An iterative procedure for the design of a polarizing beam splitter (PBS) that uses a form-birefringent, subwavelength-structured, one-dimensional photonic-crystal layer (SWS 1-D PCL) embedded in a high-index cubical prism is presented. The PBS is based on index matching and total transmission for the p polarization and total internal reflection for the s polarization at the prism-PCL interface...

We study finite foldable cubical complexes of nonpositive curvature (in the sense of A.D. Alexandrov). We show that such a complex X admits a graph of spaces decomposition. It is also shown that when dimX = 3, X contains a closed rank one geodesic in the 1-skeleton unless the universal cover of X is isometric to the product of two CAT(0) cubical complexes. AMS Classification 20F65, 20F67; 53C20

We describe an algorithm to compute the geodesics in an arbitrary CAT(0) cubical complex. A key tool is a correspondence between cubical complexes of global non-positive curvature and posets with inconsistent pairs. This correspondence also gives an explicit realization of such a complex as the state complex of a reconfigurable system, and a way to embed any interval in the integer lattice cubi...

The cubical sets model of Homotopy Type Theory was introduced by Bezem, Coquand and Huber using a particular category of presheaves. We show that this category is equivalent to a category of sets whose elements have a finite support property with respect to an action of a monoid of name substitutions; and that this is isomorphic to a category of nominal sets equipped with source and target maps...

Bezem, Coquand, and Huber have recently given a constructively valid model of higher type theory in a category of nominal cubical sets satisfying a novel condition, called the uniform Kan condition (UKC), which generalizes the standard cubical Kan condition (as considered by, for example, Williamson in his survey of combinatorial homotopy theory) to admit phantom “additional” dimensions in open...

We establish sufficient conditions implying semistability and connectivity at infinity properties for CAT(0) cubical complexes. We use this, along with the geometry of cubical K(π, 1)’s to give a complete description of the higher connectivity at infinity properties of right angled Artin groups. Among other things, this determines which right angled Artin groups are duality groups. Applications...

the crystals of [ws (cuncs) ] anion have been isolated from ch ,ci solution and examined by x-ray structural analysis as well as by ir spectroscopy. the unit cell is monoclinic with a= 14.3796(13), b= 18.039(1 i), c= 22.5956(23)& p= 96.053(8)', space group p2,/n (14), z= 4. the crystal structure was refined by the least-squares calculations to a final r-value of 0.0398(rw= 0.0443) for 2777...