Electrochemically initiated tagging of thiols using an electrospray ionization based liquid microjunction surface sampling probe two‐electrode cell

This paper reports on the conversion of a liquid microjunction surface sampling probe (LMJ‐SSP) into a two‐electrode electrochemical cell using a conductive sample surface and the probe as the two electrodes with an appropriate battery powered circuit. With this LMJ‐SSP, two‐electrode cell arrangement, tagging of analyte thiol functionalities (in this case peptide cysteine residues) with hydroquinone tags was initiated electrochemically using a hydroquinone‐doped solution when the analyte either was initially in solution or was sampled from a surface. Efficient tagging (～90%), at flow rates of 5–10 µL/min, could be achieved for up to at least two cysteines on a peptide. The high tagging efficiency observed was explained with a simple kinetic model. In general, the incorporation of a two‐electrode electrochemical cell, or other multiple electrode arrangement, into the LMJ‐SSP is expected to add to the versatility of this approach for surface sampling and ionization coupled with mass spectrometric detection. Published in 2009 by John Wiley & Sons, Ltd.     

Universality and fine zero spacing on general sets

A recent approach of D. S. Lubinsky yields universality in random matrix theory and fine zero spacing of orthogonal polynomials under very mild hypothesis on the weight function, provided the support of the generating measure μ is [-1,1]. This paper provides a method with which analogous results can be proven on general compact subsets of R. Both universality and fine zero spacing involves the equilibrium measure of the support of μ. The method is based on taking polynomial inverse images, by which results can be transferred from [-1,1] to a system of intervals, and then to general sets.     

Weighted polynomial inequalities

For the weights exp (?|x|^λ), 0<λ≤1, we prove the exact analogue of the Markov-Bernstein inequality. The Markov-Bernstein constant turns out to be of order logn for λ=1 and of order 1 for 0<λ<1. The proof is based on the solution of the problem of how fast a polynomialP _n can decrease on [?1,1] ifP _n (0)=1. The answer to this problem has several other consequences in different directions; among others, it leads to a general theorem about the incompleteness of the set of polynomials in weightedL ^p spaces.