Theory of pixel lensing towards M31 - I. The density contribution and mass of MACHOs

POINT-AGAPE is an Angle-French collaboration which is employing the Isaac Newton Telescope (INT) to conduct a pixel-lensing survey towards M31. Pixel lensing is a technique which permits the detection of microlensing against unresolved stellar fields. The survey aims to constrain the stellar population in M31, and also the distribution and nature of massive compact halo objects (MACHOs) in both M31 and the Galaxy.

R-matrix-Floquet theory of multiphoton processes:VIII. A linear equations method

A new linear equations method for calculating the R-matrix, which arises in the R-matrix-Floquet theory of multiphoton processes, is introduced. This method replaces the diagonalization of the Floquet Hamiltonian matrix by the solution of a set of linear simultaneous equations which are solved, in the present work, by the conjugate gradient method. This approach uses considerably less computer memory and can be readily ported onto parallel computers. It will thus enable much larger problems of current interest to be treated. This new method is tested by applying it to three-photon ionization of helium at frequencies where double resonances with a bound state and autoionizing states are important. Finally, an alternative linear equations method, which avoids the explicit calculation of the R-matrix by incorporating the boundary conditions directly, is described in an appendix.

Computational techniques for a simple theory of conditional preferences

A simple logic of conditional preferences is defined, with a language that allows the compact representation of certain kinds of conditional preference statements, a semantics and a proof theory. CP-nets and TCP-nets can be mapped into this logic, and the semantics and proof theory generalise those of CP-nets and TCP-nets. The system can also express preferences of a lexicographic kind. The paper derives various sufficient conditions for a set of conditional preferences to be consistent, along with algorithmic techniques for checking such conditions and hence confirming consistency. These techniques can also be used for totally ordering outcomes in a way that is consistent with the set of preferences, and they are further developed to give an approach to the problem of constrained optimisation for conditional preferences.