collocation procedure are studied by considering function approxima- tion. The problem being discussed here is one of rectangular plates with one- side edge crack, and the Williams stress function is used as approximating function. For examining the validity of the results a criterion, based on considering uniform approximation of functions, is put forward. Suppose that in the problem the boundary condition is known as f(s) (where...

In the present paper the convergence and validity of the results of boundary collocation procedure are studied by considering function approxima- tion. The problem being discussed here is one of rectangular plates with one- side edge crack, and the Williams stress function is used as approximating function. For examining the validity of the results a criterion, based on considering uniform approximation of functions, is put forward. Suppose that in the problem the boundary condition is known as f(s) (where s represents points on the boundary B), which-is approximated by the Williams stress function W_m (s). Now if the solution of the boundary value problem is stable, then a small difference between W_m (s) and f(s) would cause only a small deviation ω(γ,θ) of the calculated solution from the exact solution, where γ, θ are polar coordinates of points in domain D bounded by boundary B. Hence the mag- nitude of |δ(s)|_(max) represents a measure of the quality of the solution in domain D. For the convenience of calculation, |δ(s)|_(max) is replaced by the relative mean square error M_δ, as "criterion of validity". The criterion can be given as M_δ=(∫_B δ~2 (s)ds)/(∫_B f~2 (s)ds ≤ε where ε is a small value depending upon the accuracy required in the calcula- tion. With the help of this criterion, a judgement about the validity of the results can be obtained from the calculation itself, without having to rely on previously known analytic solution. The effectiveness of the criterion put forward is proved in numerical examples given in this paper. The difference in convergence of two different approximations usually used, i, e., interpolation approximation and average approximation, is discussed. It is well known that the results of interpolation approximation are not always convergent. This is usually explained as follows: "As in the coefficient matrix the differences between two adjacent columns are very small, the results become unstable". That is to say, divergence occurs because of the errors in matrix calculation. However, it is found in our calculations that the errors of the approximating function W_m(s) at all the nodes are negligibly small (δ(s)→0 at nodes). This clearly shows that the errors in matrix calculation appear to be not the real reason of the divergence. It is shown in the present paper that, at least for the problem studied, the divergence results from the the fluctuation of the approximating function between the nodes, and that the situation becomes worse as the number of nodes increases. This is known as "Runge phenomenon" in algebraic interpo- lation. For average approximation, there will be no fluctuation in general, and the solutions can be shown to be always convergent, but it may or may not converge to the exact solution of the problem This seems to be an indication of the incompleteness of the Williams function.

本文从函数逼近的观点研究了边界配置法解的有效性及收敛性。具体讨论矩形板单边裂纹问题,以Williams应力函数作为逼近函数。文中从函数一致逼近的概念出发,提出了判断计算结果的有效性标准。从而使边界配置数值解法可自行判断解的有效性,而不必依赖于解析解。文中的算例表明这个标准是正确的。文中区分了由插值逼近(“精确”配置边界点)和平均逼近(最小二乘法)两种不同方法所得到的两种Williams应力函数不同的收敛性质。解释了由插值逼近得到的函数不收敛的原因是节点间的振荡现象,也就是高次代数插值中的“龙格现象”。平均逼近得到的函数,不会发生“龙格现象”。可以证明它是收敛的,但是计算表明它不能保证总是收敛于准确解,这说明Williams函数各函数项构成的函数组是不完备的。

Corporate governance problems include two types: one is the agent type corporate governance,facing relationship between stockholder and manager;the other type is the deprivation type corporate governance.And the main characteristic of modern corporate is the separation of ownership and management power,appearing principal-agent relationship.Through analysis about traditional principal-agent model,finding out unreasonable factors,for example,expectation effectiveness function and the wealth maximum of stockholder.And...

Corporate governance problems include two types: one is the agent type corporate governance,facing relationship between stockholder and manager;the other type is the deprivation type corporate governance.And the main characteristic of modern corporate is the separation of ownership and management power,appearing principal-agent relationship.Through analysis about traditional principal-agent model,finding out unreasonable factors,for example,expectation effectiveness function and the wealth maximum of stockholder.And it is infeasible.Because of these reasons,putting forward Runge phenomenon,designing a principal-agent range model.On base of this model,to make consignor and agent aim same,to increase corporate value,put forward two ways of reducing contract effective angle,including executive stock options and construction of independent director.

公司治理问题有两类:一类是代理型公司治理问题,面对的是股东与经理之间的关系;另一类是剥夺型公司治理问题,涉及到大股东与小股东之间的利益关系。现代公司主要的特征是所有权与经营权相分离,产生了委托———代理关系。经过对传统的委托代理模型的分析认为:传统的委托———代理模型存在着假设条件———期望效用函数和股东财富最大化的不合理性,不具有可操作性。由此提出了龙格现象,设计了委托———代理区间化模型,并相应地提出了减小契约效力角,使委托人与代理人目标趋于一致,增加公司价值的两种方法:经理股票期权激励和加强独立董事建设。

 
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