Physical Sciences and Mathematics Commons^™

Calculating The Conformal Modulus Of Complex Tori And An Application To Graph Theory, Jason Howard

Masters Theses

In 1985 William Thurston conjectured that conformal mappings could be approximated using infintessimal circles. With this, the area of mathematics called Cirle Packing was born. The advantage of this technique is that it gives a computational method of understanding manifolds. In particular, we attempt to gain some insight of complex tori via Circle Packing. In practice, it is difficult to imagine what these tori look like. Computational techniques of Circle Packing will help us visualise these tori as points in moduli space by beginning with an initial triangulation of the torus. We then experiment with triangulations on a set number …

Individual-Based Modeling: Comparing Model Outputs To Telemetry Data With Application To The Florida Panther, Dinesh Raj Sharma

Masters Theses

Mean distance of the locations of an animal from the boundaries of its home range was presented as a measure of its space-use preference. Methods for evaluating the predictive ability of an individual-based model were also presented. These methods were applied to data on the Florida panther and some interesting results were obtained.

A strong negative correlation was observed between age and home range size of the panther, indicating constrained mobility of the panther during its old age. Space-use preference was also highly dependent on age of the panther. A general trend was found for panthers, which indicates they stay …

Theoretical Issues In The Economics Of International Trade And Environment., Meeta Keswani Mehra Dr.

Doctoral Theses

In the wake of substantial trade liberalization in the world economy over the last two decades and growing environmental consciousness, the issues of the impacts of international goods trade and foreign direct investment (FDI) on local and global environment are becoming increasingly contentious. Whilst trade and FDI have been said to bring higher incomes and well-being for all, these are seen to act as "magnifiers" of environmental deterioration - especially in the developing countries. On the other hand, growing environmentalism is perceived to act as an impediment to freer trade and investment flows across countries. Hence, the central issues are …

Environmental Regulation In The Presence Of Environmentally Conscious Consumers., Sangeeta Bansal Dr.

Doctoral Theses

The Problem and Literature Review There is a growing concern for the environmental degradation caused by various economic activities. Clean environment, once regarded as a free good, has now become a scarce resource due to cumulative accumulation of pollution over the years. Being a public good, it may not be possible to assign clear property rights to environment. Hence, even though it has become a scarce resource, economic agents continue to regard it as a free good and tend to ignore the harmful effects of their activities on the environment. This causes a distortion between the market and socially optimal …

Pattern Recognition For Electric Power System Protection, Yong Sheng

Doctoral Dissertations

The objective of this research is to demonstrate pattern recognition tools such as decision trees (DTs) and neural networks that will improve and automate the design of relay protection functions in electric power systems. Protection functions that will benefit from the research include relay algorithms for high voltage transformer protection (TP) and for high impedance fault (HIF) detection. A methodology, which uses DTs and wavelet analysis to distinguish transformer internal faults from other conditions that are easily mistaken for internal faults, has been developed. Also, a DT based solution is proposed to discriminate HIFs from normal operations that may confuse …

Optimal Path Planning And The Fast Marching Method, J. J. Clark

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

The problem of determining an optimal path for an object moving through some obstacle space presents several nontrivial subproblems. The foremost being the computational complexity that is involved and how to best deal with the associated large data volume. For example, a non-symmetric object moving in three dimensions possesses six degrees of freedom. This can lead to a computational grid that may easily be on the order of 10¹². Furthermore, for every point in the computational domain, several complex calculations must be performed. These include performing tests to determine if the object and obstacles intersect, and numerically solving …

Separable Preference Orders, Jonathan K. Hodge

Dissertations

Whenever a decision-maker must express simultaneously his or her preferences on several possibly related issues, the existence of interdependence among these preferences can lead to collective decisions that are unsatisfactory or even paradoxical. Intuitively, an individual’s preferences are said to be separable on a subset of issues if they do not depend on the choice of alternatives for issues outside the subset. Here we explore from a mathematical standpoint the properties of separable and nonseparable preference orders. We begin by formulating a general model of multidimensional preferences and we formally introduce the notions of separability and noninfluentiality. We study the …

