Orbifold Triangulations and Crystallographic Groups

Given a triangulation of a 3-dimensional euclidean orbifold, e.g. in terms of the Delaney symbol of a periodic tiling, a method is discussed for identifying the isomorphism type of the corresponding space group. Of the 219 types of groups, 175 can be recognized solely by considering the orbifold graph associated with the given triangulation. Simple algebraic invariants distinguish between the remaining 44 cases. The graphs and invariants are listed.     

Decomposition in general mathematical programming

In this paper a unifying framework is presented for the generalization of the decomposition methods originally developed by Benders (1962) and Dantzig and Wolfe (1960). These generalizations, calledVariable Decomposition andConstraint Decomposition respectively, are based on the general duality theory developed by Tind and Wolsey. The framework presented is of a general nature since there are no restrictive conditions imposed on problem structure; moreover, inaccuracies and duality gaps that are encountered during computations are accounted for. The two decomposition methods are proven not to cycle if certain (fairly general) conditions are met. Furthermore, finite convergence can be ensured under the traditional finiteness conditions and asymptotic convergence can be guaranteed once certain continuity conditions are met. The obvious symmetry between both types of decomposition methods is explained by establishing a duality relation between the two, which extends a similar result in Linear Programming. A remaining asymmetry in the asymptotic convergence results is argued to be a direct consequence of a fundamental asymmetry that resides in the Tind-Wolsey duality theory. It can be shown that in case the latter asymmetry disappears, the former does too. Other decomposition techniques, such as Lagrangean Decomposition and Cross Decomposition, turn out to be captured by the general framework presented here as well.This study was supported by the Netherlands Foundation for Mathematics (SMC) with financial aid from the Netherlands Organization for Scientific Research (NWO).Part of this work was done while on leave at the Wharton School of the University of Pennsylvania.     

Konfigurationen einander meidender Kreise in miquelschen Möbiusebenen ungerader Ordnung

Ohne Zusammenfassung     

Spezielle Sobolev-Räume von Beurling-Distributionen

Ohne Zusammenfassung