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Now showing items 11-20 of 36
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 ...
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 ...
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 IS-LM (investment saving/liquid money) model, ...
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 ...
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. ...
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 ...
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 ...
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 ...
Solutions of a Class of Multiplicatively Advanced Differential Equations II: Fourier Transforms
(2022-07-07)
For a wide class of solutions to multiplicatively advanced differential equations (MADEs), a comprehensive set of relations is established between their Fourier transforms and Jacobi theta functions. In demonstrating this ...