Partial Differential Equation(PDE) based methods in image processing
have been actively studied in the past few years. One of the
effective methods is the method based on a total variation
introduced by Rudin, Oshera and Fatemi (ROF) \cite{ROF}. This method
is a well known edge preserving model and an useful tool for image
removals and decompositions..........？

Main Purpose of this paper is to define an elliptic analogue of the Hardy sums. Some results, which are related to
elliptic analogue of the Hardy sums, are given

We study the gravitational collapse problem of rotating shells in three-dimensional Einstein gravity
with and without a cosmological constant. Taking the exterior and interior metrics to be those of
stationary metrics with asymptotically constant curvature, we solve the equations of motion for the
shells from the Darmois-Israel junction conditions in the co-rotating frame. We study various
collapse scenarios with arbitrary angular momentum for a variety of geometric configurations,
including anti-de Sitter, de Sitter, and flat spaces. We find that the collapsing shells can form
a BTZ black hole, a three-dimensional Kerr-dS spacetime, and an horizonless geometry of
point masses under certain initial conditions. For pressureless dust shells, the curvature
singularity is not formed due to the angular momentum barrier near the origin. However
when the shell pressure is nonvanishing, we find that for all types of shells with polytropic-type
equations of state (including the perfect fluid and the generalized Chaplygin gas), collapse to
a naked singularity is possible under generic initial conditions. We conclude that in three
dimensions angular momentum does not in general guard against violation of cosmic censorship.