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We introduce real second-order freeness in second-order noncommutative probability spaces. We demonstrate that under this definition, independent ensembles of the three real models of random matrices which we consider, namely real Ginibre matrices, Gaussian orthogonal matrices, and real Wishart matrices, are asymptotically second-order free. These ensembles do not satisfy the complex definition of second-order freeness satisfied by their complex analogues. This definition may be used to calculate the asymptotic fluctuations of products of matrices in terms of the fluctuations of each ensemble. We use a combinatorial approach to the matrix calculations similar to genus expansion, but in which nonorientable surfaces appear, demonstrating the commonality between the real ensembles and the distinction from their complex analogues, motivating this distinct definition. We generalize the description of graphs on surfaces in terms of the symmetric group to the nonorientable case. In the real case we find, in addition to the terms appearing in the complex case corresponding to annular spoke diagrams, an extra set of terms corresponding to annular spoke diagrams in which the two circles of the annulus are oppositely oriented, and in which the matrix transpose appears. / Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2011-09-09 11:07:37.414

Regression models with correlated errors lead to nonadditivity of the information matrix. This makes the usual approach of design optimization (approximation with a continuous design, application of an equivalence theorem, numerical calculations by a gradient algorithm) impossible. A method is presented that allows the construction of a gradient algorithm by altering the information matrices through adding of supplementary noise. A heuristic is formulated to circumvent the nonconvexity problem and the method is applied to typical examples from the literature. (author's abstract) / Series: Forschungsberichte / Institut für Statistik

This thesis is dedicated to the study of flows on a network. In the first part of the work, we describe notation and give the necessary results from graph theory and operator theory that will be used in the rest of the thesis. Next, we consider the flow of particles between vertices along an edge, which occurs instantaneously, and this flow is described by a system of first order ordinary differential equations. For this system, we extend the results of Perthame [48] to arbitrary nonnegative off-diagonal matrices (ML matrices). In particular, we show that the results that were obtained in [48] for positive off diagonal matrices hold for irreducible ML matrices. For reducible matrices, the results in [48], presented in the same form are only satisfied in certain invariant subspaces and do not hold for the whole matrix space in general. Next, we consider a system of transport equations on a network with Kirchoff-type conditions which allow for amplification and/or absorption at the boundary, and extend the results obtained in [33] to connected graphs with no sinks. We prove that the abstract Cauchy problem associated with the flow problem generates a strongly continuous semigroup provided the network has no sinks. We also prove that the acyclic part of the graph will be depleted in finite time, explicitly given by the length of the longest path in the acyclic part. / Thesis (Ph.D)-University of KwaZulu-Natal, Durban, 2013.

No description available.

No description available.

There are many examples where creation and usage of porous substrates play important roles in various fields of application in material science and technology. In the manufacture of ceramic products, as an alternative to the plaster molds, porous resin molds are used in order to resolve the drawbacks that result A porous substrate can be produced by various ways. In this study, porous polymeric matrices of poly(methyl methacrylate) (PMMA) and poly(methyl methacrylate-co-2-hydroxyethyl methacrylate) [poly(MMA-HEMA)] polymers were prepared by connecting the polymer microspheres to each other by an epoxy adhesive. To improve the surface properties, methyl methacrylate (MMA) was copolymerized with 2-hydroxyethyl methacrylate (HEMA). The microspheres used were synthesized by suspension polymerization and characterization was done by Nuclear Magnetic Resonance (NMR), Particle Size Analyzer and Scanning Electron Microscope (SEM). The porous samples were prepared with PMMA and poly(MMA-HEMA) copolymer microspheres with two different HEMA contents and their surface energies were measured. In addition, the effect of mean particle diameter of the microspheres used and the epoxy content of the solution used to bind the microspheres, on the impregnation capacity, morphology and the impact strength of the porous samples prepared, were studied. Inclusion of HEMA into the formulation improved the impregnation capacity of the samples. Using microspheres with narrower particle size distribution resulted in larger representative capillary radii and higher rate of impregnation of the samples. Increasing the epoxy content of the solution used to bind the beads, increased the impact strengths of the samples prepared.

CD-ROM in pocket on back end paper. / Bibliography: leaves 254-259. / xiv, 259 leaves : ill. ; 30 cm + 1 computer optical disc (4 3/4 in.) / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Proposes a specialized matrix processor architecture that targets numerically intensive algorithms that can be cast in matrix terms. / Thesis (Ph.D.)--University of Adelaide, Dept. of Electrical and Electronic Engineering, Advisory Centre for University Education, 2000

The main work of this thesis involves the calculation, using the Bethe ansatz, of two of the signature quantities of the one-dimensional delta-function Bose gas. These are the density matrix and concomitantly its Fourier transform the occupation numbers, and the correlation function and concomitantly its Fourier transform the structure factor. The coefficient of the delta-function is called the coupling constant; these quantities are calculated in the finite-coupling regime, both expansions around zero coupling and infinite coupling are considered. Further to this, the density matrix in the infinite coupling limit, and its first order correction, is recast into Toeplitz determinant form. From this the occupation numbers are calculated up to 36 particles for the ground state and up to 26 particles for the first and second excited states. This data is used to fit the coefficients of an ansatz for the occupation numbers. The correlation function in the infinite coupling limit, and its first order correction, is recast into a form which is easy to calculate for any N, and is determined explicitly in the thermodynamic limit.

CD-ROM in pocket on back end paper. / Bibliography: leaves 254-259. / xiv, 259 leaves : ill. ; 30 cm + 1 computer optical disc (4 3/4 in.) / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Proposes a specialized matrix processor architecture that targets numerically intensive algorithms that can be cast in matrix terms. / Thesis (Ph.D.)--University of Adelaide, Dept. of Electrical and Electronic Engineering, Advisory Centre for University Education, 2000