Convexes divisibles III

Let Δ₀ be a group of finite type and FΔ₀⊂Hom(Δ₀,PGL(Rm)) be the subset of faithful representations for which there exists a properly convex Δ₀-invariant open subset Ω in P(Rm) such that the quotient Δ₀\Ω is compact. Koszul has proved in [J.L. Koszul, Déformation des connexions localement plates, Ann. Inst. Fourier 18 (1968) 103-114] that this subset FΔ₀ is open. We describe the closure of FΔ₀. As a consequence, we show that this subset FΔ₀ is closed if and only if the virtual center of Δ₀ is trivial. This condition is satisfied if and only if FΔ₀ contains a strongly¹ irreducible representation.     

New Syntheses of Retinal and Its Acyclic Analog γ‐Retinal by an Extended Aldol Reaction with a C6 Building Block That Incorporates a C5 Unit after Decarboxylation. A Formal Route to Lycopene and β‐Carotene

Since the C₁₅ β‐end‐group aldehyde 10 ((β‐ionylidene)acetaldehyde), an excellent intermediate in the syntheses of retinoids, can be synthesized in many ways from β‐ionone, and since the corresponding acyclic C₁₅ ψ‐end‐group aldehyde 5 can easily be synthesized from citral ( 1 ) (Scheme 3), we applied the C₁₅+C₅ route to the syntheses of γ‐retinal ((all‐E)‐ 8 ) (Scheme 3) and retinal ((all‐E)‐ 13 ) (Scheme 4), and therefore, by coupling (2×C₂₀→C₄₀), to the preparation of lycopene ( 14 ) and β‐carotene ( 15 ) (Scheme 5). Our new syntheses of retinal ((all‐E)‐ 13 ) and γ‐retinal ((all‐E)‐ 8 use an extended aldol reaction with a C₆ building block that incorporates a C₅ unit after decarboxylation.     

Atypical Oxidation Reaction by Thionyl Chloride: Easy Two‐Step Synthesis of N‐Alkyl‐1,4‐dithiines

Easy two‐step synthesis of a series of dithiines was performed from succinic anhydride via cyclization of the corresponding 4‐(alkylamino)‐4‐oxobutanoic acids (succinamic acids). The reaction, carried out in polar aprotic solvents, gave 4,8‐dithiine‐indacene‐1,3,5,7‐tetraones (diimides 3) via 3,7‐bis‐4,8‐dithia‐indacene‐1,5‐diones (diisoimides 2), which could be isolated. Surprisingly, in this reaction, thionyl chloride appeared as an oxidant, and this process seemed to be useful for the syntheses of S‐containing heterocyclic compounds such as 1,4‐dithiins. A mechanistic pathway was considered.     

Synthesis of a New C-15 Phosphorus Ylide Used for the Preparation of Some β-End-Group Retinoid Derivatives

A synthesis of a new C-15 phosphorus ylide from a C-14 enaminone is reported. This reagent, which undergoes selective 1,2- or 1,4-additions with saturated and unsaturated aldehydes, may find some synthetic use for the preparation of β-end-group retinoid derivatives.     

Maximal Hilbert Functions

The set of Hilbert functions of standard graded algebras is considered as a partially ordered set under numerical comparison. For the set of algebras H(d, e₀), of a given dimension d and multiplicity e₀, we describe the requirements its maximal elements must satisfy; under fairly general conditions, the extremal functions arise from Cohen-Macaulay algebras. We also examine the subset H(d, e₀, e₁), of those functions whose first two coefficients of their Hilbert polynomials are assigned. Finally, we show how these results and the use of certain extended multiplicities can be used to prove finiteness theorems for the number of corresponding functions.     

Integrated circuit thermal analysis: A new thermal technique for polymer characterization

Polymer characterization has largely helped in the development of thermal analyzers and calorimeters, based mainly on the thermocouple technology, or more recently the semiconductor technology. With the use of an integrated silicon thermopile as a detector, a new thermal technique is appearing, to give more possibilities of investigations in the field of polymeric materials. Combining high sensitivity and use of small amount of sample, the originality of the new design comes from its low power consumption, giving rise to a portable version of the instrument. With such a concept, the thermal analysis technique is carried on the industrial site, to perform online measurements.Melting and crystallization, glass transition, control of reticulation are a promising field of applications for the characterization of polymeric materials on industrial sites.This revised version was published online in November 2005 with corrections to the Cover Date.     

Catalytic wet air oxidation of oleic acid on ceria-supported platinum catalyst.effect of pH

Summary Catalytic wet air oxidation (CWAO) of oleic acid was carried out in a batch reactor on platinum supported ceria catalyst (Pt/CeO₂). Oleic acid is a water insoluble linear unsaturated fatty acid of 18 carbon atoms. To increase the homogeneity of the solution by saponification, the influence of NaOH additions in oleic acid CWAO mechanism and catalyst performances have been investigated. The oxidation of such molecule occurs by two types of mechanisms: successive carboxy-decarboxylation which leads essentially to CO₂and/or C-C bonds splitting in the alkyl chain inducing a high formation of acetic acid. With or without NaOH, the 5%Pt/CeO₂catalyst is active in the conversion of oleic acid and selective to carbon dioxide. In alkaline medium, oleic acid is initially saponified which increases the solubility of the reactant before it to be oxidized. Finally the oxidation is slightly delayed by the presence of NaOH. The catalyst characterizations show no significant difference before and after reaction.</o:p>     

First examples of neutral rhenium(V) complexes with a novel semi-rigid ligand containing a P,N,N,S donor atom set: Synthesis,characterisation and crystal structure

A new PN₂S ligand, N-[2-(diphenylphosphino)phenyl]-2-[(S-trityl)acetylamino]ethanamide [Ph-P(Ph₂)N₂S(Trt)], was synthesised and reacted with Re^V precursors. The reaction of both tritylated and detritylated ligands with ReOCl₃(PPh₃)₂ gave the same expected neutral complex [ReO{Ph-P(Ph₂)N₂S}] (4) in good yield. An unexpected neutral and diamagnetic species, [ReN{Ph-P(Ph₂)N₂S(Trt)}] (5), has been isolated during the complexation of the tritylated ligand with ReNCl₂(PPh₃)₂. The complexes, characterized by classical spectroscopic methods and X-ray analysis for 4, are the first examples of neutral semi-rigid-PN₂S rhenium(V) complexes.     

Amino acid-pyrrole N-conjugates; a new class of antioxidants II. Effectiveness of singlet oxygen quenching by luminescence measurements

The pyrrole-amino acid and peptide N-conjugates synthesized from tyrosine, histidine and glutathione very effectively quench the 1270 nm singlet oxygen luminescence, at rates ranging from 10⁸ to 10⁹ M⁻¹ s⁻¹. Nuclear magnetic resonance spectroscopy suggests that the electron-donating properties of the methyl groups after 2,5-dimethyl substitution on the pyrrole ring are probably an important determinant of the reactivity of singlet oxygen with the N-conjugate of glutathione. However, intramolecular interactions between the pyrrole ring and the side chain may also modulate the reactivity of the antioxidant as suggested by absorption and fluorescence spectroscopies carried out on tyrosine derivatives. Efficient fluorescence quenching of the phenol ring by the pyrrole ring occurs in the tyrosine derivatives. The reactivities of these antioxidants with ¹O₂ are comparable in methanol, ethanol and D₂O.     

Ueber die Bestimmung des Gerbstoffs in Gerbstoffmaterialien

Ohne Zusammenfassung