Discrete approximation of integral operators

A method to approximate the eigenvalues of linear operators depending on an unknown distribution is introduced and applied to weighted sums of squared normally distributed random variables. This area of application includes the approximation of the asymptotic null distribution of certain degenerated U- and V-statistics.

     

A Simpler Proof of the Excluded Minor Theorem for Higher Surfaces

We give a simple proof of the fact (which follows from the Robertson–Seymour theory) that a graph which is minimal of genusgcannot contain a subdivision of a large grid. Combining this with the tree-width theorem and the quasi-wellordering of graphs of bounded tree-width in the Robertson–Seymour theory, we obtain a simpler proof of the generalized Kuratowski theorem for each fixed surface. The proof requires no previous knowledge of graph embeddings.     

Rigid nitronyl-nitroxide-labelled anchoring molecules: syntheses, structural and magnetic investigations

The syntheses of two rigid organic molecular rods bearing a nitronyl-nitroxide radical and a terminal nitrogen-based functionality like a pyridine or a cyano group are reported. Both new paramagnetic molecules are fully characterized, including crystal structure analysis. Furthermore their magnetic behaviours in the crystalline state are investigated and their spin concentration corroborate their excellent purity. While the pyridine functionalized rod is synthesized by converting the corresponding benzaldehyde to the phenyl-nitronyl-nitroxide radical, the synthesis of the cyano functionalized rod demonstrates the accessibility of highly sophisticated spin-labelled molecules via cross-coupling reaction with a meta-iodo-phenyl-nitronyl-nitroxide moiety.     

Surface bodies and p-affine surface area

The surface body is a generalization of the floating body. Its relation to p-affine surface area is studied.     

Simultaneous analysis of oxidized and reduced glutathione in cell extracts by capillary zone electrophoresis

Glutathione (GSH) and glutathione disulfide (GSSG) levels in cells constitute a thiol redox system. They can be used as an indicator of oxidative stress of the cell. In this study, a capillary zone electrophoresis (CZE) method is described that enables quantitation of GSH and GSSG from cellular extracts. The CZE buffer used was 20 mM ammonium acetate containing 5% (v/v) acetic acid at pH 3.1 in conjunction with a polybrene coated capillary operated in reverse polarity mode. Effects of different acids used to prepare cell samples were investigated on CZE performance. The acids include meta phosphoric acid (MPA), trichloroacetic acid (TCA), phosphoric acid (PA) and sulfosalicylic acid (SSA) and are used to stabilize GSH and GSSG before performing CZE analysis. The method features a limit of detection of 4 microM and a limit of quantitation of 12 microM for both GSSG and GSH and recoveries of 94% for GSH and 100% for GSSG. Quantitative analysis of GSSG and GSH in HaCaT cell extracts (5% SSA, w/v) was performed with this method and changes in the ratio of GSH to GSSG in N-ethylmaleimide treated cell sample was observed by comparing with control cell samples.