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A generalized mathematical model was developed to describe the distribution of over-potential.Dimensionless variables μ and ω that characterize the polarization and influence of side electrode reaction in the system,were derived from modeling.Adomian's decomposition methodADM）was used to solve the nonlinear differential equation of the model to obtain an approximate analytical solution,which was in the form of algebraic expressions of infinite power series.By the solution,the relationship between over-potential distribution and average selectivity could be easily calculated without solving the nonlinear model time and again.

建立了描述超电势分布的普遍化数学模型，归纳出表征电极极化和副反应影响的量纲1数μ和ω，并用ADM（Adomian's decomposition method）对该非线性微分方程模型求解；所获得的逼近解代数表达式，可方便地计算不同参数下超电势分布对平均选择性的影响，而毋需反复求解模型微分方程。

The traditional method is to transfer the differential equation into the algebraic equation via orthogonal function. This paper adopts the advantage of Slant function including:(1) The characteristic that Slant operational matrix of integration changes fast can simplify the question.

传统的特性技巧是透过正交函将微分方程式转换为一个代方程式，本文采用其优点有：(1)用Slant 积分运算矩阵快速转换的特性可以简化问题。

Quantity and space both play a role in analytic geometry , differential geometry , and algebraic geometry .

数量和空间在解析几何，微分几何和代数几何中都发挥作用。

Manifolds occur in algebraic geometry, differential equations, and classical dynamics..

流形出现于代数几何、微分方程式和经典动力学中。

One has its origin in algebraic geometry, whereas the other one comes from differential geometry.

借助于它们上面的Hermitian度量我们可以定义两个模空间：一个联系着代数几何；一个联系着微分几何。

The hybrid model is a combination of non-linear algebraic equation group and differential or difference equation group, and possesses the ability to integrate equations in inhomogeneous expression form.

本课题抓住这一前沿研究，从经验知识与经验数据的综合利用入手，对软测量模型的结构、模型构建方法以及软测量系统的关键技术进行深入研究。

Chapter 4 presents five design criteria of S-boxes of block ciphers, develops a method of constructing large S-box by use of algebraic group operation, proves the balance property of these large S-box, tests the strict avalanche and independence of avalanche variables properties of S-boxes in NEA cipher, analyses the nonlinearity and best linear approximation of the S-box, and finally defines the differential of input/output of S-boxes of this cipher and analyses the distribution of them.

第二部分即第三章，提出了一种新的分组密码类NEA(NEA-4A，NEA-8A，NEA-4B，NEA-8B)，完整地描述了该密码类的加解密过程和密钥协议；证明了NEA-4B和NEA-8B的完全对合性和没有不动点的性质；分析了该密码类的安全特征；具体地介绍了实现该类密码的途径；给出了NEA-4A的计算机C语言程序和样本数据。

Basic Mathematics has undergone an amazing evolution and born fruit on fields such as algebra, functional analysis, dynamic system, algebraic number theory and differential geometry.

基础数学的研究经过多年工作积累，在代数学、泛函分析、动力系统，代数数论，微分几何等领域在国内外有一定影响。

The system of differential equations for a geodesic line on an algebraic surface was discredited into a nonlinear system. Then it was solved numerically based on iterative methods.

在算法中，把决定代数曲面测地线的微分方程组离散为一个非线性方程组，然后采用迭代数值方法求解。

In the chapter7 and 8, the numerical algorithm for the variable delay differential algebraic system is studied.

在第七、八章，本文就变延迟微分代数系统的数值算法展开了研究。

Continuously improve the production mechanism, to provide customers with better quality products and services.

不断的完善生产机制，给客户提供更优质的产品及服务。

B:Yes, he was the very prize-winner in the court tennis ten years ago?

是的，他是十年前的世界网球冠军。