以下为句子列表：
英文: A unit-image and unit-features are first proposed, and multi-description of image is established at various layers from various angles, based on the multi-description, the similarity between images is measured by Euclidean distance.
中文: 摘要提出了单元图像和单元特征的概念，并在不同层次上从不同角度对图像进行多重描述，根据这些描述用欧氏距离来度量图像间的相似性。
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英文: Abstract: In this paper,empirical Euclidean likelihood ratio statistics are constructed for parametric components in a partly linear model,and its theory asymptotic confidence regions are constructed for parametric components in a partly linear model.
中文: 文摘:构造了部分线性模型参数的经验欧氏似然比统计量，并讨论了它的极限分布，由此可构造部分线性模型参数的渐近置信域.
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英文: During the recognition phase, Euclidean Distance representing VQ distortion in this project is calculated.
中文: 在认识阶段期间，通过对欧几里德距离代表VQ的计算来减少失真。
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英文: Economics is not a straightforward discipline like Newtonian mechanics or Euclidean geometry.
中文: 经济学不像牛顿力学或者欧几里德几何，它不是门直观的学科。
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英文: Given the name “fractals” by their discoverer, Benoit Mandelbrot, the new forms looked nothing like traditional Euclidean shapes.
中文: 这种图像与传统欧氏空间中的形体有天壤之别，它们的发现者曼德布洛称之为「碎形」。
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