Instabilities for supercritical Schrödinger equations in analytic manifolds

In this paper we consider supercritical nonlinear Schrödinger equations in an analytic Riemannian manifold (Md,g), where the metric g is analytic. Using an analytic WKB method, we are able to construct an Ansatz for the semiclassical equation for times independent of the small parameter. These approximate solutions will help to show two different types of instabilities. The first is in the energy space, and the second is an immediate loss of regularity in higher Sobolev norms.     

Detection of Frozen–Thawed Duck Fatty Liver by MALDI-TOF Mass Spectrometry: A Chemometrics Study

The marketing of poultry livers is only authorized as fresh, frozen, or deep-frozen. The higher consumer demand for these products for a short period of time may lead to the marketing of frozen–thawed poultry livers: this constitutes fraud. The aim of this study was to design a method for distinguishing frozen–thawed livers from fresh livers. For this, the spectral fingerprint of liver proteins was acquired using Matrix-Assisted Laser Dissociation Ionization-Time-Of-Flight mass spectrometry. The spectra were analyzed using the chemometrics approach. First, principal component analysis studied the expected variability of commercial conditions before and after freezing–thawing. Then, the discriminant power of spectral fingerprint of liver proteins was assessed using supervised model generation. The combined approach of mass spectrometry and chemometrics successfully described the evolution of protein profile during storage time, before and after freezing-thawing, and successfully discriminated the fresh and frozen–thawed livers. These results are promising in terms of fraud detection, providing an opportunity for implementation of a reference method for agencies to fight fraud.     

Optimization of capacity expansion planning for gas transportation networks

This paper presents techniques for solving the problem of minimizing investment costs on an existing gas transportation network. The goal of this program is to find, first, the optimal location of pipeline segments to be reinforced and, second, the optimal sizes (among a discrete commercial list of diameters) under the constraint of satisfaction of demands with high enough pressure for all users.     

Rigidity of Poisson structures

We study germs of analytic Poisson structures which are suitable perturbations of a quasihomogeneous Poisson structure in a neighborhood of the origin of ℝ ⁿ or ℂ ⁿ , a fixed point of the Poisson structures. We define a “diophantine condition” relative to the quasihomogeneous initial part ie256-1 which ensures that such a good perturbation of 256-2 which is formally conjugate to 256-3 is also analytically conjugate to it.     

Numerical approximations of one-dimensional linear conservation equations with discontinuous coefficients

Conservative linear equations arise in many areas of application, including continuum mechanics or high-frequency geometrical optics approximations. This kind of equation admits most of the time solutions which are only bounded measures in the space variable known as duality solutions. In this paper, we study the convergence of a class of finite-difference numerical schemes and introduce an appropriate concept of consistency with the continuous problem. Some basic examples including computational results are also supplied.