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Now showing items 1-10 of 36
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 ...
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 ...
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 ...
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 ...
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 ...
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 q-Advanced Special Functions
(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 ...
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 ...
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 ...
Irredundant and Mixed Ramsey Numbers
(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 ...