It is well known that each positive integer n can be expressed uniquely as a sum n = d0 + d1b + . . . + dhb h with an integral base number b ≥ 2, dh 6= 0 and di ∈ {0, . . . , b − 1}. This concept can… (More)

Discretisation methods to simulate stochastic differential equations belong to the main tools in mathematical finance. For Itô processes, there exist several Euleror Runge-Kutta-like methods which… (More)

Shift radix systems provide a unified notation to study several important types of number systems. However, the classification of such systems is already hard in two dimensions. In this paper, we… (More)

Let T be a tile of a self-affine lattice tiling. We give an algorithm that allows to determine all neighbours of T in the tiling. This can be used to characterize the sets VL of points, where T meets… (More)

In this paper we study properties of the fundamental domain Fβ of number systems, which are defined in rings of integers of number fields. First we construct addition automata for these number… (More)

This paper extends some results of Allouche and Shallit for q-regular sequences to numeration systems in algebraic number elds and to linear numeration systems. We also construct automata that… (More)

Recent results in the theory of quasi-Monte Carlo methods have shown that the weighted Koksma-Hlawka inequality gives better estimates for the error of quasi-Monte Carlo algorithms. We present a… (More)

Eswerden einige elementareUngleichungen auf hyperkomplexe Systeme Ïbertragen. Insbesondere werden Ungleichungen fÏr MÎbius-Transformationen in diesem allgemeinen Kontext gezeigt. 1. Introduction In… (More)

In a recent paper Cristea and Tichy introduced several types of discrepancies of point sets on the s-dimensional Sierpiński carpet and proved various relations between these discrepancies. In the… (More)

The present paper deals with β-expansions in algebraic function fields. If β is a Pisot unit, we characterise the elements whose β-expansion is purely periodic. In order to pursue this… (More)