Bush型函数图像的K-维数  

K-Dimension of the Graphs of a Class of Bush Functions

作　　者：王宏勇[1] 许绍元[2] 

机构地区：[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

出　　处：《西南交通大学学报》2005年第6期825-828,共4页Journal of Southwest Jiaotong University

基　　金：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)

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.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 K-dimension 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.

关 键 词：Bush型函数 分形函数 K-维数 分形维散 

分 类 号：O174.4[理学—数学]