Spectrally bounded operators from von Neumann algebras

We prove that every unital spectrally bounded operator from a properly infinite von Neumann algebra onto a semisimple Banach algebra is a Jordan homomorphism.

Deep sampling and testing in soft stratified clay

A 37-m thick layer of stratified clay encountered during a site investigation at Swann's Bridge, near the sea-coast at Limavady, Northern Ireland, is one of the deepest and thickest layers of this type of material recorded in Ireland. A study of the relevant literature and stratigraphic evidence obtained from the site investigation showed that despite being close to the current shoreline, the clay was deposited in a fresh-water glacial lake formed approximately 13 000 BP. The 37-m layer of clay can be divided into two separate zones. The lower zone was deposited as a series of laminated layers of sand, silt, and clay, whereas the upper zone was deposited as a largely homogeneous mixture. A comprehensive series of tests was carried out on carefully selected samples from the full thickness of the deposit. The results obtained from these tests were complex and confusing, particularly the results of tests done on samples from the lower zone. The results of one-dimensional compression tests, unconsolidated undrained triaxial tests, and consolidated undrained triaxial compression tests showed that despite careful sampling, all of the specimens from the lower zone exhibited behaviour similar to that of reconstituted clays. It was immediately clear that the results needed explanation. This paper studies possible causes of the results from tests carried out on the lower Limavady clay. It suggests a possible mechanism based on anisotropic elasticity, yielding, and destructuring that provides an understanding of the observed behaviour.Key words: clay, laminations, disturbance, yielding, destructuring, reconstituted.

An analogue of the Magnus problem for associative algebras

We prove an analogue of Magnus theorem for associative algebras without unity over arbitrary fields. Namely, if an algebra is given by $n+k$ generators and $k$ relations and has an $n$-element system of generators, then this algebra is a free algebra of rank $n$.

A comparison of a range of models for dispersion in a partially stratified room

A comparative study of models used to predict contaminant dispersion in a partially stratified room is presented. The experiments were carried out in a ventilated test room, with an initially evenly dispersed pollutant. Air was extracted from the outlet in the ceiling of the room at 1 and 3 air changes per hour. A small temperature difference between the top and bottom of the room causes very low air velocities, and higher concentrations, in the lower half of the room. Grid-independent CFD calculations were compared with predictions from a zonal model and from CFD using a very coarse grid. All the calculations show broadly similar contaminant concentration decay rates for the three locations monitored in the experiments, with the zonal model performing surprisingly well. For the lower air change rate, the models predict a less well mixed contaminant distribution than the experimental measurements suggest. With run times of less than a few minutes, the zonal model is around two orders of magnitude faster than coarse-grid CFD and could therefore be used more easily in parametric studies and sensitivity analyses. For a more detailed picture of internal dispersion, a CFD study using coarse and standard grids may be more appropriate.