Local-Global Principles for Diophantine Equations

The real number field, denoted ℝ, is the most well-known extension field of ℚ, the field of rational numbers, but it is not the only one. For each prime p, there exists an extension field ℚp of ℚ, and these fields, known as the p-adic fields, have some properties substantially different from ℝ. In this paper, we construct the p-adic numbers from the ground up and discuss the local-global principle, which concerns connections between solutions of equations found in ℚ and in ℚp. We state the Hasse-Minkowski theorem, which addresses a type of Diophantine equation to which the local-global principle applies, and conclude with a computation in which we apply the theorem followed by Selmer’s famous counterexample for cubic curves

Collective action initiatives to improve marketing performance: Lessons from farmer groups in Tanzania

"The primary inquiry of this study is to identify and understand the underlying factors that enable smallholder farmer groups to improve their market situation. The specific objective of this paper is to examine to what extent certain group characteristics and asset endowments facilitate collective action initiatives to improve group marketing performance. This objective is approached through an evaluation of a government-led program in Tanzania, which is attempting to increase smallholder farmers' incomes and food security through a market-oriented intervention. Findings suggest that more mature groups with strong internal institutions, functioning group activities, and a good asset base of natural capital are more likely to improve their market situation. Gender composition of groups also factors in group marketing performance. It acts as an enabling factor for male-dominated groups and as a disabling factor for female-only groups. Structural social capital in the form of membership in other groups and ties to external service providers, and cognitive social capital in the form of intragroup trust and altruistic behavior are not significant factors in a group's ability to improve its market situation." authors' abstractCollective action, Agricultural marketing, Farmer groups, Social capital, Planned change initiatives, Gender, Marketing,

Young People’s Workforce Reform Programme : evaluation report

"The Children's Workforce Development Council (CWDC) commissioned Ecorys and H.J. Giller & Associates to independently evaluate the 2008–2011 Young People's Workforce Reform Programme (YPWRP). The YPWRP was introduced in 2008 as part of a ten year government strategy to help develop help develop a more skilled, confident workforce able to work in an effective and integrated way to deliver the best possible outcomes for young people. The main evaluation methodology used was semi-structured interviews with stakeholders, supplemented by telephone surveys and a small number of focus groups and event observations. Desk review of programme information was also undertaken. This summary assesses the main YPWRP strands and workstreams along with its cross cutting themes of communications and data collation in light of intended outcomes. It concludes by assessing the outcomes of the programme overall." - page iv