We investigate the long-time behavior of a system of viscoelastic particles modeledwith the homogeneous Boltzmann equation.We prove the existence of a universal Maxwellian intermediate asymptotic state with explicit rate of convergence towards it. Exponential lower pointwise bounds and propagation of regularity are also studied. These results can be seen as a generalization of several classical...

We show that if R is a Jordan Szabó algebraic covariant derivative curvature tensor on a vector space of signature (p, q), where q ≡ 1 mod 2 and p < q or q ≡ 2 mod 4 and p < q − 1, then R = 0. This algebraic result yields an elementary proof of the geometrical fact that any pointwise totally isotropic pseudo-Riemannian manifold with such a signature (p, q) is locally symmetric.

Abstract. We prove Strichartz estimates for the absolutely continuous evolution of a Schrödinger operator H = (i∇ + A) + V in R, n ≥ 3. Both the magnetic and electric potentials are time-independent and satisfy pointwise polynomial decay bounds. The vector potential A(x) is assumed to be continuous but need not possess any Sobolev regularity. This work is a refinement of previous methods, which...

In this paper, we show that a pointwise symmetric pre-isotonic preclosure function is uniquely determined the pairs of sets it separates. We then show that when the preclosure function of the domain is pre-isotonic and the pre-closure function of the codomain is pre-isotonic and pointwise-pre-symmetric, functions which separate only those pairs of sets which are already separated are precontinu...

in this paper, the urysohn and completely hausdorff axioms in general topology are generalized to l-topological spaces so as to be compatible with pointwise metrics. some properties and characterizations are also derived