The growth rate and dimension theory of beta-expansions

In a recent paper of Feng and Sidorov they show that for β∈(1,(1+5√)/2) the set of β-expansions grows exponentially for every x∈(0,1/(β−1)). In this paper we study this growth rate further. We also consider the set of β-expansions from a dimension theory perspective.

Adapting to new challenges: extension theory and practice for the 21st century

Twenty first century challenges facing agriculture include climate change, threats to food security for a growing population and downward economic pressures on rural livelihoods. Addressing these challenges will require innovation in extension theory, policy and education, at a time when the dominance of the state in the provision of knowledge and information services to farmers and rural entrepreneurs continues to decline. This paper suggests that extension theory is catching up with and helping us to understand innovative extension practice, and therefore provides a platform for improving rural development policies and strategies. Innovation is now less likely to be spoken of as something to be passed on to farmers, than as a continuing process of creativity and adaptation that can be nurtured and sustained. Innovation systems and innovation platforms are concepts that recognise the multiple factors that lead to farmers’ developing, adapting and applying new ideas and the importance of linking all actors in the value chain to ensure producers can access appropriate information and advice for decision making at all stages in the production process. Concepts of social learning, group development and solidarity, social capital, collective action and empowerment all help to explain and therefore to apply more effectively group extension approaches in building confidence and sustaining innovation. A challenge facing educators is to ensure the curricula for aspiring extension professionals in our higher education institutions are regularly reviewed and keep up with current and future developments in theory, policy and practice.

Characterizing intuition in information systems research

The study of intuition is an emerging area of research in psychology, social sciences, and business studies. It is increasingly of interest to the study of management, for example in decision-making as a counterpoint to structured approaches. Recently work has been undertaken to conceptualize a construct for the intuitive nature of technology. However to-date there is no common under-standing of the term intuition in information systems (IS) research. This paper extends the study of intuition in IS research by using exploratory research to cate-gorize the use of the word “intuition” and related terms in papers published in two prominent IS journals over a ten year period. The entire text of MIS Quarterly and Information Systems Research was reviewed for the years 1999 through 2008 using searchable PDF versions of these publications. As far as could be deter-mined, this is the first application of this approach in the analysis of the text of IS academic journals. The use of the word “intuition” and related terms was catego-rized using coding consistent with Grounded Theory. The focus of this research was on the first two stages of Grounded Theory analysis - the development of codes and constructs. Saturation of coding was not reached: an extended review of these publications would be required to enable theory development. Over 400 incidents of the use of “intuition”, and related terms were found in the articles reviewed. The most prominent use of the term of “intuition” was coded as “Intui-tion as Authority” in which intuition was used to validate a research objective or finding; representing approximately 37 per cent of codes assigned. The second most common coding occurred in research articles with mathematical analysis, representing about 19 per cent of the codes assigned, for example where a ma-thematical formulation or result was “intuitive”. The possibly most impactful use of the term “intuition” was “Intuition as Outcome”, representing approximately 7 per cent of all coding, which characterized research results as adding to the intui-tive understanding of a research topic or phenomena. This research contributes to a greater theoretical understanding of intuition enabling insight into the use of intuition, and the eventual development of a theory on the use of intuition in academic IS research publications. It also provides potential benefits to practi-tioners by providing insight into and validation of the use of intuition in IS man-agement. Research directions include the creation of reflective and/or formative constructs for intuition in information systems research.