Browsing Mathematics by Issue Date
Now showing items 120 of 23

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 ... 
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 ... 
Random Walks on Finite Fields and Heisenberg Groups
(East Carolina University, 2011)Let H be a finite group and [mu] a probability measure on H. This data determines an invariant random walk on H beginning from the identity element. The probability distribution for the state of the random walk after n ... 
Fourier Analysis on SU(2)
(East Carolina University, 2012)The set SU(2) of 2x2 unitary matrices with determinant one forms a compact nonabelian Lie group diffeomorphic to the three dimensional sphere. This thesis surveys general theory concerning analysis on compact Lie groups ... 
Diophantine Generation, Galois Theory, and Hilbert's Tenth Problem
(East Carolina University, 2012)Hilbert's Tenth Problem was a question concerning existence of an algorithm to determine if there were integer solutions to arbitrary polynomial equations over the integers. Building on the work by Martin Davis, Hilary ... 
Newton Polygons on padic Number Fields
(East Carolina University, 2012)This thesis offers a clear introduction to padic number fields, and the method of Newton polygons to approximate the size of roots of polynomials in the completion of the algebraic closure of padic number fields. Ostrowski's ... 
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 ... 
The Effect of the Mathematics of Finance on the Dynamics of a Credit Economy
(East Carolina University, 2012)The general equilibrium theory of J.M. Keynes was developed in the 1930's to help explain the great depression and prevent future economic downturns. Out of this came the ISLM (investment saving/liquid money) model, ... 
Mathematical Analysis of Tsunami and Rogue Waves
(East Carolina University, 2012)In this thesis both forced and nonlinear 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 ... 
Irredundant and Mixed Ramsey Numbers
(East Carolina University, 2013)The irredundant Ramsey number, s(m,n), is the smallest p such that in every twocoloring of the edges of K[subscript]p using colors red (R) and blue (B), either the blue subgraph contains an melement irredundant set or ... 
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 ... 
Improved Tsunami Modeling Via qAdvanced Special Functions
(East Carolina University, 2013)This thesis studies qadvanced functions that are used as forcing terms in the forced wave equation and the Kortewegde Vries equation in modeling tsunamis. The model improves existing tsunami models and is compared to ... 
Applications of Stochastic Processes to Cancer Research
(East Carolina University, 2013)The purpose of this thesis is to implement stochastic models that are currently used to analyze the impact of different drug treatments on cancer and to model drug resistance by cancer cells. Mathematical models are used ... 
Theoretical aspects and modelling of cellular decision making, cell killing and informationprocessing in photodynamic therapy of cancer
(2013)BACKGROUND: The aim of this report is to provide a mathematical model of the mechanism for making binary fate decisions about cell death or survival, during and after Photodynamic Therapy (PDT) treatment, and to supply ... 
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 ... 
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 ... 
Economic Design of CUSUM Control Charts
(East Carolina University, 2014)In statistical process control, control charts are one tool for monitoring the control status of a process. One such type of chart is the cumulative sum (CUSUM) chart which has advantages over other styles of control chart. ... 
COLLEGE ALGEBRA REDESIGN: IMPROVE STUDENT LEARNING AND SUCCESS USING A HYBRID EMPORIUM MODEL
(2015)The purpose of this project is to describe a learningbased college algebra (Math 1065) course redesign at East Carolina University. Historically, East Carolina University’s College Algebra program maintained a high ... 
Eigenvalues for Sums of Hermitian Matrices
(East Carolina University, 2015)In this thesis we explore how the eigenvalues of nxn Hermitian matrices A,B relate to the eigenvalues of their sum C=A+B. We mainly focus on inequalities bounding sums of r eigenvalues for C by sums of r eigenvalues for A ... 
Modeling Tsunami Waves Using QAdvanced Waves in 2D
(East Carolina University, 20151215)A twodimensional numerical approximation for modeling tsunamis is developed. New qadvanced functions are used to model the forcing due to an earthquake. These results are used to model the Japanese tsunami of 2011, and ...