We study the asymptotic behavior at small diffusivity of the solutions, u, to a convection-diffusion equation in a rectangular domain Ω. The diffusive equation is supplemented with a Dirichlet boundary condition, which is smooth along the edges and continuous at the corners. To resolve the discrepancy, on ∂Ω, between uε and the corresponding limit solution, u, we propose asymptotic expansions o...

A rectangular drawing of a plane graph G is a drawing of G such that each vertex is drawn as a point, each edge is drawn as a horizontal or a vertical line segment, and the contour of each face is drawn as a rectangle. A necessary and sufficient condition for the existence of a rectangular drawing has been known only for the case where exactly four vertices of degree 2 are designated as corners...

The previously unknown crystal structure of barium perchlorate anhydrate, determined and refined from laboratory X-ray powder diffraction data, represents a new structure type. The title compound was obtained by heating hydrated barium perchlorate [Ba(ClO4)2·xH2O] at 423 K in vacuo for 6 h. It crystallizes in the ortho-rhom-bic space group Fddd. The asymmetric unit contains one Ba (site symmetr...

sl 3-Foams and the Khovanov-Lauda categorification of quantum sl k. Abstract In this paper I define certain interesting 2-functors from the Khovanov-Lauda 2-category which categorifies quantum sl k , for any k > 1, to a 2-category of universal sl 3 foams with corners. For want of a better name I use the term foamation to indicate those 2-functors. I conjecture the existence of similar 2-functor...

The role of environmental geometry in maintaining spatial orientation was measured in immersive virtual reality using a spatial updating task (requiring maintenance of orientation during locomotion) within rooms varying in rotational symmetry (the number of room orientations providing the same perspective). Spatial updating was equally good in trapezoidal, rectangular and square rooms (one-fold...