AN ALGORITHM FOR CONSTRUCTING CERTAIN DIFFERENTIAL OPERATORS IN POSITIVE CHARACTERISTIC

Given a non-zero polynomial f in a polynomial ring R with coefficients in a finite field of prime characteristic p, we present an algorithm to compute a differential operator delta which raises 1/f to its pth power. For some specific families of polynomials, we also study the level of such a differential operator delta, i.e., the least integer e such that delta is R-pe -linear. In particular, we obtain a characterization of supersingular elliptic curves in terms of the level of the associated differential operator

Reversals in nature and the nature of reversals

The asymmetric shape of reversals of the Earth's magnetic field indicates a possible connection with relaxation oscillations as they were early discussed by van der Pol. A simple mean-field dynamo model with a spherically symmetric $\alpha$ coefficient is analysed with view on this similarity, and a comparison of the time series and the phase space trajectories with those of paleomagnetic measurements is carried out. For highly supercritical dynamos a very good agreement with the data is achieved. Deviations of numerical reversal sequences from Poisson statistics are analysed and compared with paleomagnetic data. The role of the inner core is discussed in a spectral theoretical context and arguments and numerical evidence is compiled that the growth of the inner core might be important for the long term changes of the reversal rate and the occurrence of superchrons.Comment: 24 pages, 12 figure

Local cohomology and Lyubeznik numbers of F-pure rings

In this article, we study certain local cohomology modules over F-pure rings. We give sufficient conditions for the vanishing of some Lyubeznik numbers, derive a formula for computing these invariants when the F-pure ring is standard graded and, by its means, we provide some new examples of Lyubeznik tables. We study associated primes of certain Ext-modules, showing that they are all compatible ideals. Finally, we focus on properties that Lyubeznik numbers detect over a globally F-split projective variety

Avaliação da influência da suplementação alimentar sobre a estimativa da taxa de lotação animal em pastagens.

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Non-alcoholic beverages and risk of bladder cancer in Uruguay

BACKGROUND: Bladder cancer is the fourth most frequent malignancy among Uruguayan men. A previous study from Uruguay suggested a high risk of bladder cancer associated with maté drinking. We conducted an additional case-control study in order to further explore the role of non-alcoholic beverages in bladder carcinogenesis. METHODS: In the time period 1996–2000, 255 incident cases with transitional cell carcinoma of the bladder and 501 patients treated in the same hospitals and in the same time period were frequency matched on age, sex, and residence. Both cases and controls were face-to-face interviewed on occupation, tobacco smoking, alcohol drinking and intake of maté, coffee, tea, and soft drinks. Statistical analysis was carried out by unconditional multiple logistic regression. RESULTS: Ever maté drinking was positively associated with bladder cancer (odds ratio [OR] 2.2, 95% confidence interval [CI] 1.2–3.9) and the risk increased for increasing duration and amount of maté drinking. Both coffee and tea were strongly associated with bladder cancer risk (OR for coffee drinking 1.6, 95% CI 1.2–2.3; OR for tea drinking 2.3, 95% CI 1.5–3.4). These results were confirmed in a separate analysis of never-smokers. CONCLUSION: Our results suggest that drinking of maté, coffee and tea may be risk factors for bladder carcinoma in Uruguay

Linear magnetic resonance imaging measurements of the hippocampal formation differ in young versus old dogs

Age-related hippocampal formation (HF) atrophy has been documented on MRI studies using volumetric analysis and visual rating scales.This retrospective cross-sectional study aimed to compare linear MRI measurements of the HF between young (1–3 years) and old (>10 years) non-brachycephalic dogs, with normal brain anatomy and cerebrospinal fluid (CSF) analysis. Right and left hippocampal formation height (HFH), height of the brain (HB) and mean HFH/HB ratio were measured by two observers on a transverse T2 fluid-attenuated inversion recovery sequence containing rostral colliculi and mesencephalic aqueduct.119 MRI studies were enrolled: 75 young and 44 old dogs. Left and right HFH were greater (p<0.0001) in young, while HB was greater in old dogs (p=0.024). Mean HFH/HB ratio was 15.66 per cent and 18.30 per cent in old and young dogs (p<0.0001). No differences were found comparing measurements between epileptic and non-epileptic dogs.Old dogs have a greater HB; this may represent the different study populations or a statistical phenomenon. Ageing affects HF linear measurements. A reduction of mean HFH/HB ratio between 18.30 per cent and 15.66 per cent should be considered a physiological age-related process of the canine lifespan. The use of mean HFH/HB ratio could be considered for quantifying brain atrophy in elderly dogs