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Gradient Flows, Convexity, and Adjoint Orbits
(2012-06-19)
This dissertation studies some matrix results and gives their Generalizations in the context of semisimple Lie groups. The adjoint orbit is the primary object in our study.
The dissertation consists of four chapters. ...
Cycle Systems
(2012-01-18)
In this dissertation the author has found the necessary and sufficient conditions for obtaining a 6-cycle system of the Cartesian product of two complete graphs covering 2-paths in the corresponding bipartite graph. She ...
A Robust Version of Hotelling's T2 Control Chart for Retrospective Location Analysis of Individuals Using BACON Estimators
(2012-02-13)
Hotelling's T2 chart is commonly used for Phase I analysis of individual multivariate normally distributed data. However, the presence of only a few outliers can significantly distort classical estimates of location and ...
Simple Techniques for Detecting Decomposability or Indecomposability of Generalized Inverse Limits
(2012-05-01)
A continuum X is said to be decomposable if it can be written as a union of two proper subcontinua; otherwise, X is said to be indecomposable. For years, topologists have used inverse limits with continuous bonding functions ...
Rank-Based Regression for Nonlinear and Missing Response Models
(2012-07-09)
This dissertation is mainly concerned with the rank-based estimation of model parameters in complex regression models: a general nonlinear regression model and a semi-parametric regression model with missing responses. For ...
Upper Bounds on the Coarsening Rates for Some Non-Conserving Equations
(2012-08-02)
In this thesis, we prove one-sided bounds on the coarsening rates for two models of
non-conserved curvature driven dynamics by following a strategy developed by Kohn and
Otto in [20].
In the rst part, we analyze the ...
Security, (F,I)-security, and Ultra-security in Graphs
(2012-08-02)
Let G=(V,E) be a graph and S a subset of V. The notion of security in graphs was first presented by Brigham et al [3]. A set S is secure if every attack on S is defendable. The cardinality of a smallest secure set of G ...
Nim on Graphs
(2012-08-02)
Winning strategies for the Game of Nim on Graphs are discussed. Graphs considered are distinguished from those previously studied in that they may have loops. Winning strategies are found for graphs that have loops and ...
A New Solution to the Intersection Problem of Mendelsohn Triple Systems
(2012-03-29)
The thesis provides an alternate solution to the intersection problem, in which the goal is to determine the set of all values for which there exists a pair of Mendelsohn Triple Systems having this exact value of cyclic ...
The Metamorphosis of Maximum Packings of 2Kn with Triples into Maximum Packings of 2Kn with 4-cycles
(2012-05-07)
In this work, the problem of constructing a maximum packing of 2Kn with triples having a metamorphosis into a maximum packing of 2Kn with 4-cycles is concluded by solving the problem for every n ≥ 11 such that n ≡ 2, 5, ...