Frobenius–Witt differentials and regularity

Organismal Differentials and Organ Differentials.

Strong Topological Regularity and Weak Regularity of Banach Algebras

In this article we study two different generalizations of von Neumann regularity, namely strong topological regularity and weak regularity, in the Banach algebra context. We show that both are hereditary properties and under certain assumptions, weak regularity implies strong topological regularity. Then we consider strong topological regularity of certain concrete algebras. Moreover we obtain ...

Proving Regularity and Non-regularity

This does not make it look any easier to use; it makes it look even more foreboding. However, it is useful for the following reason. To use the pumping lemma to show that L is not regular, you have to show it does not satisfy the pumping lemma. Therefore you have to show that the NEGATION of the conclusion of the lemma is true. If you can intuitively understand how to form the negation of a log...

Selection and mortality differentials.

The Office of Population Censuses and Surveys Longitudinal Study provides reliable mortality data by a much wider range of characteristics than are available for other national sources. Although it is based on only a 1% sample of the population, it broadens the scope of mortality analysis and permits study of changes in relationships using different aspects of the time dimension. Data from this...

Differentials and Derivations

Quasicoherent sheaves should be thought of as the scheme-theoretic analogs of vector bundles. This analogy might lead one to think that vector bundles over a scheme X should be locally free OX-modules, but this turns out not to be an abelian category, and the category of quasicoherent sheaves contains the category of locally free OX-modules. There are two different different definitions we coul...