Browsing Mathematics by Submit Date
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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 ... 
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, ... 
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 ... 
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 ... 
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 ...