Local exact Lagrangian controllability of the Burgers viscous equation

We study and give the definition of the exact Lagrangian controllability of the viscous Burgers equation and prove a local result. We give similar results for the heat equation in dimension 1.     

Synthèse et étude de modèles de NADH à noyaux accolés en série pyrrolo[2,3-b] et [3,2-b]pyridines

Pyrrolo[2,3-b] and [3,2-b]pyridines derivatives, precursors for annealated NADH models have been prepared. Several methods for building a pyridinic annealates ring have been used starting from 2- or 3-aminopyrrole. The corresponding dihydropyridine structure leads to highly reactive NADH models compounds and are very much more stable than common models.     

Synthesis of vulpinic acids from dimethyl tartrate

A series of vulpinic acids differing by the aryl or heteroaryl groups placed in the ester α-position were prepared by Suzuki-Miyaura cross-coupling involving a common iodide and the corresponding aryl boronates. The preparation of the iodide precursor from (+)-dimethyl l-tartrate required four steps: the esterification of one hydroxyl group, a Dieckmann cyclization allowing the construction of the tetronic acid moiety, a dehydration leading to the installation of the exocyclic double bond and lastly, an N-iodosuccinimide-mediated iodation of the alkene obtained.     

Functionalized poly(phenylene‐alt‐bithiophenes): Synthesis,chiroptical properties,and interaction with chiral amines

New functionalized, (a)chiral poly(phenylene‐alt‐bithiophene)s were prepared and their chiroptical properties were studied. The polymers were prepared by a Stille coupling reaction and were functionalized with protected carboxylic acid and amino functions (tert‐butyl ester and BOC respectively). The polymers are present as well conjugated rigid rods in solution, which (chirally) aggregate in nonsolvents and film. In a next step, the protecting group (tert‐butyl ester in case of the carboxylic acid) was removed. Aggregation of this polymer can be induced by addition of amines; if chiral amines are used, the polymer chains chirally stack. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 4817–4829, 2008     

Sur un théorème de Castelnuovo

We continue the study of G. Castelnuovo on the group of birational transformations of the complex plane that fix each point of a curve of genus > 1 ; we use adjoint linear system of the curve as Castelnuovo does. We prove that these groups are abelian, and that these are either finite, of order 2 or 3, or conjuguate to a subgroup of the de Jonquières group. We show also that these results do not generalise to curves of genus ≤ 1. *Partiellement soutenu par le CNPq-Brasil et la Section de Mathématiques de l'Université de Genève.     

A Matrix Interpolation between Classical and Free Max Operations. I. The Univariate Case

Recently, Ben Arous and Voiculescu considered taking the maximum of two free random variables and brought to light a deep analogy with the operation of taking the maximum of two independent random variables. We present here a new insight on this analogy: its concrete realization based on random matrices giving an interpolation between classical and free settings.     

Large Deviation Techniques Applied to Systems with Long-Range Interactions

We discuss a method to solve models with long-range interactions in the microcanonical and canonical ensemble. The method closely follows the one introduced by R.S. Ellis, Physica D 133:106 (1999), which uses large deviation techniques. We show how it can be adapted to obtain the solution of a large class of simple models, which can show ensemble inequivalence. The model Hamiltonian can have both discrete (Ising, Potts) and continuous (HMF, Free Electron Laser) state variables. This latter extension gives access to the comparison with dynamics and to the study of non-equilibrium effects. We treat both infinite range and slowly decreasing interactions and, in particular, we present the solution of the α-Ising model in one-dimension with 0 ⩽ α < 1.     

An Ultrasensitive Virus ELISA Based on a magnetic Mesoporous Silica Nanoprobe

Detection of infectious viruses relies on quantitative polymerase chain reaction (qPCR). However, qPCR requires costly equipment, a clean operating environment and experienced technicians, limiting its wide applicability. On the other hand, enzyme-linked immunosorbent assay (ELISA) is widely used in biological laboratories due to its relatively high sensitivity and ease of operation. However, ELISA-based detection of the virus is hampered because it is lower sensitive than qPCR. Herein, a nanoprobe ELISA (NP-ELISA) based on a mesoporous silica nanoprobe, which is constructed by first being loaded with peroxidase and further coated with positively charged polymer polyethyleneimine, and finally functionalized with antivirus antibodies, is designed. Results show that each NP probe is encapsulating 170 peroxidase molecules and presents 200 antibody molecules on the surface. The limit of detection (LOD) of NP-ELISA (LOD = 1450 PFU mL⁻¹) for the detection of real virus samples is tenfold sensitive than that of standard ELISA (LOD = 14, 414 PFU mL⁻¹) and the assay time for NP-ELISA is reduced by 1 h as compared with standard one. Therefore, the NP-ELISA provides a rapid and sensitive immunoassay platform that can readily be implemented for biological laboratory research as well as for on-site clinical diagnostics.