A cubical analogue of Stanley’s theorem expressing the cd-index of an Eulerian simplicial poset in terms of its h-vector is presented. This result implies that the cd-index conjecture for Gorenstein∗ cubical posets follows from Ron Adin’s conjecture on the non-negativity of his cubical h-vector for Cohen-Macaulay cubical posets. For cubical spheres the standard definition of shelling is shown t...

It is verified that the number of vertices in a d-dimensional cubical pseudomanifold is at least 2d+1. Using Adin’s cubical h-vector, it is established that the cubical Generalized Lower Bound Conjecture (GLBC) holds for all 4-spheres, as well as some special cases of the cubical GLBC in higher dimensions.

Face numbers of triangulations of simplicial complexes were studied by Stanley by use of his concept of a local h-vector. It is shown that a parallel theory exists for cubical subdivisions of cubical complexes, in which the role of the h-vector of a simplicial complex is played by the (short or long) cubical h-vector of a cubical complex, defined by Adin, and the role of the local h-vector of a...

microwave irradiation is used in the synthesis of four tricyclic chromanones 11-14. the chromanone 14 and 12 are selectively formed thermally and under microwave in the presence of polyphosphoric acid (ppa) from the same dicarboxylic acid 9, respectively. the crystal structures of the two diacids are also reported. the corresponding ortho and meta isomers of diacids crystallize in the space gro...

Topological spaces—such as classifying spaces, configuration spaces and spacetimes—often admit directionality. Qualitative invariants on such directed spaces often are more informative, yet more difficult, to calculate than classical homotopy invariants because directed spaces rarely decompose as homotopy colimits of simpler directed spaces. Directed spaces often arise as geometric realizations...

A conformal cubical transformation-based metamaterial invisibility cloak is presented and verified, in the near and the far field, by a rigorous full-wave numerical technique based on a higher-order, large-domain finite element method, employing large anisotropic, continuously inhomogeneous generalized hexahedral finite elements, with no need for discretization of the permittivity and permeabil...

The paper deals with combinatorial and stochastic structures of cubical token systems. A cubical token system is an instance of a token system, which in turn is an instance of a transition system. It is shown that some basic results of combinatorial and stochastic parts of media theory hold almost in identical form for cubical token systems, although some underlying concepts are quite different...

Crystal structures have inspired developments in geometry since the Ancient Greeks conceived of Platonic solids after observing tetrahedral, cubical and octahedral mineral forms in their local environment. The internal structure of crystals became accessible with the development of x-ray diffraction techniques just over 100 years ago, and a key step in developing this method was understanding t...

We prove that the neighborly cubical polytopes studied by Günter M. Ziegler and the first author [14] arise as a special case of the neighborly cubical spheres constructed by Babson, Billera, and Chan [4]. By relating the two constructions we obtain an explicit description of a non-polytopal neighborly cubical sphere and, further, a new proof of the fact that the cubical equivelar surfaces of M...

We construct a model of cubical type theory with a univalent and impredicative universe in a category of cubical assemblies. We show that the cubical assembly model does not satisfy the propositional resizing axiom.