Autour de la conjecture de L. Markus sur les variétés affines

Summary For any subgroupG of (n), we introduce some integer discGn called thediscompacity ofG. This number measures to what extent the closure ofG is not compact. The Markus' conjecture says that a compact affinely flat unimodular manifold is complete. Our main result (called the discompact theorem) is that this conjecture is true under the assumption that the linear holonomy i.e. the parallel transport has discompacity 1. Because discSO(n–1, 1)=1, this ensures that a compact flat Lorentz manifoldM is geodesically complete. Hence, by a previous result of W. Goldman and Y. Kamishima [GK], such aM is, up to finite covering, a solvmanifold. This achieves the proof of a Bieberbach's theorem for compact Lorentz flat manifolds.     

The crystal structure of bis(triphenylphosphine)-(η-cyclohexa-1,3-diene)rhenium trihydride

Bis(triphenylphosphine)(η-cyclohexa-1,3-diene)rhenium trihydride, (Ph₃P)₂(η-C₆H₈)ReH₃ (I) crystallises in the space group C2/c with cell dimensions a 22.76(2), b 10.14(1) c 29.813(6) Å, β 97.69(8)°. The final refinement of 126 variables using 1580 non-zero reflections resulted in a final R value of 0.064. In spite of uncertainties in some of the atomic positions, the structure of I is compatible with a trihydrido diene compound with a distorted pentagonal bipyramidal configuration, rather than with a dihydrido cyclohexenyl compound having an “agostic” CH ? Re interaction. The factors which govern the structure of the complexes (Ph₃P)₂(η-1,3-diene)ReH₃ are discussed.     

Enzymatic synthesis of neopentylpolyol esters in organic media

Utilization of lipases for synthesis of esters of hydrophilic polyols has been investigated. The choice of a suitable solvent is crucial in this type of reaction. An interesting case is fatty acid esters from neopentylpolyols, such as trimethylolpropane, which are of great interest as high temperature lubricants. Enzymatic synthesis of trimethylolpropane tricaprylate was studied as an alternative to chemical manufacturing. Triester production occurred only if the water produced by esterification was continuously removed from the medium. In these condition, kinetics of appearance and transformation of mono-, di- and triesters were determined in order to define optimal conditions.     

Ylures sans sel,evolution en phosphoranes et equilibre ylure ⇌ phosphorane : I Synthese et structure

Synthesis of new salt-free ylids $\text{9}$,$\text{12}$ to $\text{16}$, $\text{19}$, $\text{20}$, $\text{22}$, $\text{27}$ and $\text{29}$ and phoiphoranes $\text{10}$, $\text{17}$, $\text{18}$, $\text{21}$, $\text{23}$, $\text{30}$ to $\text{33}$ by addition of a trivalent phosphorus compound (phosphites and amino-phosphines ) $\text{1}$ to $\text{7}$ with dimethyl acetylencedicartboxylate in presence of a protic trapping reagent are described. The results are consistent with trapping of carbanionic species. In relation with the. cyclic of acyclic structure of the triivalent phosphorus compound and the protic trapping reagent ie : methanol, phenol, carboxylic acid, etc.., several pathways are involved. Clearly), three phenomena are shown : one can obtain an ylid via a phosphorane or conversely a phosphorane via an ylid or an equilibrium Phoiphorane ? ylid. Results are dealing with thermodynamic or kinetically controlled reactions.     

Synthesis and crystal structures of heterobimetallic Fe-Cd,Fe-Zn,and Fe-In complexes containing hemilabile phosphorus/oxygen and silicon/oxygen bridging ligands

The reactions of K[Fe{Si(OMe)₃}(CO)₃(PY)][PY=Ph₂PCH₂C(O)Ph, Ph₂PCH₂C(O)[(-C₅H₄)FeCp] (Cp=⁵-C₅H₅), Ph₂P(CH₂)₂CN] with CdCl₂·2.5H₂O, ZnX ₂ (X=Cl, I) or InCl₃ afforded Fe-Cd-Fe or Fe-M(-X)₂ M-Fe (M=Cd, Zn, In;X=Cl, I) and Fe-InCl₂ complexes. Some of them contain an unusual and labile -²-SiO alkoxysilyl bridge which may be associated with a bridging mode for the ketophosphine ligand (first such example structurally established), thus providing original results in bimetallic chemistry on the intramolecular coordination of oxygendonor functions ofchemically different hemilabile ligands firmly attached to a neighboring metal center. The structures of the trinuclear complex (3), of the chlorobenzene solvate of the tetranuclear complex (4a·C₆H₅Cl) and of [mer-(OC)₃{(EtO)₃Si} (4e) have been determined by X-ray diffraction. Crystals of 3 are orthorhombic, space groupPbcn, witha=19.010(4),b=11.766(5),c=26.998(7)Å, andZ=4. Crystals of4a·C₆H₅Cl are monoclinic, space groupC2/c witha=22.455(3),b=17.680(2),c=16.627(4)Å, =90.80(4)°, andZ=4. Crystals of4e are monoclinic, space groupC2/c witha=25.392(5),b=18.554(6),c=16.28(1)Å, =120.73(3)°, andZ=4. The structures were solved using direct methods and Fourier difference techniques and refined by blocked full-matrix least squares toR=0.035 (R _w =0.049) for 2719 observed reflections, toR=0.042 (R _w =0.056) for 3082 observed reflections, and toR=0.057 (R _w =0.075) for 1850 observed reflections for3, 4a·C₆H₅Cl and4e, respectively. The Fe-Zn complexes (9a), (9b) and (9c) were prepared and characterized by spectroscopic methods.Part 21 in the Series: Complexes with Functional Phosphines. Part 20: P. Braunstein, S. Coco Cea, A. DeCian, and J. Fischer (1992).Inorg. Chem. 31, 4203.     

