Physical Sciences and Mathematics Commons^™

Empirical Determination And Forecastability Of Foreign Exchange Rate Of India., Rituparna Kar Dr.

Doctoral Theses

The first chapter of this thesis begins with a brief review of the existing literature on foreign exchange rate models and their forecasting performance. Thereafter it presents the motivation as well as the main aspects of this study. The format of this chapter is as follows. A brief review of the relevant literature is presented in the first section. This review includes the important theoretical / structural as well as time series models of exchange rate. The motivation of the thesis is discussed in Section 1.2. Section 1.3 presents a brief account of the Indian economic reforms since 1993 with …

Midwave Infrared Imaging Fourier Transform Spectrometry Of Combustion Plumes, Kenneth C. Bradley

Theses and Dissertations

A midwave infrared (MWIR) imaging Fourier transform spectrometer (IFTS) was used to successfully capture and analyze hyperspectral imagery of combustion plumes. Jet engine exhaust data from a small turbojet engine burning diesel fuel at a flow rate of 300 cm³/min was collected at 1 cm⁻¹ resolution from a side-plume vantage point on a 200x64 pixel window at a range of 11.2 meters. Spectral features of water, CO, and CO² were present, and showed spatial variability within the plume structure. An array of thermocouple probes was positioned within the plume to aid in temperature analysis. A single-temperature …

Some Contributions In Statistical Discrimination Of Different Pathogens Using Observations Through Ftir, Dongmei Wang

Mathematics Theses

Fourier Transform Infrared (FTIR) has been use to discriminate different pathogens by signals from cells infected with these versus normal cells as references. To do the statistical analysis, Partial Least Square Regression (PLSR) was utilized to distinguish any two kinds of virus‐infected cells and normal cells. Validation using Bootstrap method and Cross‐validations were employed to calculate the shrinkages of Area Under the ROC Curve (AUC) and specificities corresponding to 80%, 90%, and 95% sensitivities. The result shows that our procedure can significantly discriminate these pathogens when we compare infected cells with the normal cells. On the height of this success, …

Theoretical And Numerical Study Of Tikhonov's Regularization And Morozov's Discrepancy Principle, Marygeorge L. Whitney

Mathematics Theses

A concept of a well-posed problem was initially introduced by J. Hadamard in 1923, who expressed the idea that every mathematical model should have a unique solution, stable with respect to noise in the input data. If at least one of those properties is violated, the problem is ill-posed (and unstable). There are numerous examples of ill- posed problems in computational mathematics and applications. Classical numerical algorithms, when used for an ill-posed model, turn out to be divergent. Hence one has to develop special regularization techniques, which take advantage of an a priori information (normally available), in order to solve …

Analyzing Gene Expression Data In Terms Of Gene Sets: Gene Set Enrichment Analysis, Wei Li

Mathematics Theses

The DNA microarray biotechnology simultaneously monitors the expression of thousands of genes and aims to identify genes that are differently expressed under different conditions. From the statistical point of view, it can be restated as identify genes strongly associated with the response or covariant of interest. The Gene Set Enrichment Analysis (GSEA) method is one method which focuses the analysis at the functional related gene sets level instead of single genes. It helps biologists to interpret the DNA microarray data by their previous biological knowledge of the genes in a gene set. GSEA has been shown to efficiently identify gene …

Analysis Of The Total Food Folate Intake Data From The National Health And Nutrition Exa-Amination Survey (Nhanes) Using Generalized Linear Model, Kyung Ah Lee

Mathematics Theses

The National health and nutrition examination survey (NHANES) is a respected nation-wide program in charge of assessing the health and nutritional status of adults and children in United States. Recent cal research found that folic acid play an important role in preventing baby birth defects. In this paper, we use the generalized estimating equation (GEE) method to study the generalized linear model (GLM) with compound symmetric correlation matrix for the NHANES data and investigate significant factors to ence the intake of food folic acid.

Comparative Studies Between Robotic Laparoscopic Myomectomy And Abdominal Myomectomy With Factors Affecting Short-Term Surgical Outcomes, Amy N. Fomo

Mathematics Theses

The purpose of this study is to compare short-term surgical outcomes of robotic and abdominal myomectomy and to analyze the factors affecting the total operative time, estimated blood loss and length of hospital stay from a retrospective study of a consecutive case series of 122 pa-tients with symptomatic leiomyomata. Wilcoxon, t tests, multiple linear and logistic regressions analyses were performed. Patients in abdominal group had larger number of leiomyomata, larger tumor size and BMI. The operative time was longer in robotic group and was affected by the size and number of tumors, parity and interaction between parity and BMI. Estimated …

Exploring Some Inattended Affective Factors In Performing Nonroutine Mathematical Tasks, John Douglas Butler

Master's Theses, Dissertations, Graduate Research and Major Papers Overview

Describes students' attempts to solve nonroutine math problems and explores possible correlates of their performance, focusing on inattended (i.e., intentionally avoided) dimensions underrepresented in the literature, including attitudes, interests, values, aesthetics, metacognition, and representation. Analyzes objective and subjective data gathered from a sample of 9th-grade students at a high school in Rhode Island. Finds strong evidence of students' math-aesthetics in problem solving.

