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Let β > 1 be a non-integer. We consider expansions of the form ∞ i=1 d i β i , where the digits (di) i≥1 are generated by means of a Borel map K β defined on {0, 1} N × [0, β/(β − 1)]. We show existence and uniqueness of an absolutely continuous K β-invariant probability measure w.r.t. mp ⊗ λ, where mp is the Bernoulli measure on {0, 1} N with parameter p… (More)

- Martijn de Vries
- 2004

The Generic Haskell programming language allows functions to be defined by induction on the structure of data types. This gives rise to generic functions which can be applied to values of any conceivable data type. Compiling a Generic Haskell program amounts to generating a Haskell program in which all generic functions have been translated to ordinary… (More)

- Dunstano del Puerto-Flores, Jacquelien M. A. Scherpen, Marco Liserre, Martijn M. J. de Vries, Marco J. Kransse, Vito Giuseppe Monopoli
- IEEE Trans. Contr. Sys. Techn.
- 2014

- MARTIJN DE VRIES
- 2006

Consider the set U of real numbers q ≥ 1 for which only one sequence (c i) of integers 0 ≤ c i ≤ q satisfies the equality P ∞ i=1 c i q −i = 1. In this note we show that the set of algebraic numbers in U is dense in the closure U of U .

- MARTIJN DE VRIES
- 2008

Let q > 1 be a real number and let m = m(q) be the largest integer smaller than q. It is well known that each number x ∈ Jq := [0, P ∞ i=1 mq −i ] can be written as x = P ∞ i=1 c i q −i with integer coefficients 0 ≤ c i < q. If q is a non-integer, then almost every x ∈ Jq has continuum many expansions of this form. In this note we consider some properties… (More)

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