2-adic slopes of Hilbert modular forms over Q(√5)

We show that for arithmetic weights with a fixed finite order character, the slopes of U_{p} for p = 2 (which is inert) acting on overconvergent Hilbert modular forms of level U_{0}(4) are independent of the (algebraic part of the) weight and can be obtained by a simple recipe from the classical slopes in parallel weight 3

The Determination of Deuterium and Tritium in Effluent Wastewater by Pulsed Nuclear Magnetic Resonance Spectroscopy

A pulsed nuclear magnetic resonance (NMR) procedure was developed for the quantitative determination of deuterium and tritium in radioactive, effluent, wastewater to aid in the design of an efficient combined electrolytic/catalytic exchange system for the recovery of these hydrogen isotopes. The deuterium and tritium NMR signals were observed at 9.210 and 45.7 MHz, respectively. Ten different effluent water samples were analyzed for deuterium and tritium to establish base-line data for the preparation of standard reference samples. The hydrogen isotope concentrations ranged from 0.11 to 2.40 g deuterium and from 2.0 to 21.0 mg tritium per liter of processed sample. The standard deviation of the hydrogen isotope determinations is +- 0.017 g deuterium and +- 0.06 mg tritium per liter of processed effluent water. In the future, the effectiveness of specially prepared and analyzed (calorimetry) effluent samples as tritium standards will be investigated

A universally applicable method of operon map prediction on minimally annotated genomes using conserved genomic context.

An important step in understanding the regulation of a prokaryotic genome is the generation of its transcription unit map. The current strongest operon predictor depends on the distributions of intergenic distances (IGD) separating adjacent genes within and between operons. Unfortunately, experimental data on these distance distributions are limited to Escherichia coli and Bacillus subtilis. We suggest a new graph algorithmic approach based on comparative genomics to identify clusters of conserved genes independent of IGD and conservation of gene order. As a consequence, distance distributions of operon pairs for any arbitrary prokaryotic genome can be inferred. For E.coli, the algorithm predicts 854 conserved adjacent pairs with a precision of 85%. The IGD distribution for these pairs is virtually identical to the E.coli operon pair distribution. Statistical analysis of the predicted pair IGD distribution allows estimation of a genome-specific operon IGD cut-off, obviating the requirement for a training set in IGD-based operon prediction. We apply the method to a representative set of eight genomes, and show that these genome-specific IGD distributions differ considerably from each other and from the distribution in E.coli

Extensions of vector bundles on the Fargues-Fontaine curve

We completely classify the possible extensions between semistable vector bundles on the Fargues-Fontaine curve (over an algebraically closed perfectoid field), in terms of a simple condition on Harder-Narasimhan polygons. Our arguments rely on a careful study of various moduli spaces of bundle maps, which we define and analyze using Scholze's language of diamonds. This analysis reduces our main results to a somewhat involved combinatorial problem, which we then solve via a reinterpretation in terms of the euclidean geometry of Harder-Narasimhan polygons