In this paper, we introduce a new variant of the BFGS method designed to perform well when gradient measurements are corrupted by noise. We show that treating secant condition with penalty approach motivated regularized least squares estimation generates parametric family original update at one extreme and not updating inverse Hessian approximation other extreme. Furthermore, find curvature is ...

For an irreducible projective variety X, we study the family of h-planes contained in the secant variety Sec k (X), for 0 < h < k. These families have an expected dimension and we study varieties for which the expected dimension is not attained; for these varieties, making general consecutive projections to lower dimensional spaces, we do not get the expected singularities. In particular, we ex...

We give a sharp bound on the regularity of the secant variety to a smooth curve embedded by a line bundle of large (effective) degree.

MATILDE LALÍN, FRANCIS RODRIGUE, AND MATHEW ROGERS Abstract. We study the series ψs(z) := ∑∞ n=1 sec(nπz)n −s, and prove that it converges under mild restrictions on z and s. The function possesses a modular transformation property, which allows us to evaluate ψs(z) explicitly at certain quadratic irrational values of z. This supports our conjecture that πψk( √ j) ∈ Q whenever k and j are posit...

We propose a class of projective manifolds with degenerate secant varieties, which class is wider than that of Scorza varieties , and study some properties of this class of manifolds. For example, we show that there is a strong restriction on dimensions of manifolds in this class. We also give classiications of such manifolds of low dimensions.