Two inverse problems induced by multifractal phenomena

Within the frame of phenomena revealing multifractality, two inverse problems were formulated and their solution is outlined, namely, (i) to what extent the indices characterizing scaling properties of dynamical fluctuations (specified by factorial moments) are determined by means of the power law indices γ(q) which characterize the scaling properties of the associated frequency moments, the latter moments representing asymptotics (for sufficiently large multiplicities) of the former, and (ii) to what extent the scaling indices γ(q) are determined by their asymptotic properties (at large absolute values of the order q ascribed to the associated frequency moments and taken at a finite and fixed energy). (author)