Locally conformal symplectic nilmanifolds with no locally conformal K\"ahler metrics

We obtain an example of a compact locally conformal symplectic nilmanifold which admits no locally conformal K\"ahler metrics. This gives a new positive answer to a question raised by L. Ornea and M. Verbitsky.Comment: 7 pages, no figures. Comments are welcome

Some linear Jacobi structures on vector bundles

We study Jacobi structures on the dual bundle $A^\ast$ to a vector bundle $A$ such that the Jacobi bracket of linear functions is again linear and the Jacobi bracket of a linear function and the constant function 1 is a basic function. We prove that a Lie algebroid structure on $A$ and a 1-cocycle $\phi \in \Gamma (A^\ast)$ induce a Jacobi structure on $A^\ast$ satisfying the above conditions. Moreover, we show that this correspondence is a bijection. Finally, we discuss some examples and applications.Comment: 6 pages, To appear in C. R. Acad. Sci. Paris, S\'erie

Poisson-Lie groups, bi-Hamiltonian systems and integrable deformations

Given a Lie-Poisson completely integrable bi-Hamiltonian system on $\mathbb{R}^n$, we present a method which allows us to construct, under certain conditions, a completely integrable bi-Hamiltonian deformation of the initial Lie-Poisson system on a non-abelian Poisson-Lie group $G_\eta$ of dimension $n$, where $\eta \in \mathbb{R}$ is the deformation parameter. Moreover, we show that from the two multiplicative (Poisson-Lie) Hamiltonian structures on $G_\eta$ that underly the dynamics of the deformed system and by making use of the group law on $G_\eta$, one may obtain two completely integrable Hamiltonian systems on $G_\eta \times G_\eta$. By construction, both systems admit reduction, via the multiplication in $G_\eta$, to the deformed bi-Hamiltonian system in $G_\eta$. The previous approach is applied to two relevant Lie-Poisson completely integrable bi-Hamiltonian systems: the Lorenz and Euler top systems.Comment: 23 pages, 2 figures. Revised versio

Non-existence of an invariant measure for a homogeneous ellipsoid rolling on the plane

It is known that the reduced equations for an axially symmetric homogeneous ellipsoid that rolls without slipping on the plane possess a smooth invariant measure. We show that such an invariant measure does not exist in the case when all of the semi-axes of the ellipsoid have different length.Comment: v2: Minor changes after journal review. This text uses the theory developed in arXiv:1304.1788 for the specific example of a homogeneous ellipsoid rolling on the plan

Inequality of opportunity in Europe: Economic and policy facts

In this paper we consider the main factors that have influenced inequality of opportunity (IO) in Europe. Based on the EU-SILC database, we find that the various levels of development, education and social protection expenditure in 23 European countries significantly affect IO. Dropping out from school, reaching at least secondary levels of education, social spending to promote social integration and child care are the most important variables of those analyzed. The functioning of the labor market and the tax structure, on the other hand, do not have a significant bearing on IO. Lastly, we note that IO and total inequality exhibit differentiated explanatory patterns, which signifies that means of redistribution that serve to reduce overall inequality do not necessarily reduce IO.inequality of opportunity; growth; education; public expenditure; labor market.