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, ...

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 ...

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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 ...

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 ...

Two discrete functional analysis tools are established for spaces of piecewise polynomial functions on general meshes: (i) a discrete counterpart of the continuous Sobolev embeddings, in both ...

The famed Navier-Stokes equations can lead to cases where more than one result is possible, but only in an extremely narrow set of situations. For nearly two centuries, all kinds of researchers ...

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 ...