Lattices in function fields and applications

In recent decades, the use of ideas from Minkowski's Geometry of Numbers has gained recognition as a helpful tool in bounding the number of solutions to modular congruences with variables from short intervals. In 1941, Mahler introduced an analogue to the Geometry of Numbers in function fields over finite fields. Here, we build on Mahler's ideas and develop results useful for bounding the sizes of intersections of lattices and convex bodies in $\mathbb{F}_q((1/T))^d$, which are more precise than what is known over $\mathbb{R}^d$. These results are then applied to various problems regarding bounding the number of solutions to congruences in $\mathbb{F}_q[T]$, such as the number of points on polynomial curves in low dimensional subspaces of finite fields. Our results improve on a number of previous bounds due to Bagshaw, Cilleruelo, Shparlinski and Zumalac\'{a}rregui. We also present previous techniques developed by various authors for estimating certain energy/point counts in a unified manner

Aquatic fungi

Seventy-one percent of our planet’s surface consist of water, but only 0.6% are lentic and lotic freshwater habitats. Often taken for granted, freshwaters are immensely diverse habitats and host >10% of all animal and >35% of all vertebrate species worldwide. However, no other major components of global biodiversity are declining as fast and massively as freshwater species and ecosystems. Urbanisation, economic growth, and climate change have increased pressure on freshwater resources, whilst biodiversity has given way to the increasing demands of a growing human population. The adverse impacts on aquatic ecosystems include habitat fragmentation, eutrophication, habitat loss, and invasion of pathogenic as well as toxic species. Although there is increasing evidence that freshwater fungal diversity is high, the study of the biodiversity of freshwater fungi is still in its infancy. In light of the rapid decline in freshwater biodiversity, it is timely and necessary to increase our efforts to evaluate the diversity and potential ecological function of this fascinating and diverse group of freshwater organisms

Line intensity enhancements in stellar coronal X-ray spectra due to opacity effects

Context. The I(15.01 A)/I(16.78 A) emission line intensity ratio in Fe XVII has been reported to deviate from its theoretical value in solar and stellar X-ray spectra. This is attributed to opacity in the 15.01 A line, leading to a reduction in its intensity, and was interpreted in terms of a geometry in which the emitters and absorbers are spatially distinct. Aims. We study the I(15.01 A)/I(16.78 A) intensity ratio for the active cool dwarf EV Lac, in both flare and quiescent spectra. Methods. The observations were obtained with the Reflection Grating Spectrometer on the XMM-Newton satellite. The emission measure distribution versus temperature reconstruction technique is used for our analysis. Results. We find that the 15.01 A line exhibits a significant enhancement in intensity over the optically thin value. To our knowledge, this is the first time that such an enhancement has been detected on such a sound statistical basis. We interpret this enhancement in terms of a geometry in which the emitters and absorbers are not spatially distinct, and where the geometry is such that resonant pumping of the upper level has a greater effect on the observed line intensity than resonant absorption in the line-of-sight.Comment: accepted for publication in A&

Millisecond minority carrier lifetimes in n-type multicrystalline silicon

Exceptionally high minority carrier lifetimes have been measured in n-type multicrystalline silicon (mc-Si) grown by directional solidification and subjected to phosphorus gettering. The highest effective lifetimes, up to 1.6 ms averaged over several grains and 2.8 ms within some of them, were measured for relatively lowly doped, 2–3 Ωcm, wafers. The lifetime was found to decrease for lower resistivities, still reaching 500 μs for 0.9 Ωcm and 100 μs for 0.36 Ωcm. Several important findings are reported here: (i) achievement of carrier lifetimes in the millisecond range for mc-Si, (ii) effectiveness of phosphorus gettering in n-type mc-Si, and (iii) demonstration of good stability under illumination for n-type mc-Si.This work has been partially supported by the Australian Research Council

A search for line intensity enhancements in the far-UV spectra of active late-type stars arising from opacity

Radiative transfer calculations have predicted intensity enhancements for optically thick emission lines, as opposed to the normal intensity reductions, for astrophysical plasmas under certain conditions. In particular, the results are predicted to be dependent both on the geometry of the emitting plasma and the orientation of the observer. Hence in principle the detection of intensity enhancement may provide a way of determining the geometry of an unresolved astronomical source. To investigate such enhancements we have analyzed a sample of active late-type stars observed in the far ultraviolet spectral region. Emission lines of O VI in the FUSE satellite spectra of epsilon Eri, II Peg and Prox Cen were searched for intensity enhancements due to opacity. We have found strong evidence for line intensity enhancements due to opacity during active or flare-like activity for all three stars. The O VI 1032/1038 line intensity ratios, predicted to have a value of 2.0 in the optically thin case, are found to be up to ~30% larger during several orbital phases. Our measurements, combined with radiative transfer models, allow us to constrain both the geometry of the O VI emitting regions in our stellar sources and the orientation of the observer. A spherical emitting plasma can be ruled out, as this would lead to no intensity enhancement. In addition, the theory tells us that the line-of-sight to the plasma must be close to perpendicular to its surface, as observations at small angles to the surface lead to either no intensity enhancement or the usual line intensity decrease over the optically thin value. For the future, we outline a laboratory experiment, that could be undertaken with current facilities, which would provide an unequivocal test of predictions of line intensity enhancement due to opacity, in particular the dependence on plasma geometry.Comment: 10 Pages, 8 Figures, and 2 Tables; Accepted in A&

Impact of preeclampsia on cardiovascular events: an analysis of the Generation Scotland: Scottish Family Health Study

Preeclampsia is a recognised cause of an increased risk of major adverse cardiovascular events when compared to the background risk in women who did not have hypertensive disorders during pregnancy. The Generation Scotland: Scottish Family Health Study (GS:SFHS) is a population cohort of more than 20,000 members of the Scottish population. Using the Scottish Morbidity Records, we linked the women in the GS:SFHS cohort to validated maternity and inpatient admission data. This allowed us to robustly identify cardiovascular outcomes in the form of inpatient admission for cardiovascular events, We also aimed to explore the risk of pregnancy on future cardiovascular events, using data from nulliparous and parous women.In total, 9732 women were selected. 3693 women were nulliparous, and after study exclusion, 5253 women with 9583 pregnancies remained. Pregnancies from 1980 until the end of the study period of 1st of July 2013 were included. Cardiovascular events occurred in 9.0% of nulliparous women, 4.2% of women with pregnancies and in 7.6% of women with a history of preeclampsia. A total of 218 parous women experienced cardiovascular events, 25 in the preeclampsia group and 193 in the normotensive group.Survival analysis was undertaken, with index pregnancy taken as first pregnancy in normotensive controls and first preeclampsia pregnancy in cases. Endpoint of interest was admission to hospital with first cardiovascular event. After further exclusions a total of 169 cardiovascular events occurred in the normotensive pregnancy group and 20 in the preeclampsia group. Women with a history of preeclampsia were more likely to have cardiovascular events later in life than women with normotensive deliveries., This was statistically significantly different on Kaplan Meier survival analysis, (log rank Mantel-Cox p-value < 0.001). The women in our study were middle-aged, within 33 years of pregnancy, with a mean age of 53 years in the preeclampsia cardiovascular events group.Our study supports the urgent need for uniform guidelines and implementation to improve the health in women with this medical history. Increased awareness among the public of the cardiovascular risk associated with PE is vital to aid uptake of cardiovascular prevention programmes