1,138 research outputs found
The algebro-geometric study of range maps
Localizing a radiant source is a widespread problem to many scientific and
technological research areas. E.g. localization based on range measurements
stays at the core of technologies like radar, sonar and wireless sensors
networks. In this manuscript we study in depth the model for source
localization based on range measurements obtained from the source signal, from
the point of view of algebraic geometry. In the case of three receivers, we
find unexpected connections between this problem and the geometry of Kummer's
and Cayley's surfaces. Our work gives new insights also on the localization
based on range differences.Comment: 38 pages, 18 figure
Geometric T-Dualization
In this article we realize T-duality as a geometric transform of bundles of
abelian group stacks. The transform applies in the algebro-geometric setting as
well as the topological setting, and thus makes precise the link between the
models of T-duality in these two settings, which are superficially quite
different. The transform is also valid for torus bundles with affine structure
group, and thus provides a constructive method of producing T-duals in the
affine case.Comment: Comments welcom
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