Averages and moments associated to class numbers of imaginary quadratic fields

For any odd prime $\ell$, let $h_\ell(-d)$ denote the $\ell$-part of the class number of the imaginary quadratic field $\mathbb{Q}(\sqrt{-d})$. Nontrivial pointwise upper bounds are known only for $\ell =3$; nontrivial upper bounds for averages of $h_\ell(-d)$ have previously been known only for $\ell =3,5$. In this paper we prove nontrivial upper bounds for the average of $h_\ell(-d)$ for all primes $\ell \geq 7$, as well as nontrivial upper bounds for certain higher moments for all primes $\ell \geq 3$.Comment: 26 pages; minor edits to exposition and notation, to agree with published versio

Simultaneous Integer Values of Pairs of Quadratic Forms

We prove that a pair of integral quadratic forms in 5 or more variables will simultaneously represent "almost all" pairs of integers that satisfy the necessary local conditions, provided that the forms satisfy a suitable nonsingularity condition. In particular such forms simultaneously attain prime values if the obvious local conditions hold. The proof uses the circle method, and in particular pioneers a two-dimensional version of a Kloosterman refinement.Comment: 63 page

Receiver-Based Auralization of Broadband Aircraft Flyover Noise Using the NASA Auralization Framework

The NASA Auralization Framework (NAF) consists of a set of dynamic link libraries (DLLs) to facilitate auralization of aircraft noise. Advanced capabilities for synthesis, propagation, and external interfaces are provided by the NAF Advanced Plugin Libraries (APL); a separate set of DLLs that are made accessible through the NAFs plugin architecture. In the typical time domain use case, the sound is first synthesized at the source location based on a source noise definition, and is then propagated in the time domain to a receiver on or near the ground. Alternatively, it may be desirable to synthesize the sound at the receiver, after it has been propagated in the frequency domain, e.g., when the source definition is inaccessible or when alternative propagation methods are needed. Receiver-based auralization requires three new developments in the NAF APL: a component plugin to interpolate the propagated noise spectra as a function of time for input to sound synthesis, and a path finder and path traversal plugin to calculate the effects of the differential propagation path length between the direct and ground reflected rays. This paper describes those developments and demonstrates their use in the auralization of broadband flyover noise

The Dynamical Mean Field Theory phase space extension and critical properties of the finite temperature Mott transition

We consider the finite temperature metal-insulator transition in the half filled paramagnetic Hubbard model on the infinite dimensional Bethe lattice. A new method for calculating the Dynamical Mean Field Theory fixpoint surface in the phase diagram is presented and shown to be free from the convergence problems of standard forward recursion. The fixpoint equation is then analyzed using dynamical systems methods. On the fixpoint surface the eigenspectra of its Jacobian is used to characterize the hysteresis boundaries of the first order transition line and its second order critical end point. The critical point is shown to be a cusp catastrophe in the parameter space, opening a pitchfork bifurcation along the first order transition line, while the hysteresis boundaries are shown to be saddle-node bifurcations of two merging fixpoints. Using Landau theory the properties of the critical end point is determined and related to the critical eigenmode of the Jacobian. Our findings provide new insights into basic properties of this intensively studied transition.Comment: 11 pages, 12 figures, 1 tabl

Molecular transport junctions: Current from electronic excitations in the leads

Using a model comprising a 2-level bridge connecting free electron reservoirs we show that coupling of a molecular bridge to electron-hole excitations in the leads can markedly effect the source-drain current through a molecular junction.In some cases, e.g. molecules that exhibit strong charge transfer transitions, the contribution from electron-hole excitations can exceed the Landauer elastic current and dominate the observed conduction.Comment: 4 pages, 2 figures, submitted to PR

Bone mineral density, rib pain and other features of the female athlete triad in elite lightweight rowers

Objective: To determine bone mineral density (BMD) and the associations among BMD, menstrual history, disordered eating (DE), training history, intentional weight loss (IWL) and rib pain for the first time in female lightweight rowers. Setting: 9 lightweight rowing clubs, UK. Participants: 29 Caucasian female lightweight rowers volunteered. 21 (12 active, 9 retired) completed the study. Inclusion criteria: female lightweight rowers aged over 18 years. Exclusion criteria: participants with a history of bone disease, used medications known to influence BMD or if they were pregnant, lactating or postmenopausal. Main outcome measures: Dual-energy X-ray absorptiometry measured total body (TB) composition and BMD at the spine, femoral neck (FN), radius and TB. DE, oligomenorrhoea/amenorrhoea years; rib pain and training history. Results: DE was reported in six of the rowers. The active with DE started rowing younger (p<0.05) than those without, and their amount of IWL was associated with Eating Attitudes Test-26 score (p<0.05). Some participants reported a history of oligomenorrhoea/amenorrhoea 17 (76%) and/or rib pain 7 (32%) with those with rib pain having lower spine and TB Z-scores (p<0.05) than those without. Those with oligomenorrhoea/amenorrhoea had lower spine Z-scores (p<0.01) than those without. Twelve participants had low BMD; three at spine; one at FN; and eight at radius. Thirteen per cent of mean total training hours (18.6±9.1 h/week) were spent strength training (2.4±2.2 h/week). Conclusions: Upper body exercises incorporating multidimensional high peak bone strain were not reported and may need to be considered in their strength training to improve radial BMD. Results suggest IWL and high level training at a young age increases the likelihood of DE and there may be a lack of quality nutritional support for these athletes. Thus, multidisciplinary sport science support should be offered at a young age and perhaps also to consider changing the weight rules to prevent the development of the Triad