Relative Equilibria in the Four-Vortex Problem with Two Pairs of Equal Vorticities

We examine in detail the relative equilibria in the four-vortex problem where two pairs of vortices have equal strength, that is, \Gamma_1 = \Gamma_2 = 1 and \Gamma_3 = \Gamma_4 = m where m is a nonzero real parameter. One main result is that for m > 0, the convex configurations all contain a line of symmetry, forming a rhombus or an isosceles trapezoid. The rhombus solutions exist for all m but the isosceles trapezoid case exists only when m is positive. In fact, there exist asymmetric convex configurations when m < 0. In contrast to the Newtonian four-body problem with two equal pairs of masses, where the symmetry of all convex central configurations is unproven, the equations in the vortex case are easier to handle, allowing for a complete classification of all solutions. Precise counts on the number and type of solutions (equivalence classes) for different values of m, as well as a description of some of the bifurcations that occur, are provided. Our techniques involve a combination of analysis and modern and computational algebraic geometry

On the central configurations of the planar 1 + 3 body problem

We consider the Newtonian four-body problem in the plane with a dominat mass M. We study the planar central configurations of this problem when the remaining masses are infinitesimal. We obtain two different classes of central configurations depending on the mutual distances between the infinitesimal masses. Both classes exhibit symmetric and nonsymmetric configurations. And when two infinitesimal masses are equal, with the help of extended precision arithmetics, we provide evidence that the number of central configurations varies from five to seven

Tratamiento de la anemia posthemorragia digestiva aguda: ferroterapia oral vs. intravenosa. resultados preliminares

El tratamiento de la anemia ferropénica por pérdidas digestivas exige la corrección de la causa junto a la administración de suplementos de Fe. En muchos casos, ésta puede realizarse por vía oral, pero si la tolerancia es inadecuada, se precisa gran cantidad de Fe y/o conseguir una respuesta rápida, puede ser necesaria la vía endovenosa (IV).Ferrer Barceló, L.; Sanchís Artero, L.; Pérez Zahonero, M.; Canelles Gamir, P.; Monzó Gallego, A.; Huguet Malavés, J.; Luján Sanchís, M.... (2013). Tratamiento de la anemia posthemorragia digestiva aguda: ferroterapia oral vs. intravenosa. resultados preliminares. Revista Española de Enfermedades Digestivas. 105(Sup. 1):240-241. http://hdl.handle.net/10251/63692240241105Sup.