Manjul Bhargava and I have recently proved a result on the average order of the 2-Selmer groups of the Jacobians of hyperelliptic curves of a fixed genus n ≥ 1 over Q, with a rational Weierstrass point [2, Thm 1]. A surprising fact which emerges is that the average order of this finite group is equal to 3, independent of the genus n. This gives us a uniform upper bound of 3 2 on the average ran...

The arithmetic of quaternions is recalled from a constructive point of view. A Hecke module is introduced, defined as a free abelian group on right ideal classes of a quaternion order, together with a natural action of Hecke operators. An equivalent construction in terms of Shimura curves is then introduced, and the quaternion construction is applied to the analysis of specific modular and Shim...

AIM Compare the planning target volume (PTV) coverage in three different shielding techniques in cranial irradiation. SETTINGS AND DESIGN Tertiary care center, prospective study. MATERIALS AND METHODS The whole brain and meninges were contoured in ten planning CT scans, and expanded by 5 mm for the PTV. Shielding was designed using the French Society of Pediatric Oncology (SFOP) guidelines ...

background: field matching problems in abutting electron fields can be managed by using spoilers. objective: the aim of this study was to design a monte carlo framework for the assessment of spoiler application in abutting electron fields. methods: a siemens primus treatment head was simulated for a 5 mev electron beam using beamnrc and dosxyznrc, egsnrc user codes. validation of beam model was...

BACKGROUND To identify optimization of dose distributions of target volumes and decrease of radiation doses to normal tissues during stereotactic body radiation therapy (SBRT) for pancreatic cancer with dose-limiting auto-shells. METHODS With the same prescription dose, dose constraints of normal organs and calculation algorithm, treatment plans of each eligible patient were re-generated with...

A simple and parsimonious model which originated from the Weibull frequency distribution was proposed to describe nonlinear survival curves of spores. This model was suitable for downward concavity curves (Bacillus cereus and Bacillus pumilus), as well as for upward concavity curves (Clostridium botulinum). It was shown that traditional F values calculated from this new model were no longer add...

By combining experiments with simple model calculations, we obtain new insight in spin transport through hybrid, CoFeB/Al2O3(1.5 nm)/tris(8-hydroxyquinoline)aluminium (Alq3)/Co spin valves. We have measured the characteristic changes in the I-V behavior as well as the intrinsic loss of magnetoresistance at the onset of multiple-step tunneling. In the regime of multiple-step tunneling, under the...

Sarabia et al. (1999) present a basic model to create ordered families of Lorenz curves, along with basic theorems that describe the conditions for the models to satisfy the definition of the Lorenz curve. Using these basic models, they suggest a family which includes several well-known Lorenz models as special cases. This paper first shows that their basic theorems can be generalized. The pape...