Browsing Mathematics by Title
Now showing items 11-30 of 36
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ESTIMATION OF THE PROBABILITY A BROWNIAN BRIDGE CROSSES A CONCAVE BOUNDARY
(East Carolina University, 2010)This thesis studies a new method to estimate the probability that a Brownian bridge crosses a concave boundary. We show that a Brownian bridge crosses a concave boundary if and only if its least concave majorant crosses ... -
AN EXPOSITION OF THE RIEMANN ZETA FUNCTION
(East Carolina University, 2014)This thesis is an exposition of the Riemann zeta function. Included are techniques of analytic continuation and relationships to special functions. Some generalizations of the Riemann zeta function are outlined, as well ... -
Financial Market Analysis Using a Kinetics Model
(East Carolina University, 2013)Over the past several decades physicists have used models and techniques that were developed in the sciences in order to analyze the price and volume behavior of financial markets. These models and techniques ... -
First Order Definition of Rings Using Group of Units
(East Carolina University, 2023-05-03)We discuss the technical background and relevant research regarding the undecidability of $O_{\mathbb{Q}^{\text{ab}}}$. Given an algebraic extension $K/\mathbb{Q}$, we consider the subring defined by $$R_K=\{x\in O_K\,|\,\forall ... -
Fourier Analysis on SU(2)
(East Carolina University, 2012)The set SU(2) of 2x2 unitary matrices with determinant one forms a compact non-abelian Lie group diffeomorphic to the three dimensional sphere. This thesis surveys general theory concerning analysis on compact Lie groups ... -
Idempotents in Cyclic Codes
(East Carolina University, 2012)Cyclic codes give us the most probable method by which we may detect and correct data transmission errors. These codes depend on the development of advanced mathematical concepts. It is shown that cyclic codes, when viewed ... -
IDENTIFYING SUBJECTIVE VALUE IN WOMEN’S COLLEGE GOLF RECRUITING REGARDLESS OF SOCIO-ECONOMIC CLASS
(East Carolina University, 2018-05-03)College athletics have grown into a major industry and athletic departments are pushing coaches to recruit the top talent. To recruit golfers, college coaches depend on multiple ranking systems. These systems are bias ... -
Improved Tsunami Modeling Via q-Advanced Special Functions
(East Carolina University, 2013)This thesis studies q-advanced functions that are used as forcing terms in the forced wave equation and the Korteweg-de Vries equation in modeling tsunamis. The model improves existing tsunami models and is compared to ... -
Inferences Over Fields: A Preliminary Investigation into the Deductive Capabilities of Field-Theoretically Defined Logical Connectives
(East Carolina University, 2023-05-03)In this paper, we will be concerned with developing an inferential structure over the field with four elements in characteristic $2$. We begin by discussing the historical context in which this research occurs. In subsequent ... -
Irredundant and Mixed Ramsey Numbers
(East Carolina University, 2013)The irredundant Ramsey number, s(m,n), is the smallest p such that in every two-coloring of the edges of K[subscript]p using colors red (R) and blue (B), either the blue subgraph contains an m-element irredundant set or ... -
Markov Chains, Random Walks, and Card Shuffling
(East Carolina University, 2016)A common question in the study of random processes pertains to card shuffling. Whether or not a deck of cards is random can have huge implications on any game being played with those particular cards. This thesis explores ... -
Mathematical Analysis of Tsunami and Rogue Waves
(East Carolina University, 2012)In this thesis both forced and non-linear wave equations will be studied. Actual data from tsunami and rogue waves will be used and a signal analysis will be performed using wavelets. Main results show that a different ... -
Mathematical Aspects of Image Processing
(East Carolina University, 2014)In this thesis, image processing is explored from a mathematical point of view. After defining a digitized image, techniques for adjusting resolution are discussed. Image transformations defined on a neighborhood centered ... -
Modeling Tsunami Waves Using Q-Advanced Waves in 2-D
(East Carolina University, 2015-12-15)A two-dimensional numerical approximation for modeling tsunamis is developed. New q-advanced functions are used to model the forcing due to an earthquake. These results are used to model the Japanese tsunami of 2011, and ... -
Newton Polygons on p-adic Number Fields
(East Carolina University, 2012)This thesis offers a clear introduction to p-adic number fields, and the method of Newton polygons to approximate the size of roots of polynomials in the completion of the algebraic closure of p-adic number fields. Ostrowski's ... -
A PRIMER FOR THE FOUNDATIONS OF ALGEBRAIC GEOMETRY
(East Carolina University, 2010)The purpose of this thesis is to define the basic objects of study in algebraic geometry, namely, schemes and quasicoherent sheaves over schemes. We start by discussing algebraic sets as common zeros of polynomials and ...