A martingale decomposition for quadratic forms of Markov chains (with applications)

We develop a martingale-based decomposition for a general class of quadratic forms of Markov chains, which resembles the well-known Hoeffding decomposition of U$U$-statistics of i.i.d. data up to a reminder term. To illustrate the applicability of our results, we discuss how this decomposition may be used to studying the large-sample properties of certain statistics in two problems: (i) we examine the asymptotic behavior of lag-window estimators in time series, and (ii) we derive an asymptotic linear representation and limiting distribution of U$U$-statistics with varying kernels in time series. We also discuss simplified examples of interest in statistics and econometrics.     

Structural characterization of a spin-assisted colloid-polyelectrolyte assembly: stratified multilayer thin films

The assembly of polyelectrolytes and gold nanoparticles yields stratified multilayers with very low roughness and high structural perfection. The films are prepared by spin-assisted layer-by-layer self-assembly (LbL) and are characterized by X-ray reflectivity (XRR), UV-vis spectroscopy, atomic force microscopy (AFM), and transmission electron microscopy (TEM). Typical structures have four repeat units, each of which consists of eight double layers (DL) of poly(sodium 4-styrenesulfonate)/poly(allylamine hydrochloride), one monolayer of gold nanoparticles (10 nm diameter), and another layer of poly(allylamine hydrochloride). XRR scans show small-angle Bragg peaks up to seventh order, evidencing the highly stratified structure. Pronounced Kiessig fringes indicate a low global roughness, which is confirmed by local AFM measurements. TEM images corroborate the layered structure in the growth direction and nicely show the distinct separation of the individual particle layers. An AFM study reveals the lateral gold particle distribution within one individual particle layer. Interestingly, the spin-assisted deposition of polyelectrolytes reduces the roughness induced by the particle layers, leading to self-healing of roughness defects and a rather perfect stratification.     

An experimental and computational study on the dissociation behavior of hydroxypyridine N‐oxides in atmospheric pressure ionization mass spectrometry

A tandem mass spectrometric study of protonated isomeric hydroxypyridine N‐oxides was carried out with a hybrid quadrupole/time‐of‐flight mass spectrometer coupled with different atmospheric pressure ionization sources. The behavior observed in the collision‐induced dissociation (CID) mass spectra of the parent cations, was similar irrespective of the source employed. However, there were intrinsic differences in the intensities of the two fragments observed for each isomer. The major fragment because of elimination of a hydroxyl radical, dominated the CID spectra (in contrast with weaker water loss) at different energy thresholds. Therefore, it was possible to differentiate both isomers at collision energies above 13 eV by comparing the ratio of intensities of the major fragment relative to the precursor cation. In addition, quantum chemical calculations at the B3LYP/6‐31 + + G(d,p) level of theory were performed for the protonated isomers of hydroxypyridine N‐oxide and their radical cation products in order to gain insight into the major routes of dissociation. The results suggest that dissociation from the lowest triplet excited state of the protonated species would provide a reasonable rationalization for the difference in behavior of both isomers. Copyright © 2010 John Wiley & Sons, Ltd.     

SYNTHESIS OF METAL OXIDE PARTICLES FROM AQUEOUS MEDIA: THE HOMOGENEOUS ALKALIN1ZAT1ON METHOD

An analysis of the urea method as a way to synthesize uniform colloidal particles is presented. Various selected cases of precipitation and coprecipitation are reviewed to illustrate the inherent complexities of the method. The importance of the kinetics of urea hydrolysis is recognized. The concept of trajectory is used to rationalized the evolution of the systems upon aging. The influence of thermodynamic and kinetic factors in the definition of the nature of the precipitating solid phases is analyzed; the overriding role of the latter is stressed. The factors that influence particle morphology are also addressed.     

New way to quantify multiple steroidal compounds in wastewater by comprehensive two-dimensional gas chromatography–time-of-flight mass spectrometry

The applicability of comprehensive two-dimensional gas chromatography coupled with time-of-flight mass spectrometry to the screening of steroidal compounds in wastewater is demonstrated. Advanced software was utilized to identify unknown compounds in complex two-dimensional chromatograms exploiting retention indices and two different mass spectral databases. Response factors calculated as a function of the individual mass spectra of six commercial standards at different concentrations were used to develop a model allowing the quantitation of all steroidal compounds identified in the sample. The model, based on partial least squares regression equations, provided good accuracy (prediction error < 16%) in the quantitation of steroidal compounds, so offering a valuable alternative to conventional quantitation methods where reference compounds are required for the verification of analytical measurements. Special attention was paid to the development of an exhaustive sample preparation method for the separate analysis of conjugated and free steroids in both water phase and suspended solid particles. The method, including the exploitation of chemometrics, was successfully applied to the determination of steroidal compounds in effluent and influent waters collected at a local wastewater treatment plant.     

On stars and links of shellable polytopal complexes

The vertex stars of shellable polytopal complexes are shown to be shellable. The link of a vertex v of a shellable polytopal complex is also shown to be shellable, provided that all facets of the star of v are simple polytopes, or (more generally) if there exists a shelling F₁,…,F_n of the star of v such that, for every 1<j?n, the intersection of F_j with the previous facets is an initial segment of a line shelling of the boundary complex of F_j.