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>     

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.     

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.     

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.     

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.     

On the Development of Titanium κ1-Amidinate Complexes,Commercialized as Keltan ACE™ Technology,Enabling the Production of an Unprecedented Large Variety of EPDM Polymer Structures

ARLANXEO Elastomers has developed and commercialized Keltan ACE™ technology, a class of half-sandwich cyclopentadienyl κ¹-amidinate metal complexes, which are extremely active for the production of first-class ethylene/propylene/diene copolymers (EPDM). In this review, the development and some of the key features of the Keltan ACE™ catalyst system are presented. Many different ACE catalysts have been synthesized over the past years, including bridged and bimetallic catalysts. With Keltan ACE™, a complete range of EPDM products with similar polymer characteristics as their Ziegler–Natta (ZN) counterparts can be produced, including variations containing very high 5-ethylidene-2-norbornene (ENB) contents, controlled long chain branching, very high molecular weight, as well as oil-extended products. Moreover, other EPDM structures can be polymerized. The Keltan ACE™ catalyst technology also allows the production of EPDMs with very high amounts of dicyclopentadiene (DCPD) or 5-vinyl 2-norbornene (VNB) without excessive gelation and reactor fouling, that is, products that cannot or are extremely difficult to obtain via classical ZN catalysis. In a next step, high-VNB-EPDM can be postreactor modified, for example, via metathesis chemistry. In addition, EPDM polymers with a very broad or even bimodal molecular weight distribution can be obtained in a single reactor with certain ACE catalyst structures at particular activator/precatalyst ratios. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2017 , 55, 2877–2891