Only the leading seven terms of a continued fraction are needed to perform on-line arithmetic, provided the continued fractions are of the correct form. This forms the basis of a proof that there is an effective representation of the computable reals as continued fractions: we also demonstrate that the basic arithmetic operations are computable using this representation.

The world average values for the probabilities that a charm quark fragments into D and D s have been calculated to be f(c → D) = 0.235± 0.007 (±0.007) and f(c → D s ) = 0.101± 0.009 (±0.025), respectively. The average values for D, D and Λ c have been also calculated. [email protected] On leave from Moscow State University, supported by GIF, contract I-0444-176.07/95 Introduction The probab...

The continued fraction expansion of a real number is a fundamental and revealing expansion through its connection with Euclidean algorithm and with ``best'' rational approximations (see [HW]). At the same time, it is very poorly understood for some interesting numbers. We know that it is essentially unique and finite (i.e., terminating) exactly for rational numbers and periodic exactly for quad...

This section of Resonance presents thought-provoking questions, and discusses answers a few months later. Readers are invited to send new solutions old ones comments, ‘Think It Over’, Resonance, Indian Academy Sciences, Bangalore 560 080. Items illustrating ideas concepts will generally be chosen.