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...

background:  radiochromic film is used for radiation dose measurement, xr-rv3 is used in fluoroscopy and ebt2 film in radiation therapy. the aim was to determine if the dosimetric properties of these two films are comparable in megavolt photon beams. materials and methods: comparison measurements included: calibration curves, heterogeneous phantom dose profiles, and nasopharynx dose distributio...

in the United Kingdom of those days. There was a time when Sir Robert Peel, the Prime Minister was told by a President of one of the then Royal Colleges: "No man who has an academic education ought to practise obstetrics." The same gentleman stated amidst applause in a subsequent meeting: "Obstetrics is no calling for a gentleman". The story in the book tells us how in 1946 in the same kingdom ...

We solve for the effective actions on the Coulomb branches of a class of N = 2 supersymmetric theories by finding the complex structure of an M5 brane in an appropriate background hyperkahler geometry corresponding to the lift of two O6 orientifolds and four D6 branes to M theory. The resulting Seiberg-Witten curves are of finite genus, unlike other solutions proposed in the literature. The sim...

‎in this work‎, ‎first the differential equation characterizing position vector‎ ‎of spacelike curve is obtained in lorentzian plane $mathbb{l}^{2}.$ then the‎ ‎special curves mentioned above are studied in lorentzian plane $mathbb{l}%‎‎^{2}.$ finally some characterizations of these special curves are given in‎ ‎$mathbb{l}^{2}.$‎

From the Departments of Neurology and Pathology, Cornell University Medical College, New York, N. 1. Supported in part by Research Grants HE-04872 and NB-03346, NB-04161 from USPHS and from the Winthrop Laboratories. Dr. Kutt is a recipient of a Research Career Development Award JKO 3 NB 35003, NINDB, USPH. First submitted October 2, 1968; accepted for publication December 13, 1968. KARL VEREBE...