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微分代数
    Differential Algebra Analysis for High Order Combined Geometric-chromatic Aberrations
    微分代数在高阶复合几何像差-色像差分析中的应用
    Arbitrary order transfer properties of the system can be expressed in term of Differential Algebra. The corresponding differential algebraic coefficients of the 1st to the 3rd order combined geometric chromatic aberrations were given.
    本文根据微分代数的基本原理 ,研究了它在高阶复合几何像差 色像差分析计算中的应用 ,得到了系统的任意阶传递性质的微分代数表示 ,并具体给出了一至三阶复合几何像差 色像差所对应的微分代数系数。
    AN AUTOMATIC DIFFERENTIATION TECHNIQUE: DIFFERENTIAL ALGEBRA AND ITS APPLICATION IN CHARGED PARTICLE OPTICS
    一种自动微分技术:微分代数及其在带电粒子光学中的应用
    Application of Differential Algebra to Calculation of High Order Aberration of Realistic Electron Lenses
    利用微分代数方法计算实际电子透镜的高阶像差
    Another method that combines Singh algorithm with differential algebra also can decouple nonlinear systems. The method can find the certain part of output be decouplled structure of original system by Singh algorithm calculating essentiality of the decouplled system matrix.
    另一种方法是采用Singh算法与微分代数理论相结合对非线性系统进行解耦设计,通过对采用Singh算法后得到的解耦系统的矩阵,来计算其本性耦合关系,寻找出某个分划是原非线性系统的解耦结构,并以交流伺服电动机为例进行了分析。
    With the development of the computer and the constantly expanding of it's applied domain, symbol computation present gradually powerful bioenergy. In this paper, using the computer algebra as the tool and the differential algebra as the background , we discuss the theory of "AC=BD" and the differential characteristic method and their application in the differential equations .
    随着计算机的发展和应用领域的不断扩大,符号计算在数学领域中体现出了日益强大的生命力,本文就是以计算机代数为工具,微分代数为理论背景,讨论了“AC=BD”理论及微分特征列法的相关理论问题以及它们在微分方程组中的应用。
    Differential algebra is a new mathematical method and a promising tool in charged particle optics.
    微分代数是带电粒子光学中新近出现的一个很有前途的数学工具。
    High order combined geometric chromatic aberrations were calculated with Differential Algebra,a method which is capable of directly evaluating arbitrarily high order derivatives with accuracy up to the upper limit of the computer to be used.
    微分代数是计算机数值计算领域中的一种强有力的新型数学方法 ,它为任意高阶微分的计算提供了一种可达到机器精度的极为简便的手段。
    The arbitrary high order aberrations are conveniently calculated by differential algebra method and the fifth-order aberration diagrams are given.
    同时结合微分代数方法可以很方便地计算到任意高阶像差的特性,给出了所研究的透镜全部五阶像差的分布图形.
    The dimension of the differential ideal is an important concept in Differential Algebra. Much work has been done in computing the dimension by using Hilbert polynomial.
    微分理想的维数是微分代数中一个重要的概念 ,利用 Hilbert多项式来计算微分理想的维数 ,计算量较大 .
    Differential algebraic strategy can be applied to address the dynamic feedback control problems effectively in the nonlinear systems, with Flatness an important concept in the differential algebra.
    微分代数采用动态反馈控制实现一类非线性系统的控制,平滑性是微分代数的重要概念。
    Since the floating frame,which is linearized Tisserand frame,was reasonably selected,the constraint formulations caused by the floating frame of reference formulation can come into existence automatically. Then flight dynamics model of differential algebra equations was transferred into differential equations that will greatly simplify dynamics model.
    采用了合适的浮动框架———线性化Tisserand框架,使得浮动框架引出的约束方程自动满足,飞行力学求解由微分代数混合方程组化为微分方程组;
 

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