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differential algebra
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  微分代数
     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。
短句来源
     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.
短句来源
     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。
短句来源
     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
短句来源
     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。
短句来源
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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。
短句来源
     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。
短句来源
     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.
短句来源
     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。
短句来源
     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 .
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  “differential algebra”译为未确定词的双语例句
     Since the different dynamics methods such as Newton-Euler method, Lagrange's equations and other methods can be used to develop the dynamic equations of global system, the two different forms of the dynamic equations are ordinary differential equations and differential algebra equations.
     本文在多体系统传递矩阵法的基础上,首先推导小运动空间多体系统元件如弹簧、集中质量、刚体、非均匀欧拉梁等的传递矩阵,将图论描述方法引入线性多体系统传递矩阵法,采用规则标号方法和宽度编码原则,发现了总体传递矩阵与系统拓扑结构之间的相似关系,形成了程式化的链式、分叉、网络多体系统总体传递矩阵拼装方法。
短句来源
     To obtain state matrix A of linear differential algebra equation, the equation set of the model, then the eigenvalue of state matrix A and its effection on sensitivity of excition system are calculated by QR method.
     对模型方程组进行线性化,得到线性微分-代数方程的状态矩阵A; 使用QR法,计算状态矩阵A的特征值及特征值对发电机励磁系统参数灵敏度。
短句来源
     The connection is obtained based on techniques of differential algebra. Applying the result to Burgers equation and Burgers KdV equation,we prove that both equations have only one conservation law.
     通过文本给出的结果 ,我们研究了Burgers方程和Burgers KdV方程的可积性 ,证明了这两类方程都只有一个守恒率 .
短句来源
     For multi-body systems with unilateral constraints,due to their unilateral features,the systems can be formulated into mixed framework combining the differential algebra equations(DAE) with complementary problems(CP). But for the bilateral constraint systems with friction,the method for representing the CP of bilateral constraints is a difficult point.
     对于单边约束的多体系统,可以根据其单边特性,将该系统描述为微分代数方程组(DAE)与互补条件(CP)结合的混合框架,但用该方法处理含摩擦的双面约束系统时,双面约束的CP表示方法是个难点。
短句来源
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  differential algebra
The present method depends on a result from differential algebra andp-adic analysis.
      
The Heisenberg double of these two exterior Hopf algebras defines the differential algebra for the Cartan differential calculus on .
      
In the approach based on the global covariance with respect to the stability subgroup U(1), we show that the gauge-covariant exterior differential algebra on SUq(2) is uniquely determined.
      
Each system of partial differential equations generates an ideal in some differential algebra.
      
We consider tensors with coefficients in a commutative differential algebra A.
      
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A negative exponential corrector for the mixed differential-algebra equations of the largedeployable antenna of satellite is presented. The corrector reduces the parameter range of the oscillatory-type corrector and makes the numerical integration of models of dynamics of flexible multi-body systems simple and reliable.

采用具有单调速降性质的负指数函数对混合方程组进行违约修正,缩小了振荡型违约修正的参数范围,使模型计算更加简单、可靠.

By using pseudodivision algorithm of matrix multivariate polynomial and way of differential algebra,the sufficient and necessary conditions for transform a class of partial differential equations into infinite demensional Hamiltonian system and Hamiltonian forms are given,and give some examples to justify this method.

利用矩阵多元多项式的带余除法以及微分代数的观点得到把一类偏微分方程(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.

Differential algebra is a new mathematical method and a promising tool in charged particle optics. As a kind of automatic differentiation techniques, it is based on the nonstandard analysis and normal power series theory. It presents a straightforward method for the study of arbitrary order property of nonlinear systems, with accuracy limited only by the computer. The differential algebraic method is widely applicable, and it is an effective and elegant tool for the tracking, analysis and correction of...

Differential algebra is a new mathematical method and a promising tool in charged particle optics. As a kind of automatic differentiation techniques, it is based on the nonstandard analysis and normal power series theory. It presents a straightforward method for the study of arbitrary order property of nonlinear systems, with accuracy limited only by the computer. The differential algebraic method is widely applicable, and it is an effective and elegant tool for the tracking, analysis and correction of high_order aberrations, sensitivity analysis and optimization of structure design, etc., of the charged particle optical systems. The principle and virtues of differential algebra are summarized. The application of differential algebra method in charged particle optics and its implementation in various computer languages are analysed. Some new research subjects in this field are discussed.

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。作为一种自动微分技术,它结合了非标准分析、简正级数理论等的思想。微分代数提供了一种可达到机器精度的研究非线性系统任意阶性质的极为简便的方法,故应用领域非常广泛,对带电粒子光学中的轨迹追踪、高阶像差分析与校正、灵敏度分析与结构优化设计等都是一个很有效的工具。综述了微分代数的基本原理和独特性,分析了它在带电粒子光学中的应用,以及在不同计算机语言中的软件实现,提出了今后的一些发展方向。

 
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