Nearly Balanced And Resolvable Block Designs, Brian Henry Reck

Mathematics & Statistics Theses & Dissertations

One of the fundamental principles of experimental design is the separation of heterogeneous experimental units into subsets of more homogeneous units or blocks in order to isolate identifiable, unwanted, but unavoidable, variation in measurements made from the units. Given v treatments to compare, and having available b blocks of k experimental units each, the thoughtful statistician asks, “What is the optimal allocation of the treatments to the units?” This is the basic block design problem. Let n_ij be the number of times treatment i is used in block j and let N be the v x b matrix N …

Nonlinear Interfacial Stability Of Core-Annular Film Flows In The Presence Of Surfactants, Said A. Kas-Danouche

Dissertations

This work is an analytical and computational study of the nonlinear interfacial instabilities found in core-annular flows in the presence of surfactants. Core-annular flows arise when two immiscible fluids (for example water and oil) are caused to flow in a pipe under the action of ail axial pressure gradient. In one typical type of flow regime, the fluids arrange themselves so that the less viscous (e.g. water) lies in the region of high shear near the pipe wall, with the more viscous fluid occupying the core region. Tech nologically, this arrangement provides an advantage since the highly viscous fluid is …

Temporal Synchronization Of Ca1 Pyramidal Cells By High-Frequency, Depressing Inhibition, In The Presence Of Intracellular Noise, Stephen A. Kunec

Dissertations

The Sharp Wave-associated Ripple is a high-frequency, extracellular recording observed in the rat hippocampus during periods of immobility. During the ripple, pyramidal cells synchronize over a short period of time despite the fact that these cells have sparse recurrent connections. Additionally, the timing of synchronized pyramidal cell spiking may be critical for encoding information that is passed on to post-hippocampal targets. Both the synchronization and precision of pyramidal cells is believed to be coordinated by inhibition provided by a vast array of interneurons. This dissertation proposes a minimal model consisting of a single interneuron which synapses onto a network of …

Instability Of Electrified Viscous Films, Knograt Savettaseranee

Dissertations

We examine the stability of a thin two-dimensional liquid film with a regular electric field applied in a direction parallel to an initially flat bounding fluid interface. We study the distinct physical effects of surface tension, van der Waals and electrically induced forces for a viscous incompressible fluid. The film is assumed to be sufficiently thin, and the surface tension and electrically induced forces are large enough that gravity can be ignored to the leading order. Our target is to analyse the nonlinear stability of the flow. We attain this by deriving and numerically solving a set of nonlinear evolution …

Slippage And Change Point Problem With Directional Data., Arnab Kumar Laha Dr.

Doctoral Theses

In this thesis we develop statistical methods for dealing with two problems namely (1) THE SLIPPAGE PROBLEM and (2) THE CHANGE POINT PROB- LEM in the set-up of directional data. In this chapter, we provide an intro- duction to these problems and discuss the importance of the present work. The slippage problem is basically a problem to detect whether any unspecified observation in a given random sample comes from a distribution different from that for all the other remaining observations. This can also be viewed as a problem of outlier detection or that of spuriosity. This problem assumes great importance …

Communicator-In-Chief: Presidential Use Of Television Past, Present, And Future, Jenna Wasson

Honors Theses

This thesis seeks to determine how television has changed as a communication medium for presidents over the past half century. An evaluation of the evolving ways presidents use television to communicate with and to build support from the American people has been conducted. Presidential communication strategies have been identified by drawing primarily from primary sources written by presidents and White House staff. Television technology and the television audience have changed over the years. Presidents have taken a more pro-active, aggressive role in their efforts to harness television for their own purposes. Why have these changes occurred? What impact have these …

N-Person Cooperative Game Theory Solutions, Coalitions, And Applications, Ragan Nicole Brackin

Masters Theses

This study explores the topic of N-person cooperative game theory. The following paper begins with an introduction to the basic definitions and the- orems of game theory. These definitions and theorems are then used to in- troduce various solution methods and methods of coalition formation. These results are then applied to the airport game, to the supplier-firm-buyer game, and to evolutionary games.

Using The Maple Computer Algebra System As A Tool For Studying Group Theory, Thomas Edmond Cooper, Iii

Masters Theses

The purpose of this study was to show that computers can be powerful tools for studying group theory. Specifically the author examined ways that the computer algebra system Maple can be used to assist in the study of group theory. The study consists of four main parts.

