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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 ...
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 ...
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 ...
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 ...