We use Mellin transforms to compute a full asymptotic expansion for the tail of the Laplace transform of the squared L2-norm of any multiply-integrated Brownian sheet. Through reversion we obtain corresponding strong small-deviation estimates. AMS 2000 subject classifications. Primary 60G15, 41A60; secondary 60E10, 44A15, 41A27.

We resolve a conjecture proposed by D.E. Knuth concerning a recurrence arising in the satisfiability problem. Knuth’s recurrence resembles recurrences arising in the analysis of tries, in particular PATRICIA tries, and asymmetric leader election. We solve Knuth’s recurrence exactly and asymptotically, using analytic techniques such as the Mellin transform and analytic depoissonization.

The compound models of clutter statistics are found suitable to describe the nonstationary nature of radar backscattering from high-resolution observations. In this letter, we show that the properties of Mellin transform can be utilized to generate higher order moments of simple and compound models of clutter statistics in a compact manner.

We prove that a certain vector valued double Dirichlet series satisfying appropriate functional equations is a Mellin transform of a vector valued metaplectic Eisenstein series. We establish an analogous result for scalar double Dirichlet series of the type studied by Siegel.

The precise analysis of the variance of the profile of a suffix tree has been a longstanding open problem. We analyze three regimes of the asymptotic growth of the variance of the profile of a suffix tree built from a randomly generated binary string, in the nonuniform case. We utilize combinatorics on words, singularity analysis, and the Mellin transform.

This work concerns an extension of usual radar imaging in which the pictures of the target do not simply exhibit the position of elementary reflectors but also give the behavior of these reflectors when the frequency and the direction of illumination vary. Essentially, the technique consists in describing the target by a generalized image which can be computed from the knowledge of the backscat...

The most existing digital watermarking methods were robust to general attacks such as additive noise, image filtering, JPEG compression and so on, but resisting to geometric attacks is still a difficult challenge. This paper proposed a watermarking algorithm resisting to geometrical attacks. The Radon transform was employed to project two dimension image onto projection space. Then the rotation...

Abstract We offer a solution to functional equation using properties of the Mellin transform. A new criteria for Riemann Hypothesis is offered as an application our main result, through relationship with xi function.

We revisit the image charge method for the Green’s function problem of the PoissonBoltzmann equation for a dielectric sphere immersed in ionic solutions. Using finite Mellin transformation, we represent the reaction potential due to a source charge inside the sphere in terms of one dimensional distribution of image charges. The image charges are generically composed of a point image at the Kelv...