In this paper we present a new highly efficient calculation method for the far field amplitude pattern that arises from scattering problems governed by the d-dimensional Helmholtz equation and, by extension, Schrödinger’s equation. The new technique is based upon a reformulation of the classical real-valued Green’s function integral for the far field amplitude to an equivalent integral over a c...

Contour Crafting is an emerging technology that uses robotics to construct free form building structures by repeatedly laying down layers of material such as concrete. The Contour Crafting technology scales up automated additive fabrication from building small industrial parts to constructing buildings. Tool path planning and optimization for Contour Crafting benefit the technology by increasin...

Work supported in part by the Long Term Research Project Alcom-IT (# 20244) of the European Union. This paper develops an approach to the evaluation of Euler sums that involve harmonic numbers, either linearly or nonlinearly. We give explicit formulæ for several classes of Euler sums in terms of Riemann zeta values. The approach is based on simple contour integral representations and residue co...

in this article using the inverse laplace transform, we show analytical solutions for the generalized mass transfers with (and without) a chemical reaction. these transfers have been expressed as the couette flow with the fractional derivative of the caputo sense. also, using the hankel contour for the bromwich's integral, the solutions are given in terms of the generalized airy functions.

A recently discovered transform approach allows a large class of initial and initialboundary value problems to be solved in terms of contour integrals. We introduce here a spectrally accurate numerical discretization of this approach for the case of Laplace’s equation on a polygonal domain, and compare it against an also spectrally accurate implementation of the traditional boundary integral fo...