A strong correspondence principle for smooth, monotone environments

A Correspondence Principle

A single mathematical theme underpins disparate physical phenomena in classical, quantum and statistical mechanical contexts. This mathematical “correspondence principle”, a kind of wave–particle duality with glorious realizations in classical and modern mathematical analysis, embodies fundamental geometrical and physical order, and yet in some sense sits on the edge of chaos. Illustrative case...

A Weak-to-Strong Convergence Principle for Fejé-Monotone Methods in Hilbert Spaces

where Pi denotes the projector onto Si and where the mod m function takes values in 0 m−1 , converges weakly to a point in S =⋂mi=1 Si. In Gubin et al. (1967) (see also Bauschke 1995, Bauschke and Borwein 1996, Bauschke et al. 1997, and Combettes 1997), certain regularity conditions on the sets were described that guaranteed strong convergence of the iterations. To this day, however, it remains...

A Weak-to-strong Convergence Principle for Fej Er-monotone Methods in Hilbert Spaces

Correspondence Principle

The Correspondence Principle is the relation, which exists in certain economic models, between comparative statics of equilibria and the properties of out-of-equilibrium dynamics. The Correspondence Principle (CP) implies that one obtains unambiguous comparative statics by selecting equilibria with desirable dynamic properties. Generally, the CP determines comparative statics in models with a o...

Strong Correspondence for HOPLA

We show that the operational semantics for HOPLA is in strong correspondence with its presheaf semantics [2, 1]. The proof is a fairly standard logical relations proof, exploiting the path semantics of the language [3, 4]. Strong correspondence can be proved for full HOPLA by making use of the path semantics to get a logical relations proof off the ground. We’ll use the notation J−K for the pat...