An admissible Poisson algebra (or briefly, an adm-Poisson algebra) gives equivalent presentation with only one operation for a algebra. We establish bialgebra theory algebras independently and systematically, including but beyond the corresponding results on bialgebras given in [27]. Explicitly, we introduce notion of which are to Manin triples as well bialgebras. The direct correspondence betw...

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 ...

We introduce methods for identifying operator preconditions that need not be expanded further. The methods are proved to be admissible , that is, they will not cause a solution to be missed when one exists. In certain cases, the methods also identify operator reformulations that increase the number of nonexpandable preconditions. This approach provides effective loop control in common situation...