Elliptic problems appear naturally in physics mainly in two situations: as equations which describe equilibrium (for example, stationary solutions in General Relativity) and as constraints for the evolutions equations (for example, constraint equations in Electromagnetism and General Relativity). In addition, in General Relativity they appear often as gauge conditions for the evolutions equatio...

Using a post-Newtonian diagnostic tool developed by Mora and Will, we examine numerically generated quasiequilibrium initial data sets that have been used in recently successful numerical evolutions of binary black holes through plunge, merger and ringdown. We show that a small but significant orbital eccentricity is required to match post-Newtonian and quasiequilibrium calculations. If this pr...

Adiabatic evolutions with a gap condition have, under a range of circumstances, exponentially small tails that describe the leaking out of the spectral subspace. Adiabatic evolutions without a gap condition do not seem to have this feature in general. This is a known fact for eigenvalue crossing. We show that this is also the case for eigenvalues at the threshold of the continuous spectrum by c...

We construct a scalar field based cosmological model, possessing a cosmological singularity characterized by a finite value of the cosmological radius and an infinite scalar curvature. Using the methods of the qualitative theory of differential equations, we give a complete description of the cosmological evolutions in the model under consideration. There are four classes of evolutions, two of ...

Adiabatic evolutions with a gap condition have, under a range of circumstances, exponentially small tails that describe the leaking out of the spectral subspace. Adiabatic evolutions without a gap condition do not seem to have this feature in general. This is a known fact for eigenvalue crossing. We show that this is also the case for eigenvalues at the threshold of the continuous spectrum by c...

The course will give a brief overview of the variational theory for gradient flows and rate-independent evolutions, trying to focus on the most important aspects: variational approximations, convergence results, energy-dissipation inequalities and metric characterization for gradient flows; energetic descriptions, BV solutions and optimal jump transitions, viscous approximations in the case of ...

The widespread deployment of communication networks has facilitated the sharing and exchange of spatial data between producers and users spread out over different locations. These users are not necessarily located at the same sites neither belong to the same organizations, but must cooperate. Spatial data is used to help user making decision in this context. Data is updated in parallel, dependi...

In software product line (SPL) development, evolutions occur in core assets and application products. How to ensure their alignment in evolution is a big challenge. Products in an SPL share a reference architecture, which centers in SPL development and evolution, so architectural evolution management is a natural and essential choice for SPL. In this paper, we propose an architecture-based evol...

Tandem duplication is an evolutionary process whereby a segment of DNA is replicated and proximally inserted. The different configurations that can arise from this process give rise to some interesting combinatorial questions. Firstly, we introduce an algebraic formalism to represent this process as a word producing automaton. The number of words arising from n tandem duplications can then be r...

Nowadays, the industrial and technological context is characterised by the uncertainty and the complexity of its evolutions. In this boarder, companies, particularly in the manufacturing and product design fields, need flexible and adaptable Information Systems (IS) to support their business strategies as well as to facilitate their adaptation to the evolutions of the external environment. In t...