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微分代数的
    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。
    Differential algebra provides a new and promising mathematical method based on the nonstandard analysis and power series theory. The underlying principle is studied for calculating the transfer properties of nonlinear systems. Using the object oriented programming technique and Visual C++ ,a DA/TLC package was developed, and it could implemen differential algebra up to arbitrary high order.
    为给研究非线性系统传递性质提供一个简便、有效的工具 ,研究了新近出现的微分代数的基本理论 ,在VC ++环境中编制了一个DA/TLC软件包 ,实现了任意高阶微分代数的功能 .
    Pseudo_division algorithm for matrix multivariable polynomial are given, thereby with the view of differential algebra, the sufficient and necessary conditions for transforming a class of partial differential equations into infinite dimensional Hamiltonian system and its concrete form are obtained. Then by combining this method with Wu's method, a new method of constructing general solution of a class of mechanical equations is got, which several examples show very effective.
    给出矩阵多元多项式的带余除法 ,从而用微分代数的观点 ,得到把一类微分方程 (组 )化为无穷维Hamilton系统的充要条件及其具体无穷维Hamilton系统形式· 再把此方法和吴方法相结合获得构造一类微分方程 (组 )的通解的新方法· 几个例子表明这些方法都很有效的·
    Basing on wu's method, a mechanically prove the completeness of the solutions of completeness of the Hu's solutions in elasticity with the view of the differential algebra.
    在吴方法的基础上,从微分代数的观点出发,机械化证明了各项同性弹性力学方程组的胡海昌解的完备性问题.
    A symbolic computation method to decide whether the solutions to the system of linear partial differential equation is complete via using differential algebra and characteristic set is presented. This is a mechanization method,and it can be carried out on the computer in the Maple environment.
    从微分代数的角度出发 ,借助于吴微分特征集理论 ,对于线性偏微分方程组 ,给出了判定它的解的完备性的一个符号计算方法· 这个算法是一个机械化的算法 ,借助于符号计算软件Maple ,可以在计算机上实现
    By combining the standard form algorithm with the pseudo division algorithm for matrix multivariable polynomial,a new method of constructing the general solutions of a class of the partial differential equations is obtained,thereby with the view of the differential algebra and a mechanical algorithm for auto deducing the mechanical equations is got on the basis of the standard form algorithm.
    用微分代数的观点 ,把标准型算法和矩阵多元多项式的带余除法相结合 ,获得构造一类微分方程组的通解的新方法 ,并在标准型算法的基础上给出了力学方程的推理的机械化方法。
    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。
 

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