Linear discrepancy of basic totally unimodular matrices.
Low-Discrepancy Point Sets.
Low-discrepancy point sets for non-uniform measures
We prove several results concerning the existence of low-discrepancy point sets with respect to an arbitrary non-uniform measure μ on the d-dimensional unit cube. We improve a theorem of Beck, by showing that for any d ≥ 1, N ≥ 1, and any non-negative, normalized Borel measure μ on there exists a point set whose star-discrepancy with respect to μ is of order . For the proof we use a theorem of Banaszczyk concerning the balancing of vectors, which implies an upper bound for the linear discrepancy...
Low-discrepancy point sets obtained by digital constructions over finite fields
Low-discrepancy sequences obtained from algebraic function fields over finite fields
Low-discrepancy sequences using duality and global function fields
Lower bounds for the discrepancy of some sequences
Mean-Square Discrepancies of the Hammersley and Zaremba Sequences for Arbitrary Radix.
Metric results on a new notion of discrepancy
Minoration de discrépance en dimension deux
Minoration de la discrépance d'une suite quelconque sur T
Note on Irregularities of Distibution.
Odometers and systems of numeration
On a form of the Erdős-Turán inequality
On a Problem of Erdös in the Theory of Irregularities of Distribution.
On a problem of K. F. Roth concerning irregularities of point distribution.
On a problem of W. M. Schmidt concerning one-sided ireegularities of point distrubitions.
On absolute (j, ε)-normality in the rational fractions with applications to normal numbers
On existence and discrepancy of certain digital Niederreiter-Halton sequences
On functions with bounded remainder
Let be a von Neumann-Kakutani - adic adding machine transformation and let . PutWe study three questions:1. When will be bounded?2. What can be said about limit points of 3. When will the skew product be ergodic on