Convexity and Weighted Integral Inequalities for Energy Decay Rates of Nonlinear Dissipative Hyperbolic Systems

This work is concerned with the stabilization of hyperbolic systems by a nonlinear feedback which can be localized on a part of the boundary or locally distributed. We show that general weighted integral inequalities together with convexity arguments allow us to produce a general semi-explicit formula which leads to decay rates of the energy in terms of the behavior of the nonlinear feedback close to the origin. This formula allows us to unify for instance the cases where the feedback has a polynomial growth at the origin, with the cases where it goes exponentially fast to zero at the origin. We also give three other significant examples of nonpolynomial growth at the origin. Our work completes the work of [15] and improves the results of [21] and [22] (see also [23] and [10]). We also prove the optimality of our results for the one-dimensional wave equation with nonlinear boundary dissipation. The key property for obtaining our general energy decay formula is the understanding between convexity properties of an explicit function connected to the feedback and the dissipation of energy.     

Prediction of Continuous Time Autoregressive Processes via the Reproducing Kernel Spaces

We study the statistical prediction of a continuous time stochastic process admitting a functional autoregressive representation. We construct an approximation of Parzen's optimal predictor in reproducing kernel spaces framework. This approach did not require an estimation of the operator of the autoregressive representation. This revised version was published online in August 2006 with corrections to the Cover Date.     

On the existence of multiple steady-state solutions in the theory of electrodiffusion. Part I: the nonelectroneutral case. Part II: a constructive method for the electroneutral case

We give a constructive method for giving examples of doping functions and geometry of the device for which the nonelectroneutral voltage driven equations have multiple solutions. We show in particular, by performing a singular perturbation analysis of the current driven equations that if the electroneutral voltage driven equations have multiple solutions then the nonelectroneutral voltage driven equations have multiple solutions for sufficiently small normed Debye length. We then give a constructive method for giving examples of data for which the electroneutral voltage driven equations have multiple solutions.

     

ACTION DU REACTIF DE LAWESSON SUR LES HYDRAZONATES ET LES HYDROXYMATES: SYNTHESE DE SULFURES DE 1,3,4,2-THIADIAZAPHOSPHOLINES ET DE SULFURES DE 1,3,5,2-OXATHIAZAPHOSPHOLINES

Abstract

The Lawesson Reagent (L.R) 1 reacts with hydrazonates 2 and hydroxymates 3 to give 1,3,4,2-thiadiazaphospholines 4 and 1,3,5,2-oxathiazaphospholines 5 derivatives. The structure of products 4 and 5 is confirmed by IR and NMR spectroscopy.     

Sharp energy estimates for nonlinearly locally damped PDEs via observability for the associated undamped system

We consider the problem of sharp energy decay rates for nonlinearly damped abstract infinite-dimensional systems. Direct methods for nonlinear stabilization generally rely on multiplier techniques, and thus are valid under restrictive geometric conditions compared to the optimal geometric optics condition of Bardos et al. (1992) [10]. We prove sharp, simple and quasi-optimal energy decay rates through an indirect method, namely an observability estimate for the corresponding undamped system. One of the main advantage of these results is that they allow to combine optimal geometric conditions, as for instance that of Bardos et al. (1992) [10] and the optimal-weight convexity method of the first author (Alabau-Boussouira, 2010 [6], Alabau-Boussouira, 2005 [2]) to deduce very simple and quasi-optimal energy decay rates for nonlinearly locally damped systems. We also show that using arguments based on Russell's principle (Russell, 1978 [24]), one can deduce sharp energy decay rates from the exponential stabilization of the linearly damped system. Our results extend to nonlinearly damped systems, those of Haraux (1989) [14] and Ammari and Tucsnak (2001) [9] which concern linearly damped systems.     

Extended cooperative networks games

We present here a pricing model which is an extension of the Cooperative Game concept and which includes a notion of Price-Dependent Demand. We present some existence results as well as some algorithms, and conclude by discussing a specific problem related to Network Pricing.     

Light-induced layer by layer thickening in photosensitive liquid crystal membranes

Photosensitive smectic membranes of pure liquid crystal (LC) were studied under white light illumination. A thickness increase is observed in the illuminated film area. Appropriate light and thermal conditions lead to a thickening layer by layer process. This unusual phenomenon is opposite to the well-known step-by-step thinning transitions under heating. We give a phenomenological interpretation for thickening based on layer transport of LC matter towards the illuminated area.     

Intraspecific variability of carbon isotope discrimination and its correlation with grain yield in safflower: prospects for selection in a Mediterranean climate

The goals of the present study were to obtain a first estimate of intraspecific variability of carbon isotope discrimination (Δ) in safflower, a thistle-like herbaceous plant, and to determine the statistical relationship between Δ and grain yield as well as its components in a collection of 45 accessions of different origins. Grain yield and aboveground biomass, harvest index, average grain weight, and Δ (measured on the bulk leaf organic matter) were investigated in experimental field conditions. A large variability was noted for all traits but a principal component analysis (PCA) allowed to identify several homogeneous groups of accessions. Average grain yield per plant varied between 1 and 39 g. Δ varied between 21.3 and 25.2?‰, i.e. a large variation of 3.9?‰. In our experiment, the variation of Δ was not significantly related to that of grain yield in the whole accession sample. However, we found contrasting trends for this relation within accession groups. These initial results motivate further experiments to assess more in depth correlation between Δ and yield in safflower and are encouraging regarding the possibility of using Δ as an effective selection index in safflower to obtain genotypes that efficiently consume water. This study also highlighted one accession that combines the two characters required in the Mediterranean regions, i.e. high yield performance and high water-use efficiency.     

Criteria determination to choose piezoelectric materials for BAW resonator applications via colored picosecond acoustics

A great number of piezoelectric materials which could be used in the fabrication of BAW resonators were investigated via colored picosecond acoustics technique in order to study the required parameters for designing and fabricating improved devices. These parameters concerns acoustic longitudinal velocity, v_L, elastic stiffness constant, C^D₃₃, intrinsic mechanical loss, tanδ, and electromechanical coupling coefficient, k²_t. We first quantify the effect of the ratio between the wavelength pulse of a femtosecond laser and the period of Brillouin oscillations, λ_p/T. It is found that C^D₃₃ depends linearly on λ_p/T. Then, we deduced novel relations for stiffness constant and mechanical coupling coefficient. Moreover, the determination of different parameters (density, refractive index and v_L) of piezoelectric film is achieved, with good agreement with literature. The optimized conditions for the parameter choice of BAW resonators are found to be: 300?GPa?<?C^D₃₃?<?500?GPa and 1.7?GPa?<?e²₃₃/ε^s₃₃?<?28.5?GPa with λ_p/T?>?37 10³?m/s where e₃₃ and ε^s₃₃ are the piezoelectric constant and the materials permittivity in the direction 3, respectively.