Position Finding Without an Horizon

Finding Points in General Position

We study the General Position Subset Selection problem: Given a set of points in the plane, find a maximum-cardinality subset of points in general position. We prove that General Position Subset Selection is NP-hard, APX-hard, and present several fixed-parameter tractability results for the problem.

Finding without Searching

Quantization without position operators

We formulate quantum mechanics in the two-dimensional torus without using position operators. We define an algebra with only momentum operators and shift operators and construct irreducible representation of the algebra. We show that it realizes quantum mechanics of a charged particle in a uniform magnetic field. We prove that any irreducible representation of the algebra is unitary equivalent ...

Economic receding horizon control without terminal constraints

We consider a receding horizon control scheme without terminal constraints in which the stage cost is defined by economic criteria, i.e., not necessarily linked to a stabilization or tracking problem. We analyze the performance of the resulting receding horizon controller with a particular focus on the case of optimal steady states for the corresponding averaged infinite horizon problem. Using ...

Cauchy horizon singularity without mass inflation.

A perturbed Reissner-Nordström-de Sitter solution is used to emphasize the nature of the singularity along the Cauchy horizon of a charged spherically symmetric black hole. For these solutions, conditions may prevail under which the mass function is bounded and yet the curvature scalar R αβγδ R αβγδ diverges.