We use Lie-theoretic methods to explicitly compute the full spectrum of Laplace--Beltrami operator on homogeneous spheres which occur as geodesic distance in (compact or noncompact) symmetric spaces rank one, and provide a single unified formula for all cases. As an application, we find resonant radii compact case, i.e., where there is bifurcation embedded constant mean curvature spheres, show ...

On the structure of non-full-rank perfect codes Denis S. Krotov Sobolev Institute of Mathematics and Mechanics and Mathematics Department, Novosibirsk State University Novosibirsk, Russia The Krotov combining construction of perfect 1-error-correcting binary codes from 2000 and a theorem of Heden saying that every non-full-rank perfect 1-errorcorrecting binary code can be constructed by this co...

In this article we introduce a full-rank representation of the Drazin inverse AD of a given complex matrix A, which is based on an arbitrary full-rank decomposition of Al, l ≥ k, where k is the index of A. We show that the known representation of the Drazin inverse of A, devised in [7], represents a partial case of this result. Using this general representation, we introduce a determinantal rep...

We present a joint spatial and spectral denoising front-end for Track 1 of the 2nd CHiME Speech Separation and Recognition Challenge based on the Flexible Audio Source Separation Toolbox (FASST). We represent the sources by nonnegative matrix factorization (NMF) and full-rank spatial covariances, which are known to be appropriate for the modeling of small source movements. We then learn acousti...