THE PARAMETERS OF THE LEWIS METRIC FOR THE WEYL CLASS

We provide physical interpretation for the four parameters of the stationary Lewis metric restricted to the Weyl class. Matching this spacetime to a completely anisotropic, rigidly rotating, fluid cylinder, we obtain from the junction conditions that one of these parameters is proportional to the vorticity of the source. From the Newtonian approximation a second parameter is found to be proportional to the energy per unit of length. The remaining two parameters may be associated to a gravitational analog of the Aharanov-Bohm effect. We prove, using the Cartan scalars, that the Weyl class metric and static Levi-Civita metric are locally equivalent, i.e., indistinguishable in terms of its curvature.

Structure and luminescence of Eu3+-doped class I siloxane-poly(ethylene glycol) hybrids

Transparent, flexible, and luminescent EU3+-doped siloxane-poly(ethylene glycol) (PEG) nanocomposites have been obtained by the sol-gel process. The inorganic (siloxane) and organic PEG phases are usually linked by weak bonds (hydrogen bonds or van der Waals forces), and small-angle X-ray scattering (SAXS) measurements suggest that the structure of these materials consists of fractal siloxane aggregates embedded in the PEG matrix. For low Eu3+ contents, n = 300 and n = 80, the aggregates are small and isolated and their fractal dimensions are 2.1 and 1.7, respectively. These values are close to those expected for gelation mechanisms consisting of reaction-limited cluster-cluster aggregation (RLCCA) and diffusion-limited cluster-cluster aggregation (DLCCA). For high Eu3+ content, SAYS results are consistent with a two-level structure: a primary level of siloxane aggregates and a second level, much larger, formed by the coalescence of the primary ones. The observed increase in the glass transition temperature for increasing Eu3+ content is consistent with the structural model derived from SAXS measurements. Extended X-ray absorption fine structure (EXAFS) and luminescence spectroscopy measurements indicate that under the experimental conditions utilized here Eu3+ ions do not strongly interact with the polymeric phase.

Hopf-zero bifurcations of reversible vector fields

We study the dynamics of a class of reversible vector fields having eigenvalues (0, alphai, -alphai) around their symmetric equilibria. We give a complete list of all normal forms for such vector fields, their versal unfoldings, and the corresponding bifurcation diagrams of the codimensional-one case. We also obtain some important conclusions on the existence of homoclinic and heteroclinic orbits, invariant tori and symmetric periodic orbits.

The application of preprocessing and cutting plane techniques for a class of production planning problems

This paper investigates properties of integer programming models for a class of production planning problems. The models are developed within a decision support system to advise a sales team of the products on which to focus their efforts in gaining new orders in the short term. The products generally require processing on several manufacturing cells and involve precedence relationships. The cells are already (partially) committed with products for stock and to satisfy existing orders and therefore only the residual capacities of each cell in each time period of the planning horizon are considered. The determination of production recommendations to the sales team that make use of residual capacities is a nontrivial optimization problem. Solving such models is computationally demanding and techniques for speeding up solution times are highly desirable. An integer programming model is developed and various preprocessing techniques are investigated and evaluated. In addition, a number of cutting plane approaches have been applied. The performance of these approaches which are both general and application specific is examined.

Combinatorial and geometrical properties of a class of tilings

In this paper, we consider a tiling generated by a Pisot unit number of degree d >= 3 which has a finite expansible property. We compute the states of a finite automaton which recognizes the boundary of the central tile. We also prove in the case d = 3 that the interior of each tile is simply connected.

Bound states of the Dirac equation for a class of effective quadratic plus inversely quadratic potentials

The Dirac equation is exactly solved for a pseudoscalar linear plus Coulomb-like potential in a two-dimensional world. This sort of potential gives rise to an effective quadratic plus inversely quadratic potential in a Sturm-Liouville problem, regardless the sign of the parameter of the linear potential, in sharp contrast with the Schrodinger case. The generalized Dirac oscillator already analyzed in a previous work is obtained as a particular case. (C) 2004 Elsevier B.V. All rights reserved.