Addendum to `Fake Projective Planes'

The addendum updates the results presented in the paper `Fake Projective Plane, Invent Math 168, 321-370 (2007)' and makes some additions and corrections. The fake projective planes are classified into twenty six classes. Together with a recent work of Donald Cartwright and Tim Steger, there is now a complete list of fake projective planes. There are precisely one hundred fake projective planes as complex surfaces classified up to biholomorphism.Comment: A more refined classification is given in the new versio

Fragmentation of 7^7Li Relativistic Nuclei on a Proton into the 3^3H+4^4He Channel

In a track nuclear photoemulsion exposed to a beamof $^7$Li nuclei accelerated to a momentum of 3 GeV/$c$ per nucleon at the synchrophasotron of the Joint Institute for Nuclear Research (JINR, Dubna), 13 events in which $^7$Li nuclei interacting with protons break up into $^3$H and $^4$He fragments were detected among 3730 inelastic-interaction events. For this fragmentation channel, the cross section was found to be $8\pm2$ mb. The average value of the fragment total transverse momentum was $214\pm5$ MeV/$c$. This value exceedsmarkedly the average value of the transverse-momentumtransfer in the coherent dissociation of $^7$Li nuclei on track-emulsion nuclei ($166\pm5$ MeV/$c$). The recoil-proton transverse momentum was on average 98% of the total proton momentum. The longitudinal-momentum distribution of protons was characterized by a variance of 16 MeV/$c$ and a mean value of $37\pm2$ MeV/$c$.Comment: ISSN 1063-778

Updating DL-Lite ontologies through first-order queries

In this paper we study instance-level update in DL-LiteA, the description logic underlying the OWL 2 QL standard. In particular we focus on formula-based approaches to ABox insertion and deletion. We show that DL-LiteA, which is well-known for enjoying first-order rewritability of query answering, enjoys a first-order rewritability property also for updates. That is, every update can be reformulated into a set of insertion and deletion instructions computable through a nonrecursive datalog program. Such a program is readily translatable into a first-order query over the ABox considered as a database, and hence into SQL. By exploiting this result, we implement an update component for DLLiteA-based systems and perform some experiments showing that the approach works in practice.Peer ReviewedPostprint (author's final draft

INCMap: A Journey towards ontology-based data integration

Ontology-based data integration (OBDI) allows users to federate over heterogeneous data sources using a semantic rich conceptual data model. An important challenge in ODBI is the curation of mappings between the data sources and the global ontology. In the last years, we have built IncMap, a system to semi-automatically create mappings between relational data sources and a global ontology. IncMap has since been put into practice, both for academic and in industrial applications. Based on the experience of the last years, we have extended the original version of IncMap in several dimensions to enhance the mapping quality: (1) IncMap can detect and leverage semantic-rich patterns in the relational data sources such as inheritance for the mapping creation. (2) IncMap is able to leverage reasoning rules in the ontology to overcome structural differences from the relational data sources. (3) IncMap now includes a fully automatic mode that is often necessary to bootstrap mappings for a new data source. Our experimental evaluation shows that the new version of IncMap outperforms its previous version as well as other state-of-the-art systems

Topology of energy surfaces and existence of transversal Poincar\'e sections

Two questions on the topology of compact energy surfaces of natural two degrees of freedom Hamiltonian systems in a magnetic field are discussed. We show that the topology of this 3-manifold (if it is not a unit tangent bundle) is uniquely determined by the Euler characteristic of the accessible region in configuration space. In this class of 3-manifolds for most cases there does not exist a transverse and complete Poincar\'e section. We show that there are topological obstacles for its existence such that only in the cases of $S^1\times S^2$ and $T^3$ such a Poincar\'e section can exist.Comment: 10 pages, LaTe

Special features of the 9^9Be→\to2He fragmentation in emulsion at an energy of 1.2~A~GeV

The results of investigations of the relativistic $^9$Be nucleus fragmentation in emulsion which entails the production of two He fragments of an energy of 1.2~A~GeV are presented. The results of the angular measurements of the $^9$Be$\to$2He events are analyzed. The $^9$Be$\to^8$Be+n fragmentation channel involving the $^8$Be decay from the ground (0$^+$) and the first excited (2$^+$) states to two $\alpha$ particles is observed to be predominant.Comment: 10 pages, 6 figures, conference: Conference on Physics of Fundamental Interactions, Moscow, Russia, 5-9 Dec 2005 (Author's translation