### Localized Radial Solutions for Nonlinear p-Laplacian Equation in RN

**Date:**May 2008

**Creator:**Pudipeddi, Sridevi

**Description:**We establish the existence of radial solutions to the p-Laplacian equation ∆p u + f(u)=0 in RN, where f behaves like |u|q-1 u when u is large and f(u) < 0 for small positive u. We show that for each nonnegative integer n, there is a localized solution u which has exactly n zeros. Also, we look for radial solutions of a superlinear Dirichlet problem in a ball. We show that for each nonnegative integer n, there is a solution u which has exactly n zeros. Here we give an alternate proof to that which was given by Castro and Kurepa.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc6059/

### Infinite Planar Graphs

**Date:**May 2000

**Creator:**Aurand, Eric William

**Description:**How many equivalence classes of geodesic rays does a graph contain? How many bounded automorphisms does a planar graph have? Neimayer and Watkins studied these two questions and answered them for a certain class of graphs. Using the concept of excess of a vertex, the class of graphs that Neimayer and Watkins studied are extended to include graphs with positive excess at each vertex. The results of this paper show that there are an uncountable number of geodesic fibers for graphs in this extended class and that for any graph in this extended class the only bounded automorphism is the identity automorphism.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc2545/

### Determining Properties of Synaptic Structure in a Neural Network through Spike Train Analysis

**Date:**May 2007

**Creator:**Brooks, Evan

**Description:**A "complex" system typically has a relatively large number of dynamically interacting components and tends to exhibit emergent behavior that cannot be explained by analyzing each component separately. A biological neural network is one example of such a system. A multi-agent model of such a network is developed to study the relationships between a network's structure and its spike train output. Using this model, inferences are made about the synaptic structure of networks through cluster analysis of spike train summary statistics A complexity measure for the network structure is also presented which has a one-to-one correspondence with the standard time series complexity measure sample entropy.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc3702/

### Analysis Of Sequential Barycenter Random Probability Measures via Discrete Constructions

**Date:**December 2002

**Creator:**Valdes, LeRoy I.

**Description:**Hill and Monticino (1998) introduced a constructive method for generating random probability measures with a prescribed mean or distribution on the mean. The method involves sequentially generating an array of barycenters that uniquely defines a probability measure. This work analyzes statistical properties of the measures generated by sequential barycenter array constructions. Specifically, this work addresses how changing the base measures of the construction affects the statististics of measures generated by the SBA construction. A relationship between statistics associated with a finite level version of the SBA construction and the full construction is developed. Monte Carlo statistical experiments are used to simulate the effect changing base measures has on the statistics associated with the finite level construction.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc3304/

### Developing Criteria for Extracting Principal Components and Assessing Multiple Significance Tests in Knowledge Discovery Applications

**Date:**August 1999

**Creator:**Keeling, Kellie Bliss

**Description:**With advances in computer technology, organizations are able to store large amounts of data in data warehouses. There are two fundamental issues researchers must address: the dimensionality of data and the interpretation of multiple statistical tests. The first issue addressed by this research is the determination of the number of components to retain in principal components analysis. This research establishes regression, asymptotic theory, and neural network approaches for estimating mean and 95th percentile eigenvalues for implementing Horn's parallel analysis procedure for retaining components. Certain methods perform better for specific combinations of sample size and numbers of variables. The adjusted normal order statistic estimator (ANOSE), an asymptotic procedure, performs the best overall. Future research is warranted on combining methods to increase accuracy. The second issue involves interpreting multiple statistical tests. This study uses simulation to show that Parker and Rothenberg's technique using a density function with a mixture of betas to model p-values is viable for p-values from central and non-central t distributions. The simulation study shows that final estimates obtained in the proposed mixture approach reliably estimate the true proportion of the distributions associated with the null and nonnull hypotheses. Modeling the density of p-values allows for better control of ...

