| Bush型函数图像的K-维数 |
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| 引用本文： | 王宏勇,许绍元.Bush型函数图像的K-维数[J].西南交通大学学报,2005,40(6):825-828. |
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| 作者姓名： | 王宏勇 许绍元 |
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| 作者单位： | 1. 南京财经大学应用数学系,江苏,南京,210046
2. 淮北煤炭师范学院数学系,安徽,淮北,235000 |
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| 基金项目： | 国家自然科学基金资助项目(10171080)，安徽省教育厅重点科研基金资助项目(2003kj047zd) |
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| 摘 要： | 研究一类基于实数的Cantor级数表示的分形函数———Bush型函数图像的K-维数.得到了这类函数图像的K-维数的上、下界估计式.指出在基于实数的b进制表示的情形下,这类函数图像的K-维数等于其box维数与pack ing维数.
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| 关 键 词： | Bush型函数 分形函数 K-维数 分形维数 |
| 文章编号： | 0258-2724（2005）06-0825-04 |
| 收稿时间： | 2005-03-28 |
| 修稿时间： | 2005-03-28 |
K-Dimension of the Graphs of a Class of Bush Functions |
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| WANG Hong-yong,XU Shao-yuan.K-Dimension of the Graphs of a Class of Bush Functions[J].Journal of Southwest Jiaotong University,2005,40(6):825-828. |
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| Authors: | WANG Hong-yong XU Shao-yuan |
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| Institution: | 1. Dept. of Appl. Mathematics, Nanjing University of Finance and Economics, Nanjing 210046, China; 2. Dept. of Mathematics, Huaibei Coal Industry Teachers College, Huaibei 235000, China |
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| Abstract: | The K-dimension of the graphs of a class of Bush functions was studied.These fractal functions are defined by using the expression of the Cantor series of real numbers.The expressions of the upper and lower boundaries for the Kdimension of such graphs were obtained.It is shown that the K-dimension of the graphs of such functions is equal to their box dimension and packing dimension when the functions are defined by the b-adic expression of real numbers. |
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| Keywords: | Bush type function fractal function K-dimension fractal dimension |
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