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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。

Compared with traditional formula of general affine Hausdorff box distance, search range of distance is reduced.

与传统的基于广义仿射变换的Hausdorff盒距离变换公式相比，缩小了搜索距离空间。

The perspective transform can be replaced approximately with affine transform when the distance between the camera and the object is larger than the dimension of the object.

当摄像机与景物之间的距离远远大于景物的尺寸时，射影变换可用仿射变换来近似代替。

After extracting target image gradient,this mehtod can put image gradient into CPM,and then figure out the affine transform parameter of the precongnition model and target image.

最后采用模板图像轮廓线在电场化后的梯度图像中的最大能量熵值，利用遗传算法确定先验模板图像与目标图像之间的仿射变换参数，达到轮廓匹配的目的。

In order to reduce conservativity, use Lyapunov function affine to the uncertain parameter.

为减少保守性，采用了与参数相关的Lyapunov仿射函数。

In this paper, the linear equivalence of output coordinate functions of affine inverse function s and the S-box of Camellia are discussed.

有限域上的逆函数左右复合一个仿射置换而成的仿射逆函数具有很好的密码学性质。

A method which combined Wavelet Affine Invariant Function with Convex Hull for object recognition is proposed.

提出一种将小波仿射不变函数与凸壳相结合进行目标识别的方法。

In the third part, we discuss a simple class of Sturm-Liouville problems with Dirichlet boundary condition in the first boundary condition and an affine function in the second one.

第三部分我们讨论了一类参数边界条件的Sturm-Liouville问题，其第一边界条件为Dirichlet条件，第二个边界条件为特征值参数的线性函数。

The stress field is achieved by affine transformation through the complex function theory.The stress is analyzed in the composite material plate with circular hole by the model above.

由于复合材料具有十分鲜明的各向异性特性，在应用上提出了许多亟待研究解决的新课题，例如结构的开口问题。

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