Invariance principles for Gaussian sequences

An almost sure invariance principle is proved for stationary Gaussian sequences whose covariances r(n) satisfy r(n) = O (n ^–1–)for some >0.     

Preparation of thin silica films with controlled thickness and tunable refractive index

Silica films with controlled thickness and refractive index have been formed by the sequential adsorption of a cationic polyelectrolyte and silica sols. The conditions used to prepare the sol were varied, and allowed films with refractive indices as low as 1.16 to be obtained. The sequential adsorption technique allows the thickness of these films to be controlled in increments of 5-10 nm, depending on the desired refractive index. Scanning electron microscopy revealed that a low packing density of constituent silica particles was responsible for the low indices of these films. The as-adsorbed films are thermally robust; calcination at 500 degrees C resulted in only very small decreases in film thickness (by < or =1.8%) and refractive index (to as low as 1.14). After calcination, the silica films remained hydrophilic and sorbed water vapor from the atmosphere. As a result, the refractive indices of these films increased with increasing relative humidity (RH). The dependence of the refractive index on RH was eliminated by treating the calcined films with trimethylchlorosilane.     

Computational and ESR studies of electron attachment to decafluorocyclopentane, octafluorocyclobutane, and hexafluorocyclopropane: electron affinities of the molecules and the structures of their stable negative ions as determined from 13C and 19F hyperfine coupling constants

High-resolution ESR spectra of the ground-state negative ions of hexafluorocyclopropane (c-C3F6*-), octafluorocyclobutane (c-C4F8*-), and decafluorocyclopentane (c-C5F10*-) are reported and their isotropic 19F hyperfine coupling constants (hfcc) of 198.6 +/- 0.4 G, 147.6 +/- 0.4 G, and 117.9 +/- 0.4 G, respectively, are in inverse ratio to the total number of fluorine atoms per anion. Together with the small value of 5.2 +/- 0.4 G determined for the isotropic 13C hfcc of c-C4F8*-, these results indicate that in each case the singly occupied molecular orbital (SOMO) is delocalized over the equivalent fluorines and possesses a nodal plane through the carbon atoms of a time-averaged D(nh) structure. A series of quantum chemical computations were carried out to further characterize these anions and their neutral counterparts. Both the B3LYP density functional and second-order M?ller-Plesset perturbation theory (MP2) indicate that c-C3F6*- adopts a D(3h) geometry and a (2)A2' ground electronic state, that c-C4F8*- adopts a D(4h) geometry and a (2)A2u ground electronic state, and that c-C5F10*- adopts a C(s) structure and a (2)A' electronic state. Moreover, the 19F hyperfine coupling constants computed with the MP2 method and a high quality triple-zeta basis set are within 1% of the experimental values. Also, the values computed for the 13C hfcc of c-C4F8*- are consistent with the experimental value of 5.2 G. Therefore, in keeping with the ESR results, these negative ions derived from first-row elements can be characterized as pi* species. In addition, the hypervalency of these perfluorocycloalkane radical anions has been clarified.     

Application of headspace solid-phase microextraction and gas chromatography-mass spectrometry for detection of the chemical warfare agent bis(2-chloroethyl) sulfide in soil

A field expedient analytical method for detecting the chemical warfare agent (CWA) sulfur mustard as a soil contaminant was developed using solid-phase microextraction (SPME) and gas chromatography-mass spectrometry (GC-MS). Five commercially available SPME fibers were investigated to determine the optimal fiber, and extraction conditions. Polyacrylate and carbowax-divinylbenzene fiber coatings gave a statistically indistinguishable and best response compared to the other three types examined in a simple system studied without soil. The polyacrylate fiber coating was selected for study of a system in which sulfur mustard was spiked to an agricultural soil (Standard Reference Material 2709, San Joaquin type). With soil samples, the greatest sensitivity occurred by the addition of deionized water to spiked soil and extraction at ambient temperature for 20 min or longer. SPME sampling with GC-MS analyses afforded good reproducibility (relative standard deviation between 2 and 10%), and analyte concentrations as low as 237 ng/g were detected in soil (total ion chromatograms). As completed here, total time for sampling and analysis was just under 1 h, and use of organic solvents or special sample introduction equipment was avoided.     

Activity-based protein profiling in vivo using a copper(i)-catalyzed azide-alkyne [3 + 2] cycloaddition

Toward the goal of assigning function to the tens of thousands of protein products encoded by eukaryotic and prokaryotic genomes, the field of proteomics requires new technologies that can functionally characterize proteins within the dynamic environment of the cell, where these biomolecules are subject to myriad posttranslational modifications and the actions of endogenous activators and inhibitors. Here, we report an advanced strategy for activity-based protein profiling (ABPP) that addresses this important need. We show that several enzymes can be labeled in an activity-based manner both in vitro and in vivo by an azido-sulfonate ester probe and that these labeling events can be detected in whole proteomes by copper-catalyzed ligation with a rhodamine-alkyne reagent. This click chemistry-based strategy for ABPP represents a unique and versatile method for functional proteome analysis.