We study a two-dimensional fluid of particles interacting through a spherically symmetric and marginally soft two-body repulsion. This model can exist in three different crystal phases, one of them with square symmetry and the other two triangular. We show that, while the triangular solids first melt into a hexatic fluid, the square solid is directly transformed on heating into an isotropic flu...

The paper deals with modeling of human head surface on the basis of quadratic triangular B-splines for the standard videocodec MPEG-4 SNHC. First, we define a triangular B-spline surface of any degree and then we present its calculation for modeling of the quadratic form. Next, we apply the quadratic triangular B-splines on modeling of the human head surface using 3D polygonal model Candide 3-1...

We show that the Glauber dynamics on proper 9-colourings of the triangular lattice is rapidly mixing, which allows for efficient sampling. Consequently, there is a fully polynomial randomised approximation scheme (FPRAS) for counting proper 9-colourings of the triangular lattice. Proper colourings correspond to configurations in the zero-temperature anti-ferromagnetic Potts model. We show that ...