Thesis (Ph.D.)--University of Melbourne, Dept. of Mathematics and Statistics, 2005. / Typescript. Includes bibliographical references (leaves [237]-245).

Thesis (Ph. D.)--Dept. of Physics and Dept. of Mathematics. University of Missouri--Kansas City, 2008. / "A dissertation in physics and mathematics." Advisor: James M. Phillips. Typescript. Vita. Title from "catalog record" of the print edition Description based on contents viewed Sept. 12, 2008. Includes bibliographical references (leaves 79-83). Online version of the print edition.

Thesis (Ph. D.)--University of Texas at Austin, 2000. / Vita. Includes bibliographical references (leaves 228-242). Available also in a digital version from Dissertation Abstracts.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1960. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1981. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 243-246).

In this thesis we consider the following model for a three-dimensional r ˣ s ˣ t contingency table: [formula omitted]. A dot indicates summation over the replaced subscript. The f[formula omitted]’s represent the frequencies and the P[formula omitted]'s represent the proportions. The problem we are concerned with is testing the hypothesis H₀: [formula omitted] = 0 for all i, j, k. i.e. no second order interaction is present. We then seek to extend the model and problem to a w-way table. We use the method of the likelihood ratio . To assist us in determining the numerator of the likelihood ratio we reformulate a theorem about constrained extrema and Lagrange multipliers and prove this reformulation. Some general conclusions we draw are: there are two extensions to our 3-way model; results we obtain using our model and methods are in close agreement with results obtained using the models and methods of other statisticians. / Science, Faculty of / Mathematics, Department of / Graduate

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No description available.

Density functional theory of statistical mechanics in a square gradient approximation was used to study nucleation in confined systems such as a cylindrical pore and in-between two cylindrical disks. This approximation was further applied to study the evaporation and condensation in nanopores with finite lengths. Confinement effects induced nucleation phenomena that are not observed in more open systems. Density functional theory was also used to explore the solvation properties of a spherical solute immersed in a supercritical diatomic fluid. The solute was modeled as a hard core Yukawa particle surrounded by a diatomic Lennard-Jones fluid represented by two fused tangent spheres using an interaction site approximation. The results of this study indicate that local density augmentation and the solvation free energies are particularly sensitive to changes in solute and solvent particle geometry and solute/solvent anisotropic interactions. Density functional theory allowed us to systematically study the effect of a variety of geometric and interaction parameters on the properties and behavior of all the systems. Although more sophisticated, but computationally more demanding, theoretical approaches can be used, our results provide fundamental physical insights into the behavior of real systems and create a solid basis for the development of more realistic models.

Com base em exemplos, nos fundamentos da Mecânica estatística e na teoria ergódiga, é dada uma definição de atrator como uma medida invariante. Vários resultados que corroboram esta definição são demostrados. Caos é relacionado à presença de um atrator com entropia métrica maior que zero. O papel dos expoentes de Lyapunov é analisado e é provado que um atrator caótica possui expoentes de Lyapunov positivos em quase todo ponto, e também que, se um atrator possui todos expoentes de Lyapunov estritamente negativos num conjunto de medida atratora maior que zero, então seu suporte é uma órbita periódica assintoticamente estável. / Here, a definition of an attractor as an invariant measure is given based on Ergodic Theory, foundations of Statistical Mechanics and some examples. Chaos is related to the presence of an attractor with metric entropy grater zero. It is proved that a chaotic attractor has positive Lyapunov exponents almost everywhere, and that, if an attractor has every Lyapunov exponents less than zero in a set of nonzero measure then the support set of the attractor is an asymptotic stable periodic orbit.