Universal vector bundle over the reals

Universal Vector Bundle over the Reals

Let XR be a geometrically irreducible smooth projective curve, defined over R, such that XR does not have any real points. Let X = XR×R C be the complex curve. We show that there is a universal real algebraic line bundle over XR × Pic d(XR) if and only if χ(L) is odd for L ∈ Picd(XR). There is a universal quaternionic algebraic line bundle over X × Pic(X) if and only if the degree d is odd. Tak...

Supermanifolds Corresponding to the Trivial Vector Bundle over Complex Torus

δ-Decidability over the Reals∗

Given any collection F of computable functions over the reals, we show that there exists an algorithm that, given any LF -sentence φ containing only bounded quantifiers, and any positive rational number δ, decides either “φ is true”, or “a δ-strengthening of φ is false”’. Under mild assumptions, for a C-computable signature F , the δ-decision problem for bounded Σk-sentences in LF resides in (Σ...

Universal minimal dynamical system for reals

Our aim is to give a description of S(R) and M(R), the phase space of universal ambit and the phase space of universal minimal dynamical system for the group of real numbers with the usual topology.

Concurrent Cooperating Solvers over Reals

Systems combining an interval narrowing solver and a linear programming solver can tackle constraints over the reals that none of these solvers can handle on their own. In this paper we introduce a cooperating scheme where an interval narrowing solver and a linear programming solver work concurrently. Information exchanged by the solvers is therefore handled as soon as it becomes available. Mor...