Preparative and electrochemical investigations on the electron sponge behavior of cobalt telluride clusters: CO substitution in [Co11Te7(CO)10]n- ions (n=1, 2) by PMe2Ph and crystal structure of [Co11Te7(CO)5(PMe2Ph)5

The reaction of the cluster salts [Cp(2*) Nb(CO)(2)](n)[Co(11)Te(7)(CO)(10)] (Cp*=C(5)Me(5); n=1, 2) with excess PMe(2)Ph gave the neutral, dark brown clusters [Co(11)Te(7)(CO)(6)(PMe(2)Ph)(4)] (5) and [Co(11)Te(7)(CO)(5)(PMe(2)Ph)(5)] (6) with 147 metal valence electrons. The new compounds were characterized by IR spectroscopy, elemental analyses, and mass spectrometry. The molecular structure of 6 was determined by X-ray crystallography. Like its precursor anion, it consists of a pentagonal-prismatic [Co(11)Te(7)] core, but with a ligand sphere composed of five CO and five PMe(2)Ph ligands. Detailed electrochemical studies of both reactions reveal that a stepwise substitution of CO ligands in the initial cluster anions takes place leading to intermediate [Co(11)Te(7)(CO)(10-m)(PMe(2)Ph)(m)](n-) ions (m=1-5; n=1, 2). Each of these intermediates is distinguished by at least one oxidation and two reduction waves, giving rise to a total of 21 redox couples and 27 electroactive species. The electron sponge character of the new compounds is particularly pronounced in 5, which exhibits charges n between +1 and -4 corresponding to metal valence electron counts of between 146 and 151.     

Metallic Particles from Complexing Microcapsules Dispersed in a Silica Gel

A new process to control the distribution of metal nanoparticles is proposed. It involves the use of complexing microcapsules obtained by interfacial polycondensation. The latter are hollow spheres constituted of a polymer membrane, containing an insoluble active ingredient, such as a polyacrylic acid, which can complex Co²⁺ ions. These capsules are dispersed in a silica sol followed by thermal treatments and reduction under H₂ which results in metallic Co nanoparticles confined in the capsules domains. The particles do not diffuse in the matrix.     

Half-Projected and Projected Hartree-Fock Calculations for Singlet Ground States. i. four-Electron Atomic Systems

The half-projected Hartree-Fock function (HPHF ) for singlet states is defined as a linear combination of two Slater determinants, which contains only spin eigenfunctions with even quantum number. Using a self-consistent procedure based on the generalized Brillouin's theorem, the RHF , HPHF and PHF functions are deduced for the ground states of the Li^?, Be, B⁺, and C²⁺ systems, in a limited basis set. It is found that the HPHF function yields better energy values than the RHF function, very close to that of the PHF one. The HPHF scheme seems thus to be useful as a substitute for the PHF model, specially in the case of large electronic systems in which the latter method becomes unmanageable.     

In vitro determination of the release kinetics of peptides and free amino acids during the digestion of food proteins

The kinetics of peptide release during in vitro digestion of 4 protein sources (casein, cod protein, soy protein, and gluten) were investigated. Samples were sequentially hydrolyzed with pepsin (30 min) and pancreatin (2, 4, or 6 h) in a dialysis cell with continuous removal of digestion products. Nondialyzed digests were fractionated by ion-exchange chromatography and ultrafiltration. Animal proteins were digested at a greater rate than plant proteins. Target amino acids of specific enzymes appeared more rapidly in the dialyzed fractions when compared to other amino acids. Throughout the hydrolysis, nondialyzed digests contained a higher proportion of peptide mixtures with basic-neutral properties. Except for gluten, peptide fractions with molecular weights that exceeded 10 kDa (basic-neutral, BN > 10) were rapidly hydrolyzed during the first 2 h of pancreatin digestion. The kinetics of release and the composition of peptide fractions were different when the protein sources were compared. The analysis of amino acids revealed that threonine and proline proportions were relatively high in BN > 10 and in peptide fractions with molecular weight between 10-1 kDa (BN 10-1), while tyrosine, phenylalanine, lysine, and arginine predominated in the low molecular weight (<1 kDa) fractions. More resistant peptides were generally rich in proline and glutamic acid. The role of in vitro digestion assays in dietary protein quality evaluation is discussed.     

One-dimensional quantum description of the bending vibrations of HCN/CNH for high values of the total angular momentum

For high values of the quantum number of the total angular momentum J (up to J = 20), quantum mechanical eigenstates (eigenvalues and eigenfunctions) are calculated by the method of Gatti et al. (J. Mol. Spectrosc. 181 (1997) 403) for the bending deformations of HCN and CNH. In particular, we have examined the l-type resonances in highly excited rovibrational states within the framework of a one-dimensional model, i.e. along the reaction pathway for the isomerization reaction HCN/CNH. The potential energy surface used is that of Bowman et al. (J. Chem. Phys. 99 (1993) 308).