An explicit vertex operator algebra construction is given of a class of irreducible modules for toroidal Lie algebras. AMS (MOS) Subject Classifications:17B69, 17B68, 17B66, 17B10.

We derive formulas for (i) the number of distinct toroidal n × n binary arrays, allowing rotation of rows and/or columns as well as matrix transposition, and (ii) the number of distinct toroidal n × n binary arrays, allowing rotation and/or reflection of rows and/or columns as well as matrix transposition.

We prove that if G is a triangulation of the torus and χ(G) 6= 5, then there is a 3-coloring of the edges of G so that the edges bounding every face are assigned three different colors.

We present a geometric approach for tonality analysis called symmetry model. To derive the symmetry model, Carol L.Krumhansl andE.J.Kessler’s toroidal Multi Dimensional Scaling (MDS) solution is separated into a key spanning and a key related component. While the key spanning component represents relationships betweendifferent keys, the key related component is suitable for the analysis of inne...

für Naturforschung in cooperation with the Max Planck Society for the Advancement of Science under a Creative Commons Attribution 4.0 International License. Dieses Werk wurde im Jahr 2013 vom Verlag Zeitschrift für Naturforschung in Zusammenarbeit mit der Max-Planck-Gesellschaft zur Förderung der Wissenschaften e.V. digitalisiert und unter folgender Lizenz veröffentlicht: Creative Commons Namen...

We show that a k x n diagonal mesh is isomorphic to a 9 x 9 -9 x 9 twisted toroidal mesh, i.e., a network similar to a standard 9 x 9 toroidal mesh, but with opposite handed twists of 9 in the two directions, which results in a loss of (9)2 nodes

0. Introduction. In this article we show how to construct hierarchies of partial differential equations and their soliton-type solutions from the vertex operator representations of toroidal Lie algebras. Soliton theory was given a new impetus when it was linked with the representation theory of infinite-dimensional Lie algebras in the works of Sato [S], Date-Jimbo-Kashiwara-Miwa [DJKM] and Drin...

Using a unified framework, we show that a pruned 3D torus can be. explicitly specified by its pruning direction along which the links are uniformly removed from a complete 3D torus. The resulting networks, that offer the advantages of lower node degree and simpler layout, are inherently node-symmetric and maintain the same diameter as the original torus. It nuns out that the simplest pruning sc...

We investigate the Tits buildings of the paramodular groups with or without canonical level structure, respectively. These give important combinatorical information about the boundary of the toroidal compactification of the moduli spaces of non-principally polarised Abelian varieties. We give a full classification of the isotropic lines for all of these groups. Furthermore, for square-free, cop...

0.2. Structure of the proof. 1. As in [dJ], we choose a projection X 99K P of relative dimension 1, and apply semistable reduction to obtain a model X ′ → B over a suitable Galois base change B → P , with Galois group G. 2. We apply induction on the dimension to B , therefore we may assume that B is smooth, and that the discriminant locus of X ′ → B is a G-strict divisor of normal crossings. 3....