The intimate connection between the Banach space wavelet reconstruction method for each unitary representation of a given group and homogenous space, and the quantum entanglement description using group theory were both studied in our previous articles. Here, we present a universal description of quantum entanglement using group theory and non-commutative characteristic functions for homogenous space and projective representation of compact groups on Banach spaces for some well known examples, such as: Moyal representation for a spin; Dihedral and Permutation groups.
In experimental thin film physics, there is a demand to characterize a growing thin film or the thin film resulting from an experiment. While methods for discontinuous, island-like thin films have been developed, there is a lack of results directly applicable to semicontinuous thin film description. In this contribution, a unique combination of image processing methods is collected and further developed, which results in a novel set of semicontinuous thin film descriptors. In particular, the shape of the thin film contours and the thin film image intensity profiles are analyzed in a multiscale manner. The descriptiveness of the proposed features is demonstrated on a few thin film photographs from real experiments. This work establishes a basis for further measurement, description, simulation or other processing in the physics of semicontinuous thin films, using any direct imaging modality.