We introduce a notion of an asymptotically compact (AC) random dynamical system (RDS). We prove that for an AC RDS the Ω-limit set $\Omega _{B}(\omega)$ of any bounded set B is nonempty, compact, ...

This is a preview. Log in through your library . Abstract We develop a general method to prove the existence of spectral gaps for Markov semigroups on Banach spaces. Unlike most previous work, the ...

The axisymmetric Navier-Stokes equations describe the motion of incompressible fluids under the assumption of rotational symmetry around a fixed axis. This reduction in dimensional complexity retains ...

As we celebrate the International Year of Quantum Science and Technology (IYQ) in 2025, we look back on a century of quantum mechanics—a field that has fundamentally changed the way we understand ...

Jim Denier receives funding from the Australian Research Council. MILLENNIUM PRIZE SERIES: The Millennium Prize Problems are seven mathematics problems laid out by the Clay Mathematics Institute in ...

Erica Grace Cabanilla, my ERDT administrator, who took charge of all my stipends, reminded me gently that I am supposed to give my exit report on Jan. 26 as Visiting Researcher, although my ...

Rose Yu has a plan for how to make AI better, faster and smarter — and it’s already yielding results. In math and computer science, researchers have long understood that some questions are ...