Non-explosion en temps grand et stabilité de solutions globales des équations de Navier–StokesNon-blowup at large times and stability for global solutions to the Navier–Stokes equations

Suppose there exists a global solution u to the incompressible Navier–Stokes equations, such that $\text{u∈}\text{C}{}_{\mathrm{t}}\text{(}\text{H}\text{?}{}^{\mathrm{1/2}}\text{)}$. We prove that its $\text{H}\text{?}{}^{\mathrm{1/2}}$ norm goes to 0 at infinity. We next use this fact to control the $\text{L}{}^2{}_{\mathrm{t}}\text{(}\text{H}\text{?}{}^{\mathrm{3/2}}\text{)}$ norm of u, and finally we prove that such a solution is stable. To cite this article: I. Gallagher et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 289–292.     

Domain decomposition for an asymptotic geological fault modeling

We present in this paper a domain decomposition method to treat faults in geological basin modeling. The particularity of this model is that the faults whose widths are very small in comparison with the basin size, are not characterized as subdomains any more but as interfaces between sedimentary blocks. The originality of this work lies in the formulation of this new fault model and in the definition and the computation of the interface conditions between the subdomains. To cite this article: E. Flauraud et al., C. R. Mecanique 331 (2003).     

Self-energy of one electron in non-relativistic QED

We investigate the self-energy of one electron coupled to a quantized radiation field by extending the ideas developed in Hainzl (Ann. H. Poincaré, in press). We fix an arbitrary cut-off parameter Λ and recover the α²-term of the self-energy, where α is the coupling parameter representing the fine structure constant. Thereby we develop a method which allows to expand the self-energy up to any power of α. This implies that perturbation theory in α is correct if Λ is fix. As an immediate consequence we obtain enhanced binding for electrons.     

An existence result for a quadrature surface free boundary problem

The aim of this paper is to present two different approachs in order to obtain an existence result to the so-called quadrature surface free boundary problem. The first one requires the shape derivative calculus while the second one depends strongly on the compatibility condition of the Neumann problem. A necessary and sufficient condition of existences is given in the radial case.     

New access to H-phosphonates via metal-catalyzed phosphorus-oxygen bond formation

A novel approach to H-phosphonates from hypophosphorous acid using a transfer hydrogenation process was developed. This method is atom-economical, environmentally friendly, catalytic, and efficient, leading easily to H-phosphonate monoesters or ammonium salt in moderate to good yields.     

THE PHOTOTOXICITY OF 2,5-DIPHENYLOXAZOLE (POP) AND 1,4-BIS(5-PHENYLOXAZOL-2-YL)BENZENE (POPOP)

Abstract 2,5-Diphenyloxazole (POP) is widely used for the determination of radioactivity by scintillation counting. It has been found to be phototoxic to the yeasts Saccharomyces cerevisiae and Candida utilis , to the first instar larvae of the mosquito Aedes aegypti , to the crustaceans Daphnia magna and Artemia salida , as well as to the eggs of Drosophila melanogaster . The related molecule 1,4-bis(5-phenyloxazol-2-yl)benzene (POPOP) is also phototoxic, but to a lesser degree. Both POP and POPOP can sensitize the formation of singlet oxygen.     

Expedient synthesis of substituted imidazoles from nitriles

Expedient and practical new methodology for the synthesis of substituted imidazoles was developed to provide a rapid access to a variety of 2-substituted, 1,2-disubstituted and 1,2,4-trisubstituted imidazoles by the direct CuCl-mediated reaction of nitriles with α-amino acetals in an intermolecular as well as intramolecular fashion.     

In situ preparation of protein-"smart" polymer conjugates with retention of bioactivity

Protein-polymer conjugates are widely used in biotechnology and medicine, and new methods to prepare the bioconjugates would be advantageous for these applications. In this report, we demonstrate that bioactive "smart" polymer conjugates can be synthesized by polymerizing from defined initiation sites on proteins, thus preparing the polymer conjugates in situ. In particular, free cysteines, Cys-34 of bovine serum albumin (BSA) and Cys-131 of T4 lysozyme V131C, were modified with initiators for atom transfer radical polymerization (ATRP) either through a reversible disulfide linkage or irreversible bond by reaction with pyridyl disulfide- and maleimide-functionalized initiators, respectively. Initiator conjugation was verified by electrospray-ionization mass spectroscopy (ESI-MS), and the location of the modification was confirmed by muLC-MSMS (tandem mass spectrometry) analysis of the trypsin-digested protein macroinitiators. Polymerization of N-isopropylacrylamide (NIPAAm) from the protein macroinitiators resulted in thermosensitive BSA-polyNIPAAm and lysozyme-polyNIPAAm in greater than 65% yield. The resultant conjugates were characterized by gel electrophoresis and size exclusion chromatography (SEC) and easily purified by preparative SEC. The identity of polymer isolated from the BSA conjugate was confirmed by (1)H NMR, and the polydispersity index was determined by gel permeation chromatography (GPC) to be as low as 1.34. Lytic activities of the lysozyme conjugates were determined by two standard assays and compared to that of the unmodified enzyme prior to polymerization; no statistical differences in bioactivity were observed.