Modular Curves Of Genus 2

We prove that there is only a finite number of genus 2 curves C defined over Q such that there exists a nonconstant morphism pi:X_1(N) --->C defined over Q and the jacobian of C, J(C), is a Q-factor of the new part of the jacobian of X_1(N), J_1(N)^{new}. Moreover, we prove that there are only 149 genus two curves of this kind with the additional requeriment that their jacobians are Q-simple. We determine the corresponding newforms and present equations for all these curves

Covering techniques and rational points on some genus 5 curves

We describe a method that allows, under some hypotheses, to compute all the rational points of some genus 5 curves defined over a number field. This method is used to solve some arithmetic problems that remained open.Comment: Contemporary Mathematics AMS, to appea

Study of the Effect of Hot Rolling Processing Parameters on the Variability of HSLA Steels

The effect of different hot mill processing parameters and their influence on the variability of mechanical properties of HSLA steels has been studied. This work presents an analysis of the relative contribution of the different hot mill processing parameters to the variability of HSLA steels. The experimental design includes variation of Reheating, Roughing, Finishing, and Coiling temperatures, as well as Cooling Rate through the austenite to ferrite transformation, and from coiling to room temperature. The variation in finishing and coiling temperature results in an average variation of 12% in mechanical properties. The variation of the cooling rate, through the austenite to ferrite transformation, and from coiling to room temperature, has the largest impact on the variability of microstructure and properties. A correlation between the various microstructural features, dislocation densities and precipitation behavior, with mechanical properties is presented

On symmetric square values of quadratic polynomials

We prove that there does not exist a non-square quadratic polynomial with integer coefficients and an axis of symmetry which takes square values for N consecutive integers for N=7 or N >= 9. At the opposite, if N <= 6 or N=8 there are infinitely many