Blow-up results of viriel type for Zakharov equations

We consider the Zakharov equations in ^N (for N=2,N=3). We first establish a viriel identity for such equations and then prove a blow-up result for solutions with a negative energy.     

Multiplicative -quotients

Let be the Dedekind -function. In this work we exhibit all modular forms of integral weight , for positive integers and and arbitrary integers , such that both and its image under the Fricke involution are eigenforms of all Hecke operators. We also relate most of these modular forms with the Conway group via a generalized McKay-Thompson series.

     

Recherches sur la structure électronique de composés soufrés (méthode L.C.A.O. améliorée)

Improved L.C.A.O. method primitively built for conjugated molecules holding only atoms of second row in the periodic classification is extended to molecules holding atoms of the third row. The application is done for thiophen, thioketones, SO₂ and SO₃. d orbitals are not introduced in this study. Discussion about results shows that d orbitals must be introduced when the sulphur atom is strongly positively charged like in sulphur oxides.     

Superoxide radical anion adduct of 5,5-dimethyl-1-pyrroline N-oxide (DMPO). 2. The thermodynamics of decay and EPR spectral properties

The formation of the superoxide radical anion (O2*-) adduct of the nitrone 5,5-dimethyl-1-pyrroline N-oxide (DMPO) as detected by electron paramagnetic resonance (EPR) spectroscopy is one of the most common techniques for O2*- detection in chemical and biological systems. However, the nature of DMPO-O2H has confounded spin-trapping investigators over the years, since there has been no independently synthesized DMPO-O2H to date. A density functional theory (DFT) approach was used to predict the isotropic hyperfine coupling constants arising from the N, beta-H, and gamma-H nuclei of DMPO-O2H using explicit interactions with water molecules as well as via a bulk dielectric effect employing the polarizable continuum model (PCM). Theoretical calculation on the thermodynamics of DMPO-O2H decay shows favorable intramolecular rearrangement to form a nitrosoaldehyde and a hydroxyl radical as products, consistent with experimental observations. Some pathways for the bimolecular decomposition of DMPO-O2H and DMPO-OH have also been computed.     

Anderson localization for multi-dimensional systems at large disorder or large energy

We prove that discrete Schrödinger operators on ^d with a random-potential have almost-surely only pure point spectrum and exponentially decaying eigenfunctions for large disorder or large energy. This is the first proof of localization for multi-dimensional Anderson models.Groupe de recherche 048 du CNRS     

Reversible dynamics and the macroscopic rate law for a solvable Kolmogorov system: The three bakers' reaction

We investigate a piecewise linear (area-preserving) mapT describing two coupled baker transformations on two squares, with coupling parameter 0c1. The resulting dynamical system is Kolmogorov for anyc0. For rational values ofc, we construct a generating partition on whichT induces a Markov chain. This Markov structure is used to discuss the decay of correlation functions: exponential decay is found for a class of functions related to the partition. Explicit results are given forc=2^–n. The macroscopic analog of our model is a leaking process between two (badly) stirred containers: according to the Markov analysis, the corresponding progress variable decays exponentially, but the rate coefficients characterizing this decay are not those determined from the one-way flux across the cell boundary. The validity of the macroscopic rate law is discussed.     

New approach to calibrating conductivity meters in the low conductivity range

There is currently a major issue with the calibration of conductivity meters used for high purity water: the lack of availability of a reference material or reference methods for low conductivity ranges (conductivity below 1 S cm^–1 at 25.0 °C, resistivity >1 M cm at 25.0 °C). This paper describes the current status of conductivity measurements in high purity water. A new and improved approach, currently being investigated, should allow us to make the calibration of conductivity meters used for low conductivity ranges traceable to the SI.Milipore, Milli-Q and Elix are registered trademarks of Millipore Corporation.     

Mild cleavage of methoxymethyl (MOM) ethers with trimethylsilyl bromide

Trimethylsilyl bromide is an effective reagent for the deprotection of methoxymethyl ethers under mild conditions.