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Compact hyperbolic tetrahedra with non-obtuse dihedral angles.

Roland K.W. Roeder (2006)

Publicacions Matemàtiques

Given a combinatorial description C of a polyhedron having E edges, the space of dihedral angles of all compact hyperbolic polyhedra that realize C is generally not a convex subset of RE. If C has five or more faces, Andreev's Theorem states that the corresponding space of dihedral angles AC obtained by restricting to non-obtuse angles is a convex polytope. In this paper we explain why Andreev did not consider tetrahedra, the only polyhedra having fewer than five faces, by demonstrating that the...

Computing homology.

Kaczynski, Tomasz, Mischaikow, Konstantin, Mrozek, Marian (2003)

Homology, Homotopy and Applications

Configuration spaces and limits of voronoi diagrams

Roderik Lindenbergh, Wilberd van der Kallen, Dirk Siersma (2003)

Banach Center Publications

The Voronoi diagram of n distinct generating points divides the plane into cells, each of which consists of points most close to one particular generator. After introducing 'limit Voronoi diagrams' by analyzing diagrams of moving and coinciding points, we define compactifications of the configuration space of n distinct, labeled points. On elements of these compactifications we define Voronoi diagrams.

Construction de facettes pour le polytope du sac-à-dos quadratique en 0-1

Alain Faye, Olivier Boyer (2010)

RAIRO - Operations Research

Nous construisons des familles de facettes du polytope du sac-à-dos quadratique en 0-1 selon les deux approches suivantes. Le Boolean quadric polytope (introduit dans le cas sans contraintes par Padberg [12]) contenant le polytope du sac-à-dos quadratique, une première approche consiste à se demander sous quelles conditions une facette du premier est aussi une facette du second et quand ces conditions ne sont pas remplies quels liftings permettent d'en faire une facette. Des réponses à ces questions...

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