The Characterization of Two-direction Vector-valued Wavelets and Its applications in Material Engineering

摘要

Material science is an interdisciplinary field applying the properties of matter to various areas of science and engineering. In this work, we study construction and properties of orthogonal two-direction vector-valued wavelet with poly-scale. Firstly, the concepts concerning two-directional vector-valued waelets and wavelet wraps with multi-scale are provided. Secondly, we propose a construction algorism for compactly supported orthogonal two-directional vector-valued wave lets. Lastly, properties of a sort of orthogonal two-directional vector-valued wavelet wraps are characterized by virtue of the matrix theory and the time-frequency analysis method.