Browsing School of Mathematics Theses and Dissertations by Title
Now showing items 120 of 351

5listcoloring graphs on surfaces
(Georgia Institute of Technology, 20120823)Thomassen proved that there are only finitely many 6critical graphs embeddable on a fixed surface. He also showed that planar graphs are 5listcolorable. This thesis develops new techniques to prove general theorems for ... 
A nonasymptotic study of lowrank estimation of smooth kernels on graphs
(Georgia Institute of Technology, 20140723)This dissertation investigates the problem of estimating a kernel over a large graph based on a sample of noisy observations of linear measurements of the kernel. We are interested in solving this estimation problem in the ... 
A numerical study of vorticityenhanced heat transfer
(Georgia Institute of Technology, 20140626)In this work, we have numerically studied the effect of the vorticity on the enhancement of heat transfer in a channel flow. In the first part of the work, we focus on the investigation of a channel flow with a vortex ... 
A study of stochastic differential equations and FokkerPlanck equations with applications
(Georgia Institute of Technology, 20160415)FokkerPlanck equations, along with stochastic differential equations, play vital roles in physics, population modeling, game theory and optimization (finite or infinite dimensional). In this thesis, we study three topics, ... 
Accelerated algorithms for composite saddlepoint problems and applications
(Georgia Institute of Technology, 20141113)This dissertation considers the composite saddlepoint (CSP) problem which is motivated by realworld applications in the areas of machine learning and image processing. Two new accelerated algorithms for solving composite ... 
Adaptive iterative filtering methods for nonlinear signal analysis and applications
(Georgia Institute of Technology, 20130607)Timefrequency analysis for nonlinear and nonstationary signals is extraordinarily challenging. To capture the changes in these types of signals, it is necessary for the analysis methods to be local, adaptive and stable. ... 
Addition theorems from the standpoint of Abel's theorem
(Georgia Institute of Technology, 193408) 
Additive stucture, rich lines, and exponential setexpansion
(Georgia Institute of Technology, 20090519)We will survey some of the major directions of research in arithmetic combinatorics and their connections to other fields. We will then discuss three new results. The first result will generalize a structural theorem ... 
Algebraic degrees of stretch factors in mapping class groups
(Georgia Institute of Technology, 20140408)Given a closed surface Sg of genus g, a mapping class f in \MCG(Sg) is said to be pseudoAnosov if it preserves a pair of transverse measured foliations such that one is expanding and the other one is contracting by a ... 
An algorithm for finite dimensional approximations of solutions to infinite dimensional problems
(Georgia Institute of Technology, 198012) 
Algorithmic and topological aspects of semialgebraic sets defined by quadratic polynomials
(Georgia Institute of Technology, 20070822)In this thesis, we consider semialgebraic sets over a real closed field R defined by quadratic polynomials. Semialgebraic sets of R^k are defined as the smallest family of sets in R^k that contains the algebraic sets as ... 
An analysis of the oregonator
(Georgia Institute of Technology, 199605) 
An application of a pointwise variational principle in elastodynamics
(Georgia Institute of Technology, 197705) 
An application of Hilbert's projective metric to positive operators
(Georgia Institute of Technology, 196712) 
An Application of the ergodic theorem to information theory
(Georgia Institute of Technology, 197305) 
Applications of reproducing kernels in Hilbert spaces
(Georgia Institute of Technology, 197205) 
Applications of the Monge  Kantorovich theory
(Georgia Institute of Technology, 200205) 
Applications of the topological index in complex function theory
(Georgia Institute of Technology, 196008) 
Approximate feedback linearization of nonlinear control systems
(Georgia Institute of Technology, 199505) 
Approximating the circumference of 3connected clawfree graphs
(Georgia Institute of Technology, 20080825)Jackson and Wormald show that every 3connected K_1,dfree graph, on n vertices, contains a cycle of length at least 1/2 n^g(d) where g(d) = (log_2 6 + 2 log_2 (2d+1))^1. For d = 3, g(d) ~ 0.122. Improving this bound, ...