Categorical Structures in Non-Commutative Measure Theory.

In this paper, we investigate effect algebras and base normed spaces from the categorical point of view. We prove that the category of effect algebras is complete and cocomplete as well as the category of base normed spaces is complete, and discuss the contravariant functor from the category of effect algebras to the category of base normed spaces.

Examples of PDEs all whose points are characteristic

Let π : FM ! M be the bundle of linear frames of a manifold M. A basis Lijk , j < k, of diffeomorphism invariant Lagrangians on J1 (FM) was determined in [J. Muñoz Masqué, M. E. Rosado, Invariant variational problems on linear frame bundles, J. Phys. A35 (2002) 2013-2036]. The notion of a characteristic hypersurface for an arbitrary first-order PDE system on an ar- bitrary bred manifold π : P → M, is introduced and for the systems dened by the Euler-Lagrange equations of Lijk every hypersurface is shown to be characteristic. The Euler-Lagrange equations of the natural basis of Lagrangian densities Lijk on the bundle of linear frames of a manifold M which are invariant under diffeomorphisms, are shown to be an underdetermined PDEs systems such that every hypersurface of M is characteristic for such equations. This explains why these systems cannot be written in the Cauchy-Kowaleska form, although they are known to be formally integrable by using the tools of geometric theory of partial differential equations, see [J. Muñoz Masqué, M. E. Rosado, Integrability of the eld equations of invariant variational problems on linear frame bundles, J. Geom. Phys. 49 (2004), 119-155]

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

Water, agriculture and ecosystem services in climate change vulnerable agricultural regions of Spain and Jordan

Irrigated agricultural landscapes generate a valuable set of ecosystem services, which are threatened by water scarcity in many aridand semi‐arid regions of the world. In the Mediterranean region, climate change is expected to decrease water availability through reduced precipitation and more frequent drought spells. At the same time, climate change, demographic and economic development and an agricultural sector highly dependent on irrigation, will raise water demand, increasing experienced water scarcity and affecting the provision of ecosystem services from water resources and agro-ecosystems. In this context, policy makers face the challenge of balancing the provision of different ecosystem services, including agricultural income and production and also water ecosystem protection.