In several problems of interest in computational modeling there is a media that is either infinite or semi-infinite. Some examples include: modeling the ocean when doing ship analysis, modeling the soil underneath a footing, and modeling the air around an airplane. However, every finite element model must be terminated at some finite boundary. Unfortunately, for problems involving wave propagat...

Variational multiscale methods lead to stable finite element approximations of the Navier-Stokes equations, both dealing with the indefinite nature of the system (pressure stability) and the velocity stability loss for high Reynolds numbers. These methods enrich the Galerkin formulation with a sub-grid component that is modeled. In fact, the effect of the sub-grid scale on the captured scales h...

We show that in the setting of fair-coin measure on the power set of the natural numbers, each sufficiently random set has an infinite subset that computes no random set. That is, there is an almost sure event A such that if X ∈ A then X has an infinite subset Y such that no element of A is Turing computable from Y .

In previous work we have introduced dynamic limited-memory influence diagrams (DLIMIDs) as an extension of LIMIDs aimed at representing infinite-horizon decision processes. If a DLIMID respects the first-order Markov assumption then it can be represented by 2TLIMIDS. Given that the treatment selection algorithm for LIMIDs, called single policy updating (SPU), can be infeasible even for small fi...

Monotonicity of optimal solutions to finite horizon dynamic optimization problems is used to prove the existence of a forecast horizon, i.e a long enough planning horizon that ensures that a first period optimal action for the infinite horizon and the finite horizon problem agree, regardless of problem parameter changes in the tail. The existence of extremal monotone optimal solutions motivates...