We introduce a cohomology, called extendable cohomology, for abstract complex singular varieties based on suitable differential forms. Beside a study of the general properties of such a cohomology, we show that, given a complex vector bundle, one can compute its topological Chern classes using the extendable Chern classes, defined via a Chern-Weil type theory. We also prove that the localizatio...

We present optimal, up to poly-logarithmic factors, bit complexity results for basic operations, matrix-vector multiplication and solving non-singular linear systems, with structured matrices.

Using new and emerging ideas about the growth of singular vectors (‘optimal perturbations’) in dynamical systems, the dynamics of error growth and predictability in an intermediate coupled model of the El Niiio Southern Oscillation (ENSO) is investigated. A mechanism is identified for error growth associated with penetrative-convection anomalies in the atmosphere. Conditions for error growth vi...

When a plane undergoes a deformation that can be represented by a planar linear vector eld, the projected vector eld on the image plane of an optical device is at most quadratic. This 2D motion eld has one singular point, with eigenvalues identical to those of the singular point describing the deformation. As a consequence, the nature of the singular point of the deformation is a projective inv...

This paper examines the problem of relative attitude observability for formations of three, four and five vehicle formations. The analysis is rooted in within the principles of maximum likelihood estimation insomuch as the metric for observability is the resulting Fisher information matrix for the small attitude errors. For formations of three and four vehicles it is shown that the relative att...

This paper is concerned with approximating the dominant left singular vector space of a real matrix A of arbitrary dimension, from block Krylov spaces generated by the matrix AAT and the block vector AX. Two classes of results are presented. First are bounds on the distance, in the two and Frobenius norms, between the Krylov space and the target space. The distance is expressed in terms of prin...

We present a framework that yields a variety of weighted and vector-valued estimates for maximally modulated Calderón-Zygmund singular (and maximal singular) integrals from a single a priori weak type unweighted estimate for the maximal modulations of such operators. We discuss two approaches, one based on the good-λ method of Coifman and Fefferman [CF] and an alternative method employing the s...

A stability analysis is made for a non-singular pre-big-bang like cosmological model based on 1-loop corrected string effective action. Its homogeneous and isotropic solution realizes non-singular transition from de Sitter universe to Friedmann-like universe, via super inflation phase. We are interested in whether the non-singular nature of the solution would be stable or not in more general in...