We show that one can find two nonisomorphic curves over a field K that become isomorphic to one another over two finite extensions of K whose degrees over K are coprime to one another. More specifically, let K0 be an arbitrary prime field and let r > 1 and s > 1 be integers that are coprime to one another. We show that one can find a finite extension K of K0, a degree-r extension L of K, a degr...

This talk gives an introduction into the subject of Seiberg-Witten curves and their relation to integrable systems. We discuss some motivations and origins of this relation and consider explicit construction of various families of Seiberg-Witten curves in terms of corresponding integrable models.

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...

BACKGROUND The purposes of this study are to evaluate the prognostic value of posttreatment (18)F-FDG PET/CT in predicting the survival of patients with ovarian carcinoma and to determine incremental value of combining posttreatment PET/CT with traditional prognostic factors in a multivariate model. METHODS This was an IRB-approved retrospective study. From July 2001 to July 2011, 48 patients...

Abstract A brief description of the marine hazard forecast methods and technology for Sea Okhotsk developed in Federal State Budgetary Institution “ Far Eastern Regional Hydrometeorological Research Institute (FERHRI)” is presented. These provide numerical prognostic products following parameters: wave height, period direction; sea ice concentration, thickness, drift compression; level storm su...

We consider a one-parameter family of two-dimensional ordinary di erential equations with a slow parameter drift. Our equation assumes that when there is no parameter drift, there are two invariant curves consisting of equilibria, one of which is normally hyperbolic and whose stable and unstable manifolds intersect transversely. The slow parameter drift is introduced in a way that it creates tw...

Some internal transport barriers in tokamaks have been related to the vicinity of extrema plasma equilibrium profiles. This effect is numerically investigated by considering guiding-center trajectories particles undergoing ExB drift motion, that electric field has a stationary nonmonotonic radial profile and an electrostatic fluctuation. In addition, configuration safety factor profile. The num...

Probabilistic volcanic hazard analysis is becoming an increasingly popular component of volcanic risk reduction strategies worldwide. While probabilistic hazard analyses offer many advantages for decision-making, displaying the statistical results of these analyses on a map presents new hazard communication challenges. Probabilistic information is complex, difficult to interpret, and associated...

Semi-active base isolation system has been proposed mainly to mitigate the base drift of isolated structures while in most cases, its application causes the maximum acceleration of superstructure to be increased. In this paper, designing optimal semi-active base isolation system composed of linear base isolation system with low damping and magneto-rheological (MR) damper has been studied for co...