Search Our Scientific Publications & Authors

Arch Math 2022 1;118(2):169-179. Epub 2022 Feb 1.

Institute of Financial Mathematics and Applied Number Theory, Johannes Kepler University Linz, Altenberger Straße 69, 4040 Linz, Austria.

We study the extreme discrepancy of infinite sequences in the -dimensional unit cube, which uses arbitrary sub-intervals of the unit cube as test sets. This is in contrast to the classical star discrepancy, which uses exclusively intervals that are anchored in the origin as test sets. We show that for any dimension and any , the extreme discrepancy of every infinite sequence in is at least of order of magnitude , where is the number of considered initial terms of the sequence. Read More

Arch Math 2013 Jan 13;100(1):95-99. Epub 2012 Dec 13.

Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Madison WI 53706,

We show that, for any ≠ 2, most orientation preserving homeomorphisms of the sphere have a Cantor set of fixed points. In other words, the set of such homeomorphisms that do have a Cantor set of fixed points is of the first Baire category within the set of all homeomorphisms. Similarly, most orientation reversing homeomorphisms of the sphere have a Cantor set of fixed points for any ≠ 0. Read More