Invariant metrics and Laplacians on Siegel-Jacobi space

In this paper, we compute Riemannian metrics on the Siegel-Jacobi space which are invariant under the natural action of the Jacobi group explicitly and also provide the Laplacians of these invariant metrics. These are expressed in terms of the trace form.Comment: 18 pages ; Added contents, Added references ; typographical error [1] page 2, -line 5 (insert 4

Designing learning object repositories : a thesis presented in partial fulfilment of the requirements for the degree of Master of Information Science in Information Sciences at Massey University

Learning object repositories are expanding rapidly into the role of independent educational systems that not only are a supplement to a traditional way of learning, but also allow users to search, exchange and re-use learning objects. The intention of this innovative technology is to have such repositories to collect a database of learning objects catalogued by the learning content management system. However, for users to perform an efficient search, these learning objects would need to use metadata standards or specifications to describe their properties. For learning objects stored within the repositories, metadata standards are often used to descibe them so users of the respositories are able to find the accurate resources they required, hence metadata standards are important elements of any learning object repository. In this paper, a courseware example is used to demonstrate how to define a set of characteristics that we want to describe for our courseware, and attempt to map the data schema in the database with the available metadata standards. The outcome is to identify a set of metadata elements that would fully describe our learning objects stored within the learning object repository, and these metadata elements will also assist instructors to create adaptable courseware that can be reused by different instructors. Metadata standard is known as a critical element for the management of learning objects, not only will it increase the accuracy of the search results, it will also provide more relevant and descriptive information about the learning objects to the searchers

Exchange-Correlation Energy from Pairing Matrix Fluctuation and the Particle-Particle Random Phase Approximation

We formulate an adiabatic connection for the exchange-correlation energy in terms of pairing matrix fluctuation. This connection opens new channels for density functional approximations based on pairing interactions. Even the simplest approximation to the pairing matrix fluctuation, the particle-particle Random Phase Approximation (pp-RPA), has some highly desirable properties. It has no delocalization error with a nearly linear energy behavior for systems with fractional charges, describes van der Waals interactions similarly and thermodynamic properties significantly better than particle-hole RPA, and eliminates static correlation error for single-bond systems. Most significantly, the pp-RPA is the first known functional that has an explicit and closed-form dependence on the occupied and unoccupied orbitals and captures the energy derivative discontinuity in strongly correlated systems. These findings illlustrate the potential of including pairing interactions within a density functional framework