Hydrogen migrations in mass spectrometry. IV—formation of [C6H7]+ in the chemical ionization mass spectra of alkylbenzenes

Using specific deuterium labelling the mechanisms of the olefin elimination reactions leading to formation of [C₆H₇]+ in the H₂ and CH₄ chemical ionizatin mass spectra of ethylbenzene and n-propylbenzene (and to [C₂H₅C₆H₆]+ in the CH₄ chemical ionization mass spectra) have been investigated. The results show that the reaction does not occur by specific migration of H from the β position of the alkyl group to the benzene ring. For ethylbenzene 23–29% of the migrating H originates from the α-position, while for n-propylbenzene H migration from all propyl positions is observed in the approximate ratio, position 1:position 2:position 3=0.30:0.22:0.48. It is proposed that the results can be explained on the basis of competing H migration from each alkyl position involving cyclic transition states of different ring sizes, rather than by H randomization within the alkyl chain.     

On the curvature of minimal submanifolds in a sphere

S. T. Yau proved inAmer. J. Math. 97 (1975), p. 95, Theorem 15 that if the sectional curvature of ann-dimensional compact minimal submanifold in the (n + p)-dimensional unit sphere is everywhere greater than (p – 1)/(2p – 1), then this minimal submanifold is totally geodesic. In this note we improve this bound for the casep 2 to (3p – 2)/(6p).     

On "the complete basis set limit" and plane-wave methods in first-principles simulations of water

Water structure, measured by the height of the first peak in oxygen-oxygen radial distributions, is converged with respect to plane-wave basis energy cutoffs for ab initio molecular dynamics simulations, confirming the reliability of plane-wave methods.     

Spectral analysis of Brownian motion with jump boundary

Consider a family of probability measures, indexed by , on a bounded open region with a smooth boundary. For any starting point inside , we run a standard -dimensional Brownian motion in until it first exits , at which time it jumps to a point inside the domain according to the jump measure at the exit point and starts a new Brownian motion. The same evolution is repeated independently each time the process reaches the boundary. We study the exponential rate at which the transition distribution of the process converges to its invariant measure, in terms of the spectral gap of the generator. In particular, we prove two conjectures of I. Ben-Ari and R. Pinsky for an interval (see J. Funct. Anal. 251 (2007), 122-140, and preprint (2007)) by studying when a combination of the sine and cosine transforms of probability measures on an interval has only real zeros.