A Hahn-Banach theorem for integral polynomials

We study the problem of extendibility of polynomials over Banach spaces: when can a polynomial defined over a Banach space be extended to a polynomial over any larger Banach space? To this end, we identify all spaces of polynomials as the topological duals of a space spanned by evaluations, with Hausdorff locally convex topologies. We prove that all integral polynomials over a Banach space are extendible. Finally, we study the Aron-Berner extension of integral polynomials, and give an equivalence for non-containment of .

     

QPECgen, a MATLAB Generator for Mathematical Programs with Quadratic Objectives and Affine Variational Inequality Constraints

We describe a technique for generating a special class, called QPEC, of mathematical programs with equilibrium constraints, MPEC. A QPEC is a quadratic MPEC, that is an optimization problem whose objective function is quadratic, first-level constraints are linear, and second-level (equilibrium) constraints are given by a parametric affine variational inequality or one of its specialisations. The generator, written in MATLAB, allows the user to control different properties of the QPEC and its solution. Options include the proportion of degenerate constraints in both the first and second level, ill-conditioning, convexity of the objective, monotonicity and symmetry of the second-level problem, and so on. We believe these properties may substantially effect efficiency of existing methods for MPEC, and illustrate this numerically by applying several methods to generator test problems. Documentation and relevant codes can be found by visiting http://www.ms.unimelb.edu.au/danny/qpecgendoc.html.     

On the optimal local regularity for the Yang-Mills equations in

The aim of the paper is to develop the Fourier Analysis techniques needed in the study of optimal well-posedness and global regularity properties of the Yang-Mills equations in Minkowski space-time , for the case of the critical dimension . We introduce new functional spaces and prove new bilinear estimates for solutions of the homogeneous wave equation, which can be viewed as generalizations of the well-known Strichartz-Pecher inequalities.

     

Spectral properties of dissipative chaotic quantum maps

I examine spectral properties of a dissipative chaotic quantum map with the help of a recently discovered semiclassical trace formula. I show that in the presence of a small amount of dissipation the traces of any finite power of the propagator of the reduced density matrix, and traces of its classical counterpart, the Frobenius-Perron operator, are identical in the limit of variant Planck's over 2pi -->0. Numerically I find that even for finite variant Planck's over 2pi the agreement can be very good. This holds in particular if the classical phase space contains a strange attractor, as long as one stays clear of bifurcations. Traces of the quantum propagator for iterations of the map agree well with the corresponding traces of the Frobenius-Perron operator if the classical dynamics is dominated by a strong point attractor. (c) 1999 American Institute of Physics.     

Nanocomposite Mullite/Mullite Powders by Spray Pyrolysis

A mullite/mullite nanocomposite powder has been synthesized, composed of nanometer-size 3Al₂O₃·2SiO₂ (3/2) mullite precipitates within a matrix of the high alumina 2Al₂O₃·SiO₂ (2:1) mullite. Historically, the transition from the metastable high-alumina phase to the thermodynamically stable 3:2 phase of mullite has been thought to be a continuous process, involving a continuous solid solution between the two forms of mullite. In contradiction to this widely held view, our high resolution transmission electron microscopic characterization confirms that a first order phase transition between two distinct mullites occurs. The high degree of interface coherence between the precipitates and the matrix allows us to speculate that the mechanical properties of the matrix could be enhanced by a process similar to the precipitation hardening of metals.     

Spanning network games

We study fundamental properties of monotone network enterprises which contain public vertices and have positive and negative costs on edges and vertices. Among the properties studied are the nonemptiness of the core, characterization of nonredundant core constraints, ease of computation of the core and the nucleolus, and cases of decomposition of the core and the nucleolus. Received December 1994/Final version March 1998     

The number of rounds needed to exchange information within a graph

In [3] Cederbaum proposes the problem of finding a labelling of a connected graph G which minimizes the number of rounds needed to exchange information between all the points, where a round consists of the vertices of G each broadcasting once in order of their labels. In this paper we give a complete solution to the problem.     

An outdoor smog chamber and modeling study of toluene–NOx photooxidation

An experimental investigation of the gas-phase photooxidation of toluene–NO_x–air mixtures at part-per-million concentrations has been carried out in a 65-m³, outdoor smog chamber to assess our understanding of the atmospheric chemistry of toluene. In addition, six CO? NO_x–air irradiations were conducted to characterize the chamber with regard to any wall radical sources. Measured parameters in the toluene–NO_x experiments included O₃, NO, NO₂, HNO₃, peroxyacetyl nitrate (PAN), CO, toluene, benzaldehyde, o-cresol, m-nitrotoluene, peroxybenzoyl nitrate (PBZN), temperature, relative humidity, aerosol size distributions, and particulate organic carbon. Predictions of the reaction mechanism of Leone and Seinfeld [7] are found to be in good agreement with the data under a variety of initial conditions. Additional simulations are used to investigate various mechanistic pathways in areas where our understanding of toluene chemistry is still incomplete.