Isoperimetric Regions in Rn\mathbb{R}^n with density rpr^p

We show that the unique isoperimetric hypersurfaces in $\mathbb{R}^n$ with density $r^p$ for $n \ge 3$ and $p>0$ are spheres that pass through the origin.Comment: published online in Analysis and Geometry in Metric Spaces, revised according to referee report, 29 pages, 10 figure

Simplicity, primitivity and semiprimitivity of etale groupoid algebras with applications to inverse semigroup algebras

This paper studies simplicity, primitivity and semiprimitivity of algebras associated to \'etale groupoids. Applications to inverse semigroup algebras are presented. The results also recover the semiprimitivity of Leavitt path algebras and can be used to recover the known primitivity criterion for Leavitt path algebras.Comment: Updated after referee report and corrected misprint

Polarization analysis of K-edge resonant x-ray scattering of germanium

The polarization of K-edge resonant scattering at the space group ``forbidden'' (0 0 6) reflection of Ge was measured as function of the azimuthal angle, psi. The experimental results are compared to model calculations based on symmetry analysis of the resonant scattering tensors.Comment: 4 pages, 3 figures. Submitted to Phys. Rev. B Rapid Communications V2: Updated after referee report

Algebras of Quasi-Pl\"ucker Coordinates are Koszul

Motivated by the theory of quasi-determinants, we study non-commutative algebras of quasi-Pl\"ucker coordinates. We prove that these algebras provide new examples of non-homogeneous quadratic Koszul algebras by showing that their quadratic duals have quadratic Gr\"obner bases.Comment: 15 pages, AMS tex, tikz figures. V2: small corrections based on referee report. V3: Further minor changes. To appear in J. Pure Appl. Algebr

K1K_1-groups via binary complexes of fixed length

We modify Grayson's model of $K_1$ of an exact category to give a presentation whose generators are binary acyclic complexes of length at most $k$ for any given $k \ge 2$. As a corollary, we obtain another, very short proof of the identification of Nenashev's and Grayson's presentations.Comment: 10 pages, minor changes following a referee report, to appear in HH

Many intermingled basins in dimension 3

We construct a diffeomorphism of $\mathbb{T}^3$ admitting any finite or countable number of physical measures with intermingled basins. The examples are partially hyperbolic with splitting $T\mathbb{T}^3 = E^{cs} \oplus E^u$ and can be made volume hyperbolic and topologically mixing.Comment: 20 pages, 4 figures. Some changes made after referee report. To appear in Israel J. of Mat