Contractibility of Efficient Frontier of Simply Shaded Sets

In finite dimensional Euclidean space, we prove the contractibility of the efficient frontier of simply shaded sets. This work extends the result of Peleg [7], which confirms the contractibility of the efficient frontier in the convex case.     

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.     

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>     

Synthesis and structural characterization of new oxorhenium and oxotechnetium complexes with XN2S-tetradentate semi-rigid ligands (X = O, S, N)

Twelve novel oxo-technetium and oxo-rhenium complexes based on N2S2-, N2SO- or N3S-tetradentate semi-rigid ligands have been synthesised and studied herein. By reacting the ligands with a slight excess of suitable [MO]3+ precursor (ReOCl3(PPh3)2 or [NBu4][99gTcOCl4]), the monoanionic complexes of general formula [MO(Ph-XN2S)]- could be easily produced in high yield. The complexes have been characterized by means of IR, electrospray mass spectrometry, elemental analysis, NMR and conductimetry. The crystal structures of [PPh4][ReO(Ph-ON2S)] 1b and [NBu4][99gTcO(Ph-ON2S)] 1c have been established. The [MO]3+ moiety was coordinated via the two deprotonated amide nitrogens, the oxygen and the terminal sulfur atoms in 1b and 1c. In both compounds, the ON2S coordination set is in the equatorial plane, and the complexes adopted a distorted square-pyramidal geometry with an axial oxo-group. The chemical and structural identity of the different prototypic complexes (rhenium, 99gTc complexes and their corresponding 99mTc radiocomplexes) have been also established by a comparative HPLC study.     

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.     

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.     

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.     

Dependence of collision‐induced dissociation energy on molecular degrees of freedom as a means to assess relative binding affinity in multivalent complexes

In collision‐induced dissociation mass spectrometry experiments, the collision energy required for dissociation linearly depends on the degrees of freedom in the precursor ion. The magnitude of the slope of this relationship previously has been shown to qualitatively correlate to the relative binding strength of a noncovalently bound, monovalent complex. The goal of the work presented here is to determine if a similar methodology can be applied for assessing relative binding strengths in multivalent species. We have tested the method on complexes formed from 18‐crown‐6 and a variety of protonated, primary alkylamines, [C_nH_2n+1NH₃]⁺ (n = 9, 12, 14, 16 and 18) and alkyldiamines, [H₃NC_nH_2nNH₃]²⁺ (n = 3, 5, 6, 9 and 12), and compared our results with dissociation energies calculated using density functional theory at the B3LYP/6‐31G* level. We found that the method correctly assessed the stronger crown ether/headgroup interaction in the two divalent species (1:1 and 2:1 complexes formed from the diaminoalkanes) compared with the weaker interaction in the monovalent species (1:1 complexes formed from mono‐aminoalkanes). However, the experimental method could not distinguish between the binding strengths of the two divalent complexes, perhaps because their calculated dissociation energies were quite similar. Our preliminary results suggest that this method could potentially be used for a quick and simple analysis of binding strengths in multivalent species if the binding strengths of the species are significantly different from one another. Copyright © 2011 John Wiley & Sons, Ltd.     

Intramolecular reduction of the nitro group into phosphoraneimine mediated by a rhenium(v) complex. Synthesis and structure of the novel phosphoraneimine oxorhenium(v) complex [ReOCl[o-(PPh3=N)C6H4(NCH2CH2N(CH2CO2H)CH2CO2]

The title compound was synthesised via an unexpected intramolecular reduction of a nitro group in the oxo-Re(v) coordination sphere.     

Design and synthesis of a novel family of semi-rigid ligands: versatile compounds for the preparation of 99mTc radiopharmaceuticals

Synthetic pathways to a range of novel semi-rigid tetradentate ligands, with sulfur, amido or amino donor groups, designed to coordinate technetium 99m have been developed. The technetium-99m complexes have been prepared and their stabilities in serum and by metathesis reaction via cysteine exchange reactions were compared. HPLC comparison of two (99m)Tc-complexes and their rhenium analogues led to the first proof of the nature of our radioactive complexes.