Direction of light propagation to order G^2 in static, spherically symmetric spacetimes: a new derivation

A procedure avoiding any integration of the null geodesic equations is used to derive the direction of light propagation in a three-parameter family of static, spherically symmetric spacetimes within the post-post-Minkowskian approximation. Quasi-Cartesian isotropic coordinates adapted to the symmetries of spacetime are systematically used. It is found that the expression of the angle formed by two light rays as measured by a static observer staying at a given point is remarkably simple in these coordinates. The attention is mainly focused on the null geodesic paths that we call the "quasi-Minkowskian light rays". The vector-like functions characterizing the direction of propagation of such light rays at their points of emission and reception are firstly obtained in the generic case where these points are both located at a finite distance from the centre of symmetry. The direction of propagation of the quasi-Minkowskian light rays emitted at infinity is then straightforwardly deduced. An intrinsic definition of the gravitational deflection angle relative to a static observer located at a finite distance is proposed for these rays. The expression inferred from this definition extends the formula currently used in VLBI astrometry up to the second order in the gravitational constant G.Comment: 19 pages; revised introduction; added references for introduction; corrected typos; published in Class. Quantum Gra

A computational analysis of lower bounds for big bucket production planning problems

In this paper, we analyze a variety of approaches to obtain lower bounds for multi-level production planning problems with big bucket capacities, i.e., problems in which multiple items compete for the same resources. We give an extensive survey of both known and new methods, and also establish relationships between some of these methods that, to our knowledge, have not been presented before. As will be highlighted, understanding the substructures of difficult problems provide crucial insights on why these problems are hard to solve, and this is addressed by a thorough analysis in the paper. We conclude with computational results on a variety of widely used test sets, and a discussion of future research

First measurements of the ^16O(e,e'pn)^14N reaction

This paper reports on the first measurement of the ^16O(e,e'pn)^14N reaction. Data were measured in kinematics centred on a super-parallel geometry at energy and momentum transfers of 215 MeV and 316 MeV/c. The experimental resolution was sufficient to distinguish groups of states in the residual nucleus but not good enough to separate individual states. The data show a strong dependence on missing momentum and this dependence appears to be different for two groups of states in the residual nucleus. Theoretical calculations of the reaction using the Pavia code do not reproduce the shape or the magnitude of the data.Comment: 10 pages, 11 figures, 2 tables, Accepted for publication in EPJ

Investigation of the Exclusive 3He(e,e'pp)n Reaction

Cross sections for the 3He(e,e'pp)n reaction were measured over a wide range of energy and three- momentum transfer. At a momentum transfer q=375 MeV/c, data were taken at transferred energies omega ranging from 170 to 290 MeV. At omega=220 MeV, measurements were performed at three q values (305, 375, and 445 MeV/c). The results are presented as a function of the neutron momentum in the final-state, as a function of the energy and momentum transfer, and as a function of the relative momentum of the two-proton system. The data at neutron momenta below 100 MeV/c, obtained for two values of the momentum transfer at omega=220 MeV, are well described by the results of continuum-Faddeev calculations. These calculations indicate that the cross section in this domain is dominated by direct two-proton emission induced by a one-body hadronic current. Cross section distributions determined as a function of the relative momentum of the two protons are fairly well reproduced by continuum-Faddeev calculations based on various realistic nucleon-nucleon potential models. At higher neutron momentum and at higher energy transfer, deviations between data and calculations are observed that may be due to contributions of isobar currents.Comment: 14 pages, 1 table, 17 figure