Using Hart Smith’s, curvelet, and shearlet transforms, we investigate L functions with sufficiently smooth background and present here sufficient and necessary conditions, which include the special case with 1-dimensional singularity line. Specifically, we consider the situation where regularity on a line in a non-parallel direction is much lower than directional regularity along the line in a ...

Sobolev wavefront sets and 2-microlocal spaces play a key role in describing analyzing the singularities of distributions microlocal analysis solutions partial differential equations. Employing continuous shearlet transform to spaces, this paper we characterize sets, local Hölder distributions/functions. We then establish connections among through transform.

this paper is a continuation of [uniformities and covering properties for partial frames (i)], in which we make use of the notion of a partial frame, which is a meet-semilattice in which certain designated subsets are required to have joins, and finite meets distribute over these. after presenting there our axiomatization of partial frames, which we call $sels$-frames, we added structure, in th...

Microseismic noise suppression is widely used in the exploration of unconventional oil and gas resources. The effective microseismic downhole signals have extremely weak energy are contaminated by strong interference, making data processing interpretation difficult. need for high-frequency signal reservation presents a basic problem design methods. represent as continuous reflection event more ...