Using online STACK assessment to teach complex analysis: a prototype course design?

We describe a new course design, informed by our experience of the pandemic, that we think could be used in other high-level mathematics courses. The course’s main resource was a set of interactive STACK workbooks containing the course notes, automatically-marked comprehension and practice questions for self-assessment, and short videos of examples, calculations, and high-level motivation. This freed up synchronous class time to address conceptual understanding using interactive polling. We describe the course and discuss how it worked in practice

The Kenyan IPP experience

Public and concessionary finance for the expansion of power systems in Kenya dwindled in the 1990s. Meanwhile, demand for electricity services was on the rise. Private investment emerged to fill the gap with four Independent Power Producers (IPPs) established in the country by the second half of the decade. From 2000, the private market appears to have collapsed. Expansion of the power sector is once again led by the incumbent state-owned utility. This paper examines the investment and development outcomes of the four IPP projects, and highlights a number of interesting features of this experience. Firstly, the regulator matters. Established after the first wave of IPP developments, the regulator helped to bring tariffs of the second wave down. Secondly, the tendering process (i.e. an international competitive bid) does not ensure competition for a country that has significant political risk. Bidders self select well before the tender begins, a process which led one Kenyan tender to attract only two bidders (one of which was non-compliant). Thirdly, local partners matter. Half of the projects had local partners, and those that did faired better in the long run. The impact of project financing, public perception and currency devaluation is also evaluated to glean lessons learned of past projects and help pave the way for a more sustainable future for the Kenyan power sector—which presently serves only 15% of the population

Singular minimizers in the calculus of variations

This thesis examines the possible failure of regularity for minimizers of onedimensional variational problems. The direct method of the calculus of variations gives rigorous assurance that minimizers exist, but necessarily admits the possibility that minimizers might not be smooth. Regularity theory seeks to assert some extra smoothness of minimizers. Tonelli's partial regularity theorem states that any absolutely continuous minimizer has a (possibly infinite) classical derivative everywhere, and this derivative is continuous as a function into the extended real line. We examine the limits of this theorem. We find an example of a reasonable problem where partial regularity fails, and examples where partial regularity holds, but the infinite derivatives of minimizers permitted by the theorem occur very often, in precise senses. We construct continuous Lagrangians, strictly convex and superlinear in the third variable, such that the associated variational problems have minimizers nondifferentiable on dense second category sets. Thus mere continuity is an insufficient smoothness assumption for Tonelli's partial regularity theorem. Davie showed that any compact null set can occur as the singular set of a minimizer to a problem given via a smooth Lagrangian with quadratic growth. The proof relies on enforcing the occurrence of the Lavrentiev phenomenon. We give a new proof of the result, but constructing also a Lagrangian with arbitrary superlinear growth, and in which the Lavrentiev phenomenon does not occur in the problem. Universal singular sets record how often a given Lagrangian can have minimizers with infinite derivative. Despite being negligible in terms of both topology and category, they can have dimension two: any compact purely unrectifiable set can lie inside the universal singular set of a Lagrangian with arbitrary superlinearity. We show this also to be true of Fσ purely unrectifiable sets, suggesting a possible characterization of universal singular sets.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

The Kenyan IPP experience

Public and concessionary finance for the expansion of power systems in Kenya dwindled in the 1990s. Meanwhile, demand for electricity services was on the rise. Private investment emerged to fill the gap with four Independent Power Producers (IPPs) established in the country by the second half of the decade. From 2000, the private market appears to have collapsed. Expansion of the power sector is once again led by the incumbent state-owned utility. This paper examines the investment and development outcomes of the four IPP projects, and highlights a number of interesting features of this experience. Firstly, the regulator matters. Established after the first wave of IPP developments, the regulator helped to bring tariffs of the second wave down. Secondly, the tendering process (i.e. an international competitive bid) does not ensure competition for a country that has significant political risk. Bidders self select well before the tender begins, a process which led one Kenyan tender to attract only two bidders (one of which was non-compliant). Thirdly, local partners matter. Half of the projects had local partners, and those that did faired better in the long run. The impact of project financing, public perception and currency devaluation is also evaluated to glean lessons learned of past projects and help pave the way for a more sustainable future for the Kenyan power sector—which presently serves only 15% of the population

Perceived psychosocial impairment associated with eating disorder features: responses to a mental health literacy intervention

BACKGROUND: Whether and to what extent young adults are aware of the adverse impact of eating disorder features (EDF) on psychosocial functioning is unclear, although such awareness may affect the experience and behavior of sufferers. The aim of the current study was to examine young adults’ perceptions of psychosocial impairment associated with EDF, and the potential effect on these perceptions of an eating disorders “mental health literacy” (ED-MHL) intervention. METHODS: Undergraduate students (male: n = 35; female: n = 141) completed self-report questionnaires prior to, immediately following, and 3 months after completion of a 3-h ED-MHL intervention. Perceived psychosocial impairment associated with EDF–binge eating, purging, extreme dietary restriction, overvaluation of weight/shape, and excessive exercise–was assessed at each time point. RESULTS: At all 3 time points, EDF were considered to have a ‘slightly negative’ to ‘very negative’ impact on psychosocial functioning. Prior to the intervention, binge eating, purging and extreme dietary restriction were generally considered to have a greater negative impact than excessive exercise and overvaluation of weight/shape. Three months after the ED-MHL intervention, participants reported greater perceived impairment associated with excessive exercise and overvaluation; while perceptions of psychosocial impairment associated with binge eating, purging and dietary restriction remained largely unchanged. Females perceived greater impairment associated with EDF than males did immediately after the intervention, but not at the 3-month follow-up. CONCLUSIONS: The adverse effects on psychosocial functioning of binge eating, purging and extreme dietary restriction appear to be readily recognized by young people. Awareness of the adverse effects of excessive exercise and overvaluation may be poorer, but amenable to improvement by means of a relatively simple intervention. These features may warrant particular attention in health promotion programs