This paper provides a computational method to model a three-dimensional static electromagnetic field within a finite source free volume starting from discrete field information on its surface. The method uses the Helmholtz vector decomposition theorem and the differential algebraic framework of COSY INFINITY to determine a solution to the Laplace equation. The solution is locally expressed as a...

Relativistic and non-relativistic ratios of Laplace transform QCD moment sum rules for charmonium are used in order to determine the value of the on-shell charmquark mass. The validity of the non-relativistic version of QCD sum rules in this particular application is discussed. After using current values of the perturbative and non-perturbative QCD parameters, as well as experimental data on th...

We introduce stochastic Discrete Laplacian Growth and consider its deterministic continuous version. These are reminiscent respectively to well-known Diffusion Limited Aggregation and Hele-Shaw free boundary problem for the interface propagation. We study correlation between stability of deterministic free-boundary problem and macroscopic fractal growth in the corresponding discrete problem. It...

We relate the fractional powers of the discrete Laplacian with a standard time-fractional derivative in the sense of Liouville by encoding the iterative nature of the discrete operator through a time-fractional memory term.

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.

This paper deals with the investigation of a closed form solution of a generalized fractional reaction-diffusion equation. The solution of the proposed problem is developed in a compact form in terms of the H-function by the application of direct and inverse Laplace and Fourier transforms. Fractional order moments and the asymptotic expansion of the solution are also obtained.

The stability of n-dimensional linear fractional differential systems with commensurate order 1 < α < 2 and the corresponding perturbed systems is investigated. By using the Laplace transform, the asymptotic expansion of the Mittag-Leffler function, and the Gronwall inequality, some conditions on stability and asymptotic stability are given.

Ramanujan graphs have extremal spectral properties, which imply a remarkable combinatorial behavior. In this paper we compute the high-dimensional Laplace spectrum of Ramanujan triangle complexes, and show that it implies a combinatorial expansion property, and a pseudo-randomness result. For this purpose we prove a Cheeger-type inequality and a mixing lemma of independent interest.

This paper deals with the investigation of a closed form solution of a generalized fractional reaction-diffusion equation. The solution of the proposed problem is developed in a compact form in terms of the H-function by the application of direct and inverse Laplace and Fourier transforms. Fractional order moments and the asymptotic expansion of the solution are also obtained.