Singular equivalence and the (Fg) condition

Singular gradient flow of the distance function and homotopy equivalence

It is a generally shared opinion that significant information about the topology of a bounded domain Ω of a riemannian manifold M is encoded into the properties of the distance, d∂Ω, from the boundary of Ω. To confirm such an idea we propose an approach based on the invariance of the singular set of the distance function with respect to the generalized gradient flow of of d∂Ω. As an application...

A Necessary Condition for Dynamic Equivalence

If two control systems on manifolds of the same dimension are dynamic equivalent, we prove that either they are static equivalent –i.e. equivalent via a classical diffeomorphism– or they are both ruled; for systems of different dimensions, the one of higher dimension must be ruled. A ruled system is one whose equations define at each point in the state manifold, a ruled submanifold of the tange...

On Hörmander’s Condition for Singular Integrals

Singular Failures of GCH and Level by Level Equivalence ∗†

We construct a model for the level by level equivalence between strong compactness and supercompactness in which below the least supercompact cardinal κ, there is an unbounded set of singular cardinals which witness the only failures of GCH in the universe. In this model, the structure of the class of supercompact cardinals can be arbitrary.

A Sufficient Condition for the Observational Equivalence of Processes

The article deals with the problem of proving observational equivalence for the class of computational processes called processes with message passing. These processes can execute actions of the following forms: sending or receiving of messages, checking logical conditions and updating values of internal variables of processes. Our main result is a theorem that reduces the problem of proving ob...