Norms of powers of the Volterra operator

The norms of them-th powers of the Volterra operatorV onL ²[0, 1] are computed form=1,...,10. These numbers suggest that the sequencem!V is bounded above and below, which is shown, and that this sequence converges to 1/2, which is conjectured.     

Wasseranalyse

Ohne Zusammenfassung     

The existence of approximate solutions to mixed boundary value problems

Approximate solutions, similar to the type used in the Complex Variable Boundary Element Method, are shown to exist for two dimensional mixed boundary value potential problems on multiply connected domains. These approximate solutions can be used numerically to obtain least squares solutions or solutions which interpolate given boundary conditions. Areas of application include fluid flow around obstacles and heat flow in a domain with insulated boundary segments. © 1999 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 15: 191–199, 1999     

Angle-resolved photoelectron spectroscopy of cyclopropane

The angular distribution parameter, β, determined for the valence orbitals (IP < 18 eV) of cyclopropane in the 10–30 eV photon energy range using dispersed polarized synchrotron radiation. The energy dependence of β for photoelectron energies between, 2 and 10 eV above threshold was found to be similar to those found previously for other σ orbitals. The effects of Jahn-Teller splitting on β for the 3e′ orbital were found to be small but definitely present. The overall shape and magnitude of the β(hv) curve are, however, sufficiently for the different Jahn-Teller components that, for purposes of orbital assignments using β(hv) curves the shape and magnitude of the curves can be considered associated only with the initial state. Resonance photoionization features at a photon ener of ≈ 18 eV were observed in the 3e′ and 3a′₁ orbitals and tentatively assigned to autoionization.     

Use of automatic relevance determination in QSAR studies using Bayesian neural networks

We describe the use of Bayesian regularized artificial neural networks (BRANNs) coupled with automatic relevance determination (ARD) in the development of quantitative structure-activity relationship (QSAR) models. These BRANN-ARD networks have the potential to solve a number of problems which arise in QSAR modeling such as the following: choice of model; robustness of model; choice of validation set; size of validation effort; and optimization of network architecture. The ARD method ensures that irrelevant or highly correlated indices used in the modeling are neglected as well as showing which are the most important variables in modeling the activity data. The application of the methods to QSAR of compounds active at the benzodiazepine and muscarinic receptors as well as some toxicological data of the effect of substituted benzenes on Tetetrahymena pyriformis is illustrated.     

Multiple solvation configurations around phthalocyanine in helium droplets

Recent measurements of the emission spectrum of phthalocyanine solvated in superfluid helium nanodroplets exhibit a constant 10.3 cm(-1) splitting of each emission line relative to the absorption spectrum. This splitting has been attributed to two distinct helium environments near the surface of the phthalocyanine molecule. Rigid-body path-integral Monte Carlo provides a means of investigating the origin of the splitting on a detailed microscopic level. Path-integral Monte Carlo simulations of 4He(N)-phthalocyanine at 0.625 K with N ranging from 24 to 150 show two distinct helium configurations. One configuration is commensurate with the molecular substrate and the other is a triangular lattice. We investigate the energetics of these two configurations and use a method for calculating electronic spectral shifts for aromatic molecule-rare-gas clusters due to dispersive interactions to estimate the spectral splitting that would arise from the two helium configurations seen for N=150. The results are in reasonable agreement with the experimentally measured splitting, supporting the existence of two distinct local helium environments near the surface of the molecule in the nanodroplets.     

Numerical solutions of the Dirichlet problem via a density theorem

Under mild conditions a certain subspace M, consisting of functions which are analytic in a simply connected domain Ω and continuous on the boundary Gamma;, is shown to have real parts which are dense, in the sup norm, in the set of all solutions to the Dirichlet problem for continuous boundary data. Similar results hold for L^p boundary data. Numerical solutions of sample Dirichlet problems are computed. © 1994 John Wiley & Sons, Inc.     

The Riemann Hypothesis, the Generalized Riemann Hypothesis, and the Cesáro Operator

A result due to Nyman establishes the equivalence of the Riemann hypothesis with the density of a set of functions in L ²[0, 1]. Here a large class of analytic functions is considered, which includes the Riemann zeta function and the Dirichlet L-functions as well as functions not given by a Dirichlet series. For each such function there is an associated integral operator T on L ²[0, 1] such that has no zeros in Re(s) > 1/2 iff the operator T has dense range iff a specified set of functions is dense in L ²[0, 1].