This work contributes to modeling, theoretical, and practical aspects of structured Mathematical Programming problems. Many real-world applications have nonlinear characteristics and can be modeled as Mixed Integer Nonlinear Programming problems (MINLP). Modern global solvers have significant difficulty handling large-scale instances of them. Several convexification and underestimation techniques were proposed in the last decade as a part of the solution process, and we join this trend. The thesis has three major parts. The first part considers MINLP problems containing convex (in the sense of continuous relaxations) and posynomial terms (also called monomials), i.e. products of variables with some powers. Recently, a linear Mixed Integer Programming (MIP) approach was introduced for minimization the number of variables and transformations for convexification and underestimation of these structured problems. We provide polyhedral analysis together with separation for solving our variant of this minimization subproblem, containing binary and bounded continuous variables. Our novel mixed hyperedge method allows to outperform modern commercial MIP software, providing new families of facet-defining inequalities. As a byproduct, we introduce a new research area called mixed conflict hypergraphs. It merges mixed conflict graphs and 0-1 conflict hypergraphs. The second part applies our mixed hyperedge method to a linear subproblem of the same purpose for another class of structured MINLP problems. They contain signomial terms, i.e. posynomial terms of both positive and negative signs. We obtain new facet-defining inequalities in addition to those families from the first part. The final part is dedicated to managing guest flow in Georgia Aquarium after the Dolphin Tales opening with applying a large-scale MINLP. We consider arrival and departure processes related to scheduled shows and develop three stochastic models for them. If demand for the shows is high, all processes become interconnected and require a generalized model. We provide and solve a Signomial Programming problem with mixed variables for minimization resources to prevent and control congestions.

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"Building design and site features have an influence on helping or hindering fire fighting operations. Traditional studies relating to building performance evaluation for fire department operations do not address the influence of building site and architectural design on local fire department suppression techniques. These studies also do not relate fire fighting analysis to anticipated fire size. The goal of this dissertation is to develop an analytical procedure by which the size of a specified design fire can be predicted for the time at which fire fighting attack water application is likely to occur. The delays encountered due to building configuration and specified design fire conditions are incorporated in the analysis. Discrete Event Simulation is used to compute time durations for fire fighting operations. The results of this dissertation may be used as a stand alone technical analysis for any office building or as a part of a more complete building performance evaluation. "

A Hamilton cycle in a graph is a cycle that passes through every vertex of the graph. A graph is called Hamiltonian if it contains such a cycle. The problem of determining if a graph is Hamiltonian has been studied extensively, and there are many known sufficient conditions for Hamiltonicity. A large portion of these conditions relate the degrees of vertices of the graph to the number of vertices in the entire graph, and thus they can only apply to a limited set of graphs with high edge density. In a series of papers, Asratian and Khachatryan developed local analogues of some of these criteria. These results do not suffer from the same drawbacks as their global counterparts, and apply to wider classes of graphs. In this thesis we study this approach of creating local conditions for Hamiltonicity, and use it to develop local analogues of some classic results. We also study how local criteria can influence other global properties of graphs. Finally, we will see how these local conditions can allow us to extend theorems on Hamiltonicity to infinite graphs.

Fast algorithms for N-point shifted discrete Fourier transform (SDFT) are proposed by efficient matrix factorization¡DThe resulted matrix decomposition is realized by a cascade of several basic computation blocks with each block implemented by a parameterized IP module¡DBy combining these modules with different parameters, it is easy to implement a wide variety of digital transforms, such as DCT/IDCT in image/video coding, and modified DCT (MDCT) in audio coding¡D The transform processors realized using the parameterized IP modules have advantages of locality¡Amodularity¡Aregularity¡Alow-cost¡Aand high-throughput¡D Furthermore ¡Athe computation accuracy can be easily controlled by selecting different numbers of IP modules with proper parameters in the processors.

Thesis (Ph. D.)--University of Washington, 2002. / Vita. Includes bibliographical references (leaves 87-88).

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