We show that the Zariski canonical stratification of complex hypersurfaces is locally bi-Lipschitz trivial along strata codimension two. More precisely, we study equisingular families surface, not necessarily isolated, singularities in ${\\mathbb{C}^3}$. a natural such family, given by singular set and generic family polar curves, provides Lipschitz sense Mostowski. In particular are trivial, w...

This is the second part of a two-part paper on Birkhoff systems. A Birkhoff system is an algebra that has two binary operations · and +, with each being commutative, associative, and idempotent, and together satisfying x · (x + y) = x + (x · y). The first part of this paper described the lattice of subvarieties of Birkhoff systems. This second part continues the investigation of subvarieties of...

Finite monoids that generate monoid varieties with uncountably many subvarieties seem rare, and surprisingly, no finite monoid is known to generate a monoid variety with countably infinitely many subvarieties. In the present article, it is shown that there are, nevertheless, many finite monoids that generate monoid varieties with continuum many subvarieties; these include any finite inherently ...