Density Functions of Periodic Sequences of Continuous Events

Abstract Periodic Geometry studies isometry invariants of periodic point sets that are also continuous under perturbations. The motivations come from crystals whose structures determined in a rigid form, but any minimal cells can discontinuously change due to small noise measurements. For integer $$k\ge 0$$ k ≥ 0 , the density function set S was previously defined as fractional volume all k -fold intersections (within cell) balls have variable radius t and centers at points . This paper introduces functions for with different initial radii motivated by atomic chemical elements events occupying disjoint intervals time series. contributions explicit descriptions densities sequences intervals. new strictly stronger distinguish identical case zero radii.