Deformations of constant mean curvature 1/2 surfaces in H2xR with vertical ends at infinity

We study constant mean curvature 1/2 surfaces in H2xR that admit a compactification of the mean curvature operator. We show that a particular family of complete entire graphs over H2 admits a structure of infinite dimensional manifold with local control on the behaviors at infinity. These graphs also appear to have a half-space property and we deduce a uniqueness result at infinity. Deforming non degenerate constant mean curvature 1/2 annuli, we provide a large class of (non rotational) examples and construct (possibly embedded) annuli without axis, i.e. with two vertical, asymptotically rotational, non aligned ends.Comment: 35 pages. Addition of a half-space theore

Optimal Control for a Class of Infinite Dimensional Systems Involving an L∞L^\infty-term in the Cost Functional

An optimal control problem with a time-parameter is considered. The functional to be optimized includes the maximum over time-horizon reached by a function of the state variable, and so an $L^\infty$-term. In addition to the classical control function, the time at which this maximum is reached is considered as a free parameter. The problem couples the behavior of the state and the control, with this time-parameter. A change of variable is introduced to derive first and second-order optimality conditions. This allows the implementation of a Newton method. Numerical simulations are developed, for selected ordinary differential equations and a partial differential equation, which illustrate the influence of the additional parameter and the original motivation.Comment: 21 pages, 8 figure

Bridging the Gap Between Ox and Gauss using OxGauss

The purpose of this paper is to review and discuss the key improvements brought to OxGauss. Without having to install Gauss on his or her machine, the OxGauss user can run under Ox a wide range of Gauss programs and codes. Even with the console Ox version (free for academics), Gauss codes can either be called from Ox programs or run and executed on their own. While the new OxGauss version is very powerful in most circumstances, it is of little use once the purpose is to execute programs that attempt to solve optimization problems using Cml, Maxlik or Optmum. In this paper we propose a set of additional procedures that contribute to bridge the gap between Ox and three well-known Gauss application modules: Cml, Maxlik or Optmum.The effectiveness of our procedures is illustrated by revisiting a large number of freely available Gauss codes in which numerical optimization relies on the above Gauss application modules. The Gauss codes include many programs dealing with non-linear models such as the Markov regime-switching models STAR models and various GARCH-type models. These illustrations highlight a further potentially interesting implication of OxGauss: it enables non-Gauss users to replicate existing empirical results using freely available Gauss codes.econometrics;

Momentum distribution of a dilute unitary Bose gas with three-body losses

Using Boltzmann's equation, we study the effect of three-body losses on the momentum distribution of a homogeneous unitary Bose gas in the dilute limit where quantum correlations are negligible. We calculate the momentum distribution of the gas and show that inelastic collisions are quantitatively as important as a second order virial correction.Comment: 4 pages + supplemental materia

Overcoming limitations of nanomechanical resonators with simultaneous resonances

Dynamic stabilization by simultaneous primary and superharmonic resonances for high order nonlinearity cancellation is demonstrated with an electrostatically-actuated, piezoresistively-transduced nanomechanical resonator. We prove experimentally how the combination of both the third-order nonlinearity cancellation and simultaneous resonances can be used to linearly drive a nanocantilever up to very large amplitudes compared to fundamental limits like pull-in occurrence, opening the way towards resonators with high frequency stability for high-performance sensing or time reference

BEAT: An Open-Source Web-Based Open-Science Platform

With the increased interest in computational sciences, machine learning (ML), pattern recognition (PR) and big data, governmental agencies, academia and manufacturers are overwhelmed by the constant influx of new algorithms and techniques promising improved performance, generalization and robustness. Sadly, result reproducibility is often an overlooked feature accompanying original research publications, competitions and benchmark evaluations. The main reasons behind such a gap arise from natural complications in research and development in this area: the distribution of data may be a sensitive issue; software frameworks are difficult to install and maintain; Test protocols may involve a potentially large set of intricate steps which are difficult to handle. Given the raising complexity of research challenges and the constant increase in data volume, the conditions for achieving reproducible research in the domain are also increasingly difficult to meet. To bridge this gap, we built an open platform for research in computational sciences related to pattern recognition and machine learning, to help on the development, reproducibility and certification of results obtained in the field. By making use of such a system, academic, governmental or industrial organizations enable users to easily and socially develop processing toolchains, re-use data, algorithms, workflows and compare results from distinct algorithms and/or parameterizations with minimal effort. This article presents such a platform and discusses some of its key features, uses and limitations. We overview a currently operational prototype and provide design insights.Comment: References to papers published on the platform incorporate

AURELL, Martin. La Noblesse en Occident (VIe - XVe siécle) París: Armand Coün (coll. CURSUS, serie Histoire), 1996

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