Non-convex functions that yet satisfy a condition of uniform convexity for non-close points can arise in discrete constructions. We prove this sort is inherited by the convex envelope, which key to obtain other remarkable properties such as coercivity. Our techniques allow retrieve Enflo's uniformly renorming super-reflexive Banach spaces regularization raw function built from trees. Among appl...

A bstract We show that the two-point function of protected bi-scalar operators in $$ \mathcal{N} N = 4 SYM evaluated dimensional regularization exhibits a uniform transcendental weight up to three-loop order. conjecture this property holds for whole perturbative series and leverage explicit results postulate ...

the notion of a bead metric space is defined as a nice generalization of the uniformly convex normed space such as $cat(0)$ space, where the curvature is bounded from above by zero. in fact, the bead spaces themselves can be considered in particular as natural extensions of convex sets in uniformly convex spaces and normed bead spaces are identical with uniformly convex spaces. in this paper, w...

We study a specific family of uniformly isochronous polynomial systems. Our results permit us to solve a problem about centers of such systems. We consider the composition conjecture for uniformly isochronous polynomial systems.