On the cohomological equation for nilflows

Let X be a vector field on a compact connected manifold M. An important question in dynamical systems is to know when a function g:M -> R is a coboundary for the flow generated by X, i.e. when there exists a function f: M->R such that Xf=g. In this article we investigate this question for nilflows on nilmanifolds. We show that there exists countably many independent Schwartz distributions D_n such that any sufficiently smooth function g is a coboundary iff it belongs to the kernel of all the distributions D_n.Comment: 27 page

Invariant Distributions for homogeneous flows

We prove that every homogeneous flow on a finite-volume homogeneous manifold has countably many independent invariant distributions unless it is conjugate to a linear flow on a torus. We also prove that the same conclusion holds for every affine transformation of a homogenous space which is not conjugate to a toral translation. As a part of the proof, we have that any smooth partially hyperbolic flow on any compact manifold has countably many distinct minimal sets, hence countably many distinct ergodic probability measures. As a consequence, the Katok and Greenfield-Wallach conjectures hold in all of the above cases.Comment: 43 page

Linearization of Cohomology-free Vector Fields

We study the cohomological equation for a smooth vector field on a compact manifold. We show that if the vector field is cohomology free, then it can be embedded continuously in a linear flow on an Abelian group

Results from a combined test of an electromagnetic liquid argon calorimeter with a hadronic scintillating-tile calorimeter

The first combined test of an electromagnetic liquid argon accordion calorimeter and a hadronic scintillating-tile calorimeter was carried out at the CERN SPS. These devices are prototypes of the barrel calorimeter of the future ATLAS experiment at the LHC. The energy resolution of pions in the energy range from 20 to 300~GeV at an incident angle $\theta$ of about 11$^\circ$ is well-described by the expression \sigma/E = ((46.5 \pm 6.0)\%/\sqrt{E} +(1.2 \pm 0.3)\%) \oplus (3.2 \pm 0.4)~\mbox{GeV}/E. Shower profiles, shower leakage, and the angular resolution of hadronic showers were also studied