the characteristic scale function of the scale function has the following characteristics: scale invariance, and the scale function remains unchanged on different scales, that is, for any positive number $
scale function is a mathematical tool to describe complex systems. it reveals the regularity of different scales in the system. understanding scale functions is crucial to understanding various natural and social phenomena, such as turbulence, earthquakes and financial markets. the definition of scale refers to the range or degree of measurement or observation. in scale functions, scales are usually expressed as $.
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