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The Calkin-Wilf Tree: Extensions and Applications
No full textContinued fractions are of current interest in mathematics. In a recent publication, Jack E. Graver describes a method for computing terms in the Calkin-Wilf sequence, a list of the positive rationals introduced by Neil Calkin and Herbert S. Wilf in 2000. This paper explores an original method which uses continued fractions to evaluate and locate terms in the Calkin-Wilf sequence, as well as its natural extension to include all of the rational numbers. A generalization of the Calkin-Wilf tree leads to a characterization of rational numbers by continued fractions with integer coefficients. Finally, the meaning of infinite continued fractions and irrational numbers is studied using the structure of the Calkin-Wilf tree. We characterize the irrational numbers which have periodic continued fractions by developing a matrix representation of the setup, and we explain why irrational square root numbers have periodic continued fractions with palindromic coefficients
Calkin-Wilf enumeration
No full textCilj zavrˇsnog rada je dokazati prebrojivost skupa racionalnih brojeva, na specifiˇcan
naˇcin. Gradi se enumeracija skupa Q te se pridruˇzuje binarno stablo. Enumeracija se
naziva Calkin-Wilf enumeracija prema matematiˇcarima Neil Calkinu i Herbert Wilfu
te joj je pridruˇzeno i Calkin-Wilf stablo. Postoje i generalizacije navedene enumeracije.
U tim sluˇcajevima prebrojivost se dokazuje pomo´cu Pontonovog ternarnog i kvinarnog
stabla te pripadaju´cih nizova. Nizove formiramo poˇcevˇsi od korijena, s lijeva na desno,
po razinama. Radi lakˇseg razumijevanja rada, prvo se uvode osnovni pojmovi te nakon
toga slijede dokazi navedenih tvrdnji. Takoder, na temelju Calkin-Wilf stabla gradi se
pobjedniˇcka strategija u igri Euclid koju su razvili matematiˇcari A. J. Cole i A. J. T.
Davie
Facing the Future: the Changing Shape of Academic Skills Support at Bournemouth University
No full textThis paper explores the potential impact of changes to higher education in England on student expectations, engagement, lifestyles and diversity, and outlines implications for the development of digital literacy within academic skills support at Bournemouth University (BU). We will investigate how tackling resource constraints with organisational change can also enable efficient, centralised provision of support materials that utilise networks to overcome the risk of fragmented support for digital literacy. We will also look at how changing delivery modes for support can accommodate changing student lifestyles whilst tackling a weakness of centralised support for digital literacy: that it can become detached from the student’s subject-focused academic practice. Finally we will explore how involving students in developing support can help us to face changes to student expectations and engagement whilst ensuring that materials are authentic and speak to learners in their own voice
Why Privacy Matters: An Interview with Neil Richards
No full textProfessor Daniel J. Solove discusses the book \u27Why Privacy Matters\u27 and the future of privacy with the author, Professor Neil Richards
Interview with AntipodeFoundation.org: “Much More Than You Think: The Spatialities of Italian Autonomy” – Interview with Neil Gray, author of “Beyond the Right to the City: Territorial Autogestion and the Take over the City Movement in 1970s Italy”
No full textNo abstract available
Jere Nash Interview with Neil McMillen (Part 2 of 2)
No full textInterview conducted by author Jere Nash with University of Southern Mississippi history professor Neil R. McMillen in the process of writing Mississippi Politics: The Struggle for Power, 1976-2006. Topics discussed include Aaron Henry; race relations after the civil rights movement; and William Winter
Maximizing Research Impact Through Institutional and National Open-Access Self-Archiving Mandates
No full textNo research institution can afford all the journals its researchers may need, so all articles are losing research impact (usage and citations). Articles made “Open Access,” (OA) by self-archiving them on the web are cited twice as much, but only 15% of articles are being spontaneously self-archived. The only institutions approaching 100% self-archiving are those that mandate it. Surveys show that 95% of authors will comply with a self-archiving mandate; the actual expe-rience of institutions with mandates has confirmed this. What institutions and funders need to mandate is that (1) immediately upon acceptance for publication, (2) the author’s final draft must be (3) deposited into the Institutional Repository. Only the depositing needs to be mandated; set-ting access privileges to the full-text as either OA or Restricted Access (RA) can be left up to the author. For articles published in the 93% of journals that have already endorsed self-archiving, access can be set as OA immediately; for the remaining 7%, authors can email the eprint in re-sponse to individual email requests automatically forwarded by the Repository
On the expected performance of a parallel algorithm for finding maximal independent subsets of a random graph
No full textAbstract: "We consider the parallel greedy algorithm of Coppersmith, Raghavan and Tompa [CRT] for finding the lexicographically first maximal independent set of a graph. We prove an [omega](log n) bound on the expected number if [sic] iterations for most edge densities. This complements the O(log n) bound proved in Calkin and Frieze [CF].
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