Quantifier Elimination and Rectilinearisation Theorem for Generalised Quasianalytic Algebras

An algebra of germs of real functions is generalised quasianalytic if to each element of the algebra we can associate, injectively, a power series with nonnegative real exponents. We prove a quantifier elimination and a rectilinearisation result for generalised quasianalytic algebras

Fixed Parameter Undecidability for Wang Tilesets

Deciding if a given set of Wang tiles admits a tiling of the plane is decidable if the number of Wang tiles (or the number of colors) is bounded, for a trivial reason, as there are only finitely many such tilesets. We prove however that the tiling problem remains undecidable if the difference between the number of tiles and the number of colors is bounded by 43. One of the main new tool is the concept of Wang bars, which are equivalently inflated Wang tiles or thin polyominoes.Comment: In Proceedings AUTOMATA&JAC 2012, arXiv:1208.249

Transition maps at non-resonant hyperbolic singularities are o-minimal

We construct a model complete and o-minimal expansion of the field of real numbers such that, for any planar analytic vector field X and any isolated, non-resonant hyperbolic singularity p of X, a transition map for X at p is definable in this structure. This structure also defines all convergent generalized power series with natural support and is polynomially bounded.Comment: 49 pages, 2 figure

In Situ Fabrication Technologies

A manufacturing system is described that is internal to controlled cabin environments which will produce functional parts to net shape with sufficient tolerance, strength and integrity to meet application specific needs such as CEV ECLS components, robotic arm or rover components, EVA suit items, unforeseen tools, conformal repair patches, and habitat fittings among others. Except for start-up and shut-down, fabrication will be automatic without crew intervention under nominal scenarios. Off-nominal scenarios may require crew and/or Earth control intervention. System will have the ability to fabricate using both provisioned feedstock materials and feedstock refined from in situ regolith