We study the Lozi mapping f(x,y) = (1+by-a|x|,x) acting on a compact trapping region in R² and prove that its Sinai-Bowen-Ruelle measure is stable under small random perturbations. This extends the results of Kifer and Young [Y2] for Axiom A attractors to a piecewise hyperbolic setting.

Thesis (Ph.D.) -- University of Rhode Island, 2009. / Typescript. Includes bibliographical references (leaves 62-64).

Thesis (Ph.D.) -- University of Rhode Island, 2009. / Typescript. Includes bibliographical references (leaves 108-111).

Thesis (Ph. D.)--University of Oregon, 2005. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 88-90). Also available for download via the World Wide Web; free to University of Oregon users.

Thesis (Ph. D.)--University of Rhode Island, 2005. / Typescript. Includes bibliographical references (leaves 55-57).

No description available.

Thesis (Ph. D.)--State University of New York at Binghamton, Department of Mathematical Sciences, 2008. / Includes bibliographical references.

Thesis (M.S.) University of Missouri-Columbia, 2006. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on August 21, 2007) Includes bibliographical references.

Specialized techniques are needed to solve global optimization problems, due to the existence of multiple local optima or numerical noise in the objective function. The complexity of the problem is aggravated when discontinuities and constraints are present, or when evaluation of the objective function is computationally expensive. The global (minimization) programming problem is defined as finding the variable set for which the objective function obtains not only a local minimum, but also the smallest value, the global minimum. From a mathematical point of view, the global programming problem is essentially unsolvable, due to a lack of mathematical conditions characterizing the global optimum. In this study, the unconstrained global programming problem is addressed using a number of novel heuristic approaches. Firstly, a probabilistic global stopping criterion is presented for multi-start algorithms. This rule, denoted the unified Bayesian stopping criterion, is based on the single mild assumption that the probability of convergence to the global minimum is comparable to the probability of convergence to any other local minimum. This rule was previously presented for use in combination with a specific global optimization algorithm, and is now shown to be effective when used in a general multi-start approach. The suitability of the unified Bayesian stopping criterion is demonstrated for a number of algorithms using standard test functions. Secondly, multi-start global optimization algorithms based on multiple local searches, com¬bined with the unified Bayesian stopping criterion, are presented. Numerical results reveal that these simple multi-start algorithms outperform a number of leading contenders. Thirdly, parallelization of the sequential multi-start algorithms is shown to effectively re¬duce the apparent computational time associated with solving expensive global programming problems. Fourthly, two algorithms simulating natural phenomena are implemented, namely the rel¬atively new particle swarm optimization method and the well known genetic algorithm. For the current implementations, numerical results indicate that the computational effort associated with these methods is comparable. Fifthly, the observation that no single global optimization algorithm can consistently out¬perform any other algorithm when a large set of problems is considered, leads to the de¬velopment of a parallel competing algorithm infrastructure. In this infrastructure different algorithms, ranging from deterministic to stochastic, compete simultaneously for a contri¬bution to the unified Bayesian global stopping criterion. This is an important step towards facilitating an infrastructure that is suitable for a range of problems in different classes. In the sixth place, the constrained global programming problems is addressed using con¬strained algorithms in the parallel competing algorithm infrastructure. The developed methods are extensively tested using standard test functions, for both serial and parallel implementations. An optimization procedure is also presented to solve the slope stability problem faced in civil engineering. This new procedure determines the factor of safety of slopes using a global optimization approach. / Dissertation (MEng (Mechanical Engineering))--University of Pretoria, 2006. / Mechanical and Aeronautical Engineering / unrestricted

Since the discovery in the 1960's that the proton is not a fundamental particle but instead composed of even smaller particles known as quarks and gluons, there has been a concerted effort to understand the proton's internal structure. There still remain many mysteries about the proton and the theory that describes the interactions within: Quantum Chromodynamics (QCD). The distributions of quarks and gluons are encoded in objects known as parton correlation functions. Physicists use high-energy scattering experiments to access these functions by means of QCD factorization. This process of extracting information is known as a global QCD analysis. Further insight can be gained through first-principles calculations in lattice QCD as well as models for the strong interaction. In this thesis, we will use global QCD analyses to provide information on the one-dimensional (1D) structure of the proton using the latest experimental data available. Among the mysteries that remain within the proton, we provide insight on the non-perturbative nature of the proton's sea quarks, for both cases where the proton is unpolarized and longitudinally polarized. We also bring new information on the "proton spin puzzle," which concerns the delegation of the proton's spin into its constituent quarks and gluons. We shed light on the proton's transversely polarized structure, where current results from global QCD analyses and lattice QCD fail to paint a consistent picture. Our analyses also reveal a new feature of nuclear effects within light, highly asymmetric nuclei such as helium and tritium. Finally, we perform derivations in a spectator diquark model to glean information on the proton's 3D structure, and calculate moments that can be used in future lattice QCD studies. / Physics