A Comparison Theorem For The Topological And Algebraic Classification Of Quaternionic Toric 8-Manifolds, Piotr Runge

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

In order to discuss topological properties of quaternionic toric 8-manifolds, we introduce the notion of an algebraic morphism in the category of toric spaces. We show that the classification of quaternionic toric 8-manifolds with respect to an algebraic isomorphism is finer than the oriented topological classification. We construct infinite families of quaternionic toric 8-manifolds in the same oriented homeomorphism type but algebraically distinct. To prove that the elements within each family are of the same oriented homeomorphism type, and that we have representatives of all such types of a quaternionic toric 8-manifold, we present and use a method of evaluating …

Intersection Numbers, Embedded Spheres And Geosphere Laminations For Free Groups., Suhas Pandit Dr.

Doctoral Theses

Topological and geometric methods have played a major role in the study of infinite groups since the time of Poincar´e and Klein, with the work of Nielsen, Dehn, Stallings and Gromov showing particularly deep connections with the topology of surfaces and three-manifolds. This is in part because a surface or a 3-manifold is essentially determined by its fundamental group, and has a geometric structure due to the Poincar´e-K¨obe-Klein uniformisation theorem for surfaces and Thurston’s geometrisation conjecture, which is now a theorem of Perelman, for 3-manifolds.A particularly fruitful instance of such an interplay is the relation between intersection numbers of simple …

Hokua – A Wavelet Method For Audio Fingerprinting, Steven S. Lutz

Theses and Dissertations

In recent years, multimedia identification has become important as the volume of digital media has dramatically increased. With music files, one method of identification is audio fingerprinting. The underlying method for most algorithms is the Fourier transform. However, due to a lack of temporal resolution, these algorithms rely on the short-time Fourier transform. We propose an audio fingerprinting algorithm that uses a wavelet transform, which has good temporal resolution. In this thesis, we examine the basics of certain topics that are needed in understanding audio fingerprinting techniques. We also look at a brief history of work done in this field. …

Comparing Cognitive Decision Models Of Iowa Gambling Task In Indivituals Following Temporal Lobectomy, Jenny Vennukkah Jeyarajah

Mathematics Theses

This study examined the theoretical basis for decision making behavior of patients with right or left temporal lobectomy and a control group when they participated in the Iowa Gambling Task. Two cognitive decision models, Expectancy Valence Model and Strategy Switching Heuristic Choice Model, were compared for best fit. The best fitting model was then chosen to provide the basis for parameter estimation (sources of decision making, i.e. cognitive, motivational, and response processes) and interpretation. Both models outperformed the baseline model. However comparison of G2 means between the two cognitive decision models showed the expectancy valence model having a higher mean …

Growth And Geodesics Of Thompson's Group F, Jennifer L. Schofield

Theses and Dissertations

In this paper our goal is to describe how to find the growth of Thompson's group F with generators a and b. Also, by studying elements through pipe systems, we describe how adding a third generator c affects geodesic length. We model the growth of Thompson's group F by producing a grammar for reduced pairs of trees based on Blake Fordham's tree structure. Then we change this grammar into a system of equations that describes the growth of Thompson's group F and simplify. To complete our second goal, we present and discuss a computer program that has led to some …

Banach Spaces On Infinitely Branching Trees, Annette B. Locke

Electronic Theses and Dissertations

An example of a Banach space, X_∞, with a nonseparable dual such that l₁ does not imbed in X_∞ is investigated. Not every weakly null sequence has a subsequence equivalent to the usual basis of c₀, but c₀ imbeds in many subspaces of X_∞. The space l₁ does imbed in X_∞^∗, the dual space of X_∞, yet weakly converging sequences in X_∞^∗ need not converge in norm.

