Non-algebraic Examples of Manifolds with the Volume Density Property

Some Stein manifolds (with a volume form) have a large group of (volume-preserving) automorphisms: this is formalized by the (volume) density property, which has remarkable consequences. Until now all known manifolds with the volume density property are algebraic, and the tools used to establish this property are algebraic in nature. In this note we adapt a known criterion to the holomorphic case, and give the first known examples of non-algebraic manifolds with the volume density property: they arise as suspensions or pseudo-affine modifications over Stein manifolds satisfying some technical properties. As an application we show that there are such manifolds that are potential counterexamples to the Zariski Cancellation Problem, a variant of the Toth-Varolin conjecture, and the problem of linearization of C*-actions on C^3

Flory-Huggins theory for athermal mixtures of hard spheres and larger flexible polymers

A simple analytic theory for mixtures of hard spheres and larger polymers with excluded volume interactions is developed. The mixture is shown to exhibit extensive immiscibility. For large polymers with strong excluded volume interactions, the density of monomers at the critical point for demixing decreases as one over the square root of the length of the polymer, while the density of spheres tends to a constant. This is very different to the behaviour of mixtures of hard spheres and ideal polymers, these mixtures although even less miscible than those with polymers with excluded volume interactions, have a much higher polymer density at the critical point of demixing. The theory applies to the complete range of mixtures of spheres with flexible polymers, from those with strong excluded volume interactions to ideal polymers.Comment: 9 pages, 4 figure

Morphometric brain changes during aging: Results from a Brazilian necropsy sample.

The present study aimed to establish the morphometric brain changes during aging in a necropsy series from Brazil and determine whether sexual dimorphisms interfere in these changes. Methods:A cross-sectional study was conducted at the São Paulo Autopsy Service in Brazil where, after informed consent, data was gathered from next of kin interview with reference to clinical status prior to death. Brain weight, volume and density measurements were taken and then adjusted for head circumference. Descriptive statistics and tests of hypothesis and correlations were applied, considering a p-value of 0.05. Results:414 subjects, mostly men (60.4%), with a mean age of 67.1 years, were included. The mean brain weight of the sample was 1219.2g±140.9and mean volume was 1217mL±152.3. The mean brain density of the sample was 1.0g/mL±0.09. Values differed between males and females in terms of weight and volume. Brain weight decreased during aging by about 45g per decade (r= -0.300; p<0.01) and volume by about 43mL (r= -0.278; p<0.00). Mean density of the sample was 1.0 g/mL in both genders. Conclusions:Brain weight and volume (with or without corrections) decreased during aging, and these reductions were more pronounced in women. Density remained unchanged for both genders. Further studies are needed to investigate factors associated to these reductions