Characters of Binary Vector-valued Wavelets and Applications in Education Technology and Theoretical Physics

Information science is an interdisciplinary science. New physics emerge because of the diverse new material properties which need to be explained. In this article, the notion of vector-valued multiresolution analysis and biorthogonal binary vector-valued wavelets are introduced. The existence of finitely supported biorthogonal vector-valued wavelets associated with a pair of biorthogonal finitely supported vector-valued scaling functions is investigated. A new method for constructing a class of biorthogonal finitely supported vector-valued wavelet functions is proposed by using multiresolution analysis and functional analysis as well as matrix theory.