A Finitely Convergent Duality Theory for Zero-One Integer Programming

Given an integer programming problem, a constructive procedure is presented for generating a finite sequence of increasingly stronger dual problems to the given problem. The last dual problem in the sequence yields an optimal solution to the given integer programming problem. It is shown that this dual problem approximates the convex hull of the feasible integer solutions in a neighborhood of the optimal solution it finds. The theory is applicable to any bounded integer programming problem with rational data

Nuclear Reactor Refueling Optimization

In a 1971 paper, Suzuki and Kiyose give a model for light water moderated atomic reactor refueling optimization. Specifically, they present a linear programming formulation for minimizing the number of fresh fuel assemblies required by a reactor over a finite planning horizon subject to power generation and safety requirements and reactor design specifications. The optimal refueling policies found by Suzuki and Kiyose were useful in reducing the fresh fuel required, but two difficulties were encountered. First, the optimal linear programming solutions included small fractional numbers of fresh fuel assemblies which were difficult to round off. The second difficulty was that their formulation had approximately 165H constraints where H is the length of the planning horizon. The problems solved had H=10, but it was desired to analyze the problem for longer planning horizons of 20 to 30 stages without solving prohibitively large mathematical programming problems. In this paper, we give a reformulation of the reactor refueling optimization problem that consists of approximately 15H constraints and a large number of columns. This reformulation is required because the state-of-the-art of integer programming does not usually permit the solution of integer programs with thousands or even many hundreds of constraints. Moreover, the reformulation should permit the linear programming approximation to be more easily solved, at least approximately. Finally, the reformulation identifies and analyzes explicitly the fundamental activity in refueling optimization; namely, the introduction, degradation and removal of fuel assemblies. This should make it easier to modify the model to take into account additional features of the problem such as a cost for moving an assembly from one location to another

A high-flux source of polarization-entangled photons from a periodically-poled KTP parametric downconverter

We have demonstrated a high-flux source of polarization-entangled photons using a type-II phase-matched periodically-poled KTP parametric downconverter in a collinearly propagating configuration. We have observed quantum interference between the single-beam downconverted photons with a visibility of 99% and a measured coincidence flux of 300/s/mW of pump. The Clauser-Horne-Shimony-Holt version of Bell's inequality was violated with a value of 2.711 +/- 0.017.Comment: 7 pages submitted to Physical Review

Energy levels and lifetimes of Gd IV and enhancement of the electron dipole moment

We have calculated energy levels and lifetimes of 4f7 and 4f6 5d configurations of Gd IV using Hartree-Fock and configuration interaction methods. This allows us to reduce significantly the uncertainty of the theoretical determination of the electron electric dipole moment (EDM) enhancement factor in this ion and, correspondingly, in gadolinium-containing garnets for which such measurements were recently proposed. Our new value for the EDM enhancement factor of Gd+3 is -2.2 +- 0.5. Calculations of energy levels and lifetimes for Eu~III are used to control the accuracy.Comment: Submitted to Phys. Rev. A 6 pages, 0 figures, 3 table

Analysing the elasticity difference tensor of general relativity

The elasticity difference tensor, used in [1] to describe elasticity properties of a continuous medium filling a space-time, is here analysed from the point of view of the space-time connection. Principal directions associated with this tensor are compared with eigendirections of the material metric. Examples concerning spherically symmetric and axially symmetric space-times are then presented.Comment: 17 page