F-regularity Does Not Deform

Lack of Regularity of the Transport Density in the Monge Problem

In this paper, we provide a family of counter-examples to the regularity of the transport density in the classical Monge-Kantorovich problem. We prove that the W 1,p regularity of the source and target measures f± does not imply that the transport density σ is W 1,p, that the BV regularity of f± does not imply that σ is BV and that f± ∈ C∞ does not imply that σ is W 1,p, for large p.

F-regularity relative to modules

In this paper we will generalize  some of known results on the tight closure of an ideal to the tight closure of an ideal relative to a module .

A Syzygetic Approach to the Smoothability of 0-schemes of Regularity Two

We consider the question of which zero dimensional schemes deform to a collection of distinct points; equivalently, we ask which Artinian k-algebras deform to a product of fields. We introduce a syzygetic invariant which sheds light on this question for 0-schemes of regularity two. This invariant imposes obstructions for smoothability in general, and it completely answers the question of smooth...

Extension on Regularity Condition in DEA Models

Regularity of Bounded Tri-Linear Maps and the Fourth Adjoint of a Tri-Derivation

In this Article, we give a simple criterion for the regularity of a tri-linear mapping. We provide if f : X × Y × Z −→ W is a bounded tri-linear mapping and h : W −→ S is a bounded linear mapping, then f is regular if and only if hof is regular. We also shall give some necessary and sufficient conditions such that the fourth adjoint D^∗∗∗∗ of a tri-derivation D is again tri-derivation.