El que parte y reparte… ¿se lleva la mejor parte?

La semifinal de la XXV Olimpiada Matemática Aragonesa de 2º de E.S.O fue celebrada el 16 de abril de 2016 en diferentes institutos de la comunidad de Aragón. En estas líneas analizaremos el segundo problema de dicha prueba. Estudiaremos las distintas respuestas aportadas por los alumnos de cara a observar los principales errores cometidos en la resolución del problema así como los resultados obtenidos

Computation-free presentation of the fundamental group of generic (p,q)(p,q)-torus curves

In this note, we present a new method for computing fundamental groups of curve complements using a variation of the Zariski-Van Kampen method on general ruled surfaces. As an application we give an alternative (computation-free) proof for the fundamental group of generic $(p,q)$-torus curves.Comment: 7 pages, 3 figure

Cartier and Weil Divisors on Varieties with Quotient Singularities

The main goal of this paper is to show that the notions of Weil and Cartier $\mathbb{Q}$-divisors coincide for $V$-manifolds and give a procedure to express a rational Weil divisor as a rational Cartier divisor. The theory is illustrated on weighted projective spaces and weighted blow-ups.Comment: 16 page

«Pentagoneando» la circunferencia

En este artículo se estudiará el tercer problema de la final de la XXVIII Olimpiada Matemática Aragonesa de 2º de ESO. En él se mostrarán las resoluciones más interesantes propuestas por los alumnos. Así mismo, se analizarán y valorarán los resultados globales obtenidos

An algebraic approach to the minimum-cost multi-impulse orbit transfer problem

A purely algebraic formulation (i.e., polynomial equations only) of the minimum-cost multi-impulse orbit-transfer problem without time constraints is presented, while keeping all the variables with a precise physical meaning. General algebraic techniques are applied to solve these equations (resultants, Gröbner bases, etc.) in several situations of practical interest of different degrees of generality. For instance, a proof of the optimality of the Hohmann transfer for the minimum-fuel two-impulse circular-to-circular orbit-transfer problem is provided. Finally, a general formula is also provided for the optimal two-impulse in-plane transfer between two rotated elliptical orbits under a mild symmetry assumption on the two points where the impulses are applied (which, it is conjectured, can be removed)