Model Reduction For Simulation, Optimization And Control, Oleg Edward Roderick

Dissertations and Theses

Many tasks of simulation, optimization and control can be performed more efficiently if the intermediate complexity of the numerical model is reduced. In our work, we investigate model reduction, as applied to reaction-transport systems of atmospheric chemistry. We use a Proper Orthogonal Decomposition-based approach to extract information from a set of model observations, and to project the model equations onto a reduced order space chosen in such a way that the essential model behavior is preserved in the solution of the reduced version. We examine and improve many features of the method. In particular, we show how to measure sensitivities …

The Multilevel Structures Of Nurbs And Nurblets On Intervals, Weiwei Zhu

Dissertations

This dissertation is concerned with the problem of constructing biorthogonal wavelets based on non-uniform rational cubic B-Splines on intervals. We call non-uniform rational B-Splines ``NURBs", and such biorthogonal wavelets ``NURBlets". Constructing NURBlets is useful in designing and representing an arbitrary shape of an object in the industry, especially when exactness of the shape is critical such as the shape of an aircraft. As we know presently most popular wavelet models in the industry are approximated at boundaries. In this dissertation a new model is presented that is well suited for generating arbitrary shapes in the industry with mathematical exactness throughout …

Geometric Characterization Of Digital Objects: Algorithms And Applications To Image Analysis., Arindam Biswas Dr.

Doctoral Theses

Several problems of characterizing a digital object, and particularly, those related to boundary description, have been studied in this thesis. New algorithms and their applications to various aspects of image analysis and retrieval have been reported. A combinatorial technique for constructing the outer and inner isothetic covers of a digital object has been developed. The resolution of the background 2D grid can be changed by varying the grid spacing, and this procedure can be used to extract shape and topological information about the object. Next, an algorithm has been designed for constructing the orthogonal (convex) hull of a digital object …

On The Discrete Differential Geometry Of Surfaces In S4, George Shapiro

Open Access Dissertations

The Grassmannian space GC(2, 4) embedded in CP5 as the Klein quadric of twistor theory has a natural interpretation in terms of the geometry of “round” 2-spheres in S4. The incidence of two lines in CP3 corresponds to the contact properties of two 2- spheres, where contact is generalized from tangency to include “half-tangency:” 2-spheres may be in contact at two isolated points. There is a connection between the contact properties of 2-spheres and soliton geometry through the classical Ribaucour and Darboux transformations. The transformation theory of surfaces in S4 is investigated using the recently developed theory of “Discrete Differential …

Reduced Order Models For Fluid-Structure Interaction Systems By Mixed Finite Element Formulation, Ye Yang

Dissertations

In this work, mixed finite element formulations are introduced for acoustoelastic fluid- structure interaction (FSI) systems. For acoustic fluid, in addition to displacement- pressure (u/p) mixed formulation, a three-field formulation, namely, displacement-pressure-vorticity moment formulation (u - p -Λ) is employed to eliminate some zero frequencies. This formulation is introduced in order to compute the coupled frequencies without the contamination of nonphysical spurious non-zero frequencies. Furthermore, gravitational forces are introduced to include the coupled sloshing mode. In addition, u/p mixed formulation is the first time employed in solid. The numerical examples will demonstrate that the mixed formulations are capable of predicted …

Normal Surfaces And Heegaard Splittings Of 3-Manifolds., Tejas Kalelkar Dr.

Doctoral Theses

This thesis deals with various questions regarding normal surfaces and Heegaard splittings of 3-manifolds.Chapter 1The first chapter is divided into two parts. In the first, we give an outline of normal surface theory and mention some of its important applications. The second part gives an overview of the theory of Heegaard splitting surfaces and a few of its applications. None of the material covered in this chapter is original and it is meant solely as an exposition of known results.Chapter 2In this chapter, we give a lower bound on the Euler characteristic of a normal surface, a topological invariant, in …

Application Of Dual-Tree Complex Wavelet Transforms To Burst Detection And Rf Fingerprint Classification, Randall W. Klein

Theses and Dissertations

This work addresses various Open Systems Interconnection (OSI) Physical (PHY) layer mechanisms to extract and exploit RF waveform features (”fingerprints”) that are inherently unique to specific devices and that may be used to provide hardware specific identification (manufacturer, model, and/or serial number). This is addressed by applying a Dual-Tree Complex Wavelet Transform (DT-CWT) to improve burst detection and RF fingerprint classification. A ”Denoised VT” technique is introduced to improve performance at lower SNRs, with denoising implemented using a DT-CWT decomposition prior to Traditional VT processing. A newly developed Wavelet Domain (WD) fingerprinting technique is presented using statistical WD fingerprints with …

Human Capital And Economic Growth: Theory And Policy., Bidisha Chakraborty Dr.

