Fractional Fourier Transform of Cantor Sets

Chin. Phys. Lett.

2005, Vol. 22

Issue (9): 2316-2319 DOI:

Original Articles

Fractional Fourier Transform of Cantor Sets

LIAO Tian-He;GAO Qiong

Department of Physics, Information Engineering University, Zhengzhou 450001

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LIAO Tian-He, GAO Qiong 2005 Chin. Phys. Lett. 22 2316-2319

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Abstract A new kind of multifractal is constructed by fractional Fourier transform of Cantor sets. The wavelet transform modulus maxima method is applied to calculate the singularity spectrum under an operational definition of multifractal. In particular, an analysing procedure to determine the spectrum is suggested for practice. Nonanalyticities of singularity spectra or phase transitions are discovered, which are interpreted as some indications on the range of Boltzmann temperature q, on which the scaling relation of partition function holds.

Keywords: 47.53.+n 02.30.Nw

Published: 01 September 2005

PACS:	47.53.+n	(Fractals in fluid dynamics)
	02.30.Nw	(Fourier analysis)

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https://cpl.iphy.ac.cn/ OR https://cpl.iphy.ac.cn/Y2005/V22/I9/02316

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