Salem numbers and Pisot numbers via interlacing

We present a general construction of Salem numbers via rational functions whose zeros and poles mostly lie on the unit circle and satisfy an interlacing condition. This extends and unifies earlier work. We then consider the "obvious" limit points of the set of Salem numbers produced by our theorems, and show that these are all Pisot numbers, in support of a conjecture of Boyd. We then show that all Pisot numbers arise in this way. Combining this with a theorem of Boyd, we show that all Salem numbers are produced via an interlacing construction.Comment: 21 pages, 5 figures, updated in response to reviewer comment

Pinning it down: An evaluation of Pinterest’s function in the British academic library

University libraries have found a useful resource for themselves in many social media platforms. At Leeds Beckett University Library (formerly Leeds Metropolitan University), Twitter has proved a popular way to connect with students, other libraries and universities. Our Twitter following has exceeded 3,800, and our library Facebook had over 1,100 followers by May 2014. While we continue to develop these two sites, however, we acknowledge that we are not part of a stable environment. Social media is faddish; the favoured platforms change frequently. Facebook has largely taken custom away from Myspace, while Myspace used to tussle for users with Bebo, and Google Plus has taken their share of professional networks away from other platforms. With this in mind, any organisation using social media has to think about whether they should use – and if so, how to use – emerging virtual social networks