The patchwork divergence theorem

The Divergence Theorem for Unbounded Vector Fields

In the context of Lebesgue integration, we derive the divergence theorem for unbounded vector fields that can have singularities at every point of a compact set whose Minkowski content of codimension greater than two is finite. The resulting integration by parts theorem is applied to removable sets of holomorphic and harmonic functions. In the context of Lebesgue integration, powerful divergenc...

Graphene patchwork.

Graphene oxide (GO) holds tremendous potential for large-area electronics, high strength and conducting fillers in composites, and high-surface-area electrodes for energy storage. Graphene oxide for such applications will require manufacturing methods that are industrially compatible but also preserve its unique properties. Recent work by Korkut et al. describes a promising new scheme for conti...

The Patchwork Mandate

One Australian university (Queensland University of Technology) that mandates deposit of its publications is leading the world in collecting 70% of its annual research output and the fraction is rising. This level of success is surprising, since the researcher's world is hemmed in with requirements to teach, to ask for student evaluations, to write and mark examinations, to supervise Ph.D. stud...

Science fraud: from patchwork mouse to patchwork data.

Patchwork Terrains

We present a radically new method for the management, multi-resolution representation and rendering of large terrain databases. Our method has two main benefits: it provides a Ck representation of terrain, with k depending on the type of base patches; and it supports efficient updates of the database as new data come in. We assume terrain data to come as a collection of regularly sampled overla...