Relatively few families of Bell inequalities have previously been identified. Some examples are the trivial, CHSH, Imm22, and CGLMP inequalities. This paper presents a large number of new families of tight Bell inequalities for the case of many observables. For example, 44,368,793 inequivalent tight Bell inequalities other than CHSH are obtained for the case of 2 parties each with 10 2-valued o...

• Sd: A d-Simplex The simplest convex polytope in R. A d-simplex is always the convex hull of some d + 1 affinely independent points. For example, a line segment is a 1− simplex i.e., the smallest convex subspace which contains two points. A triangle is a 2 − simplex and a tetrahedron is a 3− simplex. • P: A Simplicial Polytope. A polytope where each facet is a d− 1 simplex. By our assumption, ...

Given a finite collection P of convex n-polytopes in RP (n ≥ 2), we consider a real projective manifold M which is obtained by gluing together the polytopes in P along their facets in such a way that the union of any two adjacent polytopes sharing a common facet is convex. We prove that the real projective structure on M is 1. convex if P contains no triangular polytope, and 2. properly convex ...

Concave gold nanoplates are obtained in hexagonal liquid crystal (LLC) made of SDS (sodium dodecyl sulfate)/glycine/HAuCl(4) aqueous solution system where glycine plays the key role. All plates are single-crystals, characterized by {111} facets, with concave centers of regular hexagonal or triangular shapes, and with better electrocatalytic activity than gold nanoplates.

The shape of interfacial voids formed in the epitaxial SiC/Si(111) heterosystem just underneath the SiC film has been investigated using optical microscopy and transmission electron microscopy (TEM). SiC films are grown on Si(111) substrates at two different substrate temperatures (specimen type 1 at 850°C, specimen type 2 at 1050°C) using solid-source molecular-beam epitaxy (MBE). At 850°C sub...

Two {110}-faceted gold nanostructures--rhombic dodecahedra and obtuse triangular bipyramids--have been synthesized via a Ag-assisted, seed-mediated growth method. The combination of a Cl(-)-containing surfactant with a low concentration of Ag(+) plays a role in the stabilization of the {110} facets. To the best of our knowledge, this is the first reported synthesis of a {110}-faceted bipyramid ...

This paper describes the construction, properties and potential applications of a cartographic projection recently developed by the author, called the Zenithial Orthotriangular (ZOT) projection of an Octahedron. ZOT maps a planet to a plane by modelling it as an octahedron (a regular solid having 8 equilateral triangular facets), which is then unfolded and stretched to fit within a square. As d...