Embeddings and hyperplanes of the Lie incidence geometry of type E7,1

This paper continues a program to show that for most of the standard Lie incidence geometries, all geometric hyperplanes arise from a necessarily absolutely universal embedding, by addingE _7,1 to the list. It follows from [5, 12] that any projective embedding of this point line geometry is a homomorphic image of the one afforded by the 56-dimensional module for the groupE ₇(K).This work was supported by a grant from the National Science Foundation.     

Ernest Julius Wilczynski (in Memoriam)

Ringrazio il collega dell'Università di Chicago di avermi permesso di pubblicare qui un breve sunto della commemorazione da lui scritta; e sono dolente che lo spazio concessomi non me ne abbia permesso la pubblicazione integrale.Guido Fubini     

Asymptotic analysis and estimates of blow‐up time for the radial symmetric semilinear heat equation in the open‐spectrum case

We estimate the blow‐up time for the reaction diffusion equation u_t=Δu+ λf(u), for the radial symmetric case, where f is a positive, increasing and convex function growing fast enough at infinity. Here λ>λ^*, where λ^* is the ‘extremal’ (critical) value for λ, such that there exists an ‘extremal’ weak but not a classical steady‐state solution at λ=λ^* with ∥w(?, λ)∥_∞→∞ as 0<λ→λ^*?. Estimates of the blow‐up time are obtained by using comparison methods. Also an asymptotic analysis is applied when f(s)=e^s, for λ?λ^*?1, regarding the form of the solution during blow‐up and an asymptotic estimate of blow‐up time is obtained. Finally, some numerical results are also presented. Copyright © 2007 John Wiley & Sons, Ltd.     

Oriented immobilization of Desulfovibrio gigas hydrogenase onto carbon electrodes by covalent bonds for nonmediated oxidation of H2

The orientation of hydrogenase bound covalently to a pyrolytic graphite edge electrode modified with a 4-aminophenyl monolayer can be modulated via electrostatic interactions during the immobilization step. At low ionic strength and when the amino groups of the electrode surface are mostly protonated, the hydrogenase is immobilized with the negatively charged region that surrounds its 4Fe4S cluster nearer to the protein surface facing the electrode. This allows direct electron transfer between the immobilized hydrogenase and the electrode, which is observed by the strong catalytic currents measured in the presence of the H2 substrate. Therefore, a very stable enzymatic electrode is produced that catalyzes nonmediated H2 oxidation.     

2-Oxocephems. Synthesis and Properties of 7-Acylamino-2-oxocephem-4-carboxylic Acids

A synthesis of (6 R, 7 R)-7-acylamino-2-oxocephem-4-carboxylic acids from penicillins is reported based on the formation of the 2-oxocephem system in an intramolecular Wittig condensation. An interesting steric effect of the acylamino grouping on the course of this key step was used to advantage. Some physical and biological properties of this new type of Δ³-cephem are described.     

Combined capillary gas chromatography/ion trap mass spectrometry quantitative methods using labeled or unlabeled internal standards

Three methods of operating an ion trap mass spectrometer (ITMS) were investigated for the determination of quantitative information by combined capillary GC/MS and GC/MS/MS. Separate regression Lines for a hexynone drug were examined by using bath unlabeled and stable-isotope-labeled internal standards. The ITMS modes of operation examined were (1) the full-scan, rf-voltage-only mode, useful on ion trap detectors as well as on the ITMS, (2) a scan using combined rf and dc voltages (rf/dc) for mass-selective storage analyses, and (3) rf/dc followed by collision-induced dissociation, Results of over 200 analyses in the 0.1–10 ng on-column range, with 5 ng of internal standard, showed that the unlabeled internal standard, separated by retention time on the capillary GC column, gave the best relative standard deviatiod (less than 5% over the range) and linear correlations (r ² typically > 0.9992).