Let G be a simple connected complex Lie group. The additive eigencone $$ \overline{\Gamma} n(G) is polyhedral cone containing the set of solutions to eigenvalue problem, generalization Hermitian problem. functorial, and for certain subgroups satisfies stronger functoriality property: subgroup determined by inequalities larger eigencone. Belkale Kumar first studied this property invariant under ...

Automated program verification often proceeds by exhibiting inductive invariants entailing the desired properties. For numerical properties, a classical class of invariants is convex polyhedra: solution sets of system of linear (in)equalities. Forty years of research on convex polyhedral invariants have focused, on the one hand, on identifying “easier” subclasses, on the other hand on heuristic...

The 3-D reconstruction of visible polyhedral faces from a pair of general perspective views with the aid of a calibration plate is addressed. A polyhedron is placed on a planar calibration plate and two side views of both the polyhedron and the calibration plate are taken. Through proper arrangements we may assume that in the two views a number of polyhedral edges lying on the calibration plate...

We study rigidity of polyhedral surfaces and the moduli space of polyhedral surfaces using variational principles. Curvature like quantities for polyhedral surfaces are introduced. Many of them are shown to determine the polyhedral metric up to isometry. The action functionals in the variational approaches are derived from the cosine law and the Lengendre transformation of them. These include e...

This paper is concerned with the unique determination of a threedimensional polyhedral bi-periodic diffraction grating by the scattered electromagnetic fields measured above the grating. It is shown that the uniqueness by any given incident field fails for seven simple classes of regular polyhedral gratings. Moreover, if a regular bi-periodic polyhedral grating is not uniquely identifiable by a...

We prove that, both in the Lobachevskij and spherical 3-spaces, there exist nonconvex compact boundary-free polyhedral surfaces without selfintersections which admit nontrivial continuous deformations preserving all dihedral angles and study properties of such polyhedral surfaces. In particular, we prove that the volume of the domain, bounded by such a polyhedral surface, is necessarily constan...

Ten years after the discovery of metallocarboranes, this field of chemistry is still advancing at a rapid pace. While the polyhedral expansion of carboranes has proved to be a general method for the synthesis of metallocarboranes, polymetallic compounds may be synthesized by polyhedral expansion of monometallocarboranes, sometimes producing supraicosahedral complexes. The polyhedral contraction...

We introduce a new variety of flexatube, a rhomboflexatube. It is obtained from a cardboard rhombohedron by removing a pair of opposite faces (rhombi), and then subdividing the remaining four faces by pairs of diagonals. It is reversible, that is, it can be turned inside out by a series of folds, using edges and diagonals of the rhombi. To turn a rhomboflexatube inside out is quite a challengin...

horizon map Representing the Visibility Structure of a Polyhedral Terrain through a Horizon Map We present a model for describing the visibility of a polyhedral terrain from a xed viewpoint, based on a collection of nested horizons. We brie y introduce the concepts of mathematical and digital terrain models, and some background notions for visibility problems on terrains. Then, we de ne horizon...