We introduce a Mellin transform of functions which live on all of R and discuss its applications to the limiting theory of Bellman-Harris processes, and specifically Luria-Delbrück processes. More precisely, we calculate the life-time distribution of particles in a Bellman-Harris process from their first-generation offspring and limiting distributions, and prove a formula for the Laplace transf...

This paper is concerned with the Simultaneous Localization And Mapping (SLAM) problem using data obtained from a microwave radar sensor. The radar scanner is based on Frequency Modulated Continuous Wave (FMCW) technology. In order to meet the needs of radar image analysis complexity, a trajectoryoriented EKF-SLAM technique using data from a 360◦ field of view radar sensor has been developed. Th...

This paper has four interrelated themes: (1) express Laplace and Mellin transforms of sums of positive random variables in terms of the Mellin transform of the summands; (2) show the equivalence of the two Barnes’ lemmas with known properties of gamma distributions; (3) establish properties of the sum of two reciprocal gamma variables, and related results; (4) study the G distributions (whose M...

We hear phonemes pronounced by men, women and children as approximately the same although the length of the vocal tract varies considerably from group to group. At the same time, we can identify the speaker group. This suggests that we extract and separate the size and shape information of sound sources. The impulse response of the vocal tract is compressed or expanded in time when the length o...

We study the distribution of Mahler’s measures of reciprocal polynomials with complex coefficients and bounded even degree. We discover that the distribution function associated to Mahler’s measure restricted to monic reciprocal polynomials is a reciprocal (or anti-reciprocal) Laurent polynomial on [1,∞) and identically zero on [0, 1). Moreover, the coefficients of this Laurent polynomial are r...

One-sided variations on path length in a trie (a sort of digital trees) are investigated: They include imbalance factors, climbing under different strategies, and key sampling. For the imbalance factor accurate asymptotics for the mean are derived for a randomly chosen key in the trie via poissonization and the Mellin transform, and the inverse of the two operations. It is also shown from an an...

We hear phonemes pronounced by men, women and children as approximately the same although the length of the vocal tract varies considerably from group to group. At the same time, we can identify the speaker group. This suggests that we extract and separate the size and shape information of sound sources. The impulse response of the vocal tract is compressed or expanded in time when the length o...

A bstract We present a method to calculate the x -space expressions of massless or massive operator matrix elements in QCD and QED containing local composite insertions, depending on discrete Mellin index N , directly, without computing Mellin-space explicit form analytically. Here belongs either even odd positive integers. The is based resummation operators into effective propagators relies an...