On Borel fixed ideals generated in one degree

We construct a (shellable) polyhedral cell complex that supports a minimal free resolution of a Borel fixed ideal, which is minimally generated (in the Borel sense) by just one monomial in S=k[x_1,x_2,...,x_n]; this includes the case of powers of the homogeneous maximal ideal (x_1,x_2,...,x_n) as a special case. In our most general result we prove that for any Borel fixed ideal I generated in one degree, there exists a polyhedral cell complex that supports a minimal free resolution of I.Comment: 18 pages, 6 figure

A note on supersymmetric AdS_6 solutions of massive type IIA supergravity

Motivated by the AdS_6/CFT_5 correspondence, we study general supersymmetric solutions of massive type IIA supergravity, consisting of a warped product of six-dimensional anti-de Sitter space AdS_6 with a four-dimensional Riemannian manifold M_4, and fluxes compatible with the SO(5,2) symmetry. We find that the only local solution of this form is the warped AdS_6 x_w S^4 solution, originally discovered by Brandhuber and Oz. We discuss the supersymmetric properties of this solution.Comment: 18 page

Science and Technology Parks in Two Lagging Regions of Spain: A Comparative Evaluation Using an Innovation Network Approach

Science and Technology Parks (STPs) have been widely used as innovation support and regional development instruments in most European countries. In Objective 1 regions of South Europe STPs projects were developed during the 90s through regional, national or EU structural funds as tools for promoting innovation and technology upgrade. Most existing studies cast doubt on the effectiveness of parks in achieving their goals, focussing on the traditional measures of the parks added-value (profitability and growth) to the tenant companies, the university-industry linkages developed. However, more recent developments of territorial innovation models stress the role of networks and interactions for knowledge creation and diffusion. While these approaches imply that the Parks – in their strict spatial nature – may become redundant in a networked space, they can also be used to identify additional performance assessment criteria focusing on the role of the park for the development of interactions, linkages and cooperation inside as well as outside its area. The quantity and quality of linkages inside and outside the STP area and its operation as an innovation cooperation promoter in the regional and broader space are used in this assessment. The present work assesses the performance of STPs in Objective 1 regions of South Europe. It develops an evaluation framework that integrates – together with the traditional linear performance criteria – the concepts of networking, interaction and cooperation and uses it to compare the performance of Parks in two regions in Greece (Thessaloniki and Crete) and two in Spain (Asturias and Andalusia). Our preliminary results from in depth analysis show that while there are different levels of success in terms of the traditional metrics/criteria, we observe in general low levels of interaction and cooperation developed inside the parks as well as with the broader region. The Parks do not seem to operate – at least so far – as places that facilitate intensive knowledge exchange inside and outside their area.