Development and evaluation of a high‐performance liquid chromatography/isotope ratio mass spectrometry methodology for δ13C analyses of amino sugars in soil

Amino sugars have been used as biomarkers to assess the relative contribution of dead microbial biomass of different functional groups of microorganisms to soil carbon pools. However, little is known about the dynamics of these compounds in soil. The isotopic composition of individual amino sugars can be used as a tool to determine the turnover of these compounds. Methods to determine the δ¹³C of amino sugars using gas chromatography/combustion/isotope ratio mass spectrometry (GC/C/IRMS) have been proposed in literature. However, due to derivatization, the uncertainty on the obtained δ¹³C is too high to be used for natural abundance studies. Therefore, a new high‐performance liquid chromatography/isotope ratio mass spectrometry (HPLC/IRMS) methodology, with increased accuracy and precision, has been developed. The repeatability on the obtained δ¹³C values when pure amino sugars were analyzed were not significantly concentration‐dependent as long as the injected amount was higher than 1.5 nmol. The δ¹³C value of the same amino sugar spiked to a soil deviated by only 0.3‰ from the theoretical value. Copyright © 2009 John Wiley & Sons, Ltd.     

Synthesis of biotinylated tumor-associated carbohydrate antigens for immunological studies

Syntheses of several biotinylated human cancer-associated carbohydrate antigens for immunological studies are described.     

Distinguishing a phosphate ester prodrug from its isobaric sulfate metabolite by mass spectrometry without the metabolite standard

A phosphate prodrug of a phenolic or alcoholic drug is isobaric with the putative sulfate metabolite of the drug. During liquid chromatography/tandem mass spectrometry (LC/MS/MS) analysis of biological samples obtained after the administration of a phosphate prodrug, a product ion arising from the parent drug portion of the prodrug molecule is commonly used in selected reaction monitoring (SRM) utilized for the simultaneous quantitation of the prodrug and the in vivo generated parent drug. While the advantage of using a drug moiety‐specific LC‐SRM method is obvious, one drawback is that the sulfate metabolite will also respond to such an SRM transition since the metabolite will invariably yield the same product ion as the prodrug. Thus, the sulfate metabolite could be mistaken for the prodrug unless chromatographic separation between the two is achieved. In the absence of a reference standard for the sulfate metabolite to demonstrate chromatographic separation, it is important to establish a procedure that can ascertain the absence of the sulfate metabolite in the study samples to ensure the specificity of the method for the prodrug. To this end, we studied the MS/MS behavior of model phosphate and sulfate ester compounds and developed a procedure based on phosphate‐specific and sulfate‐specific product ions for distinguishing the phosphate prodrug from the sulfate metabolite. Copyright © 2009 John Wiley & Sons, Ltd.     

Material order‐independent interface reconstruction using power diagrams

We have developed a new, multi‐material, piecewise linear interface reconstruction method that correctly locates the position of each material in the mesh cell and matches the required volume fractions with no material ordering required. This is different from other volume tracking interface reconstruction methods in which an improper material ordering may result in materials being incorrectly located within the cell. The new method utilizes a type of weighted Voronoi diagram, known as a power diagram, to reconstruct the interface from approximate material locations derived either from a particle model or quadrature formula. It works on structured and general polygonal grids, for an arbitrary number of materials and can be naturally extended to three dimensions. Published in 2007 by John Wiley & Sons, Ltd.     

The Laplacian of a Graph as a Density Matrix: A Basic Combinatorial Approach to Separability of Mixed States

We study entanglement properties of mixed density matrices obtained from combinatorial Laplacians. This is done by introducing the notion of the density matrix of a graph. We characterize the graphs with pure density matrices and show that the density matrix of a graph can be always written as a uniform mixture of pure density matrices of graphs. We consider the von Neumann entropy of these matrices and we characterize the graphs for which the minimum and maximum values are attained. We then discuss the problem of separability by pointing out that separability of density matrices of graphs does not always depend on the labelling of the vertices. We consider graphs with a tensor product structure and simple cases for which combinatorial properties are linked to the entanglement of the state. We calculate the concurrence of all graphs on four vertices representing entangled states. It turns out that for these graphs the value of the concurrence is exactly fractional. Received July 28, 2004     

Guided elastic waves and perfectly matched layers

Elastic waveguides support propagating modes that have two possible features, negative group velocities and long wavelengths that, for some frequencies, degrade the accuracy or otherwise poison existing numerical schemes that utilise perfectly matched layers (PMLs) to mimic infinite domains. We illustrate why negative group velocities and long waves are potentially an issue and describe how these problems are overcome. Detailed numerical simulations confirm the accuracy of the modified scheme and provide both theoretical and pragmatic estimates for the parameters within the PML model, in particular for the damping function. We also contrast and compare different implementations of the PML model using spectral and finite difference methods.     

Grunsky inequalities and quasiconformal extension

The Grunsky coefficient inequalities play a crucial role in various problems and are intrinsically connected with the integrable holomorphic quadratic differentials having only zeros of even order. For the functions with quasi-conformal extensions, the Grunsky constant ℵ(f) and the extremal dilatationk(f) are related by ℵ(f)≤k(f). In 1985, Jürgen Moser conjectured that any univalent functionf(z)=z+b ₀+b ₁ z ⁻¹+… on Δ*={|z|>1} can be approximated locally uniformly by functions with ℵ(f)<k(f). In this paper, we prove a theorem confirming Moser’s conjecture, which sheds new light on the features of Grunsky coefficients. In memory of Jürgen Moser The research was supported by the RiP program of the Volkswagen-Stiftung in the Mathematisches Forschungsinstitut Oberwolfach.