Prophet inequalities for averages of independent non-negative random variables

Mathematische Zeitschrift -     

Synthesis and characterization of novel PDMS nanocomposites using POSS derivatives as cross‐linking filler

We report the synthesis and characterization of novel elastomeric nanocomposites containing polyhedral oligomeric silsesquioxanes (POSS) as both the cross‐linker and filler within a polydimethylsiloxane (PDMS) polymer matrix. These polymer composites were prepared through the reaction of octasilane‐POSS (OS‐POSS) with vinyl‐terminated PDMS chains using hydrosilylation chemistry. In addition, larger super‐POSS cross‐linkers, consisting of two pendant hepta(isobutyl)POSS molecules attached to a central octasilane‐POSS core, were also used in the fabrication of the PDMS composites. The chemical incorporation of these POSS cross‐linkers into the PDMS network was verified by solid‐state ¹H magic angle spinning NMR. Based on dynamic mechanical analysis, the PDMS nanocomposites prepared with the octafunctional OS‐POSS cross‐linker exhibited enhanced mechanical properties relative to polymer systems prepared with the tetrafunctional TDSS cross‐linker at equivalent loading levels. The observed improvements in mechanical properties can be attributed to the increased dimensionality of the POSS cross‐linker. The PDMS elastomers synthesized from the larger super‐POSS molecule showed improved mechanical properties relative to both the TDSS and OS‐POSS composites due to the increased volume‐fraction of POSS filler in the polymer matrix. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 2589–2596, 2009     

Evaluation of different machines used to quantify genetic modification by real-time PCR

Quantification of genetic modification (GM) is often undertaken to test for compliance with the European Union GM labeling threshold in food. Different control laboratories will often use common validated methods, but with different models of real-time PCR machines. We performed two separate ring trials to evaluate the relative precision and accuracy of different types of real-time PCR machines used to quantify the concentration of GM maize. Both trials used dual-labeled fluorogenic probes for quantification. The first ring trial used separate GM and reference assays (a single fluorescence channel), and the second used a combined duplex assay (two simultaneous fluorescence channels). Five manufacturers and seven models--including a 96-well microtiter-plate, rotary, and portable machines--were examined. In one trial, the machine used had a significant effect on precision, but in the other it did not. Overall, the degree of variation due to the machine model was lower than other factors. No significant repeatable difference in accuracy was observed between machine models. It was not possible to use sufficient replication of machine type in each laboratory to examine all sources of variation in this study, but the results strongly indicate that factors other than machine type or manufacturer (e.g., method or laboratory) contribute more to variation in a GM quantification result.     

Absorption and Circular Dichroism Spectra of La<Subscript>3</Subscript>Ga<Subscript>5</Subscript>SiO<Subscript>14</Subscript> Crystals Doped with Pr<Superscript>3+</Superscript>, Ho<Superscript>3+</Superscript>, and Er<Superscript>3+</Superscript> Ions

The absorption and circular dichroism (CD) spectra of La₃Ga₅SiO₁₄ langasite crystals doped with Pr³⁺, Ho³⁺, and Er³⁺ ions have been studied in the wavelength range of 350–700 nm. The electronic transitions of these ions, which replace La3+ ions in the 3e position with the symmetry 2, are observed in the spectra. All transitions are active in both the absorption and CD spectra. The dipole strengths D _om, rotational strengths R _om, and anisotropy factors g have been calculated for well-resolved bands. Some features are noted for the spectra that were obtained, and their relationship with the structure disorder is considered     

On the extent of star countable spaces

For a topological property P, we say that a space X is star Pif for every open cover Uof the space X there exists Y ? X such that St(Y,U) = X and Y has P. We consider star countable and star Lindelöf spaces establishing, among other things, that there exists first countable pseudocompact spaces which are not star Lindelöf. We also describe some classes of spaces in which star countability is equivalent to countable extent and show that a star countable space with a dense σ-compact subspace can have arbitrary extent. It is proved that for any ω ₁-monolithic compact space X, if C _p (X)is star countable then it is Lindelöf.     

