space $X$ consisting of unit balls is called completely saturated (resp. completely reduced) if no finite set of its members can be replaced by a more numerous (resp. less numerous) set of unit balls of $X$ without losing the packing property (resp. covering property) of $\\mathcal F...
(1988) A polyhedron algorithm for finding space groups. Proc. of Third Int. Conf. on Engineering Graphics and Descriptive Geometry, Vienna Vol.2, pp. 37–44. Molnár, E. — Prok, I. (1994) Classification of solid transitive simplex tilings in simply connected 3-spaces, Part I. The comb...
Online publication date: 1-Dec-2011. [CrossRef] Daniel Lenz, Fabian Schwarzenberger, Ivan Veselić. (2011) A Banach space-valued ergodic theorem and the uniform approximation of the integrated density of states. Geometriae Dedicata 150, 1-34. Online publication date: 1-Feb-2011. [CrossRef]...
tilings,consistingofcongruentcopiesofasingletriangularprism,wasanalyzedin[CoR].LetG(p,q)bethegroupofrotationsin3-spacegeneratedbyrotations,aboutperpendicularaxes,by2π/pand2π/q.InaquaquaversaltilingtheorientationsofanytwoprismsarerelatedbyanelementofG(6,4).Moreprecisely,inanycubeofside2n,therelative...
balldefinesacompactzerodimensionalmetricspaceΩ,itshull,anda(reduced)groupoid-C∗-algebraAT.ThehullisthesetofalltilingswhicharelocallyhomomorphictoTandsuchthatoneoftheirpunctureslieson0.ThegroupoidR⊂Ω×ΩisthegroupoidoftheequivalencerelationT∼T′wheneverT′isatranslateofT.Wereferforthedetails,...
Consideration of the discriminantal arrangements for some particular octagons leads to a previously announced counterexample to the conjecture by Saito [ER2] that the complexified complement of a real free arrangement is aK (π, 1) space. Article PDF Similar content being viewed by others Rhombus...
Lastly we show that the orbits of any free measure-preserving action of n on a Lebesgue probability space can be measurably tiled so as to obtain the above structure.doi:10.1007/BFb0082854Daniel J. RudolphRudolph, D.J.: Rectangular tilings of R n and free R n actions. In: Alexander, J...
Such a covering of Euclidean space by a discrete set of translations is called a k -tiling. The investigation of simple tilings by translations (which we call 1-tilings in this context) began with the work of Fedorov [5] and Minkowski [15], and was later extended by Venkov and McMullen...
These tilings can be used to extend a fractal transformation defined on the attractor of a contractive IFS to a fractal transformation on the entire space upon which the IFS acts.doi:10.1007/s00454-014-9589-2Barnsley, MichaelVince, Andrew...