Gl2 of rings with many units

This paper describes the generiators and normal subgroups of GL₂(R) where R is a commutative ring with “many units”.     

Developing Interdisciplinary Units: Strategies and Examples

The authors use a common theme of SHARKS to illustrate the process of developing an interdisciplinary unit for middle school instruction. A model is presented for teams to use in developing integrated curriculum. Focusing on a central theme or topic, a web of disciplines and key concepts is developed. As activities evolve, a concept map is created to illustrate the relationships and integration of ideas and activities.     

Phase behaviour of lithium and sodium salts of phenylstearic acid

Phenylstearic acid, prepared from oleic acid and benzene, using the Friedel-Crafts reaction, has been confirmed to be a reproducible mixture of twelve positional isomers. Lithium and sodium salts of this acid are semi-crystalline solids which behave in many ways like pure single substances. The thermotropic polymorphism of these soaps has been studied using DSC and polarizing microscopy (as well as X-ray diffraction and ⁷Li NMR spectroscopy for the former soap). Both soaps exhibit characteristic stepwise melting behaviour and form stable reversed hexagonal mesophases at elevated temperatures, in contrast to the lamellar phases exhibited by the unsubstituted soaps.     

Cuprate Fermi orbits and Fermi arcs: the effect of short-range antiferromagnetic order

We consider the effect of a short antiferromagnetic correlation length xi on the electronic band structure of the underdoped cuprates. Starting with a Fermi-surface topology consistent with magnetic-quantum-oscillation data, we show that a reduced xi gives an asymmetric broadening of the quasiparticle dispersion, resulting in simulated ARPES data very similar to those observed in experiment. Predicted features include "Fermi arcs" close to ak=(pi/2,pi/2), where a is the in-plane lattice parameter, without the need to invoke a d-wave pseudogap order parameter. The statistical variation in the k-space areas of the reconstructed Fermi-surface pockets causes the quantum oscillations to be strongly damped, even in very strong magnetic fields, in agreement with experiment.     

On the effect of quarter-wave-plate errors in stress-holo-interferometry

The purpose of this paper is to analyze the influence of imperfect quarter-wave plates on the fringe configuration which is obtained in holographic interferometry. It has been found that isopachics may be substantially shifted by very small errors in the retardation of the quarter-wave plates. An alternative multiexposure technique using plane-polarized light is proposed. This technique eliminates the quarter-wave-plate error and preserves the full-field character of the interferometic method. The technique is proven analytically and experimentally.     

Dynamic load and inflation pressure effects on contact pressures of a forestry forwarder tire

A Trelleborg Twin 421 Mark II 600/55-26.5 steel-reinforced bias-ply forwarder drive tire at inflation pressures of 100 and 240 kPa and dynamic loads of 23.9 and 40 kN was used at 5% travel reduction on a firm clay soil. Effects of dynamic load and inflation pressure on soil–tire contact pressures were determined using six pressure transducers mounted on the tire tread. Three were mounted on the face of a lug and three at corresponding locations on the undertread. Contact angles increased with decreases in inflation pressure and increases in dynamic load. Contact pressures on a lug at the edge of the tire increased as dynamic load increased. Mean and peak pressures on the undertread generally were less than those on a lug. The peak pressures on a lug occurred forward of the axle in nearly all combinations of dynamic load, inflation pressure, and pressure sensor location, and peak pressures on the undertread occurred to the rear of the axle in most of the combinations. Ratios of the peak contact pressure to the inflation pressure ranged from 0 at the edge of the undertread for three combinations of dynamic load and inflation pressure to 8.39 for the pressure sensor on a lug, near the tire centerline, when the tire was underinflated. At constant dynamic load, net traction and tractive efficiency decreased as inflation pressure increased.