Superrigid subgroups of solvable Lie groups

Let be a discrete subgroup of a simply connected, solvable Lie group , such that has the same Zariski closure as . If is any finite-dimensional representation of , we show that virtually extends to a continuous representation of . Furthermore, the image of is contained in the Zariski closure of the image of . When is not discrete, the same conclusions are true if we make the additional assumption that the closure of is a finite-index subgroup of (and is closed and is continuous).

     

Use of environmentally-responsive smart glasses in controlled release: Diffusion of molecules under applied stimuli

The use of organosilica sol-gels as environmentally-responsive materials for stimuli-controlled release of encapsulated molecules is reported. These sol-gels exhibit bulk volume changes with respect to applied stimuli such as pH, temperature, salt, and solvents. These volume changes result in expulsion/intake of solvent molecules which can be utilized as a means for externally-regulated release and delivery of dopant molecular entities. For these materials, which undergo a volume transition in response to environmental changes, the magnitude and response time of the material is related to diffusion of solvent molecules in and out of the material. The release of encapsulated molecules and diffusion of solvent accompanies the volume transitions, which can be initiated by changes in temperature or ionic concentration. The kinetics and mechanism of volume changes of organosilica network consisting of hydrophilic and hydrophobic segments are investigated which provide critical insights into the nature of underlying factors that influence release of encapsulated entities. The diffusion coefficient of water molecules in these gels is determined to be considerably faster as compared to organic polymer gels and silica gels indicating rapid volume responses which can be utilized as efficient trigger mechanisms for release of molecules. The results validate preliminary feasibility of stimuli-controlled release of molecules with these gels initiated by the diffusional flow of solvent established by the volume changes.     

Determination of oestrogen concentrations in bovine plasma by a recombinant oestrogen receptor-reporter gene yeast bioassay.

A recombinant cell yeast bioassay (RCBA) was applied to the generic measurement of bovine plasma oestrogen concentration. Samples were prepared by diethyl ether extraction of plasma following addition of [3H]17 beta-oestradiol as internal standard; organic and aqueous phases were separated by freezing (recovery 97.1 +/- 0.7%) and dried extract reconstituted in culture medium (recovery 31.4 +/- 4.5%). Plasma oestrogen concentrations were measured by incubation of extracts with yeast containing a stable human oestrogen receptor (hER) and a reporter construct comprising an hER response element regulating beta-galactosidase expression. The linearity of response for the analysis of spiked plasma samples using the RCBA, following corrections, is described by y = 0.8994x - 0.111 (r2 = 0.9776, P < 0.0001). Inter-assay variation for endogenous oestrogen was 11.5% for > 1 pg ml-1. Plasma oestrogen concentrations for intact (n = 5) and castrated (n = 3) males were < 0.5 pg ml-1, and 3.7 +/- 2.6 pg ml-1 for luteal phase females (n = 10). Analysis by RCBA of sequential samples from heifers during the reproductive cycle failed to detect the pre-ovulatory increase in plasma 17 beta-oestradiol as determined by radioimmunoassay (RIA) (maximal concentrations 2.09 +/- 2.1 pg ml-1 and 32.6 +/- 14.6 pg ml-1, respectively). Interestingly, when samples were hydrolysed using Helix pomatia glucuronidase the RCBA gave concentrations (29.5 +/- 8.9 pg ml-1) not significantly different to those obtained by RIA. These preliminary findings suggest that a substantial proportion of plasma oestrogen during the pre-ovulatory period may be conjugated. These data indicate the potential of the RCBA to measure biologically active and physiological levels of plasma oestrogens in cattle. One potentially valuable application of this generic oestrogen assay could be in surveillance programmes to detect illegal use of anabolic oestrogens in live-stock where the identity of the analyte may be unknown.     

