Parallel addition in integer base is used for speeding up multiplication and division algorithms. k-block parallel addition has been introduced by Kornerup in [14]: instead of manipulating single digits, one works with blocks of fixed length k. The aim of this paper is to investigate how such notion influences the relationship between the base and the cardinality of the alphabet allowing block ...

We study the palindromic complexity of infinite words uβ , the fixed points of the substitution over a binary alphabet, φ(0) = 01, φ(1) = 01, with a − 1 ≥ b ≥ 1, which are canonically associated with quadratic non-simple Parry numbers β. 1991 Mathematics Subject Classification. 68R15, 11A63 .

Pisot numbers, primitive matrices and beta-conjugates. We show that given a Pisot number β, for any integer n large enough, there is a nonnegative primitive square matrix whose order is equal to the degree of β, and the matrix admits β for eingenvalue. Let β = a1/β + a2/β + · · ·+ an/β + · · · be the β-expansion of β. For any Pisot number β, the sequence (an)n≥1 is ultimately periodic i.e., for...

Laboratory experiments to determine the preferred orientation of free-falling hexagonal prisms were performed at Reynolds numbers appropriate to falling ice crystals in the atmosphere. Hexagonal plates orient with their c axis vertical for aspect ratios < 0.9, whilst hexagonal columns fall with their c axis horizontal. A secondary alignment is also observed: regular hexagonal columns fall prefe...