We extend in several directions invariant theory results of Chevalley, Shephard and Todd, Mitchell and Springer. Their results compare the group algebra for a finite reflection group with its coinvariant algebra, and compare a group representation with its module of relative coinvariants. Our extensions apply to arbitrary finite groups in any characteristic.

Starting with a measurable cardinal κ of the Mitchell order κ++ we construct a model with a precipitous ideal on א1 but without normal precipitous ideals. This answers a question by T. Jech and K. Prikry. In the constructed model there are no Q–point precipitous filters on א1, i.e. those isomorphic to extensions of Cubא1 .

Prof Ortwin Renn was one of my PhD supervisors at Clark University (along with Robert Mitchell and Roger Kasperson) where I studied risk research energy policy between 1988 1992. ...

The state of Michigan occupies an area between the Great Plains and the northeastern United States, bordering four Great Lakes, with diverse biogeographical regions. Michigan also has the second most diverse agriculture in the country, with many crops that depend on bees for pollination. This unique combination provides a wide range of opportunities for bees to persist, yet there is no current ...

standing of the power and limitations of learning algorithms. Machine learning draws on multiple disciplines. Mitchell provides the necessary background in both statistics and computational learning theory (a chapter on each) so that results from these fields can be understood and applied. He does not go overboard and overwhelm students in these areas. Instead, Mitchell takes the practical poin...