代数

This paper studies the construction principle and main algebraic properties of AES S-box,points out the S-box has these characteristics that periods of affine transformed pair is 4,periods of iterative-output is less than 88,strict avalanche criterion distance is 432,the algebraic expression has only 9 items and so on.

研究了AES S盒的构造原理和主要代数性质，指出了AES S盒的仿射变换对周期为4，迭代输出周期不大于88，严格雪崩准则距离为432，代数表达式只有9项等。

This process is actually the process of algebraic extension; also it is the basic way of algebra: organizing some objects into an operation system, and then study the relationship between elements or parts of the system.

这实际上是代数扩张的做法，也是代数的本质：将一些对象组织成一个运算体系，研究这个体系中各个个体之间以及部分与全体之间的关系。

cryptography ; algebraic attack ; Boolean function ; algebraic immune degree

本文研究了具有1型线性结构的布尔函数f的代数免疫阶，揭示了布尔函数的线性结构对其代数免

Given a planar point set,the moving least squaremethod is adopted to denoise and resample it so that the resulting point set is with low noise and uniform sampling density.Then the reliable signed distance field of the preprocessed point set is constructed by using the Level Set method.Finally,an algebraic B-spline function is adopted to fit the signed distance field by solving a linear equation system.

首先给定一个表示封闭曲线、可能带有噪音且分布不均匀的平面点云，采用移动最小平方(moving least square，简称MLS)方法对点云去噪、重采样，得到一个低噪音、分布均匀的"线状"点云，再通过Level Set方法建立该"线状"点云的离散几何距离场，最后用一个代数B-样条函数光顺拟合该离散距离场，代数函数的零点集即为重建曲线。

It has developed from two sources: algebraic geometry and algebraic member theory.

它由两个方面发展而来，代数几何和代数数论。

Methods of algebraic geometry rely heavily on sheaf theory and other parts of homological algebra .

代数几何方法在很大程度上依赖束理论和其他地区的同调代数。

The parameters of codes on the curves over finite fields is always the important problem in algebraic geometry codes.

有限域上代数曲线上的码的参数问题一直是代数几何码研究中的重点问题。

In this paper, we use some algebraic geometry methods to study the construction of χ-invariant algebras of some linear corresponding moduli space of these systems. Moreover, we completely determine the stable and semistable locus of these systems.

本文，我们以代数几何中的一些方法来研究某些线性动力系统的χ-不变代数的构造，并给出这类系统的相应的参量空间的刻划，进一步，完全决定了这类系统的稳定点、半稳定点的轨迹。

On the other hand, equivariant algebraic topology concerns the study of algebraic invariants of space with group actions. It is really a study of symmetries on spaces, and has always occupied a central role in mathematics.

在另一方面，等变代数拓扑关注于带有群作用的拓扑空间代数不变量的研究，其更深刻的本质在于对空间对称性的揭示，因此从来都在数学研究中占有重要的地位。

It's really the natural setting for algebraic topology because the traditional algebraic invariants (fundamental group, homolog group,etc.) arc isomorphic not only for homeomorphic spaces but for spaces of the same homotopy type. Homtopy epimorphisms and monomorphisms are special morphisms in the category of topological spaces and the initial research of them may be traceable to S.T.

同伦论的本质是利用比同胚关系更广泛的等价关系—同伦关系来对拓扑空间进行研究，这也是代数拓扑研究中一种自然的考虑，因为传统的代数不变量不仅在同胚的空间之间保持同构，而且在具有相同伦型的空间之间也保持同构。

I will endeavour to find you some assistance.

我尽力帮你找人帮忙。

At first I only know bruck is the idol of American younglings, afterwards I returned back to Taiwan ,even in Beijing last year ,I saw her poster everywhere, I was so surprised at her charm.

起初我只晓得布鲁克雷德丝是美国少男少女崇拜的偶像，后来回台湾，甚至去年在北京，居然也四处看见她的海报，才惊讶她的魅力之大。