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解析微分
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  analytic differential
     A solution of the real analytic differential equation x=f(t, x) may not be analytic.
     实解析微分方程x=f(t,x)的解不一定实解析.
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  “解析微分”译为未确定词的双语例句
     The SPH is one kind of particle method, somewhat similar to particle grid method, but the main difference is that SPH's method needn't use any grid and can be replaced by the analysis of differential formula of the interpolation formula when calculating the derivative in space, thus we can avoid grid intertwist and deforming appearing in high degree Lagrange interpolation grid method, which makes us most headache.
     SPH是一种质点方法,有点类似质点网格法,但根本的不同点在于SPH方法中计算空间导数时不需要使用任何网格,而被插值公式中的解析微分式子所替代,从而避免了高维拉氏差分网格法中网格缠结和扭曲等最令人头痛的问题.
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  相似匹配句对
     THE DIFFERENTIAL MEAN VALUE THEOREM OF ANALYTIC FUNCTION
     解析函数的微分中值定理
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     On differential analysis of the Solow model and draw from certain experience
     Solow模型的微分解析及其借鉴
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     Dilemma for Clubs
     俱乐部解析
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     Analysis of the Stairs
     楼梯解析
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     The Pattern of Differential
     微分模式
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  analytic differential
Singular perturbation problems of systems of two ordinary analytic differential equations
      
Suppose that an analytic differential equation for which a first integral is known is subject to an analytical perturbation.
      
The underlying method is essentially algebraic and based on a certain nonlinear extension of similarity (gauge) transformations in the ring of analytic differential operators.
      
On the principle of subordination in the theory of analytic differential equations
      
Remarks on the topology of singular points of analytic differential equations in the complex domain and Ladis' theorem
      
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In the paper,using the famous Lie-series formal solution of Cauchy problem of real analytic ordi- nary differential systems we derive firstly finite formulas for general solutions to two-dimensional systems of autonomuous linear inhomogencous diffe■cntial equations.Al- though such problems were known long ago to be solvable.But,however,it is unclear before weather or not the general solution can be formulated directly in terms of initial da- ta and the coefficients of the system under consideration.We discover...

In the paper,using the famous Lie-series formal solution of Cauchy problem of real analytic ordi- nary differential systems we derive firstly finite formulas for general solutions to two-dimensional systems of autonomuous linear inhomogencous diffe■cntial equations.Al- though such problems were known long ago to be solvable.But,however,it is unclear before weather or not the general solution can be formulated directly in terms of initial da- ta and the coefficients of the system under consideration.We discover that,there are six different cases distinguished by some coefficient conditions.In each case the general solution is given by a finite formula and can be calculated by simple substitution.Such results are new to the literature.

利用李群方法对实解析微分系统导出的李级数型形式解,给出了二阶线性非齐次驻定微分系统的通解公式、结果深刻完整地展示出通解与系统的系数和初始值之间的内在联系,作为特殊情形概括了 Hill,Larsen 和 Jensen 等的近期工作.

The sensitivity partial derivatives of doublet strength density with respect to the parameters of wing planfomi(bi-direction perturbation) which are needed to build the general senaitivity equations can be calculated with analytic method based on the intemal Dirichlet prob-leni fonnufation and analytical differentiation cascaded on singular integral8,and then the solu-tion of doublct strength distribution is generated for any perturbed wing planform by linear extrapolation.Thus the pressure distrlbuti on,lift...

The sensitivity partial derivatives of doublet strength density with respect to the parameters of wing planfomi(bi-direction perturbation) which are needed to build the general senaitivity equations can be calculated with analytic method based on the intemal Dirichlet prob-leni fonnufation and analytical differentiation cascaded on singular integral8,and then the solu-tion of doublct strength distribution is generated for any perturbed wing planform by linear extrapolation.Thus the pressure distrlbuti on,lift and pitehing moment coefflcients are deter-mined very rapidly.The comparison between the calculated results of the present perturbation panel method and the corresponding lower-order panel method shows that the present algorithm is of fine accuracy and can substantially reduce computing cost required(CPU time req uired for perturbation extrapolation is two orders of magnitude less than that of the corresponding lower-order panel method).

在内部Dirichiet边界条件的基础上,藉助于对奇异积分的解析微分,可用解析法计算偶强密度对机翼平面形状乡数的敏感性偏导致(建立一般敏感性方程所需)。机翼平面形状参数摄动后其偶强分布即可藉线性外推得出。从而,压力分布、升力和俯仰力矩系数即可快速确定。振动面元法与相应的低阶面无法计算结果表明,该方法有良好的准确度且使计算工作量大大减少(摄动外推所需CPU时间比相应的低阶面元法少两个量级)。

In this paper, a high order CMAC(HCMAC) neural network is proposed, in which the high order activation functions are utilized as the receptive field functions. The method of address mapping used by CMAC is adopted in the new network. Because of enhancement of the input pattern, the physical address in HCMAC is reduced highly, and by using HCMAC the approximation of complex functions can be obtained which is more continuous than using CMAC and has analytic derivatives. As a result of these characters, the computing...

In this paper, a high order CMAC(HCMAC) neural network is proposed, in which the high order activation functions are utilized as the receptive field functions. The method of address mapping used by CMAC is adopted in the new network. Because of enhancement of the input pattern, the physical address in HCMAC is reduced highly, and by using HCMAC the approximation of complex functions can be obtained which is more continuous than using CMAC and has analytic derivatives. As a result of these characters, the computing amount and learning time are reduced more than RBF neural networks. This paper also introduces originally the Kalman filter algorithm to the CMAC like networks, so learning effectiveness is improved further. By simulating, it is proved that HCMAC is feasible in many fields.

提出了一种高阶CMAC(HCMAC)神经网络.它是采用高阶的径向基函数作为接收域函数,为了进一步增强对输入模式的表达,还可以用接收域函数与输入模式向量构成张量积,这时产生的是高维的增强表达,同时HCMAC沿用CMAC的地址映射方法.由于高阶接收域函数的引入,使其可以获得较CMAC连续性强且有解析微分的复杂函数近似.HCMAC在不改变CMAC简单结构的基础上较RBF网络有计算量少,学习效率高等优点.文中还首次将用于参数估计的Kalman滤波学习算法引入到这种类CMAC的网络学习中,这使HCMAC有更高的学习速度.通过仿真研究表明HCMAC除拥有CMAC和RBF网络两者的优点外,还有较这两者更多的优良特性

 
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