After a brief introduction in chapter one, chapter two discusses simple procedures written by the author to study small finite groups. These procedures rely on the fact that for small finite groups, the elements can all be stored on a computer and tested for various properties. All of the procedures are contained in …

Third Order Opial Inequalities, Brandi Michelle Gierhart

Masters Theses

The purpose of the thesis was to find extremals y and constants K for a basic problem and for several variations of the problem. The basic problem was the third order opial inequality. We proved the existence of an extremal of this problem and other related problems. We conjectured that the extremal was a quintic spline with at most one knot, then found the quintic splines and constants for the basic problem and several variations. Maple was an important tool in finding these extremals and constants due to the complexity of the equations. We also proved that these extremals can …

Optimal Control Problems In Pde And Ode Systems, Hem Raj Joshi

Doctoral Dissertations

This dissertation contains three separate optimal control problems involving partial differential equations (PDEs) or ordinary differential equations (ODEs). In each problem, an objective functional representing the goal of the control process is minimized. First, a system of ordinary differential equations which describe the interaction of Human Immunodeficiency Virus (HIV) and CD4+T-cells in the human immune system is studied. Two controls representing drug treatment strategies of this model are explored. Existence and uniqueness results for the optimal control pair are established. The optimality system is derived and then solved numerically using an iterative method with the Runge-Kutta fourth order scheme.

Second, …

On Reproducing Kernels And Invariant Subspaces Of The Bergman Shift, George Chailos

Doctoral Dissertations

No abstract provided.

Essays In Indian Corporate Finance., K. V. S. Vinay Dr.

Doctoral Theses

This thesis comprises of three essays in corporate finance focusing on the Indian economy. The first essay contains a theoretical model while the second and the third essays are empirical exercises. In the subsequent paragraphs of this section, we examine the broader issues to which the contents of the thesis contribute.The past few years have seen rising interest in studies of financial insti- tutions and corporate financial policies in countries other than the United States. One of the reasons for such a shift in attention is the diversity in the size and structure of financial arrangements all over the world. …

Fuzzy Product -Limit Estimators: Soft Computing In The Presence Of Very Small And Highly Censored Data Sets, Kian Lawrence Pokorny

Doctoral Dissertations

When very few data are available and a high proportion of the data is censored, accurate estimates of reliability are problematic. Standard statistical methods require a more complete data set, and with any fewer data, expert knowledge or heuristic methods are required. In the current research a computational system is developed that obtains a survival curve, point estimate, and confidence interval about the point estimate.

The system uses numerical methods to define fuzzy membership functions about each data point that quantify uncertainty due to censoring. The “fuzzy” data are then used to estimate a survival curve, and the mean survival …

Modeling And Experimental Verification Of Growth Of An Axisymmetric Cylindrical Rod By Three-Dimensional Laser-Induced Chemical Vapor Deposition, Qing Chen

Doctoral Dissertations

Three-dimensional laser-induced chemical vapor deposition (3D-LCVD) is a recently developed micro-manufacturing process that holds great potential for the production of complex microstructures with high aspect ratio. A laser beam is focused through a vacuum chamber window onto a movable substrate. The heat from the laser at or near the focal spot on the substrate induces the decomposition reaction of precursor gas in the chamber. As a result, solid-phase reaction products are deposited on the substrate to form the microstructure. In this dissertation, a numerical model is developed for simulating kinetically-limited growth of an axisymmetric cylindrical rod by pre-specifying the surface …

Self-Similarity In Network Traffic, Francisco Chinchilla

Honors Theses

It is critical to properly understand the nature of network traffic in order to effectively design models describing network behavior. These models are usually used to simulate network traffic, which in turn are used to construct congestion control techniques, perform capacity planning studies, and/or evaluate the behavior of new protocols. Using the wrong models could lead to potentially serious problems such as delayed packet transmissions or an increase in packet drop rates.

Traditionally, packet arrivals were assumed to follow a Poisson arrival process. Although Poisson processes have several properties that make them easy to work with, they do not accurately …

Zero-Cycles And K-Theory On Normal Surfaces., Amalendu Krishna Dr.

