Image sampling with quasicrystals.
In a continuum theory of crystals with defects, invariant line integrals measure the line defects of the lattice structure. It is shown that the integrands of invariant line integrals can always be taken to have the transformation properties of covariant vector-valued functions.
A linearly convergent iterative algorithm that approximates the rank-1 convex envelope of a given function , i.e. the largest function below which is convex along all rank-1 lines, is established. The proposed algorithm is a modified version of an approximation scheme due to Dolzmann and Walkington.
A linearly convergent iterative algorithm that approximates the rank-1 convex envelope of a given function , i.e. the largest function below f which is convex along all rank-1 lines, is established. The proposed algorithm is a modified version of an approximation scheme due to Dolzmann and Walkington.
We consider a motion of spiral-shaped piecewise linear curves governed by a crystalline curvature flow with a driving force and a tip motion which is a simple model of a step motion of a crystal surface. We extend our previous result on global existence of a spiral-shaped solution to a linear crystalline motion for a power type nonlinear crystalline motion with a given rotating tip motion. We show that self-intersection of the solution curves never occurs and also show that facet extinction never...