We study a new Radon-like transform that averages projected pforms in Rn over affine (n − k)-spaces. We then prove an explicit inversion formula for our transform on the space of rapidly-decaying smooth p-forms. Our transform differs from the one in the work by Gelfand, Graev and Shapiro (1969). Moreover, if it can be extended to a somewhat larger space of p-forms, our inversion formula will al...

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...

Moebius syndrome, a rare congenital disorder of varying severity, involves multiple cranial nerves and is characterised predominantly by bilateral or unilateral paralysis of the facial and abducens nerves. Facial paralysis causes inability to smile and bilabial incompetence with speech difficulties, oral incompetence, problems with eating and drinking, including pocketing of food in the cheek a...

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...