Discussion on complexity and TCAS indicators for coherent safety net transitions

Transition between Separation Management in ATM and Collision Avoidance constitutes a source of potential risks due to non-coherent detection and resolution clearances between them. To explore an operational integration between these two safety nets, a complexity metric tailored for both Separation Management and Collision Avoidance, based on the intrinsic complexity, is proposed. To establish the framework to compare the complexity metric with current Collision Avoidance detection metrics, a basic pair-wise encounter model has been considered. Then, main indicators for horizontal detection of TCAS, i.e. tau and taumod, have been contrasted with the complexity metric. A simple method for determining the range locus for specific TCAS tau values, depending on relative speeds and encounter angles, was defined. In addition, range values when detection thresholds were infringed have been found to be similar, as well as its sensitivity to relative angles. Further work should be conducted for establishing a framework for the evaluation and validation of this complexity metric. This paper defines basic principles for an extended evaluation, including multi-encounter scenarios and longer look ahead times

Some results on rational surfaces and Fano varieties

The goal of this article is to study the equations and syzygies of embeddings of rational surfaces and certain Fano varieties. Given a rational surface X and an ample and base-point-free line bundle L on X, we give an optimal numerical criterion for L to satisfy property Np. This criterion turns out to be a characterization of property Np if X is anticanonical. We also prove syzygy results for adjunction bundles and a Reider type theorem for higher syzygies. For certain Fano varieties we also prove results on very ampleness and higher syzygies.Comment: 26 pages, AMSTe