The definition of an S-category is proposed by weakening the axioms of a Q-category introduced by Kontsevich and Rosenberg. Examples of Qand S-categories and (co)smooth objects in such categories are given.

Variable projection is a powerful technique in optimization. Over the last 30 years, it has been applied broadly, with empirical and theoretical results demonstrating both greater efficacy and greater stability than competing approaches. In this paper, we illustrate the technique on a large class of structured nonsmooth optimization problems, with numerical examples in sparse deconvolution and ...

Gompf’s end-sum techniques are used to establish the existence of an infinity of non-diffeomorphic manifolds, all having the same trivial R topology, but for which the exotic differentiable structure is confined to a region which is spatially limited. Thus, the smoothness is standard outside of a region which is topologically (but not smoothly) B ×R, where B is the compact three ball. The exter...