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.     

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.     

Systematische Studie zu den Koordinationseigenschaften des Guanidin‐Liganden Bis(tetramethylguanidino)propan mit den Metallen Mangan,Cobalt, Nickel,Zink, Cadmium,Quecksilber und Silber

The transition metal complexes with the ligand 1,3‐bis(N,N,N′,N′‐tetramethylguanidino)propane (btmgp), [Mn(btmgp)Br₂] ( 1 ), [Co(btmgp)Cl₂] ( 2 ), [Ni(btmgp)I₂] ( 3 ), [Zn(btmgp)Cl₂] ( 4 ), [Zn(btmgp)(O₂CCH₃)₂] ( 5 ), [Cd(btmgp)Cl₂] ( 6 ), [Hg(btmgp)Cl₂] ( 7 ) and [Ag₂(btmgp)₂][ClO₄]₂·2MeCN ( 8 ), were prepared and characterised for the first time. The stoichiometric reaction of the corresponding water‐free metal salts with the ligand btmgp in dry MeCN or THF resulted in the straightforward formation of the mononuclear complexes 1 – 7 and the binuclear complex 8 . In complexes with M^II the metal ion shows a distorted tetrahedral coordination whereas in 8 , the coordination of the M^I ion is almost linear. The coordination behavior of btmgp and resulting structural parameters of the corresponding complexes were discussed in an comparative approach together with already described complexes of btmgp and the bisguanidine ligand N¹,N²‐bis(1,3‐dimethylimidazolidin‐2‐ylidene)‐ethane‐1,2‐diamine (DMEG₂e), respectively.     

OH-radical induced degradation of hydroxybenzoic- and hydroxycinnamic acids and formation of aromatic products—A gamma radiolysis study

The OH-radical induced degradation of hydroxybenzoic acids (HBA), hydroxycinnamic acids (HCiA) and methoxylated derivatives, as well as of chlorogenic acid and rosmarinic acid was studied by gamma radiolysis in aerated aqueous solutions. Primary aromatic products resulting from an OH-radical attachment to the ring (hydroxylation), to the position occupied by the methoxyl group (replacement –OCH₃ by ?OH) as well as to the propenoic acid side chain of the cinnamic acids (benzaldehyde formations) were analysed by HPLC–UV and LC–ESI–MS. A comparison of the extent of these processes is given for 3,4-dihydroxybenzoic acid, vanillic acid, isovanillic acid, syringic acid, cinnamic acid, 4-hydroxycinnamic acid, caffeic acid, ferulic acid, isoferulic acid, chlorogenic acid, and rosmarinic acid. For all cinnamic acids and derivatives benzaldehydes were significant oxidation products. With the release of caffeic acid from chlorogenic acid the cleavage of a phenolic glycoside could be demonstrated. Reaction mechanisms are discussed.     

Simplified formulas for non-normal reflection from monoclinic crystals

Based on Berreman's 4 × 4 matrix formalism [W. Berreman, J. Opt. Soc. Am. 62, 502 (1972)] we derive simplified expressions for the reflection formulas from the a-c crystal surface for non-normal incidence. The computational effort to apply the formulas was found to be only insignificantly higher than those for normal incidence, but considerably lower than for the general expressions. Consequently, the simplified formulas can be readily applied for dispersion analysis of spectra gained by spectroscopic ellipsometry or attenuated total reflection.     

On the planarity of Hanoi graphs

Hanoi graphs are the state graphs for Tower of Hanoi problems with three or more pegs. We prove hamiltonicity and present a complete analysis of planarity of these graphs.     

On-target fraction collection for the off-line coupling of capillary isoelectric focusing with matrix-assisted laser desorption/ionization mass spectrometry.

In the present work, we describe a collection system for the off-line coupling of capillary isoelectric focusing (CIEF) with matrix-assisted laser desorption/ionization time-of-flight (MALDI-TOF) mass spectrometry. In this system, the capillary effluent is directly deposited in fractions onto the MALDI target via the use of a sheath liquid. The collected fractions are subsequently supplemented with matrix and further analysed by MALDI-TOF mass spectrometry for mass assignment. The experimental set-up includes a fiber optic based UV detector operating at 280 nm, which allows the study of the influence of the sheath liquid composition on the CIEF separation. The influence of the carrier ampholyte concentration on the protein MALDI spectra was also evaluated and the feasibility of the collection method was finally demonstrated with a mixture of four standard proteins.