Existence of Pseudo Almost Periodic Solutions to Some Classes of Partial Hyperbolic Evolution Equations

The paper examines the existence of pseudo almost periodic solutions to some classes of partial hyperbolic evolution equations. Namely, sufficient conditions for the existence and uniqueness of pseudo almost periodic solutions to those classes of hyperbolic evolution equations are given. Applications include the existence of pseudo almost periodic solutions to the transport and heat equations with delay.Comment: 12 page

Algebraic Sum of Unbounded Normal Operators and the Square Root Problem of Kato

We prove that the algebraic sum of unbounded normal operators satisfies the square root problem of Kato under appropriate hypotheses. As application, we consider perturbed Schrodinger operators.Comment: 9 page

Managing a peer-to-peer backup system: does imposed fairness socially outperform a revenue-driven monopoly ?

International audienceWe study a peer-to-peer backup system, where users offer some of their storage space to provide service for the others. The economic model for such a system is different from the ones applicable to peer-to-peer file sharing systems, since the storage capacity is a private good here. We study two mechanisms aimed at incentivizing users to offer some of their capacity: a price-based scheme (here a revenue-driven monopoly) and a more classical symmetric scheme (imposing users to contribute to the service at least as much as use it). We compare the outcomes of such mechanisms to the socially optimal situation that could be attained if users were not selfish, and show that depending on user heterogeneity, a revenue maximizing monopoly can be a worse or a better (in terms of social welfare) way to manage the system than a symmetric scheme