Une classe de séries trigonométriques qui convergent presque partout vers zéro

Sans résumé     

First Total Syntheses of Novel Non-Enzymatic Polyunsaturated Fatty Acid Metabolites and Their Identification in Edible Oils

Oxidative stress (OS) is an in vivo process leading to free radical overproduction, which triggers polyunsaturated fatty acid (PUFA) peroxidation resulting in the formation of racemic non-enzymatic oxygenated metabolites. As potential biomarkers of OS, their in vivo quantification is of great interest. However, since a large number of isomeric metabolites is formed in parallel, their quantification remains difficult without primary standards. Three new PUFA-metabolites, namely 18-F_3t-isoprostane (IsoP) from eicosapentaenoic acid (EPA), 20-F_4t-neuroprostane (NeuroP) from docosahexaenoic acid (DHA) and 20-F_3t-NeuroP from docosapentaenoic acid (DPA_n-3) were synthesized by two complementary synthetic strategies. The first one relied on a racemic approach to 18(RS)-18-F_3t-IsoP using an oxidative radical anion cyclization as a key step, whereas the second used an enzymatic deracemization of a bicyclo[3.3.0]octene intermediate obtained from cyclooctadiene to pursue an asymmetric synthesis. The synthesized metabolites were applied in targeted lipidomics to prove lipid peroxidation in edible oils of commercial nutraceuticals.     

Foliations invariant under Lie group transverse actions

In this paper we study (smooth and holomorphic) foliations which are invariant under transverse actions of Lie groups. Authors’ address: Alexandre Behague and Bruno Scárdua, Instituto de Matemática, Universidade Federal do Rio de Janeiro, Caixa Postal 68530, 21945-970 Rio de Janeiro, RJ, Brazil     

Odd character correspondences in solvable groups

Let G be a finite solvable group, p be some prime, let P be a Sylow p-subgroup of G, and let N be its normalizer in G. Assume that N has odd order. Then, we prove that there exists a bijection from the set of all irreducible characters of G of degree prime to p to the set of all the irreducible characters of degree prime to p of N such that it preserves ± the degree modulo p, the field of values, and the Schur index over every field of characteristic zero. This strengthens a more general recent result [A. Turull, Character correspondences in solvable groups, J. Algebra 295 (2006) 157–178], but only for the case under consideration here. In addition, we prove some other strong character correspondences that have very good rationality properties. As one consequence, we prove that a solvable group G has a non-trivial rational irreducible character with degree prime to p if and only if the order of the normalizer of a Sylow p-subgroup of G has even order.     

Ultraviolet photodissociation of protonated pharmaceuticals in a pressurized linear quadrupole ion trap

Ultraviolet photodissociation (UVPD) was evaluated as a technique for generating ion fragmentation information that is alternative and/or complementary to the information obtained by collision‐induced dissociation (CID). Ions trapped in a pressurized linear ion trap were dissociated using a 355 nm or a 266 nm pulsed laser. Comparisons of UVPD and CID spectra using a set of aromatic chromophore‐containing compounds (desmethyl bosentan, haloperidol, nelfinavir) demonstrated distinct characteristic fragmentation patterns resulting from photodissociation. The wavelength of light and the pressure of the buffer gas in the UVPD cell are important parameters that control fragmentation pathways. The wavelength effect is related to the absorption cross section, location of the chromophore and the energy carried by one photon. Thus, UV irradiation wavelength affects fragmentation pathways as well as the fragmentation rate. The pressure effect can be explained by collisional quenching of ‘slow’ fragmentation pathways. We observed that higher pressure of the buffer gas during UVPD experiments highlights unique fragment ions by suppressing slow fragmentation pathways responsible for CID‐like fragmentation patterns. Copyright © 2010 John Wiley & Sons, Ltd.