Une formule de Landau–Zener pour un croisement non dégénéré et involutif de codimension 3Landau–Zener formula for non-degenerate involutive codimension 3 crossings

In this Note, we study a 2×2 system of evolution equations with some codimension 3 crossing. We derive two conditions of non-degeneracy. We focus on one of them and reduce our system to some Landau–Zener's type system. Using this reduction, we describe the energy transfer at the crossing by Landau–Zener formula for 2-scales semi-classical measures. To cite this article: C. Fermanian Kammerer, P. Gérard, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 915–920.     

Characteristics of immunosorbents used as a new approach to selective solid-phase extraction in environmental analysis

Summary The trace-level determination of organic pollutants in complex matrices is difficult and often not reliable because theccurrent extraction procedures are non-selective. New extraction sorbents involving antigen-antibody interactions, called immunosorbents (ISs), have been synthesised in order to trap a group of structurally related pollutants. The IS capacity is always high for the analyte-antigen used to make the antibodies, but can be low for some related compounds. In this work, we show the relationship that exists between capacity, break-through volume and recovery of analytes because of the competition between the structurally related compounds for antibody sites. Breakthrough due to the overloading of the column should be avoided because calibration curves are no longer linear. The capacity of two ISs, one made for trapping the triazine pesticide group and the second for the phenylurea, group, have been optimised by selecting silica with 50 nm pore size. Calibration curves are linear for all the compounds in a mixture of ten phenylureas up to a concentration of 5 to 10 μg L⁻¹ for each compound when handling 50 mL water samples through a precolumn packed with 0.22 g of IS. Under these conditions, reliable quantitative results are obtained because calibration curves are similar when compounds are alone or in a mixture. Application to the clean-up of soil extracts illustrates the high selectivity and the high potential of these new sorbents in environmental analysis. Presented at the 21^st ISC held in Stuttgart, Germany, 15^th–20^th September, 1996     

Immuno-based sample preparation for trace analysis

Immuno-based sample preparation techniques are based upon molecular recognition. Thanks to the high affinity and high selectivity of the antigen–antibody interaction, they have been shown to be a unique tool in the sampling area. Immuno-based sample preparation methods include the widely encountered immunoaffinity extraction sorbents, so-called immunosorbents, as well as membrane-based or ultrafiltration techniques. This review describes the new developments and applications that have occurred in recent years with emphasis on (i) the antigen–antibody interactions, (ii) and their importance for the properties and use of immunosorbents, (iii) multiresidue extractions, (iv) the on-line coupling to chromatographic or electrophoretic separations, and (v) the high potential for improving MS detection. The recent use of artificial antibodies for sample pretreatment, so-called molecularly imprinted polymers, is also described.     

Refined inequalities on graded Lie groups

We construct a Littlewood–Paley decomposition associated to a Rockland operator on graded Lie groups, which allows us to deduce refined Gagliardo–Nirenberg, Sobolev and Hardy inequalities.     

Relevance and truthfulness in information correction and fusion

A general approach to information correction and fusion for belief functions is proposed, where not only may the information items be irrelevant, but sources may lie as well. We introduce a new correction scheme, which takes into account uncertain metaknowledge on the source’s relevance and truthfulness and that generalizes Shafer’s discounting operation. We then show how to reinterpret all connectives of Boolean logic in terms of source behavior assumptions with respect to relevance and truthfulness. We are led to generalize the unnormalized Dempster’s rule to all Boolean connectives, while taking into account the uncertainties pertaining to assumptions concerning the behavior of sources. Eventually, we further extend this approach to an even more general setting, where source behavior assumptions do not have to be restricted to relevance and truthfulness. We also establish the commutativity property between correction and fusion processes, when the behaviors of the sources are independent.     

Characterization of oligosorbents and application to the purification of ochratoxin A from wheat extracts

The aim of this work was to optimize the preparation of an anti-ochratoxin A (OTA) oligosorbent (OS), a solid-phase extraction sorbent based on OTA aptamers covalently immobilized on sepharose. Different syntheses were carried out by modifying the side of the oligonucleotide chain bound to the sepharose, the length of the spacer arm between the aptamer and the sepharose and the amount of the aptamers introduced during the covalent grafting. Indeed, the capacity of OSs prepared using 3′- or 5′-amino-modified sequences with a C6 or a C12 was studied. In the best conditions, the concentration of aptamers sequence used during their grafting was increased and a capacity close to 40 nmol g^?1 of OS was reached. The potential of the resulting OSs was also studied in pure media. For this, their selectivity was checked by comparing them to a control sorbent prepared without immobilizing aptamers. Extraction recoveries close to 100 % were obtained on all OSs, while no retention was observed on the control sorbent. OS does not demonstrate any cross-reactivity towards OTA metabolites, i.e., ochratoxin B and ochratoxin hydroquinone. The oligosorbent was finally applied to the clean-up of OTA from wheat sample extracts. Extraction recoveries were not affected by matrix interferences and the resulting chromatogram clearly highlights the selectivity of the sorbent that allows the removal of matrix components thus improving the reliability of the quantitation of OTA in real samples.     

Click approaches in sol–gel chemistry

The combination of the copper-catalyzed alkyne-azide cycloaddition (CuAAC) reaction with sol–gel processing enables the versatile preparation of sol–gel materials under different shapes with targeted functionalities through a diversity-oriented approach. In this account, the development of the CuAAC reaction under anhydrous conditions for the synthesis of sol–gel precursors and for the assembling of magnetic nanoparticles on self-assembled monolayers is related, as well as the use of the classical CuAAC methodologies for the functionalization of mesoporous silica nanoparticles and microdots arrays. Coupling CuAAC and Sol–Gel will result in simplified preparations of multifunctional materials with controlled morphologies.     

Semi-Classical Analysis of a Dirac Equation Without Adiabatic Decoupling

We study adiabatic decoupling for Dirac equation with some scaling which yields that the mass appears with a coefficient where is the semi-classical parameter and > 0. Therefore, the system presents an avoided crossing. The scale = 1/2 is critical: adiabatic decoupling holds for (0,1/2) while for 1/2, there is energy transfer at leading order between the two modes. We describe this transfer in terms of two-scale Wigner measures by means of Landau-Zener formula which takes into account the change of polarization of the measures after the crossing.