We show that, contrary to popular assumptions, predictions from machine learning potentials built upon high-dimensional atom-density representations almost exclusively occur in regions of the representation space which lie outside convex hull defined by training set points. then propose a perspective rationalize domain robust extrapolation and accurate prediction atomistic terms probability den...

It is known that a uniformly convex Banach space is reflexive and strictly convex. E is said to be smooth provided limt→ ‖x+ty‖–‖x‖ t exists for all x, y ∈UE . It is also said to be uniformly smooth if the limit is attained uniformly for all x, y ∈UE . It is well known that if E* is strictly convex, then J is single valued; if E* is reflexive, and smooth, then J is single valued and demicontin...

begin{abstract} in this paper, we prove some strong and weak convergence of three step random iterative scheme with errors to common random fixed points of three asymptotically nonexpansive nonself random mappings in a real uniformly convex separable banach space. end{abstract}

in this paper, we introduce a one-step iterative scheme for finding a common fixed point of a finite family of multivalued quasi-nonexpansive mappings in a real uniformly convex banach space. we establish weak and strong convergence theorems of the propose iterative scheme under some appropriate conditions.

We establish a solution to the Monge problem in N , with an asymmetric, strictly convex norm cost function, when the initial measure is absolutely continuous. We focus on the strategy, based on disintegration of measures, initially proposed by Sudakov. As known, there is a gap to fill. The missing step is completed when the unit ball is strictly convex, but not necessarily differentiable nor un...