| 分形中的局部维数及其动力学方程 |
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| 引用本文： | 徐宝民,张丽清,刘永清.分形中的局部维数及其动力学方程[J].华南理工大学学报(自然科学版),1998(1). |
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| 作者姓名： | 徐宝民 张丽清 刘永清 |
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| 作者单位： | 华南理工大学自动化系 |
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| 摘 要： | 提出了局部维数的概念，并在对Ｈａｕｓｄｏｒｆ维数推广的基础上推导出局部信息维数及局部填充维数与维数ｎ及概率密度的关系，进而推导出了经典分形场的动力学方程及量子体系分形场方程，从而有效地诠释了一些自然现象及生物现象中存在自相似结构的动力学机制。
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| 关 键 词： | 分形 维数 局部维数 避雷针效应 |
LOCAL DIMENSION AND ITS DYNAMIC EQUATION IN FRACTAL |
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| Xu Baomin,Zhang Liqing,Liu Yongqing.LOCAL DIMENSION AND ITS DYNAMIC EQUATION IN FRACTAL[J].Journal of South China University of Technology(Natural Science Edition),1998(1). |
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| Authors: | Xu Baomin Zhang Liqing Liu Yongqing |
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| Abstract: | This paper puts forward the concept of local dimension, and, based on the extension of Hausdorff dimension, derives the relationship between local information dimension, local stuff dimension and dimension n , possibility density. Further, the paper derives the dynamic equations in the classical fractal field and in the quantum fractal system, thus annotating structure_self_resembling dynamic mechanisms of the natural and biological phenomena efficiently. |
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| Keywords: | fractal dimension local dimension lightning rod effect |
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