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The first example of a closed orientable hyperbolic 3-manifold was constructed by F. Lobell in 1931 from eight copies of the right-angled 14-hedron. We consider the family of hyperbolic polyhedra which generalize the Lambert cube and the Lobell polyhedron. ...
We develop an analytical model to predict equilibrium shapes of two-component heterogeneous vesicles or capsules. Using a free energy functional including the bending energies of the two components and line tension contributions, the model describes shape ...
We derive a new upper bound on the diameter of a polyhedron , where . The bound is polynomial in and the largest absolute value of a sub-determinant of , denoted by . More precisely, we show that the diameter of is bounded by . If is bounded, then we show ...
We investigate the diameter of a natural abstraction of the 1-skeleton of polyhedra. Even if this abstraction is more general than other abstractions previously studied in the literature, known upper bounds on the diameter of polyhedra continue to hold her ...
We investigate the diameter of a natural abstraction of the 1-skeleton of polyhedra. Although this abstraction is simpler than other abstractions that were previously studied in the literature, the best upper bounds on the diameter of polyhedra continue to ...
We demonstrate that it is possible to record site-specific spin-lattice relaxation rates for the majority of C-13 sites in uniformly C-13 and N-15 labeled solid proteins as a result of the slowing down of proton-driven spin diffusion at sample spinning fre ...
Spheropolyhedra are bodies obtained as Minkowski sums of polyhedra with spheres. They are simple, yet flexible models of non-spherical particles for granular media simulated with the Distinct Element Method (DEM). We here give an analytical method for the ...
This thesis deals with the numerical modeling and simulation of granular media with large populations of non-spherical particles. Granular media are highly pervasive in nature and play an important role in technology. They are present in fields as diverse ...
Polyhedral operations play a central role in constrained control. One of the most fundamental operations is that of projection, required both by addition and multiplication. This thesis investigates projection and its relation to multi-parametric linear op ...
Convex polyhedra are important objects in various areas of mathematics and other disciplines. A fundamental result, known as Minkowski-Weyl theorem, states that every polyhedron admits two types of representations, either as the solution set to a finite sy ...
