A Two-Sided Absorption Problem

On a Two-Sided Turan Problem

Given positive integers n, k, t, with 2 ≤ k ≤ n, and t < 2, let m(n, k, t) be the minimum size of a family F of nonempty subsets of [n] such that every k-set in [n] contains at least t sets from F , and every (k − 1)-set in [n] contains at most t− 1 sets from F . Sloan et. al [11] determined m(n, 3, 2) and Füredi et. al [6] studied m(n, 4, t) for t = 2, 3. We consider m(n, 3, t) and m(n, 4, t) ...

A Two–Sided Contracting Stefan Problem

We study a novel two–sided Stefan problem – motivated by the study of certain 2D interfaces – in which boundaries at both sides of the sample encroach into the bulk with rate equal to the boundary value of the gradient. Here the density is in [0, 1] and takes the two extreme values at the two free boundaries. It is noted that the problem is borderline ill–posed: densities in excess of unity lia...

The Patent System’s Two-Sided Agency Problem

Two-Sided Model Matching Problem with Preview

The H 2 optimization problem with preview and asymptotic behavior constraints is considered in a general two-sided model matching setting. The solution is obtained in terms of two constrained Sylvester equations, associated with asymptotic behavior, and stabilizing solutions of two algebraic Riccati equations. The Riccati equations do not depend on the preview length, yet are affected by asympt...

A Two-Sided Ontological Solution to the Sleeping Beauty Problem

I describe in this paper an ontological solution to the Sleeping Beauty problem. I begin with describing the Entanglement urn experiment. I restate first the Sleeping Beauty problem from a wider perspective than the usual opposition between halfers and thirders. I also argue that the Sleeping Beauty experiment is best modelled with the Entanglement urn. I draw then the consequences of consideri...