Lp-solutions to BSDEs with super-linear growth coefficient. Application to degenerate semilinear PDEs.

We consider multidimensional backward stochastic differential equations (BSDEs). We prove the existence and uniqueness of solutions when the coefficient grow super-linearly, and moreover, can be neither locally Lipschitz in the variable y nor in the variable z. This is done with super-linear growth coefficient and a p-integrable terminal condition (p & 1). As application, we establish the existence and uniqueness of solutions to degenerate semilinear PDEs with superlinear growth generator and an Lp-terminal data, p & 1. Our result cover, for instance, the case of PDEs with logarithmic nonlinearities.

Constant coefficient tests for random coefficient regression

Random coefficient regression models have been applied in differentfields and they constitute a unifying setup for many statisticalproblems. The nonparametric study of this model started with Beranand Hall (1992) and it has become a fruitful framework. In thispaper we propose and study statistics for testing a basic hypothesisconcerning this model: the constancy of coefficients. The asymptoticbehavior of the statistics is investigated and bootstrapapproximations are used in order to determine the critical values ofthe test statistics. A simulation study illustrates the performanceof the proposals.

Comparative study of the LC-MS/MS and UPLC-MS/MS for the multi-residue analysis of quinolones, penicillins and cephalosporins in cow milk, and validation according to the regulation 2002/657/EC

The aim of this study was to develop and validate an analytical method to simultaneously determine European Union-regulated beta-lactams (penicillins and cephalosporins) and quinolones in cow milk. The procedure involves a new solid phase extraction (SPE) to clean-up and pre-concentrate the three series of antibiotics before analysis by liquid chromatography¿tandem mass spectrometry (LC-MS/MS) and ultra-high-performance liquid chromatography¿tandem mass spectrometry (UPLC-MS/MS). LC-MS/MS and UPLC-MS/MS techniques were also compared. The method was validated according to the Directive 2002/657/EC and subsequently applied to 56 samples of raw cow milk supplied by the Laboratori Interprofessional Lleter de Catalunya (ALLIC) (Laboratori Interprofessional Lleter de Catalunya, Control Laboratory Interprofessional of Milk of Catalunya).