Structure and magnetism of orthorhombic epitaxial FeMnAs

The molecular beam epitaxy growth of Fe on MnAs/GaAs(001) leads to the formation of an epitaxial FeMnAs phase at the Fe/MnAs interface. The investigation of the structure by high angle annular dark field imaging in a scanning transmission electron microscope reveals an unusual orthorhombic structure, with vacancy ordering. Ab initio calculations show an antiferromagnetic ground state for this orthorhombic FeMnAs.Fil: Demaille, Dominique. Laboratorio Internacional Franco-Argentino en Nanociencias; Francia. Universite Pierre et Marie Curie. Institut des Nanosciences de Paris; FranciaFil: Patriarche, Gilles. Centre National de la Recherche Scientifique; FranciaFil: Helman, Christian. Comisión Nacional de Energía Atómica; Argentina. Laboratorio Internacional Franco-Argentino en Nanociencias; FranciaFil: Eddrief, Mahmoud. Laboratorio Internacional Franco-Argentino en Nanociencias; Francia. Universite Pierre et Marie Curie. Institut des Nanosciences de Paris; FranciaFil: Etgens, Hugo. Laboratorio Internacional Franco-Argentino en Nanociencias; Francia. Universite Pierre et Marie Curie. Institut des Nanosciences de Paris; FranciaFil: Sacchi, Maurizio. Laboratorio Internacional Franco-Argentino en Nanociencias; Francia. Universite Pierre et Marie Curie. Institut des Nanosciences de Paris; Francia. L’Orme des merisiers Saint-Aubin. Synchrotron SOLEIL; FranciaFil: Llois, Ana Maria. Comisión Nacional de Energía Atómica; Argentina. Laboratorio Internacional Franco-Argentino en Nanociencias; Francia. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Marangolo, Massimiliano. Laboratorio Internacional Franco-Argentino en Nanociencias; Francia. Universite Pierre et Marie Curie. Institut des Nanosciences de Paris; Franci

Global existence results for nonlinear Schrodinger equations with quadratic potentials

We prove that no finite time blow up can occur for nonlinear Schroedinger equations with quadratic potentials, provided that the potential has a sufficiently strong repulsive component. This is not obvious in general, since the energy associated to the linear equation is not positive. The proof relies essentially on two arguments: global in time Strichartz estimates, and a refined analysis of the linear equation, which makes it possible to use continuity arguments and to control the nonlinear effects.Comment: Some typos fixed, Proposition 1.1 extended. Final version to appear in DCD

Infinitesimal Hecke Algebras II

For W a finite (2-)reflection group and B its (generalized) braid group, we determine the Zariski closure of the image of B inside the corresponding Iwahori-Hecke algebra. The Lie algebra of this closure is reductive and generated in the group algebra of W by the reflections of W. We determine its decomposition in simple factors. In case W is a Coxeter group, we prove that the representations involved are unitarizable when the parameters of the representations have modulus 1 and are close to 1. We consequently determine the topological closure in this case

Key Polynomials

The notion of key polynomials was first introduced in 1936 by S. Maclane in the case of discrete rank 1 valuations. . Let K -> L be a field extension and {\nu} a valuation of K. The original motivation for introducing key polynomials was the problem of describing all the extensions {\mu} of {\nu} to L. Take a valuation {\mu} of L extending the valuation {\nu}. In the case when {\nu} is discrete of rank 1 and L is a simple algebraic extension of K Maclane introduced the notions of key polynomials for {\mu} and augmented valuations and proved that {\mu} is obtained as a limit of a family of augmented valuations on the polynomial ring K[x]. In a series of papers, M. Vaqui\'e generalized MacLane's notion of key polynomials to the case of arbitrary valuations {\nu} (that is, valuations which are not necessarily discrete of rank 1). In the paper Valuations in algebraic field extensions, published in the Journal of Algebra in 2007, F.J. Herrera Govantes, M.A. Olalla Acosta and M. Spivakovsky develop their own notion of key polynomials for extensions (K, {\nu}) -> (L, {\mu}) of valued fields, where {\nu} is of archimedian rank 1 (not necessarily discrete) and give an explicit description of the limit key polynomials. Our purpose in this paper is to clarify the relationship between the two notions of key polynomials already developed by vaqui\'e and by F.J. Herrera Govantes, M.A. Olalla Acosta and M. Spivakovsky.Comment: arXiv admin note: text overlap with arXiv:math/0605193 by different author

Representations of stack triangulations in the plane

Stack triangulations appear as natural objects when defining an increasing family of triangulations by successive additions of vertices. We consider two different probability distributions for such objects. We represent, or "draw" these random stack triangulations in the plane $\R^2$ and study the asymptotic properties of these drawings, viewed as random compact metric spaces. We also look at the occupation measure of the vertices, and show that for these two distributions it converges to some random limit measure.Comment: 29 pages, 13 figure

