仿射坐标

The geometric detail is represented as the set of the local affine coordinates of the base surface and extracted effectively and efficiently in user specified frequency band of geometric signal.

通过基曲面上的局部仿射坐标，则可以得到与之对应的多分辨率几何细节表示，曲面的低频信息和高频信息易被用户所指定的频段分离。

Based on the idea, this paper proposed an efficient algorithm to compute 3P+Q directly over F in terms of affine coordinates, its computational complexity was 1I+3S+16M, saving one field inversion compared to Ciet's method.

根据这种思想，提出了素域F上用仿射坐标直接计算3P+Q的算法，其运算量为1I+3S+16M，比Ciet等人提出的方法节省了一次求逆运算。

This gives a new description of human recognition mechanism from the view of information geometrical and algebraic topological treatment, the results include Propose a structure representation and system identification approach for neural networks, based on the concept of simplical complexes and dual affine coordinates in the dual flat manifold.

主要的结果包括：提出用对偶平坦流形上的单、复形结构和对偶平坦流形的对偶仿射坐标作为神经网络内在结构表示的一种方法，具有广泛的意义。

That is that information processing of neural networks is viewed as the composition of the two steps: field organization and field action, in which, field organization transformation converts input pattern into relevant structure representation, extracting the underlying architecture features and forms a architecture representation in action transformation space; The field action transformation converts the features representation into expected output. In strategies, we use the dual affine coordinates in dual flat manifold as way of representation of field organization system and field action system, which established a theoretical framework of analysis the coupling mechanism of information processing from the view of point of structure representation and model generation.

在具体人工神经网络结构描述的策略上，利用对偶流形空间上的对偶仿射坐标概念分别表示场组织变换系统和场反应变换系统，建立起从问题的结构表示和模型生成两种观点来分析信息处理的理论框架；分析了有监督和非监督学习人工神经网络模型在神经场变换机理下的形式化描述。

Furthermore we discussed the problem whether I1 ,12,13 are the invariant under affine coordinate transformation.

此外，我们讨论了，I1，I2，I3是否为仿射坐标变换下的不变量这一问题。。

Firstly, some basic concepts about ECC are introduced;then the scalar multiplication under affine coordinate is discussed, we make a research and analysis of the side channel attack of scalar multiplication used in portable device, give out a new scalar multiplication algorithm which has the advantage of efficiency over other protected algorithm; and an improvement of the standard scalar multiplication algorithm proposed by IEEE1363 is made with the efficiency increasing by about 10%; at last, we deal with the using of complex multiplication in scalar multiplication algorithm, we generalize the methods and deduce a complete computing procedure, with proposing a new method which used several different fast endomorphism ,we give out an approach to boost the scalar multiplication with fast endomorphism.

本文首先介绍了椭圆曲线密码的有关基本概念；其次介绍了椭圆曲线上点的标量乘法在仿射坐标下的计算，对一般便携设备上的椭圆曲线点的标量乘法的边信道攻击做了研究与分析，给出了一种在效率上优于其它可抵抗边信道攻击的标量乘法的新算法，并对IEEE P1363 标准给出的标量乘法做了改进，使得标量乘法的运算效率提高了近10%；最后介绍了利用复乘计算标量乘法的方法，对已有的方法进行总结归纳，得出完整的计算过程，并针对两类超奇异椭圆曲线给出了一种利用多个可快速计算的复乘的标量乘法，得出一类普遍的结果，并给出了进一步用复乘加快标量乘法的思路。

In chapter 1,we find out a kind of two-parameter invariant cubic curve family of a certainquadratic system which is important one for studying the distribution of limit cycles.

第二章讨论一般的二次系统具有三次代数曲线同宿环的充要条件，针对问题，我们采用了具有双曲鞍点的二次系统的标准形，利用仿射坐标变换，我们把系统和曲线同时简化，使问题得到了完满解决。

With the assumption that electric field is constant within each element, the relationship of the degrees of freedom over each element is determined by introducing a local affine coordinate system.

在单元内部电场为常量场的假设下，使用局部仿射坐标架，确定出每个单元上自由度所服从的约束关系，由此导出对角化质量矩阵的公式。

Including: basic coordinate changing: MOVE (move the entire or a part of figure to other location of coordinate); ZOOM (used for export map with different size); CIRCUMROTATION;仿射变换 integration move, zoom and circumrotation

坐标变换包括：基本坐标变换：平移（将图形的一部分或全部移动到迪卡尔坐标系中另外的位置）、缩放（用于输出大小不同的图形）、旋转；仿射变换（综合考虑图形的平移、旋转和缩放的变换）。

Including: basic coordinate changing: MOVE (move the entire or a part of figure to other location of coordinate); ZOOM (used for export map with different size); CIRCUMROTATION;仿射变换 integration move, zoom and circumrotation

包括：基本坐标变换：平移（将图形的一部分或全部移动到迪卡尔坐标系中另外的位置）、缩放（用于输出大小不同的图形）、旋转；仿射变换（综合考虑图形的平移、旋转和缩放的变换）。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失