In situ synchrotron SAXS/WAXD studies during melt spinning of modified carbon nanofiber and isotactic polypropylene nanocomposite

The structural development of a nanocomposite, containing 95 wt% isotactic polypropylene (iPP) and 5 wt% modified carbon nanofiber (MCNF), during fiber spinning was investigated by in situ synchrotron small-angle X-ray scattering (SAXS) and wide-angle X-ray diffraction (WAXD) techniques. The modification of carbon nanofibers (CNFs) was accomplished by a chemical surface treatment using in situ polymerization of olefin segments to enhance its compatibility with iPP, where the iPP/MCNF nanocomposite was prepared by twostep blending to ensure the dispersion of MCNF. X-ray results showed that at low spin-draw ratios, the iPP/MCNF nanocomposite fiber exhibited much higher iPP crystalline orientation than the control iPP fiber. At higher spin-draw ratios, the crystalline orientation of the nanocomposite fiber and that of the pure iPP fiber was about the same. The crystallinity of the composite fiber was higher than that of the control iPP fiber, indicating the nucleating effect of the modified carbon nanofibers. The nanocomposite fiber also showed larger long periods at low spin-draw ratios. Measurements of mechanical properties indicated that the nanocomposite fiber with 5 wt% MCNF had much higher tensile strength, modulus and longer elongation to break. The mechanical enhancement can be attributed to the dispersion of MCNF in the matrix, which was confirmed by SEM results.Dedicated to Prof. E D. Fischer on his 75th birthday.     

Factors influencing the transport of short-chain alcohols through mesoporous gamma-alumina membranes

The pressure-driven transport of water, ethanol, and 1-propanol through supported gamma-alumina membranes with different pore diameters is reported. Water and alcohols had similar permeabilities when they were transported through gamma-alumina membranes with average pore diameters of 4.4 and 6.0 nm, and the permeability coefficient was found to be proportional to the square of pore size, in accordance with a viscous flow mechanism. For transport through membranes with an average diameter of 3.2 nm, the behavior of water was in accordance with the viscous flow mechanism, but the permeability of the membrane for ethanol and 1-propanol was much smaller than expected and could not be explained in terms of viscous flow. Although the low permeability of the membrane with 3.2 nm pores for ethanol and 1-propanol was partly due to the presence of small amounts of water in the alcohols, the permeability coefficients were still substantially smaller when water was absent. This intrinsic difference between water and alcohol may be due to differences in molecular size, chemisorption of alcohols on the oxide pore wall, which would lead to a reduction of the effective pore size, and/or a certain degree of translational ordering of the alcohol molecules inside the membrane pores, which leads to an effectively higher viscosity and, therefore, to a higher transport resistance.     

Manipulation of the stereochemical outcome and product distribution in the Henry reaction using CO2 pressure

The rate and stereocontrol of the Henry reaction in the presence of CO(2) can be controlled simply by manipulation of CO(2) pressure, and can be understood by consideration of the kinetic and thermodynamic aspects of the reaction.     

Facile synthesis of polymer–peptide conjugates via direct amino acid coupling chemistry

Polymer–peptide conjugates (also known as biohybrids) are attracting considerable attention as injectable materials owing to the self‐assembling behavior of the peptide and the ability to control the material properties using the polymer component. To this end, a simple method for preparing poly(ethylene oxide)‐oligophenylalanine polymer–peptide conjugates (mPEO_m‐F_n‐OEt) using isobutylchloroformate as the activating reagent has been identified and developed. The synthetic approach reported employs an industrially viable route to produce conjugates with high yield and purity. Moreover, the approach allows judicious selection of the precursor building blocks to produce libraries of polymer–peptide conjugates with complete control over the molecular composition. Control over the molecular make‐up of the conjugates allows fine control of the physicochemical properties, which will be exploited in future studies into the prominent self‐assembling behavior of such materials. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013 , 51, 4853–4859     

Improving the accuracy of 1H–19F internuclear distance measurement using 2D 1H–19F HOESY

With the rise in fluorinated pharmaceuticals, it is becoming increasingly important to develop new ¹⁹F NMR-based methods to assist in their analysis. Crucially, obtaining information regarding the conformational dynamics of a molecule in solution can aid the design of strongly binding therapeutics. Herein, we report the development of a 2D ¹H–¹⁹F Heteronuclear Overhauser Spectroscopy (HOESY) experiment to measure ¹H–¹⁹F internuclear distances, with accuracies of ~5% when compared with ¹H–¹⁹F internuclear distances calculated by quantum chemical methods. We demonstrate that correcting for cross-relaxation of ¹H, using the diagonal peaks from the 2D ¹H–¹H Nuclear Overhauser Enhancement Spectroscopy (NOESY), is critical in obtaining accurate values for ¹H–¹⁹F internuclear distances. Finally, we show that by using the proposed method to measure ¹H–¹⁹F internuclear distances, we are able to determine the relative stereochemistry of two fluorinated pharmaceuticals.