Time decay for nonlinear wave equations in two space dimensions

The Cauchy Problem for the equation u_tt–u+|u|^p–1u=0 (x², t>0, >1) is studied. Smooth Cauchy data is prescribed, and no smallness condition is imposed. For >5, it is shown that the maximum amplitude of such a wave decays at the expected rate t^–1/2 as t. For 1+8<5, the maximum amplitude still decays, but at a slower rate. These results are then used to demonstrate the existence of the scattering operator when >_o, where _o is the root of the cubic equation ³-2²-7-8=0; thus _o4.15.Alfred P. Sloan Research Fellow     

Measures of distance for atomic charge and momentum densities and their relationship to physical properties

Atomic charge and momentum densities of 91 atoms (He? U) are classified in terms of their L₁, L₂, and entropic measures of distance from the densities of the preceding atoms. The relationship between these distances and the first ionization energies is also considered. © 1995 John Wiley & Sons, Inc.     

Organometallic complex compounds,part 51. Ligand property controlled CO-insertion in nickel complexes: Separation of electronic and steric effects

Summary The influence of twenty phosphorus-containing ligands on the CO insertion with four-coordinated Ni¹¹ complexes as starting reagents is reported. Quantitative separation of the electronic and steric effects by a multilinear regression analysis (55% electronic and 45% steric influence) is presented together with a three dimensional representation. An increase in donor-capacity favours CO insertion and an increase in steric hindrance leads to a decrease in the fraction of the corresponding ketone.     

Acoustic excitations in a self-assembled block copolymer photonic crystal

High resolution Brillouin light scattering can sensitively detect acoustic phonons in concentrated solutions of a high molecular weight poly(styrene-b-isoprene) symmetric copolymer in toluene. This block copolymer lamellar forming system also possesses a photonic stop band in the visible spectrum. Based on the low but finite contrast in mechanical properties between the styrene and isoprene components and taking into account the geometrical characteristics of the layered microstructure, we calculate the acoustic band structure and represent the observed acousticlike and opticlike phonons.