Boundary stabilization and control of wave equations by means of a general multiplier method

We describe a general multiplier method to obtain boundary stabilization of the wave equation by means of a (linear or quasi-linear) Neumann feedback. This also enables us to get Dirichlet boundary control of the wave equation. This method leads to new geometrical cases concerning the "active" part of the boundary where the feedback (or control) is applied. Due to mixed boundary conditions, the Neumann feedback case generate singularities. Under a simple geometrical condition concerning the orientation of the boundary, we obtain a stabilization result in linear or quasi-linear cases

Liapunov Multipliers and Decay of Correlations in Dynamical Systems

The essential decorrelation rate of a hyperbolic dynamical system is the decay rate of time-correlations one expects to see stably for typical observables once resonances are projected out. We define and illustrate these notions and study the conjecture that for observables in $C^1$, the essential decorrelation rate is never faster than what is dictated by the {\em smallest} unstable Liapunov multiplier

Scale Invariant Cosmology

An attempt is made here to extend to the microscopic domain the scale invariant character of gravitation - which amounts to consider expansion as applying to any physical scale. Surprisingly, this hypothesis does not prevent the redshift from being obtained. It leads to strong restrictions concerning the choice between the presently available cosmological models and to new considerations about the notion of time. Moreover, there is no horizon problem and resorting to inflation is not necessary.Comment: TeX, 20 page

Extensive Properties of the Complex Ginzburg-Landau Equation

We study the set of solutions of the complex Ginzburg-Landau equation in $\real^d, d<3$. We consider the global attracting set (i.e., the forward map of the set of bounded initial data), and restrict it to a cube $Q_L$ of side $L$. We cover this set by a (minimal) number $N_{Q_L}(\epsilon)$ of balls of radius $\epsilon$ in \Linfty(Q_L). We show that the Kolmogorov $\epsilon$-entropy per unit length, $H_\epsilon =\lim_{L\to\infty} L^{-d} \log N_{Q_L}(\epsilon)$ exists. In particular, we bound $H_\epsilon$ by \OO(\log(1/\epsilon), which shows that the attracting set is smaller than the set of bounded analytic functions in a strip. We finally give a positive lower bound: H_\epsilon>\OO(\log(1/\epsilon))Comment: 24 page

Eligible assets, investment strategies and investor protection in light of modern portfolio theory: Towards a risk-based approach for UCITS. ECMI Policy Briefs No. 2, 18 September 2006

As the European Commission is currently in the process of preparing its White Paper on the enhancement of the EU framework for investment funds (scheduled for November 2006), now is a good time to reflect on whether the UCITS framework needs a radical overhaul if the regulatory landscape is going to adapt itself to the reality of market evolutions. European Capital Markets Institute (ECMI) Head of Research Jean-Pierre Casey contributes to this important debate with the second ECMI Policy Brief, in which he argues that UCITS ought to move to a risk-based approach as opposed to a reliance on the product approach. Casey concludes that both the product approach, which necessitates defining eligible assets – a laborious exercise – and the investment restrictions which form the other cornerstone of investor protection in UCITS, are outdated and out of sync with the lessons of modern portfolio theory. ECMI is an independent research body specialising in research on capital markets. It is managed by CEPS staff