Measures on double or resonant eigenvalues for linear Schrödinger operator

In this paper we consider linear Schrödinger operator with double or resonant eigenvalues. The main result is the bound of the measure (in a suitable space of functions) of the potentials leading to such double or resonant eigenvalues. Namely we present measure type estimates evaluating neighborhoods of the so-called double or resonant set.     

Two new tetrahydrofuran derivatives from the fungus Mucor spp. SNB-VECD11D isolated from the Chrysomelidae Acalymma bivittula

Two new tetrahydrofuran derivatives, mucorinic acids A (1) and B (2) as well as the three known secondary metabolites dehydroabietic acid (3), Δ8-dihydroabietic acid (4) and 8-pimarenic acid (5) were isolated from a solid culture of the fungus Mucor spp. isolated on insect Acalymma bivittula. The structure of these compounds was elucidated by analysis of NMR and MS spectroscopic data. Compounds were tested in antimicrobial and insecticidal assays. Dehydroabietic acid exhibited moderate larvicidal activity on Aedes aegypti larvae with 65% mortality at 10 ppm. Both new compounds 1 and 2 showed interesting antibacterial activity on Staphylococcus aureus and methicillin resistant S. aureus with MIC values in the 8–16 μg/ml.     

Quelques modèles diffusifs capillaires de type KortewegSome diffusive capillary models of Korteweg type.

The purpose of this Note is to propose new diffusive capillary models of Korteweg type and discuss their mathematical properties. More precisely, we introduce viscous models which provide some additional information on the behavior of the density close to vacuum. We actually prove that if some compatibility conditions between diffusion and capillarity are satisfied, some extra regularity information on a quantity involving the density is available. We obtain a non-trivial equality deduced from the special structure of the momentum equation. This Note generalizes to some extent the authors' previous works on the Korteweg model (with constant capillary coefficient) and on the shallow water equation. To cite this article: D. Bresch, B. Desjardins, C. R. Mecanique 332 (2004).     

"Click" synthesis and properties of carborane-appended large dendrimers

Large dendrimers, noted G(n)-3(n+2)cage, containing 3(n+2) o-carborane cluster cages MeC(2)B(10)H(10) at their peripheries (n = number of generation noted G(n)) have been synthesized by Huisgen-type azide alkyne Cu(I)-catalyzed dipolar "click" cycloaddition reactions (CuAAC) between an o-carborane monomeric cluster containing an ethynyl group and arene-centered azido-terminated dendrimers G(n)-3(n+2)N(3) of generations 0, 1, and 2. Attempts to synthesize higher-generation dendrimers of this family yielded insoluble materials. The carborane dendrimers G(0)-9cage, G(1)-27cage, and G(2)-81cage have been characterized by (1)H, (13)C, (11)B NMR, elemental analysis, matrix-assisted laser desorption/ionization time of flight (MALDI-TOF) mass spectroscopy, and size exclusion chromatography (SEC) showing low polydispersities, dynamic light scattering (DLS) showing hydrodynamic diameters of 5.7 nm for the G(1)-27cage and the 12.9 nm for the G(2)-81cage. These dendrimers are extremely robust thermally, with 10% mass loss temperatures of 411 °C for the G(0)-9cage, 371 °C for the G(1)-27cage, and 392 °C for the G(2)-81cage. They all showed a strong absorption in the UV region peaking at 258 nm, whereas emission spectra of low intensities were observed between 280 and 480 nm.     

Memory of chirality in cascade rearrangements of enediynes

The cascade rearrangement of chiral enediynes 1c-e, involving successively 1,3-proton shift, Saito-Myers cyclization, 1,5-hydrogen atom transfer, and intramolecular coupling of the resulting biradical, proceeded at 80 °C to form tri- and tetracyclic heterocycles possessing a quaternary stereogenic center with a very high level of memory of chirality.     

Electron affinities of biscyclopentadienyl and phospholyl uranium(IV) borohydride complexes: Experimental and DFT studies

Electron affinities (EAs) of a series of biscyclopentadienyl and phospholyl uranium(IV) complexes L₂U(BH₄)₂ [L₂ = Cp₂, (tmp)₂, (tBuCp)₂, (Cp*)(tmp) and Cp*₂] related to the U(III)/U(IV) redox system were calculated using relativistic Density Functional Theory (DFT) based methods coupled with the Conductor-like Screening Model for Real Solvents (COSMO-RS) approach. Electrochemical measurements of half-wave potentials in solution (tetrahydrofuran THF) were carried out for all these compounds under the same rigorous conditions. A good correlation (r² = 0.99) is obtained between the calculated EA values, at the ZORA/BP86/TZ2P level, and the half-wave reduction potentials measured by electrochemistry. The investigations bring to light the importance of spin-orbit coupling and solvent effect and the use of a large basis set in order to achieve such a good agreement between theory and experiment. The study confirms the instability of the Cp₂U(BH₄)₂ complex during the reduction process. The influence of the substituted aromatic ligand L₂, namely their electron donating ability, on EA was studied. The role of involved orbitals (singled occupied molecular orbital –SOMO– of anionic species or lowest unoccupied molecular orbital –LUMO– of neutral species) in the redox process was revealed.     

Supercritical fluid chromatography hyphenated with twin comprehensive two-dimensional gas chromatography for ultimate analysis of middle distillates

This paper reports the conditions of online hyphenation of supercritical fluid chromatography (SFC) with twin comprehensive two-dimensional gas chromatography (twin-GC × GC) for detailed characterization of middle distillates; this is essential for a better understanding of reactions involved in refining processes. In this configuration, saturated and unsaturated compounds that have been fractionated by SFC are transferred on two different GC × GC columns sets (twin-GC × GC) placed in the same GC oven. Cryogenic focusing is used for transfer of fractions into the first dimension columns before simultaneous GC × GC analysis of both saturated and unsaturated fractions. The benefits of SFC–twin-GC × GC are demonstrated for the extended alkane, iso-alkane, alkene, naphthenes and aromatics analysis (so-called PIONA analysis) of diesel samples which can be achieved in one single injection. For that purpose, saturated and unsaturated compounds have been separated by SFC using a silver loaded silica column prior to GC × GC analysis. Alkenes and naphthenes are quantitatively recovered in the unsaturated and saturated fractions, respectively, allowing their identification in various diesel samples. Thus, resolution between each class of compounds is significantly improved compared to a single GC × GC run, and for the first time, an extended PIONA analysis of diesel samples is presented.