The prospects of a direct extraction of the proton’s gluon density in next-to-leading order via jet rates in deeply inelastic scattering are studied. The employed method is based on the Mellin transform, and can be applied, in principle, to all infra-red-safe observables of hadronic final states. We investigate the dependence of the error band on the extracted gluon distribution on the statisti...

We define generalized Mellin transforms of mixed cusp forms, show its convergence, and prove that the function obtained by such a Mellin transform of a mixed cusp form satisfies a certain functional equation. We also prove that a mixed cusp form can be identified with a holomorphic form of the highest degree on an elliptic variety.

We propose new sets of Fourier-Mellin descriptors for color images. They are constructed using the Clifford Fourier Transform of Batard et al. (2010) and are an extension of the classical Fourier-Mellin descriptors for grayscale images. These are invariant under direct similarity transformations (translations, rotations, scale) and marginal treatment of colors images is avoided. An implementati...

This paper proposes an automatic hand detection system that combines the Fourier-Mellin Transform along with other computer vision techniques to achieve hand detection in cluttered scene color images. The proposed system uses the Fourier-Mellin Transform as an invariant feature extractor to perform RST invariant hand detection. In a first stage of the system a simple non-adaptive skin color-bas...

We analyse a stack protocol of the Capetanakis-Tsybakov-Mikhailov type for resolving collisions in a random multiple-access channel. We obtain a functional equation for the generating function of the expected collision resolution interval (CRI) durations, which is non-local with a noncommutative iteration semigroup. Using Mellin transform techniques and geometric properties of the iteration sem...

We present explicit expressions for the Mellin transforms of Laguerre and Hermite functions in terms of a variety of special functions. We show that many of the properties of the resulting functions, including functional equations and reciprocity laws, are direct consequences of transformation formulae of hypergeometric functions. Interest in these results is reinforced by the fact that polynom...

For any α-stable Lévy process with jumps on both sides, where α ∈ (1, 2), we find the Mellin transform of the first hitting time of the origin and give an expression for its density. This complements existing work in the symmetric case and the spectrally one-sided case; cf. [38, 19] and [33, 36], respectively. We appeal to the Lamperti– Kiu representation of Chaumont et al. [16] for real-valued...