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc2231/

### An Empirical Investigation of Portfolios with Little Idiosyncratic Risk

**Date:**May 2004

**Creator:**Benjelloun, Hicham

**Description:**The objective of this study is to answer the following research question: How large is a diversified portfolio? Although previous work is abundant, very little progress has been made in answering this question since the seminal work of Evans and Archer (1968). This study proposes two approaches to address the research question. The first approach is to measure the rate of risk reduction as diversification increases. For the first approach, I identify two kinds of risks: (1) risk that portfolio returns vary across time (Evans and Archer (1968), and Campbell et al. (2001)); and (2) risk that returns vary across portfolios of the same size (Elton and Gruber (1977), and O'Neil (1997)). I show that the times series risk reaches an asymptote as portfolio size increases. Cross sectional risk, on the other hand, does not appears to reach an asymptote as portfolio size increases. The second approach consists of comparing portfolios' performance to a benchmark portfolio that is assumed to be diversified (Statman (1987)). I develop a performance index. The performance index is calculated, for any given test portfolio, as the ratio of the Sharpe-like measure of the test portfolio to the Sharpe-like measure of the benchmark portfolio that is ...

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc4536/

### Landscape forest modeling of the Luquillo Experimental Forest, Puerto Rico.

**Date:**December 2002

**Creator:**Abbott-Wood, Chris

**Description:**This thesis contributes to modeling the dynamics of forest community response to environmental gradients and disturbances over a mountain landscape. A gap model (FACET) was parameterized for species of various forest types (Tabonuco, Colorado, Dwarf and Palm), for many terrain conditions and was modified and extended to include species response to excess soil moisture and hurricanes. Landscape cover types were defined by dominance of species of each forest type and canopy height. Parameters of the landscape model (MOSAIC) were calculated from multiple runs of FACET. These runs were determined by combining terrain variables (elevation and soil) and hurricane risk. MOSAIC runs were analyzed for distribution patterns. Geographic Information Systems software was used to process terrain variables, hurricane risk and MOSAIC model output.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc3362/

### Cycles and Cliques in Steinhaus Graphs

**Date:**December 1994

**Creator:**Lim, Daekeun

**Description:**In this dissertation several results in Steinhaus graphs are investigated. First under some further conditions imposed on the induced cycles in steinhaus graphs, the order of induced cycles in Steinhaus graphs is at most [(n+3)/2]. Next the results of maximum clique size in Steinhaus graphs are used to enumerate the Steinhaus graphs having maximal cliques. Finally the concept of jumbled graphs and Posa's Lemma are used to show that almost all Steinhaus graphs are Hamiltonian.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc278469/

### Three Essays in Corporate Governance

**Date:**December 1993

**Creator:**Forjan, James M. (James Martin)

**Description:**Corporate governance issues have become increasingly important to financial managers and shareholders. Firms that are plagued by poor performance, incompetent managers, or excess agency costs have become the subject of a dramatic increase in shareholder activism. Dissident shareholders, who are unable to launch costly takeover bids or proxy contests, have initiated a process of governance reform through the use of shareholder sponsored proposals. Shareholder proposals are a direct attempt to reverse operating or voting policies, such as a proposal to repeal a classified board. Managers announce shareholder proposals in a proxy statement and typically include a vote recommendation against the proposal. In the first essay, I find an unfavorable stock price reaction to the announcement of a shareholder proposal. In some cases, however, management supports the proposal and negotiates an agreement with the proposing shareholder. Stock prices react favorably to a settlement announcement. If managers are willing to negotiate with shareholders, they are perceived to be acting in the best interest of shareholders. If managers are unwilling, shareholders believe a severe agency problem exists. In the second essay, the effect that ownership structure has on voting outcomes of shareholder proposals is examined. I find a direct relationship between the percentage ...

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc279351/

### Applications of Rapidly Mixing Markov Chains to Problems in Graph Theory

**Date:**August 1993

**Creator:**Simmons, Dayton C. (Dayton Cooper)

**Description:**In this dissertation the results of Jerrum and Sinclair on the conductance of Markov chains are used to prove that almost all generalized Steinhaus graphs are rapidly mixing and an algorithm for the uniform generation of 2 - (4k + 1,4,1) cyclic Mendelsohn designs is developed.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc277740/