以下为句子列表：
英文: The fractal theory provides an important method in study of irregular objects of self-similarity and self-affinity.
中文: 摘要分形理论是分析和研究自然界中具有“自相似性”、“自仿射性”不规则形体的重要手段。
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英文: The research shows that the fractal theory can be used to describe quantificationally differentiate and anomalistic micro cracks of concrete that formed in injury evolution.
中文: 研究表明，用分形理论方法可以定量描述和区分混凝土在损伤演化期间形成的极其不规则的微裂纹。
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英文: The results show that the method of the mechanical fault diagnosis based on fractal theory is more sensitive to initial fault type of complicated mechanical system.
中文: 研究结果表明：基于分形的机械故障诊断方法对复杂机械系统的早期故障更爲敏感。
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英文: This paper connects the fractal theory with the mechanical fault diagnosis, discusses the basic concept of the fractal dimension, and makes a comprehensive analysis on diagnostic procedure based on the fractal theory, including the technique of the phase
中文: 摘要将分形的有关理论与复杂机械故障诊断联系起来，论述了分形维数的基本概念，研究了几种分形诊断方法：重构相空间求取关联维数，小波分形技术，分形模糊神经网络的诊断技术，并给出了相关算法。
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英文: Analyses of Heat Effect of Laser Acting on Enzyme by Fractal Theory and Soliton Theory
中文: 激光对酶热作用效应的分形及孤子理论分析
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