Bush型函数图像的K-维数
K-Dimension of the Graphs of a C lass ofBush Functions
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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 packing维数.Abstract: TheK-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 lowerboundaries for theK-dimension ofsuch graphswere 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 theb-adic expression of realnumbers.
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Key words:
- Bush type function /
- fractal function /
- K-dimension /
- fractal dimension
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