Various properties of the Misner-Sharp spherically symmetric gravitational energy E are derived, and known properties reviewed. In the Newtonian limit, E yields the Newtonian mass to leading order and the Newtonian kinetic and potential energy to the next order. In vacuo, E reduces to the Schwarzschild parameter. At null and spatial infinity, E reduces to the Bondi-Sachs and Arnowitt-Deser-Misn...

In this paper, we combine separate works on (a) the transfer of infinitesimal rigidity results from an Euclidean space to the next higher dimension by coning [28], (b) the further transfer of these results to spherical space via associated rigidity matrices [19], and (c) the prediction of finite motions from symmetric infinitesimal motions at regular points of the symmetryderived orbit rigidity...

The development of a sound theory that predicts and veriies existing evolutionary algorithms is one of the most important research issues in the eld today. In mathematical proofs, the assumption of spherical symmetry is probably one of the most widely-used simpliications. This paper discusses to which extend spherical symmetry is appropriate for certain evolutionary algorithms. It turns out tha...

In this article we consider weak solutions of the three-dimensional incompressible fluid flow equations with initial data admitting a one-dimensional symmetry group. We examine both the viscous and inviscid cases. For the case of viscous flows, we prove that Leray-Hopf weak solutions of the threedimensional Navier-Stokes equations preserve initially imposed symmetry and that such symmetric flow...

We consider the complex eigenvalues of induced spherical Ginibre ensemble with symplectic symmetry and establish local universality these point processes along real axis. derive scaling limits all correlation functions at regular points both in strong weak non-unitary regimes as well origin having spectral singularity. A key ingredient our proof is a derivation differential equation satisfied b...