Extension of charge-state-distribution calculations for ion-solid collisions towards low velocities and many-electron ions

Knowledge of the detailed evolution of the whole charge-state distribution of projectile ions colliding with targets is required in several fields of research such as material science and atomic and nuclear physics but also in accelerator physics, and in particular in regard to the several foreseen large-scale facilities. However, there is a lack of data for collisions in the nonperturbative energy domain and that involve many-electron projectiles. Starting from the etacha model we developed [Rozet, Nucl. Instrum. Methods Phys. Res., Sect. B 107, 67 (1996)10.1016/0168-583X(95)00800-4], we present an extension of its validity domain towards lower velocities and larger distortions. Moreover, the system of rate equations is able to take into account ions with up to 60 orbital states of electrons. The computed data from the different new versions of the etacha code are compared to some test collision systems. The improvements made are clearly illustrated by 28.9MeVu-1Pb56+ ions, and laser-generated carbon ion beams of 0.045 to 0.5MeVu-1, passing through carbon or aluminum targets, respectively. Hence, those new developments can efficiently sustain the experimental programs that are currently in progress on the "next-generation" accelerators or laser facilities.Fil: Lamour, E.. Centre National de la Recherche Scientifique; Francia. Universite de Paris; FranciaFil: Fainstein, Pablo Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; ArgentinaFil: Galassi, Mariel Elisa. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Instituto de Física de Rosario. Universidad Nacional de Rosario. Instituto de Física de Rosario; ArgentinaFil: Prigent, C.. Centre National de la Recherche Scientifique; Francia. Universite de Paris; FranciaFil: Ramirez, C. A.. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Instituto de Física de Rosario. Universidad Nacional de Rosario. Instituto de Física de Rosario; ArgentinaFil: Rivarola, Roberto Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Instituto de Física de Rosario. Universidad Nacional de Rosario. Instituto de Física de Rosario; ArgentinaFil: Rozet, J. P.. Centre National de la Recherche Scientifique; Francia. Universite de Paris; FranciaFil: Trassinelli, M.. Centre National de la Recherche Scientifique; Francia. Universite de Paris; FranciaFil: Vernhet, D.. Centre National de la Recherche Scientifique; Francia. Universite de Paris; Franci

Rates of convergence for the posterior distributions of mixtures of Betas and adaptive nonparametric estimation of the density

In this paper, we investigate the asymptotic properties of nonparametric Bayesian mixtures of Betas for estimating a smooth density on $[0,1]$. We consider a parametrization of Beta distributions in terms of mean and scale parameters and construct a mixture of these Betas in the mean parameter, while putting a prior on this scaling parameter. We prove that such Bayesian nonparametric models have good frequentist asymptotic properties. We determine the posterior rate of concentration around the true density and prove that it is the minimax rate of concentration when the true density belongs to a H\"{o}lder class with regularity $\beta$, for all positive $\beta$, leading to a minimax adaptive estimating procedure of the density. We also believe that the approximating results obtained on these mixtures of Beta densities can be of interest in a frequentist framework.Comment: Published in at http://dx.doi.org/10.1214/09-AOS703 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Homogeneous and locally homogeneous solutions to symplectic curvature flow

J. Streets and G. Tian recently introduced symplectic curvature flow, a geometric flow on almost K\"ahler manifolds generalising K\"ahler-Ricci flow. The present article gives examples of explicit solutions to this flow of non-K\"ahler structures on several nilmanifolds and on twistor fibrations over hyperbolic space studied by J. Fine and D. Panov. The latter lead to examples of non-K\"ahler static solutions of symplectic curvature flow which can be seen as analogues of K\"ahler-Einstein manifolds in K\"ahler-Ricci flow.Comment: 15 page

Braids inside the Birman-Wenzl-Murakami algebra

We determine the Zariski closure of the representations of the braid groups that factorize through the Birman-Wenzl-Murakami algebra, for generic values of the parameters $\alpha,s$. For $\alpha,s$ of modulus 1 and close to 1, we prove that these representations are unitarizable, thus deducing the topological closure of the image when in addition $\alpha,s$ are algebraically independent

Towards a statement of the S-adic conjecture through examples

The $S$-adic conjecture claims that there exists a condition $C$ such that a sequence has a sub-linear complexity if and only if it is an $S$-adic sequence satisfying Condition $C$ for some finite set $S$ of morphisms. We present an overview of the factor complexity of $S$-adic sequences and we give some examples that either illustrate some interesting properties or that are counter-examples to what could be believed to be "a good Condition $C$".Comment: 2