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...

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...

Two cyanobiphenyl liquid crystals (LCs), 5CB (4-cyano-4'-pentylbiphenyl) and 8CB (4-cyano-4'-octylbiphenyl), are introduced as additives into Co(II/III) electrolytes for dye-sensitized solar cells (DSCs). An electrolyte containing a combination of these LCs and 4-tert-butylpyridine (TBP) exhibits higher photovoltage than one with only TBP, resulting in higher power conversion efficiency.

A dye-sensitized solar cell (DSSC) fabricated by using a novel silyl-anchor coumarin dye with alkyl-chain substitutes, a Br3-/Br- redox electrolyte solution containing water, and a Mg2+-doped anatase-TiO2 electrode with twofold surface modification by MgO and Al2O3 exhibited an open-circuit photovoltage over 1.4 V, demonstrating the possibility of DSSCs as practical photovoltaic devices.

The lateral photovoltaic effect (LPE) can be used in position-sensitive detectors to detect very small displacements due to its output of lateral photovoltage changing linearly with light spot position. In this review, we will summarize some of our recent works regarding LPE in metal-semiconductor and metal-oxide-semiconductor structures, and give a theoretical model of LPE in these two structu...