Abstract:
For any elliptic curve E defined over the rationals with complex multiplication and for every prime p, we describe the image of the mod p Galois representation attached to E. We deduce information about the field of definition of torsion points of these curves, in particular we classify all cases where there are torsion points over Galois number fields not containing the field of definition of the CM.

Abstract:
We evaluate the neutral current quasi-elastic neutrino cross section within two nuclear models: the SuSA model, based on the superscaling behavior of electron scattering data, and the RMF model, based on relativistic mean field theory. We also estimate the ratio $(\nu p \to \nu p)/(\nu N \to \nu N)$ and compare with the MiniBooNE experimental data, performing a fit of the parameters $M_A$ and $g_A^{(s)}$ within the two models. Finally, we present our predictions for antineutrino scattering.

Abstract:
mechanical alloying (ma) is a powder processing technique, which allows us to induce solid state reactions in binary systems immiscible in equilibrium. fe and ag have a mutually repulsive nature that makes them completely immiscible under thermodynamically stable conditions. the ball milling process being a non-equilibrium technique seems promising in obtaining at least a partial solid solution in this system. mixtures of fe and ag powders with 75 wt% ag were studied by x-ray diffraction (xrd), scanning electron microscopy (sem) and transmission electron microscopy (tem). we have found that it is possible to obtain a small mutual solid solution in this system by ma. this is also confirmed by m？ssbauer spectroscopy.

Abstract:
Mechanical alloying (MA) is a powder processing technique, which allows us to induce solid state reactions in binary systems immiscible in equilibrium. Fe and Ag have a mutually repulsive nature that makes them completely immiscible under thermodynamically stable conditions. The ball milling process being a non-equilibrium technique seems promising in obtaining at least a partial solid solution in this system. Mixtures of Fe and Ag powders with 75 wt% Ag were studied by x-ray diffraction (XRD), scanning electron microscopy (SEM) and transmission electron microscopy (TEM). We have found that it is possible to obtain a small mutual solid solution in this system by MA. This is also confirmed by M ssbauer spectroscopy. Aleación Mecánica (AM) es una técnica de procesamiento de polvos, la cual nos permite inducir reacciones de estado sólido en sistemas binarios inmiscibles en el equilibrio. Fe y Ag tienen una naturaleza mutuamente repulsiva que las hace completamente inmiscibles bajo condiciones termodinámicamente estables. El proceso de molienda por bolas, siendo una técnica fuera del equilibrio, parece prometedor para obtener al menos una solución sólida parcial en este sistema. Mezclas de polvos de Fe y Ag con 75 % en peso de Ag fueron estudiados mediante difracción de rayos x (DRX), microscopía electrónica de barrido (MEB), y microscopía electrónica de transmisión (MET). Hemos encontrado que es posible obtener una peque a solución sólida parcial en este sistema mediante AM. Esto es confirmado mediante espectroscopia M ssbauer.

Abstract:
Let m be a positive integer and a,q two rational numbers. Denote by AP_m(a,q) the set of rational numbers d such that a,a+q,...,a+(m-1)q form an arithmetic progression in the Edwards curve E_d:x^2+y^2=1+d x^2 y^2. We study the set AP_m(a,q) and we parametrize it by the rational points of an algebraic curve.

Abstract:
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.

Abstract:
We study the problem of the existence of arithmetic progressions of three cubes over quadratic number fields Q(sqrt(D)), where D is a squarefree integer. For this purpose, we give a characterization in terms of Q(sqrt(D))-rational points on the elliptic curve E:y^2=x^3-27. We compute the torsion subgroup of the Mordell-Weil group of this elliptic curve over Q(sqrt(D)) and we give partial answers to the finiteness of the free part of E(Q(sqrt(D))). This last task will be translated to compute if the rank of the quadratic D-twist of the modular curve X_0(36) is zero or not.

Abstract:
The relativistic mean field (RMF) model is used to describe nucleons in the nucleus and thereby to evaluate the effects of having dynamically off-shell spinors. Compared with free, on-shell nucleons as employed in some other models, within the RMF nucleons are described by relativistic spinors with strongly enhanced lower components. In this work it is seen that for MiniBooNE kinematics, neutrino charged-current quasielastic cross sections show some sensitivity to these off-shell effects, while for the antineutrino-nucleus case the total cross sections are seen to be essentially independent of the enhancement of the lower components. As was found to be the case when comparing the RMF results with the neutrino-nucleus data, the present impulse approximation predictions within the RMF also fall short of the MiniBooNE antineutrino-nucleus data.

Abstract:
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.

Abstract:
The superscaling approach (SuSA) to neutrino-nucleus scattering, based on the assumed universality of the scaling function for electromagnetic and weak interactions, is reviewed. The predictions of the SuSA model for bot CC and NC differential and total cross sections are presented and compared with the MiniBooNE data. The role of scaling violations, in particular the contribution of meson exchange currents in the two-particle two-hole sector, is explored.