We give some new characterizations of exactness for locally compact second countable groups. In particular, we prove that a locally compact group is exact if and only if it admits a topologically amenable action on a compact Hausdorff space. This answers an open question by Anantharaman-Delaroche.

We present an entropy-stable semi-discretization of the Euler equations. The scheme is based on high-order summation-by-parts (SBP) operators for triangular and tetrahedral elements, although the theory is applicable to multidimensional SBP operators on more general elements. While there are established methods for proving stability of linear equations, such as energy analysis, they are not ade...

We focus on rational solutions or nearly-feasible that serve as certificates of feasibility for polynomial optimization problems. show that, under some separability conditions, certain cubic polynomially constrained sets admit solutions. However, we in other cases it is NP Hard to detect if exist they any reasonable size. extend this idea various settings including near feasible, but super opti...