Gradient estimates for some diffusion semigroups

 Consider the semigroup $P_t$ of an elliptic diffusion; we describe a simple stochastic method providing gradient estimates on $P_tf$. If $N$ is a manifold endowed with a connection, the method can also be applied to the associated nonlinear semigroup $Q_t$ acting on $N$-valued maps. With a localization technique, we deduce gradient estimates for real harmonic functions or $N$-valued harmonic maps. Moreover, the results are extended to a class of hypoelliptic diffusions. Received: 31 July 2000 / Revised version: 20 September 2001 / Published online: 15 March 2002     

Measurement of unimolecular decay in peptides of masses greater than 1200 units by a reflecting time-of-flight mass spectrometer

Daughter ions from decomposition of [M + H]+ parent ions have been observed in a time-of-flight mass spectrometer fitted with an ion mirror. Unit mass resolution is obtained for parent ions of masses up to several thousand u when the mirror voltage is set at a value determined by the usual velocity-focusing criterion for parent ions. Under this condition the daughter-ion resolution in the low-mass range suffers. Considerable improvement is obtained when the daughter-ion spectrum is examined in several segments, with the mirror voltage optimized for each segment. The daughter-ion spectrum from decay of metastable [M + H]+ parent ions in Substance P is measured using this technique. Reasons are suggested for differences between the spectrum obtained and a spectrum for the same compound recently obtained using a tandem double-focusing instrument.     

First order ordinary differential equations with several periodic solutions

The method of upper and lower solutions and convexity arguments are used to prove sharp results for the existence and multiplicity of periodic solutions for first order ordinary differential equations depending upon a parameter.Dedicated to Professor H. W. Knobloch for his sixtieth birthday     

Influence of the seed polymer on the chromatographic properties of size monodisperse polymeric separation media prepared by a multi-step swelling and polymerization method

Monodisperse polymer particle-based separation media were prepared by a multi-step swelling and polymerization method with two pairs of monomers and two porogenic solvents. Their chromatographic properties were compared to those of beads prepared by a corresponding suspension polymerization method without the use of seed polymer to ascertain the influence of the seed polymer on their porous structures. A large change in porous structure was observed when the swollen particle consisting of monomers and porogenic solvents contained at least one good solvent for the polystyrene seed polymer, allowing it to remain in the polymerizing medium. In contrast, when the polystyrene seed particle was excluded from the swollen oil droplets, due to its poor solubility in the monomers and the porogenic solvents, there was no difference in the chromatographic properties such as pore volume, pore size, pore size distribution, or retention selectivity between the multi-step swelling and polymerization method and the suspension polymerization method. Since the only difference between the multi-step swelling and polymerization method and the suspension method is the use of the seed polymer, it appears that a very small amount (< 1% v/v) of seed polymers in the enlarged swollen droplets plays an important role as a porogen and affects the porous structure as well as the chromatographic properties of the monodisperse polymer particle-based separation media. © 1993 John Wiley & Sons, Inc.     

Hardy-type estimates for Dirac operators

We prove some Hardy type inequalities related to the Dirac operator by elementary methods, for a large class of potentials, which even includes measure valued potentials. Optimality is achieved by the Coulomb potential. When potentials are smooth enough, our estimates provide some spectral information on the operator.     

Long-Time Bath Correlations in the Pollak–Grabert–Hänggi Theory

We analyze some cases for which the Pollak–Grabert–Hänggi theory on the activated rate processes for generalized Langevin dynamics exhibits unexplained disagreements with numerical results. First we analyze carefully the PGH theory and we show that a kind of Markovian hypothesis implicitly made in the reasoning is sometimes violated. Then we propose modifications of the original theory in order to take into account the possible effects caused by this violation, and we compare the corrected results with simulations.