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CATEGORICAL PROPERTIES OF LATTICE-VALUED CONVERGENCE SPACES
Title
CATEGORICAL PROPERTIES OF LATTICE-VALUED CONVERGENCE SPACES.
Creator
Flores, Paul, Richardson, Gary, University of Central Florida
Abstract / Description
This work can be roughly divided into two parts. Initially, it may be considered a continuation of the very interesting research on the topic of Lattice-Valued Convergence Spaces given by Jäger [2001, 2005]. The alternate axioms presented here seem to lead to theorems having proofs more closely related to standard arguments used in Convergence Space theory when the Lattice is L=.Various Subcategories are investigated. One such subconstruct is shown to be isomorphic to the category of...
Show moreThis work can be roughly divided into two parts. Initially, it may be considered a continuation of the very interesting research on the topic of Lattice-Valued Convergence Spaces given by Jäger [2001, 2005]. The alternate axioms presented here seem to lead to theorems having proofs more closely related to standard arguments used in Convergence Space theory when the Lattice is L=.Various Subcategories are investigated. One such subconstruct is shown to be isomorphic to the category of Lattice Valued Fuzzy Convergence Spaces defined and studied by Jäger . Our principal category is shown to be a topological universe and contains a subconstruct isomorphic to the category of probabilistic convergence spaces discussed in Kent and Richardson when L=. Fundamental work in lattice-valued convergence from the more general perspective of monads can be found in Gähler . Secondly, diagonal axioms are defined in the category whose objects consist of all the lattice valued convergence spaces. When the latter lattice is linearly ordered, a diagonal condition is given which characterizes those objects in the category that are determined by probabilistic convergence spaces which are topological. Certain background information regarding filters, convergence spaces, and diagonal axioms with its dual are given in Chapter 1. Chapter 2 describes Probabilistic Convergence and associated Diagonal axioms. Chapter 3 defines Jäger convergence and proves that Jäger's construct is isomorphic to a bireflective subconstruct of SL-CS. Furthermore, connections between the diagonal axioms discussed and those given by Gähler are explored. In Chapter 4, further categorical properties of SL-CS are discussed and in particular, it is shown that SL-CS is topological, cartesian closed, and extensional. Chapter 5 explores connections between diagonal axioms for objects in the sub construct δ(PCS) and SL-CS. Finally, recommendations for further research are provided.
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Date Issued
2007
Identifier
CFE0001715, ucf:47292
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0001715
Application of Modeling and Simulation to Reduce Costs of Acquisition within Triple Constraints
Title
Application of Modeling and Simulation to Reduce Costs of Acquisition within Triple Constraints.
Creator
Mohammad, Syed, Kincaid, John, Shumaker, Randall, Wiegand, Rudolf, Richardson, Paul, University of Central Florida
Abstract / Description
A key component of defense acquisition programs operating using the Integrated Defense Acquisition, Technology, and Logistics Life Cycle Management System is the reliance on the triple constraints of cost, schedule, and performance. While the use of Modeling and Simulation tools and capabilities is prevalent and well established in the Research and Development, Analysis, and Training domains, acquisition programs have been reluctant to use Modeling and Simulation in any great depth due to...
Show moreA key component of defense acquisition programs operating using the Integrated Defense Acquisition, Technology, and Logistics Life Cycle Management System is the reliance on the triple constraints of cost, schedule, and performance. While the use of Modeling and Simulation tools and capabilities is prevalent and well established in the Research and Development, Analysis, and Training domains, acquisition programs have been reluctant to use Modeling and Simulation in any great depth due to inaccessibility of tools, Subject Matter Experts, and implications to cost and schedule. This presents a unique Simulation Management challenge which requires an in-depth understanding of the technical capabilities available within an organization, their applicability to support immediate needs, and the flexibility to utilize these capabilities within the programmatic environment to provide a value added service. The focus of this dissertation is to study the use of Modeling and Simulation in the Defense arena, and to review the applicability of Modeling and Simulation within programmatic acquisition environments which are constrained by cost, schedule, and performance. This research draws comparisons between Modeling and Simulation to other Process Improvement initiatives, such as Lean and Six Sigma, and reviews case studies involving the application of Modeling and Simulation within triple constrained environments. The development of alternate scenarios allows cost benefit analysis to be conducted for each scenario and alternate scenario, developing a case for whether or not the application of Modeling and Simulation within the triple constrained environment delivered any consequential benefit to the acquisition process. Observations are made regarding the level of Modeling and Simulation as applied within each case study, and generalized recommendations are made for the inclusion of cost benefit analysis methodologies for analyzing proposed Modeling and Simulation activities within acquisition programs. Limitations and shortcomings of the research activity are discussed, along with recommendations for potential future work in the Simulation Management field, both with respect to the specific case studies reviewed in this study and the general field.
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Date Issued
2012
Identifier
CFE0004415, ucf:49396
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0004415