Browsing Master's Theses by Author "Mathematics"

Now showing items 1-20 of 26

  • Applications of Stochastic Processes to Cancer Research 

    Steely, Kristin Michelle (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 ...

  • Diophantine Generation, Galois Theory, and Hilbert's Tenth Problem 

    Kennedy, Kendra (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 ...

  • Economic Design of a Single CUSUM Chart with Combined One-sided Monitoring of Process Mean 

    Bergenn, Matthew (East Carolina University, 2019-04-30)
    A single, two-sided CUSUM chart utilizing continuously variable sampling intervals and continuously variable sample sizes monitors a process mean and is optimized through an economic design metric. The combined CUSUM ...

  • Economic Design of CUSUM Control Charts 

    Croskery, Thomas (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. ...

  • The Effect of the Mathematics of Finance on the Dynamics of a Credit Economy 

    Bennett, Jessica J. (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 IS-LM (investment saving/liquid money) model, ...

  • Eigenvalues for Sums of Hermitian Matrices 

    Taylor, James M. (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 ...

  • ESTIMATION OF THE PROBABILITY A BROWNIAN BRIDGE CROSSES A CONCAVE BOUNDARY 

    Yang, Fan (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 

    Molokach, John (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 

    Brown, Frank R., Jr. (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 

    Kardos, Michael (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) 

    Leaser, Tyler (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 

    Brame, Benjamin (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 ...

  • Improved Tsunami Modeling Via q-Advanced Special Functions 

    Olivo, James M. (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 

    Crumpler, Charles Wingate (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 

    Clifton, Ann Wells (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 ...

  • Lie Algebra Representation Theory 

    Clark, Erica (East Carolina University, 2019-04-30)
    We give a brief introduction to structure theory of Lie algebras, followed by representation theory. This thesis culminates in the presentation of the Theorem of the Highest Weight for a Lie algebra.

  • Markov Chains, Random Walks, and Card Shuffling 

    Outlaw, Nolan (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 

    Eidschun, Bradley (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 

    Kirk, Samantha (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 ...

  • Mathematical Techniques for the Analysis of Partial Differential Equations 

    Tran, Kevin K (East Carolina University, 2018-04-25)
    This thesis explores various solution methods for partial differential equations. The heat equation, wave equation and Laplace equation are analyzed using techniques from functional analysis, Fourier series, and Fourier ...