The general three-vertex,BRS identities and renormalizability of the light-cone gauge

The general one-loop three-vertexГ _μeλ ^abc (p, q, r) in the four-component formulation of the Yang-Mills theory is calculated in the light-cone gauge. The nonvanishing counter Lagrangian constructed from this three-vertex and the self-energy is proportional to the original Lagrangian, the single renormalization constant being -11g² C _YM Г(2?ω)/48π². Gauge dependent and nonlocal counterterms do not contribute to the renormalization constant, but are needed to verify the appropriate Slavnov-Taylor (ST) and Becchi-Rouet-Stora (BRS) identities.     

Comment on a paper of Rao et al., an entry of Ramanujan and a new 3F2(1)

A hypergeometric transformation formula is developed that simultaneously simplifies and generalizes arguments and identities in a previous paper of Rao et al. [An entry of Ramanujan on hypergeometric series in his notebooks, J. Comput. Appl. Math. 173(2) (2005) 239–246].     

The nonadditivity of the genus

A class of cubic graphs is introduced for which the genus is a nonadditive function of the genus of subgraphs. This provides a small (28 node) counterexample to Duke’s conjecture concerning the relation of the Betti number to the genus of a graph.     

Catalytic conjugate additions of carbonyl anions under neutral aqueous conditions

The conjugate addition of carbonyl anions catalyzed by thiazolium salts that is fully operative under neutral aqueous conditions has been accomplished. The combination of alpha-keto carboxylates and thiazolium-derived zwitterions produces reactive carbonyl anions in a buffered protic environment that readily undergo conjugate additions to substituted alpha,beta-unsaturated 2-acyl imidazoles. The scope of the reaction has been examined and found to accommodate various alpha-keto carboxylates and beta-aryl substituted unsaturated 2-acyl imidazoles. The optimal precatalyst for this process is the commercially available thiazolium salt 5, a simple analogue of thiamin diphosphate. In this process, no benzoin products from carbonyl anion dimerization are observed. The corresponding 1,4-dicarbonyl compounds can be efficiently converted into esters and amides by way of activation of the N-methylimidazole ring via alkylation.     

The homotopy type of rational functions

During the preparation of this work each of the authors was supported by an NSF grant, the second author by an NSF-PYI award, and the first and fourth authors by the S.F.B. 170 in G?ttingen     

Matrix-assisted laser desorption/ionization directed nano-electrospray ionization tandem mass spectrometric analysis for protein identification

In those cases where the information obtained by peptide mass fingerprinting or matrix-assisted laser desorption/ionization tandem mass spectrometry (MALDI-MS/MS) is not sufficient for unambiguous protein identification, nano-electrospray ionization (nano-ESI) and/or electrospray ionization tandem mass spectrometry (ESI-MS/MS) analysis must be performed. The sensitivity of nano-ESI/MS, however, is lower than that of MALDI-MS, especially at very low analyte concentrations and/or in the presence of contaminants, such as salt and detergents. Moreover, to perform ESI-MS/MS, the peptide masses of the precursor ions must be known. The approach described in this paper, MALDI-directed nano-ESI-MS/MS, makes use of information obtained from the more sensitive MALDI-MS experiments in order to direct subsequent nano-ESI-MS/MS experiments. Peptide molecular ions found in the MALDI-MS analysis are then selected, as their (+2) precursor ions, for nano-ESI-MS/MS sequencing, even though these ions cannot be detected in the ESI-MS spectra. This method, originally proposed by Tempst et al. (Anal. Chem. 2000, 72: 777-790), has been extended to provide better sensitivity and shorter analysis times; also, a comparison with liquid chromatography/tandem mass spectrometry (LC/MS/MS) has been performed. These experiments, performed using quadrupole time-of-flight instruments equipped with commercially available nano-ESI sources, have allowed the unambiguous identification of in-gel digested proteins at levels below their ESI-MS detection limits, even in the presence of salts and detergents.     

Quantitation of ion abundances in fourier transform ion cyclotron resonance mass spectrometry

To improve the analytical usefulness of Fourier transform ion cyclotron resonance mass spectrometry (FTICR-MS), an extensive survey of various methods for quantitation of peak magnitudes has been undertaken using a series of simulated transient response signals with varying signal-to-noise ratio. Both peak height (five methods) and peak area (four methods) were explored for a range of conditions to determine the optimum methodology for quantitation. Variables included dataset size, apodization function, damping constant, and zero filling. Based on the results obtained, recommended procedures for optimal quantitation include: apodization using a function appropriate for the peak height ratios observed in the spectrum (i.e., Hanning for ratios of about 1:10, three-term Blackman-Harris for ratios of ～1:100, or Kaiser-Bessel for ratios of ～1:1000); zero filling until the peaks of interest are represented by 10–15 points (generally obtained with one order of zero filling); and use of the polynomial y=(ax ²+bx+c) ⁿ and the three data points of highest intensity of the peak to locate the peak maximum, Y _max=(?b ²/4a+c) ⁿ . In this peak fitting procedure, which we have termed the “Comisarow method,” n is 5.5, 9.5, and 12.5 for the Hanning, three-term Blackman-Harris, and Kaiser-Bessel apodization functions, respectively. Accuracy of quantitation using an optimal peak height determination is about equal to that for peak area measurements. These recommendations were found to be valid when tested with real FTICR-MS spectra of xenon isotopes.