We study the Selmer varieties of smooth projective curves genus at least two defined over $\mathbb{Q}$ which geometrically dominate a curve with CM Jacobian. extend result Coates and Kim to show that Kim's non-abelian Chabauty method applies such curve. By combining this results Bogomolov-Tschinkel Poonen on unramified correspondences, we deduce any cover $\mathbf{P}^1$ solvable Galois group, i...

Charge movement was measured in frog cut twitch fibers with the double Vaseline-gap technique. Steady-state inactivation of charge movement was studied by changing the holding potential from -90 mV to a level ranging from -70 to -30 mV. Q beta and Q gamma at each holding potential were separated by fitting the Q-V plot with a sum of two Boltzmann distribution functions. At -70 mV Q beta and Q g...

1. Introduction. If we wish to write the equations of curves of genus 1 that give elements of the Shafarevich-Tate group of an elliptic curve over a number field K, a choice of ways is open to us. For example, if the element in question is of order 3 the curve of genus 1 corresponding to it occurs as a smooth plane cubic curve over K. In a recent article [C-M] we raised the question of when one...

The summary receiver operating characteristic (SROC) curve has been recommended to represent the performance of a diagnostic test, based on data from a meta-analysis. However, little is known about the basic properties of the SROC curve or its estimate. In this paper, the position of the SROC curve is characterized in terms of the overall diagnostic odds ratio and the magnitude of inter-study h...

This paper gives a fairly detailed description of an algorithm that computes (the size of) the 2-Selmer group of the Jacobian of a hyperellitptic curve over Q. The curve is assumed to have even genus or to possess a Q-rational Weierstraa point.

self compacting concrete (scc) specimens with limestone (l) and quartz (q) powders were formulated. the influence of the type of the powder on the properties of fresh and hardened concrete was evaluated. dense packing theories were used for mix design of samples. the equation of fuller and thompson for particle size distribution (psd) of aggregates was modified with considering fine particles a...

We construct an infinite family {Ca,b}a,b∈Q of curves of genus 2 defined over Q, with two independent morphisms to a family of elliptic curves {Ea,b}a,b∈Q. When any of these elliptic curves Ea,b has rank 1 over Q, we obtain (modulo a conjecture of S. Lang, proved for special cases) a uniform bound for the number of rational points of the curve Ca,b, and an algorithm which finds all the rational...

The genus 4 modular curve Xns(11) attached to a non-split Cartan group of level 11 admits a model defined over Q. We compute generators for its function field in terms of Siegel modular functions. We also show that its Jacobian is isomorphic over Q to the new part of the Jacobian of the classical modular curve X0(121).

In this paper, we consider the average size of the 2-Selmer groups of a class of quadratic twists of each elliptic curve over Q with Q-torsion group Z2 × Z2. We prove the existence of a positive proportion of quadratic twists of such a curve, each of which has rank 0 Mordell-Weil group.

Given an odd surjective Galois representation ̺ : GQ → PGL2(F3) and a positive integer N, there exists a twisted modular curve X(N, 3)̺ defined over Q whose rational points classify the quadratic Q-curves of degree N realizing ̺. The paper gives a method to provide an explicit plane quartic model for this curve in the genus-three case N= 5.