Analysis of a Poisson system with boundary conditions

We consider a class of problems originating from a Raman laser amplification model, for which the equations can be written as a Poisson system with boundary conditions. Once reformulated, this system becomes an integro-differential equation that we study here in some detail. In particular, we show the existence of a smooth solution under general assumptions, and prove its uniqueness for boundary values that are not too far apart. Eventually, we completely solve the question of uniqueness for systems of dimensions one and two. To cite this article: F. Castella et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Synthesis of (-)-ilimaquinone via a radical decarboxylation and quinone addition reaction

[reaction: see text] A stereoselective synthesis of (-)-ilimaquinone (4) is presented. The synthetic strategy is based on a novel radical decarboxylation and quinone addition methodology that produces quinone 7 from reaction of thiohydroxamic acid derivative 8 with benzoquinone (9). Final functionalization of 7 to ilimaquinone (4) is achieved by exploring the electronic effects of the residual thiopyridyl group.     

Ultra performance liquid chromatography – mass spectrometry studies of formalin‐induced alterations of human brain lipidome

The development of ‘omics’ sciences offers new opportunities for the study of neurodegenerative diseases but increases at the same time the sample demand on brain banks that collect and store valuable human post‐mortem tissue. Our study aims to evaluate in lipidomics the potential of formalin‐fixed tissue compared with the cryopreservation method, considered as the gold standard for biochemical research. Two complementary liquid chromatography/mass spectrometry analytical platforms were used on the basis of hybrid quadrupole time‐of‐flight and triple quadrupole mass spectrometers. Untargeted fingerprinting, semitargeted profiling of specific lipid classes and targeted monitoring of lipid species were performed in formalin‐fixed and cryopreserved samples to provide detailed information at the molecular level on the formalin‐induced alterations of the brain tissue. In vitro incubations of lipid standards were also performed to further describe the degradation processes induced by formaldehyde. Phospholipid compounds were found to be extensively hydrolysed, whilst the sphingolipid ones were preserved. N‐methylation and N‐formylation of amine‐containing phospholipids have also been evidenced. These findings show that the potential detrimental effect of formalin on the analytes of interest must be taken into account when analysing formalin‐fixed samples. Copyright © 2014 John Wiley & Sons, Ltd.     

CoI-Catalyzed Barbier Reactions of Aromatic Halides with Aromatic Aldehydes and Imines

The reductive Barbier coupling of aromatic halides and electrophiles has been achieved using a CoBr₂/1,10-phenanthroline catalytic system and over stoichiometric amounts of zinc. The reaction displayed a broad scope of substrates, including (hetero)aryl chlorides as pro-nucleophiles and aldehydes or imines as electrophiles, leading to diarylmethanols and diarylmethylamines in moderate to excellent yields, respectively.     

Landau Damping in Sobolev Spaces for the Vlasov-HMF Model

We consider the Vlasov-HMF (Hamiltonian Mean-Field) model. We consider solutions starting in a small Sobolev neighborhood of a spatially homogeneous state satisfying a linearized stability criterion (Penrose criterion). We prove that these solutions exhibit a scattering behavior to a modified state, which implies a nonlinear Landau damping effect with polynomial rate of damping.     

Energy Conservation with Non-Symplectic Methods: Examples and Counter-Examples

Energy conservation of numerical integrators is well understood for symplectic one-step methods. This article provides new insight into energy conservation with non-symplectic methods. Sufficient conditions and counter-examples are presented. AMS subject classification (2000) 65L06, 65P10, 37J99.Submitted June 2004. Accepted October 2004. Communicated by Syvert Nørsett.     

Excavations in molecular crystals

Single crystals built from porous molecular networks can react with agents that penetrate the crystals, cleave fragments from the network, and thereby increase the volume available for guests, all without loss of crystallinity.     

An Algebraic Approach to Invariant Preserving Integators: The Case of Quadratic and Hamiltonian Invariants

In this article, conditions for the preservation of quadratic and Hamiltonian invariants by numerical methods which can be written as B-series are derived in a purely algebraical way. The existence of a modified invariant is also investigated and turns out to be equivalent, up to a conjugation, to the preservation of the exact invariant. A striking corollary is that a symplectic method is formally conjugate to a method that preserves the Hamitonian exactly. Another surprising consequence is that the underlying one-step method of a symmetric multistep scheme is formally conjugate to a symplectic P-series when applied to Newton’s equations of motion.