Sound speed in water-saturated glass beads as a function of frequency and porosity

Sound propagation in water-saturated granular sediments is known to depend on the sediment porosity, but few data in the literature address both the frequency and porosity dependency. To begin to address this deficiency, a fluidized bed technique was used to control the porosity of an artificial sediment composed of glass spheres of 265 μm diameter. Time-of-flight measurements and the Fourier phase technique were utilized to determine the sound speed for frequencies from 300 to 800 kHz and porosities from 0.37 to 0.43. A Biot-based model qualitatively describes the porosity dependence.     

Detection of undistorted continuous wave (CW) electron paramagnetic resonance (EPR) spectra with non-adiabatic rapid sweep (NARS) of the magnetic field

A continuous wave (CW) electron paramagnetic resonance (EPR) spectrum is typically displayed as the first harmonic response to the application of 100 kHz magnetic field modulation, which is used to enhance sensitivity by reducing the level of 1/f noise. However, magnetic field modulation of any amplitude causes spectral broadening and sacrifices EPR spectral intensity by at least a factor of two. In the work presented here, a CW rapid-scan spectroscopic technique that avoids these compromises and also provides a means of avoiding 1/f noise is developed. This technique, termed non-adiabatic rapid sweep (NARS) EPR, consists of repetitively sweeping the polarizing magnetic field in a linear manner over a spectral fragment with a small coil at a repetition rate that is sufficiently high that receiver noise, microwave phase noise, and environmental microphonics, each of which has 1/f characteristics, are overcome. Nevertheless, the rate of sweep is sufficiently slow that adiabatic responses are avoided and the spin system is always close to thermal equilibrium. The repetitively acquired spectra from the spectral fragment are averaged. Under these conditions, undistorted pure absorption spectra are obtained without broadening or loss of signal intensity. A digital filter such as a moving average is applied to remove high frequency noise, which is approximately equivalent in bandwidth to use of an integrating time constant in conventional field modulation with lock-in detection. Nitroxide spectra at L- and X-band are presented.     

Spin-label saturation-recovery EPR at W-band: applications to eye lens lipid membranes

Saturation-recovery (SR) EPR at W-band (94 GHz) to obtain profiles of the membrane fluidity and profiles of the oxygen transport parameter is demonstrated for lens lipid membranes using phosphatidylcholine (n-PC), stearic acid (n-SASL), and cholesterol analog (ASL and CSL) spin labels, and compared with results obtained in parallel experiments at X-band (9.4 GHz). Membranes were derived from the total lipids extracted from 2-year-old porcine lens cortex and nucleus. Two findings are especially significant. First, measurements of the spin-lattice relaxation times T1 for n-PCs allowed T1 profiles across the membrane to be obtained. These profiles reflect local membrane properties differently than profiles of the order parameter. Profiles obtained at W-band are, however, shifted to longer T1 values compared to those obtained at X-band. Second, using cholesterol analog spin labels and relaxation agents (hydrophobic oxygen and water-soluble NiEDDA), the cholesterol bilayer domain was discriminated in membranes made from lipids of the lens nucleus. However, membranes made from cortical lipids show a single homogeneous environment. Profiles of the oxygen transport parameter obtained from W-band measurements are practically identical to those obtained from X-band measurements, and are very similar to those obtained earlier at X-band for membranes made of 2-year-old bovine cortical and nuclear lens lipids (M. Raguz, J. Widomska, J. Dillon, E.R. Gaillard, W.K. Subczynski, Biochim. Biophys. Acta 1788 (2009) 2380-2388). Results demonstrate that SR EPR at W-band has the potential to be a powerful tool for studying samples of small volume, ～30 nL, compared with the sample volume of ～3 μL at X-band.