The main purpose of this paper is to look at the notion of partial transpose from the combinatorial side. In this perspective, we solve some basic enumeration problems involving partial transpose of permutation matrices. Specifically, we count the number of permutations matrices which are invariant under partial transpose. We count the number of permutation matrices which are still permutation ...

We investigate the singularity formation of a 3D model that was recently proposed by Hou and Lei (2009) in [15] for axisymmetric 3D incompressible Navier–Stokes equations with swirl. The main difference between the 3D model of Hou and Lei and the reformulated 3D Navier–Stokes equations is that the convection term is neglected in the 3D model. This model shares many properties of the 3D incompre...

By performing estimates on the integral of the absolute value of vorticity along a local vortex line segment, we establish a relatively sharp dynamic growth estimate of maximum vorticity under some assumptions on the local geometric regularity of the vorticity vector. Our analysis applies to both the 3D incompressible Euler equations and the surface quasi-geostrophic model (SQG). As an applicat...

’n Opname is gedoen onder voormalige studentverpleegkundiges van een hospitaal om die faktore wat met die hoë stakingssyfer verband hou te bepaal. Die volgende is enkele van die belangrikste bevindings: — daar was betekenisvolle ontevredenheid oor werksomstandighede in die atgemeen; — ’n klein maar betekenisvolle groep kon nie met die akademiese eise van verpleegkunde tred hou nie; — dit blyk o...