Beltrami’s completeness for 𝕃p symmetric matrix fields

Abstract

Geymonat extended Gurtin’s result on Beltrami’s completeness to [Formula: see text]-case. The first objective of this paper is to generalize Geymonat’s result to [Formula: see text]-case with tangential and normal boundary conditions. Maggiani et al. proposed an extension of Beltrami’s-type decomposition for symmetric matrix fields in [Formula: see text] when [Formula: see text] is simply connected domain and of class [Formula: see text]. The second objective of this paper is to present more extensions of the above decomposition when the domain [Formula: see text] is only of class [Formula: see text] and not necessarily simply connected. The third objective of this paper is to use the previous characterizations of matrix fields to solve some variants of the bi-Laplacian problem.

The Integration Strategy of Vocal Music Teaching and Traditional Music Culture in Colleges and Universities under the Background of Big Data Informatisation

“…Matrix decomposition is an important statistical signal-processing method widely used in speech, image, signal processing and other fields [13]. In music emotion feature learning, matrix decomposition can reduce multidimensional music data for subsequent learning.…”