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An m-cycle of the 3n+1-problem is defined as a periodic orbit with m local minima. In this article we derive lower and upper bounds for the cycle length and the elements of (hypothetical) m-cycles. In particular, we prove that there do not exist nontrivial m-cycles for 1 ≤ m ≤ 68. Our proofs are based on transcendental number theory, computational(More)
BACKGROUND Caring for a baby can provoke or intensify discord between parents, with adverse effects on their own well-being and their parenting. AIM The aim of this study was to appraise evidence obtained from 450 mothers on the quality of the parents' relationship during the postnatal period and the value of support provided by health visitors in cases(More)
Optical proximity communication (OPxC) with reflecting mirrors is presented. Direct optical links are demonstrated for silicon chips with better than -2.5dB coupling loss, excluding surface losses. OPxC is a true broadband solution with little impairment to the signal integrity for high-speed optical transmission. With wavelength division multiplexing (WDM)(More)