ON THE EXISTENCE OF ZERO POINTS OF A CONTINUOUS FUNCTION

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Continuation methods in Banach manifolds

Sufficient conditions are given to assert that a perturbed mapping has a zero in a Banach manifold modelled over ℝⁿ. The zero is estimated by means of sequences of Newton's iterations. The proof of the result is constructive and is based upon continuation methods. This work is partially supported by D.G.E.S. Pb 96-1338-CO 2-01 and the Junta de Andalucia.     

A REGULAR VALUE OF COMPACT DEFORMATION

Sufficient conditions were given to assert that between any two Banach spaces over K, Fredholm mappings share at least one value in a specific open ball. The proof of the result is constructive and based upon continuation methods.     

Apparent viscosity of a mixture of a Newtonian fluid and interacting particles

We investigate the behavior of fluid–particle mixtures subject to shear stress, by mean of direct simulation. This approach is meant to give some hints to explain the influence of interacting red cells on the global behavior of the blood. We concentrate on the apparent viscosity, which we define as a macroscopic quantity which characterizes the resistance of a mixture against externally imposed shear motion. Our main purpose is to explain the non-monotonous variations of this apparent viscosity when a mixture of fluid and interacting particles is submitted to shear stress during a certain time interval. Our analysis of these variations is based on preliminary theoretical remarks, and some computations for some well-chosen static configurations. To cite this article: A. Lefebvre, B. Maury, C. R. Mecanique 333 (2005).     

Aminoglycoside analysis in food of animal origin with a zwitterionic stationary phase and liquid chromatography–tandem mass spectrometry

In this study, fourteen highly polar aminoglycoside (AGs) antibiotics were selected. Various stationary phases were tested, including Obelisc R, ZIC-HILIC, BEH amide and aminopropyl. The nature of the stationary phase, mobile phase (water or buffer solutions and acetonitrile), pH (percentage of formic acid), gradient conditions and injection solvents were systematically studied as relevant parameters for tuning retention selectivity and detectability of AGs in liquid chromatography electrospray tandem mass spectrometry (LC–(ESI)–MS/MS). Only the two zwitterionic phases (Obelisc R and ZIC-HILIC) achieved a proper chromatographic separation considering interferences due to the crosstalk effect in low resolution mass spectrometers. The water/acetonitrile mobile phase containing 1% formic acid used with Obelisc R provided more sensitivity than the highly concentrated buffered mobile phases required for ZIC-HILIC. A solid phase extraction (SPE) clean-up procedure with polymeric weak cation exchange (WCX) cartridges was optimized for honey, milk and liver samples. Different brands of cartridges and elution solvents were tested, and the Taurus WCX offered the best recovery rate with a buffer elution at pH 3. The final optimized method was validated in these matrices according to Decision 2002/657/EC. A monitoring campaign for sixty honey, milk and liver samples was carried out at the Food Authority Control in Geneva. The concentration of dihydrostreptomycin (DSTP) found in one ovine liver exceeded the established maximum residue levels (MRLs) within the European and Swiss legislations but it was compliant taking into account the validation data.     

Approximations in Sobolev spaces by prolate spheroidal wave functions

Recently, there is a growing interest in the spectral approximation by the Prolate Spheroidal Wave Functions (PSWFs) ${\psi }_{n,c},c>0$. This is due to the promising new contributions of these functions in various classical as well as emerging applications from Signal Processing, Geophysics, Numerical Analysis, etc. The PSWFs form a basis with remarkable properties not only for the space of band-limited functions with bandwidth c, but also for the Sobolev space $H^s([?1,1])$. The quality of the spectral approximation and the choice of the parameter c when approximating a function in $H^s([?1,1])$ by its truncated PSWFs series expansion, are the main issues. By considering a function $f\in H^s([?1,1])$ as the restriction to $[?1,1]$ of an almost time-limited and band-limited function, we try to give satisfactory answers to these two issues. Also, we illustrate the different results of this work by some numerical examples.     

Functionalized carbon dots as sensors for gold nanoparticles in spiked samples: Formation of nanohybrids

This paper reports the synthesis, passivation and functionalization of luminescent carbon dots (CDs) possessing surface thiol ending groups. A simple procedure involving amidation of passivated carbon dots (p-CDs) with cysteamine boosts their photoluminescent properties and enables their use as easily controlled fluorescent nanosensors for determining citrate–gold nanoparticles (AuNPs). The mechanism behind the quenching phenomenon was established from fluorescence measurements at high temperatures and lifetime tests, and found to involve static quenching leading to the formation of CD–AuNP nanohybrids. A method for determining AuNPs in complex matrices was developed and validated by application to spiked drinking water and mussel tissues. The limits of detection and quantitation for AuNPs thus obtained were 0.20 and 0.66 nmol L^–1, respectively.