Abstract
This short article exhibits that there exists critical point of the power for the generalized function t-a for a>0. The present results show that it is long-range dependent if 0<a<1 and short-range dependent when a>1. My motivation of studying that dependence issue comes from the power-law type functions in fractal time series. The present results may yet be useful to investigate fractal behavior of fractal time series from a new point of view.
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