Cergy-Pontoise University

About: Cergy-Pontoise University is a based out in . It is known for research contribution in the topics: Population & Sobolev space. The organization has 2028 authors who have published 5021 publications receiving 110856 citations. The organization is also known as: Université de Cergy-Pontoise & Universite de Cergy-Pontoise.

Global well-posedness, scattering and blow-up for the energy-critical, focusing, non-linear Schrödinger equation in the radial case

Abstract: We prove, for the energy critical, focusing NLS, that for data whose energy is smaller than that of the standing wave, and whose homogeneous Sobolev norm H^1 is smaller than that of the standing wave and which is radial, we have global well-posedness and scattering in dimensions 3, 4 and 5. This is sharp since if the data is in the inhomogeneous Sobolev space H^1, of energy smaller than the standing wave but of larger homogeneous H^1 norm, we have blow-up in finite time. The result follows from a general method that we introduce into this type of critical problem. By concentration-compactness we produce a critical element, which modulo the symmetries of the equation is compact, has minimal energy among those which fail to have the conclusion of our theorem. In addition, we show that the dilation parameter in the symmetry, for this solution, can be taken strictly positive.We then establish a rigidity theorem that shows that no such compact, modulo symmetries, object can exist. It is only at this step that we use the radial hypothesis.The same analysis, in a simplified form, applies also to the defocusing case, giving a new proof of results of Bourgain and Tao.

FPGA Design Methodology for Industrial Control Systems—A Review

Abstract: This paper reviews the state of the art of field- programmable gate array (FPGA) design methodologies with a focus on industrial control system applications. This paper starts with an overview of FPGA technology development, followed by a presentation of design methodologies, development tools and relevant CAD environments, including the use of portable hardware description languages and system level programming/design tools. They enable a holistic functional approach with the major advantage of setting up a unique modeling and evaluation environment for complete industrial electronics systems. Three main design rules are then presented. These are algorithm refinement, modularity, and systematic search for the best compromise between the control performance and the architectural constraints. An overview of contributions and limits of FPGAs is also given, followed by a short survey of FPGA-based intelligent controllers for modern industrial systems. Finally, two complete and timely case studies are presented to illustrate the benefits of an FPGA implementation when using the proposed system modeling and design methodology. These consist of the direct torque control for induction motor drives and the control of a diesel-driven synchronous stand-alone generator with the help of fuzzy logic.

Nonlinear analysis on manifolds: Sobolev spaces and inequalities

Abstract: Elements of Riemannian geometry Sobolev spaces: The compact setting Sobolev spaces: The noncompact setting Best constants in the compact setting I Best constants in the compact setting II Optimal inequalities with constraints Best constants in the noncompact setting Euclidean-type Sobolev inequalities The influence of symmetries Manifolds with boundary Bibliography.

The mechanisms of pyrrole electropolymerization

Abstract: Over the past twenty years, polypyrrole has appeared as the most extensively studied conducting polymer. However, despite the volume of work already done in this area, there has been little focus put on the mechanism of polypyrrole synthesis, especially concerning the most efficient method, electropolymerization. Numerous analytical techniques have been used to study polypyrrole electrodeposition and/or doping. However, the mechanism itself is still a controversial subject as there is not one mechanism which is universally accepted. The mechanism proposed by Diaz is the one most commonly referred to in the literature although several other mechanisms are not lacking in support. The controversy lies in the initiation step as each mechanism proposes a different way of beginning the reaction, varying between electron transfer, proton transfer and direct radical pyrrole formation. Without considering the initiation step, there are many other factors including electrolyte, solvent, temperature and pH which can influence the reaction mechanism during the electropolymerization of pyrrole, thus impacting the characteristics of the polymer formed at the electrode.