In a previous paper MR] the authors introduced the inverse measure y of a probability measure on 0; 1]. It was argued that the respective multifractal spectra are linked by thèinversion formula' f y () = f(1==). Here, the statements of MR] are put in more mathematical terms and proofs are given for the inversion formula in the case of continuous measures. Thereby, f may stand for the Hausdorr s...

Non-adiabatic transitions are studied in a spin-boson model with multiple scattering points. In order to generalize the Landau–Zener formula, which describes the case of a single scattering point, we define an “effective gap” for a set of scattering points. The generalized formula agrees very well with numerical results of the nonadiabatic dynamics, which we obtained by a direct numerical metho...

A formula for evaluation of the distribution of a linear combination of independent inverted gamma random variables by one-dimensional numerical integration is presented. The formula is direct application of the inversion formula given by Gil–Pelaez [4]. This method is applied to computation of the generalized p-values used for exact significance testing and interval estimation of the parameter...

In an earlier paper MR the authors introduced the inverse measure y dt of a given measure dt on and presented the inversion formula f f which was argued to link the respective multifractal spectra of and y A second paper RM established the formula under the assumption that and y are continuous measures Here we investigate the general case which reveals telling details of interest to the full un...