Doctoral Theses

Growth theory is one of the most important branches of macroeconomics. Growth theory helps us to understand the intertemporal behaviour of a dynamic economy and to understand the properties of the long-run rate of economic growth. It identifies the factors causing the deviation of the actual rate of growth from the socially efficient rate of growth and analyses the effectiveness of various policies in removing this gap. It analyses the condition of stability of the long-run equilibrium and also attempts to establish links between the long run equilibrium and the persistence of underdevelopment.With the emergence of the ‘new’ growth theory, …

The Last Of The Mixed Triple Systems., Ernest Jum

Electronic Theses and Dissertations

In this thesis, we consider the decomposition of the complete mixed graph on v vertices denoted M_v, into every possible mixed graph on three vertices which has (like M_v) twice as many arcs as edges. Direct constructions are given in most cases. Decompositions of theλ-fold complete mixed graph λM_v, are also studied.

Independent Domination In Complementary Prisms., Joel Agustin Gongora

Electronic Theses and Dissertations

Let G be a graph and G̅ be the complement of G. The complementary prism GG̅ of G is the graph formed from the disjoint union of G and G̅ by adding the edges of a perfect matching between the corresponding vertices of G and G̅. For example, if G is a 5-cycle, then GG̅ is the Petersen graph. In this paper we investigate independent domination in complementary prisms.

A Dna Approach To The Road-Coloring Problem, Arindam Roy

Theses and Dissertations - UTB/UTPA

The Road-Coloring Problem in graph theory can be stated as follows: Is any irreducible aperiodic directed graph with constant outdegree 2 road-colorable? In other words, does such a graph have a synchronizing instruction? That is to say: can we label (or color) the two outgoing edges at each vertex, one with “b” or blue color and the other with “r” or red color, in such a manner that there will be an instruction in the form of a finite sequence in “b”s and “r”s (example: rrbrbbbr) such that this instruction will lead each vertex to the same “target” vertex? This …

Solvability Characterizations Of Pell Like Equations, Jason Smith

Boise State University Theses and Dissertations

Pell's equation has intrigued mathematicians for centuries. First stated as Archimedes' Cattle Problem, Pell's equation, in its most general form, X² – P • Y² = 1, where P is any square free positive integer and solutions are pairs of integers, has seen many approaches but few general solutions. The eleventh century Indian mathematician Bhaskara solved X² – 61 • Y² = 1 and, in response to Fermat's challenge, Wallis and Brouncker gave solutions to X² – 151 • Y² = 1 and X² –313 • Y² = 1. Fermat claimed to …

Transparency In Formal Proof, Cap Petschulat

Boise State University Theses and Dissertations

The oft-emphasized virtue of formal proof is correctness; a machine-checked proof adds greatly to our confidence in a result. But the rigors of formalization give rise to another possible virtue, namely clarity. Given the state of the art, clarity and formality are at odds: complexity of formalization obscures the content of proof. To address this, we develop a notion of proof strategies which extend the well-known notion of proof tactics. Beginning with the foundations of logic, we describe the methods and structures necessary to implement proof strategies, concluding with a proof-of-concept implementation in CheQED, a web-based proof assistant.

Structure And Properties Of Maximal Outerplanar Graphs., Benjamin Allgeier

Electronic Theses and Dissertations

Outerplanar graphs are planar graphs that have a plane embedding in which each vertex lies on the boundary of the exterior region. An outerplanar graph is maximal outerplanar if the graph obtained by adding an edge is not outerplanar. Maximal outerplanar graphs are also known as triangulations of polygons. The spine of a maximal outerplanar graph G is the dual graph of G without the vertex that corresponds to the exterior region. In this thesis we study metric properties involving geodesic intervals, geodetic sets, Steiner sets, different concepts of boundary, and also relationships between the independence numbers and domination numbers …

Some Congruence Modulo 2 Statements Of Primitive Conway Vassiliev Invariants., James M. Dawson

Masters Theses

Polynomial knot invariants can often be used to define Vassiliev invariants on singu- lar knots. Here Vassiliev invariants form the Conway, Jones, HOMFLY, and Kauffman polynomials are explored. Also, some explanation is given about how symbols of the Jones and Conway polynomial can evaluated on suitable chord diagrams. These in- variants are further used to find expressions that are congruent modulo 2 to some low degree invariants derived from the Primitive Conway polynomial.

Optimal Control Applied To Population And Disease Models, Rachael Lynn Miller Neilan

Doctoral Dissertations

This dissertation considers the use of optimal control theory in population models for the purpose of characterizing strategies of control which minimize an invasive or infected population with the least cost. Three different models and optimal control problems are presented. Each model describes population dynamics via a system of differential equations and includes the effects of one or more control methods.

The first model is a system of two ordinary differential equations describing dynamics between a native population and an invasive population. Population growth terms are functions of the control, constructed so that the value of the control may affect …