On the controllability of the 2-D Vlasov-Stokes system

In this paper we prove an exact controllability result for the Vlasov-Stokes system in the two-dimensional torus with small data by means of an internal control. We show that one can steer, in arbitrarily small time, any initial datum of class C 1 satisfying a smallness condition in certain weighted spaces to any final state satisfying the same conditions. The proof of the main result is achieved thanks to the return method and a Leray-Schauder fixed-point argument

Fractional ideals and integration with respect to the generalised Euler characteristic

Let $b$ be a fractional ideal of a one-dimensional Cohen-Macaulay local ring $O$ containing a perfect field $k$. This paper is devoted to the study some $O$-modules associated with $b$. In addition, different motivic Poincar\'e series are introduced by considering ideal filtrations associated with $b$; the corresponding functional equations of these Poincar\'e series are also described

The universal zeta function for curve singularities and its relation with global zeta functions

The purpose of this note is to give a brief overview on zeta functions of curve singularities and to provide some evidences on how these and global zeta functions associated to singular algebraic curves over perfect fields relate to each other.Comment: Survey on the "universal zeta function" defined for curve singularities by W. Z\'u\~niga and the author in their paper "Motivic zeta functions for curve singularities" [Nagoya Math. J. 198 (2010), 47-75]; a poster of it was presented in the "Workshop on Positivity and Valuations" held at the Centre de Recerca Matem\`atica, Barcelona, in 2016 February 22nd-26t

Melting of Lennard-Jones rare gas clusters doped with a single impurity atom

Single impurity effect on the melting process of magic number Lennard-Jones, rare gas, clusters of up to 309 atoms is studied on the basis of Parallel Tempering Monte Carlo simulations in the canonical ensemble. A decrease on the melting temperature range is prevalent, although such effect is dependent on the size of the impurity atom relative to the cluster size. Additionally, the difference between the atomic sizes of the impurity and the main component of the cluster should be considered. We demonstrate that solid-solid transitions due to migrations of the impurity become apparent and are clearly differentiated from the melting up to cluster sizes of 147 atoms

Towards Understanding Reasoning Complexity in Practice

Although the computational complexity of the logic underlying the standard OWL 2 for the Web Ontology Language (OWL) appears discouraging for real applications, several contributions have shown that reasoning with OWL ontologies is feasible in practice. It turns out that reasoning in practice is often far less complex than is suggested by the established theoretical complexity bound, which reflects the worstcase scenario. State-of-the reasoners like FACT++, HERMIT, PELLET and RACER have demonstrated that, even with fairly expressive fragments of OWL 2, acceptable performances can be achieved. However, it is still not well understood why reasoning is feasible in practice and it is rather unclear how to study this problem. In this paper, we suggest first steps that in our opinion could lead to a better understanding of practical complexity. We also provide and discuss some initial empirical results with HERMIT on prominent ontologie

Lattice paths with given number of turns and semimodules over numerical semigroups

Let \Gamma= be a numerical semigroup. In this article we consider several relations between the so-called \Gamma-semimodules and lattice paths from (0,\alpha) to (\beta,0): we investigate isomorphism classes of \Gamma-semimodules as well as certain subsets of the set of gaps of \Gamma, and finally syzygies of \Gamma-semimodules. In particular we compute the number of \Gamma-semimodules which are isomorphic with their k-th syzygy for some k.Comment: 15 pages. Extended version of our previous submission "Lattice paths with given number of turns and numerical semigroups