In [11] Zarrabi-Zadeh and Chan proposed an algorithm to compute an approximate minimum spanning ball in the streaming model of computation and showed by an elegant analysis that the radius of the approximate ball is to within 3/2 of the exact one. Inspired by this result, in this paper we consider the extension of this result to computing approximate minimum spanning ellipses. The ball algorith...

We study structure properties of reductive group schemes defined over a local ring and splitting over its étale quadratic extension. As an application we prove Serre–Grothendieck conjecture on rationally trivial torsors over a local regular ring containing a field of characteristic 0 for group schemes of type F4 with trivial g3 invariant. 2010 Mathematics Subject Classification: 20G07, 20G10, 2...

We study structure properties of reductive group schemes defined over a local ring and splitting over its étale quadratic extension. As an application we prove Serre–Grothendieck conjecture on rationally trivial torsors over a local regular ring containing a field of characteristic 0 for group schemes of type F4 with trivial g3 invariant.

We show how to produce SO3-equivariant vector fields on non-trivial SO3-torsors which correspond to quadratic forms non-equivalent to the unit form. We then show an example of a Picard-Vessiot extension with group SO3 which is the function field of a non-trivial SO3-torsor.

A primitive word w is a Lyndon word if w is minimal among all its conjugates with respect to some lexicographic order. A word w is bordered if there is a nonempty word u such that w = uvu for some word v. A right extension of a word w of length n is a word wu where all factors longer than n are bordered. A right extension wu of w is called trivial if there exists a positive integer k such that ...