M-matrix asymptotics for Sturm–Liouville problems on graphs

We consider a system formulation for Sturm–Liouville operators with formally self-adjoint boundary conditions on a graph. An M-matrix associated with the boundary value problem is defined and related to the matrix Prüfer angle associated with the system boundary value problem, and consequently with the boundary value problem on the graph. Asymptotics for the M-matrix are obtained as the eigenparameter tends to negative infinity. We show that the boundary conditions may be recovered, up to a unitary equivalence, from the M-matrix and that the M-matrix is a Herglotz function. This is the first in a series of papers devoted to the reconstruction of the Sturm–Liouville problem on a graph from its M-matrix.     

Pulse sequence optimization for T2-weighted MR imaging of the brain

The authors implemented bipolar velocity compensated pulse techniques for T2-weighted MR imaging of the brain. Signal-to-noise (S/N) and image quality was compared for pulse sequences with standard and optimized RF pulses, low and regular bandwidth versions and cardiac triggering. Images from bipolar velocity compensated sequences allowed better visualization of vessels and basilar cisterns and improved image quality relative to standard sequences without velocity compensation. The implementation of optimized RF pulses with bipolar sequences resulted in further improvement in image quality. Single echo sequences consistently had improved image quality and signal-to-noise relative to the second echo of a double echo sequence. Low bandwidth bipolar sequences with extended sampling period had 30% higher S/N, but at the cost of slight loss in edge definition. The highest image quality was obtained with the bipolar, optimized RF, single echo sequence. Using this technique contiguous high quality image slices could be obtained with velocity compensation. The addition of cardiac triggering to bipolar sequences resulted in slight improvement in image quality, but this difference was marginal and probably rarely necessary for MR imaging of the brain.     

Phosphorylated serine and threonine residues promote site‐specific fragmentation of singly charged,arginine‐containing peptide ions

In order to investigate gas‐phase fragmentation reactions of phosphorylated peptide ions, matrix‐assisted laser desorption/ionization (MALDI) and electrospray ionization (ESI) tandem mass (MS/MS) spectra were recorded from synthetic phosphopeptides and from phosphopeptides isolated from natural sources. MALDI‐TOF/TOF (TOF: time‐of‐flight) spectra of synthetic arginine‐containing phosphopeptides revealed a significant increase of y ions resulting from bond cleavages on the C‐terminal side of phosphothreonine or phosphoserine. The same effect was found in ESI‐MS/MS spectra recorded from the singly charged but not from the doubly charged ions of these phosphopeptides. ESI‐MS/MS spectra of doubly charged phosphopeptides containing two arginine residues support the following general fragmentation rule: Increased amide bond cleavage on the C‐terminal side of phosphorylated serines or threonines mainly occurs in peptide ions which do not contain mobile protons. In MALDI‐TOF/TOF spectra of phosphopeptides displaying N‐terminal fragment ions, abundant b–H₃PO₄ ions resulting from the enhanced dissociation of the pSer/pThr–X bond were detected (X denotes amino acids). Cleavages at phosphoamino acids were found to be particularly predominant in spectra of phosphopeptides containing pSer/pThr–Pro bonds. A quantitative evaluation of a larger set of MALDI‐TOF/TOF spectra recorded from phosphopeptides indicated that phosphoserine residues in arginine‐containing peptides increase the signal intensities of the respective y ions by almost a factor of 3. A less pronounced cleavage‐enhancing effect was observed in some lysine‐containing phosphopeptides without arginine. The proposed peptide fragmentation pathways involve a nucleophilic attack by phosphate oxygen on the carbon center of the peptide backbone amide, which eventually leads to cleavage of the amide bond. Copyright © 2009 John Wiley & Sons, Ltd.     

Untersuchungen an oxidischen Katalysatoren. XLIV. Beeinflussung des katalytischen Verhaltens modifizierter Zeolithe vom Typ ZSM-5 durch thermische Behandlung

Studies on Oxide Catalysts. XLIV. Modification of the Catalytic Behavior of Modified ZSM-5 Zeolites by Thermal Treatment The catalytic activity, the shape selectivity, and the deactivation behavior of ZSM-5 in paraffin cracking reactions can be regulated by a thermal pretreatment. A minimum of the deactivation rate as a function of zeolite pretreatment time at 600°C found in the hexane cracking could be verified in the methanol conversion reaction to gasoline.     

Short‐term dynamics of isotopic composition of leaf‐respired CO2 upon darkening: measurements and implications

Recent advances in understanding the metabolic origin and the temporal dynamics in δ¹³C of dark‐respired CO₂ (δ¹³C_res) have led to an increasing awareness of the importance of plant isotopic fractionation in respiratory processes. Pronounced dynamics in δ¹³C_res have been observed in a number of species and three main hypotheses have been proposed: first, diurnal changes in δ¹³C of respiratory substrates; second, post‐photosynthetic discrimination in respiratory pathways; and third, dynamic decarboxylation of enriched carbon pools during the post‐illumination respiration period. Since different functional groups exhibit distinct diurnal patterns in δ¹³C_res (ranging from 0 to 10‰ diurnal increase), we explored these hypotheses for different ecotypes and environmental (i.e. growth light) conditions. Mass balance calculations revealed that the effect of respiratory substrates on diurnal changes in δ¹³C_res was negligible in all investigated species. Further, rapid post‐illumination changes in δ¹³C_res (30 min), which increased from 2.6‰ to 5‰ over the course of the day, were examined by positional ¹³C‐labelling to quantify changes in pyruvate dehydrogenase (PDH) and Krebs cycle (KC) activity. We investigated the origin of these dynamics with Rayleigh mass balance calculations based on theoretical assumptions on fractionation processes. Neither the estimated changes of PDH and KC, nor decarboxylation of a malate pool entirely explained the observed pattern in δ¹³C_res. However, a Rayleigh fractionation of ¹²C‐discriminating enzymes and/or a rapid decline in the decarboxylation rate of an enriched substrate pool may explain the post‐illumination peak in δ¹³C_res. These results are highly relevant since δ¹³C_res is used in large‐scale carbon cycle studies. Copyright © 2009 John Wiley & Sons, Ltd.