Pseudo-differential Operators with Semi-Quasielliptic Symbols Over p-adic Fields

In this article, we study pseudo-differential equations involving semi-quasielliptic symbols over p-adics. We determine the function spaces where such equations have solutions. We introduce the space of infinitely pseudo-differentiable functions with respect to a semi-quasielliptic operator. By using these spaces we show the existence of a regularization effect for certain parabolic equations over p-adics.Comment: Accepted in Journal of Mathemaatical Analysis and its Application

Quasi-isotropic spacecraft antenna system Final report

Spacecraft quasi-isotropic antenna system for space telemetr

Molecular dynamics simulations of complex shaped particles using Minkowski operators

The Minkowski operators (addition and substraction of sets in vectorial spaces) has been extensively used for Computer Graphics and Image Processing to represent complex shapes. Here we propose to apply those mathematical concepts to extend the Molecular Dynamics (MD) Methods for simulations with complex-shaped particles. A new concept of Voronoi-Minkowski diagrams is introduced to generate random packings of complex-shaped particles with tunable particle roundness. By extending the classical concept of Verlet list we achieve numerical efficiencies that do not grow quadratically with the body number of sides. Simulations of dissipative granular materials under shear demonstrate that the method complies with the first law of thermodynamics for energy balance.Comment: Submitted to Phys. Rev.

The Majorization Arrow in Quantum Algorithm Design

We apply majorization theory to study the quantum algorithms known so far and find that there is a majorization principle underlying the way they operate. Grover's algorithm is a neat instance of this principle where majorization works step by step until the optimal target state is found. Extensions of this situation are also found in algorithms based in quantum adiabatic evolution and the family of quantum phase-estimation algorithms, including Shor's algorithm. We state that in quantum algorithms the time arrow is a majorization arrow.Comment: REVTEX4.b4 file, 4 color figures (typos corrected.