Lusternik-Schnirelmann category of simplicial complexes and finite spaces

In this paper we establish a natural definition of Lusternik-Schnirelmann category for simplicial complexes via the well known notion of contiguity. This category has the property of being homotopy invariant under strong equivalences, and only depends on the simplicial structure rather than its geometric realization. In a similar way to the classical case, we also develop a notion of geometric category for simplicial complexes. We prove that the maximum value over the homotopy class of a given complex is attained in the core of the complex. Finally, by means of well known relations between simplicial complexes and posets, specific new results for the topological notion of category are obtained in the setting of finite topological spaces.Comment: 18 pages, 10 figures, this is a new version with some minor changes and a new exampl

MIMAC-He3 : A Micro-TPC Matrix of Chambers of He3 for direct detection of Wimps

The project of a micro-TPC matrix of chambers of \hetrois for direct detection of non-baryonic dark matter is presented. The privileged properties of He3 are highlighted. The double detection (ionization - projection of tracks) is explained and its rejection evaluated. The potentialities of MIMAC-He3 for supersymmetric dark matter search are discussed.Comment: to appear in Proc. of the 9th International Conference on Topics in Astroparticle and Underground Physics (TAUP 2005), Zaragoza, Sept. 200

A basic reference state suitable for anomaly-coupled ocean-atmosphere climate models

AbstractA large class of ocean-atmosphere models exists in which the ocean state is coupled to the model of the atmosphere only through the anomalies of the ocean state. The sea surface temperatures are defined with respect to a mean reference state, i.e., they are the difference between the ocean state and a reference state. Due to coupled model drift, the choice of reference state is important and it can have a large impact on the variability in the model. The reference state can be calculated as an average throughout the coupled simulation and various methods of doing this (moving average, exponentially weighted moving average and accumulated mean) are compared in this note. The accumulated mean method appears to be the sole method of the three which gives both unbiased anomalies and a convergent reference state. It is recommended for use in anomaly-coupled models for improving variability and predictability

Evolution and assessment of a nitrate vulnerable zone over 20 years: Gallocanta groundwater body (Spain)

Nitrate pollution from agricultural sources is one of the biggest issues facing groundwater management in the European Union (EU). During the last three decades, tens of nitrate vulnerable zones (NVZ) have been designated across the EU, aiming to make the problem more manageable. The Gallocanta Groundwater Body in NE Spain was declared as an NVZ in 1997, and after more than 20 years, significant improvements in water quality were expected to be observed. In the present study, the spatiotemporal trend of nitrate concentration within the Gallocanta NVZ in the last 38 years was assessed, and the effectiveness of the NVZ implementation was tested. Data from the official Ebro Basin Confederation monitoring network from 1980 to 2018 were used, and the results showed an increasing but fluctuating trend in nitrate concentration since 1980. Although a slight improvement was detected after the NVZ designation in 1997, the low rate of improvement would take decades to reach desirable levels in most of the area. The lack of update and control of action programmes, the inappropriate NVZ delimitation, and the influence of natural factors seem to be the reasons for the failure of the nitrate reduction measures. Currently, nitrate pollution and groundwater management are a matter of concern for the EU, so given the recurring problems in water supply in the area and the nonfulfillment of the goal of good quality status, more demanding measures are needed to be implemented in the short term

Supersymmetric FRW model and the ground state of supergravity

In this work we construct the vacuum configuration of supergravity interacting with homogeneous complex scalar matter fields. The corresponding configuration is of the FRW model invariant under the $n=2$ local conformal time supersymmetry, which is a subgroup of the four dimensional space-time supersymmetry. We show, that the potential of the scalar matter fields is a function of the K\"ahler potential and of the arbitrary parameter $\alpha$. This parameter enumerates the vacuum states. The scalar matter potential induces the spontaneous breaking of supersymmetry in supergravity. On the quantum level our model is a specific supersymmetric quantum mechanics, which admits quantum states in supergravity, and the states with zero energy are described by the wave function of the FRW universe.Comment: 18 pages, Revtex, submitted to PR