Geometry in preduals of spaces of 2-homogeneous polynomials on Hilbert spaces

Let H be a (real or complex) Hilbert space. Using spectral theory and properties of the Schatten–Von Neumann operators, we prove that every symmetric tensor of unit norm in HoH is an infinite absolute convex combination of points of the form xox with x in the unit sphere of the Hilbert space. We use this to obtain explicit characterizations of the smooth points of the unit ball of HoH .

The Co-Entrapment of a Homogeneous Catalyst and an Ionic Liquid by a Sol-gel Method: Recyclable Ionogel Hydrogenation Catalysts

Molecular hydrogenation catalysts have been co-entrapped with the ionic liquid [Bmim]NTf(2) inside a silica matrix by a sot-gel method. These catalytic ionogels have been compared to simple catalyst-doped glasses, the parent homogeneous catalysts, commercial heterogeneous catalysts, and Rh-doped mesoporous silica. The most active ionogel has been characterised by transmission electron microscopy, X-ray photoelectron spectroscopy, and solid state NMR before and after catalysis. The ionogel catalysts were found to be remarkably active, recyclable and resistant to chemical change.

Solventless continuous flow homogeneous hydroformylation of 1-octene

The hydroformylation of 1-octene under continuous flow conditions is described. The system involves dissolving the catalyst, made in situ from [ Rh(acac)(CO)(2)] (acacH = 2,4- pentanedione) and [RMIM][TPPMS] ( RMIM = 1-propyl (Pr), 1-pentyl (Pn) or 1-octyl (O)-3-methyl imidazolium, TPPMS = Ph2P(3-C6H4SO3)), in a mixture of nonanal and 1-octene and passing the substrate, 1-octene, together with CO and H-2 through the system dissolved in supercritical CO2 (scCO(2)). [PrMIM][TPPMS] is poorly soluble in the medium so heavy rhodium leaching (as complexes not containing phosphine) occurs in the early part of the reaction. [PnMIM][ PPMS] affords good rates at relatively low catalyst loadings and relatively low overall pressure (125 bar) with rhodium losses <1 ppm, but the catalyst precipitates at higher catalyst loadings, leading to lower reaction rates. [OMIM][ TPPMS] is the most soluble ligand and promotes high reaction rates, although preliminary experiments suggested that rhodium leaching was high at 5-10 ppm. Optimisation aimed at balancing flows so that the level within the reactor remained constant involved a reactor set up based around a reactor fitted with a sight glass and sparging stirrer with the CO2 being fed by a cooled head HPLC pump, 1-octene by a standard HPLC pump and CO/H-2 through a mass flow controller. The pressure was controlled by a back pressure regulator. Using this set up, [OMIM][ TPPMS] as the ligand and a total pressure of 140 bar, it was possible to control the level within the reactor and obtain a turnover frequency of ca. 180 h(-1). Rhodium losses in the optimised system were 100 ppb. Transport studies showed that 1-octene is preferentially transported over the aldehydes at all pressures, although the difference in mol fraction in the mobile phase was less at lower pressures. Nonanal in the mobile phase suppresses the extraction of 1-octene to some extent, so it is better to operate at high conversion and low pressure to optimise the extraction of the products relative to the substrate. CO and H2 in the mobile phase also suppress the extraction effciency by as much as 80%.

Heat capacities of common ionic liquids - Potential applications as thermal fluids?

Ionic liquids generally have wide liquid ranges and negligible vapour pressures; attractive characteristics for use as media for heat transfer and short heat term storage systems. This review of the limited literature available shows that many common ionic liquids have heat capacities, and thus potential thermal energy storage capabilities, that surpass those of commercial hot-oil and synthetic heat transfer fluids and suggests that there is a role for ionic liquids as novel thermal fluids.

Homogeneous habitat can meet the discrete and varied resource requirements of hares but may set an ecological trap

In common with other farmland species, hares (Lepus spp.) are in widespread decline in agricultural landscapes due to agricultural intensification and habitat loss. We examined the importance of habitat heterogeneity to the Irish hare (Lepus timidus hibernicus) in a pastoral landscape. We used radio-tracking during nocturnal active and diurnal inactive periods throughout one year. In autumn, winter and spring, hares occupied a heterogeneous combination of improved grassland, providing food, and Juncus-dominated rough pasture, providing refuge. In summer, hares significantly increased their use of improved grassland. This homogeneous habitat can fulfil the discrete and varied resource requirements of hares for feeding and shelter at certain times of year. However, improved grassland may be a risky habitat for hares as silage harvesting occurs during their peak birthing period of late spring and early summer. We therefore posit the existence of a putative ecological trap inherent to a homogeneous habitat of perceived high value that satisfies the hares' habitat requirements but which presents risks at a critical time of year. To test this hypothesis in relation to hare populations, work is required to provide data on differential leveret mortality between habitat types.

Supercritical fluids: A route to palladium-aerogel nanocomposites

Supercritical carbon dioxide (scCO(2)) is used to prepare novel silica aerogel composites containing nanoparticles of palladium. The material produced has been found to exhibit a Pd loading of 8% by wt. The particles deposited fit within two discrete size ranges of

CsF and alumina: A mixed homogeneous-heterogeneous catalytic system for the transesterification of sunflower oil with methanol

The activity and nature (i e heterogeneous and/or homogeneous) of catalysts based on CsF supported on alpha-Al2O3 were investigated for the transesterification of vegetable oil with methanol. The effect of the activation temperature, CsF loading and the reusability in a recirculating reactor were first studied CsF/alpha-Al2O3 exhibited the highest activity for a CsF loading of 0 6 mmol/g and when activated at 120 degrees C An important aspect of this study is the effect of CsF leaching into the reaction mixture, which is attributed to the high solubility of CsF in methanol, leading to a complete loss of activity after one run It was Identified that the activity of the catalyst resulted from a synergy between alumina and dissolved CsF, the presence of both compounds being absolutely necessary to observe any conversion The use of an alumina with a higher surface area resulted in a far greater reaction rate, showing that the concentration of surface site on the oxide (probably surface hydroxyl) was rate-limiting in the case of the experiments using the low surface area alpha-Al2O3 This work emphasizes that combined homogeneous-heterogeneous catalytic systems made from the blending of the respective catalysts can be used to obtain high conversion of vegetable oil to biodiesel. Despite the homogeneous/heterogeneous dual character, such a catalytic system may prove valuable in developing a simple and cost-effective continuous catalytic process for biodiesel production (C) 2010 Elsevier B V All rights reserved