A stratification of a set, e.g. an analytic variety, is, roughly, a partition of it into manifolds so that these manifolds fit together “regularly”. Stratification theory was originated by Thom and Whitney for algebraic and analytic sets. It was one of the key ingredients in Mather’s proof of the topological stability theorem [Ma] (see [GM] and [PW] for the history and further applications of s...

The Loomis-Whitney inequality, and the more general Uniform Cover inequality, bound the volume of a body in terms of a product of the volumes of lowerdimensional projections of the body. In this paper, we prove stability versions of these inequalities, showing that when they are close to being tight, the body in question is close in symmetric difference to a box. Our results are best possible u...

BACKGROUND Research suggests that participants do not always adequately understand studies. While some consent interventions increase understanding, methodologic challenges have been raised in studying consent outside of actual trial settings. This study examined the feasibility of testing two consent interventions in actual studies and measured effectiveness of interventions in improving under...

In this paper, we establish an extended Loomis–Whitney inequality for positive double John bases, which generalises Ball’s result [1]. Moreover, a different extension of the Loomis–Whitney inequality is deduced. 2010 Mathematics Subject Classification. 52A20, 52A21, 52A40.