Normal forms for rational difference equations with applications to the global periodicity problem

We propose a classification and derive the associated normal forms for rational difference equations with complex coefficients. As an application, we study the global periodicity problem for second order rational difference equations with complex coefficients. We find new necessary conditions as well as some new examples of globally periodic equations.

Polynomial and linearized normal forms for almost periodic differential systems

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CM points and weight 3=2 modular forms

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Multimarket contact in pharmaceutical markets

The purpose of this paper is to analyze the effect of multimarket contact on the behavior of pharmaceutical firms controlling for different levels of regulatory constraints using IMS MIDAS database. Theoretically, firms that meet in several markets are expected to be capable of sustaining implicitly more profitable out- comes, even if perfect monitoring is not possible. Firms may find it profitable to redistribute their market power among markets where they are operating. We present evidence for nine OECD countries with different degrees of regulation and show that regulation affects the importance of economic forces on firms' price setting behavior. Furthermore, our results confirms the presence of the predictions of the multimarket theory for more market friendly countries (U.S. and Canada) and less regulated ones (U.K., Germany, Netherlands), in contrast, for highly regulated countries (Japan, France, Italy and Spain) the results are less clear with some countries being

Complex contact manifolds and S1 actions

We prove rigidity and vanishing theorems for several holomorphic Euler characteristics on complex contact manifolds admitting holomorphic circle actions preserving the contact structure. Such vanishings are reminiscent of those of LeBrun and Salamon on Fano contact manifolds but under a symmetry assumption instead of a curvature condition.

Adobe Forms

La tramitació de les Ajudes i Subvencions es considera un dels procediments claus sobre els quals s'ha d'implementar iniciatives d'Administració Electrònica i d'optimització de la gestió. L'objectiu d'aquest projecte és desenvolupar un pilot amb la tecnologia Adobe Forms que implementi el servei de Formularis Electrònics.

Coefficients of Drinfeld modular forms and Hecke operators

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Explicit methods for Hilbert modular forms

We exhibit algorithms to compute systems of Hecke eigenvalues for spaces of Hilbert modular forms over a totally real field. We provide many explicit examples as well as applications to modularity and Galois representations.

Contact melting of a three-dimensional phase change material on a flat substrate

In this paper a model is developed to describe the three dimensional contact melting process of a cuboid on a heated surface. The mathematical description involves two heat equations (one in the solid and one in the melt), the Navier-Stokes equations for the flow in the melt, a Stefan condition at the phase change interface and a force balance between the weight of the solid and the countering pressure in the melt. In the solid an optimised heat balance integral method is used to approximate the temperature. In the liquid the small aspect ratio allows the Navier-Stokes and heat equations to be simplified considerably so that the liquid pressure may be determined using an igenfunction expansion and finally the problem is reduced to solving three first order ordinary differential equations. Results are presented showing the evolution of the melting process. Further reductions to the system are made to provide simple guidelines concerning the process. Comparison of the solutions with experimental data on the melting of n-octadecane shows excellent agreement.

Normal forms, stability and splitting of invariant manifolds I. Gevrey Hamiltonians

In this paper, we give a new construction of resonant normal forms with a small remainder for near-integrable Hamiltonians at a quasi-periodic frequency. The construction is based on the special case of a periodic frequency, a Diophantine result concerning the approximation of a vector by independent periodic vectors and a technique of composition of periodic averaging. It enables us to deal with non-analytic Hamiltonians, and in this first part we will focus on Gevrey Hamiltonians and derive normal forms with an exponentially small remainder. This extends a result which was known for analytic Hamiltonians, and only in the periodic case for Gevrey Hamiltonians. As applications, we obtain an exponentially large upper bound on the stability time for the evolution of the action variables and an exponentially small upper bound on the splitting of invariant manifolds for hyperbolic tori, generalizing corresponding results for analytic Hamiltonians.

Normal forms, stability and splitting of invariant manifolds II. Finitely differentiable Hamiltonians

This paper is a sequel to ``Normal forms, stability and splitting of invariant manifolds I. Gevrey Hamiltonians", in which we gave a new construction of resonant normal forms with an exponentially small remainder for near-integrable Gevrey Hamiltonians at a quasi-periodic frequency, using a method of periodic approximations. In this second part we focus on finitely differentiable Hamiltonians, and we derive normal forms with a polynomially small remainder. As applications, we obtain a polynomially large upper bound on the stability time for the evolution of the action variables and a polynomially small upper bound on the splitting of invariant manifolds for hyperbolic tori.

Implementació d'un contact center per empreses basat en software lliure

El proyecto consiste en la creación de un CRM de contact center con canal de telefonía y correo electrónico. Se ha llevado a cabo utilizando software libre. Se integra con centralita telefónica para permitir la realización de llamadas por Voip.