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...

Manual fingerprint classification proceeds by carefully inspecting the geometric characteristics of major ridge curves in a fingerprint image. We propose an automatic approach of identifying the geometric characteristics of ridges based on curves generated by the orientation field called orientation field flow curves (OFFCs). The geometric characteristics of OFFCs are analyzed by studying the i...

purpose : to evaluate orbital blood flow velocities and optic nerve diameter with doppler and gray-scale sonography in patients with acute unilateral optic neuritis (on) methods : orbital doppler and gray-scale sonography was performed in 46 eyes of 23 patients aged 19-47 with acute unilateral on. on was diagnosed by an ophthalmologist on the basis of clinical presentation, presence of decrease...

quantification of the habitat available for fish species named rainbow trout (oncorhynchusmykiss) were evaluated in lees ferry, colorado river using water depth, water temperature, sediment transport,flow velocity in 2004 as environmental index. for the flow velocity and temperature distribution calculationsin the river, the navier-stokes equation and energy conservation equations with finite v...

In 10 cardiac patients in whom an organic lesion of the mitral valve was exluded by standard investigation procedures during which a diagnostic transseptal catheterization for pressure measurements in the left heart was performed, the authors placed a directional Doppler ultrasonic catheter tip velocimeter at the site of the mitral ring and recorded the mitral flow velocity traces. The pattern ...

this work is a primary achievement in studying the co2 and n2–oil systems. to predict gas-liquid relative permeability curves, a shan-chen type multicomponent multiphase lattice boltzmann model for two-phase flow through 2d porous media is developed. periodic and bounce back boundary conditions are applied to the model with the guo scheme for the external body force (i.e., the pressure gradient...

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...