An explicit formula for the Webster torsion of a pseudo-hermitian manifold and its application to torsion-free hypersurfaces Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

This paper gives an explicit formula for calculating the Webster pseudo torsion for a strictly pseudoconvex pseudo-hermitian hypersurface. As applications, we are able to classify some pseudo torsion-free hypersurfaces, which include real ellipsoids.

A TV-Based Iterative Regularization Method for the Solutions of Thermal Convection Problems

Linear/nonlinear and Stokes based-stabilizations for the filter equations for damping out primitive variable(PV)solutions corrupted by uniformly distributed randomnoises are numerically studied through the natural convection(NC)aswell as the mixed convection(MC)environment.The most recognizable filter-scheme is based on a combination of the negative Laplace equation multiplied with the selection of the spatial scale and a linear function in order to preserve the uniqueness of the filtered solution.A more complicated filter-scheme,based on a Stokes problem which couples a filtered velocity and a filtered(artificial)pressure(or Lagrange multiplier)in order to enforce the incompressibility constraint,is also studied.Linear and Stokes basedfilters via nested iterative(NI)filters and the consistent splitting scheme(CSS)are proposed for the NC/MC problems.Inspired by the total-variation(TV)model of image diffusion,well preserved feature flow patterns from the corrupted NC/MC environment are obtained by TV-Stokes based-filters together with the CSS.Our experimental results show that our proposed algorithms are effective and efficient in eliminating the unwanted spurious oscillations and preserving the accuracy of thermal convective fluid flows.