Zonoids whose polars are zonoids, cannot have proper faces other than vertices or facets. However, there exist non–smooth zonoids whose polars are zonoids. Examples in R and R are given.

We devise a stabilized method to weakly enforce bound constraints in the discrete solution of advection-dominated diffusion problems. This combines nonlinear penalty formulation with discontinuous Galerkin-based residual minimization method. illustrate efficiency this scheme for both uniform and adaptive meshes through proper numerical examples.

In this article a novel characterization of Bose-Einstein condensates is proposed. Instead relying on occupation numbers few dominant modes, which become macroscopic in the limit infinite particle numbers, it focuses regular excitations whose stay bounded limit. manner, subspaces global, respectively local wave functions are identified. Their orthogonal complements determine particles forming p...

All known proper ferroelectrics are unable to polarize normal to a surface or interface if the resulting depolarization field is unscreened, but there is no fundamental principle that enforces this behavior. In this work, we introduce hyperferroelectrics, a new class of proper ferroelectrics which polarize even when the depolarization field is unscreened, this condition being equivalent to inst...

Prediction markets provide an efficient means to assess uncertain quantities from forecasters. Traditional and competitive strictly proper scoring rules have been shown to incentivize players to provide truthful probabilistic forecasts. However, we show that when those players can cooperate, these mechanisms can instead discourage them from reporting what they really believe. When players with ...