In this article, we are concerned with a class of nonlinear partial differential elliptic equations with Dirichlet boundary data. The key feature of this paper consists in competition effects of two generalized differential operators, which extend the standard operators with variable exponent. This class of problems is motivated by phenomena arising in non-Newtonian fluids or image reconstructi...

Machine learning potentials (MLPs) for atomistic simulations have an enormous prospective impact on materials modeling, offering orders of magnitude speedup over density functional theory without appreciably sacrificing accuracy material property prediction.

The purpose of this article is to present a short model-theoretic proof of the valuation property for a polynomially bounded, o-minimal theory T . The valuation property was conjectured by van den Dries [1], and proved for the polynomially bounded case by van den Dries– Speissegger [4] and for the power bounded case by Tyne [11]. Our proof uses the transfer principle for the theory Tconv (theor...