Doctoral Theses

The main theme of this thesis is to study the theory of algebraic cycles on singular varieties over a field. This has been studied before extensively by Collins, Barbieri-Viale, Levine, Srinivas among several others. Our interest in this thesis is to address some well known problems in the theory of zero-cycles over nominal varieties. The use of K- theoretic techniques in our proofs illustrate the interplay between the study of algebraic cycles and algebraic K-theory.For a quasi-projective surface X over a field k, we define FA,(X) to be the subgroup of the Grothendieck group Ko(X) of vector bundies generated by …

Essay On Trade In Goods And Factor Movements Under Increasing Returns To Scale., Brati Sankar Chakraborty Dr.

Doctoral Theses

The central issues that have engaged trade theorists from its inception can broadly be classified under three leads. First, to identify, what countries trade with each other, or what has come to be known as the question of pattern of trade. Second, the consequent gains that trade allows for. And the third, which is an immediate appendage to the second is to identify the redistribution of income due to trade.The first and the third, as is immediately evident, are issues in positive trade theory. The second is a normative issue, which evidently brings in questions of welfare change of the …

A New Theory Of Premixed Flames In Near-Stoichiometric Mixtures, Eliana S. Antoniou

Dissertations

In this dissertation, a new model of premixed flames in near-stoichiometric mixtures is derived. Unlike most previous theories, which are valid only for very lean or very rich, i.e. off-stoichiometric conditions, our model remains valid over the entire spectrum of mixture compositions, from lean to rich, including the near-stoichiometric regime. Since fuel-mixture composition is known to have a significant effect on flame behavior, such a model is expected to contribute new insights into classical problems in premixed combustion.

In the first part of this dissertation, we describe the derivation of a model for premixed flames in two-reactant mixtures in a …

Essays On Cooperative Behaviour And Collective Action., Anindya Bhattacharya Dr.

Doctoral Theses

This dissertation explores some issues concerning the behaviour of coalitions of individuals in a game theoretic set-up and also studies one aspect of a society facing collective action of the masses. The common feature of the issues explored in the dissertation is that it investigates the properties of stable social states. Chapter 2 introduces a notion of a social state that is unlikely to be displaced by any coalition of agents endowed with a certain notion of rationality and a certain degree of farsightedness and explores the properties of such states. Chapter 3 is also concerned with coalitionally stable social …

A Recommendation For Determining The Efficacy Of Weight Removal Estimates For The Pacific Cod Longline Cdq Fishery, Anna L. Furniss

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

In January 2000, the Alaska Department of Community and Economic Development contacted the National Marine Fisheries Service (NMFS) regarding concerns over the methods used to determine catch estimates for the Pacific Cod Community Development Quota (CDQ) fishery. Currently, NMFS determines catch estimates for the Pacific Cod CDQ fishery based on the data collected by observers from the North Pacific Groundfish Observer Program (NPGOP).

Observer estimates for catch are based on the random sampling methods for a longline fishing vessel as described in the North Pacific Groundfish Observer Manual. These sampling methods provide an official total catch (OTC) estimate for each …

The Classification Of Low Dimensional Nilpotent Lie Algebras, Kimberli C. Tripp

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Nilpotent Lie algebras are the fundamental building blocks for generic (not semi-simple) Lie algebras. In particular, the classification of nilpotent algebras is the first step in classifying and identifying solvable Lie Algebras. The problem of classifying nilpotent Lie algebras was first studied by Umlauf [9] in 1891. More recently, classifications have been given up to dimension six using different techniques by Morosov (1958) [7], Skjelbred and Sund (1977) [8], and up to dimension five by Dixmier (1958) [2]. Using Morosov's method of classification by maximal abelian ideals, Winternitz reproduced the Morosov classification obtaining different canonical forms for the algebras. The …

1p Spaces, Anh Tuyet Tran

Theses Digitization Project

In this paper we will study the 1p spaces. We will begin with definitions and different examples of 1p spaces. In particular, we will prove Holder's and Minkowski's inequalities for 1p sequence.

Fundamental Theorem Of Algebra, Paul Shibalovich

Theses Digitization Project

The fundamental theorem of algebra (FTA) is an important theorem in algebra. This theorem asserts that the complex field is algebracially closed. This thesis will include historical research of proofs of the fundamental theorem of algebra and provide information about the first proof given by Gauss of the theorem and the time when it was proved.