We consider a leader election algorithm in which a set ofdistributed 'ob· jects (people, computers, elc.) try to identify one object as their leader. The election process is randomized, that is, at every stage of the algorithm. those objects that survived so far flip abiased coin, and those who received, say a tail. survive for the next round. The process .continues until only one objects remai...

A specific form of the Mellin transform, referred to as the “scale transform,” is known to be a natural complement to the Fourier transform for wideband analytic signals. In this paper, limitations for the simultaneous localization of scale transform pairs are investigated. A number of inequalities are established and discussed, based on various measures of spread (Heisenberg-type inequalities ...

This paper addresses the use of spatiotemporal transform methods applied to the analysis of dynamic image sequences and the characterization of image motion. Image motion including a divergent component (resulting from a looming camera component) is analyzed in the spatiotemporal Mellin Transform (MT) domain, resulting in the separation of the spectrum into two parts: a structural term correspo...

The navigational tasks of computing time-to-impact and controlling movements within specific range are addressed here. By using specially designed lenses various components of these procedures, consisting of mathematical transformations, can be provided at image acquisition time, and therefore, speed up execution time. This s t u 4 discusses the optical implementation of different correlators b...

We recall the notion of cuspform for Γ = SL2(Z) acting on the upper half-plane, and prove that the orthogonal complement in L(Γ\H) to cuspforms is spanned by pseudo-Eisenstein series, which in turn are expressible as wave packets of Eisenstein series Es. Further we have a Plancherel theorem for this space. The non-trivial harmonic analysis resides in the application of the Fourier transform on ...

We obtain representations for the Mellin transform of the product of generalized hypergeometric functions 0 F1[ ax]1 F2[ b2x2] for a;b > 0. The later transform is a generalization of the discontinuous integral of Weber and Schafheitlin; in addition to reducing to other known integrals (for example, integrals involving products of powers, Bessel and Lommel functions), it contains numerous integr...

We derive a compact expression for the Borel sum of a QCD amplitude in terms of the inverse Mellin transform of the corresponding Borel function. The result allows us to investigate the momentum-plane analyticity properties of the Borel-summed Green functions in perturbative QCD. An interesting connection between the asymptotic behaviour of the Borel transform and the Landau singularities in th...

In this note, we state a representation of the Mellin transform of the exponential functional of Lévy processes in terms of generalized Weierstrass products. As by-product, we obtain a multiplicative Wiener-Hopf factorization generalizing previous results obtained by the authors in [14] as well as smoothness properties of its distribution. Résumé. Fonctionnelle exponentielle des processus de Lé...