Characterization of isoperimetric sets inside almost-convex cones

In this note we characterize isoperimetric regions inside almost-convex cones. More precisely, as in the case of convex cones, we show that isoperimetric sets are given by intersecting the cone with a ball centered at the origin.Comment: To appear in Discrete Contin. Dyn. Syst.; 15 page

An investigation of photon correlation spectroscopy data analysis packages discrete and contin using the Schulz-Zimm distribution

DISCRETE and CONTIN are standard data analysis packages used in Photon Correlation Spectroscopy for inversion of noisy autocorrelation functions. Their resolution was studied using simulated autocorrelation data based on the Schulz-Zimm distribution of polymer radii; Autocorrelation functions with various noise levels were fitted to both programs. The CONTIN output was compared with the original distribution. Autocorrelation functions calculated for broader distributions of radii yielded correspondingly broader functions in the radius space. Features like the skewness of the original Schulz-Zimm distribution were not recovered except in the case of narrow, approximately monodisperse radius distributions. Addition of noise was not found to seriously affect the performance of DISCRETE and CONTIN, however, a narrowing of the recovered radius distribution, attributable to the CONTIN feature of parsimony, was observed; It was concluded that although CONTIN results are affected by the breadth of the original radius distribution, an exact correspondence is hard to find

A remark on reaction-diffusion equations in unbounded domains

We prove the existence of a compact L^2-H^1 attractor for a reaction-diffusion equation in R^n. This improves a previous result of B. Wang concerning the existence of a compact L^2-L^2 attractor for the same equation.Comment: 6 pages; to appear on "Discr. Contin. Dynam. Systems (DCDS-A)"; two references adde

Mild mixing property for special flows under piecewise constant functions

We give a condition on a piecewise constant roof function and an irrational rotation by $\alpha$ on the circle to give rise to a special flow having the mild mixing property. Such flows will also satisfy Ratner's property. As a consequence we obtain a class of mildly mixing singular flows on the two-torus that arise from quasi-periodic Hamiltonians flows by velocity changes.Comment: Accepted for publication in Discrete Contin. Dyn. Sys

Global existence for the system of the macroscopic balance equations of charge transport in semiconductors

AbstractGlobal existence of a solution to the nonlinear balance equations of charge transport in semiconductors based on the maximum entropy principle [Contin. Mech. Thermodyn. 11 (1999) 307–325; Contin. Mech. Thermodyn. 12 (2000) 31–51] is proven for a typical 1D problem under certain restrictions on the doping profile and the initial data