Improved state space relaxation for constrained two-dimensional guillotine cutting problems

Christofides and Hadjiconstantinou (1995) introduced a dynamic programming state space relaxation for obtaining upper bounds for the Constrained Two-dimensional Guillotine Cutting Problem. The quality of those bounds depend on the chosen item weights, they are adjusted using a subgradient-like algorithm. This paper proposes Algorithm X, a new weight adjusting algorithm based on integer programming that provably obtains the optimal weights. In order to obtain even better upper bounds, that algorithm is generalized into Algorithm X2 for obtaining optimal two-dimensional item weights. We also present a full hybrid method, called Algorithm X2D, that computes those strong upper bounds but also provides feasible solutions obtained by: (1) exploring the suboptimal solutions hidden in the dynamic programming matrices; (2) performing a number of iterations of a GRASP based primal heuristic; and (3) executing X2H, an adaptation of Algorithm X2 to transform it into a primal heuristic. Extensive experiments with instances from the literature and on newly proposed instances, for both variants with and without item rotation, show that X2D can consistently deliver high-quality solutions and sharp upper bounds. In many cases the provided solutions are certified to be optimal.     

On Jacobi fields

We define curves on a Riemannian manifold as integrals of generalized Jacobi fields. We show that the force term that deviates the trajectory from the geodesic motion can be constructed as a functional of the metric tensor. These curves can be interpreted as particles (observers) coupled nonminimally with gravitation that can provide a class of residual observers for the inevitable singularity—as shown in the text.This essay received an honorable mention (1976) from the Gravity Research Foundation-Ed.     

Thermodynamics of the xenon + methyl chloride system

The total vapour pressure of the xenon + methyl chloride system has been measured as a function of composition at 175.44 and 182.32 K. The resulting data have been used to evaluate the excess Gibbs functions G^E at the same temperatures. The excess enthalpy and excess molar volume have also been measured at 182.32 K. The system shows large positive deviations from Raoult's law but negative volumes on mixing. These results are compared with theoretical predictions of a recent molecular theory and of standard engineering methods. The calculations show the superiority of the molecular theory over more empirical procedures such as those based on the Redlich-Kwong equation of state or the regular-solution model.     

On the index of a holomorphic vector field tangent to a singular variety

In this article we define and compute an index for a holomorphic vector field on a (possibly singular) subvariety of a complex manifold, provided the subvariety is a local complete intersection. This index reduces to the usual Poincaré-Hopf index in case the subvariety is smooth, and is equal more generally to the index defined in [GSV] and [SS].     

An adaptive discretization of shallow‐water equations based on discontinuous Galerkin methods

In this paper, we present a discontinuous Galerkin formulation of the shallow‐water equations. An orthogonal basis is used for the spatial discretization and an explicit Runge–Kutta scheme is used for time discretization. Some results of second‐order anisotropic adaptive calculations are presented for dam breaking problems. The adaptive procedure uses an error indicator that concentrates the computational effort near discontinuities like hydraulic jumps. Copyright © 2006 John Wiley & Sons, Ltd.     

The electric quadrupole interaction of the 134 keV state of197Hg in the metal hosts Cd,Zn, Sn and Ti studied by e−-γ TDPAC measurements

The electric quadrupole coupling constants of the lowest excited 5/2^? state in¹⁹⁷Hg have been measured by the e^?-γ TDPAC method for the hosts Ti and Sn at room temperature and for Zn and Cd at various temperatures. The observed temperature dependences are approximately the same as those known for other impurities in the same host lattices. They are well described by a simpleT ^3/2 relation.     

First-order kinetic approximation for a reactive gas mixture

A multicomponent reacting gas with an arbitrary number of chemical species and one reversible reaction is studied at a kinetic level in the frame of discrete velocity models of the Boltzmann equation, with the main objective of deriving the reactive Navier Stokes equations of the model, and characterizing the dissipative terms related to shear viscosity, thermal conductivity and thermal diffusion. The closure of the system formed by conservation and chemical rate equations is based on a first-order Chapman-Enskog method, to be applied in the strong reaction regime, and on a convenient representation of the density vector space in terms of the macroscopic variables. A mathematical procedure is proposed which leads to identification of the transport coefficients, and may be applied to a quite large variety of reactive gas flows. Moreover, it allows characterization of the functional form of the transport coefficients in dependence on the local gas concentrations, once the model is specified.Received: 4 October 2004, Accepted: 3 December 2004, Published online: 18 March 2005PACS: 51.10. + y, 51.20. + d, 47.70.Fw Correspondence to: A.J. Soares