Abstract
A new kind of multifractal is constructed by fractional Fouriertransform of Cantor sets. The wavelet transform modulus maxima methodis applied to calculate the singularity spectrum under an operationaldefinition of multifractal. In particular, an analysing procedure todetermine the spectrum is suggested for practice. Nonanalyticities ofsingularity spectra or phase transitions are discovered, which areinterpreted as some indications on the range of Boltzmann temperatureq, on which the scaling relation of partition function holds.
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