Matrix formulation of the motion equations of a rigid body and identification of the ten inertia characteristics

The motion equations of a rigid body involve ten inertial characteristics: the mass, the mass center position and the inertia matrix. In order to identify these ten inertia characteristics, we propose an approach unifying them in a 4 × 4 positive definite symmetric matrix. The translation vector and the rotation matrix of the rigid body are also gathered in a 4 × 4 matrix. Therefore the motion equations are formulated as an equality between 4 × 4 skew–symmetric matrices: one representing the sum of external forces and torques, the second representing the dynamic force and torque. The identification is performed by a projected conjugate gradient algorithm developped in the 10–dimensional linear space of 4 × 4 symmetric matrices. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Construction of a bipotential for a multivalued constitutive law

Bipotentials are non smooth mechanics tools, which allows modelling various non associative multivalued constitutive laws of dissipative materials (friction contact, soils, cyclic plasticity of metals, damage). We answer the following question: given a graph M representing a material behaviour, is there a bipotential b for which M is the set of (x, y) such that b (x, y) = 〈x, y 〉? We state a simple necessary and sufficient condition for the existence of b. If it is fulfilled, we construct the bipotential. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Density functional theory analysis of the reaction pathway for methane oxidation to acetic acid catalyzed by Pd2+ in sulfuric acid

Density functional theory has been used to investigate the thermodynamics and activation barriers associated with the direct oxidation of methane to acetic acid catalyzed by Pd2+ cation in concentrated sulfuric acid. Pd2+ cations in such solutions are ligated by two bisulfate anions and by one or two molecules of sulfuric acid. Methane oxidation is initiated by the addition of CH4 across one of the Pd-O bonds of a bisulfate ligand to form Pd(HSO4)(CH3)(H2SO4)2. The latter species will react with CO to produce Pd(HSO4)(CH3CO)(H2SO4)2. The most likely path to the final products is found to be via oxidation of Pd(HSO4)(CH3)(H2SO4)2 and Pd(HSO4)(CH3CO)(H2SO4)2 to form Pd(eta2-HSO4)(HSO4)2(CH3)(H2SO4) and Pd(eta2-HSO4)(HSO4)2(CH3CO)(H2SO4), respectively. CH3HSO4 or CH3COHSO4 is then produced by reductive elimination from the latter two species, and CH(3)COOH is then formed by hydrolysis of CH3COHSO4. The loss of Pd2+ from solution to form Pd(0) or Pd-black is predicted to occur via reduction with CO. This process is offset, though, by reoxidation of palladium by either H2SO4 or O2.     

Prenylated xanthone derivatives with antiplasmodial activity from Allanblackia monticola STANER L.C

Further study of the methanol extract of the stem bark of Allanblackia monticola STANER L.C. resulted in the isolation of a new prenylated xanthenedione, designated allanxanthone C, together with the five known xanthones, garciniafuran, tovophyllin A, rubraxanthone, norcowanin and mangostin and one saponin, stigmasterol-3-O-beta-D-glucopyranoside. The structure of the new compound was established by detailed spectroscopic analysis to be 1,2-dihydro-3,6,8-trihydroxy-1,1,7-tri(3-methylbut-2-enyl)xanthen-2,9-dione (3-hydroxyapetalinone C). The methanol extract and pure compounds were tested on two strains of Plasmodium falciparum, F32 (chloroquine sensitive) and FcM29 (chloroquine resistant). The IC50 values obtained ranged from 0.6 to 8.9 microg/ml. Their cytotoxicity was estimated on human melanoma cells (A375) and the cytotoxicity/antiplasmodial ratio was found to be between 15.45 and 30.46. The antimicrobial activities against a range of microorganisms of the crude extract and some of these compounds are also reported.     

