Given a regular matrix pencil A + μE, we consider the problem of determining the nearest singular matrix pencil with respect to the Frobenius norm. We present new approaches based on the solution of matrix differential equations for determining the nearest singular pencil A+∆A+ μ(E +∆E), one approach for general singular pencils and another one such that A+∆A and E + ∆E have a common left/right...

The Mα energy which is usually minimized in branched transport problems among singular 1-dimensional rectifiable vector measures with prescribed divergence is approximated (and convergence is proved) by means of a sequence of elliptic energies, defined on more regular vector fields. The procedure recalls the Modica-Mortola one for approximating the perimeter, and the double-well potential is re...

The Topological N=2 Superconformal algebra has 29 different types of singular vectors (in complete Verma modules) distinguished by the relative U(1) charge and the BRST-invariance properties of the vector and of the primary on which it is built. Whereas one of these types only exists at level zero, the remaining 28 types exist for general levels and can be constructed already at level 1. In thi...

An attractor Λ for a 3-vector field X is singular-hyperbolic if all its singularities are hyperbolic and it is partially hyperbolic with volume expanding central direction. We prove that C singularhyperbolic attractors, for some α > 0, always have zero volume, thus extending an analogous result for uniformly hyperbolic attractors. The same result holds for a class of higher dimensional singular...

We shall give a simple criterion for a given singular point on a surface to be a cuspidal cross cap. As an application, we show that the singularities of spacelike maximal surfaces in Lorentz-Minkowski 3-space generically consist of cuspidal edges, swallowtails and cuspidal cross caps. The same result holds for spacelike mean curvature one surfaces in de Sitter 3-space. Introduction Let U be a ...

We give expressions for the singular vectors in the highest weight representations of the Virasoro algebra. We verify that the expressions — which take the form of a product of operators applied to the highest weight vector — do indeed define singular vectors. These results explain the patterns of embeddings amongst Virasoro algebra highest weight representations. Conformal field theory relies ...

We extend Turaev’s definition of torsion invariants of 3-dimensional manifolds equipped with non-singular vector fields, by allowing (suitable) tangency circles to the boundary, and manifolds with non-zero Euler characteristic. We show that these invariants apply in particular to (the exterior of) Legendrian links in contact 3-manifolds. Our approach uses a combinatorial encoding of vector fiel...

In this paper, the regularized solutions of an ill{conditioned system of linear equations are computed for several values of the regularization parameter. Then, these solutions are extrapolated at = 0 by various vector rational extrapolations techniques built for that purpose. These techniques are justiied by an analysis of the regularized solutions based on the singular value decomposition and...

MOTIVATION Systematic differences due to experimental features of microarray experiments are present in most large microarray data sets. Many different experimental features can cause biases including different sources of RNA, different production lots of microarrays or different microarray platforms. These systematic effects present a substantial hurdle to the analysis of microarray data. RE...

The paper provides a condition for differentiability as well as an equivalent criterion for Lipschitz continuity of singular normal distributions. Such distributions are of interest, for instance, in stochastic optimization problems with probabilistic constraints, where a comparatively small (nondegenerate-) normally distributed random vector induces a large number of linear inequality constrai...