Rational invariants on the space of all structures of algebras on a two-dimensional vector space

Rational invariants on the space of all structures of algebras on a two-dimensional vector space

The Spanish water ?pressure cooker?: Threading the interplay between resource resilient water governance outcomes by strengthening the robustness of water governance processes.

This paper uses the metaphor of a pressure cooker to highlight how water problems in Spain are highly geographical and sectorial in nature, with some specific hotspots which raise the temperature of the whole water complex system, turning many potentially solvable water problems into ?wicked problems?. The paper discusses the tendency for water governance to be hydrocentric, when often the drivers and in turn the ?solutions? to Spanish water problems lie outside the water sphere. The paper analyzes of the current water governance system by looking at water governance as both a process, and its key attributes like participation, trans- parency, equity and rule of law, as well as an analysis of water governance as an outcome by looking at efficiency and sustainability of water use in Spain. It concludes on the need to have a deeper knowledge on the interactions of water governance as a process and as an outcome and potential synergies and arguing that water governance is an inherently political process which calls for strengthening the capacity of the system by looking at the interactions of these different governance attributes.

Solution of optimal continuous low-thrust transfer using Lie transforms

This paper addresses the problem of optimal constant continuous low-thrust transfer in the context of the restricted two-body problem (R2BP). Using the Pontryagin’s principle, the problem is formulated as a two point boundary value problem (TPBVP) for a Hamiltonian system. Lie transforms obtained through the Deprit method allow us to obtain the canonical mapping of the phase flow as a series in terms of the order of magnitude of the thrust applied. The reachable set of states starting from a given initial condition using optimal control policy is obtained analytically. In addition, a particular optimal transfer can be computed as the solution of a non-linear algebraic equation. Se investiga el uso de series y transformadas de Lie en problemas de optimización de trayectorias de satélites impulsados por motores de bajo empuje