Some genus 3 curves with many points

Using an explicit family of plane quartic curves, we prove the existence of a genus 3 curve over any finite field of characteristic 3 whose number of rational points stays within a fixed distance from the Hasse-Weil-Serre upper bound. We also provide an intrinsic characterization of so-called Legendre elliptic curves

Tannakian approach to linear differential algebraic groups

Tannaka's Theorem states that a linear algebraic group G is determined by the category of finite dimensional G-modules and the forgetful functor. We extend this result to linear differential algebraic groups by introducing a category corresponding to their representations and show how this category determines such a group.Comment: 31 pages; corrected misprint

Pulmonary function in patients with trophoblastic disease treated with low-dose methotrexate

The Sheffield Trophoblastic Disease Centre treats about 25 patients with persistent trophoblastic disease each year. A total of 75% of patients are classified as low risk according to the Charing Cross Hospital prognostic scoring system and receive methotrexate (MTX) 50 mg, i.m., on days 1, 3, 5, 7 with folinic acid 7.5 mg orally 24 h after each methotrexate injection. There is a 7-day rest between treatment cycles. Remission is achieved in 85% of cases. Approximately 20% of patients experienced pleuritic chest pain and dyspnoea. We have evaluated prospectively lung function in 16 low-risk patients receiving methotrexate. All patients had pulmonary function tests [spirometry-forced expiratory volume in 1 s (FEV1), forced vital capacity (FVC), peak expiratory flow rate (PEFR), and transfer factor - TLCO, kCO] performed before and after completed treatment. A mean of 7.5 cycles of MTX were administered (range 4-11). There was a significant reduction in the mean TLCO (mean pre/post 8.15/7.38 mmol min-1 kPa-1, P = 0.01), but there were no other statistically significant changes. Three patients experienced respiratory symptoms and were found to have a 39%, 28%, and 11% reduction in TLCO from baseline, improving on follow up to pretreatment levels. Low-dose MTX is an effective therapy but may cause troublesome pulmonary toxicity

Gauss Sums and Quantum Mechanics

By adapting Feynman's sum over paths method to a quantum mechanical system whose phase space is a torus, a new proof of the Landsberg-Schaar identity for quadratic Gauss sums is given. In contrast to existing non-elementary proofs, which use infinite sums and a limiting process or contour integration, only finite sums are involved. The toroidal nature of the classical phase space leads to discrete position and momentum, and hence discrete time. The corresponding `path integrals' are finite sums whose normalisations are derived and which are shown to intertwine cyclicity and discreteness to give a finite version of Kelvin's method of images.Comment: 14 pages, LaTe

Predicting the Effects of Management on Upland Birds, Economy and Employment

Livestock farming systems play a significant role in the economy and conservation of the UK uplands and rely heavily upon public financial support. Changes in that support could have far-reaching impacts on the wildlife interest and socio-economics of upland areas. Predicting the impacts of such changes is difficult, since they arise from responses to new economic circumstances. The effect of management change is also influenced by natural variation, such as the mosaic of plant communities, already present in the upland landscape. This paper sets out an approach that integrates theoretical models with field studies to investigate the effects of management change on birds, economics and employment in the UK uplands

On representations of super coalgebras

The general structure of the representation theory of a $Z_2$-graded coalgebra is discussed. The result contains the structure of Fourier analysis on compact supergroups and quantisations thereof as a special case. The general linear supergroups serve as an explicit illustration and the simplest example is carried out in detail.Comment: 18 pages, LaTeX, KCL-TH-94-

Directional wetting in anisotropic inverse opals

Porous materials display interesting transport phenomena due to the restricted motion of fluids within the nano- to micro-scale voids. Here, we investigate how liquid wetting in highly ordered inverse opals is affected by anisotropy in pore geometry. We compare samples with different degrees of pore asphericity and find different wetting patterns depending on the pore shape. Highly anisotropic structures are infiltrated more easily than their isotropic counterparts. Further, the wetting of anisotropic inverse opals is directional, with liquids filling from the side more easily. This effect is supported by percolation simulations as well as direct observations of wetting using time-resolved optical microscopy

Rational isogenies from irrational endomorphisms

In this paper, we introduce a polynomial-time algorithm to compute a connecting $\mathcal{O}$-ideal between two supersingular elliptic curves over $\mathbb{F}_p$ with common $\mathbb{F}_p$-endomorphism ring $\mathcal{O}$, given a description of their full endomorphism rings. This algorithm provides a reduction of the security of the CSIDH cryptosystem to the problem of computing endomorphism rings of supersingular elliptic curves. A similar reduction for SIDH appeared at Asiacrypt 2016, but relies on totally different techniques. Furthermore, we also show that any supersingular elliptic curve constructed using the complex-multiplication method can be located precisely in the supersingular isogeny graph by explicitly deriving a path to a known base curve. This result prohibits the use of such curves as a building block for a hash function into the supersingular isogeny graph