Convergent Star Product Algebras on ‘ax+b’

We define nontempered (exponential growth) function spaces on the Lie group ax+b which are stable under some left-invariant (convergent) star product. The techniques used to achieved the latter come from symmetric spaces geometry and star representation theory.     

Characterization of nonstoichiometric nickel manganite spinels NixMn3−x□3δ/4O4+δ by temperature programmed reduction

Cation deficient spinels Ni_xMn_3−x□_3δ/4O_4+δ (0≤x≤1) have been prepared by thermal decomposition of mixed oxalates Ni_x/3Mn_(3−x)/3(C₂O₄)·nH₂O in air at 623 K. They have been characterised by temperature programmed reduction (TPR) under H₂, the reaction being followed by gravimetric and powder X-ray diffraction measurements. It has been shown that TPR proceeds in several steps. The first steps correspond to the loss of nonstoichiometric oxygen leading to the formation of a stoichiometric oxide. During the following stages the manganese cations are reduced, causing the spinel structure to be destroyed, and the formation of solid solution of NiO in a cubic MnO. Subsequently, Ni²⁺ cations undergo a reduction to metallic nickel, and, finally, a mixture of nonstoichiometric MnO_1−δ and metallic nickel is formed. These oxides contain a high level of vacancies which vary with the nickel content with a maximum of δ≈1 near x=0.6. This nonstoichiometry is ascribed both to the presence of Ni³⁺ and excess of Mn⁴⁺.     

Reactions de photoaddition de benzo[b]selenophenes avec l'acetylene dicarboxylate de methyle et avec le dichloro-1,2 ethylene

Photoirradiated in presence of acetophenone, benzo[b]selenophene and its 3-methyl derivative add to dimethyl acetylenedicarboxylate. In each ease, the primary reaction product is unstable and has not been isolated. Photoexeited in its triplet state (the energy of which is in the neighbourhood of 69 $\text{kcal}\text{mole}$) benzo[b]selenophene and its 2- and 3-methyl, 2,3 dimethyl, 3 acetoxy and 2-methyl-3-acetoxy derivatives add to 1,2 dichloroethylene leading to cyclobutanes. Neither cyclo-addition occurs in absence of photosensitiser. Single-crystal X-ray analysis gave the structures of the two adducts of 3-acetoxybenzo[b]selenophene with trans-1,2-dichloroethylene. In both compounds the chlorine atoms are trans.     

Identification of a chemical indicator of the rupture of 1,4-β-glycosidic bonds of cellulose in an oil-impregnated insulating paper system

In this study, headspace gas chromatography/mass spectrometry has been used to assess the volatile by-products generated by the ageing of oil-impregnated paper insulation of power transformers. Sealed-glass ampoules were used to age under oxidative conditions 0.5-g specimens of insulating paper in 9 mL of inhibited mineral oil in a temperature range of 60–120 °C and moisture of 0.5, 1 and 2% (w/w). A linear relationship between one of the oil-soluble degradation by-products, i.e. methanol, and the number of ruptured 1,4-β-glycosidic bonds of cellulose, regardless of the type of paper (ordinary Kraft or thermally-upgraded (TU) Kraft paper), was established for the first time in this field. Ageing at 130 °C of model compounds of the Kraft paper constituents (α-cellulose, hemicellulose and lignin) and two cellulosic breakdown by-products (D-(+)-glucose and 1,6-anhydro-β-d-glucopyranose) confirmed that the α-cellulose degradation was mostly responsible for the presence of this molecule in the system. Furthermore, additional 130 °C-tests with six different papers and pressboard samples under a tight control of initial moisture indicated that at least one molecule of methanol is formed for each rupture of 1,4-β-glucosidic bond of the molecular chains. Stability tests showed that the ageing indicator is stable under the oxygen and temperature conditions of open-breathing transformers. The presence of methanol was detected in 94% of oil samples collected from over than 900 in-service pieces of equipment, confirming the potential for this application. Lastly, the tests have shown that oil-oxidation by-products and TU-nitrogenous agents modify the methanol partitioning coefficients in the paper/oil/air system, which makes their study essential over a range of field conditions encountered by power transformers. Results are presented and discussed in comparison with 2-furfuraldehyde, which is the current reference in the domain.     

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.