Class Notes for Math 905: Commutative Algebra, Instructor Sylvia Wiegand

Topics include: Rings, ideals, algebraic sets and affine varieties, modules, localizations, tensor products, intersection multiplicities, primary decomposition, the Nullstellensat

Class Notes for Math 901/902: Abstract Algebra, Instructor Tom Marley

Topics include: Free groups and presentations; Automorphism groups; Semidirect products; Classification of groups of small order; Normal series: composition, derived, and solvable series; Algebraic field extensions, splitting fields, algebraic closures; Separable algebraic extensions, the Primitive Element Theorem; Inseparability, purely inseparable extensions; Finite fields; Cyclotomic field extensions; Galois theory; Norm and trace maps of an algebraic field extension; Solvability by radicals, Galois\u27 theorem; Transcendence degree; Rings and modules: Examples and basic properties; Exact sequences, split short exact sequences; Free modules, projective modules; Localization of (commutative) rings and modules; The prime spectrum of a ring; Nakayama\u27s lemma; Basic category theory; The Hom functors; Tensor products, adjointness; Left/right Noetherian and Artinian modules; Composition series, the Jordan-Holder Theorem; Semisimple rings; The Artin-Wedderburn Theorem; The Density Theorem; The Jacobson radical; Artinian rings; von Neumann regular rings; Wedderburn\u27s theorem on finite division rings; Group representations, character theory; Integral ring extensions; Burnside\u27s paqb Theorem; Injective modules

Effects of dietary fibre and the provision of a foraging substrate on the welfare of sows in different grouping systems

End of project reportThere are no clear guidelines on how best to meet the EU legislative requirement (Council Directive 2001/88/EC) that pregnant sows and gilts should be provided with sufficient amounts of bulky or high fibre diets and high energy food to satisfy hunger and the motivation to chew. Therefore the aim of this project was to investigate the effect of increasing dietary fibre levels and providing access to a foraging substrate on the welfare of sows housed in dynamic and static groups. To achieve this a review paper was compiled and three experiments were conducted. The aim of the review paper was to assess the effectiveness of increasing dietary fibre levels on the welfare of pregnant sows. Previous research found that increasing dietary fibre levels decrease activity levels and the performance of stereotypic behaviour, and increase resting behaviour. However, high fibre diets do not appear to reduce aggression between group-housed pregnant sows. The research clearly showed that the effectiveness of high fibre diets is influenced by the source of fibre, with soluble fibres being more effective in reducing stereotypic behaviours than insoluble fibres. However the optimum fibrous ingredient, or combination of ingredients, and the optimum dietary inclusion rate for these ingredients remains unclear

Effects of husbandry and low-dose lipopolysaccharide challenge on the acute phase response of young pigs

End of project reportIn recent years, concern has grown for the welfare of domesticated animals in different production systems (Appleby and Hughes, 1997). Poor welfare can result in poor performance and productivity. However, the consumers are also requesting more welfare-friendly systems, as reflected by the importance that ‘organic’ and ‘free-range’ products have gained in our markets. Furthermore, there are ethical reasons for safeguarding the welfare of animals in our care. Thus, it is scientists’ task to be able to develop methods and techniques that can help to assess the welfare objectively. Traditionally, welfare assessment relied on the study of behaviour and the measurement of endocrine parameters. Acute phase response mediators and products, such as pro-inflammatory cytokines and acute phase proteins, emerged recently as potential indicators of infection and herd health status (Eckersall, 2000; Petersen et al., 2004). Thus, investigating the effects of husbandry and low-dose lipopolysaccharide (LPS) challenge on the acute phase response of young pigs can give valuable information on the use of these immune parameters as health and welfare indicators in pigs.Teagasc acknowledges the support of National Development Programme Funds (NDP) in the financing of this research projec

Studies on growth rates in pigs and the effect of birth weight

End of project reportThe purpose of this study was to assess some environmental and management factors that affect growth performance on commercial pig units. In experiment 1, a survey was carried out on 22 pig units of known growth performance in south-west Ireland to compare management factors between those showing poor and good growth rates. Low growth rate appears to be due to the cumulative effect of a combination of factors. Experiment 2 was conducted to determine the effects of providing an additional feeder on performance of weaned piglets. No benefits were recorded. Feed consumed from the additional feeder was a replacement for feed that otherwise would have been consumed from the control hopper feeder. Experiment 3 was designed to determine if pig performance and efficiency of growth were affected by weight at birth and at weaning. Lightweight pigs showed inferior growth performance up to the finisher period. Although they compensated some of the inferior growth towards the time of slaughter, they never reached the weights of the heavy birth-weight animals. Males were either significantly heavier or tended to be heavier than females throughout. There was no significant difference between the sexes in the number of days to slaughter. Light and heavy pigs did not differ in the levels of IGF-1 in their blood plasma; however lightweight pigs had significantly lower IgG preweaning. Experiment 4 aimed to determine whether piglet birth weight influenced growth performance, plasma IGF-1 concentrations and muscle fibre characteristics at day 42 of life. At slaughter (Day 42) light birth weight pigs were significantly (P < 0.001) lighter. Plasma IGF-1 concentration was lower by 28% (P=0.06) in light pigs. Muscle fibre cross sectional area and total fibre number were not significantly different between groups. This study should be repeated with bigger numbers

The Impact of the North Atlantic Oscillation on Electricity Markets: A Case Study on Ireland. ESRI WP509. July 2015

The North Atlantic Oscillation (NAO) is a large-scale circulation pattern driving climate variability in north-western Europe. As the deployment of wind-powered generation expands on electricity networks across Europe the impacts of the NAO on the electricity system will be amplified. This study assesses the impact of NAO, via wind-power generation, on the electricity market considering thermal generation costs, wholesale electricity prices and wind generation subsidies. A Monte Carlo approach is used to model NAO phases and generate hourly wind speed time-series data, electricity demand and fuel input data. A least-cost unit commitment and economic dispatch model is used to simulate an island electricity system, modelled on the all-island Irish electricity system. The impact of NAO obviously depends on the level of wind capacity within an electricity system. Our results indicate that NAO phases can affect thermal generation costs by up to 8%, wholesale electricity prices by as much as €1.5/MWh, and that wind power generators receive on average 12% higher remuneration

Carbon Dioxide (CO2) Emissions from Electricity: The Influence of The North Atlantic Oscillation. ESRI WP510. August 2015

The North Atlantic Oscillation (NAO) is a large-scale circulation pattern driving climate variability in north-western Europe. In recent years there has been an increasing deployment of wind-powered generation technology, i.e. wind farms, on electricity networks across Europe. As this deployment increases it is important to understand how climate variability will affect both wind- powered and non-renewable power generation. This study extends the literature by assessing the impact of NAO, via wind-power generation, on carbon dioxide emissions from the wider electricity system. A Monte Carlo approach is used to model NAO phases, generate hourly wind speed time- series data, electricity demand and fuel input data. A unit commitment, least-cost economic dispatch model is used to simulate an entire electricity system, modelled on the all-island Irish electricity system. Our results confirm that the NAO has a significant impact on monthly mean wind speeds, wind power output, and carbon dioxide emissions from the entire electricity system. The impact of NAO on emissions obviously depends on the level of wind penetration within an electricity system but our results indicate that emissions intensity within the Irish electricity system could vary by as much as 10% depending on the NAO phase within the next few years. The emissions intensity of the electricity system will vary with the NAO phase