Effects of methanol on the thermodynamics of iron(III) [tetrakis(pentafluorophenyl)]porphyrin chloride dissociation and the creation of catalytically active species for the epoxidation of cyclooctene

In a previous study, the authors showed that iron(III) [tetrakis(pentafluorophenyl)]porphyrin chloride [(F20TPP)FeCl] is catalytically inactive for cyclooctene epoxidation by hydrogen peroxide in acetonitrile but is catalytically active if the solvent contains methanol. It was suggested that the precursor to the active species is (F20TPP)Fe(OCH3) in methanol-containing solvents. The present study was aimed at evaluating this hypothesis. (F20TPP)Fe(OCH3) was synthesized and characterized by 1H NMR but was found to be inactive in both acetonitrile and methanol. Further investigation of the interactions of (F20TPP)FeCl with methanol in acetonitrile/methanol mixtures was then carried out using NMR. Two species, characterized by 1H NMR resonances at 82 and 65 ppm, were observed. The first resonance is attributed to the beta-pyrrole protons on molecularly dissolved (F20TPP)FeCl, whereas the second is attributed to beta-pyrrole protons of [(F20TPP)Fe]+ cations that are stabilized by coordination with a molecule of methanol, viz., [(F20TPP)Fe(CH3OH)]+. The relative concentration of [(F20TPP)Fe(CH3OH)]+ increases as the fraction of methanol in the solvent increases, suggesting that methanol facilitates the dissociation of (F20TPP)FeCl into cations and anions. A thermodynamic model of the dissociation is proposed and found to describe successfully the experimental observation over a range of solvent compositions, porphyrin concentrations, and temperatures. UV-visible spectroscopy was also used to validate the developed model. In addition, the observed rate constant for cyclooctene epoxidation was found to be proportional to the concentration of [(F20TPP)Fe(CH3OH)]+ calculated using the thermodynamic model, suggesting that this intermediate is a precursor to the species that catalyzes olefin epoxidation. The catalytic activity of [(F20TPP)Fe(CH3OH)]+ was further confirmed through experiments in which (F20TPP)Fe(OCH3) dissolved in methanol was reacted with HCl(aq). This reaction produced a product with an NMR peak at 65 ppm attributable to [(F20TPP)Fe(CH3OH)]+, and this mixture was found to have activity for cyclooctene epoxidation similar to that of (F20TPP)FeCl dissolved in methanol.     

Forcing and velocity correlations in a vibrated granular monolayer

The role of forcing on the dynamics of a vertically shaken granular monolayer is investigated. Using a flat plate, surprising negative velocity correlations are measured. A mechanism for this anticorrelation is proposed with support from both experimental results and molecular dynamics simulations. Using a rough plate, velocity correlations are positive, and the velocity distribution evolves from a Gaussian at very low densities to a broader distribution at high densities. These results are interpreted as a balance between stochastic forcing, interparticle collisions, and friction with the plate.     

The probabilistic analysis of a greedy satisfiability algorithm

On input a random 3‐CNF formula of clauses‐to‐variables ratio r₃ applies repeatedly the following simple heuristic: Set to True a literal that appears in the maximum number of clauses, irrespective of their size and the number of occurrences of the negation of the literal (ties are broken randomly; 1‐clauses when they appear get priority). We prove that for r₃ < 3.42 this heuristic succeeds with probability asymptotically bounded away from zero. Previously, heuristics of increasing sophistication were shown to succeed for r₃ < 3.26. We improve up to r₃ < 3.52 by further exploiting the degree of the negation of the evaluated to True literal. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2006     

tert-Butyl (phenylsulfonyl)alkyl-N-hydroxycarbamates: the first class of N-(Boc) nitrone equivalents

[reaction: see text] tert-Butyl (phenylsulfonyl)alkyl-N-hydroxycarbamates 1 have been easily prepared from aldehydes and tert-butyl N-hydroxycarbamate in a methanol-water mixture using sodium benzenesulfinate and formic acid. These sulfones 1 behave as N-(Boc)-protected nitrones 4 in the reaction with organometallics to give N-(Boc)hydroxylamines. Some chemical transformations showing their interest as building blocks in organic synthesis are described.     

Indium(I) trifluoromethanesulfonate and other soluble salts for univalent indium chemistry

Herein we report the synthesis, structure and preliminary reactivity studies of a series of unusually soluble indium(i) salts that are improved alternatives to indium(i) halide reagents.