Abstract We study a minimisation problem in L p and ∞ for certain cost functionals, where the class of admissible mappings is constrained by Navier–Stokes equations. Problems this type are motivated variational data assimilation atmospheric flows arising weather forecasting. Herein we establish existence PDE-constrained minimisers all , also that converge to as → ∞. further show solve an Euler–...

To effectively measure the power of discrimination of terms is a crucial issue in information retrieval (IR). Term mismatch and ambiguity have long been troublesome, and the improvement of retrieval performance by increased precision through query expansion is of interest. This report focuses on a discrimination measure for use with query expansion. The discrimination measure is derived from a ...

In this paper we reconsider the standard formulation of the Second Law of Thermodynamics in the general framework of fields with divergence measure, using Geometric Measure Theory and some recent results on Cauchy interactions. To our knowledge, the first attempt to put the Second Law of Thermodynamics within the framework of Geometric Measure Theory is Gurtin, Williams, Ziemer. Recently, the p...