Principal bundles on the affine line

We prove that any principal bundle on the affine line over a perfect field with a reductive group as structure group comes from the base field by base change.     

Modelling the Chemistry of Zeolites by Computer Graphics

The unique structural, adsorptive, and catalytic properties of zeolites are particularly amenable to illustration by computer (especially color) graphics. The siting of cations, the accommodation of guest reactant or product species, as well as the occurrence of various kinds of intergrowths (e.g. twin planes and coincidence boundaries) within these microporous solids can all be effectively portrayed by graphical means in such a manner as to emphasize the shape-selective character of the host zeolite. The dynamics of translational and angular motion of guest species (for example benzene) in a channel of molecular dimensions within a typical zeolitic solid (for example silicalite) can also be probed interactively using appropriate potential functions.     

Some polishing experiments on copper in a hyperbolic cell

Some polishing experiments have been carried out on copper anodes in a hyperbolic cell designed by Gilmont and Walton, using orthophosphoric acid as the electrolyte. The results obtained have been compared to those obtained in similar experiments in a Hull cell. It has been found that very similar bands of different reflectivity and polishes are found to form in both the cells. These bands shift with time and a study of such displacements has been made. The results are briefly discussed.     

Analysis of a model for transport of charged particles in a random magnetic field

A model for the transport of charged particles in a random magnetic field is a Volterra integrodifferential equation with a long-range kernel. The integrodifferential equation is solved numerically with the method of Bellman, Kalaba, and Lockett (“Numerical Inversion of the Laplace Transform,” Elsevier, New York, 1966). The results are shown to be in excellent agreement with analytical asymptotic results.     

Surface criticality and multifractality at localization transitions

We develop the concept of surface multifractality for localization-delocalization (LD) transitions in disordered electronic systems. We point out that the critical behavior of various observables related to wave functions near a boundary at a LD transition is different from that in the bulk. We illustrate this point with a calculation of boundary critical and multifractal behavior at the 2D spin quantum Hall transition and in a 2D metal at scales below the localization length.