A Radial Basis Function Generated Finite-Differences (RBF-FD) inspired technique for evaluating definite integrals over bounded volumes that have smooth boundaries in three dimensions is described. key aspect of this approach it allows the user to approximate value integral without explicit knowledge an expression boundary surface. Instead, a tesselation node set utilized inform algorithm domai...

We develop approximate counting of sets definable by Boolean circuits in bounded arithmetic using the dual weak pigeonhole principle (dWPHP(PV )), as a generalization of results from [15]. We discuss applications to formalization of randomized complexity classes (such as BPP , APP , MA, AM ) in PV1 + dWPHP(PV ).

Let S be a locally compact foundation semigroup with identity and                          be its semigroup algebra. Let X be a weak*-closed left translation invariant subspace of    In this paper, we prove that  X  is invariantly  complemented in   if and  only if  the left ideal  of    has a bounded approximate identity. We also prove that a foundation semigroup with identity S is left amenab...

In this paper, we study the relation between uniform Roe algebra and quasi-local associated to a metric space of bounded geometry. process, introduce weakening notion expanders, called asymptotic expanders. We show that being sequence expanders is coarse property under certain connectedness condition, it implies non-uniformly local amenability. Moreover, also analyse some $C^*$-algebraic proper...

In a recent paper, the authors proved that no spin foliation on compact enlargeable manifold with Hausdorff homotopy graph admits metric of positive scalar curvature its leaves. This result extends groundbreaking results Lichnerowicz, Gromov and Lawson, Connes non-existence metrics curvature. this paper we review in more detail material needed for proof our theorem extend to non-compact manifol...