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Ciudad Universitaria, Mexico

Hubard I.,Institute Matematicas | Mixer M.,Wentworth Institute of Technology | Pellicer D.,National Autonomous University of Mexico | Weiss A.I.,York University
Discrete and Computational Geometry

Up to isomorphism, there are six fixed-point free crystallographic groups in Euclidean 3-space (Formula presented.) generated by twists (screw motions). In each case, an orientable 3-manifold is obtained as the quotient of (Formula presented.) by such a group. The cubic tessellation of (Formula presented.) induces tessellations on each such manifold. The corresponding classification for the 3-torus and the didicosm were classified as ‘equivelar toroids’ and ‘cubic tessellation of the didicosm’ in previous works. This paper concludes the classification of cubic tessellations on the remaining four orientable manifolds. © 2015, Springer Science+Business Media New York. Source

Castillo Villalba C.M.P.,Institute Matematicas | Colombo F.,Polytechnic of Milan | Gantner J.,Vienna University of Technology | Gonzalez-Cervantes J.O.,E.S.F.M. del I.P.N.
Complex Analysis and Operator Theory

In this paper we begin the study of some important Banach spaces of slice hyperholomorphic functions, namely the Bloch, Besov and weighted Bergman spaces, and we also consider the Dirichlet space, which is a Hilbert space. The importance of these spaces is well known, and thus their study in the framework of slice hyperholomorphic functions is relevant, especially in view of the fact that this class of functions has recently found several applications in operator theory and in Schur analysis. We also discuss the property of invariance of these function spaces with respect to Möbius maps by using a suitable notion of composition. © 2014, Springer Basel. Source

Pellicer D.,Institute Matematicas | Williams G.,University of Alaska Fairbanks
Electronic Journal of Combinatorics

We discuss representations of non-finite polyhedra as quotients of regular polytopes. We provide some structural results about the minimal regular covers of non-finite polyhedra and about the stabilizer subgroups of their flags under the flag action of the automorphism group of the covering polytope. As motivating examples we discuss the minimal regular covers of the Archimedean tilings, and we construct explicit minimal regular covers for three of them. Source

O'Reilly-Regueiro E.,Institute Matematicas
Designs, Codes, and Cryptography

It has been shown that if a (v, k, λ)-symmetric design with λ ≤ 3 admits a flag-transitive automorphism group G which acts primitively on points, then G must be of affine or almost simple type. Here we extend the result to λ = 4. © 2009 Springer Science+Business Media, LLC. Source

Kotani M.,Tohoku University | Schulz-Baldes H.,Friedrich - Alexander - University, Erlangen - Nuremberg | Villegas-Blas C.,Institute Matematicas
Journal of Mathematical Physics

At the interface of two two-dimensional quantum systems, there may exist interface currents similar to edge currents in quantum Hall systems. It is proved that these interface currents are macroscopically quantized by an integer that is given by the difference of the Chern numbers of the two systems. It is also argued that at the interface between two time-reversal invariant systems with half-integer spin, one of which is trivial and the other non-trivial, there are dissipationless spin-polarized interface currents. © 2014 AIP Publishing LLC. Source

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