Models of topological space geometries

We study a special class of models of R³-spaces in the sense of Betten. We single out some of the properties of these models, and use these properties as additional axioms for general R³-spaces. Then we investigate the consequences of these new axioms in general R³-spaces. We prove the continuity of the geometric operations which involve planes, and we characterize the planes in incidence geometric terms. Using these results, we study the topology of the space of planes and of line pencils, and we prove the continuity of collineations. The obtained results are applied to our concrete examples.     

On the convex hull of the simple integer recourse objective function

We consider the objective function of a simple integer recourse problem with fixed technology matrix.Using properties of the expected value function, we prove a relation between the convex hull of this function and the expected value function of a continuous simple recourse program.We present an algorithm to compute the convex hull of the expected value function in case of discrete right-hand side random variables. Allowing for restrictions on the first stage decision variables, this result is then extended to the convex hull of the objective function.Supported by the National Operations Research Network in the Netherlands (LNMB).     

Degradation behaviour of polymeric materials found in auto Shredder residue wastes

The thermogravimetry of a series of 50/50 mixtures of polypropylene, acrylonitrile/butadiene/styrene, polyvinyl chloride and polyurethane polymers have been studied as representative of the major polymeric materials found in automobile shredder residues. The weight loss behaviour of these polymeric mixes have been compared with the results calculated from the individual polymeric components. This comparison of the thermogravimetry curves and the calculated kinetic parameters indicates that interactions occur between the individual polymers when heated together. The extent of these interactions are dependent upon the polymeric mixtures being considered, but in most cases the changes in the degradation kinetic parameters were not large. Issued as NRCC #35741     

Phase shifting at 94 GHz using the electro-optic effect in bulk crystals

We have measured electro-optic coefficients at 94 GHz for several orientations in LiNbO₃ and LiTaO₃. These coefficients are considerably enhanced over their values in the visible, due to contributions from lattice vibrations. A scaling law is developed which allows the calculation of these coefficients in terms of the linear susceptibility. The phase shifting performance of a number of promising materials is discussed.     

Stochastic processes associated with quantum systems

Stochastic processes have been useful in constructing and studying states in Quantum Field Theory (e.g., the Erice Lectures [3], Simon [2], Glimm and Jaffle [6] and in Quantum Statistical Mechanics (e.g., Ginibre [5], Høegh-Khron [7], Fröhlich [4], Driessler, Landau and Perez [2]). By analytically continuing into imaginary time, we may in certain cases replace the non-commulative algebra of observables of the quantum system by a commulative algebra consisting of functions of a stochastic process.In this article we are going to discuss an appropriate mathematical framework for this connection between quantum systems and stochastic processes.