Symmetry Properties of Autonomous Integrating Factors

We study the symmetry properties of autonomous integrating factors from an algebraic point of view. The symmetries are delineated for the resulting integrals treated as equations and symmetries of the integrals treated as functions or configurational invariants. The succession of terms (pattern) is noted. The general pattern for the solution symmetries for equations in the simplest form of maximal order is given and the properties of the associated integrals resulting from this analysis are given.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Linking academic emotions and student engagement: mature-aged distance students’ transition to university

This is an Accepted Manuscript of an article published by Taylor & Francis in Journal of Further and Higher Education on 2013, available online: https://www.tandfonline.com/doi/full/10.1080/0309877X.2014.895305Research into both student engagement and student emotions is increasing, with widespread agreement that both are critical determinants of student success in higher education. Less researched are the complex, reciprocal relationships between these important influences. Two theoretical frameworks inform this paper: Pekrun’s taxonomy of academic emotions and Kahu’s conceptual framework of student engagement. The prospective qualitative design aims to allow a rich understanding of the fluctuating and diverse emotions that students experience during the transition to university and to explore the relationships between academic emotions and student engagement. The study follows 19 mature-aged (aged 24 and over) distance students throughout their first semester at university, using video diaries to collect data on their emotional experiences and their engagement with their study. Pre and post-semester interviews were also conducted. Findings highlight that different emotions have different links to engagement: as important elements in emotional engagement, as inhibitors of engagement and as outcomes that reciprocally influence engagement. There are two key conclusions. First, student emotions are the point of intersection between the university factors such as course design and student variables such as motivation and background. Second, the flow of influence between emotions, engagement, and learning is reciprocal and complex and can spiral upwards towards ideal engagement or downwards towards disengagement and withdrawal.Publishe